LMFDB - Embedded newform 630.2.bk.b.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bk (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.b.131.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.582530 + 1.63115i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.63115 - 0.582530i) q^{6} +(-1.91453 - 1.82609i) q^{7} +1.00000i q^{8} +(-2.32132 + 1.90039i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.582530 + 1.63115i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.63115 - 0.582530i) q^{6} +(-1.91453 - 1.82609i) q^{7} +1.00000i q^{8} +(-2.32132 + 1.90039i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-0.382566 + 0.220875i) q^{11} +(-0.582530 - 1.63115i) q^{12} +(-3.17590 + 1.83361i) q^{13} +(-1.82609 + 1.91453i) q^{14} +(-1.70388 - 0.311090i) q^{15} +1.00000 q^{16} +(-0.136107 + 0.235743i) q^{17} +(1.90039 + 2.32132i) q^{18} +(-3.25564 + 1.87965i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.86336 - 4.18663i) q^{21} +(0.220875 + 0.382566i) q^{22} +(-2.24789 - 1.29782i) q^{23} +(-1.63115 + 0.582530i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.83361 + 3.17590i) q^{26} +(-4.45207 - 2.67939i) q^{27} +(1.91453 + 1.82609i) q^{28} +(-2.38822 - 1.37884i) q^{29} +(-0.311090 + 1.70388i) q^{30} +8.74919i q^{31} -1.00000i q^{32} +(-0.583137 - 0.495358i) q^{33} +(0.235743 + 0.136107i) q^{34} +(2.53870 - 0.744985i) q^{35} +(2.32132 - 1.90039i) q^{36} +(0.0597017 + 0.103406i) q^{37} +(1.87965 + 3.25564i) q^{38} +(-4.84095 - 4.11225i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(-3.93435 - 6.81449i) q^{41} +(-4.18663 - 1.86336i) q^{42} +(0.849825 - 1.47194i) q^{43} +(0.382566 - 0.220875i) q^{44} +(-0.485129 - 2.96052i) q^{45} +(-1.29782 + 2.24789i) q^{46} -7.89512 q^{47} +(0.582530 + 1.63115i) q^{48} +(0.330818 + 6.99218i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-0.463820 - 0.0846828i) q^{51} +(3.17590 - 1.83361i) q^{52} +(-0.0822585 - 0.0474920i) q^{53} +(-2.67939 + 4.45207i) q^{54} -0.441750i q^{55} +(1.82609 - 1.91453i) q^{56} +(-4.96250 - 4.21550i) q^{57} +(-1.37884 + 2.38822i) q^{58} +3.21065 q^{59} +(1.70388 + 0.311090i) q^{60} +13.0013i q^{61} +8.74919 q^{62} +(7.91450 + 0.600577i) q^{63} -1.00000 q^{64} -3.66721i q^{65} +(-0.495358 + 0.583137i) q^{66} -0.537467 q^{67} +(0.136107 - 0.235743i) q^{68} +(0.807478 - 4.42267i) q^{69} +(-0.744985 - 2.53870i) q^{70} -3.75218i q^{71} +(-1.90039 - 2.32132i) q^{72} +(9.64229 + 5.56698i) q^{73} +(0.103406 - 0.0597017i) q^{74} +(1.12135 - 1.32006i) q^{75} +(3.25564 - 1.87965i) q^{76} +(1.13577 + 0.275729i) q^{77} +(-4.11225 + 4.84095i) q^{78} +3.02791 q^{79} +(-0.500000 + 0.866025i) q^{80} +(1.77702 - 8.82282i) q^{81} +(-6.81449 + 3.93435i) q^{82} +(4.29210 - 7.43413i) q^{83} +(-1.86336 + 4.18663i) q^{84} +(-0.136107 - 0.235743i) q^{85} +(-1.47194 - 0.849825i) q^{86} +(0.857885 - 4.69876i) q^{87} +(-0.220875 - 0.382566i) q^{88} +(6.35119 + 11.0006i) q^{89} +(-2.96052 + 0.485129i) q^{90} +(9.42867 + 2.28898i) q^{91} +(2.24789 + 1.29782i) q^{92} +(-14.2713 + 5.09667i) q^{93} +7.89512i q^{94} -3.75929i q^{95} +(1.63115 - 0.582530i) q^{96} +(12.9284 + 7.46424i) q^{97} +(6.99218 - 0.330818i) q^{98} +(0.468309 - 1.23975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * q^96 + 72 * q^97 + 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.582530	+	1.63115i	0.336324	+	0.941746i
$3$	0.582530	+	1.63115i	0.336324	+	0.941746i
$4$	−1.00000			−0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.63115	−	0.582530i	0.665915	−	0.237817i
$7$	−1.91453	−	1.82609i	−0.723623	−	0.690196i
$7$	−1.91453	−	1.82609i	−0.723623	−	0.690196i
$8$			1.00000i			0.353553i
$9$	−2.32132	+	1.90039i	−0.773772	+	0.633464i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	−0.382566	+	0.220875i	−0.115348	+	0.0665963i	−0.556564	−	0.830805i	$-0.687881\pi$
$11$	−0.382566	+	0.220875i	−0.115348	+	0.0665963i	0.441216	+	0.897401i	$0.354547\pi$
$12$	−0.582530	−	1.63115i	−0.168162	−	0.470873i
$13$	−3.17590	+	1.83361i	−0.880836	+	0.508551i	−0.870934	−	0.491400i	$-0.836485\pi$
$13$	−3.17590	+	1.83361i	−0.880836	+	0.508551i	−0.00990217	+	0.999951i	$0.503152\pi$
$14$	−1.82609	+	1.91453i	−0.488042	+	0.511679i
$15$	−1.70388	−	0.311090i	−0.439941	−	0.0803231i
$16$	1.00000			0.250000
$17$	−0.136107	+	0.235743i	−0.0330107	+	0.0571762i	−0.882059	−	0.471139i	$-0.843843\pi$
$17$	−0.136107	+	0.235743i	−0.0330107	+	0.0571762i	0.849048	+	0.528316i	$0.177176\pi$
$18$	1.90039	+	2.32132i	0.447927	+	0.547140i
$19$	−3.25564	+	1.87965i	−0.746896	+	0.431221i	−0.824571	−	0.565758i	$-0.808584\pi$
$19$	−3.25564	+	1.87965i	−0.746896	+	0.431221i	0.0776753	+	0.996979i	$0.475250\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	1.86336	−	4.18663i	0.406618	−	0.913598i
$22$	0.220875	+	0.382566i	0.0470907	+	0.0815634i
$23$	−2.24789	−	1.29782i	−0.468717	−	0.270614i	0.246985	−	0.969019i	$-0.420560\pi$
$23$	−2.24789	−	1.29782i	−0.468717	−	0.270614i	−0.715703	+	0.698405i	$0.753893\pi$
$24$	−1.63115	+	0.582530i	−0.332958	+	0.118908i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.83361	+	3.17590i	0.359600	+	0.622845i
$27$	−4.45207	−	2.67939i	−0.856800	−	0.515648i
$28$	1.91453	+	1.82609i	0.361811	+	0.345098i
$29$	−2.38822	−	1.37884i	−0.443481	−	0.256044i	0.261592	−	0.965178i	$-0.415752\pi$
$29$	−2.38822	−	1.37884i	−0.443481	−	0.256044i	−0.705073	+	0.709135i	$0.749086\pi$
$30$	−0.311090	+	1.70388i	−0.0567970	+	0.311085i
$31$			8.74919i			1.57140i	0.618608	+	0.785700i	$0.287697\pi$
$31$			8.74919i			1.57140i	−0.618608	+	0.785700i	$0.712303\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.583137	−	0.495358i	−0.101511	−	0.0862307i
$34$	0.235743	+	0.136107i	0.0404297	+	0.0233421i
$35$	2.53870	−	0.744985i	0.429119	−	0.125925i
$36$	2.32132	−	1.90039i	0.386886	−	0.316732i
$37$	0.0597017	+	0.103406i	0.00981490	+	0.0169999i	0.870891	−	0.491476i	$-0.163542\pi$
$37$	0.0597017	+	0.103406i	0.00981490	+	0.0169999i	−0.861076	+	0.508476i	$0.830209\pi$
$38$	1.87965	+	3.25564i	0.304919	+	0.528135i
$39$	−4.84095	−	4.11225i	−0.775172	−	0.658486i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	−3.93435	−	6.81449i	−0.614442	−	1.06424i	−0.990482	−	0.137641i	$-0.956048\pi$
$41$	−3.93435	−	6.81449i	−0.614442	−	1.06424i	0.376041	−	0.926603i	$-0.377285\pi$
$42$	−4.18663	−	1.86336i	−0.646012	−	0.287522i
$43$	0.849825	−	1.47194i	0.129597	−	0.224469i	−0.793923	−	0.608018i	$-0.791965\pi$
$43$	0.849825	−	1.47194i	0.129597	−	0.224469i	0.923521	+	0.383549i	$0.125298\pi$
$44$	0.382566	−	0.220875i	0.0576741	−	0.0332981i
$45$	−0.485129	−	2.96052i	−0.0723187	−	0.441328i
$46$	−1.29782	+	2.24789i	−0.191353	+	0.331433i
$47$	−7.89512			−1.15162			−0.575811	−	0.817583i	$-0.695314\pi$
$47$	−7.89512			−1.15162			−0.575811	+	0.817583i	$0.695314\pi$
$48$	0.582530	+	1.63115i	0.0840810	+	0.235437i
$49$	0.330818	+	6.99218i	0.0472597	+	0.998883i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−0.463820	−	0.0846828i	−0.0649477	−	0.0118580i
$52$	3.17590	−	1.83361i	0.440418	−	0.254276i
$53$	−0.0822585	−	0.0474920i	−0.0112991	−	0.00652352i	0.494340	−	0.869269i	$-0.335410\pi$
$53$	−0.0822585	−	0.0474920i	−0.0112991	−	0.00652352i	−0.505639	+	0.862745i	$0.668743\pi$
$54$	−2.67939	+	4.45207i	−0.364618	+	0.605849i
$55$		−	0.441750i		−	0.0595655i
$56$	1.82609	−	1.91453i	0.244021	−	0.255839i
$57$	−4.96250	−	4.21550i	−0.657299	−	0.558357i
$58$	−1.37884	+	2.38822i	−0.181050	+	0.313588i
$59$	3.21065			0.417991			0.208995	−	0.977917i	$-0.432981\pi$
$59$	3.21065			0.417991			0.208995	+	0.977917i	$0.432981\pi$
$60$	1.70388	+	0.311090i	0.219971	+	0.0401616i
$61$			13.0013i			1.66465i	0.554291	+	0.832323i	$0.312989\pi$
$61$			13.0013i			1.66465i	−0.554291	+	0.832323i	$0.687011\pi$
$62$	8.74919			1.11115
$63$	7.91450	+	0.600577i	0.997133	+	0.0756655i
$64$	−1.00000			−0.125000
$65$		−	3.66721i		−	0.454862i
$66$	−0.495358	+	0.583137i	−0.0609743	+	0.0717792i
$67$	−0.537467			−0.0656620			−0.0328310	−	0.999461i	$-0.510452\pi$
$67$	−0.537467			−0.0656620			−0.0328310	+	0.999461i	$0.510452\pi$
$68$	0.136107	−	0.235743i	0.0165053	−	0.0285881i
$69$	0.807478	−	4.42267i	0.0972089	−	0.532427i
$70$	−0.744985	−	2.53870i	−0.0890427	−	0.303433i
$71$		−	3.75218i		−	0.445302i	−0.974898	−	0.222651i	$-0.928529\pi$
$71$		−	3.75218i		−	0.445302i	0.974898	−	0.222651i	$-0.0714711\pi$
$72$	−1.90039	−	2.32132i	−0.223963	−	0.273570i
$73$	9.64229	+	5.56698i	1.12854	+	0.651565i	0.943568	−	0.331178i	$-0.107446\pi$
$73$	9.64229	+	5.56698i	1.12854	+	0.651565i	0.184976	+	0.982743i	$0.440779\pi$
$74$	0.103406	−	0.0597017i	0.0120207	−	0.00694018i
$75$	1.12135	−	1.32006i	0.129483	−	0.152428i
$76$	3.25564	−	1.87965i	0.373448	−	0.215610i
$77$	1.13577	+	0.275729i	0.129433	+	0.0314222i
$78$	−4.11225	+	4.84095i	−0.465620	+	0.548130i
$79$	3.02791			0.340666			0.170333	−	0.985387i	$-0.445516\pi$
$79$	3.02791			0.340666			0.170333	+	0.985387i	$0.445516\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	1.77702	−	8.82282i	0.197447	−	0.980314i
$82$	−6.81449	+	3.93435i	−0.752534	+	0.434476i
$83$	4.29210	−	7.43413i	0.471119	−	0.816002i	−0.528335	−	0.849036i	$-0.677184\pi$
$83$	4.29210	−	7.43413i	0.471119	−	0.816002i	0.999454	+	0.0330340i	$0.0105170\pi$
$84$	−1.86336	+	4.18663i	−0.203309	+	0.456799i
$85$	−0.136107	−	0.235743i	−0.0147628	−	0.0255700i
$86$	−1.47194	−	0.849825i	−0.158723	−	0.0916389i
$87$	0.857885	−	4.69876i	0.0919750	−	0.503760i
$88$	−0.220875	−	0.382566i	−0.0235453	−	0.0407817i
$89$	6.35119	+	11.0006i	0.673225	+	1.16606i	0.976984	+	0.213311i	$0.0684247\pi$
$89$	6.35119	+	11.0006i	0.673225	+	1.16606i	−0.303760	+	0.952749i	$0.598242\pi$
$90$	−2.96052	+	0.485129i	−0.312066	+	0.0511371i
$91$	9.42867	+	2.28898i	0.988393	+	0.239950i
$92$	2.24789	+	1.29782i	0.234359	+	0.135307i
$93$	−14.2713	+	5.09667i	−1.47986	+	0.528500i
$94$			7.89512i			0.814320i
$95$		−	3.75929i		−	0.385695i
$96$	1.63115	−	0.582530i	0.166479	−	0.0594542i
$97$	12.9284	+	7.46424i	1.31268	+	0.757879i	0.982540	−	0.186052i	$-0.0595693\pi$
$97$	12.9284	+	7.46424i	1.31268	+	0.757879i	0.330144	+	0.943930i	$0.392903\pi$
$98$	6.99218	−	0.330818i	0.706317	−	0.0334176i
$99$	0.468309	−	1.23975i	0.0470669	−	0.124599i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	2.28878	+	3.96428i	0.227742	+	0.394460i	0.957138	−	0.289631i	$-0.0935325\pi$
$101$	2.28878	+	3.96428i	0.227742	+	0.394460i	−0.729397	+	0.684091i	$0.760199\pi$
$102$	−0.0846828	+	0.463820i	−0.00838485	+	0.0459250i
$103$	−3.98557	−	2.30107i	−0.392710	−	0.226731i	0.290624	−	0.956837i	$-0.406137\pi$
$103$	−3.98557	−	2.30107i	−0.392710	−	0.226731i	−0.683334	+	0.730106i	$0.739471\pi$
$104$	−1.83361	−	3.17590i	−0.179800	−	0.311423i
$105$	2.69405	+	3.70703i	0.262913	+	0.361769i
$106$	−0.0474920	+	0.0822585i	−0.00461283	+	0.00798965i
$107$	14.0223	−	8.09579i	1.35559	−	0.782650i	0.366563	−	0.930393i	$-0.380534\pi$
$107$	14.0223	−	8.09579i	1.35559	−	0.782650i	0.989026	+	0.147743i	$0.0472010\pi$
$108$	4.45207	+	2.67939i	0.428400	+	0.257824i
$109$	−1.37107	+	2.37476i	−0.131325	+	0.227461i	−0.924187	−	0.381939i	$-0.875256\pi$
$109$	−1.37107	+	2.37476i	−0.131325	+	0.227461i	0.792863	+	0.609400i	$0.208590\pi$
$110$	−0.441750			−0.0421192
$111$	−0.133894	+	0.157620i	−0.0127086	+	0.0149606i
$112$	−1.91453	−	1.82609i	−0.180906	−	0.172549i
$113$	−2.85536	+	1.64854i	−0.268610	+	0.155082i	−0.628256	−	0.778007i	$-0.716231\pi$
$113$	−2.85536	+	1.64854i	−0.268610	+	0.155082i	0.359646	+	0.933089i	$0.382898\pi$
$114$	−4.21550	+	4.96250i	−0.394818	+	0.464781i
$115$	2.24789	−	1.29782i	0.209617	−	0.121022i
$116$	2.38822	+	1.37884i	0.221740	+	0.128022i
$117$	3.88770	−	10.2918i	0.359418	−	0.951481i
$118$		−	3.21065i		−	0.295564i
$119$	0.691067	−	0.202795i	0.0633500	−	0.0185902i
$120$	0.311090	−	1.70388i	0.0283985	−	0.155543i
$121$	−5.40243	+	9.35728i	−0.491130	+	0.850662i
$122$	13.0013			1.17708
$123$	8.82359	−	10.3872i	0.795596	−	0.936579i
$124$		−	8.74919i		−	0.785700i
$125$	1.00000			0.0894427
$126$	0.600577	−	7.91450i	0.0535036	−	0.705080i
$127$	−21.1104			−1.87325			−0.936623	−	0.350339i	$-0.886066\pi$
$127$	−21.1104			−1.87325			−0.936623	+	0.350339i	$0.886066\pi$
$128$			1.00000i			0.0883883i
$129$	2.89601	+	0.528744i	0.254979	+	0.0465533i
$130$	−3.66721			−0.321636
$131$	2.54266	−	4.40402i	0.222153	−	0.384781i	−0.733308	−	0.679896i	$-0.762025\pi$
$131$	2.54266	−	4.40402i	0.222153	−	0.384781i	0.955462	+	0.295115i	$0.0953581\pi$
$132$	0.583137	+	0.495358i	0.0507556	+	0.0431154i
$133$	9.66541	+	2.34645i	0.838097	+	0.203463i
$134$			0.537467i			0.0464301i
$135$	4.54645	−	2.51591i	0.391296	−	0.216535i
$136$	−0.235743	−	0.136107i	−0.0202148	−	0.0116710i
$137$	−11.8142	+	6.82095i	−1.00936	+	0.582753i	−0.911003	−	0.412399i	$-0.864691\pi$
$137$	−11.8142	+	6.82095i	−1.00936	+	0.582753i	−0.0983540	+	0.995151i	$0.531358\pi$
$138$	−4.42267	−	0.807478i	−0.376483	−	0.0687371i
$139$	8.22684	−	4.74977i	0.697791	−	0.402870i	−0.108733	−	0.994071i	$-0.534679\pi$
$139$	8.22684	−	4.74977i	0.697791	−	0.402870i	0.806524	+	0.591201i	$0.201346\pi$
$140$	−2.53870	+	0.744985i	−0.214559	+	0.0629627i
$141$	−4.59915	−	12.8782i	−0.387318	−	1.08454i
$142$	−3.75218			−0.314876
$143$	0.809995	−	1.40295i	0.0677352	−	0.117321i
$144$	−2.32132	+	1.90039i	−0.193443	+	0.158366i
$145$	2.38822	−	1.37884i	0.198331	−	0.114506i
$146$	5.56698	−	9.64229i	0.460726	−	0.798001i
$147$	−11.2126	+	4.61277i	−0.924799	+	0.380455i
$148$	−0.0597017	−	0.103406i	−0.00490745	−	0.00849995i
$149$	12.4227	+	7.17226i	1.01771	+	0.587574i	0.913439	−	0.406975i	$-0.133416\pi$
$149$	12.4227	+	7.17226i	1.01771	+	0.587574i	0.104269	+	0.994549i	$0.466750\pi$
$150$	−1.32006	−	1.12135i	−0.107783	−	0.0915582i
$151$	−0.339894	−	0.588715i	−0.0276602	−	0.0479089i	0.851864	−	0.523763i	$-0.175472\pi$
$151$	−0.339894	−	0.588715i	−0.0276602	−	0.0479089i	−0.879524	+	0.475854i	$0.842139\pi$
$152$	−1.87965	−	3.25564i	−0.152459	−	0.264068i
$153$	−0.132058	−	0.805891i	−0.0106763	−	0.0651524i
$154$	0.275729	−	1.13577i	0.0222189	−	0.0915229i
$155$	−7.57702	−	4.37459i	−0.608601	−	0.351376i
$156$	4.84095	+	4.11225i	0.387586	+	0.329243i
$157$		−	23.8829i		−	1.90606i	−0.302875	−	0.953030i	$-0.597946\pi$
$157$		−	23.8829i		−	1.90606i	0.302875	−	0.953030i	$-0.402054\pi$
$158$		−	3.02791i		−	0.240887i
$159$	0.0295486	−	0.161842i	0.00234335	−	0.0128349i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	1.93371	+	6.58955i	0.152398	+	0.519329i
$162$	−8.82282	−	1.77702i	−0.693186	−	0.139616i
$163$	−7.98983	−	13.8388i	−0.625812	−	1.08394i	−0.988383	−	0.151982i	$-0.951434\pi$
$163$	−7.98983	−	13.8388i	−0.625812	−	1.08394i	0.362571	−	0.931956i	$-0.381899\pi$
$164$	3.93435	+	6.81449i	0.307221	+	0.532122i
$165$	0.720561	−	0.257333i	0.0560956	−	0.0200333i
$166$	−7.43413	−	4.29210i	−0.577000	−	0.333131i
$167$	−2.36183	−	4.09080i	−0.182764	−	0.316556i	0.760057	−	0.649856i	$-0.225171\pi$
$167$	−2.36183	−	4.09080i	−0.182764	−	0.316556i	−0.942821	+	0.333300i	$0.891838\pi$
$168$	4.18663	+	1.86336i	0.323006	+	0.143761i
$169$	0.224227	−	0.388373i	0.0172483	−	0.0298749i
$170$	−0.235743	+	0.136107i	−0.0180807	+	0.0104389i
$171$	3.98532	−	10.5503i	0.304765	−	0.806798i
$172$	−0.849825	+	1.47194i	−0.0647985	+	0.112234i
$173$	−20.2799			−1.54185			−0.770925	−	0.636926i	$-0.780206\pi$
$173$	−20.2799			−1.54185			−0.770925	+	0.636926i	$0.780206\pi$
$174$	−4.69876	−	0.857885i	−0.356212	−	0.0650361i
$175$	−0.624174	+	2.57107i	−0.0471831	+	0.194355i
$176$	−0.382566	+	0.220875i	−0.0288370	+	0.0166491i
$177$	1.87030	+	5.23705i	0.140580	+	0.393641i
$178$	11.0006	−	6.35119i	0.824529	−	0.476042i
$179$	13.2165	+	7.63053i	0.987846	+	0.570333i	0.904630	−	0.426199i	$-0.140148\pi$
$179$	13.2165	+	7.63053i	0.987846	+	0.570333i	0.0832159	+	0.996532i	$0.473481\pi$
$180$	0.485129	+	2.96052i	0.0361594	+	0.220664i
$181$			24.7207i			1.83748i	0.394866	+	0.918739i	$0.370791\pi$
$181$			24.7207i			1.83748i	−0.394866	+	0.918739i	$0.629209\pi$
$182$	2.28898	−	9.42867i	0.169671	−	0.698899i
$183$	−21.2071	+	7.57365i	−1.56767	+	0.559860i
$184$	1.29782	−	2.24789i	0.0956765	−	0.165717i
$185$	−0.119403			−0.00877871
$186$	5.09667	+	14.2713i	0.373706	+	1.04642i
$187$		−	0.120250i		−	0.00879355i
$188$	7.89512			0.575811
$189$	3.63080	+	13.2596i	0.264102	+	0.964495i
$190$	−3.75929			−0.272728
$191$		−	5.50470i		−	0.398306i	−0.979968	−	0.199153i	$-0.936181\pi$
$191$		−	5.50470i		−	0.398306i	0.979968	−	0.199153i	$-0.0638191\pi$
$192$	−0.582530	−	1.63115i	−0.0420405	−	0.117718i
$193$	−15.0469			−1.08310			−0.541549	−	0.840669i	$-0.682162\pi$
$193$	−15.0469			−1.08310			−0.541549	+	0.840669i	$0.682162\pi$
$194$	7.46424	−	12.9284i	0.535901	−	0.928208i
$195$	5.98178	−	2.13626i	0.428364	−	0.152981i
$196$	−0.330818	−	6.99218i	−0.0236298	−	0.499441i
$197$		−	19.6584i		−	1.40061i	−0.713846	−	0.700303i	$-0.753048\pi$
$197$		−	19.6584i		−	1.40061i	0.713846	−	0.700303i	$-0.246952\pi$
$198$	−1.23975	−	0.468309i	−0.0881050	−	0.0332813i
$199$	−9.23999	−	5.33471i	−0.655005	−	0.378168i	0.135366	−	0.990796i	$-0.456779\pi$
$199$	−9.23999	−	5.33471i	−0.655005	−	0.378168i	−0.790371	+	0.612628i	$0.790112\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−0.313091	−	0.876690i	−0.0220837	−	0.0618370i
$202$	3.96428	−	2.28878i	0.278926	−	0.161038i
$203$	2.05443	+	7.00091i	0.144192	+	0.491367i
$204$	0.463820	+	0.0846828i	0.0324739	+	0.00592898i
$205$	7.86869			0.549573
$206$	−2.30107	+	3.98557i	−0.160323	+	0.277688i
$207$	7.68443	−	1.25922i	0.534105	−	0.0875218i
$208$	−3.17590	+	1.83361i	−0.220209	+	0.127138i
$209$	0.830333	−	1.43818i	0.0574354	−	0.0994810i
$210$	3.70703	−	2.69405i	0.255809	−	0.185907i
$211$	−0.581500	−	1.00719i	−0.0400321	−	0.0693376i	0.845315	−	0.534268i	$-0.179413\pi$
$211$	−0.581500	−	1.00719i	−0.0400321	−	0.0693376i	−0.885347	+	0.464930i	$0.846079\pi$
$212$	0.0822585	+	0.0474920i	0.00564954	+	0.00326176i
$213$	6.12039	−	2.18576i	0.419362	−	0.149766i
$214$	−8.09579	−	14.0223i	−0.553417	−	0.958546i
$215$	0.849825	+	1.47194i	0.0579575	+	0.100385i
$216$	2.67939	−	4.45207i	0.182309	−	0.302925i
$217$	15.9768	−	16.7505i	1.08457	−	1.13710i
$218$	2.37476	+	1.37107i	0.160839	+	0.0928605i
$219$	−3.46366	+	18.9710i	−0.234053	+	1.28194i
$220$			0.441750i			0.0297828i
$221$		−	0.998264i		−	0.0671505i
$222$	0.157620	+	0.133894i	0.0105788	+	0.00898635i
$223$	2.45476	+	1.41726i	0.164383	+	0.0949066i	0.579935	−	0.814663i	$-0.303078\pi$
$223$	2.45476	+	1.41726i	0.164383	+	0.0949066i	−0.415552	+	0.909570i	$0.636411\pi$
$224$	−1.82609	+	1.91453i	−0.122011	+	0.127920i
$225$	2.80645	+	1.06012i	0.187096	+	0.0706749i
$226$	1.64854	+	2.85536i	0.109660	+	0.189936i
$227$	5.62480	+	9.74244i	0.373331	+	0.646628i	0.990076	−	0.140535i	$-0.0448822\pi$
$227$	5.62480	+	9.74244i	0.373331	+	0.646628i	−0.616745	+	0.787163i	$0.711549\pi$
$228$	4.96250	+	4.21550i	0.328650	+	0.279178i
$229$	14.0269	+	8.09843i	0.926924	+	0.535160i	0.885837	−	0.463996i	$-0.153585\pi$
$229$	14.0269	+	8.09843i	0.926924	+	0.535160i	0.0410863	+	0.999156i	$0.486918\pi$
$230$	−1.29782	−	2.24789i	−0.0855757	−	0.148221i
$231$	0.211865	+	2.01323i	0.0139397	+	0.132461i
$232$	1.37884	−	2.38822i	0.0905251	−	0.156794i
$233$	−3.21321	+	1.85515i	−0.210504	+	0.121535i	−0.601546	−	0.798838i	$-0.705448\pi$
$233$	−3.21321	+	1.85515i	−0.210504	+	0.121535i	0.391042	+	0.920373i	$0.372115\pi$
$234$	−10.2918	−	3.88770i	−0.672798	−	0.254147i
$235$	3.94756	−	6.83738i	0.257511	−	0.446021i
$236$	−3.21065			−0.208995
$237$	1.76385	+	4.93898i	0.114574	+	0.320821i
$238$	−0.202795	−	0.691067i	−0.0131452	−	0.0447952i
$239$	7.04916	−	4.06984i	0.455972	−	0.263256i	−0.254377	−	0.967105i	$-0.581870\pi$
$239$	7.04916	−	4.06984i	0.455972	−	0.263256i	0.710349	+	0.703849i	$0.248537\pi$
$240$	−1.70388	−	0.311090i	−0.109985	−	0.0200808i
$241$	−24.6585	+	14.2366i	−1.58839	+	0.917058i	−0.594819	+	0.803860i	$0.702776\pi$
$241$	−24.6585	+	14.2366i	−1.58839	+	0.917058i	−0.993572	+	0.113198i	$0.963891\pi$
$242$	9.35728	+	5.40243i	0.601509	+	0.347281i
$243$	15.4265	−	2.24096i	0.989613	−	0.143758i
$244$		−	13.0013i		−	0.832323i
$245$	−6.22081	−	3.20959i	−0.397433	−	0.205053i
$246$	−10.3872	−	8.82359i	−0.662261	−	0.562572i
$247$	6.89307	−	11.9391i	0.438595	−	0.759669i
$248$	−8.74919			−0.555574
$249$	14.6265	+	2.67046i	0.926915	+	0.169233i
$250$		−	1.00000i		−	0.0632456i
$251$	−4.61055			−0.291015			−0.145508	−	0.989357i	$-0.546482\pi$
$251$	−4.61055			−0.291015			−0.145508	+	0.989357i	$0.546482\pi$
$252$	−7.91450	−	0.600577i	−0.498567	−	0.0378328i
$253$	1.14662			0.0720876
$254$			21.1104i			1.32458i
$255$	0.305247	−	0.359338i	0.0191153	−	0.0225026i
$256$	1.00000			0.0625000
$257$	13.6473	−	23.6379i	0.851297	−	1.47449i	−0.0287418	−	0.999587i	$-0.509150\pi$
$257$	13.6473	−	23.6379i	0.851297	−	1.47449i	0.880039	−	0.474902i	$-0.157517\pi$
$258$	0.528744	−	2.89601i	0.0329182	−	0.180297i
$259$	0.0745285	−	0.306995i	0.00463098	−	0.0190757i
$260$			3.66721i			0.227431i
$261$	8.16414	−	1.33783i	0.505347	−	0.0828094i
$262$	−4.40402	−	2.54266i	−0.272081	−	0.157086i
$263$	−25.9006	+	14.9537i	−1.59710	+	0.922086i	−0.605057	+	0.796182i	$0.706850\pi$
$263$	−25.9006	+	14.9537i	−1.59710	+	0.922086i	−0.992042	+	0.125904i	$0.959817\pi$
$264$	0.495358	−	0.583137i	0.0304872	−	0.0358896i
$265$	0.0822585	−	0.0474920i	0.00505310	−	0.00291741i
$266$	2.34645	−	9.66541i	0.143870	−	0.592624i
$267$	−14.2439	+	16.7679i	−0.871711	+	1.02618i
$268$	0.537467			0.0328310
$269$	−6.84004	+	11.8473i	−0.417044	+	0.722342i	−0.995641	−	0.0932721i	$-0.970267\pi$
$269$	−6.84004	+	11.8473i	−0.417044	+	0.722342i	0.578596	+	0.815614i	$0.303601\pi$
$270$	−2.51591	−	4.54645i	−0.153113	−	0.276688i
$271$	−2.74454	+	1.58456i	−0.166719	+	0.0962551i	−0.581038	−	0.813877i	$-0.697353\pi$
$271$	−2.74454	+	1.58456i	−0.166719	+	0.0962551i	0.414319	+	0.910132i	$0.364020\pi$
$272$	−0.136107	+	0.235743i	−0.00825267	+	0.0142940i
$273$	1.75881	+	16.7130i	0.106448	+	1.01152i
$274$	6.82095	+	11.8142i	0.412068	+	0.713724i
$275$	0.382566	+	0.220875i	0.0230696	+	0.0133193i
$276$	−0.807478	+	4.42267i	−0.0486045	+	0.266213i
$277$	−0.758800	−	1.31428i	−0.0455919	−	0.0789674i	0.842329	−	0.538964i	$-0.181184\pi$
$277$	−0.758800	−	1.31428i	−0.0455919	−	0.0789674i	−0.887921	+	0.459996i	$0.847851\pi$
$278$	−4.74977	−	8.22684i	−0.284872	−	0.493413i
$279$	−16.6269	−	20.3096i	−0.995425	−	1.21591i
$280$	0.744985	+	2.53870i	0.0445214	+	0.151716i
$281$	3.08954	+	1.78375i	0.184307	+	0.106409i	0.589315	−	0.807904i	$-0.299398\pi$
$281$	3.08954	+	1.78375i	0.184307	+	0.106409i	−0.405008	+	0.914313i	$0.632731\pi$
$282$	−12.8782	+	4.59915i	−0.766883	+	0.273875i
$283$			13.1970i			0.784482i	0.919863	+	0.392241i	$0.128300\pi$
$283$			13.1970i			0.784482i	−0.919863	+	0.392241i	$0.871700\pi$
$284$			3.75218i			0.222651i
$285$	6.13198	−	2.18990i	0.363227	−	0.129719i
$286$	−1.40295	−	0.809995i	−0.0829583	−	0.0478960i
$287$	−4.91143	+	20.2310i	−0.289913	+	1.19420i
$288$	1.90039	+	2.32132i	0.111982	+	0.136785i
$289$	8.46295	+	14.6583i	0.497821	+	0.862251i
$290$	−1.37884	−	2.38822i	−0.0809681	−	0.140241i
$291$	−4.64410	+	25.4364i	−0.272242	+	1.49111i
$292$	−9.64229	−	5.56698i	−0.564272	−	0.325783i
$293$	−11.0248	−	19.0955i	−0.644074	−	1.11557i	−0.984515	−	0.175303i	$-0.943910\pi$
$293$	−11.0248	−	19.0955i	−0.644074	−	1.11557i	0.340440	−	0.940266i	$-0.389424\pi$
$294$	4.61277	+	11.2126i	0.269022	+	0.653932i
$295$	−1.60532	+	2.78050i	−0.0934655	+	0.161887i
$296$	−0.103406	+	0.0597017i	−0.00601037	+	0.00347009i
$297$	2.29502	+	0.0416940i	0.133171	+	0.00241933i
$298$	7.17226	−	12.4227i	0.415478	−	0.719629i
$299$	9.51876			0.550484
$300$	−1.12135	+	1.32006i	−0.0647414	+	0.0762138i
$301$	−4.31490	+	1.26621i	−0.248707	+	0.0729833i
$302$	−0.588715	+	0.339894i	−0.0338767	+	0.0195587i
$303$	−5.13306	+	6.04265i	−0.294886	+	0.347141i
$304$	−3.25564	+	1.87965i	−0.186724	+	0.107805i
$305$	−11.2595	−	6.50065i	−0.644715	−	0.372226i
$306$	−0.805891	+	0.132058i	−0.0460697	+	0.00754928i
$307$		−	29.2097i		−	1.66709i	−0.552453	−	0.833544i	$-0.686308\pi$
$307$		−	29.2097i		−	1.66709i	0.552453	−	0.833544i	$-0.313692\pi$
$308$	−1.13577	−	0.275729i	−0.0647165	−	0.0157111i
$309$	1.43168	−	7.84152i	0.0814455	−	0.446088i
$310$	−4.37459	+	7.57702i	−0.248460	+	0.430346i
$311$	−24.7927			−1.40587			−0.702933	−	0.711256i	$-0.748127\pi$
$311$	−24.7927			−1.40587			−0.702933	+	0.711256i	$0.748127\pi$
$312$	4.11225	−	4.84095i	0.232810	−	0.274065i
$313$			33.8917i			1.91567i	0.287319	+	0.957835i	$0.407236\pi$
$313$			33.8917i			1.91567i	−0.287319	+	0.957835i	$0.592764\pi$
$314$	−23.8829			−1.34779
$315$	−4.47736	+	6.55387i	−0.252271	+	0.369269i
$316$	−3.02791			−0.170333
$317$			34.1775i			1.91960i	0.280687	+	0.959799i	$0.409438\pi$
$317$			34.1775i			1.91960i	−0.280687	+	0.959799i	$0.590562\pi$
$318$	−0.161842	−	0.0295486i	−0.00907563	−	0.00165700i
$319$	1.21820			0.0682062
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	21.3739	+	18.1565i	1.19297	+	1.01340i
$322$	6.58955	−	1.93371i	0.367221	−	0.107762i
$323$		−	1.02333i		−	0.0569395i
$324$	−1.77702	+	8.82282i	−0.0987236	+	0.490157i
$325$	3.17590	+	1.83361i	0.176167	+	0.101710i
$326$	−13.8388	+	7.98983i	−0.766460	+	0.442516i
$327$	−4.67229	−	0.853053i	−0.258378	−	0.0471739i
$328$	6.81449	−	3.93435i	0.376267	−	0.217238i
$329$	15.1154	+	14.4172i	0.833340	+	0.794845i
$330$	−0.257333	−	0.720561i	−0.0141657	−	0.0396656i
$331$	−18.1882			−0.999712			−0.499856	−	0.866108i	$-0.666614\pi$
$331$	−18.1882			−0.999712			−0.499856	+	0.866108i	$0.666614\pi$
$332$	−4.29210	+	7.43413i	−0.235559	+	0.408001i
$333$	−0.335099	−	0.126582i	−0.0183633	−	0.00693667i
$334$	−4.09080	+	2.36183i	−0.223839	+	0.129233i
$335$	0.268733	−	0.465460i	0.0146825	−	0.0254308i
$336$	1.86336	−	4.18663i	0.101654	−	0.228400i
$337$	1.19477	+	2.06941i	0.0650834	+	0.112728i	0.896731	−	0.442576i	$-0.145935\pi$
$337$	1.19477	+	2.06941i	0.0650834	+	0.112728i	−0.831648	+	0.555304i	$0.812602\pi$
$338$	−0.388373	−	0.224227i	−0.0211247	−	0.0121964i
$339$	−4.35236	−	3.69721i	−0.236388	−	0.200805i
$340$	0.136107	+	0.235743i	0.00738141	+	0.0127850i
$341$	−1.93248	−	3.34715i	−0.104649	−	0.181258i
$342$	−10.5503	−	3.98532i	−0.570492	−	0.215501i
$343$	12.1350	−	13.9908i	0.655226	−	0.755433i
$344$	1.47194	+	0.849825i	0.0793616	+	0.0458195i
$345$	3.42641	+	2.91063i	0.184471	+	0.156703i
$346$			20.2799i			1.09025i
$347$			24.5163i			1.31610i	0.752973	+	0.658052i	$0.228619\pi$
$347$			24.5163i			1.31610i	−0.752973	+	0.658052i	$0.771381\pi$
$348$	−0.857885	+	4.69876i	−0.0459875	+	0.251880i
$349$	17.2041	+	9.93277i	0.920912	+	0.531689i	0.883926	−	0.467627i	$-0.154891\pi$
$349$	17.2041	+	9.93277i	0.920912	+	0.531689i	0.0369861	+	0.999316i	$0.488224\pi$
$350$	2.57107	+	0.624174i	0.137430	+	0.0333635i
$351$	19.0523	+	0.346125i	1.01693	+	0.0184748i
$352$	0.220875	+	0.382566i	0.0117727	+	0.0203909i
$353$	16.0741	+	27.8411i	0.855535	+	1.48183i	0.876147	+	0.482043i	$0.160105\pi$
$353$	16.0741	+	27.8411i	0.855535	+	1.48183i	−0.0206119	+	0.999788i	$0.506561\pi$
$354$	5.23705	−	1.87030i	0.278346	−	0.0994053i
$355$	3.24949	+	1.87609i	0.172465	+	0.0995726i
$356$	−6.35119	−	11.0006i	−0.336612	−	0.583030i
$357$	0.733357	+	1.00910i	0.0388133	+	0.0534074i
$358$	7.63053	−	13.2165i	0.403286	−	0.698512i
$359$	24.4812	−	14.1342i	1.29207	−	0.745976i	0.313048	−	0.949737i	$-0.398650\pi$
$359$	24.4812	−	14.1342i	1.29207	−	0.745976i	0.979021	+	0.203761i	$0.0653166\pi$
$360$	2.96052	−	0.485129i	0.156033	−	0.0255685i
$361$	−2.43386	+	4.21556i	−0.128098	+	0.221872i
$362$	24.7207			1.29929
$363$	−18.4102	−	3.36129i	−0.966286	−	0.176422i
$364$	−9.42867	−	2.28898i	−0.494196	−	0.119975i
$365$	−9.64229	+	5.56698i	−0.504700	+	0.291389i
$366$	7.57365	+	21.2071i	0.395881	+	1.10851i
$367$	−29.1506	+	16.8301i	−1.52165	+	0.878524i	−0.521974	+	0.852961i	$0.674804\pi$
$367$	−29.1506	+	16.8301i	−1.52165	+	0.878524i	−0.999673	+	0.0255626i	$0.991862\pi$
$368$	−2.24789	−	1.29782i	−0.117179	−	0.0676535i
$369$	22.0831	+	8.34179i	1.14960	+	0.434256i
$370$			0.119403i			0.00620749i
$371$	0.0707616	+	0.241136i	0.00367376	+	0.0125191i
$372$	14.2713	−	5.09667i	0.739930	−	0.264250i
$373$	5.98701	−	10.3698i	0.309996	−	0.536928i	−0.668365	−	0.743833i	$-0.733006\pi$
$373$	5.98701	−	10.3698i	0.309996	−	0.536928i	0.978361	+	0.206905i	$0.0663391\pi$
$374$	−0.120250			−0.00621798
$375$	0.582530	+	1.63115i	0.0300817	+	0.0842324i
$376$		−	7.89512i		−	0.407160i
$377$	10.1130			0.520845
$378$	13.2596	−	3.63080i	0.682001	−	0.186748i
$379$	−10.9629			−0.563126			−0.281563	−	0.959543i	$-0.590853\pi$
$379$	−10.9629			−0.563126			−0.281563	+	0.959543i	$0.590853\pi$
$380$			3.75929i			0.192848i
$381$	−12.2975	−	34.4343i	−0.630018	−	1.76412i
$382$	−5.50470			−0.281645
$383$	−10.0626	+	17.4289i	−0.514174	+	0.890575i	0.485691	+	0.874131i	$0.338568\pi$
$383$	−10.0626	+	17.4289i	−0.514174	+	0.890575i	−0.999865	+	0.0164445i	$0.994765\pi$
$384$	−1.63115	+	0.582530i	−0.0832394	+	0.0297271i
$385$	−0.806673	+	0.845741i	−0.0411119	+	0.0431030i
$386$			15.0469i			0.765866i
$387$	0.824549	+	5.03184i	0.0419142	+	0.255783i
$388$	−12.9284	−	7.46424i	−0.656342	−	0.378939i
$389$	−23.6779	+	13.6704i	−1.20052	+	0.693119i	−0.960670	−	0.277692i	$-0.910431\pi$
$389$	−23.6779	+	13.6704i	−1.20052	+	0.693119i	−0.239847	+	0.970811i	$0.577097\pi$
$390$	−2.13626	−	5.98178i	−0.108174	−	0.302899i
$391$	0.611905	−	0.353283i	0.0309454	−	0.0178663i
$392$	−6.99218	+	0.330818i	−0.353158	+	0.0167088i
$393$	8.66480	+	1.58199i	0.437082	+	0.0798011i
$394$	−19.6584			−0.990378
$395$	−1.51395	+	2.62224i	−0.0761753	+	0.131939i
$396$	−0.468309	+	1.23975i	−0.0235334	+	0.0622996i
$397$	13.5525	−	7.82456i	0.680182	−	0.392703i	−0.119742	−	0.992805i	$-0.538207\pi$
$397$	13.5525	−	7.82456i	0.680182	−	0.392703i	0.799924	+	0.600102i	$0.204873\pi$
$398$	−5.33471	+	9.23999i	−0.267405	+	0.463159i
$399$	1.80297	+	17.1326i	0.0902614	+	0.857705i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−33.9071	−	19.5763i	−1.69324	−	0.977592i	−0.951874	−	0.306490i	$-0.900845\pi$
$401$	−33.9071	−	19.5763i	−1.69324	−	0.977592i	−0.741365	−	0.671102i	$-0.765821\pi$
$402$	−0.876690	+	0.313091i	−0.0437253	+	0.0156155i
$403$	−16.0426	−	27.7865i	−0.799137	−	1.38415i
$404$	−2.28878	−	3.96428i	−0.113871	−	0.197230i
$405$	6.75228	+	5.95036i	0.335523	+	0.295676i
$406$	7.00091	−	2.05443i	0.347449	−	0.101959i
$407$	−0.0456797	−	0.0263732i	−0.00226426	−	0.00130727i
$408$	0.0846828	−	0.463820i	0.00419242	−	0.0229625i
$409$		−	26.2289i		−	1.29694i	−0.761242	−	0.648468i	$-0.775410\pi$
$409$		−	26.2289i		−	1.29694i	0.761242	−	0.648468i	$-0.224590\pi$
$410$		−	7.86869i		−	0.388607i
$411$	−18.0082	−	15.2974i	−0.888277	−	0.754565i
$412$	3.98557	+	2.30107i	0.196355	+	0.113366i
$413$	−6.14687	−	5.86292i	−0.302467	−	0.288495i
$414$	−1.25922	−	7.68443i	−0.0618873	−	0.377669i
$415$	4.29210	+	7.43413i	0.210691	+	0.364927i
$416$	1.83361	+	3.17590i	0.0899000	+	0.155711i
$417$	12.5400	+	10.6523i	0.614085	+	0.521648i
$418$	−1.43818	−	0.830333i	−0.0703437	−	0.0406129i
$419$	−18.3795	−	31.8342i	−0.897897	−	1.55520i	−0.830177	−	0.557500i	$-0.811761\pi$
$419$	−18.3795	−	31.8342i	−0.897897	−	1.55520i	−0.0677203	−	0.997704i	$-0.521573\pi$
$420$	−2.69405	−	3.70703i	−0.131456	−	0.180885i
$421$	6.54747	−	11.3406i	0.319104	−	0.552705i	−0.661197	−	0.750212i	$-0.729951\pi$
$421$	6.54747	−	11.3406i	0.319104	−	0.552705i	0.980301	+	0.197507i	$0.0632847\pi$
$422$	−1.00719	+	0.581500i	−0.0490291	+	0.0283070i
$423$	18.3271	−	15.0038i	0.891093	−	0.729511i
$424$	0.0474920	−	0.0822585i	0.00230641	−	0.00399483i
$425$	0.272213			0.0132043
$426$	−2.18576	−	6.12039i	−0.105900	−	0.296534i
$427$	23.7415	−	24.8913i	1.14893	−	1.20458i
$428$	−14.0223	+	8.09579i	−0.677795	+	0.391325i
$429$	2.76028	+	0.503963i	0.133267	+	0.0243316i
$430$	1.47194	−	0.849825i	0.0709832	−	0.0409822i
$431$	−17.9103	−	10.3405i	−0.862710	−	0.498086i	0.00220853	−	0.999998i	$-0.499297\pi$
$431$	−17.9103	−	10.3405i	−0.862710	−	0.498086i	−0.864919	+	0.501911i	$0.832630\pi$
$432$	−4.45207	−	2.67939i	−0.214200	−	0.128912i
$433$			5.36529i			0.257839i	0.991655	+	0.128920i	$0.0411509\pi$
$433$			5.36529i			0.257839i	−0.991655	+	0.128920i	$0.958849\pi$
$434$	−16.7505	−	15.9768i	−0.804052	−	0.766909i
$435$	3.64030	+	3.09233i	0.174539	+	0.148266i
$436$	1.37107	−	2.37476i	0.0656623	−	0.113730i
$437$	9.75777			0.466777
$438$	18.9710	+	3.46366i	0.906468	+	0.165500i
$439$			10.4796i			0.500163i	0.968225	+	0.250082i	$0.0804575\pi$
$439$			10.4796i			0.500163i	−0.968225	+	0.250082i	$0.919543\pi$
$440$	0.441750			0.0210596
$441$	−14.0558	−	15.6024i	−0.669324	−	0.742970i
$442$	−0.998264			−0.0474826
$443$		−	7.77742i		−	0.369516i	−0.982784	−	0.184758i	$-0.940850\pi$
$443$		−	7.77742i		−	0.369516i	0.982784	−	0.184758i	$-0.0591502\pi$
$444$	0.133894	−	0.157620i	0.00635431	−	0.00748031i
$445$	−12.7024			−0.602151
$446$	1.41726	−	2.45476i	0.0671091	−	0.116236i
$447$	−4.46244	+	24.4414i	−0.211066	+	1.15604i
$448$	1.91453	+	1.82609i	0.0904528	+	0.0862745i
$449$			3.73404i			0.176220i	0.996111	+	0.0881102i	$0.0280828\pi$
$449$			3.73404i			0.176220i	−0.996111	+	0.0881102i	$0.971917\pi$
$450$	1.06012	−	2.80645i	0.0499747	−	0.132297i
$451$	3.01030	+	1.73800i	0.141749	+	0.0818390i
$452$	2.85536	−	1.64854i	0.134305	−	0.0775410i
$453$	0.762284	−	0.897364i	0.0358152	−	0.0421618i
$454$	9.74244	−	5.62480i	0.457235	−	0.263985i
$455$	−6.69665	+	7.02097i	−0.313944	+	0.329148i
$456$	4.21550	−	4.96250i	0.197409	−	0.232390i
$457$	2.90786			0.136024			0.0680121	−	0.997684i	$-0.478334\pi$
$457$	2.90786			0.136024			0.0680121	+	0.997684i	$0.478334\pi$
$458$	8.09843	−	14.0269i	0.378415	−	0.655434i
$459$	1.23760	−	0.684863i	0.0577664	−	0.0319667i
$460$	−2.24789	+	1.29782i	−0.104808	+	0.0605111i
$461$	4.88443	−	8.46009i	0.227491	−	0.394026i	−0.729573	−	0.683903i	$-0.760281\pi$
$461$	4.88443	−	8.46009i	0.227491	−	0.394026i	0.957064	+	0.289877i	$0.0936145\pi$
$462$	2.01323	−	0.211865i	0.0936641	−	0.00985684i
$463$	1.43617	+	2.48752i	0.0667446	+	0.115605i	0.897467	−	0.441083i	$-0.145405\pi$
$463$	1.43617	+	2.48752i	0.0667446	+	0.115605i	−0.830722	+	0.556688i	$0.812072\pi$
$464$	−2.38822	−	1.37884i	−0.110870	−	0.0640109i
$465$	2.72179	−	14.9076i	0.126220	−	0.691324i
$466$	1.85515	+	3.21321i	0.0859379	+	0.148849i
$467$	−1.92955	−	3.34208i	−0.0892890	−	0.154653i	0.817922	−	0.575329i	$-0.195126\pi$
$467$	−1.92955	−	3.34208i	−0.0892890	−	0.154653i	−0.907211	+	0.420676i	$0.861793\pi$
$468$	−3.88770	+	10.2918i	−0.179709	+	0.475740i
$469$	1.02899	+	0.981461i	0.0475145	+	0.0453196i
$470$	−6.83738	−	3.94756i	−0.315385	−	0.182087i
$471$	38.9566	−	13.9125i	1.79503	−	0.641054i
$472$			3.21065i			0.147782i
$473$			0.750819i			0.0345227i
$474$	4.93898	−	1.76385i	0.226855	−	0.0810162i
$475$	3.25564	+	1.87965i	0.149379	+	0.0862441i
$476$	−0.691067	+	0.202795i	−0.0316750	+	0.00929508i
$477$	0.281201	−	0.0460795i	0.0128753	−	0.00210983i
$478$	−4.06984	−	7.04916i	−0.186150	−	0.322421i
$479$	−8.16437	−	14.1411i	−0.373039	−	0.646123i	0.616992	−	0.786969i	$-0.288351\pi$
$479$	−8.16437	−	14.1411i	−0.373039	−	0.646123i	−0.990031	+	0.140846i	$0.955018\pi$
$480$	−0.311090	+	1.70388i	−0.0141993	+	0.0777713i
$481$	−0.379213	−	0.218939i	−0.0172906	−	0.00998276i
$482$	14.2366	+	24.6585i	0.648458	+	1.12316i
$483$	−9.62211	+	6.99279i	−0.437821	+	0.318183i
$484$	5.40243	−	9.35728i	0.245565	−	0.425331i
$485$	−12.9284	+	7.46424i	−0.587050	+	0.338934i
$486$	−2.24096	−	15.4265i	−0.101652	−	0.699762i
$487$	7.05835	−	12.2254i	0.319844	−	0.553987i	−0.660611	−	0.750728i	$-0.729703\pi$
$487$	7.05835	−	12.2254i	0.319844	−	0.553987i	0.980455	+	0.196742i	$0.0630360\pi$
$488$	−13.0013			−0.588541
$489$	17.9189	−	21.0942i	0.810319	−	0.953911i
$490$	−3.20959	+	6.22081i	−0.144995	+	0.281028i
$491$	−9.00388	+	5.19839i	−0.406339	+	0.234600i	−0.689216	−	0.724556i	$-0.742045\pi$
$491$	−9.00388	+	5.19839i	−0.406339	+	0.234600i	0.282876	+	0.959156i	$0.408711\pi$
$492$	−8.82359	+	10.3872i	−0.397798	+	0.468289i
$493$	0.650104	−	0.375337i	0.0292792	−	0.0169043i
$494$	−11.9391	−	6.89307i	−0.537167	−	0.310134i
$495$	0.839497	+	1.02544i	0.0377326	+	0.0460901i
$496$			8.74919i			0.392850i
$497$	−6.85181	+	7.18365i	−0.307346	+	0.322231i
$498$	2.67046	−	14.6265i	0.119666	−	0.655428i
$499$	7.93948	−	13.7516i	0.355420	−	0.615605i	−0.631770	−	0.775156i	$-0.717671\pi$
$499$	7.93948	−	13.7516i	0.355420	−	0.615605i	0.987190	+	0.159551i	$0.0510046\pi$
$500$	−1.00000			−0.0447214
$501$	5.29689	−	6.23552i	0.236648	−	0.278582i
$502$			4.61055i			0.205779i
$503$	0.0186342			0.000830858			0.000415429	−	1.00000i	$-0.499868\pi$
$503$	0.0186342			0.000830858			0.000415429		1.00000i	$0.499868\pi$
$504$	−0.600577	+	7.91450i	−0.0267518	+	0.352540i
$505$	−4.57755			−0.203698
$506$		−	1.14662i		−	0.0509736i
$507$	0.764116	+	0.139510i	0.0339356	+	0.00619585i
$508$	21.1104			0.936623
$509$	16.4809	−	28.5457i	0.730502	−	1.26527i	−0.226167	−	0.974088i	$-0.572620\pi$
$509$	16.4809	−	28.5457i	0.730502	−	1.26527i	0.956669	−	0.291178i	$-0.0940471\pi$
$510$	−0.359338	−	0.305247i	−0.0159118	−	0.0135166i
$511$	−8.29463	−	28.2658i	−0.366933	−	1.25040i
$512$		−	1.00000i		−	0.0441942i
$513$	19.5306	+	0.354816i	0.862299	+	0.0156655i
$514$	−23.6379	−	13.6473i	−1.04262	−	0.601958i
$515$	3.98557	−	2.30107i	0.175625	−	0.101397i
$516$	−2.89601	−	0.528744i	−0.127490	−	0.0232767i
$517$	3.02041	−	1.74383i	0.132837	−	0.0766937i
$518$	−0.306995	−	0.0745285i	−0.0134886	−	0.00327460i
$519$	−11.8136	−	33.0795i	−0.518561	−	1.45203i
$520$	3.66721			0.160818
$521$	−3.94706	+	6.83651i	−0.172924	+	0.299513i	−0.939441	−	0.342711i	$-0.888655\pi$
$521$	−3.94706	+	6.83651i	−0.172924	+	0.299513i	0.766517	+	0.642224i	$0.221988\pi$
$522$	−1.33783	−	8.16414i	−0.0585551	−	0.357334i
$523$	2.84277	−	1.64127i	0.124306	−	0.0717679i	−0.436558	−	0.899676i	$-0.643803\pi$
$523$	2.84277	−	1.64127i	0.124306	−	0.0717679i	0.560864	+	0.827908i	$0.310469\pi$
$524$	−2.54266	+	4.40402i	−0.111077	+	0.192390i
$525$	−4.55741	+	0.479603i	−0.198902	+	0.0209316i
$526$	14.9537	+	25.9006i	0.652013	+	1.12932i
$527$	−2.06256	−	1.19082i	−0.0898467	−	0.0518730i
$528$	−0.583137	−	0.495358i	−0.0253778	−	0.0215577i
$529$	−8.13133	−	14.0839i	−0.353536	−	0.612342i
$530$	−0.0474920	−	0.0822585i	−0.00206292	−	0.00357308i
$531$	−7.45293	+	6.10149i	−0.323430	+	0.264782i
$532$	−9.66541	−	2.34645i	−0.419049	−	0.101732i
$533$	24.9902	+	14.4281i	1.08244	+	0.624950i
$534$	16.7679	+	14.2439i	0.725619	+	0.616393i
$535$			16.1916i			0.700023i
$536$		−	0.537467i		−	0.0232150i
$537$	−4.74757	+	26.0031i	−0.204873	+	1.12212i
$538$	11.8473	+	6.84004i	0.510773	+	0.294895i
$539$	−1.67096	−	2.60190i	−0.0719732	−	0.112072i
$540$	−4.54645	+	2.51591i	−0.195648	+	0.108267i
$541$	7.89978	+	13.6828i	0.339638	+	0.588270i	0.984365	−	0.176143i	$-0.0563621\pi$
$541$	7.89978	+	13.6828i	0.339638	+	0.588270i	−0.644727	+	0.764413i	$0.723029\pi$
$542$	1.58456	+	2.74454i	0.0680626	+	0.117888i
$543$	−40.3233	+	14.4006i	−1.73044	+	0.617988i
$544$	0.235743	+	0.136107i	0.0101074	+	0.00583552i
$545$	−1.37107	−	2.37476i	−0.0587302	−	0.101724i
$546$	16.7130	−	1.75881i	0.715250	−	0.0752700i
$547$	−8.85022	+	15.3290i	−0.378408	+	0.655422i	−0.990831	−	0.135108i	$-0.956862\pi$
$547$	−8.85022	+	15.3290i	−0.378408	+	0.655422i	0.612423	+	0.790531i	$0.290195\pi$
$548$	11.8142	−	6.82095i	0.504679	−	0.291376i
$549$	−24.7076	−	30.1801i	−1.05449	−	1.28806i
$550$	0.220875	−	0.382566i	0.00941814	−	0.0163127i
$551$	10.3669			0.441645
$552$	4.42267	+	0.807478i	0.188241	+	0.0343685i
$553$	−5.79701	−	5.52922i	−0.246514	−	0.235126i
$554$	−1.31428	+	0.758800i	−0.0558384	+	0.0322383i
$555$	−0.0695561	−	0.194765i	−0.00295249	−	0.00826732i
$556$	−8.22684	+	4.74977i	−0.348896	+	0.201435i
$557$	−27.5064	−	15.8808i	−1.16548	−	0.672892i	−0.212871	−	0.977080i	$-0.568281\pi$
$557$	−27.5064	−	15.8808i	−1.16548	−	0.672892i	−0.952612	+	0.304188i	$0.901615\pi$
$558$	−20.3096	+	16.6269i	−0.859775	+	0.703872i
$559$			6.23298i			0.263627i
$560$	2.53870	−	0.744985i	0.107280	−	0.0314814i
$561$	0.196146	−	0.0700493i	0.00828130	−	0.00295748i
$562$	1.78375	−	3.08954i	0.0752429	−	0.130324i
$563$	42.6170			1.79609			0.898046	−	0.439902i	$-0.144987\pi$
$563$	42.6170			1.79609			0.898046	+	0.439902i	$0.144987\pi$
$564$	4.59915	+	12.8782i	0.193659	+	0.542268i
$565$		−	3.29709i		−	0.138710i
$566$	13.1970			0.554712
$567$	−19.5134	+	13.6465i	−0.819485	+	0.573100i
$568$	3.75218			0.157438
$569$		−	17.1292i		−	0.718092i	−0.933320	−	0.359046i	$-0.883102\pi$
$569$		−	17.1292i		−	0.718092i	0.933320	−	0.359046i	$-0.116898\pi$
$570$	−2.18990	−	6.13198i	−0.0917249	−	0.256840i
$571$	14.8144			0.619963			0.309981	−	0.950743i	$-0.399677\pi$
$571$	14.8144			0.619963			0.309981	+	0.950743i	$0.399677\pi$
$572$	−0.809995	+	1.40295i	−0.0338676	+	0.0586604i
$573$	8.97900	−	3.20665i	0.375103	−	0.133960i
$574$	20.2310	+	4.91143i	0.844424	+	0.204999i
$575$			2.59564i			0.108246i
$576$	2.32132	−	1.90039i	0.0967215	−	0.0791830i
$577$	29.2079	+	16.8632i	1.21594	+	0.702025i	0.964048	−	0.265730i	$-0.0856129\pi$
$577$	29.2079	+	16.8632i	1.21594	+	0.702025i	0.251895	+	0.967755i	$0.418946\pi$
$578$	14.6583	−	8.46295i	0.609703	−	0.352012i
$579$	−8.76526	−	24.5438i	−0.364272	−	1.02000i
$580$	−2.38822	+	1.37884i	−0.0991653	+	0.0572531i
$581$	−21.7927	+	6.39509i	−0.904113	+	0.265313i
$582$	25.4364	+	4.64410i	1.05437	+	0.192504i
$583$	0.0419591			0.00173777
$584$	−5.56698	+	9.64229i	−0.230363	+	0.399001i
$585$	6.96914	+	8.51276i	0.288139	+	0.351960i
$586$	−19.0955	+	11.0248i	−0.788826	+	0.455429i
$587$	−5.76762	+	9.98982i	−0.238055	+	0.412324i	−0.960156	−	0.279464i	$-0.909843\pi$
$587$	−5.76762	+	9.98982i	−0.238055	+	0.412324i	0.722101	+	0.691788i	$0.243177\pi$
$588$	11.2126	−	4.61277i	0.462400	−	0.190227i
$589$	−16.4454	−	28.4842i	−0.677620	−	1.17367i
$590$	2.78050	+	1.60532i	0.114471	+	0.0660901i
$591$	32.0659	−	11.4516i	1.31902	−	0.471057i
$592$	0.0597017	+	0.103406i	0.00245373	+	0.00424998i
$593$	11.7771	+	20.3985i	0.483627	+	0.837666i	0.999823	−	0.0188043i	$-0.00598596\pi$
$593$	11.7771	+	20.3985i	0.483627	+	0.837666i	−0.516197	+	0.856470i	$0.672653\pi$
$594$	0.0416940	−	2.29502i	0.00171072	−	0.0941658i
$595$	−0.169908	+	0.699879i	−0.00696557	+	0.0286922i
$596$	−12.4227	−	7.17226i	−0.508854	−	0.293787i
$597$	3.31915	−	18.1795i	0.135844	−	0.744036i
$598$		−	9.51876i		−	0.389251i
$599$			36.8548i			1.50585i	0.658108	+	0.752923i	$0.271357\pi$
$599$			36.8548i			1.50585i	−0.658108	+	0.752923i	$0.728643\pi$
$600$	1.32006	+	1.12135i	0.0538913	+	0.0457791i
$601$	3.58818	+	2.07164i	0.146365	+	0.0845039i	0.571394	−	0.820676i	$-0.306403\pi$
$601$	3.58818	+	2.07164i	0.146365	+	0.0845039i	−0.425029	+	0.905180i	$0.639736\pi$
$602$	1.26621	+	4.31490i	0.0516070	+	0.175862i
$603$	1.24763	−	1.02140i	0.0508075	−	0.0415945i
$604$	0.339894	+	0.588715i	0.0138301	+	0.0239545i
$605$	−5.40243	−	9.35728i	−0.219640	−	0.380428i
$606$	6.04265	+	5.13306i	0.245466	+	0.208516i
$607$	17.0808	+	9.86160i	0.693288	+	0.400270i	0.804843	−	0.593488i	$-0.202250\pi$
$607$	17.0808	+	9.86160i	0.693288	+	0.400270i	−0.111555	+	0.993758i	$0.535583\pi$
$608$	1.87965	+	3.25564i	0.0762297	+	0.132034i
$609$	−10.2228	+	7.42932i	−0.414248	+	0.301051i
$610$	−6.50065	+	11.2595i	−0.263204	+	0.455882i
$611$	25.0741	−	14.4766i	1.01439	−	0.585659i
$612$	0.132058	+	0.805891i	0.00533815	+	0.0325762i
$613$	3.80772	−	6.59516i	0.153792	−	0.266376i	−0.778826	−	0.627240i	$-0.784185\pi$
$613$	3.80772	−	6.59516i	0.153792	−	0.266376i	0.932619	+	0.360864i	$0.117518\pi$
$614$	−29.2097			−1.17881
$615$	4.58375	+	12.8350i	0.184835	+	0.517559i
$616$	−0.275729	+	1.13577i	−0.0111094	+	0.0457615i
$617$	32.0531	−	18.5058i	1.29041	−	0.745017i	0.311681	−	0.950187i	$-0.399108\pi$
$617$	32.0531	−	18.5058i	1.29041	−	0.745017i	0.978726	+	0.205170i	$0.0657747\pi$
$618$	−7.84152	−	1.43168i	−0.315432	−	0.0575906i
$619$	−18.1979	+	10.5065i	−0.731434	+	0.422294i	−0.818947	−	0.573870i	$-0.805442\pi$
$619$	−18.1979	+	10.5065i	−0.731434	+	0.422294i	0.0875124	+	0.996163i	$0.472108\pi$
$620$	7.57702	+	4.37459i	0.304300	+	0.175688i
$621$	6.53039	+	11.8009i	0.262056	+	0.473555i
$622$			24.7927i			0.994097i
$623$	7.92850	−	32.6587i	0.317649	−	1.30844i
$624$	−4.84095	−	4.11225i	−0.193793	−	0.164622i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	33.8917			1.35458
$627$	2.82958	+	0.516617i	0.113003	+	0.0206317i
$628$			23.8829i			0.953030i
$629$	−0.0325032			−0.00129599
$630$	6.55387	+	4.47736i	0.261112	+	0.178382i
$631$	24.9229			0.992166			0.496083	−	0.868275i	$-0.334771\pi$
$631$	24.9229			0.992166			0.496083	+	0.868275i	$0.334771\pi$
$632$			3.02791i			0.120444i
$633$	1.30413	−	1.53523i	0.0518347	−	0.0610200i
$634$	34.1775			1.35736
$635$	10.5552	−	18.2821i	0.418870	−	0.725505i
$636$	−0.0295486	+	0.161842i	−0.00117168	+	0.00641744i
$637$	−13.8715	−	21.5999i	−0.549611	−	0.855818i
$638$		−	1.21820i		−	0.0482291i
$639$	7.13062	+	8.71001i	0.282083	+	0.344563i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	−5.56315	+	3.21189i	−0.219731	+	0.126862i	−0.605826	−	0.795597i	$-0.707157\pi$
$641$	−5.56315	+	3.21189i	−0.219731	+	0.126862i	0.386095	+	0.922459i	$0.373824\pi$
$642$	18.1565	−	21.3739i	0.716580	−	0.843560i
$643$	−34.0574	+	19.6630i	−1.34309	+	0.775434i	−0.987260	−	0.159116i	$-0.949136\pi$
$643$	−34.0574	+	19.6630i	−1.34309	+	0.775434i	−0.355832	+	0.934550i	$0.615802\pi$
$644$	−1.93371	−	6.58955i	−0.0761989	−	0.259665i
$645$	−1.90591	+	2.24364i	−0.0750451	+	0.0883433i
$646$	−1.02333			−0.0402623
$647$	−13.4151	+	23.2356i	−0.527401	+	0.913486i	0.472089	+	0.881551i	$0.343500\pi$
$647$	−13.4151	+	23.2356i	−0.527401	+	0.913486i	−0.999490	+	0.0319349i	$0.989833\pi$
$648$	8.82282	+	1.77702i	0.346593	+	0.0698081i
$649$	−1.22829	+	0.709151i	−0.0482144	+	0.0278366i
$650$	1.83361	−	3.17590i	0.0719200	−	0.124569i
$651$	36.6296	+	16.3028i	1.43563	+	0.638959i
$652$	7.98983	+	13.8388i	0.312906	+	0.541969i
$653$	−34.8263	−	20.1070i	−1.36286	−	0.786846i	−0.372855	−	0.927890i	$-0.621621\pi$
$653$	−34.8263	−	20.1070i	−1.36286	−	0.786846i	−0.990003	+	0.141043i	$0.954954\pi$
$654$	−0.853053	+	4.67229i	−0.0333570	+	0.182701i
$655$	2.54266	+	4.40402i	0.0993500	+	0.172079i
$656$	−3.93435	−	6.81449i	−0.153610	−	0.266061i
$657$	−32.9622	+	5.40140i	−1.28598	+	0.210729i
$658$	14.4172	−	15.1154i	0.562040	−	0.589260i
$659$	18.2869	+	10.5580i	0.712357	+	0.411280i	0.811933	−	0.583750i	$-0.198415\pi$
$659$	18.2869	+	10.5580i	0.712357	+	0.411280i	−0.0995760	+	0.995030i	$0.531749\pi$
$660$	−0.720561	+	0.257333i	−0.0280478	+	0.0100167i
$661$			26.5110i			1.03116i	0.856842	+	0.515580i	$0.172423\pi$
$661$			26.5110i			1.03116i	−0.856842	+	0.515580i	$0.827577\pi$
$662$			18.1882i			0.706903i
$663$	1.62832	−	0.581519i	0.0632387	−	0.0225843i
$664$	7.43413	+	4.29210i	0.288500	+	0.166566i
$665$	−6.86479	+	7.19726i	−0.266205	+	0.279098i
$666$	−0.126582	+	0.335099i	−0.00490497	+	0.0129848i
$667$	3.57896	+	6.19895i	0.138578	+	0.240024i
$668$	2.36183	+	4.09080i	0.0913818	+	0.158278i
$669$	−0.881790	+	4.82969i	−0.0340920	+	0.186726i
$670$	−0.465460	−	0.268733i	−0.0179823	−	0.0103821i
$671$	−2.87166	−	4.97386i	−0.110859	−	0.192014i
$672$	−4.18663	−	1.86336i	−0.161503	−	0.0718805i
$673$	17.0764	−	29.5771i	0.658245	−	1.14011i	−0.322824	−	0.946459i	$-0.604632\pi$
$673$	17.0764	−	29.5771i	0.658245	−	1.14011i	0.981070	−	0.193655i	$-0.0620344\pi$
$674$	2.06941	−	1.19477i	0.0797105	−	0.0460209i
$675$	−0.0943837	+	5.19530i	−0.00363283	+	0.199967i
$676$	−0.224227	+	0.388373i	−0.00862413	+	0.0149374i
$677$	−7.46837			−0.287033			−0.143516	−	0.989648i	$-0.545841\pi$
$677$	−7.46837			−0.287033			−0.143516	+	0.989648i	$0.545841\pi$
$678$	−3.69721	+	4.35236i	−0.141990	+	0.167152i
$679$	−11.1215	−	37.8989i	−0.426804	−	1.45443i
$680$	0.235743	−	0.136107i	0.00904035	−	0.00521945i
$681$	−12.6148	+	14.8502i	−0.483400	+	0.569060i
$682$	−3.34715	+	1.93248i	−0.128169	+	0.0739983i
$683$	20.4287	+	11.7945i	0.781681	+	0.451304i	0.837026	−	0.547163i	$-0.184292\pi$
$683$	20.4287	+	11.7945i	0.781681	+	0.451304i	−0.0553445	+	0.998467i	$0.517626\pi$
$684$	−3.98532	+	10.5503i	−0.152382	+	0.403399i
$685$		−	13.6419i		−	0.521230i
$686$	−13.9908	−	12.1350i	−0.534172	−	0.463315i
$687$	−5.03869	+	27.5976i	−0.192238	+	1.05291i
$688$	0.849825	−	1.47194i	0.0323993	−	0.0561172i
$689$	0.348326			0.0132702
$690$	2.91063	−	3.42641i	0.110806	−	0.130441i
$691$		−	16.2816i		−	0.619383i	−0.950837	−	0.309692i	$-0.899774\pi$
$691$		−	16.2816i		−	0.619383i	0.950837	−	0.309692i	$-0.100226\pi$
$692$	20.2799			0.770925
$693$	−3.16047	+	1.51835i	−0.120056	+	0.0576775i
$694$	24.5163			0.930626
$695$			9.49953i			0.360338i
$696$	4.69876	+	0.857885i	0.178106	+	0.0325181i
$697$	2.14196			0.0811326
$698$	9.93277	−	17.2041i	0.375961	−	0.651183i
$699$	−4.89781	−	4.16055i	−0.185252	−	0.157366i
$700$	0.624174	−	2.57107i	0.0235916	−	0.0971774i
$701$			4.22872i			0.159717i	0.996806	+	0.0798583i	$0.0254468\pi$
$701$			4.22872i			0.159717i	−0.996806	+	0.0798583i	$0.974553\pi$
$702$	0.346125	−	19.0523i	0.0130637	−	0.719081i
$703$	−0.388735	−	0.224436i	−0.0146614	−	0.00846477i
$704$	0.382566	−	0.220875i	0.0144185	−	0.00832453i
$705$	13.4524	+	2.45610i	0.506646	+	0.0925019i
$706$	27.8411	−	16.0741i	1.04781	−	0.604955i
$707$	2.85719	−	11.7692i	0.107456	−	0.442627i
$708$	−1.87030	−	5.23705i	−0.0702901	−	0.196821i
$709$	−5.78403			−0.217224			−0.108612	−	0.994084i	$-0.534641\pi$
$709$	−5.78403			−0.217224			−0.108612	+	0.994084i	$0.534641\pi$
$710$	1.87609	−	3.24949i	0.0704085	−	0.121951i
$711$	−7.02873	+	5.75421i	−0.263598	+	0.215800i
$712$	−11.0006	+	6.35119i	−0.412264	+	0.238021i
$713$	11.3549	−	19.6672i	0.425243	−	0.736543i
$714$	1.00910	−	0.733357i	0.0377647	−	0.0274452i
$715$	0.809995	+	1.40295i	0.0302921	+	0.0524675i
$716$	−13.2165	−	7.63053i	−0.493923	−	0.285166i
$717$	10.7449	+	9.12745i	0.401275	+	0.340871i
$718$	−14.1342	−	24.4812i	−0.527485	−	0.913630i
$719$	7.58926	+	13.1450i	0.283032	+	0.490225i	0.972130	−	0.234443i	$-0.0753265\pi$
$719$	7.58926	+	13.1450i	0.283032	+	0.490225i	−0.689098	+	0.724668i	$0.741993\pi$
$720$	−0.485129	−	2.96052i	−0.0180797	−	0.110332i
$721$	3.42852	+	11.6835i	0.127685	+	0.435115i
$722$	4.21556	+	2.43386i	0.156887	+	0.0905787i
$723$	−37.5863	−	31.9285i	−1.39785	−	1.18743i
$724$		−	24.7207i		−	0.918739i
$725$			2.75767i			0.102417i
$726$	−3.36129	+	18.4102i	−0.124749	+	0.683268i
$727$	−23.3867	−	13.5023i	−0.867364	−	0.500773i	−0.000892806	−	1.00000i	$-0.500284\pi$
$727$	−23.3867	−	13.5023i	−0.867364	−	0.500773i	−0.866471	+	0.499227i	$0.833618\pi$
$728$	−2.28898	+	9.42867i	−0.0848353	+	0.349450i
$729$	12.6418	+	23.8576i	0.468214	+	0.883615i
$730$	5.56698	+	9.64229i	0.206043	+	0.356877i
$731$	0.231333	+	0.400681i	0.00855617	+	0.0148197i
$732$	21.2071	−	7.57365i	0.783837	−	0.279930i
$733$	−15.7191	−	9.07542i	−0.580598	−	0.335208i	0.180773	−	0.983525i	$-0.442140\pi$
$733$	−15.7191	−	9.07542i	−0.580598	−	0.335208i	−0.761371	+	0.648317i	$0.775473\pi$
$734$	16.8301	+	29.1506i	0.621210	+	1.07597i
$735$	1.61152	−	12.0168i	0.0594419	−	0.443246i
$736$	−1.29782	+	2.24789i	−0.0478383	+	0.0828583i
$737$	0.205617	−	0.118713i	0.00757399	−	0.00437285i
$738$	8.34179	−	22.0831i	0.307065	−	0.812889i
$739$	2.83491	−	4.91021i	0.104284	−	0.180625i	−0.809162	−	0.587586i	$-0.800078\pi$
$739$	2.83491	−	4.91021i	0.104284	−	0.180625i	0.913445	+	0.406961i	$0.133412\pi$
$740$	0.119403			0.00438936
$741$	23.4900	+	4.28873i	0.862926	+	0.157550i
$742$	0.241136	−	0.0707616i	0.00885237	−	0.00259774i
$743$	14.9685	−	8.64209i	0.549142	−	0.317047i	−0.199634	−	0.979871i	$-0.563975\pi$
$743$	14.9685	−	8.64209i	0.549142	−	0.317047i	0.748776	+	0.662823i	$0.230642\pi$
$744$	−5.09667	−	14.2713i	−0.186853	−	0.523210i
$745$	−12.4227	+	7.17226i	−0.455133	+	0.262771i
$746$	−10.3698	−	5.98701i	−0.379665	−	0.219200i
$747$	4.16444	+	25.4136i	0.152369	+	0.929836i
$748$			0.120250i			0.00439678i
$749$	−41.6297	−	10.1064i	−1.52112	−	0.369279i
$750$	1.63115	−	0.582530i	0.0595613	−	0.0212710i
$751$	19.4141	−	33.6261i	0.708429	−	1.22703i	−0.257011	−	0.966408i	$-0.582738\pi$
$751$	19.4141	−	33.6261i	0.708429	−	1.22703i	0.965440	−	0.260626i	$-0.0839290\pi$
$752$	−7.89512			−0.287906
$753$	−2.68578	−	7.52051i	−0.0978754	−	0.274063i
$754$		−	10.1130i		−	0.368293i
$755$	0.679789			0.0247401
$756$	−3.63080	−	13.2596i	−0.132051	−	0.482247i
$757$	−33.5417			−1.21910			−0.609548	−	0.792749i	$-0.708649\pi$
$757$	−33.5417			−1.21910			−0.609548	+	0.792749i	$0.708649\pi$
$758$			10.9629i			0.398190i
$759$	0.667942	+	1.87032i	0.0242448	+	0.0678882i
$760$	3.75929			0.136364
$761$	−13.3464	+	23.1166i	−0.483806	+	0.837977i	−0.999827	−	0.0185992i	$-0.994079\pi$
$761$	−13.3464	+	23.1166i	−0.483806	+	0.837977i	0.516021	+	0.856576i	$0.327413\pi$
$762$	−34.4343	+	12.2975i	−1.24742	+	0.445490i
$763$	6.96147	−	2.04285i	0.252022	−	0.0739562i
$764$			5.50470i			0.199153i
$765$	0.763951	+	0.288580i	0.0276207	+	0.0104336i
$766$	17.4289	+	10.0626i	0.629732	+	0.363576i
$767$	−10.1967	+	5.88706i	−0.368181	+	0.212570i
$768$	0.582530	+	1.63115i	0.0210203	+	0.0588591i
$769$	−36.2335	+	20.9194i	−1.30661	+	0.754373i	−0.981529	−	0.191313i	$-0.938726\pi$
$769$	−36.2335	+	20.9194i	−1.30661	+	0.754373i	−0.325083	+	0.945685i	$0.605392\pi$
$770$	0.845741	+	0.806673i	0.0304784	+	0.0290705i
$771$	46.5069	+	8.49110i	1.67491	+	0.305799i
$772$	15.0469			0.541549
$773$	−0.0374243	+	0.0648208i	−0.00134606	+	0.00233144i	−0.866698	−	0.498834i	$-0.833762\pi$
$773$	−0.0374243	+	0.0648208i	−0.00134606	+	0.00233144i	0.865352	+	0.501165i	$0.167095\pi$
$774$	5.03184	−	0.824549i	0.180866	−	0.0296378i
$775$	7.57702	−	4.37459i	0.272175	−	0.157140i
$776$	−7.46424	+	12.9284i	−0.267951	+	0.464104i
$777$	0.544170	−	0.0572663i	0.0195220	−	0.00205442i
$778$	13.6704	+	23.6779i	0.490109	+	0.848894i
$779$	25.6177	+	14.7904i	0.917848	+	0.529920i
$780$	−5.98178	+	2.13626i	−0.214182	+	0.0764905i
$781$	0.828763	+	1.43546i	0.0296555	+	0.0513648i
$782$	−0.353283	−	0.611905i	−0.0126334	−	0.0218817i
$783$	6.93806	+	12.5376i	0.247946	+	0.448058i
$784$	0.330818	+	6.99218i	0.0118149	+	0.249721i
$785$	20.6832	+	11.9414i	0.738214	+	0.426208i
$786$	1.58199	−	8.66480i	0.0564279	−	0.309063i
$787$		−	33.3832i		−	1.18998i	−0.803733	−	0.594991i	$-0.797156\pi$
$787$		−	33.3832i		−	1.18998i	0.803733	−	0.594991i	$-0.202844\pi$
$788$			19.6584i			0.700303i
$789$	−39.4797	−	33.5368i	−1.40551	−	1.19394i
$790$	2.62224	+	1.51395i	0.0932953	+	0.0538640i
$791$	8.47705	+	2.05796i	0.301409	+	0.0731726i
$792$	1.23975	+	0.468309i	0.0440525	+	0.0166406i
$793$	−23.8393	−	41.2908i	−0.846557	−	1.46628i
$794$	−7.82456	−	13.5525i	−0.277683	−	0.480961i
$795$	0.125385	+	0.106511i	0.00444694	+	0.00377754i
$796$	9.23999	+	5.33471i	0.327503	+	0.189084i
$797$	15.3572	+	26.5995i	0.543980	+	0.942201i	0.998670	+	0.0515514i	$0.0164166\pi$
$797$	15.3572	+	26.5995i	0.543980	+	0.942201i	−0.454690	+	0.890650i	$0.650250\pi$
$798$	17.1326	−	1.80297i	0.606489	−	0.0638244i
$799$	1.07458	−	1.86122i	0.0380158	−	0.0658454i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−35.6485	−	13.4661i	−1.25958	−	0.475801i
$802$	−19.5763	+	33.9071i	−0.691262	+	1.19730i
$803$	−4.91842			−0.173567
$804$	0.313091	+	0.876690i	0.0110419	+	0.0309185i
$805$	−6.67357	−	1.62013i	−0.235213	−	0.0571021i
$806$	−27.7865	+	16.0426i	−0.978739	+	0.565075i
$807$	−23.3093	−	4.25574i	−0.820525	−	0.149809i
$808$	−3.96428	+	2.28878i	−0.139463	+	0.0805189i
$809$	8.63831	+	4.98733i	0.303707	+	0.175345i	0.644107	−	0.764936i	$-0.277229\pi$
$809$	8.63831	+	4.98733i	0.303707	+	0.175345i	−0.340400	+	0.940281i	$0.610563\pi$
$810$	5.95036	−	6.75228i	0.209074	−	0.237251i
$811$			56.5329i			1.98514i	0.121685	+	0.992569i	$0.461170\pi$
$811$			56.5329i			1.98514i	−0.121685	+	0.992569i	$0.538830\pi$
$812$	−2.05443	−	7.00091i	−0.0720962	−	0.245684i
$813$	−4.18343	−	3.55370i	−0.146719	−	0.124634i
$814$	−0.0263732	+	0.0456797i	−0.000924381	+	0.00160107i
$815$	15.9797			0.559743
$816$	−0.463820	−	0.0846828i	−0.0162369	−	0.00296449i
$817$			6.38948i			0.223540i
$818$	−26.2289			−0.917072
$819$	−26.2369	+	12.6047i	−0.916791	+	0.440444i
$820$	−7.86869			−0.274787
$821$		−	41.3245i		−	1.44223i	−0.692813	−	0.721117i	$-0.743629\pi$
$821$		−	41.3245i		−	1.44223i	0.692813	−	0.721117i	$-0.256371\pi$
$822$	−15.2974	+	18.0082i	−0.533558	+	0.628106i
$823$	−27.1596			−0.946726			−0.473363	−	0.880868i	$-0.656960\pi$
$823$	−27.1596			−0.946726			−0.473363	+	0.880868i	$0.656960\pi$
$824$	2.30107	−	3.98557i	0.0801616	−	0.138844i
$825$	−0.137424	+	0.752691i	−0.00478449	+	0.0262053i
$826$	−5.86292	+	6.14687i	−0.203997	+	0.213877i
$827$		−	5.74951i		−	0.199930i	−0.994991	−	0.0999650i	$-0.968127\pi$
$827$		−	5.74951i		−	0.199930i	0.994991	−	0.0999650i	$-0.0318731\pi$
$828$	−7.68443	+	1.25922i	−0.267052	+	0.0437609i
$829$	−26.3765	−	15.2285i	−0.916093	−	0.528907i	−0.0337068	−	0.999432i	$-0.510731\pi$
$829$	−26.3765	−	15.2285i	−0.916093	−	0.528907i	−0.882387	+	0.470525i	$0.844065\pi$
$830$	7.43413	−	4.29210i	0.258042	−	0.148981i
$831$	1.70177	−	2.00333i	0.0590336	−	0.0694946i
$832$	3.17590	−	1.83361i	0.110105	−	0.0635689i
$833$	−1.69339	−	0.873693i	−0.0586724	−	0.0302717i
$834$	10.6523	−	12.5400i	0.368861	−	0.434224i
$835$	4.72365			0.163469
$836$	−0.830333	+	1.43818i	−0.0287177	+	0.0497405i
$837$	23.4424	−	38.9520i	0.810290	−	1.34638i
$838$	−31.8342	+	18.3795i	−1.09970	+	0.634909i
$839$	15.5311	−	26.9006i	0.536193	−	0.928713i	−0.462912	−	0.886404i	$-0.653195\pi$
$839$	15.5311	−	26.9006i	0.536193	−	0.928713i	0.999105	−	0.0423086i	$-0.0134713\pi$
$840$	−3.70703	+	2.69405i	−0.127905	+	0.0929537i
$841$	−10.6976	−	18.5288i	−0.368883	−	0.638925i
$842$	−11.3406	−	6.54747i	−0.390821	−	0.225641i
$843$	−1.10981	+	6.07860i	−0.0382240	+	0.209358i
$844$	0.581500	+	1.00719i	0.0200160	+	0.0346688i
$845$	0.224227	+	0.388373i	0.00771366	+	0.0133605i
$846$	−15.0038	−	18.3271i	−0.515842	−	0.630098i
$847$	27.4303	−	8.04945i	0.942516	−	0.276583i
$848$	−0.0822585	−	0.0474920i	−0.00282477	−	0.00163088i
$849$	−21.5264	+	7.68767i	−0.738783	+	0.263840i
$850$		−	0.272213i		−	0.00933683i
$851$		−	0.309928i		−	0.0106242i
$852$	−6.12039	+	2.18576i	−0.209681	+	0.0748830i
$853$	44.5942	+	25.7465i	1.52688	+	0.881542i	0.999491	+	0.0319155i	$0.0101607\pi$
$853$	44.5942	+	25.7465i	1.52688	+	0.881542i	0.527385	+	0.849626i	$0.323173\pi$
$854$	−24.8913	−	23.7415i	−0.851764	−	0.812417i
$855$	7.14413	+	8.72651i	0.244324	+	0.298440i
$856$	8.09579	+	14.0223i	0.276708	+	0.479273i
$857$	8.93235	+	15.4713i	0.305123	+	0.528489i	0.977289	−	0.211912i	$-0.0679690\pi$
$857$	8.93235	+	15.4713i	0.305123	+	0.528489i	−0.672165	+	0.740401i	$0.734636\pi$
$858$	0.503963	−	2.76028i	0.0172050	−	0.0942343i
$859$	1.09664	+	0.633147i	0.0374170	+	0.0216027i	0.518592	−	0.855022i	$-0.326456\pi$
$859$	1.09664	+	0.633147i	0.0374170	+	0.0216027i	−0.481175	+	0.876625i	$0.659790\pi$
$860$	−0.849825	−	1.47194i	−0.0289788	−	0.0501927i
$861$	−35.8608	+	3.77385i	−1.22213	+	0.128613i
$862$	−10.3405	+	17.9103i	−0.352200	+	0.610028i
$863$	35.3845	−	20.4293i	1.20450	−	0.695420i	0.242949	−	0.970039i	$-0.421885\pi$
$863$	35.3845	−	20.4293i	1.20450	−	0.695420i	0.961553	+	0.274619i	$0.0885518\pi$
$864$	−2.67939	+	4.45207i	−0.0911546	+	0.151462i
$865$	10.1399	−	17.5629i	0.344768	−	0.597156i
$866$	5.36529			0.182320
$867$	−18.9799	+	22.3432i	−0.644592	+	0.758816i
$868$	−15.9768	+	16.7505i	−0.542287	+	0.568550i
$869$	−1.15838	+	0.668788i	−0.0392952	+	0.0226871i
$870$	3.09233	−	3.64030i	0.104840	−	0.123418i
$871$	1.70694	−	0.985503i	0.0578375	−	0.0333925i
$872$	−2.37476	−	1.37107i	−0.0804196	−	0.0464303i
$873$	−44.1960	+	7.24223i	−1.49581	+	0.245113i
$874$		−	9.75777i		−	0.330061i
$875$	−1.91453	−	1.82609i	−0.0647228	−	0.0617330i
$876$	3.46366	−	18.9710i	0.117026	−	0.640970i
$877$	−10.0424	+	17.3939i	−0.339107	+	0.587350i	−0.984265	−	0.176699i	$-0.943458\pi$
$877$	−10.0424	+	17.3939i	−0.339107	+	0.587350i	0.645158	+	0.764049i	$0.276791\pi$
$878$	10.4796			0.353669
$879$	24.7254	−	29.1068i	0.833965	−	0.981747i
$880$		−	0.441750i		−	0.0148914i
$881$	−26.6064			−0.896393			−0.448196	−	0.893935i	$-0.647933\pi$
$881$	−26.6064			−0.896393			−0.448196	+	0.893935i	$0.647933\pi$
$882$	−15.6024	+	14.0558i	−0.525359	+	0.473284i
$883$	−27.6319			−0.929887			−0.464943	−	0.885340i	$-0.653925\pi$
$883$	−27.6319			−0.929887			−0.464943	+	0.885340i	$0.653925\pi$
$884$			0.998264i			0.0335752i
$885$	−5.47057	−	0.998801i	−0.183891	−	0.0335743i
$886$	−7.77742			−0.261287
$887$	4.49355	−	7.78306i	0.150879	−	0.261330i	−0.780672	−	0.624941i	$-0.785123\pi$
$887$	4.49355	−	7.78306i	0.150879	−	0.261330i	0.931551	+	0.363611i	$0.118456\pi$
$888$	−0.157620	−	0.133894i	−0.00528938	−	0.00449317i
$889$	40.4164	+	38.5494i	1.35552	+	1.29291i
$890$			12.7024i			0.425785i
$891$	1.26891	+	3.76782i	0.0425101	+	0.126227i
$892$	−2.45476	−	1.41726i	−0.0821915	−	0.0474533i
$893$	25.7037	−	14.8400i	0.860142	−	0.496603i
$894$	24.4414	+	4.46244i	0.817443	+	0.149246i
$895$	−13.2165	+	7.63053i	−0.441778	+	0.255061i
$896$	1.82609	−	1.91453i	0.0610053	−	0.0639598i
$897$	5.54497	+	15.5266i	0.185141	+	0.518417i
$898$	3.73404			0.124607
$899$	12.0637	−	20.8949i	0.402347	−	0.696885i
$900$	−2.80645	−	1.06012i	−0.0935482	−	0.0353375i
$901$	0.0223918	−	0.0129279i	0.000745981	−	0.000430692i
$902$	1.73800	−	3.01030i	0.0578689	−	0.100232i
$903$	−4.57895	−	6.30065i	−0.152378	−	0.209673i
$904$	−1.64854	−	2.85536i	−0.0548298	−	0.0949680i
$905$	−21.4088	−	12.3604i	−0.711652	−	0.410872i
$906$	−0.897364	−	0.762284i	−0.0298129	−	0.0253252i
$907$	−15.1074	−	26.1667i	−0.501631	−	0.868851i	−0.999998	−	0.00188486i	$-0.999400\pi$
$907$	−15.1074	−	26.1667i	−0.501631	−	0.868851i	0.498367	−	0.866966i	$-0.333933\pi$
$908$	−5.62480	−	9.74244i	−0.186666	−	0.323314i
$909$	−12.8467	−	4.85277i	−0.426097	−	0.160956i
$910$	7.02097	+	6.69665i	0.232743	+	0.221992i
$911$	25.4482	+	14.6925i	0.843135	+	0.486784i	0.858329	−	0.513100i	$-0.171503\pi$
$911$	25.4482	+	14.6925i	0.843135	+	0.486784i	−0.0151935	+	0.999885i	$0.504836\pi$
$912$	−4.96250	−	4.21550i	−0.164325	−	0.139589i
$913$			3.79207i			0.125499i
$914$		−	2.90786i		−	0.0961836i
$915$	4.04458	−	22.1527i	0.133710	−	0.732346i
$916$	−14.0269	−	8.09843i	−0.463462	−	0.267580i
$917$	−12.9101	+	3.78849i	−0.426329	+	0.125107i
$918$	−0.684863	−	1.23760i	−0.0226039	−	0.0408470i
$919$	15.7829	+	27.3368i	0.520630	+	0.901758i	0.999712	+	0.0239876i	$0.00763621\pi$
$919$	15.7829	+	27.3368i	0.520630	+	0.901758i	−0.479082	+	0.877770i	$0.659030\pi$
$920$	1.29782	+	2.24789i	0.0427878	+	0.0741107i
$921$	47.6455	−	17.0156i	1.56997	−	0.560682i
$922$	−8.46009	−	4.88443i	−0.278618	−	0.160860i
$923$	6.88003	+	11.9166i	0.226459	+	0.392238i
$924$	−0.211865	−	2.01323i	−0.00696984	−	0.0662305i
$925$	0.0597017	−	0.103406i	0.00196298	−	0.00339998i
$926$	2.48752	−	1.43617i	0.0817451	−	0.0471956i
$927$	13.6247	−	2.23263i	0.447494	−	0.0733292i
$928$	−1.37884	+	2.38822i	−0.0452625	+	0.0783970i
$929$	50.8244			1.66749			0.833747	−	0.552147i	$-0.186191\pi$
$929$	50.8244			1.66749			0.833747	+	0.552147i	$0.186191\pi$
$930$	−14.9076	−	2.72179i	−0.488840	−	0.0892509i
$931$	−14.2199	−	22.1422i	−0.466037	−	0.725682i
$932$	3.21321	−	1.85515i	0.105252	−	0.0607673i
$933$	−14.4425	−	40.4407i	−0.472827	−	1.32397i
$934$	−3.34208	+	1.92955i	−0.109356	+	0.0631369i
$935$	0.104140	+	0.0601250i	0.00340573	+	0.00196630i
$936$	10.2918	+	3.88770i	0.336399	+	0.127073i
$937$			19.6915i			0.643294i	0.946860	+	0.321647i	$0.104236\pi$
$937$			19.6915i			0.643294i	−0.946860	+	0.321647i	$0.895764\pi$
$938$	0.981461	−	1.02899i	0.0320458	−	0.0335978i
$939$	−55.2825	+	19.7429i	−1.80407	+	0.644286i
$940$	−3.94756	+	6.83738i	−0.128755	+	0.223011i
$941$	27.1831			0.886145			0.443072	−	0.896486i	$-0.353888\pi$
$941$	27.1831			0.886145			0.443072	+	0.896486i	$0.353888\pi$
$942$	−13.9125	−	38.9566i	−0.453294	−	1.26927i
$943$			20.4243i			0.665106i
$944$	3.21065			0.104498
$945$	−13.2986	−	3.48544i	−0.432602	−	0.113381i
$946$	0.750819			0.0244112
$947$		−	7.85273i		−	0.255180i	−0.991827	−	0.127590i	$-0.959276\pi$
$947$		−	7.85273i		−	0.255180i	0.991827	−	0.127590i	$-0.0407241\pi$
$948$	−1.76385	−	4.93898i	−0.0572871	−	0.160411i
$949$	−40.8306			−1.32542
$950$	1.87965	−	3.25564i	0.0609838	−	0.105627i
$951$	−55.7487	+	19.9094i	−1.80778	+	0.645607i
$952$	0.202795	+	0.691067i	0.00657261	+	0.0223976i
$953$		−	14.7756i		−	0.478628i	−0.970942	−	0.239314i	$-0.923078\pi$
$953$		−	14.7756i		−	0.478628i	0.970942	−	0.239314i	$-0.0769225\pi$
$954$	−0.0460795	−	0.281201i	−0.00149188	−	0.00910423i
$955$	4.76721	+	2.75235i	0.154263	+	0.0890639i
$956$	−7.04916	+	4.06984i	−0.227986	+	0.131628i
$957$	0.709639	+	1.98707i	0.0229394	+	0.0642329i
$958$	−14.1411	+	8.16437i	−0.456878	+	0.263779i
$959$	35.0743	+	8.51492i	1.13261	+	0.274961i
$960$	1.70388	+	0.311090i	0.0549926	+	0.0100404i
$961$	−45.5483			−1.46930
$962$	−0.218939	+	0.379213i	−0.00705887	+	0.0122263i
$963$	−17.1651	+	45.4408i	−0.553137	+	1.46431i
$964$	24.6585	−	14.2366i	0.794195	−	0.458529i
$965$	7.52344	−	13.0310i	0.242188	−	0.419482i
$966$	6.99279	+	9.62211i	0.224989	+	0.309586i
$967$	11.9085	+	20.6261i	0.382950	+	0.663290i	0.991483	−	0.130240i	$-0.0415747\pi$
$967$	11.9085	+	20.6261i	0.382950	+	0.663290i	−0.608532	+	0.793529i	$0.708241\pi$
$968$	−9.35728	−	5.40243i	−0.300754	−	0.173641i
$969$	1.66921	−	0.596120i	0.0536226	−	0.0191501i
$970$	7.46424	+	12.9284i	0.239662	+	0.415107i
$971$	14.5985	+	25.2854i	0.468489	+	0.811446i	0.999351	−	0.0360115i	$-0.0114653\pi$
$971$	14.5985	+	25.2854i	0.468489	+	0.811446i	−0.530863	+	0.847458i	$0.678132\pi$
$972$	−15.4265	+	2.24096i	−0.494806	+	0.0718789i
$973$	−24.4240	−	5.92936i	−0.782997	−	0.190087i
$974$	−12.2254	−	7.05835i	−0.391728	−	0.226164i
$975$	−1.14083	+	6.24851i	−0.0365359	+	0.200112i
$976$			13.0013i			0.416161i
$977$			31.0707i			0.994040i	0.867739	+	0.497020i	$0.165573\pi$
$977$			31.0707i			0.994040i	−0.867739	+	0.497020i	$0.834427\pi$
$978$	−21.0942	−	17.9189i	−0.674517	−	0.572982i
$979$	−4.85950	−	2.80564i	−0.155310	−	0.0896685i
$980$	6.22081	+	3.20959i	0.198717	+	0.102527i
$981$	−1.33029	−	8.11814i	−0.0424729	−	0.259192i
$982$	5.19839	+	9.00388i	0.165887	+	0.287325i
$983$	15.1694	+	26.2741i	0.483827	+	0.838013i	0.999827	−	0.0185751i	$-0.00591299\pi$
$983$	15.1694	+	26.2741i	0.483827	+	0.838013i	−0.516000	+	0.856588i	$0.672580\pi$
$984$	10.3872	+	8.82359i	0.331131	+	0.281286i
$985$	17.0247	+	9.82922i	0.542452	+	0.313185i
$986$	−0.375337	−	0.650104i	−0.0119532	−	0.0207035i
$987$	−14.7114	+	33.0540i	−0.468270	+	1.05212i
$988$	−6.89307	+	11.9391i	−0.219298	+	0.379835i
$989$	−3.82062	+	2.20584i	−0.121489	+	0.0701416i
$990$	1.02544	−	0.839497i	0.0325907	−	0.0266810i
$991$	14.0266	−	24.2947i	0.445568	−	0.771747i	−0.552523	−	0.833497i	$-0.686335\pi$
$991$	14.0266	−	24.2947i	0.445568	−	0.771747i	0.998092	+	0.0617506i	$0.0196683\pi$
$992$	8.74919			0.277787
$993$	−10.5952	−	29.6677i	−0.336227	−	0.941475i
$994$	7.18365	+	6.85181i	0.227852	+	0.217326i
$995$	9.23999	−	5.33471i	0.292927	−	0.169122i
$996$	−14.6265	−	2.67046i	−0.463458	−	0.0846167i
$997$	26.1381	−	15.0908i	0.827801	−	0.477931i	−0.0252978	−	0.999680i	$-0.508053\pi$
$997$	26.1381	−	15.0908i	0.827801	−	0.477931i	0.853099	+	0.521749i	$0.174720\pi$
$998$	−13.7516	−	7.93948i	−0.435299	−	0.251320i
$999$	0.0112697	−	0.620336i	0.000356559	−	0.0196266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.b.101.4	yes	28
3.2	odd	2		1890.2.bk.b.521.8		28
7.5	odd	6		630.2.t.b.551.7	yes	28
9.4	even	3		1890.2.t.b.1151.10		28
9.5	odd	6		630.2.t.b.311.7	✓	28
21.5	even	6		1890.2.t.b.1601.10		28
63.5	even	6	inner	630.2.bk.b.131.11	yes	28
63.40	odd	6		1890.2.bk.b.341.8		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.7	✓	28	9.5	odd	6
630.2.t.b.551.7	yes	28	7.5	odd	6
630.2.bk.b.101.4	yes	28	1.1	even	1	trivial
630.2.bk.b.131.11	yes	28	63.5	even	6	inner
1890.2.t.b.1151.10		28	9.4	even	3
1890.2.t.b.1601.10		28	21.5	even	6
1890.2.bk.b.341.8		28	63.40	odd	6
1890.2.bk.b.521.8		28	3.2	odd	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.582530 + 1.63115i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.63115 - 0.582530i) q^{6} +(-1.91453 - 1.82609i) q^{7} +1.00000i q^{8} +(-2.32132 + 1.90039i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.582530 + 1.63115i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.63115 - 0.582530i) q^{6} +(-1.91453 - 1.82609i) q^{7} +1.00000i q^{8} +(-2.32132 + 1.90039i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-0.382566 + 0.220875i) q^{11} +(-0.582530 - 1.63115i) q^{12} +(-3.17590 + 1.83361i) q^{13} +(-1.82609 + 1.91453i) q^{14} +(-1.70388 - 0.311090i) q^{15} +1.00000 q^{16} +(-0.136107 + 0.235743i) q^{17} +(1.90039 + 2.32132i) q^{18} +(-3.25564 + 1.87965i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.86336 - 4.18663i) q^{21} +(0.220875 + 0.382566i) q^{22} +(-2.24789 - 1.29782i) q^{23} +(-1.63115 + 0.582530i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.83361 + 3.17590i) q^{26} +(-4.45207 - 2.67939i) q^{27} +(1.91453 + 1.82609i) q^{28} +(-2.38822 - 1.37884i) q^{29} +(-0.311090 + 1.70388i) q^{30} +8.74919i q^{31} -1.00000i q^{32} +(-0.583137 - 0.495358i) q^{33} +(0.235743 + 0.136107i) q^{34} +(2.53870 - 0.744985i) q^{35} +(2.32132 - 1.90039i) q^{36} +(0.0597017 + 0.103406i) q^{37} +(1.87965 + 3.25564i) q^{38} +(-4.84095 - 4.11225i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(-3.93435 - 6.81449i) q^{41} +(-4.18663 - 1.86336i) q^{42} +(0.849825 - 1.47194i) q^{43} +(0.382566 - 0.220875i) q^{44} +(-0.485129 - 2.96052i) q^{45} +(-1.29782 + 2.24789i) q^{46} -7.89512 q^{47} +(0.582530 + 1.63115i) q^{48} +(0.330818 + 6.99218i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-0.463820 - 0.0846828i) q^{51} +(3.17590 - 1.83361i) q^{52} +(-0.0822585 - 0.0474920i) q^{53} +(-2.67939 + 4.45207i) q^{54} -0.441750i q^{55} +(1.82609 - 1.91453i) q^{56} +(-4.96250 - 4.21550i) q^{57} +(-1.37884 + 2.38822i) q^{58} +3.21065 q^{59} +(1.70388 + 0.311090i) q^{60} +13.0013i q^{61} +8.74919 q^{62} +(7.91450 + 0.600577i) q^{63} -1.00000 q^{64} -3.66721i q^{65} +(-0.495358 + 0.583137i) q^{66} -0.537467 q^{67} +(0.136107 - 0.235743i) q^{68} +(0.807478 - 4.42267i) q^{69} +(-0.744985 - 2.53870i) q^{70} -3.75218i q^{71} +(-1.90039 - 2.32132i) q^{72} +(9.64229 + 5.56698i) q^{73} +(0.103406 - 0.0597017i) q^{74} +(1.12135 - 1.32006i) q^{75} +(3.25564 - 1.87965i) q^{76} +(1.13577 + 0.275729i) q^{77} +(-4.11225 + 4.84095i) q^{78} +3.02791 q^{79} +(-0.500000 + 0.866025i) q^{80} +(1.77702 - 8.82282i) q^{81} +(-6.81449 + 3.93435i) q^{82} +(4.29210 - 7.43413i) q^{83} +(-1.86336 + 4.18663i) q^{84} +(-0.136107 - 0.235743i) q^{85} +(-1.47194 - 0.849825i) q^{86} +(0.857885 - 4.69876i) q^{87} +(-0.220875 - 0.382566i) q^{88} +(6.35119 + 11.0006i) q^{89} +(-2.96052 + 0.485129i) q^{90} +(9.42867 + 2.28898i) q^{91} +(2.24789 + 1.29782i) q^{92} +(-14.2713 + 5.09667i) q^{93} +7.89512i q^{94} -3.75929i q^{95} +(1.63115 - 0.582530i) q^{96} +(12.9284 + 7.46424i) q^{97} +(6.99218 - 0.330818i) q^{98} +(0.468309 - 1.23975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * q^96 + 72 * q^97 + 24 * q^98 - 42 * q^99

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