LMFDB - Embedded newform 1155.2.q.j.331.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(331,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1155.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.q (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 13 x^{14} + 116 x^{12} + 545 x^{10} - 6 x^{9} + 1849 x^{8} + 78 x^{7} + 3192 x^{6} + 636 x^{5} + \cdots + 576 $ x^16 + 13x^14 + 116x^12 + 545x^10 - 6x^9 + 1849x^8 + 78x^7 + 3192x^6 + 636x^5 + 3912x^4 + 432x^3 + 1764x^2 - 144x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.5
Root			$0.307276 + 0.532217i$ of defining polynomial
Character	$\chi$	$=$	1155.331
Dual form			1155.2.q.j.991.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.307276 - 0.532217i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.811163 + 1.40498i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.614552 q^{6} +(-2.24946 + 1.39281i) q^{7} +2.22611 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.307276 - 0.532217i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.811163 + 1.40498i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.614552 q^{6} +(-2.24946 + 1.39281i) q^{7} +2.22611 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.307276 - 0.532217i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.811163 - 1.40498i) q^{12} -3.55599 q^{13} +(0.0500738 + 1.62518i) q^{14} -1.00000 q^{15} +(-0.938298 + 1.62518i) q^{16} +(2.62233 + 4.54200i) q^{17} +(0.307276 + 0.532217i) q^{18} +(-3.53435 + 6.12167i) q^{19} +1.62233 q^{20} +(2.33094 + 1.25168i) q^{21} +0.614552 q^{22} +(2.20233 - 3.81454i) q^{23} +(-1.11305 - 1.92786i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.09267 + 1.89256i) q^{26} +1.00000 q^{27} +(-3.78155 - 2.03064i) q^{28} -3.14266 q^{29} +(-0.307276 + 0.532217i) q^{30} +(2.94399 + 5.09915i) q^{31} +(2.80274 + 4.85449i) q^{32} +(0.500000 - 0.866025i) q^{33} +3.22311 q^{34} +(0.0814802 + 2.64450i) q^{35} -1.62233 q^{36} +(1.94901 - 3.37579i) q^{37} +(2.17204 + 3.76208i) q^{38} +(1.77799 + 3.07957i) q^{39} +(1.11305 - 1.92786i) q^{40} -7.75042 q^{41} +(1.38241 - 0.855955i) q^{42} +5.22043 q^{43} +(-0.811163 + 1.40498i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-1.35344 - 2.34423i) q^{46} +(-5.57213 + 9.65122i) q^{47} +1.87660 q^{48} +(3.12015 - 6.26615i) q^{49} -0.614552 q^{50} +(2.62233 - 4.54200i) q^{51} +(-2.88448 - 4.99607i) q^{52} +(1.59836 + 2.76845i) q^{53} +(0.307276 - 0.532217i) q^{54} +1.00000 q^{55} +(-5.00754 + 3.10055i) q^{56} +7.06870 q^{57} +(-0.965664 + 1.67258i) q^{58} +(2.17271 + 3.76325i) q^{59} +(-0.811163 - 1.40498i) q^{60} +(-6.99976 + 12.1239i) q^{61} +3.61847 q^{62} +(-0.0814802 - 2.64450i) q^{63} -0.308336 q^{64} +(-1.77799 + 3.07957i) q^{65} +(-0.307276 - 0.532217i) q^{66} +(-1.05195 - 1.82203i) q^{67} +(-4.25427 + 7.36861i) q^{68} -4.40465 q^{69} +(1.43248 + 0.769225i) q^{70} +9.22691 q^{71} +(-1.11305 + 1.92786i) q^{72} +(-3.26892 - 5.66194i) q^{73} +(-1.19777 - 2.07460i) q^{74} +(-0.500000 + 0.866025i) q^{75} -11.4677 q^{76} +(-2.33094 - 1.25168i) q^{77} +2.18534 q^{78} +(3.97301 - 6.88145i) q^{79} +(0.938298 + 1.62518i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.38152 + 4.12491i) q^{82} +9.86824 q^{83} +(0.132187 + 4.29024i) q^{84} +5.24465 q^{85} +(1.60411 - 2.77841i) q^{86} +(1.57133 + 2.72163i) q^{87} +(1.11305 + 1.92786i) q^{88} +(-2.28231 + 3.95307i) q^{89} +0.614552 q^{90} +(7.99905 - 4.95282i) q^{91} +7.14579 q^{92} +(2.94399 - 5.09915i) q^{93} +(3.42436 + 5.93117i) q^{94} +(3.53435 + 6.12167i) q^{95} +(2.80274 - 4.85449i) q^{96} +11.0580 q^{97} +(-2.37621 - 3.58603i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.307276	−	0.532217i	0.217277	−	0.376334i	−0.736698	−	0.676222i	$-0.763616\pi$
$2$	0.307276	−	0.532217i	0.217277	−	0.376334i	0.953974	+	0.299888i	$0.0969492\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.811163	+	1.40498i	0.405582	+	0.702488i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.614552			−0.250890
$7$	−2.24946	+	1.39281i	−0.850216	+	0.526433i
$7$	−2.24946	+	1.39281i	−0.850216	+	0.526433i
$8$	2.22611			0.787047
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.307276	−	0.532217i	−0.0971691	−	0.168302i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.811163	−	1.40498i	0.234163	−	0.405582i
$13$	−3.55599			−0.986253			−0.493126	−	0.869958i	$-0.664146\pi$
$13$	−3.55599			−0.986253			−0.493126	+	0.869958i	$0.664146\pi$
$14$	0.0500738	+	1.62518i	0.0133828	+	0.434347i
$15$	−1.00000			−0.258199
$16$	−0.938298	+	1.62518i	−0.234574	+	0.406295i
$17$	2.62233	+	4.54200i	0.636008	+	1.10160i	0.986301	+	0.164957i	$0.0527486\pi$
$17$	2.62233	+	4.54200i	0.636008	+	1.10160i	−0.350293	+	0.936640i	$0.613918\pi$
$18$	0.307276	+	0.532217i	0.0724256	+	0.125445i
$19$	−3.53435	+	6.12167i	−0.810835	+	1.40441i	0.101445	+	0.994841i	$0.467653\pi$
$19$	−3.53435	+	6.12167i	−0.810835	+	1.40441i	−0.912280	+	0.409567i	$0.865680\pi$
$20$	1.62233			0.362763
$21$	2.33094	+	1.25168i	0.508653	+	0.273140i
$22$	0.614552			0.131023
$23$	2.20233	−	3.81454i	0.459217	−	0.795387i	−0.539703	−	0.841856i	$-0.681463\pi$
$23$	2.20233	−	3.81454i	0.459217	−	0.795387i	0.998920	+	0.0464686i	$0.0147967\pi$
$24$	−1.11305	−	1.92786i	−0.227201	−	0.393524i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.09267	+	1.89256i	−0.214290	+	0.371161i
$27$	1.00000			0.192450
$28$	−3.78155	−	2.03064i	−0.714645	−	0.383755i
$29$	−3.14266			−0.583578			−0.291789	−	0.956483i	$-0.594250\pi$
$29$	−3.14266			−0.583578			−0.291789	+	0.956483i	$0.594250\pi$
$30$	−0.307276	+	0.532217i	−0.0561006	+	0.0971691i
$31$	2.94399	+	5.09915i	0.528757	+	0.915834i	0.999438	+	0.0335303i	$0.0106750\pi$
$31$	2.94399	+	5.09915i	0.528757	+	0.915834i	−0.470681	+	0.882304i	$0.655992\pi$
$32$	2.80274	+	4.85449i	0.495459	+	0.858160i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	3.22311			0.552759
$35$	0.0814802	+	2.64450i	0.0137727	+	0.447001i
$36$	−1.62233			−0.270388
$37$	1.94901	−	3.37579i	0.320416	−	0.554976i	−0.660158	−	0.751127i	$-0.729511\pi$
$37$	1.94901	−	3.37579i	0.320416	−	0.554976i	0.980574	+	0.196150i	$0.0628441\pi$
$38$	2.17204	+	3.76208i	0.352351	+	0.610290i
$39$	1.77799	+	3.07957i	0.284707	+	0.493126i
$40$	1.11305	−	1.92786i	0.175989	−	0.304822i
$41$	−7.75042			−1.21041			−0.605206	−	0.796069i	$-0.706909\pi$
$41$	−7.75042			−1.21041			−0.605206	+	0.796069i	$0.706909\pi$
$42$	1.38241	−	0.855955i	0.213310	−	0.132077i
$43$	5.22043			0.796109			0.398054	−	0.917362i	$-0.369686\pi$
$43$	5.22043			0.796109			0.398054	+	0.917362i	$0.369686\pi$
$44$	−0.811163	+	1.40498i	−0.122287	+	0.211808i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	−1.35344	−	2.34423i	−0.199554	−	0.345638i
$47$	−5.57213	+	9.65122i	−0.812779	+	1.40778i	0.0981321	+	0.995173i	$0.468713\pi$
$47$	−5.57213	+	9.65122i	−0.812779	+	1.40778i	−0.910911	+	0.412602i	$0.864620\pi$
$48$	1.87660			0.270863
$49$	3.12015	−	6.26615i	0.445736	−	0.895165i
$50$	−0.614552			−0.0869107
$51$	2.62233	−	4.54200i	0.367199	−	0.636008i
$52$	−2.88448	−	4.99607i	−0.400006	−	0.692831i
$53$	1.59836	+	2.76845i	0.219552	+	0.380276i	0.954671	−	0.297663i	$-0.0962070\pi$
$53$	1.59836	+	2.76845i	0.219552	+	0.380276i	−0.735119	+	0.677938i	$0.762874\pi$
$54$	0.307276	−	0.532217i	0.0418149	−	0.0724256i
$55$	1.00000			0.134840
$56$	−5.00754	+	3.10055i	−0.669161	+	0.414328i
$57$	7.06870			0.936272
$58$	−0.965664	+	1.67258i	−0.126798	+	0.219620i
$59$	2.17271	+	3.76325i	0.282863	+	0.489934i	0.972089	−	0.234613i	$-0.0753824\pi$
$59$	2.17271	+	3.76325i	0.282863	+	0.489934i	−0.689225	+	0.724547i	$0.742049\pi$
$60$	−0.811163	−	1.40498i	−0.104721	−	0.181382i
$61$	−6.99976	+	12.1239i	−0.896228	+	1.55231i	−0.0639506	+	0.997953i	$0.520370\pi$
$61$	−6.99976	+	12.1239i	−0.896228	+	1.55231i	−0.832277	+	0.554359i	$0.812963\pi$
$62$	3.61847			0.459546
$63$	−0.0814802	−	2.64450i	−0.0102655	−	0.333175i
$64$	−0.308336			−0.0385420
$65$	−1.77799	+	3.07957i	−0.220533	+	0.381974i
$66$	−0.307276	−	0.532217i	−0.0378230	−	0.0655114i
$67$	−1.05195	−	1.82203i	−0.128516	−	0.222596i	0.794586	−	0.607152i	$-0.207688\pi$
$67$	−1.05195	−	1.82203i	−0.128516	−	0.222596i	−0.923102	+	0.384556i	$0.874355\pi$
$68$	−4.25427	+	7.36861i	−0.515906	+	0.893575i
$69$	−4.40465			−0.530258
$70$	1.43248	+	0.769225i	0.171215	+	0.0919399i
$71$	9.22691			1.09503			0.547516	−	0.836795i	$-0.315573\pi$
$71$	9.22691			1.09503			0.547516	+	0.836795i	$0.315573\pi$
$72$	−1.11305	+	1.92786i	−0.131175	+	0.227201i
$73$	−3.26892	−	5.66194i	−0.382599	−	0.662680i	0.608834	−	0.793297i	$-0.291637\pi$
$73$	−3.26892	−	5.66194i	−0.382599	−	0.662680i	−0.991433	+	0.130617i	$0.958304\pi$
$74$	−1.19777	−	2.07460i	−0.139238	−	0.241167i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−11.4677			−1.31544
$77$	−2.33094	−	1.25168i	−0.265635	−	0.142643i
$78$	2.18534			0.247441
$79$	3.97301	−	6.88145i	0.446998	−	0.774224i	−0.551191	−	0.834379i	$-0.685826\pi$
$79$	3.97301	−	6.88145i	0.446998	−	0.774224i	0.998189	+	0.0601556i	$0.0191597\pi$
$80$	0.938298	+	1.62518i	0.104905	+	0.181701i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.38152	+	4.12491i	−0.262994	+	0.455520i
$83$	9.86824			1.08318			0.541590	−	0.840643i	$-0.317822\pi$
$83$	9.86824			1.08318			0.541590	+	0.840643i	$0.317822\pi$
$84$	0.132187	+	4.29024i	0.0144228	+	0.468103i
$85$	5.24465			0.568862
$86$	1.60411	−	2.77841i	0.172976	−	0.299603i
$87$	1.57133	+	2.72163i	0.168464	+	0.291789i
$88$	1.11305	+	1.92786i	0.118652	+	0.205511i
$89$	−2.28231	+	3.95307i	−0.241924	+	0.419025i	−0.961262	−	0.275635i	$-0.911112\pi$
$89$	−2.28231	+	3.95307i	−0.241924	+	0.419025i	0.719338	+	0.694660i	$0.244445\pi$
$90$	0.614552			0.0647794
$91$	7.99905	−	4.95282i	0.838528	−	0.519197i
$92$	7.14579			0.745000
$93$	2.94399	−	5.09915i	0.305278	−	0.528757i
$94$	3.42436	+	5.93117i	0.353196	+	0.611754i
$95$	3.53435	+	6.12167i	0.362617	+	0.628070i
$96$	2.80274	−	4.85449i	0.286053	−	0.495459i
$97$	11.0580			1.12277			0.561384	−	0.827555i	$-0.310269\pi$
$97$	11.0580			1.12277			0.561384	+	0.827555i	$0.310269\pi$
$98$	−2.37621	−	3.58603i	−0.240033	−	0.362244i
$99$	−1.00000			−0.100504
$100$	0.811163	−	1.40498i	0.0811163	−	0.140498i
$101$	6.44577	+	11.1644i	0.641378	+	1.11090i	0.985125	+	0.171837i	$0.0549704\pi$
$101$	6.44577	+	11.1644i	0.641378	+	1.11090i	−0.343747	+	0.939062i	$0.611696\pi$
$102$	−1.61155	−	2.79129i	−0.159568	−	0.276379i
$103$	6.52248	−	11.2973i	0.642680	−	1.11315i	−0.342153	−	0.939644i	$-0.611156\pi$
$103$	6.52248	−	11.2973i	0.642680	−	1.11315i	0.984832	−	0.173509i	$-0.0555106\pi$
$104$	−7.91600			−0.776228
$105$	2.24946	−	1.39281i	0.219525	−	0.135925i
$106$	1.96456			0.190814
$107$	4.79437	−	8.30409i	0.463489	−	0.802786i	−0.535643	−	0.844444i	$-0.679931\pi$
$107$	4.79437	−	8.30409i	0.463489	−	0.802786i	0.999132	+	0.0416583i	$0.0132641\pi$
$108$	0.811163	+	1.40498i	0.0780542	+	0.135194i
$109$	2.72869	+	4.72622i	0.261361	+	0.452690i	0.966604	−	0.256276i	$-0.0824955\pi$
$109$	2.72869	+	4.72622i	0.261361	+	0.452690i	−0.705243	+	0.708966i	$0.749162\pi$
$110$	0.307276	−	0.532217i	0.0292976	−	0.0507449i
$111$	−3.89802			−0.369984
$112$	−0.152905	−	4.96265i	−0.0144482	−	0.468926i
$113$	−18.8123			−1.76972			−0.884858	−	0.465861i	$-0.845745\pi$
$113$	−18.8123			−1.76972			−0.884858	+	0.465861i	$0.845745\pi$
$114$	2.17204	−	3.76208i	0.203430	−	0.352351i
$115$	−2.20233	−	3.81454i	−0.205368	−	0.355708i
$116$	−2.54921	−	4.41537i	−0.236688	−	0.409956i
$117$	1.77799	−	3.07957i	0.164375	−	0.284707i
$118$	2.67049			0.245839
$119$	−12.2250	−	6.56465i	−1.12066	−	0.601780i
$120$	−2.22611			−0.203215
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	4.30172	+	7.45079i	0.389459	+	0.674563i
$123$	3.87521	+	6.71206i	0.349416	+	0.605206i
$124$	−4.77612	+	8.27248i	−0.428908	+	0.742891i
$125$	−1.00000			−0.0894427
$126$	−1.43248	−	0.769225i	−0.127616	−	0.0685280i
$127$	8.89453			0.789262			0.394631	−	0.918840i	$-0.370872\pi$
$127$	8.89453			0.789262			0.394631	+	0.918840i	$0.370872\pi$
$128$	−5.70022	+	9.87307i	−0.503833	+	0.872665i
$129$	−2.61022	−	4.52103i	−0.229817	−	0.398054i
$130$	1.09267	+	1.89256i	0.0958333	+	0.165988i
$131$	6.90394	−	11.9580i	0.603200	−	1.04477i	−0.389133	−	0.921182i	$-0.627225\pi$
$131$	6.90394	−	11.9580i	0.603200	−	1.04477i	0.992333	−	0.123592i	$-0.0394413\pi$
$132$	1.62233			0.141205
$133$	−0.575959	−	18.6931i	−0.0499419	−	1.62090i
$134$	−1.29295			−0.111694
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	5.83758	+	10.1110i	0.500568	+	0.867009i
$137$	−7.90118	−	13.6852i	−0.675043	−	1.16921i	−0.976456	−	0.215716i	$-0.930792\pi$
$137$	−7.90118	−	13.6852i	−0.675043	−	1.16921i	0.301413	−	0.953494i	$-0.402542\pi$
$138$	−1.35344	+	2.34423i	−0.115213	+	0.199554i
$139$	−20.2079			−1.71401			−0.857007	−	0.515304i	$-0.827679\pi$
$139$	−20.2079			−1.71401			−0.857007	+	0.515304i	$0.827679\pi$
$140$	−3.64936	+	2.25960i	−0.308427	+	0.190971i
$141$	11.1443			0.938517
$142$	2.83521	−	4.91072i	0.237925	−	0.412099i
$143$	−1.77799	−	3.07957i	−0.148683	−	0.257527i
$144$	−0.938298	−	1.62518i	−0.0781915	−	0.135432i
$145$	−1.57133	+	2.72163i	−0.130492	+	0.226019i
$146$	−4.01785			−0.332519
$147$	−6.98672	+	0.430948i	−0.576255	+	0.0355440i
$148$	6.32387			0.519819
$149$	−8.78961	+	15.2241i	−0.720073	+	1.24720i	0.240897	+	0.970551i	$0.422558\pi$
$149$	−8.78961	+	15.2241i	−0.720073	+	1.24720i	−0.960970	+	0.276652i	$0.910775\pi$
$150$	0.307276	+	0.532217i	0.0250890	+	0.0434554i
$151$	5.41220	+	9.37421i	0.440439	+	0.762863i	0.997722	−	0.0674600i	$-0.0214895\pi$
$151$	5.41220	+	9.37421i	0.440439	+	0.762863i	−0.557283	+	0.830323i	$0.688156\pi$
$152$	−7.86784	+	13.6275i	−0.638166	+	1.10534i
$153$	−5.24465			−0.424005
$154$	−1.38241	+	0.855955i	−0.111398	+	0.0689748i
$155$	5.88799			0.472935
$156$	−2.88448	+	4.99607i	−0.230944	+	0.400006i
$157$	−1.69133	−	2.92947i	−0.134983	−	0.233798i	0.790608	−	0.612323i	$-0.209765\pi$
$157$	−1.69133	−	2.92947i	−0.134983	−	0.233798i	−0.925591	+	0.378525i	$0.876431\pi$
$158$	−2.44162	−	4.22901i	−0.194245	−	0.336442i
$159$	1.59836	−	2.76845i	0.126759	−	0.219552i
$160$	5.60548			0.443152
$161$	0.358892	+	11.6481i	0.0282846	+	0.917998i
$162$	−0.614552			−0.0482837
$163$	−4.15221	+	7.19185i	−0.325227	+	0.563309i	−0.981558	−	0.191164i	$-0.938774\pi$
$163$	−4.15221	+	7.19185i	−0.325227	+	0.563309i	0.656332	+	0.754473i	$0.272107\pi$
$164$	−6.28685	−	10.8892i	−0.490921	−	0.850300i
$165$	−0.500000	−	0.866025i	−0.0389249	−	0.0674200i
$166$	3.03227	−	5.25205i	0.235350	−	0.407638i
$167$	14.4832			1.12075			0.560373	−	0.828240i	$-0.310658\pi$
$167$	14.4832			1.12075			0.560373	+	0.828240i	$0.310658\pi$
$168$	5.18892	+	2.78638i	0.400334	+	0.214974i
$169$	−0.354967			−0.0273051
$170$	1.61155	−	2.79129i	0.123601	−	0.214083i
$171$	−3.53435	−	6.12167i	−0.270278	−	0.468136i
$172$	4.23462	+	7.33458i	0.322887	+	0.559257i
$173$	2.50212	−	4.33380i	0.190233	−	0.329493i	−0.755095	−	0.655616i	$-0.772409\pi$
$173$	2.50212	−	4.33380i	0.190233	−	0.329493i	0.945327	+	0.326123i	$0.105742\pi$
$174$	1.93133			0.146414
$175$	2.33094	+	1.25168i	0.176203	+	0.0946184i
$176$	−1.87660			−0.141454
$177$	2.17271	−	3.76325i	0.163311	−	0.282863i
$178$	1.40260	+	2.42937i	0.105129	+	0.182089i
$179$	2.46905	+	4.27652i	0.184546	+	0.319642i	0.943423	−	0.331591i	$-0.107585\pi$
$179$	2.46905	+	4.27652i	0.184546	+	0.319642i	−0.758878	+	0.651233i	$0.774252\pi$
$180$	−0.811163	+	1.40498i	−0.0604605	+	0.104721i
$181$	6.81318			0.506419			0.253210	−	0.967411i	$-0.418514\pi$
$181$	6.81318			0.506419			0.253210	+	0.967411i	$0.418514\pi$
$182$	−0.178062	−	5.77911i	−0.0131988	−	0.428376i
$183$	13.9995			1.03487
$184$	4.90261	−	8.49158i	0.361425	−	0.626007i
$185$	−1.94901	−	3.37579i	−0.143294	−	0.248193i
$186$	−1.80924	−	3.13369i	−0.132660	−	0.229773i
$187$	−2.62233	+	4.54200i	−0.191763	+	0.332144i
$188$	−18.0796			−1.31859
$189$	−2.24946	+	1.39281i	−0.163624	+	0.101312i
$190$	4.34408			0.315153
$191$	−0.0155336	+	0.0269051i	−0.00112398	+	0.00194678i	−0.866587	−	0.499026i	$-0.833691\pi$
$191$	−0.0155336	+	0.0269051i	−0.00112398	+	0.00194678i	0.865463	+	0.500973i	$0.167024\pi$
$192$	0.154168	+	0.267027i	0.0111261	+	0.0192710i
$193$	−10.2888	−	17.8207i	−0.740603	−	1.28276i	−0.952221	−	0.305409i	$-0.901207\pi$
$193$	−10.2888	−	17.8207i	−0.740603	−	1.28276i	0.211619	−	0.977352i	$-0.432127\pi$
$194$	3.39785	−	5.88525i	0.243952	−	0.422536i
$195$	3.55599			0.254649
$196$	11.3347	−	0.699138i	0.809625	−	0.0499384i
$197$	15.0800			1.07441			0.537203	−	0.843453i	$-0.319481\pi$
$197$	15.0800			1.07441			0.537203	+	0.843453i	$0.319481\pi$
$198$	−0.307276	+	0.532217i	−0.0218371	+	0.0378230i
$199$	−8.81979	−	15.2763i	−0.625219	−	1.08291i	−0.988499	−	0.151230i	$-0.951676\pi$
$199$	−8.81979	−	15.2763i	−0.625219	−	1.08291i	0.363280	−	0.931680i	$-0.381657\pi$
$200$	−1.11305	−	1.92786i	−0.0787047	−	0.136321i
$201$	−1.05195	+	1.82203i	−0.0741988	+	0.128516i
$202$	7.92252			0.557426
$203$	7.06930	−	4.37714i	0.496167	−	0.307215i
$204$	8.50854			0.595717
$205$	−3.87521	+	6.71206i	−0.270656	+	0.468791i
$206$	−4.00840	−	6.94276i	−0.279279	−	0.483725i
$207$	2.20233	+	3.81454i	0.153072	+	0.265129i
$208$	3.33657	−	5.77911i	0.231350	−	0.400709i
$209$	−7.06870			−0.488952
$210$	−0.0500738	−	1.62518i	−0.00345542	−	0.112148i
$211$	−5.69620			−0.392143			−0.196071	−	0.980590i	$-0.562818\pi$
$211$	−5.69620			−0.392143			−0.196071	+	0.980590i	$0.562818\pi$
$212$	−2.59307	+	4.49133i	−0.178093	+	0.308466i
$213$	−4.61345	−	7.99074i	−0.316109	−	0.547516i
$214$	−2.94639	−	5.10329i	−0.201411	−	0.348854i
$215$	2.61022	−	4.52103i	0.178015	−	0.308332i
$216$	2.22611			0.151467
$217$	−13.7246	−	7.36990i	−0.931683	−	0.500302i
$218$	3.35384			0.227150
$219$	−3.26892	+	5.66194i	−0.220893	+	0.382599i
$220$	0.811163	+	1.40498i	0.0546886	+	0.0947235i
$221$	−9.32495	−	16.1513i	−0.627264	−	1.08645i
$222$	−1.19777	+	2.07460i	−0.0803890	+	0.139238i
$223$	−11.5635			−0.774351			−0.387176	−	0.922006i	$-0.626549\pi$
$223$	−11.5635			−0.774351			−0.387176	+	0.922006i	$0.626549\pi$
$224$	−13.0660	−	7.01629i	−0.873011	−	0.468795i
$225$	1.00000			0.0666667
$226$	−5.78058	+	10.0123i	−0.384518	+	0.666005i
$227$	−3.61867	−	6.26772i	−0.240180	−	0.416003i	0.720586	−	0.693366i	$-0.243873\pi$
$227$	−3.61867	−	6.26772i	−0.240180	−	0.416003i	−0.960765	+	0.277363i	$0.910540\pi$
$228$	5.73387	+	9.93135i	0.379735	+	0.657720i
$229$	9.59092	−	16.6120i	0.633786	−	1.09775i	−0.352986	−	0.935629i	$-0.614834\pi$
$229$	9.59092	−	16.6120i	0.633786	−	1.09775i	0.986771	−	0.162120i	$-0.0518331\pi$
$230$	−2.70689			−0.178487
$231$	0.0814802	+	2.64450i	0.00536100	+	0.173995i
$232$	−6.99590			−0.459303
$233$	−8.25420	+	14.2967i	−0.540751	+	0.936608i	0.458110	+	0.888895i	$0.348527\pi$
$233$	−8.25420	+	14.2967i	−0.540751	+	0.936608i	−0.998861	+	0.0477126i	$0.984807\pi$
$234$	−1.09267	−	1.89256i	−0.0714300	−	0.123720i
$235$	5.57213	+	9.65122i	0.363486	+	0.629576i
$236$	−3.52485	+	6.10522i	−0.229448	+	0.397416i
$237$	−7.94601			−0.516149
$238$	−7.25026	+	4.48919i	−0.469964	+	0.290991i
$239$	−22.0074			−1.42354			−0.711772	−	0.702411i	$-0.752107\pi$
$239$	−22.0074			−1.42354			−0.711772	+	0.702411i	$0.752107\pi$
$240$	0.938298	−	1.62518i	0.0605669	−	0.104905i
$241$	−3.54788	−	6.14511i	−0.228539	−	0.395842i	0.728836	−	0.684688i	$-0.240062\pi$
$241$	−3.54788	−	6.14511i	−0.228539	−	0.395842i	−0.957375	+	0.288847i	$0.906728\pi$
$242$	0.307276	+	0.532217i	0.0197524	+	0.0342122i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−22.7118			−1.45397
$245$	−3.86657	−	5.83520i	−0.247026	−	0.372798i
$246$	4.76303			0.303680
$247$	12.5681	−	21.7686i	0.799689	−	1.38510i
$248$	6.55364	+	11.3512i	0.416157	+	0.720805i
$249$	−4.93412	−	8.54615i	−0.312687	−	0.541590i
$250$	−0.307276	+	0.532217i	−0.0194338	+	0.0336604i
$251$	23.1244			1.45960			0.729801	−	0.683660i	$-0.239613\pi$
$251$	23.1244			1.45960			0.729801	+	0.683660i	$0.239613\pi$
$252$	3.64936	−	2.25960i	0.229888	−	0.142341i
$253$	4.40465			0.276918
$254$	2.73307	−	4.73382i	0.171488	−	0.297027i
$255$	−2.62233	−	4.54200i	−0.164216	−	0.284431i
$256$	3.19474	+	5.53346i	0.199672	+	0.345841i
$257$	2.32766	−	4.03162i	0.145195	−	0.251486i	−0.784251	−	0.620444i	$-0.786952\pi$
$257$	2.32766	−	4.03162i	0.145195	−	0.251486i	0.929446	+	0.368959i	$0.120286\pi$
$258$	−3.20823			−0.199735
$259$	0.317612	+	10.3083i	0.0197354	+	0.640527i
$260$	−5.76897			−0.357776
$261$	1.57133	−	2.72163i	0.0972630	−	0.168464i
$262$	−4.24283	−	7.34879i	−0.262123	−	0.454010i
$263$	3.08275	+	5.33947i	0.190090	+	0.329246i	0.945280	−	0.326260i	$-0.105789\pi$
$263$	3.08275	+	5.33947i	0.190090	+	0.329246i	−0.755190	+	0.655506i	$0.772455\pi$
$264$	1.11305	−	1.92786i	0.0685037	−	0.118652i
$265$	3.19673			0.196374
$266$	−10.1258	−	5.43742i	−0.620852	−	0.333389i
$267$	4.56462			0.279350
$268$	1.70661	−	2.95593i	0.104248	−	0.180562i
$269$	−5.41557	−	9.38005i	−0.330193	−	0.571912i	0.652356	−	0.757913i	$-0.273781\pi$
$269$	−5.41557	−	9.38005i	−0.330193	−	0.571912i	−0.982550	+	0.186001i	$0.940447\pi$
$270$	−0.307276	−	0.532217i	−0.0187002	−	0.0323897i
$271$	−11.8676	+	20.5553i	−0.720906	+	1.24865i	0.239731	+	0.970839i	$0.422941\pi$
$271$	−11.8676	+	20.5553i	−0.720906	+	1.24865i	−0.960637	+	0.277807i	$0.910393\pi$
$272$	−9.84209			−0.596764
$273$	−8.28879	−	4.45097i	−0.501661	−	0.269385i
$274$	−9.71136			−0.586685
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	−3.57289	−	6.18843i	−0.215063	−	0.372500i
$277$	−9.12439	−	15.8039i	−0.548231	−	0.949564i	−0.998396	−	0.0566187i	$-0.981968\pi$
$277$	−9.12439	−	15.8039i	−0.548231	−	0.949564i	0.450165	−	0.892946i	$-0.351365\pi$
$278$	−6.20941	+	10.7550i	−0.372416	+	0.645043i
$279$	−5.88799			−0.352505
$280$	0.181383	+	5.88693i	0.0108397	+	0.351811i
$281$	16.8180			1.00327			0.501637	−	0.865078i	$-0.332731\pi$
$281$	16.8180			1.00327			0.501637	+	0.865078i	$0.332731\pi$
$282$	3.42436	−	5.93117i	0.203918	−	0.353196i
$283$	−13.4031	−	23.2148i	−0.796730	−	1.37998i	−0.921735	−	0.387821i	$-0.873228\pi$
$283$	−13.4031	−	23.2148i	−0.796730	−	1.37998i	0.125004	−	0.992156i	$-0.460106\pi$
$284$	7.48453	+	12.9636i	0.444125	+	0.769247i
$285$	3.53435	−	6.12167i	0.209357	−	0.362617i
$286$	−2.18534			−0.129222
$287$	17.4343	−	10.7949i	1.02911	−	0.637201i
$288$	−5.60548			−0.330306
$289$	−5.25319	+	9.09879i	−0.309011	+	0.535223i
$290$	0.965664	+	1.67258i	0.0567058	+	0.0982172i
$291$	−5.52899	−	9.57650i	−0.324115	−	0.561384i
$292$	5.30326	−	9.18552i	0.310350	−	0.537542i
$293$	7.50417			0.438399			0.219199	−	0.975680i	$-0.429656\pi$
$293$	7.50417			0.438399			0.219199	+	0.975680i	$0.429656\pi$
$294$	−1.91749	+	3.85087i	−0.111830	+	0.224588i
$295$	4.34543			0.253001
$296$	4.33871	−	7.51486i	0.252182	−	0.436793i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	5.40167	+	9.35596i	0.312910	+	0.541976i
$299$	−7.83144	+	13.5645i	−0.452904	+	0.784453i
$300$	−1.62233			−0.0936651
$301$	−11.7432	+	7.27108i	−0.676865	+	0.419098i
$302$	6.65216			0.382789
$303$	6.44577	−	11.1644i	0.370300	−	0.641378i
$304$	−6.63254	−	11.4879i	−0.380402	−	0.658876i
$305$	6.99976	+	12.1239i	0.400805	+	0.694215i
$306$	−1.61155	+	2.79129i	−0.0921265	+	0.159568i
$307$	15.6121			0.891031			0.445516	−	0.895274i	$-0.353020\pi$
$307$	15.6121			0.891031			0.445516	+	0.895274i	$0.353020\pi$
$308$	−0.132187	−	4.29024i	−0.00753208	−	0.244459i
$309$	−13.0450			−0.742102
$310$	1.80924	−	3.13369i	0.102758	−	0.177982i
$311$	−12.5763	−	21.7827i	−0.713134	−	1.23518i	−0.963675	−	0.267078i	$-0.913942\pi$
$311$	−12.5763	−	21.7827i	−0.713134	−	1.23518i	0.250541	−	0.968106i	$-0.419392\pi$
$312$	3.95800	+	6.85546i	0.224078	+	0.388114i
$313$	−11.1627	+	19.3343i	−0.630950	+	1.09284i	0.356408	+	0.934331i	$0.384001\pi$
$313$	−11.1627	+	19.3343i	−0.630950	+	1.09284i	−0.987358	+	0.158507i	$0.949332\pi$
$314$	−2.07882			−0.117315
$315$	−2.33094	−	1.25168i	−0.131334	−	0.0705244i
$316$	12.8910			0.725177
$317$	0.296488	−	0.513532i	0.0166524	−	0.0288428i	−0.857579	−	0.514352i	$-0.828032\pi$
$317$	0.296488	−	0.513532i	0.0166524	−	0.0288428i	0.874232	+	0.485509i	$0.161366\pi$
$318$	−0.982278	−	1.70135i	−0.0550834	−	0.0954072i
$319$	−1.57133	−	2.72163i	−0.0879777	−	0.152382i
$320$	−0.154168	+	0.267027i	−0.00861825	+	0.0149273i
$321$	−9.58873			−0.535191
$322$	6.30959	+	3.38817i	0.351620	+	0.188815i
$323$	−37.0729			−2.06279
$324$	0.811163	−	1.40498i	0.0450646	−	0.0780542i
$325$	1.77799	+	3.07957i	0.0986253	+	0.170824i
$326$	2.55175	+	4.41976i	0.141328	+	0.244788i
$327$	2.72869	−	4.72622i	0.150897	−	0.261361i
$328$	−17.2533			−0.952652
$329$	−0.908037	−	29.4710i	−0.0500617	−	1.62479i
$330$	−0.614552			−0.0338300
$331$	8.76222	−	15.1766i	0.481615	−	0.834182i	−0.518162	−	0.855282i	$-0.673384\pi$
$331$	8.76222	−	15.1766i	0.481615	−	0.834182i	0.999777	+	0.0211005i	$0.00671700\pi$
$332$	8.00476	+	13.8646i	0.439318	+	0.760921i
$333$	1.94901	+	3.37579i	0.106805	+	0.184992i
$334$	4.45035	−	7.70822i	0.243512	−	0.421775i
$335$	−2.10390			−0.114948
$336$	−4.22133	+	2.61374i	−0.230292	+	0.142591i
$337$	−4.23837			−0.230879			−0.115439	−	0.993315i	$-0.536828\pi$
$337$	−4.23837			−0.230879			−0.115439	+	0.993315i	$0.536828\pi$
$338$	−0.109073	+	0.188920i	−0.00593277	+	0.0102759i
$339$	9.40617	+	16.2920i	0.510873	+	0.884858i
$340$	4.25427	+	7.36861i	0.230720	+	0.399619i
$341$	−2.94399	+	5.09915i	−0.159426	+	0.276134i
$342$	−4.34408			−0.234901
$343$	1.70892	+	18.4412i	0.0922730	+	0.995734i
$344$	11.6212			0.626575
$345$	−2.20233	+	3.81454i	−0.118569	+	0.205368i
$346$	−1.53768	−	2.66334i	−0.0826663	−	0.143182i
$347$	9.26605	+	16.0493i	0.497427	+	0.861569i	0.999996	−	0.00296808i	$-0.000944772\pi$
$347$	9.26605	+	16.0493i	0.497427	+	0.861569i	−0.502568	+	0.864538i	$0.667611\pi$
$348$	−2.54921	+	4.41537i	−0.136652	+	0.236688i
$349$	34.0136			1.82071			0.910353	−	0.413832i	$-0.135810\pi$
$349$	34.0136			1.82071			0.910353	+	0.413832i	$0.135810\pi$
$350$	1.38241	−	0.855955i	0.0738929	−	0.0457527i
$351$	−3.55599			−0.189804
$352$	−2.80274	+	4.85449i	−0.149386	+	0.258745i
$353$	2.98303	+	5.16675i	0.158770	+	0.274999i	0.934426	−	0.356158i	$-0.115914\pi$
$353$	2.98303	+	5.16675i	0.158770	+	0.274999i	−0.775655	+	0.631157i	$0.782580\pi$
$354$	−1.33525	−	2.31271i	−0.0709675	−	0.122919i
$355$	4.61345	−	7.99074i	0.244857	−	0.424104i
$356$	−7.40530			−0.392480
$357$	0.427335	+	13.8695i	0.0226170	+	0.734050i
$358$	3.03472			0.160390
$359$	2.43946	−	4.22526i	0.128750	−	0.223001i	−0.794443	−	0.607339i	$-0.792237\pi$
$359$	2.43946	−	4.22526i	0.128750	−	0.223001i	0.923192	+	0.384338i	$0.125570\pi$
$360$	1.11305	+	1.92786i	0.0586631	+	0.101607i
$361$	−15.4832	−	26.8178i	−0.814907	−	1.41146i
$362$	2.09352	−	3.62609i	0.110033	−	0.190583i
$363$	1.00000			0.0524864
$364$	13.4471	+	7.22093i	0.704821	+	0.378479i
$365$	−6.53785			−0.342207
$366$	4.30172	−	7.45079i	0.224854	−	0.389459i
$367$	13.5806	+	23.5223i	0.708901	+	1.22785i	0.965265	+	0.261272i	$0.0841418\pi$
$367$	13.5806	+	23.5223i	0.708901	+	1.22785i	−0.256365	+	0.966580i	$0.582525\pi$
$368$	4.13288	+	7.15835i	0.215441	+	0.373155i
$369$	3.87521	−	6.71206i	0.201735	−	0.349416i
$370$	−2.39554			−0.124538
$371$	−7.45139	−	4.00130i	−0.386857	−	0.207737i
$372$	9.55224			0.495261
$373$	−0.332032	+	0.575097i	−0.0171920	+	0.0297774i	−0.874493	−	0.485037i	$-0.838806\pi$
$373$	−0.332032	+	0.575097i	−0.0171920	+	0.0297774i	0.857301	+	0.514815i	$0.172139\pi$
$374$	1.61155	+	2.79129i	0.0833315	+	0.144334i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−12.4042	+	21.4846i	−0.639696	+	1.10799i
$377$	11.1753			0.575555
$378$	0.0500738	+	1.62518i	0.00257552	+	0.0835902i
$379$	5.77483			0.296633			0.148317	−	0.988940i	$-0.452615\pi$
$379$	5.77483			0.296633			0.148317	+	0.988940i	$0.452615\pi$
$380$	−5.73387	+	9.93135i	−0.294141	+	0.509467i
$381$	−4.44727	−	7.70289i	−0.227840	−	0.394631i
$382$	0.00954623	+	0.0165346i	0.000488427	+	0.000845981i
$383$	−6.50495	+	11.2669i	−0.332387	+	0.575712i	−0.982979	−	0.183716i	$-0.941187\pi$
$383$	−6.50495	+	11.2669i	−0.332387	+	0.575712i	0.650592	+	0.759427i	$0.274521\pi$
$384$	11.4004			0.581776
$385$	−2.24946	+	1.39281i	−0.114643	+	0.0709843i
$386$	−12.6460			−0.643663
$387$	−2.61022	+	4.52103i	−0.132685	+	0.229817i
$388$	8.96983	+	15.5362i	0.455374	+	0.788731i
$389$	13.1828	+	22.8333i	0.668396	+	1.15770i	0.978352	+	0.206946i	$0.0663523\pi$
$389$	13.1828	+	22.8333i	0.668396	+	1.15770i	−0.309956	+	0.950751i	$0.600314\pi$
$390$	1.09267	−	1.89256i	0.0553294	−	0.0958333i
$391$	23.1009			1.16826
$392$	6.94578	−	13.9491i	0.350815	−	0.704537i
$393$	−13.8079			−0.696515
$394$	4.63372	−	8.02584i	0.233444	−	0.404336i
$395$	−3.97301	−	6.88145i	−0.199904	−	0.346243i
$396$	−0.811163	−	1.40498i	−0.0407625	−	0.0706027i
$397$	−3.55079	+	6.15015i	−0.178209	+	0.308667i	−0.941267	−	0.337663i	$-0.890364\pi$
$397$	−3.55079	+	6.15015i	−0.178209	+	0.308667i	0.763058	+	0.646330i	$0.223697\pi$
$398$	−10.8404			−0.543382
$399$	−15.9008	+	9.84537i	−0.796034	+	0.492885i
$400$	1.87660			0.0938298
$401$	−3.84058	+	6.65209i	−0.191790	+	0.332189i	−0.945843	−	0.324623i	$-0.894762\pi$
$401$	−3.84058	+	6.65209i	−0.191790	+	0.332189i	0.754054	+	0.656813i	$0.228096\pi$
$402$	0.646477	+	1.11973i	0.0322434	+	0.0558471i
$403$	−10.4688	−	18.1325i	−0.521488	−	0.903244i
$404$	−10.4571	+	18.1123i	−0.520262	+	0.901121i
$405$	−1.00000			−0.0496904
$406$	−0.157365	−	5.10739i	−0.00780989	−	0.253476i
$407$	3.89802			0.193218
$408$	5.83758	−	10.1110i	0.289003	−	0.500568i
$409$	−10.9216	−	18.9167i	−0.540038	−	0.935373i	−0.998901	−	0.0468659i	$-0.985077\pi$
$409$	−10.9216	−	18.9167i	−0.540038	−	0.935373i	0.458864	−	0.888507i	$-0.348257\pi$
$410$	2.38152	+	4.12491i	0.117615	+	0.203715i
$411$	−7.90118	+	13.6852i	−0.389736	+	0.675043i
$412$	21.1632			1.04264
$413$	−10.1289	−	5.43910i	−0.498412	−	0.267641i
$414$	2.70689			0.133036
$415$	4.93412	−	8.54615i	0.242206	−	0.419514i
$416$	−9.96650	−	17.2625i	−0.488648	−	0.846363i
$417$	10.1040	+	17.5006i	0.494793	+	0.857007i
$418$	−2.17204	+	3.76208i	−0.106238	+	0.184009i
$419$	37.1892			1.81681			0.908406	−	0.418088i	$-0.137300\pi$
$419$	37.1892			1.81681			0.908406	+	0.418088i	$0.137300\pi$
$420$	3.78155	+	2.03064i	0.184521	+	0.0990851i
$421$	23.7268			1.15637			0.578187	−	0.815904i	$-0.303760\pi$
$421$	23.7268			1.15637			0.578187	+	0.815904i	$0.303760\pi$
$422$	−1.75031	+	3.03162i	−0.0852035	+	0.147577i
$423$	−5.57213	−	9.65122i	−0.270926	−	0.469258i
$424$	3.55813	+	6.16286i	0.172798	+	0.299295i
$425$	2.62233	−	4.54200i	0.127202	−	0.220319i
$426$	−5.67041			−0.274732
$427$	−1.14068	−	37.0217i	−0.0552016	−	1.79161i
$428$	15.5561			0.751930
$429$	−1.77799	+	3.07957i	−0.0858423	+	0.148683i
$430$	−1.60411	−	2.77841i	−0.0773572	−	0.133987i
$431$	6.97754	+	12.0855i	0.336096	+	0.582136i	0.983695	−	0.179846i	$-0.0575599\pi$
$431$	6.97754	+	12.0855i	0.336096	+	0.582136i	−0.647599	+	0.761982i	$0.724227\pi$
$432$	−0.938298	+	1.62518i	−0.0451439	+	0.0781915i
$433$	−36.4828			−1.75325			−0.876625	−	0.481173i	$-0.840211\pi$
$433$	−36.4828			−1.75325			−0.876625	+	0.481173i	$0.840211\pi$
$434$	−8.13961	+	5.03985i	−0.390714	+	0.241921i
$435$	3.14266			0.150679
$436$	−4.42682	+	7.66747i	−0.212006	+	0.367205i
$437$	15.5676	+	26.9638i	0.744698	+	1.28986i
$438$	2.00892	+	3.47956i	0.0959900	+	0.166260i
$439$	15.5447	−	26.9242i	0.741909	−	1.28502i	−0.209717	−	0.977762i	$-0.567254\pi$
$439$	15.5447	−	26.9242i	0.741909	−	1.28502i	0.951625	−	0.307261i	$-0.0994125\pi$
$440$	2.22611			0.106125
$441$	3.86657	+	5.83520i	0.184123	+	0.277867i
$442$	−11.4613			−0.545160
$443$	7.77456	−	13.4659i	0.369380	−	0.639786i	−0.620088	−	0.784532i	$-0.712903\pi$
$443$	7.77456	−	13.4659i	0.369380	−	0.639786i	0.989469	+	0.144746i	$0.0462366\pi$
$444$	−3.16193	−	5.47663i	−0.150059	−	0.259909i
$445$	2.28231	+	3.95307i	0.108192	+	0.187394i
$446$	−3.55319	+	6.15431i	−0.168249	+	0.291415i
$447$	17.5792			0.831469
$448$	0.693590	−	0.429454i	0.0327690	−	0.0202898i
$449$	16.8570			0.795530			0.397765	−	0.917487i	$-0.369786\pi$
$449$	16.8570			0.795530			0.397765	+	0.917487i	$0.369786\pi$
$450$	0.307276	−	0.532217i	0.0144851	−	0.0250890i
$451$	−3.87521	−	6.71206i	−0.182476	−	0.316059i
$452$	−15.2599	−	26.4309i	−0.717764	−	1.24320i
$453$	5.41220	−	9.37421i	0.254288	−	0.440439i
$454$	−4.44772			−0.208742
$455$	−0.289742	−	9.40379i	−0.0135833	−	0.440857i
$456$	15.7357			0.736890
$457$	−17.1236	+	29.6590i	−0.801010	+	1.38739i	0.117942	+	0.993021i	$0.462370\pi$
$457$	−17.1236	+	29.6590i	−0.801010	+	1.38739i	−0.918952	+	0.394370i	$0.870963\pi$
$458$	−5.89411	−	10.2089i	−0.275414	−	0.477031i
$459$	2.62233	+	4.54200i	0.122400	+	0.212003i
$460$	3.57289	−	6.18843i	0.166587	−	0.288537i
$461$	5.99719			0.279317			0.139659	−	0.990200i	$-0.455400\pi$
$461$	5.99719			0.279317			0.139659	+	0.990200i	$0.455400\pi$
$462$	1.43248	+	0.769225i	0.0666452	+	0.0357876i
$463$	26.2935			1.22196			0.610980	−	0.791646i	$-0.290775\pi$
$463$	26.2935			1.22196			0.610980	+	0.791646i	$0.290775\pi$
$464$	2.94875	−	5.10739i	0.136892	−	0.237105i
$465$	−2.94399	−	5.09915i	−0.136524	−	0.236467i
$466$	5.07263	+	8.78606i	0.234985	+	0.407006i
$467$	0.0195279	−	0.0338233i	0.000903643	−	0.00156516i	−0.865573	−	0.500782i	$-0.833046\pi$
$467$	0.0195279	−	0.0338233i	0.000903643	−	0.00156516i	0.866477	+	0.499217i	$0.166379\pi$
$468$	5.76897			0.266671
$469$	4.90406	+	2.63342i	0.226449	+	0.121600i
$470$	6.84873			0.315908
$471$	−1.69133	+	2.92947i	−0.0779325	+	0.134983i
$472$	4.83669	+	8.37740i	0.222627	+	0.385601i
$473$	2.61022	+	4.52103i	0.120018	+	0.207877i
$474$	−2.44162	+	4.22901i	−0.112147	+	0.194245i
$475$	7.06870			0.324334
$476$	−0.693277	−	22.5008i	−0.0317763	−	1.03132i
$477$	−3.19673			−0.146368
$478$	−6.76236	+	11.7127i	−0.309303	+	0.535728i
$479$	7.42611	+	12.8624i	0.339308	+	0.587698i	0.984303	−	0.176489i	$-0.0564739\pi$
$479$	7.42611	+	12.8624i	0.339308	+	0.587698i	−0.644995	+	0.764187i	$0.723141\pi$
$480$	−2.80274	−	4.85449i	−0.127927	−	0.221576i
$481$	−6.93066	+	12.0043i	−0.316011	+	0.547347i
$482$	−4.36071			−0.198625
$483$	9.90810	−	6.13485i	0.450834	−	0.279146i
$484$	−1.62233			−0.0737421
$485$	5.52899	−	9.57650i	0.251059	−	0.434846i
$486$	0.307276	+	0.532217i	0.0139383	+	0.0241419i
$487$	9.35541	+	16.2040i	0.423934	+	0.734275i	0.996320	−	0.0857088i	$-0.0273155\pi$
$487$	9.35541	+	16.2040i	0.423934	+	0.734275i	−0.572386	+	0.819984i	$0.693982\pi$
$488$	−15.5822	+	26.9892i	−0.705374	+	1.22174i
$489$	8.30443			0.375539
$490$	−4.29370	+	0.264840i	−0.193970	+	0.0119642i
$491$	18.8041			0.848618			0.424309	−	0.905517i	$-0.360517\pi$
$491$	18.8041			0.848618			0.424309	+	0.905517i	$0.360517\pi$
$492$	−6.28685	+	10.8892i	−0.283433	+	0.490921i
$493$	−8.24109	−	14.2740i	−0.371160	−	0.642868i
$494$	−7.72374	−	13.3779i	−0.347508	−	0.601901i
$495$	−0.500000	+	0.866025i	−0.0224733	+	0.0389249i
$496$	−11.0494			−0.496131
$497$	−20.7556	+	12.8514i	−0.931015	+	0.576462i
$498$	−6.06454			−0.271759
$499$	11.8987	−	20.6092i	0.532661	−	0.922596i	−0.466612	−	0.884462i	$-0.654525\pi$
$499$	11.8987	−	20.6092i	0.532661	−	0.922596i	0.999273	−	0.0381336i	$-0.0121413\pi$
$500$	−0.811163	−	1.40498i	−0.0362763	−	0.0628324i
$501$	−7.24161	−	12.5428i	−0.323531	−	0.560373i
$502$	7.10558	−	12.3072i	0.317138	−	0.549299i
$503$	18.7373			0.835453			0.417727	−	0.908573i	$-0.362827\pi$
$503$	18.7373			0.835453			0.417727	+	0.908573i	$0.362827\pi$
$504$	−0.181383	−	5.88693i	−0.00807946	−	0.262225i
$505$	12.8915			0.573666
$506$	1.35344	−	2.34423i	0.0601679	−	0.104214i
$507$	0.177483	+	0.307410i	0.00788232	+	0.0136526i
$508$	7.21492	+	12.4966i	0.320110	+	0.554447i
$509$	−18.0975	+	31.3458i	−0.802157	+	1.38938i	0.116036	+	0.993245i	$0.462981\pi$
$509$	−18.0975	+	31.3458i	−0.802157	+	1.38938i	−0.918194	+	0.396132i	$0.870352\pi$
$510$	−3.22311			−0.142722
$511$	15.2393	+	8.18332i	0.674149	+	0.362009i
$512$	−18.8742			−0.834130
$513$	−3.53435	+	6.12167i	−0.156045	+	0.270278i
$514$	−1.43047	−	2.47764i	−0.0630951	−	0.109284i
$515$	−6.52248	−	11.2973i	−0.287415	−	0.497817i
$516$	4.23462	−	7.33458i	0.186419	−	0.322887i
$517$	−11.1443			−0.490124
$518$	5.58386	+	2.99846i	0.245341	+	0.131745i
$519$	−5.00424			−0.219662
$520$	−3.95800	+	6.85546i	−0.173570	+	0.300632i
$521$	−5.55256	−	9.61731i	−0.243262	−	0.421342i	0.718380	−	0.695651i	$-0.244884\pi$
$521$	−5.55256	−	9.61731i	−0.243262	−	0.421342i	−0.961642	+	0.274309i	$0.911551\pi$
$522$	−0.965664	−	1.67258i	−0.0422660	−	0.0732068i
$523$	−8.14003	+	14.0989i	−0.355938	+	0.616504i	−0.987278	−	0.159003i	$-0.949172\pi$
$523$	−8.14003	+	14.0989i	−0.355938	+	0.616504i	0.631340	+	0.775506i	$0.282505\pi$
$524$	22.4009			0.978587
$525$	−0.0814802	−	2.64450i	−0.00355609	−	0.115415i
$526$	3.78901			0.165209
$527$	−15.4402	+	26.7433i	−0.672587	+	1.16495i
$528$	0.938298	+	1.62518i	0.0408342	+	0.0707269i
$529$	1.79951	+	3.11685i	0.0782397	+	0.135515i
$530$	0.982278	−	1.70135i	0.0426674	−	0.0739021i
$531$	−4.34543			−0.188576
$532$	25.7962	−	15.9724i	1.11841	−	0.692491i
$533$	27.5604			1.19377
$534$	1.40260	−	2.42937i	0.0606963	−	0.105129i
$535$	−4.79437	−	8.30409i	−0.207279	−	0.359017i
$536$	−2.34175	−	4.05603i	−0.101148	−	0.175194i
$537$	2.46905	−	4.27652i	0.106547	−	0.184546i
$538$	−6.65630			−0.286973
$539$	6.98672	−	0.430948i	0.300939	−	0.0185622i
$540$	1.62233			0.0698138
$541$	−15.3153	+	26.5268i	−0.658455	+	1.14048i	0.322560	+	0.946549i	$0.395457\pi$
$541$	−15.3153	+	26.5268i	−0.658455	+	1.14048i	−0.981016	+	0.193929i	$0.937877\pi$
$542$	7.29326	+	12.6323i	0.313272	+	0.542604i
$543$	−3.40659	−	5.90038i	−0.146191	−	0.253210i
$544$	−14.6994	+	25.4601i	−0.630231	+	1.09159i
$545$	5.45737			0.233768
$546$	−4.91583	+	3.04376i	−0.210378	+	0.130261i
$547$	33.7600			1.44348			0.721738	−	0.692167i	$-0.243344\pi$
$547$	33.7600			1.44348			0.721738	+	0.692167i	$0.243344\pi$
$548$	12.8183	−	22.2019i	0.547570	−	0.948419i
$549$	−6.99976	−	12.1239i	−0.298743	−	0.517437i
$550$	−0.307276	−	0.532217i	−0.0131023	−	0.0226938i
$551$	11.1073	−	19.2383i	0.473185	−	0.819581i
$552$	−9.80523			−0.417338
$553$	0.647442	+	21.0132i	0.0275321	+	0.893572i
$554$	−11.2148			−0.476472
$555$	−1.94901	+	3.37579i	−0.0827310	+	0.143294i
$556$	−16.3919	−	28.3917i	−0.695173	−	1.20407i
$557$	12.2577	+	21.2310i	0.519376	+	0.899585i	0.999746	+	0.0225195i	$0.00716879\pi$
$557$	12.2577	+	21.2310i	0.519376	+	0.899585i	−0.480371	+	0.877066i	$0.659498\pi$
$558$	−1.80924	+	3.13369i	−0.0765911	+	0.132660i
$559$	−18.5638			−0.785165
$560$	−4.37423	−	2.34891i	−0.184845	−	0.0992594i
$561$	5.24465			0.221429
$562$	5.16775	−	8.95081i	0.217988	−	0.377567i
$563$	3.82774	+	6.62984i	0.161320	+	0.279414i	0.935342	−	0.353744i	$-0.115092\pi$
$563$	3.82774	+	6.62984i	0.161320	+	0.279414i	−0.774022	+	0.633158i	$0.781758\pi$
$564$	9.03982	+	15.6574i	0.380645	+	0.659297i
$565$	−9.40617	+	16.2920i	−0.395721	+	0.685408i
$566$	−16.4738			−0.692444
$567$	2.33094	+	1.25168i	0.0978903	+	0.0525658i
$568$	20.5401			0.861843
$569$	9.10512	−	15.7705i	0.381706	−	0.661135i	−0.609600	−	0.792709i	$-0.708670\pi$
$569$	9.10512	−	15.7705i	0.381706	−	0.661135i	0.991306	+	0.131574i	$0.0420032\pi$
$570$	−2.17204	−	3.76208i	−0.0909767	−	0.157576i
$571$	3.52555	+	6.10643i	0.147540	+	0.255546i	0.930318	−	0.366755i	$-0.119531\pi$
$571$	3.52555	+	6.10643i	0.147540	+	0.255546i	−0.782778	+	0.622301i	$0.786198\pi$
$572$	2.88448	−	4.99607i	0.120606	−	0.208896i
$573$	0.0310673			0.00129785
$574$	−0.388093	−	12.5958i	−0.0161987	−	0.525739i
$575$	−4.40465			−0.183687
$576$	0.154168	−	0.267027i	0.00642367	−	0.0111261i
$577$	−23.9156	−	41.4230i	−0.995620	−	1.72446i	−0.578780	−	0.815484i	$-0.696471\pi$
$577$	−23.9156	−	41.4230i	−0.995620	−	1.72446i	−0.416840	−	0.908980i	$-0.636863\pi$
$578$	3.22836	+	5.59168i	0.134282	+	0.232583i
$579$	−10.2888	+	17.8207i	−0.427587	+	0.740603i
$580$	−5.09842			−0.211701
$581$	−22.1982	+	13.7446i	−0.920938	+	0.570222i
$582$	−6.79570			−0.281691
$583$	−1.59836	+	2.76845i	−0.0661975	+	0.114657i
$584$	−7.27697	−	12.6041i	−0.301123	−	0.521561i
$585$	−1.77799	−	3.07957i	−0.0735110	−	0.127325i
$586$	2.30585	−	3.99385i	0.0952538	−	0.164984i
$587$	33.0232			1.36301			0.681507	−	0.731811i	$-0.261325\pi$
$587$	33.0232			1.36301			0.681507	+	0.731811i	$0.261325\pi$
$588$	−6.27284	−	9.46661i	−0.258688	−	0.390396i
$589$	−41.6204			−1.71494
$590$	1.33525	−	2.31271i	0.0549712	−	0.0952129i
$591$	−7.54000	−	13.0597i	−0.310154	−	0.537203i
$592$	3.65751	+	6.33499i	0.150323	+	0.260366i
$593$	6.55842	−	11.3595i	0.269322	−	0.466480i	−0.699365	−	0.714765i	$-0.746534\pi$
$593$	6.55842	−	11.3595i	0.269322	−	0.466480i	0.968687	+	0.248285i	$0.0798670\pi$
$594$	0.614552			0.0252154
$595$	−11.7976	+	7.30482i	−0.483656	+	0.299468i
$596$	−28.5192			−1.16819
$597$	−8.81979	+	15.2763i	−0.360970	+	0.625219i
$598$	4.81283	+	8.33606i	0.196811	+	0.340887i
$599$	9.83894	+	17.0415i	0.402008	+	0.696299i	0.993968	−	0.109669i	$-0.0349790\pi$
$599$	9.83894	+	17.0415i	0.402008	+	0.696299i	−0.591960	+	0.805967i	$0.701646\pi$
$600$	−1.11305	+	1.92786i	−0.0454402	+	0.0787047i
$601$	25.5309			1.04143			0.520714	−	0.853731i	$-0.325666\pi$
$601$	25.5309			1.04143			0.520714	+	0.853731i	$0.325666\pi$
$602$	0.261407	+	8.48414i	0.0106541	+	0.345788i
$603$	2.10390			0.0856774
$604$	−8.78036	+	15.2080i	−0.357268	+	0.618806i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	−3.96126	−	6.86110i	−0.160915	−	0.278713i
$607$	−14.8999	+	25.8074i	−0.604768	+	1.04749i	0.387320	+	0.921945i	$0.373401\pi$
$607$	−14.8999	+	25.8074i	−0.604768	+	1.04749i	−0.992088	+	0.125544i	$0.959932\pi$
$608$	−39.6234			−1.60694
$609$	−7.32536	−	3.93362i	−0.296839	−	0.159398i
$610$	8.60343			0.348343
$611$	19.8144	−	34.3196i	0.801606	−	1.38842i
$612$	−4.25427	−	7.36861i	−0.171969	−	0.297858i
$613$	9.22800	+	15.9834i	0.372715	+	0.645562i	0.989982	−	0.141192i	$-0.0450934\pi$
$613$	9.22800	+	15.9834i	0.372715	+	0.645562i	−0.617267	+	0.786754i	$0.711760\pi$
$614$	4.79723	−	8.30905i	0.193600	−	0.335326i
$615$	7.75042			0.312527
$616$	−5.18892	−	2.78638i	−0.209068	−	0.112267i
$617$	5.33228			0.214669			0.107335	−	0.994223i	$-0.465768\pi$
$617$	5.33228			0.214669			0.107335	+	0.994223i	$0.465768\pi$
$618$	−4.00840	+	6.94276i	−0.161242	+	0.279279i
$619$	−7.47118	−	12.9405i	−0.300292	−	0.520121i	0.675910	−	0.736984i	$-0.263751\pi$
$619$	−7.47118	−	12.9405i	−0.300292	−	0.520121i	−0.976202	+	0.216863i	$0.930417\pi$
$620$	4.77612	+	8.27248i	0.191814	+	0.332231i
$621$	2.20233	−	3.81454i	0.0883763	−	0.153072i
$622$	−15.4575			−0.619790
$623$	−0.371926	−	12.0711i	−0.0149009	−	0.483619i
$624$	−6.67315			−0.267140
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.86002	+	11.8819i	0.274182	+	0.474897i
$627$	3.53435	+	6.12167i	0.141148	+	0.244476i
$628$	2.74389	−	4.75256i	0.109493	−	0.189648i
$629$	20.4438			0.815147
$630$	−1.38241	+	0.855955i	−0.0550765	+	0.0341021i
$631$	40.9589			1.63055			0.815274	−	0.579075i	$-0.196586\pi$
$631$	40.9589			1.63055			0.815274	+	0.579075i	$0.196586\pi$
$632$	8.84434	−	15.3188i	0.351809	−	0.609351i
$633$	2.84810	+	4.93306i	0.113202	+	0.196071i
$634$	−0.182207	−	0.315592i	−0.00723637	−	0.0125338i
$635$	4.44727	−	7.70289i	0.176484	−	0.305680i
$636$	5.18614			0.205644
$637$	−11.0952	+	22.2823i	−0.439608	+	0.882859i
$638$	−1.93133			−0.0764620
$639$	−4.61345	+	7.99074i	−0.182505	+	0.316109i
$640$	5.70022	+	9.87307i	0.225321	+	0.390268i
$641$	8.72949	+	15.1199i	0.344794	+	0.597201i	0.985316	−	0.170739i	$-0.0546154\pi$
$641$	8.72949	+	15.1199i	0.344794	+	0.597201i	−0.640522	+	0.767940i	$0.721282\pi$
$642$	−2.94639	+	5.10329i	−0.116285	+	0.201411i
$643$	43.2616			1.70607			0.853035	−	0.521853i	$-0.174759\pi$
$643$	43.2616			1.70607			0.853035	+	0.521853i	$0.174759\pi$
$644$	−16.0742	+	9.95274i	−0.633411	+	0.392193i
$645$	−5.22043			−0.205554
$646$	−11.3916	+	19.7308i	−0.448196	+	0.776299i
$647$	3.72140	+	6.44565i	0.146303	+	0.253405i	0.929858	−	0.367918i	$-0.119929\pi$
$647$	3.72140	+	6.44565i	0.146303	+	0.253405i	−0.783555	+	0.621322i	$0.786596\pi$
$648$	−1.11305	−	1.92786i	−0.0437249	−	0.0757337i
$649$	−2.17271	+	3.76325i	−0.0852865	+	0.147721i
$650$	2.18534			0.0857160
$651$	0.479754	+	15.5708i	0.0188031	+	0.610266i
$652$	−13.4725			−0.527624
$653$	10.2984	−	17.8373i	0.403007	−	0.698029i	−0.591080	−	0.806613i	$-0.701298\pi$
$653$	10.2984	−	17.8373i	0.403007	−	0.698029i	0.994087	+	0.108584i	$0.0346317\pi$
$654$	−1.67692	−	2.90451i	−0.0655727	−	0.113575i
$655$	−6.90394	−	11.9580i	−0.269759	−	0.467237i
$656$	7.27220	−	12.5958i	0.283932	−	0.491784i
$657$	6.53785			0.255066
$658$	−15.9640	−	8.57245i	−0.622341	−	0.334189i
$659$	−29.9225			−1.16561			−0.582807	−	0.812610i	$-0.698046\pi$
$659$	−29.9225			−1.16561			−0.582807	+	0.812610i	$0.698046\pi$
$660$	0.811163	−	1.40498i	0.0315745	−	0.0546886i
$661$	0.252760	+	0.437792i	0.00983121	+	0.0170282i	0.870899	−	0.491462i	$-0.163537\pi$
$661$	0.252760	+	0.437792i	0.00983121	+	0.0170282i	−0.861068	+	0.508490i	$0.830204\pi$
$662$	−5.38484	−	9.32681i	−0.209288	−	0.362497i
$663$	−9.32495	+	16.1513i	−0.362151	+	0.627264i
$664$	21.9678			0.852514
$665$	−16.4767	−	8.84778i	−0.638940	−	0.343102i
$666$	2.39554			0.0928252
$667$	−6.92117	+	11.9878i	−0.267989	+	0.464170i
$668$	11.7483	+	20.3486i	0.454554	+	0.787310i
$669$	5.78176	+	10.0143i	0.223536	+	0.387176i
$670$	−0.646477	+	1.11973i	−0.0249756	+	0.0432590i
$671$	−13.9995			−0.540446
$672$	0.456735	+	14.8237i	0.0176189	+	0.571835i
$673$	19.3382			0.745433			0.372717	−	0.927945i	$-0.378426\pi$
$673$	19.3382			0.745433			0.372717	+	0.927945i	$0.378426\pi$
$674$	−1.30235	+	2.25573i	−0.0501645	+	0.0868875i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−0.287936	−	0.498720i	−0.0110745	−	0.0191815i
$677$	18.4400	−	31.9390i	0.708706	−	1.22751i	−0.256632	−	0.966509i	$-0.582613\pi$
$677$	18.4400	−	31.9390i	0.708706	−	1.22751i	0.965338	−	0.261005i	$-0.0840538\pi$
$678$	11.5612			0.444003
$679$	−24.8745	+	15.4017i	−0.954596	+	0.591063i
$680$	11.6752			0.447722
$681$	−3.61867	+	6.26772i	−0.138668	+	0.240180i
$682$	1.80924	+	3.13369i	0.0692792	+	0.119995i
$683$	2.34485	+	4.06140i	0.0897231	+	0.155405i	0.907394	−	0.420281i	$-0.138068\pi$
$683$	2.34485	+	4.06140i	0.0897231	+	0.155405i	−0.817671	+	0.575686i	$0.804735\pi$
$684$	5.73387	−	9.93135i	0.219240	−	0.379735i
$685$	−15.8024			−0.603777
$686$	10.3399	+	4.75703i	0.394778	+	0.181624i
$687$	−19.1818			−0.731832
$688$	−4.89832	+	8.48414i	−0.186747	+	0.323455i
$689$	−5.68376	−	9.84456i	−0.216534	−	0.375048i
$690$	1.35344	+	2.34423i	0.0515247	+	0.0892434i
$691$	−19.2866	+	33.4054i	−0.733697	+	1.27080i	0.221596	+	0.975138i	$0.428873\pi$
$691$	−19.2866	+	33.4054i	−0.733697	+	1.27080i	−0.955293	+	0.295661i	$0.904460\pi$
$692$	8.11851			0.308619
$693$	2.24946	−	1.39281i	0.0854500	−	0.0529086i
$694$	11.3889			0.432318
$695$	−10.1040	+	17.5006i	−0.383265	+	0.663835i
$696$	3.49795	+	6.05863i	0.132589	+	0.229652i
$697$	−20.3241	−	35.2024i	−0.769831	−	1.33339i
$698$	10.4516	−	18.1026i	0.395597	−	0.685195i
$699$	16.5084			0.624405
$700$	0.132187	+	4.29024i	0.00499621	+	0.162156i
$701$	−19.6110			−0.740698			−0.370349	−	0.928893i	$-0.620762\pi$
$701$	−19.6110			−0.740698			−0.370349	+	0.928893i	$0.620762\pi$
$702$	−1.09267	+	1.89256i	−0.0412401	+	0.0714300i
$703$	13.7770	+	23.8624i	0.519609	+	0.899988i
$704$	−0.154168	−	0.267027i	−0.00581043	−	0.0100640i
$705$	5.57213	−	9.65122i	0.209859	−	0.363486i
$706$	3.66645			0.137989
$707$	−30.0494	−	16.1361i	−1.13012	−	0.606862i
$708$	7.04970			0.264944
$709$	1.44626	−	2.50500i	0.0543155	−	0.0940773i	−0.837589	−	0.546301i	$-0.816036\pi$
$709$	1.44626	−	2.50500i	0.0543155	−	0.0940773i	0.891905	+	0.452223i	$0.149369\pi$
$710$	−2.83521	−	4.91072i	−0.106403	−	0.184296i
$711$	3.97301	+	6.88145i	0.148999	+	0.258075i
$712$	−5.08066	+	8.79996i	−0.190406	+	0.329793i
$713$	25.9346			0.971257
$714$	7.51288	+	4.03432i	0.281162	+	0.150980i
$715$	−3.55599			−0.132986
$716$	−4.00561	+	6.93792i	−0.149697	+	0.259282i
$717$	11.0037	+	19.0590i	0.410942	+	0.711772i
$718$	−1.49917	−	2.59664i	−0.0559486	−	0.0969058i
$719$	−1.10132	+	1.90754i	−0.0410723	+	0.0711393i	−0.885831	−	0.464008i	$-0.846411\pi$
$719$	−1.10132	+	1.90754i	−0.0410723	+	0.0711393i	0.844758	+	0.535148i	$0.179744\pi$
$720$	−1.87660			−0.0699366
$721$	1.06291	+	34.4974i	0.0395847	+	1.28475i
$722$	−19.0305			−0.708242
$723$	−3.54788	+	6.14511i	−0.131947	+	0.228539i
$724$	5.52660	+	9.57235i	0.205394	+	0.355754i
$725$	1.57133	+	2.72163i	0.0583578	+	0.101079i
$726$	0.307276	−	0.532217i	0.0114041	−	0.0197524i
$727$	−31.2118			−1.15758			−0.578791	−	0.815476i	$-0.696475\pi$
$727$	−31.2118			−1.15758			−0.578791	+	0.815476i	$0.696475\pi$
$728$	17.8067	−	11.0255i	0.659962	−	0.408632i
$729$	1.00000			0.0370370
$730$	−2.00892	+	3.47956i	−0.0743536	+	0.128784i
$731$	13.6897	+	23.7112i	0.506331	+	0.876991i
$732$	11.3559	+	19.6690i	0.419726	+	0.726987i
$733$	1.30500	−	2.26033i	0.0482014	−	0.0834873i	−0.840918	−	0.541162i	$-0.817984\pi$
$733$	1.30500	−	2.26033i	0.0482014	−	0.0834873i	0.889119	+	0.457675i	$0.151318\pi$
$734$	16.6919			0.616111
$735$	−3.12015	+	6.26615i	−0.115088	+	0.231131i
$736$	24.6902			0.910092
$737$	1.05195	−	1.82203i	0.0387491	−	0.0671153i
$738$	−2.38152	−	4.12491i	−0.0876648	−	0.151840i
$739$	26.8715	+	46.5428i	0.988484	+	1.71211i	0.625292	+	0.780391i	$0.284980\pi$
$739$	26.8715	+	46.5428i	0.988484	+	1.71211i	0.363192	+	0.931714i	$0.381687\pi$
$740$	3.16193	−	5.47663i	0.116235	−	0.201325i
$741$	−25.1362			−0.923401
$742$	−4.41919	+	2.73626i	−0.162234	+	0.100451i
$743$	−26.3101			−0.965225			−0.482613	−	0.875834i	$-0.660312\pi$
$743$	−26.3101			−0.965225			−0.482613	+	0.875834i	$0.660312\pi$
$744$	6.55364	−	11.3512i	0.240268	−	0.416157i
$745$	8.78961	+	15.2241i	0.322026	+	0.557766i
$746$	0.204051	+	0.353427i	0.00747084	+	0.0129399i
$747$	−4.93412	+	8.54615i	−0.180530	+	0.312687i
$748$	−8.50854			−0.311103
$749$	0.781291	+	25.3574i	0.0285478	+	0.926538i
$750$	0.614552			0.0224403
$751$	−22.7478	+	39.4003i	−0.830079	+	1.43774i	0.0678967	+	0.997692i	$0.478371\pi$
$751$	−22.7478	+	39.4003i	−0.830079	+	1.43774i	−0.897975	+	0.440046i	$0.854962\pi$
$752$	−10.4566	−	18.1114i	−0.381315	−	0.660456i
$753$	−11.5622	−	20.0264i	−0.421351	−	0.729801i
$754$	3.43389	−	5.94767i	0.125055	−	0.216601i
$755$	10.8244			0.393941
$756$	−3.78155	−	2.03064i	−0.137534	−	0.0738537i
$757$	5.41391			0.196772			0.0983859	−	0.995148i	$-0.468632\pi$
$757$	5.41391			0.196772			0.0983859	+	0.995148i	$0.468632\pi$
$758$	1.77447	−	3.07346i	0.0644515	−	0.111633i
$759$	−2.20233	−	3.81454i	−0.0799394	−	0.138459i
$760$	7.86784	+	13.6275i	0.285396	+	0.494321i
$761$	−15.3115	+	26.5203i	−0.555041	+	0.961359i	0.442860	+	0.896591i	$0.353964\pi$
$761$	−15.3115	+	26.5203i	−0.555041	+	0.961359i	−0.997900	+	0.0647679i	$0.979369\pi$
$762$	−5.46615			−0.198018
$763$	−12.7208	−	6.83091i	−0.460524	−	0.247295i
$764$	−0.0504013			−0.00182345
$765$	−2.62233	+	4.54200i	−0.0948104	+	0.164216i
$766$	3.99762	+	6.92409i	0.144440	+	0.250178i
$767$	−7.72614	−	13.3821i	−0.278975	−	0.483198i
$768$	3.19474	−	5.53346i	0.115280	−	0.199672i
$769$	−34.8540			−1.25687			−0.628434	−	0.777863i	$-0.716304\pi$
$769$	−34.8540			−1.25687			−0.628434	+	0.777863i	$0.716304\pi$
$770$	0.0500738	+	1.62518i	0.00180453	+	0.0585674i
$771$	−4.65531			−0.167657
$772$	16.6918	−	28.9110i	0.600750	−	1.04053i
$773$	10.3018	+	17.8433i	0.370530	+	0.641778i	0.989647	−	0.143521i	$-0.0458426\pi$
$773$	10.3018	+	17.8433i	0.370530	+	0.641778i	−0.619117	+	0.785299i	$0.712509\pi$
$774$	1.60411	+	2.77841i	0.0576587	+	0.0998677i
$775$	2.94399	−	5.09915i	0.105751	−	0.183167i
$776$	24.6163			0.883672
$777$	8.76845	−	5.42922i	0.314567	−	0.194772i
$778$	16.2031			0.580908
$779$	27.3927	−	47.4455i	0.981445	−	1.69991i
$780$	2.88448	+	4.99607i	0.103281	+	0.178888i
$781$	4.61345	+	7.99074i	0.165082	+	0.285931i
$782$	7.09834	−	12.2947i	0.253836	−	0.439657i
$783$	−3.14266			−0.112310
$784$	7.25599	+	10.9503i	0.259143	+	0.391083i
$785$	−3.38267			−0.120733
$786$	−4.24283	+	7.34879i	−0.151337	+	0.262123i
$787$	−25.1270	−	43.5213i	−0.895682	−	1.55137i	−0.832958	−	0.553336i	$-0.813355\pi$
$787$	−25.1270	−	43.5213i	−0.895682	−	1.55137i	−0.0627238	−	0.998031i	$-0.519979\pi$
$788$	12.2323	+	21.1870i	0.435759	+	0.754757i
$789$	3.08275	−	5.33947i	0.109749	−	0.190090i
$790$	−4.88324			−0.173738
$791$	42.3176	−	26.2021i	1.50464	−	0.931638i
$792$	−2.22611			−0.0791012
$793$	24.8911	−	43.1126i	0.883908	−	1.53097i
$794$	2.18215	+	3.77959i	0.0774414	+	0.134132i
$795$	−1.59836	−	2.76845i	−0.0566882	−	0.0981868i
$796$	14.3086	−	24.7832i	0.507154	−	0.878417i
$797$	47.7164			1.69020			0.845101	−	0.534606i	$-0.179540\pi$
$797$	47.7164			1.69020			0.845101	+	0.534606i	$0.179540\pi$
$798$	0.353956	+	11.4879i	0.0125299	+	0.406667i
$799$	−58.4478			−2.06774
$800$	2.80274	−	4.85449i	0.0990918	−	0.171632i
$801$	−2.28231	−	3.95307i	−0.0806414	−	0.139675i
$802$	2.36024	+	4.08805i	0.0833428	+	0.144354i
$803$	3.26892	−	5.66194i	0.115358	−	0.199806i
$804$	−3.41321			−0.120375
$805$	10.2670	+	5.51324i	0.361864	+	0.194316i
$806$	−12.8672			−0.453229
$807$	−5.41557	+	9.38005i	−0.190637	+	0.330193i
$808$	14.3490	+	24.8531i	0.504795	+	0.874331i
$809$	2.57153	+	4.45402i	0.0904102	+	0.156595i	0.907684	−	0.419655i	$-0.137849\pi$
$809$	2.57153	+	4.45402i	0.0904102	+	0.156595i	−0.817274	+	0.576250i	$0.804516\pi$
$810$	−0.307276	+	0.532217i	−0.0107966	+	0.0187002i
$811$	29.2009			1.02538			0.512692	−	0.858573i	$-0.328648\pi$
$811$	29.2009			1.02538			0.512692	+	0.858573i	$0.328648\pi$
$812$	11.8841	+	6.38162i	0.417051	+	0.223951i
$813$	23.7352			0.832431
$814$	1.19777	−	2.07460i	0.0419818	−	0.0727146i
$815$	4.15221	+	7.19185i	0.145446	+	0.251919i
$816$	4.92105	+	8.52350i	0.172271	+	0.298382i
$817$	−18.4508	+	31.9578i	−0.645513	+	1.11806i
$818$	−13.4238			−0.469351
$819$	0.289742	+	9.40379i	0.0101244	+	0.328595i
$820$	−12.5737			−0.439093
$821$	22.1435	−	38.3537i	0.772814	−	1.33855i	−0.163201	−	0.986593i	$-0.552182\pi$
$821$	22.1435	−	38.3537i	0.772814	−	1.33855i	0.936015	−	0.351960i	$-0.114485\pi$
$822$	4.85568	+	8.41029i	0.169361	+	0.293342i
$823$	−14.2084	−	24.6096i	−0.495272	−	0.857837i	0.504713	−	0.863287i	$-0.331598\pi$
$823$	−14.2084	−	24.6096i	−0.495272	−	0.857837i	−0.999985	+	0.00545059i	$0.998265\pi$
$824$	14.5197	−	25.1489i	0.505819	−	0.876105i
$825$	−1.00000			−0.0348155
$826$	−6.00716	+	3.71949i	−0.209016	+	0.129418i
$827$	−8.39069			−0.291773			−0.145887	−	0.989301i	$-0.546603\pi$
$827$	−8.39069			−0.291773			−0.145887	+	0.989301i	$0.546603\pi$
$828$	−3.57289	+	6.18843i	−0.124167	+	0.215063i
$829$	4.25334	+	7.36699i	0.147724	+	0.255866i	0.930386	−	0.366581i	$-0.119472\pi$
$829$	4.25334	+	7.36699i	0.147724	+	0.255866i	−0.782662	+	0.622447i	$0.786138\pi$
$830$	−3.03227	−	5.25205i	−0.105252	−	0.182301i
$831$	−9.12439	+	15.8039i	−0.316521	+	0.548231i
$832$	1.09644			0.0380122
$833$	36.6429	−	2.26017i	1.26960	−	0.0783103i
$834$	12.4188			0.430029
$835$	7.24161	−	12.5428i	0.250606	−	0.434063i
$836$	−5.73387	−	9.93135i	−0.198310	−	0.343483i
$837$	2.94399	+	5.09915i	0.101759	+	0.176252i
$838$	11.4273	−	19.7927i	0.394751	−	0.683729i
$839$	7.12029			0.245820			0.122910	−	0.992418i	$-0.460777\pi$
$839$	7.12029			0.245820			0.122910	+	0.992418i	$0.460777\pi$
$840$	5.00754	−	3.10055i	0.172777	−	0.106979i
$841$	−19.1237			−0.659437
$842$	7.29067	−	12.6278i	0.251253	−	0.435183i
$843$	−8.40898	−	14.5648i	−0.289621	−	0.501637i
$844$	−4.62055	−	8.00303i	−0.159046	−	0.275476i
$845$	−0.177483	+	0.307410i	−0.00610562	+	0.0105752i
$846$	−6.84873			−0.235464
$847$	−0.0814802	−	2.64450i	−0.00279969	−	0.0908660i
$848$	−5.99897			−0.206005
$849$	−13.4031	+	23.2148i	−0.459992	+	0.796730i
$850$	−1.61155	−	2.79129i	−0.0552759	−	0.0957406i
$851$	−8.58472	−	14.8692i	−0.294281	−	0.509709i
$852$	7.48453	−	12.9636i	0.256416	−	0.444125i
$853$	−40.2329			−1.37755			−0.688775	−	0.724976i	$-0.741851\pi$
$853$	−40.2329			−1.37755			−0.688775	+	0.724976i	$0.741851\pi$
$854$	−20.0541	−	10.7688i	−0.686237	−	0.368500i
$855$	−7.06870			−0.241744
$856$	10.6728	−	18.4858i	0.364788	−	0.631831i
$857$	18.5924	+	32.2030i	0.635106	+	1.10004i	0.986493	+	0.163805i	$0.0523768\pi$
$857$	18.5924	+	32.2030i	0.635106	+	1.10004i	−0.351387	+	0.936230i	$0.614290\pi$
$858$	1.09267	+	1.89256i	0.0373031	+	0.0646108i
$859$	14.0188	−	24.2813i	0.478315	−	0.828466i	−0.521376	−	0.853327i	$-0.674581\pi$
$859$	14.0188	−	24.2813i	0.478315	−	0.828466i	0.999691	+	0.0248610i	$0.00791432\pi$
$860$	8.46925			0.288799
$861$	−18.0658	−	9.70108i	−0.615680	−	0.330612i
$862$	8.57611			0.292104
$863$	−3.87127	+	6.70524i	−0.131780	+	0.228249i	−0.924363	−	0.381515i	$-0.875402\pi$
$863$	−3.87127	+	6.70524i	−0.131780	+	0.228249i	0.792583	+	0.609764i	$0.208736\pi$
$864$	2.80274	+	4.85449i	0.0953511	+	0.165153i
$865$	−2.50212	−	4.33380i	−0.0850746	−	0.147354i
$866$	−11.2103	+	19.4168i	−0.380941	+	0.659809i
$867$	10.5064			0.356815
$868$	−0.778318	−	25.2609i	−0.0264178	−	0.857410i
$869$	7.94601			0.269550
$870$	0.965664	−	1.67258i	0.0327391	−	0.0567058i
$871$	3.74072	+	6.47911i	0.126749	+	0.219536i
$872$	6.07434	+	10.5211i	0.205703	+	0.356288i
$873$	−5.52899	+	9.57650i	−0.187128	+	0.324115i
$874$	19.1342			0.647223
$875$	2.24946	−	1.39281i	0.0760457	−	0.0470856i
$876$	−10.6065			−0.358361
$877$	−2.28687	+	3.96098i	−0.0772222	+	0.133753i	−0.902050	−	0.431631i	$-0.857938\pi$
$877$	−2.28687	+	3.96098i	−0.0772222	+	0.133753i	0.824828	+	0.565383i	$0.191272\pi$
$878$	−9.55303	−	16.5463i	−0.322399	−	0.558412i
$879$	−3.75209	−	6.49881i	−0.126555	−	0.219199i
$880$	−0.938298	+	1.62518i	−0.0316300	+	0.0547848i
$881$	19.0331			0.641242			0.320621	−	0.947208i	$-0.396108\pi$
$881$	19.0331			0.641242			0.320621	+	0.947208i	$0.396108\pi$
$882$	4.29370	−	0.264840i	0.144576	−	0.00891762i
$883$	16.9105			0.569083			0.284542	−	0.958664i	$-0.408159\pi$
$883$	16.9105			0.569083			0.284542	+	0.958664i	$0.408159\pi$
$884$	15.1281	−	26.2027i	0.508814	−	0.881291i
$885$	−2.17271	−	3.76325i	−0.0730350	−	0.126500i
$886$	−4.77787	−	8.27551i	−0.160516	−	0.278021i
$887$	−17.5626	+	30.4193i	−0.589695	+	1.02138i	0.404577	+	0.914504i	$0.367419\pi$
$887$	−17.5626	+	30.4193i	−0.589695	+	1.02138i	−0.994272	+	0.106878i	$0.965915\pi$
$888$	−8.67742			−0.291195
$889$	−20.0079	+	12.3884i	−0.671044	+	0.415494i
$890$	2.80519			0.0940303
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−9.37991	−	16.2465i	−0.314063	−	0.543972i
$893$	−39.3877	−	68.2216i	−1.31806	−	2.28295i
$894$	5.40167	−	9.35596i	0.180659	−	0.312910i
$895$	4.93811			0.165063
$896$	−0.928910	−	30.1484i	−0.0310327	−	1.00719i
$897$	15.6629			0.522969
$898$	5.17974	−	8.97157i	0.172850	−	0.299385i
$899$	−9.25198	−	16.0249i	−0.308571	−	0.534460i
$900$	0.811163	+	1.40498i	0.0270388	+	0.0468325i
$901$	−8.38287	+	14.5196i	−0.279274	+	0.483716i
$902$	−4.76303			−0.158592
$903$	12.1685	+	6.53434i	0.404943	+	0.217449i
$904$	−41.8783			−1.39285
$905$	3.40659	−	5.90038i	0.113239	−	0.196135i
$906$	−3.32608	−	5.76094i	−0.110502	−	0.191394i
$907$	−13.8949	−	24.0667i	−0.461373	−	0.799121i	0.537657	−	0.843164i	$-0.319310\pi$
$907$	−13.8949	−	24.0667i	−0.461373	−	0.799121i	−0.999030	+	0.0440426i	$0.985976\pi$
$908$	5.87066	−	10.1683i	0.194825	−	0.337446i
$909$	−12.8915			−0.427585
$910$	−5.09389	−	2.73535i	−0.168861	−	0.0906760i
$911$	−19.6672			−0.651605			−0.325802	−	0.945438i	$-0.605634\pi$
$911$	−19.6672			−0.651605			−0.325802	+	0.945438i	$0.605634\pi$
$912$	−6.63254	+	11.4879i	−0.219625	+	0.380402i
$913$	4.93412	+	8.54615i	0.163296	+	0.282836i
$914$	10.5234	+	18.2270i	0.348082	+	0.602895i
$915$	6.99976	−	12.1239i	0.231405	−	0.400805i
$916$	31.1192			1.02821
$917$	1.12507	+	36.5149i	0.0371530	+	1.20583i
$918$	3.22311			0.106378
$919$	−2.07661	+	3.59679i	−0.0685010	+	0.118647i	−0.898242	−	0.439502i	$-0.855155\pi$
$919$	−2.07661	+	3.59679i	−0.0685010	+	0.118647i	0.829741	+	0.558149i	$0.188488\pi$
$920$	−4.90261	−	8.49158i	−0.161634	−	0.279959i
$921$	−7.80606	−	13.5205i	−0.257219	−	0.445516i
$922$	1.84279	−	3.19181i	0.0606891	−	0.105117i
$923$	−32.8108			−1.07998
$924$	−3.64936	+	2.25960i	−0.120055	+	0.0743352i
$925$	−3.89802			−0.128166
$926$	8.07934	−	13.9938i	0.265504	−	0.459866i
$927$	6.52248	+	11.2973i	0.214227	+	0.371051i
$928$	−8.80806	−	15.2560i	−0.289139	−	0.500803i
$929$	−4.64447	+	8.04445i	−0.152380	+	0.263930i	−0.932102	−	0.362196i	$-0.882027\pi$
$929$	−4.64447	+	8.04445i	−0.152380	+	0.263930i	0.779722	+	0.626126i	$0.215360\pi$
$930$	−3.61847			−0.118654
$931$	27.3316	+	41.2473i	0.895758	+	1.35183i
$932$	−26.7820			−0.877274
$933$	−12.5763	+	21.7827i	−0.411728	+	0.713134i
$934$	−0.0120009	−	0.0207862i	−0.000392681	−	0.000680144i
$935$	2.62233	+	4.54200i	0.0857592	+	0.148539i
$936$	3.95800	−	6.85546i	0.129371	−	0.224078i
$937$	−9.51463			−0.310829			−0.155415	−	0.987849i	$-0.549671\pi$
$937$	−9.51463			−0.310829			−0.155415	+	0.987849i	$0.549671\pi$
$938$	2.90845	−	1.80084i	0.0949643	−	0.0587996i
$939$	22.3253			0.728559
$940$	−9.03982	+	15.6574i	−0.294846	+	0.510689i
$941$	6.95637	+	12.0488i	0.226771	+	0.392779i	0.956849	−	0.290584i	$-0.0938497\pi$
$941$	6.95637	+	12.0488i	0.226771	+	0.392779i	−0.730078	+	0.683364i	$0.760516\pi$
$942$	1.03941	+	1.80031i	0.0338658	+	0.0586574i
$943$	−17.0690	+	29.5643i	−0.555842	+	0.962746i
$944$	−8.15461			−0.265410
$945$	0.0814802	+	2.64450i	0.00265055	+	0.0860255i
$946$	3.20823			0.104308
$947$	27.1807	−	47.0783i	0.883254	−	1.52984i	0.0355513	−	0.999368i	$-0.488681\pi$
$947$	27.1807	−	47.0783i	0.883254	−	1.52984i	0.847702	−	0.530472i	$-0.177985\pi$
$948$	−6.44551	−	11.1640i	−0.209341	−	0.362588i
$949$	11.6242	+	20.1338i	0.377339	+	0.653570i
$950$	2.17204	−	3.76208i	0.0704703	−	0.122058i
$951$	−0.592976			−0.0192286
$952$	−27.2141	−	14.6136i	−0.882014	−	0.473630i
$953$	−4.47098			−0.144829			−0.0724146	−	0.997375i	$-0.523070\pi$
$953$	−4.47098			−0.144829			−0.0724146	+	0.997375i	$0.523070\pi$
$954$	−0.982278	+	1.70135i	−0.0318024	+	0.0550834i
$955$	0.0155336	+	0.0269051i	0.000502657	+	0.000870627i
$956$	−17.8516	−	30.9199i	−0.577363	−	1.00002i
$957$	−1.57133	+	2.72163i	−0.0507939	+	0.0879777i
$958$	9.12746			0.294895
$959$	36.8344	+	19.7796i	1.18944	+	0.638715i
$960$	0.308336			0.00995150
$961$	−1.83420	+	3.17694i	−0.0591679	+	0.102482i
$962$	4.25925	+	7.37723i	0.137324	+	0.237852i
$963$	4.79437	+	8.30409i	0.154496	+	0.267595i
$964$	5.75582	−	9.96938i	0.185383	−	0.321092i
$965$	−20.5776			−0.662415
$966$	−0.220558	−	7.15835i	−0.00709632	−	0.230316i
$967$	0.0950267			0.00305585			0.00152793	−	0.999999i	$-0.499514\pi$
$967$	0.0950267			0.00305585			0.00152793	+	0.999999i	$0.499514\pi$
$968$	−1.11305	+	1.92786i	−0.0357749	+	0.0619639i
$969$	18.5364	+	32.1060i	0.595476	+	1.03139i
$970$	−3.39785	−	5.88525i	−0.109098	−	0.188964i
$971$	25.4711	−	44.1172i	0.817406	−	1.41579i	−0.0901818	−	0.995925i	$-0.528745\pi$
$971$	25.4711	−	44.1172i	0.817406	−	1.41579i	0.907588	−	0.419863i	$-0.137922\pi$
$972$	−1.62233			−0.0520361
$973$	45.4570	−	28.1459i	1.45728	−	0.902315i
$974$	11.4988			0.368444
$975$	1.77799	−	3.07957i	0.0569413	−	0.0986253i
$976$	−13.1357	−	22.7517i	−0.420464	−	0.728266i
$977$	−0.820271	−	1.42075i	−0.0262428	−	0.0454539i	0.852606	−	0.522555i	$-0.175021\pi$
$977$	−0.820271	−	1.42075i	−0.0262428	−	0.0454539i	−0.878849	+	0.477101i	$0.841688\pi$
$978$	2.55175	−	4.41976i	0.0815960	−	0.141328i
$979$	−4.56462			−0.145886
$980$	5.06190	−	10.1657i	0.161696	−	0.324733i
$981$	−5.45737			−0.174240
$982$	5.77805	−	10.0079i	0.184385	−	0.319364i
$983$	−3.58045	−	6.20152i	−0.114199	−	0.197798i	0.803261	−	0.595628i	$-0.203097\pi$
$983$	−3.58045	−	6.20152i	−0.114199	−	0.197798i	−0.917459	+	0.397830i	$0.869763\pi$
$984$	8.62663	+	14.9418i	0.275007	+	0.476326i
$985$	7.54000	−	13.0597i	0.240244	−	0.416116i
$986$	−10.1291			−0.322578
$987$	−25.0686	+	15.5219i	−0.797942	+	0.494067i
$988$	40.7791			1.29736
$989$	11.4971	−	19.9136i	0.365587	−	0.633215i
$990$	0.307276	+	0.532217i	0.00976587	+	0.0169150i
$991$	23.0906	+	39.9941i	0.733496	+	1.27045i	0.955380	+	0.295380i	$0.0954462\pi$
$991$	23.0906	+	39.9941i	0.733496	+	1.27045i	−0.221883	+	0.975073i	$0.571220\pi$
$992$	−16.5025	+	28.5832i	−0.523955	+	0.907516i
$993$	−17.5244			−0.556121
$994$	0.462026	+	14.9954i	0.0146546	+	0.475625i
$995$	−17.6396			−0.559213
$996$	8.00476	−	13.8646i	0.253640	−	0.439318i
$997$	−19.5857	−	33.9235i	−0.620286	−	1.07437i	−0.989432	−	0.144996i	$-0.953683\pi$
$997$	−19.5857	−	33.9235i	−0.620286	−	1.07437i	0.369146	−	0.929371i	$-0.379650\pi$
$998$	−7.31239	−	12.6654i	−0.231470	−	0.400917i
$999$	1.94901	−	3.37579i	0.0616640	−	0.106805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.q.j.331.5	✓	16
7.2	even	3		8085.2.a.cf.1.4		8
7.4	even	3	inner	1155.2.q.j.991.5	yes	16
7.5	odd	6		8085.2.a.ce.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.j.331.5	✓	16	1.1	even	1	trivial
1155.2.q.j.991.5	yes	16	7.4	even	3	inner
8085.2.a.ce.1.4		8	7.5	odd	6
8085.2.a.cf.1.4		8	7.2	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.307276 - 0.532217i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.811163 + 1.40498i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.614552 q^{6} +(-2.24946 + 1.39281i) q^{7} +2.22611 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.307276 - 0.532217i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.811163 + 1.40498i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.614552 q^{6} +(-2.24946 + 1.39281i) q^{7} +2.22611 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.307276 - 0.532217i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.811163 - 1.40498i) q^{12} -3.55599 q^{13} +(0.0500738 + 1.62518i) q^{14} -1.00000 q^{15} +(-0.938298 + 1.62518i) q^{16} +(2.62233 + 4.54200i) q^{17} +(0.307276 + 0.532217i) q^{18} +(-3.53435 + 6.12167i) q^{19} +1.62233 q^{20} +(2.33094 + 1.25168i) q^{21} +0.614552 q^{22} +(2.20233 - 3.81454i) q^{23} +(-1.11305 - 1.92786i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.09267 + 1.89256i) q^{26} +1.00000 q^{27} +(-3.78155 - 2.03064i) q^{28} -3.14266 q^{29} +(-0.307276 + 0.532217i) q^{30} +(2.94399 + 5.09915i) q^{31} +(2.80274 + 4.85449i) q^{32} +(0.500000 - 0.866025i) q^{33} +3.22311 q^{34} +(0.0814802 + 2.64450i) q^{35} -1.62233 q^{36} +(1.94901 - 3.37579i) q^{37} +(2.17204 + 3.76208i) q^{38} +(1.77799 + 3.07957i) q^{39} +(1.11305 - 1.92786i) q^{40} -7.75042 q^{41} +(1.38241 - 0.855955i) q^{42} +5.22043 q^{43} +(-0.811163 + 1.40498i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-1.35344 - 2.34423i) q^{46} +(-5.57213 + 9.65122i) q^{47} +1.87660 q^{48} +(3.12015 - 6.26615i) q^{49} -0.614552 q^{50} +(2.62233 - 4.54200i) q^{51} +(-2.88448 - 4.99607i) q^{52} +(1.59836 + 2.76845i) q^{53} +(0.307276 - 0.532217i) q^{54} +1.00000 q^{55} +(-5.00754 + 3.10055i) q^{56} +7.06870 q^{57} +(-0.965664 + 1.67258i) q^{58} +(2.17271 + 3.76325i) q^{59} +(-0.811163 - 1.40498i) q^{60} +(-6.99976 + 12.1239i) q^{61} +3.61847 q^{62} +(-0.0814802 - 2.64450i) q^{63} -0.308336 q^{64} +(-1.77799 + 3.07957i) q^{65} +(-0.307276 - 0.532217i) q^{66} +(-1.05195 - 1.82203i) q^{67} +(-4.25427 + 7.36861i) q^{68} -4.40465 q^{69} +(1.43248 + 0.769225i) q^{70} +9.22691 q^{71} +(-1.11305 + 1.92786i) q^{72} +(-3.26892 - 5.66194i) q^{73} +(-1.19777 - 2.07460i) q^{74} +(-0.500000 + 0.866025i) q^{75} -11.4677 q^{76} +(-2.33094 - 1.25168i) q^{77} +2.18534 q^{78} +(3.97301 - 6.88145i) q^{79} +(0.938298 + 1.62518i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.38152 + 4.12491i) q^{82} +9.86824 q^{83} +(0.132187 + 4.29024i) q^{84} +5.24465 q^{85} +(1.60411 - 2.77841i) q^{86} +(1.57133 + 2.72163i) q^{87} +(1.11305 + 1.92786i) q^{88} +(-2.28231 + 3.95307i) q^{89} +0.614552 q^{90} +(7.99905 - 4.95282i) q^{91} +7.14579 q^{92} +(2.94399 - 5.09915i) q^{93} +(3.42436 + 5.93117i) q^{94} +(3.53435 + 6.12167i) q^{95} +(2.80274 - 4.85449i) q^{96} +11.0580 q^{97} +(-2.37621 - 3.58603i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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