LMFDB - Embedded newform 980.2.x.k.67.7

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			67.7
Character	$\chi$	$=$	980.67
Dual form			980.2.x.k.863.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.763272 + 1.19055i) q^{2} +(3.11677 - 0.835136i) q^{3} +(-0.834830 - 1.81743i) q^{4} +(-1.95767 + 1.08052i) q^{5} +(-1.38467 + 4.34811i) q^{6} +(2.80095 + 0.393286i) q^{8} +(6.41872 - 3.70585i) q^{9} +O(q^{10})$	\(q+(-0.763272 + 1.19055i) q^{2} +(3.11677 - 0.835136i) q^{3} +(-0.834830 - 1.81743i) q^{4} +(-1.95767 + 1.08052i) q^{5} +(-1.38467 + 4.34811i) q^{6} +(2.80095 + 0.393286i) q^{8} +(6.41872 - 3.70585i) q^{9} +(0.207827 - 3.15544i) q^{10} +(1.21832 + 0.703395i) q^{11} +(-4.11978 - 4.96732i) q^{12} +(-0.699298 + 0.699298i) q^{13} +(-5.19924 + 5.00264i) q^{15} +(-2.60612 + 3.03449i) q^{16} +(4.46506 - 1.19641i) q^{17} +(-0.487224 + 10.4704i) q^{18} +(1.40337 + 2.43071i) q^{19} +(3.59809 + 2.65589i) q^{20} +(-1.76734 + 0.913587i) q^{22} +(0.543980 - 2.03016i) q^{23} +(9.05837 - 1.11339i) q^{24} +(2.66497 - 4.23059i) q^{25} +(-0.298796 - 1.36631i) q^{26} +(10.0659 - 10.0659i) q^{27} -4.85706i q^{29} +(-1.98747 - 10.0083i) q^{30} +(3.18470 + 1.83869i) q^{31} +(-1.62355 - 5.41886i) q^{32} +(4.38464 + 1.17486i) q^{33} +(-1.98367 + 6.22907i) q^{34} +(-12.0937 - 8.57184i) q^{36} +(-2.14283 + 7.99714i) q^{37} +(-3.96504 - 0.184507i) q^{38} +(-1.59554 + 2.76356i) q^{39} +(-5.90830 + 2.25655i) q^{40} +3.53368 q^{41} +(2.49869 + 2.49869i) q^{43} +(0.261285 - 2.80142i) q^{44} +(-8.56153 + 14.1904i) q^{45} +(2.00181 + 2.19720i) q^{46} +(2.55312 + 0.684106i) q^{47} +(-5.58845 + 11.6343i) q^{48} +(3.00265 + 6.40188i) q^{50} +(12.9174 - 7.45786i) q^{51} +(1.85472 + 0.687131i) q^{52} +(-0.254952 - 0.951495i) q^{53} +(4.30095 + 19.6670i) q^{54} +(-3.14510 - 0.0606082i) q^{55} +(6.40395 + 6.40395i) q^{57} +(5.78258 + 3.70726i) q^{58} +(-3.53286 + 6.11910i) q^{59} +(13.4324 + 5.27291i) q^{60} +(-1.09916 - 1.90379i) q^{61} +(-4.61985 + 2.38814i) q^{62} +(7.69065 + 2.20315i) q^{64} +(0.613394 - 2.12460i) q^{65} +(-4.74541 + 4.32341i) q^{66} +(-0.827081 - 3.08671i) q^{67} +(-5.90196 - 7.11614i) q^{68} -6.78184i q^{69} -12.1891i q^{71} +(19.4360 - 7.85551i) q^{72} +(1.71613 + 6.40469i) q^{73} +(-7.88545 - 8.65515i) q^{74} +(4.77298 - 15.4114i) q^{75} +(3.24607 - 4.57976i) q^{76} +(-2.07233 - 4.00892i) q^{78} +(-0.299644 - 0.518999i) q^{79} +(1.82311 - 8.75650i) q^{80} +(11.8491 - 20.5233i) q^{81} +(-2.69716 + 4.20703i) q^{82} +(-4.53764 - 4.53764i) q^{83} +(-7.44839 + 7.16674i) q^{85} +(-4.88200 + 1.06764i) q^{86} +(-4.05630 - 15.1383i) q^{87} +(3.13581 + 2.44932i) q^{88} +(-0.401553 + 0.231837i) q^{89} +(-10.3596 - 21.0241i) q^{90} +(-4.14381 + 0.706194i) q^{92} +(11.4615 + 3.07111i) q^{93} +(-2.76319 + 2.51746i) q^{94} +(-5.37376 - 3.24217i) q^{95} +(-9.58571 - 15.5335i) 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 $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.763272	+	1.19055i	−0.539715	+	0.841848i
$2$	−0.763272	+	1.19055i	−0.539715	+	0.841848i
$3$	3.11677	−	0.835136i	1.79947	−	0.482166i	0.805573	−	0.592497i	$-0.201858\pi$
$3$	3.11677	−	0.835136i	1.79947	−	0.482166i	0.993895	+	0.110331i	$0.0351911\pi$
$4$	−0.834830	−	1.81743i	−0.417415	−	0.908716i
$5$	−1.95767	+	1.08052i	−0.875498	+	0.483221i
$5$	−1.95767	+	1.08052i	−0.875498	+	0.483221i
$6$	−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
$10$	0.207827	−	3.15544i	0.0657208	−	0.997838i
$11$	1.21832	+	0.703395i	0.367336	+	0.212082i	0.672294	−	0.740284i	$-0.265309\pi$
$11$	1.21832	+	0.703395i	0.367336	+	0.212082i	−0.304958	+	0.952366i	$0.598642\pi$
$12$	−4.11978	−	4.96732i	−1.18928	−	1.43394i
$13$	−0.699298	+	0.699298i	−0.193950	+	0.193950i	−0.797401	−	0.603450i	$-0.793792\pi$
$13$	−0.699298	+	0.699298i	−0.193950	+	0.193950i	0.603450	+	0.797401i	$0.293792\pi$
$14$		0			0
$15$	−5.19924	+	5.00264i	−1.34244	+	1.29168i
$16$	−2.60612	+	3.03449i	−0.651529	+	0.758624i
$17$	4.46506	−	1.19641i	1.08294	−	0.290172i	0.327138	−	0.944977i	$-0.393916\pi$
$17$	4.46506	−	1.19641i	1.08294	−	0.290172i	0.755798	+	0.654805i	$0.227249\pi$
$18$	−0.487224	+	10.4704i	−0.114840	+	2.46790i
$19$	1.40337	+	2.43071i	0.321955	+	0.557643i	0.980891	−	0.194556i	$-0.0623266\pi$
$19$	1.40337	+	2.43071i	0.321955	+	0.557643i	−0.658936	+	0.752199i	$0.728993\pi$
$20$	3.59809	+	2.65589i	0.804557	+	0.593875i
$21$		0			0
$22$	−1.76734	+	0.913587i	−0.376797	+	0.194777i
$23$	0.543980	−	2.03016i	0.113428	−	0.423318i	−0.885737	−	0.464188i	$-0.846346\pi$
$23$	0.543980	−	2.03016i	0.113428	−	0.423318i	0.999164	+	0.0408699i	$0.0130129\pi$
$24$	9.05837	−	1.11339i	1.84903	−	0.227270i
$25$	2.66497	−	4.23059i	0.532994	−	0.846119i
$26$	−0.298796	−	1.36631i	−0.0585987	−	0.267954i
$27$	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	$-0.148921\pi$
$30$	−1.98747	−	10.0083i	−0.362861	−	1.82727i
$31$	3.18470	+	1.83869i	0.571990	+	0.330238i	0.757944	−	0.652320i	$-0.226204\pi$
$31$	3.18470	+	1.83869i	0.571990	+	0.330238i	−0.185954	+	0.982558i	$0.559538\pi$
$32$	−1.62355	−	5.41886i	−0.287005	−	0.957929i
$33$	4.38464	+	1.17486i	0.763268	+	0.204517i
$34$	−1.98367	+	6.22907i	−0.340196	+	1.06828i
$35$		0			0
$36$	−12.0937	−	8.57184i	−2.01561	−	1.42864i
$37$	−2.14283	+	7.99714i	−0.352279	+	1.31472i	0.531596	+	0.846998i	$0.321592\pi$
$37$	−2.14283	+	7.99714i	−0.352279	+	1.31472i	−0.883875	+	0.467724i	$0.845074\pi$
$38$	−3.96504	−	0.184507i	−0.643214	−	0.0299310i
$39$	−1.59554	+	2.76356i	−0.255491	+	0.442523i
$40$	−5.90830	+	2.25655i	−0.934184	+	0.356791i
$41$	3.53368			0.551868			0.275934	−	0.961177i	$-0.411013\pi$
$41$	3.53368			0.551868			0.275934	+	0.961177i	$0.411013\pi$
$42$		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	$0.663161\pi$
$44$	0.261285	−	2.80142i	0.0393903	−	0.422330i
$45$	−8.56153	+	14.1904i	−1.27628	+	2.11538i
$46$	2.00181	+	2.19720i	0.295151	+	0.323960i
$47$	2.55312	+	0.684106i	0.372411	+	0.0997872i	0.440170	−	0.897915i	$-0.354918\pi$
$47$	2.55312	+	0.684106i	0.372411	+	0.0997872i	−0.0677590	+	0.997702i	$0.521585\pi$
$48$	−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
$52$	1.85472	+	0.687131i	0.257203	+	0.0952879i
$53$	−0.254952	−	0.951495i	−0.0350204	−	0.130698i	0.946203	−	0.323575i	$-0.104885\pi$
$53$	−0.254952	−	0.951495i	−0.0350204	−	0.130698i	−0.981223	+	0.192877i	$0.938218\pi$
$54$	4.30095	+	19.6670i	0.585286	+	2.67634i
$55$	−3.14510	−	0.0606082i	−0.424085	−	0.00817240i
$56$		0			0
$57$	6.40395	+	6.40395i	0.848224	+	0.848224i
$58$	5.78258	+	3.70726i	0.759291	+	0.486787i
$59$	−3.53286	+	6.11910i	−0.459940	+	0.796639i	−0.998957	−	0.0456557i	$-0.985462\pi$
$59$	−3.53286	+	6.11910i	−0.459940	+	0.796639i	0.539018	+	0.842294i	$0.318796\pi$
$60$	13.4324	+	5.27291i	1.73412	+	0.680729i
$61$	−1.09916	−	1.90379i	−0.140732	−	0.243756i	0.787040	−	0.616902i	$-0.211612\pi$
$61$	−1.09916	−	1.90379i	−0.140732	−	0.243756i	−0.927773	+	0.373146i	$0.878279\pi$
$62$	−4.61985	+	2.38814i	−0.586722	+	0.303294i
$63$		0			0
$64$	7.69065	+	2.20315i	0.961331	+	0.275394i
$65$	0.613394	−	2.12460i	0.0760822	−	0.263524i
$66$	−4.74541	+	4.32341i	−0.584120	+	0.532175i
$67$	−0.827081	−	3.08671i	−0.101044	−	0.377101i	0.896822	−	0.442391i	$-0.145870\pi$
$67$	−0.827081	−	3.08671i	−0.101044	−	0.377101i	−0.997866	+	0.0652895i	$0.979203\pi$
$68$	−5.90196	−	7.11614i	−0.715717	−	0.862959i
$69$		−	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	$-0.257370\pi$
$72$	19.4360	−	7.85551i	2.29055	−	0.925781i
$73$	1.71613	+	6.40469i	0.200858	+	0.749612i	0.990672	+	0.136266i	$0.0435102\pi$
$73$	1.71613	+	6.40469i	0.200858	+	0.749612i	−0.789814	+	0.613346i	$0.789823\pi$
$74$	−7.88545	−	8.65515i	−0.916665	−	1.00614i
$75$	4.77298	−	15.4114i	0.551136	−	1.77956i
$76$	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	0.848677	−	0.528912i	$-0.177400\pi$
$79$	−0.299644	−	0.518999i	−0.0337126	−	0.0583919i	−0.882389	+	0.470520i	$0.844066\pi$
$80$	1.82311	−	8.75650i	0.203829	−	0.979006i
$81$	11.8491	−	20.5233i	1.31657	−	2.28036i
$82$	−2.69716	+	4.20703i	−0.297852	+	0.464589i
$83$	−4.53764	−	4.53764i	−0.498071	−	0.498071i	0.412766	−	0.910837i	$-0.364563\pi$
$83$	−4.53764	−	4.53764i	−0.498071	−	0.498071i	−0.910837	+	0.412766i	$0.864563\pi$
$84$		0			0
$85$	−7.44839	+	7.16674i	−0.807891	+	0.777342i
$86$	−4.88200	+	1.06764i	−0.526440	+	0.115127i
$87$	−4.05630	−	15.1383i	−0.434882	−	1.62300i
$88$	3.13581	+	2.44932i	0.334278	+	0.261099i
$89$	−0.401553	+	0.231837i	−0.0425645	+	0.0245746i	−0.521131	−	0.853477i	$-0.674490\pi$
$89$	−0.401553	+	0.231837i	−0.0425645	+	0.0245746i	0.478567	+	0.878051i	$0.341156\pi$
$90$	−10.3596	−	21.0241i	−1.09200	−	2.21613i
$91$		0			0
$92$	−4.14381	+	0.706194i	−0.432022	+	0.0736258i
$93$	11.4615	+	3.07111i	1.18851	+	0.318459i
$94$	−2.76319	+	2.51746i	−0.285001	+	0.259657i
$95$	−5.37376	−	3.24217i	−0.551336	−	0.332640i
$96$	−9.58571	−	15.5335i	−0.978338	−	1.58538i
$97$	8.00558	+	8.00558i	0.812843	+	0.812843i	0.985059	−	0.172216i	$-0.0550927\pi$
$97$	8.00558	+	8.00558i	0.812843	+	0.812843i	−0.172216	+	0.985059i	$0.555093\pi$
$98$		0			0
$99$	10.4267			1.04792
$100$	−9.91362	−	1.31157i	−0.991362	−	0.131157i
$101$	3.01549	−	5.22299i	0.300053	−	0.519707i	−0.676095	−	0.736815i	$-0.736329\pi$
$101$	3.01549	−	5.22299i	0.300053	−	0.519707i	0.976148	+	0.217108i	$0.0696624\pi$
$102$	−0.980516	+	21.0712i	−0.0970856	+	2.08636i
$103$	−3.64227	+	13.5932i	−0.358884	+	1.33937i	0.516642	+	0.856202i	$0.327182\pi$
$103$	−3.64227	+	13.5932i	−0.358884	+	1.33937i	−0.875526	+	0.483171i	$0.839485\pi$
$104$	−2.23372	+	1.68367i	−0.219035	+	0.165098i
$105$		0			0
$106$	1.32740	+	0.422716i	0.128929	+	0.0410578i
$107$	−19.3758	−	5.19174i	−1.87313	−	0.501905i	−0.999893	−	0.0146144i	$-0.995348\pi$
$107$	−19.3758	−	5.19174i	−1.87313	−	0.501905i	−0.873240	−	0.487290i	$-0.837985\pi$
$108$	−26.6974	−	9.89076i	−2.56896	−	0.951739i
$109$	0.879139	+	0.507571i	0.0842062	+	0.0486165i	0.541512	−	0.840693i	$-0.317852\pi$
$109$	0.879139	+	0.507571i	0.0842062	+	0.0486165i	−0.457306	+	0.889310i	$0.651185\pi$
$110$	2.47272	−	3.69814i	0.235765	−	0.352604i
$111$			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	$0.0863372\pi$
$114$	−12.5122	+	2.73628i	−1.17188	+	0.256276i
$115$	1.12869	+	4.56217i	0.105251	+	0.425425i
$116$	−8.82737	+	4.05482i	−0.819601	+	0.376481i
$117$	−1.89711	+	7.08009i	−0.175387	+	0.654555i
$118$	−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
$122$	3.10552	+	0.144511i	0.281161	+	0.0130834i
$123$	11.0137	−	2.95110i	0.993069	−	0.266092i
$124$	0.683006	−	7.32298i	0.0613357	−	0.657623i
$125$	−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	$0.0621014\pi$
$128$	−8.49303	+	7.47452i	−0.750685	+	0.660661i
$129$	9.87458	+	5.70109i	0.869408	+	0.501953i
$130$	2.06126	+	2.35193i	0.180784	+	0.206278i
$131$	−11.3871	+	6.57436i	−0.994898	+	0.574404i	−0.906735	−	0.421702i	$-0.861433\pi$
$131$	−11.3871	+	6.57436i	−0.994898	+	0.574404i	−0.0881630	+	0.996106i	$0.528100\pi$
$132$	−1.52520	−	8.94960i	−0.132752	−	0.778962i
$133$		0			0
$134$	4.30618	+	1.37132i	0.371997	+	0.118464i
$135$	−8.82937	+	30.5821i	−0.759912	+	2.63209i
$136$	12.9769	−	1.59504i	1.11276	−	0.136773i
$137$	−6.75090	+	1.80890i	−0.576769	+	0.154545i	−0.535399	−	0.844599i	$-0.679839\pi$
$137$	−6.75090	+	1.80890i	−0.576769	+	0.154545i	−0.0413695	+	0.999144i	$0.513172\pi$
$138$	8.07414	+	5.17640i	0.687317	+	0.440644i
$139$	−21.2377			−1.80136			−0.900679	−	0.434485i	$-0.856931\pi$
$139$	−21.2377			−1.80136			−0.900679	+	0.434485i	$0.856931\pi$
$140$		0			0
$141$	8.52881			0.718255
$142$	14.5117	+	9.30359i	1.21780	+	0.780740i
$143$	−1.34385	+	0.360083i	−0.112378	+	0.0301117i
$144$	−5.48256	+	29.1355i	−0.456880	+	2.42796i
$145$	5.24813	+	9.50854i	0.435833	+	0.789641i
$146$	−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	$-0.754408\pi$
$149$	−5.75434	+	3.32227i	−0.471414	+	0.272171i	0.245418	+	0.969417i	$0.421075\pi$
$150$	14.7050	+	17.4456i	1.20066	+	1.42443i
$151$	−17.6555	−	10.1934i	−1.43679	−	0.829529i	−0.439161	−	0.898408i	$-0.644724\pi$
$151$	−17.6555	−	10.1934i	−1.43679	−	0.829529i	−0.997625	+	0.0688796i	$0.978058\pi$
$152$	2.97481	+	7.36022i	0.241289	+	0.596993i
$153$	24.2263	−	24.2263i	1.95858	−	1.95858i
$154$		0			0
$155$	−8.22134	−	0.158431i	−0.660354	−	0.0127255i
$156$	6.35458	+	0.592685i	0.508774	+	0.0474528i
$157$	−17.1639	+	4.59905i	−1.36983	+	0.367044i	−0.867416	−	0.497584i	$-0.834221\pi$
$157$	−17.1639	+	4.59905i	−1.36983	+	0.367044i	−0.502412	+	0.864628i	$0.667554\pi$
$158$	0.846605	+	0.0393955i	0.0673523	+	0.00313413i
$159$	−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
$163$	4.50039	−	16.7957i	0.352498	−	1.31554i	−0.531106	−	0.847305i	$-0.678224\pi$
$163$	4.50039	−	16.7957i	0.352498	−	1.31554i	0.883604	−	0.468235i	$-0.155110\pi$
$164$	−2.95002	−	6.42222i	−0.230358	−	0.501491i
$165$	−9.85315	+	2.43768i	−0.767067	+	0.189773i
$166$	8.86575	−	1.93884i	0.688116	−	0.150483i
$167$	−6.88960	+	6.88960i	−0.533133	+	0.533133i	−0.921503	−	0.388370i	$-0.873038\pi$
$167$	−6.88960	+	6.88960i	−0.533133	+	0.533133i	0.388370	+	0.921503i	$0.373038\pi$
$168$		0			0
$169$			12.0220i			0.924767i
$170$	−2.84724	−	14.3379i	−0.218373	−	1.09966i
$171$	18.0157	+	10.4014i	1.37769	+	0.795412i
$172$	2.45521	−	6.62718i	0.187208	−	0.505318i
$173$	23.8977	+	6.40337i	1.81691	+	0.486839i	0.996399	−	0.0847922i	$-0.0270226\pi$
$173$	23.8977	+	6.40337i	1.81691	+	0.486839i	0.820510	+	0.571632i	$0.193689\pi$
$174$	21.1190	+	6.72543i	1.60103	+	0.509854i
$175$		0			0
$176$	−5.30952	+	1.86384i	−0.400220	+	0.140493i
$177$	−5.90084	+	22.0222i	−0.443534	+	1.65529i
$178$	0.0304805	−	0.655024i	0.00228461	−	0.0490961i
$179$	−10.2777	+	17.8015i	−0.768192	+	1.33055i	0.170350	+	0.985384i	$0.445510\pi$
$179$	−10.2777	+	17.8015i	−0.768192	+	1.33055i	−0.938542	+	0.345164i	$0.887823\pi$
$180$	32.9375	+	3.71344i	2.45501	+	0.276784i
$181$	−7.85989			−0.584221			−0.292110	−	0.956385i	$-0.594357\pi$
$181$	−7.85989			−0.584221			−0.292110	+	0.956385i	$0.594357\pi$
$182$		0			0
$183$	−5.01574	−	5.01574i	−0.370774	−	0.370774i
$184$	2.32210	−	5.47244i	0.171187	−	0.403434i
$185$	−4.44608	−	17.9711i	−0.326882	−	1.32127i
$186$	−12.4046	+	11.3015i	−0.909549	+	0.828664i
$187$	6.28140	+	1.68310i	0.459342	+	0.123080i
$188$	−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	$-0.768255\pi$
$191$	−7.51061	+	4.33625i	−0.543449	+	0.313760i	0.203027	+	0.979173i	$0.434922\pi$
$192$	25.8099	+	0.443974i	1.86267	+	0.0320411i
$193$	−1.37318	−	5.12478i	−0.0988437	−	0.368890i	0.898730	−	0.438502i	$-0.144491\pi$
$193$	−1.37318	−	5.12478i	−0.0988437	−	0.368890i	−0.997574	+	0.0696118i	$0.977824\pi$
$194$	−15.6415	+	3.42062i	−1.12299	+	0.245586i
$195$	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	$0.963625\pi$
$198$	−7.95842	+	12.4136i	−0.565581	+	0.882193i
$199$	2.14941	−	3.72289i	0.152368	−	0.263909i	−0.779730	−	0.626116i	$-0.784644\pi$
$199$	2.14941	−	3.72289i	0.152368	−	0.263909i	0.932097	+	0.362208i	$0.117977\pi$
$200$	9.12829	−	10.8016i	0.645467	−	0.763788i
$201$	−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
$205$	−6.91779	+	3.81820i	−0.483159	+	0.266674i
$206$	−13.4033	−	14.7116i	−0.933853	−	1.02501i
$207$	−4.03182	−	15.0470i	−0.280231	−	1.04584i
$208$	−0.299564	−	3.94447i	−0.0207710	−	0.273500i
$209$			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	$0.765041\pi$
$212$	−1.51643	+	1.25769i	−0.104149	+	0.0863788i
$213$	−10.1795	−	37.9906i	−0.697490	−	2.60307i
$214$	20.9701	−	19.1052i	1.43349	−	1.30601i
$215$	−7.59149	−	2.19174i	−0.517735	−	0.149476i
$216$	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
$220$	2.51547	+	5.76659i	0.169593	+	0.388784i
$221$	−2.28576	+	3.95905i	−0.153757	+	0.266315i
$222$	−31.8054	−	20.3907i	−2.13464	−	1.36853i
$223$	9.54503	+	9.54503i	0.639183	+	0.639183i	0.950354	−	0.311171i	$-0.100721\pi$
$223$	9.54503	+	9.54503i	0.639183	+	0.639183i	−0.311171	+	0.950354i	$0.600721\pi$
$224$		0			0
$225$	1.42776	−	37.0310i	0.0951838	−	2.46873i
$226$	3.15908	+	14.4455i	0.210139	+	0.960901i
$227$	−4.77541	−	17.8221i	−0.316955	−	1.18289i	−0.922155	−	0.386819i	$-0.873574\pi$
$227$	−4.77541	−	17.8221i	−0.316955	−	1.18289i	0.605200	−	0.796073i	$-0.293093\pi$
$228$	6.29253	−	16.9850i	0.416733	−	1.12486i
$229$	−13.5250	+	7.80865i	−0.893755	+	0.516010i	−0.875169	−	0.483817i	$-0.839250\pi$
$229$	−13.5250	+	7.80865i	−0.893755	+	0.516010i	−0.0185864	+	0.999827i	$0.505917\pi$
$230$	−6.29300	−	2.13842i	−0.414948	−	0.141003i
$231$		0			0
$232$	1.91021	−	13.6044i	0.125412	−	0.893172i
$233$	−3.69263	−	0.989436i	−0.241912	−	0.0648201i	0.135826	−	0.990733i	$-0.456631\pi$
$233$	−3.69263	−	0.989436i	−0.241912	−	0.0648201i	−0.377738	+	0.925913i	$0.623298\pi$
$234$	−6.98121	−	7.66264i	−0.456376	−	0.500923i
$235$	−5.73736	+	1.41943i	−0.374264	+	0.0925934i
$236$	14.0704	+	1.31233i	0.915904	+	0.0854253i
$237$	−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	$0.666852\pi$
$240$	−1.63067	−	28.8145i	−0.105259	−	1.85997i
$241$	−14.3810	+	24.9086i	−0.926361	+	1.60450i	−0.137004	+	0.990570i	$0.543747\pi$
$241$	−14.3810	+	24.9086i	−0.926361	+	1.60450i	−0.789357	+	0.613934i	$0.789586\pi$
$242$	12.7437	+	0.593010i	0.819199	+	0.0381202i
$243$	8.73814	−	32.6112i	0.560552	−	2.09201i
$244$	−2.54241	+	3.58699i	−0.162761	+	0.229633i
$245$		0			0
$246$	−4.89298	+	15.3648i	−0.311965	+	0.979626i
$247$	−2.68116	−	0.718415i	−0.170598	−	0.0457117i
$248$	8.19707	+	6.40258i	0.520514	+	0.406564i
$249$	−17.9323	−	10.3532i	−1.13641	−	0.656109i
$250$	−12.7955	−	9.28839i	−0.809261	−	0.587450i
$251$		−	26.0285i		−	1.64291i	−0.570277	−	0.821453i	$-0.693164\pi$
$251$		−	26.0285i		−	1.64291i	0.570277	−	0.821453i	$-0.306836\pi$
$252$		0			0
$253$	2.09075	−	2.09075i	0.131444	−	0.131444i
$254$	3.79037	+	17.3322i	0.237829	+	1.08752i
$255$	−17.2297	+	28.5575i	−1.07897	+	1.78834i
$256$	−2.41631	−	15.8165i	−0.151020	−	0.988531i
$257$	5.97352	−	22.2935i	0.372618	−	1.39063i	−0.484176	−	0.874971i	$-0.660881\pi$
$257$	5.97352	−	22.2935i	0.372618	−	1.39063i	0.856794	−	0.515659i	$-0.172453\pi$
$258$	−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
$262$	0.864358	−	18.5750i	0.0534002	−	1.14757i
$263$	10.9633	−	2.93759i	0.676023	−	0.181140i	0.0955566	−	0.995424i	$-0.469537\pi$
$263$	10.9633	−	2.93759i	0.676023	−	0.181140i	0.580466	+	0.814284i	$0.302870\pi$
$264$	11.8191	+	5.01515i	0.727416	+	0.308661i
$265$	1.52722	+	1.58724i	0.0938163	+	0.0975031i
$266$		0			0
$267$	−1.05793	+	1.05793i	−0.0647444	+	0.0647444i
$268$	−4.91941	+	4.08004i	−0.300501	+	0.249228i
$269$	23.5713	+	13.6089i	1.43717	+	0.829749i	0.997652	−	0.0684854i	$-0.0218167\pi$
$269$	23.5713	+	13.6089i	1.43717	+	0.829749i	0.439516	+	0.898235i	$0.355150\pi$
$270$	−29.6704	−	33.8543i	−1.80568	−	2.06031i
$271$	0.134959	−	0.0779185i	0.00819817	−	0.00473321i	−0.495895	−	0.868382i	$-0.665160\pi$
$271$	0.134959	−	0.0779185i	0.00819817	−	0.00473321i	0.504093	+	0.863649i	$0.331827\pi$
$272$	−8.00597	+	16.6672i	−0.485433	+	1.01060i
$273$		0			0
$274$	2.99919	−	9.41799i	0.181188	−	0.568961i
$275$	6.22256	−	3.27967i	0.375234	−	0.197772i
$276$	−12.3255	+	5.66169i	−0.741910	+	0.340794i
$277$	20.2196	−	5.41783i	1.21488	−	0.325526i	0.406204	−	0.913782i	$-0.366852\pi$
$277$	20.2196	−	5.41783i	1.21488	−	0.325526i	0.808674	+	0.588256i	$0.200185\pi$
$278$	16.2102	−	25.2846i	0.972220	−	1.51647i
$279$	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	$0.524363\pi$
$282$	−6.50980	+	10.1540i	−0.387653	+	0.604661i
$283$	−19.8738	+	5.32518i	−1.18138	+	0.316549i	−0.795472	−	0.605990i	$-0.792777\pi$
$283$	−19.8738	+	5.32518i	−1.18138	+	0.316549i	−0.385904	+	0.922539i	$0.626111\pi$
$284$	−22.1528	+	10.1758i	−1.31453	+	0.603824i
$285$	−19.4564	−	5.61728i	−1.15250	−	0.332739i
$286$	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
$290$	−15.3262	−	1.00943i	−0.899983	−	0.0592758i
$291$	31.6373	+	18.2658i	1.85461	+	1.07076i
$292$	10.2074	−	8.46578i	0.597343	−	0.495422i
$293$	4.71102	−	4.71102i	0.275221	−	0.275221i	−0.555977	−	0.831198i	$-0.687656\pi$
$293$	4.71102	−	4.71102i	0.275221	−	0.275221i	0.831198	+	0.555977i	$0.187656\pi$
$294$		0			0
$295$	0.304410	−	15.7965i	0.0177234	−	0.919708i
$296$	−9.14712	+	21.5569i	−0.531666	+	1.25297i
$297$	19.3437	−	5.18314i	1.12244	−	0.300756i
$298$	0.436793	−	9.38664i	0.0253027	−	0.543753i
$299$	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
$303$	5.03669	−	18.7972i	0.289350	−	1.07987i
$304$	−11.0333	−	2.07619i	−0.632804	−	0.119078i
$305$	4.20887	+	2.53935i	0.240999	+	0.145403i
$306$	10.3514	+	47.3339i	0.591750	+	2.70590i
$307$	16.8508	−	16.8508i	0.961723	−	0.961723i	−0.0375706	−	0.999294i	$-0.511962\pi$
$307$	16.8508	−	16.8508i	0.961723	−	0.961723i	0.999294	+	0.0375706i	$0.0119619\pi$
$308$		0			0
$309$			45.4085i			2.58320i
$310$	6.46375	−	9.66702i	0.367116	−	0.549050i
$311$	−15.7287	−	9.08099i	−0.891895	−	0.514936i	−0.0173329	−	0.999850i	$-0.505518\pi$
$311$	−15.7287	−	9.08099i	−0.891895	−	0.514936i	−0.874562	+	0.484914i	$0.838851\pi$
$312$	−5.55590	+	7.11309i	−0.314541	+	0.402699i
$313$	1.51498	+	0.405938i	0.0856319	+	0.0229450i	0.301381	−	0.953504i	$-0.402553\pi$
$313$	1.51498	+	0.405938i	0.0856319	+	0.0229450i	−0.215749	+	0.976449i	$0.569219\pi$
$314$	7.62532	−	23.9449i	0.430322	−	1.35129i
$315$		0			0
$316$	−0.693093	+	0.977859i	−0.0389895	+	0.0550088i
$317$	7.64549	−	28.5334i	0.429414	−	1.60259i	−0.324678	−	0.945825i	$-0.605256\pi$
$317$	7.64549	−	28.5334i	0.429414	−	1.60259i	0.754092	−	0.656769i	$-0.228077\pi$
$318$	4.49023	+	0.208946i	0.251800	+	0.0117171i
$319$	3.41643	−	5.91743i	0.191283	−	0.331313i
$320$	−17.4363	+	3.99682i	−0.974720	+	0.223429i
$321$	−64.7258			−3.61264
$322$		0			0
$323$	9.17425	+	9.17425i	0.510469	+	0.510469i
$324$	−47.1917	−	4.40151i	−2.62176	−	0.244528i
$325$	1.09484	+	4.82205i	0.0607306	+	0.267479i
$326$	16.5611	+	18.1776i	0.917236	+	1.00677i
$327$	3.16396	+	0.847782i	0.174968	+	0.0468824i
$328$	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	$-0.553809\pi$
$331$	10.9400	−	6.31623i	0.601319	−	0.347172i	0.769560	+	0.638574i	$0.220475\pi$
$332$	−4.45869	+	12.0350i	−0.244703	+	0.660507i
$333$	15.8820	+	59.2724i	0.870328	+	3.24811i
$334$	−2.94379	−	13.4611i	−0.161077	−	0.736557i
$335$	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	$0.699452\pi$
$338$	−14.3128	−	9.17603i	−0.778513	−	0.499111i
$339$	16.8692	−	29.2182i	0.916207	−	1.58692i
$340$	19.2432	+	7.55392i	1.04361	+	0.409669i
$341$	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
$345$	7.32789	+	13.2766i	0.394520	+	0.714790i
$346$	−25.8640	+	23.5640i	−1.39046	+	1.26681i
$347$	3.82255	+	14.2660i	0.205205	+	0.765837i	0.989387	+	0.145305i	$0.0464164\pi$
$347$	3.82255	+	14.2660i	0.205205	+	0.765837i	−0.784182	+	0.620531i	$0.786917\pi$
$348$	−24.1266	+	20.0100i	−1.29332	+	1.07265i
$349$		−	5.05181i		−	0.270417i	−0.990817	−	0.135209i	$-0.956830\pi$
$349$		−	5.05181i		−	0.270417i	0.990817	−	0.135209i	$-0.0431705\pi$
$350$		0			0
$351$			14.0781i			0.751434i
$352$	1.83361	−	7.74389i	0.0977317	−	0.412751i
$353$	2.81454	+	10.5040i	0.149803	+	0.559072i	0.999495	+	0.0317919i	$0.0101214\pi$
$353$	2.81454	+	10.5040i	0.149803	+	0.559072i	−0.849692	+	0.527280i	$0.823212\pi$
$354$	−21.7147	−	23.8342i	−1.15412	−	1.26677i
$355$	13.1705	+	23.8622i	0.699017	+	1.26648i
$356$	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	0.792699	−	0.609613i	$-0.208675\pi$
$359$	−2.49329	−	4.31850i	−0.131591	−	0.227922i	−0.924290	+	0.381691i	$0.875342\pi$
$360$	−29.5613	+	36.3794i	−1.55802	+	1.91736i
$361$	5.56111	−	9.63212i	0.292690	−	0.506954i
$362$	5.99923	−	9.35761i	0.315313	−	0.491825i
$363$	−20.5825	−	20.5825i	−1.08030	−	1.08030i
$364$		0			0
$365$	−10.2800	−	10.6840i	−0.538079	−	0.559225i
$366$	9.79988	−	2.14313i	0.512248	−	0.112023i
$367$	4.12420	+	15.3917i	0.215282	+	0.803442i	0.986067	+	0.166347i	$0.0531972\pi$
$367$	4.12420	+	15.3917i	0.215282	+	0.803442i	−0.770786	+	0.637094i	$0.780136\pi$
$368$	4.74284	+	6.94154i	0.247238	+	0.361853i
$369$	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
$373$	0.569126	+	0.152497i	0.0294682	+	0.00789599i	0.273523	−	0.961865i	$-0.411811\pi$
$373$	0.569126	+	0.152497i	0.0294682	+	0.00789599i	−0.244055	+	0.969761i	$0.578478\pi$
$374$	−6.79823	+	6.19368i	−0.351528	+	0.320267i
$375$	7.30833	+	35.3278i	0.377400	+	1.82432i
$376$	6.88211	+	2.92025i	0.354918	+	0.150601i
$377$	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	$0.708907\pi$
$380$	−1.40624	+	12.4731i	−0.0721388	+	0.639857i
$381$	20.2402	−	35.0570i	1.03694	−	1.79603i
$382$	0.570105	−	12.2515i	0.0291691	−	0.626842i
$383$	−1.11189	+	4.14964i	−0.0568151	+	0.212037i	−0.988498	−	0.151237i	$-0.951674\pi$
$383$	−1.11189	+	4.14964i	−0.0568151	+	0.212037i	0.931682	+	0.363274i	$0.118341\pi$
$384$	−20.2286	+	30.3892i	−1.03229	+	1.55079i
$385$		0			0
$386$	7.14943	+	2.27676i	0.363896	+	0.115884i
$387$	25.2982	+	6.77862i	1.28598	+	0.344577i
$388$	7.86629	−	21.2329i	0.399350	−	1.07794i
$389$	21.8152	+	12.5950i	1.10608	+	0.638593i	0.937810	−	0.347148i	$-0.112850\pi$
$389$	21.8152	+	12.5950i	1.10608	+	0.638593i	0.168266	+	0.985742i	$0.446183\pi$
$390$	8.38865	+	5.60898i	0.424776	+	0.284022i
$391$		−	9.71561i		−	0.491340i
$392$		0			0
$393$	−30.0006	+	30.0006i	−1.51333	+	1.51333i
$394$	24.1174	−	5.27421i	1.21502	−	0.265711i
$395$	1.14739	+	0.692260i	0.0577315	+	0.0348314i
$396$	−8.70454	−	18.9498i	−0.437419	−	0.952265i
$397$	−1.00160	+	3.73802i	−0.0502689	+	0.187606i	−0.986495	−	0.163793i	$-0.947627\pi$
$397$	−1.00160	+	3.73802i	−0.0502689	+	0.187606i	0.936226	+	0.351399i	$0.114294\pi$
$398$	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	0.926364	−	0.376630i	$-0.122917\pi$
$401$	2.74364	+	4.75213i	0.137011	+	0.237310i	−0.789353	+	0.613940i	$0.789584\pi$
$402$	14.5666	+	0.677834i	0.726516	+	0.0338073i
$403$	−3.51285	+	0.941265i	−0.174987	+	0.0468877i
$404$	−12.0098	−	1.12014i	−0.597512	−	0.0557293i
$405$	−1.02098	+	52.9811i	−0.0507330	+	2.63265i
$406$		0			0
$407$	−8.23579	+	8.23579i	−0.408233	+	0.408233i
$408$	39.1141	−	15.8089i	1.93643	−	0.782656i
$409$	−14.7164	−	8.49650i	−0.727678	−	0.420125i	0.0898942	−	0.995951i	$-0.471347\pi$
$409$	−14.7164	−	8.49650i	−0.727678	−	0.420125i	−0.817572	+	0.575826i	$0.804680\pi$
$410$	0.734395	−	11.1503i	0.0362692	−	0.550675i
$411$	−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
$415$	13.7862	+	3.98023i	0.676738	+	0.195382i
$416$	4.92474	+	2.65406i	0.241455	+	0.130126i
$417$	−66.1930	+	17.7364i	−3.24149	+	0.868554i
$418$	−4.70089	−	3.01378i	−0.229928	−	0.147409i
$419$	−3.87556			−0.189334			−0.0946668	−	0.995509i	$-0.530179\pi$
$419$	−3.87556			−0.189334			−0.0946668	+	0.995509i	$0.530179\pi$
$420$		0			0
$421$	20.7160			1.00964			0.504818	−	0.863226i	$-0.331560\pi$
$421$	20.7160			1.00964			0.504818	+	0.863226i	$0.331560\pi$
$422$	−23.2745	−	14.9215i	−1.13299	−	0.726367i
$423$	18.9230	−	5.07039i	0.920066	−	0.246531i
$424$	−0.339899	−	2.76536i	−0.0165069	−	0.134298i
$425$	6.83773	−	22.0782i	0.331679	−	1.07095i
$426$	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
$430$	8.40376	−	7.36517i	0.405265	−	0.355180i
$431$	−8.46015	−	4.88447i	−0.407511	−	0.235277i	0.282209	−	0.959353i	$-0.408933\pi$
$431$	−8.46015	−	4.88447i	−0.407511	−	0.235277i	−0.689720	+	0.724076i	$0.742266\pi$
$432$	4.31201	+	56.7778i	0.207462	+	2.73172i
$433$	7.00877	−	7.00877i	0.336820	−	0.336820i	−0.518349	−	0.855169i	$-0.673453\pi$
$433$	7.00877	−	7.00877i	0.336820	−	0.336820i	0.855169	+	0.518349i	$0.173453\pi$
$434$		0			0
$435$	24.2981	+	25.2530i	1.16501	+	1.21079i
$436$	0.188544	−	2.02151i	0.00902962	−	0.0968128i
$437$	5.69814	−	1.52681i	0.272579	−	0.0730373i
$438$	−30.2246	−	1.40645i	−1.44419	−	0.0672030i
$439$	−2.21290	−	3.83285i	−0.105616	−	0.182932i	0.808374	−	0.588670i	$-0.200348\pi$
$439$	−2.21290	−	3.83285i	−0.105616	−	0.182932i	−0.913990	+	0.405737i	$0.867015\pi$
$440$	−8.78542	−	1.40668i	−0.418828	−	0.0670610i
$441$		0			0
$442$	−2.96880	−	5.74315i	−0.141211	−	0.273174i
$443$	−1.13928	+	4.25183i	−0.0541286	+	0.202011i	−0.987695	−	0.156395i	$-0.950013\pi$
$443$	−1.13928	+	4.25183i	−0.0541286	+	0.202011i	0.933566	+	0.358405i	$0.116679\pi$
$444$	48.5523	−	22.3023i	2.30419	−	1.05842i
$445$	0.535606	−	0.887745i	0.0253902	−	0.0420831i
$446$	−18.6493	+	4.07840i	−0.883071	+	0.193118i
$447$	−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	$-0.172297\pi$
$450$	42.9976	+	29.9646i	2.02693	+	1.41254i
$451$	4.30514	+	2.48557i	0.202721	+	0.117041i
$452$	−19.6094	−	7.26482i	−0.922348	−	0.341708i
$453$	−63.5411	−	17.0258i	−2.98542	−	0.799941i
$454$	24.8631	+	7.91772i	1.16688	+	0.371597i
$455$		0			0
$456$	15.4186	+	20.4557i	0.722041	+	0.957928i
$457$	−5.70175	+	21.2792i	−0.266717	+	0.995400i	0.694475	+	0.719517i	$0.255637\pi$
$457$	−5.70175	+	21.2792i	−0.266717	+	0.995400i	−0.961191	+	0.275883i	$0.911030\pi$
$458$	1.02664	−	22.0623i	0.0479715	−	1.03090i
$459$	32.9019	−	56.9877i	1.53573	−	2.65996i
$460$	7.34918	−	5.85995i	0.342657	−	0.273222i
$461$	−19.7670			−0.920641			−0.460321	−	0.887753i	$-0.652266\pi$
$461$	−19.7670			−0.920641			−0.460321	+	0.887753i	$0.652266\pi$
$462$		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	$0.908379\pi$
$464$	14.7387	+	12.6581i	0.684228	+	0.587636i
$465$	−25.7563	+	6.37215i	−1.19442	+	0.295501i
$466$	3.99645	−	3.64106i	0.185132	−	0.168669i
$467$	27.2315	+	7.29665i	1.26012	+	0.337649i	0.826239	−	0.563320i	$-0.190476\pi$
$467$	27.2315	+	7.29665i	1.26012	+	0.337649i	0.433884	+	0.900969i	$0.357143\pi$
$468$	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
$472$	−12.3019	+	15.7499i	−0.566242	+	0.724946i
$473$	1.28663	+	4.80176i	0.0591592	+	0.220785i
$474$	2.67157	−	0.584244i	0.122709	−	0.0268352i
$475$	14.0233	+	0.540678i	0.643432	+	0.0248080i
$476$		0			0
$477$	−5.16257	−	5.16257i	−0.236378	−	0.236378i
$478$	11.8118	−	18.4241i	0.540260	−	0.842698i
$479$	−0.709375	+	1.22867i	−0.0324122	+	0.0561395i	−0.881776	−	0.471668i	$-0.843652\pi$
$479$	−0.709375	+	1.22867i	−0.0324122	+	0.0561395i	0.849364	+	0.527807i	$0.176986\pi$
$480$	35.5499	+	20.0519i	1.62262	+	0.915242i
$481$	−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
$485$	−24.3225	−	7.02215i	−1.10443	−	0.318860i
$486$	32.1557	+	35.2944i	1.45861	+	1.60099i
$487$	8.71188	+	32.5132i	0.394773	+	1.47331i	0.822166	+	0.569247i	$0.192765\pi$
$487$	8.71188	+	32.5132i	0.394773	+	1.47331i	−0.427393	+	0.904066i	$0.640568\pi$
$488$	−2.32995	−	5.76471i	−0.105472	−	0.260956i
$489$		−	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	$0.977235\pi$
$492$	−14.5580	−	17.5529i	−0.656324	−	0.791346i
$493$	−5.81103	−	21.6871i	−0.261716	−	0.976736i
$494$	2.90177	−	2.64372i	0.130557	−	0.118946i
$495$	−20.4121	+	11.2662i	−0.917456	+	0.506379i
$496$	−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	0.937269	−	0.348607i	$-0.113345\pi$
$499$	3.72451	+	6.45105i	0.166732	+	0.288789i	−0.770537	+	0.637395i	$0.780012\pi$
$500$	20.8248	−	8.14418i	0.931313	−	0.364219i
$501$	−15.7195	+	27.2270i	−0.702297	+	1.21641i
$502$	30.9883	+	19.8668i	1.38308	+	0.886701i
$503$	19.3043	+	19.3043i	0.860736	+	0.860736i	0.991424	−	0.130687i	$-0.0417184\pi$
$503$	19.3043	+	19.3043i	0.860736	+	0.860736i	−0.130687	+	0.991424i	$0.541718\pi$
$504$		0			0
$505$	−0.259830	+	13.4832i	−0.0115623	+	0.599994i
$506$	0.893334	+	4.08495i	0.0397135	+	0.181598i
$507$	10.0400	+	37.4697i	0.445891	+	1.66409i
$508$	−23.5280	−	8.71658i	−1.04389	−	0.386736i
$509$	9.85817	−	5.69161i	0.436956	−	0.252276i	−0.265350	−	0.964152i	$-0.585487\pi$
$509$	9.85817	−	5.69161i	0.436956	−	0.252276i	0.702305	+	0.711876i	$0.252154\pi$
$510$	−20.8482	−	42.3100i	−0.923176	−	1.87352i
$511$		0			0
$512$	20.6747	+	9.19554i	0.913700	+	0.406390i
$513$	38.5934	+	10.3411i	1.70394	+	0.456570i
$514$	21.9821	+	24.1278i	0.969590	+	1.06423i
$515$	−7.55723	−	30.5465i	−0.333011	−	1.34604i
$516$	2.11775	−	22.7058i	0.0932286	−	0.999568i
$517$	2.62931	+	2.62931i	0.115637	+	0.115637i
$518$		0			0
$519$	79.8313			3.50421
$520$	2.55366	−	5.70966i	0.111986	−	0.250385i
$521$	0.617798	−	1.07006i	0.0270662	−	0.0468801i	−0.852175	−	0.523257i	$-0.824717\pi$
$521$	0.617798	−	1.07006i	0.0270662	−	0.0468801i	0.879241	+	0.476377i	$0.158050\pi$
$522$	50.8554	+	2.36648i	2.22588	+	0.103578i
$523$	−1.63395	+	6.09797i	−0.0714474	+	0.266646i	−0.992404	−	0.123019i	$-0.960742\pi$
$523$	−1.63395	+	6.09797i	−0.0714474	+	0.266646i	0.920957	+	0.389665i	$0.127409\pi$
$524$	21.4548	+	15.2068i	0.937256	+	0.664314i
$525$		0			0
$526$	−4.87059	+	15.2945i	−0.212368	+	0.666872i
$527$	16.4197	+	4.39965i	0.715254	+	0.191652i
$528$	−14.9920	+	10.2433i	−0.652443	+	0.445784i
$529$	16.0929	+	9.29126i	0.699693	+	0.403968i
$530$	−3.05537	+	0.606740i	−0.132717	+	0.0263551i
$531$			52.3691i			2.27262i
$532$		0			0
$533$	−2.47109	+	2.47109i	−0.107035	+	0.107035i
$534$	−0.452033	−	2.06702i	−0.0195614	−	0.0894485i
$535$	43.5413	−	10.7722i	1.88246	−	0.465722i
$536$	−1.10265	−	8.97100i	−0.0476274	−	0.387488i
$537$	−17.1666	+	64.0665i	−0.740792	+	2.76467i
$538$	−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	0.970611	+	0.240656i	$0.0773624\pi$
$541$	16.1355	+	27.9475i	0.693719	+	1.20156i	−0.276891	+	0.960901i	$0.589304\pi$
$542$	−0.0102443	+	0.220149i	−0.000440029	+	0.00945620i
$543$	−24.4975	+	6.56407i	−1.05129	+	0.281691i
$544$	−13.7324	−	22.2531i	−0.588772	−	0.954095i
$545$	−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	$0.0711069\pi$
$548$	8.92341	+	10.7592i	0.381189	+	0.459609i
$549$	−14.1104	−	8.14662i	−0.602215	−	0.347689i
$550$	−0.844882	+	9.91157i	−0.0360259	+	0.422631i
$551$	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
$555$	−28.8658	−	52.2988i	−1.22528	−	2.21996i
$556$	17.7299	+	38.5981i	0.751914	+	1.63692i
$557$	−5.98149	+	1.60273i	−0.253444	+	0.0679101i	−0.383304	−	0.923622i	$-0.625214\pi$
$557$	−5.98149	+	1.60273i	−0.253444	+	0.0679101i	0.129860	+	0.991532i	$0.458547\pi$
$558$	−20.8035	+	32.4493i	−0.880682	+	1.37369i
$559$	−3.49465			−0.147808
$560$		0			0
$561$	20.9833			0.885915
$562$	1.95669	−	3.05205i	0.0825380	−	0.128743i
$563$	−4.96172	+	1.32949i	−0.209112	+	0.0560313i	−0.361854	−	0.932235i	$-0.617856\pi$
$563$	−4.96172	+	1.32949i	−0.209112	+	0.0560313i	0.152742	+	0.988266i	$0.451189\pi$
$564$	−7.12011	−	15.5005i	−0.299811	−	0.652690i
$565$	−6.48523	+	22.4627i	−0.272835	+	0.945014i
$566$	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	$-0.407839\pi$
$569$	30.0136	−	17.3284i	1.25824	−	0.726442i	0.972731	+	0.231935i	$0.0745057\pi$
$570$	21.5382	−	18.8764i	0.902136	−	0.790644i
$571$	−28.9237	−	16.6991i	−1.21042	−	0.698836i	−0.247569	−	0.968870i	$-0.579632\pi$
$571$	−28.9237	−	16.6991i	−1.21042	−	0.698836i	−0.962851	+	0.270034i	$0.912965\pi$
$572$	1.77631	+	2.14174i	0.0742713	+	0.0895508i
$573$	−19.7875	+	19.7875i	−0.826634	+	0.826634i
$574$		0			0
$575$	−7.13910	−	7.71168i	−0.297721	−	0.321599i
$576$	57.5287	−	14.3590i	2.39703	−	0.598292i
$577$	33.2773	−	8.91664i	1.38535	−	0.371204i	0.512291	−	0.858812i	$-0.328797\pi$
$577$	33.2773	−	8.91664i	1.38535	−	0.371204i	0.873063	+	0.487608i	$0.162130\pi$
$578$	−0.287149	+	6.17080i	−0.0119438	+	0.256672i
$579$	−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
$583$	0.358664	−	1.33855i	0.0148544	−	0.0554372i
$584$	2.28792	+	18.6141i	0.0946749	+	0.770259i
$585$	−3.93624	−	15.9104i	−0.162743	−	0.657812i
$586$	2.01292	+	9.20450i	0.0831531	+	0.380234i
$587$	−23.3690	+	23.3690i	−0.964544	+	0.964544i	−0.999393	−	0.0348489i	$-0.988905\pi$
$587$	−23.3690	+	23.3690i	−0.964544	+	0.964544i	0.0348489	+	0.999393i	$0.488905\pi$
$588$		0			0
$589$			10.3214i			0.425288i
$590$	18.5742	+	12.4195i	0.764689	+	0.511301i
$591$	−48.7811	−	28.1638i	−2.00659	−	1.15850i
$592$	−18.6828	−	27.3439i	−0.767859	−	1.12383i
$593$	6.26739	+	1.67934i	0.257371	+	0.0689623i	0.385197	−	0.922834i	$-0.374133\pi$
$593$	6.26739	+	1.67934i	0.257371	+	0.0689623i	−0.127826	+	0.991797i	$0.540800\pi$
$594$	−8.59374	+	26.9859i	−0.352606	+	1.10724i
$595$		0			0
$596$	10.8419	+	7.68459i	0.444101	+	0.314773i
$597$	3.59010	−	13.3984i	0.146933	−	0.548362i
$598$	−2.93636	−	0.136639i	−0.120077	−	0.00558758i
$599$	−8.75860	+	15.1703i	−0.357867	+	0.619843i	−0.987604	−	0.156965i	$-0.949829\pi$
$599$	−8.75860	+	15.1703i	−0.357867	+	0.619843i	0.629737	+	0.776808i	$0.283162\pi$
$600$	19.4300	−	41.2894i	0.793225	−	1.68563i
$601$	2.55297			0.104138			0.0520689	−	0.998643i	$-0.483418\pi$
$601$	2.55297			0.104138			0.0520689	+	0.998643i	$0.483418\pi$
$602$		0			0
$603$	−16.7477	−	16.7477i	−0.682018	−	0.682018i
$604$	−3.78648	+	40.5975i	−0.154070	+	1.65189i
$605$	17.2714	+	10.4204i	0.702183	+	0.423650i
$606$	18.5347	+	20.3438i	0.752920	+	0.826412i
$607$	−21.3783	−	5.72830i	−0.867718	−	0.232504i	−0.202617	−	0.979258i	$-0.564945\pi$
$607$	−21.3783	−	5.72830i	−0.867718	−	0.232504i	−0.665101	+	0.746754i	$0.731611\pi$
$608$	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
$612$	−64.2544	−	23.8048i	−2.59733	−	0.962250i
$613$	2.08760	+	7.79104i	0.0843175	+	0.314677i	0.995184	−	0.0980238i	$-0.0312521\pi$
$613$	2.08760	+	7.79104i	0.0843175	+	0.314677i	−0.910867	+	0.412701i	$0.864585\pi$
$614$	7.19999	+	32.9234i	0.290568	+	1.32868i
$615$	−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	$0.950701\pi$
$618$	−54.0612	−	34.6591i	−2.17466	−	1.39419i
$619$	−15.2502	+	26.4141i	−0.612956	+	1.06167i	0.377784	+	0.925894i	$0.376686\pi$
$619$	−15.2502	+	26.4141i	−0.612956	+	1.06167i	−0.990739	+	0.135777i	$0.956647\pi$
$620$	6.57549	+	15.0740i	0.264078	+	0.605386i
$621$	−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
$625$	−10.7959	−	22.5488i	−0.431834	−	0.901953i
$626$	−1.63964	+	1.49382i	−0.0655330	+	0.0597052i
$627$	3.29753	+	12.3065i	0.131691	+	0.491476i
$628$	22.6874	+	27.3548i	0.905326	+	1.09157i
$629$			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	$-0.160651\pi$
$632$	−0.635173	−	1.57154i	−0.0252658	−	0.0625123i
$633$	16.3264	+	60.9309i	0.648915	+	2.42178i
$634$	28.1349	+	30.8811i	1.11738	+	1.22644i
$635$	−7.78120	+	26.9515i	−0.308787	+	1.06954i
$636$	−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
$640$	8.55024	−	23.8095i	0.337978	−	0.941154i
$641$	−11.2086	+	19.4138i	−0.442712	+	0.766800i	−0.997890	−	0.0649320i	$-0.979317\pi$
$641$	−11.2086	+	19.4138i	−0.442712	+	0.766800i	0.555178	+	0.831732i	$0.312650\pi$
$642$	49.4035	−	77.0595i	1.94980	−	3.04130i
$643$	−3.56268	−	3.56268i	−0.140498	−	0.140498i	0.633359	−	0.773858i	$-0.281675\pi$
$643$	−3.56268	−	3.56268i	−0.140498	−	0.140498i	−0.773858	+	0.633359i	$0.781675\pi$
$644$		0			0
$645$	−25.4913	−	0.491236i	−1.00372	−	0.0193424i
$646$	−17.9249	+	3.91997i	−0.705245	+	0.154229i
$647$	−4.29327	−	16.0227i	−0.168786	−	0.629918i	−0.997527	−	0.0702854i	$-0.977609\pi$
$647$	−4.29327	−	16.0227i	−0.168786	−	0.629918i	0.828741	−	0.559632i	$-0.189058\pi$
$648$	41.2603	−	52.8246i	1.62086	−	2.07515i
$649$	−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
$653$	12.1210	+	3.24782i	0.474332	+	0.127097i	0.488062	−	0.872809i	$-0.337704\pi$
$653$	12.1210	+	3.24782i	0.474332	+	0.127097i	−0.0137300	+	0.999906i	$0.504371\pi$
$654$	−3.42430	+	3.11978i	−0.133901	+	0.121993i
$655$	15.1886	−	25.1744i	0.593467	−	0.983646i
$656$	−9.20918	+	10.7229i	−0.359558	+	0.418660i
$657$	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	$0.725284\pi$
$660$	12.6560	+	15.8724i	0.492635	+	0.617832i
$661$	3.47890	−	6.02563i	0.135313	−	0.234370i	−0.790404	−	0.612586i	$-0.790129\pi$
$661$	3.47890	−	6.02563i	0.135313	−	0.234370i	0.925717	+	0.378217i	$0.123463\pi$
$662$	−0.830422	+	17.8457i	−0.0322753	+	0.693593i
$663$	−3.81784	+	14.2484i	−0.148273	+	0.553361i
$664$	−10.9251	−	14.4943i	−0.423977	−	0.562488i
$665$		0			0
$666$	−82.6892	−	26.3327i	−3.20414	−	1.02037i
$667$	−9.86062	−	2.64214i	−0.381805	−	0.102304i
$668$	18.2730	+	6.76973i	0.707005	+	0.261929i
$669$	37.7211	+	21.7783i	1.45838	+	0.841997i
$670$	−9.91181	+	1.96830i	−0.382927	+	0.0760421i
$671$		−	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	$0.296575\pi$
$674$	−8.02127	+	1.75416i	−0.308968	+	0.0675679i
$675$	−15.7594	−	69.4100i	−0.606579	−	2.67159i
$676$	21.8491	−	10.0363i	0.840350	−	0.386012i
$677$	7.76868	−	28.9931i	0.298575	−	1.11430i	−0.639762	−	0.768573i	$-0.720967\pi$
$677$	7.76868	−	28.9931i	0.298575	−	1.11430i	0.938337	−	0.345723i	$-0.112366\pi$
$678$	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
$682$	−7.30825	−	0.340078i	−0.279847	−	0.0130223i
$683$	18.3967	−	4.92938i	0.703930	−	0.188618i	0.110940	−	0.993827i	$-0.464614\pi$
$683$	18.3967	−	4.92938i	0.703930	−	0.188618i	0.592990	+	0.805210i	$0.297947\pi$
$684$	3.86372	−	41.4257i	0.147733	−	1.58395i
$685$	11.2615	−	10.8357i	0.430281	−	0.414010i
$686$		0			0
$687$	−35.6329	+	35.6329i	−1.35948	+	1.35948i
$688$	−14.0941	+	1.07038i	−0.537334	+	0.0408080i
$689$	0.843665	+	0.487090i	0.0321411	+	0.0185567i
$690$	−21.3997	−	1.40945i	−0.814673	−	0.0536570i
$691$	24.4705	−	14.1281i	0.930903	−	0.537457i	0.0438058	−	0.999040i	$-0.486052\pi$
$691$	24.4705	−	14.1281i	0.930903	−	0.537457i	0.887097	+	0.461583i	$0.152718\pi$
$692$	−8.31284	−	48.7782i	−0.316007	−	1.85427i
$693$		0			0
$694$	−19.9020	−	6.33786i	−0.755470	−	0.240582i
$695$	41.5765	−	22.9477i	1.57709	−	0.870455i
$696$	−5.40781	−	43.9970i	−0.204983	−	1.66770i
$697$	15.7781	−	4.22772i	0.597638	−	0.160136i
$698$	6.01445	+	3.85591i	0.227650	+	0.145948i
$699$	−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	$0.663472\pi$
$702$	−16.7607	−	10.7454i	−0.632593	−	0.405560i
$703$	−22.4459	+	6.01436i	−0.846563	+	0.226836i
$704$	7.81996	+	8.09370i	0.294726	+	0.305043i
$705$	−16.6966	+	9.21551i	−0.628831	+	0.347076i
$706$	−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	$-0.559416\pi$
$709$	15.2471	−	8.80290i	0.572616	−	0.330600i	0.758193	+	0.652030i	$0.226082\pi$
$710$	−38.4619	−	2.53323i	−1.44345	−	0.0950703i
$711$	−3.84667	−	2.22087i	−0.144261	−	0.0832893i
$712$	−1.21591	+	0.491438i	−0.0455681	+	0.0184174i
$713$	5.46525	−	5.46525i	0.204675	−	0.204675i
$714$		0			0
$715$	2.24174	−	2.15697i	0.0838363	−	0.0806663i
$716$	40.9332	+	3.81779i	1.52975	+	0.142678i
$717$	−48.2328	+	12.9239i	−1.80129	+	0.482653i
$718$	7.04445	+	0.327803i	0.262897	+	0.0122335i
$719$	−11.5866	−	20.0685i	−0.432106	−	0.748429i	0.564949	−	0.825126i	$-0.308896\pi$
$719$	−11.5866	−	20.0685i	−0.432106	−	0.748429i	−0.997054	+	0.0766969i	$0.975563\pi$
$720$	−20.7483	−	62.9617i	−0.773243	−	2.34644i
$721$		0			0
$722$	7.22290	+	13.9727i	0.268809	+	0.520011i
$723$	−24.0202	+	89.6445i	−0.893320	+	3.33391i
$724$	6.56167	+	14.2848i	0.243863	+	0.530891i
$725$	−20.5482	−	12.9439i	−0.763143	−	0.480725i
$726$	40.2146	−	8.79448i	1.49250	−	0.326394i
$727$	15.3777	−	15.3777i	0.570326	−	0.570326i	−0.361893	−	0.932220i	$-0.617869\pi$
$727$	15.3777	−	15.3777i	0.570326	−	0.570326i	0.932220	+	0.361893i	$0.117869\pi$
$728$		0			0
$729$		−	37.8443i		−	1.40164i
$730$	20.5663	−	4.08408i	0.761192	−	0.151159i
$731$	14.1462	+	8.16734i	0.523218	+	0.302080i
$732$	−4.92847	+	13.3031i	−0.182162	+	0.491695i
$733$	40.3490	+	10.8115i	1.49032	+	0.399331i	0.909847	−	0.414944i	$-0.136199\pi$
$733$	40.3490	+	10.8115i	1.49032	+	0.399331i	0.580478	+	0.814276i	$0.302866\pi$
$734$	−21.4725	−	6.83800i	−0.792566	−	0.252395i
$735$		0			0
$736$	−11.8844	+	0.348310i	−0.438063	+	0.0128389i
$737$	1.16353	−	4.34235i	0.0428592	−	0.159953i
$738$	−1.72169	+	36.9990i	−0.0633764	+	1.36195i
$739$	−14.4738	+	25.0693i	−0.532426	+	0.922189i	0.466857	+	0.884333i	$0.345386\pi$
$739$	−14.4738	+	25.0693i	−0.532426	+	0.922189i	−0.999283	+	0.0378565i	$0.987947\pi$
$740$	−28.9496	+	23.0833i	−1.06421	+	0.848559i
$741$	−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	$0.542243\pi$
$744$	30.8954	+	13.1097i	1.13268	+	0.480625i
$745$	7.67535	−	12.7216i	0.281203	−	0.466082i
$746$	−0.615954	+	0.561178i	−0.0225517	+	0.0205462i
$747$	−45.9417	−	12.3100i	−1.68092	−	0.450401i
$748$	−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	$-0.963462\pi$
$751$	−38.1178	+	22.0073i	−1.39094	+	0.803059i	−0.397520	+	0.917593i	$0.630129\pi$
$752$	−8.72964	+	5.96457i	−0.318337	+	0.217505i
$753$	−21.7373	−	81.1249i	−0.792153	−	2.95636i
$754$	−6.63623	+	1.45127i	−0.241677	+	0.0528521i
$755$	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	$0.531019\pi$
$758$	18.1341	−	28.2855i	0.658659	−	1.02738i
$759$	4.77032	−	8.26243i	0.173152	−	0.299907i
$760$	−13.7765	−	11.1946i	−0.499727	−	0.406070i
$761$	2.24848	+	3.89448i	0.0815073	+	0.141175i	0.903898	−	0.427749i	$-0.140693\pi$
$761$	2.24848	+	3.89448i	0.0815073	+	0.141175i	−0.822390	+	0.568924i	$0.807360\pi$
$762$	26.2885	+	50.8551i	0.952331	+	1.84229i
$763$		0			0
$764$	14.1509	+	10.0300i	0.511963	+	0.362872i
$765$	−21.2503	+	73.6040i	−0.768304	+	2.66116i
$766$	−4.09169	−	4.49108i	−0.147839	−	0.162269i
$767$	−1.80855	−	6.74959i	−0.0653029	−	0.243714i
$768$	−20.7400	−	47.2784i	−0.748391	−	1.70601i
$769$		−	14.9079i		−	0.537593i	−0.963197	−	0.268797i	$-0.913374\pi$
$769$		−	14.9079i		−	0.537593i	0.963197	−	0.268797i	$-0.0866259\pi$
$770$		0			0
$771$		−	74.4723i		−	2.68206i
$772$	−8.16757	+	6.77398i	−0.293957	+	0.243801i
$773$	7.16881	+	26.7544i	0.257844	+	0.962287i	0.966486	+	0.256719i	$0.0826415\pi$
$773$	7.16881	+	26.7544i	0.257844	+	0.962287i	−0.708642	+	0.705568i	$0.750692\pi$
$774$	−27.3797	+	24.9449i	−0.984143	+	0.896624i
$775$	16.2659	−	8.57314i	0.584288	−	0.307956i
$776$	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
$780$	−13.0806	+	5.70595i	−0.468361	+	0.204306i
$781$	8.57374	−	14.8502i	0.306793	−	0.531380i
$782$	11.5669	+	7.41566i	0.413633	+	0.265183i
$783$	−48.8906	−	48.8906i	−1.74721	−	1.74721i
$784$		0			0
$785$	28.6320	−	27.5493i	1.02192	−	0.983277i
$786$	−12.8186	−	58.6158i	−0.457226	−	2.09076i
$787$	−1.45499	−	5.43008i	−0.0518646	−	0.193561i	0.935133	−	0.354297i	$-0.115280\pi$
$787$	−1.45499	−	5.43008i	−0.0518646	−	0.193561i	−0.986997	+	0.160736i	$0.948613\pi$
$788$	−12.1289	+	32.7387i	−0.432075	+	1.16627i
$789$	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
$793$	2.09996	+	0.562681i	0.0745716	+	0.0199814i
$794$	−3.68582	−	4.04559i	−0.130805	−	0.143572i
$795$	6.08554	+	3.67161i	0.215832	+	0.130219i
$796$	−8.56049	−	0.798427i	−0.303419	−	0.0282995i
$797$	−10.9874	−	10.9874i	−0.389195	−	0.389195i	0.485205	−	0.874400i	$-0.338745\pi$
$797$	−10.9874	−	10.9874i	−0.389195	−	0.389195i	−0.874400	+	0.485205i	$0.838745\pi$
$798$		0			0
$799$	12.2183			0.432252
$800$	−27.2517	−	7.57254i	−0.963494	−	0.267730i
$801$	−1.71830	+	2.97619i	−0.0607133	+	0.105159i
$802$	−7.75180	−	0.360718i	−0.273726	−	0.0127374i
$803$	−2.41424	+	9.01005i	−0.0851965	+	0.317958i
$804$	−11.9253	+	16.8249i	−0.420572	+	0.593369i
$805$		0			0
$806$	1.56063	−	4.90067i	0.0549710	−	0.172619i
$807$	84.8316	+	22.7306i	2.98621	+	0.800154i
$808$	10.5004	−	13.4434i	0.369402	−	0.472936i
$809$	−14.4297	−	8.33096i	−0.507320	−	0.292901i	0.224412	−	0.974494i	$-0.427954\pi$
$809$	−14.4297	−	8.33096i	−0.507320	−	0.292901i	−0.731731	+	0.681593i	$0.761287\pi$
$810$	−62.2974	−	41.6545i	−2.18891	−	1.46359i
$811$			30.5372i			1.07231i	0.844120	+	0.536154i	$0.180123\pi$
$811$			30.5372i			1.07231i	−0.844120	+	0.536154i	$0.819877\pi$
$812$		0			0
$813$	0.355563	−	0.355563i	0.0124701	−	0.0124701i
$814$	−3.51899	−	16.0913i	−0.123341	−	0.564000i
$815$	9.33771	+	37.7432i	0.327086	+	1.32209i
$816$	−11.0334	+	58.6338i	−0.386246	+	2.05259i
$817$	−2.56700	+	9.58017i	−0.0898079	+	0.335168i
$818$	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	0.981015	−	0.193933i	$-0.0621243\pi$
$821$	9.24225	+	16.0080i	0.322557	+	0.558685i	−0.658458	+	0.752617i	$0.728791\pi$
$822$	1.48248	−	31.8584i	0.0517075	−	1.11119i
$823$	41.3323	−	11.0750i	1.44075	−	0.386049i	0.547957	−	0.836507i	$-0.315406\pi$
$823$	41.3323	−	11.0750i	1.44075	−	0.386049i	0.892798	+	0.450457i	$0.148739\pi$
$824$	−15.5478	+	36.6413i	−0.541634	+	1.27646i
$825$	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	$0.439427\pi$
$828$	−23.9809	+	19.8892i	−0.833395	+	0.691198i
$829$	−29.0025	−	16.7446i	−1.00730	−	0.581563i	−0.0968981	−	0.995294i	$-0.530892\pi$
$829$	−29.0025	−	16.7446i	−1.00730	−	0.581563i	−0.910399	+	0.413731i	$0.864225\pi$
$830$	−15.2613	+	13.3752i	−0.529728	+	0.464260i
$831$	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
$835$	6.04327	−	20.9319i	0.209136	−	0.724379i
$836$	7.17612	−	3.29632i	0.248191	−	0.114006i
$837$	50.5649	−	13.5488i	1.74778	−	0.468316i
$838$	2.95811	−	4.61406i	0.102186	−	0.159390i
$839$	6.43773			0.222255			0.111127	−	0.993806i	$-0.464554\pi$
$839$	6.43773			0.222255			0.111127	+	0.993806i	$0.464554\pi$
$840$		0			0
$841$	5.40897			0.186516
$842$	−15.8119	+	24.6635i	−0.544916	+	0.849959i
$843$	−7.99001	+	2.14092i	−0.275190	+	0.0737371i
$844$	35.5296	−	16.3204i	1.22298	−	0.561772i
$845$	−12.9899	−	23.5351i	−0.446867	−	0.809631i
$846$	−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
$850$	21.0663	+	24.9924i	0.722567	+	0.857232i
$851$	15.0698	+	8.70057i	0.516587	+	0.298252i
$852$	−60.5471	+	50.2163i	−2.07431	+	1.72038i
$853$	10.0581	−	10.0581i	0.344383	−	0.344383i	−0.513629	−	0.858012i	$-0.671699\pi$
$853$	10.0581	−	10.0581i	0.344383	−	0.344383i	0.858012	+	0.513629i	$0.171699\pi$
$854$		0			0
$855$	−46.5077	−	0.896235i	−1.59053	−	0.0306506i
$856$	−52.2289	−	22.1621i	−1.78515	−	0.757484i
$857$	0.503168	−	0.134823i	0.0171879	−	0.00460548i	−0.250215	−	0.968190i	$-0.580501\pi$
$857$	0.503168	−	0.134823i	0.0171879	−	0.00460548i	0.267403	+	0.963585i	$0.413835\pi$
$858$	0.295106	−	6.34180i	0.0100747	−	0.216506i
$859$	−2.00473	−	3.47230i	−0.0684006	−	0.118473i	0.829797	−	0.558066i	$-0.188456\pi$
$859$	−2.00473	−	3.47230i	−0.0684006	−	0.118473i	−0.898197	+	0.439592i	$0.855123\pi$
$860$	2.35426	+	15.6267i	0.0802796	+	0.532868i
$861$		0			0
$862$	12.2726	−	6.34407i	0.418007	−	0.216080i
$863$	−3.83800	+	14.3236i	−0.130647	+	0.487581i	−0.999978	−	0.00664926i	$-0.997883\pi$
$863$	−3.83800	+	14.3236i	−0.130647	+	0.487581i	0.869331	+	0.494231i	$0.164550\pi$
$864$	−70.8882	−	38.2032i	−2.41166	−	1.29970i
$865$	−53.7029	+	13.2861i	−1.82595	+	0.451742i
$866$	2.99471	+	13.6939i	0.101764	+	0.465338i
$867$	9.96649	−	9.96649i	0.338480	−	0.338480i
$868$		0			0
$869$		−	0.843073i		−	0.0285993i
$870$	−48.6111	+	9.65327i	−1.64807	+	0.327276i
$871$	2.73690	+	1.58015i	0.0927364	+	0.0535414i
$872$	2.26280	+	1.76744i	0.0766282	+	0.0598529i
$873$	81.0531	+	21.7181i	2.74323	+	0.735046i
$874$	−2.53148	+	7.94930i	−0.0856287	+	0.268889i
$875$		0			0
$876$	24.7440	−	34.9104i	0.836024	−	1.17951i
$877$	−8.02646	+	29.9552i	−0.271034	+	1.01151i	0.687418	+	0.726262i	$0.258744\pi$
$877$	−8.02646	+	29.9552i	−0.271034	+	1.01151i	−0.958453	+	0.285252i	$0.907923\pi$
$878$	6.25225	+	0.290939i	0.211003	+	0.00981871i
$879$	10.7488	−	18.6175i	0.362548	−	0.627952i
$880$	8.38040	−	9.38582i	0.282503	−	0.316396i
$881$	26.6186			0.896802			0.448401	−	0.893833i	$-0.351994\pi$
$881$	26.6186			0.896802			0.448401	+	0.893833i	$0.351994\pi$
$882$		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	$0.589722\pi$
$884$	9.10352	+	0.849075i	0.306185	+	0.0285575i
$885$	−12.2435	−	49.4883i	−0.411559	−	1.66353i
$886$	−4.19245	−	4.60167i	−0.140848	−	0.154596i
$887$	−41.2767	−	11.0601i	−1.38594	−	0.371361i	−0.512663	−	0.858590i	$-0.671341\pi$
$887$	−41.2767	−	11.0601i	−1.38594	−	0.371361i	−0.873274	+	0.487229i	$0.838008\pi$
$888$	−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
$892$	9.37896	−	25.3159i	0.314031	−	0.847640i
$893$	1.92011	+	7.16594i	0.0642540	+	0.239799i
$894$	−6.47774	−	29.6208i	−0.216648	−	0.990667i
$895$	0.885581	−	45.9548i	0.0296017	−	1.53610i
$896$		0			0
$897$	4.74253	+	4.74253i	0.158348	+	0.158348i
$898$	25.9963	+	16.6664i	0.867508	+	0.556166i
$899$	8.93063	−	15.4683i	0.297853	−	0.515897i
$900$	−68.4933	+	28.3198i	−2.28311	+	0.943992i
$901$	−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
$905$	15.3871	−	8.49273i	0.511484	−	0.282308i
$906$	68.7692	−	62.6537i	2.28471	−	2.08153i
$907$	0.317430	+	1.18466i	0.0105401	+	0.0393361i	0.970996	−	0.239097i	$-0.0768515\pi$
$907$	0.317430	+	1.18466i	0.0105401	+	0.0393361i	−0.960456	+	0.278433i	$0.910185\pi$
$908$	−28.4037	+	23.5574i	−0.942611	+	0.781780i
$909$		−	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	$0.928620\pi$
$912$	−36.1222	+	2.74331i	−1.19613	+	0.0908401i
$913$	−2.33653	−	8.72004i	−0.0773277	−	0.288591i
$914$	−20.9820	−	23.0301i	−0.694024	−	0.761767i
$915$	15.2388	+	4.39960i	0.503778	+	0.145446i
$916$	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	0.997124	−	0.0757845i	$-0.0241461\pi$
$919$	13.1243	+	22.7320i	0.432931	+	0.749858i	−0.564193	+	0.825643i	$0.690813\pi$
$920$	1.36716	+	13.2223i	0.0450738	+	0.435927i
$921$	38.4473	−	66.5926i	1.26688	−	2.19430i
$922$	15.0876	−	23.5337i	0.496884	−	0.775040i
$923$	8.52380	+	8.52380i	0.280564	+	0.280564i
$924$		0			0
$925$	28.1221	+	30.3776i	0.924649	+	0.998809i
$926$	28.3772	−	6.20577i	0.932532	−	0.203934i
$927$	26.9955	+	100.748i	0.886647	+	3.30901i
$928$	−26.3197	+	7.88567i	−0.863988	+	0.258860i
$929$	17.2412	−	9.95422i	0.565666	−	0.326587i	−0.189751	−	0.981832i	$-0.560768\pi$
$929$	17.2412	−	9.95422i	0.565666	−	0.326587i	0.755416	+	0.655245i	$0.227435\pi$
$930$	12.0727	−	35.5280i	0.395881	−	1.16501i
$931$		0			0
$932$	1.28448	+	7.53711i	0.0420747	+	0.246886i
$933$	−56.6067	−	15.1677i	−1.85322	−	0.496569i
$934$	−29.4721	+	26.8512i	−0.964356	+	0.878597i
$935$	−14.1155	+	3.49220i	−0.461628	+	0.114207i
$936$	−8.09820	+	19.0849i	−0.264698	+	0.623809i
$937$	−3.76752	−	3.76752i	−0.123080	−	0.123080i	0.642884	−	0.765964i	$-0.277738\pi$
$937$	−3.76752	−	3.76752i	−0.123080	−	0.123080i	−0.765964	+	0.642884i	$0.777738\pi$
$938$		0			0
$939$	5.06087			0.165155
$940$	7.36944	+	9.24228i	0.240365	+	0.301450i
$941$	−2.41962	+	4.19090i	−0.0788772	+	0.136619i	−0.902766	−	0.430133i	$-0.858467\pi$
$941$	−2.41962	+	4.19090i	−0.0788772	+	0.136619i	0.823889	+	0.566752i	$0.191800\pi$
$942$	3.76915	−	80.9988i	0.122806	−	2.63908i
$943$	1.92225	−	7.17394i	0.0625971	−	0.233616i
$944$	−9.36132	−	26.6675i	−0.304685	−	0.867954i
$945$		0			0
$946$	−6.69879	−	2.13325i	−0.217797	−	0.0693580i
$947$	−29.9595	−	8.02761i	−0.973551	−	0.260862i	−0.263225	−	0.964735i	$-0.584786\pi$
$947$	−29.9595	−	8.02761i	−0.973551	−	0.260862i	−0.710327	+	0.703872i	$0.751453\pi$
$948$	−1.34357	+	3.62659i	−0.0436370	+	0.117786i
$949$	−5.67887	−	3.27870i	−0.184344	−	0.106431i
$950$	−11.3473	+	16.2828i	−0.368155	+	0.528283i
$951$		−	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	$0.0789947\pi$
$954$	10.0868	−	2.20586i	0.326571	−	0.0714174i
$955$	10.0179	−	16.6043i	0.324173	−	0.537303i
$956$	12.9192	+	28.1252i	0.417837	+	0.909634i
$957$	5.70637	−	21.2965i	0.184461	−	0.688417i
$958$	−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
$962$	11.5668	+	0.538243i	0.372929	+	0.0173537i
$963$	−143.608	+	38.4796i	−4.62770	+	1.23999i
$964$	57.2754	+	5.34201i	1.84472	+	0.172055i
$965$	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	$0.314544\pi$
$968$	−9.56111	−	23.6560i	−0.307306	−	0.760331i
$969$	36.2558	+	20.9323i	1.16470	+	0.672442i
$970$	26.9249	−	23.5973i	0.864506	−	0.757665i
$971$	8.19063	−	4.72886i	0.262850	−	0.151756i	−0.362784	−	0.931873i	$-0.618174\pi$
$971$	8.19063	−	4.72886i	0.262850	−	0.151756i	0.625634	+	0.780117i	$0.284840\pi$
$972$	−66.5634	+	11.3438i	−2.13502	+	0.363854i
$973$		0			0
$974$	−45.3582	−	14.4445i	−1.45337	−	0.462831i
$975$	7.43942	+	14.1149i	0.238252	+	0.452038i
$976$	8.64158	+	1.62613i	0.276610	+	0.0520510i
$977$	59.6654	−	15.9873i	1.90886	−	0.511479i	0.914624	−	0.404305i	$-0.132487\pi$
$977$	59.6654	−	15.9873i	1.90886	−	0.511479i	0.994240	−	0.107173i	$-0.0341799\pi$
$978$	66.7980	+	42.8247i	2.13596	+	1.36938i
$979$	−0.652291			−0.0208473
$980$		0			0
$981$	7.52393			0.240221
$982$	−3.77016	−	2.41708i	−0.120311	−	0.0771321i
$983$	57.3012	−	15.3538i	1.82762	−	0.489710i	0.829947	−	0.557842i	$-0.188370\pi$
$983$	57.3012	−	15.3538i	1.82762	−	0.489710i	0.997676	+	0.0681315i	$0.0217038\pi$
$984$	32.0094	−	3.93437i	1.02042	−	0.125423i
$985$	37.5025	+	10.8274i	1.19493	+	0.344989i
$986$	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
$990$	2.16696	−	32.9009i	0.0688704	−	1.04566i
$991$	−15.0202	−	8.67190i	−0.477131	−	0.275472i	0.242089	−	0.970254i	$-0.422167\pi$
$991$	−15.0202	−	8.67190i	−0.477131	−	0.275472i	−0.719220	+	0.694782i	$0.755501\pi$
$992$	4.79309	−	20.2427i	0.152181	−	0.642706i
$993$	28.8227	−	28.8227i	0.914660	−	0.914660i
$994$		0			0
$995$	−0.185204	+	9.61068i	−0.00587137	+	0.304679i
$996$	−3.84584	+	41.2340i	−0.121860	+	1.30655i
$997$	−14.9024	+	3.99308i	−0.471964	+	0.126462i	−0.486958	−	0.873425i	$-0.661894\pi$
$997$	−14.9024	+	3.99308i	−0.471964	+	0.126462i	0.0149945	+	0.999888i	$0.495227\pi$
$998$	−10.5231	−	0.489677i	−0.333104	−	0.0155005i
$999$	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.k.67.7		72
4.3	odd	2	inner	980.2.x.k.67.10		72
5.3	odd	4	inner	980.2.x.k.263.16		72
7.2	even	3	inner	980.2.x.k.667.18		72
7.3	odd	6		980.2.k.l.687.6		36
7.4	even	3		140.2.k.a.127.6	yes	36
7.5	odd	6		980.2.x.l.667.18		72
7.6	odd	2		980.2.x.l.67.7		72
20.3	even	4	inner	980.2.x.k.263.18		72
28.3	even	6		980.2.k.l.687.3		36
28.11	odd	6		140.2.k.a.127.3	yes	36
28.19	even	6		980.2.x.l.667.16		72
28.23	odd	6	inner	980.2.x.k.667.16		72
28.27	even	2		980.2.x.l.67.10		72
35.3	even	12		980.2.k.l.883.3		36
35.4	even	6		700.2.k.b.407.13		36
35.13	even	4		980.2.x.l.263.16		72
35.18	odd	12		140.2.k.a.43.3	✓	36
35.23	odd	12	inner	980.2.x.k.863.10		72
35.32	odd	12		700.2.k.b.43.16		36
35.33	even	12		980.2.x.l.863.10		72
140.3	odd	12		980.2.k.l.883.6		36
140.23	even	12	inner	980.2.x.k.863.7		72
140.39	odd	6		700.2.k.b.407.16		36
140.67	even	12		700.2.k.b.43.13		36
140.83	odd	4		980.2.x.l.263.18		72
140.103	odd	12		980.2.x.l.863.7		72
140.123	even	12		140.2.k.a.43.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.3	✓	36	35.18	odd	12
140.2.k.a.43.6	yes	36	140.123	even	12
140.2.k.a.127.3	yes	36	28.11	odd	6
140.2.k.a.127.6	yes	36	7.4	even	3
700.2.k.b.43.13		36	140.67	even	12
700.2.k.b.43.16		36	35.32	odd	12
700.2.k.b.407.13		36	35.4	even	6
700.2.k.b.407.16		36	140.39	odd	6
980.2.k.l.687.3		36	28.3	even	6
980.2.k.l.687.6		36	7.3	odd	6
980.2.k.l.883.3		36	35.3	even	12
980.2.k.l.883.6		36	140.3	odd	12
980.2.x.k.67.7		72	1.1	even	1	trivial
980.2.x.k.67.10		72	4.3	odd	2	inner
980.2.x.k.263.16		72	5.3	odd	4	inner
980.2.x.k.263.18		72	20.3	even	4	inner
980.2.x.k.667.16		72	28.23	odd	6	inner
980.2.x.k.667.18		72	7.2	even	3	inner
980.2.x.k.863.7		72	140.23	even	12	inner
980.2.x.k.863.10		72	35.23	odd	12	inner
980.2.x.l.67.7		72	7.6	odd	2
980.2.x.l.67.10		72	28.27	even	2
980.2.x.l.263.16		72	35.13	even	4
980.2.x.l.263.18		72	140.83	odd	4
980.2.x.l.667.16		72	28.19	even	6
980.2.x.l.667.18		72	7.5	odd	6
980.2.x.l.863.7		72	140.103	odd	12
980.2.x.l.863.10		72	35.33	even	12

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)

\(f(q)\)	\(=\)	\(q+(-0.763272 + 1.19055i) q^{2} +(3.11677 - 0.835136i) q^{3} +(-0.834830 - 1.81743i) q^{4} +(-1.95767 + 1.08052i) q^{5} +(-1.38467 + 4.34811i) q^{6} +(2.80095 + 0.393286i) q^{8} +(6.41872 - 3.70585i) q^{9} +O(q^{10})\)	\(q+(-0.763272 + 1.19055i) q^{2} +(3.11677 - 0.835136i) q^{3} +(-0.834830 - 1.81743i) q^{4} +(-1.95767 + 1.08052i) q^{5} +(-1.38467 + 4.34811i) q^{6} +(2.80095 + 0.393286i) q^{8} +(6.41872 - 3.70585i) q^{9} +(0.207827 - 3.15544i) q^{10} +(1.21832 + 0.703395i) q^{11} +(-4.11978 - 4.96732i) q^{12} +(-0.699298 + 0.699298i) q^{13} +(-5.19924 + 5.00264i) q^{15} +(-2.60612 + 3.03449i) q^{16} +(4.46506 - 1.19641i) q^{17} +(-0.487224 + 10.4704i) q^{18} +(1.40337 + 2.43071i) q^{19} +(3.59809 + 2.65589i) q^{20} +(-1.76734 + 0.913587i) q^{22} +(0.543980 - 2.03016i) q^{23} +(9.05837 - 1.11339i) q^{24} +(2.66497 - 4.23059i) q^{25} +(-0.298796 - 1.36631i) q^{26} +(10.0659 - 10.0659i) q^{27} -4.85706i q^{29} +(-1.98747 - 10.0083i) q^{30} +(3.18470 + 1.83869i) q^{31} +(-1.62355 - 5.41886i) q^{32} +(4.38464 + 1.17486i) q^{33} +(-1.98367 + 6.22907i) q^{34} +(-12.0937 - 8.57184i) q^{36} +(-2.14283 + 7.99714i) q^{37} +(-3.96504 - 0.184507i) q^{38} +(-1.59554 + 2.76356i) q^{39} +(-5.90830 + 2.25655i) q^{40} +3.53368 q^{41} +(2.49869 + 2.49869i) q^{43} +(0.261285 - 2.80142i) q^{44} +(-8.56153 + 14.1904i) q^{45} +(2.00181 + 2.19720i) q^{46} +(2.55312 + 0.684106i) q^{47} +(-5.58845 + 11.6343i) q^{48} +(3.00265 + 6.40188i) q^{50} +(12.9174 - 7.45786i) q^{51} +(1.85472 + 0.687131i) q^{52} +(-0.254952 - 0.951495i) q^{53} +(4.30095 + 19.6670i) q^{54} +(-3.14510 - 0.0606082i) q^{55} +(6.40395 + 6.40395i) q^{57} +(5.78258 + 3.70726i) q^{58} +(-3.53286 + 6.11910i) q^{59} +(13.4324 + 5.27291i) q^{60} +(-1.09916 - 1.90379i) q^{61} +(-4.61985 + 2.38814i) q^{62} +(7.69065 + 2.20315i) q^{64} +(0.613394 - 2.12460i) q^{65} +(-4.74541 + 4.32341i) q^{66} +(-0.827081 - 3.08671i) q^{67} +(-5.90196 - 7.11614i) q^{68} -6.78184i q^{69} -12.1891i q^{71} +(19.4360 - 7.85551i) q^{72} +(1.71613 + 6.40469i) q^{73} +(-7.88545 - 8.65515i) q^{74} +(4.77298 - 15.4114i) q^{75} +(3.24607 - 4.57976i) q^{76} +(-2.07233 - 4.00892i) q^{78} +(-0.299644 - 0.518999i) q^{79} +(1.82311 - 8.75650i) q^{80} +(11.8491 - 20.5233i) q^{81} +(-2.69716 + 4.20703i) q^{82} +(-4.53764 - 4.53764i) q^{83} +(-7.44839 + 7.16674i) q^{85} +(-4.88200 + 1.06764i) q^{86} +(-4.05630 - 15.1383i) q^{87} +(3.13581 + 2.44932i) q^{88} +(-0.401553 + 0.231837i) q^{89} +(-10.3596 - 21.0241i) q^{90} +(-4.14381 + 0.706194i) q^{92} +(11.4615 + 3.07111i) q^{93} +(-2.76319 + 2.51746i) q^{94} +(-5.37376 - 3.24217i) q^{95} +(-9.58571 - 15.5335i) 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

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