LMFDB - Embedded newform 1001.2.i.a.144.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(144,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("1001.144");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.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:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			144.3
Root			$1.19003 + 0.764088i$ of defining polynomial
Character	$\chi$	$=$	1001.144
Dual form			1001.2.i.a.716.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0667052 + 0.115537i) q^{2} +(1.25673 - 2.17673i) q^{3} +(0.991101 - 1.71664i) q^{4} +(-1.25673 - 2.17673i) q^{5} +0.335323 q^{6} +(-2.00000 + 1.73205i) q^{7} +0.531267 q^{8} +(-1.65876 - 2.87306i) q^{9} +O(q^{10})$	\(q+(0.0667052 + 0.115537i) q^{2} +(1.25673 - 2.17673i) q^{3} +(0.991101 - 1.71664i) q^{4} +(-1.25673 - 2.17673i) q^{5} +0.335323 q^{6} +(-2.00000 + 1.73205i) q^{7} +0.531267 q^{8} +(-1.65876 - 2.87306i) q^{9} +(0.167661 - 0.290398i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-2.49110 - 4.31471i) q^{12} -1.00000 q^{13} +(-0.333526 - 0.115537i) q^{14} -6.31752 q^{15} +(-1.94676 - 3.37189i) q^{16} +(-1.23437 + 2.13799i) q^{17} +(0.221296 - 0.383296i) q^{18} +(1.03544 + 1.79343i) q^{19} -4.98220 q^{20} +(1.25673 + 6.53018i) q^{21} +0.133410 q^{22} +(-2.55781 - 4.43025i) q^{23} +(0.667661 - 1.15642i) q^{24} +(-0.658762 + 1.14101i) q^{25} +(-0.0667052 - 0.115537i) q^{26} -0.798088 q^{27} +(0.991101 + 5.14991i) q^{28} -3.53127 q^{29} +(-0.421412 - 0.729906i) q^{30} +(2.74665 - 4.75733i) q^{31} +(0.790985 - 1.37003i) q^{32} +(-1.25673 - 2.17673i) q^{33} -0.329355 q^{34} +(6.28367 + 2.17673i) q^{35} -6.57600 q^{36} +(2.60553 + 4.51290i) q^{37} +(-0.138138 + 0.239262i) q^{38} +(-1.25673 + 2.17673i) q^{39} +(-0.667661 - 1.15642i) q^{40} -0.397857 q^{41} +(-0.670645 + 0.580796i) q^{42} +2.99403 q^{43} +(-0.991101 - 1.71664i) q^{44} +(-4.16925 + 7.22135i) q^{45} +(0.341238 - 0.591041i) q^{46} +(-0.924396 - 1.60110i) q^{47} -9.78626 q^{48} +(1.00000 - 6.92820i) q^{49} -0.175771 q^{50} +(3.10254 + 5.37376i) q^{51} +(-0.991101 + 1.71664i) q^{52} +(4.98101 - 8.62737i) q^{53} +(-0.0532366 - 0.0922085i) q^{54} -2.51347 q^{55} +(-1.06253 + 0.920181i) q^{56} +5.20508 q^{57} +(-0.235554 - 0.407991i) q^{58} +(-3.04474 + 5.27364i) q^{59} +(-6.26130 + 10.8449i) q^{60} +(0.814540 + 1.41083i) q^{61} +0.732863 q^{62} +(8.29381 + 2.87306i) q^{63} -7.57600 q^{64} +(1.25673 + 2.17673i) q^{65} +(0.167661 - 0.290398i) q^{66} +(-1.69420 + 2.93444i) q^{67} +(2.44676 + 4.23792i) q^{68} -12.8579 q^{69} +(0.167661 + 0.871194i) q^{70} +12.5673 q^{71} +(-0.881245 - 1.52636i) q^{72} +(-4.60254 + 7.97184i) q^{73} +(-0.347604 + 0.602068i) q^{74} +(1.65578 + 2.86789i) q^{75} +4.10489 q^{76} +(0.500000 + 2.59808i) q^{77} -0.335323 q^{78} +(1.55324 + 2.69028i) q^{79} +(-4.89313 + 8.47515i) q^{80} +(3.97330 - 6.88196i) q^{81} +(-0.0265391 - 0.0459671i) q^{82} -9.19922 q^{83} +(12.4555 + 4.31471i) q^{84} +6.20508 q^{85} +(0.199717 + 0.345921i) q^{86} +(-4.43786 + 7.68661i) q^{87} +(0.265633 - 0.460091i) q^{88} +(5.90778 + 10.2326i) q^{89} -1.11244 q^{90} +(2.00000 - 1.73205i) q^{91} -10.1402 q^{92} +(-6.90361 - 11.9574i) q^{93} +(0.123324 - 0.213603i) q^{94} +(2.60254 - 4.50773i) q^{95} +(-1.98812 - 3.44352i) q^{96} +8.21105 q^{97} +(0.867167 - 0.346610i) q^{98} -3.31752 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9	\( 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} + 4 q^{11} - 8 q^{12} - 8 q^{13} + 10 q^{14} - 30 q^{15} + 4 q^{16} - 9 q^{17} - 5 q^{18} + 4 q^{19} - 16 q^{20} - q^{21} - 4 q^{22} - 6 q^{23} + 7 q^{24} + 5 q^{25} + 2 q^{26} + 2 q^{27} - 4 q^{28} - 30 q^{29} + 11 q^{30} + 10 q^{31} + 2 q^{32} + q^{33} + 4 q^{34} - 5 q^{35} - 34 q^{36} - 9 q^{37} - 14 q^{38} + q^{39} - 7 q^{40} - 10 q^{41} - 12 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} + 13 q^{46} + 2 q^{47} - 56 q^{48} + 8 q^{49} + 2 q^{50} - 10 q^{51} + 4 q^{52} + 27 q^{53} - 20 q^{54} + 2 q^{55} - 12 q^{56} - 28 q^{57} + 10 q^{58} - 4 q^{59} - 5 q^{60} - 19 q^{61} - 88 q^{62} + 15 q^{63} - 42 q^{64} - q^{65} + 3 q^{66} + q^{67} - 16 q^{69} + 3 q^{70} - 10 q^{71} + 21 q^{72} - 2 q^{73} + 5 q^{74} - 2 q^{75} + 38 q^{76} + 4 q^{77} - 6 q^{78} + 32 q^{79} - 28 q^{80} - 4 q^{81} + 16 q^{82} + 40 q^{84} - 20 q^{85} + 22 q^{86} - 4 q^{87} + 3 q^{88} + 3 q^{89} - 58 q^{90} + 16 q^{91} - 30 q^{92} - 17 q^{93} - 5 q^{94} - 14 q^{95} + q^{96} + 6 q^{97} - 26 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9 + 3 * q^10 + 4 * q^11 - 8 * q^12 - 8 * q^13 + 10 * q^14 - 30 * q^15 + 4 * q^16 - 9 * q^17 - 5 * q^18 + 4 * q^19 - 16 * q^20 - q^21 - 4 * q^22 - 6 * q^23 + 7 * q^24 + 5 * q^25 + 2 * q^26 + 2 * q^27 - 4 * q^28 - 30 * q^29 + 11 * q^30 + 10 * q^31 + 2 * q^32 + q^33 + 4 * q^34 - 5 * q^35 - 34 * q^36 - 9 * q^37 - 14 * q^38 + q^39 - 7 * q^40 - 10 * q^41 - 12 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 + 13 * q^46 + 2 * q^47 - 56 * q^48 + 8 * q^49 + 2 * q^50 - 10 * q^51 + 4 * q^52 + 27 * q^53 - 20 * q^54 + 2 * q^55 - 12 * q^56 - 28 * q^57 + 10 * q^58 - 4 * q^59 - 5 * q^60 - 19 * q^61 - 88 * q^62 + 15 * q^63 - 42 * q^64 - q^65 + 3 * q^66 + q^67 - 16 * q^69 + 3 * q^70 - 10 * q^71 + 21 * q^72 - 2 * q^73 + 5 * q^74 - 2 * q^75 + 38 * q^76 + 4 * q^77 - 6 * q^78 + 32 * q^79 - 28 * q^80 - 4 * q^81 + 16 * q^82 + 40 * q^84 - 20 * q^85 + 22 * q^86 - 4 * q^87 + 3 * q^88 + 3 * q^89 - 58 * q^90 + 16 * q^91 - 30 * q^92 - 17 * q^93 - 5 * q^94 - 14 * q^95 + q^96 + 6 * q^97 - 26 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1001\mathbb{Z}\right)^\times$.

$n$	$365$	$430$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0667052	+	0.115537i	0.0471677	+	0.0816968i	0.888645	−	0.458595i	$-0.151647\pi$
$2$	0.0667052	+	0.115537i	0.0471677	+	0.0816968i	−0.841478	+	0.540292i	$0.818314\pi$
$3$	1.25673	−	2.17673i	0.725576	−	1.25673i	−0.233161	−	0.972438i	$-0.574907\pi$
$3$	1.25673	−	2.17673i	0.725576	−	1.25673i	0.958737	−	0.284296i	$-0.0917599\pi$
$4$	0.991101	−	1.71664i	0.495550	−	0.858319i
$5$	−1.25673	−	2.17673i	−0.562029	−	0.973462i	−0.997319	−	0.0731722i	$-0.976688\pi$
$5$	−1.25673	−	2.17673i	−0.562029	−	0.973462i	0.435291	−	0.900290i	$-0.356646\pi$
$6$	0.335323			0.136895
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	0.531267			0.187831
$9$	−1.65876	−	2.87306i	−0.552921	−	0.957687i
$10$	0.167661	−	0.290398i	0.0530192	−	0.0918319i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−2.49110	−	4.31471i	−0.719119	−	1.24555i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−0.333526	−	0.115537i	−0.0891385	−	0.0308785i
$15$	−6.31752			−1.63118
$16$	−1.94676	−	3.37189i	−0.486691	−	0.842973i
$17$	−1.23437	+	2.13799i	−0.299378	+	0.518538i	−0.975994	−	0.217798i	$-0.930112\pi$
$17$	−1.23437	+	2.13799i	−0.299378	+	0.518538i	0.676616	+	0.736336i	$0.263446\pi$
$18$	0.221296	−	0.383296i	0.0521600	−	0.0903437i
$19$	1.03544	+	1.79343i	0.237546	+	0.411441i	0.960009	−	0.279967i	$-0.0903237\pi$
$19$	1.03544	+	1.79343i	0.237546	+	0.411441i	−0.722464	+	0.691409i	$0.756990\pi$
$20$	−4.98220			−1.11405
$21$	1.25673	+	6.53018i	0.274242	+	1.42500i
$22$	0.133410			0.0284432
$23$	−2.55781	−	4.43025i	−0.533339	−	0.923771i	−0.999242	−	0.0389348i	$-0.987604\pi$
$23$	−2.55781	−	4.43025i	−0.533339	−	0.923771i	0.465902	−	0.884836i	$-0.345730\pi$
$24$	0.667661	−	1.15642i	0.136286	−	0.236054i
$25$	−0.658762	+	1.14101i	−0.131752	+	0.228202i
$26$	−0.0667052	−	0.115537i	−0.0130820	−	0.0226586i
$27$	−0.798088			−0.153592
$28$	0.991101	+	5.14991i	0.187300	+	0.973242i
$29$	−3.53127			−0.655740			−0.327870	−	0.944723i	$-0.606331\pi$
$29$	−3.53127			−0.655740			−0.327870	+	0.944723i	$0.606331\pi$
$30$	−0.421412	−	0.729906i	−0.0769389	−	0.133262i
$31$	2.74665	−	4.75733i	0.493313	−	0.854442i	−0.506658	−	0.862147i	$-0.669119\pi$
$31$	2.74665	−	4.75733i	0.493313	−	0.854442i	0.999970	+	0.00770489i	$0.00245257\pi$
$32$	0.790985	−	1.37003i	0.139828	−	0.242189i
$33$	−1.25673	−	2.17673i	−0.218769	−	0.378920i
$34$	−0.329355			−0.0564838
$35$	6.28367	+	2.17673i	1.06213	+	0.367934i
$36$	−6.57600			−1.09600
$37$	2.60553	+	4.51290i	0.428346	+	0.741917i	0.996726	−	0.0808491i	$-0.0257632\pi$
$37$	2.60553	+	4.51290i	0.428346	+	0.741917i	−0.568381	+	0.822766i	$0.692430\pi$
$38$	−0.138138	+	0.239262i	−0.0224090	+	0.0388135i
$39$	−1.25673	+	2.17673i	−0.201239	+	0.348555i
$40$	−0.667661	−	1.15642i	−0.105567	−	0.182847i
$41$	−0.397857			−0.0621348			−0.0310674	−	0.999517i	$-0.509891\pi$
$41$	−0.397857			−0.0621348			−0.0310674	+	0.999517i	$0.509891\pi$
$42$	−0.670645	+	0.580796i	−0.103483	+	0.0896188i
$43$	2.99403			0.456586			0.228293	−	0.973593i	$-0.426686\pi$
$43$	2.99403			0.456586			0.228293	+	0.973593i	$0.426686\pi$
$44$	−0.991101	−	1.71664i	−0.149414	−	0.258793i
$45$	−4.16925	+	7.22135i	−0.621515	+	1.07649i
$46$	0.341238	−	0.591041i	0.0503128	−	0.0871443i
$47$	−0.924396	−	1.60110i	−0.134837	−	0.233544i	0.790698	−	0.612206i	$-0.209718\pi$
$47$	−0.924396	−	1.60110i	−0.134837	−	0.233544i	−0.925535	+	0.378662i	$0.876384\pi$
$48$	−9.78626			−1.41252
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	−0.175771			−0.0248578
$51$	3.10254	+	5.37376i	0.434443	+	0.752477i
$52$	−0.991101	+	1.71664i	−0.137441	+	0.238055i
$53$	4.98101	−	8.62737i	0.684195	−	1.18506i	−0.289494	−	0.957180i	$-0.593487\pi$
$53$	4.98101	−	8.62737i	0.684195	−	1.18506i	0.973689	−	0.227881i	$-0.0731796\pi$
$54$	−0.0532366	−	0.0922085i	−0.00724458	−	0.0125480i
$55$	−2.51347			−0.338916
$56$	−1.06253	+	0.920181i	−0.141987	+	0.122964i
$57$	5.20508			0.689430
$58$	−0.235554	−	0.407991i	−0.0309297	−	0.0535719i
$59$	−3.04474	+	5.27364i	−0.396391	+	0.686569i	−0.993278	−	0.115756i	$-0.963071\pi$
$59$	−3.04474	+	5.27364i	−0.396391	+	0.686569i	0.596887	+	0.802325i	$0.296404\pi$
$60$	−6.26130	+	10.8449i	−0.808331	+	1.40007i
$61$	0.814540	+	1.41083i	0.104291	+	0.180638i	0.913448	−	0.406955i	$-0.133409\pi$
$61$	0.814540	+	1.41083i	0.104291	+	0.180638i	−0.809157	+	0.587592i	$0.800076\pi$
$62$	0.732863			0.0930736
$63$	8.29381	+	2.87306i	1.04492	+	0.361972i
$64$	−7.57600			−0.947000
$65$	1.25673	+	2.17673i	0.155879	+	0.269990i
$66$	0.167661	−	0.290398i	0.0206377	−	0.0357455i
$67$	−1.69420	+	2.93444i	−0.206980	+	0.358499i	−0.950762	−	0.309923i	$-0.899697\pi$
$67$	−1.69420	+	2.93444i	−0.206980	+	0.358499i	0.743782	+	0.668422i	$0.233030\pi$
$68$	2.44676	+	4.23792i	0.296714	+	0.513923i
$69$	−12.8579			−1.54791
$70$	0.167661	+	0.871194i	0.0200394	+	0.104128i
$71$	12.5673			1.49147			0.745735	−	0.666243i	$-0.232099\pi$
$71$	12.5673			1.49147			0.745735	+	0.666243i	$0.232099\pi$
$72$	−0.881245	−	1.52636i	−0.103856	−	0.179883i
$73$	−4.60254	+	7.97184i	−0.538687	+	0.933033i	0.460288	+	0.887769i	$0.347746\pi$
$73$	−4.60254	+	7.97184i	−0.538687	+	0.933033i	−0.998975	+	0.0452633i	$0.985587\pi$
$74$	−0.347604	+	0.602068i	−0.0404082	+	0.0699890i
$75$	1.65578	+	2.86789i	0.191193	+	0.331156i
$76$	4.10489			0.470864
$77$	0.500000	+	2.59808i	0.0569803	+	0.296078i
$78$	−0.335323			−0.0379678
$79$	1.55324	+	2.69028i	0.174753	+	0.302681i	0.940076	−	0.340966i	$-0.110754\pi$
$79$	1.55324	+	2.69028i	0.174753	+	0.302681i	−0.765323	+	0.643647i	$0.777421\pi$
$80$	−4.89313	+	8.47515i	−0.547068	+	0.947550i
$81$	3.97330	−	6.88196i	0.441478	−	0.764662i
$82$	−0.0265391	−	0.0459671i	−0.00293075	−	0.00507621i
$83$	−9.19922			−1.00975			−0.504873	−	0.863194i	$-0.668461\pi$
$83$	−9.19922			−1.00975			−0.504873	+	0.863194i	$0.668461\pi$
$84$	12.4555	+	4.31471i	1.35901	+	0.470774i
$85$	6.20508			0.673036
$86$	0.199717	+	0.345921i	0.0215361	+	0.0373016i
$87$	−4.43786	+	7.68661i	−0.475789	+	0.824091i
$88$	0.265633	−	0.460091i	0.0283166	−	0.0490458i
$89$	5.90778	+	10.2326i	0.626224	+	1.08465i	0.988303	+	0.152504i	$0.0487338\pi$
$89$	5.90778	+	10.2326i	0.626224	+	1.08465i	−0.362079	+	0.932147i	$0.617933\pi$
$90$	−1.11244			−0.117262
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$	−10.1402			−1.05719
$93$	−6.90361	−	11.9574i	−0.715871	−	1.23993i
$94$	0.123324	−	0.213603i	0.0127199	−	0.0220315i
$95$	2.60254	−	4.50773i	0.267015	−	0.462484i
$96$	−1.98812	−	3.44352i	−0.202911	−	0.351453i
$97$	8.21105			0.833706			0.416853	−	0.908974i	$-0.363133\pi$
$97$	8.21105			0.833706			0.416853	+	0.908974i	$0.363133\pi$
$98$	0.867167	−	0.346610i	0.0875971	−	0.0350129i
$99$	−3.31752			−0.333424
$100$	1.30580	+	2.26171i	0.130580	+	0.226171i
$101$	5.27612	−	9.13850i	0.524993	−	0.909315i	−0.474583	−	0.880211i	$-0.657401\pi$
$101$	5.27612	−	9.13850i	0.524993	−	0.909315i	0.999576	−	0.0291044i	$-0.00926553\pi$
$102$	−0.413911	+	0.716915i	−0.0409833	+	0.0709852i
$103$	−5.26130	−	9.11285i	−0.518412	−	0.897915i	−0.999771	−	0.0213921i	$-0.993190\pi$
$103$	−5.26130	−	9.11285i	−0.518412	−	0.897915i	0.481360	−	0.876523i	$-0.340143\pi$
$104$	−0.531267			−0.0520950
$105$	12.6350	−	10.9423i	1.23305	−	1.06786i
$106$	1.32904			0.129088
$107$	−4.60671	−	7.97906i	−0.445348	−	0.771365i	0.552729	−	0.833361i	$-0.313587\pi$
$107$	−4.60671	−	7.97906i	−0.445348	−	0.771365i	−0.998076	+	0.0619964i	$0.980253\pi$
$108$	−0.790985	+	1.37003i	−0.0761126	+	0.131831i
$109$	4.52654	−	7.84020i	0.433564	−	0.750955i	−0.563613	−	0.826039i	$-0.690589\pi$
$109$	4.52654	−	7.84020i	0.433564	−	0.750955i	0.997177	+	0.0750842i	$0.0239225\pi$
$110$	−0.167661	−	0.290398i	−0.0159859	−	0.0276884i
$111$	13.0978			1.24319
$112$	9.73382	+	3.37189i	0.919759	+	0.318614i
$113$	10.2431			0.963585			0.481793	−	0.876285i	$-0.339986\pi$
$113$	10.2431			0.963585			0.481793	+	0.876285i	$0.339986\pi$
$114$	0.347206	+	0.601378i	0.0325188	+	0.0563242i
$115$	−6.42897	+	11.1353i	−0.599504	+	1.03837i
$116$	−3.49984	+	6.06190i	−0.324952	+	0.562834i
$117$	1.65876	+	2.87306i	0.153353	+	0.265615i
$118$	−0.812398			−0.0747873
$119$	−1.23437	−	6.41396i	−0.113154	−	0.587966i
$120$	−3.35629			−0.306386
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.108668	+	0.188219i	−0.00983835	+	0.0170405i
$123$	−0.500000	+	0.866025i	−0.0450835	+	0.0780869i
$124$	−5.44441	−	9.42999i	−0.488922	−	0.846839i
$125$	−9.25579			−0.827863
$126$	0.221296	+	1.14989i	0.0197146	+	0.102440i
$127$	−9.06930			−0.804770			−0.402385	−	0.915471i	$-0.631819\pi$
$127$	−9.06930			−0.804770			−0.402385	+	0.915471i	$0.631819\pi$
$128$	−2.08733	−	3.61536i	−0.184496	−	0.319556i
$129$	3.76270	−	6.51719i	0.331287	−	0.573807i
$130$	−0.167661	+	0.290398i	−0.0147049	+	0.0254696i
$131$	−9.47196	−	16.4059i	−0.827569	−	1.43339i	−0.899940	−	0.436013i	$-0.856390\pi$
$131$	−9.47196	−	16.4059i	−0.827569	−	1.43339i	0.0723715	−	0.997378i	$-0.476943\pi$
$132$	−4.98220			−0.433645
$133$	−5.17719	−	1.79343i	−0.448919	−	0.155510i
$134$	−0.452048			−0.0390510
$135$	1.00298	+	1.73722i	0.0863231	+	0.149516i
$136$	−0.655778	+	1.13584i	−0.0562325	+	0.0973976i
$137$	9.76548	−	16.9143i	0.834321	−	1.44509i	−0.0602614	−	0.998183i	$-0.519193\pi$
$137$	9.76548	−	16.9143i	0.834321	−	1.44509i	0.894582	−	0.446903i	$-0.147473\pi$
$138$	−0.857690	−	1.48556i	−0.0730115	−	0.126460i
$139$	10.2938			0.873105			0.436553	−	0.899679i	$-0.356199\pi$
$139$	10.2938			0.873105			0.436553	+	0.899679i	$0.356199\pi$
$140$	9.96440	−	8.62943i	0.842146	−	0.729320i
$141$	−4.64688			−0.391338
$142$	0.838307	+	1.45199i	0.0703491	+	0.121848i
$143$	−0.500000	+	0.866025i	−0.0418121	+	0.0724207i
$144$	−6.45844	+	11.1863i	−0.538203	+	0.932195i
$145$	4.43786	+	7.68661i	0.368545	+	0.638338i
$146$	−1.22805			−0.101634
$147$	−13.8241	−	10.8836i	−1.14019	−	0.897667i
$148$	10.3294			0.849068
$149$	−9.51983	−	16.4888i	−0.779895	−	1.35082i	−0.932002	−	0.362454i	$-0.881939\pi$
$149$	−9.51983	−	16.4888i	−0.779895	−	1.35082i	0.152106	−	0.988364i	$-0.451394\pi$
$150$	−0.220898	+	0.382606i	−0.0180362	+	0.0312397i
$151$	10.6172	−	18.3895i	0.864015	−	1.49652i	−0.00400637	−	0.999992i	$-0.501275\pi$
$151$	10.6172	−	18.3895i	0.864015	−	1.49652i	0.868022	−	0.496526i	$-0.165391\pi$
$152$	0.550094	+	0.952791i	0.0446185	+	0.0772815i
$153$	8.19008			0.662129
$154$	−0.266821	+	0.231074i	−0.0215010	+	0.0186204i
$155$	−13.8072			−1.10902
$156$	2.49110	+	4.31471i	0.199448	+	0.345454i
$157$	−11.9820	+	20.7535i	−0.956271	+	1.65631i	−0.224839	+	0.974396i	$0.572186\pi$
$157$	−11.9820	+	20.7535i	−0.956271	+	1.65631i	−0.731432	+	0.681914i	$0.761148\pi$
$158$	−0.207218	+	0.358912i	−0.0164854	+	0.0285535i
$159$	−12.5196	−	21.6846i	−0.992871	−	1.71970i
$160$	−3.97623			−0.314349
$161$	12.7890	+	4.43025i	1.00792	+	0.349153i
$162$	1.06016			0.0832940
$163$	8.82344	+	15.2826i	0.691105	+	1.19703i	0.971476	+	0.237137i	$0.0762092\pi$
$163$	8.82344	+	15.2826i	0.691105	+	1.19703i	−0.280371	+	0.959892i	$0.590457\pi$
$164$	−0.394316	+	0.682975i	−0.0307909	+	0.0533314i
$165$	−3.15876	+	5.47114i	−0.245909	+	0.425927i
$166$	−0.613636	−	1.06285i	−0.0476274	−	0.0824930i
$167$	4.58514			0.354809			0.177404	−	0.984138i	$-0.443230\pi$
$167$	4.58514			0.354809			0.177404	+	0.984138i	$0.443230\pi$
$168$	0.667661	+	3.46927i	0.0515112	+	0.267660i
$169$	1.00000			0.0769231
$170$	0.413911	+	0.716915i	0.0317455	+	0.0549849i
$171$	3.43509	−	5.94975i	0.262688	−	0.454989i
$172$	2.96739	−	5.13967i	0.226261	−	0.391896i
$173$	−6.77020	−	11.7263i	−0.514729	−	0.891537i	−0.999854	−	0.0170919i	$-0.994559\pi$
$173$	−6.77020	−	11.7263i	−0.514729	−	0.891537i	0.485125	−	0.874445i	$-0.338774\pi$
$174$	−1.18411			−0.0897675
$175$	−0.658762	−	3.42303i	−0.0497977	−	0.258757i
$176$	−3.89353			−0.293486
$177$	7.65285	+	13.2551i	0.575223	+	0.996316i
$178$	−0.788160	+	1.36513i	−0.0590751	+	0.102321i
$179$	0.600347	−	1.03983i	0.0448720	−	0.0777206i	−0.842717	−	0.538357i	$-0.819045\pi$
$179$	0.600347	−	1.03983i	0.0448720	−	0.0777206i	0.887589	+	0.460636i	$0.152379\pi$
$180$	8.26429	+	14.3142i	0.615984	+	1.06691i
$181$	8.23482			0.612089			0.306045	−	0.952017i	$-0.400994\pi$
$181$	8.23482			0.612089			0.306045	+	0.952017i	$0.400994\pi$
$182$	0.333526	+	0.115537i	0.0247226	+	0.00856415i
$183$	4.09464			0.302685
$184$	−1.35888	−	2.35365i	−0.100178	−	0.173513i
$185$	6.54891	−	11.3430i	0.481485	−	0.833957i
$186$	0.921013	−	1.59524i	0.0675320	−	0.116969i
$187$	1.23437	+	2.13799i	0.0902658	+	0.156345i
$188$	−3.66468			−0.267274
$189$	1.59618	−	1.38233i	0.116105	−	0.100550i
$190$	0.694412			0.0503779
$191$	8.79201	+	15.2282i	0.636168	+	1.10187i	0.986266	+	0.165162i	$0.0528147\pi$
$191$	8.79201	+	15.2282i	0.636168	+	1.10187i	−0.350099	+	0.936713i	$0.613852\pi$
$192$	−9.52102	+	16.4909i	−0.687121	+	1.19013i
$193$	2.16190	−	3.74453i	0.155617	−	0.269537i	−0.777666	−	0.628677i	$-0.783597\pi$
$193$	2.16190	−	3.74453i	0.155617	−	0.269537i	0.933284	+	0.359140i	$0.116930\pi$
$194$	0.547720	+	0.948678i	0.0393240	+	0.0681111i
$195$	6.31752			0.452407
$196$	−10.9021	−	8.58319i	−0.778722	−	0.613085i
$197$	−7.52778			−0.536332			−0.268166	−	0.963373i	$-0.586418\pi$
$197$	−7.52778			−0.536332			−0.268166	+	0.963373i	$0.586418\pi$
$198$	−0.221296	−	0.383296i	−0.0157268	−	0.0272397i
$199$	−7.27099	+	12.5937i	−0.515427	+	0.892746i	0.484413	+	0.874840i	$0.339033\pi$
$199$	−7.27099	+	12.5937i	−0.515427	+	0.892746i	−0.999840	+	0.0179061i	$0.994300\pi$
$200$	−0.349979	+	0.606181i	−0.0247472	+	0.0428634i
$201$	4.25832	+	7.37563i	0.300359	+	0.520237i
$202$	1.40778			0.0990509
$203$	7.06253	−	6.11633i	0.495693	−	0.429282i
$204$	12.2997			0.861153
$205$	0.500000	+	0.866025i	0.0349215	+	0.0604858i
$206$	0.701912	−	1.21575i	0.0489046	−	0.0847052i
$207$	−8.48558	+	14.6975i	−0.589789	+	1.02154i
$208$	1.94676	+	3.37189i	0.134984	+	0.233799i
$209$	2.07088			0.143246
$210$	2.10706	+	0.729906i	0.145401	+	0.0503683i
$211$	24.8932			1.71372			0.856860	−	0.515550i	$-0.172412\pi$
$211$	24.8932			1.71372			0.856860	+	0.515550i	$0.172412\pi$
$212$	−9.87338	−	17.1012i	−0.678106	−	1.17451i
$213$	15.7938	−	27.3557i	1.08217	−	1.87438i
$214$	0.614583	−	1.06449i	0.0420120	−	0.0727670i
$215$	−3.76270	−	6.51719i	−0.256614	−	0.444469i
$216$	−0.423998			−0.0288494
$217$	2.74665	+	14.2720i	0.186455	+	0.968847i
$218$	1.20777			0.0818008
$219$	11.5683	+	20.0370i	0.781716	+	1.35397i
$220$	−2.49110	+	4.31471i	−0.167950	+	0.290898i
$221$	1.23437	−	2.13799i	0.0830325	−	0.143816i
$222$	0.873692	+	1.51328i	0.0586384	+	0.101565i
$223$	−8.68802			−0.581793			−0.290896	−	0.956755i	$-0.593954\pi$
$223$	−8.68802			−0.581793			−0.290896	+	0.956755i	$0.593954\pi$
$224$	0.790985	+	4.11008i	0.0528499	+	0.274616i
$225$	4.37092			0.291395
$226$	0.683265	+	1.18345i	0.0454501	+	0.0787219i
$227$	−4.45172	+	7.71061i	−0.295471	+	0.511771i	−0.975094	−	0.221790i	$-0.928810\pi$
$227$	−4.45172	+	7.71061i	−0.295471	+	0.511771i	0.679623	+	0.733561i	$0.262143\pi$
$228$	5.15876	−	8.93524i	0.341647	−	0.591751i
$229$	3.10035	+	5.36996i	0.204877	+	0.354857i	0.950093	−	0.311965i	$-0.100987\pi$
$229$	3.10035	+	5.36996i	0.204877	+	0.354857i	−0.745217	+	0.666822i	$0.767654\pi$
$230$	−1.71538			−0.113109
$231$	6.28367	+	2.17673i	0.413435	+	0.143218i
$232$	−1.87605			−0.123168
$233$	5.35455	+	9.27435i	0.350788	+	0.607583i	0.986388	−	0.164436i	$-0.0525804\pi$
$233$	5.35455	+	9.27435i	0.350788	+	0.607583i	−0.635600	+	0.772019i	$0.719247\pi$
$234$	−0.221296	+	0.383296i	−0.0144666	+	0.0250568i
$235$	−2.32344	+	4.02432i	−0.151564	+	0.262517i
$236$	6.03528	+	10.4534i	0.392863	+	0.680459i
$237$	7.80802			0.507186
$238$	0.658709	−	0.570459i	0.0426978	−	0.0369774i
$239$	−7.63933			−0.494147			−0.247074	−	0.968997i	$-0.579469\pi$
$239$	−7.63933			−0.494147			−0.247074	+	0.968997i	$0.579469\pi$
$240$	12.2987	+	21.3020i	0.793879	+	1.37504i
$241$	−1.65583	+	2.86798i	−0.106661	+	0.184743i	−0.914416	−	0.404776i	$-0.867349\pi$
$241$	−1.65583	+	2.86798i	−0.106661	+	0.184743i	0.807754	+	0.589519i	$0.200683\pi$
$242$	0.0667052	−	0.115537i	0.00428797	−	0.00742698i
$243$	−11.1839	−	19.3711i	−0.717448	−	1.24266i
$244$	3.22917			0.206726
$245$	−16.3375	+	6.53018i	−1.04377	+	0.417198i
$246$	−0.133410			−0.00850593
$247$	−1.03544	−	1.79343i	−0.0658834	−	0.114113i
$248$	1.45920	−	2.52741i	0.0926595	−	0.160491i
$249$	−11.5610	+	20.0242i	−0.732647	+	1.26898i
$250$	−0.617409	−	1.06938i	−0.0390484	−	0.0676338i
$251$	12.4245			0.784226			0.392113	−	0.919917i	$-0.371744\pi$
$251$	12.4245			0.784226			0.392113	+	0.919917i	$0.371744\pi$
$252$	13.1520	−	11.3900i	0.828498	−	0.717501i
$253$	−5.11561			−0.321616
$254$	−0.604969	−	1.04784i	−0.0379591	−	0.0657472i
$255$	7.79814	−	13.5068i	0.488339	−	0.845827i
$256$	−7.29753	+	12.6397i	−0.456096	+	0.789981i
$257$	1.40422	+	2.43219i	0.0875930	+	0.151716i	0.906493	−	0.422220i	$-0.138749\pi$
$257$	1.40422	+	2.43219i	0.0875930	+	0.151716i	−0.818900	+	0.573936i	$0.805416\pi$
$258$	1.00397			0.0625042
$259$	−13.0276	−	4.51290i	−0.809497	−	0.280418i
$260$	4.98220			0.308983
$261$	5.85753	+	10.1455i	0.362572	+	0.627993i
$262$	1.26366	−	2.18872i	0.0780690	−	0.135219i
$263$	5.52873	−	9.57605i	0.340916	−	0.590484i	−0.643687	−	0.765289i	$-0.722596\pi$
$263$	5.52873	−	9.57605i	0.340916	−	0.590484i	0.984603	+	0.174805i	$0.0559294\pi$
$264$	−0.667661	−	1.15642i	−0.0410917	−	0.0711729i
$265$	−25.0392			−1.53815
$266$	−0.138138	−	0.717787i	−0.00846980	−	0.0440103i
$267$	29.6981			1.81749
$268$	3.35825	+	5.81665i	0.205138	+	0.355309i
$269$	4.10964	−	7.11811i	0.250569	−	0.433999i	−0.713113	−	0.701049i	$-0.752716\pi$
$269$	4.10964	−	7.11811i	0.250569	−	0.433999i	0.963683	+	0.267050i	$0.0860488\pi$
$270$	−0.133808	+	0.231763i	−0.00814332	+	0.0141047i
$271$	12.2116	+	21.1512i	0.741804	+	1.28484i	0.951673	+	0.307112i	$0.0993627\pi$
$271$	12.2116	+	21.1512i	0.741804	+	1.28484i	−0.209870	+	0.977729i	$0.567304\pi$
$272$	9.61208			0.582818
$273$	−1.25673	−	6.53018i	−0.0760610	−	0.395225i
$274$	2.60563			0.157412
$275$	0.658762	+	1.14101i	0.0397249	+	0.0688055i
$276$	−12.7435	+	22.0724i	−0.767069	+	1.32860i
$277$	0.823439	−	1.42624i	0.0494757	−	0.0856944i	−0.840227	−	0.542235i	$-0.817578\pi$
$277$	0.823439	−	1.42624i	0.0494757	−	0.0856944i	0.889703	+	0.456540i	$0.150912\pi$
$278$	0.686647	+	1.18931i	0.0411823	+	0.0713299i
$279$	−18.2241			−1.09105
$280$	3.33831	+	1.15642i	0.199502	+	0.0691095i
$281$	−10.5733			−0.630751			−0.315375	−	0.948967i	$-0.602130\pi$
$281$	−10.5733			−0.630751			−0.315375	+	0.948967i	$0.602130\pi$
$282$	−0.309971	−	0.536885i	−0.0184585	−	0.0319711i
$283$	−10.9229	+	18.9190i	−0.649299	+	1.12462i	0.333992	+	0.942576i	$0.391604\pi$
$283$	−10.9229	+	18.9190i	−0.649299	+	1.12462i	−0.983291	+	0.182042i	$0.941729\pi$
$284$	12.4555	−	21.5736i	0.739098	−	1.28016i
$285$	−6.54141	−	11.3300i	−0.387479	−	0.671134i
$286$	−0.133410			−0.00788872
$287$	0.795713	−	0.689108i	0.0469695	−	0.0406767i
$288$	−5.24823			−0.309255
$289$	5.45268	+	9.44432i	0.320746	+	0.555548i
$290$	−0.592057	+	1.02547i	−0.0347668	+	0.0602178i
$291$	10.3191	−	17.8732i	0.604917	−	1.04775i
$292$	9.12317	+	15.8018i	0.533893	+	0.924730i
$293$	5.05060			0.295059			0.147530	−	0.989058i	$-0.452868\pi$
$293$	5.05060			0.295059			0.147530	+	0.989058i	$0.452868\pi$
$294$	0.335323	−	2.32318i	0.0195564	−	0.135491i
$295$	15.3057			0.891132
$296$	1.38423	+	2.39756i	0.0804567	+	0.139355i
$297$	−0.399044	+	0.691164i	−0.0231549	+	0.0401054i
$298$	1.27004	−	2.19978i	0.0735717	−	0.127430i
$299$	2.55781	+	4.43025i	0.147922	+	0.256208i
$300$	6.56417			0.378983
$301$	−5.98806	+	5.18582i	−0.345146	+	0.298905i
$302$	2.83289			0.163014
$303$	−13.2614	−	22.9693i	−0.761845	−	1.31955i
$304$	4.03151	−	6.98277i	0.231223	−	0.400490i
$305$	2.04732	−	3.54606i	0.117229	−	0.203047i
$306$	0.546321	+	0.946256i	0.0312311	+	0.0540938i
$307$	33.9744			1.93902			0.969512	−	0.245044i	$-0.0788024\pi$
$307$	33.9744			1.93902			0.969512	+	0.245044i	$0.0788024\pi$
$308$	4.95550	+	1.71664i	0.282366	+	0.0978145i
$309$	−26.4482			−1.50459
$310$	−0.921013	−	1.59524i	−0.0523100	−	0.0906037i
$311$	13.3544	−	23.1305i	0.757258	−	1.31161i	−0.186986	−	0.982363i	$-0.559872\pi$
$311$	13.3544	−	23.1305i	0.757258	−	1.31161i	0.944244	−	0.329247i	$-0.106795\pi$
$312$	−0.667661	+	1.15642i	−0.0377989	+	0.0654696i
$313$	11.7140	+	20.2893i	0.662116	+	1.14682i	0.980059	+	0.198709i	$0.0636749\pi$
$313$	11.7140	+	20.2893i	0.662116	+	1.14682i	−0.317942	+	0.948110i	$0.602992\pi$
$314$	−3.19706			−0.180420
$315$	−4.16925	−	21.6640i	−0.234910	−	1.22063i
$316$	6.15766			0.346395
$317$	−3.55482	−	6.15713i	−0.199659	−	0.345819i	0.748759	−	0.662842i	$-0.230650\pi$
$317$	−3.55482	−	6.15713i	−0.199659	−	0.345819i	−0.948418	+	0.317023i	$0.897317\pi$
$318$	1.67025	−	2.89295i	0.0936628	−	0.162229i
$319$	−1.76563	+	3.05817i	−0.0988565	+	0.171224i
$320$	9.52102	+	16.4909i	0.532241	+	0.921869i
$321$	−23.1577			−1.29253
$322$	0.341238	+	1.77312i	0.0190164	+	0.0988123i
$323$	−5.11244			−0.284464
$324$	−7.87589	−	13.6414i	−0.437549	−	0.757858i
$325$	0.658762	−	1.14101i	0.0365416	−	0.0632918i
$326$	−1.17714	+	2.03886i	−0.0651957	+	0.112922i
$327$	−11.3773	−	19.7061i	−0.629167	−	1.08975i
$328$	−0.211368			−0.0116708
$329$	4.62198	+	1.60110i	0.254818	+	0.0882715i
$330$	−0.842823			−0.0463959
$331$	5.67358	+	9.82692i	0.311848	+	0.540137i	0.978762	−	0.204998i	$-0.0657187\pi$
$331$	5.67358	+	9.82692i	0.311848	+	0.540137i	−0.666914	+	0.745134i	$0.732385\pi$
$332$	−9.11736	+	15.7917i	−0.500380	+	0.866683i
$333$	8.64389	−	14.9717i	0.473683	−	0.820442i
$334$	0.305853	+	0.529752i	0.0167355	+	0.0289868i
$335$	8.51664			0.465314
$336$	19.5725	−	16.9503i	1.06777	−	0.924714i
$337$	−30.3350			−1.65245			−0.826227	−	0.563338i	$-0.809517\pi$
$337$	−30.3350			−1.65245			−0.826227	+	0.563338i	$0.809517\pi$
$338$	0.0667052	+	0.115537i	0.00362828	+	0.00628437i
$339$	12.8728	−	22.2963i	0.699154	−	1.21097i
$340$	6.14986	−	10.6519i	0.333523	−	0.577679i
$341$	−2.74665	−	4.75733i	−0.148739	−	0.257624i
$342$	0.916554			0.0495615
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	1.59063			0.0857610
$345$	16.1590	+	27.9882i	0.869971	+	1.50683i
$346$	0.903215	−	1.56441i	0.0485571	−	0.0841034i
$347$	3.51127	−	6.08170i	0.188495	−	0.326483i	−0.756254	−	0.654279i	$-0.772972\pi$
$347$	3.51127	−	6.08170i	0.188495	−	0.326483i	0.944749	+	0.327796i	$0.106306\pi$
$348$	8.79674	+	15.2364i	0.471555	+	0.816757i
$349$	−35.2681			−1.88786			−0.943929	−	0.330149i	$-0.892901\pi$
$349$	−35.2681			−1.88786			−0.943929	+	0.330149i	$0.892901\pi$
$350$	0.351543	−	0.304445i	0.0187908	−	0.0162733i
$351$	0.798088			0.0425988
$352$	−0.790985	−	1.37003i	−0.0421597	−	0.0730227i
$353$	−1.58710	+	2.74893i	−0.0844726	+	0.146311i	−0.905166	−	0.425057i	$-0.860254\pi$
$353$	−1.58710	+	2.74893i	−0.0844726	+	0.146311i	0.820694	+	0.571368i	$0.193587\pi$
$354$	−1.02097	+	1.76837i	−0.0542639	+	0.0939878i
$355$	−15.7938	−	27.3557i	−0.838248	−	1.45189i
$356$	23.4208			1.24130
$357$	−15.5127	−	5.37376i	−0.821020	−	0.284410i
$358$	0.160185			0.00846603
$359$	8.49190	+	14.7084i	0.448185	+	0.776280i	0.998268	−	0.0588306i	$-0.0187372\pi$
$359$	8.49190	+	14.7084i	0.448185	+	0.776280i	−0.550083	+	0.835110i	$0.685404\pi$
$360$	−2.21498	+	3.83646i	−0.116740	+	0.202199i
$361$	7.35574	−	12.7405i	0.387144	−	0.670553i
$362$	0.549305	+	0.951424i	0.0288708	+	0.0500057i
$363$	−2.51347			−0.131923
$364$	−0.991101	−	5.14991i	−0.0519478	−	0.269929i
$365$	23.1367			1.21103
$366$	0.273134	+	0.473082i	0.0142769	+	0.0247284i
$367$	−10.7251	+	18.5765i	−0.559847	+	0.969684i	0.437661	+	0.899140i	$0.355807\pi$
$367$	−10.7251	+	18.5765i	−0.559847	+	0.969684i	−0.997509	+	0.0705440i	$0.977526\pi$
$368$	−9.95889	+	17.2493i	−0.519143	+	0.899182i
$369$	0.659949	+	1.14307i	0.0343556	+	0.0595056i
$370$	1.74738			0.0908422
$371$	4.98101	+	25.8821i	0.258601	+	1.34373i
$372$	−27.3687			−1.41900
$373$	8.71702	+	15.0983i	0.451350	+	0.781761i	0.998470	−	0.0552928i	$-0.0176092\pi$
$373$	8.71702	+	15.0983i	0.451350	+	0.781761i	−0.547120	+	0.837054i	$0.684276\pi$
$374$	−0.164677	+	0.285229i	−0.00851526	+	0.0147489i
$375$	−11.6321	+	20.1473i	−0.600677	+	1.04040i
$376$	−0.491101	−	0.850612i	−0.0253266	−	0.0438669i
$377$	3.53127			0.181869
$378$	0.266183	+	0.0922085i	0.0136910	+	0.00474269i
$379$	0.821072			0.0421756			0.0210878	−	0.999778i	$-0.493287\pi$
$379$	0.821072			0.0421756			0.0210878	+	0.999778i	$0.493287\pi$
$380$	−5.15876	−	8.93524i	−0.264639	−	0.458368i
$381$	−11.3977	+	19.7414i	−0.583922	+	1.01138i
$382$	−1.17295	+	2.03160i	−0.0600131	+	0.103946i
$383$	18.0106	+	31.1952i	0.920297	+	1.59400i	0.798955	+	0.601390i	$0.205386\pi$
$383$	18.0106	+	31.1952i	0.920297	+	1.59400i	0.121341	+	0.992611i	$0.461280\pi$
$384$	−10.4929			−0.535462
$385$	5.02694	−	4.35346i	0.256196	−	0.221873i
$386$	0.576841			0.0293604
$387$	−4.96639	−	8.60203i	−0.252456	−	0.437266i
$388$	8.13798	−	14.0954i	0.413143	−	0.715585i
$389$	7.48632	−	12.9667i	0.379571	−	0.657437i	−0.611428	−	0.791300i	$-0.709405\pi$
$389$	7.48632	−	12.9667i	0.379571	−	0.657437i	0.991000	+	0.133863i	$0.0427381\pi$
$390$	0.421412	+	0.729906i	0.0213390	+	0.0369602i
$391$	12.6291			0.638680
$392$	0.531267	−	3.68073i	0.0268330	−	0.185905i
$393$	−47.6149			−2.40186
$394$	−0.502142	−	0.869735i	−0.0252975	−	0.0438166i
$395$	3.90401	−	6.76195i	0.196432	−	0.340230i
$396$	−3.28800	+	5.69499i	−0.165228	+	0.286184i
$397$	0.225919	+	0.391302i	0.0113385	+	0.0196389i	0.871639	−	0.490148i	$-0.163057\pi$
$397$	0.225919	+	0.391302i	0.0113385	+	0.0196389i	−0.860300	+	0.509787i	$0.829724\pi$
$398$	−1.94005			−0.0972460
$399$	−10.4102	+	9.01547i	−0.521160	+	0.451338i
$400$	5.12982			0.256491
$401$	7.42778	+	12.8653i	0.370926	+	0.642462i	0.989708	−	0.143100i	$-0.0457072\pi$
$401$	7.42778	+	12.8653i	0.370926	+	0.642462i	−0.618783	+	0.785562i	$0.712374\pi$
$402$	−0.568104	+	0.983985i	−0.0283344	+	0.0490767i
$403$	−2.74665	+	4.75733i	−0.136820	+	0.236980i
$404$	−10.4583	−	18.1144i	−0.520321	−	0.901223i
$405$	−19.9735			−0.992493
$406$	1.17777	+	0.407991i	0.0584517	+	0.0202483i
$407$	5.21105			0.258302
$408$	1.64828	+	2.85490i	0.0816019	+	0.141339i
$409$	−1.70901	+	2.96010i	−0.0845053	+	0.146368i	−0.905180	−	0.425028i	$-0.860264\pi$
$409$	−1.70901	+	2.96010i	−0.0845053	+	0.146368i	0.820675	+	0.571395i	$0.193598\pi$
$410$	−0.0667052	+	0.115537i	−0.00329433	+	0.00570595i
$411$	−24.5452	−	42.5136i	−1.21073	−	2.09704i
$412$	−20.8579			−1.02760
$413$	−3.04474	−	15.8209i	−0.149822	−	0.778496i
$414$	−2.26413			−0.111276
$415$	11.5610	+	20.0242i	0.567506	+	0.982949i
$416$	−0.790985	+	1.37003i	−0.0387812	+	0.0671711i
$417$	12.9365	−	22.4067i	0.633504	−	1.09726i
$418$	0.138138	+	0.239262i	0.00675656	+	0.0117027i
$419$	−17.0685			−0.833851			−0.416925	−	0.908941i	$-0.636892\pi$
$419$	−17.0685			−0.833851			−0.416925	+	0.908941i	$0.636892\pi$
$420$	−6.26130	−	32.5347i	−0.305520	−	1.58753i
$421$	12.6684			0.617422			0.308711	−	0.951156i	$-0.400102\pi$
$421$	12.6684			0.617422			0.308711	+	0.951156i	$0.400102\pi$
$422$	1.66051	+	2.87608i	0.0808322	+	0.140005i
$423$	−3.06671	+	5.31169i	−0.149108	+	0.258263i
$424$	2.64625	−	4.58344i	0.128513	−	0.222591i
$425$	−1.62631	−	2.81685i	−0.0788875	−	0.136637i
$426$	4.21412			0.204175
$427$	−4.07270	−	1.41083i	−0.197092	−	0.0682746i
$428$	−18.2629			−0.882769
$429$	1.25673	+	2.17673i	0.0606757	+	0.105093i
$430$	0.501983	−	0.869461i	0.0242078	−	0.0419291i
$431$	−14.6457	+	25.3671i	−0.705458	+	1.22189i	0.261068	+	0.965320i	$0.415925\pi$
$431$	−14.6457	+	25.3671i	−0.705458	+	1.22189i	−0.966526	+	0.256569i	$0.917408\pi$
$432$	1.55369	+	2.69107i	0.0747518	+	0.129474i
$433$	−24.2210			−1.16399			−0.581993	−	0.813194i	$-0.697727\pi$
$433$	−24.2210			−1.16399			−0.581993	+	0.813194i	$0.697727\pi$
$434$	−1.46573	+	1.26936i	−0.0703571	+	0.0609310i
$435$	22.3089			1.06963
$436$	−8.97251	−	15.5408i	−0.429705	−	0.744272i
$437$	5.29690	−	9.17450i	0.253385	−	0.438876i
$438$	−1.54334	+	2.67314i	−0.0737435	+	0.127727i
$439$	−10.5410	−	18.2575i	−0.503094	−	0.871384i	−0.999994	−	0.00357598i	$-0.998862\pi$
$439$	−10.5410	−	18.2575i	−0.503094	−	0.871384i	0.496900	−	0.867808i	$-0.334472\pi$
$440$	−1.33532			−0.0636590
$441$	−21.5639	+	8.61918i	−1.02685	+	0.410437i
$442$	0.329355			0.0156658
$443$	19.6832	+	34.0922i	0.935175	+	1.61977i	0.774321	+	0.632793i	$0.218092\pi$
$443$	19.6832	+	34.0922i	0.935175	+	1.61977i	0.160855	+	0.986978i	$0.448575\pi$
$444$	12.9813	−	22.4842i	0.616063	−	1.06705i
$445$	14.8490	−	25.7193i	0.703912	−	1.21921i
$446$	−0.579536	−	1.00379i	−0.0274418	−	0.0475306i
$447$	−47.8556			−2.26349
$448$	15.1520	−	13.1220i	0.715865	−	0.619957i
$449$	−9.05556			−0.427358			−0.213679	−	0.976904i	$-0.568545\pi$
$449$	−9.05556			−0.427358			−0.213679	+	0.976904i	$0.568545\pi$
$450$	0.291563	+	0.505002i	0.0137444	+	0.0238060i
$451$	−0.198928	+	0.344554i	−0.00936717	+	0.0162244i
$452$	10.1519	−	17.5836i	0.477505	−	0.827063i
$453$	−26.6860	−	46.2215i	−1.25382	−	2.17168i
$454$	−1.18781			−0.0557468
$455$	−6.28367	−	2.17673i	−0.294583	−	0.102047i
$456$	2.76529			0.129496
$457$	12.4054	+	21.4868i	0.580301	+	1.00511i	0.995443	+	0.0953539i	$0.0303983\pi$
$457$	12.4054	+	21.4868i	0.580301	+	1.00511i	−0.415143	+	0.909756i	$0.636268\pi$
$458$	−0.413618	+	0.716408i	−0.0193271	+	0.0334755i
$459$	0.985133	−	1.70630i	0.0459821	−	0.0796433i
$460$	12.7435	+	22.0724i	0.594169	+	1.02913i
$461$	−32.4372			−1.51075			−0.755376	−	0.655292i	$-0.772546\pi$
$461$	−32.4372			−1.51075			−0.755376	+	0.655292i	$0.772546\pi$
$462$	0.167661	+	0.871194i	0.00780031	+	0.0405316i
$463$	6.66310			0.309660			0.154830	−	0.987941i	$-0.450517\pi$
$463$	6.66310			0.309660			0.154830	+	0.987941i	$0.450517\pi$
$464$	6.87454	+	11.9071i	0.319143	+	0.552771i
$465$	−17.3520	+	30.0546i	−0.804680	+	1.39375i
$466$	−0.714352	+	1.23729i	−0.0330917	+	0.0573165i
$467$	6.16830	+	10.6838i	0.285435	+	0.494388i	0.972715	−	0.232005i	$-0.0745286\pi$
$467$	6.16830	+	10.6838i	0.285435	+	0.494388i	−0.687280	+	0.726393i	$0.741195\pi$
$468$	6.57600			0.303976
$469$	−1.69420	−	8.80332i	−0.0782309	−	0.406500i
$470$	−0.619942			−0.0285958
$471$	30.1165	+	52.1633i	1.38769	+	2.40356i
$472$	−1.61757	+	2.80171i	−0.0744546	+	0.128959i
$473$	1.49702	−	2.59291i	0.0688329	−	0.119222i
$474$	0.520836	+	0.902114i	0.0239228	+	0.0414354i
$475$	−2.72843			−0.125189
$476$	−12.2338	−	4.23792i	−0.560736	−	0.194245i
$477$	−33.0493			−1.51322
$478$	−0.509583	−	0.882624i	−0.0233078	−	0.0403703i
$479$	18.7855	−	32.5374i	0.858331	−	1.48667i	−0.0151891	−	0.999885i	$-0.504835\pi$
$479$	18.7855	−	32.5374i	0.858331	−	1.48667i	0.873520	−	0.486788i	$-0.161832\pi$
$480$	−4.99707	+	8.65518i	−0.228084	+	0.395053i
$481$	−2.60553	−	4.51290i	−0.118802	−	0.205771i
$482$	−0.441810			−0.0201239
$483$	25.7159	−	22.2706i	1.17011	−	1.01335i
$484$	−1.98220			−0.0901001
$485$	−10.3191	−	17.8732i	−0.468567	−	0.811581i
$486$	1.49205	−	2.58430i	0.0676807	−	0.117226i
$487$	6.91196	−	11.9719i	0.313211	−	0.542497i	−0.665845	−	0.746090i	$-0.731929\pi$
$487$	6.91196	−	11.9719i	0.313211	−	0.542497i	0.979056	+	0.203593i	$0.0652621\pi$
$488$	0.432738	+	0.749525i	0.0195891	+	0.0339294i
$489$	44.3549			2.00580
$490$	−1.84427	−	1.45199i	−0.0833159	−	0.0655942i
$491$	−10.2413			−0.462182			−0.231091	−	0.972932i	$-0.574229\pi$
$491$	−10.2413			−0.462182			−0.231091	+	0.972932i	$0.574229\pi$
$492$	0.991101	+	1.71664i	0.0446823	+	0.0773920i
$493$	4.35888	−	7.54980i	0.196314	−	0.340026i
$494$	0.138138	−	0.239262i	0.00621513	−	0.0107649i
$495$	4.16925	+	7.22135i	0.187394	+	0.324575i
$496$	−21.3883			−0.960363
$497$	−25.1347	+	21.7673i	−1.12744	+	0.976396i
$498$	−3.08471			−0.138229
$499$	15.9996	+	27.7122i	0.716242	+	1.24057i	0.962479	+	0.271358i	$0.0874726\pi$
$499$	15.9996	+	27.7122i	0.716242	+	1.24057i	−0.246237	+	0.969210i	$0.579194\pi$
$500$	−9.17342	+	15.8888i	−0.410248	+	0.710570i
$501$	5.76230	−	9.98060i	0.257441	−	0.445900i
$502$	0.828777	+	1.43548i	0.0369901	+	0.0640688i
$503$	21.0024			0.936450			0.468225	−	0.883609i	$-0.344894\pi$
$503$	21.0024			0.936450			0.468225	+	0.883609i	$0.344894\pi$
$504$	4.40623	+	1.52636i	0.196269	+	0.0679896i
$505$	−26.5227			−1.18025
$506$	−0.341238	−	0.591041i	−0.0151699	−	0.0262750i
$507$	1.25673	−	2.17673i	0.0558135	−	0.0966719i
$508$	−8.98859	+	15.5687i	−0.398804	+	0.690749i
$509$	−4.19516	−	7.26622i	−0.185947	−	0.322070i	0.757948	−	0.652315i	$-0.226202\pi$
$509$	−4.19516	−	7.26622i	−0.185947	−	0.322070i	−0.943895	+	0.330245i	$0.892869\pi$
$510$	2.08071			0.0921352
$511$	−4.60254	−	23.9155i	−0.203604	−	1.05796i
$512$	−10.2964			−0.455043
$513$	−0.826370	−	1.43132i	−0.0364851	−	0.0631941i
$514$	−0.187338	+	0.324479i	−0.00826312	+	0.0143121i
$515$	−13.2241	+	22.9049i	−0.582724	+	1.00931i
$516$	−7.45844	−	12.9184i	−0.328339	−	0.568700i
$517$	−1.84879			−0.0813097
$518$	−0.347604	−	1.80620i	−0.0152728	−	0.0793600i
$519$	−34.0334			−1.49390
$520$	0.667661	+	1.15642i	0.0292789	+	0.0507125i
$521$	10.2441	−	17.7433i	0.448803	−	0.777349i	−0.549506	−	0.835490i	$-0.685184\pi$
$521$	10.2441	−	17.7433i	0.448803	−	0.777349i	0.998308	+	0.0581408i	$0.0185172\pi$
$522$	−0.781455	+	1.35352i	−0.0342034	+	0.0592420i
$523$	16.3600	+	28.3363i	0.715371	+	1.23906i	0.962816	+	0.270158i	$0.0870758\pi$
$523$	16.3600	+	28.3363i	0.715371	+	1.23906i	−0.247445	+	0.968902i	$0.579591\pi$
$524$	−37.5507			−1.64041
$525$	−8.27889	−	2.86789i	−0.361320	−	0.125165i
$526$	1.47518			0.0643209
$527$	6.78074	+	11.7446i	0.295374	+	0.511602i
$528$	−4.89313	+	8.47515i	−0.212946	+	0.368833i
$529$	−1.58474	+	2.74486i	−0.0689019	+	0.119342i
$530$	−1.67025	−	2.89295i	−0.0725509	−	0.125662i
$531$	20.2020			0.876691
$532$	−8.20979	+	7.10989i	−0.355940	+	0.308253i
$533$	0.397857			0.0172331
$534$	1.98101	+	3.43122i	0.0857269	+	0.148483i
$535$	−11.5788	+	20.0551i	−0.500596	+	0.867058i
$536$	−0.900073	+	1.55897i	−0.0388772	+	0.0673373i
$537$	−1.50895	−	2.61358i	−0.0651161	−	0.112784i
$538$	1.09654			0.0472751
$539$	−5.50000	−	4.33013i	−0.236902	−	0.186512i
$540$	3.97623			0.171110
$541$	−14.0130	−	24.2712i	−0.602465	−	1.04350i	−0.992447	−	0.122677i	$-0.960852\pi$
$541$	−14.0130	−	24.2712i	−0.602465	−	1.04350i	0.389982	−	0.920823i	$-0.372481\pi$
$542$	−1.62916	+	2.82178i	−0.0699783	+	0.121206i
$543$	10.3490	−	17.9250i	0.444117	−	0.769233i
$544$	1.95273	+	3.38223i	0.0837227	+	0.145012i
$545$	−22.7546			−0.974701
$546$	0.670645	−	0.580796i	0.0287010	−	0.0248558i
$547$	37.9946			1.62453			0.812267	−	0.583286i	$-0.198233\pi$
$547$	37.9946			1.62453			0.812267	+	0.583286i	$0.198233\pi$
$548$	−19.3571	−	33.5276i	−0.826896	−	1.43223i
$549$	2.70226	−	4.68045i	0.115330	−	0.199757i
$550$	−0.0878857	+	0.152222i	−0.00374746	+	0.00649079i
$551$	−3.65641	−	6.33309i	−0.155768	−	0.269799i
$552$	−6.83099			−0.290746
$553$	−7.76618	−	2.69028i	−0.330252	−	0.114403i
$554$	0.219711			0.00933461
$555$	−16.4605	−	28.5104i	−0.698708	−	1.21020i
$556$	10.2022	−	17.6706i	0.432668	−	0.749402i
$557$	3.75916	−	6.51106i	0.159281	−	0.275882i	−0.775329	−	0.631558i	$-0.782416\pi$
$557$	3.75916	−	6.51106i	0.159281	−	0.275882i	0.934610	+	0.355675i	$0.115749\pi$
$558$	−1.21564	−	2.10556i	−0.0514623	−	0.0891354i
$559$	−2.99403			−0.126634
$560$	−4.89313	−	25.4254i	−0.206772	−	1.07442i
$561$	6.20508			0.261979
$562$	−0.705295	−	1.22161i	−0.0297511	−	0.0515303i
$563$	14.1678	−	24.5394i	0.597104	−	1.03421i	−0.396143	−	0.918189i	$-0.629651\pi$
$563$	14.1678	−	24.5394i	0.597104	−	1.03421i	0.993246	−	0.116025i	$-0.0370152\pi$
$564$	−4.60553	+	7.97700i	−0.193928	+	0.335892i
$565$	−12.8728	−	22.2963i	−0.541563	−	0.938014i
$566$	−2.91445			−0.122504
$567$	3.97330	+	20.6459i	0.166863	+	0.867046i
$568$	6.67661			0.280144
$569$	−4.71343	−	8.16389i	−0.197597	−	0.342248i	0.750152	−	0.661266i	$-0.229980\pi$
$569$	−4.71343	−	8.16389i	−0.197597	−	0.342248i	−0.947749	+	0.319018i	$0.896647\pi$
$570$	0.872691	−	1.51155i	0.0365530	−	0.0633117i
$571$	6.64514	−	11.5097i	0.278091	−	0.481667i	−0.692820	−	0.721111i	$-0.743632\pi$
$571$	6.64514	−	11.5097i	0.278091	−	0.481667i	0.970910	+	0.239444i	$0.0769651\pi$
$572$	0.991101	+	1.71664i	0.0414400	+	0.0717762i
$573$	44.1969			1.84635
$574$	0.132695	+	0.0459671i	0.00553860	+	0.00191863i
$575$	6.73994			0.281075
$576$	12.5668	+	21.7663i	0.523616	+	0.906930i
$577$	3.96147	−	6.86147i	0.164918	−	0.285647i	−0.771708	−	0.635977i	$-0.780597\pi$
$577$	3.96147	−	6.86147i	0.164918	−	0.285647i	0.936626	+	0.350330i	$0.113931\pi$
$578$	−0.727444	+	1.25997i	−0.0302577	+	0.0524078i
$579$	−5.43388	−	9.41176i	−0.225824	−	0.391139i
$580$	17.5935			0.730530
$581$	18.3984	−	15.9335i	0.763296	−	0.661034i
$582$	2.75335			0.114130
$583$	−4.98101	−	8.62737i	−0.206293	−	0.357309i
$584$	−2.44518	+	4.23517i	−0.101182	+	0.175253i
$585$	4.16925	−	7.22135i	0.172377	−	0.298566i
$586$	0.336901	+	0.583530i	0.0139173	+	0.0241054i
$587$	−27.6474			−1.14113			−0.570564	−	0.821253i	$-0.693275\pi$
$587$	−27.6474			−1.14113			−0.570564	+	0.821253i	$0.693275\pi$
$588$	−32.3843	+	12.9441i	−1.33551	+	0.533807i
$589$	11.3759			0.468737
$590$	1.02097	+	1.76837i	0.0420326	+	0.0728026i
$591$	−9.46042	+	16.3859i	−0.389150	+	0.674027i
$592$	10.1447	−	17.5711i	0.416944	−	0.722168i
$593$	8.66885	+	15.0149i	0.355987	+	0.616587i	0.987286	−	0.158952i	$-0.0508114\pi$
$593$	8.66885	+	15.0149i	0.355987	+	0.616587i	−0.631299	+	0.775539i	$0.717478\pi$
$594$	−0.106473			−0.00436865
$595$	−12.4102	+	10.7475i	−0.508767	+	0.440605i
$596$	−37.7405			−1.54591
$597$	18.2754	+	31.6539i	0.747963	+	1.29551i
$598$	−0.341238	+	0.591041i	−0.0139543	+	0.0241695i
$599$	−2.03629	+	3.52695i	−0.0832005	+	0.144107i	−0.904623	−	0.426213i	$-0.859848\pi$
$599$	−2.03629	+	3.52695i	−0.0832005	+	0.144107i	0.821423	+	0.570320i	$0.193181\pi$
$600$	0.879660	+	1.52362i	0.0359120	+	0.0622014i
$601$	−3.26455			−0.133164			−0.0665819	−	0.997781i	$-0.521209\pi$
$601$	−3.26455			−0.133164			−0.0665819	+	0.997781i	$0.521209\pi$
$602$	−0.998587	−	0.345921i	−0.0406994	−	0.0140987i
$603$	11.2411			0.457773
$604$	−21.0454	−	36.4517i	−0.856326	−	1.48320i
$605$	−1.25673	+	2.17673i	−0.0510935	+	0.0884966i
$606$	1.76920	−	3.06435i	0.0718689	−	0.124481i
$607$	−13.3690	−	23.1558i	−0.542632	−	0.939866i	−0.998752	−	0.0499478i	$-0.984095\pi$
$607$	−13.3690	−	23.1558i	−0.542632	−	0.939866i	0.456120	−	0.889918i	$-0.349239\pi$
$608$	3.27607			0.132862
$609$	−4.43786	−	23.0598i	−0.179831	−	0.934431i
$610$	0.546268			0.0221177
$611$	0.924396	+	1.60110i	0.0373970	+	0.0647736i
$612$	8.11720	−	14.0594i	0.328118	−	0.568317i
$613$	−0.616620	+	1.06802i	−0.0249050	+	0.0431368i	−0.878209	−	0.478277i	$-0.841262\pi$
$613$	−0.616620	+	1.06802i	−0.0249050	+	0.0431368i	0.853304	+	0.521413i	$0.174595\pi$
$614$	2.26627	+	3.92530i	0.0914593	+	0.158412i
$615$	2.51347			0.101353
$616$	0.265633	+	1.38027i	0.0107027	+	0.0556127i
$617$	−26.3974			−1.06272			−0.531360	−	0.847146i	$-0.678319\pi$
$617$	−26.3974			−1.06272			−0.531360	+	0.847146i	$0.678319\pi$
$618$	−1.76423	−	3.05574i	−0.0709679	−	0.122920i
$619$	3.08213	−	5.33840i	0.123881	−	0.214569i	−0.797414	−	0.603433i	$-0.793799\pi$
$619$	3.08213	−	5.33840i	0.123881	−	0.214569i	0.921295	+	0.388864i	$0.127132\pi$
$620$	−13.6844	+	23.7020i	−0.549577	+	0.951895i
$621$	2.04135	+	3.53573i	0.0819167	+	0.141884i
$622$	3.56323			0.142872
$623$	−29.5389	−	10.2326i	−1.18345	−	0.409960i
$624$	9.78626			0.391764
$625$	14.9259	+	25.8524i	0.597035	+	1.03410i
$626$	−1.56277	+	2.70680i	−0.0624610	+	0.108186i
$627$	2.60254	−	4.50773i	0.103935	−	0.180022i
$628$	23.7508	+	41.1376i	0.947761	+	1.64157i
$629$	−12.8647			−0.512949
$630$	2.22488	−	1.92680i	0.0886414	−	0.0767657i
$631$	28.9135			1.15103			0.575514	−	0.817792i	$-0.304802\pi$
$631$	28.9135			1.15103			0.575514	+	0.817792i	$0.304802\pi$
$632$	0.825183	+	1.42926i	0.0328240	+	0.0568529i
$633$	31.2842	−	54.1857i	1.24343	−	2.15369i
$634$	0.474250	−	0.821425i	0.0188349	−	0.0326230i
$635$	11.3977	+	19.7414i	0.452304	+	0.783413i
$636$	−49.6328			−1.96807
$637$	−1.00000	+	6.92820i	−0.0396214	+	0.274505i
$638$	−0.471108			−0.0186513
$639$	−20.8462	−	36.1067i	−0.824664	−	1.42836i
$640$	−5.24644	+	9.08709i	−0.207384	+	0.359199i
$641$	−16.9892	+	29.4262i	−0.671033	+	1.16226i	0.306579	+	0.951845i	$0.400816\pi$
$641$	−16.9892	+	29.4262i	−0.671033	+	1.16226i	−0.977612	+	0.210418i	$0.932518\pi$
$642$	−1.54474	−	2.67556i	−0.0609658	−	0.105596i
$643$	−6.18163			−0.243780			−0.121890	−	0.992544i	$-0.538895\pi$
$643$	−6.18163			−0.243780			−0.121890	+	0.992544i	$0.538895\pi$
$644$	20.2803	−	17.5633i	0.799158	−	0.692091i
$645$	−18.9149			−0.744772
$646$	−0.341026	−	0.590675i	−0.0134175	−	0.0232398i
$647$	4.03111	−	6.98208i	0.158479	−	0.274494i	−0.775841	−	0.630928i	$-0.782674\pi$
$647$	4.03111	−	6.98208i	0.158479	−	0.274494i	0.934320	+	0.356434i	$0.116008\pi$
$648$	2.11088	−	3.65616i	0.0829234	−	0.143627i
$649$	3.04474	+	5.27364i	0.119516	+	0.207008i
$650$	0.175771			0.00689432
$651$	34.5181	+	11.9574i	1.35287	+	0.468648i
$652$	34.9797			1.36991
$653$	11.6386	+	20.1587i	0.455454	+	0.788870i	0.998714	−	0.0506946i	$-0.0161435\pi$
$653$	11.6386	+	20.1587i	0.455454	+	0.788870i	−0.543260	+	0.839565i	$0.682810\pi$
$654$	1.51785	−	2.62900i	0.0593527	−	0.102802i
$655$	−23.8075	+	41.2357i	−0.930235	+	1.61121i
$656$	0.774533	+	1.34153i	0.0302404	+	0.0523779i
$657$	30.5381			1.19140
$658$	0.123324	+	0.640810i	0.00480767	+	0.0249814i
$659$	40.7325			1.58671			0.793357	−	0.608756i	$-0.208331\pi$
$659$	40.7325			1.58671			0.793357	+	0.608756i	$0.208331\pi$
$660$	6.26130	+	10.8449i	0.243721	+	0.422137i
$661$	−8.08234	+	13.9990i	−0.314366	+	0.544499i	−0.979303	−	0.202402i	$-0.935125\pi$
$661$	−8.08234	+	13.9990i	−0.314366	+	0.544499i	0.664936	+	0.746900i	$0.268459\pi$
$662$	−0.756914	+	1.31101i	−0.0294183	+	0.0509540i
$663$	−3.10254	−	5.37376i	−0.120493	−	0.208700i
$664$	−4.88724			−0.189662
$665$	2.60254	+	13.5232i	0.100922	+	0.524407i
$666$	2.30637			0.0893700
$667$	9.03230	+	15.6444i	0.349732	+	0.605753i
$668$	4.54434	−	7.87102i	0.175826	−	0.304539i
$669$	−10.9185	+	18.9115i	−0.422135	+	0.731159i
$670$	0.568104	+	0.983985i	0.0219478	+	0.0380147i
$671$	1.62908			0.0628900
$672$	9.94058	+	3.44352i	0.383466	+	0.132837i
$673$	11.3291			0.436706			0.218353	−	0.975870i	$-0.429932\pi$
$673$	11.3291			0.436706			0.218353	+	0.975870i	$0.429932\pi$
$674$	−2.02350	−	3.50481i	−0.0779424	−	0.135000i
$675$	0.525750	−	0.910626i	0.0202361	−	0.0350500i
$676$	0.991101	−	1.71664i	0.0381193	−	0.0660245i
$677$	9.92704	+	17.1941i	0.381527	+	0.660825i	0.991281	−	0.131767i	$-0.0420649\pi$
$677$	9.92704	+	17.1941i	0.381527	+	0.660825i	−0.609754	+	0.792591i	$0.708732\pi$
$678$	3.43473			0.131910
$679$	−16.4221	+	14.2220i	−0.630222	+	0.545789i
$680$	3.29656			0.126417
$681$	11.1893	+	19.3804i	0.428774	+	0.742658i
$682$	0.366431	−	0.634678i	0.0140314	−	0.0243031i
$683$	−13.4596	+	23.3127i	−0.515018	+	0.892038i	0.484830	+	0.874608i	$0.338881\pi$
$683$	−13.4596	+	23.3127i	−0.515018	+	0.892038i	−0.999848	+	0.0174292i	$0.994452\pi$
$684$	−6.80904	−	11.7936i	−0.260350	−	0.450940i
$685$	−49.0904			−1.87565
$686$	−1.13399	+	2.19520i	−0.0432959	+	0.0838131i
$687$	15.5852			0.594614
$688$	−5.82867	−	10.0956i	−0.222216	−	0.384889i
$689$	−4.98101	+	8.62737i	−0.189762	+	0.328677i
$690$	−2.15578	+	3.73392i	−0.0820691	+	0.142148i
$691$	−16.0137	−	27.7366i	−0.609190	−	1.05515i	−0.991374	−	0.131062i	$-0.958161\pi$
$691$	−16.0137	−	27.7366i	−0.609190	−	1.05515i	0.382184	−	0.924086i	$-0.375172\pi$
$692$	−26.8398			−1.02030
$693$	6.63505	−	5.74612i	0.252045	−	0.218277i
$694$	0.936880			0.0355635
$695$	−12.9365	−	22.4067i	−0.490710	−	0.849935i
$696$	−2.35769	+	4.08364i	−0.0893680	+	0.154790i
$697$	0.491101	−	0.850612i	0.0186018	−	0.0322192i
$698$	−2.35256	−	4.07476i	−0.0890459	−	0.154232i
$699$	26.9170			1.01809
$700$	−6.52900	−	2.26171i	−0.246773	−	0.0854846i
$701$	28.3723			1.07161			0.535804	−	0.844343i	$-0.320009\pi$
$701$	28.3723			1.07161			0.535804	+	0.844343i	$0.320009\pi$
$702$	0.0532366	+	0.0922085i	0.00200929	+	0.00348018i
$703$	−5.39572	+	9.34566i	−0.203504	+	0.352478i
$704$	−3.78800	+	6.56101i	−0.142766	+	0.247277i
$705$	5.83989	+	10.1150i	0.219943	+	0.380953i
$706$	−0.423470			−0.0159375
$707$	5.27612	+	27.4155i	0.198429	+	1.03107i
$708$	30.3390			1.14021
$709$	−20.1983	−	34.9844i	−0.758562	−	1.31387i	−0.943584	−	0.331134i	$-0.892569\pi$
$709$	−20.1983	−	34.9844i	−0.758562	−	1.31387i	0.185022	−	0.982734i	$-0.440764\pi$
$710$	2.10706	−	3.64953i	0.0790765	−	0.136964i
$711$	5.15290	−	8.92509i	0.193249	−	0.334717i
$712$	3.13861	+	5.43623i	0.117624	+	0.203731i
$713$	−28.1016			−1.05241
$714$	−0.413911	−	2.15075i	−0.0154902	−	0.0804896i
$715$	2.51347			0.0939984
$716$	−1.19001	−	2.06115i	−0.0444727	−	0.0770290i
$717$	−9.60061	+	16.6287i	−0.358541	+	0.621012i
$718$	−1.13291	+	1.96225i	−0.0422797	+	0.0732306i
$719$	4.15871	+	7.20310i	0.155094	+	0.268630i	0.933093	−	0.359635i	$-0.117099\pi$
$719$	4.15871	+	7.20310i	0.155094	+	0.268630i	−0.777999	+	0.628265i	$0.783765\pi$
$720$	32.4661			1.20994
$721$	26.3065	+	9.11285i	0.979706	+	0.339380i
$722$	1.96266			0.0730427
$723$	4.16188	+	7.20859i	0.154782	+	0.268090i
$724$	8.16153	−	14.1362i	0.303321	−	0.525367i
$725$	2.32627	−	4.02921i	0.0863953	−	0.149641i
$726$	−0.167661	−	0.290398i	−0.00622250	−	0.0107777i
$727$	49.7655			1.84570			0.922849	−	0.385161i	$-0.125854\pi$
$727$	49.7655			1.84570			0.922849	+	0.385161i	$0.125854\pi$
$728$	1.06253	−	0.920181i	0.0393801	−	0.0341042i
$729$	−32.3810			−1.19929
$730$	1.54334	+	2.67314i	0.0571215	+	0.0989373i
$731$	−3.69573	+	6.40120i	−0.136692	+	0.236757i
$732$	4.05820	−	7.02902i	0.149996	−	0.259800i
$733$	21.7516	+	37.6749i	0.803414	+	1.39155i	0.917356	+	0.398067i	$0.130319\pi$
$733$	21.7516	+	37.6749i	0.803414	+	1.39155i	−0.113942	+	0.993487i	$0.536348\pi$
$734$	−2.86169			−0.105627
$735$	−6.31752	+	43.7691i	−0.233025	+	1.61445i
$736$	−8.09275			−0.298303
$737$	1.69420	+	2.93444i	0.0624067	+	0.108092i
$738$	−0.0880441	+	0.152497i	−0.00324095	+	0.00561349i
$739$	10.9230	−	18.9192i	0.401809	−	0.695953i	−0.592135	−	0.805839i	$-0.701715\pi$
$739$	10.9230	−	18.9192i	0.401809	−	0.695953i	0.993944	+	0.109885i	$0.0350483\pi$
$740$	−12.9813	−	22.4842i	−0.477200	−	0.826535i
$741$	−5.20508			−0.191214
$742$	−2.65808	+	2.30196i	−0.0975810	+	0.0845076i
$743$	−46.9852			−1.72372			−0.861859	−	0.507148i	$-0.830700\pi$
$743$	−46.9852			−1.72372			−0.861859	+	0.507148i	$0.830700\pi$
$744$	−3.66766	−	6.35258i	−0.134463	−	0.232897i
$745$	−23.9278	+	41.4442i	−0.876647	+	1.51840i
$746$	−1.16294	+	2.01427i	−0.0425783	+	0.0737477i
$747$	15.2593	+	26.4299i	0.558309	+	0.967020i
$748$	4.89353			0.178925
$749$	23.0336	+	7.97906i	0.841628	+	0.291549i
$750$	−3.10368			−0.113330
$751$	1.30654	+	2.26299i	0.0476762	+	0.0825775i	0.888879	−	0.458143i	$-0.151485\pi$
$751$	1.30654	+	2.26299i	0.0476762	+	0.0825775i	−0.841203	+	0.540720i	$0.818152\pi$
$752$	−3.59916	+	6.23393i	−0.131248	+	0.227328i
$753$	15.6143	−	27.0447i	0.569015	−	0.985564i
$754$	0.235554	+	0.407991i	0.00857836	+	0.0148582i
$755$	−53.3720			−1.94241
$756$	−0.790985	−	4.11008i	−0.0287679	−	0.149482i
$757$	−36.0352			−1.30972			−0.654860	−	0.755750i	$-0.727273\pi$
$757$	−36.0352			−1.30972			−0.654860	+	0.755750i	$0.727273\pi$
$758$	0.0547698	+	0.0948640i	0.00198933	+	0.00344562i
$759$	−6.42897	+	11.1353i	−0.233357	+	0.404186i
$760$	1.38264	−	2.39481i	0.0501538	−	0.0868689i
$761$	3.84547	+	6.66055i	0.139398	+	0.241445i	0.927269	−	0.374396i	$-0.122150\pi$
$761$	3.84547	+	6.66055i	0.139398	+	0.241445i	−0.787871	+	0.615841i	$0.788817\pi$
$762$	−3.04114			−0.110169
$763$	4.52654	+	23.5206i	0.163872	+	0.851502i
$764$	34.8551			1.26101
$765$	−10.2928	−	17.8276i	−0.372135	−	0.644557i
$766$	−2.40280	+	4.16176i	−0.0868165	+	0.150371i
$767$	3.04474	−	5.27364i	0.109939	−	0.190420i
$768$	18.3421	+	31.7695i	0.661864	+	1.14638i
$769$	−29.9181			−1.07888			−0.539438	−	0.842026i	$-0.681363\pi$
$769$	−29.9181			−1.07888			−0.539438	+	0.842026i	$0.681363\pi$
$770$	0.838307	+	0.290398i	0.0302105	+	0.0104652i
$771$	7.05894			0.254222
$772$	−4.28533	−	7.42241i	−0.154232	−	0.267138i
$773$	12.8797	−	22.3083i	0.463250	−	0.802373i	−0.535870	−	0.844300i	$-0.680016\pi$
$773$	12.8797	−	22.3083i	0.463250	−	0.802373i	0.999121	+	0.0419273i	$0.0133498\pi$
$774$	0.662567	−	1.14760i	0.0238155	−	0.0412496i
$775$	3.61878	+	6.26790i	0.129990	+	0.225150i
$776$	4.36226			0.156596
$777$	−26.1956	+	22.6861i	−0.939763	+	0.813859i
$778$	1.99751			0.0716140
$779$	−0.411956	−	0.713529i	−0.0147599	−	0.0255648i
$780$	6.26130	−	10.8449i	0.224191	−	0.388310i
$781$	6.28367	−	10.8836i	0.224847	−	0.389447i
$782$	0.842425	+	1.45912i	0.0301251	+	0.0521781i
$783$	2.81826			0.100716
$784$	−25.3079	+	10.1157i	−0.903854	+	0.361274i
$785$	60.2330			2.14981
$786$	−3.17616	−	5.50127i	−0.113290	−	0.196224i
$787$	−3.82920	+	6.63236i	−0.136496	+	0.236418i	−0.926168	−	0.377111i	$-0.876917\pi$
$787$	−3.82920	+	6.63236i	−0.136496	+	0.236418i	0.789672	+	0.613529i	$0.210251\pi$
$788$	−7.46079	+	12.9225i	−0.265780	+	0.460344i
$789$	−13.8963	−	24.0691i	−0.494721	−	0.856883i
$790$	1.04167			0.0370610
$791$	−20.4861	+	17.7415i	−0.728402	+	0.630815i
$792$	−1.76249			−0.0626274
$793$	−0.814540	−	1.41083i	−0.0289252	−	0.0500999i
$794$	−0.0301399	+	0.0522038i	−0.00106962	+	0.00185264i
$795$	−31.4677	+	54.5036i	−1.11604	+	1.93304i
$796$	14.4126	+	24.9633i	0.510840	+	0.884801i
$797$	20.5158			0.726708			0.363354	−	0.931651i	$-0.381631\pi$
$797$	20.5158			0.726708			0.363354	+	0.931651i	$0.381631\pi$
$798$	−1.73603	−	0.601378i	−0.0614548	−	0.0212886i
$799$	4.56417			0.161469
$800$	1.04214	+	1.80504i	0.0368453	+	0.0638179i
$801$	19.5992	−	33.9468i	0.692504	−	1.19945i
$802$	−0.990942	+	1.71636i	−0.0349914	+	0.0606069i
$803$	4.60254	+	7.97184i	0.162420	+	0.281320i
$804$	16.8817			0.595372
$805$	−6.42897	−	33.4059i	−0.226591	−	1.17740i
$806$	−0.732863			−0.0258140
$807$	−10.3295	−	17.8912i	−0.363614	−	0.629798i
$808$	2.80303	−	4.85499i	0.0986101	−	0.170798i
$809$	10.3227	−	17.8794i	0.362925	−	0.628605i	−0.625516	−	0.780211i	$-0.715111\pi$
$809$	10.3227	−	17.8794i	0.362925	−	0.628605i	0.988441	+	0.151607i	$0.0484448\pi$
$810$	−1.33234	−	2.30768i	−0.0468136	−	0.0810835i
$811$	−28.9757			−1.01747			−0.508737	−	0.860922i	$-0.669888\pi$
$811$	−28.9757			−1.01747			−0.508737	+	0.860922i	$0.669888\pi$
$812$	−3.49984	−	18.1857i	−0.122820	−	0.638193i
$813$	61.3871			2.15294
$814$	0.347604	+	0.602068i	0.0121835	+	0.0211025i
$815$	22.1774	−	38.4124i	0.776842	−	1.34553i
$816$	12.0798	−	20.9229i	0.422879	−	0.732447i
$817$	3.10014	+	5.36959i	0.108460	+	0.187858i
$818$	−0.456000			−0.0159437
$819$	−8.29381	−	2.87306i	−0.289809	−	0.100393i
$820$	1.98220			0.0692215
$821$	−15.6403	−	27.0897i	−0.545849	−	0.945438i	−0.998553	−	0.0537770i	$-0.982874\pi$
$821$	−15.6403	−	27.0897i	−0.545849	−	0.945438i	0.452704	−	0.891661i	$-0.350459\pi$
$822$	3.27459	−	5.67175i	0.114214	−	0.197825i
$823$	−19.4991	+	33.7733i	−0.679694	+	1.17726i	0.295379	+	0.955380i	$0.404554\pi$
$823$	−19.4991	+	33.7733i	−0.679694	+	1.17726i	−0.975073	+	0.221885i	$0.928779\pi$
$824$	−2.79516	−	4.84135i	−0.0973739	−	0.168657i
$825$	3.31156			0.115294
$826$	1.62480	−	1.40712i	0.0565339	−	0.0489598i
$827$	−40.6886			−1.41488			−0.707441	−	0.706772i	$-0.750150\pi$
$827$	−40.6886			−1.41488			−0.707441	+	0.706772i	$0.750150\pi$
$828$	16.8201	+	29.1333i	0.584540	+	1.01245i
$829$	4.83527	−	8.37493i	0.167936	−	0.290873i	−0.769758	−	0.638336i	$-0.779623\pi$
$829$	4.83527	−	8.37493i	0.167936	−	0.290873i	0.937694	+	0.347462i	$0.112957\pi$
$830$	−1.54235	+	2.67144i	−0.0535359	+	0.0927269i
$831$	−2.06969	−	3.58481i	−0.0717967	−	0.124356i
$832$	7.57600			0.262651
$833$	13.5780	+	10.6899i	0.470451	+	0.370384i
$834$	3.45173			0.119524
$835$	−5.76230	−	9.98060i	−0.199413	−	0.345393i
$836$	2.05245	−	3.55494i	0.0709854	−	0.122950i
$837$	−2.19207	+	3.79677i	−0.0757689	+	0.131236i
$838$	−1.13856	−	1.97204i	−0.0393308	−	0.0681230i
$839$	34.9304			1.20593			0.602966	−	0.797767i	$-0.293985\pi$
$839$	34.9304			1.20593			0.602966	+	0.797767i	$0.293985\pi$
$840$	6.71258	−	5.81327i	0.231606	−	0.200577i
$841$	−16.5302			−0.570005
$842$	0.845050	+	1.46367i	0.0291223	+	0.0504414i
$843$	−13.2878	+	23.0152i	−0.457658	+	0.792686i
$844$	24.6717	−	42.7326i	0.849234	−	1.47092i
$845$	−1.25673	−	2.17673i	−0.0432330	−	0.0748817i
$846$	−0.818260			−0.0281324
$847$	2.50000	+	0.866025i	0.0859010	+	0.0297570i
$848$	−38.7874			−1.33197
$849$	27.4543	+	47.5523i	0.942231	+	1.63199i
$850$	0.216966	−	0.375797i	0.00744188	−	0.0128897i
$851$	13.3289	−	23.0863i	0.456907	−	0.791387i
$852$	−31.3065	−	54.2245i	−1.07254	−	1.85770i
$853$	3.33051			0.114034			0.0570172	−	0.998373i	$-0.481841\pi$
$853$	3.33051			0.114034			0.0570172	+	0.998373i	$0.481841\pi$
$854$	−0.108668	−	0.564656i	−0.00371855	−	0.0193221i
$855$	−17.2680			−0.590553
$856$	−2.44739	−	4.23901i	−0.0836502	−	0.144886i
$857$	−9.18092	+	15.9018i	−0.313614	+	0.543196i	−0.979142	−	0.203177i	$-0.934873\pi$
$857$	−9.18092	+	15.9018i	−0.313614	+	0.543196i	0.665528	+	0.746373i	$0.268207\pi$
$858$	−0.167661	+	0.290398i	−0.00572386	+	0.00991402i
$859$	25.9219	+	44.8980i	0.884444	+	1.53190i	0.846350	+	0.532627i	$0.178795\pi$
$859$	25.9219	+	44.8980i	0.884444	+	1.53190i	0.0380934	+	0.999274i	$0.487872\pi$
$860$	−14.9169			−0.508661
$861$	−0.500000	−	2.59808i	−0.0170400	−	0.0885422i
$862$	−3.90777			−0.133099
$863$	17.4680	+	30.2554i	0.594617	+	1.02991i	0.993601	+	0.112948i	$0.0360295\pi$
$863$	17.4680	+	30.2554i	0.594617	+	1.02991i	−0.398984	+	0.916958i	$0.630637\pi$
$864$	−0.631276	+	1.09340i	−0.0214764	+	0.0371983i
$865$	−17.0167	+	29.4738i	−0.578585	+	1.00214i
$866$	−1.61567	−	2.79841i	−0.0549025	−	0.0950940i
$867$	27.4103			0.930902
$868$	27.2221	+	9.42999i	0.923977	+	0.320075i
$869$	3.10647			0.105380
$870$	1.48812	+	2.57749i	0.0504519	+	0.0873852i
$871$	1.69420	−	2.93444i	0.0574058	−	0.0994297i
$872$	2.40480	−	4.16524i	0.0814368	−	0.141053i
$873$	−13.6202	−	23.5908i	−0.460973	−	0.798429i
$874$	1.41332			0.0478064
$875$	18.5116	−	16.0315i	0.625805	−	0.541963i
$876$	45.8616			1.54952
$877$	−21.0595	−	36.4761i	−0.711129	−	1.23171i	−0.964434	−	0.264325i	$-0.914851\pi$
$877$	−21.0595	−	36.4761i	−0.711129	−	1.23171i	0.253305	−	0.967387i	$-0.418482\pi$
$878$	1.40628	−	2.43574i	0.0474595	−	0.0822023i
$879$	6.34726	−	10.9938i	0.214088	−	0.370811i
$880$	4.89313	+	8.47515i	0.164947	+	0.285697i
$881$	−16.1207			−0.543119			−0.271560	−	0.962422i	$-0.587539\pi$
$881$	−16.1207			−0.543119			−0.271560	+	0.962422i	$0.587539\pi$
$882$	−2.43426	−	1.91648i	−0.0819657	−	0.0645312i
$883$	15.2029			0.511617			0.255809	−	0.966727i	$-0.417658\pi$
$883$	15.2029			0.511617			0.255809	+	0.966727i	$0.417658\pi$
$884$	−2.44676	−	4.23792i	−0.0822936	−	0.142537i
$885$	19.2352	−	33.3163i	0.646584	−	1.11992i
$886$	−2.62594	+	4.54826i	−0.0882201	+	0.152802i
$887$	9.00542	+	15.5978i	0.302372	+	0.523724i	0.976673	−	0.214733i	$-0.0688881\pi$
$887$	9.00542	+	15.5978i	0.302372	+	0.523724i	−0.674300	+	0.738457i	$0.735555\pi$
$888$	6.95844			0.233510
$889$	18.1386	−	15.7085i	0.608349	−	0.526846i
$890$	3.96203			0.132808
$891$	−3.97330	−	6.88196i	−0.133111	−	0.230554i
$892$	−8.61070	+	14.9142i	−0.288308	+	0.499364i
$893$	1.91431	−	3.31568i	0.0640599	−	0.110955i
$894$	−3.19222	−	5.52908i	−0.106764	−	0.184920i
$895$	−3.01790			−0.100877
$896$	10.4366	+	3.61536i	0.348664	+	0.120781i
$897$	12.8579			0.429314
$898$	−0.604053	−	1.04625i	−0.0201575	−	0.0349138i
$899$	−9.69915	+	16.7994i	−0.323485	+	0.560292i
$900$	4.33202	−	7.50328i	0.144401	−	0.250109i
$901$	12.2968	+	21.2987i	0.409666	+	0.709562i
$902$	−0.0530782			−0.00176731
$903$	3.76270	+	19.5516i	0.125215	+	0.650636i
$904$	5.44180			0.180991
$905$	−10.3490	−	17.9250i	−0.344012	−	0.595846i
$906$	3.56019	−	6.16643i	0.118279	−	0.204866i
$907$	10.2356	−	17.7285i	0.339866	−	0.588665i	−0.644541	−	0.764570i	$-0.722952\pi$
$907$	10.2356	−	17.7285i	0.339866	−	0.588665i	0.984407	+	0.175904i	$0.0562849\pi$
$908$	8.82421	+	15.2840i	0.292842	+	0.507217i
$909$	−35.0073			−1.16112
$910$	−0.167661	−	0.871194i	−0.00555792	−	0.0288798i
$911$	−44.4704			−1.47337			−0.736685	−	0.676237i	$-0.763610\pi$
$911$	−44.4704			−1.47337			−0.736685	+	0.676237i	$0.763610\pi$
$912$	−10.1331	−	17.5510i	−0.335539	−	0.581171i
$913$	−4.59961	+	7.96676i	−0.152225	+	0.263661i
$914$	−1.65501	+	2.86656i	−0.0547429	+	0.0948174i
$915$	−5.14588	−	8.91292i	−0.170117	−	0.294652i
$916$	12.2910			0.406107
$917$	47.3598	+	16.4059i	1.56396	+	0.541771i
$918$	0.262854			0.00867547
$919$	−14.3624	−	24.8765i	−0.473773	−	0.820599i	0.525776	−	0.850623i	$-0.323775\pi$
$919$	−14.3624	−	24.8765i	−0.473773	−	0.820599i	−0.999549	+	0.0300239i	$0.990442\pi$
$920$	−3.41550	+	5.91581i	−0.112606	+	0.195039i
$921$	42.6968	−	73.9531i	1.40691	−	2.43684i
$922$	−2.16373	−	3.74769i	−0.0712586	−	0.123424i
$923$	−12.5673			−0.413659
$924$	9.96440	−	8.62943i	0.327805	−	0.283887i
$925$	−6.86569			−0.225742
$926$	0.444463	+	0.769833i	0.0146060	+	0.0252983i
$927$	−17.4545	+	30.2321i	−0.573281	+	0.992952i
$928$	−2.79318	+	4.83793i	−0.0916906	+	0.158813i
$929$	−1.95944	−	3.39385i	−0.0642872	−	0.111349i	0.832090	−	0.554640i	$-0.187144\pi$
$929$	−1.95944	−	3.39385i	−0.0642872	−	0.111349i	−0.896378	+	0.443291i	$0.853811\pi$
$930$	−4.62988			−0.151820
$931$	13.4607	−	5.38029i	0.441157	−	0.176332i
$932$	21.2276			0.695333
$933$	−33.5658	−	58.1377i	−1.09890	−	1.90334i
$934$	−0.822915	+	1.42533i	−0.0269266	+	0.0466382i
$935$	3.10254	−	5.37376i	0.101464	−	0.175741i
$936$	0.881245	+	1.52636i	0.0288044	+	0.0498907i
$937$	23.9106			0.781125			0.390562	−	0.920576i	$-0.372281\pi$
$937$	23.9106			0.781125			0.390562	+	0.920576i	$0.372281\pi$
$938$	0.904096	−	0.782970i	0.0295198	−	0.0255649i
$939$	58.8857			1.92166
$940$	4.60553	+	7.97700i	0.150216	+	0.260181i
$941$	12.7785	−	22.1330i	0.416567	−	0.721515i	−0.579025	−	0.815310i	$-0.696566\pi$
$941$	12.7785	−	22.1330i	0.416567	−	0.721515i	0.995592	+	0.0937950i	$0.0298998\pi$
$942$	−4.01785	+	6.95912i	−0.130909	+	0.226740i
$943$	1.01764	+	1.76260i	0.0331389	+	0.0573983i
$944$	23.7095			0.771679
$945$	−5.01492	−	1.73722i	−0.163135	−	0.0565118i
$946$	0.399435			0.0129867
$947$	−1.72949	−	2.99556i	−0.0562008	−	0.0973426i	0.836556	−	0.547881i	$-0.184565\pi$
$947$	−1.72949	−	2.99556i	−0.0562008	−	0.0973426i	−0.892757	+	0.450538i	$0.851232\pi$
$948$	7.73854	−	13.4035i	0.251336	−	0.435327i
$949$	4.60254	−	7.97184i	0.149405	−	0.258777i
$950$	−0.182000	−	0.315234i	−0.00590487	−	0.0102275i
$951$	−17.8699			−0.579470
$952$	−0.655778	−	3.40752i	−0.0212539	−	0.110438i
$953$	10.1258			0.328006			0.164003	−	0.986460i	$-0.447559\pi$
$953$	10.1258			0.328006			0.164003	+	0.986460i	$0.447559\pi$
$954$	−2.20456	−	3.81841i	−0.0713752	−	0.123625i
$955$	22.0985	−	38.2756i	0.715089	−	1.23857i
$956$	−7.57135	+	13.1140i	−0.244875	+	0.424136i
$957$	4.43786	+	7.68661i	0.143456	+	0.248473i
$958$	5.01236			0.161942
$959$	9.76548	+	50.7429i	0.315344	+	1.63857i
$960$	47.8616			1.54473
$961$	0.411851	+	0.713346i	0.0132855	+	0.0230112i
$962$	0.347604	−	0.602068i	0.0112072	−	0.0194114i
$963$	−15.2829	+	26.4707i	−0.492484	+	0.853007i
$964$	3.28219	+	5.68492i	0.105712	+	0.183099i
$965$	−10.8678			−0.349846
$966$	4.28845	+	1.48556i	0.137979	+	0.0477972i
$967$	−4.60855			−0.148201			−0.0741005	−	0.997251i	$-0.523609\pi$
$967$	−4.60855			−0.148201			−0.0741005	+	0.997251i	$0.523609\pi$
$968$	−0.265633	−	0.460091i	−0.00853778	−	0.0147879i
$969$	−6.42498	+	11.1284i	−0.206400	+	0.357495i
$970$	1.37668	−	2.38447i	0.0442024	−	0.0765608i
$971$	−28.6176	−	49.5671i	−0.918381	−	1.59068i	−0.801875	−	0.597492i	$-0.796164\pi$
$971$	−28.6176	−	49.5671i	−0.918381	−	1.59068i	−0.116506	−	0.993190i	$-0.537170\pi$
$972$	−44.3375			−1.42213
$973$	−20.5875	+	17.8293i	−0.660005	+	0.571581i
$974$	1.84425			0.0590937
$975$	−1.65578	−	2.86789i	−0.0530273	−	0.0918460i
$976$	3.17143	−	5.49309i	0.101515	−	0.175829i
$977$	−8.47611	+	14.6810i	−0.271175	+	0.469688i	−0.969163	−	0.246421i	$-0.920745\pi$
$977$	−8.47611	+	14.6810i	−0.271175	+	0.469688i	0.697988	+	0.716109i	$0.254079\pi$
$978$	2.95870	+	5.12462i	0.0946088	+	0.163867i
$979$	11.8156			0.377627
$980$	−4.98220	+	34.5177i	−0.159151	+	1.10263i
$981$	−30.0338			−0.958906
$982$	−0.683145	−	1.18324i	−0.0218000	−	0.0377588i
$983$	−10.5716	+	18.3106i	−0.337182	+	0.584017i	−0.983902	−	0.178711i	$-0.942807\pi$
$983$	−10.5716	+	18.3106i	−0.337182	+	0.584017i	0.646719	+	0.762728i	$0.276141\pi$
$984$	−0.265633	+	0.460091i	−0.00846809	+	0.0146672i
$985$	9.46042	+	16.3859i	0.301434	+	0.522099i
$986$	1.16304			0.0370387
$987$	9.29376	−	8.04863i	0.295824	−	0.256191i
$988$	−4.10489			−0.130594
$989$	−7.65815	−	13.2643i	−0.243515	−	0.421780i
$990$	−0.556221	+	0.963402i	−0.0176779	+	0.0306189i
$991$	−5.40599	+	9.36345i	−0.171727	+	0.297440i	−0.939024	−	0.343852i	$-0.888268\pi$
$991$	−5.40599	+	9.36345i	−0.171727	+	0.297440i	0.767297	+	0.641292i	$0.221601\pi$
$992$	−4.34512	−	7.52596i	−0.137958	−	0.238950i
$993$	28.5207			0.905077
$994$	−4.19153	−	1.45199i	−0.132947	−	0.0460543i
$995$	36.5508			1.15874
$996$	22.9162	+	39.6920i	0.726127	+	1.25769i
$997$	−8.30920	+	14.3920i	−0.263155	+	0.455798i	−0.967079	−	0.254478i	$-0.918096\pi$
$997$	−8.30920	+	14.3920i	−0.263155	+	0.455798i	0.703924	+	0.710276i	$0.251430\pi$
$998$	−2.13452	+	3.69709i	−0.0675669	+	0.117029i
$999$	−2.07944	−	3.60169i	−0.0657905	−	0.113952i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.a.144.3	✓	8
7.2	even	3	inner	1001.2.i.a.716.3	yes	8
7.3	odd	6		7007.2.a.l.1.2		4
7.4	even	3		7007.2.a.m.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.a.144.3	✓	8	1.1	even	1	trivial
1001.2.i.a.716.3	yes	8	7.2	even	3	inner
7007.2.a.l.1.2		4	7.3	odd	6
7007.2.a.m.1.2		4	7.4	even	3

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:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0667052 + 0.115537i) q^{2} +(1.25673 - 2.17673i) q^{3} +(0.991101 - 1.71664i) q^{4} +(-1.25673 - 2.17673i) q^{5} +0.335323 q^{6} +(-2.00000 + 1.73205i) q^{7} +0.531267 q^{8} +(-1.65876 - 2.87306i) q^{9} +O(q^{10})\)	\(q+(0.0667052 + 0.115537i) q^{2} +(1.25673 - 2.17673i) q^{3} +(0.991101 - 1.71664i) q^{4} +(-1.25673 - 2.17673i) q^{5} +0.335323 q^{6} +(-2.00000 + 1.73205i) q^{7} +0.531267 q^{8} +(-1.65876 - 2.87306i) q^{9} +(0.167661 - 0.290398i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-2.49110 - 4.31471i) q^{12} -1.00000 q^{13} +(-0.333526 - 0.115537i) q^{14} -6.31752 q^{15} +(-1.94676 - 3.37189i) q^{16} +(-1.23437 + 2.13799i) q^{17} +(0.221296 - 0.383296i) q^{18} +(1.03544 + 1.79343i) q^{19} -4.98220 q^{20} +(1.25673 + 6.53018i) q^{21} +0.133410 q^{22} +(-2.55781 - 4.43025i) q^{23} +(0.667661 - 1.15642i) q^{24} +(-0.658762 + 1.14101i) q^{25} +(-0.0667052 - 0.115537i) q^{26} -0.798088 q^{27} +(0.991101 + 5.14991i) q^{28} -3.53127 q^{29} +(-0.421412 - 0.729906i) q^{30} +(2.74665 - 4.75733i) q^{31} +(0.790985 - 1.37003i) q^{32} +(-1.25673 - 2.17673i) q^{33} -0.329355 q^{34} +(6.28367 + 2.17673i) q^{35} -6.57600 q^{36} +(2.60553 + 4.51290i) q^{37} +(-0.138138 + 0.239262i) q^{38} +(-1.25673 + 2.17673i) q^{39} +(-0.667661 - 1.15642i) q^{40} -0.397857 q^{41} +(-0.670645 + 0.580796i) q^{42} +2.99403 q^{43} +(-0.991101 - 1.71664i) q^{44} +(-4.16925 + 7.22135i) q^{45} +(0.341238 - 0.591041i) q^{46} +(-0.924396 - 1.60110i) q^{47} -9.78626 q^{48} +(1.00000 - 6.92820i) q^{49} -0.175771 q^{50} +(3.10254 + 5.37376i) q^{51} +(-0.991101 + 1.71664i) q^{52} +(4.98101 - 8.62737i) q^{53} +(-0.0532366 - 0.0922085i) q^{54} -2.51347 q^{55} +(-1.06253 + 0.920181i) q^{56} +5.20508 q^{57} +(-0.235554 - 0.407991i) q^{58} +(-3.04474 + 5.27364i) q^{59} +(-6.26130 + 10.8449i) q^{60} +(0.814540 + 1.41083i) q^{61} +0.732863 q^{62} +(8.29381 + 2.87306i) q^{63} -7.57600 q^{64} +(1.25673 + 2.17673i) q^{65} +(0.167661 - 0.290398i) q^{66} +(-1.69420 + 2.93444i) q^{67} +(2.44676 + 4.23792i) q^{68} -12.8579 q^{69} +(0.167661 + 0.871194i) q^{70} +12.5673 q^{71} +(-0.881245 - 1.52636i) q^{72} +(-4.60254 + 7.97184i) q^{73} +(-0.347604 + 0.602068i) q^{74} +(1.65578 + 2.86789i) q^{75} +4.10489 q^{76} +(0.500000 + 2.59808i) q^{77} -0.335323 q^{78} +(1.55324 + 2.69028i) q^{79} +(-4.89313 + 8.47515i) q^{80} +(3.97330 - 6.88196i) q^{81} +(-0.0265391 - 0.0459671i) q^{82} -9.19922 q^{83} +(12.4555 + 4.31471i) q^{84} +6.20508 q^{85} +(0.199717 + 0.345921i) q^{86} +(-4.43786 + 7.68661i) q^{87} +(0.265633 - 0.460091i) q^{88} +(5.90778 + 10.2326i) q^{89} -1.11244 q^{90} +(2.00000 - 1.73205i) q^{91} -10.1402 q^{92} +(-6.90361 - 11.9574i) q^{93} +(0.123324 - 0.213603i) q^{94} +(2.60254 - 4.50773i) q^{95} +(-1.98812 - 3.44352i) q^{96} +8.21105 q^{97} +(0.867167 - 0.346610i) q^{98} -3.31752 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9	\( 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} + 4 q^{11} - 8 q^{12} - 8 q^{13} + 10 q^{14} - 30 q^{15} + 4 q^{16} - 9 q^{17} - 5 q^{18} + 4 q^{19} - 16 q^{20} - q^{21} - 4 q^{22} - 6 q^{23} + 7 q^{24} + 5 q^{25} + 2 q^{26} + 2 q^{27} - 4 q^{28} - 30 q^{29} + 11 q^{30} + 10 q^{31} + 2 q^{32} + q^{33} + 4 q^{34} - 5 q^{35} - 34 q^{36} - 9 q^{37} - 14 q^{38} + q^{39} - 7 q^{40} - 10 q^{41} - 12 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} + 13 q^{46} + 2 q^{47} - 56 q^{48} + 8 q^{49} + 2 q^{50} - 10 q^{51} + 4 q^{52} + 27 q^{53} - 20 q^{54} + 2 q^{55} - 12 q^{56} - 28 q^{57} + 10 q^{58} - 4 q^{59} - 5 q^{60} - 19 q^{61} - 88 q^{62} + 15 q^{63} - 42 q^{64} - q^{65} + 3 q^{66} + q^{67} - 16 q^{69} + 3 q^{70} - 10 q^{71} + 21 q^{72} - 2 q^{73} + 5 q^{74} - 2 q^{75} + 38 q^{76} + 4 q^{77} - 6 q^{78} + 32 q^{79} - 28 q^{80} - 4 q^{81} + 16 q^{82} + 40 q^{84} - 20 q^{85} + 22 q^{86} - 4 q^{87} + 3 q^{88} + 3 q^{89} - 58 q^{90} + 16 q^{91} - 30 q^{92} - 17 q^{93} - 5 q^{94} - 14 q^{95} + q^{96} + 6 q^{97} - 26 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9 + 3 * q^10 + 4 * q^11 - 8 * q^12 - 8 * q^13 + 10 * q^14 - 30 * q^15 + 4 * q^16 - 9 * q^17 - 5 * q^18 + 4 * q^19 - 16 * q^20 - q^21 - 4 * q^22 - 6 * q^23 + 7 * q^24 + 5 * q^25 + 2 * q^26 + 2 * q^27 - 4 * q^28 - 30 * q^29 + 11 * q^30 + 10 * q^31 + 2 * q^32 + q^33 + 4 * q^34 - 5 * q^35 - 34 * q^36 - 9 * q^37 - 14 * q^38 + q^39 - 7 * q^40 - 10 * q^41 - 12 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 + 13 * q^46 + 2 * q^47 - 56 * q^48 + 8 * q^49 + 2 * q^50 - 10 * q^51 + 4 * q^52 + 27 * q^53 - 20 * q^54 + 2 * q^55 - 12 * q^56 - 28 * q^57 + 10 * q^58 - 4 * q^59 - 5 * q^60 - 19 * q^61 - 88 * q^62 + 15 * q^63 - 42 * q^64 - q^65 + 3 * q^66 + q^67 - 16 * q^69 + 3 * q^70 - 10 * q^71 + 21 * q^72 - 2 * q^73 + 5 * q^74 - 2 * q^75 + 38 * q^76 + 4 * q^77 - 6 * q^78 + 32 * q^79 - 28 * q^80 - 4 * q^81 + 16 * q^82 + 40 * q^84 - 20 * q^85 + 22 * q^86 - 4 * q^87 + 3 * q^88 + 3 * q^89 - 58 * q^90 + 16 * q^91 - 30 * q^92 - 17 * q^93 - 5 * q^94 - 14 * q^95 + q^96 + 6 * q^97 - 26 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more