LMFDB - Embedded newform 630.2.i.i.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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([2, 0, 2]))

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

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

chi := DirichletCharacter("630.121");

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.i (of order $3$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561 $ x^16 - x^15 + 2x^14 - 4x^13 + 5x^12 + 2x^11 - 35x^10 + 81x^9 - 66x^8 + 243x^7 - 315x^6 + 54x^5 + 405x^4 - 972x^3 + 1458x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-0.579249 - 1.63232i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.i.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.70326 + 0.314515i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.70326 - 0.314515i) q^{6} +(2.48140 + 0.917950i) q^{7} -1.00000 q^{8} +(2.80216 - 1.07140i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.70326 + 0.314515i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.70326 - 0.314515i) q^{6} +(2.48140 + 0.917950i) q^{7} -1.00000 q^{8} +(2.80216 - 1.07140i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.14860 + 1.98944i) q^{11} +(-1.70326 + 0.314515i) q^{12} +(-0.845351 + 1.46419i) q^{13} +(-2.48140 - 0.917950i) q^{14} +(-1.12401 - 1.31780i) q^{15} +1.00000 q^{16} +(0.372166 + 0.644610i) q^{17} +(-2.80216 + 1.07140i) q^{18} +(3.89868 - 6.75271i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.51518 - 0.783063i) q^{21} +(1.14860 - 1.98944i) q^{22} +(-1.07539 - 1.86262i) q^{23} +(1.70326 - 0.314515i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.845351 - 1.46419i) q^{26} +(-4.43582 + 2.70619i) q^{27} +(2.48140 + 0.917950i) q^{28} +(2.61618 + 4.53135i) q^{29} +(1.12401 + 1.31780i) q^{30} +4.29720 q^{31} -1.00000 q^{32} +(1.33065 - 3.74977i) q^{33} +(-0.372166 - 0.644610i) q^{34} +(0.445734 + 2.60793i) q^{35} +(2.80216 - 1.07140i) q^{36} +(-5.40503 + 9.36179i) q^{37} +(-3.89868 + 6.75271i) q^{38} +(0.979338 - 2.75977i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.14946 + 3.72298i) q^{41} +(4.51518 + 0.783063i) q^{42} +(4.16353 + 7.21144i) q^{43} +(-1.14860 + 1.98944i) q^{44} +(2.32894 + 1.89104i) q^{45} +(1.07539 + 1.86262i) q^{46} -8.18236 q^{47} +(-1.70326 + 0.314515i) q^{48} +(5.31474 + 4.55561i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.836633 - 0.980883i) q^{51} +(-0.845351 + 1.46419i) q^{52} +(6.31906 + 10.9449i) q^{53} +(4.43582 - 2.70619i) q^{54} -2.29720 q^{55} +(-2.48140 - 0.917950i) q^{56} +(-4.51662 + 12.7278i) q^{57} +(-2.61618 - 4.53135i) q^{58} +0.635800 q^{59} +(-1.12401 - 1.31780i) q^{60} +6.90519 q^{61} -4.29720 q^{62} +(7.93678 - 0.0863357i) q^{63} +1.00000 q^{64} -1.69070 q^{65} +(-1.33065 + 3.74977i) q^{66} +9.77125 q^{67} +(0.372166 + 0.644610i) q^{68} +(2.41748 + 2.83430i) q^{69} +(-0.445734 - 2.60793i) q^{70} +2.50553 q^{71} +(-2.80216 + 1.07140i) q^{72} +(-3.42499 - 5.93225i) q^{73} +(5.40503 - 9.36179i) q^{74} +(0.579249 - 1.63232i) q^{75} +(3.89868 - 6.75271i) q^{76} +(-4.67635 + 3.88224i) q^{77} +(-0.979338 + 2.75977i) q^{78} -9.30803 q^{79} +(0.500000 + 0.866025i) q^{80} +(6.70420 - 6.00447i) q^{81} +(2.14946 - 3.72298i) q^{82} +(-0.645374 - 1.11782i) q^{83} +(-4.51518 - 0.783063i) q^{84} +(-0.372166 + 0.644610i) q^{85} +(-4.16353 - 7.21144i) q^{86} +(-5.88120 - 6.89522i) q^{87} +(1.14860 - 1.98944i) q^{88} +(0.165401 - 0.286482i) q^{89} +(-2.32894 - 1.89104i) q^{90} +(-3.44171 + 2.85726i) q^{91} +(-1.07539 - 1.86262i) q^{92} +(-7.31923 + 1.35154i) q^{93} +8.18236 q^{94} +7.79736 q^{95} +(1.70326 - 0.314515i) q^{96} +(3.18123 + 5.51006i) q^{97} +(-5.31474 - 4.55561i) q^{98} +(-1.08708 + 6.80533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) $ 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9 - 8 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 + 16 * q^16 + 11 * q^17 + 6 * q^18 - 2 * q^19 + 8 * q^20 - 15 * q^21 - q^22 + 11 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 30 * q^31 - 16 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^40 + 7 * q^41 + 15 * q^42 - 13 * q^43 + q^44 + 3 * q^45 - 11 * q^46 + 10 * q^47 + 2 * q^48 - 14 * q^49 + 8 * q^50 - 3 * q^51 + 2 * q^52 + 18 * q^53 + 7 * q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 - 17 * q^58 - 2 * q^59 + q^60 + 54 * q^61 - 30 * q^62 + 41 * q^63 + 16 * q^64 + 4 * q^65 - 5 * q^66 + 20 * q^67 + 11 * q^68 - 14 * q^69 + 4 * q^70 - 38 * q^71 + 6 * q^72 - 8 * q^73 + 2 * q^74 - q^75 - 2 * q^76 - 7 * q^77 + 50 * q^79 + 8 * q^80 - 6 * q^81 - 7 * q^82 + 2 * q^83 - 15 * q^84 - 11 * q^85 + 13 * q^86 - 32 * q^87 - q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 - 6 * q^93 - 10 * q^94 - 4 * q^95 - 2 * q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.70326	+	0.314515i	−0.983375	+	0.181586i
$3$	−1.70326	+	0.314515i	−0.983375	+	0.181586i
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	1.70326	−	0.314515i	0.695351	−	0.128400i
$7$	2.48140	+	0.917950i	0.937883	+	0.346952i
$7$	2.48140	+	0.917950i	0.937883	+	0.346952i
$8$	−1.00000			−0.353553
$9$	2.80216	−	1.07140i	0.934053	−	0.357134i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−1.14860	+	1.98944i	−0.346316	+	0.599837i	−0.985592	−	0.169140i	$-0.945901\pi$
$11$	−1.14860	+	1.98944i	−0.346316	+	0.599837i	0.639276	+	0.768978i	$0.279234\pi$
$12$	−1.70326	+	0.314515i	−0.491688	+	0.0907928i
$13$	−0.845351	+	1.46419i	−0.234458	+	0.406093i	−0.959115	−	0.283016i	$-0.908665\pi$
$13$	−0.845351	+	1.46419i	−0.234458	+	0.406093i	0.724657	+	0.689110i	$0.241998\pi$
$14$	−2.48140	−	0.917950i	−0.663183	−	0.245332i
$15$	−1.12401	−	1.31780i	−0.290217	−	0.340256i
$16$	1.00000			0.250000
$17$	0.372166	+	0.644610i	0.0902634	+	0.156341i	0.907622	−	0.419789i	$-0.137896\pi$
$17$	0.372166	+	0.644610i	0.0902634	+	0.156341i	−0.817359	+	0.576129i	$0.804562\pi$
$18$	−2.80216	+	1.07140i	−0.660475	+	0.252532i
$19$	3.89868	−	6.75271i	0.894419	−	1.54918i	0.0598963	−	0.998205i	$-0.480923\pi$
$19$	3.89868	−	6.75271i	0.894419	−	1.54918i	0.834522	−	0.550974i	$-0.185744\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−4.51518	−	0.783063i	−0.985292	−	0.170878i
$22$	1.14860	−	1.98944i	0.244883	−	0.424149i
$23$	−1.07539	−	1.86262i	−0.224234	−	0.388384i	0.731856	−	0.681460i	$-0.238655\pi$
$23$	−1.07539	−	1.86262i	−0.224234	−	0.388384i	−0.956089	+	0.293076i	$0.905321\pi$
$24$	1.70326	−	0.314515i	0.347676	−	0.0642002i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.845351	−	1.46419i	0.165787	−	0.287151i
$27$	−4.43582	+	2.70619i	−0.853675	+	0.520807i
$28$	2.48140	+	0.917950i	0.468941	+	0.173476i
$29$	2.61618	+	4.53135i	0.485812	+	0.841450i	0.999867	−	0.0163066i	$-0.00519078\pi$
$29$	2.61618	+	4.53135i	0.485812	+	0.841450i	−0.514055	+	0.857757i	$0.671857\pi$
$30$	1.12401	+	1.31780i	0.205215	+	0.240597i
$31$	4.29720			0.771800			0.385900	−	0.922541i	$-0.373891\pi$
$31$	4.29720			0.771800			0.385900	+	0.922541i	$0.373891\pi$
$32$	−1.00000			−0.176777
$33$	1.33065	−	3.74977i	0.231637	−	0.652751i
$34$	−0.372166	−	0.644610i	−0.0638259	−	0.110550i
$35$	0.445734	+	2.60793i	0.0753428	+	0.440821i
$36$	2.80216	−	1.07140i	0.467027	−	0.178567i
$37$	−5.40503	+	9.36179i	−0.888582	+	1.53907i	−0.0470293	+	0.998894i	$0.514975\pi$
$37$	−5.40503	+	9.36179i	−0.888582	+	1.53907i	−0.841553	+	0.540175i	$0.818358\pi$
$38$	−3.89868	+	6.75271i	−0.632450	+	1.09543i
$39$	0.979338	−	2.75977i	0.156820	−	0.441916i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−2.14946	+	3.72298i	−0.335690	+	0.581431i	−0.983617	−	0.180271i	$-0.942303\pi$
$41$	−2.14946	+	3.72298i	−0.335690	+	0.581431i	0.647927	+	0.761702i	$0.275636\pi$
$42$	4.51518	+	0.783063i	0.696707	+	0.120829i
$43$	4.16353	+	7.21144i	0.634932	+	1.09973i	0.986530	+	0.163583i	$0.0523051\pi$
$43$	4.16353	+	7.21144i	0.634932	+	1.09973i	−0.351598	+	0.936151i	$0.614362\pi$
$44$	−1.14860	+	1.98944i	−0.173158	+	0.299919i
$45$	2.32894	+	1.89104i	0.347178	+	0.281900i
$46$	1.07539	+	1.86262i	0.158557	+	0.274629i
$47$	−8.18236			−1.19352			−0.596760	−	0.802420i	$-0.703545\pi$
$47$	−8.18236			−1.19352			−0.596760	+	0.802420i	$0.703545\pi$
$48$	−1.70326	+	0.314515i	−0.245844	+	0.0453964i
$49$	5.31474	+	4.55561i	0.759248	+	0.650801i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−0.836633	−	0.980883i	−0.117152	−	0.137351i
$52$	−0.845351	+	1.46419i	−0.117229	+	0.203047i
$53$	6.31906	+	10.9449i	0.867990	+	1.50340i	0.864047	+	0.503411i	$0.167922\pi$
$53$	6.31906	+	10.9449i	0.867990	+	1.50340i	0.00394299	+	0.999992i	$0.498745\pi$
$54$	4.43582	−	2.70619i	0.603639	−	0.368266i
$55$	−2.29720			−0.309755
$56$	−2.48140	−	0.917950i	−0.331592	−	0.122666i
$57$	−4.51662	+	12.7278i	−0.598241	+	1.68584i
$58$	−2.61618	−	4.53135i	−0.343521	−	0.594995i
$59$	0.635800			0.0827741			0.0413870	−	0.999143i	$-0.486822\pi$
$59$	0.635800			0.0827741			0.0413870	+	0.999143i	$0.486822\pi$
$60$	−1.12401	−	1.31780i	−0.145109	−	0.170128i
$61$	6.90519			0.884118			0.442059	−	0.896986i	$-0.354248\pi$
$61$	6.90519			0.884118			0.442059	+	0.896986i	$0.354248\pi$
$62$	−4.29720			−0.545745
$63$	7.93678	−	0.0863357i	0.999941	−	0.0108773i
$64$	1.00000			0.125000
$65$	−1.69070			−0.209706
$66$	−1.33065	+	3.74977i	−0.163792	+	0.461565i
$67$	9.77125			1.19375			0.596874	−	0.802335i	$-0.296409\pi$
$67$	9.77125			1.19375			0.596874	+	0.802335i	$0.296409\pi$
$68$	0.372166	+	0.644610i	0.0451317	+	0.0781704i
$69$	2.41748	+	2.83430i	0.291031	+	0.341210i
$70$	−0.445734	−	2.60793i	−0.0532754	−	0.311708i
$71$	2.50553			0.297351			0.148676	−	0.988886i	$-0.452499\pi$
$71$	2.50553			0.297351			0.148676	+	0.988886i	$0.452499\pi$
$72$	−2.80216	+	1.07140i	−0.330238	+	0.126266i
$73$	−3.42499	−	5.93225i	−0.400865	−	0.694318i	0.592966	−	0.805228i	$-0.297957\pi$
$73$	−3.42499	−	5.93225i	−0.400865	−	0.694318i	−0.993830	+	0.110910i	$0.964624\pi$
$74$	5.40503	−	9.36179i	0.628322	−	1.08829i
$75$	0.579249	−	1.63232i	0.0668860	−	0.188484i
$76$	3.89868	−	6.75271i	0.447209	−	0.774589i
$77$	−4.67635	+	3.88224i	−0.532919	+	0.442422i
$78$	−0.979338	+	2.75977i	−0.110888	+	0.312482i
$79$	−9.30803			−1.04724			−0.523618	−	0.851953i	$-0.675418\pi$
$79$	−9.30803			−1.04724			−0.523618	+	0.851953i	$0.675418\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	6.70420	−	6.00447i	0.744911	−	0.667164i
$82$	2.14946	−	3.72298i	0.237368	−	0.411134i
$83$	−0.645374	−	1.11782i	−0.0708390	−	0.122697i	0.828430	−	0.560092i	$-0.189234\pi$
$83$	−0.645374	−	1.11782i	−0.0708390	−	0.122697i	−0.899269	+	0.437395i	$0.855901\pi$
$84$	−4.51518	−	0.783063i	−0.492646	−	0.0854392i
$85$	−0.372166	+	0.644610i	−0.0403670	+	0.0699177i
$86$	−4.16353	−	7.21144i	−0.448965	−	0.777629i
$87$	−5.88120	−	6.89522i	−0.630530	−	0.739245i
$88$	1.14860	−	1.98944i	0.122441	−	0.212075i
$89$	0.165401	−	0.286482i	0.0175324	−	0.0303671i	−0.857126	−	0.515107i	$-0.827752\pi$
$89$	0.165401	−	0.286482i	0.0175324	−	0.0303671i	0.874659	+	0.484740i	$0.161086\pi$
$90$	−2.32894	−	1.89104i	−0.245492	−	0.199333i
$91$	−3.44171	+	2.85726i	−0.360789	+	0.299522i
$92$	−1.07539	−	1.86262i	−0.112117	−	0.194192i
$93$	−7.31923	+	1.35154i	−0.758969	+	0.140148i
$94$	8.18236			0.843946
$95$	7.79736			0.799992
$96$	1.70326	−	0.314515i	0.173838	−	0.0321001i
$97$	3.18123	+	5.51006i	0.323005	+	0.559462i	0.981107	−	0.193468i	$-0.0619735\pi$
$97$	3.18123	+	5.51006i	0.323005	+	0.559462i	−0.658101	+	0.752929i	$0.728640\pi$
$98$	−5.31474	−	4.55561i	−0.536869	−	0.460186i
$99$	−1.08708	+	6.80533i	−0.109256	+	0.683961i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−7.42615	+	12.8625i	−0.738930	+	1.27986i	0.214048	+	0.976823i	$0.431335\pi$
$101$	−7.42615	+	12.8625i	−0.738930	+	1.27986i	−0.952978	+	0.303041i	$0.901998\pi$
$102$	0.836633	+	0.980883i	0.0828390	+	0.0971219i
$103$	−5.09421	−	8.82343i	−0.501947	−	0.869398i	−0.999997	−	0.00225005i	$-0.999284\pi$
$103$	−5.09421	−	8.82343i	−0.501947	−	0.869398i	0.498050	−	0.867148i	$-0.334050\pi$
$104$	0.845351	−	1.46419i	0.0828934	−	0.143576i
$105$	−1.57944	−	4.30179i	−0.154137	−	0.419812i
$106$	−6.31906	−	10.9449i	−0.613762	−	1.06307i
$107$	−6.45353	+	11.1778i	−0.623887	+	1.08060i	0.364868	+	0.931059i	$0.381114\pi$
$107$	−6.45353	+	11.1778i	−0.623887	+	1.08060i	−0.988755	+	0.149544i	$0.952219\pi$
$108$	−4.43582	+	2.70619i	−0.426837	+	0.260403i
$109$	1.12676	+	1.95161i	0.107924	+	0.186930i	0.914929	−	0.403614i	$-0.132246\pi$
$109$	1.12676	+	1.95161i	0.107924	+	0.186930i	−0.807005	+	0.590545i	$0.798913\pi$
$110$	2.29720			0.219030
$111$	6.26172	−	17.6455i	0.594337	−	1.67484i
$112$	2.48140	+	0.917950i	0.234471	+	0.0867381i
$113$	9.72776	−	16.8490i	0.915111	−	1.58502i	0.108372	−	0.994110i	$-0.465436\pi$
$113$	9.72776	−	16.8490i	0.915111	−	1.58502i	0.806739	−	0.590908i	$-0.201230\pi$
$114$	4.51662	−	12.7278i	0.423020	−	1.19207i
$115$	1.07539	−	1.86262i	0.100280	−	0.173691i
$116$	2.61618	+	4.53135i	0.242906	+	0.420725i
$117$	−0.800073	+	5.00860i	−0.0739668	+	0.463046i
$118$	−0.635800			−0.0585301
$119$	0.331774	+	1.94117i	0.0304137	+	0.177946i
$120$	1.12401	+	1.31780i	0.102607	+	0.120299i
$121$	2.86143	+	4.95614i	0.260130	+	0.450558i
$122$	−6.90519			−0.625166
$123$	2.49015	−	7.01722i	0.224529	−	0.632722i
$124$	4.29720			0.385900
$125$	−1.00000			−0.0894427
$126$	−7.93678	+	0.0863357i	−0.707065	+	0.00769139i
$127$	−12.7583			−1.13212			−0.566058	−	0.824366i	$-0.691532\pi$
$127$	−12.7583			−1.13212			−0.566058	+	0.824366i	$0.691532\pi$
$128$	−1.00000			−0.0883883
$129$	−9.35966	−	10.9734i	−0.824072	−	0.966157i
$130$	1.69070			0.148284
$131$	−5.24391	−	9.08272i	−0.458163	−	0.793561i	0.540701	−	0.841215i	$-0.318159\pi$
$131$	−5.24391	−	9.08272i	−0.458163	−	0.793561i	−0.998864	+	0.0476537i	$0.984826\pi$
$132$	1.33065	−	3.74977i	0.115819	−	0.326376i
$133$	15.8729	−	13.1774i	1.37635	−	1.14263i
$134$	−9.77125			−0.844108
$135$	−4.56154	−	2.48844i	−0.392595	−	0.214171i
$136$	−0.372166	−	0.644610i	−0.0319129	−	0.0552748i
$137$	1.09980	−	1.90491i	0.0939621	−	0.162747i	−0.815213	−	0.579161i	$-0.803380\pi$
$137$	1.09980	−	1.90491i	0.0939621	−	0.162747i	0.909175	+	0.416414i	$0.136713\pi$
$138$	−2.41748	−	2.83430i	−0.205790	−	0.241272i
$139$	1.22903	−	2.12875i	0.104245	−	0.180558i	−0.809184	−	0.587555i	$-0.800091\pi$
$139$	1.22903	−	2.12875i	0.104245	−	0.180558i	0.913430	+	0.406997i	$0.133424\pi$
$140$	0.445734	+	2.60793i	0.0376714	+	0.220411i
$141$	13.9366	−	2.57348i	1.17368	−	0.216726i
$142$	−2.50553			−0.210259
$143$	−1.94194	−	3.36354i	−0.162393	−	0.281273i
$144$	2.80216	−	1.07140i	0.233513	−	0.0892834i
$145$	−2.61618	+	4.53135i	−0.217262	+	0.376308i
$146$	3.42499	+	5.93225i	0.283454	+	0.490957i
$147$	−10.4852	−	6.08780i	−0.864802	−	0.502113i
$148$	−5.40503	+	9.36179i	−0.444291	+	0.769534i
$149$	−5.10818	−	8.84763i	−0.418479	−	0.724826i	0.577308	−	0.816526i	$-0.304103\pi$
$149$	−5.10818	−	8.84763i	−0.418479	−	0.724826i	−0.995787	+	0.0917002i	$0.970770\pi$
$150$	−0.579249	+	1.63232i	−0.0472955	+	0.133278i
$151$	1.40160	−	2.42764i	0.114061	−	0.197559i	−0.803343	−	0.595516i	$-0.796948\pi$
$151$	1.40160	−	2.42764i	0.114061	−	0.197559i	0.917404	+	0.397958i	$0.130281\pi$
$152$	−3.89868	+	6.75271i	−0.316225	+	0.547717i
$153$	1.73350	+	1.40756i	0.140145	+	0.113795i
$154$	4.67635	−	3.88224i	0.376831	−	0.312840i
$155$	2.14860	+	3.72149i	0.172580	+	0.298917i
$156$	0.979338	−	2.75977i	0.0784098	−	0.220958i
$157$	6.15451			0.491183			0.245592	−	0.969373i	$-0.421018\pi$
$157$	6.15451			0.491183			0.245592	+	0.969373i	$0.421018\pi$
$158$	9.30803			0.740507
$159$	−14.2053	−	16.6546i	−1.12656	−	1.32079i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−0.958673	−	5.60907i	−0.0755540	−	0.442057i
$162$	−6.70420	+	6.00447i	−0.526732	+	0.471756i
$163$	2.75802	−	4.77703i	0.216025	−	0.374166i	−0.737564	−	0.675277i	$-0.764024\pi$
$163$	2.75802	−	4.77703i	0.216025	−	0.374166i	0.953589	+	0.301111i	$0.0973574\pi$
$164$	−2.14946	+	3.72298i	−0.167845	+	0.290716i
$165$	3.91272	−	0.722506i	0.304605	−	0.0562470i
$166$	0.645374	+	1.11782i	0.0500908	+	0.0867597i
$167$	5.03727	−	8.72480i	0.389795	−	0.675145i	−0.602626	−	0.798023i	$-0.705879\pi$
$167$	5.03727	−	8.72480i	0.389795	−	0.675145i	0.992422	+	0.122878i	$0.0392124\pi$
$168$	4.51518	+	0.783063i	0.348353	+	0.0604146i
$169$	5.07076	+	8.78282i	0.390059	+	0.675602i
$170$	0.372166	−	0.644610i	0.0285438	−	0.0494393i
$171$	3.68987	−	23.0992i	0.282171	−	1.76644i
$172$	4.16353	+	7.21144i	0.317466	+	0.549867i
$173$	20.7789			1.57979			0.789895	−	0.613242i	$-0.210135\pi$
$173$	20.7789			1.57979			0.789895	+	0.613242i	$0.210135\pi$
$174$	5.88120	+	6.89522i	0.445852	+	0.522725i
$175$	−2.03567	+	1.68998i	−0.153882	+	0.127751i
$176$	−1.14860	+	1.98944i	−0.0865791	+	0.149959i
$177$	−1.08293	+	0.199969i	−0.0813980	+	0.0150306i
$178$	−0.165401	+	0.286482i	−0.0123973	+	0.0214728i
$179$	1.39534	+	2.41679i	0.104292	+	0.180640i	0.913449	−	0.406954i	$-0.133409\pi$
$179$	1.39534	+	2.41679i	0.104292	+	0.180640i	−0.809157	+	0.587593i	$0.800076\pi$
$180$	2.32894	+	1.89104i	0.173589	+	0.140950i
$181$	−22.2958			−1.65723			−0.828616	−	0.559817i	$-0.810871\pi$
$181$	−22.2958			−1.65723			−0.828616	+	0.559817i	$0.810871\pi$
$182$	3.44171	−	2.85726i	0.255117	−	0.211794i
$183$	−11.7613	+	2.17179i	−0.869420	+	0.160543i
$184$	1.07539	+	1.86262i	0.0792785	+	0.137314i
$185$	−10.8101			−0.794772
$186$	7.31923	−	1.35154i	0.536672	−	0.0990995i
$187$	−1.70988			−0.125039
$188$	−8.18236			−0.596760
$189$	−13.4912	+	2.64329i	−0.981342	+	0.192271i
$190$	−7.79736			−0.565680
$191$	14.5124			1.05008			0.525040	−	0.851078i	$-0.324050\pi$
$191$	14.5124			1.05008			0.525040	+	0.851078i	$0.324050\pi$
$192$	−1.70326	+	0.314515i	−0.122922	+	0.0226982i
$193$	6.32879			0.455556			0.227778	−	0.973713i	$-0.426854\pi$
$193$	6.32879			0.455556			0.227778	+	0.973713i	$0.426854\pi$
$194$	−3.18123	−	5.51006i	−0.228399	−	0.395599i
$195$	2.87970	−	0.531752i	0.206219	−	0.0380795i
$196$	5.31474	+	4.55561i	0.379624	+	0.325401i
$197$	−9.15021			−0.651925			−0.325963	−	0.945383i	$-0.605688\pi$
$197$	−9.15021			−0.651925			−0.325963	+	0.945383i	$0.605688\pi$
$198$	1.08708	−	6.80533i	0.0772555	−	0.483634i
$199$	2.96846	+	5.14152i	0.210428	+	0.364472i	0.951849	−	0.306568i	$-0.0991808\pi$
$199$	2.96846	+	5.14152i	0.210428	+	0.364472i	−0.741420	+	0.671041i	$0.765847\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−16.6429	+	3.07321i	−1.17390	+	0.216768i
$202$	7.42615	−	12.8625i	0.522502	−	0.905000i
$203$	2.33224	+	13.6456i	0.163691	+	0.957735i
$204$	−0.836633	−	0.980883i	−0.0585760	−	0.0686756i
$205$	−4.29892			−0.300250
$206$	5.09421	+	8.82343i	0.354930	+	0.614757i
$207$	−5.00902	−	4.06720i	−0.348151	−	0.282690i
$208$	−0.845351	+	1.46419i	−0.0586145	+	0.101523i
$209$	8.95606	+	15.5123i	0.619504	+	1.07301i
$210$	1.57944	+	4.30179i	0.108991	+	0.296852i
$211$	−7.14767	+	12.3801i	−0.492066	+	0.852283i	−0.999958	−	0.00913776i	$-0.997091\pi$
$211$	−7.14767	+	12.3801i	−0.492066	+	0.852283i	0.507893	+	0.861420i	$0.330425\pi$
$212$	6.31906	+	10.9449i	0.433995	+	0.751702i
$213$	−4.26756	+	0.788027i	−0.292408	+	0.0539947i
$214$	6.45353	−	11.1778i	0.441154	−	0.764102i
$215$	−4.16353	+	7.21144i	−0.283950	+	0.491816i
$216$	4.43582	−	2.70619i	0.301820	−	0.184133i
$217$	10.6631	+	3.94462i	0.723858	+	0.267778i
$218$	−1.12676	−	1.95161i	−0.0763139	−	0.132180i
$219$	7.69942	+	9.02693i	0.520278	+	0.609984i
$220$	−2.29720			−0.154877
$221$	−1.25844			−0.0846520
$222$	−6.26172	+	17.6455i	−0.420259	+	1.18429i
$223$	−8.91331	−	15.4383i	−0.596879	−	1.03383i	−0.993279	−	0.115747i	$-0.963074\pi$
$223$	−8.91331	−	15.4383i	−0.596879	−	1.03383i	0.396399	−	0.918078i	$-0.370260\pi$
$224$	−2.48140	−	0.917950i	−0.165796	−	0.0613331i
$225$	−0.473220	+	2.96244i	−0.0315480	+	0.197496i
$226$	−9.72776	+	16.8490i	−0.647081	+	1.12078i
$227$	10.3752	−	17.9705i	0.688629	−	1.19274i	−0.283652	−	0.958927i	$-0.591546\pi$
$227$	10.3752	−	17.9705i	0.688629	−	1.19274i	0.972281	−	0.233814i	$-0.0751206\pi$
$228$	−4.51662	+	12.7278i	−0.299120	+	0.842919i
$229$	−10.0604	−	17.4251i	−0.664811	−	1.15149i	−0.979337	−	0.202237i	$-0.935179\pi$
$229$	−10.0604	−	17.4251i	−0.664811	−	1.15149i	0.314526	−	0.949249i	$-0.398154\pi$
$230$	−1.07539	+	1.86262i	−0.0709089	+	0.122818i
$231$	6.74399	−	8.08322i	0.443722	−	0.531837i
$232$	−2.61618	−	4.53135i	−0.171760	−	0.297498i
$233$	7.70836	−	13.3513i	0.504992	−	0.874671i	−0.494992	−	0.868898i	$-0.664829\pi$
$233$	7.70836	−	13.3513i	0.504992	−	0.874671i	0.999983	−	0.00577334i	$-0.00183772\pi$
$234$	0.800073	−	5.00860i	0.0523024	−	0.327423i
$235$	−4.09118	−	7.08613i	−0.266879	−	0.462248i
$236$	0.635800			0.0413870
$237$	15.8540	−	2.92752i	1.02983	−	0.190163i
$238$	−0.331774	−	1.94117i	−0.0215057	−	0.125827i
$239$	9.63173	−	16.6826i	0.623025	−	1.07911i	−0.365895	−	0.930656i	$-0.619237\pi$
$239$	9.63173	−	16.6826i	0.623025	−	1.07911i	0.988919	−	0.148454i	$-0.0474297\pi$
$240$	−1.12401	−	1.31780i	−0.0725543	−	0.0850639i
$241$	−13.3167	+	23.0653i	−0.857807	+	1.48576i	0.0162101	+	0.999869i	$0.494840\pi$
$241$	−13.3167	+	23.0653i	−0.857807	+	1.48576i	−0.874017	+	0.485896i	$0.838493\pi$
$242$	−2.86143	−	4.95614i	−0.183940	−	0.318593i
$243$	−9.53047	+	12.3357i	−0.611380	+	0.791337i
$244$	6.90519			0.442059
$245$	−1.28791	+	6.88050i	−0.0822813	+	0.439579i
$246$	−2.49015	+	7.01722i	−0.158766	+	0.447402i
$247$	6.59150	+	11.4168i	0.419407	+	0.726435i
$248$	−4.29720			−0.272873
$249$	1.45081	+	1.70095i	0.0919413	+	0.107794i
$250$	1.00000			0.0632456
$251$	12.9943			0.820191			0.410095	−	0.912043i	$-0.365495\pi$
$251$	12.9943			0.820191			0.410095	+	0.912043i	$0.365495\pi$
$252$	7.93678	−	0.0863357i	0.499970	−	0.00543863i
$253$	4.94076			0.310623
$254$	12.7583			0.800526
$255$	0.431153	−	1.21499i	0.0269999	−	0.0760854i
$256$	1.00000			0.0625000
$257$	−12.5561	−	21.7479i	−0.783230	−	1.35659i	−0.930051	−	0.367431i	$-0.880237\pi$
$257$	−12.5561	−	21.7479i	−0.783230	−	1.35659i	0.146821	−	0.989163i	$-0.453096\pi$
$258$	9.35966	+	10.9734i	0.582707	+	0.683176i
$259$	−22.0057	+	18.2688i	−1.36737	+	1.13517i
$260$	−1.69070			−0.104853
$261$	12.1858	+	9.89459i	0.754284	+	0.612460i
$262$	5.24391	+	9.08272i	0.323970	+	0.561132i
$263$	12.9324	−	22.3995i	0.797444	−	1.38121i	−0.123831	−	0.992303i	$-0.539518\pi$
$263$	12.9324	−	22.3995i	0.797444	−	1.38121i	0.921276	−	0.388910i	$-0.127148\pi$
$264$	−1.33065	+	3.74977i	−0.0818960	+	0.230782i
$265$	−6.31906	+	10.9449i	−0.388177	+	0.672342i
$266$	−15.8729	+	13.1774i	−0.973227	+	0.807959i
$267$	−0.191616	+	0.539974i	−0.0117267	+	0.0330459i
$268$	9.77125			0.596874
$269$	5.30556	+	9.18949i	0.323485	+	0.560293i	0.981205	−	0.192970i	$-0.0618120\pi$
$269$	5.30556	+	9.18949i	0.323485	+	0.560293i	−0.657719	+	0.753263i	$0.728479\pi$
$270$	4.56154	+	2.48844i	0.277607	+	0.151442i
$271$	6.58607	−	11.4074i	0.400075	−	0.692951i	−0.593659	−	0.804716i	$-0.702317\pi$
$271$	6.58607	−	11.4074i	0.400075	−	0.692951i	0.993735	+	0.111766i	$0.0356506\pi$
$272$	0.372166	+	0.644610i	0.0225659	+	0.0390852i
$273$	4.96346	−	5.94911i	0.300402	−	0.360057i
$274$	−1.09980	+	1.90491i	−0.0664412	+	0.115080i
$275$	−1.14860	−	1.98944i	−0.0692633	−	0.119967i
$276$	2.41748	+	2.83430i	0.145515	+	0.170605i
$277$	−15.8627	+	27.4750i	−0.953096	+	1.65081i	−0.214429	+	0.976740i	$0.568789\pi$
$277$	−15.8627	+	27.4750i	−0.953096	+	1.65081i	−0.738667	+	0.674071i	$0.764544\pi$
$278$	−1.22903	+	2.12875i	−0.0737126	+	0.127674i
$279$	12.0414	−	4.60403i	0.720903	−	0.275636i
$280$	−0.445734	−	2.60793i	−0.0266377	−	0.155854i
$281$	10.3107	+	17.8586i	0.615084	+	1.06536i	0.990370	+	0.138448i	$0.0442113\pi$
$281$	10.3107	+	17.8586i	0.615084	+	1.06536i	−0.375285	+	0.926909i	$0.622455\pi$
$282$	−13.9366	+	2.57348i	−0.829915	+	0.153248i
$283$	−4.35025			−0.258595			−0.129298	−	0.991606i	$-0.541272\pi$
$283$	−4.35025			−0.258595			−0.129298	+	0.991606i	$0.541272\pi$
$284$	2.50553			0.148676
$285$	−13.2809	+	2.45239i	−0.786693	+	0.145267i
$286$	1.94194	+	3.36354i	0.114829	+	0.198890i
$287$	−8.75119	+	7.26511i	−0.516566	+	0.428846i
$288$	−2.80216	+	1.07140i	−0.165119	+	0.0631329i
$289$	8.22299	−	14.2426i	0.483705	−	0.837802i
$290$	2.61618	−	4.53135i	0.153627	−	0.266090i
$291$	−7.15145	−	8.38449i	−0.419226	−	0.491507i
$292$	−3.42499	−	5.93225i	−0.200432	−	0.347159i
$293$	−0.408724	+	0.707931i	−0.0238779	+	0.0413578i	−0.877717	−	0.479179i	$-0.840935\pi$
$293$	−0.408724	+	0.707931i	−0.0238779	+	0.0413578i	0.853840	+	0.520536i	$0.174268\pi$
$294$	10.4852	+	6.08780i	0.611507	+	0.355048i
$295$	0.317900	+	0.550619i	0.0185088	+	0.0320583i
$296$	5.40503	−	9.36179i	0.314161	−	0.544143i
$297$	−0.288803	−	11.9331i	−0.0167580	−	0.692430i
$298$	5.10818	+	8.84763i	0.295909	+	0.512530i
$299$	3.63631			0.210293
$300$	0.579249	−	1.63232i	0.0334430	−	0.0942421i
$301$	3.71165	+	21.7164i	0.213936	+	1.25171i
$302$	−1.40160	+	2.42764i	−0.0806530	+	0.139695i
$303$	8.60319	−	24.2437i	0.494240	−	1.39277i
$304$	3.89868	−	6.75271i	0.223605	−	0.387295i
$305$	3.45259	+	5.98007i	0.197695	+	0.342418i
$306$	−1.73350	−	1.40756i	−0.0990978	−	0.0804649i
$307$	10.7190			0.611765			0.305882	−	0.952069i	$-0.401049\pi$
$307$	10.7190			0.611765			0.305882	+	0.952069i	$0.401049\pi$
$308$	−4.67635	+	3.88224i	−0.266460	+	0.221211i
$309$	11.4518	+	13.4263i	0.651473	+	0.763798i
$310$	−2.14860	−	3.72149i	−0.122032	−	0.211366i
$311$	−3.27621			−0.185777			−0.0928884	−	0.995677i	$-0.529610\pi$
$311$	−3.27621			−0.185777			−0.0928884	+	0.995677i	$0.529610\pi$
$312$	−0.979338	+	2.75977i	−0.0554441	+	0.156241i
$313$	22.8568			1.29194			0.645971	−	0.763362i	$-0.276453\pi$
$313$	22.8568			1.29194			0.645971	+	0.763362i	$0.276453\pi$
$314$	−6.15451			−0.347319
$315$	4.04316	+	6.83029i	0.227806	+	0.384843i
$316$	−9.30803			−0.523618
$317$	−23.0268			−1.29331			−0.646657	−	0.762781i	$-0.723834\pi$
$317$	−23.0268			−1.29331			−0.646657	+	0.762781i	$0.723834\pi$
$318$	14.2053	+	16.6546i	0.796596	+	0.933943i
$319$	−12.0198			−0.672978
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	7.47641	−	21.0685i	0.417293	−	1.17593i
$322$	0.958673	+	5.60907i	0.0534248	+	0.312581i
$323$	5.80382			0.322933
$324$	6.70420	−	6.00447i	0.372456	−	0.333582i
$325$	−0.845351	−	1.46419i	−0.0468916	−	0.0812187i
$326$	−2.75802	+	4.77703i	−0.152753	+	0.264575i
$327$	−2.53297	−	2.96970i	−0.140074	−	0.164225i
$328$	2.14946	−	3.72298i	0.118684	−	0.205567i
$329$	−20.3037	−	7.51099i	−1.11938	−	0.414094i
$330$	−3.91272	+	0.722506i	−0.215388	+	0.0397726i
$331$	−24.0419			−1.32146			−0.660732	−	0.750622i	$-0.729754\pi$
$331$	−24.0419			−1.32146			−0.660732	+	0.750622i	$0.729754\pi$
$332$	−0.645374	−	1.11782i	−0.0354195	−	0.0613484i
$333$	−5.11554	+	32.0242i	−0.280330	+	1.75491i
$334$	−5.03727	+	8.72480i	−0.275627	+	0.477400i
$335$	4.88563	+	8.46215i	0.266930	+	0.462337i
$336$	−4.51518	−	0.783063i	−0.246323	−	0.0427196i
$337$	2.92411	−	5.06471i	0.159287	−	0.275892i	−0.775325	−	0.631562i	$-0.782414\pi$
$337$	2.92411	−	5.06471i	0.159287	−	0.275892i	0.934612	+	0.355670i	$0.115747\pi$
$338$	−5.07076	−	8.78282i	−0.275813	−	0.477723i
$339$	−11.2696	+	31.7576i	−0.612081	+	1.72484i
$340$	−0.372166	+	0.644610i	−0.0201835	+	0.0349589i
$341$	−4.93577	+	8.54901i	−0.267287	+	0.462955i
$342$	−3.68987	+	23.0992i	−0.199525	+	1.24906i
$343$	9.00619	+	16.1830i	0.486288	+	0.873798i
$344$	−4.16353	−	7.21144i	−0.224482	−	0.388815i
$345$	−1.24583	+	3.51075i	−0.0670734	+	0.189012i
$346$	−20.7789			−1.11708
$347$	32.4523			1.74213			0.871065	−	0.491168i	$-0.163430\pi$
$347$	32.4523			1.74213			0.871065	+	0.491168i	$0.163430\pi$
$348$	−5.88120	−	6.89522i	−0.315265	−	0.369622i
$349$	−1.58495	−	2.74522i	−0.0848405	−	0.146948i	0.820483	−	0.571671i	$-0.193705\pi$
$349$	−1.58495	−	2.74522i	−0.0848405	−	0.146948i	−0.905323	+	0.424723i	$0.860371\pi$
$350$	2.03567	−	1.68998i	0.108811	−	0.0903335i
$351$	−0.212554	−	8.78257i	−0.0113453	−	0.468779i
$352$	1.14860	−	1.98944i	0.0612207	−	0.106037i
$353$	6.51501	−	11.2843i	0.346759	−	0.600604i	−0.638913	−	0.769279i	$-0.720616\pi$
$353$	6.51501	−	11.2843i	0.346759	−	0.600604i	0.985672	+	0.168675i	$0.0539489\pi$
$354$	1.08293	−	0.199969i	0.0575571	−	0.0106282i
$355$	1.25276	+	2.16985i	0.0664898	+	0.115164i
$356$	0.165401	−	0.286482i	0.00876622	−	0.0151835i
$357$	−1.17562	−	3.20196i	−0.0622206	−	0.169465i
$358$	−1.39534	−	2.41679i	−0.0737458	−	0.127732i
$359$	3.51577	−	6.08949i	0.185555	−	0.321391i	−0.758208	−	0.652012i	$-0.773925\pi$
$359$	3.51577	−	6.08949i	0.185555	−	0.321391i	0.943763	+	0.330621i	$0.107258\pi$
$360$	−2.32894	−	1.89104i	−0.122746	−	0.0996666i
$361$	−20.8994	−	36.1989i	−1.09997	−	1.90520i
$362$	22.2958			1.17184
$363$	−6.43253	−	7.54161i	−0.337620	−	0.395832i
$364$	−3.44171	+	2.85726i	−0.180395	+	0.149761i
$365$	3.42499	−	5.93225i	0.179272	−	0.310508i
$366$	11.7613	−	2.17179i	0.614773	−	0.113521i
$367$	−4.71676	+	8.16967i	−0.246213	+	0.426453i	−0.962472	−	0.271381i	$-0.912520\pi$
$367$	−4.71676	+	8.16967i	−0.246213	+	0.426453i	0.716259	+	0.697835i	$0.245853\pi$
$368$	−1.07539	−	1.86262i	−0.0560584	−	0.0970960i
$369$	−2.03434	+	12.7353i	−0.105903	+	0.662974i
$370$	10.8101			0.561988
$371$	5.63325	+	32.9594i	0.292464	+	1.71117i
$372$	−7.31923	+	1.35154i	−0.379485	+	0.0700739i
$373$	−18.8628	−	32.6713i	−0.976678	−	1.69166i	−0.674281	−	0.738475i	$-0.735546\pi$
$373$	−18.8628	−	32.6713i	−0.976678	−	1.69166i	−0.302397	−	0.953182i	$-0.597787\pi$
$374$	1.70988			0.0884158
$375$	1.70326	−	0.314515i	0.0879557	−	0.0162415i
$376$	8.18236			0.421973
$377$	−8.84634			−0.455610
$378$	13.4912	−	2.64329i	0.693913	−	0.135956i
$379$	6.94296			0.356636			0.178318	−	0.983973i	$-0.442934\pi$
$379$	6.94296			0.356636			0.178318	+	0.983973i	$0.442934\pi$
$380$	7.79736			0.399996
$381$	21.7306	−	4.01268i	1.11329	−	0.205576i
$382$	−14.5124			−0.742519
$383$	13.5881	+	23.5353i	0.694320	+	1.20260i	0.970409	+	0.241465i	$0.0776280\pi$
$383$	13.5881	+	23.5353i	0.694320	+	1.20260i	−0.276090	+	0.961132i	$0.589039\pi$
$384$	1.70326	−	0.314515i	0.0869189	−	0.0160501i
$385$	−5.70029	−	2.10872i	−0.290514	−	0.107470i
$386$	−6.32879			−0.322127
$387$	19.3932	+	15.7468i	0.985812	+	0.800455i
$388$	3.18123	+	5.51006i	0.161503	+	0.279731i
$389$	13.5440	−	23.4590i	0.686710	−	1.18942i	−0.286186	−	0.958174i	$-0.592388\pi$
$389$	13.5440	−	23.4590i	0.686710	−	1.18942i	0.972896	−	0.231243i	$-0.0742791\pi$
$390$	−2.87970	+	0.531752i	−0.145819	+	0.0269263i
$391$	0.800444	−	1.38641i	0.0404802	−	0.0701137i
$392$	−5.31474	−	4.55561i	−0.268435	−	0.230093i
$393$	11.7884	+	13.8209i	0.594645	+	0.697172i
$394$	9.15021			0.460981
$395$	−4.65402	−	8.06099i	−0.234169	−	0.405593i
$396$	−1.08708	+	6.80533i	−0.0546279	+	0.341981i
$397$	18.7475	−	32.4716i	0.940908	−	1.62970i	0.177164	−	0.984181i	$-0.443308\pi$
$397$	18.7475	−	32.4716i	0.940908	−	1.62970i	0.763744	−	0.645519i	$-0.223359\pi$
$398$	−2.96846	−	5.14152i	−0.148795	−	0.257721i
$399$	−22.8910	+	27.4368i	−1.14598	+	1.37356i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	6.34260	+	10.9857i	0.316735	+	0.548600i	0.979805	−	0.199957i	$-0.0640802\pi$
$401$	6.34260	+	10.9857i	0.316735	+	0.548600i	−0.663070	+	0.748557i	$0.730747\pi$
$402$	16.6429	−	3.07321i	0.830075	−	0.153278i
$403$	−3.63264	+	6.29192i	−0.180955	+	0.313423i
$404$	−7.42615	+	12.8625i	−0.369465	+	0.639932i
$405$	8.55213	+	2.80377i	0.424959	+	0.139321i
$406$	−2.33224	−	13.6456i	−0.115747	−	0.677221i
$407$	−12.4165	−	21.5059i	−0.615461	−	1.06601i
$408$	0.836633	+	0.980883i	0.0414195	+	0.0485610i
$409$	12.0211			0.594406			0.297203	−	0.954814i	$-0.403946\pi$
$409$	12.0211			0.594406			0.297203	+	0.954814i	$0.403946\pi$
$410$	4.29892			0.212309
$411$	−1.27412	+	3.59045i	−0.0628475	+	0.177104i
$412$	−5.09421	−	8.82343i	−0.250974	−	0.434699i
$413$	1.57768	+	0.583632i	0.0776324	+	0.0287187i
$414$	5.00902	+	4.06720i	0.246180	+	0.199892i
$415$	0.645374	−	1.11782i	0.0316802	−	0.0548717i
$416$	0.845351	−	1.46419i	0.0414467	−	0.0717878i
$417$	−1.42384	+	4.01236i	−0.0697255	+	0.196486i
$418$	−8.95606	−	15.5123i	−0.438055	−	0.758734i
$419$	−0.923993	+	1.60040i	−0.0451400	+	0.0781848i	−0.887713	−	0.460398i	$-0.847707\pi$
$419$	−0.923993	+	1.60040i	−0.0451400	+	0.0781848i	0.842573	+	0.538583i	$0.181040\pi$
$420$	−1.57944	−	4.30179i	−0.0770685	−	0.209906i
$421$	−3.88451	−	6.72817i	−0.189320	−	0.327911i	0.755704	−	0.654913i	$-0.227295\pi$
$421$	−3.88451	−	6.72817i	−0.189320	−	0.327911i	−0.945024	+	0.327002i	$0.893962\pi$
$422$	7.14767	−	12.3801i	0.347943	−	0.602655i
$423$	−22.9283	+	8.76658i	−1.11481	+	0.426246i
$424$	−6.31906	−	10.9449i	−0.306881	−	0.531533i
$425$	−0.744331			−0.0361054
$426$	4.26756	−	0.788027i	0.206764	−	0.0381801i
$427$	17.1346	+	6.33861i	0.829199	+	0.306747i
$428$	−6.45353	+	11.1778i	−0.311943	+	0.540302i
$429$	4.36551	+	5.11820i	0.210769	+	0.247109i
$430$	4.16353	−	7.21144i	0.200783	−	0.347766i
$431$	6.54581	+	11.3377i	0.315301	+	0.546117i	0.979501	−	0.201437i	$-0.0645613\pi$
$431$	6.54581	+	11.3377i	0.315301	+	0.546117i	−0.664201	+	0.747554i	$0.731228\pi$
$432$	−4.43582	+	2.70619i	−0.213419	+	0.130202i
$433$	−29.2502			−1.40567			−0.702836	−	0.711352i	$-0.748083\pi$
$433$	−29.2502			−1.40567			−0.702836	+	0.711352i	$0.748083\pi$
$434$	−10.6631	−	3.94462i	−0.511845	−	0.189348i
$435$	3.03084	−	8.54087i	0.145317	−	0.409504i
$436$	1.12676	+	1.95161i	0.0539621	+	0.0934651i
$437$	−16.7704			−0.802235
$438$	−7.69942	−	9.02693i	−0.367892	−	0.431324i
$439$	−14.9451			−0.713293			−0.356646	−	0.934239i	$-0.616080\pi$
$439$	−14.9451			−0.713293			−0.356646	+	0.934239i	$0.616080\pi$
$440$	2.29720			0.109515
$441$	19.7736	+	7.07134i	0.941601	+	0.336730i
$442$	1.25844			0.0598580
$443$	−23.2840			−1.10625			−0.553127	−	0.833097i	$-0.686566\pi$
$443$	−23.2840			−1.10625			−0.553127	+	0.833097i	$0.686566\pi$
$444$	6.26172	−	17.6455i	0.297168	−	0.837418i
$445$	0.330801			0.0156815
$446$	8.91331	+	15.4383i	0.422057	+	0.731025i
$447$	11.4833	+	13.4632i	0.543140	+	0.636786i
$448$	2.48140	+	0.917950i	0.117235	+	0.0433691i
$449$	−13.2825			−0.626839			−0.313419	−	0.949615i	$-0.601475\pi$
$449$	−13.2825			−0.626839			−0.313419	+	0.949615i	$0.601475\pi$
$450$	0.473220	−	2.96244i	0.0223078	−	0.139651i
$451$	−4.93775	−	8.55243i	−0.232510	−	0.402718i
$452$	9.72776	−	16.8490i	0.457555	−	0.792509i
$453$	−1.62375	+	4.57572i	−0.0762905	+	0.214986i
$454$	−10.3752	+	17.9705i	−0.486935	+	0.843395i
$455$	−4.19531	−	1.55198i	−0.196679	−	0.0727579i
$456$	4.51662	−	12.7278i	0.211510	−	0.596033i
$457$	35.0984			1.64183			0.820916	−	0.571048i	$-0.193463\pi$
$457$	35.0984			1.64183			0.820916	+	0.571048i	$0.193463\pi$
$458$	10.0604	+	17.4251i	0.470092	+	0.814223i
$459$	−3.39530	−	1.85222i	−0.158479	−	0.0864544i
$460$	1.07539	−	1.86262i	0.0501401	−	0.0868453i
$461$	−4.53012	−	7.84640i	−0.210989	−	0.365443i	0.741036	−	0.671466i	$-0.234335\pi$
$461$	−4.53012	−	7.84640i	−0.210989	−	0.365443i	−0.952024	+	0.306023i	$0.901002\pi$
$462$	−6.74399	+	8.08322i	−0.313759	+	0.376066i
$463$	−21.1130	+	36.5688i	−0.981204	+	1.69950i	−0.323484	+	0.946234i	$0.604854\pi$
$463$	−21.1130	+	36.5688i	−0.981204	+	1.69950i	−0.657721	+	0.753262i	$0.728479\pi$
$464$	2.61618	+	4.53135i	0.121453	+	0.210363i
$465$	−4.83008	−	5.66287i	−0.223990	−	0.262610i
$466$	−7.70836	+	13.3513i	−0.357083	+	0.618486i
$467$	5.26870	−	9.12565i	0.243806	−	0.422285i	−0.717989	−	0.696054i	$-0.754937\pi$
$467$	5.26870	−	9.12565i	0.243806	−	0.422285i	0.961795	+	0.273770i	$0.0882706\pi$
$468$	−0.800073	+	5.00860i	−0.0369834	+	0.231523i
$469$	24.2464	+	8.96952i	1.11960	+	0.414174i
$470$	4.09118	+	7.08613i	0.188712	+	0.326859i
$471$	−10.4827	+	1.93569i	−0.483017	+	0.0891918i
$472$	−0.635800			−0.0292651
$473$	−19.1289			−0.879549
$474$	−15.8540	+	2.92752i	−0.728197	+	0.134465i
$475$	3.89868	+	6.75271i	0.178884	+	0.309836i
$476$	0.331774	+	1.94117i	0.0152068	+	0.0889732i
$477$	29.4334	+	23.8992i	1.34766	+	1.09427i
$478$	−9.63173	+	16.6826i	−0.440545	+	0.763046i
$479$	18.7128	−	32.4116i	0.855011	−	1.48092i	−0.0216236	−	0.999766i	$-0.506884\pi$
$479$	18.7128	−	32.4116i	0.855011	−	1.48092i	0.876635	−	0.481157i	$-0.159783\pi$
$480$	1.12401	+	1.31780i	0.0513036	+	0.0601493i
$481$	−9.13829	−	15.8280i	−0.416670	−	0.721694i
$482$	13.3167	−	23.0653i	0.606561	−	1.05059i
$483$	3.39701	+	9.25217i	0.154569	+	0.420988i
$484$	2.86143	+	4.95614i	0.130065	+	0.225279i
$485$	−3.18123	+	5.51006i	−0.144452	+	0.250199i
$486$	9.53047	−	12.3357i	0.432311	−	0.559560i
$487$	7.69208	+	13.3231i	0.348561	+	0.603726i	0.985994	−	0.166780i	$-0.0533370\pi$
$487$	7.69208	+	13.3231i	0.348561	+	0.603726i	−0.637433	+	0.770506i	$0.720004\pi$
$488$	−6.90519			−0.312583
$489$	−3.19516	+	9.00395i	−0.144490	+	0.407173i
$490$	1.28791	−	6.88050i	0.0581817	−	0.310829i
$491$	11.7768	−	20.3981i	0.531481	−	0.920551i	−0.467844	−	0.883811i	$-0.654969\pi$
$491$	11.7768	−	20.3981i	0.531481	−	0.920551i	0.999325	−	0.0367405i	$-0.0116975\pi$
$492$	2.49015	−	7.01722i	0.112265	−	0.316361i
$493$	−1.94730	+	3.37282i	−0.0877020	+	0.151904i
$494$	−6.59150	−	11.4168i	−0.296566	−	0.513667i
$495$	−6.43713	+	2.46122i	−0.289327	+	0.110624i
$496$	4.29720			0.192950
$497$	6.21723	+	2.29995i	0.278881	+	0.103167i
$498$	−1.45081	−	1.70095i	−0.0650123	−	0.0762216i
$499$	3.43382	+	5.94754i	0.153719	+	0.266249i	0.932592	−	0.360933i	$-0.117542\pi$
$499$	3.43382	+	5.94754i	0.153719	+	0.266249i	−0.778873	+	0.627182i	$0.784208\pi$
$500$	−1.00000			−0.0447214
$501$	−5.83567	+	16.4449i	−0.260718	+	0.734702i
$502$	−12.9943			−0.579962
$503$	−19.9980			−0.891665			−0.445833	−	0.895116i	$-0.647092\pi$
$503$	−19.9980			−0.891665			−0.445833	+	0.895116i	$0.647092\pi$
$504$	−7.93678	+	0.0863357i	−0.353532	+	0.00384570i
$505$	−14.8523			−0.660919
$506$	−4.94076			−0.219644
$507$	−11.3991	−	13.3646i	−0.506254	−	0.593541i
$508$	−12.7583			−0.566058
$509$	2.15505	+	3.73266i	0.0955210	+	0.165447i	0.909826	−	0.414990i	$-0.136215\pi$
$509$	2.15505	+	3.73266i	0.0955210	+	0.165447i	−0.814305	+	0.580437i	$0.802882\pi$
$510$	−0.431153	+	1.21499i	−0.0190918	+	0.0538005i
$511$	−3.05327	−	17.8643i	−0.135069	−	0.790270i
$512$	−1.00000			−0.0441942
$513$	0.980280	+	40.5044i	0.0432804	+	1.78831i
$514$	12.5561	+	21.7479i	0.553827	+	0.959257i
$515$	5.09421	−	8.82343i	0.224478	−	0.388807i
$516$	−9.35966	−	10.9734i	−0.412036	−	0.483078i
$517$	9.39826	−	16.2783i	0.413335	−	0.715918i
$518$	22.0057	−	18.2688i	0.966876	−	0.802687i
$519$	−35.3918	+	6.53528i	−1.55353	+	0.286867i
$520$	1.69070			0.0741421
$521$	−9.77625	−	16.9330i	−0.428305	−	0.741847i	0.568417	−	0.822740i	$-0.307556\pi$
$521$	−9.77625	−	16.9330i	−0.428305	−	0.741847i	−0.996723	+	0.0808936i	$0.974223\pi$
$522$	−12.1858	−	9.89459i	−0.533359	−	0.433075i
$523$	13.2331	−	22.9204i	0.578643	−	1.00224i	−0.416992	−	0.908910i	$-0.636916\pi$
$523$	13.2331	−	22.9204i	0.578643	−	1.00224i	0.995635	−	0.0933291i	$-0.0297509\pi$
$524$	−5.24391	−	9.08272i	−0.229081	−	0.396780i
$525$	2.93574	−	3.51873i	0.128126	−	0.153570i
$526$	−12.9324	+	22.3995i	−0.563878	+	0.976666i
$527$	1.59927	+	2.77002i	0.0696653	+	0.120664i
$528$	1.33065	−	3.74977i	0.0579093	−	0.163188i
$529$	9.18709	−	15.9125i	0.399439	−	0.691848i
$530$	6.31906	−	10.9449i	0.274483	−	0.475418i
$531$	1.78161	−	0.681196i	0.0773154	−	0.0295614i
$532$	15.8729	−	13.1774i	0.688176	−	0.571314i
$533$	−3.63410	−	6.29444i	−0.157410	−	0.272643i
$534$	0.191616	−	0.539974i	0.00829206	−	0.0233669i
$535$	−12.9071			−0.558021
$536$	−9.77125			−0.422054
$537$	−3.13673	−	3.67756i	−0.135360	−	0.158699i
$538$	−5.30556	−	9.18949i	−0.228739	−	0.396187i
$539$	−15.1676	+	5.34075i	−0.653315	+	0.230042i
$540$	−4.56154	−	2.48844i	−0.196298	−	0.107085i
$541$	−9.96183	+	17.2544i	−0.428292	+	0.741824i	−0.996722	−	0.0809080i	$-0.974218\pi$
$541$	−9.96183	+	17.2544i	−0.428292	+	0.741824i	0.568429	+	0.822732i	$0.307551\pi$
$542$	−6.58607	+	11.4074i	−0.282896	+	0.489990i
$543$	37.9754	−	7.01237i	1.62968	−	0.300930i
$544$	−0.372166	−	0.644610i	−0.0159565	−	0.0276374i
$545$	−1.12676	+	1.95161i	−0.0482652	+	0.0835977i
$546$	−4.96346	+	5.94911i	−0.212416	+	0.254599i
$547$	−2.95824	−	5.12382i	−0.126485	−	0.219079i	0.795827	−	0.605524i	$-0.207036\pi$
$547$	−2.95824	−	5.12382i	−0.126485	−	0.219079i	−0.922313	+	0.386445i	$0.873703\pi$
$548$	1.09980	−	1.90491i	0.0469811	−	0.0813736i
$549$	19.3494	−	7.39822i	0.825814	−	0.315748i
$550$	1.14860	+	1.98944i	0.0489765	+	0.0848298i
$551$	40.7985			1.73808
$552$	−2.41748	−	2.83430i	−0.102895	−	0.120636i
$553$	−23.0970	−	8.54431i	−0.982184	−	0.363341i
$554$	15.8627	−	27.4750i	0.673940	−	1.16730i
$555$	18.4123	−	3.39993i	0.781559	−	0.144319i
$556$	1.22903	−	2.12875i	0.0521227	−	0.0902791i
$557$	−2.53724	−	4.39463i	−0.107506	−	0.186206i	0.807253	−	0.590205i	$-0.200953\pi$
$557$	−2.53724	−	4.39463i	−0.107506	−	0.186206i	−0.914759	+	0.403999i	$0.867620\pi$
$558$	−12.0414	+	4.60403i	−0.509755	+	0.194904i
$559$	−14.0786			−0.595459
$560$	0.445734	+	2.60793i	0.0188357	+	0.110205i
$561$	2.91236	−	0.537784i	0.122960	−	0.0227052i
$562$	−10.3107	−	17.8586i	−0.434930	−	0.753321i
$563$	−20.0992			−0.847080			−0.423540	−	0.905877i	$-0.639213\pi$
$563$	−20.0992			−0.847080			−0.423540	+	0.905877i	$0.639213\pi$
$564$	13.9366	−	2.57348i	0.586839	−	0.108363i
$565$	19.4555			0.818500
$566$	4.35025			0.182854
$567$	22.1476	−	8.74540i	0.930113	−	0.367272i
$568$	−2.50553			−0.105130
$569$	−3.42146			−0.143435			−0.0717176	−	0.997425i	$-0.522848\pi$
$569$	−3.42146			−0.143435			−0.0717176	+	0.997425i	$0.522848\pi$
$570$	13.2809	−	2.45239i	0.556276	−	0.102719i
$571$	−7.87737			−0.329658			−0.164829	−	0.986322i	$-0.552707\pi$
$571$	−7.87737			−0.329658			−0.164829	+	0.986322i	$0.552707\pi$
$572$	−1.94194	−	3.36354i	−0.0811966	−	0.140637i
$573$	−24.7183	+	4.56437i	−1.03262	+	0.190679i
$574$	8.75119	−	7.26511i	0.365268	−	0.303240i
$575$	2.15077			0.0896934
$576$	2.80216	−	1.07140i	0.116757	−	0.0446417i
$577$	−4.38883	−	7.60168i	−0.182709	−	0.316462i	0.760093	−	0.649814i	$-0.225153\pi$
$577$	−4.38883	−	7.60168i	−0.182709	−	0.316462i	−0.942802	+	0.333353i	$0.891820\pi$
$578$	−8.22299	+	14.2426i	−0.342031	+	0.592415i
$579$	−10.7795	+	1.99050i	−0.447982	+	0.0827224i
$580$	−2.61618	+	4.53135i	−0.108631	+	0.188154i
$581$	−0.575331	−	3.36619i	−0.0238687	−	0.139653i
$582$	7.15145	+	8.38449i	0.296437	+	0.347548i
$583$	−29.0323			−1.20240
$584$	3.42499	+	5.93225i	0.141727	+	0.245478i
$585$	−4.73762	+	1.81142i	−0.195876	+	0.0748929i
$586$	0.408724	−	0.707931i	0.0168842	−	0.0292444i
$587$	−13.3521	−	23.1266i	−0.551102	−	0.954536i	−0.998195	−	0.0600488i	$-0.980874\pi$
$587$	−13.3521	−	23.1266i	−0.551102	−	0.954536i	0.447094	−	0.894487i	$-0.352459\pi$
$588$	−10.4852	−	6.08780i	−0.432401	−	0.251057i
$589$	16.7534	−	29.0178i	0.690313	−	1.19566i
$590$	−0.317900	−	0.550619i	−0.0130877	−	0.0226686i
$591$	15.5851	−	2.87788i	0.641087	−	0.118380i
$592$	−5.40503	+	9.36179i	−0.222145	+	0.384767i
$593$	2.36570	−	4.09751i	0.0971477	−	0.168265i	−0.813355	−	0.581767i	$-0.802361\pi$
$593$	2.36570	−	4.09751i	0.0971477	−	0.168265i	0.910503	+	0.413503i	$0.135695\pi$
$594$	0.288803	+	11.9331i	0.0118497	+	0.489622i
$595$	−1.51521	+	1.25791i	−0.0621177	+	0.0515692i
$596$	−5.10818	−	8.84763i	−0.209239	−	0.362413i
$597$	−6.67313	−	7.82369i	−0.273113	−	0.320202i
$598$	−3.63631			−0.148700
$599$	4.00470			0.163628			0.0818138	−	0.996648i	$-0.473929\pi$
$599$	4.00470			0.163628			0.0818138	+	0.996648i	$0.473929\pi$
$600$	−0.579249	+	1.63232i	−0.0236478	+	0.0666392i
$601$	−7.44908	−	12.9022i	−0.303854	−	0.526291i	0.673151	−	0.739505i	$-0.264940\pi$
$601$	−7.44908	−	12.9022i	−0.303854	−	0.526291i	−0.977006	+	0.213214i	$0.931607\pi$
$602$	−3.71165	−	21.7164i	−0.151276	−	0.885095i
$603$	27.3806	−	10.4689i	1.11502	−	0.426328i
$604$	1.40160	−	2.42764i	0.0570303	−	0.0987793i
$605$	−2.86143	+	4.95614i	−0.116334	+	0.201496i
$606$	−8.60319	+	24.2437i	−0.349481	+	0.984834i
$607$	−1.22205	−	2.11665i	−0.0496014	−	0.0859121i	0.840159	−	0.542341i	$-0.182462\pi$
$607$	−1.22205	−	2.11665i	−0.0496014	−	0.0859121i	−0.889760	+	0.456428i	$0.849128\pi$
$608$	−3.89868	+	6.75271i	−0.158112	+	0.273859i
$609$	−8.26416	−	22.5085i	−0.334881	−	0.912089i
$610$	−3.45259	−	5.98007i	−0.139791	−	0.242126i
$611$	6.91696	−	11.9805i	0.279830	−	0.484680i
$612$	1.73350	+	1.40756i	0.0700727	+	0.0568973i
$613$	−4.65652	−	8.06533i	−0.188075	−	0.325755i	0.756533	−	0.653955i	$-0.226891\pi$
$613$	−4.65652	−	8.06533i	−0.188075	−	0.325755i	−0.944608	+	0.328200i	$0.893558\pi$
$614$	−10.7190			−0.432583
$615$	7.32217	−	1.35208i	0.295258	−	0.0545211i
$616$	4.67635	−	3.88224i	0.188415	−	0.156420i
$617$	17.1834	−	29.7625i	0.691777	−	1.19819i	−0.279479	−	0.960152i	$-0.590162\pi$
$617$	17.1834	−	29.7625i	0.691777	−	1.19819i	0.971255	−	0.238040i	$-0.0765050\pi$
$618$	−11.4518	−	13.4263i	−0.460661	−	0.540087i
$619$	−7.91488	+	13.7090i	−0.318126	+	0.551010i	−0.980097	−	0.198519i	$-0.936387\pi$
$619$	−7.91488	+	13.7090i	−0.318126	+	0.551010i	0.661971	+	0.749529i	$0.269720\pi$
$620$	2.14860	+	3.72149i	0.0862899	+	0.149458i
$621$	9.81084	+	5.35207i	0.393695	+	0.214771i
$622$	3.27621			0.131364
$623$	0.673402	−	0.559049i	0.0269793	−	0.0223978i
$624$	0.979338	−	2.75977i	0.0392049	−	0.110479i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−22.8568			−0.913541
$627$	−20.1333	−	23.6047i	−0.804048	−	0.942680i
$628$	6.15451			0.245592
$629$	−8.04627			−0.320826
$630$	−4.04316	−	6.83029i	−0.161083	−	0.272125i
$631$	−1.08144			−0.0430515			−0.0215257	−	0.999768i	$-0.506852\pi$
$631$	−1.08144			−0.0430515			−0.0215257	+	0.999768i	$0.506852\pi$
$632$	9.30803			0.370254
$633$	8.28056	−	23.3346i	0.329123	−	0.927466i
$634$	23.0268			0.914511
$635$	−6.37915	−	11.0490i	−0.253149	−	0.438466i
$636$	−14.2053	−	16.6546i	−0.563278	−	0.660397i
$637$	−11.1631	+	3.93070i	−0.442298	+	0.155740i
$638$	12.0198			0.475867
$639$	7.02089	−	2.68442i	0.277742	−	0.106194i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−14.7672	+	25.5775i	−0.583267	+	1.01025i	0.411822	+	0.911264i	$0.364893\pi$
$641$	−14.7672	+	25.5775i	−0.583267	+	1.01025i	−0.995089	+	0.0989843i	$0.968441\pi$
$642$	−7.47641	+	21.0685i	−0.295070	+	0.831506i
$643$	13.0513	−	22.6055i	0.514693	−	0.891474i	−0.485162	−	0.874424i	$-0.661239\pi$
$643$	13.0513	−	22.6055i	0.514693	−	0.891474i	0.999855	−	0.0170499i	$-0.00542741\pi$
$644$	−0.958673	−	5.60907i	−0.0377770	−	0.221028i
$645$	4.82344	−	13.5924i	0.189923	−	0.535201i
$646$	−5.80382			−0.228348
$647$	−13.1677	−	22.8071i	−0.517675	−	0.896639i	−0.999789	−	0.0205305i	$-0.993464\pi$
$647$	−13.1677	−	22.8071i	−0.517675	−	0.896639i	0.482115	−	0.876108i	$-0.339869\pi$
$648$	−6.70420	+	6.00447i	−0.263366	+	0.235878i
$649$	−0.730281	+	1.26488i	−0.0286660	+	0.0496510i
$650$	0.845351	+	1.46419i	0.0331574	+	0.0574303i
$651$	−19.4026	−	3.36498i	−0.760449	−	0.131884i
$652$	2.75802	−	4.77703i	0.108012	−	0.187083i
$653$	21.1219	+	36.5842i	0.826565	+	1.43165i	0.900718	+	0.434405i	$0.143041\pi$
$653$	21.1219	+	36.5842i	0.826565	+	1.43165i	−0.0741528	+	0.997247i	$0.523625\pi$
$654$	2.53297	+	2.96970i	0.0990471	+	0.116125i
$655$	5.24391	−	9.08272i	0.204897	−	0.354891i
$656$	−2.14946	+	3.72298i	−0.0839224	+	0.145358i
$657$	−15.9532	−	12.9536i	−0.622393	−	0.505368i
$658$	20.3037	+	7.51099i	0.791522	+	0.292809i
$659$	−4.06632	−	7.04308i	−0.158401	−	0.274359i	0.775891	−	0.630867i	$-0.217301\pi$
$659$	−4.06632	−	7.04308i	−0.158401	−	0.274359i	−0.934292	+	0.356508i	$0.883967\pi$
$660$	3.91272	−	0.722506i	0.152303	−	0.0281235i
$661$	45.2240			1.75901			0.879504	−	0.475891i	$-0.157874\pi$
$661$	45.2240			1.75901			0.879504	+	0.475891i	$0.157874\pi$
$662$	24.0419			0.934416
$663$	2.14345	−	0.395799i	0.0832446	−	0.0153716i
$664$	0.645374	+	1.11782i	0.0250454	+	0.0433799i
$665$	19.3484	+	7.15759i	0.750299	+	0.277559i
$666$	5.11554	−	32.0242i	0.198223	−	1.24091i
$667$	5.62680	−	9.74590i	0.217871	−	0.377363i
$668$	5.03727	−	8.72480i	0.194898	−	0.337573i
$669$	20.0372	+	23.4920i	0.774684	+	0.908254i
$670$	−4.88563	−	8.46215i	−0.188748	−	0.326921i
$671$	−7.93130	+	13.7374i	−0.306185	+	0.530327i
$672$	4.51518	+	0.783063i	0.174177	+	0.0302073i
$673$	−15.9941	−	27.7025i	−0.616526	−	1.06785i	−0.990115	−	0.140260i	$-0.955206\pi$
$673$	−15.9941	−	27.7025i	−0.616526	−	1.06785i	0.373589	−	0.927594i	$-0.378127\pi$
$674$	−2.92411	+	5.06471i	−0.112633	+	0.195085i
$675$	−0.125719	−	5.19463i	−0.00483894	−	0.199941i
$676$	5.07076	+	8.78282i	0.195029	+	0.337801i
$677$	1.14830			0.0441326			0.0220663	−	0.999757i	$-0.492976\pi$
$677$	1.14830			0.0441326			0.0220663	+	0.999757i	$0.492976\pi$
$678$	11.2696	−	31.7576i	0.432806	−	1.21964i
$679$	2.83597	+	16.5929i	0.108835	+	0.636777i
$680$	0.372166	−	0.644610i	0.0142719	−	0.0247197i
$681$	−12.0197	+	33.8715i	−0.460596	+	1.29796i
$682$	4.93577	−	8.54901i	0.189000	−	0.327358i
$683$	8.62552	+	14.9398i	0.330046	+	0.571657i	0.982521	−	0.186154i	$-0.0596023\pi$
$683$	8.62552	+	14.9398i	0.330046	+	0.571657i	−0.652474	+	0.757811i	$0.726269\pi$
$684$	3.68987	−	23.0992i	0.141086	−	0.883221i
$685$	2.19960			0.0840423
$686$	−9.00619	−	16.1830i	−0.343858	−	0.617869i
$687$	22.6159	+	26.5153i	0.862851	+	1.01162i
$688$	4.16353	+	7.21144i	0.158733	+	0.274934i
$689$	−21.3673			−0.814029
$690$	1.24583	−	3.51075i	0.0474281	−	0.133652i
$691$	−15.8952			−0.604681			−0.302340	−	0.953200i	$-0.597768\pi$
$691$	−15.8952			−0.604681			−0.302340	+	0.953200i	$0.597768\pi$
$692$	20.7789			0.789895
$693$	−8.94444	+	15.8889i	−0.339771	+	0.603569i
$694$	−32.4523			−1.23187
$695$	2.45807			0.0932399
$696$	5.88120	+	6.89522i	0.222926	+	0.261363i
$697$	−3.19982			−0.121202
$698$	1.58495	+	2.74522i	0.0599913	+	0.103908i
$699$	−8.93013	+	25.1650i	−0.337768	+	0.951829i
$700$	−2.03567	+	1.68998i	−0.0769411	+	0.0638754i
$701$	−8.85839			−0.334577			−0.167288	−	0.985908i	$-0.553501\pi$
$701$	−8.85839			−0.334577			−0.167288	+	0.985908i	$0.553501\pi$
$702$	0.212554	+	8.78257i	0.00802233	+	0.331477i
$703$	42.1450	+	72.9973i	1.58953	+	2.75314i
$704$	−1.14860	+	1.98944i	−0.0432895	+	0.0749797i
$705$	9.19702	+	10.7827i	0.346380	+	0.406102i
$706$	−6.51501	+	11.2843i	−0.245196	+	0.424691i
$707$	−30.2344	+	25.1002i	−1.13708	+	0.943989i
$708$	−1.08293	+	0.199969i	−0.0406990	+	0.00751529i
$709$	27.7440			1.04195			0.520973	−	0.853573i	$-0.325569\pi$
$709$	27.7440			1.04195			0.520973	+	0.853573i	$0.325569\pi$
$710$	−1.25276	−	2.16985i	−0.0470154	−	0.0814331i
$711$	−26.0826	+	9.97263i	−0.978174	+	0.374003i
$712$	−0.165401	+	0.286482i	−0.00619865	+	0.0107364i
$713$	−4.62115	−	8.00407i	−0.173064	−	0.299755i
$714$	1.17562	+	3.20196i	0.0439966	+	0.119830i
$715$	1.94194	−	3.36354i	0.0726245	−	0.125789i
$716$	1.39534	+	2.41679i	0.0521462	+	0.0903198i
$717$	−11.1583	+	31.4441i	−0.416716	+	1.17430i
$718$	−3.51577	+	6.08949i	−0.131207	+	0.227258i
$719$	−23.7618	+	41.1566i	−0.886166	+	1.53488i	−0.0417937	+	0.999126i	$0.513307\pi$
$719$	−23.7618	+	41.1566i	−0.886166	+	1.53488i	−0.844372	+	0.535758i	$0.820026\pi$
$720$	2.32894	+	1.89104i	0.0867945	+	0.0704750i
$721$	−4.54133	−	26.5707i	−0.169128	−	0.989545i
$722$	20.8994	+	36.1989i	0.777796	+	1.34718i
$723$	15.4274	−	43.4744i	0.573752	−	1.61683i
$724$	−22.2958			−0.828616
$725$	−5.23235			−0.194325
$726$	6.43253	+	7.54161i	0.238734	+	0.279896i
$727$	4.61919	+	8.00066i	0.171316	+	0.296728i	0.938880	−	0.344244i	$-0.111865\pi$
$727$	4.61919	+	8.00066i	0.171316	+	0.296728i	−0.767564	+	0.640972i	$0.778531\pi$
$728$	3.44171	−	2.85726i	0.127558	−	0.105897i
$729$	12.3531	−	24.0084i	0.457520	−	0.889199i
$730$	−3.42499	+	5.93225i	−0.126765	+	0.219563i
$731$	−3.09904	+	5.36770i	−0.114622	+	0.198532i
$732$	−11.7613	+	2.17179i	−0.434710	+	0.0802716i
$733$	23.6098	+	40.8933i	0.872047	+	1.51043i	0.859876	+	0.510504i	$0.170541\pi$
$733$	23.6098	+	40.8933i	0.872047	+	1.51043i	0.0121713	+	0.999926i	$0.496126\pi$
$734$	4.71676	−	8.16967i	0.174099	−	0.301548i
$735$	0.0296089	−	12.1243i	0.00109214	−	0.447212i
$736$	1.07539	+	1.86262i	0.0396393	+	0.0686572i
$737$	−11.2233	+	19.4393i	−0.413415	+	0.716055i
$738$	2.03434	−	12.7353i	0.0748850	−	0.468793i
$739$	−11.3561	−	19.6693i	−0.417740	−	0.723546i	0.577972	−	0.816057i	$-0.303844\pi$
$739$	−11.3561	−	19.6693i	−0.417740	−	0.723546i	−0.995712	+	0.0925102i	$0.970511\pi$
$740$	−10.8101			−0.397386
$741$	−14.8178	−	17.3726i	−0.544345	−	0.638200i
$742$	−5.63325	−	32.9594i	−0.206803	−	1.20998i
$743$	7.29685	−	12.6385i	0.267696	−	0.463662i	−0.700571	−	0.713583i	$-0.747071\pi$
$743$	7.29685	−	12.6385i	0.267696	−	0.463662i	0.968266	+	0.249921i	$0.0804045\pi$
$744$	7.31923	−	1.35154i	0.268336	−	0.0495497i
$745$	5.10818	−	8.84763i	0.187149	−	0.324152i
$746$	18.8628	+	32.6713i	0.690616	+	1.19618i
$747$	−3.00608	−	2.44086i	−0.109987	−	0.0893064i
$748$	−1.70988			−0.0625194
$749$	−26.2745	+	21.8127i	−0.960050	+	0.797020i
$750$	−1.70326	+	0.314515i	−0.0621941	+	0.0114845i
$751$	11.6728	+	20.2179i	0.425946	+	0.737761i	0.996508	−	0.0834937i	$-0.0266079\pi$
$751$	11.6728	+	20.2179i	0.425946	+	0.737761i	−0.570562	+	0.821255i	$0.693275\pi$
$752$	−8.18236			−0.298380
$753$	−22.1326	+	4.08690i	−0.806555	+	0.148935i
$754$	8.84634			0.322165
$755$	2.80320			0.102019
$756$	−13.4912	+	2.64329i	−0.490671	+	0.0961356i
$757$	8.35341			0.303610			0.151805	−	0.988410i	$-0.451491\pi$
$757$	8.35341			0.303610			0.151805	+	0.988410i	$0.451491\pi$
$758$	−6.94296			−0.252180
$759$	−8.41538	+	1.55395i	−0.305459	+	0.0564047i
$760$	−7.79736			−0.282840
$761$	18.5913	+	32.2012i	0.673936	+	1.16729i	0.976779	+	0.214251i	$0.0687309\pi$
$761$	18.5913	+	32.2012i	0.673936	+	1.16729i	−0.302843	+	0.953040i	$0.597936\pi$
$762$	−21.7306	+	4.01268i	−0.787218	+	0.145364i
$763$	1.00447	+	5.87704i	0.0363643	+	0.212763i
$764$	14.5124			0.525040
$765$	−0.352232	+	2.20504i	−0.0127350	+	0.0797233i
$766$	−13.5881	−	23.5353i	−0.490958	−	0.850365i
$767$	−0.537474	+	0.930932i	−0.0194071	+	0.0336140i
$768$	−1.70326	+	0.314515i	−0.0614609	+	0.0113491i
$769$	−8.53353	+	14.7805i	−0.307727	+	0.532998i	−0.977865	−	0.209238i	$-0.932902\pi$
$769$	−8.53353	+	14.7805i	−0.307727	+	0.532998i	0.670138	+	0.742237i	$0.266235\pi$
$770$	5.70029	+	2.10872i	0.205424	+	0.0759929i
$771$	28.2263	+	33.0931i	1.01655	+	1.19182i
$772$	6.32879			0.227778
$773$	−14.2643	−	24.7066i	−0.513052	−	0.888633i	−0.999885	−	0.0151379i	$-0.995181\pi$
$773$	−14.2643	−	24.7066i	−0.513052	−	0.888633i	0.486833	−	0.873495i	$-0.338152\pi$
$774$	−19.3932	−	15.7468i	−0.697074	−	0.566007i
$775$	−2.14860	+	3.72149i	−0.0771800	+	0.133680i
$776$	−3.18123	−	5.51006i	−0.114200	−	0.197800i
$777$	31.7355	−	38.0376i	1.13851	−	1.36459i
$778$	−13.5440	+	23.4590i	−0.485577	+	0.841045i
$779$	16.7601	+	29.0294i	0.600494	+	1.04009i
$780$	2.87970	−	0.531752i	0.103110	−	0.0190398i
$781$	−2.87785	+	4.98459i	−0.102978	+	0.178363i
$782$	−0.800444	+	1.38641i	−0.0286238	+	0.0495779i
$783$	−23.8676	−	13.0204i	−0.852958	−	0.465311i
$784$	5.31474	+	4.55561i	0.189812	+	0.162700i
$785$	3.07725	+	5.32996i	0.109832	+	0.190234i
$786$	−11.7884	−	13.8209i	−0.420478	−	0.492975i
$787$	36.7423			1.30972			0.654861	−	0.755749i	$-0.272727\pi$
$787$	36.7423			1.30972			0.654861	+	0.755749i	$0.272727\pi$
$788$	−9.15021			−0.325963
$789$	−14.9821	+	42.2195i	−0.533378	+	1.50306i
$790$	4.65402	+	8.06099i	0.165582	+	0.286797i
$791$	39.6050	−	32.8795i	1.40819	−	1.16906i
$792$	1.08708	−	6.80533i	0.0386278	−	0.241817i
$793$	−5.83730	+	10.1105i	−0.207289	+	0.359035i
$794$	−18.7475	+	32.4716i	−0.665322	+	1.15237i
$795$	7.32063	−	20.6295i	0.259636	−	0.731652i
$796$	2.96846	+	5.14152i	0.105214	+	0.182236i
$797$	−1.29107	+	2.23620i	−0.0457320	+	0.0792102i	−0.887985	−	0.459872i	$-0.847895\pi$
$797$	−1.29107	+	2.23620i	−0.0457320	+	0.0792102i	0.842253	+	0.539082i	$0.181229\pi$
$798$	22.8910	−	27.4368i	0.810334	−	0.971251i
$799$	−3.04519	−	5.27443i	−0.107731	−	0.186596i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	0.156542	−	0.979980i	0.00553113	−	0.0346259i
$802$	−6.34260	−	10.9857i	−0.223965	−	0.387919i
$803$	15.7358			0.555304
$804$	−16.6429	+	3.07321i	−0.586951	+	0.108384i
$805$	4.37826	−	3.63477i	0.154314	−	0.128109i
$806$	3.63264	−	6.29192i	0.127954	−	0.221623i
$807$	−11.9270	−	13.9834i	−0.419849	−	0.492238i
$808$	7.42615	−	12.8625i	0.261251	−	0.452500i
$809$	−16.3871	−	28.3832i	−0.576139	−	0.997901i	−0.995917	−	0.0902748i	$-0.971225\pi$
$809$	−16.3871	−	28.3832i	−0.576139	−	0.997901i	0.419778	−	0.907627i	$-0.362108\pi$
$810$	−8.55213	−	2.80377i	−0.300491	−	0.0985145i
$811$	−15.6307			−0.548868			−0.274434	−	0.961606i	$-0.588490\pi$
$811$	−15.6307			−0.548868			−0.274434	+	0.961606i	$0.588490\pi$
$812$	2.33224	+	13.6456i	0.0818455	+	0.478868i
$813$	−7.62996	+	21.5012i	−0.267594	+	0.754078i
$814$	12.4165	+	21.5059i	0.435196	+	0.753782i
$815$	5.51604			0.193219
$816$	−0.836633	−	0.980883i	−0.0292880	−	0.0343378i
$817$	64.9290			2.27158
$818$	−12.0211			−0.420309
$819$	−6.58295	+	11.6939i	−0.230027	+	0.408620i
$820$	−4.29892			−0.150125
$821$	−43.1413			−1.50564			−0.752820	−	0.658226i	$-0.771307\pi$
$821$	−43.1413			−1.50564			−0.752820	+	0.658226i	$0.771307\pi$
$822$	1.27412	−	3.59045i	0.0444399	−	0.125231i
$823$	−4.99058			−0.173961			−0.0869803	−	0.996210i	$-0.527722\pi$
$823$	−4.99058			−0.173961			−0.0869803	+	0.996210i	$0.527722\pi$
$824$	5.09421	+	8.82343i	0.177465	+	0.307379i
$825$	2.58207	+	3.02726i	0.0898961	+	0.105396i
$826$	−1.57768	−	0.583632i	−0.0548944	−	0.0203072i
$827$	−34.1979			−1.18918			−0.594589	−	0.804030i	$-0.702685\pi$
$827$	−34.1979			−1.18918			−0.594589	+	0.804030i	$0.702685\pi$
$828$	−5.00902	−	4.06720i	−0.174076	−	0.141345i
$829$	13.9941	+	24.2385i	0.486036	+	0.841839i	0.999871	−	0.0160499i	$-0.00510906\pi$
$829$	13.9941	+	24.2385i	0.486036	+	0.841839i	−0.513835	+	0.857889i	$0.671776\pi$
$830$	−0.645374	+	1.11782i	−0.0224013	+	0.0388001i
$831$	18.3769	−	51.7859i	0.637487	−	1.79643i
$832$	−0.845351	+	1.46419i	−0.0293073	+	0.0507617i
$833$	−0.958629	+	5.12137i	−0.0332145	+	0.177445i
$834$	1.42384	−	4.01236i	0.0493034	−	0.138937i
$835$	10.0745			0.348644
$836$	8.95606	+	15.5123i	0.309752	+	0.536506i
$837$	−19.0616	+	11.6291i	−0.658866	+	0.401959i
$838$	0.923993	−	1.60040i	0.0319188	−	0.0552850i
$839$	20.9174	+	36.2300i	0.722149	+	1.25080i	0.960137	+	0.279531i	$0.0901789\pi$
$839$	20.9174	+	36.2300i	0.722149	+	1.25080i	−0.237988	+	0.971268i	$0.576488\pi$
$840$	1.57944	+	4.30179i	0.0544957	+	0.148426i
$841$	0.811251	−	1.40513i	0.0279742	−	0.0484527i
$842$	3.88451	+	6.72817i	0.133869	+	0.231868i
$843$	−23.1786	−	27.1750i	−0.798312	−	0.935955i
$844$	−7.14767	+	12.3801i	−0.246033	+	0.426141i
$845$	−5.07076	+	8.78282i	−0.174440	+	0.302138i
$846$	22.9283	−	8.76658i	0.788290	−	0.301401i
$847$	2.55088	+	14.9248i	0.0876491	+	0.512824i
$848$	6.31906	+	10.9449i	0.216998	+	0.375851i
$849$	7.40958	−	1.36822i	0.254296	−	0.0469572i
$850$	0.744331			0.0255304
$851$	23.2500			0.796999
$852$	−4.26756	+	0.788027i	−0.146204	+	0.0269974i
$853$	−6.54489	−	11.3361i	−0.224093	−	0.388140i	0.731954	−	0.681354i	$-0.238609\pi$
$853$	−6.54489	−	11.3361i	−0.224093	−	0.388140i	−0.956047	+	0.293214i	$0.905275\pi$
$854$	−17.1346	−	6.33861i	−0.586332	−	0.216903i
$855$	21.8495	−	8.35410i	0.747236	−	0.285704i
$856$	6.45353	−	11.1778i	0.220577	−	0.382051i
$857$	5.65687	−	9.79798i	0.193235	−	0.334693i	−0.753086	−	0.657923i	$-0.771435\pi$
$857$	5.65687	−	9.79798i	0.193235	−	0.334693i	0.946320	+	0.323230i	$0.104769\pi$
$858$	−4.36551	−	5.11820i	−0.149036	−	0.174732i
$859$	−19.5181	−	33.8063i	−0.665948	−	1.15346i	−0.979027	−	0.203728i	$-0.934694\pi$
$859$	−19.5181	−	33.8063i	−0.665948	−	1.15346i	0.313080	−	0.949727i	$-0.398639\pi$
$860$	−4.16353	+	7.21144i	−0.141975	+	0.245908i
$861$	12.6205	−	15.1267i	0.430106	−	0.515518i
$862$	−6.54581	−	11.3377i	−0.222951	−	0.386163i
$863$	−3.61316	+	6.25818i	−0.122993	+	0.213031i	−0.920947	−	0.389688i	$-0.872583\pi$
$863$	−3.61316	+	6.25818i	−0.122993	+	0.213031i	0.797953	+	0.602719i	$0.205916\pi$
$864$	4.43582	−	2.70619i	0.150910	−	0.0920665i
$865$	10.3894	+	17.9951i	0.353252	+	0.611850i
$866$	29.2502			0.993961
$867$	−9.52632	+	26.8451i	−0.323531	+	0.911707i
$868$	10.6631	+	3.94462i	0.361929	+	0.133889i
$869$	10.6912	−	18.5177i	0.362675	−	0.628171i
$870$	−3.03084	+	8.54087i	−0.102755	+	0.289563i
$871$	−8.26013	+	14.3070i	−0.279884	+	0.484773i
$872$	−1.12676	−	1.95161i	−0.0381570	−	0.0660898i
$873$	14.8178	+	12.0317i	0.501507	+	0.407211i
$874$	16.7704			0.567266
$875$	−2.48140	−	0.917950i	−0.0838868	−	0.0310324i
$876$	7.69942	+	9.02693i	0.260139	+	0.304992i
$877$	11.0757	+	19.1837i	0.374000	+	0.647787i	0.990177	−	0.139821i	$-0.0446526\pi$
$877$	11.0757	+	19.1837i	0.374000	+	0.647787i	−0.616177	+	0.787608i	$0.711319\pi$
$878$	14.9451			0.504374
$879$	0.473506	−	1.33434i	0.0159710	−	0.0450061i
$880$	−2.29720			−0.0774387
$881$	−18.1808			−0.612526			−0.306263	−	0.951947i	$-0.599079\pi$
$881$	−18.1808			−0.612526			−0.306263	+	0.951947i	$0.599079\pi$
$882$	−19.7736	−	7.07134i	−0.665813	−	0.238104i
$883$	28.6224			0.963219			0.481610	−	0.876386i	$-0.340052\pi$
$883$	28.6224			0.963219			0.481610	+	0.876386i	$0.340052\pi$
$884$	−1.25844			−0.0423260
$885$	−0.714643	−	0.837860i	−0.0240225	−	0.0281644i
$886$	23.2840			0.782240
$887$	22.0202	+	38.1401i	0.739366	+	1.28062i	0.952781	+	0.303658i	$0.0982081\pi$
$887$	22.0202	+	38.1401i	0.739366	+	1.28062i	−0.213415	+	0.976962i	$0.568459\pi$
$888$	−6.26172	+	17.6455i	−0.210130	+	0.592144i
$889$	−31.6585	−	11.7115i	−1.06179	−	0.392790i
$890$	−0.330801			−0.0110885
$891$	4.24506	+	20.2343i	0.142215	+	0.677875i
$892$	−8.91331	−	15.4383i	−0.298440	−	0.516913i
$893$	−31.9004	+	55.2531i	−1.06751	+	1.84897i
$894$	−11.4833	−	13.4632i	−0.384058	−	0.450276i
$895$	−1.39534	+	2.41679i	−0.0466410	+	0.0807845i
$896$	−2.48140	−	0.917950i	−0.0828979	−	0.0306666i
$897$	−6.19357	+	1.14368i	−0.206797	+	0.0381863i
$898$	13.2825			0.443242
$899$	11.2422	+	19.4721i	0.374950	+	0.649432i
$900$	−0.473220	+	2.96244i	−0.0157740	+	0.0987481i
$901$	−4.70348	+	8.14666i	−0.156696	+	0.271405i
$902$	4.93775	+	8.55243i	0.164409	+	0.284765i
$903$	−13.1520	−	35.8212i	−0.437672	−	1.19206i
$904$	−9.72776	+	16.8490i	−0.323540	+	0.560389i
$905$	−11.1479	−	19.3087i	−0.370568	−	0.641843i
$906$	1.62375	−	4.57572i	0.0539455	−	0.152018i
$907$	−27.5380	+	47.6972i	−0.914383	+	1.58376i	−0.106582	+	0.994304i	$0.533991\pi$
$907$	−27.5380	+	47.6972i	−0.914383	+	1.58376i	−0.807801	+	0.589455i	$0.799343\pi$
$908$	10.3752	−	17.9705i	0.344315	−	0.596371i
$909$	−7.02841	+	43.9991i	−0.233118	+	1.45936i
$910$	4.19531	+	1.55198i	0.139073	+	0.0514476i
$911$	7.85937	+	13.6128i	0.260393	+	0.451013i	0.966346	−	0.257245i	$-0.0828147\pi$
$911$	7.85937	+	13.6128i	0.260393	+	0.451013i	−0.705954	+	0.708258i	$0.749481\pi$
$912$	−4.51662	+	12.7278i	−0.149560	+	0.421459i
$913$	2.96511			0.0981308
$914$	−35.0984			−1.16095
$915$	−7.76147	−	9.09969i	−0.256586	−	0.300826i
$916$	−10.0604	−	17.4251i	−0.332405	−	0.575743i
$917$	−4.67478	−	27.3516i	−0.154375	−	0.903228i
$918$	3.39530	+	1.85222i	0.112062	+	0.0611325i
$919$	−2.47726	+	4.29074i	−0.0817172	+	0.141538i	−0.903988	−	0.427559i	$-0.859374\pi$
$919$	−2.47726	+	4.29074i	−0.0817172	+	0.141538i	0.822270	+	0.569097i	$0.192707\pi$
$920$	−1.07539	+	1.86262i	−0.0354544	+	0.0614089i
$921$	−18.2572	+	3.37129i	−0.601594	+	0.111088i
$922$	4.53012	+	7.84640i	0.149192	+	0.258407i
$923$	−2.11805	+	3.66857i	−0.0697165	+	0.120752i
$924$	6.74399	−	8.08322i	0.221861	−	0.265919i
$925$	−5.40503	−	9.36179i	−0.177716	−	0.307814i
$926$	21.1130	−	36.5688i	0.693816	−	1.20172i
$927$	−23.7282	−	19.2667i	−0.779337	−	0.632802i
$928$	−2.61618	−	4.53135i	−0.0858802	−	0.148749i
$929$	49.6074			1.62757			0.813784	−	0.581168i	$-0.197404\pi$
$929$	49.6074			1.62757			0.813784	+	0.581168i	$0.197404\pi$
$930$	4.83008	+	5.66287i	0.158385	+	0.185693i
$931$	51.4832	−	18.1280i	1.68729	−	0.594122i
$932$	7.70836	−	13.3513i	0.252496	−	0.437335i
$933$	5.58022	−	1.03042i	0.182688	−	0.0337344i
$934$	−5.26870	+	9.12565i	−0.172397	+	0.298600i
$935$	−0.854940	−	1.48080i	−0.0279595	−	0.0484273i
$936$	0.800073	−	5.00860i	0.0261512	−	0.163711i
$937$	−8.05753			−0.263228			−0.131614	−	0.991301i	$-0.542016\pi$
$937$	−8.05753			−0.263228			−0.131614	+	0.991301i	$0.542016\pi$
$938$	−24.2464	−	8.96952i	−0.791674	−	0.292865i
$939$	−38.9309	+	7.18881i	−1.27046	+	0.234598i
$940$	−4.09118	−	7.08613i	−0.133440	−	0.231124i
$941$	18.5344			0.604205			0.302102	−	0.953276i	$-0.402312\pi$
$941$	18.5344			0.604205			0.302102	+	0.953276i	$0.402312\pi$
$942$	10.4827	−	1.93569i	0.341545	−	0.0630681i
$943$	9.24601			0.301091
$944$	0.635800			0.0206935
$945$	−9.03477	−	10.3621i	−0.293901	−	0.337079i
$946$	19.1289			0.621935
$947$	−56.4089			−1.83304			−0.916521	−	0.399987i	$-0.869015\pi$
$947$	−56.4089			−1.83304			−0.916521	+	0.399987i	$0.869015\pi$
$948$	15.8540	−	2.92752i	0.514913	−	0.0950815i
$949$	11.5813			0.375944
$950$	−3.89868	−	6.75271i	−0.126490	−	0.219087i
$951$	39.2205	−	7.24229i	1.27181	−	0.234847i
$952$	−0.331774	−	1.94117i	−0.0107529	−	0.0629136i
$953$	44.4290			1.43920			0.719599	−	0.694390i	$-0.244326\pi$
$953$	44.4290			1.43920			0.719599	+	0.694390i	$0.244326\pi$
$954$	−29.4334	−	23.8992i	−0.952943	−	0.773766i
$955$	7.25620	+	12.5681i	0.234805	+	0.406694i
$956$	9.63173	−	16.6826i	0.311512	−	0.539555i
$957$	20.4727	−	3.78040i	0.661790	−	0.122203i
$958$	−18.7128	+	32.4116i	−0.604584	+	1.04717i
$959$	4.47765	−	3.71728i	0.144591	−	0.120037i
$960$	−1.12401	−	1.31780i	−0.0362771	−	0.0425320i
$961$	−12.5341			−0.404324
$962$	9.13829	+	15.8280i	0.294630	+	0.510315i
$963$	−6.10788	+	38.2364i	−0.196824	+	1.23215i
$964$	−13.3167	+	23.0653i	−0.428903	+	0.742882i
$965$	3.16439	+	5.48089i	0.101865	+	0.176436i
$966$	−3.39701	−	9.25217i	−0.109297	−	0.297684i
$967$	−10.3142	+	17.8647i	−0.331681	+	0.574489i	−0.982842	−	0.184451i	$-0.940949\pi$
$967$	−10.3142	+	17.8647i	−0.331681	+	0.574489i	0.651160	+	0.758940i	$0.274282\pi$
$968$	−2.86143	−	4.95614i	−0.0919699	−	0.159296i
$969$	−9.88539	+	1.82539i	−0.317564	+	0.0586400i
$970$	3.18123	−	5.51006i	0.102143	−	0.176917i
$971$	−23.0979	+	40.0067i	−0.741247	+	1.28388i	0.210681	+	0.977555i	$0.432432\pi$
$971$	−23.0979	+	40.0067i	−0.741247	+	1.28388i	−0.951928	+	0.306322i	$0.900902\pi$
$972$	−9.53047	+	12.3357i	−0.305690	+	0.395669i
$973$	5.00382	−	4.15410i	0.160415	−	0.133174i
$974$	−7.69208	−	13.3231i	−0.246470	−	0.426899i
$975$	1.90036	+	2.22801i	0.0608602	+	0.0713536i
$976$	6.90519			0.221030
$977$	−31.3887			−1.00421			−0.502106	−	0.864806i	$-0.667441\pi$
$977$	−31.3887			−1.00421			−0.502106	+	0.864806i	$0.667441\pi$
$978$	3.19516	−	9.00395i	0.102170	−	0.287915i
$979$	0.379959	+	0.658108i	0.0121435	+	0.0210332i
$980$	−1.28791	+	6.88050i	−0.0411406	+	0.219790i
$981$	5.24832	+	4.26151i	0.167566	+	0.136059i
$982$	−11.7768	+	20.3981i	−0.375814	+	0.650928i
$983$	−12.1817	+	21.0993i	−0.388535	+	0.672962i	−0.992253	−	0.124236i	$-0.960352\pi$
$983$	−12.1817	+	21.0993i	−0.388535	+	0.672962i	0.603718	+	0.797198i	$0.293685\pi$
$984$	−2.49015	+	7.01722i	−0.0793831	+	0.223701i
$985$	−4.57510	−	7.92431i	−0.145775	−	0.252490i
$986$	1.94730	−	3.37282i	0.0620147	−	0.107413i
$987$	36.9448	+	6.40730i	1.17597	+	0.203947i
$988$	6.59150	+	11.4168i	0.209704	+	0.363217i
$989$	8.95480	−	15.5102i	0.284746	−	0.493195i
$990$	6.43713	−	2.46122i	0.204585	−	0.0782228i
$991$	−29.1185	−	50.4348i	−0.924981	−	1.60211i	−0.791592	−	0.611050i	$-0.790748\pi$
$991$	−29.1185	−	50.4348i	−0.924981	−	1.60211i	−0.133388	−	0.991064i	$-0.542586\pi$
$992$	−4.29720			−0.136436
$993$	40.9496	−	7.56156i	1.29950	−	0.239959i
$994$	−6.21723	−	2.29995i	−0.197199	−	0.0729500i
$995$	−2.96846	+	5.14152i	−0.0941064	+	0.162997i
$996$	1.45081	+	1.70095i	0.0459707	+	0.0538968i
$997$	18.9778	−	32.8705i	0.601032	−	1.04102i	−0.391633	−	0.920122i	$-0.628090\pi$
$997$	18.9778	−	32.8705i	0.601032	−	1.04102i	0.992665	−	0.120897i	$-0.0385771\pi$
$998$	−3.43382	−	5.94754i	−0.108696	−	0.188266i
$999$	−1.35903	−	56.1543i	−0.0429980	−	1.77664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.i.121.1	✓	16
3.2	odd	2		1890.2.i.i.1171.7		16
7.4	even	3		630.2.l.i.571.6	yes	16
9.2	odd	6		1890.2.l.i.1801.4		16
9.7	even	3		630.2.l.i.331.6	yes	16
21.11	odd	6		1890.2.l.i.361.4		16
63.11	odd	6		1890.2.i.i.991.7		16
63.25	even	3	inner	630.2.i.i.151.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.i.121.1	✓	16	1.1	even	1	trivial
630.2.i.i.151.1	yes	16	63.25	even	3	inner
630.2.l.i.331.6	yes	16	9.7	even	3
630.2.l.i.571.6	yes	16	7.4	even	3
1890.2.i.i.991.7		16	63.11	odd	6
1890.2.i.i.1171.7		16	3.2	odd	2
1890.2.l.i.361.4		16	21.11	odd	6
1890.2.l.i.1801.4		16	9.2	odd	6

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.70326 + 0.314515i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.70326 - 0.314515i) q^{6} +(2.48140 + 0.917950i) q^{7} -1.00000 q^{8} +(2.80216 - 1.07140i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.70326 + 0.314515i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.70326 - 0.314515i) q^{6} +(2.48140 + 0.917950i) q^{7} -1.00000 q^{8} +(2.80216 - 1.07140i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.14860 + 1.98944i) q^{11} +(-1.70326 + 0.314515i) q^{12} +(-0.845351 + 1.46419i) q^{13} +(-2.48140 - 0.917950i) q^{14} +(-1.12401 - 1.31780i) q^{15} +1.00000 q^{16} +(0.372166 + 0.644610i) q^{17} +(-2.80216 + 1.07140i) q^{18} +(3.89868 - 6.75271i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.51518 - 0.783063i) q^{21} +(1.14860 - 1.98944i) q^{22} +(-1.07539 - 1.86262i) q^{23} +(1.70326 - 0.314515i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.845351 - 1.46419i) q^{26} +(-4.43582 + 2.70619i) q^{27} +(2.48140 + 0.917950i) q^{28} +(2.61618 + 4.53135i) q^{29} +(1.12401 + 1.31780i) q^{30} +4.29720 q^{31} -1.00000 q^{32} +(1.33065 - 3.74977i) q^{33} +(-0.372166 - 0.644610i) q^{34} +(0.445734 + 2.60793i) q^{35} +(2.80216 - 1.07140i) q^{36} +(-5.40503 + 9.36179i) q^{37} +(-3.89868 + 6.75271i) q^{38} +(0.979338 - 2.75977i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.14946 + 3.72298i) q^{41} +(4.51518 + 0.783063i) q^{42} +(4.16353 + 7.21144i) q^{43} +(-1.14860 + 1.98944i) q^{44} +(2.32894 + 1.89104i) q^{45} +(1.07539 + 1.86262i) q^{46} -8.18236 q^{47} +(-1.70326 + 0.314515i) q^{48} +(5.31474 + 4.55561i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.836633 - 0.980883i) q^{51} +(-0.845351 + 1.46419i) q^{52} +(6.31906 + 10.9449i) q^{53} +(4.43582 - 2.70619i) q^{54} -2.29720 q^{55} +(-2.48140 - 0.917950i) q^{56} +(-4.51662 + 12.7278i) q^{57} +(-2.61618 - 4.53135i) q^{58} +0.635800 q^{59} +(-1.12401 - 1.31780i) q^{60} +6.90519 q^{61} -4.29720 q^{62} +(7.93678 - 0.0863357i) q^{63} +1.00000 q^{64} -1.69070 q^{65} +(-1.33065 + 3.74977i) q^{66} +9.77125 q^{67} +(0.372166 + 0.644610i) q^{68} +(2.41748 + 2.83430i) q^{69} +(-0.445734 - 2.60793i) q^{70} +2.50553 q^{71} +(-2.80216 + 1.07140i) q^{72} +(-3.42499 - 5.93225i) q^{73} +(5.40503 - 9.36179i) q^{74} +(0.579249 - 1.63232i) q^{75} +(3.89868 - 6.75271i) q^{76} +(-4.67635 + 3.88224i) q^{77} +(-0.979338 + 2.75977i) q^{78} -9.30803 q^{79} +(0.500000 + 0.866025i) q^{80} +(6.70420 - 6.00447i) q^{81} +(2.14946 - 3.72298i) q^{82} +(-0.645374 - 1.11782i) q^{83} +(-4.51518 - 0.783063i) q^{84} +(-0.372166 + 0.644610i) q^{85} +(-4.16353 - 7.21144i) q^{86} +(-5.88120 - 6.89522i) q^{87} +(1.14860 - 1.98944i) q^{88} +(0.165401 - 0.286482i) q^{89} +(-2.32894 - 1.89104i) q^{90} +(-3.44171 + 2.85726i) q^{91} +(-1.07539 - 1.86262i) q^{92} +(-7.31923 + 1.35154i) q^{93} +8.18236 q^{94} +7.79736 q^{95} +(1.70326 - 0.314515i) q^{96} +(3.18123 + 5.51006i) q^{97} +(-5.31474 - 4.55561i) q^{98} +(-1.08708 + 6.80533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9 - 8 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 + 16 * q^16 + 11 * q^17 + 6 * q^18 - 2 * q^19 + 8 * q^20 - 15 * q^21 - q^22 + 11 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 30 * q^31 - 16 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^40 + 7 * q^41 + 15 * q^42 - 13 * q^43 + q^44 + 3 * q^45 - 11 * q^46 + 10 * q^47 + 2 * q^48 - 14 * q^49 + 8 * q^50 - 3 * q^51 + 2 * q^52 + 18 * q^53 + 7 * q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 - 17 * q^58 - 2 * q^59 + q^60 + 54 * q^61 - 30 * q^62 + 41 * q^63 + 16 * q^64 + 4 * q^65 - 5 * q^66 + 20 * q^67 + 11 * q^68 - 14 * q^69 + 4 * q^70 - 38 * q^71 + 6 * q^72 - 8 * q^73 + 2 * q^74 - q^75 - 2 * q^76 - 7 * q^77 + 50 * q^79 + 8 * q^80 - 6 * q^81 - 7 * q^82 + 2 * q^83 - 15 * q^84 - 11 * q^85 + 13 * q^86 - 32 * q^87 - q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 - 6 * q^93 - 10 * q^94 - 4 * q^95 - 2 * q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

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