LMFDB - Embedded newform 315.2.bl.i.41.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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([5, 0, 3]))

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

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

chi := DirichletCharacter("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (of order $6$, 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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.10
Character	$\chi$	$=$	315.41
Dual form			315.2.bl.i.146.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.94805 - 1.12471i) q^{2} +(-0.913713 - 1.47144i) q^{3} +(1.52994 - 2.64993i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-3.43490 - 1.83878i) q^{6} +(-2.43271 - 1.04016i) q^{7} -2.38412i q^{8} +(-1.33026 + 2.68894i) q^{9} +O(q^{10})$	\(q+(1.94805 - 1.12471i) q^{2} +(-0.913713 - 1.47144i) q^{3} +(1.52994 - 2.64993i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-3.43490 - 1.83878i) q^{6} +(-2.43271 - 1.04016i) q^{7} -2.38412i q^{8} +(-1.33026 + 2.68894i) q^{9} -2.24942i q^{10} +(2.13353 - 1.23180i) q^{11} +(-5.29714 + 0.170069i) q^{12} +(0.336443 + 0.194245i) q^{13} +(-5.90892 + 0.709797i) q^{14} +(-1.73116 + 0.0555801i) q^{15} +(0.378445 + 0.655486i) q^{16} +4.81075 q^{17} +(0.432869 + 6.73436i) q^{18} -1.11761i q^{19} +(-1.52994 - 2.64993i) q^{20} +(0.692264 + 4.52999i) q^{21} +(2.77082 - 4.79920i) q^{22} +(-1.85078 - 1.06855i) q^{23} +(-3.50808 + 2.17840i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.873878 q^{26} +(5.17209 - 0.499535i) q^{27} +(-6.47826 + 4.85513i) q^{28} +(-4.02738 + 2.32521i) q^{29} +(-3.30988 + 2.05532i) q^{30} +(5.61553 + 3.24213i) q^{31} +(5.60387 + 3.23540i) q^{32} +(-3.76195 - 2.01385i) q^{33} +(9.37160 - 5.41070i) q^{34} +(-2.11716 + 1.58671i) q^{35} +(5.09031 + 7.63902i) q^{36} +4.29543 q^{37} +(-1.25698 - 2.17716i) q^{38} +(-0.0215924 - 0.672539i) q^{39} +(-2.06470 - 1.19206i) q^{40} +(-0.476591 + 0.825479i) q^{41} +(6.44348 + 8.04606i) q^{42} +(-5.21348 - 9.03002i) q^{43} -7.53829i q^{44} +(1.66357 + 2.49651i) q^{45} -4.80723 q^{46} +(-2.81296 - 4.87220i) q^{47} +(0.618716 - 1.15578i) q^{48} +(4.83613 + 5.06082i) q^{49} +(-1.94805 - 1.12471i) q^{50} +(-4.39565 - 7.07872i) q^{51} +(1.02947 - 0.594368i) q^{52} +9.72792i q^{53} +(9.51367 - 6.79021i) q^{54} -2.46359i q^{55} +(-2.47987 + 5.79985i) q^{56} +(-1.64449 + 1.02117i) q^{57} +(-5.23036 + 9.05925i) q^{58} +(-6.18688 + 10.7160i) q^{59} +(-2.50129 + 4.67249i) q^{60} +(0.631916 - 0.364837i) q^{61} +14.5858 q^{62} +(6.03306 - 5.15773i) q^{63} +13.0417 q^{64} +(0.336443 - 0.194245i) q^{65} +(-9.59347 + 0.308005i) q^{66} +(5.73742 - 9.93750i) q^{67} +(7.36016 - 12.7482i) q^{68} +(0.118780 + 3.69966i) q^{69} +(-2.33976 + 5.47217i) q^{70} +15.1436i q^{71} +(6.41075 + 3.17148i) q^{72} +10.5746i q^{73} +(8.36772 - 4.83111i) q^{74} +(-0.817446 + 1.52702i) q^{75} +(-2.96158 - 1.70987i) q^{76} +(-6.47152 + 0.777379i) q^{77} +(-0.798474 - 1.28586i) q^{78} +(7.35947 + 12.7470i) q^{79} +0.756890 q^{80} +(-5.46084 - 7.15397i) q^{81} +2.14410i q^{82} +(-5.97335 - 10.3461i) q^{83} +(13.0633 + 5.09616i) q^{84} +(2.40538 - 4.16623i) q^{85} +(-20.3123 - 11.7273i) q^{86} +(7.10126 + 3.80146i) q^{87} +(-2.93674 - 5.08659i) q^{88} -14.2521 q^{89} +(6.04856 + 2.99230i) q^{90} +(-0.616420 - 0.822497i) q^{91} +(-5.66317 + 3.26963i) q^{92} +(-0.360396 - 11.2253i) q^{93} +(-10.9596 - 6.32753i) q^{94} +(-0.967875 - 0.558803i) q^{95} +(-0.359648 - 11.2020i) q^{96} +(-3.46717 + 2.00177i) q^{97} +(15.1130 + 4.41951i) q^{98} +(0.474084 + 7.37555i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9	$ 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 q^{21} - 9 q^{22} + 9 q^{23} + 7 q^{24} - 12 q^{25} + 18 q^{26} + 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} + 42 q^{31} + 18 q^{32} - 13 q^{33} + 39 q^{34} + 9 q^{35} - 21 q^{36} + 12 q^{38} - 21 q^{39} + 6 q^{40} + 33 q^{41} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 q^{84} - 9 q^{85} - 102 q^{86} - 10 q^{87} - 9 q^{88} - 102 q^{89} + 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} + 156 q^{94} - 18 q^{95} + 42 q^{96} + 45 q^{97} - 3 q^{98} + 23 q^{99}+O(q^{100}) $ 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9 + 9 * q^11 + 18 * q^12 - 3 * q^13 + 9 * q^14 + 2 * q^15 - 18 * q^16 - 18 * q^17 + 2 * q^18 - 18 * q^20 + 4 * q^21 - 9 * q^22 + 9 * q^23 + 7 * q^24 - 12 * q^25 + 18 * q^26 + 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 + 42 * q^31 + 18 * q^32 - 13 * q^33 + 39 * q^34 + 9 * q^35 - 21 * q^36 + 12 * q^38 - 21 * q^39 + 6 * q^40 + 33 * q^41 + 26 * q^42 + 18 * q^43 - q^45 - 30 * q^46 + 17 * q^48 - 6 * q^50 - 12 * q^51 - 129 * q^52 - 52 * q^54 + 6 * q^56 + 6 * q^57 - 15 * q^58 - 12 * q^59 + 15 * q^60 + 15 * q^61 - 12 * q^62 - 83 * q^63 - 60 * q^64 - 3 * q^65 - 29 * q^66 - 15 * q^67 - 9 * q^68 - 61 * q^69 + 18 * q^70 + 61 * q^72 - 18 * q^74 + 7 * q^75 - 54 * q^76 - 57 * q^77 - 66 * q^78 + 21 * q^79 - 36 * q^80 + q^81 + 30 * q^83 - 42 * q^84 - 9 * q^85 - 102 * q^86 - 10 * q^87 - 9 * q^88 - 102 * q^89 + 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 + 156 * q^94 - 18 * q^95 + 42 * q^96 + 45 * q^97 - 3 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.94805	−	1.12471i	1.37748	−	0.795289i	0.385626	−	0.922655i	$-0.373986\pi$
$2$	1.94805	−	1.12471i	1.37748	−	0.795289i	0.991856	+	0.127366i	$0.0406523\pi$
$3$	−0.913713	−	1.47144i	−0.527533	−	0.849535i
$3$	−0.913713	−	1.47144i	−0.527533	−	0.849535i
$4$	1.52994	−	2.64993i	0.764970	−	1.32497i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−3.43490	−	1.83878i	−1.40229	−	0.750677i
$7$	−2.43271	−	1.04016i	−0.919477	−	0.393144i
$7$	−2.43271	−	1.04016i	−0.919477	−	0.393144i
$8$		−	2.38412i		−	0.842912i
$9$	−1.33026	+	2.68894i	−0.443419	+	0.896315i
$10$		−	2.24942i		−	0.711328i
$11$	2.13353	−	1.23180i	0.643284	−	0.371400i	−0.142594	−	0.989781i	$-0.545544\pi$
$11$	2.13353	−	1.23180i	0.643284	−	0.371400i	0.785878	+	0.618381i	$0.212211\pi$
$12$	−5.29714	+	0.170069i	−1.52915	+	0.0490946i
$13$	0.336443	+	0.194245i	0.0933124	+	0.0538740i	0.545930	−	0.837831i	$-0.316176\pi$
$13$	0.336443	+	0.194245i	0.0933124	+	0.0538740i	−0.452618	+	0.891705i	$0.649510\pi$
$14$	−5.90892	+	0.709797i	−1.57923	+	0.189701i
$15$	−1.73116	+	0.0555801i	−0.446983	+	0.0143507i
$16$	0.378445	+	0.655486i	0.0946113	+	0.163872i
$17$	4.81075			1.16678			0.583389	−	0.812193i	$-0.301726\pi$
$17$	4.81075			1.16678			0.583389	+	0.812193i	$0.301726\pi$
$18$	0.432869	+	6.73436i	0.102028	+	1.58730i
$19$		−	1.11761i		−	0.256396i	−0.991749	−	0.128198i	$-0.959081\pi$
$19$		−	1.11761i		−	0.256396i	0.991749	−	0.128198i	$-0.0409194\pi$
$20$	−1.52994	−	2.64993i	−0.342105	−	0.592543i
$21$	0.692264	+	4.52999i	0.151064	+	0.988524i
$22$	2.77082	−	4.79920i	0.590741	−	1.02319i
$23$	−1.85078	−	1.06855i	−0.385915	−	0.222808i	0.294474	−	0.955660i	$-0.404856\pi$
$23$	−1.85078	−	1.06855i	−0.385915	−	0.222808i	−0.680388	+	0.732852i	$0.738189\pi$
$24$	−3.50808	+	2.17840i	−0.716083	+	0.444664i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.873878			0.171382
$27$	5.17209	−	0.499535i	0.995368	−	0.0961355i
$28$	−6.47826	+	4.85513i	−1.22428	+	0.917533i
$29$	−4.02738	+	2.32521i	−0.747865	+	0.431780i	−0.824922	−	0.565247i	$-0.808781\pi$
$29$	−4.02738	+	2.32521i	−0.747865	+	0.431780i	0.0770570	+	0.997027i	$0.475448\pi$
$30$	−3.30988	+	2.05532i	−0.604298	+	0.375249i
$31$	5.61553	+	3.24213i	1.00858	+	0.582303i	0.910775	−	0.412902i	$-0.135485\pi$
$31$	5.61553	+	3.24213i	1.00858	+	0.582303i	0.0978037	+	0.995206i	$0.468818\pi$
$32$	5.60387	+	3.23540i	0.990634	+	0.571943i
$33$	−3.76195	−	2.01385i	−0.654871	−	0.350566i
$34$	9.37160	−	5.41070i	1.60722	−	0.927927i
$35$	−2.11716	+	1.58671i	−0.357865	+	0.268202i
$36$	5.09031	+	7.63902i	0.848385	+	1.27317i
$37$	4.29543			0.706164			0.353082	−	0.935592i	$-0.385134\pi$
$37$	4.29543			0.706164			0.353082	+	0.935592i	$0.385134\pi$
$38$	−1.25698	−	2.17716i	−0.203909	−	0.353181i
$39$	−0.0215924	−	0.672539i	−0.00345755	−	0.107692i
$40$	−2.06470	−	1.19206i	−0.326458	−	0.188481i
$41$	−0.476591	+	0.825479i	−0.0744310	+	0.128918i	−0.900839	−	0.434154i	$-0.857047\pi$
$41$	−0.476591	+	0.825479i	−0.0744310	+	0.128918i	0.826408	+	0.563072i	$0.190381\pi$
$42$	6.44348	+	8.04606i	0.994251	+	1.24153i
$43$	−5.21348	−	9.03002i	−0.795049	−	1.37706i	−0.922808	−	0.385259i	$-0.874112\pi$
$43$	−5.21348	−	9.03002i	−0.795049	−	1.37706i	0.127760	−	0.991805i	$-0.459221\pi$
$44$		−	7.53829i		−	1.13644i
$45$	1.66357	+	2.49651i	0.247990	+	0.372157i
$46$	−4.80723			−0.708787
$47$	−2.81296	−	4.87220i	−0.410313	−	0.710683i	0.584611	−	0.811314i	$-0.301247\pi$
$47$	−2.81296	−	4.87220i	−0.410313	−	0.710683i	−0.994924	+	0.100631i	$0.967914\pi$
$48$	0.618716	−	1.15578i	0.0893040	−	0.166823i
$49$	4.83613	+	5.06082i	0.690875	+	0.722974i
$50$	−1.94805	−	1.12471i	−0.275496	−	0.159058i
$51$	−4.39565	−	7.07872i	−0.615514	−	0.991219i
$52$	1.02947	−	0.594368i	0.142762	−	0.0824239i
$53$			9.72792i			1.33623i	0.744057	+	0.668117i	$0.232899\pi$
$53$			9.72792i			1.33623i	−0.744057	+	0.668117i	$0.767101\pi$
$54$	9.51367	−	6.79021i	1.29465	−	0.924031i
$55$		−	2.46359i		−	0.332190i
$56$	−2.47987	+	5.79985i	−0.331386	+	0.775038i
$57$	−1.64449	+	1.02117i	−0.217818	+	0.135257i
$58$	−5.23036	+	9.05925i	−0.686780	+	1.18954i
$59$	−6.18688	+	10.7160i	−0.805463	+	1.39510i	0.110515	+	0.993875i	$0.464750\pi$
$59$	−6.18688	+	10.7160i	−0.805463	+	1.39510i	−0.915978	+	0.401229i	$0.868583\pi$
$60$	−2.50129	+	4.67249i	−0.322915	+	0.603216i
$61$	0.631916	−	0.364837i	0.0809085	−	0.0467125i	−0.459000	−	0.888436i	$-0.651792\pi$
$61$	0.631916	−	0.364837i	0.0809085	−	0.0467125i	0.539908	+	0.841724i	$0.318459\pi$
$62$	14.5858			1.85240
$63$	6.03306	−	5.15773i	0.760094	−	0.649813i
$64$	13.0417			1.63022
$65$	0.336443	−	0.194245i	0.0417306	−	0.0240932i
$66$	−9.59347	+	0.308005i	−1.18087	+	0.0379128i
$67$	5.73742	−	9.93750i	0.700937	−	1.21406i	−0.267201	−	0.963641i	$-0.586099\pi$
$67$	5.73742	−	9.93750i	0.700937	−	1.21406i	0.968138	−	0.250418i	$-0.0805679\pi$
$68$	7.36016	−	12.7482i	0.892551	−	1.54594i
$69$	0.118780	+	3.69966i	0.0142995	+	0.445386i
$70$	−2.33976	+	5.47217i	−0.279655	+	0.654050i
$71$			15.1436i			1.79721i	0.438754	+	0.898607i	$0.355420\pi$
$71$			15.1436i			1.79721i	−0.438754	+	0.898607i	$0.644580\pi$
$72$	6.41075	+	3.17148i	0.755514	+	0.373763i
$73$			10.5746i			1.23766i	0.785524	+	0.618831i	$0.212393\pi$
$73$			10.5746i			1.23766i	−0.785524	+	0.618831i	$0.787607\pi$
$74$	8.36772	−	4.83111i	0.972728	−	0.561605i
$75$	−0.817446	+	1.52702i	−0.0943905	+	0.176325i
$76$	−2.96158	−	1.70987i	−0.339717	−	0.196136i
$77$	−6.47152	+	0.777379i	−0.737499	+	0.0885905i
$78$	−0.798474	−	1.28586i	−0.0904093	−	0.145595i
$79$	7.35947	+	12.7470i	0.828005	+	1.43415i	0.899601	+	0.436713i	$0.143857\pi$
$79$	7.35947	+	12.7470i	0.828005	+	1.43415i	−0.0715959	+	0.997434i	$0.522809\pi$
$80$	0.756890			0.0846229
$81$	−5.46084	−	7.15397i	−0.606760	−	0.794885i
$82$			2.14410i			0.236777i
$83$	−5.97335	−	10.3461i	−0.655660	−	1.13564i	−0.981728	−	0.190291i	$-0.939057\pi$
$83$	−5.97335	−	10.3461i	−0.655660	−	1.13564i	0.326067	−	0.945347i	$-0.394276\pi$
$84$	13.0633	+	5.09616i	1.42532	+	0.556036i
$85$	2.40538	−	4.16623i	0.260900	−	0.451891i
$86$	−20.3123	−	11.7273i	−2.19033	−	1.26459i
$87$	7.10126	+	3.80146i	0.761335	+	0.407559i
$88$	−2.93674	−	5.08659i	−0.313058	−	0.542232i
$89$	−14.2521			−1.51072			−0.755362	−	0.655308i	$-0.772539\pi$
$89$	−14.2521			−1.51072			−0.755362	+	0.655308i	$0.772539\pi$
$90$	6.04856	+	2.99230i	0.637574	+	0.315416i
$91$	−0.616420	−	0.822497i	−0.0646184	−	0.0862211i
$92$	−5.66317	+	3.26963i	−0.590426	+	0.340883i
$93$	−0.360396	−	11.2253i	−0.0373713	−	1.16401i
$94$	−10.9596	−	6.32753i	−1.13040	−	0.652635i
$95$	−0.967875	−	0.558803i	−0.0993019	−	0.0573320i
$96$	−0.359648	−	11.2020i	−0.0367064	−	1.14330i
$97$	−3.46717	+	2.00177i	−0.352038	+	0.203249i	−0.665582	−	0.746324i	$-0.731817\pi$
$97$	−3.46717	+	2.00177i	−0.352038	+	0.203249i	0.313545	+	0.949573i	$0.398483\pi$
$98$	15.1130	+	4.41951i	1.52664	+	0.446437i
$99$	0.474084	+	7.37555i	0.0476472	+	0.741271i
$100$	−3.05988			−0.305988
$101$	−3.71469	−	6.43403i	−0.369625	−	0.640210i	0.619882	−	0.784695i	$-0.287181\pi$
$101$	−3.71469	−	6.43403i	−0.369625	−	0.640210i	−0.989507	+	0.144485i	$0.953847\pi$
$102$	−16.5245	−	8.84590i	−1.63616	−	0.875874i
$103$	−7.59032	−	4.38227i	−0.747896	−	0.431798i	0.0770370	−	0.997028i	$-0.475454\pi$
$103$	−7.59032	−	4.38227i	−0.747896	−	0.431798i	−0.824933	+	0.565230i	$0.808787\pi$
$104$	0.463103	−	0.802118i	0.0454110	−	0.0786542i
$105$	4.26921	+	1.66547i	0.416633	+	0.162534i
$106$	10.9411	+	18.9505i	1.06269	+	1.84064i
$107$		−	4.06484i		−	0.392963i	−0.980508	−	0.196482i	$-0.937048\pi$
$107$		−	4.06484i		−	0.392963i	0.980508	−	0.196482i	$-0.0629516\pi$
$108$	6.58925	−	14.4699i	0.634051	−	1.39237i
$109$	11.3809			1.09009			0.545046	−	0.838406i	$-0.316512\pi$
$109$	11.3809			1.09009			0.545046	+	0.838406i	$0.316512\pi$
$110$	−2.77082	−	4.79920i	−0.264188	−	0.457586i
$111$	−3.92479	−	6.32045i	−0.372524	−	0.599911i
$112$	−0.238834	−	1.98825i	−0.0225677	−	0.187872i
$113$	−7.59510	−	4.38503i	−0.714487	−	0.412509i	0.0982332	−	0.995163i	$-0.468681\pi$
$113$	−7.59510	−	4.38503i	−0.714487	−	0.412509i	−0.812720	+	0.582654i	$0.802014\pi$
$114$	−2.05503	+	3.83887i	−0.192471	+	0.359543i
$115$	−1.85078	+	1.06855i	−0.172586	+	0.0996427i
$116$			14.2297i			1.32120i
$117$	−0.969870	+	0.646280i	−0.0896645	+	0.0597486i
$118$			27.8338i			2.56231i
$119$	−11.7031	−	5.00396i	−1.07283	−	0.458712i
$120$	0.132509	+	4.12728i	0.0120964	+	0.376768i
$121$	−2.46536	+	4.27013i	−0.224124	+	0.388194i
$122$	0.820670	−	1.42144i	0.0743000	−	0.128691i
$123$	1.65011	−	0.0529780i	0.148785	−	0.00477686i
$124$	17.1829	−	9.92053i	1.54307	−	0.890889i
$125$	−1.00000			−0.0894427
$126$	5.95178	−	16.8330i	0.530226	−	1.49960i
$127$	−5.13475			−0.455635			−0.227818	−	0.973704i	$-0.573159\pi$
$127$	−5.13475			−0.455635			−0.227818	+	0.973704i	$0.573159\pi$
$128$	14.1983	−	8.19737i	1.25496	−	0.724552i
$129$	−8.52348	+	15.9222i	−0.750450	+	1.40187i
$130$	0.436939	−	0.756800i	0.0383221	−	0.0663758i
$131$	6.25464	−	10.8334i	0.546470	−	0.946514i	−0.452042	−	0.891996i	$-0.649304\pi$
$131$	6.25464	−	10.8334i	0.546470	−	0.946514i	0.998513	−	0.0545179i	$-0.0173622\pi$
$132$	−11.0921	+	6.88784i	−0.965446	+	0.599509i
$133$	−1.16249	+	2.71881i	−0.100801	+	0.235751i
$134$		−	25.8117i		−	2.22979i
$135$	2.15343	−	4.72892i	0.185338	−	0.407001i
$136$		−	11.4694i		−	0.983492i
$137$	−6.12680	+	3.53731i	−0.523448	+	0.302213i	−0.738344	−	0.674424i	$-0.764392\pi$
$137$	−6.12680	+	3.53731i	−0.523448	+	0.302213i	0.214896	+	0.976637i	$0.431059\pi$
$138$	4.39243	+	7.07353i	0.373908	+	0.602139i
$139$	−9.58572	−	5.53432i	−0.813050	−	0.469415i	0.0349638	−	0.999389i	$-0.488868\pi$
$139$	−9.58572	−	5.53432i	−0.813050	−	0.469415i	−0.848014	+	0.529974i	$0.822202\pi$
$140$	0.965536	+	8.03790i	0.0816027	+	0.679327i
$141$	−4.59889	+	8.59089i	−0.387296	+	0.723483i
$142$	17.0321	+	29.5005i	1.42931	+	2.47563i
$143$	0.957082			0.0800352
$144$	−2.26599	+	0.145653i	−0.188833	+	0.0121377i
$145$			4.65041i			0.386196i
$146$	11.8933	+	20.5999i	0.984299	+	1.70486i
$147$	3.02784	−	11.7402i	0.249732	−	0.968315i
$148$	6.57175	−	11.3826i	0.540194	−	0.935644i
$149$	−7.40128	−	4.27313i	−0.606336	−	0.350068i	0.165194	−	0.986261i	$-0.447175\pi$
$149$	−7.40128	−	4.27313i	−0.606336	−	0.350068i	−0.771530	+	0.636193i	$0.780508\pi$
$150$	0.125023	+	3.89410i	0.0102081	+	0.317952i
$151$	−7.86677	−	13.6256i	−0.640188	−	1.10884i	−0.985390	−	0.170311i	$-0.945523\pi$
$151$	−7.86677	−	13.6256i	−0.640188	−	1.10884i	0.345202	−	0.938528i	$-0.387810\pi$
$152$	−2.66450			−0.216120
$153$	−6.39953	+	12.9358i	−0.517372	+	1.04580i
$154$	−11.7325	+	8.79296i	−0.945436	+	0.708557i
$155$	5.61553	−	3.24213i	0.451050	−	0.260414i
$156$	−1.81522	−	0.971726i	−0.145334	−	0.0778004i
$157$	17.2311	+	9.94836i	1.37519	+	0.793966i	0.991576	−	0.129528i	$-0.0413464\pi$
$157$	17.2311	+	9.94836i	1.37519	+	0.793966i	0.383613	+	0.923494i	$0.374680\pi$
$158$	28.6733	+	16.5545i	2.28112	+	1.31701i
$159$	14.3140	−	8.88853i	1.13518	−	0.704906i
$160$	5.60387	−	3.23540i	0.443025	−	0.255781i
$161$	3.39094	+	4.52458i	0.267244	+	0.356587i
$162$	−18.6841	−	7.79446i	−1.46796	−	0.612391i
$163$	0.220738			0.0172895			0.00864477	−	0.999963i	$-0.497248\pi$
$163$	0.220738			0.0172895			0.00864477	+	0.999963i	$0.497248\pi$
$164$	1.45831	+	2.52587i	0.113875	+	0.197237i
$165$	−3.62502	+	2.25102i	−0.282207	+	0.175241i
$166$	−23.2728	−	13.4366i	−1.80632	−	1.04288i
$167$	−12.6948	+	21.9881i	−0.982356	+	1.70149i	−0.329215	+	0.944255i	$0.606784\pi$
$167$	−12.6948	+	21.9881i	−0.982356	+	1.70149i	−0.653141	+	0.757236i	$0.726549\pi$
$168$	10.8000	−	1.65044i	0.833239	−	0.127334i
$169$	−6.42454	−	11.1276i	−0.494195	−	0.855971i
$170$		−	10.8214i		−	0.829963i
$171$	3.00518	+	1.48670i	0.229812	+	0.113691i
$172$	−31.9053			−2.43275
$173$	7.26041	+	12.5754i	0.551999	+	0.956090i	0.998130	+	0.0611226i	$0.0194681\pi$
$173$	7.26041	+	12.5754i	0.551999	+	0.956090i	−0.446131	+	0.894967i	$0.647199\pi$
$174$	18.1092	−	0.581408i	1.37285	−	0.0440765i
$175$	0.315547	+	2.62687i	0.0238531	+	0.198572i
$176$	1.61485	+	0.932334i	0.121724	+	0.0702773i
$177$	21.4209	−	0.687735i	1.61010	−	0.0516934i
$178$	−27.7639	+	16.0295i	−2.08099	+	1.20146i
$179$			15.0447i			1.12449i	0.826971	+	0.562245i	$0.190062\pi$
$179$			15.0447i			1.12449i	−0.826971	+	0.562245i	$0.809938\pi$
$180$	9.16074	−	0.588832i	0.682801	−	0.0438889i
$181$			18.1625i			1.35001i	0.737813	+	0.675006i	$0.235859\pi$
$181$			18.1625i			1.35001i	−0.737813	+	0.675006i	$0.764141\pi$
$182$	−2.12589	−	0.908974i	−0.157581	−	0.0673776i
$183$	−1.11422	−	0.596468i	−0.0823658	−	0.0440922i
$184$	−2.54754	+	4.41248i	−0.187807	+	0.325292i
$185$	2.14771	−	3.71995i	0.157903	−	0.273496i
$186$	−13.3272	−	21.4621i	−0.977201	−	1.57368i
$187$	10.2639	−	5.92586i	0.750570	−	0.433342i
$188$	−17.2147			−1.25551
$189$	−13.1018	−	4.16458i	−0.953013	−	0.302929i
$190$	−2.51396			−0.182382
$191$	−1.71849	+	0.992168i	−0.124345	+	0.0717908i	−0.560882	−	0.827895i	$-0.689538\pi$
$191$	−1.71849	+	0.992168i	−0.124345	+	0.0717908i	0.436537	+	0.899686i	$0.356205\pi$
$192$	−11.9164	−	19.1901i	−0.859993	−	1.38493i
$193$	6.61042	−	11.4496i	0.475829	−	0.824159i	−0.523788	−	0.851849i	$-0.675482\pi$
$193$	6.61042	−	11.4496i	0.475829	−	0.824159i	0.999617	+	0.0276894i	$0.00881495\pi$
$194$	−4.50282	+	7.79911i	−0.323284	+	0.559943i
$195$	−0.593232	−	0.317570i	−0.0424822	−	0.0227417i
$196$	20.8098	−	5.07267i	1.48642	−	0.362334i
$197$		−	16.1651i		−	1.15172i	−0.817550	−	0.575858i	$-0.804668\pi$
$197$		−	16.1651i		−	1.15172i	0.817550	−	0.575858i	$-0.195332\pi$
$198$	9.21889	+	13.8348i	0.655158	+	0.983193i
$199$		−	27.3385i		−	1.93798i	−0.247107	−	0.968988i	$-0.579480\pi$
$199$		−	27.3385i		−	1.93798i	0.247107	−	0.968988i	$-0.420520\pi$
$200$	−2.06470	+	1.19206i	−0.145997	+	0.0842912i
$201$	−19.8648	+	0.637773i	−1.40115	+	0.0449850i
$202$	−14.4728	−	8.35589i	−1.01830	−	0.587918i
$203$	12.2160	−	1.46742i	0.857396	−	0.102993i
$204$	−25.4832	+	0.818158i	−1.78418	+	0.0572825i
$205$	0.476591	+	0.825479i	0.0332865	+	0.0576540i
$206$	−19.7151			−1.37362
$207$	5.33528	−	3.55520i	0.370828	−	0.247104i
$208$			0.294045i			0.0203883i
$209$	−1.37666	−	2.38445i	−0.0952257	−	0.164936i
$210$	10.1898	−	1.55719i	0.703165	−	0.107456i
$211$	−0.788116	+	1.36506i	−0.0542561	+	0.0939744i	−0.891878	−	0.452276i	$-0.850612\pi$
$211$	−0.788116	+	1.36506i	−0.0542561	+	0.0939744i	0.837622	+	0.546251i	$0.183945\pi$
$212$	25.7784	+	14.8831i	1.77047	+	1.02218i
$213$	22.2829	−	13.8369i	1.52680	−	0.948089i
$214$	−4.57176	−	7.91853i	−0.312519	−	0.541299i
$215$	−10.4270			−0.711113
$216$	−1.19095	−	12.3308i	−0.0810337	−	0.839008i
$217$	−10.2886	−	13.7282i	−0.698436	−	0.931931i
$218$	22.1706	−	12.8002i	1.50158	−	0.866939i
$219$	15.5598	−	9.66214i	1.05144	−	0.652907i
$220$	−6.52835	−	3.76915i	−0.440141	−	0.254116i
$221$	1.61854	+	0.934466i	0.108875	+	0.0628590i
$222$	−14.7544	−	7.89833i	−0.990248	−	0.530101i
$223$	12.6487	−	7.30272i	0.847019	−	0.489026i	−0.0126252	−	0.999920i	$-0.504019\pi$
$223$	12.6487	−	7.30272i	0.847019	−	0.489026i	0.859644	+	0.510894i	$0.170686\pi$
$224$	−10.2672	−	13.6997i	−0.686009	−	0.915350i
$225$	2.99382	−	0.192436i	0.199588	−	0.0128291i
$226$	−19.7275			−1.31226
$227$	1.45581	+	2.52154i	0.0966257	+	0.167361i	0.910286	−	0.413980i	$-0.135862\pi$
$227$	1.45581	+	2.52154i	0.0966257	+	0.167361i	−0.813660	+	0.581341i	$0.802528\pi$
$228$	0.190070	+	5.92012i	0.0125877	+	0.392069i
$229$	−16.2387	−	9.37541i	−1.07308	−	0.619545i	−0.144061	−	0.989569i	$-0.546016\pi$
$229$	−16.2387	−	9.37541i	−1.07308	−	0.619545i	−0.929022	+	0.370024i	$0.879349\pi$
$230$	−2.40361	+	4.16318i	−0.158490	+	0.274512i
$231$	7.05698	+	8.81214i	0.464315	+	0.579796i
$232$	5.54356	+	9.60173i	0.363953	+	0.630384i
$233$			5.14191i			0.336858i	0.985714	+	0.168429i	$0.0538693\pi$
$233$			5.14191i			0.336858i	−0.985714	+	0.168429i	$0.946131\pi$
$234$	−1.16248	+	2.34981i	−0.0759938	+	0.153612i
$235$	−5.62593			−0.366995
$236$	18.9311	+	32.7897i	1.23231	+	2.13443i
$237$	12.0319	−	22.4761i	0.781558	−	1.45998i
$238$	−28.4264	+	3.41466i	−1.84261	+	0.221339i
$239$	14.7909	+	8.53953i	0.956743	+	0.552376i	0.895169	−	0.445726i	$-0.147055\pi$
$239$	14.7909	+	8.53953i	0.956743	+	0.552376i	0.0615742	+	0.998103i	$0.480388\pi$
$240$	−0.691580	−	1.11372i	−0.0446413	−	0.0718901i
$241$	18.1230	−	10.4633i	1.16740	−	0.674000i	0.214335	−	0.976760i	$-0.431241\pi$
$241$	18.1230	−	10.4633i	1.16740	−	0.674000i	0.953067	+	0.302760i	$0.0979081\pi$
$242$			11.0913i			0.712973i
$243$	−5.53698	+	14.5720i	−0.355197	+	0.934791i
$244$		−	2.23271i		−	0.142935i
$245$	6.80086	−	1.65780i	0.434491	−	0.105913i
$246$	3.15491	−	1.95910i	0.201150	−	0.124907i
$247$	0.217090	−	0.376010i	0.0138131	−	0.0239250i
$248$	7.72961	−	13.3881i	0.490831	−	0.850143i
$249$	−9.76578	+	18.2428i	−0.618881	+	1.15609i
$250$	−1.94805	+	1.12471i	−0.123206	+	0.0711328i
$251$	3.52350			0.222401			0.111201	−	0.993798i	$-0.464530\pi$
$251$	3.52350			0.222401			0.111201	+	0.993798i	$0.464530\pi$
$252$	−4.43743	−	23.8782i	−0.279532	−	1.50419i
$253$	−5.26493			−0.331004
$254$	−10.0028	+	5.77510i	−0.627629	+	0.362362i
$255$	−8.32817	+	0.267382i	−0.521531	+	0.0167441i
$256$	5.39757	−	9.34886i	0.337348	−	0.584304i
$257$	−0.354048	+	0.613230i	−0.0220849	+	0.0382522i	−0.876857	−	0.480752i	$-0.840364\pi$
$257$	−0.354048	+	0.613230i	−0.0220849	+	0.0382522i	0.854772	+	0.519004i	$0.173697\pi$
$258$	1.30361	+	40.6036i	0.0811592	+	2.52787i
$259$	−10.4495	−	4.46794i	−0.649301	−	0.277624i
$260$		−	1.18874i		−	0.0737222i
$261$	−0.894907	−	13.9225i	−0.0553934	−	0.861782i
$262$		−	28.1386i		−	1.73841i
$263$	8.83427	−	5.10047i	0.544744	−	0.314508i	−0.202255	−	0.979333i	$-0.564827\pi$
$263$	8.83427	−	5.10047i	0.544744	−	0.314508i	0.747000	+	0.664825i	$0.231494\pi$
$264$	−4.80125	+	8.96891i	−0.295497	+	0.551998i
$265$	8.42463	+	4.86396i	0.517521	+	0.298791i
$266$	0.793274	+	6.60385i	0.0486387	+	0.404908i
$267$	13.0224	+	20.9711i	0.796956	+	1.28341i
$268$	−17.5558	−	30.4076i	−1.07239	−	1.85744i
$269$	30.0939			1.83486			0.917429	−	0.397900i	$-0.130261\pi$
$269$	30.0939			1.83486			0.917429	+	0.397900i	$0.130261\pi$
$270$	−1.12366	−	11.6342i	−0.0683839	−	0.708034i
$271$		−	6.23015i		−	0.378455i	−0.981933	−	0.189227i	$-0.939402\pi$
$271$		−	6.23015i		−	0.378455i	0.981933	−	0.189227i	$-0.0605983\pi$
$272$	1.82061	+	3.15338i	0.110390	+	0.191202i
$273$	−0.647021	+	1.65855i	−0.0391595	+	0.100380i
$274$	−7.95689	+	13.7817i	−0.480693	+	0.832585i
$275$	−2.13353	−	1.23180i	−0.128657	−	0.0742800i
$276$	9.98557	+	5.34549i	0.601061	+	0.321761i
$277$	−0.132848	−	0.230100i	−0.00798208	−	0.0138254i	0.862007	−	0.506897i	$-0.169207\pi$
$277$	−0.132848	−	0.230100i	−0.00798208	−	0.0138254i	−0.869989	+	0.493071i	$0.835874\pi$
$278$	−24.8980			−1.49328
$279$	−16.1880	+	10.7870i	−0.969150	+	0.645800i
$280$	3.78289	+	5.04755i	0.226071	+	0.301649i
$281$	12.0611	−	6.96348i	0.719505	−	0.415406i	−0.0950655	−	0.995471i	$-0.530306\pi$
$281$	12.0611	−	6.96348i	0.719505	−	0.415406i	0.814570	+	0.580065i	$0.196973\pi$
$282$	0.703370	+	21.9079i	0.0418851	+	1.30460i
$283$	13.7248	+	7.92403i	0.815856	+	0.471035i	0.848985	−	0.528416i	$-0.177214\pi$
$283$	13.7248	+	7.92403i	0.815856	+	0.471035i	−0.0331293	+	0.999451i	$0.510547\pi$
$284$	40.1295	+	23.1688i	2.38125	+	1.37482i
$285$	0.0621167	+	1.93475i	0.00367948	+	0.114605i
$286$	1.86445	−	1.07644i	0.110247	−	0.0636511i
$287$	2.01804	−	1.51242i	0.119121	−	0.0892752i
$288$	−16.1544	+	10.7646i	−0.951906	+	0.634309i
$289$	6.14333			0.361372
$290$	5.23036	+	9.05925i	0.307137	+	0.531978i
$291$	6.11348	+	3.27268i	0.358378	+	0.191848i
$292$	28.0220	+	16.1785i	1.63986	+	0.946775i
$293$	3.37071	−	5.83823i	0.196919	−	0.341073i	−0.750609	−	0.660747i	$-0.770240\pi$
$293$	3.37071	−	5.83823i	0.196919	−	0.341073i	0.947528	+	0.319673i	$0.103573\pi$
$294$	−7.30590	−	26.2760i	−0.426089	−	1.53245i
$295$	6.18688	+	10.7160i	0.360214	+	0.623909i
$296$		−	10.2408i		−	0.595234i
$297$	10.4195	−	7.43672i	0.604600	−	0.431522i
$298$	−19.2241			−1.11362
$299$	−0.415121	−	0.719011i	−0.0240071	−	0.0415815i
$300$	2.79585	+	4.50242i	0.161419	+	0.259948i
$301$	3.29020	+	27.3903i	0.189644	+	1.57875i
$302$	−30.6498	−	17.6956i	−1.76370	−	1.01827i
$303$	−6.07311	+	11.3448i	−0.348891	+	0.651741i
$304$	0.732575	−	0.422953i	0.0420161	−	0.0242580i
$305$		−	0.729673i		−	0.0417810i
$306$	2.08243	+	32.3973i	0.119044	+	1.85203i
$307$			1.61431i			0.0921335i	0.998938	+	0.0460668i	$0.0146687\pi$
$307$			1.61431i			0.0921335i	−0.998938	+	0.0460668i	$0.985331\pi$
$308$	−7.84104	+	18.3385i	−0.446785	+	1.04493i
$309$	0.487135	+	15.1728i	0.0277121	+	0.863151i
$310$	7.29290	−	12.6317i	0.414209	−	0.717431i
$311$	7.87129	−	13.6335i	0.446340	−	0.773083i	−0.551805	−	0.833973i	$-0.686061\pi$
$311$	7.87129	−	13.6335i	0.446340	−	0.773083i	0.998144	+	0.0608901i	$0.0193939\pi$
$312$	−1.60341	+	0.0514787i	−0.0907752	+	0.00291441i
$313$	−3.38500	+	1.95433i	−0.191332	+	0.110465i	−0.592606	−	0.805493i	$-0.701901\pi$
$313$	−3.38500	+	1.95433i	−0.191332	+	0.110465i	0.401274	+	0.915958i	$0.368567\pi$
$314$	44.7560			2.52573
$315$	−1.45020	−	7.80365i	−0.0817093	−	0.439686i
$316$	45.0382			2.53360
$317$	−21.3367	+	12.3187i	−1.19839	+	0.691889i	−0.960195	−	0.279330i	$-0.909888\pi$
$317$	−21.3367	+	12.3187i	−1.19839	+	0.691889i	−0.238191	+	0.971218i	$0.576554\pi$
$318$	17.8875	−	33.4145i	1.00308	−	1.87379i
$319$	−5.72836	+	9.92180i	−0.320726	+	0.555514i
$320$	6.52087	−	11.2945i	0.364528	−	0.631380i
$321$	−5.98116	+	3.71410i	−0.333836	+	0.207301i
$322$	11.6946	+	5.00029i	0.651713	+	0.278655i
$323$		−	5.37653i		−	0.299158i
$324$	−27.3123	+	3.52571i	−1.51735	+	0.195873i
$325$		−	0.388491i		−	0.0215496i
$326$	0.430010	−	0.248266i	0.0238160	−	0.0137502i
$327$	−10.3989	−	16.7463i	−0.575059	−	0.926071i
$328$	1.96804	+	1.13625i	0.108667	+	0.0627388i
$329$	1.77524	+	14.7786i	0.0978724	+	0.814769i
$330$	−4.52999	+	8.46219i	−0.249368	+	0.465828i
$331$	−4.61821	−	7.99898i	−0.253840	−	0.439664i	0.710740	−	0.703455i	$-0.248360\pi$
$331$	−4.61821	−	7.99898i	−0.253840	−	0.439664i	−0.964580	+	0.263791i	$0.915027\pi$
$332$	−36.5555			−2.00624
$333$	−5.71402	+	11.5502i	−0.313126	+	0.632945i
$334$			57.1120i			3.12503i
$335$	−5.73742	−	9.93750i	−0.313469	−	0.542943i
$336$	−2.70736	+	2.16812i	−0.147699	+	0.118281i
$337$	1.28651	−	2.22831i	0.0700809	−	0.121384i	−0.828856	−	0.559462i	$-0.811008\pi$
$337$	1.28651	−	2.22831i	0.0700809	−	0.121384i	0.898937	+	0.438079i	$0.144341\pi$
$338$	−25.0307	−	14.4515i	−1.36149	−	0.786056i
$339$	0.487442	+	15.1824i	0.0264742	+	0.824594i
$340$	−7.36016	−	12.7482i	−0.399161	−	0.691367i
$341$	15.9745			0.865070
$342$	7.52636	−	0.483777i	0.406979	−	0.0261597i
$343$	−6.50081	−	17.3418i	−0.351011	−	0.936371i
$344$	−21.5286	+	12.4295i	−1.16074	+	0.670156i
$345$	3.26339	+	1.74696i	0.175695	+	0.0940532i
$346$	28.2873	+	16.3317i	1.52074	+	0.877998i
$347$	−16.4541	−	9.49979i	−0.883303	−	0.509975i	−0.0115570	−	0.999933i	$-0.503679\pi$
$347$	−16.4541	−	9.49979i	−0.883303	−	0.509975i	−0.871746	+	0.489958i	$0.837012\pi$
$348$	20.9381	−	13.0019i	1.12240	−	0.696974i
$349$	−9.19557	+	5.30906i	−0.492227	+	0.284188i	−0.725498	−	0.688224i	$-0.758391\pi$
$349$	−9.19557	+	5.30906i	−0.492227	+	0.284188i	0.233271	+	0.972412i	$0.425057\pi$
$350$	3.56916	+	4.76238i	0.190780	+	0.254560i
$351$	1.83714	+	0.836589i	0.0980594	+	0.0446538i
$352$	15.9414			0.849679
$353$	0.838153	+	1.45172i	0.0446104	+	0.0772674i	0.887468	−	0.460869i	$-0.152462\pi$
$353$	0.838153	+	1.45172i	0.0446104	+	0.0772674i	−0.842858	+	0.538136i	$0.819129\pi$
$354$	40.9556	−	25.4321i	2.17677	−	1.35170i
$355$	13.1147	+	7.57180i	0.696058	+	0.401869i
$356$	−21.8049	+	37.7672i	−1.15566	+	2.00166i
$357$	3.33031	+	21.7926i	0.176259	+	1.15339i
$358$	16.9209	+	29.3078i	0.894295	+	1.54896i
$359$			20.7692i			1.09616i	0.836428	+	0.548078i	$0.184640\pi$
$359$			20.7692i			1.09616i	−0.836428	+	0.548078i	$0.815360\pi$
$360$	5.95196	−	3.96613i	0.313696	−	0.209034i
$361$	17.7510			0.934261
$362$	20.4276	+	35.3816i	1.07365	+	1.85962i
$363$	8.53586	−	0.274050i	0.448017	−	0.0143839i
$364$	−3.12265	+	0.375102i	−0.163671	+	0.0196607i
$365$	9.15786	+	5.28729i	0.479344	+	0.276750i
$366$	−2.84142	+	0.0912259i	−0.148523	+	0.00476846i
$367$	−25.5963	+	14.7780i	−1.33612	+	0.771407i	−0.986229	−	0.165385i	$-0.947113\pi$
$367$	−25.5963	+	14.7780i	−1.33612	+	0.771407i	−0.349886	+	0.936792i	$0.613780\pi$
$368$		−	1.61755i		−	0.0843205i
$369$	−1.58568	−	2.37962i	−0.0825472	−	0.123878i
$370$		−	9.66221i		−	0.502314i
$371$	10.1186	−	23.6652i	0.525332	−	1.22864i
$372$	−30.2976	−	16.2190i	−1.57086	−	0.840915i
$373$	−5.41206	+	9.37397i	−0.280226	+	0.485366i	−0.971440	−	0.237284i	$-0.923743\pi$
$373$	−5.41206	+	9.37397i	−0.280226	+	0.485366i	0.691214	+	0.722650i	$0.257076\pi$
$374$	13.3297	−	23.0878i	0.689264	−	1.19384i
$375$	0.913713	+	1.47144i	0.0471839	+	0.0759847i
$376$	−11.6159	+	6.70643i	−0.599043	+	0.345858i
$377$	−1.80664			−0.0930468
$378$	−30.2069	+	6.62284i	−1.55367	+	0.340642i
$379$	30.6805			1.57595			0.787976	−	0.615706i	$-0.211129\pi$
$379$	30.6805			1.57595			0.787976	+	0.615706i	$0.211129\pi$
$380$	−2.96158	+	1.70987i	−0.151926	+	0.0877145i
$381$	4.69169	+	7.55546i	0.240362	+	0.387078i
$382$	−2.23180	+	3.86559i	−0.114189	+	0.197781i
$383$	7.24288	−	12.5450i	0.370094	−	0.641022i	−0.619486	−	0.785008i	$-0.712659\pi$
$383$	7.24288	−	12.5450i	0.370094	−	0.641022i	0.989580	+	0.143986i	$0.0459921\pi$
$384$	−25.0350	−	13.4018i	−1.27756	−	0.683908i
$385$	−2.56253	+	5.99319i	−0.130599	+	0.305441i
$386$		−	29.7392i		−	1.51369i
$387$	31.2165	−	2.00652i	1.58682	−	0.101997i
$388$			12.2504i			0.621918i
$389$	−16.0958	+	9.29294i	−0.816092	+	0.471171i	−0.849067	−	0.528285i	$-0.822835\pi$
$389$	−16.0958	+	9.29294i	−0.816092	+	0.471171i	0.0329752	+	0.999456i	$0.489502\pi$
$390$	−1.51282	+	0.0485703i	−0.0766047	+	0.00245945i
$391$	−8.90365	−	5.14052i	−0.450277	−	0.259967i
$392$	12.0656	−	11.5299i	0.609403	−	0.582347i
$393$	−21.6555	+	0.695267i	−1.09238	+	0.0350716i
$394$	−18.1810	−	31.4905i	−0.915947	−	1.58647i
$395$	14.7189			0.740590
$396$	20.2700	+	10.0279i	1.01861	+	0.503919i
$397$		−	10.0525i		−	0.504521i	−0.967659	−	0.252261i	$-0.918826\pi$
$397$		−	10.0525i		−	0.504521i	0.967659	−	0.252261i	$-0.0811740\pi$
$398$	−30.7479	−	53.2569i	−1.54125	−	2.66953i
$399$	5.06274	−	0.773678i	0.253454	−	0.0387324i
$400$	0.378445	−	0.655486i	0.0189223	−	0.0327743i
$401$	−16.3738	−	9.45340i	−0.817667	−	0.472080i	0.0319444	−	0.999490i	$-0.489830\pi$
$401$	−16.3738	−	9.45340i	−0.817667	−	0.472080i	−0.849611	+	0.527410i	$0.823163\pi$
$402$	−37.9803	+	23.5845i	−1.89428	+	1.17629i
$403$	1.25954	+	2.18158i	0.0627420	+	0.108672i
$404$	−22.7330			−1.13101
$405$	−8.92594	+	1.15224i	−0.443533	+	0.0572552i
$406$	22.1470	−	16.5981i	1.09914	−	0.823749i
$407$	9.16443	−	5.29109i	0.454264	−	0.262269i
$408$	−16.8765	+	10.4797i	−0.835511	+	0.518824i
$409$	−4.97809	−	2.87410i	−0.246151	−	0.142115i	0.371850	−	0.928293i	$-0.378724\pi$
$409$	−4.97809	−	2.87410i	−0.246151	−	0.142115i	−0.618000	+	0.786178i	$0.712057\pi$
$410$	1.85685	+	1.07205i	0.0917032	+	0.0529449i
$411$	10.8031	+	5.78312i	0.532876	+	0.285260i
$412$	−23.2255	+	13.4092i	−1.14424	+	0.660625i
$413$	26.1972	−	19.6335i	1.28908	−	0.966102i
$414$	6.39484	−	12.9264i	0.314289	−	0.635296i
$415$	−11.9467			−0.586440
$416$	1.25692	+	2.17705i	0.0616256	+	0.106739i
$417$	0.615196	+	19.1616i	0.0301263	+	0.938346i
$418$	−5.36362	−	3.09669i	−0.262343	−	0.151464i
$419$	3.76615	−	6.52317i	0.183989	−	0.318678i	−0.759247	−	0.650803i	$-0.774432\pi$
$419$	3.76615	−	6.52317i	0.183989	−	0.318678i	0.943235	+	0.332125i	$0.107766\pi$
$420$	10.9450	−	8.76506i	0.534063	−	0.427691i
$421$	4.57617	+	7.92615i	0.223029	+	0.386297i	0.955726	−	0.294257i	$-0.0950723\pi$
$421$	4.57617	+	7.92615i	0.223029	+	0.386297i	−0.732697	+	0.680554i	$0.761739\pi$
$422$			3.54560i			0.172597i
$423$	16.8430	−	1.08263i	0.818936	−	0.0526394i
$424$	23.1925			1.12633
$425$	−2.40538	−	4.16623i	−0.116678	−	0.202092i
$426$	27.8457	−	52.0167i	1.34913	−	2.52022i
$427$	−1.91675	+	0.230246i	−0.0927583	+	0.0111424i
$428$	−10.7716	−	6.21897i	−0.520663	−	0.300605i
$429$	−0.874498	−	1.40829i	−0.0422212	−	0.0679927i
$430$	−20.3123	+	11.7273i	−0.979545	+	0.565541i
$431$		−	5.09485i		−	0.245410i	−0.992443	−	0.122705i	$-0.960843\pi$
$431$		−	5.09485i		−	0.245410i	0.992443	−	0.122705i	$-0.0391570\pi$
$432$	2.28479	+	3.20118i	0.109927	+	0.154017i
$433$		−	35.8805i		−	1.72430i	−0.506649	−	0.862152i	$-0.669116\pi$
$433$		−	35.8805i		−	1.72430i	0.506649	−	0.862152i	$-0.330884\pi$
$434$	−35.4830	−	15.1716i	−1.70324	−	0.728260i
$435$	6.84279	−	4.24914i	0.328087	−	0.203731i
$436$	17.4121	−	30.1586i	0.833888	−	1.44434i
$437$	−1.19422	+	2.06844i	−0.0571271	+	0.0989471i
$438$	19.4443	−	36.3227i	0.929085	−	1.73556i
$439$	−0.641214	+	0.370205i	−0.0306035	+	0.0176689i	−0.515224	−	0.857056i	$-0.672291\pi$
$439$	−0.641214	+	0.370205i	−0.0306035	+	0.0176689i	0.484620	+	0.874725i	$0.338958\pi$
$440$	−5.87348			−0.280007
$441$	−20.0415	+	6.27189i	−0.954359	+	0.298661i
$442$	4.20401			0.199964
$443$	−14.9440	+	8.62790i	−0.710009	+	0.409924i	−0.811064	−	0.584957i	$-0.801111\pi$
$443$	−14.9440	+	8.62790i	−0.710009	+	0.409924i	0.101056	+	0.994881i	$0.467778\pi$
$444$	−22.7535	+	0.730517i	−1.07983	+	0.0346688i
$445$	−7.12607	+	12.3427i	−0.337808	+	0.585101i
$446$	16.4269	−	28.4522i	0.777835	−	1.34725i
$447$	0.475002	+	14.7949i	0.0224668	+	0.699776i
$448$	−31.7267	−	13.5655i	−1.49895	−	0.640910i
$449$		−	20.5062i		−	0.967747i	−0.875138	−	0.483874i	$-0.839229\pi$
$449$		−	20.5062i		−	0.967747i	0.875138	−	0.483874i	$-0.160771\pi$
$450$	5.61569	−	3.74205i	0.264726	−	0.176402i
$451$			2.34825i			0.110575i
$452$	−23.2401	+	13.4177i	−1.09312	+	0.631115i
$453$	−12.8613	+	24.0254i	−0.604277	+	1.12881i
$454$	5.67200	+	3.27473i	0.266200	+	0.153691i
$455$	−1.02051	+	0.122587i	−0.0478424	+	0.00574697i
$456$	2.43459	+	3.92065i	0.114010	+	0.183601i
$457$	4.57715	+	7.92786i	0.214110	+	0.370849i	0.952997	−	0.302980i	$-0.0979816\pi$
$457$	4.57715	+	7.92786i	0.214110	+	0.370849i	−0.738887	+	0.673829i	$0.764648\pi$
$458$	−42.1785			−1.97087
$459$	24.8816	−	2.40314i	1.16137	−	0.112169i
$460$			6.53927i			0.304895i
$461$	5.07463	+	8.78951i	0.236349	+	0.409368i	0.959664	−	0.281150i	$-0.0907158\pi$
$461$	5.07463	+	8.78951i	0.236349	+	0.409368i	−0.723315	+	0.690518i	$0.757382\pi$
$462$	23.6585	+	9.22947i	1.10069	+	0.429394i
$463$	−0.613755	+	1.06305i	−0.0285236	+	0.0494043i	−0.879935	−	0.475094i	$-0.842414\pi$
$463$	−0.613755	+	1.06305i	−0.0285236	+	0.0494043i	0.851411	+	0.524499i	$0.175747\pi$
$464$	−3.04828	−	1.75993i	−0.141513	−	0.0817025i
$465$	−9.90157	−	5.30053i	−0.459174	−	0.245806i
$466$	5.78315	+	10.0167i	0.267899	+	0.464015i
$467$	−23.2327			−1.07508			−0.537540	−	0.843238i	$-0.680646\pi$
$467$	−23.2327			−1.07508			−0.537540	+	0.843238i	$0.680646\pi$
$468$	0.228756	+	3.55886i	0.0105742	+	0.164508i
$469$	−24.2941	+	18.2072i	−1.12180	+	0.840729i
$470$	−10.9596	+	6.32753i	−0.505529	+	0.291867i
$471$	−1.10586	−	34.4444i	−0.0509555	−	1.58711i
$472$	25.5482	+	14.7502i	1.17595	+	0.678935i
$473$	−22.2463	−	12.8439i	−1.02288	−	0.590562i
$474$	−1.84021	−	57.3170i	−0.0845234	−	2.63266i
$475$	−0.967875	+	0.558803i	−0.0444092	+	0.0256396i
$476$	−31.1653	+	23.3568i	−1.42846	+	1.07056i
$477$	−26.1578	−	12.9406i	−1.19769	−	0.592511i
$478$	38.4179			1.75720
$479$	15.6175	+	27.0504i	0.713583	+	1.23596i	0.963503	+	0.267696i	$0.0862623\pi$
$479$	15.6175	+	27.0504i	0.713583	+	1.23596i	−0.249920	+	0.968266i	$0.580404\pi$
$480$	−9.88101	−	5.28952i	−0.451005	−	0.241433i
$481$	1.44517	+	0.834367i	0.0658939	+	0.0380438i
$482$	23.5363	−	40.7661i	1.07205	−	1.85684i
$483$	3.55928	−	9.12373i	0.161953	−	0.415144i
$484$	7.54371	+	13.0661i	0.342896	+	0.593913i
$485$			4.00354i			0.181791i
$486$	5.60288	+	34.6144i	0.254152	+	1.57014i
$487$	−10.7164			−0.485605			−0.242802	−	0.970076i	$-0.578067\pi$
$487$	−10.7164			−0.485605			−0.242802	+	0.970076i	$0.578067\pi$
$488$	−0.869813	−	1.50656i	−0.0393746	−	0.0681988i
$489$	−0.201691	−	0.324802i	−0.00912080	−	0.0146881i
$490$	11.3839	−	10.8785i	0.514272	−	0.491439i
$491$	−0.912341	−	0.526740i	−0.0411734	−	0.0237715i	0.479272	−	0.877666i	$-0.340901\pi$
$491$	−0.912341	−	0.526740i	−0.0411734	−	0.0237715i	−0.520445	+	0.853895i	$0.674234\pi$
$492$	2.38418	−	4.45373i	0.107487	−	0.200790i
$493$	−19.3747	+	11.1860i	−0.872593	+	0.503792i
$494$		−	0.976651i		−	0.0439416i
$495$	6.62446	+	3.27721i	0.297747	+	0.147299i
$496$			4.90787i			0.220370i
$497$	15.7518	−	36.8399i	0.706564	−	1.65250i
$498$	1.49361	+	46.5216i	0.0669304	+	2.08468i
$499$	−2.52065	+	4.36589i	−0.112840	+	0.195444i	−0.916914	−	0.399085i	$-0.869328\pi$
$499$	−2.52065	+	4.36589i	−0.112840	+	0.195444i	0.804074	+	0.594529i	$0.202661\pi$
$500$	−1.52994	+	2.64993i	−0.0684210	+	0.118509i
$501$	43.9536	−	1.41116i	1.96370	−	0.0630461i
$502$	6.86396	−	3.96291i	0.306354	−	0.176873i
$503$	−34.8769			−1.55508			−0.777542	−	0.628831i	$-0.783534\pi$
$503$	−34.8769			−1.55508			−0.777542	+	0.628831i	$0.783534\pi$
$504$	−12.2966	−	14.3835i	−0.547735	−	0.640693i
$505$	−7.42938			−0.330603
$506$	−10.2564	+	5.92152i	−0.455951	+	0.263244i
$507$	−10.5034	+	19.6208i	−0.466473	+	0.871389i
$508$	−7.85586	+	13.6067i	−0.348547	+	0.603702i
$509$	−3.07394	+	5.32422i	−0.136250	+	0.235992i	−0.926074	−	0.377341i	$-0.876838\pi$
$509$	−3.07394	+	5.32422i	−0.136250	+	0.235992i	0.789824	+	0.613333i	$0.210172\pi$
$510$	−15.9230	+	9.88765i	−0.705082	+	0.437832i
$511$	10.9993	−	25.7249i	0.486580	−	1.13800i
$512$			8.50671i			0.375947i
$513$	−0.558283	−	5.78035i	−0.0246488	−	0.255209i
$514$			1.59280i			0.0702556i
$515$	−7.59032	+	4.38227i	−0.334469	+	0.193106i
$516$	29.1523	+	46.9466i	1.28336	+	2.06671i
$517$	−12.0031	−	6.92999i	−0.527896	−	0.304781i
$518$	−25.3813	+	3.04888i	−1.11519	+	0.133960i
$519$	11.8700	−	22.1736i	0.521034	−	0.973311i
$520$	−0.463103	−	0.802118i	−0.0203084	−	0.0351752i
$521$	−20.2902			−0.888932			−0.444466	−	0.895796i	$-0.646606\pi$
$521$	−20.2902			−0.888932			−0.444466	+	0.895796i	$0.646606\pi$
$522$	−17.4021	−	26.1153i	−0.761669	−	1.14303i
$523$		−	15.6812i		−	0.685690i	−0.939392	−	0.342845i	$-0.888609\pi$
$523$		−	15.6812i		−	0.685690i	0.939392	−	0.342845i	$-0.111391\pi$
$524$	−19.1385	−	33.1488i	−0.836067	−	1.44811i
$525$	3.57695	−	2.86451i	0.156111	−	0.125018i
$526$	11.4731	−	19.8720i	0.500250	−	0.866459i
$527$	27.0149	+	15.5971i	1.17679	+	0.679419i
$528$	−0.103638	−	3.22803i	−0.00451029	−	0.140482i
$529$	−9.21641	−	15.9633i	−0.400713	−	0.694056i
$530$	21.8822			0.950501
$531$	−20.5846	−	30.8912i	−0.893294	−	1.34056i
$532$	5.42612	+	7.24014i	0.235252	+	0.313900i
$533$	−0.320691	+	0.185151i	−0.0138907	+	0.00801978i
$534$	48.9547	+	26.2065i	2.11848	+	1.13407i
$535$	−3.52026	−	2.03242i	−0.152194	−	0.0878692i
$536$	−23.6921	−	13.6787i	−1.02334	−	0.590828i
$537$	22.1373	−	13.7465i	0.955294	−	0.593205i
$538$	58.6245	−	33.8469i	2.52748	−	1.45924i
$539$	16.5519	+	4.84030i	0.712942	+	0.208486i
$540$	−9.23672	−	12.9414i	−0.397485	−	0.556910i
$541$	19.2258			0.826583			0.413291	−	0.910599i	$-0.364379\pi$
$541$	19.2258			0.826583			0.413291	+	0.910599i	$0.364379\pi$
$542$	−7.00711	−	12.1367i	−0.300981	−	0.521314i
$543$	26.7250	−	16.5954i	1.14688	−	0.712175i
$544$	26.9588	+	15.5647i	1.15585	+	0.667331i
$545$	5.69045	−	9.85615i	0.243752	−	0.422191i
$546$	0.604954	+	3.95865i	0.0258896	+	0.169415i
$547$	−12.9816	−	22.4848i	−0.555053	−	0.961379i	−0.997899	−	0.0647821i	$-0.979365\pi$
$547$	−12.9816	−	22.4848i	−0.555053	−	0.961379i	0.442847	−	0.896597i	$-0.353969\pi$
$548$			21.6475i			0.924735i
$549$	0.140416	+	2.18451i	0.00599279	+	0.0932327i
$550$	−5.54164			−0.236296
$551$	2.59866	+	4.50102i	0.110707	+	0.191750i
$552$	8.82041	−	0.283186i	0.375421	−	0.0120532i
$553$	−4.64452	−	38.6647i	−0.197505	−	1.64419i
$554$	−0.517591	−	0.298831i	−0.0219903	−	0.0126961i
$555$	−7.43607	+	0.238740i	−0.315643	+	0.0101340i
$556$	−29.3312	+	16.9344i	−1.24392	+	0.718177i
$557$		−	5.78189i		−	0.244987i	−0.992469	−	0.122493i	$-0.960911\pi$
$557$		−	5.78189i		−	0.244987i	0.992469	−	0.122493i	$-0.0390890\pi$
$558$	−19.4029	+	39.2204i	−0.821388	+	1.66033i
$559$		−	4.05078i		−	0.171330i
$560$	−1.84129	−	0.787288i	−0.0778088	−	0.0332690i
$561$	−18.0978	−	9.68814i	−0.764089	−	0.409033i
$562$	15.6638	−	27.1305i	0.660737	−	1.14443i
$563$	−18.8450	+	32.6404i	−0.794220	+	1.37563i	0.129113	+	0.991630i	$0.458787\pi$
$563$	−18.8450	+	32.6404i	−0.794220	+	1.37563i	−0.923333	+	0.384000i	$0.874546\pi$
$564$	15.7293	+	25.3303i	0.662322	+	1.06660i
$565$	−7.59510	+	4.38503i	−0.319528	+	0.184480i
$566$	35.6489			1.49844
$567$	5.84333	+	23.0837i	0.245397	+	0.969423i
$568$	36.1041			1.51489
$569$	11.9150	−	6.87915i	0.499504	−	0.288389i	−0.229005	−	0.973425i	$-0.573547\pi$
$569$	11.9150	−	6.87915i	0.499504	−	0.288389i	0.728509	+	0.685037i	$0.240214\pi$
$570$	2.29704	+	3.69914i	0.0962125	+	0.154940i
$571$	−10.5199	+	18.2211i	−0.440246	+	0.762528i	−0.997707	−	0.0676747i	$-0.978442\pi$
$571$	−10.5199	+	18.2211i	−0.440246	+	0.762528i	0.557462	+	0.830203i	$0.311775\pi$
$572$	1.46428	−	2.53620i	0.0612245	−	0.106044i
$573$	3.03012	+	1.62209i	0.126585	+	0.0677636i
$574$	2.23021	−	5.21598i	0.0930874	−	0.217711i
$575$			2.13710i			0.0891231i
$576$	−17.3489	+	35.0685i	−0.722869	+	1.46119i
$577$			12.0259i			0.500643i	0.968163	+	0.250321i	$0.0805363\pi$
$577$			12.0259i			0.500643i	−0.968163	+	0.250321i	$0.919464\pi$
$578$	11.9675	−	6.90946i	0.497784	−	0.287396i
$579$	−22.8874	+	0.734816i	−0.951167	+	0.0305379i
$580$	12.3233	+	7.11485i	0.511697	+	0.295428i
$581$	3.76975	+	31.3824i	0.156395	+	1.30196i
$582$	15.5902	−	0.500535i	0.646234	−	0.0207478i
$583$	11.9828	+	20.7548i	0.496277	+	0.859577i
$584$	25.2110			1.04324
$585$	0.0747596	+	1.16307i	0.00309093	+	0.0480871i
$586$		−	15.1643i		−	0.626429i
$587$	0.136440	+	0.236321i	0.00563148	+	0.00975402i	0.868827	−	0.495115i	$-0.164874\pi$
$587$	0.136440	+	0.236321i	0.00563148	+	0.00975402i	−0.863196	+	0.504869i	$0.831541\pi$
$588$	−26.4783	−	25.9854i	−1.09195	−	1.07162i
$589$	3.62342	−	6.27595i	0.149300	−	0.258596i
$590$	24.1047	+	13.9169i	0.992377	+	0.572949i
$591$	−23.7859	+	14.7703i	−0.978423	+	0.607568i
$592$	1.62558	+	2.81559i	0.0668111	+	0.115720i
$593$	3.61889			0.148610			0.0743050	−	0.997236i	$-0.476326\pi$
$593$	3.61889			0.148610			0.0743050	+	0.997236i	$0.476326\pi$
$594$	11.9336	−	26.2060i	0.489640	−	1.07525i
$595$	−10.1851	+	7.63324i	−0.417550	+	0.312933i
$596$	−22.6470	+	13.0753i	−0.927658	+	0.535584i
$597$	−40.2269	+	24.9796i	−1.64638	+	1.02235i
$598$	−1.61736	−	0.933781i	−0.0661386	−	0.0381852i
$599$	−21.6954	−	12.5258i	−0.886448	−	0.511791i	−0.0136692	−	0.999907i	$-0.504351\pi$
$599$	−21.6954	−	12.5258i	−0.886448	−	0.511791i	−0.872779	+	0.488115i	$0.837685\pi$
$600$	3.64059	+	1.94888i	0.148626	+	0.0795629i
$601$	−17.6859	+	10.2110i	−0.721424	+	0.416515i	−0.815277	−	0.579072i	$-0.803415\pi$
$601$	−17.6859	+	10.2110i	−0.721424	+	0.416515i	0.0938524	+	0.995586i	$0.470082\pi$
$602$	37.2155	+	49.6571i	1.51679	+	2.02387i
$603$	19.0891	+	28.6470i	0.777370	+	1.16660i
$604$	−48.1427			−1.95890
$605$	2.46536	+	4.27013i	0.100231	+	0.173606i
$606$	0.928843	+	28.9307i	0.0377317	+	1.17523i
$607$	−20.8266	−	12.0243i	−0.845327	−	0.488050i	0.0137445	−	0.999906i	$-0.495625\pi$
$607$	−20.8266	−	12.0243i	−0.845327	−	0.488050i	−0.859071	+	0.511856i	$0.828958\pi$
$608$	3.61590	−	6.26292i	0.146644	−	0.253995i
$609$	−13.3212	−	16.6343i	−0.539801	−	0.674056i
$610$	−0.820670	−	1.42144i	−0.0332280	−	0.0575525i
$611$		−	2.18562i		−	0.0884207i
$612$	24.4882	+	36.7494i	0.989878	+	1.48551i
$613$	19.0207			0.768239			0.384120	−	0.923283i	$-0.374505\pi$
$613$	19.0207			0.768239			0.384120	+	0.923283i	$0.374505\pi$
$614$	1.81563	+	3.14476i	0.0732728	+	0.126912i
$615$	0.779174	−	1.45552i	0.0314193	−	0.0586924i
$616$	1.85336	+	15.4289i	0.0746740	+	0.621646i
$617$	−28.5311	−	16.4725i	−1.14862	−	0.663157i	−0.200070	−	0.979782i	$-0.564117\pi$
$617$	−28.5311	−	16.4725i	−1.14862	−	0.663157i	−0.948551	+	0.316625i	$0.897450\pi$
$618$	18.0140	+	29.0096i	0.724628	+	1.16694i
$619$	17.7455	−	10.2454i	0.713253	−	0.411797i	−0.0990114	−	0.995086i	$-0.531568\pi$
$619$	17.7455	−	10.2454i	0.713253	−	0.411797i	0.812264	+	0.583290i	$0.198235\pi$
$620$		−	19.8411i		−	0.796836i
$621$	−10.1062	−	4.60210i	−0.405547	−	0.184676i
$622$		−	35.4116i		−	1.41988i
$623$	34.6713	+	14.8245i	1.38907	+	0.593932i
$624$	0.432668	−	0.268673i	0.0173206	−	0.0107555i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.39611	+	7.61429i	−0.175704	+	0.304328i
$627$	−2.25069	+	4.20437i	−0.0898840	+	0.167907i
$628$	52.7250	−	30.4408i	2.10396	−	1.21472i
$629$	20.6642			0.823937
$630$	−11.6019	−	13.5709i	−0.462230	−	0.540677i
$631$	−47.0272			−1.87212			−0.936061	−	0.351838i	$-0.885557\pi$
$631$	−47.0272			−1.87212			−0.936061	+	0.351838i	$0.885557\pi$
$632$	30.3903	−	17.5458i	1.20886	−	0.697935i
$633$	2.72871	−	0.0876072i	0.108456	−	0.00348207i
$634$	−27.7100	+	47.9951i	−1.10050	+	1.90613i
$635$	−2.56737	+	4.44682i	−0.101883	+	0.176467i
$636$	−1.65441	−	51.5302i	−0.0656018	−	2.04330i
$637$	0.644040	+	2.64207i	0.0255178	+	0.104683i
$638$			25.7709i			1.02028i
$639$	−40.7203	−	20.1449i	−1.61087	−	0.796918i
$640$		−	16.3947i		−	0.648059i
$641$	−1.78047	+	1.02796i	−0.0703244	+	0.0406018i	−0.534750	−	0.845010i	$-0.679594\pi$
$641$	−1.78047	+	1.02796i	−0.0703244	+	0.0406018i	0.464426	+	0.885612i	$0.346261\pi$
$642$	−7.47434	+	13.9623i	−0.294989	+	0.551049i
$643$	38.6058	+	22.2891i	1.52246	+	0.878995i	0.999647	+	0.0265505i	$0.00845227\pi$
$643$	38.6058	+	22.2891i	1.52246	+	0.878995i	0.522817	+	0.852445i	$0.324881\pi$
$644$	17.1778	−	2.06345i	0.676899	−	0.0813112i
$645$	9.52726	+	15.3426i	0.375135	+	0.604115i
$646$	−6.04703	−	10.4738i	−0.237917	−	0.412084i
$647$	−8.06386			−0.317023			−0.158512	−	0.987357i	$-0.550670\pi$
$647$	−8.06386			−0.317023			−0.158512	+	0.987357i	$0.550670\pi$
$648$	−17.0559	+	13.0193i	−0.670019	+	0.511445i
$649$			30.4839i			1.19660i
$650$	−0.436939	−	0.756800i	−0.0171382	−	0.0296842i
$651$	−10.7994	+	27.6827i	−0.423260	+	1.08497i
$652$	0.337716	−	0.584942i	0.0132260	−	0.0229081i
$653$	−10.8478	−	6.26301i	−0.424509	−	0.245090i	0.272496	−	0.962157i	$-0.412151\pi$
$653$	−10.8478	−	6.26301i	−0.424509	−	0.245090i	−0.697005	+	0.717067i	$0.745484\pi$
$654$	−39.0923	−	20.9269i	−1.52863	−	0.818308i
$655$	−6.25464	−	10.8334i	−0.244389	−	0.423294i
$656$	−0.721454			−0.0281680
$657$	−28.4345	−	14.0669i	−1.10933	−	0.548803i
$658$	20.0799	+	26.7928i	0.782794	+	1.04449i
$659$	5.31567	−	3.06900i	0.207069	−	0.119551i	−0.392880	−	0.919590i	$-0.628521\pi$
$659$	5.31567	−	3.06900i	0.207069	−	0.119551i	0.599949	+	0.800039i	$0.295188\pi$
$660$	0.418979	+	13.0500i	0.0163088	+	0.507970i
$661$	5.75735	+	3.32400i	0.223935	+	0.129289i	0.607771	−	0.794112i	$-0.292064\pi$
$661$	5.75735	+	3.32400i	0.223935	+	0.129289i	−0.383836	+	0.923401i	$0.625397\pi$
$662$	−17.9930	−	10.3883i	−0.699319	−	0.403752i
$663$	−0.103876	−	3.23542i	−0.00403419	−	0.125653i
$664$	−24.6664	+	14.2412i	−0.957242	+	0.552664i
$665$	1.77331	+	2.36615i	0.0687661	+	0.0917554i
$666$	1.85936	+	28.9269i	0.0720487	+	1.12090i
$667$	9.93839			0.384816
$668$	38.8447	+	67.2810i	1.50295	+	2.60318i
$669$	−22.3028	−	11.9392i	−0.862275	−	0.461594i
$670$	−22.3536	−	12.9058i	−0.863594	−	0.498596i
$671$	0.898808	−	1.55678i	0.0346981	−	0.0600989i
$672$	−10.7769	+	27.6252i	−0.415730	+	1.06567i
$673$	0.875991	+	1.51726i	0.0337670	+	0.0584861i	0.882415	−	0.470472i	$-0.155916\pi$
$673$	0.875991	+	1.51726i	0.0337670	+	0.0584861i	−0.848648	+	0.528958i	$0.822583\pi$
$674$		−	5.78781i		−	0.222938i
$675$	−3.01865	−	4.22939i	−0.116188	−	0.162789i
$676$	−39.3166			−1.51218
$677$	7.49127	+	12.9753i	0.287913	+	0.498680i	0.973311	−	0.229488i	$-0.0737053\pi$
$677$	7.49127	+	12.9753i	0.287913	+	0.498680i	−0.685398	+	0.728168i	$0.740372\pi$
$678$	18.0253	+	29.0278i	0.692258	+	1.11481i
$679$	10.5168	−	1.26331i	0.403597	−	0.0484812i
$680$	−9.93278	−	5.73469i	−0.380905	−	0.219915i
$681$	2.38010	−	4.44611i	0.0912055	−	0.170375i
$682$	31.1193	−	17.9667i	1.19162	−	0.687981i
$683$		−	11.6024i		−	0.443954i	−0.975052	−	0.221977i	$-0.928749\pi$
$683$		−	11.6024i		−	0.443954i	0.975052	−	0.221977i	$-0.0712509\pi$
$684$	8.53741	−	5.68896i	0.326436	−	0.217523i
$685$			7.07462i			0.270307i
$686$	−32.1685	−	26.4713i	−1.22820	−	1.01068i
$687$	1.04217	+	32.4607i	0.0397614	+	1.23845i
$688$	3.94603	−	6.83473i	0.150441	−	0.260572i
$689$	−1.88960	+	3.27289i	−0.0719882	+	0.124687i
$690$	8.32207	−	0.267186i	0.316816	−	0.0101716i
$691$	−7.00564	+	4.04471i	−0.266507	+	0.153868i	−0.627299	−	0.778778i	$-0.715840\pi$
$691$	−7.00564	+	4.04471i	−0.266507	+	0.153868i	0.360792	+	0.932646i	$0.382506\pi$
$692$	44.4320			1.68905
$693$	6.51846	−	18.4357i	0.247616	−	0.700313i
$694$	−42.7380			−1.62231
$695$	−9.58572	+	5.53432i	−0.363607	+	0.209929i
$696$	9.06312	−	16.9302i	0.343537	−	0.641739i
$697$	−2.29276	+	3.97118i	−0.0868445	+	0.150419i
$698$	−11.9423	+	20.6847i	−0.452023	+	0.782926i
$699$	7.56600	−	4.69823i	0.286172	−	0.177703i
$700$	7.44379	+	3.18277i	0.281349	+	0.120297i
$701$		−	39.1808i		−	1.47984i	−0.672696	−	0.739919i	$-0.734864\pi$
$701$		−	39.1808i		−	1.47984i	0.672696	−	0.739919i	$-0.265136\pi$
$702$	4.51977	−	0.436532i	0.170588	−	0.0164758i
$703$		−	4.80060i		−	0.181058i
$704$	27.8250	−	16.0647i	1.04869	−	0.605463i
$705$	5.14048	+	8.27820i	0.193602	+	0.311775i
$706$	3.26553	+	1.88536i	0.122900	+	0.0709563i
$707$	2.34432	+	19.5160i	0.0881672	+	0.733974i
$708$	30.9503	−	57.8163i	1.16318	−	2.17287i
$709$	7.25588	+	12.5676i	0.272500	+	0.471984i	0.969501	−	0.245086i	$-0.0788161\pi$
$709$	7.25588	+	12.5676i	0.272500	+	0.471984i	−0.697001	+	0.717070i	$0.745483\pi$
$710$	34.0643			1.27841
$711$	−44.0659	+	2.83246i	−1.65260	+	0.106225i
$712$			33.9787i			1.27341i
$713$	−6.92874	−	12.0009i	−0.259484	−	0.449439i
$714$	30.9980	+	38.7076i	1.16007	+	1.44859i
$715$	0.478541	−	0.828857i	0.0178964	−	0.0309975i
$716$	39.8674	+	23.0174i	1.48991	+	0.860202i
$717$	−0.949256	−	29.5666i	−0.0354506	−	1.10418i
$718$	23.3593	+	40.4595i	0.871760	+	1.50993i
$719$	19.8590			0.740618			0.370309	−	0.928909i	$-0.379252\pi$
$719$	19.8590			0.740618			0.370309	+	0.928909i	$0.379252\pi$
$720$	−1.00686	+	2.03523i	−0.0375234	+	0.0758487i
$721$	13.9067	+	18.5559i	0.517914	+	0.691059i
$722$	34.5798	−	19.9647i	1.28693	−	0.743008i
$723$	−31.9553	−	17.1063i	−1.18843	−	0.636192i
$724$	48.1295	+	27.7876i	1.78872	+	1.03272i
$725$	4.02738	+	2.32521i	0.149573	+	0.0863560i
$726$	16.3201	−	10.1342i	0.605695	−	0.376116i
$727$	−35.4470	+	20.4653i	−1.31466	+	0.759017i	−0.982864	−	0.184335i	$-0.940987\pi$
$727$	−35.4470	+	20.4653i	−1.31466	+	0.759017i	−0.331793	+	0.943352i	$0.607654\pi$
$728$	−1.96093	+	1.46962i	−0.0726768	+	0.0544676i
$729$	26.5009	−	5.16727i	0.981516	−	0.191380i
$730$	23.7867			0.880384
$731$	−25.0808	−	43.4412i	−0.927646	−	1.60673i
$732$	−3.28530	+	2.04006i	−0.121428	+	0.0754028i
$733$	22.0712	+	12.7428i	0.815217	+	0.470666i	0.848764	−	0.528772i	$-0.177347\pi$
$733$	22.0712	+	12.7428i	0.815217	+	0.470666i	−0.0335476	+	0.999437i	$0.510681\pi$
$734$	−33.2420	+	57.5768i	−1.22698	+	2.12520i
$735$	−8.65339	−	8.49229i	−0.319185	−	0.313243i
$736$	−6.91436	−	11.9760i	−0.254867	−	0.441442i
$737$		−	28.2693i		−	1.04131i
$738$	−5.76537	−	2.85221i	−0.212226	−	0.104991i
$739$	22.6712			0.833973			0.416986	−	0.908913i	$-0.363086\pi$
$739$	22.6712			0.833973			0.416986	+	0.908913i	$0.363086\pi$
$740$	−6.57175	−	11.3826i	−0.241582	−	0.418433i
$741$	−0.751634	+	0.0241318i	−0.0276120	+	0.000886502i
$742$	−6.90485	−	57.4815i	−0.253485	−	2.11021i
$743$	1.37485	+	0.793772i	0.0504385	+	0.0291207i	0.525007	−	0.851098i	$-0.324063\pi$
$743$	1.37485	+	0.793772i	0.0504385	+	0.0291207i	−0.474569	+	0.880218i	$0.657396\pi$
$744$	−26.7624	+	0.859225i	−0.981156	+	0.0315007i
$745$	−7.40128	+	4.27313i	−0.271162	+	0.156555i
$746$			24.3480i			0.891443i
$747$	35.7663	−	2.29898i	1.30862	−	0.0841152i
$748$		−	36.2649i		−	1.32597i
$749$	−4.22809	+	9.88857i	−0.154491	+	0.361321i
$750$	3.43490	+	1.83878i	0.125425	+	0.0671426i
$751$	−18.8024	+	32.5667i	−0.686109	+	1.18838i	0.286978	+	0.957937i	$0.407349\pi$
$751$	−18.8024	+	32.5667i	−0.686109	+	1.18838i	−0.973087	+	0.230439i	$0.925984\pi$
$752$	2.12910	−	3.68772i	0.0776404	−	0.134477i
$753$	−3.21947	−	5.18461i	−0.117324	−	0.188938i
$754$	−3.51943	+	2.03195i	−0.128170	+	0.0739991i
$755$	−15.7335			−0.572602
$756$	−31.0808	+	28.3473i	−1.13040	+	1.03098i
$757$	10.5426			0.383178			0.191589	−	0.981475i	$-0.438636\pi$
$757$	10.5426			0.383178			0.191589	+	0.981475i	$0.438636\pi$
$758$	59.7672	−	34.5066i	2.17084	−	1.25334i
$759$	4.81064	+	7.74702i	0.174615	+	0.281199i
$760$	−1.33225	+	2.30753i	−0.0483258	+	0.0837028i
$761$	9.26305	−	16.0441i	0.335785	−	0.581597i	−0.647850	−	0.761768i	$-0.724332\pi$
$761$	9.26305	−	16.0441i	0.335785	−	0.581597i	0.983635	+	0.180171i	$0.0576650\pi$
$762$	17.6373	+	9.44166i	0.638934	+	0.342035i
$763$	−27.6864	−	11.8380i	−1.00231	−	0.428563i
$764$			6.07183i			0.219671i
$765$	8.00300	+	12.0101i	0.289349	+	0.434225i
$766$		−	32.5845i		−	1.17733i
$767$	−4.16306	+	2.40355i	−0.150319	+	0.0867870i
$768$	−18.6881	+	0.599995i	−0.674348	+	0.0216505i
$769$	−28.4505	−	16.4259i	−1.02595	−	0.592333i	−0.110129	−	0.993917i	$-0.535126\pi$
$769$	−28.4505	−	16.4259i	−1.02595	−	0.592333i	−0.915822	+	0.401584i	$0.868460\pi$
$770$	1.74865	+	14.5572i	0.0630170	+	0.524604i
$771$	1.22583	−	0.0393561i	0.0441471	−	0.00141738i
$772$	−20.2271	−	35.0344i	−0.727989	−	1.26091i
$773$	27.5217			0.989887			0.494944	−	0.868925i	$-0.335189\pi$
$773$	27.5217			0.989887			0.494944	+	0.868925i	$0.335189\pi$
$774$	58.5546	−	39.0183i	2.10470	−	1.40248i
$775$		−	6.48426i		−	0.232921i
$776$	4.77245	+	8.26613i	0.171321	+	0.296737i
$777$	2.97357	+	19.4582i	0.106676	+	0.698060i
$778$	−20.9037	+	36.2063i	−0.749434	+	1.29806i
$779$	0.922561	+	0.532641i	0.0330542	+	0.0190838i
$780$	−1.74915	+	1.08616i	−0.0626296	+	0.0388909i
$781$	18.6538	+	32.3093i	0.667486	+	1.15612i
$782$	−23.1264			−0.826997
$783$	−19.6684	+	14.0380i	−0.702892	+	0.501676i
$784$	−1.48709	+	5.08526i	−0.0531102	+	0.181616i
$785$	17.2311	−	9.94836i	0.615003	−	0.355072i
$786$	−41.4042	+	25.7106i	−1.47684	+	0.917067i
$787$	8.80451	+	5.08329i	0.313847	+	0.181200i	0.648647	−	0.761090i	$-0.275335\pi$
$787$	8.80451	+	5.08329i	0.313847	+	0.181200i	−0.334800	+	0.942289i	$0.608669\pi$
$788$	−42.8365	−	24.7316i	−1.52599	−	0.881028i
$789$	−15.5770	−	8.33871i	−0.554556	−	0.296866i
$790$	28.6733	−	16.5545i	1.02015	−	0.588983i
$791$	13.9155	+	18.5676i	0.494779	+	0.660189i
$792$	17.5842	−	1.13027i	0.624826	−	0.0401624i
$793$	0.283471			0.0100664
$794$	−11.3061	−	19.5828i	−0.401240	−	0.694968i
$795$	−0.540679	−	16.8406i	−0.0191759	−	0.597274i
$796$	−72.4453	−	41.8263i	−2.56776	−	1.48249i
$797$	11.2524	−	19.4897i	0.398580	−	0.690362i	−0.594971	−	0.803747i	$-0.702836\pi$
$797$	11.2524	−	19.4897i	0.398580	−	0.690362i	0.993551	+	0.113386i	$0.0361696\pi$
$798$	8.99232	−	7.20128i	0.318325	−	0.254922i
$799$	−13.5325	−	23.4389i	−0.478744	−	0.829210i
$800$		−	6.47079i		−	0.228777i
$801$	18.9590	−	38.3232i	0.669883	−	1.35408i
$802$	−42.5293			−1.50176
$803$	13.0257	+	22.5612i	0.459668	+	0.796168i
$804$	−28.7018	+	53.6161i	−1.01224	+	1.89089i
$805$	5.61387	−	0.674355i	0.197863	−	0.0237679i
$806$	4.90729	+	2.83322i	0.172852	+	0.0997960i
$807$	−27.4972	−	44.2813i	−0.967947	−	1.55878i
$808$	−15.3395	+	8.85625i	−0.539641	+	0.311562i
$809$		−	24.8607i		−	0.874056i	−0.899448	−	0.437028i	$-0.856031\pi$
$809$		−	24.8607i		−	0.874056i	0.899448	−	0.437028i	$-0.143969\pi$
$810$	−16.0923	+	12.2837i	−0.565425	+	0.431605i
$811$		−	40.0552i		−	1.40653i	−0.710928	−	0.703264i	$-0.751725\pi$
$811$		−	40.0552i		−	1.40653i	0.710928	−	0.703264i	$-0.248275\pi$
$812$	14.8012	−	34.6167i	0.519420	−	1.21481i
$813$	−9.16728	+	5.69257i	−0.321510	+	0.199647i
$814$	11.9019	−	20.6146i	0.417160	−	0.722543i
$815$	0.110369	−	0.191165i	0.00386606	−	0.00669621i
$816$	2.97649	−	5.56019i	0.104198	−	0.194646i
$817$	−10.0920	+	5.82662i	−0.353074	+	0.203848i
$818$	−12.9301			−0.452091
$819$	3.03164	−	0.563387i	0.105934	−	0.0196863i
$820$	2.91662			0.101853
$821$	29.4435	−	16.9992i	1.02759	−	0.593277i	0.111294	−	0.993788i	$-0.464501\pi$
$821$	29.4435	−	16.9992i	1.02759	−	0.593277i	0.916292	+	0.400511i	$0.131167\pi$
$822$	27.5493	−	0.884490i	0.960891	−	0.0308501i
$823$	15.2864	−	26.4768i	0.532850	−	0.922923i	−0.466414	−	0.884566i	$-0.654454\pi$
$823$	15.2864	−	26.4768i	0.532850	−	0.922923i	0.999264	−	0.0383565i	$-0.0122122\pi$
$824$	−10.4478	+	18.0962i	−0.363968	+	0.630411i
$825$	0.136927	+	4.26487i	0.00476718	+	0.148484i
$826$	28.9516	−	67.7114i	1.00736	−	2.35598i
$827$			36.8463i			1.28127i	0.767845	+	0.640635i	$0.221329\pi$
$827$			36.8463i			1.28127i	−0.767845	+	0.640635i	$0.778671\pi$
$828$	−1.25839	−	19.5774i	−0.0437321	−	0.680361i
$829$		−	41.5579i		−	1.44337i	−0.692224	−	0.721683i	$-0.743369\pi$
$829$		−	41.5579i		−	1.44337i	0.692224	−	0.721683i	$-0.256631\pi$
$830$	−23.2728	+	13.4366i	−0.807811	+	0.466390i
$831$	−0.217192	+	0.405723i	−0.00753432	+	0.0140744i
$832$	4.38780	+	2.53330i	0.152120	+	0.0878262i
$833$	23.2654	+	24.3463i	0.806099	+	0.843551i
$834$	22.7496	+	36.6358i	0.787755	+	1.26860i
$835$	12.6948	+	21.9881i	0.439323	+	0.760930i
$836$	−8.42484			−0.291379
$837$	30.6636	+	13.9634i	1.05989	+	0.482646i
$838$		−	16.9433i		−	0.585297i
$839$	13.2465	+	22.9437i	0.457321	+	0.792103i	0.998818	−	0.0485991i	$-0.0154757\pi$
$839$	13.2465	+	22.9437i	0.457321	+	0.792103i	−0.541497	+	0.840703i	$0.682142\pi$
$840$	3.97068	−	10.1783i	0.137002	−	0.351185i
$841$	−3.68683	+	6.38578i	−0.127132	+	0.220199i
$842$	17.8292	+	10.2937i	0.614436	+	0.354745i
$843$	−21.2667	−	11.3845i	−0.732464	−	0.392104i
$844$	2.41154	+	4.17691i	0.0830086	+	0.143775i
$845$	−12.8491			−0.442022
$846$	31.5935	−	21.0525i	1.08621	−	0.723801i
$847$	10.4391	−	7.82360i	0.358693	−	0.268822i
$848$	−6.37652	+	3.68148i	−0.218971	+	0.126423i
$849$	−0.880837	−	27.4355i	−0.0302303	−	0.941584i
$850$	−9.37160	−	5.41070i	−0.321443	−	0.185585i
$851$	−7.94990	−	4.58987i	−0.272519	−	0.157339i
$852$	−2.57545	−	80.2177i	−0.0882335	−	2.74821i
$853$	2.66454	−	1.53837i	0.0912321	−	0.0526729i	−0.453690	−	0.891160i	$-0.649893\pi$
$853$	2.66454	−	1.53837i	0.0912321	−	0.0526729i	0.544922	+	0.838487i	$0.316559\pi$
$854$	−3.47498	+	2.60432i	−0.118911	+	0.0891181i
$855$	2.79011	−	1.85921i	0.0954198	−	0.0635837i
$856$	−9.69105			−0.331233
$857$	−0.835486	−	1.44710i	−0.0285397	−	0.0494321i	0.851403	−	0.524512i	$-0.175752\pi$
$857$	−0.835486	−	1.44710i	−0.0285397	−	0.0494321i	−0.879942	+	0.475080i	$0.842419\pi$
$858$	−3.28748	−	1.75986i	−0.112233	−	0.0600806i
$859$	30.7586	+	17.7585i	1.04947	+	0.605911i	0.922501	−	0.385996i	$-0.126142\pi$
$859$	30.7586	+	17.7585i	1.04947	+	0.605911i	0.126968	+	0.991907i	$0.459475\pi$
$860$	−15.9526	+	27.6308i	−0.543980	+	0.942202i
$861$	−4.06934	−	1.58750i	−0.138683	−	0.0541019i
$862$	−5.73023	−	9.92504i	−0.195172	−	0.338048i
$863$			29.1514i			0.992325i	0.868230	+	0.496162i	$0.165258\pi$
$863$			29.1514i			0.992325i	−0.868230	+	0.496162i	$0.834742\pi$
$864$	30.5999	+	13.9344i	1.04103	+	0.474059i
$865$	14.5208			0.493723
$866$	−40.3551	−	69.8970i	−1.37132	−	2.37520i
$867$	−5.61324	−	9.03953i	−0.190636	−	0.306998i
$868$	−52.1198	+	6.26079i	−1.76906	+	0.212505i
$869$	31.4033	+	18.1307i	1.06528	+	0.615042i
$870$	8.55107	−	15.9737i	0.289908	−	0.541559i
$871$	3.86062	−	2.22893i	0.130812	−	0.0755245i
$872$		−	27.1334i		−	0.918852i
$873$	−0.770426	−	11.9859i	−0.0260750	−	0.405661i
$874$			5.37259i			0.181730i
$875$	2.43271	+	1.04016i	0.0822405	+	0.0351639i
$876$	−1.79841	−	56.0151i	−0.0607625	−	1.89257i
$877$	−3.35894	+	5.81786i	−0.113423	+	0.196455i	−0.917148	−	0.398546i	$-0.869515\pi$
$877$	−3.35894	+	5.81786i	−0.113423	+	0.196455i	0.803725	+	0.595001i	$0.202848\pi$
$878$	−0.832745	+	1.44236i	−0.0281038	+	0.0486772i
$879$	−11.6705	+	0.374689i	−0.393635	+	0.0126379i
$880$	1.61485	−	0.932334i	0.0544366	−	0.0314290i
$881$	−1.09027			−0.0367322			−0.0183661	−	0.999831i	$-0.505846\pi$
$881$	−1.09027			−0.0367322			−0.0183661	+	0.999831i	$0.505846\pi$
$882$	−31.9879	+	34.7589i	−1.07709	+	1.17039i
$883$	−6.11832			−0.205898			−0.102949	−	0.994687i	$-0.532828\pi$
$883$	−6.11832			−0.205898			−0.102949	+	0.994687i	$0.532828\pi$
$884$	4.95255	−	2.85935i	0.166572	−	0.0961705i
$885$	10.1149	−	18.8950i	0.340008	−	0.635147i
$886$	−19.4077	+	33.6152i	−0.652016	+	1.12932i
$887$	−22.6970	+	39.3124i	−0.762091	+	1.31998i	0.179679	+	0.983725i	$0.442494\pi$
$887$	−22.6970	+	39.3124i	−0.762091	+	1.31998i	−0.941771	+	0.336256i	$0.890839\pi$
$888$	−15.0687	+	9.35715i	−0.505672	+	0.314005i
$889$	12.4913	+	5.34097i	0.418946	+	0.179130i
$890$			32.0590i			1.07462i
$891$	−20.4631	−	8.53659i	−0.685539	−	0.285986i
$892$		−	44.6909i		−	1.49636i
$893$	−5.44520	+	3.14379i	−0.182217	+	0.105203i
$894$	17.5653	+	28.2871i	0.587472	+	0.946061i
$895$	13.0291	+	7.52233i	0.435513	+	0.251444i
$896$	−43.0668	+	5.17331i	−1.43876	+	0.172828i
$897$	−0.678678	+	1.26779i	−0.0226604	+	0.0423304i
$898$	−23.0635	−	39.9472i	−0.769639	−	1.33305i
$899$	−30.1545			−1.00571
$900$	4.07043	−	8.22785i	0.135681	−	0.274262i
$901$			46.7986i			1.55909i
$902$	2.64110	+	4.57451i	0.0879389	+	0.152315i
$903$	37.2967	−	29.8682i	1.24116	−	0.993950i
$904$	−10.4544	+	18.1076i	−0.347709	+	0.602250i
$905$	15.7292	+	9.08127i	0.522857	+	0.301872i
$906$	1.96705	+	61.2680i	0.0653510	+	2.03549i
$907$	4.94352	+	8.56242i	0.164147	+	0.284311i	0.936352	−	0.351063i	$-0.114180\pi$
$907$	4.94352	+	8.56242i	0.164147	+	0.284311i	−0.772205	+	0.635373i	$0.780846\pi$
$908$	8.90923			0.295663
$909$	22.2422	−	1.42968i	0.737728	−	0.0474195i
$910$	−1.85014	+	1.38659i	−0.0613315	+	0.0459649i
$911$	−34.9512	+	20.1791i	−1.15798	+	0.668563i	−0.950820	−	0.309743i	$-0.899757\pi$
$911$	−34.9512	+	20.1791i	−1.15798	+	0.668563i	−0.207165	+	0.978306i	$0.566424\pi$
$912$	−1.29171	−	0.691481i	−0.0427729	−	0.0228972i
$913$	−25.4887	−	14.7159i	−0.843552	−	0.487025i
$914$	17.8331	+	10.2959i	0.589865	+	0.340559i
$915$	−1.07367	+	0.666712i	−0.0354944	+	0.0220408i
$916$	−49.6885	+	28.6877i	−1.64175	+	0.947867i
$917$	−26.4841	+	19.8485i	−0.874583	+	0.655456i
$918$	45.7679	−	32.6660i	1.51057	−	1.07814i
$919$	20.1949			0.666167			0.333084	−	0.942897i	$-0.391911\pi$
$919$	20.1949			0.666167			0.333084	+	0.942897i	$0.391911\pi$
$920$	2.54754	+	4.41248i	0.0839900	+	0.145475i
$921$	2.37536	−	1.47502i	0.0782706	−	0.0486034i
$922$	19.7713	+	11.4150i	0.651133	+	0.375932i
$923$	−2.94157	+	5.09495i	−0.0968230	+	0.167702i
$924$	34.1484	−	5.21849i	1.12340	−	0.171676i
$925$	−2.14771	−	3.71995i	−0.0706164	−	0.122311i
$926$			2.76118i			0.0907381i
$927$	21.8808	−	14.5804i	0.718658	−	0.478883i
$928$	−30.0919			−0.987814
$929$	2.47705	+	4.29038i	0.0812694	+	0.140763i	0.903795	−	0.427965i	$-0.140769\pi$
$929$	2.47705	+	4.29038i	0.0812694	+	0.140763i	−0.822526	+	0.568727i	$0.807436\pi$
$930$	−25.2503	+	0.810681i	−0.827991	+	0.0265833i
$931$	5.65600	−	5.40489i	0.185368	−	0.177138i
$932$	13.6257	+	7.86681i	0.446325	+	0.257686i
$933$	−27.2529	+	0.874975i	−0.892220	+	0.0286454i
$934$	−45.2585	+	26.1300i	−1.48090	+	0.854999i
$935$		−	11.8517i		−	0.387593i
$936$	1.54081	+	2.31228i	0.0503628	+	0.0755793i
$937$			32.1771i			1.05118i	0.850738	+	0.525590i	$0.176155\pi$
$937$			32.1771i			1.05118i	−0.850738	+	0.525590i	$0.823845\pi$
$938$	−26.8483	+	62.7923i	−0.876629	+	2.05024i
$939$	5.96860	+	3.19512i	0.194778	+	0.104269i
$940$	−8.60733	+	14.9083i	−0.280740	+	0.486256i
$941$	9.92726	−	17.1945i	0.323619	−	0.560525i	−0.657613	−	0.753356i	$-0.728434\pi$
$941$	9.92726	−	17.1945i	0.323619	−	0.560525i	0.981232	+	0.192831i	$0.0617669\pi$
$942$	−40.8942	−	65.8557i	−1.33240	−	2.14569i
$943$	1.76413	−	1.01852i	0.0574480	−	0.0331676i
$944$	−9.36558			−0.304824
$945$	−10.1575	+	9.26417i	−0.330424	+	0.301363i
$946$	−57.7825			−1.87867
$947$	−9.34865	+	5.39744i	−0.303790	+	0.175393i	−0.644144	−	0.764904i	$-0.722786\pi$
$947$	−9.34865	+	5.39744i	−0.303790	+	0.175393i	0.340354	+	0.940297i	$0.389453\pi$
$948$	−41.1520	−	66.2709i	−1.33655	−	2.15238i
$949$	−2.05406	+	3.55774i	−0.0666777	+	0.115489i
$950$	−1.25698	+	2.17716i	−0.0407819	+	0.0706363i
$951$	37.6218	+	20.1398i	1.21997	+	0.653077i
$952$	−11.9300	+	27.9017i	−0.386654	+	0.904298i
$953$			16.7368i			0.542157i	0.962557	+	0.271079i	$0.0873804\pi$
$953$			16.7368i			0.542157i	−0.962557	+	0.271079i	$0.912620\pi$
$954$	−65.5113	+	4.21092i	−2.12101	+	0.136334i
$955$			1.98434i			0.0642116i
$956$	45.2584	−	26.1299i	1.46376	−	0.845103i
$957$	19.8334	−	0.636766i	0.641122	−	0.0205837i
$958$	60.8476	+	35.1304i	1.96590	+	1.13501i
$959$	18.5841	−	2.23238i	0.600111	−	0.0720872i
$960$	−22.5773	+	0.724862i	−0.728680	+	0.0233948i
$961$	5.52279	+	9.56574i	0.178154	+	0.308572i
$962$	3.75368			0.121023
$963$	10.9301	+	5.40728i	0.352219	+	0.174247i
$964$		−	64.0329i		−	2.06236i
$965$	−6.61042	−	11.4496i	−0.212797	−	0.368575i
$966$	−3.32787	−	21.7767i	−0.107072	−	0.700653i
$967$	−25.6781	+	44.4758i	−0.825752	+	1.43024i	0.0755915	+	0.997139i	$0.475915\pi$
$967$	−25.6781	+	44.4758i	−0.825752	+	1.43024i	−0.901343	+	0.433105i	$0.857418\pi$
$968$	10.1805	+	5.87771i	0.327213	+	0.188917i
$969$	−7.91122	+	4.91260i	−0.254145	+	0.157816i
$970$	4.50282	+	7.79911i	0.144577	+	0.250414i
$971$	5.95642			0.191151			0.0955753	−	0.995422i	$-0.469531\pi$
$971$	5.95642			0.191151			0.0955753	+	0.995422i	$0.469531\pi$
$972$	30.1435	+	36.9669i	0.966853	+	1.18571i
$973$	17.5627	+	23.4341i	0.563033	+	0.751262i
$974$	−20.8760	+	12.0528i	−0.668911	+	0.386196i
$975$	−0.571640	+	0.354969i	−0.0183071	+	0.0113681i
$976$	0.478291	+	0.276141i	0.0153097	+	0.00883907i
$977$	−18.8015	−	10.8550i	−0.601512	−	0.347283i	0.168124	−	0.985766i	$-0.446229\pi$
$977$	−18.8015	−	10.8550i	−0.601512	−	0.347283i	−0.769636	+	0.638483i	$0.779562\pi$
$978$	−0.758214	−	0.405888i	−0.0242450	−	0.0129789i
$979$	−30.4074	+	17.5557i	−0.971824	+	0.561083i
$980$	6.01185	−	20.5582i	0.192041	−	0.656707i
$981$	−15.1395	+	30.6026i	−0.483367	+	0.977066i
$982$	−2.36972			−0.0756207
$983$	−6.84543	−	11.8566i	−0.218335	−	0.378168i	0.735964	−	0.677021i	$-0.236729\pi$
$983$	−6.84543	−	11.8566i	−0.218335	−	0.378168i	−0.954299	+	0.298853i	$0.903396\pi$
$984$	−0.126306	−	3.93405i	−0.00402648	−	0.125413i
$985$	−13.9994	−	8.08255i	−0.446058	−	0.257531i
$986$	−25.1620	+	43.5818i	−0.801320	+	1.38793i
$987$	20.1237	−	16.1155i	0.640543	−	0.512963i
$988$	−0.664269	−	1.15055i	−0.0211332	−	0.0366038i
$989$			22.2834i			0.708572i
$990$	16.5907	−	1.06641i	0.527287	−	0.0338928i
$991$	25.1854			0.800040			0.400020	−	0.916506i	$-0.369003\pi$
$991$	25.1854			0.800040			0.400020	+	0.916506i	$0.369003\pi$
$992$	20.9791	+	36.3369i	0.666088	+	1.15370i
$993$	−7.55027	+	14.1042i	−0.239601	+	0.447583i
$994$	−10.7489	−	89.4823i	−0.340934	−	2.83821i
$995$	−23.6759	−	13.6693i	−0.750575	−	0.433345i
$996$	33.4012	+	53.7891i	1.05836	+	1.70437i
$997$	24.4950	−	14.1422i	0.775766	−	0.447888i	−0.0591620	−	0.998248i	$-0.518843\pi$
$997$	24.4950	−	14.1422i	0.775766	−	0.447888i	0.834927	+	0.550360i	$0.185510\pi$
$998$			11.3400i			0.358961i
$999$	22.2163	−	2.14571i	0.702893	−	0.0678874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.i.41.10	✓	24
3.2	odd	2		945.2.bl.i.881.3		24
7.6	odd	2		315.2.bl.j.41.10	yes	24
9.2	odd	6		315.2.bl.j.146.10	yes	24
9.7	even	3		945.2.bl.j.251.3		24
21.20	even	2		945.2.bl.j.881.3		24
63.20	even	6	inner	315.2.bl.i.146.10	yes	24
63.34	odd	6		945.2.bl.i.251.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.10	✓	24	1.1	even	1	trivial
315.2.bl.i.146.10	yes	24	63.20	even	6	inner
315.2.bl.j.41.10	yes	24	7.6	odd	2
315.2.bl.j.146.10	yes	24	9.2	odd	6
945.2.bl.i.251.3		24	63.34	odd	6
945.2.bl.i.881.3		24	3.2	odd	2
945.2.bl.j.251.3		24	9.7	even	3
945.2.bl.j.881.3		24	21.20	even	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.94805 - 1.12471i) q^{2} +(-0.913713 - 1.47144i) q^{3} +(1.52994 - 2.64993i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-3.43490 - 1.83878i) q^{6} +(-2.43271 - 1.04016i) q^{7} -2.38412i q^{8} +(-1.33026 + 2.68894i) q^{9} +O(q^{10})\)	\(q+(1.94805 - 1.12471i) q^{2} +(-0.913713 - 1.47144i) q^{3} +(1.52994 - 2.64993i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-3.43490 - 1.83878i) q^{6} +(-2.43271 - 1.04016i) q^{7} -2.38412i q^{8} +(-1.33026 + 2.68894i) q^{9} -2.24942i q^{10} +(2.13353 - 1.23180i) q^{11} +(-5.29714 + 0.170069i) q^{12} +(0.336443 + 0.194245i) q^{13} +(-5.90892 + 0.709797i) q^{14} +(-1.73116 + 0.0555801i) q^{15} +(0.378445 + 0.655486i) q^{16} +4.81075 q^{17} +(0.432869 + 6.73436i) q^{18} -1.11761i q^{19} +(-1.52994 - 2.64993i) q^{20} +(0.692264 + 4.52999i) q^{21} +(2.77082 - 4.79920i) q^{22} +(-1.85078 - 1.06855i) q^{23} +(-3.50808 + 2.17840i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.873878 q^{26} +(5.17209 - 0.499535i) q^{27} +(-6.47826 + 4.85513i) q^{28} +(-4.02738 + 2.32521i) q^{29} +(-3.30988 + 2.05532i) q^{30} +(5.61553 + 3.24213i) q^{31} +(5.60387 + 3.23540i) q^{32} +(-3.76195 - 2.01385i) q^{33} +(9.37160 - 5.41070i) q^{34} +(-2.11716 + 1.58671i) q^{35} +(5.09031 + 7.63902i) q^{36} +4.29543 q^{37} +(-1.25698 - 2.17716i) q^{38} +(-0.0215924 - 0.672539i) q^{39} +(-2.06470 - 1.19206i) q^{40} +(-0.476591 + 0.825479i) q^{41} +(6.44348 + 8.04606i) q^{42} +(-5.21348 - 9.03002i) q^{43} -7.53829i q^{44} +(1.66357 + 2.49651i) q^{45} -4.80723 q^{46} +(-2.81296 - 4.87220i) q^{47} +(0.618716 - 1.15578i) q^{48} +(4.83613 + 5.06082i) q^{49} +(-1.94805 - 1.12471i) q^{50} +(-4.39565 - 7.07872i) q^{51} +(1.02947 - 0.594368i) q^{52} +9.72792i q^{53} +(9.51367 - 6.79021i) q^{54} -2.46359i q^{55} +(-2.47987 + 5.79985i) q^{56} +(-1.64449 + 1.02117i) q^{57} +(-5.23036 + 9.05925i) q^{58} +(-6.18688 + 10.7160i) q^{59} +(-2.50129 + 4.67249i) q^{60} +(0.631916 - 0.364837i) q^{61} +14.5858 q^{62} +(6.03306 - 5.15773i) q^{63} +13.0417 q^{64} +(0.336443 - 0.194245i) q^{65} +(-9.59347 + 0.308005i) q^{66} +(5.73742 - 9.93750i) q^{67} +(7.36016 - 12.7482i) q^{68} +(0.118780 + 3.69966i) q^{69} +(-2.33976 + 5.47217i) q^{70} +15.1436i q^{71} +(6.41075 + 3.17148i) q^{72} +10.5746i q^{73} +(8.36772 - 4.83111i) q^{74} +(-0.817446 + 1.52702i) q^{75} +(-2.96158 - 1.70987i) q^{76} +(-6.47152 + 0.777379i) q^{77} +(-0.798474 - 1.28586i) q^{78} +(7.35947 + 12.7470i) q^{79} +0.756890 q^{80} +(-5.46084 - 7.15397i) q^{81} +2.14410i q^{82} +(-5.97335 - 10.3461i) q^{83} +(13.0633 + 5.09616i) q^{84} +(2.40538 - 4.16623i) q^{85} +(-20.3123 - 11.7273i) q^{86} +(7.10126 + 3.80146i) q^{87} +(-2.93674 - 5.08659i) q^{88} -14.2521 q^{89} +(6.04856 + 2.99230i) q^{90} +(-0.616420 - 0.822497i) q^{91} +(-5.66317 + 3.26963i) q^{92} +(-0.360396 - 11.2253i) q^{93} +(-10.9596 - 6.32753i) q^{94} +(-0.967875 - 0.558803i) q^{95} +(-0.359648 - 11.2020i) q^{96} +(-3.46717 + 2.00177i) q^{97} +(15.1130 + 4.41951i) q^{98} +(0.474084 + 7.37555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9	\( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 q^{21} - 9 q^{22} + 9 q^{23} + 7 q^{24} - 12 q^{25} + 18 q^{26} + 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} + 42 q^{31} + 18 q^{32} - 13 q^{33} + 39 q^{34} + 9 q^{35} - 21 q^{36} + 12 q^{38} - 21 q^{39} + 6 q^{40} + 33 q^{41} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 q^{84} - 9 q^{85} - 102 q^{86} - 10 q^{87} - 9 q^{88} - 102 q^{89} + 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} + 156 q^{94} - 18 q^{95} + 42 q^{96} + 45 q^{97} - 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9 + 9 * q^11 + 18 * q^12 - 3 * q^13 + 9 * q^14 + 2 * q^15 - 18 * q^16 - 18 * q^17 + 2 * q^18 - 18 * q^20 + 4 * q^21 - 9 * q^22 + 9 * q^23 + 7 * q^24 - 12 * q^25 + 18 * q^26 + 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 + 42 * q^31 + 18 * q^32 - 13 * q^33 + 39 * q^34 + 9 * q^35 - 21 * q^36 + 12 * q^38 - 21 * q^39 + 6 * q^40 + 33 * q^41 + 26 * q^42 + 18 * q^43 - q^45 - 30 * q^46 + 17 * q^48 - 6 * q^50 - 12 * q^51 - 129 * q^52 - 52 * q^54 + 6 * q^56 + 6 * q^57 - 15 * q^58 - 12 * q^59 + 15 * q^60 + 15 * q^61 - 12 * q^62 - 83 * q^63 - 60 * q^64 - 3 * q^65 - 29 * q^66 - 15 * q^67 - 9 * q^68 - 61 * q^69 + 18 * q^70 + 61 * q^72 - 18 * q^74 + 7 * q^75 - 54 * q^76 - 57 * q^77 - 66 * q^78 + 21 * q^79 - 36 * q^80 + q^81 + 30 * q^83 - 42 * q^84 - 9 * q^85 - 102 * q^86 - 10 * q^87 - 9 * q^88 - 102 * q^89 + 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 + 156 * q^94 - 18 * q^95 + 42 * q^96 + 45 * q^97 - 3 * q^98 + 23 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more