LMFDB - Embedded newform 462.2.j.h.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (of order $5$, degree $4$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.20164000000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 76x^{4} + 781x^{2} + 5041 $ x^8 + 6x^6 + 76x^4 + 781*x^2 + 5041
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.1
Root			$-2.50900 - 1.82290i$ of defining polynomial
Character	$\chi$	$=$	462.421
Dual form			462.2.j.h.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-3.31802 - 2.41068i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-3.31802 - 2.41068i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -4.10130 q^{10} +(-1.81802 + 2.77395i) q^{11} -1.00000 q^{12} +(1.37640 - 1.00002i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-1.26737 + 3.90056i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.50000 - 1.08981i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(-0.901312 - 2.77395i) q^{19} +(-3.31802 + 2.41068i) q^{20} +1.00000 q^{21} +(0.159681 + 3.31278i) q^{22} -7.57343 q^{23} +(-0.809017 + 0.587785i) q^{24} +(3.65277 + 11.2421i) q^{25} +(0.525739 - 1.61806i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-0.0570413 + 0.175555i) q^{29} +(1.26737 + 3.90056i) q^{30} +(4.95062 - 3.59683i) q^{31} -1.00000 q^{32} +(3.19998 + 0.871839i) q^{33} -1.85410 q^{34} +(3.31802 - 2.41068i) q^{35} +(0.309017 + 0.951057i) q^{36} +(3.03130 - 9.32939i) q^{37} +(-2.35966 - 1.71440i) q^{38} +(-1.37640 - 1.00002i) q^{39} +(-1.26737 + 3.90056i) q^{40} +(-2.74719 - 8.45499i) q^{41} +(0.809017 - 0.587785i) q^{42} -10.0069 q^{43} +(2.07639 + 2.58624i) q^{44} +4.10130 q^{45} +(-6.12703 + 4.45155i) q^{46} +(0.560993 + 1.72656i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(9.56309 + 6.94799i) q^{50} +(-0.572949 + 1.76336i) q^{51} +(-0.525739 - 1.61806i) q^{52} +(6.94640 - 5.04685i) q^{53} +1.00000 q^{54} +(12.7193 - 4.82136i) q^{55} +1.00000 q^{56} +(-2.35966 + 1.71440i) q^{57} +(0.0570413 + 0.175555i) q^{58} +(1.94296 - 5.97981i) q^{59} +(3.31802 + 2.41068i) q^{60} +(-7.11030 - 5.16593i) q^{61} +(1.89097 - 5.81980i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} -6.97765 q^{65} +(3.10130 - 1.17557i) q^{66} +4.31667 q^{67} +(-1.50000 + 1.08981i) q^{68} +(2.34032 + 7.20276i) q^{69} +(1.26737 - 3.90056i) q^{70} +(8.87210 + 6.44596i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-3.32492 + 10.2331i) q^{73} +(-3.03130 - 9.32939i) q^{74} +(9.56309 - 6.94799i) q^{75} -2.91671 q^{76} +(-2.07639 - 2.58624i) q^{77} -1.70133 q^{78} +(9.98796 - 7.25668i) q^{79} +(1.26737 + 3.90056i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-7.19225 - 5.22547i) q^{82} +(-1.87423 - 1.36171i) q^{83} +(0.309017 - 0.951057i) q^{84} +(2.34983 + 7.23204i) q^{85} +(-8.09573 + 5.88189i) q^{86} +0.184589 q^{87} +(3.19998 + 0.871839i) q^{88} -8.52883 q^{89} +(3.31802 - 2.41068i) q^{90} +(0.525739 + 1.61806i) q^{91} +(-2.34032 + 7.20276i) q^{92} +(-4.95062 - 3.59683i) q^{93} +(1.46870 + 1.06707i) q^{94} +(-3.69655 + 11.3768i) q^{95} +(0.309017 + 0.951057i) q^{96} +(0.390967 - 0.284054i) q^{97} -1.00000 q^{98} +(-0.159681 - 3.31278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} - 8 q^{10} + 10 q^{11} - 8 q^{12} + 10 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 12 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 4 q^{25} + 2 q^{27} + 2 q^{28} - 2 q^{29} - 2 q^{30} - 4 q^{31} - 8 q^{32} + 10 q^{33} + 12 q^{34} + 2 q^{35} - 2 q^{36} + 30 q^{37} - 2 q^{38} - 10 q^{39} + 2 q^{40} - 24 q^{41} + 2 q^{42} - 20 q^{43} + 8 q^{45} - 20 q^{46} - 6 q^{47} + 2 q^{48} - 2 q^{49} + 14 q^{50} - 18 q^{51} + 24 q^{53} + 8 q^{54} + 68 q^{55} + 8 q^{56} - 2 q^{57} + 2 q^{58} + 14 q^{59} + 2 q^{60} - 12 q^{61} + 4 q^{62} + 2 q^{63} - 2 q^{64} - 44 q^{65} - 12 q^{67} - 12 q^{68} + 20 q^{69} - 2 q^{70} + 4 q^{71} + 2 q^{72} - 34 q^{73} - 30 q^{74} + 14 q^{75} - 8 q^{76} - 20 q^{78} - 22 q^{79} - 2 q^{80} - 2 q^{81} - 6 q^{82} + 12 q^{83} - 2 q^{84} + 18 q^{85} - 30 q^{86} - 8 q^{87} + 10 q^{88} + 44 q^{89} + 2 q^{90} - 20 q^{92} + 4 q^{93} + 6 q^{94} - 44 q^{95} - 2 q^{96} - 8 q^{97} - 8 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 - 8 * q^10 + 10 * q^11 - 8 * q^12 + 10 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 12 * q^17 + 2 * q^18 + 2 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 4 * q^25 + 2 * q^27 + 2 * q^28 - 2 * q^29 - 2 * q^30 - 4 * q^31 - 8 * q^32 + 10 * q^33 + 12 * q^34 + 2 * q^35 - 2 * q^36 + 30 * q^37 - 2 * q^38 - 10 * q^39 + 2 * q^40 - 24 * q^41 + 2 * q^42 - 20 * q^43 + 8 * q^45 - 20 * q^46 - 6 * q^47 + 2 * q^48 - 2 * q^49 + 14 * q^50 - 18 * q^51 + 24 * q^53 + 8 * q^54 + 68 * q^55 + 8 * q^56 - 2 * q^57 + 2 * q^58 + 14 * q^59 + 2 * q^60 - 12 * q^61 + 4 * q^62 + 2 * q^63 - 2 * q^64 - 44 * q^65 - 12 * q^67 - 12 * q^68 + 20 * q^69 - 2 * q^70 + 4 * q^71 + 2 * q^72 - 34 * q^73 - 30 * q^74 + 14 * q^75 - 8 * q^76 - 20 * q^78 - 22 * q^79 - 2 * q^80 - 2 * q^81 - 6 * q^82 + 12 * q^83 - 2 * q^84 + 18 * q^85 - 30 * q^86 - 8 * q^87 + 10 * q^88 + 44 * q^89 + 2 * q^90 - 20 * q^92 + 4 * q^93 + 6 * q^94 - 44 * q^95 - 2 * q^96 - 8 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−3.31802	−	2.41068i	−1.48386	−	1.07809i	−0.976287	−	0.216482i	$-0.930542\pi$
$5$	−3.31802	−	2.41068i	−1.48386	−	1.07809i	−0.507576	−	0.861607i	$-0.669458\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−4.10130			−1.29694
$11$	−1.81802	+	2.77395i	−0.548153	+	0.836378i
$11$	−1.81802	+	2.77395i	−0.548153	+	0.836378i
$12$	−1.00000			−0.288675
$13$	1.37640	−	1.00002i	0.381746	−	0.277354i	−0.380319	−	0.924855i	$-0.624186\pi$
$13$	1.37640	−	1.00002i	0.381746	−	0.277354i	0.762065	+	0.647501i	$0.224186\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	−1.26737	+	3.90056i	−0.327234	+	1.00712i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.50000	−	1.08981i	−0.363803	−	0.264319i	0.390833	−	0.920461i	$-0.372187\pi$
$17$	−1.50000	−	1.08981i	−0.363803	−	0.264319i	−0.754637	+	0.656143i	$0.772187\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	−0.901312	−	2.77395i	−0.206775	−	0.636388i	−0.999636	−	0.0269854i	$-0.991409\pi$
$19$	−0.901312	−	2.77395i	−0.206775	−	0.636388i	0.792861	−	0.609403i	$-0.208591\pi$
$20$	−3.31802	+	2.41068i	−0.741931	+	0.539045i
$21$	1.00000			0.218218
$22$	0.159681	+	3.31278i	0.0340441	+	0.706287i
$23$	−7.57343			−1.57917			−0.789585	−	0.613641i	$-0.789704\pi$
$23$	−7.57343			−1.57917			−0.789585	+	0.613641i	$0.789704\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	3.65277	+	11.2421i	0.730555	+	2.24842i
$26$	0.525739	−	1.61806i	0.103106	−	0.317327i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	−0.0570413	+	0.175555i	−0.0105923	+	0.0325998i	−0.956213	−	0.292672i	$-0.905456\pi$
$29$	−0.0570413	+	0.175555i	−0.0105923	+	0.0325998i	0.945621	+	0.325271i	$0.105456\pi$
$30$	1.26737	+	3.90056i	0.231389	+	0.712142i
$31$	4.95062	−	3.59683i	0.889157	−	0.646010i	−0.0465012	−	0.998918i	$-0.514807\pi$
$31$	4.95062	−	3.59683i	0.889157	−	0.646010i	0.935658	+	0.352908i	$0.114807\pi$
$32$	−1.00000			−0.176777
$33$	3.19998	+	0.871839i	0.557046	+	0.151768i
$34$	−1.85410			−0.317976
$35$	3.31802	−	2.41068i	0.560847	−	0.407479i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	3.03130	−	9.32939i	0.498343	−	1.53374i	−0.313338	−	0.949642i	$-0.601447\pi$
$37$	3.03130	−	9.32939i	0.498343	−	1.53374i	0.811681	−	0.584100i	$-0.198553\pi$
$38$	−2.35966	−	1.71440i	−0.382788	−	0.278112i
$39$	−1.37640	−	1.00002i	−0.220401	−	0.160131i
$40$	−1.26737	+	3.90056i	−0.200389	+	0.616733i
$41$	−2.74719	−	8.45499i	−0.429040	−	1.32045i	−0.899073	−	0.437799i	$-0.855758\pi$
$41$	−2.74719	−	8.45499i	−0.429040	−	1.32045i	0.470033	−	0.882649i	$-0.344242\pi$
$42$	0.809017	−	0.587785i	0.124834	−	0.0906972i
$43$	−10.0069			−1.52603			−0.763017	−	0.646378i	$-0.776283\pi$
$43$	−10.0069			−1.52603			−0.763017	+	0.646378i	$0.776283\pi$
$44$	2.07639	+	2.58624i	0.313027	+	0.389890i
$45$	4.10130			0.611385
$46$	−6.12703	+	4.45155i	−0.903382	+	0.656345i
$47$	0.560993	+	1.72656i	0.0818292	+	0.251844i	0.983598	−	0.180374i	$-0.0577309\pi$
$47$	0.560993	+	1.72656i	0.0818292	+	0.251844i	−0.901769	+	0.432219i	$0.857731\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	9.56309	+	6.94799i	1.35242	+	0.982594i
$51$	−0.572949	+	1.76336i	−0.0802289	+	0.246919i
$52$	−0.525739	−	1.61806i	−0.0729069	−	0.224384i
$53$	6.94640	−	5.04685i	0.954161	−	0.693239i	0.00237364	−	0.999997i	$-0.499244\pi$
$53$	6.94640	−	5.04685i	0.954161	−	0.693239i	0.951787	+	0.306759i	$0.0992444\pi$
$54$	1.00000			0.136083
$55$	12.7193	−	4.82136i	1.71507	−	0.650112i
$56$	1.00000			0.133631
$57$	−2.35966	+	1.71440i	−0.312545	+	0.227077i
$58$	0.0570413	+	0.175555i	0.00748989	+	0.0230515i
$59$	1.94296	−	5.97981i	0.252952	−	0.778505i	−0.741275	−	0.671202i	$-0.765778\pi$
$59$	1.94296	−	5.97981i	0.252952	−	0.778505i	0.994226	−	0.107303i	$-0.0342216\pi$
$60$	3.31802	+	2.41068i	0.428354	+	0.311218i
$61$	−7.11030	−	5.16593i	−0.910380	−	0.661430i	0.0307308	−	0.999528i	$-0.490217\pi$
$61$	−7.11030	−	5.16593i	−0.910380	−	0.661430i	−0.941111	+	0.338098i	$0.890217\pi$
$62$	1.89097	−	5.81980i	0.240153	−	0.739115i
$63$	−0.309017	−	0.951057i	−0.0389325	−	0.119822i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−6.97765			−0.865471
$66$	3.10130	−	1.17557i	0.381743	−	0.144703i
$67$	4.31667			0.527366			0.263683	−	0.964609i	$-0.415063\pi$
$67$	4.31667			0.527366			0.263683	+	0.964609i	$0.415063\pi$
$68$	−1.50000	+	1.08981i	−0.181902	+	0.132159i
$69$	2.34032	+	7.20276i	0.281741	+	0.867111i
$70$	1.26737	−	3.90056i	0.151480	−	0.466207i
$71$	8.87210	+	6.44596i	1.05292	+	0.764995i	0.972766	−	0.231787i	$-0.0744574\pi$
$71$	8.87210	+	6.44596i	1.05292	+	0.764995i	0.0801585	+	0.996782i	$0.474457\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	−3.32492	+	10.2331i	−0.389153	+	1.19769i	0.544269	+	0.838910i	$0.316807\pi$
$73$	−3.32492	+	10.2331i	−0.389153	+	1.19769i	−0.933422	+	0.358779i	$0.883193\pi$
$74$	−3.03130	−	9.32939i	−0.352382	−	1.08452i
$75$	9.56309	−	6.94799i	1.10425	−	0.802285i
$76$	−2.91671			−0.334569
$77$	−2.07639	−	2.58624i	−0.236626	−	0.294729i
$78$	−1.70133			−0.192637
$79$	9.98796	−	7.25668i	1.12373	−	0.816440i	0.138963	−	0.990298i	$-0.455623\pi$
$79$	9.98796	−	7.25668i	1.12373	−	0.816440i	0.984771	+	0.173857i	$0.0556232\pi$
$80$	1.26737	+	3.90056i	0.141696	+	0.436096i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−7.19225	−	5.22547i	−0.794251	−	0.577057i
$83$	−1.87423	−	1.36171i	−0.205723	−	0.149467i	0.480153	−	0.877185i	$-0.340581\pi$
$83$	−1.87423	−	1.36171i	−0.205723	−	0.149467i	−0.685877	+	0.727718i	$0.740581\pi$
$84$	0.309017	−	0.951057i	0.0337165	−	0.103769i
$85$	2.34983	+	7.23204i	0.254875	+	0.784425i
$86$	−8.09573	+	5.88189i	−0.872985	+	0.634261i
$87$	0.184589			0.0197901
$88$	3.19998	+	0.871839i	0.341119	+	0.0929384i
$89$	−8.52883			−0.904054			−0.452027	−	0.892004i	$-0.649299\pi$
$89$	−8.52883			−0.904054			−0.452027	+	0.892004i	$0.649299\pi$
$90$	3.31802	−	2.41068i	0.349750	−	0.254108i
$91$	0.525739	+	1.61806i	0.0551124	+	0.169619i
$92$	−2.34032	+	7.20276i	−0.243995	+	0.750940i
$93$	−4.95062	−	3.59683i	−0.513355	−	0.372974i
$94$	1.46870	+	1.06707i	0.151485	+	0.110060i
$95$	−3.69655	+	11.3768i	−0.379258	+	1.16723i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	0.390967	−	0.284054i	0.0396967	−	0.0288413i	−0.567760	−	0.823194i	$-0.692190\pi$
$97$	0.390967	−	0.284054i	0.0396967	−	0.0288413i	0.607457	+	0.794353i	$0.292190\pi$
$98$	−1.00000			−0.101015
$99$	−0.159681	−	3.31278i	−0.0160485	−	0.332947i
$100$	11.8206			1.18206
$101$	6.41931	−	4.66390i	0.638746	−	0.464076i	−0.220673	−	0.975348i	$-0.570826\pi$
$101$	6.41931	−	4.66390i	0.638746	−	0.464076i	0.859419	+	0.511272i	$0.170826\pi$
$102$	0.572949	+	1.76336i	0.0567304	+	0.174598i
$103$	−4.49309	+	13.8283i	−0.442718	+	1.36254i	0.442250	+	0.896892i	$0.354180\pi$
$103$	−4.49309	+	13.8283i	−0.442718	+	1.36254i	−0.884967	+	0.465653i	$0.845820\pi$
$104$	−1.37640	−	1.00002i	−0.134967	−	0.0980596i
$105$	−3.31802	−	2.41068i	−0.323805	−	0.235258i
$106$	2.65329	−	8.16598i	0.257710	−	0.793150i
$107$	0.130504	+	0.401649i	0.0126163	+	0.0388289i	0.957166	−	0.289538i	$-0.0935017\pi$
$107$	0.130504	+	0.401649i	0.0126163	+	0.0388289i	−0.944550	+	0.328367i	$0.893502\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	−5.13477			−0.491822			−0.245911	−	0.969292i	$-0.579087\pi$
$109$	−5.13477			−0.491822			−0.245911	+	0.969292i	$0.579087\pi$
$110$	7.45623	−	11.3768i	0.710923	−	1.08474i
$111$	−9.80950			−0.931076
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	−3.11752	−	9.59474i	−0.293272	−	0.902597i	−0.983797	−	0.179289i	$-0.942620\pi$
$113$	−3.11752	−	9.59474i	−0.293272	−	0.902597i	0.690525	−	0.723309i	$-0.257380\pi$
$114$	−0.901312	+	2.77395i	−0.0844156	+	0.259804i
$115$	25.1288	+	18.2571i	2.34327	+	1.70249i
$116$	0.149336	+	0.108499i	0.0138655	+	0.0100739i
$117$	−0.525739	+	1.61806i	−0.0486046	+	0.149590i
$118$	−1.94296	−	5.97981i	−0.178864	−	0.550486i
$119$	1.50000	−	1.08981i	0.137505	−	0.0999031i
$120$	4.10130			0.374395
$121$	−4.38962	−	10.0862i	−0.399057	−	0.916926i
$122$	−8.78881			−0.795701
$123$	−7.19225	+	5.22547i	−0.648503	+	0.471165i
$124$	−1.89097	−	5.81980i	−0.169814	−	0.522633i
$125$	8.64426	−	26.6043i	0.773166	−	2.37956i
$126$	−0.809017	−	0.587785i	−0.0720730	−	0.0523641i
$127$	8.59700	+	6.24608i	0.762860	+	0.554250i	0.899786	−	0.436331i	$-0.143722\pi$
$127$	8.59700	+	6.24608i	0.762860	+	0.554250i	−0.136926	+	0.990581i	$0.543722\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	3.09229	+	9.51710i	0.272261	+	0.837934i
$130$	−5.64504	+	4.10136i	−0.495102	+	0.359713i
$131$	13.5707			1.18568			0.592841	−	0.805320i	$-0.298006\pi$
$131$	13.5707			1.18568			0.592841	+	0.805320i	$0.298006\pi$
$132$	1.81802	−	2.77395i	0.158238	−	0.241442i
$133$	2.91671			0.252910
$134$	3.49226	−	2.53728i	0.301686	−	0.219187i
$135$	−1.26737	−	3.90056i	−0.109078	−	0.335707i
$136$	−0.572949	+	1.76336i	−0.0491300	+	0.151207i
$137$	−2.98544	−	2.16905i	−0.255063	−	0.185314i	0.452905	−	0.891559i	$-0.350388\pi$
$137$	−2.98544	−	2.16905i	−0.255063	−	0.185314i	−0.707968	+	0.706245i	$0.750388\pi$
$138$	6.12703	+	4.45155i	0.521568	+	0.378941i
$139$	1.81802	−	5.59528i	0.154202	−	0.474586i	−0.843877	−	0.536537i	$-0.819732\pi$
$139$	1.81802	−	5.59528i	0.154202	−	0.474586i	0.998079	+	0.0619510i	$0.0197323\pi$
$140$	−1.26737	−	3.90056i	−0.107112	−	0.329658i
$141$	1.46870	−	1.06707i	0.123687	−	0.0898636i
$142$	10.9665			0.920290
$143$	0.271670	+	5.63612i	0.0227182	+	0.471316i
$144$	1.00000			0.0833333
$145$	0.612471	−	0.444986i	0.0508630	−	0.0369541i
$146$	3.32492	+	10.2331i	0.275173	+	0.846895i
$147$	−0.309017	+	0.951057i	−0.0254873	+	0.0784418i
$148$	−7.93605	−	5.76588i	−0.652339	−	0.473952i
$149$	7.23607	+	5.25731i	0.592802	+	0.430696i	0.843317	−	0.537417i	$-0.180600\pi$
$149$	7.23607	+	5.25731i	0.592802	+	0.430696i	−0.250515	+	0.968113i	$0.580600\pi$
$150$	3.65277	−	11.2421i	0.298248	−	0.917912i
$151$	3.30767	+	10.1800i	0.269175	+	0.828434i	0.990702	+	0.136049i	$0.0434403\pi$
$151$	3.30767	+	10.1800i	0.269175	+	0.828434i	−0.721528	+	0.692386i	$0.756560\pi$
$152$	−2.35966	+	1.71440i	−0.191394	+	0.139056i
$153$	1.85410			0.149895
$154$	−3.19998	−	0.871839i	−0.257862	−	0.0702548i
$155$	−25.0970			−2.01584
$156$	−1.37640	+	1.00002i	−0.110200	+	0.0800653i
$157$	4.60525	+	14.1735i	0.367539	+	1.13117i	0.948376	+	0.317148i	$0.102725\pi$
$157$	4.60525	+	14.1735i	0.367539	+	1.13117i	−0.580837	+	0.814020i	$0.697275\pi$
$158$	3.81506	−	11.7416i	0.303510	−	0.934108i
$159$	−6.94640	−	5.04685i	−0.550885	−	0.400241i
$160$	3.31802	+	2.41068i	0.262312	+	0.190581i
$161$	2.34032	−	7.20276i	0.184443	−	0.567657i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	14.5623	−	10.5801i	1.14061	−	0.828700i	0.153404	−	0.988164i	$-0.450976\pi$
$163$	14.5623	−	10.5801i	1.14061	−	0.828700i	0.987204	+	0.159463i	$0.0509764\pi$
$164$	−8.89011			−0.694201
$165$	−8.51588	−	10.6069i	−0.662960	−	0.825747i
$166$	−2.31667			−0.179809
$167$	−12.5047	+	9.08520i	−0.967643	+	0.703034i	−0.954913	−	0.296885i	$-0.904052\pi$
$167$	−12.5047	+	9.08520i	−0.967643	+	0.703034i	−0.0127297	+	0.999919i	$0.504052\pi$
$168$	−0.309017	−	0.951057i	−0.0238412	−	0.0733756i
$169$	−3.12277	+	9.61089i	−0.240213	+	0.739299i
$170$	6.15194	+	4.46965i	0.471833	+	0.342806i
$171$	2.35966	+	1.71440i	0.180448	+	0.131103i
$172$	−3.09229	+	9.51710i	−0.235785	+	0.725672i
$173$	−7.10046	−	21.8530i	−0.539838	−	1.66145i	−0.732956	−	0.680276i	$-0.761860\pi$
$173$	−7.10046	−	21.8530i	−0.539838	−	1.66145i	0.193118	−	0.981176i	$-0.438140\pi$
$174$	0.149336	−	0.108499i	0.0113211	−	0.00822529i
$175$	−11.8206			−0.893555
$176$	3.10130	−	1.17557i	0.233769	−	0.0886120i
$177$	−6.28755			−0.472601
$178$	−6.89997	+	5.01312i	−0.517174	+	0.375749i
$179$	5.32097	+	16.3763i	0.397708	+	1.22402i	0.926832	+	0.375476i	$0.122521\pi$
$179$	5.32097	+	16.3763i	0.397708	+	1.22402i	−0.529124	+	0.848544i	$0.677479\pi$
$180$	1.26737	−	3.90056i	0.0944642	−	0.290731i
$181$	−7.41509	−	5.38738i	−0.551160	−	0.400441i	0.277053	−	0.960855i	$-0.410642\pi$
$181$	−7.41509	−	5.38738i	−0.551160	−	0.400441i	−0.828213	+	0.560414i	$0.810642\pi$
$182$	1.37640	+	1.00002i	0.102026	+	0.0741261i
$183$	−2.71589	+	8.35865i	−0.200764	+	0.617890i
$184$	2.34032	+	7.20276i	0.172531	+	0.530995i
$185$	−32.5481	+	23.6476i	−2.39298	+	1.73860i
$186$	−6.11930			−0.448689
$187$	5.75012	−	2.17963i	0.420490	−	0.159390i
$188$	1.81541			0.132402
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	3.69655	+	11.3768i	0.268176	+	0.825360i
$191$	6.74507	−	20.7592i	0.488056	−	1.50208i	−0.339449	−	0.940624i	$-0.610241\pi$
$191$	6.74507	−	20.7592i	0.488056	−	1.50208i	0.827505	−	0.561458i	$-0.189759\pi$
$192$	0.809017	+	0.587785i	0.0583858	+	0.0424197i
$193$	−18.6824	−	13.5735i	−1.34479	−	0.977045i	−0.999253	−	0.0386391i	$-0.987698\pi$
$193$	−18.6824	−	13.5735i	−1.34479	−	0.977045i	−0.345534	−	0.938406i	$-0.612302\pi$
$194$	0.149336	−	0.459609i	0.0107217	−	0.0329980i
$195$	2.15621	+	6.63614i	0.154410	+	0.475224i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	19.6661			1.40115			0.700577	−	0.713577i	$-0.252926\pi$
$197$	19.6661			1.40115			0.700577	+	0.713577i	$0.252926\pi$
$198$	−2.07639	−	2.58624i	−0.147562	−	0.183796i
$199$	−7.07904			−0.501820			−0.250910	−	0.968010i	$-0.580730\pi$
$199$	−7.07904			−0.501820			−0.250910	+	0.968010i	$0.580730\pi$
$200$	9.56309	−	6.94799i	0.676212	−	0.491297i
$201$	−1.33393	−	4.10540i	−0.0940879	−	0.289573i
$202$	2.45196	−	7.54636i	0.172519	−	0.530960i
$203$	−0.149336	−	0.108499i	−0.0104813	−	0.00761514i
$204$	1.50000	+	1.08981i	0.105021	+	0.0763022i
$205$	−11.2671	+	34.6764i	−0.786925	+	2.42191i
$206$	4.49309	+	13.8283i	0.313049	+	0.963465i
$207$	6.12703	−	4.45155i	0.425858	−	0.309404i
$208$	−1.70133			−0.117966
$209$	9.33341	+	2.54290i	0.645606	+	0.175896i
$210$	−4.10130			−0.283016
$211$	−17.6296	+	12.8086i	−1.21367	+	0.881782i	−0.995559	−	0.0941420i	$-0.969989\pi$
$211$	−17.6296	+	12.8086i	−1.21367	+	0.881782i	−0.218110	+	0.975924i	$0.569989\pi$
$212$	−2.65329	−	8.16598i	−0.182229	−	0.560842i
$213$	3.38884	−	10.4298i	0.232200	−	0.714637i
$214$	0.341663	+	0.248233i	0.0233556	+	0.0169688i
$215$	33.2030	+	24.1234i	2.26443	+	1.64520i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	1.89097	+	5.81980i	0.128367	+	0.395074i
$218$	−4.15412	+	3.01814i	−0.281352	+	0.204414i
$219$	10.7597			0.727072
$220$	−0.654899	−	13.5867i	−0.0441533	−	0.916014i
$221$	−3.15444			−0.212190
$222$	−7.93605	+	5.76588i	−0.532633	+	0.386980i
$223$	−4.62620	−	14.2380i	−0.309794	−	0.953446i	−0.977845	−	0.209331i	$-0.932871\pi$
$223$	−4.62620	−	14.2380i	−0.309794	−	0.953446i	0.668051	−	0.744115i	$-0.267129\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	−9.56309	−	6.94799i	−0.637539	−	0.463199i
$226$	−8.16177	−	5.92988i	−0.542913	−	0.394450i
$227$	−3.81850	+	11.7521i	−0.253443	+	0.780017i	0.740690	+	0.671847i	$0.234499\pi$
$227$	−3.81850	+	11.7521i	−0.253443	+	0.780017i	−0.994132	+	0.108169i	$0.965501\pi$
$228$	0.901312	+	2.77395i	0.0596908	+	0.183709i
$229$	8.37984	−	6.08831i	0.553755	−	0.402327i	−0.275413	−	0.961326i	$-0.588815\pi$
$229$	8.37984	−	6.08831i	0.553755	−	0.402327i	0.829168	+	0.558999i	$0.188815\pi$
$230$	31.0609			2.04809
$231$	−1.81802	+	2.77395i	−0.119617	+	0.182513i
$232$	0.184589			0.0121189
$233$	−9.60600	+	6.97917i	−0.629310	+	0.457220i	−0.856161	−	0.516709i	$-0.827157\pi$
$233$	−9.60600	+	6.97917i	−0.629310	+	0.457220i	0.226851	+	0.973929i	$0.427157\pi$
$234$	0.525739	+	1.61806i	0.0343686	+	0.105776i
$235$	2.30080	−	7.08112i	0.150087	−	0.461922i
$236$	−5.08673	−	3.69573i	−0.331118	−	0.240571i
$237$	−9.98796	−	7.25668i	−0.648788	−	0.471372i
$238$	0.572949	−	1.76336i	0.0371388	−	0.114301i
$239$	7.64587	+	23.5316i	0.494570	+	1.52213i	0.817626	+	0.575750i	$0.195290\pi$
$239$	7.64587	+	23.5316i	0.494570	+	1.52213i	−0.323056	+	0.946380i	$0.604710\pi$
$240$	3.31802	−	2.41068i	0.214177	−	0.155609i
$241$	−2.44726			−0.157642			−0.0788209	−	0.996889i	$-0.525116\pi$
$241$	−2.44726			−0.157642			−0.0788209	+	0.996889i	$0.525116\pi$
$242$	−9.47979	−	5.57974i	−0.609384	−	0.358679i
$243$	−1.00000			−0.0641500
$244$	−7.11030	+	5.16593i	−0.455190	+	0.330715i
$245$	1.26737	+	3.90056i	0.0809693	+	0.249198i
$246$	−2.74719	+	8.45499i	−0.175155	+	0.539071i
$247$	−4.01456	−	2.91675i	−0.255441	−	0.185588i
$248$	−4.95062	−	3.59683i	−0.314364	−	0.228399i
$249$	−0.715892	+	2.20329i	−0.0453678	+	0.139628i
$250$	−8.64426	−	26.6043i	−0.546711	−	1.68260i
$251$	−0.642510	+	0.466811i	−0.0405549	+	0.0294648i	−0.607878	−	0.794030i	$-0.707979\pi$
$251$	−0.642510	+	0.466811i	−0.0405549	+	0.0294648i	0.567323	+	0.823495i	$0.307979\pi$
$252$	−1.00000			−0.0629941
$253$	13.7686	−	21.0083i	0.865627	−	1.32078i
$254$	10.6265			0.666764
$255$	6.15194	−	4.46965i	0.385250	−	0.279900i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−4.51556	+	13.8975i	−0.281673	+	0.866900i	0.705703	+	0.708507i	$0.250631\pi$
$257$	−4.51556	+	13.8975i	−0.281673	+	0.866900i	−0.987376	+	0.158393i	$0.949369\pi$
$258$	8.09573	+	5.88189i	0.504018	+	0.366191i
$259$	7.93605	+	5.76588i	0.493122	+	0.358274i
$260$	−2.15621	+	6.63614i	−0.133723	+	0.411556i
$261$	−0.0570413	−	0.175555i	−0.00353077	−	0.0108666i
$262$	10.9790	−	7.97668i	0.678283	−	0.492801i
$263$	−5.86523			−0.361665			−0.180833	−	0.983514i	$-0.557879\pi$
$263$	−5.86523			−0.361665			−0.180833	+	0.983514i	$0.557879\pi$
$264$	−0.159681	−	3.31278i	−0.00982768	−	0.203887i
$265$	−35.2146			−2.16322
$266$	2.35966	−	1.71440i	0.144680	−	0.105116i
$267$	2.63555	+	8.11140i	0.161293	+	0.496410i
$268$	1.33393	−	4.10540i	0.0814825	−	0.250777i
$269$	−12.5236	−	9.09894i	−0.763578	−	0.554772i	0.136428	−	0.990650i	$-0.456438\pi$
$269$	−12.5236	−	9.09894i	−0.763578	−	0.554772i	−0.900006	+	0.435878i	$0.856438\pi$
$270$	−3.31802	−	2.41068i	−0.201928	−	0.146709i
$271$	−1.54935	+	4.76842i	−0.0941165	+	0.289661i	−0.987022	−	0.160582i	$-0.948663\pi$
$271$	−1.54935	+	4.76842i	−0.0941165	+	0.289661i	0.892906	+	0.450243i	$0.148663\pi$
$272$	0.572949	+	1.76336i	0.0347401	+	0.106919i
$273$	1.37640	−	1.00002i	0.0833037	−	0.0605237i
$274$	−3.69020			−0.222933
$275$	−37.8258	−	10.3057i	−2.28098	−	0.621456i
$276$	7.57343			0.455867
$277$	17.7962	−	12.9297i	1.06927	−	0.776870i	0.0934891	−	0.995620i	$-0.470198\pi$
$277$	17.7962	−	12.9297i	1.06927	−	0.776870i	0.975781	+	0.218750i	$0.0701980\pi$
$278$	−1.81802	−	5.59528i	−0.109037	−	0.335583i
$279$	−1.89097	+	5.81980i	−0.113209	+	0.348422i
$280$	−3.31802	−	2.41068i	−0.198289	−	0.144066i
$281$	10.8340	+	7.87134i	0.646301	+	0.469565i	0.862009	−	0.506893i	$-0.169206\pi$
$281$	10.8340	+	7.87134i	0.646301	+	0.469565i	−0.215708	+	0.976458i	$0.569206\pi$
$282$	0.560993	−	1.72656i	0.0334066	−	0.102815i
$283$	−9.79999	−	30.1613i	−0.582549	−	1.79290i	−0.608899	−	0.793248i	$-0.708389\pi$
$283$	−9.79999	−	30.1613i	−0.582549	−	1.79290i	0.0263505	−	0.999653i	$-0.491611\pi$
$284$	8.87210	−	6.44596i	0.526462	−	0.382497i
$285$	11.9623			0.708584
$286$	3.53262	+	4.40004i	0.208888	+	0.260180i
$287$	8.89011			0.524766
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	−4.19098	−	12.8985i	−0.246528	−	0.758736i
$290$	0.233943	−	0.720003i	0.0137376	−	0.0422800i
$291$	−0.390967	−	0.284054i	−0.0229189	−	0.0166515i
$292$	8.70477	+	6.32438i	0.509408	+	0.370107i
$293$	−0.267370	+	0.822880i	−0.0156199	+	0.0480732i	−0.958563	−	0.284882i	$-0.908046\pi$
$293$	−0.267370	+	0.822880i	−0.0156199	+	0.0480732i	0.942943	+	0.332955i	$0.108046\pi$
$294$	0.309017	+	0.951057i	0.0180222	+	0.0554667i
$295$	−20.8622	+	15.1573i	−1.21464	+	0.882490i
$296$	−9.80950			−0.570166
$297$	−3.10130	+	1.17557i	−0.179955	+	0.0682135i
$298$	8.94427			0.518128
$299$	−10.4241	+	7.57355i	−0.602841	+	0.437990i
$300$	−3.65277	−	11.2421i	−0.210893	−	0.649062i
$301$	3.09229	−	9.51710i	0.178237	−	0.548557i
$302$	8.65960	+	6.29157i	0.498304	+	0.362039i
$303$	−6.41931	−	4.66390i	−0.368780	−	0.267934i
$304$	−0.901312	+	2.77395i	−0.0516938	+	0.159097i
$305$	11.1387	+	34.2813i	0.637799	+	1.96294i
$306$	1.50000	−	1.08981i	0.0857493	−	0.0623005i
$307$	−7.28911			−0.416011			−0.208006	−	0.978128i	$-0.566697\pi$
$307$	−7.28911			−0.416011			−0.208006	+	0.978128i	$0.566697\pi$
$308$	−3.10130	+	1.17557i	−0.176713	+	0.0669843i
$309$	14.5400			0.827149
$310$	−20.3039	+	14.7517i	−1.15319	+	0.837839i
$311$	0.0342266	+	0.105339i	0.00194081	+	0.00597321i	0.952022	−	0.306029i	$-0.0990004\pi$
$311$	0.0342266	+	0.105339i	0.00194081	+	0.00597321i	−0.950081	+	0.312002i	$0.899000\pi$
$312$	−0.525739	+	1.61806i	−0.0297641	+	0.0916046i
$313$	4.98887	+	3.62463i	0.281988	+	0.204876i	0.719784	−	0.694198i	$-0.244241\pi$
$313$	4.98887	+	3.62463i	0.281988	+	0.204876i	−0.437796	+	0.899074i	$0.644241\pi$
$314$	12.0567	+	8.75970i	0.680399	+	0.494338i
$315$	−1.26737	+	3.90056i	−0.0714082	+	0.219772i
$316$	−3.81506	−	11.7416i	−0.214614	−	0.660514i
$317$	−2.79093	+	2.02773i	−0.156754	+	0.113889i	−0.663398	−	0.748267i	$-0.730886\pi$
$317$	−2.79093	+	2.02773i	−0.156754	+	0.113889i	0.506643	+	0.862156i	$0.330886\pi$
$318$	−8.58622			−0.481491
$319$	−0.383279	−	0.477392i	−0.0214595	−	0.0267288i
$320$	4.10130			0.229269
$321$	0.341663	−	0.248233i	0.0190698	−	0.0138550i
$322$	−2.34032	−	7.20276i	−0.130421	−	0.401394i
$323$	−1.67112	+	5.14319i	−0.0929838	+	0.286175i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	16.2699	+	11.8208i	0.902494	+	0.655700i
$326$	5.56231	−	17.1190i	0.308068	−	0.948135i
$327$	1.58673	+	4.88346i	0.0877465	+	0.270056i
$328$	−7.19225	+	5.22547i	−0.397125	+	0.288528i
$329$	−1.81541			−0.100087
$330$	−13.1241	−	3.57567i	−0.722457	−	0.196834i
$331$	12.4196			0.682645			0.341322	−	0.939946i	$-0.389125\pi$
$331$	12.4196			0.682645			0.341322	+	0.939946i	$0.389125\pi$
$332$	−1.87423	+	1.36171i	−0.102862	+	0.0747334i
$333$	3.03130	+	9.32939i	0.166114	+	0.511247i
$334$	−4.77637	+	14.7002i	−0.261351	+	0.804357i
$335$	−14.3228	−	10.4061i	−0.782538	−	0.568547i
$336$	−0.809017	−	0.587785i	−0.0441355	−	0.0320663i
$337$	−5.79867	+	17.8465i	−0.315874	+	0.972160i	0.659519	+	0.751687i	$0.270760\pi$
$337$	−5.79867	+	17.8465i	−0.315874	+	0.972160i	−0.975393	+	0.220472i	$0.929240\pi$
$338$	3.12277	+	9.61089i	0.169856	+	0.522763i
$339$	−8.16177	+	5.92988i	−0.443287	+	0.322067i
$340$	7.60422			0.412397
$341$	0.977135	+	20.2719i	0.0529148	+	1.09778i
$342$	2.91671			0.157717
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	3.09229	+	9.51710i	0.166725	+	0.513128i
$345$	9.59834	−	29.5407i	0.516757	−	1.59042i
$346$	−18.5893	−	13.5059i	−0.999365	−	0.726081i
$347$	1.54165	+	1.12007i	0.0827599	+	0.0601286i	0.628396	−	0.777894i	$-0.283712\pi$
$347$	1.54165	+	1.12007i	0.0827599	+	0.0601286i	−0.545636	+	0.838022i	$0.683712\pi$
$348$	0.0570413	−	0.175555i	0.00305773	−	0.00941074i
$349$	3.80985	+	11.7255i	0.203936	+	0.627652i	0.999755	+	0.0221172i	$0.00704071\pi$
$349$	3.80985	+	11.7255i	0.203936	+	0.627652i	−0.795819	+	0.605535i	$0.792959\pi$
$350$	−9.56309	+	6.94799i	−0.511168	+	0.371386i
$351$	1.70133			0.0908102
$352$	1.81802	−	2.77395i	0.0969007	−	0.147852i
$353$	−12.6747			−0.674608			−0.337304	−	0.941396i	$-0.609515\pi$
$353$	−12.6747			−0.674608			−0.337304	+	0.941396i	$0.609515\pi$
$354$	−5.08673	+	3.69573i	−0.270357	+	0.196426i
$355$	−13.8986	−	42.7756i	−0.737663	−	2.27029i
$356$	−2.63555	+	8.11140i	−0.139684	+	0.429903i
$357$	−1.50000	−	1.08981i	−0.0793884	−	0.0576791i
$358$	13.9305	+	10.1211i	0.736249	+	0.534916i
$359$	6.07556	−	18.6986i	0.320656	−	0.986876i	−0.652708	−	0.757610i	$-0.726367\pi$
$359$	6.07556	−	18.6986i	0.320656	−	0.986876i	0.973364	−	0.229267i	$-0.0736329\pi$
$360$	−1.26737	−	3.90056i	−0.0667963	−	0.205578i
$361$	8.48887	−	6.16753i	0.446783	−	0.324607i
$362$	−9.16556			−0.481731
$363$	−8.23607	+	7.29158i	−0.432281	+	0.382709i
$364$	1.70133			0.0891738
$365$	35.7008	−	25.9382i	1.86867	−	1.35767i
$366$	2.71589	+	8.35865i	0.141962	+	0.436914i
$367$	7.52013	−	23.1446i	0.392547	−	1.20814i	−0.538308	−	0.842748i	$-0.680936\pi$
$367$	7.52013	−	23.1446i	0.392547	−	1.20814i	0.930855	−	0.365388i	$-0.119064\pi$
$368$	6.12703	+	4.45155i	0.319394	+	0.232053i
$369$	7.19225	+	5.22547i	0.374413	+	0.272027i
$370$	−12.4323	+	38.2626i	−0.646323	+	1.98918i
$371$	2.65329	+	8.16598i	0.137752	+	0.423957i
$372$	−4.95062	+	3.59683i	−0.256677	+	0.186487i
$373$	−14.7209			−0.762219			−0.381109	−	0.924530i	$-0.624458\pi$
$373$	−14.7209			−0.762219			−0.381109	+	0.924530i	$0.624458\pi$
$374$	3.37079	−	5.14319i	0.174299	−	0.265948i
$375$	−27.9734			−1.44454
$376$	1.46870	−	1.06707i	0.0757423	−	0.0550300i
$377$	0.0970459	+	0.298677i	0.00499812	+	0.0153826i
$378$	−0.309017	+	0.951057i	−0.0158941	+	0.0489171i
$379$	4.35628	+	3.16502i	0.223767	+	0.162576i	0.694021	−	0.719955i	$-0.255838\pi$
$379$	4.35628	+	3.16502i	0.223767	+	0.162576i	−0.470254	+	0.882531i	$0.655838\pi$
$380$	9.67768	+	7.03125i	0.496455	+	0.360695i
$381$	3.28376	−	10.1064i	0.168232	−	0.517765i
$382$	−6.74507	−	20.7592i	−0.345108	−	1.06213i
$383$	9.58891	−	6.96675i	0.489970	−	0.355984i	−0.315203	−	0.949024i	$-0.602072\pi$
$383$	9.58891	−	6.96675i	0.489970	−	0.355984i	0.805173	+	0.593040i	$0.202072\pi$
$384$	1.00000			0.0510310
$385$	0.654899	+	13.5867i	0.0333767	+	0.692442i
$386$	−23.0927			−1.17539
$387$	8.09573	−	5.88189i	0.411529	−	0.298993i
$388$	−0.149336	−	0.459609i	−0.00758139	−	0.0233331i
$389$	6.14899	−	18.9246i	0.311766	−	0.959517i	−0.665299	−	0.746577i	$-0.731696\pi$
$389$	6.14899	−	18.9246i	0.311766	−	0.959517i	0.977065	−	0.212940i	$-0.0683040\pi$
$390$	5.64504	+	4.10136i	0.285848	+	0.207680i
$391$	11.3601	+	8.25363i	0.574507	+	0.417404i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$	−4.19359	−	12.9065i	−0.211539	−	0.651049i
$394$	15.9102	−	11.5595i	0.801546	−	0.582357i
$395$	−50.6338			−2.54766
$396$	−3.19998	−	0.871839i	−0.160805	−	0.0438116i
$397$	−21.5750			−1.08282			−0.541409	−	0.840759i	$-0.682109\pi$
$397$	−21.5750			−1.08282			−0.541409	+	0.840759i	$0.682109\pi$
$398$	−5.72707	+	4.16096i	−0.287072	+	0.208570i
$399$	−0.901312	−	2.77395i	−0.0451220	−	0.138871i
$400$	3.65277	−	11.2421i	0.182639	−	0.562104i
$401$	13.4005	+	9.73606i	0.669191	+	0.486195i	0.869754	−	0.493485i	$-0.164277\pi$
$401$	13.4005	+	9.73606i	0.669191	+	0.486195i	−0.200564	+	0.979681i	$0.564277\pi$
$402$	−3.49226	−	2.53728i	−0.174178	−	0.126548i
$403$	3.21715	−	9.90138i	0.160258	−	0.493223i
$404$	−2.45196	−	7.54636i	−0.121990	−	0.375445i
$405$	−3.31802	+	2.41068i	−0.164874	+	0.119788i
$406$	−0.184589			−0.00916102
$407$	20.3683	+	25.3697i	1.00962	+	1.25753i
$408$	1.85410			0.0917917
$409$	19.0970	−	13.8748i	0.944288	−	0.686065i	−0.00516090	−	0.999987i	$-0.501643\pi$
$409$	19.0970	−	13.8748i	0.944288	−	0.686065i	0.949449	+	0.313921i	$0.101643\pi$
$410$	11.2671	+	34.6764i	0.556440	+	1.71255i
$411$	−1.14034	+	3.50959i	−0.0562486	+	0.173115i
$412$	11.7631	+	8.54637i	0.579525	+	0.421049i
$413$	5.08673	+	3.69573i	0.250302	+	0.181855i
$414$	2.34032	−	7.20276i	0.115020	−	0.353996i
$415$	2.93608	+	9.03633i	0.144127	+	0.443576i
$416$	−1.37640	+	1.00002i	−0.0674837	+	0.0490298i
$417$	−5.88323			−0.288103
$418$	9.04557	−	3.42879i	0.442433	−	0.167708i
$419$	22.5775			1.10298			0.551492	−	0.834180i	$-0.314059\pi$
$419$	22.5775			1.10298			0.551492	+	0.834180i	$0.314059\pi$
$420$	−3.31802	+	2.41068i	−0.161903	+	0.117629i
$421$	−6.80770	−	20.9520i	−0.331787	−	1.02114i	−0.968283	−	0.249856i	$-0.919617\pi$
$421$	−6.80770	−	20.9520i	−0.331787	−	1.02114i	0.636496	−	0.771280i	$-0.280383\pi$
$422$	−6.73389	+	20.7248i	−0.327801	+	1.00887i
$423$	−1.46870	−	1.06707i	−0.0714105	−	0.0518828i
$424$	−6.94640	−	5.04685i	−0.337347	−	0.245097i
$425$	6.77262	−	20.8440i	0.328520	−	1.01108i
$426$	−3.38884	−	10.4298i	−0.164190	−	0.505325i
$427$	7.11030	−	5.16593i	0.344091	−	0.249997i
$428$	0.422319			0.0204136
$429$	5.27632	−	2.00003i	0.254743	−	0.0965624i
$430$	41.0412			1.97918
$431$	6.05191	−	4.39697i	0.291510	−	0.211795i	−0.432412	−	0.901676i	$-0.642337\pi$
$431$	6.05191	−	4.39697i	0.291510	−	0.211795i	0.723922	+	0.689882i	$0.242337\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	4.66051	−	14.3436i	0.223970	−	0.689308i	−0.774425	−	0.632666i	$-0.781961\pi$
$433$	4.66051	−	14.3436i	0.223970	−	0.689308i	0.998395	−	0.0566423i	$-0.0180395\pi$
$434$	4.95062	+	3.59683i	0.237637	+	0.172653i
$435$	−0.612471	−	0.444986i	−0.0293657	−	0.0213355i
$436$	−1.58673	+	4.88346i	−0.0759907	+	0.233875i
$437$	6.82602	+	21.0083i	0.326533	+	1.00497i
$438$	8.70477	−	6.32438i	0.415930	−	0.302191i
$439$	19.6576			0.938206			0.469103	−	0.883144i	$-0.344577\pi$
$439$	19.6576			0.938206			0.469103	+	0.883144i	$0.344577\pi$
$440$	−8.51588	−	10.6069i	−0.405978	−	0.505665i
$441$	1.00000			0.0476190
$442$	−2.55199	+	1.85413i	−0.121386	+	0.0881920i
$443$	−4.85837	−	14.9525i	−0.230828	−	0.710416i	−0.997647	−	0.0685530i	$-0.978162\pi$
$443$	−4.85837	−	14.9525i	−0.230828	−	0.710416i	0.766819	−	0.641863i	$-0.221838\pi$
$444$	−3.03130	+	9.32939i	−0.143859	+	0.442753i
$445$	28.2988	+	20.5603i	1.34149	+	0.974651i
$446$	−12.1116	−	8.79956i	−0.573499	−	0.416671i
$447$	2.76393	−	8.50651i	0.130729	−	0.402344i
$448$	−0.309017	−	0.951057i	−0.0145997	−	0.0449332i
$449$	32.2960	−	23.4644i	1.52414	−	1.10736i	0.564759	−	0.825256i	$-0.308969\pi$
$449$	32.2960	−	23.4644i	1.52414	−	1.10736i	0.959385	−	0.282100i	$-0.0910309\pi$
$450$	−11.8206			−0.557230
$451$	28.4482	+	7.75074i	1.33957	+	0.364968i
$452$	−10.0885			−0.474524
$453$	8.65960	−	6.29157i	0.406863	−	0.295604i
$454$	3.81850	+	11.7521i	0.179211	+	0.551555i
$455$	2.15621	−	6.63614i	0.101085	−	0.311107i
$456$	2.35966	+	1.71440i	0.110501	+	0.0802840i
$457$	−18.1469	−	13.1845i	−0.848874	−	0.616743i	0.0759610	−	0.997111i	$-0.475798\pi$
$457$	−18.1469	−	13.1845i	−0.848874	−	0.616743i	−0.924835	+	0.380367i	$0.875798\pi$
$458$	3.20081	−	9.85109i	0.149564	−	0.460311i
$459$	−0.572949	−	1.76336i	−0.0267430	−	0.0823064i
$460$	25.1288	−	18.2571i	1.17164	−	0.851243i
$461$	13.7718			0.641418			0.320709	−	0.947178i	$-0.396079\pi$
$461$	13.7718			0.641418			0.320709	+	0.947178i	$0.396079\pi$
$462$	0.159681	+	3.31278i	0.00742903	+	0.154124i
$463$	−15.7733			−0.733049			−0.366525	−	0.930408i	$-0.619452\pi$
$463$	−15.7733			−0.733049			−0.366525	+	0.930408i	$0.619452\pi$
$464$	0.149336	−	0.108499i	0.00693275	−	0.00503694i
$465$	7.75541	+	23.8687i	0.359649	+	1.10688i
$466$	−3.66916	+	11.2925i	−0.169971	+	0.523116i
$467$	−6.09229	−	4.42631i	−0.281918	−	0.204825i	0.437836	−	0.899055i	$-0.355745\pi$
$467$	−6.09229	−	4.42631i	−0.281918	−	0.204825i	−0.719753	+	0.694230i	$0.755745\pi$
$468$	1.37640	+	1.00002i	0.0636243	+	0.0462257i
$469$	−1.33393	+	4.10540i	−0.0615950	+	0.189570i
$470$	−2.30080	−	7.08112i	−0.106128	−	0.326628i
$471$	12.0567	−	8.75970i	0.555543	−	0.403626i
$472$	−6.28755			−0.289408
$473$	18.1927	−	27.7586i	0.836500	−	1.27634i
$474$	−12.3458			−0.567061
$475$	27.8927	−	20.2652i	1.27981	−	0.929833i
$476$	−0.572949	−	1.76336i	−0.0262611	−	0.0808233i
$477$	−2.65329	+	8.16598i	−0.121486	+	0.373894i
$478$	20.0171	+	14.5433i	0.915563	+	0.665195i
$479$	16.9151	+	12.2896i	0.772873	+	0.561525i	0.902831	−	0.429995i	$-0.141485\pi$
$479$	16.9151	+	12.2896i	0.772873	+	0.561525i	−0.129959	+	0.991519i	$0.541485\pi$
$480$	1.26737	−	3.90056i	0.0578473	−	0.178036i
$481$	−5.15724	−	15.8723i	−0.235150	−	0.723717i
$482$	−1.97987	+	1.43846i	−0.0901808	+	0.0655202i
$483$	−7.57343			−0.344603
$484$	−10.9490	+	1.05798i	−0.497682	+	0.0480898i
$485$	−1.98200			−0.0899979
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−0.271321	−	0.835042i	−0.0122947	−	0.0378393i	0.944721	−	0.327876i	$-0.106333\pi$
$487$	−0.271321	−	0.835042i	−0.0122947	−	0.0378393i	−0.957016	+	0.290036i	$0.906333\pi$
$488$	−2.71589	+	8.35865i	−0.122943	+	0.378379i
$489$	−14.5623	−	10.5801i	−0.658530	−	0.478450i
$490$	3.31802	+	2.41068i	0.149893	+	0.108903i
$491$	10.4668	−	32.2136i	0.472362	−	1.45378i	−0.377121	−	0.926164i	$-0.623086\pi$
$491$	10.4668	−	32.2136i	0.472362	−	1.45378i	0.849483	−	0.527616i	$-0.176914\pi$
$492$	2.74719	+	8.45499i	0.123853	+	0.381180i
$493$	0.276884	−	0.201168i	0.0124702	−	0.00906016i
$494$	−4.96227			−0.223263
$495$	−7.45623	+	11.3768i	−0.335133	+	0.511349i
$496$	−6.11930			−0.274765
$497$	−8.87210	+	6.44596i	−0.397968	+	0.289141i
$498$	0.715892	+	2.20329i	0.0320799	+	0.0987317i
$499$	−8.51295	+	26.2002i	−0.381092	+	1.17288i	0.558184	+	0.829717i	$0.311498\pi$
$499$	−8.51295	+	26.2002i	−0.381092	+	1.17288i	−0.939276	+	0.343163i	$0.888502\pi$
$500$	−22.6310	−	16.4424i	−1.01209	−	0.735324i
$501$	12.5047	+	9.08520i	0.558669	+	0.405897i
$502$	−0.245417	+	0.755316i	−0.0109535	+	0.0337114i
$503$	7.62937	+	23.4808i	0.340177	+	1.04696i	0.964115	+	0.265484i	$0.0855316\pi$
$503$	7.62937	+	23.4808i	0.340177	+	1.04696i	−0.623938	+	0.781474i	$0.714468\pi$
$504$	−0.809017	+	0.587785i	−0.0360365	+	0.0261820i
$505$	−32.5426			−1.44813
$506$	−1.20933	−	25.0891i	−0.0537614	−	1.11535i
$507$	10.1055			0.448800
$508$	8.59700	−	6.24608i	0.381430	−	0.277125i
$509$	11.5454	+	35.5329i	0.511739	+	1.57497i	0.789138	+	0.614215i	$0.210527\pi$
$509$	11.5454	+	35.5329i	0.511739	+	1.57497i	−0.277400	+	0.960755i	$0.589473\pi$
$510$	2.34983	−	7.23204i	0.104052	−	0.320240i
$511$	−8.70477	−	6.32438i	−0.385076	−	0.279774i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	0.901312	−	2.77395i	0.0397939	−	0.122473i
$514$	4.51556	+	13.8975i	0.199173	+	0.612991i
$515$	48.2438	−	35.0512i	2.12588	−	1.54454i
$516$	10.0069			0.440528
$517$	−5.80928	−	1.58275i	−0.255492	−	0.0696091i
$518$	9.80950			0.431005
$519$	−18.5893	+	13.5059i	−0.815978	+	0.592843i
$520$	2.15621	+	6.63614i	0.0945562	+	0.291014i
$521$	−0.590170	+	1.81636i	−0.0258558	+	0.0795760i	−0.963152	−	0.268958i	$-0.913321\pi$
$521$	−0.590170	+	1.81636i	−0.0258558	+	0.0795760i	0.937296	+	0.348534i	$0.113321\pi$
$522$	−0.149336	−	0.108499i	−0.00653626	−	0.00474887i
$523$	11.2498	+	8.17344i	0.491918	+	0.357399i	0.805921	−	0.592022i	$-0.201670\pi$
$523$	11.2498	+	8.17344i	0.491918	+	0.357399i	−0.314003	+	0.949422i	$0.601670\pi$
$524$	4.19359	−	12.9065i	0.183198	−	0.563825i
$525$	3.65277	+	11.2421i	0.159420	+	0.490645i
$526$	−4.74507	+	3.44749i	−0.206895	+	0.150318i
$527$	−11.3458			−0.494231
$528$	−2.07639	−	2.58624i	−0.0903631	−	0.112551i
$529$	34.3569			1.49378
$530$	−28.4892	+	20.6986i	−1.23749	+	0.899091i
$531$	1.94296	+	5.97981i	0.0843172	+	0.259502i
$532$	0.901312	−	2.77395i	0.0390768	−	0.120266i
$533$	−12.2364	−	8.89024i	−0.530016	−	0.385079i
$534$	6.89997	+	5.01312i	0.298591	+	0.216939i
$535$	0.535234	−	1.64728i	0.0231402	−	0.0712182i
$536$	−1.33393	−	4.10540i	−0.0576168	−	0.177326i
$537$	13.9305	−	10.1211i	0.601145	−	0.436757i
$538$	−15.4800			−0.667392
$539$	3.10130	−	1.17557i	0.133582	−	0.0506354i
$540$	−4.10130			−0.176492
$541$	−4.74302	+	3.44601i	−0.203919	+	0.148156i	−0.685058	−	0.728489i	$-0.740223\pi$
$541$	−4.74302	+	3.44601i	−0.203919	+	0.148156i	0.481139	+	0.876644i	$0.340223\pi$
$542$	1.54935	+	4.76842i	0.0665504	+	0.204821i
$543$	−2.83231	+	8.71697i	−0.121546	+	0.374081i
$544$	1.50000	+	1.08981i	0.0643120	+	0.0467254i
$545$	17.0373	+	12.3783i	0.729796	+	0.530228i
$546$	0.525739	−	1.61806i	0.0224996	−	0.0692465i
$547$	−6.47523	−	19.9287i	−0.276861	−	0.852089i	−0.988721	−	0.149769i	$-0.952147\pi$
$547$	−6.47523	−	19.9287i	−0.276861	−	0.852089i	0.711860	−	0.702321i	$-0.247853\pi$
$548$	−2.98544	+	2.16905i	−0.127532	+	0.0926571i
$549$	8.78881			0.375097
$550$	−36.6593	+	13.8960i	−1.56316	+	0.592526i
$551$	0.538393			0.0229363
$552$	6.12703	−	4.45155i	0.260784	−	0.189471i
$553$	3.81506	+	11.7416i	0.162233	+	0.499302i
$554$	6.79754	−	20.9207i	0.288800	−	0.888835i
$555$	32.5481	+	23.6476i	1.38159	+	1.00378i
$556$	−4.75963	−	3.45808i	−0.201853	−	0.146655i
$557$	−11.4525	+	35.2471i	−0.485257	+	1.49347i	0.346352	+	0.938105i	$0.387420\pi$
$557$	−11.4525	+	35.2471i	−0.485257	+	1.49347i	−0.831609	+	0.555362i	$0.812580\pi$
$558$	1.89097	+	5.81980i	0.0800510	+	0.246372i
$559$	−13.7735	+	10.0070i	−0.582557	+	0.423252i
$560$	−4.10130			−0.173311
$561$	−3.84983	−	4.79515i	−0.162540	−	0.202451i
$562$	13.3915			0.564888
$563$	−4.85532	+	3.52759i	−0.204627	+	0.148670i	−0.685379	−	0.728186i	$-0.740364\pi$
$563$	−4.85532	+	3.52759i	−0.204627	+	0.148670i	0.480752	+	0.876856i	$0.340364\pi$
$564$	−0.560993	−	1.72656i	−0.0236221	−	0.0727012i
$565$	−12.7859	+	39.3509i	−0.537906	+	1.65550i
$566$	−25.6567	−	18.6407i	−1.07843	−	0.783526i
$567$	0.809017	+	0.587785i	0.0339755	+	0.0246847i
$568$	3.38884	−	10.4298i	0.142193	−	0.437624i
$569$	3.09127	+	9.51394i	0.129593	+	0.398845i	0.994710	−	0.102725i	$-0.0327560\pi$
$569$	3.09127	+	9.51394i	0.129593	+	0.398845i	−0.865117	+	0.501570i	$0.832756\pi$
$570$	9.67768	−	7.03125i	0.405354	−	0.294507i
$571$	−25.4693			−1.06586			−0.532928	−	0.846160i	$-0.678908\pi$
$571$	−25.4693			−1.06586			−0.532928	+	0.846160i	$0.678908\pi$
$572$	5.44422	+	1.48328i	0.227634	+	0.0620192i
$573$	−21.8275			−0.911857
$574$	7.19225	−	5.22547i	0.300199	−	0.218107i
$575$	−27.6640	−	85.1411i	−1.15367	−	3.55063i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−8.14377	−	5.91680i	−0.339030	−	0.246320i	0.405223	−	0.914218i	$-0.367194\pi$
$577$	−8.14377	−	5.91680i	−0.339030	−	0.246320i	−0.744252	+	0.667899i	$0.767194\pi$
$578$	−10.9721	−	7.97172i	−0.456381	−	0.331580i
$579$	−7.13604	+	21.9625i	−0.296564	+	0.912729i
$580$	−0.233943	−	0.720003i	−0.00971396	−	0.0298965i
$581$	1.87423	−	1.36171i	0.0777561	−	0.0564931i
$582$	−0.483262			−0.0200318
$583$	1.37106	+	28.4442i	0.0567833	+	1.17804i
$584$	10.7597			0.445239
$585$	5.64504	−	4.10136i	0.233394	−	0.169570i
$586$	0.267370	+	0.822880i	0.0110450	+	0.0339929i
$587$	−14.7177	+	45.2963i	−0.607463	+	1.86958i	−0.128584	+	0.991699i	$0.541043\pi$
$587$	−14.7177	+	45.2963i	−0.607463	+	1.86958i	−0.478879	+	0.877881i	$0.658957\pi$
$588$	0.809017	+	0.587785i	0.0333633	+	0.0242399i
$589$	−14.4395	−	10.4909i	−0.594969	−	0.432270i
$590$	−7.96865	+	24.5250i	−0.328064	+	1.00968i
$591$	−6.07717	−	18.7036i	−0.249981	−	0.769363i
$592$	−7.93605	+	5.76588i	−0.326170	+	0.236976i
$593$	−27.1543			−1.11509			−0.557546	−	0.830146i	$-0.688257\pi$
$593$	−27.1543			−1.11509			−0.557546	+	0.830146i	$0.688257\pi$
$594$	−1.81802	+	2.77395i	−0.0745942	+	0.113817i
$595$	−7.60422			−0.311743
$596$	7.23607	−	5.25731i	0.296401	−	0.215348i
$597$	2.18755	+	6.73257i	0.0895303	+	0.275546i
$598$	−3.98165	+	12.2543i	−0.162822	+	0.501114i
$599$	−1.83949	−	1.33647i	−0.0751595	−	0.0546065i	0.549571	−	0.835447i	$-0.314791\pi$
$599$	−1.83949	−	1.33647i	−0.0751595	−	0.0546065i	−0.624731	+	0.780840i	$0.714791\pi$
$600$	−9.56309	−	6.94799i	−0.390411	−	0.283650i
$601$	−4.26686	+	13.1320i	−0.174049	+	0.535667i	−0.999589	−	0.0286767i	$-0.990871\pi$
$601$	−4.26686	+	13.1320i	−0.174049	+	0.535667i	0.825540	+	0.564344i	$0.190871\pi$
$602$	−3.09229	−	9.51710i	−0.126033	−	0.387888i
$603$	−3.49226	+	2.53728i	−0.142216	+	0.103326i
$604$	10.7039			0.435534
$605$	−9.74974	+	44.0481i	−0.396383	+	1.79081i
$606$	−7.93471			−0.322325
$607$	10.7658	−	7.82178i	0.436969	−	0.317476i	−0.347461	−	0.937695i	$-0.612956\pi$
$607$	10.7658	−	7.82178i	0.436969	−	0.317476i	0.784429	+	0.620218i	$0.212956\pi$
$608$	0.901312	+	2.77395i	0.0365530	+	0.112499i
$609$	−0.0570413	+	0.175555i	−0.00231143	+	0.00711385i
$610$	29.1614	+	21.1870i	1.18071	+	0.857837i
$611$	2.49874	+	1.81544i	0.101088	+	0.0734448i
$612$	0.572949	−	1.76336i	0.0231601	−	0.0712794i
$613$	−5.86181	−	18.0408i	−0.236756	−	0.728661i	−0.996884	−	0.0788866i	$-0.974863\pi$
$613$	−5.86181	−	18.0408i	−0.236756	−	0.728661i	0.760127	−	0.649774i	$-0.225137\pi$
$614$	−5.89701	+	4.28443i	−0.237984	+	0.172906i
$615$	36.4609			1.47025
$616$	−1.81802	+	2.77395i	−0.0732500	+	0.111766i
$617$	−9.30545			−0.374623			−0.187312	−	0.982301i	$-0.559977\pi$
$617$	−9.30545			−0.374623			−0.187312	+	0.982301i	$0.559977\pi$
$618$	11.7631	−	8.54637i	0.473180	−	0.343785i
$619$	−2.05412	−	6.32192i	−0.0825619	−	0.254099i	0.901251	−	0.433297i	$-0.142650\pi$
$619$	−2.05412	−	6.32192i	−0.0825619	−	0.254099i	−0.983813	+	0.179198i	$0.942650\pi$
$620$	−7.75541	+	23.8687i	−0.311465	+	0.958590i
$621$	−6.12703	−	4.45155i	−0.245869	−	0.178635i
$622$	0.0896065	+	0.0651029i	0.00359289	+	0.00261039i
$623$	2.63555	−	8.11140i	0.105591	−	0.324976i
$624$	0.525739	+	1.61806i	0.0210464	+	0.0647742i
$625$	−45.0008	+	32.6950i	−1.80003	+	1.30780i
$626$	6.16659			0.246466
$627$	−0.465742	−	9.66240i	−0.0186000	−	0.385879i
$628$	14.9029			0.594690
$629$	−14.7142	+	10.6905i	−0.586696	+	0.426259i
$630$	1.26737	+	3.90056i	0.0504932	+	0.155402i
$631$	0.0830787	−	0.255690i	0.00330731	−	0.0101789i	−0.949389	−	0.314102i	$-0.898297\pi$
$631$	0.0830787	−	0.255690i	0.00330731	−	0.0101789i	0.952697	+	0.303923i	$0.0982966\pi$
$632$	−9.98796	−	7.25668i	−0.397300	−	0.288655i
$633$	17.6296	+	12.8086i	0.700712	+	0.509097i
$634$	−1.06604	+	3.28094i	−0.0423379	+	0.130303i
$635$	−13.4677	−	41.4492i	−0.534448	−	1.64486i
$636$	−6.94640	+	5.04685i	−0.275443	+	0.200121i
$637$	−1.70133			−0.0674091
$638$	−0.590683	−	0.160932i	−0.0233854	−	0.00637137i
$639$	−10.9665			−0.433829
$640$	3.31802	−	2.41068i	0.131156	−	0.0952905i
$641$	−14.1662	−	43.5992i	−0.559533	−	1.72206i	−0.683662	−	0.729799i	$-0.739614\pi$
$641$	−14.1662	−	43.5992i	−0.559533	−	1.72206i	0.124129	−	0.992266i	$-0.460386\pi$
$642$	0.130504	−	0.401649i	0.00515057	−	0.0158518i
$643$	−26.5956	−	19.3228i	−1.04883	−	0.762017i	−0.0768379	−	0.997044i	$-0.524482\pi$
$643$	−26.5956	−	19.3228i	−1.04883	−	0.762017i	−0.971989	+	0.235026i	$0.924482\pi$
$644$	−6.12703	−	4.45155i	−0.241439	−	0.175416i
$645$	12.6824	−	39.0325i	0.499370	−	1.53690i
$646$	1.67112	+	5.14319i	0.0657495	+	0.202356i
$647$	31.6559	−	22.9994i	1.24452	−	0.904198i	0.246631	−	0.969109i	$-0.420676\pi$
$647$	31.6559	−	22.9994i	1.24452	−	0.904198i	0.997891	+	0.0649109i	$0.0206763\pi$
$648$	−1.00000			−0.0392837
$649$	13.0554	+	16.2611i	0.512468	+	0.638303i
$650$	20.1108			0.788809
$651$	4.95062	−	3.59683i	0.194030	−	0.140971i
$652$	−5.56231	−	17.1190i	−0.217837	−	0.670432i
$653$	12.3395	−	37.9770i	0.482881	−	1.48616i	−0.352144	−	0.935946i	$-0.614547\pi$
$653$	12.3395	−	37.9770i	0.482881	−	1.48616i	0.835026	−	0.550211i	$-0.185453\pi$
$654$	4.15412	+	3.01814i	0.162439	+	0.118019i
$655$	−45.0280	−	32.7147i	−1.75939	−	1.27827i
$656$	−2.74719	+	8.45499i	−0.107260	+	0.330112i
$657$	−3.32492	−	10.2331i	−0.129718	−	0.399230i
$658$	−1.46870	+	1.06707i	−0.0572558	+	0.0415988i
$659$	0.286582			0.0111636			0.00558182	−	0.999984i	$-0.498223\pi$
$659$	0.286582			0.0111636			0.00558182	+	0.999984i	$0.498223\pi$
$660$	−12.7193	+	4.82136i	−0.495099	+	0.187671i
$661$	12.8164			0.498502			0.249251	−	0.968439i	$-0.419816\pi$
$661$	12.8164			0.498502			0.249251	+	0.968439i	$0.419816\pi$
$662$	10.0477	−	7.30008i	0.390515	−	0.283726i
$663$	0.974774	+	3.00005i	0.0378571	+	0.116512i
$664$	−0.715892	+	2.20329i	−0.0277820	+	0.0855041i
$665$	−9.67768	−	7.03125i	−0.375284	−	0.272660i
$666$	7.93605	+	5.76588i	0.307516	+	0.223423i
$667$	0.431998	−	1.32955i	0.0167270	−	0.0514805i
$668$	4.77637	+	14.7002i	0.184803	+	0.568766i
$669$	−12.1116	+	8.79956i	−0.468260	+	0.340211i
$670$	−17.7040			−0.683963
$671$	27.2567	−	10.3319i	1.05223	−	0.398857i
$672$	−1.00000			−0.0385758
$673$	−18.0456	+	13.1109i	−0.695606	+	0.505387i	−0.878498	−	0.477746i	$-0.841454\pi$
$673$	−18.0456	+	13.1109i	−0.695606	+	0.505387i	0.182893	+	0.983133i	$0.441454\pi$
$674$	5.79867	+	17.8465i	0.223357	+	0.687421i
$675$	−3.65277	+	11.2421i	−0.140595	+	0.432708i
$676$	8.17551	+	5.93985i	0.314443	+	0.228456i
$677$	−27.3718	−	19.8868i	−1.05198	−	0.764311i	−0.0793952	−	0.996843i	$-0.525299\pi$
$677$	−27.3718	−	19.8868i	−1.05198	−	0.764311i	−0.972589	+	0.232532i	$0.925299\pi$
$678$	−3.11752	+	9.59474i	−0.119728	+	0.368484i
$679$	0.149336	+	0.459609i	0.00573099	+	0.0176382i
$680$	6.15194	−	4.46965i	0.235916	−	0.171403i
$681$	12.3569			0.473518
$682$	12.7060	+	15.8259i	0.486539	+	0.606007i
$683$	11.9967			0.459042			0.229521	−	0.973304i	$-0.426284\pi$
$683$	11.9967			0.459042			0.229521	+	0.973304i	$0.426284\pi$
$684$	2.35966	−	1.71440i	0.0902240	−	0.0655516i
$685$	4.67685	+	14.3939i	0.178693	+	0.549961i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−8.37984	−	6.08831i	−0.319711	−	0.232284i
$688$	8.09573	+	5.88189i	0.308647	+	0.224245i
$689$	4.51411	−	13.8930i	0.171974	−	0.529281i
$690$	−9.59834	−	29.5407i	−0.365403	−	1.12459i
$691$	−21.0137	+	15.2673i	−0.799399	+	0.580797i	−0.910738	−	0.412985i	$-0.864486\pi$
$691$	−21.0137	+	15.2673i	−0.799399	+	0.580797i	0.111339	+	0.993783i	$0.464486\pi$
$692$	−22.9776			−0.873477
$693$	3.19998	+	0.871839i	0.121557	+	0.0331184i
$694$	1.90558			0.0723348
$695$	−19.5207	+	14.1826i	−0.740461	+	0.537976i
$696$	−0.0570413	−	0.175555i	−0.00216214	−	0.00665440i
$697$	−5.09358	+	15.6764i	−0.192933	+	0.593787i
$698$	9.97431	+	7.24676i	0.377533	+	0.274294i
$699$	9.60600	+	6.97917i	0.363332	+	0.263976i
$700$	−3.65277	+	11.2421i	−0.138062	+	0.424911i
$701$	12.0421	+	37.0619i	0.454825	+	1.39981i	0.871341	+	0.490679i	$0.163251\pi$
$701$	12.0421	+	37.0619i	0.454825	+	1.39981i	−0.416516	+	0.909129i	$0.636749\pi$
$702$	1.37640	−	1.00002i	0.0519490	−	0.0377432i
$703$	−28.6114			−1.07910
$704$	−0.159681	−	3.31278i	−0.00601820	−	0.124855i
$705$	−7.44554			−0.280415
$706$	−10.2541	+	7.45002i	−0.385917	+	0.280385i
$707$	2.45196	+	7.54636i	0.0922154	+	0.283810i
$708$	−1.94296	+	5.97981i	−0.0730209	+	0.224735i
$709$	18.3497	+	13.3318i	0.689136	+	0.500687i	0.876376	−	0.481627i	$-0.159954\pi$
$709$	18.3497	+	13.3318i	0.689136	+	0.500687i	−0.187240	+	0.982314i	$0.559954\pi$
$710$	−36.3871	−	26.4368i	−1.36558	−	0.992155i
$711$	−3.81506	+	11.7416i	−0.143076	+	0.440343i
$712$	2.63555	+	8.11140i	0.0987715	+	0.303988i
$713$	−37.4931	+	27.2404i	−1.40413	+	1.02016i
$714$	−1.85410			−0.0693880
$715$	12.6855	−	19.3557i	0.474410	−	0.723861i
$716$	17.2190			0.643505
$717$	20.0171	−	14.5433i	0.747554	−	0.543130i
$718$	−6.07556	−	18.6986i	−0.226738	−	0.697827i
$719$	−13.3021	+	40.9397i	−0.496085	+	1.52679i	0.319174	+	0.947696i	$0.396595\pi$
$719$	−13.3021	+	40.9397i	−0.496085	+	1.52679i	−0.815259	+	0.579096i	$0.803405\pi$
$720$	−3.31802	−	2.41068i	−0.123655	−	0.0898408i
$721$	−11.7631	−	8.54637i	−0.438080	−	0.318283i
$722$	3.24246	−	9.97927i	0.120672	−	0.371390i
$723$	0.756244	+	2.32748i	0.0281250	+	0.0865600i
$724$	−7.41509	+	5.38738i	−0.275580	+	0.200220i
$725$	−2.18196			−0.0810361
$726$	−2.37723	+	10.7401i	−0.0882274	+	0.398601i
$727$	32.4730			1.20436			0.602178	−	0.798362i	$-0.294300\pi$
$727$	32.4730			1.20436			0.602178	+	0.798362i	$0.294300\pi$
$728$	1.37640	−	1.00002i	0.0510129	−	0.0370630i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	13.6365	−	41.9688i	0.504709	−	1.55334i
$731$	15.0103	+	10.9056i	0.555177	+	0.403359i
$732$	7.11030	+	5.16593i	0.262804	+	0.190938i
$733$	−10.6845	+	32.8836i	−0.394642	+	1.21458i	0.534597	+	0.845107i	$0.320463\pi$
$733$	−10.6845	+	32.8836i	−0.394642	+	1.21458i	−0.929240	+	0.369478i	$0.879537\pi$
$734$	−7.52013	−	23.1446i	−0.277573	−	0.854282i
$735$	3.31802	−	2.41068i	0.122387	−	0.0889193i
$736$	7.57343			0.279160
$737$	−7.84779	+	11.9742i	−0.289077	+	0.441077i
$738$	8.89011			0.327249
$739$	−10.7956	+	7.84345i	−0.397122	+	0.288526i	−0.768368	−	0.640009i	$-0.778931\pi$
$739$	−10.7956	+	7.84345i	−0.397122	+	0.288526i	0.371246	+	0.928535i	$0.378931\pi$
$740$	12.4323	+	38.2626i	0.457019	+	1.40656i
$741$	−1.53343	+	4.71940i	−0.0563318	+	0.173372i
$742$	6.94640	+	5.04685i	0.255010	+	0.185276i
$743$	−29.2252	−	21.2334i	−1.07217	−	0.778976i	−0.0958682	−	0.995394i	$-0.530563\pi$
$743$	−29.2252	−	21.2334i	−1.07217	−	0.778976i	−0.976301	+	0.216418i	$0.930563\pi$
$744$	−1.89097	+	5.81980i	−0.0693262	+	0.213364i
$745$	−11.3357	−	34.8877i	−0.415308	−	1.27819i
$746$	−11.9095	+	8.65272i	−0.436036	+	0.316799i
$747$	2.31667			0.0847627
$748$	−0.296065	−	6.14223i	−0.0108252	−	0.224582i
$749$	−0.422319			−0.0154312
$750$	−22.6310	+	16.4424i	−0.826366	+	0.600390i
$751$	−15.1071	−	46.4948i	−0.551265	−	1.69662i	−0.705609	−	0.708602i	$-0.749326\pi$
$751$	−15.1071	−	46.4948i	−0.551265	−	1.69662i	0.154344	−	0.988017i	$-0.450674\pi$
$752$	0.560993	−	1.72656i	0.0204573	−	0.0629611i
$753$	0.642510	+	0.466811i	0.0234144	+	0.0170115i
$754$	0.254070	+	0.184592i	0.00925267	+	0.00672246i
$755$	13.5657	−	41.7511i	0.493708	−	1.51948i
$756$	0.309017	+	0.951057i	0.0112388	+	0.0345896i
$757$	16.7712	−	12.1850i	0.609558	−	0.442870i	−0.239701	−	0.970847i	$-0.577049\pi$
$757$	16.7712	−	12.1850i	0.609558	−	0.442870i	0.849259	+	0.527977i	$0.177049\pi$
$758$	5.38465			0.195579
$759$	−24.2349	−	6.60281i	−0.879670	−	0.239667i
$760$	11.9623			0.433917
$761$	−30.3966	+	22.0844i	−1.10188	+	0.800559i	−0.981365	−	0.192153i	$-0.938453\pi$
$761$	−30.3966	+	22.0844i	−1.10188	+	0.800559i	−0.120510	+	0.992712i	$0.538453\pi$
$762$	−3.28376	−	10.1064i	−0.118958	−	0.366115i
$763$	1.58673	−	4.88346i	0.0574436	−	0.176793i
$764$	−17.6588	−	12.8299i	−0.638874	−	0.464169i
$765$	−6.15194	−	4.46965i	−0.222424	−	0.161600i
$766$	3.66264	−	11.2724i	0.132336	−	0.407290i
$767$	−3.30561	−	10.1736i	−0.119359	−	0.367348i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	30.2933			1.09240			0.546202	−	0.837653i	$-0.316073\pi$
$769$	30.2933			1.09240			0.546202	+	0.837653i	$0.316073\pi$
$770$	8.51588	+	10.6069i	0.306891	+	0.382247i
$771$	14.6127			0.526262
$772$	−18.6824	+	13.5735i	−0.672394	+	0.488523i
$773$	−11.6307	−	35.7957i	−0.418328	−	1.28748i	−0.909240	−	0.416272i	$-0.863336\pi$
$773$	−11.6307	−	35.7957i	−0.418328	−	1.28748i	0.490912	−	0.871209i	$-0.336664\pi$
$774$	3.09229	−	9.51710i	0.111150	−	0.342085i
$775$	58.5194	+	42.5168i	2.10208	+	1.52725i
$776$	−0.390967	−	0.284054i	−0.0140349	−	0.0101969i
$777$	3.03130	−	9.32939i	0.108747	−	0.334690i
$778$	−6.14899	−	18.9246i	−0.220452	−	0.678481i
$779$	−20.9777	+	15.2412i	−0.751603	+	0.546072i
$780$	6.97765			0.249840
$781$	−34.0104	+	12.8919i	−1.21699	+	0.461309i
$782$	14.0419			0.502138
$783$	−0.149336	+	0.108499i	−0.00533683	+	0.00387744i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	18.8875	−	58.1297i	0.674123	−	2.07474i
$786$	−10.9790	−	7.97668i	−0.391607	−	0.284519i
$787$	28.9315	+	21.0199i	1.03129	+	0.749280i	0.968567	−	0.248751i	$-0.0800201\pi$
$787$	28.9315	+	21.0199i	1.03129	+	0.749280i	0.0627275	+	0.998031i	$0.480020\pi$
$788$	6.07717	−	18.7036i	0.216490	−	0.666288i
$789$	1.81245	+	5.57816i	0.0645251	+	0.198588i
$790$	−40.9636	+	29.7618i	−1.45742	+	1.05888i
$791$	10.0885			0.358706
$792$	−3.10130	+	1.17557i	−0.110200	+	0.0417721i
$793$	−14.9526			−0.530984
$794$	−17.4545	+	12.6815i	−0.619438	+	0.450048i
$795$	10.8819	+	33.4911i	0.385942	+	1.18781i
$796$	−2.18755	+	6.73257i	−0.0775355	+	0.238630i
$797$	−28.6468	−	20.8131i	−1.01472	−	0.737238i	−0.0495270	−	0.998773i	$-0.515771\pi$
$797$	−28.6468	−	20.8131i	−1.01472	−	0.737238i	−0.965194	+	0.261535i	$0.915771\pi$
$798$	−2.35966	−	1.71440i	−0.0835312	−	0.0606890i
$799$	1.04014	−	3.20121i	0.0367974	−	0.113251i
$800$	−3.65277	−	11.2421i	−0.129145	−	0.397468i
$801$	6.89997	−	5.01312i	0.243798	−	0.177130i
$802$	16.5640			0.584894
$803$	−22.3413	−	27.8271i	−0.788406	−	0.981996i
$804$	−4.31667			−0.152237
$805$	−25.1288	+	18.2571i	−0.885673	+	0.643479i
$806$	−3.21715	−	9.90138i	−0.113319	−	0.348761i
$807$	−4.78360	+	14.7224i	−0.168391	+	0.518253i
$808$	−6.41931	−	4.66390i	−0.225831	−	0.164076i
$809$	−9.48457	−	6.89095i	−0.333460	−	0.242273i	0.408437	−	0.912786i	$-0.366074\pi$
$809$	−9.48457	−	6.89095i	−0.333460	−	0.242273i	−0.741897	+	0.670514i	$0.766074\pi$
$810$	−1.26737	+	3.90056i	−0.0445308	+	0.137052i
$811$	9.07572	+	27.9322i	0.318692	+	0.980832i	0.974208	+	0.225651i	$0.0724510\pi$
$811$	9.07572	+	27.9322i	0.318692	+	0.980832i	−0.655516	+	0.755181i	$0.727549\pi$
$812$	−0.149336	+	0.108499i	−0.00524067	+	0.00380757i
$813$	5.01381			0.175842
$814$	31.3902	+	8.55231i	1.10023	+	0.299758i
$815$	−73.8233			−2.58592
$816$	1.50000	−	1.08981i	0.0525105	−	0.0381511i
$817$	9.01931	+	27.7586i	0.315546	+	0.971150i
$818$	7.29442	−	22.4499i	0.255044	−	0.784943i
$819$	−1.37640	−	1.00002i	−0.0480954	−	0.0349434i
$820$	29.4975	+	21.4312i	1.03010	+	0.748410i
$821$	0.524928	−	1.61556i	0.0183201	−	0.0563835i	−0.941479	−	0.337073i	$-0.890563\pi$
$821$	0.524928	−	1.61556i	0.0183201	−	0.0563835i	0.959799	+	0.280689i	$0.0905631\pi$
$822$	1.14034	+	3.50959i	0.0397738	+	0.122411i
$823$	28.0691	−	20.3934i	0.978428	−	0.710870i	0.0210716	−	0.999778i	$-0.493292\pi$
$823$	28.0691	−	20.3934i	0.978428	−	0.710870i	0.957357	+	0.288908i	$0.0932922\pi$
$824$	14.5400			0.506523
$825$	1.88753	+	39.1591i	0.0657153	+	1.36335i
$826$	6.28755			0.218772
$827$	−41.6120	+	30.2329i	−1.44699	+	1.05130i	−0.460469	+	0.887676i	$0.652319\pi$
$827$	−41.6120	+	30.2329i	−1.44699	+	1.05130i	−0.986523	+	0.163625i	$0.947681\pi$
$828$	−2.34032	−	7.20276i	−0.0813317	−	0.250313i
$829$	14.3121	−	44.0480i	0.497079	−	1.52985i	−0.316613	−	0.948555i	$-0.602546\pi$
$829$	14.3121	−	44.0480i	0.497079	−	1.52985i	0.813692	−	0.581297i	$-0.197454\pi$
$830$	7.68676	+	5.58476i	0.266811	+	0.193850i
$831$	−17.7962	−	12.9297i	−0.617343	−	0.448526i
$832$	−0.525739	+	1.61806i	−0.0182267	+	0.0560961i
$833$	0.572949	+	1.76336i	0.0198515	+	0.0610967i
$834$	−4.75963	+	3.45808i	−0.164813	+	0.119743i
$835$	63.3923			2.19378
$836$	5.30262	−	8.09080i	0.183395	−	0.279826i
$837$	6.11930			0.211514
$838$	18.2656	−	13.2707i	0.630975	−	0.458430i
$839$	−0.281768	−	0.867194i	−0.00972773	−	0.0299389i	0.946075	−	0.323948i	$-0.105010\pi$
$839$	−0.281768	−	0.867194i	−0.00972773	−	0.0299389i	−0.955803	+	0.294009i	$0.905010\pi$
$840$	−1.26737	+	3.90056i	−0.0437284	+	0.134582i
$841$	23.4339	+	17.0257i	0.808066	+	0.587095i
$842$	−17.8228	−	12.9490i	−0.614214	−	0.446253i
$843$	4.13821	−	12.7361i	0.142528	−	0.438655i
$844$	6.73389	+	20.7248i	0.231790	+	0.713377i
$845$	33.5302	−	24.3611i	1.15347	−	0.838047i
$846$	−1.81541			−0.0624151
$847$	10.9490	−	1.05798i	0.376212	−	0.0363525i
$848$	−8.58622			−0.294852
$849$	−25.6567	+	18.6407i	−0.880535	+	0.639746i
$850$	−6.77262	−	20.8440i	−0.232299	−	0.714942i
$851$	−22.9574	+	70.6555i	−0.786968	+	2.42204i
$852$	−8.87210	−	6.44596i	−0.303953	−	0.220835i
$853$	−15.6042	−	11.3371i	−0.534278	−	0.388176i	0.287677	−	0.957727i	$-0.407117\pi$
$853$	−15.6042	−	11.3371i	−0.534278	−	0.388176i	−0.821956	+	0.569551i	$0.807117\pi$
$854$	2.71589	−	8.35865i	0.0929359	−	0.286027i
$855$	−3.69655	−	11.3768i	−0.126419	−	0.389078i
$856$	0.341663	−	0.248233i	0.0116778	−	0.00848442i
$857$	−5.21919			−0.178284			−0.0891421	−	0.996019i	$-0.528413\pi$
$857$	−5.21919			−0.178284			−0.0891421	+	0.996019i	$0.528413\pi$
$858$	3.09304	−	4.71940i	0.105595	−	0.161118i
$859$	−43.5639			−1.48638			−0.743190	−	0.669080i	$-0.766688\pi$
$859$	−43.5639			−1.48638			−0.743190	+	0.669080i	$0.766688\pi$
$860$	33.2030	−	24.1234i	1.13221	−	0.822601i
$861$	−2.74719	−	8.45499i	−0.0936241	−	0.288145i
$862$	2.31162	−	7.11445i	0.0787342	−	0.242319i
$863$	−2.85201	−	2.07211i	−0.0970835	−	0.0705353i	0.538185	−	0.842827i	$-0.319110\pi$
$863$	−2.85201	−	2.07211i	−0.0970835	−	0.0705353i	−0.635268	+	0.772292i	$0.719110\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−29.1211	+	89.6255i	−0.990147	+	3.04736i
$866$	−4.66051	−	14.3436i	−0.158371	−	0.487415i
$867$	−10.9721	+	7.97172i	−0.372633	+	0.270734i
$868$	6.11930			0.207702
$869$	1.97139	+	40.8989i	0.0668748	+	1.38740i
$870$	−0.757056			−0.0256666
$871$	5.94148	−	4.31674i	0.201319	−	0.146267i
$872$	1.58673	+	4.88346i	0.0537335	+	0.165375i
$873$	−0.149336	+	0.459609i	−0.00505426	+	0.0155554i
$874$	17.8708	+	12.9839i	0.604487	+	0.439186i
$875$	22.6310	+	16.4424i	0.765066	+	0.555853i
$876$	3.32492	−	10.2331i	0.112339	−	0.345743i
$877$	0.210494	+	0.647834i	0.00710787	+	0.0218758i	0.954548	−	0.298059i	$-0.0963391\pi$
$877$	0.210494	+	0.647834i	0.00710787	+	0.0218758i	−0.947440	+	0.319934i	$0.896339\pi$
$878$	15.9033	−	11.5544i	0.536711	−	0.389944i
$879$	0.865228			0.0291834
$880$	−13.1241	−	3.57567i	−0.442413	−	0.120536i
$881$	49.3785			1.66360			0.831802	−	0.555072i	$-0.187309\pi$
$881$	49.3785			1.66360			0.831802	+	0.555072i	$0.187309\pi$
$882$	0.809017	−	0.587785i	0.0272410	−	0.0197918i
$883$	−5.14837	−	15.8451i	−0.173256	−	0.533229i	0.826293	−	0.563240i	$-0.190446\pi$
$883$	−5.14837	−	15.8451i	−0.173256	−	0.533229i	−0.999550	+	0.0300118i	$0.990446\pi$
$884$	−0.974774	+	3.00005i	−0.0327852	+	0.100902i
$885$	20.8622	+	15.1573i	0.701275	+	0.509506i
$886$	−12.7194	−	9.24117i	−0.427316	−	0.310463i
$887$	−3.35083	+	10.3128i	−0.112510	+	0.346270i	−0.991420	−	0.130719i	$-0.958272\pi$
$887$	−3.35083	+	10.3128i	−0.112510	+	0.346270i	0.878910	+	0.476988i	$0.158272\pi$
$888$	3.03130	+	9.32939i	0.101724	+	0.313074i
$889$	−8.59700	+	6.24608i	−0.288334	+	0.209487i
$890$	34.9792			1.17251
$891$	2.07639	+	2.58624i	0.0695616	+	0.0866422i
$892$	−14.9707			−0.501256
$893$	4.28376	−	3.11233i	0.143351	−	0.104150i
$894$	−2.76393	−	8.50651i	−0.0924397	−	0.284500i
$895$	21.8229	−	67.1639i	0.729459	−	2.24504i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	10.4241	+	7.57355i	0.348050	+	0.252873i
$898$	12.3360	−	37.9663i	0.411657	−	1.26695i
$899$	0.349053	+	1.07427i	0.0116416	+	0.0358290i
$900$	−9.56309	+	6.94799i	−0.318770	+	0.231600i
$901$	−15.9197			−0.530363
$902$	27.5708	−	10.4509i	0.918009	−	0.347978i
$903$	−10.0069			−0.333008
$904$	−8.16177	+	5.92988i	−0.271457	+	0.197225i
$905$	11.6162	+	35.7509i	0.386134	+	1.18840i
$906$	3.30767	−	10.1800i	0.109890	−	0.338207i
$907$	−0.885755	−	0.643539i	−0.0294110	−	0.0213684i	0.572983	−	0.819568i	$-0.305786\pi$
$907$	−0.885755	−	0.643539i	−0.0294110	−	0.0213684i	−0.602394	+	0.798199i	$0.705786\pi$
$908$	9.99696	+	7.26322i	0.331761	+	0.241038i
$909$	−2.45196	+	7.54636i	−0.0813264	+	0.250297i
$910$	−2.15621	−	6.63614i	−0.0714777	−	0.219986i
$911$	−6.59160	+	4.78907i	−0.218389	+	0.158669i	−0.691601	−	0.722279i	$-0.743094\pi$
$911$	−6.59160	+	4.78907i	−0.218389	+	0.158669i	0.473212	+	0.880949i	$0.343094\pi$
$912$	2.91671			0.0965818
$913$	7.18469	−	2.72341i	0.237779	−	0.0901318i
$914$	−22.4308			−0.741943
$915$	29.1614	−	21.1870i	0.964047	−	0.700421i
$916$	−3.20081	−	9.85109i	−0.105758	−	0.325489i
$917$	−4.19359	+	12.9065i	−0.138485	+	0.426212i
$918$	−1.50000	−	1.08981i	−0.0495074	−	0.0359692i
$919$	27.1308	+	19.7117i	0.894963	+	0.650229i	0.937167	−	0.348880i	$-0.113438\pi$
$919$	27.1308	+	19.7117i	0.894963	+	0.650229i	−0.0422041	+	0.999109i	$0.513438\pi$
$920$	9.59834	−	29.5407i	0.316448	−	0.973926i
$921$	2.25246	+	6.93235i	0.0742210	+	0.228429i
$922$	11.1416	−	8.09488i	0.366931	−	0.266591i
$923$	18.6577			0.614124
$924$	2.07639	+	2.58624i	0.0683081	+	0.0850809i
$925$	115.954			3.81256
$926$	−12.7609	+	9.27133i	−0.419349	+	0.304675i
$927$	−4.49309	−	13.8283i	−0.147573	−	0.454182i
$928$	0.0570413	−	0.175555i	0.00187247	−	0.00576288i
$929$	−12.9945	−	9.44105i	−0.426335	−	0.309751i	0.353847	−	0.935303i	$-0.384874\pi$
$929$	−12.9945	−	9.44105i	−0.426335	−	0.309751i	−0.780182	+	0.625553i	$0.784874\pi$
$930$	20.3039	+	14.7517i	0.665792	+	0.483726i
$931$	−0.901312	+	2.77395i	−0.0295393	+	0.0909126i
$932$	3.66916	+	11.2925i	0.120187	+	0.369899i
$933$	0.0896065	−	0.0651029i	0.00293358	−	0.00213137i
$934$	−7.53049			−0.246405
$935$	−24.3334	−	6.62966i	−0.795787	−	0.216813i
$936$	1.70133			0.0556096
$937$	28.7768	−	20.9075i	0.940096	−	0.683020i	−0.00834764	−	0.999965i	$-0.502657\pi$
$937$	28.7768	−	20.9075i	0.940096	−	0.683020i	0.948444	+	0.316945i	$0.102657\pi$
$938$	1.33393	+	4.10540i	0.0435542	+	0.134046i
$939$	1.90558	−	5.86477i	0.0621863	−	0.191390i
$940$	−6.02356	−	4.37638i	−0.196467	−	0.142742i
$941$	−34.2392	−	24.8762i	−1.11617	−	0.810942i	−0.132543	−	0.991177i	$-0.542314\pi$
$941$	−34.2392	−	24.8762i	−1.11617	−	0.810942i	−0.983624	+	0.180235i	$0.942314\pi$
$942$	4.60525	−	14.1735i	0.150047	−	0.461797i
$943$	20.8057	+	64.0333i	0.677526	+	2.08521i
$944$	−5.08673	+	3.69573i	−0.165559	+	0.120286i
$945$	4.10130			0.133415
$946$	−1.59791	−	33.1506i	−0.0519525	−	1.07782i
$947$	−1.52265			−0.0494795			−0.0247397	−	0.999694i	$-0.507876\pi$
$947$	−1.52265			−0.0494795			−0.0247397	+	0.999694i	$0.507876\pi$
$948$	−9.98796	+	7.25668i	−0.324394	+	0.235686i
$949$	5.65679	+	17.4098i	0.183627	+	0.565146i
$950$	10.6541	−	32.7898i	0.345664	−	1.06384i
$951$	2.79093	+	2.02773i	0.0905022	+	0.0657537i
$952$	−1.50000	−	1.08981i	−0.0486153	−	0.0353211i
$953$	0.797061	−	2.45310i	0.0258193	−	0.0794637i	−0.937317	−	0.348479i	$-0.886698\pi$
$953$	0.797061	−	2.45310i	0.0258193	−	0.0794637i	0.963136	+	0.269015i	$0.0866982\pi$
$954$	2.65329	+	8.16598i	0.0859034	+	0.264383i
$955$	−72.4240	+	52.6191i	−2.34359	+	1.70272i
$956$	24.7425			0.800231
$957$	−0.335587	+	0.512042i	−0.0108480	+	0.0165520i
$958$	20.9083			0.675516
$959$	2.98544	−	2.16905i	0.0964048	−	0.0700422i
$960$	−1.26737	−	3.90056i	−0.0409042	−	0.125890i
$961$	1.99186	−	6.13032i	0.0642536	−	0.197752i
$962$	−13.5018	−	9.80965i	−0.435316	−	0.316276i
$963$	−0.341663	−	0.248233i	−0.0110099	−	0.00799919i
$964$	−0.756244	+	2.32748i	−0.0243570	+	0.0749631i
$965$	29.2670	+	90.0745i	0.942138	+	2.89960i
$966$	−6.12703	+	4.45155i	−0.197134	+	0.143226i
$967$	−9.51179			−0.305879			−0.152939	−	0.988236i	$-0.548874\pi$
$967$	−9.51179			−0.305879			−0.152939	+	0.988236i	$0.548874\pi$
$968$	−8.23607	+	7.29158i	−0.264717	+	0.234360i
$969$	5.40787			0.173726
$970$	−1.60347	+	1.16499i	−0.0514843	+	0.0374056i
$971$	−3.54884	−	10.9222i	−0.113888	−	0.350510i	0.877826	−	0.478980i	$-0.158993\pi$
$971$	−3.54884	−	10.9222i	−0.113888	−	0.350510i	−0.991713	+	0.128470i	$0.958993\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	4.75963	+	3.45808i	0.152587	+	0.110861i
$974$	−0.710329	−	0.516084i	−0.0227604	−	0.0165364i
$975$	6.21457	−	19.1265i	0.199025	−	0.612537i
$976$	2.71589	+	8.35865i	0.0869336	+	0.267554i
$977$	25.3005	−	18.3819i	0.809436	−	0.588090i	−0.104231	−	0.994553i	$-0.533238\pi$
$977$	25.3005	−	18.3819i	0.809436	−	0.588090i	0.913667	+	0.406463i	$0.133238\pi$
$978$	−18.0000			−0.575577
$979$	15.5056	−	23.6586i	0.495560	−	0.756131i
$980$	4.10130			0.131011
$981$	4.15412	−	3.01814i	0.132631	−	0.0963619i
$982$	−10.4668	−	32.2136i	−0.334010	−	1.02798i
$983$	−5.79472	+	17.8343i	−0.184823	+	0.568826i	−0.999945	−	0.0104624i	$-0.996670\pi$
$983$	−5.79472	+	17.8343i	−0.184823	+	0.568826i	0.815122	+	0.579289i	$0.196670\pi$
$984$	7.19225	+	5.22547i	0.229280	+	0.166582i
$985$	−65.2526	−	47.4088i	−2.07912	−	1.51057i
$986$	0.105760	−	0.325497i	0.00336810	−	0.0103659i
$987$	0.560993	+	1.72656i	0.0178566	+	0.0549569i
$988$	−4.01456	+	2.91675i	−0.127720	+	0.0927942i
$989$	75.7864			2.40987
$990$	0.654899	+	13.5867i	0.0208141	+	0.431813i
$991$	−7.90542			−0.251124			−0.125562	−	0.992086i	$-0.540073\pi$
$991$	−7.90542			−0.251124			−0.125562	+	0.992086i	$0.540073\pi$
$992$	−4.95062	+	3.59683i	−0.157182	+	0.114200i
$993$	−3.83788	−	11.8118i	−0.121791	−	0.374835i
$994$	−3.38884	+	10.4298i	−0.107488	+	0.330813i
$995$	23.4884	+	17.0653i	0.744632	+	0.541007i
$996$	1.87423	+	1.36171i	0.0593872	+	0.0431473i
$997$	7.51961	−	23.1430i	0.238149	−	0.732946i	−0.758540	−	0.651627i	$-0.774087\pi$
$997$	7.51961	−	23.1430i	0.238149	−	0.732946i	0.996688	−	0.0813189i	$-0.0259132\pi$
$998$	8.51295	+	26.2002i	0.269473	+	0.829352i
$999$	7.93605	−	5.76588i	0.251086	−	0.182424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.h.421.1	yes	8
11.2	odd	10		5082.2.a.cd.1.4		4
11.4	even	5	inner	462.2.j.h.169.1	✓	8
11.9	even	5		5082.2.a.by.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.h.169.1	✓	8	11.4	even	5	inner
462.2.j.h.421.1	yes	8	1.1	even	1	trivial
5082.2.a.by.1.4		4	11.9	even	5
5082.2.a.cd.1.4		4	11.2	odd	10

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-3.31802 - 2.41068i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-3.31802 - 2.41068i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -4.10130 q^{10} +(-1.81802 + 2.77395i) q^{11} -1.00000 q^{12} +(1.37640 - 1.00002i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-1.26737 + 3.90056i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.50000 - 1.08981i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(-0.901312 - 2.77395i) q^{19} +(-3.31802 + 2.41068i) q^{20} +1.00000 q^{21} +(0.159681 + 3.31278i) q^{22} -7.57343 q^{23} +(-0.809017 + 0.587785i) q^{24} +(3.65277 + 11.2421i) q^{25} +(0.525739 - 1.61806i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-0.0570413 + 0.175555i) q^{29} +(1.26737 + 3.90056i) q^{30} +(4.95062 - 3.59683i) q^{31} -1.00000 q^{32} +(3.19998 + 0.871839i) q^{33} -1.85410 q^{34} +(3.31802 - 2.41068i) q^{35} +(0.309017 + 0.951057i) q^{36} +(3.03130 - 9.32939i) q^{37} +(-2.35966 - 1.71440i) q^{38} +(-1.37640 - 1.00002i) q^{39} +(-1.26737 + 3.90056i) q^{40} +(-2.74719 - 8.45499i) q^{41} +(0.809017 - 0.587785i) q^{42} -10.0069 q^{43} +(2.07639 + 2.58624i) q^{44} +4.10130 q^{45} +(-6.12703 + 4.45155i) q^{46} +(0.560993 + 1.72656i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(9.56309 + 6.94799i) q^{50} +(-0.572949 + 1.76336i) q^{51} +(-0.525739 - 1.61806i) q^{52} +(6.94640 - 5.04685i) q^{53} +1.00000 q^{54} +(12.7193 - 4.82136i) q^{55} +1.00000 q^{56} +(-2.35966 + 1.71440i) q^{57} +(0.0570413 + 0.175555i) q^{58} +(1.94296 - 5.97981i) q^{59} +(3.31802 + 2.41068i) q^{60} +(-7.11030 - 5.16593i) q^{61} +(1.89097 - 5.81980i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} -6.97765 q^{65} +(3.10130 - 1.17557i) q^{66} +4.31667 q^{67} +(-1.50000 + 1.08981i) q^{68} +(2.34032 + 7.20276i) q^{69} +(1.26737 - 3.90056i) q^{70} +(8.87210 + 6.44596i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-3.32492 + 10.2331i) q^{73} +(-3.03130 - 9.32939i) q^{74} +(9.56309 - 6.94799i) q^{75} -2.91671 q^{76} +(-2.07639 - 2.58624i) q^{77} -1.70133 q^{78} +(9.98796 - 7.25668i) q^{79} +(1.26737 + 3.90056i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-7.19225 - 5.22547i) q^{82} +(-1.87423 - 1.36171i) q^{83} +(0.309017 - 0.951057i) q^{84} +(2.34983 + 7.23204i) q^{85} +(-8.09573 + 5.88189i) q^{86} +0.184589 q^{87} +(3.19998 + 0.871839i) q^{88} -8.52883 q^{89} +(3.31802 - 2.41068i) q^{90} +(0.525739 + 1.61806i) q^{91} +(-2.34032 + 7.20276i) q^{92} +(-4.95062 - 3.59683i) q^{93} +(1.46870 + 1.06707i) q^{94} +(-3.69655 + 11.3768i) q^{95} +(0.309017 + 0.951057i) q^{96} +(0.390967 - 0.284054i) q^{97} -1.00000 q^{98} +(-0.159681 - 3.31278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} - 8 q^{10} + 10 q^{11} - 8 q^{12} + 10 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 12 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 4 q^{25} + 2 q^{27} + 2 q^{28} - 2 q^{29} - 2 q^{30} - 4 q^{31} - 8 q^{32} + 10 q^{33} + 12 q^{34} + 2 q^{35} - 2 q^{36} + 30 q^{37} - 2 q^{38} - 10 q^{39} + 2 q^{40} - 24 q^{41} + 2 q^{42} - 20 q^{43} + 8 q^{45} - 20 q^{46} - 6 q^{47} + 2 q^{48} - 2 q^{49} + 14 q^{50} - 18 q^{51} + 24 q^{53} + 8 q^{54} + 68 q^{55} + 8 q^{56} - 2 q^{57} + 2 q^{58} + 14 q^{59} + 2 q^{60} - 12 q^{61} + 4 q^{62} + 2 q^{63} - 2 q^{64} - 44 q^{65} - 12 q^{67} - 12 q^{68} + 20 q^{69} - 2 q^{70} + 4 q^{71} + 2 q^{72} - 34 q^{73} - 30 q^{74} + 14 q^{75} - 8 q^{76} - 20 q^{78} - 22 q^{79} - 2 q^{80} - 2 q^{81} - 6 q^{82} + 12 q^{83} - 2 q^{84} + 18 q^{85} - 30 q^{86} - 8 q^{87} + 10 q^{88} + 44 q^{89} + 2 q^{90} - 20 q^{92} + 4 q^{93} + 6 q^{94} - 44 q^{95} - 2 q^{96} - 8 q^{97} - 8 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 - 8 * q^10 + 10 * q^11 - 8 * q^12 + 10 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 12 * q^17 + 2 * q^18 + 2 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 4 * q^25 + 2 * q^27 + 2 * q^28 - 2 * q^29 - 2 * q^30 - 4 * q^31 - 8 * q^32 + 10 * q^33 + 12 * q^34 + 2 * q^35 - 2 * q^36 + 30 * q^37 - 2 * q^38 - 10 * q^39 + 2 * q^40 - 24 * q^41 + 2 * q^42 - 20 * q^43 + 8 * q^45 - 20 * q^46 - 6 * q^47 + 2 * q^48 - 2 * q^49 + 14 * q^50 - 18 * q^51 + 24 * q^53 + 8 * q^54 + 68 * q^55 + 8 * q^56 - 2 * q^57 + 2 * q^58 + 14 * q^59 + 2 * q^60 - 12 * q^61 + 4 * q^62 + 2 * q^63 - 2 * q^64 - 44 * q^65 - 12 * q^67 - 12 * q^68 + 20 * q^69 - 2 * q^70 + 4 * q^71 + 2 * q^72 - 34 * q^73 - 30 * q^74 + 14 * q^75 - 8 * q^76 - 20 * q^78 - 22 * q^79 - 2 * q^80 - 2 * q^81 - 6 * q^82 + 12 * q^83 - 2 * q^84 + 18 * q^85 - 30 * q^86 - 8 * q^87 + 10 * q^88 + 44 * q^89 + 2 * q^90 - 20 * q^92 + 4 * q^93 + 6 * q^94 - 44 * q^95 - 2 * q^96 - 8 * q^97 - 8 * q^98

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