LMFDB - Embedded newform 180.2.k.e.127.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,2,Mod(127,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("180.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$180 = 2^{2} \cdot 3^{2} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	180.k (of order $4$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64$ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{5}$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.5
Root			$1.19252 - 0.760198i$ of defining polynomial
Character	$\chi$	$=$	180.127
Dual form			180.2.k.e.163.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19252 - 0.760198i) q^{2} +(0.844199 - 1.81310i) q^{4} +(-0.432320 - 2.19388i) q^{5} +(-0.611393 + 0.611393i) q^{7} +(-0.371591 - 2.80391i) q^{8} +(-2.18333 - 2.28759i) q^{10} +5.12822i q^{11} +(1.76156 - 1.76156i) q^{13} +(-0.264318 + 1.19388i) q^{14} +(-2.57466 - 3.06123i) q^{16} +(3.76156 + 3.76156i) q^{17} +1.22279 q^{19} +(-4.34268 - 1.06823i) q^{20} +(3.89846 + 6.11549i) q^{22} +(-1.07700 - 1.07700i) q^{23} +(-4.62620 + 1.89692i) q^{25} +(0.761557 - 3.43982i) q^{26} +(0.592379 + 1.62465i) q^{28} +0.864641i q^{29} +7.81086i q^{31} +(-5.39747 - 1.69333i) q^{32} +(7.34525 + 1.62620i) q^{34} +(1.60564 + 1.07700i) q^{35} +(-1.76156 - 1.76156i) q^{37} +(1.45820 - 0.929560i) q^{38} +(-5.99079 + 2.02741i) q^{40} -5.52311 q^{41} +(-6.20522 - 6.20522i) q^{43} +(9.29797 + 4.32924i) q^{44} +(-2.10308 - 0.465611i) q^{46} +(2.29979 - 2.29979i) q^{47} +6.25240i q^{49} +(-4.07479 + 5.77893i) q^{50} +(-1.70677 - 4.68098i) q^{52} +(2.62620 - 2.62620i) q^{53} +(11.2507 - 2.21703i) q^{55} +(1.94148 + 1.48710i) q^{56} +(0.657298 + 1.03110i) q^{58} -0.528636 q^{59} +4.98168 q^{61} +(5.93780 + 9.31460i) q^{62} +(-7.72384 + 2.08382i) q^{64} +(-4.62620 - 3.10308i) q^{65} +(6.20522 - 6.20522i) q^{67} +(9.99558 - 3.64457i) q^{68} +(2.73349 + 0.0637434i) q^{70} -8.10243i q^{71} +(-2.25240 + 2.25240i) q^{73} +(-3.43982 - 0.761557i) q^{74} +(1.03228 - 2.21703i) q^{76} +(-3.13536 - 3.13536i) q^{77} -15.9133 q^{79} +(-5.60289 + 6.97191i) q^{80} +(-6.58641 + 4.19866i) q^{82} +(-7.95665 - 7.95665i) q^{83} +(6.62620 - 9.87859i) q^{85} +(-12.1170 - 2.68264i) q^{86} +(14.3791 - 1.90560i) q^{88} +7.25240i q^{89} +2.15401i q^{91} +(-2.86192 + 1.04351i) q^{92} +(0.994247 - 4.49084i) q^{94} +(-0.528636 - 2.68264i) q^{95} +(0.793833 + 0.793833i) q^{97} +(4.75306 + 7.45610i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q + 12 q^{8} - 8 q^{10} - 4 q^{13} + 12 q^{16} + 20 q^{17} - 20 q^{20} + 12 q^{22} - 20 q^{25} - 16 q^{26} - 4 q^{28} - 20 q^{32} + 4 q^{37} - 16 q^{38} - 8 q^{40} - 16 q^{41} - 40 q^{46} + 16 q^{50}+ \cdots - 24 q^{98}+O(q^{100})$ 12 * q + 12 * q^8 - 8 * q^10 - 4 * q^13 + 12 * q^16 + 20 * q^17 - 20 * q^20 + 12 * q^22 - 20 * q^25 - 16 * q^26 - 4 * q^28 - 20 * q^32 + 4 * q^37 - 16 * q^38 - 8 * q^40 - 16 * q^41 - 40 * q^46 + 16 * q^50 - 8 * q^52 - 4 * q^53 + 64 * q^56 - 20 * q^58 - 32 * q^61 + 56 * q^62 - 20 * q^65 + 16 * q^68 + 44 * q^70 + 44 * q^73 + 8 * q^76 - 48 * q^77 - 4 * q^80 + 16 * q^82 + 44 * q^85 - 64 * q^86 + 60 * q^88 - 56 * q^92 - 20 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$ .

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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

)

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

$2$	1.19252	−	0.760198i	0.843238	−	0.537541i
$2$	1.19252	−	0.760198i	0.843238	−	0.537541i
$3$		0			0
$3$		0			0
$4$	0.844199	−	1.81310i	0.422099	−	0.906550i
$5$	−0.432320	−	2.19388i	−0.193340	−	0.981132i
$5$	−0.432320	−	2.19388i	−0.193340	−	0.981132i
$6$		0			0
$7$	−0.611393	+	0.611393i	−0.231085	+	0.231085i	−0.813145	−	0.582060i	$-0.802247\pi$
$7$	−0.611393	+	0.611393i	−0.231085	+	0.231085i	0.582060	+	0.813145i	$0.302247\pi$
$8$	−0.371591	−	2.80391i	−0.131377	−	0.991332i
$9$		0			0
$10$	−2.18333	−	2.28759i	−0.690430	−	0.723399i
$11$			5.12822i			1.54622i	0.634274	+	0.773108i	$0.281299\pi$
$11$			5.12822i			1.54622i	−0.634274	+	0.773108i	$0.718701\pi$
$12$		0			0
$13$	1.76156	−	1.76156i	0.488568	−	0.488568i	−0.419286	−	0.907854i	$-0.637720\pi$
$13$	1.76156	−	1.76156i	0.488568	−	0.488568i	0.907854	+	0.419286i	$0.137720\pi$
$14$	−0.264318	+	1.19388i	−0.0706419	+	0.319077i
$15$		0			0
$16$	−2.57466	−	3.06123i	−0.643664	−	0.765308i
$17$	3.76156	+	3.76156i	0.912312	+	0.912312i	0.996454	−	0.0841421i	$-0.0268150\pi$
$17$	3.76156	+	3.76156i	0.912312	+	0.912312i	−0.0841421	+	0.996454i	$0.526815\pi$
$18$		0			0
$19$	1.22279			0.280527			0.140263	−	0.990114i	$-0.455205\pi$
$19$	1.22279			0.280527			0.140263	+	0.990114i	$0.455205\pi$
$20$	−4.34268	−	1.06823i	−0.971053	−	0.238863i
$21$		0			0
$22$	3.89846	+	6.11549i	0.831154	+	1.30383i
$23$	−1.07700	−	1.07700i	−0.224571	−	0.224571i	0.585849	−	0.810420i	$-0.300761\pi$
$23$	−1.07700	−	1.07700i	−0.224571	−	0.224571i	−0.810420	+	0.585849i	$0.800761\pi$
$24$		0			0
$25$	−4.62620	+	1.89692i	−0.925240	+	0.379383i
$26$	0.761557	−	3.43982i	0.149354	−	0.674604i
$27$		0			0
$28$	0.592379	+	1.62465i	0.111949	+	0.307031i
$29$			0.864641i			0.160560i	0.996772	+	0.0802799i	$0.0255814\pi$
$29$			0.864641i			0.160560i	−0.996772	+	0.0802799i	$0.974419\pi$
$30$		0			0
$31$			7.81086i			1.40287i	0.712732	+	0.701436i	$0.247457\pi$
$31$			7.81086i			1.40287i	−0.712732	+	0.701436i	$0.752543\pi$
$32$	−5.39747	−	1.69333i	−0.954146	−	0.299341i
$33$		0			0
$34$	7.34525	+	1.62620i	1.25970	+	0.278891i
$35$	1.60564	+	1.07700i	0.271403	+	0.182047i
$36$		0			0
$37$	−1.76156	−	1.76156i	−0.289598	−	0.289598i	0.547323	−	0.836921i	$-0.315647\pi$
$37$	−1.76156	−	1.76156i	−0.289598	−	0.289598i	−0.836921	+	0.547323i	$0.815647\pi$
$38$	1.45820	−	0.929560i	0.236551	−	0.150795i
$39$		0			0
$40$	−5.99079	+	2.02741i	−0.947227	+	0.320562i
$41$	−5.52311			−0.862566			−0.431283	−	0.902217i	$-0.641939\pi$
$41$	−5.52311			−0.862566			−0.431283	+	0.902217i	$0.641939\pi$
$42$		0			0
$43$	−6.20522	−	6.20522i	−0.946288	−	0.946288i	0.0523416	−	0.998629i	$-0.483332\pi$
$43$	−6.20522	−	6.20522i	−0.946288	−	0.946288i	−0.998629	+	0.0523416i	$0.983332\pi$
$44$	9.29797	+	4.32924i	1.40172	+	0.652657i
$45$		0			0
$46$	−2.10308	−	0.465611i	−0.310083	−	0.0686506i
$47$	2.29979	−	2.29979i	0.335459	−	0.335459i	−0.519196	−	0.854655i	$-0.673769\pi$
$47$	2.29979	−	2.29979i	0.335459	−	0.335459i	0.854655	+	0.519196i	$0.173769\pi$
$48$		0			0
$49$			6.25240i			0.893199i
$50$	−4.07479	+	5.77893i	−0.576263	+	0.817264i
$51$		0			0
$52$	−1.70677	−	4.68098i	−0.236687	−	0.649135i
$53$	2.62620	−	2.62620i	0.360736	−	0.360736i	−0.503348	−	0.864084i	$-0.667899\pi$
$53$	2.62620	−	2.62620i	0.360736	−	0.360736i	0.864084	+	0.503348i	$0.167899\pi$
$54$		0			0
$55$	11.2507	−	2.21703i	1.51704	−	0.298945i
$56$	1.94148	+	1.48710i	0.259441	+	0.198723i
$57$		0			0
$58$	0.657298	+	1.03110i	0.0863075	+	0.135390i
$59$	−0.528636			−0.0688225			−0.0344113	−	0.999408i	$-0.510956\pi$
$59$	−0.528636			−0.0688225			−0.0344113	+	0.999408i	$0.510956\pi$
$60$		0			0
$61$	4.98168			0.637838			0.318919	−	0.947782i	$-0.396680\pi$
$61$	4.98168			0.637838			0.318919	+	0.947782i	$0.396680\pi$
$62$	5.93780	+	9.31460i	0.754101	+	1.18295i
$63$		0			0
$64$	−7.72384	+	2.08382i	−0.965480	+	0.260477i
$65$	−4.62620	−	3.10308i	−0.573809	−	0.384890i
$66$		0			0
$67$	6.20522	−	6.20522i	0.758089	−	0.758089i	−0.217886	−	0.975974i	$-0.569916\pi$
$67$	6.20522	−	6.20522i	0.758089	−	0.758089i	0.975974	+	0.217886i	$0.0699160\pi$
$68$	9.99558	−	3.64457i	1.21214	−	0.441969i
$69$		0			0
$70$	2.73349	+	0.0637434i	0.326715	+	0.00761879i
$71$		−	8.10243i		−	0.961581i	−0.876835	−	0.480791i	$-0.840350\pi$
$71$		−	8.10243i		−	0.961581i	0.876835	−	0.480791i	$-0.159650\pi$
$72$		0			0
$73$	−2.25240	+	2.25240i	−0.263623	+	0.263623i	−0.826524	−	0.562901i	$-0.809685\pi$
$73$	−2.25240	+	2.25240i	−0.263623	+	0.263623i	0.562901	+	0.826524i	$0.309685\pi$
$74$	−3.43982	−	0.761557i	−0.399871	−	0.0885292i
$75$		0			0
$76$	1.03228	−	2.21703i	0.118410	−	0.254311i
$77$	−3.13536	−	3.13536i	−0.357307	−	0.357307i
$78$		0			0
$79$	−15.9133			−1.79039			−0.895193	−	0.445680i	$-0.852962\pi$
$79$	−15.9133			−1.79039			−0.895193	+	0.445680i	$0.852962\pi$
$80$	−5.60289	+	6.97191i	−0.626423	+	0.779484i
$81$		0			0
$82$	−6.58641	+	4.19866i	−0.727348	+	0.463664i
$83$	−7.95665	−	7.95665i	−0.873355	−	0.873355i	0.119481	−	0.992836i	$-0.461877\pi$
$83$	−7.95665	−	7.95665i	−0.873355	−	0.873355i	−0.992836	+	0.119481i	$0.961877\pi$
$84$		0			0
$85$	6.62620	−	9.87859i	0.718712	−	1.07148i
$86$	−12.1170	−	2.68264i	−1.30661	−	0.289277i
$87$		0			0
$88$	14.3791	−	1.90560i	1.53281	−	0.203138i
$89$			7.25240i			0.768752i	0.923177	+	0.384376i	$0.125583\pi$
$89$			7.25240i			0.768752i	−0.923177	+	0.384376i	$0.874417\pi$
$90$		0			0
$91$			2.15401i			0.225801i
$92$	−2.86192	+	1.04351i	−0.298376	+	0.108793i
$93$		0			0
$94$	0.994247	−	4.49084i	0.102549	−	0.463195i
$95$	−0.528636	−	2.68264i	−0.0542369	−	0.275234i
$96$		0			0
$97$	0.793833	+	0.793833i	0.0806015	+	0.0806015i	0.746258	−	0.665657i	$-0.231848\pi$
$97$	0.793833	+	0.793833i	0.0806015	+	0.0806015i	−0.665657	+	0.746258i	$0.731848\pi$
$98$	4.75306	+	7.45610i	0.480131	+	0.753179i
$99$		0			0
$100$	−0.466135	+	9.98913i	−0.0466135	+	0.998913i
$101$	10.1170			1.00668			0.503341	−	0.864088i	$-0.332104\pi$
$101$	10.1170			1.00668			0.503341	+	0.864088i	$0.332104\pi$
$102$		0			0
$103$	−3.82267	−	3.82267i	−0.376659	−	0.376659i	0.493236	−	0.869895i	$-0.335814\pi$
$103$	−3.82267	−	3.82267i	−0.376659	−	0.376659i	−0.869895	+	0.493236i	$0.835814\pi$
$104$	−5.59383	−	4.28467i	−0.548520	−	0.420147i
$105$		0			0
$106$	1.13536	−	5.12822i	0.110276	−	0.498097i
$107$	5.51107	−	5.51107i	0.532775	−	0.532775i	−0.388622	−	0.921397i	$-0.627049\pi$
$107$	5.51107	−	5.51107i	0.532775	−	0.532775i	0.921397	+	0.388622i	$0.127049\pi$
$108$		0			0
$109$		−	7.31695i		−	0.700836i	−0.936593	−	0.350418i	$-0.886039\pi$
$109$		−	7.31695i		−	0.700836i	0.936593	−	0.350418i	$-0.113961\pi$
$110$	11.7313	−	11.1966i	1.11853	−	1.06755i
$111$		0			0
$112$	3.44575	+	0.297490i	0.325592	+	0.0281101i
$113$	0.509161	−	0.509161i	0.0478978	−	0.0478978i	−0.682752	−	0.730650i	$-0.739217\pi$
$113$	0.509161	−	0.509161i	0.0478978	−	0.0478978i	0.730650	+	0.682752i	$0.239217\pi$
$114$		0			0
$115$	−1.89721	+	2.82843i	−0.176915	+	0.263752i
$116$	1.56768	+	0.729929i	0.145555	+	0.0677722i
$117$		0			0
$118$	−0.630408	+	0.401868i	−0.0580337	+	0.0369949i
$119$	−4.59958			−0.421643
$120$		0			0
$121$	−15.2986			−1.39078
$122$	5.94074	−	3.78706i	0.537849	−	0.342864i
$123$		0			0
$124$	14.1619	+	6.59392i	1.27177	+	0.592152i
$125$	6.16160	+	9.32924i	0.551110	+	0.834432i
$126$		0			0
$127$	7.49103	−	7.49103i	0.664722	−	0.664722i	−0.291767	−	0.956489i	$-0.594243\pi$
$127$	7.49103	−	7.49103i	0.664722	−	0.664722i	0.956489	+	0.291767i	$0.0942433\pi$
$128$	−7.62671	+	8.35664i	−0.674112	+	0.738629i
$129$		0			0
$130$	−7.87578	−	0.183659i	−0.690752	−	0.0161079i
$131$			13.9964i			1.22287i	0.791296	+	0.611434i	$0.209407\pi$
$131$			13.9964i			1.22287i	−0.791296	+	0.611434i	$0.790593\pi$
$132$		0			0
$133$	−0.747604	+	0.747604i	−0.0648255	+	0.0648255i
$134$	2.68264	−	12.1170i	0.231745	−	1.04675i
$135$		0			0
$136$	9.14931	−	11.9448i	0.784547	−	1.02426i
$137$	−7.01395	−	7.01395i	−0.599242	−	0.599242i	0.340869	−	0.940111i	$-0.389279\pi$
$137$	−7.01395	−	7.01395i	−0.599242	−	0.599242i	−0.940111	+	0.340869i	$0.889279\pi$
$138$		0			0
$139$	2.28006			0.193392			0.0966960	−	0.995314i	$-0.469173\pi$
$139$	2.28006			0.193392			0.0966960	+	0.995314i	$0.469173\pi$
$140$	3.30820	−	2.00198i	0.279594	−	0.169198i
$141$		0			0
$142$	−6.15945	−	9.66229i	−0.516889	−	0.810842i
$143$	9.03365	+	9.03365i	0.755432	+	0.755432i
$144$		0			0
$145$	1.89692	−	0.373802i	0.157530	−	0.0310426i
$146$	−0.973757	+	4.39829i	−0.0805887	+	0.364005i
$147$		0			0
$148$	−4.68098	+	1.70677i	−0.384774	+	0.140296i
$149$		−	10.1170i		−	0.828820i	−0.910090	−	0.414410i	$-0.863988\pi$
$149$		−	10.1170i		−	0.828820i	0.910090	−	0.414410i	$-0.136012\pi$
$150$		0			0
$151$			7.93691i			0.645897i	0.946417	+	0.322948i	$0.104674\pi$
$151$			7.93691i			0.645897i	−0.946417	+	0.322948i	$0.895326\pi$
$152$	−0.454377	−	3.42859i	−0.0368548	−	0.278095i
$153$		0			0
$154$	−6.12247	−	1.35548i	−0.493362	−	0.109228i
$155$	17.1361	−	3.37680i	1.37640	−	0.271231i
$156$		0			0
$157$	9.01395	+	9.01395i	0.719392	+	0.719392i	0.968481	−	0.249089i	$-0.0801311\pi$
$157$	9.01395	+	9.01395i	0.719392	+	0.719392i	−0.249089	+	0.968481i	$0.580131\pi$
$158$	−18.9769	+	12.0972i	−1.50972	+	0.962405i
$159$		0			0
$160$	−1.38152	+	12.5734i	−0.109219	+	0.994018i
$161$	1.31695			0.103790
$162$		0			0
$163$	13.0849	+	13.0849i	1.02489	+	1.02489i	0.999682	+	0.0252033i	$0.00802331\pi$
$163$	13.0849	+	13.0849i	1.02489	+	1.02489i	0.0252033	+	0.999682i	$0.491977\pi$
$164$	−4.66261	+	10.0140i	−0.364088	+	0.781958i
$165$		0			0
$166$	−15.5371	−	3.43982i	−1.20591	−	0.266982i
$167$	−11.3334	+	11.3334i	−0.877008	+	0.877008i	−0.993224	−	0.116216i	$-0.962924\pi$
$167$	−11.3334	+	11.3334i	−0.877008	+	0.877008i	0.116216	+	0.993224i	$0.462924\pi$
$168$		0			0
$169$			6.79383i			0.522603i
$170$	0.392177	−	16.8176i	0.0300786	−	1.28985i
$171$		0			0
$172$	−16.4891	+	6.01224i	−1.25728	+	0.458429i
$173$	−7.96772	+	7.96772i	−0.605775	+	0.605775i	−0.941839	−	0.336064i	$-0.890904\pi$
$173$	−7.96772	+	7.96772i	−0.605775	+	0.605775i	0.336064	+	0.941839i	$0.390904\pi$
$174$		0			0
$175$	1.66866	−	3.98819i	0.126139	−	0.301479i
$176$	15.6987	−	13.2034i	1.18333	−	0.995244i
$177$		0			0
$178$	5.51325	+	8.64861i	0.413236	+	0.648241i
$179$	−12.6475			−0.945320			−0.472660	−	0.881245i	$-0.656706\pi$
$179$	−12.6475			−0.945320			−0.472660	+	0.881245i	$0.656706\pi$
$180$		0			0
$181$	7.72928			0.574513			0.287256	−	0.957854i	$-0.407257\pi$
$181$	7.72928			0.574513			0.287256	+	0.957854i	$0.407257\pi$
$182$	1.63747	+	2.56869i	0.121378	+	0.190404i
$183$		0			0
$184$	−2.61962	+	3.42003i	−0.193121	+	0.252128i
$185$	−3.10308	+	4.62620i	−0.228143	+	0.340125i
$186$		0			0
$187$	−19.2901	+	19.2901i	−1.41063	+	1.41063i
$188$	−2.22827	−	6.11123i	−0.162513	−	0.445707i
$189$		0			0
$190$	−2.66975	−	2.79723i	−0.193684	−	0.202933i
$191$			7.04516i			0.509770i	0.966971	+	0.254885i	$0.0820376\pi$
$191$			7.04516i			0.509770i	−0.966971	+	0.254885i	$0.917962\pi$
$192$		0			0
$193$	−11.5048	+	11.5048i	−0.828133	+	0.828133i	−0.987258	−	0.159125i	$-0.949133\pi$
$193$	−11.5048	+	11.5048i	−0.828133	+	0.828133i	0.159125	+	0.987258i	$0.449133\pi$
$194$	1.55013	+	0.343190i	0.111293	+	0.0246396i
$195$		0			0
$196$	11.3362	+	5.27827i	0.809730	+	0.377019i
$197$	−7.87859	−	7.87859i	−0.561327	−	0.561327i	0.368358	−	0.929684i	$-0.379920\pi$
$197$	−7.87859	−	7.87859i	−0.561327	−	0.561327i	−0.929684	+	0.368358i	$0.879920\pi$
$198$		0			0
$199$	11.4792			0.813741			0.406870	−	0.913486i	$-0.366620\pi$
$199$	11.4792			0.813741			0.406870	+	0.913486i	$0.366620\pi$
$200$	7.03784	+	12.2666i	0.497650	+	0.867378i
$201$		0			0
$202$	12.0648	−	7.69095i	0.848873	−	0.541133i
$203$	−0.528636	−	0.528636i	−0.0371030	−	0.0371030i
$204$		0			0
$205$	2.38776	+	12.1170i	0.166768	+	0.846291i
$206$	−7.46460	−	1.65262i	−0.520083	−	0.115143i
$207$		0			0
$208$	−9.92794	−	0.857132i	−0.688379	−	0.0594314i
$209$			6.27072i			0.433755i
$210$		0			0
$211$		−	5.49134i		−	0.378039i	−0.981973	−	0.189020i	$-0.939469\pi$
$211$		−	5.49134i		−	0.378039i	0.981973	−	0.189020i	$-0.0605310\pi$
$212$	−2.54452	−	6.97859i	−0.174759	−	0.479292i
$213$		0			0
$214$	2.38255	−	10.7616i	0.162868	−	0.735645i
$215$	−10.9309	+	16.2961i	−0.745478	+	1.11139i
$216$		0			0
$217$	−4.77551	−	4.77551i	−0.324183	−	0.324183i
$218$	−5.56233	−	8.72559i	−0.376728	−	0.590972i
$219$		0			0
$220$	5.47811	−	22.2702i	0.369334	−	1.50146i
$221$	13.2524			0.891453
$222$		0			0
$223$	−10.8678	−	10.8678i	−0.727764	−	0.727764i	0.242410	−	0.970174i	$-0.422062\pi$
$223$	−10.8678	−	10.8678i	−0.727764	−	0.727764i	−0.970174	+	0.242410i	$0.922062\pi$
$224$	4.33526	−	2.26469i	0.289662	−	0.151316i
$225$		0			0
$226$	0.220121	−	0.994247i	0.0146422	−	0.0661363i
$227$	−4.98244	+	4.98244i	−0.330696	+	0.330696i	−0.852851	−	0.522155i	$-0.825128\pi$
$227$	−4.98244	+	4.98244i	−0.330696	+	0.330696i	0.522155	+	0.852851i	$0.325128\pi$
$228$		0			0
$229$		−	25.7572i		−	1.70208i	−0.525098	−	0.851041i	$-0.675972\pi$
$229$		−	25.7572i		−	1.70208i	0.525098	−	0.851041i	$-0.324028\pi$
$230$	−0.112288	+	4.81520i	−0.00740403	+	0.317505i
$231$		0			0
$232$	2.42438	−	0.321293i	0.159168	−	0.0210939i
$233$	0.715328	−	0.715328i	0.0468627	−	0.0468627i	−0.683287	−	0.730150i	$-0.739450\pi$
$233$	0.715328	−	0.715328i	0.0468627	−	0.0468627i	0.730150	+	0.683287i	$0.239450\pi$
$234$		0			0
$235$	−6.03971	−	4.05121i	−0.393987	−	0.264272i
$236$	−0.446274	+	0.958469i	−0.0290499	+	0.0623910i
$237$		0			0
$238$	−5.48509	+	3.49659i	−0.355545	+	0.226650i
$239$	26.9354			1.74231			0.871154	−	0.491009i	$-0.163372\pi$
$239$	26.9354			1.74231			0.871154	+	0.491009i	$0.163372\pi$
$240$		0			0
$241$	14.0925			0.907775			0.453887	−	0.891059i	$-0.350037\pi$
$241$	14.0925			0.907775			0.453887	+	0.891059i	$0.350037\pi$
$242$	−18.2439	+	11.6300i	−1.17276	+	0.747603i
$243$		0			0
$244$	4.20553	−	9.03228i	0.269231	−	0.578232i
$245$	13.7170	−	2.70304i	0.876346	−	0.172691i
$246$		0			0
$247$	2.15401	−	2.15401i	0.137056	−	0.137056i
$248$	21.9010	−	2.90245i	1.39071	−	0.184306i
$249$		0			0
$250$	14.4399	+	6.44125i	0.913259	+	0.407380i
$251$		−	17.2471i		−	1.08863i	−0.838882	−	0.544314i	$-0.816790\pi$
$251$		−	17.2471i		−	1.08863i	0.838882	−	0.544314i	$-0.183210\pi$
$252$		0			0
$253$	5.52311	−	5.52311i	0.347235	−	0.347235i
$254$	3.23853	−	14.6279i	0.203203	−	0.917834i
$255$		0			0
$256$	−2.74229	+	15.7632i	−0.171393	+	0.985203i
$257$	15.0140	+	15.0140i	0.936545	+	0.936545i	0.998103	−	0.0615588i	$-0.0196072\pi$
$257$	15.0140	+	15.0140i	0.936545	+	0.936545i	−0.0615588	+	0.998103i	$0.519607\pi$
$258$		0			0
$259$	2.15401			0.133844
$260$	−9.53163	+	5.76814i	−0.591127	+	0.357725i
$261$		0			0
$262$	10.6400	+	16.6909i	0.657341	+	1.03117i
$263$	6.73386	+	6.73386i	0.415228	+	0.415228i	0.883555	−	0.468327i	$-0.155143\pi$
$263$	6.73386	+	6.73386i	0.415228	+	0.415228i	−0.468327	+	0.883555i	$0.655143\pi$
$264$		0			0
$265$	−6.89692	−	4.62620i	−0.423674	−	0.284185i
$266$	−0.323204	+	1.45986i	−0.0198169	+	0.0895096i
$267$		0			0
$268$	−6.01224	−	16.4891i	−0.367256	−	1.00723i
$269$		−	25.7047i		−	1.56724i	−0.621238	−	0.783622i	$-0.713370\pi$
$269$		−	25.7047i		−	1.56724i	0.621238	−	0.783622i	$-0.286630\pi$
$270$		0			0
$271$		−	0.931222i		−	0.0565677i	−0.999600	−	0.0282839i	$-0.990996\pi$
$271$		−	0.931222i		−	0.0565677i	0.999600	−	0.0282839i	$-0.00900423\pi$
$272$	1.83029	−	21.1997i	0.110977	−	1.28542i
$273$		0			0
$274$	−13.6963	−	3.03228i	−0.827421	−	0.183186i
$275$	−9.72780	−	23.7242i	−0.586608	−	1.43062i
$276$		0			0
$277$	−22.0602	−	22.0602i	−1.32547	−	1.32547i	−0.909277	−	0.416190i	$-0.863365\pi$
$277$	−22.0602	−	22.0602i	−1.32547	−	1.32547i	−0.416190	−	0.909277i	$-0.636635\pi$
$278$	2.71901	−	1.73330i	0.163075	−	0.103956i
$279$		0			0
$280$	2.42318	−	4.90228i	0.144813	−	0.292967i
$281$	−8.56934			−0.511204			−0.255602	−	0.966782i	$-0.582274\pi$
$281$	−8.56934			−0.511204			−0.255602	+	0.966782i	$0.582274\pi$
$282$		0			0
$283$	11.5705	+	11.5705i	0.687796	+	0.687796i	0.961744	−	0.273949i	$-0.0883299\pi$
$283$	11.5705	+	11.5705i	0.687796	+	0.687796i	−0.273949	+	0.961744i	$0.588330\pi$
$284$	−14.6905	−	6.84006i	−0.871721	−	0.405883i
$285$		0			0
$286$	17.6402	+	3.90543i	1.04308	+	0.230933i
$287$	3.37680	−	3.37680i	0.199326	−	0.199326i
$288$		0			0
$289$			11.2986i			0.664625i
$290$	1.97794	−	1.88780i	0.116149	−	0.110855i
$291$		0			0
$292$	2.18235	+	5.98529i	0.127712	+	0.350262i
$293$	−12.8969	+	12.8969i	−0.753446	+	0.753446i	−0.975121	−	0.221675i	$-0.928848\pi$
$293$	−12.8969	+	12.8969i	−0.753446	+	0.753446i	0.221675	+	0.975121i	$0.428848\pi$
$294$		0			0
$295$	0.228540	+	1.15976i	0.0133061	+	0.0675240i
$296$	−4.28467	+	5.59383i	−0.249041	+	0.325135i
$297$		0			0
$298$	−7.69095	−	12.0648i	−0.445525	−	0.698892i
$299$	−3.79441			−0.219436
$300$		0			0
$301$	7.58767			0.437346
$302$	6.03362	+	9.46491i	0.347196	+	0.544644i
$303$		0			0
$304$	−3.14826	−	3.74324i	−0.180565	−	0.214689i
$305$	−2.15368	−	10.9292i	−0.123319	−	0.625804i
$306$		0			0
$307$	1.60564	−	1.60564i	0.0916387	−	0.0916387i	−0.659801	−	0.751440i	$-0.729360\pi$
$307$	1.60564	−	1.60564i	0.0916387	−	0.0916387i	0.751440	+	0.659801i	$0.229360\pi$
$308$	−8.33158	+	3.03785i	−0.474736	+	0.173098i
$309$		0			0
$310$	17.8681	−	17.0537i	1.01484	−	0.968585i
$311$		−	19.4161i		−	1.10099i	−0.834839	−	0.550494i	$-0.814439\pi$
$311$		−	19.4161i		−	1.10099i	0.834839	−	0.550494i	$-0.185561\pi$
$312$		0			0
$313$	17.7110	−	17.7110i	1.00108	−	1.00108i	0.00108322	−	0.999999i	$-0.499655\pi$
$313$	17.7110	−	17.7110i	1.00108	−	1.00108i	0.999999	−	0.00108322i	$-0.000344798\pi$
$314$	17.6017	+	3.89692i	0.993321	+	0.219916i
$315$		0			0
$316$	−13.4340	+	28.8524i	−0.755721	+	1.62307i
$317$	7.78946	+	7.78946i	0.437500	+	0.437500i	0.891170	−	0.453670i	$-0.149885\pi$
$317$	7.78946	+	7.78946i	0.437500	+	0.437500i	−0.453670	+	0.891170i	$0.649885\pi$
$318$		0			0
$319$	−4.43407			−0.248260
$320$	7.91081	+	16.0443i	0.442228	+	0.896903i
$321$		0			0
$322$	1.57048	−	1.00114i	0.0875196	−	0.0557914i
$323$	4.59958	+	4.59958i	0.255928	+	0.255928i
$324$		0			0
$325$	−4.80779	+	11.4908i	−0.266688	+	0.637397i
$326$	25.5510	+	5.65685i	1.41514	+	0.313304i
$327$		0			0
$328$	2.05234	+	15.4863i	0.113322	+	0.855089i
$329$			2.81215i			0.155039i
$330$		0			0
$331$		−	31.7005i		−	1.74242i	−0.490912	−	0.871209i	$-0.663336\pi$
$331$		−	31.7005i		−	1.74242i	0.490912	−	0.871209i	$-0.336664\pi$
$332$	−21.1432	+	7.70919i	−1.16038	+	0.423097i
$333$		0			0
$334$	−4.89968	+	22.1310i	−0.268098	+	1.21095i
$335$	−16.2961	−	10.9309i	−0.890353	−	0.597216i
$336$		0			0
$337$	18.9634	+	18.9634i	1.03300	+	1.03300i	0.999437	+	0.0335632i	$0.0106855\pi$
$337$	18.9634	+	18.9634i	1.03300	+	1.03300i	0.0335632	+	0.999437i	$0.489314\pi$
$338$	5.16466	+	8.10177i	0.280920	+	0.440678i
$339$		0			0
$340$	−12.3170	−	20.3535i	−0.667985	−	1.10382i
$341$	−40.0558			−2.16914
$342$		0			0
$343$	−8.10243	−	8.10243i	−0.437490	−	0.437490i
$344$	−15.0931	+	19.7047i	−0.813765	+	1.06241i
$345$		0			0
$346$	−3.44461	+	15.5587i	−0.185183	+	0.836441i
$347$	7.71957	−	7.71957i	0.414408	−	0.414408i	−0.468863	−	0.883271i	$-0.655336\pi$
$347$	7.71957	−	7.71957i	0.414408	−	0.414408i	0.883271	+	0.468863i	$0.155336\pi$
$348$		0			0
$349$			27.0741i			1.44925i	0.689146	+	0.724623i	$0.257986\pi$
$349$			27.0741i			1.44925i	−0.689146	+	0.724623i	$0.742014\pi$
$350$	−1.04190	−	6.02450i	−0.0556918	−	0.322023i
$351$		0			0
$352$	8.68375	−	27.6794i	0.462846	−	1.47532i
$353$	9.96772	−	9.96772i	0.530528	−	0.530528i	−0.390201	−	0.920730i	$-0.627595\pi$
$353$	9.96772	−	9.96772i	0.530528	−	0.530528i	0.920730	+	0.390201i	$0.127595\pi$
$354$		0			0
$355$	−17.7757	+	3.50285i	−0.943438	+	0.185912i
$356$	13.1493	+	6.12247i	0.696912	+	0.324490i
$357$		0			0
$358$	−15.0824	+	9.61461i	−0.797129	+	0.508148i
$359$	−14.2334			−0.751211			−0.375606	−	0.926780i	$-0.622565\pi$
$359$	−14.2334			−0.751211			−0.375606	+	0.926780i	$0.622565\pi$
$360$		0			0
$361$	−17.5048			−0.921305
$362$	9.21731	−	5.87578i	0.484451	−	0.308824i
$363$		0			0
$364$	3.90543	+	1.81841i	0.204700	+	0.0953107i
$365$	5.91524	+	3.96772i	0.309618	+	0.207680i
$366$		0			0
$367$	2.89145	−	2.89145i	0.150933	−	0.150933i	−0.627602	−	0.778534i	$-0.715963\pi$
$367$	2.89145	−	2.89145i	0.150933	−	0.150933i	0.778534	+	0.627602i	$0.215963\pi$
$368$	−0.524045	+	6.06988i	−0.0273177	+	0.316414i
$369$		0			0
$370$	−0.183659	+	7.87578i	−0.00954795	+	0.409442i
$371$			3.21128i			0.166721i
$372$		0			0
$373$	−11.2847	+	11.2847i	−0.584298	+	0.584298i	−0.936081	−	0.351783i	$-0.885575\pi$
$373$	−11.2847	+	11.2847i	−0.584298	+	0.584298i	0.351783	+	0.936081i	$0.385575\pi$
$374$	−8.33950	+	37.6681i	−0.431225	+	1.94777i
$375$		0			0
$376$	−7.30299	−	5.59383i	−0.376623	−	0.288480i
$377$	1.52311	+	1.52311i	0.0784444	+	0.0784444i
$378$		0			0
$379$	15.4562			0.793932			0.396966	−	0.917833i	$-0.370063\pi$
$379$	15.4562			0.793932			0.396966	+	0.917833i	$0.370063\pi$
$380$	−5.31017	−	1.30622i	−0.272406	−	0.0670075i
$381$		0			0
$382$	5.35571	+	8.40148i	0.274022	+	0.429857i
$383$	−12.5562	−	12.5562i	−0.641593	−	0.641593i	0.309354	−	0.950947i	$-0.399887\pi$
$383$	−12.5562	−	12.5562i	−0.641593	−	0.641593i	−0.950947	+	0.309354i	$0.899887\pi$
$384$		0			0
$385$	−5.52311	+	8.23407i	−0.281484	+	0.419647i
$386$	−4.97376	+	22.4656i	−0.253158	+	1.14347i
$387$		0			0
$388$	2.10945	−	0.769144i	0.107091	−	0.0390474i
$389$			5.16327i			0.261788i	0.991396	+	0.130894i	$0.0417848\pi$
$389$			5.16327i			0.261788i	−0.991396	+	0.130894i	$0.958215\pi$
$390$		0			0
$391$		−	8.10243i		−	0.409757i
$392$	17.5312	−	2.32333i	0.885458	−	0.117346i
$393$		0			0
$394$	−15.3847	−	3.40608i	−0.775068	−	0.171596i
$395$	6.87964	+	34.9118i	0.346152	+	1.75660i
$396$		0			0
$397$	−3.46293	−	3.46293i	−0.173800	−	0.173800i	0.614847	−	0.788646i	$-0.289218\pi$
$397$	−3.46293	−	3.46293i	−0.173800	−	0.173800i	−0.788646	+	0.614847i	$0.789218\pi$
$398$	13.6892	−	8.72648i	0.686177	−	0.437419i
$399$		0			0
$400$	17.7178	+	9.27796i	0.885889	+	0.463898i
$401$	−3.49521			−0.174542			−0.0872712	−	0.996185i	$-0.527815\pi$
$401$	−3.49521			−0.174542			−0.0872712	+	0.996185i	$0.527815\pi$
$402$		0			0
$403$	13.7593	+	13.7593i	0.685399	+	0.685399i
$404$	8.54079	−	18.3432i	0.424920	−	0.912608i
$405$		0			0
$406$	−1.03228	−	0.228540i	−0.0512310	−	0.0113423i
$407$	9.03365	−	9.03365i	0.447781	−	0.447781i
$408$		0			0
$409$		−	14.8034i		−	0.731982i	−0.930618	−	0.365991i	$-0.880730\pi$
$409$		−	14.8034i		−	0.731982i	0.930618	−	0.365991i	$-0.119270\pi$
$410$	12.0588	+	12.6346i	0.595541	+	0.623979i
$411$		0			0
$412$	−10.1580	+	3.70379i	−0.500448	+	0.182473i
$413$	0.323204	−	0.323204i	0.0159039	−	0.0159039i
$414$		0			0
$415$	−14.0161	+	20.8957i	−0.688023	+	1.02573i
$416$	−12.4908	+	6.52505i	−0.612414	+	0.319917i
$417$		0			0
$418$	4.76699	+	7.47795i	0.233161	+	0.365758i
$419$	19.0701			0.931634			0.465817	−	0.884881i	$-0.345760\pi$
$419$	19.0701			0.931634			0.465817	+	0.884881i	$0.345760\pi$
$420$		0			0
$421$	−20.8034			−1.01390			−0.506948	−	0.861976i	$-0.669226\pi$
$421$	−20.8034			−1.01390			−0.506948	+	0.861976i	$0.669226\pi$
$422$	−4.17450	−	6.54852i	−0.203212	−	0.318777i
$423$		0			0
$424$	−8.33950	−	6.38776i	−0.405002	−	0.310217i
$425$	−24.5371	−	10.2663i	−1.19022	−	0.497991i
$426$		0			0
$427$	−3.04577	+	3.04577i	−0.147395	+	0.147395i
$428$	−5.33968	−	14.6446i	−0.258103	−	0.707872i
$429$		0			0
$430$	−0.646951	+	27.7431i	−0.0311988	+	1.33789i
$431$		−	15.3302i		−	0.738428i	−0.929344	−	0.369214i	$-0.879627\pi$
$431$		−	15.3302i		−	0.738428i	0.929344	−	0.369214i	$-0.120373\pi$
$432$		0			0
$433$	16.2803	−	16.2803i	0.782381	−	0.782381i	−0.197851	−	0.980232i	$-0.563396\pi$
$433$	16.2803	−	16.2803i	0.782381	−	0.782381i	0.980232	+	0.197851i	$0.0633961\pi$
$434$	−9.32521	−	2.06455i	−0.447625	−	0.0991016i
$435$		0			0
$436$	−13.2663	−	6.17696i	−0.635343	−	0.295823i
$437$	−1.31695	−	1.31695i	−0.0629981	−	0.0629981i
$438$		0			0
$439$	24.6554			1.17674			0.588368	−	0.808593i	$-0.299770\pi$
$439$	24.6554			1.17674			0.588368	+	0.808593i	$0.299770\pi$
$440$	−10.3970	−	30.7221i	−0.495659	−	1.46462i
$441$		0			0
$442$	15.8037	−	10.0744i	0.751706	−	0.479192i
$443$	−1.77116	−	1.77116i	−0.0841501	−	0.0841501i	0.663779	−	0.747929i	$-0.268952\pi$
$443$	−1.77116	−	1.77116i	−0.0841501	−	0.0841501i	−0.747929	+	0.663779i	$0.768952\pi$
$444$		0			0
$445$	15.9109	−	3.13536i	0.754248	−	0.148630i
$446$	−21.2218	−	4.69839i	−1.00488	−	0.222475i
$447$		0			0
$448$	3.44827	−	5.99634i	0.162916	−	0.283300i
$449$			33.1512i			1.56450i	0.622963	+	0.782251i	$0.285929\pi$
$449$			33.1512i			1.56450i	−0.622963	+	0.782251i	$0.714071\pi$
$450$		0			0
$451$		−	28.3237i		−	1.33371i
$452$	−0.493326	−	1.35299i	−0.0232041	−	0.0636394i
$453$		0			0
$454$	−2.15401	+	9.72928i	−0.101093	+	0.456618i
$455$	4.72563	−	0.931222i	0.221541	−	0.0436564i
$456$		0			0
$457$	−7.50479	−	7.50479i	−0.351059	−	0.351059i	0.509444	−	0.860504i	$-0.329851\pi$
$457$	−7.50479	−	7.50479i	−0.351059	−	0.351059i	−0.860504	+	0.509444i	$0.829851\pi$
$458$	−19.5806	−	30.7159i	−0.914939	−	1.43526i
$459$		0			0
$460$	3.52660	+	5.82758i	0.164429	+	0.271712i
$461$	27.0216			1.25852			0.629262	−	0.777193i	$-0.283357\pi$
$461$	27.0216			1.25852			0.629262	+	0.777193i	$0.283357\pi$
$462$		0			0
$463$	27.7123	+	27.7123i	1.28790	+	1.28790i	0.936059	+	0.351843i	$0.114445\pi$
$463$	27.7123	+	27.7123i	1.28790	+	1.28790i	0.351843	+	0.936059i	$0.385555\pi$
$464$	2.64687	−	2.22615i	0.122878	−	0.103347i
$465$		0			0
$466$	0.309251	−	1.39683i	0.0143258	−	0.0647070i
$467$	2.00823	−	2.00823i	0.0929296	−	0.0929296i	−0.659114	−	0.752043i	$-0.729068\pi$
$467$	2.00823	−	2.00823i	0.0929296	−	0.0929296i	0.752043	+	0.659114i	$0.229068\pi$
$468$		0			0
$469$			7.58767i			0.350366i
$470$	−10.2822	−	0.239774i	−0.474282	−	0.0110600i
$471$		0			0
$472$	0.196436	+	1.48225i	0.00904172	+	0.0682260i
$473$	31.8217	−	31.8217i	1.46317	−	1.46317i
$474$		0			0
$475$	−5.65685	+	2.31952i	−0.259554	+	0.106427i
$476$	−3.88296	+	8.33950i	−0.177975	+	0.382240i
$477$		0			0
$478$	32.1210	−	20.4763i	1.46918	−	0.936562i
$479$	13.7593			0.628678			0.314339	−	0.949311i	$-0.398217\pi$
$479$	13.7593			0.628678			0.314339	+	0.949311i	$0.398217\pi$
$480$		0			0
$481$	−6.20617			−0.282977
$482$	16.8055	−	10.7131i	0.765470	−	0.487966i
$483$		0			0
$484$	−12.9151	+	27.7379i	−0.587049	+	1.26081i
$485$	1.39838	−	2.08476i	0.0634972	−	0.0946641i
$486$		0			0
$487$	−24.3355	+	24.3355i	−1.10275	+	1.10275i	−0.108671	+	0.994078i	$0.534660\pi$
$487$	−24.3355	+	24.3355i	−1.10275	+	1.10275i	−0.994078	+	0.108671i	$0.965340\pi$
$488$	−1.85115	−	13.9682i	−0.0837975	−	0.632310i
$489$		0			0
$490$	14.3029	−	13.6510i	0.646140	−	0.616691i
$491$			28.8918i			1.30387i	0.758275	+	0.651935i	$0.226043\pi$
$491$			28.8918i			1.30387i	−0.758275	+	0.651935i	$0.773957\pi$
$492$		0			0
$493$	−3.25240	+	3.25240i	−0.146481	+	0.146481i
$494$	0.931222	−	4.20617i	0.0418977	−	0.189244i
$495$		0			0
$496$	23.9109	−	20.1103i	1.07363	−	0.902979i
$497$	4.95377	+	4.95377i	0.222207	+	0.222207i
$498$		0			0
$499$	−12.5365			−0.561211			−0.280605	−	0.959823i	$-0.590535\pi$
$499$	−12.5365			−0.561211			−0.280605	+	0.959823i	$0.590535\pi$
$500$	22.1164	−	3.29586i	0.989078	−	0.147395i
$501$		0			0
$502$	−13.1112	−	20.5675i	−0.585182	−	0.917972i
$503$	9.01392	+	9.01392i	0.401911	+	0.401911i	0.878906	−	0.476995i	$-0.158274\pi$
$503$	9.01392	+	9.01392i	0.401911	+	0.401911i	−0.476995	+	0.878906i	$0.658274\pi$
$504$		0			0
$505$	−4.37380	−	22.1955i	−0.194632	−	0.987689i
$506$	2.38776	−	10.7851i	0.106149	−	0.479455i
$507$		0			0
$508$	−7.25806	−	19.9059i	−0.322025	−	0.883182i
$509$			22.5448i			0.999279i	0.866233	+	0.499640i	$0.166534\pi$
$509$			22.5448i			0.999279i	−0.866233	+	0.499640i	$0.833466\pi$
$510$		0			0
$511$		−	2.75420i		−	0.121839i
$512$	8.71295	+	20.8826i	0.385062	+	0.922891i
$513$		0			0
$514$	29.3180	+	6.49084i	1.29316	+	0.286299i
$515$	−6.73386	+	10.0391i	−0.296729	+	0.442376i
$516$		0			0
$517$	11.7938	+	11.7938i	0.518692	+	0.518692i
$518$	2.56869	−	1.63747i	0.112862	−	0.0719464i
$519$		0			0
$520$	−6.98172	+	14.1245i	−0.306169	+	0.619402i
$521$	18.9046			0.828226			0.414113	−	0.910225i	$-0.364092\pi$
$521$	18.9046			0.828226			0.414113	+	0.910225i	$0.364092\pi$
$522$		0			0
$523$	−21.8269	−	21.8269i	−0.954426	−	0.954426i	0.0445800	−	0.999006i	$-0.485805\pi$
$523$	−21.8269	−	21.8269i	−0.954426	−	0.954426i	−0.999006	+	0.0445800i	$0.985805\pi$
$524$	25.3768	+	11.8157i	1.10859	+	0.516172i
$525$		0			0
$526$	13.1493	+	2.91118i	0.573337	+	0.126934i
$527$	−29.3810	+	29.3810i	−1.27986	+	1.27986i
$528$		0			0
$529$		−	20.6801i		−	0.899136i
$530$	−11.7415	−	0.273805i	−0.510019	−	0.0118933i
$531$		0			0
$532$	0.724353	+	1.98661i	0.0314047	+	0.0861303i
$533$	−9.72928	+	9.72928i	−0.421422	+	0.421422i
$534$		0			0
$535$	−14.4732	−	9.70807i	−0.625730	−	0.419716i
$536$	−19.7047	−	15.0931i	−0.851114	−	0.651922i
$537$		0			0
$538$	−19.5407	−	30.6533i	−0.842457	−	1.32156i
$539$	−32.0637			−1.38108
$540$		0			0
$541$	7.85838			0.337858			0.168929	−	0.985628i	$-0.445969\pi$
$541$	7.85838			0.337858			0.168929	+	0.985628i	$0.445969\pi$
$542$	−0.707913	−	1.11050i	−0.0304075	−	0.0477000i
$543$		0			0
$544$	−13.9333	−	26.6724i	−0.597387	−	1.14357i
$545$	−16.0525	+	3.16327i	−0.687613	+	0.135499i
$546$		0			0
$547$	17.8105	−	17.8105i	0.761522	−	0.761522i	−0.215076	−	0.976597i	$-0.569000\pi$
$547$	17.8105	−	17.8105i	0.761522	−	0.761522i	0.976597	+	0.215076i	$0.0689998\pi$
$548$	−18.6382	+	6.79582i	−0.796183	+	0.290303i
$549$		0			0
$550$	−29.6356	−	20.8964i	−1.26367	−	0.891027i
$551$			1.05727i			0.0450413i
$552$		0			0
$553$	9.72928	−	9.72928i	0.413731	−	0.413731i
$554$	−43.0773	−	9.53707i	−1.83018	−	0.405191i
$555$		0			0
$556$	1.92482	−	4.13397i	0.0816307	−	0.175319i
$557$	−23.3372	−	23.3372i	−0.988827	−	0.988827i	0.0111112	−	0.999938i	$-0.496463\pi$
$557$	−23.3372	−	23.3372i	−0.988827	−	0.988827i	−0.999938	+	0.0111112i	$0.996463\pi$
$558$		0			0
$559$	−21.8617			−0.924652
$560$	−0.837010	−	7.68815i	−0.0353701	−	0.324884i
$561$		0			0
$562$	−10.2191	+	6.51439i	−0.431067	+	0.274793i
$563$	5.27400	+	5.27400i	0.222273	+	0.222273i	0.809455	−	0.587182i	$-0.199763\pi$
$563$	5.27400	+	5.27400i	0.222273	+	0.222273i	−0.587182	+	0.809455i	$0.699763\pi$
$564$		0			0
$565$	−1.33716	−	0.896916i	−0.0562546	−	0.0377336i
$566$	22.5939	+	5.00217i	0.949693	+	0.210257i
$567$		0			0
$568$	−22.7185	+	3.01079i	−0.953247	+	0.126330i
$569$		−	28.5606i		−	1.19732i	−0.801002	−	0.598661i	$-0.795699\pi$
$569$		−	28.5606i		−	1.19732i	0.801002	−	0.598661i	$-0.204301\pi$
$570$		0			0
$571$			32.2837i			1.35103i	0.737347	+	0.675515i	$0.236078\pi$
$571$			32.2837i			1.35103i	−0.737347	+	0.675515i	$0.763922\pi$
$572$	24.0051	−	8.75270i	1.00370	−	0.365969i
$573$		0			0
$574$	1.45986	−	6.59392i	0.0609333	−	0.275225i
$575$	7.02542	+	2.93945i	0.292980	+	0.122583i
$576$		0			0
$577$	27.0279	+	27.0279i	1.12519	+	1.12519i	0.990949	+	0.134237i	$0.0428584\pi$
$577$	27.0279	+	27.0279i	1.12519	+	1.12519i	0.134237	+	0.990949i	$0.457142\pi$
$578$	8.58919	+	13.4738i	0.357263	+	0.560437i
$579$		0			0
$580$	0.923635	−	3.75486i	0.0383518	−	0.155912i
$581$	9.72928			0.403639
$582$		0			0
$583$	13.4677	+	13.4677i	0.557776	+	0.557776i
$584$	7.15249	+	5.47855i	0.295972	+	0.226704i
$585$		0			0
$586$	−5.57560	+	25.1840i	−0.230326	+	1.04034i
$587$	−17.1558	+	17.1558i	−0.708096	+	0.708096i	−0.966135	−	0.258039i	$-0.916924\pi$
$587$	−17.1558	+	17.1558i	−0.708096	+	0.708096i	0.258039	+	0.966135i	$0.416924\pi$
$588$		0			0
$589$			9.55102i			0.393543i
$590$	1.15419	+	1.20930i	0.0475171	+	0.0497862i
$591$		0			0
$592$	−0.857132	+	9.92794i	−0.0352279	+	0.408036i
$593$	21.5833	−	21.5833i	0.886320	−	0.886320i	−0.107848	−	0.994167i	$-0.534396\pi$
$593$	21.5833	−	21.5833i	0.886320	−	0.886320i	0.994167	+	0.107848i	$0.0343959\pi$
$594$		0			0
$595$	1.98849	+	10.0909i	0.0815203	+	0.413687i
$596$	−18.3432	−	8.54079i	−0.751366	−	0.349844i
$597$		0			0
$598$	−4.52490	+	2.88450i	−0.185037	+	0.117956i
$599$	23.7636			0.970955			0.485478	−	0.874249i	$-0.338646\pi$
$599$	23.7636			0.970955			0.485478	+	0.874249i	$0.338646\pi$
$600$		0			0
$601$	22.1695			0.904314			0.452157	−	0.891938i	$-0.350655\pi$
$601$	22.1695			0.904314			0.452157	+	0.891938i	$0.350655\pi$
$602$	9.04843	−	5.76813i	0.368786	−	0.235091i
$603$		0			0
$604$	14.3904	+	6.70033i	0.585537	+	0.272633i
$605$	6.61391	+	33.5633i	0.268894	+	1.36454i
$606$		0			0
$607$	9.35348	−	9.35348i	0.379646	−	0.379646i	−0.491328	−	0.870974i	$-0.663489\pi$
$607$	9.35348	−	9.35348i	0.379646	−	0.379646i	0.870974	+	0.491328i	$0.163489\pi$
$608$	−6.59995	−	2.07058i	−0.267663	−	0.0839731i
$609$		0			0
$610$	−10.8767	−	11.3960i	−0.440383	−	0.461412i
$611$		−	8.10243i		−	0.327789i
$612$		0			0
$613$	−24.1247	+	24.1247i	−0.974389	+	0.974389i	−0.999680	−	0.0252913i	$-0.991949\pi$
$613$	−24.1247	+	24.1247i	−0.974389	+	0.974389i	0.0252913	+	0.999680i	$0.491949\pi$
$614$	0.694151	−	3.13536i	0.0280137	−	0.126533i
$615$		0			0
$616$	−7.62620	+	9.95634i	−0.307268	+	0.401152i
$617$	−3.82611	−	3.82611i	−0.154033	−	0.154033i	0.625883	−	0.779917i	$-0.284739\pi$
$617$	−3.82611	−	3.82611i	−0.154033	−	0.154033i	−0.779917	+	0.625883i	$0.784739\pi$
$618$		0			0
$619$	30.1297			1.21101			0.605507	−	0.795840i	$-0.292971\pi$
$619$	30.1297			1.21101			0.605507	+	0.795840i	$0.292971\pi$
$620$	8.34379	−	33.9201i	0.335095	−	1.36226i
$621$		0			0
$622$	−14.7601	−	23.1541i	−0.591826	−	0.928395i
$623$	−4.43407	−	4.43407i	−0.177647	−	0.177647i
$624$		0			0
$625$	17.8034	−	17.5510i	0.712137	−	0.702041i
$626$	7.65681	−	34.5845i	0.306028	−	1.38227i
$627$		0			0
$628$	23.9528	−	8.73362i	0.955819	−	0.348509i
$629$		−	13.2524i		−	0.528408i
$630$		0			0
$631$			21.5701i			0.858694i	0.903140	+	0.429347i	$0.141256\pi$
$631$			21.5701i			0.858694i	−0.903140	+	0.429347i	$0.858744\pi$
$632$	5.91324	+	44.6195i	0.235216	+	1.77487i
$633$		0			0
$634$	15.2106	+	3.36754i	0.604090	+	0.133742i
$635$	−19.6729	−	13.1959i	−0.780697	−	0.523663i
$636$		0			0
$637$	11.0140	+	11.0140i	0.436389	+	0.436389i
$638$	−5.28771	+	3.37077i	−0.209342	+	0.133450i
$639$		0			0
$640$	21.6306	+	13.1193i	0.855025	+	0.518586i
$641$	−48.3911			−1.91133			−0.955666	−	0.294452i	$-0.904863\pi$
$641$	−48.3911			−1.91133			−0.955666	+	0.294452i	$0.904863\pi$
$642$		0			0
$643$	−23.3413	−	23.3413i	−0.920491	−	0.920491i	0.0765729	−	0.997064i	$-0.475602\pi$
$643$	−23.3413	−	23.3413i	−0.920491	−	0.920491i	−0.997064	+	0.0765729i	$0.975602\pi$
$644$	1.11177	−	2.38776i	0.0438097	−	0.0940907i
$645$		0			0
$646$	8.98168	+	1.98849i	0.353379	+	0.0782362i
$647$	32.4465	−	32.4465i	1.27560	−	1.27560i	0.332501	−	0.943103i	$-0.392108\pi$
$647$	32.4465	−	32.4465i	1.27560	−	1.27560i	0.943103	−	0.332501i	$-0.107892\pi$
$648$		0			0
$649$		−	2.71096i		−	0.106414i
$650$	3.00194	+	17.3579i	0.117746	+	0.680833i
$651$		0			0
$652$	34.7704	−	12.6779i	1.36171	−	0.496506i
$653$	−18.4725	+	18.4725i	−0.722885	+	0.722885i	−0.969192	−	0.246307i	$-0.920783\pi$
$653$	−18.4725	+	18.4725i	−0.722885	+	0.722885i	0.246307	+	0.969192i	$0.420783\pi$
$654$		0			0
$655$	30.7063	−	6.05091i	1.19979	−	0.236429i
$656$	14.2201	+	16.9075i	0.555202	+	0.660128i
$657$		0			0
$658$	2.13779	+	3.35355i	0.0833399	+	0.130735i
$659$	47.5028			1.85045			0.925223	−	0.379423i	$-0.123878\pi$
$659$	47.5028			1.85045			0.925223	+	0.379423i	$0.123878\pi$
$660$		0			0
$661$	−46.1204			−1.79387			−0.896937	−	0.442158i	$-0.854213\pi$
$661$	−46.1204			−1.79387			−0.896937	+	0.442158i	$0.854213\pi$
$662$	−24.0987	−	37.8035i	−0.936621	−	1.46927i
$663$		0			0
$664$	−19.3531	+	25.2663i	−0.751046	+	0.980525i
$665$	1.96336	+	1.31695i	0.0761357	+	0.0510690i
$666$		0			0
$667$	0.931222	−	0.931222i	0.0360571	−	0.0360571i
$668$	10.9810	+	30.1163i	0.424867	+	1.16524i
$669$		0			0
$670$	−27.7431	−	0.646951i	−1.07181	−	0.0249939i
$671$			25.5471i			0.986236i
$672$		0			0
$673$	3.60599	−	3.60599i	0.139001	−	0.139001i	−0.634183	−	0.773183i	$-0.718663\pi$
$673$	3.60599	−	3.60599i	0.139001	−	0.139001i	0.773183	+	0.634183i	$0.218663\pi$
$674$	37.0300	+	8.19825i	1.42634	+	0.315785i
$675$		0			0
$676$	12.3179	+	5.73535i	0.473765	+	0.220590i
$677$	8.26635	+	8.26635i	0.317702	+	0.317702i	0.847884	−	0.530182i	$-0.177876\pi$
$677$	8.26635	+	8.26635i	0.317702	+	0.317702i	−0.530182	+	0.847884i	$0.677876\pi$
$678$		0			0
$679$	−0.970688			−0.0372516
$680$	−30.1609	−	14.9085i	−1.15662	−	0.571714i
$681$		0			0
$682$	−47.7673	+	30.4503i	−1.82910	+	1.16600i
$683$	8.43079	+	8.43079i	0.322595	+	0.322595i	0.849762	−	0.527167i	$-0.176746\pi$
$683$	8.43079	+	8.43079i	0.322595	+	0.322595i	−0.527167	+	0.849762i	$0.676746\pi$
$684$		0			0
$685$	−12.3555	+	18.4200i	−0.472079	+	0.703793i
$686$	−15.8217	−	3.50285i	−0.604077	−	0.133739i
$687$		0			0
$688$	−3.01932	+	34.9719i	−0.115110	+	1.33329i
$689$		−	9.25240i		−	0.352488i
$690$		0			0
$691$			21.9182i			0.833809i	0.908950	+	0.416905i	$0.136885\pi$
$691$			21.9182i			0.833809i	−0.908950	+	0.416905i	$0.863115\pi$
$692$	7.71993	+	21.1726i	0.293468	+	0.804862i
$693$		0			0
$694$	3.33733	−	15.0741i	0.126683	−	0.572206i
$695$	−0.985716	−	5.00217i	−0.0373903	−	0.189743i
$696$		0			0
$697$	−20.7755	−	20.7755i	−0.786929	−	0.786929i
$698$	20.5817	+	32.2864i	0.779029	+	1.22206i
$699$		0			0
$700$	−5.82230	−	6.39228i	−0.220062	−	0.241605i
$701$	21.8184			0.824070			0.412035	−	0.911168i	$-0.364818\pi$
$701$	21.8184			0.824070			0.412035	+	0.911168i	$0.364818\pi$
$702$		0			0
$703$	−2.15401	−	2.15401i	−0.0812400	−	0.0812400i
$704$	−10.6863	−	39.6095i	−0.402754	−	1.49284i
$705$		0			0
$706$	4.30925	−	19.4641i	0.162181	−	0.732542i
$707$	−6.18549	+	6.18549i	−0.232629	+	0.232629i
$708$		0			0
$709$		−	31.7938i		−	1.19404i	−0.802225	−	0.597021i	$-0.796351\pi$
$709$		−	31.7938i		−	1.19404i	0.802225	−	0.597021i	$-0.203649\pi$
$710$	−18.5350	+	17.6903i	−0.695607	+	0.663904i
$711$		0			0
$712$	20.3351	−	2.69493i	0.762089	−	0.100997i
$713$	8.41233	−	8.41233i	0.315044	−	0.315044i
$714$		0			0
$715$	15.9133	−	23.7242i	0.595123	−	0.887233i
$716$	−10.6770	+	22.9312i	−0.399019	+	0.856979i
$717$		0			0
$718$	−16.9736	+	10.8202i	−0.633450	+	0.403807i
$719$	−52.0874			−1.94253			−0.971265	−	0.237999i	$-0.923508\pi$
$719$	−52.0874			−1.94253			−0.971265	+	0.237999i	$0.923508\pi$
$720$		0			0
$721$	4.67432			0.174081
$722$	−20.8748	+	13.3071i	−0.776879	+	0.495239i
$723$		0			0
$724$	6.52505	−	14.0140i	0.242502	−	0.520824i
$725$	−1.64015	−	4.00000i	−0.0609137	−	0.148556i
$726$		0			0
$727$	−8.13069	+	8.13069i	−0.301551	+	0.301551i	−0.841620	−	0.540070i	$-0.818398\pi$
$727$	−8.13069	+	8.13069i	−0.301551	+	0.301551i	0.540070	+	0.841620i	$0.318398\pi$
$728$	6.03965	−	0.800411i	0.223844	−	0.0296652i
$729$		0			0
$730$	10.0703	+	0.234833i	0.372718	+	0.00869156i
$731$		−	46.6826i		−	1.72662i
$732$		0			0
$733$	−29.9956	+	29.9956i	−1.10791	+	1.10791i	−0.114489	+	0.993424i	$0.536523\pi$
$733$	−29.9956	+	29.9956i	−1.10791	+	1.10791i	−0.993424	+	0.114489i	$0.963477\pi$
$734$	1.25003	−	5.64618i	0.0461396	−	0.208404i
$735$		0			0
$736$	3.98937	+	7.63682i	0.147050	+	0.281497i
$737$	31.8217	+	31.8217i	1.17217	+	1.17217i
$738$		0			0
$739$	−39.4719			−1.45200			−0.725999	−	0.687696i	$-0.758622\pi$
$739$	−39.4719			−1.45200			−0.725999	+	0.687696i	$0.758622\pi$
$740$	5.76814	+	9.53163i	0.212041	+	0.350390i
$741$		0			0
$742$	2.44121	+	3.82951i	0.0896196	+	0.140586i
$743$	−12.2252	−	12.2252i	−0.448499	−	0.448499i	0.446356	−	0.894855i	$-0.352721\pi$
$743$	−12.2252	−	12.2252i	−0.448499	−	0.448499i	−0.894855	+	0.446356i	$0.852721\pi$
$744$		0			0
$745$	−22.1955	+	4.37380i	−0.813182	+	0.160244i
$746$	−4.87859	+	22.0358i	−0.178618	+	0.806786i
$747$		0			0
$748$	18.6902	+	51.2595i	0.683380	+	1.87423i
$749$			6.73887i			0.246233i
$750$		0			0
$751$		−	28.9069i		−	1.05483i	−0.849609	−	0.527413i	$-0.823162\pi$
$751$		−	28.9069i		−	1.05483i	0.849609	−	0.527413i	$-0.176838\pi$
$752$	−12.9614	−	1.11902i	−0.472652	−	0.0408066i
$753$		0			0
$754$	2.97421	+	0.658473i	0.108314	+	0.0239802i
$755$	17.4126	−	3.43129i	0.633710	−	0.124877i
$756$		0			0
$757$	−16.2018	−	16.2018i	−0.588864	−	0.588864i	0.348459	−	0.937324i	$-0.386705\pi$
$757$	−16.2018	−	16.2018i	−0.588864	−	0.588864i	−0.937324	+	0.348459i	$0.886705\pi$
$758$	18.4318	−	11.7498i	0.669474	−	0.426771i
$759$		0			0
$760$	−7.32546	+	2.47909i	−0.265722	+	0.0899262i
$761$	6.64641			0.240932			0.120466	−	0.992717i	$-0.461561\pi$
$761$	6.64641			0.240932			0.120466	+	0.992717i	$0.461561\pi$
$762$		0			0
$763$	4.47353	+	4.47353i	0.161953	+	0.161953i
$764$	12.7736	+	5.94751i	0.462131	+	0.215173i
$765$		0			0
$766$	−24.5187	−	5.42831i	−0.885898	−	0.196133i
$767$	−0.931222	+	0.931222i	−0.0336245	+	0.0336245i
$768$		0			0
$769$			29.3449i			1.05820i	0.848559	+	0.529101i	$0.177471\pi$
$769$			29.3449i			1.05820i	−0.848559	+	0.529101i	$0.822529\pi$
$770$	−0.326890	+	14.0179i	−0.0117803	+	0.505172i
$771$		0			0
$772$	11.1470	+	30.5717i	0.401189	+	1.10030i
$773$	−37.5833	+	37.5833i	−1.35178	+	1.35178i	−0.468104	+	0.883674i	$0.655063\pi$
$773$	−37.5833	+	37.5833i	−1.35178	+	1.35178i	−0.883674	+	0.468104i	$0.844937\pi$
$774$		0			0
$775$	−14.8166	−	36.1346i	−0.532226	−	1.29799i
$776$	1.93086	−	2.52082i	0.0693137	−	0.0904921i
$777$		0			0
$778$	3.92510	+	6.15729i	0.140722	+	0.220749i
$779$	−6.75359			−0.241973
$780$		0			0
$781$	41.5510			1.48681
$782$	−6.15945	−	9.66229i	−0.220261	−	0.345523i
$783$		0			0
$784$	19.1400	−	16.0978i	0.683573	−	0.574920i
$785$	15.8786	−	23.6724i	0.566731	−	0.844905i
$786$		0			0
$787$	−7.59353	+	7.59353i	−0.270680	+	0.270680i	−0.829374	−	0.558694i	$-0.811303\pi$
$787$	−7.59353	+	7.59353i	−0.270680	+	0.270680i	0.558694	+	0.829374i	$0.311303\pi$
$788$	−20.9358	+	7.63357i	−0.745806	+	0.271935i
$789$		0			0
$790$	34.7440	+	36.4031i	1.23614	+	1.29516i
$791$			0.622595i			0.0221369i
$792$		0			0
$793$	8.77551	−	8.77551i	0.311628	−	0.311628i
$794$	−6.76212	−	1.49710i	−0.239979	−	0.0531300i
$795$		0			0
$796$	9.69075	−	20.8130i	0.343479	−	0.737696i
$797$	−27.4908	−	27.4908i	−0.973775	−	0.973775i	0.0258893	−	0.999665i	$-0.491758\pi$
$797$	−27.4908	−	27.4908i	−0.973775	−	0.973775i	−0.999665	+	0.0258893i	$0.991758\pi$
$798$		0			0
$799$	17.3016			0.612086
$800$	28.1818	−	2.40487i	0.996379	−	0.0850251i
$801$		0			0
$802$	−4.16810	+	2.65705i	−0.147181	+	0.0938237i
$803$	−11.5508	−	11.5508i	−0.407618	−	0.407618i
$804$		0			0
$805$	−0.569343	−	2.88922i	−0.0200667	−	0.101832i
$806$	26.8680	+	5.94842i	0.946384	+	0.209524i
$807$		0			0
$808$	−3.75940	−	28.3673i	−0.132255	−	0.997957i
$809$			47.7205i			1.67776i	0.544313	+	0.838882i	$0.316791\pi$
$809$			47.7205i			1.67776i	−0.544313	+	0.838882i	$0.683209\pi$
$810$		0			0
$811$			37.3179i			1.31041i	0.755451	+	0.655205i	$0.227418\pi$
$811$			37.3179i			1.31041i	−0.755451	+	0.655205i	$0.772582\pi$
$812$	−1.40474	+	0.512195i	−0.0492968	+	0.0179745i
$813$		0			0
$814$	3.90543	−	17.6402i	0.136885	−	0.618287i
$815$	23.0497	−	34.3634i	0.807397	−	1.20370i
$816$		0			0
$817$	−7.58767	−	7.58767i	−0.265459	−	0.265459i
$818$	−11.2535	−	17.6533i	−0.393470	−	0.617235i
$819$		0			0
$820$	23.9851	+	5.89995i	0.837597	+	0.206035i
$821$	0.686380			0.0239548			0.0119774	−	0.999928i	$-0.496187\pi$
$821$	0.686380			0.0239548			0.0119774	+	0.999928i	$0.496187\pi$
$822$		0			0
$823$	−27.2553	−	27.2553i	−0.950059	−	0.950059i	0.0487521	−	0.998811i	$-0.484476\pi$
$823$	−27.2553	−	27.2553i	−0.950059	−	0.950059i	−0.998811	+	0.0487521i	$0.984476\pi$
$824$	−9.29797	+	12.1389i	−0.323910	+	0.422879i
$825$		0			0
$826$	0.139728	−	0.631126i	0.00486175	−	0.0219597i
$827$	31.4437	−	31.4437i	1.09341	−	1.09341i	0.0982432	−	0.995162i	$-0.468678\pi$
$827$	31.4437	−	31.4437i	1.09341	−	1.09341i	0.995162	−	0.0982432i	$-0.0313223\pi$
$828$		0			0
$829$		−	0.270718i		−	0.00940243i	−0.999989	−	0.00470122i	$-0.998504\pi$
$829$		−	0.270718i		−	0.00940243i	0.999989	−	0.00470122i	$-0.00149645\pi$
$830$	−0.829553	+	35.5735i	−0.0287942	+	1.23478i
$831$		0			0
$832$	−9.93522	+	17.2767i	−0.344442	+	0.598964i
$833$	−23.5187	+	23.5187i	−0.814876	+	0.814876i
$834$		0			0
$835$	29.7639	+	19.9645i	1.03002	+	0.690900i
$836$	11.3694	+	5.29373i	0.393220	+	0.183088i
$837$		0			0
$838$	22.7414	−	14.4970i	0.785589	−	0.500792i
$839$	−31.0214			−1.07098			−0.535489	−	0.844542i	$-0.679873\pi$
$839$	−31.0214			−1.07098			−0.535489	+	0.844542i	$0.679873\pi$
$840$		0			0
$841$	28.2524			0.974221
$842$	−24.8085	+	15.8147i	−0.854956	+	0.545011i
$843$		0			0
$844$	−9.95634	−	4.63578i	−0.342711	−	0.159570i
$845$	14.9048	−	2.93711i	0.512742	−	0.101040i
$846$		0			0
$847$	9.35348	−	9.35348i	0.321389	−	0.321389i
$848$	−14.8010	−	1.27785i	−0.508267	−	0.0438814i
$849$		0			0
$850$	−37.0654	+	6.41021i	−1.27133	+	0.219869i
$851$			3.79441i			0.130071i
$852$		0			0
$853$	3.82611	−	3.82611i	0.131003	−	0.131003i	−0.638565	−	0.769568i	$-0.720472\pi$
$853$	3.82611	−	3.82611i	0.131003	−	0.131003i	0.769568	+	0.638565i	$0.220472\pi$
$854$	−1.31675	+	5.94751i	−0.0450581	+	0.203520i
$855$		0			0
$856$	−17.5004	−	13.4047i	−0.598152	−	0.458163i
$857$	−20.7711	−	20.7711i	−0.709529	−	0.709529i	0.256907	−	0.966436i	$-0.417296\pi$
$857$	−20.7711	−	20.7711i	−0.709529	−	0.709529i	−0.966436	+	0.256907i	$0.917296\pi$
$858$		0			0
$859$	1.69693			0.0578985			0.0289492	−	0.999581i	$-0.490784\pi$
$859$	1.69693			0.0578985			0.0289492	+	0.999581i	$0.490784\pi$
$860$	20.3187	+	33.5759i	0.692862	+	1.14493i
$861$		0			0
$862$	−11.6540	−	18.2815i	−0.396935	−	0.622670i
$863$	−5.92869	−	5.92869i	−0.201815	−	0.201815i	0.598962	−	0.800777i	$-0.295580\pi$
$863$	−5.92869	−	5.92869i	−0.201815	−	0.201815i	−0.800777	+	0.598962i	$0.795580\pi$
$864$		0			0
$865$	20.9248	+	14.0356i	0.711465	+	0.477225i
$866$	7.03831	−	31.7908i	0.239171	−	1.08030i
$867$		0			0
$868$	−12.6900	+	4.62699i	−0.430725	+	0.157050i
$869$		−	81.6068i		−	2.76832i
$870$		0			0
$871$		−	21.8617i		−	0.740756i
$872$	−20.5161	+	2.71891i	−0.694762	+	0.0920740i
$873$		0			0
$874$	−2.57162	−	0.569343i	−0.0869865	−	0.0192583i
$875$	−9.47100	−	1.93667i	−0.320178	−	0.0654714i
$876$		0			0
$877$	−10.0323	−	10.0323i	−0.338766	−	0.338766i	0.517137	−	0.855903i	$-0.326998\pi$
$877$	−10.0323	−	10.0323i	−0.338766	−	0.338766i	−0.855903	+	0.517137i	$0.826998\pi$
$878$	29.4020	−	18.7430i	0.992269	−	0.632544i
$879$		0			0
$880$	−35.7535	−	28.7329i	−1.20525	−	0.968585i
$881$	29.8130			1.00443			0.502213	−	0.864744i	$-0.332519\pi$
$881$	29.8130			1.00443			0.502213	+	0.864744i	$0.332519\pi$
$882$		0			0
$883$	−5.56557	−	5.56557i	−0.187296	−	0.187296i	0.607230	−	0.794526i	$-0.292281\pi$
$883$	−5.56557	−	5.56557i	−0.187296	−	0.187296i	−0.794526	+	0.607230i	$0.792281\pi$
$884$	11.1877	−	24.0279i	0.376282	−	0.808146i
$885$		0			0
$886$	−3.45856	−	0.765707i	−0.116193	−	0.0257244i
$887$	−8.59630	+	8.59630i	−0.288636	+	0.288636i	−0.836541	−	0.547905i	$-0.815426\pi$
$887$	−8.59630	+	8.59630i	−0.288636	+	0.288636i	0.547905	+	0.836541i	$0.315426\pi$
$888$		0			0
$889$			9.15994i			0.307214i
$890$	16.5905	−	15.8344i	0.556115	−	0.530770i
$891$		0			0
$892$	−28.8791	+	10.5298i	−0.966943	+	0.352565i
$893$	2.81215	−	2.81215i	0.0941052	−	0.0941052i
$894$		0			0
$895$	5.46778	+	27.7471i	0.182768	+	0.927483i
$896$	−0.446274	−	9.77211i	−0.0149090	−	0.326463i
$897$		0			0
$898$	25.2015	+	39.5334i	0.840984	+	1.31925i
$899$	−6.75359			−0.225245
$900$		0			0
$901$	19.7572			0.658207
$902$	−21.5316	−	33.7766i	−0.716925	−	1.12464i
$903$		0			0
$904$	−1.61684	−	1.23844i	−0.0537754	−	0.0411900i
$905$	−3.34153	−	16.9571i	−0.111076	−	0.563673i
$906$		0			0
$907$	31.6263	−	31.6263i	1.05013	−	1.05013i	0.0514592	−	0.998675i	$-0.483613\pi$
$907$	31.6263	−	31.6263i	1.05013	−	1.05013i	0.998675	−	0.0514592i	$-0.0163872\pi$
$908$	4.82748	+	13.2398i	0.160206	+	0.439379i
$909$		0			0
$910$	4.92749	−	4.70291i	0.163345	−	0.155900i
$911$			42.2656i			1.40032i	0.713985	+	0.700161i	$0.246888\pi$
$911$			42.2656i			1.40032i	−0.713985	+	0.700161i	$0.753112\pi$
$912$		0			0
$913$	40.8034	−	40.8034i	1.35040	−	1.35040i
$914$	−14.6547	−	3.24448i	−0.484735	−	0.107318i
$915$		0			0
$916$	−46.7003	−	21.7442i	−1.54302	−	0.718448i
$917$	−8.55728	−	8.55728i	−0.282586	−	0.282586i
$918$		0			0
$919$	−31.2829			−1.03193			−0.515964	−	0.856610i	$-0.672566\pi$
$919$	−31.2829			−1.03193			−0.515964	+	0.856610i	$0.672566\pi$
$920$	8.63564	+	4.26858i	0.284709	+	0.140731i
$921$		0			0
$922$	32.2238	−	20.5418i	1.06123	−	0.676508i
$923$	−14.2729	−	14.2729i	−0.469798	−	0.469798i
$924$		0			0
$925$	11.4908	+	4.80779i	0.377816	+	0.158079i
$926$	54.1143	+	11.9806i	1.77831	+	0.393707i
$927$		0			0
$928$	1.46412	−	4.66687i	0.0480621	−	0.153198i
$929$		−	22.1050i		−	0.725241i	−0.931937	−	0.362620i	$-0.881882\pi$
$929$		−	22.1050i		−	0.725241i	0.931937	−	0.362620i	$-0.118118\pi$
$930$		0			0
$931$			7.64535i			0.250566i
$932$	−0.693082	−	1.90084i	−0.0227026	−	0.0622641i
$933$		0			0
$934$	0.868197	−	3.92150i	0.0284083	−	0.128315i
$935$	50.6596	+	33.9806i	1.65675	+	1.11128i
$936$		0			0
$937$	−15.2986	−	15.2986i	−0.499784	−	0.499784i	0.411586	−	0.911371i	$-0.364975\pi$
$937$	−15.2986	−	15.2986i	−0.499784	−	0.499784i	−0.911371	+	0.411586i	$0.864975\pi$
$938$	5.76813	+	9.04843i	0.188336	+	0.295442i
$939$		0			0
$940$	−12.4440	+	7.53056i	−0.405877	+	0.245620i
$941$	−25.5264			−0.832138			−0.416069	−	0.909333i	$-0.636593\pi$
$941$	−25.5264			−0.832138			−0.416069	+	0.909333i	$0.636593\pi$
$942$		0			0
$943$	5.94842	+	5.94842i	0.193707	+	0.193707i
$944$	1.36106	+	1.61828i	0.0442986	+	0.0526704i
$945$		0			0
$946$	13.7572	−	62.1388i	0.447285	−	2.02031i
$947$	−11.9881	+	11.9881i	−0.389562	+	0.389562i	−0.874531	−	0.484969i	$-0.838831\pi$
$947$	−11.9881	+	11.9881i	−0.389562	+	0.389562i	0.484969	+	0.874531i	$0.338831\pi$
$948$		0			0
$949$			7.93545i			0.257596i
$950$	−4.98260	+	7.06640i	−0.161657	+	0.229264i
$951$		0			0
$952$	1.70916	+	12.8968i	0.0553943	+	0.417988i
$953$	−5.99563	+	5.99563i	−0.194218	+	0.194218i	−0.797516	−	0.603298i	$-0.793853\pi$
$953$	−5.99563	+	5.99563i	−0.194218	+	0.194218i	0.603298	+	0.797516i	$0.293853\pi$
$954$		0			0
$955$	15.4562	−	3.04577i	0.500151	−	0.0985586i
$956$	22.7389	−	48.8366i	0.735427	−	1.57949i
$957$		0			0
$958$	16.4082	−	10.4598i	0.530125	−	0.337940i
$959$	8.57657			0.276952
$960$		0			0
$961$	−30.0096			−0.968051
$962$	−7.40097	+	4.71791i	−0.238617	+	0.152112i
$963$		0			0
$964$	11.8968	−	25.5510i	0.383171	−	0.822943i
$965$	30.2139	+	20.2663i	0.972619	+	0.652397i
$966$		0			0
$967$	−1.66866	+	1.66866i	−0.0536606	+	0.0536606i	−0.733428	−	0.679767i	$-0.762081\pi$
$967$	−1.66866	+	1.66866i	−0.0536606	+	0.0536606i	0.679767	+	0.733428i	$0.262081\pi$
$968$	5.68483	+	42.8960i	0.182717	+	1.37873i
$969$		0			0
$970$	0.0827643	−	3.54916i	0.00265740	−	0.113957i
$971$		−	4.79719i		−	0.153949i	−0.997033	−	0.0769745i	$-0.975474\pi$
$971$		−	4.79719i		−	0.153949i	0.997033	−	0.0769745i	$-0.0245260\pi$
$972$		0			0
$973$	−1.39401	+	1.39401i	−0.0446900	+	0.0446900i
$974$	−10.5208	+	47.5204i	−0.337107	+	1.52265i
$975$		0			0
$976$	−12.8261	−	15.2501i	−0.410554	−	0.488143i
$977$	25.0140	+	25.0140i	0.800267	+	0.800267i	0.983137	−	0.182870i	$-0.0585387\pi$
$977$	25.0140	+	25.0140i	0.800267	+	0.800267i	−0.182870	+	0.983137i	$0.558539\pi$
$978$		0			0
$979$	−37.1919			−1.18866
$980$	6.67899	−	27.1522i	0.213353	−	0.867344i
$981$		0			0
$982$	21.9635	+	34.4540i	0.700884	+	1.09947i
$983$	30.9151	+	30.9151i	0.986038	+	0.986038i	0.999904	−	0.0138655i	$-0.00441368\pi$
$983$	30.9151	+	30.9151i	0.986038	+	0.986038i	−0.0138655	+	0.999904i	$0.504414\pi$
$984$		0			0
$985$	−13.8786	+	20.6907i	−0.442209	+	0.659262i
$986$	−1.40608	+	6.35101i	−0.0447786	+	0.202257i
$987$		0			0
$988$	−2.08702	−	5.72384i	−0.0663969	−	0.182100i
$989$			13.3661i			0.425017i
$990$		0			0
$991$		−	26.5873i		−	0.844575i	−0.906462	−	0.422287i	$-0.861227\pi$
$991$		−	26.5873i		−	0.844575i	0.906462	−	0.422287i	$-0.138773\pi$
$992$	13.2264	−	42.1589i	0.419937	−	1.33855i
$993$		0			0
$994$	9.67331	+	2.14162i	0.306819	+	0.0679280i
$995$	−4.96270	−	25.1840i	−0.157328	−	0.798387i
$996$		0			0
$997$	−2.47252	−	2.47252i	−0.0783054	−	0.0783054i	0.666869	−	0.745175i	$-0.267634\pi$
$997$	−2.47252	−	2.47252i	−0.0783054	−	0.0783054i	−0.745175	+	0.666869i	$0.767634\pi$
$998$	−14.9500	+	9.53021i	−0.473234	+	0.301674i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.k.e.127.5		12
3.2	odd	2		60.2.j.a.7.2	✓	12
4.3	odd	2	inner	180.2.k.e.127.2		12
5.2	odd	4		900.2.k.n.343.5		12
5.3	odd	4	inner	180.2.k.e.163.2		12
5.4	even	2		900.2.k.n.307.2		12
12.11	even	2		60.2.j.a.7.5	yes	12
15.2	even	4		300.2.j.d.43.2		12
15.8	even	4		60.2.j.a.43.5	yes	12
15.14	odd	2		300.2.j.d.7.5		12
20.3	even	4	inner	180.2.k.e.163.5		12
20.7	even	4		900.2.k.n.343.2		12
20.19	odd	2		900.2.k.n.307.5		12
24.5	odd	2		960.2.w.g.127.2		12
24.11	even	2		960.2.w.g.127.5		12
60.23	odd	4		60.2.j.a.43.2	yes	12
60.47	odd	4		300.2.j.d.43.5		12
60.59	even	2		300.2.j.d.7.2		12
120.53	even	4		960.2.w.g.703.5		12
120.83	odd	4		960.2.w.g.703.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.2	✓	12	3.2	odd	2
60.2.j.a.7.5	yes	12	12.11	even	2
60.2.j.a.43.2	yes	12	60.23	odd	4
60.2.j.a.43.5	yes	12	15.8	even	4
180.2.k.e.127.2		12	4.3	odd	2	inner
180.2.k.e.127.5		12	1.1	even	1	trivial
180.2.k.e.163.2		12	5.3	odd	4	inner
180.2.k.e.163.5		12	20.3	even	4	inner
300.2.j.d.7.2		12	60.59	even	2
300.2.j.d.7.5		12	15.14	odd	2
300.2.j.d.43.2		12	15.2	even	4
300.2.j.d.43.5		12	60.47	odd	4
900.2.k.n.307.2		12	5.4	even	2
900.2.k.n.307.5		12	20.19	odd	2
900.2.k.n.343.2		12	20.7	even	4
900.2.k.n.343.5		12	5.2	odd	4
960.2.w.g.127.2		12	24.5	odd	2
960.2.w.g.127.5		12	24.11	even	2
960.2.w.g.703.2		12	120.83	odd	4
960.2.w.g.703.5		12	120.53	even	4

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	180.2.k.e.127.5

Level	$180$
Weight	$2$
Character	180.127
Analytic conductor	$1.437$
Analytic rank	$0$
Dimension	$12$
Inner twists	$4$