LMFDB - Embedded newform 880.2.bk.b.243.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(243,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.243"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bk (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [236] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$236$
Relative dimension:	$118$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.11
Character	$\chi$	$=$	880.243
Dual form			880.2.bk.b.507.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35246 - 0.413341i) q^{2} +2.75998 q^{3} +(1.65830 + 1.11806i) q^{4} +(2.15400 - 0.600239i) q^{5} +(-3.73277 - 1.14082i) q^{6} +(-0.140016 + 0.140016i) q^{7} +(-1.78064 - 2.19757i) q^{8} +4.61751 q^{9} +(-3.16130 - 0.0785374i) q^{10} +(0.707107 + 0.707107i) q^{11} +(4.57688 + 3.08582i) q^{12} +0.570496i q^{13} +(0.247241 - 0.131492i) q^{14} +(5.94500 - 1.65665i) q^{15} +(1.49990 + 3.70814i) q^{16} +(-1.55040 + 1.55040i) q^{17} +(-6.24500 - 1.90861i) q^{18} +(0.0194447 + 0.0194447i) q^{19} +(4.24307 + 1.41292i) q^{20} +(-0.386443 + 0.386443i) q^{21} +(-0.664057 - 1.24861i) q^{22} +(1.45195 + 1.45195i) q^{23} +(-4.91455 - 6.06526i) q^{24} +(4.27943 - 2.58583i) q^{25} +(0.235810 - 0.771573i) q^{26} +4.46431 q^{27} +(-0.388734 + 0.0756426i) q^{28} +(4.12978 - 4.12978i) q^{29} +(-8.72514 - 0.216762i) q^{30} -1.03083i q^{31} +(-0.495831 - 5.63508i) q^{32} +(1.95160 + 1.95160i) q^{33} +(2.73770 - 1.45601i) q^{34} +(-0.217552 + 0.385638i) q^{35} +(7.65721 + 5.16264i) q^{36} -1.59977i q^{37} +(-0.0182609 - 0.0343355i) q^{38} +1.57456i q^{39} +(-5.15457 - 3.66475i) q^{40} -2.73891i q^{41} +(0.682381 - 0.362915i) q^{42} +8.22338i q^{43} +(0.382009 + 1.96318i) q^{44} +(9.94612 - 2.77161i) q^{45} +(-1.36356 - 2.56386i) q^{46} +(-6.69403 - 6.69403i) q^{47} +(4.13971 + 10.2344i) q^{48} +6.96079i q^{49} +(-6.85658 + 1.72837i) q^{50} +(-4.27907 + 4.27907i) q^{51} +(-0.637847 + 0.946053i) q^{52} -4.51442 q^{53} +(-6.03780 - 1.84528i) q^{54} +(1.94754 + 1.09867i) q^{55} +(0.557014 + 0.0583765i) q^{56} +(0.0536671 + 0.0536671i) q^{57} +(-7.29237 + 3.87835i) q^{58} +(0.812680 - 0.812680i) q^{59} +(11.7108 + 3.89963i) q^{60} +(-5.47096 - 5.47096i) q^{61} +(-0.426084 + 1.39415i) q^{62} +(-0.646527 + 0.646527i) q^{63} +(-1.65862 + 7.82617i) q^{64} +(0.342434 + 1.22885i) q^{65} +(-1.83279 - 3.44615i) q^{66} +1.15518i q^{67} +(-4.30445 + 0.837590i) q^{68} +(4.00737 + 4.00737i) q^{69} +(0.453630 - 0.431637i) q^{70} -1.27659 q^{71} +(-8.22214 - 10.1473i) q^{72} +(-6.01688 + 6.01688i) q^{73} +(-0.661253 + 2.16363i) q^{74} +(11.8111 - 7.13685i) q^{75} +(0.0105049 + 0.0539854i) q^{76} -0.198013 q^{77} +(0.650831 - 2.12953i) q^{78} -14.2754 q^{79} +(5.45656 + 7.08703i) q^{80} -1.53111 q^{81} +(-1.13210 + 3.70426i) q^{82} +4.45552 q^{83} +(-1.07290 + 0.208772i) q^{84} +(-2.40895 + 4.27017i) q^{85} +(3.39906 - 11.1218i) q^{86} +(11.3981 - 11.3981i) q^{87} +(0.294812 - 2.81302i) q^{88} +13.7128 q^{89} +(-14.5974 - 0.362647i) q^{90} +(-0.0798787 - 0.0798787i) q^{91} +(0.784406 + 4.03114i) q^{92} -2.84507i q^{93} +(6.28649 + 11.8203i) q^{94} +(0.0535554 + 0.0302124i) q^{95} +(-1.36848 - 15.5527i) q^{96} +(-7.26431 + 7.26431i) q^{97} +(2.87718 - 9.41419i) q^{98} +(3.26507 + 3.26507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) $ 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.35246	−	0.413341i	−0.956334	−	0.292277i
$2$	−1.35246	−	0.413341i	−0.956334	−	0.292277i
$3$	2.75998			1.59348			0.796739	−	0.604324i	$-0.206557\pi$
$3$	2.75998			1.59348			0.796739	+	0.604324i	$0.206557\pi$
$4$	1.65830	+	1.11806i	0.829149	+	0.559028i
$5$	2.15400	−	0.600239i	0.963298	−	0.268435i
$5$	2.15400	−	0.600239i	0.963298	−	0.268435i
$6$	−3.73277	−	1.14082i	−1.52390	−	0.465736i
$7$	−0.140016	+	0.140016i	−0.0529212	+	0.0529212i	−0.733072	−	0.680151i	$-0.761914\pi$
$7$	−0.140016	+	0.140016i	−0.0529212	+	0.0529212i	0.680151	+	0.733072i	$0.261914\pi$
$8$	−1.78064	−	2.19757i	−0.629552	−	0.776958i
$9$	4.61751			1.53917
$10$	−3.16130	−	0.0785374i	−0.999692	−	0.0248357i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	4.57688	+	3.08582i	1.32123	+	0.890799i
$13$			0.570496i			0.158227i	0.996866	+	0.0791136i	$0.0252090\pi$
$13$			0.570496i			0.158227i	−0.996866	+	0.0791136i	$0.974791\pi$
$14$	0.247241	−	0.131492i	0.0660779	−	0.0351427i
$15$	5.94500	−	1.65665i	1.53499	−	0.427745i
$16$	1.49990	+	3.70814i	0.374976	+	0.927035i
$17$	−1.55040	+	1.55040i	−0.376027	+	0.376027i	−0.869666	−	0.493640i	$-0.835666\pi$
$17$	−1.55040	+	1.55040i	−0.376027	+	0.376027i	0.493640	+	0.869666i	$0.335666\pi$
$18$	−6.24500	−	1.90861i	−1.47196	−	0.449864i
$19$	0.0194447	+	0.0194447i	0.00446092	+	0.00446092i	0.709334	−	0.704873i	$-0.248996\pi$
$19$	0.0194447	+	0.0194447i	0.00446092	+	0.00446092i	−0.704873	+	0.709334i	$0.748996\pi$
$20$	4.24307	+	1.41292i	0.948780	+	0.315938i
$21$	−0.386443	+	0.386443i	−0.0843287	+	0.0843287i
$22$	−0.664057	−	1.24861i	−0.141577	−	0.266205i
$23$	1.45195	+	1.45195i	0.302753	+	0.302753i	0.842090	−	0.539337i	$-0.181325\pi$
$23$	1.45195	+	1.45195i	0.302753	+	0.302753i	−0.539337	+	0.842090i	$0.681325\pi$
$24$	−4.91455	−	6.06526i	−1.00318	−	1.23807i
$25$	4.27943	−	2.58583i	0.855885	−	0.517166i
$26$	0.235810	−	0.771573i	0.0462461	−	0.151318i
$27$	4.46431			0.859157
$28$	−0.388734	+	0.0756426i	−0.0734639	+	0.0142951i
$29$	4.12978	−	4.12978i	0.766881	−	0.766881i	−0.210675	−	0.977556i	$-0.567566\pi$
$29$	4.12978	−	4.12978i	0.766881	−	0.766881i	0.977556	+	0.210675i	$0.0675663\pi$
$30$	−8.72514	−	0.216762i	−1.59299	−	0.0395751i
$31$		−	1.03083i		−	0.185142i	−0.995706	−	0.0925711i	$-0.970491\pi$
$31$		−	1.03083i		−	0.185142i	0.995706	−	0.0925711i	$-0.0295085\pi$
$32$	−0.495831	−	5.63508i	−0.0876513	−	0.996151i
$33$	1.95160	+	1.95160i	0.339731	+	0.339731i
$34$	2.73770	−	1.45601i	0.469511	−	0.249703i
$35$	−0.217552	+	0.385638i	−0.0367729	+	0.0651847i
$36$	7.65721	+	5.16264i	1.27620	+	0.860440i
$37$		−	1.59977i		−	0.263001i	−0.991316	−	0.131501i	$-0.958020\pi$
$37$		−	1.59977i		−	0.263001i	0.991316	−	0.131501i	$-0.0419795\pi$
$38$	−0.0182609	−	0.0343355i	−0.00296231	−	0.00556996i
$39$			1.57456i			0.252131i
$40$	−5.15457	−	3.66475i	−0.815009	−	0.579448i
$41$		−	2.73891i		−	0.427745i	−0.976862	−	0.213873i	$-0.931392\pi$
$41$		−	2.73891i		−	0.427745i	0.976862	−	0.213873i	$-0.0686078\pi$
$42$	0.682381	−	0.362915i	0.105294	−	0.0559991i
$43$			8.22338i			1.25405i	0.778998	+	0.627027i	$0.215728\pi$
$43$			8.22338i			1.25405i	−0.778998	+	0.627027i	$0.784272\pi$
$44$	0.382009	+	1.96318i	0.0575900	+	0.295960i
$45$	9.94612	−	2.77161i	1.48268	−	0.413168i
$46$	−1.36356	−	2.56386i	−0.201045	−	0.378021i
$47$	−6.69403	−	6.69403i	−0.976425	−	0.976425i	0.0233037	−	0.999728i	$-0.492582\pi$
$47$	−6.69403	−	6.69403i	−0.976425	−	0.976425i	−0.999728	+	0.0233037i	$0.992582\pi$
$48$	4.13971	+	10.2344i	0.597515	+	1.47721i
$49$			6.96079i			0.994399i
$50$	−6.85658	+	1.72837i	−0.969667	+	0.244428i
$51$	−4.27907	+	4.27907i	−0.599190	+	0.599190i
$52$	−0.637847	+	0.946053i	−0.0884534	+	0.131194i
$53$	−4.51442			−0.620103			−0.310052	−	0.950720i	$-0.600346\pi$
$53$	−4.51442			−0.620103			−0.310052	+	0.950720i	$0.600346\pi$
$54$	−6.03780	−	1.84528i	−0.821641	−	0.251111i
$55$	1.94754	+	1.09867i	0.262606	+	0.148145i
$56$	0.557014	+	0.0583765i	0.0744341	+	0.00780088i
$57$	0.0536671	+	0.0536671i	0.00710838	+	0.00710838i
$58$	−7.29237	+	3.87835i	−0.957535	+	0.509253i
$59$	0.812680	−	0.812680i	0.105802	−	0.105802i	−0.652224	−	0.758026i	$-0.726164\pi$
$59$	0.812680	−	0.812680i	0.105802	−	0.105802i	0.758026	+	0.652224i	$0.226164\pi$
$60$	11.7108	+	3.89963i	1.51186	+	0.503440i
$61$	−5.47096	−	5.47096i	−0.700484	−	0.700484i	0.264030	−	0.964514i	$-0.414948\pi$
$61$	−5.47096	−	5.47096i	−0.700484	−	0.700484i	−0.964514	+	0.264030i	$0.914948\pi$
$62$	−0.426084	+	1.39415i	−0.0541127	+	0.177058i
$63$	−0.646527	+	0.646527i	−0.0814547	+	0.0814547i
$64$	−1.65862	+	7.82617i	−0.207328	+	0.978272i
$65$	0.342434	+	1.22885i	0.0424737	+	0.152420i
$66$	−1.83279	−	3.44615i	−0.225601	−	0.424191i
$67$			1.15518i			0.141128i	0.997507	+	0.0705638i	$0.0224798\pi$
$67$			1.15518i			0.141128i	−0.997507	+	0.0705638i	$0.977520\pi$
$68$	−4.30445	+	0.837590i	−0.521992	+	0.101573i
$69$	4.00737	+	4.00737i	0.482430	+	0.482430i
$70$	0.453630	−	0.431637i	0.0542192	−	0.0515905i
$71$	−1.27659			−0.151503			−0.0757515	−	0.997127i	$-0.524136\pi$
$71$	−1.27659			−0.151503			−0.0757515	+	0.997127i	$0.524136\pi$
$72$	−8.22214	−	10.1473i	−0.968989	−	1.19587i
$73$	−6.01688	+	6.01688i	−0.704223	+	0.704223i	−0.965314	−	0.261092i	$-0.915918\pi$
$73$	−6.01688	+	6.01688i	−0.704223	+	0.704223i	0.261092	+	0.965314i	$0.415918\pi$
$74$	−0.661253	+	2.16363i	−0.0768691	+	0.251517i
$75$	11.8111	−	7.13685i	1.36383	−	0.824092i
$76$	0.0105049	+	0.0539854i	0.00120499	+	0.00619255i
$77$	−0.198013			−0.0225657
$78$	0.650831	−	2.12953i	0.0736921	−	0.241122i
$79$	−14.2754			−1.60610			−0.803052	−	0.595909i	$-0.796792\pi$
$79$	−14.2754			−1.60610			−0.803052	+	0.595909i	$0.796792\pi$
$80$	5.45656	+	7.08703i	0.610062	+	0.792354i
$81$	−1.53111			−0.170124
$82$	−1.13210	+	3.70426i	−0.125020	+	0.409067i
$83$	4.45552			0.489057			0.244528	−	0.969642i	$-0.421367\pi$
$83$	4.45552			0.489057			0.244528	+	0.969642i	$0.421367\pi$
$84$	−1.07290	+	0.208772i	−0.117063	+	0.0227789i
$85$	−2.40895	+	4.27017i	−0.261287	+	0.463165i
$86$	3.39906	−	11.1218i	0.366531	−	1.19929i
$87$	11.3981	−	11.3981i	1.22201	−	1.22201i
$88$	0.294812	−	2.81302i	0.0314270	−	0.299869i
$89$	13.7128			1.45355			0.726775	−	0.686876i	$-0.241018\pi$
$89$	13.7128			1.45355			0.726775	+	0.686876i	$0.241018\pi$
$90$	−14.5974	−	0.362647i	−1.53870	−	0.0382264i
$91$	−0.0798787	−	0.0798787i	−0.00837356	−	0.00837356i
$92$	0.784406	+	4.03114i	0.0817800	+	0.420275i
$93$		−	2.84507i		−	0.295020i
$94$	6.28649	+	11.8203i	0.648402	+	1.21917i
$95$	0.0535554	+	0.0302124i	0.00549467	+	0.00309973i
$96$	−1.36848	−	15.5527i	−0.139670	−	1.58734i
$97$	−7.26431	+	7.26431i	−0.737579	+	0.737579i	−0.972109	−	0.234530i	$-0.924645\pi$
$97$	−7.26431	+	7.26431i	−0.737579	+	0.737579i	0.234530	+	0.972109i	$0.424645\pi$
$98$	2.87718	−	9.41419i	0.290639	−	0.950977i
$99$	3.26507	+	3.26507i	0.328152	+	0.328152i
$100$	9.98766	+	0.496561i	0.998766	+	0.0496561i
$101$	5.25513	−	5.25513i	0.522905	−	0.522905i	−0.395543	−	0.918448i	$-0.629443\pi$
$101$	5.25513	−	5.25513i	0.522905	−	0.522905i	0.918448	+	0.395543i	$0.129443\pi$
$102$	7.55600	−	4.01856i	0.748155	−	0.397897i
$103$	−2.72104	−	2.72104i	−0.268112	−	0.268112i	0.560227	−	0.828339i	$-0.310714\pi$
$103$	−2.72104	−	2.72104i	−0.268112	−	0.268112i	−0.828339	+	0.560227i	$0.810714\pi$
$104$	1.25371	−	1.01585i	0.122936	−	0.0996123i
$105$	−0.600439	+	1.06435i	−0.0585968	+	0.103870i
$106$	6.10557	+	1.86600i	0.593026	+	0.181242i
$107$	16.5058			1.59567			0.797837	−	0.602873i	$-0.205978\pi$
$107$	16.5058			1.59567			0.797837	+	0.602873i	$0.205978\pi$
$108$	7.40316	+	4.99135i	0.712369	+	0.480293i
$109$	8.89192	−	8.89192i	0.851692	−	0.851692i	−0.138650	−	0.990341i	$-0.544276\pi$
$109$	8.89192	−	8.89192i	0.851692	−	0.851692i	0.990341	+	0.138650i	$0.0442763\pi$
$110$	−2.17984	−	2.29091i	−0.207840	−	0.218430i
$111$		−	4.41535i		−	0.419086i
$112$	−0.729210	−	0.309189i	−0.0689039	−	0.0292156i
$113$	−9.94560	−	9.94560i	−0.935603	−	0.935603i	0.0624451	−	0.998048i	$-0.480110\pi$
$113$	−9.94560	−	9.94560i	−0.935603	−	0.935603i	−0.998048	+	0.0624451i	$0.980110\pi$
$114$	−0.0503998	−	0.0947655i	−0.00472037	−	0.00887560i
$115$	3.99903	+	2.25599i	0.372911	+	0.210372i
$116$	11.4657	−	2.23108i	1.06457	−	0.207150i
$117$			2.63427i			0.243539i
$118$	−1.43503	+	0.763203i	−0.132105	+	0.0702585i
$119$		−	0.434162i		−	0.0397995i
$120$	−14.2265	−	10.1147i	−1.29870	−	0.923337i
$121$			1.00000i			0.0909091i
$122$	5.13788	+	9.66063i	0.465162	+	0.874632i
$123$		−	7.55934i		−	0.681603i
$124$	1.15252	−	1.70942i	0.103500	−	0.153510i
$125$	7.66576	−	8.13856i	0.685647	−	0.727935i
$126$	1.14164	−	0.607165i	0.101705	−	0.0540906i
$127$	−10.6479	−	10.6479i	−0.944847	−	0.944847i	0.0537097	−	0.998557i	$-0.482895\pi$
$127$	−10.6479	−	10.6479i	−0.944847	−	0.944847i	−0.998557	+	0.0537097i	$0.982895\pi$
$128$	5.47810	−	9.89901i	0.484200	−	0.874957i
$129$			22.6964i			1.99831i
$130$	0.0448053	−	1.80351i	0.00392968	−	0.158178i
$131$	−5.49210	+	5.49210i	−0.479847	+	0.479847i	−0.905083	−	0.425236i	$-0.860191\pi$
$131$	−5.49210	+	5.49210i	−0.479847	+	0.479847i	0.425236	+	0.905083i	$0.360191\pi$
$132$	1.05434	+	5.41834i	0.0917683	+	0.471606i
$133$	−0.00544515			−0.000472155
$134$	0.477483	−	1.56233i	0.0412483	−	0.134965i
$135$	9.61612	−	2.67965i	0.827624	−	0.230628i
$136$	6.16781	+	0.646402i	0.528886	+	0.0554285i
$137$	−10.9783	−	10.9783i	−0.937935	−	0.937935i	0.0602480	−	0.998183i	$-0.480811\pi$
$137$	−10.9783	−	10.9783i	−0.937935	−	0.937935i	−0.998183	+	0.0602480i	$0.980811\pi$
$138$	−3.76339	−	7.07622i	−0.320361	−	0.602368i
$139$	−7.14356	+	7.14356i	−0.605909	+	0.605909i	−0.941874	−	0.335965i	$-0.890937\pi$
$139$	−7.14356	+	7.14356i	−0.605909	+	0.605909i	0.335965	+	0.941874i	$0.390937\pi$
$140$	−0.791930	+	0.396268i	−0.0669303	+	0.0334907i
$141$	−18.4754	−	18.4754i	−1.55591	−	1.55591i
$142$	1.72653	+	0.527666i	0.144887	+	0.0442808i
$143$	−0.403402	+	0.403402i	−0.0337341	+	0.0337341i
$144$	6.92582	+	17.1224i	0.577151	+	1.42686i
$145$	6.41668	−	11.3744i	0.532877	−	0.944592i
$146$	10.6246	−	5.65057i	0.879300	−	0.467644i
$147$			19.2117i			1.58455i
$148$	1.78864	−	2.65290i	0.147025	−	0.218067i
$149$	8.48977	+	8.48977i	0.695509	+	0.695509i	0.963439	−	0.267929i	$-0.0863393\pi$
$149$	8.48977	+	8.48977i	0.695509	+	0.695509i	−0.267929	+	0.963439i	$0.586339\pi$
$150$	−18.9241	+	4.77027i	−1.54514	+	0.389491i
$151$	22.7826			1.85402			0.927011	−	0.375035i	$-0.122369\pi$
$151$	22.7826			1.85402			0.927011	+	0.375035i	$0.122369\pi$
$152$	0.00810702	−	0.0773552i	0.000657566	−	0.00627434i
$153$	−7.15898	+	7.15898i	−0.578769	+	0.578769i
$154$	0.267804	+	0.0818469i	0.0215803	+	0.00659541i
$155$	−0.618744	−	2.22040i	−0.0496987	−	0.178347i
$156$	−1.76045	+	2.61109i	−0.140949	+	0.209055i
$157$	−8.02532			−0.640490			−0.320245	−	0.947335i	$-0.603765\pi$
$157$	−8.02532			−0.640490			−0.320245	+	0.947335i	$0.603765\pi$
$158$	19.3069	+	5.90060i	1.53597	+	0.469427i
$159$	−12.4597			−0.988121
$160$	−4.45042	−	11.8403i	−0.351836	−	0.936062i
$161$	−0.406594			−0.0320441
$162$	2.07077	+	0.632872i	0.162695	+	0.0497231i
$163$	−20.0328			−1.56909			−0.784545	−	0.620072i	$-0.787103\pi$
$163$	−20.0328			−1.56909			−0.784545	+	0.620072i	$0.787103\pi$
$164$	3.06225	−	4.54192i	0.239122	−	0.354665i
$165$	5.37518	+	3.03232i	0.418457	+	0.236066i
$166$	−6.02591	−	1.84165i	−0.467701	−	0.142940i
$167$	−14.2903	+	14.2903i	−1.10582	+	1.10582i	−0.112121	+	0.993695i	$0.535764\pi$
$167$	−14.2903	+	14.2903i	−1.10582	+	1.10582i	−0.993695	+	0.112121i	$0.964236\pi$
$168$	1.53735	+	0.161118i	0.118609	+	0.0124305i
$169$	12.6745			0.974964
$170$	5.02304	−	4.77951i	0.385250	−	0.366572i
$171$	0.0897862	+	0.0897862i	0.00686613	+	0.00686613i
$172$	−9.19420	+	13.6368i	−0.701051	+	1.03980i
$173$			13.5907i			1.03328i	0.856203	+	0.516640i	$0.172817\pi$
$173$			13.5907i			1.03328i	−0.856203	+	0.516640i	$0.827183\pi$
$174$	−20.1268	+	10.7042i	−1.52581	+	0.811483i
$175$	−0.237131	+	0.961247i	−0.0179254	+	0.0726634i
$176$	−1.56146	+	3.68264i	−0.117699	+	0.277590i
$177$	2.24298	−	2.24298i	0.168593	−	0.168593i
$178$	−18.5460	−	5.66805i	−1.39008	−	0.424839i
$179$	13.5540	+	13.5540i	1.01307	+	1.01307i	0.999913	+	0.0131575i	$0.00418830\pi$
$179$	13.5540	+	13.5540i	1.01307	+	1.01307i	0.0131575	+	0.999913i	$0.495812\pi$
$180$	19.5924	+	6.52416i	1.46033	+	0.486282i
$181$	7.21737	−	7.21737i	0.536463	−	0.536463i	−0.386025	−	0.922488i	$-0.626152\pi$
$181$	7.21737	−	7.21737i	0.536463	−	0.536463i	0.922488	+	0.386025i	$0.126152\pi$
$182$	0.0750156	+	0.141050i	0.00556053	+	0.0104553i
$183$	−15.0998	−	15.0998i	−1.11621	−	1.11621i
$184$	0.605358	−	5.77618i	0.0446276	−	0.425825i
$185$	−0.960247	−	3.44591i	−0.0705988	−	0.253348i
$186$	−1.17599	+	3.84784i	−0.0862274	+	0.282138i
$187$	−2.19259			−0.160338
$188$	−3.61639	−	18.5850i	−0.263753	−	1.35545i
$189$	−0.625076	+	0.625076i	−0.0454676	+	0.0454676i
$190$	−0.0599435	−	0.0629978i	−0.00434876	−	0.00457034i
$191$			8.31703i			0.601799i	0.953656	+	0.300900i	$0.0972869\pi$
$191$			8.31703i			0.601799i	−0.953656	+	0.300900i	$0.902713\pi$
$192$	−4.57777	+	21.6001i	−0.330372	+	1.55885i
$193$	−6.19275	−	6.19275i	−0.445764	−	0.445764i	0.448180	−	0.893944i	$-0.352072\pi$
$193$	−6.19275	−	6.19275i	−0.445764	−	0.445764i	−0.893944	+	0.448180i	$0.852072\pi$
$194$	12.8273	−	6.82205i	0.920949	−	0.489795i
$195$	0.945113	+	3.39160i	0.0676810	+	0.242878i
$196$	−7.78255	+	11.5431i	−0.555897	+	0.824505i
$197$		−	21.3784i		−	1.52315i	−0.648078	−	0.761574i	$-0.724427\pi$
$197$		−	21.3784i		−	1.52315i	0.648078	−	0.761574i	$-0.275573\pi$
$198$	−3.06629	−	5.76547i	−0.217912	−	0.409734i
$199$			25.8891i			1.83523i	0.397469	+	0.917616i	$0.369889\pi$
$199$			25.8891i			1.83523i	−0.397469	+	0.917616i	$0.630111\pi$
$200$	−13.3027	−	4.79989i	−0.940641	−	0.339404i
$201$			3.18827i			0.224884i
$202$	−9.27952	+	4.93519i	−0.652905	+	0.347239i
$203$			1.15647i			0.0811684i
$204$	−11.8802	+	2.31173i	−0.831782	+	0.161854i
$205$	−1.64400	−	5.89960i	−0.114822	−	0.412046i
$206$	2.55538	+	4.80481i	0.178042	+	0.334767i
$207$	6.70441	+	6.70441i	0.465989	+	0.465989i
$208$	−2.11548	+	0.855689i	−0.146682	+	0.0593313i
$209$			0.0274990i			0.00190214i
$210$	1.25201	−	1.19131i	0.0863970	−	0.0822083i
$211$	−16.5135	+	16.5135i	−1.13683	+	1.13683i	−0.147819	+	0.989014i	$0.547225\pi$
$211$	−16.5135	+	16.5135i	−1.13683	+	1.13683i	−0.989014	+	0.147819i	$0.952775\pi$
$212$	−7.48625	−	5.04737i	−0.514158	−	0.346655i
$213$	−3.52336			−0.241417
$214$	−22.3234	−	6.82252i	−1.52600	−	0.466378i
$215$	4.93600	+	17.7132i	0.336632	+	1.20803i
$216$	−7.94934	−	9.81063i	−0.540884	−	0.667529i
$217$	0.144333	+	0.144333i	0.00979794	+	0.00979794i
$218$	−15.7014	+	8.35057i	−1.06343	+	0.565572i
$219$	−16.6065	+	16.6065i	−1.12216	+	1.12216i
$220$	2.00122	+	3.99939i	0.134922	+	0.269639i
$221$	−0.884496	−	0.884496i	−0.0594977	−	0.0594977i
$222$	−1.82505	+	5.97159i	−0.122489	+	0.400787i
$223$	−3.70237	+	3.70237i	−0.247929	+	0.247929i	−0.820120	−	0.572191i	$-0.806093\pi$
$223$	−3.70237	+	3.70237i	−0.247929	+	0.247929i	0.572191	+	0.820120i	$0.306093\pi$
$224$	0.858427	+	0.719579i	0.0573561	+	0.0480789i
$225$	19.7603	−	11.9401i	1.31735	−	0.796007i
$226$	9.34010	+	17.5620i	0.621294	+	1.16820i
$227$			8.45393i			0.561107i	0.959838	+	0.280554i	$0.0905181\pi$
$227$			8.45393i			0.561107i	−0.959838	+	0.280554i	$0.909482\pi$
$228$	0.0289932	+	0.148999i	0.00192012	+	0.00986769i
$229$	−19.6399	−	19.6399i	−1.29784	−	1.29784i	−0.929815	−	0.368027i	$-0.880033\pi$
$229$	−19.6399	−	19.6399i	−1.29784	−	1.29784i	−0.368027	−	0.929815i	$-0.619967\pi$
$230$	−4.47603	−	4.70410i	−0.295141	−	0.310179i
$231$	−0.546512			−0.0359579
$232$	−16.4291	−	1.72181i	−1.07863	−	0.113043i
$233$	8.28654	−	8.28654i	0.542869	−	0.542869i	−0.381500	−	0.924369i	$-0.624592\pi$
$233$	8.28654	−	8.28654i	0.542869	−	0.542869i	0.924369	+	0.381500i	$0.124592\pi$
$234$	1.08885	−	3.56275i	0.0711807	−	0.232904i
$235$	−18.4370	−	10.4009i	−1.20269	−	0.678481i
$236$	2.25629	−	0.439043i	0.146872	−	0.0285793i
$237$	−39.3998			−2.55929
$238$	−0.179457	+	0.587186i	−0.0116325	+	0.0380616i
$239$	−13.0043			−0.841178			−0.420589	−	0.907251i	$-0.638177\pi$
$239$	−13.0043			−0.841178			−0.420589	+	0.907251i	$0.638177\pi$
$240$	15.0600	+	19.5601i	0.972120	+	1.26260i
$241$	1.02567			0.0660691			0.0330345	−	0.999454i	$-0.489483\pi$
$241$	1.02567			0.0660691			0.0330345	+	0.999454i	$0.489483\pi$
$242$	0.413341	−	1.35246i	0.0265706	−	0.0869394i
$243$	−17.6188			−1.13025
$244$	−2.95564	−	15.1893i	−0.189215	−	0.972396i
$245$	4.17814	+	14.9935i	0.266932	+	0.957902i
$246$	−3.12459	+	10.2237i	−0.199217	+	0.651840i
$247$	−0.0110931	+	0.0110931i	−0.000705840	+	0.000705840i
$248$	−2.26532	+	1.83554i	−0.143848	+	0.116557i
$249$	12.2972			0.779301
$250$	−13.7316	+	7.83850i	−0.868465	+	0.495750i
$251$	−18.0813	−	18.0813i	−1.14128	−	1.14128i	−0.988216	−	0.153064i	$-0.951086\pi$
$251$	−18.0813	−	18.0813i	−1.14128	−	1.14128i	−0.153064	−	0.988216i	$-0.548914\pi$
$252$	−1.79499	+	0.349281i	−0.113074	+	0.0220026i
$253$			2.05337i			0.129094i
$254$	9.99963	+	18.8021i	0.627432	+	1.17975i
$255$	−6.64865	+	11.7856i	−0.416355	+	0.738042i
$256$	−11.5006	+	11.1237i	−0.718787	+	0.695231i
$257$	5.81381	−	5.81381i	0.362656	−	0.362656i	−0.502134	−	0.864790i	$-0.667452\pi$
$257$	5.81381	−	5.81381i	0.362656	−	0.362656i	0.864790	+	0.502134i	$0.167452\pi$
$258$	9.38137	−	30.6960i	0.584058	−	1.91105i
$259$	0.223994	+	0.223994i	0.0139183	+	0.0139183i
$260$	−0.806063	+	2.42066i	−0.0499899	+	0.150123i
$261$	19.0693	−	19.0693i	1.18036	−	1.18036i
$262$	9.69796	−	5.15773i	0.599142	−	0.318646i
$263$	−1.45231	−	1.45231i	−0.0895530	−	0.0895530i	0.660911	−	0.750464i	$-0.270170\pi$
$263$	−1.45231	−	1.45231i	−0.0895530	−	0.0895530i	−0.750464	+	0.660911i	$0.770170\pi$
$264$	0.813675	−	7.76389i	0.0500783	−	0.477835i
$265$	−9.72406	+	2.70973i	−0.597344	+	0.166458i
$266$	0.00736435	+	0.00225071i	0.000451537	+	0.000138000i
$267$	37.8470			2.31620
$268$	−1.29155	+	1.91563i	−0.0788942	+	0.117016i
$269$	−1.13531	+	1.13531i	−0.0692212	+	0.0692212i	−0.740870	−	0.671649i	$-0.765586\pi$
$269$	−1.13531	+	1.13531i	−0.0692212	+	0.0692212i	0.671649	+	0.740870i	$0.265586\pi$
$270$	−14.1130	−	0.350615i	−0.858892	−	0.0213378i
$271$			3.48320i			0.211589i	0.994388	+	0.105795i	$0.0337386\pi$
$271$			3.48320i			0.211589i	−0.994388	+	0.105795i	$0.966261\pi$
$272$	−8.07454	−	3.42365i	−0.489591	−	0.207589i
$273$	−0.220464	−	0.220464i	−0.0133431	−	0.0133431i
$274$	10.3099	+	19.3854i	0.622843	+	1.17112i
$275$	4.85447	+	1.19755i	0.292735	+	0.0722152i
$276$	2.16495	+	11.1259i	0.130315	+	0.669699i
$277$		−	9.52689i		−	0.572415i	−0.958168	−	0.286208i	$-0.907605\pi$
$277$		−	9.52689i		−	0.572415i	0.958168	−	0.286208i	$-0.0923947\pi$
$278$	12.6141	−	6.70865i	0.756544	−	0.402358i
$279$		−	4.75986i		−	0.284966i
$280$	1.23485	−	0.208599i	0.0737963	−	0.0124662i
$281$		−	2.85462i		−	0.170292i	−0.996368	−	0.0851461i	$-0.972864\pi$
$281$		−	2.85462i		−	0.170292i	0.996368	−	0.0851461i	$-0.0271357\pi$
$282$	17.3506	+	32.6239i	1.03321	+	1.94273i
$283$			31.1764i			1.85325i	0.375992	+	0.926623i	$0.377302\pi$
$283$			31.1764i			1.85325i	−0.375992	+	0.926623i	$0.622698\pi$
$284$	−2.11696	−	1.42730i	−0.125619	−	0.0846944i
$285$	0.147812	+	0.0833858i	0.00875563	+	0.00493935i
$286$	0.712328	−	0.378842i	0.0421208	−	0.0224014i
$287$	0.383491	+	0.383491i	0.0226368	+	0.0226368i
$288$	−2.28950	−	26.0201i	−0.134910	−	1.53325i
$289$			12.1925i			0.717208i
$290$	−13.3798	+	12.7311i	−0.785690	+	0.747598i
$291$	−20.0494	+	20.0494i	−1.17532	+	1.17532i
$292$	−16.7050	+	3.25057i	−0.977585	+	0.190225i
$293$	19.5119			1.13990			0.569949	−	0.821680i	$-0.306963\pi$
$293$	19.5119			1.13990			0.569949	+	0.821680i	$0.306963\pi$
$294$	7.94098	−	25.9830i	0.463127	−	1.51536i
$295$	1.26271	−	2.23831i	0.0735178	−	0.130320i
$296$	−3.51561	+	2.84863i	−0.204341	+	0.165573i
$297$	3.15674	+	3.15674i	0.183173	+	0.183173i
$298$	−7.97291	−	14.9913i	−0.461858	−	0.868420i
$299$	−0.828334	+	0.828334i	−0.0479038	+	0.0479038i
$300$	27.5658	+	1.37050i	1.59151	+	0.0791259i
$301$	−1.15141	−	1.15141i	−0.0663660	−	0.0663660i
$302$	−30.8126	−	9.41699i	−1.77306	−	0.541887i
$303$	14.5041	−	14.5041i	0.833238	−	0.833238i
$304$	−0.0429385	+	0.101269i	−0.00246269	+	0.00580817i
$305$	−15.0683	−	8.50056i	−0.862810	−	0.486740i
$306$	12.6413	−	6.72314i	0.722658	−	0.384336i
$307$		−	15.7762i		−	0.900397i	−0.892928	−	0.450199i	$-0.851353\pi$
$307$		−	15.7762i		−	0.900397i	0.892928	−	0.450199i	$-0.148647\pi$
$308$	−0.328364	−	0.221389i	−0.0187103	−	0.0126148i
$309$	−7.51002	−	7.51002i	−0.427230	−	0.427230i
$310$	−0.0809585	+	3.25876i	−0.00459814	+	0.185085i
$311$	26.9472			1.52804			0.764018	−	0.645194i	$-0.223224\pi$
$311$	26.9472			1.52804			0.764018	+	0.645194i	$0.223224\pi$
$312$	3.46021	−	2.80373i	0.195896	−	0.158730i
$313$	−11.0430	+	11.0430i	−0.624185	+	0.624185i	−0.946599	−	0.322414i	$-0.895506\pi$
$313$	−11.0430	+	11.0430i	−0.624185	+	0.624185i	0.322414	+	0.946599i	$0.395506\pi$
$314$	10.8539	+	3.31720i	0.612523	+	0.187200i
$315$	−1.00455	+	1.78069i	−0.0565998	+	0.100330i
$316$	−23.6728	−	15.9607i	−1.33170	−	0.897857i
$317$	−25.7723			−1.44752			−0.723759	−	0.690053i	$-0.757587\pi$
$317$	−25.7723			−1.44752			−0.723759	+	0.690053i	$0.757587\pi$
$318$	16.8513	+	5.15012i	0.944973	+	0.288805i
$319$	5.84039			0.326999
$320$	1.12491	+	17.8531i	0.0628841	+	0.998021i
$321$	45.5557			2.54267
$322$	0.549902	+	0.168062i	0.0306448	+	0.00936574i
$323$	−0.0602941			−0.00335485
$324$	−2.53904	−	1.71187i	−0.141058	−	0.0951039i
$325$	1.47521	+	2.44140i	0.0818297	+	0.135424i
$326$	27.0936	+	8.28038i	1.50057	+	0.458608i
$327$	24.5416	−	24.5416i	1.35715	−	1.35715i
$328$	−6.01894	+	4.87702i	−0.332340	+	0.269288i
$329$	1.87455			0.103347
$330$	−6.01633	−	6.32288i	−0.331188	−	0.348063i
$331$	22.7527	+	22.7527i	1.25060	+	1.25060i	0.955450	+	0.295152i	$0.0953703\pi$
$331$	22.7527	+	22.7527i	1.25060	+	1.25060i	0.295152	+	0.955450i	$0.404630\pi$
$332$	7.38858	+	4.98152i	0.405501	+	0.273396i
$333$		−	7.38698i		−	0.404804i
$334$	25.2338	−	13.4203i	1.38073	−	0.734325i
$335$	0.693384	+	2.48825i	0.0378836	+	0.135948i
$336$	−2.01261	−	0.853357i	−0.109797	−	0.0465544i
$337$	7.07442	−	7.07442i	0.385368	−	0.385368i	−0.487664	−	0.873032i	$-0.662151\pi$
$337$	7.07442	−	7.07442i	0.385368	−	0.385368i	0.873032	+	0.487664i	$0.162151\pi$
$338$	−17.1418	−	5.23891i	−0.932391	−	0.284959i
$339$	−27.4497	−	27.4497i	−1.49086	−	1.49086i
$340$	−8.76903	+	4.38787i	−0.475568	+	0.237966i
$341$	0.728906	−	0.728906i	0.0394724	−	0.0394724i
$342$	−0.0843200	−	0.158545i	−0.00455950	−	0.00857312i
$343$	−1.95474	−	1.95474i	−0.105546	−	0.105546i
$344$	18.0715	−	14.6429i	0.974347	−	0.789493i
$345$	11.0372	+	6.22649i	0.594225	+	0.335223i
$346$	5.61759	−	18.3808i	0.302003	−	0.988160i
$347$	−2.13391			−0.114554			−0.0572771	−	0.998358i	$-0.518242\pi$
$347$	−2.13391			−0.114554			−0.0572771	+	0.998358i	$0.518242\pi$
$348$	31.6452	−	6.15774i	1.69636	−	0.330090i
$349$	−5.62057	+	5.62057i	−0.300862	+	0.300862i	−0.841351	−	0.540489i	$-0.818239\pi$
$349$	−5.62057	+	5.62057i	−0.300862	+	0.300862i	0.540489	+	0.841351i	$0.318239\pi$
$350$	0.718033	−	1.20203i	0.0383805	−	0.0642513i
$351$			2.54687i			0.135942i
$352$	3.63400	−	4.33521i	0.193693	−	0.231067i
$353$	7.04955	+	7.04955i	0.375210	+	0.375210i	0.869370	−	0.494161i	$-0.164525\pi$
$353$	7.04955	+	7.04955i	0.375210	+	0.375210i	−0.494161	+	0.869370i	$0.664525\pi$
$354$	−3.96066	+	2.10643i	−0.210507	+	0.111955i
$355$	−2.74977	+	0.766258i	−0.145943	+	0.0406687i
$356$	22.7398	+	15.3316i	1.20521	+	0.812575i
$357$		−	1.19828i		−	0.0634197i
$358$	−12.7288	−	23.9336i	−0.672737	−	1.26493i
$359$		−	12.5765i		−	0.663760i	−0.943322	−	0.331880i	$-0.892317\pi$
$359$		−	12.5765i		−	0.663760i	0.943322	−	0.331880i	$-0.107683\pi$
$360$	−23.8013	−	16.9220i	−1.25444	−	0.891870i
$361$		−	18.9992i		−	0.999960i
$362$	−12.7444	+	6.77797i	−0.669833	+	0.356242i
$363$			2.75998i			0.144862i
$364$	−0.0431538	−	0.221772i	−0.00226187	−	0.0116240i
$365$	−9.34879	+	16.5719i	−0.489338	+	0.867414i
$366$	14.1805	+	26.6632i	0.741225	+	1.39371i
$367$	3.07549	+	3.07549i	0.160539	+	0.160539i	0.782806	−	0.622266i	$-0.213788\pi$
$367$	3.07549	+	3.07549i	0.160539	+	0.160539i	−0.622266	+	0.782806i	$0.713788\pi$
$368$	−3.20626	+	7.56183i	−0.167138	+	0.394188i
$369$		−	12.6469i		−	0.658373i
$370$	−0.125642	+	5.05737i	−0.00653182	+	0.262920i
$371$	0.632092	−	0.632092i	0.0328166	−	0.0328166i
$372$	3.18095	−	4.71797i	0.164924	−	0.244615i
$373$	−5.56460			−0.288124			−0.144062	−	0.989569i	$-0.546016\pi$
$373$	−5.56460			−0.288124			−0.144062	+	0.989569i	$0.546016\pi$
$374$	2.96540	+	0.906290i	0.153337	+	0.0468631i
$375$	21.1574	−	22.4623i	1.09256	−	1.15995i
$376$	−2.79092	+	26.6303i	−0.143931	+	1.37335i
$377$	2.35602	+	2.35602i	0.121341	+	0.121341i
$378$	1.10376	−	0.587020i	0.0567713	−	0.0301931i
$379$	−11.0691	+	11.0691i	−0.568580	+	0.568580i	−0.931731	−	0.363150i	$-0.881701\pi$
$379$	−11.0691	+	11.0691i	−0.568580	+	0.568580i	0.363150	+	0.931731i	$0.381701\pi$
$380$	0.0550316	+	0.109979i	0.00282306	+	0.00564181i
$381$	−29.3880	−	29.3880i	−1.50559	−	1.50559i
$382$	3.43777	−	11.2485i	0.175892	−	0.575521i
$383$	−4.52046	+	4.52046i	−0.230985	+	0.230985i	−0.813104	−	0.582119i	$-0.802224\pi$
$383$	−4.52046	+	4.52046i	−0.230985	+	0.230985i	0.582119	+	0.813104i	$0.302224\pi$
$384$	15.1195	−	27.3211i	0.771563	−	1.39422i
$385$	−0.426519	+	0.118855i	−0.0217374	+	0.00605742i
$386$	5.81573	+	10.9352i	0.296013	+	0.556585i
$387$			37.9716i			1.93020i
$388$	−20.1683	+	3.92448i	−1.02389	+	0.199235i
$389$	−23.5877	−	23.5877i	−1.19595	−	1.19595i	−0.975370	−	0.220576i	$-0.929206\pi$
$389$	−23.5877	−	23.5877i	−1.19595	−	1.19595i	−0.220576	−	0.975370i	$-0.570794\pi$
$390$	0.123662	−	4.97766i	0.00626186	−	0.252054i
$391$	−4.50221			−0.227687
$392$	15.2968	−	12.3947i	0.772606	−	0.626026i
$393$	−15.1581	+	15.1581i	−0.764625	+	0.764625i
$394$	−8.83658	+	28.9134i	−0.445180	+	1.45664i
$395$	−30.7491	+	8.56864i	−1.54716	+	0.431135i
$396$	1.76393	+	9.06500i	0.0886408	+	0.455533i
$397$	4.78652			0.240228			0.120114	−	0.992760i	$-0.461674\pi$
$397$	4.78652			0.240228			0.120114	+	0.992760i	$0.461674\pi$
$398$	10.7010	−	35.0140i	0.536395	−	1.75509i
$399$	−0.0150285			−0.000752368
$400$	16.0073	+	11.9902i	0.800367	+	0.599511i
$401$	29.9895			1.49760			0.748801	−	0.662795i	$-0.230630\pi$
$401$	29.9895			1.49760			0.748801	+	0.662795i	$0.230630\pi$
$402$	1.31785	−	4.31201i	0.0657282	−	0.215064i
$403$	0.588084			0.0292945
$404$	14.5901	−	2.83904i	0.725885	−	0.141248i
$405$	−3.29802	+	0.919034i	−0.163880	+	0.0456672i
$406$	0.478018	−	1.56408i	0.0237236	−	0.0776241i
$407$	1.13121	−	1.13121i	0.0560720	−	0.0560720i
$408$	17.0231	+	1.78406i	0.842767	+	0.0883241i
$409$	36.0665			1.78337			0.891686	−	0.452654i	$-0.149523\pi$
$409$	36.0665			1.78337			0.891686	+	0.452654i	$0.149523\pi$
$410$	−0.215107	+	8.65851i	−0.0106234	+	0.427613i
$411$	−30.2998	−	30.2998i	−1.49458	−	1.49458i
$412$	−1.47002	−	7.55456i	−0.0724226	−	0.372186i
$413$			0.227577i			0.0111983i
$414$	−6.29624	−	11.8387i	−0.309443	−	0.581839i
$415$	9.59718	−	2.67438i	0.471107	−	0.131280i
$416$	3.21479	−	0.282869i	0.157618	−	0.0138688i
$417$	−19.7161	+	19.7161i	−0.965502	+	0.965502i
$418$	0.0113665	−	0.0371913i	0.000555952	−	0.00181909i
$419$	1.42937	+	1.42937i	0.0698293	+	0.0698293i	0.741159	−	0.671330i	$-0.234276\pi$
$419$	1.42937	+	1.42937i	0.0698293	+	0.0698293i	−0.671330	+	0.741159i	$0.734276\pi$
$420$	−2.18571	+	1.09369i	−0.106652	+	0.0533668i
$421$	−18.8889	+	18.8889i	−0.920589	+	0.920589i	−0.997071	−	0.0764823i	$-0.975631\pi$
$421$	−18.8889	+	18.8889i	−0.920589	+	0.920589i	0.0764823	+	0.997071i	$0.475631\pi$
$422$	29.1595	−	15.5081i	1.41946	−	0.754922i
$423$	−30.9098	−	30.9098i	−1.50288	−	1.50288i
$424$	8.03857	+	9.92075i	0.390387	+	0.481794i
$425$	−2.62575	+	10.6439i	−0.127367	+	0.516304i
$426$	4.76520	+	1.45635i	0.230875	+	0.0705604i
$427$	1.53205			0.0741409
$428$	27.3715	+	18.4544i	1.32305	+	0.892026i
$429$	−1.11338	+	1.11338i	−0.0537546	+	0.0537546i
$430$	0.645843	−	25.9966i	0.0311453	−	1.25367i
$431$		−	15.0218i		−	0.723573i	−0.932261	−	0.361787i	$-0.882167\pi$
$431$		−	15.0218i		−	0.723573i	0.932261	−	0.361787i	$-0.117833\pi$
$432$	6.69603	+	16.5543i	0.322163	+	0.796468i
$433$	5.48731	+	5.48731i	0.263703	+	0.263703i	0.826557	−	0.562854i	$-0.190297\pi$
$433$	5.48731	+	5.48731i	0.263703	+	0.263703i	−0.562854	+	0.826557i	$0.690297\pi$
$434$	−0.135545	−	0.254863i	−0.00650639	−	0.0122338i
$435$	17.7099	−	31.3932i	0.849127	−	1.50519i
$436$	24.6871	−	4.80379i	1.18230	−	0.230060i
$437$			0.0564656i			0.00270112i
$438$	29.3238	−	15.5955i	1.40114	−	0.745180i
$439$		−	13.0263i		−	0.621709i	−0.950457	−	0.310855i	$-0.899385\pi$
$439$		−	13.0263i		−	0.621709i	0.950457	−	0.310855i	$-0.100615\pi$
$440$	−1.05346	−	6.23620i	−0.0502218	−	0.297299i
$441$			32.1415i			1.53055i
$442$	0.830647	+	1.56185i	0.0395099	+	0.0742894i
$443$		−	4.29913i		−	0.204258i	−0.994771	−	0.102129i	$-0.967435\pi$
$443$		−	4.29913i		−	0.204258i	0.994771	−	0.102129i	$-0.0325654\pi$
$444$	4.93661	−	7.32196i	0.234281	−	0.347485i
$445$	29.5373	−	8.23094i	1.40020	−	0.390184i
$446$	6.53765	−	3.47696i	0.309567	−	0.164639i
$447$	23.4316	+	23.4316i	1.10828	+	1.10828i
$448$	−0.863557	−	1.32802i	−0.0407992	−	0.0627433i
$449$		−	22.6148i		−	1.06726i	−0.845718	−	0.533630i	$-0.820827\pi$
$449$		−	22.6148i		−	1.06726i	0.845718	−	0.533630i	$-0.179173\pi$
$450$	−31.6604	+	7.98076i	−1.49248	+	0.376217i
$451$	1.93670	−	1.93670i	0.0911956	−	0.0911956i
$452$	−5.37303	−	27.6125i	−0.252726	−	1.29878i
$453$	62.8796			2.95434
$454$	3.49436	−	11.4336i	0.163999	−	0.536606i
$455$	−0.220005	−	0.124112i	−0.0103140	−	0.00581848i
$456$	0.0223752	−	0.213499i	0.00104782	−	0.00999802i
$457$	7.61254	+	7.61254i	0.356099	+	0.356099i	0.862373	−	0.506274i	$-0.168977\pi$
$457$	7.61254	+	7.61254i	0.356099	+	0.356099i	−0.506274	+	0.862373i	$0.668977\pi$
$458$	18.4442	+	34.6802i	0.861842	+	1.62050i
$459$	−6.92146	+	6.92146i	−0.323066	+	0.323066i
$460$	4.10926	+	8.21223i	0.191595	+	0.382897i
$461$	−13.4947	−	13.4947i	−0.628509	−	0.628509i	0.319184	−	0.947693i	$-0.396591\pi$
$461$	−13.4947	−	13.4947i	−0.628509	−	0.628509i	−0.947693	+	0.319184i	$0.896591\pi$
$462$	0.739136	+	0.225896i	0.0343877	+	0.0105096i
$463$	15.8225	−	15.8225i	0.735335	−	0.735335i	−0.236337	−	0.971671i	$-0.575947\pi$
$463$	15.8225	−	15.8225i	0.735335	−	0.735335i	0.971671	+	0.236337i	$0.0759468\pi$
$464$	21.5081	+	9.11953i	0.998486	+	0.423363i
$465$	−1.70772	−	6.12828i	−0.0791937	−	0.284192i
$466$	−14.6324	+	7.78205i	−0.677832	+	0.360496i
$467$			14.3620i			0.664594i	0.943175	+	0.332297i	$0.107824\pi$
$467$			14.3620i			0.664594i	−0.943175	+	0.332297i	$0.892176\pi$
$468$	−2.94527	+	4.36841i	−0.136145	+	0.201930i
$469$	−0.161744	−	0.161744i	−0.00746863	−	0.00746863i
$470$	20.6361	+	21.6876i	0.951873	+	1.00037i
$471$	−22.1498			−1.02061
$472$	−3.23301	−	0.338828i	−0.148811	−	0.0155958i
$473$	−5.81481	+	5.81481i	−0.267365	+	0.267365i
$474$	53.2867	+	16.2856i	2.44754	+	0.748021i
$475$	0.133493	+	0.0329315i	0.00612508	+	0.00151100i
$476$	0.485417	−	0.719969i	0.0222491	−	0.0329997i
$477$	−20.8454			−0.954445
$478$	17.5878	+	5.37521i	0.804447	+	0.245857i
$479$	−14.8014			−0.676293			−0.338146	−	0.941094i	$-0.609800\pi$
$479$	−14.8014			−0.676293			−0.338146	+	0.941094i	$0.609800\pi$
$480$	−12.2831	−	32.6792i	−0.560643	−	1.49159i
$481$	0.912665			0.0416139
$482$	−1.38718	−	0.423951i	−0.0631841	−	0.0193104i
$483$	−1.12219			−0.0510615
$484$	−1.11806	+	1.65830i	−0.0508207	+	0.0753772i
$485$	−11.2870	+	20.0076i	−0.512516	+	0.908500i
$486$	23.8287	+	7.28257i	1.08089	+	0.330344i
$487$	6.83833	−	6.83833i	0.309874	−	0.309874i	−0.534986	−	0.844861i	$-0.679683\pi$
$487$	6.83833	−	6.83833i	0.309874	−	0.309874i	0.844861	+	0.534986i	$0.179683\pi$
$488$	−2.28099	+	21.7646i	−0.103255	+	0.985239i
$489$	−55.2902			−2.50031
$490$	0.546682	−	22.0052i	0.0246966	−	0.994092i
$491$	−3.57853	−	3.57853i	−0.161497	−	0.161497i	0.621733	−	0.783229i	$-0.286429\pi$
$491$	−3.57853	−	3.57853i	−0.161497	−	0.161497i	−0.783229	+	0.621733i	$0.786429\pi$
$492$	8.45177	−	12.5356i	0.381035	−	0.565150i
$493$			12.8056i			0.576735i
$494$	0.0195883	−	0.0104178i	0.000881319	−	0.000468718i
$495$	8.99279	+	5.07314i	0.404196	+	0.228021i
$496$	3.82245	−	1.54614i	0.171633	−	0.0694238i
$497$	0.178743	−	0.178743i	0.00801771	−	0.00801771i
$498$	−16.6314	−	5.08293i	−0.745272	−	0.227771i
$499$	−15.8373	−	15.8373i	−0.708974	−	0.708974i	0.257346	−	0.966319i	$-0.417152\pi$
$499$	−15.8373	−	15.8373i	−0.708974	−	0.708974i	−0.966319	+	0.257346i	$0.917152\pi$
$500$	21.8115	−	4.92540i	0.975439	−	0.220270i
$501$	−39.4410	+	39.4410i	−1.76209	+	1.76209i
$502$	16.9805	+	31.9279i	0.757875	+	1.42501i
$503$	14.9752	+	14.9752i	0.667712	+	0.667712i	0.957186	−	0.289474i	$-0.0934804\pi$
$503$	14.9752	+	14.9752i	0.667712	+	0.667712i	−0.289474	+	0.957186i	$0.593480\pi$
$504$	2.57202	+	0.269554i	0.114567	+	0.0120069i
$505$	8.16521	−	14.4739i	0.363347	−	0.644079i
$506$	0.848744	−	2.77710i	0.0377313	−	0.123457i
$507$	34.9815			1.55358
$508$	−5.75243	−	29.5623i	−0.255223	−	1.31161i
$509$	11.2971	−	11.2971i	0.500736	−	0.500736i	−0.410930	−	0.911667i	$-0.634796\pi$
$509$	11.2971	−	11.2971i	0.500736	−	0.500736i	0.911667	+	0.410930i	$0.134796\pi$
$510$	13.8635	−	13.1914i	0.613887	−	0.584124i
$511$		−	1.68492i		−	0.0745365i
$512$	20.1520	−	10.2907i	0.890600	−	0.454788i
$513$	0.0868073	+	0.0868073i	0.00383263	+	0.00383263i
$514$	−10.2660	+	5.45986i	−0.452816	+	0.240824i
$515$	−7.49438	−	4.22784i	−0.330242	−	0.186301i
$516$	−25.3758	+	37.6374i	−1.11711	+	1.65689i
$517$		−	9.46679i		−	0.416349i
$518$	−0.210357	−	0.395529i	−0.00924256	−	0.0173786i
$519$			37.5100i			1.64651i
$520$	2.09073	−	2.94066i	0.0916844	−	0.128957i
$521$			5.01183i			0.219572i	0.993955	+	0.109786i	$0.0350166\pi$
$521$			5.01183i			0.219572i	−0.993955	+	0.109786i	$0.964983\pi$
$522$	−33.6726	+	17.9083i	−1.47381	+	0.783827i
$523$			11.6975i			0.511496i	0.966743	+	0.255748i	$0.0823218\pi$
$523$			11.6975i			0.511496i	−0.966743	+	0.255748i	$0.917678\pi$
$524$	−15.2480	+	2.96706i	−0.666112	+	0.129617i
$525$	−0.654477	+	2.65303i	−0.0285637	+	0.115788i
$526$	1.36389	+	2.56448i	0.0594683	+	0.111817i
$527$	1.59819	+	1.59819i	0.0696184	+	0.0696184i
$528$	−4.30960	+	10.1640i	−0.187551	+	0.442333i
$529$		−	18.7837i		−	0.816681i
$530$	14.2714	+	0.354551i	0.619912	+	0.0154007i
$531$	3.75256	−	3.75256i	0.162847	−	0.162847i
$532$	−0.00902968	−	0.00608798i	−0.000391486	−	0.000263948i
$533$	1.56254			0.0676810
$534$	−51.1866	−	15.6437i	−2.21506	−	0.676971i
$535$	35.5534	−	9.90742i	1.53711	−	0.428335i
$536$	2.53858	−	2.05696i	0.109650	−	0.0888472i
$537$	37.4087	+	37.4087i	1.61431	+	1.61431i
$538$	2.00474	−	1.06619i	0.0864303	−	0.0459668i
$539$	−4.92202	+	4.92202i	−0.212007	+	0.212007i
$540$	18.9424	+	6.30770i	0.815151	+	0.271440i
$541$	29.6989	+	29.6989i	1.27686	+	1.27686i	0.942417	+	0.334440i	$0.108547\pi$
$541$	29.6989	+	29.6989i	1.27686	+	1.27686i	0.334440	+	0.942417i	$0.391453\pi$
$542$	1.43975	−	4.71089i	0.0618426	−	0.202350i
$543$	19.9198	−	19.9198i	0.854842	−	0.854842i
$544$	9.50536	+	7.96789i	0.407539	+	0.341620i
$545$	13.8159	−	24.4905i	0.591809	−	1.04906i
$546$	0.207042	+	0.389296i	0.00886057	+	0.0166603i
$547$		−	2.18513i		−	0.0934293i	−0.998908	−	0.0467147i	$-0.985125\pi$
$547$		−	2.18513i		−	0.0934293i	0.998908	−	0.0467147i	$-0.0148751\pi$
$548$	−5.93091	−	30.4795i	−0.253356	−	1.30202i
$549$	−25.2622	−	25.2622i	−1.07817	−	1.07817i
$550$	−6.07048	−	3.62620i	−0.258846	−	0.154622i
$551$	0.160605			0.00684199
$552$	1.67078	−	15.9422i	0.0711130	−	0.678543i
$553$	1.99878	−	1.99878i	0.0849969	−	0.0849969i
$554$	−3.93786	+	12.8847i	−0.167304	+	0.547420i
$555$	−2.65027	−	9.51066i	−0.112498	−	0.403705i
$556$	−19.8330	+	3.85925i	−0.841109	+	0.163669i
$557$	0.599018			0.0253812			0.0126906	−	0.999919i	$-0.495960\pi$
$557$	0.599018			0.0253812			0.0126906	+	0.999919i	$0.495960\pi$
$558$	−1.96745	+	6.43752i	−0.0832887	+	0.272522i
$559$	−4.69141			−0.198425
$560$	−1.75631	−	0.228292i	−0.0742174	−	0.00964710i
$561$	−6.05152			−0.255496
$562$	−1.17993	+	3.86076i	−0.0497724	+	0.162856i
$563$	18.4868			0.779128			0.389564	−	0.920999i	$-0.372626\pi$
$563$	18.4868			0.779128			0.389564	+	0.920999i	$0.372626\pi$
$564$	−9.98119	−	51.2943i	−0.420284	−	2.15988i
$565$	−27.3926	−	15.4531i	−1.15241	−	0.650116i
$566$	12.8865	−	42.1649i	0.541660	−	1.77232i
$567$	0.214381	−	0.214381i	0.00900314	−	0.00900314i
$568$	2.27315	+	2.80539i	0.0953791	+	0.117711i
$569$	−0.845321			−0.0354377			−0.0177189	−	0.999843i	$-0.505640\pi$
$569$	−0.845321			−0.0354377			−0.0177189	+	0.999843i	$0.505640\pi$
$570$	−0.165443	−	0.173873i	−0.00692965	−	0.00728273i
$571$	−21.5317	−	21.5317i	−0.901074	−	0.901074i	0.0944552	−	0.995529i	$-0.469889\pi$
$571$	−21.5317	−	21.5317i	−0.901074	−	0.901074i	−0.995529	+	0.0944552i	$0.969889\pi$
$572$	−1.11999	+	0.217934i	−0.0468290	+	0.00911230i
$573$			22.9549i			0.958954i
$574$	−0.360144	−	0.677170i	−0.0150321	−	0.0282645i
$575$	9.96803	+	2.45902i	0.415696	+	0.102548i
$576$	−7.65871	+	36.1375i	−0.319113	+	1.50573i
$577$	32.9762	−	32.9762i	1.37282	−	1.37282i	0.516580	−	0.856239i	$-0.327205\pi$
$577$	32.9762	−	32.9762i	1.37282	−	1.37282i	0.856239	−	0.516580i	$-0.172795\pi$
$578$	5.03968	−	16.4899i	0.209623	−	0.685890i
$579$	−17.0919	−	17.0919i	−0.710315	−	0.710315i
$580$	23.3580	−	11.6879i	0.969887	−	0.485315i
$581$	−0.623845	+	0.623845i	−0.0258814	+	0.0258814i
$582$	35.4032	−	18.8288i	1.46751	−	0.780477i
$583$	−3.19218	−	3.19218i	−0.132206	−	0.132206i
$584$	23.9364	+	2.50860i	0.990496	+	0.103806i
$585$	1.58119	+	5.67422i	0.0653744	+	0.234600i
$586$	−26.3891	−	8.06508i	−1.09012	−	0.333166i
$587$	−5.92738			−0.244649			−0.122325	−	0.992490i	$-0.539035\pi$
$587$	−5.92738			−0.244649			−0.122325	+	0.992490i	$0.539035\pi$
$588$	−21.4797	+	31.8587i	−0.885809	+	1.31383i
$589$	0.0200442	−	0.0200442i	0.000825905	−	0.000825905i
$590$	−2.63295	+	2.50530i	−0.108397	+	0.103142i
$591$		−	59.0040i		−	2.42710i
$592$	5.93218	−	2.39950i	0.243811	−	0.0986190i
$593$	−9.11761	−	9.11761i	−0.374415	−	0.374415i	0.494667	−	0.869082i	$-0.335290\pi$
$593$	−9.11761	−	9.11761i	−0.374415	−	0.374415i	−0.869082	+	0.494667i	$0.835290\pi$
$594$	−2.96456	−	5.57418i	−0.121637	−	0.228712i
$595$	−0.260601	−	0.935184i	−0.0106836	−	0.0383388i
$596$	4.58653	+	23.5706i	0.187872	+	0.965490i
$597$			71.4536i			2.92440i
$598$	1.46267	−	0.777904i	0.0598132	−	0.0318109i
$599$			28.8016i			1.17680i	0.808569	+	0.588401i	$0.200242\pi$
$599$			28.8016i			1.17680i	−0.808569	+	0.588401i	$0.799758\pi$
$600$	−36.7152	−	13.2476i	−1.49889	−	0.540832i
$601$		−	2.50539i		−	0.102197i	−0.998694	−	0.0510984i	$-0.983728\pi$
$601$		−	2.50539i		−	0.102197i	0.998694	−	0.0510984i	$-0.0162722\pi$
$602$	1.08131	+	2.03316i	0.0440708	+	0.0828652i
$603$			5.33405i			0.217219i
$604$	37.7803	+	25.4722i	1.53726	+	1.03645i
$605$	0.600239	+	2.15400i	0.0244032	+	0.0875725i
$606$	−25.6113	+	13.6211i	−1.04039	+	0.553317i
$607$	21.3036	+	21.3036i	0.864688	+	0.864688i	0.991878	−	0.127190i	$-0.0405959\pi$
$607$	21.3036	+	21.3036i	0.864688	+	0.864688i	−0.127190	+	0.991878i	$0.540596\pi$
$608$	0.0999313	−	0.119214i	0.00405275	−	0.00483476i
$609$			3.19184i			0.129340i
$610$	16.8657	+	17.7250i	0.682871	+	0.717665i
$611$	3.81892	−	3.81892i	0.154497	−	0.154497i
$612$	−19.8759	+	3.86758i	−0.803434	+	0.156338i
$613$	−21.4899			−0.867969			−0.433984	−	0.900920i	$-0.642893\pi$
$613$	−21.4899			−0.867969			−0.433984	+	0.900920i	$0.642893\pi$
$614$	−6.52097	+	21.3367i	−0.263165	+	0.861081i
$615$	−4.53741	−	16.2828i	−0.182966	−	0.656586i
$616$	0.352590	+	0.435147i	0.0142063	+	0.0175326i
$617$	−12.4679	−	12.4679i	−0.501937	−	0.501937i	0.410102	−	0.912039i	$-0.365493\pi$
$617$	−12.4679	−	12.4679i	−0.501937	−	0.501937i	−0.912039	+	0.410102i	$0.865493\pi$
$618$	7.05280	+	13.2612i	0.283705	+	0.533444i
$619$	1.77556	−	1.77556i	0.0713656	−	0.0713656i	−0.670523	−	0.741889i	$-0.733930\pi$
$619$	1.77556	−	1.77556i	0.0713656	−	0.0713656i	0.741889	+	0.670523i	$0.233930\pi$
$620$	1.45647	−	4.37388i	0.0584934	−	0.175659i
$621$	6.48197	+	6.48197i	0.260112	+	0.260112i
$622$	−36.4450	−	11.1384i	−1.46131	−	0.446609i
$623$	−1.92001	+	1.92001i	−0.0769235	+	0.0769235i
$624$	−5.83869	+	2.36169i	−0.233735	+	0.0945431i
$625$	11.6270	−	22.1317i	0.465079	−	0.885269i
$626$	19.4997	−	10.3706i	0.779363	−	0.414494i
$627$			0.0758968i			0.00303103i
$628$	−13.3084	−	8.97276i	−0.531062	−	0.358052i
$629$	2.48029	+	2.48029i	0.0988955	+	0.0988955i
$630$	2.09464	−	1.99309i	0.0834526	−	0.0794066i
$631$	17.6754			0.703647			0.351824	−	0.936066i	$-0.385562\pi$
$631$	17.6754			0.703647			0.351824	+	0.936066i	$0.385562\pi$
$632$	25.4193	+	31.3711i	1.01113	+	1.24788i
$633$	−45.5769	+	45.5769i	−1.81152	+	1.81152i
$634$	34.8561	+	10.6528i	1.38431	+	0.423076i
$635$	−29.3268	−	16.5443i	−1.16380	−	0.656539i
$636$	−20.6619	−	13.9307i	−0.819299	−	0.552387i
$637$	−3.97110			−0.157341
$638$	−7.89889	−	2.41407i	−0.312720	−	0.0955741i
$639$	−5.89466			−0.233189
$640$	5.85805	−	24.6106i	0.231560	−	0.972821i
$641$	−26.4635			−1.04525			−0.522623	−	0.852564i	$-0.675046\pi$
$641$	−26.4635			−1.04525			−0.522623	+	0.852564i	$0.675046\pi$
$642$	−61.6123	−	18.8301i	−2.43164	−	0.743163i
$643$	−10.7417			−0.423610			−0.211805	−	0.977312i	$-0.567934\pi$
$643$	−10.7417			−0.423610			−0.211805	+	0.977312i	$0.567934\pi$
$644$	−0.674254	−	0.454595i	−0.0265693	−	0.0179135i
$645$	13.6233	+	48.8880i	0.536416	+	1.92496i
$646$	0.0815454	+	0.0249221i	0.00320836	+	0.000980545i
$647$	−17.7408	+	17.7408i	−0.697464	+	0.697464i	−0.963863	−	0.266399i	$-0.914166\pi$
$647$	−17.7408	+	17.7408i	−0.697464	+	0.697464i	0.266399	+	0.963863i	$0.414166\pi$
$648$	2.72636	+	3.36473i	0.107102	+	0.132179i
$649$	1.14930			0.0451141
$650$	−0.986028	−	3.91166i	−0.0386752	−	0.153428i
$651$	0.398356	+	0.398356i	0.0156128	+	0.0156128i
$652$	−33.2203	−	22.3978i	−1.30101	−	0.877165i
$653$			24.4157i			0.955460i	0.878507	+	0.477730i	$0.158540\pi$
$653$			24.4157i			0.955460i	−0.878507	+	0.477730i	$0.841460\pi$
$654$	−43.3355	+	23.0474i	−1.69455	+	0.901226i
$655$	−8.53340	+	15.1265i	−0.333428	+	0.591043i
$656$	10.1562	−	4.10809i	0.396535	−	0.160394i
$657$	−27.7830	+	27.7830i	−1.08392	+	1.08392i
$658$	−2.53525	−	0.774827i	−0.0988343	−	0.0302059i
$659$	−18.8135	−	18.8135i	−0.732868	−	0.732868i	0.238319	−	0.971187i	$-0.423404\pi$
$659$	−18.8135	−	18.8135i	−0.732868	−	0.732868i	−0.971187	+	0.238319i	$0.923404\pi$
$660$	5.52334	+	11.0382i	0.214996	+	0.429663i
$661$	−24.0145	+	24.0145i	−0.934056	+	0.934056i	−0.997956	−	0.0639004i	$-0.979646\pi$
$661$	−24.0145	+	24.0145i	−0.934056	+	0.934056i	0.0639004	+	0.997956i	$0.479646\pi$
$662$	−21.3675	−	40.1768i	−0.830472	−	1.56151i
$663$	−2.44120	−	2.44120i	−0.0948082	−	0.0948082i
$664$	−7.93369	−	9.79131i	−0.307887	−	0.379977i
$665$	−0.0117289	+	0.00326839i	−0.000454825	+	0.000126743i
$666$	−3.05334	+	9.99059i	−0.118315	+	0.387128i
$667$	11.9925			0.464351
$668$	−39.6749	+	7.72021i	−1.53507	+	0.298704i
$669$	−10.2185	+	10.2185i	−0.395069	+	0.395069i
$670$	0.0907247	−	3.65187i	0.00350500	−	0.141084i
$671$		−	7.73710i		−	0.298688i
$672$	2.36925	+	1.98603i	0.0913956	+	0.0766126i
$673$	22.9707	+	22.9707i	0.885457	+	0.885457i	0.994083	−	0.108626i	$-0.0346451\pi$
$673$	22.9707	+	22.9707i	0.885457	+	0.885457i	−0.108626	+	0.994083i	$0.534645\pi$
$674$	−12.4920	+	6.64372i	−0.481175	+	0.255907i
$675$	19.1047	−	11.5439i	0.735340	−	0.444327i
$676$	21.0181	+	14.1708i	0.808390	+	0.545032i
$677$			6.71129i			0.257936i	0.991649	+	0.128968i	$0.0411664\pi$
$677$			6.71129i			0.257936i	−0.991649	+	0.128968i	$0.958834\pi$
$678$	25.7785	+	48.4707i	0.990018	+	1.86151i
$679$		−	2.03424i		−	0.0780670i
$680$	13.6735	−	2.30981i	0.524353	−	0.0885773i
$681$			23.3327i			0.894112i
$682$	−1.28710	+	0.684529i	−0.0492857	+	0.0262120i
$683$		−	37.8889i		−	1.44978i	−0.688865	−	0.724889i	$-0.741891\pi$
$683$		−	37.8889i		−	1.44978i	0.688865	−	0.724889i	$-0.258109\pi$
$684$	0.0485063	+	0.249278i	0.00185468	+	0.00953140i
$685$	−30.2367	−	17.0576i	−1.15529	−	0.651736i
$686$	1.83573	+	3.45168i	0.0700885	+	0.131786i
$687$	−54.2059	−	54.2059i	−2.06808	−	2.06808i
$688$	−30.4934	+	12.3343i	−1.16255	+	0.470240i
$689$		−	2.57546i		−	0.0981172i
$690$	−12.3538	−	12.9832i	−0.470300	−	0.494263i
$691$	31.1784	−	31.1784i	1.18608	−	1.18608i	0.207940	−	0.978142i	$-0.433324\pi$
$691$	31.1784	−	31.1784i	1.18608	−	1.18608i	0.978142	−	0.207940i	$-0.0666760\pi$
$692$	−15.1951	+	22.5374i	−0.577632	+	0.856743i
$693$	−0.914327			−0.0347324
$694$	2.88603	+	0.882033i	0.109552	+	0.0334815i
$695$	−11.0994	+	19.6751i	−0.421023	+	0.746318i
$696$	−45.3442	−	4.75218i	−1.71877	−	0.180131i
$697$	4.24640	+	4.24640i	0.160844	+	0.160844i
$698$	9.92482	−	5.27839i	0.375660	−	0.199790i
$699$	22.8707	−	22.8707i	0.865050	−	0.865050i
$700$	−1.46796	+	1.32891i	−0.0554837	+	0.0502280i
$701$	−5.12726	−	5.12726i	−0.193654	−	0.193654i	0.603619	−	0.797273i	$-0.293725\pi$
$701$	−5.12726	−	5.12726i	−0.193654	−	0.193654i	−0.797273	+	0.603619i	$0.793725\pi$
$702$	1.05273	−	3.44454i	0.0397327	−	0.130006i
$703$	0.0311071	−	0.0311071i	0.00117323	−	0.00117323i
$704$	−6.70676	+	4.36112i	−0.252771	+	0.164366i
$705$	−50.8857	−	28.7064i	−1.91647	−	1.08114i
$706$	−6.62036	−	12.4481i	−0.249161	−	0.468491i
$707$			1.47161i			0.0553455i
$708$	6.22731	−	1.21175i	0.234037	−	0.0455405i
$709$	33.8473	+	33.8473i	1.27116	+	1.27116i	0.945479	+	0.325683i	$0.105594\pi$
$709$	33.8473	+	33.8473i	1.27116	+	1.27116i	0.325683	+	0.945479i	$0.394406\pi$
$710$	4.03568	+	0.100260i	0.151456	+	0.00376268i
$711$	−65.9167			−2.47207
$712$	−24.4175	−	30.1347i	−0.915086	−	1.12935i
$713$	1.49671	−	1.49671i	0.0560524	−	0.0560524i
$714$	−0.495299	+	1.62063i	−0.0185361	+	0.0606504i
$715$	−0.626789	+	1.11106i	−0.0234406	+	0.0415515i
$716$	7.32242	+	37.6306i	0.273652	+	1.40632i
$717$	−35.8916			−1.34040
$718$	−5.19837	+	17.0092i	−0.194002	+	0.634776i
$719$	10.2185			0.381086			0.190543	−	0.981679i	$-0.438975\pi$
$719$	10.2185			0.381086			0.190543	+	0.981679i	$0.438975\pi$
$720$	25.1957	+	32.7244i	0.938989	+	1.21957i
$721$	0.761978			0.0283776
$722$	−7.85318	+	25.6957i	−0.292265	+	0.956296i
$723$	2.83083			0.105280
$724$	20.0380	−	3.89913i	0.744705	−	0.144910i
$725$	6.99417	−	28.3520i	0.259757	−	1.05297i
$726$	1.14082	−	3.73277i	0.0423397	−	0.138536i
$727$	5.64423	−	5.64423i	0.209333	−	0.209333i	−0.594651	−	0.803984i	$-0.702710\pi$
$727$	5.64423	−	5.64423i	0.209333	−	0.209333i	0.803984	+	0.594651i	$0.202710\pi$
$728$	−0.0333036	+	0.317774i	−0.00123431	+	0.0117775i
$729$	−44.0342			−1.63090
$730$	19.4937	−	18.5486i	0.721495	−	0.686515i
$731$	−12.7495	−	12.7495i	−0.471558	−	0.471558i
$732$	−8.15752	−	41.9223i	−0.301511	−	1.54949i
$733$			22.7837i			0.841535i	0.907169	+	0.420767i	$0.138239\pi$
$733$			22.7837i			0.841535i	−0.907169	+	0.420767i	$0.861761\pi$
$734$	−2.88825	−	5.43071i	−0.106607	−	0.200451i
$735$	11.5316	+	41.3819i	0.425350	+	1.52640i
$736$	7.46195	−	8.90180i	0.275051	−	0.328125i
$737$	−0.816835	+	0.816835i	−0.0300885	+	0.0300885i
$738$	−5.22750	+	17.1045i	−0.192427	+	0.629625i
$739$	9.59846	+	9.59846i	0.353085	+	0.353085i	0.861256	−	0.508171i	$-0.169678\pi$
$739$	9.59846	+	9.59846i	0.353085	+	0.353085i	−0.508171	+	0.861256i	$0.669678\pi$
$740$	2.26035	−	6.78796i	0.0830920	−	0.249530i
$741$	−0.0306169	+	0.0306169i	−0.00112474	+	0.00112474i
$742$	−1.11615	+	0.593609i	−0.0409751	+	0.0217921i
$743$	23.7768	+	23.7768i	0.872288	+	0.872288i	0.992721	−	0.120434i	$-0.0384285\pi$
$743$	23.7768	+	23.7768i	0.872288	+	0.872288i	−0.120434	+	0.992721i	$0.538429\pi$
$744$	−6.25224	+	5.06605i	−0.229218	+	0.185730i
$745$	23.3829	+	13.1911i	0.856682	+	0.483283i
$746$	7.52590	+	2.30008i	0.275543	+	0.0842119i
$747$	20.5734			0.752742
$748$	−3.63597	−	2.45144i	−0.132944	−	0.0896336i
$749$	−2.31108	+	2.31108i	−0.0844449	+	0.0844449i
$750$	−37.8991	+	21.6341i	−1.38388	+	0.789967i
$751$		−	28.6759i		−	1.04640i	−0.852210	−	0.523199i	$-0.824738\pi$
$751$		−	28.6759i		−	1.04640i	0.852210	−	0.523199i	$-0.175262\pi$
$752$	14.7820	−	34.8628i	0.539044	−	1.27131i
$753$	−49.9040	−	49.9040i	−1.81860	−	1.81860i
$754$	−2.21259	−	4.16027i	−0.0805776	−	0.151508i
$755$	49.0737	−	13.6750i	1.78597	−	0.497685i
$756$	−1.73543	+	0.337692i	−0.0631170	+	0.0122817i
$757$			29.0633i			1.05632i	0.849144	+	0.528162i	$0.177119\pi$
$757$			29.0633i			1.05632i	−0.849144	+	0.528162i	$0.822881\pi$
$758$	19.5458	−	10.3952i	0.709935	−	0.377570i
$759$			5.66727i			0.205709i
$760$	−0.0289691	−	0.171489i	−0.00105082	−	0.00622057i
$761$		−	50.4514i		−	1.82886i	−0.404743	−	0.914431i	$-0.632639\pi$
$761$		−	50.4514i		−	1.82886i	0.404743	−	0.914431i	$-0.367361\pi$
$762$	27.5988	+	51.8934i	0.999800	+	1.87990i
$763$			2.49003i			0.0901450i
$764$	−9.29890	+	13.7921i	−0.336423	+	0.498981i
$765$	−11.1233	+	19.7175i	−0.402165	+	0.712889i
$766$	7.98224	−	4.24525i	0.288410	−	0.153387i
$767$	0.463631	+	0.463631i	0.0167407	+	0.0167407i
$768$	−31.7414	+	30.7012i	−1.14537	+	1.10783i
$769$			34.6495i			1.24949i	0.780828	+	0.624746i	$0.214797\pi$
$769$			34.6495i			1.24949i	−0.780828	+	0.624746i	$0.785203\pi$
$770$	0.625978	+	0.0155514i	0.0225587	+	0.000560434i
$771$	16.0460	−	16.0460i	0.577884	−	0.577884i
$772$	−3.34558	−	17.1933i	−0.120410	−	0.618799i
$773$	40.3554			1.45148			0.725742	−	0.687967i	$-0.241497\pi$
$773$	40.3554			1.45148			0.725742	+	0.687967i	$0.241497\pi$
$774$	15.6952	−	51.3550i	0.564153	−	1.84592i
$775$	−2.66555	−	4.41135i	−0.0957493	−	0.158460i
$776$	28.8990	+	3.02868i	1.03741	+	0.108723i
$777$	0.618221	+	0.618221i	0.0221785	+	0.0221785i
$778$	22.1517	+	41.6513i	0.794176	+	1.49327i
$779$	0.0532573	−	0.0532573i	0.00190814	−	0.00190814i
$780$	−2.22472	+	6.68098i	−0.0796578	+	0.239217i
$781$	−0.902683	−	0.902683i	−0.0323005	−	0.0323005i
$782$	6.08906	+	1.86095i	0.217744	+	0.0665475i
$783$	18.4366	−	18.4366i	0.658871	−	0.658871i
$784$	−25.8116	+	10.4405i	−0.921842	+	0.372875i
$785$	−17.2865	+	4.81711i	−0.616983	+	0.171930i
$786$	26.7662	−	14.2353i	0.954719	−	0.507755i
$787$		−	53.5155i		−	1.90762i	−0.300409	−	0.953810i	$-0.597123\pi$
$787$		−	53.5155i		−	1.90762i	0.300409	−	0.953810i	$-0.402877\pi$
$788$	23.9022	−	35.4518i	0.851482	−	1.26292i
$789$	−4.00834	−	4.00834i	−0.142701	−	0.142701i
$790$	45.1288	+	1.12115i	1.60561	+	0.0398887i
$791$	2.78509			0.0990264
$792$	1.36130	−	12.9892i	0.0483716	−	0.461550i
$793$	3.12116	−	3.12116i	0.110836	−	0.110836i
$794$	−6.47357	−	1.97847i	−0.229739	−	0.0702131i
$795$	−26.8382	+	7.47882i	−0.951854	+	0.265246i
$796$	−28.9455	+	42.9319i	−1.02595	+	1.52168i
$797$	21.7656			0.770976			0.385488	−	0.922713i	$-0.374033\pi$
$797$	21.7656			0.770976			0.385488	+	0.922713i	$0.374033\pi$
$798$	0.0203255	+	0.00621192i	0.000719515	+	0.000219899i
$799$	20.7568			0.734324
$800$	−16.6932	−	22.8328i	−0.590195	−	0.807261i
$801$	63.3189			2.23726
$802$	−40.5596	−	12.3959i	−1.43221	−	0.437714i
$803$	−8.50915			−0.300281
$804$	−3.56467	+	5.28711i	−0.125716	+	0.186462i
$805$	−0.875803	+	0.244054i	−0.0308680	+	0.00860176i
$806$	−0.795360	−	0.243079i	−0.0280153	−	0.00856210i
$807$	−3.13344	+	3.13344i	−0.110302	+	0.110302i
$808$	−20.9060	−	2.19100i	−0.735471	−	0.0770792i
$809$	10.2152			0.359148			0.179574	−	0.983744i	$-0.442528\pi$
$809$	10.2152			0.359148			0.179574	+	0.983744i	$0.442528\pi$
$810$	4.84031	+	0.120250i	0.170071	+	0.00422514i
$811$	−1.10510	−	1.10510i	−0.0388052	−	0.0388052i	0.687438	−	0.726243i	$-0.258735\pi$
$811$	−1.10510	−	1.10510i	−0.0388052	−	0.0388052i	−0.726243	+	0.687438i	$0.758735\pi$
$812$	−1.29300	+	1.91777i	−0.0453754	+	0.0673007i
$813$			9.61358i			0.337163i
$814$	−1.99749	+	1.06234i	−0.0700121	+	0.0372350i
$815$	−43.1506	+	12.0245i	−1.51150	+	0.421199i
$816$	−22.2856	−	9.44921i	−0.780152	−	0.330788i
$817$	−0.159901	+	0.159901i	−0.00559424	+	0.00559424i
$818$	−48.7785	−	14.9078i	−1.70550	−	0.521238i
$819$	−0.368841	−	0.368841i	−0.0128883	−	0.0128883i
$820$	3.86985	−	11.6214i	0.135141	−	0.405836i
$821$	−6.60603	+	6.60603i	−0.230552	+	0.230552i	−0.812923	−	0.582371i	$-0.802125\pi$
$821$	−6.60603	+	6.60603i	−0.230552	+	0.230552i	0.582371	+	0.812923i	$0.302125\pi$
$822$	28.4551	+	53.5034i	0.992486	+	1.86615i
$823$	25.7130	+	25.7130i	0.896301	+	0.896301i	0.995107	−	0.0988061i	$-0.0315024\pi$
$823$	25.7130	+	25.7130i	0.896301	+	0.896301i	−0.0988061	+	0.995107i	$0.531502\pi$
$824$	−1.13447	+	10.8249i	−0.0395212	+	0.377102i
$825$	13.3983	+	3.30523i	0.466467	+	0.115073i
$826$	0.0940668	−	0.307788i	0.00327300	−	0.0107093i
$827$	9.95386			0.346130			0.173065	−	0.984910i	$-0.444633\pi$
$827$	9.95386			0.346130			0.173065	+	0.984910i	$0.444633\pi$
$828$	3.62200	+	18.6138i	0.125873	+	0.646875i
$829$	16.4770	−	16.4770i	0.572269	−	0.572269i	−0.360493	−	0.932762i	$-0.617391\pi$
$829$	16.4770	−	16.4770i	0.572269	−	0.572269i	0.932762	+	0.360493i	$0.117391\pi$
$830$	−14.0852	−	0.349925i	−0.488906	−	0.0121461i
$831$		−	26.2941i		−	0.912131i
$832$	−4.46480	−	0.946238i	−0.154789	−	0.0328049i
$833$	−10.7920	−	10.7920i	−0.373921	−	0.373921i
$834$	34.8147	−	18.5158i	1.20554	−	0.641149i
$835$	−22.2037	+	39.3589i	−0.768390	+	1.36207i
$836$	−0.0307454	+	0.0456015i	−0.00106335	+	0.00157716i
$837$		−	4.60194i		−	0.159066i
$838$	−1.34235	−	2.52399i	−0.0463707	−	0.0871896i
$839$			43.0584i			1.48654i	0.668992	+	0.743270i	$0.266726\pi$
$839$			43.0584i			1.48654i	−0.668992	+	0.743270i	$0.733274\pi$
$840$	3.40816	−	0.575730i	0.117593	−	0.0198646i
$841$		−	5.11014i		−	0.176212i
$842$	33.3541	−	17.7389i	1.14946	−	0.611324i
$843$		−	7.87870i		−	0.271357i
$844$	−45.8472	+	8.92126i	−1.57813	+	0.307082i
$845$	27.3009	−	7.60775i	0.939181	−	0.261715i
$846$	29.0279	+	54.5805i	0.998001	+	1.87652i
$847$	−0.140016	−	0.140016i	−0.00481101	−	0.00481101i
$848$	−6.77119	−	16.7401i	−0.232524	−	0.574857i
$849$			86.0464i			2.95311i
$850$	7.95078	−	13.3101i	0.272709	−	0.456532i
$851$	2.32280	−	2.32280i	0.0796244	−	0.0796244i
$852$	−5.84278	−	3.93931i	−0.200170	−	0.134959i
$853$	−0.642584			−0.0220017			−0.0110008	−	0.999939i	$-0.503502\pi$
$853$	−0.642584			−0.0220017			−0.0110008	+	0.999939i	$0.503502\pi$
$854$	−2.07203	−	0.633258i	−0.0709034	−	0.0216696i
$855$	0.247293	+	0.139506i	0.00845723	+	0.00477101i
$856$	−29.3909	−	36.2726i	−1.00456	−	1.23977i
$857$	23.4155	+	23.4155i	0.799858	+	0.799858i	0.983073	−	0.183215i	$-0.0586505\pi$
$857$	23.4155	+	23.4155i	0.799858	+	0.799858i	−0.183215	+	0.983073i	$0.558651\pi$
$858$	1.96601	−	1.04560i	0.0671186	−	0.0356961i
$859$	40.2351	−	40.2351i	1.37280	−	1.37280i	0.516541	−	0.856263i	$-0.327220\pi$
$859$	40.2351	−	40.2351i	1.37280	−	1.37280i	0.856263	−	0.516541i	$-0.172780\pi$
$860$	−11.6189	+	34.8924i	−0.396203	+	1.18982i
$861$	1.05843	+	1.05843i	0.0360712	+	0.0360712i
$862$	−6.20912	+	20.3163i	−0.211483	+	0.691978i
$863$	5.26168	−	5.26168i	0.179110	−	0.179110i	−0.611858	−	0.790968i	$-0.709578\pi$
$863$	5.26168	−	5.26168i	0.179110	−	0.179110i	0.790968	+	0.611858i	$0.209578\pi$
$864$	−2.21354	−	25.1568i	−0.0753062	−	0.855850i
$865$	8.15766	+	29.2743i	0.277369	+	0.995356i
$866$	−5.15323	−	9.68949i	−0.175114	−	0.329262i
$867$			33.6512i			1.14285i
$868$	0.0779745	+	0.400718i	0.00264663	+	0.0136013i
$869$	−10.0942	−	10.0942i	−0.342423	−	0.342423i
$870$	−36.9281	+	35.1377i	−1.25198	+	1.19128i
$871$	−0.659025			−0.0223302
$872$	−35.3739	−	3.70728i	−1.19791	−	0.125544i
$873$	−33.5430	+	33.5430i	−1.13526	+	1.13526i
$874$	0.0233396	−	0.0763675i	0.000789474	−	0.00258317i
$875$	0.0661987	+	2.21286i	0.00223792	+	0.0748083i
$876$	−46.1055	+	8.97152i	−1.55776	+	0.303120i
$877$	49.9187			1.68563			0.842817	−	0.538200i	$-0.180896\pi$
$877$	49.9187			1.68563			0.842817	+	0.538200i	$0.180896\pi$
$878$	−5.38429	+	17.6175i	−0.181711	+	0.594562i
$879$	53.8526			1.81640
$880$	−1.15292	+	8.86966i	−0.0388648	+	0.298996i
$881$	14.2647			0.480591			0.240295	−	0.970700i	$-0.422756\pi$
$881$	14.2647			0.480591			0.240295	+	0.970700i	$0.422756\pi$
$882$	13.2854	−	43.4702i	0.447344	−	1.46372i
$883$	36.7057			1.23525			0.617623	−	0.786474i	$-0.288096\pi$
$883$	36.7057			1.23525			0.617623	+	0.786474i	$0.288096\pi$
$884$	−0.477842	−	2.45567i	−0.0160716	−	0.0825933i
$885$	3.48506	−	6.17771i	0.117149	−	0.207661i
$886$	−1.77701	+	5.81440i	−0.0596998	+	0.195339i
$887$	20.8967	−	20.8967i	0.701644	−	0.701644i	−0.263119	−	0.964763i	$-0.584751\pi$
$887$	20.8967	−	20.8967i	0.701644	−	0.701644i	0.964763	+	0.263119i	$0.0847513\pi$
$888$	−9.70304	+	7.86216i	−0.325613	+	0.263837i
$889$	2.98175			0.100005
$890$	−43.3502	−	1.07696i	−1.45310	−	0.0360999i
$891$	−1.08266	−	1.08266i	−0.0362705	−	0.0362705i
$892$	−10.2791	+	2.00017i	−0.344169	+	0.0669708i
$893$		−	0.260327i		−	0.00871151i
$894$	−22.0051	−	41.3756i	−0.735960	−	1.38381i
$895$	37.3309	+	21.0596i	1.24783	+	0.703945i
$896$	0.618999	+	2.15304i	0.0206793	+	0.0719282i
$897$	−2.28619	+	2.28619i	−0.0763336	+	0.0763336i
$898$	−9.34765	+	30.5857i	−0.311935	+	1.02066i
$899$	−4.25709	−	4.25709i	−0.141982	−	0.141982i
$900$	46.1182	+	2.29288i	1.53727	+	0.0764292i
$901$	6.99915	−	6.99915i	0.233175	−	0.233175i
$902$	−3.41983	+	1.81879i	−0.113868	+	0.0605591i
$903$	−3.17786	−	3.17786i	−0.105753	−	0.105753i
$904$	−4.14658	+	39.5657i	−0.137913	+	1.31594i
$905$	11.2141	−	19.8784i	0.372768	−	0.660779i
$906$	−85.0422	−	25.9907i	−2.82534	−	0.863485i
$907$	34.1766			1.13482			0.567408	−	0.823437i	$-0.307946\pi$
$907$	34.1766			1.13482			0.567408	+	0.823437i	$0.307946\pi$
$908$	−9.45197	+	14.0191i	−0.313675	+	0.465242i
$909$	24.2656	−	24.2656i	0.804840	−	0.804840i
$910$	0.246247	+	0.258794i	0.00816302	+	0.00857894i
$911$		−	11.7387i		−	0.388920i	−0.980910	−	0.194460i	$-0.937705\pi$
$911$		−	11.7387i		−	0.388920i	0.980910	−	0.194460i	$-0.0622955\pi$
$912$	−0.118510	+	0.279501i	−0.00392425	+	0.00925519i
$913$	3.15053	+	3.15053i	0.104267	+	0.104267i
$914$	−7.14908	−	13.4422i	−0.236470	−	0.444629i
$915$	−41.5883	−	23.4614i	−1.37487	−	0.775610i
$916$	−10.6103	−	54.5273i	−0.350574	−	1.80163i
$917$		−	1.53797i		−	0.0507881i
$918$	12.2219	−	6.50007i	0.403384	−	0.214534i
$919$		−	18.7391i		−	0.618146i	−0.951038	−	0.309073i	$-0.899981\pi$
$919$		−	18.7391i		−	0.618146i	0.951038	−	0.309073i	$-0.100019\pi$
$920$	−2.16315	−	12.8052i	−0.0713169	−	0.422176i
$921$		−	43.5422i		−	1.43476i
$922$	12.6731	+	23.8289i	0.417366	+	0.784763i
$923$		−	0.728288i		−	0.0239719i
$924$	−0.906280	−	0.611031i	−0.0298144	−	0.0201015i
$925$	−4.13674	−	6.84611i	−0.136015	−	0.225099i
$926$	−27.9394	+	14.8592i	−0.918146	+	0.488304i
$927$	−12.5644	−	12.5644i	−0.412670	−	0.412670i
$928$	−25.3193	−	21.2240i	−0.831147	−	0.696711i
$929$		−	17.3125i		−	0.568006i	−0.958823	−	0.284003i	$-0.908337\pi$
$929$		−	17.3125i		−	0.568006i	0.958823	−	0.284003i	$-0.0916626\pi$
$930$	−0.223444	+	8.99412i	−0.00732703	+	0.294929i
$931$	−0.135351	+	0.135351i	−0.00443594	+	0.00443594i
$932$	23.0064	−	4.47674i	0.753599	−	0.146640i
$933$	74.3739			2.43489
$934$	5.93641	−	19.4240i	0.194245	−	0.635573i
$935$	−4.72285	+	1.31608i	−0.154454	+	0.0430405i
$936$	5.78900	−	4.69070i	0.189219	−	0.153320i
$937$	−10.2211	−	10.2211i	−0.333907	−	0.333907i	0.520161	−	0.854068i	$-0.325872\pi$
$937$	−10.2211	−	10.2211i	−0.333907	−	0.333907i	−0.854068	+	0.520161i	$0.825872\pi$
$938$	0.151897	+	0.285607i	0.00495960	+	0.00932541i
$939$	−30.4784	+	30.4784i	−0.994624	+	0.994624i
$940$	−18.9452	−	37.8614i	−0.617923	−	1.23490i
$941$	16.7496	+	16.7496i	0.546021	+	0.546021i	0.925288	−	0.379266i	$-0.123824\pi$
$941$	16.7496	+	16.7496i	0.546021	+	0.546021i	−0.379266	+	0.925288i	$0.623824\pi$
$942$	29.9567	+	9.15542i	0.976041	+	0.298300i
$943$	3.97676	−	3.97676i	0.129501	−	0.129501i
$944$	4.23247	+	1.79459i	0.137755	+	0.0584089i
$945$	−0.971218	+	1.72161i	−0.0315937	+	0.0560039i
$946$	10.2678	−	5.46080i	0.333835	−	0.177546i
$947$			37.1258i			1.20643i	0.797579	+	0.603214i	$0.206114\pi$
$947$			37.1258i			1.20643i	−0.797579	+	0.603214i	$0.793886\pi$
$948$	−65.3366	−	44.0512i	−2.12203	−	1.43072i
$949$	−3.43261	−	3.43261i	−0.111427	−	0.111427i
$950$	−0.166932	−	0.0997167i	−0.00541599	−	0.00323524i
$951$	−71.1312			−2.30659
$952$	−0.954100	+	0.773087i	−0.0309226	+	0.0250559i
$953$	−4.52997	+	4.52997i	−0.146740	+	0.146740i	−0.776660	−	0.629920i	$-0.783088\pi$
$953$	−4.52997	+	4.52997i	−0.146740	+	0.146740i	0.629920	+	0.776660i	$0.283088\pi$
$954$	28.1926	+	8.61627i	0.912768	+	0.278962i
$955$	4.99221	+	17.9149i	0.161544	+	0.579712i
$956$	−21.5650	−	14.5395i	−0.697462	−	0.470242i
$957$	16.1194			0.521066
$958$	20.0183	+	6.11803i	0.646762	+	0.197665i
$959$	3.07427			0.0992732
$960$	3.10472	+	49.2744i	0.100204	+	1.59032i
$961$	29.9374			0.965722
$962$	−1.23434	−	0.377242i	−0.0397968	−	0.0121628i
$963$	76.2156			2.45601
$964$	1.70086	+	1.14675i	0.0547811	+	0.0369345i
$965$	−17.0563	−	9.62205i	−0.549062	−	0.309745i
$966$	1.51772	+	0.463849i	0.0488319	+	0.0149241i
$967$	43.3440	−	43.3440i	1.39385	−	1.39385i	0.577354	−	0.816494i	$-0.304085\pi$
$967$	43.3440	−	43.3440i	1.39385	−	1.39385i	0.816494	−	0.577354i	$-0.195915\pi$
$968$	2.19757	−	1.78064i	0.0706326	−	0.0572320i
$969$	−0.166411			−0.00534589
$970$	23.5352	−	22.3942i	0.755670	−	0.719033i
$971$	−5.32899	−	5.32899i	−0.171016	−	0.171016i	0.616410	−	0.787425i	$-0.288586\pi$
$971$	−5.32899	−	5.32899i	−0.171016	−	0.171016i	−0.787425	+	0.616410i	$0.788586\pi$
$972$	−29.2172	−	19.6988i	−0.937141	−	0.631839i
$973$		−	2.00043i		−	0.0641308i
$974$	−12.0751	+	6.42200i	−0.386912	+	0.205774i
$975$	4.07155	+	6.73821i	0.130394	+	0.215796i
$976$	12.0812	−	28.4930i	0.386709	−	0.912038i
$977$	12.0760	−	12.0760i	0.386344	−	0.386344i	−0.487037	−	0.873381i	$-0.661922\pi$
$977$	12.0760	−	12.0760i	0.386344	−	0.386344i	0.873381	+	0.487037i	$0.161922\pi$
$978$	74.7778	+	22.8537i	2.39113	+	0.730782i
$979$	9.69639	+	9.69639i	0.309898	+	0.309898i
$980$	−9.83501	+	29.5351i	−0.314168	+	0.943466i
$981$	41.0586	−	41.0586i	1.31090	−	1.31090i
$982$	3.36066	+	6.31897i	0.107243	+	0.201647i
$983$	−0.832518	−	0.832518i	−0.0265532	−	0.0265532i	0.693706	−	0.720259i	$-0.255977\pi$
$983$	−0.832518	−	0.832518i	−0.0265532	−	0.0265532i	−0.720259	+	0.693706i	$0.755977\pi$
$984$	−16.6122	+	13.4605i	−0.529577	+	0.429105i
$985$	−12.8322	−	46.0491i	−0.408867	−	1.46725i
$986$	5.29309	−	17.3191i	0.168566	−	0.551551i
$987$	5.17372			0.164681
$988$	−0.0307985	+	0.00599298i	−0.000979830	+	0.000190662i
$989$	−11.9400	+	11.9400i	−0.379669	+	0.379669i
$990$	−10.0655	−	10.5783i	−0.319901	−	0.336201i
$991$		−	21.9258i		−	0.696497i	−0.937402	−	0.348249i	$-0.886776\pi$
$991$		−	21.9258i		−	0.696497i	0.937402	−	0.348249i	$-0.113224\pi$
$992$	−5.80880	+	0.511116i	−0.184430	+	0.0162280i
$993$	62.7971	+	62.7971i	1.99281	+	1.99281i
$994$	−0.315624	+	0.167861i	−0.0100110	+	0.00532422i
$995$	15.5397	+	55.7651i	0.492641	+	1.76787i
$996$	20.3924	+	13.7489i	0.646156	+	0.435651i
$997$		−	43.6596i		−	1.38271i	−0.722514	−	0.691357i	$-0.757013\pi$
$997$		−	43.6596i		−	1.38271i	0.722514	−	0.691357i	$-0.242987\pi$
$998$	14.8731	+	27.9655i	0.470799	+	0.885232i
$999$		−	7.14189i		−	0.225959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bk.b.243.11	yes	236
5.2	odd	4		880.2.s.b.67.70	✓	236
16.11	odd	4		880.2.s.b.683.70	yes	236
80.27	even	4	inner	880.2.bk.b.507.11	yes	236

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.s.b.67.70	✓	236	5.2	odd	4
880.2.s.b.683.70	yes	236	16.11	odd	4
880.2.bk.b.243.11	yes	236	1.1	even	1	trivial
880.2.bk.b.507.11	yes	236	80.27	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35246 - 0.413341i) q^{2} +2.75998 q^{3} +(1.65830 + 1.11806i) q^{4} +(2.15400 - 0.600239i) q^{5} +(-3.73277 - 1.14082i) q^{6} +(-0.140016 + 0.140016i) q^{7} +(-1.78064 - 2.19757i) q^{8} +4.61751 q^{9} +(-3.16130 - 0.0785374i) q^{10} +(0.707107 + 0.707107i) q^{11} +(4.57688 + 3.08582i) q^{12} +0.570496i q^{13} +(0.247241 - 0.131492i) q^{14} +(5.94500 - 1.65665i) q^{15} +(1.49990 + 3.70814i) q^{16} +(-1.55040 + 1.55040i) q^{17} +(-6.24500 - 1.90861i) q^{18} +(0.0194447 + 0.0194447i) q^{19} +(4.24307 + 1.41292i) q^{20} +(-0.386443 + 0.386443i) q^{21} +(-0.664057 - 1.24861i) q^{22} +(1.45195 + 1.45195i) q^{23} +(-4.91455 - 6.06526i) q^{24} +(4.27943 - 2.58583i) q^{25} +(0.235810 - 0.771573i) q^{26} +4.46431 q^{27} +(-0.388734 + 0.0756426i) q^{28} +(4.12978 - 4.12978i) q^{29} +(-8.72514 - 0.216762i) q^{30} -1.03083i q^{31} +(-0.495831 - 5.63508i) q^{32} +(1.95160 + 1.95160i) q^{33} +(2.73770 - 1.45601i) q^{34} +(-0.217552 + 0.385638i) q^{35} +(7.65721 + 5.16264i) q^{36} -1.59977i q^{37} +(-0.0182609 - 0.0343355i) q^{38} +1.57456i q^{39} +(-5.15457 - 3.66475i) q^{40} -2.73891i q^{41} +(0.682381 - 0.362915i) q^{42} +8.22338i q^{43} +(0.382009 + 1.96318i) q^{44} +(9.94612 - 2.77161i) q^{45} +(-1.36356 - 2.56386i) q^{46} +(-6.69403 - 6.69403i) q^{47} +(4.13971 + 10.2344i) q^{48} +6.96079i q^{49} +(-6.85658 + 1.72837i) q^{50} +(-4.27907 + 4.27907i) q^{51} +(-0.637847 + 0.946053i) q^{52} -4.51442 q^{53} +(-6.03780 - 1.84528i) q^{54} +(1.94754 + 1.09867i) q^{55} +(0.557014 + 0.0583765i) q^{56} +(0.0536671 + 0.0536671i) q^{57} +(-7.29237 + 3.87835i) q^{58} +(0.812680 - 0.812680i) q^{59} +(11.7108 + 3.89963i) q^{60} +(-5.47096 - 5.47096i) q^{61} +(-0.426084 + 1.39415i) q^{62} +(-0.646527 + 0.646527i) q^{63} +(-1.65862 + 7.82617i) q^{64} +(0.342434 + 1.22885i) q^{65} +(-1.83279 - 3.44615i) q^{66} +1.15518i q^{67} +(-4.30445 + 0.837590i) q^{68} +(4.00737 + 4.00737i) q^{69} +(0.453630 - 0.431637i) q^{70} -1.27659 q^{71} +(-8.22214 - 10.1473i) q^{72} +(-6.01688 + 6.01688i) q^{73} +(-0.661253 + 2.16363i) q^{74} +(11.8111 - 7.13685i) q^{75} +(0.0105049 + 0.0539854i) q^{76} -0.198013 q^{77} +(0.650831 - 2.12953i) q^{78} -14.2754 q^{79} +(5.45656 + 7.08703i) q^{80} -1.53111 q^{81} +(-1.13210 + 3.70426i) q^{82} +4.45552 q^{83} +(-1.07290 + 0.208772i) q^{84} +(-2.40895 + 4.27017i) q^{85} +(3.39906 - 11.1218i) q^{86} +(11.3981 - 11.3981i) q^{87} +(0.294812 - 2.81302i) q^{88} +13.7128 q^{89} +(-14.5974 - 0.362647i) q^{90} +(-0.0798787 - 0.0798787i) q^{91} +(0.784406 + 4.03114i) q^{92} -2.84507i q^{93} +(6.28649 + 11.8203i) q^{94} +(0.0535554 + 0.0302124i) q^{95} +(-1.36848 - 15.5527i) q^{96} +(-7.26431 + 7.26431i) q^{97} +(2.87718 - 9.41419i) q^{98} +(3.26507 + 3.26507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) \) 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

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