LMFDB - Embedded newform 630.2.l.i.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(331,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 2]))

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

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

chi := DirichletCharacter("630.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561 $ x^16 - x^15 + 2x^14 - 4x^13 + 5x^12 + 2x^11 - 35x^10 + 81x^9 - 66x^8 + 243x^7 - 315x^6 + 54x^5 + 405x^4 - 972x^3 + 1458x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.1
Root			$-0.803168 - 1.53458i$ of defining polynomial
Character	$\chi$	$=$	630.331
Dual form			630.2.l.i.571.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.73057 + 0.0717234i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.927397 - 1.46285i) q^{6} +(-2.59109 + 0.535003i) q^{7} -1.00000 q^{8} +(2.98971 - 0.248244i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.73057 + 0.0717234i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.927397 - 1.46285i) q^{6} +(-2.59109 + 0.535003i) q^{7} -1.00000 q^{8} +(2.98971 - 0.248244i) q^{9} +(-0.500000 - 0.866025i) q^{10} +0.379264 q^{11} +(0.803168 - 1.53458i) q^{12} +(-0.308106 - 0.533656i) q^{13} +(-1.75887 - 1.97645i) q^{14} +(1.73057 - 0.0717234i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.97521 - 3.42117i) q^{17} +(1.70984 + 2.46504i) q^{18} +(2.57037 - 4.45201i) q^{19} +(0.500000 - 0.866025i) q^{20} +(4.44569 - 1.11170i) q^{21} +(0.189632 + 0.328453i) q^{22} +2.74084 q^{23} +(1.73057 - 0.0717234i) q^{24} +1.00000 q^{25} +(0.308106 - 0.533656i) q^{26} +(-5.15609 + 0.644035i) q^{27} +(0.832221 - 2.51146i) q^{28} +(3.69460 - 6.39923i) q^{29} +(0.927397 + 1.46285i) q^{30} +(-1.18963 + 2.06050i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.656342 + 0.0272021i) q^{33} +(1.97521 - 3.42117i) q^{34} +(2.59109 - 0.535003i) q^{35} +(-1.27987 + 2.71329i) q^{36} +(3.99026 - 6.91133i) q^{37} +5.14074 q^{38} +(0.571473 + 0.901427i) q^{39} +1.00000 q^{40} +(-3.63844 - 6.30196i) q^{41} +(3.18560 + 3.29423i) q^{42} +(-2.57500 + 4.46002i) q^{43} +(-0.189632 + 0.328453i) q^{44} +(-2.98971 + 0.248244i) q^{45} +(1.37042 + 2.37364i) q^{46} +(-3.72254 - 6.44763i) q^{47} +(0.927397 + 1.46285i) q^{48} +(6.42754 - 2.77249i) q^{49} +(0.500000 + 0.866025i) q^{50} +(3.66361 + 5.77889i) q^{51} +0.616212 q^{52} +(-0.998199 - 1.72893i) q^{53} +(-3.13579 - 4.14328i) q^{54} -0.379264 q^{55} +(2.59109 - 0.535003i) q^{56} +(-4.12888 + 7.88885i) q^{57} +7.38920 q^{58} +(-0.115881 + 0.200711i) q^{59} +(-0.803168 + 1.53458i) q^{60} +(5.76782 + 9.99016i) q^{61} -2.37926 q^{62} +(-7.61381 + 2.24273i) q^{63} +1.00000 q^{64} +(0.308106 + 0.533656i) q^{65} +(-0.351729 - 0.554808i) q^{66} +(-6.70314 + 11.6102i) q^{67} +3.95043 q^{68} +(-4.74320 + 0.196583i) q^{69} +(1.75887 + 1.97645i) q^{70} -11.2870 q^{71} +(-2.98971 + 0.248244i) q^{72} +(-3.58534 - 6.20999i) q^{73} +7.98051 q^{74} +(-1.73057 + 0.0717234i) q^{75} +(2.57037 + 4.45201i) q^{76} +(-0.982710 + 0.202908i) q^{77} +(-0.494922 + 0.945624i) q^{78} +(-3.01763 - 5.22670i) q^{79} +(0.500000 + 0.866025i) q^{80} +(8.87675 - 1.48436i) q^{81} +(3.63844 - 6.30196i) q^{82} +(4.29143 - 7.43298i) q^{83} +(-1.26008 + 4.40593i) q^{84} +(1.97521 + 3.42117i) q^{85} -5.14999 q^{86} +(-5.93477 + 11.3393i) q^{87} -0.379264 q^{88} +(6.26653 - 10.8540i) q^{89} +(-1.70984 - 2.46504i) q^{90} +(1.08384 + 1.21791i) q^{91} +(-1.37042 + 2.37364i) q^{92} +(1.91095 - 3.65116i) q^{93} +(3.72254 - 6.44763i) q^{94} +(-2.57037 + 4.45201i) q^{95} +(-0.803168 + 1.53458i) q^{96} +(-0.792120 + 1.37199i) q^{97} +(5.61482 + 4.18017i) q^{98} +(1.13389 - 0.0941502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - q^{3} - 8 q^{4} - 16 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} + 9 q^{9}+O(q^{10}) $ 16 * q + 8 * q^2 - q^3 - 8 * q^4 - 16 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 + 9 * q^9	\( 16 q + 8 q^{2} - q^{3} - 8 q^{4} - 16 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} + 9 q^{9} - 8 q^{10} - 2 q^{11} - q^{12} + 2 q^{13} + 8 q^{14} + q^{15} - 8 q^{16} + 11 q^{17} + 3 q^{18} - 2 q^{19} + 8 q^{20} - q^{22} - 22 q^{23} + q^{24} + 16 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} + 2 q^{30} - 15 q^{31} + 8 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} - 4 q^{38} + 33 q^{39} + 16 q^{40} + 7 q^{41} - 9 q^{42} - 13 q^{43} + q^{44} - 9 q^{45} - 11 q^{46} - 5 q^{47} + 2 q^{48} + 10 q^{49} + 8 q^{50} + 30 q^{51} - 4 q^{52} + 18 q^{53} + q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} + 34 q^{58} + q^{59} + q^{60} - 27 q^{61} - 30 q^{62} + 14 q^{63} + 16 q^{64} - 2 q^{65} + 10 q^{66} - 10 q^{67} - 22 q^{68} - 14 q^{69} - 8 q^{70} - 38 q^{71} - 9 q^{72} - 8 q^{73} - 4 q^{74} - q^{75} - 2 q^{76} - 19 q^{77} - 25 q^{79} + 8 q^{80} + 9 q^{81} - 7 q^{82} + 2 q^{83} - 9 q^{84} - 11 q^{85} - 26 q^{86} + 58 q^{87} + 2 q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} + 3 q^{93} + 5 q^{94} + 2 q^{95} + q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - q^3 - 8 * q^4 - 16 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 + 9 * q^9 - 8 * q^10 - 2 * q^11 - q^12 + 2 * q^13 + 8 * q^14 + q^15 - 8 * q^16 + 11 * q^17 + 3 * q^18 - 2 * q^19 + 8 * q^20 - q^22 - 22 * q^23 + q^24 + 16 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 + 2 * q^30 - 15 * q^31 + 8 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^38 + 33 * q^39 + 16 * q^40 + 7 * q^41 - 9 * q^42 - 13 * q^43 + q^44 - 9 * q^45 - 11 * q^46 - 5 * q^47 + 2 * q^48 + 10 * q^49 + 8 * q^50 + 30 * q^51 - 4 * q^52 + 18 * q^53 + q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 + 34 * q^58 + q^59 + q^60 - 27 * q^61 - 30 * q^62 + 14 * q^63 + 16 * q^64 - 2 * q^65 + 10 * q^66 - 10 * q^67 - 22 * q^68 - 14 * q^69 - 8 * q^70 - 38 * q^71 - 9 * q^72 - 8 * q^73 - 4 * q^74 - q^75 - 2 * q^76 - 19 * q^77 - 25 * q^79 + 8 * q^80 + 9 * q^81 - 7 * q^82 + 2 * q^83 - 9 * q^84 - 11 * q^85 - 26 * q^86 + 58 * q^87 + 2 * q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 + 3 * q^93 + 5 * q^94 + 2 * q^95 + q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.73057	+	0.0717234i	−0.999142	+	0.0414095i
$3$	−1.73057	+	0.0717234i	−0.999142	+	0.0414095i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.927397	−	1.46285i	−0.378608	−	0.597207i
$7$	−2.59109	+	0.535003i	−0.979342	+	0.202212i
$7$	−2.59109	+	0.535003i	−0.979342	+	0.202212i
$8$	−1.00000			−0.353553
$9$	2.98971	−	0.248244i	0.996570	−	0.0827480i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	0.379264			0.114353			0.0571763	−	0.998364i	$-0.481790\pi$
$11$	0.379264			0.114353			0.0571763	+	0.998364i	$0.481790\pi$
$12$	0.803168	−	1.53458i	0.231855	−	0.442994i
$13$	−0.308106	−	0.533656i	−0.0854533	−	0.148009i	0.820131	−	0.572176i	$-0.193901\pi$
$13$	−0.308106	−	0.533656i	−0.0854533	−	0.148009i	−0.905584	+	0.424166i	$0.860567\pi$
$14$	−1.75887	−	1.97645i	−0.470079	−	0.528229i
$15$	1.73057	−	0.0717234i	0.446830	−	0.0185189i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.97521	−	3.42117i	−0.479060	−	0.829756i	0.520652	−	0.853769i	$-0.325689\pi$
$17$	−1.97521	−	3.42117i	−0.479060	−	0.829756i	−0.999712	+	0.0240132i	$0.992356\pi$
$18$	1.70984	+	2.46504i	0.403014	+	0.581016i
$19$	2.57037	−	4.45201i	0.589684	−	1.02136i	−0.404590	−	0.914498i	$-0.632586\pi$
$19$	2.57037	−	4.45201i	0.589684	−	1.02136i	0.994274	−	0.106864i	$-0.0340809\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	4.44569	−	1.11170i	0.970128	−	0.242593i
$22$	0.189632	+	0.328453i	0.0404297	+	0.0700263i
$23$	2.74084			0.571505			0.285752	−	0.958303i	$-0.407756\pi$
$23$	2.74084			0.571505			0.285752	+	0.958303i	$0.407756\pi$
$24$	1.73057	−	0.0717234i	0.353250	−	0.0146405i
$25$	1.00000			0.200000
$26$	0.308106	−	0.533656i	0.0604246	−	0.104658i
$27$	−5.15609	+	0.644035i	−0.992289	+	0.123945i
$28$	0.832221	−	2.51146i	0.157275	−	0.474620i
$29$	3.69460	−	6.39923i	0.686070	−	1.18831i	−0.287029	−	0.957922i	$-0.592668\pi$
$29$	3.69460	−	6.39923i	0.686070	−	1.18831i	0.973099	−	0.230386i	$-0.0739989\pi$
$30$	0.927397	+	1.46285i	0.169319	+	0.267079i
$31$	−1.18963	+	2.06050i	−0.213664	+	0.370077i	−0.952859	−	0.303415i	$-0.901873\pi$
$31$	−1.18963	+	2.06050i	−0.213664	+	0.370077i	0.739194	+	0.673492i	$0.235207\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.656342	+	0.0272021i	−0.114254	+	0.00473529i
$34$	1.97521	−	3.42117i	0.338746	−	0.586726i
$35$	2.59109	−	0.535003i	0.437975	−	0.0904320i
$36$	−1.27987	+	2.71329i	−0.213312	+	0.452215i
$37$	3.99026	−	6.91133i	0.655994	−	1.13621i	−0.325650	−	0.945491i	$-0.605583\pi$
$37$	3.99026	−	6.91133i	0.655994	−	1.13621i	0.981644	−	0.190724i	$-0.0610837\pi$
$38$	5.14074			0.833938
$39$	0.571473	+	0.901427i	0.0915090	+	0.144344i
$40$	1.00000			0.158114
$41$	−3.63844	−	6.30196i	−0.568229	−	0.984201i	−0.996741	−	0.0806654i	$-0.974295\pi$
$41$	−3.63844	−	6.30196i	−0.568229	−	0.984201i	0.428512	−	0.903536i	$-0.359038\pi$
$42$	3.18560	+	3.29423i	0.491549	+	0.508310i
$43$	−2.57500	+	4.46002i	−0.392683	+	0.680147i	−0.992802	−	0.119763i	$-0.961786\pi$
$43$	−2.57500	+	4.46002i	−0.392683	+	0.680147i	0.600119	+	0.799911i	$0.295120\pi$
$44$	−0.189632	+	0.328453i	−0.0285881	+	0.0495161i
$45$	−2.98971	+	0.248244i	−0.445680	+	0.0370061i
$46$	1.37042	+	2.37364i	0.202058	+	0.349974i
$47$	−3.72254	−	6.44763i	−0.542988	−	0.940483i	−0.998731	−	0.0503712i	$-0.983960\pi$
$47$	−3.72254	−	6.44763i	−0.542988	−	0.940483i	0.455743	−	0.890112i	$-0.349374\pi$
$48$	0.927397	+	1.46285i	0.133858	+	0.211144i
$49$	6.42754	−	2.77249i	0.918221	−	0.396070i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	3.66361	+	5.77889i	0.513009	+	0.809207i
$52$	0.616212			0.0854533
$53$	−0.998199	−	1.72893i	−0.137113	−	0.237487i	0.789290	−	0.614021i	$-0.210449\pi$
$53$	−0.998199	−	1.72893i	−0.137113	−	0.237487i	−0.926403	+	0.376534i	$0.877116\pi$
$54$	−3.13579	−	4.14328i	−0.426727	−	0.563829i
$55$	−0.379264			−0.0511400
$56$	2.59109	−	0.535003i	0.346250	−	0.0714928i
$57$	−4.12888	+	7.88885i	−0.546884	+	1.04490i
$58$	7.38920			0.970249
$59$	−0.115881	+	0.200711i	−0.0150864	+	0.0261303i	−0.873470	−	0.486878i	$-0.838136\pi$
$59$	−0.115881	+	0.200711i	−0.0150864	+	0.0261303i	0.858384	+	0.513008i	$0.171469\pi$
$60$	−0.803168	+	1.53458i	−0.103689	+	0.198113i
$61$	5.76782	+	9.99016i	0.738494	+	1.27911i	0.953173	+	0.302424i	$0.0977959\pi$
$61$	5.76782	+	9.99016i	0.738494	+	1.27911i	−0.214680	+	0.976685i	$0.568871\pi$
$62$	−2.37926			−0.302167
$63$	−7.61381	+	2.24273i	−0.959250	+	0.282557i
$64$	1.00000			0.125000
$65$	0.308106	+	0.533656i	0.0382159	+	0.0661918i
$66$	−0.351729	−	0.554808i	−0.0432948	−	0.0682921i
$67$	−6.70314	+	11.6102i	−0.818919	+	1.41841i	0.0875599	+	0.996159i	$0.472093\pi$
$67$	−6.70314	+	11.6102i	−0.818919	+	1.41841i	−0.906479	+	0.422251i	$0.861240\pi$
$68$	3.95043			0.479060
$69$	−4.74320	+	0.196583i	−0.571015	+	0.0236658i
$70$	1.75887	+	1.97645i	0.210226	+	0.236231i
$71$	−11.2870			−1.33952			−0.669758	−	0.742580i	$-0.733602\pi$
$71$	−11.2870			−1.33952			−0.669758	+	0.742580i	$0.733602\pi$
$72$	−2.98971	+	0.248244i	−0.352341	+	0.0292559i
$73$	−3.58534	−	6.20999i	−0.419632	−	0.726824i	0.576270	−	0.817259i	$-0.304508\pi$
$73$	−3.58534	−	6.20999i	−0.419632	−	0.726824i	−0.995902	+	0.0904348i	$0.971174\pi$
$74$	7.98051			0.927716
$75$	−1.73057	+	0.0717234i	−0.199828	+	0.00828191i
$76$	2.57037	+	4.45201i	0.294842	+	0.510681i
$77$	−0.982710	+	0.202908i	−0.111990	+	0.0231235i
$78$	−0.494922	+	0.945624i	−0.0560389	+	0.107071i
$79$	−3.01763	−	5.22670i	−0.339510	−	0.588049i	0.644830	−	0.764326i	$-0.276928\pi$
$79$	−3.01763	−	5.22670i	−0.339510	−	0.588049i	−0.984341	+	0.176276i	$0.943595\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	8.87675	−	1.48436i	0.986306	−	0.164929i
$82$	3.63844	−	6.30196i	0.401799	−	0.695935i
$83$	4.29143	−	7.43298i	0.471046	−	0.815876i	−0.528405	−	0.848992i	$-0.677210\pi$
$83$	4.29143	−	7.43298i	0.471046	−	0.815876i	0.999452	+	0.0331163i	$0.0105432\pi$
$84$	−1.26008	+	4.40593i	−0.137486	+	0.480726i
$85$	1.97521	+	3.42117i	0.214242	+	0.371078i
$86$	−5.14999			−0.555338
$87$	−5.93477	+	11.3393i	−0.636274	+	1.21570i
$88$	−0.379264			−0.0404297
$89$	6.26653	−	10.8540i	0.664251	−	1.15052i	−0.315237	−	0.949013i	$-0.602084\pi$
$89$	6.26653	−	10.8540i	0.664251	−	1.15052i	0.979488	−	0.201504i	$-0.0645828\pi$
$90$	−1.70984	−	2.46504i	−0.180233	−	0.259838i
$91$	1.08384	+	1.21791i	0.113617	+	0.127672i
$92$	−1.37042	+	2.37364i	−0.142876	+	0.247469i
$93$	1.91095	−	3.65116i	0.198156	−	0.378608i
$94$	3.72254	−	6.44763i	0.383951	−	0.665022i
$95$	−2.57037	+	4.45201i	−0.263715	+	0.456767i
$96$	−0.803168	+	1.53458i	−0.0819730	+	0.156622i
$97$	−0.792120	+	1.37199i	−0.0804276	+	0.139305i	−0.903434	−	0.428728i	$-0.858962\pi$
$97$	−0.792120	+	1.37199i	−0.0804276	+	0.139305i	0.823006	+	0.568033i	$0.192295\pi$
$98$	5.61482	+	4.18017i	0.567182	+	0.422261i
$99$	1.13389	−	0.0941502i	0.113960	−	0.00946245i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−12.0666			−1.20067			−0.600337	−	0.799747i	$-0.704967\pi$
$101$	−12.0666			−1.20067			−0.600337	+	0.799747i	$0.704967\pi$
$102$	−3.17286	+	6.06223i	−0.314160	+	0.600250i
$103$	−11.4690			−1.13007			−0.565036	−	0.825066i	$-0.691138\pi$
$103$	−11.4690			−1.13007			−0.565036	+	0.825066i	$0.691138\pi$
$104$	0.308106	+	0.533656i	0.0302123	+	0.0523292i
$105$	−4.44569	+	1.11170i	−0.433855	+	0.108491i
$106$	0.998199	−	1.72893i	0.0969537	−	0.167929i
$107$	2.31889	−	4.01643i	0.224175	−	0.388283i	−0.731896	−	0.681416i	$-0.761365\pi$
$107$	2.31889	−	4.01643i	0.224175	−	0.388283i	0.956072	+	0.293133i	$0.0946979\pi$
$108$	2.02029	−	4.78732i	0.194403	−	0.460660i
$109$	6.78033	+	11.7439i	0.649438	+	1.12486i	0.983257	+	0.182222i	$0.0583290\pi$
$109$	6.78033	+	11.7439i	0.649438	+	1.12486i	−0.333820	+	0.942637i	$0.608338\pi$
$110$	−0.189632	−	0.328453i	−0.0180807	−	0.0313167i
$111$	−6.40969	+	12.2467i	−0.608381	+	1.16240i
$112$	1.75887	+	1.97645i	0.166198	+	0.186757i
$113$	−7.78805	−	13.4893i	−0.732638	−	1.26897i	−0.955752	−	0.294174i	$-0.904956\pi$
$113$	−7.78805	−	13.4893i	−0.732638	−	1.26897i	0.223114	−	0.974792i	$-0.428378\pi$
$114$	−8.89639	+	0.368712i	−0.833223	+	0.0345330i
$115$	−2.74084			−0.255585
$116$	3.69460	+	6.39923i	0.343035	+	0.594154i
$117$	−1.05363	−	1.51899i	−0.0974077	−	0.140431i
$118$	−0.231761			−0.0213353
$119$	6.94830	+	7.80783i	0.636950	+	0.715743i
$120$	−1.73057	+	0.0717234i	−0.157978	+	0.00654742i
$121$	−10.8562			−0.986924
$122$	−5.76782	+	9.99016i	−0.522194	+	0.904467i
$123$	6.74856	+	10.6450i	0.608497	+	0.959827i
$124$	−1.18963	−	2.06050i	−0.106832	−	0.185039i
$125$	−1.00000			−0.0894427
$126$	−5.74917	−	5.47239i	−0.512177	−	0.487519i
$127$	8.57545			0.760948			0.380474	−	0.924792i	$-0.375761\pi$
$127$	8.57545			0.760948			0.380474	+	0.924792i	$0.375761\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	4.13631	−	7.90305i	0.364182	−	0.695825i
$130$	−0.308106	+	0.533656i	−0.0270227	+	0.0468047i
$131$	−13.8186			−1.20734			−0.603669	−	0.797235i	$-0.706295\pi$
$131$	−13.8186			−1.20734			−0.603669	+	0.797235i	$0.706295\pi$
$132$	0.304613	−	0.582010i	0.0265132	−	0.0506574i
$133$	−4.27823	+	12.9107i	−0.370970	+	1.11950i
$134$	−13.4063			−1.15813
$135$	5.15609	−	0.644035i	0.443765	−	0.0554297i
$136$	1.97521	+	3.42117i	0.169373	+	0.293363i
$137$	9.32960			0.797082			0.398541	−	0.917151i	$-0.369517\pi$
$137$	9.32960			0.797082			0.398541	+	0.917151i	$0.369517\pi$
$138$	−2.54185	−	4.00944i	−0.216376	−	0.341307i
$139$	−4.87554	−	8.44469i	−0.413538	−	0.716269i	0.581736	−	0.813378i	$-0.302374\pi$
$139$	−4.87554	−	8.44469i	−0.413538	−	0.716269i	−0.995274	+	0.0971088i	$0.969041\pi$
$140$	−0.832221	+	2.51146i	−0.0703355	+	0.212257i
$141$	6.90454	+	10.8910i	0.581467	+	0.917191i
$142$	−5.64348	−	9.77479i	−0.473590	−	0.820283i
$143$	−0.116854	−	0.202397i	−0.00977180	−	0.0169253i
$144$	−1.70984	−	2.46504i	−0.142487	−	0.205420i
$145$	−3.69460	+	6.39923i	−0.306820	+	0.531427i
$146$	3.58534	−	6.20999i	0.296725	−	0.513943i
$147$	−10.9244	+	5.25897i	−0.901032	+	0.433753i
$148$	3.99026	+	6.91133i	0.327997	+	0.568107i
$149$	−6.25399			−0.512346			−0.256173	−	0.966631i	$-0.582462\pi$
$149$	−6.25399			−0.512346			−0.256173	+	0.966631i	$0.582462\pi$
$150$	−0.927397	−	1.46285i	−0.0757216	−	0.119441i
$151$	21.9891			1.78945			0.894723	−	0.446622i	$-0.147373\pi$
$151$	21.9891			1.78945			0.894723	+	0.446622i	$0.147373\pi$
$152$	−2.57037	+	4.45201i	−0.208485	+	0.361106i
$153$	−6.75461	−	9.73798i	−0.546078	−	0.787269i
$154$	−0.667078	−	0.749598i	−0.0537547	−	0.0604043i
$155$	1.18963	−	2.06050i	0.0955536	−	0.165504i
$156$	−1.06640	+	0.0441969i	−0.0853800	+	0.00353858i
$157$	−7.97995	+	13.8217i	−0.636869	+	1.10309i	0.349247	+	0.937031i	$0.386438\pi$
$157$	−7.97995	+	13.8217i	−0.636869	+	1.10309i	−0.986116	+	0.166059i	$0.946896\pi$
$158$	3.01763	−	5.22670i	0.240070	−	0.415814i
$159$	1.85145	+	2.92044i	0.146830	+	0.231606i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−7.10178	+	1.46636i	−0.559699	+	0.115565i
$162$	5.72387	+	6.94531i	0.449709	+	0.545675i
$163$	−3.60765	+	6.24864i	−0.282573	+	0.489431i	−0.972018	−	0.234907i	$-0.924521\pi$
$163$	−3.60765	+	6.24864i	−0.282573	+	0.489431i	0.689444	+	0.724339i	$0.257855\pi$
$164$	7.27688			0.568229
$165$	0.656342	−	0.0272021i	0.0510961	−	0.00211768i
$166$	8.58287			0.666160
$167$	5.11565	+	8.86057i	0.395861	+	0.685652i	0.993211	−	0.116329i	$-0.0371128\pi$
$167$	5.11565	+	8.86057i	0.395861	+	0.685652i	−0.597350	+	0.801981i	$0.703779\pi$
$168$	−4.44569	+	1.11170i	−0.342992	+	0.0857695i
$169$	6.31014	−	10.9295i	0.485395	−	0.840730i
$170$	−1.97521	+	3.42117i	−0.151492	+	0.262392i
$171$	6.57948	−	13.9483i	0.503146	−	1.06665i
$172$	−2.57500	−	4.46002i	−0.196342	−	0.340074i
$173$	−2.12875	−	3.68710i	−0.161846	−	0.280325i	0.773685	−	0.633571i	$-0.218411\pi$
$173$	−2.12875	−	3.68710i	−0.161846	−	0.280325i	−0.935531	+	0.353245i	$0.885078\pi$
$174$	−12.7875	+	0.529979i	−0.969417	+	0.0401776i
$175$	−2.59109	+	0.535003i	−0.195868	+	0.0404424i
$176$	−0.189632	−	0.328453i	−0.0142941	−	0.0247580i
$177$	0.186143	−	0.355655i	0.0139914	−	0.0267326i
$178$	12.5331			0.939393
$179$	1.87410	+	3.24604i	0.140077	+	0.242621i	0.927525	−	0.373760i	$-0.121932\pi$
$179$	1.87410	+	3.24604i	0.140077	+	0.242621i	−0.787448	+	0.616381i	$0.788598\pi$
$180$	1.27987	−	2.71329i	0.0953959	−	0.202237i
$181$	19.5320			1.45180			0.725899	−	0.687801i	$-0.241424\pi$
$181$	19.5320			1.45180			0.725899	+	0.687801i	$0.241424\pi$
$182$	−0.512825	+	1.54759i	−0.0380131	+	0.114715i
$183$	−10.6981	−	16.8749i	−0.790828	−	1.24743i
$184$	−2.74084			−0.202058
$185$	−3.99026	+	6.91133i	−0.293369	+	0.508131i
$186$	4.11747	−	0.170649i	0.301908	−	0.0125126i
$187$	−0.749128	−	1.29753i	−0.0547817	−	0.0948847i
$188$	7.44508			0.542988
$189$	13.0153	−	4.42728i	0.946727	−	0.322037i
$190$	−5.14074			−0.372949
$191$	−3.86820	−	6.69992i	−0.279893	−	0.484790i	0.691465	−	0.722410i	$-0.256966\pi$
$191$	−3.86820	−	6.69992i	−0.279893	−	0.484790i	−0.971358	+	0.237621i	$0.923632\pi$
$192$	−1.73057	+	0.0717234i	−0.124893	+	0.00517619i
$193$	−0.601243	+	1.04138i	−0.0432784	+	0.0749605i	−0.886853	−	0.462051i	$-0.847114\pi$
$193$	−0.601243	+	1.04138i	−0.0432784	+	0.0749605i	0.843575	+	0.537012i	$0.180447\pi$
$194$	−1.58424			−0.113742
$195$	−0.571473	−	0.901427i	−0.0409241	−	0.0645525i
$196$	−0.812728	+	6.95266i	−0.0580520	+	0.496619i
$197$	−18.2839			−1.30268			−0.651339	−	0.758787i	$-0.725792\pi$
$197$	−18.2839			−1.30268			−0.651339	+	0.758787i	$0.725792\pi$
$198$	0.648482	+	0.934903i	0.0460856	+	0.0664407i
$199$	−4.34213	−	7.52079i	−0.307806	−	0.533135i	0.670076	−	0.742292i	$-0.266261\pi$
$199$	−4.34213	−	7.52079i	−0.307806	−	0.533135i	−0.977882	+	0.209157i	$0.932928\pi$
$200$	−1.00000			−0.0707107
$201$	10.7675	−	20.5730i	0.759481	−	1.45110i
$202$	−6.03331	−	10.4500i	−0.424502	−	0.735259i
$203$	−6.14945	+	18.5576i	−0.431607	+	1.30249i
$204$	−6.83647	+	0.283338i	−0.478649	+	0.0198376i
$205$	3.63844	+	6.30196i	0.254120	+	0.440148i
$206$	−5.73449	−	9.93243i	−0.399541	−	0.692025i
$207$	8.19433	−	0.680398i	0.569545	−	0.0472909i
$208$	−0.308106	+	0.533656i	−0.0213633	+	0.0370024i
$209$	0.974850	−	1.68849i	0.0674318	−	0.116795i
$210$	−3.18560	−	3.29423i	−0.219828	−	0.227323i
$211$	−7.54299	−	13.0648i	−0.519281	−	0.899421i	−0.999749	−	0.0224087i	$-0.992866\pi$
$211$	−7.54299	−	13.0648i	−0.519281	−	0.899421i	0.480468	−	0.877012i	$-0.340467\pi$
$212$	1.99640			0.137113
$213$	19.5328	−	0.809539i	1.33837	−	0.0554687i
$214$	4.63777			0.317032
$215$	2.57500	−	4.46002i	0.175613	−	0.304171i
$216$	5.15609	−	0.644035i	0.350827	−	0.0438210i
$217$	1.98007	−	5.97542i	0.134416	−	0.405638i
$218$	−6.78033	+	11.7439i	−0.459222	+	0.795396i
$219$	6.65007	+	10.4896i	0.449370	+	0.708824i
$220$	0.189632	−	0.328453i	0.0127850	−	0.0221443i
$221$	−1.21715	+	2.10817i	−0.0818745	+	0.141811i
$222$	−13.8108	+	0.572390i	−0.926920	+	0.0384163i
$223$	11.1346	−	19.2857i	0.745629	−	1.29147i	−0.204271	−	0.978914i	$-0.565482\pi$
$223$	11.1346	−	19.2857i	0.745629	−	1.29147i	0.949900	−	0.312553i	$-0.101184\pi$
$224$	−0.832221	+	2.51146i	−0.0556051	+	0.167804i
$225$	2.98971	−	0.248244i	0.199314	−	0.0165496i
$226$	7.78805	−	13.4893i	0.518053	−	0.897295i
$227$	2.90402			0.192747			0.0963734	−	0.995345i	$-0.469276\pi$
$227$	2.90402			0.192747			0.0963734	+	0.995345i	$0.469276\pi$
$228$	−4.76751	−	7.52014i	−0.315736	−	0.498034i
$229$	14.8090			0.978606			0.489303	−	0.872114i	$-0.337251\pi$
$229$	14.8090			0.978606			0.489303	+	0.872114i	$0.337251\pi$
$230$	−1.37042	−	2.37364i	−0.0903629	−	0.156513i
$231$	1.68609	−	0.421628i	0.110937	−	0.0277411i
$232$	−3.69460	+	6.39923i	−0.242562	+	0.420130i
$233$	9.63735	−	16.6924i	0.631364	−	1.09355i	−0.355909	−	0.934521i	$-0.615829\pi$
$233$	9.63735	−	16.6924i	0.631364	−	1.09355i	0.987273	−	0.159034i	$-0.0508379\pi$
$234$	0.788672	−	1.67196i	0.0515571	−	0.109300i
$235$	3.72254	+	6.44763i	0.242832	+	0.420597i
$236$	−0.115881	−	0.200711i	−0.00754318	−	0.0130652i
$237$	5.59709	+	8.82870i	0.363570	+	0.573486i
$238$	−3.28763	+	9.92132i	−0.213105	+	0.643104i
$239$	5.41490	+	9.37888i	0.350261	+	0.606669i	0.986295	−	0.164991i	$-0.0527597\pi$
$239$	5.41490	+	9.37888i	0.350261	+	0.606669i	−0.636034	+	0.771661i	$0.719426\pi$
$240$	−0.927397	−	1.46285i	−0.0598632	−	0.0944267i
$241$	−6.98664			−0.450049			−0.225025	−	0.974353i	$-0.572246\pi$
$241$	−6.98664			−0.450049			−0.225025	+	0.974353i	$0.572246\pi$
$242$	−5.42808	−	9.40171i	−0.348930	−	0.604365i
$243$	−15.2553	+	3.20545i	−0.978630	+	0.205630i
$244$	−11.5356			−0.738494
$245$	−6.42754	+	2.77249i	−0.410641	+	0.177128i
$246$	−5.84456	+	11.1669i	−0.372636	+	0.711977i
$247$	−3.16779			−0.201562
$248$	1.18963	−	2.06050i	0.0755417	−	0.130842i
$249$	−6.89349	+	13.1711i	−0.436857	+	0.834682i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	17.4193			1.09950			0.549749	−	0.835330i	$-0.314723\pi$
$251$	17.4193			1.09950			0.549749	+	0.835330i	$0.314723\pi$
$252$	1.86465	−	7.71512i	0.117462	−	0.486007i
$253$	1.03950			0.0653530
$254$	4.28773	+	7.42656i	0.269036	+	0.465984i
$255$	−3.66361	−	5.77889i	−0.229424	−	0.361888i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.1140			0.818031			0.409016	−	0.912527i	$-0.365872\pi$
$257$	13.1140			0.818031			0.409016	+	0.912527i	$0.365872\pi$
$258$	8.91240	−	0.369375i	0.554862	−	0.0229963i
$259$	−6.64155	+	20.0427i	−0.412686	+	1.24539i
$260$	−0.616212			−0.0382159
$261$	9.45721	−	20.0490i	0.585387	−	1.24100i
$262$	−6.90931	−	11.9673i	−0.426859	−	0.739341i
$263$	−4.80299			−0.296165			−0.148083	−	0.988975i	$-0.547310\pi$
$263$	−4.80299			−0.296165			−0.148083	+	0.988975i	$0.547310\pi$
$264$	0.656342	−	0.0272021i	0.0403950	−	0.00167418i
$265$	0.998199	+	1.72893i	0.0613189	+	0.106207i
$266$	−13.3201	+	2.75031i	−0.816711	+	0.168632i
$267$	−10.0662	+	19.2329i	−0.616039	+	1.17704i
$268$	−6.70314	−	11.6102i	−0.409460	−	0.709205i
$269$	−4.56270	−	7.90283i	−0.278193	−	0.481844i	0.692743	−	0.721185i	$-0.256402\pi$
$269$	−4.56270	−	7.90283i	−0.278193	−	0.481844i	−0.970936	+	0.239341i	$0.923069\pi$
$270$	3.13579	+	4.14328i	0.190838	+	0.252152i
$271$	−13.2680	+	22.9808i	−0.805973	+	1.39599i	0.109659	+	0.993969i	$0.465024\pi$
$271$	−13.2680	+	22.9808i	−0.805973	+	1.39599i	−0.915632	+	0.402017i	$0.868309\pi$
$272$	−1.97521	+	3.42117i	−0.119765	+	0.207439i
$273$	−1.96301	−	2.02994i	−0.118807	−	0.122858i
$274$	4.66480	+	8.07967i	0.281811	+	0.488111i
$275$	0.379264			0.0228705
$276$	2.20136	−	4.20603i	0.132506	−	0.253173i
$277$	−2.34121			−0.140669			−0.0703347	−	0.997523i	$-0.522407\pi$
$277$	−2.34121			−0.140669			−0.0703347	+	0.997523i	$0.522407\pi$
$278$	4.87554	−	8.44469i	0.292416	−	0.506479i
$279$	−3.04515	+	6.45563i	−0.182308	+	0.386488i
$280$	−2.59109	+	0.535003i	−0.154848	+	0.0319725i
$281$	8.99372	−	15.5776i	0.536520	−	0.929280i	−0.462568	−	0.886584i	$-0.653072\pi$
$281$	8.99372	−	15.5776i	0.536520	−	0.929280i	0.999088	−	0.0426963i	$-0.0135948\pi$
$282$	−5.97965	+	11.4250i	−0.356083	+	0.680351i
$283$	3.96265	−	6.86351i	0.235555	−	0.407993i	−0.723879	−	0.689927i	$-0.757643\pi$
$283$	3.96265	−	6.86351i	0.235555	−	0.407993i	0.959434	+	0.281934i	$0.0909759\pi$
$284$	5.64348	−	9.77479i	0.334879	−	0.580027i
$285$	4.12888	−	7.88885i	0.244574	−	0.467295i
$286$	0.116854	−	0.202397i	0.00690970	−	0.0119680i
$287$	12.7991	+	14.3824i	0.755508	+	0.848967i
$288$	1.27987	−	2.71329i	0.0754171	−	0.159882i
$289$	0.697058	−	1.20734i	0.0410034	−	0.0710200i
$290$	−7.38920			−0.433909
$291$	1.27241	−	2.43113i	0.0745901	−	0.142516i
$292$	7.17068			0.419632
$293$	13.3538	+	23.1294i	0.780135	+	1.35123i	0.931863	+	0.362811i	$0.118183\pi$
$293$	13.3538	+	23.1294i	0.780135	+	1.35123i	−0.151728	+	0.988422i	$0.548484\pi$
$294$	−10.0166	−	6.83135i	−0.584181	−	0.398412i
$295$	0.115881	−	0.200711i	0.00674683	−	0.0116858i
$296$	−3.99026	+	6.91133i	−0.231929	+	0.401713i
$297$	−1.95552	+	0.244260i	−0.113471	+	0.0141734i
$298$	−3.12699	−	5.41611i	−0.181142	−	0.313747i
$299$	−0.844470	−	1.46267i	−0.0488370	−	0.0845881i
$300$	0.803168	−	1.53458i	0.0463709	−	0.0885987i
$301$	4.28593	−	12.9340i	0.247037	−	0.745502i
$302$	10.9945	+	19.0431i	0.632665	+	1.09581i
$303$	20.8821	−	0.865459i	1.19964	−	0.0497193i
$304$	−5.14074			−0.294842
$305$	−5.76782	−	9.99016i	−0.330264	−	0.572035i
$306$	5.05603	−	10.7187i	0.289034	−	0.612744i
$307$	17.6963			1.00998			0.504991	−	0.863125i	$-0.331496\pi$
$307$	17.6963			1.00998			0.504991	+	0.863125i	$0.331496\pi$
$308$	0.315632	−	0.952506i	0.0179848	−	0.0542740i
$309$	19.8478	−	0.822595i	1.12910	−	0.0467958i
$310$	2.37926			0.135133
$311$	−8.21246	+	14.2244i	−0.465686	+	0.806592i	−0.999232	−	0.0391790i	$-0.987526\pi$
$311$	−8.21246	+	14.2244i	−0.465686	+	0.806592i	0.533546	+	0.845771i	$0.320859\pi$
$312$	−0.571473	−	0.901427i	−0.0323533	−	0.0510333i
$313$	5.94794	+	10.3021i	0.336197	+	0.582311i	0.983714	−	0.179741i	$-0.0575258\pi$
$313$	5.94794	+	10.3021i	0.336197	+	0.582311i	−0.647517	+	0.762051i	$0.724192\pi$
$314$	−15.9599			−0.900669
$315$	7.61381	−	2.24273i	0.428990	−	0.126363i
$316$	6.03527			0.339510
$317$	12.8943	+	22.3336i	0.724216	+	1.25438i	0.959296	+	0.282403i	$0.0911314\pi$
$317$	12.8943	+	22.3336i	0.724216	+	1.25438i	−0.235080	+	0.971976i	$0.575535\pi$
$318$	−1.60344	+	3.06362i	−0.0899167	+	0.171800i
$319$	1.40123	−	2.42700i	0.0784538	−	0.135886i
$320$	−1.00000			−0.0559017
$321$	−3.72491	+	7.11701i	−0.207904	+	0.397233i
$322$	−4.82079	−	5.41714i	−0.268652	−	0.301886i
$323$	−20.3081			−1.12997
$324$	−3.15288	+	8.42967i	−0.175160	+	0.468315i
$325$	−0.308106	−	0.533656i	−0.0170907	−	0.0296019i
$326$	−7.21531			−0.399619
$327$	−12.5761	−	19.8372i	−0.695461	−	1.09700i
$328$	3.63844	+	6.30196i	0.200899	+	0.347968i
$329$	13.0949	+	14.7148i	0.721948	+	0.811255i
$330$	0.351729	+	0.554808i	0.0193620	+	0.0305412i
$331$	0.0130328	+	0.0225735i	0.000716347	+	0.00124075i	0.866383	−	0.499379i	$-0.166439\pi$
$331$	0.0130328	+	0.0225735i	0.000716347	+	0.00124075i	−0.865667	+	0.500620i	$0.833105\pi$
$332$	4.29143	+	7.43298i	0.235523	+	0.407938i
$333$	10.2140	−	21.6534i	0.559725	−	1.18660i
$334$	−5.11565	+	8.86057i	−0.279916	+	0.484829i
$335$	6.70314	−	11.6102i	0.366232	−	0.634332i
$336$	−3.18560	−	3.29423i	−0.173789	−	0.179715i
$337$	−9.33400	−	16.1670i	−0.508455	−	0.880671i	−0.999952	−	0.00979108i	$-0.996883\pi$
$337$	−9.33400	−	16.1670i	−0.508455	−	0.880671i	0.491497	−	0.870879i	$-0.336450\pi$
$338$	12.6203			0.686453
$339$	14.4452	+	22.7855i	0.784557	+	1.23754i
$340$	−3.95043			−0.214242
$341$	−0.451185	+	0.781476i	−0.0244330	+	0.0423193i
$342$	15.3693	−	1.27616i	0.831078	−	0.0690068i
$343$	−15.1711	+	10.6225i	−0.819162	+	0.573563i
$344$	2.57500	−	4.46002i	0.138834	−	0.240468i
$345$	4.74320	−	0.196583i	0.255366	−	0.0105836i
$346$	2.12875	−	3.68710i	0.114442	−	0.198220i
$347$	16.9496	−	29.3576i	0.909904	−	1.57600i	0.0957083	−	0.995409i	$-0.469488\pi$
$347$	16.9496	−	29.3576i	0.909904	−	1.57600i	0.814196	−	0.580591i	$-0.197178\pi$
$348$	−6.85272	−	10.8093i	−0.367344	−	0.579439i
$349$	3.64339	−	6.31054i	0.195026	−	0.337796i	−0.751883	−	0.659297i	$-0.770854\pi$
$349$	3.64339	−	6.31054i	0.195026	−	0.337796i	0.946909	+	0.321501i	$0.104187\pi$
$350$	−1.75887	−	1.97645i	−0.0940157	−	0.105646i
$351$	1.93231	+	2.55314i	0.103139	+	0.136277i
$352$	0.189632	−	0.328453i	0.0101074	−	0.0175066i
$353$	5.56083			0.295973			0.147987	−	0.988989i	$-0.452721\pi$
$353$	5.56083			0.295973			0.147987	+	0.988989i	$0.452721\pi$
$354$	0.401078	−	0.0166227i	0.0213170	−	0.000883486i
$355$	11.2870			0.599050
$356$	6.26653	+	10.8540i	0.332126	+	0.575258i
$357$	−12.5845	−	13.0136i	−0.666042	−	0.688753i
$358$	−1.87410	+	3.24604i	−0.0990495	+	0.171559i
$359$	0.698378	−	1.20963i	0.0368590	−	0.0638416i	−0.847007	−	0.531581i	$-0.821598\pi$
$359$	0.698378	−	1.20963i	0.0368590	−	0.0638416i	0.883866	+	0.467739i	$0.154931\pi$
$360$	2.98971	−	0.248244i	0.157572	−	0.0130836i
$361$	−3.71361	−	6.43217i	−0.195453	−	0.338535i
$362$	9.76598	+	16.9152i	0.513288	+	0.889041i
$363$	18.7873	−	0.778641i	0.986077	−	0.0408680i
$364$	−1.59666	+	0.329675i	−0.0836880	+	0.0172797i
$365$	3.58534	+	6.20999i	0.187665	+	0.325046i
$366$	9.26506	−	17.7023i	0.484293	−	0.925315i
$367$	−28.0892			−1.46625			−0.733123	−	0.680096i	$-0.761938\pi$
$367$	−28.0892			−1.46625			−0.733123	+	0.680096i	$0.761938\pi$
$368$	−1.37042	−	2.37364i	−0.0714381	−	0.123734i
$369$	−12.4423	−	17.9378i	−0.647721	−	0.933806i
$370$	−7.98051			−0.414887
$371$	3.51141	+	3.94579i	0.182303	+	0.204855i
$372$	2.20652	+	3.48051i	0.114403	+	0.180456i
$373$	11.2252			0.581220			0.290610	−	0.956842i	$-0.406142\pi$
$373$	11.2252			0.581220			0.290610	+	0.956842i	$0.406142\pi$
$374$	0.749128	−	1.29753i	0.0387365	−	0.0670936i
$375$	1.73057	−	0.0717234i	0.0893660	−	0.00370378i
$376$	3.72254	+	6.44763i	0.191975	+	0.332511i
$377$	−4.55332			−0.234508
$378$	10.3418	+	9.05798i	0.531925	+	0.465892i
$379$	−13.2661			−0.681435			−0.340718	−	0.940166i	$-0.610670\pi$
$379$	−13.2661			−0.681435			−0.340718	+	0.940166i	$0.610670\pi$
$380$	−2.57037	−	4.45201i	−0.131857	−	0.228383i
$381$	−14.8404	+	0.615061i	−0.760296	+	0.0315105i
$382$	3.86820	−	6.69992i	0.197914	−	0.342798i
$383$	17.5244			0.895455			0.447727	−	0.894170i	$-0.352233\pi$
$383$	17.5244			0.895455			0.447727	+	0.894170i	$0.352233\pi$
$384$	−0.927397	−	1.46285i	−0.0473260	−	0.0746508i
$385$	0.982710	−	0.202908i	0.0500835	−	0.0103411i
$386$	−1.20249			−0.0612050
$387$	−6.59132	+	13.9734i	−0.335056	+	0.710308i
$388$	−0.792120	−	1.37199i	−0.0402138	−	0.0696523i
$389$	9.42441			0.477836			0.238918	−	0.971040i	$-0.423207\pi$
$389$	9.42441			0.477836			0.238918	+	0.971040i	$0.423207\pi$
$390$	0.494922	−	0.945624i	0.0250614	−	0.0478835i
$391$	−5.41375	−	9.37689i	−0.273785	−	0.474210i
$392$	−6.42754	+	2.77249i	−0.324640	+	0.140032i
$393$	23.9140	−	0.991119i	1.20630	−	0.0499953i
$394$	−9.14197	−	15.8344i	−0.460566	−	0.797724i
$395$	3.01763	+	5.22670i	0.151834	+	0.262984i
$396$	−0.485409	+	1.02905i	−0.0243927	+	0.0517119i
$397$	3.03378	−	5.25466i	0.152261	−	0.263724i	−0.779797	−	0.626032i	$-0.784678\pi$
$397$	3.03378	−	5.25466i	0.152261	−	0.263724i	0.932058	+	0.362308i	$0.118011\pi$
$398$	4.34213	−	7.52079i	0.217651	−	0.376983i
$399$	6.47776	−	22.6497i	0.324294	−	1.13390i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−39.1787			−1.95649			−0.978246	−	0.207450i	$-0.933484\pi$
$401$	−39.1787			−1.95649			−0.978246	+	0.207450i	$0.933484\pi$
$402$	23.2005	−	0.961545i	1.15713	−	0.0479575i
$403$	1.46613			0.0730332
$404$	6.03331	−	10.4500i	0.300168	−	0.519907i
$405$	−8.87675	+	1.48436i	−0.441089	+	0.0737583i
$406$	−19.1461	+	3.95324i	−0.950206	+	0.196196i
$407$	1.51336	−	2.62122i	0.0750146	−	0.129929i
$408$	−3.66361	−	5.77889i	−0.181376	−	0.286098i
$409$	−0.403682	+	0.699198i	−0.0199608	+	0.0345731i	−0.875833	−	0.482614i	$-0.839687\pi$
$409$	−0.403682	+	0.699198i	−0.0199608	+	0.0345731i	0.855872	+	0.517187i	$0.173021\pi$
$410$	−3.63844	+	6.30196i	−0.179690	+	0.311232i
$411$	−16.1455	+	0.669151i	−0.796398	+	0.0330068i
$412$	5.73449	−	9.93243i	0.282518	−	0.489336i
$413$	0.192876	−	0.582058i	0.00949083	−	0.0286412i
$414$	4.68640	+	6.75630i	0.230324	+	0.332054i
$415$	−4.29143	+	7.43298i	−0.210658	+	0.364871i
$416$	−0.616212			−0.0302123
$417$	9.04313	+	14.2644i	0.442844	+	0.698530i
$418$	1.94970			0.0953630
$419$	15.1172	+	26.1838i	0.738524	+	1.27916i	0.953160	+	0.302467i	$0.0978104\pi$
$419$	15.1172	+	26.1838i	0.738524	+	1.27916i	−0.214635	+	0.976694i	$0.568856\pi$
$420$	1.26008	−	4.40593i	0.0614857	−	0.214987i
$421$	−13.5938	+	23.5451i	−0.662519	+	1.14752i	0.317432	+	0.948281i	$0.397179\pi$
$421$	−13.5938	+	23.5451i	−0.662519	+	1.14752i	−0.979951	+	0.199236i	$0.936154\pi$
$422$	7.54299	−	13.0648i	0.367187	−	0.635987i
$423$	−12.7299	−	18.3524i	−0.618949	−	0.892326i
$424$	0.998199	+	1.72893i	0.0484769	+	0.0839644i
$425$	−1.97521	−	3.42117i	−0.0958120	−	0.165951i
$426$	10.4675	+	16.5111i	0.507152	+	0.799968i
$427$	−20.2897	−	22.7996i	−0.981889	−	1.10335i
$428$	2.31889	+	4.01643i	0.112088	+	0.194141i
$429$	0.216740	+	0.341879i	0.0104643	+	0.0165061i
$430$	5.14999			0.248355
$431$	−18.3346	−	31.7564i	−0.883145	−	1.52965i	−0.847826	−	0.530275i	$-0.822089\pi$
$431$	−18.3346	−	31.7564i	−0.883145	−	1.52965i	−0.0353190	−	0.999376i	$-0.511245\pi$
$432$	3.13579	+	4.14328i	0.150871	+	0.199344i
$433$	−24.3601			−1.17067			−0.585336	−	0.810791i	$-0.699037\pi$
$433$	−24.3601			−1.17067			−0.585336	+	0.810791i	$0.699037\pi$
$434$	6.16490	−	1.27291i	0.295925	−	0.0611018i
$435$	5.93477	−	11.3393i	0.284550	−	0.543677i
$436$	−13.5607			−0.649438
$437$	7.04498	−	12.2023i	0.337007	−	0.583713i
$438$	−5.75926	+	11.0039i	−0.275188	+	0.525789i
$439$	−11.2295	−	19.4501i	−0.535956	−	0.928302i	−0.999116	−	0.0420280i	$-0.986618\pi$
$439$	−11.2295	−	19.4501i	−0.535956	−	0.928302i	0.463161	−	0.886274i	$-0.346715\pi$
$440$	0.379264			0.0180807
$441$	18.5282	−	9.88454i	0.882297	−	0.470692i
$442$	−2.43430			−0.115788
$443$	9.25796	+	16.0353i	0.439859	+	0.761858i	0.997678	−	0.0681044i	$-0.0216951\pi$
$443$	9.25796	+	16.0353i	0.439859	+	0.761858i	−0.557819	+	0.829962i	$0.688362\pi$
$444$	−7.40110	−	11.6743i	−0.351241	−	0.554038i
$445$	−6.26653	+	10.8540i	−0.297062	+	0.514527i
$446$	22.2692			1.05448
$447$	10.8229	−	0.448557i	0.511907	−	0.0212160i
$448$	−2.59109	+	0.535003i	−0.122418	+	0.0252765i
$449$	−27.6845			−1.30651			−0.653257	−	0.757136i	$-0.726598\pi$
$449$	−27.6845			−1.30651			−0.653257	+	0.757136i	$0.726598\pi$
$450$	1.70984	+	2.46504i	0.0806027	+	0.116203i
$451$	−1.37993	−	2.39011i	−0.0649784	−	0.112546i
$452$	15.5761			0.732638
$453$	−38.0535	+	1.57713i	−1.78791	+	0.0741001i
$454$	1.45201	+	2.51496i	0.0681463	+	0.118033i
$455$	−1.08384	−	1.21791i	−0.0508112	−	0.0570967i
$456$	4.12888	−	7.88885i	0.193353	−	0.369429i
$457$	5.69023	+	9.85576i	0.266178	+	0.461033i	0.967871	−	0.251446i	$-0.0809059\pi$
$457$	5.69023	+	9.85576i	0.266178	+	0.461033i	−0.701694	+	0.712479i	$0.747573\pi$
$458$	7.40450	+	12.8250i	0.345989	+	0.599271i
$459$	12.3877	+	16.3677i	0.578210	+	0.763981i
$460$	1.37042	−	2.37364i	0.0638962	−	0.110671i
$461$	−11.2662	+	19.5136i	−0.524720	+	0.908841i	0.474866	+	0.880058i	$0.342496\pi$
$461$	−11.2662	+	19.5136i	−0.524720	+	0.908841i	−0.999586	+	0.0287830i	$0.990837\pi$
$462$	1.20819	+	1.24938i	0.0562099	+	0.0581266i
$463$	−8.51644	−	14.7509i	−0.395793	−	0.685533i	0.597409	−	0.801936i	$-0.296197\pi$
$463$	−8.51644	−	14.7509i	−0.395793	−	0.685533i	−0.993202	+	0.116404i	$0.962863\pi$
$464$	−7.38920			−0.343035
$465$	−1.91095	+	3.65116i	−0.0886182	+	0.169318i
$466$	19.2747			0.892883
$467$	3.14018	−	5.43895i	0.145310	−	0.251685i	−0.784178	−	0.620535i	$-0.786915\pi$
$467$	3.14018	−	5.43895i	0.145310	−	0.251685i	0.929489	+	0.368851i	$0.120249\pi$
$468$	1.84230	−	0.152971i	0.0851602	−	0.00707109i
$469$	11.1570	−	33.6693i	0.515182	−	1.55470i
$470$	−3.72254	+	6.44763i	−0.171708	+	0.297407i
$471$	12.8185	−	24.4917i	0.590644	−	1.12852i
$472$	0.115881	−	0.200711i	0.00533383	−	0.00923847i
$473$	−0.976604	+	1.69153i	−0.0449043	+	0.0777766i
$474$	−4.84734	+	9.26157i	−0.222646	+	0.425398i
$475$	2.57037	−	4.45201i	0.117937	−	0.204272i
$476$	−10.2359	+	2.11349i	−0.469163	+	0.0968717i
$477$	−3.41353	−	4.92121i	−0.156295	−	0.225327i
$478$	−5.41490	+	9.37888i	−0.247672	+	0.428980i
$479$	2.96967			0.135688			0.0678438	−	0.997696i	$-0.478388\pi$
$479$	2.96967			0.135688			0.0678438	+	0.997696i	$0.478388\pi$
$480$	0.803168	−	1.53458i	0.0366594	−	0.0700434i
$481$	−4.91769			−0.224227
$482$	−3.49332	−	6.05061i	−0.159116	−	0.275598i
$483$	12.1849	−	3.04699i	0.554433	−	0.138643i
$484$	5.42808	−	9.40171i	0.246731	−	0.427350i
$485$	0.792120	−	1.37199i	0.0359683	−	0.0622989i
$486$	−10.4037	−	11.6088i	−0.471920	−	0.526585i
$487$	7.50526	+	12.9995i	0.340096	+	0.589063i	0.984450	−	0.175664i	$-0.0562071\pi$
$487$	7.50526	+	12.9995i	0.340096	+	0.589063i	−0.644354	+	0.764727i	$0.722874\pi$
$488$	−5.76782	−	9.99016i	−0.261097	−	0.452233i
$489$	5.79511	−	11.0724i	0.262064	−	0.500713i
$490$	−5.61482	−	4.18017i	−0.253652	−	0.188841i
$491$	−6.41840	−	11.1170i	−0.289658	−	0.501703i	0.684070	−	0.729417i	$-0.260208\pi$
$491$	−6.41840	−	11.1170i	−0.289658	−	0.501703i	−0.973728	+	0.227714i	$0.926875\pi$
$492$	−12.5931	+	0.521923i	−0.567742	+	0.0235301i
$493$	−29.1905			−1.31467
$494$	−1.58389	−	2.74339i	−0.0712628	−	0.123431i
$495$	−1.13389	+	0.0941502i	−0.0509646	+	0.00423174i
$496$	2.37926			0.106832
$497$	29.2456	−	6.03856i	1.31184	−	0.270866i
$498$	−14.8532	+	0.615593i	−0.665588	+	0.0275854i
$499$	−23.3565			−1.04558			−0.522791	−	0.852461i	$-0.675109\pi$
$499$	−23.3565			−1.04558			−0.522791	+	0.852461i	$0.675109\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−9.48848	−	14.9669i	−0.423914	−	0.668671i
$502$	8.70967	+	15.0856i	0.388731	+	0.673303i
$503$	18.9067			0.843007			0.421503	−	0.906827i	$-0.361503\pi$
$503$	18.9067			0.843007			0.421503	+	0.906827i	$0.361503\pi$
$504$	7.61381	−	2.24273i	0.339146	−	0.0998991i
$505$	12.0666			0.536958
$506$	0.519752	+	0.900237i	0.0231058	+	0.0400204i
$507$	−10.1362	+	19.3668i	−0.450165	+	0.860108i
$508$	−4.28773	+	7.42656i	−0.190237	+	0.329500i
$509$	34.8111			1.54297			0.771487	−	0.636245i	$-0.219513\pi$
$509$	34.8111			1.54297			0.771487	+	0.636245i	$0.219513\pi$
$510$	3.17286	−	6.06223i	0.140497	−	0.268440i
$511$	12.6123	+	14.1725i	0.557936	+	0.626955i
$512$	−1.00000			−0.0441942
$513$	−10.3858	+	24.6104i	−0.458544	+	1.08657i
$514$	6.55702	+	11.3571i	0.289218	+	0.500940i
$515$	11.4690			0.505384
$516$	4.77609	+	7.53367i	0.210255	+	0.331652i
$517$	−1.41183	−	2.44535i	−0.0620920	−	0.107547i
$518$	−20.6783	+	4.26960i	−0.908551	+	0.187595i
$519$	3.94839	+	6.22809i	0.173315	+	0.273383i
$520$	−0.308106	−	0.533656i	−0.0135113	−	0.0234023i
$521$	17.3804	+	30.1037i	0.761449	+	1.31887i	0.942104	+	0.335321i	$0.108845\pi$
$521$	17.3804	+	30.1037i	0.761449	+	1.31887i	−0.180655	+	0.983546i	$0.557822\pi$
$522$	22.0916	−	1.83433i	0.966922	−	0.0802862i
$523$	−15.7294	+	27.2442i	−0.687800	+	1.19130i	0.284748	+	0.958602i	$0.408090\pi$
$523$	−15.7294	+	27.2442i	−0.687800	+	1.19130i	−0.972548	+	0.232702i	$0.925243\pi$
$524$	6.90931	−	11.9673i	0.301835	−	0.522793i
$525$	4.44569	−	1.11170i	0.194026	−	0.0485186i
$526$	−2.40150	−	4.15951i	−0.104710	−	0.181363i
$527$	9.39911			0.409432
$528$	0.351729	+	0.554808i	0.0153070	+	0.0241449i
$529$	−15.4878			−0.673382
$530$	−0.998199	+	1.72893i	−0.0433590	+	0.0751000i
$531$	−0.296624	+	0.628835i	−0.0128724	+	0.0272891i
$532$	−9.04192	−	10.1604i	−0.392017	−	0.440511i
$533$	−2.24205	+	3.88335i	−0.0971140	+	0.168206i
$534$	−21.6893	+	0.898914i	−0.938587	+	0.0388998i
$535$	−2.31889	+	4.01643i	−0.100254	+	0.173645i
$536$	6.70314	−	11.6102i	0.289532	−	0.501484i
$537$	−3.47608	−	5.48307i	−0.150004	−	0.236612i
$538$	4.56270	−	7.90283i	0.196712	−	0.340715i
$539$	2.43774	−	1.05151i	0.105001	−	0.0452916i
$540$	−2.02029	+	4.78732i	−0.0869395	+	0.206013i
$541$	−14.7606	+	25.5662i	−0.634609	+	1.09918i	0.351989	+	0.936004i	$0.385506\pi$
$541$	−14.7606	+	25.5662i	−0.634609	+	1.09918i	−0.986598	+	0.163171i	$0.947828\pi$
$542$	−26.5360			−1.13982
$543$	−33.8013	+	1.40090i	−1.45055	+	0.0601183i
$544$	−3.95043			−0.169373
$545$	−6.78033	−	11.7439i	−0.290437	−	0.503052i
$546$	0.776479	−	2.71499i	0.0332302	−	0.116191i
$547$	10.2744	−	17.7958i	0.439301	−	0.760892i	−0.558334	−	0.829616i	$-0.688559\pi$
$547$	10.2744	−	17.7958i	0.439301	−	0.760892i	0.997636	+	0.0687237i	$0.0218927\pi$
$548$	−4.66480	+	8.07967i	−0.199270	+	0.345147i
$549$	19.7241	+	28.4359i	0.841805	+	1.21361i
$550$	0.189632	+	0.328453i	0.00808594	+	0.0140053i
$551$	−18.9930	−	32.8968i	−0.809128	−	1.40145i
$552$	4.74320	−	0.196583i	0.201884	−	0.00836711i
$553$	10.6153	+	11.9284i	0.451407	+	0.507248i
$554$	−1.17060	−	2.02754i	−0.0497342	−	0.0861421i
$555$	6.40969	−	12.2467i	0.272076	−	0.519843i
$556$	9.75109			0.413538
$557$	−12.1130	−	20.9803i	−0.513243	−	0.888963i	−0.999882	−	0.0153595i	$-0.995111\pi$
$557$	−12.1130	−	20.9803i	−0.513243	−	0.888963i	0.486639	−	0.873603i	$-0.338223\pi$
$558$	−7.11331	+	0.590638i	−0.301131	+	0.0250037i
$559$	3.17349			0.134224
$560$	−1.75887	−	1.97645i	−0.0743260	−	0.0835204i
$561$	1.38948	+	2.19173i	0.0586638	+	0.0925348i
$562$	17.9874			0.758754
$563$	7.29569	−	12.6365i	0.307477	−	0.532565i	−0.670333	−	0.742060i	$-0.733849\pi$
$563$	7.29569	−	12.6365i	0.307477	−	0.532565i	0.977810	+	0.209495i	$0.0671820\pi$
$564$	−12.8842	+	0.533986i	−0.542522	+	0.0224849i
$565$	7.78805	+	13.4893i	0.327646	+	0.567499i
$566$	7.92530			0.333125
$567$	−22.2064	+	8.59520i	−0.932580	+	0.360964i
$568$	11.2870			0.473590
$569$	−3.35828	−	5.81670i	−0.140786	−	0.243849i	0.787007	−	0.616944i	$-0.211630\pi$
$569$	−3.35828	−	5.81670i	−0.140786	−	0.243849i	−0.927793	+	0.373096i	$0.878296\pi$
$570$	8.89639	−	0.368712i	0.372629	−	0.0154436i
$571$	17.9126	−	31.0255i	0.749619	−	1.29838i	−0.198387	−	0.980124i	$-0.563570\pi$
$571$	17.9126	−	31.0255i	0.749619	−	1.29838i	0.948005	−	0.318254i	$-0.103097\pi$
$572$	0.233707			0.00977180
$573$	7.17472	+	11.3172i	0.299728	+	0.472783i
$574$	−6.05597	+	18.2756i	−0.252771	+	0.762807i
$575$	2.74084			0.114301
$576$	2.98971	−	0.248244i	0.124571	−	0.0103435i
$577$	−5.90753	−	10.2321i	−0.245934	−	0.425970i	0.716460	−	0.697628i	$-0.245761\pi$
$577$	−5.90753	−	10.2321i	−0.245934	−	0.425970i	−0.962394	+	0.271659i	$0.912428\pi$
$578$	1.39412			0.0579876
$579$	0.965799	−	1.84531i	0.0401372	−	0.0766883i
$580$	−3.69460	−	6.39923i	−0.153410	−	0.265714i
$581$	−7.14285	+	21.5555i	−0.296335	+	0.894273i
$582$	2.74163	−	0.113627i	0.113644	−	0.00471000i
$583$	−0.378582	−	0.655722i	−0.0156792	−	0.0271572i
$584$	3.58534	+	6.20999i	0.148362	+	0.256971i
$585$	1.05363	+	1.51899i	0.0435621	+	0.0628025i
$586$	−13.3538	+	23.1294i	−0.551639	+	0.955466i
$587$	−7.21091	+	12.4897i	−0.297626	+	0.515503i	−0.975592	−	0.219590i	$-0.929528\pi$
$587$	−7.21091	+	12.4897i	−0.297626	+	0.515503i	0.677966	+	0.735093i	$0.262862\pi$
$588$	0.907810	−	12.0903i	0.0374374	−	0.498596i
$589$	6.11559	+	10.5925i	0.251989	+	0.436457i
$590$	0.231761			0.00954145
$591$	31.6416	−	1.31139i	1.30156	−	0.0539433i
$592$	−7.98051			−0.327997
$593$	−15.5047	+	26.8549i	−0.636701	+	1.10280i	0.349451	+	0.936955i	$0.386368\pi$
$593$	−15.5047	+	26.8549i	−0.636701	+	1.10280i	−0.986152	+	0.165844i	$0.946965\pi$
$594$	−1.18929	−	1.57140i	−0.0487974	−	0.0644753i
$595$	−6.94830	−	7.80783i	−0.284853	−	0.320090i
$596$	3.12699	−	5.41611i	0.128087	−	0.221853i
$597$	8.05376	+	12.7038i	0.329618	+	0.519931i
$598$	0.844470	−	1.46267i	0.0345330	−	0.0598128i
$599$	−23.6350	+	40.9371i	−0.965701	+	1.67264i	−0.257982	+	0.966150i	$0.583057\pi$
$599$	−23.6350	+	40.9371i	−0.965701	+	1.67264i	−0.707719	+	0.706494i	$0.750276\pi$
$600$	1.73057	−	0.0717234i	0.0706500	−	0.00292810i
$601$	−21.3039	+	36.8994i	−0.869004	+	1.50516i	−0.00598892	+	0.999982i	$0.501906\pi$
$601$	−21.3039	+	36.8994i	−0.869004	+	1.50516i	−0.863015	+	0.505178i	$0.831427\pi$
$602$	13.3441	−	2.75526i	0.543866	−	0.112296i
$603$	−17.1583	+	36.3751i	−0.698740	+	1.48131i
$604$	−10.9945	+	19.0431i	−0.447361	+	0.774853i
$605$	10.8562			0.441366
$606$	11.1905	+	17.6517i	0.454585	+	0.717050i
$607$	−0.622142			−0.0252520			−0.0126260	−	0.999920i	$-0.504019\pi$
$607$	−0.622142			−0.0252520			−0.0126260	+	0.999920i	$0.504019\pi$
$608$	−2.57037	−	4.45201i	−0.104242	−	0.180553i
$609$	9.31100	−	32.5563i	0.377301	−	1.31925i
$610$	5.76782	−	9.99016i	0.233532	−	0.404490i
$611$	−2.29387	+	3.97311i	−0.0928002	+	0.160735i
$612$	11.8106	−	0.980671i	0.477417	−	0.0396413i
$613$	−16.3060	−	28.2428i	−0.658593	−	1.14072i	−0.980980	−	0.194108i	$-0.937819\pi$
$613$	−16.3060	−	28.2428i	−0.658593	−	1.14072i	0.322387	−	0.946608i	$-0.395515\pi$
$614$	8.84815	+	15.3254i	0.357082	+	0.618485i
$615$	−6.74856	−	10.6450i	−0.272128	−	0.429248i
$616$	0.982710	−	0.202908i	0.0395945	−	0.00817538i
$617$	−5.77847	−	10.0086i	−0.232632	−	0.402931i	0.725950	−	0.687748i	$-0.241401\pi$
$617$	−5.77847	−	10.0086i	−0.232632	−	0.402931i	−0.958582	+	0.284817i	$0.908067\pi$
$618$	10.6363	+	16.7774i	0.427855	+	0.674887i
$619$	−30.3806			−1.22110			−0.610551	−	0.791977i	$-0.709052\pi$
$619$	−30.3806			−1.22110			−0.610551	+	0.791977i	$0.709052\pi$
$620$	1.18963	+	2.06050i	0.0477768	+	0.0827518i
$621$	−14.1320	+	1.76520i	−0.567098	+	0.0708350i
$622$	−16.4249			−0.658580
$623$	−10.4303	+	31.4762i	−0.417880	+	1.26107i
$624$	0.494922	−	0.945624i	0.0198127	−	0.0378553i
$625$	1.00000			0.0400000
$626$	−5.94794	+	10.3021i	−0.237727	+	0.411756i
$627$	−1.56594	+	2.99196i	−0.0625375	+	0.119487i
$628$	−7.97995	−	13.8217i	−0.318435	−	0.551545i
$629$	−31.5264			−1.25704
$630$	5.74917	+	5.47239i	0.229052	+	0.218025i
$631$	38.4859			1.53210			0.766050	−	0.642781i	$-0.222219\pi$
$631$	38.4859			1.53210			0.766050	+	0.642781i	$0.222219\pi$
$632$	3.01763	+	5.22670i	0.120035	+	0.207907i
$633$	13.9907	+	22.0686i	0.556080	+	0.877146i
$634$	−12.8943	+	22.3336i	−0.512098	+	0.886980i
$635$	−8.57545			−0.340306
$636$	−3.45490	+	0.143189i	−0.136996	+	0.00567780i
$637$	−3.45992	−	2.57587i	−0.137087	−	0.102060i
$638$	2.80246			0.110950
$639$	−33.7448	+	2.80192i	−1.33492	+	0.110842i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−48.2156			−1.90440			−0.952201	−	0.305473i	$-0.901186\pi$
$641$	−48.2156			−1.90440			−0.952201	+	0.305473i	$0.901186\pi$
$642$	−8.02597	+	0.332637i	−0.316760	+	0.0131281i
$643$	13.1515	+	22.7790i	0.518643	+	0.898316i	0.999765	+	0.0216625i	$0.00689593\pi$
$643$	13.1515	+	22.7790i	0.518643	+	0.898316i	−0.481122	+	0.876653i	$0.659771\pi$
$644$	2.28099	−	6.88350i	0.0898835	−	0.271248i
$645$	−4.13631	+	7.90305i	−0.162867	+	0.311182i
$646$	−10.1541	−	17.5874i	−0.399506	−	0.691965i
$647$	10.4110	+	18.0323i	0.409298	+	0.708924i	0.994811	−	0.101738i	$-0.0324404\pi$
$647$	10.4110	+	18.0323i	0.409298	+	0.708924i	−0.585514	+	0.810663i	$0.699107\pi$
$648$	−8.87675	+	1.48436i	−0.348712	+	0.0583110i
$649$	−0.0439494	+	0.0761225i	−0.00172516	+	0.00298807i
$650$	0.308106	−	0.533656i	0.0120849	−	0.0209317i
$651$	−2.99807	+	10.4829i	−0.117504	+	0.410856i
$652$	−3.60765	−	6.24864i	−0.141287	−	0.244716i
$653$	−22.9920			−0.899748			−0.449874	−	0.893092i	$-0.648531\pi$
$653$	−22.9920			−0.899748			−0.449874	+	0.893092i	$0.648531\pi$
$654$	10.8915	−	20.8099i	0.425891	−	0.813730i
$655$	13.8186			0.539938
$656$	−3.63844	+	6.30196i	−0.142057	+	0.246050i
$657$	−12.2607	−	17.6760i	−0.478336	−	0.689608i
$658$	−6.19595	+	18.6980i	−0.241543	+	0.728923i
$659$	1.13866	−	1.97221i	0.0443557	−	0.0768263i	−0.842995	−	0.537921i	$-0.819210\pi$
$659$	1.13866	−	1.97221i	0.0443557	−	0.0768263i	0.887351	+	0.461095i	$0.152543\pi$
$660$	−0.304613	+	0.582010i	−0.0118571	+	0.0226547i
$661$	−24.6335	+	42.6665i	−0.958132	+	1.65953i	−0.231101	+	0.972930i	$0.574233\pi$
$661$	−24.6335	+	42.6665i	−0.958132	+	1.65953i	−0.727032	+	0.686604i	$0.759101\pi$
$662$	−0.0130328	+	0.0225735i	−0.000506534	+	0.000877342i
$663$	1.95515	−	3.73562i	0.0759319	−	0.145079i
$664$	−4.29143	+	7.43298i	−0.166540	+	0.288456i
$665$	4.27823	−	12.9107i	0.165903	−	0.500657i
$666$	23.8594	−	1.98112i	0.924534	−	0.0767666i
$667$	10.1263	−	17.5393i	0.392092	−	0.679124i
$668$	−10.2313			−0.395861
$669$	−17.8859	+	34.1738i	−0.691511	+	1.32124i
$670$	13.4063			0.517930
$671$	2.18753	+	3.78891i	0.0844486	+	0.146269i
$672$	1.26008	−	4.40593i	0.0486087	−	0.169962i
$673$	23.7608	−	41.1550i	0.915913	−	1.58641i	0.110355	−	0.993892i	$-0.464801\pi$
$673$	23.7608	−	41.1550i	0.915913	−	1.58641i	0.805559	−	0.592516i	$-0.201865\pi$
$674$	9.33400	−	16.1670i	0.359532	−	0.622728i
$675$	−5.15609	+	0.644035i	−0.198458	+	0.0247889i
$676$	6.31014	+	10.9295i	0.242698	+	0.420365i
$677$	11.0948	+	19.2167i	0.426406	+	0.738558i	0.996551	−	0.0829870i	$-0.0264460\pi$
$677$	11.0948	+	19.2167i	0.426406	+	0.738558i	−0.570144	+	0.821545i	$0.693113\pi$
$678$	−12.5102	+	23.9027i	−0.480452	+	0.917977i
$679$	1.31844	−	3.97875i	0.0505970	−	0.152690i
$680$	−1.97521	−	3.42117i	−0.0757460	−	0.131196i
$681$	−5.02560	+	0.208287i	−0.192581	+	0.00798156i
$682$	−0.902370			−0.0345535
$683$	9.12399	+	15.8032i	0.349120	+	0.604693i	0.986093	−	0.166192i	$-0.0531473\pi$
$683$	9.12399	+	15.8032i	0.349120	+	0.604693i	−0.636974	+	0.770886i	$0.719814\pi$
$684$	8.78985	+	12.6722i	0.336088	+	0.484532i
$685$	−9.32960			−0.356466
$686$	−16.7849	−	7.82728i	−0.640851	−	0.298847i
$687$	−25.6279	+	1.06215i	−0.977766	+	0.0405236i
$688$	5.14999			0.196342
$689$	−0.615103	+	1.06539i	−0.0234336	+	0.0405881i
$690$	2.54185	+	4.00944i	0.0967665	+	0.152637i
$691$	13.2691	+	22.9827i	0.504779	+	0.874304i	0.999985	+	0.00552760i	$0.00175950\pi$
$691$	13.2691	+	22.9827i	0.504779	+	0.874304i	−0.495205	+	0.868776i	$0.664907\pi$
$692$	4.25750			0.161846
$693$	−2.88765	+	0.850587i	−0.109693	+	0.0323111i
$694$	33.8993			1.28680
$695$	4.87554	+	8.44469i	0.184940	+	0.320325i
$696$	5.93477	−	11.3393i	0.224957	−	0.429814i
$697$	−14.3734	+	24.8955i	−0.544431	+	0.942983i
$698$	7.28679			0.275809
$699$	−15.4808	+	29.5785i	−0.585539	+	1.11876i
$700$	0.832221	−	2.51146i	0.0314550	−	0.0949241i
$701$	−11.5095			−0.434708			−0.217354	−	0.976093i	$-0.569743\pi$
$701$	−11.5095			−0.434708			−0.217354	+	0.976093i	$0.569743\pi$
$702$	−1.24493	+	2.95000i	−0.0469868	+	0.111341i
$703$	−20.5129	−	35.5293i	−0.773658	−	1.34001i
$704$	0.379264			0.0142941
$705$	−6.90454	−	10.8910i	−0.260040	−	0.410180i
$706$	2.78042	+	4.81582i	0.104642	+	0.181246i
$707$	31.2658	−	6.45568i	1.17587	−	0.242791i
$708$	0.214934	+	0.339032i	0.00807773	+	0.0127416i
$709$	6.60117	+	11.4336i	0.247912	+	0.429397i	0.962946	−	0.269693i	$-0.0869222\pi$
$709$	6.60117	+	11.4336i	0.247912	+	0.429397i	−0.715034	+	0.699090i	$0.753589\pi$
$710$	5.64348	+	9.77479i	0.211796	+	0.366841i
$711$	−10.3194	−	14.8772i	−0.387006	−	0.557939i
$712$	−6.26653	+	10.8540i	−0.234848	+	0.406769i
$713$	−3.26059	+	5.64751i	−0.122110	+	0.211501i
$714$	4.97787	−	17.4053i	0.186292	−	0.651377i
$715$	0.116854	+	0.202397i	0.00437008	+	0.00756920i
$716$	−3.74821			−0.140077
$717$	−10.0435	−	15.8424i	−0.375082	−	0.591645i
$718$	1.39676			0.0521264
$719$	21.8952	−	37.9237i	0.816555	−	1.41431i	−0.0916513	−	0.995791i	$-0.529215\pi$
$719$	21.8952	−	37.9237i	0.816555	−	1.41431i	0.908206	−	0.418523i	$-0.137452\pi$
$720$	1.70984	+	2.46504i	0.0637220	+	0.0918668i
$721$	29.7172	−	6.13594i	1.10673	−	0.228514i
$722$	3.71361	−	6.43217i	0.138206	−	0.239381i
$723$	12.0908	−	0.501106i	0.449663	−	0.0186363i
$724$	−9.76598	+	16.9152i	−0.362950	+	0.628647i
$725$	3.69460	−	6.39923i	0.137214	−	0.237662i
$726$	10.0680	+	15.8809i	0.373657	+	0.589397i
$727$	14.4786	−	25.0776i	0.536980	−	0.930076i	−0.462085	−	0.886836i	$-0.652898\pi$
$727$	14.4786	−	25.0776i	0.536980	−	0.930076i	0.999065	−	0.0432406i	$-0.0137682\pi$
$728$	−1.08384	−	1.21791i	−0.0401698	−	0.0451389i
$729$	26.1704	−	6.64140i	0.969275	−	0.245978i
$730$	−3.58534	+	6.20999i	−0.132699	+	0.229842i
$731$	20.3447			0.752475
$732$	19.9632	−	0.827376i	0.737860	−	0.0305807i
$733$	35.7333			1.31984			0.659920	−	0.751336i	$-0.270590\pi$
$733$	35.7333			1.31984			0.659920	+	0.751336i	$0.270590\pi$
$734$	−14.0446	−	24.3260i	−0.518396	−	0.897888i
$735$	10.9244	−	5.25897i	0.402954	−	0.193980i
$736$	1.37042	−	2.37364i	0.0505144	−	0.0874935i
$737$	−2.54226	+	4.40333i	−0.0936455	+	0.162199i
$738$	9.31346	−	19.7443i	0.342833	−	0.726797i
$739$	5.27465	+	9.13596i	0.194031	+	0.336072i	0.946582	−	0.322462i	$-0.104510\pi$
$739$	5.27465	+	9.13596i	0.194031	+	0.336072i	−0.752551	+	0.658534i	$0.771177\pi$
$740$	−3.99026	−	6.91133i	−0.146685	−	0.254065i
$741$	5.48206	−	0.227205i	0.201389	−	0.00834657i
$742$	−1.66145	+	5.01387i	−0.0609936	+	0.184065i
$743$	−9.55767	−	16.5544i	−0.350637	−	0.607321i	0.635724	−	0.771916i	$-0.280702\pi$
$743$	−9.55767	−	16.5544i	−0.350637	−	0.607321i	−0.986361	+	0.164595i	$0.947368\pi$
$744$	−1.91095	+	3.65116i	−0.0700588	+	0.133858i
$745$	6.25399			0.229128
$746$	5.61261	+	9.72133i	0.205492	+	0.355923i
$747$	10.9850	−	23.2878i	0.401919	−	0.852056i
$748$	1.49826			0.0547817
$749$	−3.85965	+	11.6476i	−0.141029	+	0.425593i
$750$	0.927397	+	1.46285i	0.0338637	+	0.0534158i
$751$	11.3285			0.413383			0.206692	−	0.978406i	$-0.433730\pi$
$751$	11.3285			0.413383			0.206692	+	0.978406i	$0.433730\pi$
$752$	−3.72254	+	6.44763i	−0.135747	+	0.235121i
$753$	−30.1453	+	1.24937i	−1.09856	+	0.0455297i
$754$	−2.27666	−	3.94329i	−0.0829110	−	0.143606i
$755$	−21.9891			−0.800264
$756$	−2.67354	+	13.4853i	−0.0972357	+	0.490454i
$757$	11.7276			0.426248			0.213124	−	0.977025i	$-0.431636\pi$
$757$	11.7276			0.426248			0.213124	+	0.977025i	$0.431636\pi$
$758$	−6.63306	−	11.4888i	−0.240924	−	0.417292i
$759$	−1.79893	+	0.0745568i	−0.0652970	+	0.00270624i
$760$	2.57037	−	4.45201i	0.0932372	−	0.161491i
$761$	−3.60028			−0.130510			−0.0652551	−	0.997869i	$-0.520786\pi$
$761$	−3.60028			−0.130510			−0.0652551	+	0.997869i	$0.520786\pi$
$762$	−7.95285	−	12.5446i	−0.288101	−	0.454443i
$763$	−23.8515	−	26.8020i	−0.863482	−	0.970297i
$764$	7.73641			0.279893
$765$	6.75461	+	9.73798i	0.244213	+	0.352077i
$766$	8.76220	+	15.1766i	0.316591	+	0.548352i
$767$	0.142814			0.00515672
$768$	0.803168	−	1.53458i	0.0289818	−	0.0553742i
$769$	−19.2146	−	33.2806i	−0.692896	−	1.20013i	−0.970885	−	0.239546i	$-0.923001\pi$
$769$	−19.2146	−	33.2806i	−0.692896	−	1.20013i	0.277989	−	0.960584i	$-0.410332\pi$
$770$	0.667078	+	0.749598i	0.0240398	+	0.0270136i
$771$	−22.6947	+	0.940584i	−0.817330	+	0.0338743i
$772$	−0.601243	−	1.04138i	−0.0216392	−	0.0374802i
$773$	12.7904	+	22.1536i	0.460038	+	0.796810i	0.998962	−	0.0455446i	$-0.0145023\pi$
$773$	12.7904	+	22.1536i	0.460038	+	0.796810i	−0.538924	+	0.842354i	$0.681169\pi$
$774$	−15.3970	+	1.27846i	−0.553433	+	0.0459531i
$775$	−1.18963	+	2.06050i	−0.0427329	+	0.0740155i
$776$	0.792120	−	1.37199i	0.0284354	−	0.0492516i
$777$	10.0561	−	35.1615i	0.360761	−	1.26141i
$778$	4.71220	+	8.16178i	0.168941	+	0.292614i
$779$	−37.4086			−1.34030
$780$	1.06640	−	0.0441969i	0.0381831	−	0.00158250i
$781$	−4.28074			−0.153177
$782$	5.41375	−	9.37689i	0.193595	−	0.335317i
$783$	−14.9283	+	35.3745i	−0.533495	+	1.26418i
$784$	−5.61482	−	4.18017i	−0.200529	−	0.149292i
$785$	7.97995	−	13.8217i	0.284817	−	0.493317i
$786$	12.8153	+	20.2146i	0.457108	+	0.721031i
$787$	18.1550	−	31.4453i	0.647155	−	1.12091i	−0.336644	−	0.941632i	$-0.609292\pi$
$787$	18.1550	−	31.4453i	0.647155	−	1.12091i	0.983799	−	0.179274i	$-0.0573748\pi$
$788$	9.14197	−	15.8344i	0.325669	−	0.564076i
$789$	8.31189	−	0.344487i	0.295911	−	0.0122641i
$790$	−3.01763	+	5.22670i	−0.107363	+	0.185958i
$791$	27.3964	+	30.7854i	0.974103	+	1.09460i
$792$	−1.13389	+	0.0941502i	−0.0402911	+	0.00334548i
$793$	3.55420	−	6.15606i	0.126213	−	0.218608i
$794$	6.06756			0.215330
$795$	−1.85145	−	2.92044i	−0.0656643	−	0.103577i
$796$	8.68426			0.307806
$797$	−25.0226	−	43.3404i	−0.886345	−	1.53520i	−0.844164	−	0.536085i	$-0.819903\pi$
$797$	−25.0226	−	43.3404i	−0.886345	−	1.53520i	−0.0421813	−	0.999110i	$-0.513431\pi$
$798$	22.8541	−	5.71496i	0.809027	−	0.202307i
$799$	−14.7056	+	25.4709i	−0.520247	+	0.901095i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	16.0407	−	34.0058i	0.566770	−	1.20154i
$802$	−19.5894	−	33.9298i	−0.691724	−	1.19810i
$803$	−1.35979	−	2.35523i	−0.0479860	−	0.0831142i
$804$	12.4329	+	19.6114i	0.438476	+	0.691641i
$805$	7.10178	−	1.46636i	0.250305	−	0.0516823i
$806$	0.733066	+	1.26971i	0.0258212	+	0.0447235i
$807$	8.46286	+	13.3491i	0.297907	+	0.469911i
$808$	12.0666			0.424502
$809$	19.2324	+	33.3115i	0.676175	+	1.17117i	0.976124	+	0.217215i	$0.0696971\pi$
$809$	19.2324	+	33.3115i	0.676175	+	1.17117i	−0.299949	+	0.953955i	$0.596970\pi$
$810$	−5.72387	−	6.94531i	−0.201116	−	0.244033i
$811$	−3.66567			−0.128719			−0.0643595	−	0.997927i	$-0.520500\pi$
$811$	−3.66567			−0.128719			−0.0643595	+	0.997927i	$0.520500\pi$
$812$	−12.9967	−	14.6044i	−0.456094	−	0.512514i
$813$	21.3129	−	40.7215i	0.747475	−	1.42816i
$814$	3.02672			0.106087
$815$	3.60765	−	6.24864i	0.126371	−	0.218880i
$816$	3.17286	−	6.06223i	0.111072	−	0.212220i
$817$	13.2374	+	22.9278i	0.463118	+	0.802143i
$818$	−0.807364			−0.0282288
$819$	3.54271	+	3.37216i	0.123792	+	0.117833i
$820$	−7.27688			−0.254120
$821$	24.8368	+	43.0185i	0.866809	+	1.50136i	0.865240	+	0.501358i	$0.167166\pi$
$821$	24.8368	+	43.0185i	0.866809	+	1.50136i	0.00156914	+	0.999999i	$0.499501\pi$
$822$	−8.65225	−	13.6478i	−0.301782	−	0.476023i
$823$	11.7326	−	20.3215i	0.408974	−	0.708364i	−0.585801	−	0.810455i	$-0.699220\pi$
$823$	11.7326	−	20.3215i	0.408974	−	0.708364i	0.994775	+	0.102091i	$0.0325532\pi$
$824$	11.4690			0.399541
$825$	−0.656342	+	0.0272021i	−0.0228509	+	0.000947057i
$826$	0.600515	−	0.123993i	0.0208946	−	0.00431426i
$827$	−7.31763			−0.254459			−0.127230	−	0.991873i	$-0.540608\pi$
$827$	−7.31763			−0.254459			−0.127230	+	0.991873i	$0.540608\pi$
$828$	−3.50792	+	7.43669i	−0.121909	+	0.258443i
$829$	−3.79583	−	6.57457i	−0.131835	−	0.228344i	0.792549	−	0.609808i	$-0.208753\pi$
$829$	−3.79583	−	6.57457i	−0.131835	−	0.228344i	−0.924384	+	0.381464i	$0.875420\pi$
$830$	−8.58287			−0.297916
$831$	4.05161	−	0.167919i	0.140549	−	0.00582506i
$832$	−0.308106	−	0.533656i	−0.0106817	−	0.0185012i
$833$	−22.1809	−	16.5135i	−0.768524	−	0.572158i
$834$	−7.83176	+	14.9638i	−0.271192	+	0.518153i
$835$	−5.11565	−	8.86057i	−0.177035	−	0.306633i
$836$	0.974850	+	1.68849i	0.0337159	+	0.0583977i
$837$	4.80681	−	11.3903i	0.166148	−	0.393706i
$838$	−15.1172	+	26.1838i	−0.522216	+	0.904504i
$839$	−24.3324	+	42.1449i	−0.840047	+	1.45500i	0.0498072	+	0.998759i	$0.484139\pi$
$839$	−24.3324	+	42.1449i	−0.840047	+	1.45500i	−0.889854	+	0.456245i	$0.849194\pi$
$840$	4.44569	−	1.11170i	0.153391	−	0.0383573i
$841$	−12.8001	−	22.1705i	−0.441384	−	0.764499i
$842$	−27.1875			−0.936944
$843$	−14.4469	+	27.6031i	−0.497579	+	0.950700i
$844$	15.0860			0.519281
$845$	−6.31014	+	10.9295i	−0.217075	+	0.375986i
$846$	9.52873	−	20.2006i	0.327604	−	0.694512i
$847$	28.1293	−	5.80808i	0.966535	−	0.199568i
$848$	−0.998199	+	1.72893i	−0.0342783	+	0.0593718i
$849$	−6.36535	+	12.1620i	−0.218458	+	0.417398i
$850$	1.97521	−	3.42117i	0.0677493	−	0.117345i
$851$	10.9367	−	18.9428i	0.374904	−	0.649352i
$852$	−9.06533	+	17.3207i	−0.310573	+	0.593397i
$853$	17.4299	−	30.1895i	0.596790	−	1.03367i	−0.396502	−	0.918034i	$-0.629776\pi$
$853$	17.4299	−	30.1895i	0.596790	−	1.03367i	0.993292	−	0.115636i	$-0.0368907\pi$
$854$	9.60021	−	28.9713i	0.328512	−	0.991376i
$855$	−6.57948	+	13.9483i	−0.225014	+	0.477022i
$856$	−2.31889	+	4.01643i	−0.0792579	+	0.137279i
$857$	16.1207			0.550672			0.275336	−	0.961348i	$-0.411211\pi$
$857$	16.1207			0.550672			0.275336	+	0.961348i	$0.411211\pi$
$858$	−0.187706	+	0.358642i	−0.00640819	+	0.0122438i
$859$	5.86219			0.200015			0.100008	−	0.994987i	$-0.468113\pi$
$859$	5.86219			0.200015			0.100008	+	0.994987i	$0.468113\pi$
$860$	2.57500	+	4.46002i	0.0878066	+	0.152086i
$861$	−23.1813	−	23.9717i	−0.790015	−	0.816953i
$862$	18.3346	−	31.7564i	0.624478	−	1.08163i
$863$	5.81678	−	10.0750i	0.198006	−	0.342956i	−0.749876	−	0.661578i	$-0.769887\pi$
$863$	5.81678	−	10.0750i	0.198006	−	0.342956i	0.947882	+	0.318623i	$0.103220\pi$
$864$	−2.02029	+	4.78732i	−0.0687317	+	0.162868i
$865$	2.12875	+	3.68710i	0.0723797	+	0.125365i
$866$	−12.1801	−	21.0965i	−0.413895	−	0.716887i
$867$	−1.11971	+	2.13938i	−0.0380273	+	0.0726570i
$868$	4.18483	+	4.70250i	0.142042	+	0.159613i
$869$	−1.14448	−	1.98230i	−0.0388239	−	0.0672449i
$870$	12.7875	−	0.529979i	0.433537	−	0.0179680i
$871$	8.26112			0.279917
$872$	−6.78033	−	11.7439i	−0.229611	−	0.397698i
$873$	−2.02762	+	4.29850i	−0.0686246	+	0.145482i
$874$	14.0900			0.476600
$875$	2.59109	−	0.535003i	0.0875950	−	0.0180864i
$876$	−12.4093	+	0.514306i	−0.419272	+	0.0173768i
$877$	50.3730			1.70097			0.850487	−	0.525996i	$-0.176307\pi$
$877$	50.3730			1.70097			0.850487	+	0.525996i	$0.176307\pi$
$878$	11.2295	−	19.4501i	0.378978	−	0.656409i
$879$	−24.7685	−	39.0691i	−0.835419	−	1.31777i
$880$	0.189632	+	0.328453i	0.00639250	+	0.0110721i
$881$	17.7576			0.598269			0.299135	−	0.954211i	$-0.403302\pi$
$881$	17.7576			0.598269			0.299135	+	0.954211i	$0.403302\pi$
$882$	17.8244	+	11.1037i	0.600178	+	0.373880i
$883$	43.0049			1.44723			0.723614	−	0.690204i	$-0.242479\pi$
$883$	43.0049			1.44723			0.723614	+	0.690204i	$0.242479\pi$
$884$	−1.21715	−	2.10817i	−0.0409372	−	0.0709054i
$885$	−0.186143	+	0.355655i	−0.00625713	+	0.0119552i
$886$	−9.25796	+	16.0353i	−0.311027	+	0.538715i
$887$	34.9062			1.17204			0.586018	−	0.810298i	$-0.300695\pi$
$887$	34.9062			1.17204			0.586018	+	0.810298i	$0.300695\pi$
$888$	6.40969	−	12.2467i	0.215095	−	0.410972i
$889$	−22.2198	+	4.58789i	−0.745228	+	0.153873i
$890$	−12.5331			−0.420109
$891$	3.36664	−	0.562964i	0.112787	−	0.0188600i
$892$	11.1346	+	19.2857i	0.372815	+	0.645734i
$893$	−38.2732			−1.28076
$894$	5.79993	+	9.14865i	0.193979	+	0.305977i
$895$	−1.87410	−	3.24604i	−0.0626444	−	0.108503i
$896$	−1.75887	−	1.97645i	−0.0587598	−	0.0660286i
$897$	1.56632	+	2.47067i	0.0522978	+	0.0824932i
$898$	−13.8423	−	23.9755i	−0.461922	−	0.800073i
$899$	8.79043	+	15.2255i	0.293177	+	0.507798i
$900$	−1.27987	+	2.71329i	−0.0426623	+	0.0904429i
$901$	−3.94332	+	6.83002i	−0.131371	+	0.227541i
$902$	1.37993	−	2.39011i	0.0459467	−	0.0795820i
$903$	−6.48942	+	22.6905i	−0.215954	+	0.755092i
$904$	7.78805	+	13.4893i	0.259027	+	0.448647i
$905$	−19.5320			−0.649264
$906$	−20.3926	−	32.1668i	−0.677499	−	1.06867i
$907$	−34.4295			−1.14321			−0.571606	−	0.820528i	$-0.693679\pi$
$907$	−34.4295			−1.14321			−0.571606	+	0.820528i	$0.693679\pi$
$908$	−1.45201	+	2.51496i	−0.0481867	+	0.0834618i
$909$	−36.0757	+	2.99547i	−1.19656	+	0.0993534i
$910$	0.512825	−	1.54759i	0.0170000	−	0.0513021i
$911$	10.1847	−	17.6405i	0.337436	−	0.584456i	−0.646514	−	0.762902i	$-0.723774\pi$
$911$	10.1847	−	17.6405i	0.337436	−	0.584456i	0.983950	+	0.178446i	$0.0571071\pi$
$912$	8.89639	−	0.368712i	0.294589	−	0.0122093i
$913$	1.62759	−	2.81907i	0.0538653	−	0.0932975i
$914$	−5.69023	+	9.85576i	−0.188216	+	0.326000i
$915$	10.6981	+	16.8749i	0.353669	+	0.557868i
$916$	−7.40450	+	12.8250i	−0.244651	+	0.423749i
$917$	35.8054	−	7.39300i	1.18240	−	0.244138i
$918$	−7.98102	+	18.9120i	−0.263413	+	0.624188i
$919$	21.3909	−	37.0501i	0.705619	−	1.22217i	−0.260848	−	0.965380i	$-0.584002\pi$
$919$	21.3909	−	37.0501i	0.705619	−	1.22217i	0.966468	−	0.256789i	$-0.0826644\pi$
$920$	2.74084			0.0903629
$921$	−30.6246	+	1.26924i	−1.00911	+	0.0418229i
$922$	−22.5324			−0.742066
$923$	3.47758	+	6.02335i	0.114466	+	0.198261i
$924$	−0.477905	+	1.67101i	−0.0157219	+	0.0549722i
$925$	3.99026	−	6.91133i	0.131199	−	0.227243i
$926$	8.51644	−	14.7509i	0.279868	−	0.484745i
$927$	−34.2890	+	2.84711i	−1.12620	+	0.0935113i
$928$	−3.69460	−	6.39923i	−0.121281	−	0.210065i
$929$	−9.82148	−	17.0113i	−0.322232	−	0.558123i	0.658716	−	0.752392i	$-0.271100\pi$
$929$	−9.82148	−	17.0113i	−0.322232	−	0.558123i	−0.980948	+	0.194269i	$0.937767\pi$
$930$	−4.11747	+	0.170649i	−0.135017	+	0.00559580i
$931$	4.17802	−	35.7418i	0.136929	−	1.17139i
$932$	9.63735	+	16.6924i	0.315682	+	0.546777i
$933$	13.1920	−	25.2053i	0.431886	−	0.825184i
$934$	6.28036			0.205500
$935$	0.749128	+	1.29753i	0.0244991	+	0.0424337i
$936$	1.05363	+	1.51899i	0.0344388	+	0.0496498i
$937$	25.9493			0.847726			0.423863	−	0.905726i	$-0.360674\pi$
$937$	25.9493			0.847726			0.423863	+	0.905726i	$0.360674\pi$
$938$	34.7370	−	7.17240i	1.13420	−	0.234187i
$939$	−11.0322	−	17.4019i	−0.360022	−	0.567889i
$940$	−7.44508			−0.242832
$941$	3.01076	−	5.21479i	0.0981479	−	0.169997i	−0.812770	−	0.582584i	$-0.802042\pi$
$941$	3.01076	−	5.21479i	0.0981479	−	0.169997i	0.910918	+	0.412587i	$0.135375\pi$
$942$	27.6196	−	1.14470i	0.899897	−	0.0372963i
$943$	−9.97239	−	17.2727i	−0.324746	−	0.562476i
$944$	0.231761			0.00754318
$945$	−13.0153	+	4.42728i	−0.423389	+	0.144019i
$946$	−1.95321			−0.0635043
$947$	−24.0909	−	41.7267i	−0.782850	−	1.35594i	−0.930275	−	0.366863i	$-0.880432\pi$
$947$	−24.0909	−	41.7267i	−0.782850	−	1.35594i	0.147424	−	0.989073i	$-0.452902\pi$
$948$	−10.4444	+	0.432870i	−0.339219	+	0.0140590i
$949$	−2.20933	+	3.82667i	−0.0717179	+	0.124219i
$950$	5.14074			0.166788
$951$	−23.9163	−	37.7249i	−0.775538	−	1.22331i
$952$	−6.94830	−	7.80783i	−0.225196	−	0.253053i
$953$	−9.73496			−0.315346			−0.157673	−	0.987491i	$-0.550399\pi$
$953$	−9.73496			−0.315346			−0.157673	+	0.987491i	$0.550399\pi$
$954$	2.55513	−	5.41681i	0.0827254	−	0.175376i
$955$	3.86820	+	6.69992i	0.125172	+	0.216804i
$956$	−10.8298			−0.350261
$957$	−2.25085	+	4.30059i	−0.0727596	+	0.139018i
$958$	1.48483	+	2.57181i	0.0479728	+	0.0830914i
$959$	−24.1739	+	4.99137i	−0.780616	+	0.161180i
$960$	1.73057	−	0.0717234i	0.0558538	−	0.00231486i
$961$	12.6696	+	21.9443i	0.408695	+	0.707881i
$962$	−2.45884	−	4.25884i	−0.0792763	−	0.137311i
$963$	5.93575	−	12.5836i	0.191277	−	0.405501i
$964$	3.49332	−	6.05061i	0.112512	−	0.194877i
$965$	0.601243	−	1.04138i	0.0193547	−	0.0335233i
$966$	8.73123	+	9.02895i	0.280923	+	0.290502i
$967$	5.59665	+	9.69367i	0.179976	+	0.311728i	0.941872	−	0.335972i	$-0.109065\pi$
$967$	5.59665	+	9.69367i	0.179976	+	0.311728i	−0.761896	+	0.647699i	$0.775731\pi$
$968$	10.8562			0.348930
$969$	35.1445	−	1.45657i	1.12901	−	0.0467917i
$970$	1.58424			0.0508669
$971$	27.9680	−	48.4420i	0.897535	−	1.55458i	0.0668998	−	0.997760i	$-0.478689\pi$
$971$	27.9680	−	48.4420i	0.897535	−	1.55458i	0.830635	−	0.556817i	$-0.187977\pi$
$972$	4.85167	−	14.8142i	0.155617	−	0.475167i
$973$	17.1509	+	19.2726i	0.549834	+	0.617850i
$974$	−7.50526	+	12.9995i	−0.240484	+	0.416531i
$975$	0.571473	+	0.901427i	0.0183018	+	0.0288688i
$976$	5.76782	−	9.99016i	0.184623	−	0.319777i
$977$	25.9833	−	45.0043i	0.831279	−	1.43982i	−0.0657463	−	0.997836i	$-0.520943\pi$
$977$	25.9833	−	45.0043i	0.831279	−	1.43982i	0.897025	−	0.441980i	$-0.145724\pi$
$978$	12.4866	−	0.517507i	0.399276	−	0.0165480i
$979$	2.37667	−	4.11652i	0.0759588	−	0.131564i
$980$	0.812728	−	6.95266i	0.0259616	−	0.222095i
$981$	23.1866	+	33.4276i	0.740290	+	1.06726i
$982$	6.41840	−	11.1170i	0.204819	−	0.354758i
$983$	−15.3080			−0.488250			−0.244125	−	0.969744i	$-0.578501\pi$
$983$	−15.3080			−0.488250			−0.244125	+	0.969744i	$0.578501\pi$
$984$	−6.74856	−	10.6450i	−0.215136	−	0.339350i
$985$	18.2839			0.582575
$986$	−14.5953	−	25.2797i	−0.464807	−	0.805070i
$987$	−23.7171	−	24.5258i	−0.754922	−	0.780664i
$988$	1.58389	−	2.74339i	0.0503904	−	0.0872787i
$989$	−7.05766	+	12.2242i	−0.224420	+	0.388708i
$990$	−0.648482	−	0.934903i	−0.0206101	−	0.0297132i
$991$	9.70464	+	16.8089i	0.308278	+	0.533953i	0.977986	−	0.208672i	$-0.0669140\pi$
$991$	9.70464	+	16.8089i	0.308278	+	0.533953i	−0.669708	+	0.742625i	$0.733581\pi$
$992$	1.18963	+	2.06050i	0.0377709	+	0.0654210i
$993$	−0.0241731	−	0.0381301i	−0.000767111	−	0.00121002i
$994$	19.8523	+	22.3081i	0.629678	+	0.707571i
$995$	4.34213	+	7.52079i	0.137655	+	0.238425i
$996$	−7.95973	−	12.5555i	−0.252214	−	0.397835i
$997$	9.90519			0.313701			0.156850	−	0.987622i	$-0.449866\pi$
$997$	9.90519			0.313701			0.156850	+	0.987622i	$0.449866\pi$
$998$	−11.6783	−	20.2273i	−0.369669	−	0.640285i
$999$	−16.1230	+	38.2052i	−0.510108	+	1.20876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.l.i.331.1	yes	16
3.2	odd	2		1890.2.l.i.1801.1		16
7.4	even	3		630.2.i.i.151.6	yes	16
9.4	even	3		630.2.i.i.121.6	✓	16
9.5	odd	6		1890.2.i.i.1171.5		16
21.11	odd	6		1890.2.i.i.991.5		16
63.4	even	3	inner	630.2.l.i.571.1	yes	16
63.32	odd	6		1890.2.l.i.361.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.i.121.6	✓	16	9.4	even	3
630.2.i.i.151.6	yes	16	7.4	even	3
630.2.l.i.331.1	yes	16	1.1	even	1	trivial
630.2.l.i.571.1	yes	16	63.4	even	3	inner
1890.2.i.i.991.5		16	21.11	odd	6
1890.2.i.i.1171.5		16	9.5	odd	6
1890.2.l.i.361.1		16	63.32	odd	6
1890.2.l.i.1801.1		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.73057 + 0.0717234i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.927397 - 1.46285i) q^{6} +(-2.59109 + 0.535003i) q^{7} -1.00000 q^{8} +(2.98971 - 0.248244i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.73057 + 0.0717234i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.927397 - 1.46285i) q^{6} +(-2.59109 + 0.535003i) q^{7} -1.00000 q^{8} +(2.98971 - 0.248244i) q^{9} +(-0.500000 - 0.866025i) q^{10} +0.379264 q^{11} +(0.803168 - 1.53458i) q^{12} +(-0.308106 - 0.533656i) q^{13} +(-1.75887 - 1.97645i) q^{14} +(1.73057 - 0.0717234i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.97521 - 3.42117i) q^{17} +(1.70984 + 2.46504i) q^{18} +(2.57037 - 4.45201i) q^{19} +(0.500000 - 0.866025i) q^{20} +(4.44569 - 1.11170i) q^{21} +(0.189632 + 0.328453i) q^{22} +2.74084 q^{23} +(1.73057 - 0.0717234i) q^{24} +1.00000 q^{25} +(0.308106 - 0.533656i) q^{26} +(-5.15609 + 0.644035i) q^{27} +(0.832221 - 2.51146i) q^{28} +(3.69460 - 6.39923i) q^{29} +(0.927397 + 1.46285i) q^{30} +(-1.18963 + 2.06050i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.656342 + 0.0272021i) q^{33} +(1.97521 - 3.42117i) q^{34} +(2.59109 - 0.535003i) q^{35} +(-1.27987 + 2.71329i) q^{36} +(3.99026 - 6.91133i) q^{37} +5.14074 q^{38} +(0.571473 + 0.901427i) q^{39} +1.00000 q^{40} +(-3.63844 - 6.30196i) q^{41} +(3.18560 + 3.29423i) q^{42} +(-2.57500 + 4.46002i) q^{43} +(-0.189632 + 0.328453i) q^{44} +(-2.98971 + 0.248244i) q^{45} +(1.37042 + 2.37364i) q^{46} +(-3.72254 - 6.44763i) q^{47} +(0.927397 + 1.46285i) q^{48} +(6.42754 - 2.77249i) q^{49} +(0.500000 + 0.866025i) q^{50} +(3.66361 + 5.77889i) q^{51} +0.616212 q^{52} +(-0.998199 - 1.72893i) q^{53} +(-3.13579 - 4.14328i) q^{54} -0.379264 q^{55} +(2.59109 - 0.535003i) q^{56} +(-4.12888 + 7.88885i) q^{57} +7.38920 q^{58} +(-0.115881 + 0.200711i) q^{59} +(-0.803168 + 1.53458i) q^{60} +(5.76782 + 9.99016i) q^{61} -2.37926 q^{62} +(-7.61381 + 2.24273i) q^{63} +1.00000 q^{64} +(0.308106 + 0.533656i) q^{65} +(-0.351729 - 0.554808i) q^{66} +(-6.70314 + 11.6102i) q^{67} +3.95043 q^{68} +(-4.74320 + 0.196583i) q^{69} +(1.75887 + 1.97645i) q^{70} -11.2870 q^{71} +(-2.98971 + 0.248244i) q^{72} +(-3.58534 - 6.20999i) q^{73} +7.98051 q^{74} +(-1.73057 + 0.0717234i) q^{75} +(2.57037 + 4.45201i) q^{76} +(-0.982710 + 0.202908i) q^{77} +(-0.494922 + 0.945624i) q^{78} +(-3.01763 - 5.22670i) q^{79} +(0.500000 + 0.866025i) q^{80} +(8.87675 - 1.48436i) q^{81} +(3.63844 - 6.30196i) q^{82} +(4.29143 - 7.43298i) q^{83} +(-1.26008 + 4.40593i) q^{84} +(1.97521 + 3.42117i) q^{85} -5.14999 q^{86} +(-5.93477 + 11.3393i) q^{87} -0.379264 q^{88} +(6.26653 - 10.8540i) q^{89} +(-1.70984 - 2.46504i) q^{90} +(1.08384 + 1.21791i) q^{91} +(-1.37042 + 2.37364i) q^{92} +(1.91095 - 3.65116i) q^{93} +(3.72254 - 6.44763i) q^{94} +(-2.57037 + 4.45201i) q^{95} +(-0.803168 + 1.53458i) q^{96} +(-0.792120 + 1.37199i) q^{97} +(5.61482 + 4.18017i) q^{98} +(1.13389 - 0.0941502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - q^{3} - 8 q^{4} - 16 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} + 9 q^{9}+O(q^{10}) \) 16 * q + 8 * q^2 - q^3 - 8 * q^4 - 16 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 + 9 * q^9	\( 16 q + 8 q^{2} - q^{3} - 8 q^{4} - 16 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} + 9 q^{9} - 8 q^{10} - 2 q^{11} - q^{12} + 2 q^{13} + 8 q^{14} + q^{15} - 8 q^{16} + 11 q^{17} + 3 q^{18} - 2 q^{19} + 8 q^{20} - q^{22} - 22 q^{23} + q^{24} + 16 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} + 2 q^{30} - 15 q^{31} + 8 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} - 4 q^{38} + 33 q^{39} + 16 q^{40} + 7 q^{41} - 9 q^{42} - 13 q^{43} + q^{44} - 9 q^{45} - 11 q^{46} - 5 q^{47} + 2 q^{48} + 10 q^{49} + 8 q^{50} + 30 q^{51} - 4 q^{52} + 18 q^{53} + q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} + 34 q^{58} + q^{59} + q^{60} - 27 q^{61} - 30 q^{62} + 14 q^{63} + 16 q^{64} - 2 q^{65} + 10 q^{66} - 10 q^{67} - 22 q^{68} - 14 q^{69} - 8 q^{70} - 38 q^{71} - 9 q^{72} - 8 q^{73} - 4 q^{74} - q^{75} - 2 q^{76} - 19 q^{77} - 25 q^{79} + 8 q^{80} + 9 q^{81} - 7 q^{82} + 2 q^{83} - 9 q^{84} - 11 q^{85} - 26 q^{86} + 58 q^{87} + 2 q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} + 3 q^{93} + 5 q^{94} + 2 q^{95} + q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - q^3 - 8 * q^4 - 16 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 + 9 * q^9 - 8 * q^10 - 2 * q^11 - q^12 + 2 * q^13 + 8 * q^14 + q^15 - 8 * q^16 + 11 * q^17 + 3 * q^18 - 2 * q^19 + 8 * q^20 - q^22 - 22 * q^23 + q^24 + 16 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 + 2 * q^30 - 15 * q^31 + 8 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^38 + 33 * q^39 + 16 * q^40 + 7 * q^41 - 9 * q^42 - 13 * q^43 + q^44 - 9 * q^45 - 11 * q^46 - 5 * q^47 + 2 * q^48 + 10 * q^49 + 8 * q^50 + 30 * q^51 - 4 * q^52 + 18 * q^53 + q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 + 34 * q^58 + q^59 + q^60 - 27 * q^61 - 30 * q^62 + 14 * q^63 + 16 * q^64 - 2 * q^65 + 10 * q^66 - 10 * q^67 - 22 * q^68 - 14 * q^69 - 8 * q^70 - 38 * q^71 - 9 * q^72 - 8 * q^73 - 4 * q^74 - q^75 - 2 * q^76 - 19 * q^77 - 25 * q^79 + 8 * q^80 + 9 * q^81 - 7 * q^82 + 2 * q^83 - 9 * q^84 - 11 * q^85 - 26 * q^86 + 58 * q^87 + 2 * q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 + 3 * q^93 + 5 * q^94 + 2 * q^95 + q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

Introduction

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