LMFDB - Embedded newform 546.2.bq.c.419.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(419,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("546.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bq (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			419.18
Character	$\chi$	$=$	546.419
Dual form			546.2.bq.c.503.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.64235 - 0.550175i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.64213 q^{5} +(-1.69740 + 0.344709i) q^{6} +(-1.55066 - 2.14370i) q^{7} -1.00000i q^{8} +(2.39462 + 1.80716i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.64235 - 0.550175i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.64213 q^{5} +(-1.69740 + 0.344709i) q^{6} +(-1.55066 - 2.14370i) q^{7} -1.00000i q^{8} +(2.39462 + 1.80716i) q^{9} +(-1.42213 + 0.821065i) q^{10} +(-4.72128 + 2.72583i) q^{11} +(-1.29764 + 1.14723i) q^{12} +(3.02729 + 1.95845i) q^{13} +(-2.41476 - 1.08117i) q^{14} +(2.69695 + 0.903458i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00196 + 1.73544i) q^{17} +(2.97738 + 0.367735i) q^{18} +(0.710134 + 0.409996i) q^{19} +(-0.821065 + 1.42213i) q^{20} +(1.36732 + 4.37384i) q^{21} +(-2.72583 + 4.72128i) q^{22} +(-7.99723 + 4.61721i) q^{23} +(-0.550175 + 1.64235i) q^{24} -2.30341 q^{25} +(3.60093 + 0.182427i) q^{26} +(-2.93854 - 4.28544i) q^{27} +(-2.63183 + 0.271064i) q^{28} +(3.90054 - 2.25198i) q^{29} +(2.78735 - 0.566057i) q^{30} +7.82978i q^{31} +(-0.866025 - 0.500000i) q^{32} +(9.25367 - 1.87924i) q^{33} +2.00392i q^{34} +(2.54639 + 3.52023i) q^{35} +(2.76235 - 1.17022i) q^{36} +(-2.70458 - 4.68447i) q^{37} +0.819992 q^{38} +(-3.89437 - 4.88200i) q^{39} +1.64213i q^{40} +(-2.57673 - 4.46303i) q^{41} +(3.37105 + 3.10419i) q^{42} +(1.26790 - 2.19606i) q^{43} +5.45167i q^{44} +(-3.93227 - 2.96758i) q^{45} +(-4.61721 + 7.99723i) q^{46} -8.88055 q^{47} +(0.344709 + 1.69740i) q^{48} +(-2.19089 + 6.64831i) q^{49} +(-1.99481 + 1.15171i) q^{50} +(2.60036 - 2.29895i) q^{51} +(3.20971 - 1.64248i) q^{52} -1.04342i q^{53} +(-4.68757 - 2.24203i) q^{54} +(7.75296 - 4.47617i) q^{55} +(-2.14370 + 1.55066i) q^{56} +(-0.940718 - 1.06405i) q^{57} +(2.25198 - 3.90054i) q^{58} +(3.15112 - 5.45790i) q^{59} +(2.13089 - 1.88390i) q^{60} +(0.0774854 + 0.0447362i) q^{61} +(3.91489 + 6.78079i) q^{62} +(0.160757 - 7.93563i) q^{63} -1.00000 q^{64} +(-4.97120 - 3.21603i) q^{65} +(7.07430 - 6.25431i) q^{66} +(-0.687189 - 1.19025i) q^{67} +(1.00196 + 1.73544i) q^{68} +(15.6745 - 3.18318i) q^{69} +(3.96535 + 1.77541i) q^{70} +(-6.98942 - 4.03534i) q^{71} +(1.80716 - 2.39462i) q^{72} +1.33316i q^{73} +(-4.68447 - 2.70458i) q^{74} +(3.78300 + 1.26728i) q^{75} +(0.710134 - 0.409996i) q^{76} +(13.1645 + 5.89416i) q^{77} +(-5.81362 - 2.28075i) q^{78} +6.63038 q^{79} +(0.821065 + 1.42213i) q^{80} +(2.46837 + 8.65489i) q^{81} +(-4.46303 - 2.57673i) q^{82} +2.51709 q^{83} +(4.47151 + 1.00278i) q^{84} +(1.64535 - 2.84983i) q^{85} -2.53580i q^{86} +(-7.64503 + 1.55256i) q^{87} +(2.72583 + 4.72128i) q^{88} +(2.76731 + 4.79312i) q^{89} +(-4.88924 - 0.603869i) q^{90} +(-0.495967 - 9.52649i) q^{91} +9.23441i q^{92} +(4.30774 - 12.8592i) q^{93} +(-7.69078 + 4.44027i) q^{94} +(-1.16613 - 0.673266i) q^{95} +(1.14723 + 1.29764i) q^{96} +(-16.3882 - 9.46172i) q^{97} +(1.42679 + 6.85305i) q^{98} +(-16.2317 - 2.00477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.64235	−	0.550175i	−0.948210	−	0.317643i
$3$	−1.64235	−	0.550175i	−0.948210	−	0.317643i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.64213			−0.734383			−0.367191	−	0.930145i	$-0.619681\pi$
$5$	−1.64213			−0.734383			−0.367191	+	0.930145i	$0.619681\pi$
$6$	−1.69740	+	0.344709i	−0.692962	+	0.140727i
$7$	−1.55066	−	2.14370i	−0.586096	−	0.810242i
$7$	−1.55066	−	2.14370i	−0.586096	−	0.810242i
$8$		−	1.00000i		−	0.353553i
$9$	2.39462	+	1.80716i	0.798205	+	0.602386i
$10$	−1.42213	+	0.821065i	−0.449716	+	0.259643i
$11$	−4.72128	+	2.72583i	−1.42352	+	0.821870i	−0.996598	−	0.0824185i	$-0.973736\pi$
$11$	−4.72128	+	2.72583i	−1.42352	+	0.821870i	−0.426922	+	0.904288i	$0.640402\pi$
$12$	−1.29764	+	1.14723i	−0.374596	+	0.331176i
$13$	3.02729	+	1.95845i	0.839618	+	0.543177i
$13$	3.02729	+	1.95845i	0.839618	+	0.543177i
$14$	−2.41476	−	1.08117i	−0.645373	−	0.288954i
$15$	2.69695	+	0.903458i	0.696349	+	0.233272i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00196	+	1.73544i	−0.243011	+	0.420907i	−0.961570	−	0.274558i	$-0.911468\pi$
$17$	−1.00196	+	1.73544i	−0.243011	+	0.420907i	0.718560	+	0.695465i	$0.244802\pi$
$18$	2.97738	+	0.367735i	0.701774	+	0.0866761i
$19$	0.710134	+	0.409996i	0.162916	+	0.0940595i	0.579241	−	0.815156i	$-0.303349\pi$
$19$	0.710134	+	0.409996i	0.162916	+	0.0940595i	−0.416325	+	0.909216i	$0.636682\pi$
$20$	−0.821065	+	1.42213i	−0.183596	+	0.317997i
$21$	1.36732	+	4.37384i	0.298374	+	0.954449i
$22$	−2.72583	+	4.72128i	−0.581150	+	1.00658i
$23$	−7.99723	+	4.61721i	−1.66754	+	0.962754i	−0.698580	+	0.715532i	$0.746184\pi$
$23$	−7.99723	+	4.61721i	−1.66754	+	0.962754i	−0.968959	+	0.247222i	$0.920482\pi$
$24$	−0.550175	+	1.64235i	−0.112304	+	0.335243i
$25$	−2.30341			−0.460682
$26$	3.60093	+	0.182427i	0.706201	+	0.0357769i
$27$	−2.93854	−	4.28544i	−0.565523	−	0.824733i
$28$	−2.63183	+	0.271064i	−0.497369	+	0.0512263i
$29$	3.90054	−	2.25198i	0.724313	−	0.418182i	−0.0920252	−	0.995757i	$-0.529334\pi$
$29$	3.90054	−	2.25198i	0.724313	−	0.418182i	0.816338	+	0.577574i	$0.196001\pi$
$30$	2.78735	−	0.566057i	0.508899	−	0.103347i
$31$			7.82978i			1.40627i	0.711057	+	0.703135i	$0.248217\pi$
$31$			7.82978i			1.40627i	−0.711057	+	0.703135i	$0.751783\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	9.25367	−	1.87924i	1.61086	−	0.327133i
$34$			2.00392i			0.343669i
$35$	2.54639	+	3.52023i	0.430418	+	0.595028i
$36$	2.76235	−	1.17022i	0.460392	−	0.195037i
$37$	−2.70458	−	4.68447i	−0.444631	−	0.770123i	0.553396	−	0.832918i	$-0.313332\pi$
$37$	−2.70458	−	4.68447i	−0.444631	−	0.770123i	−0.998026	+	0.0627955i	$0.979998\pi$
$38$	0.819992			0.133020
$39$	−3.89437	−	4.88200i	−0.623598	−	0.781745i
$40$			1.64213i			0.259643i
$41$	−2.57673	−	4.46303i	−0.402417	−	0.697008i	0.591600	−	0.806232i	$-0.298497\pi$
$41$	−2.57673	−	4.46303i	−0.402417	−	0.697008i	−0.994017	+	0.109224i	$0.965163\pi$
$42$	3.37105	+	3.10419i	0.520165	+	0.478987i
$43$	1.26790	−	2.19606i	0.193353	−	0.334897i	−0.753007	−	0.658013i	$-0.771397\pi$
$43$	1.26790	−	2.19606i	0.193353	−	0.334897i	0.946359	+	0.323116i	$0.104731\pi$
$44$			5.45167i			0.821870i
$45$	−3.93227	−	2.96758i	−0.586188	−	0.442381i
$46$	−4.61721	+	7.99723i	−0.680770	+	1.17913i
$47$	−8.88055			−1.29536			−0.647680	−	0.761912i	$-0.724261\pi$
$47$	−8.88055			−1.29536			−0.647680	+	0.761912i	$0.724261\pi$
$48$	0.344709	+	1.69740i	0.0497545	+	0.244999i
$49$	−2.19089	+	6.64831i	−0.312984	+	0.949758i
$50$	−1.99481	+	1.15171i	−0.282109	+	0.162876i
$51$	2.60036	−	2.29895i	0.364124	−	0.321918i
$52$	3.20971	−	1.64248i	0.445107	−	0.227771i
$53$		−	1.04342i		−	0.143324i	−0.997429	−	0.0716621i	$-0.977170\pi$
$53$		−	1.04342i		−	0.143324i	0.997429	−	0.0716621i	$-0.0228303\pi$
$54$	−4.68757	−	2.24203i	−0.637898	−	0.305101i
$55$	7.75296	−	4.47617i	1.04541	−	0.603567i
$56$	−2.14370	+	1.55066i	−0.286464	+	0.207216i
$57$	−0.940718	−	1.06405i	−0.124601	−	0.140937i
$58$	2.25198	−	3.90054i	0.295699	−	0.512166i
$59$	3.15112	−	5.45790i	0.410241	−	0.710558i	−0.584675	−	0.811268i	$-0.698778\pi$
$59$	3.15112	−	5.45790i	0.410241	−	0.710558i	0.994916	+	0.100710i	$0.0321113\pi$
$60$	2.13089	−	1.88390i	0.275097	−	0.243210i
$61$	0.0774854	+	0.0447362i	0.00992099	+	0.00572789i	0.504952	−	0.863147i	$-0.331510\pi$
$61$	0.0774854	+	0.0447362i	0.00992099	+	0.00572789i	−0.495031	+	0.868875i	$0.664843\pi$
$62$	3.91489	+	6.78079i	0.497191	+	0.861161i
$63$	0.160757	−	7.93563i	0.0202535	−	0.999795i
$64$	−1.00000			−0.125000
$65$	−4.97120	−	3.21603i	−0.616601	−	0.398900i
$66$	7.07430	−	6.25431i	0.870786	−	0.769852i
$67$	−0.687189	−	1.19025i	−0.0839535	−	0.145412i	0.820991	−	0.570941i	$-0.193421\pi$
$67$	−0.687189	−	1.19025i	−0.0839535	−	0.145412i	−0.904945	+	0.425529i	$0.860088\pi$
$68$	1.00196	+	1.73544i	0.121505	+	0.210454i
$69$	15.6745	−	3.18318i	1.88699	−	0.383210i
$70$	3.96535	+	1.77541i	0.473950	+	0.212203i
$71$	−6.98942	−	4.03534i	−0.829491	−	0.478907i	0.0241871	−	0.999707i	$-0.492300\pi$
$71$	−6.98942	−	4.03534i	−0.829491	−	0.478907i	−0.853679	+	0.520800i	$0.825634\pi$
$72$	1.80716	−	2.39462i	0.212975	−	0.282208i
$73$			1.33316i			0.156034i	0.996952	+	0.0780172i	$0.0248589\pi$
$73$			1.33316i			0.156034i	−0.996952	+	0.0780172i	$0.975141\pi$
$74$	−4.68447	−	2.70458i	−0.544559	−	0.314401i
$75$	3.78300	+	1.26728i	0.436824	+	0.146333i
$76$	0.710134	−	0.409996i	0.0814579	−	0.0470298i
$77$	13.1645	+	5.89416i	1.50023	+	0.671702i
$78$	−5.81362	−	2.28075i	−0.658263	−	0.258244i
$79$	6.63038			0.745976			0.372988	−	0.927836i	$-0.378333\pi$
$79$	6.63038			0.745976			0.372988	+	0.927836i	$0.378333\pi$
$80$	0.821065	+	1.42213i	0.0917978	+	0.158999i
$81$	2.46837	+	8.65489i	0.274263	+	0.961655i
$82$	−4.46303	−	2.57673i	−0.492859	−	0.284552i
$83$	2.51709			0.276286			0.138143	−	0.990412i	$-0.455887\pi$
$83$	2.51709			0.276286			0.138143	+	0.990412i	$0.455887\pi$
$84$	4.47151	+	1.00278i	0.487882	+	0.109413i
$85$	1.64535	−	2.84983i	0.178463	−	0.309107i
$86$		−	2.53580i		−	0.273442i
$87$	−7.64503	+	1.55256i	−0.819634	+	0.166451i
$88$	2.72583	+	4.72128i	0.290575	+	0.503290i
$89$	2.76731	+	4.79312i	0.293334	+	0.508070i	0.974596	−	0.223970i	$-0.0719018\pi$
$89$	2.76731	+	4.79312i	0.293334	+	0.508070i	−0.681262	+	0.732040i	$0.738568\pi$
$90$	−4.88924	−	0.603869i	−0.515371	−	0.0636534i
$91$	−0.495967	−	9.52649i	−0.0519915	−	0.998648i
$92$			9.23441i			0.962754i
$93$	4.30774	−	12.8592i	0.446692	−	1.33344i
$94$	−7.69078	+	4.44027i	−0.793243	+	0.457979i
$95$	−1.16613	−	0.673266i	−0.119643	−	0.0690757i
$96$	1.14723	+	1.29764i	0.117088	+	0.132440i
$97$	−16.3882	−	9.46172i	−1.66397	−	0.960692i	−0.970792	−	0.239922i	$-0.922878\pi$
$97$	−16.3882	−	9.46172i	−1.66397	−	0.960692i	−0.693175	−	0.720770i	$-0.743789\pi$
$98$	1.42679	+	6.85305i	0.144127	+	0.692262i
$99$	−16.2317	−	2.00477i	−1.63134	−	0.201487i
$100$	−1.15171	+	1.99481i	−0.115171	+	0.199481i
$101$	1.04627	+	1.81218i	0.104107	+	0.180319i	0.913373	−	0.407123i	$-0.133468\pi$
$101$	1.04627	+	1.81218i	0.104107	+	0.180319i	−0.809266	+	0.587443i	$0.800135\pi$
$102$	1.10251	−	3.29113i	0.109164	−	0.325871i
$103$		−	16.9309i		−	1.66825i	−0.551574	−	0.834126i	$-0.685973\pi$
$103$		−	16.9309i		−	1.66825i	0.551574	−	0.834126i	$-0.314027\pi$
$104$	1.95845	−	3.02729i	0.192042	−	0.296850i
$105$	−2.24532	−	7.18240i	−0.219120	−	0.700931i
$106$	−0.521708	−	0.903625i	−0.0506728	−	0.0877678i
$107$	−3.07883	+	1.77757i	−0.297642	+	0.171844i	−0.641383	−	0.767221i	$-0.721639\pi$
$107$	−3.07883	+	1.77757i	−0.297642	+	0.171844i	0.343741	+	0.939064i	$0.388306\pi$
$108$	−5.18057	+	0.402133i	−0.498500	+	0.0386953i
$109$	−9.56379			−0.916045			−0.458023	−	0.888941i	$-0.651442\pi$
$109$	−9.56379			−0.916045			−0.458023	+	0.888941i	$0.651442\pi$
$110$	4.47617	−	7.75296i	0.426786	−	0.739215i
$111$	1.86459	+	9.18153i	0.176979	+	0.871472i
$112$	−1.08117	+	2.41476i	−0.102161	+	0.228174i
$113$	−0.168421	−	0.0972380i	−0.0158437	−	0.00914738i	0.492057	−	0.870563i	$-0.336245\pi$
$113$	−0.168421	−	0.0972380i	−0.0158437	−	0.00914738i	−0.507901	+	0.861415i	$0.669578\pi$
$114$	−1.34671	−	0.451139i	−0.126131	−	0.0422530i
$115$	13.1325	−	7.58205i	1.22461	−	0.707030i
$116$		−	4.50396i		−	0.418182i
$117$	3.70996	+	10.1605i	0.342986	+	0.939341i
$118$		−	6.30224i		−	0.580168i
$119$	5.27397	−	0.543191i	0.483464	−	0.0497942i
$120$	0.903458	−	2.69695i	0.0824740	−	0.246197i
$121$	9.36034	−	16.2126i	0.850940	−	1.47387i
$122$	0.0894724			0.00810045
$123$	1.77644	+	8.74749i	0.160177	+	0.788735i
$124$	6.78079	+	3.91489i	0.608933	+	0.351567i
$125$	11.9931			1.07270
$126$	−3.82859	−	6.95283i	−0.341078	−	0.619408i
$127$	8.79671	+	15.2363i	0.780582	+	1.35201i	0.931603	+	0.363477i	$0.118410\pi$
$127$	8.79671	+	15.2363i	0.780582	+	1.35201i	−0.151022	+	0.988530i	$0.548256\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−3.29055	+	2.90914i	−0.289717	+	0.256135i
$130$	−5.91320	−	0.299569i	−0.518622	−	0.0262739i
$131$	−1.13610			−0.0992613			−0.0496306	−	0.998768i	$-0.515804\pi$
$131$	−1.13610			−0.0992613			−0.0496306	+	0.998768i	$0.515804\pi$
$132$	2.99937	−	8.95354i	0.261062	−	0.779305i
$133$	−0.222270	−	2.15808i	−0.0192733	−	0.187129i
$134$	−1.19025	−	0.687189i	−0.102822	−	0.0593641i
$135$	4.82547	+	7.03724i	0.415310	+	0.605669i
$136$	1.73544	+	1.00196i	0.148813	+	0.0859173i
$137$	−18.0084	−	10.3972i	−1.53856	−	0.888290i	−0.998923	−	0.0463939i	$-0.985227\pi$
$137$	−18.0084	−	10.3972i	−1.53856	−	0.888290i	−0.539640	−	0.841896i	$-0.681440\pi$
$138$	11.9829	−	10.5940i	1.02006	−	0.901819i
$139$	0.0859214	+	0.0496067i	0.00728776	+	0.00420759i	0.503639	−	0.863914i	$-0.331994\pi$
$139$	0.0859214	+	0.0496067i	0.00728776	+	0.00420759i	−0.496352	+	0.868122i	$0.665327\pi$
$140$	4.32180	−	0.445122i	0.365259	−	0.0376197i
$141$	14.5850	+	4.88585i	1.22827	+	0.411463i
$142$	−8.07069			−0.677277
$143$	−19.6311	−	0.994532i	−1.64163	−	0.0831669i
$144$	0.367735	−	2.97738i	0.0306446	−	0.248115i
$145$	−6.40520	+	3.69804i	−0.531923	+	0.307106i
$146$	0.666579	+	1.15455i	0.0551665	+	0.0955512i
$147$	7.25593	−	9.71347i	0.598459	−	0.801153i
$148$	−5.40917			−0.444631
$149$	12.8477	+	7.41763i	1.05253	+	0.607676i	0.923355	−	0.383947i	$-0.125435\pi$
$149$	12.8477	+	7.41763i	1.05253	+	0.607676i	0.129170	+	0.991622i	$0.458769\pi$
$150$	3.90982	−	0.794006i	0.319235	−	0.0648304i
$151$	−21.8848			−1.78096			−0.890481	−	0.455020i	$-0.849632\pi$
$151$	−21.8848			−1.78096			−0.890481	+	0.455020i	$0.849632\pi$
$152$	0.409996	−	0.710134i	0.0332551	−	0.0575995i
$153$	−5.53553	+	2.34503i	−0.447521	+	0.189584i
$154$	14.3479	−	1.47775i	1.15618	−	0.119081i
$155$		−	12.8575i		−	1.03274i
$156$	−6.17512	+	0.931622i	−0.494405	+	0.0745895i
$157$		−	0.0759287i		−	0.00605977i	−0.999995	−	0.00302989i	$-0.999036\pi$
$157$		−	0.0759287i		−	0.00605977i	0.999995	−	0.00302989i	$-0.000964444\pi$
$158$	5.74208	−	3.31519i	0.456815	−	0.263742i
$159$	−0.574061	+	1.71365i	−0.0455260	+	0.135901i
$160$	1.42213	+	0.821065i	0.112429	+	0.0649109i
$161$	22.2989	+	9.98393i	1.75740	+	0.786844i
$162$	6.46512	+	6.26117i	0.507948	+	0.491924i
$163$	7.42791	−	12.8655i	0.581799	−	1.00770i	−0.413468	−	0.910519i	$-0.635683\pi$
$163$	7.42791	−	12.8655i	0.581799	−	1.00770i	0.995266	−	0.0971859i	$-0.0309841\pi$
$164$	−5.15346			−0.402417
$165$	−15.1957	+	3.08595i	−1.18299	+	0.240241i
$166$	2.17986	−	1.25854i	0.169190	−	0.0976819i
$167$	3.11992	+	5.40385i	0.241426	+	0.418163i	0.961121	−	0.276128i	$-0.0890515\pi$
$167$	3.11992	+	5.40385i	0.241426	+	0.418163i	−0.719694	+	0.694291i	$0.755718\pi$
$168$	4.37384	−	1.36732i	0.337449	−	0.105491i
$169$	5.32892	+	11.8576i	0.409917	+	0.912123i
$170$		−	3.29069i		−	0.252385i
$171$	0.959571	+	2.26511i	0.0733802	+	0.173217i
$172$	−1.26790	−	2.19606i	−0.0966763	−	0.167448i
$173$	−7.62087	+	13.1997i	−0.579404	+	1.00356i	0.416144	+	0.909299i	$0.363381\pi$
$173$	−7.62087	+	13.1997i	−0.579404	+	1.00356i	−0.995548	+	0.0942586i	$0.969952\pi$
$174$	−5.84452	+	5.16707i	−0.443072	+	0.391715i
$175$	3.57181	+	4.93782i	0.270004	+	0.373264i
$176$	4.72128	+	2.72583i	0.355880	+	0.205467i
$177$	−8.17803	+	7.23010i	−0.614698	+	0.543448i
$178$	4.79312	+	2.76731i	0.359260	+	0.207419i
$179$	−14.4202	+	8.32552i	−1.07782	+	0.622279i	−0.930307	−	0.366782i	$-0.880460\pi$
$179$	−14.4202	+	8.32552i	−1.07782	+	0.622279i	−0.147511	+	0.989060i	$0.547126\pi$
$180$	−4.53614	+	1.92165i	−0.338104	+	0.143232i
$181$		−	4.84052i		−	0.359793i	−0.983686	−	0.179897i	$-0.942424\pi$
$181$		−	4.84052i		−	0.359793i	0.983686	−	0.179897i	$-0.0575763\pi$
$182$	−5.19277	−	8.00220i	−0.384913	−	0.593162i
$183$	−0.102645	−	0.116103i	−0.00758776	−	0.00858258i
$184$	4.61721	+	7.99723i	0.340385	+	0.589564i
$185$	4.44128	+	7.69251i	0.326529	+	0.565565i
$186$	−2.69899	−	13.2903i	−0.197900	−	0.974491i
$187$		−	10.9247i		−	0.798893i
$188$	−4.44027	+	7.69078i	−0.323840	+	0.560908i
$189$	−4.63000	+	12.9446i	−0.336783	+	0.941582i
$190$	−1.34653			−0.0976878
$191$	12.7889	+	7.38366i	0.925371	+	0.534263i	0.885344	−	0.464936i	$-0.153923\pi$
$191$	12.7889	+	7.38366i	0.925371	+	0.534263i	0.0400262	+	0.999199i	$0.487256\pi$
$192$	1.64235	+	0.550175i	0.118526	+	0.0397054i
$193$	5.83945	+	10.1142i	0.420333	+	0.728038i	0.995972	−	0.0896659i	$-0.0285799\pi$
$193$	5.83945	+	10.1142i	0.420333	+	0.728038i	−0.575639	+	0.817704i	$0.695247\pi$
$194$	−18.9234			−1.35862
$195$	6.39506	+	8.01687i	0.457959	+	0.574100i
$196$	4.66216	+	5.22152i	0.333011	+	0.372966i
$197$	9.81078	−	5.66426i	0.698989	−	0.403561i	−0.107982	−	0.994153i	$-0.534439\pi$
$197$	9.81078	−	5.66426i	0.698989	−	0.403561i	0.806971	+	0.590591i	$0.201105\pi$
$198$	−15.0594	+	6.37965i	−1.07023	+	0.453382i
$199$	−19.2194	−	11.0963i	−1.36243	−	0.786598i	−0.372481	−	0.928040i	$-0.621493\pi$
$199$	−19.2194	−	11.0963i	−1.36243	−	0.786598i	−0.989947	+	0.141442i	$0.954826\pi$
$200$			2.30341i			0.162876i
$201$	0.473761	+	2.33287i	0.0334165	+	0.164548i
$202$	1.81218	+	1.04627i	0.127505	+	0.0736150i
$203$	−10.8760	−	4.86953i	−0.763345	−	0.341774i
$204$	−0.690769	−	3.40146i	−0.0483635	−	0.238150i
$205$	4.23132	+	7.32887i	0.295528	+	0.511870i
$206$	−8.46546	−	14.6626i	−0.589816	−	1.02159i
$207$	−27.4943	−	3.39582i	−1.91099	−	0.236026i
$208$	0.182427	−	3.60093i	0.0126490	−	0.249680i
$209$	−4.47032			−0.309219
$210$	−5.53570	−	5.09749i	−0.382000	−	0.351760i
$211$	8.97860	+	15.5514i	0.618112	+	1.07060i	0.989830	+	0.142256i	$0.0454356\pi$
$211$	8.97860	+	15.5514i	0.618112	+	1.07060i	−0.371718	+	0.928346i	$0.621231\pi$
$212$	−0.903625	−	0.521708i	−0.0620612	−	0.0358311i
$213$	9.25892	+	10.4728i	0.634411	+	0.717587i
$214$	−1.77757	+	3.07883i	−0.121512	+	0.210465i
$215$	−2.08205	+	3.60622i	−0.141995	+	0.245942i
$216$	−4.28544	+	2.93854i	−0.291587	+	0.199942i
$217$	16.7847	−	12.1413i	1.13942	−	0.824208i
$218$	−8.28249	+	4.78190i	−0.560961	+	0.323871i
$219$	0.733470	−	2.18951i	0.0495633	−	0.147953i
$220$		−	8.95234i		−	0.603567i
$221$	−6.43201	+	3.29140i	−0.432664	+	0.221403i
$222$	6.20555	+	7.01915i	0.416489	+	0.471094i
$223$	−13.8338	+	7.98696i	−0.926381	+	0.534846i	−0.885665	−	0.464325i	$-0.846297\pi$
$223$	−13.8338	+	7.98696i	−0.926381	+	0.534846i	−0.0407157	+	0.999171i	$0.512964\pi$
$224$	0.271064	+	2.63183i	0.0181112	+	0.175846i
$225$	−5.51578	−	4.16262i	−0.367719	−	0.277508i
$226$	−0.194476			−0.0129363
$227$	9.91906	−	17.1803i	0.658351	−	1.14030i	−0.322692	−	0.946504i	$-0.604588\pi$
$227$	9.91906	−	17.1803i	0.658351	−	1.14030i	0.981042	−	0.193793i	$-0.0620790\pi$
$228$	−1.39186	+	0.282659i	−0.0921779	+	0.0187195i
$229$			25.8572i			1.70869i	0.519704	+	0.854347i	$0.326042\pi$
$229$			25.8572i			1.70869i	−0.519704	+	0.854347i	$0.673958\pi$
$230$	7.58205	−	13.1325i	0.499946	−	0.865931i
$231$	−18.3779	−	16.9230i	−1.20917	−	1.11345i
$232$	−2.25198	−	3.90054i	−0.147850	−	0.256083i
$233$			11.0842i			0.726151i	0.931760	+	0.363075i	$0.118273\pi$
$233$			11.0842i			0.726151i	−0.931760	+	0.363075i	$0.881727\pi$
$234$	8.29318	+	6.94429i	0.542142	+	0.453963i
$235$	14.5830			0.951291
$236$	−3.15112	−	5.45790i	−0.205120	−	0.355279i
$237$	−10.8894	−	3.64787i	−0.707342	−	0.236954i
$238$	4.29580	−	3.10740i	0.278455	−	0.201423i
$239$			15.9911i			1.03438i	0.855872	+	0.517188i	$0.173021\pi$
$239$			15.9911i			1.03438i	−0.855872	+	0.517188i	$0.826979\pi$
$240$	−0.566057	−	2.78735i	−0.0365388	−	0.179923i
$241$	16.5559	+	9.55856i	1.06646	+	0.615721i	0.927212	−	0.374536i	$-0.122198\pi$
$241$	16.5559	+	9.55856i	1.06646	+	0.615721i	0.139248	+	0.990258i	$0.455531\pi$
$242$		−	18.7207i		−	1.20341i
$243$	0.707777	−	15.5724i	0.0454039	−	0.998969i
$244$	0.0774854	−	0.0447362i	0.00496050	−	0.00286394i
$245$	3.59772	−	10.9174i	0.229850	−	0.697486i
$246$	5.91219	+	6.68733i	0.376948	+	0.426369i
$247$	1.34682	+	2.63194i	0.0856961	+	0.167466i
$248$	7.82978			0.497191
$249$	−4.13393	−	1.38484i	−0.261977	−	0.0877605i
$250$	10.3864	−	5.99657i	0.656892	−	0.379257i
$251$	5.97786	−	10.3540i	0.377319	−	0.653536i	−0.613352	−	0.789810i	$-0.710179\pi$
$251$	5.97786	−	10.3540i	0.377319	−	0.653536i	0.990671	+	0.136274i	$0.0435127\pi$
$252$	−6.79208	−	4.10703i	−0.427861	−	0.258719i
$253$	25.1715	−	43.5983i	1.58252	−	2.74100i
$254$	15.2363	+	8.79671i	0.956013	+	0.551955i
$255$	−4.27013	+	3.77518i	−0.267406	+	0.236411i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.49214	+	4.31652i	0.155456	+	0.269257i	0.933225	−	0.359293i	$-0.116982\pi$
$257$	2.49214	+	4.31652i	0.155456	+	0.269257i	−0.777769	+	0.628550i	$0.783649\pi$
$258$	−1.39513	+	4.16466i	−0.0868570	+	0.259280i
$259$	−5.84821	+	13.0619i	−0.363390	+	0.811624i
$260$	−5.27076	+	2.69717i	−0.326879	+	0.167271i
$261$	13.4100	+	1.65627i	0.830057	+	0.102520i
$262$	−0.983889	+	0.568048i	−0.0607849	+	0.0350942i
$263$	24.6591	−	14.2369i	1.52054	−	0.877885i	0.520836	−	0.853657i	$-0.325620\pi$
$263$	24.6591	−	14.2369i	1.52054	−	0.877885i	0.999706	−	0.0242286i	$-0.00771297\pi$
$264$	−1.87924	−	9.25367i	−0.115659	−	0.569524i
$265$			1.71342i			0.105255i
$266$	−1.27153	−	1.75782i	−0.0779626	−	0.107779i
$267$	−1.90783	−	9.39448i	−0.116757	−	0.574933i
$268$	−1.37438			−0.0839535
$269$	−4.26305	+	7.38382i	−0.259923	+	0.450200i	−0.966221	−	0.257715i	$-0.917030\pi$
$269$	−4.26305	+	7.38382i	−0.259923	+	0.450200i	0.706298	+	0.707914i	$0.250364\pi$
$270$	7.69760	+	3.68170i	0.468461	+	0.224061i
$271$	−24.1477	+	13.9417i	−1.46687	+	0.846896i	−0.999313	−	0.0370693i	$-0.988198\pi$
$271$	−24.1477	+	13.9417i	−1.46687	+	0.846896i	−0.467553	+	0.883965i	$0.654864\pi$
$272$	2.00392			0.121505
$273$	−4.42668	+	15.9187i	−0.267915	+	0.963443i
$274$	−20.7943			−1.25623
$275$	10.8751	−	6.27871i	0.655790	−	0.378621i
$276$	5.08054	−	15.1661i	0.305812	−	0.912893i
$277$	−3.11730	+	5.39932i	−0.187300	+	0.324414i	−0.944349	−	0.328944i	$-0.893307\pi$
$277$	−3.11730	+	5.39932i	−0.187300	+	0.324414i	0.757049	+	0.653358i	$0.226640\pi$
$278$	0.0992134			0.00595043
$279$	−14.1496	+	18.7493i	−0.847116	+	1.12249i
$280$	3.52023	−	2.54639i	0.210374	−	0.152176i
$281$		−	26.9354i		−	1.60683i	−0.595418	−	0.803416i	$-0.703014\pi$
$281$		−	26.9354i		−	1.60683i	0.595418	−	0.803416i	$-0.296986\pi$
$282$	15.0739	−	3.06120i	0.897635	−	0.182292i
$283$	−0.515082	+	0.297383i	−0.0306185	+	0.0176776i	−0.515231	−	0.857051i	$-0.672294\pi$
$283$	−0.515082	+	0.297383i	−0.0306185	+	0.0176776i	0.484613	+	0.874729i	$0.338961\pi$
$284$	−6.98942	+	4.03534i	−0.414746	+	0.239454i
$285$	1.54478	+	1.74731i	0.0915049	+	0.103502i
$286$	−17.4983	+	8.95426i	−1.03470	+	0.529476i
$287$	−5.57174	+	12.4444i	−0.328890	+	0.734569i
$288$	−1.17022	−	2.76235i	−0.0689559	−	0.162773i
$289$	6.49215	+	11.2447i	0.381891	+	0.661455i
$290$	−3.69804	+	6.40520i	−0.217157	+	0.376126i
$291$	21.7095	+	24.5558i	1.27263	+	1.43949i
$292$	1.15455	+	0.666579i	0.0675649	+	0.0390086i
$293$	−2.75106	+	4.76497i	−0.160718	+	0.278373i	−0.935127	−	0.354314i	$-0.884714\pi$
$293$	−2.75106	+	4.76497i	−0.160718	+	0.278373i	0.774408	+	0.632686i	$0.218048\pi$
$294$	1.42709	−	12.0401i	0.0832295	−	0.702191i
$295$	−5.17455	+	8.96257i	−0.301274	+	0.521821i
$296$	−4.68447	+	2.70458i	−0.272280	+	0.157201i
$297$	25.5551	+	12.2228i	1.48286	+	0.709238i
$298$	14.8353			0.859383
$299$	−33.2525	−	1.68461i	−1.92304	−	0.0974233i
$300$	2.98900	−	2.64254i	0.172570	−	0.152567i
$301$	−6.67378	+	0.687363i	−0.384670	+	0.0396190i
$302$	−18.9528	+	10.9424i	−1.09061	+	0.629665i
$303$	−0.721314	−	3.55187i	−0.0414384	−	0.204049i
$304$		−	0.819992i		−	0.0470298i
$305$	−0.127241	−	0.0734627i	−0.00728580	−	0.00420646i
$306$	−3.62140	+	4.79862i	−0.207021	+	0.274319i
$307$		−	10.2749i		−	0.586419i	−0.956048	−	0.293210i	$-0.905277\pi$
$307$		−	10.2749i		−	0.586419i	0.956048	−	0.293210i	$-0.0947234\pi$
$308$	11.6867	−	8.45370i	0.665913	−	0.481694i
$309$	−9.31496	+	27.8065i	−0.529909	+	1.58185i
$310$	−6.42875	−	11.1349i	−0.365129	−	0.632421i
$311$	4.74366			0.268988			0.134494	−	0.990914i	$-0.457059\pi$
$311$	4.74366			0.268988			0.134494	+	0.990914i	$0.457059\pi$
$312$	−4.88200	+	3.89437i	−0.276389	+	0.220475i
$313$			12.1163i			0.684852i	0.939545	+	0.342426i	$0.111249\pi$
$313$			12.1163i			0.684852i	−0.939545	+	0.342426i	$0.888751\pi$
$314$	−0.0379644	−	0.0657562i	−0.00214245	−	0.00371084i
$315$	−0.263984	+	13.0313i	−0.0148738	+	0.734232i
$316$	3.31519	−	5.74208i	0.186494	−	0.323017i
$317$		−	28.9636i		−	1.62676i	−0.581736	−	0.813378i	$-0.697626\pi$
$317$		−	28.9636i		−	1.62676i	0.581736	−	0.813378i	$-0.302374\pi$
$318$	0.359675	+	1.77110i	0.0201696	+	0.0993182i
$319$	−12.2770	+	21.2645i	−0.687383	+	1.19058i
$320$	1.64213			0.0917978
$321$	6.03449	−	1.22549i	0.336812	−	0.0683999i
$322$	24.3034	−	2.50312i	1.35438	−	0.139493i
$323$	−1.42305	+	0.821599i	−0.0791807	+	0.0457150i
$324$	8.72954	+	2.18977i	0.484975	+	0.121654i
$325$	−6.97308	−	4.51112i	−0.386797	−	0.250232i
$326$		−	14.8558i		−	0.822787i
$327$	15.7071	+	5.26176i	0.868604	+	0.290976i
$328$	−4.46303	+	2.57673i	−0.246429	+	0.142276i
$329$	13.7707	+	19.0372i	0.759205	+	1.04956i
$330$	−11.6169	+	10.2704i	−0.639490	+	0.565366i
$331$	6.51282	−	11.2805i	0.357977	−	0.620035i	−0.629646	−	0.776882i	$-0.716800\pi$
$331$	6.51282	−	11.2805i	0.357977	−	0.620035i	0.987623	+	0.156848i	$0.0501332\pi$
$332$	1.25854	−	2.17986i	0.0690715	−	0.119635i
$333$	1.98914	−	16.1051i	0.109004	−	0.882555i
$334$	5.40385	+	3.11992i	0.295686	+	0.170714i
$335$	1.12845	+	1.95454i	0.0616540	+	0.106788i
$336$	3.10419	−	3.37105i	0.169348	−	0.183906i
$337$	−14.5560			−0.792915			−0.396458	−	0.918053i	$-0.629761\pi$
$337$	−14.5560			−0.792915			−0.396458	+	0.918053i	$0.629761\pi$
$338$	10.5438	+	7.60452i	0.573506	+	0.413631i
$339$	0.223108	+	0.252360i	0.0121176	+	0.0137063i
$340$	−1.64535	−	2.84983i	−0.0892315	−	0.154553i
$341$	−21.3427	−	36.9666i	−1.15577	−	2.00185i
$342$	1.96357	+	1.48185i	0.106177	+	0.0801295i
$343$	17.6493	−	5.61268i	0.952973	−	0.303056i
$344$	−2.19606	−	1.26790i	−0.118404	−	0.0683605i
$345$	−25.7396	+	5.22720i	−1.38577	+	0.281423i
$346$			15.2417i			0.819401i
$347$	6.40167	+	3.69601i	0.343660	+	0.198412i	0.661889	−	0.749602i	$-0.269755\pi$
$347$	6.40167	+	3.69601i	0.343660	+	0.198412i	−0.318229	+	0.948014i	$0.603088\pi$
$348$	−2.47796	+	7.39707i	−0.132833	+	0.396525i
$349$	−30.0059	+	17.3239i	−1.60618	+	0.927329i	−0.615966	+	0.787772i	$0.711234\pi$
$349$	−30.0059	+	17.3239i	−1.60618	+	0.927329i	−0.990214	+	0.139556i	$0.955432\pi$
$350$	5.56219	+	2.49037i	0.297312	+	0.133116i
$351$	−0.502979	−	18.7282i	−0.0268471	−	0.999640i
$352$	5.45167			0.290575
$353$	4.08453	+	7.07462i	0.217398	+	0.376544i	0.954012	−	0.299770i	$-0.0969098\pi$
$353$	4.08453	+	7.07462i	0.217398	+	0.376544i	−0.736614	+	0.676313i	$0.763576\pi$
$354$	−3.46733	+	10.3505i	−0.184287	+	0.550121i
$355$	11.4775	+	6.62656i	0.609164	+	0.351701i
$356$	5.53462			0.293334
$357$	−8.96055	−	2.00950i	−0.474243	−	0.106354i
$358$	−8.32552	+	14.4202i	−0.440017	+	0.762133i
$359$			9.96368i			0.525863i	0.964815	+	0.262931i	$0.0846893\pi$
$359$			9.96368i			0.525863i	−0.964815	+	0.262931i	$0.915311\pi$
$360$	−2.96758	+	3.93227i	−0.156405	+	0.207249i
$361$	−9.16381	−	15.8722i	−0.482306	−	0.835378i
$362$	−2.42026	−	4.19201i	−0.127206	−	0.220327i
$363$	−24.2927	+	21.4769i	−1.27504	+	1.12724i
$364$	−8.49817	−	4.33373i	−0.445425	−	0.227149i
$365$		−	2.18922i		−	0.114589i
$366$	−0.146945	−	0.0492255i	−0.00768093	−	0.00257306i
$367$	28.2897	−	16.3331i	1.47671	−	0.852581i	0.477059	−	0.878872i	$-0.341703\pi$
$367$	28.2897	−	16.3331i	1.47671	−	0.852581i	0.999654	+	0.0262909i	$0.00836963\pi$
$368$	7.99723	+	4.61721i	0.416885	+	0.240688i
$369$	1.89511	−	15.3438i	0.0986555	−	0.798766i
$370$	7.69251	+	4.44128i	0.399915	+	0.230891i
$371$	−2.23677	+	1.61799i	−0.116127	+	0.0840017i
$372$	−8.98254	−	10.1602i	−0.465723	−	0.526783i
$373$	−11.1251	+	19.2692i	−0.576033	+	0.997719i	0.419895	+	0.907573i	$0.362067\pi$
$373$	−11.1251	+	19.2692i	−0.576033	+	0.997719i	−0.995929	+	0.0901465i	$0.971266\pi$
$374$	−5.46235	−	9.46107i	−0.282451	−	0.489220i
$375$	−19.6969	−	6.59832i	−1.01714	−	0.340736i
$376$			8.88055i			0.457979i
$377$	16.2185	+	0.821644i	0.835293	+	0.0423168i
$378$	2.46261	+	13.5254i	0.126663	+	0.695670i
$379$	−7.15982	−	12.4012i	−0.367775	−	0.637005i	0.621442	−	0.783460i	$-0.286547\pi$
$379$	−7.15982	−	12.4012i	−0.367775	−	0.637005i	−0.989217	+	0.146455i	$0.953214\pi$
$380$	−1.16613	+	0.673266i	−0.0598213	+	0.0345378i
$381$	−6.06461	−	29.8631i	−0.310699	−	1.52993i
$382$	14.7673			0.755562
$383$	4.62087	−	8.00358i	0.236115	−	0.408964i	−0.723481	−	0.690344i	$-0.757459\pi$
$383$	4.62087	−	8.00358i	0.236115	−	0.408964i	0.959596	+	0.281381i	$0.0907923\pi$
$384$	1.69740	−	0.344709i	0.0866202	−	0.0175909i
$385$	−21.6178	−	9.67897i	−1.10174	−	0.493286i
$386$	10.1142	+	5.83945i	0.514801	+	0.297220i
$387$	7.00476	−	2.96744i	0.356072	−	0.150843i
$388$	−16.3882	+	9.46172i	−0.831983	+	0.480346i
$389$		−	4.72915i		−	0.239777i	−0.992787	−	0.119889i	$-0.961746\pi$
$389$		−	4.72915i		−	0.239777i	0.992787	−	0.119889i	$-0.0382538\pi$
$390$	9.54672	+	3.74529i	0.483417	+	0.189650i
$391$		−	18.5050i		−	0.935839i
$392$	6.64831	+	2.19089i	0.335790	+	0.110657i
$393$	1.86587	+	0.625052i	0.0941205	+	0.0315297i
$394$	5.66426	−	9.81078i	0.285361	−	0.494260i
$395$	−10.8879			−0.547832
$396$	−9.85202	+	13.0546i	−0.495082	+	0.656021i
$397$	−17.5022	−	10.1049i	−0.878410	−	0.507150i	−0.00827590	−	0.999966i	$-0.502634\pi$
$397$	−17.5022	−	10.1049i	−0.878410	−	0.507150i	−0.870134	+	0.492816i	$0.835968\pi$
$398$	−22.1927			−1.11242
$399$	−0.822275	+	3.66660i	−0.0411652	+	0.183560i
$400$	1.15171	+	1.99481i	0.0575853	+	0.0997406i
$401$	1.50582	−	0.869384i	0.0751969	−	0.0434150i	−0.461930	−	0.886916i	$-0.652843\pi$
$401$	1.50582	−	0.869384i	0.0751969	−	0.0434150i	0.537127	+	0.843501i	$0.319510\pi$
$402$	1.57673	+	1.78345i	0.0786399	+	0.0889503i
$403$	−15.3343	+	23.7030i	−0.763853	+	1.18073i
$404$	2.09253			0.104107
$405$	−4.05338	−	14.2125i	−0.201414	−	0.706222i
$406$	−11.8537	+	1.22086i	−0.588287	+	0.0605904i
$407$	25.5382	+	14.7445i	1.26588	+	0.730857i
$408$	−2.29895	−	2.60036i	−0.113815	−	0.128737i
$409$	17.5356	+	10.1242i	0.867078	+	0.500608i	0.866376	−	0.499392i	$-0.166443\pi$
$409$	17.5356	+	10.1242i	0.867078	+	0.500608i	0.000701977		1.00000i	$0.499777\pi$
$410$	7.32887	+	4.23132i	0.361947	+	0.208970i
$411$	23.8558	+	26.9835i	1.17672	+	1.33100i
$412$	−14.6626	−	8.46546i	−0.722374	−	0.417063i
$413$	−16.5864	+	1.70831i	−0.816164	+	0.0840605i
$414$	−25.5087	+	10.8063i	−1.25368	+	0.531100i
$415$	−4.13338			−0.202900
$416$	−1.64248	−	3.20971i	−0.0805292	−	0.157369i
$417$	−0.113820	−	0.128743i	−0.00557381	−	0.00630459i
$418$	−3.87141	+	2.23516i	−0.189357	+	0.109325i
$419$	16.4439	+	28.4817i	0.803338	+	1.39142i	0.917408	+	0.397949i	$0.130278\pi$
$419$	16.4439	+	28.4817i	0.803338	+	1.39142i	−0.114070	+	0.993473i	$0.536389\pi$
$420$	−7.34280	−	1.64670i	−0.358292	−	0.0803508i
$421$	−15.5310			−0.756933			−0.378466	−	0.925615i	$-0.623548\pi$
$421$	−15.5310			−0.756933			−0.378466	+	0.925615i	$0.623548\pi$
$422$	15.5514	+	8.97860i	0.757030	+	0.437071i
$423$	−21.2655	−	16.0485i	−1.03396	−	0.780307i
$424$	−1.04342			−0.0506728
$425$	2.30792	−	3.99744i	0.111951	−	0.193904i
$426$	13.2549	+	4.44029i	0.642201	+	0.215133i
$427$	−0.0242528	−	0.235476i	−0.00117367	−	0.0113955i
$428$			3.55513i			0.171844i
$429$	31.6939	+	12.4339i	1.53020	+	0.600314i
$430$			4.16411i			0.200811i
$431$	7.05106	−	4.07093i	0.339638	−	0.196090i	−0.320474	−	0.947257i	$-0.603842\pi$
$431$	7.05106	−	4.07093i	0.339638	−	0.196090i	0.660112	+	0.751167i	$0.270509\pi$
$432$	−2.24203	+	4.68757i	−0.107870	+	0.225531i
$433$	−10.1353	−	5.85161i	−0.487070	−	0.281210i	0.236288	−	0.971683i	$-0.424069\pi$
$433$	−10.1353	−	5.85161i	−0.487070	−	0.281210i	−0.723358	+	0.690473i	$0.757402\pi$
$434$	8.46529	−	18.9071i	0.406347	−	0.907568i
$435$	12.5541	−	2.54950i	0.601925	−	0.122239i
$436$	−4.78190	+	8.28249i	−0.229011	+	0.396659i
$437$	−7.57214			−0.362225
$438$	−0.459552	−	2.26291i	−0.0219582	−	0.108126i
$439$	6.79275	−	3.92180i	0.324200	−	0.187177i	−0.329063	−	0.944308i	$-0.606733\pi$
$439$	6.79275	−	3.92180i	0.324200	−	0.187177i	0.653263	+	0.757131i	$0.273400\pi$
$440$	−4.47617	−	7.75296i	−0.213393	−	0.369608i
$441$	−17.2609	+	11.9609i	−0.821946	+	0.569565i
$442$	−3.92458	+	6.06644i	−0.186673	+	0.288551i
$443$		−	23.4522i		−	1.11425i	−0.830430	−	0.557124i	$-0.811905\pi$
$443$		−	23.4522i		−	1.11425i	0.830430	−	0.557124i	$-0.188095\pi$
$444$	8.88373	+	2.97599i	0.421603	+	0.141234i
$445$	−4.54428	−	7.87092i	−0.215420	−	0.373118i
$446$	−7.98696	+	13.8338i	−0.378193	+	0.655050i
$447$	−17.0194	−	19.2508i	−0.804991	−	0.910532i
$448$	1.55066	+	2.14370i	0.0732619	+	0.101280i
$449$	−14.3032	−	8.25793i	−0.675007	−	0.389716i	0.122964	−	0.992411i	$-0.460760\pi$
$449$	−14.3032	−	8.25793i	−0.675007	−	0.389716i	−0.797971	+	0.602695i	$0.794093\pi$
$450$	−6.85812	−	0.847046i	−0.323295	−	0.0399301i
$451$	24.3309	+	14.0475i	1.14570	+	0.661470i
$452$	−0.168421	+	0.0972380i	−0.00792186	+	0.00457369i
$453$	35.9425	+	12.0405i	1.68873	+	0.565711i
$454$		−	19.8381i		−	0.931049i
$455$	0.814442	+	15.6437i	0.0381816	+	0.733389i
$456$	−1.06405	+	0.940718i	−0.0498289	+	0.0440531i
$457$	3.49048	+	6.04568i	0.163278	+	0.282805i	0.936042	−	0.351887i	$-0.114460\pi$
$457$	3.49048	+	6.04568i	0.163278	+	0.282805i	−0.772765	+	0.634693i	$0.781127\pi$
$458$	12.9286	+	22.3930i	0.604114	+	1.04636i
$459$	10.3814	−	0.805843i	0.484564	−	0.0376135i
$460$		−	15.1641i		−	0.707030i
$461$	10.4364	−	18.0764i	0.486072	−	0.841901i	−0.513800	−	0.857910i	$-0.671763\pi$
$461$	10.4364	−	18.0764i	0.486072	−	0.841901i	0.999872	+	0.0160089i	$0.00509602\pi$
$462$	−24.3772	−	5.46684i	−1.13413	−	0.254341i
$463$	−0.653244			−0.0303588			−0.0151794	−	0.999885i	$-0.504832\pi$
$463$	−0.653244			−0.0303588			−0.0151794	+	0.999885i	$0.504832\pi$
$464$	−3.90054	−	2.25198i	−0.181078	−	0.104546i
$465$	−7.07387	+	21.1165i	−0.328043	+	0.979254i
$466$	5.54210	+	9.59921i	0.256733	+	0.444675i
$467$	15.6587			0.724600			0.362300	−	0.932062i	$-0.381992\pi$
$467$	15.6587			0.724600			0.362300	+	0.932062i	$0.381992\pi$
$468$	10.6542	+	1.86734i	0.492493	+	0.0863181i
$469$	−1.48593	+	3.31880i	−0.0686139	+	0.153248i
$470$	12.6293	−	7.29150i	0.582544	−	0.336332i
$471$	−0.0417741	+	0.124701i	−0.00192485	+	0.00574594i
$472$	−5.45790	−	3.15112i	−0.251220	−	0.145042i
$473$			13.8243i			0.635643i
$474$	−11.2544	+	2.28555i	−0.516933	+	0.104979i
$475$	−1.63573	−	0.944389i	−0.0750524	−	0.0433315i
$476$	2.16657	−	4.83899i	0.0993045	−	0.221795i
$477$	1.88562	−	2.49858i	0.0863364	−	0.114402i
$478$	7.99553	+	13.8487i	0.365707	+	0.633423i
$479$	−5.63585	−	9.76157i	−0.257508	−	0.446018i	0.708065	−	0.706147i	$-0.249568\pi$
$479$	−5.63585	−	9.76157i	−0.257508	−	0.446018i	−0.965574	+	0.260129i	$0.916235\pi$
$480$	−1.88390	−	2.13089i	−0.0859877	−	0.0972615i
$481$	0.986778	−	19.4780i	0.0449932	−	0.888122i
$482$	19.1171			0.870761
$483$	−31.1297	−	28.6654i	−1.41645	−	1.30432i
$484$	−9.36034	−	16.2126i	−0.425470	−	0.736935i
$485$	26.9115	+	15.5374i	1.22199	+	0.705515i
$486$	−7.17324	−	13.8400i	−0.325385	−	0.627794i
$487$	−6.11110	+	10.5847i	−0.276920	+	0.479640i	−0.970618	−	0.240627i	$-0.922647\pi$
$487$	−6.11110	+	10.5847i	−0.276920	+	0.479640i	0.693698	+	0.720266i	$0.255980\pi$
$488$	0.0447362	−	0.0774854i	0.00202511	−	0.00350760i
$489$	−19.2775	+	17.0430i	−0.871758	+	0.770711i
$490$	−2.34297	−	11.2536i	−0.105845	−	0.508386i
$491$	10.7390	−	6.20019i	0.484646	−	0.279811i	−0.237704	−	0.971338i	$-0.576395\pi$
$491$	10.7390	−	6.20019i	0.484646	−	0.279811i	0.722351	+	0.691527i	$0.243062\pi$
$492$	8.46377	+	2.83530i	0.381576	+	0.127825i
$493$			9.02557i			0.406491i
$494$	2.48235	+	1.60592i	0.111686	+	0.0722536i
$495$	26.6545	+	3.29209i	1.19803	+	0.147969i
$496$	6.78079	−	3.91489i	0.304466	−	0.175784i
$497$	2.18767	+	21.2407i	0.0981306	+	0.952774i
$498$	−4.27251	+	0.867662i	−0.191456	+	0.0388809i
$499$	4.12872			0.184827			0.0924135	−	0.995721i	$-0.470542\pi$
$499$	4.12872			0.184827			0.0924135	+	0.995721i	$0.470542\pi$
$500$	5.99657	−	10.3864i	0.268175	−	0.464493i
$501$	−2.15093	−	10.5915i	−0.0960963	−	0.473194i
$502$		−	11.9557i		−	0.533610i
$503$	−4.60121	+	7.96953i	−0.205158	+	0.355344i	−0.950183	−	0.311693i	$-0.899104\pi$
$503$	−4.60121	+	7.96953i	−0.205158	+	0.355344i	0.745025	+	0.667036i	$0.232437\pi$
$504$	−7.93563	−	0.160757i	−0.353481	−	0.00716068i
$505$	−1.71810	−	2.97584i	−0.0764546	−	0.132423i
$506$		−	50.3429i		−	2.23802i
$507$	−2.22820	−	22.4061i	−0.0989578	−	0.995092i
$508$	17.5934			0.780582
$509$	−16.2637	−	28.1696i	−0.720876	−	1.24859i	−0.960649	−	0.277765i	$-0.910406\pi$
$509$	−16.2637	−	28.1696i	−0.720876	−	1.24859i	0.239773	−	0.970829i	$-0.422927\pi$
$510$	−1.81046	+	5.40447i	−0.0801684	+	0.239314i
$511$	2.85789	−	2.06728i	0.126426	−	0.0914511i
$512$			1.00000i			0.0441942i
$513$	−0.329746	−	4.24802i	−0.0145586	−	0.187555i
$514$	4.31652	+	2.49214i	0.190394	+	0.109924i
$515$			27.8027i			1.22514i
$516$	0.874112	+	4.30427i	0.0384806	+	0.189485i
$517$	41.9276	−	24.2069i	1.84397	−	1.06462i
$518$	1.46623	+	14.2360i	0.0644225	+	0.625494i
$519$	19.7783	−	17.4858i	0.868170	−	0.767540i
$520$	−3.21603	+	4.97120i	−0.141032	+	0.218001i
$521$	−8.56893			−0.375412			−0.187706	−	0.982225i	$-0.560105\pi$
$521$	−8.56893			−0.375412			−0.187706	+	0.982225i	$0.560105\pi$
$522$	12.4415	−	5.27062i	0.544551	−	0.230689i
$523$	19.6060	−	11.3195i	0.857310	−	0.494968i	−0.00580042	−	0.999983i	$-0.501846\pi$
$523$	19.6060	−	11.3195i	0.857310	−	0.494968i	0.863111	+	0.505015i	$0.168513\pi$
$524$	−0.568048	+	0.983889i	−0.0248153	+	0.0429814i
$525$	−3.14950	−	10.0747i	−0.137455	−	0.439698i
$526$	14.2369	−	24.6591i	0.620759	−	1.07519i
$527$	−13.5881	−	7.84512i	−0.591909	−	0.341739i
$528$	−6.25431	−	7.07430i	−0.272184	−	0.307869i
$529$	31.1372	−	53.9312i	1.35379	−	2.34483i
$530$	0.856712	+	1.48387i	0.0372132	+	0.0644551i
$531$	17.4090	−	7.37500i	0.755486	−	0.320048i
$532$	−1.98009	−	0.886547i	−0.0858476	−	0.0384367i
$533$	0.940130	−	18.5573i	0.0407216	−	0.803804i
$534$	−6.34947	−	7.18194i	−0.274768	−	0.310793i
$535$	5.05584	−	2.91899i	0.218583	−	0.126199i
$536$	−1.19025	+	0.687189i	−0.0514108	+	0.0296821i
$537$	28.2635	−	5.73976i	1.21966	−	0.247689i
$538$			8.52610i			0.367586i
$539$	−7.77838	−	37.3605i	−0.335038	−	1.60923i
$540$	8.50716	−	0.660355i	0.366090	−	0.0284172i
$541$	−30.2986			−1.30264			−0.651318	−	0.758805i	$-0.725784\pi$
$541$	−30.2986			−1.30264			−0.651318	+	0.758805i	$0.725784\pi$
$542$	−13.9417	+	24.1477i	−0.598846	+	1.03723i
$543$	−2.66313	+	7.94982i	−0.114286	+	0.341160i
$544$	1.73544	−	1.00196i	0.0744066	−	0.0429587i
$545$	15.7050			0.672728
$546$	4.12572	+	15.9993i	0.176565	+	0.684708i
$547$	−20.3506			−0.870127			−0.435064	−	0.900400i	$-0.643274\pi$
$547$	−20.3506			−0.870127			−0.435064	+	0.900400i	$0.643274\pi$
$548$	−18.0084	+	10.3972i	−0.769282	+	0.444145i
$549$	0.104702	+	0.247154i	0.00446859	+	0.0105483i
$550$	6.27871	−	10.8751i	0.267725	−	0.463714i
$551$	3.69321			0.157336
$552$	−3.18318	−	15.6745i	−0.135485	−	0.667152i
$553$	−10.2815	−	14.2135i	−0.437213	−	0.604421i
$554$			6.23460i			0.264883i
$555$	−3.06190	−	15.0773i	−0.129970	−	0.639994i
$556$	0.0859214	−	0.0496067i	0.00364388	−	0.00210379i
$557$	8.68060	−	5.01174i	0.367809	−	0.212354i	−0.304692	−	0.952451i	$-0.598554\pi$
$557$	8.68060	−	5.01174i	0.367809	−	0.212354i	0.672501	+	0.740097i	$0.265220\pi$
$558$	−2.87929	+	23.3122i	−0.121890	+	0.986884i
$559$	8.13918	−	4.16499i	0.344251	−	0.176161i
$560$	1.77541	−	3.96535i	0.0750250	−	0.167567i
$561$	−6.01049	+	17.9422i	−0.253763	+	0.757519i
$562$	−13.4677	−	23.3268i	−0.568101	−	0.983980i
$563$	19.0902	−	33.0653i	0.804558	−	1.39354i	−0.112031	−	0.993705i	$-0.535736\pi$
$563$	19.0902	−	33.0653i	0.804558	−	1.39354i	0.916589	−	0.399830i	$-0.130931\pi$
$564$	11.5237	−	10.1880i	0.485237	−	0.428993i
$565$	0.276569	+	0.159677i	0.0116354	+	0.00671768i
$566$	−0.297383	+	0.515082i	−0.0124999	+	0.0216505i
$567$	14.7259	−	18.7123i	0.618428	−	0.785841i
$568$	−4.03534	+	6.98942i	−0.169319	+	0.293270i
$569$	−1.39347	+	0.804521i	−0.0584173	+	0.0337273i	−0.528924	−	0.848669i	$-0.677404\pi$
$569$	−1.39347	+	0.804521i	−0.0584173	+	0.0337273i	0.470507	+	0.882396i	$0.344071\pi$
$570$	2.21148	+	0.740828i	0.0926285	+	0.0310299i
$571$	14.6931			0.614888			0.307444	−	0.951566i	$-0.400526\pi$
$571$	14.6931			0.614888			0.307444	+	0.951566i	$0.400526\pi$
$572$	−10.6768	+	16.5038i	−0.446421	+	0.690057i
$573$	−16.9415	−	19.1627i	−0.707741	−	0.800532i
$574$	1.39692	+	13.5630i	0.0583062	+	0.566110i
$575$	18.4209	−	10.6353i	0.768205	−	0.443524i
$576$	−2.39462	−	1.80716i	−0.0997757	−	0.0752982i
$577$		−	8.58712i		−	0.357486i	−0.983896	−	0.178743i	$-0.942797\pi$
$577$		−	8.58712i		−	0.357486i	0.983896	−	0.178743i	$-0.0572031\pi$
$578$	11.2447	+	6.49215i	0.467720	+	0.270038i
$579$	−4.02582	−	19.8238i	−0.167308	−	0.823849i
$580$			7.39609i			0.307106i
$581$	−3.90315	−	5.39587i	−0.161930	−	0.223859i
$582$	31.0789	+	10.4112i	1.28826	+	0.431558i
$583$	2.84418	+	4.92626i	0.117794	+	0.204025i
$584$	1.33316			0.0551665
$585$	−6.09223	−	16.6849i	−0.251883	−	0.689835i
$586$			5.50211i			0.227290i
$587$	18.5941	+	32.2059i	0.767460	+	1.32928i	0.938936	+	0.344091i	$0.111813\pi$
$587$	18.5941	+	32.2059i	0.767460	+	1.32928i	−0.171477	+	0.985188i	$0.554854\pi$
$588$	−4.78414	−	11.1406i	−0.197295	−	0.459429i
$589$	−3.21018	+	5.56019i	−0.132273	+	0.229104i
$590$			10.3491i			0.426065i
$591$	−19.2290	+	3.90504i	−0.790977	+	0.160632i
$592$	−2.70458	+	4.68447i	−0.111158	+	0.192531i
$593$	2.36671			0.0971893			0.0485946	−	0.998819i	$-0.484526\pi$
$593$	2.36671			0.0971893			0.0485946	+	0.998819i	$0.484526\pi$
$594$	28.2427	−	2.19230i	1.15881	−	0.0899510i
$595$	−8.66055	+	0.891989i	−0.355048	+	0.0365680i
$596$	12.8477	−	7.41763i	0.526263	−	0.303838i
$597$	25.4600	+	28.7981i	1.04201	+	1.17863i
$598$	−29.6398	+	15.1673i	−1.21206	+	0.620239i
$599$			33.8591i			1.38344i	0.722164	+	0.691722i	$0.243148\pi$
$599$			33.8591i			1.38344i	−0.722164	+	0.691722i	$0.756852\pi$
$600$	1.26728	−	3.78300i	0.0517364	−	0.154440i
$601$	8.39643	−	4.84768i	0.342497	−	0.197741i	−0.318878	−	0.947796i	$-0.603306\pi$
$601$	8.39643	−	4.84768i	0.342497	−	0.197741i	0.661376	+	0.750055i	$0.269973\pi$
$602$	−5.43598	+	3.93217i	−0.221554	+	0.160263i
$603$	0.505408	−	4.09204i	0.0205818	−	0.166641i
$604$	−10.9424	+	18.9528i	−0.445241	+	0.771179i
$605$	−15.3709	+	26.6232i	−0.624915	+	1.08239i
$606$	−2.40061	−	2.71535i	−0.0975181	−	0.110304i
$607$	−39.9962	−	23.0918i	−1.62340	−	0.937269i	−0.986002	−	0.166732i	$-0.946678\pi$
$607$	−39.9962	−	23.0918i	−1.62340	−	0.937269i	−0.637395	−	0.770537i	$-0.719988\pi$
$608$	−0.409996	−	0.710134i	−0.0166275	−	0.0287997i
$609$	15.1831	+	13.9812i	0.615250	+	0.566545i
$610$	−0.146925			−0.00594883
$611$	−26.8840	−	17.3921i	−1.08761	−	0.703610i
$612$	−0.736912	+	5.96642i	−0.0297879	+	0.241178i
$613$	−10.0107	−	17.3390i	−0.404329	−	0.700318i	0.589915	−	0.807466i	$-0.299161\pi$
$613$	−10.0107	−	17.3390i	−0.404329	−	0.700318i	−0.994243	+	0.107148i	$0.965828\pi$
$614$	−5.13745	−	8.89832i	−0.207330	−	0.359107i
$615$	−2.91715	−	14.3645i	−0.117631	−	0.579233i
$616$	5.89416	−	13.1645i	0.237482	−	0.530412i
$617$	−16.7758	−	9.68554i	−0.675370	−	0.389925i	0.122738	−	0.992439i	$-0.460832\pi$
$617$	−16.7758	−	9.68554i	−0.675370	−	0.389925i	−0.798108	+	0.602514i	$0.794166\pi$
$618$	5.83624	+	28.7386i	0.234768	+	1.15603i
$619$			14.4256i			0.579816i	0.957055	+	0.289908i	$0.0936247\pi$
$619$			14.4256i			0.579816i	−0.957055	+	0.289908i	$0.906375\pi$
$620$	−11.1349	−	6.42875i	−0.447189	−	0.258185i
$621$	43.2870	+	20.7038i	1.73705	+	0.830815i
$622$	4.10813	−	2.37183i	0.164721	−	0.0951017i
$623$	5.98384	−	13.3648i	0.239738	−	0.535449i
$624$	−2.28075	+	5.81362i	−0.0913031	+	0.232731i
$625$	−8.17724			−0.327090
$626$	6.05813	+	10.4930i	0.242132	+	0.419385i
$627$	7.34183	+	2.45946i	0.293204	+	0.0982213i
$628$	−0.0657562	−	0.0379644i	−0.00262396	−	0.00151494i
$629$	10.8395			0.432200
$630$	6.28705	+	11.4175i	0.250482	+	0.454882i
$631$	−3.41727	+	5.91888i	−0.136039	+	0.235627i	−0.925994	−	0.377538i	$-0.876771\pi$
$631$	−3.41727	+	5.91888i	−0.136039	+	0.235627i	0.789955	+	0.613165i	$0.210104\pi$
$632$		−	6.63038i		−	0.263742i
$633$	−6.19001	−	30.4806i	−0.246031	−	1.21149i
$634$	−14.4818	−	25.0832i	−0.575145	−	0.996180i
$635$	−14.4453	−	25.0201i	−0.573246	−	0.992891i
$636$	1.19704	+	1.35398i	0.0474656	+	0.0536887i
$637$	−19.6528	+	15.8356i	−0.778674	+	0.627429i
$638$			24.5541i			0.972106i
$639$	−9.44448	−	22.2941i	−0.373618	−	0.881940i
$640$	1.42213	−	0.821065i	0.0562145	−	0.0324554i
$641$	13.7700	+	7.95011i	0.543882	+	0.314010i	0.746651	−	0.665216i	$-0.231661\pi$
$641$	13.7700	+	7.95011i	0.543882	+	0.314010i	−0.202769	+	0.979227i	$0.564994\pi$
$642$	4.61328	−	4.07855i	0.182072	−	0.160967i
$643$	40.7351	+	23.5184i	1.60643	+	0.927475i	0.990159	+	0.139944i	$0.0446923\pi$
$643$	40.7351	+	23.5184i	1.60643	+	0.927475i	0.616275	+	0.787531i	$0.288641\pi$
$644$	19.7958	−	14.3195i	0.780064	−	0.564266i
$645$	5.40351	−	4.77718i	0.212763	−	0.188101i
$646$	−0.821599	+	1.42305i	−0.0323254	+	0.0559892i
$647$	−7.57114	−	13.1136i	−0.297652	−	0.515549i	0.677946	−	0.735112i	$-0.262870\pi$
$647$	−7.57114	−	13.1136i	−0.297652	−	0.515549i	−0.975598	+	0.219563i	$0.929537\pi$
$648$	8.65489	−	2.46837i	0.339996	−	0.0969668i
$649$			34.3577i			1.34866i
$650$	−8.29443	−	0.420204i	−0.325334	−	0.0164818i
$651$	−34.2462	+	10.7058i	−1.34221	+	0.419594i
$652$	−7.42791	−	12.8655i	−0.290899	−	0.503852i
$653$	−28.5931	+	16.5082i	−1.11893	+	0.646017i	−0.941129	−	0.338048i	$-0.890233\pi$
$653$	−28.5931	+	16.5082i	−1.11893	+	0.646017i	−0.177806	+	0.984066i	$0.556900\pi$
$654$	16.2336	−	3.29673i	0.634784	−	0.128912i
$655$	1.86562			0.0728957
$656$	−2.57673	+	4.46303i	−0.100604	+	0.174252i
$657$	−2.40923	+	3.19240i	−0.0939929	+	0.124547i
$658$	21.4444	+	9.60135i	0.835990	+	0.374299i
$659$	−21.1756	−	12.2258i	−0.824886	−	0.476248i	0.0272128	−	0.999630i	$-0.491337\pi$
$659$	−21.1756	−	12.2258i	−0.824886	−	0.476248i	−0.852098	+	0.523382i	$0.824670\pi$
$660$	−4.92535	+	14.7029i	−0.191719	+	0.572308i
$661$	10.1405	−	5.85461i	0.394419	−	0.227718i	−0.289654	−	0.957131i	$-0.593540\pi$
$661$	10.1405	−	5.85461i	0.394419	−	0.227718i	0.684073	+	0.729414i	$0.260207\pi$
$662$		−	13.0256i		−	0.506256i
$663$	12.3744	−	1.86690i	0.480583	−	0.0725042i
$664$		−	2.51709i		−	0.0976819i
$665$	0.364997	+	3.54384i	0.0141540	+	0.137424i
$666$	−6.32991	−	14.9420i	−0.245279	−	0.578991i
$667$	−20.7957	+	36.0192i	−0.805213	+	1.39467i
$668$	6.23983			0.241426
$669$	27.1142	−	5.50635i	1.04829	−	0.212888i
$670$	1.95454	+	1.12845i	0.0755104	+	0.0435960i
$671$	−0.487774			−0.0188303
$672$	1.00278	−	4.47151i	0.0386832	−	0.172492i
$673$	15.6498	+	27.1063i	0.603257	+	1.04487i	0.992324	+	0.123663i	$0.0394641\pi$
$673$	15.6498	+	27.1063i	0.603257	+	1.04487i	−0.389067	+	0.921209i	$0.627203\pi$
$674$	−12.6059	+	7.27800i	−0.485559	+	0.280338i
$675$	6.76867	+	9.87112i	0.260526	+	0.379940i
$676$	12.9334	+	1.31382i	0.497440	+	0.0505314i
$677$	−10.5864			−0.406868			−0.203434	−	0.979089i	$-0.565210\pi$
$677$	−10.5864			−0.406868			−0.203434	+	0.979089i	$0.565210\pi$
$678$	0.319397	+	0.106996i	0.0122664	+	0.00410915i
$679$	5.12946	+	49.8032i	0.196851	+	1.91127i
$680$	−2.84983	−	1.64535i	−0.109286	−	0.0630962i
$681$	−25.7427	+	22.7588i	−0.986463	+	0.872121i
$682$	−36.9666	−	21.3427i	−1.41552	−	0.817253i
$683$	−16.4793	−	9.51432i	−0.630562	−	0.364055i	0.150408	−	0.988624i	$-0.451941\pi$
$683$	−16.4793	−	9.51432i	−0.630562	−	0.364055i	−0.780970	+	0.624569i	$0.785275\pi$
$684$	2.44142	+	0.301540i	0.0933502	+	0.0115297i
$685$	29.5722	+	17.0735i	1.12989	+	0.652345i
$686$	12.4784	−	13.6854i	0.476428	−	0.522510i
$687$	14.2260	−	42.4666i	0.542755	−	1.62020i
$688$	−2.53580			−0.0966763
$689$	2.04348	−	3.15872i	0.0778504	−	0.120338i
$690$	−19.6775	+	17.3967i	−0.749111	+	0.662280i
$691$	−4.63524	+	2.67616i	−0.176333	+	0.101806i	−0.585569	−	0.810623i	$-0.699129\pi$
$691$	−4.63524	+	2.67616i	−0.176333	+	0.101806i	0.409236	+	0.912429i	$0.365795\pi$
$692$	7.62087	+	13.1997i	0.289702	+	0.501779i
$693$	20.8722	+	37.9045i	0.792870	+	1.43987i
$694$	7.39202			0.280597
$695$	−0.141094	−	0.0814607i	−0.00535200	−	0.00308998i
$696$	1.55256	+	7.64503i	0.0588495	+	0.289784i
$697$	10.3271			0.391167
$698$	−17.3239	+	30.0059i	−0.655720	+	1.13574i
$699$	6.09825	−	18.2041i	0.230657	−	0.688544i
$700$	6.06218	−	0.624372i	0.229129	−	0.0235990i
$701$			22.1372i			0.836112i	0.908421	+	0.418056i	$0.137288\pi$
$701$			22.1372i			0.836112i	−0.908421	+	0.418056i	$0.862712\pi$
$702$	−9.79971	−	15.9676i	−0.369866	−	0.602660i
$703$		−	4.43547i		−	0.167287i
$704$	4.72128	−	2.72583i	0.177940	−	0.102734i
$705$	−23.9504	−	8.02320i	−0.902023	−	0.302171i
$706$	7.07462	+	4.08453i	0.266257	+	0.153723i
$707$	2.26237	−	5.05296i	0.0850853	−	0.190036i
$708$	2.17244	+	10.6974i	0.0816452	+	0.402034i
$709$	16.0279	−	27.7611i	0.601940	−	1.04259i	−0.390587	−	0.920566i	$-0.627728\pi$
$709$	16.0279	−	27.7611i	0.601940	−	1.04259i	0.992527	−	0.122025i	$-0.0389388\pi$
$710$	13.2531			0.497380
$711$	15.8772	+	11.9821i	0.595442	+	0.449365i
$712$	4.79312	−	2.76731i	0.179630	−	0.103709i
$713$	−36.1517	−	62.6166i	−1.35389	−	2.34501i
$714$	−8.76481	+	2.74000i	−0.328015	+	0.102542i
$715$	32.2368	+	1.63315i	1.20559	+	0.0610763i
$716$			16.6510i			0.622279i
$717$	8.79788	−	26.2629i	0.328563	−	0.980806i
$718$	4.98184	+	8.62880i	0.185921	+	0.322024i
$719$	−24.1515	+	41.8316i	−0.900698	+	1.56005i	−0.0741070	+	0.997250i	$0.523611\pi$
$719$	−24.1515	+	41.8316i	−0.900698	+	1.56005i	−0.826591	+	0.562804i	$0.809723\pi$
$720$	−0.603869	+	4.88924i	−0.0225049	+	0.182211i
$721$	−36.2948	+	26.2541i	−1.35169	+	0.977755i
$722$	−15.8722	−	9.16381i	−0.590701	−	0.341042i
$723$	−21.9317	−	24.8071i	−0.815649	−	0.922587i
$724$	−4.19201	−	2.42026i	−0.155795	−	0.0899483i
$725$	−8.98455	+	5.18723i	−0.333678	+	0.192649i
$726$	−10.2996	+	30.7459i	−0.382255	+	1.14109i
$727$			26.7232i			0.991107i	0.868577	+	0.495554i	$0.165035\pi$
$727$			26.7232i			0.991107i	−0.868577	+	0.495554i	$0.834965\pi$
$728$	−9.52649	+	0.495967i	−0.353075	+	0.0183818i
$729$	−9.72994	+	25.1859i	−0.360368	+	0.932810i
$730$	−1.09461	−	1.89592i	−0.0405133	−	0.0701711i
$731$	2.54077	+	4.40073i	0.0939736	+	0.162767i
$732$	−0.151871	+	0.0308420i	−0.00561331	+	0.00113995i
$733$		−	24.6343i		−	0.909889i	−0.890520	−	0.454944i	$-0.849659\pi$
$733$		−	24.6343i		−	0.909889i	0.890520	−	0.454944i	$-0.150341\pi$
$734$	16.3331	−	28.2897i	0.602866	−	1.04419i
$735$	−11.9152	+	15.9508i	−0.439498	+	0.588353i
$736$	9.23441			0.340385
$737$	6.48883	+	3.74633i	0.239019	+	0.137998i
$738$	−6.03068	−	14.2357i	−0.221992	−	0.524022i
$739$	14.0369	+	24.3126i	0.516356	+	0.894354i	0.999820	+	0.0189899i	$0.00604503\pi$
$739$	14.0369	+	24.3126i	0.516356	+	0.894354i	−0.483464	+	0.875364i	$0.660622\pi$
$740$	8.88255			0.326529
$741$	−0.763922	−	5.06355i	−0.0280634	−	0.186014i
$742$	−1.12811	+	2.51960i	−0.0414141	+	0.0924975i
$743$	−33.7678	+	19.4958i	−1.23882	+	0.715233i	−0.968853	−	0.247636i	$-0.920346\pi$
$743$	−33.7678	+	19.4958i	−1.23882	+	0.715233i	−0.269967	+	0.962869i	$0.587013\pi$
$744$	−12.8592	−	4.30774i	−0.471442	−	0.157930i
$745$	−21.0976	−	12.1807i	−0.772956	−	0.446266i
$746$			22.2501i			0.814634i
$747$	6.02745	+	4.54877i	0.220533	+	0.166431i
$748$	−9.46107	−	5.46235i	−0.345931	−	0.199723i
$749$	8.58480	+	3.84369i	0.313682	+	0.140445i
$750$	−20.3572	+	4.13415i	−0.743340	+	0.150958i
$751$	8.82433	+	15.2842i	0.322005	+	0.557728i	0.980902	−	0.194505i	$-0.0623100\pi$
$751$	8.82433	+	15.2842i	0.322005	+	0.557728i	−0.658897	+	0.752233i	$0.728977\pi$
$752$	4.44027	+	7.69078i	0.161920	+	0.280454i
$753$	−15.5142	+	13.7159i	−0.565369	+	0.499836i
$754$	14.4564	−	7.39766i	0.526472	−	0.269407i
$755$	35.9377			1.30791
$756$	8.89537	+	10.4820i	0.323521	+	0.381227i
$757$	−9.91031	−	17.1652i	−0.360196	−	0.623879i	0.627797	−	0.778378i	$-0.283957\pi$
$757$	−9.91031	−	17.1652i	−0.360196	−	0.623879i	−0.987993	+	0.154499i	$0.950624\pi$
$758$	−12.4012	−	7.15982i	−0.450431	−	0.260056i
$759$	−65.3270	+	57.7548i	−2.37122	+	2.09637i
$760$	−0.673266	+	1.16613i	−0.0244219	+	0.0423000i
$761$	7.57620	−	13.1224i	0.274637	−	0.475685i	−0.695407	−	0.718617i	$-0.744776\pi$
$761$	7.57620	−	13.1224i	0.274637	−	0.475685i	0.970043	+	0.242931i	$0.0781090\pi$
$762$	−20.1837	−	22.8299i	−0.731177	−	0.827040i
$763$	14.8302	+	20.5019i	0.536890	+	0.742218i
$764$	12.7889	−	7.38366i	0.462685	−	0.267131i
$765$	9.09006	−	3.85084i	0.328652	−	0.139227i
$766$		−	9.24174i		−	0.333918i
$767$	20.2284	−	10.3513i	0.730404	−	0.373764i
$768$	1.29764	−	1.14723i	0.0468245	−	0.0413970i
$769$	−8.59424	+	4.96189i	−0.309916	+	0.178930i	−0.646889	−	0.762584i	$-0.723930\pi$
$769$	−8.59424	+	4.96189i	−0.309916	+	0.178930i	0.336973	+	0.941514i	$0.390597\pi$
$770$	−23.5610	+	2.42666i	−0.849081	+	0.0874507i
$771$	−1.71813	−	8.46034i	−0.0618769	−	0.304692i
$772$	11.6789			0.420333
$773$	−9.40902	+	16.2969i	−0.338419	+	0.586159i	−0.984136	−	0.177418i	$-0.943225\pi$
$773$	−9.40902	+	16.2969i	−0.338419	+	0.586159i	0.645717	+	0.763577i	$0.276559\pi$
$774$	4.58258	−	6.07226i	0.164717	−	0.218263i
$775$		−	18.0352i		−	0.647843i
$776$	−9.46172	+	16.3882i	−0.339656	+	0.588301i
$777$	16.7911	−	18.2346i	0.602377	−	0.654162i
$778$	−2.36457	−	4.09556i	−0.0847741	−	0.146833i
$779$		−	4.22579i		−	0.151405i
$780$	10.1403	−	1.52984i	0.363083	−	0.0547772i
$781$	43.9987			1.57440
$782$	−9.25251	−	16.0258i	−0.330869	−	0.573082i
$783$	−21.1126	−	10.0980i	−0.754504	−	0.360873i
$784$	6.85305	−	1.42679i	0.244752	−	0.0509568i
$785$			0.124685i			0.00445019i
$786$	1.92841	−	0.391623i	0.0687842	−	0.0139687i
$787$	4.22052	+	2.43672i	0.150445	+	0.0868596i	0.573333	−	0.819323i	$-0.305650\pi$
$787$	4.22052	+	2.43672i	0.150445	+	0.0868596i	−0.422888	+	0.906182i	$0.638984\pi$
$788$		−	11.3285i		−	0.403561i
$789$	−48.3315	+	9.81518i	−1.72065	+	0.349430i
$790$	−9.42924	+	5.44397i	−0.335477	+	0.193688i
$791$	0.0527154	+	0.511827i	0.00187435	+	0.0181985i
$792$	−2.00477	+	16.2317i	−0.0712365	+	0.576767i
$793$	0.146957	+	0.287181i	0.00521859	+	0.0101981i
$794$	−20.2098			−0.717218
$795$	0.942682	−	2.81404i	0.0334335	−	0.0998037i
$796$	−19.2194	+	11.0963i	−0.681214	+	0.393299i
$797$	−21.6580	+	37.5127i	−0.767165	+	1.32877i	0.171929	+	0.985109i	$0.445000\pi$
$797$	−21.6580	+	37.5127i	−0.767165	+	1.32877i	−0.939094	+	0.343660i	$0.888333\pi$
$798$	1.12119	+	3.58651i	0.0396897	+	0.126961i
$799$	8.89795	−	15.4117i	0.314787	−	0.545227i
$800$	1.99481	+	1.15171i	0.0705273	+	0.0407189i
$801$	−2.03528	+	16.4786i	−0.0719129	+	0.582244i
$802$	0.869384	−	1.50582i	0.0306990	−	0.0531723i
$803$	−3.63397	−	6.29422i	−0.128240	−	0.222118i
$804$	2.25721	+	0.756148i	0.0796056	+	0.0266673i
$805$	−36.6177	−	16.3949i	−1.29060	−	0.577845i
$806$	−1.42836	+	28.1945i	−0.0503119	+	0.993109i
$807$	11.0638	−	9.78138i	0.389464	−	0.344321i
$808$	1.81218	−	1.04627i	0.0637524	−	0.0368075i
$809$	−1.09649	+	0.633061i	−0.0385507	+	0.0222572i	−0.519151	−	0.854682i	$-0.673752\pi$
$809$	−1.09649	+	0.633061i	−0.0385507	+	0.0222572i	0.480601	+	0.876939i	$0.340419\pi$
$810$	−10.6166	−	10.2817i	−0.373028	−	0.361260i
$811$			32.1785i			1.12994i	0.825112	+	0.564969i	$0.191112\pi$
$811$			32.1785i			1.12994i	−0.825112	+	0.564969i	$0.808888\pi$
$812$	−9.65513	+	6.98412i	−0.338829	+	0.245095i
$813$	47.3292	−	9.61163i	1.65991	−	0.337095i
$814$	29.4890			1.03359
$815$	−12.1976	+	21.1268i	−0.427263	+	0.740041i
$816$	−3.29113	−	1.10251i	−0.115213	−	0.0385954i
$817$	1.80075	−	1.03967i	0.0630004	−	0.0363733i
$818$	20.2483			0.707966
$819$	16.0282	−	23.7086i	0.560071	−	0.828445i
$820$	8.46265			0.295528
$821$	17.6248	−	10.1757i	0.615109	−	0.355133i	−0.159853	−	0.987141i	$-0.551102\pi$
$821$	17.6248	−	10.1757i	0.615109	−	0.355133i	0.774962	+	0.632007i	$0.217769\pi$
$822$	34.1515	+	11.4405i	1.19117	+	0.399034i
$823$	−4.90216	+	8.49079i	−0.170879	+	0.295970i	−0.938727	−	0.344661i	$-0.887994\pi$
$823$	−4.90216	+	8.49079i	−0.170879	+	0.295970i	0.767849	+	0.640631i	$0.221327\pi$
$824$	−16.9309			−0.589816
$825$	−21.3150	+	4.32866i	−0.742094	+	0.150705i
$826$	−13.5101	+	9.77265i	−0.470076	+	0.340034i
$827$			27.5072i			0.956518i	0.878219	+	0.478259i	$0.158732\pi$
$827$			27.5072i			0.956518i	−0.878219	+	0.478259i	$0.841268\pi$
$828$	−16.6880	+	22.1129i	−0.579949	+	0.768475i
$829$	−28.4015	+	16.3976i	−0.986425	+	0.569513i	−0.904204	−	0.427102i	$-0.859535\pi$
$829$	−28.4015	+	16.3976i	−0.986425	+	0.569513i	−0.0822210	+	0.996614i	$0.526201\pi$
$830$	−3.57961	+	2.06669i	−0.124250	+	0.0717359i
$831$	8.09026	−	7.15251i	0.280648	−	0.248118i
$832$	−3.02729	−	1.95845i	−0.104952	−	0.0678971i
$833$	−9.34259	−	10.4635i	−0.323702	−	0.362539i
$834$	−0.162943	−	0.0545847i	−0.00564226	−	0.00189011i
$835$	−5.12331	−	8.87382i	−0.177299	−	0.307091i
$836$	−2.23516	+	3.87141i	−0.0773047	+	0.133896i
$837$	33.5540	−	23.0081i	1.15980	−	0.795277i
$838$	28.4817	+	16.4439i	0.983884	+	0.568045i
$839$	−20.3368	+	35.2245i	−0.702106	+	1.21608i	0.265620	+	0.964078i	$0.414423\pi$
$839$	−20.3368	+	35.2245i	−0.702106	+	1.21608i	−0.967726	+	0.252005i	$0.918910\pi$
$840$	−7.18240	+	2.24532i	−0.247816	+	0.0774708i
$841$	−4.35717	+	7.54684i	−0.150247	+	0.260236i
$842$	−13.4502	+	7.76548i	−0.463525	+	0.267616i
$843$	−14.8192	+	44.2373i	−0.510400	+	1.52361i
$844$	17.9572			0.618112
$845$	−8.75078	−	19.4717i	−0.301036	−	0.669847i
$846$	−26.4407	−	3.26569i	−0.909051	−	0.112277i
$847$	−49.2696	+	5.07450i	−1.69292	+	0.174362i
$848$	−0.903625	+	0.521708i	−0.0310306	+	0.0179155i
$849$	1.00956	−	0.205021i	0.0346479	−	0.00703631i
$850$		−	4.61585i		−	0.158322i
$851$	43.2584	+	24.9752i	1.48288	+	0.856140i
$852$	13.6992	−	2.78204i	0.469327	−	0.0953111i
$853$		−	22.2614i		−	0.762217i	−0.924530	−	0.381108i	$-0.875542\pi$
$853$		−	22.2614i		−	0.762217i	0.924530	−	0.381108i	$-0.124458\pi$
$854$	−0.138742	−	0.191802i	−0.00474764	−	0.00656333i
$855$	−1.57574	−	3.71960i	−0.0538892	−	0.127208i
$856$	1.77757	+	3.07883i	0.0607559	+	0.105232i
$857$	−10.1508			−0.346743			−0.173372	−	0.984856i	$-0.555466\pi$
$857$	−10.1508			−0.346743			−0.173372	+	0.984856i	$0.555466\pi$
$858$	33.6647	−	5.07889i	1.14929	−	0.173391i
$859$			41.7571i			1.42473i	0.701808	+	0.712366i	$0.252376\pi$
$859$			41.7571i			1.42473i	−0.701808	+	0.712366i	$0.747624\pi$
$860$	2.08205	+	3.60622i	0.0709974	+	0.122971i
$861$	15.9973	−	17.3726i	0.545187	−	0.592056i
$862$	4.07093	−	7.05106i	0.138656	−	0.240160i
$863$		−	36.7875i		−	1.25226i	−0.779718	−	0.626131i	$-0.784638\pi$
$863$		−	36.7875i		−	1.25226i	0.779718	−	0.626131i	$-0.215362\pi$
$864$	0.402133	+	5.18057i	0.0136809	+	0.176247i
$865$	12.5145	−	21.6757i	0.425504	−	0.736995i
$866$	−11.7032			−0.397691
$867$	−4.47581	−	22.0396i	−0.152006	−	0.748504i
$868$	−2.12237	−	20.6066i	−0.0720380	−	0.699435i
$869$	−31.3039	+	18.0733i	−1.06191	+	0.613095i
$870$	9.59745	−	8.48500i	0.325384	−	0.287668i
$871$	0.250724	−	4.94904i	0.00849545	−	0.167692i
$872$			9.56379i			0.323871i
$873$	−22.1446	−	52.2732i	−0.749480	−	1.76918i
$874$	−6.55767	+	3.78607i	−0.221816	+	0.128066i
$875$	−18.5973	−	25.7097i	−0.628704	−	0.869146i
$876$	−1.52944	−	1.72996i	−0.0516749	−	0.0584499i
$877$	−21.5811	+	37.3796i	−0.728743	+	1.26222i	0.228672	+	0.973504i	$0.426562\pi$
$877$	−21.5811	+	37.3796i	−0.728743	+	1.26222i	−0.957415	+	0.288716i	$0.906772\pi$
$878$	3.92180	−	6.79275i	0.132354	−	0.229244i
$879$	7.13976	−	6.31218i	0.240818	−	0.212905i
$880$	−7.75296	−	4.47617i	−0.261352	−	0.150892i
$881$	−5.89735	−	10.2145i	−0.198687	−	0.344136i	0.749416	−	0.662099i	$-0.230334\pi$
$881$	−5.89735	−	10.2145i	−0.198687	−	0.344136i	−0.948103	+	0.317964i	$0.897001\pi$
$882$	−8.96792	+	18.9888i	−0.301966	+	0.639388i
$883$	40.3326			1.35730			0.678649	−	0.734462i	$-0.262566\pi$
$883$	40.3326			1.35730			0.678649	+	0.734462i	$0.262566\pi$
$884$	−0.365569	+	7.21598i	−0.0122954	+	0.242700i
$885$	13.4294	−	11.8728i	0.451424	−	0.399099i
$886$	−11.7261	−	20.3102i	−0.393946	−	0.682334i
$887$	19.5819	+	33.9169i	0.657497	+	1.13882i	0.981262	+	0.192681i	$0.0617181\pi$
$887$	19.5819	+	33.9169i	0.657497	+	1.13882i	−0.323765	+	0.946138i	$0.604949\pi$
$888$	9.18153	−	1.86459i	0.308112	−	0.0625715i
$889$	19.0214	−	42.4839i	0.637958	−	1.42487i
$890$	−7.87092	−	4.54428i	−0.263834	−	0.152325i
$891$	−35.2457	−	34.1338i	−1.18077	−	1.14353i
$892$			15.9739i			0.534846i
$893$	−6.30638	−	3.64099i	−0.211035	−	0.121841i
$894$	−24.3647	−	8.16198i	−0.814876	−	0.272977i
$895$	23.6799	−	13.6716i	0.791531	−	0.456991i
$896$	2.41476	+	1.08117i	0.0806716	+	0.0361192i
$897$	53.6854	+	21.0614i	1.79250	+	0.703219i
$898$	−16.5159			−0.551141
$899$	17.6325	+	30.5404i	0.588077	+	1.01858i
$900$	−6.36283	+	2.69550i	−0.212094	+	0.0898499i
$901$	1.81079	+	1.04546i	0.0603262	+	0.0348293i
$902$	28.0949			0.935459
$903$	11.3388	+	2.54285i	0.377333	+	0.0846209i
$904$	−0.0972380	+	0.168421i	−0.00323409	+	0.00560160i
$905$			7.94876i			0.264226i
$906$	37.1474	−	7.54390i	1.23414	−	0.250629i
$907$	−24.7300	−	42.8337i	−0.821147	−	1.42227i	−0.904829	−	0.425776i	$-0.860001\pi$
$907$	−24.7300	−	42.8337i	−0.821147	−	1.42227i	0.0836816	−	0.996493i	$-0.473332\pi$
$908$	−9.91906	−	17.1803i	−0.329175	−	0.570149i
$909$	−0.769498	+	6.23025i	−0.0255226	+	0.206644i
$910$	8.52719	+	13.1406i	0.282674	+	0.435608i
$911$		−	17.4206i		−	0.577169i	−0.957454	−	0.288585i	$-0.906815\pi$
$911$		−	17.4206i		−	0.577169i	0.957454	−	0.288585i	$-0.0931847\pi$
$912$	−0.451139	+	1.34671i	−0.0149387	+	0.0445941i
$913$	−11.8839	+	6.86116i	−0.393299	+	0.227071i
$914$	6.04568	+	3.49048i	0.199973	+	0.115455i
$915$	0.168557	+	0.190656i	0.00557232	+	0.00630290i
$916$	22.3930	+	12.9286i	0.739886	+	0.427173i
$917$	1.76170	+	2.43545i	0.0581766	+	0.0804256i
$918$	8.58767	−	5.88860i	0.283435	−	0.194353i
$919$	10.4031	−	18.0186i	0.343165	−	0.594380i	−0.641853	−	0.766827i	$-0.721834\pi$
$919$	10.4031	−	18.0186i	0.343165	−	0.594380i	0.985019	+	0.172448i	$0.0551675\pi$
$920$	−7.58205	−	13.1325i	−0.249973	−	0.432966i
$921$	−5.65299	+	16.8750i	−0.186272	+	0.556049i
$922$		−	20.8728i		−	0.687409i
$923$	−13.2559	−	25.9046i	−0.436325	−	0.852660i
$924$	−23.8447	+	7.45417i	−0.784433	+	0.245224i
$925$	6.22977	+	10.7903i	0.204833	+	0.354782i
$926$	−0.565726	+	0.326622i	−0.0185909	+	0.0107335i
$927$	30.5968	−	40.5430i	1.00493	−	1.33161i
$928$	−4.50396			−0.147850
$929$	−15.2776	+	26.4615i	−0.501240	+	0.868174i	0.498759	+	0.866741i	$0.333789\pi$
$929$	−15.2776	+	26.4615i	−0.501240	+	0.868174i	−0.999999	+	0.00143280i	$0.999544\pi$
$930$	4.43210	+	21.8244i	0.145334	+	0.715649i
$931$	−4.28160	+	3.82293i	−0.140324	+	0.125292i
$932$	9.59921	+	5.54210i	0.314432	+	0.181538i
$933$	−7.79074	−	2.60984i	−0.255057	−	0.0854423i
$934$	13.5609	−	7.82936i	0.443725	−	0.256185i
$935$			17.9398i			0.586693i
$936$	10.1605	−	3.70996i	0.332107	−	0.121264i
$937$			1.74410i			0.0569772i	0.999594	+	0.0284886i	$0.00906944\pi$
$937$			1.74410i			0.0569772i	−0.999594	+	0.0284886i	$0.990931\pi$
$938$	0.372545	+	3.61713i	0.0121640	+	0.118103i
$939$	6.66606	−	19.8991i	0.217539	−	0.649384i
$940$	7.29150	−	12.6293i	0.237823	−	0.411921i
$941$	12.9915			0.423512			0.211756	−	0.977323i	$-0.432082\pi$
$941$	12.9915			0.423512			0.211756	+	0.977323i	$0.432082\pi$
$942$	0.0261733	+	0.128882i	0.000852773	+	0.00419919i
$943$	41.2134	+	23.7946i	1.34209	+	0.774858i
$944$	−6.30224			−0.205120
$945$	7.60306	−	21.2567i	0.247327	−	0.691482i
$946$	6.91216	+	11.9722i	0.224734	+	0.389250i
$947$	−45.4118	+	26.2185i	−1.47569	+	0.851988i	−0.999624	−	0.0274231i	$-0.991270\pi$
$947$	−45.4118	+	26.2185i	−1.47569	+	0.851988i	−0.476063	+	0.879411i	$0.657937\pi$
$948$	−8.60384	+	7.60656i	−0.279440	+	0.247050i
$949$	−2.61093	+	4.03585i	−0.0847543	+	0.131009i
$950$	−1.88878			−0.0612801
$951$	−15.9350	+	47.5683i	−0.516728	+	1.54251i
$952$	−0.543191	−	5.27397i	−0.0176049	−	0.170930i
$953$	38.6381	+	22.3077i	1.25161	+	0.722618i	0.971429	−	0.237329i	$-0.0762721\pi$
$953$	38.6381	+	22.3077i	1.25161	+	0.722618i	0.280181	+	0.959947i	$0.409605\pi$
$954$	0.383701	−	3.10664i	0.0124228	−	0.100581i
$955$	−21.0010	−	12.1249i	−0.679576	−	0.392353i
$956$	13.8487	+	7.99553i	0.447898	+	0.258594i
$957$	31.8624	−	28.1691i	1.02996	−	0.910579i
$958$	−9.76157	−	5.63585i	−0.315382	−	0.182086i
$959$	5.63660	+	54.7271i	0.182015	+	1.76723i
$960$	−2.69695	−	0.903458i	−0.0870436	−	0.0291590i
$961$	−30.3054			−0.977594
$962$	−8.88445	−	17.3619i	−0.286446	−	0.559769i
$963$	−10.5850	−	1.30735i	−0.341096	−	0.0421287i
$964$	16.5559	−	9.55856i	0.533230	−	0.307861i
$965$	−9.58914	−	16.6089i	−0.308685	−	0.534659i
$966$	−41.2918	−	9.26012i	−1.32854	−	0.297939i
$967$	−31.6290			−1.01712			−0.508559	−	0.861027i	$-0.669822\pi$
$967$	−31.6290			−1.01712			−0.508559	+	0.861027i	$0.669822\pi$
$968$	−16.2126	−	9.36034i	−0.521092	−	0.300853i
$969$	2.78917	−	0.566425i	0.0896010	−	0.0181962i
$970$	31.0747			0.997749
$971$	−10.8750	+	18.8361i	−0.348996	+	0.604478i	−0.986071	−	0.166323i	$-0.946811\pi$
$971$	−10.8750	+	18.8361i	−0.348996	+	0.604478i	0.637076	+	0.770801i	$0.280144\pi$
$972$	−13.1322	−	8.39914i	−0.421215	−	0.269403i
$973$	−0.0268932	−	0.261113i	−0.000862157	−	0.00837089i
$974$			12.2222i			0.391624i
$975$	8.97033	+	11.2452i	0.287280	+	0.360136i
$976$		−	0.0894724i		−	0.00286394i
$977$	−35.9958	+	20.7822i	−1.15161	+	0.664881i	−0.949278	−	0.314437i	$-0.898184\pi$
$977$	−35.9958	+	20.7822i	−1.15161	+	0.664881i	−0.202329	+	0.979318i	$0.564851\pi$
$978$	−8.17329	+	24.3984i	−0.261353	+	0.780175i
$979$	−26.1305	−	15.0865i	−0.835134	−	0.482165i
$980$	−7.65587	−	8.57441i	−0.244558	−	0.273900i
$981$	−22.9016	−	17.2833i	−0.731192	−	0.551812i
$982$	6.20019	−	10.7390i	0.197856	−	0.342697i
$983$	−40.2905			−1.28507			−0.642533	−	0.766258i	$-0.722116\pi$
$983$	−40.2905			−1.28507			−0.642533	+	0.766258i	$0.722116\pi$
$984$	8.74749	−	1.77644i	0.278860	−	0.0566309i
$985$	−16.1106	+	9.30144i	−0.513325	+	0.296369i
$986$	4.51279	+	7.81637i	0.143716	+	0.248924i
$987$	−12.1426	−	38.8420i	−0.386502	−	1.23636i
$988$	2.95274	+	0.149589i	0.0939391	+	0.00475905i
$989$			23.4166i			0.744604i
$990$	24.7295	−	10.4762i	0.785956	−	0.332956i
$991$	−1.18400	−	2.05076i	−0.0376111	−	0.0651444i	0.846607	−	0.532218i	$-0.178641\pi$
$991$	−1.18400	−	2.05076i	−0.0376111	−	0.0651444i	−0.884218	+	0.467074i	$0.845308\pi$
$992$	3.91489	−	6.78079i	0.124298	−	0.215290i
$993$	−16.9026	+	14.9434i	−0.536388	+	0.474214i
$994$	12.5149	+	17.3011i	0.396949	+	0.548758i
$995$	31.5607	+	18.2216i	1.00054	+	0.577664i
$996$	−3.26627	+	2.88767i	−0.103496	+	0.0914994i
$997$	20.6745	+	11.9364i	0.654769	+	0.378031i	0.790281	−	0.612745i	$-0.209935\pi$
$997$	20.6745	+	11.9364i	0.654769	+	0.378031i	−0.135512	+	0.990776i	$0.543268\pi$
$998$	3.57558	−	2.06436i	0.113183	−	0.0653462i
$999$	−12.1275	+	25.3558i	−0.383697	+	0.802223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bq.c.419.18	yes	64
3.2	odd	2	inner	546.2.bq.c.419.7	✓	64
7.6	odd	2	inner	546.2.bq.c.419.31	yes	64
13.9	even	3	inner	546.2.bq.c.503.10	yes	64
21.20	even	2	inner	546.2.bq.c.419.10	yes	64
39.35	odd	6	inner	546.2.bq.c.503.31	yes	64
91.48	odd	6	inner	546.2.bq.c.503.7	yes	64
273.230	even	6	inner	546.2.bq.c.503.18	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bq.c.419.7	✓	64	3.2	odd	2	inner
546.2.bq.c.419.10	yes	64	21.20	even	2	inner
546.2.bq.c.419.18	yes	64	1.1	even	1	trivial
546.2.bq.c.419.31	yes	64	7.6	odd	2	inner
546.2.bq.c.503.7	yes	64	91.48	odd	6	inner
546.2.bq.c.503.10	yes	64	13.9	even	3	inner
546.2.bq.c.503.18	yes	64	273.230	even	6	inner
546.2.bq.c.503.31	yes	64	39.35	odd	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.64235 - 0.550175i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.64213 q^{5} +(-1.69740 + 0.344709i) q^{6} +(-1.55066 - 2.14370i) q^{7} -1.00000i q^{8} +(2.39462 + 1.80716i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.64235 - 0.550175i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.64213 q^{5} +(-1.69740 + 0.344709i) q^{6} +(-1.55066 - 2.14370i) q^{7} -1.00000i q^{8} +(2.39462 + 1.80716i) q^{9} +(-1.42213 + 0.821065i) q^{10} +(-4.72128 + 2.72583i) q^{11} +(-1.29764 + 1.14723i) q^{12} +(3.02729 + 1.95845i) q^{13} +(-2.41476 - 1.08117i) q^{14} +(2.69695 + 0.903458i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00196 + 1.73544i) q^{17} +(2.97738 + 0.367735i) q^{18} +(0.710134 + 0.409996i) q^{19} +(-0.821065 + 1.42213i) q^{20} +(1.36732 + 4.37384i) q^{21} +(-2.72583 + 4.72128i) q^{22} +(-7.99723 + 4.61721i) q^{23} +(-0.550175 + 1.64235i) q^{24} -2.30341 q^{25} +(3.60093 + 0.182427i) q^{26} +(-2.93854 - 4.28544i) q^{27} +(-2.63183 + 0.271064i) q^{28} +(3.90054 - 2.25198i) q^{29} +(2.78735 - 0.566057i) q^{30} +7.82978i q^{31} +(-0.866025 - 0.500000i) q^{32} +(9.25367 - 1.87924i) q^{33} +2.00392i q^{34} +(2.54639 + 3.52023i) q^{35} +(2.76235 - 1.17022i) q^{36} +(-2.70458 - 4.68447i) q^{37} +0.819992 q^{38} +(-3.89437 - 4.88200i) q^{39} +1.64213i q^{40} +(-2.57673 - 4.46303i) q^{41} +(3.37105 + 3.10419i) q^{42} +(1.26790 - 2.19606i) q^{43} +5.45167i q^{44} +(-3.93227 - 2.96758i) q^{45} +(-4.61721 + 7.99723i) q^{46} -8.88055 q^{47} +(0.344709 + 1.69740i) q^{48} +(-2.19089 + 6.64831i) q^{49} +(-1.99481 + 1.15171i) q^{50} +(2.60036 - 2.29895i) q^{51} +(3.20971 - 1.64248i) q^{52} -1.04342i q^{53} +(-4.68757 - 2.24203i) q^{54} +(7.75296 - 4.47617i) q^{55} +(-2.14370 + 1.55066i) q^{56} +(-0.940718 - 1.06405i) q^{57} +(2.25198 - 3.90054i) q^{58} +(3.15112 - 5.45790i) q^{59} +(2.13089 - 1.88390i) q^{60} +(0.0774854 + 0.0447362i) q^{61} +(3.91489 + 6.78079i) q^{62} +(0.160757 - 7.93563i) q^{63} -1.00000 q^{64} +(-4.97120 - 3.21603i) q^{65} +(7.07430 - 6.25431i) q^{66} +(-0.687189 - 1.19025i) q^{67} +(1.00196 + 1.73544i) q^{68} +(15.6745 - 3.18318i) q^{69} +(3.96535 + 1.77541i) q^{70} +(-6.98942 - 4.03534i) q^{71} +(1.80716 - 2.39462i) q^{72} +1.33316i q^{73} +(-4.68447 - 2.70458i) q^{74} +(3.78300 + 1.26728i) q^{75} +(0.710134 - 0.409996i) q^{76} +(13.1645 + 5.89416i) q^{77} +(-5.81362 - 2.28075i) q^{78} +6.63038 q^{79} +(0.821065 + 1.42213i) q^{80} +(2.46837 + 8.65489i) q^{81} +(-4.46303 - 2.57673i) q^{82} +2.51709 q^{83} +(4.47151 + 1.00278i) q^{84} +(1.64535 - 2.84983i) q^{85} -2.53580i q^{86} +(-7.64503 + 1.55256i) q^{87} +(2.72583 + 4.72128i) q^{88} +(2.76731 + 4.79312i) q^{89} +(-4.88924 - 0.603869i) q^{90} +(-0.495967 - 9.52649i) q^{91} +9.23441i q^{92} +(4.30774 - 12.8592i) q^{93} +(-7.69078 + 4.44027i) q^{94} +(-1.16613 - 0.673266i) q^{95} +(1.14723 + 1.29764i) q^{96} +(-16.3882 - 9.46172i) q^{97} +(1.42679 + 6.85305i) q^{98} +(-16.2317 - 2.00477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

Introduction

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