LMFDB - Embedded newform 416.2.bf.a.53.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(53,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("416.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$416 = 2^{5} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	416.bf (of order $8$ , degree $4$ , 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			53.12
Character	$\chi$	$=$	416.53
Dual form			416.2.bf.a.157.12

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.948103 - 1.04933i) q^{2} +(-0.976242 + 0.404373i) q^{3} +(-0.202200 + 1.98975i) q^{4} +(-0.597830 + 1.44329i) q^{5} +(1.34990 + 0.641016i) q^{6} +(2.62460 + 2.62460i) q^{7} +(2.27962 - 1.67432i) q^{8} +(-1.33179 + 1.33179i) q^{9} +(2.08130 - 0.741064i) q^{10} +(-5.89298 - 2.44095i) q^{11} +(-0.607205 - 2.02424i) q^{12} +(-0.382683 - 0.923880i) q^{13} +(0.265687 - 5.24247i) q^{14} -1.65074i q^{15} +(-3.91823 - 0.804655i) q^{16} -6.51659i q^{17} +(2.66017 + 0.134817i) q^{18} +(-0.250211 - 0.604064i) q^{19} +(-2.75091 - 1.48137i) q^{20} +(-3.62356 - 1.50093i) q^{21} +(3.02578 + 8.49797i) q^{22} +(-5.18047 + 5.18047i) q^{23} +(-1.54841 + 2.55635i) q^{24} +(1.80985 + 1.80985i) q^{25} +(-0.606634 + 1.27750i) q^{26} +(1.97473 - 4.76741i) q^{27} +(-5.75299 + 4.69161i) q^{28} +(-3.12542 + 1.29459i) q^{29} +(-1.73218 + 1.56508i) q^{30} -2.92892 q^{31} +(2.87054 + 4.87443i) q^{32} +6.74002 q^{33} +(-6.83807 + 6.17840i) q^{34} +(-5.35711 + 2.21899i) q^{35} +(-2.38064 - 2.91922i) q^{36} +(0.285686 - 0.689708i) q^{37} +(-0.396638 + 0.835270i) q^{38} +(0.747183 + 0.747183i) q^{39} +(1.05370 + 4.29111i) q^{40} +(-1.01306 + 1.01306i) q^{41} +(1.86053 + 5.22535i) q^{42} +(-10.8876 - 4.50980i) q^{43} +(6.04845 - 11.2320i) q^{44} +(-1.12597 - 2.71834i) q^{45} +(10.3477 + 0.524417i) q^{46} +3.32378i q^{47} +(4.15052 - 0.798887i) q^{48} +6.77702i q^{49} +(0.183211 - 3.61506i) q^{50} +(2.63513 + 6.36176i) q^{51} +(1.91567 - 0.574637i) q^{52} +(3.29436 + 1.36457i) q^{53} +(-6.87485 + 2.44785i) q^{54} +(7.04599 - 7.04599i) q^{55} +(10.3775 + 1.58868i) q^{56} +(0.488534 + 0.488534i) q^{57} +(4.32168 + 2.05220i) q^{58} +(-2.22325 + 5.36739i) q^{59} +(3.28457 + 0.333780i) q^{60} +(11.6680 - 4.83305i) q^{61} +(2.77691 + 3.07341i) q^{62} -6.99082 q^{63} +(2.39333 - 7.63361i) q^{64} +1.56220 q^{65} +(-6.39024 - 7.07253i) q^{66} +(-12.4084 + 5.13974i) q^{67} +(12.9664 + 1.31765i) q^{68} +(2.96255 - 7.15223i) q^{69} +(7.40756 + 3.51757i) q^{70} +(-9.04213 - 9.04213i) q^{71} +(-0.806137 + 5.26581i) q^{72} +(-3.21819 + 3.21819i) q^{73} +(-0.994593 + 0.354134i) q^{74} +(-2.49871 - 1.03500i) q^{75} +(1.25253 - 0.375717i) q^{76} +(-9.06018 - 21.8732i) q^{77} +(0.0756371 - 1.49245i) q^{78} +5.71407i q^{79} +(3.50378 - 5.17409i) q^{80} -0.197632i q^{81} +(2.02352 + 0.102552i) q^{82} +(2.54562 + 6.14568i) q^{83} +(3.71915 - 6.90649i) q^{84} +(9.40532 + 3.89581i) q^{85} +(5.59031 + 15.7005i) q^{86} +(2.52767 - 2.52767i) q^{87} +(-17.5207 + 4.30227i) q^{88} +(4.16399 + 4.16399i) q^{89} +(-1.78491 + 3.75879i) q^{90} +(1.42042 - 3.42920i) q^{91} +(-9.26036 - 11.3553i) q^{92} +(2.85933 - 1.18437i) q^{93} +(3.48775 - 3.15128i) q^{94} +1.02142 q^{95} +(-4.77342 - 3.59785i) q^{96} -9.16804 q^{97} +(7.11135 - 6.42532i) q^{98} +(11.0990 - 4.59737i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51}+ \cdots + 56 q^{98}+O(q^{100})$ 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$ .

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.948103	−	1.04933i	−0.670410	−	0.741991i
$2$	−0.948103	−	1.04933i	−0.670410	−	0.741991i
$3$	−0.976242	+	0.404373i	−0.563633	+	0.233465i	−0.646262	−	0.763116i	$-0.723669\pi$
$3$	−0.976242	+	0.404373i	−0.563633	+	0.233465i	0.0826283	+	0.996580i	$0.473669\pi$
$4$	−0.202200	+	1.98975i	−0.101100	+	0.994876i
$5$	−0.597830	+	1.44329i	−0.267358	+	0.645458i	−0.999357	−	0.0358466i	$-0.988587\pi$
$5$	−0.597830	+	1.44329i	−0.267358	+	0.645458i	0.732000	+	0.681305i	$0.238587\pi$
$6$	1.34990	+	0.641016i	0.551094	+	0.261694i
$7$	2.62460	+	2.62460i	0.992005	+	0.992005i	0.999968	−	0.00796378i	$-0.00253498\pi$
$7$	2.62460	+	2.62460i	0.992005	+	0.992005i	−0.00796378	+	0.999968i	$0.502535\pi$
$8$	2.27962	−	1.67432i	0.805967	−	0.591960i
$9$	−1.33179	+	1.33179i	−0.443930	+	0.443930i
$10$	2.08130	−	0.741064i	0.658163	−	0.234345i
$11$	−5.89298	−	2.44095i	−1.77680	−	0.735974i	−0.993433	−	0.114413i	$-0.963501\pi$
$11$	−5.89298	−	2.44095i	−1.77680	−	0.735974i	−0.783366	−	0.621561i	$-0.786499\pi$
$12$	−0.607205	−	2.02424i	−0.175285	−	0.584349i
$13$	−0.382683	−	0.923880i	−0.106137	−	0.256238i
$13$	−0.382683	−	0.923880i	−0.106137	−	0.256238i
$14$	0.265687	−	5.24247i	0.0710079	−	1.40111i
$15$		−	1.65074i		−	0.426220i
$16$	−3.91823	−	0.804655i	−0.979558	−	0.201164i
$17$		−	6.51659i		−	1.58050i	−0.612782	−	0.790252i	$-0.709950\pi$
$17$		−	6.51659i		−	1.58050i	0.612782	−	0.790252i	$-0.290050\pi$
$18$	2.66017	+	0.134817i	0.627007	+	0.0317766i
$19$	−0.250211	−	0.604064i	−0.0574024	−	0.138582i	0.892576	−	0.450897i	$-0.148896\pi$
$19$	−0.250211	−	0.604064i	−0.0574024	−	0.138582i	−0.949979	+	0.312315i	$0.898896\pi$
$20$	−2.75091	−	1.48137i	−0.615121	−	0.331244i
$21$	−3.62356	−	1.50093i	−0.790725	−	0.327529i
$22$	3.02578	+	8.49797i	0.645099	+	1.81177i
$23$	−5.18047	+	5.18047i	−1.08020	+	1.08020i	−0.0837121	+	0.996490i	$0.526678\pi$
$23$	−5.18047	+	5.18047i	−1.08020	+	1.08020i	−0.996490	+	0.0837121i	$0.973322\pi$
$24$	−1.54841	+	2.55635i	−0.316068	+	0.521813i
$25$	1.80985	+	1.80985i	0.361970	+	0.361970i
$26$	−0.606634	+	1.27750i	−0.118971	+	0.250538i
$27$	1.97473	−	4.76741i	0.380036	−	0.917489i
$28$	−5.75299	+	4.69161i	−1.08721	+	0.886630i
$29$	−3.12542	+	1.29459i	−0.580377	+	0.240400i	−0.653504	−	0.756923i	$-0.726702\pi$
$29$	−3.12542	+	1.29459i	−0.580377	+	0.240400i	0.0731278	+	0.997323i	$0.476702\pi$
$30$	−1.73218	+	1.56508i	−0.316252	+	0.285743i
$31$	−2.92892			−0.526049			−0.263024	−	0.964789i	$-0.584720\pi$
$31$	−2.92892			−0.526049			−0.263024	+	0.964789i	$0.584720\pi$
$32$	2.87054	+	4.87443i	0.507444	+	0.861685i
$33$	6.74002			1.17329
$34$	−6.83807	+	6.17840i	−1.17272	+	1.05959i
$35$	−5.35711	+	2.21899i	−0.905518	+	0.375078i
$36$	−2.38064	−	2.91922i	−0.396774	−	0.486537i
$37$	0.285686	−	0.689708i	0.0469665	−	0.113387i	−0.898655	−	0.438656i	$-0.855455\pi$
$37$	0.285686	−	0.689708i	0.0469665	−	0.113387i	0.945622	+	0.325269i	$0.105455\pi$
$38$	−0.396638	+	0.835270i	−0.0643432	+	0.135499i
$39$	0.747183	+	0.747183i	0.119645	+	0.119645i
$40$	1.05370	+	4.29111i	0.166604	+	0.678483i
$41$	−1.01306	+	1.01306i	−0.158213	+	0.158213i	−0.781775	−	0.623561i	$-0.785685\pi$
$41$	−1.01306	+	1.01306i	−0.158213	+	0.158213i	0.623561	+	0.781775i	$0.285685\pi$
$42$	1.86053	+	5.22535i	0.287087	+	0.806289i
$43$	−10.8876	−	4.50980i	−1.66035	−	0.687739i	−0.662244	−	0.749288i	$-0.730396\pi$
$43$	−10.8876	−	4.50980i	−1.66035	−	0.687739i	−0.998104	+	0.0615492i	$0.980396\pi$
$44$	6.04845	−	11.2320i	0.911838	−	1.69329i
$45$	−1.12597	−	2.71834i	−0.167850	−	0.405226i
$46$	10.3477	+	0.524417i	1.52568	+	0.0773211i
$47$			3.32378i			0.484823i	0.970174	+	0.242411i	$0.0779383\pi$
$47$			3.32378i			0.484823i	−0.970174	+	0.242411i	$0.922062\pi$
$48$	4.15052	−	0.798887i	0.599076	−	0.115309i
$49$			6.77702i			0.968146i
$50$	0.183211	−	3.61506i	0.0259099	−	0.511247i
$51$	2.63513	+	6.36176i	0.368992	+	0.890825i
$52$	1.91567	−	0.574637i	0.265656	−	0.0796878i
$53$	3.29436	+	1.36457i	0.452515	+	0.187438i	0.597288	−	0.802027i	$-0.296245\pi$
$53$	3.29436	+	1.36457i	0.452515	+	0.187438i	−0.144773	+	0.989465i	$0.546245\pi$
$54$	−6.87485	+	2.44785i	−0.935549	+	0.333111i
$55$	7.04599	−	7.04599i	0.950082	−	0.950082i
$56$	10.3775	+	1.58868i	1.38675	+	0.212296i
$57$	0.488534	+	0.488534i	0.0647079	+	0.0647079i
$58$	4.32168	+	2.05220i	0.567465	+	0.269467i
$59$	−2.22325	+	5.36739i	−0.289442	+	0.698775i	−0.999988	−	0.00487584i	$-0.998448\pi$
$59$	−2.22325	+	5.36739i	−0.289442	+	0.698775i	0.710546	+	0.703651i	$0.248448\pi$
$60$	3.28457	+	0.333780i	0.424037	+	0.0430908i
$61$	11.6680	−	4.83305i	1.49394	−	0.618809i	0.521767	−	0.853088i	$-0.325273\pi$
$61$	11.6680	−	4.83305i	1.49394	−	0.618809i	0.972169	+	0.234279i	$0.0752729\pi$
$62$	2.77691	+	3.07341i	0.352668	+	0.390323i
$63$	−6.99082			−0.880761
$64$	2.39333	−	7.63361i	0.299166	−	0.954201i
$65$	1.56220			0.193768
$66$	−6.39024	−	7.07253i	−0.786584	−	0.870568i
$67$	−12.4084	+	5.13974i	−1.51593	+	0.627919i	−0.976771	−	0.214285i	$-0.931258\pi$
$67$	−12.4084	+	5.13974i	−1.51593	+	0.627919i	−0.539159	+	0.842204i	$0.681258\pi$
$68$	12.9664	+	1.31765i	1.57241	+	0.159789i
$69$	2.96255	−	7.15223i	0.356649	−	0.861027i
$70$	7.40756	+	3.51757i	0.885372	+	0.420430i
$71$	−9.04213	−	9.04213i	−1.07310	−	1.07310i	−0.997108	−	0.0759957i	$-0.975786\pi$
$71$	−9.04213	−	9.04213i	−1.07310	−	1.07310i	−0.0759957	−	0.997108i	$-0.524214\pi$
$72$	−0.806137	+	5.26581i	−0.0950041	+	0.620582i
$73$	−3.21819	+	3.21819i	−0.376660	+	0.376660i	−0.869896	−	0.493236i	$-0.835814\pi$
$73$	−3.21819	+	3.21819i	−0.376660	+	0.376660i	0.493236	+	0.869896i	$0.335814\pi$
$74$	−0.994593	+	0.354134i	−0.115619	+	0.0411673i
$75$	−2.49871	−	1.03500i	−0.288526	−	0.119511i
$76$	1.25253	−	0.375717i	0.143675	−	0.0430977i
$77$	−9.06018	−	21.8732i	−1.03250	−	2.49268i
$78$	0.0756371	−	1.49245i	0.00856421	−	0.168987i
$79$			5.71407i			0.642883i	0.946929	+	0.321442i	$0.104167\pi$
$79$			5.71407i			0.642883i	−0.946929	+	0.321442i	$0.895833\pi$
$80$	3.50378	−	5.17409i	0.391735	−	0.578481i
$81$		−	0.197632i		−	0.0219591i
$82$	2.02352	+	0.102552i	0.223461	+	0.0113249i
$83$	2.54562	+	6.14568i	0.279419	+	0.674576i	0.999820	−	0.0189813i	$-0.00604231\pi$
$83$	2.54562	+	6.14568i	0.279419	+	0.674576i	−0.720401	+	0.693558i	$0.756042\pi$
$84$	3.71915	−	6.90649i	0.405793	−	0.753560i
$85$	9.40532	+	3.89581i	1.02015	+	0.422560i
$86$	5.59031	+	15.7005i	0.602819	+	1.69303i
$87$	2.52767	−	2.52767i	0.270995	−	0.270995i
$88$	−17.5207	+	4.30227i	−1.86771	+	0.458623i
$89$	4.16399	+	4.16399i	0.441382	+	0.441382i	0.892476	−	0.451094i	$-0.148966\pi$
$89$	4.16399	+	4.16399i	0.441382	+	0.441382i	−0.451094	+	0.892476i	$0.648966\pi$
$90$	−1.78491	+	3.75879i	−0.188146	+	0.396211i
$91$	1.42042	−	3.42920i	0.148901	−	0.359478i
$92$	−9.26036	−	11.3553i	−0.965459	−	1.18388i
$93$	2.85933	−	1.18437i	0.296499	−	0.122814i
$94$	3.48775	−	3.15128i	0.359734	−	0.325030i
$95$	1.02142			0.104796
$96$	−4.77342	−	3.59785i	−0.487185	−	0.367204i
$97$	−9.16804			−0.930873			−0.465437	−	0.885081i	$-0.654103\pi$
$97$	−9.16804			−0.930873			−0.465437	+	0.885081i	$0.654103\pi$
$98$	7.11135	−	6.42532i	0.718355	−	0.649055i
$99$	11.0990	−	4.59737i	1.11550	−	0.462053i
$100$	−3.96711	+	3.23521i	−0.396711	+	0.323521i
$101$	2.28957	−	5.52751i	0.227821	−	0.550007i	−0.768091	−	0.640341i	$-0.778793\pi$
$101$	2.28957	−	5.52751i	0.227821	−	0.550007i	0.995912	+	0.0903332i	$0.0287932\pi$
$102$	4.17723	−	8.79674i	0.413608	−	0.871007i
$103$	8.18709	+	8.18709i	0.806698	+	0.806698i	0.984133	−	0.177435i	$-0.0567798\pi$
$103$	8.18709	+	8.18709i	0.806698	+	0.806698i	−0.177435	+	0.984133i	$0.556780\pi$
$104$	−2.41924	−	1.46536i	−0.237226	−	0.143690i
$105$	4.33254	−	4.33254i	0.422813	−	0.422813i
$106$	−1.69151	−	4.75063i	−0.164294	−	0.461422i
$107$	7.28976	+	3.01952i	0.704727	+	0.291908i	0.706121	−	0.708091i	$-0.250444\pi$
$107$	7.28976	+	3.01952i	0.704727	+	0.291908i	−0.00139340	+	0.999999i	$0.500444\pi$
$108$	9.08668	+	4.89319i	0.874366	+	0.470847i
$109$	1.51517	+	3.65794i	0.145127	+	0.350367i	0.979682	−	0.200557i	$-0.0642753\pi$
$109$	1.51517	+	3.65794i	0.145127	+	0.350367i	−0.834555	+	0.550924i	$0.814275\pi$
$110$	−14.0739	−	0.713264i	−1.34190	−	0.0680070i
$111$			0.788845i			0.0748739i
$112$	−8.17188	−	12.3957i	−0.772170	−	1.17128i
$113$		−	1.01935i		−	0.0958925i	−0.998850	−	0.0479462i	$-0.984732\pi$
$113$		−	1.01935i		−	0.0958925i	0.998850	−	0.0479462i	$-0.0152676\pi$
$114$	0.0494541	−	0.975815i	0.00463180	−	0.0913935i
$115$	−4.37987	−	10.5739i	−0.408425	−	0.986026i
$116$	−1.94396	−	6.48059i	−0.180492	−	0.601707i
$117$	1.74007	+	0.720759i	0.160869	+	0.0666342i
$118$	7.74005	−	2.75592i	0.712529	−	0.253703i
$119$	17.1034	−	17.1034i	1.56787	−	1.56787i
$120$	−2.76387	−	3.76307i	−0.252306	−	0.343520i
$121$	20.9908	+	20.9908i	1.90825	+	1.90825i
$122$	−16.1340	−	7.66141i	−1.46070	−	0.693631i
$123$	0.579338	−	1.39865i	0.0522371	−	0.126112i
$124$	0.592226	−	5.82782i	0.0531835	−	0.523353i
$125$	−10.9106	+	4.51930i	−0.975871	+	0.404219i
$126$	6.62802	+	7.33570i	0.590471	+	0.653516i
$127$	−6.14933			−0.545664			−0.272832	−	0.962062i	$-0.587960\pi$
$127$	−6.14933			−0.545664			−0.272832	+	0.962062i	$0.587960\pi$
$128$	−10.2793	+	4.72605i	−0.908572	+	0.417728i
$129$	12.4526			1.09639
$130$	−1.48113	−	1.63927i	−0.129904	−	0.143774i
$131$	−1.77577	+	0.735547i	−0.155149	+	0.0642650i	−0.458907	−	0.888484i	$-0.651759\pi$
$131$	−1.77577	+	0.735547i	−0.155149	+	0.0642650i	0.303757	+	0.952749i	$0.401759\pi$
$132$	−1.36283	+	13.4110i	−0.118619	+	1.16728i
$133$	0.928720	−	2.24213i	0.0805303	−	0.194417i
$134$	17.1578	+	8.14757i	1.48221	+	0.703843i
$135$	5.70020	+	5.70020i	0.490595	+	0.490595i
$136$	−10.9108	−	14.8553i	−0.935596	−	1.27383i
$137$	−3.05899	+	3.05899i	−0.261347	+	0.261347i	−0.825601	−	0.564254i	$-0.809164\pi$
$137$	−3.05899	+	3.05899i	−0.261347	+	0.261347i	0.564254	+	0.825601i	$0.309164\pi$
$138$	−10.3139	+	3.67235i	−0.877975	+	0.312611i
$139$	11.0433	+	4.57430i	0.936683	+	0.387987i	0.798210	−	0.602380i	$-0.205781\pi$
$139$	11.0433	+	4.57430i	0.936683	+	0.387987i	0.138473	+	0.990366i	$0.455781\pi$
$140$	−3.33203	−	11.1080i	−0.281608	−	0.938798i
$141$	−1.34404	−	3.24481i	−0.113189	−	0.273262i
$142$	−0.915332	+	18.0611i	−0.0768130	+	1.51565i
$143$			6.37851i			0.533398i
$144$	6.28989	−	4.14663i	0.524158	−	0.345552i
$145$		−	5.28484i		−	0.438882i
$146$	6.42812	+	0.325776i	0.531995	+	0.0269614i
$147$	−2.74044	−	6.61601i	−0.226028	−	0.545679i
$148$	1.31458	+	0.707904i	0.108058	+	0.0581893i
$149$	−6.38457	−	2.64457i	−0.523044	−	0.216652i	0.105509	−	0.994418i	$-0.466353\pi$
$149$	−6.38457	−	2.64457i	−0.523044	−	0.216652i	−0.628554	+	0.777766i	$0.716353\pi$
$150$	1.28297	+	3.60326i	0.104754	+	0.294205i
$151$	10.5457	−	10.5457i	0.858194	−	0.858194i	−0.132931	−	0.991125i	$-0.542439\pi$
$151$	10.5457	−	10.5457i	0.858194	−	0.858194i	0.991125	+	0.132931i	$0.0424390\pi$
$152$	−1.58178	−	0.958103i	−0.128299	−	0.0777124i
$153$	8.67872	+	8.67872i	0.701633	+	0.701633i
$154$	−14.3623	+	30.2452i	−1.15735	+	2.43723i
$155$	1.75099	−	4.22727i	0.140643	−	0.339543i
$156$	−1.63779	+	1.33563i	−0.131128	+	0.106936i
$157$	−9.12313	+	3.77892i	−0.728105	+	0.301591i	−0.715773	−	0.698333i	$-0.753925\pi$
$157$	−9.12313	+	3.77892i	−0.728105	+	0.301591i	−0.0123318	+	0.999924i	$0.503925\pi$
$158$	5.99597	−	5.41753i	0.477013	−	0.430996i
$159$	−3.76788			−0.298812
$160$	−8.75130	+	1.22894i	−0.691851	+	0.0971560i
$161$	−27.1933			−2.14313
$162$	−0.207382	+	0.187376i	−0.0162935	+	0.0147216i
$163$	−9.44232	+	3.91114i	−0.739580	+	0.306344i	−0.720482	−	0.693474i	$-0.756079\pi$
$163$	−9.44232	+	3.91114i	−0.739580	+	0.306344i	−0.0190977	+	0.999818i	$0.506079\pi$
$164$	−1.81090	−	2.22058i	−0.141407	−	0.173398i
$165$	−4.02939	+	9.72780i	−0.313687	+	0.757308i
$166$	4.03535	−	8.49795i	0.313204	−	0.659569i
$167$	−4.18543	−	4.18543i	−0.323879	−	0.323879i	0.526374	−	0.850253i	$-0.323551\pi$
$167$	−4.18543	−	4.18543i	−0.323879	−	0.323879i	−0.850253	+	0.526374i	$0.823551\pi$
$168$	−10.7734	+	2.64544i	−0.831182	+	0.204100i
$169$	−0.707107	+	0.707107i	−0.0543928	+	0.0543928i
$170$	−4.82921	−	13.5629i	−0.370384	−	1.04023i
$171$	1.13772	+	0.471257i	0.0870032	+	0.0360379i
$172$	11.1749	−	20.7518i	0.852076	−	1.58231i
$173$	6.85935	+	16.5599i	0.521507	+	1.25903i	0.936967	+	0.349418i	$0.113621\pi$
$173$	6.85935	+	16.5599i	0.521507	+	1.25903i	−0.415460	+	0.909611i	$0.636379\pi$
$174$	−5.04886	−	0.255875i	−0.382753	−	0.0193979i
$175$			9.50026i			0.718152i
$176$	21.1259	+	14.3060i	1.59243	+	1.07836i
$177$		−	6.13889i		−	0.461427i
$178$	0.421520	−	8.31731i	0.0315942	−	0.623409i
$179$	6.26096	+	15.1153i	0.467966	+	1.12977i	0.965050	+	0.262067i	$0.0844043\pi$
$179$	6.26096	+	15.1153i	0.467966	+	1.12977i	−0.497083	+	0.867703i	$0.665596\pi$
$180$	5.63650	−	1.69076i	0.420120	−	0.126022i
$181$	−22.2238	−	9.20539i	−1.65188	−	0.684231i	−0.654466	−	0.756091i	$-0.727107\pi$
$181$	−22.2238	−	9.20539i	−1.65188	−	0.684231i	−0.997415	+	0.0718598i	$0.977107\pi$
$182$	−4.94508	+	1.76074i	−0.366554	+	0.130515i
$183$	−9.43645	+	9.43645i	−0.697563	+	0.697563i
$184$	−3.13575	+	20.4832i	−0.231171	+	1.51004i
$185$	0.824656	+	0.824656i	0.0606299	+	0.0606299i
$186$	−3.95374	−	1.87748i	−0.289902	−	0.137664i
$187$	−15.9067	+	38.4021i	−1.16321	+	2.80824i
$188$	−6.61349	−	0.672067i	−0.482338	−	0.0490155i
$189$	17.6954	−	7.32968i	1.28715	−	0.533155i
$190$	−0.968414	−	1.07181i	−0.0702562	−	0.0777575i
$191$	20.7281			1.49983			0.749915	−	0.661535i	$-0.230094\pi$
$191$	20.7281			1.49983			0.749915	+	0.661535i	$0.230094\pi$
$192$	0.750353	+	8.42004i	0.0541520	+	0.607664i
$193$	16.6997			1.20207			0.601035	−	0.799223i	$-0.294755\pi$
$193$	16.6997			1.20207			0.601035	+	0.799223i	$0.294755\pi$
$194$	8.69225	+	9.62032i	0.624067	+	0.690699i
$195$	−1.52509	+	0.631713i	−0.109214	+	0.0452379i
$196$	−13.4846	−	1.37031i	−0.963185	−	0.0978795i
$197$	1.42194	−	3.43287i	0.101309	−	0.244582i	−0.865096	−	0.501607i	$-0.832742\pi$
$197$	1.42194	−	3.43287i	0.101309	−	0.244582i	0.966405	+	0.257025i	$0.0827424\pi$
$198$	−15.3472	−	7.28780i	−1.09068	−	0.517922i
$199$	3.26775	+	3.26775i	0.231645	+	0.231645i	0.813379	−	0.581734i	$-0.197626\pi$
$199$	3.26775	+	3.26775i	0.231645	+	0.231645i	−0.581734	+	0.813379i	$0.697626\pi$
$200$	7.15604	+	1.09551i	0.506008	+	0.0774642i
$201$	10.0353	−	10.0353i	0.707832	−	0.707832i
$202$	−7.97094	+	2.83813i	−0.560834	+	0.199690i
$203$	−11.6008	−	4.80519i	−0.814214	−	0.337258i
$204$	−13.1912	+	3.95691i	−0.923566	+	0.277039i
$205$	−0.856501	−	2.06778i	−0.0598206	−	0.144420i
$206$	0.828776	−	16.3532i	0.0577436	−	1.13938i
$207$		−	13.7986i		−	0.959068i
$208$	0.756037	+	3.92790i	0.0524218	+	0.272351i
$209$			4.17049i			0.288479i
$210$	−8.65397	−	0.438582i	−0.597181	−	0.0302650i
$211$	2.48177	+	5.99153i	0.170852	+	0.412474i	0.985992	−	0.166790i	$-0.0533401\pi$
$211$	2.48177	+	5.99153i	0.170852	+	0.412474i	−0.815140	+	0.579264i	$0.803340\pi$
$212$	−3.38127	+	6.27904i	−0.232227	+	0.431246i
$213$	12.4837	+	5.17092i	0.855369	+	0.354305i
$214$	−3.74297	−	10.5122i	−0.255864	−	0.718599i
$215$	13.0179	−	13.0179i	0.887814	−	0.887814i
$216$	−3.48053	−	14.1742i	−0.236820	−	0.964433i
$217$	−7.68722	−	7.68722i	−0.521843	−	0.521843i
$218$	2.40186	−	5.05802i	0.162675	−	0.342572i
$219$	1.84038	−	4.44307i	0.124361	−	0.300235i
$220$	12.5951	+	15.4445i	0.849160	+	1.04127i
$221$	−6.02054	+	2.49379i	−0.404985	+	0.167750i
$222$	0.827761	−	0.747907i	0.0555557	−	0.0501962i
$223$	−16.1538			−1.08174			−0.540870	−	0.841106i	$-0.681905\pi$
$223$	−16.1538			−1.08174			−0.540870	+	0.841106i	$0.681905\pi$
$224$	−5.25940	+	20.3274i	−0.351409	+	1.35818i
$225$	−4.82068			−0.321379
$226$	−1.06964	+	0.966450i	−0.0711513	+	0.0642873i
$227$	−19.1776	+	7.94363i	−1.27286	+	0.527237i	−0.913834	−	0.406089i	$-0.866892\pi$
$227$	−19.1776	+	7.94363i	−1.27286	+	0.527237i	−0.359030	+	0.933326i	$0.616892\pi$
$228$	−1.07084	+	0.873280i	−0.0709183	+	0.0578344i
$229$	−9.41379	+	22.7269i	−0.622080	+	1.50184i	0.227176	+	0.973854i	$0.427051\pi$
$229$	−9.41379	+	22.7269i	−0.622080	+	1.50184i	−0.849256	+	0.527981i	$0.822949\pi$
$230$	−6.94302	+	14.6211i	−0.457809	+	0.964089i
$231$	17.6898	+	17.6898i	1.16391	+	1.16391i
$232$	−4.95722	+	8.18413i	−0.325457	+	0.537314i
$233$	14.6261	−	14.6261i	0.958186	−	0.958186i	−0.0409739	−	0.999160i	$-0.513046\pi$
$233$	14.6261	−	14.6261i	0.958186	−	0.958186i	0.999160	+	0.0409739i	$0.0130460\pi$
$234$	−0.893447	−	2.50926i	−0.0584064	−	0.164036i
$235$	−4.79717	−	1.98705i	−0.312933	−	0.129621i
$236$	−10.2302	−	5.50900i	−0.665932	−	0.358605i
$237$	−2.31061	−	5.57832i	−0.150091	−	0.362351i
$238$	−34.1630	−	1.73137i	−2.21446	−	0.112228i
$239$		−	15.3952i		−	0.995833i	−0.867225	−	0.497916i	$-0.834099\pi$
$239$		−	15.3952i		−	0.995833i	0.867225	−	0.497916i	$-0.165901\pi$
$240$	−1.32828	+	6.46800i	−0.0857401	+	0.417507i
$241$			7.17624i			0.462263i	0.972923	+	0.231131i	$0.0742427\pi$
$241$			7.17624i			0.462263i	−0.972923	+	0.231131i	$0.925757\pi$
$242$	2.12489	−	41.9277i	0.136593	−	2.69521i
$243$	6.00410	+	14.4952i	0.385163	+	0.929866i
$244$	7.25731	+	24.1937i	0.464601	+	1.54884i
$245$	−9.78120	−	4.05151i	−0.624898	−	0.258841i
$246$	−2.01692	+	0.718142i	−0.128594	+	0.0457871i
$247$	−0.462331	+	0.462331i	−0.0294174	+	0.0294174i
$248$	−6.67681	+	4.90393i	−0.423978	+	0.311400i
$249$	−4.97029	−	4.97029i	−0.314979	−	0.314979i
$250$	15.0866	+	7.16405i	0.954160	+	0.453094i
$251$	4.76537	−	11.5046i	0.300787	−	0.726165i	−0.699150	−	0.714975i	$-0.746438\pi$
$251$	4.76537	−	11.5046i	0.300787	−	0.726165i	0.999937	−	0.0111900i	$-0.00356196\pi$
$252$	1.41354	−	13.9100i	0.0890448	−	0.876248i
$253$	43.1736	−	17.8831i	2.71430	−	1.12430i
$254$	5.83020	+	6.45269i	0.365819	+	0.404878i
$255$	−10.7572			−0.673643
$256$	14.7051	+	6.30565i	0.919066	+	0.394103i
$257$	−14.5268			−0.906160			−0.453080	−	0.891470i	$-0.649675\pi$
$257$	−14.5268			−0.906160			−0.453080	+	0.891470i	$0.649675\pi$
$258$	−11.8064	−	13.0669i	−0.735032	−	0.813511i
$259$	2.56002	−	1.06039i	0.159072	−	0.0658896i
$260$	−0.315877	+	3.10840i	−0.0195899	+	0.192775i
$261$	2.43828	−	5.88653i	0.150926	−	0.364367i
$262$	2.45544	+	1.16600i	0.151698	+	0.0720355i
$263$	11.9439	+	11.9439i	0.736495	+	0.736495i	0.971898	−	0.235403i	$-0.0756409\pi$
$263$	11.9439	+	11.9439i	0.736495	+	0.736495i	−0.235403	+	0.971898i	$0.575641\pi$
$264$	15.3647	−	11.2849i	0.945631	−	0.694539i
$265$	−3.93893	+	3.93893i	−0.241967	+	0.241967i
$266$	−3.23326	+	1.15123i	−0.198244	+	0.0705866i
$267$	−5.74887	−	2.38126i	−0.351825	−	0.145731i
$268$	−7.71782	−	25.7289i	−0.471441	−	1.57165i
$269$	1.72631	+	4.16768i	0.105255	+	0.254108i	0.967729	−	0.251993i	$-0.0810861\pi$
$269$	1.72631	+	4.16768i	0.105255	+	0.254108i	−0.862474	+	0.506101i	$0.831086\pi$
$270$	0.577030	−	11.3858i	0.0351169	−	0.692917i
$271$			9.45765i			0.574511i	0.957854	+	0.287256i	$0.0927429\pi$
$271$			9.45765i			0.574511i	−0.957854	+	0.287256i	$0.907257\pi$
$272$	−5.24361	+	25.5335i	−0.317940	+	1.54820i
$273$			3.92211i			0.237377i
$274$	6.11014	+	0.309661i	0.369127	+	0.0187073i
$275$	−6.24765	−	15.0832i	−0.376748	−	0.909549i
$276$	13.6321	+	7.34092i	0.820558	+	0.441871i
$277$	2.33882	+	0.968773i	0.140526	+	0.0582079i	0.451838	−	0.892100i	$-0.350768\pi$
$277$	2.33882	+	0.968773i	0.140526	+	0.0582079i	−0.311312	+	0.950308i	$0.600768\pi$
$278$	−5.67026	−	15.9250i	−0.340079	−	0.955120i
$279$	3.90070	−	3.90070i	0.233529	−	0.233529i
$280$	−8.49689	+	14.0280i	−0.507786	+	0.838331i
$281$	19.5935	+	19.5935i	1.16885	+	1.16885i	0.982479	+	0.186372i	$0.0596730\pi$
$281$	19.5935	+	19.5935i	1.16885	+	1.16885i	0.186372	+	0.982479i	$0.440327\pi$
$282$	−2.13059	+	4.48676i	−0.126875	+	0.267183i
$283$	7.55259	−	18.2336i	0.448955	−	1.08387i	−0.523759	−	0.851866i	$-0.675471\pi$
$283$	7.55259	−	18.2336i	0.448955	−	1.08387i	0.972714	−	0.232007i	$-0.0745292\pi$
$284$	19.8199	−	16.1633i	1.17610	−	0.959115i
$285$	−0.997155	+	0.413035i	−0.0590664	+	0.0244661i
$286$	6.69318	−	6.04749i	0.395776	−	0.357595i
$287$	−5.31775			−0.313897
$288$	−10.3147	−	2.66876i	−0.607797	−	0.157258i
$289$	−25.4659			−1.49799
$290$	−5.54555	+	5.01057i	−0.325646	+	0.294231i
$291$	8.95022	−	3.70730i	0.524671	−	0.217326i
$292$	−5.75268	−	7.05411i	−0.336650	−	0.412811i
$293$	−9.10839	+	21.9896i	−0.532118	+	1.28465i	0.398000	+	0.917385i	$0.369704\pi$
$293$	−9.10839	+	21.9896i	−0.532118	+	1.28465i	−0.930118	+	0.367261i	$0.880296\pi$
$294$	−4.34418	+	9.14830i	−0.253358	+	0.533540i
$295$	−6.41757	−	6.41757i	−0.373646	−	0.373646i
$296$	−0.503533	−	2.05060i	−0.0292672	−	0.119189i
$297$	−23.2740	+	23.2740i	−1.35050	+	1.35050i
$298$	3.27819	+	9.20687i	0.189900	+	0.533340i
$299$	6.76861	+	2.80365i	0.391439	+	0.162139i
$300$	2.56463	−	4.76253i	0.148069	−	0.274965i
$301$	−16.7392	−	40.4121i	−0.964833	−	2.32931i
$302$	−21.0643	−	1.06753i	−1.21211	−	0.0614297i
$303$			6.32202i			0.363191i
$304$	0.494323	+	2.56820i	0.0283514	+	0.147296i
$305$			19.7297i			1.12972i
$306$	0.878544	−	17.3352i	0.0502230	−	0.990987i
$307$	0.950305	+	2.29424i	0.0542368	+	0.130939i	0.948675	−	0.316252i	$-0.102424\pi$
$307$	0.950305	+	2.29424i	0.0542368	+	0.130939i	−0.894439	+	0.447191i	$0.852424\pi$
$308$	45.3542	−	13.6048i	2.58430	−	0.775203i
$309$	−11.3032	−	4.68194i	−0.643017	−	0.266347i
$310$	−6.09594	+	2.17051i	−0.346226	+	0.123277i
$311$	6.11886	−	6.11886i	0.346969	−	0.346969i	−0.512011	−	0.858979i	$-0.671099\pi$
$311$	6.11886	−	6.11886i	0.346969	−	0.346969i	0.858979	+	0.512011i	$0.171099\pi$
$312$	2.95431	+	0.452272i	0.167255	+	0.0256049i
$313$	−12.6856	−	12.6856i	−0.717034	−	0.717034i	0.250963	−	0.967997i	$-0.419253\pi$
$313$	−12.6856	−	12.6856i	−0.717034	−	0.717034i	−0.967997	+	0.250963i	$0.919253\pi$
$314$	12.6150	+	5.99039i	0.711906	+	0.338057i
$315$	4.17932	−	10.0898i	0.235478	−	0.568494i
$316$	−11.3696	−	1.15538i	−0.639590	−	0.0649955i
$317$	−1.11612	+	0.462311i	−0.0626875	+	0.0259660i	−0.413807	−	0.910365i	$-0.635801\pi$
$317$	−1.11612	+	0.462311i	−0.0626875	+	0.0259660i	0.351119	+	0.936331i	$0.385801\pi$
$318$	3.57234	+	3.95376i	0.200327	+	0.221716i
$319$	21.5781			1.20814
$320$	9.58670	+	8.01787i	0.535913	+	0.448212i
$321$	−8.33757			−0.465358
$322$	25.7820	+	28.5348i	1.43678	+	1.59018i
$323$	−3.93643	+	1.63052i	−0.219029	+	0.0907248i
$324$	0.393239	+	0.0399612i	0.0218466	+	0.00222006i
$325$	0.979485	−	2.36469i	0.0543320	−	0.131169i
$326$	13.0564	+	6.19998i	0.723126	+	0.343385i
$327$	−2.95834	−	2.95834i	−0.163597	−	0.163597i
$328$	−0.613209	+	4.00557i	−0.0338588	+	0.221171i
$329$	−8.72357	+	8.72357i	−0.480946	+	0.480946i
$330$	14.0280	−	4.99479i	0.772215	−	0.274954i
$331$	−9.83435	−	4.07352i	−0.540545	−	0.223901i	0.0956699	−	0.995413i	$-0.469501\pi$
$331$	−9.83435	−	4.07352i	−0.540545	−	0.223901i	−0.636215	+	0.771512i	$0.719501\pi$
$332$	−12.7431	+	3.82251i	−0.699369	+	0.209787i
$333$	0.538072	+	1.29902i	0.0294861	+	0.0711858i
$334$	−0.423690	+	8.36014i	−0.0231833	+	0.457446i
$335$		−	20.9816i		−	1.14635i
$336$	12.9902	+	8.79669i	0.708674	+	0.479899i
$337$		−	1.25645i		−	0.0684434i	−0.999414	−	0.0342217i	$-0.989105\pi$
$337$		−	1.25645i		−	0.0684434i	0.999414	−	0.0342217i	$-0.0108952\pi$
$338$	1.41240	+	0.0715802i	0.0768245	+	0.00389345i
$339$	0.412197	+	0.995133i	0.0223875	+	0.0540482i
$340$	−9.65345	+	17.9265i	−0.523532	+	0.972202i
$341$	17.2600	+	7.14934i	0.934683	+	0.387158i
$342$	−0.584166	−	1.64064i	−0.0315881	−	0.0887158i
$343$	0.585229	−	0.585229i	0.0315994	−	0.0315994i
$344$	−32.3705	+	7.94870i	−1.74530	+	0.428565i
$345$	8.55163	+	8.55163i	0.460404	+	0.460404i
$346$	10.8735	−	22.8983i	0.584564	−	1.23102i
$347$	3.65323	−	8.81968i	0.196116	−	0.473465i	−0.794977	−	0.606640i	$-0.792517\pi$
$347$	3.65323	−	8.81968i	0.196116	−	0.473465i	0.991093	+	0.133174i	$0.0425171\pi$
$348$	4.51835	+	5.54054i	0.242209	+	0.297004i
$349$	18.8523	−	7.80886i	1.00914	−	0.417999i	0.183998	−	0.982927i	$-0.441096\pi$
$349$	18.8523	−	7.80886i	1.00914	−	0.417999i	0.825140	+	0.564928i	$0.191096\pi$
$350$	9.96894	−	9.00723i	0.532862	−	0.481457i
$351$	−5.16021			−0.275432
$352$	−5.01777	−	35.7317i	−0.267448	−	1.90451i
$353$	−29.5885			−1.57484			−0.787420	−	0.616417i	$-0.788583\pi$
$353$	−29.5885			−1.57484			−0.787420	+	0.616417i	$0.788583\pi$
$354$	−6.44174	+	5.82030i	−0.342375	+	0.309346i
$355$	18.4561	−	7.64475i	0.979546	−	0.405741i
$356$	−9.12728	+	7.44336i	−0.483745	+	0.394497i
$357$	−9.78092	+	23.6132i	−0.517661	+	1.24974i
$358$	9.92494	−	20.9007i	0.524549	−	1.10464i
$359$	−20.6058	−	20.6058i	−1.08753	−	1.08753i	−0.995782	−	0.0917506i	$-0.970754\pi$
$359$	−20.6058	−	20.6058i	−1.08753	−	1.08753i	−0.0917506	−	0.995782i	$-0.529246\pi$
$360$	−7.11815	−	4.31155i	−0.375160	−	0.227238i
$361$	13.1327	−	13.1327i	0.691197	−	0.691197i
$362$	11.4109	+	32.0478i	0.599745	+	1.68440i
$363$	−28.9801	−	12.0040i	−1.52106	−	0.630045i
$364$	6.53605	+	3.51967i	0.342582	+	0.184481i
$365$	−2.72085	−	6.56870i	−0.142416	−	0.343822i
$366$	18.8487	+	0.955249i	0.985238	+	0.0499317i
$367$		−	23.0872i		−	1.20514i	−0.798065	−	0.602571i	$-0.794143\pi$
$367$		−	23.0872i		−	1.20514i	0.798065	−	0.602571i	$-0.205857\pi$
$368$	24.4668	−	16.1298i	1.27542	−	0.840823i
$369$		−	2.69837i		−	0.140471i
$370$	0.0834796	−	1.64720i	0.00433990	−	0.0856337i
$371$	5.06492	+	12.2278i	0.262958	+	0.634836i
$372$	1.77845	+	5.92884i	0.0922085	+	0.307396i
$373$	−7.68995	−	3.18528i	−0.398171	−	0.164928i	0.174607	−	0.984638i	$-0.444134\pi$
$373$	−7.68995	−	3.18528i	−0.398171	−	0.164928i	−0.572778	+	0.819710i	$0.694134\pi$
$374$	55.3777	−	19.7178i	2.86351	−	1.01958i
$375$	8.82387	−	8.82387i	0.455663	−	0.455663i
$376$	5.56505	+	7.57694i	0.286996	+	0.390751i
$377$	2.39210	+	2.39210i	0.123199	+	0.123199i
$378$	−24.4683	−	11.6191i	−1.25852	−	0.597621i
$379$	6.10751	−	14.7448i	0.313722	−	0.757391i	−0.685839	−	0.727753i	$-0.740565\pi$
$379$	6.10751	−	14.7448i	0.313722	−	0.757391i	0.999561	−	0.0296377i	$-0.00943536\pi$
$380$	−0.206531	+	2.03238i	−0.0105948	+	0.104259i
$381$	6.00323	−	2.48662i	0.307555	−	0.127393i
$382$	−19.6523	−	21.7506i	−1.00550	−	1.11286i
$383$	7.73928			0.395458			0.197729	−	0.980257i	$-0.436643\pi$
$383$	7.73928			0.395458			0.197729	+	0.980257i	$0.436643\pi$
$384$	8.12402	−	8.77044i	0.414577	−	0.447565i
$385$	36.9858			1.88497
$386$	−15.8330	−	17.5235i	−0.805880	−	0.891924i
$387$	20.5061	−	8.49392i	1.04239	−	0.431770i
$388$	1.85378	−	18.2421i	0.0941112	−	0.926104i
$389$	−5.09911	+	12.3103i	−0.258535	+	0.624159i	−0.998842	−	0.0481102i	$-0.984680\pi$
$389$	−5.09911	+	12.3103i	−0.258535	+	0.624159i	0.740307	+	0.672269i	$0.234680\pi$
$390$	2.10882	+	1.00140i	0.106784	+	0.0507077i
$391$	33.7590	+	33.7590i	1.70726	+	1.70726i
$392$	11.3469	+	15.4490i	0.573104	+	0.780294i
$393$	1.43614	−	1.43614i	0.0724438	−	0.0724438i
$394$	−4.95037	+	1.76262i	−0.249396	+	0.0887997i
$395$	−8.24706	−	3.41604i	−0.414955	−	0.171880i
$396$	6.90341	+	23.0139i	0.346909	+	1.15649i
$397$	0.461745	+	1.11475i	0.0231743	+	0.0559478i	0.935043	−	0.354534i	$-0.115361\pi$
$397$	0.461745	+	1.11475i	0.0231743	+	0.0559478i	−0.911869	+	0.410482i	$0.865361\pi$
$398$	0.330793	−	6.52713i	0.0165812	−	0.327175i
$399$			2.56441i			0.128381i
$400$	−5.63511	−	8.54772i	−0.281755	−	0.427386i
$401$			13.2668i			0.662510i	0.943541	+	0.331255i	$0.107472\pi$
$401$			13.2668i			0.662510i	−0.943541	+	0.331255i	$0.892528\pi$
$402$	−20.0448	−	1.01587i	−0.999743	−	0.0506667i
$403$	1.12085	+	2.70596i	0.0558334	+	0.134794i
$404$	10.5354	+	5.67334i	0.524157	+	0.282259i
$405$	0.285240	+	0.118150i	0.0141737	+	0.00587094i
$406$	5.95648	+	16.7289i	0.295615	+	0.830241i
$407$	−3.36708	+	3.36708i	−0.166900	+	0.166900i
$408$	16.6587	+	10.0904i	0.824728	+	0.499547i
$409$	−25.6267	−	25.6267i	−1.26716	−	1.26716i	−0.947548	−	0.319612i	$-0.896447\pi$
$409$	−25.6267	−	25.6267i	−1.26716	−	1.26716i	−0.319612	−	0.947548i	$-0.603553\pi$
$410$	−1.35773	+	2.85922i	−0.0670537	+	0.141207i
$411$	1.74934	−	4.22329i	0.0862887	−	0.208319i
$412$	−17.9457	+	14.6349i	−0.884122	+	0.721008i
$413$	−19.9224	+	8.25211i	−0.980316	+	0.406060i
$414$	−14.4793	+	13.0825i	−0.711619	+	0.642969i
$415$	−10.3918			−0.510116
$416$	3.40487	−	4.51739i	0.166938	−	0.221483i
$417$	−12.6307			−0.618527
$418$	4.37623	−	3.95405i	0.214048	−	0.193399i
$419$	−10.6196	+	4.39877i	−0.518800	+	0.214894i	−0.626690	−	0.779269i	$-0.715591\pi$
$419$	−10.6196	+	4.39877i	−0.518800	+	0.214894i	0.107890	+	0.994163i	$0.465591\pi$
$420$	7.74464	+	9.49672i	0.377900	+	0.463393i
$421$	2.25698	−	5.44882i	0.109998	−	0.265559i	−0.859289	−	0.511490i	$-0.829094\pi$
$421$	2.25698	−	5.44882i	0.109998	−	0.265559i	0.969287	+	0.245931i	$0.0790936\pi$
$422$	3.93413	−	8.28480i	0.191511	−	0.403298i
$423$	−4.42657	−	4.42657i	−0.215227	−	0.215227i
$424$	9.79460	−	2.40510i	0.475668	−	0.116802i
$425$	11.7941	−	11.7941i	0.572096	−	0.572096i
$426$	−6.40982	−	18.0021i	−0.310557	−	0.872206i
$427$	43.3087	+	17.9390i	2.09585	+	0.868131i
$428$	−7.48208	+	13.8943i	−0.361660	+	0.671605i
$429$	−2.57929	−	6.22697i	−0.124530	−	0.300641i
$430$	−26.0024	−	1.31780i	−1.25395	−	0.0635499i
$431$		−	9.97586i		−	0.480520i	−0.970709	−	0.240260i	$-0.922767\pi$
$431$		−	9.97586i		−	0.480520i	0.970709	−	0.240260i	$-0.0772327\pi$
$432$	−11.5736	+	17.0908i	−0.556833	+	0.822284i
$433$		−	16.3135i		−	0.783976i	−0.919970	−	0.391988i	$-0.871787\pi$
$433$		−	16.3135i		−	0.783976i	0.919970	−	0.391988i	$-0.128213\pi$
$434$	−0.778175	+	15.3547i	−0.0373536	+	0.737051i
$435$	2.13704	+	5.15928i	0.102463	+	0.247368i
$436$	−7.58476	+	2.27518i	−0.363244	+	0.108961i
$437$	4.42555	+	1.83312i	0.211703	+	0.0876901i
$438$	−6.40714	+	2.28132i	−0.306145	+	0.109006i
$439$	−20.1673	+	20.1673i	−0.962533	+	0.962533i	−0.999323	−	0.0367903i	$-0.988287\pi$
$439$	−20.1673	+	20.1673i	−0.962533	+	0.962533i	0.0367903	+	0.999323i	$0.488287\pi$
$440$	4.26496	−	27.8594i	0.203324	−	1.32814i
$441$	−9.02557	−	9.02557i	−0.429789	−	0.429789i
$442$	8.32491	+	3.95318i	0.395976	+	0.188034i
$443$	−4.56877	+	11.0300i	−0.217069	+	0.524050i	−0.994478	−	0.104945i	$-0.966533\pi$
$443$	−4.56877	+	11.0300i	−0.217069	+	0.524050i	0.777409	+	0.628995i	$0.216533\pi$
$444$	−1.56961	−	0.159504i	−0.0744902	−	0.00756974i
$445$	−8.49921	+	3.52049i	−0.402901	+	0.166887i
$446$	15.3155	+	16.9507i	0.725210	+	0.802641i
$447$	7.30227			0.345386
$448$	26.3167	−	13.7536i	1.24335	−	0.649797i
$449$	−16.0396			−0.756957			−0.378479	−	0.925610i	$-0.623553\pi$
$449$	−16.0396			−0.756957			−0.378479	+	0.925610i	$0.623553\pi$
$450$	4.57051	+	5.05850i	0.215456	+	0.238460i
$451$	8.44277	−	3.49711i	0.397554	−	0.164672i
$452$	2.02826	+	0.206113i	0.0954011	+	0.00969472i
$453$	−6.03074	+	14.5595i	−0.283349	+	0.684065i
$454$	26.5179	+	12.5923i	1.24455	+	0.590987i
$455$	4.10016	+	4.10016i	0.192218	+	0.192218i
$456$	1.93163	+	0.295711i	0.0904569	+	0.0138479i
$457$	−8.99028	+	8.99028i	−0.420547	+	0.420547i	−0.885392	−	0.464845i	$-0.846110\pi$
$457$	−8.99028	+	8.99028i	−0.420547	+	0.420547i	0.464845	+	0.885392i	$0.346110\pi$
$458$	32.7733	−	11.6692i	1.53140	−	0.545268i
$459$	−31.0673	−	12.8685i	−1.45010	−	0.600649i
$460$	21.9251	−	6.57681i	1.02227	−	0.306645i
$461$	1.36185	+	3.28780i	0.0634277	+	0.153128i	0.952415	−	0.304803i	$-0.0985907\pi$
$461$	1.36185	+	3.28780i	0.0634277	+	0.153128i	−0.888988	+	0.457931i	$0.848591\pi$
$462$	1.79074	−	35.3343i	0.0833126	−	1.64390i
$463$			15.4779i			0.719321i	0.933083	+	0.359660i	$0.117107\pi$
$463$			15.4779i			0.719321i	−0.933083	+	0.359660i	$0.882893\pi$
$464$	13.2878	−	2.55762i	0.616872	−	0.118735i
$465$			4.83489i			0.224213i
$466$	−29.2147	−	1.48059i	−1.35334	−	0.0685871i
$467$	12.8577	+	31.0413i	0.594985	+	1.43642i	0.878636	+	0.477492i	$0.158454\pi$
$467$	12.8577	+	31.0413i	0.594985	+	1.43642i	−0.283651	+	0.958928i	$0.591546\pi$
$468$	−1.78597	+	3.31657i	−0.0825567	+	0.153308i
$469$	−46.0569	−	19.0774i	−2.12671	−	0.880911i
$470$	2.46313	+	6.91776i	0.113616	+	0.319092i
$471$	7.37828	−	7.37828i	0.339973	−	0.339973i
$472$	3.91855	+	15.9580i	0.180366	+	0.734528i
$473$	53.1523	+	53.1523i	2.44395	+	2.44395i
$474$	−3.66281	+	7.71343i	−0.168238	+	0.354289i
$475$	0.640420	−	1.54611i	0.0293845	−	0.0709405i
$476$	30.5733	+	37.4899i	1.40132	+	1.71835i
$477$	−6.20471	+	2.57007i	−0.284094	+	0.117676i
$478$	−16.1547	+	14.5962i	−0.738898	+	0.667616i
$479$	0.156320			0.00714242			0.00357121	−	0.999994i	$-0.498863\pi$
$479$	0.156320			0.00714242			0.00357121	+	0.999994i	$0.498863\pi$
$480$	8.04643	−	4.73852i	0.367268	−	0.216283i
$481$	−0.746534			−0.0340390
$482$	7.53027	−	6.80382i	0.342994	−	0.309906i
$483$	26.5472	−	10.9962i	1.20794	−	0.500345i
$484$	−46.0107	+	37.5221i	−2.09140	+	1.70555i
$485$	5.48093	−	13.2321i	0.248876	−	0.600840i
$486$	9.51776	−	20.0432i	0.431734	−	0.909179i
$487$	−12.4935	−	12.4935i	−0.566136	−	0.566136i	0.364908	−	0.931044i	$-0.381100\pi$
$487$	−12.4935	−	12.4935i	−0.566136	−	0.566136i	−0.931044	+	0.364908i	$0.881100\pi$
$488$	18.5066	−	30.5535i	0.837754	−	1.38309i
$489$	7.63643	−	7.63643i	0.345331	−	0.345331i
$490$	5.02221	+	14.1050i	0.226880	+	0.637198i
$491$	−15.0055	−	6.21550i	−0.677191	−	0.280502i	0.0174612	−	0.999848i	$-0.494442\pi$
$491$	−15.0055	−	6.21550i	−0.677191	−	0.280502i	−0.694652	+	0.719346i	$0.744442\pi$
$492$	2.66582	+	1.43554i	0.120184	+	0.0647194i
$493$	8.43633	+	20.3671i	0.379953	+	0.917288i
$494$	0.923476	+	0.0468016i	0.0415491	+	0.00210570i
$495$			18.7676i			0.843539i
$496$	11.4762	+	2.35677i	0.515295	+	0.105822i
$497$		−	47.4639i		−	2.12905i
$498$	−0.503141	+	9.92784i	−0.0225463	+	0.444877i
$499$	7.53020	+	18.1795i	0.337098	+	0.813827i	0.997992	+	0.0633469i	$0.0201775\pi$
$499$	7.53020	+	18.1795i	0.337098	+	0.813827i	−0.660894	+	0.750480i	$0.729823\pi$
$500$	−6.78618	−	22.6231i	−0.303487	−	1.01174i
$501$	5.77847	+	2.39352i	0.258163	+	0.106935i
$502$	−16.5902	+	5.90711i	−0.740459	+	0.263647i
$503$	−21.1088	+	21.1088i	−0.941193	+	0.941193i	−0.998364	−	0.0571712i	$-0.981792\pi$
$503$	−21.1088	+	21.1088i	−0.941193	+	0.941193i	0.0571712	+	0.998364i	$0.481792\pi$
$504$	−15.9364	+	11.7048i	−0.709864	+	0.521375i
$505$	6.60902	+	6.60902i	0.294097	+	0.294097i
$506$	−59.6984	−	28.3485i	−2.65392	−	1.26024i
$507$	0.404373	−	0.976242i	0.0179588	−	0.0433564i
$508$	1.24339	−	12.2356i	0.0551666	−	0.542869i
$509$	4.29098	−	1.77738i	0.190194	−	0.0787811i	−0.285553	−	0.958363i	$-0.592177\pi$
$509$	4.29098	−	1.77738i	0.190194	−	0.0787811i	0.475748	+	0.879582i	$0.342177\pi$
$510$	10.1990	+	11.2879i	0.451617	+	0.499837i
$511$	−16.8929			−0.747297
$512$	−7.32519	−	21.4089i	−0.323731	−	0.946149i
$513$	−3.37392			−0.148962
$514$	13.7729	+	15.2435i	0.607499	+	0.672362i
$515$	−16.7108	+	6.92185i	−0.736367	+	0.305013i
$516$	−2.51791	+	24.7776i	−0.110845	+	1.09077i
$517$	8.11317	−	19.5869i	0.356817	−	0.861432i
$518$	−3.53987	−	1.68095i	−0.155533	−	0.0738566i
$519$	−13.3928	−	13.3928i	−0.587877	−	0.587877i
$520$	3.56123	−	2.61562i	0.156170	−	0.114703i
$521$	−14.2560	+	14.2560i	−0.624566	+	0.624566i	−0.946695	−	0.322130i	$-0.895601\pi$
$521$	−14.2560	+	14.2560i	−0.624566	+	0.624566i	0.322130	+	0.946695i	$0.395601\pi$
$522$	−8.48868	+	3.02247i	−0.371539	+	0.132290i
$523$	23.0950	+	9.56627i	1.00987	+	0.418304i	0.825409	−	0.564535i	$-0.190945\pi$
$523$	23.0950	+	9.56627i	1.00987	+	0.418304i	0.184465	+	0.982839i	$0.440945\pi$
$524$	−1.10450	−	3.68206i	−0.0482501	−	0.160852i
$525$	−3.84165	−	9.27455i	−0.167663	−	0.404775i
$526$	1.20908	−	23.8573i	0.0527185	−	1.04023i
$527$			19.0865i			0.831422i
$528$	−26.4090	−	5.42339i	−1.14930	−	0.236023i
$529$		−	30.6745i		−	1.33367i
$530$	7.86776	+	0.398736i	0.341754	+	0.0173200i
$531$	−4.18734	−	10.1091i	−0.181715	−	0.438699i
$532$	4.27349	+	2.30128i	0.185279	+	0.0997732i
$533$	1.32363	+	0.548264i	0.0573326	+	0.0237480i
$534$	2.95179	+	8.29016i	0.127736	+	0.358750i
$535$	−8.71607	+	8.71607i	−0.376828	+	0.376828i
$536$	−19.6809	+	32.4923i	−0.850087	+	1.40345i
$537$	−12.2244	−	12.2244i	−0.527523	−	0.527523i
$538$	2.73656	−	5.76287i	0.117982	−	0.248455i
$539$	16.5424	−	39.9368i	0.712530	−	1.72020i
$540$	−12.4946	+	10.1894i	−0.537681	+	0.438483i
$541$	3.03280	−	1.25623i	0.130390	−	0.0540093i	−0.316534	−	0.948581i	$-0.602519\pi$
$541$	3.03280	−	1.25623i	0.130390	−	0.0540093i	0.446924	+	0.894572i	$0.352519\pi$
$542$	9.92423	−	8.96683i	0.426282	−	0.385158i
$543$	25.4182			1.09080
$544$	31.7646	−	18.7061i	1.36190	−	0.802017i
$545$	−6.18528			−0.264948
$546$	4.11560	−	3.71857i	0.176131	−	0.159140i
$547$	−13.1061	+	5.42874i	−0.560378	+	0.232116i	−0.644849	−	0.764310i	$-0.723080\pi$
$547$	−13.1061	+	5.42874i	−0.560378	+	0.232116i	0.0844711	+	0.996426i	$0.473080\pi$
$548$	−5.46811	−	6.70516i	−0.233586	−	0.286430i
$549$	−9.10274	+	21.9760i	−0.388495	+	0.937911i
$550$	−9.90385	+	20.8563i	−0.422302	+	0.889315i
$551$	1.56403	+	1.56403i	0.0666301	+	0.0666301i
$552$	−5.22160	−	21.2646i	−0.222246	−	0.905081i
$553$	−14.9971	+	14.9971i	−0.637743	+	0.637743i
$554$	−1.20088	−	3.37270i	−0.0510206	−	0.143292i
$555$	−1.13853	−	0.471595i	−0.0483280	−	0.0200181i
$556$	−11.3347	+	21.0486i	−0.480697	+	0.892658i
$557$	−0.703935	−	1.69945i	−0.0298267	−	0.0720080i	0.908264	−	0.418397i	$-0.137408\pi$
$557$	−0.703935	−	1.69945i	−0.0298267	−	0.0720080i	−0.938091	+	0.346389i	$0.887408\pi$
$558$	−7.79140	−	0.394866i	−0.329836	−	0.0167160i
$559$			11.7847i			0.498439i
$560$	22.7759	−	4.38388i	0.962459	−	0.185253i
$561$		−	43.9219i		−	1.85439i
$562$	1.98345	−	39.1368i	0.0836666	−	1.65089i
$563$	−8.09682	−	19.5475i	−0.341240	−	0.823827i	−0.997591	−	0.0693710i	$-0.977901\pi$
$563$	−8.09682	−	19.5475i	−0.341240	−	0.823827i	0.656351	−	0.754456i	$-0.272099\pi$
$564$	6.72813	−	2.01821i	0.283305	−	0.0849822i
$565$	1.47122	+	0.609398i	0.0618946	+	0.0256376i
$566$	−26.2937	+	9.36213i	−1.10521	+	0.393520i
$567$	0.518704	−	0.518704i	0.0217835	−	0.0217835i
$568$	−35.7520	−	5.47323i	−1.50012	−	0.229652i
$569$	−21.2211	−	21.2211i	−0.889633	−	0.889633i	0.104854	−	0.994488i	$-0.466562\pi$
$569$	−21.2211	−	21.2211i	−0.889633	−	0.889633i	−0.994488	+	0.104854i	$0.966562\pi$
$570$	1.37882	+	0.654748i	0.0577523	+	0.0274244i
$571$	9.77130	−	23.5900i	0.408916	−	0.987211i	−0.576507	−	0.817092i	$-0.695585\pi$
$571$	9.77130	−	23.5900i	0.408916	−	0.987211i	0.985424	−	0.170119i	$-0.0544153\pi$
$572$	−12.6917	−	1.28973i	−0.530665	−	0.0539265i
$573$	−20.2356	+	8.38186i	−0.845354	+	0.350157i
$574$	5.04178	+	5.58009i	0.210440	+	0.232908i
$575$	−18.7518			−0.782002
$576$	6.97895	+	13.3538i	0.290789	+	0.556407i
$577$	−10.7911			−0.449239			−0.224619	−	0.974447i	$-0.572114\pi$
$577$	−10.7911			−0.449239			−0.224619	+	0.974447i	$0.572114\pi$
$578$	24.1443	+	26.7222i	1.00427	+	1.11150i
$579$	−16.3029	+	6.75290i	−0.677527	+	0.280641i
$580$	10.5155	+	1.06859i	0.436633	+	0.0443709i
$581$	−9.44870	+	22.8112i	−0.391998	+	0.946367i
$582$	−12.3759	−	5.87686i	−0.512999	−	0.243604i
$583$	−16.0827	−	16.0827i	−0.666078	−	0.666078i
$584$	−1.94798	+	12.7245i	−0.0806079	+	0.526544i
$585$	−2.08053	+	2.08053i	−0.0860192	+	0.0860192i
$586$	31.7101	−	11.2907i	1.30993	−	0.466414i
$587$	30.3635	+	12.5770i	1.25323	+	0.519107i	0.907826	−	0.419346i	$-0.137741\pi$
$587$	30.3635	+	12.5770i	1.25323	+	0.519107i	0.345408	+	0.938453i	$0.387741\pi$
$588$	13.7183	−	4.11504i	0.565735	−	0.169702i
$589$	0.732848	+	1.76925i	0.0301965	+	0.0729008i
$590$	−0.649649	+	12.8187i	−0.0267456	+	0.527737i
$591$			3.92630i			0.161506i
$592$	−1.67436	+	2.47255i	−0.0688158	+	0.101621i
$593$			39.2423i			1.61149i	0.592264	+	0.805744i	$0.298234\pi$
$593$			39.2423i			1.61149i	−0.592264	+	0.805744i	$0.701766\pi$
$594$	46.4884	+	2.35602i	1.90744	+	0.0966688i
$595$	14.4602	+	34.9101i	0.592812	+	1.43117i
$596$	6.55301	−	12.1690i	0.268422	−	0.498461i
$597$	−4.51150	−	1.86873i	−0.184644	−	0.0764819i
$598$	−3.47538	−	9.76067i	−0.142119	−	0.399144i
$599$	21.2256	−	21.2256i	0.867255	−	0.867255i	−0.124912	−	0.992168i	$-0.539865\pi$
$599$	21.2256	−	21.2256i	0.867255	−	0.867255i	0.992168	+	0.124912i	$0.0398650\pi$
$600$	−7.42902	+	1.82422i	−0.303288	+	0.0744736i
$601$	−14.1105	−	14.1105i	−0.575579	−	0.575579i	0.358103	−	0.933682i	$-0.383424\pi$
$601$	−14.1105	−	14.1105i	−0.575579	−	0.575579i	−0.933682	+	0.358103i	$0.883424\pi$
$602$	−26.5352	+	55.8798i	−1.08149	+	2.27749i
$603$	9.68036	−	23.3705i	0.394215	−	0.951719i
$604$	18.8509	+	23.1156i	0.767033	+	0.940560i
$605$	−42.8446	+	17.7468i	−1.74188	+	0.721511i
$606$	6.63391	−	5.99393i	0.269484	−	0.243487i
$607$	−27.6602			−1.12269			−0.561346	−	0.827581i	$-0.689716\pi$
$607$	−27.6602			−1.12269			−0.561346	+	0.827581i	$0.689716\pi$
$608$	2.22622	−	2.95362i	0.0902853	−	0.119785i
$609$	13.2682			0.537656
$610$	20.7030	−	18.7058i	0.838239	−	0.757374i
$611$	3.07077	−	1.27195i	0.124230	−	0.0514578i
$612$	−19.0233	+	15.5137i	−0.768973	+	0.627103i
$613$	9.09593	−	21.9595i	0.367381	−	0.886937i	−0.626796	−	0.779183i	$-0.715634\pi$
$613$	9.09593	−	21.9595i	0.367381	−	0.886937i	0.994178	−	0.107754i	$-0.0343658\pi$
$614$	1.50643	−	3.17236i	0.0607947	−	0.128026i
$615$	1.67230	+	1.67230i	0.0674338	+	0.0674338i
$616$	−57.2764	−	34.6930i	−2.30773	−	1.39782i
$617$	−8.20331	+	8.20331i	−0.330253	+	0.330253i	−0.852682	−	0.522430i	$-0.825026\pi$
$617$	−8.20331	+	8.20331i	−0.330253	+	0.330253i	0.522430	+	0.852682i	$0.325026\pi$
$618$	5.80370	+	16.2998i	0.233459	+	0.655674i
$619$	8.55452	+	3.54340i	0.343835	+	0.142421i	0.547917	−	0.836533i	$-0.315421\pi$
$619$	8.55452	+	3.54340i	0.343835	+	0.142421i	−0.204082	+	0.978954i	$0.565421\pi$
$620$	8.05717	+	4.33880i	0.323584	+	0.174250i
$621$	14.4674	+	34.9274i	0.580557	+	1.40159i
$622$	−12.2220	−	0.619410i	−0.490059	−	0.0248361i
$623$			21.8576i			0.875707i
$624$	−2.32641	−	3.52886i	−0.0931310	−	0.141267i
$625$		−	5.65129i		−	0.226052i
$626$	−1.28416	+	25.3387i	−0.0513254	+	1.01274i
$627$	−1.68643	−	4.07140i	−0.0673496	−	0.162596i
$628$	−5.67443	−	18.9169i	−0.226434	−	0.754865i
$629$	−4.49454	−	1.86170i	−0.179209	−	0.0742308i
$630$	−14.5500	+	5.18065i	−0.579685	+	0.206402i
$631$	−11.3714	+	11.3714i	−0.452689	+	0.452689i	−0.896246	−	0.443557i	$-0.853716\pi$
$631$	−11.3714	+	11.3714i	−0.452689	+	0.452689i	0.443557	+	0.896246i	$0.353716\pi$
$632$	9.56717	+	13.0259i	0.380561	+	0.518143i
$633$	−4.84562	−	4.84562i	−0.192596	−	0.192596i
$634$	1.54331	+	0.732861i	0.0612929	+	0.0291056i
$635$	3.67625	−	8.87525i	0.145888	−	0.352204i
$636$	0.761865	−	7.49715i	0.0302099	−	0.297281i
$637$	6.26115	−	2.59345i	0.248076	−	0.102756i
$638$	−20.4583	−	22.6426i	−0.809950	−	0.896429i
$639$	24.0844			0.952766
$640$	−0.675769	−	17.6614i	−0.0267121	−	0.698128i
$641$	−23.0743			−0.911379			−0.455690	−	0.890139i	$-0.650607\pi$
$641$	−23.0743			−0.911379			−0.455690	+	0.890139i	$0.650607\pi$
$642$	7.90488	+	8.74889i	0.311981	+	0.345291i
$643$	5.53781	−	2.29384i	0.218390	−	0.0904600i	−0.270806	−	0.962634i	$-0.587290\pi$
$643$	5.53781	−	2.29384i	0.218390	−	0.0904600i	0.489196	+	0.872174i	$0.337290\pi$
$644$	5.49848	−	54.1079i	0.216670	−	2.13215i
$645$	−7.44454	+	17.9727i	−0.293128	+	0.707674i
$646$	5.44311	+	2.58473i	0.214156	+	0.101695i
$647$	6.25142	+	6.25142i	0.245769	+	0.245769i	0.819232	−	0.573463i	$-0.194400\pi$
$647$	6.25142	+	6.25142i	0.245769	+	0.245769i	−0.573463	+	0.819232i	$0.694400\pi$
$648$	−0.330899	−	0.450526i	−0.0129989	−	0.0176983i
$649$	26.2031	−	26.2031i	1.02856	−	1.02856i
$650$	−3.41000	+	1.21416i	−0.133751	+	0.0476233i
$651$	10.6131	+	4.39609i	0.415960	+	0.172296i
$652$	−5.87296	−	19.5787i	−0.230003	−	0.766762i
$653$	−7.50447	−	18.1174i	−0.293673	−	0.708989i	−0.999999	−	0.00110260i	$-0.999649\pi$
$653$	−7.50447	−	18.1174i	−0.293673	−	0.708989i	0.706327	−	0.707886i	$-0.250351\pi$
$654$	−0.299472	+	5.90910i	−0.0117103	+	0.231064i
$655$		−	3.00268i		−	0.117324i
$656$	4.78457	−	3.15424i	0.186806	−	0.123152i
$657$		−	8.57190i		−	0.334422i
$658$	17.4248	+	0.883084i	0.679289	+	0.0344262i
$659$	5.90745	+	14.2618i	0.230122	+	0.555563i	0.996191	−	0.0871948i	$-0.0277903\pi$
$659$	5.90745	+	14.2618i	0.230122	+	0.555563i	−0.766070	+	0.642758i	$0.777790\pi$
$660$	−18.5412	−	9.98444i	−0.721714	−	0.388644i
$661$	35.9768	+	14.9021i	1.39934	+	0.579624i	0.949579	−	0.313527i	$-0.101511\pi$
$661$	35.9768	+	14.9021i	1.39934	+	0.579624i	0.449757	+	0.893151i	$0.351511\pi$
$662$	5.04950	+	14.1816i	0.196254	+	0.551184i
$663$	4.86908	−	4.86908i	0.189100	−	0.189100i
$664$	16.0929	+	9.74764i	0.624525	+	0.378282i
$665$	2.68082	+	2.68082i	0.103958	+	0.103958i
$666$	0.852957	−	1.79622i	0.0330514	−	0.0696022i
$667$	9.48456	−	22.8978i	0.367244	−	0.886604i
$668$	9.17427	−	7.48168i	0.354963	−	0.289475i
$669$	15.7700	−	6.53216i	0.609705	−	0.252548i
$670$	−22.0167	+	19.8928i	−0.850580	+	0.768524i
$671$	−80.5566			−3.10985
$672$	−3.08540	−	21.9712i	−0.119022	−	0.847558i
$673$	19.0113			0.732830			0.366415	−	0.930451i	$-0.380585\pi$
$673$	19.0113			0.732830			0.366415	+	0.930451i	$0.380585\pi$
$674$	−1.31844	+	1.19125i	−0.0507844	+	0.0458852i
$675$	12.2023	−	5.05435i	0.469666	−	0.194542i
$676$	−1.26399	−	1.54994i	−0.0486150	−	0.0596132i
$677$	0.889957	−	2.14855i	0.0342038	−	0.0825754i	−0.905855	−	0.423589i	$-0.860770\pi$
$677$	0.889957	−	2.14855i	0.0342038	−	0.0825754i	0.940058	+	0.341013i	$0.110770\pi$
$678$	0.653420	−	1.37602i	0.0250944	−	0.0528458i
$679$	−24.0624	−	24.0624i	−0.923430	−	0.923430i
$680$	27.9634	−	6.86651i	1.07235	−	0.263319i
$681$	15.5098	−	15.5098i	0.594337	−	0.594337i
$682$	−8.86225	−	24.8898i	−0.339353	−	0.953081i
$683$	−13.9472	−	5.77712i	−0.533675	−	0.221055i	0.0995371	−	0.995034i	$-0.468264\pi$
$683$	−13.9472	−	5.77712i	−0.533675	−	0.221055i	−0.633212	+	0.773979i	$0.718264\pi$
$684$	−1.16773	+	2.16848i	−0.0446493	+	0.0829140i
$685$	−2.58625	−	6.24377i	−0.0988156	−	0.238562i
$686$	−1.16896	−	0.0592425i	−0.0446310	−	0.00226189i
$687$		−	25.9936i		−	0.991718i
$688$	39.0314	+	26.4312i	1.48806	+	1.00768i
$689$		−	3.56579i		−	0.135846i
$690$	0.865678	−	17.0813i	0.0329558	−	0.650275i
$691$	−15.8806	−	38.3392i	−0.604127	−	1.45849i	−0.869298	−	0.494289i	$-0.835428\pi$
$691$	−15.8806	−	38.3392i	−0.604127	−	1.45849i	0.265171	−	0.964201i	$-0.414572\pi$
$692$	−34.3371	+	10.3000i	−1.30530	+	0.391547i
$693$	41.1967	+	17.0643i	1.56494	+	0.648217i
$694$	−12.7184	+	4.52851i	−0.482785	+	0.171900i
$695$	−13.2041	+	13.2041i	−0.500859	+	0.500859i
$696$	1.53001	−	9.99425i	0.0579948	−	0.378831i
$697$	6.60169	+	6.60169i	0.250057	+	0.250057i
$698$	−26.0680	−	12.3787i	−0.986688	−	0.468540i
$699$	−8.36420	+	20.1930i	−0.316363	+	0.763768i
$700$	−18.9032	−	1.92095i	−0.714473	−	0.0726051i
$701$	15.0532	−	6.23525i	0.568553	−	0.235502i	−0.0798409	−	0.996808i	$-0.525441\pi$
$701$	15.0532	−	6.23525i	0.568553	−	0.235502i	0.648393	+	0.761305i	$0.275441\pi$
$702$	4.89241	+	5.41478i	0.184652	+	0.204368i
$703$	−0.488110			−0.0184094
$704$	−32.7371	+	39.1427i	−1.23383	+	1.47524i
$705$	5.48671			0.206641
$706$	28.0530	+	31.0482i	1.05579	+	1.16852i
$707$	20.5167	−	8.49828i	0.771609	−	0.319611i
$708$	12.2149	+	1.24128i	0.459063	+	0.0466503i
$709$	4.62814	−	11.1733i	0.173813	−	0.419622i	−0.812834	−	0.582496i	$-0.802076\pi$
$709$	4.62814	−	11.1733i	0.173813	−	0.419622i	0.986647	+	0.162873i	$0.0520762\pi$
$710$	−25.5202	−	12.1185i	−0.957754	−	0.454801i
$711$	−7.60994	−	7.60994i	−0.285395	−	0.285395i
$712$	16.4642	+	2.52048i	0.617021	+	0.0944590i
$713$	15.1731	−	15.1731i	0.568239	−	0.568239i
$714$	34.0514	−	12.1243i	1.27434	−	0.453742i
$715$	−9.20603	−	3.81326i	−0.344286	−	0.142608i
$716$	−31.3417	+	9.40145i	−1.17129	+	0.351349i
$717$	6.22540	+	15.0294i	0.232492	+	0.561284i
$718$	−2.08592	+	41.1588i	−0.0778458	+	1.53603i
$719$		−	33.9003i		−	1.26427i	−0.774860	−	0.632133i	$-0.782179\pi$
$719$		−	33.9003i		−	1.26427i	0.774860	−	0.632133i	$-0.217821\pi$
$720$	2.22450	+	11.5571i	0.0829021	+	0.430708i
$721$			42.9756i			1.60050i
$722$	−26.2318	−	1.32942i	−0.976247	−	0.0494760i
$723$	−2.90188	−	7.00575i	−0.107922	−	0.260547i
$724$	22.8101	−	42.3585i	0.847731	−	1.57424i
$725$	−7.99958	−	3.31353i	−0.297097	−	0.123062i
$726$	14.8800	+	41.7908i	0.552249	+	1.55100i
$727$	16.8428	−	16.8428i	0.624664	−	0.624664i	−0.322056	−	0.946721i	$-0.604374\pi$
$727$	16.8428	−	16.8428i	0.624664	−	0.624664i	0.946721	+	0.322056i	$0.104374\pi$
$728$	−2.50355	−	10.1955i	−0.0927876	−	0.377871i
$729$	−11.3037	−	11.3037i	−0.418654	−	0.418654i
$730$	−4.31311	+	9.08288i	−0.159635	+	0.336172i
$731$	−29.3885	+	70.9502i	−1.08697	+	2.62419i
$732$	−16.8682	−	20.6843i	−0.623465	−	0.764512i
$733$	2.72156	−	1.12731i	0.100523	−	0.0416381i	−0.331855	−	0.943330i	$-0.607674\pi$
$733$	2.72156	−	1.12731i	0.100523	−	0.0416381i	0.432378	+	0.901692i	$0.357674\pi$
$734$	−24.2262	+	21.8891i	−0.894204	+	0.807940i
$735$	11.1871			0.412644
$736$	−40.1225	−	10.3811i	−1.47894	−	0.382652i
$737$	85.6684			3.15564
$738$	−2.83148	+	2.55833i	−0.104228	+	0.0941734i
$739$	−36.2250	+	15.0049i	−1.33256	+	0.551963i	−0.931384	−	0.364038i	$-0.881398\pi$
$739$	−36.2250	+	15.0049i	−1.33256	+	0.551963i	−0.401174	+	0.916002i	$0.631398\pi$
$740$	−1.80761	+	1.47412i	−0.0664489	+	0.0541896i
$741$	0.264393	−	0.638300i	0.00971270	−	0.0234485i
$742$	8.02897	−	16.9080i	0.294753	−	0.620712i
$743$	23.7148	+	23.7148i	0.870012	+	0.870012i	0.992473	−	0.122461i	$-0.0390788\pi$
$743$	23.7148	+	23.7148i	0.870012	+	0.870012i	−0.122461	+	0.992473i	$0.539079\pi$
$744$	4.53517	−	7.48734i	0.166267	−	0.274499i
$745$	7.63377	−	7.63377i	0.279680	−	0.279680i
$746$	3.94845	+	11.0893i	0.144563	+	0.406008i
$747$	−11.5750	−	4.79452i	−0.423507	−	0.175422i
$748$	−73.1943	−	39.4152i	−2.67625	−	1.44116i
$749$	11.2077	+	27.0577i	0.409519	+	0.988666i
$750$	−17.6251	−	0.893237i	−0.643578	−	0.0326164i
$751$			1.76215i			0.0643017i	0.999483	+	0.0321508i	$0.0102357\pi$
$751$			1.76215i			0.0643017i	−0.999483	+	0.0321508i	$0.989764\pi$
$752$	2.67449	−	13.0233i	0.0975288	−	0.474912i
$753$			13.1583i			0.479514i
$754$	0.242151	−	4.77806i	0.00881862	−	0.174007i
$755$	8.91593	+	21.5249i	0.324484	+	0.783373i
$756$	11.0062	+	36.6915i	0.400293	+	1.33446i
$757$	36.1620	+	14.9788i	1.31433	+	0.544413i	0.926145	−	0.377169i	$-0.123102\pi$
$757$	36.1620	+	14.9788i	1.31433	+	0.544413i	0.388184	+	0.921582i	$0.373102\pi$
$758$	−21.2628	+	7.57081i	−0.772299	+	0.274984i
$759$	−34.9165	+	34.9165i	−1.26739	+	1.26739i
$760$	2.32845	−	1.71018i	0.0844619	−	0.0620349i
$761$	11.2621	+	11.2621i	0.408251	+	0.408251i	0.881128	−	0.472877i	$-0.156785\pi$
$761$	11.2621	+	11.2621i	0.408251	+	0.408251i	−0.472877	+	0.881128i	$0.656785\pi$
$762$	−8.30097	−	3.94181i	−0.300713	−	0.142797i
$763$	−5.62391	+	13.5773i	−0.203599	+	0.491532i
$764$	−4.19121	+	41.2437i	−0.151633	+	1.49214i
$765$	−17.7143	+	7.33750i	−0.640462	+	0.265288i
$766$	−7.33763	−	8.12108i	−0.265119	−	0.293426i
$767$	5.80962			0.209773
$768$	−16.9055	−	0.209515i	−0.610026	−	0.00756022i
$769$	21.6884			0.782104			0.391052	−	0.920369i	$-0.372111\pi$
$769$	21.6884			0.782104			0.391052	+	0.920369i	$0.372111\pi$
$770$	−35.0664	−	38.8104i	−1.26370	−	1.39863i
$771$	14.1817	−	5.87426i	0.510742	−	0.211556i
$772$	−3.37667	+	33.2282i	−0.121529	+	1.19591i
$773$	−13.5282	+	32.6599i	−0.486575	+	1.17470i	0.469857	+	0.882742i	$0.344305\pi$
$773$	−13.5282	+	32.6599i	−0.486575	+	1.17470i	−0.956432	+	0.291954i	$0.905695\pi$
$774$	−28.3549	−	13.4647i	−1.01920	−	0.483977i
$775$	−5.30090	−	5.30090i	−0.190414	−	0.190414i
$776$	−20.8996	+	15.3502i	−0.750253	+	0.551040i
$777$	−2.07040	+	2.07040i	−0.0742752	+	0.0742752i
$778$	17.7521	−	6.32081i	0.636444	−	0.226612i
$779$	0.865432	+	0.358474i	0.0310073	+	0.0128437i
$780$	−0.948579	−	3.16228i	−0.0339646	−	0.113228i
$781$	31.2137	+	75.3565i	1.11691	+	2.69647i
$782$	3.41741	−	67.4314i	0.122206	−	2.41134i
$783$			17.4567i			0.623850i
$784$	5.45317	−	26.5539i	0.194756	−	0.948355i
$785$		−	15.4265i		−	0.550594i
$786$	−2.86860	−	0.145380i	−0.102320	−	0.00518554i
$787$	−7.10154	−	17.1446i	−0.253142	−	0.611140i	0.745312	−	0.666716i	$-0.232301\pi$
$787$	−7.10154	−	17.1446i	−0.253142	−	0.611140i	−0.998454	+	0.0555759i	$0.982301\pi$
$788$	6.54304	+	3.52343i	0.233086	+	0.125517i
$789$	−16.4900	−	6.83037i	−0.587059	−	0.243168i
$790$	4.23450	+	11.8927i	0.150657	+	0.423122i
$791$	2.67539	−	2.67539i	0.0951257	−	0.0951257i
$792$	17.6041	−	29.0636i	0.625535	−	1.03273i
$793$	−8.93031	−	8.93031i	−0.317125	−	0.317125i
$794$	0.731964	−	1.54142i	0.0259764	−	0.0547031i
$795$	2.25255	−	5.43814i	0.0798898	−	0.192871i
$796$	−7.16276	+	5.84128i	−0.253877	+	0.207039i
$797$	3.95932	−	1.64000i	0.140246	−	0.0580919i	−0.311456	−	0.950260i	$-0.600817\pi$
$797$	3.95932	−	1.64000i	0.140246	−	0.0580919i	0.451703	+	0.892169i	$0.350817\pi$
$798$	2.69092	−	2.43132i	0.0952575	−	0.0860680i
$799$	21.6597			0.766264
$800$	−3.62674	+	14.0172i	−0.128225	+	0.495584i
$801$	−11.0911			−0.391886
$802$	13.9213	−	12.5783i	0.491576	−	0.444154i
$803$	26.8201	−	11.1093i	0.946462	−	0.392037i
$804$	17.9385	+	21.9968i	0.632644	+	0.775767i
$805$	16.2570	−	39.2478i	0.572982	−	1.38330i
$806$	1.77678	−	3.74168i	0.0625844	−	0.131795i
$807$	−3.37059	−	3.37059i	−0.118650	−	0.118650i
$808$	−4.03545	−	16.4341i	−0.141967	−	0.578149i
$809$	30.9716	−	30.9716i	1.08890	−	1.08890i	0.0932602	−	0.995642i	$-0.470271\pi$
$809$	30.9716	−	30.9716i	1.08890	−	1.08890i	0.995642	−	0.0932602i	$-0.0297289\pi$
$810$	−0.146458	−	0.411331i	−0.00514601	−	0.0144527i
$811$	17.3191	+	7.17381i	0.608156	+	0.251907i	0.665440	−	0.746451i	$-0.268244\pi$
$811$	17.3191	+	7.17381i	0.608156	+	0.251907i	−0.0572836	+	0.998358i	$0.518244\pi$
$812$	11.9068	−	22.1110i	0.417847	−	0.775945i
$813$	−3.82441	−	9.23295i	−0.134128	−	0.323814i
$814$	6.72554	+	0.340849i	0.235730	+	0.0119467i
$815$		−	15.9662i		−	0.559271i
$816$	−5.20602	−	27.0472i	−0.182247	−	0.946842i
$817$			7.70523i			0.269572i
$818$	−2.59419	+	51.1878i	−0.0907036	+	1.78974i
$819$	2.67527	+	6.45868i	0.0934816	+	0.225684i
$820$	4.28755	−	1.28612i	0.149728	−	0.0449133i
$821$	−25.7593	−	10.6698i	−0.899004	−	0.372380i	−0.115167	−	0.993346i	$-0.536740\pi$
$821$	−25.7593	−	10.6698i	−0.899004	−	0.372380i	−0.783837	+	0.620966i	$0.786740\pi$
$822$	−6.09019	+	2.16847i	−0.212420	+	0.0756341i
$823$	5.78434	−	5.78434i	0.201629	−	0.201629i	−0.599069	−	0.800698i	$-0.704462\pi$
$823$	5.78434	−	5.78434i	0.201629	−	0.201629i	0.800698	+	0.599069i	$0.204462\pi$
$824$	32.3712	+	4.95567i	1.12771	+	0.172639i
$825$	12.1984	+	12.1984i	0.424695	+	0.424695i
$826$	27.5477	+	13.0813i	0.958506	+	0.455158i
$827$	−4.56797	+	11.0281i	−0.158844	+	0.383483i	−0.983186	−	0.182609i	$-0.941546\pi$
$827$	−4.56797	+	11.0281i	−0.158844	+	0.383483i	0.824342	+	0.566093i	$0.191546\pi$
$828$	27.4558	+	2.79007i	0.954154	+	0.0969617i
$829$	29.3977	−	12.1769i	1.02103	−	0.422923i	0.191560	−	0.981481i	$-0.438645\pi$
$829$	29.3977	−	12.1769i	1.02103	−	0.422923i	0.829465	+	0.558558i	$0.188645\pi$
$830$	9.85254	+	10.9045i	0.341987	+	0.378501i
$831$	−2.67500			−0.0927948
$832$	−7.96842	+	0.710106i	−0.276255	+	0.0246185i
$833$	44.1630			1.53016
$834$	11.9752	+	13.2538i	0.414667	+	0.458941i
$835$	8.54297	−	3.53861i	0.295642	−	0.122459i
$836$	−8.29824	−	0.843272i	−0.287001	−	0.0291652i
$837$	−5.78381	+	13.9633i	−0.199918	+	0.482644i
$838$	14.6842	+	6.97297i	0.507258	+	0.240877i
$839$	31.2187	+	31.2187i	1.07779	+	1.07779i	0.996707	+	0.0810835i	$0.0258381\pi$
$839$	31.2187	+	31.2187i	1.07779	+	1.07779i	0.0810835	+	0.996707i	$0.474162\pi$
$840$	2.62250	−	17.1306i	0.0904849	−	0.591061i
$841$	−12.4138	+	12.4138i	−0.428062	+	0.428062i
$842$	−7.85748	+	2.79773i	−0.270787	+	0.0964161i
$843$	−27.0511	−	11.2049i	−0.931689	−	0.385918i
$844$	−12.4235	+	3.72663i	−0.427634	+	0.128276i
$845$	−0.597830	−	1.44329i	−0.0205660	−	0.0496506i
$846$	−0.448100	+	8.84179i	−0.0154060	+	0.303987i
$847$			110.185i			3.78599i
$848$	−11.8100	−	7.99751i	−0.405559	−	0.274636i
$849$			20.8544i			0.715722i
$850$	−23.5579	−	1.19391i	−0.808028	−	0.0409507i
$851$	2.09302	+	5.05300i	0.0717478	+	0.173214i
$852$	−12.8130	+	23.7939i	−0.438968	+	0.815166i
$853$	25.6414	+	10.6210i	0.877946	+	0.363657i	0.775700	−	0.631102i	$-0.217397\pi$
$853$	25.6414	+	10.6210i	0.877946	+	0.363657i	0.102246	+	0.994759i	$0.467397\pi$
$854$	−22.2371	−	62.4533i	−0.760937	−	2.13711i
$855$	−1.36032	+	1.36032i	−0.0465220	+	0.0465220i
$856$	21.6735	−	5.32201i	0.740785	−	0.181903i
$857$	−26.6776	−	26.6776i	−0.911290	−	0.911290i	0.0850835	−	0.996374i	$-0.472884\pi$
$857$	−26.6776	−	26.6776i	−0.911290	−	0.911290i	−0.996374	+	0.0850835i	$0.972884\pi$
$858$	−4.08873	+	8.61035i	−0.139587	+	0.293952i
$859$	−4.97513	+	12.0110i	−0.169749	+	0.409811i	−0.985745	−	0.168247i	$-0.946189\pi$
$859$	−4.97513	+	12.0110i	−0.169749	+	0.409811i	0.815995	+	0.578058i	$0.196189\pi$
$860$	23.2702	+	28.5346i	0.793507	+	0.973022i
$861$	5.19141	−	2.15035i	0.176923	−	0.0732838i
$862$	−10.4680	+	9.45815i	−0.356541	+	0.322146i
$863$	4.11170			0.139964			0.0699820	−	0.997548i	$-0.477706\pi$
$863$	4.11170			0.139964			0.0699820	+	0.997548i	$0.477706\pi$
$864$	28.9069	−	4.05937i	0.983434	−	0.138103i
$865$	−28.0015			−0.952080
$866$	−17.1183	+	15.4669i	−0.581703	+	0.525586i
$867$	24.8609	−	10.2977i	0.844319	−	0.349729i
$868$	16.8500	−	13.7413i	0.571927	−	0.466411i
$869$	13.9478	−	33.6729i	0.473146	−	1.14227i
$870$	3.38766	−	7.13400i	0.114853	−	0.241865i
$871$	9.49700	+	9.49700i	0.321793	+	0.321793i
$872$	9.57856	+	5.80184i	0.324371	+	0.196475i
$873$	12.2099	−	12.2099i	0.413242	−	0.413242i
$874$	−2.27232	−	6.38186i	−0.0768624	−	0.215870i
$875$	−40.4972	−	16.7745i	−1.36906	−	0.567081i
$876$	8.46849	+	4.56029i	0.286124	+	0.154078i
$877$	−1.24049	−	2.99480i	−0.0418882	−	0.101127i	0.901551	−	0.432673i	$-0.142430\pi$
$877$	−1.24049	−	2.99480i	−0.0418882	−	0.101127i	−0.943439	+	0.331546i	$0.892430\pi$
$878$	40.2829	+	2.04153i	1.35948	+	0.0688983i
$879$		−	25.1504i		−	0.848300i
$880$	−33.2774	+	21.9382i	−1.12178	+	0.739538i
$881$		−	1.38657i		−	0.0467148i	−0.999727	−	0.0233574i	$-0.992564\pi$
$881$		−	1.38657i		−	0.0467148i	0.999727	−	0.0233574i	$-0.00743557\pi$
$882$	−0.913655	+	18.0280i	−0.0307644	+	0.607034i
$883$	3.94680	+	9.52841i	0.132820	+	0.320657i	0.976272	−	0.216549i	$-0.0694800\pi$
$883$	3.94680	+	9.52841i	0.132820	+	0.320657i	−0.843451	+	0.537205i	$0.819480\pi$
$884$	−3.74467	−	12.4836i	−0.125947	−	0.419870i
$885$	8.86019	+	3.67001i	0.297832	+	0.123366i
$886$	15.9058	−	5.66340i	0.534365	−	0.190266i
$887$	−18.2122	+	18.2122i	−0.611507	+	0.611507i	−0.943339	−	0.331832i	$-0.892333\pi$
$887$	−18.2122	+	18.2122i	−0.611507	+	0.611507i	0.331832	+	0.943339i	$0.392333\pi$
$888$	1.32078	+	1.79827i	0.0443223	+	0.0603459i
$889$	−16.1395	−	16.1395i	−0.541302	−	0.541302i
$890$	11.7523	+	5.58071i	0.393938	+	0.187066i
$891$	−0.482410	+	1.16464i	−0.0161613	+	0.0390169i
$892$	3.26630	−	32.1421i	0.109364	−	1.07620i
$893$	2.00777	−	0.831647i	0.0671876	−	0.0278300i
$894$	−6.92331	−	7.66252i	−0.231550	−	0.256273i
$895$	−25.5587			−0.854334
$896$	−39.3831	−	14.5751i	−1.31570	−	0.486920i
$897$	−7.74151			−0.258482
$898$	15.2072	+	16.8309i	0.507472	+	0.561655i
$899$	9.15410	−	3.79175i	0.305306	−	0.126462i
$900$	0.974741	−	9.59197i	0.0324914	−	0.319732i
$901$	8.89232	−	21.4680i	0.296246	−	0.715201i
$902$	−11.6742	−	5.54365i	−0.388710	−	0.184584i
$903$	32.6831	+	32.6831i	1.08762	+	1.08762i
$904$	−1.70672	−	2.32373i	−0.0567645	−	0.0772862i
$905$	26.5721	−	26.5721i	0.883286	−	0.883286i
$906$	20.9955	−	7.47565i	0.697529	−	0.248362i
$907$	16.7742	+	6.94809i	0.556977	+	0.230708i	0.643372	−	0.765553i	$-0.277535\pi$
$907$	16.7742	+	6.94809i	0.556977	+	0.230708i	−0.0863951	+	0.996261i	$0.527535\pi$
$908$	−11.9282	−	39.7649i	−0.395850	−	1.31965i
$909$	4.31225	+	10.4107i	0.143028	+	0.345301i
$910$	0.415058	−	8.18980i	0.0137590	−	0.271489i
$911$		−	4.98783i		−	0.165254i	−0.996581	−	0.0826272i	$-0.973669\pi$
$911$		−	4.98783i		−	0.165254i	0.996581	−	0.0826272i	$-0.0263311\pi$
$912$	−1.52109	−	2.30729i	−0.0503682	−	0.0764020i
$913$		−	42.4301i		−	1.40423i
$914$	17.9575	+	0.910083i	0.593982	+	0.0301029i
$915$	−7.97813	−	19.2609i	−0.263749	−	0.636746i
$916$	−43.3174	−	23.3265i	−1.43125	−	0.770728i
$917$	−6.59119	−	2.73016i	−0.217660	−	0.0901578i
$918$	15.9517	+	44.8005i	0.526483	+	1.47864i
$919$	−24.5686	+	24.5686i	−0.810442	+	0.810442i	−0.984700	−	0.174258i	$-0.944247\pi$
$919$	−24.5686	+	24.5686i	−0.810442	+	0.810442i	0.174258	+	0.984700i	$0.444247\pi$
$920$	−27.6886	−	16.7713i	−0.912865	−	0.552933i
$921$	−1.85545	−	1.85545i	−0.0611393	−	0.0611393i
$922$	2.15882	−	4.54621i	0.0710969	−	0.149721i
$923$	−4.89357	+	11.8141i	−0.161074	+	0.388866i
$924$	−38.7753	+	31.6215i	−1.27561	+	1.04027i
$925$	1.76532	−	0.731219i	0.0580433	−	0.0240423i
$926$	16.2415	−	14.6747i	0.533729	−	0.482240i
$927$	−21.8070			−0.716235
$928$	−15.2820	−	11.5185i	−0.501658	−	0.378112i
$929$	−20.7133			−0.679580			−0.339790	−	0.940501i	$-0.610356\pi$
$929$	−20.7133			−0.679580			−0.339790	+	0.940501i	$0.610356\pi$
$930$	5.07341	−	4.58398i	0.166364	−	0.150315i
$931$	4.09375	−	1.69569i	0.134167	−	0.0555739i
$932$	26.1449	+	32.0597i	0.856404	+	1.05015i
$933$	−3.49919	+	8.44778i	−0.114558	+	0.276568i
$934$	20.3822	−	42.9224i	0.666926	−	1.40446i
$935$	−45.9158	−	45.9158i	−1.50161	−	1.50161i
$936$	5.17347	−	1.27037i	0.169100	−	0.0415232i
$937$	−2.25200	+	2.25200i	−0.0735697	+	0.0735697i	−0.742934	−	0.669364i	$-0.766566\pi$
$937$	−2.25200	+	2.25200i	−0.0735697	+	0.0735697i	0.669364	+	0.742934i	$0.266566\pi$
$938$	23.6481	+	66.4163i	0.772139	+	2.16857i
$939$	17.5140	+	7.25452i	0.571547	+	0.236742i
$940$	4.92373	−	9.14340i	0.160594	−	0.298225i
$941$	−9.57071	−	23.1057i	−0.311996	−	0.753226i	−0.999631	−	0.0271687i	$-0.991351\pi$
$941$	−9.57071	−	23.1057i	−0.311996	−	0.753226i	0.687635	−	0.726057i	$-0.258649\pi$
$942$	−14.7377	−	0.746901i	−0.480179	−	0.0243354i
$943$		−	10.4962i		−	0.341805i
$944$	13.0301	−	19.2417i	0.424093	−	0.626265i
$945$			29.9215i			0.973346i
$946$	5.38059	−	106.168i	0.174938	−	3.45183i
$947$	−14.1208	−	34.0907i	−0.458865	−	1.10780i	−0.968857	−	0.247619i	$-0.920352\pi$
$947$	−14.1208	−	34.0907i	−0.458865	−	1.10780i	0.509993	−	0.860179i	$-0.329648\pi$
$948$	11.5667	−	3.46962i	0.375668	−	0.112688i
$949$	4.20476	+	1.74167i	0.136492	+	0.0565370i
$950$	−2.22957	+	0.793860i	−0.0723368	+	0.0257562i
$951$	0.902655	−	0.902655i	0.0292706	−	0.0292706i
$952$	10.3528	−	67.6258i	0.335535	−	2.19176i
$953$	−26.8920	−	26.8920i	−0.871117	−	0.871117i	0.121478	−	0.992594i	$-0.461237\pi$
$953$	−26.8920	−	26.8920i	−0.871117	−	0.871117i	−0.992594	+	0.121478i	$0.961237\pi$
$954$	8.57957	+	4.07411i	0.277774	+	0.131904i
$955$	−12.3918	+	29.9166i	−0.400991	+	0.968077i
$956$	30.6326	+	3.11291i	0.990730	+	0.100679i
$957$	−21.0654	+	8.72559i	−0.680949	+	0.282058i
$958$	−0.148207	−	0.164031i	−0.00478835	−	0.00529961i
$959$	−16.0572			−0.518515
$960$	−12.6011	−	3.95078i	−0.406700	−	0.127511i
$961$	−22.4215			−0.723273
$962$	0.707792	+	0.783363i	0.0228201	+	0.0252566i
$963$	−13.7298	+	5.68706i	−0.442436	+	0.183263i
$964$	−14.2790	−	1.45104i	−0.459894	−	0.0467347i
$965$	−9.98357	+	24.1025i	−0.321383	+	0.775886i
$966$	−36.7082	−	17.4313i	−1.18107	−	0.560844i
$967$	−4.71007	−	4.71007i	−0.151466	−	0.151466i	0.627307	−	0.778772i	$-0.284157\pi$
$967$	−4.71007	−	4.71007i	−0.151466	−	0.151466i	−0.778772	+	0.627307i	$0.784157\pi$
$968$	82.9961	+	12.7058i	2.66760	+	0.408379i
$969$	3.18357	−	3.18357i	0.102271	−	0.102271i
$970$	−19.0814	+	6.79411i	−0.612667	+	0.218146i
$971$	1.25749	+	0.520868i	0.0403547	+	0.0167155i	0.402770	−	0.915301i	$-0.368048\pi$
$971$	1.25749	+	0.520868i	0.0403547	+	0.0167155i	−0.362415	+	0.932017i	$0.618048\pi$
$972$	−30.0558	+	9.01575i	−0.964042	+	0.289180i
$973$	16.9786	+	40.9900i	0.544309	+	1.31408i
$974$	−1.26472	+	24.9550i	−0.0405241	+	0.799611i
$975$			2.70458i			0.0866159i
$976$	−49.6069	+	9.54828i	−1.58788	+	0.305633i
$977$			32.9112i			1.05292i	0.850199	+	0.526462i	$0.176482\pi$
$977$			32.9112i			1.05292i	−0.850199	+	0.526462i	$0.823518\pi$
$978$	−15.2533	−	0.773033i	−0.487746	−	0.0247189i
$979$	−14.3742	−	34.7024i	−0.459402	−	1.10909i
$980$	10.0392	−	18.6430i	0.320692	−	0.595527i
$981$	−6.88949	−	2.85372i	−0.219965	−	0.0911123i
$982$	7.70468	+	21.6388i	0.245866	+	0.690520i
$983$	38.4387	−	38.4387i	1.22600	−	1.22600i	0.260540	−	0.965463i	$-0.416099\pi$
$983$	38.4387	−	38.4387i	1.22600	−	1.22600i	0.965463	−	0.260540i	$-0.0839006\pi$
$984$	−1.02110	−	4.15837i	−0.0325516	−	0.132564i
$985$	4.10454	+	4.10454i	0.130782	+	0.130782i
$986$	13.3734	−	28.1626i	0.425894	−	0.896881i
$987$	4.98874	−	12.0439i	0.158793	−	0.383361i
$988$	−0.826440	−	1.01341i	−0.0262926	−	0.0322408i
$989$	79.7659	−	33.0401i	2.53641	−	1.05061i
$990$	19.6934	−	17.7936i	0.625898	−	0.565517i
$991$	44.8381			1.42433			0.712164	−	0.702013i	$-0.247715\pi$
$991$	44.8381			1.42433			0.712164	+	0.702013i	$0.247715\pi$
$992$	−8.40756	−	14.2768i	−0.266940	−	0.453288i
$993$	11.2479			0.356942
$994$	−49.8055	+	45.0007i	−1.57973	+	1.42734i
$995$	−6.66987	+	2.76275i	−0.211449	+	0.0875851i
$996$	10.8946	−	8.88466i	0.345210	−	0.281521i
$997$	10.2131	−	24.6566i	0.323452	−	0.780881i	−0.675597	−	0.737271i	$-0.736114\pi$
$997$	10.2131	−	24.6566i	0.323452	−	0.780881i	0.999049	−	0.0436102i	$-0.0138860\pi$
$998$	11.9370	−	25.1377i	0.377858	−	0.795721i
$999$	−2.72397	−	2.72397i	−0.0861826	−	0.0861826i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bf.a.53.12	✓	192
32.29	even	8	inner	416.2.bf.a.157.12	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bf.a.53.12	✓	192	1.1	even	1	trivial
416.2.bf.a.157.12	yes	192	32.29	even	8	inner

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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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Fields

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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	416.2.bf.a.53.12

Level	$416$
Weight	$2$
Character	416.53
Analytic conductor	$3.322$
Analytic rank	$0$
Dimension	$192$
Inner twists	$2$