LMFDB - Embedded newform 399.2.k.c.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [399,2,Mod(64,399)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(399, base_ring=CyclotomicField(6))

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("399.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.k (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:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 11 x^{10} - 10 x^{9} + 90 x^{8} - 79 x^{7} + 275 x^{6} - 177 x^{5} + 560 x^{4} + \cdots + 9 $ x^12 - x^11 + 11x^10 - 10x^9 + 90x^8 - 79x^7 + 275x^6 - 177x^5 + 560x^4 - 320x^3 + 421x^2 + 57x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			64.1
Root			$1.34639 + 2.33202i$ of defining polynomial
Character	$\chi$	$=$	399.64
Dual form			399.2.k.c.106.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34639 - 2.33202i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.62554 + 4.54758i) q^{4} +(-1.03963 - 1.80069i) q^{5} +(-1.34639 + 2.33202i) q^{6} -1.00000 q^{7} +8.75448 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.34639 - 2.33202i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.62554 + 4.54758i) q^{4} +(-1.03963 - 1.80069i) q^{5} +(-1.34639 + 2.33202i) q^{6} -1.00000 q^{7} +8.75448 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.79950 + 4.84888i) q^{10} -1.81905 q^{11} +5.25109 q^{12} +(-3.30361 + 5.72202i) q^{13} +(1.34639 + 2.33202i) q^{14} +(-1.03963 + 1.80069i) q^{15} +(-6.53587 - 11.3205i) q^{16} +(1.08591 + 1.88086i) q^{17} +2.69278 q^{18} +(4.30847 - 0.661119i) q^{19} +10.9184 q^{20} +(0.500000 + 0.866025i) q^{21} +(2.44916 + 4.24207i) q^{22} +(-0.173960 + 0.301308i) q^{23} +(-4.37724 - 7.58160i) q^{24} +(0.338332 - 0.586008i) q^{25} +17.7918 q^{26} +1.00000 q^{27} +(2.62554 - 4.54758i) q^{28} +(-0.164372 + 0.284700i) q^{29} +5.59901 q^{30} +1.56957 q^{31} +(-8.84522 + 15.3204i) q^{32} +(0.909526 + 1.57535i) q^{33} +(2.92413 - 5.06474i) q^{34} +(1.03963 + 1.80069i) q^{35} +(-2.62554 - 4.54758i) q^{36} -11.3128 q^{37} +(-7.34263 - 9.15731i) q^{38} +6.60722 q^{39} +(-9.10143 - 15.7641i) q^{40} +(-1.47677 - 2.55783i) q^{41} +(1.34639 - 2.33202i) q^{42} +(3.46388 + 5.99961i) q^{43} +(4.77600 - 8.27228i) q^{44} +2.07926 q^{45} +0.936875 q^{46} +(-4.16437 + 7.21290i) q^{47} +(-6.53587 + 11.3205i) q^{48} +1.00000 q^{49} -1.82211 q^{50} +(1.08591 - 1.88086i) q^{51} +(-17.3475 - 30.0468i) q^{52} +(0.705792 - 1.22247i) q^{53} +(-1.34639 - 2.33202i) q^{54} +(1.89114 + 3.27556i) q^{55} -8.75448 q^{56} +(-2.72678 - 3.40069i) q^{57} +0.885234 q^{58} +(5.33278 + 9.23664i) q^{59} +(-5.45920 - 9.45561i) q^{60} +(3.25565 - 5.63895i) q^{61} +(-2.11326 - 3.66027i) q^{62} +(0.500000 - 0.866025i) q^{63} +21.4931 q^{64} +13.7382 q^{65} +(2.44916 - 4.24207i) q^{66} +(-7.97715 + 13.8168i) q^{67} -11.4044 q^{68} +0.347920 q^{69} +(2.79950 - 4.84888i) q^{70} +(-7.16625 - 12.4123i) q^{71} +(-4.37724 + 7.58160i) q^{72} +(7.60311 + 13.1690i) q^{73} +(15.2314 + 26.3816i) q^{74} -0.676663 q^{75} +(-8.30559 + 21.3289i) q^{76} +1.81905 q^{77} +(-8.89591 - 15.4082i) q^{78} +(4.47320 + 7.74780i) q^{79} +(-13.5898 + 23.5382i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.97661 + 6.88770i) q^{82} -4.59810 q^{83} -5.25109 q^{84} +(2.25790 - 3.91079i) q^{85} +(9.32747 - 16.1557i) q^{86} +0.328743 q^{87} -15.9249 q^{88} +(-1.43291 + 2.48188i) q^{89} +(-2.79950 - 4.84888i) q^{90} +(3.30361 - 5.72202i) q^{91} +(-0.913480 - 1.58219i) q^{92} +(-0.784786 - 1.35929i) q^{93} +22.4275 q^{94} +(-5.66970 - 7.07092i) q^{95} +17.6904 q^{96} +(-0.444846 - 0.770496i) q^{97} +(-1.34639 - 2.33202i) q^{98} +(0.909526 - 1.57535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} - 6 q^{3} - 9 q^{4} - q^{6} - 12 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q - q^2 - 6 * q^3 - 9 * q^4 - q^6 - 12 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q - q^{2} - 6 q^{3} - 9 q^{4} - q^{6} - 12 q^{7} - 6 q^{8} - 6 q^{9} - 4 q^{10} + 8 q^{11} + 18 q^{12} - 2 q^{13} + q^{14} - 19 q^{16} + 3 q^{17} + 2 q^{18} + 3 q^{19} - 26 q^{20} + 6 q^{21} + 2 q^{22} + 5 q^{23} + 3 q^{24} - 16 q^{25} + 98 q^{26} + 12 q^{27} + 9 q^{28} + 11 q^{29} + 8 q^{30} - 10 q^{31} - 4 q^{33} - 6 q^{34} - 9 q^{36} - 10 q^{37} - 26 q^{38} + 4 q^{39} - 62 q^{40} + 5 q^{41} + q^{42} - q^{43} + 15 q^{44} - 24 q^{46} - 37 q^{47} - 19 q^{48} + 12 q^{49} + 6 q^{50} + 3 q^{51} + 9 q^{52} + 9 q^{53} - q^{54} + 9 q^{55} + 6 q^{56} + 3 q^{57} + 18 q^{58} + 6 q^{59} + 13 q^{60} + 19 q^{61} + 5 q^{62} + 6 q^{63} + 118 q^{64} + 48 q^{65} + 2 q^{66} + 8 q^{67} - 130 q^{68} - 10 q^{69} + 4 q^{70} - 19 q^{71} + 3 q^{72} + 24 q^{73} + 15 q^{74} + 32 q^{75} - 6 q^{76} - 8 q^{77} - 49 q^{78} + 27 q^{79} - 11 q^{80} - 6 q^{81} - 46 q^{82} + 70 q^{83} - 18 q^{84} - 59 q^{85} - 3 q^{86} - 22 q^{87} - 14 q^{88} - 4 q^{89} - 4 q^{90} + 2 q^{91} - 9 q^{92} + 5 q^{93} + 34 q^{94} - 55 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - q^2 - 6 * q^3 - 9 * q^4 - q^6 - 12 * q^7 - 6 * q^8 - 6 * q^9 - 4 * q^10 + 8 * q^11 + 18 * q^12 - 2 * q^13 + q^14 - 19 * q^16 + 3 * q^17 + 2 * q^18 + 3 * q^19 - 26 * q^20 + 6 * q^21 + 2 * q^22 + 5 * q^23 + 3 * q^24 - 16 * q^25 + 98 * q^26 + 12 * q^27 + 9 * q^28 + 11 * q^29 + 8 * q^30 - 10 * q^31 - 4 * q^33 - 6 * q^34 - 9 * q^36 - 10 * q^37 - 26 * q^38 + 4 * q^39 - 62 * q^40 + 5 * q^41 + q^42 - q^43 + 15 * q^44 - 24 * q^46 - 37 * q^47 - 19 * q^48 + 12 * q^49 + 6 * q^50 + 3 * q^51 + 9 * q^52 + 9 * q^53 - q^54 + 9 * q^55 + 6 * q^56 + 3 * q^57 + 18 * q^58 + 6 * q^59 + 13 * q^60 + 19 * q^61 + 5 * q^62 + 6 * q^63 + 118 * q^64 + 48 * q^65 + 2 * q^66 + 8 * q^67 - 130 * q^68 - 10 * q^69 + 4 * q^70 - 19 * q^71 + 3 * q^72 + 24 * q^73 + 15 * q^74 + 32 * q^75 - 6 * q^76 - 8 * q^77 - 49 * q^78 + 27 * q^79 - 11 * q^80 - 6 * q^81 - 46 * q^82 + 70 * q^83 - 18 * q^84 - 59 * q^85 - 3 * q^86 - 22 * q^87 - 14 * q^88 - 4 * q^89 - 4 * q^90 + 2 * q^91 - 9 * q^92 + 5 * q^93 + 34 * q^94 - 55 * q^97 - q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.34639	−	2.33202i	−0.952043	−	1.64899i	−0.740994	−	0.671511i	$-0.765645\pi$
$2$	−1.34639	−	2.33202i	−0.952043	−	1.64899i	−0.211049	−	0.977476i	$-0.567688\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−2.62554	+	4.54758i	−1.31277	+	2.27379i
$5$	−1.03963	−	1.80069i	−0.464937	−	0.805295i	0.534261	−	0.845319i	$-0.320590\pi$
$5$	−1.03963	−	1.80069i	−0.464937	−	0.805295i	−0.999199	+	0.0400241i	$0.987257\pi$
$6$	−1.34639	+	2.33202i	−0.549662	+	0.952043i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	8.75448			3.09518
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.79950	+	4.84888i	−0.885281	+	1.53335i
$11$	−1.81905			−0.548465			−0.274232	−	0.961663i	$-0.588424\pi$
$11$	−1.81905			−0.548465			−0.274232	+	0.961663i	$0.588424\pi$
$12$	5.25109			1.51586
$13$	−3.30361	+	5.72202i	−0.916257	+	1.58700i	−0.111206	+	0.993797i	$0.535471\pi$
$13$	−3.30361	+	5.72202i	−0.916257	+	1.58700i	−0.805051	+	0.593206i	$0.797862\pi$
$14$	1.34639	+	2.33202i	0.359838	+	0.623258i
$15$	−1.03963	+	1.80069i	−0.268432	+	0.464937i
$16$	−6.53587	−	11.3205i	−1.63397	−	2.83012i
$17$	1.08591	+	1.88086i	0.263372	+	0.456174i	0.967136	−	0.254260i	$-0.0818319\pi$
$17$	1.08591	+	1.88086i	0.263372	+	0.456174i	−0.703764	+	0.710434i	$0.748499\pi$
$18$	2.69278			0.634695
$19$	4.30847	−	0.661119i	0.988431	−	0.151671i
$19$	4.30847	−	0.661119i	0.988431	−	0.151671i
$20$	10.9184			2.44143
$21$	0.500000	+	0.866025i	0.109109	+	0.188982i
$22$	2.44916	+	4.24207i	0.522162	+	0.904411i
$23$	−0.173960	+	0.301308i	−0.0362732	+	0.0628270i	−0.883592	−	0.468257i	$-0.844882\pi$
$23$	−0.173960	+	0.301308i	−0.0362732	+	0.0628270i	0.847319	+	0.531084i	$0.178215\pi$
$24$	−4.37724	−	7.58160i	−0.893500	−	1.54759i
$25$	0.338332	−	0.586008i	0.0676663	−	0.117202i
$26$	17.7918			3.48926
$27$	1.00000			0.192450
$28$	2.62554	−	4.54758i	0.496181	−	0.859411i
$29$	−0.164372	+	0.284700i	−0.0305230	+	0.0528674i	−0.880883	−	0.473333i	$-0.843051\pi$
$29$	−0.164372	+	0.284700i	−0.0305230	+	0.0528674i	0.850360	+	0.526201i	$0.176384\pi$
$30$	5.59901			1.02223
$31$	1.56957			0.281904			0.140952	−	0.990016i	$-0.454984\pi$
$31$	1.56957			0.281904			0.140952	+	0.990016i	$0.454984\pi$
$32$	−8.84522	+	15.3204i	−1.56363	+	2.70828i
$33$	0.909526	+	1.57535i	0.158328	+	0.274232i
$34$	2.92413	−	5.06474i	0.501484	−	0.868595i
$35$	1.03963	+	1.80069i	0.175730	+	0.304373i
$36$	−2.62554	−	4.54758i	−0.437591	−	0.757929i
$37$	−11.3128			−1.85981			−0.929905	−	0.367800i	$-0.880111\pi$
$37$	−11.3128			−1.85981			−0.929905	+	0.367800i	$0.880111\pi$
$38$	−7.34263	−	9.15731i	−1.19113	−	1.48551i
$39$	6.60722			1.05800
$40$	−9.10143	−	15.7641i	−1.43906	−	2.49253i
$41$	−1.47677	−	2.55783i	−0.230632	−	0.399467i	0.727362	−	0.686254i	$-0.240746\pi$
$41$	−1.47677	−	2.55783i	−0.230632	−	0.399467i	−0.957994	+	0.286787i	$0.907413\pi$
$42$	1.34639	−	2.33202i	0.207753	−	0.359838i
$43$	3.46388	+	5.99961i	0.528236	+	0.914932i	0.999458	+	0.0329171i	$0.0104797\pi$
$43$	3.46388	+	5.99961i	0.528236	+	0.914932i	−0.471222	+	0.882015i	$0.656187\pi$
$44$	4.77600	−	8.27228i	0.720009	−	1.24709i
$45$	2.07926			0.309958
$46$	0.936875			0.138135
$47$	−4.16437	+	7.21290i	−0.607436	+	1.05211i	0.384225	+	0.923239i	$0.374469\pi$
$47$	−4.16437	+	7.21290i	−0.607436	+	1.05211i	−0.991661	+	0.128871i	$0.958865\pi$
$48$	−6.53587	+	11.3205i	−0.943372	+	1.63397i
$49$	1.00000			0.142857
$50$	−1.82211			−0.257685
$51$	1.08591	−	1.88086i	0.152058	−	0.263372i
$52$	−17.3475	−	30.0468i	−2.40567	−	4.16675i
$53$	0.705792	−	1.22247i	0.0969480	−	0.167919i	−0.813472	−	0.581604i	$-0.802425\pi$
$53$	0.705792	−	1.22247i	0.0969480	−	0.167919i	0.910420	+	0.413685i	$0.135759\pi$
$54$	−1.34639	−	2.33202i	−0.183221	−	0.317348i
$55$	1.89114	+	3.27556i	0.255002	+	0.441676i
$56$	−8.75448			−1.16987
$57$	−2.72678	−	3.40069i	−0.361171	−	0.450432i
$58$	0.885234			0.116237
$59$	5.33278	+	9.23664i	0.694268	+	1.20251i	0.970427	+	0.241396i	$0.0776053\pi$
$59$	5.33278	+	9.23664i	0.694268	+	1.20251i	−0.276158	+	0.961112i	$0.589061\pi$
$60$	−5.45920	−	9.45561i	−0.704779	−	1.22071i
$61$	3.25565	−	5.63895i	0.416843	−	0.721994i	−0.578777	−	0.815486i	$-0.696470\pi$
$61$	3.25565	−	5.63895i	0.416843	−	0.721994i	0.995620	+	0.0934924i	$0.0298031\pi$
$62$	−2.11326	−	3.66027i	−0.268384	−	0.464855i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	21.4931			2.68663
$65$	13.7382			1.70401
$66$	2.44916	−	4.24207i	0.301470	−	0.522162i
$67$	−7.97715	+	13.8168i	−0.974563	+	1.68799i	−0.293195	+	0.956053i	$0.594719\pi$
$67$	−7.97715	+	13.8168i	−0.974563	+	1.68799i	−0.681368	+	0.731941i	$0.738615\pi$
$68$	−11.4044			−1.38299
$69$	0.347920			0.0418847
$70$	2.79950	−	4.84888i	0.334605	−	0.579552i
$71$	−7.16625	−	12.4123i	−0.850477	−	1.47307i	−0.880778	−	0.473529i	$-0.842980\pi$
$71$	−7.16625	−	12.4123i	−0.850477	−	1.47307i	0.0303010	−	0.999541i	$-0.490353\pi$
$72$	−4.37724	+	7.58160i	−0.515863	+	0.893500i
$73$	7.60311	+	13.1690i	0.889877	+	1.54131i	0.840019	+	0.542556i	$0.182543\pi$
$73$	7.60311	+	13.1690i	0.889877	+	1.54131i	0.0498579	+	0.998756i	$0.484123\pi$
$74$	15.2314	+	26.3816i	1.77062	+	3.06680i
$75$	−0.676663			−0.0781344
$76$	−8.30559	+	21.3289i	−0.952717	+	2.44659i
$77$	1.81905			0.207300
$78$	−8.89591	−	15.4082i	−1.00726	−	1.74463i
$79$	4.47320	+	7.74780i	0.503274	+	0.871696i	0.999993	+	0.00378441i	$0.00120462\pi$
$79$	4.47320	+	7.74780i	0.503274	+	0.871696i	−0.496719	+	0.867911i	$0.665462\pi$
$80$	−13.5898	+	23.5382i	−1.51939	+	2.63165i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.97661	+	6.88770i	−0.439144	+	0.760619i
$83$	−4.59810			−0.504707			−0.252353	−	0.967635i	$-0.581205\pi$
$83$	−4.59810			−0.504707			−0.252353	+	0.967635i	$0.581205\pi$
$84$	−5.25109			−0.572941
$85$	2.25790	−	3.91079i	0.244903	−	0.424185i
$86$	9.32747	−	16.1557i	1.00581	−	1.74211i
$87$	0.328743			0.0352450
$88$	−15.9249			−1.69760
$89$	−1.43291	+	2.48188i	−0.151888	+	0.263078i	−0.931922	−	0.362660i	$-0.881869\pi$
$89$	−1.43291	+	2.48188i	−0.151888	+	0.263078i	0.780033	+	0.625738i	$0.215202\pi$
$90$	−2.79950	−	4.84888i	−0.295094	−	0.511117i
$91$	3.30361	−	5.72202i	0.346312	−	0.599831i
$92$	−0.913480	−	1.58219i	−0.0952369	−	0.164955i
$93$	−0.784786	−	1.35929i	−0.0813786	−	0.140952i
$94$	22.4275			2.31322
$95$	−5.66970	−	7.07092i	−0.581699	−	0.725461i
$96$	17.6904			1.80552
$97$	−0.444846	−	0.770496i	−0.0451673	−	0.0782321i	0.842558	−	0.538606i	$-0.181049\pi$
$97$	−0.444846	−	0.770496i	−0.0451673	−	0.0782321i	−0.887725	+	0.460374i	$0.847715\pi$
$98$	−1.34639	−	2.33202i	−0.136006	−	0.235570i
$99$	0.909526	−	1.57535i	0.0914108	−	0.158328i
$100$	1.77661	+	3.07718i	0.177661	+	0.307718i
$101$	−7.96908	+	13.8029i	−0.792954	+	1.37344i	0.131177	+	0.991359i	$0.458124\pi$
$101$	−7.96908	+	13.8029i	−0.792954	+	1.37344i	−0.924131	+	0.382077i	$0.875209\pi$
$102$	−5.84826			−0.579064
$103$	−1.27080			−0.125216			−0.0626080	−	0.998038i	$-0.519942\pi$
$103$	−1.27080			−0.125216			−0.0626080	+	0.998038i	$0.519942\pi$
$104$	−28.9214	+	50.0933i	−2.83598	+	4.91205i
$105$	1.03963	−	1.80069i	0.101458	−	0.175730i
$106$	−3.80109			−0.369195
$107$	−0.695303			−0.0672175			−0.0336087	−	0.999435i	$-0.510700\pi$
$107$	−0.695303			−0.0672175			−0.0336087	+	0.999435i	$0.510700\pi$
$108$	−2.62554	+	4.54758i	−0.252643	+	0.437591i
$109$	−1.41617	−	2.45289i	−0.135645	−	0.234944i	0.790199	−	0.612851i	$-0.209977\pi$
$109$	−1.41617	−	2.45289i	−0.135645	−	0.234944i	−0.925844	+	0.377907i	$0.876644\pi$
$110$	5.09244	−	8.82037i	0.485546	−	0.840990i
$111$	5.65639	+	9.79716i	0.536881	+	0.929905i
$112$	6.53587	+	11.3205i	0.617582	+	1.06968i
$113$	−13.9069			−1.30825			−0.654127	−	0.756385i	$-0.726964\pi$
$113$	−13.9069			−1.30825			−0.654127	+	0.756385i	$0.726964\pi$
$114$	−4.25915	+	10.9376i	−0.398906	+	1.02440i
$115$	0.723418			0.0674591
$116$	−0.863129	−	1.49498i	−0.0801395	−	0.138806i
$117$	−3.30361	−	5.72202i	−0.305419	−	0.529001i
$118$	14.3600	−	24.8723i	1.32195	−	2.28968i
$119$	−1.08591	−	1.88086i	−0.0995454	−	0.172418i
$120$	−9.10143	+	15.7641i	−0.830843	+	1.43906i
$121$	−7.69105			−0.699186
$122$	−17.5335			−1.58741
$123$	−1.47677	+	2.55783i	−0.133156	+	0.230632i
$124$	−4.12098	+	7.13775i	−0.370075	+	0.640989i
$125$	−11.8033			−1.05572
$126$	−2.69278			−0.239892
$127$	−6.69260	+	11.5919i	−0.593872	+	1.02862i	0.399833	+	0.916588i	$0.369068\pi$
$127$	−6.69260	+	11.5919i	−0.593872	+	1.02862i	−0.993705	+	0.112029i	$0.964265\pi$
$128$	−11.2476	−	19.4815i	−0.994160	−	1.72194i
$129$	3.46388	−	5.99961i	0.304977	−	0.528236i
$130$	−18.4969	−	32.0376i	−1.62229	−	2.80989i
$131$	8.19664	+	14.1970i	0.716144	+	1.24040i	0.962517	+	0.271222i	$0.0874279\pi$
$131$	8.19664	+	14.1970i	0.716144	+	1.24040i	−0.246373	+	0.969175i	$0.579239\pi$
$132$	−9.55200			−0.831395
$133$	−4.30847	+	0.661119i	−0.373592	+	0.0573263i
$134$	42.9615			3.71131
$135$	−1.03963	−	1.80069i	−0.0894773	−	0.154979i
$136$	9.50660	+	16.4659i	0.815184	+	1.41194i
$137$	7.54771	−	13.0730i	0.644844	−	1.11690i	−0.339493	−	0.940609i	$-0.610255\pi$
$137$	7.54771	−	13.0730i	0.644844	−	1.11690i	0.984337	−	0.176295i	$-0.0564112\pi$
$138$	−0.468437	−	0.811357i	−0.0398760	−	0.0690673i
$139$	−2.82847	+	4.89906i	−0.239908	+	0.415533i	−0.960688	−	0.277631i	$-0.910451\pi$
$139$	−2.82847	+	4.89906i	−0.239908	+	0.415533i	0.720780	+	0.693164i	$0.243784\pi$
$140$	−10.9184			−0.922773
$141$	8.32874			0.701407
$142$	−19.2972	+	33.4237i	−1.61938	+	2.80485i
$143$	6.00944	−	10.4087i	0.502535	−	0.870416i
$144$	13.0717			1.08931
$145$	0.683543			0.0567652
$146$	20.4735	−	35.4612i	1.69440	−	2.93479i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$	29.7022	−	51.4457i	2.44151	−	4.22881i
$149$	−7.19308	−	12.4588i	−0.589280	−	1.02066i	−0.994327	−	0.106367i	$-0.966078\pi$
$149$	−7.19308	−	12.4588i	−0.589280	−	1.02066i	0.405047	−	0.914296i	$-0.367255\pi$
$150$	0.911054	+	1.57799i	0.0743873	+	0.128843i
$151$	−3.66213			−0.298020			−0.149010	−	0.988836i	$-0.547609\pi$
$151$	−3.66213			−0.298020			−0.149010	+	0.988836i	$0.547609\pi$
$152$	37.7184	−	5.78775i	3.05937	−	0.469449i
$153$	−2.17182			−0.175582
$154$	−2.44916	−	4.24207i	−0.197359	−	0.341835i
$155$	−1.63178	−	2.82632i	−0.131068	−	0.227016i
$156$	−17.3475	+	30.0468i	−1.38892	+	2.40567i
$157$	2.64186	+	4.57584i	0.210843	+	0.365191i	0.951979	−	0.306164i	$-0.0990457\pi$
$157$	2.64186	+	4.57584i	0.210843	+	0.365191i	−0.741135	+	0.671356i	$0.765712\pi$
$158$	12.0454	−	20.8632i	0.958277	−	1.65978i
$159$	−1.41158			−0.111946
$160$	36.7831			2.90796
$161$	0.173960	−	0.301308i	0.0137100	−	0.0237464i
$162$	−1.34639	+	2.33202i	−0.105783	+	0.183221i
$163$	17.1383			1.34238			0.671188	−	0.741287i	$-0.265784\pi$
$163$	17.1383			1.34238			0.671188	+	0.741287i	$0.265784\pi$
$164$	15.5093			1.21107
$165$	1.89114	−	3.27556i	0.147225	−	0.255002i
$166$	6.19084	+	10.7229i	0.480503	+	0.832255i
$167$	8.65153	−	14.9849i	0.669476	−	1.15957i	−0.308575	−	0.951200i	$-0.599852\pi$
$167$	8.65153	−	14.9849i	0.669476	−	1.15957i	0.978051	−	0.208366i	$-0.0668145\pi$
$168$	4.37724	+	7.58160i	0.337711	+	0.584933i
$169$	−15.3277	−	26.5483i	−1.17905	−	2.04218i
$170$	−12.1601			−0.932634
$171$	−1.58169	+	4.06180i	−0.120955	+	0.310614i
$172$	−36.3782			−2.77381
$173$	−3.72606	−	6.45372i	−0.283287	−	0.490667i	0.688905	−	0.724851i	$-0.258092\pi$
$173$	−3.72606	−	6.45372i	−0.283287	−	0.490667i	−0.972192	+	0.234184i	$0.924758\pi$
$174$	−0.442617	−	0.766635i	−0.0335547	−	0.0581185i
$175$	−0.338332	+	0.586008i	−0.0255755	+	0.0442980i
$176$	11.8891	+	20.5925i	0.896174	+	1.55222i
$177$	5.33278	−	9.23664i	0.400836	−	0.694268i
$178$	7.71705			0.578417
$179$	−20.3004			−1.51732			−0.758662	−	0.651484i	$-0.774147\pi$
$179$	−20.3004			−1.51732			−0.758662	+	0.651484i	$0.774147\pi$
$180$	−5.45920	+	9.45561i	−0.406905	+	0.704779i
$181$	−2.81951	+	4.88353i	−0.209572	+	0.362990i	−0.951580	−	0.307402i	$-0.900541\pi$
$181$	−2.81951	+	4.88353i	−0.209572	+	0.362990i	0.742008	+	0.670392i	$0.233874\pi$
$182$	−17.7918			−1.31882
$183$	−6.51130			−0.481329
$184$	−1.52293	+	2.63779i	−0.112272	+	0.194461i
$185$	11.7611	+	20.3709i	0.864695	+	1.49770i
$186$	−2.11326	+	3.66027i	−0.154952	+	0.268384i
$187$	−1.97533	−	3.42137i	−0.144451	−	0.250196i
$188$	−21.8675	−	37.8756i	−1.59485	−	2.76236i
$189$	−1.00000			−0.0727393
$190$	−8.85589	+	22.7421i	−0.642474	+	1.64988i
$191$	19.3899			1.40300			0.701501	−	0.712669i	$-0.252514\pi$
$191$	19.3899			1.40300			0.701501	+	0.712669i	$0.252514\pi$
$192$	−10.7465	−	18.6135i	−0.775564	−	1.34332i
$193$	−11.4356	−	19.8071i	−0.823154	−	1.42574i	−0.903322	−	0.428963i	$-0.858879\pi$
$193$	−11.4356	−	19.8071i	−0.823154	−	1.42574i	0.0801677	−	0.996781i	$-0.474454\pi$
$194$	−1.19788	+	2.07478i	−0.0860024	+	0.148961i
$195$	−6.86908	−	11.8976i	−0.491905	−	0.852004i
$196$	−2.62554	+	4.54758i	−0.187539	+	0.324827i
$197$	−9.21162			−0.656301			−0.328150	−	0.944626i	$-0.606425\pi$
$197$	−9.21162			−0.656301			−0.328150	+	0.944626i	$0.606425\pi$
$198$	−4.89832			−0.348108
$199$	−3.28246	+	5.68539i	−0.232688	+	0.403027i	−0.958598	−	0.284762i	$-0.908085\pi$
$199$	−3.28246	+	5.68539i	−0.232688	+	0.403027i	0.725911	+	0.687789i	$0.241419\pi$
$200$	2.96192	−	5.13019i	0.209439	−	0.362759i
$201$	15.9543			1.12533
$202$	42.9181			3.01970
$203$	0.164372	−	0.284700i	0.0115366	−	0.0199820i
$204$	5.70222	+	9.87654i	0.399235	+	0.691496i
$205$	−3.07059	+	5.31841i	−0.214459	+	0.371454i
$206$	1.71100	+	2.96354i	0.119211	+	0.206479i
$207$	−0.173960	−	0.301308i	−0.0120911	−	0.0209423i
$208$	86.3679			5.98854
$209$	−7.83733	+	1.20261i	−0.542120	+	0.0831863i
$210$	−5.59901			−0.386368
$211$	−3.31643	−	5.74423i	−0.228313	−	0.395449i	0.728996	−	0.684518i	$-0.239987\pi$
$211$	−3.31643	−	5.74423i	−0.228313	−	0.395449i	−0.957308	+	0.289069i	$0.906654\pi$
$212$	3.70617	+	6.41928i	0.254541	+	0.440878i
$213$	−7.16625	+	12.4123i	−0.491023	+	0.850477i
$214$	0.936151	+	1.62146i	0.0639939	+	0.110841i
$215$	7.20231	−	12.4748i	0.491193	−	0.850772i
$216$	8.75448			0.595667
$217$	−1.56957			−0.106550
$218$	−3.81345	+	6.60510i	−0.258280	+	0.447354i
$219$	7.60311	−	13.1690i	0.513771	−	0.889877i
$220$	−19.8611			−1.33904
$221$	−14.3497			−0.965267
$222$	15.2314	−	26.3816i	1.02227	−	1.77062i
$223$	6.56242	+	11.3664i	0.439452	+	0.761153i	0.997647	−	0.0685564i	$-0.0218393\pi$
$223$	6.56242	+	11.3664i	0.439452	+	0.761153i	−0.558195	+	0.829710i	$0.688506\pi$
$224$	8.84522	−	15.3204i	0.590996	−	1.02364i
$225$	0.338332	+	0.586008i	0.0225554	+	0.0390672i
$226$	18.7242	+	32.4312i	1.24551	+	2.15729i
$227$	−13.3182			−0.883959			−0.441980	−	0.897025i	$-0.645724\pi$
$227$	−13.3182			−0.883959			−0.441980	+	0.897025i	$0.645724\pi$
$228$	22.6242	−	3.47160i	1.49832	−	0.229912i
$229$	−2.94994			−0.194937			−0.0974687	−	0.995239i	$-0.531075\pi$
$229$	−2.94994			−0.194937			−0.0974687	+	0.995239i	$0.531075\pi$
$230$	−0.974004	−	1.68703i	−0.0642240	−	0.111239i
$231$	−0.909526	−	1.57535i	−0.0598424	−	0.103650i
$232$	−1.43899	+	2.49240i	−0.0944741	+	0.163634i
$233$	−4.33566	−	7.50958i	−0.284038	−	0.491969i	0.688337	−	0.725391i	$-0.258341\pi$
$233$	−4.33566	−	7.50958i	−0.284038	−	0.491969i	−0.972376	+	0.233422i	$0.925008\pi$
$234$	−8.89591	+	15.4082i	−0.581544	+	1.00726i
$235$	17.3177			1.12968
$236$	−56.0058			−3.64566
$237$	4.47320	−	7.74780i	0.290565	−	0.503274i
$238$	−2.92413	+	5.06474i	−0.189543	+	0.328298i
$239$	14.3796			0.930137			0.465068	−	0.885275i	$-0.346030\pi$
$239$	14.3796			0.930137			0.465068	+	0.885275i	$0.346030\pi$
$240$	27.1796			1.75444
$241$	6.28065	−	10.8784i	0.404572	−	0.700740i	−0.589699	−	0.807623i	$-0.700754\pi$
$241$	6.28065	−	10.8784i	0.404572	−	0.700740i	0.994272	+	0.106883i	$0.0340870\pi$
$242$	10.3552	+	17.9357i	0.665655	+	1.15295i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	17.0957	+	29.6106i	1.09444	+	1.89563i
$245$	−1.03963	−	1.80069i	−0.0664196	−	0.115042i
$246$	7.95323			0.507079
$247$	−10.4506	+	26.8372i	−0.664954	+	1.70761i
$248$	13.7408			0.872541
$249$	2.29905	+	3.98207i	0.145696	+	0.252353i
$250$	15.8918	+	27.5255i	1.00509	+	1.74086i
$251$	0.925040	−	1.60222i	0.0583880	−	0.101131i	−0.835354	−	0.549712i	$-0.814737\pi$
$251$	0.925040	−	1.60222i	0.0583880	−	0.101131i	0.893742	+	0.448582i	$0.148071\pi$
$252$	2.62554	+	4.54758i	0.165394	+	0.286470i
$253$	0.316443	−	0.548095i	0.0198946	−	0.0344584i
$254$	36.0434			2.26157
$255$	−4.51580			−0.282790
$256$	−8.79440	+	15.2324i	−0.549650	+	0.952022i
$257$	−11.8564	+	20.5359i	−0.739583	+	1.28100i	0.213100	+	0.977030i	$0.431644\pi$
$257$	−11.8564	+	20.5359i	−0.739583	+	1.28100i	−0.952683	+	0.303965i	$0.901689\pi$
$258$	−18.6549			−1.16141
$259$	11.3128			0.702942
$260$	−36.0701	+	62.4753i	−2.23697	+	3.87455i
$261$	−0.164372	−	0.284700i	−0.0101743	−	0.0176225i
$262$	22.0718	−	38.2295i	1.36360	−	2.36182i
$263$	−3.65216	−	6.32573i	−0.225202	−	0.390061i	0.731178	−	0.682187i	$-0.238971\pi$
$263$	−3.65216	−	6.32573i	−0.225202	−	0.390061i	−0.956380	+	0.292126i	$0.905637\pi$
$264$	7.96243	+	13.7913i	0.490054	+	0.848798i
$265$	−2.93505			−0.180299
$266$	7.34263	+	9.15731i	0.450206	+	0.561471i
$267$	2.86582			0.175386
$268$	−41.8887	−	72.5533i	−2.55876	−	4.43190i
$269$	0.358407	+	0.620779i	0.0218524	+	0.0378495i	0.876745	−	0.480956i	$-0.159710\pi$
$269$	0.358407	+	0.620779i	0.0218524	+	0.0378495i	−0.854892	+	0.518805i	$0.826377\pi$
$270$	−2.79950	+	4.84888i	−0.170372	+	0.295094i
$271$	−3.47326	−	6.01586i	−0.210985	−	0.365438i	0.741038	−	0.671463i	$-0.234334\pi$
$271$	−3.47326	−	6.01586i	−0.210985	−	0.365438i	−0.952023	+	0.306026i	$0.901001\pi$
$272$	14.1948	−	24.5861i	0.860684	−	1.49075i
$273$	−6.60722			−0.399887
$274$	−40.6487			−2.45568
$275$	−0.615443	+	1.06598i	−0.0371126	+	0.0642809i
$276$	−0.913480	+	1.58219i	−0.0549850	+	0.0952369i
$277$	12.6155			0.757989			0.378995	−	0.925399i	$-0.376270\pi$
$277$	12.6155			0.757989			0.378995	+	0.925399i	$0.376270\pi$
$278$	15.2329			0.913611
$279$	−0.784786	+	1.35929i	−0.0469839	+	0.0813786i
$280$	9.10143	+	15.7641i	0.543915	+	0.942088i
$281$	6.33213	−	10.9676i	0.377743	−	0.654270i	−0.612991	−	0.790090i	$-0.710034\pi$
$281$	6.33213	−	10.9676i	0.377743	−	0.654270i	0.990733	+	0.135820i	$0.0433670\pi$
$282$	−11.2138	−	19.4228i	−0.667769	−	1.15661i
$283$	7.19010	+	12.4536i	0.427407	+	0.740291i	0.996642	−	0.0818842i	$-0.0260938\pi$
$283$	7.19010	+	12.4536i	0.427407	+	0.740291i	−0.569235	+	0.822175i	$0.692760\pi$
$284$	75.2612			4.46593
$285$	−3.28875	+	8.44556i	−0.194809	+	0.500272i
$286$	−32.3643			−1.91374
$287$	1.47677	+	2.55783i	0.0871708	+	0.150984i
$288$	−8.84522	−	15.3204i	−0.521210	−	0.902762i
$289$	6.14159	−	10.6375i	0.361270	−	0.625738i
$290$	−0.920317	−	1.59404i	−0.0540429	−	0.0936051i
$291$	−0.444846	+	0.770496i	−0.0260774	+	0.0451673i
$292$	−79.8492			−4.67282
$293$	−20.3785			−1.19052			−0.595262	−	0.803532i	$-0.702952\pi$
$293$	−20.3785			−1.19052			−0.595262	+	0.803532i	$0.702952\pi$
$294$	−1.34639	+	2.33202i	−0.0785232	+	0.136006i
$295$	11.0882	−	19.2054i	0.645583	−	1.11818i
$296$	−99.0375			−5.75644
$297$	−1.81905			−0.105552
$298$	−19.3694	+	33.5488i	−1.12204	+	1.94343i
$299$	−1.14939	−	1.99081i	−0.0664711	−	0.115131i
$300$	1.77661	−	3.07718i	0.102573	−	0.177661i
$301$	−3.46388	−	5.99961i	−0.199654	−	0.345812i
$302$	4.93067	+	8.54017i	0.283728	+	0.491431i
$303$	15.9382			0.915624
$304$	−35.6438	−	44.4529i	−2.04431	−	2.54955i
$305$	−13.5387			−0.775224
$306$	2.92413	+	5.06474i	0.167161	+	0.289532i
$307$	−9.20768	−	15.9482i	−0.525510	−	0.910210i	−0.999559	−	0.0297112i	$-0.990541\pi$
$307$	−9.20768	−	15.9482i	−0.525510	−	0.910210i	0.474049	−	0.880499i	$-0.342792\pi$
$308$	−4.77600	+	8.27228i	−0.272138	+	0.471357i
$309$	0.635401	+	1.10055i	0.0361467	+	0.0626080i
$310$	−4.39403	+	7.61068i	−0.249564	+	0.432257i
$311$	−5.39233			−0.305771			−0.152886	−	0.988244i	$-0.548857\pi$
$311$	−5.39233			−0.305771			−0.152886	+	0.988244i	$0.548857\pi$
$312$	57.8428			3.27470
$313$	9.94802	−	17.2305i	0.562295	−	0.973924i	−0.435001	−	0.900430i	$-0.643252\pi$
$313$	9.94802	−	17.2305i	0.562295	−	0.973924i	0.997296	−	0.0734936i	$-0.0234149\pi$
$314$	7.11396	−	12.3217i	0.401464	−	0.695356i
$315$	−2.07926			−0.117153
$316$	−46.9783			−2.64274
$317$	−4.50450	+	7.80202i	−0.252998	+	0.438205i	−0.964350	−	0.264631i	$-0.914750\pi$
$317$	−4.50450	+	7.80202i	−0.252998	+	0.438205i	0.711352	+	0.702836i	$0.248083\pi$
$318$	1.90055	+	3.29184i	0.106577	+	0.184597i
$319$	0.299000	−	0.517884i	0.0167408	−	0.0289959i
$320$	−22.3449	−	38.7024i	−1.24912	−	2.16353i
$321$	0.347652	+	0.602150i	0.0194040	+	0.0336087i
$322$	−0.936875			−0.0522100
$323$	5.92209	+	7.38569i	0.329514	+	0.410951i
$324$	5.25109			0.291727
$325$	2.23543	+	3.87188i	0.123999	+	0.214773i
$326$	−23.0749	−	39.9669i	−1.27800	−	2.21356i
$327$	−1.41617	+	2.45289i	−0.0783147	+	0.135645i
$328$	−12.9283	−	22.3925i	−0.713847	−	1.23642i
$329$	4.16437	−	7.21290i	0.229589	−	0.397660i
$330$	−10.1849			−0.560660
$331$	22.2854			1.22492			0.612458	−	0.790503i	$-0.290181\pi$
$331$	22.2854			1.22492			0.612458	+	0.790503i	$0.290181\pi$
$332$	12.0725	−	20.9102i	0.662565	−	1.14760i
$333$	5.65639	−	9.79716i	0.309968	−	0.536881i
$334$	−46.5934			−2.54948
$335$	33.1732			1.81244
$336$	6.53587	−	11.3205i	0.356561	−	0.617582i
$337$	5.74699	+	9.95407i	0.313058	+	0.542233i	0.979023	−	0.203750i	$-0.0653131\pi$
$337$	5.74699	+	9.95407i	0.313058	+	0.542233i	−0.665964	+	0.745983i	$0.731980\pi$
$338$	−41.2742	+	71.4889i	−2.24502	+	3.88849i
$339$	6.95346	+	12.0437i	0.377660	+	0.654127i
$340$	11.8564	+	20.5359i	0.643005	+	1.11372i
$341$	−2.85514			−0.154614
$342$	11.6018	−	1.78025i	0.627353	−	0.0962650i
$343$	−1.00000			−0.0539949
$344$	30.3244	+	52.5234i	1.63498	+	2.83187i
$345$	−0.361709	−	0.626498i	−0.0194738	−	0.0337295i
$346$	−10.0335	+	17.3785i	−0.539403	+	0.934273i
$347$	16.2544	+	28.1535i	0.872583	+	1.51136i	0.859316	+	0.511446i	$0.170890\pi$
$347$	16.2544	+	28.1535i	0.872583	+	1.51136i	0.0132671	+	0.999912i	$0.495777\pi$
$348$	−0.863129	+	1.49498i	−0.0462686	+	0.0801395i
$349$	−6.88550			−0.368572			−0.184286	−	0.982873i	$-0.558997\pi$
$349$	−6.88550			−0.368572			−0.184286	+	0.982873i	$0.558997\pi$
$350$	1.82211			0.0973958
$351$	−3.30361	+	5.72202i	−0.176334	+	0.305419i
$352$	16.0899	−	27.8686i	0.857596	−	1.48540i
$353$	11.0287			0.586998			0.293499	−	0.955959i	$-0.405180\pi$
$353$	11.0287			0.586998			0.293499	+	0.955959i	$0.405180\pi$
$354$	−28.7200			−1.52645
$355$	−14.9005	+	25.8085i	−0.790837	+	1.36977i
$356$	−7.52435	−	13.0326i	−0.398790	−	0.690724i
$357$	−1.08591	+	1.88086i	−0.0574726	+	0.0995454i
$358$	27.3323	+	47.3410i	1.44456	+	2.50205i
$359$	−8.62492	−	14.9388i	−0.455206	−	0.788440i	0.543494	−	0.839413i	$-0.317101\pi$
$359$	−8.62492	−	14.9388i	−0.455206	−	0.788440i	−0.998700	+	0.0509731i	$0.983768\pi$
$360$	18.2029			0.959375
$361$	18.1258	−	5.69683i	0.953992	−	0.299833i
$362$	15.1847			0.798088
$363$	3.84552	+	6.66064i	0.201838	+	0.349593i
$364$	17.3475	+	30.0468i	0.909259	+	1.57488i
$365$	15.8089	−	27.3818i	0.827475	−	1.43323i
$366$	8.76676	+	15.1845i	0.458246	+	0.793705i
$367$	4.10950	−	7.11786i	0.214514	−	0.371549i	−0.738608	−	0.674135i	$-0.764517\pi$
$367$	4.10950	−	7.11786i	0.214514	−	0.371549i	0.953122	+	0.302586i	$0.0978499\pi$
$368$	4.54793			0.237077
$369$	2.95353			0.153755
$370$	31.6702	−	54.8544i	1.64645	−	2.85174i
$371$	−0.705792	+	1.22247i	−0.0366429	+	0.0634673i
$372$	8.24196			0.427326
$373$	−4.05835			−0.210133			−0.105067	−	0.994465i	$-0.533506\pi$
$373$	−4.05835			−0.210133			−0.105067	+	0.994465i	$0.533506\pi$
$374$	−5.31914	+	9.21302i	−0.275046	+	0.476394i
$375$	5.90164	+	10.2219i	0.304759	+	0.527859i
$376$	−36.4569	+	63.1452i	−1.88012	+	3.25647i
$377$	−1.08604	−	1.88107i	−0.0559339	−	0.0968803i
$378$	1.34639	+	2.33202i	0.0692509	+	0.119946i
$379$	−11.9539			−0.614030			−0.307015	−	0.951705i	$-0.599330\pi$
$379$	−11.9539			−0.614030			−0.307015	+	0.951705i	$0.599330\pi$
$380$	47.0416	−	7.21836i	2.41318	−	0.370294i
$381$	13.3852			0.685744
$382$	−26.1064	−	45.2175i	−1.33572	−	2.31353i
$383$	2.88263	+	4.99287i	0.147296	+	0.255124i	0.930227	−	0.366984i	$-0.119610\pi$
$383$	2.88263	+	4.99287i	0.147296	+	0.255124i	−0.782931	+	0.622108i	$0.786276\pi$
$384$	−11.2476	+	19.4815i	−0.573978	+	0.994160i
$385$	−1.89114	−	3.27556i	−0.0963817	−	0.166938i
$386$	−30.7937	+	53.3362i	−1.56736	+	2.71474i
$387$	−6.92775			−0.352157
$388$	4.67185			0.237177
$389$	−13.9947	+	24.2396i	−0.709560	+	1.22899i	0.255460	+	0.966820i	$0.417773\pi$
$389$	−13.9947	+	24.2396i	−0.709560	+	1.22899i	−0.965020	+	0.262175i	$0.915560\pi$
$390$	−18.4969	+	32.0376i	−0.936629	+	1.62229i
$391$	−0.755622			−0.0382134
$392$	8.75448			0.442168
$393$	8.19664	−	14.1970i	0.413466	−	0.716144i
$394$	12.4025	+	21.4817i	0.624827	+	1.08223i
$395$	9.30095	−	16.1097i	0.467982	−	0.810568i
$396$	4.77600	+	8.27228i	0.240003	+	0.415698i
$397$	−6.06886	−	10.5116i	−0.304587	−	0.527561i	0.672582	−	0.740022i	$-0.265185\pi$
$397$	−6.06886	−	10.5116i	−0.304587	−	0.527561i	−0.977169	+	0.212462i	$0.931852\pi$
$398$	17.6779			0.886114
$399$	2.72678	+	3.40069i	0.136510	+	0.170247i
$400$	−8.84517			−0.442259
$401$	12.0759	+	20.9162i	0.603044	+	1.04450i	0.992357	+	0.123398i	$0.0393790\pi$
$401$	12.0759	+	20.9162i	0.603044	+	1.04450i	−0.389313	+	0.921105i	$0.627288\pi$
$402$	−21.4807	−	37.2057i	−1.07136	−	1.85565i
$403$	−5.18526	+	8.98113i	−0.258296	+	0.447382i
$404$	−41.8464	−	72.4800i	−2.08193	−	3.60602i
$405$	−1.03963	+	1.80069i	−0.0516597	+	0.0894773i
$406$	−0.885234			−0.0439334
$407$	20.5785			1.02004
$408$	9.50660	−	16.4659i	0.470647	−	0.815184i
$409$	10.9922	−	19.0391i	0.543530	−	0.941422i	−0.455168	−	0.890406i	$-0.650421\pi$
$409$	10.9922	−	19.0391i	0.543530	−	0.941422i	0.998698	−	0.0510161i	$-0.0162460\pi$
$410$	16.5369			0.816697
$411$	−15.0954			−0.744602
$412$	3.33655	−	5.77907i	0.164380	−	0.284714i
$413$	−5.33278	−	9.23664i	−0.262409	−	0.454505i
$414$	−0.468437	+	0.811357i	−0.0230224	+	0.0398760i
$415$	4.78033	+	8.27977i	0.234657	+	0.406438i
$416$	−58.4423	−	101.225i	−2.86537	−	4.96297i
$417$	5.65695			0.277022
$418$	13.3566	+	16.6576i	0.653294	+	0.814751i
$419$	0.167650			0.00819025			0.00409512	−	0.999992i	$-0.498696\pi$
$419$	0.167650			0.00819025			0.00409512	+	0.999992i	$0.498696\pi$
$420$	5.45920	+	9.45561i	0.266382	+	0.461386i
$421$	1.58228	+	2.74059i	0.0771157	+	0.133568i	0.902004	−	0.431727i	$-0.142096\pi$
$421$	1.58228	+	2.74059i	0.0771157	+	0.133568i	−0.824889	+	0.565295i	$0.808762\pi$
$422$	−8.93044	+	15.4680i	−0.434727	+	0.752969i
$423$	−4.16437	−	7.21290i	−0.202479	−	0.350703i
$424$	6.17884	−	10.7021i	0.300071	−	0.519738i
$425$	1.46959			0.0712858
$426$	38.5943			1.86990
$427$	−3.25565	+	5.63895i	−0.157552	+	0.272888i
$428$	1.82555	−	3.16194i	0.0882412	−	0.152838i
$429$	−12.0189			−0.580277
$430$	−38.7885			−1.87055
$431$	2.20657	−	3.82188i	0.106287	−	0.184094i	−0.807977	−	0.589215i	$-0.799437\pi$
$431$	2.20657	−	3.82188i	0.106287	−	0.184094i	0.914263	+	0.405121i	$0.132771\pi$
$432$	−6.53587	−	11.3205i	−0.314457	−	0.544656i
$433$	−8.34477	+	14.4536i	−0.401024	+	0.694594i	−0.993850	−	0.110737i	$-0.964679\pi$
$433$	−8.34477	+	14.4536i	−0.401024	+	0.694594i	0.592826	+	0.805331i	$0.298012\pi$
$434$	2.11326	+	3.66027i	0.101440	+	0.175699i
$435$	−0.341772	−	0.591966i	−0.0163867	−	0.0283826i
$436$	14.8729			0.712284
$437$	−0.550302	+	1.41318i	−0.0263245	+	0.0676018i
$438$	−40.9471			−1.95653
$439$	4.25269	+	7.36588i	0.202970	+	0.351554i	0.949484	−	0.313815i	$-0.101607\pi$
$439$	4.25269	+	7.36588i	0.202970	+	0.351554i	−0.746514	+	0.665370i	$0.768274\pi$
$440$	16.5560	+	28.6758i	0.789276	+	1.36707i
$441$	−0.500000	+	0.866025i	−0.0238095	+	0.0412393i
$442$	19.3204	+	33.4638i	0.918976	+	1.59171i
$443$	−4.52265	+	7.83346i	−0.214878	+	0.372179i	−0.953235	−	0.302231i	$-0.902269\pi$
$443$	−4.52265	+	7.83346i	−0.214878	+	0.372179i	0.738357	+	0.674410i	$0.235602\pi$
$444$	−59.4044			−2.81921
$445$	5.95880			0.282474
$446$	17.6712	−	30.6074i	0.836755	−	1.44930i
$447$	−7.19308	+	12.4588i	−0.340221	+	0.589280i
$448$	−21.4931			−1.01545
$449$	−30.2418			−1.42720			−0.713601	−	0.700553i	$-0.752937\pi$
$449$	−30.2418			−1.42720			−0.713601	+	0.700553i	$0.752937\pi$
$450$	0.911054	−	1.57799i	0.0429475	−	0.0743873i
$451$	2.68632	+	4.65284i	0.126494	+	0.219093i
$452$	36.5132	−	63.2428i	1.71744	−	2.97469i
$453$	1.83107	+	3.17150i	0.0860310	+	0.149010i
$454$	17.9315	+	31.0583i	0.841567	+	1.45764i
$455$	−13.7382			−0.644055
$456$	−23.8716	−	29.7712i	−1.11789	−	1.39417i
$457$	−20.0678			−0.938731			−0.469365	−	0.883004i	$-0.655517\pi$
$457$	−20.0678			−0.938731			−0.469365	+	0.883004i	$0.655517\pi$
$458$	3.97178	+	6.87932i	0.185589	+	0.321449i
$459$	1.08591	+	1.88086i	0.0506860	+	0.0877908i
$460$	−1.89937	+	3.28980i	−0.0885584	+	0.153388i
$461$	10.5822	+	18.3289i	0.492862	+	0.853663i	0.999966	−	0.00822223i	$-0.00261725\pi$
$461$	10.5822	+	18.3289i	0.492862	+	0.853663i	−0.507104	+	0.861885i	$0.669284\pi$
$462$	−2.44916	+	4.24207i	−0.113945	+	0.197359i
$463$	24.1680			1.12318			0.561592	−	0.827415i	$-0.310189\pi$
$463$	24.1680			1.12318			0.561592	+	0.827415i	$0.310189\pi$
$464$	4.29725			0.199495
$465$	−1.63178	+	2.82632i	−0.0756719	+	0.131068i
$466$	−11.6750	+	20.2217i	−0.540834	+	0.936751i
$467$	11.6250			0.537942			0.268971	−	0.963148i	$-0.413316\pi$
$467$	11.6250			0.537942			0.268971	+	0.963148i	$0.413316\pi$
$468$	34.6951			1.60378
$469$	7.97715	−	13.8168i	0.368350	−	0.638002i
$470$	−23.3164	−	40.3851i	−1.07550	−	1.86283i
$471$	2.64186	−	4.57584i	0.121730	−	0.210843i
$472$	46.6857	+	80.8620i	2.14888	+	3.72197i
$473$	−6.30097	−	10.9136i	−0.289719	−	0.501808i
$474$	−24.0907			−1.10652
$475$	1.07027	−	2.74847i	0.0491074	−	0.126109i
$476$	11.4044			0.522722
$477$	0.705792	+	1.22247i	0.0323160	+	0.0559729i
$478$	−19.3605	−	33.5334i	−0.885530	−	1.53378i
$479$	−1.03459	+	1.79196i	−0.0472716	+	0.0818768i	−0.888693	−	0.458503i	$-0.848386\pi$
$479$	−1.03459	+	1.79196i	−0.0472716	+	0.0818768i	0.841421	+	0.540379i	$0.181719\pi$
$480$	−18.3915	−	31.8551i	−0.839455	−	1.45398i
$481$	37.3730	−	64.7320i	1.70406	−	2.95152i
$482$	−33.8249			−1.54068
$483$	−0.347920			−0.0158309
$484$	20.1932	−	34.9756i	0.917872	−	1.58980i
$485$	−0.924953	+	1.60207i	−0.0419999	+	0.0727460i
$486$	2.69278			0.122147
$487$	−23.7932			−1.07818			−0.539088	−	0.842250i	$-0.681231\pi$
$487$	−23.7932			−1.07818			−0.539088	+	0.842250i	$0.681231\pi$
$488$	28.5015	−	49.3661i	1.29020	−	2.23470i
$489$	−8.56916	−	14.8422i	−0.387511	−	0.671188i
$490$	−2.79950	+	4.84888i	−0.126469	+	0.219050i
$491$	−5.08247	−	8.80310i	−0.229369	−	0.397278i	0.728252	−	0.685309i	$-0.240333\pi$
$491$	−5.08247	−	8.80310i	−0.229369	−	0.397278i	−0.957621	+	0.288031i	$0.907000\pi$
$492$	−7.75463	−	13.4314i	−0.349606	−	0.605535i
$493$	−0.713972			−0.0321557
$494$	76.6555	−	11.7625i	3.44890	−	0.529221i
$495$	−3.78229			−0.170001
$496$	−10.2585	−	17.7683i	−0.460622	−	0.797820i
$497$	7.16625	+	12.4123i	0.321450	+	0.556768i
$498$	6.19084	−	10.7229i	0.277418	−	0.480503i
$499$	−13.3208	−	23.0722i	−0.596319	−	1.03286i	−0.993359	−	0.115054i	$-0.963296\pi$
$499$	−13.3208	−	23.0722i	−0.596319	−	1.03286i	0.397040	−	0.917801i	$-0.370037\pi$
$500$	30.9900	−	53.6763i	1.38592	−	2.40048i
$501$	−17.3031			−0.773044
$502$	−4.98186			−0.222352
$503$	−19.1566	+	33.1802i	−0.854151	+	1.47943i	0.0232791	+	0.999729i	$0.492589\pi$
$503$	−19.1566	+	33.1802i	−0.854151	+	1.47943i	−0.877430	+	0.479704i	$0.840744\pi$
$504$	4.37724	−	7.58160i	0.194978	−	0.337711i
$505$	33.1397			1.47470
$506$	−1.70422			−0.0757620
$507$	−15.3277	+	26.5483i	−0.680726	+	1.17905i
$508$	−35.1434	−	60.8702i	−1.55924	−	2.70068i
$509$	−18.0527	+	31.2681i	−0.800171	+	1.38594i	0.119333	+	0.992854i	$0.461924\pi$
$509$	−18.0527	+	31.2681i	−0.800171	+	1.38594i	−0.919503	+	0.393082i	$0.871409\pi$
$510$	6.08003	+	10.5309i	0.269228	+	0.466317i
$511$	−7.60311	−	13.1690i	−0.336342	−	0.582561i
$512$	2.37233			0.104843
$513$	4.30847	−	0.661119i	0.190224	−	0.0291891i
$514$	63.8536			2.81646
$515$	1.32117	+	2.28833i	0.0582176	+	0.100836i
$516$	18.1891	+	31.5045i	0.800731	+	1.38691i
$517$	7.57521	−	13.1206i	0.333157	−	0.577045i
$518$	−15.2314	−	26.3816i	−0.669231	−	1.15914i
$519$	−3.72606	+	6.45372i	−0.163556	+	0.283287i
$520$	120.270			5.27421
$521$	17.8977			0.784113			0.392056	−	0.919941i	$-0.371764\pi$
$521$	17.8977			0.784113			0.392056	+	0.919941i	$0.371764\pi$
$522$	−0.442617	+	0.766635i	−0.0193728	+	0.0335547i
$523$	19.9424	−	34.5412i	0.872019	−	1.51038i	0.0121134	−	0.999927i	$-0.496144\pi$
$523$	19.9424	−	34.5412i	0.872019	−	1.51038i	0.859905	−	0.510454i	$-0.170523\pi$
$524$	−86.0826			−3.76053
$525$	0.676663			0.0295320
$526$	−9.83448	+	17.0338i	−0.428804	+	0.742710i
$527$	1.70442	+	2.95214i	0.0742456	+	0.128597i
$528$	11.8891	−	20.5925i	0.517407	−	0.896174i
$529$	11.4395	+	19.8138i	0.497369	+	0.861468i
$530$	3.95173	+	6.84460i	0.171652	+	0.297311i
$531$	−10.6656			−0.462846
$532$	8.30559	−	21.3289i	0.360093	−	0.924725i
$533$	19.5146			0.845273
$534$	−3.85852	−	6.68316i	−0.166975	−	0.289209i
$535$	0.722859	+	1.25203i	0.0312519	+	0.0541299i
$536$	−69.8358	+	120.959i	−3.01645	+	5.22464i
$537$	10.1502	+	17.5807i	0.438014	+	0.758662i
$538$	0.965112	−	1.67162i	0.0416089	−	0.0720688i
$539$	−1.81905			−0.0783521
$540$	10.9184			0.469853
$541$	−12.3864	+	21.4539i	−0.532533	+	0.922374i	0.466745	+	0.884392i	$0.345427\pi$
$541$	−12.3864	+	21.4539i	−0.532533	+	0.922374i	−0.999278	+	0.0379827i	$0.987907\pi$
$542$	−9.35274	+	16.1994i	−0.401735	+	0.695825i
$543$	5.63901			0.241993
$544$	−38.4205			−1.64727
$545$	−2.94460	+	5.10020i	−0.126133	+	0.218468i
$546$	8.89591	+	15.4082i	0.380710	+	0.659409i
$547$	−1.20025	+	2.07889i	−0.0513188	+	0.0888868i	−0.890544	−	0.454898i	$-0.849676\pi$
$547$	−1.20025	+	2.07889i	−0.0513188	+	0.0888868i	0.839225	+	0.543785i	$0.183009\pi$
$548$	39.6337	+	68.6476i	1.69307	+	2.93248i
$549$	3.25565	+	5.63895i	0.138948	+	0.240665i
$550$	3.31451			0.141331
$551$	−0.519969	+	1.33529i	−0.0221514	+	0.0568853i
$552$	3.04586			0.129640
$553$	−4.47320	−	7.74780i	−0.190220	−	0.329470i
$554$	−16.9853	−	29.4195i	−0.721638	−	1.24991i
$555$	11.7611	−	20.3709i	0.499232	−	0.864695i
$556$	−14.8526	−	25.7254i	−0.629889	−	1.09100i
$557$	−3.82254	+	6.62083i	−0.161966	+	0.280534i	−0.935574	−	0.353131i	$-0.885117\pi$
$557$	−3.82254	+	6.62083i	−0.161966	+	0.280534i	0.773608	+	0.633665i	$0.218450\pi$
$558$	4.22652			0.178923
$559$	−45.7732			−1.93600
$560$	13.5898	−	23.5382i	0.574274	−	0.994672i
$561$	−1.97533	+	3.42137i	−0.0833985	+	0.144451i
$562$	−34.1021			−1.43851
$563$	−34.8166			−1.46734			−0.733672	−	0.679504i	$-0.762195\pi$
$563$	−34.8166			−1.46734			−0.733672	+	0.679504i	$0.762195\pi$
$564$	−21.8675	+	37.8756i	−0.920787	+	1.59485i
$565$	14.4581	+	25.0421i	0.608256	+	1.05353i
$566$	19.3614	−	33.5349i	0.813820	−	1.40958i
$567$	0.500000	+	0.866025i	0.0209980	+	0.0363696i
$568$	−62.7368	−	108.663i	−2.63238	−	4.55941i
$569$	−4.11846			−0.172655			−0.0863274	−	0.996267i	$-0.527513\pi$
$569$	−4.11846			−0.172655			−0.0863274	+	0.996267i	$0.527513\pi$
$570$	24.1232	−	3.70161i	1.01041	−	0.155043i
$571$	14.1922			0.593924			0.296962	−	0.954889i	$-0.404027\pi$
$571$	14.1922			0.593924			0.296962	+	0.954889i	$0.404027\pi$
$572$	31.5561	+	54.6568i	1.31943	+	2.28531i
$573$	−9.69493	−	16.7921i	−0.405012	−	0.701501i
$574$	3.97661	−	6.88770i	0.165981	−	0.287487i
$575$	0.117712	+	0.203884i	0.00490895	+	0.00850255i
$576$	−10.7465	+	18.6135i	−0.447772	+	0.775564i
$577$	−0.345930			−0.0144013			−0.00720064	−	0.999974i	$-0.502292\pi$
$577$	−0.345930			−0.0144013			−0.00720064	+	0.999974i	$0.502292\pi$
$578$	−33.0760			−1.37578
$579$	−11.4356	+	19.8071i	−0.475248	+	0.823154i
$580$	−1.79467	+	3.10847i	−0.0745197	+	0.129072i
$581$	4.59810			0.190761
$582$	2.39575			0.0993071
$583$	−1.28387	+	2.22373i	−0.0531726	+	0.0920976i
$584$	66.5613	+	115.288i	2.75433	+	4.77063i
$585$	−6.86908	+	11.8976i	−0.284001	+	0.491905i
$586$	27.4374	+	47.5230i	1.13343	+	1.96316i
$587$	19.9921	+	34.6274i	0.825163	+	1.42922i	0.901794	+	0.432165i	$0.142250\pi$
$587$	19.9921	+	34.6274i	0.825163	+	1.42922i	−0.0766311	+	0.997060i	$0.524416\pi$
$588$	5.25109			0.216551
$589$	6.76246	−	1.03767i	0.278642	−	0.0427566i
$590$	−59.7165			−2.45849
$591$	4.60581	+	7.97750i	0.189458	+	0.328150i
$592$	73.9389	+	128.066i	3.03887	+	5.26348i
$593$	15.0050	−	25.9895i	0.616183	−	1.06726i	−0.373993	−	0.927432i	$-0.622012\pi$
$593$	15.0050	−	25.9895i	0.616183	−	1.06726i	0.990176	−	0.139828i	$-0.0446551\pi$
$594$	2.44916	+	4.24207i	0.100490	+	0.174054i
$595$	−2.25790	+	3.91079i	−0.0925648	+	0.160327i
$596$	75.5430			3.09436
$597$	6.56493			0.268684
$598$	−3.09507	+	5.36082i	−0.126567	+	0.219220i
$599$	5.70926	−	9.88873i	0.233274	−	0.404043i	−0.725496	−	0.688227i	$-0.758389\pi$
$599$	5.70926	−	9.88873i	0.233274	−	0.404043i	0.958770	+	0.284184i	$0.0917227\pi$
$600$	−5.92384			−0.241840
$601$	15.2836			0.623429			0.311715	−	0.950176i	$-0.399097\pi$
$601$	15.2836			0.623429			0.311715	+	0.950176i	$0.399097\pi$
$602$	−9.32747	+	16.1557i	−0.380159	+	0.658455i
$603$	−7.97715	−	13.8168i	−0.324854	−	0.562664i
$604$	9.61509	−	16.6538i	0.391233	−	0.677635i
$605$	7.99586	+	13.8492i	0.325078	+	0.563051i
$606$	−21.4590	−	37.1681i	−0.871713	−	1.50985i
$607$	16.6552			0.676014			0.338007	−	0.941144i	$-0.390247\pi$
$607$	16.6552			0.676014			0.338007	+	0.941144i	$0.390247\pi$
$608$	−27.9808	+	71.8551i	−1.13477	+	2.91411i
$609$	−0.328743			−0.0133213
$610$	18.2284	+	31.5725i	0.738047	+	1.27833i
$611$	−27.5149	−	47.6572i	−1.11313	−	1.92801i
$612$	5.70222	−	9.87654i	0.230499	−	0.399235i
$613$	−17.2759	−	29.9227i	−0.697766	−	1.20857i	−0.969239	−	0.246121i	$-0.920844\pi$
$613$	−17.2759	−	29.9227i	−0.697766	−	1.20857i	0.271473	−	0.962446i	$-0.412489\pi$
$614$	−24.7943	+	42.9450i	−1.00062	+	1.73312i
$615$	6.14117			0.247636
$616$	15.9249			0.641631
$617$	7.76673	−	13.4524i	0.312677	−	0.541572i	−0.666264	−	0.745716i	$-0.732108\pi$
$617$	7.76673	−	13.4524i	0.312677	−	0.541572i	0.978941	+	0.204144i	$0.0654411\pi$
$618$	1.71100	−	2.96354i	0.0688265	−	0.119211i
$619$	32.8322			1.31964			0.659819	−	0.751425i	$-0.270633\pi$
$619$	32.8322			1.31964			0.659819	+	0.751425i	$0.270633\pi$
$620$	17.1372			0.688247
$621$	−0.173960	+	0.301308i	−0.00698078	+	0.0120911i
$622$	7.26020	+	12.5750i	0.291107	+	0.504213i
$623$	1.43291	−	2.48188i	0.0574084	−	0.0994343i
$624$	−43.1840	−	74.7968i	−1.72874	−	2.99427i
$625$	10.5794	+	18.3241i	0.423176	+	0.732963i
$626$	−53.5757			−2.14132
$627$	4.96016	+	6.18603i	0.198090	+	0.247046i
$628$	−27.7453			−1.10716
$629$	−12.2847	−	21.2777i	−0.489823	−	0.848398i
$630$	2.79950	+	4.84888i	0.111535	+	0.193184i
$631$	0.447179	−	0.774536i	0.0178019	−	0.0308338i	−0.856987	−	0.515338i	$-0.827667\pi$
$631$	0.447179	−	0.774536i	0.0178019	−	0.0308338i	0.874789	+	0.484504i	$0.161000\pi$
$632$	39.1605	+	67.8280i	1.55772	+	2.69805i
$633$	−3.31643	+	5.74423i	−0.131816	+	0.228313i
$634$	24.2593			0.963459
$635$	27.8313			1.10445
$636$	3.70617	−	6.41928i	0.146959	−	0.254541i
$637$	−3.30361	+	5.72202i	−0.130894	+	0.226715i
$638$	−1.61029			−0.0637519
$639$	14.3325			0.566985
$640$	−23.3868	+	40.5071i	−0.924444	+	1.60118i
$641$	12.1034	+	20.9637i	0.478055	+	0.828016i	0.999684	−	0.0251571i	$-0.00800860\pi$
$641$	12.1034	+	20.9637i	0.478055	+	0.828016i	−0.521628	+	0.853173i	$0.674675\pi$
$642$	0.936151	−	1.62146i	0.0369469	−	0.0639939i
$643$	10.9152	+	18.9056i	0.430452	+	0.745564i	0.996912	−	0.0785247i	$-0.0250210\pi$
$643$	10.9152	+	18.9056i	0.430452	+	0.745564i	−0.566460	+	0.824089i	$0.691688\pi$
$644$	0.913480	+	1.58219i	0.0359962	+	0.0623472i
$645$	−14.4046			−0.567181
$646$	9.25012	−	23.7545i	0.363941	−	0.934607i
$647$	−4.28554			−0.168482			−0.0842411	−	0.996445i	$-0.526847\pi$
$647$	−4.28554			−0.168482			−0.0842411	+	0.996445i	$0.526847\pi$
$648$	−4.37724	−	7.58160i	−0.171954	−	0.297833i
$649$	−9.70060	−	16.8019i	−0.380782	−	0.659534i
$650$	6.01954	−	10.4261i	0.236106	−	0.408947i
$651$	0.784786	+	1.35929i	0.0307582	+	0.0532748i
$652$	−44.9974	+	77.9378i	−1.76223	+	3.05228i
$653$	−4.45533			−0.174350			−0.0871752	−	0.996193i	$-0.527784\pi$
$653$	−4.45533			−0.174350			−0.0871752	+	0.996193i	$0.527784\pi$
$654$	7.62691			0.298236
$655$	17.0430	−	29.5193i	0.665924	−	1.15341i
$656$	−19.3039	+	33.4354i	−0.753692	+	1.30543i
$657$	−15.2062			−0.593252
$658$	−22.4275			−0.874315
$659$	−23.4498	+	40.6162i	−0.913473	+	1.58218i	−0.104350	+	0.994541i	$0.533276\pi$
$659$	−23.4498	+	40.6162i	−0.913473	+	1.58218i	−0.809122	+	0.587640i	$0.800057\pi$
$660$	9.93057	+	17.2002i	0.386547	+	0.669519i
$661$	9.86580	−	17.0881i	0.383735	−	0.664649i	−0.607858	−	0.794046i	$-0.707971\pi$
$661$	9.86580	−	17.0881i	0.383735	−	0.664649i	0.991593	+	0.129397i	$0.0413043\pi$
$662$	−30.0049	−	51.9700i	−1.16617	−	2.01987i
$663$	7.17486	+	12.4272i	0.278649	+	0.482633i
$664$	−40.2540			−1.56216
$665$	5.66970	+	7.07092i	0.219861	+	0.274199i
$666$	−30.4629			−1.18041
$667$	−0.0571882	−	0.0990529i	−0.00221434	−	0.00383534i
$668$	45.4300	+	78.6870i	1.75774	+	3.04449i
$669$	6.56242	−	11.3664i	0.253718	−	0.439452i
$670$	−44.6641	−	77.3605i	−1.72552	−	2.98870i
$671$	−5.92220	+	10.2575i	−0.228624	+	0.395988i
$672$	−17.6904			−0.682424
$673$	−24.6144			−0.948816			−0.474408	−	0.880305i	$-0.657338\pi$
$673$	−24.6144			−0.948816			−0.474408	+	0.880305i	$0.657338\pi$
$674$	15.4754	−	26.8042i	0.596090	−	1.03246i
$675$	0.338332	−	0.586008i	0.0130224	−	0.0225554i
$676$	160.974			6.19131
$677$	−17.5627			−0.674988			−0.337494	−	0.941328i	$-0.609579\pi$
$677$	−17.5627			−0.674988			−0.337494	+	0.941328i	$0.609579\pi$
$678$	18.7242	−	32.4312i	0.719097	−	1.24551i
$679$	0.444846	+	0.770496i	0.0170716	+	0.0295689i
$680$	19.7667	−	34.2370i	0.758019	−	1.31293i
$681$	6.65909	+	11.5339i	0.255177	+	0.441980i
$682$	3.84413	+	6.65823i	0.147199	+	0.254957i
$683$	4.65125			0.177975			0.0889876	−	0.996033i	$-0.471637\pi$
$683$	4.65125			0.177975			0.0889876	+	0.996033i	$0.471637\pi$
$684$	−14.3186	−	17.8573i	−0.547484	−	0.682791i
$685$	−31.3874			−1.19925
$686$	1.34639	+	2.33202i	0.0514055	+	0.0890369i
$687$	1.47497	+	2.55472i	0.0562736	+	0.0974687i
$688$	45.2789	−	78.4254i	1.72624	−	2.98994i
$689$	4.66332	+	8.07711i	0.177658	+	0.307713i
$690$	−0.974004	+	1.68703i	−0.0370797	+	0.0642240i
$691$	16.1793			0.615490			0.307745	−	0.951469i	$-0.400426\pi$
$691$	16.1793			0.615490			0.307745	+	0.951469i	$0.400426\pi$
$692$	39.1317			1.48756
$693$	−0.909526	+	1.57535i	−0.0345500	+	0.0598424i
$694$	43.7696	−	75.8112i	1.66147	−	2.87776i
$695$	11.7623			0.446169
$696$	2.87797			0.109089
$697$	3.20728	−	5.55517i	0.121484	−	0.210417i
$698$	9.27058	+	16.0571i	0.350897	+	0.607771i
$699$	−4.33566	+	7.50958i	−0.163990	+	0.284038i
$700$	−1.77661	−	3.07718i	−0.0671495	−	0.116306i
$701$	−4.91661	−	8.51582i	−0.185698	−	0.321638i	0.758114	−	0.652122i	$-0.226121\pi$
$701$	−4.91661	−	8.51582i	−0.185698	−	0.321638i	−0.943811	+	0.330484i	$0.892788\pi$
$702$	17.7918			0.671509
$703$	−48.7408	+	7.47910i	−1.83829	+	0.282080i
$704$	−39.0970			−1.47352
$705$	−8.65883	−	14.9975i	−0.326110	−	0.564840i
$706$	−14.8489	−	25.7191i	−0.558847	−	0.967952i
$707$	7.96908	−	13.8029i	0.299708	−	0.519110i
$708$	28.0029	+	48.5024i	1.05241	+	1.82283i
$709$	−5.31978	+	9.21414i	−0.199789	+	0.346044i	−0.948460	−	0.316897i	$-0.897359\pi$
$709$	−5.31978	+	9.21414i	−0.199789	+	0.346044i	0.748671	+	0.662942i	$0.230692\pi$
$710$	80.2478			3.01165
$711$	−8.94639			−0.335516
$712$	−12.5444	+	21.7275i	−0.470121	+	0.814274i
$713$	−0.273043	+	0.472925i	−0.0102255	+	0.0177112i
$714$	5.84826			0.218865
$715$	−24.9904			−0.934589
$716$	53.2996	−	92.3177i	1.99190	−	3.45007i
$717$	−7.18978	−	12.4531i	−0.268507	−	0.465068i
$718$	−23.2251	+	40.2270i	−0.866751	+	1.50126i
$719$	−17.9967	−	31.1713i	−0.671165	−	1.16249i	−0.977574	−	0.210592i	$-0.932461\pi$
$719$	−17.9967	−	31.1713i	−0.671165	−	1.16249i	0.306409	−	0.951900i	$-0.400873\pi$
$720$	−13.5898	−	23.5382i	−0.506462	−	0.877218i
$721$	1.27080			0.0473272
$722$	−37.6896	−	34.5997i	−1.40266	−	1.28767i
$723$	−12.5613			−0.467160
$724$	−14.8055	−	25.6438i	−0.550241	−	0.953046i
$725$	0.111224	+	0.192646i	0.00413076	+	0.00715469i
$726$	10.3552	−	17.9357i	0.384316	−	0.665655i
$727$	−8.53497	−	14.7830i	−0.316545	−	0.548271i	0.663220	−	0.748424i	$-0.269189\pi$
$727$	−8.53497	−	14.7830i	−0.316545	−	0.548271i	−0.979765	+	0.200153i	$0.935856\pi$
$728$	28.9214	−	50.0933i	1.07190	−	1.85658i
$729$	1.00000			0.0370370
$730$	−85.1398			−3.15117
$731$	−7.52293	+	13.0301i	−0.278246	+	0.481936i
$732$	17.0957	−	29.6106i	0.631875	−	1.09444i
$733$	18.0341			0.666106			0.333053	−	0.942908i	$-0.391921\pi$
$733$	18.0341			0.666106			0.333053	+	0.942908i	$0.391921\pi$
$734$	−22.1320			−0.816906
$735$	−1.03963	+	1.80069i	−0.0383474	+	0.0664196i
$736$	−3.07743	−	5.33027i	−0.113436	−	0.196476i
$737$	14.5108	−	25.1335i	0.534514	−	0.925805i
$738$	−3.97661	−	6.88770i	−0.146381	−	0.253540i
$739$	−2.13504	−	3.69800i	−0.0785387	−	0.136033i	0.824081	−	0.566472i	$-0.191692\pi$
$739$	−2.13504	−	3.69800i	−0.0785387	−	0.136033i	−0.902620	+	0.430439i	$0.858359\pi$
$740$	−123.517			−4.54059
$741$	28.4670	−	4.36816i	1.04576	−	0.160468i
$742$	3.80109			0.139542
$743$	−14.5064	−	25.1258i	−0.532188	−	0.921776i	−0.999294	−	0.0375748i	$-0.988037\pi$
$743$	−14.5064	−	25.1258i	−0.532188	−	0.921776i	0.467106	−	0.884201i	$-0.345297\pi$
$744$	−6.87040	−	11.8999i	−0.251881	−	0.436271i
$745$	−14.9563	+	25.9051i	−0.547957	+	0.949089i
$746$	5.46413	+	9.46415i	0.200056	+	0.346507i
$747$	2.29905	−	3.98207i	0.0841178	−	0.145696i
$748$	20.7453			0.758522
$749$	0.695303			0.0254058
$750$	15.8918	−	27.5255i	0.580288	−	1.00509i
$751$	−4.23617	+	7.33726i	−0.154580	+	0.267740i	−0.932906	−	0.360120i	$-0.882736\pi$
$751$	−4.23617	+	7.33726i	−0.154580	+	0.267740i	0.778326	+	0.627860i	$0.216069\pi$
$752$	108.871			3.97013
$753$	−1.85008			−0.0674206
$754$	−2.92447	+	5.06533i	−0.106503	+	0.184468i
$755$	3.80727	+	6.59439i	0.138561	+	0.239994i
$756$	2.62554	−	4.54758i	0.0954901	−	0.165394i
$757$	−19.2553	−	33.3512i	−0.699846	−	1.21217i	−0.968519	−	0.248938i	$-0.919918\pi$
$757$	−19.2553	−	33.3512i	−0.699846	−	1.21217i	0.268673	−	0.963231i	$-0.413415\pi$
$758$	16.0946	+	27.8767i	0.584583	+	1.01253i
$759$	−0.632885			−0.0229723
$760$	−49.6352	−	61.9022i	−1.80046	−	2.24543i
$761$	−44.9608			−1.62983			−0.814914	−	0.579582i	$-0.803216\pi$
$761$	−44.9608			−1.62983			−0.814914	+	0.579582i	$0.803216\pi$
$762$	−18.0217	−	31.2145i	−0.652858	−	1.13078i
$763$	1.41617	+	2.45289i	0.0512690	+	0.0888005i
$764$	−50.9089	+	88.1769i	−1.84182	+	3.19013i
$765$	2.25790	+	3.91079i	0.0816345	+	0.141395i
$766$	7.76231	−	13.4447i	0.280464	−	0.485777i
$767$	−70.4697			−2.54451
$768$	17.5888			0.634682
$769$	−14.6312	+	25.3419i	−0.527613	+	0.913852i	0.471869	+	0.881669i	$0.343579\pi$
$769$	−14.6312	+	25.3419i	−0.527613	+	0.913852i	−0.999482	+	0.0321836i	$0.989754\pi$
$770$	−5.09244	+	8.82037i	−0.183519	+	0.317864i
$771$	23.7128			0.853997
$772$	120.099			4.32245
$773$	13.6650	−	23.6685i	0.491496	−	0.851296i	−0.508456	−	0.861088i	$-0.669784\pi$
$773$	13.6650	−	23.6685i	0.491496	−	0.851296i	0.999952	+	0.00979211i	$0.00311697\pi$
$774$	9.32747	+	16.1557i	0.335269	+	0.580703i
$775$	0.531036	−	0.919782i	0.0190754	−	0.0330395i
$776$	−3.89440	−	6.74529i	−0.139801	−	0.242142i
$777$	−5.65639	−	9.79716i	−0.202922	−	0.351471i
$778$	75.3695			2.70213
$779$	−8.05364	−	10.0440i	−0.288552	−	0.359865i
$780$	72.1403			2.58304
$781$	13.0358	+	22.5786i	0.466457	+	0.807927i
$782$	1.01736	+	1.76213i	0.0363808	+	0.0630135i
$783$	−0.164372	+	0.284700i	−0.00587416	+	0.0101743i
$784$	−6.53587	−	11.3205i	−0.233424	−	0.404302i
$785$	5.49312	−	9.51437i	0.196058	−	0.339582i
$786$	−44.1436			−1.57455
$787$	−10.0026			−0.356556			−0.178278	−	0.983980i	$-0.557053\pi$
$787$	−10.0026			−0.356556			−0.178278	+	0.983980i	$0.557053\pi$
$788$	24.1855	−	41.8905i	0.861573	−	1.49229i
$789$	−3.65216	+	6.32573i	−0.130020	+	0.225202i
$790$	−50.0909			−1.78215
$791$	13.9069			0.494473
$792$	7.96243	−	13.7913i	0.282933	−	0.490054i
$793$	21.5108	+	37.2578i	0.763871	+	1.32306i
$794$	−16.3421	+	28.3054i	−0.579960	+	1.00452i
$795$	1.46753	+	2.54183i	0.0520478	+	0.0901495i
$796$	−17.2365	−	29.8545i	−0.610932	−	1.05816i
$797$	−11.7330			−0.415603			−0.207801	−	0.978171i	$-0.566631\pi$
$797$	−11.7330			−0.415603			−0.207801	+	0.978171i	$0.566631\pi$
$798$	4.25915	−	10.9376i	0.150772	−	0.387186i
$799$	−18.0886			−0.639928
$800$	5.98524	+	10.3667i	0.211610	+	0.366519i
$801$	−1.43291	−	2.48188i	−0.0506295	−	0.0876928i
$802$	32.5179	−	56.3227i	1.14825	−	1.98882i
$803$	−13.8305	−	23.9551i	−0.488066	−	0.845356i
$804$	−41.8887	+	72.5533i	−1.47730	+	2.55876i
$805$	−0.723418			−0.0254971
$806$	27.9256			0.983636
$807$	0.358407	−	0.620779i	0.0126165	−	0.0218524i
$808$	−69.7652	+	120.837i	−2.45433	+	4.25103i
$809$	−7.48387			−0.263119			−0.131560	−	0.991308i	$-0.541998\pi$
$809$	−7.48387			−0.263119			−0.131560	+	0.991308i	$0.541998\pi$
$810$	5.59901			0.196729
$811$	−2.87915	+	4.98683i	−0.101101	+	0.175111i	−0.912138	−	0.409882i	$-0.865570\pi$
$811$	−2.87915	+	4.98683i	−0.101101	+	0.175111i	0.811038	+	0.584994i	$0.198903\pi$
$812$	0.863129	+	1.49498i	0.0302899	+	0.0524636i
$813$	−3.47326	+	6.01586i	−0.121813	+	0.210985i
$814$	−27.7068	−	47.9896i	−0.971123	−	1.68203i
$815$	−17.8175	−	30.8609i	−0.624121	−	1.08101i
$816$	−28.3895			−0.993833
$817$	18.8905	+	23.5591i	0.660894	+	0.824229i
$818$	−59.1993			−2.06986
$819$	3.30361	+	5.72202i	0.115437	+	0.199944i
$820$	−16.1239	−	27.9275i	−0.563072	−	0.975269i
$821$	19.2186	−	33.2876i	0.670734	−	1.16174i	−0.306963	−	0.951722i	$-0.599313\pi$
$821$	19.2186	−	33.2876i	0.670734	−	1.16174i	0.977696	−	0.210023i	$-0.0673539\pi$
$822$	20.3244	+	35.2028i	0.708893	+	1.22784i
$823$	−1.25480	+	2.17338i	−0.0437396	+	0.0757592i	−0.887066	−	0.461642i	$-0.847261\pi$
$823$	−1.25480	+	2.17338i	−0.0437396	+	0.0757592i	0.843327	+	0.537401i	$0.180594\pi$
$824$	−11.1252			−0.387565
$825$	1.23089			0.0428540
$826$	−14.3600	+	24.8723i	−0.499649	+	0.865417i
$827$	−1.27616	+	2.21037i	−0.0443765	+	0.0768623i	−0.887360	−	0.461076i	$-0.847463\pi$
$827$	−1.27616	+	2.21037i	−0.0443765	+	0.0768623i	0.842984	+	0.537939i	$0.180797\pi$
$828$	1.82696			0.0634913
$829$	−0.370818			−0.0128790			−0.00643952	−	0.999979i	$-0.502050\pi$
$829$	−0.370818			−0.0128790			−0.00643952	+	0.999979i	$0.502050\pi$
$830$	12.8724	−	22.2956i	0.446807	−	0.773893i
$831$	−6.30773	−	10.9253i	−0.218813	−	0.378995i
$832$	−71.0047	+	122.984i	−2.46164	+	4.26369i
$833$	1.08591	+	1.88086i	0.0376246	+	0.0651678i
$834$	−7.61647	−	13.1921i	−0.263737	−	0.456806i
$835$	−35.9776			−1.24506
$836$	15.1083	−	38.7984i	0.522532	−	1.34187i
$837$	1.56957			0.0542524
$838$	−0.225723	−	0.390963i	−0.00779747	−	0.0135056i
$839$	0.327853	+	0.567859i	0.0113188	+	0.0196047i	0.871629	−	0.490166i	$-0.163064\pi$
$839$	0.327853	+	0.567859i	0.0113188	+	0.0196047i	−0.860311	+	0.509770i	$0.829730\pi$
$840$	9.10143	−	15.7641i	0.314029	−	0.543915i
$841$	14.4460	+	25.0211i	0.498137	+	0.862798i
$842$	4.26074	−	7.37982i	0.146835	−	0.254326i
$843$	−12.6643			−0.436180
$844$	34.8297			1.19889
$845$	−31.8703	+	55.2010i	−1.09637	+	1.89897i
$846$	−11.2138	+	19.4228i	−0.385537	+	0.667769i
$847$	7.69105			0.264268
$848$	−18.4519			−0.633640
$849$	7.19010	−	12.4536i	0.246764	−	0.427407i
$850$	−1.97865	−	3.42712i	−0.0678671	−	0.117549i
$851$	1.96797	−	3.40863i	0.0674613	−	0.116846i
$852$	−37.6306	−	65.1781i	−1.28920	−	2.23297i
$853$	−3.87514	−	6.71195i	−0.132682	−	0.229813i	0.792027	−	0.610486i	$-0.209026\pi$
$853$	−3.87514	−	6.71195i	−0.132682	−	0.229813i	−0.924710	+	0.380673i	$0.875692\pi$
$854$	17.5335			0.599985
$855$	8.95845	−	1.37464i	0.306372	−	0.0470117i
$856$	−6.08702			−0.208050
$857$	12.6461	+	21.9036i	0.431982	+	0.748214i	0.997044	−	0.0768341i	$-0.0244812\pi$
$857$	12.6461	+	21.9036i	0.431982	+	0.748214i	−0.565062	+	0.825048i	$0.691148\pi$
$858$	16.1821	+	28.0283i	0.552449	+	0.956869i
$859$	2.58290	−	4.47372i	0.0881275	−	0.152641i	−0.818592	−	0.574375i	$-0.805245\pi$
$859$	2.58290	−	4.47372i	0.0881275	−	0.152641i	0.906720	+	0.421734i	$0.138578\pi$
$860$	37.8200	+	65.5061i	1.28965	+	2.23374i
$861$	1.47677	−	2.55783i	0.0503281	−	0.0871708i
$862$	−11.8836			−0.404757
$863$	11.2311			0.382311			0.191156	−	0.981560i	$-0.438777\pi$
$863$	11.2311			0.382311			0.191156	+	0.981560i	$0.438777\pi$
$864$	−8.84522	+	15.3204i	−0.300921	+	0.521210i
$865$	−7.74746	+	13.4190i	−0.263421	+	0.456259i
$866$	44.9413			1.52717
$867$	−12.2832			−0.417159
$868$	4.12098	−	7.13775i	0.139875	−	0.242271i
$869$	−8.13698	−	14.0937i	−0.276028	−	0.478095i
$870$	−0.920317	+	1.59404i	−0.0312017	+	0.0540429i
$871$	−52.7068	−	91.2908i	−1.78590	−	3.09327i
$872$	−12.3979	−	21.4737i	−0.419845	−	0.727193i
$873$	0.889693			0.0301115
$874$	4.03650	−	0.619386i	0.136537	−	0.0209510i
$875$	11.8033			0.399024
$876$	39.9246	+	69.1515i	1.34893	+	2.33641i
$877$	−5.57514	−	9.65642i	−0.188259	−	0.326074i	0.756411	−	0.654097i	$-0.226951\pi$
$877$	−5.57514	−	9.65642i	−0.188259	−	0.326074i	−0.944670	+	0.328023i	$0.893618\pi$
$878$	11.4516	−	19.8347i	0.386472	−	0.669390i
$879$	10.1892	+	17.6483i	0.343675	+	0.595262i
$880$	24.7206	−	42.8173i	0.833330	−	1.44337i
$881$	52.2845			1.76151			0.880755	−	0.473572i	$-0.157036\pi$
$881$	52.2845			1.76151			0.880755	+	0.473572i	$0.157036\pi$
$882$	2.69278			0.0906708
$883$	−12.1610	+	21.0634i	−0.409250	+	0.708841i	−0.994806	−	0.101791i	$-0.967543\pi$
$883$	−12.1610	+	21.0634i	−0.409250	+	0.708841i	0.585556	+	0.810632i	$0.300876\pi$
$884$	37.6758	−	65.2565i	1.26718	−	2.19481i
$885$	−22.1765			−0.745455
$886$	24.3570			0.818291
$887$	26.9742	−	46.7206i	0.905703	−	1.56872i	0.0857334	−	0.996318i	$-0.472677\pi$
$887$	26.9742	−	46.7206i	0.905703	−	1.56872i	0.819970	−	0.572406i	$-0.193990\pi$
$888$	49.5188	+	85.7690i	1.66174	+	2.87822i
$889$	6.69260	−	11.5919i	0.224463	−	0.388781i
$890$	−8.02289	−	13.8960i	−0.268928	−	0.465797i
$891$	0.909526	+	1.57535i	0.0304703	+	0.0527761i
$892$	−68.9197			−2.30760
$893$	−13.1735	+	33.8297i	−0.440834	+	1.13207i
$894$	38.7388			1.29562
$895$	21.1050	+	36.5549i	0.705461	+	1.22189i
$896$	11.2476	+	19.4815i	0.375757	+	0.650830i
$897$	−1.14939	+	1.99081i	−0.0383771	+	0.0664711i
$898$	40.7174	+	70.5246i	1.35876	+	2.35344i
$899$	−0.257993	+	0.446857i	−0.00860455	+	0.0149035i
$900$	−3.55322			−0.118441
$901$	3.06571			0.102134
$902$	7.23367	−	12.5291i	0.240855	−	0.417173i
$903$	−3.46388	+	5.99961i	−0.115271	+	0.199654i
$904$	−121.748			−4.04927
$905$	11.7250			0.389752
$906$	4.93067	−	8.54017i	0.163810	−	0.283728i
$907$	−2.04325	−	3.53901i	−0.0678450	−	0.117511i	0.830107	−	0.557603i	$-0.188279\pi$
$907$	−2.04325	−	3.53901i	−0.0678450	−	0.117511i	−0.897952	+	0.440092i	$0.854946\pi$
$908$	34.9675	−	60.5655i	1.16044	−	2.00994i
$909$	−7.96908	−	13.8029i	−0.264318	−	0.457812i
$910$	18.4969	+	32.0376i	0.613168	+	1.06204i
$911$	46.2425			1.53208			0.766041	−	0.642792i	$-0.222224\pi$
$911$	46.2425			1.53208			0.766041	+	0.642792i	$0.222224\pi$
$912$	−20.6754	+	53.0949i	−0.684632	+	1.75815i
$913$	8.36418			0.276814
$914$	27.0191	+	46.7984i	0.893712	+	1.54795i
$915$	6.76935	+	11.7249i	0.223788	+	0.387612i
$916$	7.74520	−	13.4151i	0.255908	−	0.443246i
$917$	−8.19664	−	14.1970i	−0.270677	−	0.468826i
$918$	2.92413	−	5.06474i	0.0965106	−	0.167161i
$919$	37.2204			1.22779			0.613894	−	0.789388i	$-0.289602\pi$
$919$	37.2204			1.22779			0.613894	+	0.789388i	$0.289602\pi$
$920$	6.33315			0.208798
$921$	−9.20768	+	15.9482i	−0.303403	+	0.525510i
$922$	28.4956	−	49.3558i	0.938453	−	1.62545i
$923$	94.6980			3.11702
$924$	9.55200			0.314238
$925$	−3.82747	+	6.62938i	−0.125847	+	0.217973i
$926$	−32.5396	−	56.3603i	−1.06932	−	1.85211i
$927$	0.635401	−	1.10055i	0.0208693	−	0.0361467i
$928$	−2.90781	−	5.03647i	−0.0954534	−	0.165330i
$929$	18.8563	+	32.6601i	0.618656	+	1.07154i	0.989731	+	0.142941i	$0.0456560\pi$
$929$	18.8563	+	32.6601i	0.618656	+	1.07154i	−0.371075	+	0.928603i	$0.621011\pi$
$930$	8.78805			0.288172
$931$	4.30847	−	0.661119i	0.141204	−	0.0216673i
$932$	45.5338			1.49151
$933$	2.69617	+	4.66990i	0.0882685	+	0.152886i
$934$	−15.6519	−	27.1098i	−0.512144	−	0.887060i
$935$	−4.10723	+	7.11394i	−0.134321	+	0.232651i
$936$	−28.9214	−	50.0933i	−0.945325	−	1.63735i
$937$	−8.04097	+	13.9274i	−0.262687	+	0.454987i	−0.966955	−	0.254947i	$-0.917942\pi$
$937$	−8.04097	+	13.9274i	−0.262687	+	0.454987i	0.704268	+	0.709934i	$0.251275\pi$
$938$	−42.9615			−1.40274
$939$	−19.8960			−0.649283
$940$	−45.4683	+	78.7533i	−1.48301	+	2.56865i
$941$	10.5257	−	18.2311i	0.343129	−	0.594316i	−0.641883	−	0.766802i	$-0.721847\pi$
$941$	10.5257	−	18.2311i	0.343129	−	0.594316i	0.985012	+	0.172486i	$0.0551800\pi$
$942$	−14.2279			−0.463571
$943$	1.02759			0.0334631
$944$	69.7087	−	120.739i	2.26883	−	3.92972i
$945$	1.03963	+	1.80069i	0.0338192	+	0.0585766i
$946$	−16.9672	+	29.3880i	−0.551650	+	0.955486i
$947$	−1.60308	−	2.77662i	−0.0520932	−	0.0902280i	0.838803	−	0.544435i	$-0.183256\pi$
$947$	−1.60308	−	2.77662i	−0.0520932	−	0.0902280i	−0.890896	+	0.454207i	$0.849923\pi$
$948$	23.4891	+	40.6844i	0.762892	+	1.32137i
$949$	−100.471			−3.26142
$950$	−7.85050	+	1.20463i	−0.254704	+	0.0390834i
$951$	9.00900			0.292137
$952$	−9.50660	−	16.4659i	−0.308111	−	0.533663i
$953$	22.5385	+	39.0378i	0.730094	+	1.26456i	0.956843	+	0.290606i	$0.0938570\pi$
$953$	22.5385	+	39.0378i	0.730094	+	1.26456i	−0.226749	+	0.973953i	$0.572810\pi$
$954$	1.90055	−	3.29184i	0.0615324	−	0.106577i
$955$	−20.1583	−	34.9152i	−0.652308	−	1.12983i
$956$	−37.7542	+	65.3921i	−1.22106	+	2.11493i
$957$	−0.598001			−0.0193306
$958$	5.57185			0.180018
$959$	−7.54771	+	13.0730i	−0.243728	+	0.422150i
$960$	−22.3449	+	38.7024i	−0.721177	+	1.24912i
$961$	−28.5364			−0.920530
$962$	−201.275			−6.48937
$963$	0.347652	−	0.602150i	0.0112029	−	0.0194040i
$964$	32.9803	+	57.1235i	1.06222	+	1.83982i
$965$	−23.7777	+	41.1841i	−0.765430	+	1.32576i
$966$	0.468437	+	0.811357i	0.0150717	+	0.0261050i
$967$	20.6984	+	35.8507i	0.665616	+	1.15288i	0.979118	+	0.203294i	$0.0651646\pi$
$967$	20.6984	+	35.8507i	0.665616	+	1.15288i	−0.313502	+	0.949588i	$0.601502\pi$
$968$	−67.3311			−2.16410
$969$	3.43515	−	8.82153i	0.110353	−	0.283388i
$970$	4.98140			0.159943
$971$	−7.55206	−	13.0806i	−0.242357	−	0.419775i	0.719028	−	0.694981i	$-0.244587\pi$
$971$	−7.55206	−	13.0806i	−0.242357	−	0.419775i	−0.961385	+	0.275206i	$0.911254\pi$
$972$	−2.62554	−	4.54758i	−0.0842144	−	0.145864i
$973$	2.82847	−	4.89906i	0.0906767	−	0.157057i
$974$	32.0350	+	55.4863i	1.02647	+	1.77790i
$975$	2.23543	−	3.87188i	0.0715911	−	0.123999i
$976$	−85.1141			−2.72443
$977$	−8.03822			−0.257166			−0.128583	−	0.991699i	$-0.541043\pi$
$977$	−8.03822			−0.257166			−0.128583	+	0.991699i	$0.541043\pi$
$978$	−23.0749	+	39.9669i	−0.737854	+	1.27800i
$979$	2.60654	−	4.51466i	0.0833054	−	0.144289i
$980$	10.9184			0.348775
$981$	2.83235			0.0904300
$982$	−13.6860	+	23.7049i	−0.436738	+	0.756452i
$983$	−2.22751	−	3.85815i	−0.0710464	−	0.123056i	0.828314	−	0.560264i	$-0.189301\pi$
$983$	−2.22751	−	3.85815i	−0.0710464	−	0.123056i	−0.899360	+	0.437209i	$0.855967\pi$
$984$	−12.9283	+	22.3925i	−0.412140	+	0.713847i
$985$	9.57669	+	16.5873i	0.305139	+	0.528516i
$986$	0.961287	+	1.66500i	0.0306136	+	0.0530243i
$987$	−8.32874			−0.265107
$988$	−94.6060	−	117.987i	−3.00982	−	3.75367i
$989$	−2.41031			−0.0766433
$990$	5.09244	+	8.82037i	0.161849	+	0.280330i
$991$	25.4907	+	44.1512i	0.809739	+	1.40251i	0.913045	+	0.407860i	$0.133725\pi$
$991$	25.4907	+	44.1512i	0.809739	+	1.40251i	−0.103306	+	0.994650i	$0.532942\pi$
$992$	−13.8832	+	24.0464i	−0.440793	+	0.763475i
$993$	−11.1427	−	19.2997i	−0.353603	−	0.612458i
$994$	19.2972	−	33.4237i	0.612069	−	1.06013i
$995$	13.6502			0.432741
$996$	−24.1450			−0.765064
$997$	16.0713	−	27.8364i	0.508985	−	0.881587i	−0.490961	−	0.871181i	$-0.663354\pi$
$997$	16.0713	−	27.8364i	0.508985	−	0.881587i	0.999946	−	0.0104058i	$-0.00331232\pi$
$998$	−35.8699	+	62.1286i	−1.13544	+	1.96665i
$999$	−11.3128			−0.357921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.k.c.64.1	✓	12
3.2	odd	2		1197.2.k.i.64.6		12
19.7	even	3		7581.2.a.bc.1.6		6
19.11	even	3	inner	399.2.k.c.106.1	yes	12
19.12	odd	6		7581.2.a.ba.1.1		6
57.11	odd	6		1197.2.k.i.505.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.k.c.64.1	✓	12	1.1	even	1	trivial
399.2.k.c.106.1	yes	12	19.11	even	3	inner
1197.2.k.i.64.6		12	3.2	odd	2
1197.2.k.i.505.6		12	57.11	odd	6
7581.2.a.ba.1.1		6	19.12	odd	6
7581.2.a.bc.1.6		6	19.7	even	3

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:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34639 - 2.33202i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.62554 + 4.54758i) q^{4} +(-1.03963 - 1.80069i) q^{5} +(-1.34639 + 2.33202i) q^{6} -1.00000 q^{7} +8.75448 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.34639 - 2.33202i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.62554 + 4.54758i) q^{4} +(-1.03963 - 1.80069i) q^{5} +(-1.34639 + 2.33202i) q^{6} -1.00000 q^{7} +8.75448 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.79950 + 4.84888i) q^{10} -1.81905 q^{11} +5.25109 q^{12} +(-3.30361 + 5.72202i) q^{13} +(1.34639 + 2.33202i) q^{14} +(-1.03963 + 1.80069i) q^{15} +(-6.53587 - 11.3205i) q^{16} +(1.08591 + 1.88086i) q^{17} +2.69278 q^{18} +(4.30847 - 0.661119i) q^{19} +10.9184 q^{20} +(0.500000 + 0.866025i) q^{21} +(2.44916 + 4.24207i) q^{22} +(-0.173960 + 0.301308i) q^{23} +(-4.37724 - 7.58160i) q^{24} +(0.338332 - 0.586008i) q^{25} +17.7918 q^{26} +1.00000 q^{27} +(2.62554 - 4.54758i) q^{28} +(-0.164372 + 0.284700i) q^{29} +5.59901 q^{30} +1.56957 q^{31} +(-8.84522 + 15.3204i) q^{32} +(0.909526 + 1.57535i) q^{33} +(2.92413 - 5.06474i) q^{34} +(1.03963 + 1.80069i) q^{35} +(-2.62554 - 4.54758i) q^{36} -11.3128 q^{37} +(-7.34263 - 9.15731i) q^{38} +6.60722 q^{39} +(-9.10143 - 15.7641i) q^{40} +(-1.47677 - 2.55783i) q^{41} +(1.34639 - 2.33202i) q^{42} +(3.46388 + 5.99961i) q^{43} +(4.77600 - 8.27228i) q^{44} +2.07926 q^{45} +0.936875 q^{46} +(-4.16437 + 7.21290i) q^{47} +(-6.53587 + 11.3205i) q^{48} +1.00000 q^{49} -1.82211 q^{50} +(1.08591 - 1.88086i) q^{51} +(-17.3475 - 30.0468i) q^{52} +(0.705792 - 1.22247i) q^{53} +(-1.34639 - 2.33202i) q^{54} +(1.89114 + 3.27556i) q^{55} -8.75448 q^{56} +(-2.72678 - 3.40069i) q^{57} +0.885234 q^{58} +(5.33278 + 9.23664i) q^{59} +(-5.45920 - 9.45561i) q^{60} +(3.25565 - 5.63895i) q^{61} +(-2.11326 - 3.66027i) q^{62} +(0.500000 - 0.866025i) q^{63} +21.4931 q^{64} +13.7382 q^{65} +(2.44916 - 4.24207i) q^{66} +(-7.97715 + 13.8168i) q^{67} -11.4044 q^{68} +0.347920 q^{69} +(2.79950 - 4.84888i) q^{70} +(-7.16625 - 12.4123i) q^{71} +(-4.37724 + 7.58160i) q^{72} +(7.60311 + 13.1690i) q^{73} +(15.2314 + 26.3816i) q^{74} -0.676663 q^{75} +(-8.30559 + 21.3289i) q^{76} +1.81905 q^{77} +(-8.89591 - 15.4082i) q^{78} +(4.47320 + 7.74780i) q^{79} +(-13.5898 + 23.5382i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.97661 + 6.88770i) q^{82} -4.59810 q^{83} -5.25109 q^{84} +(2.25790 - 3.91079i) q^{85} +(9.32747 - 16.1557i) q^{86} +0.328743 q^{87} -15.9249 q^{88} +(-1.43291 + 2.48188i) q^{89} +(-2.79950 - 4.84888i) q^{90} +(3.30361 - 5.72202i) q^{91} +(-0.913480 - 1.58219i) q^{92} +(-0.784786 - 1.35929i) q^{93} +22.4275 q^{94} +(-5.66970 - 7.07092i) q^{95} +17.6904 q^{96} +(-0.444846 - 0.770496i) q^{97} +(-1.34639 - 2.33202i) q^{98} +(0.909526 - 1.57535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} - 6 q^{3} - 9 q^{4} - q^{6} - 12 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q - q^2 - 6 * q^3 - 9 * q^4 - q^6 - 12 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q - q^{2} - 6 q^{3} - 9 q^{4} - q^{6} - 12 q^{7} - 6 q^{8} - 6 q^{9} - 4 q^{10} + 8 q^{11} + 18 q^{12} - 2 q^{13} + q^{14} - 19 q^{16} + 3 q^{17} + 2 q^{18} + 3 q^{19} - 26 q^{20} + 6 q^{21} + 2 q^{22} + 5 q^{23} + 3 q^{24} - 16 q^{25} + 98 q^{26} + 12 q^{27} + 9 q^{28} + 11 q^{29} + 8 q^{30} - 10 q^{31} - 4 q^{33} - 6 q^{34} - 9 q^{36} - 10 q^{37} - 26 q^{38} + 4 q^{39} - 62 q^{40} + 5 q^{41} + q^{42} - q^{43} + 15 q^{44} - 24 q^{46} - 37 q^{47} - 19 q^{48} + 12 q^{49} + 6 q^{50} + 3 q^{51} + 9 q^{52} + 9 q^{53} - q^{54} + 9 q^{55} + 6 q^{56} + 3 q^{57} + 18 q^{58} + 6 q^{59} + 13 q^{60} + 19 q^{61} + 5 q^{62} + 6 q^{63} + 118 q^{64} + 48 q^{65} + 2 q^{66} + 8 q^{67} - 130 q^{68} - 10 q^{69} + 4 q^{70} - 19 q^{71} + 3 q^{72} + 24 q^{73} + 15 q^{74} + 32 q^{75} - 6 q^{76} - 8 q^{77} - 49 q^{78} + 27 q^{79} - 11 q^{80} - 6 q^{81} - 46 q^{82} + 70 q^{83} - 18 q^{84} - 59 q^{85} - 3 q^{86} - 22 q^{87} - 14 q^{88} - 4 q^{89} - 4 q^{90} + 2 q^{91} - 9 q^{92} + 5 q^{93} + 34 q^{94} - 55 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - q^2 - 6 * q^3 - 9 * q^4 - q^6 - 12 * q^7 - 6 * q^8 - 6 * q^9 - 4 * q^10 + 8 * q^11 + 18 * q^12 - 2 * q^13 + q^14 - 19 * q^16 + 3 * q^17 + 2 * q^18 + 3 * q^19 - 26 * q^20 + 6 * q^21 + 2 * q^22 + 5 * q^23 + 3 * q^24 - 16 * q^25 + 98 * q^26 + 12 * q^27 + 9 * q^28 + 11 * q^29 + 8 * q^30 - 10 * q^31 - 4 * q^33 - 6 * q^34 - 9 * q^36 - 10 * q^37 - 26 * q^38 + 4 * q^39 - 62 * q^40 + 5 * q^41 + q^42 - q^43 + 15 * q^44 - 24 * q^46 - 37 * q^47 - 19 * q^48 + 12 * q^49 + 6 * q^50 + 3 * q^51 + 9 * q^52 + 9 * q^53 - q^54 + 9 * q^55 + 6 * q^56 + 3 * q^57 + 18 * q^58 + 6 * q^59 + 13 * q^60 + 19 * q^61 + 5 * q^62 + 6 * q^63 + 118 * q^64 + 48 * q^65 + 2 * q^66 + 8 * q^67 - 130 * q^68 - 10 * q^69 + 4 * q^70 - 19 * q^71 + 3 * q^72 + 24 * q^73 + 15 * q^74 + 32 * q^75 - 6 * q^76 - 8 * q^77 - 49 * q^78 + 27 * q^79 - 11 * q^80 - 6 * q^81 - 46 * q^82 + 70 * q^83 - 18 * q^84 - 59 * q^85 - 3 * q^86 - 22 * q^87 - 14 * q^88 - 4 * q^89 - 4 * q^90 + 2 * q^91 - 9 * q^92 + 5 * q^93 + 34 * q^94 - 55 * q^97 - q^98 - 4 * q^99

Introduction

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