LMFDB - Embedded newform 315.2.i.d.211.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(106,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("315.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.3
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	315.211
Dual form			315.2.i.d.106.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.669131 + 1.15897i) q^{2} +(0.704489 + 1.58231i) q^{3} +(0.104528 - 0.181049i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.36245 + 1.87525i) q^{6} +(0.500000 + 0.866025i) q^{7} +2.95630 q^{8} +(-2.00739 + 2.22943i) q^{9} +O(q^{10})$	\(q+(0.669131 + 1.15897i) q^{2} +(0.704489 + 1.58231i) q^{3} +(0.104528 - 0.181049i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.36245 + 1.87525i) q^{6} +(0.500000 + 0.866025i) q^{7} +2.95630 q^{8} +(-2.00739 + 2.22943i) q^{9} +1.33826 q^{10} +(-0.330869 - 0.573083i) q^{11} +(0.360114 + 0.0378495i) q^{12} +(-0.891693 + 1.54446i) q^{13} +(-0.669131 + 1.15897i) q^{14} +(1.72256 + 0.181049i) q^{15} +(1.76909 + 3.06415i) q^{16} +1.33826 q^{17} +(-3.92705 - 0.834720i) q^{18} -4.32157 q^{19} +(-0.104528 - 0.181049i) q^{20} +(-1.01807 + 1.40126i) q^{21} +(0.442790 - 0.766934i) q^{22} +(2.60686 - 4.51522i) q^{23} +(2.08268 + 4.67777i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.38664 q^{26} +(-4.94183 - 1.60570i) q^{27} +0.209057 q^{28} +(-2.46086 - 4.26234i) q^{29} +(0.942790 + 2.11754i) q^{30} +(-0.344375 + 0.596475i) q^{31} +(0.588790 - 1.01981i) q^{32} +(0.673699 - 0.927267i) q^{33} +(0.895472 + 1.55100i) q^{34} +1.00000 q^{35} +(0.193806 + 0.596475i) q^{36} -6.53818 q^{37} +(-2.89169 - 5.00856i) q^{38} +(-3.07199 - 0.322880i) q^{39} +(1.47815 - 2.56023i) q^{40} +(0.409767 - 0.709737i) q^{41} +(-2.30524 - 0.242290i) q^{42} +(0.819699 + 1.41976i) q^{43} -0.138341 q^{44} +(0.927051 + 2.85317i) q^{45} +6.97733 q^{46} +(-6.08406 - 10.5379i) q^{47} +(-3.60213 + 4.95791i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.669131 - 1.15897i) q^{50} +(0.942790 + 2.11754i) q^{51} +(0.186415 + 0.322880i) q^{52} +13.8223 q^{53} +(-1.44578 - 6.80185i) q^{54} -0.661739 q^{55} +(1.47815 + 2.56023i) q^{56} +(-3.04449 - 6.83805i) q^{57} +(3.29328 - 5.70413i) q^{58} +(-2.74898 + 4.76138i) q^{59} +(0.212835 - 0.292943i) q^{60} +(5.87218 + 10.1709i) q^{61} -0.921727 q^{62} +(-2.93444 - 0.623735i) q^{63} +8.65227 q^{64} +(0.891693 + 1.54446i) q^{65} +(1.52547 + 0.160333i) q^{66} +(3.30902 - 5.73139i) q^{67} +(0.139886 - 0.242290i) q^{68} +(8.98097 + 0.943938i) q^{69} +(0.669131 + 1.15897i) q^{70} +5.79659 q^{71} +(-5.93444 + 6.59087i) q^{72} +0.0885901 q^{73} +(-4.37490 - 7.57754i) q^{74} +(1.01807 - 1.40126i) q^{75} +(-0.451727 + 0.782414i) q^{76} +(0.330869 - 0.573083i) q^{77} +(-1.68136 - 3.77639i) q^{78} +(-5.78477 - 10.0195i) q^{79} +3.53818 q^{80} +(-0.940756 - 8.95070i) q^{81} +1.09675 q^{82} +(-0.978938 - 1.69557i) q^{83} +(0.147278 + 0.330792i) q^{84} +(0.669131 - 1.15897i) q^{85} +(-1.09697 + 1.90001i) q^{86} +(5.01068 - 6.89661i) q^{87} +(-0.978148 - 1.69420i) q^{88} -13.1606 q^{89} +(-2.68641 + 2.98357i) q^{90} -1.78339 q^{91} +(-0.544983 - 0.943938i) q^{92} +(-1.18641 - 0.124697i) q^{93} +(8.14206 - 14.1025i) q^{94} +(-2.16078 + 3.74259i) q^{95} +(2.02845 + 0.213199i) q^{96} +(8.33761 + 14.4412i) q^{97} -1.33826 q^{98} +(1.94183 + 0.412750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9	$ 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9} + 2 q^{10} - 7 q^{11} + 3 q^{12} + 8 q^{13} - q^{14} + 3 q^{15} + 9 q^{16} + 2 q^{17} - 18 q^{18} + 6 q^{19} + q^{20} - 7 q^{22} + 8 q^{23} + 6 q^{24} - 4 q^{25} - 6 q^{26} - 2 q^{28} - q^{29} - 3 q^{30} + 9 q^{34} + 8 q^{35} - 6 q^{36} - 42 q^{37} - 8 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} + 3 q^{42} + 7 q^{43} + 6 q^{44} - 6 q^{45} - 46 q^{46} + 2 q^{47} + 30 q^{48} - 4 q^{49} + q^{50} - 3 q^{51} + 7 q^{52} - 16 q^{53} - 36 q^{54} - 14 q^{55} + 3 q^{56} - 24 q^{57} + 19 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 30 q^{62} + 3 q^{63} - 14 q^{64} - 8 q^{65} - 9 q^{66} + 22 q^{67} + q^{68} + 51 q^{69} + q^{70} + 26 q^{71} - 21 q^{72} - 8 q^{73} - 9 q^{74} + 13 q^{76} + 7 q^{77} - 21 q^{78} + 24 q^{79} + 18 q^{80} + 9 q^{81} + 19 q^{83} - 12 q^{84} + q^{85} + 27 q^{86} + 45 q^{87} + q^{88} + 30 q^{89} - 27 q^{90} + 16 q^{91} - 3 q^{92} - 15 q^{93} + 7 q^{94} + 3 q^{95} + 30 q^{96} + 12 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) $ 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9 + 2 * q^10 - 7 * q^11 + 3 * q^12 + 8 * q^13 - q^14 + 3 * q^15 + 9 * q^16 + 2 * q^17 - 18 * q^18 + 6 * q^19 + q^20 - 7 * q^22 + 8 * q^23 + 6 * q^24 - 4 * q^25 - 6 * q^26 - 2 * q^28 - q^29 - 3 * q^30 + 9 * q^34 + 8 * q^35 - 6 * q^36 - 42 * q^37 - 8 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 + 3 * q^42 + 7 * q^43 + 6 * q^44 - 6 * q^45 - 46 * q^46 + 2 * q^47 + 30 * q^48 - 4 * q^49 + q^50 - 3 * q^51 + 7 * q^52 - 16 * q^53 - 36 * q^54 - 14 * q^55 + 3 * q^56 - 24 * q^57 + 19 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 30 * q^62 + 3 * q^63 - 14 * q^64 - 8 * q^65 - 9 * q^66 + 22 * q^67 + q^68 + 51 * q^69 + q^70 + 26 * q^71 - 21 * q^72 - 8 * q^73 - 9 * q^74 + 13 * q^76 + 7 * q^77 - 21 * q^78 + 24 * q^79 + 18 * q^80 + 9 * q^81 + 19 * q^83 - 12 * q^84 + q^85 + 27 * q^86 + 45 * q^87 + q^88 + 30 * q^89 - 27 * q^90 + 16 * q^91 - 3 * q^92 - 15 * q^93 + 7 * q^94 + 3 * q^95 + 30 * q^96 + 12 * q^97 - 2 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.669131	+	1.15897i	0.473147	+	0.819514i	0.999528	−	0.0307347i	$-0.00978469\pi$
$2$	0.669131	+	1.15897i	0.473147	+	0.819514i	−0.526381	+	0.850249i	$0.676451\pi$
$3$	0.704489	+	1.58231i	0.406737	+	0.913545i
$3$	0.704489	+	1.58231i	0.406737	+	0.913545i
$4$	0.104528	−	0.181049i	0.0522642	−	0.0905243i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.36245	+	1.87525i	−0.556217	+	0.765568i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	2.95630			1.04521
$9$	−2.00739	+	2.22943i	−0.669131	+	0.743145i
$10$	1.33826			0.423195
$11$	−0.330869	−	0.573083i	−0.0997609	−	0.172791i	0.811825	−	0.583901i	$-0.198474\pi$
$11$	−0.330869	−	0.573083i	−0.0997609	−	0.172791i	−0.911586	+	0.411110i	$0.865141\pi$
$12$	0.360114	+	0.0378495i	0.103956	+	0.0109262i
$13$	−0.891693	+	1.54446i	−0.247311	+	0.428355i	−0.962779	−	0.270290i	$-0.912880\pi$
$13$	−0.891693	+	1.54446i	−0.247311	+	0.428355i	0.715468	+	0.698646i	$0.246214\pi$
$14$	−0.669131	+	1.15897i	−0.178833	+	0.309747i
$15$	1.72256	+	0.181049i	0.444764	+	0.0467465i
$16$	1.76909	+	3.06415i	0.442273	+	0.766039i
$17$	1.33826			0.324576			0.162288	−	0.986743i	$-0.448113\pi$
$17$	1.33826			0.324576			0.162288	+	0.986743i	$0.448113\pi$
$18$	−3.92705	−	0.834720i	−0.925615	−	0.196745i
$19$	−4.32157			−0.991436			−0.495718	−	0.868484i	$-0.665095\pi$
$19$	−4.32157			−0.991436			−0.495718	+	0.868484i	$0.665095\pi$
$20$	−0.104528	−	0.181049i	−0.0233733	−	0.0404837i
$21$	−1.01807	+	1.40126i	−0.222162	+	0.305780i
$22$	0.442790	−	0.766934i	0.0944031	−	0.163511i
$23$	2.60686	−	4.51522i	0.543569	−	0.941489i	−0.455127	−	0.890427i	$-0.650406\pi$
$23$	2.60686	−	4.51522i	0.543569	−	0.941489i	0.998695	−	0.0510619i	$-0.0162606\pi$
$24$	2.08268	+	4.67777i	0.425124	+	0.954845i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.38664			−0.468058
$27$	−4.94183	−	1.60570i	−0.951057	−	0.309017i
$28$	0.209057			0.0395080
$29$	−2.46086	−	4.26234i	−0.456971	−	0.791497i	0.541828	−	0.840489i	$-0.317732\pi$
$29$	−2.46086	−	4.26234i	−0.456971	−	0.791497i	−0.998799	+	0.0489924i	$0.984399\pi$
$30$	0.942790	+	2.11754i	0.172129	+	0.386608i
$31$	−0.344375	+	0.596475i	−0.0618516	+	0.107130i	−0.895293	−	0.445478i	$-0.853034\pi$
$31$	−0.344375	+	0.596475i	−0.0618516	+	0.107130i	0.833441	+	0.552608i	$0.186367\pi$
$32$	0.588790	−	1.01981i	0.104084	−	0.180279i
$33$	0.673699	−	0.927267i	0.117276	−	0.161416i
$34$	0.895472	+	1.55100i	0.153572	+	0.265995i
$35$	1.00000			0.169031
$36$	0.193806	+	0.596475i	0.0323011	+	0.0994125i
$37$	−6.53818			−1.07487			−0.537435	−	0.843305i	$-0.680607\pi$
$37$	−6.53818			−1.07487			−0.537435	+	0.843305i	$0.680607\pi$
$38$	−2.89169	−	5.00856i	−0.469095	−	0.812496i
$39$	−3.07199	−	0.322880i	−0.491913	−	0.0517021i
$40$	1.47815	−	2.56023i	0.233716	−	0.404807i
$41$	0.409767	−	0.709737i	0.0639949	−	0.110842i	−0.832253	−	0.554396i	$-0.812949\pi$
$41$	0.409767	−	0.709737i	0.0639949	−	0.110842i	0.896248	+	0.443554i	$0.146283\pi$
$42$	−2.30524	−	0.242290i	−0.355706	−	0.0373862i
$43$	0.819699	+	1.41976i	0.125003	+	0.216511i	0.921734	−	0.387822i	$-0.126773\pi$
$43$	0.819699	+	1.41976i	0.125003	+	0.216511i	−0.796731	+	0.604334i	$0.793439\pi$
$44$	−0.138341			−0.0208557
$45$	0.927051	+	2.85317i	0.138197	+	0.425325i
$46$	6.97733			1.02875
$47$	−6.08406	−	10.5379i	−0.887451	−	1.53711i	−0.842879	−	0.538104i	$-0.819141\pi$
$47$	−6.08406	−	10.5379i	−0.887451	−	1.53711i	−0.0445722	−	0.999006i	$-0.514192\pi$
$48$	−3.60213	+	4.95791i	−0.519923	+	0.715612i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.669131	−	1.15897i	0.0946294	−	0.163903i
$51$	0.942790	+	2.11754i	0.132017	+	0.296515i
$52$	0.186415	+	0.322880i	0.0258511	+	0.0447753i
$53$	13.8223			1.89864			0.949319	−	0.314314i	$-0.101774\pi$
$53$	13.8223			1.89864			0.949319	+	0.314314i	$0.101774\pi$
$54$	−1.44578	−	6.80185i	−0.196745	−	0.925615i
$55$	−0.661739			−0.0892288
$56$	1.47815	+	2.56023i	0.197526	+	0.342125i
$57$	−3.04449	−	6.83805i	−0.403253	−	0.905721i
$58$	3.29328	−	5.70413i	0.432429	−	0.748988i
$59$	−2.74898	+	4.76138i	−0.357887	+	0.619879i	−0.987608	−	0.156943i	$-0.949836\pi$
$59$	−2.74898	+	4.76138i	−0.357887	+	0.619879i	0.629721	+	0.776822i	$0.283169\pi$
$60$	0.212835	−	0.292943i	0.0274769	−	0.0378188i
$61$	5.87218	+	10.1709i	0.751855	+	1.30225i	0.946923	+	0.321461i	$0.104174\pi$
$61$	5.87218	+	10.1709i	0.751855	+	1.30225i	−0.195068	+	0.980790i	$0.562493\pi$
$62$	−0.921727			−0.117059
$63$	−2.93444	−	0.623735i	−0.369705	−	0.0785832i
$64$	8.65227			1.08153
$65$	0.891693	+	1.54446i	0.110601	+	0.191566i
$66$	1.52547	+	0.160333i	0.187772	+	0.0197356i
$67$	3.30902	−	5.73139i	0.404261	−	0.700200i	−0.589974	−	0.807422i	$-0.700862\pi$
$67$	3.30902	−	5.73139i	0.404261	−	0.700200i	0.994235	+	0.107222i	$0.0341955\pi$
$68$	0.139886	−	0.242290i	0.0169637	−	0.0293820i
$69$	8.98097	+	0.943938i	1.08118	+	0.113637i
$70$	0.669131	+	1.15897i	0.0799764	+	0.138523i
$71$	5.79659			0.687929			0.343964	−	0.938983i	$-0.388230\pi$
$71$	5.79659			0.687929			0.343964	+	0.938983i	$0.388230\pi$
$72$	−5.93444	+	6.59087i	−0.699381	+	0.776741i
$73$	0.0885901			0.0103687			0.00518434	−	0.999987i	$-0.498350\pi$
$73$	0.0885901			0.0103687			0.00518434	+	0.999987i	$0.498350\pi$
$74$	−4.37490	−	7.57754i	−0.508571	−	0.880872i
$75$	1.01807	−	1.40126i	0.117557	−	0.161803i
$76$	−0.451727	+	0.782414i	−0.0518166	+	0.0897490i
$77$	0.330869	−	0.573083i	0.0377061	−	0.0653088i
$78$	−1.68136	−	3.77639i	−0.190376	−	0.427592i
$79$	−5.78477	−	10.0195i	−0.650837	−	1.12728i	−0.982920	−	0.184033i	$-0.941085\pi$
$79$	−5.78477	−	10.0195i	−0.650837	−	1.12728i	0.332083	−	0.943250i	$-0.392249\pi$
$80$	3.53818			0.395581
$81$	−0.940756	−	8.95070i	−0.104528	−	0.994522i
$82$	1.09675			0.121116
$83$	−0.978938	−	1.69557i	−0.107452	−	0.186113i	0.807285	−	0.590162i	$-0.200936\pi$
$83$	−0.978938	−	1.69557i	−0.107452	−	0.186113i	−0.914737	+	0.404049i	$0.867603\pi$
$84$	0.147278	+	0.330792i	0.0160694	+	0.0360924i
$85$	0.669131	−	1.15897i	0.0725774	−	0.125708i
$86$	−1.09697	+	1.90001i	−0.118289	+	0.204883i
$87$	5.01068	−	6.89661i	0.537202	−	0.739394i
$88$	−0.978148	−	1.69420i	−0.104271	−	0.180602i
$89$	−13.1606			−1.39502			−0.697508	−	0.716577i	$-0.745708\pi$
$89$	−13.1606			−1.39502			−0.697508	+	0.716577i	$0.745708\pi$
$90$	−2.68641	+	2.98357i	−0.283173	+	0.314495i
$91$	−1.78339			−0.186950
$92$	−0.544983	−	0.943938i	−0.0568184	−	0.0984123i
$93$	−1.18641	−	0.124697i	−0.123025	−	0.0129305i
$94$	8.14206	−	14.1025i	0.839789	−	1.45456i
$95$	−2.16078	+	3.74259i	−0.221692	+	0.383981i
$96$	2.02845	+	0.213199i	0.207028	+	0.0217595i
$97$	8.33761	+	14.4412i	0.846556	+	1.46628i	0.884263	+	0.466989i	$0.154661\pi$
$97$	8.33761	+	14.4412i	0.846556	+	1.46628i	−0.0377074	+	0.999289i	$0.512005\pi$
$98$	−1.33826			−0.135185
$99$	1.94183	+	0.412750i	0.195162	+	0.0414829i
$100$	−0.209057			−0.0209057
$101$	0.651358	+	1.12819i	0.0648126	+	0.112259i	0.896611	−	0.442819i	$-0.146022\pi$
$101$	0.651358	+	1.12819i	0.0648126	+	0.112259i	−0.831798	+	0.555078i	$0.812688\pi$
$102$	−1.82331	+	2.50957i	−0.180535	+	0.248485i
$103$	−7.68704	+	13.3143i	−0.757426	+	1.31190i	0.186732	+	0.982411i	$0.440210\pi$
$103$	−7.68704	+	13.3143i	−0.757426	+	1.31190i	−0.944159	+	0.329490i	$0.893123\pi$
$104$	−2.63611	+	4.56587i	−0.258492	+	0.447721i
$105$	0.704489	+	1.58231i	0.0687510	+	0.154417i
$106$	9.24892	+	16.0196i	0.898335	+	1.55596i
$107$	−14.8776			−1.43827			−0.719137	−	0.694868i	$-0.755463\pi$
$107$	−14.8776			−1.43827			−0.719137	+	0.694868i	$0.755463\pi$
$108$	−0.807272	+	0.726871i	−0.0776798	+	0.0699432i
$109$	−2.65727			−0.254521			−0.127260	−	0.991869i	$-0.540618\pi$
$109$	−2.65727			−0.254521			−0.127260	+	0.991869i	$0.540618\pi$
$110$	−0.442790	−	0.766934i	−0.0422183	−	0.0731243i
$111$	−4.60607	−	10.3454i	−0.437189	−	0.981943i
$112$	−1.76909	+	3.06415i	−0.167163	+	0.289535i
$113$	6.57969	−	11.3964i	0.618965	−	1.07208i	−0.370710	−	0.928749i	$-0.620886\pi$
$113$	6.57969	−	11.3964i	0.618965	−	1.07208i	0.989675	−	0.143330i	$-0.0457810\pi$
$114$	5.88791	−	8.10402i	0.551454	−	0.759011i
$115$	−2.60686	−	4.51522i	−0.243091	−	0.421046i
$116$	−1.02892			−0.0955329
$117$	−1.65329	−	5.08830i	−0.152847	−	0.470414i
$118$	−7.35772			−0.677333
$119$	0.669131	+	1.15897i	0.0613391	+	0.106242i
$120$	5.09240	+	0.535233i	0.464871	+	0.0488599i
$121$	5.28105	−	9.14705i	0.480096	−	0.831550i
$122$	−7.85851	+	13.6113i	−0.711476	+	1.23231i
$123$	1.41170	+	0.148375i	0.127289	+	0.0133786i
$124$	0.0719940	+	0.124697i	0.00646525	+	0.0111981i
$125$	−1.00000			−0.0894427
$126$	−1.24064	−	3.81829i	−0.110525	−	0.340160i
$127$	−11.0026			−0.976319			−0.488159	−	0.872754i	$-0.662332\pi$
$127$	−11.0026			−0.976319			−0.488159	+	0.872754i	$0.662332\pi$
$128$	4.61192	+	7.98808i	0.407640	+	0.706053i
$129$	−1.66903	+	2.29722i	−0.146950	+	0.202259i
$130$	−1.19332	+	2.06689i	−0.104661	+	0.181278i
$131$	−4.31651	+	7.47642i	−0.377135	+	0.653218i	−0.990644	−	0.136470i	$-0.956424\pi$
$131$	−4.31651	+	7.47642i	−0.377135	+	0.653218i	0.613509	+	0.789688i	$0.289757\pi$
$132$	−0.0974597	−	0.218898i	−0.00848278	−	0.0190526i
$133$	−2.16078	−	3.74259i	−0.187364	−	0.324523i
$134$	8.85666			0.765099
$135$	−3.86149	+	3.47690i	−0.332344	+	0.299244i
$136$	3.95630			0.339250
$137$	6.55248	+	11.3492i	0.559816	+	0.969630i	0.997511	+	0.0705062i	$0.0224615\pi$
$137$	6.55248	+	11.3492i	0.559816	+	0.969630i	−0.437695	+	0.899123i	$0.644205\pi$
$138$	4.91545	+	11.0403i	0.418431	+	0.939811i
$139$	−2.84565	+	4.92882i	−0.241365	+	0.418057i	−0.961103	−	0.276189i	$-0.910928\pi$
$139$	−2.84565	+	4.92882i	−0.241365	+	0.418057i	0.719738	+	0.694246i	$0.244262\pi$
$140$	0.104528	−	0.181049i	0.00883427	−	0.0153014i
$141$	12.3880	−	17.0507i	1.04326	−	1.43593i
$142$	3.87868	+	6.71806i	0.325491	+	0.563767i
$143$	1.18014			0.0986879
$144$	−10.3826	−	2.20689i	−0.865216	−	0.183907i
$145$	−4.92173			−0.408727
$146$	0.0592784	+	0.102673i	0.00490591	+	0.00849729i
$147$	−1.72256	−	0.181049i	−0.142075	−	0.0149326i
$148$	−0.683426	+	1.18373i	−0.0561773	+	0.0973019i
$149$	−4.81135	+	8.33351i	−0.394161	+	0.682707i	−0.992994	−	0.118167i	$-0.962298\pi$
$149$	−4.81135	+	8.33351i	−0.394161	+	0.682707i	0.598832	+	0.800874i	$0.295632\pi$
$150$	2.30524	+	0.242290i	0.188222	+	0.0197829i
$151$	3.62309	+	6.27538i	0.294843	+	0.510683i	0.974948	−	0.222431i	$-0.0713993\pi$
$151$	3.62309	+	6.27538i	0.294843	+	0.510683i	−0.680105	+	0.733114i	$0.738066\pi$
$152$	−12.7758			−1.03626
$153$	−2.68641	+	2.98357i	−0.217184	+	0.241207i
$154$	0.885579			0.0713620
$155$	0.344375	+	0.596475i	0.0276609	+	0.0479100i
$156$	−0.379568	+	0.522430i	−0.0303897	+	0.0418279i
$157$	9.54870	−	16.5388i	0.762069	−	1.31994i	−0.179713	−	0.983719i	$-0.557517\pi$
$157$	9.54870	−	16.5388i	0.762069	−	1.31994i	0.941782	−	0.336223i	$-0.109150\pi$
$158$	7.74153	−	13.4087i	0.615883	−	1.06674i
$159$	9.73765	+	21.8711i	0.772246	+	1.73449i
$160$	−0.588790	−	1.01981i	−0.0465479	−	0.0806234i
$161$	5.21373			0.410899
$162$	9.74408	−	7.07949i	0.765568	−	0.556217i
$163$	−17.7525			−1.39048			−0.695242	−	0.718776i	$-0.744703\pi$
$163$	−17.7525			−1.39048			−0.695242	+	0.718776i	$0.744703\pi$
$164$	−0.0856646	−	0.148375i	−0.00668928	−	0.0115862i
$165$	−0.466187	−	1.04707i	−0.0362926	−	0.0815146i
$166$	1.31007	−	2.26911i	0.101681	−	0.176117i
$167$	1.93822	−	3.35710i	0.149984	−	0.259780i	−0.781237	−	0.624234i	$-0.785411\pi$
$167$	1.93822	−	3.35710i	0.149984	−	0.259780i	0.931221	+	0.364454i	$0.118744\pi$
$168$	−3.00973	+	4.14253i	−0.232205	+	0.319603i
$169$	4.90977	+	8.50397i	0.377674	+	0.654151i
$170$	1.79094			0.137359
$171$	8.67508	−	9.63465i	0.663400	−	0.736780i
$172$	0.342728			0.0261327
$173$	7.23560	+	12.5324i	0.550113	+	0.952823i	0.998266	+	0.0588662i	$0.0187485\pi$
$173$	7.23560	+	12.5324i	0.550113	+	0.952823i	−0.448153	+	0.893957i	$0.647918\pi$
$174$	11.3458	+	1.19249i	0.860119	+	0.0904022i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	1.17068	−	2.02767i	0.0882430	−	0.152841i
$177$	−9.47059	−	0.995399i	−0.711853	−	0.0748188i
$178$	−8.80613	−	15.2527i	−0.660047	−	1.14324i
$179$	5.15248			0.385114			0.192557	−	0.981286i	$-0.438322\pi$
$179$	5.15248			0.385114			0.192557	+	0.981286i	$0.438322\pi$
$180$	0.613466	+	0.130396i	0.0457250	+	0.00971915i
$181$	−20.8252			−1.54792			−0.773962	−	0.633232i	$-0.781728\pi$
$181$	−20.8252			−1.54792			−0.773962	+	0.633232i	$0.781728\pi$
$182$	−1.19332	−	2.06689i	−0.0884546	−	0.153208i
$183$	−11.9566	+	16.4569i	−0.883859	+	1.21653i
$184$	7.70666	−	13.3483i	0.568142	−	0.984052i
$185$	−3.26909	+	5.66223i	−0.240348	+	0.416296i
$186$	−0.649346	−	1.45846i	−0.0476124	−	0.106939i
$187$	−0.442790	−	0.766934i	−0.0323800	−	0.0560838i
$188$	−2.54383			−0.185528
$189$	−1.08034	−	5.08260i	−0.0785832	−	0.369705i
$190$	−5.78339			−0.419571
$191$	9.32177	+	16.1458i	0.674499	+	1.16827i	0.976615	+	0.214996i	$0.0689738\pi$
$191$	9.32177	+	16.1458i	0.674499	+	1.16827i	−0.302116	+	0.953271i	$0.597693\pi$
$192$	6.09543	+	13.6906i	0.439899	+	0.988030i
$193$	−6.92735	+	11.9985i	−0.498642	+	0.863673i	−0.999999	−	0.00156765i	$-0.999501\pi$
$193$	−6.92735	+	11.9985i	−0.498642	+	0.863673i	0.501357	+	0.865241i	$0.332834\pi$
$194$	−11.1579	+	19.3260i	−0.801090	+	1.38753i
$195$	−1.81562	+	2.49899i	−0.130019	+	0.178956i
$196$	0.104528	+	0.181049i	0.00746632	+	0.0129320i
$197$	10.7261			0.764206			0.382103	−	0.924120i	$-0.375200\pi$
$197$	10.7261			0.764206			0.382103	+	0.924120i	$0.375200\pi$
$198$	0.820977	+	2.52671i	0.0583443	+	0.179565i
$199$	6.26970			0.444447			0.222224	−	0.974996i	$-0.428668\pi$
$199$	6.26970			0.444447			0.222224	+	0.974996i	$0.428668\pi$
$200$	−1.47815	−	2.56023i	−0.104521	−	0.181035i
$201$	11.4000	+	1.19819i	0.804092	+	0.0845135i
$202$	−0.871688	+	1.50981i	−0.0613317	+	0.106230i
$203$	2.46086	−	4.26234i	0.172719	−	0.299158i
$204$	0.481926	+	0.0506525i	0.0337416	+	0.00354638i
$205$	−0.409767	−	0.709737i	−0.0286194	−	0.0495702i
$206$	−20.5745			−1.43350
$207$	4.83339	+	14.8756i	0.335944	+	1.03393i
$208$	−6.30994			−0.437516
$209$	1.42987	+	2.47662i	0.0989065	+	0.171311i
$210$	−1.36245	+	1.87525i	−0.0940179	+	0.129405i
$211$	−5.16168	+	8.94028i	−0.355344	+	0.615475i	−0.987177	−	0.159630i	$-0.948970\pi$
$211$	−5.16168	+	8.94028i	−0.355344	+	0.615475i	0.631832	+	0.775105i	$0.282303\pi$
$212$	1.44482	−	2.50251i	0.0992309	−	0.171873i
$213$	4.08363	+	9.17199i	0.279806	+	0.628454i
$214$	−9.95507	−	17.2427i	−0.680515	−	1.17869i
$215$	1.63940			0.111806
$216$	−14.6095	−	4.74692i	−0.994052	−	0.322987i
$217$	−0.688750			−0.0467554
$218$	−1.77806	−	3.07969i	−0.120426	−	0.208583i
$219$	0.0624107	+	0.140177i	0.00421733	+	0.00947227i
$220$	−0.0691705	+	0.119807i	−0.00466348	+	0.00807738i
$221$	−1.19332	+	2.06689i	−0.0802713	+	0.139034i
$222$	8.90794	−	12.2607i	0.597862	−	0.822886i
$223$	−2.42626	−	4.20241i	−0.162474	−	0.281414i	0.773281	−	0.634063i	$-0.218614\pi$
$223$	−2.42626	−	4.20241i	−0.162474	−	0.281414i	−0.935756	+	0.352649i	$0.885281\pi$
$224$	1.17758			0.0786803
$225$	2.93444	+	0.623735i	0.195630	+	0.0415823i
$226$	17.6107			1.17145
$227$	4.88588	+	8.46259i	0.324287	+	0.561682i	0.981368	−	0.192138i	$-0.0615422\pi$
$227$	4.88588	+	8.46259i	0.324287	+	0.561682i	−0.657081	+	0.753820i	$0.728209\pi$
$228$	−1.55626	−	0.163569i	−0.103066	−	0.0108326i
$229$	−8.07427	+	13.9850i	−0.533563	+	0.924157i	0.465669	+	0.884959i	$0.345814\pi$
$229$	−8.07427	+	13.9850i	−0.533563	+	0.924157i	−0.999231	+	0.0391984i	$0.987520\pi$
$230$	3.48866	−	6.04254i	0.230036	−	0.398434i
$231$	1.13989	+	0.119807i	0.0749990	+	0.00788271i
$232$	−7.27504	−	12.6007i	−0.477630	−	0.827279i
$233$	5.76414			0.377621			0.188811	−	0.982014i	$-0.439537\pi$
$233$	5.76414			0.377621			0.188811	+	0.982014i	$0.439537\pi$
$234$	4.79091	−	5.32085i	0.313192	−	0.347835i
$235$	−12.1681			−0.793760
$236$	0.574694	+	0.995399i	0.0374094	+	0.0647950i
$237$	11.7786	−	16.2119i	0.765105	−	1.05308i
$238$	−0.895472	+	1.55100i	−0.0580448	+	0.100537i
$239$	−0.0605219	+	0.104827i	−0.00391484	+	0.00678070i	−0.867976	−	0.496606i	$-0.834579\pi$
$239$	−0.0605219	+	0.104827i	−0.00391484	+	0.00678070i	0.864061	+	0.503387i	$0.167913\pi$
$240$	2.49261	+	5.59849i	0.160897	+	0.361381i
$241$	−10.4808	−	18.1533i	−0.675128	−	1.16936i	−0.976431	−	0.215828i	$-0.930755\pi$
$241$	−10.4808	−	18.1533i	−0.675128	−	1.16936i	0.301303	−	0.953528i	$-0.402578\pi$
$242$	14.1349			0.908623
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	2.45524			0.157181
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$	0.772648	+	1.73540i	0.0492622	+	0.110645i
$247$	3.85351	−	6.67448i	0.245193	−	0.424687i
$248$	−1.01807	+	1.76336i	−0.0646478	+	0.111973i
$249$	1.99326	−	2.74349i	0.126318	−	0.173862i
$250$	−0.669131	−	1.15897i	−0.0423195	−	0.0732996i
$251$	−15.1644			−0.957170			−0.478585	−	0.878041i	$-0.658850\pi$
$251$	−15.1644			−0.957170			−0.478585	+	0.878041i	$0.658850\pi$
$252$	−0.419659	+	0.466079i	−0.0264360	+	0.0293602i
$253$	−3.45013			−0.216908
$254$	−7.36215	−	12.7516i	−0.461942	−	0.800107i
$255$	2.30524	+	0.242290i	0.144360	+	0.0151728i
$256$	2.48032	−	4.29604i	0.155020	−	0.268502i
$257$	10.9827	−	19.0225i	0.685080	−	1.18659i	−0.288331	−	0.957531i	$-0.593100\pi$
$257$	10.9827	−	19.0225i	0.685080	−	1.18659i	0.973412	−	0.229063i	$-0.0735663\pi$
$258$	−3.77920	−	0.397210i	−0.235283	−	0.0247292i
$259$	−3.26909	−	5.66223i	−0.203131	−	0.351834i
$260$	0.372829			0.0231219
$261$	14.4425	+	3.06985i	0.893970	+	0.190019i
$262$	−11.5532			−0.713761
$263$	16.0183	+	27.7446i	0.987733	+	1.71080i	0.629099	+	0.777325i	$0.283424\pi$
$263$	16.0183	+	27.7446i	0.987733	+	1.71080i	0.358633	+	0.933478i	$0.383243\pi$
$264$	1.99165	−	2.74128i	0.122578	−	0.168714i
$265$	6.91115	−	11.9705i	0.424548	−	0.735339i
$266$	2.89169	−	5.00856i	0.177301	−	0.307094i
$267$	−9.27146	−	20.8240i	−0.567404	−	1.27441i
$268$	−0.691773	−	1.19819i	−0.0422568	−	0.0731908i
$269$	4.59293			0.280036			0.140018	−	0.990149i	$-0.455284\pi$
$269$	4.59293			0.280036			0.140018	+	0.990149i	$0.455284\pi$
$270$	−6.61347	−	2.14885i	−0.402483	−	0.130775i
$271$	16.2926			0.989708			0.494854	−	0.868976i	$-0.335222\pi$
$271$	16.2926			0.989708			0.494854	+	0.868976i	$0.335222\pi$
$272$	2.36751	+	4.10064i	0.143551	+	0.248638i
$273$	−1.25638	−	2.82186i	−0.0760393	−	0.170787i
$274$	−8.76893	+	15.1882i	−0.529750	+	0.917554i
$275$	−0.330869	+	0.573083i	−0.0199522	+	0.0345582i
$276$	1.10967	−	1.52732i	0.0667940	−	0.0919341i
$277$	15.5820	+	26.9889i	0.936234	+	1.62161i	0.772418	+	0.635114i	$0.219047\pi$
$277$	15.5820	+	26.9889i	0.936234	+	1.62161i	0.163816	+	0.986491i	$0.447620\pi$
$278$	−7.61645			−0.456805
$279$	−0.638506	−	1.96512i	−0.0382264	−	0.117649i
$280$	2.95630			0.176672
$281$	−9.74628	−	16.8811i	−0.581415	−	1.00704i	−0.995312	−	0.0967160i	$-0.969166\pi$
$281$	−9.74628	−	16.8811i	−0.581415	−	1.00704i	0.413898	−	0.910323i	$-0.364167\pi$
$282$	28.0504	+	2.94822i	1.67038	+	0.175564i
$283$	15.1440	−	26.2302i	0.900219	−	1.55922i	0.0730095	−	0.997331i	$-0.476740\pi$
$283$	15.1440	−	26.2302i	0.900219	−	1.55922i	0.827209	−	0.561894i	$-0.189927\pi$
$284$	0.605909	−	1.04946i	0.0359541	−	0.0622743i
$285$	−7.44417	−	0.782414i	−0.440955	−	0.0463462i
$286$	0.789665	+	1.36774i	0.0466939	+	0.0808762i
$287$	0.819534			0.0483756
$288$	1.09168	+	3.35983i	0.0643276	+	0.197980i
$289$	−15.2091			−0.894650
$290$	−3.29328	−	5.70413i	−0.193388	−	0.334958i
$291$	−16.9766	+	23.3663i	−0.995186	+	1.36976i
$292$	0.00926019	−	0.0160391i	0.000541912	−	0.000938618i
$293$	12.3622	−	21.4119i	0.722206	−	1.25090i	−0.237907	−	0.971288i	$-0.576461\pi$
$293$	12.3622	−	21.4119i	0.722206	−	1.25090i	0.960114	−	0.279610i	$-0.0902052\pi$
$294$	−0.942790	−	2.11754i	−0.0549846	−	0.123497i
$295$	2.74898	+	4.76138i	0.160052	+	0.277218i
$296$	−19.3288			−1.12346
$297$	0.714903	+	3.36336i	0.0414829	+	0.195162i
$298$	−12.8777			−0.745985
$299$	4.64904	+	8.05238i	0.268861	+	0.465681i
$300$	−0.147278	−	0.330792i	−0.00850311	−	0.0190983i
$301$	−0.819699	+	1.41976i	−0.0472467	+	0.0818336i
$302$	−4.84864	+	8.39809i	−0.279008	+	0.483256i
$303$	−1.32626	+	1.82544i	−0.0761918	+	0.104869i
$304$	−7.64524	−	13.2420i	−0.438485	−	0.759478i
$305$	11.7444			0.672480
$306$	−5.25542	−	1.11707i	−0.300432	−	0.0638589i
$307$	10.1284			0.578060			0.289030	−	0.957320i	$-0.406667\pi$
$307$	10.1284			0.578060			0.289030	+	0.957320i	$0.406667\pi$
$308$	−0.0691705	−	0.119807i	−0.00394136	−	0.00682663i
$309$	−26.4828	−	2.78346i	−1.50655	−	0.158345i
$310$	−0.460864	+	0.798239i	−0.0261753	+	0.0453369i
$311$	−6.67150	+	11.5554i	−0.378306	+	0.655245i	−0.990816	−	0.135218i	$-0.956827\pi$
$311$	−6.67150	+	11.5554i	−0.378306	+	0.655245i	0.612510	+	0.790463i	$0.290160\pi$
$312$	−9.08172	−	0.954527i	−0.514151	−	0.0540395i
$313$	−8.22745	−	14.2504i	−0.465043	−	0.805478i	0.534160	−	0.845383i	$-0.320628\pi$
$313$	−8.22745	−	14.2504i	−0.465043	−	0.805478i	−0.999203	+	0.0399048i	$0.987295\pi$
$314$	25.5573			1.44228
$315$	−2.00739	+	2.22943i	−0.113104	+	0.125614i
$316$	−2.41869			−0.136062
$317$	8.81216	+	15.2631i	0.494940	+	0.857262i	0.999983	−	0.00583249i	$-0.00185655\pi$
$317$	8.81216	+	15.2631i	0.494940	+	0.857262i	−0.505043	+	0.863094i	$0.668523\pi$
$318$	−18.8322	+	25.9203i	−1.05606	+	1.45354i
$319$	−1.62845	+	2.82056i	−0.0911756	+	0.157921i
$320$	4.32614	−	7.49309i	0.241838	−	0.418876i
$321$	−10.4811	−	23.5410i	−0.584999	−	1.31393i
$322$	3.48866	+	6.04254i	0.194416	+	0.336738i
$323$	−5.78339			−0.321796
$324$	−1.71885	−	0.765280i	−0.0954915	−	0.0425156i
$325$	1.78339			0.0989245
$326$	−11.8787	−	20.5746i	−0.657903	−	1.13952i
$327$	−1.87202	−	4.20462i	−0.103523	−	0.232516i
$328$	1.21139	−	2.09819i	0.0668879	−	0.115853i
$329$	6.08406	−	10.5379i	0.335425	−	0.580973i
$330$	0.901585	−	1.24093i	0.0496306	−	0.0683107i
$331$	−5.54082	−	9.59698i	−0.304551	−	0.527498i	0.672610	−	0.739997i	$-0.265173\pi$
$331$	−5.54082	−	9.59698i	−0.304551	−	0.527498i	−0.977161	+	0.212499i	$0.931840\pi$
$332$	−0.409307			−0.0224637
$333$	13.1247	−	14.5764i	0.719229	−	0.798784i
$334$	5.18769			0.283858
$335$	−3.30902	−	5.73139i	−0.180791	−	0.313139i
$336$	−6.09474	−	0.640583i	−0.332495	−	0.0349467i
$337$	9.46448	−	16.3930i	0.515563	−	0.892981i	−0.484274	−	0.874916i	$-0.660916\pi$
$337$	9.46448	−	16.3930i	0.515563	−	0.892981i	0.999837	−	0.0180647i	$-0.00575049\pi$
$338$	−6.57055	+	11.3805i	−0.357391	+	0.619019i
$339$	22.6678	+	2.38249i	1.23115	+	0.129399i
$340$	−0.139886	−	0.242290i	−0.00758640	−	0.0131400i
$341$	0.455772			0.0246815
$342$	16.9710	+	3.60730i	0.917687	+	0.195060i
$343$	−1.00000			−0.0539949
$344$	2.42327	+	4.19723i	0.130654	+	0.226300i
$345$	5.30796	−	7.30578i	0.285771	−	0.393330i
$346$	−9.68312	+	16.7717i	−0.520568	+	0.901650i
$347$	−9.71113	+	16.8202i	−0.521321	+	0.902954i	0.478372	+	0.878157i	$0.341227\pi$
$347$	−9.71113	+	16.8202i	−0.521321	+	0.902954i	−0.999693	+	0.0247966i	$0.992106\pi$
$348$	−0.724863	−	1.62807i	−0.0388567	−	0.0872737i
$349$	11.2191	+	19.4320i	0.600544	+	1.04017i	0.992739	+	0.120290i	$0.0383826\pi$
$349$	11.2191	+	19.4320i	0.600544	+	1.04017i	−0.392195	+	0.919882i	$0.628284\pi$
$350$	1.33826			0.0715331
$351$	6.88653	−	6.20066i	0.367576	−	0.330967i
$352$	−0.779250			−0.0415342
$353$	−6.72055	−	11.6403i	−0.357699	−	0.619552i	0.629877	−	0.776695i	$-0.283105\pi$
$353$	−6.72055	−	11.6403i	−0.357699	−	0.619552i	−0.987576	+	0.157142i	$0.949772\pi$
$354$	−5.18343	−	11.6422i	−0.275496	−	0.618774i
$355$	2.89829	−	5.01999i	0.153826	−	0.266434i
$356$	−1.37565	+	2.38270i	−0.0729094	+	0.126283i
$357$	−1.36245	+	1.87525i	−0.0721084	+	0.0992488i
$358$	3.44768	+	5.97156i	0.182216	+	0.315607i
$359$	−15.0019			−0.791771			−0.395885	−	0.918300i	$-0.629562\pi$
$359$	−15.0019			−0.791771			−0.395885	+	0.918300i	$0.629562\pi$
$360$	2.74064	+	8.43481i	0.144444	+	0.444554i
$361$	−0.324055			−0.0170555
$362$	−13.9348	−	24.1357i	−0.732395	−	1.26855i
$363$	18.1939	+	1.91225i	0.954931	+	0.100367i
$364$	−0.186415	+	0.322880i	−0.00977078	+	0.0169235i
$365$	0.0442951	−	0.0767213i	0.00231851	−	0.00401578i
$366$	−27.0735	−	2.84554i	−1.41516	−	0.148739i
$367$	−1.22382	−	2.11972i	−0.0638828	−	0.110648i	0.832315	−	0.554303i	$-0.187015\pi$
$367$	−1.22382	−	2.11972i	−0.0638828	−	0.110648i	−0.896198	+	0.443655i	$0.853682\pi$
$368$	18.4471			0.961622
$369$	0.759750	+	2.33827i	0.0395510	+	0.121725i
$370$	−8.74979			−0.454880
$371$	6.91115	+	11.9705i	0.358809	+	0.621475i
$372$	−0.146590	+	0.201764i	−0.00760036	+	0.0104610i
$373$	9.56227	−	16.5623i	0.495115	−	0.857565i	−0.504869	−	0.863196i	$-0.668459\pi$
$373$	9.56227	−	16.5623i	0.495115	−	0.857565i	0.999984	+	0.00563108i	$0.00179244\pi$
$374$	0.592568	−	1.02636i	0.0306410	−	0.0530717i
$375$	−0.704489	−	1.58231i	−0.0363796	−	0.0817100i
$376$	−17.9863	−	31.1531i	−0.927571	−	1.60660i
$377$	8.77734			0.452056
$378$	5.16769	−	4.65301i	0.265797	−	0.239325i
$379$	−3.51235			−0.180417			−0.0902087	−	0.995923i	$-0.528753\pi$
$379$	−3.51235			−0.180417			−0.0902087	+	0.995923i	$0.528753\pi$
$380$	0.451727	+	0.782414i	0.0231731	+	0.0401370i
$381$	−7.75117	−	17.4094i	−0.397105	−	0.891912i
$382$	−12.4750	+	21.6073i	−0.638274	+	1.10552i
$383$	14.3290	−	24.8185i	0.732176	−	1.26817i	−0.223776	−	0.974641i	$-0.571838\pi$
$383$	14.3290	−	24.8185i	0.732176	−	1.26817i	0.955951	−	0.293525i	$-0.0948283\pi$
$384$	−9.39055	+	12.9250i	−0.479210	+	0.659575i
$385$	−0.330869	−	0.573083i	−0.0168627	−	0.0292070i
$386$	−18.5412			−0.943723
$387$	−4.81072	−	1.02255i	−0.244543	−	0.0519791i
$388$	3.48607			0.176978
$389$	−3.60861	−	6.25029i	−0.182964	−	0.316902i	0.759925	−	0.650011i	$-0.225236\pi$
$389$	−3.60861	−	6.25029i	−0.182964	−	0.316902i	−0.942888	+	0.333109i	$0.891902\pi$
$390$	−4.11113	−	0.432097i	−0.208175	−	0.0218801i
$391$	3.48866	−	6.04254i	0.176429	−	0.305585i
$392$	−1.47815	+	2.56023i	−0.0746577	+	0.129311i
$393$	−14.8709	−	1.56300i	−0.750139	−	0.0788427i
$394$	7.17719	+	12.4313i	0.361582	+	0.626278i
$395$	−11.5695			−0.582126
$396$	0.277705	−	0.308422i	0.0139552	−	0.0154988i
$397$	19.8031			0.993890			0.496945	−	0.867782i	$-0.334455\pi$
$397$	19.8031			0.993890			0.496945	+	0.867782i	$0.334455\pi$
$398$	4.19525	+	7.26639i	0.210289	+	0.364231i
$399$	4.39968	−	6.05563i	0.220259	−	0.303161i
$400$	1.76909	−	3.06415i	0.0884545	−	0.153208i
$401$	4.53946	−	7.86257i	0.226690	−	0.392638i	−0.730135	−	0.683303i	$-0.760543\pi$
$401$	4.53946	−	7.86257i	0.226690	−	0.392638i	0.956825	+	0.290664i	$0.0938763\pi$
$402$	6.23941	+	14.0140i	0.311194	+	0.698952i
$403$	−0.614153	−	1.06374i	−0.0305932	−	0.0529889i
$404$	0.272342			0.0135495
$405$	−8.22191	−	3.66063i	−0.408550	−	0.181898i
$406$	6.58656			0.326885
$407$	2.16328	+	3.74692i	0.107230	+	0.185728i
$408$	2.78716	+	6.26007i	0.137985	+	0.309920i
$409$	−10.1702	+	17.6154i	−0.502886	+	0.871024i	0.497108	+	0.867689i	$0.334395\pi$
$409$	−10.1702	+	17.6154i	−0.502886	+	0.871024i	−0.999994	+	0.00333589i	$0.998938\pi$
$410$	0.548375	−	0.949814i	0.0270823	−	0.0469080i
$411$	−13.3418	+	18.3634i	−0.658103	+	0.905801i
$412$	1.60703	+	2.78346i	0.0791726	+	0.137131i
$413$	−5.49797			−0.270537
$414$	−14.0062	+	15.5555i	−0.688369	+	0.764511i
$415$	−1.95788			−0.0961083
$416$	1.05004	+	1.81872i	0.0514824	+	0.0891702i
$417$	−9.80363	−	1.03040i	−0.480086	−	0.0504591i
$418$	−1.91355	+	3.31436i	−0.0935946	+	0.162111i
$419$	−2.90773	+	5.03634i	−0.142052	+	0.246041i	−0.928269	−	0.371909i	$-0.878703\pi$
$419$	−2.90773	+	5.03634i	−0.142052	+	0.246041i	0.786217	+	0.617950i	$0.212037\pi$
$420$	0.360114	+	0.0378495i	0.0175717	+	0.00184686i
$421$	16.6573	+	28.8513i	0.811827	+	1.40613i	0.911584	+	0.411115i	$0.134860\pi$
$421$	16.6573	+	28.8513i	0.811827	+	1.40613i	−0.0997562	+	0.995012i	$0.531806\pi$
$422$	−13.8153			−0.672520
$423$	35.7066	+	7.58968i	1.73612	+	0.369023i
$424$	40.8628			1.98447
$425$	−0.669131	−	1.15897i	−0.0324576	−	0.0562182i
$426$	−7.89756	+	10.8701i	−0.382638	+	0.526656i
$427$	−5.87218	+	10.1709i	−0.284175	+	0.492205i
$428$	−1.55514	+	2.69357i	−0.0751703	+	0.130199i
$429$	0.831392	+	1.86734i	0.0401400	+	0.0901559i
$430$	1.09697	+	1.90001i	0.0529007	+	0.0916266i
$431$	−33.1633			−1.59742			−0.798710	−	0.601716i	$-0.794484\pi$
$431$	−33.1633			−1.59742			−0.798710	+	0.601716i	$0.794484\pi$
$432$	−3.82244	−	17.9832i	−0.183907	−	0.865216i
$433$	33.2920			1.59991			0.799955	−	0.600060i	$-0.204856\pi$
$433$	33.2920			1.59991			0.799955	+	0.600060i	$0.204856\pi$
$434$	−0.460864	−	0.798239i	−0.0221222	−	0.0383167i
$435$	−3.46730	−	7.78768i	−0.166244	−	0.373391i
$436$	−0.277761	+	0.481095i	−0.0133023	+	0.0230403i
$437$	−11.2657	+	19.5128i	−0.538913	+	0.933425i
$438$	−0.120699	+	0.166129i	−0.00576724	+	0.00793793i
$439$	13.1127	+	22.7118i	0.625834	+	1.08398i	0.988379	+	0.152009i	$0.0485744\pi$
$439$	13.1127	+	22.7118i	0.625834	+	1.08398i	−0.362546	+	0.931966i	$0.618092\pi$
$440$	−1.95630			−0.0932627
$441$	−0.927051	−	2.85317i	−0.0441453	−	0.135865i
$442$	−3.19394			−0.151920
$443$	−7.86257	−	13.6184i	−0.373562	−	0.647029i	0.616549	−	0.787317i	$-0.288530\pi$
$443$	−7.86257	−	13.6184i	−0.373562	−	0.647029i	−0.990111	+	0.140288i	$0.955197\pi$
$444$	−2.35449	−	0.247467i	−0.111739	−	0.0117442i
$445$	−6.58028	+	11.3974i	−0.311935	+	0.540287i
$446$	3.24697	−	5.62392i	0.153749	−	0.266300i
$447$	−16.5757	−	1.74218i	−0.784004	−	0.0824022i
$448$	4.32614	+	7.49309i	0.204391	+	0.354015i
$449$	38.5915			1.82125			0.910624	−	0.413236i	$-0.135602\pi$
$449$	38.5915			1.82125			0.910624	+	0.413236i	$0.135602\pi$
$450$	1.24064	+	3.81829i	0.0584842	+	0.179996i
$451$	−0.542317			−0.0255367
$452$	−1.37553	−	2.38249i	−0.0646995	−	0.112063i
$453$	−7.37715	+	10.1538i	−0.346609	+	0.477066i
$454$	−6.53859	+	11.3252i	−0.306871	+	0.531516i
$455$	−0.891693	+	1.54446i	−0.0418032	+	0.0724053i
$456$	−9.00043	−	20.2153i	−0.421484	−	0.946667i
$457$	20.7219	+	35.8913i	0.969328	+	1.67893i	0.697507	+	0.716578i	$0.254292\pi$
$457$	20.7219	+	35.8913i	0.969328	+	1.67893i	0.271821	+	0.962348i	$0.412374\pi$
$458$	−21.6110			−1.00981
$459$	−6.61347	−	2.14885i	−0.308690	−	0.100300i
$460$	−1.08997			−0.0508199
$461$	9.80816	+	16.9882i	0.456812	+	0.791221i	0.998790	−	0.0491711i	$-0.0156580\pi$
$461$	9.80816	+	16.9882i	0.456812	+	0.791221i	−0.541979	+	0.840392i	$0.682325\pi$
$462$	0.623880	+	1.40126i	0.0290255	+	0.0651924i
$463$	−3.04373	+	5.27189i	−0.141454	+	0.245005i	−0.928044	−	0.372470i	$-0.878511\pi$
$463$	−3.04373	+	5.27189i	−0.141454	+	0.245005i	0.786590	+	0.617475i	$0.211844\pi$
$464$	8.70698	−	15.0809i	0.404211	−	0.700115i
$465$	−0.701198	+	0.965117i	−0.0325173	+	0.0447562i
$466$	3.85696	+	6.68045i	0.178670	+	0.309466i
$467$	−20.9548			−0.969672			−0.484836	−	0.874605i	$-0.661121\pi$
$467$	−20.9548			−0.969672			−0.484836	+	0.874605i	$0.661121\pi$
$468$	−1.09405	−	0.232547i	−0.0505723	−	0.0107495i
$469$	6.61803			0.305592
$470$	−8.14206	−	14.1025i	−0.375565	−	0.650498i
$471$	32.8965	+	3.45756i	1.51579	+	0.159316i
$472$	−8.12681	+	14.0760i	−0.374067	+	0.647902i
$473$	0.542427	−	0.939511i	0.0249408	−	0.0431987i
$474$	26.6705	+	2.80319i	1.22502	+	0.128755i
$475$	2.16078	+	3.74259i	0.0991436	+	0.171722i
$476$	0.279773			0.0128234
$477$	−27.7468	+	30.8159i	−1.27044	+	1.41096i
$478$	−0.161988			−0.00740917
$479$	−12.8915	−	22.3287i	−0.589026	−	1.02022i	−0.994360	−	0.106055i	$-0.966178\pi$
$479$	−12.8915	−	22.3287i	−0.589026	−	1.02022i	0.405334	−	0.914169i	$-0.367155\pi$
$480$	1.19886	−	1.65009i	0.0547204	−	0.0753161i
$481$	5.83005	−	10.0979i	0.265827	−	0.460427i
$482$	14.0261	−	24.2938i	0.638869	−	1.10655i
$483$	3.67301	+	8.24972i	0.167128	+	0.375375i
$484$	−1.10404	−	1.91225i	−0.0501836	−	0.0869206i
$485$	16.6752			0.757183
$486$	18.0665	+	10.4307i	0.819514	+	0.473147i
$487$	27.1083			1.22840			0.614198	−	0.789152i	$-0.289480\pi$
$487$	27.1083			1.22840			0.614198	+	0.789152i	$0.289480\pi$
$488$	17.3599	+	30.0682i	0.785845	+	1.36112i
$489$	−12.5064	−	28.0899i	−0.565561	−	1.27027i
$490$	−0.669131	+	1.15897i	−0.0302282	+	0.0523568i
$491$	−11.2506	+	19.4866i	−0.507732	+	0.879417i	0.492228	+	0.870466i	$0.336183\pi$
$491$	−11.2506	+	19.4866i	−0.507732	+	0.879417i	−0.999960	+	0.00895100i	$0.997151\pi$
$492$	0.174426	−	0.240077i	0.00786372	−	0.0108235i
$493$	−3.29328	−	5.70413i	−0.148322	−	0.256901i
$494$	10.3140			0.464049
$495$	1.32837	−	1.47530i	0.0597057	−	0.0663100i
$496$	−2.43692			−0.109421
$497$	2.89829	+	5.01999i	0.130006	+	0.225178i
$498$	4.51337	+	0.474374i	0.202249	+	0.0212572i
$499$	−3.15174	+	5.45898i	−0.141091	+	0.244378i	−0.927908	−	0.372809i	$-0.878394\pi$
$499$	−3.15174	+	5.45898i	−0.141091	+	0.244378i	0.786816	+	0.617187i	$0.211728\pi$
$500$	−0.104528	+	0.181049i	−0.00467465	+	0.00809674i
$501$	6.67741	+	0.701825i	0.298325	+	0.0313552i
$502$	−10.1470	−	17.5751i	−0.452882	−	0.784414i
$503$	−29.9283			−1.33443			−0.667217	−	0.744863i	$-0.732515\pi$
$503$	−29.9283			−1.33443			−0.667217	+	0.744863i	$0.732515\pi$
$504$	−8.67508	−	1.84395i	−0.386419	−	0.0821358i
$505$	1.30272			0.0579701
$506$	−2.30858	−	3.99859i	−0.102629	−	0.177759i
$507$	−9.99701	+	13.7597i	−0.443983	+	0.611090i
$508$	−1.15008	+	1.99200i	−0.0510266	+	0.0883806i
$509$	11.0491	−	19.1376i	0.489743	−	0.848259i	−0.510187	−	0.860063i	$-0.670424\pi$
$509$	11.0491	−	19.1376i	0.489743	−	0.848259i	0.999930	+	0.0118037i	$0.00375733\pi$
$510$	1.26170	+	2.83382i	0.0558690	+	0.125484i
$511$	0.0442951	+	0.0767213i	0.00195950	+	0.00339395i
$512$	25.0863			1.10867
$513$	21.3565	+	6.93914i	0.942911	+	0.306370i
$514$	29.3954			1.29657
$515$	7.68704	+	13.3143i	0.338731	+	0.586700i
$516$	0.241448	+	0.542300i	0.0106291	+	0.0238734i
$517$	−4.02606	+	6.97333i	−0.177066	+	0.306687i
$518$	4.37490	−	7.57754i	0.192222	−	0.332938i
$519$	−14.7328	+	20.2779i	−0.646696	+	0.890101i
$520$	2.63611	+	4.56587i	0.115601	+	0.200227i
$521$	−18.7772			−0.822644			−0.411322	−	0.911490i	$-0.634933\pi$
$521$	−18.7772			−0.822644			−0.411322	+	0.911490i	$0.634933\pi$
$522$	6.10607	+	18.7926i	0.267256	+	0.822528i
$523$	21.9797			0.961104			0.480552	−	0.876966i	$-0.340436\pi$
$523$	21.9797			0.961104			0.480552	+	0.876966i	$0.340436\pi$
$524$	0.902396	+	1.56300i	0.0394214	+	0.0682798i
$525$	1.72256	+	0.181049i	0.0751788	+	0.00790161i
$526$	−21.4367	+	37.1295i	−0.934685	+	1.61892i
$527$	−0.460864	+	0.798239i	−0.0200755	+	0.0347718i
$528$	4.03312	+	0.423898i	0.175519	+	0.0184478i
$529$	−2.09148	−	3.62254i	−0.0909338	−	0.157502i
$530$	18.4978			0.803495
$531$	−5.09690	−	15.6866i	−0.221186	−	0.680742i
$532$	−0.903454			−0.0391697
$533$	0.730773	+	1.26574i	0.0316533	+	0.0548251i
$534$	17.9306	−	24.6793i	0.775932	−	1.06798i
$535$	−7.43881	+	12.8844i	−0.321608	+	0.557041i
$536$	9.78243	−	16.9437i	0.422537	−	0.731855i
$537$	3.62986	+	8.15280i	0.156640	+	0.351819i
$538$	3.07327	+	5.32306i	0.132498	+	0.229494i
$539$	0.661739			0.0285031
$540$	0.225853	+	1.06255i	0.00971915	+	0.0457250i
$541$	1.77587			0.0763507			0.0381753	−	0.999271i	$-0.487845\pi$
$541$	1.77587			0.0763507			0.0381753	+	0.999271i	$0.487845\pi$
$542$	10.9019	+	18.8827i	0.468277	+	0.811080i
$543$	−14.6711	−	32.9518i	−0.629597	−	1.41410i
$544$	0.787955	−	1.36478i	0.0337833	−	0.0585143i
$545$	−1.32864	+	2.30127i	−0.0569125	+	0.0985754i
$546$	2.42977	−	3.34429i	0.103985	−	0.143123i
$547$	−8.58281	−	14.8659i	−0.366975	−	0.635619i	0.622116	−	0.782925i	$-0.286273\pi$
$547$	−8.58281	−	14.8659i	−0.366975	−	0.635619i	−0.989091	+	0.147306i	$0.952940\pi$
$548$	2.73968			0.117033
$549$	−34.4631	−	7.32536i	−1.47085	−	0.312639i
$550$	−0.885579			−0.0377612
$551$	10.6348	+	18.4200i	0.453057	+	0.784718i
$552$	26.5504	+	2.79056i	1.13006	+	0.118774i
$553$	5.78477	−	10.0195i	0.245993	−	0.426073i
$554$	−20.8528	+	36.1182i	−0.885952	+	1.53451i
$555$	−11.2624	−	1.18373i	−0.478063	−	0.0502465i
$556$	0.594903	+	1.03040i	0.0252295	+	0.0436988i
$557$	−24.2342			−1.02684			−0.513419	−	0.858138i	$-0.671621\pi$
$557$	−24.2342			−1.02684			−0.513419	+	0.858138i	$0.671621\pi$
$558$	1.85027	−	2.05493i	0.0783281	−	0.0869921i
$559$	−2.92368			−0.123658
$560$	1.76909	+	3.06415i	0.0747577	+	0.129484i
$561$	0.901585	−	1.24093i	0.0380650	−	0.0523919i
$562$	13.0431	−	22.5913i	0.550189	−	0.952955i
$563$	−5.73052	+	9.92556i	−0.241513	+	0.418312i	−0.961145	−	0.276043i	$-0.910977\pi$
$563$	−5.73052	+	9.92556i	−0.241513	+	0.418312i	0.719633	+	0.694355i	$0.244310\pi$
$564$	−1.79210	−	4.02512i	−0.0754609	−	0.169488i
$565$	−6.57969	−	11.3964i	−0.276810	−	0.479448i
$566$	40.5333			1.70374
$567$	7.28115	−	5.29007i	0.305780	−	0.222162i
$568$	17.1364			0.719029
$569$	−11.2104	−	19.4170i	−0.469966	−	0.814005i	0.529444	−	0.848345i	$-0.322400\pi$
$569$	−11.2104	−	19.4170i	−0.469966	−	0.814005i	−0.999410	+	0.0343398i	$0.989067\pi$
$570$	−4.07433	−	9.15109i	−0.170655	−	0.383297i
$571$	5.44697	−	9.43443i	0.227949	−	0.394819i	−0.729251	−	0.684246i	$-0.760131\pi$
$571$	5.44697	−	9.43443i	0.227949	−	0.394819i	0.957200	+	0.289427i	$0.0934648\pi$
$572$	0.123358	−	0.213662i	0.00515785	−	0.00893365i
$573$	−18.9805	+	26.1244i	−0.792922	+	1.09136i
$574$	0.548375	+	0.949814i	0.0228887	+	0.0396445i
$575$	−5.21373			−0.217427
$576$	−17.3685	+	19.2897i	−0.723687	+	0.803736i
$577$	−2.67343			−0.111296			−0.0556482	−	0.998450i	$-0.517723\pi$
$577$	−2.67343			−0.111296			−0.0556482	+	0.998450i	$0.517723\pi$
$578$	−10.1768	−	17.6268i	−0.423301	−	0.733179i
$579$	−23.8656	−	2.50838i	−0.991820	−	0.104245i
$580$	−0.514461	+	0.891072i	−0.0213618	+	0.0369997i
$581$	0.978938	−	1.69557i	0.0406132	−	0.0703441i
$582$	−38.4403	−	4.04024i	−1.59340	−	0.167473i
$583$	−4.57337	−	7.92132i	−0.189410	−	0.328067i
$584$	0.261899			0.0108374
$585$	−5.23324	−	1.11236i	−0.216368	−	0.0459904i
$586$	33.0877			1.36684
$587$	−7.58940	−	13.1452i	−0.313248	−	0.542562i	0.665815	−	0.746116i	$-0.268084\pi$
$587$	−7.58940	−	13.1452i	−0.313248	−	0.542562i	−0.979064	+	0.203555i	$0.934750\pi$
$588$	−0.212835	+	0.292943i	−0.00877718	+	0.0120808i
$589$	1.48824	−	2.57771i	0.0613218	−	0.106213i
$590$	−3.67886	+	6.37197i	−0.151456	+	0.262330i
$591$	7.55645	+	16.9721i	0.310831	+	0.698137i
$592$	−11.5666	−	20.0340i	−0.475386	−	0.823392i
$593$	−4.47015			−0.183567			−0.0917835	−	0.995779i	$-0.529257\pi$
$593$	−4.47015			−0.183567			−0.0917835	+	0.995779i	$0.529257\pi$
$594$	−3.41966	+	3.07907i	−0.140310	+	0.126336i
$595$	1.33826			0.0548634
$596$	1.00585	+	1.74218i	0.0412011	+	0.0713624i
$597$	4.41693	+	9.92059i	0.180773	+	0.406023i
$598$	−6.22164	+	10.7762i	−0.254422	+	0.440671i
$599$	13.7861	−	23.8783i	0.563287	−	0.975641i	−0.433920	−	0.900951i	$-0.642870\pi$
$599$	13.7861	−	23.8783i	0.563287	−	0.975641i	0.997207	−	0.0746898i	$-0.0237967\pi$
$600$	3.00973	−	4.14253i	0.122872	−	0.169118i
$601$	−6.64711	−	11.5131i	−0.271141	−	0.469631i	0.698013	−	0.716085i	$-0.254068\pi$
$601$	−6.64711	−	11.5131i	−0.271141	−	0.469631i	−0.969154	+	0.246454i	$0.920734\pi$
$602$	−2.19394			−0.0894184
$603$	6.13525	+	18.8824i	0.249847	+	0.768950i
$604$	1.51486			0.0616390
$605$	−5.28105	−	9.14705i	−0.214705	−	0.371880i
$606$	−3.00307	−	0.315636i	−0.121992	−	0.0128218i
$607$	21.6602	−	37.5166i	0.879161	−	1.52275i	0.0268988	−	0.999638i	$-0.491437\pi$
$607$	21.6602	−	37.5166i	0.879161	−	1.52275i	0.852263	−	0.523114i	$-0.175230\pi$
$608$	−2.54449	+	4.40719i	−0.103193	+	0.178735i
$609$	8.47798	+	0.891072i	0.343545	+	0.0361081i
$610$	7.85851	+	13.6113i	0.318182	+	0.551107i
$611$	21.7004			0.877906
$612$	0.259364	+	0.798239i	0.0104842	+	0.0322669i
$613$	−34.4529			−1.39154			−0.695769	−	0.718265i	$-0.744936\pi$
$613$	−34.4529			−1.39154			−0.695769	+	0.718265i	$0.744936\pi$
$614$	6.77724	+	11.7385i	0.273507	+	0.473729i
$615$	0.834346	−	1.14838i	0.0336441	−	0.0463071i
$616$	0.978148	−	1.69420i	0.0394107	−	0.0682613i
$617$	5.22770	−	9.05464i	0.210459	−	0.364526i	−0.741399	−	0.671064i	$-0.765837\pi$
$617$	5.22770	−	9.05464i	0.210459	−	0.364526i	0.951858	+	0.306538i	$0.0991707\pi$
$618$	−14.4945	−	32.5552i	−0.583055	−	1.30956i
$619$	−16.6377	−	28.8174i	−0.668726	−	1.15827i	−0.978261	−	0.207379i	$-0.933507\pi$
$619$	−16.6377	−	28.8174i	−0.668726	−	1.15827i	0.309535	−	0.950888i	$-0.399827\pi$
$620$	0.143988			0.00578269
$621$	−20.1328	+	18.1276i	−0.807900	+	0.727437i
$622$	−17.8564			−0.715977
$623$	−6.58028	−	11.3974i	−0.263633	−	0.456626i
$624$	−4.44528	−	9.98427i	−0.177954	−	0.399691i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	11.0105	−	19.0707i	0.440067	−	0.762219i
$627$	−2.91144	+	4.00725i	−0.116272	+	0.160034i
$628$	−1.99622	−	3.45756i	−0.0796579	−	0.137972i
$629$	−8.74979			−0.348877
$630$	−3.92705	−	0.834720i	−0.156457	−	0.0332561i
$631$	−31.7046			−1.26214			−0.631070	−	0.775726i	$-0.717384\pi$
$631$	−31.7046			−1.26214			−0.631070	+	0.775726i	$0.717384\pi$
$632$	−17.1015	−	29.6206i	−0.680260	−	1.17825i
$633$	−17.7826	−	1.86903i	−0.706796	−	0.0742872i
$634$	−11.7930	+	20.4260i	−0.468359	+	0.811221i
$635$	−5.50128	+	9.52849i	−0.218312	+	0.378127i
$636$	4.97760	+	0.523166i	0.197375	+	0.0207449i
$637$	−0.891693	−	1.54446i	−0.0353302	−	0.0611936i
$638$	−4.35858			−0.172558
$639$	−11.6360	+	12.9231i	−0.460314	+	0.511231i
$640$	9.22384			0.364604
$641$	−21.9256	−	37.9763i	−0.866009	−	1.49997i	−0.866042	−	0.499972i	$-0.833344\pi$
$641$	−21.9256	−	37.9763i	−0.866009	−	1.49997i	3.25004e−5	−	1.00000i	$-0.499990\pi$
$642$	20.2700	−	27.8993i	0.799993	−	1.10110i
$643$	5.20666	−	9.01820i	0.205331	−	0.355643i	−0.744907	−	0.667168i	$-0.767506\pi$
$643$	5.20666	−	9.01820i	0.205331	−	0.355643i	0.950238	+	0.311525i	$0.100840\pi$
$644$	0.544983	−	0.943938i	0.0214753	−	0.0371964i
$645$	1.15494	+	2.59403i	0.0454756	+	0.102140i
$646$	−3.86984	−	6.70276i	−0.152257	−	0.263717i
$647$	4.14378			0.162909			0.0814545	−	0.996677i	$-0.474043\pi$
$647$	4.14378			0.162909			0.0814545	+	0.996677i	$0.474043\pi$
$648$	−2.78115	−	26.4609i	−0.109254	−	1.03948i
$649$	3.63822			0.142813
$650$	1.19332	+	2.06689i	0.0468058	+	0.0810700i
$651$	−0.485216	−	1.08981i	−0.0190171	−	0.0427132i
$652$	−1.85564	+	3.21407i	−0.0726726	+	0.125873i
$653$	2.13377	−	3.69580i	0.0835010	−	0.144628i	−0.821250	−	0.570568i	$-0.806723\pi$
$653$	2.13377	−	3.69580i	0.0835010	−	0.144628i	0.904751	+	0.425940i	$0.140056\pi$
$654$	3.62040	−	4.98305i	0.141569	−	0.194853i
$655$	4.31651	+	7.47642i	0.168660	+	0.292128i
$656$	2.89966			0.113213
$657$	−0.177835	+	0.197506i	−0.00693801	+	0.00770544i
$658$	16.2841			0.634821
$659$	−8.97045	−	15.5373i	−0.349439	−	0.605247i	0.636711	−	0.771103i	$-0.280295\pi$
$659$	−8.97045	−	15.5373i	−0.349439	−	0.605247i	−0.986150	+	0.165856i	$0.946961\pi$
$660$	−0.238301	−	0.0250465i	−0.00927586	−	0.000974932i
$661$	−14.1837	+	24.5668i	−0.551681	+	0.955539i	0.446473	+	0.894797i	$0.352680\pi$
$661$	−14.1837	+	24.5668i	−0.551681	+	0.955539i	−0.998154	+	0.0607417i	$0.980653\pi$
$662$	7.41506	−	12.8433i	0.288195	−	0.499168i
$663$	−4.11113	−	0.432097i	−0.159663	−	0.0167813i
$664$	−2.89403	−	5.01260i	−0.112310	−	0.194527i
$665$	−4.32157			−0.167583
$666$	25.6758	+	5.45755i	0.994916	+	0.211476i
$667$	−25.6605			−0.993580
$668$	−0.405199	−	0.701825i	−0.0156776	−	0.0271544i
$669$	4.94023	−	6.79964i	0.191000	−	0.262889i
$670$	4.42833	−	7.67009i	0.171081	−	0.296321i
$671$	3.88585	−	6.73048i	0.150011	−	0.259827i
$672$	0.829591	+	1.86329i	0.0320022	+	0.0718781i
$673$	−9.33425	−	16.1674i	−0.359809	−	0.623208i	0.628120	−	0.778117i	$-0.283825\pi$
$673$	−9.33425	−	16.1674i	−0.359809	−	0.623208i	−0.987929	+	0.154909i	$0.950492\pi$
$674$	25.3319			0.975748
$675$	1.08034	+	5.08260i	0.0415823	+	0.195630i
$676$	2.05284			0.0789554
$677$	2.08162	+	3.60547i	0.0800031	+	0.138569i	0.903251	−	0.429113i	$-0.141174\pi$
$677$	2.08162	+	3.60547i	0.0800031	+	0.138569i	−0.823248	+	0.567682i	$0.807840\pi$
$678$	12.4065	+	27.8655i	0.476470	+	1.07017i
$679$	−8.33761	+	14.4412i	−0.319968	+	0.554201i
$680$	1.97815	−	3.42625i	0.0758585	−	0.131391i
$681$	−9.94838	+	13.6928i	−0.381223	+	0.524708i
$682$	0.304971	+	0.528226i	0.0116780	+	0.0202268i
$683$	−28.2844			−1.08227			−0.541137	−	0.840934i	$-0.682006\pi$
$683$	−28.2844			−1.08227			−0.541137	+	0.840934i	$0.682006\pi$
$684$	−0.837548	−	2.57771i	−0.0320244	−	0.0985611i
$685$	13.1050			0.500715
$686$	−0.669131	−	1.15897i	−0.0255475	−	0.0442496i
$687$	−27.8169	−	2.92367i	−1.06128	−	0.111545i
$688$	−2.90024	+	5.02337i	−0.110571	+	0.191514i
$689$	−12.3252	+	21.3479i	−0.469554	+	0.813292i
$690$	12.0189	+	1.26324i	0.457551	+	0.0480906i
$691$	−16.6210	−	28.7884i	−0.632292	−	1.09516i	−0.987082	−	0.160215i	$-0.948781\pi$
$691$	−16.6210	−	28.7884i	−0.632292	−	1.09516i	0.354790	−	0.934946i	$-0.384552\pi$
$692$	3.02531			0.115005
$693$	0.613466	+	1.88805i	0.0233036	+	0.0717212i
$694$	−25.9921			−0.986645
$695$	2.84565	+	4.92882i	0.107942	+	0.186961i
$696$	14.8131	−	20.3884i	0.561487	−	0.772821i
$697$	0.548375	−	0.949814i	0.0207712	−	0.0359768i
$698$	−15.0141	+	26.0051i	−0.568291	+	0.984309i
$699$	4.06077	+	9.12063i	0.153592	+	0.344974i
$700$	−0.104528	−	0.181049i	−0.00395080	−	0.00684299i
$701$	23.1546			0.874535			0.437268	−	0.899331i	$-0.355946\pi$
$701$	23.1546			0.874535			0.437268	+	0.899331i	$0.355946\pi$
$702$	11.7944	+	3.83222i	0.445150	+	0.144638i
$703$	28.2552			1.06566
$704$	−2.86277	−	4.95847i	−0.107895	−	0.186879i
$705$	−8.57230	−	19.2537i	−0.322851	−	0.725136i
$706$	8.99385	−	15.5778i	0.338488	−	0.586279i
$707$	−0.651358	+	1.12819i	−0.0244969	+	0.0424298i
$708$	−1.17016	+	1.61059i	−0.0439774	+	0.0605297i
$709$	−3.31151	−	5.73570i	−0.124366	−	0.215409i	0.797119	−	0.603823i	$-0.206356\pi$
$709$	−3.31151	−	5.73570i	−0.124366	−	0.215409i	−0.921485	+	0.388414i	$0.873023\pi$
$710$	7.75735			0.291128
$711$	33.9501	+	7.21632i	1.27323	+	0.270633i
$712$	−38.9065			−1.45808
$713$	1.79548	+	3.10986i	0.0672411	+	0.116465i
$714$	−3.08501	−	0.324248i	−0.115454	−	0.0121347i
$715$	0.590068	−	1.02203i	0.0220673	−	0.0382217i
$716$	0.538581	−	0.932849i	0.0201277	−	0.0348622i
$717$	−0.208506	−	0.0219148i	−0.00778679	−	0.000818424i
$718$	−10.0382	−	17.3867i	−0.374624	−	0.648867i
$719$	38.0335			1.41841			0.709205	−	0.705002i	$-0.249054\pi$
$719$	38.0335			1.41841			0.709205	+	0.705002i	$0.249054\pi$
$720$	−7.10252	+	7.88814i	−0.264695	+	0.293974i
$721$	−15.3741			−0.572561
$722$	−0.216835	−	0.375569i	−0.00806976	−	0.0139772i
$723$	21.3405	−	29.3726i	0.793661	−	1.09238i
$724$	−2.17682	+	3.77037i	−0.0809010	+	0.140125i
$725$	−2.46086	+	4.26234i	−0.0913942	+	0.158299i
$726$	9.95784	+	22.3657i	0.369570	+	0.830068i
$727$	−0.855278	−	1.48138i	−0.0317205	−	0.0549415i	0.849729	−	0.527219i	$-0.176765\pi$
$727$	−0.855278	−	1.48138i	−0.0317205	−	0.0549415i	−0.881450	+	0.472278i	$0.843432\pi$
$728$	−5.27222			−0.195401
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$	0.118557			0.00438798
$731$	1.09697	+	1.90001i	0.0405730	+	0.0702744i
$732$	1.72969	+	3.88494i	0.0639311	+	0.143592i
$733$	−19.7037	+	34.1277i	−0.727771	+	1.26054i	0.230052	+	0.973178i	$0.426110\pi$
$733$	−19.7037	+	34.1277i	−0.727771	+	1.26054i	−0.957823	+	0.287358i	$0.907223\pi$
$734$	1.63779	−	2.83674i	0.0604519	−	0.104706i
$735$	−1.01807	+	1.40126i	−0.0375522	+	0.0516862i
$736$	−3.06979	−	5.31703i	−0.113154	−	0.195988i
$737$	−4.37941			−0.161318
$738$	−2.20161	+	2.44513i	−0.0810423	+	0.0900066i
$739$	2.91159			0.107104			0.0535522	−	0.998565i	$-0.482946\pi$
$739$	2.91159			0.107104			0.0535522	+	0.998565i	$0.482946\pi$
$740$	0.683426	+	1.18373i	0.0251232	+	0.0435147i
$741$	13.2758	+	1.39535i	0.487700	+	0.0512593i
$742$	−9.24892	+	16.0196i	−0.339539	+	0.588098i
$743$	−5.63117	+	9.75347i	−0.206588	+	0.357820i	−0.950637	−	0.310304i	$-0.899569\pi$
$743$	−5.63117	+	9.75347i	−0.206588	+	0.357820i	0.744050	+	0.668124i	$0.232903\pi$
$744$	−3.50739	−	0.368642i	−0.128587	−	0.0135151i
$745$	4.81135	+	8.33351i	0.176274	+	0.305316i
$746$	25.5936			0.937049
$747$	5.74527	+	1.22120i	0.210209	+	0.0446812i
$748$	−0.185136			−0.00676926
$749$	−7.43881	−	12.8844i	−0.271808	−	0.470786i
$750$	1.36245	−	1.87525i	0.0497496	−	0.0684744i
$751$	23.4586	−	40.6315i	0.856016	−	1.48266i	−0.0196831	−	0.999806i	$-0.506266\pi$
$751$	23.4586	−	40.6315i	0.856016	−	1.48266i	0.875699	−	0.482857i	$-0.160401\pi$
$752$	21.5265	−	37.2850i	0.784990	−	1.35964i
$753$	−10.6832	−	23.9948i	−0.389316	−	0.874418i
$754$	5.87319	+	10.1727i	0.213889	+	0.370466i
$755$	7.24618			0.263716
$756$	−1.03312	−	0.335683i	−0.0375744	−	0.0122087i
$757$	28.9715			1.05299			0.526494	−	0.850179i	$-0.323506\pi$
$757$	28.9715			1.05299			0.526494	+	0.850179i	$0.323506\pi$
$758$	−2.35022	−	4.07070i	−0.0853639	−	0.147855i
$759$	−2.43057	−	5.45916i	−0.0882242	−	0.198155i
$760$	−6.38791	+	11.0642i	−0.231714	+	0.401340i
$761$	10.3462	−	17.9202i	0.375050	−	0.649606i	−0.615284	−	0.788305i	$-0.710959\pi$
$761$	10.3462	−	17.9202i	0.375050	−	0.649606i	0.990335	+	0.138699i	$0.0442921\pi$
$762$	14.9904	−	20.6325i	0.543046	−	0.747438i
$763$	−1.32864	−	2.30127i	−0.0480999	−	0.0833114i
$764$	3.89756			0.141009
$765$	1.24064	+	3.81829i	0.0448553	+	0.138050i
$766$	38.3518			1.38571
$767$	−4.90250	−	8.49138i	−0.177019	−	0.306606i
$768$	8.54500	+	0.898116i	0.308341	+	0.0324080i
$769$	7.93589	−	13.7454i	0.286175	−	0.495670i	−0.686718	−	0.726924i	$-0.740949\pi$
$769$	7.93589	−	13.7454i	0.286175	−	0.495670i	0.972894	+	0.231253i	$0.0742827\pi$
$770$	0.442790	−	0.766934i	0.0159570	−	0.0276384i
$771$	37.8367	+	3.97680i	1.36265	+	0.143221i
$772$	1.44821	+	2.50838i	0.0521223	+	0.0902784i
$773$	2.13874			0.0769251			0.0384626	−	0.999260i	$-0.487754\pi$
$773$	2.13874			0.0769251			0.0384626	+	0.999260i	$0.487754\pi$
$774$	−2.03390	−	6.25969i	−0.0731069	−	0.225000i
$775$	0.688750			0.0247406
$776$	24.6484	+	42.6923i	0.884827	+	1.53257i
$777$	6.65635	−	9.16168i	0.238795	−	0.328674i
$778$	4.82926	−	8.36453i	0.173137	−	0.299883i
$779$	−1.77084	+	3.06718i	−0.0634468	+	0.109893i
$780$	0.262654	+	0.589930i	0.00940452	+	0.0211229i
$781$	−1.91791	−	3.32192i	−0.0686284	−	0.118868i
$782$	9.33749			0.333908
$783$	5.31714	+	25.0152i	0.190019	+	0.893970i
$784$	−3.53818			−0.126364
$785$	−9.54870	−	16.5388i	−0.340808	−	0.590296i
$786$	−8.13912	−	18.2808i	−0.290313	−	0.652054i
$787$	11.1445	−	19.3029i	0.397259	−	0.688073i	−0.596128	−	0.802890i	$-0.703295\pi$
$787$	11.1445	−	19.3029i	0.397259	−	0.688073i	0.993387	+	0.114817i	$0.0366281\pi$
$788$	1.12119	−	1.94195i	0.0399407	−	0.0691792i
$789$	−32.6157	+	44.8917i	−1.16115	+	1.59819i
$790$	−7.74153	−	13.4087i	−0.275431	−	0.477061i
$791$	13.1594			0.467894
$792$	5.74064	+	1.22021i	0.203985	+	0.0433583i
$793$	−20.9447			−0.743769
$794$	13.2509	+	22.9512i	0.470256	+	0.814507i
$795$	23.8098	+	2.50251i	0.844445	+	0.0887548i
$796$	0.655362	−	1.13512i	0.0232287	−	0.0402333i
$797$	−10.3177	+	17.8707i	−0.365470	+	0.633013i	−0.988851	−	0.148905i	$-0.952425\pi$
$797$	−10.3177	+	17.8707i	−0.365470	+	0.633013i	0.623381	+	0.781918i	$0.285758\pi$
$798$	9.96224	+	1.04707i	0.352660	+	0.0370660i
$799$	−8.14206	−	14.1025i	−0.288045	−	0.498909i
$800$	−1.17758			−0.0416337
$801$	26.4184	−	29.3406i	0.933448	−	1.03670i
$802$	12.1500			0.429030
$803$	−0.0293118	−	0.0507695i	−0.00103439	−	0.00179161i
$804$	1.40855	−	1.93871i	0.0496758	−	0.0683729i
$805$	2.60686	−	4.51522i	0.0918799	−	0.159141i
$806$	0.821898	−	1.42357i	0.0289501	−	0.0501431i
$807$	3.23567	+	7.26743i	0.113901	+	0.255826i
$808$	1.92561	+	3.33525i	0.0677426	+	0.117334i
$809$	15.4866			0.544479			0.272240	−	0.962229i	$-0.412236\pi$
$809$	15.4866			0.544479			0.272240	+	0.962229i	$0.412236\pi$
$810$	−1.25898	−	11.9784i	−0.0442360	−	0.420877i
$811$	−2.30279			−0.0808617			−0.0404309	−	0.999182i	$-0.512873\pi$
$811$	−2.30279			−0.0808617			−0.0404309	+	0.999182i	$0.512873\pi$
$812$	−0.514461	−	0.891072i	−0.0180540	−	0.0312705i
$813$	11.4780	+	25.7800i	0.402550	+	0.904143i
$814$	−2.89504	+	5.01435i	−0.101471	+	0.175753i
$815$	−8.87626	+	15.3741i	−0.310922	+	0.538532i
$816$	−4.82059	+	6.63497i	−0.168754	+	0.232271i
$817$	−3.54238	−	6.13559i	−0.123932	−	0.214657i
$818$	−27.2209			−0.951756
$819$	3.57995	−	3.97594i	0.125094	−	0.138931i
$820$	−0.171329			−0.00598308
$821$	−0.147155	−	0.254880i	−0.00513574	−	0.00889536i	0.863446	−	0.504441i	$-0.168301\pi$
$821$	−0.147155	−	0.254880i	−0.00513574	−	0.00889536i	−0.868582	+	0.495546i	$0.834968\pi$
$822$	−30.2100	−	3.17520i	−1.05370	−	0.110748i
$823$	−24.5553	+	42.5310i	−0.855943	+	1.48254i	0.0198242	+	0.999803i	$0.493689\pi$
$823$	−24.5553	+	42.5310i	−0.855943	+	1.48254i	−0.875767	+	0.482733i	$0.839644\pi$
$824$	−22.7252	+	39.3611i	−0.791668	+	1.37121i
$825$	−1.13989	−	0.119807i	−0.0396858	−	0.00417114i
$826$	−3.67886	−	6.37197i	−0.128004	−	0.221709i
$827$	51.5805			1.79363			0.896815	−	0.442405i	$-0.145875\pi$
$827$	51.5805			1.79363			0.896815	+	0.442405i	$0.145875\pi$
$828$	3.19844	+	0.679850i	0.111154	+	0.0236264i
$829$	−39.4858			−1.37140			−0.685699	−	0.727885i	$-0.740503\pi$
$829$	−39.4858			−1.37140			−0.685699	+	0.727885i	$0.740503\pi$
$830$	−1.31007	−	2.26911i	−0.0454733	−	0.0787621i
$831$	−31.7273	+	43.6689i	−1.10061	+	1.51486i
$832$	−7.71517	+	13.3631i	−0.267475	+	0.463281i
$833$	−0.669131	+	1.15897i	−0.0231840	+	0.0401559i
$834$	−5.36570	−	12.0516i	−0.185799	−	0.417312i
$835$	−1.93822	−	3.35710i	−0.0670749	−	0.116177i
$836$	0.597850			0.0206771
$837$	2.65960	−	2.39472i	0.0919293	−	0.0827735i
$838$	−7.78261			−0.268846
$839$	−23.7956	−	41.2152i	−0.821516	−	1.42291i	−0.904553	−	0.426360i	$-0.859796\pi$
$839$	−23.7956	−	41.2152i	−0.821516	−	1.42291i	0.0830379	−	0.996546i	$-0.473538\pi$
$840$	2.08268	+	4.67777i	0.0718592	+	0.161398i
$841$	2.38830	−	4.13666i	0.0823552	−	0.142643i
$842$	−22.2918	+	38.6106i	−0.768227	+	1.33061i
$843$	19.8449	−	27.3141i	0.683494	−	0.940748i
$844$	1.07908	+	1.86903i	0.0371436	+	0.0643346i
$845$	9.81953			0.337802
$846$	15.0962	+	46.4613i	0.519018	+	1.59737i
$847$	10.5621			0.362918
$848$	24.4529	+	42.3537i	0.839716	+	1.45443i
$849$	52.1731	+	5.48361i	1.79057	+	0.188197i
$850$	0.895472	−	1.55100i	0.0307144	−	0.0531989i
$851$	−17.0441	+	29.5213i	−0.584266	+	1.01198i
$852$	2.08743	+	0.219398i	0.0715142	+	0.00751645i
$853$	11.5193	+	19.9520i	0.394414	+	0.683145i	0.993026	−	0.117894i	$-0.0376144\pi$
$853$	11.5193	+	19.9520i	0.394414	+	0.683145i	−0.598612	+	0.801039i	$0.704281\pi$
$854$	−15.7170			−0.537825
$855$	−4.00631	−	12.3302i	−0.137013	−	0.421683i
$856$	−43.9826			−1.50330
$857$	5.61860	+	9.73171i	0.191928	+	0.332429i	0.945889	−	0.324490i	$-0.105193\pi$
$857$	5.61860	+	9.73171i	0.191928	+	0.332429i	−0.753961	+	0.656919i	$0.771859\pi$
$858$	−1.60787	+	2.21305i	−0.0548919	+	0.0755523i
$859$	−1.46731	+	2.54145i	−0.0500639	+	0.0867132i	−0.889971	−	0.456016i	$-0.849276\pi$
$859$	−1.46731	+	2.54145i	−0.0500639	+	0.0867132i	0.839907	+	0.542730i	$0.182609\pi$
$860$	0.171364	−	0.296811i	0.00584346	−	0.0101212i
$861$	0.577352	+	1.29675i	0.0196761	+	0.0441933i
$862$	−22.1906	−	38.4352i	−0.755814	−	1.30911i
$863$	−36.2827			−1.23508			−0.617539	−	0.786540i	$-0.711870\pi$
$863$	−36.2827			−1.23508			−0.617539	+	0.786540i	$0.711870\pi$
$864$	−4.54722	+	4.09433i	−0.154699	+	0.139292i
$865$	14.4712			0.492036
$866$	22.2767	+	38.5844i	0.756993	+	1.31115i
$867$	−10.7146	−	24.0654i	−0.363887	−	0.817304i
$868$	−0.0719940	+	0.124697i	−0.00244363	+	0.00423250i
$869$	−3.82800	+	6.63030i	−0.129856	+	0.224917i
$870$	6.70560	−	9.22947i	0.227341	−	0.312908i
$871$	5.90125	+	10.2213i	0.199956	+	0.346335i
$872$	−7.85568			−0.266027
$873$	−48.9325	−	10.4009i	−1.65611	−	0.352018i
$874$	−30.1530			−1.01994
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$	0.0319025	+	0.00335309i	0.00107789	+	0.000113290i
$877$	−18.1302	+	31.4024i	−0.612213	+	1.06038i	0.378654	+	0.925538i	$0.376387\pi$
$877$	−18.1302	+	31.4024i	−0.612213	+	1.06038i	−0.990867	+	0.134846i	$0.956946\pi$
$878$	−17.5482	+	30.3943i	−0.592222	+	1.02576i
$879$	42.5893	+	4.47631i	1.43650	+	0.150982i
$880$	−1.17068	−	2.02767i	−0.0394635	−	0.0683527i
$881$	50.7854			1.71101			0.855503	−	0.517799i	$-0.173248\pi$
$881$	50.7854			1.71101			0.855503	+	0.517799i	$0.173248\pi$
$882$	2.68641	−	2.98357i	0.0904563	−	0.100462i
$883$	14.4337			0.485734			0.242867	−	0.970060i	$-0.421912\pi$
$883$	14.4337			0.485734			0.242867	+	0.970060i	$0.421912\pi$
$884$	0.249471	+	0.432097i	0.00839063	+	0.0145330i
$885$	−5.59734	+	7.70407i	−0.188152	+	0.258970i
$886$	10.5222	−	18.2249i	0.353499	−	0.612279i
$887$	8.66324	−	15.0052i	0.290883	−	0.503824i	−0.683136	−	0.730292i	$-0.739384\pi$
$887$	8.66324	−	15.0052i	0.290883	−	0.503824i	0.974019	+	0.226467i	$0.0727176\pi$
$888$	−13.6169	−	30.5841i	−0.456954	−	1.02633i
$889$	−5.50128	−	9.52849i	−0.184507	−	0.319575i
$890$	−17.6123			−0.590364
$891$	−4.81822	+	3.50064i	−0.161416	+	0.117276i
$892$	−1.01445			−0.0339664
$893$	26.2927	+	45.5402i	0.879850	+	1.52395i
$894$	−9.07219	−	20.3765i	−0.303419	−	0.681491i
$895$	2.57624	−	4.46218i	0.0861142	−	0.149154i
$896$	−4.61192	+	7.98808i	−0.154073	+	0.266863i
$897$	−9.46614	+	13.0290i	−0.316065	+	0.435027i
$898$	25.8228	+	44.7264i	0.861717	+	1.49254i
$899$	3.38984			0.113057
$900$	0.419659	−	0.466079i	0.0139886	−	0.0155360i
$901$	18.4978			0.616252
$902$	−0.362881	−	0.628529i	−0.0120826	−	0.0209277i
$903$	−2.82397	−	0.296811i	−0.0939757	−	0.00987724i
$904$	19.4515	−	33.6910i	0.646947	−	1.12055i
$905$	−10.4126	+	18.0351i	−0.346126	+	0.599508i
$906$	−16.7042	−	1.75568i	−0.554959	−	0.0583285i
$907$	−22.3839	−	38.7700i	−0.743245	−	1.28734i	−0.951010	−	0.309159i	$-0.899952\pi$
$907$	−22.3839	−	38.7700i	−0.743245	−	1.28734i	0.207766	−	0.978179i	$-0.433381\pi$
$908$	2.04285			0.0677945
$909$	−3.82275	−	0.812550i	−0.126793	−	0.0269506i
$910$	−2.38664			−0.0791162
$911$	−21.8640	−	37.8695i	−0.724385	−	1.25467i	−0.959226	−	0.282639i	$-0.908790\pi$
$911$	−21.8640	−	37.8695i	−0.724385	−	1.25467i	0.234841	−	0.972034i	$-0.424543\pi$
$912$	15.5668	−	21.4259i	0.515470	−	0.709483i
$913$	−0.647801	+	1.12202i	−0.0214391	+	0.0371336i
$914$	−27.7313	+	48.0320i	−0.917269	+	1.58876i
$915$	8.27376	+	18.5832i	0.273522	+	0.614341i
$916$	1.68798	+	2.92367i	0.0557725	+	0.0966008i
$917$	−8.63302			−0.285087
$918$	−1.93483	−	9.10265i	−0.0638589	−	0.300432i
$919$	23.3354			0.769764			0.384882	−	0.922966i	$-0.374242\pi$
$919$	23.3354			0.769764			0.384882	+	0.922966i	$0.374242\pi$
$920$	−7.70666	−	13.3483i	−0.254081	−	0.440081i
$921$	7.13536	+	16.0263i	0.235118	+	0.528084i
$922$	−13.1259	+	22.7347i	−0.432278	+	0.748727i
$923$	−5.16878	+	8.95259i	−0.170132	+	0.294678i
$924$	0.140841	−	0.193852i	0.00463334	−	0.00637725i
$925$	3.26909	+	5.66223i	0.107487	+	0.186173i
$926$	−8.14660			−0.267714
$927$	−14.2526	−	43.8649i	−0.468115	−	1.44071i
$928$	−5.79573			−0.190254
$929$	−17.8371	−	30.8947i	−0.585215	−	1.01362i	−0.994849	−	0.101372i	$-0.967677\pi$
$929$	−17.8371	−	30.8947i	−0.585215	−	1.01362i	0.409634	−	0.912250i	$-0.365656\pi$
$930$	−1.58773	−	0.166877i	−0.0520638	−	0.00547213i
$931$	2.16078	−	3.74259i	0.0708168	−	0.122658i
$932$	0.602516	−	1.04359i	0.0197361	−	0.0341839i
$933$	−22.9842	−	2.41573i	−0.752467	−	0.0790875i
$934$	−14.0215	−	24.2859i	−0.458797	−	0.794660i
$935$	−0.885579			−0.0289615
$936$	−4.88761	−	15.0425i	−0.159757	−	0.491680i
$937$	−53.4359			−1.74567			−0.872837	−	0.488011i	$-0.837723\pi$
$937$	−53.4359			−1.74567			−0.872837	+	0.488011i	$0.837723\pi$
$938$	4.42833	+	7.67009i	0.144590	+	0.250437i
$939$	16.7523	−	23.0576i	0.546691	−	0.752456i
$940$	−1.27191	+	2.20302i	−0.0414853	+	0.0718546i
$941$	10.0914	−	17.4789i	0.328971	−	0.569795i	−0.653337	−	0.757067i	$-0.726631\pi$
$941$	10.0914	−	17.4789i	0.328971	−	0.569795i	0.982308	+	0.187273i	$0.0599648\pi$
$942$	18.0048	+	40.4395i	0.586629	+	1.31759i
$943$	−2.13641	−	3.70038i	−0.0695712	−	0.120501i
$944$	−19.4528			−0.633135
$945$	−4.94183	−	1.60570i	−0.160758	−	0.0522334i
$946$	1.45182			0.0472026
$947$	16.6730	+	28.8786i	0.541801	+	0.938427i	0.998801	+	0.0489603i	$0.0155908\pi$
$947$	16.6730	+	28.8786i	0.541801	+	0.938427i	−0.457000	+	0.889467i	$0.651076\pi$
$948$	−1.70394	−	3.82711i	−0.0553414	−	0.124299i
$949$	−0.0789952	+	0.136824i	−0.00256429	+	0.00444148i
$950$	−2.89169	+	5.00856i	−0.0938189	+	0.162499i
$951$	−17.9429	+	24.6962i	−0.581837	+	0.800830i
$952$	1.97815	+	3.42625i	0.0641121	+	0.111045i
$953$	−29.0960			−0.942513			−0.471257	−	0.881996i	$-0.656199\pi$
$953$	−29.0960			−0.942513			−0.471257	+	0.881996i	$0.656199\pi$
$954$	−54.2809	−	11.5378i	−1.75741	−	0.373549i
$955$	18.6435			0.603291
$956$	0.0126525	+	0.0219148i	0.000409212	+	0.000708776i
$957$	−5.61021	−	0.589657i	−0.181352	−	0.0190609i
$958$	17.2521	−	29.8816i	0.557392	−	0.965431i
$959$	−6.55248	+	11.3492i	−0.211591	+	0.366486i
$960$	14.9041	+	1.56648i	0.481027	+	0.0505580i
$961$	15.2628	+	26.4360i	0.492349	+	0.852773i
$962$	15.6043			0.503102
$963$	29.8652	−	33.1687i	0.962393	−	1.06885i
$964$	−4.38217			−0.141140
$965$	6.92735	+	11.9985i	0.222999	+	0.386246i
$966$	−7.10344	+	9.77704i	−0.228549	+	0.314571i
$967$	18.0186	−	31.2091i	0.579439	−	1.00362i	−0.416105	−	0.909317i	$-0.636605\pi$
$967$	18.0186	−	31.2091i	0.579439	−	1.00362i	0.995544	−	0.0943013i	$-0.0300617\pi$
$968$	15.6123	−	27.0414i	0.501800	−	0.869143i
$969$	−4.07433	−	9.15109i	−0.130886	−	0.293975i
$970$	11.1579	+	19.3260i	0.358258	+	0.620522i
$971$	4.97188			0.159555			0.0797776	−	0.996813i	$-0.474579\pi$
$971$	4.97188			0.159555			0.0797776	+	0.996813i	$0.474579\pi$
$972$		−	3.25887i		−	0.104528i
$973$	−5.69131			−0.182455
$974$	18.1390	+	31.4177i	0.581211	+	1.00669i
$975$	1.25638	+	2.82186i	0.0402362	+	0.0903720i
$976$	−20.7768	+	35.9865i	−0.665050	+	1.15190i
$977$	−3.27500	+	5.67247i	−0.104777	+	0.181479i	−0.913647	−	0.406509i	$-0.866746\pi$
$977$	−3.27500	+	5.67247i	−0.104777	+	0.181479i	0.808870	+	0.587987i	$0.200079\pi$
$978$	24.1869	−	33.2904i	0.773411	−	1.06451i
$979$	4.35443	+	7.54209i	0.139168	+	0.241046i
$980$	0.209057			0.00667808
$981$	5.33419	−	5.92421i	0.170307	−	0.189146i
$982$	−30.1124			−0.960927
$983$	−28.5941	−	49.5264i	−0.912010	−	1.57965i	−0.811221	−	0.584739i	$-0.801197\pi$
$983$	−28.5941	−	49.5264i	−0.912010	−	1.57965i	−0.100788	−	0.994908i	$-0.532136\pi$
$984$	4.17340	+	0.438642i	0.133043	+	0.0139834i
$985$	5.36307	−	9.28912i	0.170882	−	0.295976i
$986$	4.40727	−	7.63361i	0.140356	−	0.243104i
$987$	20.9603	+	2.20302i	0.667175	+	0.0701229i
$988$	−0.805603	−	1.39535i	−0.0256297	−	0.0443919i
$989$	8.54738			0.271791
$990$	2.59868	+	0.552367i	0.0825915	+	0.0175554i
$991$	24.1639			0.767591			0.383796	−	0.923418i	$-0.374617\pi$
$991$	24.1639			0.767591			0.383796	+	0.923418i	$0.374617\pi$
$992$	0.405529	+	0.702397i	0.0128756	+	0.0223011i
$993$	11.2819	−	15.5282i	0.358021	−	0.492774i
$994$	−3.87868	+	6.71806i	−0.123024	+	0.213084i
$995$	3.13485	−	5.42972i	0.0993815	−	0.172134i
$996$	−0.288352	−	0.647650i	−0.00913679	−	0.0205216i
$997$	3.04761	+	5.27861i	0.0965187	+	0.167175i	0.910241	−	0.414078i	$-0.135896\pi$
$997$	3.04761	+	5.27861i	0.0965187	+	0.167175i	−0.813723	+	0.581253i	$0.802563\pi$
$998$	−8.43571			−0.267028
$999$	32.3106	+	10.4984i	1.02226	+	0.332153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.i.d.211.3	yes	8
3.2	odd	2		945.2.i.c.631.2		8
9.2	odd	6		945.2.i.c.316.2		8
9.4	even	3		2835.2.a.l.1.2		4
9.5	odd	6		2835.2.a.q.1.3		4
9.7	even	3	inner	315.2.i.d.106.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.d.106.3	✓	8	9.7	even	3	inner
315.2.i.d.211.3	yes	8	1.1	even	1	trivial
945.2.i.c.316.2		8	9.2	odd	6
945.2.i.c.631.2		8	3.2	odd	2
2835.2.a.l.1.2		4	9.4	even	3
2835.2.a.q.1.3		4	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.669131 + 1.15897i) q^{2} +(0.704489 + 1.58231i) q^{3} +(0.104528 - 0.181049i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.36245 + 1.87525i) q^{6} +(0.500000 + 0.866025i) q^{7} +2.95630 q^{8} +(-2.00739 + 2.22943i) q^{9} +O(q^{10})\)	\(q+(0.669131 + 1.15897i) q^{2} +(0.704489 + 1.58231i) q^{3} +(0.104528 - 0.181049i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.36245 + 1.87525i) q^{6} +(0.500000 + 0.866025i) q^{7} +2.95630 q^{8} +(-2.00739 + 2.22943i) q^{9} +1.33826 q^{10} +(-0.330869 - 0.573083i) q^{11} +(0.360114 + 0.0378495i) q^{12} +(-0.891693 + 1.54446i) q^{13} +(-0.669131 + 1.15897i) q^{14} +(1.72256 + 0.181049i) q^{15} +(1.76909 + 3.06415i) q^{16} +1.33826 q^{17} +(-3.92705 - 0.834720i) q^{18} -4.32157 q^{19} +(-0.104528 - 0.181049i) q^{20} +(-1.01807 + 1.40126i) q^{21} +(0.442790 - 0.766934i) q^{22} +(2.60686 - 4.51522i) q^{23} +(2.08268 + 4.67777i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.38664 q^{26} +(-4.94183 - 1.60570i) q^{27} +0.209057 q^{28} +(-2.46086 - 4.26234i) q^{29} +(0.942790 + 2.11754i) q^{30} +(-0.344375 + 0.596475i) q^{31} +(0.588790 - 1.01981i) q^{32} +(0.673699 - 0.927267i) q^{33} +(0.895472 + 1.55100i) q^{34} +1.00000 q^{35} +(0.193806 + 0.596475i) q^{36} -6.53818 q^{37} +(-2.89169 - 5.00856i) q^{38} +(-3.07199 - 0.322880i) q^{39} +(1.47815 - 2.56023i) q^{40} +(0.409767 - 0.709737i) q^{41} +(-2.30524 - 0.242290i) q^{42} +(0.819699 + 1.41976i) q^{43} -0.138341 q^{44} +(0.927051 + 2.85317i) q^{45} +6.97733 q^{46} +(-6.08406 - 10.5379i) q^{47} +(-3.60213 + 4.95791i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.669131 - 1.15897i) q^{50} +(0.942790 + 2.11754i) q^{51} +(0.186415 + 0.322880i) q^{52} +13.8223 q^{53} +(-1.44578 - 6.80185i) q^{54} -0.661739 q^{55} +(1.47815 + 2.56023i) q^{56} +(-3.04449 - 6.83805i) q^{57} +(3.29328 - 5.70413i) q^{58} +(-2.74898 + 4.76138i) q^{59} +(0.212835 - 0.292943i) q^{60} +(5.87218 + 10.1709i) q^{61} -0.921727 q^{62} +(-2.93444 - 0.623735i) q^{63} +8.65227 q^{64} +(0.891693 + 1.54446i) q^{65} +(1.52547 + 0.160333i) q^{66} +(3.30902 - 5.73139i) q^{67} +(0.139886 - 0.242290i) q^{68} +(8.98097 + 0.943938i) q^{69} +(0.669131 + 1.15897i) q^{70} +5.79659 q^{71} +(-5.93444 + 6.59087i) q^{72} +0.0885901 q^{73} +(-4.37490 - 7.57754i) q^{74} +(1.01807 - 1.40126i) q^{75} +(-0.451727 + 0.782414i) q^{76} +(0.330869 - 0.573083i) q^{77} +(-1.68136 - 3.77639i) q^{78} +(-5.78477 - 10.0195i) q^{79} +3.53818 q^{80} +(-0.940756 - 8.95070i) q^{81} +1.09675 q^{82} +(-0.978938 - 1.69557i) q^{83} +(0.147278 + 0.330792i) q^{84} +(0.669131 - 1.15897i) q^{85} +(-1.09697 + 1.90001i) q^{86} +(5.01068 - 6.89661i) q^{87} +(-0.978148 - 1.69420i) q^{88} -13.1606 q^{89} +(-2.68641 + 2.98357i) q^{90} -1.78339 q^{91} +(-0.544983 - 0.943938i) q^{92} +(-1.18641 - 0.124697i) q^{93} +(8.14206 - 14.1025i) q^{94} +(-2.16078 + 3.74259i) q^{95} +(2.02845 + 0.213199i) q^{96} +(8.33761 + 14.4412i) q^{97} -1.33826 q^{98} +(1.94183 + 0.412750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9	\( 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9} + 2 q^{10} - 7 q^{11} + 3 q^{12} + 8 q^{13} - q^{14} + 3 q^{15} + 9 q^{16} + 2 q^{17} - 18 q^{18} + 6 q^{19} + q^{20} - 7 q^{22} + 8 q^{23} + 6 q^{24} - 4 q^{25} - 6 q^{26} - 2 q^{28} - q^{29} - 3 q^{30} + 9 q^{34} + 8 q^{35} - 6 q^{36} - 42 q^{37} - 8 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} + 3 q^{42} + 7 q^{43} + 6 q^{44} - 6 q^{45} - 46 q^{46} + 2 q^{47} + 30 q^{48} - 4 q^{49} + q^{50} - 3 q^{51} + 7 q^{52} - 16 q^{53} - 36 q^{54} - 14 q^{55} + 3 q^{56} - 24 q^{57} + 19 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 30 q^{62} + 3 q^{63} - 14 q^{64} - 8 q^{65} - 9 q^{66} + 22 q^{67} + q^{68} + 51 q^{69} + q^{70} + 26 q^{71} - 21 q^{72} - 8 q^{73} - 9 q^{74} + 13 q^{76} + 7 q^{77} - 21 q^{78} + 24 q^{79} + 18 q^{80} + 9 q^{81} + 19 q^{83} - 12 q^{84} + q^{85} + 27 q^{86} + 45 q^{87} + q^{88} + 30 q^{89} - 27 q^{90} + 16 q^{91} - 3 q^{92} - 15 q^{93} + 7 q^{94} + 3 q^{95} + 30 q^{96} + 12 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9 + 2 * q^10 - 7 * q^11 + 3 * q^12 + 8 * q^13 - q^14 + 3 * q^15 + 9 * q^16 + 2 * q^17 - 18 * q^18 + 6 * q^19 + q^20 - 7 * q^22 + 8 * q^23 + 6 * q^24 - 4 * q^25 - 6 * q^26 - 2 * q^28 - q^29 - 3 * q^30 + 9 * q^34 + 8 * q^35 - 6 * q^36 - 42 * q^37 - 8 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 + 3 * q^42 + 7 * q^43 + 6 * q^44 - 6 * q^45 - 46 * q^46 + 2 * q^47 + 30 * q^48 - 4 * q^49 + q^50 - 3 * q^51 + 7 * q^52 - 16 * q^53 - 36 * q^54 - 14 * q^55 + 3 * q^56 - 24 * q^57 + 19 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 30 * q^62 + 3 * q^63 - 14 * q^64 - 8 * q^65 - 9 * q^66 + 22 * q^67 + q^68 + 51 * q^69 + q^70 + 26 * q^71 - 21 * q^72 - 8 * q^73 - 9 * q^74 + 13 * q^76 + 7 * q^77 - 21 * q^78 + 24 * q^79 + 18 * q^80 + 9 * q^81 + 19 * q^83 - 12 * q^84 + q^85 + 27 * q^86 + 45 * q^87 + q^88 + 30 * q^89 - 27 * q^90 + 16 * q^91 - 3 * q^92 - 15 * q^93 + 7 * q^94 + 3 * q^95 + 30 * q^96 + 12 * q^97 - 2 * q^98 - 24 * q^99

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