LMFDB - Embedded newform 280.2.s.c.13.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(13,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3, 2]))

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

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

chi := DirichletCharacter("280.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.15
Character	$\chi$	$=$	280.13
Dual form			280.2.s.c.237.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.349904 + 1.37024i) q^{2} +(-0.152811 - 0.152811i) q^{3} +(-1.75513 - 0.958907i) q^{4} +(-2.05351 + 0.884920i) q^{5} +(0.262858 - 0.155920i) q^{6} +(-0.192988 - 2.63870i) q^{7} +(1.92806 - 2.06944i) q^{8} -2.95330i q^{9} +O(q^{10})$	\(q+(-0.349904 + 1.37024i) q^{2} +(-0.152811 - 0.152811i) q^{3} +(-1.75513 - 0.958907i) q^{4} +(-2.05351 + 0.884920i) q^{5} +(0.262858 - 0.155920i) q^{6} +(-0.192988 - 2.63870i) q^{7} +(1.92806 - 2.06944i) q^{8} -2.95330i q^{9} +(-0.494024 - 3.12345i) q^{10} -1.71191i q^{11} +(0.121673 + 0.414737i) q^{12} +(2.61784 + 2.61784i) q^{13} +(3.68319 + 0.658852i) q^{14} +(0.449026 + 0.178574i) q^{15} +(2.16100 + 3.36602i) q^{16} +(-3.67050 - 3.67050i) q^{17} +(4.04674 + 1.03337i) q^{18} -4.22745i q^{19} +(4.45275 + 0.415973i) q^{20} +(-0.373733 + 0.432715i) q^{21} +(2.34573 + 0.599003i) q^{22} +(2.74570 + 2.74570i) q^{23} +(-0.610864 + 0.0216035i) q^{24} +(3.43383 - 3.63439i) q^{25} +(-4.50307 + 2.67108i) q^{26} +(-0.909732 + 0.909732i) q^{27} +(-2.19155 + 4.81634i) q^{28} -10.0191 q^{29} +(-0.401806 + 0.552792i) q^{30} -8.50400i q^{31} +(-5.36841 + 1.78331i) q^{32} +(-0.261599 + 0.261599i) q^{33} +(6.31380 - 3.74516i) q^{34} +(2.73135 + 5.24783i) q^{35} +(-2.83194 + 5.18343i) q^{36} +(-2.20040 - 2.20040i) q^{37} +(5.79264 + 1.47920i) q^{38} -0.800071i q^{39} +(-2.12802 + 5.95580i) q^{40} +3.07334i q^{41} +(-0.462154 - 0.663514i) q^{42} +(4.25689 - 4.25689i) q^{43} +(-1.64156 + 3.00463i) q^{44} +(2.61343 + 6.06463i) q^{45} +(-4.72301 + 2.80155i) q^{46} +(7.96917 + 7.96917i) q^{47} +(0.184142 - 0.844592i) q^{48} +(-6.92551 + 1.01848i) q^{49} +(3.77849 + 5.97687i) q^{50} +1.12179i q^{51} +(-2.08440 - 7.10492i) q^{52} +(-1.49101 + 1.49101i) q^{53} +(-0.928236 - 1.56487i) q^{54} +(1.51490 + 3.51543i) q^{55} +(-5.83272 - 4.68821i) q^{56} +(-0.646003 + 0.646003i) q^{57} +(3.50571 - 13.7286i) q^{58} -9.80345i q^{59} +(-0.616866 - 0.743996i) q^{60} -5.41890 q^{61} +(11.6525 + 2.97558i) q^{62} +(-7.79288 + 0.569950i) q^{63} +(-0.565140 - 7.98001i) q^{64} +(-7.69234 - 3.05919i) q^{65} +(-0.266920 - 0.449989i) q^{66} +(5.57302 + 5.57302i) q^{67} +(2.92256 + 9.96189i) q^{68} -0.839149i q^{69} +(-8.14652 + 1.90637i) q^{70} -6.76483 q^{71} +(-6.11166 - 5.69415i) q^{72} +(-3.80923 + 3.80923i) q^{73} +(3.78501 - 2.24516i) q^{74} +(-1.08011 + 0.0306476i) q^{75} +(-4.05373 + 7.41974i) q^{76} +(-4.51722 + 0.330377i) q^{77} +(1.09629 + 0.279948i) q^{78} +6.18844i q^{79} +(-7.41629 - 4.99986i) q^{80} -8.58186 q^{81} +(-4.21123 - 1.07537i) q^{82} +(-2.48782 - 2.48782i) q^{83} +(1.07089 - 0.401098i) q^{84} +(10.7855 + 4.28932i) q^{85} +(4.34348 + 7.32249i) q^{86} +(1.53103 + 1.53103i) q^{87} +(-3.54269 - 3.30067i) q^{88} +12.4324 q^{89} +(-9.22448 + 1.45900i) q^{90} +(6.40249 - 7.41291i) q^{91} +(-2.18620 - 7.45195i) q^{92} +(-1.29951 + 1.29951i) q^{93} +(-13.7081 + 8.13126i) q^{94} +(3.74096 + 8.68112i) q^{95} +(1.09286 + 0.547844i) q^{96} +(2.43265 + 2.43265i) q^{97} +(1.02770 - 9.84601i) q^{98} -5.05577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.349904	+	1.37024i	−0.247419	+	0.968909i
$2$	−0.349904	+	1.37024i	−0.247419	+	0.968909i
$3$	−0.152811	−	0.152811i	−0.0882257	−	0.0882257i	0.661617	−	0.749842i	$-0.269871\pi$
$3$	−0.152811	−	0.152811i	−0.0882257	−	0.0882257i	−0.749842	+	0.661617i	$0.769871\pi$
$4$	−1.75513	−	0.958907i	−0.877567	−	0.479453i
$5$	−2.05351	+	0.884920i	−0.918359	+	0.395748i
$5$	−2.05351	+	0.884920i	−0.918359	+	0.395748i
$6$	0.262858	−	0.155920i	0.107311	−	0.0636539i
$7$	−0.192988	−	2.63870i	−0.0729425	−	0.997336i
$7$	−0.192988	−	2.63870i	−0.0729425	−	0.997336i
$8$	1.92806	−	2.06944i	0.681673	−	0.731657i
$9$		−	2.95330i		−	0.984432i
$10$	−0.494024	−	3.12345i	−0.156224	−	0.987722i
$11$		−	1.71191i		−	0.516160i	−0.966124	−	0.258080i	$-0.916910\pi$
$11$		−	1.71191i		−	0.516160i	0.966124	−	0.258080i	$-0.0830898\pi$
$12$	0.121673	+	0.414737i	0.0351239	+	0.119724i
$13$	2.61784	+	2.61784i	0.726058	+	0.726058i	0.969832	−	0.243774i	$-0.0783856\pi$
$13$	2.61784	+	2.61784i	0.726058	+	0.726058i	−0.243774	+	0.969832i	$0.578386\pi$
$14$	3.68319	+	0.658852i	0.984375	+	0.176086i
$15$	0.449026	+	0.178574i	0.115938	+	0.0461077i
$16$	2.16100	+	3.36602i	0.540249	+	0.841505i
$17$	−3.67050	−	3.67050i	−0.890227	−	0.890227i	0.104317	−	0.994544i	$-0.466734\pi$
$17$	−3.67050	−	3.67050i	−0.890227	−	0.890227i	−0.994544	+	0.104317i	$0.966734\pi$
$18$	4.04674	+	1.03337i	0.953825	+	0.243568i
$19$		−	4.22745i		−	0.969843i	−0.874558	−	0.484922i	$-0.838848\pi$
$19$		−	4.22745i		−	0.969843i	0.874558	−	0.484922i	$-0.161152\pi$
$20$	4.45275	+	0.415973i	0.995665	+	0.0930144i
$21$	−0.373733	+	0.432715i	−0.0815553	+	0.0944261i
$22$	2.34573	+	0.599003i	0.500112	+	0.127708i
$23$	2.74570	+	2.74570i	0.572518	+	0.572518i	0.932831	−	0.360313i	$-0.117330\pi$
$23$	2.74570	+	2.74570i	0.572518	+	0.572518i	−0.360313	+	0.932831i	$0.617330\pi$
$24$	−0.610864	+	0.0216035i	−0.124692	+	0.00440979i
$25$	3.43383	−	3.63439i	0.686766	−	0.726878i
$26$	−4.50307	+	2.67108i	−0.883124	+	0.523843i
$27$	−0.909732	+	0.909732i	−0.175078	+	0.175078i
$28$	−2.19155	+	4.81634i	−0.414164	+	0.910202i
$29$	−10.0191			−1.86049			−0.930247	−	0.366933i	$-0.880408\pi$
$29$	−10.0191			−1.86049			−0.930247	+	0.366933i	$0.880408\pi$
$30$	−0.401806	+	0.552792i	−0.0733595	+	0.100925i
$31$		−	8.50400i		−	1.52736i	−0.645593	−	0.763682i	$-0.723390\pi$
$31$		−	8.50400i		−	1.52736i	0.645593	−	0.763682i	$-0.276610\pi$
$32$	−5.36841	+	1.78331i	−0.949010	+	0.315247i
$33$	−0.261599	+	0.261599i	−0.0455386	+	0.0455386i
$34$	6.31380	−	3.74516i	1.08281	−	0.642289i
$35$	2.73135	+	5.24783i	0.461682	+	0.887046i
$36$	−2.83194	+	5.18343i	−0.471989	+	0.863906i
$37$	−2.20040	−	2.20040i	−0.361744	−	0.361744i	0.502711	−	0.864455i	$-0.332336\pi$
$37$	−2.20040	−	2.20040i	−0.361744	−	0.361744i	−0.864455	+	0.502711i	$0.832336\pi$
$38$	5.79264	+	1.47920i	0.939690	+	0.239958i
$39$		−	0.800071i		−	0.128114i
$40$	−2.12802	+	5.95580i	−0.336469	+	0.941695i
$41$			3.07334i			0.479976i	0.970776	+	0.239988i	$0.0771434\pi$
$41$			3.07334i			0.479976i	−0.970776	+	0.239988i	$0.922857\pi$
$42$	−0.462154	−	0.663514i	−0.0713119	−	0.102382i
$43$	4.25689	−	4.25689i	0.649170	−	0.649170i	−0.303622	−	0.952793i	$-0.598196\pi$
$43$	4.25689	−	4.25689i	0.649170	−	0.649170i	0.952793	+	0.303622i	$0.0981960\pi$
$44$	−1.64156	+	3.00463i	−0.247475	+	0.452965i
$45$	2.61343	+	6.06463i	0.389588	+	0.904062i
$46$	−4.72301	+	2.80155i	−0.696370	+	0.413066i
$47$	7.96917	+	7.96917i	1.16242	+	1.16242i	0.983944	+	0.178479i	$0.0571178\pi$
$47$	7.96917	+	7.96917i	1.16242	+	1.16242i	0.178479	+	0.983944i	$0.442882\pi$
$48$	0.184142	−	0.844592i	0.0265785	−	0.121906i
$49$	−6.92551	+	1.01848i	−0.989359	+	0.145496i
$50$	3.77849	+	5.97687i	0.534359	+	0.845258i
$51$			1.12179i			0.157082i
$52$	−2.08440	−	7.10492i	−0.289054	−	0.985275i
$53$	−1.49101	+	1.49101i	−0.204806	+	0.204806i	−0.802056	−	0.597249i	$-0.796260\pi$
$53$	−1.49101	+	1.49101i	−0.204806	+	0.204806i	0.597249	+	0.802056i	$0.296260\pi$
$54$	−0.928236	−	1.56487i	−0.126317	−	0.212952i
$55$	1.51490	+	3.51543i	0.204269	+	0.474020i
$56$	−5.83272	−	4.68821i	−0.779430	−	0.626489i
$57$	−0.646003	+	0.646003i	−0.0855652	+	0.0855652i
$58$	3.50571	−	13.7286i	0.460322	−	1.80265i
$59$		−	9.80345i		−	1.27630i	−0.769912	−	0.638150i	$-0.779700\pi$
$59$		−	9.80345i		−	1.27630i	0.769912	−	0.638150i	$-0.220300\pi$
$60$	−0.616866	−	0.743996i	−0.0796370	−	0.0960495i
$61$	−5.41890			−0.693819			−0.346910	−	0.937899i	$-0.612769\pi$
$61$	−5.41890			−0.693819			−0.346910	+	0.937899i	$0.612769\pi$
$62$	11.6525	+	2.97558i	1.47988	+	0.377899i
$63$	−7.79288	+	0.569950i	−0.981810	+	0.0718070i
$64$	−0.565140	−	7.98001i	−0.0706425	−	0.997502i
$65$	−7.69234	−	3.05919i	−0.954118	−	0.379445i
$66$	−0.266920	−	0.449989i	−0.0328556	−	0.0553898i
$67$	5.57302	+	5.57302i	0.680852	+	0.680852i	0.960192	−	0.279340i	$-0.0901157\pi$
$67$	5.57302	+	5.57302i	0.680852	+	0.680852i	−0.279340	+	0.960192i	$0.590116\pi$
$68$	2.92256	+	9.96189i	0.354412	+	1.20806i
$69$		−	0.839149i		−	0.101022i
$70$	−8.14652	+	1.90637i	−0.973695	+	0.227855i
$71$	−6.76483			−0.802837			−0.401419	−	0.915895i	$-0.631483\pi$
$71$	−6.76483			−0.802837			−0.401419	+	0.915895i	$0.631483\pi$
$72$	−6.11166	−	5.69415i	−0.720266	−	0.671061i
$73$	−3.80923	+	3.80923i	−0.445836	+	0.445836i	−0.893968	−	0.448131i	$-0.852090\pi$
$73$	−3.80923	+	3.80923i	−0.445836	+	0.445836i	0.448131	+	0.893968i	$0.352090\pi$
$74$	3.78501	−	2.24516i	0.439999	−	0.260994i
$75$	−1.08011	+	0.0306476i	−0.124720	+	0.00353888i
$76$	−4.05373	+	7.41974i	−0.464995	+	0.851103i
$77$	−4.51722	+	0.330377i	−0.514785	+	0.0376500i
$78$	1.09629	+	0.279948i	0.124131	+	0.0316979i
$79$			6.18844i			0.696253i	0.937447	+	0.348127i	$0.113182\pi$
$79$			6.18844i			0.696253i	−0.937447	+	0.348127i	$0.886818\pi$
$80$	−7.41629	−	4.99986i	−0.829167	−	0.559001i
$81$	−8.58186			−0.953540
$82$	−4.21123	−	1.07537i	−0.465052	−	0.118755i
$83$	−2.48782	−	2.48782i	−0.273074	−	0.273074i	0.557263	−	0.830336i	$-0.311852\pi$
$83$	−2.48782	−	2.48782i	−0.273074	−	0.273074i	−0.830336	+	0.557263i	$0.811852\pi$
$84$	1.07089	−	0.401098i	0.116843	−	0.0437633i
$85$	10.7855	+	4.28932i	1.16985	+	0.465242i
$86$	4.34348	+	7.32249i	0.468369	+	0.789604i
$87$	1.53103	+	1.53103i	0.164143	+	0.164143i
$88$	−3.54269	−	3.30067i	−0.377652	−	0.351852i
$89$	12.4324			1.31783			0.658914	−	0.752218i	$-0.271016\pi$
$89$	12.4324			1.31783			0.658914	+	0.752218i	$0.271016\pi$
$90$	−9.22448	+	1.45900i	−0.972345	+	0.153792i
$91$	6.40249	−	7.41291i	0.671163	−	0.777084i
$92$	−2.18620	−	7.45195i	−0.227928	−	0.776919i
$93$	−1.29951	+	1.29951i	−0.134753	+	0.134753i
$94$	−13.7081	+	8.13126i	−1.41389	+	0.838676i
$95$	3.74096	+	8.68112i	0.383814	+	0.890664i
$96$	1.09286	+	0.547844i	0.111540	+	0.0559141i
$97$	2.43265	+	2.43265i	0.246998	+	0.246998i	0.819737	−	0.572740i	$-0.194119\pi$
$97$	2.43265	+	2.43265i	0.246998	+	0.246998i	−0.572740	+	0.819737i	$0.694119\pi$
$98$	1.02770	−	9.84601i	0.103814	−	0.994597i
$99$	−5.05577			−0.508124
$100$	−9.51188	+	3.08612i	−0.951188	+	0.308612i
$101$	12.1473			1.20870			0.604349	−	0.796720i	$-0.293433\pi$
$101$	12.1473			1.20870			0.604349	+	0.796720i	$0.293433\pi$
$102$	−1.53712	−	0.392518i	−0.152198	−	0.0388651i
$103$	8.19252	−	8.19252i	0.807233	−	0.807233i	−0.176981	−	0.984214i	$-0.556633\pi$
$103$	8.19252	−	8.19252i	0.807233	−	0.807233i	0.984214	+	0.176981i	$0.0566331\pi$
$104$	10.4648	−	0.370093i	1.02616	−	0.0362906i
$105$	0.384548	−	1.21931i	0.0375281	−	0.118992i
$106$	−1.52134	−	2.56476i	−0.147766	−	0.249112i
$107$	−0.582094	−	0.582094i	−0.0562731	−	0.0562731i	0.678410	−	0.734683i	$-0.262669\pi$
$107$	−0.582094	−	0.582094i	−0.0562731	−	0.0562731i	−0.734683	+	0.678410i	$0.762669\pi$
$108$	2.46905	−	0.724354i	0.237584	−	0.0697010i
$109$	−1.61076			−0.154283			−0.0771415	−	0.997020i	$-0.524579\pi$
$109$	−1.61076			−0.154283			−0.0771415	+	0.997020i	$0.524579\pi$
$110$	−5.34706	+	0.845725i	−0.509822	+	0.0806367i
$111$			0.672493i			0.0638302i
$112$	8.46488	−	6.35183i	0.799856	−	0.600191i
$113$	5.51278	+	5.51278i	0.518599	+	0.518599i	0.917147	−	0.398549i	$-0.130486\pi$
$113$	5.51278	+	5.51278i	0.518599	+	0.518599i	−0.398549	+	0.917147i	$0.630486\pi$
$114$	−0.659142	−	1.11122i	−0.0617343	−	0.104075i
$115$	−8.06806	−	3.20861i	−0.752350	−	0.299204i
$116$	17.5848	+	9.60735i	1.63271	+	0.892020i
$117$	7.73125	−	7.73125i	0.714755	−	0.714755i
$118$	13.4331	+	3.43026i	1.23662	+	0.315781i
$119$	−8.97700	+	10.3937i	−0.822920	+	0.952791i
$120$	1.23530	−	0.584929i	0.112767	−	0.0533965i
$121$	8.06937			0.733579
$122$	1.89609	−	7.42521i	0.171664	−	0.672247i
$123$	0.469642	−	0.469642i	0.0423462	−	0.0423462i
$124$	−8.15454	+	14.9257i	−0.732299	+	1.34036i
$125$	−3.83527	+	10.5019i	−0.343037	+	0.939322i
$126$	1.94579	−	10.8776i	0.173344	−	0.969051i
$127$	3.34067	−	3.34067i	0.296436	−	0.296436i	−0.543180	−	0.839616i	$-0.682780\pi$
$127$	3.34067	−	3.34067i	0.296436	−	0.296436i	0.839616	+	0.543180i	$0.182780\pi$
$128$	11.1323	+	2.01786i	0.983966	+	0.178355i
$129$	−1.30100			−0.114547
$130$	6.88341	−	9.46996i	0.603715	−	0.830571i
$131$	17.0862			1.49283			0.746414	−	0.665482i	$-0.231774\pi$
$131$	17.0862			1.49283			0.746414	+	0.665482i	$0.231774\pi$
$132$	0.709991	−	0.208293i	0.0617968	−	0.0181296i
$133$	−11.1550	+	0.815846i	−0.967260	+	0.0707428i
$134$	−9.58641	+	5.68637i	−0.828140	+	0.491228i
$135$	1.06311	−	2.67319i	0.0914976	−	0.230071i
$136$	−14.6728	+	0.518911i	−1.25818	+	0.0444963i
$137$	−3.73179	+	3.73179i	−0.318829	+	0.318829i	−0.848317	−	0.529488i	$-0.822384\pi$
$137$	−3.73179	+	3.73179i	−0.318829	+	0.318829i	0.529488	+	0.848317i	$0.322384\pi$
$138$	1.14984	+	0.293621i	0.0978808	+	0.0249947i
$139$			3.65962i			0.310405i	0.987883	+	0.155202i	$0.0496030\pi$
$139$			3.65962i			0.310405i	−0.987883	+	0.155202i	$0.950397\pi$
$140$	0.238303	−	11.8298i	0.0201403	−	0.999797i
$141$		−	2.43556i		−	0.205111i
$142$	2.36704	−	9.26946i	0.198637	−	0.777876i
$143$	4.48150	−	4.48150i	0.374762	−	0.374762i
$144$	9.94086	−	6.38206i	0.828405	−	0.531839i
$145$	20.5743	−	8.86608i	1.70860	−	0.736288i
$146$	−3.88671	−	6.55243i	−0.321666	−	0.542283i
$147$	1.21393	+	0.902663i	0.100123	+	0.0744504i
$148$	1.75202	+	5.97198i	0.144015	+	0.490894i
$149$	16.0306			1.31328			0.656640	−	0.754204i	$-0.271977\pi$
$149$	16.0306			1.31328			0.656640	+	0.754204i	$0.271977\pi$
$150$	0.335938	−	1.49073i	0.0274292	−	0.121718i
$151$	−0.815065			−0.0663291			−0.0331645	−	0.999450i	$-0.510559\pi$
$151$	−0.815065			−0.0663291			−0.0331645	+	0.999450i	$0.510559\pi$
$152$	−8.74844	−	8.15079i	−0.709592	−	0.661117i
$153$	−10.8401	+	10.8401i	−0.876369	+	0.876369i
$154$	1.12789	−	6.30529i	0.0908883	−	0.508095i
$155$	7.52536	+	17.4631i	0.604451	+	1.40267i
$156$	−0.767194	+	1.40423i	−0.0614246	+	0.112429i
$157$	1.16402	−	1.16402i	0.0928987	−	0.0928987i	−0.659130	−	0.752029i	$-0.729075\pi$
$157$	1.16402	−	1.16402i	0.0928987	−	0.0928987i	0.752029	+	0.659130i	$0.229075\pi$
$158$	−8.47966	−	2.16536i	−0.674606	−	0.172267i
$159$	0.455688			0.0361384
$160$	9.44601	−	8.41266i	0.746773	−	0.665079i
$161$	6.71520	−	7.77498i	0.529232	−	0.612754i
$162$	3.00282	−	11.7592i	0.235924	−	0.923893i
$163$	−0.325734	+	0.325734i	−0.0255135	+	0.0255135i	−0.719748	−	0.694235i	$-0.755743\pi$
$163$	−0.325734	+	0.325734i	−0.0255135	+	0.0255135i	0.694235	+	0.719748i	$0.255743\pi$
$164$	2.94705	−	5.39413i	0.230126	−	0.421211i
$165$	0.305703	−	0.768692i	0.0237989	−	0.0598426i
$166$	4.27942	−	2.53842i	0.332147	−	0.197020i
$167$	2.84550	+	2.84550i	0.220191	+	0.220191i	0.808579	−	0.588388i	$-0.200237\pi$
$167$	2.84550	+	2.84550i	0.220191	+	0.220191i	−0.588388	+	0.808579i	$0.700237\pi$
$168$	0.174894	+	1.60772i	0.0134934	+	0.124038i
$169$			0.706149i			0.0543192i
$170$	−9.65131	+	13.2779i	−0.740222	+	1.01837i
$171$	−12.4849			−0.954745
$172$	−11.5534	+	3.38946i	−0.880938	+	0.258444i
$173$	−16.0862	−	16.0862i	−1.22301	−	1.22301i	−0.966557	−	0.256450i	$-0.917447\pi$
$173$	−16.0862	−	16.0862i	−1.22301	−	1.22301i	−0.256450	−	0.966557i	$-0.582553\pi$
$174$	−2.63359	+	1.56217i	−0.199652	+	0.118428i
$175$	−10.2528	−	8.35947i	−0.775036	−	0.631917i
$176$	5.76232	−	3.69943i	0.434351	−	0.278855i
$177$	−1.49808	+	1.49808i	−0.112603	+	0.112603i
$178$	−4.35013	+	17.0354i	−0.326056	+	1.27686i
$179$	−6.09026			−0.455207			−0.227604	−	0.973754i	$-0.573089\pi$
$179$	−6.09026			−0.455207			−0.227604	+	0.973754i	$0.573089\pi$
$180$	1.22849	−	13.1503i	0.0915664	−	0.980165i
$181$	6.92171			0.514487			0.257243	−	0.966347i	$-0.417186\pi$
$181$	6.92171			0.514487			0.257243	+	0.966347i	$0.417186\pi$
$182$	7.91724	+	11.3668i	0.586865	+	0.842561i
$183$	0.828070	+	0.828070i	0.0612127	+	0.0612127i
$184$	10.9759	−	0.388169i	0.809157	−	0.0286162i
$185$	6.46573	+	2.57137i	0.475370	+	0.189051i
$186$	−1.32594	−	2.23535i	−0.0972226	−	0.163903i
$187$	−6.28356	+	6.28356i	−0.459500	+	0.459500i
$188$	−6.34528	−	21.6287i	−0.462777	−	1.57743i
$189$	2.57608	+	2.22495i	0.187382	+	0.161841i
$190$	−13.2042	+	2.08846i	−0.957935	+	0.151513i
$191$	−13.8061			−0.998971			−0.499485	−	0.866322i	$-0.666478\pi$
$191$	−13.8061			−0.998971			−0.499485	+	0.866322i	$0.666478\pi$
$192$	−1.13308	+	1.30580i	−0.0817728	+	0.0942378i
$193$	6.64743	+	6.64743i	0.478493	+	0.478493i	0.904649	−	0.426157i	$-0.140133\pi$
$193$	6.64743	+	6.64743i	0.478493	+	0.478493i	−0.426157	+	0.904649i	$0.640133\pi$
$194$	−4.18451	+	2.48213i	−0.300430	+	0.178206i
$195$	0.707999	+	1.64296i	0.0507009	+	0.117655i
$196$	13.1318	+	4.85336i	0.937988	+	0.346668i
$197$	2.90160	+	2.90160i	0.206730	+	0.206730i	0.802876	−	0.596146i	$-0.203302\pi$
$197$	2.90160	+	2.90160i	0.206730	+	0.206730i	−0.596146	+	0.802876i	$0.703302\pi$
$198$	1.76903	−	6.92764i	0.125720	−	0.492326i
$199$	4.16130			0.294987			0.147493	−	0.989063i	$-0.452880\pi$
$199$	4.16130			0.294987			0.147493	+	0.989063i	$0.452880\pi$
$200$	−0.900495	−	14.1134i	−0.0636746	−	0.997971i
$201$		−	1.70324i		−	0.120137i
$202$	−4.25037	+	16.6447i	−0.299055	+	1.17112i
$203$	1.93356	+	26.4374i	0.135709	+	1.85554i
$204$	1.07569	−	1.96889i	0.0753134	−	0.137850i
$205$	−2.71966	−	6.31115i	−0.189950	−	0.440790i
$206$	8.35916	+	14.0923i	0.582410	+	0.981860i
$207$	8.10887	−	8.10887i	0.563606	−	0.563606i
$208$	−3.15456	+	14.4688i	−0.218729	+	1.00323i
$209$	−7.23701			−0.500594
$210$	1.53620	+	0.953566i	0.106008	+	0.0658023i
$211$		−	20.9585i		−	1.44284i	−0.692497	−	0.721420i	$-0.743490\pi$
$211$		−	20.9585i		−	1.44284i	0.692497	−	0.721420i	$-0.256510\pi$
$212$	4.04667	−	1.18719i	0.277926	−	0.0815363i
$213$	1.03374	+	1.03374i	0.0708309	+	0.0708309i
$214$	1.00129	−	0.593933i	0.0684466	−	0.0406004i
$215$	−4.97458	+	12.5086i	−0.339263	+	0.853080i
$216$	0.128612	+	3.63665i	0.00875093	+	0.247443i
$217$	−22.4395	+	1.64117i	−1.52329	+	0.111410i
$218$	0.563611	−	2.20714i	0.0381726	−	0.149486i
$219$	1.16419			0.0786685
$220$	0.712108	−	7.62270i	0.0480103	−	0.513922i
$221$		−	19.2176i		−	1.29271i
$222$	−0.921479	−	0.235308i	−0.0618456	−	0.0157928i
$223$	−0.851522	+	0.851522i	−0.0570221	+	0.0570221i	−0.735043	−	0.678021i	$-0.762838\pi$
$223$	−0.851522	+	0.851522i	−0.0570221	+	0.0570221i	0.678021	+	0.735043i	$0.262838\pi$
$224$	5.74166	+	13.8215i	0.383631	+	0.923487i
$225$	−10.7334	−	10.1411i	−0.715562	−	0.676075i
$226$	−9.48279	+	5.62491i	−0.630786	+	0.374163i
$227$	−6.56802	+	6.56802i	−0.435935	+	0.435935i	−0.890641	−	0.454706i	$-0.849744\pi$
$227$	−6.56802	+	6.56802i	−0.435935	+	0.435935i	0.454706	+	0.890641i	$0.349744\pi$
$228$	1.75328	−	0.514366i	0.116114	−	0.0340647i
$229$		−	23.9684i		−	1.58387i	−0.610603	−	0.791937i	$-0.709073\pi$
$229$		−	23.9684i		−	1.58387i	0.610603	−	0.791937i	$-0.290927\pi$
$230$	7.21962	−	9.93250i	0.476047	−	0.654930i
$231$	0.740768	+	0.639797i	0.0487390	+	0.0420956i
$232$	−19.3174	+	20.7338i	−1.26825	+	1.36124i
$233$	4.18024	+	4.18024i	0.273857	+	0.273857i	0.830651	−	0.556794i	$-0.187969\pi$
$233$	4.18024	+	4.18024i	0.273857	+	0.273857i	−0.556794	+	0.830651i	$0.687969\pi$
$234$	7.88851	+	13.2989i	0.515688	+	0.869376i
$235$	−23.4169	−	9.31272i	−1.52755	−	0.607495i
$236$	−9.40060	+	17.2064i	−0.611927	+	1.12004i
$237$	0.945664	−	0.945664i	0.0614275	−	0.0614275i
$238$	−11.1008	−	15.9375i	−0.719561	−	1.03307i
$239$		−	14.1601i		−	0.915943i	−0.888967	−	0.457971i	$-0.848576\pi$
$239$		−	14.1601i		−	0.915943i	0.888967	−	0.457971i	$-0.151424\pi$
$240$	0.369259	+	1.89733i	0.0238356	+	0.122472i
$241$			20.6566i			1.33061i	0.746572	+	0.665305i	$0.231698\pi$
$241$			20.6566i			1.33061i	−0.746572	+	0.665305i	$0.768302\pi$
$242$	−2.82350	+	11.0570i	−0.181502	+	0.710771i
$243$	4.04060	+	4.04060i	0.259205	+	0.259205i
$244$	9.51090	+	5.19622i	0.608873	+	0.332654i
$245$	13.3204	−	8.21998i	0.851007	−	0.525155i
$246$	0.479194	+	0.807853i	0.0305523	+	0.0515069i
$247$	11.0668	−	11.0668i	0.704162	−	0.704162i
$248$	−17.5985	−	16.3963i	−1.11751	−	1.04116i
$249$			0.760335i			0.0481843i
$250$	−13.0482	−	8.92993i	−0.825243	−	0.564778i
$251$	11.9637			0.755140			0.377570	−	0.925981i	$-0.376760\pi$
$251$	11.9637			0.755140			0.377570	+	0.925981i	$0.376760\pi$
$252$	14.2241	+	6.47230i	0.896033	+	0.407717i
$253$	4.70039	−	4.70039i	0.295511	−	0.295511i
$254$	3.40861	+	5.74644i	0.213875	+	0.360564i
$255$	−0.992694	−	2.30361i	−0.0621649	−	0.144258i
$256$	−6.66019	+	14.5479i	−0.416262	+	0.909245i
$257$	−1.88138	−	1.88138i	−0.117357	−	0.117357i	0.645989	−	0.763346i	$-0.276445\pi$
$257$	−1.88138	−	1.88138i	−0.117357	−	0.117357i	−0.763346	+	0.645989i	$0.776445\pi$
$258$	0.455226	−	1.78269i	0.0283412	−	0.110986i
$259$	−5.38156	+	6.23086i	−0.334394	+	0.387167i
$260$	10.5676	+	12.7455i	0.655376	+	0.790444i
$261$			29.5893i			1.83153i
$262$	−5.97852	+	23.4122i	−0.369354	+	1.44641i
$263$	−20.4931	−	20.4931i	−1.26366	−	1.26366i	−0.949307	−	0.314352i	$-0.898213\pi$
$263$	−20.4931	−	20.4931i	−1.26366	−	1.26366i	−0.314352	−	0.949307i	$-0.601787\pi$
$264$	0.0369832	+	1.04574i	0.00227616	+	0.0643610i
$265$	1.74239	−	4.38124i	0.107034	−	0.269137i
$266$	2.78526	−	15.5705i	0.170775	−	0.954690i
$267$	−1.89981	−	1.89981i	−0.116266	−	0.116266i
$268$	−4.43739	−	15.1254i	−0.271057	−	0.923931i
$269$			16.2322i			0.989692i	0.868981	+	0.494846i	$0.164776\pi$
$269$			16.2322i			0.989692i	−0.868981	+	0.494846i	$0.835224\pi$
$270$	3.29093	+	2.39207i	0.200280	+	0.145577i
$271$		−	13.2089i		−	0.802381i	−0.915995	−	0.401191i	$-0.868597\pi$
$271$		−	13.2089i		−	0.802381i	0.915995	−	0.401191i	$-0.131403\pi$
$272$	4.42304	−	20.2869i	0.268186	−	1.23008i
$273$	−2.11115	+	0.154404i	−0.127773	+	0.00934495i
$274$	−3.80770	−	6.41924i	−0.230031	−	0.387800i
$275$	−6.22174	−	5.87841i	−0.375185	−	0.354481i
$276$	−0.804666	+	1.47282i	−0.0484352	+	0.0886533i
$277$	16.4789	+	16.4789i	0.990120	+	0.990120i	0.999952	−	0.00983184i	$-0.00312962\pi$
$277$	16.4789	+	16.4789i	0.990120	+	0.990120i	−0.00983184	+	0.999952i	$0.503130\pi$
$278$	−5.01457	−	1.28051i	−0.300754	−	0.0768001i
$279$	−25.1148			−1.50359
$280$	16.1263	+	4.46581i	0.963729	+	0.266883i
$281$	3.18695			0.190117			0.0950586	−	0.995472i	$-0.469696\pi$
$281$	3.18695			0.190117			0.0950586	+	0.995472i	$0.469696\pi$
$282$	3.33731	+	0.852212i	0.198734	+	0.0507485i
$283$	−18.4759	−	18.4759i	−1.09828	−	1.09828i	−0.994612	−	0.103669i	$-0.966942\pi$
$283$	−18.4759	−	18.4759i	−1.09828	−	1.09828i	−0.103669	−	0.994612i	$-0.533058\pi$
$284$	11.8732	+	6.48684i	0.704544	+	0.384923i
$285$	0.754914	−	1.89824i	0.0447173	−	0.112442i
$286$	4.57265	+	7.70884i	0.270387	+	0.455833i
$287$	8.10964	−	0.593118i	0.478697	−	0.0350106i
$288$	5.26664	+	15.8545i	0.310340	+	0.934236i
$289$			9.94515i			0.585009i
$290$	4.94966	+	31.2941i	0.290654	+	1.83765i
$291$		−	0.743473i		−	0.0435831i
$292$	10.3384	−	3.03301i	0.605009	−	0.177494i
$293$	−2.20948	−	2.20948i	−0.129079	−	0.129079i	0.639616	−	0.768695i	$-0.279094\pi$
$293$	−2.20948	−	2.20948i	−0.129079	−	0.129079i	−0.768695	+	0.639616i	$0.779094\pi$
$294$	−1.66163	+	1.34754i	−0.0969081	+	0.0785900i
$295$	8.67527	+	20.1315i	0.505094	+	1.17210i
$296$	−8.79611	+	0.311078i	−0.511263	+	0.0180811i
$297$	1.55738	+	1.55738i	0.0903682	+	0.0903682i
$298$	−5.60918	+	21.9659i	−0.324931	+	1.27245i
$299$			14.3756i			0.831362i
$300$	1.92512	+	0.981930i	0.111147	+	0.0566917i
$301$	−12.0542	−	10.4112i	−0.694793	−	0.600089i
$302$	0.285194	−	1.11684i	0.0164111	−	0.0642668i
$303$	−1.85624	−	1.85624i	−0.106638	−	0.106638i
$304$	14.2297	−	9.13550i	0.816128	−	0.523957i
$305$	11.1278	−	4.79529i	0.637175	−	0.274578i
$306$	−11.0606	−	18.6465i	−0.632290	−	1.06595i
$307$	−16.9811	+	16.9811i	−0.969164	+	0.969164i	−0.999539	−	0.0303745i	$-0.990330\pi$
$307$	−16.9811	+	16.9811i	−0.969164	+	0.969164i	0.0303745	+	0.999539i	$0.490330\pi$
$308$	8.24513	+	3.75173i	0.469810	+	0.213775i
$309$	−2.50382			−0.142438
$310$	−26.5618	+	4.20118i	−1.50861	+	0.238611i
$311$		−	8.25825i		−	0.468283i	−0.972203	−	0.234141i	$-0.924772\pi$
$311$		−	8.25825i		−	0.468283i	0.972203	−	0.234141i	$-0.0752278\pi$
$312$	−1.65570	−	1.54259i	−0.0937354	−	0.0873319i
$313$	17.0913	−	17.0913i	0.966059	−	0.966059i	−0.0333835	−	0.999443i	$-0.510628\pi$
$313$	17.0913	−	17.0913i	0.966059	−	0.966059i	0.999443	+	0.0333835i	$0.0106283\pi$
$314$	1.18769	+	2.00228i	0.0670254	+	0.112995i
$315$	15.4984	−	8.06647i	0.873237	−	0.454494i
$316$	5.93413	−	10.8615i	0.333821	−	0.611009i
$317$	−23.5652	−	23.5652i	−1.32355	−	1.32355i	−0.910878	−	0.412675i	$-0.864594\pi$
$317$	−23.5652	−	23.5652i	−1.32355	−	1.32355i	−0.412675	−	0.910878i	$-0.635406\pi$
$318$	−0.159447	+	0.624403i	−0.00894133	+	0.0350148i
$319$			17.1517i			0.960312i
$320$	8.22220	+	15.8870i	0.459635	+	0.888108i
$321$			0.177901i			0.00992947i
$322$	8.30394	+	11.9220i	0.462760	+	0.664385i
$323$	−15.5169	+	15.5169i	−0.863381	+	0.863381i
$324$	15.0623	+	8.22920i	0.836795	+	0.457178i
$325$	18.5035	−	0.525029i	1.02639	−	0.0291234i
$326$	−0.332360	−	0.560311i	−0.0184077	−	0.0310327i
$327$	0.246143	+	0.246143i	0.0136117	+	0.0136117i
$328$	6.36009	+	5.92560i	0.351177	+	0.327187i
$329$	19.4903	−	22.5662i	1.07454	−	1.24412i
$330$	0.946329	+	0.687856i	0.0520937	+	0.0378652i
$331$			17.7443i			0.975315i	0.873035	+	0.487658i	$0.162149\pi$
$331$			17.7443i			0.975315i	−0.873035	+	0.487658i	$0.837851\pi$
$332$	1.98087	+	6.75205i	0.108715	+	0.370567i
$333$	−6.49844	+	6.49844i	−0.356112	+	0.356112i
$334$	−4.89468	+	2.90338i	−0.267825	+	0.158866i
$335$	−16.3759	−	6.51259i	−0.894713	−	0.355821i
$336$	−2.26416	−	0.322899i	−0.123520	−	0.0176156i
$337$	7.91903	−	7.91903i	0.431377	−	0.431377i	−0.457720	−	0.889097i	$-0.651334\pi$
$337$	7.91903	−	7.91903i	0.431377	−	0.431377i	0.889097	+	0.457720i	$0.151334\pi$
$338$	−0.967596	−	0.247084i	−0.0526303	−	0.0134396i
$339$		−	1.68483i		−	0.0915075i
$340$	−14.8170	−	17.8706i	−0.803564	−	0.969172i
$341$	−14.5581			−0.788363
$342$	4.36852	−	17.1074i	0.236222	−	0.925061i
$343$	4.02399	+	18.0778i	0.217275	+	0.976110i
$344$	−0.601812	−	17.0169i	−0.0324475	−	0.917492i
$345$	0.742580	+	1.72320i	0.0399792	+	0.0927742i
$346$	27.6706	−	16.4133i	1.48758	−	0.882387i
$347$	17.9361	+	17.9361i	0.962862	+	0.962862i	0.999335	−	0.0364727i	$-0.0116122\pi$
$347$	17.9361	+	17.9361i	0.962862	+	0.962862i	−0.0364727	+	0.999335i	$0.511612\pi$
$348$	−1.21905	−	4.15527i	−0.0653478	−	0.222746i
$349$			14.9911i			0.802455i	0.915978	+	0.401228i	$0.131416\pi$
$349$			14.9911i			0.802455i	−0.915978	+	0.401228i	$0.868584\pi$
$350$	15.0420	−	11.1238i	0.804028	−	0.594591i
$351$	−4.76306			−0.254233
$352$	3.05286	+	9.19022i	0.162718	+	0.489841i
$353$	−11.5185	+	11.5185i	−0.613069	+	0.613069i	−0.943744	−	0.330676i	$-0.892723\pi$
$353$	−11.5185	+	11.5185i	−0.613069	+	0.613069i	0.330676	+	0.943744i	$0.392723\pi$
$354$	−1.52855	−	2.57692i	−0.0812416	−	0.136962i
$355$	13.8917	−	5.98633i	0.737293	−	0.317722i
$356$	−21.8205	−	11.9215i	−1.15648	−	0.631837i
$357$	2.96007	−	0.216492i	0.156663	−	0.0114580i
$358$	2.13100	−	8.34514i	0.112627	−	0.441054i
$359$		−	24.0496i		−	1.26929i	−0.772804	−	0.634645i	$-0.781146\pi$
$359$		−	24.0496i		−	1.26929i	0.772804	−	0.634645i	$-0.218854\pi$
$360$	17.5892	+	6.28467i	0.927035	+	0.331231i
$361$	1.12867			0.0594037
$362$	−2.42193	+	9.48443i	−0.127294	+	0.498491i
$363$	−1.23309	−	1.23309i	−0.0647206	−	0.0647206i
$364$	−18.3455	+	6.87127i	−0.961566	+	0.360152i
$365$	4.45144	−	11.1932i	0.232999	−	0.585877i
$366$	−1.42440	+	0.844913i	−0.0744547	+	0.0441643i
$367$	13.1810	+	13.1810i	0.688045	+	0.688045i	0.961800	−	0.273755i	$-0.0882656\pi$
$367$	13.1810	+	13.1810i	0.688045	+	0.688045i	−0.273755	+	0.961800i	$0.588266\pi$
$368$	−3.30864	+	15.1755i	−0.172475	+	0.791080i
$369$	9.07650			0.472503
$370$	−5.78579	+	7.95990i	−0.300789	+	0.413815i
$371$	4.22209	+	3.64659i	0.219200	+	0.189322i
$372$	3.52692	−	1.03471i	0.182862	−	0.0536470i
$373$	9.36808	−	9.36808i	0.485061	−	0.485061i	−0.421683	−	0.906743i	$-0.638560\pi$
$373$	9.36808	−	9.36808i	0.485061	−	0.485061i	0.906743	+	0.421683i	$0.138560\pi$
$374$	−6.41137	−	10.8087i	−0.331524	−	0.558902i
$375$	2.19089	−	1.01874i	0.113137	−	0.0526076i
$376$	31.8568	−	1.12663i	1.64289	−	0.0581014i
$377$	−26.2283	−	26.2283i	−1.35083	−	1.35083i
$378$	−3.95010	+	2.75134i	−0.203171	+	0.141514i
$379$	−14.7091			−0.755557			−0.377778	−	0.925896i	$-0.623312\pi$
$379$	−14.7091			−0.755557			−0.377778	+	0.925896i	$0.623312\pi$
$380$	1.75850	−	18.8238i	0.0902094	−	0.965639i
$381$	−1.02098			−0.0523066
$382$	4.83079	−	18.9177i	0.247165	−	0.967911i
$383$	−14.4565	+	14.4565i	−0.738691	+	0.738691i	−0.972325	−	0.233634i	$-0.924938\pi$
$383$	−14.4565	+	14.4565i	−0.738691	+	0.738691i	0.233634	+	0.972325i	$0.424938\pi$
$384$	−1.39279	−	2.00950i	−0.0710756	−	0.102547i
$385$	8.98381	−	4.67581i	0.457857	−	0.238301i
$386$	−11.4346	+	6.78264i	−0.582004	+	0.345227i
$387$	−12.5719	−	12.5719i	−0.639064	−	0.639064i
$388$	−1.93694	−	6.60230i	−0.0983333	−	0.335181i
$389$	14.3214			0.726125			0.363062	−	0.931765i	$-0.381731\pi$
$389$	14.3214			0.726125			0.363062	+	0.931765i	$0.381731\pi$
$390$	−2.49898	+	0.395255i	−0.126541	+	0.0200145i
$391$		−	20.1562i		−	1.01934i
$392$	−11.2452	+	16.2956i	−0.567966	+	0.823052i
$393$	−2.61097	−	2.61097i	−0.131706	−	0.131706i
$394$	−4.99118	+	2.96062i	−0.251452	+	0.149154i
$395$	−5.47627	−	12.7080i	−0.275541	−	0.639411i
$396$	8.87357	+	4.84802i	0.445913	+	0.243622i
$397$	−13.6522	+	13.6522i	−0.685183	+	0.685183i	−0.961163	−	0.275980i	$-0.910998\pi$
$397$	−13.6522	+	13.6522i	−0.685183	+	0.685183i	0.275980	+	0.961163i	$0.410998\pi$
$398$	−1.45605	+	5.70199i	−0.0729854	+	0.285815i
$399$	1.82928	+	1.57994i	0.0915786	+	0.0790959i
$400$	19.6539	+	3.70445i	0.982697	+	0.185222i
$401$	14.9713			0.747633			0.373817	−	0.927503i	$-0.378049\pi$
$401$	14.9713			0.747633			0.373817	+	0.927503i	$0.378049\pi$
$402$	2.33386	+	0.595970i	0.116402	+	0.0297243i
$403$	22.2621	−	22.2621i	1.10895	−	1.10895i
$404$	−21.3201	−	11.6481i	−1.06071	−	0.579514i
$405$	17.6230	−	7.59426i	0.875692	−	0.377362i
$406$	−36.9022	−	6.60108i	−1.83142	−	0.327606i
$407$	−3.76689	+	3.76689i	−0.186718	+	0.186718i
$408$	2.32147	+	2.16288i	0.114930	+	0.107079i
$409$	1.03720			0.0512864			0.0256432	−	0.999671i	$-0.491837\pi$
$409$	1.03720			0.0512864			0.0256432	+	0.999671i	$0.491837\pi$
$410$	9.59943	−	1.51831i	0.474082	−	0.0749838i
$411$	1.14052			0.0562578
$412$	−22.2348	+	6.52312i	−1.09543	+	0.321371i
$413$	−25.8684	+	1.89195i	−1.27290	+	0.0930966i
$414$	8.27380	+	13.9485i	0.406635	+	0.685529i
$415$	7.31029	+	2.90725i	0.358848	+	0.142711i
$416$	−18.7220	−	9.38521i	−0.917923	−	0.460148i
$417$	0.559231	−	0.559231i	0.0273857	−	0.0273857i
$418$	2.53226	−	9.91646i	0.123857	−	0.485030i
$419$		−	12.3869i		−	0.605140i	−0.953127	−	0.302570i	$-0.902155\pi$
$419$		−	12.3869i		−	0.605140i	0.953127	−	0.302570i	$-0.0978446\pi$
$420$	−1.84414	+	1.77131i	−0.0899847	+	0.0864309i
$421$			1.01412i			0.0494251i	0.999695	+	0.0247126i	$0.00786705\pi$
$421$			1.01412i			0.0494251i	−0.999695	+	0.0247126i	$0.992133\pi$
$422$	28.7182	+	7.33345i	1.39798	+	0.356987i
$423$	23.5353	−	23.5353i	1.14433	−	1.14433i
$424$	0.210789	+	5.96032i	0.0102368	+	0.289459i
$425$	−25.9439	+	0.736150i	−1.25846	+	0.0357085i
$426$	−1.77819	+	1.05477i	−0.0861536	+	0.0511037i
$427$	1.04578	+	14.2989i	0.0506089	+	0.691971i
$428$	0.463479	+	1.57983i	0.0224031	+	0.0763638i
$429$	−1.36965			−0.0661273
$430$	−15.3992	−	11.1932i	−0.742616	−	0.539783i
$431$	3.24993			0.156544			0.0782718	−	0.996932i	$-0.475060\pi$
$431$	3.24993			0.156544			0.0782718	+	0.996932i	$0.475060\pi$
$432$	−5.02810	−	1.09625i	−0.241915	−	0.0527433i
$433$	−0.344934	+	0.344934i	−0.0165765	+	0.0165765i	−0.715346	−	0.698770i	$-0.753731\pi$
$433$	−0.344934	+	0.344934i	−0.0165765	+	0.0165765i	0.698770	+	0.715346i	$0.253731\pi$
$434$	5.60287	−	31.3219i	0.268947	−	1.50350i
$435$	−4.49883	−	1.78915i	−0.215702	−	0.0857831i
$436$	2.82710	+	1.54457i	0.135394	+	0.0739715i
$437$	11.6073	−	11.6073i	0.555253	−	0.555253i
$438$	−0.407353	+	1.59522i	−0.0194641	+	0.0762226i
$439$	2.24250			0.107028			0.0535142	−	0.998567i	$-0.482958\pi$
$439$	2.24250			0.107028			0.0535142	+	0.998567i	$0.482958\pi$
$440$	10.1958	+	3.64297i	0.486065	+	0.173672i
$441$	3.00786	+	20.4531i	0.143231	+	0.973957i
$442$	26.3327	+	6.72429i	1.25252	+	0.319842i
$443$	14.6819	−	14.6819i	0.697559	−	0.697559i	−0.266325	−	0.963883i	$-0.585809\pi$
$443$	14.6819	−	14.6819i	0.697559	−	0.697559i	0.963883	+	0.266325i	$0.0858094\pi$
$444$	0.644858	−	1.18032i	0.0306036	−	0.0560153i
$445$	−25.5300	+	11.0017i	−1.21024	+	0.521529i
$446$	−0.868842	−	1.46474i	−0.0411409	−	0.0693576i
$447$	−2.44966	−	2.44966i	−0.115865	−	0.115865i
$448$	−20.9478	+	3.03128i	−0.989692	+	0.143215i
$449$			13.9894i			0.660203i	0.943945	+	0.330101i	$0.107083\pi$
$449$			13.9894i			0.660203i	−0.943945	+	0.330101i	$0.892917\pi$
$450$	17.6515	−	11.1590i	0.832099	−	0.526040i
$451$	5.26128			0.247744
$452$	−4.38943	−	14.9619i	−0.206461	−	0.703749i
$453$	0.124551	+	0.124551i	0.00585193	+	0.00585193i
$454$	−6.70162	−	11.2980i	−0.314522	−	0.530240i
$455$	−6.58776	+	20.8882i	−0.308839	+	0.979254i
$456$	0.0913276	+	2.58240i	0.00427681	+	0.120932i
$457$	−20.0794	+	20.0794i	−0.939272	+	0.939272i	−0.998259	−	0.0589864i	$-0.981213\pi$
$457$	−20.0794	+	20.0794i	−0.939272	+	0.939272i	0.0589864	+	0.998259i	$0.481213\pi$
$458$	32.8425	+	8.38662i	1.53463	+	0.391881i
$459$	6.67834			0.311718
$460$	11.0838	+	13.3681i	0.516784	+	0.623289i
$461$	−10.8457			−0.505136			−0.252568	−	0.967579i	$-0.581275\pi$
$461$	−10.8457			−0.505136			−0.252568	+	0.967579i	$0.581275\pi$
$462$	−1.13588	+	0.791165i	−0.0528457	+	0.0368083i
$463$	5.62656	+	5.62656i	0.261489	+	0.261489i	0.825659	−	0.564170i	$-0.190804\pi$
$463$	5.62656	+	5.62656i	0.261489	+	0.261489i	−0.564170	+	0.825659i	$0.690804\pi$
$464$	−21.6512	−	33.7244i	−1.00513	−	1.56562i
$465$	1.51860	−	3.81852i	0.0704232	−	0.177080i
$466$	−7.19063	+	4.26526i	−0.333099	+	0.197585i
$467$	16.3696	−	16.3696i	0.757497	−	0.757497i	−0.218369	−	0.975866i	$-0.570074\pi$
$467$	16.3696	−	16.3696i	0.757497	−	0.757497i	0.975866	+	0.218369i	$0.0700738\pi$
$468$	−20.9829	+	6.15584i	−0.969937	+	0.284554i
$469$	13.6300	−	15.7811i	0.629375	−	0.728702i
$470$	20.9543	−	28.8283i	0.966552	−	1.32975i
$471$	−0.355751			−0.0163921
$472$	−20.2876	−	18.9017i	−0.933814	−	0.870020i
$473$	−7.28741	−	7.28741i	−0.335076	−	0.335076i
$474$	0.964899	+	1.62668i	0.0443193	+	0.0747159i
$475$	−15.3642	−	14.5164i	−0.704958	−	0.666056i
$476$	25.7225	−	9.63428i	1.17899	−	0.441587i
$477$	4.40340	+	4.40340i	0.201618	+	0.201618i
$478$	19.4028	+	4.95468i	0.887465	+	0.226622i
$479$	13.2284			0.604421			0.302210	−	0.953241i	$-0.402276\pi$
$479$	13.2284			0.604421			0.302210	+	0.953241i	$0.402276\pi$
$480$	−2.72901	−	0.157908i	−0.124562	−	0.00720749i
$481$		−	11.5206i		−	0.525294i
$482$	−28.3046	−	7.22782i	−1.28924	−	0.329218i
$483$	−2.21427	+	0.161946i	−0.100753	+	0.00736878i
$484$	−14.1628	−	7.73777i	−0.643765	−	0.351717i
$485$	−7.14817	−	2.84277i	−0.324582	−	0.129084i
$486$	−6.95043	+	4.12279i	−0.315278	+	0.187013i
$487$	11.6840	−	11.6840i	0.529454	−	0.529454i	−0.390955	−	0.920410i	$-0.627855\pi$
$487$	11.6840	−	11.6840i	0.529454	−	0.529454i	0.920410	+	0.390955i	$0.127855\pi$
$488$	−10.4480	+	11.2141i	−0.472958	+	0.507637i
$489$	0.0995518			0.00450189
$490$	6.60253	+	21.1283i	0.298272	+	0.954481i
$491$		−	7.55735i		−	0.341059i	−0.985353	−	0.170529i	$-0.945452\pi$
$491$		−	7.55735i		−	0.341059i	0.985353	−	0.170529i	$-0.0545477\pi$
$492$	−1.27463	+	0.373942i	−0.0574647	+	0.0168586i
$493$	36.7750	+	36.7750i	1.65626	+	1.65626i
$494$	11.2919	+	19.0365i	0.508045	+	0.856492i
$495$	10.3821	−	4.47396i	0.466641	−	0.201089i
$496$	28.6246	−	18.3771i	1.28528	−	0.825156i
$497$	1.30553	+	17.8504i	0.0585610	+	0.800699i
$498$	−1.04184	−	0.266044i	−0.0466861	−	0.0119217i
$499$	32.0611			1.43525			0.717627	−	0.696428i	$-0.245228\pi$
$499$	32.0611			1.43525			0.717627	+	0.696428i	$0.245228\pi$
$500$	16.8018	−	14.7546i	0.751399	−	0.659848i
$501$		−	0.869650i		−	0.0388531i
$502$	−4.18613	+	16.3931i	−0.186836	+	0.731661i
$503$	11.5818	−	11.5818i	0.516408	−	0.516408i	−0.400074	−	0.916483i	$-0.631016\pi$
$503$	11.5818	−	11.5818i	0.516408	−	0.516408i	0.916483	+	0.400074i	$0.131016\pi$
$504$	−13.8457	+	17.2258i	−0.616736	+	0.767297i
$505$	−24.9445	+	10.7494i	−1.11002	+	0.478340i
$506$	4.79599	+	8.08536i	0.213208	+	0.359438i
$507$	0.107908	−	0.107908i	0.00479235	−	0.00479235i
$508$	−9.06671	+	2.65993i	−0.402270	+	0.118015i
$509$			19.9081i			0.882409i	0.897407	+	0.441204i	$0.145449\pi$
$509$			19.9081i			0.882409i	−0.897407	+	0.441204i	$0.854551\pi$
$510$	3.50385	−	0.554191i	0.155153	−	0.0245400i
$511$	10.7866	+	9.31629i	0.477169	+	0.412128i
$512$	−17.6038	−	14.2165i	−0.777984	−	0.628284i
$513$	3.84585	+	3.84585i	0.169798	+	0.169798i
$514$	3.23625	−	1.91965i	0.142745	−	0.0846719i
$515$	−9.57373	+	24.0732i	−0.421869	+	1.06079i
$516$	2.28344	+	1.24754i	0.100523	+	0.0549200i
$517$	13.6425	−	13.6425i	0.599996	−	0.599996i
$518$	−6.65477	−	9.55424i	−0.292394	−	0.419789i
$519$			4.91630i			0.215802i
$520$	−21.1621	+	10.0205i	−0.928020	+	0.439428i
$521$			3.54619i			0.155362i	0.996978	+	0.0776808i	$0.0247515\pi$
$521$			3.54619i			0.155362i	−0.996978	+	0.0776808i	$0.975248\pi$
$522$	−40.5445	−	10.3534i	−1.77459	−	0.453156i
$523$	15.4155	+	15.4155i	0.674073	+	0.674073i	0.958652	−	0.284580i	$-0.0918540\pi$
$523$	15.4155	+	15.4155i	0.674073	+	0.674073i	−0.284580	+	0.958652i	$0.591854\pi$
$524$	−29.9886	−	16.3841i	−1.31006	−	0.715741i
$525$	0.289317	+	2.84416i	0.0126268	+	0.124129i
$526$	35.2511	−	20.9099i	1.53702	−	0.911716i
$527$	−31.2139	+	31.2139i	−1.35970	+	1.35970i
$528$	−1.44586	−	0.315233i	−0.0629231	−	0.0137188i
$529$		−	7.92225i		−	0.344446i
$530$	5.39370	+	3.92051i	0.234287	+	0.170296i
$531$	−28.9525			−1.25643
$532$	20.3608	+	9.26467i	0.882754	+	0.401674i
$533$	−8.04551	+	8.04551i	−0.348490	+	0.348490i
$534$	3.26795	−	1.93845i	0.141418	−	0.0838850i
$535$	1.71044	+	0.680230i	0.0739489	+	0.0294089i
$536$	22.2781	−	0.787876i	0.962269	−	0.0340311i
$537$	0.930661	+	0.930661i	0.0401610	+	0.0401610i
$538$	−22.2420	−	5.67969i	−0.958921	−	0.244869i
$539$	1.74354	+	11.8558i	0.0750994	+	0.510667i
$540$	−4.42923	+	3.67238i	−0.190604	+	0.158034i
$541$			39.8565i			1.71357i	0.515677	+	0.856783i	$0.327540\pi$
$541$			39.8565i			1.71357i	−0.515677	+	0.856783i	$0.672460\pi$
$542$	18.0994	+	4.62183i	0.777434	+	0.198525i
$543$	−1.05772	−	1.05772i	−0.0453910	−	0.0453910i
$544$	26.2504	+	13.1591i	1.12548	+	0.564192i
$545$	3.30772	−	1.42540i	0.141687	−	0.0610572i
$546$	0.527128	−	2.94682i	0.0225590	−	0.126112i
$547$	16.1872	+	16.1872i	0.692115	+	0.692115i	0.962697	−	0.270582i	$-0.0872160\pi$
$547$	16.1872	+	16.1872i	0.692115	+	0.692115i	−0.270582	+	0.962697i	$0.587216\pi$
$548$	10.1282	−	2.97136i	0.432657	−	0.126930i
$549$			16.0036i			0.683018i
$550$	10.2319	−	6.46843i	0.436288	−	0.275815i
$551$			42.3551i			1.80439i
$552$	−1.73657	−	1.61793i	−0.0739132	−	0.0688638i
$553$	16.3294	−	1.19429i	0.694399	−	0.0507865i
$554$	−28.3461	+	16.8141i	−1.20431	+	0.714361i
$555$	−0.595103	−	1.38097i	−0.0252607	−	0.0586191i
$556$	3.50923	−	6.42312i	0.148825	−	0.272401i
$557$	−16.0139	−	16.0139i	−0.678530	−	0.678530i	0.281137	−	0.959668i	$-0.409288\pi$
$557$	−16.0139	−	16.0139i	−0.678530	−	0.678530i	−0.959668	+	0.281137i	$0.909288\pi$
$558$	8.78777	−	34.4134i	0.372016	−	1.45684i
$559$	22.2877			0.942670
$560$	−11.7619	+	20.5343i	−0.497031	+	0.867733i
$561$	1.92040			0.0810794
$562$	−1.11512	+	4.36689i	−0.0470387	+	0.184206i
$563$	−5.89268	−	5.89268i	−0.248347	−	0.248347i	0.571945	−	0.820292i	$-0.306189\pi$
$563$	−5.89268	−	5.89268i	−0.248347	−	0.248347i	−0.820292	+	0.571945i	$0.806189\pi$
$564$	−2.33548	+	4.27474i	−0.0983413	+	0.179999i
$565$	−16.1989	−	6.44219i	−0.681494	−	0.271025i
$566$	31.7813	−	18.8517i	1.33587	−	0.792398i
$567$	1.65619	+	22.6450i	0.0695536	+	0.951000i
$568$	−13.0430	+	13.9994i	−0.547273	+	0.587401i
$569$		−	23.9740i		−	1.00504i	−0.864565	−	0.502522i	$-0.832406\pi$
$569$		−	23.9740i		−	1.00504i	0.864565	−	0.502522i	$-0.167594\pi$
$570$	2.33690	+	1.69862i	0.0978819	+	0.0711472i
$571$		−	9.98784i		−	0.417978i	−0.977918	−	0.208989i	$-0.932983\pi$
$571$		−	9.98784i		−	0.417978i	0.977918	−	0.208989i	$-0.0670173\pi$
$572$	−12.1630	+	3.56830i	−0.508559	+	0.149198i
$573$	2.10972	+	2.10972i	0.0881349	+	0.0881349i
$574$	−2.02488	+	11.3197i	−0.0845168	+	0.472476i
$575$	19.4072	−	0.550673i	0.809337	−	0.0229647i
$576$	−23.5674	+	1.66903i	−0.981973	+	0.0695428i
$577$	5.82269	+	5.82269i	0.242402	+	0.242402i	0.817843	−	0.575441i	$-0.195170\pi$
$577$	5.82269	+	5.82269i	0.242402	+	0.242402i	−0.575441	+	0.817843i	$0.695170\pi$
$578$	−13.6273	−	3.47985i	−0.566820	−	0.144743i
$579$		−	2.03161i		−	0.0844308i
$580$	−44.6124	−	4.16766i	−1.85243	−	0.173053i
$581$	−6.08450	+	7.04474i	−0.252428	+	0.292265i
$582$	1.01874	+	0.260144i	0.0422281	+	0.0107833i
$583$	2.55248	+	2.55248i	0.105713	+	0.105713i
$584$	0.538523	+	15.2274i	0.0222843	+	0.630114i
$585$	−9.03469	+	22.7178i	−0.373538	+	0.939264i
$586$	3.80063	−	2.25442i	0.157003	−	0.0931293i
$587$	33.5181	−	33.5181i	1.38344	−	1.38344i	0.545010	−	0.838429i	$-0.316526\pi$
$587$	33.5181	−	33.5181i	1.38344	−	1.38344i	0.838429	−	0.545010i	$-0.183474\pi$
$588$	−1.26505	−	2.74834i	−0.0521696	−	0.113340i
$589$	−35.9502			−1.48130
$590$	−30.6206	+	4.84315i	−1.26063	+	0.199389i
$591$		−	0.886795i		−	0.0364779i
$592$	2.65154	−	12.1617i	0.108978	−	0.499841i
$593$	−21.8516	+	21.8516i	−0.897338	+	0.897338i	−0.995200	−	0.0978624i	$-0.968800\pi$
$593$	−21.8516	+	21.8516i	−0.897338	+	0.897338i	0.0978624	+	0.995200i	$0.468800\pi$
$594$	−2.67892	+	1.58905i	−0.109917	+	0.0651997i
$595$	9.23677	−	29.2876i	0.378671	−	1.20067i
$596$	−28.1359	−	15.3719i	−1.15249	−	0.629657i
$597$	−0.635894	−	0.635894i	−0.0260254	−	0.0260254i
$598$	−19.6981	−	5.03008i	−0.805514	−	0.205695i
$599$			33.7846i			1.38040i	0.723617	+	0.690202i	$0.242478\pi$
$599$			33.7846i			1.38040i	−0.723617	+	0.690202i	$0.757522\pi$
$600$	−2.01909	+	2.29430i	−0.0824290	+	0.0936644i
$601$			30.8760i			1.25946i	0.776815	+	0.629729i	$0.216834\pi$
$601$			30.8760i			1.25946i	−0.776815	+	0.629729i	$0.783166\pi$
$602$	18.4836	−	12.8743i	0.753337	−	0.524717i
$603$	16.4588	−	16.4588i	0.670253	−	0.670253i
$604$	1.43055	+	0.781571i	0.0582082	+	0.0318017i
$605$	−16.5706	+	7.14075i	−0.673689	+	0.290313i
$606$	3.19301	−	1.89400i	0.129707	−	0.0769383i
$607$	−5.62936	−	5.62936i	−0.228489	−	0.228489i	0.583572	−	0.812061i	$-0.301654\pi$
$607$	−5.62936	−	5.62936i	−0.228489	−	0.228489i	−0.812061	+	0.583572i	$0.801654\pi$
$608$	7.53884	+	22.6947i	0.305741	+	0.920391i
$609$	3.74446	−	4.33540i	0.151733	−	0.175679i
$610$	2.67707	+	16.9257i	0.108391	+	0.685300i
$611$			41.7240i			1.68797i
$612$	29.4204	−	8.63118i	1.18925	−	0.348895i
$613$	23.8846	−	23.8846i	0.964692	−	0.964692i	−0.0347060	−	0.999398i	$-0.511049\pi$
$613$	23.8846	−	23.8846i	0.964692	−	0.964692i	0.999398	+	0.0347060i	$0.0110495\pi$
$614$	−17.3265	−	29.2100i	−0.699241	−	1.17882i
$615$	−0.548820	+	1.38001i	−0.0221306	+	0.0556474i
$616$	−8.02579	+	9.98509i	−0.323368	+	0.402311i
$617$	17.8039	−	17.8039i	0.716759	−	0.716759i	−0.251181	−	0.967940i	$-0.580819\pi$
$617$	17.8039	−	17.8039i	0.716759	−	0.716759i	0.967940	+	0.251181i	$0.0808189\pi$
$618$	0.876097	−	3.43085i	0.0352418	−	0.138009i
$619$		−	35.0721i		−	1.40967i	−0.709373	−	0.704834i	$-0.751022\pi$
$619$		−	35.0721i		−	1.40967i	0.709373	−	0.704834i	$-0.248978\pi$
$620$	3.53743	−	37.8662i	0.142067	−	1.52074i
$621$	−4.99570			−0.200471
$622$	11.3158	+	2.88959i	0.453723	+	0.115862i
$623$	−2.39930	−	32.8053i	−0.0961258	−	1.31432i
$624$	2.69306	−	1.72895i	0.107809	−	0.0692134i
$625$	−1.41759	−	24.9598i	−0.0567036	−	0.998391i
$626$	17.4390	+	29.3996i	0.697001	+	1.17504i
$627$	1.10590	+	1.10590i	0.0441653	+	0.0441653i
$628$	−3.15919	+	0.926824i	−0.126066	+	0.0369843i
$629$			16.1532i			0.644068i
$630$	5.63008	+	24.0591i	0.224308	+	0.958537i
$631$	−22.7618			−0.906131			−0.453066	−	0.891477i	$-0.649670\pi$
$631$	−22.7618			−0.906131			−0.453066	+	0.891477i	$0.649670\pi$
$632$	12.8066	+	11.9317i	0.509418	+	0.474618i
$633$	−3.20269	+	3.20269i	−0.127296	+	0.127296i
$634$	40.5356	−	24.0445i	1.60987	−	0.954930i
$635$	−3.90388	+	9.81632i	−0.154921	+	0.389549i
$636$	−0.799793	−	0.436962i	−0.0317139	−	0.0173267i
$637$	−20.7961	−	15.4637i	−0.823970	−	0.612693i
$638$	−23.5020	−	6.00145i	−0.930455	−	0.237600i
$639$			19.9785i			0.790339i
$640$	−24.6460	+	5.70751i	−0.974218	+	0.225609i
$641$	−17.2614			−0.681784			−0.340892	−	0.940102i	$-0.610729\pi$
$641$	−17.2614			−0.681784			−0.340892	+	0.940102i	$0.610729\pi$
$642$	−0.243768	−	0.0622483i	−0.00962075	−	0.00245674i
$643$	20.2694	+	20.2694i	0.799348	+	0.799348i	0.982993	−	0.183645i	$-0.0587897\pi$
$643$	20.2694	+	20.2694i	0.799348	+	0.799348i	−0.183645	+	0.982993i	$0.558790\pi$
$644$	−19.2416	+	7.20688i	−0.758224	+	0.283991i
$645$	2.67163	−	1.15129i	0.105195	−	0.0453318i
$646$	−15.8325	−	26.6913i	−0.622920	−	1.05015i
$647$	−18.8673	−	18.8673i	−0.741752	−	0.741752i	0.231163	−	0.972915i	$-0.425747\pi$
$647$	−18.8673	−	18.8673i	−0.741752	−	0.741752i	−0.972915	+	0.231163i	$0.925747\pi$
$648$	−16.5464	+	17.7596i	−0.650003	+	0.697664i
$649$	−16.7826			−0.658775
$650$	−5.75501	+	25.5380i	−0.225730	+	1.00168i
$651$	3.67981	+	3.17823i	0.144223	+	0.124565i
$652$	0.884056	−	0.259359i	0.0346223	−	0.0101573i
$653$	5.92133	−	5.92133i	0.231719	−	0.231719i	−0.581691	−	0.813410i	$-0.697609\pi$
$653$	5.92133	−	5.92133i	0.231719	−	0.231719i	0.813410	+	0.581691i	$0.197609\pi$
$654$	−0.423402	+	0.251149i	−0.0165563	+	0.00982071i
$655$	−35.0867	+	15.1199i	−1.37095	+	0.590784i
$656$	−10.3449	+	6.64148i	−0.403902	+	0.259306i
$657$	11.2498	+	11.2498i	0.438896	+	0.438896i
$658$	24.1015	+	34.6025i	0.939574	+	1.34895i
$659$	48.8385			1.90248			0.951239	−	0.308455i	$-0.0998119\pi$
$659$	48.8385			1.90248			0.951239	+	0.308455i	$0.0998119\pi$
$660$	−1.27365	+	1.05602i	−0.0495769	+	0.0411054i
$661$	7.96281			0.309717			0.154859	−	0.987937i	$-0.450508\pi$
$661$	7.96281			0.309717			0.154859	+	0.987937i	$0.450508\pi$
$662$	−24.3140	−	6.20880i	−0.944991	−	0.241312i
$663$	−2.93666	+	2.93666i	−0.114051	+	0.114051i
$664$	−9.94506	+	0.351712i	−0.385943	+	0.0136491i
$665$	22.1850	−	11.5466i	0.860295	−	0.447759i
$666$	−6.63062	−	11.1783i	−0.256931	−	0.433149i
$667$	−27.5094	−	27.5094i	−1.06517	−	1.06517i
$668$	−2.26567	−	7.72280i	−0.0876613	−	0.298804i
$669$	0.260245			0.0100616
$670$	14.6538	−	20.1602i	0.566127	−	0.778858i
$671$			9.27666i			0.358122i
$672$	1.23469	−	2.98947i	0.0476292	−	0.115321i
$673$	−23.8193	−	23.8193i	−0.918166	−	0.918166i	0.0787302	−	0.996896i	$-0.474913\pi$
$673$	−23.8193	−	23.8193i	−0.918166	−	0.918166i	−0.996896	+	0.0787302i	$0.974913\pi$
$674$	8.08010	+	13.6219i	0.311234	+	0.524696i
$675$	0.182454	+	6.43019i	0.00702267	+	0.247498i
$676$	0.677131	−	1.23939i	0.0260435	−	0.0476687i
$677$	9.69645	−	9.69645i	0.372665	−	0.372665i	−0.495782	−	0.868447i	$-0.665119\pi$
$677$	9.69645	−	9.69645i	0.372665	−	0.372665i	0.868447	+	0.495782i	$0.165119\pi$
$678$	2.30863	+	0.589529i	0.0886624	+	0.0226407i
$679$	5.94956	−	6.88851i	0.228323	−	0.264357i
$680$	29.6717	−	14.0499i	1.13786	−	0.538788i
$681$	2.00734			0.0769214
$682$	5.09392	−	19.9481i	0.195056	−	0.763852i
$683$	8.38005	−	8.38005i	0.320654	−	0.320654i	−0.528364	−	0.849018i	$-0.677194\pi$
$683$	8.38005	−	8.38005i	0.320654	−	0.320654i	0.849018	+	0.528364i	$0.177194\pi$
$684$	21.9127	+	11.9719i	0.837853	+	0.457756i
$685$	4.36095	−	10.9656i	0.166623	−	0.418975i
$686$	−26.1790	−	0.811645i	−0.999520	−	0.0309887i
$687$	−3.66264	+	3.66264i	−0.139738	+	0.139738i
$688$	23.5279	+	5.12966i	0.896994	+	0.195567i
$689$	−7.80646			−0.297402
$690$	−2.62104	+	0.414560i	−0.0997813	+	0.0157820i
$691$	−26.6705			−1.01459			−0.507296	−	0.861772i	$-0.669355\pi$
$691$	−26.6705			−1.01459			−0.507296	+	0.861772i	$0.669355\pi$
$692$	12.8083	+	43.6585i	0.486897	+	1.65965i
$693$	0.975703	+	13.3407i	0.0370639	+	0.506771i
$694$	−30.8528	+	18.3009i	−1.17116	+	0.694695i
$695$	−3.23847	−	7.51507i	−0.122842	−	0.285063i
$696$	6.12029	−	0.216447i	0.231989	−	0.00820439i
$697$	11.2807	−	11.2807i	0.427287	−	0.427287i
$698$	−20.5415	−	5.24544i	−0.777506	−	0.198543i
$699$		−	1.27758i		−	0.0483224i
$700$	9.97903	+	24.5034i	0.377172	+	0.926143i
$701$		−	18.4558i		−	0.697067i	−0.937296	−	0.348533i	$-0.886680\pi$
$701$		−	18.4558i		−	0.697067i	0.937296	−	0.348533i	$-0.113320\pi$
$702$	1.66661	−	6.52655i	0.0629023	−	0.246329i
$703$	−9.30209	+	9.30209i	−0.350835	+	0.350835i
$704$	−13.6611	+	0.967468i	−0.514870	+	0.0364628i
$705$	2.15528	+	5.00146i	0.0811725	+	0.188366i
$706$	−11.7528	−	19.8135i	−0.442323	−	0.745693i
$707$	−2.34427	−	32.0530i	−0.0881654	−	1.20548i
$708$	4.06585	−	1.19281i	0.152804	−	0.0448287i
$709$	−0.657870			−0.0247068			−0.0123534	−	0.999924i	$-0.503932\pi$
$709$	−0.657870			−0.0247068			−0.0123534	+	0.999924i	$0.503932\pi$
$710$	3.34199	+	21.1296i	0.125423	+	0.792980i
$711$	18.2763			0.685415
$712$	23.9704	−	25.7280i	0.898329	−	0.964198i
$713$	23.3494	−	23.3494i	0.874443	−	0.874443i
$714$	−0.739093	+	4.13177i	−0.0276599	+	0.154627i
$715$	−5.23705	+	13.1686i	−0.195854	+	0.492477i
$716$	10.6892	+	5.83999i	0.399475	+	0.218251i
$717$	−2.16383	+	2.16383i	−0.0808097	+	0.0808097i
$718$	32.9538	+	8.41505i	1.22983	+	0.314047i
$719$	−38.6915			−1.44295			−0.721475	−	0.692440i	$-0.756536\pi$
$719$	−38.6915			−1.44295			−0.721475	+	0.692440i	$0.756536\pi$
$720$	−14.7661	+	21.9025i	−0.550299	+	0.816259i
$721$	−23.1987	−	20.0366i	−0.863965	−	0.746201i
$722$	−0.394926	+	1.54655i	−0.0146976	+	0.0575567i
$723$	3.15657	−	3.15657i	0.117394	−	0.117394i
$724$	−12.1485	−	6.63727i	−0.451497	−	0.246672i
$725$	−34.4038	+	36.4132i	−1.27773	+	1.35235i
$726$	2.12110	−	1.25817i	0.0787214	−	0.0466952i
$727$	10.4894	+	10.4894i	0.389030	+	0.389030i	0.874341	−	0.485311i	$-0.161294\pi$
$727$	10.4894	+	10.4894i	0.389030	+	0.389030i	−0.485311	+	0.874341i	$0.661294\pi$
$728$	−2.99614	−	27.5421i	−0.111045	−	1.02078i
$729$			24.5107i			0.907803i
$730$	13.7798	+	10.0161i	0.510013	+	0.370712i
$731$	−31.2499			−1.15582
$732$	−0.659333	−	2.24742i	−0.0243696	−	0.0830669i
$733$	16.6784	+	16.6784i	0.616032	+	0.616032i	0.944511	−	0.328479i	$-0.106536\pi$
$733$	16.6784	+	16.6784i	0.616032	+	0.616032i	−0.328479	+	0.944511i	$0.606536\pi$
$734$	−22.6733	+	13.4491i	−0.836888	+	0.496417i
$735$	−3.29161	−	0.779397i	−0.121413	−	0.0287485i
$736$	−19.6365	−	9.84361i	−0.723810	−	0.362840i
$737$	9.54049	−	9.54049i	0.351429	−	0.351429i
$738$	−3.17590	+	12.4370i	−0.116906	+	0.457813i
$739$	−40.9779			−1.50740			−0.753698	−	0.657221i	$-0.771732\pi$
$739$	−40.9779			−1.50740			−0.753698	+	0.657221i	$0.771732\pi$
$740$	−8.88253	−	10.7131i	−0.326528	−	0.393823i
$741$	−3.38226			−0.124250
$742$	−6.47404	+	4.50933i	−0.237670	+	0.165543i
$743$	3.14702	+	3.14702i	0.115453	+	0.115453i	0.762473	−	0.647020i	$-0.223985\pi$
$743$	3.14702	+	3.14702i	0.115453	+	0.115453i	−0.647020	+	0.762473i	$0.723985\pi$
$744$	0.183716	+	5.19479i	0.00673535	+	0.190450i
$745$	−32.9191	+	14.1858i	−1.20606	+	0.519729i
$746$	9.55862	+	16.1145i	0.349966	+	0.589993i
$747$	−7.34727	+	7.34727i	−0.268823	+	0.268823i
$748$	17.0538	−	5.00315i	0.623550	−	0.182933i
$749$	−1.42364	+	1.64831i	−0.0520185	+	0.0602279i
$750$	0.629325	+	3.35851i	0.0229797	+	0.122636i
$751$	42.9924			1.56881			0.784407	−	0.620247i	$-0.212968\pi$
$751$	42.9924			1.56881			0.784407	+	0.620247i	$0.212968\pi$
$752$	−9.60305	+	44.0457i	−0.350187	+	1.60618i
$753$	−1.82819	−	1.82819i	−0.0666228	−	0.0666228i
$754$	45.1165	−	26.7618i	1.64305	−	0.974606i
$755$	1.67375	−	0.721268i	0.0609139	−	0.0262496i
$756$	−2.38785	−	6.37530i	−0.0868454	−	0.231867i
$757$	21.5801	+	21.5801i	0.784341	+	0.784341i	0.980560	−	0.196219i	$-0.0628664\pi$
$757$	21.5801	+	21.5801i	0.784341	+	0.784341i	−0.196219	+	0.980560i	$0.562866\pi$
$758$	5.14677	−	20.1551i	0.186939	−	0.732065i
$759$	−1.43655			−0.0521433
$760$	25.1778	+	8.99609i	0.913296	+	0.326322i
$761$			15.0620i			0.545998i	0.962014	+	0.272999i	$0.0880156\pi$
$761$			15.0620i			0.545998i	−0.962014	+	0.272999i	$0.911984\pi$
$762$	0.357246	−	1.39900i	0.0129417	−	0.0506803i
$763$	0.310857	+	4.25032i	0.0112538	+	0.153872i
$764$	24.2315	+	13.2387i	0.876664	+	0.478960i
$765$	12.6676	−	31.8529i	0.458000	−	1.15164i
$766$	−14.7505	−	24.8673i	−0.532958	−	0.898491i
$767$	25.6639	−	25.6639i	0.926668	−	0.926668i
$768$	3.24084	−	1.20533i	0.116944	−	0.0434938i
$769$	−5.14329			−0.185472			−0.0927359	−	0.995691i	$-0.529561\pi$
$769$	−5.14329			−0.185472			−0.0927359	+	0.995691i	$0.529561\pi$
$770$	3.26353	+	13.9461i	0.117610	+	0.502582i
$771$			0.574992i			0.0207078i
$772$	−5.29287	−	18.0414i	−0.190495	−	0.649325i
$773$	−1.64198	−	1.64198i	−0.0590581	−	0.0590581i	0.676961	−	0.736019i	$-0.263297\pi$
$773$	−1.64198	−	1.64198i	−0.0590581	−	0.0590581i	−0.736019	+	0.676961i	$0.763297\pi$
$774$	21.6255	−	12.8276i	0.777312	−	0.461078i
$775$	−30.9069	−	29.2013i	−1.11021	−	1.04894i
$776$	9.72451	−	0.343911i	0.349090	−	0.0123457i
$777$	1.77451	−	0.129783i	0.0636602	−	0.00465594i
$778$	−5.01112	+	19.6238i	−0.179657	+	0.703549i
$779$	12.9924			0.465501
$780$	0.332808	−	3.56252i	0.0119164	−	0.127559i
$781$			11.5808i			0.414392i
$782$	27.6189	+	7.05273i	0.987650	+	0.252205i
$783$	9.11467	−	9.11467i	0.325732	−	0.325732i
$784$	−18.3942	−	21.1105i	−0.656936	−	0.753946i
$785$	−1.36026	+	3.42039i	−0.0485499	+	0.122079i
$786$	4.49124	−	2.66407i	0.160197	−	0.0950243i
$787$	0.419726	−	0.419726i	0.0149616	−	0.0149616i	−0.699586	−	0.714548i	$-0.746632\pi$
$787$	0.419726	−	0.419726i	0.0149616	−	0.0149616i	0.714548	+	0.699586i	$0.246632\pi$
$788$	−2.31034	−	7.87506i	−0.0823023	−	0.280537i
$789$			6.26316i			0.222974i
$790$	19.3293	−	3.05724i	0.687705	−	0.108772i
$791$	13.4827	−	15.6105i	0.479389	−	0.555045i
$792$	−9.74786	+	10.4626i	−0.346375	+	0.371773i
$793$	−14.1858	−	14.1858i	−0.503753	−	0.503753i
$794$	−13.9299	−	23.4838i	−0.494352	−	0.833407i
$795$	−0.935760	+	0.403247i	−0.0331880	+	0.0143017i
$796$	−7.30364	−	3.99030i	−0.258871	−	0.141432i
$797$	−23.4757	+	23.4757i	−0.831552	+	0.831552i	−0.987729	−	0.156177i	$-0.950083\pi$
$797$	−23.4757	+	23.4757i	−0.831552	+	0.831552i	0.156177	+	0.987729i	$0.450083\pi$
$798$	−2.80497	+	1.95373i	−0.0992950	+	0.0691614i
$799$		−	58.5017i		−	2.06964i
$800$	−11.9530	+	25.6345i	−0.422602	+	0.906316i
$801$		−	36.7165i		−	1.29731i
$802$	−5.23853	+	20.5144i	−0.184979	+	0.724388i
$803$	6.52105	+	6.52105i	0.230123	+	0.230123i
$804$	−1.63325	+	2.98942i	−0.0576003	+	0.105429i
$805$	−6.90952	+	21.9084i	−0.243529	+	0.772171i
$806$	22.7149	+	38.2941i	0.800098	+	1.34885i
$807$	2.48046	−	2.48046i	0.0873163	−	0.0873163i
$808$	23.4207	−	25.1380i	0.823937	−	0.884351i
$809$		−	19.4837i		−	0.685011i	−0.939516	−	0.342506i	$-0.888724\pi$
$809$		−	19.4837i		−	0.685011i	0.939516	−	0.342506i	$-0.111276\pi$
$810$	4.23965	+	26.8050i	0.148966	+	0.941832i
$811$	−7.78374			−0.273324			−0.136662	−	0.990618i	$-0.543637\pi$
$811$	−7.78374			−0.273324			−0.136662	+	0.990618i	$0.543637\pi$
$812$	21.9573	−	48.2552i	0.770550	−	1.69343i
$813$	−2.01847	+	2.01847i	−0.0707907	+	0.0707907i
$814$	−3.84350	−	6.47960i	−0.134715	−	0.227110i
$815$	0.380651	−	0.957148i	0.0133336	−	0.0335274i
$816$	−3.77597	+	2.42418i	−0.132185	+	0.0848634i
$817$	−17.9958	−	17.9958i	−0.629594	−	0.629594i
$818$	−0.362921	+	1.42122i	−0.0126892	+	0.0496918i
$819$	−21.8925	−	18.9084i	−0.764987	−	0.660715i
$820$	−1.27843	+	13.6848i	−0.0446446	+	0.477895i
$821$		−	6.61421i		−	0.230837i	−0.993317	−	0.115419i	$-0.963179\pi$
$821$		−	6.61421i		−	0.230837i	0.993317	−	0.115419i	$-0.0368210\pi$
$822$	−0.399073	+	1.56279i	−0.0139193	+	0.0545087i
$823$	1.82220	+	1.82220i	0.0635181	+	0.0635181i	0.738152	−	0.674634i	$-0.235699\pi$
$823$	1.82220	+	1.82220i	0.0635181	+	0.0635181i	−0.674634	+	0.738152i	$0.735699\pi$
$824$	−1.15820	−	32.7496i	−0.0403480	−	1.14089i
$825$	0.0524659	+	1.84904i	0.00182663	+	0.0643754i
$826$	6.45902	−	36.1080i	0.224738	−	1.25636i
$827$	−19.9956	−	19.9956i	−0.695315	−	0.695315i	0.268082	−	0.963396i	$-0.413610\pi$
$827$	−19.9956	−	19.9956i	−0.695315	−	0.695315i	−0.963396	+	0.268082i	$0.913610\pi$
$828$	−22.0078	+	6.45651i	−0.764824	+	0.224379i
$829$		−	28.0242i		−	0.973322i	−0.873591	−	0.486661i	$-0.838215\pi$
$829$		−	28.0242i		−	0.973322i	0.873591	−	0.486661i	$-0.161785\pi$
$830$	−6.54154	+	8.99963i	−0.227060	+	0.312382i
$831$		−	5.03632i		−	0.174708i
$832$	19.4109	−	22.3698i	0.672953	−	0.775534i
$833$	29.1584	+	21.6818i	1.01028	+	0.751229i
$834$	0.570606	+	0.961960i	0.0197585	+	0.0333100i
$835$	−8.36131	−	3.32523i	−0.289355	−	0.115074i
$836$	12.7019	+	6.93961i	0.439305	+	0.240012i
$837$	7.73636	+	7.73636i	0.267408	+	0.267408i
$838$	16.9731	+	4.33423i	0.586325	+	0.149723i
$839$	51.6008			1.78146			0.890729	−	0.454535i	$-0.150194\pi$
$839$	51.6008			1.78146			0.890729	+	0.454535i	$0.150194\pi$
$840$	−1.78185	−	3.14671i	−0.0614797	−	0.108572i
$841$	71.3817			2.46144
$842$	−1.38959	−	0.354844i	−0.0478884	−	0.0122287i
$843$	−0.487002	−	0.487002i	−0.0167732	−	0.0167732i
$844$	−20.0972	+	36.7849i	−0.691775	+	1.26619i
$845$	−0.624886	−	1.45009i	−0.0214967	−	0.0498845i
$846$	24.0140	+	40.4842i	0.825620	+	1.39188i
$847$	−1.55729	−	21.2927i	−0.0535091	−	0.731625i
$848$	−8.24085	−	1.79671i	−0.282992	−	0.0616992i
$849$			5.64667i			0.193793i
$850$	8.06917	−	35.8071i	0.276770	−	1.22817i
$851$		−	12.0833i		−	0.414210i
$852$	−0.823095	−	2.80562i	−0.0281988	−	0.0961190i
$853$	−2.85870	−	2.85870i	−0.0978801	−	0.0978801i	0.656471	−	0.754351i	$-0.272048\pi$
$853$	−2.85870	−	2.85870i	−0.0978801	−	0.0978801i	−0.754351	+	0.656471i	$0.772048\pi$
$854$	−19.9589	−	3.57025i	−0.682978	−	0.122172i
$855$	25.6379	−	11.0482i	0.876799	−	0.377839i
$856$	−2.32692	+	0.0822925i	−0.0795325	+	0.00281270i
$857$	−5.73997	−	5.73997i	−0.196074	−	0.196074i	0.602241	−	0.798315i	$-0.294275\pi$
$857$	−5.73997	−	5.73997i	−0.196074	−	0.196074i	−0.798315	+	0.602241i	$0.794275\pi$
$858$	0.479245	−	1.87675i	0.0163612	−	0.0640713i
$859$			42.4707i			1.44908i	0.689232	+	0.724540i	$0.257948\pi$
$859$			42.4707i			1.44908i	−0.689232	+	0.724540i	$0.742052\pi$
$860$	20.7256	−	17.1841i	0.706738	−	0.585974i
$861$	−1.32988	−	1.14861i	−0.0453222	−	0.0391446i
$862$	−1.13716	+	4.45320i	−0.0387319	+	0.151677i
$863$	18.5623	+	18.5623i	0.631870	+	0.631870i	0.948537	−	0.316667i	$-0.102564\pi$
$863$	18.5623	+	18.5623i	0.631870	+	0.631870i	−0.316667	+	0.948537i	$0.602564\pi$
$864$	3.26148	−	6.50615i	0.110958	−	0.221344i
$865$	47.2681	+	18.7982i	1.60716	+	0.639157i
$866$	−0.351950	−	0.593337i	−0.0119597	−	0.0201624i
$867$	1.51973	−	1.51973i	0.0516129	−	0.0516129i
$868$	40.9581	+	18.6369i	1.39021	+	0.632579i
$869$	10.5940			0.359378
$870$	4.02573	−	5.53846i	0.136485	−	0.187771i
$871$			29.1785i			0.988676i
$872$	−3.10565	+	3.33337i	−0.105171	+	0.112882i
$873$	7.18433	−	7.18433i	0.243153	−	0.243153i
$874$	11.8434	+	19.9663i	0.400609	+	0.675370i
$875$	28.4517	+	8.09340i	0.961842	+	0.273607i
$876$	−2.04331	−	1.11635i	−0.0690369	−	0.0377179i
$877$	−8.94806	−	8.94806i	−0.302154	−	0.302154i	0.539702	−	0.841856i	$-0.318537\pi$
$877$	−8.94806	−	8.94806i	−0.302154	−	0.302154i	−0.841856	+	0.539702i	$0.818537\pi$
$878$	−0.784658	+	3.07277i	−0.0264809	+	0.103701i
$879$			0.675268i			0.0227762i
$880$	−8.55930	+	12.6960i	−0.288534	+	0.427983i
$881$		−	42.1652i		−	1.42058i	−0.703908	−	0.710291i	$-0.748563\pi$
$881$		−	42.1652i		−	1.42058i	0.703908	−	0.710291i	$-0.251437\pi$
$882$	−29.0782	−	3.03511i	−0.979113	−	0.102198i
$883$	−12.9060	+	12.9060i	−0.434321	+	0.434321i	−0.890095	−	0.455774i	$-0.849362\pi$
$883$	−12.9060	+	12.9060i	−0.434321	+	0.434321i	0.455774	+	0.890095i	$0.349362\pi$
$884$	−18.4278	+	33.7294i	−0.619795	+	1.13444i
$885$	1.75065	−	4.40201i	0.0588473	−	0.147972i
$886$	14.9805	+	25.2550i	0.503281	+	0.848460i
$887$	−22.9714	−	22.9714i	−0.771303	−	0.771303i	0.207031	−	0.978334i	$-0.433620\pi$
$887$	−22.9714	−	22.9714i	−0.771303	−	0.771303i	−0.978334	+	0.207031i	$0.933620\pi$
$888$	1.39168	+	1.29661i	0.0467018	+	0.0435114i
$889$	−9.45973	−	8.17032i	−0.317269	−	0.274024i
$890$	−6.14189	−	38.8319i	−0.205877	−	1.30165i
$891$			14.6914i			0.492179i
$892$	2.31107	−	0.678006i	0.0773802	−	0.0227013i
$893$	33.6893	−	33.6893i	1.12737	−	1.12737i
$894$	4.21378	−	2.49949i	0.140930	−	0.0835955i
$895$	12.5064	−	5.38939i	0.418044	−	0.180147i
$896$	3.17613	−	29.7643i	0.106107	−	0.994355i
$897$	2.19676	−	2.19676i	0.0733476	−	0.0733476i
$898$	−19.1689	−	4.89496i	−0.639676	−	0.163347i
$899$			85.2021i			2.84165i
$900$	9.11423	+	28.0914i	0.303808	+	0.936380i
$901$	10.9455			0.364648
$902$	−1.84094	+	7.20924i	−0.0612967	+	0.240041i
$903$	0.251078	+	3.43297i	0.00835535	+	0.114242i
$904$	22.0373	−	0.779360i	0.732951	−	0.0259211i
$905$	−14.2138	+	6.12516i	−0.472484	+	0.203607i
$906$	−0.214247	+	0.127085i	−0.00711787	+	0.00422210i
$907$	24.6489	+	24.6489i	0.818453	+	0.818453i	0.985884	−	0.167431i	$-0.0535471\pi$
$907$	24.6489	+	24.6489i	0.818453	+	0.818453i	−0.167431	+	0.985884i	$0.553547\pi$
$908$	17.8259	−	5.22965i	0.591573	−	0.173552i
$909$		−	35.8745i		−	1.18988i
$910$	−26.3168	−	16.3357i	−0.872395	−	0.541523i
$911$	−10.8180			−0.358416			−0.179208	−	0.983811i	$-0.557353\pi$
$911$	−10.8180			−0.358416			−0.179208	+	0.983811i	$0.557353\pi$
$912$	−3.57047	−	0.778449i	−0.118230	−	0.0257770i
$913$	−4.25892	+	4.25892i	−0.140950	+	0.140950i
$914$	−20.4878	−	34.5394i	−0.677675	−	1.14246i
$915$	−2.43323	−	0.967677i	−0.0804401	−	0.0319904i
$916$	−22.9834	+	42.0677i	−0.759394	+	1.38996i
$917$	−3.29743	−	45.0854i	−0.108891	−	1.48885i
$918$	−2.33678	+	9.15096i	−0.0771252	+	0.302027i
$919$		−	37.9739i		−	1.25264i	−0.779565	−	0.626321i	$-0.784560\pi$
$919$		−	37.9739i		−	1.25264i	0.779565	−	0.626321i	$-0.215440\pi$
$920$	−22.1957	+	10.5099i	−0.731772	+	0.346503i
$921$	5.18982			0.171010
$922$	3.79496	−	14.8613i	0.124980	−	0.489431i
$923$	−17.7092	−	17.7092i	−0.582906	−	0.582906i
$924$	−0.686642	−	1.83326i	−0.0225889	−	0.0603098i
$925$	−15.5529	+	0.441309i	−0.511377	+	0.0145101i
$926$	−9.67852	+	5.74101i	−0.318056	+	0.188661i
$927$	−24.1950	−	24.1950i	−0.794667	−	0.794667i
$928$	53.7865	−	17.8671i	1.76563	−	0.586516i
$929$	−29.5862			−0.970691			−0.485345	−	0.874323i	$-0.661306\pi$
$929$	−29.5862			−0.970691			−0.485345	+	0.874323i	$0.661306\pi$
$930$	4.70094	+	3.41696i	0.154150	+	0.112047i
$931$	4.30555	+	29.2773i	0.141109	+	0.959523i
$932$	−3.32842	−	11.3453i	−0.109026	−	0.371629i
$933$	−1.26196	+	1.26196i	−0.0413146	+	0.0413146i
$934$	16.7026	+	28.1582i	0.546526	+	0.921364i
$935$	7.34293	−	18.4638i	0.240139	−	0.603832i
$936$	−1.09299	−	30.9057i	−0.0357256	−	1.01018i
$937$	36.4385	+	36.4385i	1.19039	+	1.19039i	0.976957	+	0.213437i	$0.0684657\pi$
$937$	36.4385	+	36.4385i	1.19039	+	1.19039i	0.213437	+	0.976957i	$0.431534\pi$
$938$	16.8547	+	24.1983i	0.550326	+	0.790102i
$939$	−5.22350			−0.170463
$940$	32.1698	+	38.7997i	1.04926	+	1.26551i
$941$	−17.6470			−0.575276			−0.287638	−	0.957739i	$-0.592870\pi$
$941$	−17.6470			−0.575276			−0.287638	+	0.957739i	$0.592870\pi$
$942$	0.124478	−	0.487465i	0.00405573	−	0.0158825i
$943$	−8.43848	+	8.43848i	−0.274795	+	0.274795i
$944$	32.9986	−	21.1852i	1.07401	−	0.689520i
$945$	−7.25891	−	2.28933i	−0.236133	−	0.0744719i
$946$	12.5354	−	7.43564i	0.407562	−	0.241753i
$947$	−14.3693	−	14.3693i	−0.466938	−	0.466938i	0.433983	−	0.900921i	$-0.357108\pi$
$947$	−14.3693	−	14.3693i	−0.466938	−	0.466938i	−0.900921	+	0.433983i	$0.857108\pi$
$948$	−2.56657	+	0.752964i	−0.0833584	+	0.0244551i
$949$	−19.9439			−0.647406
$950$	25.2669	−	15.9734i	0.819767	−	0.518245i
$951$			7.20206i			0.233543i
$952$	4.20093	+	38.6171i	0.136153	+	1.25159i
$953$	−19.0634	−	19.0634i	−0.617525	−	0.617525i	0.327371	−	0.944896i	$-0.393837\pi$
$953$	−19.0634	−	19.0634i	−0.617525	−	0.617525i	−0.944896	+	0.327371i	$0.893837\pi$
$954$	−7.57450	+	4.49297i	−0.245234	+	0.145465i
$955$	28.3509	−	12.2173i	0.917414	−	0.395341i
$956$	−13.5782	+	24.8529i	−0.439152	+	0.803801i
$957$	2.62098	−	2.62098i	0.0847243	−	0.0847243i
$958$	−4.62866	+	18.1261i	−0.149545	+	0.585628i
$959$	10.5673	+	9.12691i	0.341236	+	0.294723i
$960$	1.17126	−	3.68416i	0.0378024	−	0.118906i
$961$	−41.3180			−1.33284
$962$	15.7860	+	4.03110i	0.508961	+	0.129968i
$963$	−1.71910	+	1.71910i	−0.0553971	+	0.0553971i
$964$	19.8078	−	36.2551i	0.637965	−	1.16770i
$965$	−19.5330	−	7.76814i	−0.628791	−	0.250065i
$966$	0.552875	−	3.09075i	0.0177885	−	0.0994432i
$967$	−31.7288	+	31.7288i	−1.02033	+	1.02033i	−0.0205405	+	0.999789i	$0.506539\pi$
$967$	−31.7288	+	31.7288i	−1.02033	+	1.02033i	−0.999789	+	0.0205405i	$0.993461\pi$
$968$	15.5583	−	16.6991i	0.500061	−	0.536728i
$969$	4.74231			0.152345
$970$	6.39646	−	8.80004i	0.205378	−	0.282552i
$971$	24.9149			0.799556			0.399778	−	0.916612i	$-0.369087\pi$
$971$	24.9149			0.799556			0.399778	+	0.916612i	$0.369087\pi$
$972$	−3.21724	−	10.9664i	−0.103193	−	0.351746i
$973$	9.65664	−	0.706261i	0.309578	−	0.0226417i
$974$	11.9217	+	20.0983i	0.381996	+	0.643990i
$975$	−2.90777	−	2.74731i	−0.0931232	−	0.0879844i
$976$	−11.7102	−	18.2401i	−0.374835	−	0.583852i
$977$	−11.2699	+	11.2699i	−0.360555	+	0.360555i	−0.864017	−	0.503462i	$-0.832059\pi$
$977$	−11.2699	+	11.2699i	−0.360555	+	0.360555i	0.503462	+	0.864017i	$0.332059\pi$
$978$	−0.0348335	+	0.136410i	−0.00111385	+	0.00436192i
$979$		−	21.2831i		−	0.680210i
$980$	−31.2612	+	1.65419i	−0.998603	+	0.0528411i
$981$			4.75706i			0.151881i
$982$	10.3554	+	2.64435i	0.330455	+	0.0843845i
$983$	−28.1976	+	28.1976i	−0.899365	+	0.899365i	−0.995380	−	0.0960152i	$-0.969390\pi$
$983$	−28.1976	+	28.1976i	−0.899365	+	0.899365i	0.0960152	+	0.995380i	$0.469390\pi$
$984$	−0.0663949	−	1.87739i	−0.00211659	−	0.0598491i
$985$	−8.52616	−	3.39079i	−0.271666	−	0.108040i
$986$	−63.2584	+	37.5230i	−2.01456	+	1.19498i
$987$	−6.42672	+	0.470034i	−0.204565	+	0.0149613i
$988$	−30.0357	+	8.81168i	−0.955563	+	0.280337i
$989$	23.3763			0.743324
$990$	2.49768	+	15.7915i	0.0793814	+	0.501886i
$991$	−53.1218			−1.68747			−0.843735	−	0.536760i	$-0.819648\pi$
$991$	−53.1218			−1.68747			−0.843735	+	0.536760i	$0.819648\pi$
$992$	15.1652	+	45.6529i	0.481497	+	1.44948i
$993$	2.71153	−	2.71153i	0.0860479	−	0.0860479i
$994$	−24.9162	−	4.45702i	−0.790293	−	0.141368i
$995$	−8.54528	+	3.68242i	−0.270904	+	0.116740i
$996$	0.729090	−	1.33449i	0.0231021	−	0.0422849i
$997$	−18.9505	+	18.9505i	−0.600168	+	0.600168i	−0.940357	−	0.340189i	$-0.889509\pi$
$997$	−18.9505	+	18.9505i	−0.600168	+	0.600168i	0.340189	+	0.940357i	$0.389509\pi$
$998$	−11.2183	+	43.9316i	−0.355110	+	1.39063i
$999$	4.00355			0.126667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.s.c.13.15	yes	72
4.3	odd	2		1120.2.w.c.433.19		72
5.2	odd	4	inner	280.2.s.c.237.5	yes	72
7.6	odd	2	inner	280.2.s.c.13.16	yes	72
8.3	odd	2		1120.2.w.c.433.18		72
8.5	even	2	inner	280.2.s.c.13.6	yes	72
20.7	even	4		1120.2.w.c.657.20		72
28.27	even	2		1120.2.w.c.433.17		72
35.27	even	4	inner	280.2.s.c.237.6	yes	72
40.27	even	4		1120.2.w.c.657.17		72
40.37	odd	4	inner	280.2.s.c.237.16	yes	72
56.13	odd	2	inner	280.2.s.c.13.5	✓	72
56.27	even	2		1120.2.w.c.433.20		72
140.27	odd	4		1120.2.w.c.657.18		72
280.27	odd	4		1120.2.w.c.657.19		72
280.237	even	4	inner	280.2.s.c.237.15	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.s.c.13.5	✓	72	56.13	odd	2	inner
280.2.s.c.13.6	yes	72	8.5	even	2	inner
280.2.s.c.13.15	yes	72	1.1	even	1	trivial
280.2.s.c.13.16	yes	72	7.6	odd	2	inner
280.2.s.c.237.5	yes	72	5.2	odd	4	inner
280.2.s.c.237.6	yes	72	35.27	even	4	inner
280.2.s.c.237.15	yes	72	280.237	even	4	inner
280.2.s.c.237.16	yes	72	40.37	odd	4	inner
1120.2.w.c.433.17		72	28.27	even	2
1120.2.w.c.433.18		72	8.3	odd	2
1120.2.w.c.433.19		72	4.3	odd	2
1120.2.w.c.433.20		72	56.27	even	2
1120.2.w.c.657.17		72	40.27	even	4
1120.2.w.c.657.18		72	140.27	odd	4
1120.2.w.c.657.19		72	280.27	odd	4
1120.2.w.c.657.20		72	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.349904 + 1.37024i) q^{2} +(-0.152811 - 0.152811i) q^{3} +(-1.75513 - 0.958907i) q^{4} +(-2.05351 + 0.884920i) q^{5} +(0.262858 - 0.155920i) q^{6} +(-0.192988 - 2.63870i) q^{7} +(1.92806 - 2.06944i) q^{8} -2.95330i q^{9} +O(q^{10})\)	\(q+(-0.349904 + 1.37024i) q^{2} +(-0.152811 - 0.152811i) q^{3} +(-1.75513 - 0.958907i) q^{4} +(-2.05351 + 0.884920i) q^{5} +(0.262858 - 0.155920i) q^{6} +(-0.192988 - 2.63870i) q^{7} +(1.92806 - 2.06944i) q^{8} -2.95330i q^{9} +(-0.494024 - 3.12345i) q^{10} -1.71191i q^{11} +(0.121673 + 0.414737i) q^{12} +(2.61784 + 2.61784i) q^{13} +(3.68319 + 0.658852i) q^{14} +(0.449026 + 0.178574i) q^{15} +(2.16100 + 3.36602i) q^{16} +(-3.67050 - 3.67050i) q^{17} +(4.04674 + 1.03337i) q^{18} -4.22745i q^{19} +(4.45275 + 0.415973i) q^{20} +(-0.373733 + 0.432715i) q^{21} +(2.34573 + 0.599003i) q^{22} +(2.74570 + 2.74570i) q^{23} +(-0.610864 + 0.0216035i) q^{24} +(3.43383 - 3.63439i) q^{25} +(-4.50307 + 2.67108i) q^{26} +(-0.909732 + 0.909732i) q^{27} +(-2.19155 + 4.81634i) q^{28} -10.0191 q^{29} +(-0.401806 + 0.552792i) q^{30} -8.50400i q^{31} +(-5.36841 + 1.78331i) q^{32} +(-0.261599 + 0.261599i) q^{33} +(6.31380 - 3.74516i) q^{34} +(2.73135 + 5.24783i) q^{35} +(-2.83194 + 5.18343i) q^{36} +(-2.20040 - 2.20040i) q^{37} +(5.79264 + 1.47920i) q^{38} -0.800071i q^{39} +(-2.12802 + 5.95580i) q^{40} +3.07334i q^{41} +(-0.462154 - 0.663514i) q^{42} +(4.25689 - 4.25689i) q^{43} +(-1.64156 + 3.00463i) q^{44} +(2.61343 + 6.06463i) q^{45} +(-4.72301 + 2.80155i) q^{46} +(7.96917 + 7.96917i) q^{47} +(0.184142 - 0.844592i) q^{48} +(-6.92551 + 1.01848i) q^{49} +(3.77849 + 5.97687i) q^{50} +1.12179i q^{51} +(-2.08440 - 7.10492i) q^{52} +(-1.49101 + 1.49101i) q^{53} +(-0.928236 - 1.56487i) q^{54} +(1.51490 + 3.51543i) q^{55} +(-5.83272 - 4.68821i) q^{56} +(-0.646003 + 0.646003i) q^{57} +(3.50571 - 13.7286i) q^{58} -9.80345i q^{59} +(-0.616866 - 0.743996i) q^{60} -5.41890 q^{61} +(11.6525 + 2.97558i) q^{62} +(-7.79288 + 0.569950i) q^{63} +(-0.565140 - 7.98001i) q^{64} +(-7.69234 - 3.05919i) q^{65} +(-0.266920 - 0.449989i) q^{66} +(5.57302 + 5.57302i) q^{67} +(2.92256 + 9.96189i) q^{68} -0.839149i q^{69} +(-8.14652 + 1.90637i) q^{70} -6.76483 q^{71} +(-6.11166 - 5.69415i) q^{72} +(-3.80923 + 3.80923i) q^{73} +(3.78501 - 2.24516i) q^{74} +(-1.08011 + 0.0306476i) q^{75} +(-4.05373 + 7.41974i) q^{76} +(-4.51722 + 0.330377i) q^{77} +(1.09629 + 0.279948i) q^{78} +6.18844i q^{79} +(-7.41629 - 4.99986i) q^{80} -8.58186 q^{81} +(-4.21123 - 1.07537i) q^{82} +(-2.48782 - 2.48782i) q^{83} +(1.07089 - 0.401098i) q^{84} +(10.7855 + 4.28932i) q^{85} +(4.34348 + 7.32249i) q^{86} +(1.53103 + 1.53103i) q^{87} +(-3.54269 - 3.30067i) q^{88} +12.4324 q^{89} +(-9.22448 + 1.45900i) q^{90} +(6.40249 - 7.41291i) q^{91} +(-2.18620 - 7.45195i) q^{92} +(-1.29951 + 1.29951i) q^{93} +(-13.7081 + 8.13126i) q^{94} +(3.74096 + 8.68112i) q^{95} +(1.09286 + 0.547844i) q^{96} +(2.43265 + 2.43265i) q^{97} +(1.02770 - 9.84601i) q^{98} -5.05577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

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