LMFDB - Embedded newform 630.2.bk.b.101.1

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			101.1
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.b.131.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.68763 - 0.389766i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.389766 + 1.68763i) q^{6} +(0.408654 - 2.61400i) q^{7} +1.00000i q^{8} +(2.69616 + 1.31556i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.68763 - 0.389766i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.389766 + 1.68763i) q^{6} +(0.408654 - 2.61400i) q^{7} +1.00000i q^{8} +(2.69616 + 1.31556i) q^{9} +(0.866025 + 0.500000i) q^{10} +(3.42673 - 1.97842i) q^{11} +(1.68763 + 0.389766i) q^{12} +(2.82686 - 1.63209i) q^{13} +(-2.61400 - 0.408654i) q^{14} +(1.18136 - 1.26664i) q^{15} +1.00000 q^{16} +(-0.497322 + 0.861388i) q^{17} +(1.31556 - 2.69616i) q^{18} +(-4.90846 + 2.83390i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.70850 + 4.25218i) q^{21} +(-1.97842 - 3.42673i) q^{22} +(-6.67695 - 3.85494i) q^{23} +(0.389766 - 1.68763i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.63209 - 2.82686i) q^{26} +(-4.03736 - 3.27105i) q^{27} +(-0.408654 + 2.61400i) q^{28} +(-4.10273 - 2.36871i) q^{29} +(-1.26664 - 1.18136i) q^{30} -5.58041i q^{31} -1.00000i q^{32} +(-6.55415 + 2.00321i) q^{33} +(0.861388 + 0.497322i) q^{34} +(2.05946 + 1.66090i) q^{35} +(-2.69616 - 1.31556i) q^{36} +(-5.05548 - 8.75634i) q^{37} +(2.83390 + 4.90846i) q^{38} +(-5.40682 + 1.65254i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(5.16567 + 8.94721i) q^{41} +(4.25218 + 1.70850i) q^{42} +(5.10292 - 8.83852i) q^{43} +(-3.42673 + 1.97842i) q^{44} +(-2.48739 + 1.67717i) q^{45} +(-3.85494 + 6.67695i) q^{46} -4.73926 q^{47} +(-1.68763 - 0.389766i) q^{48} +(-6.66600 - 2.13644i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(1.17503 - 1.25986i) q^{51} +(-2.82686 + 1.63209i) q^{52} +(8.82289 + 5.09390i) q^{53} +(-3.27105 + 4.03736i) q^{54} +3.95684i q^{55} +(2.61400 + 0.408654i) q^{56} +(9.38820 - 2.86941i) q^{57} +(-2.36871 + 4.10273i) q^{58} -3.40720 q^{59} +(-1.18136 + 1.26664i) q^{60} -6.29939i q^{61} -5.58041 q^{62} +(4.54067 - 6.51017i) q^{63} -1.00000 q^{64} +3.26418i q^{65} +(2.00321 + 6.55415i) q^{66} +9.22190 q^{67} +(0.497322 - 0.861388i) q^{68} +(9.76567 + 9.10814i) q^{69} +(1.66090 - 2.05946i) q^{70} -2.74965i q^{71} +(-1.31556 + 2.69616i) q^{72} +(-12.7539 - 7.36348i) q^{73} +(-8.75634 + 5.05548i) q^{74} +(0.506266 + 1.65641i) q^{75} +(4.90846 - 2.83390i) q^{76} +(-3.77125 - 9.76595i) q^{77} +(1.65254 + 5.40682i) q^{78} -1.84147 q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.53861 + 7.09393i) q^{81} +(8.94721 - 5.16567i) q^{82} +(-0.789829 + 1.36802i) q^{83} +(1.70850 - 4.25218i) q^{84} +(-0.497322 - 0.861388i) q^{85} +(-8.83852 - 5.10292i) q^{86} +(6.00064 + 5.59661i) q^{87} +(1.97842 + 3.42673i) q^{88} +(6.92781 + 11.9993i) q^{89} +(1.67717 + 2.48739i) q^{90} +(-3.11107 - 8.05637i) q^{91} +(6.67695 + 3.85494i) q^{92} +(-2.17506 + 9.41764i) q^{93} +4.73926i q^{94} -5.66780i q^{95} +(-0.389766 + 1.68763i) q^{96} +(-0.776974 - 0.448586i) q^{97} +(-2.13644 + 6.66600i) q^{98} +(11.8417 - 0.826087i) 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
$3$	−1.68763	−	0.389766i	−0.974351	−	0.225032i
$3$	−1.68763	−	0.389766i	−0.974351	−	0.225032i
$4$	−1.00000			−0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.389766	+	1.68763i	−0.159121	+	0.688971i
$7$	0.408654	−	2.61400i	0.154457	−	0.988000i
$7$	0.408654	−	2.61400i	0.154457	−	0.988000i
$8$			1.00000i			0.353553i
$9$	2.69616	+	1.31556i	0.898722	+	0.438520i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	3.42673	−	1.97842i	1.03320	−	0.596516i	0.115298	−	0.993331i	$-0.463218\pi$
$11$	3.42673	−	1.97842i	1.03320	−	0.596516i	0.917899	+	0.396815i	$0.129884\pi$
$12$	1.68763	+	0.389766i	0.487176	+	0.112516i
$13$	2.82686	−	1.63209i	0.784030	−	0.452660i	−0.0538267	−	0.998550i	$-0.517142\pi$
$13$	2.82686	−	1.63209i	0.784030	−	0.452660i	0.837857	+	0.545890i	$0.183809\pi$
$14$	−2.61400	−	0.408654i	−0.698621	−	0.109217i
$15$	1.18136	−	1.26664i	0.305026	−	0.327046i
$16$	1.00000			0.250000
$17$	−0.497322	+	0.861388i	−0.120618	+	0.208917i	−0.920012	−	0.391891i	$-0.871821\pi$
$17$	−0.497322	+	0.861388i	−0.120618	+	0.208917i	0.799393	+	0.600808i	$0.205154\pi$
$18$	1.31556	−	2.69616i	0.310080	−	0.635492i
$19$	−4.90846	+	2.83390i	−1.12608	+	0.650141i	−0.942945	−	0.332947i	$-0.891957\pi$
$19$	−4.90846	+	2.83390i	−1.12608	+	0.650141i	−0.183132	+	0.983088i	$0.558624\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−1.70850	+	4.25218i	−0.372826	+	0.927901i
$22$	−1.97842	−	3.42673i	−0.421801	−	0.730580i
$23$	−6.67695	−	3.85494i	−1.39224	−	0.803810i	−0.398677	−	0.917092i	$-0.630530\pi$
$23$	−6.67695	−	3.85494i	−1.39224	−	0.803810i	−0.993563	+	0.113282i	$0.963864\pi$
$24$	0.389766	−	1.68763i	0.0795607	−	0.344485i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.63209	−	2.82686i	−0.320079	−	0.554393i
$27$	−4.03736	−	3.27105i	−0.776990	−	0.629513i
$28$	−0.408654	+	2.61400i	−0.0772283	+	0.494000i
$29$	−4.10273	−	2.36871i	−0.761858	−	0.439859i	0.0681041	−	0.997678i	$-0.478305\pi$
$29$	−4.10273	−	2.36871i	−0.761858	−	0.439859i	−0.829963	+	0.557819i	$0.811638\pi$
$30$	−1.26664	−	1.18136i	−0.231257	−	0.215686i
$31$		−	5.58041i		−	1.00227i	−0.865369	−	0.501135i	$-0.832916\pi$
$31$		−	5.58041i		−	1.00227i	0.865369	−	0.501135i	$-0.167084\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−6.55415	+	2.00321i	−1.14093	+	0.348715i
$34$	0.861388	+	0.497322i	0.147727	+	0.0852901i
$35$	2.05946	+	1.66090i	0.348113	+	0.280744i
$36$	−2.69616	−	1.31556i	−0.449361	−	0.219260i
$37$	−5.05548	−	8.75634i	−0.831115	−	1.43953i	−0.897155	−	0.441717i	$-0.854370\pi$
$37$	−5.05548	−	8.75634i	−0.831115	−	1.43953i	0.0660393	−	0.997817i	$-0.478964\pi$
$38$	2.83390	+	4.90846i	0.459719	+	0.796257i
$39$	−5.40682	+	1.65254i	−0.865783	+	0.264618i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	5.16567	+	8.94721i	0.806743	+	1.39732i	0.915108	+	0.403208i	$0.132105\pi$
$41$	5.16567	+	8.94721i	0.806743	+	1.39732i	−0.108365	+	0.994111i	$0.534562\pi$
$42$	4.25218	+	1.70850i	0.656125	+	0.263628i
$43$	5.10292	−	8.83852i	0.778188	−	1.34786i	−0.154797	−	0.987946i	$-0.549472\pi$
$43$	5.10292	−	8.83852i	0.778188	−	1.34786i	0.932985	−	0.359915i	$-0.117194\pi$
$44$	−3.42673	+	1.97842i	−0.516598	+	0.298258i
$45$	−2.48739	+	1.67717i	−0.370798	+	0.250017i
$46$	−3.85494	+	6.67695i	−0.568379	+	0.984462i
$47$	−4.73926			−0.691293			−0.345646	−	0.938365i	$-0.612340\pi$
$47$	−4.73926			−0.691293			−0.345646	+	0.938365i	$0.612340\pi$
$48$	−1.68763	−	0.389766i	−0.243588	−	0.0562579i
$49$	−6.66600	−	2.13644i	−0.952286	−	0.305206i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	1.17503	−	1.25986i	0.164538	−	0.176416i
$52$	−2.82686	+	1.63209i	−0.392015	+	0.226330i
$53$	8.82289	+	5.09390i	1.21192	+	0.699701i	0.963177	−	0.268869i	$-0.0866500\pi$
$53$	8.82289	+	5.09390i	1.21192	+	0.699701i	0.248741	+	0.968570i	$0.419983\pi$
$54$	−3.27105	+	4.03736i	−0.445133	+	0.549415i
$55$			3.95684i			0.533540i
$56$	2.61400	+	0.408654i	0.349311	+	0.0546086i
$57$	9.38820	−	2.86941i	1.24350	−	0.380063i
$58$	−2.36871	+	4.10273i	−0.311027	+	0.538715i
$59$	−3.40720			−0.443580			−0.221790	−	0.975094i	$-0.571190\pi$
$59$	−3.40720			−0.443580			−0.221790	+	0.975094i	$0.571190\pi$
$60$	−1.18136	+	1.26664i	−0.152513	+	0.163523i
$61$		−	6.29939i		−	0.806554i	−0.915078	−	0.403277i	$-0.867871\pi$
$61$		−	6.29939i		−	0.806554i	0.915078	−	0.403277i	$-0.132129\pi$
$62$	−5.58041			−0.708713
$63$	4.54067	−	6.51017i	0.572071	−	0.820204i
$64$	−1.00000			−0.125000
$65$			3.26418i			0.404871i
$66$	2.00321	+	6.55415i	0.246578	+	0.806761i
$67$	9.22190			1.12663			0.563317	−	0.826241i	$-0.309525\pi$
$67$	9.22190			1.12663			0.563317	+	0.826241i	$0.309525\pi$
$68$	0.497322	−	0.861388i	0.0603092	−	0.104459i
$69$	9.76567	+	9.10814i	1.17565	+	1.09649i
$70$	1.66090	−	2.05946i	0.198516	−	0.246153i
$71$		−	2.74965i		−	0.326324i	−0.986599	−	0.163162i	$-0.947831\pi$
$71$		−	2.74965i		−	0.326324i	0.986599	−	0.163162i	$-0.0521693\pi$
$72$	−1.31556	+	2.69616i	−0.155040	+	0.317746i
$73$	−12.7539	−	7.36348i	−1.49273	−	0.861830i	−0.492767	−	0.870161i	$-0.664015\pi$
$73$	−12.7539	−	7.36348i	−1.49273	−	0.861830i	−0.999965	+	0.00833139i	$0.997348\pi$
$74$	−8.75634	+	5.05548i	−1.01790	+	0.587687i
$75$	0.506266	+	1.65641i	0.0584585	+	0.191266i
$76$	4.90846	−	2.83390i	0.563039	−	0.325071i
$77$	−3.77125	−	9.76595i	−0.429774	−	1.11293i
$78$	1.65254	+	5.40682i	0.187113	+	0.612201i
$79$	−1.84147			−0.207182			−0.103591	−	0.994620i	$-0.533033\pi$
$79$	−1.84147			−0.207182			−0.103591	+	0.994620i	$0.533033\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	5.53861	+	7.09393i	0.615401	+	0.788214i
$82$	8.94721	−	5.16567i	0.988054	−	0.570453i
$83$	−0.789829	+	1.36802i	−0.0866950	+	0.150160i	−0.906112	−	0.423037i	$-0.860964\pi$
$83$	−0.789829	+	1.36802i	−0.0866950	+	0.150160i	0.819417	+	0.573198i	$0.194297\pi$
$84$	1.70850	−	4.25218i	0.186413	−	0.463951i
$85$	−0.497322	−	0.861388i	−0.0539422	−	0.0934306i
$86$	−8.83852	−	5.10292i	−0.953082	−	0.550262i
$87$	6.00064	+	5.59661i	0.643336	+	0.600020i
$88$	1.97842	+	3.42673i	0.210900	+	0.365290i
$89$	6.92781	+	11.9993i	0.734347	+	1.27193i	0.955009	+	0.296576i	$0.0958447\pi$
$89$	6.92781	+	11.9993i	0.734347	+	1.27193i	−0.220663	+	0.975350i	$0.570822\pi$
$90$	1.67717	+	2.48739i	0.176789	+	0.262194i
$91$	−3.11107	−	8.05637i	−0.326129	−	0.844537i
$92$	6.67695	+	3.85494i	0.696120	+	0.401905i
$93$	−2.17506	+	9.41764i	−0.225543	+	0.976564i
$94$			4.73926i			0.488818i
$95$		−	5.66780i		−	0.581504i
$96$	−0.389766	+	1.68763i	−0.0397804	+	0.172243i
$97$	−0.776974	−	0.448586i	−0.0788897	−	0.0455470i	0.460036	−	0.887900i	$-0.347836\pi$
$97$	−0.776974	−	0.448586i	−0.0788897	−	0.0455470i	−0.538926	+	0.842353i	$0.681170\pi$
$98$	−2.13644	+	6.66600i	−0.215813	+	0.673368i
$99$	11.8417	−	0.826087i	1.19014	−	0.0830249i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−0.107847	−	0.186797i	−0.0107312	−	0.0185870i	0.860610	−	0.509265i	$-0.170083\pi$
$101$	−0.107847	−	0.186797i	−0.0107312	−	0.0185870i	−0.871341	+	0.490678i	$0.836749\pi$
$102$	−1.25986	−	1.17503i	−0.124745	−	0.116346i
$103$	−9.83240	−	5.67674i	−0.968816	−	0.559346i	−0.0699406	−	0.997551i	$-0.522281\pi$
$103$	−9.83240	−	5.67674i	−0.968816	−	0.559346i	−0.898875	+	0.438205i	$0.855614\pi$
$104$	1.63209	+	2.82686i	0.160039	+	0.277196i
$105$	−2.82824	−	3.60570i	−0.276008	−	0.351880i
$106$	5.09390	−	8.82289i	0.494763	−	0.856955i
$107$	5.53564	−	3.19600i	0.535151	−	0.308969i	−0.207961	−	0.978137i	$-0.566683\pi$
$107$	5.53564	−	3.19600i	0.535151	−	0.308969i	0.743111	+	0.669168i	$0.233349\pi$
$108$	4.03736	+	3.27105i	0.388495	+	0.314757i
$109$	0.615666	−	1.06636i	0.0589701	−	0.102139i	−0.835033	−	0.550199i	$-0.814552\pi$
$109$	0.615666	−	1.06636i	0.0589701	−	0.102139i	0.894003	+	0.448060i	$0.147885\pi$
$110$	3.95684			0.377270
$111$	5.11883	+	16.7479i	0.485858	+	1.58964i
$112$	0.408654	−	2.61400i	0.0386141	−	0.247000i
$113$	−7.32005	+	4.22623i	−0.688612	+	0.397571i	−0.803092	−	0.595855i	$-0.796813\pi$
$113$	−7.32005	+	4.22623i	−0.688612	+	0.397571i	0.114480	+	0.993426i	$0.463480\pi$
$114$	−2.86941	−	9.38820i	−0.268745	−	0.879286i
$115$	6.67695	−	3.85494i	0.622628	−	0.359475i
$116$	4.10273	+	2.36871i	0.380929	+	0.219930i
$117$	9.76879	−	0.681476i	0.903125	−	0.0630025i
$118$			3.40720i			0.313658i
$119$	2.04844	+	1.65201i	0.187780	+	0.151440i
$120$	1.26664	+	1.18136i	0.115628	+	0.107843i
$121$	2.32830	−	4.03273i	0.211664	−	0.366612i
$122$	−6.29939			−0.570320
$123$	−5.23041	−	17.1130i	−0.471610	−	1.54302i
$124$			5.58041i			0.501135i
$125$	1.00000			0.0894427
$126$	−6.51017	−	4.54067i	−0.579972	−	0.404515i
$127$	20.5777			1.82598			0.912988	−	0.407985i	$-0.133769\pi$
$127$	20.5777			1.82598			0.912988	+	0.407985i	$0.133769\pi$
$128$			1.00000i			0.0883883i
$129$	−12.0568	+	12.9272i	−1.06154	+	1.13817i
$130$	3.26418			0.286287
$131$	2.50459	−	4.33807i	0.218827	−	0.379019i	−0.735623	−	0.677391i	$-0.763110\pi$
$131$	2.50459	−	4.33807i	0.218827	−	0.379019i	0.954450	+	0.298372i	$0.0964437\pi$
$132$	6.55415	−	2.00321i	0.570466	−	0.174357i
$133$	5.40196	+	13.9888i	0.468409	+	1.21298i
$134$		−	9.22190i		−	0.796651i
$135$	4.85149	−	1.86093i	0.417550	−	0.160163i
$136$	−0.861388	−	0.497322i	−0.0738634	−	0.0426450i
$137$	7.99924	−	4.61836i	0.683421	−	0.394573i	−0.117722	−	0.993047i	$-0.537559\pi$
$137$	7.99924	−	4.61836i	0.683421	−	0.394573i	0.801143	+	0.598473i	$0.204226\pi$
$138$	9.10814	−	9.76567i	0.775336	−	0.831309i
$139$	11.2919	−	6.51936i	0.957763	−	0.552965i	0.0622791	−	0.998059i	$-0.480163\pi$
$139$	11.2919	−	6.51936i	0.957763	−	0.552965i	0.895484	+	0.445094i	$0.146830\pi$
$140$	−2.05946	−	1.66090i	−0.174057	−	0.140372i
$141$	7.99811	+	1.84721i	0.673562	+	0.155563i
$142$	−2.74965			−0.230746
$143$	6.45792	−	11.1854i	0.540038	−	0.935373i
$144$	2.69616	+	1.31556i	0.224680	+	0.109630i
$145$	4.10273	−	2.36871i	0.340713	−	0.196711i
$146$	−7.36348	+	12.7539i	−0.609406	+	1.05552i
$147$	10.4170	+	6.20370i	0.859181	+	0.511672i
$148$	5.05548	+	8.75634i	0.415558	+	0.719767i
$149$	−19.1098	−	11.0331i	−1.56554	−	0.903863i	−0.996679	−	0.0814277i	$-0.974052\pi$
$149$	−19.1098	−	11.0331i	−1.56554	−	0.903863i	−0.568858	−	0.822436i	$-0.692615\pi$
$150$	1.65641	−	0.506266i	0.135245	−	0.0413364i
$151$	−2.76891	−	4.79589i	−0.225331	−	0.390284i	0.731088	−	0.682283i	$-0.239013\pi$
$151$	−2.76891	−	4.79589i	−0.225331	−	0.390284i	−0.956419	+	0.291999i	$0.905680\pi$
$152$	−2.83390	−	4.90846i	−0.229860	−	0.398128i
$153$	−2.47407	+	1.66819i	−0.200017	+	0.134865i
$154$	−9.76595	+	3.77125i	−0.786963	+	0.303896i
$155$	4.83278	+	2.79020i	0.388178	+	0.224115i
$156$	5.40682	−	1.65254i	0.432892	−	0.132309i
$157$			16.7972i			1.34056i	0.742107	+	0.670281i	$0.233827\pi$
$157$			16.7972i			1.34056i	−0.742107	+	0.670281i	$0.766173\pi$
$158$			1.84147i			0.146500i
$159$	−12.9043	−	12.0355i	−1.02338	−	0.954474i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−12.8054	+	15.8782i	−1.00920	+	1.25138i
$162$	7.09393	−	5.53861i	0.557352	−	0.435154i
$163$	0.864749	+	1.49779i	0.0677324	+	0.117316i	0.897903	−	0.440194i	$-0.145090\pi$
$163$	0.864749	+	1.49779i	0.0677324	+	0.117316i	−0.830170	+	0.557510i	$0.811757\pi$
$164$	−5.16567	−	8.94721i	−0.403371	−	0.698660i
$165$	1.54224	−	6.67767i	0.120064	−	0.519856i
$166$	1.36802	+	0.789829i	0.106179	+	0.0613026i
$167$	0.371022	+	0.642629i	0.0287105	+	0.0497281i	0.880024	−	0.474930i	$-0.157527\pi$
$167$	0.371022	+	0.642629i	0.0287105	+	0.0497281i	−0.851313	+	0.524658i	$0.824193\pi$
$168$	−4.25218	−	1.70850i	−0.328063	−	0.131814i
$169$	−1.17257	+	2.03096i	−0.0901981	+	0.156228i
$170$	−0.861388	+	0.497322i	−0.0660654	+	0.0381429i
$171$	−16.9622	+	1.18329i	−1.29713	+	0.0904885i
$172$	−5.10292	+	8.83852i	−0.389094	+	0.673930i
$173$	0.964238			0.0733097			0.0366548	−	0.999328i	$-0.488330\pi$
$173$	0.964238			0.0733097			0.0366548	+	0.999328i	$0.488330\pi$
$174$	5.59661	−	6.00064i	0.424278	−	0.454907i
$175$	−2.46812	+	0.953096i	−0.186572	+	0.0720473i
$176$	3.42673	−	1.97842i	0.258299	−	0.149129i
$177$	5.75008	+	1.32801i	0.432203	+	0.0998195i
$178$	11.9993	−	6.92781i	0.899387	−	0.519262i
$179$	0.186006	+	0.107391i	0.0139028	+	0.00802676i	0.506935	−	0.861984i	$-0.330778\pi$
$179$	0.186006	+	0.107391i	0.0139028	+	0.00802676i	−0.493033	+	0.870011i	$0.664112\pi$
$180$	2.48739	−	1.67717i	0.185399	−	0.125009i
$181$		−	11.1757i		−	0.830681i	−0.909666	−	0.415341i	$-0.863662\pi$
$181$		−	11.1757i		−	0.830681i	0.909666	−	0.415341i	$-0.136338\pi$
$182$	−8.05637	+	3.11107i	−0.597178	+	0.230608i
$183$	−2.45529	+	10.6310i	−0.181500	+	0.785867i
$184$	3.85494	−	6.67695i	0.284190	−	0.492231i
$185$	10.1110			0.743372
$186$	9.41764	+	2.17506i	0.690535	+	0.159483i
$187$			3.93565i			0.287803i
$188$	4.73926			0.345646
$189$	−10.2004	+	9.21693i	−0.741970	+	0.670433i
$190$	−5.66780			−0.411185
$191$			18.8822i			1.36627i	0.730294	+	0.683133i	$0.239383\pi$
$191$			18.8822i			1.36627i	−0.730294	+	0.683133i	$0.760617\pi$
$192$	1.68763	+	0.389766i	0.121794	+	0.0281290i
$193$	−5.89018			−0.423985			−0.211992	−	0.977271i	$-0.567995\pi$
$193$	−5.89018			−0.423985			−0.211992	+	0.977271i	$0.567995\pi$
$194$	−0.448586	+	0.776974i	−0.0322066	+	0.0557835i
$195$	1.27227	−	5.50871i	0.0911089	−	0.394487i
$196$	6.66600	+	2.13644i	0.476143	+	0.152603i
$197$		−	24.0786i		−	1.71553i	−0.514043	−	0.857764i	$-0.671853\pi$
$197$		−	24.0786i		−	1.71553i	0.514043	−	0.857764i	$-0.328147\pi$
$198$	−0.826087	−	11.8417i	−0.0587074	−	0.841556i
$199$	13.1750	+	7.60658i	0.933950	+	0.539216i	0.888059	−	0.459730i	$-0.152054\pi$
$199$	13.1750	+	7.60658i	0.933950	+	0.539216i	0.0458914	+	0.998946i	$0.485387\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−15.5631	−	3.59439i	−1.09774	−	0.253528i
$202$	−0.186797	+	0.107847i	−0.0131430	+	0.00758812i
$203$	−7.86842	+	9.75657i	−0.552255	+	0.684777i
$204$	−1.17503	+	1.25986i	−0.0822688	+	0.0882079i
$205$	−10.3313			−0.721573
$206$	−5.67674	+	9.83240i	−0.395517	+	0.685056i
$207$	−12.9307	−	19.1775i	−0.898749	−	1.33293i
$208$	2.82686	−	1.63209i	0.196007	−	0.113165i
$209$	−11.2133	+	19.4220i	−0.775640	+	1.34345i
$210$	−3.60570	+	2.82824i	−0.248817	+	0.195167i
$211$	−3.11109	−	5.38856i	−0.214176	−	0.370964i	0.738841	−	0.673879i	$-0.235373\pi$
$211$	−3.11109	−	5.38856i	−0.214176	−	0.370964i	−0.953017	+	0.302916i	$0.902040\pi$
$212$	−8.82289	−	5.09390i	−0.605959	−	0.349850i
$213$	−1.07172	+	4.64039i	−0.0734332	+	0.317954i
$214$	−3.19600	−	5.53564i	−0.218474	−	0.378409i
$215$	5.10292	+	8.83852i	0.348016	+	0.602782i
$216$	3.27105	−	4.03736i	0.222567	−	0.274707i
$217$	−14.5872	−	2.28045i	−0.990243	−	0.154807i
$218$	−1.06636	−	0.615666i	−0.0722233	−	0.0416982i
$219$	18.6538	+	17.3978i	1.26051	+	1.17564i
$220$		−	3.95684i		−	0.266770i
$221$			3.24670i			0.218396i
$222$	16.7479	−	5.11883i	1.12404	−	0.343553i
$223$	4.37102	+	2.52361i	0.292705	+	0.168994i	0.639161	−	0.769073i	$-0.279282\pi$
$223$	4.37102	+	2.52361i	0.292705	+	0.168994i	−0.346456	+	0.938066i	$0.612615\pi$
$224$	−2.61400	−	0.408654i	−0.174655	−	0.0273043i
$225$	−0.208774	−	2.99273i	−0.0139183	−	0.199515i
$226$	4.22623	+	7.32005i	0.281125	+	0.486922i
$227$	−2.53981	−	4.39908i	−0.168573	−	0.291977i	0.769345	−	0.638833i	$-0.220583\pi$
$227$	−2.53981	−	4.39908i	−0.168573	−	0.291977i	−0.937918	+	0.346856i	$0.887249\pi$
$228$	−9.38820	+	2.86941i	−0.621749	+	0.190031i
$229$	25.6828	+	14.8280i	1.69716	+	0.979859i	0.948429	+	0.316991i	$0.102672\pi$
$229$	25.6828	+	14.8280i	1.69716	+	0.979859i	0.748736	+	0.662868i	$0.230661\pi$
$230$	−3.85494	−	6.67695i	−0.254187	−	0.440265i
$231$	2.55802	+	17.9512i	0.168306	+	1.18110i
$232$	2.36871	−	4.10273i	0.155514	−	0.269358i
$233$	15.8420	−	9.14639i	1.03784	−	0.599200i	0.118622	−	0.992939i	$-0.462152\pi$
$233$	15.8420	−	9.14639i	1.03784	−	0.599200i	0.919222	+	0.393740i	$0.128819\pi$
$234$	−0.681476	−	9.76879i	−0.0445495	−	0.638606i
$235$	2.36963	−	4.10432i	0.154578	−	0.267737i
$236$	3.40720			0.221790
$237$	3.10772	+	0.717744i	0.201868	+	0.0466225i
$238$	1.65201	−	2.04844i	0.107084	−	0.132780i
$239$	6.05638	−	3.49665i	0.391755	−	0.226180i	−0.291165	−	0.956673i	$-0.594043\pi$
$239$	6.05638	−	3.49665i	0.391755	−	0.226180i	0.682920	+	0.730493i	$0.260710\pi$
$240$	1.18136	−	1.26664i	0.0762565	−	0.0817615i
$241$	4.77687	−	2.75793i	0.307705	−	0.177654i	−0.338194	−	0.941076i	$-0.609816\pi$
$241$	4.77687	−	2.75793i	0.307705	−	0.177654i	0.645899	+	0.763423i	$0.276483\pi$
$242$	−4.03273	−	2.32830i	−0.259234	−	0.149669i
$243$	−6.58212	−	14.1307i	−0.422243	−	0.906483i
$244$			6.29939i			0.403277i
$245$	5.18322	−	4.70471i	0.331143	−	0.300573i
$246$	−17.1130	+	5.23041i	−1.09108	+	0.333479i
$247$	−9.25035	+	16.0221i	−0.588586	+	1.01946i
$248$	5.58041			0.354356
$249$	1.86615	−	2.00087i	0.118262	−	0.126800i
$250$		−	1.00000i		−	0.0632456i
$251$	−0.276363			−0.0174439			−0.00872195	−	0.999962i	$-0.502776\pi$
$251$	−0.276363			−0.0174439			−0.00872195	+	0.999962i	$0.502776\pi$
$252$	−4.54067	+	6.51017i	−0.286035	+	0.410102i
$253$	−30.5068			−1.91794
$254$		−	20.5777i		−	1.29116i
$255$	0.503554	+	1.64754i	0.0315338	+	0.103173i
$256$	1.00000			0.0625000
$257$	−8.24562	+	14.2818i	−0.514348	+	0.890876i	0.485514	+	0.874229i	$0.338633\pi$
$257$	−8.24562	+	14.2818i	−0.514348	+	0.890876i	−0.999861	+	0.0166473i	$0.994701\pi$
$258$	12.9272	+	12.0568i	0.804810	+	0.750622i
$259$	−24.9550	+	9.63671i	−1.55063	+	0.598796i
$260$		−	3.26418i		−	0.202436i
$261$	−7.94546	−	11.7838i	−0.491812	−	0.729401i
$262$	−4.33807	−	2.50459i	−0.268007	−	0.154734i
$263$	−2.17310	+	1.25464i	−0.133999	+	0.0773646i	−0.565501	−	0.824748i	$-0.691317\pi$
$263$	−2.17310	+	1.25464i	−0.133999	+	0.0773646i	0.431502	+	0.902112i	$0.357984\pi$
$264$	−2.00321	−	6.55415i	−0.123289	−	0.403380i
$265$	−8.82289	+	5.09390i	−0.541986	+	0.312916i
$266$	13.9888	−	5.40196i	0.857708	−	0.331215i
$267$	−7.01463	−	22.9506i	−0.429288	−	1.40455i
$268$	−9.22190			−0.563317
$269$	13.3603	−	23.1408i	0.814594	−	1.41092i	−0.0950245	−	0.995475i	$-0.530293\pi$
$269$	13.3603	−	23.1408i	0.814594	−	1.41092i	0.909619	−	0.415444i	$-0.136374\pi$
$270$	−1.86093	−	4.85149i	−0.113253	−	0.295252i
$271$	12.9500	−	7.47668i	0.786656	−	0.454176i	−0.0521278	−	0.998640i	$-0.516600\pi$
$271$	12.9500	−	7.47668i	0.786656	−	0.454176i	0.838784	+	0.544464i	$0.183267\pi$
$272$	−0.497322	+	0.861388i	−0.0301546	+	0.0522293i
$273$	2.11023	+	14.8087i	0.127717	+	0.896266i
$274$	−4.61836	−	7.99924i	−0.279005	−	0.483252i
$275$	−3.42673	−	1.97842i	−0.206639	−	0.119303i
$276$	−9.76567	−	9.10814i	−0.587824	−	0.548246i
$277$	7.11465	+	12.3229i	0.427478	+	0.740414i	0.996648	−	0.0818060i	$-0.0260688\pi$
$277$	7.11465	+	12.3229i	0.427478	+	0.740414i	−0.569170	+	0.822220i	$0.692735\pi$
$278$	−6.51936	−	11.2919i	−0.391005	−	0.677241i
$279$	7.34136	−	15.0457i	0.439516	−	0.900762i
$280$	−1.66090	+	2.05946i	−0.0992581	+	0.123077i
$281$	21.5588	+	12.4470i	1.28609	+	0.742524i	0.977954	−	0.208819i	$-0.0669620\pi$
$281$	21.5588	+	12.4470i	1.28609	+	0.742524i	0.308135	+	0.951343i	$0.400295\pi$
$282$	1.84721	−	7.99811i	0.109999	−	0.476280i
$283$			17.1797i			1.02122i	0.859811	+	0.510612i	$0.170581\pi$
$283$			17.1797i			1.02122i	−0.859811	+	0.510612i	$0.829419\pi$
$284$			2.74965i			0.163162i
$285$	−2.20912	+	9.56513i	−0.130857	+	0.566589i
$286$	−11.1854	−	6.45792i	−0.661409	−	0.381865i
$287$	25.4990	−	9.84677i	1.50516	−	0.581236i
$288$	1.31556	−	2.69616i	0.0775201	−	0.158873i
$289$	8.00534	+	13.8657i	0.470902	+	0.815627i
$290$	−2.36871	−	4.10273i	−0.139096	−	0.240921i
$291$	1.13640	+	1.05988i	0.0666168	+	0.0621315i
$292$	12.7539	+	7.36348i	0.746366	+	0.430915i
$293$	3.98706	+	6.90578i	0.232926	+	0.403440i	0.958668	−	0.284527i	$-0.0918366\pi$
$293$	3.98706	+	6.90578i	0.232926	+	0.403440i	−0.725742	+	0.687967i	$0.758503\pi$
$294$	6.20370	−	10.4170i	0.361807	−	0.607532i
$295$	1.70360	−	2.95072i	0.0991875	−	0.171798i
$296$	8.75634	−	5.05548i	0.508952	−	0.293844i
$297$	−20.3064	−	3.22139i	−1.17830	−	0.186924i
$298$	−11.0331	+	19.1098i	−0.639128	+	1.10700i
$299$	−25.1664			−1.45541
$300$	−0.506266	−	1.65641i	−0.0292293	−	0.0956329i
$301$	−21.0186	−	16.9509i	−1.21149	−	0.977035i
$302$	−4.79589	+	2.76891i	−0.275973	+	0.159333i
$303$	0.109199	+	0.357279i	0.00627331	+	0.0205252i
$304$	−4.90846	+	2.83390i	−0.281519	+	0.162535i
$305$	5.45543	+	3.14969i	0.312377	+	0.180351i
$306$	1.66819	+	2.47407i	0.0953638	+	0.141433i
$307$		−	15.5665i		−	0.888429i	−0.895920	−	0.444215i	$-0.853483\pi$
$307$		−	15.5665i		−	0.888429i	0.895920	−	0.444215i	$-0.146517\pi$
$308$	3.77125	+	9.76595i	0.214887	+	0.556467i
$309$	14.3808	+	13.4126i	0.818096	+	0.763014i
$310$	2.79020	−	4.83278i	0.158473	−	0.274483i
$311$	−20.1669			−1.14356			−0.571779	−	0.820408i	$-0.693747\pi$
$311$	−20.1669			−1.14356			−0.571779	+	0.820408i	$0.693747\pi$
$312$	−1.65254	−	5.40682i	−0.0935567	−	0.306101i
$313$			6.67203i			0.377125i	0.982061	+	0.188563i	$0.0603829\pi$
$313$			6.67203i			0.377125i	−0.982061	+	0.188563i	$0.939617\pi$
$314$	16.7972			0.947921
$315$	3.36764	+	7.18742i	0.189745	+	0.404965i
$316$	1.84147			0.103591
$317$			25.5416i			1.43456i	0.696786	+	0.717279i	$0.254613\pi$
$317$			25.5416i			1.43456i	−0.696786	+	0.717279i	$0.745387\pi$
$318$	−12.0355	+	12.9043i	−0.674915	+	0.723638i
$319$	−18.7453			−1.04953
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−10.5878	+	3.23605i	−0.590953	+	0.180619i
$322$	15.8782	+	12.8054i	0.884858	+	0.713615i
$323$		−	5.63745i		−	0.313676i
$324$	−5.53861	−	7.09393i	−0.307700	−	0.394107i
$325$	−2.82686	−	1.63209i	−0.156806	−	0.0905320i
$326$	1.49779	−	0.864749i	0.0829549	−	0.0478940i
$327$	−1.45465	+	1.55966i	−0.0804422	+	0.0862494i
$328$	−8.94721	+	5.16567i	−0.494027	+	0.285227i
$329$	−1.93672	+	12.3884i	−0.106775	+	0.682997i
$330$	−6.67767	−	1.54224i	−0.367594	−	0.0848977i
$331$	1.81278			0.0996394			0.0498197	−	0.998758i	$-0.484135\pi$
$331$	1.81278			0.0996394			0.0498197	+	0.998758i	$0.484135\pi$
$332$	0.789829	−	1.36802i	0.0433475	−	0.0750801i
$333$	−2.11091	−	30.2593i	−0.115677	−	1.65820i
$334$	0.642629	−	0.371022i	0.0351631	−	0.0203014i
$335$	−4.61095	+	7.98640i	−0.251923	+	0.436344i
$336$	−1.70850	+	4.25218i	−0.0932065	+	0.231975i
$337$	7.15488	+	12.3926i	0.389751	+	0.675069i	0.992416	−	0.122926i	$-0.0392277\pi$
$337$	7.15488	+	12.3926i	0.389751	+	0.675069i	−0.602665	+	0.797995i	$0.705894\pi$
$338$	2.03096	+	1.17257i	0.110470	+	0.0637797i
$339$	14.0007	−	4.27919i	0.760416	−	0.232414i
$340$	0.497322	+	0.861388i	0.0269711	+	0.0467153i
$341$	−11.0404	−	19.1225i	−0.597871	−	1.03554i
$342$	1.18329	+	16.9622i	0.0639850	+	0.917209i
$343$	−8.30875	+	16.5519i	−0.448630	+	0.893717i
$344$	8.83852	+	5.10292i	0.476541	+	0.275131i
$345$	−12.7707	+	3.90324i	−0.687552	+	0.210144i
$346$		−	0.964238i		−	0.0518378i
$347$			6.00500i			0.322365i	0.986925	+	0.161183i	$0.0515308\pi$
$347$			6.00500i			0.322365i	−0.986925	+	0.161183i	$0.948469\pi$
$348$	−6.00064	−	5.59661i	−0.321668	−	0.300010i
$349$	11.6157	+	6.70633i	0.621775	+	0.358982i	0.777560	−	0.628809i	$-0.216457\pi$
$349$	11.6157	+	6.70633i	0.621775	+	0.358982i	−0.155785	+	0.987791i	$0.549791\pi$
$350$	0.953096	+	2.46812i	0.0509451	+	0.131926i
$351$	−16.7517	−	2.65747i	−0.894139	−	0.141845i
$352$	−1.97842	−	3.42673i	−0.105450	−	0.182645i
$353$	−0.252692	−	0.437675i	−0.0134494	−	0.0232951i	0.859222	−	0.511602i	$-0.170948\pi$
$353$	−0.252692	−	0.437675i	−0.0134494	−	0.0232951i	−0.872672	+	0.488307i	$0.837615\pi$
$354$	1.32801	−	5.75008i	0.0705831	−	0.305614i
$355$	2.38127	+	1.37483i	0.126385	+	0.0729683i
$356$	−6.92781	−	11.9993i	−0.367173	−	0.635963i
$357$	−2.81310	−	3.58639i	−0.148885	−	0.189812i
$358$	0.107391	−	0.186006i	0.00567578	−	0.00983073i
$359$	−11.2748	+	6.50952i	−0.595062	+	0.343559i	−0.767097	−	0.641532i	$-0.778299\pi$
$359$	−11.2748	+	6.50952i	−0.595062	+	0.343559i	0.172034	+	0.985091i	$0.444966\pi$
$360$	−1.67717	−	2.48739i	−0.0883945	−	0.131097i
$361$	6.56197	−	11.3657i	0.345367	−	0.598193i
$362$	−11.1757			−0.587380
$363$	−5.50112	+	5.89826i	−0.288734	+	0.309578i
$364$	3.11107	+	8.05637i	0.163065	+	0.422269i
$365$	12.7539	−	7.36348i	0.667570	−	0.385422i
$366$	10.6310	+	2.45529i	0.555692	+	0.128340i
$367$	−27.7376	+	16.0143i	−1.44789	+	0.835942i	−0.998356	−	0.0573200i	$-0.981744\pi$
$367$	−27.7376	+	16.0143i	−1.44789	+	0.835942i	−0.449537	+	0.893262i	$0.648411\pi$
$368$	−6.67695	−	3.85494i	−0.348060	−	0.200952i
$369$	2.15692	+	30.9189i	0.112285	+	1.60957i
$370$		−	10.1110i		−	0.525643i
$371$	16.9210	−	20.9814i	0.878493	−	1.08930i
$372$	2.17506	−	9.41764i	0.112771	−	0.488282i
$373$	−3.40038	+	5.88964i	−0.176065	+	0.304954i	−0.940529	−	0.339712i	$-0.889670\pi$
$373$	−3.40038	+	5.88964i	−0.176065	+	0.304954i	0.764464	+	0.644666i	$0.223004\pi$
$374$	3.93565			0.203508
$375$	−1.68763	−	0.389766i	−0.0871486	−	0.0201274i
$376$		−	4.73926i		−	0.244409i
$377$	−15.4638			−0.796426
$378$	9.21693	+	10.2004i	0.474068	+	0.524652i
$379$	2.14646			0.110256			0.0551281	−	0.998479i	$-0.482443\pi$
$379$	2.14646			0.110256			0.0551281	+	0.998479i	$0.482443\pi$
$380$			5.66780i			0.290752i
$381$	−34.7275	−	8.02050i	−1.77914	−	0.410903i
$382$	18.8822			0.966096
$383$	0.355273	−	0.615351i	0.0181536	−	0.0314430i	−0.856806	−	0.515639i	$-0.827555\pi$
$383$	0.355273	−	0.615351i	0.0181536	−	0.0314430i	0.874959	+	0.484196i	$0.160888\pi$
$384$	0.389766	−	1.68763i	0.0198902	−	0.0861213i
$385$	10.3432	+	1.61698i	0.527138	+	0.0824088i
$386$			5.89018i			0.299802i
$387$	25.3859	−	17.1169i	1.29044	−	0.870101i
$388$	0.776974	+	0.448586i	0.0394449	+	0.0227735i
$389$	16.9870	−	9.80747i	0.861277	−	0.497258i	−0.00316299	−	0.999995i	$-0.501007\pi$
$389$	16.9870	−	9.80747i	0.861277	−	0.497258i	0.864440	+	0.502737i	$0.167673\pi$
$390$	−5.50871	−	1.27227i	−0.278944	−	0.0644237i
$391$	6.64119	−	3.83429i	0.335859	−	0.193908i
$392$	2.13644	−	6.66600i	0.107907	−	0.336684i
$393$	−5.91764	+	6.34484i	−0.298505	+	0.320055i
$394$	−24.0786			−1.21306
$395$	0.920736	−	1.59476i	0.0463273	−	0.0802412i
$396$	−11.8417	+	0.826087i	−0.595070	+	0.0415124i
$397$	20.7322	−	11.9697i	1.04052	−	0.600743i	0.120538	−	0.992709i	$-0.461538\pi$
$397$	20.7322	−	11.9697i	1.04052	−	0.600743i	0.919980	+	0.391965i	$0.128205\pi$
$398$	7.60658	−	13.1750i	0.381284	−	0.660402i
$399$	−3.66412	−	25.7134i	−0.183436	−	1.28728i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	0.585108	+	0.337812i	0.0292189	+	0.0168696i	0.514538	−	0.857467i	$-0.327963\pi$
$401$	0.585108	+	0.337812i	0.0292189	+	0.0168696i	−0.485319	+	0.874337i	$0.661297\pi$
$402$	−3.59439	+	15.5631i	−0.179272	+	0.776218i
$403$	−9.10772	−	15.7750i	−0.453688	−	0.785810i
$404$	0.107847	+	0.186797i	0.00536561	+	0.00929351i
$405$	−8.91283	+	1.24961i	−0.442882	+	0.0620936i
$406$	9.75657	+	7.86842i	0.484210	+	0.390503i
$407$	−34.6475	−	20.0037i	−1.71741	−	0.991548i
$408$	1.25986	+	1.17503i	0.0623724	+	0.0581729i
$409$		−	30.3557i		−	1.50099i	−0.660874	−	0.750497i	$-0.729814\pi$
$409$		−	30.3557i		−	1.50099i	0.660874	−	0.750497i	$-0.270186\pi$
$410$			10.3313i			0.510229i
$411$	−15.2998	+	4.67624i	−0.754684	+	0.230662i
$412$	9.83240	+	5.67674i	0.484408	+	0.279673i
$413$	−1.39237	+	8.90643i	−0.0685138	+	0.438257i
$414$	−19.1775	+	12.9307i	−0.942521	+	0.635512i
$415$	−0.789829	−	1.36802i	−0.0387712	−	0.0671537i
$416$	−1.63209	−	2.82686i	−0.0800197	−	0.138598i
$417$	−21.5975	+	6.60105i	−1.05763	+	0.323255i
$418$	19.4220	+	11.2133i	0.949961	+	0.548460i
$419$	5.87786	+	10.1808i	0.287152	+	0.497363i	0.973129	−	0.230261i	$-0.0739581\pi$
$419$	5.87786	+	10.1808i	0.287152	+	0.497363i	−0.685976	+	0.727624i	$0.740625\pi$
$420$	2.82824	+	3.60570i	0.138004	+	0.175940i
$421$	14.4557	−	25.0380i	0.704526	−	1.22028i	−0.262336	−	0.964977i	$-0.584493\pi$
$421$	14.4557	−	25.0380i	0.704526	−	1.22028i	0.966862	−	0.255299i	$-0.0821739\pi$
$422$	−5.38856	+	3.11109i	−0.262311	+	0.151445i
$423$	−12.7778	−	6.23478i	−0.621280	−	0.303146i
$424$	−5.09390	+	8.82289i	−0.247382	+	0.428477i
$425$	0.994645			0.0482474
$426$	4.64039	+	1.07172i	0.224828	+	0.0519251i
$427$	−16.4666	−	2.57427i	−0.796875	−	0.124577i
$428$	−5.53564	+	3.19600i	−0.267575	+	0.154485i
$429$	−15.2583	+	16.3598i	−0.736676	+	0.789857i
$430$	8.83852	−	5.10292i	0.426231	−	0.246085i
$431$	17.2762	+	9.97444i	0.832167	+	0.480452i	0.854594	−	0.519297i	$-0.173806\pi$
$431$	17.2762	+	9.97444i	0.832167	+	0.480452i	−0.0224273	+	0.999748i	$0.507139\pi$
$432$	−4.03736	−	3.27105i	−0.194247	−	0.157378i
$433$		−	28.8157i		−	1.38479i	−0.721517	−	0.692397i	$-0.756555\pi$
$433$		−	28.8157i		−	1.38479i	0.721517	−	0.692397i	$-0.243445\pi$
$434$	−2.28045	+	14.5872i	−0.109465	+	0.700208i
$435$	−7.84713	+	2.39840i	−0.376241	+	0.114994i
$436$	−0.615666	+	1.06636i	−0.0294851	+	0.0510696i
$437$	43.6980			2.09036
$438$	17.3978	−	18.6538i	0.831301	−	0.891313i
$439$		−	8.17520i		−	0.390181i	−0.980785	−	0.195091i	$-0.937500\pi$
$439$		−	8.17520i		−	0.390181i	0.980785	−	0.195091i	$-0.0625001\pi$
$440$	−3.95684			−0.188635
$441$	−15.1620	−	14.5297i	−0.722001	−	0.691892i
$442$	3.24670			0.154430
$443$		−	26.2700i		−	1.24813i	−0.781374	−	0.624063i	$-0.785481\pi$
$443$		−	26.2700i		−	1.24813i	0.781374	−	0.624063i	$-0.214519\pi$
$444$	−5.11883	−	16.7479i	−0.242929	−	0.794820i
$445$	−13.8556			−0.656820
$446$	2.52361	−	4.37102i	0.119496	−	0.206974i
$447$	27.9499	+	26.0680i	1.32199	+	1.23298i
$448$	−0.408654	+	2.61400i	−0.0193071	+	0.123500i
$449$		−	6.39690i		−	0.301888i	−0.988542	−	0.150944i	$-0.951769\pi$
$449$		−	6.39690i		−	0.301888i	0.988542	−	0.150944i	$-0.0482314\pi$
$450$	−2.99273	+	0.208774i	−0.141078	+	0.00984171i
$451$	35.4027	+	20.4398i	1.66705	+	0.962471i
$452$	7.32005	−	4.22623i	0.344306	−	0.198785i
$453$	2.80361	+	9.17290i	0.131725	+	0.430980i
$454$	−4.39908	+	2.53981i	−0.206459	+	0.119199i
$455$	8.53256	+	1.33392i	0.400013	+	0.0625350i
$456$	2.86941	+	9.38820i	0.134373	+	0.439643i
$457$	−10.3267			−0.483065			−0.241532	−	0.970393i	$-0.577650\pi$
$457$	−10.3267			−0.483065			−0.241532	+	0.970393i	$0.577650\pi$
$458$	14.8280	−	25.6828i	0.692865	−	1.20008i
$459$	4.82551	−	1.85096i	0.225235	−	0.0863956i
$460$	−6.67695	+	3.85494i	−0.311314	+	0.179737i
$461$	−4.00379	+	6.93476i	−0.186475	+	0.322984i	−0.944073	−	0.329738i	$-0.893040\pi$
$461$	−4.00379	+	6.93476i	−0.186475	+	0.322984i	0.757598	+	0.652722i	$0.226373\pi$
$462$	17.9512	−	2.55802i	0.835165	−	0.119010i
$463$	15.2865	+	26.4770i	0.710425	+	1.23049i	0.964698	+	0.263359i	$0.0848304\pi$
$463$	15.2865	+	26.4770i	0.710425	+	1.23049i	−0.254273	+	0.967132i	$0.581836\pi$
$464$	−4.10273	−	2.36871i	−0.190465	−	0.109965i
$465$	−7.06839	−	6.59247i	−0.327789	−	0.305719i
$466$	−9.14639	−	15.8420i	−0.423698	−	0.733867i
$467$	−3.61017	−	6.25300i	−0.167059	−	0.289354i	0.770326	−	0.637651i	$-0.220094\pi$
$467$	−3.61017	−	6.25300i	−0.167059	−	0.289354i	−0.937385	+	0.348296i	$0.886760\pi$
$468$	−9.76879	+	0.681476i	−0.451562	+	0.0315012i
$469$	3.76856	−	24.1061i	0.174016	−	1.11311i
$470$	−4.10432	−	2.36963i	−0.189318	−	0.109303i
$471$	6.54698	−	28.3474i	0.301669	−	1.30618i
$472$		−	3.40720i		−	0.156829i
$473$		−	40.3829i		−	1.85681i
$474$	0.717744	−	3.10772i	0.0329671	−	0.142742i
$475$	4.90846	+	2.83390i	0.225215	+	0.130028i
$476$	−2.04844	−	1.65201i	−0.0938899	−	0.0757198i
$477$	17.0866	+	25.3410i	0.782344	+	1.16029i
$478$	−3.49665	−	6.05638i	−0.159933	−	0.277012i
$479$	9.13594	+	15.8239i	0.417432	+	0.723013i	0.995680	−	0.0928475i	$-0.0295969\pi$
$479$	9.13594	+	15.8239i	0.417432	+	0.723013i	−0.578248	+	0.815861i	$0.696264\pi$
$480$	−1.26664	−	1.18136i	−0.0578141	−	0.0539215i
$481$	−28.5822	−	16.5020i	−1.30324	−	0.752425i
$482$	−2.75793	−	4.77687i	−0.125620	−	0.217581i
$483$	27.7995	−	21.8054i	1.26492	−	0.992179i
$484$	−2.32830	+	4.03273i	−0.105832	+	0.183306i
$485$	0.776974	−	0.448586i	0.0352806	−	0.0203692i
$486$	−14.1307	+	6.58212i	−0.640980	+	0.298571i
$487$	−19.2868	+	33.4057i	−0.873967	+	1.51375i	−0.0161074	+	0.999870i	$0.505127\pi$
$487$	−19.2868	+	33.4057i	−0.873967	+	1.51375i	−0.857859	+	0.513885i	$0.828206\pi$
$488$	6.29939			0.285160
$489$	−0.875586	−	2.86476i	−0.0395954	−	0.129549i
$490$	−4.70471	−	5.18322i	−0.212537	−	0.234154i
$491$	21.3449	−	12.3235i	0.963282	−	0.556151i	0.0661005	−	0.997813i	$-0.478944\pi$
$491$	21.3449	−	12.3235i	0.963282	−	0.556151i	0.897182	+	0.441662i	$0.145611\pi$
$492$	5.23041	+	17.1130i	0.235805	+	0.771512i
$493$	4.08076	−	2.35603i	0.183788	−	0.106110i
$494$	16.0221	+	9.25035i	0.720867	+	0.416193i
$495$	−5.20546	+	10.6683i	−0.233968	+	0.479504i
$496$		−	5.58041i		−	0.250568i
$497$	−7.18760	−	1.12366i	−0.322408	−	0.0504029i
$498$	−2.00087	−	1.86615i	−0.0896609	−	0.0836240i
$499$	−5.25899	+	9.10884i	−0.235425	+	0.407768i	−0.959396	−	0.282062i	$-0.908981\pi$
$499$	−5.25899	+	9.10884i	−0.235425	+	0.407768i	0.723971	+	0.689830i	$0.242315\pi$
$500$	−1.00000			−0.0447214
$501$	−0.375671	−	1.22913i	−0.0167838	−	0.0549134i
$502$			0.276363i			0.0123347i
$503$	−19.4315			−0.866406			−0.433203	−	0.901296i	$-0.642617\pi$
$503$	−19.4315			−0.866406			−0.433203	+	0.901296i	$0.642617\pi$
$504$	6.51017	+	4.54067i	0.289986	+	0.202258i
$505$	0.215695			0.00959830
$506$			30.5068i			1.35619i
$507$	2.77047	−	2.97047i	0.123041	−	0.131923i
$508$	−20.5777			−0.912988
$509$	11.6664	−	20.2068i	0.517105	−	0.895652i	−0.482698	−	0.875787i	$-0.660343\pi$
$509$	11.6664	−	20.2068i	0.517105	−	0.895652i	0.999803	−	0.0198652i	$-0.00632372\pi$
$510$	1.64754	−	0.503554i	0.0729543	−	0.0222978i
$511$	−24.4601	+	30.3296i	−1.08205	+	1.34170i
$512$		−	1.00000i		−	0.0441942i
$513$	29.0870	+	4.61433i	1.28422	+	0.203728i
$514$	14.2818	+	8.24562i	0.629945	+	0.363699i
$515$	9.83240	−	5.67674i	0.433268	−	0.250147i
$516$	12.0568	−	12.9272i	0.530770	−	0.569087i
$517$	−16.2402	+	9.37626i	−0.714241	+	0.412367i
$518$	9.63671	+	24.9550i	0.423413	+	1.09646i
$519$	−1.62727	−	0.375828i	−0.0714294	−	0.0164970i
$520$	−3.26418			−0.143144
$521$	11.8637	−	20.5486i	0.519759	−	0.900249i	−0.479977	−	0.877281i	$-0.659355\pi$
$521$	11.8637	−	20.5486i	0.519759	−	0.900249i	0.999736	−	0.0229682i	$-0.00731164\pi$
$522$	−11.7838	+	7.94546i	−0.515764	+	0.347763i
$523$	15.7239	−	9.07818i	0.687556	−	0.396961i	−0.115140	−	0.993349i	$-0.536732\pi$
$523$	15.7239	−	9.07818i	0.687556	−	0.396961i	0.802696	+	0.596388i	$0.203398\pi$
$524$	−2.50459	+	4.33807i	−0.109413	+	0.189510i
$525$	4.53675	−	0.646481i	0.198000	−	0.0282147i
$526$	1.25464	+	2.17310i	0.0547050	+	0.0947519i
$527$	4.80689	+	2.77526i	0.209392	+	0.120892i
$528$	−6.55415	+	2.00321i	−0.285233	+	0.0871787i
$529$	18.2211	+	31.5598i	0.792221	+	1.37217i
$530$	5.09390	+	8.82289i	0.221265	+	0.383242i
$531$	−9.18638	−	4.48238i	−0.398655	−	0.194519i
$532$	−5.40196	−	13.9888i	−0.234205	−	0.606491i
$533$	29.2053	+	16.8617i	1.26502	+	0.730360i
$534$	−22.9506	+	7.01463i	−0.993170	+	0.303553i
$535$			6.39201i			0.276351i
$536$			9.22190i			0.398325i
$537$	−0.272052	−	0.253734i	−0.0117399	−	0.0109494i
$538$	−23.1408	−	13.3603i	−0.997670	−	0.576005i
$539$	−27.0694	+	5.86716i	−1.16596	+	0.252717i
$540$	−4.85149	+	1.86093i	−0.208775	+	0.0800817i
$541$	5.56494	+	9.63875i	0.239255	+	0.414402i	0.960501	−	0.278277i	$-0.0897634\pi$
$541$	5.56494	+	9.63875i	0.239255	+	0.414402i	−0.721245	+	0.692680i	$0.756430\pi$
$542$	−7.47668	−	12.9500i	−0.321151	−	0.556250i
$543$	−4.35590	+	18.8604i	−0.186930	+	0.809376i
$544$	0.861388	+	0.497322i	0.0369317	+	0.0213225i
$545$	0.615666	+	1.06636i	0.0263722	+	0.0456781i
$546$	14.8087	−	2.11023i	0.633756	−	0.0903094i
$547$	−15.8512	+	27.4550i	−0.677747	+	1.17389i	0.297911	+	0.954594i	$0.403710\pi$
$547$	−15.8512	+	27.4550i	−0.677747	+	1.17389i	−0.975658	+	0.219299i	$0.929623\pi$
$548$	−7.99924	+	4.61836i	−0.341711	+	0.197287i
$549$	8.28722	−	16.9842i	0.353690	−	0.724867i
$550$	−1.97842	+	3.42673i	−0.0843602	+	0.146116i
$551$	26.8508			1.14388
$552$	−9.10814	+	9.76567i	−0.387668	+	0.415654i
$553$	−0.752524	+	4.81361i	−0.0320006	+	0.204696i
$554$	12.3229	−	7.11465i	0.523552	−	0.302273i
$555$	−17.0635	−	3.94091i	−0.724306	−	0.167282i
$556$	−11.2919	+	6.51936i	−0.478881	+	0.276482i
$557$	28.2949	+	16.3360i	1.19889	+	0.692181i	0.960308	−	0.278941i	$-0.0899835\pi$
$557$	28.2949	+	16.3360i	1.19889	+	0.692181i	0.238584	+	0.971122i	$0.423317\pi$
$558$	−15.0457	−	7.34136i	−0.636935	−	0.310785i
$559$		−	33.3137i		−	1.40902i
$560$	2.05946	+	1.66090i	0.0870283	+	0.0701860i
$561$	1.53398	−	6.64191i	0.0647649	−	0.280422i
$562$	12.4470	−	21.5588i	0.525044	−	0.909402i
$563$	−24.4996			−1.03253			−0.516267	−	0.856428i	$-0.672679\pi$
$563$	−24.4996			−1.03253			−0.516267	+	0.856428i	$0.672679\pi$
$564$	−7.99811	−	1.84721i	−0.336781	−	0.0777814i
$565$		−	8.45246i		−	0.355598i
$566$	17.1797			0.722115
$567$	20.8069	−	11.5790i	0.873808	−	0.486271i
$568$	2.74965			0.115373
$569$			21.3621i			0.895548i	0.894147	+	0.447774i	$0.147783\pi$
$569$			21.3621i			0.895548i	−0.894147	+	0.447774i	$0.852217\pi$
$570$	9.56513	+	2.20912i	0.400639	+	0.0925297i
$571$	−16.4486			−0.688354			−0.344177	−	0.938905i	$-0.611842\pi$
$571$	−16.4486			−0.688354			−0.344177	+	0.938905i	$0.611842\pi$
$572$	−6.45792	+	11.1854i	−0.270019	+	0.467687i
$573$	7.35963	−	31.8661i	0.307453	−	1.33122i
$574$	−9.84677	−	25.4990i	−0.410996	−	1.06431i
$575$			7.70987i			0.321524i
$576$	−2.69616	−	1.31556i	−0.112340	−	0.0548150i
$577$	17.2606	+	9.96542i	0.718569	+	0.414866i	0.814226	−	0.580549i	$-0.197162\pi$
$577$	17.2606	+	9.96542i	0.718569	+	0.414866i	−0.0956570	+	0.995414i	$0.530495\pi$
$578$	13.8657	−	8.00534i	0.576735	−	0.332978i
$579$	9.94043	+	2.29579i	0.413110	+	0.0954100i
$580$	−4.10273	+	2.36871i	−0.170357	+	0.0983555i
$581$	3.25325	+	2.62366i	0.134968	+	0.108848i
$582$	1.05988	−	1.13640i	0.0439336	−	0.0471052i
$583$	40.3115			1.66953
$584$	7.36348	−	12.7539i	0.304703	−	0.527761i
$585$	−4.29422	+	8.80076i	−0.177544	+	0.363867i
$586$	6.90578	−	3.98706i	0.285275	−	0.164704i
$587$	−1.94532	+	3.36939i	−0.0802918	+	0.139070i	−0.903375	−	0.428851i	$-0.858919\pi$
$587$	−1.94532	+	3.36939i	−0.0802918	+	0.139070i	0.823083	+	0.567920i	$0.192252\pi$
$588$	−10.4170	−	6.20370i	−0.429590	−	0.255836i
$589$	15.8143	+	27.3912i	0.651618	+	1.12863i
$590$	−2.95072	−	1.70360i	−0.121479	−	0.0701362i
$591$	−9.38502	+	40.6357i	−0.386048	+	1.67153i
$592$	−5.05548	−	8.75634i	−0.207779	−	0.359883i
$593$	7.52066	+	13.0262i	0.308836	+	0.534920i	0.978108	−	0.208097i	$-0.0667271\pi$
$593$	7.52066	+	13.0262i	0.308836	+	0.534920i	−0.669272	+	0.743018i	$0.733394\pi$
$594$	−3.22139	+	20.3064i	−0.132175	+	0.833183i
$595$	−2.45490	+	0.947992i	−0.100641	+	0.0388639i
$596$	19.1098	+	11.0331i	0.782769	+	0.451932i
$597$	−19.2697	−	17.9722i	−0.788655	−	0.735555i
$598$			25.1664i			1.02913i
$599$		−	27.3275i		−	1.11657i	−0.829649	−	0.558286i	$-0.811459\pi$
$599$		−	27.3275i		−	1.11657i	0.829649	−	0.558286i	$-0.188541\pi$
$600$	−1.65641	+	0.506266i	−0.0676227	+	0.0206682i
$601$	10.2307	+	5.90670i	0.417319	+	0.240939i	0.693930	−	0.720043i	$-0.255878\pi$
$601$	10.2307	+	5.90670i	0.417319	+	0.240939i	−0.276610	+	0.960982i	$0.589211\pi$
$602$	−16.9509	+	21.0186i	−0.690868	+	0.856653i
$603$	24.8638	+	12.1320i	1.01253	+	0.494052i
$604$	2.76891	+	4.79589i	0.112665	+	0.195142i
$605$	2.32830	+	4.03273i	0.0946589	+	0.163954i
$606$	0.357279	−	0.109199i	0.0145135	−	0.00443590i
$607$	0.641040	+	0.370104i	0.0260190	+	0.0150221i	0.512953	−	0.858417i	$-0.328551\pi$
$607$	0.641040	+	0.370104i	0.0260190	+	0.0150221i	−0.486934	+	0.873439i	$0.661885\pi$
$608$	2.83390	+	4.90846i	0.114930	+	0.199064i
$609$	17.0817	−	13.3986i	0.692187	−	0.542938i
$610$	3.14969	−	5.45543i	0.127527	−	0.220884i
$611$	−13.3972	+	7.73490i	−0.541994	+	0.312920i
$612$	2.47407	−	1.66819i	0.100008	−	0.0674324i
$613$	8.29710	−	14.3710i	0.335117	−	0.580439i	−0.648390	−	0.761308i	$-0.724558\pi$
$613$	8.29710	−	14.3710i	0.335117	−	0.580439i	0.983507	+	0.180869i	$0.0578909\pi$
$614$	−15.5665			−0.628214
$615$	17.4355	+	4.02681i	0.703065	+	0.162377i
$616$	9.76595	−	3.77125i	0.393482	−	0.151948i
$617$	−40.0027	+	23.0956i	−1.61045	+	0.929793i	−0.621184	+	0.783665i	$0.713348\pi$
$617$	−40.0027	+	23.0956i	−1.61045	+	0.929793i	−0.989266	+	0.146128i	$0.953319\pi$
$618$	13.4126	−	14.3808i	0.539532	−	0.578481i
$619$	15.6722	−	9.04833i	0.629917	−	0.363683i	−0.150803	−	0.988564i	$-0.548186\pi$
$619$	15.6722	−	9.04833i	0.629917	−	0.363683i	0.780720	+	0.624881i	$0.214852\pi$
$620$	−4.83278	−	2.79020i	−0.194089	−	0.112057i
$621$	14.3475	+	37.4044i	0.575747	+	1.50099i
$622$			20.1669i			0.808618i
$623$	34.1973	−	13.2057i	1.37009	−	0.529077i
$624$	−5.40682	+	1.65254i	−0.216446	+	0.0661546i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.67203			0.266668
$627$	26.4939	−	28.4065i	1.05806	−	1.13445i
$628$		−	16.7972i		−	0.670281i
$629$	10.0568			0.400991
$630$	7.18742	−	3.36764i	0.286354	−	0.134170i
$631$	8.36756			0.333107			0.166554	−	0.986032i	$-0.446736\pi$
$631$	8.36756			0.333107			0.166554	+	0.986032i	$0.446736\pi$
$632$		−	1.84147i		−	0.0732498i
$633$	3.15007	+	10.3065i	0.125204	+	0.409645i
$634$	25.5416			1.01439
$635$	−10.2889	+	17.8208i	−0.408301	+	0.707198i
$636$	12.9043	+	12.0355i	0.511689	+	0.477237i
$637$	−22.3307	+	4.84009i	−0.884775	+	0.191771i
$638$			18.7453i			0.742132i
$639$	3.61733	−	7.41352i	0.143100	−	0.293274i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	14.8984	−	8.60160i	0.588451	−	0.339743i	−0.176034	−	0.984384i	$-0.556327\pi$
$641$	14.8984	−	8.60160i	0.588451	−	0.339743i	0.764485	+	0.644642i	$0.222993\pi$
$642$	3.23605	+	10.5878i	0.127717	+	0.417867i
$643$	33.1046	−	19.1129i	1.30552	−	0.753740i	0.324172	−	0.945998i	$-0.394914\pi$
$643$	33.1046	−	19.1129i	1.30552	−	0.753740i	0.981344	+	0.192258i	$0.0615809\pi$
$644$	12.8054	−	15.8782i	0.504602	−	0.625689i
$645$	−5.16687	−	16.9051i	−0.203445	−	0.665636i
$646$	−5.63745			−0.221802
$647$	7.26184	−	12.5779i	0.285492	−	0.494487i	−0.687236	−	0.726434i	$-0.741176\pi$
$647$	7.26184	−	12.5779i	0.285492	−	0.494487i	0.972728	+	0.231947i	$0.0745096\pi$
$648$	−7.09393	+	5.53861i	−0.278676	+	0.217577i
$649$	−11.6755	+	6.74088i	−0.458305	+	0.264603i
$650$	−1.63209	+	2.82686i	−0.0640158	+	0.110879i
$651$	23.7289	+	9.53415i	0.930008	+	0.373673i
$652$	−0.864749	−	1.49779i	−0.0338662	−	0.0586580i
$653$	18.0580	+	10.4258i	0.706666	+	0.407994i	0.809825	−	0.586671i	$-0.199562\pi$
$653$	18.0580	+	10.4258i	0.706666	+	0.407994i	−0.103160	+	0.994665i	$0.532895\pi$
$654$	1.55966	+	1.45465i	0.0609875	+	0.0568812i
$655$	2.50459	+	4.33807i	0.0978623	+	0.169502i
$656$	5.16567	+	8.94721i	0.201686	+	0.349330i
$657$	−24.6996	−	36.6317i	−0.963622	−	1.42914i
$658$	12.3884	+	1.93672i	0.482952	+	0.0755011i
$659$	−19.3743	−	11.1857i	−0.754715	−	0.435735i	0.0726801	−	0.997355i	$-0.476845\pi$
$659$	−19.3743	−	11.1857i	−0.754715	−	0.435735i	−0.827395	+	0.561621i	$0.810178\pi$
$660$	−1.54224	+	6.67767i	−0.0600318	+	0.259928i
$661$		−	44.5340i		−	1.73217i	−0.499894	−	0.866086i	$-0.666628\pi$
$661$		−	44.5340i		−	1.73217i	0.499894	−	0.866086i	$-0.333372\pi$
$662$		−	1.81278i		−	0.0704557i
$663$	1.26545	−	5.47921i	0.0491461	−	0.212795i
$664$	−1.36802	−	0.789829i	−0.0530896	−	0.0306513i
$665$	−14.8156	−	2.31617i	−0.574526	−	0.0898171i
$666$	−30.2593	+	2.11091i	−1.17252	+	0.0817960i
$667$	18.2625	+	31.6316i	0.707126	+	1.22478i
$668$	−0.371022	−	0.642629i	−0.0143553	−	0.0248641i
$669$	−6.39304	−	5.96259i	−0.247169	−	0.230527i
$670$	7.98640	+	4.61095i	0.308542	+	0.178137i
$671$	−12.4628	−	21.5863i	−0.481123	−	0.833329i
$672$	4.25218	+	1.70850i	0.164031	+	0.0659070i
$673$	−2.10536	+	3.64659i	−0.0811557	+	0.140566i	−0.903747	−	0.428068i	$-0.859194\pi$
$673$	−2.10536	+	3.64659i	−0.0811557	+	0.140566i	0.822591	+	0.568634i	$0.192528\pi$
$674$	12.3926	−	7.15488i	0.477346	−	0.275596i
$675$	−0.814131	+	5.13198i	−0.0313359	+	0.197530i
$676$	1.17257	−	2.03096i	0.0450990	−	0.0781138i
$677$	−39.6564			−1.52412			−0.762059	−	0.647508i	$-0.775811\pi$
$677$	−39.6564			−1.52412			−0.762059	+	0.647508i	$0.775811\pi$
$678$	−4.27919	−	14.0007i	−0.164341	−	0.537696i
$679$	−1.49012	+	1.84769i	−0.0571855	+	0.0709080i
$680$	0.861388	−	0.497322i	0.0330327	−	0.0190714i
$681$	2.57164	+	8.41393i	0.0985453	+	0.322423i
$682$	−19.1225	+	11.0404i	−0.732240	+	0.422759i
$683$	−39.4682	−	22.7869i	−1.51021	−	0.871918i	−0.999929	−	0.0119087i	$-0.996209\pi$
$683$	−39.4682	−	22.7869i	−1.51021	−	0.871918i	−0.510278	−	0.860010i	$-0.670457\pi$
$684$	16.9622	−	1.18329i	0.648565	−	0.0452442i
$685$			9.23672i			0.352917i
$686$	16.5519	+	8.30875i	0.631954	+	0.317229i
$687$	−37.5635	−	35.0343i	−1.43314	−	1.33664i
$688$	5.10292	−	8.83852i	0.194547	−	0.336965i
$689$	33.2548			1.26691
$690$	3.90324	+	12.7707i	0.148594	+	0.486173i
$691$			19.7402i			0.750952i	0.926832	+	0.375476i	$0.122521\pi$
$691$			19.7402i			0.750952i	−0.926832	+	0.375476i	$0.877479\pi$
$692$	−0.964238			−0.0366548
$693$	2.67978	−	31.2919i	0.101796	−	1.18868i
$694$	6.00500			0.227947
$695$			13.0387i			0.494587i
$696$	−5.59661	+	6.00064i	−0.212139	+	0.227454i
$697$	−10.2760			−0.389232
$698$	6.70633	−	11.6157i	0.253838	−	0.439661i
$699$	−30.3003	+	9.26100i	−1.14606	+	0.350283i
$700$	2.46812	−	0.953096i	0.0932861	−	0.0360237i
$701$			13.6845i			0.516855i	0.966031	+	0.258427i	$0.0832043\pi$
$701$			13.6845i			0.516855i	−0.966031	+	0.258427i	$0.916796\pi$
$702$	−2.65747	+	16.7517i	−0.100300	+	0.632251i
$703$	49.6292	+	28.6534i	1.87180	+	1.08068i
$704$	−3.42673	+	1.97842i	−0.129150	+	0.0745646i
$705$	−5.59878	+	6.00296i	−0.210862	+	0.226085i
$706$	−0.437675	+	0.252692i	−0.0164721	+	0.00951017i
$707$	−0.532361	+	0.205578i	−0.0200215	+	0.00773156i
$708$	−5.75008	−	1.32801i	−0.216101	−	0.0499098i
$709$	−6.98123			−0.262185			−0.131093	−	0.991370i	$-0.541849\pi$
$709$	−6.98123			−0.262185			−0.131093	+	0.991370i	$0.541849\pi$
$710$	1.37483	−	2.38127i	0.0515963	−	0.0893675i
$711$	−4.96491	−	2.42257i	−0.186199	−	0.0908533i
$712$	−11.9993	+	6.92781i	−0.449694	+	0.259631i
$713$	−21.5121	+	37.2601i	−0.805635	+	1.39540i
$714$	−3.58639	+	2.81310i	−0.134217	+	0.105277i
$715$	6.45792	+	11.1854i	0.241512	+	0.418312i
$716$	−0.186006	−	0.107391i	−0.00695138	−	0.00401338i
$717$	−11.5838	+	3.54047i	−0.432604	+	0.132221i
$718$	6.50952	+	11.2748i	0.242933	+	0.420773i
$719$	7.49920	+	12.9890i	0.279673	+	0.484408i	0.971303	−	0.237844i	$-0.0764406\pi$
$719$	7.49920	+	12.9890i	0.279673	+	0.484408i	−0.691630	+	0.722252i	$0.743107\pi$
$720$	−2.48739	+	1.67717i	−0.0926996	+	0.0625043i
$721$	−18.8571	+	23.3821i	−0.702273	+	0.870795i
$722$	−11.3657	−	6.56197i	−0.422986	−	0.244211i
$723$	−9.13652	+	2.79249i	−0.339791	+	0.103854i
$724$			11.1757i			0.415341i
$725$			4.73743i			0.175944i
$726$	5.89826	+	5.50112i	0.218905	+	0.204166i
$727$	−22.4642	−	12.9697i	−0.833152	−	0.481020i	0.0217788	−	0.999763i	$-0.493067\pi$
$727$	−22.4642	−	12.9697i	−0.833152	−	0.481020i	−0.854931	+	0.518742i	$0.826400\pi$
$728$	8.05637	−	3.11107i	0.298589	−	0.115304i
$729$	5.60051	+	26.4128i	0.207426	+	0.978251i
$730$	−7.36348	−	12.7539i	−0.272534	−	0.472044i
$731$	5.07559	+	8.79118i	0.187728	+	0.325154i
$732$	2.45529	−	10.6310i	0.0907501	−	0.392933i
$733$	−19.6712	−	11.3572i	−0.726572	−	0.419486i	0.0905950	−	0.995888i	$-0.471123\pi$
$733$	−19.6712	−	11.3572i	−0.726572	−	0.419486i	−0.817167	+	0.576401i	$0.804456\pi$
$734$	16.0143	+	27.7376i	0.591100	+	1.02382i
$735$	−10.5811	+	5.91955i	−0.390289	+	0.218346i
$736$	−3.85494	+	6.67695i	−0.142095	+	0.246116i
$737$	31.6009	−	18.2448i	1.16404	−	0.672056i
$738$	30.9189	−	2.15692i	1.13814	−	0.0793973i
$739$	−6.74623	+	11.6848i	−0.248164	+	0.429833i	−0.963016	−	0.269443i	$-0.913161\pi$
$739$	−6.74623	+	11.6848i	−0.248164	+	0.429833i	0.714852	+	0.699275i	$0.246494\pi$
$740$	−10.1110			−0.371686
$741$	21.8560	−	23.4338i	0.802900	−	0.860862i
$742$	−20.9814	−	16.9210i	−0.770252	−	0.621188i
$743$	−32.3371	+	18.6698i	−1.18633	+	0.684930i	−0.957471	−	0.288529i	$-0.906834\pi$
$743$	−32.3371	+	18.6698i	−1.18633	+	0.684930i	−0.228862	+	0.973459i	$0.573500\pi$
$744$	−9.41764	−	2.17506i	−0.345268	−	0.0797414i
$745$	19.1098	−	11.0331i	0.700130	−	0.404220i
$746$	5.88964	+	3.40038i	0.215635	+	0.124497i
$747$	−3.92923	+	2.64935i	−0.143763	+	0.0969347i
$748$		−	3.93565i		−	0.143902i
$749$	−6.09220	−	15.7762i	−0.222604	−	0.576451i
$750$	−0.389766	+	1.68763i	−0.0142323	+	0.0616234i
$751$	15.3349	−	26.5609i	0.559579	−	0.969220i	−0.437952	−	0.898998i	$-0.644296\pi$
$751$	15.3349	−	26.5609i	0.559579	−	0.969220i	0.997531	−	0.0702215i	$-0.0223706\pi$
$752$	−4.73926			−0.172823
$753$	0.466398	+	0.107717i	0.0169965	+	0.00392543i
$754$			15.4638i			0.563159i
$755$	5.53782			0.201542
$756$	10.2004	−	9.21693i	0.370985	−	0.335217i
$757$	−22.5697			−0.820308			−0.410154	−	0.912016i	$-0.634525\pi$
$757$	−22.5697			−0.820308			−0.410154	+	0.912016i	$0.634525\pi$
$758$		−	2.14646i		−	0.0779630i
$759$	51.4840	+	11.8905i	1.86875	+	0.431598i
$760$	5.66780			0.205593
$761$	10.1156	−	17.5208i	0.366691	−	0.635127i	−0.622355	−	0.782735i	$-0.713824\pi$
$761$	10.1156	−	17.5208i	0.366691	−	0.635127i	0.989046	+	0.147608i	$0.0471574\pi$
$762$	−8.02050	+	34.7275i	−0.290552	+	1.25804i
$763$	−2.53588	−	2.04513i	−0.0918052	−	0.0740385i
$764$		−	18.8822i		−	0.683133i
$765$	−0.207656	−	2.97670i	−0.00750783	−	0.107623i
$766$	−0.615351	−	0.355273i	−0.0222335	−	0.0128365i
$767$	−9.63168	+	5.56086i	−0.347780	+	0.200791i
$768$	−1.68763	−	0.389766i	−0.0608970	−	0.0140645i
$769$	29.9888	−	17.3140i	1.08142	−	0.624359i	0.150143	−	0.988664i	$-0.452027\pi$
$769$	29.9888	−	17.3140i	1.08142	−	0.624359i	0.931280	+	0.364305i	$0.118693\pi$
$770$	1.61698	−	10.3432i	0.0582718	−	0.372743i
$771$	19.4821	−	20.8885i	0.701631	−	0.752282i
$772$	5.89018			0.211992
$773$	−9.02636	+	15.6341i	−0.324656	+	0.562320i	−0.981443	−	0.191756i	$-0.938582\pi$
$773$	−9.02636	+	15.6341i	−0.324656	+	0.562320i	0.656787	+	0.754076i	$0.271915\pi$
$774$	−17.1169	−	25.3859i	−0.615254	−	0.912477i
$775$	−4.83278	+	2.79020i	−0.173598	+	0.100227i
$776$	0.448586	−	0.776974i	0.0161033	−	0.0278917i
$777$	45.8708	−	6.53654i	1.64561	−	0.234497i
$778$	−9.80747	−	16.9870i	−0.351615	−	0.609015i
$779$	−50.7110	−	29.2780i	−1.81691	−	1.04899i
$780$	−1.27227	+	5.50871i	−0.0455544	+	0.197243i
$781$	−5.43997	−	9.42231i	−0.194658	−	0.337157i
$782$	−3.83429	−	6.64119i	−0.137114	−	0.237488i
$783$	8.81603	+	22.9836i	0.315059	+	0.821366i
$784$	−6.66600	−	2.13644i	−0.238072	−	0.0763015i
$785$	−14.5468	−	8.39860i	−0.519198	−	0.299759i
$786$	6.34484	+	5.91764i	0.226313	+	0.211075i
$787$			1.78725i			0.0637087i	0.999493	+	0.0318544i	$0.0101413\pi$
$787$			1.78725i			0.0637087i	−0.999493	+	0.0318544i	$0.989859\pi$
$788$			24.0786i			0.857764i
$789$	4.15641	−	1.27036i	0.147972	−	0.0452262i
$790$	−1.59476	−	0.920736i	−0.0567391	−	0.0327583i
$791$	8.05601	+	20.8617i	0.286439	+	0.741756i
$792$	0.826087	+	11.8417i	0.0293537	+	0.420778i
$793$	−10.2812	−	17.8075i	−0.365094	−	0.632362i
$794$	−11.9697	−	20.7322i	−0.424790	−	0.735757i
$795$	16.8752	−	5.15773i	0.598501	−	0.182926i
$796$	−13.1750	−	7.60658i	−0.466975	−	0.269608i
$797$	−21.5468	−	37.3202i	−0.763227	−	1.32195i	−0.941179	−	0.337909i	$-0.890280\pi$
$797$	−21.5468	−	37.3202i	−0.763227	−	1.32195i	0.177951	−	0.984039i	$-0.443053\pi$
$798$	−25.7134	+	3.66412i	−0.910243	+	0.129709i
$799$	2.35694	−	4.08234i	0.0833826	−	0.144423i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	2.89270	+	41.4661i	0.102208	+	1.46513i
$802$	0.337812	−	0.585108i	0.0119286	−	0.0206609i
$803$	−58.2722			−2.05638
$804$	15.5631	+	3.59439i	0.548869	+	0.126764i
$805$	−7.34825	−	19.0289i	−0.258992	−	0.670680i
$806$	−15.7750	+	9.10772i	−0.555652	+	0.320806i
$807$	−31.5668	+	33.8456i	−1.11120	+	1.19142i
$808$	0.186797	−	0.107847i	0.00657151	−	0.00379406i
$809$	31.6514	+	18.2739i	1.11280	+	0.642478i	0.939554	−	0.342400i	$-0.111240\pi$
$809$	31.6514	+	18.2739i	1.11280	+	0.642478i	0.173250	+	0.984878i	$0.444573\pi$
$810$	1.24961	+	8.91283i	0.0439068	+	0.313165i
$811$		−	0.856906i		−	0.0300900i	−0.999887	−	0.0150450i	$-0.995211\pi$
$811$		−	0.856906i		−	0.0300900i	0.999887	−	0.0150450i	$-0.00478916\pi$
$812$	7.86842	−	9.75657i	0.276127	−	0.342388i
$813$	−24.7689	+	7.57038i	−0.868684	+	0.265505i
$814$	−20.0037	+	34.6475i	−0.701130	+	1.21439i
$815$	−1.72950			−0.0605817
$816$	1.17503	−	1.25986i	0.0411344	−	0.0441039i
$817$			57.8446i			2.02373i
$818$	−30.3557			−1.06136
$819$	2.21067	−	25.8141i	0.0772471	−	0.902018i
$820$	10.3313			0.360786
$821$		−	13.5165i		−	0.471728i	−0.971786	−	0.235864i	$-0.924208\pi$
$821$		−	13.5165i		−	0.471728i	0.971786	−	0.235864i	$-0.0757921\pi$
$822$	4.67624	+	15.2998i	0.163102	+	0.533642i
$823$	−14.9733			−0.521935			−0.260968	−	0.965348i	$-0.584042\pi$
$823$	−14.9733			−0.521935			−0.260968	+	0.965348i	$0.584042\pi$
$824$	5.67674	−	9.83240i	0.197759	−	0.342528i
$825$	5.01191	+	4.67446i	0.174492	+	0.162744i
$826$	8.90643	+	1.39237i	0.309894	+	0.0484466i
$827$		−	14.6192i		−	0.508361i	−0.967157	−	0.254180i	$-0.918194\pi$
$827$		−	14.6192i		−	0.508361i	0.967157	−	0.254180i	$-0.0818057\pi$
$828$	12.9307	+	19.1775i	0.449375	+	0.666463i
$829$	3.40972	+	1.96860i	0.118425	+	0.0683724i	0.558042	−	0.829813i	$-0.311553\pi$
$829$	3.40972	+	1.96860i	0.118425	+	0.0683724i	−0.439618	+	0.898185i	$0.644886\pi$
$830$	−1.36802	+	0.789829i	−0.0474848	+	0.0274154i
$831$	−7.20381	−	23.5696i	−0.249897	−	0.817619i
$832$	−2.82686	+	1.63209i	−0.0980037	+	0.0565825i
$833$	5.15546	−	4.67951i	0.178626	−	0.162136i
$834$	6.60105	+	21.5975i	0.228576	+	0.747859i
$835$	−0.742044			−0.0256795
$836$	11.2133	−	19.4220i	0.387820	−	0.671724i
$837$	−18.2538	+	22.5301i	−0.630943	+	0.778754i
$838$	10.1808	−	5.87786i	0.351688	−	0.203047i
$839$	16.9706	−	29.3940i	0.585891	−	1.01479i	−0.408872	−	0.912592i	$-0.634078\pi$
$839$	16.9706	−	29.3940i	0.585891	−	1.01479i	0.994764	−	0.102202i	$-0.0325888\pi$
$840$	3.60570	−	2.82824i	0.124408	−	0.0975836i
$841$	−3.27839	−	5.67833i	−0.113048	−	0.195804i
$842$	−25.0380	−	14.4557i	−0.862865	−	0.498175i
$843$	−31.5318	−	29.4087i	−1.08601	−	1.01289i
$844$	3.11109	+	5.38856i	0.107088	+	0.185482i
$845$	−1.17257	−	2.03096i	−0.0403378	−	0.0698671i
$846$	−6.23478	+	12.7778i	−0.214356	+	0.439311i
$847$	−9.59010	−	7.73417i	−0.329520	−	0.265749i
$848$	8.82289	+	5.09390i	0.302979	+	0.174925i
$849$	6.69605	−	28.9928i	0.229808	−	0.995032i
$850$		−	0.994645i		−	0.0341160i
$851$			77.9542i			2.67223i
$852$	1.07172	−	4.64039i	0.0367166	−	0.158977i
$853$	27.7997	+	16.0501i	0.951843	+	0.549547i	0.893653	−	0.448759i	$-0.148134\pi$
$853$	27.7997	+	16.0501i	0.951843	+	0.549547i	0.0581898	+	0.998306i	$0.481467\pi$
$854$	−2.57427	+	16.4666i	−0.0880896	+	0.563476i
$855$	7.45633	−	15.2813i	0.255001	−	0.522610i
$856$	3.19600	+	5.53564i	0.109237	+	0.189204i
$857$	−7.37024	−	12.7656i	−0.251763	−	0.436066i	0.712249	−	0.701927i	$-0.247677\pi$
$857$	−7.37024	−	12.7656i	−0.251763	−	0.436066i	−0.964011	+	0.265862i	$0.914344\pi$
$858$	16.3598	+	15.2583i	0.558513	+	0.520908i
$859$	−1.36977	−	0.790839i	−0.0467360	−	0.0269831i	0.476450	−	0.879202i	$-0.341923\pi$
$859$	−1.36977	−	0.790839i	−0.0467360	−	0.0269831i	−0.523186	+	0.852219i	$0.675257\pi$
$860$	−5.10292	−	8.83852i	−0.174008	−	0.301391i
$861$	−46.8707	+	6.67902i	−1.59735	+	0.227620i
$862$	9.97444	−	17.2762i	0.339731	−	0.588431i
$863$	5.03980	−	2.90973i	0.171557	−	0.0990483i	−0.411763	−	0.911291i	$-0.635087\pi$
$863$	5.03980	−	2.90973i	0.171557	−	0.0990483i	0.583320	+	0.812243i	$0.301753\pi$
$864$	−3.27105	+	4.03736i	−0.111283	+	0.137354i
$865$	−0.482119	+	0.835055i	−0.0163925	+	0.0283927i
$866$	−28.8157			−0.979197
$867$	−8.10566	−	26.5203i	−0.275283	−	0.900675i
$868$	14.5872	+	2.28045i	0.495122	+	0.0774036i
$869$	−6.31022	+	3.64321i	−0.214060	+	0.123587i
$870$	2.39840	+	7.84713i	0.0813133	+	0.266042i
$871$	26.0690	−	15.0510i	0.883315	−	0.509982i
$872$	1.06636	+	0.615666i	0.0361117	+	0.0208491i
$873$	−1.50471	−	2.23162i	−0.0509266	−	0.0755288i
$874$		−	43.6980i		−	1.47811i
$875$	0.408654	−	2.61400i	0.0138150	−	0.0883694i
$876$	−18.6538	−	17.3978i	−0.630254	−	0.587819i
$877$	24.0873	−	41.7204i	0.813369	−	1.40880i	−0.0971239	−	0.995272i	$-0.530964\pi$
$877$	24.0873	−	41.7204i	0.813369	−	1.40880i	0.910493	−	0.413524i	$-0.135702\pi$
$878$	−8.17520			−0.275900
$879$	−4.03702	−	13.2084i	−0.136165	−	0.445508i
$880$			3.95684i			0.133385i
$881$	−53.9354			−1.81713			−0.908566	−	0.417742i	$-0.862822\pi$
$881$	−53.9354			−1.81713			−0.908566	+	0.417742i	$0.862822\pi$
$882$	−14.5297	+	15.1620i	−0.489241	+	0.510532i
$883$	−42.9089			−1.44400			−0.722000	−	0.691893i	$-0.756777\pi$
$883$	−42.9089			−1.44400			−0.722000	+	0.691893i	$0.756777\pi$
$884$		−	3.24670i		−	0.109198i
$885$	−4.02513	+	4.31571i	−0.135303	+	0.145071i
$886$	−26.2700			−0.882558
$887$	9.55424	−	16.5484i	0.320800	−	0.555642i	−0.659853	−	0.751394i	$-0.729382\pi$
$887$	9.55424	−	16.5484i	0.320800	−	0.555642i	0.980653	+	0.195753i	$0.0627150\pi$
$888$	−16.7479	+	5.11883i	−0.562022	+	0.171777i
$889$	8.40916	−	53.7902i	0.282034	−	1.80406i
$890$			13.8556i			0.464442i
$891$	33.0141	+	13.3513i	1.10601	+	0.447284i
$892$	−4.37102	−	2.52361i	−0.146353	−	0.0844968i
$893$	23.2625	−	13.4306i	0.778449	−	0.449438i
$894$	26.0680	−	27.9499i	0.871846	−	0.934785i
$895$	−0.186006	+	0.107391i	−0.00621750	+	0.00358968i
$896$	2.61400	+	0.408654i	0.0873277	+	0.0136522i
$897$	42.4715	+	9.80901i	1.41808	+	0.327513i
$898$	−6.39690			−0.213467
$899$	−13.2184	+	22.8949i	−0.440858	+	0.763589i
$900$	0.208774	+	2.99273i	0.00695914	+	0.0997576i
$901$	−8.77564	+	5.06662i	−0.292359	+	0.168794i
$902$	20.4398	−	35.4027i	0.680570	−	1.17878i
$903$	28.8646	+	36.7992i	0.960553	+	1.22460i
$904$	−4.22623	−	7.32005i	−0.140562	−	0.243461i
$905$	9.67842	+	5.58784i	0.321721	+	0.185746i
$906$	9.17290	−	2.80361i	0.304749	−	0.0931436i
$907$	13.5228	+	23.4221i	0.449016	+	0.777718i	0.998322	−	0.0579028i	$-0.0184413\pi$
$907$	13.5228	+	23.4221i	0.449016	+	0.777718i	−0.549306	+	0.835621i	$0.685108\pi$
$908$	2.53981	+	4.39908i	0.0842865	+	0.145989i
$909$	−0.0450316	−	0.645516i	−0.00149360	−	0.0214104i
$910$	1.33392	−	8.53256i	0.0442189	−	0.282852i
$911$	4.11941	+	2.37834i	0.136482	+	0.0787979i	0.566686	−	0.823934i	$-0.308225\pi$
$911$	4.11941	+	2.37834i	0.136482	+	0.0787979i	−0.430204	+	0.902732i	$0.641558\pi$
$912$	9.38820	−	2.86941i	0.310874	−	0.0950157i
$913$			6.25046i			0.206860i
$914$			10.3267i			0.341578i
$915$	−7.97908	−	7.44185i	−0.263780	−	0.246020i
$916$	−25.6828	−	14.8280i	−0.848582	−	0.489929i
$917$	−10.3162	−	8.31976i	−0.340671	−	0.274743i
$918$	−1.85096	−	4.82551i	−0.0610909	−	0.159265i
$919$	−17.3173	−	29.9945i	−0.571245	−	0.989426i	−0.996438	−	0.0843232i	$-0.973127\pi$
$919$	−17.3173	−	29.9945i	−0.571245	−	0.989426i	0.425193	−	0.905103i	$-0.360206\pi$
$920$	3.85494	+	6.67695i	0.127094	+	0.220132i
$921$	−6.06731	+	26.2705i	−0.199925	+	0.865643i
$922$	6.93476	+	4.00379i	0.228384	+	0.131858i
$923$	−4.48768	−	7.77289i	−0.147714	−	0.255848i
$924$	−2.55802	−	17.9512i	−0.0841528	−	0.590551i
$925$	−5.05548	+	8.75634i	−0.166223	+	0.287907i
$926$	26.4770	−	15.2865i	0.870089	−	0.502346i
$927$	−19.0417	−	28.2405i	−0.625411	−	0.927541i
$928$	−2.36871	+	4.10273i	−0.0777569	+	0.134679i
$929$	−29.2791			−0.960615			−0.480307	−	0.877100i	$-0.659475\pi$
$929$	−29.2791			−0.960615			−0.480307	+	0.877100i	$0.659475\pi$
$930$	−6.59247	+	7.06839i	−0.216176	+	0.231782i
$931$	38.7743	−	8.40415i	1.27078	−	0.275435i
$932$	−15.8420	+	9.14639i	−0.518922	+	0.299600i
$933$	34.0341	+	7.86036i	1.11423	+	0.257337i
$934$	−6.25300	+	3.61017i	−0.204604	+	0.118128i
$935$	−3.40837	−	1.96783i	−0.111466	−	0.0643548i
$936$	0.681476	+	9.76879i	0.0222747	+	0.319303i
$937$			25.3740i			0.828932i	0.910065	+	0.414466i	$0.136032\pi$
$937$			25.3740i			0.828932i	−0.910065	+	0.414466i	$0.863968\pi$
$938$	−24.1061	−	3.76856i	−0.787091	−	0.123048i
$939$	2.60053	−	11.2599i	0.0848652	−	0.367453i
$940$	−2.36963	+	4.10432i	−0.0772889	+	0.133868i
$941$	−12.1904			−0.397397			−0.198699	−	0.980061i	$-0.563671\pi$
$941$	−12.1904			−0.397397			−0.198699	+	0.980061i	$0.563671\pi$
$942$	−28.3474	−	6.54698i	−0.923608	−	0.213312i
$943$		−	79.6534i		−	2.59387i
$944$	−3.40720			−0.110895
$945$	−2.88190	−	13.4423i	−0.0937481	−	0.437277i
$946$	−40.3829			−1.31296
$947$			16.2933i			0.529461i	0.964322	+	0.264731i	$0.0852831\pi$
$947$			16.2933i			0.529461i	−0.964322	+	0.264731i	$0.914717\pi$
$948$	−3.10772	−	0.717744i	−0.100934	−	0.0233112i
$949$	−48.0714			−1.56046
$950$	2.83390	−	4.90846i	0.0919438	−	0.159251i
$951$	9.95524	−	43.1046i	0.322821	−	1.39776i
$952$	−1.65201	+	2.04844i	−0.0535420	+	0.0663902i
$953$		−	58.2513i		−	1.88695i	−0.331449	−	0.943473i	$-0.607538\pi$
$953$		−	58.2513i		−	1.88695i	0.331449	−	0.943473i	$-0.392462\pi$
$954$	25.3410	−	17.0866i	0.820446	−	0.553200i
$955$	−16.3524	−	9.44109i	−0.529153	−	0.305506i
$956$	−6.05638	+	3.49665i	−0.195877	+	0.113090i
$957$	31.6350	+	7.30627i	1.02261	+	0.236178i
$958$	15.8239	−	9.13594i	0.511248	−	0.295169i
$959$	−8.80349	−	22.7973i	−0.284279	−	0.736164i
$960$	−1.18136	+	1.26664i	−0.0381282	+	0.0408808i
$961$	−0.140960			−0.00454711
$962$	−16.5020	+	28.5822i	−0.532045	+	0.921529i
$963$	19.1295	−	1.33449i	0.616441	−	0.0430032i
$964$	−4.77687	+	2.75793i	−0.153853	+	0.0888269i
$965$	2.94509	−	5.10105i	0.0948058	−	0.164209i
$966$	−21.8054	−	27.7995i	−0.701577	−	0.894433i
$967$	5.61342	+	9.72273i	0.180515	+	0.312662i	0.942056	−	0.335455i	$-0.108890\pi$
$967$	5.61342	+	9.72273i	0.180515	+	0.312662i	−0.761541	+	0.648117i	$0.775557\pi$
$968$	4.03273	+	2.32830i	0.129617	+	0.0748344i
$969$	−2.19729	+	9.51390i	−0.0705870	+	0.305631i
$970$	−0.448586	−	0.776974i	−0.0144032	−	0.0249471i
$971$	8.18607	+	14.1787i	0.262704	+	0.455016i	0.966959	−	0.254930i	$-0.0820525\pi$
$971$	8.18607	+	14.1787i	0.262704	+	0.455016i	−0.704256	+	0.709946i	$0.748719\pi$
$972$	6.58212	+	14.1307i	0.211122	+	0.453241i
$973$	−12.4272	−	32.1811i	−0.398396	−	1.03168i
$974$	33.4057	+	19.2868i	1.07039	+	0.617988i
$975$	4.13455	+	3.85617i	0.132412	+	0.123496i
$976$		−	6.29939i		−	0.201638i
$977$			58.4624i			1.87038i	0.354149	+	0.935189i	$0.384770\pi$
$977$			58.4624i			1.87038i	−0.354149	+	0.935189i	$0.615230\pi$
$978$	−2.86476	+	0.875586i	−0.0916049	+	0.0279981i
$979$	47.4794	+	27.4123i	1.51745	+	0.876100i
$980$	−5.18322	+	4.70471i	−0.165572	+	0.150286i
$981$	3.06280	−	2.06515i	0.0977878	−	0.0659352i
$982$	−12.3235	−	21.3449i	−0.393258	−	0.681143i
$983$	−12.6833	−	21.9682i	−0.404535	−	0.700675i	0.589732	−	0.807599i	$-0.299233\pi$
$983$	−12.6833	−	21.9682i	−0.404535	−	0.700675i	−0.994267	+	0.106924i	$0.965900\pi$
$984$	17.1130	−	5.23041i	0.545541	−	0.166739i
$985$	20.8527	+	12.0393i	0.664421	+	0.383604i
$986$	−2.35603	−	4.08076i	−0.0750312	−	0.129958i
$987$	8.09705	−	20.1522i	0.257732	−	0.641451i
$988$	9.25035	−	16.0221i	0.294293	−	0.509730i
$989$	−68.1438	+	39.3429i	−2.16685	+	1.25103i
$990$	10.6683	+	5.20546i	0.339061	+	0.165440i
$991$	−11.2022	+	19.4028i	−0.355850	+	0.616349i	−0.987263	−	0.159097i	$-0.949142\pi$
$991$	−11.2022	+	19.4028i	−0.355850	+	0.616349i	0.631413	+	0.775446i	$0.282475\pi$
$992$	−5.58041			−0.177178
$993$	−3.05930	−	0.706561i	−0.0970838	−	0.0224220i
$994$	−1.12366	+	7.18760i	−0.0356402	+	0.227977i
$995$	−13.1750	+	7.60658i	−0.417675	+	0.241145i
$996$	−1.86615	+	2.00087i	−0.0591311	+	0.0633998i
$997$	21.1293	−	12.1990i	0.669172	−	0.386346i	−0.126591	−	0.991955i	$-0.540404\pi$
$997$	21.1293	−	12.1990i	0.669172	−	0.386346i	0.795763	+	0.605609i	$0.207070\pi$
$998$	9.10884	+	5.25899i	0.288335	+	0.166470i
$999$	−8.23164	+	51.8892i	−0.260438	+	1.64170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.b.101.1	yes	28
3.2	odd	2		1890.2.bk.b.521.12		28
7.5	odd	6		630.2.t.b.551.2	yes	28
9.4	even	3		1890.2.t.b.1151.9		28
9.5	odd	6		630.2.t.b.311.2	✓	28
21.5	even	6		1890.2.t.b.1601.9		28
63.5	even	6	inner	630.2.bk.b.131.8	yes	28
63.40	odd	6		1890.2.bk.b.341.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.2	✓	28	9.5	odd	6
630.2.t.b.551.2	yes	28	7.5	odd	6
630.2.bk.b.101.1	yes	28	1.1	even	1	trivial
630.2.bk.b.131.8	yes	28	63.5	even	6	inner
1890.2.t.b.1151.9		28	9.4	even	3
1890.2.t.b.1601.9		28	21.5	even	6
1890.2.bk.b.341.12		28	63.40	odd	6
1890.2.bk.b.521.12		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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.68763 - 0.389766i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.389766 + 1.68763i) q^{6} +(0.408654 - 2.61400i) q^{7} +1.00000i q^{8} +(2.69616 + 1.31556i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.68763 - 0.389766i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.389766 + 1.68763i) q^{6} +(0.408654 - 2.61400i) q^{7} +1.00000i q^{8} +(2.69616 + 1.31556i) q^{9} +(0.866025 + 0.500000i) q^{10} +(3.42673 - 1.97842i) q^{11} +(1.68763 + 0.389766i) q^{12} +(2.82686 - 1.63209i) q^{13} +(-2.61400 - 0.408654i) q^{14} +(1.18136 - 1.26664i) q^{15} +1.00000 q^{16} +(-0.497322 + 0.861388i) q^{17} +(1.31556 - 2.69616i) q^{18} +(-4.90846 + 2.83390i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.70850 + 4.25218i) q^{21} +(-1.97842 - 3.42673i) q^{22} +(-6.67695 - 3.85494i) q^{23} +(0.389766 - 1.68763i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.63209 - 2.82686i) q^{26} +(-4.03736 - 3.27105i) q^{27} +(-0.408654 + 2.61400i) q^{28} +(-4.10273 - 2.36871i) q^{29} +(-1.26664 - 1.18136i) q^{30} -5.58041i q^{31} -1.00000i q^{32} +(-6.55415 + 2.00321i) q^{33} +(0.861388 + 0.497322i) q^{34} +(2.05946 + 1.66090i) q^{35} +(-2.69616 - 1.31556i) q^{36} +(-5.05548 - 8.75634i) q^{37} +(2.83390 + 4.90846i) q^{38} +(-5.40682 + 1.65254i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(5.16567 + 8.94721i) q^{41} +(4.25218 + 1.70850i) q^{42} +(5.10292 - 8.83852i) q^{43} +(-3.42673 + 1.97842i) q^{44} +(-2.48739 + 1.67717i) q^{45} +(-3.85494 + 6.67695i) q^{46} -4.73926 q^{47} +(-1.68763 - 0.389766i) q^{48} +(-6.66600 - 2.13644i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(1.17503 - 1.25986i) q^{51} +(-2.82686 + 1.63209i) q^{52} +(8.82289 + 5.09390i) q^{53} +(-3.27105 + 4.03736i) q^{54} +3.95684i q^{55} +(2.61400 + 0.408654i) q^{56} +(9.38820 - 2.86941i) q^{57} +(-2.36871 + 4.10273i) q^{58} -3.40720 q^{59} +(-1.18136 + 1.26664i) q^{60} -6.29939i q^{61} -5.58041 q^{62} +(4.54067 - 6.51017i) q^{63} -1.00000 q^{64} +3.26418i q^{65} +(2.00321 + 6.55415i) q^{66} +9.22190 q^{67} +(0.497322 - 0.861388i) q^{68} +(9.76567 + 9.10814i) q^{69} +(1.66090 - 2.05946i) q^{70} -2.74965i q^{71} +(-1.31556 + 2.69616i) q^{72} +(-12.7539 - 7.36348i) q^{73} +(-8.75634 + 5.05548i) q^{74} +(0.506266 + 1.65641i) q^{75} +(4.90846 - 2.83390i) q^{76} +(-3.77125 - 9.76595i) q^{77} +(1.65254 + 5.40682i) q^{78} -1.84147 q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.53861 + 7.09393i) q^{81} +(8.94721 - 5.16567i) q^{82} +(-0.789829 + 1.36802i) q^{83} +(1.70850 - 4.25218i) q^{84} +(-0.497322 - 0.861388i) q^{85} +(-8.83852 - 5.10292i) q^{86} +(6.00064 + 5.59661i) q^{87} +(1.97842 + 3.42673i) q^{88} +(6.92781 + 11.9993i) q^{89} +(1.67717 + 2.48739i) q^{90} +(-3.11107 - 8.05637i) q^{91} +(6.67695 + 3.85494i) q^{92} +(-2.17506 + 9.41764i) q^{93} +4.73926i q^{94} -5.66780i q^{95} +(-0.389766 + 1.68763i) q^{96} +(-0.776974 - 0.448586i) q^{97} +(-2.13644 + 6.66600i) q^{98} +(11.8417 - 0.826087i) 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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