LMFDB - Embedded newform 630.2.bz.a.517.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(13,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9, 6]))

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

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

chi := DirichletCharacter("630.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bz (of order $12$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			517.13
Character	$\chi$	$=$	630.517
Dual form			630.2.bz.a.223.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(0.0305359 - 1.73178i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.58976 + 1.57247i) q^{5} +(1.66487 + 0.477713i) q^{6} +(1.12847 - 2.39302i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.99814 - 0.105763i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(0.0305359 - 1.73178i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.58976 + 1.57247i) q^{5} +(1.66487 + 0.477713i) q^{6} +(1.12847 - 2.39302i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.99814 - 0.105763i) q^{9} +(-1.10743 - 1.94257i) q^{10} +(-0.243530 - 0.421807i) q^{11} +(-0.892336 + 1.48450i) q^{12} +(-1.17543 + 0.314954i) q^{13} +(2.01941 + 1.70938i) q^{14} +(2.67463 + 2.80113i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.59279 + 2.59279i) q^{17} +(0.878134 - 2.86860i) q^{18} -7.77993 q^{19} +(2.16301 - 0.566923i) q^{20} +(-4.10973 - 2.02734i) q^{21} +(0.470464 - 0.126060i) q^{22} +(1.10448 + 4.12197i) q^{23} +(-1.20296 - 1.24615i) q^{24} +(0.0546582 - 4.99970i) q^{25} -1.21689i q^{26} +(-0.274709 + 5.18889i) q^{27} +(-2.17380 + 1.50818i) q^{28} +(0.0975531 - 0.0563223i) q^{29} +(-3.39793 + 1.85851i) q^{30} +(0.577525 + 0.333434i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.737913 + 0.408861i) q^{33} +(-1.83338 - 3.17551i) q^{34} +(1.96896 + 5.57882i) q^{35} +(2.54358 + 1.59066i) q^{36} +(-6.32740 - 6.32740i) q^{37} +(2.01359 - 7.51484i) q^{38} +(0.509540 + 2.04520i) q^{39} +(-0.0122221 + 2.23603i) q^{40} +(-8.77891 - 5.06851i) q^{41} +(3.02194 - 3.44498i) q^{42} +(3.51575 + 0.942044i) q^{43} +0.487060i q^{44} +(4.93262 - 4.54635i) q^{45} -4.26738 q^{46} +(-3.43155 - 0.919481i) q^{47} +(1.51503 - 0.839446i) q^{48} +(-4.45310 - 5.40092i) q^{49} +(4.81519 + 1.34681i) q^{50} +(4.41098 + 4.56933i) q^{51} +(1.17543 + 0.314954i) q^{52} +(-6.56992 + 6.56992i) q^{53} +(-4.94098 - 1.60833i) q^{54} +(1.05043 + 0.287626i) q^{55} +(-0.894170 - 2.49007i) q^{56} +(-0.237567 + 13.4731i) q^{57} +(0.0291546 + 0.108806i) q^{58} +(0.680171 - 1.17809i) q^{59} +(-0.915737 - 3.76317i) q^{60} +(-5.58015 + 3.22170i) q^{61} +(-0.471547 + 0.471547i) q^{62} +(-3.63641 + 7.05525i) q^{63} -1.00000i q^{64} +(1.37338 - 2.34903i) q^{65} +(-0.203943 - 0.818591i) q^{66} +(-13.3562 + 3.57879i) q^{67} +(3.54182 - 0.949028i) q^{68} +(7.17208 - 1.78685i) q^{69} +(-5.89833 + 0.457967i) q^{70} +4.92862 q^{71} +(-2.19479 + 2.04522i) q^{72} +(3.32627 + 3.32627i) q^{73} +(7.74945 - 4.47415i) q^{74} +(-8.65672 - 0.247326i) q^{75} +(6.73762 + 3.88997i) q^{76} +(-1.28421 + 0.106775i) q^{77} +(-2.10739 - 0.0371588i) q^{78} +(9.28025 - 5.35796i) q^{79} +(-2.15668 - 0.590534i) q^{80} +(8.97763 + 0.634184i) q^{81} +(7.16795 - 7.16795i) q^{82} +(0.950809 - 3.54847i) q^{83} +(2.54546 + 3.81059i) q^{84} +(0.0448157 - 8.19901i) q^{85} +(-1.81989 + 3.15214i) q^{86} +(-0.0945591 - 0.170661i) q^{87} +(-0.470464 - 0.126060i) q^{88} +2.14078 q^{89} +(3.11478 + 5.94122i) q^{90} +(-0.572744 + 3.16824i) q^{91} +(1.10448 - 4.12197i) q^{92} +(0.595071 - 0.989966i) q^{93} +(1.77630 - 3.07664i) q^{94} +(12.3682 - 12.2337i) q^{95} +(0.418723 + 1.68068i) q^{96} +(13.5130 + 3.62079i) q^{97} +(6.36943 - 2.90350i) q^{98} +(0.685525 + 1.29039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 24 q^{15} + 96 q^{16} - 8 q^{18} + 8 q^{23} + 48 q^{30} - 24 q^{35} + 8 q^{36} - 44 q^{42} + 48 q^{46} + 32 q^{50} - 160 q^{53} - 4 q^{56} + 88 q^{57} + 24 q^{58} + 8 q^{60} - 48 q^{63} - 8 q^{65} + 16 q^{71} + 16 q^{72} - 16 q^{77} - 16 q^{78} - 8 q^{81} - 16 q^{86} + 8 q^{92} - 120 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) $ 192 * q + 8 * q^11 + 24 * q^15 + 96 * q^16 - 8 * q^18 + 8 * q^23 + 48 * q^30 - 24 * q^35 + 8 * q^36 - 44 * q^42 + 48 * q^46 + 32 * q^50 - 160 * q^53 - 4 * q^56 + 88 * q^57 + 24 * q^58 + 8 * q^60 - 48 * q^63 - 8 * q^65 + 16 * q^71 + 16 * q^72 - 16 * q^77 - 16 * q^78 - 8 * q^81 - 16 * q^86 + 8 * q^92 - 120 * q^93 - 128 * q^95 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	0.0305359	−	1.73178i	0.0176299	−	0.999845i
$3$	0.0305359	−	1.73178i	0.0176299	−	0.999845i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−1.58976	+	1.57247i	−0.710961	+	0.703231i
$5$	−1.58976	+	1.57247i	−0.710961	+	0.703231i
$6$	1.66487	+	0.477713i	0.679680	+	0.195026i
$7$	1.12847	−	2.39302i	0.426523	−	0.904477i
$7$	1.12847	−	2.39302i	0.426523	−	0.904477i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.99814	−	0.105763i	−0.999378	−	0.0352543i
$10$	−1.10743	−	1.94257i	−0.350201	−	0.614296i
$11$	−0.243530	−	0.421807i	−0.0734271	−	0.127179i	0.826974	−	0.562240i	$-0.190060\pi$
$11$	−0.243530	−	0.421807i	−0.0734271	−	0.127179i	−0.900401	+	0.435061i	$0.856727\pi$
$12$	−0.892336	+	1.48450i	−0.257595	+	0.428538i
$13$	−1.17543	+	0.314954i	−0.326005	+	0.0873526i	−0.418109	−	0.908397i	$-0.637307\pi$
$13$	−1.17543	+	0.314954i	−0.326005	+	0.0873526i	0.0921049	+	0.995749i	$0.470640\pi$
$14$	2.01941	+	1.70938i	0.539710	+	0.456851i
$15$	2.67463	+	2.80113i	0.690588	+	0.723249i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.59279	+	2.59279i	−0.628845	+	0.628845i	−0.947777	−	0.318933i	$-0.896676\pi$
$17$	−2.59279	+	2.59279i	−0.628845	+	0.628845i	0.318933	+	0.947777i	$0.396676\pi$
$18$	0.878134	−	2.86860i	0.206978	−	0.676136i
$19$	−7.77993			−1.78484			−0.892419	−	0.451207i	$-0.850994\pi$
$19$	−7.77993			−1.78484			−0.892419	+	0.451207i	$0.850994\pi$
$20$	2.16301	−	0.566923i	0.483663	−	0.126768i
$21$	−4.10973	−	2.02734i	−0.896817	−	0.442402i
$22$	0.470464	−	0.126060i	0.100303	−	0.0268762i
$23$	1.10448	+	4.12197i	0.230300	+	0.859490i	0.980212	+	0.197952i	$0.0634292\pi$
$23$	1.10448	+	4.12197i	0.230300	+	0.859490i	−0.749912	+	0.661538i	$0.769904\pi$
$24$	−1.20296	−	1.24615i	−0.245554	−	0.254369i
$25$	0.0546582	−	4.99970i	0.0109316	−	0.999940i
$26$		−	1.21689i		−	0.238652i
$27$	−0.274709	+	5.18889i	−0.0528678	+	0.998602i
$28$	−2.17380	+	1.50818i	−0.410809	+	0.285019i
$29$	0.0975531	−	0.0563223i	0.0181152	−	0.0104588i	−0.490915	−	0.871207i	$-0.663337\pi$
$29$	0.0975531	−	0.0563223i	0.0181152	−	0.0104588i	0.509030	+	0.860749i	$0.330004\pi$
$30$	−3.39793	+	1.85851i	−0.620374	+	0.339317i
$31$	0.577525	+	0.333434i	0.103727	+	0.0598866i	0.550966	−	0.834528i	$-0.314259\pi$
$31$	0.577525	+	0.333434i	0.103727	+	0.0598866i	−0.447239	+	0.894414i	$0.647593\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−0.737913	+	0.408861i	−0.128454	+	0.0711735i
$34$	−1.83338	−	3.17551i	−0.314422	−	0.544596i
$35$	1.96896	+	5.57882i	0.332815	+	0.942992i
$36$	2.54358	+	1.59066i	0.423930	+	0.265110i
$37$	−6.32740	−	6.32740i	−1.04022	−	1.04022i	−0.999157	−	0.0410618i	$-0.986926\pi$
$37$	−6.32740	−	6.32740i	−1.04022	−	1.04022i	−0.0410618	−	0.999157i	$-0.513074\pi$
$38$	2.01359	−	7.51484i	0.326648	−	1.21907i
$39$	0.509540	+	2.04520i	0.0815916	+	0.327494i
$40$	−0.0122221	+	2.23603i	−0.00193249	+	0.353548i
$41$	−8.77891	−	5.06851i	−1.37104	−	0.791568i	−0.379977	−	0.924996i	$-0.624068\pi$
$41$	−8.77891	−	5.06851i	−1.37104	−	0.791568i	−0.991058	+	0.133428i	$0.957401\pi$
$42$	3.02194	−	3.44498i	0.466295	−	0.531572i
$43$	3.51575	+	0.942044i	0.536148	+	0.143660i	0.516726	−	0.856151i	$-0.327151\pi$
$43$	3.51575	+	0.942044i	0.536148	+	0.143660i	0.0194220	+	0.999811i	$0.493817\pi$
$44$			0.487060i			0.0734271i
$45$	4.93262	−	4.54635i	0.735311	−	0.677730i
$46$	−4.26738			−0.629190
$47$	−3.43155	−	0.919481i	−0.500543	−	0.134120i	−0.000290851	−	1.00000i	$-0.500093\pi$
$47$	−3.43155	−	0.919481i	−0.500543	−	0.134120i	−0.500252	+	0.865880i	$0.666759\pi$
$48$	1.51503	−	0.839446i	0.218676	−	0.121164i
$49$	−4.45310	−	5.40092i	−0.636157	−	0.771560i
$50$	4.81519	+	1.34681i	0.680971	+	0.190468i
$51$	4.41098	+	4.56933i	0.617661	+	0.639834i
$52$	1.17543	+	0.314954i	0.163002	+	0.0436763i
$53$	−6.56992	+	6.56992i	−0.902447	+	0.902447i	−0.995647	−	0.0932001i	$-0.970290\pi$
$53$	−6.56992	+	6.56992i	−0.902447	+	0.902447i	0.0932001	+	0.995647i	$0.470290\pi$
$54$	−4.94098	−	1.60833i	−0.672382	−	0.218866i
$55$	1.05043	+	0.287626i	0.141640	+	0.0387834i
$56$	−0.894170	−	2.49007i	−0.119489	−	0.332750i
$57$	−0.237567	+	13.4731i	−0.0314665	+	1.78456i
$58$	0.0291546	+	0.108806i	0.00382818	+	0.0142870i
$59$	0.680171	−	1.17809i	0.0885507	−	0.153374i	−0.818348	−	0.574723i	$-0.805110\pi$
$59$	0.680171	−	1.17809i	0.0885507	−	0.153374i	0.906899	+	0.421349i	$0.138443\pi$
$60$	−0.915737	−	3.76317i	−0.118221	−	0.485823i
$61$	−5.58015	+	3.22170i	−0.714465	+	0.412497i	−0.812712	−	0.582665i	$-0.802010\pi$
$61$	−5.58015	+	3.22170i	−0.714465	+	0.412497i	0.0982469	+	0.995162i	$0.468677\pi$
$62$	−0.471547	+	0.471547i	−0.0598866	+	0.0598866i
$63$	−3.63641	+	7.05525i	−0.458144	+	0.888878i
$64$		−	1.00000i		−	0.125000i
$65$	1.37338	−	2.34903i	0.170347	−	0.291361i
$66$	−0.203943	−	0.818591i	−0.0251037	−	0.100762i
$67$	−13.3562	+	3.57879i	−1.63172	+	0.437219i	−0.954416	−	0.298481i	$-0.903520\pi$
$67$	−13.3562	+	3.57879i	−1.63172	+	0.437219i	−0.677308	+	0.735700i	$0.736853\pi$
$68$	3.54182	−	0.949028i	0.429509	−	0.115087i
$69$	7.17208	−	1.78685i	0.863417	−	0.215111i
$70$	−5.89833	+	0.457967i	−0.704985	+	0.0547375i
$71$	4.92862			0.584920			0.292460	−	0.956278i	$-0.405526\pi$
$71$	4.92862			0.584920			0.292460	+	0.956278i	$0.405526\pi$
$72$	−2.19479	+	2.04522i	−0.258658	+	0.241031i
$73$	3.32627	+	3.32627i	0.389310	+	0.389310i	0.874441	−	0.485131i	$-0.161228\pi$
$73$	3.32627	+	3.32627i	0.389310	+	0.389310i	−0.485131	+	0.874441i	$0.661228\pi$
$74$	7.74945	−	4.47415i	0.900856	−	0.520109i
$75$	−8.65672	−	0.247326i	−0.999592	−	0.0285588i
$76$	6.73762	+	3.88997i	0.772858	+	0.446210i
$77$	−1.28421	+	0.106775i	−0.146349	+	0.0121682i
$78$	−2.10739	−	0.0371588i	−0.238615	−	0.00420741i
$79$	9.28025	−	5.35796i	1.04411	−	0.602817i	0.123115	−	0.992392i	$-0.460712\pi$
$79$	9.28025	−	5.35796i	1.04411	−	0.602817i	0.920995	+	0.389575i	$0.127378\pi$
$80$	−2.15668	−	0.590534i	−0.241124	−	0.0660237i
$81$	8.97763	+	0.634184i	0.997514	+	0.0704649i
$82$	7.16795	−	7.16795i	0.791568	−	0.791568i
$83$	0.950809	−	3.54847i	0.104365	−	0.389495i	−0.893907	−	0.448252i	$-0.852047\pi$
$83$	0.950809	−	3.54847i	0.104365	−	0.389495i	0.998272	+	0.0587565i	$0.0187136\pi$
$84$	2.54546	+	3.81059i	0.277732	+	0.415770i
$85$	0.0448157	−	8.19901i	0.00486094	−	0.889308i
$86$	−1.81989	+	3.15214i	−0.196244	+	0.339904i
$87$	−0.0945591	−	0.170661i	−0.0101378	−	0.0182967i
$88$	−0.470464	−	0.126060i	−0.0501516	−	0.0134381i
$89$	2.14078			0.226922			0.113461	−	0.993542i	$-0.463806\pi$
$89$	2.14078			0.226922			0.113461	+	0.993542i	$0.463806\pi$
$90$	3.11478	+	5.94122i	0.328327	+	0.626260i
$91$	−0.572744	+	3.16824i	−0.0600399	+	0.332121i
$92$	1.10448	−	4.12197i	0.115150	−	0.429745i
$93$	0.595071	−	0.989966i	0.0617059	−	0.102655i
$94$	1.77630	−	3.07664i	0.183211	−	0.317331i
$95$	12.3682	−	12.2337i	1.26895	−	1.25515i
$96$	0.418723	+	1.68068i	0.0427357	+	0.171533i
$97$	13.5130	+	3.62079i	1.37204	+	0.367636i	0.868222	−	0.496176i	$-0.165263\pi$
$97$	13.5130	+	3.62079i	1.37204	+	0.367636i	0.503814	+	0.863812i	$0.331930\pi$
$98$	6.36943	−	2.90350i	0.643410	−	0.293298i
$99$	0.685525	+	1.29039i	0.0688978	+	0.129689i
$100$	−2.54719	+	4.30254i	−0.254719	+	0.430254i
$101$	14.1717	−	8.18206i	1.41014	−	0.814146i	0.414740	−	0.909940i	$-0.363872\pi$
$101$	14.1717	−	8.18206i	1.41014	−	0.814146i	0.995401	+	0.0957943i	$0.0305391\pi$
$102$	−5.55528	+	3.07805i	−0.550054	+	0.304772i
$103$	0.294045	−	0.0787891i	0.0289731	−	0.00776333i	−0.244303	−	0.969699i	$-0.578559\pi$
$103$	0.294045	−	0.0787891i	0.0289731	−	0.00776333i	0.273276	+	0.961936i	$0.411893\pi$
$104$	−0.608445	+	1.05386i	−0.0596630	+	0.103339i
$105$	9.72142	−	3.23946i	0.948713	−	0.316139i
$106$	−4.64563	−	8.04647i	−0.451224	−	0.781542i
$107$	9.59737	+	9.59737i	0.927813	+	0.927813i	0.997564	−	0.0697513i	$-0.0222206\pi$
$107$	9.59737	+	9.59737i	0.927813	+	0.927813i	−0.0697513	+	0.997564i	$0.522221\pi$
$108$	2.83235	−	4.35635i	0.272543	−	0.419190i
$109$		−	15.3751i		−	1.47266i	−0.676620	−	0.736332i	$-0.736556\pi$
$109$		−	15.3751i		−	1.47266i	0.676620	−	0.736332i	$-0.263444\pi$
$110$	−0.549697	+	0.940198i	−0.0524116	+	0.0896443i
$111$	−11.1509	+	10.7645i	−1.05840	+	1.02172i
$112$	2.63665	−	0.219224i	0.249140	−	0.0207147i
$113$	−0.419276	−	1.56476i	−0.0394422	−	0.147200i	0.943397	−	0.331667i	$-0.107611\pi$
$113$	−0.419276	−	1.56476i	−0.0394422	−	0.147200i	−0.982839	+	0.184466i	$0.940944\pi$
$114$	−12.9526	−	3.71658i	−1.21312	−	0.348089i
$115$	−8.23754	−	4.81617i	−0.768154	−	0.449110i
$116$	−0.112645			−0.0104588
$117$	3.55740	−	0.819959i	0.328881	−	0.0758053i
$118$	0.961907	+	0.961907i	0.0885507	+	0.0885507i
$119$	3.27871	+	9.13051i	0.300559	+	0.836992i
$120$	3.87195	+	0.0894454i	0.353459	+	0.00816521i
$121$	5.38139	−	9.32083i	0.489217	−	0.847349i
$122$	−1.66768	−	6.22385i	−0.150984	−	0.563481i
$123$	−9.04562	+	15.0484i	−0.815616	+	1.35687i
$124$	−0.333434	−	0.577525i	−0.0299433	−	0.0518633i
$125$	7.77500	+	8.03426i	0.695417	+	0.718606i
$126$	−5.87368	−	5.33853i	−0.523269	−	0.475594i
$127$	−3.24885	−	3.24885i	−0.288289	−	0.288289i	0.548115	−	0.836403i	$-0.315346\pi$
$127$	−3.24885	−	3.24885i	−0.288289	−	0.288289i	−0.836403	+	0.548115i	$0.815346\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	1.73877	−	6.05975i	0.153090	−	0.533532i
$130$	1.91353	+	1.93456i	0.167827	+	0.169672i
$131$	−11.1480	−	6.43628i	−0.974002	−	0.562340i	−0.0735478	−	0.997292i	$-0.523432\pi$
$131$	−11.1480	−	6.43628i	−0.974002	−	0.562340i	−0.900454	+	0.434952i	$0.856765\pi$
$132$	0.843482	+	0.0148728i	0.0734157	+	0.00129451i
$133$	−8.77944	+	18.6175i	−0.761274	+	1.61435i
$134$		−	13.8274i		−	1.19450i
$135$	−7.72266	−	8.68104i	−0.664661	−	0.747145i
$136$			3.66676i			0.314422i
$137$	0.0408575	−	0.152482i	0.00349069	−	0.0130274i	−0.964159	−	0.265327i	$-0.914520\pi$
$137$	0.0408575	−	0.152482i	0.00349069	−	0.0130274i	0.967649	+	0.252299i	$0.0811868\pi$
$138$	−0.130308	+	7.39017i	−0.0110926	+	0.629093i
$139$	3.17401	−	5.49754i	0.269216	−	0.466295i	−0.699444	−	0.714688i	$-0.746569\pi$
$139$	3.17401	−	5.49754i	0.269216	−	0.466295i	0.968660	+	0.248392i	$0.0799022\pi$
$140$	1.08424	−	5.81588i	0.0916348	−	0.491531i
$141$	−1.69712	+	5.91461i	−0.142924	+	0.498100i
$142$	−1.27562	+	4.76068i	−0.107048	+	0.399508i
$143$	0.419102	+	0.419102i	0.0350470	+	0.0350470i
$144$	−1.40747	−	2.64934i	−0.117290	−	0.220779i
$145$	−0.0665205	+	0.242938i	−0.00552422	+	0.0201749i
$146$	−4.07383	+	2.35203i	−0.337152	+	0.194655i
$147$	−9.48919	+	7.54687i	−0.782655	+	0.622455i
$148$	2.31599	+	8.64339i	0.190373	+	0.710482i
$149$	4.18746	+	2.41763i	0.343050	+	0.198060i	0.661620	−	0.749839i	$-0.269869\pi$
$149$	4.18746	+	2.41763i	0.343050	+	0.198060i	−0.318570	+	0.947899i	$0.603203\pi$
$150$	2.47942	−	8.29774i	0.202444	−	0.677507i
$151$	3.95748	+	6.85456i	0.322056	+	0.557817i	0.980912	−	0.194452i	$-0.0622929\pi$
$151$	3.95748	+	6.85456i	0.322056	+	0.557817i	−0.658856	+	0.752269i	$0.728960\pi$
$152$	−5.50124	+	5.50124i	−0.446210	+	0.446210i
$153$	8.04777	−	7.49933i	0.650624	−	0.606284i
$154$	0.229241	−	1.26809i	0.0184727	−	0.102185i
$155$	−1.44244	+	0.378063i	−0.115860	+	0.0303667i
$156$	0.581325	−	2.02596i	0.0465432	−	0.162207i
$157$	0.723257	+	2.69923i	0.0577222	+	0.215422i	0.988763	−	0.149494i	$-0.0477644\pi$
$157$	0.723257	+	2.69923i	0.0577222	+	0.215422i	−0.931040	+	0.364916i	$0.881098\pi$
$158$	2.77348	+	10.3508i	0.220646	+	0.823464i
$159$	11.1770	+	11.5783i	0.886397	+	0.918217i
$160$	1.12860	−	1.93035i	0.0892238	−	0.152608i
$161$	11.1103	+	2.00849i	0.875617	+	0.158291i
$162$	−2.93616	+	8.50758i	−0.230686	+	0.668419i
$163$	6.84447	−	6.84447i	0.536100	−	0.536100i	−0.386281	−	0.922381i	$-0.626241\pi$
$163$	6.84447	−	6.84447i	0.536100	−	0.536100i	0.922381	+	0.386281i	$0.126241\pi$
$164$	5.06851	+	8.77891i	0.395784	+	0.685518i
$165$	0.530181	−	1.81034i	0.0412745	−	0.140935i
$166$	3.18147	+	1.83682i	0.246930	+	0.142565i
$167$	−0.808831	−	3.01860i	−0.0625892	−	0.233586i	0.927544	−	0.373713i	$-0.121916\pi$
$167$	−0.808831	−	3.01860i	−0.0625892	−	0.233586i	−0.990134	+	0.140127i	$0.955249\pi$
$168$	−4.33957	+	1.47247i	−0.334805	+	0.113604i
$169$	−9.97590	+	5.75959i	−0.767377	+	0.443045i
$170$	7.90804	+	2.16535i	0.606519	+	0.166075i
$171$	23.3253	+	0.822829i	1.78373	+	0.0629233i
$172$	−2.57371	−	2.57371i	−0.196244	−	0.196244i
$173$	−2.94333	+	10.9847i	−0.223778	+	0.835149i	0.759113	+	0.650959i	$0.225633\pi$
$173$	−2.94333	+	10.9847i	−0.223778	+	0.835149i	−0.982891	+	0.184190i	$0.941034\pi$
$174$	0.189319	−	0.0471668i	0.0143522	−	0.00357571i
$175$	−11.9027	−	5.77283i	−0.899760	−	0.436385i
$176$	0.243530	−	0.421807i	0.0183568	−	0.0317949i
$177$	−2.01943	−	1.21388i	−0.151789	−	0.0912410i
$178$	−0.554075	+	2.06784i	−0.0415297	+	0.154991i
$179$			15.9719i			1.19380i	0.802317	+	0.596898i	$0.203600\pi$
$179$			15.9719i			1.19380i	−0.802317	+	0.596898i	$0.796400\pi$
$180$	−6.54495	+	1.47094i	−0.487831	+	0.109638i
$181$		−	22.3126i		−	1.65848i	−0.558890	−	0.829242i	$-0.688773\pi$
$181$		−	22.3126i		−	1.65848i	0.558890	−	0.829242i	$-0.311227\pi$
$182$	−2.91204	−	1.37323i	−0.215855	−	0.101790i
$183$	5.40889	+	9.76198i	0.399837	+	0.721627i
$184$	3.69566	+	2.13369i	0.272447	+	0.157298i
$185$	20.0087	+	0.109367i	1.47107	+	0.00804084i
$186$	0.802218	+	0.831016i	0.0588215	+	0.0609331i
$187$	1.72508	+	0.462234i	0.126150	+	0.0338019i
$188$	2.51207	+	2.51207i	0.183211	+	0.183211i
$189$	12.1071	+	6.51290i	0.880663	+	0.473744i
$190$	8.61575	+	15.1131i	0.625052	+	1.09642i
$191$	−6.07741	−	10.5264i	−0.439746	−	0.761663i	0.557923	−	0.829892i	$-0.311598\pi$
$191$	−6.07741	−	10.5264i	−0.439746	−	0.761663i	−0.997670	+	0.0682295i	$0.978265\pi$
$192$	−1.73178	−	0.0305359i	−0.124981	−	0.00220374i
$193$	4.28374	+	15.9871i	0.308350	+	1.15078i	0.930023	+	0.367502i	$0.119787\pi$
$193$	4.28374	+	15.9871i	0.308350	+	1.15078i	−0.621673	+	0.783277i	$0.713547\pi$
$194$	−6.99484	+	12.1154i	−0.502200	+	0.869836i
$195$	−4.02606	−	2.45013i	−0.288312	−	0.175458i
$196$	1.15604	+	6.90388i	0.0825739	+	0.493134i
$197$	−17.4709	−	17.4709i	−1.24475	−	1.24475i	−0.958008	−	0.286741i	$-0.907428\pi$
$197$	−17.4709	−	17.4709i	−1.24475	−	1.24475i	−0.286741	−	0.958008i	$-0.592572\pi$
$198$	−1.42385	+	0.328189i	−0.101188	+	0.0233234i
$199$	−26.3081			−1.86493			−0.932465	−	0.361261i	$-0.882346\pi$
$199$	−26.3081			−1.86493			−0.932465	+	0.361261i	$0.882346\pi$
$200$	−3.49667	−	3.57397i	−0.247252	−	0.252718i
$201$	5.78984	+	23.2394i	0.408384	+	1.63918i
$202$	4.23535	+	15.8065i	0.297998	+	1.11214i
$203$	−0.0246944	−	0.297005i	−0.00173321	−	0.0208456i
$204$	−1.53536	−	6.16264i	−0.107497	−	0.431471i
$205$	21.9264	−	5.74690i	1.53141	−	0.401381i
$206$			0.304418i			0.0212098i
$207$	−2.87542	−	12.4750i	−0.199856	−	0.867075i
$208$	−0.860472	−	0.860472i	−0.0596630	−	0.0596630i
$209$	1.89465	+	3.28163i	0.131056	+	0.226995i
$210$	0.612988	+	10.2286i	0.0423002	+	0.705840i
$211$	−6.44404	+	11.1614i	−0.443626	+	0.768383i	−0.997955	−	0.0639143i	$-0.979642\pi$
$211$	−6.44404	+	11.1614i	−0.443626	+	0.768383i	0.554329	+	0.832298i	$0.312975\pi$
$212$	8.97467	−	2.40476i	0.616383	−	0.165159i
$213$	0.150500	−	8.53530i	0.0103121	−	0.584829i
$214$	−11.7543	+	6.78637i	−0.803510	+	0.463907i
$215$	−7.07054	+	4.03081i	−0.482207	+	0.274899i
$216$	3.47485	+	3.86335i	0.236433	+	0.262867i
$217$	1.44964	−	1.00576i	0.0984078	−	0.0682753i
$218$	14.8512	+	3.97936i	1.00585	+	0.269516i
$219$	5.86194	−	5.65880i	0.396113	−	0.382386i
$220$	−0.765889	−	0.774308i	−0.0516362	−	0.0522038i
$221$	2.23103	−	3.86425i	0.150075	−	0.259938i
$222$	−7.51161	−	13.5570i	−0.504146	−	0.909885i
$223$	0.517933	−	1.93295i	0.0346834	−	0.129440i	−0.946413	−	0.322957i	$-0.895323\pi$
$223$	0.517933	−	1.93295i	0.0346834	−	0.129440i	0.981097	+	0.193517i	$0.0619896\pi$
$224$	−0.470662	+	2.60355i	−0.0314474	+	0.173957i
$225$	−0.692656	+	14.9840i	−0.0461771	+	0.998933i
$226$	1.61996			0.107758
$227$	6.93749	+	1.85890i	0.460458	+	0.123379i	0.481588	−	0.876397i	$-0.340060\pi$
$227$	6.93749	+	1.85890i	0.460458	+	0.123379i	−0.0211309	+	0.999777i	$0.506727\pi$
$228$	6.94231	−	11.5493i	0.459766	−	0.764871i
$229$	−2.38627	+	4.13315i	−0.157689	+	0.273126i	−0.934035	−	0.357181i	$-0.883738\pi$
$229$	−2.38627	+	4.13315i	−0.157689	+	0.273126i	0.776346	+	0.630307i	$0.217071\pi$
$230$	6.78410	−	6.71034i	0.447330	−	0.442466i
$231$	0.145697	+	2.22723i	0.00958616	+	0.146541i
$232$	0.0291546	−	0.108806i	0.00191409	−	0.00714349i
$233$	−20.0083	+	20.0083i	−1.31079	+	1.31079i	−0.389954	+	0.920835i	$0.627509\pi$
$233$	−20.0083	+	20.0083i	−1.31079	+	1.31079i	−0.920835	+	0.389954i	$0.872491\pi$
$234$	−0.128702	+	3.64840i	−0.00841351	+	0.238504i
$235$	6.90119	−	3.93426i	0.450184	−	0.256643i
$236$	−1.17809	+	0.680171i	−0.0766872	+	0.0442754i
$237$	−8.99543	−	16.2350i	−0.584316	−	1.05458i
$238$	−9.66799	+	0.803843i	−0.626683	+	0.0521054i
$239$	−18.5153	−	10.6898i	−1.19766	−	0.691468i	−0.237625	−	0.971357i	$-0.576369\pi$
$239$	−18.5153	−	10.6898i	−1.19766	−	0.691468i	−0.960032	+	0.279889i	$0.909702\pi$
$240$	−1.08853	+	3.71687i	−0.0702644	+	0.239923i
$241$	23.3644	−	13.4895i	1.50504	−	0.868933i	0.505053	−	0.863088i	$-0.331473\pi$
$241$	23.3644	−	13.4895i	1.50504	−	0.868933i	0.999983	−	0.00584474i	$-0.00186045\pi$
$242$	7.61043	+	7.61043i	0.489217	+	0.489217i
$243$	1.37241	−	15.5279i	0.0880400	−	0.996117i
$244$	6.44340			0.412497
$245$	15.5721	+	1.58378i	0.994868	+	0.101184i
$246$	−12.1944	−	12.6322i	−0.777489	−	0.805400i
$247$	9.14473	−	2.45032i	0.581865	−	0.155910i
$248$	0.644146	−	0.172598i	0.0409033	−	0.0109600i
$249$	−6.11614	−	1.75495i	−0.387595	−	0.111215i
$250$	−9.77282	+	5.43065i	−0.618087	+	0.343465i
$251$		−	9.79033i		−	0.617960i	−0.951068	−	0.308980i	$-0.900012\pi$
$251$		−	9.79033i		−	0.617960i	0.951068	−	0.308980i	$-0.0999877\pi$
$252$	6.67685	−	4.29182i	0.420602	−	0.270359i
$253$	1.46970	−	1.46970i	0.0923993	−	0.0923993i
$254$	3.97901	−	2.29728i	0.249665	−	0.144144i
$255$	−14.1975	−	0.327975i	−0.889084	−	0.0205386i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.16386	−	23.0039i	−0.384491	−	1.43494i	−0.838967	−	0.544182i	$-0.816840\pi$
$257$	−6.16386	−	23.0039i	−0.384491	−	1.43494i	0.454476	−	0.890759i	$-0.349827\pi$
$258$	5.40325	+	3.24790i	0.336391	+	0.202206i
$259$	−22.2819	+	8.00130i	−1.38453	+	0.497177i
$260$	−2.36390	+	1.34762i	−0.146603	+	0.0835761i
$261$	−0.298434	+	0.158544i	−0.0184726	+	0.00981365i
$262$	9.10227	−	9.10227i	0.562340	−	0.562340i
$263$	−8.51730	−	2.28220i	−0.525199	−	0.140727i	−0.0135289	−	0.999908i	$-0.504307\pi$
$263$	−8.51730	−	2.28220i	−0.525199	−	0.140727i	−0.511671	+	0.859182i	$0.670973\pi$
$264$	−0.232675	+	0.810892i	−0.0143202	+	0.0499069i
$265$	0.113559	−	20.7756i	0.00697587	−	1.27623i
$266$	−15.7109	−	13.2989i	−0.963295	−	0.815406i
$267$	0.0653707	−	3.70737i	0.00400062	−	0.226887i
$268$	13.3562	+	3.57879i	0.815862	+	0.218610i
$269$	−15.0297			−0.916378			−0.458189	−	0.888855i	$-0.651502\pi$
$269$	−15.0297			−0.916378			−0.458189	+	0.888855i	$0.651502\pi$
$270$	10.3840	−	5.21270i	0.631951	−	0.317235i
$271$			5.21490i			0.316783i	0.987376	+	0.158391i	$0.0506308\pi$
$271$			5.21490i			0.316783i	−0.987376	+	0.158391i	$0.949369\pi$
$272$	−3.54182	−	0.949028i	−0.214755	−	0.0575433i
$273$	5.46920	+	1.08861i	0.331011	+	0.0658858i
$274$	0.136712	+	0.0789307i	0.00825907	+	0.00476838i
$275$	−2.12222	+	1.19452i	−0.127975	+	0.0720324i
$276$	−7.10463	−	2.03858i	−0.427648	−	0.122708i
$277$	−2.46367	+	9.19455i	−0.148028	+	0.552447i	0.851574	+	0.524234i	$0.175648\pi$
$277$	−2.46367	+	9.19455i	−0.148028	+	0.552447i	−0.999602	+	0.0282130i	$0.991018\pi$
$278$	4.48872	+	4.48872i	0.269216	+	0.269216i
$279$	−1.69623	−	1.06076i	−0.101551	−	0.0635062i
$280$	5.33708	+	2.55255i	0.318952	+	0.152544i
$281$	−12.4095	−	21.4939i	−0.740290	−	1.28222i	−0.952363	−	0.304966i	$-0.901355\pi$
$281$	−12.4095	−	21.4939i	−0.740290	−	1.28222i	0.212074	−	0.977254i	$-0.431978\pi$
$282$	−5.27383	−	3.17011i	−0.314052	−	0.188777i
$283$	22.2972	−	5.97451i	1.32543	−	0.355148i	0.474420	−	0.880299i	$-0.342658\pi$
$283$	22.2972	−	5.97451i	1.32543	−	0.355148i	0.851009	+	0.525151i	$0.175991\pi$
$284$	−4.26831	−	2.46431i	−0.253278	−	0.146230i
$285$	−20.8085	−	21.7926i	−1.23259	−	1.29088i
$286$	−0.513292	+	0.296350i	−0.0303516	+	0.0175235i
$287$	−22.0358	+	15.2884i	−1.30073	+	0.902448i
$288$	2.92335	−	0.673815i	0.172260	−	0.0397049i
$289$			3.55484i			0.209108i
$290$	−0.217444	−	0.127131i	−0.0127687	−	0.00746539i
$291$	6.68306	−	23.2910i	0.391768	−	1.36534i
$292$	−1.21750	−	4.54376i	−0.0712487	−	0.265904i
$293$	−19.1674	+	5.13589i	−1.11977	+	0.300042i	−0.770791	−	0.637088i	$-0.780139\pi$
$293$	−19.1674	+	5.13589i	−1.11977	+	0.300042i	−0.348980	+	0.937130i	$0.613472\pi$
$294$	−4.83373	−	11.1191i	−0.281909	−	0.648481i
$295$	0.771209	+	2.94243i	0.0449015	+	0.171315i
$296$	−8.94830			−0.520109
$297$	2.25561	−	1.14778i	0.130884	−	0.0666007i
$298$	−3.41905	+	3.41905i	−0.198060	+	0.198060i
$299$	−2.59647	−	4.49721i	−0.150157	−	0.260080i
$300$	7.37328	+	4.54255i	0.425696	+	0.262264i
$301$	6.22176	−	7.35020i	0.358617	−	0.423659i
$302$	−7.64527	+	2.04854i	−0.439936	+	0.117880i
$303$	−13.7368	−	24.7922i	−0.789158	−	1.42428i
$304$	−3.88997	−	6.73762i	−0.223105	−	0.386429i
$305$	3.80505	−	13.8964i	0.217877	−	0.795703i
$306$	5.16088	+	9.71452i	0.295028	+	0.555342i
$307$	−11.1707	+	11.1707i	−0.637545	+	0.637545i	−0.949949	−	0.312404i	$-0.898866\pi$
$307$	−11.1707	+	11.1707i	−0.637545	+	0.637545i	0.312404	+	0.949949i	$0.398866\pi$
$308$	1.16555	+	0.549635i	0.0664131	+	0.0313183i
$309$	−0.127467	−	0.511628i	−0.00725133	−	0.0291055i
$310$	0.00815055	−	1.49114i	0.000462920	−	0.0846911i
$311$	−1.58350	−	0.914234i	−0.0897920	−	0.0518415i	0.454432	−	0.890782i	$-0.349842\pi$
$311$	−1.58350	−	0.914234i	−0.0897920	−	0.0518415i	−0.544224	+	0.838940i	$0.683176\pi$
$312$	1.80647	+	1.08587i	0.102271	+	0.0614756i
$313$	−5.33710	+	19.9183i	−0.301671	+	1.12585i	0.634103	+	0.773249i	$0.281370\pi$
$313$	−5.33710	+	19.9183i	−0.301671	+	1.12585i	−0.935774	+	0.352601i	$0.885297\pi$
$314$	−2.79445			−0.157700
$315$	−5.31318	−	16.9343i	−0.299364	−	0.954139i
$316$	−10.7159			−0.602817
$317$	−5.17064	+	19.2971i	−0.290412	+	1.08383i	0.654381	+	0.756165i	$0.272929\pi$
$317$	−5.17064	+	19.2971i	−0.290412	+	1.08383i	−0.944793	+	0.327668i	$0.893737\pi$
$318$	−14.0766	+	7.79951i	−0.789376	+	0.437375i
$319$	−0.0475142	−	0.0274324i	−0.00266029	−	0.00153592i
$320$	1.57247	+	1.58976i	0.0879039	+	0.0888701i
$321$	16.9136	−	16.3275i	0.944026	−	0.911312i
$322$	−4.81562	+	10.2119i	−0.268364	+	0.569088i
$323$	20.1718	−	20.1718i	1.12239	−	1.12239i
$324$	−7.45776	−	5.03803i	−0.414320	−	0.279891i
$325$	1.51043	+	5.89399i	0.0837837	+	0.326940i
$326$	4.83977	+	8.38272i	0.268050	+	0.464276i
$327$	−26.6263	−	0.469492i	−1.47244	−	0.0259629i
$328$	−9.79160	+	2.62365i	−0.540651	+	0.144867i
$329$	−6.07275	+	7.17416i	−0.334801	+	0.395524i
$330$	1.61143	+	0.980665i	0.0887064	+	0.0539839i
$331$	0.425902	+	0.737683i	0.0234097	+	0.0405467i	0.877493	−	0.479590i	$-0.159214\pi$
$331$	0.425902	+	0.737683i	0.0234097	+	0.0405467i	−0.854083	+	0.520136i	$0.825881\pi$
$332$	−2.59766	+	2.59766i	−0.142565	+	0.142565i
$333$	18.3012	+	19.6396i	1.00290	+	1.07624i
$334$	3.12508			0.170997
$335$	15.6056	−	26.6917i	0.852626	−	1.45832i
$336$	−0.299135	−	4.57280i	−0.0163192	−	0.249467i
$337$	34.3985	−	9.21704i	1.87380	−	0.502084i	0.873933	−	0.486046i	$-0.161561\pi$
$337$	34.3985	−	9.21704i	1.87380	−	0.502084i	0.999871	−	0.0160380i	$-0.00510528\pi$
$338$	−2.98138	−	11.1267i	−0.162166	−	0.605211i
$339$	−2.72263	+	0.678314i	−0.147873	+	0.0368409i
$340$	−4.13832	+	7.07814i	−0.224432	+	0.383866i
$341$		−	0.324805i		−	0.0175892i
$342$	−6.83182	+	22.3175i	−0.369423	+	1.20679i
$343$	−17.9497	+	4.56156i	−0.969193	+	0.246301i
$344$	3.15214	−	1.81989i	0.169952	−	0.0981218i
$345$	−8.59210	+	14.1186i	−0.462583	+	0.760117i
$346$	−9.84859	−	5.68608i	−0.529463	−	0.305686i
$347$	−12.9622	+	3.47320i	−0.695846	+	0.186451i	−0.589369	−	0.807864i	$-0.700624\pi$
$347$	−12.9622	+	3.47320i	−0.695846	+	0.186451i	−0.106477	+	0.994315i	$0.533957\pi$
$348$	−0.00343970	+	0.195076i	−0.000184388	+	0.0104572i
$349$	−15.3836	−	26.6452i	−0.823466	−	1.42629i	−0.903086	−	0.429460i	$-0.858704\pi$
$349$	−15.3836	−	26.6452i	−0.823466	−	1.42629i	0.0796196	−	0.996825i	$-0.474629\pi$
$350$	8.65677	−	10.0030i	0.462724	−	0.534684i
$351$	−1.31136	−	6.18567i	−0.0699953	−	0.330167i
$352$	0.344404	+	0.344404i	0.0183568	+	0.0183568i
$353$	5.78984	−	21.6080i	0.308162	−	1.15008i	−0.622027	−	0.782996i	$-0.713691\pi$
$353$	5.78984	−	21.6080i	0.308162	−	1.15008i	0.930189	−	0.367081i	$-0.119643\pi$
$354$	1.69519	−	1.63644i	0.0900981	−	0.0869758i
$355$	−7.83531	+	7.75012i	−0.415855	+	0.411334i
$356$	−1.85397	−	1.07039i	−0.0982603	−	0.0567306i
$357$	15.9122	−	5.39920i	0.842161	−	0.285756i
$358$	−15.4277	−	4.13383i	−0.815377	−	0.218480i
$359$			15.8380i			0.835896i	0.908471	+	0.417948i	$0.137251\pi$
$359$			15.8380i			0.835896i	−0.908471	+	0.417948i	$0.862749\pi$
$360$	0.273133	−	6.70264i	0.0143954	−	0.353260i
$361$	41.5273			2.18565
$362$	21.5523	+	5.77493i	1.13277	+	0.303524i
$363$	−15.9773	−	9.60401i	−0.838592	−	0.504080i
$364$	2.08013	−	2.45740i	0.109028	−	0.128803i
$365$	−10.5184	−	0.0574935i	−0.550559	−	0.00300935i
$366$	−10.8293	+	2.69800i	−0.566055	+	0.141027i
$367$	35.1228	+	9.41111i	1.83339	+	0.491256i	0.998269	−	0.0588063i	$-0.0187294\pi$
$367$	35.1228	+	9.41111i	1.83339	+	0.491256i	0.835123	+	0.550062i	$0.185396\pi$
$368$	−3.01749	+	3.01749i	−0.157298	+	0.157298i
$369$	25.7843	+	16.1246i	1.34228	+	0.839411i
$370$	−5.28427	+	19.2986i	−0.274716	+	1.00329i
$371$	8.30797	+	23.1359i	0.431328	+	1.20116i
$372$	−1.01033	+	0.559800i	−0.0523831	+	0.0290243i
$373$	1.12353	+	4.19306i	0.0581741	+	0.217109i	0.988894	−	0.148625i	$-0.0474848\pi$
$373$	1.12353	+	4.19306i	0.0581741	+	0.217109i	−0.930720	+	0.365734i	$0.880818\pi$
$374$	−0.892968	+	1.54667i	−0.0461743	+	0.0799762i
$375$	14.1510	−	13.2193i	0.730755	−	0.682640i
$376$	−3.07664	+	1.77630i	−0.158666	+	0.0916057i
$377$	−0.0969275	+	0.0969275i	−0.00499202	+	0.00499202i
$378$	−9.42453	+	10.0089i	−0.484746	+	0.514803i
$379$			14.7134i			0.755778i	0.925851	+	0.377889i	$0.123350\pi$
$379$			14.7134i			0.755778i	−0.925851	+	0.377889i	$0.876650\pi$
$380$	−16.8280	+	4.41062i	−0.863261	+	0.226260i
$381$	−5.72550	+	5.52709i	−0.293326	+	0.283161i
$382$	11.7407	−	3.14590i	0.600705	−	0.160958i
$383$	14.7349	−	3.94821i	0.752920	−	0.201744i	0.138107	−	0.990417i	$-0.455898\pi$
$383$	14.7349	−	3.94821i	0.752920	−	0.201744i	0.614813	+	0.788673i	$0.289232\pi$
$384$	0.477713	−	1.66487i	0.0243782	−	0.0849600i
$385$	1.87368	−	2.18913i	0.0954916	−	0.111568i
$386$	−16.5511			−0.842428
$387$	−10.4411	−	3.19621i	−0.530750	−	0.162473i
$388$	−9.89219	−	9.89219i	−0.502200	−	0.502200i
$389$	−24.9706	+	14.4168i	−1.26606	+	0.730960i	−0.974240	−	0.225513i	$-0.927594\pi$
$389$	−24.9706	+	14.4168i	−1.26606	+	0.730960i	−0.291820	+	0.956473i	$0.594261\pi$
$390$	3.40867	−	3.25474i	0.172605	−	0.164810i
$391$	−13.5511	−	7.82373i	−0.685309	−	0.395663i
$392$	−6.96784	−	0.670212i	−0.351929	−	0.0338508i
$393$	−11.4866	+	19.1093i	−0.579424	+	0.963936i
$394$	21.3974	−	12.3538i	1.07798	−	0.622374i
$395$	−6.32811	+	23.1108i	−0.318402	+	1.16283i
$396$	0.0515130	−	1.46027i	0.00258862	−	0.0733815i
$397$	9.32289	−	9.32289i	0.467902	−	0.467902i	−0.433332	−	0.901234i	$-0.642662\pi$
$397$	9.32289	−	9.32289i	0.467902	−	0.467902i	0.901234	+	0.433332i	$0.142662\pi$
$398$	6.80903	−	25.4116i	0.341306	−	1.27377i
$399$	31.9734	+	15.7726i	1.60067	+	0.789617i
$400$	4.35720	−	2.45252i	0.217860	−	0.122626i
$401$	−17.7778	+	30.7920i	−0.887780	+	1.53768i	−0.0452860	+	0.998974i	$0.514420\pi$
$401$	−17.7778	+	30.7920i	−0.887780	+	1.53768i	−0.842494	+	0.538706i	$0.818913\pi$
$402$	−23.9460	−	0.422232i	−1.19432	−	0.0210590i
$403$	−0.783855	−	0.210033i	−0.0390466	−	0.0104625i
$404$	−16.3641			−0.814146
$405$	−15.2695	+	13.1089i	−0.758747	+	0.651385i
$406$	0.293276	+	0.0530175i	0.0145550	+	0.00263122i
$407$	−1.12803	+	4.20985i	−0.0559142	+	0.208675i
$408$	6.35004	+	0.111968i	0.314374	+	0.00554324i
$409$	6.70383	−	11.6114i	0.331483	−	0.574146i	−0.651320	−	0.758803i	$-0.725784\pi$
$409$	6.70383	−	11.6114i	0.331483	−	0.574146i	0.982803	+	0.184658i	$0.0591177\pi$
$410$	−0.123896	+	22.6667i	−0.00611878	+	1.11943i
$411$	−0.262818	−	0.0754125i	−0.0129639	−	0.00371982i
$412$	−0.294045	−	0.0787891i	−0.0144866	−	0.00388166i
$413$	−2.05164	−	2.95711i	−0.100955	−	0.145510i
$414$	12.7942	+	0.451331i	0.628799	+	0.0221817i
$415$	4.06831	+	7.13633i	0.199706	+	0.350308i
$416$	1.05386	−	0.608445i	0.0516696	−	0.0298315i
$417$	−9.42362	−	5.66456i	−0.461477	−	0.277395i
$418$	−3.66018	+	0.980742i	−0.179025	+	0.0479697i
$419$	−6.22294	+	10.7785i	−0.304011	+	0.526562i	−0.977041	−	0.213053i	$-0.931659\pi$
$419$	−6.22294	+	10.7785i	−0.304011	+	0.526562i	0.673030	+	0.739615i	$0.264993\pi$
$420$	−10.0387	−	2.05526i	−0.489839	−	0.100286i
$421$	−17.2735	−	29.9186i	−0.841860	−	1.45814i	−0.888320	−	0.459225i	$-0.848127\pi$
$421$	−17.2735	−	29.9186i	−0.841860	−	1.45814i	0.0464598	−	0.998920i	$-0.485206\pi$
$422$	−9.11326	−	9.11326i	−0.443626	−	0.443626i
$423$	10.1910	+	3.11966i	0.495503	+	0.151683i
$424$			9.29126i			0.451224i
$425$	12.8215	+	13.1049i	0.621933	+	0.635682i
$426$	8.20551	+	2.35447i	0.397558	+	0.114074i
$427$	1.41255	+	16.9890i	0.0683580	+	0.822157i
$428$	−3.51288	−	13.1103i	−0.169802	−	0.633708i
$429$	0.738590	−	0.712995i	0.0356595	−	0.0344237i
$430$	−2.06347	−	7.87286i	−0.0995095	−	0.379663i
$431$	31.7630			1.52997			0.764985	−	0.644048i	$-0.222746\pi$
$431$	31.7630			1.52997			0.764985	+	0.644048i	$0.222746\pi$
$432$	−4.63106	+	2.35654i	−0.222812	+	0.113379i
$433$	8.28438	+	8.28438i	0.398122	+	0.398122i	0.877570	−	0.479448i	$-0.159163\pi$
$433$	8.28438	+	8.28438i	0.398122	+	0.398122i	−0.479448	+	0.877570i	$0.659163\pi$
$434$	0.596294	+	1.66055i	0.0286230	+	0.0797090i
$435$	0.418685	+	0.122617i	0.0200744	+	0.00587905i
$436$	−7.68753	+	13.3152i	−0.368166	+	0.637682i
$437$	−8.59277	−	32.0686i	−0.411048	−	1.53405i
$438$	3.94880	+	7.12680i	0.188681	+	0.340532i
$439$	−10.8395	−	18.7745i	−0.517340	−	0.896059i	−0.999797	−	0.0201396i	$-0.993589\pi$
$439$	−10.8395	−	18.7745i	−0.517340	−	0.896059i	0.482457	−	0.875920i	$-0.339744\pi$
$440$	0.946151	−	0.539386i	0.0451060	−	0.0257142i
$441$	12.7798	+	16.6637i	0.608560	+	0.793508i
$442$	3.15515	+	3.15515i	0.150075	+	0.150075i
$443$	0.473613	+	0.126904i	0.0225020	+	0.00602940i	0.270052	−	0.962846i	$-0.412959\pi$
$443$	0.473613	+	0.126904i	0.0225020	+	0.00602940i	−0.247550	+	0.968875i	$0.579626\pi$
$444$	15.0392	−	3.74685i	0.713728	−	0.177818i
$445$	−3.40332	+	3.36632i	−0.161333	+	0.159579i
$446$	1.73304	+	1.00057i	0.0820617	+	0.0473784i
$447$	4.31467	−	7.17794i	0.204077	−	0.339505i
$448$	−2.39302	−	1.12847i	−0.113060	−	0.0533153i
$449$		−	35.0637i		−	1.65476i	−0.561644	−	0.827379i	$-0.689831\pi$
$449$		−	35.0637i		−	1.65476i	0.561644	−	0.827379i	$-0.310169\pi$
$450$	−14.2942	−	4.54720i	−0.673833	−	0.214357i
$451$			4.93734i			0.232490i
$452$	−0.419276	+	1.56476i	−0.0197211	+	0.0736002i
$453$	11.9915	−	6.64419i	0.563408	−	0.312171i
$454$	−3.59111	+	6.21999i	−0.168539	+	0.291918i
$455$	−4.07144	−	5.93735i	−0.190872	−	0.278347i
$456$	9.35897	+	9.69494i	0.438274	+	0.454007i
$457$	2.49108	−	9.29682i	0.116528	−	0.434887i	−0.882869	−	0.469619i	$-0.844391\pi$
$457$	2.49108	−	9.29682i	0.116528	−	0.434887i	0.999397	+	0.0347322i	$0.0110578\pi$
$458$	−3.37470	−	3.37470i	−0.157689	−	0.157689i
$459$	−12.7414	−	14.1660i	−0.594720	−	0.661211i
$460$	4.72583	+	8.28970i	0.220343	+	0.386509i
$461$	−16.9342	+	9.77695i	−0.788703	+	0.455358i	−0.839506	−	0.543351i	$-0.817155\pi$
$461$	−16.9342	+	9.77695i	−0.788703	+	0.455358i	0.0508028	+	0.998709i	$0.483822\pi$
$462$	−2.18905	−	0.435717i	−0.101844	−	0.0202714i
$463$	−2.28225	−	8.51747i	−0.106065	−	0.395841i	0.892399	−	0.451248i	$-0.149021\pi$
$463$	−2.28225	−	8.51747i	−0.106065	−	0.395841i	−0.998464	+	0.0554072i	$0.982354\pi$
$464$	0.0975531	+	0.0563223i	0.00452879	+	0.00261470i
$465$	0.610676	+	2.50954i	0.0283194	+	0.116377i
$466$	−14.1480	−	24.5051i	−0.655394	−	1.13518i
$467$	11.0943	−	11.0943i	0.513383	−	0.513383i	−0.402178	−	0.915561i	$-0.631747\pi$
$467$	11.0943	−	11.0943i	0.513383	−	0.513383i	0.915561	+	0.402178i	$0.131747\pi$
$468$	−3.49078	−	1.06859i	−0.161361	−	0.0493957i
$469$	−6.50803	+	36.0003i	−0.300513	+	1.66234i
$470$	2.01405	+	7.68430i	0.0929012	+	0.354450i
$471$	4.69657	−	1.17010i	0.216406	−	0.0539154i
$472$	−0.352082	−	1.31399i	−0.0162059	−	0.0604813i
$473$	−0.458832	−	1.71238i	−0.0210971	−	0.0787355i
$474$	18.0100	−	4.48699i	0.827225	−	0.206094i
$475$	−0.425237	+	38.8973i	−0.0195112	+	1.78473i
$476$	1.72581	−	9.54661i	0.0791022	−	0.437568i
$477$	20.3923	−	19.0026i	0.933701	−	0.870071i
$478$	15.1177	−	15.1177i	0.691468	−	0.691468i
$479$	12.2905	+	21.2877i	0.561566	+	0.972660i	0.997360	+	0.0726142i	$0.0231342\pi$
$479$	12.2905	+	21.2877i	0.561566	+	0.972660i	−0.435794	+	0.900046i	$0.643532\pi$
$480$	−3.30848	−	2.01344i	−0.151011	−	0.0919004i
$481$	9.43024	+	5.44455i	0.429982	+	0.248250i
$482$	6.98266	+	26.0596i	0.318052	+	1.18698i
$483$	3.81753	−	19.1793i	0.173704	−	0.872690i
$484$	−9.32083	+	5.38139i	−0.423674	+	0.244608i
$485$	−27.1760	+	15.4926i	−1.23400	+	0.703484i
$486$	14.6436	+	5.34457i	0.664248	+	0.242434i
$487$	−17.1768	−	17.1768i	−0.778357	−	0.778357i	0.201194	−	0.979551i	$-0.435518\pi$
$487$	−17.1768	−	17.1768i	−0.778357	−	0.778357i	−0.979551	+	0.201194i	$0.935518\pi$
$488$	−1.66768	+	6.22385i	−0.0754921	+	0.281740i
$489$	−11.6441	−	12.0621i	−0.526565	−	0.545468i
$490$	−5.56018	+	14.6316i	−0.251183	+	0.660989i
$491$	−16.9452	+	29.3500i	−0.764728	+	1.32455i	0.175663	+	0.984450i	$0.443793\pi$
$491$	−16.9452	+	29.3500i	−0.764728	+	1.32455i	−0.940391	+	0.340097i	$0.889540\pi$
$492$	15.3579	−	8.50948i	0.692389	−	0.383637i
$493$	−0.106903	+	0.398967i	−0.00481467	+	0.0179686i
$494$			9.46732i			0.425955i
$495$	−3.11892	−	0.973438i	−0.140185	−	0.0437528i
$496$			0.666869i			0.0299433i
$497$	5.56182	−	11.7943i	0.249482	−	0.529046i
$498$	3.27812	−	5.45352i	0.146896	−	0.244378i
$499$	10.9508	+	6.32247i	0.490227	+	0.283033i	0.724669	−	0.689098i	$-0.241993\pi$
$499$	10.9508	+	6.32247i	0.490227	+	0.283033i	−0.234442	+	0.972130i	$0.575326\pi$
$500$	−2.71622	−	10.8454i	−0.121473	−	0.485020i
$501$	−5.25225	+	1.30854i	−0.234653	+	0.0584614i
$502$	9.45674	+	2.53392i	0.422075	+	0.113095i
$503$	3.78527	+	3.78527i	0.168777	+	0.168777i	0.786442	−	0.617665i	$-0.211921\pi$
$503$	3.78527	+	3.78527i	0.168777	+	0.168777i	−0.617665	+	0.786442i	$0.711921\pi$
$504$	2.41749	+	7.56014i	0.107683	+	0.336756i
$505$	−9.66357	+	35.2922i	−0.430023	+	1.57048i
$506$	1.03924	+	1.80001i	0.0461996	+	0.0800201i
$507$	9.66973	+	17.4520i	0.429448	+	0.775069i
$508$	1.18916	+	4.43801i	0.0527605	+	0.196905i
$509$	−8.64582	+	14.9750i	−0.383219	+	0.663755i	−0.991520	−	0.129951i	$-0.958518\pi$
$509$	−8.64582	+	14.9750i	−0.383219	+	0.663755i	0.608301	+	0.793706i	$0.291851\pi$
$510$	3.99139	−	13.6289i	0.176742	−	0.603497i
$511$	11.7134	−	4.20622i	0.518172	−	0.186072i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	2.13722	−	40.3692i	0.0943605	−	1.78234i
$514$	23.8153			1.05045
$515$	−0.343567	+	0.587634i	−0.0151394	+	0.0258942i
$516$	−4.53570	+	4.37851i	−0.199673	+	0.192753i
$517$	0.447842	+	1.67137i	0.0196961	+	0.0735068i
$518$	−1.96168	−	23.5936i	−0.0861913	−	1.03664i
$519$	18.9332	+	5.43264i	0.831074	+	0.238466i
$520$	−0.689883	−	2.63214i	−0.0302534	−	0.115427i
$521$			20.8241i			0.912322i	0.889897	+	0.456161i	$0.150776\pi$
$521$			20.8241i			0.912322i	−0.889897	+	0.456161i	$0.849224\pi$
$522$	−0.0759017	−	0.329300i	−0.00332213	−	0.0144131i
$523$	17.0957	+	17.0957i	0.747544	+	0.747544i	0.974017	−	0.226473i	$-0.0727196\pi$
$523$	17.0957	+	17.0957i	0.747544	+	0.747544i	−0.226473	+	0.974017i	$0.572720\pi$
$524$	6.43628	+	11.1480i	0.281170	+	0.487001i
$525$	−10.3607	+	20.4366i	−0.452180	+	0.891927i
$526$	4.40888	−	7.63641i	0.192236	−	0.332963i
$527$	−2.36193	+	0.632877i	−0.102887	+	0.0275686i
$528$	−0.723041	−	0.434621i	−0.0314663	−	0.0189145i
$529$	4.14782	−	2.39474i	0.180340	−	0.104119i
$530$	20.0383	+	5.48681i	0.870407	+	0.238332i
$531$	−2.16384	+	3.46014i	−0.0939028	+	0.150157i
$532$	16.9120	−	11.7335i	0.733228	−	0.508713i
$533$	11.9153	+	3.19270i	0.516109	+	0.138291i
$534$	3.56412	+	1.02268i	0.154235	+	0.0442557i
$535$	−30.3491	−	0.165888i	−1.31211	−	0.00717195i
$536$	−6.91370	+	11.9749i	−0.298626	+	0.517236i
$537$	27.6598	+	0.487716i	1.19361	+	0.0210465i
$538$	3.88997	−	14.5176i	0.167709	−	0.625897i
$539$	−1.19368	+	3.19363i	−0.0514154	+	0.137559i
$540$	2.34750	+	11.3793i	0.101020	+	0.489689i
$541$	−9.75934			−0.419587			−0.209793	−	0.977746i	$-0.567279\pi$
$541$	−9.75934			−0.419587			−0.209793	+	0.977746i	$0.567279\pi$
$542$	−5.03721	−	1.34972i	−0.216367	−	0.0579753i
$543$	−38.6406	−	0.681336i	−1.65823	−	0.0292389i
$544$	1.83338	−	3.17551i	0.0786056	−	0.136149i
$545$	24.1769	+	24.4426i	1.03562	+	1.04701i
$546$	−2.46705	+	5.00109i	−0.105580	+	0.214027i
$547$	−6.71061	+	25.0443i	−0.286925	+	1.07082i	0.660496	+	0.750830i	$0.270346\pi$
$547$	−6.71061	+	25.0443i	−0.286925	+	1.07082i	−0.947421	+	0.319989i	$0.896321\pi$
$548$	−0.111625	+	0.111625i	−0.00476838	+	0.00476838i
$549$	17.0708	−	9.06893i	0.728563	−	0.387052i
$550$	−0.604550	−	2.35907i	−0.0257781	−	0.100591i
$551$	−0.758956	+	0.438184i	−0.0323326	+	0.0186673i
$552$	3.80793	−	6.33492i	0.162076	−	0.269632i
$553$	−2.34918	−	28.2541i	−0.0998975	−	1.20149i
$554$	−8.24361	−	4.75945i	−0.350237	−	0.202210i
$555$	0.800384	−	34.6474i	0.0339744	−	1.47070i
$556$	−5.49754	+	3.17401i	−0.233148	+	0.134608i
$557$	−8.05216	−	8.05216i	−0.341181	−	0.341181i	0.515630	−	0.856811i	$-0.327558\pi$
$557$	−8.05216	−	8.05216i	−0.341181	−	0.341181i	−0.856811	+	0.515630i	$0.827558\pi$
$558$	1.46363	−	1.36389i	0.0619606	−	0.0577381i
$559$	−4.42921			−0.187336
$560$	−3.84692	+	4.49458i	−0.162562	+	0.189931i
$561$	0.853165	−	2.97335i	0.0360207	−	0.125535i
$562$	23.9733	−	6.42364i	1.01125	−	0.270965i
$563$	−28.4212	+	7.61545i	−1.19781	+	0.320953i	−0.801969	−	0.597365i	$-0.796214\pi$
$563$	−28.4212	+	7.61545i	−1.19781	+	0.320953i	−0.395843	+	0.918318i	$0.629548\pi$
$564$	4.42706	−	4.27364i	0.186413	−	0.179953i
$565$	3.12709	+	1.82829i	0.131558	+	0.0769167i
$566$			23.0837i			0.970282i
$567$	11.6486	−	20.7680i	0.489196	−	0.872174i
$568$	3.48506	−	3.48506i	0.146230	−	0.146230i
$569$	−5.82551	+	3.36336i	−0.244218	+	0.140999i	−0.617114	−	0.786874i	$-0.711698\pi$
$569$	−5.82551	+	3.36336i	−0.244218	+	0.140999i	0.372896	+	0.927873i	$0.378365\pi$
$570$	26.4357	−	14.4591i	1.10727	−	0.605625i
$571$	−11.2574	+	19.4983i	−0.471106	+	0.815979i	−0.999454	−	0.0330487i	$-0.989478\pi$
$571$	−11.2574	+	19.4983i	−0.471106	+	0.815979i	0.528348	+	0.849028i	$0.322812\pi$
$572$	−0.153402	−	0.572503i	−0.00641405	−	0.0239376i
$573$	−18.4150	+	10.2033i	−0.769297	+	0.426250i
$574$	−9.06422	−	25.2419i	−0.378333	−	1.05358i
$575$	20.6690	−	5.29676i	0.861956	−	0.220890i
$576$	−0.105763	+	2.99814i	−0.00440679	+	0.124922i
$577$	−11.9758	+	11.9758i	−0.498557	+	0.498557i	−0.910989	−	0.412431i	$-0.864680\pi$
$577$	−11.9758	+	11.9758i	−0.498557	+	0.498557i	0.412431	+	0.910989i	$0.364680\pi$
$578$	−3.43371	−	0.920060i	−0.142824	−	0.0382694i
$579$	27.8170	−	6.93032i	1.15604	−	0.288014i
$580$	0.179078	−	0.177131i	0.00743579	−	0.00735495i
$581$	−7.41860	−	6.27966i	−0.307775	−	0.260524i
$582$	20.7677	+	12.4835i	0.860847	+	0.517457i
$583$	4.37121	+	1.17126i	0.181037	+	0.0485087i
$584$	4.70405			0.194655
$585$	−4.36603	+	6.89745i	−0.180513	+	0.285174i
$586$		−	19.8435i		−	0.819729i
$587$	−17.8369	−	4.77938i	−0.736208	−	0.197266i	−0.128816	−	0.991669i	$-0.541118\pi$
$587$	−17.8369	−	4.77938i	−0.736208	−	0.197266i	−0.607392	+	0.794402i	$0.707784\pi$
$588$	11.9913	−	1.79118i	0.494514	−	0.0738672i
$589$	−4.49311	−	2.59410i	−0.185135	−	0.106888i
$590$	−3.04177	−	0.0166263i	−0.125228	−	0.000684493i
$591$	−30.7892	+	29.7223i	−1.26650	+	1.22261i
$592$	2.31599	−	8.64339i	0.0951866	−	0.355241i
$593$	16.2084	+	16.2084i	0.665600	+	0.665600i	0.956694	−	0.291095i	$-0.0940195\pi$
$593$	16.2084	+	16.2084i	0.665600	+	0.665600i	−0.291095	+	0.956694i	$0.594019\pi$
$594$	0.524873	+	2.47581i	0.0215358	+	0.101584i
$595$	−19.5698	−	9.35961i	−0.802285	−	0.383707i
$596$	−2.41763	−	4.18746i	−0.0990300	−	0.171525i
$597$	−0.803341	+	45.5598i	−0.0328785	+	1.86464i
$598$	5.01599	−	1.34403i	0.205119	−	0.0549615i
$599$	7.60798	+	4.39247i	0.310854	+	0.179472i	0.647308	−	0.762228i	$-0.275895\pi$
$599$	7.60798	+	4.39247i	0.310854	+	0.179472i	−0.336455	+	0.941700i	$0.609228\pi$
$600$	−6.29611	+	5.94634i	−0.257038	+	0.242758i
$601$	−4.29376	+	2.47901i	−0.175146	+	0.101121i	−0.585010	−	0.811026i	$-0.698910\pi$
$601$	−4.29376	+	2.47901i	−0.175146	+	0.101121i	0.409864	+	0.912147i	$0.365576\pi$
$602$	5.48944	+	7.91214i	0.223733	+	0.322475i
$603$	40.4223	−	9.31711i	1.64612	−	0.379422i
$604$		−	7.91497i		−	0.322056i
$605$	6.10166	+	23.2800i	0.248068	+	0.946465i
$606$	27.5028	−	6.85203i	1.11722	−	0.278345i
$607$	−7.79474	−	29.0904i	−0.316379	−	1.18074i	−0.922699	−	0.385521i	$-0.874022\pi$
$607$	−7.79474	−	29.0904i	−0.316379	−	1.18074i	0.606320	−	0.795221i	$-0.292645\pi$
$608$	7.51484	−	2.01359i	0.304767	−	0.0816620i
$609$	−0.515102	+	0.0336960i	−0.0208730	+	0.00136543i
$610$	12.4380	+	7.27204i	0.503601	+	0.294436i
$611$	4.32312			0.174895
$612$	−10.7192	+	2.47072i	−0.433299	+	0.0998730i
$613$	8.92430	−	8.92430i	0.360449	−	0.360449i	−0.503529	−	0.863978i	$-0.667965\pi$
$613$	8.92430	−	8.92430i	0.360449	−	0.360449i	0.863978	+	0.503529i	$0.167965\pi$
$614$	−7.89887	−	13.6812i	−0.318773	−	0.552130i
$615$	−9.28284	−	38.1473i	−0.374320	−	1.53825i
$616$	−0.832572	+	0.983575i	−0.0335453	+	0.0396294i
$617$	5.65909	−	1.51635i	0.227826	−	0.0610458i	−0.143100	−	0.989708i	$-0.545707\pi$
$617$	5.65909	−	1.51635i	0.227826	−	0.0610458i	0.370926	+	0.928662i	$0.379040\pi$
$618$	0.527185	+	0.00929567i	0.0212065	+	0.000373927i
$619$	6.72545	+	11.6488i	0.270319	+	0.468206i	0.968943	−	0.247283i	$-0.0795376\pi$
$619$	6.72545	+	11.6488i	0.270319	+	0.468206i	−0.698625	+	0.715488i	$0.746204\pi$
$620$	1.43822	+	0.393809i	0.0577604	+	0.0158157i
$621$	−21.6918	+	4.59867i	−0.870464	+	0.184538i
$622$	1.29292	−	1.29292i	0.0518415	−	0.0518415i
$623$	2.41581	−	5.12294i	0.0967876	−	0.205246i
$624$	−1.51642	+	1.46387i	−0.0607055	+	0.0586018i
$625$	−24.9940	−	0.546549i	−0.999761	−	0.0218620i
$626$	−17.8583	−	10.3105i	−0.713760	−	0.412090i
$627$	5.74092	−	3.18091i	0.229270	−	0.127033i
$628$	0.723257	−	2.69923i	0.0288611	−	0.107711i
$629$	32.8113			1.30827
$630$	17.7324	−	0.749222i	0.706476	−	0.0298497i
$631$	5.44170			0.216631			0.108315	−	0.994117i	$-0.465454\pi$
$631$	5.44170			0.216631			0.108315	+	0.994117i	$0.465454\pi$
$632$	2.77348	−	10.3508i	0.110323	−	0.411732i
$633$	19.1324	+	11.5005i	0.760443	+	0.457104i
$634$	−17.3013	−	9.98891i	−0.687123	−	0.396710i
$635$	10.2736	+	0.0561553i	0.407695	+	0.00222846i
$636$	−3.89046	−	15.6156i	−0.154267	−	0.619199i
$637$	6.93533	+	4.94586i	0.274788	+	0.195962i
$638$	0.0387952	−	0.0387952i	0.00153592	−	0.00153592i
$639$	−14.7767	−	0.521266i	−0.584556	−	0.0206210i
$640$	−1.94257	+	1.10743i	−0.0767870	+	0.0437751i
$641$	−3.73637	−	6.47159i	−0.147578	−	0.255612i	0.782754	−	0.622331i	$-0.213814\pi$
$641$	−3.73637	−	6.47159i	−0.147578	−	0.255612i	−0.930332	+	0.366719i	$0.880481\pi$
$642$	11.3936	+	20.5632i	0.449669	+	0.811563i
$643$	−23.8223	+	6.38317i	−0.939461	+	0.251728i	−0.695884	−	0.718154i	$-0.744987\pi$
$643$	−23.8223	+	6.38317i	−0.939461	+	0.251728i	−0.243576	+	0.969882i	$0.578321\pi$
$644$	−8.61759	−	7.29457i	−0.339580	−	0.287446i
$645$	6.76457	+	12.3677i	0.266355	+	0.486978i
$646$	14.2636	+	24.7053i	0.561193	+	0.972015i
$647$	24.0593	−	24.0593i	0.945868	−	0.945868i	−0.0527407	−	0.998608i	$-0.516796\pi$
$647$	24.0593	−	24.0593i	0.945868	−	0.945868i	0.998608	+	0.0527407i	$0.0167957\pi$
$648$	6.79658	−	5.89971i	0.266995	−	0.231762i
$649$	−0.662569			−0.0260081
$650$	−6.08409	−	0.0665130i	−0.238638	−	0.00260886i
$651$	−1.69749	−	2.54117i	−0.0665298	−	0.0995961i
$652$	−9.34971	+	2.50525i	−0.366163	+	0.0981131i
$653$	−3.19874	−	11.9379i	−0.125176	−	0.467164i	0.874670	−	0.484720i	$-0.161078\pi$
$653$	−3.19874	−	11.9379i	−0.125176	−	0.467164i	−0.999846	+	0.0175552i	$0.994412\pi$
$654$	7.34488	−	25.5975i	0.287207	−	1.00094i
$655$	27.8434	−	7.29774i	1.08793	−	0.285146i
$656$		−	10.1370i		−	0.395784i
$657$	−9.62080	−	10.3244i	−0.375343	−	0.402793i
$658$	−5.35796	−	7.72263i	−0.208875	−	0.301059i
$659$	36.5922	−	21.1265i	1.42543	−	0.822971i	0.428673	−	0.903460i	$-0.358981\pi$
$659$	36.5922	−	21.1265i	1.42543	−	0.822971i	0.996756	+	0.0804885i	$0.0256480\pi$
$660$	−1.36432	+	1.30271i	−0.0531061	+	0.0507079i
$661$	−26.4831	−	15.2900i	−1.03007	−	0.594713i	−0.113067	−	0.993587i	$-0.536067\pi$
$661$	−26.4831	−	15.2900i	−1.03007	−	0.594713i	−0.917005	+	0.398875i	$0.869401\pi$
$662$	−0.822779	+	0.220463i	−0.0319782	+	0.00856853i
$663$	−6.62391	−	3.98165i	−0.257251	−	0.154634i
$664$	−1.83682	−	3.18147i	−0.0712825	−	0.123465i
$665$	−15.3184	−	43.4028i	−0.594022	−	1.68309i
$666$	−23.7071	+	12.5945i	−0.918632	+	0.488027i
$667$	0.339904	+	0.339904i	0.0131611	+	0.0131611i
$668$	−0.808831	+	3.01860i	−0.0312946	+	0.116793i
$669$	−3.33164	−	0.955972i	−0.128809	−	0.0369600i
$670$	21.7432	+	21.9822i	0.840013	+	0.849246i
$671$	2.71787	+	1.56916i	0.104922	+	0.0605769i
$672$	4.49441	+	0.894586i	0.173376	+	0.0345094i
$673$	−3.03721	−	0.813818i	−0.117076	−	0.0313704i	0.199805	−	0.979836i	$-0.435969\pi$
$673$	−3.03721	−	0.813818i	−0.117076	−	0.0313704i	−0.316881	+	0.948465i	$0.602636\pi$
$674$			35.6119i			1.37172i
$675$	25.9279	+	1.65708i	0.997964	+	0.0637810i
$676$	11.5192			0.443045
$677$	−17.8878	−	4.79301i	−0.687482	−	0.184210i	−0.101865	−	0.994798i	$-0.532481\pi$
$677$	−17.8878	−	4.79301i	−0.687482	−	0.184210i	−0.585617	+	0.810588i	$0.699148\pi$
$678$	0.0494669	−	2.80542i	0.00189977	−	0.107741i
$679$	23.9137	−	28.2509i	0.917723	−	1.08417i
$680$	−5.76589	−	5.82927i	−0.221112	−	0.223542i
$681$	3.43104	−	11.9575i	0.131478	−	0.458211i
$682$	0.313738	+	0.0840658i	0.0120136	+	0.00321905i
$683$	−17.7878	+	17.7878i	−0.680630	+	0.680630i	−0.960142	−	0.279512i	$-0.909827\pi$
$683$	−17.7878	+	17.7878i	−0.680630	+	0.680630i	0.279512	+	0.960142i	$0.409827\pi$
$684$	−19.7889	−	12.3752i	−0.756647	−	0.473179i
$685$	0.174821	+	0.306657i	0.00667956	+	0.0117168i
$686$	0.239598	−	18.5187i	0.00914791	−	0.707048i
$687$	7.08484	+	4.25871i	0.270304	+	0.162480i
$688$	0.942044	+	3.51575i	0.0359151	+	0.134037i
$689$	5.65322	−	9.79167i	0.215371	−	0.373033i
$690$	−11.4137	−	11.9535i	−0.434511	−	0.455061i
$691$	13.6499	−	7.88080i	0.519268	−	0.299800i	−0.217367	−	0.976090i	$-0.569747\pi$
$691$	13.6499	−	7.88080i	0.519268	−	0.299800i	0.736635	+	0.676290i	$0.236414\pi$
$692$	8.04134	−	8.04134i	0.305686	−	0.305686i
$693$	3.86153	−	0.184305i	0.146687	−	0.00700116i
$694$		−	13.4194i		−	0.509395i
$695$	3.59883	+	13.7308i	0.136512	+	0.520839i
$696$	−0.187539	−	0.0538118i	−0.00710863	−	0.00203973i
$697$	35.9035	−	9.62031i	1.35994	−	0.364395i
$698$	29.7189	−	7.96315i	1.12488	−	0.301410i
$699$	34.0391	+	35.2610i	1.28748	+	1.33369i
$700$	7.42163	+	10.9508i	0.280511	+	0.413900i
$701$	−0.834053			−0.0315017			−0.0157509	−	0.999876i	$-0.505014\pi$
$701$	−0.834053			−0.0315017			−0.0157509	+	0.999876i	$0.505014\pi$
$702$	6.31431	+	0.334291i	0.238318	+	0.0126170i
$703$	49.2268	+	49.2268i	1.85662	+	1.85662i
$704$	−0.421807	+	0.243530i	−0.0158974	+	0.00917839i
$705$	−6.60255	−	12.0715i	−0.248667	−	0.454638i
$706$	19.3732	+	11.1851i	0.729119	+	0.420957i
$707$	−3.58741	−	43.1465i	−0.134918	−	1.62269i
$708$	1.14193	+	2.06097i	0.0429165	+	0.0774558i
$709$	32.0420	−	18.4995i	1.20336	−	0.694761i	0.242061	−	0.970261i	$-0.422177\pi$
$709$	32.0420	−	18.4995i	1.20336	−	0.694761i	0.961301	+	0.275500i	$0.0888433\pi$
$710$	−5.45812	−	9.57421i	−0.204839	−	0.359314i
$711$	−28.3901	+	15.0824i	−1.06471	+	0.565633i
$712$	1.51376	−	1.51376i	0.0567306	−	0.0567306i
$713$	−0.736542	+	2.74881i	−0.0275837	+	0.102944i
$714$	1.09686	+	16.7674i	0.0410489	+	0.627504i
$715$	−1.32530	−	0.00724404i	−0.0495632	−	0.000270912i
$716$	7.98595	−	13.8321i	0.298449	−	0.516929i
$717$	−19.0778	+	31.7381i	−0.712475	+	1.18528i
$718$	−15.2983	−	4.09917i	−0.570928	−	0.152980i
$719$	−27.9794			−1.04346			−0.521728	−	0.853112i	$-0.674712\pi$
$719$	−27.9794			−1.04346			−0.521728	+	0.853112i	$0.674712\pi$
$720$	6.40356	+	1.99860i	0.238647	+	0.0744833i
$721$	0.143278	−	0.792567i	0.00533595	−	0.0295168i
$722$	−10.7481	+	40.1123i	−0.400002	+	1.49283i
$723$	−22.6474	−	40.8740i	−0.842264	−	1.52012i
$724$	−11.1563	+	19.3233i	−0.414621	+	0.718145i
$725$	−0.276263	−	0.490815i	−0.0102601	−	0.0182284i
$726$	13.4120	−	12.9472i	0.497766	−	0.480516i
$727$	24.1115	+	6.46065i	0.894246	+	0.239612i	0.676543	−	0.736403i	$-0.263477\pi$
$727$	24.1115	+	6.46065i	0.894246	+	0.239612i	0.217702	+	0.976015i	$0.430144\pi$
$728$	1.83529	+	2.64527i	0.0680204	+	0.0980403i
$729$	−26.8491	−	2.85087i	−0.994410	−	0.105588i
$730$	2.77790	−	10.1451i	0.102815	−	0.375488i
$731$	−11.5582	+	6.67310i	−0.427494	+	0.246814i
$732$	0.196755	−	11.1586i	0.00727228	−	0.412433i
$733$	−8.30597	+	2.22558i	−0.306788	+	0.0822036i	−0.408929	−	0.912566i	$-0.634098\pi$
$733$	−8.30597	+	2.22558i	−0.306788	+	0.0822036i	0.102141	+	0.994770i	$0.467431\pi$
$734$	−18.1809	+	31.4902i	−0.671068	+	1.16232i
$735$	3.21827	−	26.9192i	0.118708	−	0.992929i
$736$	−2.13369	−	3.69566i	−0.0786488	−	0.136224i
$737$	4.76220	+	4.76220i	0.175418	+	0.175418i
$738$	−22.2486	+	20.7324i	−0.818982	+	0.763170i
$739$			40.2971i			1.48235i	0.671310	+	0.741177i	$0.265732\pi$
$739$			40.2971i			1.48235i	−0.671310	+	0.741177i	$0.734268\pi$
$740$	−17.2734	−	10.0991i	−0.634981	−	0.371249i
$741$	−3.96418	−	15.9115i	−0.145628	−	0.584524i
$742$	−24.4978	+	2.03687i	−0.899344	+	0.0747758i
$743$	−8.45176	−	31.5424i	−0.310065	−	1.15718i	−0.928497	−	0.371340i	$-0.878898\pi$
$743$	−8.45176	−	31.5424i	−0.310065	−	1.15718i	0.618432	−	0.785838i	$-0.287768\pi$
$744$	−0.279233	−	1.12079i	−0.0102372	−	0.0410902i
$745$	−10.4587	+	2.74122i	−0.383177	+	0.100430i
$746$	−4.34098			−0.158934
$747$	−3.22595	+	10.5382i	−0.118031	+	0.385574i
$748$	−1.26285	−	1.26285i	−0.0461743	−	0.0461743i
$749$	33.7971	−	12.1363i	1.23492	−	0.443452i
$750$	9.10629	+	17.0902i	0.332515	+	0.624047i
$751$	−17.1975	+	29.7869i	−0.627545	+	1.08694i	0.360498	+	0.932760i	$0.382607\pi$
$751$	−17.1975	+	29.7869i	−0.627545	+	1.08694i	−0.988043	+	0.154180i	$0.950727\pi$
$752$	−0.919481	−	3.43155i	−0.0335300	−	0.125136i
$753$	−16.9547	−	0.298957i	−0.617864	−	0.0108946i
$754$	−0.0685381	−	0.118711i	−0.00249601	−	0.00432322i
$755$	−17.0701	−	4.67406i	−0.621243	−	0.170106i
$756$	−7.22861	−	11.6939i	−0.262902	−	0.425303i
$757$	22.4964	+	22.4964i	0.817647	+	0.817647i	0.985767	−	0.168120i	$-0.0537695\pi$
$757$	22.4964	+	22.4964i	0.817647	+	0.817647i	−0.168120	+	0.985767i	$0.553769\pi$
$758$	−14.2121	−	3.80812i	−0.516206	−	0.138317i
$759$	−2.50032	−	2.59008i	−0.0907559	−	0.0940139i
$760$	0.0950873	−	17.3962i	0.00344918	−	0.631026i
$761$	37.0555	+	21.3940i	1.34326	+	0.775533i	0.987285	−	0.158962i	$-0.0508148\pi$
$761$	37.0555	+	21.3940i	1.34326	+	0.775533i	0.355977	+	0.934495i	$0.384148\pi$
$762$	−3.85689	−	6.96092i	−0.139720	−	0.252168i
$763$	−36.7929	−	17.3504i	−1.33199	−	0.628125i
$764$			12.1548i			0.439746i
$765$	−1.00152	+	24.5770i	−0.0362099	+	0.888584i
$766$			15.2547i			0.551176i
$767$	−0.428446	+	1.59898i	−0.0154703	+	0.0577359i
$768$	1.48450	+	0.892336i	0.0535672	+	0.0321994i
$769$	8.76918	−	15.1887i	0.316225	−	0.547718i	−0.663472	−	0.748201i	$-0.730918\pi$
$769$	8.76918	−	15.1887i	0.316225	−	0.547718i	0.979697	+	0.200483i	$0.0642513\pi$
$770$	1.62959	+	2.37642i	0.0587265	+	0.0856404i
$771$	−40.0259	+	9.97202i	−1.44150	+	0.359134i
$772$	4.28374	−	15.9871i	0.154175	−	0.575389i
$773$	−30.8909	−	30.8909i	−1.11107	−	1.11107i	−0.993006	−	0.118061i	$-0.962332\pi$
$773$	−30.8909	−	30.8909i	−1.11107	−	1.11107i	−0.118061	−	0.993006i	$-0.537668\pi$
$774$	5.78965	−	9.25806i	0.208105	−	0.332774i
$775$	1.69864	−	2.86923i	0.0610169	−	0.103066i
$776$	12.1154	−	6.99484i	0.434918	−	0.251100i
$777$	13.1761	+	38.8317i	0.472690	+	1.39308i
$778$	−7.46268	−	27.8511i	−0.267550	−	0.998510i
$779$	68.2993	+	39.4326i	2.44708	+	1.41282i
$780$	2.26161	+	4.13491i	0.0809785	+	0.148053i
$781$	−1.20027	−	2.07893i	−0.0429490	−	0.0743898i
$782$	11.0644	−	11.0644i	0.395663	−	0.395663i
$783$	0.265451	+	0.521664i	0.00948645	+	0.0186428i
$784$	2.45078	−	6.55695i	0.0875280	−	0.234177i
$785$	−5.39427	−	3.15382i	−0.192530	−	0.112565i
$786$	−15.4852	−	16.0411i	−0.552339	−	0.572167i
$787$	−3.46100	−	12.9166i	−0.123371	−	0.460429i	0.876405	−	0.481575i	$-0.159935\pi$
$787$	−3.46100	−	12.9166i	−0.123371	−	0.460429i	−0.999776	+	0.0211463i	$0.993268\pi$
$788$	6.39479	+	23.8657i	0.227805	+	0.850179i
$789$	−4.21236	+	14.6804i	−0.149964	+	0.522637i
$790$	−20.6855	−	12.0940i	−0.735956	−	0.430285i
$791$	−4.21765	−	0.762453i	−0.149962	−	0.0271097i
$792$	1.39718	+	0.427704i	0.0496467	+	0.0151978i
$793$	5.54437	−	5.54437i	0.196886	−	0.196886i
$794$	6.59228	+	11.4182i	0.233951	+	0.405215i
$795$	−35.9753	−	0.831061i	−1.27591	−	0.0294747i
$796$	22.7835	+	13.1540i	0.807538	+	0.466232i
$797$	−2.95248	−	11.0188i	−0.104582	−	0.390306i	0.893715	−	0.448635i	$-0.148090\pi$
$797$	−2.95248	−	11.0188i	−0.104582	−	0.390306i	−0.998297	+	0.0583287i	$0.981423\pi$
$798$	−23.5105	+	26.8017i	−0.832262	+	0.948770i
$799$	11.2813	−	6.51327i	0.399104	−	0.230423i
$800$	1.24122	+	4.84349i	0.0438838	+	0.171243i
$801$	−6.41835	−	0.226416i	−0.226781	−	0.00800000i
$802$	−25.1416	−	25.1416i	−0.887780	−	0.887780i
$803$	0.592995	−	2.21309i	0.0209263	−	0.0780982i
$804$	6.60553	−	23.0208i	0.232959	−	0.811881i
$805$	−20.8210	+	14.2777i	−0.733845	+	0.503222i
$806$	0.405753	−	0.702785i	0.0142920	−	0.0247545i
$807$	−0.458946	+	26.0282i	−0.0161557	+	0.916235i
$808$	4.23535	−	15.8065i	0.148999	−	0.556072i
$809$		−	5.36557i		−	0.188643i	−0.995542	−	0.0943217i	$-0.969932\pi$
$809$		−	5.36557i		−	0.188643i	0.995542	−	0.0943217i	$-0.0300682\pi$
$810$	−8.71017	−	18.1420i	−0.306044	−	0.637446i
$811$			7.85355i			0.275776i	0.990448	+	0.137888i	$0.0440313\pi$
$811$			7.85355i			0.275776i	−0.990448	+	0.137888i	$0.955969\pi$
$812$	−0.127116	+	0.269561i	−0.00446091	+	0.00945973i
$813$	9.03107	+	0.159242i	0.316733	+	0.00558485i
$814$	−3.77445	−	2.17918i	−0.132294	−	0.0763802i
$815$	−0.118304	+	21.6438i	−0.00414403	+	0.758148i
$816$	−1.75166	+	6.10468i	−0.0613205	+	0.213707i
$817$	−27.3523	−	7.32904i	−0.956937	−	0.256410i
$818$	9.48065	+	9.48065i	0.331483	+	0.331483i
$819$	2.05225	−	9.43823i	0.0717113	−	0.329798i
$820$	−21.8623	−	5.98625i	−0.763465	−	0.209049i
$821$	−7.85403	−	13.6036i	−0.274108	−	0.474768i	0.695802	−	0.718234i	$-0.255049\pi$
$821$	−7.85403	−	13.6036i	−0.274108	−	0.474768i	−0.969910	+	0.243465i	$0.921716\pi$
$822$	0.140865	−	0.234345i	0.00491324	−	0.00817372i
$823$	6.03923	+	22.5387i	0.210514	+	0.785651i	0.987698	+	0.156376i	$0.0499812\pi$
$823$	6.03923	+	22.5387i	0.210514	+	0.785651i	−0.777183	+	0.629274i	$0.783352\pi$
$824$	0.152209	−	0.263634i	0.00530245	−	0.00918411i
$825$	2.00385	+	3.71169i	0.0697651	+	0.129225i
$826$	3.38735	−	1.21638i	0.117861	−	0.0423232i
$827$	27.3145	+	27.3145i	0.949818	+	0.949818i	0.998800	−	0.0489817i	$-0.0155976\pi$
$827$	27.3145	+	27.3145i	0.949818	+	0.949818i	−0.0489817	+	0.998800i	$0.515598\pi$
$828$	−3.74733	+	12.2414i	−0.130229	+	0.425418i
$829$	−53.3023			−1.85127			−0.925634	−	0.378421i	$-0.876467\pi$
$829$	−53.3023			−1.85127			−0.925634	+	0.378421i	$0.876467\pi$
$830$	−7.94612	+	2.08267i	−0.275814	+	0.0722906i
$831$	15.8477	+	4.54731i	0.549752	+	0.157744i
$832$	0.314954	+	1.17543i	0.0109191	+	0.0407506i
$833$	25.5494	+	2.45751i	0.885235	+	0.0851476i
$834$	7.91056	−	7.63642i	0.273920	−	0.264428i
$835$	6.03251	+	3.52697i	0.208764	+	0.122056i
$836$		−	3.78930i		−	0.131056i
$837$	−1.88880	+	2.90511i	−0.0652866	+	0.100415i
$838$	−8.80057	−	8.80057i	−0.304011	−	0.304011i
$839$	−15.1177	−	26.1847i	−0.521922	−	0.903995i	−0.999675	−	0.0255005i	$-0.991882\pi$
$839$	−15.1177	−	26.1847i	−0.521922	−	0.903995i	0.477753	−	0.878494i	$-0.341451\pi$
$840$	4.58344	−	9.16472i	0.158144	−	0.316213i
$841$	−14.4937	+	25.1037i	−0.499781	+	0.865646i
$842$	33.3699	−	8.94144i	1.15000	−	0.308142i
$843$	−37.6017	+	20.8342i	−1.29507	+	0.717569i
$844$	11.1614	−	6.44404i	0.384192	−	0.221813i
$845$	6.80247	−	24.8432i	0.234012	−	0.854631i
$846$	−5.65098	+	9.03632i	−0.194285	+	0.310675i
$847$	−16.2322	−	23.3961i	−0.557745	−	0.803899i
$848$	−8.97467	−	2.40476i	−0.308191	−	0.0825797i
$849$	−9.66568	−	38.7963i	−0.331725	−	1.33148i
$850$	−15.9768	+	8.99280i	−0.548000	+	0.308450i
$851$	19.0929	−	33.0698i	0.654496	−	1.13362i
$852$	−4.39799	+	7.31653i	−0.150672	+	0.250660i
$853$	−5.85219	+	21.8407i	−0.200375	+	0.747810i	0.790435	+	0.612546i	$0.209855\pi$
$853$	−5.85219	+	21.8407i	−0.200375	+	0.747810i	−0.990810	+	0.135263i	$0.956812\pi$
$854$	−16.7757	−	3.03267i	−0.574054	−	0.103776i
$855$	−38.3754	+	35.3703i	−1.31241	+	1.20964i
$856$	13.5727			0.463907
$857$	−19.7488	−	5.29166i	−0.674605	−	0.180760i	−0.0947765	−	0.995499i	$-0.530214\pi$
$857$	−19.7488	−	5.29166i	−0.674605	−	0.180760i	−0.579828	+	0.814739i	$0.696880\pi$
$858$	0.497539	+	0.897960i	0.0169857	+	0.0306558i
$859$	−11.6587	+	20.1934i	−0.397788	+	0.688990i	−0.993453	−	0.114244i	$-0.963556\pi$
$859$	−11.6587	+	20.1934i	−0.397788	+	0.688990i	0.595664	+	0.803234i	$0.296889\pi$
$860$	8.13867	+	0.0444858i	0.277526	+	0.00151695i
$861$	25.8034	+	38.6281i	0.879376	+	1.31644i
$862$	−8.22087	+	30.6807i	−0.280004	+	1.04499i
$863$	10.4509	−	10.4509i	0.355754	−	0.355754i	−0.506491	−	0.862245i	$-0.669058\pi$
$863$	10.4509	−	10.4509i	0.355754	−	0.355754i	0.862245	+	0.506491i	$0.169058\pi$
$864$	−1.07763	−	5.08318i	−0.0366618	−	0.172933i
$865$	−12.5939	−	22.0913i	−0.428206	−	0.751126i
$866$	−10.1462	+	5.85794i	−0.344784	+	0.199061i
$867$	6.15620	+	0.108550i	0.209076	+	0.00368656i
$868$	−1.75830	+	0.146194i	−0.0596806	+	0.00496213i
$869$	−4.52004	−	2.60965i	−0.153332	−	0.0885262i
$870$	−0.226803	+	0.372683i	−0.00768934	+	0.0126351i
$871$	14.5721	−	8.41321i	0.493757	−	0.285071i
$872$	−10.8718	−	10.8718i	−0.368166	−	0.368166i
$873$	−40.1308	−	12.2848i	−1.35822	−	0.415778i
$874$	33.1999			1.12300
$875$	28.0000	−	9.53929i	0.946574	−	0.322487i
$876$	−7.90599	+	1.96969i	−0.267118	+	0.0665498i
$877$	32.2929	−	8.65285i	1.09045	−	0.292186i	0.331581	−	0.943427i	$-0.392418\pi$
$877$	32.2929	−	8.65285i	1.09045	−	0.292186i	0.758871	+	0.651241i	$0.225751\pi$
$878$	20.9403	−	5.61093i	0.706700	−	0.189360i
$879$	8.30894	+	33.3506i	0.280254	+	1.12489i
$880$	0.276126	+	1.05351i	0.00930819	+	0.0355140i
$881$		−	16.9840i		−	0.572205i	−0.958199	−	0.286102i	$-0.907640\pi$
$881$		−	16.9840i		−	0.572205i	0.958199	−	0.286102i	$-0.0923597\pi$
$882$	−19.4035	+	8.03144i	−0.653350	+	0.270433i
$883$	16.5052	−	16.5052i	0.555444	−	0.555444i	−0.372563	−	0.928007i	$-0.621521\pi$
$883$	16.5052	−	16.5052i	0.555444	−	0.555444i	0.928007	+	0.372563i	$0.121521\pi$
$884$	−3.86425	+	2.23103i	−0.129969	+	0.0750375i
$885$	5.11920	−	1.24572i	0.172080	−	0.0418743i
$886$	−0.245160	+	0.424630i	−0.00823631	+	0.0142657i
$887$	13.1435	+	49.0524i	0.441317	+	1.64702i	0.725481	+	0.688242i	$0.241617\pi$
$887$	13.1435	+	49.0524i	0.441317	+	1.64702i	−0.284164	+	0.958776i	$0.591716\pi$
$888$	−0.273244	+	15.4965i	−0.00916948	+	0.520028i
$889$	−11.4408	+	4.10832i	−0.383712	+	0.137789i
$890$	−2.37077	−	4.15863i	−0.0794685	−	0.139397i
$891$	−1.91882	−	3.94127i	−0.0642829	−	0.132037i
$892$	−1.41502	+	1.41502i	−0.0473784	+	0.0473784i
$893$	26.6972	+	7.15350i	0.893388	+	0.239383i
$894$	5.81664	+	6.02544i	0.194537	+	0.201521i
$895$	−25.1154	−	25.3914i	−0.839514	−	0.848742i
$896$	1.70938	−	2.01941i	0.0571064	−	0.0674638i
$897$	−7.86747	+	4.35918i	−0.262687	+	0.145549i
$898$	33.8689	+	9.07515i	1.13022	+	0.302842i
$899$	0.0751192			0.00250536
$900$	8.09186	−	12.6302i	0.269729	−	0.421007i
$901$		−	34.0689i		−	1.13500i
$902$	−4.76910	−	1.27788i	−0.158794	−	0.0425486i
$903$	−12.5390	−	10.9992i	−0.417270	−	0.366030i
$904$	−1.40293	−	0.809980i	−0.0466606	−	0.0269395i
$905$	35.0860	+	35.4717i	1.16630	+	1.17912i
$906$	3.31418	+	13.3025i	0.110106	+	0.441946i
$907$	−8.63285	+	32.2182i	−0.286649	+	1.06979i	0.660977	+	0.750406i	$0.270142\pi$
$907$	−8.63285	+	32.2182i	−0.286649	+	1.06979i	−0.947626	+	0.319382i	$0.896525\pi$
$908$	−5.07860	−	5.07860i	−0.168539	−	0.168539i
$909$	−43.3542	+	23.0321i	−1.43797	+	0.763926i
$910$	6.78881	−	2.39601i	0.225047	−	0.0794270i
$911$	−0.375681	−	0.650698i	−0.0124469	−	0.0215586i	0.859735	−	0.510741i	$-0.170629\pi$
$911$	−0.375681	−	0.650698i	−0.0124469	−	0.0215586i	−0.872182	+	0.489182i	$0.837295\pi$
$912$	−11.7869	+	6.53083i	−0.390302	+	0.216257i
$913$	−1.72832	+	0.463101i	−0.0571990	+	0.0153264i
$914$	8.33530	+	4.81239i	0.275707	+	0.159180i
$915$	−23.9493	−	7.01385i	−0.791739	−	0.231871i
$916$	4.13315	−	2.38627i	0.136563	−	0.0788447i
$917$	−27.9823	+	19.4141i	−0.924057	+	0.641111i
$918$	16.9810	−	8.64087i	0.560457	−	0.285191i
$919$		−	13.3584i		−	0.440654i	−0.975426	−	0.220327i	$-0.929288\pi$
$919$		−	13.3584i		−	0.440654i	0.975426	−	0.220327i	$-0.0707125\pi$
$920$	−9.23037	+	2.41927i	−0.304316	+	0.0797611i
$921$	19.0041	+	19.6863i	0.626206	+	0.648686i
$922$	−5.06092	−	18.8876i	−0.166673	−	0.622030i
$923$	−5.79323	+	1.55229i	−0.190687	+	0.0510943i
$924$	0.987438	−	2.00169i	0.0324843	−	0.0658507i
$925$	−31.9810	+	31.2893i	−1.05153	+	1.02878i
$926$	8.81794			0.289775
$927$	−0.889920	+	0.205121i	−0.0292288	+	0.00673707i
$928$	−0.0796518	+	0.0796518i	−0.00261470	+	0.00261470i
$929$	−10.5954	−	18.3518i	−0.347624	−	0.602103i	0.638203	−	0.769868i	$-0.279678\pi$
$929$	−10.5954	−	18.3518i	−0.347624	−	0.602103i	−0.985827	+	0.167765i	$0.946345\pi$
$930$	−2.58208	−	0.0596483i	−0.0846698	−	0.00195595i
$931$	34.6448	+	42.0188i	1.13544	+	1.37711i
$932$	27.3319	−	7.32355i	0.895285	−	0.239891i
$933$	−1.63161	+	2.71436i	−0.0534164	+	0.0888641i
$934$	7.84485	+	13.5877i	0.256691	+	0.444603i
$935$	−3.46931	+	1.97780i	−0.113459	+	0.0646811i
$936$	1.93566	−	3.09526i	0.0632690	−	0.101172i
$937$	−41.2273	+	41.2273i	−1.34684	+	1.34684i	−0.457763	+	0.889074i	$0.651349\pi$
$937$	−41.2273	+	41.2273i	−1.34684	+	1.34684i	−0.889074	+	0.457763i	$0.848651\pi$
$938$	−33.0892	−	15.6038i	−1.08040	−	0.509483i
$939$	34.3312	+	9.85091i	1.12036	+	0.321472i
$940$	−7.94374	−	0.0434203i	−0.259096	−	0.00141621i
$941$	7.42601	+	4.28741i	0.242081	+	0.139765i	0.616133	−	0.787642i	$-0.288698\pi$
$941$	7.42601	+	4.28741i	0.242081	+	0.139765i	−0.374052	+	0.927408i	$0.622032\pi$
$942$	−0.0853311	+	4.83938i	−0.00278024	+	0.157675i
$943$	11.1961	−	41.7845i	0.364596	−	1.36069i
$944$	1.36034			0.0442754
$945$	−29.4887	+	8.68416i	−0.959269	+	0.282496i
$946$	1.77279			0.0576384
$947$	1.33385	−	4.97800i	0.0433443	−	0.161763i	−0.940861	−	0.338792i	$-0.889982\pi$
$947$	1.33385	−	4.97800i	0.0433443	−	0.161763i	0.984206	+	0.177029i	$0.0566485\pi$
$948$	−0.327220	+	18.5576i	−0.0106276	+	0.602723i
$949$	−4.95740	−	2.86216i	−0.160924	−	0.0929096i
$950$	−37.4619	−	10.4781i	−1.21542	−	0.339955i
$951$	33.2605	+	9.54368i	1.07854	+	0.309475i
$952$	8.77464	+	4.13785i	0.284388	+	0.134108i
$953$	12.2301	−	12.2301i	0.396170	−	0.396170i	−0.480709	−	0.876880i	$-0.659621\pi$
$953$	12.2301	−	12.2301i	0.396170	−	0.396170i	0.876880	+	0.480709i	$0.159621\pi$
$954$	13.0772	+	24.6157i	0.423390	+	0.796964i
$955$	26.2141	+	7.17784i	0.848268	+	0.232269i
$956$	10.6898	+	18.5153i	0.345734	+	0.598829i
$957$	−0.0489577	+	0.0814466i	−0.00158258	+	0.00263280i
$958$	−23.7434	+	6.36201i	−0.767113	+	0.205547i
$959$	−0.318787	−	0.269845i	−0.0102942	−	0.00871375i
$960$	2.80113	−	2.67463i	0.0904061	−	0.0863235i
$961$	−15.2776	−	26.4617i	−0.492827	−	0.853602i
$962$	−7.69975	+	7.69975i	−0.248250	+	0.248250i
$963$	−27.7592	−	29.7893i	−0.894527	−	0.959946i
$964$	−26.9789			−0.868933
$965$	−31.9494	−	18.6796i	−1.02849	−	0.601317i
$966$	17.5378	+	8.65143i	0.564269	+	0.278355i
$967$	−41.0127	+	10.9893i	−1.31888	+	0.353393i	−0.848558	−	0.529102i	$-0.822529\pi$
$967$	−41.0127	+	10.9893i	−1.31888	+	0.353393i	−0.470322	+	0.882495i	$0.655862\pi$
$968$	−2.78561	−	10.3960i	−0.0895329	−	0.334141i
$969$	−34.3171	−	35.5490i	−1.10242	−	1.14200i
$970$	−7.93106	−	30.2598i	−0.254651	−	0.971582i
$971$		−	46.8590i		−	1.50378i	−0.659291	−	0.751888i	$-0.729143\pi$
$971$		−	46.8590i		−	1.50378i	0.659291	−	0.751888i	$-0.270857\pi$
$972$	−8.95250	+	12.7614i	−0.287152	+	0.409321i
$973$	−9.57395	−	13.7993i	−0.306927	−	0.442385i
$974$	21.0373	−	12.1459i	0.674077	−	0.389179i
$975$	10.2532	−	2.43576i	0.328366	−	0.0780067i
$976$	−5.58015	−	3.22170i	−0.178616	−	0.103124i
$977$	38.7128	−	10.3731i	1.23853	−	0.331864i	0.420636	−	0.907230i	$-0.361807\pi$
$977$	38.7128	−	10.3731i	1.23853	−	0.331864i	0.817896	+	0.575366i	$0.195140\pi$
$978$	14.6648	−	8.12545i	0.468930	−	0.259823i
$979$	−0.521345	−	0.902996i	−0.0166623	−	0.0288599i
$980$	−12.6940	−	9.15766i	−0.405494	−	0.292531i
$981$	−1.62611	+	46.0965i	−0.0519178	+	1.47175i
$982$	−23.9642	−	23.9642i	−0.764728	−	0.764728i
$983$	−13.1972	+	49.2528i	−0.420927	+	1.57092i	0.351733	+	0.936100i	$0.385593\pi$
$983$	−13.1972	+	49.2528i	−0.420927	+	1.57092i	−0.772660	+	0.634820i	$0.781074\pi$
$984$	4.24460	+	17.0370i	0.135313	+	0.543121i
$985$	55.2470	+	0.301979i	1.76031	+	0.00962185i
$986$	−0.357704	−	0.206521i	−0.0113916	−	0.00657696i
$987$	12.2386	+	10.7357i	0.389560	+	0.341722i
$988$	−9.14473	−	2.45032i	−0.290933	−	0.0779552i
$989$			15.5323i			0.493898i
$990$	1.74750	−	2.76070i	0.0555393	−	0.0877409i
$991$	14.9527			0.474989			0.237495	−	0.971389i	$-0.423674\pi$
$991$	14.9527			0.474989			0.237495	+	0.971389i	$0.423674\pi$
$992$	−0.644146	−	0.172598i	−0.0204516	−	0.00548000i
$993$	1.29051	−	0.715043i	0.0409531	−	0.0226912i
$994$	9.95291	+	8.42489i	0.315687	+	0.267221i
$995$	41.8235	−	41.3687i	1.32589	−	1.31148i
$996$	4.41926	+	4.57790i	0.140029	+	0.145056i
$997$	−3.81157	−	1.02131i	−0.120714	−	0.0323451i	0.197956	−	0.980211i	$-0.436570\pi$
$997$	−3.81157	−	1.02131i	−0.120714	−	0.0323451i	−0.318670	+	0.947866i	$0.603236\pi$
$998$	−8.94132	+	8.94132i	−0.283033	+	0.283033i
$999$	34.5704	−	31.0940i	1.09376	−	0.983770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bz.a.517.13	yes	192
5.3	odd	4	inner	630.2.bz.a.13.48	yes	192
7.6	odd	2	inner	630.2.bz.a.517.12	yes	192
9.7	even	3	inner	630.2.bz.a.97.25	yes	192
35.13	even	4	inner	630.2.bz.a.13.25	✓	192
45.43	odd	12	inner	630.2.bz.a.223.12	yes	192
63.34	odd	6	inner	630.2.bz.a.97.48	yes	192
315.223	even	12	inner	630.2.bz.a.223.13	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bz.a.13.25	✓	192	35.13	even	4	inner
630.2.bz.a.13.48	yes	192	5.3	odd	4	inner
630.2.bz.a.97.25	yes	192	9.7	even	3	inner
630.2.bz.a.97.48	yes	192	63.34	odd	6	inner
630.2.bz.a.223.12	yes	192	45.43	odd	12	inner
630.2.bz.a.223.13	yes	192	315.223	even	12	inner
630.2.bz.a.517.12	yes	192	7.6	odd	2	inner
630.2.bz.a.517.13	yes	192	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.0305359 - 1.73178i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.58976 + 1.57247i) q^{5} +(1.66487 + 0.477713i) q^{6} +(1.12847 - 2.39302i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.99814 - 0.105763i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.0305359 - 1.73178i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.58976 + 1.57247i) q^{5} +(1.66487 + 0.477713i) q^{6} +(1.12847 - 2.39302i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.99814 - 0.105763i) q^{9} +(-1.10743 - 1.94257i) q^{10} +(-0.243530 - 0.421807i) q^{11} +(-0.892336 + 1.48450i) q^{12} +(-1.17543 + 0.314954i) q^{13} +(2.01941 + 1.70938i) q^{14} +(2.67463 + 2.80113i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.59279 + 2.59279i) q^{17} +(0.878134 - 2.86860i) q^{18} -7.77993 q^{19} +(2.16301 - 0.566923i) q^{20} +(-4.10973 - 2.02734i) q^{21} +(0.470464 - 0.126060i) q^{22} +(1.10448 + 4.12197i) q^{23} +(-1.20296 - 1.24615i) q^{24} +(0.0546582 - 4.99970i) q^{25} -1.21689i q^{26} +(-0.274709 + 5.18889i) q^{27} +(-2.17380 + 1.50818i) q^{28} +(0.0975531 - 0.0563223i) q^{29} +(-3.39793 + 1.85851i) q^{30} +(0.577525 + 0.333434i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.737913 + 0.408861i) q^{33} +(-1.83338 - 3.17551i) q^{34} +(1.96896 + 5.57882i) q^{35} +(2.54358 + 1.59066i) q^{36} +(-6.32740 - 6.32740i) q^{37} +(2.01359 - 7.51484i) q^{38} +(0.509540 + 2.04520i) q^{39} +(-0.0122221 + 2.23603i) q^{40} +(-8.77891 - 5.06851i) q^{41} +(3.02194 - 3.44498i) q^{42} +(3.51575 + 0.942044i) q^{43} +0.487060i q^{44} +(4.93262 - 4.54635i) q^{45} -4.26738 q^{46} +(-3.43155 - 0.919481i) q^{47} +(1.51503 - 0.839446i) q^{48} +(-4.45310 - 5.40092i) q^{49} +(4.81519 + 1.34681i) q^{50} +(4.41098 + 4.56933i) q^{51} +(1.17543 + 0.314954i) q^{52} +(-6.56992 + 6.56992i) q^{53} +(-4.94098 - 1.60833i) q^{54} +(1.05043 + 0.287626i) q^{55} +(-0.894170 - 2.49007i) q^{56} +(-0.237567 + 13.4731i) q^{57} +(0.0291546 + 0.108806i) q^{58} +(0.680171 - 1.17809i) q^{59} +(-0.915737 - 3.76317i) q^{60} +(-5.58015 + 3.22170i) q^{61} +(-0.471547 + 0.471547i) q^{62} +(-3.63641 + 7.05525i) q^{63} -1.00000i q^{64} +(1.37338 - 2.34903i) q^{65} +(-0.203943 - 0.818591i) q^{66} +(-13.3562 + 3.57879i) q^{67} +(3.54182 - 0.949028i) q^{68} +(7.17208 - 1.78685i) q^{69} +(-5.89833 + 0.457967i) q^{70} +4.92862 q^{71} +(-2.19479 + 2.04522i) q^{72} +(3.32627 + 3.32627i) q^{73} +(7.74945 - 4.47415i) q^{74} +(-8.65672 - 0.247326i) q^{75} +(6.73762 + 3.88997i) q^{76} +(-1.28421 + 0.106775i) q^{77} +(-2.10739 - 0.0371588i) q^{78} +(9.28025 - 5.35796i) q^{79} +(-2.15668 - 0.590534i) q^{80} +(8.97763 + 0.634184i) q^{81} +(7.16795 - 7.16795i) q^{82} +(0.950809 - 3.54847i) q^{83} +(2.54546 + 3.81059i) q^{84} +(0.0448157 - 8.19901i) q^{85} +(-1.81989 + 3.15214i) q^{86} +(-0.0945591 - 0.170661i) q^{87} +(-0.470464 - 0.126060i) q^{88} +2.14078 q^{89} +(3.11478 + 5.94122i) q^{90} +(-0.572744 + 3.16824i) q^{91} +(1.10448 - 4.12197i) q^{92} +(0.595071 - 0.989966i) q^{93} +(1.77630 - 3.07664i) q^{94} +(12.3682 - 12.2337i) q^{95} +(0.418723 + 1.68068i) q^{96} +(13.5130 + 3.62079i) q^{97} +(6.36943 - 2.90350i) q^{98} +(0.685525 + 1.29039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 24 q^{15} + 96 q^{16} - 8 q^{18} + 8 q^{23} + 48 q^{30} - 24 q^{35} + 8 q^{36} - 44 q^{42} + 48 q^{46} + 32 q^{50} - 160 q^{53} - 4 q^{56} + 88 q^{57} + 24 q^{58} + 8 q^{60} - 48 q^{63} - 8 q^{65} + 16 q^{71} + 16 q^{72} - 16 q^{77} - 16 q^{78} - 8 q^{81} - 16 q^{86} + 8 q^{92} - 120 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) \) 192 * q + 8 * q^11 + 24 * q^15 + 96 * q^16 - 8 * q^18 + 8 * q^23 + 48 * q^30 - 24 * q^35 + 8 * q^36 - 44 * q^42 + 48 * q^46 + 32 * q^50 - 160 * q^53 - 4 * q^56 + 88 * q^57 + 24 * q^58 + 8 * q^60 - 48 * q^63 - 8 * q^65 + 16 * q^71 + 16 * q^72 - 16 * q^77 - 16 * q^78 - 8 * q^81 - 16 * q^86 + 8 * q^92 - 120 * q^93 - 128 * q^95 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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