LMFDB - Embedded newform 980.2.x.k.263.16

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			263.16
Character	$\chi$	$=$	980.263
Dual form			980.2.x.k.667.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19055 + 0.763272i) q^{2} +(0.835136 + 3.11677i) q^{3} +(0.834830 + 1.81743i) q^{4} +(1.91459 - 1.15514i) q^{5} +(-1.38467 + 4.34811i) q^{6} +(-0.393286 + 2.80095i) q^{8} +(-6.41872 + 3.70585i) q^{9} +O(q^{10})$	\(q+(1.19055 + 0.763272i) q^{2} +(0.835136 + 3.11677i) q^{3} +(0.834830 + 1.81743i) q^{4} +(1.91459 - 1.15514i) q^{5} +(-1.38467 + 4.34811i) q^{6} +(-0.393286 + 2.80095i) q^{8} +(-6.41872 + 3.70585i) q^{9} +(3.16111 + 0.0861032i) q^{10} +(1.21832 + 0.703395i) q^{11} +(-4.96732 + 4.11978i) q^{12} +(-0.699298 - 0.699298i) q^{13} +(5.19924 + 5.00264i) q^{15} +(-2.60612 + 3.03449i) q^{16} +(-1.19641 - 4.46506i) q^{17} +(-10.4704 - 0.487224i) q^{18} +(-1.40337 - 2.43071i) q^{19} +(3.69774 + 2.51529i) q^{20} +(0.913587 + 1.76734i) q^{22} +(2.03016 + 0.543980i) q^{23} +(-9.05837 + 1.11339i) q^{24} +(2.33132 - 4.42323i) q^{25} +(-0.298796 - 1.36631i) q^{26} +(-10.0659 - 10.0659i) q^{27} +4.85706i q^{29} +(2.37159 + 9.92434i) q^{30} +(3.18470 + 1.83869i) q^{31} +(-5.41886 + 1.62355i) 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} +(0.184507 - 3.96504i) q^{38} +(1.59554 - 2.76356i) q^{39} +(2.48250 + 5.81697i) q^{40} +3.53368 q^{41} +(-2.49869 + 2.49869i) q^{43} +(-0.261285 + 2.80142i) q^{44} +(-8.00846 + 14.5097i) q^{45} +(2.00181 + 2.19720i) q^{46} +(0.684106 - 2.55312i) q^{47} +(-11.6343 - 5.58845i) q^{48} +(6.15168 - 3.48666i) q^{50} +(12.9174 - 7.45786i) q^{51} +(0.687131 - 1.85472i) q^{52} +(0.951495 - 0.254952i) q^{53} +(-4.30095 - 19.6670i) q^{54} +(3.14510 - 0.0606082i) q^{55} +(6.40395 - 6.40395i) q^{57} +(-3.70726 + 5.78258i) q^{58} +(3.53286 - 6.11910i) q^{59} +(-4.75148 + 13.6256i) q^{60} +(-1.09916 - 1.90379i) q^{61} +(2.38814 + 4.61985i) q^{62} +(-7.69065 - 2.20315i) q^{64} +(-2.14665 - 0.531084i) q^{65} +(-4.74541 + 4.32341i) q^{66} +(-3.08671 + 0.827081i) q^{67} +(7.11614 - 5.90196i) q^{68} +6.78184i q^{69} -12.1891i q^{71} +(-7.85551 - 19.4360i) q^{72} +(-6.40469 + 1.71613i) q^{73} +(7.88545 + 8.65515i) q^{74} +(15.7332 + 3.57218i) q^{75} +(3.24607 - 4.57976i) q^{76} +(4.00892 - 2.07233i) q^{78} +(0.299644 + 0.518999i) q^{79} +(-1.48439 + 8.82024i) q^{80} +(11.8491 - 20.5233i) q^{81} +(4.20703 + 2.69716i) q^{82} +(4.53764 - 4.53764i) q^{83} +(-7.44839 - 7.16674i) q^{85} +(-4.88200 + 1.06764i) q^{86} +(-15.1383 + 4.05630i) q^{87} +(-2.44932 + 3.13581i) q^{88} +(0.401553 - 0.231837i) q^{89} +(-20.6093 + 11.1619i) q^{90} +(0.706194 + 4.14381i) q^{92} +(-3.07111 + 11.4615i) q^{93} +(2.76319 - 2.51746i) q^{94} +(-5.49468 - 3.03273i) 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 $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.19055	+	0.763272i	0.841848	+	0.539715i
$2$	1.19055	+	0.763272i	0.841848	+	0.539715i
$3$	0.835136	+	3.11677i	0.482166	+	1.79947i	0.592497	+	0.805573i	$0.298142\pi$
$3$	0.835136	+	3.11677i	0.482166	+	1.79947i	−0.110331	+	0.993895i	$0.535191\pi$
$4$	0.834830	+	1.81743i	0.417415	+	0.908716i
$5$	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
$8$	−0.393286	+	2.80095i	−0.139048	+	0.990286i
$9$	−6.41872	+	3.70585i	−2.13957	+	1.23528i
$10$	3.16111	+	0.0861032i	0.999629	+	0.0272282i
$11$	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	$0.598642\pi$
$12$	−4.96732	+	4.11978i	−1.43394	+	1.18928i
$13$	−0.699298	−	0.699298i	−0.193950	−	0.193950i	0.603450	−	0.797401i	$-0.293792\pi$
$13$	−0.699298	−	0.699298i	−0.193950	−	0.193950i	−0.797401	+	0.603450i	$0.793792\pi$
$14$		0			0
$15$	5.19924	+	5.00264i	1.34244	+	1.29168i
$16$	−2.60612	+	3.03449i	−0.651529	+	0.758624i
$17$	−1.19641	−	4.46506i	−0.290172	−	1.08294i	−0.944977	−	0.327138i	$-0.893916\pi$
$17$	−1.19641	−	4.46506i	−0.290172	−	1.08294i	0.654805	−	0.755798i	$-0.272751\pi$
$18$	−10.4704	−	0.487224i	−2.46790	−	0.114840i
$19$	−1.40337	−	2.43071i	−0.321955	−	0.557643i	0.658936	−	0.752199i	$-0.271007\pi$
$19$	−1.40337	−	2.43071i	−0.321955	−	0.557643i	−0.980891	+	0.194556i	$0.937673\pi$
$20$	3.69774	+	2.51529i	0.826840	+	0.562437i
$21$		0			0
$22$	0.913587	+	1.76734i	0.194777	+	0.376797i
$23$	2.03016	+	0.543980i	0.423318	+	0.113428i	0.464188	−	0.885737i	$-0.346346\pi$
$23$	2.03016	+	0.543980i	0.423318	+	0.113428i	−0.0408699	+	0.999164i	$0.513013\pi$
$24$	−9.05837	+	1.11339i	−1.84903	+	0.227270i
$25$	2.33132	−	4.42323i	0.466263	−	0.884646i
$26$	−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	$0.148921\pi$
$29$			4.85706i			0.901933i	−0.892541	+	0.450967i	$0.851079\pi$
$30$	2.37159	+	9.92434i	0.432991	+	1.81193i
$31$	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	$0.559538\pi$
$32$	−5.41886	+	1.62355i	−0.957929	+	0.287005i
$33$	−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	0.846998	−	0.531596i	$-0.178408\pi$
$37$	7.99714	+	2.14283i	1.31472	+	0.352279i	0.467724	+	0.883875i	$0.345074\pi$
$38$	0.184507	−	3.96504i	0.0299310	−	0.643214i
$39$	1.59554	−	2.76356i	0.255491	−	0.442523i
$40$	2.48250	+	5.81697i	0.392518	+	0.919744i
$41$	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	$-0.836839\pi$
$43$	−2.49869	+	2.49869i	−0.381046	+	0.381046i	0.490433	+	0.871479i	$0.336839\pi$
$44$	−0.261285	+	2.80142i	−0.0393903	+	0.422330i
$45$	−8.00846	+	14.5097i	−1.19383	+	2.16298i
$46$	2.00181	+	2.19720i	0.295151	+	0.323960i
$47$	0.684106	−	2.55312i	0.0997872	−	0.372411i	−0.897915	−	0.440170i	$-0.854918\pi$
$47$	0.684106	−	2.55312i	0.0997872	−	0.372411i	0.997702	+	0.0677590i	$0.0215849\pi$
$48$	−11.6343	−	5.58845i	−1.67926	−	0.806623i
$49$		0			0
$50$	6.15168	−	3.48666i	0.869980	−	0.493088i
$51$	12.9174	−	7.45786i	1.80880	−	1.04431i
$52$	0.687131	−	1.85472i	0.0952879	−	0.257203i
$53$	0.951495	−	0.254952i	0.130698	−	0.0350204i	−0.192877	−	0.981223i	$-0.561782\pi$
$53$	0.951495	−	0.254952i	0.130698	−	0.0350204i	0.323575	+	0.946203i	$0.395115\pi$
$54$	−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
$58$	−3.70726	+	5.78258i	−0.486787	+	0.759291i
$59$	3.53286	−	6.11910i	0.459940	−	0.796639i	−0.539018	−	0.842294i	$-0.681204\pi$
$59$	3.53286	−	6.11910i	0.459940	−	0.796639i	0.998957	+	0.0456557i	$0.0145377\pi$
$60$	−4.75148	+	13.6256i	−0.613413	+	1.75906i
$61$	−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	$0.878279\pi$
$62$	2.38814	+	4.61985i	0.303294	+	0.586722i
$63$		0			0
$64$	−7.69065	−	2.20315i	−0.961331	−	0.275394i
$65$	−2.14665	−	0.531084i	−0.266260	−	0.0658729i
$66$	−4.74541	+	4.32341i	−0.584120	+	0.532175i
$67$	−3.08671	+	0.827081i	−0.377101	+	0.101044i	−0.442391	−	0.896822i	$-0.645870\pi$
$67$	−3.08671	+	0.827081i	−0.377101	+	0.101044i	0.0652895	+	0.997866i	$0.479203\pi$
$68$	7.11614	−	5.90196i	0.862959	−	0.715717i
$69$			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	$-0.257370\pi$
$72$	−7.85551	−	19.4360i	−0.925781	−	2.29055i
$73$	−6.40469	+	1.71613i	−0.749612	+	0.200858i	−0.613346	−	0.789814i	$-0.710177\pi$
$73$	−6.40469	+	1.71613i	−0.749612	+	0.200858i	−0.136266	+	0.990672i	$0.543510\pi$
$74$	7.88545	+	8.65515i	0.916665	+	1.00614i
$75$	15.7332	+	3.57218i	1.81671	+	0.412480i
$76$	3.24607	−	4.57976i	0.372350	−	0.525334i
$77$		0			0
$78$	4.00892	−	2.07233i	0.453921	−	0.234645i
$79$	0.299644	+	0.518999i	0.0337126	+	0.0583919i	0.882389	−	0.470520i	$-0.155934\pi$
$79$	0.299644	+	0.518999i	0.0337126	+	0.0583919i	−0.848677	+	0.528912i	$0.822600\pi$
$80$	−1.48439	+	8.82024i	−0.165960	+	0.986133i
$81$	11.8491	−	20.5233i	1.31657	−	2.28036i
$82$	4.20703	+	2.69716i	0.464589	+	0.297852i
$83$	4.53764	−	4.53764i	0.498071	−	0.498071i	−0.412766	−	0.910837i	$-0.635437\pi$
$83$	4.53764	−	4.53764i	0.498071	−	0.498071i	0.910837	+	0.412766i	$0.135437\pi$
$84$		0			0
$85$	−7.44839	−	7.16674i	−0.807891	−	0.777342i
$86$	−4.88200	+	1.06764i	−0.526440	+	0.115127i
$87$	−15.1383	+	4.05630i	−1.62300	+	0.434882i
$88$	−2.44932	+	3.13581i	−0.261099	+	0.334278i
$89$	0.401553	−	0.231837i	0.0425645	−	0.0245746i	−0.478567	−	0.878051i	$-0.658844\pi$
$89$	0.401553	−	0.231837i	0.0425645	−	0.0245746i	0.521131	+	0.853477i	$0.325510\pi$
$90$	−20.6093	+	11.1619i	−2.17242	+	1.17657i
$91$		0			0
$92$	0.706194	+	4.14381i	0.0736258	+	0.432022i
$93$	−3.07111	+	11.4615i	−0.318459	+	1.18851i
$94$	2.76319	−	2.51746i	0.285001	−	0.259657i
$95$	−5.49468	−	3.03273i	−0.563742	−	0.311151i
$96$	−9.58571	−	15.5335i	−0.978338	−	1.58538i
$97$	8.00558	−	8.00558i	0.812843	−	0.812843i	−0.172216	−	0.985059i	$-0.555093\pi$
$97$	8.00558	−	8.00558i	0.812843	−	0.812843i	0.985059	+	0.172216i	$0.0550927\pi$
$98$		0			0
$99$	−10.4267			−1.04792
$100$	9.98517	+	0.544363i	0.998517	+	0.0544363i
$101$	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	$0.0696624\pi$
$102$	21.0712	+	0.980516i	2.08636	+	0.0970856i
$103$	−13.5932	−	3.64227i	−1.33937	−	0.358884i	−0.483171	−	0.875526i	$-0.660515\pi$
$103$	−13.5932	−	3.64227i	−1.33937	−	0.358884i	−0.856202	+	0.516642i	$0.827182\pi$
$104$	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	−0.0146144	+	0.999893i	$0.504652\pi$
$107$	−5.19174	+	19.3758i	−0.501905	+	1.87313i	−0.487290	+	0.873240i	$0.662015\pi$
$108$	9.89076	−	26.6974i	0.951739	−	2.56896i
$109$	−0.879139	−	0.507571i	−0.0842062	−	0.0486165i	0.457306	−	0.889310i	$-0.348815\pi$
$109$	−0.879139	−	0.507571i	−0.0842062	−	0.0486165i	−0.541512	+	0.840693i	$0.682148\pi$
$110$	3.79066	+	2.32841i	0.361425	+	0.222005i
$111$			26.7148i			2.53566i
$112$		0			0
$113$	7.39345	+	7.39345i	0.695518	+	0.695518i	0.963440	−	0.267923i	$-0.0863372\pi$
$113$	7.39345	+	7.39345i	0.695518	+	0.695518i	−0.267923	+	0.963440i	$0.586337\pi$
$114$	12.5122	−	2.73628i	1.17188	−	0.256276i
$115$	4.51530	−	1.30362i	0.421054	−	0.121563i
$116$	−8.82737	+	4.05482i	−0.819601	+	0.376481i
$117$	7.08009	+	1.89711i	0.654555	+	0.175387i
$118$	8.87660	−	4.58857i	0.817157	−	0.422412i
$119$		0			0
$120$	−16.0569	+	12.5953i	−1.46579	+	1.14979i
$121$	−4.51047	−	7.81236i	−0.410043	−	0.710215i
$122$	0.144511	−	3.10552i	0.0130834	−	0.281161i
$123$	2.95110	+	11.0137i	0.266092	+	0.993069i
$124$	−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	$-0.437899\pi$
$127$	−8.87092	−	8.87092i	−0.787167	−	0.787167i	−0.981029	+	0.193862i	$0.937899\pi$
$128$	−7.47452	−	8.49303i	−0.660661	−	0.750685i
$129$	−9.87458	−	5.70109i	−0.869408	−	0.501953i
$130$	−2.15034	−	2.27077i	−0.188597	−	0.199159i
$131$	−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	$0.528100\pi$
$132$	−8.94960	+	1.52520i	−0.778962	+	0.132752i
$133$		0			0
$134$	−4.30618	−	1.37132i	−0.371997	−	0.118464i
$135$	−30.8996	−	7.64458i	−2.65941	−	0.657941i
$136$	12.9769	−	1.59504i	1.11276	−	0.136773i
$137$	1.80890	+	6.75090i	0.154545	+	0.576769i	0.999144	+	0.0413695i	$0.0131721\pi$
$137$	1.80890	+	6.75090i	0.154545	+	0.576769i	−0.844599	+	0.535399i	$0.820161\pi$
$138$	−5.17640	+	8.07414i	−0.440644	+	0.687317i
$139$	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
$142$	9.30359	−	14.5117i	0.780740	−	1.21780i
$143$	−0.360083	−	1.34385i	−0.0301117	−	0.112378i
$144$	5.48256	−	29.1355i	0.456880	−	2.42796i
$145$	5.61057	+	9.29928i	0.465932	+	0.772263i
$146$	−8.93499	−	2.84538i	−0.739465	−	0.235485i
$147$		0			0
$148$	2.78181	+	16.3232i	0.228664	+	1.34176i
$149$	5.75434	−	3.32227i	0.471414	−	0.272171i	−0.245418	−	0.969417i	$-0.578925\pi$
$149$	5.75434	−	3.32227i	0.471414	−	0.272171i	0.716831	+	0.697247i	$0.245592\pi$
$150$	16.0046	+	16.2615i	1.30677	+	1.32775i
$151$	−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	$0.978058\pi$
$152$	7.36022	−	2.97481i	0.596993	−	0.241289i
$153$	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
$157$	4.59905	+	17.1639i	0.367044	+	1.36983i	0.864628	+	0.502412i	$0.167554\pi$
$157$	4.59905	+	17.1639i	0.367044	+	1.36983i	−0.497584	+	0.867416i	$0.665779\pi$
$158$	−0.0393955	+	0.846605i	−0.00313413	+	0.0673523i
$159$	1.58925	+	2.75267i	0.126036	+	0.218301i
$160$	−8.49949	+	9.36796i	−0.671944	+	0.740602i
$161$		0			0
$162$	29.7719	−	15.3899i	2.33910	−	1.20915i
$163$	16.7957	+	4.50039i	1.31554	+	0.352498i	0.847305	−	0.531106i	$-0.178224\pi$
$163$	16.7957	+	4.50039i	1.31554	+	0.352498i	0.468235	+	0.883604i	$0.344890\pi$
$164$	2.95002	+	6.42222i	0.230358	+	0.501491i
$165$	2.81548	+	9.75192i	0.219185	+	0.759186i
$166$	8.86575	−	1.93884i	0.688116	−	0.150483i
$167$	6.88960	+	6.88960i	0.533133	+	0.533133i	0.921503	−	0.388370i	$-0.126962\pi$
$167$	6.88960	+	6.88960i	0.533133	+	0.533133i	−0.388370	+	0.921503i	$0.626962\pi$
$168$		0			0
$169$		−	12.0220i		−	0.924767i
$170$	−3.39752	−	14.2175i	−0.260578	−	1.09044i
$171$	18.0157	+	10.4014i	1.37769	+	0.795412i
$172$	−6.62718	−	2.45521i	−0.505318	−	0.187208i
$173$	−6.40337	+	23.8977i	−0.486839	+	1.81691i	0.0847922	+	0.996399i	$0.472977\pi$
$173$	−6.40337	+	23.8977i	−0.486839	+	1.81691i	−0.571632	+	0.820510i	$0.693689\pi$
$174$	−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
$178$	0.655024	+	0.0304805i	0.0490961	+	0.00228461i
$179$	10.2777	−	17.8015i	0.768192	−	1.33055i	−0.170350	−	0.985384i	$-0.554490\pi$
$179$	10.2777	−	17.8015i	0.768192	−	1.33055i	0.938542	−	0.345164i	$-0.112177\pi$
$180$	−33.0561	−	2.44170i	−2.46386	−	0.181994i
$181$	−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
$185$	17.7865	−	5.13516i	1.30769	−	0.377544i
$186$	−12.4046	+	11.3015i	−0.909549	+	0.828664i
$187$	1.68310	−	6.28140i	0.123080	−	0.459342i
$188$	5.21123	−	0.888105i	0.380068	−	0.0647717i
$189$		0			0
$190$	−4.22691	−	7.80456i	−0.306652	−	0.566202i
$191$	−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	$0.434922\pi$
$192$	0.443974	−	25.8099i	0.0320411	−	1.86267i
$193$	5.12478	−	1.37318i	0.368890	−	0.0988437i	−0.0696118	−	0.997574i	$-0.522176\pi$
$193$	5.12478	−	1.37318i	0.368890	−	0.0988437i	0.438502	+	0.898730i	$0.355509\pi$
$194$	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	−0.993478	−	0.114026i	$-0.963625\pi$
$197$	−12.3437	+	12.3437i	−0.879452	+	0.879452i	0.114026	+	0.993478i	$0.463625\pi$
$198$	−12.4136	−	7.95842i	−0.882193	−	0.565581i
$199$	−2.14941	+	3.72289i	−0.152368	+	0.263909i	−0.932097	−	0.362208i	$-0.882023\pi$
$199$	−2.14941	+	3.72289i	−0.152368	+	0.263909i	0.779730	+	0.626116i	$0.215356\pi$
$200$	11.4724	+	8.26950i	0.811219	+	0.584742i
$201$	−5.15564	−	8.92983i	−0.363651	−	0.629862i
$202$	7.57667	−	3.91660i	0.533092	−	0.275571i
$203$		0			0
$204$	24.3380	+	17.2504i	1.70400	+	1.20777i
$205$	6.76555	−	4.08188i	0.472527	−	0.285091i
$206$	−13.4033	−	14.7116i	−0.933853	−	1.02501i
$207$	−15.0470	+	4.03182i	−1.04584	+	0.280231i
$208$	3.94447	−	0.299564i	0.273500	−	0.0207710i
$209$		−	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	$0.765041\pi$
$212$	1.25769	+	1.51643i	0.0863788	+	0.104149i
$213$	37.9906	−	10.1795i	2.60307	−	0.697490i
$214$	−20.9701	+	19.1052i	−1.43349	+	1.30601i
$215$	−1.89764	+	7.67029i	−0.129418	+	0.523110i
$216$	32.1528	−	24.2353i	2.18772	−	1.64900i
$217$		0			0
$218$	−0.659246	−	1.27531i	−0.0446498	−	0.0863751i
$219$	−10.6976	−	18.5287i	−0.722875	−	1.25206i
$220$	2.73577	+	5.66540i	0.184446	+	0.381961i
$221$	−2.28576	+	3.95905i	−0.153757	+	0.266315i
$222$	−20.3907	+	31.8054i	−1.36853	+	2.13464i
$223$	−9.54503	+	9.54503i	−0.639183	+	0.639183i	−0.950354	−	0.311171i	$-0.899279\pi$
$223$	−9.54503	+	9.54503i	−0.639183	+	0.639183i	0.311171	+	0.950354i	$0.399279\pi$
$224$		0			0
$225$	1.42776	+	37.0310i	0.0951838	+	2.46873i
$226$	3.15908	+	14.4455i	0.210139	+	0.960901i
$227$	−17.8221	+	4.77541i	−1.18289	+	0.316955i	−0.796073	−	0.605200i	$-0.793093\pi$
$227$	−17.8221	+	4.77541i	−1.18289	+	0.316955i	−0.386819	+	0.922155i	$0.626426\pi$
$228$	16.9850	+	6.29253i	1.12486	+	0.416733i
$229$	13.5250	−	7.80865i	0.893755	−	0.516010i	0.0185864	−	0.999827i	$-0.494083\pi$
$229$	13.5250	−	7.80865i	0.893755	−	0.516010i	0.875169	+	0.483817i	$0.160750\pi$
$230$	6.37072	+	1.89438i	0.420073	+	0.124912i
$231$		0			0
$232$	−13.6044	−	1.91021i	−0.893172	−	0.125412i
$233$	0.989436	−	3.69263i	0.0648201	−	0.241912i	−0.925913	−	0.377738i	$-0.876702\pi$
$233$	0.989436	−	3.69263i	0.0648201	−	0.241912i	0.990733	+	0.135826i	$0.0433688\pi$
$234$	6.98121	+	7.66264i	0.456376	+	0.500923i
$235$	−1.63942	−	5.67842i	−0.106944	−	0.370419i
$236$	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	$-0.333148\pi$
$239$	15.4752			1.00101			0.500505	+	0.865734i	$0.333148\pi$
$240$	−28.7303	+	2.73960i	−1.85453	+	0.176840i
$241$	−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	$0.789586\pi$
$242$	0.593010	−	12.7437i	0.0381202	−	0.819199i
$243$	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
$248$	−6.40258	+	8.19707i	−0.406564	+	0.520514i
$249$	17.9323	+	10.3532i	1.13641	+	0.656109i
$250$	7.75039	−	13.7816i	0.490178	−	0.871622i
$251$		−	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
$255$	16.1167	−	29.2001i	1.00927	−	1.82858i
$256$	−2.41631	−	15.8165i	−0.151020	−	0.988531i
$257$	−22.2935	−	5.97352i	−1.39063	−	0.372618i	−0.515659	−	0.856794i	$-0.672453\pi$
$257$	−22.2935	−	5.97352i	−1.39063	−	0.372618i	−0.874971	+	0.484176i	$0.839119\pi$
$258$	−7.40472	−	14.3244i	−0.460998	−	0.891801i
$259$		0			0
$260$	−0.826882	−	4.34476i	−0.0512811	−	0.269451i
$261$	−17.9995	−	31.1761i	−1.11414	−	1.92975i
$262$	−18.5750	−	0.864358i	−1.14757	−	0.0534002i
$263$	2.93759	+	10.9633i	0.181140	+	0.676023i	0.995424	+	0.0955566i	$0.0304631\pi$
$263$	2.93759	+	10.9633i	0.181140	+	0.676023i	−0.814284	+	0.580466i	$0.802870\pi$
$264$	−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
$268$	−4.08004	−	4.91941i	−0.249228	−	0.300501i
$269$	−23.5713	−	13.6089i	−1.43717	−	0.829749i	−0.439516	−	0.898235i	$-0.644850\pi$
$269$	−23.5713	−	13.6089i	−1.43717	−	0.829749i	−0.997652	+	0.0684854i	$0.978183\pi$
$270$	−30.9526	−	32.6861i	−1.88372	−	1.98921i
$271$	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	$0.331827\pi$
$272$	16.6672	+	8.00597i	1.01060	+	0.485433i
$273$		0			0
$274$	−2.99919	+	9.41799i	−0.181188	+	0.568961i
$275$	5.95156	−	3.74906i	0.358893	−	0.226077i
$276$	−12.3255	+	5.66169i	−0.741910	+	0.340794i
$277$	−5.41783	−	20.2196i	−0.325526	−	1.21488i	−0.913782	−	0.406204i	$-0.866852\pi$
$277$	−5.41783	−	20.2196i	−0.325526	−	1.21488i	0.588256	−	0.808674i	$-0.299815\pi$
$278$	25.2846	+	16.2102i	1.51647	+	0.972220i
$279$	−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	$0.524363\pi$
$282$	10.1540	+	6.50980i	0.604661	+	0.387653i
$283$	−5.32518	−	19.8738i	−0.316549	−	1.18138i	−0.922539	−	0.385904i	$-0.873889\pi$
$283$	−5.32518	−	19.8738i	−0.316549	−	1.18138i	0.605990	−	0.795472i	$-0.292777\pi$
$284$	22.1528	−	10.1758i	1.31453	−	0.603824i
$285$	4.86351	−	19.6584i	0.288089	−	1.16446i
$286$	0.597025	−	1.87476i	0.0353028	−	0.110857i
$287$		0			0
$288$	28.7656	−	30.5026i	1.69503	−	1.79738i
$289$	−3.78292	+	2.18407i	−0.222525	+	0.128475i
$290$	−0.418208	+	15.3537i	−0.0245580	+	0.901599i
$291$	31.6373	+	18.2658i	1.85461	+	1.07076i
$292$	−8.46578	−	10.2074i	−0.495422	−	0.597343i
$293$	4.71102	+	4.71102i	0.275221	+	0.275221i	0.831198	−	0.555977i	$-0.187656\pi$
$293$	4.71102	+	4.71102i	0.275221	+	0.275221i	−0.555977	+	0.831198i	$0.687656\pi$
$294$		0			0
$295$	−0.304410	−	15.7965i	−0.0177234	−	0.919708i
$296$	−9.14712	+	21.5569i	−0.531666	+	1.25297i
$297$	−5.18314	−	19.3437i	−0.300756	−	1.12244i
$298$	9.38664	+	0.436793i	0.543753	+	0.0253027i
$299$	−1.03928	−	1.80009i	−0.0601033	−	0.104102i
$300$	6.64232	+	31.5761i	0.383495	+	1.82305i
$301$		0			0
$302$	−13.2395	−	25.6118i	−0.761846	−	1.47379i
$303$	18.7972	+	5.03669i	1.07987	+	0.289350i
$304$	11.0333	+	2.07619i	0.632804	+	0.119078i
$305$	−4.30358	−	2.37531i	−0.246422	−	0.136010i
$306$	10.3514	+	47.3339i	0.591750	+	2.70590i
$307$	−16.8508	−	16.8508i	−0.961723	−	0.961723i	0.0375706	−	0.999294i	$-0.488038\pi$
$307$	−16.8508	−	16.8508i	−0.961723	−	0.961723i	−0.999294	+	0.0375706i	$0.988038\pi$
$308$		0			0
$309$		−	45.4085i		−	2.58320i
$310$	9.90887	+	6.08651i	0.562786	+	0.345690i
$311$	−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	$0.838851\pi$
$312$	7.11309	+	5.55590i	0.402699	+	0.314541i
$313$	−0.405938	+	1.51498i	−0.0229450	+	0.0856319i	−0.976449	−	0.215749i	$-0.930781\pi$
$313$	−0.405938	+	1.51498i	−0.0229450	+	0.0856319i	0.953504	+	0.301381i	$0.0974475\pi$
$314$	−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	−0.656769	−	0.754092i	$-0.728077\pi$
$317$	−28.5334	−	7.64549i	−1.60259	−	0.429414i	−0.945825	+	0.324678i	$0.894744\pi$
$318$	−0.208946	+	4.49023i	−0.0117171	+	0.251800i
$319$	−3.41643	+	5.91743i	−0.191283	+	0.331313i
$320$	−17.2694	+	4.66562i	−0.965388	+	0.260816i
$321$	−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
$325$	−4.72344	+	1.46287i	−0.262009	+	0.0811454i
$326$	16.5611	+	18.1776i	0.917236	+	1.00677i
$327$	0.847782	−	3.16396i	0.0468824	−	0.174968i
$328$	−1.38975	+	9.89766i	−0.0767360	+	0.546507i
$329$		0			0
$330$	−4.09139	+	13.7592i	−0.225224	+	0.757416i
$331$	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	$0.220475\pi$
$332$	12.0350	+	4.45869i	0.660507	+	0.244703i
$333$	−59.2724	+	15.8820i	−3.24811	+	0.870328i
$334$	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	−0.586391	−	0.810028i	$-0.699452\pi$
$337$	4.10542	−	4.10542i	0.223636	−	0.223636i	0.810028	+	0.586391i	$0.199452\pi$
$338$	9.17603	−	14.3128i	0.499111	−	0.778513i
$339$	−16.8692	+	29.2182i	−0.916207	+	1.58692i
$340$	6.80693	−	19.5200i	0.369157	−	1.05862i
$341$	2.58665	+	4.48021i	0.140075	+	0.242617i
$342$	13.5095	+	26.1342i	0.730513	+	1.41318i
$343$		0			0
$344$	−6.01600	−	7.98140i	−0.324361	−	0.430328i
$345$	7.83396	+	12.9845i	0.421766	+	0.699060i
$346$	−25.8640	+	23.5640i	−1.39046	+	1.26681i
$347$	14.2660	−	3.82255i	0.765837	−	0.205205i	0.145305	−	0.989387i	$-0.453584\pi$
$347$	14.2660	−	3.82255i	0.765837	−	0.205205i	0.620531	+	0.784182i	$0.286917\pi$
$348$	−20.0100	−	24.1266i	−1.07265	−	1.29332i
$349$			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
$352$	−7.74389	−	1.83361i	−0.412751	−	0.0977317i
$353$	−10.5040	+	2.81454i	−0.559072	+	0.149803i	−0.527280	−	0.849692i	$-0.676788\pi$
$353$	−10.5040	+	2.81454i	−0.559072	+	0.149803i	−0.0317919	+	0.999495i	$0.510121\pi$
$354$	21.7147	+	23.8342i	1.15412	+	1.26677i
$355$	−14.0801	−	23.3371i	−0.747292	−	1.23860i
$356$	0.756576	+	0.536251i	0.0400984	+	0.0284212i
$357$		0			0
$358$	25.8236	−	13.3489i	1.36482	−	0.705514i
$359$	2.49329	+	4.31850i	0.131591	+	0.227922i	0.924290	−	0.381691i	$-0.124658\pi$
$359$	2.49329	+	4.31850i	0.131591	+	0.227922i	−0.792699	+	0.609613i	$0.791325\pi$
$360$	−37.4913	−	28.1378i	−1.97597	−	1.48299i
$361$	5.56111	−	9.63212i	0.292690	−	0.506954i
$362$	−9.35761	−	5.99923i	−0.491825	−	0.315313i
$363$	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
$367$	15.3917	−	4.12420i	0.803442	−	0.215282i	0.166347	−	0.986067i	$-0.446803\pi$
$367$	15.3917	−	4.12420i	0.803442	−	0.215282i	0.637094	+	0.770786i	$0.280136\pi$
$368$	−6.94154	+	4.74284i	−0.361853	+	0.247238i
$369$	−22.6817	+	13.0953i	−1.18076	+	0.681714i
$370$	25.0953	+	7.46228i	1.30464	+	0.387946i
$371$		0			0
$372$	−23.3944	+	3.98691i	−1.21294	+	0.206712i
$373$	−0.152497	+	0.569126i	−0.00789599	+	0.0294682i	−0.969761	−	0.244055i	$-0.921522\pi$
$373$	−0.152497	+	0.569126i	−0.00789599	+	0.0294682i	0.961865	+	0.273523i	$0.0881890\pi$
$374$	6.79823	−	6.19368i	0.351528	−	0.320267i
$375$	34.2489	−	11.3347i	1.76861	−	0.585321i
$376$	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	$-0.291093\pi$
$379$	23.7583			1.22038			0.610191	+	0.792254i	$0.291093\pi$
$380$	0.924648	−	12.5180i	0.0474335	−	0.642161i
$381$	20.2402	−	35.0570i	1.03694	−	1.79603i
$382$	−12.2515	−	0.570105i	−0.626842	−	0.0291691i
$383$	−4.14964	−	1.11189i	−0.212037	−	0.0568151i	0.151237	−	0.988498i	$-0.451674\pi$
$383$	−4.14964	−	1.11189i	−0.212037	−	0.0568151i	−0.363274	+	0.931682i	$0.618341\pi$
$384$	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
$388$	21.2329	+	7.86629i	1.07794	+	0.399350i
$389$	−21.8152	−	12.5950i	−1.10608	−	0.638593i	−0.168266	−	0.985742i	$-0.553817\pi$
$389$	−21.8152	−	12.5950i	−1.10608	−	0.638593i	−0.937810	+	0.347148i	$0.887150\pi$
$390$	5.28162	−	8.59852i	0.267445	−	0.435403i
$391$		−	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
$395$	1.17321	+	0.647540i	0.0590306	+	0.0325813i
$396$	−8.70454	−	18.9498i	−0.437419	−	0.952265i
$397$	3.73802	+	1.00160i	0.187606	+	0.0502689i	0.351399	−	0.936226i	$-0.385706\pi$
$397$	3.73802	+	1.00160i	0.187606	+	0.0502689i	−0.163793	+	0.986495i	$0.552373\pi$
$398$	−5.40057	+	2.79171i	−0.270706	+	0.139936i
$399$		0			0
$400$	7.34658	+	18.6018i	0.367329	+	0.930091i
$401$	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	$0.789584\pi$
$402$	0.677834	−	14.5666i	0.0338073	−	0.726516i
$403$	−0.941265	−	3.51285i	−0.0468877	−	0.174987i
$404$	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
$408$	15.8089	+	39.1141i	0.782656	+	1.93643i
$409$	14.7164	+	8.49650i	0.727678	+	0.420125i	0.817572	−	0.575826i	$-0.195320\pi$
$409$	14.7164	+	8.49650i	0.727678	+	0.420125i	−0.0898942	+	0.995951i	$0.528653\pi$
$410$	11.1703	+	0.304261i	0.551663	+	0.0150264i
$411$	−19.5303	+	11.2758i	−0.963360	+	0.556196i
$412$	−4.72839	−	27.7453i	−0.232951	−	1.36691i
$413$		0			0
$414$	−20.9916	−	6.68484i	−1.03168	−	0.328542i
$415$	3.44613	−	13.9293i	0.169164	−	0.683764i
$416$	4.92474	+	2.65406i	0.241455	+	0.130126i
$417$	17.7364	+	66.1930i	0.868554	+	3.24149i
$418$	3.01378	−	4.70089i	0.147409	−	0.229928i
$419$	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	$0.331560\pi$
$422$	−14.9215	+	23.2745i	−0.726367	+	1.13299i
$423$	5.07039	+	18.9230i	0.246531	+	0.920066i
$424$	0.339899	+	2.76536i	0.0165069	+	0.134298i
$425$	−22.5392	−	5.11747i	−1.09331	−	0.248234i
$426$	52.9995	+	16.8779i	2.56783	+	0.817735i
$427$		0			0
$428$	−39.5485	+	6.73991i	−1.91165	+	0.325786i
$429$	3.88775	−	2.24459i	0.187702	−	0.108370i
$430$	−8.11376	+	7.68347i	−0.391280	+	0.370530i
$431$	−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	$0.742266\pi$
$432$	56.7778	−	4.31201i	2.73172	−	0.207462i
$433$	7.00877	+	7.00877i	0.336820	+	0.336820i	0.855169	−	0.518349i	$-0.173453\pi$
$433$	7.00877	+	7.00877i	0.336820	+	0.336820i	−0.518349	+	0.855169i	$0.673453\pi$
$434$		0			0
$435$	−24.2981	+	25.2530i	−1.16501	+	1.21079i
$436$	0.188544	−	2.02151i	0.00902962	−	0.0968128i
$437$	−1.52681	−	5.69814i	−0.0730373	−	0.272579i
$438$	1.40645	−	30.2246i	0.0672030	−	1.44419i
$439$	2.21290	+	3.83285i	0.105616	+	0.182932i	0.913990	−	0.405737i	$-0.132985\pi$
$439$	2.21290	+	3.83285i	0.105616	+	0.182932i	−0.808374	+	0.588670i	$0.799652\pi$
$440$	−1.06716	+	8.83309i	−0.0508750	+	0.421101i
$441$		0			0
$442$	−5.74315	+	2.96880i	−0.273174	+	0.141211i
$443$	−4.25183	−	1.13928i	−0.202011	−	0.0541286i	0.156395	−	0.987695i	$-0.450013\pi$
$443$	−4.25183	−	1.13928i	−0.202011	−	0.0541286i	−0.358405	+	0.933566i	$0.616679\pi$
$444$	−48.5523	+	22.3023i	−2.30419	+	1.05842i
$445$	0.501006	−	0.907721i	0.0237500	−	0.0430301i
$446$	−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	$0.172297\pi$
$449$			21.8355i			1.03048i	−0.857046	+	0.515240i	$0.827703\pi$
$450$	−26.5649	+	45.1771i	−1.25228	+	2.12967i
$451$	4.30514	+	2.48557i	0.202721	+	0.117041i
$452$	−7.26482	+	19.6094i	−0.341708	+	0.922348i
$453$	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	0.719517	−	0.694475i	$-0.244363\pi$
$457$	21.2792	+	5.70175i	0.995400	+	0.266717i	0.275883	+	0.961191i	$0.411030\pi$
$458$	22.0623	+	1.02664i	1.03090	+	0.0479715i
$459$	−32.9019	+	56.9877i	−1.53573	+	2.65996i
$460$	6.13874	+	7.11795i	0.286220	+	0.331876i
$461$	−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	$-0.591621\pi$
$463$	14.5239	−	14.5239i	0.674983	−	0.674983i	0.958861	+	0.283877i	$0.0916209\pi$
$464$	−14.7387	−	12.6581i	−0.684228	−	0.587636i
$465$	7.35973	+	25.4917i	0.341299	+	1.18215i
$466$	3.99645	−	3.64106i	0.185132	−	0.168669i
$467$	7.29665	−	27.2315i	0.337649	−	1.26012i	−0.563320	−	0.826239i	$-0.690476\pi$
$467$	7.29665	−	27.2315i	0.337649	−	1.26012i	0.900969	−	0.433884i	$-0.142857\pi$
$468$	2.46282	+	14.4513i	0.113844	+	0.668014i
$469$		0			0
$470$	2.38236	−	8.01178i	0.109890	−	0.369556i
$471$	−49.6551	+	28.6684i	−2.28799	+	1.32097i
$472$	15.7499	+	12.3019i	0.724946	+	0.566242i
$473$	−4.80176	+	1.28663i	−0.220785	+	0.0591592i
$474$	−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
$478$	18.4241	+	11.8118i	0.842698	+	0.540260i
$479$	0.709375	−	1.22867i	0.0324122	−	0.0561395i	−0.849364	−	0.527807i	$-0.823014\pi$
$479$	0.709375	−	1.22867i	0.0324122	−	0.0561395i	0.881776	+	0.471668i	$0.156348\pi$
$480$	−36.2960	−	18.6674i	−1.65668	−	0.852047i
$481$	−4.09391	−	7.09086i	−0.186666	−	0.323315i
$482$	−36.1334	+	18.6784i	−1.64583	+	0.850777i
$483$		0			0
$484$	10.4330	−	14.7195i	0.474225	−	0.669067i
$485$	6.07987	−	24.5749i	0.276072	−	1.11589i
$486$	32.1557	+	35.2944i	1.45861	+	1.60099i
$487$	32.5132	−	8.71188i	1.47331	−	0.394773i	0.569247	−	0.822166i	$-0.307235\pi$
$487$	32.5132	−	8.71188i	1.47331	−	0.394773i	0.904066	+	0.427393i	$0.140568\pi$
$488$	5.76471	−	2.32995i	0.260956	−	0.105472i
$489$			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	$0.977235\pi$
$492$	−17.5529	+	14.5580i	−0.791346	+	0.656324i
$493$	21.6871	−	5.81103i	0.976736	−	0.261716i
$494$	−2.90177	+	2.64372i	−0.130557	+	0.118946i
$495$	−19.9629	+	12.0443i	−0.897265	+	0.541350i
$496$	−13.8792	+	4.87213i	−0.623195	+	0.218765i
$497$		0			0
$498$	13.4470	+	26.0133i	0.602576	+	1.16568i
$499$	−3.72451	−	6.45105i	−0.166732	−	0.288789i	0.770537	−	0.637395i	$-0.219988\pi$
$499$	−3.72451	−	6.45105i	−0.166732	−	0.288789i	−0.937269	+	0.348607i	$0.886655\pi$
$500$	19.7463	−	10.4920i	0.883083	−	0.469217i
$501$	−15.7195	+	27.2270i	−0.702297	+	1.21641i
$502$	19.8668	−	30.9883i	0.886701	−	1.38308i
$503$	−19.3043	+	19.3043i	−0.860736	+	0.860736i	−0.991424	−	0.130687i	$-0.958282\pi$
$503$	−19.3043	+	19.3043i	−0.860736	+	0.860736i	0.130687	+	0.991424i	$0.458282\pi$
$504$		0			0
$505$	−0.259830	−	13.4832i	−0.0115623	−	0.599994i
$506$	0.893334	+	4.08495i	0.0397135	+	0.181598i
$507$	37.4697	−	10.0400i	1.66409	−	0.445891i
$508$	8.71658	−	23.5280i	0.386736	−	1.04389i
$509$	−9.85817	+	5.69161i	−0.436956	+	0.252276i	−0.702305	−	0.711876i	$-0.747846\pi$
$509$	−9.85817	+	5.69161i	−0.436956	+	0.252276i	0.265350	+	0.964152i	$0.414513\pi$
$510$	41.4754	−	22.4629i	1.83656	−	0.994672i
$511$		0			0
$512$	9.19554	−	20.6747i	0.406390	−	0.913700i
$513$	−10.3411	+	38.5934i	−0.456570	+	1.70394i
$514$	−21.9821	−	24.1278i	−0.969590	−	1.06423i
$515$	−30.2326	+	8.72849i	−1.33221	+	0.384623i
$516$	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
$520$	2.33179	−	5.80380i	0.102256	−	0.254514i
$521$	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	$0.158050\pi$
$522$	2.36648	−	50.8554i	0.103578	−	2.22588i
$523$	−6.09797	−	1.63395i	−0.266646	−	0.0714474i	0.123019	−	0.992404i	$-0.460742\pi$
$523$	−6.09797	−	1.63395i	−0.266646	−	0.0714474i	−0.389665	+	0.920957i	$0.627409\pi$
$524$	−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
$528$	−10.2433	−	14.9920i	−0.445784	−	0.652443i
$529$	−16.0929	−	9.29126i	−0.699693	−	0.403968i
$530$	3.02973	−	0.724004i	0.131603	−	0.0314487i
$531$			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
$535$	12.4417	+	43.0940i	0.537901	+	1.86312i
$536$	−1.10265	−	8.97100i	−0.0476274	−	0.387488i
$537$	64.0665	+	17.1666i	2.76467	+	0.740792i
$538$	−17.6756	−	34.1934i	−0.762048	−	1.47418i
$539$		0			0
$540$	−11.9024	−	62.5398i	−0.512197	−	2.69128i
$541$	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	$0.589304\pi$
$542$	0.220149	+	0.0102443i	0.00945620	+	0.000440029i
$543$	−6.56407	−	24.4975i	−0.281691	−	1.05129i
$544$	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	$-0.428893\pi$
$547$	−17.6256	−	17.6256i	−0.753617	−	0.753617i	−0.975152	+	0.221536i	$0.928893\pi$
$548$	−10.7592	+	8.92341i	−0.459609	+	0.381189i
$549$	14.1104	+	8.14662i	0.602215	+	0.347689i
$550$	9.94719	+	0.0792139i	0.424150	+	0.00337769i
$551$	11.8061	−	6.81625i	0.502957	−	0.290382i
$552$	−18.9956	−	2.66721i	−0.808507	−	0.113524i
$553$		0			0
$554$	8.98286	−	28.2078i	0.381645	−	1.19843i
$555$	30.8593	+	51.1479i	1.30990	+	2.17111i
$556$	17.7299	+	38.5981i	0.751914	+	1.63692i
$557$	1.60273	+	5.98149i	0.0679101	+	0.253444i	0.991532	−	0.129860i	$-0.0414528\pi$
$557$	1.60273	+	5.98149i	0.0679101	+	0.253444i	−0.923622	+	0.383304i	$0.874786\pi$
$558$	−32.4493	−	20.8035i	−1.37369	−	0.880682i
$559$	3.49465			0.147808
$560$		0			0
$561$	20.9833			0.885915
$562$	−3.05205	−	1.95669i	−0.128743	−	0.0825380i
$563$	−1.32949	−	4.96172i	−0.0560313	−	0.209112i	0.932235	−	0.361854i	$-0.117856\pi$
$563$	−1.32949	−	4.96172i	−0.0560313	−	0.209112i	−0.988266	+	0.152742i	$0.951189\pi$
$564$	7.12011	+	15.5005i	0.299811	+	0.652690i
$565$	22.6959	+	5.61499i	0.954823	+	0.236224i
$566$	8.82925	−	27.7254i	0.371121	−	1.16539i
$567$		0			0
$568$	34.1410	+	4.79380i	1.43253	+	0.201143i
$569$	−30.0136	+	17.3284i	−1.25824	+	0.726442i	−0.972731	−	0.231935i	$-0.925494\pi$
$569$	−30.0136	+	17.3284i	−1.25824	+	0.726442i	−0.285504	+	0.958378i	$0.592161\pi$
$570$	20.7950	−	19.6922i	0.871005	−	0.824814i
$571$	−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	$0.912965\pi$
$572$	2.14174	−	1.77631i	0.0895508	−	0.0742713i
$573$	−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
$577$	−8.91664	−	33.2773i	−0.371204	−	1.38535i	−0.858812	−	0.512291i	$-0.828797\pi$
$577$	−8.91664	−	33.2773i	−0.371204	−	1.38535i	0.487608	−	0.873063i	$-0.337870\pi$
$578$	−6.17080	−	0.287149i	−0.256672	−	0.0119438i
$579$	8.55978	+	14.8260i	0.355732	+	0.616146i
$580$	−12.2169	+	17.9602i	−0.507281	+	0.745755i
$581$		0			0
$582$	23.7241	+	45.8942i	0.983394	+	1.90238i
$583$	1.33855	+	0.358664i	0.0554372	+	0.0148544i
$584$	−2.28792	−	18.6141i	−0.0946749	−	0.770259i
$585$	15.7469	−	4.54630i	0.651054	−	0.187966i
$586$	2.01292	+	9.20450i	0.0831531	+	0.380234i
$587$	23.3690	+	23.3690i	0.964544	+	0.964544i	0.999393	−	0.0348489i	$-0.0110950\pi$
$587$	23.3690	+	23.3690i	0.964544	+	0.964544i	−0.0348489	+	0.999393i	$0.511095\pi$
$588$		0			0
$589$		−	10.3214i		−	0.425288i
$590$	11.6946	−	19.0389i	0.481460	−	0.783820i
$591$	−48.7811	−	28.1638i	−2.00659	−	1.15850i
$592$	−27.3439	+	18.6828i	−1.12383	+	0.767859i
$593$	−1.67934	+	6.26739i	−0.0689623	+	0.257371i	−0.991797	−	0.127826i	$-0.959200\pi$
$593$	−1.67934	+	6.26739i	−0.0689623	+	0.257371i	0.922834	+	0.385197i	$0.125867\pi$
$594$	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
$598$	0.136639	−	2.93636i	0.00558758	−	0.120077i
$599$	8.75860	−	15.1703i	0.357867	−	0.619843i	−0.629737	−	0.776808i	$-0.716838\pi$
$599$	8.75860	−	15.1703i	0.357867	−	0.619843i	0.987604	+	0.156965i	$0.0501709\pi$
$600$	−16.1931	+	42.6629i	−0.661082	+	1.74171i
$601$	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
$605$	−17.6601	−	9.74727i	−0.717983	−	0.396283i
$606$	18.5347	+	20.3438i	0.752920	+	0.826412i
$607$	−5.72830	+	21.3783i	−0.232504	+	0.867718i	0.746754	+	0.665101i	$0.231611\pi$
$607$	−5.72830	+	21.3783i	−0.232504	+	0.867718i	−0.979258	+	0.202617i	$0.935055\pi$
$608$	11.5510	+	10.8932i	0.468457	+	0.441779i
$609$		0			0
$610$	−3.31062	−	6.11273i	−0.134043	−	0.247497i
$611$	−2.26378	+	1.30700i	−0.0915829	+	0.0528754i
$612$	−23.8048	+	64.2544i	−0.962250	+	2.59733i
$613$	−7.79104	+	2.08760i	−0.314677	+	0.0843175i	−0.412701	−	0.910867i	$-0.635415\pi$
$613$	−7.79104	+	2.08760i	−0.314677	+	0.0843175i	0.0980238	+	0.995184i	$0.468748\pi$
$614$	−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	−0.988031	−	0.154258i	$-0.950701\pi$
$617$	−20.7105	+	20.7105i	−0.833772	+	0.833772i	0.154258	+	0.988031i	$0.450701\pi$
$618$	34.6591	−	54.0612i	1.39419	−	2.17466i
$619$	15.2502	−	26.4141i	0.612956	−	1.06167i	−0.377784	−	0.925894i	$-0.623314\pi$
$619$	15.2502	−	26.4141i	0.612956	−	1.06167i	0.990739	−	0.135777i	$-0.0433530\pi$
$620$	7.15137	+	14.8095i	0.287206	+	0.594763i
$621$	−14.9597	−	25.9110i	−0.600314	−	1.03977i
$622$	−11.7946	−	22.8167i	−0.472921	−	0.914866i
$623$		0			0
$624$	4.22784	+	12.0438i	0.169249	+	0.482138i
$625$	−14.1299	−	20.6239i	−0.565197	−	0.824956i
$626$	−1.63964	+	1.49382i	−0.0655330	+	0.0597052i
$627$	12.3065	−	3.29753i	0.491476	−	0.131691i
$628$	−27.3548	+	22.6874i	−1.09157	+	0.905326i
$629$		−	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	$-0.160651\pi$
$632$	−1.57154	+	0.635173i	−0.0625123	+	0.0252658i
$633$	−60.9309	+	16.3264i	−2.42178	+	0.648915i
$634$	−28.1349	−	30.8811i	−1.11738	−	1.22644i
$635$	−27.2313	−	6.73706i	−1.08064	−	0.267352i
$636$	−3.67603	+	5.18637i	−0.145764	+	0.205653i
$637$		0			0
$638$	−8.58406	+	4.43735i	−0.339846	+	0.175676i
$639$	45.1709	+	78.2383i	1.78693	+	3.09506i
$640$	−24.1213	−	7.62658i	−0.953477	−	0.301467i
$641$	−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	$0.312650\pi$
$642$	−77.0595	−	49.4035i	−3.04130	−	1.94980i
$643$	3.56268	−	3.56268i	0.140498	−	0.140498i	−0.633359	−	0.773858i	$-0.718325\pi$
$643$	3.56268	−	3.56268i	0.140498	−	0.140498i	0.773858	+	0.633359i	$0.218325\pi$
$644$		0			0
$645$	−25.4913	+	0.491236i	−1.00372	+	0.0193424i
$646$	−17.9249	+	3.91997i	−0.705245	+	0.154229i
$647$	−16.0227	+	4.29327i	−0.629918	+	0.168786i	−0.559632	−	0.828741i	$-0.689058\pi$
$647$	−16.0227	+	4.29327i	−0.629918	+	0.168786i	−0.0702854	+	0.997527i	$0.522391\pi$
$648$	52.8246	+	41.2603i	2.07515	+	1.62086i
$649$	8.60829	−	4.97000i	0.337905	−	0.195089i
$650$	−6.74007	−	1.86365i	−0.264367	−	0.0730983i
$651$		0			0
$652$	5.84240	+	34.2821i	0.228806	+	1.34259i
$653$	−3.24782	+	12.1210i	−0.127097	+	0.474332i	−0.999906	−	0.0137300i	$-0.995629\pi$
$653$	−3.24782	+	12.1210i	−0.127097	+	0.474332i	0.872809	+	0.488062i	$0.162296\pi$
$654$	3.42430	−	3.11978i	0.133901	−	0.121993i
$655$	−14.2074	+	25.7409i	−0.555129	+	1.00578i
$656$	−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	$-0.274716\pi$
$659$	33.3787			1.30025			0.650126	+	0.759827i	$0.274716\pi$
$660$	−15.3730	+	13.2581i	−0.598393	+	0.516073i
$661$	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	$0.123463\pi$
$662$	17.8457	+	0.830422i	0.693593	+	0.0322753i
$663$	−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
$668$	−6.76973	+	18.2730i	−0.261929	+	0.707005i
$669$	−37.7211	−	21.7783i	−1.45838	−	0.841997i
$670$	−9.82862	+	2.34871i	−0.379713	+	0.0907387i
$671$		−	3.09256i		−	0.119387i
$672$		0			0
$673$	−5.34897	−	5.34897i	−0.206188	−	0.206188i	0.596457	−	0.802645i	$-0.296575\pi$
$673$	−5.34897	−	5.34897i	−0.206188	−	0.206188i	−0.802645	+	0.596457i	$0.796575\pi$
$674$	8.02127	−	1.75416i	0.308968	−	0.0675679i
$675$	−67.9905	+	21.0570i	−2.61696	+	0.810483i
$676$	21.8491	−	10.0363i	0.840350	−	0.386012i
$677$	−28.9931	−	7.76868i	−1.11430	−	0.298575i	−0.345723	−	0.938337i	$-0.612366\pi$
$677$	−28.9931	−	7.76868i	−1.11430	−	0.298575i	−0.768573	+	0.639762i	$0.779033\pi$
$678$	−42.3851	+	21.9101i	−1.62779	+	0.841451i
$679$		0			0
$680$	23.0030	−	18.0440i	0.882127	−	0.691955i
$681$	−29.7677	−	51.5592i	−1.14070	−	1.97575i
$682$	−0.340078	+	7.30825i	−0.0130223	+	0.279847i
$683$	4.92938	+	18.3967i	0.188618	+	0.703930i	0.993827	+	0.110940i	$0.0353861\pi$
$683$	4.92938	+	18.3967i	0.188618	+	0.703930i	−0.805210	+	0.592990i	$0.797947\pi$
$684$	−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
$688$	−1.07038	−	14.0941i	−0.0408080	−	0.537334i
$689$	−0.843665	−	0.487090i	−0.0321411	−	0.0185567i
$690$	−0.583938	+	21.4381i	−0.0222302	+	0.816135i
$691$	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	$0.152718\pi$
$692$	−48.7782	+	8.31284i	−1.85427	+	0.316007i
$693$		0			0
$694$	19.9020	+	6.33786i	0.755470	+	0.240582i
$695$	40.6615	−	24.5325i	1.54238	−	0.930569i
$696$	−5.40781	−	43.9970i	−0.204983	−	1.66770i
$697$	−4.22772	−	15.7781i	−0.160136	−	0.597638i
$698$	−3.85591	+	6.01445i	−0.145948	+	0.227650i
$699$	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	$0.663472\pi$
$702$	−10.7454	+	16.7607i	−0.405560	+	0.632593i
$703$	−6.01436	−	22.4459i	−0.226836	−	0.846563i
$704$	−7.81996	−	8.09370i	−0.294726	−	0.305043i
$705$	16.3292	−	9.85194i	0.614992	−	0.371046i
$706$	−14.6538	−	4.66656i	−0.551504	−	0.175628i
$707$		0			0
$708$	7.66046	+	44.9501i	0.287898	+	1.68933i
$709$	−15.2471	+	8.80290i	−0.572616	+	0.330600i	−0.758193	−	0.652030i	$-0.773918\pi$
$709$	−15.2471	+	8.80290i	−0.572616	+	0.330600i	0.185578	+	0.982630i	$0.440584\pi$
$710$	1.04952	−	38.5310i	0.0393877	−	1.44604i
$711$	−3.84667	−	2.22087i	−0.144261	−	0.0832893i
$712$	0.491438	+	1.21591i	0.0184174	+	0.0455681i
$713$	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
$717$	12.9239	+	48.2328i	0.482653	+	1.80129i
$718$	−0.327803	+	7.04445i	−0.0122335	+	0.262897i
$719$	11.5866	+	20.0685i	0.432106	+	0.748429i	0.997054	−	0.0766969i	$-0.0244374\pi$
$719$	11.5866	+	20.0685i	0.432106	+	0.748429i	−0.564949	+	0.825126i	$0.691104\pi$
$720$	−23.1586	−	62.1156i	−0.863070	−	2.31491i
$721$		0			0
$722$	13.9727	−	7.22290i	0.520011	−	0.268809i
$723$	−89.6445	−	24.0202i	−3.33391	−	0.893320i
$724$	−6.56167	−	14.2848i	−0.243863	−	0.530891i
$725$	21.4839	+	11.3233i	0.797892	+	0.420538i
$726$	40.2146	−	8.79448i	1.49250	−	0.326394i
$727$	−15.3777	−	15.3777i	−0.570326	−	0.570326i	0.361893	−	0.932220i	$-0.382131\pi$
$727$	−15.3777	−	15.3777i	−0.570326	−	0.570326i	−0.932220	+	0.361893i	$0.882131\pi$
$728$		0			0
$729$			37.8443i			1.40164i
$730$	−20.3937	+	4.87341i	−0.754803	+	0.180373i
$731$	14.1462	+	8.16734i	0.523218	+	0.302080i
$732$	13.3031	+	4.92847i	0.491695	+	0.182162i
$733$	−10.8115	+	40.3490i	−0.399331	+	1.49032i	0.414944	+	0.909847i	$0.363801\pi$
$733$	−10.8115	+	40.3490i	−0.399331	+	1.49032i	−0.814276	+	0.580478i	$0.802866\pi$
$734$	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
$738$	−36.9990	−	1.72169i	−1.36195	−	0.0633764i
$739$	14.4738	−	25.0693i	0.532426	−	0.922189i	−0.466857	−	0.884333i	$-0.654614\pi$
$739$	14.4738	−	25.0693i	0.532426	−	0.922189i	0.999283	−	0.0378565i	$-0.0120530\pi$
$740$	24.1815	+	28.0388i	0.888930	+	1.03073i
$741$	−8.95654			−0.329027
$742$		0			0
$743$	−23.4115	+	23.4115i	−0.858885	+	0.858885i	−0.991207	−	0.132322i	$-0.957757\pi$
$743$	−23.4115	+	23.4115i	−0.858885	+	0.858885i	0.132322	+	0.991207i	$0.457757\pi$
$744$	−30.8954	−	13.1097i	−1.13268	−	0.480625i
$745$	7.17953	−	13.0078i	0.263038	−	0.476570i
$746$	−0.615954	+	0.561178i	−0.0225517	+	0.0205462i
$747$	−12.3100	+	45.9417i	−0.450401	+	1.68092i
$748$	12.8211	−	2.18499i	0.468786	−	0.0798912i
$749$		0			0
$750$	49.4266	+	12.6467i	1.80480	+	0.461793i
$751$	−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	$0.630129\pi$
$752$	5.96457	+	8.72964i	0.217505	+	0.318337i
$753$	81.1249	−	21.7373i	2.95636	−	0.792153i
$754$	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	−0.0972943	−	0.995256i	$-0.531019\pi$
$757$	24.7062	−	24.7062i	0.897961	−	0.897961i	0.995256	+	0.0972943i	$0.0310188\pi$
$758$	28.2855	+	18.1341i	1.02738	+	0.658659i
$759$	−4.77032	+	8.26243i	−0.173152	+	0.299907i
$760$	10.6555	−	14.1976i	0.386516	−	0.515001i
$761$	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	$0.807360\pi$
$762$	50.8551	−	26.2885i	1.84229	−	0.952331i
$763$		0			0
$764$	−14.1509	−	10.0300i	−0.511963	−	0.362872i
$765$	74.3680	+	18.3987i	2.68878	+	0.665207i
$766$	−4.09169	−	4.49108i	−0.147839	−	0.162269i
$767$	−6.74959	+	1.80855i	−0.243714	+	0.0653029i
$768$	47.2784	−	20.7400i	1.70601	−	0.748391i
$769$			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
$772$	6.77398	+	8.16757i	0.243801	+	0.293957i
$773$	−26.7544	+	7.16881i	−0.962287	+	0.257844i	−0.705568	−	0.708642i	$-0.749308\pi$
$773$	−26.7544	+	7.16881i	−0.962287	+	0.257844i	−0.256719	+	0.966486i	$0.582642\pi$
$774$	27.3797	−	24.9449i	0.984143	−	0.896624i
$775$	15.5575	−	9.80011i	0.558842	−	0.352030i
$776$	19.2747	+	25.5717i	0.691923	+	0.917971i
$777$		0			0
$778$	−16.3587	−	31.6460i	−0.586489	−	1.13456i
$779$	−4.95906	−	8.58934i	−0.177677	−	0.307745i
$780$	12.8511	−	6.20567i	0.460142	−	0.222199i
$781$	8.57374	−	14.8502i	0.306793	−	0.531380i
$782$	7.41566	−	11.5669i	0.265183	−	0.413633i
$783$	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
$787$	−5.43008	+	1.45499i	−0.193561	+	0.0518646i	−0.354297	−	0.935133i	$-0.615280\pi$
$787$	−5.43008	+	1.45499i	−0.193561	+	0.0518646i	0.160736	+	0.986997i	$0.448613\pi$
$788$	−32.7387	−	12.1289i	−1.16627	−	0.432075i
$789$	−31.7166	+	18.3116i	−1.12914	+	0.651911i
$790$	0.902519	+	1.66641i	0.0321102	+	0.0592882i
$791$		0			0
$792$	4.10068	−	29.2047i	0.145711	−	1.03774i
$793$	−0.562681	+	2.09996i	−0.0199814	+	0.0745716i
$794$	3.68582	+	4.04559i	0.130805	+	0.143572i
$795$	6.22248	+	3.43443i	0.220689	+	0.121807i
$796$	−8.56049	−	0.798427i	−0.303419	−	0.0282995i
$797$	−10.9874	+	10.9874i	−0.389195	+	0.389195i	−0.874400	−	0.485205i	$-0.838745\pi$
$797$	−10.9874	+	10.9874i	−0.389195	+	0.389195i	0.485205	+	0.874400i	$0.338745\pi$
$798$		0			0
$799$	−12.2183			−0.432252
$800$	−5.45176	+	27.7539i	−0.192749	+	0.981248i
$801$	−1.71830	+	2.97619i	−0.0607133	+	0.105159i
$802$	−0.360718	+	7.75180i	−0.0127374	+	0.273726i
$803$	−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
$808$	13.4434	+	10.5004i	0.472936	+	0.369402i
$809$	14.4297	+	8.33096i	0.507320	+	0.292901i	0.731731	−	0.681593i	$-0.238713\pi$
$809$	14.4297	+	8.33096i	0.507320	+	0.292901i	−0.224412	+	0.974494i	$0.572046\pi$
$810$	39.2234	−	63.8560i	1.37817	−	2.24367i
$811$			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
$815$	37.3554	−	10.7849i	1.30850	−	0.377779i
$816$	−11.0334	+	58.6338i	−0.386246	+	2.05259i
$817$	9.58017	+	2.56700i	0.335168	+	0.0898079i
$818$	11.0355	+	21.3481i	0.385846	+	0.746420i
$819$		0			0
$820$	13.0666	+	8.88825i	0.456307	+	0.310391i
$821$	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	$0.728791\pi$
$822$	−31.8584	−	1.48248i	−1.11119	−	0.0517075i
$823$	11.0750	+	41.3323i	0.386049	+	1.44075i	0.836507	+	0.547957i	$0.184594\pi$
$823$	11.0750	+	41.3323i	0.386049	+	1.44075i	−0.450457	+	0.892798i	$0.648739\pi$
$824$	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	$-0.0605726\pi$
$827$	22.7990	+	22.7990i	0.792801	+	0.792801i	−0.189148	+	0.981949i	$0.560573\pi$
$828$	−19.8892	−	23.9809i	−0.691198	−	0.833395i
$829$	29.0025	+	16.7446i	1.00730	+	0.581563i	0.910399	−	0.413731i	$-0.135775\pi$
$829$	29.0025	+	16.7446i	1.00730	+	0.581563i	0.0968981	+	0.995294i	$0.469108\pi$
$830$	14.7347	−	13.9533i	0.511448	−	0.484324i
$831$	58.4953	−	33.7723i	2.02918	−	1.17155i
$832$	3.83740	+	6.91871i	0.133038	+	0.239863i
$833$		0			0
$834$	−29.4072	+	92.3440i	−1.01829	+	3.19761i
$835$	21.1492	+	5.23233i	0.731898	+	0.181072i
$836$	7.17612	−	3.29632i	0.248191	−	0.114006i
$837$	−13.5488	−	50.5649i	−0.468316	−	1.74778i
$838$	4.61406	+	2.95811i	0.159390	+	0.102186i
$839$	−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
$842$	24.6635	+	15.8119i	0.849959	+	0.544916i
$843$	−2.14092	−	7.99001i	−0.0737371	−	0.275190i
$844$	−35.5296	+	16.3204i	−1.22298	+	0.561772i
$845$	−13.8870	−	23.0171i	−0.477728	−	0.791814i
$846$	−8.40681	+	26.3989i	−0.289032	+	0.907612i
$847$		0			0
$848$	−1.70605	+	3.55174i	−0.0585862	+	0.121967i
$849$	57.4949	−	33.1947i	1.97322	−	1.13924i
$850$	−22.9281	−	23.2962i	−0.786426	−	0.799052i
$851$	15.0698	+	8.70057i	0.516587	+	0.298252i
$852$	50.2163	+	60.5471i	1.72038	+	2.07431i
$853$	10.0581	+	10.0581i	0.344383	+	0.344383i	0.858012	−	0.513629i	$-0.171699\pi$
$853$	10.0581	+	10.0581i	0.344383	+	0.344383i	−0.513629	+	0.858012i	$0.671699\pi$
$854$		0			0
$855$	46.5077	−	0.896235i	1.59053	−	0.0306506i
$856$	−52.2289	−	22.1621i	−1.78515	−	0.757484i
$857$	−0.134823	−	0.503168i	−0.00460548	−	0.0171879i	0.963585	−	0.267403i	$-0.0861654\pi$
$857$	−0.134823	−	0.503168i	−0.00460548	−	0.0171879i	−0.968190	+	0.250215i	$0.919499\pi$
$858$	6.34180	+	0.295106i	0.216506	+	0.0100747i
$859$	2.00473	+	3.47230i	0.0684006	+	0.118473i	0.898197	−	0.439592i	$-0.144877\pi$
$859$	2.00473	+	3.47230i	0.0684006	+	0.118473i	−0.829797	+	0.558066i	$0.811544\pi$
$860$	−15.5244	+	2.95457i	−0.529379	+	0.100750i
$861$		0			0
$862$	−6.34407	−	12.2726i	−0.216080	−	0.418007i
$863$	−14.3236	−	3.83800i	−0.487581	−	0.130647i	0.00664926	−	0.999978i	$-0.497883\pi$
$863$	−14.3236	−	3.83800i	−0.487581	−	0.130647i	−0.494231	+	0.869331i	$0.664550\pi$
$864$	70.8882	+	38.2032i	2.41166	+	1.29970i
$865$	15.3453	+	53.1511i	0.521756	+	1.80719i
$866$	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
$870$	−48.2031	+	11.5189i	−1.63424	+	0.390529i
$871$	2.73690	+	1.58015i	0.0927364	+	0.0535414i
$872$	1.76744	−	2.26280i	0.0598529	−	0.0766282i
$873$	−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	0.726262	−	0.687418i	$-0.241256\pi$
$877$	29.9552	+	8.02646i	1.01151	+	0.271034i	0.285252	+	0.958453i	$0.407923\pi$
$878$	−0.290939	+	6.25225i	−0.00981871	+	0.211003i
$879$	−10.7488	+	18.6175i	−0.362548	+	0.627952i
$880$	−8.01257	+	9.70173i	−0.270104	+	0.327045i
$881$	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	$-0.910278\pi$
$883$	−20.2772	+	20.2772i	−0.682383	+	0.682383i	0.278154	+	0.960537i	$0.410278\pi$
$884$	−9.10352	−	0.849075i	−0.306185	−	0.0285575i
$885$	48.9799	−	14.1410i	1.64644	−	0.475345i
$886$	−4.19245	−	4.60167i	−0.140848	−	0.154596i
$887$	−11.0601	+	41.2767i	−0.371361	+	1.38594i	0.487229	+	0.873274i	$0.338008\pi$
$887$	−11.0601	+	41.2767i	−0.371361	+	1.38594i	−0.858590	+	0.512663i	$0.828659\pi$
$888$	−74.8268	−	10.5066i	−2.51102	−	0.352577i
$889$		0			0
$890$	1.28931	−	0.698285i	0.0432179	−	0.0234066i
$891$	28.8720	−	16.6692i	0.967247	−	0.558440i
$892$	−25.3159	−	9.37896i	−0.847640	−	0.314031i
$893$	−7.16594	+	1.92011i	−0.239799	+	0.0642540i
$894$	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
$898$	−16.6664	+	25.9963i	−0.556166	+	0.867508i
$899$	−8.93063	+	15.4683i	−0.297853	+	0.515897i
$900$	−66.1094	+	33.5095i	−2.20365	+	1.11698i
$901$	−2.27675	−	3.94345i	−0.0758496	−	0.131375i
$902$	3.22832	+	6.24520i	0.107491	+	0.207942i
$903$		0			0
$904$	−23.6164	+	17.8010i	−0.785471	+	0.592051i
$905$	−15.0485	+	9.07925i	−0.500228	+	0.301804i
$906$	68.7692	−	62.6537i	2.28471	−	2.08153i
$907$	1.18466	−	0.317430i	0.0393361	−	0.0105401i	−0.239097	−	0.970996i	$-0.576852\pi$
$907$	1.18466	−	0.317430i	0.0393361	−	0.0105401i	0.278433	+	0.960456i	$0.410185\pi$
$908$	−23.5574	−	28.4037i	−0.781780	−	0.942611i
$909$			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	$0.928620\pi$
$912$	2.74331	+	36.1222i	0.0908401	+	1.19613i
$913$	8.72004	−	2.33653i	0.288591	−	0.0773277i
$914$	20.9820	+	23.0301i	0.694024	+	0.761767i
$915$	3.80922	−	15.3970i	0.125929	−	0.509008i
$916$	25.4827	+	18.0618i	0.841974	+	0.596779i
$917$		0			0
$918$	−82.6686	+	42.7338i	−2.72847	+	1.41042i
$919$	−13.1243	−	22.7320i	−0.432931	−	0.749858i	0.564193	−	0.825643i	$-0.309187\pi$
$919$	−13.1243	−	22.7320i	−0.432931	−	0.749858i	−0.997124	+	0.0757845i	$0.975854\pi$
$920$	1.87556	+	13.1598i	0.0618353	+	0.433867i
$921$	38.4473	−	66.5926i	1.26688	−	2.19430i
$922$	−23.5337	−	15.0876i	−0.775040	−	0.496884i
$923$	−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
$927$	100.748	−	26.9955i	3.30901	−	0.886647i
$928$	−7.88567	−	26.3197i	−0.258860	−	0.863988i
$929$	−17.2412	+	9.95422i	−0.565666	+	0.326587i	−0.755416	−	0.655245i	$-0.772565\pi$
$929$	−17.2412	+	9.95422i	−0.565666	+	0.326587i	0.189751	+	0.981832i	$0.439232\pi$
$930$	−10.6950	+	35.9667i	−0.350702	+	1.17940i
$931$		0			0
$932$	7.53711	−	1.28448i	0.246886	−	0.0420747i
$933$	15.1677	−	56.6067i	0.496569	−	1.85322i
$934$	29.4721	−	26.8512i	0.964356	−	0.878597i
$935$	−4.03344	−	13.9705i	−0.131908	−	0.456885i
$936$	−8.09820	+	19.0849i	−0.264698	+	0.623809i
$937$	−3.76752	+	3.76752i	−0.123080	+	0.123080i	−0.765964	−	0.642884i	$-0.777738\pi$
$937$	−3.76752	+	3.76752i	−0.123080	+	0.123080i	0.642884	+	0.765964i	$0.277738\pi$
$938$		0			0
$939$	−5.06087			−0.165155
$940$	8.95150	−	7.72005i	0.291966	−	0.251800i
$941$	−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	$0.191800\pi$
$942$	−80.9988	−	3.76915i	−2.63908	−	0.122806i
$943$	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	0.703872	+	0.710327i	$0.251453\pi$
$947$	−8.02761	+	29.9595i	−0.260862	+	0.973551i	−0.964735	+	0.263225i	$0.915214\pi$
$948$	−3.62659	−	1.34357i	−0.117786	−	0.0436370i
$949$	5.67887	+	3.27870i	0.184344	+	0.106431i
$950$	−17.1081	−	10.0599i	−0.555061	−	0.326386i
$951$		−	95.3170i		−	3.09086i
$952$		0			0
$953$	22.3422	+	22.3422i	0.723734	+	0.723734i	0.969364	−	0.245630i	$-0.0789947\pi$
$953$	22.3422	+	22.3422i	0.723734	+	0.723734i	−0.245630	+	0.969364i	$0.578995\pi$
$954$	−10.0868	+	2.20586i	−0.326571	+	0.0714174i
$955$	−9.37078	+	16.9779i	−0.303231	+	0.549393i
$956$	12.9192	+	28.1252i	0.417837	+	0.909634i
$957$	−21.2965	−	5.70637i	−0.688417	−	0.184461i
$958$	1.78236	−	0.921354i	0.0575855	−	0.0297676i
$959$		0			0
$960$	−28.9640	−	49.9283i	−0.934808	−	1.61143i
$961$	−8.73844	−	15.1354i	−0.281885	−	0.488239i
$962$	0.538243	−	11.5668i	0.0173537	−	0.372929i
$963$	−38.4796	−	143.608i	−1.23999	−	4.62770i
$964$	−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	$-0.185456\pi$
$967$	8.85634	+	8.85634i	0.284801	+	0.284801i	−0.550219	+	0.835020i	$0.685456\pi$
$968$	23.6560	−	9.56111i	0.760331	−	0.307306i
$969$	−36.2558	−	20.9323i	−1.16470	−	0.672442i
$970$	25.9958	−	24.6172i	0.834674	−	0.790409i
$971$	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	$0.284840\pi$
$972$	11.3438	+	66.5634i	0.363854	+	2.13502i
$973$		0			0
$974$	45.3582	+	14.4445i	1.45337	+	0.462831i
$975$	−8.50414	−	13.5002i	−0.272350	−	0.432352i
$976$	8.64158	+	1.62613i	0.276610	+	0.0520510i
$977$	−15.9873	−	59.6654i	−0.511479	−	1.90886i	−0.404305	−	0.914624i	$-0.632487\pi$
$977$	−15.9873	−	59.6654i	−0.511479	−	1.90886i	−0.107173	−	0.994240i	$-0.534180\pi$
$978$	−42.8247	+	66.7980i	−1.36938	+	2.13596i
$979$	0.652291			0.0208473
$980$		0			0
$981$	7.52393			0.240221
$982$	−2.41708	+	3.77016i	−0.0771321	+	0.120311i
$983$	15.3538	+	57.3012i	0.489710	+	1.82762i	0.557842	+	0.829947i	$0.311630\pi$
$983$	15.3538	+	57.3012i	0.489710	+	1.82762i	−0.0681315	+	0.997676i	$0.521704\pi$
$984$	−32.0094	+	3.93437i	−1.02042	+	0.125423i
$985$	−9.37447	+	37.8918i	−0.298695	+	1.20733i
$986$	30.2550	+	9.63480i	0.963515	+	0.306834i
$987$		0			0
$988$	−5.47258	+	0.932645i	−0.174106	+	0.0296714i
$989$	−6.43198	+	3.71351i	−0.204525	+	0.118083i
$990$	−32.9599	−	0.897773i	−1.04754	−	0.0285331i
$991$	−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	$0.755501\pi$
$992$	−20.2427	−	4.79309i	−0.642706	−	0.152181i
$993$	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
$997$	3.99308	+	14.9024i	0.126462	+	0.471964i	0.999888	−	0.0149945i	$-0.00477309\pi$
$997$	3.99308	+	14.9024i	0.126462	+	0.471964i	−0.873425	+	0.486958i	$0.838106\pi$
$998$	0.489677	−	10.5231i	0.0155005	−	0.333104i
$999$	−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.263.16		72
4.3	odd	2	inner	980.2.x.k.263.18		72
5.2	odd	4	inner	980.2.x.k.67.7		72
7.2	even	3	inner	980.2.x.k.863.10		72
7.3	odd	6		980.2.k.l.883.3		36
7.4	even	3		140.2.k.a.43.3	✓	36
7.5	odd	6		980.2.x.l.863.10		72
7.6	odd	2		980.2.x.l.263.16		72
20.7	even	4	inner	980.2.x.k.67.10		72
28.3	even	6		980.2.k.l.883.6		36
28.11	odd	6		140.2.k.a.43.6	yes	36
28.19	even	6		980.2.x.l.863.7		72
28.23	odd	6	inner	980.2.x.k.863.7		72
28.27	even	2		980.2.x.l.263.18		72
35.2	odd	12	inner	980.2.x.k.667.18		72
35.4	even	6		700.2.k.b.43.16		36
35.12	even	12		980.2.x.l.667.18		72
35.17	even	12		980.2.k.l.687.6		36
35.18	odd	12		700.2.k.b.407.13		36
35.27	even	4		980.2.x.l.67.7		72
35.32	odd	12		140.2.k.a.127.6	yes	36
140.27	odd	4		980.2.x.l.67.10		72
140.39	odd	6		700.2.k.b.43.13		36
140.47	odd	12		980.2.x.l.667.16		72
140.67	even	12		140.2.k.a.127.3	yes	36
140.87	odd	12		980.2.k.l.687.3		36
140.107	even	12	inner	980.2.x.k.667.16		72
140.123	even	12		700.2.k.b.407.16		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.3	✓	36	7.4	even	3
140.2.k.a.43.6	yes	36	28.11	odd	6
140.2.k.a.127.3	yes	36	140.67	even	12
140.2.k.a.127.6	yes	36	35.32	odd	12
700.2.k.b.43.13		36	140.39	odd	6
700.2.k.b.43.16		36	35.4	even	6
700.2.k.b.407.13		36	35.18	odd	12
700.2.k.b.407.16		36	140.123	even	12
980.2.k.l.687.3		36	140.87	odd	12
980.2.k.l.687.6		36	35.17	even	12
980.2.k.l.883.3		36	7.3	odd	6
980.2.k.l.883.6		36	28.3	even	6
980.2.x.k.67.7		72	5.2	odd	4	inner
980.2.x.k.67.10		72	20.7	even	4	inner
980.2.x.k.263.16		72	1.1	even	1	trivial
980.2.x.k.263.18		72	4.3	odd	2	inner
980.2.x.k.667.16		72	140.107	even	12	inner
980.2.x.k.667.18		72	35.2	odd	12	inner
980.2.x.k.863.7		72	28.23	odd	6	inner
980.2.x.k.863.10		72	7.2	even	3	inner
980.2.x.l.67.7		72	35.27	even	4
980.2.x.l.67.10		72	140.27	odd	4
980.2.x.l.263.16		72	7.6	odd	2
980.2.x.l.263.18		72	28.27	even	2
980.2.x.l.667.16		72	140.47	odd	12
980.2.x.l.667.18		72	35.12	even	12
980.2.x.l.863.7		72	28.19	even	6
980.2.x.l.863.10		72	7.5	odd	6

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)

\(f(q)\)	\(=\)	\(q+(1.19055 + 0.763272i) q^{2} +(0.835136 + 3.11677i) q^{3} +(0.834830 + 1.81743i) q^{4} +(1.91459 - 1.15514i) q^{5} +(-1.38467 + 4.34811i) q^{6} +(-0.393286 + 2.80095i) q^{8} +(-6.41872 + 3.70585i) q^{9} +O(q^{10})\)	\(q+(1.19055 + 0.763272i) q^{2} +(0.835136 + 3.11677i) q^{3} +(0.834830 + 1.81743i) q^{4} +(1.91459 - 1.15514i) q^{5} +(-1.38467 + 4.34811i) q^{6} +(-0.393286 + 2.80095i) q^{8} +(-6.41872 + 3.70585i) q^{9} +(3.16111 + 0.0861032i) q^{10} +(1.21832 + 0.703395i) q^{11} +(-4.96732 + 4.11978i) q^{12} +(-0.699298 - 0.699298i) q^{13} +(5.19924 + 5.00264i) q^{15} +(-2.60612 + 3.03449i) q^{16} +(-1.19641 - 4.46506i) q^{17} +(-10.4704 - 0.487224i) q^{18} +(-1.40337 - 2.43071i) q^{19} +(3.69774 + 2.51529i) q^{20} +(0.913587 + 1.76734i) q^{22} +(2.03016 + 0.543980i) q^{23} +(-9.05837 + 1.11339i) q^{24} +(2.33132 - 4.42323i) q^{25} +(-0.298796 - 1.36631i) q^{26} +(-10.0659 - 10.0659i) q^{27} +4.85706i q^{29} +(2.37159 + 9.92434i) q^{30} +(3.18470 + 1.83869i) q^{31} +(-5.41886 + 1.62355i) 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} +(0.184507 - 3.96504i) q^{38} +(1.59554 - 2.76356i) q^{39} +(2.48250 + 5.81697i) q^{40} +3.53368 q^{41} +(-2.49869 + 2.49869i) q^{43} +(-0.261285 + 2.80142i) q^{44} +(-8.00846 + 14.5097i) q^{45} +(2.00181 + 2.19720i) q^{46} +(0.684106 - 2.55312i) q^{47} +(-11.6343 - 5.58845i) q^{48} +(6.15168 - 3.48666i) q^{50} +(12.9174 - 7.45786i) q^{51} +(0.687131 - 1.85472i) q^{52} +(0.951495 - 0.254952i) q^{53} +(-4.30095 - 19.6670i) q^{54} +(3.14510 - 0.0606082i) q^{55} +(6.40395 - 6.40395i) q^{57} +(-3.70726 + 5.78258i) q^{58} +(3.53286 - 6.11910i) q^{59} +(-4.75148 + 13.6256i) q^{60} +(-1.09916 - 1.90379i) q^{61} +(2.38814 + 4.61985i) q^{62} +(-7.69065 - 2.20315i) q^{64} +(-2.14665 - 0.531084i) q^{65} +(-4.74541 + 4.32341i) q^{66} +(-3.08671 + 0.827081i) q^{67} +(7.11614 - 5.90196i) q^{68} +6.78184i q^{69} -12.1891i q^{71} +(-7.85551 - 19.4360i) q^{72} +(-6.40469 + 1.71613i) q^{73} +(7.88545 + 8.65515i) q^{74} +(15.7332 + 3.57218i) q^{75} +(3.24607 - 4.57976i) q^{76} +(4.00892 - 2.07233i) q^{78} +(0.299644 + 0.518999i) q^{79} +(-1.48439 + 8.82024i) q^{80} +(11.8491 - 20.5233i) q^{81} +(4.20703 + 2.69716i) q^{82} +(4.53764 - 4.53764i) q^{83} +(-7.44839 - 7.16674i) q^{85} +(-4.88200 + 1.06764i) q^{86} +(-15.1383 + 4.05630i) q^{87} +(-2.44932 + 3.13581i) q^{88} +(0.401553 - 0.231837i) q^{89} +(-20.6093 + 11.1619i) q^{90} +(0.706194 + 4.14381i) q^{92} +(-3.07111 + 11.4615i) q^{93} +(2.76319 - 2.51746i) q^{94} +(-5.49468 - 3.03273i) 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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