LMFDB - Embedded newform 630.2.i.f.151.2

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	12.0.91830304992969.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + x^{10} + 4x^{9} - 7x^{8} + x^{7} + 7x^{6} + 2x^{5} - 28x^{4} + 32x^{3} + 16x^{2} - 64x + 64 $ x^12 - 2x^11 + x^10 + 4x^9 - 7x^8 + x^7 + 7x^6 + 2x^5 - 28x^4 + 32x^3 + 16x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.2
Root			$0.683706 + 1.23796i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.f.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.554872 + 1.64077i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.554872 - 1.64077i) q^{6} +(2.32383 - 1.26483i) q^{7} -1.00000 q^{8} +(-2.38423 - 1.82083i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.554872 + 1.64077i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.554872 - 1.64077i) q^{6} +(2.32383 - 1.26483i) q^{7} -1.00000 q^{8} +(-2.38423 - 1.82083i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.25470 - 2.17320i) q^{11} +(-0.554872 + 1.64077i) q^{12} +(-2.97905 - 5.15987i) q^{13} +(-2.32383 + 1.26483i) q^{14} +(-1.14351 - 1.30092i) q^{15} +1.00000 q^{16} +(-2.65781 + 4.60347i) q^{17} +(2.38423 + 1.82083i) q^{18} +(-2.97905 - 5.15987i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.785868 + 4.51469i) q^{21} +(1.25470 + 2.17320i) q^{22} +(-0.678764 + 1.17565i) q^{23} +(0.554872 - 1.64077i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.97905 + 5.15987i) q^{26} +(4.31051 - 2.90164i) q^{27} +(2.32383 - 1.26483i) q^{28} +(3.10212 - 5.37303i) q^{29} +(1.14351 + 1.30092i) q^{30} -6.16523 q^{31} -1.00000 q^{32} +(4.26192 - 0.852819i) q^{33} +(2.65781 - 4.60347i) q^{34} +(-0.0665372 + 2.64491i) q^{35} +(-2.38423 - 1.82083i) q^{36} +(2.58315 + 4.47415i) q^{37} +(2.97905 + 5.15987i) q^{38} +(10.1191 - 2.02486i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-4.43192 - 7.67631i) q^{41} +(-0.785868 - 4.51469i) q^{42} +(0.977900 - 1.69377i) q^{43} +(-1.25470 - 2.17320i) q^{44} +(2.76900 - 1.15439i) q^{45} +(0.678764 - 1.17565i) q^{46} -2.04420 q^{47} +(-0.554872 + 1.64077i) q^{48} +(3.80039 - 5.87852i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-6.07847 - 6.91519i) q^{51} +(-2.97905 - 5.15987i) q^{52} +(-0.179671 + 0.311199i) q^{53} +(-4.31051 + 2.90164i) q^{54} +2.50940 q^{55} +(-2.32383 + 1.26483i) q^{56} +(10.1191 - 2.02486i) q^{57} +(-3.10212 + 5.37303i) q^{58} -2.86874 q^{59} +(-1.14351 - 1.30092i) q^{60} +3.82899 q^{61} +6.16523 q^{62} +(-7.84361 - 1.21565i) q^{63} +1.00000 q^{64} +5.95810 q^{65} +(-4.26192 + 0.852819i) q^{66} +12.9461 q^{67} +(-2.65781 + 4.60347i) q^{68} +(-1.55235 - 1.76603i) q^{69} +(0.0665372 - 2.64491i) q^{70} +3.52556 q^{71} +(2.38423 + 1.82083i) q^{72} +(5.60063 - 9.70058i) q^{73} +(-2.58315 - 4.47415i) q^{74} +(1.69838 - 0.339850i) q^{75} +(-2.97905 - 5.15987i) q^{76} +(-5.66445 - 3.46317i) q^{77} +(-10.1191 + 2.02486i) q^{78} -14.7994 q^{79} +(-0.500000 + 0.866025i) q^{80} +(2.36914 + 8.68258i) q^{81} +(4.43192 + 7.67631i) q^{82} +(-2.54006 + 4.39951i) q^{83} +(0.785868 + 4.51469i) q^{84} +(-2.65781 - 4.60347i) q^{85} +(-0.977900 + 1.69377i) q^{86} +(7.09461 + 8.07120i) q^{87} +(1.25470 + 2.17320i) q^{88} +(-0.367362 - 0.636290i) q^{89} +(-2.76900 + 1.15439i) q^{90} +(-13.4492 - 8.22266i) q^{91} +(-0.678764 + 1.17565i) q^{92} +(3.42092 - 10.1157i) q^{93} +2.04420 q^{94} +5.95810 q^{95} +(0.554872 - 1.64077i) q^{96} +(-6.19076 + 10.7227i) q^{97} +(-3.80039 + 5.87852i) q^{98} +(-0.965543 + 7.46602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 2 q^{19} - 6 q^{20} + 29 q^{21} + 7 q^{22} - 9 q^{23} - 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 4 q^{28} + 3 q^{29} + q^{30} + 18 q^{31} - 12 q^{32} + 27 q^{33} - q^{34} - 8 q^{35} - 4 q^{36} + 6 q^{37} + 2 q^{38} + 10 q^{39} + 6 q^{40} - 11 q^{41} - 29 q^{42} + 23 q^{43} - 7 q^{44} + 5 q^{45} + 9 q^{46} - 2 q^{47} + 2 q^{48} + 24 q^{49} + 6 q^{50} - 15 q^{51} - 2 q^{52} - 4 q^{53} - 11 q^{54} + 14 q^{55} - 4 q^{56} + 10 q^{57} - 3 q^{58} - 22 q^{59} - q^{60} + 50 q^{61} - 18 q^{62} - q^{63} + 12 q^{64} + 4 q^{65} - 27 q^{66} + 4 q^{67} + q^{68} - 12 q^{69} + 8 q^{70} + 22 q^{71} + 4 q^{72} + 24 q^{73} - 6 q^{74} - q^{75} - 2 q^{76} - 11 q^{77} - 10 q^{78} + 2 q^{79} - 6 q^{80} + 20 q^{81} + 11 q^{82} + 4 q^{83} + 29 q^{84} + q^{85} - 23 q^{86} + 7 q^{88} + 2 q^{89} - 5 q^{90} - 8 q^{91} - 9 q^{92} + 40 q^{93} + 2 q^{94} + 4 q^{95} - 2 q^{96} - 36 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^15 + 12 * q^16 + q^17 + 4 * q^18 - 2 * q^19 - 6 * q^20 + 29 * q^21 + 7 * q^22 - 9 * q^23 - 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 4 * q^28 + 3 * q^29 + q^30 + 18 * q^31 - 12 * q^32 + 27 * q^33 - q^34 - 8 * q^35 - 4 * q^36 + 6 * q^37 + 2 * q^38 + 10 * q^39 + 6 * q^40 - 11 * q^41 - 29 * q^42 + 23 * q^43 - 7 * q^44 + 5 * q^45 + 9 * q^46 - 2 * q^47 + 2 * q^48 + 24 * q^49 + 6 * q^50 - 15 * q^51 - 2 * q^52 - 4 * q^53 - 11 * q^54 + 14 * q^55 - 4 * q^56 + 10 * q^57 - 3 * q^58 - 22 * q^59 - q^60 + 50 * q^61 - 18 * q^62 - q^63 + 12 * q^64 + 4 * q^65 - 27 * q^66 + 4 * q^67 + q^68 - 12 * q^69 + 8 * q^70 + 22 * q^71 + 4 * q^72 + 24 * q^73 - 6 * q^74 - q^75 - 2 * q^76 - 11 * q^77 - 10 * q^78 + 2 * q^79 - 6 * q^80 + 20 * q^81 + 11 * q^82 + 4 * q^83 + 29 * q^84 + q^85 - 23 * q^86 + 7 * q^88 + 2 * q^89 - 5 * q^90 - 8 * q^91 - 9 * q^92 + 40 * q^93 + 2 * q^94 + 4 * q^95 - 2 * q^96 - 36 * q^97 - 24 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.554872	+	1.64077i	−0.320356	+	0.947297i
$3$	−0.554872	+	1.64077i	−0.320356	+	0.947297i
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.554872	−	1.64077i	0.226526	−	0.669840i
$7$	2.32383	−	1.26483i	0.878326	−	0.478062i
$7$	2.32383	−	1.26483i	0.878326	−	0.478062i
$8$	−1.00000			−0.353553
$9$	−2.38423	−	1.82083i	−0.794744	−	0.606944i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−1.25470	−	2.17320i	−0.378306	−	0.655245i	0.612510	−	0.790463i	$-0.290160\pi$
$11$	−1.25470	−	2.17320i	−0.378306	−	0.655245i	−0.990816	+	0.135218i	$0.956827\pi$
$12$	−0.554872	+	1.64077i	−0.160178	+	0.473649i
$13$	−2.97905	−	5.15987i	−0.826240	−	1.43109i	−0.900968	−	0.433886i	$-0.857142\pi$
$13$	−2.97905	−	5.15987i	−0.826240	−	1.43109i	0.0747277	−	0.997204i	$-0.476191\pi$
$14$	−2.32383	+	1.26483i	−0.621070	+	0.338041i
$15$	−1.14351	−	1.30092i	−0.295253	−	0.335895i
$16$	1.00000			0.250000
$17$	−2.65781	+	4.60347i	−0.644615	+	1.11651i	0.339776	+	0.940507i	$0.389649\pi$
$17$	−2.65781	+	4.60347i	−0.644615	+	1.11651i	−0.984390	+	0.175999i	$0.943684\pi$
$18$	2.38423	+	1.82083i	0.561969	+	0.429174i
$19$	−2.97905	−	5.15987i	−0.683441	−	1.18375i	−0.973924	−	0.226875i	$-0.927149\pi$
$19$	−2.97905	−	5.15987i	−0.683441	−	1.18375i	0.290483	−	0.956880i	$-0.406184\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.785868	+	4.51469i	0.171491	+	0.985186i
$22$	1.25470	+	2.17320i	0.267503	+	0.463328i
$23$	−0.678764	+	1.17565i	−0.141532	+	0.245141i	−0.928074	−	0.372397i	$-0.878536\pi$
$23$	−0.678764	+	1.17565i	−0.141532	+	0.245141i	0.786542	+	0.617537i	$0.211869\pi$
$24$	0.554872	−	1.64077i	0.113263	−	0.334920i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.97905	+	5.15987i	0.584240	+	1.01193i
$27$	4.31051	−	2.90164i	0.829558	−	0.558421i
$28$	2.32383	−	1.26483i	0.439163	−	0.239031i
$29$	3.10212	−	5.37303i	0.576049	−	0.997747i	−0.419878	−	0.907581i	$-0.637927\pi$
$29$	3.10212	−	5.37303i	0.576049	−	0.997747i	0.995927	−	0.0901657i	$-0.0287397\pi$
$30$	1.14351	+	1.30092i	0.208775	+	0.237514i
$31$	−6.16523			−1.10731			−0.553654	−	0.832747i	$-0.686767\pi$
$31$	−6.16523			−1.10731			−0.553654	+	0.832747i	$0.686767\pi$
$32$	−1.00000			−0.176777
$33$	4.26192	−	0.852819i	0.741904	−	0.148457i
$34$	2.65781	−	4.60347i	0.455811	−	0.789489i
$35$	−0.0665372	+	2.64491i	−0.0112468	+	0.447072i
$36$	−2.38423	−	1.82083i	−0.397372	−	0.303472i
$37$	2.58315	+	4.47415i	0.424668	+	0.735546i	0.996389	−	0.0849016i	$-0.0270576\pi$
$37$	2.58315	+	4.47415i	0.424668	+	0.735546i	−0.571722	+	0.820448i	$0.693724\pi$
$38$	2.97905	+	5.15987i	0.483266	+	0.837041i
$39$	10.1191	−	2.02486i	1.62036	−	0.324237i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−4.43192	−	7.67631i	−0.692149	−	1.19884i	−0.971132	−	0.238542i	$-0.923331\pi$
$41$	−4.43192	−	7.67631i	−0.692149	−	1.19884i	0.278983	−	0.960296i	$-0.410003\pi$
$42$	−0.785868	−	4.51469i	−0.121262	−	0.696632i
$43$	0.977900	−	1.69377i	0.149128	−	0.258298i	−0.781777	−	0.623558i	$-0.785687\pi$
$43$	0.977900	−	1.69377i	0.149128	−	0.258298i	0.930906	+	0.365260i	$0.119020\pi$
$44$	−1.25470	−	2.17320i	−0.189153	−	0.327623i
$45$	2.76900	−	1.15439i	0.412779	−	0.172086i
$46$	0.678764	−	1.17565i	0.100078	−	0.173341i
$47$	−2.04420			−0.298177			−0.149089	−	0.988824i	$-0.547634\pi$
$47$	−2.04420			−0.298177			−0.149089	+	0.988824i	$0.547634\pi$
$48$	−0.554872	+	1.64077i	−0.0800889	+	0.236824i
$49$	3.80039	−	5.87852i	0.542913	−	0.839789i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−6.07847	−	6.91519i	−0.851157	−	0.968321i
$52$	−2.97905	−	5.15987i	−0.413120	−	0.715545i
$53$	−0.179671	+	0.311199i	−0.0246796	+	0.0427464i	−0.878101	−	0.478475i	$-0.841190\pi$
$53$	−0.179671	+	0.311199i	−0.0246796	+	0.0427464i	0.853422	+	0.521221i	$0.174523\pi$
$54$	−4.31051	+	2.90164i	−0.586586	+	0.394863i
$55$	2.50940			0.338367
$56$	−2.32383	+	1.26483i	−0.310535	+	0.169021i
$57$	10.1191	−	2.02486i	1.34031	−	0.268199i
$58$	−3.10212	+	5.37303i	−0.407328	+	0.705513i
$59$	−2.86874			−0.373478			−0.186739	−	0.982410i	$-0.559792\pi$
$59$	−2.86874			−0.373478			−0.186739	+	0.982410i	$0.559792\pi$
$60$	−1.14351	−	1.30092i	−0.147626	−	0.167948i
$61$	3.82899			0.490252			0.245126	−	0.969491i	$-0.421171\pi$
$61$	3.82899			0.490252			0.245126	+	0.969491i	$0.421171\pi$
$62$	6.16523			0.782985
$63$	−7.84361	−	1.21565i	−0.988202	−	0.153157i
$64$	1.00000			0.125000
$65$	5.95810			0.739012
$66$	−4.26192	+	0.852819i	−0.524606	+	0.104975i
$67$	12.9461			1.58161			0.790806	−	0.612066i	$-0.209661\pi$
$67$	12.9461			1.58161			0.790806	+	0.612066i	$0.209661\pi$
$68$	−2.65781	+	4.60347i	−0.322307	+	0.558253i
$69$	−1.55235	−	1.76603i	−0.186880	−	0.212605i
$70$	0.0665372	−	2.64491i	0.00795272	−	0.316128i
$71$	3.52556			0.418407			0.209203	−	0.977872i	$-0.432913\pi$
$71$	3.52556			0.418407			0.209203	+	0.977872i	$0.432913\pi$
$72$	2.38423	+	1.82083i	0.280985	+	0.214587i
$73$	5.60063	−	9.70058i	0.655504	−	1.13537i	−0.326263	−	0.945279i	$-0.605789\pi$
$73$	5.60063	−	9.70058i	0.655504	−	1.13537i	0.981767	−	0.190088i	$-0.0608772\pi$
$74$	−2.58315	−	4.47415i	−0.300285	−	0.520110i
$75$	1.69838	−	0.339850i	0.196112	−	0.0392425i
$76$	−2.97905	−	5.15987i	−0.341721	−	0.591877i
$77$	−5.66445	−	3.46317i	−0.645524	−	0.394665i
$78$	−10.1191	+	2.02486i	−1.14577	+	0.229270i
$79$	−14.7994			−1.66506			−0.832530	−	0.553980i	$-0.813108\pi$
$79$	−14.7994			−1.66506			−0.832530	+	0.553980i	$0.813108\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	2.36914	+	8.68258i	0.263237	+	0.964731i
$82$	4.43192	+	7.67631i	0.489423	+	0.847706i
$83$	−2.54006	+	4.39951i	−0.278808	+	0.482909i	−0.971089	−	0.238719i	$-0.923273\pi$
$83$	−2.54006	+	4.39951i	−0.278808	+	0.482909i	0.692281	+	0.721628i	$0.256606\pi$
$84$	0.785868	+	4.51469i	0.0857453	+	0.492593i
$85$	−2.65781	−	4.60347i	−0.288280	−	0.499316i
$86$	−0.977900	+	1.69377i	−0.105450	+	0.182644i
$87$	7.09461	+	8.07120i	0.760622	+	0.865324i
$88$	1.25470	+	2.17320i	0.133751	+	0.231664i
$89$	−0.367362	−	0.636290i	−0.0389403	−	0.0674466i	0.845898	−	0.533344i	$-0.179065\pi$
$89$	−0.367362	−	0.636290i	−0.0389403	−	0.0674466i	−0.884839	+	0.465897i	$0.845732\pi$
$90$	−2.76900	+	1.15439i	−0.291879	+	0.121683i
$91$	−13.4492	−	8.22266i	−1.40986	−	0.861969i
$92$	−0.678764	+	1.17565i	−0.0707660	+	0.122570i
$93$	3.42092	−	10.1157i	0.354733	−	1.04895i
$94$	2.04420			0.210843
$95$	5.95810			0.611288
$96$	0.554872	−	1.64077i	0.0566314	−	0.167460i
$97$	−6.19076	+	10.7227i	−0.628576	+	1.08873i	0.359261	+	0.933237i	$0.383029\pi$
$97$	−6.19076	+	10.7227i	−0.628576	+	1.08873i	−0.987838	+	0.155489i	$0.950305\pi$
$98$	−3.80039	+	5.87852i	−0.383897	+	0.593821i
$99$	−0.965543	+	7.46602i	−0.0970407	+	0.750363i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−4.02012	−	6.96305i	−0.400017	−	0.692849i	0.593711	−	0.804679i	$-0.297662\pi$
$101$	−4.02012	−	6.96305i	−0.400017	−	0.692849i	−0.993727	+	0.111829i	$0.964329\pi$
$102$	6.07847	+	6.91519i	0.601859	+	0.684706i
$103$	−5.60483	+	9.70785i	−0.552260	+	0.956543i	0.445851	+	0.895107i	$0.352901\pi$
$103$	−5.60483	+	9.70785i	−0.552260	+	0.956543i	−0.998111	+	0.0614356i	$0.980432\pi$
$104$	2.97905	+	5.15987i	0.292120	+	0.505967i
$105$	−4.30277	−	1.57676i	−0.419907	−	0.153876i
$106$	0.179671	−	0.311199i	0.0174511	−	0.0302263i
$107$	3.76525	+	6.52160i	0.364000	+	0.630467i	0.988615	−	0.150466i	$-0.0480774\pi$
$107$	3.76525	+	6.52160i	0.364000	+	0.630467i	−0.624615	+	0.780933i	$0.714744\pi$
$108$	4.31051	−	2.90164i	0.414779	−	0.279211i
$109$	5.59671	−	9.69378i	0.536067	−	0.928496i	−0.463044	−	0.886335i	$-0.653243\pi$
$109$	5.59671	−	9.69378i	0.536067	−	0.928496i	0.999111	−	0.0421601i	$-0.0134240\pi$
$110$	−2.50940			−0.239262
$111$	−8.77436	+	1.75577i	−0.832826	+	0.166650i
$112$	2.32383	−	1.26483i	0.219581	−	0.119516i
$113$	−5.83876	−	10.1130i	−0.549264	−	0.951354i	−0.998325	−	0.0578524i	$-0.981575\pi$
$113$	−5.83876	−	10.1130i	−0.549264	−	0.951354i	0.449061	−	0.893501i	$-0.351759\pi$
$114$	−10.1191	+	2.02486i	−0.947744	+	0.189646i
$115$	−0.678764	−	1.17565i	−0.0632950	−	0.109630i
$116$	3.10212	−	5.37303i	0.288025	−	0.498873i
$117$	−2.29250	+	17.7267i	−0.211942	+	1.63883i
$118$	2.86874			0.264089
$119$	−0.353687	+	14.0594i	−0.0324225	+	1.28882i
$120$	1.14351	+	1.30092i	0.104388	+	0.118757i
$121$	2.35146	−	4.07285i	0.213769	−	0.370259i
$122$	−3.82899			−0.346661
$123$	15.0542	−	3.01237i	1.35739	−	0.271617i
$124$	−6.16523			−0.553654
$125$	1.00000			0.0894427
$126$	7.84361	+	1.21565i	0.698764	+	0.108299i
$127$	−1.08717			−0.0964710			−0.0482355	−	0.998836i	$-0.515360\pi$
$127$	−1.08717			−0.0964710			−0.0482355	+	0.998836i	$0.515360\pi$
$128$	−1.00000			−0.0883883
$129$	2.23648	+	2.54433i	0.196911	+	0.224016i
$130$	−5.95810			−0.522560
$131$	−4.30124	+	7.44996i	−0.375801	+	0.650906i	−0.990447	−	0.137897i	$-0.955966\pi$
$131$	−4.30124	+	7.44996i	−0.375801	+	0.650906i	0.614646	+	0.788803i	$0.289299\pi$
$132$	4.26192	−	0.852819i	0.370952	−	0.0742283i
$133$	−13.4492	−	8.22266i	−1.16619	−	0.712995i
$134$	−12.9461			−1.11837
$135$	0.357641	+	5.18383i	0.0307809	+	0.446153i
$136$	2.65781	−	4.60347i	0.227906	−	0.394744i
$137$	1.02295	+	1.77180i	0.0873966	+	0.151375i	0.906410	−	0.422399i	$-0.138812\pi$
$137$	1.02295	+	1.77180i	0.0873966	+	0.151375i	−0.819013	+	0.573774i	$0.805479\pi$
$138$	1.55235	+	1.76603i	0.132144	+	0.150335i
$139$	5.44268	+	9.42700i	0.461642	+	0.799588i	0.999043	−	0.0437392i	$-0.0139270\pi$
$139$	5.44268	+	9.42700i	0.461642	+	0.799588i	−0.537401	+	0.843327i	$0.680594\pi$
$140$	−0.0665372	+	2.64491i	−0.00562342	+	0.223536i
$141$	1.13427	−	3.35406i	0.0955228	−	0.282463i
$142$	−3.52556			−0.295858
$143$	−7.47562	+	12.9482i	−0.625143	+	1.08278i
$144$	−2.38423	−	1.82083i	−0.198686	−	0.151736i
$145$	3.10212	+	5.37303i	0.257617	+	0.446206i
$146$	−5.60063	+	9.70058i	−0.463512	+	0.802825i
$147$	7.53656	+	9.49738i	0.621605	+	0.783331i
$148$	2.58315	+	4.47415i	0.212334	+	0.367773i
$149$	0.250077	−	0.433146i	0.0204871	−	0.0354847i	−0.855600	−	0.517637i	$-0.826812\pi$
$149$	0.250077	−	0.433146i	0.0204871	−	0.0354847i	0.876087	+	0.482153i	$0.160145\pi$
$150$	−1.69838	+	0.339850i	−0.138672	+	0.0277486i
$151$	8.28820	+	14.3556i	0.674484	+	1.16824i	0.976619	+	0.214976i	$0.0689672\pi$
$151$	8.28820	+	14.3556i	0.674484	+	1.16824i	−0.302135	+	0.953265i	$0.597699\pi$
$152$	2.97905	+	5.15987i	0.241633	+	0.418521i
$153$	14.7190	−	6.13631i	1.18996	−	0.496091i
$154$	5.66445	+	3.46317i	0.456454	+	0.279070i
$155$	3.08262	−	5.33925i	0.247602	−	0.428859i
$156$	10.1191	−	2.02486i	0.810179	−	0.162119i
$157$	−1.10586			−0.0882570			−0.0441285	−	0.999026i	$-0.514051\pi$
$157$	−1.10586			−0.0882570			−0.0441285	+	0.999026i	$0.514051\pi$
$158$	14.7994			1.17738
$159$	−0.410910	−	0.467473i	−0.0325873	−	0.0370730i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−0.0903261	+	3.59054i	−0.00711870	+	0.282975i
$162$	−2.36914	−	8.68258i	−0.186137	−	0.682168i
$163$	−3.44888	−	5.97364i	−0.270137	−	0.467892i	0.698759	−	0.715357i	$-0.253736\pi$
$163$	−3.44888	−	5.97364i	−0.270137	−	0.467892i	−0.968897	+	0.247465i	$0.920402\pi$
$164$	−4.43192	−	7.67631i	−0.346075	−	0.599419i
$165$	−1.39240	+	4.11734i	−0.108398	+	0.320534i
$166$	2.54006	−	4.39951i	0.197147	−	0.341468i
$167$	−6.61206	−	11.4524i	−0.511657	−	0.886215i	−0.999909	−	0.0135125i	$-0.995699\pi$
$167$	−6.61206	−	11.4524i	−0.511657	−	0.886215i	0.488252	−	0.872703i	$-0.337635\pi$
$168$	−0.785868	−	4.51469i	−0.0606311	−	0.348316i
$169$	−11.2495	+	19.4847i	−0.865345	+	1.49882i
$170$	2.65781	+	4.60347i	0.203845	+	0.353070i
$171$	−2.29250	+	17.7267i	−0.175312	+	1.35559i
$172$	0.977900	−	1.69377i	0.0745642	−	0.129149i
$173$	−15.2751			−1.16135			−0.580673	−	0.814137i	$-0.697210\pi$
$173$	−15.2751			−1.16135			−0.580673	+	0.814137i	$0.697210\pi$
$174$	−7.09461	−	8.07120i	−0.537841	−	0.611876i
$175$	−2.25729	−	1.38008i	−0.170635	−	0.104324i
$176$	−1.25470	−	2.17320i	−0.0945765	−	0.163811i
$177$	1.59178	−	4.70693i	0.119646	−	0.353795i
$178$	0.367362	+	0.636290i	0.0275350	+	0.0476919i
$179$	−0.232599	+	0.402873i	−0.0173853	+	0.0301121i	−0.874587	−	0.484868i	$-0.838868\pi$
$179$	−0.232599	+	0.402873i	−0.0173853	+	0.0301121i	0.857202	+	0.514981i	$0.172201\pi$
$180$	2.76900	−	1.15439i	0.206389	−	0.0860432i
$181$	26.1282			1.94209			0.971046	−	0.238892i	$-0.0767841\pi$
$181$	26.1282			1.94209			0.971046	+	0.238892i	$0.0767841\pi$
$182$	13.4492	+	8.22266i	0.996920	+	0.609504i
$183$	−2.12460	+	6.28248i	−0.157055	+	0.464415i
$184$	0.678764	−	1.17565i	0.0500391	−	0.0866703i
$185$	−5.16631			−0.379834
$186$	−3.42092	+	10.1157i	−0.250834	+	0.741720i
$187$	13.3390			0.975446
$188$	−2.04420			−0.149089
$189$	6.34680	−	12.1950i	0.461662	−	0.887056i
$190$	−5.95810			−0.432246
$191$	−20.6483			−1.49406			−0.747029	−	0.664791i	$-0.768521\pi$
$191$	−20.6483			−1.49406			−0.747029	+	0.664791i	$0.768521\pi$
$192$	−0.554872	+	1.64077i	−0.0400445	+	0.118412i
$193$	−15.7801			−1.13587			−0.567937	−	0.823072i	$-0.692258\pi$
$193$	−15.7801			−1.13587			−0.567937	+	0.823072i	$0.692258\pi$
$194$	6.19076	−	10.7227i	0.444470	−	0.769845i
$195$	−3.30599	+	9.77586i	−0.236747	+	0.700064i
$196$	3.80039	−	5.87852i	0.271456	−	0.419895i
$197$	11.1659			0.795536			0.397768	−	0.917486i	$-0.369785\pi$
$197$	11.1659			0.795536			0.397768	+	0.917486i	$0.369785\pi$
$198$	0.965543	−	7.46602i	0.0686182	−	0.530587i
$199$	−12.9803	+	22.4825i	−0.920148	+	1.59374i	−0.120965	+	0.992657i	$0.538599\pi$
$199$	−12.9803	+	22.4825i	−0.920148	+	1.59374i	−0.799183	+	0.601087i	$0.794734\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−7.18341	+	21.2415i	−0.506679	+	1.49826i
$202$	4.02012	+	6.96305i	0.282855	+	0.489918i
$203$	0.412813	−	16.4097i	0.0289738	−	1.15173i
$204$	−6.07847	−	6.91519i	−0.425578	−	0.484160i
$205$	8.86383			0.619077
$206$	5.60483	−	9.70785i	0.390507	−	0.676378i
$207$	3.75900	−	1.56712i	0.261269	−	0.108922i
$208$	−2.97905	−	5.15987i	−0.206560	−	0.357772i
$209$	−7.47562	+	12.9482i	−0.517100	+	0.895643i
$210$	4.30277	+	1.57676i	0.296919	+	0.108807i
$211$	−2.97056	−	5.14516i	−0.204502	−	0.354207i	0.745472	−	0.666537i	$-0.232224\pi$
$211$	−2.97056	−	5.14516i	−0.204502	−	0.354207i	−0.949974	+	0.312329i	$0.898891\pi$
$212$	−0.179671	+	0.311199i	−0.0123398	+	0.0213732i
$213$	−1.95623	+	5.78462i	−0.134039	+	0.396356i
$214$	−3.76525	−	6.52160i	−0.257387	−	0.445807i
$215$	0.977900	+	1.69377i	0.0666922	+	0.115514i
$216$	−4.31051	+	2.90164i	−0.293293	+	0.197432i
$217$	−14.3270	+	7.79800i	−0.972577	+	0.529362i
$218$	−5.59671	+	9.69378i	−0.379057	+	0.656546i
$219$	12.8088	+	14.5719i	0.865535	+	0.984679i
$220$	2.50940			0.169184
$221$	31.6711			2.13043
$222$	8.77436	−	1.75577i	0.588897	−	0.117839i
$223$	−8.23601	+	14.2652i	−0.551524	+	0.955267i	0.446641	+	0.894713i	$0.352620\pi$
$223$	−8.23601	+	14.2652i	−0.551524	+	0.955267i	−0.998165	+	0.0605541i	$0.980713\pi$
$224$	−2.32383	+	1.26483i	−0.155268	+	0.0845103i
$225$	−0.384771	+	2.97522i	−0.0256514	+	0.198348i
$226$	5.83876	+	10.1130i	0.388388	+	0.672709i
$227$	−8.90835	−	15.4297i	−0.591268	−	1.02411i	−0.994062	−	0.108816i	$-0.965294\pi$
$227$	−8.90835	−	15.4297i	−0.591268	−	1.02411i	0.402794	−	0.915291i	$-0.368039\pi$
$228$	10.1191	−	2.02486i	0.670156	−	0.134100i
$229$	11.5572	−	20.0177i	0.763723	−	1.32281i	−0.177197	−	0.984175i	$-0.556703\pi$
$229$	11.5572	−	20.0177i	0.763723	−	1.32281i	0.940919	−	0.338631i	$-0.109964\pi$
$230$	0.678764	+	1.17565i	0.0447564	+	0.0775203i
$231$	8.82530	−	7.37243i	0.580662	−	0.485070i
$232$	−3.10212	+	5.37303i	−0.203664	+	0.352757i
$233$	4.94916	+	8.57219i	0.324230	+	0.561583i	0.981356	−	0.192198i	$-0.0615614\pi$
$233$	4.94916	+	8.57219i	0.324230	+	0.561583i	−0.657126	+	0.753781i	$0.728228\pi$
$234$	2.29250	−	17.7267i	0.149866	−	1.15883i
$235$	1.02210	−	1.77033i	0.0666745	−	0.115484i
$236$	−2.86874			−0.186739
$237$	8.21177	−	24.2823i	0.533412	−	1.57731i
$238$	0.353687	−	14.0594i	0.0229261	−	0.911335i
$239$	−12.6933	−	21.9855i	−0.821064	−	1.42212i	−0.904891	−	0.425644i	$-0.860048\pi$
$239$	−12.6933	−	21.9855i	−0.821064	−	1.42212i	0.0838266	−	0.996480i	$-0.473286\pi$
$240$	−1.14351	−	1.30092i	−0.0738132	−	0.0839738i
$241$	−14.3326	−	24.8249i	−0.923247	−	1.59911i	−0.794357	−	0.607451i	$-0.792192\pi$
$241$	−14.3326	−	24.8249i	−0.923247	−	1.59911i	−0.128890	−	0.991659i	$-0.541141\pi$
$242$	−2.35146	+	4.07285i	−0.151158	+	0.261813i
$243$	−15.5607	−	0.930524i	−0.998217	−	0.0596931i
$244$	3.82899			0.245126
$245$	3.19076	+	6.23049i	0.203850	+	0.398052i
$246$	−15.0542	+	3.01237i	−0.959819	+	0.192062i
$247$	−17.7495	+	30.7430i	−1.12937	+	1.95613i
$248$	6.16523			0.391493
$249$	−5.80917	−	6.60881i	−0.368141	−	0.418817i
$250$	−1.00000			−0.0632456
$251$	27.3920			1.72897			0.864484	−	0.502660i	$-0.167645\pi$
$251$	27.3920			1.72897			0.864484	+	0.502660i	$0.167645\pi$
$252$	−7.84361	−	1.21565i	−0.494101	−	0.0765787i
$253$	3.40658			0.214170
$254$	1.08717			0.0682153
$255$	9.02797	−	1.80652i	0.565353	−	0.113128i
$256$	1.00000			0.0625000
$257$	12.9546	−	22.4380i	0.808085	−	1.39964i	−0.106104	−	0.994355i	$-0.533838\pi$
$257$	12.9546	−	22.4380i	0.808085	−	1.39964i	0.914189	−	0.405289i	$-0.132829\pi$
$258$	−2.23648	−	2.54433i	−0.139237	−	0.158403i
$259$	11.6619	+	7.12992i	0.724634	+	0.443031i
$260$	5.95810			0.369506
$261$	−17.1796	+	7.16211i	−1.06339	+	0.443324i
$262$	4.30124	−	7.44996i	0.265731	−	0.460260i
$263$	−14.5434	−	25.1899i	−0.896784	−	1.55327i	−0.831582	−	0.555403i	$-0.812564\pi$
$263$	−14.5434	−	25.1899i	−0.896784	−	1.55327i	−0.0652021	−	0.997872i	$-0.520769\pi$
$264$	−4.26192	+	0.852819i	−0.262303	+	0.0524874i
$265$	−0.179671	−	0.311199i	−0.0110371	−	0.0191168i
$266$	13.4492	+	8.22266i	0.824623	+	0.504164i
$267$	1.24784	−	0.249696i	0.0763667	−	0.0152811i
$268$	12.9461			0.790806
$269$	−4.69888	+	8.13870i	−0.286496	+	0.496225i	−0.972971	−	0.230928i	$-0.925824\pi$
$269$	−4.69888	+	8.13870i	−0.286496	+	0.496225i	0.686475	+	0.727153i	$0.259157\pi$
$270$	−0.357641	−	5.18383i	−0.0217654	−	0.315478i
$271$	−0.571895	−	0.990552i	−0.0347402	−	0.0601717i	0.848133	−	0.529784i	$-0.177727\pi$
$271$	−0.571895	−	0.990552i	−0.0347402	−	0.0601717i	−0.882873	+	0.469612i	$0.844394\pi$
$272$	−2.65781	+	4.60347i	−0.161154	+	0.279126i
$273$	20.9541	−	17.5045i	1.26820	−	1.05942i
$274$	−1.02295	−	1.77180i	−0.0617987	−	0.107038i
$275$	−1.25470	+	2.17320i	−0.0756612	+	0.131049i
$276$	−1.55235	−	1.76603i	−0.0934402	−	0.106303i
$277$	3.56388	+	6.17281i	0.214133	+	0.370888i	0.953004	−	0.302958i	$-0.0979742\pi$
$277$	3.56388	+	6.17281i	0.214133	+	0.370888i	−0.738871	+	0.673847i	$0.764641\pi$
$278$	−5.44268	−	9.42700i	−0.326430	−	0.565394i
$279$	14.6993	+	11.2259i	0.880027	+	0.672074i
$280$	0.0665372	−	2.64491i	0.00397636	−	0.158064i
$281$	9.36628	−	16.2229i	0.558746	−	0.967776i	−0.438856	−	0.898557i	$-0.644616\pi$
$281$	9.36628	−	16.2229i	0.558746	−	0.967776i	0.997602	−	0.0692183i	$-0.0220505\pi$
$282$	−1.13427	+	3.35406i	−0.0675448	+	0.199731i
$283$	−31.6080			−1.87890			−0.939450	−	0.342686i	$-0.888663\pi$
$283$	−31.6080			−1.87890			−0.939450	+	0.342686i	$0.888663\pi$
$284$	3.52556			0.209203
$285$	−3.30599	+	9.77586i	−0.195830	+	0.579072i
$286$	7.47562	−	12.9482i	0.442043	−	0.765641i
$287$	−20.0083	−	12.2328i	−1.18105	−	0.722080i
$288$	2.38423	+	1.82083i	0.140492	+	0.107294i
$289$	−5.62796	−	9.74791i	−0.331056	−	0.573407i
$290$	−3.10212	−	5.37303i	−0.182163	−	0.315515i
$291$	−14.1584	−	16.1073i	−0.829979	−	0.944228i
$292$	5.60063	−	9.70058i	0.327752	−	0.567683i
$293$	−2.92595	−	5.06790i	−0.170936	−	0.296070i	0.767811	−	0.640676i	$-0.221346\pi$
$293$	−2.92595	−	5.06790i	−0.170936	−	0.296070i	−0.938747	+	0.344606i	$0.888012\pi$
$294$	−7.53656	−	9.49738i	−0.439541	−	0.553899i
$295$	1.43437	−	2.48440i	0.0835122	−	0.144647i
$296$	−2.58315	−	4.47415i	−0.150143	−	0.260055i
$297$	−11.7142	−	5.72692i	−0.679729	−	0.332310i
$298$	−0.250077	+	0.433146i	−0.0144866	+	0.0250915i
$299$	8.08829			0.467758
$300$	1.69838	−	0.339850i	0.0980561	−	0.0196212i
$301$	0.130134	−	5.17292i	0.00750077	−	0.298162i
$302$	−8.28820	−	14.3556i	−0.476932	−	0.826071i
$303$	13.6554	−	2.73247i	0.784482	−	0.156977i
$304$	−2.97905	−	5.15987i	−0.170860	−	0.295939i
$305$	−1.91450	+	3.31600i	−0.109624	+	0.189874i
$306$	−14.7190	+	6.13631i	−0.841429	+	0.350790i
$307$	18.0889			1.03239			0.516193	−	0.856472i	$-0.327349\pi$
$307$	18.0889			1.03239			0.516193	+	0.856472i	$0.327349\pi$
$308$	−5.66445	−	3.46317i	−0.322762	−	0.197332i
$309$	−12.8184	−	14.5828i	−0.729211	−	0.829589i
$310$	−3.08262	+	5.33925i	−0.175081	+	0.303249i
$311$	28.7843			1.63221			0.816105	−	0.577904i	$-0.196129\pi$
$311$	28.7843			1.63221			0.816105	+	0.577904i	$0.196129\pi$
$312$	−10.1191	+	2.02486i	−0.572883	+	0.114635i
$313$	−0.185134			−0.0104644			−0.00523219	−	0.999986i	$-0.501665\pi$
$313$	−0.185134			−0.0104644			−0.00523219	+	0.999986i	$0.501665\pi$
$314$	1.10586			0.0624071
$315$	4.97459	−	6.18494i	0.280286	−	0.348482i
$316$	−14.7994			−0.832530
$317$	5.86194			0.329239			0.164620	−	0.986357i	$-0.447360\pi$
$317$	5.86194			0.329239			0.164620	+	0.986357i	$0.447360\pi$
$318$	0.410910	+	0.467473i	0.0230427	+	0.0262146i
$319$	−15.5689			−0.871691
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−12.7897	+	2.55924i	−0.713849	+	0.142843i
$322$	0.0903261	−	3.59054i	0.00503368	−	0.200093i
$323$	31.6711			1.76223
$324$	2.36914	+	8.68258i	0.131619	+	0.482366i
$325$	−2.97905	+	5.15987i	−0.165248	+	0.286218i
$326$	3.44888	+	5.97364i	0.191016	+	0.330849i
$327$	12.7998	+	14.5617i	0.707829	+	0.805264i
$328$	4.43192	+	7.67631i	0.244712	+	0.423853i
$329$	−4.75038	+	2.58557i	−0.261897	+	0.142547i
$330$	1.39240	−	4.11734i	0.0766489	−	0.226652i
$331$	−1.74896			−0.0961314			−0.0480657	−	0.998844i	$-0.515306\pi$
$331$	−1.74896			−0.0961314			−0.0480657	+	0.998844i	$0.515306\pi$
$332$	−2.54006	+	4.39951i	−0.139404	+	0.241455i
$333$	1.98784	−	15.3709i	0.108933	−	0.842321i
$334$	6.61206	+	11.4524i	0.361796	+	0.626649i
$335$	−6.47303	+	11.2116i	−0.353659	+	0.612556i
$336$	0.785868	+	4.51469i	0.0428726	+	0.246296i
$337$	8.99813	+	15.5852i	0.490160	+	0.848981i	0.999936	−	0.0113258i	$-0.00360518\pi$
$337$	8.99813	+	15.5852i	0.490160	+	0.848981i	−0.509776	+	0.860307i	$0.670272\pi$
$338$	11.2495	−	19.4847i	0.611892	−	1.05983i
$339$	19.8329	−	3.96860i	1.07717	−	0.215545i
$340$	−2.65781	−	4.60347i	−0.144140	−	0.249658i
$341$	7.73551	+	13.3983i	0.418901	+	0.725558i
$342$	2.29250	−	17.7267i	0.123964	−	0.958549i
$343$	1.39610	−	18.4676i	0.0753825	−	0.997155i
$344$	−0.977900	+	1.69377i	−0.0527248	+	0.0913221i
$345$	2.30560	−	0.461356i	0.124129	−	0.0248386i
$346$	15.2751			0.821195
$347$	−4.14672			−0.222608			−0.111304	−	0.993786i	$-0.535503\pi$
$347$	−4.14672			−0.222608			−0.111304	+	0.993786i	$0.535503\pi$
$348$	7.09461	+	8.07120i	0.380311	+	0.432662i
$349$	−11.4215	+	19.7827i	−0.611381	+	1.05894i	0.379627	+	0.925140i	$0.376052\pi$
$349$	−11.4215	+	19.7827i	−0.611381	+	1.05894i	−0.991008	+	0.133804i	$0.957281\pi$
$350$	2.25729	+	1.38008i	0.120657	+	0.0737684i
$351$	−27.8133	−	13.5975i	−1.48456	−	0.725781i
$352$	1.25470	+	2.17320i	0.0668757	+	0.115832i
$353$	11.7572	+	20.3640i	0.625771	+	1.08387i	0.988391	+	0.151930i	$0.0485487\pi$
$353$	11.7572	+	20.3640i	0.625771	+	1.08387i	−0.362621	+	0.931937i	$0.618118\pi$
$354$	−1.59178	+	4.70693i	−0.0846024	+	0.250171i
$355$	−1.76278	+	3.05322i	−0.0935586	+	0.162048i
$356$	−0.367362	−	0.636290i	−0.0194702	−	0.0337233i
$357$	−22.8719	−	8.38148i	−1.21051	−	0.443595i
$358$	0.232599	−	0.402873i	0.0122932	−	0.0212925i
$359$	−6.12241	−	10.6043i	−0.323128	−	0.559675i	0.658003	−	0.753015i	$-0.271401\pi$
$359$	−6.12241	−	10.6043i	−0.323128	−	0.559675i	−0.981132	+	0.193340i	$0.938068\pi$
$360$	−2.76900	+	1.15439i	−0.145939	+	0.0608417i
$361$	−8.24949	+	14.2885i	−0.434184	+	0.752028i
$362$	−26.1282			−1.37327
$363$	5.37784	+	6.11811i	0.282263	+	0.321118i
$364$	−13.4492	−	8.22266i	−0.704929	−	0.430984i
$365$	5.60063	+	9.70058i	0.293150	+	0.507751i
$366$	2.12460	−	6.28248i	0.111055	−	0.328391i
$367$	5.78768	+	10.0246i	0.302114	+	0.523277i	0.976615	−	0.214997i	$-0.0689742\pi$
$367$	5.78768	+	10.0246i	0.302114	+	0.523277i	−0.674500	+	0.738275i	$0.735641\pi$
$368$	−0.678764	+	1.17565i	−0.0353830	+	0.0612852i
$369$	−3.41055	+	26.3719i	−0.177546	+	1.37287i
$370$	5.16631			0.268583
$371$	−0.0239096	+	0.950427i	−0.00124132	+	0.0493437i
$372$	3.42092	−	10.1157i	0.177366	−	0.524475i
$373$	7.15324	−	12.3898i	0.370381	−	0.641518i	−0.619243	−	0.785199i	$-0.712561\pi$
$373$	7.15324	−	12.3898i	0.370381	−	0.641518i	0.989624	+	0.143681i	$0.0458939\pi$
$374$	−13.3390			−0.689745
$375$	−0.554872	+	1.64077i	−0.0286535	+	0.0847288i
$376$	2.04420			0.105422
$377$	−36.9655			−1.90382
$378$	−6.34680	+	12.1950i	−0.326444	+	0.627243i
$379$	−5.19451			−0.266824			−0.133412	−	0.991061i	$-0.542593\pi$
$379$	−5.19451			−0.266824			−0.133412	+	0.991061i	$0.542593\pi$
$380$	5.95810			0.305644
$381$	0.603243	−	1.78380i	0.0309050	−	0.0913868i
$382$	20.6483			1.05646
$383$	−5.92200	+	10.2572i	−0.302600	+	0.524119i	−0.976724	−	0.214499i	$-0.931188\pi$
$383$	−5.92200	+	10.2572i	−0.302600	+	0.524119i	0.674124	+	0.738618i	$0.264521\pi$
$384$	0.554872	−	1.64077i	0.0283157	−	0.0837300i
$385$	5.83142	−	3.17397i	0.297197	−	0.161761i
$386$	15.7801			0.803184
$387$	−5.41562	+	2.25776i	−0.275291	+	0.114768i
$388$	−6.19076	+	10.7227i	−0.314288	+	0.544363i
$389$	−17.6616	−	30.5908i	−0.895480	−	1.55102i	−0.833209	−	0.552958i	$-0.813499\pi$
$389$	−17.6616	−	30.5908i	−0.895480	−	1.55102i	−0.0622714	−	0.998059i	$-0.519834\pi$
$390$	3.30599	−	9.77586i	0.167405	−	0.495020i
$391$	−3.60806	−	6.24934i	−0.182467	−	0.316043i
$392$	−3.80039	+	5.87852i	−0.191949	+	0.296910i
$393$	−9.83702	−	11.1911i	−0.496212	−	0.564517i
$394$	−11.1659			−0.562529
$395$	7.39969	−	12.8166i	0.372319	−	0.644875i
$396$	−0.965543	+	7.46602i	−0.0485204	+	0.375182i
$397$	−5.44065	−	9.42348i	−0.273058	−	0.472951i	0.696585	−	0.717474i	$-0.254702\pi$
$397$	−5.44065	−	9.42348i	−0.273058	−	0.472951i	−0.969643	+	0.244523i	$0.921369\pi$
$398$	12.9803	−	22.4825i	0.650643	−	1.12695i
$399$	20.9541	−	17.5045i	1.04901	−	0.876319i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−14.3646	+	24.8801i	−0.717332	+	1.24246i	0.244722	+	0.969593i	$0.421303\pi$
$401$	−14.3646	+	24.8801i	−0.717332	+	1.24246i	−0.962053	+	0.272862i	$0.912030\pi$
$402$	7.18341	−	21.2415i	0.358276	−	1.05943i
$403$	18.3665	+	31.8118i	0.914902	+	1.58466i
$404$	−4.02012	−	6.96305i	−0.200008	−	0.346425i
$405$	−8.70390	−	2.28956i	−0.432500	−	0.113769i
$406$	−0.412813	+	16.4097i	−0.0204876	+	0.814399i
$407$	6.48216	−	11.2274i	0.321309	−	0.556523i
$408$	6.07847	+	6.91519i	0.300929	+	0.342353i
$409$	2.79310			0.138110			0.0690550	−	0.997613i	$-0.478002\pi$
$409$	2.79310			0.138110			0.0690550	+	0.997613i	$0.478002\pi$
$410$	−8.86383			−0.437754
$411$	−3.47472	+	0.695299i	−0.171395	+	0.0342966i
$412$	−5.60483	+	9.70785i	−0.276130	+	0.478271i
$413$	−6.66647	+	3.62848i	−0.328035	+	0.178546i
$414$	−3.75900	+	1.56712i	−0.184745	+	0.0770196i
$415$	−2.54006	−	4.39951i	−0.124687	−	0.215964i
$416$	2.97905	+	5.15987i	0.146060	+	0.252983i
$417$	−18.4875	+	3.69939i	−0.905337	+	0.181160i
$418$	7.47562	−	12.9482i	0.365645	−	0.633315i
$419$	14.8923	+	25.7942i	0.727535	+	1.26013i	0.957922	+	0.287028i	$0.0926674\pi$
$419$	14.8923	+	25.7942i	0.727535	+	1.26013i	−0.230387	+	0.973099i	$0.573999\pi$
$420$	−4.30277	−	1.57676i	−0.209954	−	0.0769381i
$421$	10.7947	−	18.6969i	0.526101	−	0.911233i	−0.473437	−	0.880828i	$-0.656987\pi$
$421$	10.7947	−	18.6969i	0.526101	−	0.911233i	0.999538	−	0.0304053i	$-0.00967978\pi$
$422$	2.97056	+	5.14516i	0.144605	+	0.250462i
$423$	4.87385	+	3.72215i	0.236975	+	0.180977i
$424$	0.179671	−	0.311199i	0.00872557	−	0.0151131i
$425$	5.31563			0.257846
$426$	1.95623	−	5.78462i	0.0947799	−	0.280266i
$427$	8.89793	−	4.84304i	0.430601	−	0.234371i
$428$	3.76525	+	6.52160i	0.182000	+	0.315233i
$429$	−17.0969	−	19.4503i	−0.825446	−	0.939071i
$430$	−0.977900	−	1.69377i	−0.0471585	−	0.0816810i
$431$	17.4006	−	30.1387i	0.838157	−	1.45173i	−0.0532769	−	0.998580i	$-0.516967\pi$
$431$	17.4006	−	30.1387i	0.838157	−	1.45173i	0.891434	−	0.453151i	$-0.149700\pi$
$432$	4.31051	−	2.90164i	0.207389	−	0.139605i
$433$	−16.7114			−0.803098			−0.401549	−	0.915838i	$-0.631528\pi$
$433$	−16.7114			−0.803098			−0.401549	+	0.915838i	$0.631528\pi$
$434$	14.3270	−	7.79800i	0.687716	−	0.374316i
$435$	−10.5372	+	2.10851i	−0.505219	+	0.101095i
$436$	5.59671	−	9.69378i	0.268034	−	0.464248i
$437$	8.08829			0.386915
$438$	−12.8088	−	14.5719i	−0.612026	−	0.696273i
$439$	30.6286			1.46182			0.730911	−	0.682473i	$-0.239095\pi$
$439$	30.6286			1.46182			0.730911	+	0.682473i	$0.239095\pi$
$440$	−2.50940			−0.119631
$441$	−19.7648	+	7.09590i	−0.941182	+	0.337900i
$442$	−31.6711			−1.50644
$443$	27.0075			1.28316			0.641582	−	0.767055i	$-0.278278\pi$
$443$	27.0075			1.28316			0.641582	+	0.767055i	$0.278278\pi$
$444$	−8.77436	+	1.75577i	−0.416413	+	0.0833251i
$445$	0.734724			0.0348293
$446$	8.23601	−	14.2652i	0.389986	−	0.675476i
$447$	0.571930	+	0.650658i	0.0270514	+	0.0307751i
$448$	2.32383	−	1.26483i	0.109791	−	0.0597578i
$449$	40.6860			1.92009			0.960045	−	0.279845i	$-0.0902831\pi$
$449$	40.6860			1.92009			0.960045	+	0.279845i	$0.0902831\pi$
$450$	0.384771	−	2.97522i	0.0181383	−	0.140253i
$451$	−11.1214	+	19.2629i	−0.523688	+	0.907055i
$452$	−5.83876	−	10.1130i	−0.274632	−	0.475677i
$453$	−28.1531	+	5.63349i	−1.32275	+	0.264684i
$454$	8.90835	+	15.4297i	0.418090	+	0.724153i
$455$	13.8456	−	7.53601i	0.649093	−	0.353294i
$456$	−10.1191	+	2.02486i	−0.473872	+	0.0948228i
$457$	35.4495			1.65826			0.829129	−	0.559057i	$-0.188837\pi$
$457$	35.4495			1.65826			0.829129	+	0.559057i	$0.188837\pi$
$458$	−11.5572	+	20.0177i	−0.540033	+	0.935365i
$459$	1.90109	+	27.5553i	0.0887352	+	1.28617i
$460$	−0.678764	−	1.17565i	−0.0316475	−	0.0548151i
$461$	11.9946	−	20.7753i	0.558645	−	0.967601i	−0.438965	−	0.898504i	$-0.644655\pi$
$461$	11.9946	−	20.7753i	0.558645	−	0.967601i	0.997610	−	0.0690971i	$-0.0220118\pi$
$462$	−8.82530	+	7.37243i	−0.410590	+	0.342996i
$463$	6.53066	+	11.3114i	0.303506	+	0.525687i	0.976927	−	0.213571i	$-0.0685096\pi$
$463$	6.53066	+	11.3114i	0.303506	+	0.525687i	−0.673422	+	0.739258i	$0.735176\pi$
$464$	3.10212	−	5.37303i	0.144012	−	0.249437i
$465$	7.05000	+	8.02045i	0.326936	+	0.371940i
$466$	−4.94916	−	8.57219i	−0.229265	−	0.397099i
$467$	−11.0880	−	19.2050i	−0.513092	−	0.888701i	−0.999885	−	0.0151836i	$-0.995167\pi$
$467$	−11.0880	−	19.2050i	−0.513092	−	0.888701i	0.486793	−	0.873517i	$-0.338167\pi$
$468$	−2.29250	+	17.7267i	−0.105971	+	0.819416i
$469$	30.0845	−	16.3746i	1.38917	−	0.756110i
$470$	−1.02210	+	1.77033i	−0.0471460	+	0.0816592i
$471$	0.613609	−	1.81445i	0.0282736	−	0.0836056i
$472$	2.86874			0.132044
$473$	−4.90788			−0.225665
$474$	−8.21177	+	24.2823i	−0.377179	+	1.11532i
$475$	−2.97905	+	5.15987i	−0.136688	+	0.236751i
$476$	−0.353687	+	14.0594i	−0.0162112	+	0.644411i
$477$	0.995017	−	0.414820i	0.0455587	−	0.0189933i
$478$	12.6933	+	21.9855i	0.580580	+	1.00559i
$479$	16.2605	+	28.1639i	0.742959	+	1.28684i	0.951142	+	0.308753i	$0.0999116\pi$
$479$	16.2605	+	28.1639i	0.742959	+	1.28684i	−0.208183	+	0.978090i	$0.566755\pi$
$480$	1.14351	+	1.30092i	0.0521938	+	0.0593785i
$481$	15.3907	−	26.6575i	0.701755	−	1.21548i
$482$	14.3326	+	24.8249i	0.652834	+	1.13074i
$483$	−5.84113	−	2.14050i	−0.265781	−	0.0973960i
$484$	2.35146	−	4.07285i	0.106885	−	0.185130i
$485$	−6.19076	−	10.7227i	−0.281108	−	0.486893i
$486$	15.5607	+	0.930524i	0.705846	+	0.0422094i
$487$	−9.99511	+	17.3120i	−0.452922	+	0.784483i	−0.998566	−	0.0535335i	$-0.982952\pi$
$487$	−9.99511	+	17.3120i	−0.452922	+	0.784483i	0.545644	+	0.838017i	$0.316285\pi$
$488$	−3.82899			−0.173330
$489$	11.7150	−	2.34421i	0.529773	−	0.106009i
$490$	−3.19076	−	6.23049i	−0.144144	−	0.281465i
$491$	15.5637	+	26.9570i	0.702378	+	1.21655i	0.967629	+	0.252375i	$0.0812117\pi$
$491$	15.5637	+	26.9570i	0.702378	+	1.21655i	−0.265251	+	0.964179i	$0.585455\pi$
$492$	15.0542	−	3.01237i	0.678695	−	0.135808i
$493$	16.4897	+	28.5610i	0.742660	+	1.28632i
$494$	17.7495	−	30.7430i	0.798587	−	1.38319i
$495$	−5.98299	−	4.56919i	−0.268915	−	0.205370i
$496$	−6.16523			−0.276827
$497$	8.19280	−	4.45925i	0.367497	−	0.200025i
$498$	5.80917	+	6.60881i	0.260315	+	0.296148i
$499$	−7.40897	+	12.8327i	−0.331671	+	0.574471i	−0.982840	−	0.184462i	$-0.940946\pi$
$499$	−7.40897	+	12.8327i	−0.331671	+	0.574471i	0.651169	+	0.758933i	$0.274279\pi$
$500$	1.00000			0.0447214
$501$	22.4596	−	4.49422i	1.00342	−	0.200787i
$502$	−27.3920			−1.22257
$503$	−2.45622			−0.109518			−0.0547588	−	0.998500i	$-0.517439\pi$
$503$	−2.45622			−0.109518			−0.0547588	+	0.998500i	$0.517439\pi$
$504$	7.84361	+	1.21565i	0.349382	+	0.0541493i
$505$	8.04024			0.357786
$506$	−3.40658			−0.151441
$507$	−25.7278	−	29.2693i	−1.14261	−	1.29990i
$508$	−1.08717			−0.0482355
$509$	6.67596	−	11.5631i	0.295907	−	0.512526i	−0.679289	−	0.733871i	$-0.737712\pi$
$509$	6.67596	−	11.5631i	0.295907	−	0.512526i	0.975195	+	0.221345i	$0.0710448\pi$
$510$	−9.02797	+	1.80652i	−0.399765	+	0.0799939i
$511$	0.745301	−	29.6264i	0.0329702	−	1.31059i
$512$	−1.00000			−0.0441942
$513$	−27.8133	−	13.5975i	−1.22799	−	0.600345i
$514$	−12.9546	+	22.4380i	−0.571402	+	0.989698i
$515$	−5.60483	−	9.70785i	−0.246978	−	0.427779i
$516$	2.23648	+	2.54433i	0.0984554	+	0.112008i
$517$	2.56486	+	4.44246i	0.112802	+	0.195379i
$518$	−11.6619	−	7.12992i	−0.512393	−	0.313271i
$519$	8.47574	−	25.0629i	0.372044	−	1.10014i
$520$	−5.95810			−0.261280
$521$	−17.5850	+	30.4582i	−0.770415	+	1.33440i	0.166921	+	0.985970i	$0.446617\pi$
$521$	−17.5850	+	30.4582i	−0.770415	+	1.33440i	−0.937336	+	0.348427i	$0.886716\pi$
$522$	17.1796	−	7.16211i	0.751929	−	0.313477i
$523$	5.78531	+	10.0204i	0.252974	+	0.438164i	0.964343	−	0.264655i	$-0.0852580\pi$
$523$	5.78531	+	10.0204i	0.252974	+	0.438164i	−0.711369	+	0.702818i	$0.751925\pi$
$524$	−4.30124	+	7.44996i	−0.187900	+	0.325453i
$525$	3.51690	−	2.93793i	0.153490	−	0.128222i
$526$	14.5434	+	25.1899i	0.634122	+	1.09833i
$527$	16.3860	−	28.3815i	0.713787	−	1.23632i
$528$	4.26192	−	0.852819i	0.185476	−	0.0371142i
$529$	10.5786	+	18.3226i	0.459937	+	0.796635i
$530$	0.179671	+	0.311199i	0.00780439	+	0.0135176i
$531$	6.83974	+	5.22349i	0.296820	+	0.226680i
$532$	−13.4492	−	8.22266i	−0.583096	−	0.356497i
$533$	−26.4058	+	45.7362i	−1.14376	+	1.98106i
$534$	−1.24784	+	0.249696i	−0.0539994	+	0.0108054i
$535$	−7.53050			−0.325572
$536$	−12.9461			−0.559185
$537$	−0.531958	−	0.605184i	−0.0229557	−	0.0261156i
$538$	4.69888	−	8.13870i	0.202583	−	0.350884i
$539$	−17.5436	−	0.883234i	−0.755655	−	0.0380436i
$540$	0.357641	+	5.18383i	0.0153904	+	0.223077i
$541$	−2.16363	−	3.74752i	−0.0930218	−	0.161119i	0.815759	−	0.578391i	$-0.196319\pi$
$541$	−2.16363	−	3.74752i	−0.0930218	−	0.161119i	−0.908781	+	0.417273i	$0.862986\pi$
$542$	0.571895	+	0.990552i	0.0245650	+	0.0425478i
$543$	−14.4978	+	42.8703i	−0.622160	+	1.83974i
$544$	2.65781	−	4.60347i	0.113953	−	0.197372i
$545$	5.59671	+	9.69378i	0.239737	+	0.415236i
$546$	−20.9541	+	17.5045i	−0.896751	+	0.749122i
$547$	−0.544266	+	0.942697i	−0.0232711	+	0.0403068i	−0.877426	−	0.479711i	$-0.840741\pi$
$547$	−0.544266	+	0.942697i	−0.0232711	+	0.0403068i	0.854155	+	0.520018i	$0.174075\pi$
$548$	1.02295	+	1.77180i	0.0436983	+	0.0756876i
$549$	−9.12921	−	6.97195i	−0.389625	−	0.297556i
$550$	1.25470	−	2.17320i	0.0535005	−	0.0926657i
$551$	−36.9655			−1.57478
$552$	1.55235	+	1.76603i	0.0660722	+	0.0751673i
$553$	−34.3913	+	18.7188i	−1.46247	+	0.796003i
$554$	−3.56388	−	6.17281i	−0.151415	−	0.262258i
$555$	2.86664	−	8.47670i	0.121682	−	0.359816i
$556$	5.44268	+	9.42700i	0.230821	+	0.399794i
$557$	−9.25764	+	16.0347i	−0.392259	+	0.679412i	−0.992747	−	0.120221i	$-0.961640\pi$
$557$	−9.25764	+	16.0347i	−0.392259	+	0.679412i	0.600488	+	0.799633i	$0.294973\pi$
$558$	−14.6993	−	11.2259i	−0.622273	−	0.475228i
$559$	−11.6529			−0.492863
$560$	−0.0665372	+	2.64491i	−0.00281171	+	0.111768i
$561$	−7.40146	+	21.8862i	−0.312490	+	0.924038i
$562$	−9.36628	+	16.2229i	−0.395093	+	0.684321i
$563$	12.4134			0.523163			0.261581	−	0.965181i	$-0.415756\pi$
$563$	12.4134			0.523163			0.261581	+	0.965181i	$0.415756\pi$
$564$	1.13427	−	3.35406i	0.0477614	−	0.141231i
$565$	11.6775			0.491277
$566$	31.6080			1.32858
$567$	16.4875	+	17.1803i	0.692410	+	0.721504i
$568$	−3.52556			−0.147929
$569$	9.25085			0.387816			0.193908	−	0.981020i	$-0.437884\pi$
$569$	9.25085			0.387816			0.193908	+	0.981020i	$0.437884\pi$
$570$	3.30599	−	9.77586i	0.138473	−	0.409466i
$571$	−12.1307			−0.507652			−0.253826	−	0.967250i	$-0.581689\pi$
$571$	−12.1307			−0.507652			−0.253826	+	0.967250i	$0.581689\pi$
$572$	−7.47562	+	12.9482i	−0.312572	+	0.541390i
$573$	11.4572	−	33.8791i	0.478630	−	1.41532i
$574$	20.0083	+	12.2328i	0.835130	+	0.510587i
$575$	1.35753			0.0566128
$576$	−2.38423	−	1.82083i	−0.0993431	−	0.0758680i
$577$	3.58092	−	6.20234i	0.149076	−	0.258207i	−0.781810	−	0.623516i	$-0.785704\pi$
$577$	3.58092	−	6.20234i	0.149076	−	0.258207i	0.930886	+	0.365310i	$0.119037\pi$
$578$	5.62796	+	9.74791i	0.234092	+	0.405460i
$579$	8.75592	−	25.8914i	0.363884	−	1.07601i
$580$	3.10212	+	5.37303i	0.128809	+	0.223103i
$581$	−0.338017	+	13.4365i	−0.0140233	+	0.557439i
$582$	14.1584	+	16.1073i	0.586884	+	0.667670i
$583$	0.901730			0.0373458
$584$	−5.60063	+	9.70058i	−0.231756	+	0.401413i
$585$	−14.2055	−	10.8487i	−0.587325	−	0.448539i
$586$	2.92595	+	5.06790i	0.120870	+	0.209353i
$587$	−14.4975	+	25.1104i	−0.598375	+	1.03642i	0.394686	+	0.918816i	$0.370853\pi$
$587$	−14.4975	+	25.1104i	−0.598375	+	1.03642i	−0.993061	+	0.117600i	$0.962480\pi$
$588$	7.53656	+	9.49738i	0.310802	+	0.391665i
$589$	18.3665	+	31.8118i	0.756780	+	1.31078i
$590$	−1.43437	+	2.48440i	−0.0590521	+	0.102281i
$591$	−6.19564	+	18.3206i	−0.254854	+	0.753609i
$592$	2.58315	+	4.47415i	0.106167	+	0.183887i
$593$	15.1709	+	26.2768i	0.622994	+	1.07906i	0.988925	+	0.148416i	$0.0474174\pi$
$593$	15.1709	+	26.2768i	0.622994	+	1.07906i	−0.365931	+	0.930642i	$0.619249\pi$
$594$	11.7142	+	5.72692i	0.480641	+	0.234978i
$595$	−11.9989	−	7.33600i	−0.491909	−	0.300746i
$596$	0.250077	−	0.433146i	0.0102435	−	0.0177423i
$597$	−29.6862	−	33.7726i	−1.21497	−	1.38222i
$598$	−8.08829			−0.330755
$599$	−14.9439			−0.610593			−0.305297	−	0.952257i	$-0.598756\pi$
$599$	−14.9439			−0.610593			−0.305297	+	0.952257i	$0.598756\pi$
$600$	−1.69838	+	0.339850i	−0.0693362	+	0.0138743i
$601$	4.85451	−	8.40827i	0.198020	−	0.342980i	−0.749866	−	0.661589i	$-0.769882\pi$
$601$	4.85451	−	8.40827i	0.198020	−	0.342980i	0.947886	+	0.318609i	$0.103216\pi$
$602$	−0.130134	+	5.17292i	−0.00530385	+	0.210833i
$603$	−30.8664	−	23.5726i	−1.25698	−	0.959951i
$604$	8.28820	+	14.3556i	0.337242	+	0.584120i
$605$	2.35146	+	4.07285i	0.0956005	+	0.165585i
$606$	−13.6554	+	2.73247i	−0.554712	+	0.110999i
$607$	7.93110	−	13.7371i	0.321913	−	0.557570i	−0.658969	−	0.752170i	$-0.729007\pi$
$607$	7.93110	−	13.7371i	0.321913	−	0.557570i	0.980883	+	0.194599i	$0.0623407\pi$
$608$	2.97905	+	5.15987i	0.120816	+	0.209260i
$609$	26.6954	+	9.78261i	1.08175	+	0.396411i
$610$	1.91450	−	3.31600i	0.0775157	−	0.134261i
$611$	6.08978	+	10.5478i	0.246366	+	0.426718i
$612$	14.7190	−	6.13631i	0.594980	−	0.248046i
$613$	17.2918	−	29.9503i	0.698409	−	1.20968i	−0.270609	−	0.962689i	$-0.587225\pi$
$613$	17.2918	−	29.9503i	0.698409	−	1.20968i	0.969018	−	0.246991i	$-0.0794417\pi$
$614$	−18.0889			−0.730007
$615$	−4.91830	+	14.5435i	−0.198325	+	0.586450i
$616$	5.66445	+	3.46317i	0.228227	+	0.139535i
$617$	−5.89064	−	10.2029i	−0.237148	−	0.410753i	0.722747	−	0.691113i	$-0.242879\pi$
$617$	−5.89064	−	10.2029i	−0.237148	−	0.410753i	−0.959895	+	0.280360i	$0.909546\pi$
$618$	12.8184	+	14.5828i	0.515630	+	0.586608i
$619$	−17.4140	−	30.1620i	−0.699928	−	1.21231i	−0.968491	−	0.249049i	$-0.919882\pi$
$619$	−17.4140	−	30.1620i	−0.699928	−	1.21231i	0.268562	−	0.963262i	$-0.413451\pi$
$620$	3.08262	−	5.33925i	0.123801	−	0.214429i
$621$	0.485508	+	7.03719i	0.0194828	+	0.282393i
$622$	−28.7843			−1.15415
$623$	−1.65849	−	1.01398i	−0.0664460	−	0.0406242i
$624$	10.1191	−	2.02486i	0.405090	−	0.0810593i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.185134			0.00739944
$627$	−17.0969	−	19.4503i	−0.682784	−	0.776772i
$628$	−1.10586			−0.0441285
$629$	−27.4622			−1.09499
$630$	−4.97459	+	6.18494i	−0.198192	+	0.246414i
$631$	−21.5511			−0.857934			−0.428967	−	0.903320i	$-0.641122\pi$
$631$	−21.5511			−0.857934			−0.428967	+	0.903320i	$0.641122\pi$
$632$	14.7994			0.588688
$633$	10.0903	−	2.01909i	0.401053	−	0.0802516i
$634$	−5.86194			−0.232807
$635$	0.543587	−	0.941520i	0.0215716	−	0.0373631i
$636$	−0.410910	−	0.467473i	−0.0162936	−	0.0185365i
$637$	−41.6540	−	2.09708i	−1.65039	−	0.0830892i
$638$	15.5689			0.616379
$639$	−8.40575	−	6.41945i	−0.332526	−	0.253950i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	11.2726	+	19.5247i	0.445241	+	0.771180i	0.998069	−	0.0621154i	$-0.0197847\pi$
$641$	11.2726	+	19.5247i	0.445241	+	0.771180i	−0.552828	+	0.833295i	$0.686451\pi$
$642$	12.7897	−	2.55924i	0.504768	−	0.101005i
$643$	4.05308	+	7.02014i	0.159838	+	0.276847i	0.934810	−	0.355148i	$-0.115570\pi$
$643$	4.05308	+	7.02014i	0.159838	+	0.276847i	−0.774972	+	0.631995i	$0.782236\pi$
$644$	−0.0903261	+	3.59054i	−0.00355935	+	0.141487i
$645$	−3.32170	+	0.664678i	−0.130792	+	0.0261717i
$646$	−31.6711			−1.24608
$647$	13.3586	−	23.1378i	0.525180	−	0.909639i	−0.474389	−	0.880315i	$-0.657331\pi$
$647$	13.3586	−	23.1378i	0.525180	−	0.909639i	0.999570	−	0.0293242i	$-0.00933553\pi$
$648$	−2.36914	−	8.68258i	−0.0930685	−	0.341084i
$649$	3.59940	+	6.23435i	0.141289	+	0.244720i
$650$	2.97905	−	5.15987i	0.116848	−	0.202387i
$651$	−4.84506	−	27.8341i	−0.189893	−	1.09090i
$652$	−3.44888	−	5.97364i	−0.135069	−	0.233946i
$653$	−3.03938	+	5.26436i	−0.118940	+	0.206010i	−0.919348	−	0.393446i	$-0.871283\pi$
$653$	−3.03938	+	5.26436i	−0.118940	+	0.206010i	0.800408	+	0.599456i	$0.204616\pi$
$654$	−12.7998	−	14.5617i	−0.500511	−	0.569408i
$655$	−4.30124	−	7.44996i	−0.168063	−	0.291094i
$656$	−4.43192	−	7.67631i	−0.173037	−	0.299709i
$657$	−31.0163	+	12.9306i	−1.21006	+	0.504472i
$658$	4.75038	−	2.58557i	0.185189	−	0.100796i
$659$	−3.02425	+	5.23816i	−0.117808	+	0.204050i	−0.918899	−	0.394493i	$-0.870920\pi$
$659$	−3.02425	+	5.23816i	−0.117808	+	0.204050i	0.801091	+	0.598543i	$0.204253\pi$
$660$	−1.39240	+	4.11734i	−0.0541989	+	0.160267i
$661$	9.99425			0.388731			0.194366	−	0.980929i	$-0.437735\pi$
$661$	9.99425			0.388731			0.194366	+	0.980929i	$0.437735\pi$
$662$	1.74896			0.0679752
$663$	−17.5734	+	51.9648i	−0.682494	+	2.01815i
$664$	2.54006	−	4.39951i	0.0985734	−	0.170734i
$665$	13.8456	−	7.53601i	0.536910	−	0.292234i
$666$	−1.98784	+	15.3709i	−0.0770274	+	0.595611i
$667$	4.21121	+	7.29404i	0.163059	+	0.282426i
$668$	−6.61206	−	11.4524i	−0.255828	−	0.443108i
$669$	−18.8359	−	21.4287i	−0.728238	−	0.828482i
$670$	6.47303	−	11.2116i	0.250075	−	0.433142i
$671$	−4.80423	−	8.32117i	−0.185465	−	0.321235i
$672$	−0.785868	−	4.51469i	−0.0303155	−	0.174158i
$673$	2.40233	−	4.16096i	0.0926031	−	0.160393i	−0.816003	−	0.578048i	$-0.803815\pi$
$673$	2.40233	−	4.16096i	0.0926031	−	0.160393i	0.908606	+	0.417655i	$0.137148\pi$
$674$	−8.99813	−	15.5852i	−0.346595	−	0.600320i
$675$	−4.66815	−	2.28219i	−0.179677	−	0.0878415i
$676$	−11.2495	+	19.4847i	−0.432673	+	0.749411i
$677$	−48.9810			−1.88249			−0.941247	−	0.337719i	$-0.890345\pi$
$677$	−48.9810			−1.88249			−0.941247	+	0.337719i	$0.890345\pi$
$678$	−19.8329	+	3.96860i	−0.761677	+	0.152413i
$679$	−0.823832	+	32.7480i	−0.0316158	+	1.25675i
$680$	2.65781	+	4.60347i	0.101923	+	0.176535i
$681$	30.2596	−	6.05501i	1.15955	−	0.232028i
$682$	−7.73551	−	13.3983i	−0.296208	−	0.513047i
$683$	8.41351	−	14.5726i	0.321934	−	0.557606i	−0.658953	−	0.752184i	$-0.729000\pi$
$683$	8.41351	−	14.5726i	0.321934	−	0.557606i	0.980887	+	0.194578i	$0.0623338\pi$
$684$	−2.29250	+	17.7267i	−0.0876561	+	0.677797i
$685$	−2.04590			−0.0781699
$686$	−1.39610	+	18.4676i	−0.0533035	+	0.705095i
$687$	26.4316	+	30.0700i	1.00843	+	1.14724i
$688$	0.977900	−	1.69377i	0.0372821	−	0.0645745i
$689$	2.14099			0.0815653
$690$	−2.30560	+	0.461356i	−0.0877727	+	0.0175635i
$691$	13.1129			0.498840			0.249420	−	0.968395i	$-0.419760\pi$
$691$	13.1129			0.498840			0.249420	+	0.968395i	$0.419760\pi$
$692$	−15.2751			−0.580673
$693$	7.19952	+	18.5710i	0.273487	+	0.705455i
$694$	4.14672			0.157407
$695$	−10.8854			−0.412905
$696$	−7.09461	−	8.07120i	−0.268920	−	0.305938i
$697$	47.1169			1.78468
$698$	11.4215	−	19.7827i	0.432312	−	0.748786i
$699$	−16.8111	+	3.36394i	−0.635855	+	0.127236i
$700$	−2.25729	−	1.38008i	−0.0853177	−	0.0521621i
$701$	20.8396			0.787099			0.393550	−	0.919303i	$-0.371247\pi$
$701$	20.8396			0.787099			0.393550	+	0.919303i	$0.371247\pi$
$702$	27.8133	+	13.5975i	1.04975	+	0.513205i
$703$	15.3907	−	26.6575i	0.580471	−	1.00540i
$704$	−1.25470	−	2.17320i	−0.0472882	−	0.0819056i
$705$	2.33756	+	2.65934i	0.0880377	+	0.100156i
$706$	−11.7572	−	20.3640i	−0.442487	−	0.766409i
$707$	−18.1492	−	11.0962i	−0.682570	−	0.417314i
$708$	1.59178	−	4.70693i	0.0598229	−	0.176897i
$709$	−12.8592			−0.482938			−0.241469	−	0.970408i	$-0.577629\pi$
$709$	−12.8592			−0.482938			−0.241469	+	0.970408i	$0.577629\pi$
$710$	1.76278	−	3.05322i	0.0661559	−	0.114585i
$711$	35.2852	+	26.9472i	1.32330	+	1.01060i
$712$	0.367362	+	0.636290i	0.0137675	+	0.0238460i
$713$	4.18474	−	7.24817i	0.156720	−	0.271446i
$714$	22.8719	+	8.38148i	0.855960	+	0.313669i
$715$	−7.47562	−	12.9482i	−0.279573	−	0.484234i
$716$	−0.232599	+	0.402873i	−0.00869263	+	0.0150561i
$717$	43.1163	−	8.62766i	1.61021	−	0.322206i
$718$	6.12241	+	10.6043i	0.228486	+	0.395750i
$719$	9.29950	+	16.1072i	0.346813	+	0.600698i	0.985681	−	0.168618i	$-0.0539306\pi$
$719$	9.29950	+	16.1072i	0.346813	+	0.600698i	−0.638869	+	0.769316i	$0.720597\pi$
$720$	2.76900	−	1.15439i	0.103195	−	0.0430216i
$721$	−0.745860	+	29.6486i	−0.0277773	+	1.10417i
$722$	8.24949	−	14.2885i	0.307014	−	0.531764i
$723$	48.6846	−	9.74190i	1.81060	−	0.362305i
$724$	26.1282			0.971046
$725$	−6.20424			−0.230420
$726$	−5.37784	−	6.11811i	−0.199590	−	0.227064i
$727$	−7.48277	+	12.9605i	−0.277520	+	0.480680i	−0.970768	−	0.240020i	$-0.922846\pi$
$727$	−7.48277	+	12.9605i	−0.277520	+	0.480680i	0.693247	+	0.720700i	$0.256179\pi$
$728$	13.4492	+	8.22266i	0.498460	+	0.304752i
$729$	10.1610	−	25.0151i	0.376332	−	0.926485i
$730$	−5.60063	−	9.70058i	−0.207289	−	0.359034i
$731$	5.19815	+	9.00347i	0.192261	+	0.333005i
$732$	−2.12460	+	6.28248i	−0.0785275	+	0.232207i
$733$	12.4231	−	21.5174i	0.458857	−	0.794764i	−0.540043	−	0.841637i	$-0.681592\pi$
$733$	12.4231	−	21.5174i	0.458857	−	0.794764i	0.998901	+	0.0468727i	$0.0149255\pi$
$734$	−5.78768	−	10.0246i	−0.213627	−	0.370013i
$735$	−11.9933	+	1.77816i	−0.442378	+	0.0655884i
$736$	0.678764	−	1.17565i	0.0250196	−	0.0433352i
$737$	−16.2434	−	28.1344i	−0.598334	−	1.03634i
$738$	3.41055	−	26.3719i	0.125544	−	0.970762i
$739$	2.77974	−	4.81466i	0.102254	−	0.177110i	−0.810359	−	0.585934i	$-0.800728\pi$
$739$	2.77974	−	4.81466i	0.102254	−	0.177110i	0.912613	+	0.408824i	$0.134061\pi$
$740$	−5.16631			−0.189917
$741$	−40.5934	−	46.1812i	−1.49124	−	1.69651i
$742$	0.0239096	−	0.950427i	0.000877748	−	0.0348913i
$743$	−13.6878	−	23.7080i	−0.502157	−	0.869762i	−0.999997	−	0.00249280i	$-0.999207\pi$
$743$	−13.6878	−	23.7080i	−0.502157	−	0.869762i	0.497840	−	0.867269i	$-0.334127\pi$
$744$	−3.42092	+	10.1157i	−0.125417	+	0.370860i
$745$	0.250077	+	0.433146i	0.00916210	+	0.0158692i
$746$	−7.15324	+	12.3898i	−0.261899	+	0.453622i
$747$	14.0669	−	5.86444i	0.514680	−	0.214569i
$748$	13.3390			0.487723
$749$	16.9985	+	10.3927i	0.621113	+	0.379741i
$750$	0.554872	−	1.64077i	0.0202611	−	0.0599123i
$751$	20.0674	−	34.7578i	0.732271	−	1.26833i	−0.223639	−	0.974672i	$-0.571794\pi$
$751$	20.0674	−	34.7578i	0.732271	−	1.26833i	0.955910	−	0.293659i	$-0.0948731\pi$
$752$	−2.04420			−0.0745443
$753$	−15.1991	+	44.9439i	−0.553885	+	1.63785i
$754$	36.9655			1.34620
$755$	−16.5764			−0.603277
$756$	6.34680	−	12.1950i	0.230831	−	0.443528i
$757$	−2.26550			−0.0823410			−0.0411705	−	0.999152i	$-0.513109\pi$
$757$	−2.26550			−0.0823410			−0.0411705	+	0.999152i	$0.513109\pi$
$758$	5.19451			0.188673
$759$	−1.89022	+	5.58940i	−0.0686105	+	0.202882i
$760$	−5.95810			−0.216123
$761$	5.36510	−	9.29263i	0.194485	−	0.336858i	−0.752247	−	0.658882i	$-0.771030\pi$
$761$	5.36510	−	9.29263i	0.194485	−	0.336858i	0.946732	+	0.322024i	$0.104363\pi$
$762$	−0.603243	+	1.78380i	−0.0218532	+	0.0646202i
$763$	0.744779	−	29.6056i	0.0269628	−	1.07180i
$764$	−20.6483			−0.747029
$765$	−2.04530	+	15.8152i	−0.0739479	+	0.571799i
$766$	5.92200	−	10.2572i	0.213971	−	0.370608i
$767$	8.54612	+	14.8023i	0.308583	+	0.534481i
$768$	−0.554872	+	1.64077i	−0.0200222	+	0.0592061i
$769$	3.58422	+	6.20804i	0.129250	+	0.223868i	0.923386	−	0.383872i	$-0.125410\pi$
$769$	3.58422	+	6.20804i	0.129250	+	0.223868i	−0.794136	+	0.607740i	$0.792076\pi$
$770$	−5.83142	+	3.17397i	−0.210150	+	0.114382i
$771$	29.6274	+	33.7057i	1.06700	+	1.21388i
$772$	−15.7801			−0.567937
$773$	12.1491	−	21.0428i	0.436972	−	0.756859i	−0.560482	−	0.828167i	$-0.689384\pi$
$773$	12.1491	−	21.0428i	0.436972	−	0.756859i	0.997454	+	0.0713082i	$0.0227174\pi$
$774$	5.41562	−	2.25776i	0.194660	−	0.0811534i
$775$	3.08262	+	5.33925i	0.110731	+	0.191791i
$776$	6.19076	−	10.7227i	0.222235	−	0.384923i
$777$	−18.1694	+	15.1782i	−0.651823	+	0.544516i
$778$	17.6616	+	30.5908i	0.633200	+	1.09673i
$779$	−26.4058	+	45.7362i	−0.946087	+	1.63867i
$780$	−3.30599	+	9.77586i	−0.118373	+	0.350032i
$781$	−4.42351	−	7.66175i	−0.158286	−	0.274159i
$782$	3.60806	+	6.24934i	0.129024	+	0.223476i
$783$	−2.21889	−	32.1617i	−0.0792968	−	1.14937i
$784$	3.80039	−	5.87852i	0.135728	−	0.209947i
$785$	0.552928	−	0.957700i	0.0197349	−	0.0341818i
$786$	9.83702	+	11.1911i	0.350875	+	0.399174i
$787$	−39.8058			−1.41892			−0.709462	−	0.704744i	$-0.751062\pi$
$787$	−39.8058			−1.41892			−0.709462	+	0.704744i	$0.751062\pi$
$788$	11.1659			0.397768
$789$	49.4005	−	9.88514i	1.75870	−	0.351920i
$790$	−7.39969	+	12.8166i	−0.263269	+	0.455996i
$791$	−26.3596	−	16.1159i	−0.937239	−	0.573016i
$792$	0.965543	−	7.46602i	0.0343091	−	0.265293i
$793$	−11.4068	−	19.7571i	−0.405066	−	0.701595i
$794$	5.44065	+	9.42348i	0.193081	+	0.334427i
$795$	0.610299	−	0.122122i	0.0216451	−	0.00433122i
$796$	−12.9803	+	22.4825i	−0.460074	+	0.796872i
$797$	−21.8579	−	37.8591i	−0.774248	−	1.34104i	−0.935216	−	0.354077i	$-0.884795\pi$
$797$	−21.8579	−	37.8591i	−0.774248	−	1.34104i	0.160968	−	0.986960i	$-0.448538\pi$
$798$	−20.9541	+	17.5045i	−0.741765	+	0.619651i
$799$	5.43311	−	9.41042i	0.192209	−	0.332917i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−0.282700	+	2.18597i	−0.00998873	+	0.0772374i
$802$	14.3646	−	24.8801i	0.507230	−	0.878548i
$803$	−28.1084			−0.991925
$804$	−7.18341	+	21.2415i	−0.253339	+	0.749129i
$805$	−3.06434	−	1.87350i	−0.108004	−	0.0660321i
$806$	−18.3665	−	31.8118i	−0.646934	−	1.12052i
$807$	−10.7464	−	12.2257i	−0.378292	−	0.430365i
$808$	4.02012	+	6.96305i	0.141427	+	0.244959i
$809$	−8.14162	+	14.1017i	−0.286244	+	0.495789i	−0.972910	−	0.231184i	$-0.925740\pi$
$809$	−8.14162	+	14.1017i	−0.286244	+	0.495789i	0.686666	+	0.726973i	$0.259073\pi$
$810$	8.70390	+	2.28956i	0.305824	+	0.0804469i
$811$	−5.38713			−0.189168			−0.0945839	−	0.995517i	$-0.530152\pi$
$811$	−5.38713			−0.189168			−0.0945839	+	0.995517i	$0.530152\pi$
$812$	0.412813	−	16.4097i	0.0144869	−	0.575867i
$813$	1.94259	−	0.388717i	0.0681297	−	0.0136329i
$814$	−6.48216	+	11.2274i	−0.227200	+	0.393521i
$815$	6.89777			0.241618
$816$	−6.07847	−	6.91519i	−0.212789	−	0.242080i
$817$	−11.6529			−0.407682
$818$	−2.79310			−0.0976585
$819$	17.0939	+	44.0935i	0.597310	+	1.54075i
$820$	8.86383			0.309539
$821$	22.8971			0.799115			0.399557	−	0.916708i	$-0.369164\pi$
$821$	22.8971			0.799115			0.399557	+	0.916708i	$0.369164\pi$
$822$	3.47472	−	0.695299i	0.121195	−	0.0242514i
$823$	−0.900425			−0.0313869			−0.0156934	−	0.999877i	$-0.504996\pi$
$823$	−0.900425			−0.0313869			−0.0156934	+	0.999877i	$0.504996\pi$
$824$	5.60483	−	9.70785i	0.195254	−	0.338189i
$825$	−2.86952	−	3.26452i	−0.0999039	−	0.113656i
$826$	6.66647	−	3.62848i	0.231956	−	0.126251i
$827$	41.9173			1.45761			0.728803	−	0.684723i	$-0.240077\pi$
$827$	41.9173			1.45761			0.728803	+	0.684723i	$0.240077\pi$
$828$	3.75900	−	1.56712i	0.130634	−	0.0544611i
$829$	9.65386	−	16.7210i	0.335293	−	0.580744i	−0.648248	−	0.761429i	$-0.724498\pi$
$829$	9.65386	−	16.7210i	0.335293	−	0.580744i	0.983541	+	0.180685i	$0.0578315\pi$
$830$	2.54006	+	4.39951i	0.0881667	+	0.152709i
$831$	−12.1056	+	2.42237i	−0.419940	+	0.0840309i
$832$	−2.97905	−	5.15987i	−0.103280	−	0.178886i
$833$	16.9609	+	33.1190i	0.587660	+	1.14751i
$834$	18.4875	−	3.69939i	0.640170	−	0.128099i
$835$	13.2241			0.457640
$836$	−7.47562	+	12.9482i	−0.258550	+	0.447822i
$837$	−26.5753	+	17.8893i	−0.918576	+	0.618344i
$838$	−14.8923	−	25.7942i	−0.514445	−	0.891045i
$839$	26.7782	−	46.3812i	0.924486	−	1.60126i	0.132099	−	0.991236i	$-0.457828\pi$
$839$	26.7782	−	46.3812i	0.924486	−	1.60126i	0.792386	−	0.610020i	$-0.208838\pi$
$840$	4.30277	+	1.57676i	0.148460	+	0.0544035i
$841$	−4.74630	−	8.22083i	−0.163665	−	0.283477i
$842$	−10.7947	+	18.6969i	−0.372009	+	0.644339i
$843$	21.4209	+	24.3695i	0.737774	+	0.839331i
$844$	−2.97056	−	5.14516i	−0.102251	−	0.177104i
$845$	−11.2495	−	19.4847i	−0.386994	−	0.670294i
$846$	−4.87385	−	3.72215i	−0.167566	−	0.127970i
$847$	0.312919	−	12.4388i	0.0107520	−	0.427403i
$848$	−0.179671	+	0.311199i	−0.00616991	+	0.0106866i
$849$	17.5384	−	51.8614i	0.601916	−	1.77988i
$850$	−5.31563			−0.182325
$851$	−7.01340			−0.240416
$852$	−1.95623	+	5.78462i	−0.0670195	+	0.198178i
$853$	15.3011	−	26.5022i	0.523899	−	0.907419i	−0.475714	−	0.879600i	$-0.657810\pi$
$853$	15.3011	−	26.5022i	0.523899	−	0.907419i	0.999613	−	0.0278194i	$-0.00885633\pi$
$854$	−8.89793	+	4.84304i	−0.304481	+	0.165725i
$855$	−14.2055	−	10.8487i	−0.485818	−	0.371018i
$856$	−3.76525	−	6.52160i	−0.128694	−	0.222904i
$857$	15.7006	+	27.1943i	0.536323	+	0.928938i	0.999098	+	0.0424624i	$0.0135203\pi$
$857$	15.7006	+	27.1943i	0.536323	+	0.928938i	−0.462776	+	0.886476i	$0.653146\pi$
$858$	17.0969	+	19.4503i	0.583679	+	0.664024i
$859$	16.9692	−	29.3915i	0.578982	−	1.00283i	−0.416614	−	0.909083i	$-0.636783\pi$
$859$	16.9692	−	29.3915i	0.578982	−	1.00283i	0.995596	−	0.0937429i	$-0.0298832\pi$
$860$	0.977900	+	1.69377i	0.0333461	+	0.0577572i
$861$	31.1732	−	26.0413i	1.06238	−	0.887485i
$862$	−17.4006	+	30.1387i	−0.592667	+	1.02653i
$863$	−1.42043	−	2.46026i	−0.0483521	−	0.0837483i	0.840836	−	0.541289i	$-0.182064\pi$
$863$	−1.42043	−	2.46026i	−0.0483521	−	0.0837483i	−0.889189	+	0.457541i	$0.848730\pi$
$864$	−4.31051	+	2.90164i	−0.146646	+	0.0987158i
$865$	7.63756	−	13.2286i	0.259685	−	0.449787i
$866$	16.7114			0.567876
$867$	19.1169	−	3.82532i	0.649242	−	0.129915i
$868$	−14.3270	+	7.79800i	−0.486289	+	0.264681i
$869$	18.5688	+	32.1620i	0.629902	+	1.09102i
$870$	10.5372	−	2.10851i	0.357244	−	0.0714852i
$871$	−38.5670	−	66.7999i	−1.30679	−	2.26343i
$872$	−5.59671	+	9.69378i	−0.189528	+	0.328273i
$873$	34.2845	−	14.2931i	1.16035	−	0.483748i
$874$	−8.08829			−0.273590
$875$	2.32383	−	1.26483i	0.0785599	−	0.0427592i
$876$	12.8088	+	14.5719i	0.432768	+	0.492339i
$877$	−1.85738	+	3.21708i	−0.0627193	+	0.108633i	−0.895680	−	0.444699i	$-0.853311\pi$
$877$	−1.85738	+	3.21708i	−0.0627193	+	0.108633i	0.832961	+	0.553332i	$0.186644\pi$
$878$	−30.6286			−1.03366
$879$	9.93877	−	1.98877i	0.335226	−	0.0670795i
$880$	2.50940			0.0845918
$881$	−13.9925			−0.471420			−0.235710	−	0.971823i	$-0.575742\pi$
$881$	−13.9925			−0.471420			−0.235710	+	0.971823i	$0.575742\pi$
$882$	19.7648	−	7.09590i	0.665516	−	0.238931i
$883$	5.02808			0.169208			0.0846041	−	0.996415i	$-0.473037\pi$
$883$	5.02808			0.169208			0.0846041	+	0.996415i	$0.473037\pi$
$884$	31.6711			1.06521
$885$	3.28043	+	3.73199i	0.110270	+	0.125450i
$886$	−27.0075			−0.907334
$887$	−1.17692	+	2.03849i	−0.0395171	+	0.0684457i	−0.885108	−	0.465387i	$-0.845915\pi$
$887$	−1.17692	+	2.03849i	−0.0395171	+	0.0684457i	0.845590	+	0.533832i	$0.179249\pi$
$888$	8.77436	−	1.75577i	0.294448	−	0.0589197i
$889$	−2.52641	+	1.37509i	−0.0847330	+	0.0461192i
$890$	−0.734724			−0.0246280
$891$	15.8965	−	16.0426i	0.532551	−	0.537449i
$892$	−8.23601	+	14.2652i	−0.275762	+	0.477634i
$893$	6.08978	+	10.5478i	0.203787	+	0.352969i
$894$	−0.571930	−	0.650658i	−0.0191282	−	0.0217613i
$895$	−0.232599	−	0.402873i	−0.00777492	−	0.0134666i
$896$	−2.32383	+	1.26483i	−0.0776338	+	0.0422551i
$897$	−4.48797	+	13.2710i	−0.149849	+	0.443106i
$898$	−40.6860			−1.35771
$899$	−19.1253	+	33.1260i	−0.637864	+	1.10481i
$900$	−0.384771	+	2.97522i	−0.0128257	+	0.0991741i
$901$	−0.955062	−	1.65422i	−0.0318177	−	0.0551099i
$902$	11.1214	−	19.2629i	0.370304	−	0.641385i
$903$	8.41535	+	3.08383i	0.280045	+	0.102623i
$904$	5.83876	+	10.1130i	0.194194	+	0.336354i
$905$	−13.0641	+	22.6277i	−0.434265	+	0.752169i
$906$	28.1531	−	5.63349i	0.935323	−	0.187160i
$907$	−5.42043	−	9.38845i	−0.179982	−	0.311739i	0.761892	−	0.647704i	$-0.224271\pi$
$907$	−5.42043	−	9.38845i	−0.179982	−	0.311739i	−0.941874	+	0.335966i	$0.890937\pi$
$908$	−8.90835	−	15.4297i	−0.295634	−	0.512053i
$909$	−3.09365	+	23.9215i	−0.102610	+	0.793426i
$910$	−13.8456	+	7.53601i	−0.458978	+	0.249816i
$911$	10.8536	−	18.7990i	0.359597	−	0.622839i	−0.628297	−	0.777974i	$-0.716248\pi$
$911$	10.8536	−	18.7990i	0.359597	−	0.622839i	0.987893	+	0.155134i	$0.0495810\pi$
$912$	10.1191	−	2.02486i	0.335078	−	0.0670498i
$913$	12.7480			0.421899
$914$	−35.4495			−1.17257
$915$	−4.37849	−	4.98120i	−0.144748	−	0.164673i
$916$	11.5572	−	20.0177i	0.381861	−	0.661403i
$917$	−0.572385	+	22.7528i	−0.0189018	+	0.751364i
$918$	−1.90109	−	27.5553i	−0.0627453	−	0.909461i
$919$	−2.25667	−	3.90867i	−0.0744407	−	0.128935i	0.826402	−	0.563080i	$-0.190384\pi$
$919$	−2.25667	−	3.90867i	−0.0744407	−	0.128935i	−0.900843	+	0.434145i	$0.857050\pi$
$920$	0.678764	+	1.17565i	0.0223782	+	0.0387601i
$921$	−10.0370	+	29.6796i	−0.330731	+	0.977977i
$922$	−11.9946	+	20.7753i	−0.395022	+	0.684197i
$923$	−10.5028	−	18.1914i	−0.345704	−	0.598778i
$924$	8.82530	−	7.37243i	0.290331	−	0.242535i
$925$	2.58315	−	4.47415i	0.0849335	−	0.147109i
$926$	−6.53066	−	11.3114i	−0.214611	−	0.371717i
$927$	31.0396	−	12.9403i	1.01947	−	0.425016i
$928$	−3.10212	+	5.37303i	−0.101832	+	0.176378i
$929$	49.8155			1.63439			0.817196	−	0.576359i	$-0.195527\pi$
$929$	49.8155			1.63439			0.817196	+	0.576359i	$0.195527\pi$
$930$	−7.05000	−	8.02045i	−0.231179	−	0.263001i
$931$	−41.6540	−	2.09708i	−1.36515	−	0.0687289i
$932$	4.94916	+	8.57219i	0.162115	+	0.280792i
$933$	−15.9716	+	47.2284i	−0.522888	+	1.54619i
$934$	11.0880	+	19.2050i	0.362811	+	0.628406i
$935$	−6.66952	+	11.5519i	−0.218116	+	0.377789i
$936$	2.29250	−	17.7267i	0.0749328	−	0.579415i
$937$	21.8677			0.714387			0.357194	−	0.934030i	$-0.383734\pi$
$937$	21.8677			0.714387			0.357194	+	0.934030i	$0.383734\pi$
$938$	−30.0845	+	16.3746i	−0.982292	+	0.534650i
$939$	0.102726	−	0.303762i	0.00335233	−	0.00991289i
$940$	1.02210	−	1.77033i	0.0333372	−	0.0577418i
$941$	1.42852			0.0465685			0.0232842	−	0.999729i	$-0.492588\pi$
$941$	1.42852			0.0465685			0.0232842	+	0.999729i	$0.492588\pi$
$942$	−0.613609	+	1.81445i	−0.0199925	+	0.0591181i
$943$	12.0329			0.391845
$944$	−2.86874			−0.0933695
$945$	7.38778	+	11.5940i	0.240325	+	0.377153i
$946$	4.90788			0.159569
$947$	7.84837			0.255038			0.127519	−	0.991836i	$-0.459299\pi$
$947$	7.84837			0.255038			0.127519	+	0.991836i	$0.459299\pi$
$948$	8.21177	−	24.2823i	0.266706	−	0.788654i
$949$	−66.7383			−2.16642
$950$	2.97905	−	5.15987i	0.0966532	−	0.167408i
$951$	−3.25263	+	9.61807i	−0.105474	+	0.311887i
$952$	0.353687	−	14.0594i	0.0114631	−	0.455667i
$953$	−20.2969			−0.657480			−0.328740	−	0.944420i	$-0.606624\pi$
$953$	−20.2969			−0.657480			−0.328740	+	0.944420i	$0.606624\pi$
$954$	−0.995017	+	0.414820i	−0.0322149	+	0.0134303i
$955$	10.3242	−	17.8820i	0.334082	−	0.578647i
$956$	−12.6933	−	21.9855i	−0.410532	−	0.711062i
$957$	8.63876	−	25.5450i	0.279251	−	0.825751i
$958$	−16.2605	−	28.1639i	−0.525351	−	0.909935i
$959$	4.61820	+	2.82351i	0.149130	+	0.0911758i
$960$	−1.14351	−	1.30092i	−0.0369066	−	0.0419869i
$961$	7.01007			0.226131
$962$	−15.3907	+	26.6575i	−0.496216	+	0.859471i
$963$	2.89752	−	22.4049i	0.0933711	−	0.721988i
$964$	−14.3326	−	24.8249i	−0.461623	−	0.799555i
$965$	7.89003	−	13.6659i	0.253989	−	0.439922i
$966$	5.84113	+	2.14050i	0.187935	+	0.0688694i
$967$	4.14865	+	7.18567i	0.133411	+	0.231075i	0.924990	−	0.379993i	$-0.124073\pi$
$967$	4.14865	+	7.18567i	0.133411	+	0.231075i	−0.791578	+	0.611068i	$0.790740\pi$
$968$	−2.35146	+	4.07285i	−0.0755788	+	0.130906i
$969$	−17.5734	+	51.9648i	−0.564539	+	1.66935i
$970$	6.19076	+	10.7227i	0.198773	+	0.344285i
$971$	−23.9345	−	41.4558i	−0.768096	−	1.33038i	−0.938594	−	0.345023i	$-0.887871\pi$
$971$	−23.9345	−	41.4558i	−0.768096	−	1.33038i	0.170498	−	0.985358i	$-0.445462\pi$
$972$	−15.5607	−	0.930524i	−0.499108	−	0.0298466i
$973$	24.5715	+	15.0227i	0.787725	+	0.481605i
$974$	9.99511	−	17.3120i	0.320264	−	0.554713i
$975$	−6.81315	−	7.75100i	−0.218195	−	0.248231i
$976$	3.82899			0.122563
$977$	−13.1524			−0.420783			−0.210391	−	0.977617i	$-0.567474\pi$
$977$	−13.1524			−0.420783			−0.210391	+	0.977617i	$0.567474\pi$
$978$	−11.7150	+	2.34421i	−0.374606	+	0.0749594i
$979$	−0.921858	+	1.59670i	−0.0294627	+	0.0510309i
$980$	3.19076	+	6.23049i	0.101925	+	0.199026i
$981$	−30.9946	+	12.9216i	−0.989581	+	0.412554i
$982$	−15.5637	−	26.9570i	−0.496656	−	0.860234i
$983$	−26.9090	−	46.6077i	−0.858262	−	1.48655i	−0.873585	−	0.486671i	$-0.838211\pi$
$983$	−26.9090	−	46.6077i	−0.858262	−	1.48655i	0.0153228	−	0.999883i	$-0.495122\pi$
$984$	−15.0542	+	3.01237i	−0.479910	+	0.0960310i
$985$	−5.58294	+	9.66993i	−0.177887	+	0.308110i
$986$	−16.4897	−	28.5610i	−0.525140	−	0.909569i
$987$	−1.60647	−	9.22893i	−0.0511346	−	0.293760i
$988$	−17.7495	+	30.7430i	−0.564687	+	0.978066i
$989$	1.32753	+	2.29934i	0.0422129	+	0.0731148i
$990$	5.98299	+	4.56919i	0.190152	+	0.145219i
$991$	12.4080	−	21.4913i	0.394153	−	0.682693i	−0.598839	−	0.800869i	$-0.704371\pi$
$991$	12.4080	−	21.4913i	0.394153	−	0.682693i	0.992993	+	0.118176i	$0.0377046\pi$
$992$	6.16523			0.195746
$993$	0.970448	−	2.86963i	0.0307963	−	0.0910650i
$994$	−8.19280	+	4.45925i	−0.259860	+	0.141439i
$995$	−12.9803	−	22.4825i	−0.411503	−	0.712744i
$996$	−5.80917	−	6.60881i	−0.184070	−	0.209408i
$997$	−21.8366	−	37.8220i	−0.691571	−	1.19784i	−0.971323	−	0.237764i	$-0.923586\pi$
$997$	−21.8366	−	37.8220i	−0.691571	−	1.19784i	0.279752	−	0.960072i	$-0.409748\pi$
$998$	7.40897	−	12.8327i	0.234527	−	0.406212i
$999$	24.1171	+	11.7905i	0.763031	+	0.373034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.f.151.2	yes	12
3.2	odd	2		1890.2.i.h.991.6		12
7.2	even	3		630.2.l.h.331.2	yes	12
9.4	even	3		630.2.l.h.571.2	yes	12
9.5	odd	6		1890.2.l.f.361.3		12
21.2	odd	6		1890.2.l.f.1801.3		12
63.23	odd	6		1890.2.i.h.1171.6		12
63.58	even	3	inner	630.2.i.f.121.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.f.121.2	✓	12	63.58	even	3	inner
630.2.i.f.151.2	yes	12	1.1	even	1	trivial
630.2.l.h.331.2	yes	12	7.2	even	3
630.2.l.h.571.2	yes	12	9.4	even	3
1890.2.i.h.991.6		12	3.2	odd	2
1890.2.i.h.1171.6		12	63.23	odd	6
1890.2.l.f.361.3		12	9.5	odd	6
1890.2.l.f.1801.3		12	21.2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.554872 + 1.64077i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.554872 - 1.64077i) q^{6} +(2.32383 - 1.26483i) q^{7} -1.00000 q^{8} +(-2.38423 - 1.82083i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.554872 + 1.64077i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.554872 - 1.64077i) q^{6} +(2.32383 - 1.26483i) q^{7} -1.00000 q^{8} +(-2.38423 - 1.82083i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.25470 - 2.17320i) q^{11} +(-0.554872 + 1.64077i) q^{12} +(-2.97905 - 5.15987i) q^{13} +(-2.32383 + 1.26483i) q^{14} +(-1.14351 - 1.30092i) q^{15} +1.00000 q^{16} +(-2.65781 + 4.60347i) q^{17} +(2.38423 + 1.82083i) q^{18} +(-2.97905 - 5.15987i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.785868 + 4.51469i) q^{21} +(1.25470 + 2.17320i) q^{22} +(-0.678764 + 1.17565i) q^{23} +(0.554872 - 1.64077i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.97905 + 5.15987i) q^{26} +(4.31051 - 2.90164i) q^{27} +(2.32383 - 1.26483i) q^{28} +(3.10212 - 5.37303i) q^{29} +(1.14351 + 1.30092i) q^{30} -6.16523 q^{31} -1.00000 q^{32} +(4.26192 - 0.852819i) q^{33} +(2.65781 - 4.60347i) q^{34} +(-0.0665372 + 2.64491i) q^{35} +(-2.38423 - 1.82083i) q^{36} +(2.58315 + 4.47415i) q^{37} +(2.97905 + 5.15987i) q^{38} +(10.1191 - 2.02486i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-4.43192 - 7.67631i) q^{41} +(-0.785868 - 4.51469i) q^{42} +(0.977900 - 1.69377i) q^{43} +(-1.25470 - 2.17320i) q^{44} +(2.76900 - 1.15439i) q^{45} +(0.678764 - 1.17565i) q^{46} -2.04420 q^{47} +(-0.554872 + 1.64077i) q^{48} +(3.80039 - 5.87852i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-6.07847 - 6.91519i) q^{51} +(-2.97905 - 5.15987i) q^{52} +(-0.179671 + 0.311199i) q^{53} +(-4.31051 + 2.90164i) q^{54} +2.50940 q^{55} +(-2.32383 + 1.26483i) q^{56} +(10.1191 - 2.02486i) q^{57} +(-3.10212 + 5.37303i) q^{58} -2.86874 q^{59} +(-1.14351 - 1.30092i) q^{60} +3.82899 q^{61} +6.16523 q^{62} +(-7.84361 - 1.21565i) q^{63} +1.00000 q^{64} +5.95810 q^{65} +(-4.26192 + 0.852819i) q^{66} +12.9461 q^{67} +(-2.65781 + 4.60347i) q^{68} +(-1.55235 - 1.76603i) q^{69} +(0.0665372 - 2.64491i) q^{70} +3.52556 q^{71} +(2.38423 + 1.82083i) q^{72} +(5.60063 - 9.70058i) q^{73} +(-2.58315 - 4.47415i) q^{74} +(1.69838 - 0.339850i) q^{75} +(-2.97905 - 5.15987i) q^{76} +(-5.66445 - 3.46317i) q^{77} +(-10.1191 + 2.02486i) q^{78} -14.7994 q^{79} +(-0.500000 + 0.866025i) q^{80} +(2.36914 + 8.68258i) q^{81} +(4.43192 + 7.67631i) q^{82} +(-2.54006 + 4.39951i) q^{83} +(0.785868 + 4.51469i) q^{84} +(-2.65781 - 4.60347i) q^{85} +(-0.977900 + 1.69377i) q^{86} +(7.09461 + 8.07120i) q^{87} +(1.25470 + 2.17320i) q^{88} +(-0.367362 - 0.636290i) q^{89} +(-2.76900 + 1.15439i) q^{90} +(-13.4492 - 8.22266i) q^{91} +(-0.678764 + 1.17565i) q^{92} +(3.42092 - 10.1157i) q^{93} +2.04420 q^{94} +5.95810 q^{95} +(0.554872 - 1.64077i) q^{96} +(-6.19076 + 10.7227i) q^{97} +(-3.80039 + 5.87852i) q^{98} +(-0.965543 + 7.46602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 2 q^{19} - 6 q^{20} + 29 q^{21} + 7 q^{22} - 9 q^{23} - 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 4 q^{28} + 3 q^{29} + q^{30} + 18 q^{31} - 12 q^{32} + 27 q^{33} - q^{34} - 8 q^{35} - 4 q^{36} + 6 q^{37} + 2 q^{38} + 10 q^{39} + 6 q^{40} - 11 q^{41} - 29 q^{42} + 23 q^{43} - 7 q^{44} + 5 q^{45} + 9 q^{46} - 2 q^{47} + 2 q^{48} + 24 q^{49} + 6 q^{50} - 15 q^{51} - 2 q^{52} - 4 q^{53} - 11 q^{54} + 14 q^{55} - 4 q^{56} + 10 q^{57} - 3 q^{58} - 22 q^{59} - q^{60} + 50 q^{61} - 18 q^{62} - q^{63} + 12 q^{64} + 4 q^{65} - 27 q^{66} + 4 q^{67} + q^{68} - 12 q^{69} + 8 q^{70} + 22 q^{71} + 4 q^{72} + 24 q^{73} - 6 q^{74} - q^{75} - 2 q^{76} - 11 q^{77} - 10 q^{78} + 2 q^{79} - 6 q^{80} + 20 q^{81} + 11 q^{82} + 4 q^{83} + 29 q^{84} + q^{85} - 23 q^{86} + 7 q^{88} + 2 q^{89} - 5 q^{90} - 8 q^{91} - 9 q^{92} + 40 q^{93} + 2 q^{94} + 4 q^{95} - 2 q^{96} - 36 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^15 + 12 * q^16 + q^17 + 4 * q^18 - 2 * q^19 - 6 * q^20 + 29 * q^21 + 7 * q^22 - 9 * q^23 - 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 4 * q^28 + 3 * q^29 + q^30 + 18 * q^31 - 12 * q^32 + 27 * q^33 - q^34 - 8 * q^35 - 4 * q^36 + 6 * q^37 + 2 * q^38 + 10 * q^39 + 6 * q^40 - 11 * q^41 - 29 * q^42 + 23 * q^43 - 7 * q^44 + 5 * q^45 + 9 * q^46 - 2 * q^47 + 2 * q^48 + 24 * q^49 + 6 * q^50 - 15 * q^51 - 2 * q^52 - 4 * q^53 - 11 * q^54 + 14 * q^55 - 4 * q^56 + 10 * q^57 - 3 * q^58 - 22 * q^59 - q^60 + 50 * q^61 - 18 * q^62 - q^63 + 12 * q^64 + 4 * q^65 - 27 * q^66 + 4 * q^67 + q^68 - 12 * q^69 + 8 * q^70 + 22 * q^71 + 4 * q^72 + 24 * q^73 - 6 * q^74 - q^75 - 2 * q^76 - 11 * q^77 - 10 * q^78 + 2 * q^79 - 6 * q^80 + 20 * q^81 + 11 * q^82 + 4 * q^83 + 29 * q^84 + q^85 - 23 * q^86 + 7 * q^88 + 2 * q^89 - 5 * q^90 - 8 * q^91 - 9 * q^92 + 40 * q^93 + 2 * q^94 + 4 * q^95 - 2 * q^96 - 36 * q^97 - 24 * q^98 + 15 * q^99

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