LMFDB - Embedded newform 864.2.w.a.107.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.14
Character	$\chi$	$=$	864.107
Dual form			864.2.w.a.323.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.167507 + 1.40426i) q^{2} +(-1.94388 - 0.470445i) q^{4} +(-3.93413 - 1.62957i) q^{5} +(1.80111 - 1.80111i) q^{7} +(0.986240 - 2.65091i) q^{8} +O(q^{10})$	\(q+(-0.167507 + 1.40426i) q^{2} +(-1.94388 - 0.470445i) q^{4} +(-3.93413 - 1.62957i) q^{5} +(1.80111 - 1.80111i) q^{7} +(0.986240 - 2.65091i) q^{8} +(2.94733 - 5.25157i) q^{10} +(-0.527986 - 0.218699i) q^{11} +(1.75560 + 4.23839i) q^{13} +(2.22752 + 2.83092i) q^{14} +(3.55736 + 1.82898i) q^{16} -3.50487 q^{17} +(-4.81224 + 1.99330i) q^{19} +(6.88086 + 5.01848i) q^{20} +(0.395551 - 0.704796i) q^{22} +(3.23298 - 3.23298i) q^{23} +(9.28633 + 9.28633i) q^{25} +(-6.24586 + 1.75535i) q^{26} +(-4.34847 + 2.65382i) q^{28} +(3.22277 + 7.78045i) q^{29} +5.47393i q^{31} +(-3.16424 + 4.68909i) q^{32} +(0.587088 - 4.92174i) q^{34} +(-10.0208 + 4.15076i) q^{35} +(1.93653 - 4.67520i) q^{37} +(-1.99302 - 7.09152i) q^{38} +(-8.19984 + 8.82188i) q^{40} +(-2.40752 - 2.40752i) q^{41} +(0.505016 - 1.21922i) q^{43} +(0.923458 + 0.673514i) q^{44} +(3.99839 + 5.08148i) q^{46} +9.27490i q^{47} +0.512021i q^{49} +(-14.5959 + 11.4849i) q^{50} +(-1.41875 - 9.06484i) q^{52} +(-2.83647 + 6.84783i) q^{53} +(1.72078 + 1.72078i) q^{55} +(-2.99825 - 6.55090i) q^{56} +(-11.4656 + 3.22232i) q^{58} +(-0.00661636 + 0.0159733i) q^{59} +(-9.30765 + 3.85536i) q^{61} +(-7.68682 - 0.916920i) q^{62} +(-6.05466 - 5.22887i) q^{64} -19.5352i q^{65} +(-3.08636 - 7.45113i) q^{67} +(6.81305 + 1.64885i) q^{68} +(-4.15018 - 14.7671i) q^{70} +(6.99549 + 6.99549i) q^{71} +(5.27477 - 5.27477i) q^{73} +(6.24081 + 3.50252i) q^{74} +(10.2922 - 1.61084i) q^{76} +(-1.34486 + 0.557060i) q^{77} +4.36861 q^{79} +(-11.0147 - 12.9924i) q^{80} +(3.78405 - 2.97750i) q^{82} +(6.42057 + 15.5006i) q^{83} +(13.7886 + 5.71142i) q^{85} +(1.62750 + 0.913400i) q^{86} +(-1.10047 + 1.18396i) q^{88} +(2.02487 - 2.02487i) q^{89} +(10.7958 + 4.47177i) q^{91} +(-7.80547 + 4.76359i) q^{92} +(-13.0244 - 1.55361i) q^{94} +22.1802 q^{95} -8.35869 q^{97} +(-0.719010 - 0.0857670i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) $ 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−0.167507	+	1.40426i	−0.118445	+	0.992961i
$2$	−0.167507	+	1.40426i	−0.118445	+	0.992961i
$3$		0			0
$3$		0			0
$4$	−1.94388	−	0.470445i	−0.971942	−	0.235223i
$5$	−3.93413	−	1.62957i	−1.75940	−	0.728765i	−0.996624	−	0.0820966i	$-0.973838\pi$
$5$	−3.93413	−	1.62957i	−1.75940	−	0.728765i	−0.762771	−	0.646669i	$-0.776162\pi$
$6$		0			0
$7$	1.80111	−	1.80111i	0.680755	−	0.680755i	−0.279416	−	0.960170i	$-0.590141\pi$
$7$	1.80111	−	1.80111i	0.680755	−	0.680755i	0.960170	+	0.279416i	$0.0901407\pi$
$8$	0.986240	−	2.65091i	0.348688	−	0.937239i
$9$		0			0
$10$	2.94733	−	5.25157i	0.932027	−	1.66069i
$11$	−0.527986	−	0.218699i	−0.159194	−	0.0659402i	0.301664	−	0.953414i	$-0.402458\pi$
$11$	−0.527986	−	0.218699i	−0.159194	−	0.0659402i	−0.460857	+	0.887474i	$0.652458\pi$
$12$		0			0
$13$	1.75560	+	4.23839i	0.486915	+	1.17552i	0.956264	+	0.292504i	$0.0944886\pi$
$13$	1.75560	+	4.23839i	0.486915	+	1.17552i	−0.469349	+	0.883013i	$0.655511\pi$
$14$	2.22752	+	2.83092i	0.595331	+	0.756595i
$15$		0			0
$16$	3.55736	+	1.82898i	0.889341	+	0.457245i
$17$	−3.50487			−0.850055			−0.425027	−	0.905180i	$-0.639736\pi$
$17$	−3.50487			−0.850055			−0.425027	+	0.905180i	$0.639736\pi$
$18$		0			0
$19$	−4.81224	+	1.99330i	−1.10400	+	0.457293i	−0.858869	−	0.512196i	$-0.828832\pi$
$19$	−4.81224	+	1.99330i	−1.10400	+	0.457293i	−0.245135	+	0.969489i	$0.578832\pi$
$20$	6.88086	+	5.01848i	1.53861	+	1.12217i
$21$		0			0
$22$	0.395551	−	0.704796i	0.0843318	−	0.150263i
$23$	3.23298	−	3.23298i	0.674123	−	0.674123i	−0.284541	−	0.958664i	$-0.591841\pi$
$23$	3.23298	−	3.23298i	0.674123	−	0.674123i	0.958664	+	0.284541i	$0.0918413\pi$
$24$		0			0
$25$	9.28633	+	9.28633i	1.85727	+	1.85727i
$26$	−6.24586	+	1.75535i	−1.22491	+	0.344253i
$27$		0			0
$28$	−4.34847	+	2.65382i	−0.821783	+	0.501525i
$29$	3.22277	+	7.78045i	0.598453	+	1.44479i	0.875157	+	0.483839i	$0.160758\pi$
$29$	3.22277	+	7.78045i	0.598453	+	1.44479i	−0.276704	+	0.960955i	$0.589242\pi$
$30$		0			0
$31$			5.47393i			0.983148i	0.870836	+	0.491574i	$0.163578\pi$
$31$			5.47393i			0.983148i	−0.870836	+	0.491574i	$0.836422\pi$
$32$	−3.16424	+	4.68909i	−0.559364	+	0.828922i
$33$		0			0
$34$	0.587088	−	4.92174i	0.100685	−	0.844071i
$35$	−10.0208	+	4.15076i	−1.69383	+	0.701606i
$36$		0			0
$37$	1.93653	−	4.67520i	0.318364	−	0.768599i	−0.680977	−	0.732305i	$-0.738445\pi$
$37$	1.93653	−	4.67520i	0.318364	−	0.768599i	0.999341	−	0.0362941i	$-0.0115553\pi$
$38$	−1.99302	−	7.09152i	−0.323310	−	1.15040i
$39$		0			0
$40$	−8.19984	+	8.82188i	−1.29651	+	1.39486i
$41$	−2.40752	−	2.40752i	−0.375991	−	0.375991i	0.493663	−	0.869653i	$-0.335658\pi$
$41$	−2.40752	−	2.40752i	−0.375991	−	0.375991i	−0.869653	+	0.493663i	$0.835658\pi$
$42$		0			0
$43$	0.505016	−	1.21922i	0.0770143	−	0.185929i	−0.880683	−	0.473706i	$-0.842916\pi$
$43$	0.505016	−	1.21922i	0.0770143	−	0.185929i	0.957698	+	0.287777i	$0.0929161\pi$
$44$	0.923458	+	0.673514i	0.139216	+	0.101536i
$45$		0			0
$46$	3.99839	+	5.08148i	0.589531	+	0.749224i
$47$			9.27490i			1.35288i	0.736496	+	0.676441i	$0.236479\pi$
$47$			9.27490i			1.35288i	−0.736496	+	0.676441i	$0.763521\pi$
$48$		0			0
$49$			0.512021i			0.0731459i
$50$	−14.5959	+	11.4849i	−2.06418	+	1.62421i
$51$		0			0
$52$	−1.41875	−	9.06484i	−0.196745	−	1.25707i
$53$	−2.83647	+	6.84783i	−0.389619	+	0.940622i	0.600402	+	0.799698i	$0.295007\pi$
$53$	−2.83647	+	6.84783i	−0.389619	+	0.940622i	−0.990020	+	0.140924i	$0.954993\pi$
$54$		0			0
$55$	1.72078	+	1.72078i	0.232030	+	0.232030i
$56$	−2.99825	−	6.55090i	−0.400658	−	0.875401i
$57$		0			0
$58$	−11.4656	+	3.22232i	−1.50551	+	0.423112i
$59$	−0.00661636	+	0.0159733i	−0.000861377	+	0.00207955i	−0.924310	−	0.381643i	$-0.875358\pi$
$59$	−0.00661636	+	0.0159733i	−0.000861377	+	0.00207955i	0.923448	+	0.383723i	$0.125358\pi$
$60$		0			0
$61$	−9.30765	+	3.85536i	−1.19172	+	0.493628i	−0.888316	−	0.459233i	$-0.848124\pi$
$61$	−9.30765	+	3.85536i	−1.19172	+	0.493628i	−0.303407	+	0.952861i	$0.598124\pi$
$62$	−7.68682	−	0.916920i	−0.976227	−	0.116449i
$63$		0			0
$64$	−6.05466	−	5.22887i	−0.756833	−	0.653608i
$65$		−	19.5352i		−	2.42305i
$66$		0			0
$67$	−3.08636	−	7.45113i	−0.377059	−	0.910300i	−0.992514	−	0.122129i	$-0.961028\pi$
$67$	−3.08636	−	7.45113i	−0.377059	−	0.910300i	0.615456	−	0.788171i	$-0.288972\pi$
$68$	6.81305	+	1.64885i	0.826204	+	0.199952i
$69$		0			0
$70$	−4.15018	−	14.7671i	−0.496042	−	1.76501i
$71$	6.99549	+	6.99549i	0.830212	+	0.830212i	0.987546	−	0.157333i	$-0.0502897\pi$
$71$	6.99549	+	6.99549i	0.830212	+	0.830212i	−0.157333	+	0.987546i	$0.550290\pi$
$72$		0			0
$73$	5.27477	−	5.27477i	0.617366	−	0.617366i	−0.327489	−	0.944855i	$-0.606203\pi$
$73$	5.27477	−	5.27477i	0.617366	−	0.617366i	0.944855	+	0.327489i	$0.106203\pi$
$74$	6.24081	+	3.50252i	0.725480	+	0.407160i
$75$		0			0
$76$	10.2922	−	1.61084i	1.18059	−	0.184776i
$77$	−1.34486	+	0.557060i	−0.153261	+	0.0634828i
$78$		0			0
$79$	4.36861			0.491507			0.245753	−	0.969332i	$-0.420965\pi$
$79$	4.36861			0.491507			0.245753	+	0.969332i	$0.420965\pi$
$80$	−11.0147	−	12.9924i	−1.23148	−	1.45260i
$81$		0			0
$82$	3.78405	−	2.97750i	0.417878	−	0.328810i
$83$	6.42057	+	15.5006i	0.704750	+	1.70142i	0.712721	+	0.701448i	$0.247463\pi$
$83$	6.42057	+	15.5006i	0.704750	+	1.70142i	−0.00797127	+	0.999968i	$0.502537\pi$
$84$		0			0
$85$	13.7886	+	5.71142i	1.49558	+	0.619490i
$86$	1.62750	+	0.913400i	0.175498	+	0.0984945i
$87$		0			0
$88$	−1.10047	+	1.18396i	−0.117311	+	0.126210i
$89$	2.02487	−	2.02487i	0.214636	−	0.214636i	−0.591597	−	0.806234i	$-0.701502\pi$
$89$	2.02487	−	2.02487i	0.214636	−	0.214636i	0.806234	+	0.591597i	$0.201502\pi$
$90$		0			0
$91$	10.7958	+	4.47177i	1.13171	+	0.468769i
$92$	−7.80547	+	4.76359i	−0.813777	+	0.496639i
$93$		0			0
$94$	−13.0244	−	1.55361i	−1.34336	−	0.160242i
$95$	22.1802			2.27564
$96$		0			0
$97$	−8.35869			−0.848697			−0.424348	−	0.905499i	$-0.639497\pi$
$97$	−8.35869			−0.848697			−0.424348	+	0.905499i	$0.639497\pi$
$98$	−0.719010	−	0.0857670i	−0.0726310	−	0.00866377i
$99$		0			0
$100$	−13.6828	−	22.4202i	−1.36828	−	2.24202i
$101$	6.76411	+	2.80179i	0.673055	+	0.278788i	0.692920	−	0.721014i	$-0.256324\pi$
$101$	6.76411	+	2.80179i	0.673055	+	0.278788i	−0.0198656	+	0.999803i	$0.506324\pi$
$102$		0			0
$103$	11.2645	−	11.2645i	1.10993	−	1.10993i	0.116768	−	0.993159i	$-0.462747\pi$
$103$	11.2645	−	11.2645i	1.10993	−	1.10993i	0.993159	−	0.116768i	$-0.0372533\pi$
$104$	12.9670	−	0.473868i	1.27152	−	0.0464666i
$105$		0			0
$106$	−9.14100	−	5.13019i	−0.887853	−	0.498288i
$107$	−1.58115	−	0.654935i	−0.152856	−	0.0633150i	0.304944	−	0.952370i	$-0.401362\pi$
$107$	−1.58115	−	0.654935i	−0.152856	−	0.0633150i	−0.457800	+	0.889055i	$0.651362\pi$
$108$		0			0
$109$	2.77346	+	6.69572i	0.265649	+	0.641333i	0.999269	−	0.0382265i	$-0.0121708\pi$
$109$	2.77346	+	6.69572i	0.265649	+	0.641333i	−0.733620	+	0.679560i	$0.762171\pi$
$110$	−2.70466	+	2.12818i	−0.257879	+	0.202914i
$111$		0			0
$112$	9.70138	−	3.11300i	0.916695	−	0.294151i
$113$	4.67012			0.439328			0.219664	−	0.975576i	$-0.429504\pi$
$113$	4.67012			0.439328			0.219664	+	0.975576i	$0.429504\pi$
$114$		0			0
$115$	−17.9873	+	7.45059i	−1.67733	+	0.694771i
$116$	−2.60441	−	16.6404i	−0.241813	−	1.54502i
$117$		0			0
$118$	−0.0213224	−	0.0119667i	−0.00196288	−	0.00110163i
$119$	−6.31264	+	6.31264i	−0.578679	+	0.578679i
$120$		0			0
$121$	−7.54723	−	7.54723i	−0.686112	−	0.686112i
$122$	−3.85482	−	13.7161i	−0.348999	−	1.24180i
$123$		0			0
$124$	2.57519	−	10.6407i	0.231258	−	0.955562i
$125$	−13.2530	−	31.9957i	−1.18539	−	2.86178i
$126$		0			0
$127$			19.9447i			1.76981i	0.465775	+	0.884903i	$0.345776\pi$
$127$			19.9447i			1.76981i	−0.465775	+	0.884903i	$0.654224\pi$
$128$	8.35688	−	7.62644i	0.738651	−	0.674088i
$129$		0			0
$130$	27.4325	+	3.27228i	2.40599	+	0.286998i
$131$	−8.66917	+	3.59089i	−0.757429	+	0.313737i	−0.727769	−	0.685823i	$-0.759443\pi$
$131$	−8.66917	+	3.59089i	−0.757429	+	0.313737i	−0.0296603	+	0.999560i	$0.509443\pi$
$132$		0			0
$133$	−5.07722	+	12.2575i	−0.440251	+	1.06286i
$134$	10.9803	−	3.08593i	0.948553	−	0.266584i
$135$		0			0
$136$	−3.45664	+	9.29109i	−0.296404	+	0.796704i
$137$	−5.99092	−	5.99092i	−0.511838	−	0.511838i	0.403251	−	0.915089i	$-0.367880\pi$
$137$	−5.99092	−	5.99092i	−0.511838	−	0.511838i	−0.915089	+	0.403251i	$0.867880\pi$
$138$		0			0
$139$	−4.61103	+	11.1320i	−0.391103	+	0.944205i	0.598598	+	0.801050i	$0.295725\pi$
$139$	−4.61103	+	11.1320i	−0.391103	+	0.944205i	−0.989700	+	0.143155i	$0.954275\pi$
$140$	21.4320	−	3.35434i	1.81133	−	0.283494i
$141$		0			0
$142$	−10.9953	+	8.65169i	−0.922703	+	0.726034i
$143$		−	2.62176i		−	0.219242i
$144$		0			0
$145$		−	35.8610i		−	2.97810i
$146$	6.52359	+	8.29070i	0.539896	+	0.686144i
$147$		0			0
$148$	−5.96382	+	8.17702i	−0.490223	+	0.672147i
$149$	−0.505473	+	1.22032i	−0.0414100	+	0.0999725i	−0.943231	−	0.332137i	$-0.892230\pi$
$149$	−0.505473	+	1.22032i	−0.0414100	+	0.0999725i	0.901821	+	0.432109i	$0.142230\pi$
$150$		0			0
$151$	7.49947	+	7.49947i	0.610298	+	0.610298i	0.943024	−	0.332725i	$-0.107968\pi$
$151$	7.49947	+	7.49947i	0.610298	+	0.610298i	−0.332725	+	0.943024i	$0.607968\pi$
$152$	0.538027	+	14.7227i	0.0436397	+	1.19417i
$153$		0			0
$154$	−0.556983	−	1.98184i	−0.0448829	−	0.159701i
$155$	8.92015	−	21.5352i	0.716484	−	1.72975i
$156$		0			0
$157$	−22.8339	+	9.45810i	−1.82234	+	0.754839i	−0.847916	+	0.530131i	$0.822143\pi$
$157$	−22.8339	+	9.45810i	−1.82234	+	0.754839i	−0.974426	+	0.224708i	$0.927857\pi$
$158$	−0.731771	+	6.13465i	−0.0582165	+	0.488047i
$159$		0			0
$160$	20.0897	−	13.2911i	1.58823	−	1.05076i
$161$		−	11.6459i		−	0.917824i
$162$		0			0
$163$	1.38360	+	3.34030i	0.108372	+	0.261632i	0.968757	−	0.248012i	$-0.0797772\pi$
$163$	1.38360	+	3.34030i	0.108372	+	0.261632i	−0.860385	+	0.509644i	$0.829777\pi$
$164$	3.54733	+	5.81253i	0.277000	+	0.453883i
$165$		0			0
$166$	−22.8424	+	6.41969i	−1.77291	+	0.498264i
$167$	−0.682611	−	0.682611i	−0.0528220	−	0.0528220i	0.680202	−	0.733024i	$-0.261892\pi$
$167$	−0.682611	−	0.682611i	−0.0528220	−	0.0528220i	−0.733024	+	0.680202i	$0.761892\pi$
$168$		0			0
$169$	−5.68942	+	5.68942i	−0.437647	+	0.437647i
$170$	−10.3300	+	18.4060i	−0.792274	+	1.41168i
$171$		0			0
$172$	−1.55527	+	2.13243i	−0.118588	+	0.162597i
$173$	2.11886	−	0.877660i	0.161094	−	0.0667272i	−0.300679	−	0.953725i	$-0.597213\pi$
$173$	2.11886	−	0.877660i	0.161094	−	0.0667272i	0.461773	+	0.886998i	$0.347213\pi$
$174$		0			0
$175$	33.4514			2.52869
$176$	−1.47824	−	1.74367i	−0.111427	−	0.131434i
$177$		0			0
$178$	2.50427	+	3.18262i	0.187703	+	0.238548i
$179$	3.83061	+	9.24791i	0.286313	+	0.691221i	0.999957	−	0.00928754i	$-0.00295636\pi$
$179$	3.83061	+	9.24791i	0.286313	+	0.691221i	−0.713644	+	0.700509i	$0.752956\pi$
$180$		0			0
$181$	−2.97359	−	1.23170i	−0.221026	−	0.0915518i	0.269423	−	0.963022i	$-0.413167\pi$
$181$	−2.97359	−	1.23170i	−0.221026	−	0.0915518i	−0.490449	+	0.871470i	$0.663167\pi$
$182$	−8.08789	+	14.4111i	−0.599515	+	1.06822i
$183$		0			0
$184$	−5.38185	−	11.7588i	−0.396755	−	0.866872i
$185$	−15.2371	+	15.2371i	−1.12026	+	1.12026i
$186$		0			0
$187$	1.85052	+	0.766511i	0.135323	+	0.0560528i
$188$	4.36333	−	18.0293i	0.318229	−	1.31492i
$189$		0			0
$190$	−3.71533	+	31.1467i	−0.269538	+	2.25962i
$191$	−9.07372			−0.656551			−0.328276	−	0.944582i	$-0.606468\pi$
$191$	−9.07372			−0.656551			−0.328276	+	0.944582i	$0.606468\pi$
$192$		0			0
$193$	5.12981			0.369252			0.184626	−	0.982809i	$-0.440893\pi$
$193$	5.12981			0.369252			0.184626	+	0.982809i	$0.440893\pi$
$194$	1.40014	−	11.7378i	0.100524	−	0.842722i
$195$		0			0
$196$	0.240878	−	0.995310i	0.0172056	−	0.0710936i
$197$	−5.16765	−	2.14051i	−0.368180	−	0.152505i	0.190920	−	0.981606i	$-0.438853\pi$
$197$	−5.16765	−	2.14051i	−0.368180	−	0.152505i	−0.559099	+	0.829101i	$0.688853\pi$
$198$		0			0
$199$	1.57923	−	1.57923i	0.111949	−	0.111949i	−0.648914	−	0.760862i	$-0.724776\pi$
$199$	1.57923	−	1.57923i	0.111949	−	0.111949i	0.760862	+	0.648914i	$0.224776\pi$
$200$	33.7758	−	15.4587i	2.38831	−	1.09309i
$201$		0			0
$202$	−5.06747	+	9.02925i	−0.356546	+	0.635296i
$203$	19.8180	+	8.20888i	1.39095	+	0.576150i
$204$		0			0
$205$	5.54826	+	13.3947i	0.387507	+	0.935526i
$206$	13.9314	+	17.7052i	0.970648	+	1.23358i
$207$		0			0
$208$	−1.50663	+	18.2884i	−0.104466	+	1.26807i
$209$	2.97673			0.205905
$210$		0			0
$211$	1.13475	−	0.470028i	0.0781193	−	0.0323581i	−0.343282	−	0.939233i	$-0.611539\pi$
$211$	1.13475	−	0.470028i	0.0781193	−	0.0323581i	0.421401	+	0.906874i	$0.361539\pi$
$212$	8.73529	−	11.9770i	0.599942	−	0.822583i
$213$		0			0
$214$	1.18455	−	2.11064i	0.0809743	−	0.144281i
$215$	−3.97360	+	3.97360i	−0.270997	+	0.270997i
$216$		0			0
$217$	9.85915	+	9.85915i	0.669282	+	0.669282i
$218$	−9.86709	+	2.77307i	−0.668284	+	0.187816i
$219$		0			0
$220$	−2.53546	−	4.15453i	−0.170941	−	0.280098i
$221$	−6.15313	−	14.8550i	−0.413905	−	0.999254i
$222$		0			0
$223$			19.0240i			1.27394i	0.770889	+	0.636969i	$0.219812\pi$
$223$			19.0240i			1.27394i	−0.770889	+	0.636969i	$0.780188\pi$
$224$	2.74641	+	14.1447i	0.183503	+	0.945082i
$225$		0			0
$226$	−0.782275	+	6.55805i	−0.0520362	+	0.436235i
$227$	13.9428	−	5.77532i	0.925419	−	0.383321i	0.131480	−	0.991319i	$-0.458027\pi$
$227$	13.9428	−	5.77532i	0.925419	−	0.383321i	0.793939	+	0.607997i	$0.208027\pi$
$228$		0			0
$229$	9.94047	−	23.9984i	0.656885	−	1.58586i	−0.145705	−	0.989328i	$-0.546545\pi$
$229$	9.94047	−	23.9984i	0.656885	−	1.58586i	0.802589	−	0.596532i	$-0.203455\pi$
$230$	−7.44956	−	26.5069i	−0.491209	−	1.74781i
$231$		0			0
$232$	23.8037	−	0.869884i	1.56279	−	0.0571107i
$233$	−13.4161	−	13.4161i	−0.878921	−	0.878921i	0.114502	−	0.993423i	$-0.463473\pi$
$233$	−13.4161	−	13.4161i	−0.878921	−	0.878921i	−0.993423	+	0.114502i	$0.963473\pi$
$234$		0			0
$235$	15.1141	−	36.4886i	0.985934	−	2.38026i
$236$	0.0203760	−	0.0279376i	0.00132636	−	0.00181858i
$237$		0			0
$238$	−7.80717	−	9.92199i	−0.506064	−	0.643147i
$239$		−	6.40372i		−	0.414222i	−0.978317	−	0.207111i	$-0.933594\pi$
$239$		−	6.40372i		−	0.414222i	0.978317	−	0.207111i	$-0.0664061\pi$
$240$		0			0
$241$		−	4.41728i		−	0.284542i	−0.989828	−	0.142271i	$-0.954560\pi$
$241$		−	4.41728i		−	0.284542i	0.989828	−	0.142271i	$-0.0454405\pi$
$242$	11.8625	−	9.33406i	0.762549	−	0.600016i
$243$		0			0
$244$	19.9067	−	3.11562i	1.27440	−	0.199457i
$245$	0.834374	−	2.01436i	0.0533062	−	0.128693i
$246$		0			0
$247$	−16.8967	−	16.8967i	−1.07511	−	1.07511i
$248$	14.5109	+	5.39861i	0.921444	+	0.342812i
$249$		0			0
$250$	47.1502	−	13.2512i	2.98204	−	0.838080i
$251$	−5.70829	+	13.7810i	−0.360304	+	0.869851i	0.634951	+	0.772552i	$0.281020\pi$
$251$	−5.70829	+	13.7810i	−0.360304	+	0.869851i	−0.995255	+	0.0972985i	$0.968980\pi$
$252$		0			0
$253$	−2.41402	+	0.999919i	−0.151768	+	0.0628644i
$254$	−28.0075	−	3.34087i	−1.75735	−	0.209625i
$255$		0			0
$256$	9.30966	+	13.0127i	0.581854	+	0.813293i
$257$			27.1738i			1.69505i	0.530753	+	0.847526i	$0.321909\pi$
$257$			27.1738i			1.69505i	−0.530753	+	0.847526i	$0.678091\pi$
$258$		0			0
$259$	−4.93264	−	11.9085i	−0.306499	−	0.739955i
$260$	−9.19025	+	37.9742i	−0.569955	+	2.35506i
$261$		0			0
$262$	−3.59039	−	12.7753i	−0.221815	−	0.789258i
$263$	−8.60649	−	8.60649i	−0.530699	−	0.530699i	0.390081	−	0.920780i	$-0.372447\pi$
$263$	−8.60649	−	8.60649i	−0.530699	−	0.530699i	−0.920780	+	0.390081i	$0.872447\pi$
$264$		0			0
$265$	22.3180	−	22.3180i	1.37099	−	1.37099i
$266$	−16.3622	−	9.18295i	−1.00323	−	0.563043i
$267$		0			0
$268$	2.49417	+	15.9361i	0.152356	+	0.973451i
$269$	27.7138	−	11.4794i	1.68974	−	0.699913i	0.690025	−	0.723786i	$-0.257600\pi$
$269$	27.7138	−	11.4794i	1.68974	−	0.699913i	0.999715	+	0.0238727i	$0.00759963\pi$
$270$		0			0
$271$	−30.3410			−1.84308			−0.921542	−	0.388279i	$-0.873070\pi$
$271$	−30.3410			−1.84308			−0.921542	+	0.388279i	$0.873070\pi$
$272$	−12.4681	−	6.41033i	−0.755988	−	0.388683i
$273$		0			0
$274$	9.41631	−	7.40928i	0.568860	−	0.447611i
$275$	−2.87214	−	6.93397i	−0.173197	−	0.418134i
$276$		0			0
$277$	−9.64561	−	3.99534i	−0.579549	−	0.240057i	0.0735984	−	0.997288i	$-0.476552\pi$
$277$	−9.64561	−	3.99534i	−0.579549	−	0.240057i	−0.653147	+	0.757231i	$0.726552\pi$
$278$	−14.8598	−	8.33976i	−0.891234	−	0.500186i
$279$		0			0
$280$	1.12037	+	30.6579i	0.0669546	+	1.83216i
$281$	1.44386	−	1.44386i	0.0861335	−	0.0861335i	−0.662727	−	0.748861i	$-0.730601\pi$
$281$	1.44386	−	1.44386i	0.0861335	−	0.0861335i	0.748861	+	0.662727i	$0.230601\pi$
$282$		0			0
$283$	−19.8747	−	8.23236i	−1.18143	−	0.489363i	−0.296473	−	0.955041i	$-0.595810\pi$
$283$	−19.8747	−	8.23236i	−1.18143	−	0.489363i	−0.884954	+	0.465678i	$0.845810\pi$
$284$	−10.3074	−	16.8894i	−0.611633	−	1.00220i
$285$		0			0
$286$	3.68163	+	0.439162i	0.217699	+	0.0259682i
$287$	−8.67239			−0.511915
$288$		0			0
$289$	−4.71592			−0.277407
$290$	50.3581	+	6.00696i	2.95713	+	0.352741i
$291$		0			0
$292$	−12.7350	+	7.77205i	−0.745261	+	0.454825i
$293$	−0.493799	−	0.204538i	−0.0288481	−	0.0119493i	0.368213	−	0.929742i	$-0.379970\pi$
$293$	−0.493799	−	0.204538i	−0.0288481	−	0.0119493i	−0.397061	+	0.917792i	$0.629970\pi$
$294$		0			0
$295$	0.0520592	−	0.0520592i	0.00303100	−	0.00303100i
$296$	−10.4837	−	9.74445i	−0.609351	−	0.566385i
$297$		0			0
$298$	−1.62897	−	0.914226i	−0.0943639	−	0.0529597i
$299$	19.3784	+	8.02681i	1.12068	+	0.464202i
$300$		0			0
$301$	−1.28635	−	3.10553i	−0.0741442	−	0.179000i
$302$	−11.7874	+	9.27499i	−0.678289	+	0.533715i
$303$		0			0
$304$	−20.7646	−	1.71062i	−1.19093	−	0.0981107i
$305$	42.9000			2.45645
$306$		0			0
$307$	−4.88633	+	2.02398i	−0.278878	+	0.115515i	−0.517738	−	0.855539i	$-0.673226\pi$
$307$	−4.88633	+	2.02398i	−0.278878	+	0.115515i	0.238861	+	0.971054i	$0.423226\pi$
$308$	2.87632	−	0.450176i	0.163893	−	0.0256511i
$309$		0			0
$310$	28.7467	+	16.1335i	1.63271	+	0.916320i
$311$	−2.51961	+	2.51961i	−0.142874	+	0.142874i	−0.774926	−	0.632052i	$-0.782213\pi$
$311$	−2.51961	+	2.51961i	−0.142874	+	0.142874i	0.632052	+	0.774926i	$0.282213\pi$
$312$		0			0
$313$	−3.77971	−	3.77971i	−0.213642	−	0.213642i	0.592171	−	0.805812i	$-0.298271\pi$
$313$	−3.77971	−	3.77971i	−0.213642	−	0.213642i	−0.805812	+	0.592171i	$0.798271\pi$
$314$	−9.45679	−	33.6490i	−0.533678	−	1.89892i
$315$		0			0
$316$	−8.49206	−	2.05519i	−0.477716	−	0.115613i
$317$	−7.32833	−	17.6922i	−0.411600	−	0.993691i	−0.984708	−	0.174211i	$-0.944262\pi$
$317$	−7.32833	−	17.6922i	−0.411600	−	0.993691i	0.573108	−	0.819480i	$-0.305738\pi$
$318$		0			0
$319$		−	4.81279i		−	0.269464i
$320$	15.2990	+	30.4375i	0.855241	+	1.70151i
$321$		0			0
$322$	16.3538	+	1.95076i	0.911363	+	0.108712i
$323$	16.8663	−	6.98623i	0.938464	−	0.388724i
$324$		0			0
$325$	−23.0560	+	55.6621i	−1.27892	+	3.08758i
$326$	−4.92240	+	1.38340i	−0.272627	+	0.0766197i
$327$		0			0
$328$	−8.75650	+	4.00772i	−0.483497	+	0.221290i
$329$	16.7051	+	16.7051i	0.920981	+	0.920981i
$330$		0			0
$331$	−4.19347	+	10.1239i	−0.230494	+	0.556462i	−0.996236	−	0.0866867i	$-0.972372\pi$
$331$	−4.19347	+	10.1239i	−0.230494	+	0.556462i	0.765742	+	0.643148i	$0.222372\pi$
$332$	−5.18865	−	33.1520i	−0.284764	−	1.81945i
$333$		0			0
$334$	1.07290	−	0.844220i	0.0587067	−	0.0461937i
$335$			34.3431i			1.87636i
$336$		0			0
$337$		−	1.77494i		−	0.0966873i	−0.998831	−	0.0483436i	$-0.984606\pi$
$337$		−	1.77494i		−	0.0966873i	0.998831	−	0.0483436i	$-0.0153943\pi$
$338$	−7.03640	−	8.94242i	−0.382729	−	0.486404i
$339$		0			0
$340$	−24.1165	−	17.5891i	−1.30790	−	0.953903i
$341$	1.19714	−	2.89016i	0.0648290	−	0.156511i
$342$		0			0
$343$	13.5300	+	13.5300i	0.730549	+	0.730549i
$344$	−2.73397	−	2.54119i	−0.147406	−	0.137012i
$345$		0			0
$346$	0.877538	+	3.12244i	0.0471768	+	0.167863i
$347$	5.11965	−	12.3599i	0.274837	−	0.663516i	−0.724840	−	0.688917i	$-0.758086\pi$
$347$	5.11965	−	12.3599i	0.274837	−	0.663516i	0.999677	+	0.0254011i	$0.00808630\pi$
$348$		0			0
$349$	16.1690	−	6.69741i	0.865506	−	0.358504i	0.0946474	−	0.995511i	$-0.469828\pi$
$349$	16.1690	−	6.69741i	0.865506	−	0.358504i	0.770858	+	0.637007i	$0.219828\pi$
$350$	−5.60332	+	46.9744i	−0.299510	+	2.51088i
$351$		0			0
$352$	2.69618	−	1.78376i	0.143707	−	0.0950746i
$353$			11.7752i			0.626733i	0.949632	+	0.313366i	$0.101457\pi$
$353$			11.7752i			0.626733i	−0.949632	+	0.313366i	$0.898543\pi$
$354$		0			0
$355$	−16.1215	−	38.9208i	−0.855642	−	2.06570i
$356$	−4.88871	+	2.98353i	−0.259101	+	0.158127i
$357$		0			0
$358$	−13.6281	+	3.83008i	−0.720268	+	0.202426i
$359$	−16.5669	−	16.5669i	−0.874367	−	0.874367i	0.118578	−	0.992945i	$-0.462166\pi$
$359$	−16.5669	−	16.5669i	−0.874367	−	0.874367i	−0.992945	+	0.118578i	$0.962166\pi$
$360$		0			0
$361$	5.74940	−	5.74940i	0.302600	−	0.302600i
$362$	2.22773	−	3.96938i	0.117087	−	0.208626i
$363$		0			0
$364$	−18.8821	−	13.7714i	−0.989690	−	0.721820i
$365$	−29.3472	+	12.1560i	−1.53610	+	0.636275i
$366$		0			0
$367$	−6.58947			−0.343967			−0.171984	−	0.985100i	$-0.555018\pi$
$367$	−6.58947			−0.343967			−0.171984	+	0.985100i	$0.555018\pi$
$368$	17.4139	−	5.58782i	0.907764	−	0.291285i
$369$		0			0
$370$	−18.8446	−	23.9492i	−0.979682	−	1.24506i
$371$	7.22491	+	17.4425i	0.375098	+	0.905568i
$372$		0			0
$373$	9.15352	+	3.79151i	0.473951	+	0.196317i	0.606856	−	0.794812i	$-0.292430\pi$
$373$	9.15352	+	3.79151i	0.473951	+	0.196317i	−0.132905	+	0.991129i	$0.542430\pi$
$374$	−1.38635	+	2.47021i	−0.0716866	+	0.127732i
$375$		0			0
$376$	24.5869	+	9.14727i	1.26797	+	0.471734i
$377$	−27.3187	+	27.3187i	−1.40698	+	1.40698i
$378$		0			0
$379$	−24.3094	−	10.0693i	−1.24869	−	0.517224i	−0.342269	−	0.939602i	$-0.611196\pi$
$379$	−24.3094	−	10.0693i	−1.24869	−	0.517224i	−0.906420	+	0.422378i	$0.861196\pi$
$380$	−43.1157	−	10.4346i	−2.21179	−	0.535281i
$381$		0			0
$382$	1.51991	−	12.7418i	0.0777653	−	0.651930i
$383$	30.2731			1.54688			0.773442	−	0.633867i	$-0.218533\pi$
$383$	30.2731			1.54688			0.773442	+	0.633867i	$0.218533\pi$
$384$		0			0
$385$	6.19862			0.315911
$386$	−0.859277	+	7.20358i	−0.0437360	+	0.366652i
$387$		0			0
$388$	16.2483	+	3.93231i	0.824883	+	0.199633i
$389$	6.58185	+	2.72629i	0.333713	+	0.138229i	0.543247	−	0.839573i	$-0.317195\pi$
$389$	6.58185	+	2.72629i	0.333713	+	0.138229i	−0.209534	+	0.977801i	$0.567195\pi$
$390$		0			0
$391$	−11.3312	+	11.3312i	−0.573041	+	0.573041i
$392$	1.35732	+	0.504976i	0.0685552	+	0.0255051i
$393$		0			0
$394$	3.87145	−	6.89817i	0.195041	−	0.347525i
$395$	−17.1867	−	7.11895i	−0.864755	−	0.358193i
$396$		0			0
$397$	6.79902	+	16.4143i	0.341233	+	0.823810i	0.997592	+	0.0693605i	$0.0220959\pi$
$397$	6.79902	+	16.4143i	0.341233	+	0.823810i	−0.656359	+	0.754449i	$0.727904\pi$
$398$	1.95311	+	2.48218i	0.0979008	+	0.124420i
$399$		0			0
$400$	16.0503	+	50.0194i	0.802516	+	2.50097i
$401$	−12.6207			−0.630250			−0.315125	−	0.949050i	$-0.602046\pi$
$401$	−12.6207			−0.630250			−0.315125	+	0.949050i	$0.602046\pi$
$402$		0			0
$403$	−23.2007	+	9.61003i	−1.15571	+	0.478709i
$404$	−11.8306	−	8.62849i	−0.588592	−	0.429284i
$405$		0			0
$406$	−14.8470	+	26.4545i	−0.736846	+	1.31292i
$407$	−2.04493	+	2.04493i	−0.101363	+	0.101363i
$408$		0			0
$409$	−23.6256	−	23.6256i	−1.16821	−	1.16821i	−0.982628	−	0.185585i	$-0.940582\pi$
$409$	−23.6256	−	23.6256i	−1.16821	−	1.16821i	−0.185585	−	0.982628i	$-0.559418\pi$
$410$	−19.7390	+	5.54749i	−0.974838	+	0.273971i
$411$		0			0
$412$	−27.1963	+	16.5976i	−1.33986	+	0.817704i
$413$	0.0168529	+	0.0406864i	0.000829276	+	0.00200205i
$414$		0			0
$415$		−	71.4443i		−	3.50706i
$416$	−25.4293	−	5.17913i	−1.24677	−	0.253928i
$417$		0			0
$418$	−0.498622	+	4.18010i	−0.0243884	+	0.204455i
$419$	−3.41229	+	1.41342i	−0.166701	+	0.0690500i	−0.464474	−	0.885587i	$-0.653756\pi$
$419$	−3.41229	+	1.41342i	−0.166701	+	0.0690500i	0.297772	+	0.954637i	$0.403756\pi$
$420$		0			0
$421$	1.11626	−	2.69489i	0.0544031	−	0.131341i	−0.894341	−	0.447386i	$-0.852355\pi$
$421$	1.11626	−	2.69489i	0.0544031	−	0.131341i	0.948744	+	0.316045i	$0.102355\pi$
$422$	0.469963	+	1.67221i	0.0228775	+	0.0814021i
$423$		0			0
$424$	15.3556	+	14.2728i	0.745732	+	0.693150i
$425$	−32.5473	−	32.5473i	−1.57878	−	1.57878i
$426$		0			0
$427$	−9.82017	+	23.7080i	−0.475231	+	1.14731i
$428$	2.76547	+	2.01696i	0.133674	+	0.0974936i
$429$		0			0
$430$	−4.91435	−	6.24556i	−0.236991	−	0.301188i
$431$			30.6040i			1.47414i	0.675816	+	0.737071i	$0.263792\pi$
$431$			30.6040i			1.47414i	−0.675816	+	0.737071i	$0.736208\pi$
$432$		0			0
$433$		−	8.52659i		−	0.409762i	−0.978787	−	0.204881i	$-0.934319\pi$
$433$		−	8.52659i		−	0.409762i	0.978787	−	0.204881i	$-0.0656807\pi$
$434$	−15.4963	+	12.1933i	−0.743844	+	0.585298i
$435$		0			0
$436$	−2.24131	−	14.3204i	−0.107339	−	0.685825i
$437$	−9.11359	+	22.0021i	−0.435962	+	1.05251i
$438$		0			0
$439$	25.4910	+	25.4910i	1.21662	+	1.21662i	0.968808	+	0.247811i	$0.0797112\pi$
$439$	25.4910	+	25.4910i	1.21662	+	1.21662i	0.247811	+	0.968808i	$0.420289\pi$
$440$	6.25874	−	2.86453i	0.298374	−	0.136561i
$441$		0			0
$442$	21.8909	−	6.15228i	1.04124	−	0.292634i
$443$	4.70852	−	11.3674i	0.223709	−	0.540081i	−0.771679	−	0.636012i	$-0.780583\pi$
$443$	4.70852	−	11.3674i	0.223709	−	0.540081i	0.995388	+	0.0959313i	$0.0305829\pi$
$444$		0			0
$445$	−11.2658	+	4.66644i	−0.534049	+	0.221210i
$446$	−26.7146	−	3.18664i	−1.26497	−	0.150892i
$447$		0			0
$448$	−20.3229	+	1.48735i	−0.960165	+	0.0702705i
$449$		−	1.47316i		−	0.0695229i	−0.999396	−	0.0347614i	$-0.988933\pi$
$449$		−	1.47316i		−	0.0695229i	0.999396	−	0.0347614i	$-0.0110671\pi$
$450$		0			0
$451$	0.744614	+	1.79766i	0.0350625	+	0.0846484i
$452$	−9.07816	−	2.19703i	−0.427001	−	0.103340i
$453$		0			0
$454$	5.77452	+	20.5468i	0.271012	+	0.964308i
$455$	−35.1850	−	35.1850i	−1.64950	−	1.64950i
$456$		0			0
$457$	−4.10233	+	4.10233i	−0.191899	+	0.191899i	−0.796516	−	0.604617i	$-0.793326\pi$
$457$	−4.10233	+	4.10233i	−0.191899	+	0.191899i	0.604617	+	0.796516i	$0.293326\pi$
$458$	32.0349	+	17.9789i	1.49689	+	0.840098i
$459$		0			0
$460$	38.4703	−	6.02103i	1.79369	−	0.280732i
$461$	−14.5005	+	6.00631i	−0.675356	+	0.279742i	−0.693884	−	0.720087i	$-0.744102\pi$
$461$	−14.5005	+	6.00631i	−0.675356	+	0.279742i	0.0185280	+	0.999828i	$0.494102\pi$
$462$		0			0
$463$	33.2789			1.54660			0.773302	−	0.634038i	$-0.218604\pi$
$463$	33.2789			1.54660			0.773302	+	0.634038i	$0.218604\pi$
$464$	−2.76574	+	33.5723i	−0.128396	+	1.55855i
$465$		0			0
$466$	21.0870	−	16.5924i	0.976837	−	0.768630i
$467$	6.92509	+	16.7186i	0.320455	+	0.773647i	0.999228	+	0.0392982i	$0.0125122\pi$
$467$	6.92509	+	16.7186i	0.320455	+	0.773647i	−0.678773	+	0.734349i	$0.737488\pi$
$468$		0			0
$469$	−18.9791	−	7.86142i	−0.876376	−	0.363007i
$470$	48.7077	+	27.3362i	2.24672	+	1.26092i
$471$		0			0
$472$	0.0358185	+	0.0332929i	0.00164868	+	0.00153243i
$473$	−0.533283	+	0.533283i	−0.0245204	+	0.0245204i
$474$		0			0
$475$	−63.1984	−	26.1777i	−2.89974	−	1.20111i
$476$	15.2408	−	9.30128i	0.698560	−	0.426324i
$477$		0			0
$478$	8.99247	+	1.07266i	0.411306	+	0.0490625i
$479$	9.61988			0.439543			0.219772	−	0.975551i	$-0.429469\pi$
$479$	9.61988			0.439543			0.219772	+	0.975551i	$0.429469\pi$
$480$		0			0
$481$	23.2151			1.05852
$482$	6.20300	+	0.739924i	0.282539	+	0.0337026i
$483$		0			0
$484$	11.1204	+	18.2215i	0.505472	+	0.828250i
$485$	32.8842	+	13.6211i	1.49319	+	0.618501i
$486$		0			0
$487$	12.8304	−	12.8304i	0.581403	−	0.581403i	−0.353886	−	0.935289i	$-0.615140\pi$
$487$	12.8304	−	12.8304i	0.581403	−	0.581403i	0.935289	+	0.353886i	$0.115140\pi$
$488$	1.04063	+	28.4761i	0.0471071	+	1.28905i
$489$		0			0
$490$	2.68892	+	1.50910i	0.121473	+	0.0681740i
$491$	−16.5426	−	6.85218i	−0.746558	−	0.309234i	−0.0232215	−	0.999730i	$-0.507392\pi$
$491$	−16.5426	−	6.85218i	−0.746558	−	0.309234i	−0.723336	+	0.690496i	$0.757392\pi$
$492$		0			0
$493$	−11.2954	−	27.2694i	−0.508718	−	1.22815i
$494$	26.5577	−	20.8970i	1.19489	−	0.940202i
$495$		0			0
$496$	−10.0117	+	19.4728i	−0.449539	+	0.874353i
$497$	25.1993			1.13034
$498$		0			0
$499$	21.6276	−	8.95845i	0.968185	−	0.401035i	0.158149	−	0.987415i	$-0.449448\pi$
$499$	21.6276	−	8.95845i	0.968185	−	0.401035i	0.810036	+	0.586380i	$0.199448\pi$
$500$	10.7102	+	68.4307i	0.478973	+	3.06031i
$501$		0			0
$502$	−18.3959	−	10.3243i	−0.821051	−	0.460797i
$503$	−27.0985	+	27.0985i	−1.20826	+	1.20826i	−0.236671	+	0.971590i	$0.576056\pi$
$503$	−27.0985	+	27.0985i	−1.20826	+	1.20826i	−0.971590	+	0.236671i	$0.923944\pi$
$504$		0			0
$505$	−22.0452	−	22.0452i	−0.980998	−	0.980998i
$506$	−0.999780	−	3.55740i	−0.0444457	−	0.158146i
$507$		0			0
$508$	9.38289	−	38.7702i	0.416298	−	1.72015i
$509$	−12.9535	−	31.2725i	−0.574153	−	1.38613i	−0.897990	−	0.440016i	$-0.854973\pi$
$509$	−12.9535	−	31.2725i	−0.574153	−	1.38613i	0.323837	−	0.946113i	$-0.395027\pi$
$510$		0			0
$511$		−	19.0009i		−	0.840549i
$512$	−19.8326	+	10.8935i	−0.876486	+	0.481427i
$513$		0			0
$514$	−38.1590	−	4.55178i	−1.68312	−	0.200771i
$515$	−62.6724	+	25.9598i	−2.76168	+	1.14392i
$516$		0			0
$517$	2.02841	−	4.89702i	0.0892094	−	0.215371i
$518$	17.5488	−	4.93196i	0.771050	−	0.216698i
$519$		0			0
$520$	−51.7861	−	19.2664i	−2.27097	−	0.844888i
$521$	19.8283	+	19.8283i	0.868693	+	0.868693i	0.992328	−	0.123635i	$-0.0394552\pi$
$521$	19.8283	+	19.8283i	0.868693	+	0.868693i	−0.123635	+	0.992328i	$0.539455\pi$
$522$		0			0
$523$	−7.19963	+	17.3815i	−0.314818	+	0.760038i	0.684695	+	0.728830i	$0.259935\pi$
$523$	−7.19963	+	17.3815i	−0.314818	+	0.760038i	−0.999513	+	0.0312081i	$0.990065\pi$
$524$	18.5412	−	2.90190i	0.809975	−	0.126770i
$525$		0			0
$526$	13.5274	−	10.6441i	0.589822	−	0.464105i
$527$		−	19.1854i		−	0.835729i
$528$		0			0
$529$			2.09570i			0.0911175i
$530$	27.6019	+	35.0787i	1.19895	+	1.52372i
$531$		0			0
$532$	15.6360	−	21.4386i	0.677907	−	0.929481i
$533$	5.97736	−	14.4306i	0.258908	−	0.625059i
$534$		0			0
$535$	5.15320	+	5.15320i	0.222792	+	0.222792i
$536$	−22.7962	+	0.833064i	−0.984644	+	0.0359829i
$537$		0			0
$538$	11.4778	+	40.8402i	0.494845	+	1.76075i
$539$	0.111979	−	0.270340i	0.00482326	−	0.0116444i
$540$		0			0
$541$	29.2905	−	12.1325i	1.25930	−	0.521619i	0.349605	−	0.936897i	$-0.386316\pi$
$541$	29.2905	−	12.1325i	1.25930	−	0.521619i	0.909694	+	0.415279i	$0.136316\pi$
$542$	5.08232	−	42.6066i	0.218304	−	1.83011i
$543$		0			0
$544$	11.0902	−	16.4346i	0.475490	−	0.704629i
$545$		−	30.8613i		−	1.32195i
$546$		0			0
$547$	12.7177	+	30.7032i	0.543769	+	1.31278i	0.922045	+	0.387082i	$0.126517\pi$
$547$	12.7177	+	30.7032i	0.543769	+	1.31278i	−0.378276	+	0.925693i	$0.623483\pi$
$548$	8.82724	+	14.4640i	0.377081	+	0.617873i
$549$		0			0
$550$	10.2182	−	2.87175i	0.435705	−	0.122452i
$551$	−31.0175	−	31.0175i	−1.32139	−	1.32139i
$552$		0			0
$553$	7.86833	−	7.86833i	0.334596	−	0.334596i
$554$	7.22620	−	12.8757i	0.307012	−	0.547036i
$555$		0			0
$556$	14.2003	−	19.4701i	0.602227	−	0.825716i
$557$	−24.6214	+	10.1985i	−1.04324	+	0.432125i	−0.837475	−	0.546476i	$-0.815969\pi$
$557$	−24.6214	+	10.1985i	−1.04324	+	0.432125i	−0.205768	+	0.978601i	$0.565969\pi$
$558$		0			0
$559$	6.05412			0.256062
$560$	−43.2393	−	3.56212i	−1.82720	−	0.150527i
$561$		0			0
$562$	1.78570	+	2.26941i	0.0753251	+	0.0957292i
$563$	−0.901476	−	2.17636i	−0.0379927	−	0.0917225i	0.903744	−	0.428073i	$-0.140807\pi$
$563$	−0.901476	−	2.17636i	−0.0379927	−	0.0917225i	−0.941737	+	0.336350i	$0.890807\pi$
$564$		0			0
$565$	−18.3728	−	7.61028i	−0.772951	−	0.320167i
$566$	14.8895	−	26.5302i	0.625853	−	1.11515i
$567$		0			0
$568$	25.4437	−	11.6452i	1.06759	−	0.488622i
$569$	−26.1461	+	26.1461i	−1.09610	+	1.09610i	−0.101241	+	0.994862i	$0.532281\pi$
$569$	−26.1461	+	26.1461i	−1.09610	+	1.09610i	−0.994862	+	0.101241i	$0.967719\pi$
$570$		0			0
$571$	−3.62983	−	1.50352i	−0.151903	−	0.0629205i	0.305436	−	0.952212i	$-0.401198\pi$
$571$	−3.62983	−	1.50352i	−0.151903	−	0.0629205i	−0.457340	+	0.889292i	$0.651198\pi$
$572$	−1.23339	+	5.09639i	−0.0515708	+	0.213091i
$573$		0			0
$574$	1.45268	−	12.1783i	0.0606338	−	0.508312i
$575$	60.0450			2.50405
$576$		0			0
$577$	5.12912			0.213528			0.106764	−	0.994284i	$-0.465951\pi$
$577$	5.12912			0.213528			0.106764	+	0.994284i	$0.465951\pi$
$578$	0.789947	−	6.62237i	0.0328575	−	0.275454i
$579$		0			0
$580$	−16.8706	+	69.7096i	−0.700515	+	2.89453i
$581$	39.4825	+	16.3542i	1.63801	+	0.678485i
$582$		0			0
$583$	2.99523	−	2.99523i	0.124050	−	0.124050i
$584$	−8.78077	−	19.1851i	−0.363351	−	0.793887i
$585$		0			0
$586$	0.369939	−	0.659160i	0.0152821	−	0.0272297i
$587$	−39.9161	−	16.5338i	−1.64751	−	0.682422i	−0.650490	−	0.759515i	$-0.725436\pi$
$587$	−39.9161	−	16.5338i	−1.64751	−	0.682422i	−0.997024	+	0.0770926i	$0.975436\pi$
$588$		0			0
$589$	−10.9112	−	26.3419i	−0.449587	−	1.08540i
$590$	0.0643843	+	0.0818248i	0.00265066	+	0.00336868i
$591$		0			0
$592$	15.4398	−	13.0895i	0.634572	−	0.537976i
$593$	14.3658			0.589931			0.294965	−	0.955508i	$-0.404692\pi$
$593$	14.3658			0.589931			0.294965	+	0.955508i	$0.404692\pi$
$594$		0			0
$595$	35.1216	−	14.5478i	1.43985	−	0.596404i
$596$	1.55667	−	2.13436i	0.0637638	−	0.0874268i
$597$		0			0
$598$	−14.5177	+	25.8678i	−0.593674	+	1.05781i
$599$	−6.69798	+	6.69798i	−0.273672	+	0.273672i	−0.830576	−	0.556905i	$-0.811989\pi$
$599$	−6.69798	+	6.69798i	−0.273672	+	0.273672i	0.556905	+	0.830576i	$0.311989\pi$
$600$		0			0
$601$	−9.70012	−	9.70012i	−0.395676	−	0.395676i	0.481029	−	0.876705i	$-0.340263\pi$
$601$	−9.70012	−	9.70012i	−0.395676	−	0.395676i	−0.876705	+	0.481029i	$0.840263\pi$
$602$	4.57644	−	1.28618i	0.186522	−	0.0524206i
$603$		0			0
$604$	−11.0500	−	18.1062i	−0.449618	−	0.736730i
$605$	17.3930	+	41.9905i	0.707128	+	1.70716i
$606$		0			0
$607$			38.7414i			1.57247i	0.617931	+	0.786233i	$0.287971\pi$
$607$			38.7414i			1.57247i	−0.617931	+	0.786233i	$0.712029\pi$
$608$	5.88036	−	28.8723i	0.238480	−	1.17093i
$609$		0			0
$610$	−7.18604	+	60.2428i	−0.290954	+	2.43916i
$611$	−39.3106	+	16.2830i	−1.59034	+	0.658739i
$612$		0			0
$613$	−14.1998	+	34.2813i	−0.573524	+	1.38461i	0.325013	+	0.945710i	$0.394631\pi$
$613$	−14.1998	+	34.2813i	−0.573524	+	1.38461i	−0.898536	+	0.438899i	$0.855369\pi$
$614$	−2.02370	−	7.20070i	−0.0816700	−	0.290597i
$615$		0			0
$616$	0.150361	+	4.11450i	0.00605820	+	0.165778i
$617$	−9.25656	−	9.25656i	−0.372655	−	0.372655i	0.495788	−	0.868443i	$-0.334879\pi$
$617$	−9.25656	−	9.25656i	−0.372655	−	0.372655i	−0.868443	+	0.495788i	$0.834879\pi$
$618$		0			0
$619$	0.139195	−	0.336046i	0.00559470	−	0.0135068i	−0.921057	−	0.389427i	$-0.872673\pi$
$619$	0.139195	−	0.336046i	0.00559470	−	0.0135068i	0.926652	+	0.375920i	$0.122673\pi$
$620$	−27.4708	+	37.6654i	−1.10326	+	1.51268i
$621$		0			0
$622$	−3.11613	−	3.96023i	−0.124945	−	0.158791i
$623$		−	7.29403i		−	0.292229i
$624$		0			0
$625$			81.8076i			3.27230i
$626$	5.94081	−	4.67456i	0.237443	−	0.186833i
$627$		0			0
$628$	48.8359	−	7.64336i	1.94876	−	0.305003i
$629$	−6.78729	+	16.3860i	−0.270627	+	0.653351i
$630$		0			0
$631$	−8.98002	−	8.98002i	−0.357489	−	0.357489i	0.505397	−	0.862887i	$-0.331346\pi$
$631$	−8.98002	−	8.98002i	−0.357489	−	0.357489i	−0.862887	+	0.505397i	$0.831346\pi$
$632$	4.30849	−	11.5808i	0.171383	−	0.460659i
$633$		0			0
$634$	26.0719	−	7.32732i	1.03545	−	0.291005i
$635$	32.5013	−	78.4650i	1.28977	−	3.11379i
$636$		0			0
$637$	−2.17015	+	0.898904i	−0.0859843	+	0.0356159i
$638$	6.75840	+	0.806174i	0.267568	+	0.0319167i
$639$		0			0
$640$	−45.3048	+	16.3853i	−1.79083	+	0.647685i
$641$			8.03068i			0.317193i	0.987344	+	0.158596i	$0.0506969\pi$
$641$			8.03068i			0.317193i	−0.987344	+	0.158596i	$0.949303\pi$
$642$		0			0
$643$	8.46145	+	20.4278i	0.333687	+	0.805592i	0.998293	+	0.0583982i	$0.0185993\pi$
$643$	8.46145	+	20.4278i	0.333687	+	0.805592i	−0.664606	+	0.747194i	$0.731401\pi$
$644$	−5.47875	+	22.6382i	−0.215893	+	0.892072i
$645$		0			0
$646$	6.98526	+	24.8548i	0.274832	+	0.977900i
$647$	−2.49537	−	2.49537i	−0.0981030	−	0.0981030i	0.656352	−	0.754455i	$-0.272099\pi$
$647$	−2.49537	−	2.49537i	−0.0981030	−	0.0981030i	−0.754455	+	0.656352i	$0.772099\pi$
$648$		0			0
$649$	0.00698670	−	0.00698670i	0.000274252	−	0.000274252i
$650$	−74.3020	−	41.7004i	−2.91436	−	1.63562i
$651$		0			0
$652$	−1.11812	−	7.14405i	−0.0437891	−	0.279783i
$653$	35.3520	−	14.6433i	1.38343	−	0.573036i	0.438034	−	0.898958i	$-0.355675\pi$
$653$	35.3520	−	14.6433i	1.38343	−	0.573036i	0.945397	+	0.325922i	$0.105675\pi$
$654$		0			0
$655$	39.9572			1.56126
$656$	−4.16111	−	12.9677i	−0.162464	−	0.506304i
$657$		0			0
$658$	−26.2565	+	20.6600i	−1.02358	+	0.805413i
$659$	−1.57465	−	3.80154i	−0.0613397	−	0.148087i	0.890238	−	0.455496i	$-0.150538\pi$
$659$	−1.57465	−	3.80154i	−0.0613397	−	0.148087i	−0.951578	+	0.307409i	$0.900538\pi$
$660$		0			0
$661$	−31.7340	−	13.1446i	−1.23431	−	0.511267i	−0.332377	−	0.943147i	$-0.607851\pi$
$661$	−31.7340	−	13.1446i	−1.23431	−	0.511267i	−0.901932	+	0.431879i	$0.857851\pi$
$662$	−13.5142	−	7.58454i	−0.525244	−	0.294782i
$663$		0			0
$664$	47.4230	−	1.73303i	1.84037	−	0.0672546i
$665$	39.9489	−	39.9489i	1.54915	−	1.54915i
$666$		0			0
$667$	35.5732	+	14.7349i	1.37740	+	0.570537i
$668$	1.00578	+	1.64805i	0.0389150	+	0.0637648i
$669$		0			0
$670$	−48.2266	−	5.75270i	−1.86316	−	0.222246i
$671$	5.75747			0.222265
$672$		0			0
$673$	21.6309			0.833810			0.416905	−	0.908950i	$-0.363115\pi$
$673$	21.6309			0.833810			0.416905	+	0.908950i	$0.363115\pi$
$674$	2.49248	+	0.297315i	0.0960067	+	0.0114521i
$675$		0			0
$676$	13.7361	−	8.38300i	0.528312	−	0.322423i
$677$	−10.9044	−	4.51674i	−0.419089	−	0.173592i	0.163166	−	0.986599i	$-0.447829\pi$
$677$	−10.9044	−	4.51674i	−0.419089	−	0.173592i	−0.582255	+	0.813006i	$0.697829\pi$
$678$		0			0
$679$	−15.0549	+	15.0549i	−0.577754	+	0.577754i
$680$	28.7393	−	30.9195i	1.10210	−	1.18571i
$681$		0			0
$682$	3.85800	+	2.16522i	0.147731	+	0.0829106i
$683$	44.8237	+	18.5666i	1.71513	+	0.710431i	0.999934	+	0.0115104i	$0.00366397\pi$
$683$	44.8237	+	18.5666i	1.71513	+	0.710431i	0.715199	+	0.698921i	$0.246336\pi$
$684$		0			0
$685$	13.8064	+	33.3316i	0.527516	+	1.27354i
$686$	−21.2659	+	16.7332i	−0.811937	+	0.638877i
$687$		0			0
$688$	4.02645	−	3.41353i	0.153507	−	0.130140i
$689$	−34.0035			−1.29543
$690$		0			0
$691$	12.6306	−	5.23178i	0.480492	−	0.199026i	−0.129272	−	0.991609i	$-0.541264\pi$
$691$	12.6306	−	5.23178i	0.480492	−	0.199026i	0.609764	+	0.792583i	$0.291264\pi$
$692$	−4.53170	+	0.709262i	−0.172270	+	0.0269621i
$693$		0			0
$694$	16.4990	+	9.25969i	0.626292	+	0.351493i
$695$	36.2808	−	36.2808i	1.37621	−	1.37621i
$696$		0			0
$697$	8.43802	+	8.43802i	0.319613	+	0.319613i
$698$	6.69648	+	23.8273i	0.253466	+	0.901876i
$699$		0			0
$700$	−65.0255	−	15.7370i	−2.45773	−	0.594804i
$701$	−3.42768	−	8.27515i	−0.129462	−	0.312548i	0.845836	−	0.533443i	$-0.179102\pi$
$701$	−3.42768	−	8.27515i	−0.129462	−	0.312548i	−0.975298	+	0.220895i	$0.929102\pi$
$702$		0			0
$703$			26.3583i			0.994122i
$704$	2.05323	+	4.08492i	0.0773840	+	0.153956i
$705$		0			0
$706$	−16.5355	−	1.97243i	−0.622321	−	0.0742334i
$707$	17.2292	−	7.13658i	0.647972	−	0.268399i
$708$		0			0
$709$	5.69918	−	13.7590i	0.214037	−	0.516731i	−0.779999	−	0.625780i	$-0.784781\pi$
$709$	5.69918	−	13.7590i	0.214037	−	0.516731i	0.994036	+	0.109049i	$0.0347806\pi$
$710$	57.3553	−	16.1193i	2.15251	−	0.604946i
$711$		0			0
$712$	−3.37075	−	7.36477i	−0.126324	−	0.276006i
$713$	17.6971	+	17.6971i	0.662762	+	0.662762i
$714$		0			0
$715$	−4.27233	+	10.3143i	−0.159776	+	0.385734i
$716$	−3.09562	−	19.7790i	−0.115689	−	0.739174i
$717$		0			0
$718$	26.0392	−	20.4891i	0.971776	−	0.764647i
$719$		−	20.5784i		−	0.767445i	−0.923448	−	0.383722i	$-0.874642\pi$
$719$		−	20.5784i		−	0.767445i	0.923448	−	0.383722i	$-0.125358\pi$
$720$		0			0
$721$		−	40.5773i		−	1.51118i
$722$	7.11058	+	9.03671i	0.264628	+	0.336311i
$723$		0			0
$724$	5.20087	+	3.79320i	0.193289	+	0.140973i
$725$	−42.3242	+	102.180i	−1.57188	+	3.79485i
$726$		0			0
$727$	27.0543	+	27.0543i	1.00339	+	1.00339i	0.999994	+	0.00339404i	$0.00108036\pi$
$727$	27.0543	+	27.0543i	1.00339	+	1.00339i	0.00339404	+	0.999994i	$0.498920\pi$
$728$	22.5015	−	24.2085i	0.833962	−	0.897227i
$729$		0			0
$730$	−12.1543	−	43.2473i	−0.449852	−	1.60066i
$731$	−1.77001	+	4.27319i	−0.0654664	+	0.158050i
$732$		0			0
$733$	8.68221	−	3.59629i	0.320685	−	0.132832i	−0.216534	−	0.976275i	$-0.569475\pi$
$733$	8.68221	−	3.59629i	0.320685	−	0.132832i	0.537218	+	0.843443i	$0.319475\pi$
$734$	1.10378	−	9.25332i	0.0407412	−	0.341546i
$735$		0			0
$736$	4.92980	+	25.3897i	0.181715	+	0.935875i
$737$			4.60908i			0.169777i
$738$		0			0
$739$	7.29030	+	17.6003i	0.268178	+	0.647439i	0.999398	−	0.0347030i	$-0.0110485\pi$
$739$	7.29030	+	17.6003i	0.268178	+	0.647439i	−0.731220	+	0.682142i	$0.761049\pi$
$740$	36.7874	−	22.4510i	1.35233	−	0.825314i
$741$		0			0
$742$	−25.7040	+	7.22391i	−0.943622	+	0.265198i
$743$	18.2313	+	18.2313i	0.668841	+	0.668841i	0.957448	−	0.288607i	$-0.0931919\pi$
$743$	18.2313	+	18.2313i	0.668841	+	0.668841i	−0.288607	+	0.957448i	$0.593192\pi$
$744$		0			0
$745$	3.97719	−	3.97719i	0.145713	−	0.145713i
$746$	−6.85754	+	12.2188i	−0.251072	+	0.447362i
$747$		0			0
$748$	−3.23659	−	2.36058i	−0.118342	−	0.0863112i
$749$	−4.02744	+	1.66822i	−0.147159	+	0.0609554i
$750$		0			0
$751$	−10.8193			−0.394802			−0.197401	−	0.980323i	$-0.563250\pi$
$751$	−10.8193			−0.394802			−0.197401	+	0.980323i	$0.563250\pi$
$752$	−16.9636	+	32.9942i	−0.618599	+	1.20317i
$753$		0			0
$754$	−33.7864	−	42.9386i	−1.23043	−	1.56373i
$755$	−17.2830	−	41.7248i	−0.628992	−	1.51852i
$756$		0			0
$757$	47.3522	+	19.6139i	1.72105	+	0.712881i	0.999796	+	0.0202058i	$0.00643214\pi$
$757$	47.3522	+	19.6139i	1.72105	+	0.712881i	0.721250	+	0.692675i	$0.243568\pi$
$758$	18.2118	−	32.4500i	0.661484	−	1.17864i
$759$		0			0
$760$	21.8750	−	58.7977i	0.793489	−	2.13282i
$761$	−11.0778	+	11.0778i	−0.401570	+	0.401570i	−0.878786	−	0.477216i	$-0.841646\pi$
$761$	−11.0778	+	11.0778i	−0.401570	+	0.401570i	0.477216	+	0.878786i	$0.341646\pi$
$762$		0			0
$763$	17.0550	+	7.06441i	0.617432	+	0.255749i
$764$	17.6383	+	4.26869i	0.638130	+	0.154436i
$765$		0			0
$766$	−5.07095	+	42.5113i	−0.183221	+	1.53599i
$767$	−0.0793167			−0.00286396
$768$		0			0
$769$	−5.28351			−0.190528			−0.0952641	−	0.995452i	$-0.530370\pi$
$769$	−5.28351			−0.190528			−0.0952641	+	0.995452i	$0.530370\pi$
$770$	−1.03831	+	8.70446i	−0.0374181	+	0.313687i
$771$		0			0
$772$	−9.97175	−	2.41329i	−0.358891	−	0.0868563i
$773$	49.7146	+	20.5924i	1.78811	+	0.740659i	0.990505	+	0.137476i	$0.0438990\pi$
$773$	49.7146	+	20.5924i	1.78811	+	0.740659i	0.797603	+	0.603183i	$0.206101\pi$
$774$		0			0
$775$	−50.8328	+	50.8328i	−1.82597	+	1.82597i
$776$	−8.24367	+	22.1582i	−0.295931	+	0.795431i
$777$		0			0
$778$	−4.93092	+	8.78595i	−0.176782	+	0.314992i
$779$	16.3844	+	6.78666i	0.587033	+	0.243157i
$780$		0			0
$781$	−2.16362	−	5.22343i	−0.0774203	−	0.186909i
$782$	−14.0138	−	17.8099i	−0.501133	−	0.636881i
$783$		0			0
$784$	−0.936477	+	1.82145i	−0.0334456	+	0.0650516i
$785$	105.244			3.75632
$786$		0			0
$787$	−7.70131	+	3.18999i	−0.274522	+	0.113711i	−0.515697	−	0.856771i	$-0.672467\pi$
$787$	−7.70131	+	3.18999i	−0.274522	+	0.113711i	0.241175	+	0.970482i	$0.422467\pi$
$788$	9.03831	+	6.59200i	0.321977	+	0.234830i
$789$		0			0
$790$	12.8757	−	22.9420i	0.458098	−	0.816241i
$791$	8.41138	−	8.41138i	0.299074	−	0.299074i
$792$		0			0
$793$	−32.6810	−	32.6810i	−1.16054	−	1.16054i
$794$	−24.1888	+	6.79808i	−0.858428	+	0.241255i
$795$		0			0
$796$	−3.81278	+	2.32690i	−0.135140	+	0.0824746i
$797$	20.5711	+	49.6631i	0.728667	+	1.75916i	0.646990	+	0.762498i	$0.276027\pi$
$797$	20.5711	+	49.6631i	0.728667	+	1.75916i	0.0816765	+	0.996659i	$0.473973\pi$
$798$		0			0
$799$		−	32.5073i		−	1.15002i
$800$	−72.9286	+	14.1602i	−2.57842	+	0.500640i
$801$		0			0
$802$	2.11406	−	17.7228i	0.0746499	−	0.625813i
$803$	−3.93860	+	1.63142i	−0.138990	+	0.0575716i
$804$		0			0
$805$	−18.9778	+	45.8164i	−0.668879	+	1.61482i
$806$	−9.60870	−	34.1895i	−0.338452	−	1.20427i
$807$		0			0
$808$	14.0983	−	15.1678i	0.495978	−	0.533603i
$809$	−26.4554	−	26.4554i	−0.930121	−	0.930121i	0.0675917	−	0.997713i	$-0.478468\pi$
$809$	−26.4554	−	26.4554i	−0.930121	−	0.930121i	−0.997713	+	0.0675917i	$0.978468\pi$
$810$		0			0
$811$	17.4357	−	42.0936i	0.612252	−	1.47811i	−0.248269	−	0.968691i	$-0.579862\pi$
$811$	17.4357	−	42.0936i	0.612252	−	1.47811i	0.860521	−	0.509415i	$-0.170138\pi$
$812$	−34.6620	−	25.2804i	−1.21640	−	0.887167i
$813$		0			0
$814$	−2.52907	−	3.21414i	−0.0886437	−	0.112656i
$815$		−	15.3958i		−	0.539292i
$816$		0			0
$817$			6.87381i			0.240484i
$818$	37.1340	−	29.2191i	1.29836	−	1.02162i
$819$		0			0
$820$	−4.48371	−	28.6479i	−0.156578	−	1.00043i
$821$	10.4508	−	25.2305i	0.364736	−	0.880551i	−0.629858	−	0.776710i	$-0.716887\pi$
$821$	10.4508	−	25.2305i	0.364736	−	0.880551i	0.994594	−	0.103840i	$-0.0331131\pi$
$822$		0			0
$823$	21.4794	+	21.4794i	0.748725	+	0.748725i	0.974240	−	0.225515i	$-0.0724064\pi$
$823$	21.4794	+	21.4794i	0.748725	+	0.748725i	−0.225515	+	0.974240i	$0.572406\pi$
$824$	−18.7517	−	40.9708i	−0.653248	−	1.42729i
$825$		0			0
$826$	−0.0599572	+	0.0168505i	−0.00208618	+	0.000586305i
$827$	7.56490	−	18.2633i	0.263057	−	0.635077i	−0.736067	−	0.676908i	$-0.763319\pi$
$827$	7.56490	−	18.2633i	0.263057	−	0.635077i	0.999125	+	0.0418317i	$0.0133193\pi$
$828$		0			0
$829$	−15.9436	+	6.60407i	−0.553745	+	0.229369i	−0.641967	−	0.766732i	$-0.721882\pi$
$829$	−15.9436	+	6.60407i	−0.553745	+	0.229369i	0.0882219	+	0.996101i	$0.471882\pi$
$830$	100.326	+	11.9674i	3.48237	+	0.415394i
$831$		0			0
$832$	11.5324	−	34.8418i	0.399815	−	1.20792i
$833$		−	1.79457i		−	0.0621780i
$834$		0			0
$835$	1.57312	+	3.79784i	0.0544399	+	0.131430i
$836$	−5.78641	−	1.40039i	−0.200127	−	0.0484334i
$837$		0			0
$838$	−1.41322	−	5.02850i	−0.0488190	−	0.173707i
$839$	14.9035	+	14.9035i	0.514524	+	0.514524i	0.915909	−	0.401385i	$-0.131471\pi$
$839$	14.9035	+	14.9035i	0.514524	+	0.514524i	−0.401385	+	0.915909i	$0.631471\pi$
$840$		0			0
$841$	−29.6431	+	29.6431i	−1.02218	+	1.02218i
$842$	3.59734	+	2.01893i	0.123972	+	0.0695768i
$843$		0			0
$844$	−2.42694	+	0.379843i	−0.0835388	+	0.0130747i
$845$	31.6542	−	13.1116i	1.08894	−	0.451052i
$846$		0			0
$847$	−27.1868			−0.934148
$848$	−22.6149	+	19.1724i	−0.776599	+	0.658383i
$849$		0			0
$850$	51.1568	−	40.2530i	1.75466	−	1.38067i
$851$	−8.85406	−	21.3756i	−0.303513	−	0.732746i
$852$		0			0
$853$	1.48079	+	0.613364i	0.0507014	+	0.0210012i	0.407890	−	0.913031i	$-0.366265\pi$
$853$	1.48079	+	0.613364i	0.0507014	+	0.0210012i	−0.357189	+	0.934032i	$0.616265\pi$
$854$	−31.6472	−	17.7613i	−1.08294	−	0.607779i
$855$		0			0
$856$	−3.29557	+	3.54557i	−0.112640	+	0.121185i
$857$	−11.5944	+	11.5944i	−0.396059	+	0.396059i	−0.876840	−	0.480782i	$-0.840353\pi$
$857$	−11.5944	+	11.5944i	−0.396059	+	0.396059i	0.480782	+	0.876840i	$0.340353\pi$
$858$		0			0
$859$	−19.6933	−	8.15722i	−0.671926	−	0.278321i	0.0205213	−	0.999789i	$-0.493467\pi$
$859$	−19.6933	−	8.15722i	−0.671926	−	0.278321i	−0.692447	+	0.721469i	$0.743467\pi$
$860$	9.59357	−	5.85485i	0.327138	−	0.199649i
$861$		0			0
$862$	−42.9759	−	5.12637i	−1.46376	−	0.174605i
$863$	0.877535			0.0298716			0.0149358	−	0.999888i	$-0.495246\pi$
$863$	0.877535			0.0298716			0.0149358	+	0.999888i	$0.495246\pi$
$864$		0			0
$865$	−9.76606			−0.332056
$866$	11.9735	+	1.42826i	0.406877	+	0.0485343i
$867$		0			0
$868$	−14.5268	−	23.8032i	−0.493073	−	0.807934i
$869$	−2.30656	−	0.955410i	−0.0782448	−	0.0324101i
$870$		0			0
$871$	26.1624	−	26.1624i	0.886478	−	0.886478i
$872$	20.4850	−	0.748606i	0.693711	−	0.0253510i
$873$		0			0
$874$	−29.3701	−	16.4833i	−0.993459	−	0.557557i
$875$	−81.4978	−	33.7575i	−2.75513	−	1.14121i
$876$		0			0
$877$	−7.80862	−	18.8517i	−0.263678	−	0.636576i	0.735482	−	0.677544i	$-0.236956\pi$
$877$	−7.80862	−	18.8517i	−0.263678	−	0.636576i	−0.999160	+	0.0409684i	$0.986956\pi$
$878$	−40.0659	+	31.5260i	−1.35216	+	1.06395i
$879$		0			0
$880$	2.97417	+	9.26871i	0.100259	+	0.312448i
$881$	−35.4734			−1.19513			−0.597564	−	0.801821i	$-0.703865\pi$
$881$	−35.4734			−1.19513			−0.597564	+	0.801821i	$0.703865\pi$
$882$		0			0
$883$	0.754129	−	0.312371i	0.0253785	−	0.0105121i	−0.369958	−	0.929048i	$-0.620628\pi$
$883$	0.754129	−	0.312371i	0.0253785	−	0.0105121i	0.395337	+	0.918536i	$0.370628\pi$
$884$	4.97252	+	31.7711i	0.167244	+	1.06858i
$885$		0			0
$886$	15.1740	+	8.51610i	0.509782	+	0.286104i
$887$	24.7334	−	24.7334i	0.830466	−	0.830466i	−0.157115	−	0.987580i	$-0.550219\pi$
$887$	24.7334	−	24.7334i	0.830466	−	0.830466i	0.987580	+	0.157115i	$0.0502192\pi$
$888$		0			0
$889$	35.9226	+	35.9226i	1.20480	+	1.20480i
$890$	−4.66579	−	16.6017i	−0.156398	−	0.556491i
$891$		0			0
$892$	8.94973	−	36.9803i	0.299659	−	1.23819i
$893$	−18.4876	−	44.6330i	−0.618664	−	1.49359i
$894$		0			0
$895$		−	42.6247i		−	1.42479i
$896$	1.31560	−	28.7877i	0.0439510	−	0.961729i
$897$		0			0
$898$	2.06870	+	0.246764i	0.0690335	+	0.00823464i
$899$	−42.5897	+	17.6412i	−1.42045	+	0.588368i
$900$		0			0
$901$	9.94143	−	24.0007i	0.331197	−	0.799580i
$902$	−2.64910	+	0.744511i	−0.0882055	+	0.0247895i
$903$		0			0
$904$	4.60585	−	12.3801i	0.153188	−	0.411755i
$905$	9.69135	+	9.69135i	0.322152	+	0.322152i
$906$		0			0
$907$	7.96975	−	19.2407i	0.264631	−	0.638876i	−0.734583	−	0.678519i	$-0.762622\pi$
$907$	7.96975	−	19.2407i	0.264631	−	0.638876i	0.999214	+	0.0396429i	$0.0126220\pi$
$908$	−29.8202	+	4.66720i	−0.989619	+	0.154886i
$909$		0			0
$910$	55.3026	−	43.5152i	1.83326	−	1.44251i
$911$			20.9956i			0.695616i	0.937566	+	0.347808i	$0.113074\pi$
$911$			20.9956i			0.695616i	−0.937566	+	0.347808i	$0.886926\pi$
$912$		0			0
$913$		−	9.58830i		−	0.317326i
$914$	−5.07357	−	6.44791i	−0.167819	−	0.213278i
$915$		0			0
$916$	−30.6130	+	41.9737i	−1.01148	+	1.38685i
$917$	−9.14653	+	22.0817i	−0.302045	+	0.729202i
$918$		0			0
$919$	−3.84761	−	3.84761i	−0.126921	−	0.126921i	0.640793	−	0.767714i	$-0.278606\pi$
$919$	−3.84761	−	3.84761i	−0.126921	−	0.126921i	−0.767714	+	0.640793i	$0.778606\pi$
$920$	2.01105	+	55.0308i	0.0663023	+	1.81431i
$921$		0			0
$922$	−6.00548	−	21.3686i	−0.197780	−	0.703736i
$923$	−17.3683	+	41.9309i	−0.571686	+	1.38017i
$924$		0			0
$925$	61.3988	−	25.4322i	2.01878	−	0.836206i
$926$	−5.57444	+	46.7322i	−0.183188	+	1.53572i
$927$		0			0
$928$	−46.6809	−	9.50739i	−1.53237	−	0.312095i
$929$		−	7.40512i		−	0.242954i	−0.992594	−	0.121477i	$-0.961237\pi$
$929$		−	7.40512i		−	0.242954i	0.992594	−	0.121477i	$-0.0387631\pi$
$930$		0			0
$931$	−1.02061	−	2.46397i	−0.0334491	−	0.0807534i
$932$	19.7679	+	32.3910i	0.647518	+	1.06100i
$933$		0			0
$934$	−24.6373	+	6.92413i	−0.806157	+	0.226565i
$935$	−6.03110	−	6.03110i	−0.197238	−	0.197238i
$936$		0			0
$937$	26.6551	−	26.6551i	0.870783	−	0.870783i	−0.121774	−	0.992558i	$-0.538858\pi$
$937$	26.6551	−	26.6551i	0.870783	−	0.870783i	0.992558	+	0.121774i	$0.0388585\pi$
$938$	14.2186	−	25.3348i	0.464254	−	0.827210i
$939$		0			0
$940$	−46.5459	+	63.8193i	−1.51816	+	2.08156i
$941$	−7.74358	+	3.20749i	−0.252433	+	0.104561i	−0.505312	−	0.862937i	$-0.668623\pi$
$941$	−7.74358	+	3.20749i	−0.252433	+	0.104561i	0.252879	+	0.967498i	$0.418623\pi$
$942$		0			0
$943$	−15.5669			−0.506928
$944$	−0.0527517	+	0.0447217i	−0.00171692	+	0.00145557i
$945$		0			0
$946$	−0.659539	−	0.838196i	−0.0214435	−	0.0272521i
$947$	14.6443	+	35.3545i	0.475876	+	1.14887i	0.961526	+	0.274714i	$0.0885831\pi$
$947$	14.6443	+	35.3545i	0.475876	+	1.14887i	−0.485650	+	0.874154i	$0.661417\pi$
$948$		0			0
$949$	31.6169	+	13.0962i	1.02633	+	0.425119i
$950$	47.3463	−	84.3620i	1.53612	−	2.73707i
$951$		0			0
$952$	10.5085	+	22.9600i	0.340582	+	0.744139i
$953$	−1.25476	+	1.25476i	−0.0406458	+	0.0406458i	−0.727138	−	0.686492i	$-0.759150\pi$
$953$	−1.25476	+	1.25476i	−0.0406458	+	0.0406458i	0.686492	+	0.727138i	$0.259150\pi$
$954$		0			0
$955$	35.6972	+	14.7863i	1.15513	+	0.478472i
$956$	−3.01260	+	12.4481i	−0.0974344	+	0.402600i
$957$		0			0
$958$	−1.61139	+	13.5088i	−0.0520617	+	0.436449i
$959$	−21.5806			−0.696873
$960$		0			0
$961$	1.03604			0.0334206
$962$	−3.88868	+	32.6000i	−0.125376	+	1.05107i
$963$		0			0
$964$	−2.07809	+	8.58668i	−0.0669307	+	0.276558i
$965$	−20.1813	−	8.35938i	−0.649660	−	0.269098i
$966$		0			0
$967$	−7.94156	+	7.94156i	−0.255383	+	0.255383i	−0.823173	−	0.567790i	$-0.807799\pi$
$967$	−7.94156	+	7.94156i	−0.255383	+	0.255383i	0.567790	+	0.823173i	$0.307799\pi$
$968$	−27.4504	+	12.5637i	−0.882290	+	0.403812i
$969$		0			0
$970$	−24.6358	+	43.8962i	−0.791008	+	1.40942i
$971$	14.0116	+	5.80380i	0.449654	+	0.186253i	0.596006	−	0.802980i	$-0.296753\pi$
$971$	14.0116	+	5.80380i	0.449654	+	0.186253i	−0.146352	+	0.989233i	$0.546753\pi$
$972$		0			0
$973$	11.7450	+	28.3549i	0.376527	+	0.909017i
$974$	15.8681	+	20.1664i	0.508446	+	0.646175i
$975$		0			0
$976$	−40.1621	−	3.30861i	−1.28556	−	0.105906i
$977$	17.0869			0.546659			0.273330	−	0.961920i	$-0.411875\pi$
$977$	17.0869			0.546659			0.273330	+	0.961920i	$0.411875\pi$
$978$		0			0
$979$	−1.51194	+	0.626267i	−0.0483219	+	0.0200156i
$980$	−2.56957	+	3.52315i	−0.0820819	+	0.112543i
$981$		0			0
$982$	12.3932	−	22.0823i	0.395484	−	0.704675i
$983$	32.8857	−	32.8857i	1.04889	−	1.04889i	0.0501480	−	0.998742i	$-0.484031\pi$
$983$	32.8857	−	32.8857i	1.04889	−	1.04889i	0.998742	−	0.0501480i	$-0.0159693\pi$
$984$		0			0
$985$	16.8421	+	16.8421i	0.536633	+	0.536633i
$986$	40.1854	−	11.2938i	1.27976	−	0.359668i
$987$		0			0
$988$	24.8963	+	40.7942i	0.792056	+	1.29784i
$989$	−2.30900	−	5.57441i	−0.0734218	−	0.177256i
$990$		0			0
$991$			35.5028i			1.12778i	0.825849	+	0.563892i	$0.190697\pi$
$991$			35.5028i			1.12778i	−0.825849	+	0.563892i	$0.809303\pi$
$992$	−25.6678	−	17.3209i	−0.814953	−	0.549938i
$993$		0			0
$994$	−4.22104	+	35.3863i	−0.133883	+	1.12239i
$995$	−8.78635	+	3.63943i	−0.278546	+	0.115378i
$996$		0			0
$997$	−7.27295	+	17.5585i	−0.230337	+	0.556082i	−0.996217	−	0.0869012i	$-0.972304\pi$
$997$	−7.27295	+	17.5585i	−0.230337	+	0.556082i	0.765880	+	0.642983i	$0.222304\pi$
$998$	8.95721	+	31.8713i	0.283535	+	1.00887i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.a.107.14	✓	128
3.2	odd	2	inner	864.2.w.a.107.19	yes	128
32.3	odd	8	inner	864.2.w.a.323.19	yes	128
96.35	even	8	inner	864.2.w.a.323.14	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.a.107.14	✓	128	1.1	even	1	trivial
864.2.w.a.107.19	yes	128	3.2	odd	2	inner
864.2.w.a.323.14	yes	128	96.35	even	8	inner
864.2.w.a.323.19	yes	128	32.3	odd	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.167507 + 1.40426i) q^{2} +(-1.94388 - 0.470445i) q^{4} +(-3.93413 - 1.62957i) q^{5} +(1.80111 - 1.80111i) q^{7} +(0.986240 - 2.65091i) q^{8} +O(q^{10})\)	\(q+(-0.167507 + 1.40426i) q^{2} +(-1.94388 - 0.470445i) q^{4} +(-3.93413 - 1.62957i) q^{5} +(1.80111 - 1.80111i) q^{7} +(0.986240 - 2.65091i) q^{8} +(2.94733 - 5.25157i) q^{10} +(-0.527986 - 0.218699i) q^{11} +(1.75560 + 4.23839i) q^{13} +(2.22752 + 2.83092i) q^{14} +(3.55736 + 1.82898i) q^{16} -3.50487 q^{17} +(-4.81224 + 1.99330i) q^{19} +(6.88086 + 5.01848i) q^{20} +(0.395551 - 0.704796i) q^{22} +(3.23298 - 3.23298i) q^{23} +(9.28633 + 9.28633i) q^{25} +(-6.24586 + 1.75535i) q^{26} +(-4.34847 + 2.65382i) q^{28} +(3.22277 + 7.78045i) q^{29} +5.47393i q^{31} +(-3.16424 + 4.68909i) q^{32} +(0.587088 - 4.92174i) q^{34} +(-10.0208 + 4.15076i) q^{35} +(1.93653 - 4.67520i) q^{37} +(-1.99302 - 7.09152i) q^{38} +(-8.19984 + 8.82188i) q^{40} +(-2.40752 - 2.40752i) q^{41} +(0.505016 - 1.21922i) q^{43} +(0.923458 + 0.673514i) q^{44} +(3.99839 + 5.08148i) q^{46} +9.27490i q^{47} +0.512021i q^{49} +(-14.5959 + 11.4849i) q^{50} +(-1.41875 - 9.06484i) q^{52} +(-2.83647 + 6.84783i) q^{53} +(1.72078 + 1.72078i) q^{55} +(-2.99825 - 6.55090i) q^{56} +(-11.4656 + 3.22232i) q^{58} +(-0.00661636 + 0.0159733i) q^{59} +(-9.30765 + 3.85536i) q^{61} +(-7.68682 - 0.916920i) q^{62} +(-6.05466 - 5.22887i) q^{64} -19.5352i q^{65} +(-3.08636 - 7.45113i) q^{67} +(6.81305 + 1.64885i) q^{68} +(-4.15018 - 14.7671i) q^{70} +(6.99549 + 6.99549i) q^{71} +(5.27477 - 5.27477i) q^{73} +(6.24081 + 3.50252i) q^{74} +(10.2922 - 1.61084i) q^{76} +(-1.34486 + 0.557060i) q^{77} +4.36861 q^{79} +(-11.0147 - 12.9924i) q^{80} +(3.78405 - 2.97750i) q^{82} +(6.42057 + 15.5006i) q^{83} +(13.7886 + 5.71142i) q^{85} +(1.62750 + 0.913400i) q^{86} +(-1.10047 + 1.18396i) q^{88} +(2.02487 - 2.02487i) q^{89} +(10.7958 + 4.47177i) q^{91} +(-7.80547 + 4.76359i) q^{92} +(-13.0244 - 1.55361i) q^{94} +22.1802 q^{95} -8.35869 q^{97} +(-0.719010 - 0.0857670i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

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