LMFDB - Embedded newform 980.2.x.l.667.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(67,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("980.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.18
Character	$\chi$	$=$	980.667
Dual form			980.2.x.l.263.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41268 + 0.0657371i) q^{2} +(0.835136 - 3.11677i) q^{3} +(1.99136 + 0.185732i) q^{4} +(-1.91459 - 1.15514i) q^{5} +(1.38467 - 4.34811i) q^{6} +(2.80095 + 0.393286i) q^{8} +(-6.41872 - 3.70585i) q^{9} +O(q^{10})$	\(q+(1.41268 + 0.0657371i) q^{2} +(0.835136 - 3.11677i) q^{3} +(1.99136 + 0.185732i) q^{4} +(-1.91459 - 1.15514i) q^{5} +(1.38467 - 4.34811i) q^{6} +(2.80095 + 0.393286i) q^{8} +(-6.41872 - 3.70585i) q^{9} +(-2.62878 - 1.75770i) q^{10} +(-1.21832 + 0.703395i) q^{11} +(2.24194 - 6.05149i) q^{12} +(0.699298 - 0.699298i) q^{13} +(-5.19924 + 5.00264i) q^{15} +(3.93101 + 0.739716i) q^{16} +(1.19641 - 4.46506i) q^{17} +(-8.82402 - 5.65715i) q^{18} +(-1.40337 + 2.43071i) q^{19} +(-3.59809 - 2.65589i) q^{20} +(-1.76734 + 0.913587i) q^{22} +(-2.03016 + 0.543980i) q^{23} +(3.56496 - 8.40147i) q^{24} +(2.33132 + 4.42323i) q^{25} +(1.03386 - 0.941917i) q^{26} +(-10.0659 + 10.0659i) q^{27} -4.85706i q^{29} +(-7.67375 + 6.72537i) q^{30} +(3.18470 - 1.83869i) q^{31} +(5.50465 + 1.30340i) q^{32} +(1.17486 + 4.38464i) q^{33} +(1.98367 - 6.22907i) q^{34} +(-12.0937 - 8.57184i) q^{36} +(7.99714 - 2.14283i) q^{37} +(-2.14231 + 3.34157i) q^{38} +(-1.59554 - 2.76356i) q^{39} +(-4.90838 - 3.98846i) q^{40} -3.53368 q^{41} +(2.49869 + 2.49869i) q^{43} +(-2.55675 + 1.17443i) q^{44} +(8.00846 + 14.5097i) q^{45} +(-2.90374 + 0.635016i) q^{46} +(0.684106 + 2.55312i) q^{47} +(5.58845 - 11.6343i) q^{48} +(3.00265 + 6.40188i) q^{50} +(-12.9174 - 7.45786i) q^{51} +(1.52243 - 1.26267i) q^{52} +(0.951495 + 0.254952i) q^{53} +(-14.8816 + 13.5582i) q^{54} +(3.14510 + 0.0606082i) q^{55} +(6.40395 + 6.40395i) q^{57} +(0.319289 - 6.86149i) q^{58} +(3.53286 + 6.11910i) q^{59} +(-11.2827 + 8.99638i) q^{60} +(1.09916 - 1.90379i) q^{61} +(4.61985 - 2.38814i) q^{62} +(7.69065 + 2.20315i) q^{64} +(-2.14665 + 0.531084i) q^{65} +(1.37148 + 6.27135i) q^{66} +(3.08671 + 0.827081i) q^{67} +(3.21178 - 8.66931i) q^{68} +6.78184i q^{69} -12.1891i q^{71} +(-16.5211 - 12.9043i) q^{72} +(6.40469 + 1.71613i) q^{73} +(11.4383 - 2.50143i) q^{74} +(15.7332 - 3.57218i) q^{75} +(-3.24607 + 4.57976i) q^{76} +(-2.07233 - 4.00892i) q^{78} +(-0.299644 + 0.518999i) q^{79} +(-6.67180 - 5.95711i) q^{80} +(11.8491 + 20.5233i) q^{81} +(-4.99198 - 0.232294i) q^{82} +(4.53764 + 4.53764i) q^{83} +(-7.44839 + 7.16674i) q^{85} +(3.36560 + 3.69412i) q^{86} +(-15.1383 - 4.05630i) q^{87} +(-3.68908 + 1.49103i) q^{88} +(-0.401553 - 0.231837i) q^{89} +(10.3596 + 21.0241i) q^{90} +(-4.14381 + 0.706194i) q^{92} +(-3.07111 - 11.4615i) q^{93} +(0.798592 + 3.65172i) q^{94} +(5.49468 - 3.03273i) q^{95} +(8.65952 - 16.0682i) q^{96} +(-8.00558 - 8.00558i) q^{97} +10.4267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 16 q^{6}+O(q^{10}) $ 72 * q + 16 * q^6	$ 72 q + 16 q^{6} - 16 q^{10} - 16 q^{12} + 8 q^{13} + 8 q^{16} - 20 q^{17} - 28 q^{18} - 40 q^{20} + 8 q^{22} + 20 q^{25} - 32 q^{26} + 4 q^{30} - 20 q^{37} - 36 q^{40} + 20 q^{45} - 16 q^{46} + 48 q^{48} + 80 q^{50} + 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} - 64 q^{61} - 80 q^{62} - 4 q^{65} + 32 q^{66} + 80 q^{68} - 80 q^{72} + 52 q^{73} - 16 q^{76} - 152 q^{78} - 20 q^{80} + 36 q^{81} + 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} + 32 q^{90} - 112 q^{92} - 32 q^{93} + 120 q^{96} - 40 q^{97}+O(q^{100}) $ 72 * q + 16 * q^6 - 16 * q^10 - 16 * q^12 + 8 * q^13 + 8 * q^16 - 20 * q^17 - 28 * q^18 - 40 * q^20 + 8 * q^22 + 20 * q^25 - 32 * q^26 + 4 * q^30 - 20 * q^37 - 36 * q^40 + 20 * q^45 - 16 * q^46 + 48 * q^48 + 80 * q^50 + 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 - 64 * q^61 - 80 * q^62 - 4 * q^65 + 32 * q^66 + 80 * q^68 - 80 * q^72 + 52 * q^73 - 16 * q^76 - 152 * q^78 - 20 * q^80 + 36 * q^81 + 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 + 32 * q^90 - 112 * q^92 - 32 * q^93 + 120 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.41268	+	0.0657371i	0.998919	+	0.0464831i
$2$	1.41268	+	0.0657371i	0.998919	+	0.0464831i
$3$	0.835136	−	3.11677i	0.482166	−	1.79947i	−0.110331	−	0.993895i	$-0.535191\pi$
$3$	0.835136	−	3.11677i	0.482166	−	1.79947i	0.592497	−	0.805573i	$-0.298142\pi$
$4$	1.99136	+	0.185732i	0.995679	+	0.0928658i
$5$	−1.91459	−	1.15514i	−0.856231	−	0.516593i
$5$	−1.91459	−	1.15514i	−0.856231	−	0.516593i
$6$	1.38467	−	4.34811i	0.565290	−	1.77511i
$7$		0			0
$7$		0			0
$8$	2.80095	+	0.393286i	0.990286	+	0.139048i
$9$	−6.41872	−	3.70585i	−2.13957	−	1.23528i
$10$	−2.62878	−	1.75770i	−0.831293	−	0.555835i
$11$	−1.21832	+	0.703395i	−0.367336	+	0.212082i	−0.672294	−	0.740284i	$-0.734691\pi$
$11$	−1.21832	+	0.703395i	−0.367336	+	0.212082i	0.304958	+	0.952366i	$0.401358\pi$
$12$	2.24194	−	6.05149i	0.647191	−	1.74691i
$13$	0.699298	−	0.699298i	0.193950	−	0.193950i	−0.603450	−	0.797401i	$-0.706208\pi$
$13$	0.699298	−	0.699298i	0.193950	−	0.193950i	0.797401	+	0.603450i	$0.206208\pi$
$14$		0			0
$15$	−5.19924	+	5.00264i	−1.34244	+	1.29168i
$16$	3.93101	+	0.739716i	0.982752	+	0.184929i
$17$	1.19641	−	4.46506i	0.290172	−	1.08294i	−0.654805	−	0.755798i	$-0.727249\pi$
$17$	1.19641	−	4.46506i	0.290172	−	1.08294i	0.944977	−	0.327138i	$-0.106084\pi$
$18$	−8.82402	−	5.65715i	−2.07984	−	1.33340i
$19$	−1.40337	+	2.43071i	−0.321955	+	0.557643i	−0.980891	−	0.194556i	$-0.937673\pi$
$19$	−1.40337	+	2.43071i	−0.321955	+	0.557643i	0.658936	+	0.752199i	$0.271007\pi$
$20$	−3.59809	−	2.65589i	−0.804557	−	0.593875i
$21$		0			0
$22$	−1.76734	+	0.913587i	−0.376797	+	0.194777i
$23$	−2.03016	+	0.543980i	−0.423318	+	0.113428i	−0.464188	−	0.885737i	$-0.653654\pi$
$23$	−2.03016	+	0.543980i	−0.423318	+	0.113428i	0.0408699	+	0.999164i	$0.486987\pi$
$24$	3.56496	−	8.40147i	0.727694	−	1.71494i
$25$	2.33132	+	4.42323i	0.466263	+	0.884646i
$26$	1.03386	−	0.941917i	0.202756	−	0.184725i
$27$	−10.0659	+	10.0659i	−1.93718	+	1.93718i
$28$		0			0
$29$		−	4.85706i		−	0.901933i	−0.892541	−	0.450967i	$-0.851079\pi$
$29$		−	4.85706i		−	0.901933i	0.892541	−	0.450967i	$-0.148921\pi$
$30$	−7.67375	+	6.72537i	−1.40103	+	1.22788i
$31$	3.18470	−	1.83869i	0.571990	−	0.330238i	−0.185954	−	0.982558i	$-0.559538\pi$
$31$	3.18470	−	1.83869i	0.571990	−	0.330238i	0.757944	+	0.652320i	$0.226204\pi$
$32$	5.50465	+	1.30340i	0.973094	+	0.230410i
$33$	1.17486	+	4.38464i	0.204517	+	0.763268i
$34$	1.98367	−	6.22907i	0.340196	−	1.06828i
$35$		0			0
$36$	−12.0937	−	8.57184i	−2.01561	−	1.42864i
$37$	7.99714	−	2.14283i	1.31472	−	0.352279i	0.467724	−	0.883875i	$-0.345074\pi$
$37$	7.99714	−	2.14283i	1.31472	−	0.352279i	0.846998	+	0.531596i	$0.178408\pi$
$38$	−2.14231	+	3.34157i	−0.347528	+	0.542074i
$39$	−1.59554	−	2.76356i	−0.255491	−	0.442523i
$40$	−4.90838	−	3.98846i	−0.776082	−	0.630632i
$41$	−3.53368			−0.551868			−0.275934	−	0.961177i	$-0.588987\pi$
$41$	−3.53368			−0.551868			−0.275934	+	0.961177i	$0.588987\pi$
$42$		0			0
$43$	2.49869	+	2.49869i	0.381046	+	0.381046i	0.871479	−	0.490433i	$-0.163161\pi$
$43$	2.49869	+	2.49869i	0.381046	+	0.381046i	−0.490433	+	0.871479i	$0.663161\pi$
$44$	−2.55675	+	1.17443i	−0.385444	+	0.177052i
$45$	8.00846	+	14.5097i	1.19383	+	2.16298i
$46$	−2.90374	+	0.635016i	−0.428133	+	0.0936280i
$47$	0.684106	+	2.55312i	0.0997872	+	0.372411i	0.997702	−	0.0677590i	$-0.0215849\pi$
$47$	0.684106	+	2.55312i	0.0997872	+	0.372411i	−0.897915	+	0.440170i	$0.854918\pi$
$48$	5.58845	−	11.6343i	0.806623	−	1.67926i
$49$		0			0
$50$	3.00265	+	6.40188i	0.424638	+	0.905363i
$51$	−12.9174	−	7.45786i	−1.80880	−	1.04431i
$52$	1.52243	−	1.26267i	0.211123	−	0.175101i
$53$	0.951495	+	0.254952i	0.130698	+	0.0350204i	0.323575	−	0.946203i	$-0.395115\pi$
$53$	0.951495	+	0.254952i	0.130698	+	0.0350204i	−0.192877	+	0.981223i	$0.561782\pi$
$54$	−14.8816	+	13.5582i	−2.02513	+	1.84504i
$55$	3.14510	+	0.0606082i	0.424085	+	0.00817240i
$56$		0			0
$57$	6.40395	+	6.40395i	0.848224	+	0.848224i
$58$	0.319289	−	6.86149i	0.0419247	−	0.900958i
$59$	3.53286	+	6.11910i	0.459940	+	0.796639i	0.998957	−	0.0456557i	$-0.0145377\pi$
$59$	3.53286	+	6.11910i	0.459940	+	0.796639i	−0.539018	+	0.842294i	$0.681204\pi$
$60$	−11.2827	+	8.99638i	−1.45659	+	1.16143i
$61$	1.09916	−	1.90379i	0.140732	−	0.243756i	−0.787040	−	0.616902i	$-0.788388\pi$
$61$	1.09916	−	1.90379i	0.140732	−	0.243756i	0.927773	+	0.373146i	$0.121721\pi$
$62$	4.61985	−	2.38814i	0.586722	−	0.303294i
$63$		0			0
$64$	7.69065	+	2.20315i	0.961331	+	0.275394i
$65$	−2.14665	+	0.531084i	−0.266260	+	0.0658729i
$66$	1.37148	+	6.27135i	0.168817	+	0.771950i
$67$	3.08671	+	0.827081i	0.377101	+	0.101044i	0.442391	−	0.896822i	$-0.354130\pi$
$67$	3.08671	+	0.827081i	0.377101	+	0.101044i	−0.0652895	+	0.997866i	$0.520797\pi$
$68$	3.21178	−	8.66931i	0.389485	−	1.05131i
$69$			6.78184i			0.816438i
$70$		0			0
$71$		−	12.1891i		−	1.44658i	−0.690546	−	0.723289i	$-0.742630\pi$
$71$		−	12.1891i		−	1.44658i	0.690546	−	0.723289i	$-0.257370\pi$
$72$	−16.5211	−	12.9043i	−1.94703	−	1.52079i
$73$	6.40469	+	1.71613i	0.749612	+	0.200858i	0.613346	−	0.789814i	$-0.289823\pi$
$73$	6.40469	+	1.71613i	0.749612	+	0.200858i	0.136266	+	0.990672i	$0.456490\pi$
$74$	11.4383	−	2.50143i	1.32968	−	0.290785i
$75$	15.7332	−	3.57218i	1.81671	−	0.412480i
$76$	−3.24607	+	4.57976i	−0.372350	+	0.525334i
$77$		0			0
$78$	−2.07233	−	4.00892i	−0.234645	−	0.453921i
$79$	−0.299644	+	0.518999i	−0.0337126	+	0.0583919i	−0.882389	−	0.470520i	$-0.844066\pi$
$79$	−0.299644	+	0.518999i	−0.0337126	+	0.0583919i	0.848677	+	0.528912i	$0.177400\pi$
$80$	−6.67180	−	5.95711i	−0.745930	−	0.666025i
$81$	11.8491	+	20.5233i	1.31657	+	2.28036i
$82$	−4.99198	−	0.232294i	−0.551271	−	0.0256526i
$83$	4.53764	+	4.53764i	0.498071	+	0.498071i	0.910837	−	0.412766i	$-0.135437\pi$
$83$	4.53764	+	4.53764i	0.498071	+	0.498071i	−0.412766	+	0.910837i	$0.635437\pi$
$84$		0			0
$85$	−7.44839	+	7.16674i	−0.807891	+	0.777342i
$86$	3.36560	+	3.69412i	0.362922	+	0.398347i
$87$	−15.1383	−	4.05630i	−1.62300	−	0.434882i
$88$	−3.68908	+	1.49103i	−0.393257	+	0.158944i
$89$	−0.401553	−	0.231837i	−0.0425645	−	0.0245746i	0.478567	−	0.878051i	$-0.341156\pi$
$89$	−0.401553	−	0.231837i	−0.0425645	−	0.0245746i	−0.521131	+	0.853477i	$0.674490\pi$
$90$	10.3596	+	21.0241i	1.09200	+	2.21613i
$91$		0			0
$92$	−4.14381	+	0.706194i	−0.432022	+	0.0736258i
$93$	−3.07111	−	11.4615i	−0.318459	−	1.18851i
$94$	0.798592	+	3.65172i	0.0823685	+	0.376647i
$95$	5.49468	−	3.03273i	0.563742	−	0.311151i
$96$	8.65952	−	16.0682i	0.883809	−	1.63995i
$97$	−8.00558	−	8.00558i	−0.812843	−	0.812843i	0.172216	−	0.985059i	$-0.444907\pi$
$97$	−8.00558	−	8.00558i	−0.812843	−	0.812843i	−0.985059	+	0.172216i	$0.944907\pi$
$98$		0			0
$99$	10.4267			1.04792
$100$	3.82095	+	9.24123i	0.382095	+	0.924123i
$101$	−3.01549	−	5.22299i	−0.300053	−	0.519707i	0.676095	−	0.736815i	$-0.263671\pi$
$101$	−3.01549	−	5.22299i	−0.300053	−	0.519707i	−0.976148	+	0.217108i	$0.930338\pi$
$102$	−17.7579	−	11.3848i	−1.75830	−	1.12726i
$103$	−13.5932	+	3.64227i	−1.33937	+	0.358884i	−0.856202	−	0.516642i	$-0.827182\pi$
$103$	−13.5932	+	3.64227i	−1.33937	+	0.358884i	−0.483171	+	0.875526i	$0.660515\pi$
$104$	2.23372	−	1.68367i	0.219035	−	0.165098i
$105$		0			0
$106$	1.32740	+	0.422716i	0.128929	+	0.0410578i
$107$	5.19174	+	19.3758i	0.501905	+	1.87313i	0.487290	+	0.873240i	$0.337985\pi$
$107$	5.19174	+	19.3758i	0.501905	+	1.87313i	0.0146144	+	0.999893i	$0.495348\pi$
$108$	−21.9143	+	18.1752i	−2.10871	+	1.74891i
$109$	−0.879139	+	0.507571i	−0.0842062	+	0.0486165i	−0.541512	−	0.840693i	$-0.682148\pi$
$109$	−0.879139	+	0.507571i	−0.0842062	+	0.0486165i	0.457306	+	0.889310i	$0.348815\pi$
$110$	4.43904	+	0.292370i	0.423246	+	0.0278764i
$111$		−	26.7148i		−	2.53566i
$112$		0			0
$113$	7.39345	−	7.39345i	0.695518	−	0.695518i	−0.267923	−	0.963440i	$-0.586337\pi$
$113$	7.39345	−	7.39345i	0.695518	−	0.695518i	0.963440	+	0.267923i	$0.0863372\pi$
$114$	8.62579	+	9.46774i	0.807879	+	0.886735i
$115$	4.51530	+	1.30362i	0.421054	+	0.121563i
$116$	0.902109	−	9.67214i	0.0837588	−	0.898036i
$117$	−7.08009	+	1.89711i	−0.654555	+	0.175387i
$118$	4.58857	+	8.87660i	0.422412	+	0.817157i
$119$		0			0
$120$	−16.5303	+	11.9674i	−1.50900	+	1.09247i
$121$	−4.51047	+	7.81236i	−0.410043	+	0.710215i
$122$	1.67791	−	2.61721i	0.151911	−	0.236951i
$123$	−2.95110	+	11.0137i	−0.266092	+	0.993069i
$124$	6.68339	−	3.06999i	0.600186	−	0.275693i
$125$	0.645919	−	11.1617i	0.0577727	−	0.998330i
$126$		0			0
$127$	8.87092	−	8.87092i	0.787167	−	0.787167i	−0.193862	−	0.981029i	$-0.562101\pi$
$127$	8.87092	−	8.87092i	0.787167	−	0.787167i	0.981029	+	0.193862i	$0.0621014\pi$
$128$	10.7196	+	3.61792i	0.947491	+	0.319782i
$129$	9.87458	−	5.70109i	0.869408	−	0.501953i
$130$	−3.06746	+	0.609140i	−0.269034	+	0.0534251i
$131$	−11.3871	−	6.57436i	−0.994898	−	0.574404i	−0.0881630	−	0.996106i	$-0.528100\pi$
$131$	−11.3871	−	6.57436i	−0.994898	−	0.574404i	−0.906735	+	0.421702i	$0.861433\pi$
$132$	1.52520	+	8.94960i	0.132752	+	0.778962i
$133$		0			0
$134$	4.30618	+	1.37132i	0.371997	+	0.118464i
$135$	30.8996	−	7.64458i	2.65941	−	0.657941i
$136$	5.10713	−	12.0359i	0.437933	−	1.03207i
$137$	1.80890	−	6.75090i	0.154545	−	0.576769i	−0.844599	−	0.535399i	$-0.820161\pi$
$137$	1.80890	−	6.75090i	0.154545	−	0.576769i	0.999144	−	0.0413695i	$-0.0131721\pi$
$138$	−0.445819	+	9.58061i	−0.0379506	+	0.815556i
$139$	21.2377			1.80136			0.900679	−	0.434485i	$-0.143069\pi$
$139$	21.2377			1.80136			0.900679	+	0.434485i	$0.143069\pi$
$140$		0			0
$141$	8.52881			0.718255
$142$	0.801275	−	17.2193i	0.0672415	−	1.44501i
$143$	−0.360083	+	1.34385i	−0.0301117	+	0.112378i
$144$	−22.4908	−	19.3158i	−1.87423	−	1.60965i
$145$	−5.61057	+	9.29928i	−0.465932	+	0.772263i
$146$	8.93499	+	2.84538i	0.739465	+	0.235485i
$147$		0			0
$148$	16.3232	−	2.78181i	1.34176	−	0.228664i
$149$	5.75434	+	3.32227i	0.471414	+	0.272171i	0.716831	−	0.697247i	$-0.245592\pi$
$149$	5.75434	+	3.32227i	0.471414	+	0.272171i	−0.245418	+	0.969417i	$0.578925\pi$
$150$	22.4608	−	4.01211i	1.83392	−	0.327588i
$151$	17.6555	−	10.1934i	1.43679	−	0.829529i	0.439161	−	0.898408i	$-0.355276\pi$
$151$	17.6555	−	10.1934i	1.43679	−	0.829529i	0.997625	+	0.0688796i	$0.0219424\pi$
$152$	−4.88673	+	6.25637i	−0.396367	+	0.507458i
$153$	−24.2263	+	24.2263i	−1.95858	+	1.95858i
$154$		0			0
$155$	−8.22134	−	0.158431i	−0.660354	−	0.0127255i
$156$	−2.66401	−	5.79957i	−0.213292	−	0.464338i
$157$	−4.59905	+	17.1639i	−0.367044	+	1.36983i	0.497584	+	0.867416i	$0.334221\pi$
$157$	−4.59905	+	17.1639i	−0.367044	+	1.36983i	−0.864628	+	0.502412i	$0.832446\pi$
$158$	−0.457420	+	0.713484i	−0.0363904	+	0.0567617i
$159$	1.58925	−	2.75267i	0.126036	−	0.218301i
$160$	−9.03355	−	8.85410i	−0.714164	−	0.699978i
$161$		0			0
$162$	15.3899	+	29.7719i	1.20915	+	2.33910i
$163$	−16.7957	+	4.50039i	−1.31554	+	0.352498i	−0.847305	−	0.531106i	$-0.821776\pi$
$163$	−16.7957	+	4.50039i	−1.31554	+	0.352498i	−0.468235	+	0.883604i	$0.655110\pi$
$164$	−7.03682	−	0.656316i	−0.549483	−	0.0512497i
$165$	2.81548	−	9.75192i	0.219185	−	0.759186i
$166$	6.11196	+	6.70855i	0.474380	+	0.520684i
$167$	6.88960	−	6.88960i	0.533133	−	0.533133i	−0.388370	−	0.921503i	$-0.626962\pi$
$167$	6.88960	−	6.88960i	0.533133	−	0.533133i	0.921503	+	0.388370i	$0.126962\pi$
$168$		0			0
$169$			12.0220i			0.924767i
$170$	−10.9933	+	9.63472i	−0.843151	+	0.738949i
$171$	18.0157	−	10.4014i	1.37769	−	0.795412i
$172$	4.51170	+	5.43987i	0.344014	+	0.414786i
$173$	6.40337	+	23.8977i	0.486839	+	1.81691i	0.571632	+	0.820510i	$0.306311\pi$
$173$	6.40337	+	23.8977i	0.486839	+	1.81691i	−0.0847922	+	0.996399i	$0.527023\pi$
$174$	−21.1190	−	6.72543i	−1.60103	−	0.509854i
$175$		0			0
$176$	−5.30952	+	1.86384i	−0.400220	+	0.140493i
$177$	22.0222	−	5.90084i	1.65529	−	0.443534i
$178$	−0.552027	−	0.353909i	−0.0413762	−	0.0265266i
$179$	−10.2777	−	17.8015i	−0.768192	−	1.33055i	−0.938542	−	0.345164i	$-0.887823\pi$
$179$	−10.2777	−	17.8015i	−0.768192	−	1.33055i	0.170350	−	0.985384i	$-0.445510\pi$
$180$	13.2528	+	30.3814i	0.987806	+	2.26450i
$181$	7.85989			0.584221			0.292110	−	0.956385i	$-0.405643\pi$
$181$	7.85989			0.584221			0.292110	+	0.956385i	$0.405643\pi$
$182$		0			0
$183$	−5.01574	−	5.01574i	−0.370774	−	0.370774i
$184$	−5.90032	+	0.725227i	−0.434978	+	0.0534645i
$185$	−17.7865	−	5.13516i	−1.30769	−	0.377544i
$186$	−3.58506	−	16.3934i	−0.262870	−	1.20203i
$187$	1.68310	+	6.28140i	0.123080	+	0.459342i
$188$	0.888105	+	5.21123i	0.0647717	+	0.380068i
$189$		0			0
$190$	7.96161	−	3.92308i	0.577596	−	0.284610i
$191$	7.51061	+	4.33625i	0.543449	+	0.313760i	0.746475	−	0.665413i	$-0.231745\pi$
$191$	7.51061	+	4.33625i	0.543449	+	0.313760i	−0.203027	+	0.979173i	$0.565078\pi$
$192$	13.2895	−	22.1301i	0.959084	−	1.59710i
$193$	5.12478	+	1.37318i	0.368890	+	0.0988437i	0.438502	−	0.898730i	$-0.355509\pi$
$193$	5.12478	+	1.37318i	0.368890	+	0.0988437i	−0.0696118	+	0.997574i	$0.522176\pi$
$194$	−10.7831	−	11.8356i	−0.774181	−	0.849748i
$195$	−0.137480	+	7.13415i	−0.00984515	+	0.510887i
$196$		0			0
$197$	−12.3437	−	12.3437i	−0.879452	−	0.879452i	0.114026	−	0.993478i	$-0.463625\pi$
$197$	−12.3437	−	12.3437i	−0.879452	−	0.879452i	−0.993478	+	0.114026i	$0.963625\pi$
$198$	14.7297	+	0.685422i	1.04679	+	0.0487108i
$199$	−2.14941	−	3.72289i	−0.152368	−	0.263909i	0.779730	−	0.626116i	$-0.215356\pi$
$199$	−2.14941	−	3.72289i	−0.152368	−	0.263909i	−0.932097	+	0.362208i	$0.882023\pi$
$200$	4.79031	+	13.3061i	0.338726	+	0.940885i
$201$	5.15564	−	8.92983i	0.363651	−	0.629862i
$202$	−3.91660	−	7.57667i	−0.275571	−	0.533092i
$203$		0			0
$204$	−24.3380	−	17.2504i	−1.70400	−	1.20777i
$205$	6.76555	+	4.08188i	0.472527	+	0.285091i
$206$	−19.4423	+	4.25181i	−1.35461	+	0.296238i
$207$	15.0470	+	4.03182i	1.04584	+	0.280231i
$208$	3.26623	−	2.23166i	0.226472	−	0.154738i
$209$		−	3.94849i		−	0.273123i
$210$		0			0
$211$			19.5494i			1.34583i	0.739718	+	0.672917i	$0.234959\pi$
$211$			19.5494i			1.34583i	−0.739718	+	0.672917i	$0.765041\pi$
$212$	1.84741	+	0.684424i	0.126881	+	0.0470064i
$213$	−37.9906	−	10.1795i	−2.60307	−	0.697490i
$214$	6.06058	+	27.7132i	0.414293	+	1.89444i
$215$	−1.89764	−	7.67029i	−0.129418	−	0.523110i
$216$	−32.1528	+	24.2353i	−2.18772	+	1.64900i
$217$		0			0
$218$	−1.27531	+	0.659246i	−0.0863751	+	0.0446498i
$219$	10.6976	−	18.5287i	0.722875	−	1.25206i
$220$	6.25175	+	0.704836i	0.421493	+	0.0475200i
$221$	−2.28576	−	3.95905i	−0.153757	−	0.266315i
$222$	1.75615	−	37.7396i	0.117865	−	2.53292i
$223$	−9.54503	−	9.54503i	−0.639183	−	0.639183i	0.311171	−	0.950354i	$-0.399279\pi$
$223$	−9.54503	−	9.54503i	−0.639183	−	0.639183i	−0.950354	+	0.311171i	$0.899279\pi$
$224$		0			0
$225$	1.42776	−	37.0310i	0.0951838	−	2.46873i
$226$	10.9306	−	9.95860i	0.727096	−	0.662436i
$227$	−17.8221	−	4.77541i	−1.18289	−	0.316955i	−0.386819	−	0.922155i	$-0.626426\pi$
$227$	−17.8221	−	4.77541i	−1.18289	−	0.316955i	−0.796073	+	0.605200i	$0.793093\pi$
$228$	11.5631	+	13.9420i	0.765788	+	0.923330i
$229$	−13.5250	−	7.80865i	−0.893755	−	0.516010i	−0.0185864	−	0.999827i	$-0.505917\pi$
$229$	−13.5250	−	7.80865i	−0.893755	−	0.516010i	−0.875169	+	0.483817i	$0.839250\pi$
$230$	6.29300	+	2.13842i	0.414948	+	0.141003i
$231$		0			0
$232$	1.91021	−	13.6044i	0.125412	−	0.893172i
$233$	0.989436	+	3.69263i	0.0648201	+	0.241912i	0.990733	−	0.135826i	$-0.0433688\pi$
$233$	0.989436	+	3.69263i	0.0648201	+	0.241912i	−0.925913	+	0.377738i	$0.876702\pi$
$234$	−10.1266	+	2.21459i	−0.662000	+	0.144772i
$235$	1.63942	−	5.67842i	0.106944	−	0.370419i
$236$	5.89868	+	12.8415i	0.383972	+	0.835909i
$237$	1.36736	+	1.36736i	0.0888193	+	0.0888193i
$238$		0			0
$239$	−15.4752			−1.00101			−0.500505	−	0.865734i	$-0.666852\pi$
$239$	−15.4752			−1.00101			−0.500505	+	0.865734i	$0.666852\pi$
$240$	−24.1388	+	15.8195i	−1.55815	+	1.02114i
$241$	14.3810	+	24.9086i	0.926361	+	1.60450i	0.789357	+	0.613934i	$0.210414\pi$
$241$	14.3810	+	24.9086i	0.926361	+	1.60450i	0.137004	+	0.990570i	$0.456253\pi$
$242$	−6.88544	+	10.7399i	−0.442613	+	0.690387i
$243$	32.6112	−	8.73814i	2.09201	−	0.560552i
$244$	2.54241	−	3.58699i	0.162761	−	0.229633i
$245$		0			0
$246$	−4.89298	+	15.3648i	−0.311965	+	0.979626i
$247$	0.718415	+	2.68116i	0.0457117	+	0.170598i
$248$	9.64333	−	3.89758i	0.612352	−	0.247497i
$249$	17.9323	−	10.3532i	1.13641	−	0.656109i
$250$	1.64622	−	15.7255i	0.104116	−	0.994565i
$251$			26.0285i			1.64291i	0.570277	+	0.821453i	$0.306836\pi$
$251$			26.0285i			1.64291i	−0.570277	+	0.821453i	$0.693164\pi$
$252$		0			0
$253$	2.09075	−	2.09075i	0.131444	−	0.131444i
$254$	13.1150	−	11.9487i	0.822906	−	0.749726i
$255$	16.1167	+	29.2001i	1.00927	+	1.82858i
$256$	14.9056	+	5.81566i	0.931603	+	0.363479i
$257$	22.2935	−	5.97352i	1.39063	−	0.372618i	0.515659	−	0.856794i	$-0.327547\pi$
$257$	22.2935	−	5.97352i	1.39063	−	0.372618i	0.874971	+	0.484176i	$0.160881\pi$
$258$	14.3244	−	7.40472i	0.891801	−	0.460998i
$259$		0			0
$260$	−4.37339	+	0.658877i	−0.271226	+	0.0408618i
$261$	−17.9995	+	31.1761i	−1.11414	+	1.92975i
$262$	−15.6542	−	10.0361i	−0.967122	−	0.620029i
$263$	−2.93759	+	10.9633i	−0.181140	+	0.676023i	0.814284	+	0.580466i	$0.197130\pi$
$263$	−2.93759	+	10.9633i	−0.181140	+	0.676023i	−0.995424	+	0.0955566i	$0.969537\pi$
$264$	1.56631	+	12.7432i	0.0963997	+	0.784291i
$265$	−1.52722	−	1.58724i	−0.0938163	−	0.0975031i
$266$		0			0
$267$	−1.05793	+	1.05793i	−0.0647444	+	0.0647444i
$268$	5.99312	+	2.22031i	0.366088	+	0.135627i
$269$	23.5713	−	13.6089i	1.43717	−	0.829749i	0.439516	−	0.898235i	$-0.355150\pi$
$269$	23.5713	−	13.6089i	1.43717	−	0.829749i	0.997652	+	0.0684854i	$0.0218167\pi$
$270$	44.1539	−	8.76814i	2.68712	−	0.533612i
$271$	0.134959	+	0.0779185i	0.00819817	+	0.00473321i	0.504093	−	0.863649i	$-0.331827\pi$
$271$	0.134959	+	0.0779185i	0.00819817	+	0.00473321i	−0.495895	+	0.868382i	$0.665160\pi$
$272$	8.00597	−	16.6672i	0.485433	−	1.01060i
$273$		0			0
$274$	2.99919	−	9.41799i	0.181188	−	0.568961i
$275$	−5.95156	−	3.74906i	−0.358893	−	0.226077i
$276$	−1.25960	+	13.5051i	−0.0758192	+	0.812910i
$277$	−5.41783	+	20.2196i	−0.325526	+	1.21488i	0.588256	+	0.808674i	$0.299815\pi$
$277$	−5.41783	+	20.2196i	−0.325526	+	1.21488i	−0.913782	+	0.406204i	$0.866852\pi$
$278$	30.0022	+	1.39610i	1.79941	+	0.0837328i
$279$	−27.2556			−1.63175
$280$		0			0
$281$	−2.56355			−0.152929			−0.0764644	−	0.997072i	$-0.524363\pi$
$281$	−2.56355			−0.152929			−0.0764644	+	0.997072i	$0.524363\pi$
$282$	12.0485	+	0.560659i	0.717479	+	0.0333868i
$283$	−5.32518	+	19.8738i	−0.316549	+	1.18138i	0.605990	+	0.795472i	$0.292777\pi$
$283$	−5.32518	+	19.8738i	−0.316549	+	1.18138i	−0.922539	+	0.385904i	$0.873889\pi$
$284$	2.26390	−	24.2728i	0.134338	−	1.44033i
$285$	−4.86351	−	19.6584i	−0.288089	−	1.16446i
$286$	−0.597025	+	1.87476i	−0.0353028	+	0.110857i
$287$		0			0
$288$	−30.5026	−	28.7656i	−1.79738	−	1.69503i
$289$	−3.78292	−	2.18407i	−0.222525	−	0.128475i
$290$	−8.53727	+	12.7681i	−0.501326	+	0.749771i
$291$	−31.6373	+	18.2658i	−1.85461	+	1.07076i
$292$	12.4353	+	4.60698i	0.727720	+	0.269603i
$293$	−4.71102	+	4.71102i	−0.275221	+	0.275221i	−0.831198	−	0.555977i	$-0.812344\pi$
$293$	−4.71102	+	4.71102i	−0.275221	+	0.275221i	0.555977	+	0.831198i	$0.312344\pi$
$294$		0			0
$295$	0.304410	−	15.7965i	0.0177234	−	0.919708i
$296$	23.2423	−	2.85679i	1.35093	−	0.166047i
$297$	5.18314	−	19.3437i	0.300756	−	1.12244i
$298$	7.91067	+	5.07159i	0.458253	+	0.293790i
$299$	−1.03928	+	1.80009i	−0.0601033	+	0.104102i
$300$	31.9938	−	4.19134i	1.84716	−	0.241987i
$301$		0			0
$302$	25.6118	−	13.2395i	1.47379	−	0.761846i
$303$	−18.7972	+	5.03669i	−1.07987	+	0.289350i
$304$	−7.31469	+	8.51704i	−0.419526	+	0.488486i
$305$	−4.30358	+	2.37531i	−0.246422	+	0.136010i
$306$	−35.8166	+	32.6315i	−2.04750	+	1.86542i
$307$	−16.8508	+	16.8508i	−0.961723	+	0.961723i	−0.999294	−	0.0375706i	$-0.988038\pi$
$307$	−16.8508	+	16.8508i	−0.961723	+	0.961723i	0.0375706	+	0.999294i	$0.488038\pi$
$308$		0			0
$309$			45.4085i			2.58320i
$310$	−11.6038	−	0.764260i	−0.659049	−	0.0434071i
$311$	−15.7287	+	9.08099i	−0.891895	+	0.514936i	−0.874562	−	0.484914i	$-0.838851\pi$
$311$	−15.7287	+	9.08099i	−0.891895	+	0.514936i	−0.0173329	+	0.999850i	$0.505518\pi$
$312$	−3.38216	−	8.36809i	−0.191477	−	0.473750i
$313$	0.405938	+	1.51498i	0.0229450	+	0.0856319i	0.976449	−	0.215749i	$-0.0692192\pi$
$313$	0.405938	+	1.51498i	0.0229450	+	0.0856319i	−0.953504	+	0.301381i	$0.902553\pi$
$314$	−7.62532	+	23.9449i	−0.430322	+	1.35129i
$315$		0			0
$316$	−0.693093	+	0.977859i	−0.0389895	+	0.0550088i
$317$	−28.5334	+	7.64549i	−1.60259	+	0.429414i	−0.945825	−	0.324678i	$-0.894744\pi$
$317$	−28.5334	+	7.64549i	−1.60259	+	0.429414i	−0.656769	+	0.754092i	$0.728077\pi$
$318$	2.42607	−	3.78418i	0.136047	−	0.212206i
$319$	3.41643	+	5.91743i	0.191283	+	0.331313i
$320$	−12.1795	−	13.1019i	−0.680855	−	0.732418i
$321$	64.7258			3.61264
$322$		0			0
$323$	9.17425	+	9.17425i	0.510469	+	0.510469i
$324$	19.7840	+	43.0699i	1.09911	+	2.39277i
$325$	4.72344	+	1.46287i	0.262009	+	0.0811454i
$326$	−24.0229	+	5.25353i	−1.33050	+	0.290966i
$327$	0.847782	+	3.16396i	0.0468824	+	0.174968i
$328$	−9.89766	−	1.38975i	−0.546507	−	0.0767360i
$329$		0			0
$330$	4.61845	−	13.5913i	0.254238	−	0.748177i
$331$	−10.9400	−	6.31623i	−0.601319	−	0.347172i	0.168241	−	0.985746i	$-0.446191\pi$
$331$	−10.9400	−	6.31623i	−0.601319	−	0.347172i	−0.769560	+	0.638574i	$0.779525\pi$
$332$	8.19328	+	9.87885i	0.449665	+	0.542172i
$333$	−59.2724	−	15.8820i	−3.24811	−	0.870328i
$334$	10.1857	−	9.27993i	0.557339	−	0.507775i
$335$	−4.95439	−	5.14909i	−0.270687	−	0.281325i
$336$		0			0
$337$	4.10542	+	4.10542i	0.223636	+	0.223636i	0.810028	−	0.586391i	$-0.199452\pi$
$337$	4.10542	+	4.10542i	0.223636	+	0.223636i	−0.586391	+	0.810028i	$0.699452\pi$
$338$	−0.790289	+	16.9832i	−0.0429861	+	0.923767i
$339$	−16.8692	−	29.2182i	−0.916207	−	1.58692i
$340$	−16.1635	+	12.8881i	−0.876588	+	0.698958i
$341$	−2.58665	+	4.48021i	−0.140075	+	0.242617i
$342$	26.1342	−	13.5095i	1.41318	−	0.730513i
$343$		0			0
$344$	6.01600	+	7.98140i	0.324361	+	0.430328i
$345$	7.83396	−	12.9845i	0.421766	−	0.699060i
$346$	7.47498	+	34.1809i	0.401857	+	1.83757i
$347$	−14.2660	−	3.82255i	−0.765837	−	0.205205i	−0.145305	−	0.989387i	$-0.546416\pi$
$347$	−14.2660	−	3.82255i	−0.765837	−	0.205205i	−0.620531	+	0.784182i	$0.713083\pi$
$348$	−29.3925	−	10.8892i	−1.57560	−	0.583723i
$349$			5.05181i			0.270417i	0.990817	+	0.135209i	$0.0431705\pi$
$349$			5.05181i			0.270417i	−0.990817	+	0.135209i	$0.956830\pi$
$350$		0			0
$351$			14.0781i			0.751434i
$352$	−7.62321	+	2.28399i	−0.406318	+	0.121737i
$353$	10.5040	+	2.81454i	0.559072	+	0.149803i	0.527280	−	0.849692i	$-0.323212\pi$
$353$	10.5040	+	2.81454i	0.559072	+	0.149803i	0.0317919	+	0.999495i	$0.489879\pi$
$354$	31.4984	−	6.88835i	1.67412	−	0.366112i
$355$	−14.0801	+	23.3371i	−0.747292	+	1.23860i
$356$	−0.756576	−	0.536251i	−0.0400984	−	0.0284212i
$357$		0			0
$358$	−13.3489	−	25.8236i	−0.705514	−	1.36482i
$359$	−2.49329	+	4.31850i	−0.131591	+	0.227922i	−0.924290	−	0.381691i	$-0.875342\pi$
$359$	−2.49329	+	4.31850i	−0.131591	+	0.227922i	0.792699	+	0.609613i	$0.208675\pi$
$360$	16.7248	+	43.7906i	0.881477	+	2.30797i
$361$	5.56111	+	9.63212i	0.292690	+	0.506954i
$362$	11.1035	+	0.516686i	0.583589	+	0.0271564i
$363$	20.5825	+	20.5825i	1.08030	+	1.08030i
$364$		0			0
$365$	−10.2800	−	10.6840i	−0.538079	−	0.559225i
$366$	−6.75594	−	7.41538i	−0.353139	−	0.387608i
$367$	15.3917	+	4.12420i	0.803442	+	0.215282i	0.637094	−	0.770786i	$-0.280136\pi$
$367$	15.3917	+	4.12420i	0.803442	+	0.215282i	0.166347	+	0.986067i	$0.446803\pi$
$368$	−8.38297	+	0.636648i	−0.436993	+	0.0331875i
$369$	22.6817	+	13.0953i	1.18076	+	0.681714i
$370$	−24.7892	−	8.42359i	−1.28873	−	0.437922i
$371$		0			0
$372$	−3.98691	−	23.3944i	−0.206712	−	1.21294i
$373$	−0.152497	−	0.569126i	−0.00789599	−	0.0294682i	0.961865	−	0.273523i	$-0.0881890\pi$
$373$	−0.152497	−	0.569126i	−0.00789599	−	0.0294682i	−0.969761	+	0.244055i	$0.921522\pi$
$374$	1.96476	+	8.98428i	0.101596	+	0.464566i
$375$	−34.2489	−	11.3347i	−1.76861	−	0.585321i
$376$	0.912041	+	7.42021i	0.0470349	+	0.382668i
$377$	−3.39653	−	3.39653i	−0.174930	−	0.174930i
$378$		0			0
$379$	−23.7583			−1.22038			−0.610191	−	0.792254i	$-0.708907\pi$
$379$	−23.7583			−1.22038			−0.610191	+	0.792254i	$0.708907\pi$
$380$	11.5051	−	5.01871i	0.590201	−	0.257454i
$381$	−20.2402	−	35.0570i	−1.03694	−	1.79603i
$382$	10.3251	+	6.61948i	0.528277	+	0.338682i
$383$	−4.14964	+	1.11189i	−0.212037	+	0.0568151i	−0.363274	−	0.931682i	$-0.618341\pi$
$383$	−4.14964	+	1.11189i	−0.212037	+	0.0568151i	0.151237	+	0.988498i	$0.451674\pi$
$384$	20.2286	−	30.3892i	1.03229	−	1.55079i
$385$		0			0
$386$	7.14943	+	2.27676i	0.363896	+	0.115884i
$387$	−6.77862	−	25.2982i	−0.344577	−	1.28598i
$388$	−14.4551	−	17.4289i	−0.733845	−	0.884816i
$389$	−21.8152	+	12.5950i	−1.10608	+	0.638593i	−0.937810	−	0.347148i	$-0.887150\pi$
$389$	−21.8152	+	12.5950i	−1.10608	+	0.638593i	−0.168266	+	0.985742i	$0.553817\pi$
$390$	−0.663194	+	10.0693i	−0.0335822	+	0.509877i
$391$			9.71561i			0.491340i
$392$		0			0
$393$	−30.0006	+	30.0006i	−1.51333	+	1.51333i
$394$	−16.6263	−	18.2492i	−0.837622	−	0.919381i
$395$	1.17321	−	0.647540i	0.0590306	−	0.0325813i
$396$	20.7633	+	1.93657i	1.04340	+	0.0973163i
$397$	−3.73802	+	1.00160i	−0.187606	+	0.0502689i	−0.351399	−	0.936226i	$-0.614294\pi$
$397$	−3.73802	+	1.00160i	−0.187606	+	0.0502689i	0.163793	+	0.986495i	$0.447627\pi$
$398$	−2.79171	−	5.40057i	−0.139936	−	0.270706i
$399$		0			0
$400$	5.89249	+	19.1123i	0.294625	+	0.955613i
$401$	2.74364	−	4.75213i	0.137011	−	0.237310i	−0.789353	−	0.613940i	$-0.789584\pi$
$401$	2.74364	−	4.75213i	0.137011	−	0.237310i	0.926364	+	0.376630i	$0.122917\pi$
$402$	7.87032	−	12.2761i	0.392536	−	0.612277i
$403$	0.941265	−	3.51285i	0.0468877	−	0.174987i
$404$	−5.03485	−	10.9609i	−0.250493	−	0.545325i
$405$	1.02098	−	52.9811i	0.0507330	−	2.63265i
$406$		0			0
$407$	−8.23579	+	8.23579i	−0.408233	+	0.408233i
$408$	−33.2479	−	25.9693i	−1.64602	−	1.28567i
$409$	−14.7164	+	8.49650i	−0.727678	+	0.420125i	−0.817572	−	0.575826i	$-0.804680\pi$
$409$	−14.7164	+	8.49650i	−0.727678	+	0.420125i	0.0898942	+	0.995951i	$0.471347\pi$
$410$	9.28926	+	6.21116i	0.458764	+	0.306747i
$411$	−19.5303	−	11.2758i	−0.963360	−	0.556196i
$412$	−27.7453	+	4.72839i	−1.36691	+	0.232951i
$413$		0			0
$414$	20.9916	+	6.68484i	1.03168	+	0.328542i
$415$	−3.44613	−	13.9293i	−0.169164	−	0.683764i
$416$	4.76085	−	2.93792i	0.233420	−	0.144044i
$417$	17.7364	−	66.1930i	0.868554	−	3.24149i
$418$	0.259563	−	5.57798i	0.0126956	−	0.272828i
$419$	3.87556			0.189334			0.0946668	−	0.995509i	$-0.469821\pi$
$419$	3.87556			0.189334			0.0946668	+	0.995509i	$0.469821\pi$
$420$		0			0
$421$	20.7160			1.00964			0.504818	−	0.863226i	$-0.331560\pi$
$421$	20.7160			1.00964			0.504818	+	0.863226i	$0.331560\pi$
$422$	−1.28512	+	27.6171i	−0.0625586	+	1.34438i
$423$	5.07039	−	18.9230i	0.246531	−	0.920066i
$424$	2.56482	+	1.08832i	0.124559	+	0.0528534i
$425$	22.5392	−	5.11747i	1.09331	−	0.248234i
$426$	−52.9995	−	16.8779i	−2.56783	−	0.817735i
$427$		0			0
$428$	6.73991	+	39.5485i	0.325786	+	1.91165i
$429$	3.88775	+	2.24459i	0.187702	+	0.108370i
$430$	−2.17654	−	10.9605i	−0.104962	−	0.528560i
$431$	8.46015	−	4.88447i	0.407511	−	0.235277i	−0.282209	−	0.959353i	$-0.591067\pi$
$431$	8.46015	−	4.88447i	0.407511	−	0.235277i	0.689720	+	0.724076i	$0.257734\pi$
$432$	−47.0150	+	32.1232i	−2.26201	+	1.54553i
$433$	−7.00877	+	7.00877i	−0.336820	+	0.336820i	−0.855169	−	0.518349i	$-0.826547\pi$
$433$	−7.00877	+	7.00877i	−0.336820	+	0.336820i	0.518349	+	0.855169i	$0.326547\pi$
$434$		0			0
$435$	24.2981	+	25.2530i	1.16501	+	1.21079i
$436$	−1.84495	+	0.847472i	−0.0883572	+	0.0405865i
$437$	1.52681	−	5.69814i	0.0730373	−	0.272579i
$438$	16.3303	−	25.4720i	0.780293	−	1.21710i
$439$	2.21290	−	3.83285i	0.105616	−	0.182932i	−0.808374	−	0.588670i	$-0.799652\pi$
$439$	2.21290	−	3.83285i	0.105616	−	0.182932i	0.913990	+	0.405737i	$0.132985\pi$
$440$	8.78542	+	1.40668i	0.418828	+	0.0670610i
$441$		0			0
$442$	−2.96880	−	5.74315i	−0.141211	−	0.273174i
$443$	4.25183	−	1.13928i	0.202011	−	0.0541286i	−0.156395	−	0.987695i	$-0.549987\pi$
$443$	4.25183	−	1.13928i	0.202011	−	0.0541286i	0.358405	+	0.933566i	$0.383321\pi$
$444$	4.96178	−	53.1987i	0.235476	−	2.52470i
$445$	0.501006	+	0.907721i	0.0237500	+	0.0430301i
$446$	−12.8567	−	14.1116i	−0.608781	−	0.668203i
$447$	15.1604	−	15.1604i	0.717062	−	0.717062i
$448$		0			0
$449$		−	21.8355i		−	1.03048i	−0.857046	−	0.515240i	$-0.827703\pi$
$449$		−	21.8355i		−	1.03048i	0.857046	−	0.515240i	$-0.172297\pi$
$450$	4.45128	−	52.2193i	0.209835	−	2.46164i
$451$	4.30514	−	2.48557i	0.202721	−	0.117041i
$452$	16.0962	−	13.3498i	0.757102	−	0.627922i
$453$	−17.0258	−	63.5411i	−0.799941	−	2.98542i
$454$	−24.8631	−	7.91772i	−1.16688	−	0.371597i
$455$		0			0
$456$	15.4186	+	20.4557i	0.722041	+	0.957928i
$457$	21.2792	−	5.70175i	0.995400	−	0.266717i	0.275883	−	0.961191i	$-0.411030\pi$
$457$	21.2792	−	5.70175i	0.995400	−	0.266717i	0.719517	+	0.694475i	$0.244363\pi$
$458$	−18.5932	−	11.9203i	−0.868804	−	0.556997i
$459$	32.9019	+	56.9877i	1.53573	+	2.65996i
$460$	8.74946	+	3.43460i	0.407945	+	0.160139i
$461$	19.7670			0.920641			0.460321	−	0.887753i	$-0.347734\pi$
$461$	19.7670			0.920641			0.460321	+	0.887753i	$0.347734\pi$
$462$		0			0
$463$	−14.5239	−	14.5239i	−0.674983	−	0.674983i	0.283877	−	0.958861i	$-0.408379\pi$
$463$	−14.5239	−	14.5239i	−0.674983	−	0.674983i	−0.958861	+	0.283877i	$0.908379\pi$
$464$	3.59284	−	19.0931i	0.166794	−	0.886377i
$465$	−7.35973	+	25.4917i	−0.341299	+	1.18215i
$466$	1.15502	+	5.28156i	0.0535052	+	0.244663i
$467$	7.29665	+	27.2315i	0.337649	+	1.26012i	0.900969	+	0.433884i	$0.142857\pi$
$467$	7.29665	+	27.2315i	0.337649	+	1.26012i	−0.563320	+	0.826239i	$0.690476\pi$
$468$	−14.4513	+	2.46282i	−0.668014	+	0.113844i
$469$		0			0
$470$	2.68927	−	7.91404i	0.124047	−	0.365048i
$471$	49.6551	+	28.6684i	2.28799	+	1.32097i
$472$	7.48882	+	18.5287i	0.344701	+	0.852853i
$473$	−4.80176	−	1.28663i	−0.220785	−	0.0591592i
$474$	1.84176	+	2.02153i	0.0845947	+	0.0928519i
$475$	−14.0233	−	0.540678i	−0.643432	−	0.0248080i
$476$		0			0
$477$	−5.16257	−	5.16257i	−0.236378	−	0.236378i
$478$	−21.8616	−	1.01730i	−0.999928	−	0.0465301i
$479$	0.709375	+	1.22867i	0.0324122	+	0.0561395i	0.881776	−	0.471668i	$-0.156348\pi$
$479$	0.709375	+	1.22867i	0.0324122	+	0.0561395i	−0.849364	+	0.527807i	$0.823014\pi$
$480$	−35.1404	+	20.7611i	−1.60393	+	0.947610i
$481$	4.09391	−	7.09086i	0.186666	−	0.323315i
$482$	18.6784	+	36.1334i	0.850777	+	1.64583i
$483$		0			0
$484$	−10.4330	+	14.7195i	−0.474225	+	0.669067i
$485$	6.07987	+	24.5749i	0.276072	+	1.11589i
$486$	46.6437	−	10.2005i	2.11580	−	0.462703i
$487$	−32.5132	−	8.71188i	−1.47331	−	0.394773i	−0.569247	−	0.822166i	$-0.692765\pi$
$487$	−32.5132	−	8.71188i	−1.47331	−	0.394773i	−0.904066	+	0.427393i	$0.859432\pi$
$488$	3.82742	−	4.90015i	0.173259	−	0.221819i
$489$			56.1067i			2.53723i
$490$		0			0
$491$			3.16673i			0.142913i	0.997444	+	0.0714563i	$0.0227647\pi$
$491$			3.16673i			0.142913i	−0.997444	+	0.0714563i	$0.977235\pi$
$492$	−7.92228	+	21.3840i	−0.357164	+	0.964066i
$493$	−21.6871	−	5.81103i	−0.976736	−	0.261716i
$494$	0.838642	+	3.83486i	0.0377323	+	0.172539i
$495$	−19.9629	−	12.0443i	−0.897265	−	0.541350i
$496$	13.8792	−	4.87213i	0.623195	−	0.218765i
$497$		0			0
$498$	26.0133	−	13.4470i	1.16568	−	0.602576i
$499$	3.72451	−	6.45105i	0.166732	−	0.288789i	−0.770537	−	0.637395i	$-0.780012\pi$
$499$	3.72451	−	6.45105i	0.166732	−	0.288789i	0.937269	+	0.348607i	$0.113345\pi$
$500$	3.35933	−	22.1069i	0.150234	−	0.988651i
$501$	−15.7195	−	27.2270i	−0.702297	−	1.21641i
$502$	−1.71104	+	36.7701i	−0.0763674	+	1.64113i
$503$	−19.3043	−	19.3043i	−0.860736	−	0.860736i	0.130687	−	0.991424i	$-0.458282\pi$
$503$	−19.3043	−	19.3043i	−0.860736	−	0.860736i	−0.991424	+	0.130687i	$0.958282\pi$
$504$		0			0
$505$	−0.259830	+	13.4832i	−0.0115623	+	0.599994i
$506$	3.09101	−	2.81613i	0.137412	−	0.125192i
$507$	37.4697	+	10.0400i	1.66409	+	0.445891i
$508$	19.3128	−	16.0176i	0.856866	−	0.710664i
$509$	9.85817	+	5.69161i	0.436956	+	0.252276i	0.702305	−	0.711876i	$-0.252154\pi$
$509$	9.85817	+	5.69161i	0.436956	+	0.252276i	−0.265350	+	0.964152i	$0.585487\pi$
$510$	20.8482	+	42.3100i	0.923176	+	1.87352i
$511$		0			0
$512$	20.6747	+	9.19554i	0.913700	+	0.406390i
$513$	−10.3411	−	38.5934i	−0.456570	−	1.70394i
$514$	31.8863	−	6.97319i	1.40645	−	0.307574i
$515$	30.2326	+	8.72849i	1.33221	+	0.384623i
$516$	20.7227	−	9.51889i	0.912266	−	0.419046i
$517$	−2.62931	−	2.62931i	−0.115637	−	0.115637i
$518$		0			0
$519$	79.8313			3.50421
$520$	−6.22154	+	0.643292i	−0.272833	+	0.0282102i
$521$	−0.617798	−	1.07006i	−0.0270662	−	0.0468801i	0.852175	−	0.523257i	$-0.175283\pi$
$521$	−0.617798	−	1.07006i	−0.0270662	−	0.0468801i	−0.879241	+	0.476377i	$0.841950\pi$
$522$	−27.4771	+	42.8588i	−1.20264	+	1.87588i
$523$	−6.09797	+	1.63395i	−0.266646	+	0.0714474i	−0.389665	−	0.920957i	$-0.627409\pi$
$523$	−6.09797	+	1.63395i	−0.266646	+	0.0714474i	0.123019	+	0.992404i	$0.460742\pi$
$524$	−21.4548	−	15.2068i	−0.937256	−	0.664314i
$525$		0			0
$526$	−4.87059	+	15.2945i	−0.212368	+	0.666872i
$527$	−4.39965	−	16.4197i	−0.191652	−	0.715254i
$528$	1.37500	+	18.1051i	0.0598392	+	0.787924i
$529$	−16.0929	+	9.29126i	−0.699693	+	0.403968i
$530$	−2.05314	−	2.34266i	−0.0891826	−	0.101759i
$531$		−	52.3691i		−	2.27262i
$532$		0			0
$533$	−2.47109	+	2.47109i	−0.107035	+	0.107035i
$534$	−1.56407	+	1.42498i	−0.0676840	+	0.0616649i
$535$	12.4417	−	43.0940i	0.537901	−	1.86312i
$536$	8.32044	+	3.53057i	0.359388	+	0.152497i
$537$	−64.0665	+	17.1666i	−2.76467	+	0.740792i
$538$	34.1934	−	17.6756i	1.47418	−	0.762048i
$539$		0			0
$540$	62.9519	−	9.48407i	2.70902	−	0.408129i
$541$	16.1355	−	27.9475i	0.693719	−	1.20156i	−0.276891	−	0.960901i	$-0.589304\pi$
$541$	16.1355	−	27.9475i	0.693719	−	1.20156i	0.970611	−	0.240656i	$-0.0773624\pi$
$542$	0.185532	+	0.118946i	0.00796929	+	0.00510917i
$543$	6.56407	−	24.4975i	0.281691	−	1.05129i
$544$	12.4056	−	23.0192i	0.531884	−	0.986939i
$545$	2.26951	+	0.0437350i	0.0972150	+	0.00187340i
$546$		0			0
$547$	17.6256	−	17.6256i	0.753617	−	0.753617i	−0.221536	−	0.975152i	$-0.571107\pi$
$547$	17.6256	−	17.6256i	0.753617	−	0.753617i	0.975152	+	0.221536i	$0.0711069\pi$
$548$	4.85602	−	13.1075i	0.207439	−	0.559924i
$549$	−14.1104	+	8.14662i	−0.602215	+	0.347689i
$550$	−8.16123	−	5.68747i	−0.347996	−	0.242515i
$551$	11.8061	+	6.81625i	0.502957	+	0.290382i
$552$	−2.66721	+	18.9956i	−0.113524	+	0.808507i
$553$		0			0
$554$	−8.98286	+	28.2078i	−0.381645	+	1.19843i
$555$	−30.8593	+	51.1479i	−1.30990	+	2.17111i
$556$	42.2919	+	3.94451i	1.79357	+	0.167285i
$557$	1.60273	−	5.98149i	0.0679101	−	0.253444i	−0.923622	−	0.383304i	$-0.874786\pi$
$557$	1.60273	−	5.98149i	0.0679101	−	0.253444i	0.991532	+	0.129860i	$0.0414528\pi$
$558$	−38.5036	−	1.79171i	−1.62999	−	0.0758490i
$559$	3.49465			0.147808
$560$		0			0
$561$	20.9833			0.885915
$562$	−3.62149	−	0.168521i	−0.152764	−	0.00710861i
$563$	−1.32949	+	4.96172i	−0.0560313	+	0.209112i	−0.988266	−	0.152742i	$-0.951189\pi$
$563$	−1.32949	+	4.96172i	−0.0560313	+	0.209112i	0.932235	+	0.361854i	$0.117856\pi$
$564$	16.9839	+	1.58407i	0.715151	+	0.0667013i
$565$	−22.6959	+	5.61499i	−0.954823	+	0.236224i
$566$	−8.82925	+	27.7254i	−0.371121	+	1.16539i
$567$		0			0
$568$	4.79380	−	34.1410i	0.201143	−	1.43253i
$569$	−30.0136	−	17.3284i	−1.25824	−	0.726442i	−0.285504	−	0.958378i	$-0.592161\pi$
$569$	−30.0136	−	17.3284i	−1.25824	−	0.726442i	−0.972731	+	0.231935i	$0.925494\pi$
$570$	−5.57832	−	28.0908i	−0.233650	−	1.17660i
$571$	28.9237	−	16.6991i	1.21042	−	0.698836i	0.247569	−	0.968870i	$-0.420368\pi$
$571$	28.9237	−	16.6991i	1.21042	−	0.698836i	0.962851	+	0.270034i	$0.0870350\pi$
$572$	−0.966649	+	2.60920i	−0.0404176	+	0.109096i
$573$	19.7875	−	19.7875i	0.826634	−	0.826634i
$574$		0			0
$575$	−7.13910	−	7.71168i	−0.297721	−	0.321599i
$576$	−41.1996	−	42.6418i	−1.71665	−	1.77674i
$577$	8.91664	−	33.2773i	0.371204	−	1.38535i	−0.487608	−	0.873063i	$-0.662130\pi$
$577$	8.91664	−	33.2773i	0.371204	−	1.38535i	0.858812	−	0.512291i	$-0.171203\pi$
$578$	−5.20050	−	3.33408i	−0.216312	−	0.138679i
$579$	8.55978	−	14.8260i	0.355732	−	0.616146i
$580$	−12.8998	+	17.4761i	−0.535636	+	0.725657i
$581$		0			0
$582$	−45.8942	+	23.7241i	−1.90238	+	0.983394i
$583$	−1.33855	+	0.358664i	−0.0554372	+	0.0148544i
$584$	17.2643	+	7.32567i	0.714401	+	0.303138i
$585$	15.7469	+	4.54630i	0.651054	+	0.187966i
$586$	−6.96487	+	6.34549i	−0.287716	+	0.262130i
$587$	23.3690	−	23.3690i	0.964544	−	0.964544i	−0.0348489	−	0.999393i	$-0.511095\pi$
$587$	23.3690	−	23.3690i	0.964544	−	0.964544i	0.999393	+	0.0348489i	$0.0110950\pi$
$588$		0			0
$589$			10.3214i			0.425288i
$590$	1.46845	−	22.2955i	0.0604552	−	0.917890i
$591$	−48.7811	+	28.1638i	−2.00659	+	1.15850i
$592$	33.0219	−	2.50786i	1.35719	−	0.103072i
$593$	1.67934	+	6.26739i	0.0689623	+	0.257371i	0.991797	−	0.127826i	$-0.0408000\pi$
$593$	1.67934	+	6.26739i	0.0689623	+	0.257371i	−0.922834	+	0.385197i	$0.874133\pi$
$594$	8.59374	−	26.9859i	0.352606	−	1.10724i
$595$		0			0
$596$	10.8419	+	7.68459i	0.444101	+	0.314773i
$597$	−13.3984	+	3.59010i	−0.548362	+	0.146933i
$598$	−1.58651	+	2.47464i	−0.0648773	+	0.101196i
$599$	−8.75860	−	15.1703i	−0.357867	−	0.619843i	0.629737	−	0.776808i	$-0.283162\pi$
$599$	−8.75860	−	15.1703i	−0.357867	−	0.619843i	−0.987604	+	0.156965i	$0.949829\pi$
$600$	45.4727	−	3.81787i	1.85641	−	0.155864i
$601$	−2.55297			−0.104138			−0.0520689	−	0.998643i	$-0.516582\pi$
$601$	−2.55297			−0.104138			−0.0520689	+	0.998643i	$0.516582\pi$
$602$		0			0
$603$	−16.7477	−	16.7477i	−0.682018	−	0.682018i
$604$	37.0517	−	17.0196i	1.50761	−	0.692516i
$605$	17.6601	−	9.74727i	0.717983	−	0.396283i
$606$	−26.8856	+	5.87959i	−1.09215	+	0.238842i
$607$	−5.72830	−	21.3783i	−0.232504	−	0.867718i	−0.979258	−	0.202617i	$-0.935055\pi$
$607$	−5.72830	−	21.3783i	−0.232504	−	0.867718i	0.746754	−	0.665101i	$-0.231611\pi$
$608$	−10.8932	+	11.5510i	−0.441779	+	0.468457i
$609$		0			0
$610$	−6.23574	+	3.07266i	−0.252478	+	0.124408i
$611$	2.26378	+	1.30700i	0.0915829	+	0.0528754i
$612$	−52.7427	+	43.7436i	−2.13200	+	1.76823i
$613$	−7.79104	−	2.08760i	−0.314677	−	0.0843175i	0.0980238	−	0.995184i	$-0.468748\pi$
$613$	−7.79104	−	2.08760i	−0.314677	−	0.0843175i	−0.412701	+	0.910867i	$0.635415\pi$
$614$	−24.9125	+	22.6971i	−1.00539	+	0.915980i
$615$	18.3724	−	17.6777i	0.740849	−	0.712835i
$616$		0			0
$617$	−20.7105	−	20.7105i	−0.833772	−	0.833772i	0.154258	−	0.988031i	$-0.450701\pi$
$617$	−20.7105	−	20.7105i	−0.833772	−	0.833772i	−0.988031	+	0.154258i	$0.950701\pi$
$618$	−2.98502	+	64.1479i	−0.120075	+	2.58041i
$619$	15.2502	+	26.4141i	0.612956	+	1.06167i	0.990739	+	0.135777i	$0.0433530\pi$
$619$	15.2502	+	26.4141i	0.612956	+	1.06167i	−0.377784	+	0.925894i	$0.623314\pi$
$620$	−16.3422	−	1.84246i	−0.656319	−	0.0739948i
$621$	14.9597	−	25.9110i	0.600314	−	1.03977i
$622$	−22.8167	+	11.7946i	−0.914866	+	0.472921i
$623$		0			0
$624$	−4.22784	−	12.0438i	−0.169249	−	0.482138i
$625$	−14.1299	+	20.6239i	−0.565197	+	0.824956i
$626$	0.473872	+	2.16688i	0.0189398	+	0.0866059i
$627$	−12.3065	−	3.29753i	−0.491476	−	0.131691i
$628$	−12.3462	+	33.3253i	−0.492668	+	1.32982i
$629$		−	38.2714i		−	1.52598i
$630$		0			0
$631$		−	24.2931i		−	0.967092i	−0.875319	−	0.483546i	$-0.839349\pi$
$631$		−	24.2931i		−	0.967092i	0.875319	−	0.483546i	$-0.160651\pi$
$632$	−1.04340	+	1.33584i	−0.0415044	+	0.0531370i
$633$	60.9309	+	16.3264i	2.42178	+	0.648915i
$634$	−40.8113	+	8.92497i	−1.62082	+	0.354456i
$635$	−27.2313	+	6.73706i	−1.08064	+	0.267352i
$636$	3.67603	−	5.18637i	0.145764	−	0.205653i
$637$		0			0
$638$	4.43735	+	8.58406i	0.175676	+	0.339846i
$639$	−45.1709	+	78.2383i	−1.78693	+	3.09506i
$640$	−16.3445	−	19.3095i	−0.646074	−	0.763274i
$641$	−11.2086	−	19.4138i	−0.442712	−	0.766800i	0.555178	−	0.831732i	$-0.312650\pi$
$641$	−11.2086	−	19.4138i	−0.442712	−	0.766800i	−0.997890	+	0.0649320i	$0.979317\pi$
$642$	91.4372	+	4.25489i	3.60874	+	0.167927i
$643$	3.56268	+	3.56268i	0.140498	+	0.140498i	0.773858	−	0.633359i	$-0.218325\pi$
$643$	3.56268	+	3.56268i	0.140498	+	0.140498i	−0.633359	+	0.773858i	$0.718325\pi$
$644$		0			0
$645$	−25.4913	−	0.491236i	−1.00372	−	0.0193424i
$646$	12.3572	+	13.5634i	0.486189	+	0.533645i
$647$	−16.0227	−	4.29327i	−0.629918	−	0.168786i	−0.0702854	−	0.997527i	$-0.522391\pi$
$647$	−16.0227	−	4.29327i	−0.629918	−	0.168786i	−0.559632	+	0.828741i	$0.689058\pi$
$648$	25.1173	+	62.1448i	0.986700	+	2.44128i
$649$	−8.60829	−	4.97000i	−0.337905	−	0.195089i
$650$	6.57657	+	2.37708i	0.257954	+	0.0932367i
$651$		0			0
$652$	−34.2821	+	5.84240i	−1.34259	+	0.228806i
$653$	−3.24782	−	12.1210i	−0.127097	−	0.474332i	0.872809	−	0.488062i	$-0.162296\pi$
$653$	−3.24782	−	12.1210i	−0.127097	−	0.474332i	−0.999906	+	0.0137300i	$0.995629\pi$
$654$	0.989659	+	4.52542i	0.0386987	+	0.176958i
$655$	14.2074	+	25.7409i	0.555129	+	1.00578i
$656$	−13.8909	−	2.61392i	−0.542349	−	0.102056i
$657$	−34.7502	−	34.7502i	−1.35573	−	1.35573i
$658$		0			0
$659$	−33.3787			−1.30025			−0.650126	−	0.759827i	$-0.725284\pi$
$659$	−33.3787			−1.30025			−0.650126	+	0.759827i	$0.725284\pi$
$660$	7.41787	−	18.8966i	0.288740	−	0.735550i
$661$	−3.47890	−	6.02563i	−0.135313	−	0.234370i	0.790404	−	0.612586i	$-0.209871\pi$
$661$	−3.47890	−	6.02563i	−0.135313	−	0.234370i	−0.925717	+	0.378217i	$0.876537\pi$
$662$	−15.0396	−	9.64201i	−0.584531	−	0.374748i
$663$	−14.2484	+	3.81784i	−0.553361	+	0.148273i
$664$	10.9251	+	14.4943i	0.423977	+	0.562488i
$665$		0			0
$666$	−82.6892	−	26.3327i	−3.20414	−	1.02037i
$667$	2.64214	+	9.86062i	0.102304	+	0.381805i
$668$	14.9993	−	12.4400i	0.580339	−	0.481320i
$669$	−37.7211	+	21.7783i	−1.45838	+	0.841997i
$670$	−6.66051	−	7.59973i	−0.257318	−	0.293603i
$671$			3.09256i			0.119387i
$672$		0			0
$673$	−5.34897	+	5.34897i	−0.206188	+	0.206188i	−0.802645	−	0.596457i	$-0.796575\pi$
$673$	−5.34897	+	5.34897i	−0.206188	+	0.206188i	0.596457	+	0.802645i	$0.296575\pi$
$674$	5.52979	+	6.06954i	0.212999	+	0.233790i
$675$	−67.9905	−	21.0570i	−2.61696	−	0.810483i
$676$	−2.23286	+	23.9400i	−0.0858792	+	0.920770i
$677$	28.9931	−	7.76868i	1.11430	−	0.298575i	0.345723	−	0.938337i	$-0.387634\pi$
$677$	28.9931	−	7.76868i	1.11430	−	0.298575i	0.768573	+	0.639762i	$0.220967\pi$
$678$	−21.9101	−	42.3851i	−0.841451	−	1.62779i
$679$		0			0
$680$	−23.6811	+	17.1443i	−0.908131	+	0.657456i
$681$	−29.7677	+	51.5592i	−1.14070	+	1.97575i
$682$	−3.94864	+	6.15909i	−0.151201	+	0.235844i
$683$	−4.92938	+	18.3967i	−0.188618	+	0.703930i	0.805210	+	0.592990i	$0.202053\pi$
$683$	−4.92938	+	18.3967i	−0.188618	+	0.703930i	−0.993827	+	0.110940i	$0.964614\pi$
$684$	37.8075	−	17.3667i	1.44561	−	0.664034i
$685$	−11.2615	+	10.8357i	−0.430281	+	0.414010i
$686$		0			0
$687$	−35.6329	+	35.6329i	−1.35948	+	1.35948i
$688$	7.97404	+	11.6707i	0.304008	+	0.444941i
$689$	0.843665	−	0.487090i	0.0321411	−	0.0185567i
$690$	11.9205	−	17.8280i	0.453805	−	0.678699i
$691$	24.4705	+	14.1281i	0.930903	+	0.537457i	0.887097	−	0.461583i	$-0.152718\pi$
$691$	24.4705	+	14.1281i	0.930903	+	0.537457i	0.0438058	+	0.999040i	$0.486052\pi$
$692$	8.31284	+	48.7782i	0.316007	+	1.85427i
$693$		0			0
$694$	−19.9020	−	6.33786i	−0.755470	−	0.240582i
$695$	−40.6615	−	24.5325i	−1.54238	−	0.930569i
$696$	−40.8064	−	17.3152i	−1.54676	−	0.656331i
$697$	−4.22772	+	15.7781i	−0.160136	+	0.597638i
$698$	−0.332091	+	7.13662i	−0.0125698	+	0.270125i
$699$	12.3354			0.466567
$700$		0			0
$701$	−26.0149			−0.982568			−0.491284	−	0.871000i	$-0.663472\pi$
$701$	−26.0149			−0.982568			−0.491284	+	0.871000i	$0.663472\pi$
$702$	−0.925454	+	19.8879i	−0.0349290	+	0.750622i
$703$	−6.01436	+	22.4459i	−0.226836	+	0.846563i
$704$	−10.9193	+	2.72543i	−0.411538	+	0.102719i
$705$	−16.3292	−	9.85194i	−0.614992	−	0.371046i
$706$	14.6538	+	4.66656i	0.551504	+	0.175628i
$707$		0			0
$708$	44.9501	−	7.66046i	1.68933	−	0.287898i
$709$	−15.2471	−	8.80290i	−0.572616	−	0.330600i	0.185578	−	0.982630i	$-0.440584\pi$
$709$	−15.2471	−	8.80290i	−0.572616	−	0.330600i	−0.758193	+	0.652030i	$0.773918\pi$
$710$	−21.4248	+	32.0424i	−0.804058	+	1.20253i
$711$	3.84667	−	2.22087i	0.144261	−	0.0832893i
$712$	−1.03355	−	0.807288i	−0.0387340	−	0.0302544i
$713$	−5.46525	+	5.46525i	−0.204675	+	0.204675i
$714$		0			0
$715$	2.24174	−	2.15697i	0.0838363	−	0.0806663i
$716$	−17.1603	−	37.3581i	−0.641310	−	1.39614i
$717$	−12.9239	+	48.2328i	−0.482653	+	1.80129i
$718$	−3.80611	+	5.93678i	−0.142043	+	0.221558i
$719$	11.5866	−	20.0685i	0.432106	−	0.748429i	−0.564949	−	0.825126i	$-0.691104\pi$
$719$	11.5866	−	20.0685i	0.432106	−	0.748429i	0.997054	+	0.0766969i	$0.0244374\pi$
$720$	20.7483	+	62.9617i	0.773243	+	2.34644i
$721$		0			0
$722$	7.22290	+	13.9727i	0.268809	+	0.520011i
$723$	89.6445	−	24.0202i	3.33391	−	0.893320i
$724$	15.6518	+	1.45983i	0.581696	+	0.0542541i
$725$	21.4839	−	11.3233i	0.797892	−	0.420538i
$726$	27.7235	+	30.4296i	1.02892	+	1.12935i
$727$	−15.3777	+	15.3777i	−0.570326	+	0.570326i	−0.932220	−	0.361893i	$-0.882131\pi$
$727$	−15.3777	+	15.3777i	−0.570326	+	0.570326i	0.361893	+	0.932220i	$0.382131\pi$
$728$		0			0
$729$		−	37.8443i		−	1.40164i
$730$	−13.8201	−	15.7689i	−0.511503	−	0.583632i
$731$	14.1462	−	8.16734i	0.523218	−	0.302080i
$732$	−9.05655	−	10.9197i	−0.334740	−	0.403604i
$733$	10.8115	+	40.3490i	0.399331	+	1.49032i	0.814276	+	0.580478i	$0.197134\pi$
$733$	10.8115	+	40.3490i	0.399331	+	1.49032i	−0.414944	+	0.909847i	$0.636199\pi$
$734$	21.4725	+	6.83800i	0.792566	+	0.252395i
$735$		0			0
$736$	−11.8844	+	0.348310i	−0.438063	+	0.0128389i
$737$	−4.34235	+	1.16353i	−0.159953	+	0.0428592i
$738$	31.1813	+	19.9906i	1.14780	+	0.735862i
$739$	−14.4738	−	25.0693i	−0.532426	−	0.922189i	−0.999283	−	0.0378565i	$-0.987947\pi$
$739$	−14.4738	−	25.0693i	−0.532426	−	0.922189i	0.466857	−	0.884333i	$-0.345386\pi$
$740$	−34.4655	−	13.5294i	−1.26698	−	0.497352i
$741$	8.95654			0.329027
$742$		0			0
$743$	23.4115	+	23.4115i	0.858885	+	0.858885i	0.991207	−	0.132322i	$-0.0422432\pi$
$743$	23.4115	+	23.4115i	0.858885	+	0.858885i	−0.132322	+	0.991207i	$0.542243\pi$
$744$	−4.09437	−	33.3111i	−0.150107	−	1.22124i
$745$	−7.17953	−	13.0078i	−0.263038	−	0.476570i
$746$	−0.178017	−	0.814021i	−0.00651768	−	0.0298034i
$747$	−12.3100	−	45.9417i	−0.450401	−	1.68092i
$748$	2.18499	+	12.8211i	0.0798912	+	0.468786i
$749$		0			0
$750$	−47.6378	−	18.2638i	−1.73949	−	0.666898i
$751$	38.1178	+	22.0073i	1.39094	+	0.803059i	0.993419	−	0.114534i	$-0.0365376\pi$
$751$	38.1178	+	22.0073i	1.39094	+	0.803059i	0.397520	+	0.917593i	$0.369871\pi$
$752$	0.800644	+	10.5424i	0.0291965	+	0.384441i
$753$	81.1249	+	21.7373i	2.95636	+	0.792153i
$754$	−4.57495	−	5.02151i	−0.166610	−	0.182872i
$755$	−45.5779	−	0.878318i	−1.65875	−	0.0319653i
$756$		0			0
$757$	24.7062	+	24.7062i	0.897961	+	0.897961i	0.995256	−	0.0972943i	$-0.0310188\pi$
$757$	24.7062	+	24.7062i	0.897961	+	0.897961i	−0.0972943	+	0.995256i	$0.531019\pi$
$758$	−33.5630	−	1.56180i	−1.21906	−	0.0567272i
$759$	−4.77032	−	8.26243i	−0.173152	−	0.299907i
$760$	16.5831	−	6.33354i	0.601531	−	0.229742i
$761$	−2.24848	+	3.89448i	−0.0815073	+	0.141175i	−0.903898	−	0.427749i	$-0.859307\pi$
$761$	−2.24848	+	3.89448i	−0.0815073	+	0.141175i	0.822390	+	0.568924i	$0.192640\pi$
$762$	−26.2885	−	50.8551i	−0.952331	−	1.84229i
$763$		0			0
$764$	14.1509	+	10.0300i	0.511963	+	0.362872i
$765$	74.3680	−	18.3987i	2.68878	−	0.665207i
$766$	−5.93523	+	1.29797i	−0.214449	+	0.0468975i
$767$	6.74959	+	1.80855i	0.243714	+	0.0653029i
$768$	30.5743	−	41.6006i	1.10325	−	1.50113i
$769$			14.9079i			0.537593i	0.963197	+	0.268797i	$0.0866259\pi$
$769$			14.9079i			0.537593i	−0.963197	+	0.268797i	$0.913374\pi$
$770$		0			0
$771$		−	74.4723i		−	2.68206i
$772$	9.95023	+	3.68633i	0.358116	+	0.132674i
$773$	26.7544	+	7.16881i	0.962287	+	0.257844i	0.705568	−	0.708642i	$-0.250692\pi$
$773$	26.7544	+	7.16881i	0.962287	+	0.257844i	0.256719	+	0.966486i	$0.417358\pi$
$774$	−7.91303	−	36.1839i	−0.284428	−	1.30060i
$775$	15.5575	+	9.80011i	0.558842	+	0.352030i
$776$	−19.2747	−	25.5717i	−0.691923	−	0.917971i
$777$		0			0
$778$	−31.6460	+	16.3587i	−1.13456	+	0.586489i
$779$	4.95906	−	8.58934i	0.177677	−	0.307745i
$780$	−1.59881	+	14.1811i	−0.0572466	+	0.507765i
$781$	8.57374	+	14.8502i	0.306793	+	0.531380i
$782$	−0.638676	+	13.7251i	−0.0228390	+	0.490809i
$783$	48.8906	+	48.8906i	1.74721	+	1.74721i
$784$		0			0
$785$	28.6320	−	27.5493i	1.02192	−	0.983277i
$786$	−44.3535	+	40.4092i	−1.58204	+	1.44135i
$787$	−5.43008	−	1.45499i	−0.193561	−	0.0518646i	0.160736	−	0.986997i	$-0.448613\pi$
$787$	−5.43008	−	1.45499i	−0.193561	−	0.0518646i	−0.354297	+	0.935133i	$0.615280\pi$
$788$	−22.2881	−	26.8733i	−0.793980	−	0.957322i
$789$	31.7166	+	18.3116i	1.12914	+	0.651911i
$790$	1.69994	−	0.837647i	0.0604813	−	0.0298021i
$791$		0			0
$792$	29.2047	+	4.10068i	1.03774	+	0.145711i
$793$	−0.562681	−	2.09996i	−0.0199814	−	0.0745716i
$794$	−5.34649	+	1.16922i	−0.189740	+	0.0414940i
$795$	−6.22248	+	3.43443i	−0.220689	+	0.121807i
$796$	−3.58879	−	7.81282i	−0.127201	−	0.276918i
$797$	10.9874	+	10.9874i	0.389195	+	0.389195i	0.874400	−	0.485205i	$-0.161255\pi$
$797$	10.9874	+	10.9874i	0.389195	+	0.389195i	−0.485205	+	0.874400i	$0.661255\pi$
$798$		0			0
$799$	12.2183			0.432252
$800$	7.06785	+	27.3870i	0.249886	+	0.968275i
$801$	1.71830	+	2.97619i	0.0607133	+	0.105159i
$802$	4.18829	−	6.53290i	0.147894	−	0.230685i
$803$	−9.01005	+	2.41424i	−0.317958	+	0.0851965i
$804$	11.9253	−	16.8249i	0.420572	−	0.593369i
$805$		0			0
$806$	1.56063	−	4.90067i	0.0549710	−	0.172619i
$807$	−22.7306	−	84.8316i	−0.800154	−	2.98621i
$808$	−6.39212	−	15.8153i	−0.224874	−	0.556380i
$809$	14.4297	−	8.33096i	0.507320	−	0.292901i	−0.224412	−	0.974494i	$-0.572046\pi$
$809$	14.4297	−	8.33096i	0.507320	−	0.292901i	0.731731	+	0.681593i	$0.238713\pi$
$810$	4.92515	−	74.7784i	0.173052	−	2.62745i
$811$		−	30.5372i		−	1.07231i	−0.844120	−	0.536154i	$-0.819877\pi$
$811$		−	30.5372i		−	1.07231i	0.844120	−	0.536154i	$-0.180123\pi$
$812$		0			0
$813$	0.355563	−	0.355563i	0.0124701	−	0.0124701i
$814$	−12.1760	+	11.0932i	−0.426768	+	0.388816i
$815$	37.3554	+	10.7849i	1.30850	+	0.377779i
$816$	−45.2617	−	38.8721i	−1.58448	−	1.36080i
$817$	−9.58017	+	2.56700i	−0.335168	+	0.0898079i
$818$	−21.3481	+	11.0355i	−0.746420	+	0.385846i
$819$		0			0
$820$	12.7145	+	9.38507i	0.444009	+	0.327741i
$821$	9.24225	−	16.0080i	0.322557	−	0.558685i	−0.658458	−	0.752617i	$-0.728791\pi$
$821$	9.24225	−	16.0080i	0.322557	−	0.558685i	0.981015	+	0.193933i	$0.0621243\pi$
$822$	−26.8490	−	17.2131i	−0.936465	−	0.600375i
$823$	−11.0750	+	41.3323i	−0.386049	+	1.44075i	0.450457	+	0.892798i	$0.351261\pi$
$823$	−11.0750	+	41.3323i	−0.386049	+	1.44075i	−0.836507	+	0.547957i	$0.815406\pi$
$824$	−39.5062	+	4.85583i	−1.37626	+	0.169161i
$825$	−16.6553	+	15.4187i	−0.579863	+	0.536809i
$826$		0			0
$827$	−22.7990	+	22.7990i	−0.792801	+	0.792801i	−0.981949	−	0.189148i	$-0.939427\pi$
$827$	−22.7990	+	22.7990i	−0.792801	+	0.792801i	0.189148	+	0.981949i	$0.439427\pi$
$828$	29.2150	+	10.8235i	1.01529	+	0.376142i
$829$	−29.0025	+	16.7446i	−1.00730	+	0.581563i	−0.910399	−	0.413731i	$-0.864225\pi$
$829$	−29.0025	+	16.7446i	−1.00730	+	0.581563i	−0.0968981	+	0.995294i	$0.530892\pi$
$830$	−3.95262	−	19.9043i	−0.137197	−	0.690888i
$831$	58.4953	+	33.7723i	2.02918	+	1.17155i
$832$	6.91871	−	3.83740i	0.239863	−	0.133038i
$833$		0			0
$834$	29.4072	−	92.3440i	1.01829	−	3.19761i
$835$	−21.1492	+	5.23233i	−0.731898	+	0.181072i
$836$	0.733360	−	7.86286i	0.0253638	−	0.271943i
$837$	−13.5488	+	50.5649i	−0.468316	+	1.74778i
$838$	5.47495	+	0.254768i	0.189129	+	0.00880082i
$839$	−6.43773			−0.222255			−0.111127	−	0.993806i	$-0.535446\pi$
$839$	−6.43773			−0.222255			−0.111127	+	0.993806i	$0.535446\pi$
$840$		0			0
$841$	5.40897			0.186516
$842$	29.2652	+	1.36181i	1.00854	+	0.0469310i
$843$	−2.14092	+	7.99001i	−0.0737371	+	0.275190i
$844$	−3.63094	+	38.9298i	−0.124982	+	1.34002i
$845$	13.8870	−	23.0171i	0.477728	−	0.791814i
$846$	8.40681	−	26.3989i	0.289032	−	0.907612i
$847$		0			0
$848$	3.55174	+	1.70605i	0.121967	+	0.0585862i
$849$	57.4949	+	33.1947i	1.97322	+	1.13924i
$850$	32.1772	−	5.74772i	1.10367	−	0.197145i
$851$	−15.0698	+	8.70057i	−0.516587	+	0.298252i
$852$	−73.7621	−	27.3271i	−2.52705	−	0.936213i
$853$	−10.0581	+	10.0581i	−0.344383	+	0.344383i	−0.858012	−	0.513629i	$-0.828301\pi$
$853$	−10.0581	+	10.0581i	−0.344383	+	0.344383i	0.513629	+	0.858012i	$0.328301\pi$
$854$		0			0
$855$	−46.5077	−	0.896235i	−1.59053	−	0.0306506i
$856$	6.92156	+	56.3126i	0.236574	+	1.92473i
$857$	0.134823	−	0.503168i	0.00460548	−	0.0171879i	−0.963585	−	0.267403i	$-0.913835\pi$
$857$	0.134823	−	0.503168i	0.00460548	−	0.0171879i	0.968190	+	0.250215i	$0.0805013\pi$
$858$	5.34461	+	3.42647i	0.182462	+	0.116978i
$859$	2.00473	−	3.47230i	0.0684006	−	0.118473i	−0.829797	−	0.558066i	$-0.811544\pi$
$859$	2.00473	−	3.47230i	0.0684006	−	0.118473i	0.898197	+	0.439592i	$0.144877\pi$
$860$	−2.35426	−	15.6267i	−0.0802796	−	0.532868i
$861$		0			0
$862$	12.2726	−	6.34407i	0.418007	−	0.216080i
$863$	14.3236	−	3.83800i	0.487581	−	0.130647i	−0.00664926	−	0.999978i	$-0.502117\pi$
$863$	14.3236	−	3.83800i	0.487581	−	0.130647i	0.494231	+	0.869331i	$0.335450\pi$
$864$	−68.5291	+	42.2893i	−2.33141	+	1.43871i
$865$	15.3453	−	53.1511i	0.521756	−	1.80719i
$866$	−10.3619	+	9.44045i	−0.352113	+	0.320800i
$867$	−9.96649	+	9.96649i	−0.338480	+	0.338480i
$868$		0			0
$869$		−	0.843073i		−	0.0285993i
$870$	32.6655	+	37.2718i	1.10747	+	1.26363i
$871$	2.73690	−	1.58015i	0.0927364	−	0.0535414i
$872$	−2.66205	+	1.07593i	−0.0901483	+	0.0364355i
$873$	21.7181	+	81.0531i	0.735046	+	2.74323i
$874$	2.53148	−	7.94930i	0.0856287	−	0.268889i
$875$		0			0
$876$	24.7440	−	34.9104i	0.836024	−	1.17951i
$877$	29.9552	−	8.02646i	1.01151	−	0.271034i	0.285252	−	0.958453i	$-0.407923\pi$
$877$	29.9552	−	8.02646i	1.01151	−	0.271034i	0.726262	+	0.687418i	$0.241256\pi$
$878$	3.37809	−	5.26914i	0.114005	−	0.177825i
$879$	10.7488	+	18.6175i	0.362548	+	0.627952i
$880$	12.3186	+	2.56473i	0.415259	+	0.0864570i
$881$	−26.6186			−0.896802			−0.448401	−	0.893833i	$-0.648006\pi$
$881$	−26.6186			−0.896802			−0.448401	+	0.893833i	$0.648006\pi$
$882$		0			0
$883$	20.2772	+	20.2772i	0.682383	+	0.682383i	0.960537	−	0.278154i	$-0.0897224\pi$
$883$	20.2772	+	20.2772i	0.682383	+	0.682383i	−0.278154	+	0.960537i	$0.589722\pi$
$884$	−3.81644	−	8.30842i	−0.128361	−	0.279442i
$885$	−48.9799	−	14.1410i	−1.64644	−	0.475345i
$886$	6.08139	−	1.32993i	0.204308	−	0.0446800i
$887$	−11.0601	−	41.2767i	−0.371361	−	1.38594i	−0.858590	−	0.512663i	$-0.828659\pi$
$887$	−11.0601	−	41.2767i	−0.371361	−	1.38594i	0.487229	−	0.873274i	$-0.338008\pi$
$888$	10.5066	−	74.8268i	0.352577	−	2.51102i
$889$		0			0
$890$	0.648093	+	1.31526i	0.0217241	+	0.0440876i
$891$	−28.8720	−	16.6692i	−0.967247	−	0.558440i
$892$	−17.2348	−	20.7804i	−0.577062	−	0.695779i
$893$	−7.16594	−	1.92011i	−0.239799	−	0.0642540i
$894$	22.4135	−	20.4203i	0.749619	−	0.682956i
$895$	−0.885581	+	45.9548i	−0.0296017	+	1.53610i
$896$		0			0
$897$	4.74253	+	4.74253i	0.158348	+	0.158348i
$898$	1.43540	−	30.8467i	0.0479000	−	1.02937i
$899$	−8.93063	−	15.4683i	−0.297853	−	0.515897i
$900$	9.72100	−	73.4768i	0.324033	−	2.44923i
$901$	2.27675	−	3.94345i	0.0758496	−	0.131375i
$902$	6.24520	−	3.22832i	0.207942	−	0.107491i
$903$		0			0
$904$	23.6164	−	17.8010i	0.785471	−	0.592051i
$905$	−15.0485	−	9.07925i	−0.500228	−	0.301804i
$906$	−19.8751	−	90.8828i	−0.660305	−	3.01938i
$907$	−1.18466	−	0.317430i	−0.0393361	−	0.0105401i	0.239097	−	0.970996i	$-0.423148\pi$
$907$	−1.18466	−	0.317430i	−0.0393361	−	0.0105401i	−0.278433	+	0.960456i	$0.589815\pi$
$908$	−34.6032	−	12.8197i	−1.14835	−	0.425436i
$909$			44.6999i			1.48260i
$910$		0			0
$911$			13.4236i			0.444743i	0.974962	+	0.222372i	$0.0713799\pi$
$911$			13.4236i			0.444743i	−0.974962	+	0.222372i	$0.928620\pi$
$912$	20.4369	+	29.9111i	0.676733	+	0.990455i
$913$	−8.72004	−	2.33653i	−0.288591	−	0.0773277i
$914$	30.4357	−	6.65594i	1.00672	−	0.220159i
$915$	3.80922	+	15.3970i	0.125929	+	0.509008i
$916$	−25.4827	−	18.0618i	−0.841974	−	0.596779i
$917$		0			0
$918$	42.7338	+	82.6686i	1.41042	+	2.72847i
$919$	13.1243	−	22.7320i	0.432931	−	0.749858i	−0.564193	−	0.825643i	$-0.690813\pi$
$919$	13.1243	−	22.7320i	0.432931	−	0.749858i	0.997124	+	0.0757845i	$0.0241461\pi$
$920$	12.1344	+	5.42717i	0.400061	+	0.178928i
$921$	38.4473	+	66.5926i	1.26688	+	2.19430i
$922$	27.9246	+	1.29943i	0.919646	+	0.0427943i
$923$	−8.52380	−	8.52380i	−0.280564	−	0.280564i
$924$		0			0
$925$	28.1221	+	30.3776i	0.924649	+	0.998809i
$926$	−19.5629	−	21.4725i	−0.642878	−	0.705629i
$927$	100.748	+	26.9955i	3.30901	+	0.886647i
$928$	6.33068	−	26.7364i	0.207815	−	0.877666i
$929$	17.2412	+	9.95422i	0.565666	+	0.326587i	0.755416	−	0.655245i	$-0.227435\pi$
$929$	17.2412	+	9.95422i	0.565666	+	0.326587i	−0.189751	+	0.981832i	$0.560768\pi$
$930$	−12.0727	+	35.5280i	−0.395881	+	1.16501i
$931$		0			0
$932$	1.28448	+	7.53711i	0.0420747	+	0.246886i
$933$	15.1677	+	56.6067i	0.496569	+	1.85322i
$934$	8.51775	+	38.9491i	0.278709	+	1.27446i
$935$	4.03344	−	13.9705i	0.131908	−	0.456885i
$936$	−20.5771	+	2.52920i	−0.672583	+	0.0826693i
$937$	3.76752	+	3.76752i	0.123080	+	0.123080i	0.765964	−	0.642884i	$-0.222262\pi$
$937$	3.76752	+	3.76752i	0.123080	+	0.123080i	−0.642884	+	0.765964i	$0.722262\pi$
$938$		0			0
$939$	5.06087			0.165155
$940$	4.31933	−	11.0033i	0.140881	−	0.358887i
$941$	2.41962	+	4.19090i	0.0788772	+	0.136619i	0.902766	−	0.430133i	$-0.141533\pi$
$941$	2.41962	+	4.19090i	0.0788772	+	0.136619i	−0.823889	+	0.566752i	$0.808200\pi$
$942$	68.2624	+	43.7636i	2.22411	+	1.42589i
$943$	7.17394	−	1.92225i	0.233616	−	0.0625971i
$944$	9.36132	+	26.6675i	0.304685	+	0.867954i
$945$		0			0
$946$	−6.69879	−	2.13325i	−0.217797	−	0.0693580i
$947$	8.02761	+	29.9595i	0.260862	+	0.973551i	0.964735	+	0.263225i	$0.0847861\pi$
$947$	8.02761	+	29.9595i	0.260862	+	0.973551i	−0.703872	+	0.710327i	$0.748547\pi$
$948$	2.46893	+	2.97686i	0.0801872	+	0.0966838i
$949$	5.67887	−	3.27870i	0.184344	−	0.106431i
$950$	−19.7749	−	1.68566i	−0.641584	−	0.0546899i
$951$			95.3170i			3.09086i
$952$		0			0
$953$	22.3422	−	22.3422i	0.723734	−	0.723734i	−0.245630	−	0.969364i	$-0.578995\pi$
$953$	22.3422	−	22.3422i	0.723734	−	0.723734i	0.969364	+	0.245630i	$0.0789947\pi$
$954$	−6.95371	−	7.63245i	−0.225135	−	0.247110i
$955$	−9.37078	−	16.9779i	−0.303231	−	0.549393i
$956$	−30.8167	−	2.87424i	−0.996684	−	0.0929596i
$957$	21.2965	−	5.70637i	0.688417	−	0.184461i
$958$	0.921354	+	1.78236i	0.0297676	+	0.0575855i
$959$		0			0
$960$	−51.0071	+	27.0189i	−1.64625	+	0.872030i
$961$	−8.73844	+	15.1354i	−0.281885	+	0.488239i
$962$	6.24953	−	9.74802i	0.201493	−	0.314289i
$963$	38.4796	−	143.608i	1.23999	−	4.62770i
$964$	24.0114	+	52.2729i	0.773354	+	1.68360i
$965$	−8.22565	−	8.54890i	−0.264793	−	0.275199i
$966$		0			0
$967$	−8.85634	+	8.85634i	−0.284801	+	0.284801i	−0.835020	−	0.550219i	$-0.814544\pi$
$967$	−8.85634	+	8.85634i	−0.284801	+	0.284801i	0.550219	+	0.835020i	$0.314544\pi$
$968$	−15.7061	+	20.1081i	−0.504813	+	0.646300i
$969$	36.2558	−	20.9323i	1.16470	−	0.672442i
$970$	6.97345	+	35.1163i	0.223904	+	1.12752i
$971$	8.19063	+	4.72886i	0.262850	+	0.151756i	0.625634	−	0.780117i	$-0.284840\pi$
$971$	8.19063	+	4.72886i	0.262850	+	0.151756i	−0.362784	+	0.931873i	$0.618174\pi$
$972$	66.5634	−	11.3438i	2.13502	−	0.363854i
$973$		0			0
$974$	−45.3582	−	14.4445i	−1.45337	−	0.462831i
$975$	8.50414	−	13.5002i	0.272350	−	0.432352i
$976$	5.72906	−	6.67076i	0.183383	−	0.213526i
$977$	−15.9873	+	59.6654i	−0.511479	+	1.90886i	−0.107173	+	0.994240i	$0.534180\pi$
$977$	−15.9873	+	59.6654i	−0.511479	+	1.90886i	−0.404305	+	0.914624i	$0.632487\pi$
$978$	−3.68829	+	79.2611i	−0.117939	+	2.53449i
$979$	0.652291			0.0208473
$980$		0			0
$981$	7.52393			0.240221
$982$	−0.208172	+	4.47359i	−0.00664303	+	0.142758i
$983$	15.3538	−	57.3012i	0.489710	−	1.82762i	−0.0681315	−	0.997676i	$-0.521704\pi$
$983$	15.3538	−	57.3012i	0.489710	−	1.82762i	0.557842	−	0.829947i	$-0.311630\pi$
$984$	−12.5974	+	29.6881i	−0.401591	+	0.946422i
$985$	9.37447	+	37.8918i	0.298695	+	1.20733i
$986$	−30.2550	−	9.63480i	−0.963515	−	0.306834i
$987$		0			0
$988$	0.932645	+	5.47258i	0.0296714	+	0.174106i
$989$	−6.43198	−	3.71351i	−0.204525	−	0.118083i
$990$	−27.4095	−	18.3271i	−0.871132	−	0.582473i
$991$	15.0202	−	8.67190i	0.477131	−	0.275472i	−0.242089	−	0.970254i	$-0.577833\pi$
$991$	15.0202	−	8.67190i	0.477131	−	0.275472i	0.719220	+	0.694782i	$0.244499\pi$
$992$	19.9272	−	5.97040i	0.632690	−	0.189560i
$993$	−28.8227	+	28.8227i	−0.914660	+	0.914660i
$994$		0			0
$995$	−0.185204	+	9.61068i	−0.00587137	+	0.304679i
$996$	37.6326	−	17.2864i	1.19243	−	0.547740i
$997$	−3.99308	+	14.9024i	−0.126462	+	0.471964i	−0.999888	−	0.0149945i	$-0.995227\pi$
$997$	−3.99308	+	14.9024i	−0.126462	+	0.471964i	0.873425	+	0.486958i	$0.161894\pi$
$998$	5.68564	−	8.86846i	0.179976	−	0.280726i
$999$	−58.9289	+	102.068i	−1.86443	+	3.22928i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.l.667.18		72
4.3	odd	2	inner	980.2.x.l.667.16		72
5.3	odd	4	inner	980.2.x.l.863.10		72
7.2	even	3		980.2.k.l.687.6		36
7.3	odd	6		980.2.x.k.67.7		72
7.4	even	3	inner	980.2.x.l.67.7		72
7.5	odd	6		140.2.k.a.127.6	yes	36
7.6	odd	2		980.2.x.k.667.18		72
20.3	even	4	inner	980.2.x.l.863.7		72
28.3	even	6		980.2.x.k.67.10		72
28.11	odd	6	inner	980.2.x.l.67.10		72
28.19	even	6		140.2.k.a.127.3	yes	36
28.23	odd	6		980.2.k.l.687.3		36
28.27	even	2		980.2.x.k.667.16		72
35.3	even	12		980.2.x.k.263.16		72
35.12	even	12		700.2.k.b.43.16		36
35.13	even	4		980.2.x.k.863.10		72
35.18	odd	12	inner	980.2.x.l.263.16		72
35.19	odd	6		700.2.k.b.407.13		36
35.23	odd	12		980.2.k.l.883.3		36
35.33	even	12		140.2.k.a.43.3	✓	36
140.3	odd	12		980.2.x.k.263.18		72
140.19	even	6		700.2.k.b.407.16		36
140.23	even	12		980.2.k.l.883.6		36
140.47	odd	12		700.2.k.b.43.13		36
140.83	odd	4		980.2.x.k.863.7		72
140.103	odd	12		140.2.k.a.43.6	yes	36
140.123	even	12	inner	980.2.x.l.263.18		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.3	✓	36	35.33	even	12
140.2.k.a.43.6	yes	36	140.103	odd	12
140.2.k.a.127.3	yes	36	28.19	even	6
140.2.k.a.127.6	yes	36	7.5	odd	6
700.2.k.b.43.13		36	140.47	odd	12
700.2.k.b.43.16		36	35.12	even	12
700.2.k.b.407.13		36	35.19	odd	6
700.2.k.b.407.16		36	140.19	even	6
980.2.k.l.687.3		36	28.23	odd	6
980.2.k.l.687.6		36	7.2	even	3
980.2.k.l.883.3		36	35.23	odd	12
980.2.k.l.883.6		36	140.23	even	12
980.2.x.k.67.7		72	7.3	odd	6
980.2.x.k.67.10		72	28.3	even	6
980.2.x.k.263.16		72	35.3	even	12
980.2.x.k.263.18		72	140.3	odd	12
980.2.x.k.667.16		72	28.27	even	2
980.2.x.k.667.18		72	7.6	odd	2
980.2.x.k.863.7		72	140.83	odd	4
980.2.x.k.863.10		72	35.13	even	4
980.2.x.l.67.7		72	7.4	even	3	inner
980.2.x.l.67.10		72	28.11	odd	6	inner
980.2.x.l.263.16		72	35.18	odd	12	inner
980.2.x.l.263.18		72	140.123	even	12	inner
980.2.x.l.667.16		72	4.3	odd	2	inner
980.2.x.l.667.18		72	1.1	even	1	trivial
980.2.x.l.863.7		72	20.3	even	4	inner
980.2.x.l.863.10		72	5.3	odd	4	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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41268 + 0.0657371i) q^{2} +(0.835136 - 3.11677i) q^{3} +(1.99136 + 0.185732i) q^{4} +(-1.91459 - 1.15514i) q^{5} +(1.38467 - 4.34811i) q^{6} +(2.80095 + 0.393286i) q^{8} +(-6.41872 - 3.70585i) q^{9} +O(q^{10})\)	\(q+(1.41268 + 0.0657371i) q^{2} +(0.835136 - 3.11677i) q^{3} +(1.99136 + 0.185732i) q^{4} +(-1.91459 - 1.15514i) q^{5} +(1.38467 - 4.34811i) q^{6} +(2.80095 + 0.393286i) q^{8} +(-6.41872 - 3.70585i) q^{9} +(-2.62878 - 1.75770i) q^{10} +(-1.21832 + 0.703395i) q^{11} +(2.24194 - 6.05149i) q^{12} +(0.699298 - 0.699298i) q^{13} +(-5.19924 + 5.00264i) q^{15} +(3.93101 + 0.739716i) q^{16} +(1.19641 - 4.46506i) q^{17} +(-8.82402 - 5.65715i) q^{18} +(-1.40337 + 2.43071i) q^{19} +(-3.59809 - 2.65589i) q^{20} +(-1.76734 + 0.913587i) q^{22} +(-2.03016 + 0.543980i) q^{23} +(3.56496 - 8.40147i) q^{24} +(2.33132 + 4.42323i) q^{25} +(1.03386 - 0.941917i) q^{26} +(-10.0659 + 10.0659i) q^{27} -4.85706i q^{29} +(-7.67375 + 6.72537i) q^{30} +(3.18470 - 1.83869i) q^{31} +(5.50465 + 1.30340i) q^{32} +(1.17486 + 4.38464i) q^{33} +(1.98367 - 6.22907i) q^{34} +(-12.0937 - 8.57184i) q^{36} +(7.99714 - 2.14283i) q^{37} +(-2.14231 + 3.34157i) q^{38} +(-1.59554 - 2.76356i) q^{39} +(-4.90838 - 3.98846i) q^{40} -3.53368 q^{41} +(2.49869 + 2.49869i) q^{43} +(-2.55675 + 1.17443i) q^{44} +(8.00846 + 14.5097i) q^{45} +(-2.90374 + 0.635016i) q^{46} +(0.684106 + 2.55312i) q^{47} +(5.58845 - 11.6343i) q^{48} +(3.00265 + 6.40188i) q^{50} +(-12.9174 - 7.45786i) q^{51} +(1.52243 - 1.26267i) q^{52} +(0.951495 + 0.254952i) q^{53} +(-14.8816 + 13.5582i) q^{54} +(3.14510 + 0.0606082i) q^{55} +(6.40395 + 6.40395i) q^{57} +(0.319289 - 6.86149i) q^{58} +(3.53286 + 6.11910i) q^{59} +(-11.2827 + 8.99638i) q^{60} +(1.09916 - 1.90379i) q^{61} +(4.61985 - 2.38814i) q^{62} +(7.69065 + 2.20315i) q^{64} +(-2.14665 + 0.531084i) q^{65} +(1.37148 + 6.27135i) q^{66} +(3.08671 + 0.827081i) q^{67} +(3.21178 - 8.66931i) q^{68} +6.78184i q^{69} -12.1891i q^{71} +(-16.5211 - 12.9043i) q^{72} +(6.40469 + 1.71613i) q^{73} +(11.4383 - 2.50143i) q^{74} +(15.7332 - 3.57218i) q^{75} +(-3.24607 + 4.57976i) q^{76} +(-2.07233 - 4.00892i) q^{78} +(-0.299644 + 0.518999i) q^{79} +(-6.67180 - 5.95711i) q^{80} +(11.8491 + 20.5233i) q^{81} +(-4.99198 - 0.232294i) q^{82} +(4.53764 + 4.53764i) q^{83} +(-7.44839 + 7.16674i) q^{85} +(3.36560 + 3.69412i) q^{86} +(-15.1383 - 4.05630i) q^{87} +(-3.68908 + 1.49103i) q^{88} +(-0.401553 - 0.231837i) q^{89} +(10.3596 + 21.0241i) q^{90} +(-4.14381 + 0.706194i) q^{92} +(-3.07111 - 11.4615i) q^{93} +(0.798592 + 3.65172i) q^{94} +(5.49468 - 3.03273i) q^{95} +(8.65952 - 16.0682i) q^{96} +(-8.00558 - 8.00558i) q^{97} +10.4267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 16 q^{6}+O(q^{10}) \) 72 * q + 16 * q^6	\( 72 q + 16 q^{6} - 16 q^{10} - 16 q^{12} + 8 q^{13} + 8 q^{16} - 20 q^{17} - 28 q^{18} - 40 q^{20} + 8 q^{22} + 20 q^{25} - 32 q^{26} + 4 q^{30} - 20 q^{37} - 36 q^{40} + 20 q^{45} - 16 q^{46} + 48 q^{48} + 80 q^{50} + 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} - 64 q^{61} - 80 q^{62} - 4 q^{65} + 32 q^{66} + 80 q^{68} - 80 q^{72} + 52 q^{73} - 16 q^{76} - 152 q^{78} - 20 q^{80} + 36 q^{81} + 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} + 32 q^{90} - 112 q^{92} - 32 q^{93} + 120 q^{96} - 40 q^{97}+O(q^{100}) \) 72 * q + 16 * q^6 - 16 * q^10 - 16 * q^12 + 8 * q^13 + 8 * q^16 - 20 * q^17 - 28 * q^18 - 40 * q^20 + 8 * q^22 + 20 * q^25 - 32 * q^26 + 4 * q^30 - 20 * q^37 - 36 * q^40 + 20 * q^45 - 16 * q^46 + 48 * q^48 + 80 * q^50 + 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 - 64 * q^61 - 80 * q^62 - 4 * q^65 + 32 * q^66 + 80 * q^68 - 80 * q^72 + 52 * q^73 - 16 * q^76 - 152 * q^78 - 20 * q^80 + 36 * q^81 + 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 + 32 * q^90 - 112 * q^92 - 32 * q^93 + 120 * q^96 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more