LMFDB - Embedded newform 110.2.k.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(7,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("110.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$110 = 2 \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	110.k (of order $20$ , degree $8$ , 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:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	110.17
Dual form			110.2.k.a.13.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 + 0.453990i) q^{2} +(-0.216404 + 0.0342750i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.60893 - 1.55285i) q^{5} +(-0.208378 - 0.0677061i) q^{6} +(-0.0165943 + 0.104772i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-2.80751 + 0.912216i) q^{9} +(2.13855 - 0.653156i) q^{10} +(-0.733646 + 3.23447i) q^{11} +(-0.154928 - 0.154928i) q^{12} +(0.904452 - 1.77509i) q^{13} +(-0.0623513 + 0.0858193i) q^{14} +(-0.294956 + 0.391189i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-2.43444 - 4.77786i) q^{17} +(-2.91565 - 0.461794i) q^{18} +(-3.72925 - 2.70946i) q^{19} +(2.20199 + 0.388914i) q^{20} -0.0232420i q^{21} +(-2.12210 + 2.54886i) q^{22} +(-1.26420 + 1.26420i) q^{23} +(-0.0677061 - 0.208378i) q^{24} +(0.177332 - 4.99685i) q^{25} +(1.61175 - 1.17100i) q^{26} +(1.16195 - 0.592045i) q^{27} +(-0.0945166 + 0.0481586i) q^{28} +(-3.14143 + 2.28238i) q^{29} +(-0.440404 + 0.214645i) q^{30} +(2.80221 + 8.62430i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.0479025 - 0.725097i) q^{33} -5.36232i q^{34} +(0.135996 + 0.194340i) q^{35} +(-2.38821 - 1.73514i) q^{36} +(9.02408 + 1.42927i) q^{37} +(-2.09272 - 4.10719i) q^{38} +(-0.134886 + 0.415136i) q^{39} +(1.78542 + 1.34621i) q^{40} +(0.361961 - 0.498197i) q^{41} +(0.0105516 - 0.0207087i) q^{42} +(2.10353 + 2.10353i) q^{43} +(-3.04796 + 1.30764i) q^{44} +(-3.10057 + 5.82733i) q^{45} +(-1.70035 + 0.552477i) q^{46} +(-1.38892 - 8.76927i) q^{47} +(0.0342750 - 0.216404i) q^{48} +(6.64669 + 2.15964i) q^{49} +(2.42653 - 4.37172i) q^{50} +(0.690585 + 0.950509i) q^{51} +(1.96770 - 0.311653i) q^{52} +(-7.17360 - 3.65513i) q^{53} +1.30409 q^{54} +(3.84224 + 6.34328i) q^{55} -0.106078 q^{56} +(0.899893 + 0.458518i) q^{57} +(-3.83521 + 0.607438i) q^{58} +(6.35785 + 8.75082i) q^{59} +(-0.489849 - 0.00868934i) q^{60} +(-0.692750 - 0.225088i) q^{61} +(-1.41857 + 8.95649i) q^{62} +(-0.0489864 - 0.309288i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-1.30124 - 4.26047i) q^{65} +(0.371869 - 0.624319i) q^{66} +(1.43736 + 1.43736i) q^{67} +(2.43444 - 4.77786i) q^{68} +(0.230248 - 0.316909i) q^{69} +(0.0329450 + 0.234900i) q^{70} +(0.219183 - 0.674575i) q^{71} +(-1.34018 - 2.63025i) q^{72} +(13.1937 + 2.08968i) q^{73} +(7.39164 + 5.37034i) q^{74} +(0.132892 + 1.08742i) q^{75} -4.60961i q^{76} +(-0.326708 - 0.130540i) q^{77} +(-0.308652 + 0.308652i) q^{78} +(-2.31524 - 7.12558i) q^{79} +(0.979658 + 2.01004i) q^{80} +(6.93348 - 5.03747i) q^{81} +(0.548687 - 0.279570i) q^{82} +(-5.07282 + 2.58473i) q^{83} +(0.0188031 - 0.0136613i) q^{84} +(-11.3361 - 3.90695i) q^{85} +(0.919276 + 2.82924i) q^{86} +(0.601589 - 0.601589i) q^{87} +(-3.30941 - 0.218632i) q^{88} -0.464658i q^{89} +(-5.40818 + 3.78456i) q^{90} +(0.170971 + 0.124218i) q^{91} +(-1.76584 - 0.279682i) q^{92} +(-0.902007 - 1.77029i) q^{93} +(2.74363 - 8.44403i) q^{94} +(-10.2075 + 1.43162i) q^{95} +(0.128785 - 0.177257i) q^{96} +(0.809810 - 1.58934i) q^{97} +(4.94179 + 4.94179i) q^{98} +(-0.890812 - 9.75005i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36}+ \cdots + 72 q^{97}+O(q^{100})$ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$ .

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{10}\right)$

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

)

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

$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$2$	0.891007	+	0.453990i	0.630037	+	0.321020i
$3$	−0.216404	+	0.0342750i	−0.124941	+	0.0197887i	−0.218592	−	0.975816i	$-0.570146\pi$
$3$	−0.216404	+	0.0342750i	−0.124941	+	0.0197887i	0.0936508	+	0.995605i	$0.470146\pi$
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$	1.60893	−	1.55285i	0.719537	−	0.694454i
$5$	1.60893	−	1.55285i	0.719537	−	0.694454i
$6$	−0.208378	−	0.0677061i	−0.0850700	−	0.0276409i
$7$	−0.0165943	+	0.104772i	−0.00627207	+	0.0396003i	−0.990626	−	0.136603i	$-0.956382\pi$
$7$	−0.0165943	+	0.104772i	−0.00627207	+	0.0396003i	0.984354	+	0.176203i	$0.0563816\pi$
$8$	0.156434	+	0.987688i	0.0553079	+	0.349201i
$9$	−2.80751	+	0.912216i	−0.935838	+	0.304072i
$10$	2.13855	−	0.653156i	0.676268	−	0.206546i
$11$	−0.733646	+	3.23447i	−0.221203	+	0.975228i
$11$	−0.733646	+	3.23447i	−0.221203	+	0.975228i
$12$	−0.154928	−	0.154928i	−0.0447239	−	0.0447239i
$13$	0.904452	−	1.77509i	0.250850	−	0.492321i	−0.730903	−	0.682481i	$-0.760901\pi$
$13$	0.904452	−	1.77509i	0.250850	−	0.492321i	0.981753	+	0.190161i	$0.0609009\pi$
$14$	−0.0623513	+	0.0858193i	−0.0166641	+	0.0229362i
$15$	−0.294956	+	0.391189i	−0.0761573	+	0.101004i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−2.43444	−	4.77786i	−0.590439	−	1.15880i	−0.972115	−	0.234506i	$-0.924653\pi$
$17$	−2.43444	−	4.77786i	−0.590439	−	1.15880i	0.381676	−	0.924296i	$-0.375347\pi$
$18$	−2.91565	−	0.461794i	−0.687225	−	0.108846i
$19$	−3.72925	−	2.70946i	−0.855549	−	0.621593i	0.0711211	−	0.997468i	$-0.477342\pi$
$19$	−3.72925	−	2.70946i	−0.855549	−	0.621593i	−0.926671	+	0.375875i	$0.877342\pi$
$20$	2.20199	+	0.388914i	0.492379	+	0.0869638i
$21$		−	0.0232420i		−	0.00507181i
$22$	−2.12210	+	2.54886i	−0.452433	+	0.543419i
$23$	−1.26420	+	1.26420i	−0.263605	+	0.263605i	−0.826517	−	0.562912i	$-0.809681\pi$
$23$	−1.26420	+	1.26420i	−0.263605	+	0.263605i	0.562912	+	0.826517i	$0.309681\pi$
$24$	−0.0677061	−	0.208378i	−0.0138205	−	0.0425350i
$25$	0.177332	−	4.99685i	0.0354665	−	0.999371i
$26$	1.61175	−	1.17100i	0.316089	−	0.229652i
$27$	1.16195	−	0.592045i	0.223618	−	0.113939i
$28$	−0.0945166	+	0.0481586i	−0.0178620	+	0.00910112i
$29$	−3.14143	+	2.28238i	−0.583348	+	0.423827i	−0.839930	−	0.542695i	$-0.817404\pi$
$29$	−3.14143	+	2.28238i	−0.583348	+	0.423827i	0.256581	+	0.966523i	$0.417404\pi$
$30$	−0.440404	+	0.214645i	−0.0804063	+	0.0391885i
$31$	2.80221	+	8.62430i	0.503291	+	1.54897i	0.803625	+	0.595136i	$0.202902\pi$
$31$	2.80221	+	8.62430i	0.503291	+	1.54897i	−0.300334	+	0.953834i	$0.597098\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.0479025	−	0.725097i	0.00833876	−	0.126223i
$34$		−	5.36232i		−	0.919631i
$35$	0.135996	+	0.194340i	0.0229876	+	0.0328495i
$36$	−2.38821	−	1.73514i	−0.398036	−	0.289190i
$37$	9.02408	+	1.42927i	1.48355	+	0.234971i	0.845065	−	0.534664i	$-0.179562\pi$
$37$	9.02408	+	1.42927i	1.48355	+	0.234971i	0.638484	+	0.769635i	$0.279562\pi$
$38$	−2.09272	−	4.10719i	−0.339484	−	0.666275i
$39$	−0.134886	+	0.415136i	−0.0215990	+	0.0664750i
$40$	1.78542	+	1.34621i	0.282300	+	0.212854i
$41$	0.361961	−	0.498197i	0.0565289	−	0.0778053i	−0.779817	−	0.626008i	$-0.784688\pi$
$41$	0.361961	−	0.498197i	0.0565289	−	0.0778053i	0.836346	+	0.548203i	$0.184688\pi$
$42$	0.0105516	−	0.0207087i	0.00162815	−	0.00319543i
$43$	2.10353	+	2.10353i	0.320785	+	0.320785i	0.849068	−	0.528283i	$-0.177164\pi$
$43$	2.10353	+	2.10353i	0.320785	+	0.320785i	−0.528283	+	0.849068i	$0.677164\pi$
$44$	−3.04796	+	1.30764i	−0.459498	+	0.197134i
$45$	−3.10057	+	5.82733i	−0.462206	+	0.868688i
$46$	−1.70035	+	0.552477i	−0.250703	+	0.0814583i
$47$	−1.38892	−	8.76927i	−0.202594	−	1.27913i	−0.853949	−	0.520356i	$-0.825799\pi$
$47$	−1.38892	−	8.76927i	−0.202594	−	1.27913i	0.651355	−	0.758773i	$-0.274201\pi$
$48$	0.0342750	−	0.216404i	0.00494718	−	0.0312352i
$49$	6.64669	+	2.15964i	0.949528	+	0.308520i
$50$	2.42653	−	4.37172i	0.343163	−	0.618255i
$51$	0.690585	+	0.950509i	0.0967012	+	0.133098i
$52$	1.96770	−	0.311653i	0.272871	−	0.0432185i
$53$	−7.17360	−	3.65513i	−0.985370	−	0.502071i	−0.114415	−	0.993433i	$-0.536499\pi$
$53$	−7.17360	−	3.65513i	−0.985370	−	0.502071i	−0.870955	+	0.491362i	$0.836499\pi$
$54$	1.30409			0.177464
$55$	3.84224	+	6.34328i	0.518088	+	0.855327i
$56$	−0.106078			−0.0141753
$57$	0.899893	+	0.458518i	0.119194	+	0.0607322i
$58$	−3.83521	+	0.607438i	−0.503588	+	0.0797605i
$59$	6.35785	+	8.75082i	0.827721	+	1.13926i	0.988343	+	0.152244i	$0.0486500\pi$
$59$	6.35785	+	8.75082i	0.827721	+	1.13926i	−0.160622	+	0.987016i	$0.551350\pi$
$60$	−0.489849	−	0.00868934i	−0.0632392	−	0.00112179i
$61$	−0.692750	−	0.225088i	−0.0886976	−	0.0288196i	0.264332	−	0.964432i	$-0.414849\pi$
$61$	−0.692750	−	0.225088i	−0.0886976	−	0.0288196i	−0.353030	+	0.935612i	$0.614849\pi$
$62$	−1.41857	+	8.95649i	−0.180158	+	1.13747i
$63$	−0.0489864	−	0.309288i	−0.00617170	−	0.0389666i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	−1.30124	−	4.26047i	−0.161398	−	0.528447i
$66$	0.371869	−	0.624319i	0.0457739	−	0.0768484i
$67$	1.43736	+	1.43736i	0.175601	+	0.175601i	0.789435	−	0.613834i	$-0.210374\pi$
$67$	1.43736	+	1.43736i	0.175601	+	0.175601i	−0.613834	+	0.789435i	$0.710374\pi$
$68$	2.43444	−	4.77786i	0.295220	−	0.579401i
$69$	0.230248	−	0.316909i	0.0277186	−	0.0381514i
$70$	0.0329450	+	0.234900i	0.00393769	+	0.0280759i
$71$	0.219183	−	0.674575i	0.0260122	−	0.0800573i	−0.937208	−	0.348772i	$-0.886599\pi$
$71$	0.219183	−	0.674575i	0.0260122	−	0.0800573i	0.963220	+	0.268715i	$0.0865988\pi$
$72$	−1.34018	−	2.63025i	−0.157941	−	0.309978i
$73$	13.1937	+	2.08968i	1.54421	+	0.244578i	0.869658	−	0.493654i	$-0.164339\pi$
$73$	13.1937	+	2.08968i	1.54421	+	0.244578i	0.674547	+	0.738232i	$0.264339\pi$
$74$	7.39164	+	5.37034i	0.859260	+	0.624289i
$75$	0.132892	+	1.08742i	0.0153450	+	0.125564i
$76$		−	4.60961i		−	0.528759i
$77$	−0.326708	−	0.130540i	−0.0372319	−	0.0148764i
$78$	−0.308652	+	0.308652i	−0.0349480	+	0.0349480i
$79$	−2.31524	−	7.12558i	−0.260485	−	0.801691i	−0.992699	−	0.120616i	$-0.961513\pi$
$79$	−2.31524	−	7.12558i	−0.260485	−	0.801691i	0.732214	−	0.681075i	$-0.238487\pi$
$80$	0.979658	+	2.01004i	0.109529	+	0.224730i
$81$	6.93348	−	5.03747i	0.770387	−	0.559719i
$82$	0.548687	−	0.279570i	0.0605923	−	0.0308733i
$83$	−5.07282	+	2.58473i	−0.556814	+	0.283711i	−0.709666	−	0.704538i	$-0.751154\pi$
$83$	−5.07282	+	2.58473i	−0.556814	+	0.283711i	0.152852	+	0.988249i	$0.451154\pi$
$84$	0.0188031	−	0.0136613i	0.00205159	−	0.00149057i
$85$	−11.3361	−	3.90695i	−1.22958	−	0.423768i
$86$	0.919276	+	2.82924i	0.0991281	+	0.305085i
$87$	0.601589	−	0.601589i	0.0644971	−	0.0644971i
$88$	−3.30941	−	0.218632i	−0.352784	−	0.0233062i
$89$		−	0.464658i		−	0.0492537i	−0.999697	−	0.0246268i	$-0.992160\pi$
$89$		−	0.464658i		−	0.0492537i	0.999697	−	0.0246268i	$-0.00783976\pi$
$90$	−5.40818	+	3.78456i	−0.570072	+	0.398928i
$91$	0.170971	+	0.124218i	0.0179227	+	0.0130216i
$92$	−1.76584	−	0.279682i	−0.184102	−	0.0291589i
$93$	−0.902007	−	1.77029i	−0.0935338	−	0.183570i
$94$	2.74363	−	8.44403i	0.282984	−	0.870935i
$95$	−10.2075	+	1.43162i	−1.04727	+	0.146881i
$96$	0.128785	−	0.177257i	0.0131440	−	0.0180912i
$97$	0.809810	−	1.58934i	0.0822238	−	0.161373i	−0.846234	−	0.532812i	$-0.821135\pi$
$97$	0.809810	−	1.58934i	0.0822238	−	0.161373i	0.928458	+	0.371439i	$0.121135\pi$
$98$	4.94179	+	4.94179i	0.499196	+	0.499196i
$99$	−0.890812	−	9.75005i	−0.0895300	−	0.979917i
$100$	4.14677	−	2.79361i	0.414677	−	0.279361i
$101$	−9.45029	+	3.07058i	−0.940339	+	0.305535i	−0.738784	−	0.673943i	$-0.764599\pi$
$101$	−9.45029	+	3.07058i	−0.940339	+	0.305535i	−0.201555	+	0.979477i	$0.564599\pi$
$102$	0.183794	+	1.16043i	0.0181983	+	0.114900i
$103$	−0.499214	+	3.15191i	−0.0491890	+	0.310567i	0.950811	+	0.309773i	$0.100253\pi$
$103$	−0.499214	+	3.15191i	−0.0491890	+	0.310567i	−1.00000		0.000794658i	$0.999747\pi$
$104$	1.89472	+	0.615632i	0.185793	+	0.0603677i
$105$	−0.0360912	−	0.0373948i	−0.00352214	−	0.00364935i
$106$	−4.73233	−	6.51349i	−0.459645	−	0.632646i
$107$	−18.0361	+	2.85664i	−1.74361	+	0.276161i	−0.945329	−	0.326118i	$-0.894259\pi$
$107$	−18.0361	+	2.85664i	−1.74361	+	0.276161i	−0.798285	+	0.602279i	$0.794259\pi$
$108$	1.16195	+	0.592045i	0.111809	+	0.0569696i
$109$	−6.47671			−0.620357			−0.310178	−	0.950678i	$-0.600389\pi$
$109$	−6.47671			−0.620357			−0.310178	+	0.950678i	$0.600389\pi$
$110$	0.543675	+	7.39624i	0.0518374	+	0.705204i
$111$	−2.00184			−0.190006
$112$	−0.0945166	−	0.0481586i	−0.00893098	−	0.00455056i
$113$	14.8741	−	2.35583i	1.39924	−	0.221618i	0.589198	−	0.807989i	$-0.299444\pi$
$113$	14.8741	−	2.35583i	1.39924	−	0.221618i	0.810043	+	0.586371i	$0.199444\pi$
$114$	0.593647	+	0.817085i	0.0556002	+	0.0765271i
$115$	−0.0709044	+	3.99713i	−0.00661187	+	0.372735i
$116$	−3.69297	−	1.19992i	−0.342884	−	0.111410i
$117$	−0.919998	+	5.80864i	−0.0850538	+	0.537009i
$118$	1.69209	+	10.6834i	0.155770	+	0.983491i
$119$	0.540986	−	0.175777i	0.0495921	−	0.0161135i
$120$	−0.432514	−	0.230129i	−0.0394829	−	0.0210078i
$121$	−9.92353	−	4.74590i	−0.902139	−	0.431446i
$122$	−0.515057	−	0.515057i	−0.0466311	−	0.0466311i
$123$	−0.0612542	+	0.120218i	−0.00552311	+	0.0108397i
$124$	−5.33011	+	7.33627i	−0.478658	+	0.658817i
$125$	−7.47403	−	8.31497i	−0.668498	−	0.743714i
$126$	0.0967665	−	0.297817i	0.00862065	−	0.0265316i
$127$	−0.262989	−	0.516145i	−0.0233365	−	0.0458005i	0.879044	−	0.476741i	$-0.158182\pi$
$127$	−0.262989	−	0.516145i	−0.0233365	−	0.0458005i	−0.902380	+	0.430940i	$0.858182\pi$
$128$	−0.987688	−	0.156434i	−0.0873001	−	0.0138270i
$129$	−0.527311	−	0.383114i	−0.0464272	−	0.0337313i
$130$	0.774805	−	4.38686i	0.0679549	−	0.384753i
$131$		−	21.1341i		−	1.84649i	−0.384207	−	0.923247i	$-0.625525\pi$
$131$		−	21.1341i		−	1.84649i	0.384207	−	0.923247i	$-0.374475\pi$
$132$	0.614772	−	0.387447i	0.0535091	−	0.0337230i
$133$	0.345761	−	0.345761i	0.0299813	−	0.0299813i
$134$	0.628149	+	1.93324i	0.0542638	+	0.167007i
$135$	0.950151	−	2.75690i	0.0817760	−	0.237276i
$136$	4.33821	−	3.15189i	0.371998	−	0.270273i
$137$	−1.94100	+	0.988989i	−0.165831	+	0.0844950i	−0.534936	−	0.844893i	$-0.679664\pi$
$137$	−1.94100	+	0.988989i	−0.165831	+	0.0844950i	0.369105	+	0.929388i	$0.379664\pi$
$138$	0.349027	−	0.177838i	0.0297111	−	0.0151386i
$139$	9.71730	−	7.06003i	0.824211	−	0.598824i	−0.0937049	−	0.995600i	$-0.529871\pi$
$139$	9.71730	−	7.06003i	0.824211	−	0.598824i	0.917915	+	0.396776i	$0.129871\pi$
$140$	−0.0772879	+	0.224254i	−0.00653202	+	0.0189529i
$141$	0.601134	+	1.85010i	0.0506246	+	0.155806i
$142$	0.501544	−	0.501544i	0.0420886	−	0.0420886i
$143$	5.07791	+	4.22770i	0.424636	+	0.353538i
$144$		−	2.95199i		−	0.246000i
$145$	−1.51016	+	8.55035i	−0.125412	+	0.710068i
$146$	10.8070	+	7.85173i	0.894392	+	0.649814i
$147$	−1.51239	−	0.239540i	−0.124740	−	0.0197569i
$148$	4.14791	+	8.14074i	0.340956	+	0.669165i
$149$	−3.61131	+	11.1145i	−0.295850	+	0.910532i	0.687085	+	0.726577i	$0.258890\pi$
$149$	−3.61131	+	11.1145i	−0.295850	+	0.910532i	−0.982935	+	0.183955i	$0.941110\pi$
$150$	−0.375270	+	1.02923i	−0.0306406	+	0.0840361i
$151$	12.6050	−	17.3493i	1.02578	−	1.41186i	0.117708	−	0.993048i	$-0.462445\pi$
$151$	12.6050	−	17.3493i	1.02578	−	1.41186i	0.908071	−	0.418816i	$-0.137555\pi$
$152$	2.09272	−	4.10719i	0.169742	−	0.333137i
$153$	11.1932	+	11.1932i	0.904915	+	0.904915i
$154$	−0.231836	−	0.264634i	−0.0186818	−	0.0213248i
$155$	17.9008	+	9.52453i	1.43783	+	0.765029i
$156$	−0.415136	+	0.134886i	−0.0332375	+	0.0107995i
$157$	2.39160	+	15.1000i	0.190871	+	1.20511i	0.878031	+	0.478604i	$0.158857\pi$
$157$	2.39160	+	15.1000i	0.190871	+	1.20511i	−0.687160	+	0.726506i	$0.741143\pi$
$158$	1.17205	−	7.40004i	0.0932434	−	0.588716i
$159$	1.67768	+	0.545110i	0.133048	+	0.0432300i
$160$	−0.0396590	+	2.23572i	−0.00313532	+	0.176749i
$161$	−0.111475	−	0.153432i	−0.00878547	−	0.0120922i
$162$	8.46474	−	1.34068i	0.665053	−	0.105334i
$163$	−17.9490	−	9.14546i	−1.40587	−	0.716328i	−0.423963	−	0.905679i	$-0.639362\pi$
$163$	−17.9490	−	9.14546i	−1.40587	−	0.716328i	−0.981909	+	0.189351i	$0.939362\pi$
$164$	0.615806			0.0480863
$165$	−1.04889	−	1.24102i	−0.0816562	−	0.0966131i
$166$	−5.69336			−0.441890
$167$	7.49534	+	3.81907i	0.580007	+	0.295528i	0.719274	−	0.694727i	$-0.244475\pi$
$167$	7.49534	+	3.81907i	0.580007	+	0.295528i	−0.139267	+	0.990255i	$0.544475\pi$
$168$	0.0229558	−	0.00363584i	0.00177108	−	0.000280511i
$169$	5.30831	+	7.30626i	0.408331	+	0.562020i
$170$	−8.32687	−	8.62762i	−0.638641	−	0.661708i
$171$	12.9415	+	4.20496i	0.989665	+	0.321562i
$172$	−0.465368	+	2.93822i	−0.0354839	+	0.224037i
$173$	1.08335	+	6.83998i	0.0823654	+	0.520034i	0.994031	+	0.109101i	$0.0347972\pi$
$173$	1.08335	+	6.83998i	0.0823654	+	0.520034i	−0.911665	+	0.410933i	$0.865203\pi$
$174$	0.809135	−	0.262904i	0.0613404	−	0.0199307i
$175$	0.520590	+	0.101499i	0.0393529	+	0.00767260i
$176$	−2.84945	−	1.69724i	−0.214785	−	0.127935i
$177$	−1.67580	−	1.67580i	−0.125961	−	0.125961i
$178$	0.210951	−	0.414014i	0.0158114	−	0.0310316i
$179$	0.385794	−	0.531001i	0.0288356	−	0.0396888i	−0.794356	−	0.607453i	$-0.792191\pi$
$179$	0.385794	−	0.531001i	0.0288356	−	0.0396888i	0.823191	+	0.567764i	$0.192191\pi$
$180$	−6.53688	+	0.916808i	−0.487230	+	0.0683348i
$181$	0.292688	−	0.900800i	0.0217553	−	0.0669559i	−0.939589	−	0.342303i	$-0.888793\pi$
$181$	0.292688	−	0.900800i	0.0217553	−	0.0669559i	0.961345	+	0.275348i	$0.0887929\pi$
$182$	0.0959429	+	0.188299i	0.00711176	+	0.0139576i
$183$	0.157629	+	0.0249660i	0.0116523	+	0.00184554i
$184$	−1.44640	−	1.05087i	−0.106630	−	0.0774715i
$185$	16.7386	−	11.7134i	1.23065	−	0.861187i
$186$		−	1.98684i		−	0.145682i
$187$	17.2399	−	4.36886i	1.26070	−	0.319483i
$188$	6.27810	−	6.27810i	0.457878	−	0.457878i
$189$	0.0427482	+	0.131565i	0.00310947	+	0.00956997i
$190$	−9.74489	−	3.35853i	−0.706969	−	0.243653i
$191$	−9.79405	+	7.11579i	−0.708672	+	0.514881i	−0.882745	−	0.469852i	$-0.844307\pi$
$191$	−9.79405	+	7.11579i	−0.708672	+	0.514881i	0.174073	+	0.984733i	$0.444307\pi$
$192$	0.195221	−	0.0994700i	0.0140889	−	0.00717863i
$193$	−8.73594	+	4.45118i	−0.628827	+	0.320403i	−0.739199	−	0.673487i	$-0.764796\pi$
$193$	−8.73594	+	4.45118i	−0.628827	+	0.320403i	0.110372	+	0.993890i	$0.464796\pi$
$194$	1.44309	−	1.04847i	0.103608	−	0.0752756i
$195$	0.427621	+	0.877384i	0.0306226	+	0.0628308i
$196$	2.15964	+	6.64669i	0.154260	+	0.474764i
$197$	−16.8687	+	16.8687i	−1.20185	+	1.20185i	−0.228242	+	0.973604i	$0.573298\pi$
$197$	−16.8687	+	16.8687i	−1.20185	+	1.20185i	−0.973604	+	0.228242i	$0.926702\pi$
$198$	3.63271	−	9.09178i	0.258165	−	0.646124i
$199$		−	4.39456i		−	0.311522i	−0.987795	−	0.155761i	$-0.950217\pi$
$199$		−	4.39456i		−	0.311522i	0.987795	−	0.155761i	$-0.0497830\pi$
$200$	4.96308	−	0.606531i	0.350942	−	0.0428882i
$201$	−0.360316	−	0.261785i	−0.0254147	−	0.0184649i
$202$	−9.81428	−	1.55443i	−0.690531	−	0.109369i
$203$	−0.187001	−	0.367010i	−0.0131249	−	0.0257590i
$204$	−0.363062	+	1.11739i	−0.0254194	+	0.0782329i
$205$	−0.191252	−	1.36364i	−0.0133576	−	0.0952405i
$206$	−1.87574	+	2.58174i	−0.130689	+	0.179878i
$207$	2.39604	−	4.70250i	0.166536	−	0.326846i
$208$	1.40872	+	1.40872i	0.0976770	+	0.0976770i
$209$	11.4996	−	10.0744i	0.795445	−	0.696858i
$210$	−0.0151806	−	0.0497040i	−0.00104756	−	0.00342990i
$211$	−16.9189	+	5.49730i	−1.16475	+	0.378449i	−0.826680	−	0.562672i	$-0.809773\pi$
$211$	−16.9189	+	5.49730i	−1.16475	+	0.378449i	−0.338068	+	0.941122i	$0.609773\pi$
$212$	−1.25947	−	7.95200i	−0.0865010	−	0.546146i
$213$	−0.0243109	+	0.153493i	−0.00166576	+	0.0105172i
$214$	−17.3672	−	5.64293i	−1.18719	−	0.385743i
$215$	6.65090	+	0.117979i	0.453588	+	0.00804611i
$216$	0.766526	+	1.05503i	0.0521555	+	0.0717858i
$217$	−0.950090	+	0.150479i	−0.0644963	+	0.0102152i
$218$	−5.77079	−	2.94037i	−0.390847	−	0.199147i
$219$	−2.92679			−0.197774
$220$	−2.87341	+	6.83692i	−0.193725	+	0.460945i
$221$	−10.6830			−0.718614
$222$	−1.78365	−	0.908814i	−0.119711	−	0.0609956i
$223$	−22.1438	+	3.50724i	−1.48286	+	0.234862i	−0.844782	−	0.535110i	$-0.820270\pi$
$223$	−22.1438	+	3.50724i	−1.48286	+	0.234862i	−0.638078	+	0.769972i	$0.720270\pi$
$224$	−0.0623513	−	0.0858193i	−0.00416602	−	0.00573404i
$225$	4.06035	+	14.1905i	0.270690	+	0.946033i
$226$	14.3225	+	4.65365i	0.952717	+	0.309556i
$227$	3.31724	−	20.9442i	0.220173	−	1.39012i	−0.591642	−	0.806201i	$-0.701520\pi$
$227$	3.31724	−	20.9442i	0.220173	−	1.39012i	0.811814	−	0.583916i	$-0.198480\pi$
$228$	0.157995	+	0.997539i	0.0104634	+	0.0660636i
$229$	−14.3864	+	4.67441i	−0.950678	+	0.308894i	−0.742991	−	0.669301i	$-0.766594\pi$
$229$	−14.3864	+	4.67441i	−0.950678	+	0.308894i	−0.207687	+	0.978195i	$0.566594\pi$
$230$	−1.87784	+	3.52928i	−0.123821	+	0.232714i
$231$	0.0751753	+	0.0170514i	0.00494617	+	0.00112190i
$232$	−2.74571	−	2.74571i	−0.180265	−	0.180265i
$233$	10.9477	−	21.4862i	0.717211	−	1.40761i	−0.187796	−	0.982208i	$-0.560134\pi$
$233$	10.9477	−	21.4862i	0.717211	−	1.40761i	0.905007	−	0.425397i	$-0.139866\pi$
$234$	−3.45679	+	4.75786i	−0.225978	+	0.311031i
$235$	−15.8520	−	11.9524i	−1.03407	−	0.779688i
$236$	−3.34252	+	10.2872i	−0.217579	+	0.669640i
$237$	0.745258	+	1.46265i	0.0484097	+	0.0950093i
$238$	0.561824	+	0.0889841i	0.0364176	+	0.00576798i
$239$	20.9893	+	15.2496i	1.35769	+	0.986418i	0.998588	+	0.0531181i	$0.0169160\pi$
$239$	20.9893	+	15.2496i	1.35769	+	0.986418i	0.359099	+	0.933299i	$0.383084\pi$
$240$	−0.280896	−	0.401404i	−0.0181318	−	0.0259105i
$241$			19.4981i			1.25598i	0.778221	+	0.627991i	$0.216123\pi$
$241$			19.4981i			1.25598i	−0.778221	+	0.627991i	$0.783877\pi$
$242$	−6.68733	−	8.73382i	−0.429878	−	0.561431i
$243$	−4.09417	+	4.09417i	−0.262641	+	0.262641i
$244$	−0.225088	−	0.692750i	−0.0144098	−	0.0443488i
$245$	14.0477	−	6.84658i	0.897473	−	0.437412i
$246$	−0.109156	+	0.0793063i	−0.00695952	+	0.00505639i
$247$	−8.18246	+	4.16917i	−0.520638	+	0.265278i
$248$	−8.07976	+	4.11684i	−0.513065	+	0.261420i
$249$	1.00919	−	0.733217i	0.0639546	−	0.0464657i
$250$	−2.88449	−	10.8018i	−0.182431	−	0.683168i
$251$	6.30723	+	19.4117i	0.398109	+	1.22525i	0.926514	+	0.376261i	$0.122790\pi$
$251$	6.30723	+	19.4117i	0.398109	+	1.22525i	−0.528405	+	0.848992i	$0.677210\pi$
$252$	0.221426	−	0.221426i	0.0139485	−	0.0139485i
$253$	−3.16154	−	5.01650i	−0.198765	−	0.315385i
$254$		−	0.579284i		−	0.0363475i
$255$	2.58710	+	0.456932i	0.162010	+	0.0286142i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−11.8903	−	1.88324i	−0.741696	−	0.117473i	−0.225859	−	0.974160i	$-0.572519\pi$
$257$	−11.8903	−	1.88324i	−0.741696	−	0.117473i	−0.515837	+	0.856687i	$0.672519\pi$
$258$	−0.295908	−	0.580751i	−0.0184224	−	0.0361560i
$259$	−0.299497	+	0.921757i	−0.0186098	+	0.0572752i
$260$	2.68195	−	3.55697i	0.166327	−	0.220594i
$261$	6.73757	−	9.27347i	0.417045	−	0.574014i
$262$	9.59468	−	18.8306i	0.592761	−	1.16336i
$263$	−15.8387	−	15.8387i	−0.976655	−	0.976655i	0.0230786	−	0.999734i	$-0.492653\pi$
$263$	−15.8387	−	15.8387i	−0.976655	−	0.976655i	−0.999734	+	0.0230786i	$0.992653\pi$
$264$	0.723664	−	0.0661174i	0.0445384	−	0.00406925i
$265$	−17.2177	+	5.25864i	−1.05768	+	0.323036i
$266$	0.465048	−	0.151103i	0.0285139	−	0.00926473i
$267$	0.0159262	+	0.100554i	0.000974667	+	0.00615380i
$268$	−0.317990	+	2.00771i	−0.0194243	+	0.122640i
$269$	−5.93360	−	1.92794i	−0.361778	−	0.117549i	0.122487	−	0.992470i	$-0.460913\pi$
$269$	−5.93360	−	1.92794i	−0.361778	−	0.117549i	−0.484265	+	0.874921i	$0.660913\pi$
$270$	2.09820	−	2.02505i	0.127692	−	0.123241i
$271$	−9.59850	−	13.2112i	−0.583067	−	0.802523i	0.410960	−	0.911653i	$-0.365193\pi$
$271$	−9.59850	−	13.2112i	−0.583067	−	0.802523i	−0.994027	+	0.109130i	$0.965193\pi$
$272$	5.29630	−	0.838852i	0.321136	−	0.0508629i
$273$	−0.0412565	−	0.0210212i	−0.00249696	−	0.00127226i
$274$	−2.17844			−0.131604
$275$	16.0321	+	4.23950i	0.966769	+	0.255651i
$276$	0.391722			0.0235789
$277$	24.8351	+	12.6541i	1.49220	+	0.760312i	0.994269	−	0.106907i	$-0.0340948\pi$
$277$	24.8351	+	12.6541i	1.49220	+	0.760312i	0.497927	+	0.867219i	$0.334095\pi$
$278$	11.8634	−	1.87897i	0.711517	−	0.112693i
$279$	−15.7345	−	21.6566i	−0.941998	−	1.29655i
$280$	−0.170673	+	0.164724i	−0.0101997	+	0.00984412i
$281$	12.2425	+	3.97784i	0.730328	+	0.237298i	0.650495	−	0.759510i	$-0.274561\pi$
$281$	12.2425	+	3.97784i	0.730328	+	0.237298i	0.0798325	+	0.996808i	$0.474561\pi$
$282$	−0.304314	+	1.92136i	−0.0181216	+	0.114415i
$283$	−1.46814	−	9.26948i	−0.0872720	−	0.551014i	−0.992121	−	0.125282i	$-0.960017\pi$
$283$	−1.46814	−	9.26948i	−0.0872720	−	0.551014i	0.904849	−	0.425732i	$-0.139983\pi$
$284$	0.674575	−	0.219183i	0.0400287	−	0.0130061i
$285$	2.15988	−	0.659670i	0.127940	−	0.0390755i
$286$	2.60511	+	6.07224i	0.154044	+	0.359059i
$287$	0.0461908	+	0.0461908i	0.00272656	+	0.00272656i
$288$	1.34018	−	2.63025i	0.0789707	−	0.154989i
$289$	−6.90912	+	9.50959i	−0.406419	+	0.559388i
$290$	−5.22734	+	6.93282i	−0.306960	+	0.407109i
$291$	−0.120771	+	0.371696i	−0.00707975	+	0.0217892i
$292$	6.06448	+	11.9022i	0.354897	+	0.696524i
$293$	6.94825	+	1.10049i	0.405921	+	0.0642916i	0.356057	−	0.934464i	$-0.384121\pi$
$293$	6.94825	+	1.10049i	0.405921	+	0.0642916i	0.0498645	+	0.998756i	$0.484121\pi$
$294$	−1.23880	−	0.900044i	−0.0722485	−	0.0524916i
$295$	23.8180	+	4.20673i	1.38674	+	0.244925i
$296$			9.13656i			0.531052i
$297$	1.06249	+	4.19265i	0.0616517	+	0.243282i
$298$	−8.26356	+	8.26356i	−0.478695	+	0.478695i
$299$	1.10066	+	3.38748i	0.0636528	+	0.195903i
$300$	−0.801627	+	0.746680i	−0.0462820	+	0.0431096i
$301$	−0.255299	+	0.185485i	−0.0147152	+	0.0106912i
$302$	19.1075	−	9.73578i	1.09952	−	0.560231i
$303$	1.93984	−	0.988396i	0.111441	−	0.0567819i
$304$	3.72925	−	2.70946i	0.213887	−	0.155398i
$305$	−1.46412	+	0.713583i	−0.0838351	+	0.0408597i
$306$	4.89160	+	15.0548i	0.279634	+	0.860625i
$307$	0.00373246	−	0.00373246i	0.000213022	−	0.000213022i	−0.707000	−	0.707213i	$-0.749952\pi$
$307$	0.00373246	−	0.00373246i	0.000213022	−	0.000213022i	0.707213	+	0.707000i	$0.249952\pi$
$308$	−0.0864256	−	0.341042i	−0.00492456	−	0.0194327i
$309$		−	0.699198i		−	0.0397760i
$310$	11.6257	+	16.6132i	0.660294	+	0.943567i
$311$	17.1613	+	12.4684i	0.973128	+	0.707019i	0.956162	−	0.292837i	$-0.0945994\pi$
$311$	17.1613	+	12.4684i	0.973128	+	0.707019i	0.0169656	+	0.999856i	$0.494599\pi$
$312$	−0.431126	−	0.0682837i	−0.0244077	−	0.00386580i
$313$	−12.7695	−	25.0616i	−0.721777	−	1.41657i	−0.901469	−	0.432844i	$-0.857510\pi$
$313$	−12.7695	−	25.0616i	−0.721777	−	1.41657i	0.179692	−	0.983723i	$-0.442490\pi$
$314$	−4.72431	+	14.5399i	−0.266608	+	0.820536i
$315$	−0.559092	−	0.421555i	−0.0315013	−	0.0237519i
$316$	4.40385	−	6.06138i	0.247736	−	0.340979i
$317$	4.03040	−	7.91011i	0.226370	−	0.444276i	−0.749687	−	0.661793i	$-0.769796\pi$
$317$	4.03040	−	7.91011i	0.226370	−	0.444276i	0.976057	+	0.217517i	$0.0697957\pi$
$318$	1.24735	+	1.24735i	0.0699477	+	0.0699477i
$319$	−5.07758	−	11.8353i	−0.284290	−	0.662649i
$320$	−1.05033	+	1.97403i	−0.0587153	+	0.110352i
$321$	3.80517	−	1.23638i	0.212384	−	0.0690077i
$322$	−0.0296682	−	0.187318i	−0.00165335	−	0.0104388i
$323$	−3.86678	+	24.4139i	−0.215153	+	1.35843i
$324$	8.15080	+	2.64835i	0.452822	+	0.147131i
$325$	−8.70947	−	4.83420i	−0.483114	−	0.268153i
$326$	−11.8407	−	16.2973i	−0.655796	−	0.902626i
$327$	1.40159	−	0.221990i	0.0775079	−	0.0122761i
$328$	0.548687	+	0.279570i	0.0302962	+	0.0154367i
$329$	0.941825			0.0519245
$330$	−0.371160	−	1.58194i	−0.0204317	−	0.0870831i
$331$	12.4062			0.681905			0.340953	−	0.940081i	$-0.389250\pi$
$331$	12.4062			0.681905			0.340953	+	0.940081i	$0.389250\pi$
$332$	−5.07282	−	2.58473i	−0.278407	−	0.141855i
$333$	−26.6390	+	4.21921i	−1.45981	+	0.231211i
$334$	4.94458	+	6.80563i	0.270555	+	0.372387i
$335$	4.54462	+	0.0806161i	0.248299	+	0.00440453i
$336$	0.0221044	+	0.00718216i	0.00120589	+	0.000391819i
$337$	2.26742	−	14.3159i	0.123514	−	0.779838i	−0.845707	−	0.533647i	$-0.820821\pi$
$337$	2.26742	−	14.3159i	0.123514	−	0.779838i	0.969221	−	0.246191i	$-0.0791790\pi$
$338$	1.41276	+	8.91984i	0.0768442	+	0.485175i
$339$	−3.13808	+	1.01962i	−0.170437	+	0.0553783i
$340$	−3.50243	−	11.4676i	−0.189946	−	0.621917i
$341$	−29.9508	+	2.73645i	−1.62193	+	0.148187i
$342$	9.62199	+	9.62199i	0.520298	+	0.520298i
$343$	−0.673679	+	1.32217i	−0.0363752	+	0.0713904i
$344$	−1.74857	+	2.40670i	−0.0942764	+	0.129760i
$345$	−0.121658	−	0.867426i	−0.00654984	−	0.0467007i
$346$	−2.14002	+	6.58630i	−0.115048	+	0.354082i
$347$	3.54262	+	6.95278i	0.190178	+	0.373245i	0.966332	−	0.257298i	$-0.0828322\pi$
$347$	3.54262	+	6.95278i	0.190178	+	0.373245i	−0.776154	+	0.630543i	$0.782832\pi$
$348$	0.840301	+	0.133091i	0.0450448	+	0.00713440i
$349$	9.08291	+	6.59912i	0.486197	+	0.353243i	0.803720	−	0.595008i	$-0.202851\pi$
$349$	9.08291	+	6.59912i	0.486197	+	0.353243i	−0.317523	+	0.948251i	$0.602851\pi$
$350$	0.417769	+	0.326779i	0.0223307	+	0.0174671i
$351$		−	2.59805i		−	0.138673i
$352$	−1.76835	−	2.80588i	−0.0942532	−	0.149554i
$353$	14.6534	−	14.6534i	0.779921	−	0.779921i	−0.199896	−	0.979817i	$-0.564061\pi$
$353$	14.6534	−	14.6534i	0.779921	−	0.779921i	0.979817	+	0.199896i	$0.0640606\pi$
$354$	−0.732351	−	2.25394i	−0.0389240	−	0.119796i
$355$	−0.694861	−	1.42570i	−0.0368794	−	0.0756685i
$356$	0.375917	−	0.273119i	0.0199235	−	0.0144753i
$357$	−0.111047	+	0.0565812i	−0.00587723	+	0.00299460i
$358$	0.584815	−	0.297978i	0.0309084	−	0.0157486i
$359$	−12.9937	+	9.44050i	−0.685783	+	0.498250i	−0.875271	−	0.483633i	$-0.839317\pi$
$359$	−12.9937	+	9.44050i	−0.685783	+	0.498250i	0.189488	+	0.981883i	$0.439317\pi$
$360$	−6.24063	−	2.15080i	−0.328910	−	0.113357i
$361$	0.694829	+	2.13846i	0.0365700	+	0.112551i
$362$	0.669741	−	0.669741i	0.0352008	−	0.0352008i
$363$	2.31016	+	0.686903i	0.121252	+	0.0360531i
$364$			0.211332i			0.0110768i
$365$	24.4727	−	17.1256i	1.28096	−	0.896397i
$366$	0.129114	+	0.0938069i	0.00674890	+	0.00490336i
$367$	−14.6317	−	2.31743i	−0.763767	−	0.120969i	−0.237615	−	0.971359i	$-0.576366\pi$
$367$	−14.6317	−	2.31743i	−0.763767	−	0.120969i	−0.526152	+	0.850391i	$0.676366\pi$
$368$	−0.811669	−	1.59299i	−0.0423112	−	0.0830403i
$369$	−0.561748	+	1.72888i	−0.0292434	+	0.0900020i
$370$	20.2320	−	2.83756i	1.05181	−	0.147518i
$371$	0.501998	−	0.690941i	0.0260625	−	0.0358719i
$372$	0.902007	−	1.77029i	0.0467669	−	0.0917852i
$373$	20.0556	+	20.0556i	1.03844	+	1.03844i	0.999231	+	0.0392100i	$0.0124841\pi$
$373$	20.0556	+	20.0556i	1.03844	+	1.03844i	0.0392100	+	0.999231i	$0.487516\pi$
$374$	17.3442	+	3.93404i	0.896849	+	0.203425i
$375$	1.90241	+	1.54322i	0.0982399	+	0.0796916i
$376$	8.44403	−	2.74363i	0.435467	−	0.141492i
$377$	1.21015	+	7.64061i	0.0623261	+	0.393512i
$378$	−0.0216405	+	0.136633i	−0.00111307	+	0.00702764i
$379$	−5.15841	−	1.67607i	−0.264970	−	0.0860938i	0.173519	−	0.984830i	$-0.444486\pi$
$379$	−5.15841	−	1.67607i	−0.264970	−	0.0860938i	−0.438489	+	0.898737i	$0.644486\pi$
$380$	−7.15802	−	7.41656i	−0.367199	−	0.380461i
$381$	0.0746028	+	0.102682i	0.00382202	+	0.00526056i
$382$	−11.9571	+	1.89381i	−0.611777	+	0.0968959i
$383$	−10.9531	−	5.58087i	−0.559676	−	0.285169i	0.151181	−	0.988506i	$-0.451692\pi$
$383$	−10.9531	−	5.58087i	−0.559676	−	0.285169i	−0.710856	+	0.703337i	$0.751692\pi$
$384$	0.219102			0.0111810
$385$	−0.728360	+	0.297299i	−0.0371207	+	0.0151517i
$386$	−9.80458			−0.499040
$387$	−7.82456	−	3.98681i	−0.397745	−	0.202661i
$388$	1.76180	−	0.279042i	0.0894418	−	0.0141662i
$389$	−3.96143	−	5.45244i	−0.200852	−	0.276450i	0.696695	−	0.717367i	$-0.254653\pi$
$389$	−3.96143	−	5.45244i	−0.200852	−	0.276450i	−0.897548	+	0.440918i	$0.854653\pi$
$390$	−0.0173111	+	0.975891i	−0.000876584	+	0.0494161i
$391$	9.11783	+	2.96256i	0.461108	+	0.149823i
$392$	−1.09328	+	6.90270i	−0.0552190	+	0.348639i
$393$	0.724372	+	4.57350i	0.0365397	+	0.230703i
$394$	−22.6884	+	7.37190i	−1.14302	+	0.371391i
$395$	−14.7900	−	7.86937i	−0.744166	−	0.395951i
$396$	7.36435	−	6.45162i	0.370072	−	0.324206i
$397$	−5.29209	−	5.29209i	−0.265602	−	0.265602i	0.561723	−	0.827325i	$-0.310139\pi$
$397$	−5.29209	−	5.29209i	−0.265602	−	0.265602i	−0.827325	+	0.561723i	$0.810139\pi$
$398$	1.99509	−	3.91558i	0.100005	−	0.196270i
$399$	−0.0629732	+	0.0866751i	−0.00315260	+	0.00433918i
$400$	4.69749	+	1.71277i	0.234875	+	0.0856383i
$401$	6.50875	−	20.0319i	0.325031	−	1.00034i	−0.646395	−	0.763003i	$-0.723724\pi$
$401$	6.50875	−	20.0319i	0.325031	−	1.00034i	0.971426	−	0.237341i	$-0.0762758\pi$
$402$	−0.202196	−	0.396832i	−0.0100846	−	0.0197922i
$403$	17.8434	+	2.82611i	0.888841	+	0.140779i
$404$	−8.03889	−	5.84060i	−0.399950	−	0.290581i
$405$	3.33309	−	18.8716i	0.165623	−	0.937737i
$406$		−	0.411904i		−	0.0204425i
$407$	−11.2434	+	28.1395i	−0.557315	+	1.39482i
$408$	−0.830775	+	0.830775i	−0.0411295	+	0.0411295i
$409$	−0.694017	−	2.13596i	−0.0343169	−	0.105617i	0.932431	−	0.361349i	$-0.117684\pi$
$409$	−0.694017	−	2.13596i	−0.0343169	−	0.105617i	−0.966748	+	0.255732i	$0.917684\pi$
$410$	0.448671	−	1.30184i	0.0221583	−	0.0642931i
$411$	0.386143	−	0.280549i	0.0190470	−	0.0138385i
$412$	−2.84338	+	1.44878i	−0.140083	+	0.0713761i
$413$	−1.02235	+	0.520913i	−0.0503065	+	0.0256325i
$414$	4.26978	−	3.10217i	0.209848	−	0.152464i
$415$	−4.14814	+	12.0360i	−0.203624	+	0.590822i
$416$	0.615632	+	1.89472i	0.0301838	+	0.0928963i
$417$	−1.86088	+	1.86088i	−0.0911277	+	0.0911277i
$418$	14.8199	−	3.75560i	0.724864	−	0.183693i
$419$		−	18.5024i		−	0.903903i	−0.892042	−	0.451952i	$-0.850728\pi$
$419$		−	18.5024i		−	0.903903i	0.892042	−	0.451952i	$-0.149272\pi$
$420$	0.00903912	−	0.0511785i	0.000441064	−	0.00249725i
$421$	0.946673	+	0.687798i	0.0461380	+	0.0335212i	0.610615	−	0.791927i	$-0.290922\pi$
$421$	0.946673	+	0.687798i	0.0461380	+	0.0335212i	−0.564477	+	0.825449i	$0.690922\pi$
$422$	−17.5706	−	2.78291i	−0.855324	−	0.135470i
$423$	11.8989	+	23.3528i	0.578543	+	1.13545i
$424$	2.48793	−	7.65707i	0.120825	−	0.371860i
$425$	−24.3060	+	11.3173i	−1.17901	+	0.548969i
$426$	−0.0913457	+	0.125727i	−0.00442571	+	0.00609147i
$427$	0.0350788	−	0.0688460i	0.00169758	−	0.00333169i
$428$	−12.9124	−	12.9124i	−0.624145	−	0.624145i
$429$	−1.24379	−	0.740847i	−0.0600505	−	0.0357684i
$430$	5.87243	+	3.12457i	0.283194	+	0.150680i
$431$	−22.2668	+	7.23491i	−1.07255	+	0.348493i	−0.791481	−	0.611193i	$-0.790690\pi$
$431$	−22.2668	+	7.23491i	−1.07255	+	0.348493i	−0.281071	+	0.959687i	$0.590690\pi$
$432$	0.204005	+	1.28804i	0.00981519	+	0.0619707i
$433$	0.639810	−	4.03960i	0.0307473	−	0.194131i	−0.967534	−	0.252743i	$-0.918667\pi$
$433$	0.639810	−	4.03960i	0.0307473	−	0.194131i	0.998281	+	0.0586119i	$0.0186674\pi$
$434$	−0.914853	−	0.297254i	−0.0439143	−	0.0142686i
$435$	0.0337408	−	1.90209i	0.00161775	−	0.0911983i
$436$	−3.80692	−	5.23977i	−0.182318	−	0.250940i
$437$	8.13985	−	1.28923i	0.389382	−	0.0616720i
$438$	−2.60779	−	1.32874i	−0.124605	−	0.0634895i
$439$	33.8379			1.61500			0.807499	−	0.589869i	$-0.200821\pi$
$439$	33.8379			1.61500			0.807499	+	0.589869i	$0.200821\pi$
$440$	−5.66412	+	4.78725i	−0.270026	+	0.228223i
$441$	−20.6307			−0.982416
$442$	−9.51859	−	4.84996i	−0.452753	−	0.230689i
$443$	4.55789	−	0.721899i	0.216552	−	0.0342984i	−0.0472157	−	0.998885i	$-0.515035\pi$
$443$	4.55789	−	0.721899i	0.216552	−	0.0342984i	0.263768	+	0.964586i	$0.415035\pi$
$444$	−1.17665	−	1.61952i	−0.0558413	−	0.0768590i
$445$	−0.721543	−	0.747604i	−0.0342044	−	0.0354398i
$446$	−21.3225	−	6.92812i	−1.00965	−	0.328056i
$447$	0.400553	−	2.52899i	0.0189455	−	0.119617i
$448$	−0.0165943	−	0.104772i	−0.000784008	−	0.00495003i
$449$	−2.21284	+	0.718995i	−0.104430	+	0.0339315i	−0.360766	−	0.932656i	$-0.617485\pi$
$449$	−2.21284	+	0.718995i	−0.104430	+	0.0339315i	0.256336	+	0.966588i	$0.417485\pi$
$450$	−2.82455	+	14.4872i	−0.133151	+	0.682933i
$451$	1.34585	+	1.53625i	0.0633736	+	0.0723393i
$452$	10.6487	+	10.6487i	0.500873	+	0.500873i
$453$	−2.13312	+	4.18649i	−0.100223	+	0.196699i
$454$	12.4642	−	17.1554i	0.584972	−	0.805145i
$455$	0.467973	−	0.0656340i	0.0219389	−	0.00307697i
$456$	−0.312099	+	0.960541i	−0.0146154	+	0.0449815i
$457$	−14.5730	−	28.6012i	−0.681698	−	1.33791i	−0.929401	−	0.369071i	$-0.879676\pi$
$457$	−14.5730	−	28.6012i	−0.681698	−	1.33791i	0.247703	−	0.968836i	$-0.420324\pi$
$458$	−14.9405	−	2.36634i	−0.698123	−	0.110572i
$459$	−5.65742	−	4.11036i	−0.264066	−	0.191855i
$460$	−3.27543	+	2.29209i	−0.152718	+	0.106869i
$461$		−	10.2924i		−	0.479365i	−0.970851	−	0.239682i	$-0.922957\pi$
$461$		−	10.2924i		−	0.479365i	0.970851	−	0.239682i	$-0.0770433\pi$
$462$	0.0592405	+	0.0493217i	0.00275612	+	0.00229466i
$463$	14.0341	−	14.0341i	0.652221	−	0.652221i	−0.301306	−	0.953527i	$-0.597423\pi$
$463$	14.0341	−	14.0341i	0.652221	−	0.652221i	0.953527	+	0.301306i	$0.0974227\pi$
$464$	−1.19992	−	3.69297i	−0.0557048	−	0.171442i
$465$	−4.20026	−	1.44760i	−0.194782	−	0.0671307i
$466$	19.5090	−	14.1741i	0.903738	−	0.656604i
$467$	−21.7661	+	11.0904i	−1.00721	+	0.513201i	−0.878125	−	0.478432i	$-0.841205\pi$
$467$	−21.7661	+	11.0904i	−1.00721	+	0.513201i	−0.129089	+	0.991633i	$0.541205\pi$
$468$	−5.24005	+	2.66994i	−0.242221	+	0.123418i
$469$	−0.174448	+	0.126744i	−0.00805525	+	0.00585248i
$470$	−8.69796	−	17.8463i	−0.401207	−	0.823189i
$471$	−1.03510	−	3.18572i	−0.0476951	−	0.146790i
$472$	−7.64850	+	7.64850i	−0.352051	+	0.352051i
$473$	−8.34704	+	5.26055i	−0.383797	+	0.241880i
$474$			1.64157i			0.0753998i
$475$	−14.2001	+	18.1541i	−0.651545	+	0.832966i
$476$	0.460191	+	0.334348i	0.0210928	+	0.0153248i
$477$	23.4743	+	3.71796i	1.07481	+	0.170234i
$478$	11.7784	+	23.1165i	0.538733	+	1.05732i
$479$	−4.52436	+	13.9245i	−0.206723	+	0.636229i	0.792915	+	0.609332i	$0.208562\pi$
$479$	−4.52436	+	13.9245i	−0.206723	+	0.636229i	−0.999638	+	0.0268965i	$0.991438\pi$
$480$	−0.0680469	−	0.485177i	−0.00310590	−	0.0221452i
$481$	10.6989	−	14.7258i	0.487829	−	0.671440i
$482$	−8.85194	+	17.3729i	−0.403195	+	0.791315i
$483$	0.0293826	+	0.0293826i	0.00133695	+	0.00133695i
$484$	−1.99339	−	10.8179i	−0.0906085	−	0.491722i
$485$	−1.16507	−	3.81466i	−0.0529033	−	0.173215i
$486$	−5.50665	+	1.78922i	−0.249787	+	0.0811606i
$487$	−0.0991206	−	0.625823i	−0.00449158	−	0.0283587i	0.985341	−	0.170598i	$-0.0545699\pi$
$487$	−0.0991206	−	0.625823i	−0.00449158	−	0.0283587i	−0.989832	+	0.142239i	$0.954570\pi$
$488$	0.113947	−	0.719433i	0.00515814	−	0.0325672i
$489$	4.19769	+	1.36391i	0.189826	+	0.0616783i
$490$	15.6249	+	0.277166i	0.705859	+	0.0125211i
$491$	9.54067	+	13.1316i	0.430564	+	0.592621i	0.968083	−	0.250631i	$-0.0806381\pi$
$491$	9.54067	+	13.1316i	0.430564	+	0.592621i	−0.537518	+	0.843252i	$0.680638\pi$
$492$	−0.133263	+	0.0211068i	−0.00600795	+	0.000951566i
$493$	18.5525	+	9.45298i	0.835564	+	0.425741i
$494$	−9.18339			−0.413180
$495$	−16.5736	−	14.3039i	−0.744927	−	0.642912i
$496$	−9.06813			−0.407171
$497$	0.0670397	+	0.0341584i	0.00300714	+	0.00153221i
$498$	1.23207	−	0.195140i	0.0552102	−	0.00874443i
$499$	16.6574	+	22.9270i	0.745688	+	1.02635i	0.998271	+	0.0587766i	$0.0187200\pi$
$499$	16.6574	+	22.9270i	0.745688	+	1.02635i	−0.252583	+	0.967575i	$0.581280\pi$
$500$	2.33383	−	10.9340i	0.104372	−	0.488985i
$501$	−1.75292	−	0.569558i	−0.0783147	−	0.0254460i
$502$	−3.19293	+	20.1593i	−0.142507	+	0.899755i
$503$	6.16544	+	38.9270i	0.274903	+	1.73567i	0.609034	+	0.793144i	$0.291557\pi$
$503$	6.16544	+	38.9270i	0.274903	+	1.73567i	−0.334131	+	0.942527i	$0.608443\pi$
$504$	0.297817	−	0.0967665i	0.0132658	−	0.00431032i
$505$	−10.4367	+	19.6152i	−0.464429	+	0.872866i
$506$	−0.539514	−	5.90505i	−0.0239843	−	0.262511i
$507$	−1.39916	−	1.39916i	−0.0621389	−	0.0621389i
$508$	0.262989	−	0.516145i	0.0116683	−	0.0229002i
$509$	5.76334	−	7.93256i	0.255456	−	0.351605i	−0.661957	−	0.749542i	$-0.730274\pi$
$509$	5.76334	−	7.93256i	0.255456	−	0.351605i	0.917413	+	0.397937i	$0.130274\pi$
$510$	2.09768	+	1.58165i	0.0928868	+	0.0700366i
$511$	−0.437881	+	1.34766i	−0.0193707	+	0.0596169i
$512$	−0.453990	−	0.891007i	−0.0200637	−	0.0393773i
$513$	−5.93734	−	0.940383i	−0.262140	−	0.0415189i
$514$	−9.73935	−	7.07605i	−0.429584	−	0.312111i
$515$	4.09124	+	5.84642i	0.180281	+	0.257624i
$516$		−	0.651792i		−	0.0286936i
$517$	29.3829	+	1.94114i	1.29226	+	0.0853711i
$518$	−0.685323	+	0.685323i	−0.0301113	+	0.0301113i
$519$	−0.468881	−	1.44307i	−0.0205816	−	0.0633437i
$520$	4.00446	−	1.95170i	0.175607	−	0.0855877i
$521$	33.0758	−	24.0310i	1.44908	−	1.05282i	0.463031	−	0.886342i	$-0.346762\pi$
$521$	33.0758	−	24.0310i	1.44908	−	1.05282i	0.986046	−	0.166474i	$-0.0532382\pi$
$522$	10.2133	−	5.20393i	0.447024	−	0.227770i
$523$	27.2799	−	13.8998i	1.19287	−	0.607797i	0.259161	−	0.965834i	$-0.416554\pi$
$523$	27.2799	−	13.8998i	1.19287	−	0.607797i	0.933707	+	0.358037i	$0.116554\pi$
$524$	17.0978	−	12.4223i	0.746923	−	0.542671i
$525$	−0.116137	−	0.00412155i	−0.00506862	−	0.000179879i
$526$	−6.92176	−	21.3030i	−0.301803	−	0.928854i
$527$	34.3839	−	34.3839i	1.49779	−	1.49779i
$528$	0.674806	+	0.269625i	0.0293671	+	0.0117339i
$529$			19.8036i			0.861025i
$530$	−17.7285	−	3.13119i	−0.770075	−	0.136010i
$531$	−25.8324	−	18.7683i	−1.12103	−	0.814476i
$532$	0.482960	+	0.0764934i	0.0209390	+	0.00331641i
$533$	−0.556967	−	1.09311i	−0.0241249	−	0.0473478i
$534$	−0.0314602	+	0.0968246i	−0.00136142	+	0.00419001i
$535$	−24.5829	+	32.6034i	−1.06281	+	1.40957i
$536$	−1.19481	+	1.64452i	−0.0516080	+	0.0710323i
$537$	−0.0652874	+	0.128134i	−0.00281736	+	0.00552938i
$538$	−4.41161	−	4.41161i	−0.190198	−	0.190198i
$539$	−11.8616	+	19.9141i	−0.510915	+	0.857760i
$540$	2.78886	−	0.851776i	0.120014	−	0.0366546i
$541$	−1.54365	+	0.501564i	−0.0663669	+	0.0215639i	−0.342012	−	0.939695i	$-0.611108\pi$
$541$	−1.54365	+	0.501564i	−0.0663669	+	0.0215639i	0.275645	+	0.961259i	$0.411108\pi$
$542$	−2.55457	−	16.1289i	−0.109728	−	0.692795i
$543$	−0.0324638	+	0.204969i	−0.00139316	+	0.00879605i
$544$	5.09987	+	1.65705i	0.218655	+	0.0710454i
$545$	−10.4206	+	10.0573i	−0.446369	+	0.430809i
$546$	−0.0272164	−	0.0374601i	−0.00116475	−	0.00160315i
$547$	−16.1044	+	2.55068i	−0.688574	+	0.109059i	−0.490910	−	0.871210i	$-0.663335\pi$
$547$	−16.1044	+	2.55068i	−0.688574	+	0.109059i	−0.197664	+	0.980270i	$0.563335\pi$
$548$	−1.94100	−	0.988989i	−0.0829154	−	0.0422475i
$549$	2.15024			0.0917698
$550$	12.3600	+	11.0558i	0.527031	+	0.471422i
$551$	17.8992			0.762531
$552$	0.349027	+	0.177838i	0.0148556	+	0.00756928i
$553$	0.784985	−	0.124329i	0.0333809	−	0.00528702i
$554$	16.3834	+	22.5498i	0.696063	+	0.958049i
$555$	−3.22082	+	3.10854i	−0.136716	+	0.131950i
$556$	11.4234	+	3.71168i	0.484459	+	0.157410i
$557$	−1.96290	+	12.3932i	−0.0831706	+	0.525118i	0.910565	+	0.413365i	$0.135647\pi$
$557$	−1.96290	+	12.3932i	−0.0831706	+	0.525118i	−0.993736	+	0.111753i	$0.964353\pi$
$558$	−4.18761	−	26.4395i	−0.177275	−	1.11927i
$559$	5.63649	−	1.83141i	0.238398	−	0.0774603i
$560$	−0.226854	+	0.0692858i	−0.00958632	+	0.00292786i
$561$	−3.58103	+	1.53634i	−0.151191	+	0.0648642i
$562$	9.10227	+	9.10227i	0.383956	+	0.383956i
$563$	−6.98769	+	13.7141i	−0.294496	+	0.577981i	−0.990087	−	0.140457i	$-0.955143\pi$
$563$	−6.98769	+	13.7141i	−0.294496	+	0.577981i	0.695591	+	0.718438i	$0.255143\pi$
$564$	−1.14342	+	1.57379i	−0.0481469	+	0.0662685i
$565$	20.2732	−	26.8876i	0.852901	−	1.13117i
$566$	2.90013	−	8.92569i	0.121902	−	0.375175i
$567$	0.412732	+	0.810031i	0.0173331	+	0.0340181i
$568$	0.700557	+	0.110957i	0.0293947	+	0.00465567i
$569$	20.8367	+	15.1388i	0.873522	+	0.634651i	0.931530	−	0.363665i	$-0.118475\pi$
$569$	20.8367	+	15.1388i	0.873522	+	0.634651i	−0.0580079	+	0.998316i	$0.518475\pi$
$570$	2.22395	+	0.392792i	0.0931509	+	0.0164523i
$571$			1.63340i			0.0683555i	0.999416	+	0.0341778i	$0.0108812\pi$
$571$			1.63340i			0.0683555i	−0.999416	+	0.0341778i	$0.989119\pi$
$572$	−0.435564	+	6.59310i	−0.0182118	+	0.275671i
$573$	1.87558	−	1.87558i	0.0783534	−	0.0783534i
$574$	0.0201861	+	0.0621265i	0.000842553	+	0.00259311i
$575$	6.09286	+	6.54123i	0.254090	+	0.272788i
$576$	2.38821	−	1.73514i	0.0995089	−	0.0722975i
$577$	4.54545	−	2.31602i	0.189230	−	0.0964173i	−0.356809	−	0.934177i	$-0.616135\pi$
$577$	4.54545	−	2.31602i	0.189230	−	0.0964173i	0.546038	+	0.837760i	$0.316135\pi$
$578$	−10.4733	+	5.33643i	−0.435633	+	0.221966i
$579$	1.73793	−	1.26268i	0.0722259	−	0.0524752i
$580$	−7.80503	+	3.80403i	−0.324086	+	0.157954i
$581$	−0.186628	−	0.574383i	−0.00774265	−	0.0238294i
$582$	−0.276355	+	0.276355i	−0.0114553	+	0.0114553i
$583$	17.0853	−	20.5212i	0.707600	−	0.849901i
$584$			13.3582i			0.552764i
$585$	7.53971	+	10.7743i	0.311729	+	0.445464i
$586$	5.69132	+	4.13499i	0.235106	+	0.170815i
$587$	32.8854	+	5.20854i	1.35733	+	0.214979i	0.792319	−	0.610107i	$-0.208874\pi$
$587$	32.8854	+	5.20854i	1.35733	+	0.214979i	0.565007	+	0.825086i	$0.308874\pi$
$588$	−0.695171	−	1.36435i	−0.0286684	−	0.0562648i
$589$	12.9171	−	39.7547i	0.532239	−	1.63806i
$590$	19.3122	+	14.5614i	0.795071	+	0.599483i
$591$	3.07228	−	4.22863i	0.126377	−	0.173943i
$592$	−4.14791	+	8.14074i	−0.170478	+	0.334582i
$593$	−5.45354	−	5.45354i	−0.223950	−	0.223950i	0.586209	−	0.810160i	$-0.300620\pi$
$593$	−5.45354	−	5.45354i	−0.223950	−	0.223950i	−0.810160	+	0.586209i	$0.800620\pi$
$594$	−0.956741	+	4.21804i	−0.0392556	+	0.173068i
$595$	0.597456	−	1.12288i	0.0244933	−	0.0460337i
$596$	−11.1145	+	3.61131i	−0.455266	+	0.147925i
$597$	0.150624	+	0.951000i	0.00616461	+	0.0389218i
$598$	−0.557190	+	3.51796i	−0.0227852	+	0.143860i
$599$	−9.71951	−	3.15806i	−0.397129	−	0.129035i	0.103643	−	0.994615i	$-0.466950\pi$
$599$	−9.71951	−	3.15806i	−0.397129	−	0.129035i	−0.500771	+	0.865580i	$0.666950\pi$
$600$	−1.05324	+	0.301365i	−0.0429984	+	0.0123032i
$601$	16.4580	+	22.6525i	0.671337	+	0.924017i	0.999790	−	0.0205038i	$-0.00652703\pi$
$601$	16.4580	+	22.6525i	0.671337	+	0.924017i	−0.328452	+	0.944521i	$0.606527\pi$
$602$	−0.311681	+	0.0493655i	−0.0127032	+	0.00201199i
$603$	−5.34659	−	2.72422i	−0.217730	−	0.110939i
$604$	21.4449			0.872580
$605$	−23.3360	+	7.77388i	−0.948741	+	0.316053i
$606$	2.17713			0.0884398
$607$	−22.4284	−	11.4278i	−0.910341	−	0.463842i	−0.0648886	−	0.997893i	$-0.520669\pi$
$607$	−22.4284	−	11.4278i	−0.910341	−	0.463842i	−0.845453	+	0.534051i	$0.820669\pi$
$608$	4.55286	−	0.721102i	0.184643	−	0.0292445i
$609$	0.0530470	+	0.0730129i	0.00214957	+	0.00295863i
$610$	−1.62850	−	0.0288876i	−0.0659360	−	0.00116963i
$611$	−16.8224	−	5.46594i	−0.680562	−	0.221128i
$612$	−2.47629	+	15.6347i	−0.100098	+	0.631994i
$613$	−2.12862	−	13.4396i	−0.0859741	−	0.542819i	−0.992653	−	0.120997i	$-0.961391\pi$
$613$	−2.12862	−	13.4396i	−0.0859741	−	0.542819i	0.906679	−	0.421822i	$-0.138609\pi$
$614$	0.00502014	−	0.00163114i	0.000202596	−	6.58276e-5i
$615$	0.0881265	+	0.288541i	0.00355360	+	0.0116351i
$616$	0.0778240	−	0.343107i	0.00313562	−	0.0138242i
$617$	−18.5963	−	18.5963i	−0.748657	−	0.748657i	0.225570	−	0.974227i	$-0.427576\pi$
$617$	−18.5963	−	18.5963i	−0.748657	−	0.748657i	−0.974227	+	0.225570i	$0.927576\pi$
$618$	0.317429	−	0.622990i	0.0127689	−	0.0250603i
$619$	5.02643	−	6.91829i	0.202029	−	0.278069i	−0.695966	−	0.718075i	$-0.745023\pi$
$619$	5.02643	−	6.91829i	0.202029	−	0.278069i	0.897995	+	0.440005i	$0.145023\pi$
$620$	2.81631	+	20.0804i	0.113106	+	0.806449i
$621$	−0.720481	+	2.21741i	−0.0289119	+	0.0889817i
$622$	9.63029	+	18.9005i	0.386139	+	0.757841i
$623$	0.0486834	+	0.00771069i	0.00195046	+	0.000308922i
$624$	−0.353136	−	0.256568i	−0.0141368	−	0.0102710i
$625$	−24.9371	−	1.77221i	−0.997484	−	0.0708883i
$626$		−	28.1273i		−	1.12419i
$627$	−2.14326	+	2.57428i	−0.0855937	+	0.102807i
$628$	−10.8104	+	10.8104i	−0.431382	+	0.431382i
$629$	−15.1397	−	46.5953i	−0.603661	−	1.85788i
$630$	−0.306773	−	0.629431i	−0.0122221	−	0.0250771i
$631$	−13.1804	+	9.57615i	−0.524705	+	0.381221i	−0.818373	−	0.574687i	$-0.805124\pi$
$631$	−13.1804	+	9.57615i	−0.524705	+	0.381221i	0.293668	+	0.955907i	$0.405124\pi$
$632$	6.67567	−	3.40142i	0.265544	−	0.135301i
$633$	3.47291	−	1.76953i	0.138036	−	0.0703327i
$634$	7.18223	−	5.21820i	0.285243	−	0.207241i
$635$	−1.22463	−	0.422061i	−0.0485978	−	0.0167490i
$636$	0.545110	+	1.67768i	0.0216150	+	0.0665242i
$637$	9.84517	−	9.84517i	0.390080	−	0.390080i
$638$	0.848950	−	12.8505i	0.0336103	−	0.508756i
$639$			2.09382i			0.0828302i
$640$	−1.83204	+	1.28204i	−0.0724179	+	0.0506769i
$641$	11.4273	+	8.30243i	0.451352	+	0.327926i	0.790129	−	0.612940i	$-0.210013\pi$
$641$	11.4273	+	8.30243i	0.451352	+	0.327926i	−0.338777	+	0.940867i	$0.610013\pi$
$642$	3.95174	+	0.625893i	0.155963	+	0.0247020i
$643$	−9.49044	−	18.6260i	−0.374267	−	0.734539i	0.624658	−	0.780898i	$-0.285238\pi$
$643$	−9.49044	−	18.6260i	−0.374267	−	0.734539i	−0.998925	+	0.0463588i	$0.985238\pi$
$644$	0.0586059	−	0.180371i	0.00230940	−	0.00710759i
$645$	−1.44333	+	0.202429i	−0.0568309	+	0.00797062i
$646$	−14.5290	+	19.9975i	−0.571636	+	0.786790i
$647$	−5.90519	+	11.5896i	−0.232157	+	0.455633i	−0.977468	−	0.211083i	$-0.932301\pi$
$647$	−5.90519	+	11.5896i	−0.232157	+	0.455633i	0.745311	+	0.666717i	$0.232301\pi$
$648$	6.06009	+	6.06009i	0.238063	+	0.238063i
$649$	−32.9686	+	14.1442i	−1.29413	+	0.555209i
$650$	−5.56551	−	8.26132i	−0.218297	−	0.324035i
$651$	0.200446	−	0.0651288i	0.00785609	−	0.00255260i
$652$	−3.15131	−	19.8966i	−0.123415	−	0.779211i
$653$	−4.58653	+	28.9582i	−0.179485	+	1.13322i	0.719257	+	0.694744i	$0.244482\pi$
$653$	−4.58653	+	28.9582i	−0.179485	+	1.13322i	−0.898742	+	0.438479i	$0.855518\pi$
$654$	1.34960	+	0.438513i	0.0527737	+	0.0171472i
$655$	−32.8180	−	34.0033i	−1.28231	−	1.32862i
$656$	0.361961	+	0.498197i	0.0141322	+	0.0194513i
$657$	−38.9477	+	6.16871i	−1.51950	+	0.240664i
$658$	0.839173	+	0.427580i	0.0327144	+	0.0166688i
$659$	−4.17645			−0.162691			−0.0813457	−	0.996686i	$-0.525922\pi$
$659$	−4.17645			−0.162691			−0.0813457	+	0.996686i	$0.525922\pi$
$660$	0.387481	−	1.57802i	0.0150827	−	0.0614245i
$661$	−13.3436			−0.519005			−0.259503	−	0.965742i	$-0.583559\pi$
$661$	−13.3436			−0.519005			−0.259503	+	0.965742i	$0.583559\pi$
$662$	11.0540	+	5.63229i	0.429625	+	0.218905i
$663$	2.31184	−	0.366159i	0.0897843	−	0.0142204i
$664$	−3.34647	−	4.60602i	−0.129868	−	0.178748i
$665$	0.0193924	−	1.09322i	0.000752007	−	0.0423933i
$666$	−25.6510	−	8.33452i	−0.993957	−	0.322956i
$667$	1.08601	−	6.85680i	0.0420505	−	0.265496i
$668$	1.31596	+	8.30865i	0.0509160	+	0.321471i
$669$	4.67180	−	1.51796i	0.180622	−	0.0586878i
$670$	4.01268	+	2.13504i	0.155023	+	0.0824839i
$671$	1.23627	−	2.07554i	0.0477258	−	0.0801254i
$672$	0.0164345	+	0.0164345i	0.000633976	+	0.000633976i
$673$	−12.8692	+	25.2571i	−0.496070	+	0.973591i	0.498238	+	0.867040i	$0.333981\pi$
$673$	−12.8692	+	25.2571i	−0.496070	+	0.973591i	−0.994307	+	0.106551i	$0.966019\pi$
$674$	8.51958	−	11.7262i	0.328162	−	0.451676i
$675$	−2.75231	−	5.91110i	−0.105937	−	0.227518i
$676$	−2.79074	+	8.58902i	−0.107336	+	0.330347i
$677$	−15.7644	−	30.9393i	−0.605873	−	1.18909i	−0.966568	−	0.256409i	$-0.917460\pi$
$677$	−15.7644	−	30.9393i	−0.605873	−	1.18909i	0.360695	−	0.932684i	$-0.382540\pi$
$678$	−3.25895	−	0.516166i	−0.125159	−	0.0198232i
$679$	0.153081	+	0.111220i	0.00587471	+	0.00426823i
$680$	2.08548	−	11.8078i	0.0799745	−	0.452807i
$681$			4.64611i			0.178039i
$682$	−27.9287	−	11.1592i	−1.06945	−	0.427308i
$683$	17.3870	−	17.3870i	0.665293	−	0.665293i	−0.291329	−	0.956623i	$-0.594098\pi$
$683$	17.3870	−	17.3870i	0.665293	−	0.665293i	0.956623	+	0.291329i	$0.0940976\pi$
$684$	4.20496	+	12.9415i	0.160781	+	0.494832i
$685$	−1.58719	+	4.60529i	−0.0606435	+	0.175959i
$686$	−1.20050	+	0.872217i	−0.0458355	+	0.0333014i
$687$	2.95305	−	1.50466i	0.112666	−	0.0574062i
$688$	−2.65060	+	1.35055i	−0.101053	+	0.0514892i
$689$	−12.9764	+	9.42788i	−0.494360	+	0.359174i
$690$	0.285405	−	0.828114i	0.0108652	−	0.0315258i
$691$	5.45315	+	16.7831i	0.207448	+	0.638459i	0.999604	+	0.0281402i	$0.00895847\pi$
$691$	5.45315	+	16.7831i	0.207448	+	0.638459i	−0.792156	+	0.610318i	$0.791042\pi$
$692$	−4.89689	+	4.89689i	−0.186152	+	0.186152i
$693$	1.03632	+	0.0684629i	0.0393665	+	0.00260069i
$694$			7.80329i			0.296209i
$695$	4.67134	−	26.4486i	0.177194	−	1.00325i
$696$	0.688292	+	0.500073i	0.0260896	+	0.0189552i
$697$	−3.26149	−	0.516570i	−0.123538	−	0.0195665i
$698$	5.09700	+	10.0034i	0.192924	+	0.378635i
$699$	−1.63270	+	5.02493i	−0.0617543	+	0.190060i
$700$	0.223881	+	0.480826i	0.00846190	+	0.0181735i
$701$	−25.5285	+	35.1370i	−0.964200	+	1.32711i	−0.0192769	+	0.999814i	$0.506136\pi$
$701$	−25.5285	+	35.1370i	−0.964200	+	1.32711i	−0.944923	+	0.327293i	$0.893864\pi$
$702$	1.17949	−	2.31488i	0.0445169	−	0.0873694i
$703$	−29.7805	−	29.7805i	−1.12319	−	1.12319i
$704$	−0.301766	−	3.30287i	−0.0113732	−	0.124482i
$705$	3.84011	+	2.04322i	0.144627	+	0.0769520i
$706$	19.7087	−	6.40376i	0.741749	−	0.241009i
$707$	−0.164892	−	1.04108i	−0.00620138	−	0.0391540i
$708$	0.370740	−	2.34076i	0.0139333	−	0.0879711i
$709$	24.3796	+	7.92140i	0.915594	+	0.297495i	0.728658	−	0.684878i	$-0.240144\pi$
$709$	24.3796	+	7.92140i	0.915594	+	0.297495i	0.186936	+	0.982372i	$0.440144\pi$
$710$	0.0281297	−	1.58577i	0.00105569	−	0.0595129i
$711$	13.0001	+	17.8932i	0.487544	+	0.671046i
$712$	0.458938	−	0.0726886i	0.0171994	−	0.00272412i
$713$	−14.4454	−	7.36032i	−0.540986	−	0.275646i
$714$	−0.124631			−0.00466419
$715$	14.7350	−	1.08312i	0.551058	−	0.0405066i
$716$	0.656353			0.0245291
$717$	−5.06486	−	2.58068i	−0.189151	−	0.0963771i
$718$	−15.8634	+	2.51251i	−0.592017	+	0.0937662i
$719$	−10.8139	−	14.8840i	−0.403289	−	0.555079i	0.558277	−	0.829655i	$-0.311463\pi$
$719$	−10.8139	−	14.8840i	−0.403289	−	0.555079i	−0.961566	+	0.274575i	$0.911463\pi$
$720$	−4.58400	−	4.74956i	−0.170835	−	0.177006i
$721$	−0.321950	−	0.104608i	−0.0119900	−	0.00389580i
$722$	−0.351745	+	2.22083i	−0.0130906	+	0.0826508i
$723$	−0.668298	−	4.21946i	−0.0248543	−	0.156924i
$724$	0.900800	−	0.292688i	0.0334780	−	0.0108777i
$725$	10.8476	+	16.1020i	0.402871	+	0.598013i
$726$	1.74652	+	1.66083i	0.0648194	+	0.0616390i
$727$	20.0550	+	20.0550i	0.743800	+	0.743800i	0.973307	−	0.229507i	$-0.0737114\pi$
$727$	20.0550	+	20.0550i	0.743800	+	0.743800i	−0.229507	+	0.973307i	$0.573711\pi$
$728$	−0.0959429	+	0.188299i	−0.00355588	+	0.00697881i
$729$	−14.3667	+	19.7741i	−0.532102	+	0.732375i
$730$	29.5802	−	4.14867i	1.09481	−	0.153549i
$731$	4.92946	−	15.1713i	0.182323	−	0.561131i
$732$	0.0724541	+	0.142199i	0.00267798	+	0.00525583i
$733$	1.52027	+	0.240788i	0.0561526	+	0.00889369i	0.184448	−	0.982842i	$-0.440950\pi$
$733$	1.52027	+	0.240788i	0.0561526	+	0.00889369i	−0.128295	+	0.991736i	$0.540950\pi$
$734$	−11.9848	−	8.70749i	−0.442368	−	0.321399i
$735$	−2.80531	+	1.96311i	−0.103475	+	0.0724105i
$736$		−	1.78785i		−	0.0659012i
$737$	−5.70360	+	3.59458i	−0.210095	+	0.132408i
$738$	−1.28542	+	1.28542i	−0.0473169	+	0.0473169i
$739$	0.337238	+	1.03791i	0.0124055	+	0.0381802i	0.957068	−	0.289865i	$-0.0936103\pi$
$739$	0.337238	+	1.03791i	0.0124055	+	0.0381802i	−0.944662	+	0.328045i	$0.893610\pi$
$740$	19.3150	+	6.65683i	0.710035	+	0.244710i
$741$	1.62782	−	1.18268i	0.0597995	−	0.0434469i
$742$	0.760965	−	0.387731i	0.0279359	−	0.0142340i
$743$	24.4539	−	12.4599i	0.897125	−	0.457108i	0.0562991	−	0.998414i	$-0.482070\pi$
$743$	24.4539	−	12.4599i	0.897125	−	0.457108i	0.840826	+	0.541306i	$0.182070\pi$
$744$	1.60739	−	1.16784i	0.0589297	−	0.0428150i
$745$	11.4487	+	23.4902i	0.419448	+	0.860616i
$746$	8.76463	+	26.9748i	0.320896	+	0.987616i
$747$	11.8842	−	11.8842i	0.434819	−	0.434819i
$748$	13.6678	+	11.3794i	0.499745	+	0.416071i
$749$		−	1.93709i		−	0.0707797i
$750$	0.994450	+	2.23870i	0.0363122	+	0.0817456i
$751$	−13.4132	−	9.74529i	−0.489456	−	0.355611i	0.315519	−	0.948919i	$-0.397821\pi$
$751$	−13.4132	−	9.74529i	−0.489456	−	0.355611i	−0.804975	+	0.593309i	$0.797821\pi$
$752$	8.76927	+	1.38892i	0.319782	+	0.0506485i
$753$	−2.03025	−	3.98458i	−0.0739863	−	0.145206i
$754$	−2.39051	+	7.35723i	−0.0870572	+	0.267935i
$755$	−6.66019	−	47.4875i	−0.242389	−	1.72825i
$756$	−0.0813119	+	0.111916i	−0.00295728	+	0.00407035i
$757$	−8.25846	+	16.2081i	−0.300159	+	0.589095i	−0.990992	−	0.133919i	$-0.957244\pi$
$757$	−8.25846	+	16.2081i	−0.300159	+	0.589095i	0.690833	+	0.723014i	$0.257244\pi$
$758$	−3.83526	−	3.83526i	−0.139303	−	0.139303i
$759$	0.856112	+	0.977229i	0.0310749	+	0.0354712i
$760$	−3.01080	−	9.85787i	−0.109213	−	0.357583i
$761$	25.7366	−	8.36233i	0.932951	−	0.303134i	0.197182	−	0.980367i	$-0.436821\pi$
$761$	25.7366	−	8.36233i	0.932951	−	0.303134i	0.735769	+	0.677232i	$0.236821\pi$
$762$	0.0198550	+	0.125359i	0.000719270	+	0.00454129i
$763$	0.107477	−	0.678581i	0.00389092	−	0.0245663i
$764$	−11.5136	−	3.74099i	−0.416547	−	0.135344i
$765$	35.3904	+	0.627783i	1.27954	+	0.0226975i
$766$	−7.22559	−	9.94518i	−0.261071	−	0.359334i
$767$	21.2838	−	3.37103i	0.768515	−	0.121721i
$768$	0.195221	+	0.0994700i	0.00704443	+	0.00358932i
$769$	0.573262			0.0206723			0.0103362	−	0.999947i	$-0.496710\pi$
$769$	0.573262			0.0206723			0.0103362	+	0.999947i	$0.496710\pi$
$770$	−0.783944	−	0.0657735i	−0.0282514	−	0.00237031i
$771$	2.63766			0.0949928
$772$	−8.73594	−	4.45118i	−0.314413	−	0.160202i
$773$	17.8864	−	2.83293i	0.643330	−	0.101893i	0.173759	−	0.984788i	$-0.444409\pi$
$773$	17.8864	−	2.83293i	0.643330	−	0.101893i	0.469571	+	0.882895i	$0.344409\pi$
$774$	−5.16176	−	7.10456i	−0.185536	−	0.255368i
$775$	43.5913	−	12.4728i	1.56585	−	0.448038i
$776$	1.69646	+	0.551212i	0.0608993	+	0.0197874i
$777$	0.0332191	−	0.209737i	0.00119173	−	0.00752428i
$778$	−1.05430	−	6.65661i	−0.0377986	−	0.238651i
$779$	−2.69969	+	0.877183i	−0.0967265	+	0.0314284i
$780$	−0.458469	+	0.861666i	−0.0164158	+	0.0308526i
$781$	2.02109	+	1.20384i	0.0723202	+	0.0430767i
$782$	6.77907	+	6.77907i	0.242419	+	0.242419i
$783$	−2.29892	+	4.51189i	−0.0821567	+	0.161242i
$784$	−4.10788	+	5.65402i	−0.146710	+	0.201929i
$785$	27.2959	+	20.5811i	0.974232	+	0.734570i
$786$	−1.43091	+	4.40388i	−0.0510388	+	0.157081i
$787$	4.47822	+	8.78900i	0.159631	+	0.313294i	0.956944	−	0.290272i	$-0.0937458\pi$
$787$	4.47822	+	8.78900i	0.159631	+	0.313294i	−0.797313	+	0.603566i	$0.793746\pi$
$788$	−23.5623	−	3.73190i	−0.839371	−	0.132943i
$789$	3.97043	+	2.88468i	0.141351	+	0.102697i
$790$	−9.60538	−	13.7262i	−0.341744	−	0.488356i
$791$			1.59749i			0.0568003i
$792$	9.49066	−	2.40509i	0.337236	−	0.0854611i
$793$	−1.02611	+	1.02611i	−0.0364383	+	0.0364383i
$794$	−2.31273	−	7.11785i	−0.0820757	−	0.252603i
$795$	3.54574	−	1.72813i	0.125755	−	0.0612904i
$796$	3.55527	−	2.58306i	0.126013	−	0.0915540i
$797$	8.07900	−	4.11646i	0.286173	−	0.145812i	−0.305012	−	0.952349i	$-0.598660\pi$
$797$	8.07900	−	4.11646i	0.286173	−	0.145812i	0.591185	+	0.806536i	$0.298660\pi$
$798$	−0.0954592	+	0.0486389i	−0.00337922	+	0.00172180i
$799$	−38.5171	+	27.9843i	−1.36264	+	0.990014i
$800$	3.40792	+	3.65870i	0.120488	+	0.129355i
$801$	0.423869	+	1.30453i	0.0149767	+	0.0460935i
$802$	14.8936	−	14.8936i	0.525912	−	0.525912i
$803$	−16.4385	+	41.1415i	−0.580101	+	1.45185i
$804$		−	0.445375i		−	0.0157072i
$805$	−0.417613	−	0.0737586i	−0.0147189	−	0.00259965i
$806$	14.6155	+	10.6188i	0.514810	+	0.374031i
$807$	1.35014	+	0.213841i	0.0475271	+	0.00752755i
$808$	−4.51113	−	8.85359i	−0.158701	−	0.311468i
$809$	0.123448	−	0.379934i	0.00434020	−	0.0133578i	−0.948863	−	0.315688i	$-0.897765\pi$
$809$	0.123448	−	0.379934i	0.00434020	−	0.0133578i	0.953203	+	0.302330i	$0.0977646\pi$
$810$	11.5373	−	15.3015i	0.405380	−	0.537641i
$811$	15.3766	−	21.1641i	0.539946	−	0.743172i	−0.448659	−	0.893703i	$-0.648098\pi$
$811$	15.3766	−	21.1641i	0.539946	−	0.743172i	0.988605	+	0.150531i	$0.0480983\pi$
$812$	0.187001	−	0.367010i	0.00656244	−	0.0128795i
$813$	2.52997	+	2.52997i	0.0887299	+	0.0887299i
$814$	−22.7930	+	19.9681i	−0.798895	+	0.699880i
$815$	−43.0802	+	13.1576i	−1.50903	+	0.460890i
$816$	−1.11739	+	0.363062i	−0.0391165	+	0.0127097i
$817$	−2.14516	−	13.5440i	−0.0750498	−	0.473846i
$818$	0.351334	−	2.21824i	0.0122841	−	0.0775588i
$819$	−0.593319	−	0.192781i	−0.0207322	−	0.00673631i
$820$	0.990790	−	0.956252i	0.0345999	−	0.0333938i
$821$	12.7049	+	17.4868i	0.443405	+	0.610295i	0.970965	−	0.239223i	$-0.0768927\pi$
$821$	12.7049	+	17.4868i	0.443405	+	0.610295i	−0.527559	+	0.849518i	$0.676893\pi$
$822$	0.471422	−	0.0746660i	0.0164427	−	0.00260427i
$823$	33.2021	+	16.9173i	1.15735	+	0.589701i	0.923887	−	0.382664i	$-0.124993\pi$
$823$	33.2021	+	16.9173i	1.15735	+	0.589701i	0.233466	+	0.972365i	$0.424993\pi$
$824$	−3.19120			−0.111171
$825$	−3.61471	−	0.367945i	−0.125848	−	0.0128102i
$826$	−1.14741			−0.0399235
$827$	39.1773	+	19.9618i	1.36233	+	0.694141i	0.973823	−	0.227306i	$-0.0729918\pi$
$827$	39.1773	+	19.9618i	1.36233	+	0.694141i	0.388504	+	0.921447i	$0.372992\pi$
$828$	5.21276	−	0.825620i	0.181156	−	0.0286923i
$829$	−8.11023	−	11.1628i	−0.281680	−	0.387699i	0.644609	−	0.764512i	$-0.277020\pi$
$829$	−8.11023	−	11.1628i	−0.281680	−	0.387699i	−0.926289	+	0.376813i	$0.877020\pi$
$830$	−9.16023	+	8.84091i	−0.317956	+	0.306873i
$831$	−5.80813	−	1.88718i	−0.201482	−	0.0654655i
$832$	−0.311653	+	1.96770i	−0.0108046	+	0.0682177i
$833$	−5.86252	−	37.0145i	−0.203124	−	1.28248i
$834$	−2.50288	+	0.813235i	−0.0866676	+	0.0281600i
$835$	17.9899	−	5.49449i	0.622567	−	0.190145i
$836$	14.9096	+	3.38182i	0.515660	+	0.116963i
$837$	8.36201	+	8.36201i	0.289033	+	0.289033i
$838$	8.39993	−	16.4858i	0.290171	−	0.569492i
$839$	4.40717	−	6.06595i	0.152152	−	0.209420i	−0.726136	−	0.687551i	$-0.758686\pi$
$839$	4.40717	−	6.06595i	0.152152	−	0.209420i	0.878288	+	0.478131i	$0.158686\pi$
$840$	0.0312885	−	0.0414967i	0.00107955	−	0.00143177i
$841$	−4.30219	+	13.2408i	−0.148351	+	0.456579i
$842$	0.531238	+	1.04261i	0.0183077	+	0.0359308i
$843$	−2.78567	−	0.441207i	−0.0959436	−	0.0151960i
$844$	−14.3921	−	10.4565i	−0.495397	−	0.359927i
$845$	19.8862	+	3.51229i	0.684106	+	0.120827i
$846$			26.2095i			0.901101i
$847$	0.661914	−	0.960957i	0.0227436	−	0.0330189i
$848$	5.69300	−	5.69300i	0.195499	−	0.195499i
$849$	0.635424	+	1.95563i	0.0218077	+	0.0671172i
$850$	−26.7947	−	0.950913i	−0.919052	−	0.0326160i
$851$	−13.2152	+	9.60138i	−0.453010	+	0.329131i
$852$	−0.138468	+	0.0705531i	−0.00474384	+	0.00241711i
$853$	−45.6440	+	23.2568i	−1.56282	+	0.796297i	−0.999551	−	0.0299755i	$-0.990457\pi$
$853$	−45.6440	+	23.2568i	−1.56282	+	0.796297i	−0.563270	+	0.826273i	$0.690457\pi$
$854$	0.0625108	−	0.0454168i	0.00213908	−	0.00155413i
$855$	27.3517	−	13.3307i	0.935410	−	0.455902i
$856$	−5.64293	−	17.3672i	−0.192871	−	0.593597i
$857$	−11.1186	+	11.1186i	−0.379803	+	0.379803i	−0.871031	−	0.491228i	$-0.836548\pi$
$857$	−11.1186	+	11.1186i	−0.379803	+	0.379803i	0.491228	+	0.871031i	$0.336548\pi$
$858$	−0.771883	−	1.22477i	−0.0263517	−	0.0418128i
$859$			17.6506i			0.602230i	0.953588	+	0.301115i	$0.0973589\pi$
$859$			17.6506i			0.602230i	−0.953588	+	0.301115i	$0.902641\pi$
$860$	3.81385	+	5.45004i	0.130051	+	0.185845i
$861$	−0.0115791	−	0.00841269i	−0.000394614	−	0.000286704i
$862$	−23.1244	−	3.66255i	−0.787621	−	0.124747i
$863$	2.55733	+	5.01904i	0.0870525	+	0.170850i	0.930428	−	0.366474i	$-0.119435\pi$
$863$	2.55733	+	5.01904i	0.0870525	+	0.170850i	−0.843376	+	0.537324i	$0.819435\pi$
$864$	−0.402986	+	1.24026i	−0.0137099	+	0.0421947i
$865$	12.3645	+	9.32281i	0.420405	+	0.316985i
$866$	2.40401	−	3.30884i	0.0816917	−	0.112439i
$867$	1.16922	−	2.29472i	0.0397088	−	0.0779329i
$868$	−0.680189	−	0.680189i	−0.0230871	−	0.0230871i
$869$	24.7460	−	2.26092i	0.839451	−	0.0766963i
$870$	0.893595	−	1.67946i	0.0302957	−	0.0569390i
$871$	3.85146	−	1.25142i	0.130502	−	0.0424026i
$872$	−1.01318	−	6.39697i	−0.0343106	−	0.216629i
$873$	−0.823729	+	5.20082i	−0.0278790	+	0.176021i
$874$	7.83795	+	2.54671i	0.265123	+	0.0861436i
$875$	0.995207	−	0.645091i	0.0336441	−	0.0218081i
$876$	−1.72033	−	2.36783i	−0.0581244	−	0.0800014i
$877$	25.6103	−	4.05627i	0.864798	−	0.136971i	0.291752	−	0.956494i	$-0.405762\pi$
$877$	25.6103	−	4.05627i	0.864798	−	0.136971i	0.573046	+	0.819523i	$0.305762\pi$
$878$	30.1498	+	15.3621i	1.01751	+	0.518446i
$879$	−1.54135			−0.0519884
$880$	−7.22013	+	1.69401i	−0.243391	+	0.0571050i
$881$	27.0741			0.912148			0.456074	−	0.889942i	$-0.349255\pi$
$881$	27.0741			0.912148			0.456074	+	0.889942i	$0.349255\pi$
$882$	−18.3821	−	9.36616i	−0.618958	−	0.315375i
$883$	−41.6531	+	6.59720i	−1.40174	+	0.222014i	−0.811093	−	0.584918i	$-0.801127\pi$
$883$	−41.6531	+	6.59720i	−1.40174	+	0.222014i	−0.590646	+	0.806931i	$0.701127\pi$
$884$	−6.27929	−	8.64270i	−0.211195	−	0.290685i
$885$	−5.29851	−	0.0939892i	−0.178107	−	0.00315941i
$886$	4.38884	+	1.42602i	0.147446	+	0.0479081i
$887$	2.29522	−	14.4914i	0.0770658	−	0.486575i	−0.918723	−	0.394902i	$-0.870779\pi$
$887$	2.29522	−	14.4914i	0.0770658	−	0.486575i	0.995789	−	0.0916728i	$-0.0292214\pi$
$888$	−0.313156	−	1.97719i	−0.0105088	−	0.0663501i
$889$	0.0584419	−	0.0189889i	0.00196008	−	0.000636869i
$890$	−0.303495	−	0.993694i	−0.0101732	−	0.0333087i
$891$	11.2068	+	26.1218i	0.375442	+	0.875114i
$892$	−15.8532	−	15.8532i	−0.530805	−	0.530805i
$893$	−18.5804	+	36.4660i	−0.621768	+	1.22029i
$894$	1.50503	−	2.07150i	0.0503359	−	0.0692814i
$895$	−0.203845	−	1.45342i	−0.00681379	−	0.0485826i
$896$	0.0327800	−	0.100887i	0.00109510	−	0.00337038i
$897$	−0.354294	−	0.695340i	−0.0118295	−	0.0232167i
$898$	−2.29807	−	0.363978i	−0.0766876	−	0.0121461i
$899$	−28.4869	−	20.6969i	−0.950090	−	0.690281i
$900$	−9.09374	+	11.6259i	−0.303125	+	0.387529i
$901$			43.1727i			1.43829i
$902$	0.501717	+	1.97981i	0.0167054	+	0.0659206i
$903$	0.0488902	−	0.0488902i	0.00162696	−	0.00162696i
$904$	4.65365	+	14.3225i	0.154778	+	0.476358i
$905$	−0.927890	−	1.90383i	−0.0308441	−	0.0632853i
$906$	−3.80125	+	2.76177i	−0.126288	+	0.0917538i
$907$	−27.2760	+	13.8978i	−0.905684	+	0.461469i	−0.843827	−	0.536616i	$-0.819702\pi$
$907$	−27.2760	+	13.8978i	−0.905684	+	0.461469i	−0.0618575	+	0.998085i	$0.519702\pi$
$908$	18.8941	−	9.62700i	0.627021	−	0.319483i
$909$	23.7308	−	17.2414i	0.787100	−	0.571862i
$910$	0.446765	+	0.153975i	0.0148101	+	0.00510423i
$911$	−13.6769	−	42.0931i	−0.453135	−	1.39461i	−0.873311	−	0.487163i	$-0.838032\pi$
$911$	−13.6769	−	42.0931i	−0.453135	−	1.39461i	0.420176	−	0.907443i	$-0.361968\pi$
$912$	−0.714159	+	0.714159i	−0.0236482	+	0.0236482i
$913$	−4.63857	−	18.3041i	−0.153514	−	0.605778i
$914$		−	32.0999i		−	1.06177i
$915$	0.292383	−	0.204605i	0.00966588	−	0.00676403i
$916$	−12.2378	−	8.89126i	−0.404347	−	0.293776i
$917$	2.21427	+	0.350706i	0.0731217	+	0.0115813i
$918$	−3.17474	−	6.23077i	−0.104782	−	0.205646i
$919$	−13.7694	+	42.3779i	−0.454211	+	1.39792i	0.417847	+	0.908517i	$0.362785\pi$
$919$	−13.7694	+	42.3779i	−0.454211	+	1.39792i	−0.872059	+	0.489402i	$0.837215\pi$
$920$	−3.95901	+	0.555258i	−0.130525	+	0.0183063i
$921$	−0.000679789	0	0.000935649i	−2.23998e−5	0	3.08307e-5i
$922$	4.67265	−	9.17060i	0.153886	−	0.302018i
$923$	−0.999189	−	0.999189i	−0.0328887	−	0.0328887i
$924$	0.0303921	+	0.0708406i	0.000999826	+	0.00233049i
$925$	8.74213	−	44.8385i	0.287440	−	1.47428i
$926$	18.8758	−	6.13314i	0.620299	−	0.201547i
$927$	−1.47368	−	9.30443i	−0.0484019	−	0.305598i
$928$	0.607438	−	3.83521i	0.0199401	−	0.125897i
$929$	−11.5215	−	3.74356i	−0.378008	−	0.122822i	0.113849	−	0.993498i	$-0.463682\pi$
$929$	−11.5215	−	3.74356i	−0.378008	−	0.122822i	−0.491857	+	0.870676i	$0.663682\pi$
$930$	−3.08526	−	3.19670i	−0.101170	−	0.104824i
$931$	−18.9357	−	26.0628i	−0.620594	−	0.854174i
$932$	23.8176	−	3.77234i	0.780171	−	0.123567i
$933$	−4.14113	−	2.11001i	−0.135575	−	0.0690787i
$934$	−24.4286			−0.799329
$935$	20.9536	−	33.8001i	0.685256	−	1.10538i
$936$	−5.88104			−0.192228
$937$	−11.4178	−	5.81766i	−0.373003	−	0.190055i	0.257432	−	0.966296i	$-0.417124\pi$
$937$	−11.4178	−	5.81766i	−0.373003	−	0.190055i	−0.630435	+	0.776242i	$0.717124\pi$
$938$	−0.212974	+	0.0337318i	−0.00695386	+	0.00110138i
$939$	3.62237	+	4.98576i	0.118211	+	0.162704i
$940$	0.352115	−	19.8500i	0.0114847	−	0.647435i
$941$	6.81210	+	2.21339i	0.222068	+	0.0721543i	0.417938	−	0.908476i	$-0.362753\pi$
$941$	6.81210	+	2.21339i	0.222068	+	0.0721543i	−0.195870	+	0.980630i	$0.562753\pi$
$942$	0.524004	−	3.30843i	0.0170730	−	0.107794i
$943$	0.172230	+	1.08742i	0.00560857	+	0.0354111i
$944$	−10.2872	+	3.34252i	−0.334820	+	0.108790i
$945$	0.273080	+	0.145298i	0.00888329	+	0.00472656i
$946$	−9.82551	+	0.897706i	−0.319455	+	0.0291869i
$947$	−16.2126	−	16.2126i	−0.526838	−	0.526838i	0.392790	−	0.919628i	$-0.371510\pi$
$947$	−16.2126	−	16.2126i	−0.526838	−	0.526838i	−0.919628	+	0.392790i	$0.871510\pi$
$948$	−0.745258	+	1.46265i	−0.0242048	+	0.0475047i
$949$	15.6424	−	21.5300i	0.507775	−	0.698892i
$950$	−20.8942	+	9.72868i	−0.677896	+	0.315640i
$951$	−0.601076	+	1.84992i	−0.0194912	+	0.0599879i
$952$	0.258242	+	0.506828i	0.00836967	+	0.0164264i
$953$	−4.32716	−	0.685354i	−0.140170	−	0.0222008i	0.0859550	−	0.996299i	$-0.472606\pi$
$953$	−4.32716	−	0.685354i	−0.140170	−	0.0222008i	−0.226125	+	0.974098i	$0.572606\pi$
$954$	19.2278	+	13.9698i	0.622523	+	0.452289i
$955$	−4.70823	+	26.6575i	−0.152355	+	0.862616i
$956$			25.9442i			0.839097i
$957$	1.50447	+	2.38717i	0.0486324	+	0.0771663i
$958$	−10.3528	+	10.3528i	−0.334485	+	0.334485i
$959$	−0.0714092	−	0.219775i	−0.00230592	−	0.00709690i
$960$	0.159636	−	0.463189i	0.00515222	−	0.0149494i
$961$	−41.4467	+	30.1128i	−1.33699	+	0.971381i
$962$	16.2182	−	8.26359i	0.522896	−	0.266429i
$963$	48.0307	−	24.4729i	1.54777	−	0.788627i
$964$	−15.7743	+	11.4607i	−0.508055	+	0.369124i
$965$	−7.14354	+	20.7272i	−0.229959	+	0.667233i
$966$	0.0128407	+	0.0395195i	0.000413141	+	0.00127152i
$967$	−25.2637	+	25.2637i	−0.812426	+	0.812426i	−0.984997	−	0.172571i	$-0.944793\pi$
$967$	−25.2637	+	25.2637i	−0.812426	+	0.812426i	0.172571	+	0.984997i	$0.444793\pi$
$968$	3.13509	−	10.5438i	0.100766	−	0.338890i
$969$		−	5.41580i		−	0.173981i
$970$	0.693729	−	3.92782i	0.0222743	−	0.126115i
$971$	−20.7820	−	15.0990i	−0.666927	−	0.484551i	0.202068	−	0.979372i	$-0.435234\pi$
$971$	−20.7820	−	15.0990i	−0.666927	−	0.484551i	−0.868995	+	0.494820i	$0.835234\pi$
$972$	−5.71875	−	0.905760i	−0.183429	−	0.0290523i
$973$	0.578445	+	1.13526i	0.0185441	+	0.0363948i
$974$	0.195800	−	0.602612i	0.00627385	−	0.0193089i
$975$	2.05046	+	0.747623i	0.0656672	+	0.0239431i
$976$	0.428143	−	0.589289i	0.0137045	−	0.0188627i
$977$	−12.5517	+	24.6342i	−0.401566	+	0.788117i	−0.999914	−	0.0131191i	$-0.995824\pi$
$977$	−12.5517	+	24.6342i	−0.401566	+	0.788117i	0.598348	+	0.801236i	$0.295824\pi$
$978$	3.12097	+	3.12097i	0.0997976	+	0.0997976i
$979$	1.50292	+	0.340895i	0.0480336	+	0.0108950i
$980$	13.7960	+	7.34049i	0.440698	+	0.234483i
$981$	18.1835	−	5.90816i	0.580553	−	0.188633i
$982$	2.53917	+	16.0317i	0.0810283	+	0.511593i
$983$	5.50769	−	34.7742i	0.175668	−	1.10912i	−0.729472	−	0.684011i	$-0.760234\pi$
$983$	5.50769	−	34.7742i	0.175668	−	1.10912i	0.905140	−	0.425114i	$-0.139766\pi$
$984$	−0.128320	−	0.0416938i	−0.00409070	−	0.00132915i
$985$	−0.946103	+	53.3352i	−0.0301453	+	1.69940i
$986$	12.2389	+	16.8453i	0.389765	+	0.536465i
$987$	−0.203815	+	0.0322811i	−0.00648750	+	0.00102752i
$988$	−8.18246	−	4.16917i	−0.260319	−	0.132639i
$989$	−5.31858			−0.169121
$990$	−8.27335	−	20.2691i	−0.262944	−	0.644194i
$991$	7.86972			0.249990			0.124995	−	0.992157i	$-0.460109\pi$
$991$	7.86972			0.249990			0.124995	+	0.992157i	$0.460109\pi$
$992$	−8.07976	−	4.11684i	−0.256533	−	0.130710i
$993$	−2.68475	+	0.425222i	−0.0851979	+	0.0134940i
$994$	0.0442252	+	0.0608707i	0.00140274	+	0.00193070i
$995$	−6.82407	−	7.07055i	−0.216338	−	0.224151i
$996$	1.18637	+	0.385475i	0.0375916	+	0.0122142i
$997$	7.27985	−	45.9631i	0.230555	−	1.45567i	−0.552395	−	0.833583i	$-0.686286\pi$
$997$	7.27985	−	45.9631i	0.230555	−	1.45567i	0.782950	−	0.622085i	$-0.213714\pi$
$998$	4.43324	+	27.9904i	0.140332	+	0.886020i
$999$	11.3318	−	3.68191i	0.358521	−	0.116491i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.k.a.17.5	yes	48
3.2	odd	2		990.2.bh.c.127.1		48
4.3	odd	2		880.2.cm.c.17.3		48
5.2	odd	4		550.2.bh.b.193.2		48
5.3	odd	4	inner	110.2.k.a.83.5	yes	48
5.4	even	2		550.2.bh.b.457.2		48
11.2	odd	10	inner	110.2.k.a.57.5	yes	48
15.8	even	4		990.2.bh.c.523.2		48
20.3	even	4		880.2.cm.c.193.3		48
33.2	even	10		990.2.bh.c.937.2		48
44.35	even	10		880.2.cm.c.497.3		48
55.2	even	20		550.2.bh.b.343.2		48
55.13	even	20	inner	110.2.k.a.13.5	✓	48
55.24	odd	10		550.2.bh.b.57.2		48
165.68	odd	20		990.2.bh.c.343.1		48
220.123	odd	20		880.2.cm.c.673.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.13.5	✓	48	55.13	even	20	inner
110.2.k.a.17.5	yes	48	1.1	even	1	trivial
110.2.k.a.57.5	yes	48	11.2	odd	10	inner
110.2.k.a.83.5	yes	48	5.3	odd	4	inner
550.2.bh.b.57.2		48	55.24	odd	10
550.2.bh.b.193.2		48	5.2	odd	4
550.2.bh.b.343.2		48	55.2	even	20
550.2.bh.b.457.2		48	5.4	even	2
880.2.cm.c.17.3		48	4.3	odd	2
880.2.cm.c.193.3		48	20.3	even	4
880.2.cm.c.497.3		48	44.35	even	10
880.2.cm.c.673.3		48	220.123	odd	20
990.2.bh.c.127.1		48	3.2	odd	2
990.2.bh.c.343.1		48	165.68	odd	20
990.2.bh.c.523.2		48	15.8	even	4
990.2.bh.c.937.2		48	33.2	even	10

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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	110.2.k.a.17.5

Level	$110$
Weight	$2$
Character	110.17
Analytic conductor	$0.878$
Analytic rank	$0$
Dimension	$48$
Inner twists	$4$