LMFDB - Embedded newform 315.2.i.c.106.1

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:	8.0.142635249.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 3x^{6} + 3x^{5} - 11x^{4} + 6x^{3} + 12x^{2} - 24x + 16 $ x^8 - 3x^7 + 3x^6 + 3x^5 - 11x^4 + 6x^3 + 12x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			106.1
Root			$0.818235 + 1.15347i$ of defining polynomial
Character	$\chi$	$=$	315.106
Dual form			315.2.i.c.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.875400 + 1.51624i) q^{2} +(-1.16098 - 1.28535i) q^{3} +(-0.532651 - 0.922579i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.96522 - 0.635135i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.63647 q^{8} +(-0.304233 + 2.98453i) q^{9} +O(q^{10})$	\(q+(-0.875400 + 1.51624i) q^{2} +(-1.16098 - 1.28535i) q^{3} +(-0.532651 - 0.922579i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.96522 - 0.635135i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.63647 q^{8} +(-0.304233 + 2.98453i) q^{9} +1.75080 q^{10} +(3.05503 - 5.29147i) q^{11} +(-0.567434 + 1.75574i) q^{12} +(2.90805 + 5.03689i) q^{13} +(-0.875400 - 1.51624i) q^{14} +(-0.532651 + 1.64811i) q^{15} +(2.49787 - 4.32643i) q^{16} +4.73907 q^{17} +(-4.25894 - 3.07395i) q^{18} +3.68123 q^{19} +(-0.532651 + 0.922579i) q^{20} +(1.69363 - 0.362768i) q^{21} +(5.34875 + 9.26431i) q^{22} +(0.500000 + 0.866025i) q^{23} +(1.89991 + 2.10343i) q^{24} +(-0.500000 + 0.866025i) q^{25} -10.1828 q^{26} +(4.18937 - 3.07395i) q^{27} +1.06530 q^{28} +(0.839016 - 1.45322i) q^{29} +(-2.03265 - 2.25039i) q^{30} +(3.47922 + 6.02618i) q^{31} +(2.73680 + 4.74027i) q^{32} +(-10.3482 + 2.21654i) q^{33} +(-4.14858 + 7.18556i) q^{34} +1.00000 q^{35} +(2.91552 - 1.30904i) q^{36} -4.49413 q^{37} +(-3.22255 + 5.58163i) q^{38} +(3.09795 - 9.58561i) q^{39} +(0.818235 + 1.41722i) q^{40} +(1.98736 + 3.44220i) q^{41} +(-0.932566 + 2.88552i) q^{42} +(5.66350 - 9.80947i) q^{43} -6.50907 q^{44} +(2.73680 - 1.22879i) q^{45} -1.75080 q^{46} +(-2.08768 + 3.61598i) q^{47} +(-8.46095 + 1.81229i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.875400 - 1.51624i) q^{50} +(-5.50198 - 6.09135i) q^{51} +(3.09795 - 5.36581i) q^{52} -8.30597 q^{53} +(0.993464 + 9.04302i) q^{54} -6.11007 q^{55} +(0.818235 - 1.41722i) q^{56} +(-4.27385 - 4.73166i) q^{57} +(1.46895 + 2.54430i) q^{58} +(-0.418564 - 0.724974i) q^{59} +(1.80423 - 0.386458i) q^{60} +(4.62833 - 8.01651i) q^{61} -12.1828 q^{62} +(-2.43257 - 1.75574i) q^{63} +0.408295 q^{64} +(2.90805 - 5.03689i) q^{65} +(5.69804 - 17.6307i) q^{66} +(-2.25894 - 3.91259i) q^{67} +(-2.52427 - 4.37217i) q^{68} +(0.532651 - 1.64811i) q^{69} +(-0.875400 + 1.51624i) q^{70} +10.3667 q^{71} +(0.497868 - 4.88410i) q^{72} +12.2346 q^{73} +(3.93417 - 6.81418i) q^{74} +(1.69363 - 0.362768i) q^{75} +(-1.96081 - 3.39623i) q^{76} +(3.05503 + 5.29147i) q^{77} +(11.8221 + 13.0885i) q^{78} +(-4.41643 + 7.64948i) q^{79} -4.99574 q^{80} +(-8.81488 - 1.81599i) q^{81} -6.95892 q^{82} +(3.17072 - 5.49185i) q^{83} +(-1.23680 - 1.36928i) q^{84} +(-2.36954 - 4.10416i) q^{85} +(9.91566 + 17.1744i) q^{86} +(-2.84197 + 0.608737i) q^{87} +(-4.99947 + 8.65933i) q^{88} -9.66496 q^{89} +(-0.532651 + 5.22532i) q^{90} -5.81610 q^{91} +(0.532651 - 0.922579i) q^{92} +(3.70642 - 11.4683i) q^{93} +(-3.65512 - 6.33085i) q^{94} +(-1.84062 - 3.18804i) q^{95} +(2.91552 - 9.02112i) q^{96} +(4.08677 - 7.07849i) q^{97} +1.75080 q^{98} +(14.8631 + 10.7277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q + q^2 - q^3 - q^4 - 4 * q^5 + 8 * q^6 - 4 * q^7 - 6 * q^8 + 5 * q^9	\( 8 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{7} - 6 q^{8} + 5 q^{9} - 2 q^{10} + q^{11} - 17 q^{12} + 12 q^{13} + q^{14} - q^{15} + q^{16} + 10 q^{17} - 16 q^{18} - 18 q^{19} - q^{20} + 2 q^{21} + 17 q^{22} + 4 q^{23} + 6 q^{24} - 4 q^{25} - 2 q^{26} - 16 q^{27} + 2 q^{28} + 15 q^{29} - 13 q^{30} + 16 q^{31} + 2 q^{32} - 6 q^{33} + 11 q^{34} + 8 q^{35} - 14 q^{36} - 30 q^{37} - 24 q^{38} + 15 q^{39} + 3 q^{40} + 2 q^{41} + 5 q^{42} + 7 q^{43} + 6 q^{44} + 2 q^{45} + 2 q^{46} + 10 q^{47} - 14 q^{48} - 4 q^{49} + q^{50} + 37 q^{51} + 15 q^{52} - 22 q^{54} - 2 q^{55} + 3 q^{56} - 22 q^{57} - 17 q^{58} + 13 q^{59} + 7 q^{60} + 32 q^{61} - 18 q^{62} - 7 q^{63} - 30 q^{64} + 12 q^{65} + 45 q^{66} - 41 q^{68} + q^{69} + q^{70} + 26 q^{71} - 15 q^{72} - 4 q^{73} - 13 q^{74} + 2 q^{75} + 11 q^{76} + q^{77} + 51 q^{78} - 2 q^{80} - 31 q^{81} + 12 q^{82} - 17 q^{83} + 10 q^{84} - 5 q^{85} + 15 q^{86} + 11 q^{87} + 11 q^{88} - 34 q^{89} - q^{90} - 24 q^{91} + q^{92} + 5 q^{93} - 15 q^{94} + 9 q^{95} - 14 q^{96} + 4 q^{97} - 2 q^{98} + 48 q^{99}+O(q^{100}) \) 8 * q + q^2 - q^3 - q^4 - 4 * q^5 + 8 * q^6 - 4 * q^7 - 6 * q^8 + 5 * q^9 - 2 * q^10 + q^11 - 17 * q^12 + 12 * q^13 + q^14 - q^15 + q^16 + 10 * q^17 - 16 * q^18 - 18 * q^19 - q^20 + 2 * q^21 + 17 * q^22 + 4 * q^23 + 6 * q^24 - 4 * q^25 - 2 * q^26 - 16 * q^27 + 2 * q^28 + 15 * q^29 - 13 * q^30 + 16 * q^31 + 2 * q^32 - 6 * q^33 + 11 * q^34 + 8 * q^35 - 14 * q^36 - 30 * q^37 - 24 * q^38 + 15 * q^39 + 3 * q^40 + 2 * q^41 + 5 * q^42 + 7 * q^43 + 6 * q^44 + 2 * q^45 + 2 * q^46 + 10 * q^47 - 14 * q^48 - 4 * q^49 + q^50 + 37 * q^51 + 15 * q^52 - 22 * q^54 - 2 * q^55 + 3 * q^56 - 22 * q^57 - 17 * q^58 + 13 * q^59 + 7 * q^60 + 32 * q^61 - 18 * q^62 - 7 * q^63 - 30 * q^64 + 12 * q^65 + 45 * q^66 - 41 * q^68 + q^69 + q^70 + 26 * q^71 - 15 * q^72 - 4 * q^73 - 13 * q^74 + 2 * q^75 + 11 * q^76 + q^77 + 51 * q^78 - 2 * q^80 - 31 * q^81 + 12 * q^82 - 17 * q^83 + 10 * q^84 - 5 * q^85 + 15 * q^86 + 11 * q^87 + 11 * q^88 - 34 * q^89 - q^90 - 24 * q^91 + q^92 + 5 * q^93 - 15 * q^94 + 9 * q^95 - 14 * q^96 + 4 * q^97 - 2 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.875400	+	1.51624i	−0.619001	+	1.07214i	0.370667	+	0.928766i	$0.379129\pi$
$2$	−0.875400	+	1.51624i	−0.619001	+	1.07214i	−0.989668	+	0.143376i	$0.954204\pi$
$3$	−1.16098	−	1.28535i	−0.670294	−	0.742095i
$3$	−1.16098	−	1.28535i	−0.670294	−	0.742095i
$4$	−0.532651	−	0.922579i	−0.266326	−	0.461289i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	2.96522	−	0.635135i	1.21054	−	0.259293i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−1.63647			−0.578579
$9$	−0.304233	+	2.98453i	−0.101411	+	0.994845i
$10$	1.75080			0.553652
$11$	3.05503	−	5.29147i	0.921127	−	1.59544i	0.123453	−	0.992350i	$-0.460603\pi$
$11$	3.05503	−	5.29147i	0.921127	−	1.59544i	0.797674	−	0.603089i	$-0.206064\pi$
$12$	−0.567434	+	1.75574i	−0.163804	+	0.506839i
$13$	2.90805	+	5.03689i	0.806548	+	1.39698i	0.915241	+	0.402907i	$0.132000\pi$
$13$	2.90805	+	5.03689i	0.806548	+	1.39698i	−0.108693	+	0.994075i	$0.534666\pi$
$14$	−0.875400	−	1.51624i	−0.233961	−	0.405232i
$15$	−0.532651	+	1.64811i	−0.137530	+	0.425541i
$16$	2.49787	−	4.32643i	0.624467	−	1.08161i
$17$	4.73907			1.14939			0.574697	−	0.818367i	$-0.305120\pi$
$17$	4.73907			1.14939			0.574697	+	0.818367i	$0.305120\pi$
$18$	−4.25894	−	3.07395i	−1.00384	−	0.724537i
$19$	3.68123			0.844533			0.422266	−	0.906472i	$-0.361235\pi$
$19$	3.68123			0.844533			0.422266	+	0.906472i	$0.361235\pi$
$20$	−0.532651	+	0.922579i	−0.119104	+	0.206295i
$21$	1.69363	−	0.362768i	0.369581	−	0.0791625i
$22$	5.34875	+	9.26431i	1.14036	+	1.97516i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	0.913434	−	0.406986i	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$	1.89991	+	2.10343i	0.387818	+	0.429361i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−10.1828			−1.99702
$27$	4.18937	−	3.07395i	0.806245	−	0.591582i
$28$	1.06530			0.201323
$29$	0.839016	−	1.45322i	0.155801	−	0.269856i	−0.777549	−	0.628822i	$-0.783537\pi$
$29$	0.839016	−	1.45322i	0.155801	−	0.269856i	0.933351	+	0.358966i	$0.116871\pi$
$30$	−2.03265	−	2.25039i	−0.371110	−	0.410862i
$31$	3.47922	+	6.02618i	0.624886	+	1.08233i	0.988563	+	0.150809i	$0.0481879\pi$
$31$	3.47922	+	6.02618i	0.624886	+	1.08233i	−0.363677	+	0.931525i	$0.618479\pi$
$32$	2.73680	+	4.74027i	0.483802	+	0.837970i
$33$	−10.3482	+	2.21654i	−1.80139	+	0.385850i
$34$	−4.14858	+	7.18556i	−0.711476	+	1.23231i
$35$	1.00000			0.169031
$36$	2.91552	−	1.30904i	0.485920	−	0.218173i
$37$	−4.49413			−0.738831			−0.369416	−	0.929264i	$-0.620442\pi$
$37$	−4.49413			−0.738831			−0.369416	+	0.929264i	$0.620442\pi$
$38$	−3.22255	+	5.58163i	−0.522767	+	0.905459i
$39$	3.09795	−	9.58561i	0.496070	−	1.53493i
$40$	0.818235	+	1.41722i	0.129374	+	0.224083i
$41$	1.98736	+	3.44220i	0.310373	+	0.537581i	0.978443	−	0.206517i	$-0.0662128\pi$
$41$	1.98736	+	3.44220i	0.310373	+	0.537581i	−0.668070	+	0.744098i	$0.732879\pi$
$42$	−0.932566	+	2.88552i	−0.143898	+	0.445245i
$43$	5.66350	−	9.80947i	0.863676	−	1.49593i	−0.00468081	−	0.999989i	$-0.501490\pi$
$43$	5.66350	−	9.80947i	0.863676	−	1.49593i	0.868356	−	0.495941i	$-0.165177\pi$
$44$	−6.50907			−0.981279
$45$	2.73680	−	1.22879i	0.407978	−	0.183178i
$46$	−1.75080			−0.258141
$47$	−2.08768	+	3.61598i	−0.304520	+	0.527444i	−0.977154	−	0.212531i	$-0.931829\pi$
$47$	−2.08768	+	3.61598i	−0.304520	+	0.527444i	0.672634	+	0.739975i	$0.265163\pi$
$48$	−8.46095	+	1.81229i	−1.22123	+	0.261582i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.875400	−	1.51624i	−0.123800	−	0.214428i
$51$	−5.50198	−	6.09135i	−0.770432	−	0.852959i
$52$	3.09795	−	5.36581i	0.429609	−	0.744104i
$53$	−8.30597			−1.14091			−0.570457	−	0.821328i	$-0.693234\pi$
$53$	−8.30597			−1.14091			−0.570457	+	0.821328i	$0.693234\pi$
$54$	0.993464	+	9.04302i	0.135193	+	1.23060i
$55$	−6.11007			−0.823881
$56$	0.818235	−	1.41722i	0.109341	−	0.189385i
$57$	−4.27385	−	4.73166i	−0.566086	−	0.626724i
$58$	1.46895	+	2.54430i	0.192883	+	0.334082i
$59$	−0.418564	−	0.724974i	−0.0544924	−	0.0943836i	0.837492	−	0.546449i	$-0.184021\pi$
$59$	−0.418564	−	0.724974i	−0.0544924	−	0.0943836i	−0.891985	+	0.452065i	$0.850687\pi$
$60$	1.80423	−	0.386458i	0.232925	−	0.0498915i
$61$	4.62833	−	8.01651i	0.592597	−	1.02641i	−0.401284	−	0.915954i	$-0.631436\pi$
$61$	4.62833	−	8.01651i	0.592597	−	1.02641i	0.993881	−	0.110455i	$-0.0352308\pi$
$62$	−12.1828			−1.54722
$63$	−2.43257	−	1.75574i	−0.306474	−	0.221202i
$64$	0.408295			0.0510369
$65$	2.90805	−	5.03689i	0.360699	−	0.624750i
$66$	5.69804	−	17.6307i	0.701380	−	2.17019i
$67$	−2.25894	−	3.91259i	−0.275973	−	0.477999i	0.694407	−	0.719582i	$-0.255667\pi$
$67$	−2.25894	−	3.91259i	−0.275973	−	0.477999i	−0.970380	+	0.241583i	$0.922333\pi$
$68$	−2.52427	−	4.37217i	−0.306113	−	0.530203i
$69$	0.532651	−	1.64811i	0.0641237	−	0.198410i
$70$	−0.875400	+	1.51624i	−0.104630	+	0.181225i
$71$	10.3667			1.23030			0.615152	−	0.788408i	$-0.289094\pi$
$71$	10.3667			1.23030			0.615152	+	0.788408i	$0.289094\pi$
$72$	0.497868	−	4.88410i	0.0586743	−	0.575597i
$73$	12.2346			1.43195			0.715975	−	0.698126i	$-0.245983\pi$
$73$	12.2346			1.43195			0.715975	+	0.698126i	$0.245983\pi$
$74$	3.93417	−	6.81418i	0.457338	−	0.792132i
$75$	1.69363	−	0.362768i	0.195564	−	0.0418889i
$76$	−1.96081	−	3.39623i	−0.224921	−	0.389574i
$77$	3.05503	+	5.29147i	0.348153	+	0.603019i
$78$	11.8221	+	13.0885i	1.33859	+	1.48198i
$79$	−4.41643	+	7.64948i	−0.496887	+	0.860634i	−0.999994	−	0.00359042i	$-0.998857\pi$
$79$	−4.41643	+	7.64948i	−0.496887	+	0.860634i	0.503106	+	0.864225i	$0.332190\pi$
$80$	−4.99574			−0.558540
$81$	−8.81488	−	1.81599i	−0.979432	−	0.201776i
$82$	−6.95892			−0.768485
$83$	3.17072	−	5.49185i	0.348032	−	0.602809i	−0.637868	−	0.770146i	$-0.720183\pi$
$83$	3.17072	−	5.49185i	0.348032	−	0.602809i	0.985900	+	0.167337i	$0.0535168\pi$
$84$	−1.23680	−	1.36928i	−0.134946	−	0.149401i
$85$	−2.36954	−	4.10416i	−0.257012	−	0.445158i
$86$	9.91566	+	17.1744i	1.06923	+	1.85197i
$87$	−2.84197	+	0.608737i	−0.304692	+	0.0652634i
$88$	−4.99947	+	8.65933i	−0.532945	+	0.923088i
$89$	−9.66496			−1.02448			−0.512242	−	0.858841i	$-0.671185\pi$
$89$	−9.66496			−1.02448			−0.512242	+	0.858841i	$0.671185\pi$
$90$	−0.532651	+	5.22532i	−0.0561464	+	0.550797i
$91$	−5.81610			−0.609693
$92$	0.532651	−	0.922579i	0.0555327	−	0.0961855i
$93$	3.70642	−	11.4683i	0.384338	−	1.18921i
$94$	−3.65512	−	6.33085i	−0.376997	−	0.652977i
$95$	−1.84062	−	3.18804i	−0.188843	−	0.327086i
$96$	2.91552	−	9.02112i	0.297564	−	0.920714i
$97$	4.08677	−	7.07849i	0.414949	−	0.718712i	−0.580474	−	0.814278i	$-0.697133\pi$
$97$	4.08677	−	7.07849i	0.414949	−	0.718712i	0.995423	+	0.0955664i	$0.0304662\pi$
$98$	1.75080			0.176858
$99$	14.8631	+	10.7277i	1.49380	+	1.07817i
$100$	1.06530			0.106530
$101$	−6.06599	+	10.5066i	−0.603588	+	1.04545i	0.388684	+	0.921371i	$0.372930\pi$
$101$	−6.06599	+	10.5066i	−0.603588	+	1.04545i	−0.992273	+	0.124075i	$0.960404\pi$
$102$	14.0524	−	3.00995i	1.39139	−	0.298029i
$103$	0.697899	+	1.20880i	0.0687661	+	0.119106i	0.898358	−	0.439263i	$-0.144760\pi$
$103$	0.697899	+	1.20880i	0.0687661	+	0.119106i	−0.829592	+	0.558370i	$0.811427\pi$
$104$	−4.75894	−	8.24272i	−0.466652	−	0.808265i
$105$	−1.16098	−	1.28535i	−0.113300	−	0.125437i
$106$	7.27105	−	12.5938i	0.706227	−	1.22322i
$107$	−0.484840			−0.0468713			−0.0234356	−	0.999725i	$-0.507460\pi$
$107$	−0.484840			−0.0468713			−0.0234356	+	0.999725i	$0.507460\pi$
$108$	−5.06743	−	2.22768i	−0.487614	−	0.214359i
$109$	−10.7345			−1.02818			−0.514091	−	0.857736i	$-0.671870\pi$
$109$	−10.7345			−1.02818			−0.514091	+	0.857736i	$0.671870\pi$
$110$	5.34875	−	9.26431i	0.509984	−	0.883318i
$111$	5.21762	+	5.77652i	0.495234	+	0.548283i
$112$	2.49787	+	4.32643i	0.236026	+	0.408810i
$113$	0.559298	+	0.968732i	0.0526143	+	0.0911306i	0.891133	−	0.453742i	$-0.149911\pi$
$113$	0.559298	+	0.968732i	0.0526143	+	0.0911306i	−0.838519	+	0.544873i	$0.816578\pi$
$114$	10.9157	−	2.33808i	1.02234	−	0.218981i
$115$	0.500000	−	0.866025i	0.0466252	−	0.0807573i
$116$	−1.78761			−0.165976
$117$	−15.9175	+	7.14679i	−1.47157	+	0.660721i
$118$	1.46564			0.134923
$119$	−2.36954	+	4.10416i	−0.217215	+	0.376227i
$120$	0.871667	−	2.69709i	0.0795720	−	0.246209i
$121$	−13.1665	−	22.8050i	−1.19695	−	2.07318i
$122$	8.10329	+	14.0353i	0.733637	+	1.27070i
$123$	2.11713	−	6.55078i	0.190896	−	0.590664i
$124$	3.70642	−	6.41971i	0.332846	−	0.576507i
$125$	1.00000			0.0894427
$126$	4.79159	−	2.15137i	0.426869	−	0.191659i
$127$	−11.7567			−1.04324			−0.521620	−	0.853178i	$-0.674672\pi$
$127$	−11.7567			−1.04324			−0.521620	+	0.853178i	$0.674672\pi$
$128$	−5.83102	+	10.0996i	−0.515394	+	0.892689i
$129$	−19.1838	+	4.10907i	−1.68904	+	0.361784i
$130$	5.09142	+	8.81859i	0.446547	+	0.773442i
$131$	0.485084	+	0.840190i	0.0423820	+	0.0734077i	0.886438	−	0.462847i	$-0.153172\pi$
$131$	0.485084	+	0.840190i	0.0423820	+	0.0734077i	−0.844056	+	0.536255i	$0.819839\pi$
$132$	7.55692	+	8.36641i	0.657746	+	0.728202i
$133$	−1.84062	+	3.18804i	−0.159602	+	0.276438i
$134$	7.90990			0.683311
$135$	−4.75680	−	2.09113i	−0.409401	−	0.179975i
$136$	−7.75534			−0.665015
$137$	−5.38354	+	9.32456i	−0.459947	+	0.796651i	−0.998958	−	0.0456479i	$-0.985465\pi$
$137$	−5.38354	+	9.32456i	−0.459947	+	0.796651i	0.539011	+	0.842299i	$0.318798\pi$
$138$	2.03265	+	2.25039i	0.173031	+	0.191566i
$139$	5.41270	+	9.37507i	0.459099	+	0.795183i	0.998914	−	0.0466010i	$-0.0148389\pi$
$139$	5.41270	+	9.37507i	0.459099	+	0.795183i	−0.539814	+	0.841784i	$0.681506\pi$
$140$	−0.532651	−	0.922579i	−0.0450172	−	0.0779721i
$141$	7.07155	−	1.51469i	0.595532	−	0.127560i
$142$	−9.07504	+	15.7184i	−0.761560	+	1.31906i
$143$	35.5368			2.97173
$144$	12.1525	+	8.77121i	1.01270	+	0.730935i
$145$	−1.67803			−0.139353
$146$	−10.7102	+	18.5505i	−0.886378	+	1.53525i
$147$	−0.532651	+	1.64811i	−0.0439323	+	0.135934i
$148$	2.39381	+	4.14619i	0.196770	+	0.340815i
$149$	6.90752	+	11.9642i	0.565886	+	0.980143i	0.996967	+	0.0778300i	$0.0247991\pi$
$149$	6.90752	+	11.9642i	0.565886	+	0.980143i	−0.431081	+	0.902313i	$0.641868\pi$
$150$	−0.932566	+	2.88552i	−0.0761437	+	0.235602i
$151$	−5.42006	+	9.38782i	−0.441078	+	0.763970i	−0.997770	−	0.0667494i	$-0.978737\pi$
$151$	−5.42006	+	9.38782i	−0.441078	+	0.763970i	0.556692	+	0.830719i	$0.312071\pi$
$152$	−6.02423			−0.488629
$153$	−1.44178	+	14.1439i	−0.116561	+	1.14347i
$154$	−10.6975			−0.862030
$155$	3.47922	−	6.02618i	0.279458	−	0.484035i
$156$	−10.4936	+	2.24768i	−0.840161	+	0.179958i
$157$	5.53503	+	9.58695i	0.441743	+	0.765122i	0.997819	−	0.0660099i	$-0.0210269\pi$
$157$	5.53503	+	9.58695i	0.441743	+	0.765122i	−0.556076	+	0.831132i	$0.687694\pi$
$158$	−7.73229	−	13.3927i	−0.615148	−	1.06547i
$159$	9.64310	+	10.6761i	0.764748	+	0.846666i
$160$	2.73680	−	4.74027i	0.216363	−	0.374752i
$161$	−1.00000			−0.0788110
$162$	10.4700	−	11.7757i	0.822602	−	0.925190i
$163$	11.2066			0.877767			0.438883	−	0.898544i	$-0.355374\pi$
$163$	11.2066			0.877767			0.438883	+	0.898544i	$0.355374\pi$
$164$	2.11713	−	3.66698i	0.165320	−	0.286343i
$165$	7.09369	+	7.85355i	0.552243	+	0.611398i
$166$	5.55130	+	9.61513i	0.430864	+	0.746279i
$167$	−11.8200	−	20.4728i	−0.914657	−	1.58423i	−0.807403	−	0.590001i	$-0.799127\pi$
$167$	−11.8200	−	20.4728i	−0.914657	−	1.58423i	−0.107255	−	0.994232i	$-0.534206\pi$
$168$	−2.77158	+	0.593659i	−0.213832	+	0.0458018i
$169$	−10.4135	+	18.0368i	−0.801040	+	1.38744i
$170$	8.29717			0.636364
$171$	−1.11995	+	10.9868i	−0.0856449	+	0.840179i
$172$	−12.0667			−0.920075
$173$	1.54452	−	2.67519i	0.117428	−	0.203391i	−0.801320	−	0.598236i	$-0.795868\pi$
$173$	1.54452	−	2.67519i	0.117428	−	0.203391i	0.918748	+	0.394845i	$0.129202\pi$
$174$	1.56488	−	4.84200i	0.118633	−	0.367071i
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−15.2621	−	26.4348i	−1.15043	−	1.99260i
$177$	−0.445897	+	1.37968i	−0.0335157	+	0.103703i
$178$	8.46071	−	14.6544i	0.634157	−	1.09839i
$179$	22.9526			1.71556			0.857780	−	0.514017i	$-0.171843\pi$
$179$	22.9526			1.71556			0.857780	+	0.514017i	$0.171843\pi$
$180$	−2.59142	−	1.87039i	−0.193153	−	0.139411i
$181$	−4.10028			−0.304772			−0.152386	−	0.988321i	$-0.548696\pi$
$181$	−4.10028			−0.304772			−0.152386	+	0.988321i	$0.548696\pi$
$182$	5.09142	−	8.81859i	0.377401	−	0.653678i
$183$	−15.6774	+	3.35802i	−1.15891	+	0.248232i
$184$	−0.818235	−	1.41722i	−0.0603211	−	0.104479i
$185$	2.24707	+	3.89203i	0.165208	+	0.286148i
$186$	14.1441	+	15.6592i	1.03709	+	1.14819i
$187$	14.4780	−	25.0767i	1.05874	−	1.83379i
$188$	4.44803			0.324406
$189$	0.567434	+	5.16508i	0.0412748	+	0.375704i
$190$	6.44511			0.467577
$191$	4.36740	−	7.56456i	0.316014	−	0.547353i	−0.663638	−	0.748054i	$-0.730989\pi$
$191$	4.36740	−	7.56456i	0.316014	−	0.547353i	0.979653	+	0.200701i	$0.0643219\pi$
$192$	−0.474024	−	0.524801i	−0.0342097	−	0.0378742i
$193$	8.09142	+	14.0147i	0.582433	+	1.00880i	0.995190	+	0.0979624i	$0.0312325\pi$
$193$	8.09142	+	14.0147i	0.582433	+	1.00880i	−0.412757	+	0.910841i	$0.635434\pi$
$194$	7.15512	+	12.3930i	0.513708	+	0.889768i
$195$	−9.85035	+	2.10990i	−0.705399	+	0.151093i
$196$	−0.532651	+	0.922579i	−0.0380465	+	0.0658985i
$197$	−0.418652			−0.0298278			−0.0149139	−	0.999889i	$-0.504747\pi$
$197$	−0.418652			−0.0298278			−0.0149139	+	0.999889i	$0.504747\pi$
$198$	−29.2769	+	13.1450i	−2.08062	+	0.934176i
$199$	−7.48667			−0.530716			−0.265358	−	0.964150i	$-0.585490\pi$
$199$	−7.48667			−0.530716			−0.265358	+	0.964150i	$0.585490\pi$
$200$	0.818235	−	1.41722i	0.0578579	−	0.100213i
$201$	−2.40645	+	7.44598i	−0.169738	+	0.525199i
$202$	−10.6203	−	18.3950i	−0.747244	−	1.29426i
$203$	0.839016	+	1.45322i	0.0588874	+	0.101996i
$204$	−2.68911	+	8.32058i	−0.188275	+	0.582557i
$205$	1.98736	−	3.44220i	0.138803	−	0.240414i
$206$	−2.44376			−0.170265
$207$	−2.73680	+	1.22879i	−0.190221	+	0.0854071i
$208$	29.0557			2.01465
$209$	11.2463	−	19.4791i	0.777922	−	1.34740i
$210$	2.96522	−	0.635135i	0.204619	−	0.0438284i
$211$	−3.12969	−	5.42078i	−0.215457	−	0.373182i	0.737957	−	0.674848i	$-0.235791\pi$
$211$	−3.12969	−	5.42078i	−0.215457	−	0.373182i	−0.953414	+	0.301666i	$0.902457\pi$
$212$	4.42419	+	7.66291i	0.303854	+	0.526291i
$213$	−12.0356	−	13.3248i	−0.824666	−	0.913003i
$214$	0.424429	−	0.735133i	0.0290134	−	0.0502526i
$215$	−11.3270			−0.772495
$216$	−6.85578	+	5.03043i	−0.466477	+	0.342277i
$217$	−6.95844			−0.472369
$218$	9.39701	−	16.2761i	0.636446	−	1.10236i
$219$	−14.2041	−	15.7257i	−0.959827	−	1.06264i
$220$	3.25453	+	5.63702i	0.219421	+	0.380048i
$221$	13.7815	+	23.8702i	0.927041	+	1.60568i
$222$	−13.3261	+	2.85438i	−0.894388	+	0.191573i
$223$	11.6207	−	20.1277i	0.778181	−	1.34785i	−0.154808	−	0.987945i	$-0.549476\pi$
$223$	11.6207	−	20.1277i	0.778181	−	1.34785i	0.932989	−	0.359904i	$-0.117191\pi$
$224$	−5.47360			−0.365720
$225$	−2.43257	−	1.75574i	−0.162171	−	0.117049i
$226$	−1.95844			−0.130273
$227$	−9.88422	+	17.1200i	−0.656039	+	1.13629i	0.325593	+	0.945510i	$0.394436\pi$
$227$	−9.88422	+	17.1200i	−0.656039	+	1.13629i	−0.981632	+	0.190783i	$0.938897\pi$
$228$	−2.08886	+	6.46329i	−0.138338	+	0.428042i
$229$	0.00517872	+	0.00896980i	0.000342219	+	0.000592741i	0.866196	−	0.499704i	$-0.166558\pi$
$229$	0.00517872	+	0.00896980i	0.000342219	+	0.000592741i	−0.865854	+	0.500296i	$0.833224\pi$
$230$	0.875400	+	1.51624i	0.0577222	+	0.0999777i
$231$	3.25453	−	10.0701i	0.214133	−	0.662563i
$232$	−1.37302	+	2.37815i	−0.0901435	+	0.156133i
$233$	−6.48609			−0.424918			−0.212459	−	0.977170i	$-0.568147\pi$
$233$	−6.48609			−0.424918			−0.212459	+	0.977170i	$0.568147\pi$
$234$	3.09795	−	30.3910i	0.202520	−	1.98672i
$235$	4.17537			0.272371
$236$	−0.445897	+	0.772316i	−0.0290254	+	0.0502735i
$237$	14.9596	−	3.20428i	0.971733	−	0.208140i
$238$	−4.14858	−	7.18556i	−0.268913	−	0.465770i
$239$	−7.89928	−	13.6820i	−0.510962	−	0.885012i	−0.999919	−	0.0127043i	$-0.995956\pi$
$239$	−7.89928	−	13.6820i	−0.510962	−	0.885012i	0.488957	−	0.872308i	$-0.337377\pi$
$240$	5.79997	+	6.42125i	0.374386	+	0.414490i
$241$	3.20899	−	5.55814i	0.206709	−	0.358031i	−0.743967	−	0.668217i	$-0.767058\pi$
$241$	3.20899	−	5.55814i	0.206709	−	0.358031i	0.950676	+	0.310186i	$0.100391\pi$
$242$	46.1037			2.96366
$243$	7.89977	+	13.4385i	0.506770	+	0.862081i
$244$	−9.86115			−0.631295
$245$	−0.500000	+	0.866025i	−0.0319438	+	0.0553283i
$246$	8.07920	+	8.94463i	0.515111	+	0.570289i
$247$	10.7052	+	18.5420i	0.681157	+	1.17980i
$248$	−5.69363	−	9.86166i	−0.361546	−	0.626216i
$249$	−10.7401	+	2.30047i	−0.680625	+	0.145787i
$250$	−0.875400	+	1.51624i	−0.0553652	+	0.0958953i
$251$	4.15861			0.262489			0.131245	−	0.991350i	$-0.458103\pi$
$251$	4.15861			0.262489			0.131245	+	0.991350i	$0.458103\pi$
$252$	−0.324100	+	3.17943i	−0.0204164	+	0.200285i
$253$	6.11007			0.384137
$254$	10.2918	−	17.8260i	0.645767	−	1.11850i
$255$	−2.52427	+	7.81053i	−0.158076	+	0.489114i
$256$	−9.80066	−	16.9752i	−0.612541	−	1.06095i
$257$	−5.87404	−	10.1741i	−0.366413	−	0.634645i	0.622589	−	0.782549i	$-0.286081\pi$
$257$	−5.87404	−	10.1741i	−0.366413	−	0.634645i	−0.989002	+	0.147903i	$0.952748\pi$
$258$	10.5632	−	32.6843i	0.657634	−	2.03483i
$259$	2.24707	−	3.89203i	0.139626	−	0.241839i
$260$	−6.19591			−0.384254
$261$	4.08192	+	2.94619i	0.252665	+	0.182365i
$262$	−1.69857			−0.104938
$263$	6.19926	−	10.7374i	0.382263	−	0.662098i	−0.609123	−	0.793076i	$-0.708478\pi$
$263$	6.19926	−	10.7374i	0.382263	−	0.662098i	0.991385	+	0.130978i	$0.0418117\pi$
$264$	16.9345	−	3.62730i	1.04225	−	0.223245i
$265$	4.15299	+	7.19318i	0.255116	+	0.441874i
$266$	−3.22255	−	5.58163i	−0.197587	−	0.342231i
$267$	11.2209	+	12.4228i	0.686706	+	0.760265i
$268$	−2.40645	+	4.16809i	−0.146997	+	0.254607i
$269$	−18.8491			−1.14925			−0.574626	−	0.818416i	$-0.694852\pi$
$269$	−18.8491			−1.14925			−0.574626	+	0.818416i	$0.694852\pi$
$270$	7.33475	−	5.38187i	0.446379	−	0.327530i
$271$	−21.0866			−1.28092			−0.640461	−	0.767991i	$-0.721257\pi$
$271$	−21.0866			−1.28092			−0.640461	+	0.767991i	$0.721257\pi$
$272$	11.8376	−	20.5033i	0.717758	−	1.24319i
$273$	6.75240	+	7.47571i	0.408674	+	0.452450i
$274$	−9.42550	−	16.3254i	−0.569415	−	0.986256i
$275$	3.05503	+	5.29147i	0.184225	+	0.319088i
$276$	−1.80423	+	0.386458i	−0.108602	+	0.0232620i
$277$	9.24867	−	16.0192i	0.555699	−	0.962498i	−0.442150	−	0.896941i	$-0.645784\pi$
$277$	9.24867	−	16.0192i	0.555699	−	0.962498i	0.997849	−	0.0655572i	$-0.0208825\pi$
$278$	−18.9531			−1.13673
$279$	−19.0438	+	8.55048i	−1.14012	+	0.511904i
$280$	−1.63647			−0.0977978
$281$	−8.81421	+	15.2667i	−0.525812	+	0.910733i	0.473736	+	0.880667i	$0.342905\pi$
$281$	−8.81421	+	15.2667i	−0.525812	+	0.910733i	−0.999548	+	0.0300661i	$0.990428\pi$
$282$	−3.89381	+	12.0481i	−0.231873	+	0.717455i
$283$	1.89594	+	3.28386i	0.112702	+	0.195205i	0.916859	−	0.399212i	$-0.130716\pi$
$283$	1.89594	+	3.28386i	0.112702	+	0.195205i	−0.804157	+	0.594417i	$0.797383\pi$
$284$	−5.52185	−	9.56413i	−0.327662	−	0.567526i
$285$	−1.96081	+	6.06710i	−0.116149	+	0.359384i
$286$	−31.1089	+	53.8822i	−1.83951	+	3.18612i
$287$	−3.97471			−0.234620
$288$	−14.9801	+	6.72592i	−0.882713	+	0.396329i
$289$	5.45878			0.321105
$290$	1.46895	−	2.54430i	0.0862597	−	0.149406i
$291$	−13.8430	+	2.96510i	−0.811491	+	0.173817i
$292$	−6.51676	−	11.2874i	−0.381365	−	0.660543i
$293$	4.03730	+	6.99281i	0.235861	+	0.408524i	0.959523	−	0.281631i	$-0.0908755\pi$
$293$	4.03730	+	6.99281i	0.235861	+	0.408524i	−0.723661	+	0.690155i	$0.757542\pi$
$294$	−2.03265	−	2.25039i	−0.118547	−	0.131245i
$295$	−0.418564	+	0.724974i	−0.0243697	+	0.0422096i
$296$	7.35451			0.427472
$297$	−3.46706	−	31.5590i	−0.201179	−	1.83124i
$298$	−24.1874			−1.40114
$299$	−2.90805	+	5.03689i	−0.168177	+	0.291291i
$300$	−1.23680	−	1.36928i	−0.0714066	−	0.0790556i
$301$	5.66350	+	9.80947i	0.326439	+	0.565408i
$302$	−9.48944	−	16.4362i	−0.546056	−	0.945797i
$303$	20.5471	−	4.40109i	1.18040	−	0.252836i
$304$	9.19524	−	15.9266i	0.527383	−	0.913454i
$305$	−9.25667			−0.530035
$306$	−20.1834	−	14.5677i	−1.15381	−	0.832778i
$307$	−1.03255			−0.0589305			−0.0294653	−	0.999566i	$-0.509380\pi$
$307$	−1.03255			−0.0589305			−0.0294653	+	0.999566i	$0.509380\pi$
$308$	3.25453	−	5.63702i	0.185444	−	0.321199i
$309$	0.743474	−	2.30044i	0.0422947	−	0.130867i
$310$	6.09142	+	10.5506i	0.345969	+	0.599236i
$311$	−4.14471	−	7.17885i	−0.235025	−	0.407075i	0.724255	−	0.689532i	$-0.242184\pi$
$311$	−4.14471	−	7.17885i	−0.235025	−	0.407075i	−0.959280	+	0.282457i	$0.908851\pi$
$312$	−5.06971	+	15.6866i	−0.287016	+	0.888076i
$313$	−10.0346	+	17.3805i	−0.567191	+	0.982404i	0.429651	+	0.902995i	$0.358637\pi$
$313$	−10.0346	+	17.3805i	−0.567191	+	0.982404i	−0.996842	+	0.0794088i	$0.974697\pi$
$314$	−19.3815			−1.09376
$315$	−0.304233	+	2.98453i	−0.0171416	+	0.168159i
$316$	9.40967			0.529335
$317$	−10.3821	+	17.9823i	−0.583116	+	1.00999i	0.411991	+	0.911188i	$0.364833\pi$
$317$	−10.3821	+	17.9823i	−0.583116	+	1.00999i	−0.995107	+	0.0987992i	$0.968500\pi$
$318$	−24.6290	+	5.27541i	−1.38113	+	0.295830i
$319$	−5.12644	−	8.87926i	−0.287026	−	0.497143i
$320$	−0.204148	−	0.353594i	−0.0114122	−	0.0197665i
$321$	0.562891	+	0.623188i	0.0314175	+	0.0347829i
$322$	0.875400	−	1.51624i	0.0487841	−	0.0844966i
$323$	17.4456			0.970701
$324$	3.01987	+	9.09971i	0.167770	+	0.505540i
$325$	−5.81610			−0.322619
$326$	−9.81024	+	16.9918i	−0.543339	+	0.941090i
$327$	12.4626	+	13.7976i	0.689184	+	0.763008i
$328$	−3.25225	−	5.63306i	−0.179575	−	0.311033i
$329$	−2.08768	−	3.61598i	−0.115098	−	0.199355i
$330$	−18.1177	+	3.88071i	−0.997345	+	0.213626i
$331$	5.58158	−	9.66757i	0.306791	−	0.531378i	−0.670867	−	0.741577i	$-0.734078\pi$
$331$	5.58158	−	9.66757i	0.306791	−	0.531378i	0.977659	+	0.210200i	$0.0674114\pi$
$332$	−6.75555			−0.370759
$333$	1.36726	−	13.4129i	0.0749256	−	0.735022i
$334$	41.3888			2.26470
$335$	−2.25894	+	3.91259i	−0.123419	+	0.213768i
$336$	2.66098	−	8.23355i	0.145169	−	0.449177i
$337$	−3.03624	−	5.25893i	−0.165395	−	0.286472i	0.771401	−	0.636350i	$-0.219556\pi$
$337$	−3.03624	−	5.25893i	−0.165395	−	0.286472i	−0.936795	+	0.349878i	$0.886223\pi$
$338$	−18.2320	−	31.5788i	−0.991690	−	1.71766i
$339$	0.595821	−	1.84357i	0.0323606	−	0.100129i
$340$	−2.52427	+	4.37217i	−0.136898	+	0.237114i
$341$	42.5165			2.30240
$342$	−15.6781	−	11.3159i	−0.847777	−	0.611896i
$343$	1.00000			0.0539949
$344$	−9.26814	+	16.0529i	−0.499705	+	0.865514i
$345$	−1.69363	+	0.362768i	−0.0911822	+	0.0195308i
$346$	2.70415	+	4.68372i	0.145376	+	0.251798i
$347$	−9.75254	−	16.8919i	−0.523544	−	0.906804i	−0.999624	−	0.0274029i	$-0.991276\pi$
$347$	−9.75254	−	16.8919i	−0.523544	−	0.906804i	0.476081	−	0.879402i	$-0.342057\pi$
$348$	2.07539	+	2.29770i	0.111252	+	0.123170i
$349$	6.29410	−	10.9017i	0.336916	−	0.583555i	−0.646935	−	0.762545i	$-0.723950\pi$
$349$	6.29410	−	10.9017i	0.336916	−	0.583555i	0.983851	+	0.178990i	$0.0572830\pi$
$350$	1.75080			0.0935842
$351$	27.6661	+	12.1622i	1.47671	+	0.649170i
$352$	33.4440			1.78257
$353$	−8.20857	+	14.2177i	−0.436898	+	0.756729i	−0.997448	−	0.0713908i	$-0.977256\pi$
$353$	−8.20857	+	14.2177i	−0.436898	+	0.756729i	0.560550	+	0.828120i	$0.310590\pi$
$354$	−1.70159	−	1.88386i	−0.0904384	−	0.100126i
$355$	−5.18337	−	8.97785i	−0.275105	−	0.476495i
$356$	5.14805	+	8.91669i	0.272846	+	0.472583i
$357$	8.02625	−	1.71918i	0.424794	−	0.0909888i
$358$	−20.0927	+	34.8016i	−1.06193	+	1.83932i
$359$	−13.2324			−0.698381			−0.349191	−	0.937052i	$-0.613543\pi$
$359$	−13.2324			−0.698381			−0.349191	+	0.937052i	$0.613543\pi$
$360$	−4.47869	+	2.01088i	−0.236048	+	0.105983i
$361$	−5.44852			−0.286764
$362$	3.58939	−	6.21701i	0.188654	−	0.326759i
$363$	−14.0263	+	43.3997i	−0.736187	+	2.27789i
$364$	3.09795	+	5.36581i	0.162377	+	0.281245i
$365$	−6.11729	−	10.5955i	−0.320194	−	0.554591i
$366$	8.63245	−	26.7103i	0.451225	−	1.39617i
$367$	10.1362	−	17.5564i	0.529104	−	0.916436i	−0.470320	−	0.882496i	$-0.655861\pi$
$367$	10.1362	−	17.5564i	0.529104	−	0.916436i	0.999424	−	0.0339395i	$-0.0108053\pi$
$368$	4.99574			0.260421
$369$	−10.8780	+	4.88410i	−0.566285	+	0.254256i
$370$	−7.86833			−0.409055
$371$	4.15299	−	7.19318i	0.215612	−	0.373451i
$372$	−12.5546	+	2.68914i	−0.650928	+	0.139425i
$373$	−15.1254	−	26.1979i	−0.783162	−	1.35648i	−0.930091	−	0.367329i	$-0.880272\pi$
$373$	−15.1254	−	26.1979i	−0.783162	−	1.35648i	0.146929	−	0.989147i	$-0.453061\pi$
$374$	25.3481	+	43.9042i	1.31072	+	2.27023i
$375$	−1.16098	−	1.28535i	−0.0599529	−	0.0663750i
$376$	3.41643	−	5.91743i	0.176189	−	0.305168i
$377$	9.75961			0.502645
$378$	−8.32822	−	3.66114i	−0.428357	−	0.188309i
$379$	−0.698602			−0.0358848			−0.0179424	−	0.999839i	$-0.505712\pi$
$379$	−0.698602			−0.0358848			−0.0179424	+	0.999839i	$0.505712\pi$
$380$	−1.96081	+	3.39623i	−0.100588	+	0.174223i
$381$	13.6494	+	15.1115i	0.699278	+	0.774183i
$382$	7.64645	+	13.2440i	0.391226	+	0.677624i
$383$	−3.04757	−	5.27854i	−0.155723	−	0.269721i	0.777599	−	0.628761i	$-0.216438\pi$
$383$	−3.04757	−	5.27854i	−0.155723	−	0.269721i	−0.933322	+	0.359040i	$0.883104\pi$
$384$	19.7512	−	4.23062i	1.00793	−	0.215893i
$385$	3.05503	−	5.29147i	0.155699	−	0.269678i
$386$	−28.3329			−1.44211
$387$	27.5537	+	19.8873i	1.40063	+	1.01093i
$388$	−8.70729			−0.442046
$389$	−6.77943	+	11.7423i	−0.343731	+	0.595359i	−0.985122	−	0.171855i	$-0.945024\pi$
$389$	−6.77943	+	11.7423i	−0.343731	+	0.595359i	0.641392	+	0.767214i	$0.278357\pi$
$390$	5.42390	−	16.7825i	0.274650	−	0.849814i
$391$	2.36954	+	4.10416i	0.119833	+	0.207556i
$392$	0.818235	+	1.41722i	0.0413271	+	0.0715806i
$393$	0.516761	−	1.59895i	0.0260671	−	0.0806562i
$394$	0.366488	−	0.634777i	0.0184634	−	0.0319796i
$395$	8.83286			0.444430
$396$	1.98027	−	19.4265i	0.0995124	−	0.976220i
$397$	−16.4109			−0.823639			−0.411819	−	0.911265i	$-0.635107\pi$
$397$	−16.4109			−0.823639			−0.411819	+	0.911265i	$0.635107\pi$
$398$	6.55383	−	11.3516i	0.328514	−	0.569003i
$399$	6.23467	−	1.33543i	0.312124	−	0.0668553i
$400$	2.49787	+	4.32643i	0.124893	+	0.216322i
$401$	1.75042	+	3.03181i	0.0874117	+	0.151401i	0.906416	−	0.422385i	$-0.138807\pi$
$401$	1.75042	+	3.03181i	0.0874117	+	0.151401i	−0.819005	+	0.573787i	$0.805474\pi$
$402$	−9.18326	−	10.1670i	−0.458019	−	0.507082i
$403$	−20.2355	+	35.0489i	−1.00800	+	1.74591i
$404$	12.9242			0.643004
$405$	2.83475	+	8.54191i	0.140860	+	0.424451i
$406$	−2.93790			−0.145806
$407$	−13.7297	+	23.7806i	−0.680558	+	1.17876i
$408$	9.00383	+	9.96831i	0.445756	+	0.493505i
$409$	−3.37859	−	5.85188i	−0.167060	−	0.289357i	0.770325	−	0.637652i	$-0.220094\pi$
$409$	−3.37859	−	5.85188i	−0.167060	−	0.289357i	−0.937385	+	0.348295i	$0.886761\pi$
$410$	3.47946	+	6.02661i	0.171838	+	0.297633i
$411$	18.2355	−	3.90595i	0.899490	−	0.192666i
$412$	0.743474	−	1.28773i	0.0366283	−	0.0634421i
$413$	0.837128			0.0411924
$414$	0.532651	−	5.22532i	0.0261784	−	0.256811i
$415$	−6.34144			−0.311289
$416$	−15.9175	+	27.5699i	−0.780420	+	1.35173i
$417$	5.76616	−	17.8415i	0.282370	−	0.873702i
$418$	19.6900	+	34.1041i	0.963070	+	1.66809i
$419$	15.1142	+	26.1785i	0.738376	+	1.27890i	0.953226	+	0.302258i	$0.0977404\pi$
$419$	15.1142	+	26.1785i	0.738376	+	1.27890i	−0.214850	+	0.976647i	$0.568926\pi$
$420$	−0.567434	+	1.75574i	−0.0276880	+	0.0856714i
$421$	0.650611	−	1.12689i	0.0317088	−	0.0549213i	−0.849736	−	0.527209i	$-0.823238\pi$
$421$	0.650611	−	1.12689i	0.0317088	−	0.0549213i	0.881444	+	0.472288i	$0.156572\pi$
$422$	10.9589			0.533472
$423$	−10.1569	−	7.33086i	−0.493843	−	0.356439i
$424$	13.5925			0.660109
$425$	−2.36954	+	4.10416i	−0.114939	+	0.199081i
$426$	30.7396	−	6.58427i	1.48934	−	0.319009i
$427$	4.62833	+	8.01651i	0.223981	+	0.387946i
$428$	0.258251	+	0.447303i	0.0124830	+	0.0216212i
$429$	−41.2576	−	45.6771i	−1.99194	−	2.20531i
$430$	9.91566	−	17.1744i	0.478175	−	0.828224i
$431$	−6.84759			−0.329837			−0.164918	−	0.986307i	$-0.552736\pi$
$431$	−6.84759			−0.329837			−0.164918	+	0.986307i	$0.552736\pi$
$432$	−2.83475	−	25.8034i	−0.136387	−	1.24146i
$433$	−5.73858			−0.275779			−0.137889	−	0.990448i	$-0.544032\pi$
$433$	−5.73858			−0.275779			−0.137889	+	0.990448i	$0.544032\pi$
$434$	6.09142	−	10.5506i	0.292397	−	0.506447i
$435$	1.94817	+	2.15685i	0.0934075	+	0.103413i
$436$	5.71776	+	9.90345i	0.273831	+	0.474289i
$437$	1.84062	+	3.18804i	0.0880487	+	0.152505i
$438$	36.2782	−	7.77060i	1.73344	−	0.371294i
$439$	−6.16981	+	10.6864i	−0.294469	+	0.510035i	−0.974861	−	0.222813i	$-0.928476\pi$
$439$	−6.16981	+	10.6864i	−0.294469	+	0.510035i	0.680392	+	0.732848i	$0.261809\pi$
$440$	9.99894			0.476681
$441$	2.73680	−	1.22879i	0.130324	−	0.0585140i
$442$	−48.2572			−2.29536
$443$	−5.16965	+	8.95410i	−0.245618	+	0.425422i	−0.962305	−	0.271972i	$-0.912324\pi$
$443$	−5.16965	+	8.95410i	−0.245618	+	0.425422i	0.716687	+	0.697394i	$0.245657\pi$
$444$	2.55013	−	7.89053i	0.121024	−	0.374468i
$445$	4.83248	+	8.37010i	0.229082	+	0.396781i
$446$	20.3456	+	35.2395i	0.963390	+	1.66864i
$447$	7.35860	−	22.7688i	0.348050	−	1.07693i
$448$	−0.204148	+	0.353594i	−0.00964506	+	0.0167057i
$449$	24.4414			1.15346			0.576731	−	0.816934i	$-0.304328\pi$
$449$	24.4414			1.15346			0.576731	+	0.816934i	$0.304328\pi$
$450$	4.79159	−	2.15137i	0.225878	−	0.101417i
$451$	24.2857			1.14357
$452$	0.595821	−	1.03199i	0.0280251	−	0.0485408i
$453$	18.3592	−	3.93245i	0.862591	−	0.184763i
$454$	−17.3053	−	29.9737i	−0.812178	−	1.40673i
$455$	2.90805	+	5.03689i	0.136332	+	0.236133i
$456$	6.99403	+	7.74322i	0.327525	+	0.362610i
$457$	19.9778	−	34.6025i	0.934520	−	1.61864i	0.159033	−	0.987273i	$-0.449162\pi$
$457$	19.9778	−	34.6025i	0.934520	−	1.61864i	0.775487	−	0.631364i	$-0.217504\pi$
$458$	−0.0181338			−0.000847337
$459$	19.8537	−	14.5677i	0.926692	−	0.679961i
$460$	−1.06530			−0.0496700
$461$	7.58273	−	13.1337i	0.353163	−	0.611696i	−0.633639	−	0.773629i	$-0.718439\pi$
$461$	7.58273	−	13.1337i	0.353163	−	0.611696i	0.986802	+	0.161933i	$0.0517727\pi$
$462$	12.4196	+	13.7500i	0.577814	+	0.639708i
$463$	−5.21428	−	9.03139i	−0.242328	−	0.419724i	0.719049	−	0.694959i	$-0.244578\pi$
$463$	−5.21428	−	9.03139i	−0.242328	−	0.419724i	−0.961377	+	0.275235i	$0.911244\pi$
$464$	−4.19150	−	7.25990i	−0.194586	−	0.337032i
$465$	−11.7851	+	2.52430i	−0.546519	+	0.117062i
$466$	5.67793	−	9.83446i	0.263025	−	0.455573i
$467$	−27.5899			−1.27671			−0.638353	−	0.769744i	$-0.720384\pi$
$467$	−27.5899			−1.27671			−0.638353	+	0.769744i	$0.720384\pi$
$468$	15.0719	+	10.8784i	0.696701	+	0.502854i
$469$	4.51787			0.208616
$470$	−3.65512	+	6.33085i	−0.168598	+	0.292020i
$471$	5.89648	−	18.2447i	0.271695	−	0.840672i
$472$	0.684967	+	1.18640i	0.0315282	+	0.0546084i
$473$	−34.6044	−	59.9365i	−1.59111	−	2.75588i
$474$	−8.23723	+	25.4874i	−0.378348	+	1.17068i
$475$	−1.84062	+	3.18804i	−0.0844533	+	0.146277i
$476$	5.04854			0.231400
$477$	2.52695	−	24.7895i	0.115701	−	1.13503i
$478$	27.6601			1.26514
$479$	−10.7444	+	18.6099i	−0.490924	+	0.850306i	−0.999945	−	0.0104482i	$-0.996674\pi$
$479$	−10.7444	+	18.6099i	−0.490924	+	0.850306i	0.509021	+	0.860754i	$0.330008\pi$
$480$	−9.27028	+	1.98565i	−0.423128	+	0.0906320i
$481$	−13.0692	−	22.6365i	−0.595903	−	1.03213i
$482$	5.61831	+	9.73119i	0.255907	+	0.443244i
$483$	1.16098	+	1.28535i	0.0528266	+	0.0584853i
$484$	−14.0263	+	24.2942i	−0.637557	+	1.10428i
$485$	−8.17354			−0.371141
$486$	−27.2914	+	0.213844i	−1.23796	+	0.00970016i
$487$	11.6178			0.526451			0.263225	−	0.964734i	$-0.415214\pi$
$487$	11.6178			0.526451			0.263225	+	0.964734i	$0.415214\pi$
$488$	−7.57413	+	13.1188i	−0.342865	+	0.593859i
$489$	−13.0107	−	14.4043i	−0.588362	−	0.651387i
$490$	−0.875400	−	1.51624i	−0.0395466	−	0.0684966i
$491$	−17.3701	−	30.0860i	−0.783903	−	1.35776i	−0.929652	−	0.368438i	$-0.879893\pi$
$491$	−17.3701	−	30.0860i	−0.783903	−	1.35776i	0.145749	−	0.989322i	$-0.453441\pi$
$492$	−7.17130	+	1.53606i	−0.323307	+	0.0692508i
$493$	3.97616	−	6.88690i	0.179077	−	0.310171i
$494$	−37.4854			−1.68655
$495$	1.85888	−	18.2357i	0.0835506	−	0.819634i
$496$	34.7625			1.56088
$497$	−5.18337	+	8.97785i	−0.232506	+	0.402712i
$498$	5.91381	−	18.2984i	0.265004	−	0.819969i
$499$	1.51854	+	2.63020i	0.0679794	+	0.117744i	0.898012	−	0.439971i	$-0.145011\pi$
$499$	1.51854	+	2.63020i	0.0679794	+	0.117744i	−0.830032	+	0.557715i	$0.811678\pi$
$500$	−0.532651	−	0.922579i	−0.0238209	−	0.0412590i
$501$	−12.5918	+	38.9614i	−0.562562	+	1.74066i
$502$	−3.64045	+	6.30544i	−0.162481	+	0.281425i
$503$	−3.40995			−0.152042			−0.0760210	−	0.997106i	$-0.524222\pi$
$503$	−3.40995			−0.152042			−0.0760210	+	0.997106i	$0.524222\pi$
$504$	3.98082	+	2.87322i	0.177320	+	0.127983i
$505$	12.1320			0.539866
$506$	−5.34875	+	9.26431i	−0.237781	+	0.411849i
$507$	35.2734	−	7.55539i	1.56655	−	0.335547i
$508$	6.26223	+	10.8465i	0.277841	+	0.481235i
$509$	15.6708	+	27.1427i	0.694597	+	1.20308i	0.970316	+	0.241839i	$0.0777507\pi$
$509$	15.6708	+	27.1427i	0.694597	+	1.20308i	−0.275719	+	0.961238i	$0.588916\pi$
$510$	−9.63288	−	10.6647i	−0.426551	−	0.472242i
$511$	−6.11729	+	10.5955i	−0.270613	+	0.468715i
$512$	10.9939			0.485867
$513$	15.4221	−	11.3159i	0.680900	−	0.499611i
$514$	20.5686			0.907240
$515$	0.697899	−	1.20880i	0.0307531	−	0.0532660i
$516$	14.0092	+	15.5099i	0.616721	+	0.682784i
$517$	12.7559	+	22.0939i	0.561003	+	0.971686i
$518$	3.93417	+	6.81418i	0.172857	+	0.299398i
$519$	−5.23171	+	1.12061i	−0.229647	+	0.0491891i
$520$	−4.75894	+	8.24272i	−0.208693	+	0.361467i
$521$	−11.9819			−0.524936			−0.262468	−	0.964941i	$-0.584536\pi$
$521$	−11.9819			−0.524936			−0.262468	+	0.964941i	$0.584536\pi$
$522$	−8.04044	+	3.61007i	−0.351920	+	0.158009i
$523$	−23.4259			−1.02434			−0.512172	−	0.858883i	$-0.671159\pi$
$523$	−23.4259			−1.02434			−0.512172	+	0.858883i	$0.671159\pi$
$524$	0.516761	−	0.895056i	0.0225748	−	0.0391007i
$525$	−0.532651	+	1.64811i	−0.0232468	+	0.0719296i
$526$	10.8537	+	18.7991i	0.473242	+	0.819679i
$527$	16.4883	+	28.5585i	0.718240	+	1.24403i
$528$	−16.2588	+	50.3075i	−0.707573	+	2.18935i
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	−14.5421			−0.631669
$531$	2.29105	−	1.02866i	0.0994231	−	0.0446399i
$532$	3.92163			0.170024
$533$	−11.5587	+	20.0202i	−0.500661	+	0.867171i
$534$	−28.6587	+	6.13855i	−1.24018	+	0.265641i
$535$	0.242420	+	0.419884i	0.0104807	+	0.0181532i
$536$	3.69668	+	6.40284i	0.159672	+	0.276561i
$537$	−26.6476	−	29.5021i	−1.14993	−	1.27311i
$538$	16.5005	−	28.5798i	0.711389	−	1.23216i
$539$	−6.11007			−0.263179
$540$	0.604489	+	5.50237i	0.0260131	+	0.236784i
$541$	7.62446			0.327801			0.163901	−	0.986477i	$-0.447592\pi$
$541$	7.62446			0.327801			0.163901	+	0.986477i	$0.447592\pi$
$542$	18.4592	−	31.9724i	0.792893	−	1.37333i
$543$	4.76036	+	5.27029i	0.204287	+	0.226170i
$544$	12.9699	+	22.4645i	0.556079	+	0.963157i
$545$	5.36726	+	9.29637i	0.229908	+	0.398213i
$546$	−17.2460	+	3.69401i	−0.738061	+	0.158089i
$547$	−20.6792	+	35.8175i	−0.884180	+	1.53145i	−0.0375304	+	0.999295i	$0.511949\pi$
$547$	−20.6792	+	35.8175i	−0.884180	+	1.53145i	−0.846650	+	0.532150i	$0.821384\pi$
$548$	11.4702			0.489982
$549$	22.5174	+	16.2523i	0.961021	+	0.693631i
$550$	−10.6975			−0.456143
$551$	3.08861	−	5.34964i	0.131579	−	0.227902i
$552$	−0.871667	+	2.69709i	−0.0371006	+	0.114796i
$553$	−4.41643	−	7.64948i	−0.187806	−	0.325289i
$554$	16.1926	+	28.0464i	0.687956	+	1.19158i
$555$	2.39381	−	7.40685i	0.101611	−	0.314403i
$556$	5.76616	−	9.98728i	0.244540	−	0.423555i
$557$	−10.2775			−0.435472			−0.217736	−	0.976008i	$-0.569867\pi$
$557$	−10.2775			−0.435472			−0.217736	+	0.976008i	$0.569867\pi$
$558$	3.70642	−	36.3601i	0.156905	−	1.53925i
$559$	65.8790			2.78638
$560$	2.49787	−	4.32643i	0.105554	−	0.182825i
$561$	−49.0409	+	10.5043i	−2.07051	+	0.443493i
$562$	−15.4319	−	26.7289i	−0.650957	−	1.12749i
$563$	4.49496	+	7.78550i	0.189440	+	0.328120i	0.945064	−	0.326886i	$-0.105999\pi$
$563$	4.49496	+	7.78550i	0.189440	+	0.328120i	−0.755624	+	0.655006i	$0.772666\pi$
$564$	−5.16409	−	5.71726i	−0.217447	−	0.240740i
$565$	0.559298	−	0.968732i	0.0235298	−	0.0407549i
$566$	−6.63882			−0.279050
$567$	5.98013	−	6.72592i	0.251142	−	0.282462i
$568$	−16.9648			−0.711829
$569$	−3.97112	+	6.87818i	−0.166478	+	0.288348i	−0.937179	−	0.348849i	$-0.886573\pi$
$569$	−3.97112	+	6.87818i	−0.166478	+	0.288348i	0.770701	+	0.637197i	$0.219906\pi$
$570$	−7.48266	−	8.28420i	−0.313414	−	0.346987i
$571$	−19.5862	−	33.9243i	−0.819656	−	1.41969i	−0.905936	−	0.423415i	$-0.860831\pi$
$571$	−19.5862	−	33.9243i	−0.819656	−	1.41969i	0.0862797	−	0.996271i	$-0.472502\pi$
$572$	−18.9287	−	32.7855i	−0.791449	−	1.37083i
$573$	−14.7936	+	3.16871i	−0.618010	+	0.132375i
$574$	3.47946	−	6.02661i	0.145230	−	0.251546i
$575$	−1.00000			−0.0417029
$576$	−0.124217	+	1.21857i	−0.00517570	+	0.0507738i
$577$	5.80815			0.241796			0.120898	−	0.992665i	$-0.461423\pi$
$577$	5.80815			0.241796			0.120898	+	0.992665i	$0.461423\pi$
$578$	−4.77862	+	8.27681i	−0.198764	+	0.344270i
$579$	8.61980	−	26.6712i	0.358227	−	1.10842i
$580$	0.893806	+	1.54812i	0.0371133	+	0.0642821i
$581$	3.17072	+	5.49185i	0.131544	+	0.227840i
$582$	7.62236	−	23.5849i	0.315957	−	0.977626i
$583$	−25.3750	+	43.9508i	−1.05093	+	1.82026i
$584$	−20.0215			−0.828496
$585$	14.1481	+	10.2116i	0.584950	+	0.422196i
$586$	−14.1370			−0.583994
$587$	−1.00014	+	1.73229i	−0.0412802	+	0.0714993i	−0.885927	−	0.463824i	$-0.846477\pi$
$587$	−1.00014	+	1.73229i	−0.0412802	+	0.0714993i	0.844647	+	0.535323i	$0.179810\pi$
$588$	1.80423	−	0.386458i	0.0744053	−	0.0159372i
$589$	12.8078	+	22.1838i	0.527737	+	0.914067i
$590$	−0.732822	−	1.26928i	−0.0301698	−	0.0522556i
$591$	0.486049	+	0.538114i	0.0199934	+	0.0221350i
$592$	−11.2258	+	19.4436i	−0.461376	+	0.799126i
$593$	18.6458			0.765690			0.382845	−	0.923813i	$-0.374944\pi$
$593$	18.6458			0.765690			0.382845	+	0.923813i	$0.374944\pi$
$594$	50.8860	+	22.3698i	2.08788	+	0.917845i
$595$	4.73907			0.194283
$596$	7.35860	−	12.7455i	0.301420	−	0.522074i
$597$	8.69190	+	9.62297i	0.355736	+	0.393842i
$598$	−5.09142	−	8.81859i	−0.208204	−	0.360619i
$599$	−14.0200	−	24.2833i	−0.572840	−	0.992188i	−0.996273	−	0.0862606i	$-0.972508\pi$
$599$	−14.0200	−	24.2833i	−0.572840	−	0.992188i	0.423432	−	0.905928i	$-0.360825\pi$
$600$	−2.77158	+	0.593659i	−0.113149	+	0.0242360i
$601$	−14.9532	+	25.8996i	−0.609952	+	1.05647i	0.381296	+	0.924453i	$0.375478\pi$
$601$	−14.9532	+	25.8996i	−0.609952	+	1.05647i	−0.991248	+	0.132015i	$0.957855\pi$
$602$	−19.8313			−0.808264
$603$	12.3645	−	5.55153i	0.503522	−	0.226076i
$604$	11.5480			0.469882
$605$	−13.1665	+	22.8050i	−0.535293	+	0.927154i
$606$	−11.3139	+	35.0071i	−0.459594	+	1.42206i
$607$	−7.62634	−	13.2092i	−0.309544	−	0.536145i	0.668719	−	0.743515i	$-0.266843\pi$
$607$	−7.62634	−	13.2092i	−0.309544	−	0.536145i	−0.978263	+	0.207370i	$0.933510\pi$
$608$	10.0748	+	17.4501i	0.408587	+	0.707693i
$609$	0.893806	−	2.76559i	0.0362188	−	0.112067i
$610$	8.10329	−	14.0353i	0.328093	−	0.568273i
$611$	−24.2844			−0.982441
$612$	13.8168	−	6.20361i	0.558513	−	0.250766i
$613$	21.4518			0.866431			0.433215	−	0.901290i	$-0.357379\pi$
$613$	21.4518			0.866431			0.433215	+	0.901290i	$0.357379\pi$
$614$	0.903891	−	1.56559i	0.0364781	−	0.0631819i
$615$	−6.73171	+	1.44190i	−0.271449	+	0.0581429i
$616$	−4.99947	−	8.65933i	−0.201434	−	0.348894i
$617$	15.8000	+	27.3664i	0.636085	+	1.10173i	0.986284	+	0.165056i	$0.0527805\pi$
$617$	15.8000	+	27.3664i	0.636085	+	1.10173i	−0.350199	+	0.936675i	$0.613886\pi$
$618$	2.83717	+	3.14109i	0.114128	+	0.126353i
$619$	−9.37249	+	16.2336i	−0.376712	+	0.652485i	−0.990582	−	0.136923i	$-0.956279\pi$
$619$	−9.37249	+	16.2336i	−0.376712	+	0.652485i	0.613869	+	0.789408i	$0.289612\pi$
$620$	−7.41284			−0.297707
$621$	4.75680	+	2.09113i	0.190884	+	0.0839140i
$622$	14.5131			0.581923
$623$	4.83248	−	8.37010i	0.193609	−	0.335341i
$624$	−33.7332	−	37.3467i	−1.35041	−	1.49506i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−17.5686	−	30.4298i	−0.702184	−	1.21622i
$627$	−38.0942	+	8.15959i	−1.52134	+	0.325863i
$628$	5.89648	−	10.2130i	0.235295	−	0.407543i
$629$	−21.2980			−0.849208
$630$	−4.25894	−	3.07395i	−0.169680	−	0.122469i
$631$	−34.9978			−1.39324			−0.696619	−	0.717441i	$-0.745313\pi$
$631$	−34.9978			−1.39324			−0.696619	+	0.717441i	$0.745313\pi$
$632$	7.22736	−	12.5181i	0.287489	−	0.497945i
$633$	−3.33407	+	10.3162i	−0.132517	+	0.410031i
$634$	−18.1770	−	31.4834i	−0.721900	−	1.25037i
$635$	5.87836	+	10.1816i	0.233276	+	0.404045i
$636$	4.71309	−	14.5831i	0.186886	−	0.578259i
$637$	2.90805	−	5.03689i	0.115221	−	0.199569i
$638$	17.9508			0.710677
$639$	−3.15390	+	30.9399i	−0.124766	+	1.22396i
$640$	11.6620			0.460983
$641$	20.6415	−	35.7522i	0.815291	−	1.41213i	−0.0938280	−	0.995588i	$-0.529910\pi$
$641$	20.6415	−	35.7522i	0.815291	−	1.41213i	0.909119	−	0.416537i	$-0.136756\pi$
$642$	−1.43766	+	0.307939i	−0.0567397	+	0.0121534i
$643$	−2.63091	−	4.55687i	−0.103753	−	0.179705i	0.809475	−	0.587154i	$-0.199752\pi$
$643$	−2.63091	−	4.55687i	−0.103753	−	0.179705i	−0.913228	+	0.407449i	$0.866418\pi$
$644$	0.532651	+	0.922579i	0.0209894	+	0.0363547i
$645$	13.1505	+	14.5591i	0.517799	+	0.573265i
$646$	−15.2719	+	26.4517i	−0.600865	+	1.04073i
$647$	−4.79934			−0.188682			−0.0943408	−	0.995540i	$-0.530074\pi$
$647$	−4.79934			−0.188682			−0.0943408	+	0.995540i	$0.530074\pi$
$648$	14.4253	+	2.97181i	0.566679	+	0.116744i
$649$	−5.11491			−0.200778
$650$	5.09142	−	8.81859i	0.199702	−	0.345894i
$651$	8.07863	+	8.94401i	0.316627	+	0.350543i
$652$	−5.96919	−	10.3389i	−0.233772	−	0.404904i
$653$	−7.23824	−	12.5370i	−0.283254	−	0.490611i	0.688930	−	0.724828i	$-0.258081\pi$
$653$	−7.23824	−	12.5370i	−0.283254	−	0.490611i	−0.972184	+	0.234217i	$0.924747\pi$
$654$	−31.8302	+	6.81787i	−1.24466	+	0.266600i
$655$	0.485084	−	0.840190i	0.0189538	−	0.0328289i
$656$	19.8566			0.775270
$657$	−3.72216	+	36.5145i	−0.145215	+	1.42457i
$658$	7.31024			0.284983
$659$	14.0086	−	24.2636i	0.545696	−	0.945174i	−0.452866	−	0.891578i	$-0.649599\pi$
$659$	14.0086	−	24.2636i	0.545696	−	0.945174i	0.998563	−	0.0535955i	$-0.0170682\pi$
$660$	3.46706	−	10.7277i	0.134955	−	0.417575i
$661$	24.2168	+	41.9448i	0.941926	+	1.63146i	0.761792	+	0.647822i	$0.224320\pi$
$661$	24.2168	+	41.9448i	0.941926	+	1.63146i	0.180134	+	0.983642i	$0.442347\pi$
$662$	9.77222	+	16.9260i	0.379808	+	0.657847i
$663$	14.6814	−	45.4269i	0.570179	−	1.76423i
$664$	−5.18879	+	8.98725i	−0.201364	+	0.348773i
$665$	3.68123			0.142752
$666$	19.1402	+	13.8147i	0.741669	+	0.535311i
$667$	1.67803			0.0649737
$668$	−12.5918	+	21.8097i	−0.487193	+	0.843843i
$669$	−39.3625	+	8.43125i	−1.52184	+	0.325971i
$670$	−3.95495	−	6.85017i	−0.152793	−	0.264645i
$671$	−28.2794	−	48.9814i	−1.09171	−	1.89091i
$672$	6.35476	+	7.03547i	0.245140	+	0.271399i
$673$	17.9700	−	31.1250i	0.692693	−	1.19978i	−0.278259	−	0.960506i	$-0.589757\pi$
$673$	17.9700	−	31.1250i	0.692693	−	1.19978i	0.970952	−	0.239274i	$-0.0769094\pi$
$674$	10.6317			0.409518
$675$	0.567434	+	5.16508i	0.0218406	+	0.198804i
$676$	22.1871			0.853350
$677$	14.2219	−	24.6331i	0.546593	−	0.946727i	−0.451911	−	0.892063i	$-0.649258\pi$
$677$	14.2219	−	24.6331i	0.546593	−	0.946727i	0.998505	−	0.0546646i	$-0.0174089\pi$
$678$	2.27371	+	2.51727i	0.0873215	+	0.0966752i
$679$	4.08677	+	7.07849i	0.156836	+	0.271648i
$680$	3.87767	+	6.71632i	0.148702	+	0.257559i
$681$	33.4805	−	7.17136i	1.28298	−	0.274807i
$682$	−37.2190	+	64.4651i	−1.42519	+	2.46850i
$683$	−41.1926			−1.57619			−0.788096	−	0.615553i	$-0.788933\pi$
$683$	−41.1926			−1.57619			−0.788096	+	0.615553i	$0.788933\pi$
$684$	10.7327	−	4.81887i	0.410375	−	0.184254i
$685$	10.7671			0.411389
$686$	−0.875400	+	1.51624i	−0.0334229	+	0.0578902i
$687$	0.00551690	−	0.0170702i	0.000210483	−	0.000651270i
$688$	−28.2933	−	49.0055i	−1.07867	−	1.86832i
$689$	−24.1542	−	41.8363i	−0.920202	−	1.59384i
$690$	0.932566	−	2.88552i	0.0355022	−	0.109850i
$691$	3.28345	−	5.68710i	0.124908	−	0.216348i	−0.796789	−	0.604258i	$-0.793470\pi$
$691$	3.28345	−	5.68710i	0.124908	−	0.216348i	0.921697	+	0.387910i	$0.126803\pi$
$692$	−3.29076			−0.125096
$693$	−16.7220	+	7.50801i	−0.635217	+	0.285206i
$694$	34.1495			1.29630
$695$	5.41270	−	9.37507i	0.205315	−	0.355617i
$696$	4.65080	−	0.996179i	0.176288	−	0.0377601i
$697$	9.41822	+	16.3128i	0.356740	+	0.617892i
$698$	11.0197	+	19.0867i	0.417103	+	0.722443i
$699$	7.53025	+	8.33688i	0.284820	+	0.315330i
$700$	−0.532651	+	0.922579i	−0.0201323	+	0.0348702i
$701$	−2.61012			−0.0985828			−0.0492914	−	0.998784i	$-0.515696\pi$
$701$	−2.61012			−0.0985828			−0.0492914	+	0.998784i	$0.515696\pi$
$702$	−42.6597	+	31.3015i	−1.61009	+	1.18140i
$703$	−16.5440			−0.623967
$704$	1.24735	−	2.16048i	0.0470115	−	0.0814262i
$705$	−4.84754	−	5.36680i	−0.182569	−	0.202125i
$706$	−14.3716	−	24.8923i	−0.540881	−	0.936833i
$707$	−6.06599	−	10.5066i	−0.228135	−	0.395141i
$708$	1.51037	−	0.323514i	0.0567633	−	0.0121584i
$709$	6.45282	−	11.1766i	0.242341	−	0.419746i	−0.719040	−	0.694969i	$-0.755418\pi$
$709$	6.45282	−	11.1766i	0.242341	−	0.419746i	0.961381	+	0.275223i	$0.0887515\pi$
$710$	18.1501			0.681160
$711$	−21.4865	−	15.5082i	−0.805807	−	0.581603i
$712$	15.8164			0.592745
$713$	−3.47922	+	6.02618i	−0.130298	+	0.225682i
$714$	−4.41949	+	13.6747i	−0.165395	+	0.511762i
$715$	−17.7684	−	30.7757i	−0.664500	−	1.15095i
$716$	−12.2257	−	21.1756i	−0.456897	−	0.791369i
$717$	−8.41512	+	26.0378i	−0.314268	+	0.972401i
$718$	11.5837	−	20.0635i	0.432299	−	0.748764i
$719$	8.13828			0.303507			0.151753	−	0.988418i	$-0.451508\pi$
$719$	8.13828			0.303507			0.151753	+	0.988418i	$0.451508\pi$
$720$	1.51987	−	14.9099i	0.0566421	−	0.555661i
$721$	−1.39580			−0.0519823
$722$	4.76963	−	8.26125i	0.177507	−	0.307452i
$723$	−10.8697	+	2.32824i	−0.404250	+	0.0865882i
$724$	2.18402	+	3.78283i	0.0811685	+	0.140588i
$725$	0.839016	+	1.45322i	0.0311603	+	0.0539712i
$726$	−53.5256	−	59.2592i	−1.98652	−	2.19932i
$727$	−14.2624	+	24.7031i	−0.528962	+	0.916189i	0.470468	+	0.882417i	$0.344085\pi$
$727$	−14.2624	+	24.7031i	−0.528962	+	0.916189i	−0.999430	+	0.0337717i	$0.989248\pi$
$728$	9.51787			0.352756
$729$	8.10165	−	25.7558i	0.300061	−	0.953920i
$730$	21.4203			0.792801
$731$	26.8397	−	46.4878i	0.992703	−	1.71941i
$732$	11.4486	+	12.6750i	0.423154	+	0.468481i
$733$	18.9040	+	32.7427i	0.698236	+	1.20938i	0.969077	+	0.246757i	$0.0793649\pi$
$733$	18.9040	+	32.7427i	0.698236	+	1.20938i	−0.270841	+	0.962624i	$0.587302\pi$
$734$	17.7464	+	30.7377i	0.655033	+	1.13455i
$735$	1.69363	−	0.362768i	0.0624707	−	0.0133809i
$736$	−2.73680	+	4.74027i	−0.100880	+	0.174729i
$737$	−27.6045			−1.01683
$738$	2.11713	−	20.7691i	0.0779328	−	0.764523i
$739$	−39.0949			−1.43813			−0.719065	−	0.694943i	$-0.755430\pi$
$739$	−39.0949			−1.43813			−0.719065	+	0.694943i	$0.755430\pi$
$740$	2.39381	−	4.14619i	0.0879980	−	0.152417i
$741$	11.4043	−	35.2869i	0.418947	−	1.29630i
$742$	7.27105	+	12.5938i	0.266929	+	0.462334i
$743$	−4.65459	−	8.06198i	−0.170760	−	0.295765i	0.767926	−	0.640539i	$-0.221289\pi$
$743$	−4.65459	−	8.06198i	−0.170760	−	0.295765i	−0.938686	+	0.344774i	$0.887956\pi$
$744$	−6.06544	+	18.7675i	−0.222370	+	0.688051i
$745$	6.90752	−	11.9642i	0.253072	−	0.438333i
$746$	52.9630			1.93911
$747$	15.4260	+	11.1339i	0.564407	+	0.407369i
$748$	−30.8469			−1.12788
$749$	0.242420	−	0.419884i	0.00885783	−	0.0153422i
$750$	2.96522	−	0.635135i	0.108274	−	0.0231918i
$751$	8.88756	+	15.3937i	0.324312	+	0.561725i	0.981373	−	0.192113i	$-0.0615340\pi$
$751$	8.88756	+	15.3937i	0.324312	+	0.561725i	−0.657061	+	0.753837i	$0.728201\pi$
$752$	10.4295	+	18.0645i	0.380325	+	0.658743i
$753$	−4.82808	−	5.34525i	−0.175945	−	0.194792i
$754$	−8.54356	+	14.7979i	−0.311138	+	0.538907i
$755$	10.8401			0.394512
$756$	4.46295	−	3.27469i	0.162316	−	0.119099i
$757$	−11.2184			−0.407739			−0.203870	−	0.978998i	$-0.565352\pi$
$757$	−11.2184			−0.407739			−0.203870	+	0.978998i	$0.565352\pi$
$758$	0.611556	−	1.05925i	0.0222127	−	0.0384736i
$759$	−7.09369	−	7.85355i	−0.257485	−	0.285066i
$760$	3.01211	+	5.21713i	0.109261	+	0.189245i
$761$	21.0958	+	36.5391i	0.764723	+	1.32454i	0.940393	+	0.340091i	$0.110458\pi$
$761$	21.0958	+	36.5391i	0.764723	+	1.32454i	−0.175669	+	0.984449i	$0.556209\pi$
$762$	−34.8612	+	7.46710i	−1.26289	+	0.270504i
$763$	5.36726	−	9.29637i	0.194308	−	0.336551i
$764$	−9.30521			−0.336651
$765$	12.9699	−	5.82334i	0.468927	−	0.210543i
$766$	10.6714			0.385572
$767$	2.43441	−	4.21652i	0.0879015	−	0.152250i
$768$	−10.4407	+	32.3052i	−0.376745	+	1.16571i
$769$	−1.72091	−	2.98070i	−0.0620575	−	0.107487i	0.833327	−	0.552780i	$-0.186433\pi$
$769$	−1.72091	−	2.98070i	−0.0620575	−	0.107487i	−0.895385	+	0.445293i	$0.853100\pi$
$770$	5.34875	+	9.26431i	0.192756	+	0.333863i
$771$	−6.25763	+	19.3622i	−0.225363	+	0.697312i
$772$	8.61980	−	14.9299i	0.310234	−	0.537340i
$773$	20.9848			0.754770			0.377385	−	0.926056i	$-0.376823\pi$
$773$	20.9848			0.754770			0.377385	+	0.926056i	$0.376823\pi$
$774$	−54.2743	+	24.3686i	−1.95085	+	0.875911i
$775$	−6.95844			−0.249954
$776$	−6.68787	+	11.5837i	−0.240081	+	0.415832i
$777$	−7.61142	+	1.63033i	−0.273058	+	0.0584877i
$778$	−11.8694	−	20.5585i	−0.425540	−	0.737056i
$779$	7.31592	+	12.6715i	0.262120	+	0.454005i
$780$	7.19335	+	7.96389i	0.257563	+	0.285153i
$781$	31.6707	−	54.8553i	1.13327	−	1.96288i
$782$	−8.29717			−0.296706
$783$	−0.952173	−	8.66717i	−0.0340279	−	0.309739i
$784$	−4.99574			−0.178419
$785$	5.53503	−	9.58695i	0.197554	−	0.342173i
$786$	1.97201	+	2.18325i	0.0703393	+	0.0778740i
$787$	13.3900	+	23.1922i	0.477303	+	0.826713i	0.999662	−	0.0260129i	$-0.00828109\pi$
$787$	13.3900	+	23.1922i	0.477303	+	0.826713i	−0.522359	+	0.852726i	$0.674948\pi$
$788$	0.222996	+	0.386240i	0.00794389	+	0.0137592i
$789$	−20.9986	+	4.49779i	−0.747568	+	0.160125i
$790$	−7.73229	+	13.3927i	−0.275103	+	0.476492i
$791$	−1.11860			−0.0397727
$792$	−24.3231	−	17.5555i	−0.864283	−	0.623809i
$793$	53.8377			1.91183
$794$	14.3661	−	24.8828i	0.509834	−	0.883058i
$795$	4.42419	−	13.6892i	0.156910	−	0.485506i
$796$	3.98778	+	6.90704i	0.141343	+	0.244814i
$797$	−24.8167	−	42.9839i	−0.879054	−	1.52257i	−0.852380	−	0.522922i	$-0.824842\pi$
$797$	−24.8167	−	42.9839i	−0.879054	−	1.52257i	−0.0266739	−	0.999644i	$-0.508492\pi$
$798$	−3.43299	+	10.6223i	−0.121527	+	0.376024i
$799$	−9.89368	+	17.1364i	−0.350013	+	0.606241i
$800$	−5.47360			−0.193521
$801$	2.94040	−	28.8454i	0.103894	−	1.01920i
$802$	−6.12926			−0.216432
$803$	37.3770	−	64.7389i	1.31901	−	2.28459i
$804$	8.15130	−	1.74597i	0.287474	−	0.0615755i
$805$	0.500000	+	0.866025i	0.0176227	+	0.0305234i
$806$	−35.4283	−	61.3636i	−1.24791	−	2.16144i
$807$	21.8835	+	24.2277i	0.770337	+	0.852855i
$808$	9.92681	−	17.1937i	0.349224	−	0.604873i
$809$	−55.4296			−1.94880			−0.974401	−	0.224818i	$-0.927821\pi$
$809$	−55.4296			−1.94880			−0.974401	+	0.224818i	$0.927821\pi$
$810$	−15.4331	−	3.17943i	−0.542264	−	0.111714i
$811$	−51.0851			−1.79384			−0.896920	−	0.442193i	$-0.854200\pi$
$811$	−51.0851			−1.79384			−0.896920	+	0.442193i	$0.854200\pi$
$812$	0.893806	−	1.54812i	0.0313664	−	0.0543282i
$813$	24.4812	+	27.1036i	0.858595	+	0.950566i
$814$	−24.0380	−	41.6351i	−0.842532	−	1.45931i
$815$	−5.60329	−	9.70518i	−0.196275	−	0.339958i
$816$	−40.0970	+	8.58859i	−1.40368	+	0.300661i
$817$	20.8487	−	36.1109i	0.729402	−	1.26336i
$818$	11.8305			0.413642
$819$	1.76945	−	17.3584i	0.0618296	−	0.606550i
$820$	−4.23427			−0.147867
$821$	−2.55717	+	4.42914i	−0.0892457	+	0.154578i	−0.907192	−	0.420716i	$-0.861779\pi$
$821$	−2.55717	+	4.42914i	−0.0892457	+	0.154578i	0.817947	+	0.575294i	$0.195112\pi$
$822$	−10.0410	+	31.0686i	−0.350220	+	1.08364i
$823$	18.6307	+	32.2693i	0.649425	+	1.12484i	0.983260	+	0.182206i	$0.0583238\pi$
$823$	18.6307	+	32.2693i	0.649425	+	1.12484i	−0.333835	+	0.942632i	$0.608343\pi$
$824$	−1.14209	−	1.97816i	−0.0397866	−	0.0689124i
$825$	3.25453	−	10.0701i	0.113308	−	0.350596i
$826$	−0.732822	+	1.26928i	−0.0254981	+	0.0441641i
$827$	23.9366			0.832356			0.416178	−	0.909283i	$-0.363369\pi$
$827$	23.9366			0.832356			0.416178	+	0.909283i	$0.363369\pi$
$828$	2.59142	+	1.87039i	0.0900580	+	0.0650007i
$829$	−11.3556			−0.394397			−0.197198	−	0.980364i	$-0.563184\pi$
$829$	−11.3556			−0.394397			−0.197198	+	0.980364i	$0.563184\pi$
$830$	5.55130	−	9.61513i	0.192688	−	0.333746i
$831$	−31.3277	+	6.71024i	−1.08675	+	0.232776i
$832$	1.18734	+	2.05654i	0.0411637	+	0.0712976i
$833$	−2.36954	−	4.10416i	−0.0820995	−	0.142201i
$834$	22.0043	+	24.3613i	0.761945	+	0.843564i
$835$	−11.8200	+	20.4728i	−0.409047	+	0.708490i
$836$	−23.9614			−0.828722
$837$	33.0999	+	14.5510i	1.14410	+	0.502955i
$838$	−52.9238			−1.82822
$839$	18.9639	−	32.8465i	0.654707	−	1.13399i	−0.327260	−	0.944934i	$-0.606125\pi$
$839$	18.9639	−	32.8465i	0.654707	−	1.13399i	0.981967	−	0.189051i	$-0.0605413\pi$
$840$	1.89991	+	2.10343i	0.0655533	+	0.0725753i
$841$	13.0921	+	22.6762i	0.451452	+	0.781938i
$842$	1.13909	+	1.97296i	0.0392556	+	0.0679927i
$843$	29.8561	−	6.39503i	1.02830	−	0.220257i
$844$	−3.33407	+	5.77477i	−0.114763	+	0.198776i
$845$	20.8270			0.716472
$846$	20.0066	−	8.98277i	0.687843	−	0.308834i
$847$	26.3329			0.904810
$848$	−20.7472	+	35.9352i	−0.712463	+	1.23402i
$849$	2.01975	−	6.24945i	0.0693175	−	0.214480i
$850$	−4.14858	−	7.18556i	−0.142295	−	0.246463i
$851$	−2.24707	−	3.89203i	−0.0770285	−	0.133417i
$852$	−5.88244	+	18.2013i	−0.201529	+	0.623566i
$853$	−19.5193	+	33.8085i	−0.668329	+	1.15758i	0.310042	+	0.950723i	$0.399657\pi$
$853$	−19.5193	+	33.8085i	−0.668329	+	1.15758i	−0.978371	+	0.206857i	$0.933677\pi$
$854$	−16.2066			−0.554578
$855$	10.0748	−	4.52348i	0.344551	−	0.154700i
$856$	0.793426			0.0271187
$857$	−11.8587	+	20.5399i	−0.405087	+	0.701631i	−0.994332	−	0.106324i	$-0.966092\pi$
$857$	−11.8587	+	20.5399i	−0.405087	+	0.701631i	0.589245	+	0.807954i	$0.299425\pi$
$858$	105.374	−	22.5706i	3.59742	−	0.770549i
$859$	−22.8542	−	39.5847i	−0.779777	−	1.35061i	−0.932070	−	0.362278i	$-0.881999\pi$
$859$	−22.8542	−	39.5847i	−0.779777	−	1.35061i	0.152294	−	0.988335i	$-0.451334\pi$
$860$	6.03334	+	10.4500i	0.205735	+	0.356344i
$861$	4.61457	+	5.10888i	0.157264	+	0.174110i
$862$	5.99438	−	10.3826i	0.204169	−	0.353632i
$863$	−5.54957			−0.188909			−0.0944547	−	0.995529i	$-0.530111\pi$
$863$	−5.54957			−0.188909			−0.0944547	+	0.995529i	$0.530111\pi$
$864$	26.0368	+	11.4460i	0.885791	+	0.389400i
$865$	−3.08904			−0.105031
$866$	5.02356	−	8.70105i	0.170707	−	0.295674i
$867$	−6.33756	−	7.01643i	−0.215235	−	0.238290i
$868$	3.70642	+	6.41971i	0.125804	+	0.217899i
$869$	26.9847	+	46.7389i	0.915393	+	1.58551i
$870$	−4.97573	+	1.06578i	−0.168693	+	0.0361332i
$871$	13.1382	−	22.7560i	0.445171	−	0.771059i
$872$	17.5667			0.594884
$873$	19.8827	+	14.3506i	0.672927	+	0.485695i
$874$	−6.44511			−0.218009
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	−6.94232	+	21.4807i	−0.234559	+	0.725767i
$877$	−10.6589	−	18.4617i	−0.359924	−	0.623406i	0.628024	−	0.778194i	$-0.283864\pi$
$877$	−10.6589	−	18.4617i	−0.359924	−	0.623406i	−0.987948	+	0.154788i	$0.950531\pi$
$878$	−10.8021	−	18.7098i	−0.364553	−	0.631425i
$879$	4.30094	−	13.3079i	0.145067	−	0.448863i
$880$	−15.2621	+	26.4348i	−0.514487	+	0.891117i
$881$	8.12987			0.273902			0.136951	−	0.990578i	$-0.456270\pi$
$881$	8.12987			0.273902			0.136951	+	0.990578i	$0.456270\pi$
$882$	−0.532651	+	5.22532i	−0.0179353	+	0.175946i
$883$	−4.24853			−0.142975			−0.0714873	−	0.997442i	$-0.522775\pi$
$883$	−4.24853			−0.142975			−0.0714873	+	0.997442i	$0.522775\pi$
$884$	14.6814	−	25.4290i	0.493789	−	0.855268i
$885$	1.41779	−	0.303683i	0.0476584	−	0.0102082i
$886$	−9.05103	−	15.6768i	−0.304075	−	0.526674i
$887$	25.7749	+	44.6434i	0.865435	+	1.49898i	0.866614	+	0.498978i	$0.166291\pi$
$887$	25.7749	+	44.6434i	0.865435	+	1.49898i	−0.00117920	+	0.999999i	$0.500375\pi$
$888$	−8.53847	−	9.45310i	−0.286532	−	0.317225i
$889$	5.87836	−	10.1816i	0.197154	−	0.341480i
$890$	−16.9214			−0.567207
$891$	−36.5390	+	41.0958i	−1.22410	+	1.37676i
$892$	−24.7592			−0.828998
$893$	−7.68525	+	13.3113i	−0.257177	+	0.445444i
$894$	28.0812	+	31.0892i	0.939174	+	1.03978i
$895$	−11.4763	−	19.8776i	−0.383611	−	0.664433i
$896$	−5.83102	−	10.0996i	−0.194801	−	0.337405i
$897$	9.85035	−	2.10990i	0.328894	−	0.0704474i
$898$	−21.3960	+	37.0590i	−0.713995	+	1.23668i
$899$	11.6765			0.389432
$900$	−0.324100	+	3.17943i	−0.0108033	+	0.105981i
$901$	−39.3626			−1.31136
$902$	−21.2597	+	36.8230i	−0.707872	+	1.22607i
$903$	6.03334	−	18.6682i	0.200777	−	0.621239i
$904$	−0.915274	−	1.58530i	−0.0304415	−	0.0527263i
$905$	2.05014	+	3.55095i	0.0681490	+	0.118038i
$906$	−10.1091	+	31.2794i	−0.335853	+	1.03919i
$907$	1.07275	−	1.85806i	0.0356202	−	0.0616959i	−0.847666	−	0.530531i	$-0.821993\pi$
$907$	1.07275	−	1.85806i	0.0356202	−	0.0616959i	0.883286	+	0.468835i	$0.155326\pi$
$908$	21.0594			0.698880
$909$	−29.5118	−	21.3006i	−0.978846	−	0.706496i
$910$	−10.1828			−0.337558
$911$	−17.1698	+	29.7389i	−0.568860	+	0.985295i	0.427819	+	0.903865i	$0.359282\pi$
$911$	−17.1698	+	29.7389i	−0.568860	+	0.985295i	−0.996679	+	0.0814303i	$0.974051\pi$
$912$	−31.1467	+	6.67148i	−1.03137	+	0.220915i
$913$	−19.3733	−	33.5556i	−0.641163	−	1.11053i
$914$	34.9771	+	60.5821i	1.15694	+	2.00388i
$915$	10.7468	+	11.8980i	0.355280	+	0.393337i
$916$	0.00551690	−	0.00955555i	0.000182283	−	0.000315724i
$917$	−0.970168			−0.0320378
$918$	4.70810	+	42.8555i	0.155390	+	1.41444i
$919$	2.02313			0.0667370			0.0333685	−	0.999443i	$-0.489377\pi$
$919$	2.02313			0.0667370			0.0333685	+	0.999443i	$0.489377\pi$
$920$	−0.818235	+	1.41722i	−0.0269764	+	0.0467245i
$921$	1.19877	+	1.32718i	0.0395008	+	0.0437321i
$922$	13.2759	+	22.9945i	0.437217	+	0.757282i
$923$	30.1470	+	52.2161i	0.992300	+	1.71871i
$924$	−11.0240	+	2.36128i	−0.362662	+	0.0776805i
$925$	2.24707	−	3.89203i	0.0738831	−	0.127969i
$926$	18.2583			0.600006
$927$	−3.82002	+	1.71515i	−0.125466	+	0.0563329i
$928$	9.18487			0.301508
$929$	5.84648	−	10.1264i	0.191817	−	0.332237i	−0.754036	−	0.656834i	$-0.771895\pi$
$929$	5.84648	−	10.1264i	0.191817	−	0.332237i	0.945852	+	0.324597i	$0.105229\pi$
$930$	6.48920	−	20.0787i	0.212789	−	0.658407i
$931$	−1.84062	−	3.18804i	−0.0603238	−	0.104484i
$932$	3.45482	+	5.98393i	0.113167	+	0.196010i
$933$	−4.41537	+	13.6619i	−0.144553	+	0.447271i
$934$	24.1522	−	41.8328i	0.790283	−	1.36881i
$935$	−28.9560			−0.946964
$936$	26.0485	−	11.6955i	0.851422	−	0.382279i
$937$	13.5123			0.441427			0.220713	−	0.975339i	$-0.429161\pi$
$937$	13.5123			0.441427			0.220713	+	0.975339i	$0.429161\pi$
$938$	−3.95495	+	6.85017i	−0.129134	+	0.223666i
$939$	33.9900	−	7.28049i	1.10922	−	0.237590i
$940$	−2.22401	−	3.85211i	−0.0725394	−	0.125642i
$941$	2.79192	+	4.83575i	0.0910140	+	0.157641i	0.907938	−	0.419104i	$-0.137656\pi$
$941$	2.79192	+	4.83575i	0.0910140	+	0.157641i	−0.816924	+	0.576745i	$0.804323\pi$
$942$	22.5016	+	24.9119i	0.733140	+	0.811673i
$943$	−1.98736	+	3.44220i	−0.0647172	+	0.112093i
$944$	−4.18207			−0.136115
$945$	4.18937	−	3.07395i	0.136280	−	0.0999956i
$946$	121.171			3.93960
$947$	12.6053	−	21.8331i	0.409618	−	0.709480i	−0.585229	−	0.810868i	$-0.698995\pi$
$947$	12.6053	−	21.8331i	0.409618	−	0.709480i	0.994847	+	0.101389i	$0.0323286\pi$
$948$	−10.9245	−	12.0947i	−0.354810	−	0.392817i
$949$	35.5788	+	61.6243i	1.15494	+	2.00041i
$950$	−3.22255	−	5.58163i	−0.104553	−	0.181092i
$951$	35.1669	−	7.53258i	1.14037	−	0.244261i
$952$	3.87767	−	6.71632i	0.125676	−	0.217677i
$953$	32.3742			1.04870			0.524351	−	0.851502i	$-0.324308\pi$
$953$	32.3742			1.04870			0.524351	+	0.851502i	$0.324308\pi$
$954$	35.3746	+	25.5322i	1.14530	+	0.826634i
$955$	−8.73481			−0.282652
$956$	−8.41512	+	14.5754i	−0.272164	+	0.471403i
$957$	−5.46121	+	16.8979i	−0.176536	+	0.546233i
$958$	−18.8113	−	32.5821i	−0.607766	−	1.05268i
$959$	−5.38354	−	9.32456i	−0.173843	−	0.301106i
$960$	−0.217479	+	0.672917i	−0.00701910	+	0.0217183i
$961$	−8.70992	+	15.0860i	−0.280965	+	0.486646i
$962$	45.7630			1.47546
$963$	0.147504	−	1.44702i	0.00475326	−	0.0466296i
$964$	−6.83710			−0.220208
$965$	8.09142	−	14.0147i	0.260472	−	0.451151i
$966$	−2.96522	+	0.635135i	−0.0954043	+	0.0204351i
$967$	−13.7076	−	23.7423i	−0.440808	−	0.763502i	0.556942	−	0.830552i	$-0.311975\pi$
$967$	−13.7076	−	23.7423i	−0.440808	−	0.763502i	−0.997750	+	0.0670499i	$0.978641\pi$
$968$	21.5465	+	37.3196i	0.692531	+	1.19950i
$969$	−20.2541	−	22.4237i	−0.650655	−	0.720352i
$970$	7.15512	−	12.3930i	0.229737	−	0.397916i
$971$	16.6145			0.533185			0.266592	−	0.963809i	$-0.414102\pi$
$971$	16.6145			0.533185			0.266592	+	0.963809i	$0.414102\pi$
$972$	8.19027	−	14.4462i	0.262703	−	0.463362i
$973$	−10.8254			−0.347046
$974$	−10.1702	+	17.6153i	−0.325874	+	0.564430i
$975$	6.75240	+	7.47571i	0.216250	+	0.239414i
$976$	−23.1219	−	40.0484i	−0.740115	−	1.28192i
$977$	30.5289	+	52.8776i	0.976707	+	1.69171i	0.674183	+	0.738564i	$0.264496\pi$
$977$	30.5289	+	52.8776i	0.976707	+	1.69171i	0.302523	+	0.953142i	$0.402171\pi$
$978$	33.2299	−	7.11768i	1.06258	−	0.227598i
$979$	−29.5268	+	51.1419i	−0.943680	+	1.63450i
$980$	1.06530			0.0340298
$981$	3.26580	−	32.0376i	0.104269	−	1.02288i
$982$	60.8233			1.94095
$983$	−3.51023	+	6.07990i	−0.111959	+	0.193919i	−0.916560	−	0.399897i	$-0.869046\pi$
$983$	−3.51023	+	6.07990i	−0.111959	+	0.193919i	0.804601	+	0.593816i	$0.202379\pi$
$984$	−3.46462	+	10.7202i	−0.110448	+	0.341746i
$985$	0.209326	+	0.362564i	0.00666969	+	0.0115522i
$986$	6.96146	+	12.0576i	0.221698	+	0.383992i
$987$	−2.22401	+	6.88149i	−0.0707912	+	0.219040i
$988$	11.4043	−	19.7528i	0.362819	−	0.628421i
$989$	11.3270			0.360178
$990$	26.0224	+	18.7820i	0.827046	+	0.596933i
$991$	60.0698			1.90818			0.954090	−	0.299522i	$-0.0968270\pi$
$991$	60.0698			1.90818			0.954090	+	0.299522i	$0.0968270\pi$
$992$	−19.0438	+	32.9849i	−0.604643	+	1.04727i
$993$	−18.9063	+	4.04964i	−0.599973	+	0.128511i
$994$	−9.07504	−	15.7184i	−0.287843	−	0.498558i
$995$	3.74333	+	6.48365i	0.118672	+	0.205545i
$996$	7.84309	+	8.68323i	0.248518	+	0.275139i
$997$	−7.44502	+	12.8951i	−0.235786	+	0.408393i	−0.959501	−	0.281706i	$-0.909100\pi$
$997$	−7.44502	+	12.8951i	−0.235786	+	0.408393i	0.723715	+	0.690099i	$0.242433\pi$
$998$	−5.31734			−0.168317
$999$	−18.8276	+	13.8147i	−0.595679	+	0.437079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.i.c.106.1	✓	8
3.2	odd	2		945.2.i.d.316.4		8
9.2	odd	6		2835.2.a.p.1.1		4
9.4	even	3	inner	315.2.i.c.211.1	yes	8
9.5	odd	6		945.2.i.d.631.4		8
9.7	even	3		2835.2.a.m.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.c.106.1	✓	8	1.1	even	1	trivial
315.2.i.c.211.1	yes	8	9.4	even	3	inner
945.2.i.d.316.4		8	3.2	odd	2
945.2.i.d.631.4		8	9.5	odd	6
2835.2.a.m.1.4		4	9.7	even	3
2835.2.a.p.1.1		4	9.2	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)

\(f(q)\)	\(=\)	\(q+(-0.875400 + 1.51624i) q^{2} +(-1.16098 - 1.28535i) q^{3} +(-0.532651 - 0.922579i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.96522 - 0.635135i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.63647 q^{8} +(-0.304233 + 2.98453i) q^{9} +O(q^{10})\)	\(q+(-0.875400 + 1.51624i) q^{2} +(-1.16098 - 1.28535i) q^{3} +(-0.532651 - 0.922579i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.96522 - 0.635135i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.63647 q^{8} +(-0.304233 + 2.98453i) q^{9} +1.75080 q^{10} +(3.05503 - 5.29147i) q^{11} +(-0.567434 + 1.75574i) q^{12} +(2.90805 + 5.03689i) q^{13} +(-0.875400 - 1.51624i) q^{14} +(-0.532651 + 1.64811i) q^{15} +(2.49787 - 4.32643i) q^{16} +4.73907 q^{17} +(-4.25894 - 3.07395i) q^{18} +3.68123 q^{19} +(-0.532651 + 0.922579i) q^{20} +(1.69363 - 0.362768i) q^{21} +(5.34875 + 9.26431i) q^{22} +(0.500000 + 0.866025i) q^{23} +(1.89991 + 2.10343i) q^{24} +(-0.500000 + 0.866025i) q^{25} -10.1828 q^{26} +(4.18937 - 3.07395i) q^{27} +1.06530 q^{28} +(0.839016 - 1.45322i) q^{29} +(-2.03265 - 2.25039i) q^{30} +(3.47922 + 6.02618i) q^{31} +(2.73680 + 4.74027i) q^{32} +(-10.3482 + 2.21654i) q^{33} +(-4.14858 + 7.18556i) q^{34} +1.00000 q^{35} +(2.91552 - 1.30904i) q^{36} -4.49413 q^{37} +(-3.22255 + 5.58163i) q^{38} +(3.09795 - 9.58561i) q^{39} +(0.818235 + 1.41722i) q^{40} +(1.98736 + 3.44220i) q^{41} +(-0.932566 + 2.88552i) q^{42} +(5.66350 - 9.80947i) q^{43} -6.50907 q^{44} +(2.73680 - 1.22879i) q^{45} -1.75080 q^{46} +(-2.08768 + 3.61598i) q^{47} +(-8.46095 + 1.81229i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.875400 - 1.51624i) q^{50} +(-5.50198 - 6.09135i) q^{51} +(3.09795 - 5.36581i) q^{52} -8.30597 q^{53} +(0.993464 + 9.04302i) q^{54} -6.11007 q^{55} +(0.818235 - 1.41722i) q^{56} +(-4.27385 - 4.73166i) q^{57} +(1.46895 + 2.54430i) q^{58} +(-0.418564 - 0.724974i) q^{59} +(1.80423 - 0.386458i) q^{60} +(4.62833 - 8.01651i) q^{61} -12.1828 q^{62} +(-2.43257 - 1.75574i) q^{63} +0.408295 q^{64} +(2.90805 - 5.03689i) q^{65} +(5.69804 - 17.6307i) q^{66} +(-2.25894 - 3.91259i) q^{67} +(-2.52427 - 4.37217i) q^{68} +(0.532651 - 1.64811i) q^{69} +(-0.875400 + 1.51624i) q^{70} +10.3667 q^{71} +(0.497868 - 4.88410i) q^{72} +12.2346 q^{73} +(3.93417 - 6.81418i) q^{74} +(1.69363 - 0.362768i) q^{75} +(-1.96081 - 3.39623i) q^{76} +(3.05503 + 5.29147i) q^{77} +(11.8221 + 13.0885i) q^{78} +(-4.41643 + 7.64948i) q^{79} -4.99574 q^{80} +(-8.81488 - 1.81599i) q^{81} -6.95892 q^{82} +(3.17072 - 5.49185i) q^{83} +(-1.23680 - 1.36928i) q^{84} +(-2.36954 - 4.10416i) q^{85} +(9.91566 + 17.1744i) q^{86} +(-2.84197 + 0.608737i) q^{87} +(-4.99947 + 8.65933i) q^{88} -9.66496 q^{89} +(-0.532651 + 5.22532i) q^{90} -5.81610 q^{91} +(0.532651 - 0.922579i) q^{92} +(3.70642 - 11.4683i) q^{93} +(-3.65512 - 6.33085i) q^{94} +(-1.84062 - 3.18804i) q^{95} +(2.91552 - 9.02112i) q^{96} +(4.08677 - 7.07849i) q^{97} +1.75080 q^{98} +(14.8631 + 10.7277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q + q^2 - q^3 - q^4 - 4 * q^5 + 8 * q^6 - 4 * q^7 - 6 * q^8 + 5 * q^9	\( 8 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{7} - 6 q^{8} + 5 q^{9} - 2 q^{10} + q^{11} - 17 q^{12} + 12 q^{13} + q^{14} - q^{15} + q^{16} + 10 q^{17} - 16 q^{18} - 18 q^{19} - q^{20} + 2 q^{21} + 17 q^{22} + 4 q^{23} + 6 q^{24} - 4 q^{25} - 2 q^{26} - 16 q^{27} + 2 q^{28} + 15 q^{29} - 13 q^{30} + 16 q^{31} + 2 q^{32} - 6 q^{33} + 11 q^{34} + 8 q^{35} - 14 q^{36} - 30 q^{37} - 24 q^{38} + 15 q^{39} + 3 q^{40} + 2 q^{41} + 5 q^{42} + 7 q^{43} + 6 q^{44} + 2 q^{45} + 2 q^{46} + 10 q^{47} - 14 q^{48} - 4 q^{49} + q^{50} + 37 q^{51} + 15 q^{52} - 22 q^{54} - 2 q^{55} + 3 q^{56} - 22 q^{57} - 17 q^{58} + 13 q^{59} + 7 q^{60} + 32 q^{61} - 18 q^{62} - 7 q^{63} - 30 q^{64} + 12 q^{65} + 45 q^{66} - 41 q^{68} + q^{69} + q^{70} + 26 q^{71} - 15 q^{72} - 4 q^{73} - 13 q^{74} + 2 q^{75} + 11 q^{76} + q^{77} + 51 q^{78} - 2 q^{80} - 31 q^{81} + 12 q^{82} - 17 q^{83} + 10 q^{84} - 5 q^{85} + 15 q^{86} + 11 q^{87} + 11 q^{88} - 34 q^{89} - q^{90} - 24 q^{91} + q^{92} + 5 q^{93} - 15 q^{94} + 9 q^{95} - 14 q^{96} + 4 q^{97} - 2 q^{98} + 48 q^{99}+O(q^{100}) \) 8 * q + q^2 - q^3 - q^4 - 4 * q^5 + 8 * q^6 - 4 * q^7 - 6 * q^8 + 5 * q^9 - 2 * q^10 + q^11 - 17 * q^12 + 12 * q^13 + q^14 - q^15 + q^16 + 10 * q^17 - 16 * q^18 - 18 * q^19 - q^20 + 2 * q^21 + 17 * q^22 + 4 * q^23 + 6 * q^24 - 4 * q^25 - 2 * q^26 - 16 * q^27 + 2 * q^28 + 15 * q^29 - 13 * q^30 + 16 * q^31 + 2 * q^32 - 6 * q^33 + 11 * q^34 + 8 * q^35 - 14 * q^36 - 30 * q^37 - 24 * q^38 + 15 * q^39 + 3 * q^40 + 2 * q^41 + 5 * q^42 + 7 * q^43 + 6 * q^44 + 2 * q^45 + 2 * q^46 + 10 * q^47 - 14 * q^48 - 4 * q^49 + q^50 + 37 * q^51 + 15 * q^52 - 22 * q^54 - 2 * q^55 + 3 * q^56 - 22 * q^57 - 17 * q^58 + 13 * q^59 + 7 * q^60 + 32 * q^61 - 18 * q^62 - 7 * q^63 - 30 * q^64 + 12 * q^65 + 45 * q^66 - 41 * q^68 + q^69 + q^70 + 26 * q^71 - 15 * q^72 - 4 * q^73 - 13 * q^74 + 2 * q^75 + 11 * q^76 + q^77 + 51 * q^78 - 2 * q^80 - 31 * q^81 + 12 * q^82 - 17 * q^83 + 10 * q^84 - 5 * q^85 + 15 * q^86 + 11 * q^87 + 11 * q^88 - 34 * q^89 - q^90 - 24 * q^91 + q^92 + 5 * q^93 - 15 * q^94 + 9 * q^95 - 14 * q^96 + 4 * q^97 - 2 * q^98 + 48 * q^99

Introduction

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