LMFDB - Embedded newform 357.2.bf.a.29.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(29,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 0, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.29"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bf (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$36$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			29.13
Character	$\chi$	$=$	357.29
Dual form			357.2.bf.a.197.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.927040 + 0.383993i) q^{2} +(-1.08976 - 1.34627i) q^{3} +(-0.702260 + 0.702260i) q^{4} +(0.206206 - 1.03667i) q^{5} +(1.52720 + 0.829583i) q^{6} +(-0.980785 + 0.195090i) q^{7} +(1.14935 - 2.77477i) q^{8} +(-0.624860 + 2.93420i) q^{9} +(0.206911 + 1.04021i) q^{10} +(0.0513533 + 0.0343132i) q^{11} +(1.71072 + 0.180136i) q^{12} +(-1.63096 - 1.63096i) q^{13} +(0.834314 - 0.557471i) q^{14} +(-1.62034 + 0.852108i) q^{15} +1.02737i q^{16} +(-1.78393 + 3.71720i) q^{17} +(-0.547442 - 2.96007i) q^{18} +(2.41528 + 5.83101i) q^{19} +(0.583200 + 0.872821i) q^{20} +(1.33146 + 1.10780i) q^{21} +(-0.0607825 - 0.0120904i) q^{22} +(-3.28662 + 4.91878i) q^{23} +(-4.98808 + 1.47650i) q^{24} +(3.58724 + 1.48588i) q^{25} +(2.13824 + 0.885690i) q^{26} +(4.63116 - 2.35634i) q^{27} +(0.551762 - 0.825771i) q^{28} +(-8.91991 - 1.77428i) q^{29} +(1.17492 - 1.41214i) q^{30} +(5.29400 + 7.92302i) q^{31} +(1.90419 + 4.59712i) q^{32} +(-0.00976797 - 0.106528i) q^{33} +(0.226392 - 4.13101i) q^{34} +1.05698i q^{35} +(-1.62176 - 2.49939i) q^{36} +(-8.29830 + 5.54475i) q^{37} +(-4.47813 - 4.47813i) q^{38} +(-0.418355 + 3.97306i) q^{39} +(-2.63951 - 1.76366i) q^{40} +(0.960864 + 4.83059i) q^{41} +(-1.65970 - 0.515700i) q^{42} +(2.79355 - 6.74423i) q^{43} +(-0.0601601 + 0.0119666i) q^{44} +(2.91294 + 1.25282i) q^{45} +(1.15806 - 5.82194i) q^{46} +(5.94735 - 5.94735i) q^{47} +(1.38311 - 1.11958i) q^{48} +(0.923880 - 0.382683i) q^{49} -3.89608 q^{50} +(6.94839 - 1.64921i) q^{51} +2.29072 q^{52} +(-10.8609 + 4.49873i) q^{53} +(-3.38846 + 3.96276i) q^{54} +(0.0461607 - 0.0461607i) q^{55} +(-0.585932 + 2.94568i) q^{56} +(5.21801 - 9.60599i) q^{57} +(8.95042 - 1.78035i) q^{58} +(-0.00276777 + 0.00668198i) q^{59} +(0.539502 - 1.73630i) q^{60} +(0.799262 + 4.01816i) q^{61} +(-7.95013 - 5.31211i) q^{62} +(0.0404186 - 2.99973i) q^{63} +(-4.98344 - 4.98344i) q^{64} +(-2.02708 + 1.35445i) q^{65} +(0.0499613 + 0.0950050i) q^{66} -14.6304i q^{67} +(-1.35766 - 3.86322i) q^{68} +(10.2036 - 0.935607i) q^{69} +(-0.405872 - 0.979860i) q^{70} +(1.55931 + 2.33368i) q^{71} +(7.42355 + 5.10626i) q^{72} +(-5.71846 - 1.13747i) q^{73} +(5.56372 - 8.32669i) q^{74} +(-1.90883 - 6.44863i) q^{75} +(-5.79104 - 2.39873i) q^{76} +(-0.0570607 - 0.0236353i) q^{77} +(-1.13779 - 3.84383i) q^{78} +(-2.21627 + 3.31688i) q^{79} +(1.06504 + 0.211850i) q^{80} +(-8.21910 - 3.66693i) q^{81} +(-2.74567 - 4.10919i) q^{82} +(0.0440482 + 0.106342i) q^{83} +(-1.71299 + 0.157071i) q^{84} +(3.48565 + 2.61585i) q^{85} +7.32488i q^{86} +(7.33188 + 13.9421i) q^{87} +(0.154234 - 0.103056i) q^{88} +(5.11735 + 5.11735i) q^{89} +(-3.18149 - 0.0428677i) q^{90} +(1.91781 + 1.28144i) q^{91} +(-1.14620 - 5.76232i) q^{92} +(4.89732 - 15.7613i) q^{93} +(-3.22969 + 7.79717i) q^{94} +(6.54286 - 1.30146i) q^{95} +(4.11384 - 7.57329i) q^{96} +(0.869274 - 4.37013i) q^{97} +(-0.709526 + 0.709526i) q^{98} +(-0.132770 + 0.129240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 48 q^{12} - 48 q^{24} - 64 q^{25} - 64 q^{31} - 224 q^{34} + 16 q^{39} + 64 q^{40} - 64 q^{43} + 64 q^{45} + 32 q^{51} + 128 q^{52} + 112 q^{54} - 32 q^{57} + 32 q^{58} - 144 q^{60} + 32 q^{61}+ \cdots + 304 q^{96}+O(q^{100}) $ 288 * q - 48 * q^12 - 48 * q^24 - 64 * q^25 - 64 * q^31 - 224 * q^34 + 16 * q^39 + 64 * q^40 - 64 * q^43 + 64 * q^45 + 32 * q^51 + 128 * q^52 + 112 * q^54 - 32 * q^57 + 32 * q^58 - 144 * q^60 + 32 * q^61 + 64 * q^64 - 192 * q^66 - 32 * q^70 - 208 * q^72 - 128 * q^76 - 208 * q^78 - 64 * q^79 - 112 * q^81 - 256 * q^82 + 32 * q^85 + 32 * q^88 + 240 * q^90 - 96 * q^91 + 64 * q^93 + 304 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$1$	$e\left(\frac{13}{16}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.927040	+	0.383993i	−0.655517	+	0.271524i	−0.685551	−	0.728025i	$-0.740438\pi$
$2$	−0.927040	+	0.383993i	−0.655517	+	0.271524i	0.0300340	+	0.999549i	$0.490438\pi$
$3$	−1.08976	−	1.34627i	−0.629171	−	0.777267i
$3$	−1.08976	−	1.34627i	−0.629171	−	0.777267i
$4$	−0.702260	+	0.702260i	−0.351130	+	0.351130i
$5$	0.206206	−	1.03667i	0.0922181	−	0.463612i	−0.906889	−	0.421369i	$-0.861550\pi$
$5$	0.206206	−	1.03667i	0.0922181	−	0.463612i	0.999107	−	0.0422428i	$-0.0134503\pi$
$6$	1.52720	+	0.829583i	0.623479	+	0.338676i
$7$	−0.980785	+	0.195090i	−0.370702	+	0.0737372i
$7$	−0.980785	+	0.195090i	−0.370702	+	0.0737372i
$8$	1.14935	−	2.77477i	0.406355	−	0.981028i
$9$	−0.624860	+	2.93420i	−0.208287	+	0.978068i
$10$	0.206911	+	1.04021i	0.0654312	+	0.328945i
$11$	0.0513533	+	0.0343132i	0.0154836	+	0.0103458i	0.563288	−	0.826261i	$-0.309536\pi$
$11$	0.0513533	+	0.0343132i	0.0154836	+	0.0103458i	−0.547804	+	0.836606i	$0.684536\pi$
$12$	1.71072	+	0.180136i	0.493843	+	0.0520006i
$13$	−1.63096	−	1.63096i	−0.452347	−	0.452347i	0.443786	−	0.896133i	$-0.353635\pi$
$13$	−1.63096	−	1.63096i	−0.452347	−	0.452347i	−0.896133	+	0.443786i	$0.853635\pi$
$14$	0.834314	−	0.557471i	0.222980	−	0.148990i
$15$	−1.62034	+	0.852108i	−0.418371	+	0.220013i
$16$			1.02737i			0.256842i
$17$	−1.78393	+	3.71720i	−0.432666	+	0.901555i
$17$	−1.78393	+	3.71720i	−0.432666	+	0.901555i
$18$	−0.547442	−	2.96007i	−0.129033	−	0.697694i
$19$	2.41528	+	5.83101i	0.554104	+	1.33772i	0.914372	+	0.404876i	$0.132685\pi$
$19$	2.41528	+	5.83101i	0.554104	+	1.33772i	−0.360268	+	0.932849i	$0.617315\pi$
$20$	0.583200	+	0.872821i	0.130408	+	0.195169i
$21$	1.33146	+	1.10780i	0.290549	+	0.241741i
$22$	−0.0607825	−	0.0120904i	−0.0129589	−	0.00257768i
$23$	−3.28662	+	4.91878i	−0.685308	+	1.02564i	0.311838	+	0.950135i	$0.399055\pi$
$23$	−3.28662	+	4.91878i	−0.685308	+	1.02564i	−0.997146	+	0.0755006i	$0.975945\pi$
$24$	−4.98808	+	1.47650i	−1.01819	+	0.301389i
$25$	3.58724	+	1.48588i	0.717448	+	0.297177i
$26$	2.13824	+	0.885690i	0.419344	+	0.173698i
$27$	4.63116	−	2.35634i	0.891267	−	0.453478i
$28$	0.551762	−	0.825771i	0.104273	−	0.156056i
$29$	−8.91991	−	1.77428i	−1.65639	−	0.329475i	−0.723686	−	0.690130i	$-0.757553\pi$
$29$	−8.91991	−	1.77428i	−1.65639	−	0.329475i	−0.932700	+	0.360654i	$0.882553\pi$
$30$	1.17492	−	1.41214i	0.214510	−	0.257820i
$31$	5.29400	+	7.92302i	0.950830	+	1.42302i	0.905644	+	0.424038i	$0.139388\pi$
$31$	5.29400	+	7.92302i	0.950830	+	1.42302i	0.0451854	+	0.998979i	$0.485612\pi$
$32$	1.90419	+	4.59712i	0.336616	+	0.812664i
$33$	−0.00976797	−	0.106528i	−0.00170039	−	0.0185442i
$34$	0.226392	−	4.13101i	0.0388259	−	0.708463i
$35$			1.05698i			0.178662i
$36$	−1.62176	−	2.49939i	−0.270293	−	0.416565i
$37$	−8.29830	+	5.54475i	−1.36423	+	0.911551i	−0.999806	−	0.0196810i	$-0.993735\pi$
$37$	−8.29830	+	5.54475i	−1.36423	+	0.911551i	−0.364426	+	0.931232i	$0.618735\pi$
$38$	−4.47813	−	4.47813i	−0.726448	−	0.726448i
$39$	−0.418355	+	3.97306i	−0.0669904	+	0.636198i
$40$	−2.63951	−	1.76366i	−0.417343	−	0.278860i
$41$	0.960864	+	4.83059i	0.150062	+	0.754411i	0.980379	+	0.197121i	$0.0631591\pi$
$41$	0.960864	+	4.83059i	0.150062	+	0.754411i	−0.830318	+	0.557291i	$0.811841\pi$
$42$	−1.65970	−	0.515700i	−0.256098	−	0.0795743i
$43$	2.79355	−	6.74423i	0.426013	−	1.02849i	−0.554527	−	0.832166i	$-0.687101\pi$
$43$	2.79355	−	6.74423i	0.426013	−	1.02849i	0.980540	−	0.196320i	$-0.0628991\pi$
$44$	−0.0601601	+	0.0119666i	−0.00906948	+	0.00180403i
$45$	2.91294	+	1.25282i	0.434236	+	0.186760i
$46$	1.15806	−	5.82194i	0.170746	−	0.858399i
$47$	5.94735	−	5.94735i	0.867510	−	0.867510i	−0.124687	−	0.992196i	$-0.539793\pi$
$47$	5.94735	−	5.94735i	0.867510	−	0.867510i	0.992196	+	0.124687i	$0.0397926\pi$
$48$	1.38311	−	1.11958i	0.199635	−	0.161598i
$49$	0.923880	−	0.382683i	0.131983	−	0.0546691i
$50$	−3.89608			−0.550989
$51$	6.94839	−	1.64921i	0.972969	−	0.230936i
$52$	2.29072			0.317665
$53$	−10.8609	+	4.49873i	−1.49186	+	0.617948i	−0.971721	−	0.236133i	$-0.924120\pi$
$53$	−10.8609	+	4.49873i	−1.49186	+	0.617948i	−0.520139	+	0.854082i	$0.674120\pi$
$54$	−3.38846	+	3.96276i	−0.461110	+	0.539263i
$55$	0.0461607	−	0.0461607i	0.00622431	−	0.00622431i
$56$	−0.585932	+	2.94568i	−0.0782984	+	0.393633i
$57$	5.21801	−	9.60599i	0.691142	−	1.27234i
$58$	8.95042	−	1.78035i	1.17525	−	0.233771i
$59$	−0.00276777	+	0.00668198i	−0.000360333	+	0.000869920i	−0.924060	−	0.382248i	$-0.875150\pi$
$59$	−0.00276777	+	0.00668198i	−0.000360333	+	0.000869920i	0.923699	+	0.383118i	$0.125150\pi$
$60$	0.539502	−	1.73630i	0.0696494	−	0.224156i
$61$	0.799262	+	4.01816i	0.102335	+	0.514473i	0.997618	+	0.0689757i	$0.0219731\pi$
$61$	0.799262	+	4.01816i	0.102335	+	0.514473i	−0.895283	+	0.445497i	$0.853027\pi$
$62$	−7.95013	−	5.31211i	−1.00967	−	0.674638i
$63$	0.0404186	−	2.99973i	0.00509226	−	0.377930i
$64$	−4.98344	−	4.98344i	−0.622930	−	0.622930i
$65$	−2.02708	+	1.35445i	−0.251428	+	0.167999i
$66$	0.0499613	+	0.0950050i	0.00614981	+	0.0116943i
$67$		−	14.6304i		−	1.78738i	−0.448683	−	0.893691i	$-0.648107\pi$
$67$		−	14.6304i		−	1.78738i	0.448683	−	0.893691i	$-0.351893\pi$
$68$	−1.35766	−	3.86322i	−0.164641	−	0.468485i
$69$	10.2036	−	0.935607i	1.22837	−	0.112634i
$70$	−0.405872	−	0.979860i	−0.0485109	−	0.117116i
$71$	1.55931	+	2.33368i	0.185056	+	0.276956i	0.912385	−	0.409333i	$-0.134238\pi$
$71$	1.55931	+	2.33368i	0.185056	+	0.276956i	−0.727329	+	0.686289i	$0.759238\pi$
$72$	7.42355	+	5.10626i	0.874874	+	0.601778i
$73$	−5.71846	−	1.13747i	−0.669295	−	0.133131i	−0.151265	−	0.988493i	$-0.548335\pi$
$73$	−5.71846	−	1.13747i	−0.669295	−	0.133131i	−0.518030	+	0.855362i	$0.673335\pi$
$74$	5.56372	−	8.32669i	0.646769	−	0.967959i
$75$	−1.90883	−	6.44863i	−0.220412	−	0.744623i
$76$	−5.79104	−	2.39873i	−0.664278	−	0.275153i
$77$	−0.0570607	−	0.0236353i	−0.00650267	−	0.00269349i
$78$	−1.13779	−	3.84383i	−0.128830	−	0.435228i
$79$	−2.21627	+	3.31688i	−0.249350	+	0.373179i	−0.934938	−	0.354811i	$-0.884545\pi$
$79$	−2.21627	+	3.31688i	−0.249350	+	0.373179i	0.685588	+	0.727990i	$0.259545\pi$
$80$	1.06504	+	0.211850i	0.119075	+	0.0236855i
$81$	−8.21910	−	3.66693i	−0.913233	−	0.407437i
$82$	−2.74567	−	4.10919i	−0.303209	−	0.453784i
$83$	0.0440482	+	0.106342i	0.00483492	+	0.0116725i	0.926279	−	0.376840i	$-0.122989\pi$
$83$	0.0440482	+	0.106342i	0.00483492	+	0.0116725i	−0.921444	+	0.388512i	$0.872989\pi$
$84$	−1.71299	+	0.157071i	−0.186903	+	0.0171378i
$85$	3.48565	+	2.61585i	0.378072	+	0.283729i
$86$			7.32488i			0.789862i
$87$	7.33188	+	13.9421i	0.786060	+	1.49475i
$88$	0.154234	−	0.103056i	0.0164414	−	0.0109858i
$89$	5.11735	+	5.11735i	0.542438	+	0.542438i	0.924243	−	0.381805i	$-0.124697\pi$
$89$	5.11735	+	5.11735i	0.542438	+	0.542438i	−0.381805	+	0.924243i	$0.624697\pi$
$90$	−3.18149	−	0.0428677i	−0.335359	−	0.00451865i
$91$	1.91781	+	1.28144i	0.201041	+	0.134331i
$92$	−1.14620	−	5.76232i	−0.119499	−	0.600764i
$93$	4.89732	−	15.7613i	0.507829	−	1.63437i
$94$	−3.22969	+	7.79717i	−0.333117	+	0.804216i
$95$	6.54286	−	1.30146i	0.671283	−	0.133527i
$96$	4.11384	−	7.57329i	0.419867	−	0.772945i
$97$	0.869274	−	4.37013i	0.0882614	−	0.443720i	−0.911232	−	0.411893i	$-0.864868\pi$
$97$	0.869274	−	4.37013i	0.0882614	−	0.443720i	0.999493	−	0.0318265i	$-0.0101324\pi$
$98$	−0.709526	+	0.709526i	−0.0716729	+	0.0716729i
$99$	−0.132770	+	0.129240i	−0.0133439	+	0.0129891i
$100$	−3.56265	+	1.47570i	−0.356265	+	0.147570i
$101$	6.52619			0.649380			0.324690	−	0.945820i	$-0.394740\pi$
$101$	6.52619			0.649380			0.324690	+	0.945820i	$0.394740\pi$
$102$	−5.80815	+	4.19702i	−0.575093	+	0.415567i
$103$	4.60410			0.453656			0.226828	−	0.973935i	$-0.427165\pi$
$103$	4.60410			0.453656			0.226828	+	0.973935i	$0.427165\pi$
$104$	−6.40008	+	2.65100i	−0.627579	+	0.259952i
$105$	1.42297	−	1.15185i	0.138868	−	0.112409i
$106$	8.34101	−	8.34101i	0.810151	−	0.810151i
$107$	−0.240072	+	1.20692i	−0.0232087	+	0.116678i	−0.990653	−	0.136406i	$-0.956445\pi$
$107$	−0.240072	+	1.20692i	−0.0232087	+	0.116678i	0.967444	+	0.253084i	$0.0814448\pi$
$108$	−1.59752	+	4.90704i	−0.153721	+	0.472181i
$109$	−11.1565	+	2.21916i	−1.06860	+	0.212557i	−0.697899	−	0.716196i	$-0.745882\pi$
$109$	−11.1565	+	2.21916i	−1.06860	+	0.212557i	−0.370699	+	0.928753i	$0.620882\pi$
$110$	−0.0250675	+	0.0605182i	−0.00239009	+	0.00577018i
$111$	16.5078	+	5.12929i	1.56685	+	0.486851i
$112$	−0.200430	−	1.00763i	−0.0189388	−	0.0952120i
$113$	5.26075	+	3.51512i	0.494890	+	0.330675i	0.777843	−	0.628459i	$-0.216314\pi$
$113$	5.26075	+	3.51512i	0.494890	+	0.330675i	−0.282953	+	0.959134i	$0.591314\pi$
$114$	−1.14868	+	10.9088i	−0.107583	+	1.02170i
$115$	4.42142	+	4.42142i	0.412299	+	0.412299i
$116$	7.51010	−	5.01809i	0.697295	−	0.465918i
$117$	5.80469	−	3.76645i	0.536644	−	0.348208i
$118$		−	0.00725727i		−	0.000668086i
$119$	1.02446	−	3.99381i	0.0939119	−	0.366112i
$120$	0.502064	+	5.47544i	0.0458320	+	0.499837i
$121$	−4.20806	−	10.1592i	−0.382551	−	0.923559i
$122$	−2.28389	−	3.41809i	−0.206774	−	0.309459i
$123$	5.45615	−	6.55774i	0.491964	−	0.591292i
$124$	−9.28179	−	1.84626i	−0.833529	−	0.165799i
$125$	5.21620	−	7.80660i	0.466551	−	0.698243i
$126$	1.11440	+	2.79639i	0.0992790	+	0.249122i
$127$	9.80307	+	4.06056i	0.869882	+	0.360317i	0.772564	−	0.634937i	$-0.218974\pi$
$127$	9.80307	+	4.06056i	0.869882	+	0.360317i	0.0973174	+	0.995253i	$0.468974\pi$
$128$	−2.66078	−	1.10213i	−0.235182	−	0.0974157i
$129$	−12.1238	+	3.58871i	−1.06744	+	0.315968i
$130$	1.35908	−	2.03401i	0.119200	−	0.178395i
$131$	−19.5538	−	3.88949i	−1.70842	−	0.339826i	−0.758347	−	0.651851i	$-0.773993\pi$
$131$	−19.5538	−	3.88949i	−1.70842	−	0.339826i	−0.950074	+	0.312025i	$0.898993\pi$
$132$	0.0816701	+	0.0679508i	0.00710847	+	0.00591436i
$133$	−3.50645	−	5.24777i	−0.304047	−	0.455039i
$134$	5.61795	+	13.5629i	0.485317	+	1.17166i
$135$	−1.48777	−	5.28687i	−0.128047	−	0.455021i
$136$	8.26403	+	9.22233i	0.708635	+	0.790808i
$137$			12.1089i			1.03453i	0.855825	+	0.517266i	$0.173050\pi$
$137$			12.1089i			1.03453i	−0.855825	+	0.517266i	$0.826950\pi$
$138$	−9.09988	+	4.78545i	−0.774633	+	0.407365i
$139$	−10.1226	+	6.76369i	−0.858586	+	0.573689i	−0.905086	−	0.425230i	$-0.860193\pi$
$139$	−10.1226	+	6.76369i	−0.858586	+	0.573689i	0.0464997	+	0.998918i	$0.485193\pi$
$140$	−0.742273	−	0.742273i	−0.0627335	−	0.0627335i
$141$	−14.4879	−	1.52554i	−1.22010	−	0.128474i
$142$	−2.34166	−	1.56465i	−0.196508	−	0.131302i
$143$	−0.0277918	−	0.139719i	−0.00232406	−	0.0116839i
$144$	−3.01451	−	0.641962i	−0.251209	−	0.0534968i
$145$	−3.67868	+	8.88111i	−0.305497	+	0.737536i
$146$	5.73802	−	1.14136i	0.474882	−	0.0944599i
$147$	−1.52200	−	0.826755i	−0.125532	−	0.0681896i
$148$	1.93371	−	9.72142i	0.158950	−	0.799096i
$149$	−7.22425	+	7.22425i	−0.591834	+	0.591834i	−0.938126	−	0.346293i	$-0.887440\pi$
$149$	−7.22425	+	7.22425i	−0.591834	+	0.591834i	0.346293	+	0.938126i	$0.387440\pi$
$150$	4.24578	+	5.24516i	0.346667	+	0.428266i
$151$	−0.0502173	+	0.0208007i	−0.00408663	+	0.00169274i	−0.384726	−	0.923031i	$-0.625704\pi$
$151$	−0.0502173	+	0.0208007i	−0.00408663	+	0.00169274i	0.380639	+	0.924724i	$0.375704\pi$
$152$	18.9557			1.53751
$153$	−9.79233	−	7.55713i	−0.791663	−	0.610958i
$154$	0.0619733			0.00499395
$155$	9.30520	−	3.85434i	0.747411	−	0.309588i
$156$	−2.49633	−	3.08391i	−0.199866	−	0.246911i
$157$	−10.2939	+	10.2939i	−0.821544	+	0.821544i	−0.986329	−	0.164786i	$-0.947307\pi$
$157$	−10.2939	+	10.2939i	−0.821544	+	0.821544i	0.164786	+	0.986329i	$0.447307\pi$
$158$	0.780914	−	3.92592i	0.0621261	−	0.312329i
$159$	17.8922	+	9.71913i	1.41895	+	0.770777i
$160$	5.15834	−	1.02606i	0.407803	−	0.0811170i
$161$	2.26386	−	5.46545i	0.178418	−	0.430738i
$162$	9.02751	+	0.243319i	0.709268	+	0.0191170i
$163$	4.44539	+	22.3485i	0.348190	+	1.75047i	0.616706	+	0.787194i	$0.288467\pi$
$163$	4.44539	+	22.3485i	0.348190	+	1.75047i	−0.268516	+	0.963275i	$0.586533\pi$
$164$	−4.06711	−	2.71755i	−0.317588	−	0.212205i
$165$	−0.112448	−	0.0118406i	−0.00875410	−	0.000921789i
$166$	−0.0816690	−	0.0816690i	−0.00633874	−	0.00633874i
$167$	−9.77712	+	6.53286i	−0.756576	+	0.505528i	−0.873029	−	0.487668i	$-0.837848\pi$
$167$	−9.77712	+	6.53286i	−0.756576	+	0.505528i	0.116453	+	0.993196i	$0.462848\pi$
$168$	4.60419	−	2.42125i	0.355221	−	0.186804i
$169$		−	7.67993i		−	0.590764i
$170$	−4.23580	−	1.08653i	−0.324871	−	0.0833333i
$171$	−18.6186	+	3.44337i	−1.42380	+	0.263321i
$172$	2.77440	+	6.69800i	0.211546	+	0.510718i
$173$	−0.581400	−	0.870126i	−0.0442030	−	0.0661545i	0.808710	−	0.588208i	$-0.200166\pi$
$173$	−0.581400	−	0.870126i	−0.0442030	−	0.0661545i	−0.852913	+	0.522053i	$0.825166\pi$
$174$	−12.1506	−	10.1095i	−0.921135	−	0.766399i
$175$	−3.80819	−	0.757497i	−0.287872	−	0.0572614i
$176$	−0.0352523	+	0.0527588i	−0.00265724	+	0.00397684i
$177$	0.0120119	−	0.00355559i	0.000902871	−	0.000267254i
$178$	−6.70902	−	2.77897i	−0.502862	−	0.208292i
$179$	−1.38846	−	0.575120i	−0.103779	−	0.0429865i	0.330190	−	0.943914i	$-0.392887\pi$
$179$	−1.38846	−	0.575120i	−0.103779	−	0.0429865i	−0.433969	+	0.900928i	$0.642887\pi$
$180$	−2.92545	+	1.16584i	−0.218050	+	0.0868964i
$181$	0.958343	−	1.43426i	0.0712331	−	0.106608i	−0.794143	−	0.607731i	$-0.792080\pi$
$181$	0.958343	−	1.43426i	0.0712331	−	0.106608i	0.865376	+	0.501123i	$0.167080\pi$
$182$	−2.26995	−	0.451521i	−0.168260	−	0.0334689i
$183$	4.53851	−	5.45484i	0.335496	−	0.403233i
$184$	9.87099	+	14.7730i	0.727699	+	1.08908i
$185$	4.03690	+	9.74594i	0.296799	+	0.716536i
$186$	1.51220	+	16.4919i	0.110880	+	1.20924i
$187$	−0.219159	+	0.129678i	−0.0160265	+	0.00948303i
$188$			8.35317i			0.609217i
$189$	−4.08248	+	3.21456i	−0.296956	+	0.233825i
$190$	−5.56575	+	3.71891i	−0.403782	+	0.269798i
$191$	−10.6589	−	10.6589i	−0.771254	−	0.771254i	0.207072	−	0.978326i	$-0.433607\pi$
$191$	−10.6589	−	10.6589i	−0.771254	−	0.771254i	−0.978326	+	0.207072i	$0.933607\pi$
$192$	−1.27829	+	12.1398i	−0.0922529	+	0.876113i
$193$	3.74097	+	2.49964i	0.269281	+	0.179928i	0.682878	−	0.730532i	$-0.260728\pi$
$193$	3.74097	+	2.49964i	0.269281	+	0.179928i	−0.413597	+	0.910460i	$0.635728\pi$
$194$	0.872248	+	4.38509i	0.0626237	+	0.314831i
$195$	4.03247	+	1.25296i	0.288771	+	0.0897266i
$196$	−0.380060	+	0.917547i	−0.0271472	+	0.0655391i
$197$	−7.12924	+	1.41809i	−0.507938	+	0.101035i	−0.442405	−	0.896815i	$-0.645875\pi$
$197$	−7.12924	+	1.41809i	−0.507938	+	0.101035i	−0.0655326	+	0.997850i	$0.520875\pi$
$198$	0.0734563	−	0.170794i	0.00522031	−	0.0121378i
$199$	−1.95452	+	9.82604i	−0.138552	+	0.696550i	0.847590	+	0.530651i	$0.178052\pi$
$199$	−1.95452	+	9.82604i	−0.138552	+	0.696550i	−0.986143	+	0.165899i	$0.946948\pi$
$200$	8.24596	−	8.24596i	0.583077	−	0.583077i
$201$	−19.6963	+	15.9435i	−1.38927	+	1.12457i
$202$	−6.05004	+	2.50601i	−0.425680	+	0.176322i
$203$	9.09466			0.638320
$204$	−3.72140	+	6.03775i	−0.260550	+	0.422727i
$205$	5.20585			0.363592
$206$	−4.26819	+	1.76794i	−0.297379	+	0.123178i
$207$	−12.3790	−	12.7172i	−0.860401	−	0.883904i
$208$	1.67560	−	1.67560i	0.116182	−	0.116182i
$209$	−0.0760476	+	0.382317i	−0.00526032	+	0.0264454i
$210$	−0.876851	+	1.61422i	−0.0605085	+	0.111392i
$211$	16.3885	−	3.25987i	1.12823	−	0.224419i	0.404523	−	0.914528i	$-0.367438\pi$
$211$	16.3885	−	3.25987i	1.12823	−	0.224419i	0.723705	+	0.690109i	$0.242438\pi$
$212$	4.46790	−	10.7865i	0.306856	−	0.740817i
$213$	1.44247	−	4.64239i	0.0988367	−	0.318091i
$214$	−0.240894	−	1.21105i	−0.0164671	−	0.0827859i
$215$	−6.41548	−	4.28669i	−0.437532	−	0.292350i
$216$	−1.21549	−	15.5586i	−0.0827037	−	1.05863i
$217$	−6.73798	−	6.73798i	−0.457404	−	0.457404i
$218$	9.49038	−	6.34127i	0.642769	−	0.429485i
$219$	4.70039	+	8.93813i	0.317623	+	0.603983i
$220$			0.0648336i			0.00437108i
$221$	8.97213	−	3.15310i	0.603531	−	0.212101i
$222$	−17.2730	+	1.58383i	−1.15929	+	0.106300i
$223$	−2.67582	−	6.46000i	−0.179186	−	0.432594i	0.808610	−	0.588345i	$-0.200220\pi$
$223$	−2.67582	−	6.46000i	−0.179186	−	0.432594i	−0.987796	+	0.155751i	$0.950220\pi$
$224$	−2.76446	−	4.13730i	−0.184708	−	0.276435i
$225$	−6.60140	+	9.59722i	−0.440094	+	0.639815i
$226$	−6.22671	−	1.23857i	−0.414194	−	0.0823884i
$227$	14.7468	−	22.0701i	0.978776	−	1.46484i	0.0958138	−	0.995399i	$-0.469455\pi$
$227$	14.7468	−	22.0701i	0.978776	−	1.46484i	0.882963	−	0.469443i	$-0.155545\pi$
$228$	3.08150	+	10.4103i	0.204077	+	0.689439i
$229$	−6.34081	−	2.62645i	−0.419013	−	0.173561i	0.163208	−	0.986592i	$-0.447816\pi$
$229$	−6.34081	−	2.62645i	−0.419013	−	0.173561i	−0.582220	+	0.813031i	$0.697816\pi$
$230$	−5.79662	−	2.40104i	−0.382218	−	0.158320i
$231$	0.0303629	+	0.102576i	0.00199773	+	0.00674898i
$232$	−15.1753	+	22.7114i	−0.996305	+	1.49108i
$233$	−5.78237	−	1.15018i	−0.378815	−	0.0753511i	0.00201015	−	0.999998i	$-0.499360\pi$
$233$	−5.78237	−	1.15018i	−0.378815	−	0.0753511i	−0.380826	+	0.924647i	$0.624360\pi$
$234$	−3.93490	+	5.72061i	−0.257232	+	0.373968i
$235$	−4.93904	−	7.39180i	−0.322188	−	0.482188i
$236$	−0.00274880	−	0.00663618i	−0.000178931	−	0.000431979i
$237$	6.88060	−	0.630909i	0.446943	−	0.0409819i
$238$	0.583879	+	4.09580i	0.0378473	+	0.265492i
$239$			22.8783i			1.47987i	0.672677	+	0.739936i	$0.265144\pi$
$239$			22.8783i			1.47987i	−0.672677	+	0.739936i	$0.734856\pi$
$240$	−0.875430	−	1.66469i	−0.0565087	−	0.107455i
$241$	5.74187	−	3.83660i	0.369866	−	0.247137i	−0.356721	−	0.934211i	$-0.616105\pi$
$241$	5.74187	−	3.83660i	0.369866	−	0.247137i	0.726587	+	0.687074i	$0.241105\pi$
$242$	7.80208	+	7.80208i	0.501537	+	0.501537i
$243$	4.02016	+	15.0612i	0.257893	+	0.966173i
$244$	−3.38309	−	2.26051i	−0.216580	−	0.144714i
$245$	−0.206206	−	1.03667i	−0.0131740	−	0.0662303i
$246$	−2.53994	+	8.17441i	−0.161941	+	0.521182i
$247$	5.57091	−	13.4494i	0.354469	−	0.855763i
$248$	28.0692	−	5.58331i	1.78239	−	0.354540i
$249$	0.0951625	−	0.175187i	0.00603068	−	0.0111020i
$250$	−1.83795	+	9.24002i	−0.116242	+	0.584390i
$251$	−7.15548	+	7.15548i	−0.451650	+	0.451650i	−0.895902	−	0.444252i	$-0.853470\pi$
$251$	−7.15548	+	7.15548i	−0.451650	+	0.451650i	0.444252	+	0.895902i	$0.353470\pi$
$252$	2.07820	+	2.13497i	0.130915	+	0.134491i
$253$	−0.337557	+	0.139821i	−0.0212221	+	0.00879046i
$254$	−10.6471			−0.668056
$255$	−0.276886	−	7.54325i	−0.0173392	−	0.472376i
$256$	16.9852			1.06157
$257$	3.14771	−	1.30383i	0.196349	−	0.0813304i	−0.282342	−	0.959314i	$-0.591111\pi$
$257$	3.14771	−	1.30383i	0.196349	−	0.0813304i	0.478691	+	0.877983i	$0.341111\pi$
$258$	9.86123	−	7.98234i	0.613933	−	0.496958i
$259$	7.05713	−	7.05713i	0.438509	−	0.438509i
$260$	0.472360	−	2.37471i	0.0292945	−	0.147273i
$261$	10.7798	−	25.0641i	0.667252	−	1.55143i
$262$	19.6207	−	3.90279i	1.21217	−	0.241115i
$263$	3.17122	−	7.65599i	0.195546	−	0.472089i	−0.795444	−	0.606027i	$-0.792762\pi$
$263$	3.17122	−	7.65599i	0.195546	−	0.472089i	0.990990	+	0.133938i	$0.0427624\pi$
$264$	−0.306817	−	0.0953338i	−0.0188833	−	0.00586739i
$265$	2.42411	+	12.1868i	0.148912	+	0.748630i
$266$	5.26572	+	3.51844i	0.322862	+	0.215730i
$267$	1.31264	−	12.4660i	0.0803325	−	0.762906i
$268$	10.2743	+	10.2743i	0.627604	+	0.627604i
$269$	20.9611	−	14.0057i	1.27802	−	0.853946i	0.283549	−	0.958958i	$-0.408488\pi$
$269$	20.9611	−	14.0057i	1.27802	−	0.853946i	0.994471	+	0.105012i	$0.0334882\pi$
$270$	3.40934	+	4.32985i	0.207486	+	0.263506i
$271$			2.72585i			0.165583i	0.996567	+	0.0827917i	$0.0263836\pi$
$271$			2.72585i			0.165583i	−0.996567	+	0.0827917i	$0.973616\pi$
$272$	−3.81894	−	1.83275i	−0.231557	−	0.111127i
$273$	−0.364789	−	3.97833i	−0.0220780	−	0.240780i
$274$	−4.64973	−	11.2254i	−0.280900	−	0.678153i
$275$	0.133231	+	0.199394i	0.00803414	+	0.0120239i
$276$	−6.50854	+	7.82262i	−0.391768	+	0.470866i
$277$	−0.392684	−	0.0781097i	−0.0235941	−	0.00469316i	0.183279	−	0.983061i	$-0.441329\pi$
$277$	−0.392684	−	0.0781097i	−0.0235941	−	0.00469316i	−0.206873	+	0.978368i	$0.566329\pi$
$278$	6.78683	−	10.1572i	0.407047	−	0.609189i
$279$	−26.5558	+	10.5829i	−1.58985	+	0.633580i
$280$	2.93287	+	1.21483i	0.175272	+	0.0726001i
$281$	9.51385	+	3.94077i	0.567549	+	0.235086i	0.647959	−	0.761675i	$-0.275623\pi$
$281$	9.51385	+	3.94077i	0.567549	+	0.235086i	−0.0804099	+	0.996762i	$0.525623\pi$
$282$	14.0166	−	4.14899i	0.834678	−	0.247069i
$283$	14.3678	−	21.5030i	0.854078	−	1.27822i	−0.104827	−	0.994491i	$-0.533429\pi$
$283$	14.3678	−	21.5030i	0.854078	−	1.27822i	0.958905	−	0.283728i	$-0.0915712\pi$
$284$	−2.73389	−	0.543804i	−0.162226	−	0.0322689i
$285$	−8.88223	−	7.39016i	−0.526138	−	0.437755i
$286$	0.0794150	+	0.118853i	0.00469591	+	0.00702792i
$287$	−1.88480	−	4.55031i	−0.111256	−	0.268597i
$288$	−14.6787	+	2.71472i	−0.864953	+	0.159967i
$289$	−10.6352	−	13.2624i	−0.625601	−	0.780143i
$290$		−	9.64573i		−	0.566417i
$291$	−6.83066	+	3.59211i	−0.400420	+	0.210573i
$292$	4.81465	−	3.21704i	0.281756	−	0.188263i
$293$	10.8222	+	10.8222i	0.632238	+	0.632238i	0.948629	−	0.316391i	$-0.102471\pi$
$293$	10.8222	+	10.8222i	0.632238	+	0.632238i	−0.316391	+	0.948629i	$0.602471\pi$
$294$	1.72842	+	0.181999i	0.100804	+	0.0106144i
$295$	0.00635626	+	0.00424712i	0.000370076	+	0.000247277i
$296$	5.84776	+	29.3987i	0.339894	+	1.70876i
$297$	0.318679	+	0.0379039i	0.0184916	+	0.00219941i
$298$	3.92311	−	9.47123i	0.227260	−	0.548654i
$299$	13.3827	−	2.66198i	0.773941	−	0.153946i
$300$	5.86911	+	3.18812i	0.338853	+	0.184066i
$301$	−1.42414	+	7.15964i	−0.0820861	+	0.412675i
$302$	0.0385662	−	0.0385662i	0.00221923	−	0.00221923i
$303$	−7.11196	−	8.78598i	−0.408572	−	0.504742i
$304$	−5.99060	+	2.48139i	−0.343584	+	0.142317i
$305$	4.33031			0.247953
$306$	11.9798	+	3.24558i	0.684838	+	0.185538i
$307$	28.1754			1.60806			0.804029	−	0.594591i	$-0.202686\pi$
$307$	28.1754			1.60806			0.804029	+	0.594591i	$0.202686\pi$
$308$	0.0566696	−	0.0234733i	0.00322905	−	0.00133752i
$309$	−5.01735	−	6.19834i	−0.285427	−	0.352611i
$310$	−7.14625	+	7.14625i	−0.405880	+	0.405880i
$311$	−4.65894	+	23.4221i	−0.264184	+	1.32814i	0.589675	+	0.807641i	$0.299256\pi$
$311$	−4.65894	+	23.4221i	−0.264184	+	1.32814i	−0.853859	+	0.520504i	$0.825744\pi$
$312$	10.5435	+	5.72726i	0.596907	+	0.324242i
$313$	−10.1773	+	2.02439i	−0.575255	+	0.114425i	−0.474140	−	0.880449i	$-0.657241\pi$
$313$	−10.1773	+	2.02439i	−0.575255	+	0.114425i	−0.101115	+	0.994875i	$0.532241\pi$
$314$	5.59009	−	13.4957i	0.315467	−	0.761604i
$315$	−3.10139	−	0.660463i	−0.174743	−	0.0372128i
$316$	−0.772917	−	3.88571i	−0.0434800	−	0.218589i
$317$	−10.2799	−	6.86881i	−0.577377	−	0.385791i	0.232320	−	0.972639i	$-0.425368\pi$
$317$	−10.2799	−	6.86881i	−0.577377	−	0.385791i	−0.809697	+	0.586848i	$0.800368\pi$
$318$	−20.3189	−	2.13954i	−1.13943	−	0.119979i
$319$	−0.397185	−	0.397185i	−0.0222381	−	0.0222381i
$320$	−6.19379	+	4.13856i	−0.346243	+	0.231352i
$321$	1.88646	−	0.992053i	0.105292	−	0.0553710i
$322$			5.93600i			0.330800i
$323$	−25.9837	−	1.42399i	−1.44577	−	0.0792327i
$324$	8.34709	−	3.19681i	0.463727	−	0.177600i
$325$	−3.42723	−	8.27406i	−0.190108	−	0.458962i
$326$	−12.7027	−	19.0110i	−0.703538	−	1.05292i
$327$	15.1455	+	12.6012i	0.837545	+	0.696851i
$328$	14.5081	+	2.88585i	0.801077	+	0.159344i
$329$	−4.67280	+	6.99334i	−0.257620	+	0.385555i
$330$	0.108791	−	0.0322027i	0.00598874	−	0.00177270i
$331$	−9.83788	−	4.07498i	−0.540739	−	0.223981i	0.0955604	−	0.995424i	$-0.469536\pi$
$331$	−9.83788	−	4.07498i	−0.540739	−	0.223981i	−0.636299	+	0.771442i	$0.719536\pi$
$332$	−0.105613	−	0.0437463i	−0.00579626	−	0.00240089i
$333$	−11.0841	−	27.8136i	−0.607408	−	1.52418i
$334$	6.55521	−	9.81057i	0.358685	−	0.536810i
$335$	−15.1668	−	3.01687i	−0.828651	−	0.164829i
$336$	−1.13812	+	1.36790i	−0.0620893	+	0.0746252i
$337$	−7.13381	−	10.6765i	−0.388603	−	0.581586i	0.584660	−	0.811278i	$-0.301228\pi$
$337$	−7.13381	−	10.6765i	−0.388603	−	0.581586i	−0.973263	+	0.229693i	$0.926228\pi$
$338$	2.94904	+	7.11961i	0.160407	+	0.387256i
$339$	−1.00065	−	10.9130i	−0.0543481	−	0.592712i
$340$	−4.28484	+	0.610827i	−0.232378	+	0.0331267i
$341$			0.588527i			0.0318705i
$342$	15.9379	−	10.3415i	0.861825	−	0.559206i
$343$	−0.831470	+	0.555570i	−0.0448951	+	0.0299980i
$344$	−15.5029	−	15.5029i	−0.835861	−	0.835861i
$345$	1.13413	−	10.7707i	0.0610595	−	0.579873i
$346$	0.873103	+	0.583389i	0.0469383	+	0.0313632i
$347$	−2.21301	−	11.1255i	−0.118800	−	0.597250i	−0.993618	−	0.112798i	$-0.964019\pi$
$347$	−2.21301	−	11.1255i	−0.118800	−	0.597250i	0.874817	−	0.484453i	$-0.160981\pi$
$348$	−14.9399	−	4.64209i	−0.800861	−	0.248842i
$349$	0.0561102	−	0.135462i	0.00300351	−	0.00725112i	−0.922371	−	0.386306i	$-0.873751\pi$
$349$	0.0561102	−	0.135462i	0.00300351	−	0.00725112i	0.925374	+	0.379055i	$0.123751\pi$
$350$	3.82122	−	0.760088i	0.204253	−	0.0406284i
$351$	−11.3963	−	3.71014i	−0.608292	−	0.198033i
$352$	−0.0599553	+	0.301416i	−0.00319563	+	0.0160655i
$353$	−2.18236	+	2.18236i	−0.116155	+	0.116155i	−0.762795	−	0.646640i	$-0.776174\pi$
$353$	−2.18236	+	2.18236i	−0.116155	+	0.116155i	0.646640	+	0.762795i	$0.276174\pi$
$354$	−0.00977021	+	0.00790866i	−0.000519281	+	0.000420340i
$355$	2.74078	−	1.13527i	0.145466	−	0.0602539i
$356$	−7.18743			−0.380933
$357$	−6.49313	+	2.97309i	−0.343653	+	0.157352i
$358$	1.50800			0.0797004
$359$	−5.01551	+	2.07749i	−0.264708	+	0.109646i	−0.511090	−	0.859527i	$-0.670758\pi$
$359$	−5.01551	+	2.07749i	−0.264708	+	0.109646i	0.246382	+	0.969173i	$0.420758\pi$
$360$	6.82427	−	6.64281i	0.359671	−	0.350107i
$361$	−14.7320	+	14.7320i	−0.775369	+	0.775369i
$362$	−0.337677	+	1.69762i	−0.0177479	+	0.0892247i
$363$	−9.09115	+	16.7362i	−0.477162	+	0.878421i
$364$	−2.24670	+	0.446897i	−0.117759	+	0.0234238i
$365$	−2.35836	+	5.69359i	−0.123442	+	0.298016i
$366$	−2.11276	+	6.79961i	−0.110436	+	0.355421i
$367$	−4.45693	−	22.4065i	−0.232650	−	1.16961i	−0.903689	−	0.428188i	$-0.859152\pi$
$367$	−4.45693	−	22.4065i	−0.232650	−	1.16961i	0.671040	−	0.741421i	$-0.265848\pi$
$368$	−5.05340	−	3.37658i	−0.263427	−	0.176016i
$369$	−14.7743	−	0.199071i	−0.769121	−	0.0103632i
$370$	−7.48474	−	7.48474i	−0.389113	−	0.389113i
$371$	9.77455	−	6.53115i	0.507469	−	0.339080i
$372$	7.62933	+	14.5077i	0.395562	+	0.752190i
$373$		−	25.1022i		−	1.29974i	−0.760045	−	0.649871i	$-0.774823\pi$
$373$		−	25.1022i		−	1.29974i	0.760045	−	0.649871i	$-0.225177\pi$
$374$	0.153374	−	0.204373i	0.00793078	−	0.0105679i
$375$	−16.1941	+	1.48490i	−0.836262	+	0.0766801i
$376$	−9.66694	−	23.3381i	−0.498534	−	1.20357i
$377$	11.6542	+	17.4418i	0.600224	+	0.898298i
$378$	2.55025	−	4.54767i	0.131171	−	0.233907i
$379$	22.7002	+	4.51535i	1.16603	+	0.231938i	0.739896	−	0.672721i	$-0.234875\pi$
$379$	22.7002	+	4.51535i	1.16603	+	0.231938i	0.426136	+	0.904659i	$0.359875\pi$
$380$	−3.68083	+	5.50875i	−0.188823	+	0.282593i
$381$	−5.21637	−	17.6226i	−0.267242	−	0.902831i
$382$	13.9742	+	5.78831i	0.714983	+	0.296156i
$383$	22.1614	+	9.17955i	1.13239	+	0.469053i	0.868594	−	0.495525i	$-0.165024\pi$
$383$	22.1614	+	9.17955i	1.13239	+	0.469053i	0.263800	+	0.964577i	$0.415024\pi$
$384$	1.41585	+	4.78318i	0.0722520	+	0.244091i
$385$	−0.0362682	+	0.0542792i	−0.00184840	+	0.00276633i
$386$	−4.42787	−	0.880759i	−0.225373	−	0.0448294i
$387$	18.0434	+	12.4110i	0.917196	+	0.630889i
$388$	2.45851	+	3.67943i	0.124812	+	0.186795i
$389$	3.04838	+	7.35945i	0.154559	+	0.373139i	0.982125	−	0.188230i	$-0.0602750\pi$
$389$	3.04838	+	7.35945i	0.154559	+	0.373139i	−0.827566	+	0.561369i	$0.810275\pi$
$390$	−4.21939	+	0.386892i	−0.213657	+	0.0195911i
$391$	−12.4210	−	20.9918i	−0.628158	−	1.06160i
$392$		−	3.00339i		−	0.151694i
$393$	16.0726	+	30.5631i	0.810754	+	1.54171i
$394$	6.06456	−	4.05221i	0.305528	−	0.204147i
$395$	2.98150	+	2.98150i	0.150015	+	0.150015i
$396$	0.00247922	−	0.183999i	0.000124586	−	0.00924632i
$397$	−6.70485	−	4.48004i	−0.336507	−	0.224847i	0.375823	−	0.926691i	$-0.377360\pi$
$397$	−6.70485	−	4.48004i	−0.336507	−	0.224847i	−0.712330	+	0.701845i	$0.752360\pi$
$398$	−1.96121	−	9.85966i	−0.0983065	−	0.494220i
$399$	−3.24371	+	10.4394i	−0.162389	+	0.522623i
$400$	−1.52655	+	3.68542i	−0.0763276	+	0.184271i
$401$	20.5490	−	4.08746i	1.02617	−	0.204118i	0.346820	−	0.937932i	$-0.387262\pi$
$401$	20.5490	−	4.08746i	1.02617	−	0.204118i	0.679350	+	0.733814i	$0.262262\pi$
$402$	12.1371	−	22.3435i	0.605343	−	1.11439i
$403$	4.28784	−	21.5564i	0.213593	−	1.07380i
$404$	−4.58308	+	4.58308i	−0.228017	+	0.228017i
$405$	−5.49622	+	7.76433i	−0.273109	+	0.385813i
$406$	−8.43111	+	3.49228i	−0.418429	+	0.173319i
$407$	−0.616403			−0.0305540
$408$	3.40992	−	21.1757i	0.168816	−	1.04835i
$409$	−34.3808			−1.70002			−0.850012	−	0.526764i	$-0.823405\pi$
$409$	−34.3808			−1.70002			−0.850012	+	0.526764i	$0.823405\pi$
$410$	−4.82603	+	1.99901i	−0.238341	+	0.0987240i
$411$	16.3018	−	13.1957i	0.804108	−	0.650898i
$412$	−3.23328	+	3.23328i	−0.159292	+	0.159292i
$413$	0.00141100	−	0.00709355i	6.94306e−5	−	0.000349051i
$414$	16.3591	+	7.03587i	0.804008	+	0.345794i
$415$	0.119324	−	0.0237351i	0.00585739	−	0.00116511i
$416$	4.39207	−	10.6034i	0.215339	−	0.519874i
$417$	20.1369	+	6.25690i	0.986107	+	0.306401i
$418$	−0.0763078	−	0.383625i	−0.00373234	−	0.0187637i
$419$	13.6149	+	9.09718i	0.665131	+	0.444426i	0.841760	−	0.539851i	$-0.181520\pi$
$419$	13.6149	+	9.09718i	0.665131	+	0.444426i	−0.176630	+	0.984277i	$0.556520\pi$
$420$	−0.190399	+	1.80819i	−0.00929053	+	0.0882308i
$421$	13.2832	+	13.2832i	0.647383	+	0.647383i	0.952360	−	0.304977i	$-0.0986487\pi$
$421$	13.2832	+	13.2832i	0.647383	+	0.647383i	−0.304977	+	0.952360i	$0.598649\pi$
$422$	−13.9410	+	9.31508i	−0.678637	+	0.453451i
$423$	13.7345	+	21.1670i	0.667793	+	1.02917i
$424$			35.3071i			1.71466i
$425$	−11.9227	+	10.6838i	−0.578336	+	0.518240i
$426$	0.445410	+	4.85758i	0.0215802	+	0.235350i
$427$	−1.56781	−	3.78503i	−0.0758716	−	0.183170i
$428$	−0.678982	−	1.01617i	−0.0328198	−	0.0491183i
$429$	−0.157812	+	0.189674i	−0.00761924	+	0.00915756i
$430$	7.59346	+	1.51043i	0.366189	+	0.0728396i
$431$	2.71105	−	4.05737i	0.130587	−	0.195437i	−0.760414	−	0.649439i	$-0.775004\pi$
$431$	2.71105	−	4.05737i	0.130587	−	0.195437i	0.891001	+	0.454002i	$0.150004\pi$
$432$	2.42083	+	4.75791i	0.116472	+	0.228915i
$433$	9.66507	+	4.00340i	0.464474	+	0.192391i	0.602633	−	0.798019i	$-0.294118\pi$
$433$	9.66507	+	4.00340i	0.464474	+	0.192391i	−0.138159	+	0.990410i	$0.544118\pi$
$434$	8.83371	+	3.65904i	0.424032	+	0.175640i
$435$	15.9652	−	4.72578i	0.765472	−	0.226584i
$436$	6.27633	−	9.39319i	0.300582	−	0.449852i
$437$	−36.6195	−	7.28408i	−1.75175	−	0.348445i
$438$	−7.78963	−	6.48109i	−0.372203	−	0.309678i
$439$	8.07330	+	12.0826i	0.385318	+	0.576669i	0.972534	−	0.232761i	$-0.0747761\pi$
$439$	8.07330	+	12.0826i	0.385318	+	0.576669i	−0.587216	+	0.809430i	$0.699776\pi$
$440$	−0.0750305	−	0.181140i	−0.00357694	−	0.00863550i
$441$	0.545576	+	2.94997i	0.0259798	+	0.140475i
$442$	−7.10676	+	6.36829i	−0.338034	+	0.302908i
$443$			28.7795i			1.36735i	0.729784	+	0.683677i	$0.239620\pi$
$443$			28.7795i			1.36735i	−0.729784	+	0.683677i	$0.760380\pi$
$444$	−15.1949	+	7.99070i	−0.721118	+	0.379222i
$445$	6.36022	−	4.24977i	0.301504	−	0.201458i
$446$	4.96119	+	4.96119i	0.234919	+	0.234919i
$447$	17.5984	+	1.85308i	0.832377	+	0.0876477i
$448$	5.85991	+	3.91546i	0.276855	+	0.184988i
$449$	−0.514253	−	2.58533i	−0.0242691	−	0.122009i	0.966752	−	0.255717i	$-0.0823116\pi$
$449$	−0.514253	−	2.58533i	−0.0242691	−	0.122009i	−0.991021	+	0.133708i	$0.957312\pi$
$450$	2.43451	−	11.4319i	0.114764	−	0.538905i
$451$	−0.116409	+	0.281037i	−0.00548150	+	0.0132335i
$452$	−6.16294	+	1.22589i	−0.289880	+	0.0576608i
$453$	0.0827279	+	0.0449381i	0.00388690	+	0.00211138i
$454$	−5.19609	+	26.1225i	−0.243864	+	1.22599i
$455$	1.72389	−	1.72389i	0.0808171	−	0.0808171i
$456$	−20.6571	−	25.5194i	−0.967356	−	1.19505i
$457$	−21.2922	+	8.81953i	−0.996009	+	0.412560i	−0.820332	−	0.571888i	$-0.806211\pi$
$457$	−21.2922	+	8.81953i	−0.996009	+	0.412560i	−0.175677	+	0.984448i	$0.556211\pi$
$458$	6.88673			0.321796
$459$	0.497356	+	21.4185i	0.0232146	+	0.999731i
$460$	−6.20997			−0.289541
$461$	0.680280	−	0.281781i	0.0316838	−	0.0131239i	−0.366785	−	0.930306i	$-0.619542\pi$
$461$	0.680280	−	0.281781i	0.0316838	−	0.0131239i	0.398469	+	0.917182i	$0.369542\pi$
$462$	−0.0675359	−	0.0834326i	−0.00314205	−	0.00388163i
$463$	−18.5887	+	18.5887i	−0.863889	+	0.863889i	−0.991787	−	0.127898i	$-0.959177\pi$
$463$	−18.5887	+	18.5887i	−0.863889	+	0.863889i	0.127898	+	0.991787i	$0.459177\pi$
$464$	1.82284	−	9.16404i	0.0846233	−	0.425430i
$465$	−15.3294	−	8.32697i	−0.710882	−	0.386154i
$466$	5.80215	−	1.15412i	0.268779	−	0.0534635i
$467$	−6.25177	+	15.0931i	−0.289298	+	0.698426i	−0.999987	−	0.00507967i	$-0.998383\pi$
$467$	−6.25177	+	15.0931i	−0.289298	+	0.698426i	0.710690	+	0.703506i	$0.248383\pi$
$468$	−1.43138	+	6.72143i	−0.0661654	+	0.310698i
$469$	2.85424	+	14.3492i	0.131797	+	0.662586i
$470$	7.41709	+	4.95594i	0.342125	+	0.228600i
$471$	25.0762	+	2.64047i	1.15545	+	0.121667i
$472$	0.0153598	+	0.0153598i	0.000706993	+	0.000706993i
$473$	0.374874	−	0.250483i	0.0172367	−	0.0115172i
$474$	−6.13633	+	3.22698i	−0.281851	+	0.148220i
$475$			24.5060i			1.12441i
$476$	2.08526	+	3.52413i	0.0955775	+	0.161528i
$477$	−6.41366	−	34.6792i	−0.293661	−	1.58785i
$478$	−8.78508	−	21.2091i	−0.401820	−	0.970080i
$479$	−10.8606	−	16.2541i	−0.496236	−	0.742669i	0.495826	−	0.868422i	$-0.334865\pi$
$479$	−10.8606	−	16.2541i	−0.496236	−	0.742669i	−0.992062	+	0.125753i	$0.959865\pi$
$480$	−7.00268	−	5.82634i	−0.319627	−	0.265935i
$481$	22.5775	+	4.49094i	1.02944	+	0.204769i
$482$	−3.84972	+	5.76152i	−0.175350	+	0.262430i
$483$	−9.82501	+	2.90825i	−0.447053	+	0.132330i
$484$	10.0895	+	4.17922i	0.458614	+	0.189964i
$485$	−4.35113	−	1.80230i	−0.197575	−	0.0818380i
$486$	−9.51022	−	12.4186i	−0.431392	−	0.563318i
$487$	−21.1633	+	31.6732i	−0.959003	+	1.43525i	−0.0595527	+	0.998225i	$0.518967\pi$
$487$	−21.1633	+	31.6732i	−0.959003	+	1.43525i	−0.899450	+	0.437024i	$0.856033\pi$
$488$	12.0681	+	2.40049i	0.546297	+	0.108665i
$489$	25.2426	−	30.3391i	1.14151	−	1.37198i
$490$	0.589234	+	0.881851i	0.0266189	+	0.0398380i
$491$	−8.52469	−	20.5804i	−0.384714	−	0.928781i	−0.991040	−	0.133565i	$-0.957357\pi$
$491$	−8.52469	−	20.5804i	−0.384714	−	0.928781i	0.606326	−	0.795216i	$-0.292643\pi$
$492$	0.773609	+	8.43688i	0.0348770	+	0.380364i
$493$	22.5078	−	29.9919i	1.01370	−	1.35077i
$494$			14.6073i			0.657214i
$495$	0.106601	+	0.164289i	0.00479135	+	0.00738423i
$496$	−8.13987	+	5.43889i	−0.365491	+	0.244213i
$497$	−1.98463	−	1.98463i	−0.0890227	−	0.0890227i
$498$	−0.0209488	+	0.198947i	−0.000938737	+	0.00891505i
$499$	−14.3186	−	9.56738i	−0.640989	−	0.428295i	0.192145	−	0.981367i	$-0.438456\pi$
$499$	−14.3186	−	9.56738i	−0.640989	−	0.428295i	−0.833134	+	0.553072i	$0.813456\pi$
$500$	1.81913	+	9.14539i	0.0813541	+	0.408994i
$501$	19.4496	+	6.04336i	0.868946	+	0.269998i
$502$	3.88577	−	9.38107i	0.173430	−	0.418698i
$503$	1.51897	−	0.302143i	0.0677277	−	0.0134719i	−0.161110	−	0.986936i	$-0.551507\pi$
$503$	1.51897	−	0.302143i	0.0677277	−	0.0134719i	0.228838	+	0.973465i	$0.426507\pi$
$504$	−8.27709	−	3.55988i	−0.368691	−	0.158570i
$505$	1.34574	−	6.76549i	0.0598846	−	0.301060i
$506$	0.259239	−	0.259239i	0.0115246	−	0.0115246i
$507$	−10.3392	+	8.36926i	−0.459181	+	0.371692i
$508$	−9.73588	+	4.03273i	−0.431960	+	0.178924i
$509$	23.3269			1.03395			0.516973	−	0.856002i	$-0.327059\pi$
$509$	23.3269			1.03395			0.516973	+	0.856002i	$0.327059\pi$
$510$	3.15324	+	6.88657i	0.139628	+	0.304943i
$511$	5.83049			0.257926
$512$	−10.4244	+	4.31791i	−0.460696	+	0.190827i
$513$	24.9254	+	21.3131i	1.10048	+	0.940996i
$514$	−2.41740	+	2.41740i	−0.106627	+	0.106627i
$515$	0.949393	−	4.77292i	0.0418353	−	0.210320i
$516$	5.99386	−	11.0343i	0.263865	−	0.485757i
$517$	0.509488	−	0.101343i	0.0224072	−	0.00445708i
$518$	−3.83236	+	9.25213i	−0.168384	+	0.406515i
$519$	−0.537836	+	1.73094i	−0.0236084	+	0.0759800i
$520$	1.42847	+	7.18140i	0.0626425	+	0.314925i
$521$	20.6170	+	13.7759i	0.903249	+	0.603531i	0.918096	−	0.396358i	$-0.129726\pi$
$521$	20.6170	+	13.7759i	0.903249	+	0.603531i	−0.0148473	+	0.999890i	$0.504726\pi$
$522$	−0.368851	+	27.3748i	−0.0161442	+	1.19816i
$523$	18.9799	+	18.9799i	0.829934	+	0.829934i	0.987507	−	0.157573i	$-0.0503670\pi$
$523$	18.9799	+	18.9799i	0.829934	+	0.829934i	−0.157573	+	0.987507i	$0.550367\pi$
$524$	16.4633	−	11.0004i	0.719201	−	0.480555i
$525$	3.13021	+	5.95232i	0.136614	+	0.259781i
$526$			8.31514i			0.362557i
$527$	−38.8956	+	5.54478i	−1.69432	+	0.241534i
$528$	0.109444	−	0.0100353i	0.00476293	−	0.000436731i
$529$	−4.59077	−	11.0831i	−0.199599	−	0.481874i
$530$	−6.92689	−	10.3668i	−0.300885	−	0.450306i
$531$	−0.0178768	−	0.0122965i	−0.000775788	−	0.000533622i
$532$	6.14773	+	1.22286i	0.266538	+	0.0530177i
$533$	6.31137	−	9.44563i	0.273376	−	0.409136i
$534$	3.56997	+	12.0605i	0.154488	+	0.521910i
$535$	1.20168	+	0.497750i	0.0519529	+	0.0215196i
$536$	−40.5958	−	16.8153i	−1.75347	−	0.726312i
$537$	0.738823	+	2.49598i	0.0318825	+	0.107709i
$538$	−14.0537	+	21.0328i	−0.605897	+	0.906788i
$539$	0.0605753	+	0.0120492i	0.00260916	+	0.000518995i
$540$	4.75756	+	2.66795i	0.204733	+	0.114810i
$541$	2.16512	+	3.24033i	0.0930858	+	0.139313i	0.875090	−	0.483961i	$-0.160802\pi$
$541$	2.16512	+	3.24033i	0.0930858	+	0.139313i	−0.782004	+	0.623274i	$0.785802\pi$
$542$	−1.04670	−	2.52697i	−0.0449598	−	0.108543i
$543$	−2.97526	+	0.272813i	−0.127681	+	0.0117075i
$544$	−20.4854	−	1.12266i	−0.878303	−	0.0481336i
$545$			12.0232i			0.515017i
$546$	1.86582	+	3.54800i	0.0798499	+	0.151840i
$547$	−10.8073	+	7.22119i	−0.462085	+	0.308756i	−0.764733	−	0.644347i	$-0.777129\pi$
$547$	−10.8073	+	7.22119i	−0.462085	+	0.308756i	0.302648	+	0.953102i	$0.402129\pi$
$548$	−8.50359	−	8.50359i	−0.363255	−	0.363255i
$549$	−12.2895	−	0.165590i	−0.524505	−	0.00706722i
$550$	−0.200077	−	0.133687i	−0.00853129	−	0.00570043i
$551$	−11.1983	−	56.2974i	−0.477062	−	2.39835i
$552$	9.13137	−	29.3879i	0.388657	−	1.25083i
$553$	1.52659	−	3.68552i	0.0649174	−	0.156724i
$554$	0.394028	−	0.0783770i	0.0167406	−	0.00332992i
$555$	8.72138	−	16.0555i	0.370202	−	0.681516i
$556$	2.35881	−	11.8586i	0.100036	−	0.502915i
$557$	−6.06590	+	6.06590i	−0.257020	+	0.257020i	−0.823841	−	0.566821i	$-0.808173\pi$
$557$	−6.06590	+	6.06590i	−0.257020	+	0.257020i	0.566821	+	0.823841i	$0.308173\pi$
$558$	20.5545	−	20.0080i	0.870142	−	0.847005i
$559$	−15.5558	+	6.44340i	−0.657938	+	0.272527i
$560$	−1.08591			−0.0458879
$561$	0.413412	+	0.153729i	0.0174543	+	0.00649043i
$562$	−10.3330			−0.435869
$563$	2.77548	−	1.14964i	0.116972	−	0.0484515i	−0.323430	−	0.946252i	$-0.604836\pi$
$563$	2.77548	−	1.14964i	0.116972	−	0.0484515i	0.440402	+	0.897801i	$0.354836\pi$
$564$	11.2456	−	9.10292i	0.473524	−	0.383302i
$565$	4.72881	−	4.72881i	0.198942	−	0.198942i
$566$	−5.06257	+	25.4512i	−0.212796	+	1.06980i
$567$	8.77656	+	1.99301i	0.368581	+	0.0836984i
$568$	8.26759	−	1.64453i	0.346901	−	0.0690028i
$569$	7.20685	−	17.3989i	0.302127	−	0.729398i	−0.697788	−	0.716305i	$-0.745832\pi$
$569$	7.20685	−	17.3989i	0.302127	−	0.729398i	0.999914	−	0.0130936i	$-0.00416795\pi$
$570$	11.0720	+	3.44026i	0.463753	+	0.144097i
$571$	5.86878	+	29.5043i	0.245601	+	1.23472i	0.884908	+	0.465766i	$0.154221\pi$
$571$	5.86878	+	29.5043i	0.245601	+	1.23472i	−0.639307	+	0.768951i	$0.720779\pi$
$572$	0.117636	+	0.0786018i	0.00491860	+	0.00328650i
$573$	−2.73411	+	25.9654i	−0.114219	+	1.08472i
$574$	3.49458	+	3.49458i	0.145861	+	0.145861i
$575$	−19.0986	+	12.7613i	−0.796468	+	0.532183i
$576$	17.7364	−	11.5085i	0.739016	−	0.479520i
$577$		−	32.4547i		−	1.35111i	−0.737311	−	0.675553i	$-0.763905\pi$
$577$		−	32.4547i		−	1.35111i	0.737311	−	0.675553i	$-0.236095\pi$
$578$	14.9520	+	8.21096i	0.621919	+	0.341531i
$579$	−0.711575	−	7.76033i	−0.0295720	−	0.322508i
$580$	−3.65346	−	8.82024i	−0.151702	−	0.366240i
$581$	−0.0639481	−	0.0957051i	−0.00265302	−	0.00397052i
$582$	4.95295	−	5.95295i	0.205306	−	0.246758i
$583$	−0.712108	−	0.141647i	−0.0294925	−	0.00586643i
$584$	−9.72871	+	14.5600i	−0.402577	+	0.602499i
$585$	−2.70759	−	6.79420i	−0.111945	−	0.280906i
$586$	−14.1882	−	5.87696i	−0.586110	−	0.242775i
$587$	−14.0176	−	5.80627i	−0.578567	−	0.239650i	0.0741563	−	0.997247i	$-0.476374\pi$
$587$	−14.0176	−	5.80627i	−0.578567	−	0.239650i	−0.652723	+	0.757596i	$0.726374\pi$
$588$	1.64944	−	0.488241i	0.0680216	−	0.0201347i
$589$	−33.4127	+	50.0057i	−1.37675	+	2.06045i
$590$	−0.00752338	−	0.00149649i	−0.000309732	−	6.16096e-5i
$591$	9.67827	+	8.05247i	0.398111	+	0.331235i
$592$	−5.69651	−	8.52543i	−0.234125	−	0.350393i
$593$	−4.33096	−	10.4559i	−0.177851	−	0.429371i	0.809664	−	0.586893i	$-0.199649\pi$
$593$	−4.33096	−	10.4559i	−0.177851	−	0.429371i	−0.987515	+	0.157523i	$0.949649\pi$
$594$	−0.309983	+	0.0872318i	−0.0127188	+	0.00357917i
$595$	−3.92900	−	1.88557i	−0.161073	−	0.0773008i
$596$		−	10.1466i		−	0.415621i
$597$	15.3584	−	8.07669i	0.628578	−	0.330557i
$598$	−11.3841	+	7.60662i	−0.465531	+	0.311058i
$599$	13.6615	+	13.6615i	0.558196	+	0.558196i	0.928793	−	0.370598i	$-0.120847\pi$
$599$	13.6615	+	13.6615i	0.558196	+	0.558196i	−0.370598	+	0.928793i	$0.620847\pi$
$600$	−20.0873	−	2.11516i	−0.820062	−	0.0863509i
$601$	23.0963	+	15.4325i	0.942119	+	0.629504i	0.928869	−	0.370409i	$-0.120782\pi$
$601$	23.0963	+	15.4325i	0.942119	+	0.629504i	0.0132498	+	0.999912i	$0.495782\pi$
$602$	−1.42901	−	7.18413i	−0.0582422	−	0.292803i
$603$	42.9284	+	9.14192i	1.74818	+	0.372288i
$604$	0.0206581	−	0.0498731i	0.000840567	−	0.00202931i
$605$	−11.3994	+	2.26748i	−0.463451	+	0.0921862i
$606$	9.96683	+	5.41402i	0.404875	+	0.219930i
$607$	−4.70360	+	23.6466i	−0.190913	+	0.959786i	0.759904	+	0.650035i	$0.225246\pi$
$607$	−4.70360	+	23.6466i	−0.190913	+	0.959786i	−0.950818	+	0.309751i	$0.899754\pi$
$608$	−22.2067	+	22.2067i	−0.900600	+	0.900600i
$609$	−9.91097	−	12.2438i	−0.401613	−	0.496145i
$610$	−4.01437	+	1.66281i	−0.162537	+	0.0673251i
$611$	−19.3998			−0.784831
$612$	12.1838	−	1.56969i	0.492502	−	0.0634510i
$613$	17.5973			0.710749			0.355375	−	0.934724i	$-0.384353\pi$
$613$	17.5973			0.710749			0.355375	+	0.934724i	$0.384353\pi$
$614$	−26.1198	+	10.8192i	−1.05411	+	0.436626i
$615$	−5.67311	−	7.00846i	−0.228762	−	0.282608i
$616$	−0.131165	+	0.131165i	−0.00528479	+	0.00528479i
$617$	−1.87825	+	9.44262i	−0.0756157	+	0.380146i	−0.999999	−	0.00131888i	$-0.999580\pi$
$617$	−1.87825	+	9.44262i	−0.0756157	+	0.380146i	0.924383	+	0.381465i	$0.124580\pi$
$618$	7.03140	+	3.81949i	0.282845	+	0.153642i
$619$	8.52310	−	1.69535i	0.342572	−	0.0681418i	−0.0208061	−	0.999784i	$-0.506623\pi$
$619$	8.52310	−	1.69535i	0.342572	−	0.0681418i	0.363378	+	0.931642i	$0.381623\pi$
$620$	−3.82792	+	9.24142i	−0.153733	+	0.371144i
$621$	−3.63056	+	30.5241i	−0.145689	+	1.22489i
$622$	−4.67488	−	23.5022i	−0.187446	−	0.942353i
$623$	−6.01737	−	4.02068i	−0.241081	−	0.161085i
$624$	−4.08180	−	0.429805i	−0.163403	−	0.0172060i
$625$	6.71053	+	6.71053i	0.268421	+	0.268421i
$626$	8.65742	−	5.78470i	0.346020	−	0.231203i
$627$	0.597574	−	0.314252i	0.0238648	−	0.0125500i
$628$		−	14.4580i		−	0.576938i
$629$	−5.80741	−	40.7379i	−0.231557	−	1.62433i
$630$	3.12872	−	0.578634i	0.124651	−	0.0230533i
$631$	−1.22661	−	2.96130i	−0.0488305	−	0.117887i	0.897582	−	0.440847i	$-0.145322\pi$
$631$	−1.22661	−	2.96130i	−0.0488305	−	0.117887i	−0.946413	+	0.322960i	$0.895322\pi$
$632$	6.65632	+	9.96188i	0.264774	+	0.396262i
$633$	−22.2481	−	18.5108i	−0.884282	−	0.735736i
$634$	12.1675	+	2.42026i	0.483232	+	0.0961207i
$635$	6.23091	−	9.32521i	0.247266	−	0.370060i
$636$	−19.3904	+	5.73964i	−0.768878	+	0.227592i
$637$	−2.13095	−	0.882670i	−0.0844314	−	0.0349726i
$638$	0.520723	+	0.215690i	0.0206156	+	0.00853927i
$639$	−7.82183	+	3.11712i	−0.309427	+	0.123311i
$640$	−1.69122	+	2.53108i	−0.0668512	+	0.100050i
$641$	−14.6787	−	2.91977i	−0.579773	−	0.115324i	−0.103512	−	0.994628i	$-0.533008\pi$
$641$	−14.6787	−	2.91977i	−0.579773	−	0.115324i	−0.476261	+	0.879304i	$0.658008\pi$
$642$	−1.36788	+	1.64406i	−0.0539861	+	0.0648859i
$643$	−14.4060	−	21.5600i	−0.568116	−	0.850245i	0.430514	−	0.902584i	$-0.358332\pi$
$643$	−14.4060	−	21.5600i	−0.568116	−	0.850245i	−0.998629	+	0.0523390i	$0.983332\pi$
$644$	2.24835	+	5.42799i	0.0885973	+	0.213893i
$645$	1.22030	+	13.3084i	0.0480491	+	0.524017i
$646$	24.6348	−	8.65747i	0.969242	−	0.340624i
$647$		−	25.4642i		−	1.00110i	−0.865707	−	0.500551i	$-0.833131\pi$
$647$		−	25.4642i		−	1.00110i	0.865707	−	0.500551i	$-0.166869\pi$
$648$	−19.6215	+	18.5915i	−0.770804	+	0.730344i
$649$	−0.000371414	0	0.000248171i	−1.45793e−5	0	9.74155e-6i
$650$	6.35436	+	6.35436i	0.249239	+	0.249239i
$651$	−1.72835	+	16.4139i	−0.0677393	+	0.643310i
$652$	−18.8163	−	12.5726i	−0.736902	−	0.492382i
$653$	4.24335	+	21.3328i	0.166055	+	0.834816i	0.970558	+	0.240867i	$0.0774319\pi$
$653$	4.24335	+	21.3328i	0.166055	+	0.834816i	−0.804503	+	0.593949i	$0.797568\pi$
$654$	−18.8792	−	5.86612i	−0.738236	−	0.229384i
$655$	−8.06421	+	19.4687i	−0.315095	+	0.760706i
$656$	−4.96280	+	0.987162i	−0.193765	+	0.0385422i
$657$	6.91081	−	16.0684i	0.269616	−	0.626886i
$658$	1.64648	−	8.27743i	0.0641866	−	0.322688i
$659$	−19.2147	+	19.2147i	−0.748497	+	0.748497i	−0.974197	−	0.225700i	$-0.927533\pi$
$659$	−19.2147	+	19.2147i	−0.748497	+	0.748497i	0.225700	+	0.974197i	$0.427533\pi$
$660$	0.0872832	−	0.0706529i	0.00339750	−	0.00275016i
$661$	13.5763	−	5.62347i	0.528056	−	0.218728i	−0.102696	−	0.994713i	$-0.532747\pi$
$661$	13.5763	−	5.62347i	0.528056	−	0.218728i	0.630751	+	0.775985i	$0.282747\pi$
$662$	10.6849			0.415280
$663$	−14.0224	−	8.64275i	−0.544583	−	0.335657i
$664$	0.345700			0.0134158
$665$	−6.16324	+	2.55290i	−0.239000	+	0.0989971i
$666$	20.9557	+	21.5281i	0.812016	+	0.834197i
$667$	38.0436	−	38.0436i	1.47306	−	1.47306i
$668$	2.27831	−	11.4538i	0.0881505	−	0.443163i
$669$	−5.78088	+	10.6422i	−0.223502	+	0.411451i
$670$	15.2187	−	3.02719i	0.587950	−	0.116950i
$671$	−0.0968311	+	0.233771i	−0.00373812	+	0.00902463i
$672$	−2.55732	+	8.23034i	−0.0986507	+	0.317492i
$673$	−3.49292	−	17.5601i	−0.134642	−	0.676893i	−0.987861	−	0.155340i	$-0.950353\pi$
$673$	−3.49292	−	17.5601i	−0.134642	−	0.676893i	0.853219	−	0.521553i	$-0.174647\pi$
$674$	10.7130	+	7.15821i	0.412650	+	0.275724i
$675$	20.1143	−	1.57140i	0.774201	−	0.0604831i
$676$	5.39331	+	5.39331i	0.207435	+	0.207435i
$677$	18.4401	−	12.3213i	0.708712	−	0.473546i	−0.148234	−	0.988952i	$-0.547359\pi$
$677$	18.4401	−	12.3213i	0.708712	−	0.473546i	0.856946	+	0.515406i	$0.172359\pi$
$678$	5.11815	+	9.73254i	0.196562	+	0.373776i
$679$			4.45575i			0.170996i
$680$	11.2646	−	6.66535i	0.431977	−	0.255605i
$681$	−45.7826	+	4.19798i	−1.75439	+	0.160867i
$682$	−0.225990	−	0.545588i	−0.00865360	−	0.0208916i
$683$	22.3514	+	33.4512i	0.855252	+	1.27998i	0.958434	+	0.285313i	$0.0920975\pi$
$683$	22.3514	+	33.4512i	0.855252	+	1.27998i	−0.103182	+	0.994662i	$0.532903\pi$
$684$	10.6569	−	15.4932i	0.407478	−	0.592398i
$685$	12.5529	+	2.49693i	0.479622	+	0.0954027i
$686$	0.557471	−	0.834314i	0.0212843	−	0.0318543i
$687$	3.37405	+	11.3986i	0.128728	+	0.434884i
$688$	6.92882	+	2.87001i	0.264159	+	0.109418i
$689$	25.0510	+	10.3764i	0.954366	+	0.395311i
$690$	3.08447	+	10.4203i	0.117424	+	0.396696i
$691$	18.4920	−	27.6752i	0.703469	−	1.05282i	−0.291877	−	0.956456i	$-0.594280\pi$
$691$	18.4920	−	27.6752i	0.703469	−	1.05282i	0.995347	−	0.0963603i	$-0.0307201\pi$
$692$	1.01935	+	0.202761i	0.0387498	+	0.00770782i
$693$	0.105006	−	0.152659i	0.00398884	−	0.00579903i
$694$	6.32367	+	9.46405i	0.240043	+	0.359250i
$695$	4.92436	+	11.8885i	0.186792	+	0.450955i
$696$	47.1129	−	4.31996i	1.78581	−	0.163748i
$697$	−19.6704	−	5.04568i	−0.745069	−	0.191119i
$698$			0.147125i			0.00556875i
$699$	4.75292	+	9.03802i	0.179772	+	0.341849i
$700$	3.20630	−	2.14238i	0.121187	−	0.0809744i
$701$	5.20240	+	5.20240i	0.196492	+	0.196492i	0.798494	−	0.602002i	$-0.205630\pi$
$701$	5.20240	+	5.20240i	0.196492	+	0.196492i	−0.602002	+	0.798494i	$0.705630\pi$
$702$	11.9895	−	0.936661i	0.452516	−	0.0353520i
$703$	−52.3742	−	34.9953i	−1.97533	−	1.31987i
$704$	−0.0849184	−	0.426914i	−0.00320048	−	0.0160899i
$705$	−4.56897	+	14.7045i	−0.172077	+	0.553804i
$706$	1.18513	−	2.86115i	0.0446028	−	0.107681i
$707$	−6.40079	+	1.27320i	−0.240727	+	0.0478835i
$708$	−0.00593854	+	0.0109324i	−0.000223184	+	0.000410866i
$709$	−6.45001	+	32.4264i	−0.242235	+	1.21780i	0.647766	+	0.761840i	$0.275704\pi$
$709$	−6.45001	+	32.4264i	−0.242235	+	1.21780i	−0.890001	+	0.455959i	$0.849296\pi$
$710$	−2.10488	+	2.10488i	−0.0789948	+	0.0789948i
$711$	−8.34755	−	8.57558i	−0.313058	−	0.321609i
$712$	20.0811	−	8.31785i	0.752570	−	0.311725i
$713$	−56.3709			−2.11111
$714$	4.87775	−	5.24949i	0.182545	−	0.196457i
$715$	−0.150573			−0.00563109
$716$	1.37895	−	0.571178i	0.0515336	−	0.0213459i
$717$	30.8002	−	24.9317i	1.15025	−	0.931093i
$718$	3.85184	−	3.85184i	0.143749	−	0.143749i
$719$	1.32024	−	6.63729i	0.0492366	−	0.247529i	−0.948327	−	0.317295i	$-0.897225\pi$
$719$	1.32024	−	6.63729i	0.0492366	−	0.247529i	0.997563	+	0.0697662i	$0.0222253\pi$
$720$	−1.28711	+	2.99267i	−0.0479678	+	0.111530i
$721$	−4.51563	+	0.898216i	−0.168171	+	0.0334513i
$722$	8.00019	−	19.3142i	0.297736	−	0.718799i
$723$	−11.4223	−	3.54912i	−0.424801	−	0.131993i
$724$	0.334219	+	1.68023i	0.0124211	+	0.0624453i
$725$	−29.3615	−	19.6187i	−1.09046	−	0.728620i
$726$	2.00130	−	19.0060i	0.0742751	−	0.705380i
$727$	5.20419	+	5.20419i	0.193013	+	0.193013i	0.796997	−	0.603984i	$-0.206421\pi$
$727$	5.20419	+	5.20419i	0.193013	+	0.193013i	−0.603984	+	0.796997i	$0.706421\pi$
$728$	5.75992	−	3.84865i	0.213477	−	0.142641i
$729$	15.8953	−	21.8252i	0.588715	−	0.808341i
$730$		−	6.18378i		−	0.228872i
$731$	20.0862	+	22.4154i	0.742915	+	0.829064i
$732$	0.643501	+	7.01793i	0.0237845	+	0.259390i
$733$	5.07150	+	12.2437i	0.187320	+	0.452231i	0.989442	−	0.144930i	$-0.0462956\pi$
$733$	5.07150	+	12.2437i	0.187320	+	0.452231i	−0.802122	+	0.597160i	$0.796296\pi$
$734$	12.7357	+	19.0603i	0.470083	+	0.703529i
$735$	−1.17092	+	1.40732i	−0.0431899	+	0.0519099i
$736$	−28.8706	−	5.74271i	−1.06418	−	0.211679i
$737$	0.502013	−	0.751316i	0.0184919	−	0.0276751i
$738$	13.7728	−	5.48869i	0.506985	−	0.202041i
$739$	−13.8573	−	5.73986i	−0.509747	−	0.211144i	0.112959	−	0.993600i	$-0.463967\pi$
$739$	−13.8573	−	5.73986i	−0.509747	−	0.211144i	−0.622707	+	0.782455i	$0.713967\pi$
$740$	−9.67914	−	4.00923i	−0.355812	−	0.147382i
$741$	−24.1774	+	7.15662i	−0.888178	+	0.262905i
$742$	−6.55349	+	9.80799i	−0.240586	+	0.360063i
$743$	44.6446	+	8.88036i	1.63785	+	0.325789i	0.926283	−	0.376828i	$-0.122985\pi$
$743$	44.6446	+	8.88036i	1.63785	+	0.325789i	0.711568	+	0.702617i	$0.247985\pi$
$744$	−38.1052	−	31.7041i	−1.39700	−	1.16233i
$745$	5.99946	+	8.97883i	0.219803	+	0.328959i
$746$	9.63905	+	23.2707i	0.352911	+	0.852002i
$747$	−0.339553	+	0.0627977i	−0.0124236	+	0.00229765i
$748$	0.0628389	−	0.244975i	0.00229762	−	0.00895717i
$749$		−	1.23057i		−	0.0449640i
$750$	14.4424	−	7.59500i	0.527363	−	0.277330i
$751$	15.1169	−	10.1008i	0.551623	−	0.368582i	−0.248302	−	0.968683i	$-0.579873\pi$
$751$	15.1169	−	10.1008i	0.551623	−	0.368582i	0.799925	+	0.600100i	$0.204873\pi$
$752$	6.11012	+	6.11012i	0.222813	+	0.222813i
$753$	17.4309	+	1.83544i	0.635218	+	0.0668872i
$754$	−17.5015	−	11.6941i	−0.637366	−	0.425874i
$755$	0.0112083	+	0.0563479i	0.000407912	+	0.00205071i
$756$	0.609502	−	5.12442i	0.0221674	−	0.186373i
$757$	16.6843	−	40.2794i	0.606400	−	1.46398i	−0.260489	−	0.965477i	$-0.583884\pi$
$757$	16.6843	−	40.2794i	0.606400	−	1.46398i	0.866889	−	0.498502i	$-0.166116\pi$
$758$	−22.7779	+	4.53080i	−0.827330	+	0.164566i
$759$	0.556092	+	0.302071i	0.0201848	+	0.0109645i
$760$	3.90877	−	19.6507i	0.141786	−	0.712807i
$761$	13.2134	−	13.2134i	0.478984	−	0.478984i	−0.425823	−	0.904807i	$-0.640015\pi$
$761$	13.2134	−	13.2134i	0.478984	−	0.478984i	0.904807	+	0.425823i	$0.140015\pi$
$762$	11.6027	+	14.3338i	0.420322	+	0.519258i
$763$	10.5092	−	4.35305i	0.380458	−	0.157591i
$764$	14.9707			0.541621
$765$	−9.85347	+	8.59307i	−0.356253	+	0.310683i
$766$	−24.0694			−0.869662
$767$	0.0154122	−	0.00638393i	0.000556501	−	0.000230510i
$768$	−18.5097	−	22.8665i	−0.667911	−	0.825125i
$769$	24.8069	−	24.8069i	0.894560	−	0.894560i	−0.100388	−	0.994948i	$-0.532009\pi$
$769$	24.8069	−	24.8069i	0.894560	−	0.894560i	0.994948	+	0.100388i	$0.0320085\pi$
$770$	0.0127793	−	0.0642458i	0.000460533	−	0.00231526i
$771$	−5.18554	−	2.81681i	−0.186753	−	0.101445i
$772$	−4.38253	+	0.871739i	−0.157731	+	0.0313746i
$773$	−19.2910	+	46.5726i	−0.693849	+	1.67510i	0.0430299	+	0.999074i	$0.486299\pi$
$773$	−19.2910	+	46.5726i	−0.693849	+	1.67510i	−0.736879	+	0.676025i	$0.763701\pi$
$774$	−21.4927	−	4.57702i	−0.772538	−	0.164518i
$775$	7.21814	+	36.2880i	0.259283	+	1.30350i
$776$	−11.1270	−	7.43483i	−0.399436	−	0.266895i
$777$	−17.1913	−	1.81021i	−0.616735	−	0.0649410i
$778$	−5.65195	−	5.65195i	−0.202632	−	0.202632i
$779$	−25.8464	+	17.2700i	−0.926045	+	0.618763i
$780$	−3.71175	+	1.95194i	−0.132902	+	0.0698906i
$781$			0.173347i			0.00620283i
$782$	19.5755	+	14.6906i	0.700017	+	0.525336i
$783$	−45.4903	+	12.8014i	−1.62569	+	0.457484i
$784$	0.393157	+	0.949166i	0.0140413	+	0.0338988i
$785$	8.54870	+	12.7940i	0.305116	+	0.456639i
$786$	−26.6359	−	22.1615i	−0.950073	−	0.790475i
$787$	−3.71123	−	0.738210i	−0.132291	−	0.0263143i	0.128501	−	0.991709i	$-0.458984\pi$
$787$	−3.71123	−	0.738210i	−0.132291	−	0.0263143i	−0.260792	+	0.965395i	$0.583984\pi$
$788$	4.01071	−	6.00246i	0.142876	−	0.213829i
$789$	−13.7628	+	4.07387i	−0.489970	+	0.145034i
$790$	−3.90884	−	1.61910i	−0.139070	−	0.0576048i
$791$	−5.84543	−	2.42126i	−0.207840	−	0.0860900i
$792$	0.206012	+	0.516948i	0.00732031	+	0.0183690i
$793$	5.24990	−	7.85703i	0.186429	−	0.279011i
$794$	7.93597	+	1.57856i	0.281637	+	0.0560211i
$795$	13.7650	−	16.5442i	0.488194	−	0.586761i
$796$	−5.52785	−	8.27302i	−0.195930	−	0.293229i
$797$	−8.08803	−	19.5262i	−0.286493	−	0.691655i	0.713466	−	0.700689i	$-0.247124\pi$
$797$	−8.08803	−	19.5262i	−0.286493	−	0.691655i	−0.999959	+	0.00903477i	$0.997124\pi$
$798$	−1.00160	−	10.9233i	−0.0354562	−	0.386681i
$799$	11.4979	+	32.7171i	0.406766	+	1.15745i
$800$			19.3204i			0.683078i
$801$	−18.2130	+	11.8177i	−0.643524	+	0.417559i
$802$	−17.4802	+	11.6799i	−0.617249	+	0.412432i
$803$	−0.254631	−	0.254631i	−0.00898574	−	0.00898574i
$804$	2.63545	−	25.0285i	0.0929450	−	0.882685i
$805$	−5.19904	−	3.47388i	−0.183242	−	0.122438i
$806$	4.30251	+	21.6302i	0.151550	+	0.761891i
$807$	−41.6979	−	12.9563i	−1.46784	−	0.456084i
$808$	7.50085	−	18.1087i	0.263879	−	0.637060i
$809$	9.28443	−	1.84679i	0.326423	−	0.0649296i	−0.0291585	−	0.999575i	$-0.509283\pi$
$809$	9.28443	−	1.84679i	0.326423	−	0.0649296i	0.355582	+	0.934645i	$0.384283\pi$
$810$	2.11377	−	9.30836i	0.0742703	−	0.327062i
$811$	4.75896	−	23.9249i	0.167110	−	0.840116i	−0.802724	−	0.596350i	$-0.796617\pi$
$811$	4.75896	−	23.9249i	0.167110	−	0.840116i	0.969834	−	0.243766i	$-0.0783830\pi$
$812$	−6.38682	+	6.38682i	−0.224133	+	0.224133i
$813$	3.66971	−	2.97051i	0.128702	−	0.104180i
$814$	0.571430	−	0.236694i	0.0200286	−	0.00829613i
$815$	24.0846			0.843648
$816$	1.69435	+	7.13856i	0.0593141	+	0.249900i
$817$	46.0729			1.61189
$818$	31.8724	−	13.2020i	1.11439	−	0.461597i
$819$	−4.95836	+	4.82652i	−0.173259	+	0.168652i
$820$	−3.65586	+	3.65586i	−0.127668	+	0.127668i
$821$	10.0681	−	50.6159i	0.351380	−	1.76651i	−0.250695	−	0.968066i	$-0.580659\pi$
$821$	10.0681	−	50.6159i	0.351380	−	1.76651i	0.602075	−	0.798440i	$-0.294341\pi$
$822$	−10.0453	+	18.4928i	−0.350371	+	0.645009i
$823$	16.6625	−	3.31438i	0.580818	−	0.115532i	0.104067	−	0.994570i	$-0.466814\pi$
$823$	16.6625	−	3.31438i	0.580818	−	0.115532i	0.476751	+	0.879038i	$0.341814\pi$
$824$	5.29171	−	12.7753i	0.184345	−	0.445049i
$825$	0.123248	−	0.396656i	0.00429095	−	0.0138098i
$826$	0.00141582	+	0.00711782i	4.92628e−5	+	0.000247661i
$827$	−16.6105	−	11.0988i	−0.577604	−	0.385943i	0.232178	−	0.972673i	$-0.425415\pi$
$827$	−16.6105	−	11.0988i	−0.577604	−	0.385943i	−0.809782	+	0.586731i	$0.800415\pi$
$828$	17.6240	+	0.237468i	0.612478	+	0.00825258i
$829$	35.9632	+	35.9632i	1.24905	+	1.24905i	0.956139	+	0.292913i	$0.0946248\pi$
$829$	35.9632	+	35.9632i	1.24905	+	1.24905i	0.292913	+	0.956139i	$0.405375\pi$
$830$	−0.101504	+	0.0678230i	−0.00352326	+	0.00235417i
$831$	0.322774	+	0.613778i	0.0111969	+	0.0212917i
$832$			16.2556i			0.563561i
$833$	−0.225620	+	4.11693i	−0.00781726	+	0.142643i
$834$	−21.0703	+	1.93202i	−0.729605	+	0.0669002i
$835$	4.75631	+	11.4827i	0.164599	+	0.397377i
$836$	−0.215081	−	0.321891i	−0.00743873	−	0.0111328i
$837$	43.1867	+	24.2183i	1.49275	+	0.837108i
$838$	−16.1148	−	3.20543i	−0.556676	−	0.110730i
$839$	24.5227	−	36.7008i	0.846617	−	1.26705i	−0.115195	−	0.993343i	$-0.536749\pi$
$839$	24.5227	−	36.7008i	0.846617	−	1.26705i	0.961812	−	0.273710i	$-0.0882507\pi$
$840$	−1.56062	−	5.27229i	−0.0538466	−	0.181911i
$841$	49.6242	+	20.5550i	1.71118	+	0.708793i
$842$	−17.4147	−	7.21340i	−0.600150	−	0.248590i
$843$	−5.06247	−	17.1026i	−0.174361	−	0.589046i
$844$	−9.21969	+	13.7982i	−0.317355	+	0.474955i
$845$	−7.96154	−	1.58365i	−0.273885	−	0.0544792i
$846$	−20.8604	−	14.3487i	−0.717194	−	0.493319i
$847$	6.10915	+	9.14299i	0.209913	+	0.314157i
$848$	−4.62186	−	11.1582i	−0.158715	−	0.383173i
$849$	−44.6061	+	4.09011i	−1.53088	+	0.140372i
$850$	6.95032	−	14.4825i	0.238394	−	0.496747i
$851$		−	59.0410i		−	2.02390i
$852$	2.24717	+	4.27315i	0.0769868	+	0.146396i
$853$	−8.84698	+	5.91136i	−0.302915	+	0.202401i	−0.697733	−	0.716358i	$-0.745808\pi$
$853$	−8.84698	+	5.91136i	−0.302915	+	0.202401i	0.394818	+	0.918759i	$0.370808\pi$
$854$	2.90685	+	2.90685i	0.0994702	+	0.0994702i
$855$	−0.269634	+	20.0113i	−0.00922129	+	0.684372i
$856$	3.07301	+	2.05332i	0.105033	+	0.0701810i
$857$	−0.858571	−	4.31633i	−0.0293282	−	0.147443i	0.963347	−	0.268260i	$-0.0864486\pi$
$857$	−0.858571	−	4.31633i	−0.0293282	−	0.147443i	−0.992675	+	0.120817i	$0.961449\pi$
$858$	0.0734645	−	0.236434i	0.00250804	−	0.00807174i
$859$	5.07414	−	12.2501i	0.173127	−	0.417966i	−0.813369	−	0.581748i	$-0.802369\pi$
$859$	5.07414	−	12.2501i	0.173127	−	0.417966i	0.986497	+	0.163781i	$0.0523691\pi$
$860$	7.51570	−	1.49497i	0.256283	−	0.0509779i
$861$	−4.07195	+	7.49618i	−0.138772	+	0.255469i
$862$	−0.955251	+	4.80237i	−0.0325360	+	0.163569i
$863$	37.8800	−	37.8800i	1.28945	−	1.28945i	0.354332	−	0.935120i	$-0.384708\pi$
$863$	37.8800	−	37.8800i	1.28945	−	1.28945i	0.935120	−	0.354332i	$-0.115292\pi$
$864$	19.6510	+	16.8031i	0.668540	+	0.571653i
$865$	−1.02192	+	0.423293i	−0.0347463	+	0.0143924i
$866$	−10.4972			−0.356709
$867$	−6.26495	+	28.7707i	−0.212769	+	0.977103i
$868$	9.46363			0.321216
$869$	−0.227626	+	0.0942856i	−0.00772167	+	0.00319842i
$870$	−12.9857	+	10.5115i	−0.440257	+	0.356373i
$871$	−23.8615	+	23.8615i	−0.808517	+	0.808517i
$872$	−6.66501	+	33.5073i	−0.225706	+	1.13470i
$873$	12.2797	+	5.28135i	0.415605	+	0.178747i
$874$	36.7448	−	7.30900i	1.24291	−	0.247231i
$875$	−3.59298	+	8.67423i	−0.121465	+	0.293242i
$876$	−9.57779	−	2.97599i	−0.323603	−	0.100550i
$877$	−4.23657	−	21.2987i	−0.143059	−	0.719206i	−0.984013	−	0.178099i	$-0.943005\pi$
$877$	−4.23657	−	21.2987i	−0.143059	−	0.719206i	0.840954	−	0.541107i	$-0.181995\pi$
$878$	−12.1239	−	8.10092i	−0.409161	−	0.273393i
$879$	2.77598	−	26.3631i	0.0936314	−	0.889204i
$880$	0.0474241	+	0.0474241i	0.00159867	+	0.00159867i
$881$	6.25861	−	4.18187i	0.210858	−	0.140891i	−0.445657	−	0.895204i	$-0.647030\pi$
$881$	6.25861	−	4.18187i	0.210858	−	0.140891i	0.656515	+	0.754313i	$0.272030\pi$
$882$	−1.63854	−	2.52525i	−0.0551725	−	0.0850295i
$883$			17.6622i			0.594379i	0.954819	+	0.297189i	$0.0960493\pi$
$883$			17.6622i			0.594379i	−0.954819	+	0.297189i	$0.903951\pi$
$884$	−4.08647	+	8.51507i	−0.137443	+	0.286393i
$885$	−0.00120903	−	0.0131855i	−4.06412e−5	−	0.000443227i
$886$	−11.0511	−	26.6797i	−0.371269	−	0.896324i
$887$	−11.3882	−	17.0437i	−0.382380	−	0.572272i	0.589494	−	0.807773i	$-0.299327\pi$
$887$	−11.3882	−	17.0437i	−0.382380	−	0.572272i	−0.971874	+	0.235501i	$0.924327\pi$
$888$	33.2058	−	39.9101i	1.11431	−	1.33929i
$889$	−10.4069	−	2.07006i	−0.349036	−	0.0694275i
$890$	−4.26431	+	6.38198i	−0.142940	+	0.213925i
$891$	−0.296254	−	0.470332i	−0.00992487	−	0.0157567i
$892$	6.41572	+	2.65748i	0.214814	+	0.0889790i
$893$	49.0435	+	20.3145i	1.64118	+	0.679799i
$894$	−17.0260	+	5.03979i	−0.569435	+	0.168556i
$895$	−0.882518	+	1.32078i	−0.0294993	+	0.0441488i
$896$	2.82467	+	0.561863i	0.0943657	+	0.0187705i
$897$	−18.1676	−	15.1157i	−0.606599	−	0.504700i
$898$	1.46948	+	2.19923i	0.0490372	+	0.0733893i
$899$	−33.1643	−	80.0657i	−1.10609	−	2.67034i
$900$	−2.10384	−	11.3756i	−0.0701281	−	0.379188i
$901$	2.65233	−	48.3976i	0.0883620	−	1.61236i
$902$		−	0.305233i		−	0.0101631i
$903$	11.1907	−	5.88499i	0.372404	−	0.195840i
$904$	15.8001	−	10.5573i	0.525502	−	0.351129i
$905$	−1.28924	−	1.28924i	−0.0428557	−	0.0428557i
$906$	−0.0939480	−	0.00989254i	−0.00312121	−	0.000328658i
$907$	−3.50818	−	2.34409i	−0.116487	−	0.0778343i	0.495962	−	0.868344i	$-0.334816\pi$
$907$	−3.50818	−	2.34409i	−0.116487	−	0.0778343i	−0.612449	+	0.790510i	$0.709816\pi$
$908$	5.14288	+	25.8550i	0.170672	+	0.858028i
$909$	−4.07795	+	19.1492i	−0.135257	+	0.635138i
$910$	−0.936154	+	2.26007i	−0.0310332	+	0.0749208i
$911$	13.7784	−	2.74070i	0.456499	−	0.0908034i	0.0385159	−	0.999258i	$-0.487737\pi$
$911$	13.7784	−	2.74070i	0.456499	−	0.0908034i	0.417984	+	0.908455i	$0.362737\pi$
$912$	9.86890	+	5.36083i	0.326792	+	0.177515i
$913$	−0.00138690	+	0.00697243i	−4.58998e−5	+	0.000230754i
$914$	16.3521	−	16.3521i	0.540880	−	0.540880i
$915$	−4.71899	−	5.82975i	−0.156005	−	0.192726i
$916$	6.29735	−	2.60845i	0.208070	−	0.0861856i
$917$	19.9368			0.658373
$918$	−8.68562	−	19.6648i	−0.286668	−	0.649037i
$919$	1.39003			0.0458529			0.0229264	−	0.999737i	$-0.492702\pi$
$919$	1.39003			0.0458529			0.0229264	+	0.999737i	$0.492702\pi$
$920$	17.3501	−	7.18666i	0.572017	−	0.236937i
$921$	−30.7044	−	37.9316i	−1.01174	−	1.24989i
$922$	−0.522445	+	0.522445i	−0.0172058	+	0.0172058i
$923$	1.26296	−	6.34931i	0.0415707	−	0.208990i
$924$	−0.0933574	−	0.0507121i	−0.00307123	−	0.00166831i
$925$	−38.0068	+	7.56003i	−1.24966	+	0.248572i
$926$	10.0945	−	24.3704i	0.331727	−	0.800860i
$927$	−2.87692	+	13.5094i	−0.0944904	+	0.443706i
$928$	−8.82862	−	44.3845i	−0.289814	−	1.45699i
$929$	34.9654	+	23.3632i	1.14718	+	0.766521i	0.975796	−	0.218684i	$-0.0701763\pi$
$929$	34.9654	+	23.3632i	1.14718	+	0.766521i	0.171383	+	0.985204i	$0.445176\pi$
$930$	17.4084	+	1.83307i	0.570845	+	0.0601088i
$931$	4.46286	+	4.46286i	0.146264	+	0.146264i
$932$	4.86845	−	3.25300i	0.159471	−	0.106555i
$933$	36.6095	−	19.2522i	1.19854	−	0.630289i
$934$		−	16.3926i		−	0.536381i
$935$	0.0892415	+	0.253936i	0.00291851	+	0.00830459i
$936$	−3.77942	−	20.4356i	−0.123534	−	0.667959i
$937$	7.50796	+	18.1258i	0.245274	+	0.592144i	0.997791	−	0.0664285i	$-0.0211604\pi$
$937$	7.50796	+	18.1258i	0.245274	+	0.592144i	−0.752517	+	0.658573i	$0.771160\pi$
$938$	−8.15600	−	12.2063i	−0.266303	−	0.398550i
$939$	13.8161	+	11.4952i	0.450873	+	0.375133i
$940$	8.65946	+	1.72247i	0.282440	+	0.0561809i
$941$	−21.9303	+	32.8211i	−0.714909	+	1.06994i	0.279060	+	0.960274i	$0.409977\pi$
$941$	−21.9303	+	32.8211i	−0.714909	+	1.06994i	−0.993969	+	0.109663i	$0.965023\pi$
$942$	−24.2606	+	7.18125i	−0.790452	+	0.233978i
$943$	−26.9186	−	11.1500i	−0.876590	−	0.363095i
$944$	−0.00686487	−	0.00284352i	−0.000223432	−	9.25487e-5i
$945$	2.49060	+	4.89503i	0.0810192	+	0.159235i
$946$	−0.251340	+	0.376156i	−0.00817176	+	0.0122299i
$947$	16.8944	+	3.36050i	0.548993	+	0.109201i	0.461790	−	0.886989i	$-0.347207\pi$
$947$	16.8944	+	3.36050i	0.548993	+	0.109201i	0.0872026	+	0.996191i	$0.472207\pi$
$948$	−4.38891	+	5.27503i	−0.142545	+	0.171325i
$949$	7.47141	+	11.1818i	0.242532	+	0.362975i
$950$	−9.41014	−	22.7181i	−0.305305	−	0.737072i
$951$	1.95535	+	21.3248i	0.0634067	+	0.691505i
$952$	−9.90442	−	7.43290i	−0.321004	−	0.240902i
$953$			48.0708i			1.55717i	0.627541	+	0.778584i	$0.284062\pi$
$953$			48.0708i			1.55717i	−0.627541	+	0.778584i	$0.715938\pi$
$954$	19.2623	+	29.6862i	0.623639	+	0.961126i
$955$	−13.2477	+	8.85184i	−0.428686	+	0.286439i
$956$	−16.0665	−	16.0665i	−0.519627	−	0.519627i
$957$	−0.101881	+	0.967552i	−0.00329335	+	0.0312765i
$958$	16.3097	+	10.8978i	0.526943	+	0.352092i
$959$	−2.36233	−	11.8762i	−0.0762835	−	0.383503i
$960$	12.3213	+	3.82846i	0.397669	+	0.123563i
$961$	−22.8847	+	55.2486i	−0.738217	+	1.78221i
$962$	−22.6547	+	4.50630i	−0.730418	+	0.145289i
$963$	−3.39135	−	1.45858i	−0.109285	−	0.0470021i
$964$	−1.33800	+	6.72658i	−0.0430941	+	0.216648i
$965$	3.36270	−	3.36270i	0.108249	−	0.108249i
$966$	7.99143	−	6.46880i	0.257120	−	0.208130i
$967$	−15.7140	+	6.50896i	−0.505329	+	0.209314i	−0.620759	−	0.784002i	$-0.713175\pi$
$967$	−15.7140	+	6.50896i	−0.505329	+	0.209314i	0.115430	+	0.993316i	$0.463175\pi$
$968$	−33.0258			−1.06149
$969$	26.3989	+	36.5328i	0.848054	+	1.17360i
$970$	4.72574			0.151734
$971$	14.3871	−	5.95932i	0.461703	−	0.191244i	−0.139693	−	0.990195i	$-0.544611\pi$
$971$	14.3871	−	5.95932i	0.461703	−	0.191244i	0.601396	+	0.798951i	$0.294611\pi$
$972$	−13.4000	−	7.75365i	−0.429807	−	0.248698i
$973$	8.60854	−	8.60854i	0.275977	−	0.275977i
$974$	7.45700	−	37.4889i	0.238938	−	1.20122i
$975$	−7.40424	+	13.6307i	−0.237125	+	0.436531i
$976$	−4.12814	+	0.821138i	−0.132139	+	0.0262840i
$977$	−16.9670	+	40.9619i	−0.542822	+	1.31049i	0.379902	+	0.925027i	$0.375958\pi$
$977$	−16.9670	+	40.9619i	−0.542822	+	1.31049i	−0.922724	+	0.385462i	$0.874042\pi$
$978$	−11.7509	+	37.8185i	−0.375753	+	1.20930i
$979$	0.0872003	+	0.438385i	0.00278693	+	0.0140109i
$980$	0.872821	+	0.583200i	0.0278812	+	0.0186296i
$981$	0.459764	−	34.1221i	0.0146791	−	1.08943i
$982$	15.8055	+	15.8055i	0.504373	+	0.504373i
$983$	−2.78215	+	1.85897i	−0.0887367	+	0.0592920i	−0.599147	−	0.800639i	$-0.704494\pi$
$983$	−2.78215	+	1.85897i	−0.0887367	+	0.0592920i	0.510410	+	0.859931i	$0.329494\pi$
$984$	−11.9252	−	22.6766i	−0.380162	−	0.722905i
$985$			7.68308i			0.244803i
$986$	−9.34897	+	36.4466i	−0.297732	+	1.16070i
$987$	14.5071	−	1.33021i	0.461766	−	0.0423411i
$988$	5.53273	+	13.3572i	0.176020	+	0.424949i
$989$	23.9920	+	35.9066i	0.762902	+	1.14176i
$990$	−0.161909	−	0.111368i	−0.00514581	−	0.00353952i
$991$	−25.0505	−	4.98286i	−0.795757	−	0.158286i	−0.219562	−	0.975599i	$-0.570463\pi$
$991$	−25.0505	−	4.98286i	−0.795757	−	0.158286i	−0.576194	+	0.817313i	$0.695463\pi$
$992$	−26.3423	+	39.4241i	−0.836370	+	1.25172i
$993$	5.23489	+	17.6851i	0.166124	+	0.561221i
$994$	2.60191	+	1.07775i	0.0825276	+	0.0341841i
$995$	9.78330	+	4.05238i	0.310152	+	0.128469i
$996$	0.0561983	+	0.189856i	0.00178071	+	0.00601581i
$997$	−13.0019	+	19.4588i	−0.411776	+	0.616266i	−0.978155	−	0.207879i	$-0.933344\pi$
$997$	−13.0019	+	19.4588i	−0.411776	+	0.616266i	0.566379	+	0.824145i	$0.308344\pi$
$998$	16.9477	+	3.37111i	0.536471	+	0.106711i
$999$	−25.3655	+	45.2323i	−0.802528	+	1.43109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bf.a.29.13	✓	288
3.2	odd	2	inner	357.2.bf.a.29.24	yes	288
17.10	odd	16	inner	357.2.bf.a.197.24	yes	288
51.44	even	16	inner	357.2.bf.a.197.13	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bf.a.29.13	✓	288	1.1	even	1	trivial
357.2.bf.a.29.24	yes	288	3.2	odd	2	inner
357.2.bf.a.197.13	yes	288	51.44	even	16	inner
357.2.bf.a.197.24	yes	288	17.10	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bf (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.927040 + 0.383993i) q^{2} +(-1.08976 - 1.34627i) q^{3} +(-0.702260 + 0.702260i) q^{4} +(0.206206 - 1.03667i) q^{5} +(1.52720 + 0.829583i) q^{6} +(-0.980785 + 0.195090i) q^{7} +(1.14935 - 2.77477i) q^{8} +(-0.624860 + 2.93420i) q^{9} +(0.206911 + 1.04021i) q^{10} +(0.0513533 + 0.0343132i) q^{11} +(1.71072 + 0.180136i) q^{12} +(-1.63096 - 1.63096i) q^{13} +(0.834314 - 0.557471i) q^{14} +(-1.62034 + 0.852108i) q^{15} +1.02737i q^{16} +(-1.78393 + 3.71720i) q^{17} +(-0.547442 - 2.96007i) q^{18} +(2.41528 + 5.83101i) q^{19} +(0.583200 + 0.872821i) q^{20} +(1.33146 + 1.10780i) q^{21} +(-0.0607825 - 0.0120904i) q^{22} +(-3.28662 + 4.91878i) q^{23} +(-4.98808 + 1.47650i) q^{24} +(3.58724 + 1.48588i) q^{25} +(2.13824 + 0.885690i) q^{26} +(4.63116 - 2.35634i) q^{27} +(0.551762 - 0.825771i) q^{28} +(-8.91991 - 1.77428i) q^{29} +(1.17492 - 1.41214i) q^{30} +(5.29400 + 7.92302i) q^{31} +(1.90419 + 4.59712i) q^{32} +(-0.00976797 - 0.106528i) q^{33} +(0.226392 - 4.13101i) q^{34} +1.05698i q^{35} +(-1.62176 - 2.49939i) q^{36} +(-8.29830 + 5.54475i) q^{37} +(-4.47813 - 4.47813i) q^{38} +(-0.418355 + 3.97306i) q^{39} +(-2.63951 - 1.76366i) q^{40} +(0.960864 + 4.83059i) q^{41} +(-1.65970 - 0.515700i) q^{42} +(2.79355 - 6.74423i) q^{43} +(-0.0601601 + 0.0119666i) q^{44} +(2.91294 + 1.25282i) q^{45} +(1.15806 - 5.82194i) q^{46} +(5.94735 - 5.94735i) q^{47} +(1.38311 - 1.11958i) q^{48} +(0.923880 - 0.382683i) q^{49} -3.89608 q^{50} +(6.94839 - 1.64921i) q^{51} +2.29072 q^{52} +(-10.8609 + 4.49873i) q^{53} +(-3.38846 + 3.96276i) q^{54} +(0.0461607 - 0.0461607i) q^{55} +(-0.585932 + 2.94568i) q^{56} +(5.21801 - 9.60599i) q^{57} +(8.95042 - 1.78035i) q^{58} +(-0.00276777 + 0.00668198i) q^{59} +(0.539502 - 1.73630i) q^{60} +(0.799262 + 4.01816i) q^{61} +(-7.95013 - 5.31211i) q^{62} +(0.0404186 - 2.99973i) q^{63} +(-4.98344 - 4.98344i) q^{64} +(-2.02708 + 1.35445i) q^{65} +(0.0499613 + 0.0950050i) q^{66} -14.6304i q^{67} +(-1.35766 - 3.86322i) q^{68} +(10.2036 - 0.935607i) q^{69} +(-0.405872 - 0.979860i) q^{70} +(1.55931 + 2.33368i) q^{71} +(7.42355 + 5.10626i) q^{72} +(-5.71846 - 1.13747i) q^{73} +(5.56372 - 8.32669i) q^{74} +(-1.90883 - 6.44863i) q^{75} +(-5.79104 - 2.39873i) q^{76} +(-0.0570607 - 0.0236353i) q^{77} +(-1.13779 - 3.84383i) q^{78} +(-2.21627 + 3.31688i) q^{79} +(1.06504 + 0.211850i) q^{80} +(-8.21910 - 3.66693i) q^{81} +(-2.74567 - 4.10919i) q^{82} +(0.0440482 + 0.106342i) q^{83} +(-1.71299 + 0.157071i) q^{84} +(3.48565 + 2.61585i) q^{85} +7.32488i q^{86} +(7.33188 + 13.9421i) q^{87} +(0.154234 - 0.103056i) q^{88} +(5.11735 + 5.11735i) q^{89} +(-3.18149 - 0.0428677i) q^{90} +(1.91781 + 1.28144i) q^{91} +(-1.14620 - 5.76232i) q^{92} +(4.89732 - 15.7613i) q^{93} +(-3.22969 + 7.79717i) q^{94} +(6.54286 - 1.30146i) q^{95} +(4.11384 - 7.57329i) q^{96} +(0.869274 - 4.37013i) q^{97} +(-0.709526 + 0.709526i) q^{98} +(-0.132770 + 0.129240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 48 q^{12} - 48 q^{24} - 64 q^{25} - 64 q^{31} - 224 q^{34} + 16 q^{39} + 64 q^{40} - 64 q^{43} + 64 q^{45} + 32 q^{51} + 128 q^{52} + 112 q^{54} - 32 q^{57} + 32 q^{58} - 144 q^{60} + 32 q^{61}+ \cdots + 304 q^{96}+O(q^{100}) \) 288 * q - 48 * q^12 - 48 * q^24 - 64 * q^25 - 64 * q^31 - 224 * q^34 + 16 * q^39 + 64 * q^40 - 64 * q^43 + 64 * q^45 + 32 * q^51 + 128 * q^52 + 112 * q^54 - 32 * q^57 + 32 * q^58 - 144 * q^60 + 32 * q^61 + 64 * q^64 - 192 * q^66 - 32 * q^70 - 208 * q^72 - 128 * q^76 - 208 * q^78 - 64 * q^79 - 112 * q^81 - 256 * q^82 + 32 * q^85 + 32 * q^88 + 240 * q^90 - 96 * q^91 + 64 * q^93 + 304 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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