LMFDB - Embedded newform 336.2.w.b.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(85,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("336.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.w (of order $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			85.1
Character	$\chi$	$=$	336.85
Dual form			336.2.w.b.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40848 + 0.127230i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.96762 - 0.358402i) q^{4} +(-0.805240 - 0.805240i) q^{5} +(0.905980 - 1.08591i) q^{6} -1.00000i q^{7} +(-2.72576 + 0.755143i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.40848 + 0.127230i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.96762 - 0.358402i) q^{4} +(-0.805240 - 0.805240i) q^{5} +(0.905980 - 1.08591i) q^{6} -1.00000i q^{7} +(-2.72576 + 0.755143i) q^{8} -1.00000i q^{9} +(1.23661 + 1.03171i) q^{10} +(-0.326956 - 0.326956i) q^{11} +(-1.13789 + 1.64475i) q^{12} +(-3.46355 + 3.46355i) q^{13} +(0.127230 + 1.40848i) q^{14} +1.13878 q^{15} +(3.74310 - 1.41040i) q^{16} -7.57049 q^{17} +(0.127230 + 1.40848i) q^{18} +(3.34700 - 3.34700i) q^{19} +(-1.87301 - 1.29581i) q^{20} +(0.707107 + 0.707107i) q^{21} +(0.502109 + 0.418912i) q^{22} -6.11816i q^{23} +(1.39344 - 2.46137i) q^{24} -3.70318i q^{25} +(4.43766 - 5.31900i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.358402 - 1.96762i) q^{28} +(-4.51921 + 4.51921i) q^{29} +(-1.60395 + 0.144888i) q^{30} -6.80843 q^{31} +(-5.09262 + 2.46276i) q^{32} +0.462386 q^{33} +(10.6629 - 0.963195i) q^{34} +(-0.805240 + 0.805240i) q^{35} +(-0.358402 - 1.96762i) q^{36} +(-0.895292 - 0.895292i) q^{37} +(-4.28833 + 5.14001i) q^{38} -4.89819i q^{39} +(2.80296 + 1.58682i) q^{40} -10.9937i q^{41} +(-1.08591 - 0.905980i) q^{42} +(-5.85617 - 5.85617i) q^{43} +(-0.760509 - 0.526145i) q^{44} +(-0.805240 + 0.805240i) q^{45} +(0.778415 + 8.61730i) q^{46} +1.34460 q^{47} +(-1.64946 + 3.64407i) q^{48} -1.00000 q^{49} +(0.471156 + 5.21584i) q^{50} +(5.35314 - 5.35314i) q^{51} +(-5.57362 + 8.05630i) q^{52} +(2.55227 + 2.55227i) q^{53} +(-1.08591 - 0.905980i) q^{54} +0.526557i q^{55} +(0.755143 + 2.72576i) q^{56} +4.73337i q^{57} +(5.79023 - 6.94019i) q^{58} +(5.44250 + 5.44250i) q^{59} +(2.24070 - 0.408142i) q^{60} +(-6.94278 + 6.94278i) q^{61} +(9.58952 - 0.866238i) q^{62} -1.00000 q^{63} +(6.85952 - 4.11668i) q^{64} +5.57797 q^{65} +(-0.651261 + 0.0588295i) q^{66} +(2.62373 - 2.62373i) q^{67} +(-14.8959 + 2.71328i) q^{68} +(4.32619 + 4.32619i) q^{69} +(1.03171 - 1.23661i) q^{70} +2.61541i q^{71} +(0.755143 + 2.72576i) q^{72} +13.6312i q^{73} +(1.37491 + 1.14709i) q^{74} +(2.61854 + 2.61854i) q^{75} +(5.38606 - 7.78520i) q^{76} +(-0.326956 + 0.326956i) q^{77} +(0.623198 + 6.89900i) q^{78} +9.66695 q^{79} +(-4.14980 - 1.87838i) q^{80} -1.00000 q^{81} +(1.39874 + 15.4845i) q^{82} +(-0.419553 + 0.419553i) q^{83} +(1.64475 + 1.13789i) q^{84} +(6.09606 + 6.09606i) q^{85} +(8.99338 + 7.50321i) q^{86} -6.39113i q^{87} +(1.13810 + 0.644305i) q^{88} +2.60923i q^{89} +(1.03171 - 1.23661i) q^{90} +(3.46355 + 3.46355i) q^{91} +(-2.19276 - 12.0382i) q^{92} +(4.81428 - 4.81428i) q^{93} +(-1.89384 + 0.171074i) q^{94} -5.39027 q^{95} +(1.85960 - 5.34246i) q^{96} -3.48313 q^{97} +(1.40848 - 0.127230i) q^{98} +(-0.326956 + 0.326956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) $ 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

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 $

$2$	−1.40848	+	0.127230i	−0.995945	+	0.0899654i
$2$	−1.40848	+	0.127230i	−0.995945	+	0.0899654i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.96762	−	0.358402i	0.983812	−	0.179201i
$5$	−0.805240	−	0.805240i	−0.360114	−	0.360114i	0.503741	−	0.863855i	$-0.331957\pi$
$5$	−0.805240	−	0.805240i	−0.360114	−	0.360114i	−0.863855	+	0.503741i	$0.831957\pi$
$6$	0.905980	−	1.08591i	0.369865	−	0.443321i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.72576	+	0.755143i	−0.963701	+	0.266984i
$9$		−	1.00000i		−	0.333333i
$10$	1.23661	+	1.03171i	0.391052	+	0.326256i
$11$	−0.326956	−	0.326956i	−0.0985810	−	0.0985810i	0.656096	−	0.754677i	$-0.272207\pi$
$11$	−0.326956	−	0.326956i	−0.0985810	−	0.0985810i	−0.754677	+	0.656096i	$0.772207\pi$
$12$	−1.13789	+	1.64475i	−0.328481	+	0.474798i
$13$	−3.46355	+	3.46355i	−0.960615	+	0.960615i	−0.999253	−	0.0386386i	$-0.987698\pi$
$13$	−3.46355	+	3.46355i	−0.960615	+	0.960615i	0.0386386	+	0.999253i	$0.487698\pi$
$14$	0.127230	+	1.40848i	0.0340037	+	0.376432i
$15$	1.13878			0.294032
$16$	3.74310	−	1.41040i	0.935774	−	0.352601i
$17$	−7.57049			−1.83611			−0.918057	−	0.396449i	$-0.870242\pi$
$17$	−7.57049			−1.83611			−0.918057	+	0.396449i	$0.870242\pi$
$18$	0.127230	+	1.40848i	0.0299885	+	0.331982i
$19$	3.34700	−	3.34700i	0.767853	−	0.767853i	−0.209875	−	0.977728i	$-0.567306\pi$
$19$	3.34700	−	3.34700i	0.767853	−	0.767853i	0.977728	+	0.209875i	$0.0673056\pi$
$20$	−1.87301	−	1.29581i	−0.418818	−	0.289752i
$21$	0.707107	+	0.707107i	0.154303	+	0.154303i
$22$	0.502109	+	0.418912i	0.107050	+	0.0893123i
$23$		−	6.11816i		−	1.27572i	−0.770151	−	0.637862i	$-0.779819\pi$
$23$		−	6.11816i		−	1.27572i	0.770151	−	0.637862i	$-0.220181\pi$
$24$	1.39344	−	2.46137i	0.284434	−	0.502425i
$25$		−	3.70318i		−	0.740635i
$26$	4.43766	−	5.31900i	0.870297	−	1.04314i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.358402	−	1.96762i	−0.0677317	−	0.371846i
$29$	−4.51921	+	4.51921i	−0.839196	+	0.839196i	−0.988753	−	0.149557i	$-0.952215\pi$
$29$	−4.51921	+	4.51921i	−0.839196	+	0.839196i	0.149557	+	0.988753i	$0.452215\pi$
$30$	−1.60395	+	0.144888i	−0.292840	+	0.0264527i
$31$	−6.80843			−1.22283			−0.611415	−	0.791310i	$-0.709399\pi$
$31$	−6.80843			−1.22283			−0.611415	+	0.791310i	$0.709399\pi$
$32$	−5.09262	+	2.46276i	−0.900257	+	0.435358i
$33$	0.462386			0.0804910
$34$	10.6629	−	0.963195i	1.82867	−	0.165187i
$35$	−0.805240	+	0.805240i	−0.136110	+	0.136110i
$36$	−0.358402	−	1.96762i	−0.0597337	−	0.327937i
$37$	−0.895292	−	0.895292i	−0.147185	−	0.147185i	0.629674	−	0.776859i	$-0.283188\pi$
$37$	−0.895292	−	0.895292i	−0.147185	−	0.147185i	−0.776859	+	0.629674i	$0.783188\pi$
$38$	−4.28833	+	5.14001i	−0.695659	+	0.833820i
$39$		−	4.89819i		−	0.784339i
$40$	2.80296	+	1.58682i	0.443187	+	0.250898i
$41$		−	10.9937i		−	1.71693i	−0.512869	−	0.858467i	$-0.671417\pi$
$41$		−	10.9937i		−	1.71693i	0.512869	−	0.858467i	$-0.328583\pi$
$42$	−1.08591	−	0.905980i	−0.167560	−	0.139796i
$43$	−5.85617	−	5.85617i	−0.893058	−	0.893058i	0.101752	−	0.994810i	$-0.467555\pi$
$43$	−5.85617	−	5.85617i	−0.893058	−	0.893058i	−0.994810	+	0.101752i	$0.967555\pi$
$44$	−0.760509	−	0.526145i	−0.114651	−	0.0793194i
$45$	−0.805240	+	0.805240i	−0.120038	+	0.120038i
$46$	0.778415	+	8.61730i	0.114771	+	1.27055i
$47$	1.34460			0.196130			0.0980650	−	0.995180i	$-0.468735\pi$
$47$	1.34460			0.196130			0.0980650	+	0.995180i	$0.468735\pi$
$48$	−1.64946	+	3.64407i	−0.238079	+	0.525977i
$49$	−1.00000			−0.142857
$50$	0.471156	+	5.21584i	0.0666315	+	0.737632i
$51$	5.35314	−	5.35314i	0.749590	−	0.749590i
$52$	−5.57362	+	8.05630i	−0.772921	+	1.11721i
$53$	2.55227	+	2.55227i	0.350581	+	0.350581i	0.860326	−	0.509745i	$-0.170260\pi$
$53$	2.55227	+	2.55227i	0.350581	+	0.350581i	−0.509745	+	0.860326i	$0.670260\pi$
$54$	−1.08591	−	0.905980i	−0.147774	−	0.123288i
$55$			0.526557i			0.0710009i
$56$	0.755143	+	2.72576i	0.100910	+	0.364245i
$57$			4.73337i			0.626950i
$58$	5.79023	−	6.94019i	0.760295	−	0.911292i
$59$	5.44250	+	5.44250i	0.708553	+	0.708553i	0.966231	−	0.257678i	$-0.0829574\pi$
$59$	5.44250	+	5.44250i	0.708553	+	0.708553i	−0.257678	+	0.966231i	$0.582957\pi$
$60$	2.24070	−	0.408142i	0.289273	−	0.0526909i
$61$	−6.94278	+	6.94278i	−0.888933	+	0.888933i	−0.994421	−	0.105488i	$-0.966360\pi$
$61$	−6.94278	+	6.94278i	−0.888933	+	0.888933i	0.105488	+	0.994421i	$0.466360\pi$
$62$	9.58952	−	0.866238i	1.21787	−	0.110012i
$63$	−1.00000			−0.125988
$64$	6.85952	−	4.11668i	0.857440	−	0.514585i
$65$	5.57797			0.691862
$66$	−0.651261	+	0.0588295i	−0.0801646	+	0.00724141i
$67$	2.62373	−	2.62373i	0.320540	−	0.320540i	−0.528434	−	0.848974i	$-0.677221\pi$
$67$	2.62373	−	2.62373i	0.320540	−	0.320540i	0.848974	+	0.528434i	$0.177221\pi$
$68$	−14.8959	+	2.71328i	−1.80639	+	0.329034i
$69$	4.32619	+	4.32619i	0.520812	+	0.520812i
$70$	1.03171	−	1.23661i	0.123313	−	0.147804i
$71$			2.61541i			0.310392i	0.987884	+	0.155196i	$0.0496009\pi$
$71$			2.61541i			0.310392i	−0.987884	+	0.155196i	$0.950399\pi$
$72$	0.755143	+	2.72576i	0.0889945	+	0.321234i
$73$			13.6312i			1.59541i	0.603049	+	0.797704i	$0.293952\pi$
$73$			13.6312i			1.59541i	−0.603049	+	0.797704i	$0.706048\pi$
$74$	1.37491	+	1.14709i	0.159830	+	0.133347i
$75$	2.61854	+	2.61854i	0.302363	+	0.302363i
$76$	5.38606	−	7.78520i	0.617824	−	0.893024i
$77$	−0.326956	+	0.326956i	−0.0372601	+	0.0372601i
$78$	0.623198	+	6.89900i	0.0705633	+	0.781158i
$79$	9.66695			1.08762			0.543808	−	0.839209i	$-0.316982\pi$
$79$	9.66695			1.08762			0.543808	+	0.839209i	$0.316982\pi$
$80$	−4.14980	−	1.87838i	−0.463962	−	0.210009i
$81$	−1.00000			−0.111111
$82$	1.39874	+	15.4845i	0.154465	+	1.70997i
$83$	−0.419553	+	0.419553i	−0.0460519	+	0.0460519i	−0.729758	−	0.683706i	$-0.760367\pi$
$83$	−0.419553	+	0.419553i	−0.0460519	+	0.0460519i	0.683706	+	0.729758i	$0.260367\pi$
$84$	1.64475	+	1.13789i	0.179457	+	0.124154i
$85$	6.09606	+	6.09606i	0.661211	+	0.661211i
$86$	8.99338	+	7.50321i	0.969781	+	0.809092i
$87$		−	6.39113i		−	0.685201i
$88$	1.13810	+	0.644305i	0.121322	+	0.0686831i
$89$			2.60923i			0.276578i	0.990392	+	0.138289i	$0.0441603\pi$
$89$			2.60923i			0.276578i	−0.990392	+	0.138289i	$0.955840\pi$
$90$	1.03171	−	1.23661i	0.108752	−	0.130351i
$91$	3.46355	+	3.46355i	0.363078	+	0.363078i
$92$	−2.19276	−	12.0382i	−0.228611	−	1.25507i
$93$	4.81428	−	4.81428i	0.499218	−	0.499218i
$94$	−1.89384	+	0.171074i	−0.195335	+	0.0176449i
$95$	−5.39027			−0.553030
$96$	1.85960	−	5.34246i	0.189794	−	0.545263i
$97$	−3.48313			−0.353658			−0.176829	−	0.984242i	$-0.556584\pi$
$97$	−3.48313			−0.353658			−0.176829	+	0.984242i	$0.556584\pi$
$98$	1.40848	−	0.127230i	0.142278	−	0.0128522i
$99$	−0.326956	+	0.326956i	−0.0328603	+	0.0328603i
$100$	−1.32723	−	7.28646i	−0.132723	−	0.728646i
$101$	−1.81208	−	1.81208i	−0.180308	−	0.180308i	0.611182	−	0.791490i	$-0.290694\pi$
$101$	−1.81208	−	1.81208i	−0.180308	−	0.180308i	−0.791490	+	0.611182i	$0.790694\pi$
$102$	−6.85871	+	8.22087i	−0.679113	+	0.813988i
$103$		−	9.41854i		−	0.928037i	−0.885826	−	0.464018i	$-0.846407\pi$
$103$		−	9.41854i		−	0.928037i	0.885826	−	0.464018i	$-0.153593\pi$
$104$	6.82531	−	12.0563i	0.669277	−	1.18221i
$105$		−	1.13878i		−	0.111134i
$106$	−3.91954	−	3.27009i	−0.380699	−	0.317619i
$107$	9.24353	+	9.24353i	0.893606	+	0.893606i	0.994861	−	0.101255i	$-0.0322856\pi$
$107$	9.24353	+	9.24353i	0.893606	+	0.893606i	−0.101255	+	0.994861i	$0.532286\pi$
$108$	1.64475	+	1.13789i	0.158266	+	0.109494i
$109$	−4.74645	+	4.74645i	−0.454627	+	0.454627i	−0.896887	−	0.442260i	$-0.854177\pi$
$109$	−4.74645	+	4.74645i	−0.454627	+	0.454627i	0.442260	+	0.896887i	$0.354177\pi$
$110$	−0.0669939	−	0.741644i	−0.00638762	−	0.0707129i
$111$	1.26613			0.120176
$112$	−1.41040	−	3.74310i	−0.133271	−	0.353689i
$113$	16.8532			1.58542			0.792709	−	0.609600i	$-0.208670\pi$
$113$	16.8532			1.58542			0.792709	+	0.609600i	$0.208670\pi$
$114$	−0.602228	−	6.66685i	−0.0564038	−	0.624407i
$115$	−4.92659	+	4.92659i	−0.459407	+	0.459407i
$116$	−7.27242	+	10.5118i	−0.675227	+	0.975997i
$117$	3.46355	+	3.46355i	0.320205	+	0.320205i
$118$	−8.35809	−	6.97319i	−0.769425	−	0.641934i
$119$			7.57049i			0.693986i
$120$	−3.10404	+	0.859944i	−0.283359	+	0.0785018i
$121$		−	10.7862i		−	0.980564i
$122$	8.89543	−	10.6621i	0.805355	−	0.965301i
$123$	7.77375	+	7.77375i	0.700935	+	0.700935i
$124$	−13.3964	+	2.44016i	−1.20303	+	0.219132i
$125$	−7.00815	+	7.00815i	−0.626828	+	0.626828i
$126$	1.40848	−	0.127230i	0.125477	−	0.0113346i
$127$	−22.0671			−1.95814			−0.979068	−	0.203534i	$-0.934757\pi$
$127$	−22.0671			−1.95814			−0.979068	+	0.203534i	$0.934757\pi$
$128$	−9.13772	+	6.67099i	−0.807668	+	0.589638i
$129$	8.28188			0.729179
$130$	−7.85646	+	0.709687i	−0.689057	+	0.0622437i
$131$	2.79181	−	2.79181i	0.243921	−	0.243921i	−0.574549	−	0.818470i	$-0.694823\pi$
$131$	2.79181	−	2.79181i	0.243921	−	0.243921i	0.818470	+	0.574549i	$0.194823\pi$
$132$	0.909802	−	0.165720i	0.0791881	−	0.0144241i
$133$	−3.34700	−	3.34700i	−0.290221	−	0.290221i
$134$	−3.36165	+	4.02929i	−0.290403	+	0.348078i
$135$		−	1.13878i		−	0.0980107i
$136$	20.6353	−	5.71681i	1.76946	−	0.490212i
$137$		−	10.5387i		−	0.900378i	−0.892933	−	0.450189i	$-0.851357\pi$
$137$		−	10.5387i		−	0.900378i	0.892933	−	0.450189i	$-0.148643\pi$
$138$	−6.64377	−	5.54293i	−0.565555	−	0.471845i
$139$	−3.31850	−	3.31850i	−0.281472	−	0.281472i	0.552224	−	0.833696i	$-0.313779\pi$
$139$	−3.31850	−	3.31850i	−0.281472	−	0.281472i	−0.833696	+	0.552224i	$0.813779\pi$
$140$	−1.29581	+	1.87301i	−0.109516	+	0.158298i
$141$	−0.950776	+	0.950776i	−0.0800697	+	0.0800697i
$142$	−0.332759	−	3.68375i	−0.0279245	−	0.309133i
$143$	2.26485			0.189397
$144$	−1.41040	−	3.74310i	−0.117534	−	0.311925i
$145$	7.27810			0.604413
$146$	−1.73430	−	19.1992i	−0.143532	−	1.58894i
$147$	0.707107	−	0.707107i	0.0583212	−	0.0583212i
$148$	−2.08247	−	1.44072i	−0.171178	−	0.118427i
$149$	−5.98262	−	5.98262i	−0.490115	−	0.490115i	0.418227	−	0.908342i	$-0.362652\pi$
$149$	−5.98262	−	5.98262i	−0.490115	−	0.490115i	−0.908342	+	0.418227i	$0.862652\pi$
$150$	−4.02132	−	3.35500i	−0.328339	−	0.273935i
$151$		−	1.33648i		−	0.108761i	−0.998520	−	0.0543807i	$-0.982682\pi$
$151$		−	1.33648i		−	0.108761i	0.998520	−	0.0543807i	$-0.0173184\pi$
$152$	−6.59564	+	11.6506i	−0.534977	+	0.944985i
$153$			7.57049i			0.612038i
$154$	0.418912	−	0.502109i	0.0337569	−	0.0404611i
$155$	5.48242	+	5.48242i	0.440358	+	0.440358i
$156$	−1.75552	−	9.63781i	−0.140554	−	0.771642i
$157$	−9.67055	+	9.67055i	−0.771794	+	0.771794i	−0.978420	−	0.206626i	$-0.933752\pi$
$157$	−9.67055	+	9.67055i	−0.771794	+	0.771794i	0.206626	+	0.978420i	$0.433752\pi$
$158$	−13.6157	+	1.22993i	−1.08321	+	0.0978479i
$159$	−3.60945			−0.286248
$160$	6.08390	+	2.11768i	0.480974	+	0.167417i
$161$	−6.11816			−0.482178
$162$	1.40848	−	0.127230i	0.110661	−	0.00999615i
$163$	−2.15092	+	2.15092i	−0.168473	+	0.168473i	−0.786308	−	0.617835i	$-0.788010\pi$
$163$	−2.15092	+	2.15092i	−0.168473	+	0.168473i	0.617835	+	0.786308i	$0.288010\pi$
$164$	−3.94018	−	21.6316i	−0.307677	−	1.68914i
$165$	−0.372332	−	0.372332i	−0.0289860	−	0.0289860i
$166$	0.537551	−	0.644311i	0.0417221	−	0.0500082i
$167$		−	0.745529i		−	0.0576908i	−0.999584	−	0.0288454i	$-0.990817\pi$
$167$		−	0.745529i		−	0.0576908i	0.999584	−	0.0288454i	$-0.00918305\pi$
$168$	−2.46137	−	1.39344i	−0.189899	−	0.107506i
$169$		−	10.9923i		−	0.845561i
$170$	−9.36178	−	7.81057i	−0.718016	−	0.599044i
$171$	−3.34700	−	3.34700i	−0.255951	−	0.255951i
$172$	−13.6216	−	9.42388i	−1.03864	−	0.718564i
$173$	9.87906	−	9.87906i	0.751091	−	0.751091i	−0.223592	−	0.974683i	$-0.571778\pi$
$173$	9.87906	−	9.87906i	0.751091	−	0.751091i	0.974683	+	0.223592i	$0.0717783\pi$
$174$	0.813145	+	9.00177i	0.0616444	+	0.682422i
$175$	−3.70318			−0.279934
$176$	−1.68497	−	0.762688i	−0.127009	−	0.0574898i
$177$	−7.69685			−0.578531
$178$	−0.331974	−	3.67505i	−0.0248825	−	0.275457i
$179$	3.46023	−	3.46023i	0.258629	−	0.258629i	−0.565867	−	0.824496i	$-0.691458\pi$
$179$	3.46023	−	3.46023i	0.258629	−	0.258629i	0.824496	+	0.565867i	$0.191458\pi$
$180$	−1.29581	+	1.87301i	−0.0965840	+	0.139606i
$181$	−0.316769	−	0.316769i	−0.0235452	−	0.0235452i	0.695236	−	0.718781i	$-0.255300\pi$
$181$	−0.316769	−	0.316769i	−0.0235452	−	0.0235452i	−0.718781	+	0.695236i	$0.755300\pi$
$182$	−5.31900	−	4.43766i	−0.394270	−	0.328941i
$183$		−	9.81858i		−	0.725810i
$184$	4.62009	+	16.6766i	0.340597	+	1.22942i
$185$			1.44185i			0.106007i
$186$	−6.16829	+	7.39334i	−0.452281	+	0.542106i
$187$	2.47522	+	2.47522i	0.181006	+	0.181006i
$188$	2.64567	−	0.481908i	0.192955	−	0.0351467i
$189$	0.707107	−	0.707107i	0.0514344	−	0.0514344i
$190$	7.59208	−	0.685806i	0.550788	−	0.0497536i
$191$	12.6233			0.913392			0.456696	−	0.889623i	$-0.349033\pi$
$191$	12.6233			0.913392			0.456696	+	0.889623i	$0.349033\pi$
$192$	−1.93948	+	7.76134i	−0.139970	+	0.560127i
$193$	9.73534			0.700765			0.350383	−	0.936607i	$-0.386052\pi$
$193$	9.73534			0.700765			0.350383	+	0.936607i	$0.386052\pi$
$194$	4.90591	−	0.443159i	0.352224	−	0.0318170i
$195$	−3.94422	+	3.94422i	−0.282452	+	0.282452i
$196$	−1.96762	+	0.358402i	−0.140545	+	0.0256002i
$197$	9.82654	+	9.82654i	0.700112	+	0.700112i	0.964434	−	0.264322i	$-0.0851482\pi$
$197$	9.82654	+	9.82654i	0.700112	+	0.700112i	−0.264322	+	0.964434i	$0.585148\pi$
$198$	0.418912	−	0.502109i	0.0297708	−	0.0356834i
$199$			16.2398i			1.15121i	0.817728	+	0.575605i	$0.195233\pi$
$199$			16.2398i			1.15121i	−0.817728	+	0.575605i	$0.804767\pi$
$200$	2.79643	+	10.0940i	0.197737	+	0.713751i
$201$			3.71052i			0.261720i
$202$	2.78282	+	2.32172i	0.195799	+	0.163356i
$203$	4.51921	+	4.51921i	0.317186	+	0.317186i
$204$	8.61440	−	12.4516i	0.603129	−	0.871783i
$205$	−8.85260	+	8.85260i	−0.618293	+	0.618293i
$206$	1.19832	+	13.2658i	0.0834912	+	0.924273i
$207$	−6.11816			−0.425241
$208$	−8.07939	+	17.8494i	−0.560205	+	1.23763i
$209$	−2.18864			−0.151391
$210$	0.144888	+	1.60395i	0.00999819	+	0.110683i
$211$	18.5803	−	18.5803i	1.27912	−	1.27912i	0.337960	−	0.941161i	$-0.390263\pi$
$211$	18.5803	−	18.5803i	1.27912	−	1.27912i	0.941161	−	0.337960i	$-0.109737\pi$
$212$	5.93664	+	4.10716i	0.407730	+	0.282081i
$213$	−1.84937	−	1.84937i	−0.126717	−	0.126717i
$214$	−14.1954	−	11.8433i	−0.970376	−	0.809589i
$215$			9.43125i			0.643206i
$216$	−2.46137	−	1.39344i	−0.167475	−	0.0948112i
$217$			6.80843i			0.462186i
$218$	6.08138	−	7.28916i	0.411883	−	0.493684i
$219$	−9.63870	−	9.63870i	−0.651323	−	0.651323i
$220$	0.188719	+	1.03607i	0.0127234	+	0.0698515i
$221$	26.2207	−	26.2207i	1.76380	−	1.76380i
$222$	−1.78332	+	0.161091i	−0.119689	+	0.0108117i
$223$	10.8750			0.728244			0.364122	−	0.931351i	$-0.381369\pi$
$223$	10.8750			0.728244			0.364122	+	0.931351i	$0.381369\pi$
$224$	2.46276	+	5.09262i	0.164550	+	0.340265i
$225$	−3.70318			−0.246878
$226$	−23.7374	+	2.14424i	−1.57899	+	0.142633i
$227$	−5.79840	+	5.79840i	−0.384853	+	0.384853i	−0.872847	−	0.487994i	$-0.837729\pi$
$227$	−5.79840	+	5.79840i	−0.384853	+	0.384853i	0.487994	+	0.872847i	$0.337729\pi$
$228$	1.69645	+	9.31349i	0.112350	+	0.616801i
$229$	−19.7232	−	19.7232i	−1.30335	−	1.30335i	−0.926121	−	0.377226i	$-0.876878\pi$
$229$	−19.7232	−	19.7232i	−1.30335	−	1.30335i	−0.377226	−	0.926121i	$-0.623122\pi$
$230$	6.31218	−	7.56581i	0.416213	−	0.498874i
$231$		−	0.462386i		−	0.0304228i
$232$	8.90562	−	15.7309i	0.584683	−	1.03279i
$233$		−	21.3815i		−	1.40075i	−0.713776	−	0.700374i	$-0.753017\pi$
$233$		−	21.3815i		−	1.40075i	0.713776	−	0.700374i	$-0.246983\pi$
$234$	−5.31900	−	4.43766i	−0.347714	−	0.290099i
$235$	−1.08273	−	1.08273i	−0.0706293	−	0.0706293i
$236$	12.6594	+	8.75819i	0.824056	+	0.570109i
$237$	−6.83557	+	6.83557i	−0.444018	+	0.444018i
$238$	−0.963195	−	10.6629i	−0.0624347	−	0.691171i
$239$	−20.8709			−1.35002			−0.675012	−	0.737807i	$-0.735861\pi$
$239$	−20.8709			−1.35002			−0.675012	+	0.737807i	$0.735861\pi$
$240$	4.26257	−	1.60614i	0.275148	−	0.103676i
$241$	8.76736			0.564755			0.282378	−	0.959303i	$-0.408877\pi$
$241$	8.76736			0.564755			0.282378	+	0.959303i	$0.408877\pi$
$242$	1.37233	+	15.1921i	0.0882168	+	0.976587i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−11.1725	+	16.1491i	−0.715245	+	1.03384i
$245$	0.805240	+	0.805240i	0.0514449	+	0.0514449i
$246$	−11.9382	−	9.96010i	−0.761153	−	0.635033i
$247$			23.1849i			1.47522i
$248$	18.5581	−	5.14134i	1.17844	−	0.326475i
$249$		−	0.593337i		−	0.0376012i
$250$	8.97918	−	10.7625i	0.567893	−	0.680679i
$251$	9.95193	+	9.95193i	0.628160	+	0.628160i	0.947605	−	0.319445i	$-0.103496\pi$
$251$	9.95193	+	9.95193i	0.628160	+	0.628160i	−0.319445	+	0.947605i	$0.603496\pi$
$252$	−1.96762	+	0.358402i	−0.123949	+	0.0225772i
$253$	−2.00037	+	2.00037i	−0.125762	+	0.125762i
$254$	31.0810	−	2.80760i	1.95020	−	0.176164i
$255$	−8.62114			−0.539876
$256$	12.0215	−	10.5585i	0.751346	−	0.659909i
$257$	−27.8589			−1.73779			−0.868894	−	0.494998i	$-0.835169\pi$
$257$	−27.8589			−1.73779			−0.868894	+	0.494998i	$0.835169\pi$
$258$	−11.6648	+	1.05371i	−0.726222	+	0.0656008i
$259$	−0.895292	+	0.895292i	−0.0556307	+	0.0556307i
$260$	10.9754	−	1.99916i	0.680663	−	0.123983i
$261$	4.51921	+	4.51921i	0.279732	+	0.279732i
$262$	−3.57700	+	4.28740i	−0.220988	+	0.264877i
$263$		−	11.3490i		−	0.699810i	−0.936785	−	0.349905i	$-0.886214\pi$
$263$		−	11.3490i		−	0.699810i	0.936785	−	0.349905i	$-0.113786\pi$
$264$	−1.26035	+	0.349168i	−0.0775693	+	0.0214898i
$265$		−	4.11037i		−	0.252498i
$266$	5.14001	+	4.28833i	0.315154	+	0.262935i
$267$	−1.84501	−	1.84501i	−0.112913	−	0.112913i
$268$	4.22217	−	6.10287i	0.257910	−	0.372792i
$269$	9.63867	−	9.63867i	0.587680	−	0.587680i	−0.349322	−	0.937003i	$-0.613588\pi$
$269$	9.63867	−	9.63867i	0.587680	−	0.587680i	0.937003	+	0.349322i	$0.113588\pi$
$270$	0.144888	+	1.60395i	0.00881757	+	0.0976133i
$271$	−0.604488			−0.0367200			−0.0183600	−	0.999831i	$-0.505845\pi$
$271$	−0.604488			−0.0367200			−0.0183600	+	0.999831i	$0.505845\pi$
$272$	−28.3371	+	10.6774i	−1.71819	+	0.647415i
$273$	−4.89819			−0.296452
$274$	1.34084	+	14.8435i	0.0810029	+	0.896727i
$275$	−1.21078	+	1.21078i	−0.0730125	+	0.0730125i
$276$	10.0628	+	6.96181i	0.605712	+	0.419051i
$277$	7.93031	+	7.93031i	0.476486	+	0.476486i	0.904006	−	0.427520i	$-0.140613\pi$
$277$	7.93031	+	7.93031i	0.476486	+	0.476486i	−0.427520	+	0.904006i	$0.640613\pi$
$278$	5.09626	+	4.25183i	0.305653	+	0.255008i
$279$			6.80843i			0.407610i
$280$	1.58682	−	2.80296i	0.0948305	−	0.167509i
$281$			15.8543i			0.945786i	0.881120	+	0.472893i	$0.156790\pi$
$281$			15.8543i			0.945786i	−0.881120	+	0.472893i	$0.843210\pi$
$282$	1.21818	−	1.46011i	0.0725416	−	0.0869486i
$283$	−4.74918	−	4.74918i	−0.282310	−	0.282310i	0.551720	−	0.834029i	$-0.313972\pi$
$283$	−4.74918	−	4.74918i	−0.282310	−	0.282310i	−0.834029	+	0.551720i	$0.813972\pi$
$284$	0.937368	+	5.14614i	0.0556226	+	0.305367i
$285$	3.81150	−	3.81150i	0.225774	−	0.225774i
$286$	−3.19000	+	0.288158i	−0.188629	+	0.0170391i
$287$	−10.9937			−0.648940
$288$	2.46276	+	5.09262i	0.145119	+	0.300086i
$289$	40.3123			2.37131
$290$	−10.2511	+	0.925995i	−0.601962	+	0.0543763i
$291$	2.46294	−	2.46294i	0.144380	−	0.144380i
$292$	4.88545	+	26.8210i	0.285899	+	1.56958i
$293$	−6.69860	−	6.69860i	−0.391336	−	0.391336i	0.483827	−	0.875164i	$-0.339246\pi$
$293$	−6.69860	−	6.69860i	−0.391336	−	0.391336i	−0.875164	+	0.483827i	$0.839246\pi$
$294$	−0.905980	+	1.08591i	−0.0528378	+	0.0633316i
$295$		−	8.76503i		−	0.510320i
$296$	3.11642	+	1.76428i	0.181138	+	0.102546i
$297$		−	0.462386i		−	0.0268303i
$298$	9.18756	+	7.66522i	0.532221	+	0.444034i
$299$	21.1905	+	21.1905i	1.22548	+	1.22548i
$300$	6.09080	+	4.21382i	0.351652	+	0.243285i
$301$	−5.85617	+	5.85617i	−0.337544	+	0.337544i
$302$	0.170041	+	1.88241i	0.00978475	+	0.108320i
$303$	2.56266			0.147221
$304$	7.80751	−	17.2487i	0.447792	−	0.989283i
$305$	11.1812			0.640235
$306$	−0.963195	−	10.6629i	−0.0550622	−	0.609556i
$307$	−6.89318	+	6.89318i	−0.393415	+	0.393415i	−0.875903	−	0.482488i	$-0.839733\pi$
$307$	−6.89318	+	6.89318i	−0.393415	+	0.393415i	0.482488	+	0.875903i	$0.339733\pi$
$308$	−0.526145	+	0.760509i	−0.0299799	+	0.0433340i
$309$	6.65992	+	6.65992i	0.378869	+	0.378869i
$310$	−8.41940	−	7.02434i	−0.478190	−	0.398956i
$311$		−	18.9224i		−	1.07299i	−0.843902	−	0.536497i	$-0.819747\pi$
$311$		−	18.9224i		−	1.07299i	0.843902	−	0.536497i	$-0.180253\pi$
$312$	3.69884	+	13.3513i	0.209405	+	0.755868i
$313$		−	18.9646i		−	1.07194i	−0.844236	−	0.535971i	$-0.819946\pi$
$313$		−	18.9646i		−	1.07194i	0.844236	−	0.535971i	$-0.180054\pi$
$314$	12.3904	−	14.8512i	0.699230	−	0.838099i
$315$	0.805240	+	0.805240i	0.0453702	+	0.0453702i
$316$	19.0209	−	3.46466i	1.07001	−	0.194902i
$317$	−17.0892	+	17.0892i	−0.959824	+	0.959824i	−0.999224	−	0.0393992i	$-0.987456\pi$
$317$	−17.0892	+	17.0892i	−0.959824	+	0.959824i	0.0393992	+	0.999224i	$0.487456\pi$
$318$	5.08383	−	0.459231i	0.285087	−	0.0257524i
$319$	2.95517			0.165458
$320$	−8.83847	−	2.20864i	−0.494086	−	0.123467i
$321$	−13.0723			−0.729626
$322$	8.61730	−	0.778415i	0.480223	−	0.0433794i
$323$	−25.3384	+	25.3384i	−1.40987	+	1.40987i
$324$	−1.96762	+	0.358402i	−0.109312	+	0.0199112i
$325$	12.8261	+	12.8261i	0.711465	+	0.711465i
$326$	2.75587	−	3.30319i	0.152633	−	0.182947i
$327$		−	6.71249i		−	0.371201i
$328$	8.30185	+	29.9663i	0.458393	+	1.65461i
$329$		−	1.34460i		−	0.0741302i
$330$	0.571793	+	0.477049i	0.0314762	+	0.0262607i
$331$	−16.8112	−	16.8112i	−0.924028	−	0.924028i	0.0732836	−	0.997311i	$-0.476652\pi$
$331$	−16.8112	−	16.8112i	−0.924028	−	0.924028i	−0.997311	+	0.0732836i	$0.976652\pi$
$332$	−0.675154	+	0.975891i	−0.0370539	+	0.0535590i
$333$	−0.895292	+	0.895292i	−0.0490617	+	0.0490617i
$334$	0.0948539	+	1.05006i	0.00519017	+	0.0574568i
$335$	−4.22547			−0.230862
$336$	3.64407	+	1.64946i	0.198801	+	0.0899856i
$337$	8.16205			0.444615			0.222308	−	0.974977i	$-0.428641\pi$
$337$	8.16205			0.444615			0.222308	+	0.974977i	$0.428641\pi$
$338$	1.39855	+	15.4824i	0.0760712	+	0.842132i
$339$	−11.9170	+	11.9170i	−0.647244	+	0.647244i
$340$	14.1796	+	9.80992i	0.768997	+	0.532018i
$341$	2.22606	+	2.22606i	0.120548	+	0.120548i
$342$	5.14001	+	4.28833i	0.277940	+	0.231886i
$343$			1.00000i			0.0539949i
$344$	20.3848	+	11.5403i	1.09907	+	0.622209i
$345$		−	6.96725i		−	0.375104i
$346$	−12.6575	+	15.1714i	−0.680473	+	0.815617i
$347$	−1.57438	−	1.57438i	−0.0845170	−	0.0845170i	0.663584	−	0.748101i	$-0.269034\pi$
$347$	−1.57438	−	1.57438i	−0.0845170	−	0.0845170i	−0.748101	+	0.663584i	$0.769034\pi$
$348$	−2.29059	−	12.5753i	−0.122789	−	0.674109i
$349$	−2.00641	+	2.00641i	−0.107401	+	0.107401i	−0.758765	−	0.651364i	$-0.774197\pi$
$349$	−2.00641	+	2.00641i	−0.107401	+	0.107401i	0.651364	+	0.758765i	$0.274197\pi$
$350$	5.21584	−	0.471156i	0.278799	−	0.0251844i
$351$	−4.89819			−0.261446
$352$	2.47028	+	0.859851i	0.131666	+	0.0458302i
$353$	1.84561			0.0982321			0.0491160	−	0.998793i	$-0.484360\pi$
$353$	1.84561			0.0982321			0.0491160	+	0.998793i	$0.484360\pi$
$354$	10.8409	−	0.979273i	0.576185	−	0.0520478i
$355$	2.10603	−	2.10603i	0.111777	−	0.111777i
$356$	0.935155	+	5.13399i	0.0495631	+	0.272101i
$357$	−5.35314	−	5.35314i	−0.283318	−	0.283318i
$358$	−4.43341	+	5.31390i	−0.234313	+	0.280848i
$359$			29.1469i			1.53831i	0.639060	+	0.769157i	$0.279324\pi$
$359$			29.1469i			1.53831i	−0.639060	+	0.769157i	$0.720676\pi$
$360$	1.58682	−	2.80296i	0.0836327	−	0.147729i
$361$		−	3.40476i		−	0.179198i
$362$	0.486464	+	0.405859i	0.0255680	+	0.0213315i
$363$	7.62699	+	7.62699i	0.400313	+	0.400313i
$364$	8.05630	+	5.57362i	0.422265	+	0.292137i
$365$	10.9764	−	10.9764i	0.574530	−	0.574530i
$366$	1.24922	+	13.8293i	0.0652978	+	0.722867i
$367$	−1.57762			−0.0823509			−0.0411754	−	0.999152i	$-0.513110\pi$
$367$	−1.57762			−0.0823509			−0.0411754	+	0.999152i	$0.513110\pi$
$368$	−8.62907	−	22.9009i	−0.449821	−	1.19379i
$369$	−10.9937			−0.572311
$370$	−0.183447	−	2.03082i	−0.00953696	−	0.105577i
$371$	2.55227	−	2.55227i	0.132507	−	0.132507i
$372$	7.74725	−	11.1982i	0.401676	−	0.580597i
$373$	−9.84137	−	9.84137i	−0.509567	−	0.509567i	0.404826	−	0.914394i	$-0.367332\pi$
$373$	−9.84137	−	9.84137i	−0.509567	−	0.509567i	−0.914394	+	0.404826i	$0.867332\pi$
$374$	−3.80121	−	3.17137i	−0.196556	−	0.163988i
$375$		−	9.91102i		−	0.511803i
$376$	−3.66505	+	1.01537i	−0.189011	+	0.0523635i
$377$		−	31.3050i		−	1.61229i
$378$	−0.905980	+	1.08591i	−0.0465986	+	0.0558532i
$379$	−19.0833	−	19.0833i	−0.980245	−	0.980245i	0.0195633	−	0.999809i	$-0.493772\pi$
$379$	−19.0833	−	19.0833i	−0.980245	−	0.980245i	−0.999809	+	0.0195633i	$0.993772\pi$
$380$	−10.6060	+	1.93189i	−0.544078	+	0.0991036i
$381$	15.6038	−	15.6038i	0.799406	−	0.799406i
$382$	−17.7797	+	1.60607i	−0.909688	+	0.0821737i
$383$	−0.900891			−0.0460334			−0.0230167	−	0.999735i	$-0.507327\pi$
$383$	−0.900891			−0.0460334			−0.0230167	+	0.999735i	$0.507327\pi$
$384$	1.74424	−	11.1784i	0.0890103	−	0.570448i
$385$	0.526557			0.0268358
$386$	−13.7120	+	1.23863i	−0.697923	+	0.0630446i
$387$	−5.85617	+	5.85617i	−0.297686	+	0.297686i
$388$	−6.85349	+	1.24836i	−0.347933	+	0.0633759i
$389$	−15.2174	−	15.2174i	−0.771554	−	0.771554i	0.206824	−	0.978378i	$-0.433687\pi$
$389$	−15.2174	−	15.2174i	−0.771554	−	0.771554i	−0.978378	+	0.206824i	$0.933687\pi$
$390$	5.05353	−	6.05718i	0.255895	−	0.306717i
$391$			46.3175i			2.34237i
$392$	2.72576	−	0.755143i	0.137672	−	0.0381405i
$393$			3.94821i			0.199161i
$394$	−15.0907	−	12.5902i	−0.760259	−	0.634287i
$395$	−7.78422	−	7.78422i	−0.391667	−	0.391667i
$396$	−0.526145	+	0.760509i	−0.0264398	+	0.0382170i
$397$	23.5507	−	23.5507i	1.18197	−	1.18197i	0.202741	−	0.979232i	$-0.435015\pi$
$397$	23.5507	−	23.5507i	1.18197	−	1.18197i	0.979232	−	0.202741i	$-0.0649850\pi$
$398$	−2.06619	−	22.8734i	−0.103569	−	1.14654i
$399$	4.73337			0.236965
$400$	−5.22297	−	13.8613i	−0.261148	−	0.693067i
$401$	−34.4691			−1.72130			−0.860652	−	0.509194i	$-0.829944\pi$
$401$	−34.4691			−1.72130			−0.860652	+	0.509194i	$0.829944\pi$
$402$	−0.472090	−	5.22619i	−0.0235457	−	0.260659i
$403$	23.5813	−	23.5813i	1.17467	−	1.17467i
$404$	−4.21494	−	2.91603i	−0.209701	−	0.145078i
$405$	0.805240	+	0.805240i	0.0400127	+	0.0400127i
$406$	−6.94019	−	5.79023i	−0.344436	−	0.287364i
$407$			0.585442i			0.0290193i
$408$	−10.5490	+	18.6338i	−0.522253	+	0.922509i
$409$			19.9235i			0.985153i	0.870269	+	0.492577i	$0.163945\pi$
$409$			19.9235i			0.985153i	−0.870269	+	0.492577i	$0.836055\pi$
$410$	11.3424	−	13.5950i	0.560161	−	0.671410i
$411$	7.45196	+	7.45196i	0.367578	+	0.367578i
$412$	−3.37563	−	18.5322i	−0.166305	−	0.913014i
$413$	5.44250	−	5.44250i	0.267808	−	0.267808i
$414$	8.61730	−	0.778415i	0.423517	−	0.0382570i
$415$	0.675682			0.0331679
$416$	9.10867	−	26.1684i	0.446589	−	1.28301i
$417$	4.69307			0.229821
$418$	3.08265	−	0.278461i	0.150778	−	0.0136200i
$419$	−7.86410	+	7.86410i	−0.384187	+	0.384187i	−0.872608	−	0.488421i	$-0.837573\pi$
$419$	−7.86410	+	7.86410i	−0.384187	+	0.384187i	0.488421	+	0.872608i	$0.337573\pi$
$420$	−0.408142	−	2.24070i	−0.0199153	−	0.109335i
$421$	−1.36575	−	1.36575i	−0.0665627	−	0.0665627i	0.673042	−	0.739604i	$-0.264987\pi$
$421$	−1.36575	−	1.36575i	−0.0665627	−	0.0665627i	−0.739604	+	0.673042i	$0.764987\pi$
$422$	−23.8060	+	28.5339i	−1.15886	+	1.38901i
$423$		−	1.34460i		−	0.0653767i
$424$	−8.88419	−	5.02953i	−0.431454	−	0.244256i
$425$			28.0349i			1.35989i
$426$	2.84010	+	2.36951i	0.137603	+	0.114803i
$427$	6.94278	+	6.94278i	0.335985	+	0.335985i
$428$	21.5007	+	14.8749i	1.03928	+	0.719006i
$429$	−1.60149	+	1.60149i	−0.0773209	+	0.0773209i
$430$	−1.19994	−	13.2837i	−0.0578663	−	0.640598i
$431$	4.07868			0.196463			0.0982316	−	0.995164i	$-0.468681\pi$
$431$	4.07868			0.196463			0.0982316	+	0.995164i	$0.468681\pi$
$432$	3.64407	+	1.64946i	0.175326	+	0.0793598i
$433$	−4.82100			−0.231683			−0.115841	−	0.993268i	$-0.536956\pi$
$433$	−4.82100			−0.231683			−0.115841	+	0.993268i	$0.536956\pi$
$434$	−0.866238	−	9.58952i	−0.0415807	−	0.460312i
$435$	−5.14639	+	5.14639i	−0.246751	+	0.246751i
$436$	−7.63809	+	11.0404i	−0.365798	+	0.528738i
$437$	−20.4775	−	20.4775i	−0.979569	−	0.979569i
$438$	14.8022	+	12.3496i	0.707278	+	0.590085i
$439$		−	33.3378i		−	1.59113i	−0.605871	−	0.795563i	$-0.707175\pi$
$439$		−	33.3378i		−	1.59113i	0.605871	−	0.795563i	$-0.292825\pi$
$440$	−0.397626	−	1.43527i	−0.0189561	−	0.0684236i
$441$			1.00000i			0.0476190i
$442$	−33.5953	+	40.2674i	−1.59796	+	1.91533i
$443$	−24.7484	−	24.7484i	−1.17583	−	1.17583i	−0.980796	−	0.195037i	$-0.937517\pi$
$443$	−24.7484	−	24.7484i	−1.17583	−	1.17583i	−0.195037	−	0.980796i	$-0.562483\pi$
$444$	2.49128	−	0.453785i	0.118231	−	0.0215357i
$445$	2.10106	−	2.10106i	0.0995998	−	0.0995998i
$446$	−15.3172	+	1.38363i	−0.725291	+	0.0655168i
$447$	8.46070			0.400177
$448$	−4.11668	−	6.85952i	−0.194495	−	0.324082i
$449$	−8.78245			−0.414470			−0.207235	−	0.978291i	$-0.566446\pi$
$449$	−8.78245			−0.414470			−0.207235	+	0.978291i	$0.566446\pi$
$450$	5.21584	−	0.471156i	0.245877	−	0.0222105i
$451$	−3.59447	+	3.59447i	−0.169257	+	0.169257i
$452$	33.1608	−	6.04024i	1.55975	−	0.284109i
$453$	0.945035	+	0.945035i	0.0444016	+	0.0444016i
$454$	7.42919	−	8.90466i	0.348669	−	0.417916i
$455$		−	5.57797i		−	0.261499i
$456$	−3.57437	−	12.9020i	−0.167385	−	0.604192i
$457$			2.11749i			0.0990521i	0.998773	+	0.0495260i	$0.0157711\pi$
$457$			2.11749i			0.0990521i	−0.998773	+	0.0495260i	$0.984229\pi$
$458$	30.2891	+	25.2704i	1.41532	+	1.18081i
$459$	−5.35314	−	5.35314i	−0.249863	−	0.249863i
$460$	−7.92798	+	11.4594i	−0.369644	+	0.534296i
$461$	−2.23040	+	2.23040i	−0.103880	+	0.103880i	−0.757137	−	0.653256i	$-0.773402\pi$
$461$	−2.23040	+	2.23040i	−0.103880	+	0.103880i	0.653256	+	0.757137i	$0.273402\pi$
$462$	0.0588295	+	0.651261i	0.00273699	+	0.0302994i
$463$	35.5596			1.65260			0.826298	−	0.563233i	$-0.190443\pi$
$463$	35.5596			1.65260			0.826298	+	0.563233i	$0.190443\pi$
$464$	−10.5419	+	23.2897i	−0.489397	+	1.08120i
$465$	−7.75331			−0.359551
$466$	2.72037	+	30.1154i	0.126019	+	1.39507i
$467$	−3.26861	+	3.26861i	−0.151253	+	0.151253i	−0.778678	−	0.627424i	$-0.784109\pi$
$467$	−3.26861	+	3.26861i	−0.151253	+	0.151253i	0.627424	+	0.778678i	$0.284109\pi$
$468$	8.05630	+	5.57362i	0.372403	+	0.257640i
$469$	−2.62373	−	2.62373i	−0.121153	−	0.121153i
$470$	1.66275	+	1.38724i	0.0766970	+	0.0639887i
$471$		−	13.6762i		−	0.630167i
$472$	−18.9448	−	10.7251i	−0.872005	−	0.493661i
$473$			3.82942i			0.176077i
$474$	8.75806	−	10.4974i	0.402271	−	0.482163i
$475$	−12.3945	−	12.3945i	−0.568699	−	0.568699i
$476$	2.71328	+	14.8959i	0.124363	+	0.682752i
$477$	2.55227	−	2.55227i	0.116860	−	0.116860i
$478$	29.3962	−	2.65541i	1.34455	−	0.121455i
$479$	−11.9912			−0.547892			−0.273946	−	0.961745i	$-0.588329\pi$
$479$	−11.9912			−0.547892			−0.273946	+	0.961745i	$0.588329\pi$
$480$	−5.79939	+	2.80454i	−0.264705	+	0.128009i
$481$	6.20177			0.282776
$482$	−12.3486	+	1.11547i	−0.562465	+	0.0508084i
$483$	4.32619	−	4.32619i	0.196849	−	0.196849i
$484$	−3.86580	−	21.2232i	−0.175718	−	0.964691i
$485$	2.80475	+	2.80475i	0.127357	+	0.127357i
$486$	−0.905980	+	1.08591i	−0.0410961	+	0.0492579i
$487$			32.2699i			1.46229i	0.682222	+	0.731145i	$0.261014\pi$
$487$			32.2699i			1.46229i	−0.682222	+	0.731145i	$0.738986\pi$
$488$	13.6816	−	24.1672i	0.619335	−	1.09400i
$489$		−	3.04186i		−	0.137558i
$490$	−1.23661	−	1.03171i	−0.0558646	−	0.0466080i
$491$	−26.7849	−	26.7849i	−1.20878	−	1.20878i	−0.971421	−	0.237363i	$-0.923717\pi$
$491$	−26.7849	−	26.7849i	−1.20878	−	1.20878i	−0.237363	−	0.971421i	$-0.576283\pi$
$492$	18.0820	+	12.5097i	0.815197	+	0.563981i
$493$	34.2126	−	34.2126i	1.54086	−	1.54086i
$494$	−2.94983	−	32.6555i	−0.132719	−	1.46924i
$495$	0.526557			0.0236670
$496$	−25.4846	+	9.60262i	−1.14429	+	0.431170i
$497$	2.61541			0.117317
$498$	0.0754905	+	0.835703i	0.00338281	+	0.0374488i
$499$	−21.9047	+	21.9047i	−0.980590	+	0.980590i	−0.999815	−	0.0192250i	$-0.993880\pi$
$499$	−21.9047	+	21.9047i	−0.980590	+	0.980590i	0.0192250	+	0.999815i	$0.493880\pi$
$500$	−11.2777	+	16.3011i	−0.504353	+	0.729009i
$501$	0.527169	+	0.527169i	0.0235522	+	0.0235522i
$502$	−15.2833	−	12.7509i	−0.682126	−	0.569100i
$503$		−	18.0324i		−	0.804025i	−0.915634	−	0.402013i	$-0.868311\pi$
$503$		−	18.0324i		−	0.804025i	0.915634	−	0.402013i	$-0.131689\pi$
$504$	2.72576	−	0.755143i	0.121415	−	0.0336368i
$505$			2.91831i			0.129863i
$506$	2.56297	−	3.07199i	0.113938	−	0.136566i
$507$	7.77272	+	7.77272i	0.345199	+	0.345199i
$508$	−43.4197	+	7.90889i	−1.92644	+	0.350900i
$509$	−1.60938	+	1.60938i	−0.0713346	+	0.0713346i	−0.741874	−	0.670539i	$-0.766063\pi$
$509$	−1.60938	+	1.60938i	−0.0713346	+	0.0713346i	0.670539	+	0.741874i	$0.266063\pi$
$510$	12.1427	−	1.09687i	0.537687	−	0.0485702i
$511$	13.6312			0.603008
$512$	−15.5887	+	16.4010i	−0.688930	+	0.724828i
$513$	4.73337			0.208983
$514$	39.2386	−	3.54449i	1.73074	−	0.156341i
$515$	−7.58419	+	7.58419i	−0.334199	+	0.334199i
$516$	16.2956	−	2.96824i	0.717375	−	0.130670i
$517$	−0.439625	−	0.439625i	−0.0193347	−	0.0193347i
$518$	1.14709	−	1.37491i	0.0504003	−	0.0604100i
$519$			13.9711i			0.613263i
$520$	−15.2042	+	4.21217i	−0.666749	+	0.184716i
$521$			32.9752i			1.44467i	0.691543	+	0.722335i	$0.256931\pi$
$521$			32.9752i			1.44467i	−0.691543	+	0.722335i	$0.743069\pi$
$522$	−6.94019	−	5.79023i	−0.303764	−	0.253432i
$523$	−10.6099	−	10.6099i	−0.463937	−	0.463937i	0.436007	−	0.899943i	$-0.356392\pi$
$523$	−10.6099	−	10.6099i	−0.463937	−	0.463937i	−0.899943	+	0.436007i	$0.856392\pi$
$524$	4.49264	−	6.49382i	0.196262	−	0.283684i
$525$	2.61854	−	2.61854i	0.114282	−	0.114282i
$526$	1.44394	+	15.9848i	0.0629587	+	0.696972i
$527$	51.5431			2.24525
$528$	1.73075	−	0.652150i	0.0753214	−	0.0283812i
$529$	−14.4319			−0.627472
$530$	0.522964	+	5.78938i	0.0227161	+	0.251474i
$531$	5.44250	−	5.44250i	0.236184	−	0.236184i
$532$	−7.78520	−	5.38606i	−0.337531	−	0.233515i
$533$	38.0773	+	38.0773i	1.64931	+	1.64931i
$534$	2.83339	+	2.36391i	0.122613	+	0.102296i
$535$		−	14.8865i		−	0.643601i
$536$	−5.17037	+	9.13296i	−0.223326	+	0.394484i
$537$			4.89350i			0.211170i
$538$	−12.3495	+	14.8022i	−0.532426	+	0.638168i
$539$	0.326956	+	0.326956i	0.0140830	+	0.0140830i
$540$	−0.408142	−	2.24070i	−0.0175636	−	0.0964242i
$541$	−25.9308	+	25.9308i	−1.11485	+	1.11485i	−0.122365	+	0.992485i	$0.539048\pi$
$541$	−25.9308	+	25.9308i	−1.11485	+	1.11485i	−0.992485	+	0.122365i	$0.960952\pi$
$542$	0.851409	−	0.0769092i	0.0365711	−	0.00330353i
$543$	0.447978			0.0192246
$544$	38.5537	−	18.6443i	1.65297	−	0.799367i
$545$	7.64406			0.327436
$546$	6.89900	−	0.623198i	0.295250	−	0.0266704i
$547$	−19.8105	+	19.8105i	−0.847035	+	0.847035i	−0.989762	−	0.142727i	$-0.954413\pi$
$547$	−19.8105	+	19.8105i	−0.847035	+	0.847035i	0.142727	+	0.989762i	$0.454413\pi$
$548$	−3.77708	−	20.7361i	−0.161349	−	0.885803i
$549$	6.94278	+	6.94278i	0.296311	+	0.296311i
$550$	1.55130	−	1.85940i	0.0661479	−	0.0792851i
$551$			30.2516i			1.28876i
$552$	−15.0590	−	8.52526i	−0.640956	−	0.362859i
$553$		−	9.66695i		−	0.411081i
$554$	−12.1787	−	10.1607i	−0.517421	−	0.431687i
$555$	−1.01954	−	1.01954i	−0.0432772	−	0.0432772i
$556$	−7.71893	−	5.34021i	−0.327356	−	0.226475i
$557$	2.13352	−	2.13352i	0.0904002	−	0.0904002i	−0.660461	−	0.750861i	$-0.729639\pi$
$557$	2.13352	−	2.13352i	0.0904002	−	0.0904002i	0.750861	+	0.660461i	$0.229639\pi$
$558$	−0.866238	−	9.58952i	−0.0366708	−	0.405957i
$559$	40.5662			1.71577
$560$	−1.87838	+	4.14980i	−0.0793760	+	0.175361i
$561$	−3.50049			−0.147791
$562$	−2.01714	−	22.3304i	−0.0850880	−	0.941950i
$563$	23.1103	−	23.1103i	0.973984	−	0.973984i	−0.0256861	−	0.999670i	$-0.508177\pi$
$563$	23.1103	−	23.1103i	0.973984	−	0.973984i	0.999670	+	0.0256861i	$0.00817703\pi$
$564$	−1.53001	+	2.21153i	−0.0644250	+	0.0931222i
$565$	−13.5709	−	13.5709i	−0.570932	−	0.570932i
$566$	7.29336	+	6.08488i	0.306563	+	0.255767i
$567$			1.00000i			0.0419961i
$568$	−1.97501	−	7.12897i	−0.0828695	−	0.299125i
$569$			23.3513i			0.978936i	0.872021	+	0.489468i	$0.162809\pi$
$569$			23.3513i			0.978936i	−0.872021	+	0.489468i	$0.837191\pi$
$570$	−4.88348	+	5.85335i	−0.204546	+	0.245170i
$571$	4.94977	+	4.94977i	0.207142	+	0.207142i	0.803051	−	0.595910i	$-0.203208\pi$
$571$	4.94977	+	4.94977i	0.207142	+	0.207142i	−0.595910	+	0.803051i	$0.703208\pi$
$572$	4.45638	−	0.811729i	0.186331	−	0.0339401i
$573$	−8.92604	+	8.92604i	−0.372891	+	0.372891i
$574$	15.4845	−	1.39874i	0.646309	−	0.0583821i
$575$	−22.6566			−0.944846
$576$	−4.11668	−	6.85952i	−0.171528	−	0.285813i
$577$	6.97439			0.290348			0.145174	−	0.989406i	$-0.453626\pi$
$577$	6.97439			0.290348			0.145174	+	0.989406i	$0.453626\pi$
$578$	−56.7790	+	5.12895i	−2.36170	+	0.213336i
$579$	−6.88392	+	6.88392i	−0.286086	+	0.286086i
$580$	14.3206	−	2.60849i	0.594629	−	0.108312i
$581$	0.419553	+	0.419553i	0.0174060	+	0.0174060i
$582$	−3.15564	+	3.78236i	−0.130806	+	0.156784i
$583$		−	1.66896i		−	0.0691212i
$584$	−10.2935	−	37.1553i	−0.425948	−	1.53750i
$585$		−	5.57797i		−	0.230621i
$586$	10.2871	+	8.58257i	0.424956	+	0.354543i
$587$	−10.3093	−	10.3093i	−0.425511	−	0.425511i	0.461585	−	0.887096i	$-0.347281\pi$
$587$	−10.3093	−	10.3093i	−0.425511	−	0.425511i	−0.887096	+	0.461585i	$0.847281\pi$
$588$	1.13789	−	1.64475i	0.0469259	−	0.0678283i
$589$	−22.7878	+	22.7878i	−0.938954	+	0.938954i
$590$	1.11518	+	12.3454i	0.0459111	+	0.508251i
$591$	−13.8968			−0.571639
$592$	−4.61389	−	2.08844i	−0.189630	−	0.0858344i
$593$	3.39349			0.139354			0.0696770	−	0.997570i	$-0.477803\pi$
$593$	3.39349			0.139354			0.0696770	+	0.997570i	$0.477803\pi$
$594$	0.0588295	+	0.651261i	0.00241380	+	0.0267215i
$595$	6.09606	−	6.09606i	0.249914	−	0.249914i
$596$	−13.9157	−	9.62736i	−0.570011	−	0.394352i
$597$	−11.4833	−	11.4833i	−0.469979	−	0.469979i
$598$	−32.5425	−	27.1503i	−1.33076	−	1.11026i
$599$		−	29.7606i		−	1.21599i	−0.793942	−	0.607993i	$-0.791975\pi$
$599$		−	29.7606i		−	1.21599i	0.793942	−	0.607993i	$-0.208025\pi$
$600$	−9.11488	−	5.16014i	−0.372114	−	0.210662i
$601$		−	8.58619i		−	0.350238i	−0.984547	−	0.175119i	$-0.943969\pi$
$601$		−	8.58619i		−	0.350238i	0.984547	−	0.175119i	$-0.0560310\pi$
$602$	7.50321	−	8.99338i	0.305808	−	0.366543i
$603$	−2.62373	−	2.62373i	−0.106847	−	0.106847i
$604$	−0.478998	−	2.62969i	−0.0194901	−	0.107001i
$605$	−8.68548	+	8.68548i	−0.353115	+	0.353115i
$606$	−3.60945	+	0.326048i	−0.146624	+	0.0132448i
$607$	18.3434			0.744536			0.372268	−	0.928125i	$-0.378580\pi$
$607$	18.3434			0.744536			0.372268	+	0.928125i	$0.378580\pi$
$608$	−8.80216	+	25.2878i	−0.356975	+	1.02556i
$609$	−6.39113			−0.258982
$610$	−15.7485	+	1.42259i	−0.637639	+	0.0575990i
$611$	−4.65708	+	4.65708i	−0.188405	+	0.188405i
$612$	2.71328	+	14.8959i	0.109678	+	0.602130i
$613$	23.0100	+	23.0100i	0.929364	+	0.929364i	0.997665	−	0.0683006i	$-0.0217577\pi$
$613$	23.0100	+	23.0100i	0.929364	+	0.929364i	−0.0683006	+	0.997665i	$0.521758\pi$
$614$	8.83188	−	10.5859i	0.356426	−	0.427213i
$615$		−	12.5195i		−	0.504834i
$616$	0.644305	−	1.13810i	0.0259598	−	0.0458554i
$617$		−	0.121516i		−	0.00489204i	−0.999997	−	0.00244602i	$-0.999221\pi$
$617$		−	0.121516i		−	0.00489204i	0.999997	−	0.00244602i	$-0.000778594\pi$
$618$	−10.2277	−	8.53301i	−0.411418	−	0.343248i
$619$	−8.02459	−	8.02459i	−0.322536	−	0.322536i	0.527204	−	0.849739i	$-0.323241\pi$
$619$	−8.02459	−	8.02459i	−0.322536	−	0.322536i	−0.849739	+	0.527204i	$0.823241\pi$
$620$	12.7523	+	8.82243i	0.512143	+	0.354317i
$621$	4.32619	−	4.32619i	0.173604	−	0.173604i
$622$	2.40751	+	26.6519i	0.0965323	+	1.06864i
$623$	2.60923			0.104537
$624$	−6.90842	−	18.3344i	−0.276558	−	0.733964i
$625$	−7.22939			−0.289176
$626$	2.41287	+	26.7112i	0.0964377	+	1.06760i
$627$	1.54760	−	1.54760i	0.0618053	−	0.0618053i
$628$	−15.5621	+	22.4940i	−0.620994	+	0.897607i
$629$	6.77780	+	6.77780i	0.270249	+	0.270249i
$630$	−1.23661	−	1.03171i	−0.0492679	−	0.0411044i
$631$		−	1.18090i		−	0.0470111i	−0.999724	−	0.0235055i	$-0.992517\pi$
$631$		−	1.18090i		−	0.0470111i	0.999724	−	0.0235055i	$-0.00748273\pi$
$632$	−26.3498	+	7.29993i	−1.04814	+	0.290376i
$633$			26.2765i			1.04440i
$634$	21.8955	−	26.2440i	0.869581	−	1.04228i
$635$	17.7693	+	17.7693i	0.705153	+	0.705153i
$636$	−7.10204	+	1.29363i	−0.281614	+	0.0512960i
$637$	3.46355	−	3.46355i	0.137231	−	0.137231i
$638$	−4.16229	+	0.375987i	−0.164787	+	0.0148855i
$639$	2.61541			0.103464
$640$	12.7298	+	1.98631i	0.503190	+	0.0785157i
$641$	−29.4979			−1.16510			−0.582549	−	0.812796i	$-0.697945\pi$
$641$	−29.4979			−1.16510			−0.582549	+	0.812796i	$0.697945\pi$
$642$	18.4121	−	1.66320i	0.726668	−	0.0656411i
$643$	34.8146	−	34.8146i	1.37295	−	1.37295i	0.516920	−	0.856034i	$-0.327079\pi$
$643$	34.8146	−	34.8146i	1.37295	−	1.37295i	0.856034	−	0.516920i	$-0.172921\pi$
$644$	−12.0382	+	2.19276i	−0.474373	+	0.0864069i
$645$	−6.66890	−	6.66890i	−0.262588	−	0.262588i
$646$	32.4648	−	38.9124i	1.27731	−	1.53099i
$647$		−	35.4849i		−	1.39506i	−0.716558	−	0.697528i	$-0.754283\pi$
$647$		−	35.4849i		−	1.39506i	0.716558	−	0.697528i	$-0.245717\pi$
$648$	2.72576	−	0.755143i	0.107078	−	0.0296648i
$649$		−	3.55891i		−	0.139700i
$650$	−19.6972	−	16.4334i	−0.772587	−	0.644573i
$651$	−4.81428	−	4.81428i	−0.188687	−	0.188687i
$652$	−3.46131	+	5.00310i	−0.135555	+	0.195937i
$653$	5.45480	−	5.45480i	0.213463	−	0.213463i	−0.592274	−	0.805737i	$-0.701770\pi$
$653$	5.45480	−	5.45480i	0.213463	−	0.213463i	0.805737	+	0.592274i	$0.201770\pi$
$654$	0.854032	+	9.45440i	0.0333953	+	0.369696i
$655$	−4.49615			−0.175679
$656$	−15.5056	−	41.1506i	−0.605392	−	1.60666i
$657$	13.6312			0.531803
$658$	0.171074	+	1.89384i	0.00666915	+	0.0738296i
$659$	10.9383	−	10.9383i	0.426096	−	0.426096i	−0.461200	−	0.887296i	$-0.652581\pi$
$659$	10.9383	−	10.9383i	0.426096	−	0.426096i	0.887296	+	0.461200i	$0.152581\pi$
$660$	−0.866054	−	0.599165i	−0.0337111	−	0.0233224i
$661$	−1.41146	−	1.41146i	−0.0548996	−	0.0548996i	0.679124	−	0.734024i	$-0.262360\pi$
$661$	−1.41146	−	1.41146i	−0.0548996	−	0.0548996i	−0.734024	+	0.679124i	$0.762360\pi$
$662$	25.8171	+	21.5393i	1.00341	+	0.837150i
$663$			37.0817i			1.44013i
$664$	0.826777	−	1.46042i	0.0320852	−	0.0566754i
$665$			5.39027i			0.209026i
$666$	1.14709	−	1.37491i	0.0444489	−	0.0532766i
$667$	27.6492	+	27.6492i	1.07058	+	1.07058i
$668$	−0.267199	−	1.46692i	−0.0103383	−	0.0567569i
$669$	−7.68979	+	7.68979i	−0.297304	+	0.297304i
$670$	5.95149	−	0.537608i	0.229926	−	0.0207696i
$671$	4.53997			0.175264
$672$	−5.34246	−	1.85960i	−0.206090	−	0.0717355i
$673$	40.0656			1.54441			0.772207	−	0.635371i	$-0.219153\pi$
$673$	40.0656			1.54441			0.772207	+	0.635371i	$0.219153\pi$
$674$	−11.4961	+	1.03846i	−0.442812	+	0.0400000i
$675$	2.61854	−	2.61854i	0.100788	−	0.100788i
$676$	−3.93966	−	21.6287i	−0.151525	−	0.831873i
$677$	−28.2938	−	28.2938i	−1.08742	−	1.08742i	−0.995794	−	0.0916238i	$-0.970794\pi$
$677$	−28.2938	−	28.2938i	−1.08742	−	1.08742i	−0.0916238	−	0.995794i	$-0.529206\pi$
$678$	15.2687	−	18.3011i	0.586390	−	0.702849i
$679$			3.48313i			0.133670i
$680$	−21.2198	−	12.0130i	−0.813742	−	0.460677i
$681$		−	8.20018i		−	0.314232i
$682$	−3.41857	−	2.85213i	−0.130904	−	0.109214i
$683$	−17.1521	−	17.1521i	−0.656306	−	0.656306i	0.298198	−	0.954504i	$-0.403614\pi$
$683$	−17.1521	−	17.1521i	−0.656306	−	0.656306i	−0.954504	+	0.298198i	$0.903614\pi$
$684$	−7.78520	−	5.38606i	−0.297675	−	0.205941i
$685$	−8.48615	+	8.48615i	−0.324239	+	0.324239i
$686$	−0.127230	−	1.40848i	−0.00485767	−	0.0537760i
$687$	27.8929			1.06418
$688$	−30.1798	−	13.6606i	−1.15059	−	0.520807i
$689$	−17.6798			−0.673546
$690$	0.886445	+	9.81322i	0.0337464	+	0.373583i
$691$	33.9093	−	33.9093i	1.28997	−	1.28997i	0.355171	−	0.934801i	$-0.384423\pi$
$691$	33.9093	−	33.9093i	1.28997	−	1.28997i	0.934801	−	0.355171i	$-0.115577\pi$
$692$	15.8976	−	22.9790i	0.604336	−	0.873529i
$693$	0.326956	+	0.326956i	0.0124200	+	0.0124200i
$694$	2.41779	+	2.01717i	0.0917779	+	0.0765707i
$695$			5.34439i			0.202724i
$696$	4.82622	+	17.4207i	0.182937	+	0.660329i
$697$			83.2280i			3.15249i
$698$	2.57071	−	3.08127i	0.0973030	−	0.116628i
$699$	15.1190	+	15.1190i	0.571853	+	0.571853i
$700$	−7.28646	+	1.32723i	−0.275402	+	0.0501645i
$701$	−8.85810	+	8.85810i	−0.334566	+	0.334566i	−0.854317	−	0.519752i	$-0.826025\pi$
$701$	−8.85810	+	8.85810i	−0.334566	+	0.334566i	0.519752	+	0.854317i	$0.326025\pi$
$702$	6.89900	−	0.623198i	0.260386	−	0.0235211i
$703$	−5.99308			−0.226033
$704$	−3.58873	−	0.896788i	−0.135255	−	0.0337990i
$705$	1.53121			0.0576685
$706$	−2.59951	+	0.234818i	−0.0978337	+	0.00883749i
$707$	−1.81208	+	1.81208i	−0.0681501	+	0.0681501i
$708$	−15.1445	+	2.75857i	−0.569166	+	0.103673i
$709$	20.2034	+	20.2034i	0.758755	+	0.758755i	0.976096	−	0.217341i	$-0.0697383\pi$
$709$	20.2034	+	20.2034i	0.758755	+	0.758755i	−0.217341	+	0.976096i	$0.569738\pi$
$710$	−2.69835	+	3.23425i	−0.101267	+	0.121379i
$711$		−	9.66695i		−	0.362539i
$712$	−1.97035	−	7.11214i	−0.0738418	−	0.266539i
$713$			41.6550i			1.55999i
$714$	8.22087	+	6.85871i	0.307658	+	0.256681i
$715$	−1.82375	−	1.82375i	−0.0682045	−	0.0682045i
$716$	5.56827	−	8.04858i	0.208096	−	0.300790i
$717$	14.7579	−	14.7579i	0.551145	−	0.551145i
$718$	−3.70837	−	41.0528i	−0.138395	−	1.53208i
$719$	42.0375			1.56774			0.783868	−	0.620928i	$-0.213244\pi$
$719$	42.0375			1.56774			0.783868	+	0.620928i	$0.213244\pi$
$720$	−1.87838	+	4.14980i	−0.0700030	+	0.154654i
$721$	−9.41854			−0.350765
$722$	0.433189	+	4.79553i	0.0161216	+	0.178471i
$723$	−6.19946	+	6.19946i	−0.230560	+	0.230560i
$724$	−0.736812	−	0.509751i	−0.0273834	−	0.0189448i
$725$	16.7354	+	16.7354i	0.621538	+	0.621538i
$726$	−11.7128	−	9.77208i	−0.434704	−	0.362676i
$727$			33.7760i			1.25268i	0.779549	+	0.626342i	$0.215448\pi$
$727$			33.7760i			1.25268i	−0.779549	+	0.626342i	$0.784552\pi$
$728$	−12.0563	−	6.82531i	−0.446835	−	0.252963i
$729$			1.00000i			0.0370370i
$730$	−14.0635	+	16.8565i	−0.520512	+	0.623888i
$731$	44.3341	+	44.3341i	1.63976	+	1.63976i
$732$	−3.51900	−	19.3193i	−0.130066	−	0.714061i
$733$	15.4095	−	15.4095i	0.569165	−	0.569165i	−0.362730	−	0.931894i	$-0.618155\pi$
$733$	15.4095	−	15.4095i	0.569165	−	0.569165i	0.931894	+	0.362730i	$0.118155\pi$
$734$	2.22204	−	0.200720i	0.0820169	−	0.00740873i
$735$	−1.13878			−0.0420046
$736$	15.0675	+	31.1575i	0.555397	+	1.14848i
$737$	−1.71569			−0.0631983
$738$	15.4845	−	1.39874i	0.569991	−	0.0514882i
$739$	−22.2512	+	22.2512i	−0.818523	+	0.818523i	−0.985894	−	0.167371i	$-0.946472\pi$
$739$	−22.2512	+	22.2512i	−0.818523	+	0.818523i	0.167371	+	0.985894i	$0.446472\pi$
$740$	0.516763	+	2.83702i	0.0189966	+	0.104291i
$741$	−16.3942	−	16.3942i	−0.602257	−	0.602257i
$742$	−3.27009	+	3.91954i	−0.120049	+	0.143891i
$743$			11.9212i			0.437346i	0.975798	+	0.218673i	$0.0701728\pi$
$743$			11.9212i			0.437346i	−0.975798	+	0.218673i	$0.929827\pi$
$744$	−9.48710	+	16.7580i	−0.347814	+	0.614380i
$745$			9.63489i			0.352995i
$746$	15.1135	+	12.6092i	0.553344	+	0.461657i
$747$	0.419553	+	0.419553i	0.0153506	+	0.0153506i
$748$	5.75742	+	3.98318i	0.210512	+	0.145639i
$749$	9.24353	−	9.24353i	0.337751	−	0.337751i
$750$	1.26098	+	13.9595i	0.0460445	+	0.509727i
$751$	36.4598			1.33044			0.665219	−	0.746648i	$-0.268338\pi$
$751$	36.4598			1.33044			0.665219	+	0.746648i	$0.268338\pi$
$752$	5.03297	−	1.89643i	0.183533	−	0.0691556i
$753$	−14.0742			−0.512891
$754$	3.98294	+	44.0924i	0.145050	+	1.60575i
$755$	−1.07619	+	1.07619i	−0.0391665	+	0.0391665i
$756$	1.13789	−	1.64475i	0.0413847	−	0.0598190i
$757$	−16.6380	−	16.6380i	−0.604719	−	0.604719i	0.336842	−	0.941561i	$-0.390641\pi$
$757$	−16.6380	−	16.6380i	−0.604719	−	0.604719i	−0.941561	+	0.336842i	$0.890641\pi$
$758$	29.3065	+	24.4505i	1.06446	+	0.888082i
$759$		−	2.82895i		−	0.102684i
$760$	14.6926	−	4.07043i	0.532956	−	0.147650i
$761$			2.35441i			0.0853474i	0.999089	+	0.0426737i	$0.0135876\pi$
$761$			2.35441i			0.0853474i	−0.999089	+	0.0426737i	$0.986412\pi$
$762$	−19.9923	+	23.9629i	−0.724245	+	0.868083i
$763$	4.74645	+	4.74645i	0.171833	+	0.171833i
$764$	24.8380	−	4.52423i	0.898607	−	0.163681i
$765$	6.09606	−	6.09606i	0.220404	−	0.220404i
$766$	1.26889	−	0.114621i	0.0458467	−	0.00414141i
$767$	−37.7007			−1.36129
$768$	−1.03449	+	15.9665i	−0.0373288	+	0.576142i
$769$	−31.2378			−1.12646			−0.563232	−	0.826299i	$-0.690442\pi$
$769$	−31.2378			−1.12646			−0.563232	+	0.826299i	$0.690442\pi$
$770$	−0.741644	+	0.0669939i	−0.0267270	+	0.00241429i
$771$	19.6992	−	19.6992i	0.709449	−	0.709449i
$772$	19.1555	−	3.48917i	0.689421	−	0.125578i
$773$	15.4590	+	15.4590i	0.556022	+	0.556022i	0.928173	−	0.372150i	$-0.121379\pi$
$773$	15.4590	+	15.4590i	0.556022	+	0.556022i	−0.372150	+	0.928173i	$0.621379\pi$
$774$	7.50321	−	8.99338i	0.269697	−	0.323260i
$775$			25.2128i			0.905670i
$776$	9.49416	−	2.63026i	0.340820	−	0.0944208i
$777$		−	1.26613i		−	0.0454223i
$778$	23.3695	+	19.4973i	0.837838	+	0.699012i
$779$	−36.7960	−	36.7960i	−1.31835	−	1.31835i
$780$	−6.34713	+	9.17437i	−0.227264	+	0.328495i
$781$	0.855124	−	0.855124i	0.0305987	−	0.0305987i
$782$	−5.89298	−	65.2372i	−0.210733	−	2.33288i
$783$	−6.39113			−0.228400
$784$	−3.74310	+	1.41040i	−0.133682	+	0.0503715i
$785$	15.5742			0.555868
$786$	−0.502332	−	5.56097i	−0.0179176	−	0.198353i
$787$	12.0888	−	12.0888i	0.430919	−	0.430919i	−0.458022	−	0.888941i	$-0.651442\pi$
$787$	12.0888	−	12.0888i	0.430919	−	0.430919i	0.888941	+	0.458022i	$0.151442\pi$
$788$	22.8568	+	15.8131i	0.814240	+	0.563318i
$789$	8.02496	+	8.02496i	0.285696	+	0.285696i
$790$	11.9543	+	9.97352i	0.425315	+	0.354842i
$791$		−	16.8532i		−	0.599232i
$792$	0.644305	−	1.13810i	0.0228944	−	0.0404407i
$793$		−	48.0933i		−	1.70784i
$794$	−30.1742	+	36.1670i	−1.07084	+	1.28352i
$795$	2.90647	+	2.90647i	0.103082	+	0.103082i
$796$	5.82038	+	31.9538i	0.206298	+	1.13257i
$797$	4.39200	−	4.39200i	0.155573	−	0.155573i	−0.625029	−	0.780602i	$-0.714913\pi$
$797$	4.39200	−	4.39200i	0.155573	−	0.155573i	0.780602	+	0.625029i	$0.214913\pi$
$798$	−6.66685	+	0.602228i	−0.236004	+	0.0213186i
$799$	−10.1793			−0.360117
$800$	9.12002	+	18.8589i	0.322442	+	0.666762i
$801$	2.60923			0.0921927
$802$	48.5490	−	4.38551i	1.71432	−	0.154858i
$803$	4.45680	−	4.45680i	0.157277	−	0.157277i
$804$	1.32986	+	7.30091i	0.0469005	+	0.257483i
$805$	4.92659	+	4.92659i	0.173639	+	0.173639i
$806$	−30.2135	+	36.2140i	−1.06422	+	1.27558i
$807$			13.6311i			0.479839i
$808$	6.30766	+	3.57090i	0.221903	+	0.125624i
$809$			28.7534i			1.01091i	0.862852	+	0.505457i	$0.168676\pi$
$809$			28.7534i			1.01091i	−0.862852	+	0.505457i	$0.831324\pi$
$810$	−1.23661	−	1.03171i	−0.0434502	−	0.0362507i
$811$	−38.1545	−	38.1545i	−1.33979	−	1.33979i	−0.896264	−	0.443522i	$-0.853729\pi$
$811$	−38.1545	−	38.1545i	−1.33979	−	1.33979i	−0.443522	−	0.896264i	$-0.646271\pi$
$812$	10.5118	+	7.27242i	0.368892	+	0.255212i
$813$	0.427438	−	0.427438i	0.0149909	−	0.0149909i
$814$	−0.0744860	−	0.824583i	−0.00261073	−	0.0289016i
$815$	3.46402			0.121339
$816$	12.4872	−	27.5874i	0.437141	−	0.965753i
$817$	−39.2012			−1.37147
$818$	−2.53487	−	28.0618i	−0.0886297	−	0.981158i
$819$	3.46355	−	3.46355i	0.121026	−	0.121026i
$820$	−14.2458	+	20.5914i	−0.497485	+	0.719083i
$821$	22.0320	+	22.0320i	0.768923	+	0.768923i	0.977917	−	0.208994i	$-0.0670188\pi$
$821$	22.0320	+	22.0320i	0.768923	+	0.768923i	−0.208994	+	0.977917i	$0.567019\pi$
$822$	−11.4440	−	9.54781i	−0.399157	−	0.333018i
$823$		−	3.93740i		−	0.137249i	−0.997643	−	0.0686245i	$-0.978139\pi$
$823$		−	3.93740i		−	0.137249i	0.997643	−	0.0686245i	$-0.0218611\pi$
$824$	7.11235	+	25.6727i	0.247770	+	0.894350i
$825$		−	1.71230i		−	0.0596145i
$826$	−6.97319	+	8.35809i	−0.242628	+	0.290815i
$827$	−17.3878	−	17.3878i	−0.604632	−	0.604632i	0.336906	−	0.941538i	$-0.390620\pi$
$827$	−17.3878	−	17.3878i	−0.604632	−	0.604632i	−0.941538	+	0.336906i	$0.890620\pi$
$828$	−12.0382	+	2.19276i	−0.418358	+	0.0762038i
$829$	32.2931	−	32.2931i	1.12159	−	1.12159i	0.130083	−	0.991503i	$-0.458476\pi$
$829$	32.2931	−	32.2931i	1.12159	−	1.12159i	0.991503	−	0.130083i	$-0.0415243\pi$
$830$	−0.951683	+	0.0859672i	−0.0330334	+	0.00298396i
$831$	−11.2152			−0.389050
$832$	−9.49995	+	38.0165i	−0.329351	+	1.31799i
$833$	7.57049			0.262302
$834$	−6.61010	+	0.597101i	−0.228889	+	0.0206759i
$835$	−0.600330	+	0.600330i	−0.0207753	+	0.0207753i
$836$	−4.30643	+	0.784414i	−0.148941	+	0.0271295i
$837$	−4.81428	−	4.81428i	−0.166406	−	0.166406i
$838$	10.0759	−	12.0770i	0.348065	−	0.417192i
$839$			12.4459i			0.429679i	0.976649	+	0.214839i	$0.0689228\pi$
$839$			12.4459i			0.429679i	−0.976649	+	0.214839i	$0.931077\pi$
$840$	0.859944	+	3.10404i	0.0296709	+	0.107100i
$841$		−	11.8465i		−	0.408501i
$842$	2.09740	+	1.74987i	0.0722812	+	0.0603045i
$843$	−11.2107	−	11.2107i	−0.386115	−	0.386115i
$844$	29.8998	−	43.2183i	1.02919	−	1.48763i
$845$	−8.85144	+	8.85144i	−0.304499	+	0.304499i
$846$	0.171074	+	1.89384i	0.00588164	+	0.0651116i
$847$	−10.7862			−0.370618
$848$	13.1531	+	5.95365i	0.451679	+	0.204449i
$849$	6.71636			0.230505
$850$	−3.56688	−	39.4865i	−0.122343	−	1.35438i
$851$	−5.47754	+	5.47754i	−0.187768	+	0.187768i
$852$	−4.30169	−	2.97605i	−0.147374	−	0.101958i
$853$	−23.4343	−	23.4343i	−0.802376	−	0.802376i	0.181091	−	0.983466i	$-0.442037\pi$
$853$	−23.4343	−	23.4343i	−0.802376	−	0.802376i	−0.983466	+	0.181091i	$0.942037\pi$
$854$	−10.6621	−	8.89543i	−0.364849	−	0.304395i
$855$			5.39027i			0.184343i
$856$	−32.1758	−	18.2154i	−1.09975	−	0.622591i
$857$			3.15408i			0.107741i	0.998548	+	0.0538707i	$0.0171559\pi$
$857$			3.15408i			0.107741i	−0.998548	+	0.0538707i	$0.982844\pi$
$858$	2.05191	−	2.45943i	0.0700511	−	0.0839635i
$859$	22.2106	+	22.2106i	0.757815	+	0.757815i	0.975924	−	0.218109i	$-0.0699890\pi$
$859$	22.2106	+	22.2106i	0.757815	+	0.757815i	−0.218109	+	0.975924i	$0.569989\pi$
$860$	3.38018	+	18.5572i	0.115263	+	0.632794i
$861$	7.77375	−	7.77375i	0.264929	−	0.264929i
$862$	−5.74474	+	0.518932i	−0.195667	+	0.0176749i
$863$	22.4648			0.764711			0.382355	−	0.924015i	$-0.375113\pi$
$863$	22.4648			0.764711			0.382355	+	0.924015i	$0.375113\pi$
$864$	−5.34246	−	1.85960i	−0.181754	−	0.0632648i
$865$	−15.9100			−0.540957
$866$	6.79028	−	0.613377i	0.230743	−	0.0208434i
$867$	−28.5051	+	28.5051i	−0.968084	+	0.968084i
$868$	2.44016	+	13.3964i	0.0828243	+	0.454704i
$869$	−3.16067	−	3.16067i	−0.107218	−	0.107218i
$870$	6.59381	−	7.90336i	0.223551	−	0.267949i
$871$			18.1748i			0.615831i
$872$	9.35342	−	16.5219i	0.316747	−	0.559503i
$873$			3.48313i			0.117886i
$874$	31.4474	+	26.2367i	1.06372	+	0.887470i
$875$	7.00815	+	7.00815i	0.236919	+	0.236919i
$876$	−22.4199	−	15.5108i	−0.757497	−	0.524062i
$877$	−27.7008	+	27.7008i	−0.935389	+	0.935389i	−0.998036	−	0.0626468i	$-0.980046\pi$
$877$	−27.7008	+	27.7008i	−0.935389	+	0.935389i	0.0626468	+	0.998036i	$0.480046\pi$
$878$	4.24158	+	46.9556i	0.143146	+	1.58467i
$879$	9.47325			0.319525
$880$	0.742657	+	1.97095i	0.0250350	+	0.0664408i
$881$	32.3138			1.08868			0.544340	−	0.838865i	$-0.316780\pi$
$881$	32.3138			1.08868			0.544340	+	0.838865i	$0.316780\pi$
$882$	−0.127230	−	1.40848i	−0.00428407	−	0.0474259i
$883$	−19.3000	+	19.3000i	−0.649497	+	0.649497i	−0.952871	−	0.303374i	$-0.901887\pi$
$883$	−19.3000	+	19.3000i	−0.649497	+	0.649497i	0.303374	+	0.952871i	$0.401887\pi$
$884$	42.1950	−	60.9901i	1.41917	−	2.05132i
$885$	6.19782	+	6.19782i	0.208337	+	0.208337i
$886$	38.0064	+	31.7089i	1.27685	+	1.06528i
$887$		−	49.3734i		−	1.65780i	−0.559398	−	0.828899i	$-0.688968\pi$
$887$		−	49.3734i		−	1.65780i	0.559398	−	0.828899i	$-0.311032\pi$
$888$	−3.45118	+	0.956113i	−0.115814	+	0.0320851i
$889$			22.0671i			0.740106i
$890$	−2.69198	+	3.22662i	−0.0902354	+	0.108156i
$891$	0.326956	+	0.326956i	0.0109534	+	0.0109534i
$892$	21.3979	−	3.89763i	0.716456	−	0.130502i
$893$	4.50037	−	4.50037i	0.150599	−	0.150599i
$894$	−11.9167	+	1.07646i	−0.398555	+	0.0360021i
$895$	−5.57263			−0.186272
$896$	6.67099	+	9.13772i	0.222862	+	0.305270i
$897$	−29.9679			−1.00060
$898$	12.3699	−	1.11739i	0.412789	−	0.0372879i
$899$	30.7687	−	30.7687i	1.02619	−	1.02619i
$900$	−7.28646	+	1.32723i	−0.242882	+	0.0442409i
$901$	−19.3219	−	19.3219i	−0.643706	−	0.643706i
$902$	4.60541	−	5.52006i	0.153343	−	0.183798i
$903$		−	8.28188i		−	0.275604i
$904$	−45.9378	+	12.7266i	−1.52787	+	0.423281i
$905$			0.510150i			0.0169579i
$906$	−1.45130	−	1.21082i	−0.0482162	−	0.0402270i
$907$	26.6615	+	26.6615i	0.885279	+	0.885279i	0.994065	−	0.108786i	$-0.0346963\pi$
$907$	26.6615	+	26.6615i	0.885279	+	0.885279i	−0.108786	+	0.994065i	$0.534696\pi$
$908$	−9.33092	+	13.4872i	−0.309657	+	0.447590i
$909$	−1.81208	+	1.81208i	−0.0601028	+	0.0601028i
$910$	0.709687	+	7.85646i	0.0235259	+	0.260439i
$911$	3.01720			0.0999643			0.0499821	−	0.998750i	$-0.484084\pi$
$911$	3.01720			0.0999643			0.0499821	+	0.998750i	$0.484084\pi$
$912$	6.67595	+	17.7174i	0.221063	+	0.586683i
$913$	0.274351			0.00907968
$914$	−0.269409	−	2.98244i	−0.00891126	−	0.0986504i
$915$	−7.90632	+	7.90632i	−0.261375	+	0.261375i
$916$	−45.8768	−	31.7391i	−1.51581	−	1.04869i
$917$	−2.79181	−	2.79181i	−0.0921936	−	0.0921936i
$918$	8.22087	+	6.85871i	0.271329	+	0.226371i
$919$		−	5.16809i		−	0.170480i	−0.996360	−	0.0852398i	$-0.972834\pi$
$919$		−	5.16809i		−	0.170480i	0.996360	−	0.0852398i	$-0.0271657\pi$
$920$	9.70841	−	17.1490i	0.320077	−	0.565385i
$921$		−	9.74843i		−	0.321222i
$922$	2.85770	−	3.42525i	0.0941134	−	0.112805i
$923$	−9.05859	−	9.05859i	−0.298167	−	0.298167i
$924$	−0.165720	−	0.909802i	−0.00545179	−	0.0299303i
$925$	−3.31542	+	3.31542i	−0.109010	+	0.109010i
$926$	−50.0850	+	4.52426i	−1.64589	+	0.148676i
$927$	−9.41854			−0.309346
$928$	11.8849	−	34.1444i	0.390142	−	1.12084i
$929$	−10.7505			−0.352711			−0.176356	−	0.984327i	$-0.556431\pi$
$929$	−10.7505			−0.352711			−0.176356	+	0.984327i	$0.556431\pi$
$930$	10.9204	−	0.986456i	0.358093	−	0.0323472i
$931$	−3.34700	+	3.34700i	−0.109693	+	0.109693i
$932$	−7.66317	−	42.0707i	−0.251016	−	1.37807i
$933$	13.3802	+	13.3802i	0.438048	+	0.438048i
$934$	4.18790	−	5.01964i	0.137032	−	0.164248i
$935$		−	3.98629i		−	0.130366i
$936$	−12.0563	−	6.82531i	−0.394071	−	0.223092i
$937$		−	7.11251i		−	0.232355i	−0.993228	−	0.116178i	$-0.962936\pi$
$937$		−	7.11251i		−	0.232355i	0.993228	−	0.116178i	$-0.0370642\pi$
$938$	4.02929	+	3.36165i	0.131561	+	0.109762i
$939$	13.4100	+	13.4100i	0.437618	+	0.437618i
$940$	−2.51845	−	1.74235i	−0.0821428	−	0.0568291i
$941$	−40.2596	+	40.2596i	−1.31242	+	1.31242i	−0.392800	+	0.919624i	$0.628494\pi$
$941$	−40.2596	+	40.2596i	−1.31242	+	1.31242i	−0.919624	+	0.392800i	$0.871506\pi$
$942$	1.74003	+	19.2627i	0.0566932	+	0.627612i
$943$	−67.2615			−2.19033
$944$	28.0479	+	12.6957i	0.912881	+	0.413209i
$945$	−1.13878			−0.0370446
$946$	−0.487218	−	5.39366i	−0.0158408	−	0.175363i
$947$	31.9771	−	31.9771i	1.03912	−	1.03912i	0.0399126	−	0.999203i	$-0.487292\pi$
$947$	31.9771	−	31.9771i	1.03912	−	1.03912i	0.999203	−	0.0399126i	$-0.0127080\pi$
$948$	−10.9999	+	15.8997i	−0.357262	+	0.516399i
$949$	−47.2122	−	47.2122i	−1.53257	−	1.53257i
$950$	19.0344	+	15.8805i	0.617556	+	0.515230i
$951$		−	24.1678i		−	0.783693i
$952$	−5.71681	−	20.6353i	−0.185283	−	0.668795i
$953$		−	34.9288i		−	1.13145i	−0.824593	−	0.565727i	$-0.808596\pi$
$953$		−	34.9288i		−	1.13145i	0.824593	−	0.565727i	$-0.191404\pi$
$954$	−3.27009	+	3.91954i	−0.105873	+	0.126900i
$955$	−10.1648	−	10.1648i	−0.328926	−	0.328926i
$956$	−41.0660	+	7.48016i	−1.32817	+	0.241926i
$957$	−2.08962	+	2.08962i	−0.0675478	+	0.0675478i
$958$	16.8894	−	1.52564i	0.545670	−	0.0492913i
$959$	−10.5387			−0.340311
$960$	7.81149	−	4.68800i	0.252115	−	0.151304i
$961$	15.3547			0.495311
$962$	−8.73506	+	0.789053i	−0.281630	+	0.0254401i
$963$	9.24353	−	9.24353i	0.297869	−	0.297869i
$964$	17.2509	−	3.14224i	0.555613	−	0.101205i
$965$	−7.83929	−	7.83929i	−0.252356	−	0.252356i
$966$	−5.54293	+	6.64377i	−0.178341	+	0.213760i
$967$		−	51.2932i		−	1.64948i	−0.565514	−	0.824739i	$-0.691322\pi$
$967$		−	51.2932i		−	1.64948i	0.565514	−	0.824739i	$-0.308678\pi$
$968$	8.14513	+	29.4006i	0.261794	+	0.944970i
$969$		−	35.8339i		−	1.15115i
$970$	−4.30729	−	3.59359i	−0.138299	−	0.115383i
$971$	−17.6501	−	17.6501i	−0.566420	−	0.566420i	0.364704	−	0.931124i	$-0.381170\pi$
$971$	−17.6501	−	17.6501i	−0.566420	−	0.566420i	−0.931124	+	0.364704i	$0.881170\pi$
$972$	1.13789	−	1.64475i	0.0364979	−	0.0527554i
$973$	−3.31850	+	3.31850i	−0.106386	+	0.106386i
$974$	−4.10571	−	45.4515i	−0.131556	−	1.45636i
$975$	−18.1389			−0.580909
$976$	−16.1954	+	35.7796i	−0.518402	+	1.14528i
$977$	59.6247			1.90756			0.953782	−	0.300499i	$-0.0971532\pi$
$977$	59.6247			1.90756			0.953782	+	0.300499i	$0.0971532\pi$
$978$	0.387017	+	4.28440i	0.0123754	+	0.137000i
$979$	0.853105	−	0.853105i	0.0272654	−	0.0272654i
$980$	1.87301	+	1.29581i	0.0598311	+	0.0413932i
$981$	4.74645	+	4.74645i	0.151542	+	0.151542i
$982$	41.1338	+	34.3181i	1.31263	+	1.09513i
$983$		−	15.6513i		−	0.499200i	−0.968349	−	0.249600i	$-0.919701\pi$
$983$		−	15.6513i		−	0.499200i	0.968349	−	0.249600i	$-0.0802991\pi$
$984$	−27.0597	−	15.3191i	−0.862630	−	0.488354i
$985$		−	15.8255i		−	0.504241i
$986$	−43.8349	+	52.5406i	−1.39599	+	1.67324i
$987$	0.950776	+	0.950776i	0.0302635	+	0.0302635i
$988$	8.30954	+	45.6193i	0.264362	+	1.45134i
$989$	−35.8290	+	35.8290i	−1.13930	+	1.13930i
$990$	−0.741644	+	0.0669939i	−0.0235710	+	0.00212921i
$991$	−48.6107			−1.54417			−0.772084	−	0.635520i	$-0.780786\pi$
$991$	−48.6107			−1.54417			−0.772084	+	0.635520i	$0.780786\pi$
$992$	34.6728	−	16.7675i	1.10086	−	0.532369i
$993$	23.7746			0.754465
$994$	−3.68375	+	0.332759i	−0.116841	+	0.0105545i
$995$	13.0769	−	13.0769i	0.414567	−	0.414567i
$996$	−0.212653	−	1.16747i	−0.00673818	−	0.0369926i
$997$	−21.9038	−	21.9038i	−0.693701	−	0.693701i	0.269343	−	0.963044i	$-0.413193\pi$
$997$	−21.9038	−	21.9038i	−0.693701	−	0.693701i	−0.963044	+	0.269343i	$0.913193\pi$
$998$	28.0654	−	33.6393i	0.888395	−	1.06483i
$999$		−	1.26613i		−	0.0400587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.b.85.1	✓	28
4.3	odd	2		1344.2.w.b.1009.9		28
8.3	odd	2		2688.2.w.c.2017.6		28
8.5	even	2		2688.2.w.d.2017.9		28
16.3	odd	4		1344.2.w.b.337.9		28
16.5	even	4		2688.2.w.d.673.9		28
16.11	odd	4		2688.2.w.c.673.6		28
16.13	even	4	inner	336.2.w.b.253.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.b.85.1	✓	28	1.1	even	1	trivial
336.2.w.b.253.1	yes	28	16.13	even	4	inner
1344.2.w.b.337.9		28	16.3	odd	4
1344.2.w.b.1009.9		28	4.3	odd	2
2688.2.w.c.673.6		28	16.11	odd	4
2688.2.w.c.2017.6		28	8.3	odd	2
2688.2.w.d.673.9		28	16.5	even	4
2688.2.w.d.2017.9		28	8.5	even	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40848 + 0.127230i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.96762 - 0.358402i) q^{4} +(-0.805240 - 0.805240i) q^{5} +(0.905980 - 1.08591i) q^{6} -1.00000i q^{7} +(-2.72576 + 0.755143i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.40848 + 0.127230i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.96762 - 0.358402i) q^{4} +(-0.805240 - 0.805240i) q^{5} +(0.905980 - 1.08591i) q^{6} -1.00000i q^{7} +(-2.72576 + 0.755143i) q^{8} -1.00000i q^{9} +(1.23661 + 1.03171i) q^{10} +(-0.326956 - 0.326956i) q^{11} +(-1.13789 + 1.64475i) q^{12} +(-3.46355 + 3.46355i) q^{13} +(0.127230 + 1.40848i) q^{14} +1.13878 q^{15} +(3.74310 - 1.41040i) q^{16} -7.57049 q^{17} +(0.127230 + 1.40848i) q^{18} +(3.34700 - 3.34700i) q^{19} +(-1.87301 - 1.29581i) q^{20} +(0.707107 + 0.707107i) q^{21} +(0.502109 + 0.418912i) q^{22} -6.11816i q^{23} +(1.39344 - 2.46137i) q^{24} -3.70318i q^{25} +(4.43766 - 5.31900i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.358402 - 1.96762i) q^{28} +(-4.51921 + 4.51921i) q^{29} +(-1.60395 + 0.144888i) q^{30} -6.80843 q^{31} +(-5.09262 + 2.46276i) q^{32} +0.462386 q^{33} +(10.6629 - 0.963195i) q^{34} +(-0.805240 + 0.805240i) q^{35} +(-0.358402 - 1.96762i) q^{36} +(-0.895292 - 0.895292i) q^{37} +(-4.28833 + 5.14001i) q^{38} -4.89819i q^{39} +(2.80296 + 1.58682i) q^{40} -10.9937i q^{41} +(-1.08591 - 0.905980i) q^{42} +(-5.85617 - 5.85617i) q^{43} +(-0.760509 - 0.526145i) q^{44} +(-0.805240 + 0.805240i) q^{45} +(0.778415 + 8.61730i) q^{46} +1.34460 q^{47} +(-1.64946 + 3.64407i) q^{48} -1.00000 q^{49} +(0.471156 + 5.21584i) q^{50} +(5.35314 - 5.35314i) q^{51} +(-5.57362 + 8.05630i) q^{52} +(2.55227 + 2.55227i) q^{53} +(-1.08591 - 0.905980i) q^{54} +0.526557i q^{55} +(0.755143 + 2.72576i) q^{56} +4.73337i q^{57} +(5.79023 - 6.94019i) q^{58} +(5.44250 + 5.44250i) q^{59} +(2.24070 - 0.408142i) q^{60} +(-6.94278 + 6.94278i) q^{61} +(9.58952 - 0.866238i) q^{62} -1.00000 q^{63} +(6.85952 - 4.11668i) q^{64} +5.57797 q^{65} +(-0.651261 + 0.0588295i) q^{66} +(2.62373 - 2.62373i) q^{67} +(-14.8959 + 2.71328i) q^{68} +(4.32619 + 4.32619i) q^{69} +(1.03171 - 1.23661i) q^{70} +2.61541i q^{71} +(0.755143 + 2.72576i) q^{72} +13.6312i q^{73} +(1.37491 + 1.14709i) q^{74} +(2.61854 + 2.61854i) q^{75} +(5.38606 - 7.78520i) q^{76} +(-0.326956 + 0.326956i) q^{77} +(0.623198 + 6.89900i) q^{78} +9.66695 q^{79} +(-4.14980 - 1.87838i) q^{80} -1.00000 q^{81} +(1.39874 + 15.4845i) q^{82} +(-0.419553 + 0.419553i) q^{83} +(1.64475 + 1.13789i) q^{84} +(6.09606 + 6.09606i) q^{85} +(8.99338 + 7.50321i) q^{86} -6.39113i q^{87} +(1.13810 + 0.644305i) q^{88} +2.60923i q^{89} +(1.03171 - 1.23661i) q^{90} +(3.46355 + 3.46355i) q^{91} +(-2.19276 - 12.0382i) q^{92} +(4.81428 - 4.81428i) q^{93} +(-1.89384 + 0.171074i) q^{94} -5.39027 q^{95} +(1.85960 - 5.34246i) q^{96} -3.48313 q^{97} +(1.40848 - 0.127230i) q^{98} +(-0.326956 + 0.326956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) \) 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

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