LMFDB - Embedded newform 308.2.l.a.243.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(199,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("308.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.l (of order $6$, degree $2$, 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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			243.17
Character	$\chi$	$=$	308.243
Dual form			308.2.l.a.199.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.441022 + 1.34369i) q^{2} +(0.0769501 + 0.133281i) q^{3} +(-1.61100 - 1.18519i) q^{4} +(-0.742658 - 0.428774i) q^{5} +(-0.213026 + 0.0446169i) q^{6} +(2.28724 - 1.32986i) q^{7} +(2.30302 - 1.64198i) q^{8} +(1.48816 - 2.57756i) q^{9} +(0.903667 - 0.808802i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(0.0339978 - 0.305917i) q^{12} -1.56905i q^{13} +(0.778191 + 3.65984i) q^{14} -0.131977i q^{15} +(1.19063 + 3.81869i) q^{16} +(6.13912 - 3.54442i) q^{17} +(2.80713 + 3.13638i) q^{18} +(-3.26764 + 5.65971i) q^{19} +(0.688241 + 1.57095i) q^{20} +(0.353249 + 0.202514i) q^{21} +(-0.289908 - 1.38418i) q^{22} +(5.05703 + 2.91968i) q^{23} +(0.396063 + 0.180599i) q^{24} +(-2.13231 - 3.69326i) q^{25} +(2.10832 + 0.691988i) q^{26} +0.919756 q^{27} +(-5.26088 - 0.568424i) q^{28} +5.55634 q^{29} +(0.177336 + 0.0582047i) q^{30} +(-2.05600 - 3.56110i) q^{31} +(-5.65623 - 0.0842873i) q^{32} +(-0.133281 - 0.0769501i) q^{33} +(2.05511 + 9.81224i) q^{34} +(-2.26885 + 0.00692075i) q^{35} +(-5.45233 + 2.38870i) q^{36} +(-2.71052 + 4.69475i) q^{37} +(-6.16379 - 6.88675i) q^{38} +(0.209126 - 0.120739i) q^{39} +(-2.41439 + 0.231959i) q^{40} -1.53377i q^{41} +(-0.427907 + 0.385343i) q^{42} -10.7461i q^{43} +(1.98776 + 0.220908i) q^{44} +(-2.21038 + 1.27617i) q^{45} +(-6.15340 + 5.50743i) q^{46} +(-3.52639 + 6.10789i) q^{47} +(-0.417341 + 0.452538i) q^{48} +(3.46295 - 6.08342i) q^{49} +(5.90299 - 1.23634i) q^{50} +(0.944812 + 0.545488i) q^{51} +(-1.85963 + 2.52775i) q^{52} +(1.82971 + 3.16915i) q^{53} +(-0.405633 + 1.23587i) q^{54} +0.857547 q^{55} +(3.08395 - 6.81830i) q^{56} -1.00578 q^{57} +(-2.45047 + 7.46599i) q^{58} +(5.78799 + 10.0251i) q^{59} +(-0.156418 + 0.212614i) q^{60} +(-8.38317 - 4.84002i) q^{61} +(5.69176 - 1.19210i) q^{62} +(-0.0240201 - 7.87455i) q^{63} +(2.60778 - 7.56303i) q^{64} +(-0.672769 + 1.16527i) q^{65} +(0.162177 - 0.145152i) q^{66} +(10.3965 - 6.00241i) q^{67} +(-14.0909 - 1.56599i) q^{68} +0.898677i q^{69} +(0.991313 - 3.05168i) q^{70} +0.515735i q^{71} +(-0.805067 - 8.37971i) q^{72} +(-11.7319 + 6.77342i) q^{73} +(-5.11289 - 5.71258i) q^{74} +(0.328162 - 0.568394i) q^{75} +(11.9720 - 5.24501i) q^{76} +(-1.31588 + 2.29531i) q^{77} +(0.0700063 + 0.334249i) q^{78} +(-4.38476 - 2.53154i) q^{79} +(0.753121 - 3.34649i) q^{80} +(-4.39370 - 7.61011i) q^{81} +(2.06091 + 0.676428i) q^{82} -14.2549 q^{83} +(-0.329065 - 0.744919i) q^{84} -6.07902 q^{85} +(14.4394 + 4.73925i) q^{86} +(0.427561 + 0.740557i) q^{87} +(-1.17348 + 2.57351i) q^{88} +(2.37726 + 1.37251i) q^{89} +(-0.739941 - 3.53288i) q^{90} +(-2.08662 - 3.58881i) q^{91} +(-4.68648 - 10.6971i) q^{92} +(0.316419 - 0.548054i) q^{93} +(-6.65189 - 7.43209i) q^{94} +(4.85347 - 2.80215i) q^{95} +(-0.424013 - 0.760356i) q^{96} +4.10652i q^{97} +(6.64698 + 7.33605i) q^{98} +2.97631i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 12 q^{8} - 40 q^{9} - 18 q^{10} - 30 q^{12} - 4 q^{14} - 4 q^{16} - 10 q^{18} - 8 q^{21} + 40 q^{25} + 30 q^{26} + 16 q^{28} - 16 q^{29} + 36 q^{30} - 20 q^{32} - 20 q^{36} - 8 q^{37} - 12 q^{38}+ \cdots + 78 q^{98}+O(q^{100}) $ 80 * q + 12 * q^8 - 40 * q^9 - 18 * q^10 - 30 * q^12 - 4 * q^14 - 4 * q^16 - 10 * q^18 - 8 * q^21 + 40 * q^25 + 30 * q^26 + 16 * q^28 - 16 * q^29 + 36 * q^30 - 20 * q^32 - 20 * q^36 - 8 * q^37 - 12 * q^38 - 60 * q^40 + 4 * q^44 + 24 * q^45 - 10 * q^46 - 24 * q^49 - 64 * q^50 + 54 * q^52 - 30 * q^54 + 38 * q^56 + 80 * q^57 + 10 * q^58 - 12 * q^60 - 36 * q^64 - 16 * q^65 + 30 * q^66 + 60 * q^68 - 22 * q^70 - 38 * q^72 - 72 * q^73 + 28 * q^74 - 24 * q^78 + 42 * q^80 - 64 * q^81 - 90 * q^82 + 88 * q^84 - 2 * q^86 + 12 * q^88 - 120 * q^89 + 36 * q^92 + 8 * q^93 - 54 * q^94 - 42 * q^96 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.441022	+	1.34369i	−0.311850	+	0.950131i
$2$	−0.441022	+	1.34369i	−0.311850	+	0.950131i
$3$	0.0769501	+	0.133281i	0.0444272	+	0.0769501i	0.887384	−	0.461031i	$-0.152520\pi$
$3$	0.0769501	+	0.133281i	0.0444272	+	0.0769501i	−0.842957	+	0.537981i	$0.819187\pi$
$4$	−1.61100	−	1.18519i	−0.805499	−	0.592597i
$5$	−0.742658	−	0.428774i	−0.332127	−	0.191753i	0.324658	−	0.945831i	$-0.394751\pi$
$5$	−0.742658	−	0.428774i	−0.332127	−	0.191753i	−0.656785	+	0.754078i	$0.728084\pi$
$6$	−0.213026	+	0.0446169i	−0.0869673	+	0.0182148i
$7$	2.28724	−	1.32986i	0.864496	−	0.502639i
$7$	2.28724	−	1.32986i	0.864496	−	0.502639i
$8$	2.30302	−	1.64198i	0.814240	−	0.580529i
$9$	1.48816	−	2.57756i	0.496052	−	0.859188i
$10$	0.903667	−	0.808802i	0.285765	−	0.255766i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	0.0339978	−	0.305917i	0.00981433	−	0.0883106i
$13$		−	1.56905i		−	0.435178i	−0.976041	−	0.217589i	$-0.930181\pi$
$13$		−	1.56905i		−	0.435178i	0.976041	−	0.217589i	$-0.0698192\pi$
$14$	0.778191	+	3.65984i	0.207980	+	0.978133i
$15$		−	0.131977i		−	0.0340762i
$16$	1.19063	+	3.81869i	0.297658	+	0.954672i
$17$	6.13912	−	3.54442i	1.48896	−	0.859649i	0.489036	−	0.872264i	$-0.337349\pi$
$17$	6.13912	−	3.54442i	1.48896	−	0.859649i	0.999920	+	0.0126146i	$0.00401545\pi$
$18$	2.80713	+	3.13638i	0.661648	+	0.739253i
$19$	−3.26764	+	5.65971i	−0.749647	+	1.29843i	0.198344	+	0.980132i	$0.436444\pi$
$19$	−3.26764	+	5.65971i	−0.749647	+	1.29843i	−0.947992	+	0.318295i	$0.896890\pi$
$20$	0.688241	+	1.57095i	0.153895	+	0.351274i
$21$	0.353249	+	0.202514i	0.0770852	+	0.0441922i
$22$	−0.289908	−	1.38418i	−0.0618086	−	0.295108i
$23$	5.05703	+	2.91968i	1.05446	+	0.608795i	0.923895	−	0.382645i	$-0.124987\pi$
$23$	5.05703	+	2.91968i	1.05446	+	0.608795i	0.130568	+	0.991439i	$0.458320\pi$
$24$	0.396063	+	0.180599i	0.0808461	+	0.0368646i
$25$	−2.13231	−	3.69326i	−0.426461	−	0.738653i
$26$	2.10832	+	0.691988i	0.413476	+	0.135710i
$27$	0.919756			0.177007
$28$	−5.26088	−	0.568424i	−0.994214	−	0.107422i
$29$	5.55634			1.03179			0.515893	−	0.856653i	$-0.327460\pi$
$29$	5.55634			1.03179			0.515893	+	0.856653i	$0.327460\pi$
$30$	0.177336	+	0.0582047i	0.0323769	+	0.0106267i
$31$	−2.05600	−	3.56110i	−0.369269	−	0.639593i	0.620182	−	0.784458i	$-0.287059\pi$
$31$	−2.05600	−	3.56110i	−0.369269	−	0.639593i	−0.989451	+	0.144865i	$0.953725\pi$
$32$	−5.65623	−	0.0842873i	−0.999889	−	0.0149000i
$33$	−0.133281	−	0.0769501i	−0.0232013	−	0.0133953i
$34$	2.05511	+	9.81224i	0.352449	+	1.68279i
$35$	−2.26885	+	0.00692075i	−0.383505	+	0.00116982i
$36$	−5.45233	+	2.38870i	−0.908722	+	0.398116i
$37$	−2.71052	+	4.69475i	−0.445606	+	0.771813i	−0.998094	−	0.0617082i	$-0.980345\pi$
$37$	−2.71052	+	4.69475i	−0.445606	+	0.771813i	0.552488	+	0.833521i	$0.313679\pi$
$38$	−6.16379	−	6.88675i	−0.999899	−	1.11718i
$39$	0.209126	−	0.120739i	0.0334869	−	0.0193337i
$40$	−2.41439	+	0.231959i	−0.381749	+	0.0366759i
$41$		−	1.53377i		−	0.239535i	−0.992802	−	0.119767i	$-0.961785\pi$
$41$		−	1.53377i		−	0.239535i	0.992802	−	0.119767i	$-0.0382149\pi$
$42$	−0.427907	+	0.385343i	−0.0660274	+	0.0594598i
$43$		−	10.7461i		−	1.63876i	−0.573252	−	0.819379i	$-0.694318\pi$
$43$		−	10.7461i		−	1.63876i	0.573252	−	0.819379i	$-0.305682\pi$
$44$	1.98776	+	0.220908i	0.299666	+	0.0333032i
$45$	−2.21038	+	1.27617i	−0.329504	+	0.190240i
$46$	−6.15340	+	5.50743i	−0.907269	+	0.812026i
$47$	−3.52639	+	6.10789i	−0.514378	+	0.890928i	0.485483	+	0.874246i	$0.338644\pi$
$47$	−3.52639	+	6.10789i	−0.514378	+	0.890928i	−0.999861	+	0.0166821i	$0.994690\pi$
$48$	−0.417341	+	0.452538i	−0.0602380	+	0.0653182i
$49$	3.46295	−	6.08342i	0.494707	−	0.869060i
$50$	5.90299	−	1.23634i	0.834809	−	0.174846i
$51$	0.944812	+	0.545488i	0.132300	+	0.0763835i
$52$	−1.85963	+	2.52775i	−0.257885	+	0.350535i
$53$	1.82971	+	3.16915i	0.251330	+	0.435316i	0.963892	−	0.266293i	$-0.0857988\pi$
$53$	1.82971	+	3.16915i	0.251330	+	0.435316i	−0.712562	+	0.701609i	$0.752466\pi$
$54$	−0.405633	+	1.23587i	−0.0551996	+	0.168180i
$55$	0.857547			0.115632
$56$	3.08395	−	6.81830i	0.412110	−	0.911134i
$57$	−1.00578			−0.133219
$58$	−2.45047	+	7.46599i	−0.321763	+	0.980333i
$59$	5.78799	+	10.0251i	0.753532	+	1.30516i	0.946101	+	0.323872i	$0.104985\pi$
$59$	5.78799	+	10.0251i	0.753532	+	1.30516i	−0.192569	+	0.981284i	$0.561682\pi$
$60$	−0.156418	+	0.212614i	−0.0201935	+	0.0274484i
$61$	−8.38317	−	4.84002i	−1.07335	−	0.619702i	−0.144259	−	0.989540i	$-0.546080\pi$
$61$	−8.38317	−	4.84002i	−1.07335	−	0.619702i	−0.929096	+	0.369838i	$0.879413\pi$
$62$	5.69176	−	1.19210i	0.722854	−	0.151397i
$63$	−0.0240201	−	7.87455i	−0.00302624	−	0.992100i
$64$	2.60778	−	7.56303i	0.325972	−	0.945379i
$65$	−0.672769	+	1.16527i	−0.0834468	+	0.144534i
$66$	0.162177	−	0.145152i	0.0199626	−	0.0178670i
$67$	10.3965	−	6.00241i	1.27013	−	0.733311i	0.295120	−	0.955460i	$-0.404640\pi$
$67$	10.3965	−	6.00241i	1.27013	−	0.733311i	0.975013	+	0.222149i	$0.0713071\pi$
$68$	−14.0909	−	1.56599i	−1.70878	−	0.189904i
$69$			0.898677i			0.108188i
$70$	0.991313	−	3.05168i	0.118485	−	0.364745i
$71$			0.515735i			0.0612064i	0.999532	+	0.0306032i	$0.00974283\pi$
$71$			0.515735i			0.0612064i	−0.999532	+	0.0306032i	$0.990257\pi$
$72$	−0.805067	−	8.37971i	−0.0948780	−	0.987558i
$73$	−11.7319	+	6.77342i	−1.37312	+	0.792769i	−0.991319	−	0.131478i	$-0.958028\pi$
$73$	−11.7319	+	6.77342i	−1.37312	+	0.792769i	−0.381796	+	0.924247i	$0.624694\pi$
$74$	−5.11289	−	5.71258i	−0.594361	−	0.664074i
$75$	0.328162	−	0.568394i	0.0378929	−	0.0656325i
$76$	11.9720	−	5.24501i	1.37328	−	0.601644i
$77$	−1.31588	+	2.29531i	−0.149958	+	0.261575i
$78$	0.0700063	+	0.334249i	0.00792665	+	0.0378462i
$79$	−4.38476	−	2.53154i	−0.493324	−	0.284821i	0.232629	−	0.972566i	$-0.425267\pi$
$79$	−4.38476	−	2.53154i	−0.493324	−	0.284821i	−0.725952	+	0.687745i	$0.758601\pi$
$80$	0.753121	−	3.34649i	0.0842015	−	0.374149i
$81$	−4.39370	−	7.61011i	−0.488189	−	0.845567i
$82$	2.06091	+	0.676428i	0.227590	+	0.0746990i
$83$	−14.2549			−1.56467			−0.782337	−	0.622856i	$-0.785972\pi$
$83$	−14.2549			−1.56467			−0.782337	+	0.622856i	$0.785972\pi$
$84$	−0.329065	−	0.744919i	−0.0359039	−	0.0812773i
$85$	−6.07902			−0.659363
$86$	14.4394	+	4.73925i	1.55704	+	0.511047i
$87$	0.427561	+	0.740557i	0.0458393	+	0.0793961i
$88$	−1.17348	+	2.57351i	−0.125093	+	0.274337i
$89$	2.37726	+	1.37251i	0.251989	+	0.145486i	0.620675	−	0.784068i	$-0.286859\pi$
$89$	2.37726	+	1.37251i	0.251989	+	0.145486i	−0.368686	+	0.929554i	$0.620192\pi$
$90$	−0.739941	−	3.53288i	−0.0779966	−	0.372399i
$91$	−2.08662	−	3.58881i	−0.218737	−	0.376209i
$92$	−4.68648	−	10.6971i	−0.488600	−	1.11525i
$93$	0.316419	−	0.548054i	0.0328111	−	0.0568306i
$94$	−6.65189	−	7.43209i	−0.686090	−	0.766562i
$95$	4.85347	−	2.80215i	0.497956	−	0.287495i
$96$	−0.424013	−	0.760356i	−0.0432757	−	0.0776035i
$97$			4.10652i			0.416954i	0.978027	+	0.208477i	$0.0668506\pi$
$97$			4.10652i			0.416954i	−0.978027	+	0.208477i	$0.933149\pi$
$98$	6.64698	+	7.33605i	0.671446	+	0.741053i
$99$			2.97631i			0.299131i
$100$	−0.942088	+	8.47704i	−0.0942088	+	0.847704i
$101$	3.98843	−	2.30272i	0.396864	−	0.229129i	−0.288266	−	0.957550i	$-0.593079\pi$
$101$	3.98843	−	2.30272i	0.396864	−	0.229129i	0.685130	+	0.728421i	$0.259745\pi$
$102$	−1.14965	+	1.02896i	−0.113832	+	0.101882i
$103$	−7.27590	+	12.6022i	−0.716916	+	1.24173i	0.245300	+	0.969447i	$0.421113\pi$
$103$	−7.27590	+	12.6022i	−0.716916	+	1.24173i	−0.962216	+	0.272287i	$0.912220\pi$
$104$	−2.57636	−	3.61356i	−0.252633	−	0.354339i
$105$	−0.175510	−	0.301863i	−0.0171281	−	0.0294588i
$106$	−5.06529	+	1.06089i	−0.491984	+	0.103043i
$107$	0.949803	+	0.548369i	0.0918209	+	0.0530128i	0.545207	−	0.838301i	$-0.316451\pi$
$107$	0.949803	+	0.548369i	0.0918209	+	0.0530128i	−0.453386	+	0.891314i	$0.649784\pi$
$108$	−1.48173	−	1.09009i	−0.142579	−	0.104894i
$109$	7.91220	+	13.7043i	0.757851	+	1.31264i	0.943944	+	0.330105i	$0.107084\pi$
$109$	7.91220	+	13.7043i	0.757851	+	1.31264i	−0.186093	+	0.982532i	$0.559583\pi$
$110$	−0.378198	+	1.15228i	−0.0360597	+	0.109865i
$111$	−0.834298			−0.0791881
$112$	7.80158	+	7.15089i	0.737180	+	0.675696i
$113$	1.73920			0.163610			0.0818051	−	0.996648i	$-0.473931\pi$
$113$	1.73920			0.163610			0.0818051	+	0.996648i	$0.473931\pi$
$114$	0.443571	−	1.35146i	0.0415443	−	0.126575i
$115$	−2.50376	−	4.33664i	−0.233477	−	0.404394i
$116$	−8.95126	−	6.58534i	−0.831103	−	0.611433i
$117$	−4.04434	−	2.33500i	−0.373899	−	0.215871i
$118$	−16.0232	+	3.35597i	−1.47506	+	0.308942i
$119$	9.32808	−	16.2711i	0.855103	−	1.49157i
$120$	−0.216704	−	0.303945i	−0.0197822	−	0.0277462i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	10.2007	−	9.12981i	0.923524	−	0.826574i
$123$	0.204423	−	0.118024i	0.0184322	−	0.0106419i
$124$	−0.908376	+	8.17369i	−0.0815746	+	0.734019i
$125$			7.94484i			0.710608i
$126$	10.5915	+	3.44058i	0.943569	+	0.306511i
$127$			15.8144i			1.40330i	0.712521	+	0.701650i	$0.247553\pi$
$127$			15.8144i			1.40330i	−0.712521	+	0.701650i	$0.752447\pi$
$128$	9.01228	+	6.83951i	0.796580	+	0.604533i
$129$	1.43225	−	0.826910i	0.126103	−	0.0728054i
$130$	−1.26905	−	1.41790i	−0.111303	−	0.124358i
$131$	2.84946	−	4.93541i	0.248958	−	0.431209i	−0.714279	−	0.699861i	$-0.753245\pi$
$131$	2.84946	−	4.93541i	0.248958	−	0.431209i	0.963237	+	0.268653i	$0.0865784\pi$
$132$	0.123516	+	0.281931i	0.0107506	+	0.0245389i
$133$	0.0527423	+	17.2906i	0.00457334	+	1.49929i
$134$	3.48029	+	16.6168i	0.300651	+	1.43548i
$135$	−0.683064	−	0.394367i	−0.0587888	−	0.0339417i
$136$	8.31862	−	18.2432i	0.713316	−	1.56434i
$137$	7.14714	+	12.3792i	0.610622	+	1.05763i	0.991136	+	0.132853i	$0.0424137\pi$
$137$	7.14714	+	12.3792i	0.610622	+	1.05763i	−0.380514	+	0.924775i	$0.624253\pi$
$138$	−1.20754	−	0.396337i	−0.102793	−	0.0337384i
$139$	−0.675952			−0.0573335			−0.0286667	−	0.999589i	$-0.509126\pi$
$139$	−0.675952			−0.0573335			−0.0286667	+	0.999589i	$0.509126\pi$
$140$	3.66331	+	2.67787i	0.309606	+	0.226322i
$141$	−1.08543			−0.0914093
$142$	−0.692987	−	0.227450i	−0.0581542	−	0.0190872i
$143$	0.784527	+	1.35884i	0.0656055	+	0.113632i
$144$	11.6148	+	2.61388i	0.967897	+	0.217823i
$145$	−4.12646	−	2.38241i	−0.342684	−	0.197849i
$146$	−3.92733	−	18.7513i	−0.325028	−	1.55186i
$147$	1.07728	−	0.00657221i	0.0888527	−	0.000542067i
$148$	9.93083	−	4.35075i	0.816309	−	0.357630i
$149$	−6.32245	+	10.9508i	−0.517955	+	0.897124i	0.481827	+	0.876266i	$0.339973\pi$
$149$	−6.32245	+	10.9508i	−0.517955	+	0.897124i	−0.999782	+	0.0208583i	$0.993360\pi$
$150$	0.619017	+	0.691622i	0.0505426	+	0.0564707i
$151$	−0.376018	+	0.217094i	−0.0305999	+	0.0176669i	−0.515222	−	0.857057i	$-0.672291\pi$
$151$	−0.376018	+	0.217094i	−0.0305999	+	0.0176669i	0.484622	+	0.874724i	$0.338957\pi$
$152$	1.76773	+	18.3998i	0.143382	+	1.49242i
$153$		−	21.0986i		−	1.70572i
$154$	−2.50385	−	2.78042i	−0.201766	−	0.224052i
$155$			3.52624i			0.283234i
$156$	−0.480001	−	0.0533445i	−0.0384308	−	0.00427097i
$157$	−8.06953	+	4.65895i	−0.644019	+	0.371825i	−0.786161	−	0.618022i	$-0.787934\pi$
$157$	−8.06953	+	4.65895i	−0.644019	+	0.371825i	0.142142	+	0.989846i	$0.454601\pi$
$158$	5.33538	−	4.77528i	0.424460	−	0.379901i
$159$	−0.281592	+	0.487732i	−0.0223317	+	0.0386797i
$160$	4.16450	+	2.48784i	0.329233	+	0.196681i
$161$	15.4494	−	0.0471259i	1.21758	−	0.00371404i
$162$	12.1633	−	2.54753i	0.955642	−	0.200153i
$163$	−2.58288	−	1.49123i	−0.202307	−	0.116802i	0.395424	−	0.918499i	$-0.370598\pi$
$163$	−2.58288	−	1.49123i	−0.202307	−	0.116802i	−0.597731	+	0.801697i	$0.703931\pi$
$164$	−1.81782	+	2.47091i	−0.141948	+	0.192945i
$165$	0.0659883	+	0.114295i	0.00513719	+	0.00889787i
$166$	6.28671	−	19.1541i	0.487943	−	1.48665i
$167$	−23.0719			−1.78536			−0.892679	−	0.450694i	$-0.851177\pi$
$167$	−23.0719			−1.78536			−0.892679	+	0.450694i	$0.851177\pi$
$168$	1.14606	−	0.113635i	0.0884207	−	0.00876716i
$169$	10.5381			0.810621
$170$	2.68099	−	8.16832i	0.205622	−	0.626481i
$171$	9.72552	+	16.8451i	0.743729	+	1.28818i
$172$	−12.7362	+	17.3119i	−0.971123	+	1.32002i
$173$	11.3452	+	6.55017i	0.862562	+	0.498000i	0.864869	−	0.501997i	$-0.167401\pi$
$173$	11.3452	+	6.55017i	0.862562	+	0.498000i	−0.00230741	+	0.999997i	$0.500734\pi$
$174$	−1.18364	+	0.247906i	−0.0897317	+	0.0187937i
$175$	−9.78862	−	5.61172i	−0.739950	−	0.424206i
$176$	−2.94046	−	2.71177i	−0.221646	−	0.204407i
$177$	−0.890773	+	1.54286i	−0.0669546	+	0.115969i
$178$	−2.89265	+	2.58899i	−0.216813	+	0.194053i
$179$	−1.12768	+	0.651064i	−0.0842865	+	0.0486628i	−0.541551	−	0.840668i	$-0.682163\pi$
$179$	−1.12768	+	0.651064i	−0.0842865	+	0.0486628i	0.457264	+	0.889331i	$0.348829\pi$
$180$	5.07343	+	0.563831i	0.378151	+	0.0420255i
$181$			6.26285i			0.465514i	0.972535	+	0.232757i	$0.0747747\pi$
$181$			6.26285i			0.465514i	−0.972535	+	0.232757i	$0.925225\pi$
$182$	5.74249	−	1.22102i	0.425661	−	0.0905084i
$183$		−	1.48976i		−	0.110126i
$184$	16.4405	−	1.57949i	1.21201	−	0.116442i
$185$	4.02597	−	2.32440i	0.295995	−	0.170893i
$186$	0.596866	+	0.666873i	0.0437644	+	0.0488975i
$187$	−3.54442	+	6.13912i	−0.259194	+	0.448937i
$188$	12.9201	−	5.66035i	0.942292	−	0.412823i
$189$	2.10370	−	1.22315i	0.153022	−	0.0889707i
$190$	1.62473	+	7.75737i	0.117870	+	0.562779i
$191$	7.56005	+	4.36479i	0.547026	+	0.315825i	0.747922	−	0.663787i	$-0.231052\pi$
$191$	7.56005	+	4.36479i	0.547026	+	0.315825i	−0.200896	+	0.979613i	$0.564385\pi$
$192$	1.20868	−	0.234408i	0.0872290	−	0.0169169i
$193$	−2.13134	−	3.69159i	−0.153417	−	0.265726i	0.779064	−	0.626944i	$-0.215694\pi$
$193$	−2.13134	−	3.69159i	−0.153417	−	0.265726i	−0.932482	+	0.361218i	$0.882361\pi$
$194$	−5.51788	−	1.81107i	−0.396161	−	0.130027i
$195$	−0.207079			−0.0148292
$196$	−12.7888	+	5.69611i	−0.913488	+	0.406865i
$197$	−6.17673			−0.440074			−0.220037	−	0.975492i	$-0.570618\pi$
$197$	−6.17673			−0.440074			−0.220037	+	0.975492i	$0.570618\pi$
$198$	−3.99924	−	1.31262i	−0.284214	−	0.0932839i
$199$	9.23058	+	15.9878i	0.654339	+	1.13335i	0.982059	+	0.188573i	$0.0603863\pi$
$199$	9.23058	+	15.9878i	0.654339	+	1.13335i	−0.327720	+	0.944775i	$0.606280\pi$
$200$	−10.9750	−	5.00444i	−0.776051	−	0.353867i
$201$	1.60002	+	0.923772i	0.112857	+	0.0651579i
$202$	1.33515	+	6.37476i	0.0939411	+	0.448527i
$203$	12.7087	−	7.38915i	0.891976	−	0.518617i
$204$	−0.875583	−	1.99856i	−0.0613031	−	0.139928i
$205$	−0.657641	+	1.13907i	−0.0459317	+	0.0795560i
$206$	−13.7246	−	15.3344i	−0.956241	−	1.06840i
$207$	15.0513	−	8.68987i	1.04614	−	0.603988i
$208$	5.99173	−	1.86817i	0.415452	−	0.129534i
$209$		−	6.53527i		−	0.452054i
$210$	0.483013	−	0.102703i	0.0333311	−	0.00708719i
$211$		−	11.1917i		−	0.770468i	−0.922819	−	0.385234i	$-0.874121\pi$
$211$		−	11.1917i		−	0.770468i	0.922819	−	0.385234i	$-0.125879\pi$
$212$	0.808395	−	7.27405i	0.0555208	−	0.499584i
$213$	−0.0687379	+	0.0396858i	−0.00470984	+	0.00271923i
$214$	−1.15572	+	1.03440i	−0.0790035	+	0.0707099i
$215$	−4.60763	+	7.98065i	−0.314238	+	0.544276i
$216$	2.11821	−	1.51022i	0.144126	−	0.102758i
$217$	−9.43834	−	5.41091i	−0.640716	−	0.367316i
$218$	−21.9038	+	4.58762i	−1.48351	+	0.310713i
$219$	−1.80554	−	1.04243i	−0.122007	−	0.0704409i
$220$	−1.38151	−	1.01636i	−0.0931412	−	0.0685229i
$221$	−5.56140	−	9.63262i	−0.374100	−	0.647960i
$222$	0.367944	−	1.12104i	0.0246948	−	0.0752391i
$223$	−15.5034			−1.03818			−0.519091	−	0.854719i	$-0.673729\pi$
$223$	−15.5034			−1.03818			−0.519091	+	0.854719i	$0.673729\pi$
$224$	−13.0492	+	7.32920i	−0.871890	+	0.489703i
$225$	−12.6928			−0.846189
$226$	−0.767026	+	2.33694i	−0.0510218	+	0.155451i
$227$	−11.1713	−	19.3492i	−0.741465	−	1.28425i	−0.951828	−	0.306631i	$-0.900798\pi$
$227$	−11.1713	−	19.3492i	−0.741465	−	1.28425i	0.210364	−	0.977623i	$-0.432535\pi$
$228$	1.62031	+	1.19204i	0.107308	+	0.0789450i
$229$	5.16448	+	2.98171i	0.341278	+	0.197037i	0.660837	−	0.750529i	$-0.270201\pi$
$229$	5.16448	+	2.98171i	0.341278	+	0.197037i	−0.319559	+	0.947566i	$0.603535\pi$
$230$	6.93131	−	1.45172i	0.457037	−	0.0957235i
$231$	−0.407180	+	0.00124204i	−0.0267905	+	8.17200e-5i
$232$	12.7963	−	9.12342i	0.840121	−	0.598982i
$233$	−2.77699	+	4.80988i	−0.181927	+	0.315106i	−0.942537	−	0.334103i	$-0.891567\pi$
$233$	−2.77699	+	4.80988i	−0.181927	+	0.315106i	0.760610	+	0.649209i	$0.224900\pi$
$234$	4.92116	−	4.40455i	0.321706	−	0.287934i
$235$	5.23781	−	3.02405i	0.341677	−	0.197267i
$236$	2.55723	−	23.0103i	0.166462	−	1.49784i
$237$		−	0.779209i		−	0.0506151i
$238$	17.7494	+	19.7100i	1.15052	+	1.27761i
$239$			1.89135i			0.122341i	0.998127	+	0.0611705i	$0.0194833\pi$
$239$			1.89135i			0.122341i	−0.998127	+	0.0611705i	$0.980517\pi$
$240$	0.503978	−	0.157136i	0.0325316	−	0.0101431i
$241$	12.2320	−	7.06213i	0.787930	−	0.454912i	−0.0513032	−	0.998683i	$-0.516337\pi$
$241$	12.2320	−	7.06213i	0.787930	−	0.454912i	0.839233	+	0.543771i	$0.183004\pi$
$242$	0.943157	+	1.05378i	0.0606285	+	0.0677396i
$243$	2.05582	−	3.56079i	0.131881	−	0.228425i
$244$	7.76891	+	17.7329i	0.497353	+	1.13524i
$245$	−5.18020	+	3.03307i	−0.330951	+	0.193776i
$246$	0.0684321	+	0.326733i	0.00436307	+	0.0208317i
$247$	8.88040	+	5.12710i	0.565046	+	0.326230i
$248$	−10.5823	−	4.82536i	−0.671976	−	0.306410i
$249$	−1.09691	−	1.89991i	−0.0695140	−	0.120402i
$250$	−10.6754	−	3.50385i	−0.675171	−	0.221603i
$251$	−5.20466			−0.328515			−0.164258	−	0.986417i	$-0.552523\pi$
$251$	−5.20466			−0.328515			−0.164258	+	0.986417i	$0.552523\pi$
$252$	−9.29417	+	12.7144i	−0.585478	+	0.800929i
$253$	−5.83935			−0.367117
$254$	−21.2496	−	6.97450i	−1.33332	−	0.437619i
$255$	−0.467781	−	0.810221i	−0.0292936	−	0.0507380i
$256$	−13.1648	+	9.09332i	−0.822799	+	0.568332i
$257$	−5.05209	−	2.91683i	−0.315141	−	0.181947i	0.334084	−	0.942543i	$-0.391573\pi$
$257$	−5.05209	−	2.91683i	−0.315141	−	0.181947i	−0.649225	+	0.760597i	$0.724906\pi$
$258$	0.479456	+	2.28918i	0.0298496	+	0.142518i
$259$	0.0437499	+	14.3426i	0.00271849	+	0.891208i
$260$	2.46490	−	1.07989i	0.152867	−	0.0669718i
$261$	8.26871	−	14.3218i	0.511820	−	0.886499i
$262$	5.37498	+	6.00541i	0.332067	+	0.371016i
$263$	16.3652	−	9.44847i	1.00912	−	0.582617i	0.0981882	−	0.995168i	$-0.468695\pi$
$263$	16.3652	−	9.44847i	1.00912	−	0.582617i	0.910935	+	0.412550i	$0.135362\pi$
$264$	−0.433300	+	0.0416286i	−0.0266678	+	0.00256206i
$265$		−	3.13812i		−	0.192773i
$266$	−23.2565	−	7.55468i	−1.42595	−	0.463207i
$267$			0.422459i			0.0258541i
$268$	−23.8627	−	2.65197i	−1.45765	−	0.161995i
$269$	−7.13871	+	4.12153i	−0.435255	+	0.251294i	−0.701583	−	0.712588i	$-0.747523\pi$
$269$	−7.13871	+	4.12153i	−0.435255	+	0.251294i	0.266328	+	0.963882i	$0.414190\pi$
$270$	0.831153	−	0.743901i	0.0505824	−	0.0452723i
$271$	9.97766	−	17.2818i	0.606100	−	1.04980i	−0.385777	−	0.922592i	$-0.626067\pi$
$271$	9.97766	−	17.2818i	0.606100	−	1.04980i	0.991877	−	0.127203i	$-0.0406001\pi$
$272$	20.8445	+	19.2233i	1.26388	+	1.16558i
$273$	0.317756	−	0.554267i	0.0192315	−	0.0335458i
$274$	−19.7859	+	4.14402i	−1.19531	+	0.250350i
$275$	3.69326	+	2.13231i	0.222712	+	0.128583i
$276$	1.06511	−	1.44777i	0.0641119	−	0.0871454i
$277$	−5.29054	−	9.16349i	−0.317878	−	0.550581i	0.662167	−	0.749356i	$-0.269637\pi$
$277$	−5.29054	−	9.16349i	−0.317878	−	0.550581i	−0.980045	+	0.198775i	$0.936304\pi$
$278$	0.298110	−	0.908269i	0.0178794	−	0.0544743i
$279$	−12.2386			−0.732707
$280$	−5.21383	+	3.74135i	−0.311586	+	0.223588i
$281$	−9.34994			−0.557771			−0.278885	−	0.960324i	$-0.589965\pi$
$281$	−9.34994			−0.557771			−0.278885	+	0.960324i	$0.589965\pi$
$282$	0.478697	−	1.45847i	0.0285060	−	0.0868509i
$283$	−0.472499	−	0.818393i	−0.0280872	−	0.0486484i	0.851640	−	0.524127i	$-0.175608\pi$
$283$	−0.472499	−	0.818393i	−0.0280872	−	0.0486484i	−0.879727	+	0.475479i	$0.842275\pi$
$284$	0.611245	−	0.830848i	0.0362707	−	0.0493017i
$285$	0.746950	+	0.431252i	0.0442455	+	0.0255452i
$286$	−2.17185	+	0.454881i	−0.128424	+	0.0268977i
$287$	−2.03970	−	3.50811i	−0.120400	−	0.207077i
$288$	−8.63461	+	14.4539i	−0.508799	+	0.851701i
$289$	16.6259	−	28.7969i	0.977994	−	1.69393i
$290$	5.02108	−	4.49398i	0.294848	−	0.263896i
$291$	−0.547323	+	0.315997i	−0.0320846	+	0.0185241i
$292$	26.9279	+	2.99261i	1.57584	+	0.175129i
$293$		−	6.81918i		−	0.398381i	−0.979961	−	0.199190i	$-0.936169\pi$
$293$		−	6.81918i		−	0.398381i	0.979961	−	0.199190i	$-0.0638312\pi$
$294$	−0.466274	+	1.45043i	−0.0271937	+	0.0845907i
$295$		−	9.92695i		−	0.577969i
$296$	1.46634	+	15.2627i	0.0852294	+	0.887128i
$297$	−0.796532	+	0.459878i	−0.0462195	+	0.0266848i
$298$	−11.9261	−	13.3249i	−0.690862	−	0.771893i
$299$	4.58113	−	7.93475i	0.264934	−	0.458879i
$300$	−1.20233	+	0.526746i	−0.0694163	+	0.0304117i
$301$	−14.2907	−	24.5788i	−0.823705	−	1.41670i
$302$	−0.125875	−	0.600995i	−0.00724327	−	0.0345834i
$303$	0.613820	+	0.354389i	0.0352631	+	0.0203591i
$304$	−25.5032	−	5.73945i	−1.46271	−	0.329180i
$305$	4.15055	+	7.18896i	0.237660	+	0.411639i
$306$	28.3500	+	9.30497i	1.62066	+	0.531930i
$307$	18.2117			1.03939			0.519697	−	0.854350i	$-0.326045\pi$
$307$	18.2117			1.03939			0.519697	+	0.854350i	$0.326045\pi$
$308$	4.84027	−	2.13817i	0.275800	−	0.121834i
$309$	−2.23952			−0.127402
$310$	−4.73817	−	1.55515i	−0.269110	−	0.0883266i
$311$	3.33573	+	5.77765i	0.189152	+	0.327620i	0.944968	−	0.327164i	$-0.106093\pi$
$311$	3.33573	+	5.77765i	0.189152	+	0.327620i	−0.755816	+	0.654784i	$0.772760\pi$
$312$	0.283369	−	0.621445i	0.0160426	−	0.0351824i
$313$	2.94066	+	1.69779i	0.166216	+	0.0959649i	0.580800	−	0.814046i	$-0.302740\pi$
$313$	2.94066	+	1.69779i	0.166216	+	0.0959649i	−0.414584	+	0.910011i	$0.636073\pi$
$314$	−2.70133	−	12.8976i	−0.152445	−	0.727856i
$315$	−3.35856	+	5.85840i	−0.189234	+	0.330083i
$316$	4.06347	+	9.27509i	0.228588	+	0.521765i
$317$	−6.88253	+	11.9209i	−0.386561	+	0.669544i	−0.991984	−	0.126360i	$-0.959671\pi$
$317$	−6.88253	+	11.9209i	−0.386561	+	0.669544i	0.605423	+	0.795904i	$0.293004\pi$
$318$	−0.531172	−	0.593473i	−0.0297866	−	0.0332803i
$319$	−4.81193	+	2.77817i	−0.269416	+	0.155548i
$320$	−5.17952	+	4.49860i	−0.289544	+	0.251479i
$321$			0.168788i			0.00942084i
$322$	−6.75021	+	20.7800i	−0.376174	+	1.15802i
$323$			46.3276i			2.57773i
$324$	−1.94121	+	17.4673i	−0.107845	+	0.970403i
$325$	−5.79493	+	3.34571i	−0.321445	+	0.185586i
$326$	3.14285	−	2.81292i	0.174067	−	0.155793i
$327$	−1.21769	+	2.10910i	−0.0673384	+	0.116633i
$328$	−2.51843	−	3.53230i	−0.139057	−	0.195039i
$329$	0.0569189	+	18.6598i	0.00313804	+	1.02875i
$330$	−0.182679	+	0.0382611i	−0.0100562	+	0.00210620i
$331$	−16.1065	−	9.29907i	−0.885291	−	0.511123i	−0.0128920	−	0.999917i	$-0.504104\pi$
$331$	−16.1065	−	9.29907i	−0.885291	−	0.511123i	−0.872399	+	0.488794i	$0.837437\pi$
$332$	22.9645	+	16.8948i	1.26034	+	0.927220i
$333$	8.06735	+	13.9731i	0.442088	+	0.765719i
$334$	10.1752	−	31.0015i	0.556763	−	1.69632i
$335$	−10.2947			−0.562460
$336$	−0.352749	+	1.59007i	−0.0192440	+	0.0867453i
$337$	22.0770			1.20261			0.601304	−	0.799020i	$-0.294648\pi$
$337$	22.0770			1.20261			0.601304	+	0.799020i	$0.294648\pi$
$338$	−4.64752	+	14.1599i	−0.252792	+	0.770196i
$339$	0.133832	+	0.231803i	0.00726874	+	0.0125898i
$340$	9.79330	+	7.20482i	0.531116	+	0.390736i
$341$	3.56110	+	2.05600i	0.192844	+	0.111339i
$342$	−26.9237	+	5.63901i	−1.45587	+	0.304923i
$343$	−0.169476	−	18.5195i	−0.00915086	−	0.999958i
$344$	−17.6449	−	24.7484i	−0.951347	−	1.33434i
$345$	0.385329	−	0.667410i	0.0207454	−	0.0359321i
$346$	−13.8049	+	12.3557i	−0.742156	+	0.664246i
$347$	−5.28833	+	3.05322i	−0.283892	+	0.163905i	−0.635184	−	0.772361i	$-0.719076\pi$
$347$	−5.28833	+	3.05322i	−0.283892	+	0.163905i	0.351292	+	0.936266i	$0.385742\pi$
$348$	0.188904	−	1.69978i	0.0101263	−	0.0911177i
$349$		−	1.62806i		−	0.0871479i	−0.999050	−	0.0435740i	$-0.986126\pi$
$349$		−	1.62806i		−	0.0871479i	0.999050	−	0.0435740i	$-0.0138744\pi$
$350$	11.8574	−	10.6780i	0.633805	−	0.570761i
$351$		−	1.44315i		−	0.0770295i
$352$	4.94058	−	2.75512i	0.263334	−	0.146848i
$353$	20.1908	−	11.6572i	1.07465	−	0.620448i	0.145199	−	0.989402i	$-0.453618\pi$
$353$	20.1908	−	11.6572i	1.07465	−	0.620448i	0.929447	+	0.368955i	$0.120284\pi$
$354$	−1.68028	−	1.87736i	−0.0893058	−	0.0997805i
$355$	0.221133	−	0.383014i	0.0117365	−	0.0203283i
$356$	−2.20307	−	5.02863i	−0.116762	−	0.266517i
$357$	2.88644	−	0.00880461i	0.152766	−	0.000465989i
$358$	−0.377497	−	1.80238i	−0.0199513	−	0.0952587i
$359$	−22.6284	−	13.0645i	−1.19428	−	0.689519i	−0.235007	−	0.971994i	$-0.575511\pi$
$359$	−22.6284	−	13.0645i	−1.19428	−	0.689519i	−0.959275	+	0.282475i	$0.908845\pi$
$360$	−2.99511	+	6.56844i	−0.157856	+	0.346187i
$361$	−11.8549	−	20.5333i	−0.623942	−	1.08070i
$362$	−8.41532	−	2.76206i	−0.442300	−	0.145171i
$363$	0.153900			0.00807766
$364$	−0.891888	+	8.25461i	−0.0467476	+	0.432659i
$365$	11.6171			0.608064
$366$	2.00178	+	0.657018i	0.104634	+	0.0343429i
$367$	8.99434	+	15.5787i	0.469501	+	0.813199i	0.999392	−	0.0348665i	$-0.0111006\pi$
$367$	8.99434	+	15.5787i	0.469501	+	0.813199i	−0.529891	+	0.848066i	$0.677767\pi$
$368$	−5.12827	+	22.7875i	−0.267330	+	1.18788i
$369$	−3.95340	−	2.28249i	−0.205806	−	0.118822i
$370$	1.34772	+	6.43477i	0.0700647	+	0.334528i
$371$	8.39950	+	4.81535i	0.436080	+	0.250001i
$372$	−1.15930	+	0.507897i	−0.0601070	+	0.0263332i
$373$	−3.04964	+	5.28212i	−0.157904	+	0.273498i	−0.934113	−	0.356978i	$-0.883807\pi$
$373$	−3.04964	+	5.28212i	−0.157904	+	0.273498i	0.776209	+	0.630476i	$0.217140\pi$
$374$	−6.68590	−	7.47009i	−0.345720	−	0.386269i
$375$	−1.05890	+	0.611356i	−0.0546814	+	0.0315703i
$376$	1.90772	+	19.8569i	0.0983830	+	1.02404i
$377$		−	8.71820i		−	0.449010i
$378$	0.715746	+	3.36616i	0.0368140	+	0.173136i
$379$		−	0.948262i		−	0.0487089i	−0.999703	−	0.0243545i	$-0.992247\pi$
$379$		−	0.948262i		−	0.0487089i	0.999703	−	0.0243545i	$-0.00775304\pi$
$380$	−11.1400	−	1.23804i	−0.571472	−	0.0635100i
$381$	−2.10777	+	1.21692i	−0.107984	+	0.0623447i
$382$	−9.19907	+	8.23338i	−0.470666	+	0.421256i
$383$	−4.01408	+	6.95260i	−0.205110	+	0.355261i	−0.950168	−	0.311739i	$-0.899089\pi$
$383$	−4.01408	+	6.95260i	−0.205110	+	0.355261i	0.745058	+	0.667000i	$0.232422\pi$
$384$	−0.218084	+	1.72747i	−0.0111291	+	0.0881546i
$385$	1.96142	−	1.14042i	0.0999631	−	0.0581210i
$386$	5.90031	−	1.23578i	0.300318	−	0.0628997i
$387$	−27.6987	−	15.9918i	−1.40800	−	0.812910i
$388$	4.86702	−	6.61559i	0.247085	−	0.335856i
$389$	2.77339	+	4.80366i	0.140617	+	0.243555i	0.927729	−	0.373255i	$-0.121758\pi$
$389$	2.77339	+	4.80366i	0.140617	+	0.243555i	−0.787112	+	0.616810i	$0.788425\pi$
$390$	0.0913263	−	0.278249i	0.00462449	−	0.0140897i
$391$	41.3943			2.09340
$392$	−2.01363	−	19.6963i	−0.101704	−	0.994815i
$393$	0.877065			0.0442421
$394$	2.72408	−	8.29960i	0.137237	−	0.418128i
$395$	2.17092	+	3.76014i	0.109231	+	0.189193i
$396$	3.52751	−	4.79484i	0.177264	−	0.240950i
$397$	3.06972	+	1.77231i	0.154065	+	0.0889495i	0.575051	−	0.818118i	$-0.304982\pi$
$397$	3.06972	+	1.77231i	0.154065	+	0.0889495i	−0.420986	+	0.907067i	$0.638316\pi$
$398$	−25.5536	+	5.35204i	−1.28088	+	0.268273i
$399$	−2.30046	+	1.33755i	−0.115167	+	0.0669610i
$400$	11.5646	−	12.5399i	0.578232	−	0.626997i
$401$	14.0302	−	24.3010i	0.700634	−	1.21353i	−0.267610	−	0.963527i	$-0.586234\pi$
$401$	14.0302	−	24.3010i	0.700634	−	1.21353i	0.968244	−	0.250006i	$-0.0804327\pi$
$402$	−1.94691	+	1.74253i	−0.0971029	+	0.0869093i
$403$	−5.58756	+	3.22598i	−0.278336	+	0.160698i
$404$	−9.15453	−	1.01738i	−0.455455	−	0.0506166i
$405$			7.53561i			0.374447i
$406$	4.32390	+	20.3353i	0.214591	+	1.00922i
$407$		−	5.42103i		−	0.268711i
$408$	3.07160	−	0.295099i	0.152067	−	0.0146096i
$409$	14.8889	−	8.59612i	0.736210	−	0.425051i	−0.0844799	−	0.996425i	$-0.526923\pi$
$409$	14.8889	−	8.59612i	0.736210	−	0.425051i	0.820690	+	0.571374i	$0.193590\pi$
$410$	−1.24052	−	1.38602i	−0.0612648	−	0.0684506i
$411$	−1.09995	+	1.90516i	−0.0542564	+	0.0939748i
$412$	26.6575	−	11.6788i	1.31332	−	0.575374i
$413$	26.5705	+	15.2326i	1.30745	+	0.749547i
$414$	5.03852	+	24.0567i	0.247630	+	1.18232i
$415$	10.5865	+	6.11210i	0.519670	+	0.300031i
$416$	−0.132251	+	8.87493i	−0.00648416	+	0.435129i
$417$	−0.0520146	−	0.0900919i	−0.00254716	−	0.00441182i
$418$	8.78137	+	2.88220i	0.429511	+	0.140973i
$419$	−1.20436			−0.0588367			−0.0294184	−	0.999567i	$-0.509366\pi$
$419$	−1.20436			−0.0588367			−0.0294184	+	0.999567i	$0.509366\pi$
$420$	−0.0750187	+	0.694314i	−0.00366054	+	0.0338791i
$421$	−33.6225			−1.63866			−0.819329	−	0.573323i	$-0.805654\pi$
$421$	−33.6225			−1.63866			−0.819329	+	0.573323i	$0.805654\pi$
$422$	15.0382	+	4.93579i	0.732046	+	0.240270i
$423$	10.4957	+	18.1790i	0.510316	+	0.883894i
$424$	9.41754	+	4.29425i	0.457356	+	0.208547i
$425$	−26.1810	−	15.1156i	−1.26996	−	0.733214i
$426$	−0.0230105	−	0.109865i	−0.00111486	−	0.00532296i
$427$	−25.6109	+	0.0781219i	−1.23940	+	0.00378058i
$428$	−0.880208	−	2.00912i	−0.0425465	−	0.0971146i
$429$	−0.120739	+	0.209126i	−0.00582933	+	0.0100967i
$430$	−8.69144	−	9.71086i	−0.419138	−	0.468299i
$431$	23.4499	−	13.5388i	1.12954	−	0.652143i	0.185724	−	0.982602i	$-0.440537\pi$
$431$	23.4499	−	13.5388i	1.12954	−	0.652143i	0.943820	+	0.330459i	$0.107204\pi$
$432$	1.09509	+	3.51226i	0.0526876	+	0.168984i
$433$			24.8016i			1.19189i	0.803026	+	0.595944i	$0.203222\pi$
$433$			24.8016i			1.19189i	−0.803026	+	0.595944i	$0.796778\pi$
$434$	11.4331	−	10.2959i	0.548806	−	0.494217i
$435$		−	0.733307i		−	0.0351594i
$436$	3.49574	−	31.4552i	0.167416	−	1.50643i
$437$	−33.0491	+	19.0809i	−1.58095	+	0.912762i
$438$	2.19699	−	1.96635i	0.104976	−	0.0939559i
$439$	10.7133	−	18.5559i	0.511316	−	0.885625i	−0.488598	−	0.872509i	$-0.662492\pi$
$439$	10.7133	−	18.5559i	0.511316	−	0.885625i	0.999914	−	0.0131162i	$-0.00417514\pi$
$440$	1.97495	−	1.40808i	0.0941519	−	0.0671275i
$441$	−10.5270	−	17.9791i	−0.501285	−	0.856146i
$442$	15.3959	−	3.22458i	0.732310	−	0.153378i
$443$	1.74516	+	1.00757i	0.0829148	+	0.0478709i	0.540884	−	0.841097i	$-0.318090\pi$
$443$	1.74516	+	1.00757i	0.0829148	+	0.0478709i	−0.457969	+	0.888968i	$0.651423\pi$
$444$	1.34405	+	0.988805i	0.0637859	+	0.0469266i
$445$	−1.17699	−	2.03861i	−0.0557948	−	0.0966395i
$446$	6.83733	−	20.8317i	0.323757	−	0.986409i
$447$	−1.94605			−0.0920451
$448$	−4.09315	−	20.7665i	−0.193383	−	0.981123i
$449$	19.6006			0.925010			0.462505	−	0.886617i	$-0.346951\pi$
$449$	19.6006			0.925010			0.462505	+	0.886617i	$0.346951\pi$
$450$	5.59782	−	17.0552i	0.263884	−	0.803990i
$451$	0.766886	+	1.32829i	0.0361113	+	0.0625465i
$452$	−2.80185	−	2.06129i	−0.131788	−	0.0969549i
$453$	−0.0578693	−	0.0334108i	−0.00271894	−	0.00156978i
$454$	30.9261	−	6.47729i	1.45144	−	0.303994i
$455$	0.0108590	+	3.55994i	0.000509080	+	0.166893i
$456$	−2.31633	+	1.65147i	−0.108472	+	0.0773374i
$457$	−2.46006	+	4.26094i	−0.115077	+	0.199318i	−0.917810	−	0.397019i	$-0.870045\pi$
$457$	−2.46006	+	4.26094i	−0.115077	+	0.199318i	0.802734	+	0.596338i	$0.203378\pi$
$458$	−6.28414	+	5.62445i	−0.293639	+	0.262813i
$459$	5.64650	−	3.26001i	0.263556	−	0.152164i
$460$	−1.10620	+	9.95376i	−0.0515770	+	0.464097i
$461$			1.00254i			0.0466927i	0.999727	+	0.0233464i	$0.00743206\pi$
$461$			1.00254i			0.0466927i	−0.999727	+	0.0233464i	$0.992568\pi$
$462$	0.177906	−	0.547671i	0.00827696	−	0.0254799i
$463$			7.47644i			0.347459i	0.984793	+	0.173730i	$0.0555819\pi$
$463$			7.47644i			0.347459i	−0.984793	+	0.173730i	$0.944418\pi$
$464$	6.61556	+	21.2179i	0.307120	+	0.985018i
$465$	−0.469982	+	0.271344i	−0.0217949	+	0.0125833i
$466$	−5.23827	−	5.85267i	−0.242658	−	0.271120i
$467$	2.53581	−	4.39216i	0.117343	−	0.203245i	−0.801371	−	0.598168i	$-0.795896\pi$
$467$	2.53581	−	4.39216i	0.117343	−	0.203245i	0.918714	+	0.394923i	$0.129229\pi$
$468$	3.74800	+	8.55501i	0.173251	+	0.395455i
$469$	15.7969	−	27.5548i	0.729434	−	1.27236i
$470$	1.75339	+	8.37166i	0.0808779	+	0.386156i
$471$	−1.24190	−	0.717013i	−0.0572239	−	0.0330382i
$472$	29.7909	+	13.5842i	1.37124	+	0.625262i
$473$	5.37303	+	9.30636i	0.247052	+	0.427907i
$474$	1.04701	+	0.343649i	0.0480910	+	0.0157843i
$475$	27.8704			1.27878
$476$	−34.3119	+	15.1572i	−1.57269	+	0.694728i
$477$	10.8916			0.498691
$478$	−2.54138	−	0.834126i	−0.116240	−	0.0381520i
$479$	8.42548	+	14.5934i	0.384970	+	0.666788i	0.991765	−	0.128071i	$-0.0408784\pi$
$479$	8.42548	+	14.5934i	0.384970	+	0.666788i	−0.606795	+	0.794858i	$0.707545\pi$
$480$	−0.0111240	+	0.746490i	−0.000507737	+	0.0340725i
$481$	7.36632	+	4.25295i	0.335876	+	0.193918i
$482$	4.09473	+	19.5505i	0.186510	+	0.890501i
$483$	1.19511	+	2.05549i	0.0543796	+	0.0935281i
$484$	−1.83191	+	0.802569i	−0.0832685	+	0.0364804i
$485$	1.76077	−	3.04974i	0.0799523	−	0.138481i
$486$	3.87793	+	4.33278i	0.175907	+	0.196539i
$487$	−1.04845	+	0.605322i	−0.0475097	+	0.0274298i	−0.523567	−	0.851985i	$-0.675399\pi$
$487$	−1.04845	+	0.605322i	−0.0475097	+	0.0274298i	0.476057	+	0.879414i	$0.342066\pi$
$488$	−27.2538	+	2.61837i	−1.23372	+	0.118528i
$489$		−	0.459000i		−	0.0207567i
$490$	−1.79093	−	8.29823i	−0.0809058	−	0.374876i
$491$		−	19.4228i		−	0.876540i	−0.898843	−	0.438270i	$-0.855591\pi$
$491$		−	19.4228i		−	0.876540i	0.898843	−	0.438270i	$-0.144409\pi$
$492$	−0.469207	−	0.0521449i	−0.0211535	−	0.00235087i
$493$	34.1111	−	19.6940i	1.53628	−	0.886975i
$494$	−10.8057	+	9.67133i	−0.486171	+	0.435134i
$495$	1.27617	−	2.21038i	0.0573594	−	0.0993493i
$496$	11.1508	−	12.0912i	0.500686	−	0.542911i
$497$	0.685854	+	1.17961i	0.0307648	+	0.0529127i
$498$	3.03665	−	0.636007i	0.136075	−	0.0285001i
$499$	−4.61934	−	2.66698i	−0.206790	−	0.119390i	0.393029	−	0.919526i	$-0.371427\pi$
$499$	−4.61934	−	2.66698i	−0.206790	−	0.119390i	−0.599819	+	0.800136i	$0.704761\pi$
$500$	9.41618	−	12.7991i	0.421104	−	0.572395i
$501$	−1.77538	−	3.07506i	−0.0793183	−	0.137383i
$502$	2.29537	−	6.99344i	0.102447	−	0.312133i
$503$	−30.1491			−1.34428			−0.672142	−	0.740423i	$-0.734625\pi$
$503$	−30.1491			−1.34428			−0.672142	+	0.740423i	$0.734625\pi$
$504$	−12.9852	−	18.0958i	−0.578407	−	0.806051i
$505$	−3.94939			−0.175745
$506$	2.57528	−	7.84627i	0.114485	−	0.348809i
$507$	0.810905	+	1.40453i	0.0360136	+	0.0623773i
$508$	18.7431	−	25.4770i	0.831592	−	1.13036i
$509$	34.4383	+	19.8830i	1.52645	+	0.881297i	0.999507	+	0.0313977i	$0.00999584\pi$
$509$	34.4383	+	19.8830i	1.52645	+	0.881297i	0.526945	+	0.849900i	$0.323337\pi$
$510$	1.29499	−	0.271227i	0.0573430	−	0.0120101i
$511$	−17.8260	+	31.0942i	−0.788576	+	1.37553i
$512$	−6.41262	−	21.6997i	−0.283401	−	0.959002i
$513$	−3.00543	+	5.20555i	−0.132693	+	0.229831i
$514$	6.14739	−	5.50205i	0.271150	−	0.242685i
$515$	10.8070	−	6.23943i	0.476214	−	0.274942i
$516$	−3.28740	−	0.365343i	−0.144720	−	0.0160833i
$517$		−	7.05279i		−	0.310181i
$518$	−19.2913	−	6.26664i	−0.847613	−	0.275340i
$519$			2.01615i			0.0884990i
$520$	0.363956	+	3.78832i	0.0159605	+	0.166129i
$521$	−32.8835	+	18.9853i	−1.44065	+	0.831760i	−0.997893	−	0.0648815i	$-0.979333\pi$
$521$	−32.8835	+	18.9853i	−1.44065	+	0.831760i	−0.442757	+	0.896641i	$0.646000\pi$
$522$	15.5974	+	17.4268i	0.682679	+	0.762751i
$523$	2.32073	−	4.01963i	0.101479	−	0.175766i	−0.810815	−	0.585302i	$-0.800976\pi$
$523$	2.32073	−	4.01963i	0.101479	−	0.175766i	0.912294	+	0.409536i	$0.134309\pi$
$524$	−10.4399	+	4.57378i	−0.456069	+	0.199806i
$525$	−0.00529681	−	1.73646i	−0.000231172	−	0.0757855i
$526$	5.47837	+	26.1568i	0.238868	+	1.14049i
$527$	−25.2441	−	14.5747i	−1.09965	−	0.634884i
$528$	0.135159	−	0.600580i	0.00588205	−	0.0261369i
$529$	5.54901	+	9.61117i	0.241261	+	0.417877i
$530$	4.21666	+	1.38398i	0.183160	+	0.0601163i
$531$	34.4538			1.49517
$532$	20.4078	−	27.9177i	0.884789	−	1.21039i
$533$	−2.40657			−0.104240
$534$	−0.567654	−	0.186314i	−0.0245648	−	0.00806260i
$535$	−0.470252	−	0.814501i	−0.0203308	−	0.0352140i
$536$	14.0874	−	30.8945i	0.608484	−	1.33444i
$537$	−0.173550	−	0.100199i	−0.00748922	−	0.00432390i
$538$	−2.38973	−	11.4099i	−0.103029	−	0.491915i
$539$	0.0427044	+	6.99987i	0.00183941	+	0.301506i
$540$	0.633014	+	1.44489i	0.0272406	+	0.0621781i
$541$	−5.01497	+	8.68619i	−0.215611	+	0.373449i	−0.953461	−	0.301515i	$-0.902508\pi$
$541$	−5.01497	+	8.68619i	−0.215611	+	0.373449i	0.737851	+	0.674964i	$0.235841\pi$
$542$	18.8210	+	21.0285i	0.808431	+	0.903253i
$543$	−0.834722	+	0.481927i	−0.0358214	+	0.0206815i
$544$	−35.0230	+	19.5306i	−1.50160	+	0.837368i
$545$		−	13.5702i		−	0.581282i
$546$	0.604625	+	0.671409i	0.0258756	+	0.0287337i
$547$			5.93630i			0.253818i	0.991914	+	0.126909i	$0.0405056\pi$
$547$			5.93630i			0.253818i	−0.991914	+	0.126909i	$0.959494\pi$
$548$	3.15773	−	28.4136i	0.134891	−	1.21377i
$549$	−24.9509	+	14.4054i	−1.06488	+	0.614809i
$550$	−4.49397	+	4.02220i	−0.191623	+	0.171507i
$551$	−18.1561	+	31.4473i	−0.773476	+	1.33970i
$552$	1.47561	+	2.06967i	0.0628063	+	0.0880910i
$553$	−13.3956	+	0.0408611i	−0.569638	+	0.00173759i
$554$	14.6461	−	3.06754i	0.622254	−	0.130327i
$555$	0.619598	+	0.357725i	0.0263005	+	0.0151846i
$556$	1.08896	+	0.801134i	0.0461821	+	0.0339756i
$557$	17.2020	+	29.7948i	0.728874	+	1.26245i	0.957360	+	0.288899i	$0.0932891\pi$
$557$	17.2020	+	29.7948i	0.728874	+	1.26245i	−0.228486	+	0.973547i	$0.573378\pi$
$558$	5.39751	−	16.4449i	0.228495	−	0.696168i
$559$	−16.8612			−0.713151
$560$	−2.72779	−	8.65578i	−0.115270	−	0.365774i
$561$	−1.09098			−0.0460610
$562$	4.12353	−	12.5634i	0.173941	−	0.529955i
$563$	4.21861	+	7.30685i	0.177793	+	0.307947i	0.941124	−	0.338060i	$-0.109771\pi$
$563$	4.21861	+	7.30685i	0.177793	+	0.307947i	−0.763331	+	0.646007i	$0.776437\pi$
$564$	1.74862	+	1.28644i	0.0736301	+	0.0541689i
$565$	−1.29163	−	0.745723i	−0.0543393	−	0.0313728i
$566$	1.30805	−	0.273963i	0.0549814	−	0.0115155i
$567$	−20.1698	−	11.5632i	−0.847053	−	0.485607i
$568$	0.846828	+	1.18775i	0.0355321	+	0.0498367i
$569$	−5.02434	+	8.70240i	−0.210631	+	0.364824i	−0.951912	−	0.306371i	$-0.900885\pi$
$569$	−5.02434	+	8.70240i	−0.210631	+	0.364824i	0.741281	+	0.671195i	$0.234219\pi$
$570$	−0.908890	+	0.813477i	−0.0380692	+	0.0340728i
$571$	−38.5938	+	22.2821i	−1.61510	+	0.932478i	−0.626936	+	0.779071i	$0.715691\pi$
$571$	−38.5938	+	22.2821i	−1.61510	+	0.932478i	−0.988163	+	0.153407i	$0.950976\pi$
$572$	0.346617	−	3.11891i	0.0144928	−	0.130408i
$573$			1.34349i			0.0561249i
$574$	5.61336	−	1.19357i	0.234297	−	0.0498186i
$575$		−	24.9026i		−	1.03851i
$576$	−15.6134	−	17.9767i	−0.650559	−	0.749029i
$577$	−38.5366	+	22.2491i	−1.60430	+	0.926244i	−0.613688	+	0.789549i	$0.710315\pi$
$577$	−38.5366	+	22.2491i	−1.60430	+	0.926244i	−0.990613	+	0.136695i	$0.956352\pi$
$578$	31.3617	+	35.0401i	1.30447	+	1.45748i
$579$	0.328013	−	0.568136i	0.0136318	−	0.0236109i
$580$	3.82410	+	8.72872i	0.158787	+	0.362440i
$581$	−32.6043	+	18.9569i	−1.35265	+	0.786466i
$582$	−0.183220	−	0.874793i	−0.00759471	−	0.0362613i
$583$	−3.16915	−	1.82971i	−0.131253	−	0.0757787i
$584$	−15.8969	+	34.8629i	−0.657820	+	1.44264i
$585$	2.00237	+	3.46821i	0.0827880	+	0.143393i
$586$	9.16285	+	3.00741i	0.378514	+	0.124235i
$587$	−2.89174			−0.119355			−0.0596775	−	0.998218i	$-0.519007\pi$
$587$	−2.89174			−0.119355			−0.0596775	+	0.998218i	$0.519007\pi$
$588$	−1.74329	−	1.26620i	−0.0718920	−	0.0522172i
$589$	26.8731			1.10729
$590$	13.3387	+	4.37801i	0.549147	+	0.180240i
$591$	−0.475300	−	0.823244i	−0.0195512	−	0.0338637i
$592$	−21.1550	−	4.76090i	−0.869467	−	0.195672i
$593$	20.5427	+	11.8603i	0.843586	+	0.487045i	0.858482	−	0.512844i	$-0.171408\pi$
$593$	20.5427	+	11.8603i	0.843586	+	0.487045i	−0.0148955	+	0.999889i	$0.504742\pi$
$594$	−0.266644	−	1.27311i	−0.0109406	−	0.0522362i
$595$	−13.9042	+	8.08424i	−0.570017	+	0.331422i
$596$	23.1643	−	10.1484i	0.948845	−	0.415695i
$597$	−1.42059	+	2.46053i	−0.0581408	+	0.100703i
$598$	8.64146	+	9.65502i	0.353375	+	0.394823i
$599$	−4.46943	+	2.58042i	−0.182616	+	0.105433i	−0.588521	−	0.808482i	$-0.700290\pi$
$599$	−4.46943	+	2.58042i	−0.182616	+	0.105433i	0.405905	+	0.913915i	$0.366956\pi$
$600$	−0.177530	−	1.84786i	−0.00724763	−	0.0754385i
$601$			34.6827i			1.41473i	0.706846	+	0.707367i	$0.250117\pi$
$601$			34.6827i			1.41473i	−0.706846	+	0.707367i	$0.749883\pi$
$602$	39.3288	−	8.36249i	1.60292	−	0.340830i
$603$		−	35.7301i		−	1.45504i
$604$	0.863064	+	0.0959158i	0.0351176	+	0.00390276i
$605$	−0.742658	+	0.428774i	−0.0301933	+	0.0174321i
$606$	−0.746897	+	0.668490i	−0.0303406	+	0.0271555i
$607$	15.7362	−	27.2560i	0.638715	−	1.10629i	−0.347001	−	0.937865i	$-0.612800\pi$
$607$	15.7362	−	27.2560i	0.638715	−	1.10629i	0.985715	−	0.168421i	$-0.0538669\pi$
$608$	18.9595	−	31.7372i	0.768911	−	1.28711i
$609$	1.96277	+	1.12524i	0.0795355	+	0.0455969i
$610$	−11.4902	+	2.40655i	−0.465225	+	0.0974385i
$611$	9.58362	+	5.53311i	0.387712	+	0.223846i
$612$	−25.0060	+	33.9899i	−1.01081	+	1.37396i
$613$	−12.4884	−	21.6306i	−0.504403	−	0.873651i	−0.999987	−	0.00509149i	$-0.998379\pi$
$613$	−12.4884	−	21.6306i	−0.504403	−	0.873651i	0.495584	−	0.868560i	$-0.334954\pi$
$614$	−8.03175	+	24.4708i	−0.324135	+	0.987561i
$615$	−0.202422			−0.00816245
$616$	0.738371	+	7.44680i	0.0297498	+	0.300040i
$617$	−46.7565			−1.88235			−0.941174	−	0.337923i	$-0.890276\pi$
$617$	−46.7565			−1.88235			−0.941174	+	0.337923i	$0.890276\pi$
$618$	0.987680	−	3.00922i	0.0397303	−	0.121049i
$619$	−12.4453	−	21.5559i	−0.500219	−	0.866405i	−1.00000		0.000253218i	$-0.999919\pi$
$619$	−12.4453	−	21.5559i	−0.500219	−	0.866405i	0.499781	−	0.866152i	$-0.333414\pi$
$620$	4.17928	−	5.68077i	0.167844	−	0.228145i
$621$	4.65123	+	2.68539i	0.186647	+	0.107761i
$622$	−9.23449	+	1.93411i	−0.370269	+	0.0775506i
$623$	7.26261	−	0.0221534i	0.290970	−	0.000887559i
$624$	0.710057	+	0.654831i	0.0284250	+	0.0262142i
$625$	−7.25499	+	12.5660i	−0.290200	+	0.502641i
$626$	−3.57820	+	3.20257i	−0.143014	+	0.128001i
$627$	0.871031	−	0.502890i	0.0347856	−	0.0200835i
$628$	18.5218	+	2.05840i	0.739099	+	0.0821391i
$629$			38.4289i			1.53226i
$630$	−6.39066	−	7.09655i	−0.254610	−	0.282733i
$631$		−	15.6996i		−	0.624991i	−0.949919	−	0.312496i	$-0.898835\pi$
$631$		−	15.6996i		−	0.624991i	0.949919	−	0.312496i	$-0.101165\pi$
$632$	−14.2549	+	1.36952i	−0.567030	+	0.0544765i
$633$	1.49165	−	0.861202i	0.0592876	−	0.0342297i
$634$	−12.9826	−	14.5053i	−0.515605	−	0.576081i
$635$	6.78080	−	11.7447i	0.269088	−	0.466074i
$636$	1.03170	−	0.451995i	0.0409096	−	0.0179228i
$637$	−9.54522	−	5.43356i	−0.378195	−	0.215286i
$638$	−1.61083	−	7.69097i	−0.0637732	−	0.304489i
$639$	1.32934	+	0.767494i	0.0525878	+	0.0303616i
$640$	−3.76044	−	8.94364i	−0.148644	−	0.353528i
$641$	2.88024	+	4.98873i	0.113763	+	0.197043i	0.917284	−	0.398233i	$-0.130376\pi$
$641$	2.88024	+	4.98873i	0.113763	+	0.197043i	−0.803522	+	0.595275i	$0.797043\pi$
$642$	−0.226799	−	0.0744394i	−0.00895103	−	0.00293789i
$643$	25.1686			0.992553			0.496276	−	0.868165i	$-0.334700\pi$
$643$	25.1686			0.992553			0.496276	+	0.868165i	$0.334700\pi$
$644$	−24.9448	−	18.2346i	−0.982963	−	0.718544i
$645$	−1.41823			−0.0558427
$646$	−62.2498	−	20.4315i	−2.44919	−	0.803866i
$647$	14.0920	+	24.4081i	0.554014	+	0.959581i	0.997979	+	0.0635369i	$0.0202380\pi$
$647$	14.0920	+	24.4081i	0.554014	+	0.959581i	−0.443965	+	0.896044i	$0.646429\pi$
$648$	−22.6144	−	10.3118i	−0.888379	−	0.405087i
$649$	−10.0251	−	5.78799i	−0.393519	−	0.227198i
$650$	−1.93989	−	9.26212i	−0.0760888	−	0.363290i
$651$	−0.00510726	−	1.67433i	−0.000200169	−	0.0656220i
$652$	2.39363	+	5.46358i	0.0937416	+	0.213970i
$653$	4.17918	−	7.23855i	0.163544	−	0.283266i	−0.772593	−	0.634901i	$-0.781041\pi$
$653$	4.17918	−	7.23855i	0.163544	−	0.283266i	0.936137	+	0.351635i	$0.114374\pi$
$654$	−2.29695	−	2.56636i	−0.0898177	−	0.100352i
$655$	−4.23235	+	2.44355i	−0.165371	+	0.0954773i
$656$	5.85700	−	1.82616i	0.228677	−	0.0712996i
$657$			40.3196i			1.57302i
$658$	−25.0981	−	8.15292i	−0.978426	−	0.317834i
$659$			21.7381i			0.846796i	0.905944	+	0.423398i	$0.139163\pi$
$659$			21.7381i			0.846796i	−0.905944	+	0.423398i	$0.860837\pi$
$660$	0.0291547	−	0.262338i	0.00113485	−	0.0102115i
$661$	14.9532	−	8.63324i	0.581613	−	0.335794i	−0.180161	−	0.983637i	$-0.557662\pi$
$661$	14.9532	−	8.63324i	0.581613	−	0.335794i	0.761774	+	0.647843i	$0.224329\pi$
$662$	19.5984	−	17.5410i	0.761712	−	0.681749i
$663$	0.855900	−	1.48246i	0.0332404	−	0.0575741i
$664$	−32.8292	+	23.4062i	−1.27402	+	0.908338i
$665$	7.37460	−	12.8636i	0.285975	−	0.498830i
$666$	−22.3333	+	4.67758i	−0.865399	+	0.181252i
$667$	28.0986	+	16.2227i	1.08798	+	0.628146i
$668$	37.1688	+	27.3447i	1.43810	+	1.05800i
$669$	−1.19298	−	2.06631i	−0.0461235	−	0.0798882i
$670$	4.54019	−	13.8329i	0.175403	−	0.534411i
$671$	9.68005			0.373694
$672$	−1.98099	−	1.17524i	−0.0764182	−	0.0453359i
$673$	11.2376			0.433178			0.216589	−	0.976263i	$-0.430507\pi$
$673$	11.2376			0.433178			0.216589	+	0.976263i	$0.430507\pi$
$674$	−9.73643	+	29.6646i	−0.375033	+	1.14264i
$675$	−1.96120	−	3.39690i	−0.0754867	−	0.130747i
$676$	−16.9768	−	12.4896i	−0.652954	−	0.480371i
$677$	−42.5887	−	24.5886i	−1.63682	−	0.945017i	−0.981919	−	0.189300i	$-0.939378\pi$
$677$	−42.5887	−	24.5886i	−1.63682	−	0.945017i	−0.654898	−	0.755717i	$-0.727288\pi$
$678$	−0.370494	+	0.0775977i	−0.0142287	+	0.00298012i
$679$	5.46109	+	9.39260i	0.209577	+	0.360455i
$680$	−14.0001	+	9.98166i	−0.536879	+	0.382779i
$681$	1.71926	−	2.97785i	0.0658823	−	0.114112i
$682$	−4.33315	+	3.87827i	−0.165925	+	0.148507i
$683$	−23.3351	+	13.4725i	−0.892893	+	0.515512i	−0.874888	−	0.484326i	$-0.839065\pi$
$683$	−23.3351	+	13.4725i	−0.892893	+	0.515512i	−0.0180052	+	0.999838i	$0.505732\pi$
$684$	4.29689	−	38.6640i	0.164296	−	1.47836i
$685$		−	12.2580i		−	0.468355i
$686$	24.9592	+	7.93978i	0.952945	+	0.303142i
$687$			0.917772i			0.0350152i
$688$	41.0359	−	12.7946i	1.56448	−	0.487790i
$689$	4.97256	−	2.87091i	0.189440	−	0.109373i
$690$	0.726852	+	0.812105i	0.0276708	+	0.0309163i
$691$	3.18922	−	5.52390i	0.121324	−	0.210139i	−0.798966	−	0.601376i	$-0.794619\pi$
$691$	3.18922	−	5.52390i	0.121324	−	0.210139i	0.920290	+	0.391237i	$0.127953\pi$
$692$	−10.5139	−	23.9986i	−0.399680	−	0.912290i
$693$	3.95808	+	6.80755i	0.150355	+	0.258598i
$694$	−1.77030	−	8.45240i	−0.0671998	−	0.320849i
$695$	0.502001	+	0.289830i	0.0190420	+	0.0109939i
$696$	2.20066	+	1.00347i	0.0834159	+	0.0380364i
$697$	−5.43634	−	9.41602i	−0.205916	−	0.356657i
$698$	2.18760	+	0.718010i	0.0828020	+	0.0271771i
$699$	−0.854758			−0.0323299
$700$	9.11848	+	20.6419i	0.344646	+	0.780190i
$701$	47.4892			1.79364			0.896820	−	0.442395i	$-0.145871\pi$
$701$	47.4892			1.79364			0.896820	+	0.442395i	$0.145871\pi$
$702$	1.93914	+	0.636460i	0.0731882	+	0.0240216i
$703$	−17.7140	−	30.6815i	−0.668095	−	1.15717i
$704$	1.52312	+	7.85367i	0.0574046	+	0.295996i
$705$	0.806100	+	0.465402i	0.0303595	+	0.0175280i
$706$	6.75900	+	32.2712i	0.254378	+	1.21454i
$707$	6.06021	−	10.5709i	0.227918	−	0.397561i
$708$	3.26363	−	1.42981i	0.122655	−	0.0537357i
$709$	7.20292	−	12.4758i	0.270511	−	0.468540i	−0.698481	−	0.715628i	$-0.746141\pi$
$709$	7.20292	−	12.4758i	0.270511	−	0.468540i	0.968993	+	0.247089i	$0.0794739\pi$
$710$	0.417127	+	0.466052i	0.0156545	+	0.0174906i
$711$	−13.0504	+	7.53466i	−0.489429	+	0.282572i
$712$	7.72851	−	0.742504i	0.289638	−	0.0278265i
$713$		−	24.0115i		−	0.899236i
$714$	−1.26115	+	3.88235i	−0.0471974	+	0.145293i
$715$		−	1.34554i		−	0.0503203i
$716$	2.58832	+	0.287651i	0.0967301	+	0.0107500i
$717$	−0.252081	+	0.145539i	−0.00941416	+	0.00543526i
$718$	27.5343	−	24.6438i	1.02757	−	0.919698i
$719$	11.9968	−	20.7790i	0.447404	−	0.774926i	−0.550812	−	0.834629i	$-0.685682\pi$
$719$	11.9968	−	20.7790i	0.447404	−	0.774926i	0.998216	+	0.0597030i	$0.0190154\pi$
$720$	−7.50504	−	6.92132i	−0.279696	−	0.257943i
$721$	0.117439	+	38.5003i	0.00437365	+	1.43382i
$722$	32.8186	−	6.87366i	1.22138	−	0.255811i
$723$	1.88250	+	1.08686i	0.0700110	+	0.0404209i
$724$	7.42269	−	10.0894i	0.275862	−	0.374971i
$725$	−11.8478	−	20.5210i	−0.440017	−	0.762132i
$726$	−0.0678734	+	0.206794i	−0.00251902	+	0.00767484i
$727$	13.9163			0.516125			0.258063	−	0.966128i	$-0.416916\pi$
$727$	13.9163			0.516125			0.258063	+	0.966128i	$0.416916\pi$
$728$	−10.6983	−	4.83889i	−0.396505	−	0.179341i
$729$	−25.7294			−0.952941
$730$	−5.12338	+	15.6097i	−0.189625	+	0.577741i
$731$	−38.0886	−	65.9714i	−1.40876	−	2.44004i
$732$	−1.76566	+	2.40000i	−0.0652605	+	0.0887067i
$733$	−38.3853	−	22.1618i	−1.41779	−	0.818563i	−0.421688	−	0.906741i	$-0.638562\pi$
$733$	−38.3853	−	22.1618i	−1.41779	−	0.818563i	−0.996105	+	0.0881777i	$0.971896\pi$
$734$	−24.8996	+	5.21506i	−0.919060	+	0.192491i
$735$	−0.802869	−	0.457029i	−0.0296143	−	0.0168578i
$736$	−28.3576	−	16.9406i	−1.04527	−	0.624438i
$737$	−6.00241	+	10.3965i	−0.221102	+	0.382959i
$738$	4.81050	−	4.30550i	0.177077	−	0.158488i
$739$	−4.78366	+	2.76185i	−0.175970	+	0.101596i	−0.585398	−	0.810746i	$-0.699062\pi$
$739$	−4.78366	+	2.76185i	−0.175970	+	0.101596i	0.409428	+	0.912342i	$0.365728\pi$
$740$	−9.24070	−	1.02696i	−0.339695	−	0.0377517i
$741$			1.57812i			0.0579738i
$742$	−10.1747	+	9.16264i	−0.373525	+	0.336371i
$743$			9.58657i			0.351697i	0.984417	+	0.175849i	$0.0562669\pi$
$743$			9.58657i			0.351697i	−0.984417	+	0.175849i	$0.943733\pi$
$744$	−0.171177	−	1.78173i	−0.00627566	−	0.0653215i
$745$	9.39083	−	5.42180i	0.344053	−	0.198639i
$746$	−5.75257	−	6.42730i	−0.210617	−	0.235320i
$747$	−21.2135	+	36.7428i	−0.776160	+	1.34435i
$748$	12.9861	−	5.68929i	0.474819	−	0.208021i
$749$	2.90168	−	0.00885112i	0.106025	−	0.000323413i
$750$	−0.354474	−	1.69245i	−0.0129436	−	0.0617997i
$751$	11.5367	+	6.66073i	0.420981	+	0.243054i	0.695497	−	0.718529i	$-0.255184\pi$
$751$	11.5367	+	6.66073i	0.420981	+	0.243054i	−0.274516	+	0.961583i	$0.588518\pi$
$752$	−27.5228	−	6.19395i	−1.00365	−	0.225870i
$753$	−0.400499	−	0.693685i	−0.0145950	−	0.0252793i
$754$	11.7146	+	3.84492i	0.426619	+	0.140024i
$755$	0.372337			0.0135507
$756$	−4.83873	−	0.522811i	−0.175983	−	0.0190145i
$757$	−30.9744			−1.12578			−0.562891	−	0.826531i	$-0.690311\pi$
$757$	−30.9744			−1.12578			−0.562891	+	0.826531i	$0.690311\pi$
$758$	1.27417	+	0.418205i	0.0462799	+	0.0151899i
$759$	−0.449339	−	0.778277i	−0.0163100	−	0.0282497i
$760$	6.57654	−	14.4227i	0.238556	−	0.523167i
$761$	−5.81994	−	3.36014i	−0.210973	−	0.121805i	0.390791	−	0.920480i	$-0.372202\pi$
$761$	−5.81994	−	3.36014i	−0.210973	−	0.121805i	−0.601763	+	0.798674i	$0.705535\pi$
$762$	−0.705589	−	3.36887i	−0.0255608	−	0.122041i
$763$	36.3219	+	20.8230i	1.31494	+	0.753844i
$764$	−7.00610	−	15.9918i	−0.253472	−	0.578563i
$765$	−9.04654	+	15.6691i	−0.327078	+	0.566517i
$766$	−7.57183	−	8.45993i	−0.273581	−	0.305670i
$767$	15.7299	−	9.08167i	0.567975	−	0.327920i
$768$	−2.22500	−	1.05489i	−0.0802878	−	0.0380651i
$769$		−	46.6336i		−	1.68165i	−0.541306	−	0.840826i	$-0.682070\pi$
$769$		−	46.6336i		−	1.68165i	0.541306	−	0.840826i	$-0.317930\pi$
$770$	0.667336	+	3.13848i	0.0240491	+	0.113103i
$771$		−	0.897800i		−	0.0323335i
$772$	−0.941660	+	8.47319i	−0.0338911	+	0.304957i
$773$	23.7955	−	13.7383i	0.855863	−	0.494133i	−0.00676182	−	0.999977i	$-0.502152\pi$
$773$	23.7955	−	13.7383i	0.855863	−	0.494133i	0.862625	+	0.505844i	$0.168819\pi$
$774$	33.7038	−	30.1656i	1.21146	−	1.08428i
$775$	−8.76806	+	15.1867i	−0.314958	+	0.545523i
$776$	6.74284	+	9.45738i	0.242054	+	0.339500i
$777$	−1.90824	+	1.10950i	−0.0684578	+	0.0398030i
$778$	−7.67775	+	1.60806i	−0.275261	+	0.0576516i
$779$	8.68071	+	5.01181i	0.311019	+	0.179567i
$780$	0.333603	+	0.245428i	0.0119449	+	0.00878774i
$781$	−0.257867	−	0.446639i	−0.00922722	−	0.0159820i
$782$	−18.2558	+	55.6210i	−0.652826	+	1.98900i
$783$	5.11048			0.182634
$784$	27.3538	+	5.98082i	0.976921	+	0.213601i
$785$	7.99054			0.285194
$786$	−0.386805	+	1.17850i	−0.0137969	+	0.0420358i
$787$	−19.1783	−	33.2178i	−0.683632	−	1.18409i	−0.973865	−	0.227130i	$-0.927066\pi$
$787$	−19.1783	−	33.2178i	−0.683632	−	1.18409i	0.290232	−	0.956956i	$-0.406267\pi$
$788$	9.95071	+	7.32062i	0.354479	+	0.260786i
$789$	2.51861	+	1.45412i	0.0896649	+	0.0517681i
$790$	−6.00987	+	1.25873i	−0.213822	+	0.0447836i
$791$	3.97797	−	2.31289i	0.141440	−	0.0822369i
$792$	4.88706	+	6.85450i	0.173654	+	0.243564i
$793$	−7.59426	+	13.1537i	−0.269680	+	0.467100i
$794$	−3.73524	+	3.34313i	−0.132559	+	0.118643i
$795$	0.418253	−	0.241479i	0.0148339	−	0.00856437i
$796$	4.07823	−	36.6964i	0.144549	−	1.30067i
$797$		−	15.2204i		−	0.539135i	−0.962982	−	0.269567i	$-0.913119\pi$
$797$		−	15.2204i		−	0.539135i	0.962982	−	0.269567i	$-0.0868807\pi$
$798$	−0.782689	−	3.68099i	−0.0277069	−	0.130306i
$799$			49.9962i			1.76874i
$800$	11.7495	+	21.0697i	0.415408	+	0.744925i
$801$	7.07547	−	4.08503i	0.250000	−	0.144337i
$802$	26.4653	+	29.5695i	0.934524	+	1.04413i
$803$	6.77342	−	11.7319i	0.239029	−	0.414010i
$804$	−1.48278	−	3.38453i	−0.0522937	−	0.119363i
$805$	−11.4938	−	6.58930i	−0.405104	−	0.232242i
$806$	−1.87047	−	8.93068i	−0.0658847	−	0.314570i
$807$	−1.09865	−	0.634305i	−0.0386743	−	0.0223286i
$808$	5.40439	−	11.8521i	0.190126	−	0.416957i
$809$	−1.02020	−	1.76704i	−0.0358684	−	0.0621260i	0.847534	−	0.530741i	$-0.178086\pi$
$809$	−1.02020	−	1.76704i	−0.0358684	−	0.0621260i	−0.883402	+	0.468615i	$0.844753\pi$
$810$	−10.1255	−	3.32337i	−0.355774	−	0.116771i
$811$	16.5953			0.582739			0.291369	−	0.956611i	$-0.405889\pi$
$811$	16.5953			0.582739			0.291369	+	0.956611i	$0.405889\pi$
$812$	−29.2313	−	3.15836i	−1.02582	−	0.110837i
$813$	3.07113			0.107709
$814$	7.28418	+	2.39080i	0.255310	+	0.0837974i
$815$	1.27880	+	2.21494i	0.0447943	+	0.0775861i
$816$	−0.958123	+	4.25742i	−0.0335410	+	0.149040i
$817$	60.8196	+	35.1142i	2.12781	+	1.22849i
$818$	4.98417	+	23.7972i	0.174267	+	0.832048i
$819$	−12.3556	+	0.0376888i	−0.431740	+	0.00131695i
$820$	2.40947	−	1.05560i	0.0841425	−	0.0368633i
$821$	−5.66947	+	9.81981i	−0.197866	+	0.342714i	−0.947836	−	0.318758i	$-0.896734\pi$
$821$	−5.66947	+	9.81981i	−0.197866	+	0.342714i	0.749970	+	0.661471i	$0.230068\pi$
$822$	−2.07485	−	2.31821i	−0.0723685	−	0.0808567i
$823$	−31.3908	+	18.1235i	−1.09421	+	0.631745i	−0.934695	−	0.355450i	$-0.884327\pi$
$823$	−31.3908	+	18.1235i	−1.09421	+	0.631745i	−0.159518	+	0.987195i	$0.550994\pi$
$824$	3.93613	+	40.9701i	0.137122	+	1.42726i
$825$			0.656325i			0.0228503i
$826$	−32.1861	+	28.9845i	−1.11990	+	1.00850i
$827$			1.31009i			0.0455564i	0.999741	+	0.0227782i	$0.00725115\pi$
$827$			1.31009i			0.0455564i	−0.999741	+	0.0227782i	$0.992749\pi$
$828$	−34.5468	−	3.83933i	−1.20058	−	0.133426i
$829$	25.1741	−	14.5343i	0.874332	−	0.504796i	0.00554678	−	0.999985i	$-0.498234\pi$
$829$	25.1741	−	14.5343i	0.874332	−	0.504796i	0.868785	+	0.495189i	$0.164901\pi$
$830$	−12.8816	+	11.5294i	−0.447128	+	0.400190i
$831$	0.814216	−	1.41026i	0.0282448	−	0.0489215i
$832$	−11.8668	−	4.09175i	−0.411408	−	0.141856i
$833$	−0.302725	−	49.6210i	−0.0104888	−	1.71927i
$834$	0.143995	−	0.0301589i	0.00498614	−	0.00104432i
$835$	17.1345	+	9.89262i	0.592965	+	0.342348i
$836$	−7.74556	+	10.5283i	−0.267886	+	0.364129i
$837$	−1.89102	−	3.27534i	−0.0653632	−	0.113212i
$838$	0.531149	−	1.61828i	0.0183482	−	0.0559026i
$839$	14.0445			0.484871			0.242436	−	0.970167i	$-0.422054\pi$
$839$	14.0445			0.484871			0.242436	+	0.970167i	$0.422054\pi$
$840$	−0.899857	−	0.407010i	−0.0310480	−	0.0140432i
$841$	1.87292			0.0645835
$842$	14.8283	−	45.1781i	0.511016	−	1.55694i
$843$	−0.719479	−	1.24617i	−0.0247802	−	0.0429205i
$844$	−13.2643	+	18.0298i	−0.456577	+	0.620612i
$845$	−7.82618	−	4.51845i	−0.269229	−	0.155439i
$846$	−29.0558	+	6.08555i	−0.998958	+	0.209225i
$847$	−0.00807040	−	2.64574i	−0.000277302	−	0.0909087i
$848$	−9.92348	+	10.7604i	−0.340774	+	0.369513i
$849$	0.0727177	−	0.125951i	0.00249567	−	0.00432262i
$850$	31.8571	−	28.5128i	1.09269	−	0.977980i
$851$	−27.4143	+	15.8277i	−0.939751	+	0.542565i
$852$	0.157772	+	0.0175339i	0.00540518	+	0.000600700i
$853$		−	18.8052i		−	0.643877i	−0.946761	−	0.321939i	$-0.895666\pi$
$853$		−	18.8052i		−	0.643877i	0.946761	−	0.321939i	$-0.104334\pi$
$854$	11.1900	−	34.4475i	0.382914	−	1.17877i
$855$		−	16.6802i		−	0.570450i
$856$	3.08783	−	0.296658i	0.105540	−	0.0101396i
$857$	6.37694	−	3.68173i	0.217832	−	0.125765i	−0.387114	−	0.922032i	$-0.626528\pi$
$857$	6.37694	−	3.68173i	0.217832	−	0.125765i	0.604946	+	0.796266i	$0.293195\pi$
$858$	−0.227752	−	0.254465i	−0.00777531	−	0.00868728i
$859$	6.50258	−	11.2628i	0.221865	−	0.384282i	−0.733509	−	0.679680i	$-0.762119\pi$
$859$	6.50258	−	11.2628i	0.221865	−	0.384282i	0.955374	+	0.295398i	$0.0954521\pi$
$860$	16.8815	−	7.39588i	0.575654	−	0.252197i
$861$	0.310611	−	0.541804i	0.0105856	−	0.0184646i
$862$	7.85003	+	37.4804i	0.267373	+	1.27659i
$863$	15.9808	+	9.22650i	0.543991	+	0.314074i	0.746695	−	0.665167i	$-0.231639\pi$
$863$	15.9808	+	9.22650i	0.543991	+	0.314074i	−0.202704	+	0.979240i	$0.564973\pi$
$864$	−5.20235	−	0.0775237i	−0.176987	−	0.00263741i
$865$	−5.61708	−	9.72907i	−0.190987	−	0.330798i
$866$	−33.3256	−	10.9381i	−1.13245	−	0.371690i
$867$	5.11745			0.173798
$868$	8.79218	+	19.9032i	0.298426	+	0.675559i
$869$	5.06308			0.171753
$870$	0.985337	+	0.323405i	0.0334061	+	0.0109645i
$871$	−9.41811	−	16.3127i	−0.319121	−	0.552733i
$872$	40.7242	+	18.5696i	1.37910	+	0.628846i
$873$	10.5848	+	6.11114i	0.358242	+	0.206831i
$874$	−11.0634	−	52.8227i	−0.374225	−	1.78676i
$875$	10.5655	+	18.1718i	0.357180	+	0.614318i
$876$	1.67324	+	3.81927i	0.0565337	+	0.129041i
$877$	11.6968	−	20.2595i	0.394974	−	0.684115i	−0.598124	−	0.801404i	$-0.704087\pi$
$877$	11.6968	−	20.2595i	0.394974	−	0.684115i	0.993098	+	0.117289i	$0.0374203\pi$
$878$	20.2086	+	22.5789i	0.682006	+	0.761999i
$879$	0.908870	−	0.524736i	0.0306554	−	0.0176989i
$880$	1.02102	+	3.27471i	0.0344187	+	0.110390i
$881$			23.6479i			0.796717i	0.917230	+	0.398359i	$0.130420\pi$
$881$			23.6479i			0.796717i	−0.917230	+	0.398359i	$0.869580\pi$
$882$	28.8009	−	6.21582i	0.969777	−	0.209297i
$883$		−	41.4991i		−	1.39656i	−0.715826	−	0.698278i	$-0.753950\pi$
$883$		−	41.4991i		−	1.39656i	0.715826	−	0.698278i	$-0.246050\pi$
$884$	−2.45712	+	22.1095i	−0.0826418	+	0.743622i
$885$	1.32308	−	0.763880i	0.0444748	−	0.0256775i
$886$	−2.12351	+	1.90059i	−0.0713406	+	0.0638515i
$887$	13.8731	−	24.0288i	0.465812	−	0.806809i	−0.533426	−	0.845847i	$-0.679096\pi$
$887$	13.8731	−	24.0288i	0.465812	−	0.806809i	0.999238	+	0.0390373i	$0.0124291\pi$
$888$	−1.92140	+	1.36990i	−0.0644781	+	0.0459710i
$889$	21.0309	+	36.1714i	0.705354	+	1.21315i
$890$	3.25834	−	0.682439i	0.109220	−	0.0228754i
$891$	7.61011	+	4.39370i	0.254948	+	0.147194i
$892$	24.9759	+	18.3745i	0.836255	+	0.615223i
$893$	−23.0460	−	39.9168i	−0.771203	−	1.33576i
$894$	0.858252	−	2.61489i	0.0287042	−	0.0874549i
$895$	1.11664			0.0373250
$896$	29.7088	+	3.65856i	0.992503	+	0.122224i
$897$	1.41007			0.0470810
$898$	−8.64430	+	26.3371i	−0.288464	+	0.878881i
$899$	−11.4239	−	19.7867i	−0.381007	−	0.659923i
$900$	20.4481	+	15.0435i	0.681604	+	0.501449i
$901$	22.4656	+	12.9705i	0.748438	+	0.432111i
$902$	−2.12302	+	0.444653i	−0.0706887	+	0.0148053i
$903$	2.17623	−	3.79603i	0.0724204	−	0.126324i
$904$	4.00541	−	2.85574i	0.133218	−	0.0949805i
$905$	2.68535	−	4.65116i	0.0892639	−	0.154610i
$906$	0.0704154	−	0.0630234i	0.00233940	−	0.00209381i
$907$	−41.9052	+	24.1940i	−1.39144	+	0.803348i	−0.993475	−	0.114053i	$-0.963617\pi$
$907$	−41.9052	+	24.1940i	−1.39144	+	0.803348i	−0.397965	+	0.917401i	$0.630283\pi$
$908$	−4.93566	+	44.4117i	−0.163796	+	1.47386i
$909$		−	13.7072i		−	0.454641i
$910$	−4.78825	−	1.55542i	−0.158729	−	0.0515618i
$911$			59.2554i			1.96322i	0.190904	+	0.981609i	$0.438858\pi$
$911$			59.2554i			1.96322i	−0.190904	+	0.981609i	$0.561142\pi$
$912$	−1.19751	−	3.84076i	−0.0396537	−	0.127180i
$913$	12.3451	−	7.12743i	0.408562	−	0.235883i
$914$	−4.64044	−	5.18472i	−0.153492	−	0.171495i
$915$	−0.638770	+	1.10638i	−0.0211171	+	0.0365759i
$916$	−4.78606	−	10.9244i	−0.158136	−	0.360954i
$917$	−0.0459926	−	15.0779i	−0.00151881	−	0.497915i
$918$	1.89020	+	9.02487i	0.0623860	+	0.297865i
$919$	−23.1024	−	13.3382i	−0.762078	−	0.439986i	0.0679632	−	0.997688i	$-0.478350\pi$
$919$	−23.1024	−	13.3382i	−0.762078	−	0.439986i	−0.830041	+	0.557702i	$0.811683\pi$
$920$	−12.8869	−	5.87622i	−0.424868	−	0.193733i
$921$	1.40139	+	2.42728i	0.0461773	+	0.0799815i
$922$	−1.34710	−	0.442141i	−0.0443642	−	0.0145611i
$923$	0.809216			0.0266357
$924$	0.657438	+	0.480586i	0.0216281	+	0.0158101i
$925$	23.1186			0.760135
$926$	−10.0460	−	3.29728i	−0.330132	−	0.108355i
$927$	21.6554	+	37.5082i	0.711256	+	1.23193i
$928$	−31.4279	−	0.468329i	−1.03167	−	0.0153736i
$929$	20.4275	+	11.7938i	0.670204	+	0.386942i	0.796154	−	0.605094i	$-0.206865\pi$
$929$	20.4275	+	11.7938i	0.670204	+	0.386942i	−0.125950	+	0.992037i	$0.540198\pi$
$930$	−0.157330	−	0.751179i	−0.00515905	−	0.0246321i
$931$	23.1147	+	39.4777i	0.757555	+	1.29383i
$932$	10.1744	−	4.45745i	0.333272	−	0.146009i
$933$	−0.513369	+	0.889181i	−0.0168070	+	0.0291105i
$934$	4.78334	+	5.34438i	0.156516	+	0.174874i
$935$	5.26459	−	3.03951i	0.172170	−	0.0994027i
$936$	−13.1482	+	1.26319i	−0.429763	+	0.0412888i
$937$			26.2289i			0.856861i	0.903575	+	0.428430i	$0.140933\pi$
$937$			26.2289i			0.856861i	−0.903575	+	0.428430i	$0.859067\pi$
$938$	30.0583	+	33.3784i	0.981439	+	1.08984i
$939$			0.522581i			0.0170538i
$940$	−12.0222	−	1.33608i	−0.392121	−	0.0435780i
$941$	48.2399	−	27.8513i	1.57258	−	0.907927i	0.576724	−	0.816939i	$-0.304331\pi$
$941$	48.2399	−	27.8513i	1.57258	−	0.907927i	0.995852	−	0.0909880i	$-0.0290025\pi$
$942$	1.51115	−	1.35251i	0.0492359	−	0.0440672i
$943$	4.47812	−	7.75633i	0.145828	−	0.252581i
$944$	−31.3913	+	34.0387i	−1.02170	+	1.10787i
$945$	−2.08678	+	0.00636540i	−0.0678831	+	0.000207067i
$946$	−14.8745	+	3.11537i	−0.483611	+	0.101289i
$947$	20.7813	+	11.9981i	0.675302	+	0.389886i	0.798083	−	0.602548i	$-0.205848\pi$
$947$	20.7813	+	11.9981i	0.675302	+	0.389886i	−0.122780	+	0.992434i	$0.539181\pi$
$948$	−0.923513	+	1.25530i	−0.0299943	+	0.0407704i
$949$	10.6279	+	18.4080i	0.344995	+	0.597549i
$950$	−12.2915	+	37.4492i	−0.398788	+	1.21501i
$951$	−2.11844			−0.0686952
$952$	−5.23420	−	52.7892i	−0.169641	−	1.71091i
$953$	27.6586			0.895951			0.447975	−	0.894046i	$-0.352145\pi$
$953$	27.6586			0.895951			0.447975	+	0.894046i	$0.352145\pi$
$954$	−4.80343	+	14.6349i	−0.155517	+	0.473822i
$955$	−3.74302	−	6.48310i	−0.121121	−	0.209788i
$956$	2.24161	−	3.04696i	0.0724989	−	0.0985456i
$957$	−0.740557	−	0.427561i	−0.0239388	−	0.0138211i
$958$	−23.3248	+	4.88523i	−0.753589	+	0.157834i
$959$	32.8098	+	18.8096i	1.05949	+	0.607393i
$960$	−0.998144	−	0.344166i	−0.0322150	−	0.0111079i
$961$	7.04570	−	12.2035i	0.227281	−	0.393662i
$962$	−8.96335	+	8.02240i	−0.288990	+	0.258653i
$963$	2.82691	−	1.63212i	0.0910960	−	0.0525943i
$964$	−28.0757	−	3.12017i	−0.904256	−	0.100494i
$965$			3.65545i			0.117673i
$966$	−3.28901	+	0.699343i	−0.105822	+	0.0225010i
$967$		−	27.1700i		−	0.873728i	−0.899528	−	0.436864i	$-0.856089\pi$
$967$		−	27.1700i		−	0.873728i	0.899528	−	0.436864i	$-0.143911\pi$
$968$	−0.270491	−	2.81546i	−0.00869391	−	0.0904924i
$969$	−6.17461	+	3.56491i	−0.198357	+	0.114521i
$970$	3.32136	+	3.71092i	0.106642	+	0.119151i
$971$	−4.66797	+	8.08516i	−0.149802	+	0.259465i	−0.931154	−	0.364625i	$-0.881197\pi$
$971$	−4.66797	+	8.08516i	−0.149802	+	0.259465i	0.781352	+	0.624091i	$0.214530\pi$
$972$	−7.53216	+	3.29988i	−0.241594	+	0.105844i
$973$	−1.54607	+	0.898920i	−0.0495646	+	0.0288181i
$974$	−0.350975	−	1.67575i	−0.0112460	−	0.0536945i
$975$	−0.891841	−	0.514905i	−0.0285618	−	0.0164901i
$976$	8.50128	−	37.7754i	0.272119	−	1.20916i
$977$	−9.76957	−	16.9214i	−0.312556	−	0.541363i	0.666359	−	0.745631i	$-0.267852\pi$
$977$	−9.76957	−	16.9214i	−0.312556	−	0.541363i	−0.978915	+	0.204268i	$0.934519\pi$
$978$	0.616754	+	0.202429i	0.0197216	+	0.00647298i
$979$	−2.74502			−0.0877313
$980$	11.9401	+	1.25326i	0.381412	+	0.0400338i
$981$	47.0984			1.50374
$982$	26.0982	+	8.56590i	0.832828	+	0.273349i
$983$	−20.6184	−	35.7122i	−0.657626	−	1.13904i	−0.981229	−	0.192848i	$-0.938228\pi$
$983$	−20.6184	−	35.7122i	−0.657626	−	1.13904i	0.323603	−	0.946193i	$-0.395106\pi$
$984$	0.276997	−	0.607471i	0.00883035	−	0.0193655i
$985$	4.58720	+	2.64842i	0.146160	+	0.0843857i
$986$	11.4189	+	54.5202i	0.363652	+	1.73628i
$987$	−2.48263	+	1.44346i	−0.0790230	+	0.0459459i
$988$	−8.22971	−	18.7847i	−0.261822	−	0.597622i
$989$	31.3750	−	54.3431i	0.997667	−	1.72801i
$990$	2.40725	+	2.68960i	0.0765074	+	0.0854810i
$991$	12.4505	−	7.18829i	0.395503	−	0.228344i	−0.289039	−	0.957317i	$-0.593336\pi$
$991$	12.4505	−	7.18829i	0.395503	−	0.228344i	0.684542	+	0.728974i	$0.260002\pi$
$992$	11.3291	+	20.3157i	0.359698	+	0.645024i
$993$		−	2.86226i		−	0.0908310i
$994$	−1.88751	+	0.401340i	−0.0598680	+	0.0127297i
$995$		−	15.8313i		−	0.501887i
$996$	−0.484634	+	4.36080i	−0.0153562	+	0.138177i
$997$	−10.7949	+	6.23242i	−0.341877	+	0.197383i	−0.661102	−	0.750296i	$-0.729911\pi$
$997$	−10.7949	+	6.23242i	−0.341877	+	0.197383i	0.319225	+	0.947679i	$0.396577\pi$
$998$	5.62082	−	5.03076i	0.177924	−	0.159246i
$999$	−2.49301	+	4.31803i	−0.0788755	+	0.136616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.l.a.243.17	yes	80
4.3	odd	2	inner	308.2.l.a.243.11	yes	80
7.3	odd	6	inner	308.2.l.a.199.11	✓	80
28.3	even	6	inner	308.2.l.a.199.17	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.l.a.199.11	✓	80	7.3	odd	6	inner
308.2.l.a.199.17	yes	80	28.3	even	6	inner
308.2.l.a.243.11	yes	80	4.3	odd	2	inner
308.2.l.a.243.17	yes	80	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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.441022 + 1.34369i) q^{2} +(0.0769501 + 0.133281i) q^{3} +(-1.61100 - 1.18519i) q^{4} +(-0.742658 - 0.428774i) q^{5} +(-0.213026 + 0.0446169i) q^{6} +(2.28724 - 1.32986i) q^{7} +(2.30302 - 1.64198i) q^{8} +(1.48816 - 2.57756i) q^{9} +(0.903667 - 0.808802i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(0.0339978 - 0.305917i) q^{12} -1.56905i q^{13} +(0.778191 + 3.65984i) q^{14} -0.131977i q^{15} +(1.19063 + 3.81869i) q^{16} +(6.13912 - 3.54442i) q^{17} +(2.80713 + 3.13638i) q^{18} +(-3.26764 + 5.65971i) q^{19} +(0.688241 + 1.57095i) q^{20} +(0.353249 + 0.202514i) q^{21} +(-0.289908 - 1.38418i) q^{22} +(5.05703 + 2.91968i) q^{23} +(0.396063 + 0.180599i) q^{24} +(-2.13231 - 3.69326i) q^{25} +(2.10832 + 0.691988i) q^{26} +0.919756 q^{27} +(-5.26088 - 0.568424i) q^{28} +5.55634 q^{29} +(0.177336 + 0.0582047i) q^{30} +(-2.05600 - 3.56110i) q^{31} +(-5.65623 - 0.0842873i) q^{32} +(-0.133281 - 0.0769501i) q^{33} +(2.05511 + 9.81224i) q^{34} +(-2.26885 + 0.00692075i) q^{35} +(-5.45233 + 2.38870i) q^{36} +(-2.71052 + 4.69475i) q^{37} +(-6.16379 - 6.88675i) q^{38} +(0.209126 - 0.120739i) q^{39} +(-2.41439 + 0.231959i) q^{40} -1.53377i q^{41} +(-0.427907 + 0.385343i) q^{42} -10.7461i q^{43} +(1.98776 + 0.220908i) q^{44} +(-2.21038 + 1.27617i) q^{45} +(-6.15340 + 5.50743i) q^{46} +(-3.52639 + 6.10789i) q^{47} +(-0.417341 + 0.452538i) q^{48} +(3.46295 - 6.08342i) q^{49} +(5.90299 - 1.23634i) q^{50} +(0.944812 + 0.545488i) q^{51} +(-1.85963 + 2.52775i) q^{52} +(1.82971 + 3.16915i) q^{53} +(-0.405633 + 1.23587i) q^{54} +0.857547 q^{55} +(3.08395 - 6.81830i) q^{56} -1.00578 q^{57} +(-2.45047 + 7.46599i) q^{58} +(5.78799 + 10.0251i) q^{59} +(-0.156418 + 0.212614i) q^{60} +(-8.38317 - 4.84002i) q^{61} +(5.69176 - 1.19210i) q^{62} +(-0.0240201 - 7.87455i) q^{63} +(2.60778 - 7.56303i) q^{64} +(-0.672769 + 1.16527i) q^{65} +(0.162177 - 0.145152i) q^{66} +(10.3965 - 6.00241i) q^{67} +(-14.0909 - 1.56599i) q^{68} +0.898677i q^{69} +(0.991313 - 3.05168i) q^{70} +0.515735i q^{71} +(-0.805067 - 8.37971i) q^{72} +(-11.7319 + 6.77342i) q^{73} +(-5.11289 - 5.71258i) q^{74} +(0.328162 - 0.568394i) q^{75} +(11.9720 - 5.24501i) q^{76} +(-1.31588 + 2.29531i) q^{77} +(0.0700063 + 0.334249i) q^{78} +(-4.38476 - 2.53154i) q^{79} +(0.753121 - 3.34649i) q^{80} +(-4.39370 - 7.61011i) q^{81} +(2.06091 + 0.676428i) q^{82} -14.2549 q^{83} +(-0.329065 - 0.744919i) q^{84} -6.07902 q^{85} +(14.4394 + 4.73925i) q^{86} +(0.427561 + 0.740557i) q^{87} +(-1.17348 + 2.57351i) q^{88} +(2.37726 + 1.37251i) q^{89} +(-0.739941 - 3.53288i) q^{90} +(-2.08662 - 3.58881i) q^{91} +(-4.68648 - 10.6971i) q^{92} +(0.316419 - 0.548054i) q^{93} +(-6.65189 - 7.43209i) q^{94} +(4.85347 - 2.80215i) q^{95} +(-0.424013 - 0.760356i) q^{96} +4.10652i q^{97} +(6.64698 + 7.33605i) q^{98} +2.97631i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 12 q^{8} - 40 q^{9} - 18 q^{10} - 30 q^{12} - 4 q^{14} - 4 q^{16} - 10 q^{18} - 8 q^{21} + 40 q^{25} + 30 q^{26} + 16 q^{28} - 16 q^{29} + 36 q^{30} - 20 q^{32} - 20 q^{36} - 8 q^{37} - 12 q^{38}+ \cdots + 78 q^{98}+O(q^{100}) \) 80 * q + 12 * q^8 - 40 * q^9 - 18 * q^10 - 30 * q^12 - 4 * q^14 - 4 * q^16 - 10 * q^18 - 8 * q^21 + 40 * q^25 + 30 * q^26 + 16 * q^28 - 16 * q^29 + 36 * q^30 - 20 * q^32 - 20 * q^36 - 8 * q^37 - 12 * q^38 - 60 * q^40 + 4 * q^44 + 24 * q^45 - 10 * q^46 - 24 * q^49 - 64 * q^50 + 54 * q^52 - 30 * q^54 + 38 * q^56 + 80 * q^57 + 10 * q^58 - 12 * q^60 - 36 * q^64 - 16 * q^65 + 30 * q^66 + 60 * q^68 - 22 * q^70 - 38 * q^72 - 72 * q^73 + 28 * q^74 - 24 * q^78 + 42 * q^80 - 64 * q^81 - 90 * q^82 + 88 * q^84 - 2 * q^86 + 12 * q^88 - 120 * q^89 + 36 * q^92 + 8 * q^93 - 54 * q^94 - 42 * q^96 + 78 * q^98

Introduction

L-functions

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