LMFDB - Embedded newform 273.2.l.b.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.3
Root			$0.415625 + 0.719884i$ of defining polynomial
Character	$\chi$	$=$	273.16
Dual form			273.2.l.b.256.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.831251 q^{2} +(0.500000 - 0.866025i) q^{3} -1.30902 q^{4} +(-1.30847 + 2.26634i) q^{5} +(-0.415625 + 0.719884i) q^{6} +(1.78280 - 1.95490i) q^{7} +2.75063 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-0.831251 q^{2} +(0.500000 - 0.866025i) q^{3} -1.30902 q^{4} +(-1.30847 + 2.26634i) q^{5} +(-0.415625 + 0.719884i) q^{6} +(1.78280 - 1.95490i) q^{7} +2.75063 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.08767 - 1.88389i) q^{10} +(0.924183 - 1.60073i) q^{11} +(-0.654511 + 1.13365i) q^{12} +(2.74506 - 2.33765i) q^{13} +(-1.48195 + 1.62501i) q^{14} +(1.30847 + 2.26634i) q^{15} +0.331582 q^{16} +6.83128 q^{17} +(0.415625 + 0.719884i) q^{18} +(-2.53494 - 4.39065i) q^{19} +(1.71281 - 2.96668i) q^{20} +(-0.801591 - 2.52140i) q^{21} +(-0.768228 + 1.33061i) q^{22} -1.27286 q^{23} +(1.37531 - 2.38211i) q^{24} +(-0.924183 - 1.60073i) q^{25} +(-2.28184 + 1.94318i) q^{26} -1.00000 q^{27} +(-2.33372 + 2.55900i) q^{28} +(0.724496 + 1.25486i) q^{29} +(-1.08767 - 1.88389i) q^{30} +(-3.09878 - 5.36725i) q^{31} -5.77688 q^{32} +(-0.924183 - 1.60073i) q^{33} -5.67851 q^{34} +(2.09772 + 6.59834i) q^{35} +(0.654511 + 1.13365i) q^{36} +7.87843 q^{37} +(2.10717 + 3.64973i) q^{38} +(-0.651934 - 3.54612i) q^{39} +(-3.59911 + 6.23384i) q^{40} +(4.41239 + 7.64248i) q^{41} +(0.666324 + 2.09592i) q^{42} +(0.109598 - 0.189830i) q^{43} +(-1.20978 + 2.09539i) q^{44} +2.61694 q^{45} +1.05806 q^{46} +(0.624016 - 1.08083i) q^{47} +(0.165791 - 0.287158i) q^{48} +(-0.643251 - 6.97038i) q^{49} +(0.768228 + 1.33061i) q^{50} +(3.41564 - 5.91607i) q^{51} +(-3.59335 + 3.06004i) q^{52} +(1.33947 + 2.32004i) q^{53} +0.831251 q^{54} +(2.41853 + 4.18902i) q^{55} +(4.90382 - 5.37720i) q^{56} -5.06988 q^{57} +(-0.602238 - 1.04311i) q^{58} -12.0361 q^{59} +(-1.71281 - 2.96668i) q^{60} +(4.36109 + 7.55363i) q^{61} +(2.57586 + 4.46153i) q^{62} +(-2.58439 - 0.566501i) q^{63} +4.13888 q^{64} +(1.70607 + 9.27998i) q^{65} +(0.768228 + 1.33061i) q^{66} +(-6.91656 + 11.9798i) q^{67} -8.94230 q^{68} +(-0.636428 + 1.10233i) q^{69} +(-1.74373 - 5.48488i) q^{70} +(1.78833 - 3.09749i) q^{71} +(-1.37531 - 2.38211i) q^{72} +(-3.26733 - 5.65918i) q^{73} -6.54896 q^{74} -1.84837 q^{75} +(3.31829 + 5.74745i) q^{76} +(-1.48163 - 4.66047i) q^{77} +(0.541921 + 2.94772i) q^{78} +(3.08084 - 5.33616i) q^{79} +(-0.433865 + 0.751475i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.66780 - 6.35282i) q^{82} -8.67738 q^{83} +(1.04930 + 3.30057i) q^{84} +(-8.93852 + 15.4820i) q^{85} +(-0.0911037 + 0.157796i) q^{86} +1.44899 q^{87} +(2.54208 - 4.40302i) q^{88} -15.1550 q^{89} -2.17533 q^{90} +(0.324029 - 9.53389i) q^{91} +1.66620 q^{92} -6.19756 q^{93} +(-0.518714 + 0.898438i) q^{94} +13.2676 q^{95} +(-2.88844 + 5.00293i) q^{96} +(6.08221 - 10.5347i) q^{97} +(0.534703 + 5.79414i) q^{98} -1.84837 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.831251			−0.587783			−0.293892	−	0.955839i	$-0.594950\pi$
$2$	−0.831251			−0.587783			−0.293892	+	0.955839i	$0.594950\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.30902			−0.654511
$5$	−1.30847	+	2.26634i	−0.585165	+	1.01354i	0.409690	+	0.912225i	$0.365637\pi$
$5$	−1.30847	+	2.26634i	−0.585165	+	1.01354i	−0.994855	+	0.101311i	$0.967696\pi$
$6$	−0.415625	+	0.719884i	−0.169678	+	0.293892i
$7$	1.78280	−	1.95490i	0.673835	−	0.738882i
$7$	1.78280	−	1.95490i	0.673835	−	0.738882i
$8$	2.75063			0.972494
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.08767	−	1.88389i	0.343950	−	0.595739i
$11$	0.924183	−	1.60073i	0.278652	−	0.482639i	−0.692398	−	0.721516i	$-0.743446\pi$
$11$	0.924183	−	1.60073i	0.278652	−	0.482639i	0.971050	+	0.238877i	$0.0767792\pi$
$12$	−0.654511	+	1.13365i	−0.188941	+	0.327255i
$13$	2.74506	−	2.33765i	0.761344	−	0.648348i
$13$	2.74506	−	2.33765i	0.761344	−	0.648348i
$14$	−1.48195	+	1.62501i	−0.396069	+	0.434302i
$15$	1.30847	+	2.26634i	0.337845	+	0.585165i
$16$	0.331582			0.0828954
$17$	6.83128			1.65683			0.828415	−	0.560115i	$-0.189243\pi$
$17$	6.83128			1.65683			0.828415	+	0.560115i	$0.189243\pi$
$18$	0.415625	+	0.719884i	0.0979639	+	0.169678i
$19$	−2.53494	−	4.39065i	−0.581556	−	1.00728i	−0.995295	−	0.0968885i	$-0.969111\pi$
$19$	−2.53494	−	4.39065i	−0.581556	−	1.00728i	0.413740	−	0.910395i	$-0.364222\pi$
$20$	1.71281	−	2.96668i	0.382997	−	0.663370i
$21$	−0.801591	−	2.52140i	−0.174922	−	0.550214i
$22$	−0.768228	+	1.33061i	−0.163787	+	0.283687i
$23$	−1.27286			−0.265409			−0.132704	−	0.991156i	$-0.542366\pi$
$23$	−1.27286			−0.265409			−0.132704	+	0.991156i	$0.542366\pi$
$24$	1.37531	−	2.38211i	0.280735	−	0.486247i
$25$	−0.924183	−	1.60073i	−0.184837	−	0.320146i
$26$	−2.28184	+	1.94318i	−0.447505	+	0.381088i
$27$	−1.00000			−0.192450
$28$	−2.33372	+	2.55900i	−0.441032	+	0.483606i
$29$	0.724496	+	1.25486i	0.134536	+	0.233022i	0.925420	−	0.378943i	$-0.123712\pi$
$29$	0.724496	+	1.25486i	0.134536	+	0.233022i	−0.790884	+	0.611966i	$0.790379\pi$
$30$	−1.08767	−	1.88389i	−0.198580	−	0.343950i
$31$	−3.09878	−	5.36725i	−0.556557	−	0.963986i	−0.997781	−	0.0665883i	$-0.978789\pi$
$31$	−3.09878	−	5.36725i	−0.556557	−	0.963986i	0.441223	−	0.897397i	$-0.354545\pi$
$32$	−5.77688			−1.02122
$33$	−0.924183	−	1.60073i	−0.160880	−	0.278652i
$34$	−5.67851			−0.973857
$35$	2.09772	+	6.59834i	0.354579	+	1.11532i
$36$	0.654511	+	1.13365i	0.109085	+	0.188941i
$37$	7.87843			1.29521			0.647603	−	0.761978i	$-0.275771\pi$
$37$	7.87843			1.29521			0.647603	+	0.761978i	$0.275771\pi$
$38$	2.10717	+	3.64973i	0.341829	+	0.592064i
$39$	−0.651934	−	3.54612i	−0.104393	−	0.567834i
$40$	−3.59911	+	6.23384i	−0.569069	+	0.985657i
$41$	4.41239	+	7.64248i	0.689099	+	1.19355i	0.972130	+	0.234444i	$0.0753268\pi$
$41$	4.41239	+	7.64248i	0.689099	+	1.19355i	−0.283031	+	0.959111i	$0.591340\pi$
$42$	0.666324	+	2.09592i	0.102816	+	0.323407i
$43$	0.109598	−	0.189830i	0.0167136	−	0.0289488i	−0.857548	−	0.514405i	$-0.828013\pi$
$43$	0.109598	−	0.189830i	0.0167136	−	0.0289488i	0.874261	+	0.485456i	$0.161346\pi$
$44$	−1.20978	+	2.09539i	−0.182381	+	0.315892i
$45$	2.61694			0.390110
$46$	1.05806			0.156003
$47$	0.624016	−	1.08083i	0.0910220	−	0.157655i	−0.816919	−	0.576752i	$-0.804320\pi$
$47$	0.624016	−	1.08083i	0.0910220	−	0.157655i	0.907941	+	0.419097i	$0.137653\pi$
$48$	0.165791	−	0.287158i	0.0239299	−	0.0414477i
$49$	−0.643251	−	6.97038i	−0.0918930	−	0.995769i
$50$	0.768228	+	1.33061i	0.108644	+	0.188177i
$51$	3.41564	−	5.91607i	0.478286	−	0.828415i
$52$	−3.59335	+	3.06004i	−0.498308	+	0.424351i
$53$	1.33947	+	2.32004i	0.183991	+	0.318682i	0.943236	−	0.332123i	$-0.107765\pi$
$53$	1.33947	+	2.32004i	0.183991	+	0.318682i	−0.759245	+	0.650805i	$0.774432\pi$
$54$	0.831251			0.113119
$55$	2.41853	+	4.18902i	0.326114	+	0.564847i
$56$	4.90382	−	5.37720i	0.655300	−	0.718558i
$57$	−5.06988			−0.671522
$58$	−0.602238	−	1.04311i	−0.0790777	−	0.136967i
$59$	−12.0361			−1.56697			−0.783483	−	0.621414i	$-0.786559\pi$
$59$	−12.0361			−1.56697			−0.783483	+	0.621414i	$0.786559\pi$
$60$	−1.71281	−	2.96668i	−0.221123	−	0.382997i
$61$	4.36109	+	7.55363i	0.558381	+	0.967144i	0.997632	+	0.0687794i	$0.0219105\pi$
$61$	4.36109	+	7.55363i	0.558381	+	0.967144i	−0.439251	+	0.898364i	$0.644756\pi$
$62$	2.57586	+	4.46153i	0.327135	+	0.566615i
$63$	−2.58439	−	0.566501i	−0.325603	−	0.0713724i
$64$	4.13888			0.517359
$65$	1.70607	+	9.27998i	0.211612	+	1.15104i
$66$	0.768228	+	1.33061i	0.0945623	+	0.163787i
$67$	−6.91656	+	11.9798i	−0.844992	+	1.46357i	0.0406360	+	0.999174i	$0.487062\pi$
$67$	−6.91656	+	11.9798i	−0.844992	+	1.46357i	−0.885628	+	0.464395i	$0.846272\pi$
$68$	−8.94230			−1.08441
$69$	−0.636428	+	1.10233i	−0.0766170	+	0.132704i
$70$	−1.74373	−	5.48488i	−0.208415	−	0.655569i
$71$	1.78833	−	3.09749i	0.212236	−	0.367604i	−0.740178	−	0.672411i	$-0.765259\pi$
$71$	1.78833	−	3.09749i	0.212236	−	0.367604i	0.952414	+	0.304807i	$0.0985920\pi$
$72$	−1.37531	−	2.38211i	−0.162082	−	0.280735i
$73$	−3.26733	−	5.65918i	−0.382412	−	0.662357i	0.608994	−	0.793175i	$-0.291573\pi$
$73$	−3.26733	−	5.65918i	−0.382412	−	0.662357i	−0.991406	+	0.130817i	$0.958240\pi$
$74$	−6.54896			−0.761301
$75$	−1.84837			−0.213431
$76$	3.31829	+	5.74745i	0.380634	+	0.659278i
$77$	−1.48163	−	4.66047i	−0.168848	−	0.531110i
$78$	0.541921	+	2.94772i	0.0613605	+	0.333763i
$79$	3.08084	−	5.33616i	0.346621	−	0.600365i	−0.639026	−	0.769185i	$-0.720662\pi$
$79$	3.08084	−	5.33616i	0.346621	−	0.600365i	0.985647	+	0.168820i	$0.0539956\pi$
$80$	−0.433865	+	0.751475i	−0.0485075	+	0.0840175i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.66780	−	6.35282i	−0.405041	−	0.701551i
$83$	−8.67738			−0.952467			−0.476233	−	0.879319i	$-0.657998\pi$
$83$	−8.67738			−0.952467			−0.476233	+	0.879319i	$0.657998\pi$
$84$	1.04930	+	3.30057i	0.114488	+	0.360121i
$85$	−8.93852	+	15.4820i	−0.969519	+	1.67926i
$86$	−0.0911037	+	0.157796i	−0.00982396	+	0.0170156i
$87$	1.44899			0.155348
$88$	2.54208	−	4.40302i	0.270987	−	0.469363i
$89$	−15.1550			−1.60643			−0.803215	−	0.595690i	$-0.796879\pi$
$89$	−15.1550			−1.60643			−0.803215	+	0.595690i	$0.796879\pi$
$90$	−2.17533			−0.229300
$91$	0.324029	−	9.53389i	0.0339674	−	0.999423i
$92$	1.66620			0.173713
$93$	−6.19756			−0.642657
$94$	−0.518714	+	0.898438i	−0.0535012	+	0.0926668i
$95$	13.2676			1.36122
$96$	−2.88844	+	5.00293i	−0.294800	+	0.510609i
$97$	6.08221	−	10.5347i	0.617554	−	1.06964i	−0.372376	−	0.928082i	$-0.621457\pi$
$97$	6.08221	−	10.5347i	0.617554	−	1.06964i	0.989931	−	0.141554i	$-0.0452098\pi$
$98$	0.534703	+	5.79414i	0.0540132	+	0.585296i
$99$	−1.84837			−0.185768
$100$	1.20978	+	2.09539i	0.120978	+	0.209539i
$101$	2.29803	−	3.98031i	0.228663	−	0.396056i	−0.728749	−	0.684781i	$-0.759898\pi$
$101$	2.29803	−	3.98031i	0.228663	−	0.396056i	0.957412	+	0.288725i	$0.0932313\pi$
$102$	−2.83926	+	4.91774i	−0.281128	+	0.486928i
$103$	−2.22609	+	3.85570i	−0.219343	+	0.379914i	−0.954607	−	0.297867i	$-0.903725\pi$
$103$	−2.22609	+	3.85570i	−0.219343	+	0.379914i	0.735264	+	0.677781i	$0.237058\pi$
$104$	7.55065	−	6.43001i	0.740402	−	0.630515i
$105$	6.76319	+	1.48250i	0.660020	+	0.144677i
$106$	−1.11344	−	1.92853i	−0.108147	−	0.187316i
$107$	7.21387			0.697391			0.348696	−	0.937236i	$-0.386625\pi$
$107$	7.21387			0.697391			0.348696	+	0.937236i	$0.386625\pi$
$108$	1.30902			0.125961
$109$	4.34979	+	7.53406i	0.416635	+	0.721632i	0.995599	−	0.0937209i	$-0.0298761\pi$
$109$	4.34979	+	7.53406i	0.416635	+	0.721632i	−0.578964	+	0.815353i	$0.696543\pi$
$110$	−2.01041	−	3.48212i	−0.191685	−	0.332007i
$111$	3.93922	−	6.82292i	0.373894	−	0.647603i
$112$	0.591144	−	0.648208i	0.0558578	−	0.0612499i
$113$	1.82527	−	3.16146i	0.171707	−	0.297405i	−0.767310	−	0.641277i	$-0.778405\pi$
$113$	1.82527	−	3.16146i	0.171707	−	0.297405i	0.939017	+	0.343871i	$0.111738\pi$
$114$	4.21435			0.394710
$115$	1.66549	−	2.88472i	0.155308	−	0.269002i
$116$	−0.948381	−	1.64264i	−0.0880550	−	0.152516i
$117$	−3.39700	−	1.20847i	−0.314053	−	0.111723i
$118$	10.0050			0.921036
$119$	12.1788	−	13.3545i	1.11643	−	1.22420i
$120$	3.59911	+	6.23384i	0.328552	+	0.569069i
$121$	3.79177	+	6.56754i	0.344707	+	0.597049i
$122$	−3.62516	−	6.27896i	−0.328207	−	0.568471i
$123$	8.82477			0.795703
$124$	4.05637	+	7.02584i	0.364273	+	0.630939i
$125$	−8.24763			−0.737691
$126$	2.14828	+	0.470904i	0.191384	+	0.0419515i
$127$	4.80639	+	8.32491i	0.426498	+	0.738716i	0.996559	−	0.0828862i	$-0.0264138\pi$
$127$	4.80639	+	8.32491i	0.426498	+	0.738716i	−0.570061	+	0.821602i	$0.693080\pi$
$128$	8.11332			0.717123
$129$	−0.109598	−	0.189830i	−0.00964959	−	0.0167136i
$130$	−1.41817	−	7.71399i	−0.124382	−	0.676562i
$131$	8.28016	−	14.3417i	0.723441	−	1.25304i	−0.236172	−	0.971711i	$-0.575893\pi$
$131$	8.28016	−	14.3417i	0.723441	−	1.25304i	0.959613	−	0.281325i	$-0.0907738\pi$
$132$	1.20978	+	2.09539i	0.105297	+	0.182381i
$133$	−13.1026	−	2.87209i	−1.13614	−	0.249042i
$134$	5.74940	−	9.95825i	0.496672	−	0.860261i
$135$	1.30847	−	2.26634i	0.112615	−	0.195055i
$136$	18.7903			1.61126
$137$	−10.5569			−0.901934			−0.450967	−	0.892541i	$-0.648921\pi$
$137$	−10.5569			−0.901934			−0.450967	+	0.892541i	$0.648921\pi$
$138$	0.529032	−	0.916310i	0.0450342	−	0.0780015i
$139$	−4.57749	+	7.92845i	−0.388258	+	0.672482i	−0.992215	−	0.124534i	$-0.960256\pi$
$139$	−4.57749	+	7.92845i	−0.388258	+	0.672482i	0.603958	+	0.797016i	$0.293590\pi$
$140$	−2.74595	−	8.63738i	−0.232076	−	0.729992i
$141$	−0.624016	−	1.08083i	−0.0525516	−	0.0910220i
$142$	−1.48655	+	2.57479i	−0.124749	+	0.216071i
$143$	−1.20501	−	6.55453i	−0.100768	−	0.548117i
$144$	−0.165791	−	0.287158i	−0.0138159	−	0.0239299i
$145$	−3.79192			−0.314902
$146$	2.71597	+	4.70420i	0.224775	+	0.389322i
$147$	−6.35815	−	2.92812i	−0.524412	−	0.241507i
$148$	−10.3130			−0.847727
$149$	5.45367	+	9.44604i	0.446782	+	0.773850i	0.998174	−	0.0603965i	$-0.0192365\pi$
$149$	5.45367	+	9.44604i	0.446782	+	0.773850i	−0.551392	+	0.834246i	$0.685903\pi$
$150$	1.53646			0.125451
$151$	11.1702	+	19.3474i	0.909018	+	1.57447i	0.815430	+	0.578855i	$0.196500\pi$
$151$	11.1702	+	19.3474i	0.909018	+	1.57447i	0.0935880	+	0.995611i	$0.470166\pi$
$152$	−6.97268	−	12.0770i	−0.565559	−	0.979577i
$153$	−3.41564	−	5.91607i	−0.276138	−	0.478286i
$154$	1.23161	+	3.87402i	0.0992459	+	0.312177i
$155$	16.2186			1.30271
$156$	0.853396	+	4.64195i	0.0683264	+	0.371654i
$157$	−0.329586	−	0.570859i	−0.0263038	−	0.0455595i	0.852574	−	0.522607i	$-0.175040\pi$
$157$	−0.329586	−	0.570859i	−0.0263038	−	0.0455595i	−0.878878	+	0.477047i	$0.841707\pi$
$158$	−2.56095	+	4.43569i	−0.203738	+	0.352885i
$159$	2.67895			0.212455
$160$	7.55887	−	13.0924i	0.597581	−	1.03504i
$161$	−2.26925	+	2.48830i	−0.178842	+	0.196106i
$162$	0.415625	−	0.719884i	0.0326546	−	0.0565595i
$163$	−9.09253	−	15.7487i	−0.712182	−	1.23354i	−0.964036	−	0.265771i	$-0.914374\pi$
$163$	−9.09253	−	15.7487i	−0.712182	−	1.23354i	0.251854	−	0.967765i	$-0.418960\pi$
$164$	−5.77591	−	10.0042i	−0.451023	−	0.781194i
$165$	4.83706			0.376565
$166$	7.21308			0.559844
$167$	−2.21154	−	3.83050i	−0.171134	−	0.296413i	0.767683	−	0.640830i	$-0.221410\pi$
$167$	−2.21154	−	3.83050i	−0.171134	−	0.296413i	−0.938817	+	0.344417i	$0.888076\pi$
$168$	−2.20488	−	6.93543i	−0.170110	−	0.535080i
$169$	2.07076	−	12.8340i	0.159289	−	0.987232i
$170$	7.43016	−	12.8694i	0.569867	−	0.987039i
$171$	−2.53494	+	4.39065i	−0.193852	+	0.335761i
$172$	−0.143467	+	0.248491i	−0.0109392	+	0.0189473i
$173$	−1.76022	−	3.04879i	−0.133827	−	0.231795i	0.791322	−	0.611400i	$-0.209393\pi$
$173$	−1.76022	−	3.04879i	−0.133827	−	0.231795i	−0.925149	+	0.379605i	$0.876060\pi$
$174$	−1.20448			−0.0913111
$175$	−4.77690	−	1.04710i	−0.361100	−	0.0791534i
$176$	0.306442	−	0.530773i	0.0230990	−	0.0400086i
$177$	−6.01804	+	10.4236i	−0.452344	+	0.783483i
$178$	12.5976			0.944232
$179$	−5.41014	+	9.37064i	−0.404373	+	0.700395i	−0.994248	−	0.107100i	$-0.965844\pi$
$179$	−5.41014	+	9.37064i	−0.404373	+	0.700395i	0.589875	+	0.807494i	$0.299177\pi$
$180$	−3.42563			−0.255331
$181$	−23.0651			−1.71441			−0.857207	−	0.514973i	$-0.827802\pi$
$181$	−23.0651			−1.71441			−0.857207	+	0.514973i	$0.827802\pi$
$182$	−0.269349	+	7.92505i	−0.0199655	+	0.587444i
$183$	8.72218			0.644762
$184$	−3.50115			−0.258109
$185$	−10.3087	+	17.8552i	−0.757910	+	1.31274i
$186$	5.15173			0.377743
$187$	6.31336	−	10.9351i	0.461678	−	0.799650i
$188$	−0.816850	+	1.41483i	−0.0595749	+	0.103187i
$189$	−1.78280	+	1.95490i	−0.129680	+	0.142198i
$190$	−11.0287			−0.800105
$191$	0.914829	+	1.58453i	0.0661947	+	0.114653i	0.897223	−	0.441577i	$-0.145581\pi$
$191$	0.914829	+	1.58453i	0.0661947	+	0.114653i	−0.831029	+	0.556230i	$0.812247\pi$
$192$	2.06944	−	3.58437i	0.149349	−	0.258680i
$193$	−1.57976	+	2.73622i	−0.113713	+	0.196957i	−0.917265	−	0.398278i	$-0.869608\pi$
$193$	−1.57976	+	2.73622i	−0.113713	+	0.196957i	0.803551	+	0.595235i	$0.202941\pi$
$194$	−5.05584	+	8.75697i	−0.362988	+	0.628714i
$195$	8.88974	+	3.16249i	0.636607	+	0.226471i
$196$	0.842029	+	9.12438i	0.0601450	+	0.651742i
$197$	5.57597	+	9.65786i	0.397271	+	0.688094i	0.993388	−	0.114804i	$-0.0366239\pi$
$197$	5.57597	+	9.65786i	0.397271	+	0.688094i	−0.596117	+	0.802898i	$0.703291\pi$
$198$	1.53646			0.109191
$199$	20.7497			1.47090			0.735452	−	0.677577i	$-0.236970\pi$
$199$	20.7497			1.47090			0.735452	+	0.677577i	$0.236970\pi$
$200$	−2.54208	−	4.40302i	−0.179752	−	0.311340i
$201$	6.91656	+	11.9798i	0.487856	+	0.844992i
$202$	−1.91024	+	3.30864i	−0.134404	+	0.232795i
$203$	3.74476	+	0.820855i	0.262831	+	0.0576127i
$204$	−4.47115	+	7.74426i	−0.313043	+	0.542207i
$205$	−23.0939			−1.61295
$206$	1.85044	−	3.20506i	0.128926	−	0.223307i
$207$	0.636428	+	1.10233i	0.0442348	+	0.0766170i
$208$	0.910213	−	0.775123i	0.0631119	−	0.0537451i
$209$	−9.37100			−0.648206
$210$	−5.62191	−	1.23233i	−0.387949	−	0.0850387i
$211$	8.16773	+	14.1469i	0.562289	+	0.973914i	0.997296	+	0.0734866i	$0.0234126\pi$
$211$	8.16773	+	14.1469i	0.562289	+	0.973914i	−0.435007	+	0.900427i	$0.643254\pi$
$212$	−1.75340	−	3.03698i	−0.120424	−	0.208581i
$213$	−1.78833	−	3.09749i	−0.122535	−	0.212236i
$214$	−5.99654			−0.409915
$215$	0.286812	+	0.496773i	0.0195604	+	0.0338796i
$216$	−2.75063			−0.187157
$217$	−16.0169	−	3.51092i	−1.08730	−	0.238337i
$218$	−3.61577	−	6.26270i	−0.244891	−	0.424163i
$219$	−6.53466			−0.441571
$220$	−3.16591	−	5.48351i	−0.213445	−	0.369698i
$221$	18.7523	−	15.9692i	1.26142	−	1.07420i
$222$	−3.27448	+	5.67156i	−0.219769	+	0.380650i
$223$	9.30867	+	16.1231i	0.623355	+	1.07968i	0.988857	+	0.148871i	$0.0475640\pi$
$223$	9.30867	+	16.1231i	0.623355	+	1.07968i	−0.365502	+	0.930811i	$0.619103\pi$
$224$	−10.2990	+	11.2932i	−0.688133	+	0.754560i
$225$	−0.924183	+	1.60073i	−0.0616122	+	0.106715i
$226$	−1.51726	+	2.62797i	−0.100926	+	0.174810i
$227$	−22.5455			−1.49639			−0.748197	−	0.663476i	$-0.769080\pi$
$227$	−22.5455			−1.49639			−0.748197	+	0.663476i	$0.769080\pi$
$228$	6.63659			0.439519
$229$	9.62713	−	16.6747i	0.636179	−	1.10189i	−0.350085	−	0.936718i	$-0.613847\pi$
$229$	9.62713	−	16.6747i	0.636179	−	1.10189i	0.986264	−	0.165176i	$-0.0528193\pi$
$230$	−1.38444	+	2.39793i	−0.0912875	+	0.158115i
$231$	−4.77690	−	1.04710i	−0.314297	−	0.0688942i
$232$	1.99282	+	3.45166i	0.130835	+	0.226613i
$233$	−11.4276	+	19.7933i	−0.748650	+	1.29670i	0.199820	+	0.979833i	$0.435964\pi$
$233$	−11.4276	+	19.7933i	−0.748650	+	1.29670i	−0.948470	+	0.316867i	$0.897369\pi$
$234$	2.82376	+	1.00454i	0.184595	+	0.0656689i
$235$	1.63301	+	2.82846i	0.106526	+	0.184508i
$236$	15.7555			1.02560
$237$	−3.08084	−	5.33616i	−0.200122	−	0.346621i
$238$	−10.1236	+	11.1009i	−0.656219	+	0.719565i
$239$	−11.2501			−0.727705			−0.363853	−	0.931457i	$-0.618539\pi$
$239$	−11.2501			−0.727705			−0.363853	+	0.931457i	$0.618539\pi$
$240$	0.433865	+	0.751475i	0.0280058	+	0.0485075i
$241$	19.4461			1.25263			0.626316	−	0.779569i	$-0.284562\pi$
$241$	19.4461			1.25263			0.626316	+	0.779569i	$0.284562\pi$
$242$	−3.15191	−	5.45928i	−0.202613	−	0.350936i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−5.70876	−	9.88787i	−0.365466	−	0.633006i
$245$	16.6389	+	7.66271i	1.06302	+	0.489552i
$246$	−7.33560			−0.467701
$247$	−17.2224	−	6.12680i	−1.09583	−	0.389839i
$248$	−8.52359	−	14.7633i	−0.541249	−	0.937470i
$249$	−4.33869	+	7.51483i	−0.274953	+	0.476233i
$250$	6.85585			0.433602
$251$	−8.79293	+	15.2298i	−0.555005	+	0.961297i	0.442898	+	0.896572i	$0.353950\pi$
$251$	−8.79293	+	15.2298i	−0.555005	+	0.961297i	−0.997903	+	0.0647248i	$0.979383\pi$
$252$	3.38302	+	0.741562i	0.213110	+	0.0467140i
$253$	−1.17635	+	2.03750i	−0.0739566	+	0.128097i
$254$	−3.99531	−	6.92009i	−0.250688	−	0.434205i
$255$	8.93852	+	15.4820i	0.559752	+	0.969519i
$256$	−15.0220			−0.938872
$257$	15.1872			0.947353			0.473677	−	0.880699i	$-0.342927\pi$
$257$	15.1872			0.947353			0.473677	+	0.880699i	$0.342927\pi$
$258$	0.0911037	+	0.157796i	0.00567187	+	0.00982396i
$259$	14.0457	−	15.4015i	0.872755	−	0.957005i
$260$	−2.23328	−	12.1477i	−0.138502	−	0.753368i
$261$	0.724496	−	1.25486i	0.0448452	−	0.0776741i
$262$	−6.88289	+	11.9215i	−0.425226	+	0.736514i
$263$	6.98496	−	12.0983i	0.430711	−	0.746014i	−0.566223	−	0.824252i	$-0.691596\pi$
$263$	6.98496	−	12.0983i	0.430711	−	0.746014i	0.996935	+	0.0782380i	$0.0249294\pi$
$264$	−2.54208	−	4.40302i	−0.156454	−	0.270987i
$265$	−7.01065			−0.430661
$266$	10.8915	+	2.38743i	0.667802	+	0.146383i
$267$	−7.57751	+	13.1246i	−0.463736	+	0.803215i
$268$	9.05393	−	15.6819i	0.553057	−	0.957922i
$269$	−28.9256			−1.76363			−0.881813	−	0.471600i	$-0.843677\pi$
$269$	−28.9256			−1.76363			−0.881813	+	0.471600i	$0.843677\pi$
$270$	−1.08767	+	1.88389i	−0.0661933	+	0.114650i
$271$	−10.1175			−0.614595			−0.307297	−	0.951614i	$-0.599425\pi$
$271$	−10.1175			−0.614595			−0.307297	+	0.951614i	$0.599425\pi$
$272$	2.26513			0.137344
$273$	−8.09457	−	5.04756i	−0.489906	−	0.305492i
$274$	8.77541			0.530142
$275$	−3.41646			−0.206020
$276$	0.833099	−	1.44297i	0.0501466	−	0.0868565i
$277$	3.40639			0.204670			0.102335	−	0.994750i	$-0.467369\pi$
$277$	3.40639			0.204670			0.102335	+	0.994750i	$0.467369\pi$
$278$	3.80504	−	6.59053i	0.228211	−	0.395274i
$279$	−3.09878	+	5.36725i	−0.185519	+	0.321329i
$280$	5.77003	+	18.1496i	0.344825	+	1.08465i
$281$	9.40331			0.560954			0.280477	−	0.959861i	$-0.409507\pi$
$281$	9.40331			0.560954			0.280477	+	0.959861i	$0.409507\pi$
$282$	0.518714	+	0.898438i	0.0308889	+	0.0535012i
$283$	−5.23950	+	9.07507i	−0.311456	+	0.539457i	−0.978678	−	0.205402i	$-0.934150\pi$
$283$	−5.23950	+	9.07507i	−0.311456	+	0.539457i	0.667222	+	0.744859i	$0.267483\pi$
$284$	−2.34097	+	4.05468i	−0.138911	+	0.240601i
$285$	6.63379	−	11.4901i	0.392952	−	0.680612i
$286$	1.00167	+	5.44846i	0.0592299	+	0.322174i
$287$	22.8067	+	4.99924i	1.34623	+	0.295096i
$288$	2.88844	+	5.00293i	0.170203	+	0.294800i
$289$	29.6664			1.74508
$290$	3.15204			0.185094
$291$	−6.08221	−	10.5347i	−0.356545	−	0.617554i
$292$	4.27701	+	7.40799i	0.250293	+	0.433520i
$293$	−4.61007	+	7.98488i	−0.269323	+	0.466481i	−0.968687	−	0.248284i	$-0.920133\pi$
$293$	−4.61007	+	7.98488i	−0.269323	+	0.466481i	0.699364	+	0.714766i	$0.253467\pi$
$294$	5.28522	+	2.43400i	0.308240	+	0.141954i
$295$	15.7489	−	27.2778i	0.916934	−	1.58818i
$296$	21.6706			1.25958
$297$	−0.924183	+	1.60073i	−0.0536265	+	0.0928839i
$298$	−4.53337	−	7.85203i	−0.262611	−	0.454856i
$299$	−3.49407	+	2.97550i	−0.202068	+	0.172077i
$300$	2.41955			0.139693
$301$	−0.175706	−	0.552682i	−0.0101275	−	0.0318561i
$302$	−9.28524	−	16.0825i	−0.534306	−	0.925445i
$303$	−2.29803	−	3.98031i	−0.132019	−	0.228663i
$304$	−0.840540	−	1.45586i	−0.0482083	−	0.0834992i
$305$	−22.8254			−1.30698
$306$	2.83926	+	4.91774i	0.162309	+	0.281128i
$307$	−16.1499			−0.921726			−0.460863	−	0.887471i	$-0.652460\pi$
$307$	−16.1499			−0.921726			−0.460863	+	0.887471i	$0.652460\pi$
$308$	1.93949	+	6.10065i	0.110513	+	0.347617i
$309$	2.22609	+	3.85570i	0.126638	+	0.219343i
$310$	−13.4818			−0.765712
$311$	15.2138	+	26.3510i	0.862694	+	1.49423i	0.869319	+	0.494252i	$0.164558\pi$
$311$	15.2138	+	26.3510i	0.862694	+	1.49423i	−0.00662478	+	0.999978i	$0.502109\pi$
$312$	−1.79323	−	9.75406i	−0.101522	−	0.552215i
$313$	−13.6859	+	23.7047i	−0.773574	+	1.33987i	0.162018	+	0.986788i	$0.448200\pi$
$313$	−13.6859	+	23.7047i	−0.773574	+	1.33987i	−0.935592	+	0.353082i	$0.885134\pi$
$314$	0.273968	+	0.474527i	0.0154609	+	0.0267791i
$315$	4.66548	−	5.11585i	0.262870	−	0.288245i
$316$	−4.03288	+	6.98516i	−0.226867	+	0.392946i
$317$	−6.18424	+	10.7114i	−0.347342	+	0.601613i	−0.985776	−	0.168063i	$-0.946249\pi$
$317$	−6.18424	+	10.7114i	−0.347342	+	0.601613i	0.638435	+	0.769676i	$0.279582\pi$
$318$	−2.22688			−0.124877
$319$	2.67827			0.149954
$320$	−5.41559	+	9.38008i	−0.302741	+	0.524362i
$321$	3.60694	−	6.24740i	0.201320	−	0.348696i
$322$	1.88632	−	2.06841i	0.105120	−	0.115268i
$323$	−17.3169	−	29.9938i	−0.963538	−	1.66890i
$324$	0.654511	−	1.13365i	0.0363617	−	0.0629803i
$325$	−6.27890	−	2.23369i	−0.348291	−	0.123903i
$326$	7.55818	+	13.0911i	0.418609	+	0.725052i
$327$	8.69959			0.481088
$328$	12.1368	+	21.0216i	0.670144	+	1.16072i
$329$	−1.00041	−	3.14678i	−0.0551544	−	0.173488i
$330$	−4.02081			−0.221338
$331$	6.20311	+	10.7441i	0.340954	+	0.590549i	0.984610	−	0.174766i	$-0.0559168\pi$
$331$	6.20311	+	10.7441i	0.340954	+	0.590549i	−0.643656	+	0.765315i	$0.722583\pi$
$332$	11.3589			0.623400
$333$	−3.93922	−	6.82292i	−0.215868	−	0.373894i
$334$	1.83834	+	3.18411i	0.100590	+	0.174226i
$335$	−18.1002	−	31.3505i	−0.988920	−	1.71286i
$336$	−0.265793	−	0.836050i	−0.0145002	−	0.0456103i
$337$	−15.8519			−0.863506			−0.431753	−	0.901992i	$-0.642105\pi$
$337$	−15.8519			−0.863506			−0.431753	+	0.901992i	$0.642105\pi$
$338$	−1.72132	+	10.6683i	−0.0936276	+	0.580278i
$339$	−1.82527	−	3.16146i	−0.0991351	−	0.171707i
$340$	11.7007	−	20.2662i	0.634561	−	1.09909i
$341$	−11.4554			−0.620343
$342$	2.10717	−	3.64973i	0.113943	−	0.197355i
$343$	−14.7732	−	11.1693i	−0.797676	−	0.603086i
$344$	0.301464	−	0.522151i	0.0162539	−	0.0281525i
$345$	−1.66549	−	2.88472i	−0.0896672	−	0.155308i
$346$	1.46318	+	2.53431i	0.0786613	+	0.136245i
$347$	−12.9304			−0.694142			−0.347071	−	0.937839i	$-0.612824\pi$
$347$	−12.9304			−0.694142			−0.347071	+	0.937839i	$0.612824\pi$
$348$	−1.89676			−0.101677
$349$	−1.67254	−	2.89693i	−0.0895292	−	0.155069i	0.817783	−	0.575527i	$-0.195203\pi$
$349$	−1.67254	−	2.89693i	−0.0895292	−	0.155069i	−0.907312	+	0.420458i	$0.861870\pi$
$350$	3.97080	+	0.870404i	0.212248	+	0.0465250i
$351$	−2.74506	+	2.33765i	−0.146521	+	0.124775i
$352$	−5.33890	+	9.24724i	−0.284564	+	0.492880i
$353$	−3.00732	+	5.20882i	−0.160063	+	0.277238i	−0.934891	−	0.354935i	$-0.884503\pi$
$353$	−3.00732	+	5.20882i	−0.160063	+	0.277238i	0.774828	+	0.632172i	$0.217836\pi$
$354$	5.00251	−	8.66459i	0.265880	−	0.460518i
$355$	4.67996	+	8.10593i	0.248387	+	0.430218i
$356$	19.8383			1.05143
$357$	−5.47590	−	17.2244i	−0.289815	−	0.911611i
$358$	4.49719	−	7.78936i	0.237684	−	0.411680i
$359$	7.44965	−	12.9032i	0.393177	−	0.681003i	−0.599689	−	0.800233i	$-0.704709\pi$
$359$	7.44965	−	12.9032i	0.393177	−	0.681003i	0.992867	+	0.119230i	$0.0380425\pi$
$360$	7.19822			0.379380
$361$	−3.35186	+	5.80559i	−0.176414	+	0.305557i
$362$	19.1729			1.00770
$363$	7.58354			0.398033
$364$	−0.424161	+	12.4801i	−0.0222321	+	0.654133i
$365$	17.1008			0.895097
$366$	−7.25032			−0.378981
$367$	4.04076	−	6.99881i	0.210926	−	0.365335i	−0.741078	−	0.671418i	$-0.765685\pi$
$367$	4.04076	−	6.99881i	0.210926	−	0.365335i	0.952005	+	0.306084i	$0.0990187\pi$
$368$	−0.422056			−0.0220012
$369$	4.41239	−	7.64248i	0.229700	−	0.397852i
$370$	8.56911	−	14.8421i	0.445487	−	0.771605i
$371$	6.92345	+	1.51763i	0.359448	+	0.0787913i
$372$	8.11274			0.420626
$373$	5.63854	+	9.76624i	0.291953	+	0.505677i	0.974271	−	0.225378i	$-0.0723617\pi$
$373$	5.63854	+	9.76624i	0.291953	+	0.505677i	−0.682319	+	0.731055i	$0.739028\pi$
$374$	−5.24798	+	9.08977i	−0.271367	+	0.470021i
$375$	−4.12382	+	7.14266i	−0.212953	+	0.368845i
$376$	1.71643	−	2.97295i	0.0885184	−	0.153318i
$377$	4.92222	+	1.75106i	0.253507	+	0.0901843i
$378$	1.48195	−	1.62501i	0.0762235	−	0.0835815i
$379$	−8.94558	−	15.4942i	−0.459504	−	0.795884i	0.539431	−	0.842030i	$-0.318639\pi$
$379$	−8.94558	−	15.4942i	−0.459504	−	0.795884i	−0.998935	+	0.0461461i	$0.985306\pi$
$380$	−17.3675			−0.890936
$381$	9.61278			0.492477
$382$	−0.760453	−	1.31714i	−0.0389081	−	0.0673909i
$383$	−0.0190547	−	0.0330037i	−0.000973650	−	0.00168641i	0.865538	−	0.500843i	$-0.166977\pi$
$383$	−0.0190547	−	0.0330037i	−0.000973650	−	0.00168641i	−0.866512	+	0.499157i	$0.833643\pi$
$384$	4.05666	−	7.02634i	0.207016	−	0.358562i
$385$	12.5009	+	2.74020i	0.637102	+	0.139653i
$386$	1.31317	−	2.27448i	0.0668388	−	0.115768i
$387$	−0.219197			−0.0111424
$388$	−7.96174	+	13.7901i	−0.404196	+	0.700088i
$389$	19.5855	+	33.9231i	0.993025	+	1.71997i	0.598622	+	0.801032i	$0.295715\pi$
$389$	19.5855	+	33.9231i	0.993025	+	1.71997i	0.394403	+	0.918938i	$0.370951\pi$
$390$	−7.38960	−	2.62882i	−0.374187	−	0.133116i
$391$	−8.69525			−0.439737
$392$	−1.76934	−	19.1729i	−0.0893654	−	0.968379i
$393$	−8.28016	−	14.3417i	−0.417679	−	0.723441i
$394$	−4.63503	−	8.02811i	−0.233509	−	0.404450i
$395$	8.06236	+	13.9644i	0.405661	+	0.702626i
$396$	2.41955			0.121587
$397$	−4.36570	−	7.56162i	−0.219108	−	0.379507i	0.735427	−	0.677604i	$-0.236981\pi$
$397$	−4.36570	−	7.56162i	−0.219108	−	0.379507i	−0.954536	+	0.298097i	$0.903648\pi$
$398$	−17.2482			−0.864573
$399$	−9.03859	+	9.91110i	−0.452495	+	0.496176i
$400$	−0.306442	−	0.530773i	−0.0153221	−	0.0265387i
$401$	24.2837			1.21267			0.606336	−	0.795208i	$-0.292639\pi$
$401$	24.2837			1.21267			0.606336	+	0.795208i	$0.292639\pi$
$402$	−5.74940	−	9.95825i	−0.286754	−	0.496672i
$403$	−21.0531	−	7.48956i	−1.04873	−	0.373082i
$404$	−3.00818	+	5.21031i	−0.149662	+	0.259223i
$405$	−1.30847	−	2.26634i	−0.0650184	−	0.112615i
$406$	−3.11284	−	0.682337i	−0.154487	−	0.0338638i
$407$	7.28111	−	12.6113i	0.360911	−	0.625117i
$408$	9.39516	−	16.2729i	0.465130	−	0.805628i
$409$	−19.7226			−0.975221			−0.487610	−	0.873061i	$-0.662131\pi$
$409$	−19.7226			−0.975221			−0.487610	+	0.873061i	$0.662131\pi$
$410$	19.1968			0.948063
$411$	−5.27844	+	9.14252i	−0.260366	+	0.450967i
$412$	2.91400	−	5.04720i	0.143563	−	0.248658i
$413$	−21.4579	+	23.5293i	−1.05588	+	1.15780i
$414$	−0.529032	−	0.916310i	−0.0260005	−	0.0450342i
$415$	11.3541	−	19.6659i	0.557350	−	0.965359i
$416$	−15.8579	+	13.5043i	−0.777498	+	0.662105i
$417$	4.57749	+	7.92845i	0.224161	+	0.388258i
$418$	7.78965			0.381004
$419$	11.0976	+	19.2216i	0.542154	+	0.939039i	0.998780	+	0.0493798i	$0.0157245\pi$
$419$	11.0976	+	19.2216i	0.542154	+	0.939039i	−0.456626	+	0.889659i	$0.650942\pi$
$420$	−8.85317	−	1.94062i	−0.431990	−	0.0946927i
$421$	−1.85475			−0.0903949			−0.0451974	−	0.998978i	$-0.514392\pi$
$421$	−1.85475			−0.0903949			−0.0451974	+	0.998978i	$0.514392\pi$
$422$	−6.78943	−	11.7596i	−0.330504	−	0.572450i
$423$	−1.24803			−0.0606814
$424$	3.68440	+	6.38156i	0.178930	+	0.309916i
$425$	−6.31336	−	10.9351i	−0.306243	−	0.530428i
$426$	1.48655	+	2.57479i	0.0720238	+	0.124749i
$427$	22.5415	+	4.94112i	1.09086	+	0.239118i
$428$	−9.44312			−0.456450
$429$	−6.27890	−	2.23369i	−0.303148	−	0.107844i
$430$	−0.238413	−	0.412943i	−0.0114973	−	0.0199139i
$431$	18.8935	−	32.7246i	0.910069	−	1.57629i	0.0961051	−	0.995371i	$-0.469362\pi$
$431$	18.8935	−	32.7246i	0.910069	−	1.57629i	0.813964	−	0.580915i	$-0.197305\pi$
$432$	−0.331582			−0.0159532
$433$	17.5680	−	30.4286i	0.844263	−	1.46231i	−0.0419959	−	0.999118i	$-0.513372\pi$
$433$	17.5680	−	30.4286i	0.844263	−	1.46231i	0.886259	−	0.463189i	$-0.153295\pi$
$434$	13.3141	+	2.91846i	0.639096	+	0.140091i
$435$	−1.89596	+	3.28390i	−0.0909044	+	0.157451i
$436$	−5.69397	−	9.86225i	−0.272692	−	0.472316i
$437$	3.22662	+	5.58867i	0.154350	+	0.267342i
$438$	5.43194			0.259548
$439$	15.3475			0.732496			0.366248	−	0.930517i	$-0.380642\pi$
$439$	15.3475			0.732496			0.366248	+	0.930517i	$0.380642\pi$
$440$	6.65247	+	11.5224i	0.317144	+	0.549310i
$441$	−5.71490	+	4.04226i	−0.272138	+	0.192489i
$442$	−15.5879	+	13.2744i	−0.741440	+	0.631398i
$443$	−14.5356	+	25.1765i	−0.690609	+	1.19617i	0.281030	+	0.959699i	$0.409324\pi$
$443$	−14.5356	+	25.1765i	−0.690609	+	1.19617i	−0.971639	+	0.236471i	$0.924009\pi$
$444$	−5.15652	+	8.93136i	−0.244718	+	0.423863i
$445$	19.8299	−	34.3464i	0.940027	−	1.62817i
$446$	−7.73784	−	13.4023i	−0.366397	−	0.634619i
$447$	10.9073			0.515900
$448$	7.37879	−	8.09108i	0.348615	−	0.382268i
$449$	−1.18131	+	2.04609i	−0.0557494	+	0.0965607i	−0.892553	−	0.450942i	$-0.851088\pi$
$449$	−1.18131	+	2.04609i	−0.0557494	+	0.0965607i	0.836804	+	0.547503i	$0.184421\pi$
$450$	0.768228	−	1.33061i	0.0362146	−	0.0627255i
$451$	16.3114			0.768074
$452$	−2.38932	+	4.13842i	−0.112384	+	0.194655i
$453$	22.3404			1.04964
$454$	18.7409			0.879555
$455$	21.1830	+	13.2092i	0.993074	+	0.619255i
$456$	−13.9454			−0.653051
$457$	−16.7534			−0.783692			−0.391846	−	0.920031i	$-0.628163\pi$
$457$	−16.7534			−0.783692			−0.391846	+	0.920031i	$0.628163\pi$
$458$	−8.00257	+	13.8608i	−0.373935	+	0.647675i
$459$	−6.83128			−0.318857
$460$	−2.18017	+	3.77616i	−0.101651	+	0.176064i
$461$	12.5469	−	21.7318i	0.584366	−	1.01215i	−0.410588	−	0.911821i	$-0.634677\pi$
$461$	12.5469	−	21.7318i	0.584366	−	1.01215i	0.994954	−	0.100330i	$-0.0319900\pi$
$462$	3.97080	+	0.870404i	0.184738	+	0.0404948i
$463$	−0.254256			−0.0118163			−0.00590815	−	0.999983i	$-0.501881\pi$
$463$	−0.254256			−0.0118163			−0.00590815	+	0.999983i	$0.501881\pi$
$464$	0.240230	+	0.416090i	0.0111524	+	0.0193165i
$465$	8.10932	−	14.0457i	0.376061	−	0.651356i
$466$	9.49924	−	16.4532i	0.440044	−	0.762178i
$467$	−5.11155	+	8.85346i	−0.236534	+	0.409689i	−0.959717	−	0.280967i	$-0.909345\pi$
$467$	−5.11155	+	8.85346i	−0.236534	+	0.409689i	0.723183	+	0.690656i	$0.242678\pi$
$468$	4.44675	+	1.58191i	0.205551	+	0.0731240i
$469$	11.0885	+	34.8788i	0.512020	+	1.61055i
$470$	−1.35744	−	2.35116i	−0.0626141	−	0.108451i
$471$	−0.659171			−0.0303730
$472$	−33.1068			−1.52386
$473$	−0.202578	−	0.350875i	−0.00931453	−	0.0161332i
$474$	2.56095	+	4.43569i	0.117628	+	0.203738i
$475$	−4.68550	+	8.11552i	−0.214985	+	0.372366i
$476$	−15.9423	+	17.4813i	−0.730715	+	0.801253i
$477$	1.33947	−	2.32004i	0.0613303	−	0.106227i
$478$	9.35162			0.427733
$479$	6.35400	−	11.0055i	0.290322	−	0.502852i	−0.683564	−	0.729891i	$-0.739571\pi$
$479$	6.35400	−	11.0055i	0.290322	−	0.502852i	0.973886	+	0.227039i	$0.0729043\pi$
$480$	−7.55887	−	13.0924i	−0.345014	−	0.597581i
$481$	21.6268	−	18.4170i	0.986098	−	0.839745i
$482$	−16.1646			−0.736277
$483$	1.02031	+	3.20938i	0.0464258	+	0.146032i
$484$	−4.96351	−	8.59706i	−0.225614	−	0.390775i
$485$	15.9168	+	27.5686i	0.722743	+	1.25183i
$486$	−0.415625	−	0.719884i	−0.0188532	−	0.0326546i
$487$	20.4820			0.928126			0.464063	−	0.885802i	$-0.346391\pi$
$487$	20.4820			0.928126			0.464063	+	0.885802i	$0.346391\pi$
$488$	11.9957	+	20.7772i	0.543022	+	0.940541i
$489$	−18.1851			−0.822357
$490$	−13.8311	−	6.36963i	−0.624825	−	0.287751i
$491$	−9.92098	−	17.1836i	−0.447727	−	0.775487i	0.550510	−	0.834828i	$-0.314433\pi$
$491$	−9.92098	−	17.1836i	−0.447727	−	0.775487i	−0.998238	+	0.0593417i	$0.981100\pi$
$492$	−11.5518			−0.520796
$493$	4.94924	+	8.57233i	0.222902	+	0.386078i
$494$	14.3161	+	5.09291i	0.644113	+	0.229141i
$495$	2.41853	−	4.18902i	0.108705	−	0.188282i
$496$	−1.02750	−	1.77968i	−0.0461361	−	0.0799100i
$497$	−2.86703	−	9.01821i	−0.128604	−	0.404522i
$498$	3.60654	−	6.24671i	0.161613	−	0.279922i
$499$	−13.9419	+	24.1480i	−0.624124	+	1.08101i	0.364585	+	0.931170i	$0.381211\pi$
$499$	−13.9419	+	24.1480i	−0.624124	+	1.08101i	−0.988710	+	0.149845i	$0.952123\pi$
$500$	10.7963			0.482827
$501$	−4.42308			−0.197609
$502$	7.30913	−	12.6598i	0.326223	−	0.565034i
$503$	6.62277	−	11.4710i	0.295295	−	0.511465i	−0.679759	−	0.733436i	$-0.737916\pi$
$503$	6.62277	−	11.4710i	0.295295	−	0.511465i	0.975053	+	0.221970i	$0.0712489\pi$
$504$	−7.10870	−	1.55823i	−0.316647	−	0.0694092i
$505$	6.01381	+	10.4162i	0.267611	+	0.463516i
$506$	0.977844	−	1.69368i	0.0434705	−	0.0752931i
$507$	−10.0792	−	8.21034i	−0.447633	−	0.364634i
$508$	−6.29167	−	10.8975i	−0.279148	−	0.483498i
$509$	27.0750			1.20008			0.600040	−	0.799970i	$-0.295151\pi$
$509$	27.0750			1.20008			0.600040	+	0.799970i	$0.295151\pi$
$510$	−7.43016	−	12.8694i	−0.329013	−	0.569867i
$511$	−16.8881	−	3.70189i	−0.747086	−	0.163762i
$512$	−3.73962			−0.165270
$513$	2.53494	+	4.39065i	0.111920	+	0.193852i
$514$	−12.6244			−0.556838
$515$	−5.82554	−	10.0901i	−0.256704	−	0.444625i
$516$	0.143467	+	0.248491i	0.00631576	+	0.0109392i
$517$	−1.15341	−	1.99776i	−0.0507269	−	0.0878615i
$518$	−11.6755	+	12.8025i	−0.512991	+	0.562511i
$519$	−3.52044			−0.154530
$520$	4.69277	+	25.5258i	0.205791	+	1.11938i
$521$	−11.6257	−	20.1363i	−0.509331	−	0.882187i	−0.999942	−	0.0108082i	$-0.996560\pi$
$521$	−11.6257	−	20.1363i	−0.509331	−	0.882187i	0.490611	−	0.871379i	$-0.336774\pi$
$522$	−0.602238	+	1.04311i	−0.0263592	+	0.0456555i
$523$	33.5380			1.46651			0.733256	−	0.679952i	$-0.237999\pi$
$523$	33.5380			1.46651			0.733256	+	0.679952i	$0.237999\pi$
$524$	−10.8389	+	18.7735i	−0.473500	+	0.820126i
$525$	−3.29527	+	3.61337i	−0.143817	+	0.157700i
$526$	−5.80626	+	10.0567i	−0.253165	+	0.438494i
$527$	−21.1686	−	36.6652i	−0.922121	−	1.59716i
$528$	−0.306442	−	0.530773i	−0.0133362	−	0.0230990i
$529$	−21.3798			−0.929558
$530$	5.82761			0.253135
$531$	6.01804	+	10.4236i	0.261161	+	0.452344i
$532$	17.1515	+	3.75963i	0.743614	+	0.163001i
$533$	29.9777	+	10.6645i	1.29848	+	0.461929i
$534$	6.29881	−	10.9099i	0.272576	−	0.472116i
$535$	−9.43913	+	16.3491i	−0.408089	+	0.706831i
$536$	−19.0249	+	32.9521i	−0.821750	+	1.42331i
$537$	5.41014	+	9.37064i	0.233465	+	0.404373i
$538$	24.0444			1.03663
$539$	−11.7522	−	5.41224i	−0.506203	−	0.233122i
$540$	−1.71281	+	2.96668i	−0.0737078	+	0.127666i
$541$	−4.65598	+	8.06439i	−0.200176	+	0.346715i	−0.948585	−	0.316522i	$-0.897485\pi$
$541$	−4.65598	+	8.06439i	−0.200176	+	0.346715i	0.748409	+	0.663238i	$0.230818\pi$
$542$	8.41019			0.361248
$543$	−11.5325	+	19.9749i	−0.494908	+	0.857207i
$544$	−39.4635			−1.69198
$545$	−22.7663			−0.975200
$546$	6.72862	+	4.19579i	0.287958	+	0.179563i
$547$	−31.5111			−1.34732			−0.673658	−	0.739043i	$-0.735278\pi$
$547$	−31.5111			−1.34732			−0.673658	+	0.739043i	$0.735278\pi$
$548$	13.8192			0.590326
$549$	4.36109	−	7.55363i	0.186127	−	0.322381i
$550$	2.83993			0.121095
$551$	3.67311	−	6.36201i	0.156480	−	0.271031i
$552$	−1.75058	+	3.03209i	−0.0745095	+	0.129054i
$553$	−4.93914	−	15.5360i	−0.210034	−	0.660659i
$554$	−2.83157			−0.120302
$555$	10.3087	+	17.8552i	0.437579	+	0.757910i
$556$	5.99203	−	10.3785i	0.254119	−	0.440147i
$557$	−2.76650	+	4.79172i	−0.117220	+	0.203032i	−0.918665	−	0.395037i	$-0.870732\pi$
$557$	−2.76650	+	4.79172i	−0.117220	+	0.203032i	0.801445	+	0.598069i	$0.204065\pi$
$558$	2.57586	−	4.46153i	0.109045	−	0.188872i
$559$	−0.142902	−	0.777298i	−0.00604410	−	0.0328762i
$560$	0.695564	+	2.18789i	0.0293929	+	0.0924553i
$561$	−6.31336	−	10.9351i	−0.266550	−	0.461678i
$562$	−7.81651			−0.329720
$563$	12.3688			0.521281			0.260641	−	0.965436i	$-0.416066\pi$
$563$	12.3688			0.521281			0.260641	+	0.965436i	$0.416066\pi$
$564$	0.816850	+	1.41483i	0.0343956	+	0.0595749i
$565$	4.77662	+	8.27335i	0.200954	+	0.348062i
$566$	4.35534	−	7.54366i	0.183068	−	0.317084i
$567$	0.801591	+	2.52140i	0.0336637	+	0.105889i
$568$	4.91904	−	8.52003i	0.206398	−	0.357493i
$569$	1.99446			0.0836120			0.0418060	−	0.999126i	$-0.486689\pi$
$569$	1.99446			0.0836120			0.0418060	+	0.999126i	$0.486689\pi$
$570$	−5.51434	+	9.55112i	−0.230970	+	0.400052i
$571$	−11.0440	−	19.1288i	−0.462179	−	0.800517i	0.536891	−	0.843652i	$-0.319599\pi$
$571$	−11.0440	−	19.1288i	−0.462179	−	0.800517i	−0.999069	+	0.0431350i	$0.986265\pi$
$572$	1.57739	+	8.58002i	0.0659539	+	0.358749i
$573$	1.82966			0.0764351
$574$	−18.9581	−	4.15562i	−0.791294	−	0.173452i
$575$	1.17635	+	2.03750i	0.0490573	+	0.0849697i
$576$	−2.06944	−	3.58437i	−0.0862266	−	0.149349i
$577$	−4.54321	−	7.86907i	−0.189136	−	0.327594i	0.755826	−	0.654772i	$-0.227235\pi$
$577$	−4.54321	−	7.86907i	−0.189136	−	0.327594i	−0.944963	+	0.327179i	$0.893902\pi$
$578$	−24.6603			−1.02573
$579$	1.57976	+	2.73622i	0.0656525	+	0.113713i
$580$	4.96371			0.206107
$581$	−15.4700	+	16.9634i	−0.641805	+	0.703760i
$582$	5.05584	+	8.75697i	0.209571	+	0.362988i
$583$	4.95168			0.205078
$584$	−8.98721	−	15.5663i	−0.371893	−	0.644138i
$585$	7.18367	−	6.11749i	0.297008	−	0.252927i
$586$	3.83213	−	6.63744i	0.158304	−	0.274190i
$587$	−3.02112	−	5.23273i	−0.124695	−	0.215978i	0.796919	−	0.604086i	$-0.206462\pi$
$587$	−3.02112	−	5.23273i	−0.124695	−	0.215978i	−0.921614	+	0.388109i	$0.873128\pi$
$588$	8.32296	+	3.83297i	0.343233	+	0.158069i
$589$	−15.7105	+	27.2113i	−0.647338	+	1.12122i
$590$	−13.0912	+	22.6747i	−0.538958	+	0.933503i
$591$	11.1519			0.458729
$592$	2.61234			0.107367
$593$	−6.67095	+	11.5544i	−0.273943	+	0.474484i	−0.969868	−	0.243631i	$-0.921661\pi$
$593$	−6.67095	+	11.5544i	−0.273943	+	0.474484i	0.695925	+	0.718115i	$0.254995\pi$
$594$	0.768228	−	1.33061i	0.0315208	−	0.0545956i
$595$	14.3301	+	45.0752i	0.587476	+	1.84790i
$596$	−7.13898	−	12.3651i	−0.292424	−	0.506493i
$597$	10.3748	−	17.9697i	0.424614	−	0.735452i
$598$	2.90445	−	2.47338i	0.118772	−	0.101144i
$599$	−15.0725	−	26.1063i	−0.615844	−	1.06667i	−0.990236	−	0.139402i	$-0.955482\pi$
$599$	−15.0725	−	26.1063i	−0.615844	−	1.06667i	0.374392	−	0.927270i	$-0.377851\pi$
$600$	−5.08417			−0.207560
$601$	−18.9159	−	32.7634i	−0.771598	−	1.33645i	−0.936687	−	0.350168i	$-0.886125\pi$
$601$	−18.9159	−	32.7634i	−0.771598	−	1.33645i	0.165089	−	0.986279i	$-0.447209\pi$
$602$	0.146056	+	0.459417i	0.00595279	+	0.0187245i
$603$	13.8331			0.563328
$604$	−14.6220	−	25.3261i	−0.594962	−	1.03051i
$605$	−19.8457			−0.806841
$606$	1.91024	+	3.30864i	0.0775983	+	0.134404i
$607$	−3.35449	−	5.81015i	−0.136155	−	0.235827i	0.789883	−	0.613257i	$-0.210141\pi$
$607$	−3.35449	−	5.81015i	−0.136155	−	0.235827i	−0.926038	+	0.377430i	$0.876808\pi$
$608$	14.6441	+	25.3643i	0.593895	+	1.02866i
$609$	2.58326	−	2.83263i	0.104679	−	0.114784i
$610$	18.9737			0.768221
$611$	−0.813634	−	4.42567i	−0.0329161	−	0.179043i
$612$	4.47115	+	7.74426i	0.180736	+	0.313043i
$613$	10.0836	−	17.4653i	0.407272	−	0.705416i	−0.587311	−	0.809362i	$-0.699813\pi$
$613$	10.0836	−	17.4653i	0.407272	−	0.705416i	0.994583	+	0.103945i	$0.0331467\pi$
$614$	13.4247			0.541775
$615$	−11.5469	+	19.9999i	−0.465618	+	0.806474i
$616$	−4.07542	−	12.8192i	−0.164203	−	0.516501i
$617$	−2.98249	+	5.16582i	−0.120071	+	0.207968i	−0.919795	−	0.392399i	$-0.871645\pi$
$617$	−2.98249	+	5.16582i	−0.120071	+	0.207968i	0.799725	+	0.600367i	$0.204979\pi$
$618$	−1.85044	−	3.20506i	−0.0744356	−	0.128926i
$619$	4.31420	+	7.47242i	0.173402	+	0.300342i	0.939607	−	0.342255i	$-0.111191\pi$
$619$	4.31420	+	7.47242i	0.173402	+	0.300342i	−0.766205	+	0.642596i	$0.777857\pi$
$620$	−21.2305			−0.852639
$621$	1.27286			0.0510780
$622$	−12.6465	−	21.9043i	−0.507077	−	0.878283i
$623$	−27.0184	+	29.6265i	−1.08247	+	1.18696i
$624$	−0.216169	−	1.17583i	−0.00865370	−	0.0470708i
$625$	15.4127	−	26.6956i	0.616507	−	1.06782i
$626$	11.3764	−	19.7046i	0.454694	−	0.787553i
$627$	−4.68550	+	8.11552i	−0.187121	+	0.324103i
$628$	0.431435	+	0.747267i	0.0172161	+	0.0298192i
$629$	53.8198			2.14594
$630$	−3.87818	+	4.25255i	−0.154510	+	0.169426i
$631$	−1.02888	+	1.78208i	−0.0409592	+	0.0709434i	−0.885778	−	0.464109i	$-0.846375\pi$
$631$	−1.02888	+	1.78208i	−0.0409592	+	0.0709434i	0.844819	+	0.535052i	$0.179708\pi$
$632$	8.47423	−	14.6778i	0.337087	−	0.583852i
$633$	16.3355			0.649276
$634$	5.14066	−	8.90388i	0.204162	−	0.353618i
$635$	−25.1560			−0.998287
$636$	−3.50680			−0.139054
$637$	−18.0601	−	17.6305i	−0.715567	−	0.698544i
$638$	−2.22631			−0.0881405
$639$	−3.57667			−0.141491
$640$	−10.6160	+	18.3875i	−0.419635	+	0.726830i
$641$	−17.6623			−0.697618			−0.348809	−	0.937194i	$-0.613414\pi$
$641$	−17.6623			−0.697618			−0.348809	+	0.937194i	$0.613414\pi$
$642$	−2.99827	+	5.19316i	−0.118332	+	0.204957i
$643$	−24.6023	+	42.6124i	−0.970219	+	1.68047i	−0.275334	+	0.961349i	$0.588788\pi$
$643$	−24.6023	+	42.6124i	−0.970219	+	1.68047i	−0.694885	+	0.719121i	$0.744545\pi$
$644$	2.97050	−	3.25725i	0.117054	−	0.128353i
$645$	0.573624			0.0225864
$646$	14.3947	+	24.9323i	0.566352	+	0.980950i
$647$	7.74797	−	13.4199i	0.304604	−	0.527590i	−0.672569	−	0.740034i	$-0.734809\pi$
$647$	7.74797	−	13.4199i	0.304604	−	0.527590i	0.977173	+	0.212445i	$0.0681426\pi$
$648$	−1.37531	+	2.38211i	−0.0540274	+	0.0935783i
$649$	−11.1235	+	19.2666i	−0.436637	+	0.756278i
$650$	5.21934	+	1.85676i	0.204719	+	0.0728281i
$651$	−11.0490	+	12.1156i	−0.433045	+	0.474848i
$652$	11.9023	+	20.6154i	0.466131	+	0.807363i
$653$	−36.7330			−1.43748			−0.718738	−	0.695281i	$-0.755280\pi$
$653$	−36.7330			−1.43748			−0.718738	+	0.695281i	$0.755280\pi$
$654$	−7.23154			−0.282776
$655$	21.6687	+	37.5312i	0.846665	+	1.46647i
$656$	1.46307	+	2.53411i	0.0571232	+	0.0989402i
$657$	−3.26733	+	5.65918i	−0.127471	+	0.220786i
$658$	0.831593	+	2.61577i	0.0324189	+	0.101973i
$659$	−5.48070	+	9.49284i	−0.213498	+	0.369789i	−0.952807	−	0.303577i	$-0.901819\pi$
$659$	−5.48070	+	9.49284i	−0.213498	+	0.369789i	0.739309	+	0.673366i	$0.235152\pi$
$660$	−6.33182			−0.246466
$661$	−8.03552	+	13.9179i	−0.312545	+	0.541344i	−0.978913	−	0.204279i	$-0.934515\pi$
$661$	−8.03552	+	13.9179i	−0.312545	+	0.541344i	0.666367	+	0.745624i	$0.267848\pi$
$662$	−5.15634	−	8.93104i	−0.200407	−	0.347115i
$663$	−4.45355	−	24.2246i	−0.172961	−	0.940804i
$664$	−23.8682			−0.926268
$665$	23.6534	−	25.9367i	0.917240	−	1.00578i
$666$	3.27448	+	5.67156i	0.126883	+	0.219769i
$667$	−0.922180	−	1.59726i	−0.0357069	−	0.0618462i
$668$	2.89495	+	5.01421i	0.112009	+	0.194005i
$669$	18.6173			0.719788
$670$	15.0458	+	26.0601i	0.581271	+	1.00679i
$671$	16.1218			0.622375
$672$	4.63070	+	14.5658i	0.178633	+	0.561889i
$673$	14.1074	+	24.4348i	0.543802	+	0.941892i	0.998681	+	0.0513390i	$0.0163489\pi$
$673$	14.1074	+	24.4348i	0.543802	+	0.941892i	−0.454880	+	0.890553i	$0.650318\pi$
$674$	13.1769			0.507554
$675$	0.924183	+	1.60073i	0.0355718	+	0.0616122i
$676$	−2.71067	+	16.8000i	−0.104257	+	0.646154i
$677$	17.5358	−	30.3729i	0.673956	−	1.16733i	−0.302817	−	0.953049i	$-0.597927\pi$
$677$	17.5358	−	30.3729i	0.673956	−	1.16733i	0.976773	−	0.214277i	$-0.0687395\pi$
$678$	1.51726	+	2.62797i	0.0582699	+	0.100926i
$679$	−9.75089	−	30.6713i	−0.374205	−	1.17706i
$680$	−24.5866	+	42.5852i	−0.942851	+	1.63307i
$681$	−11.2727	+	19.5249i	−0.431972	+	0.748197i
$682$	9.52228			0.364627
$683$	48.3832			1.85133			0.925666	−	0.378341i	$-0.123505\pi$
$683$	48.3832			1.85133			0.925666	+	0.378341i	$0.123505\pi$
$684$	3.31829	−	5.74745i	0.126878	−	0.219759i
$685$	13.8133	−	23.9254i	0.527781	−	0.914143i
$686$	12.2802	+	9.28450i	0.468861	+	0.354484i
$687$	−9.62713	−	16.6747i	−0.367298	−	0.636179i
$688$	0.0363408	−	0.0629441i	0.00138548	−	0.00239972i
$689$	9.10039	+	3.23743i	0.346697	+	0.123336i
$690$	1.38444	+	2.39793i	0.0527049	+	0.0912875i
$691$	−24.1060			−0.917035			−0.458518	−	0.888685i	$-0.651619\pi$
$691$	−24.1060			−0.917035			−0.458518	+	0.888685i	$0.651619\pi$
$692$	2.30417	+	3.99093i	0.0875913	+	0.151713i
$693$	−3.29527	+	3.61337i	−0.125177	+	0.137260i
$694$	10.7484			0.408005
$695$	−11.9790	−	20.7483i	−0.454390	−	0.787026i
$696$	3.98564			0.151075
$697$	30.1423	+	52.2079i	1.14172	+	1.97752i
$698$	1.39030	+	2.40808i	0.0526238	+	0.0911470i
$699$	11.4276	+	19.7933i	0.432233	+	0.748650i
$700$	6.25307	+	1.37068i	0.236344	+	0.0518068i
$701$	−3.07792			−0.116251			−0.0581257	−	0.998309i	$-0.518512\pi$
$701$	−3.07792			−0.116251			−0.0581257	+	0.998309i	$0.518512\pi$
$702$	2.28184	−	1.94318i	0.0861224	−	0.0733404i
$703$	−19.9714	−	34.5914i	−0.753235	−	1.30464i
$704$	3.82508	−	6.62523i	0.144163	−	0.249698i
$705$	3.26602			0.123005
$706$	2.49983	−	4.32984i	0.0940825	−	0.162956i
$707$	−3.68417	−	11.5885i	−0.138557	−	0.435831i
$708$	7.87775	−	13.6447i	0.296064	−	0.512798i
$709$	−17.9722	−	31.1287i	−0.674959	−	1.16906i	−0.976481	−	0.215604i	$-0.930828\pi$
$709$	−17.9722	−	31.1287i	−0.674959	−	1.16906i	0.301522	−	0.953459i	$-0.402505\pi$
$710$	−3.89022	−	6.73806i	−0.145997	−	0.252875i
$711$	−6.16167			−0.231081
$712$	−41.6858			−1.56224
$713$	3.94430	+	6.83173i	0.147715	+	0.255850i
$714$	4.55185	+	14.3178i	0.170349	+	0.535830i
$715$	16.4315	+	5.84544i	0.614503	+	0.218607i
$716$	7.08200	−	12.2664i	0.264667	−	0.458416i
$717$	−5.62503	+	9.74283i	−0.210070	+	0.363853i
$718$	−6.19253	+	10.7258i	−0.231103	+	0.400282i
$719$	−5.09760	−	8.82930i	−0.190108	−	0.329278i	0.755178	−	0.655520i	$-0.227551\pi$
$719$	−5.09760	−	8.82930i	−0.190108	−	0.329278i	−0.945286	+	0.326243i	$0.894217\pi$
$720$	0.867729			0.0323384
$721$	3.56883	+	11.2257i	0.132910	+	0.418068i
$722$	2.78624	−	4.82590i	0.103693	−	0.179602i
$723$	9.72305	−	16.8408i	0.361604	−	0.626316i
$724$	30.1927			1.12210
$725$	1.33913	−	2.31945i	0.0497342	−	0.0861421i
$726$	−6.30383			−0.233957
$727$	−2.32372			−0.0861821			−0.0430911	−	0.999071i	$-0.513721\pi$
$727$	−2.32372			−0.0861821			−0.0430911	+	0.999071i	$0.513721\pi$
$728$	0.891282	−	26.2242i	0.0330331	−	0.971933i
$729$	1.00000			0.0370370
$730$	−14.2151			−0.526123
$731$	0.748697	−	1.29678i	0.0276916	−	0.0479632i
$732$	−11.4175			−0.422004
$733$	2.91958	−	5.05685i	0.107837	−	0.186779i	−0.807057	−	0.590474i	$-0.798941\pi$
$733$	2.91958	−	5.05685i	0.107837	−	0.186779i	0.914894	+	0.403695i	$0.132274\pi$
$734$	−3.35889	+	5.81777i	−0.123979	+	0.214738i
$735$	14.9555	−	10.5784i	0.551644	−	0.390188i
$736$	7.35314			0.271040
$737$	12.7843	+	22.1431i	0.470917	+	0.815652i
$738$	−3.66780	+	6.35282i	−0.135014	+	0.233850i
$739$	−0.0105714	+	0.0183102i	−0.000388875	+	0.000673551i	−0.866220	−	0.499663i	$-0.833457\pi$
$739$	−0.0105714	+	0.0183102i	−0.000388875	+	0.000673551i	0.865831	+	0.500337i	$0.166790\pi$
$740$	13.4943	−	23.3728i	0.496060	−	0.859201i
$741$	−13.9172	+	11.8516i	−0.511260	+	0.435380i
$742$	−5.75513	−	1.26153i	−0.211277	−	0.0463122i
$743$	−14.8332	−	25.6918i	−0.544176	−	0.942541i	−0.998658	−	0.0517853i	$-0.983509\pi$
$743$	−14.8332	−	25.6918i	−0.544176	−	0.942541i	0.454482	−	0.890756i	$-0.349824\pi$
$744$	−17.0472			−0.624980
$745$	−28.5439			−1.04577
$746$	−4.68704	−	8.11819i	−0.171605	−	0.297228i
$747$	4.33869	+	7.51483i	0.158744	+	0.274953i
$748$	−8.26432	+	14.3142i	−0.302173	+	0.523380i
$749$	12.8609	−	14.1024i	0.469927	−	0.515290i
$750$	3.42793	−	5.93734i	0.125170	−	0.216801i
$751$	12.6016			0.459838			0.229919	−	0.973210i	$-0.426154\pi$
$751$	12.6016			0.459838			0.229919	+	0.973210i	$0.426154\pi$
$752$	0.206912	−	0.358382i	0.00754531	−	0.0130689i
$753$	8.79293	+	15.2298i	0.320432	+	0.555005i
$754$	−4.09160	−	1.45557i	−0.149007	−	0.0530088i
$755$	−58.4635			−2.12770
$756$	2.33372	−	2.55900i	0.0848767	−	0.0930701i
$757$	−8.13319	−	14.0871i	−0.295606	−	0.512004i	0.679520	−	0.733657i	$-0.262188\pi$
$757$	−8.13319	−	14.0871i	−0.295606	−	0.512004i	−0.975126	+	0.221653i	$0.928855\pi$
$758$	7.43602	+	12.8796i	0.270089	+	0.467807i
$759$	1.17635	+	2.03750i	0.0426989	+	0.0739566i
$760$	36.4942			1.32378
$761$	−23.1276	−	40.0581i	−0.838374	−	1.45211i	−0.891254	−	0.453505i	$-0.850173\pi$
$761$	−23.1276	−	40.0581i	−0.838374	−	1.45211i	0.0528802	−	0.998601i	$-0.483160\pi$
$762$	−7.99063			−0.289470
$763$	22.4831	+	4.92832i	0.813944	+	0.178417i
$764$	−1.19753	−	2.07419i	−0.0433252	−	0.0750414i
$765$	17.8770			0.646346
$766$	0.0158392	+	0.0274344i	0.000572295	+	0.000991244i
$767$	−33.0398	+	28.1362i	−1.19300	+	1.01594i
$768$	−7.51098	+	13.0094i	−0.271029	+	0.469436i
$769$	19.2803	+	33.3944i	0.695264	+	1.20423i	0.970092	+	0.242739i	$0.0780460\pi$
$769$	19.2803	+	33.3944i	0.695264	+	1.20423i	−0.274827	+	0.961494i	$0.588621\pi$
$770$	−10.3913	−	2.27779i	−0.374478	−	0.0820859i
$771$	7.59362	−	13.1525i	0.273477	−	0.473677i
$772$	2.06794	−	3.58177i	0.0744267	−	0.128911i
$773$	−10.3545			−0.372424			−0.186212	−	0.982510i	$-0.559621\pi$
$773$	−10.3545			−0.372424			−0.186212	+	0.982510i	$0.559621\pi$
$774$	0.182207			0.00654931
$775$	−5.72768	+	9.92063i	−0.205744	+	0.356360i
$776$	16.7299	−	28.9770i	0.600568	−	1.04021i
$777$	−6.31528	−	19.8647i	−0.226560	−	0.712641i
$778$	−16.2805	−	28.1986i	−0.583683	−	1.01097i
$779$	22.3703	−	38.7465i	0.801499	−	1.38824i
$780$	−11.6369	−	4.13977i	−0.416666	−	0.148227i
$781$	−3.30550	−	5.72529i	−0.118280	−	0.204867i
$782$	7.22793			0.258470
$783$	−0.724496	−	1.25486i	−0.0258914	−	0.0448452i
$784$	−0.213290	−	2.31125i	−0.00761751	−	0.0825447i
$785$	1.72501			0.0615683
$786$	6.88289	+	11.9215i	0.245505	+	0.425226i
$787$	34.2879			1.22223			0.611116	−	0.791541i	$-0.290721\pi$
$787$	34.2879			1.22223			0.611116	+	0.791541i	$0.290721\pi$
$788$	−7.29906	−	12.6423i	−0.260018	−	0.450365i
$789$	−6.98496	−	12.0983i	−0.248671	−	0.430711i
$790$	−6.70184	−	11.6079i	−0.238441	−	0.412992i
$791$	−2.92624	−	9.20447i	−0.104045	−	0.327273i
$792$	−5.08417			−0.180658
$793$	29.6293	+	10.5405i	1.05217	+	0.374304i
$794$	3.62899	+	6.28560i	0.128788	+	0.223068i
$795$	−3.50532	+	6.07140i	−0.124321	+	0.215330i
$796$	−27.1618			−0.962723
$797$	6.60638	−	11.4426i	0.234010	−	0.405317i	−0.724975	−	0.688776i	$-0.758149\pi$
$797$	6.60638	−	11.4426i	0.234010	−	0.405317i	0.958984	+	0.283459i	$0.0914819\pi$
$798$	7.51333	−	8.23862i	0.265969	−	0.291644i
$799$	4.26283	−	7.38343i	0.150808	−	0.261207i
$800$	5.33890	+	9.24724i	0.188758	+	0.326939i
$801$	7.57751	+	13.1246i	0.267738	+	0.463736i
$802$	−20.1859			−0.712788
$803$	−12.0784			−0.426239
$804$	−9.05393	−	15.6819i	−0.319307	−	0.553057i
$805$	−2.67009	−	8.39875i	−0.0941083	−	0.296017i
$806$	17.5004	+	6.22571i	0.616426	+	0.219291i
$807$	−14.4628	+	25.0503i	−0.509115	+	0.881813i
$808$	6.32103	−	10.9484i	0.222373	−	0.385162i
$809$	25.4875	−	44.1457i	0.896094	−	1.55208i	0.0636484	−	0.997972i	$-0.479726\pi$
$809$	25.4875	−	44.1457i	0.896094	−	1.55208i	0.832445	−	0.554107i	$-0.186940\pi$
$810$	1.08767	+	1.88389i	0.0382167	+	0.0661933i
$811$	7.86969			0.276342			0.138171	−	0.990408i	$-0.455878\pi$
$811$	7.86969			0.276342			0.138171	+	0.990408i	$0.455878\pi$
$812$	−4.90197	−	1.07452i	−0.172026	−	0.0377082i
$813$	−5.05875	+	8.76202i	−0.177418	+	0.307297i
$814$	−6.05243	+	10.4831i	−0.212138	+	0.367433i
$815$	47.5892			1.66698
$816$	1.13256	−	1.96166i	0.0396477	−	0.0686718i
$817$	−1.11130			−0.0388795
$818$	16.3944			0.573218
$819$	−8.41860	+	4.48633i	−0.294170	+	0.156765i
$820$	30.2304			1.05569
$821$	−41.6714			−1.45434			−0.727171	−	0.686457i	$-0.759165\pi$
$821$	−41.6714			−1.45434			−0.727171	+	0.686457i	$0.759165\pi$
$822$	4.38770	−	7.59973i	0.153039	−	0.265071i
$823$	−15.7101			−0.547619			−0.273809	−	0.961784i	$-0.588284\pi$
$823$	−15.7101			−0.547619			−0.273809	+	0.961784i	$0.588284\pi$
$824$	−6.12315	+	10.6056i	−0.213310	+	0.369464i
$825$	−1.70823	+	2.95874i	−0.0594729	+	0.103010i
$826$	17.8369	−	19.5588i	0.620626	−	0.680537i
$827$	33.6343			1.16958			0.584789	−	0.811185i	$-0.301177\pi$
$827$	33.6343			1.16958			0.584789	+	0.811185i	$0.301177\pi$
$828$	−0.833099	−	1.44297i	−0.0289522	−	0.0501466i
$829$	25.1510	−	43.5629i	0.873532	−	1.51300i	0.0152129	−	0.999884i	$-0.495157\pi$
$829$	25.1510	−	43.5629i	0.873532	−	1.51300i	0.858319	−	0.513117i	$-0.171509\pi$
$830$	−9.43810	+	16.3473i	−0.327601	+	0.567422i
$831$	1.70320	−	2.95002i	0.0590832	−	0.102335i
$832$	11.3615	−	9.67525i	0.393889	−	0.335429i
$833$	−4.39423	−	47.6167i	−0.152251	−	1.64982i
$834$	−3.80504	−	6.59053i	−0.131758	−	0.228211i
$835$	11.5749			0.400567
$836$	12.2668			0.424258
$837$	3.09878	+	5.36725i	0.107110	+	0.185519i
$838$	−9.22491	−	15.9780i	−0.318669	−	0.551951i
$839$	−19.2875	+	33.4069i	−0.665877	+	1.15333i	0.313170	+	0.949697i	$0.398609\pi$
$839$	−19.2875	+	33.4069i	−0.665877	+	1.15333i	−0.979047	+	0.203635i	$0.934724\pi$
$840$	18.6030	+	4.07780i	0.641865	+	0.140697i
$841$	13.4502	−	23.2964i	0.463800	−	0.803326i
$842$	1.54176			0.0531326
$843$	4.70165	−	8.14351i	0.161934	−	0.280477i
$844$	−10.6917	−	18.5186i	−0.368025	−	0.637437i
$845$	26.3767	+	21.4860i	0.907384	+	0.739139i
$846$	1.03743			0.0356675
$847$	19.5988	+	4.29608i	0.673424	+	0.147615i
$848$	0.444145	+	0.769282i	0.0152520	+	0.0264173i
$849$	5.23950	+	9.07507i	0.179819	+	0.311456i
$850$	5.24798	+	9.08977i	0.180004	+	0.311777i
$851$	−10.0281			−0.343759
$852$	2.34097	+	4.05468i	0.0802003	+	0.138911i
$853$	22.6889			0.776855			0.388427	−	0.921479i	$-0.373018\pi$
$853$	22.6889			0.776855			0.388427	+	0.921479i	$0.373018\pi$
$854$	−18.7377	−	4.10731i	−0.641190	−	0.140549i
$855$	−6.63379	−	11.4901i	−0.226871	−	0.392952i
$856$	19.8427			0.678209
$857$	10.2901	+	17.8230i	0.351504	+	0.608822i	0.986513	−	0.163682i	$-0.0523371\pi$
$857$	10.2901	+	17.8230i	0.351504	+	0.608822i	−0.635009	+	0.772504i	$0.719004\pi$
$858$	5.21934	+	1.85676i	0.178185	+	0.0633887i
$859$	1.81131	−	3.13729i	0.0618012	−	0.107043i	−0.833469	−	0.552566i	$-0.813649\pi$
$859$	1.81131	−	3.13729i	0.0618012	−	0.107043i	0.895271	+	0.445523i	$0.146982\pi$
$860$	−0.375443	−	0.650286i	−0.0128025	−	0.0221746i
$861$	15.7328	−	17.2515i	0.536172	−	0.587931i
$862$	−15.7053	+	27.2023i	−0.534923	+	0.926515i
$863$	−3.99010	+	6.91105i	−0.135824	+	0.235255i	−0.925912	−	0.377739i	$-0.876702\pi$
$863$	−3.99010	+	6.91105i	−0.135824	+	0.235255i	0.790088	+	0.612994i	$0.210035\pi$
$864$	5.77688			0.196534
$865$	9.21277			0.313244
$866$	−14.6034	+	25.2938i	−0.496244	+	0.859520i
$867$	14.8332	−	25.6919i	0.503763	−	0.872542i
$868$	20.9665	+	4.59588i	0.711649	+	0.155994i
$869$	−5.69451	−	9.86318i	−0.193173	−	0.334586i
$870$	1.57602	−	2.72975i	0.0534321	−	0.0925470i
$871$	9.01828	+	49.0539i	0.305573	+	1.66213i
$872$	11.9647	+	20.7234i	0.405174	+	0.701783i
$873$	−12.1644			−0.411703
$874$	−2.68213	−	4.64558i	−0.0907244	−	0.157139i
$875$	−14.7039	+	16.1233i	−0.497082	+	0.545066i
$876$	8.55401			0.289013
$877$	6.29998	+	10.9119i	0.212735	+	0.368468i	0.952570	−	0.304321i	$-0.0984295\pi$
$877$	6.29998	+	10.9119i	0.212735	+	0.368468i	−0.739834	+	0.672789i	$0.765096\pi$
$878$	−12.7576			−0.430549
$879$	4.61007	+	7.98488i	0.155494	+	0.269323i
$880$	0.801940	+	1.38900i	0.0270334	+	0.0468232i
$881$	0.0834951	+	0.144618i	0.00281302	+	0.00487230i	0.867428	−	0.497562i	$-0.165771\pi$
$881$	0.0834951	+	0.144618i	0.00281302	+	0.00487230i	−0.864615	+	0.502434i	$0.832438\pi$
$882$	4.75052	−	3.36013i	0.159958	−	0.113142i
$883$	1.54174			0.0518836			0.0259418	−	0.999663i	$-0.491742\pi$
$883$	1.54174			0.0518836			0.0259418	+	0.999663i	$0.491742\pi$
$884$	−24.5472	+	20.9040i	−0.825611	+	0.703077i
$885$	−15.7489	−	27.2778i	−0.529392	−	0.916934i
$886$	12.0828	−	20.9280i	0.405928	−	0.703088i
$887$	−10.3337			−0.346971			−0.173485	−	0.984836i	$-0.555503\pi$
$887$	−10.3337			−0.346971			−0.173485	+	0.984836i	$0.555503\pi$
$888$	10.8353	−	18.7673i	0.363609	−	0.629790i
$889$	24.8432	+	5.44565i	0.833213	+	0.182641i
$890$	−16.4836	+	28.5504i	−0.552532	+	0.957013i
$891$	0.924183	+	1.60073i	0.0309613	+	0.0536265i
$892$	−12.1852	−	21.1055i	−0.407992	−	0.706663i
$893$	−6.32737			−0.211737
$894$	−9.06674			−0.303237
$895$	−14.1580	−	24.5224i	−0.473250	−	0.819693i
$896$	14.4644	−	15.8607i	0.483223	−	0.529869i
$897$	0.829819	+	4.51371i	0.0277068	+	0.150708i
$898$	0.981963	−	1.70081i	0.0327685	−	0.0567568i
$899$	4.49011	−	7.77709i	0.149753	−	0.259381i
$900$	1.20978	−	2.09539i	0.0403259	−	0.0698464i
$901$	9.15033	+	15.8488i	0.304842	+	0.528001i
$902$	−13.5589			−0.451461
$903$	−0.566490	−	0.124175i	−0.0188516	−	0.00413229i
$904$	5.02064	−	8.69600i	0.166984	−	0.289225i
$905$	30.1799	−	52.2732i	1.00321	−	1.73762i
$906$	−18.5705			−0.616963
$907$	−11.9496	+	20.6973i	−0.396780	+	0.687242i	−0.993327	−	0.115336i	$-0.963206\pi$
$907$	−11.9496	+	20.6973i	−0.396780	+	0.687242i	0.596547	+	0.802578i	$0.296539\pi$
$908$	29.5125			0.979406
$909$	−4.59607			−0.152442
$910$	−17.6084	−	10.9801i	−0.583712	−	0.363988i
$911$	14.3304			0.474786			0.237393	−	0.971414i	$-0.423707\pi$
$911$	14.3304			0.474786			0.237393	+	0.971414i	$0.423707\pi$
$912$	−1.68108			−0.0556662
$913$	−8.01949	+	13.8902i	−0.265406	+	0.459697i
$914$	13.9263			0.460641
$915$	−11.4127	+	19.7674i	−0.377293	+	0.653490i
$916$	−12.6021	+	21.8275i	−0.416386	+	0.721202i
$917$	−13.2746	−	41.7552i	−0.438366	−	1.37888i
$918$	5.67851			0.187419
$919$	27.1731	+	47.0652i	0.896359	+	1.55254i	0.832114	+	0.554605i	$0.187131\pi$
$919$	27.1731	+	47.0652i	0.896359	+	1.55254i	0.0642448	+	0.997934i	$0.479536\pi$
$920$	4.58115	−	7.93479i	0.151036	−	0.261602i
$921$	−8.07497	+	13.9863i	−0.266079	+	0.460863i
$922$	−10.4296	+	18.0646i	−0.343480	+	0.594926i
$923$	−2.33175	−	12.6833i	−0.0767506	−	0.417476i
$924$	6.25307	+	1.37068i	0.205711	+	0.0450920i
$925$	−7.28111	−	12.6113i	−0.239402	−	0.414656i
$926$	0.211351			0.00694542
$927$	4.45218			0.146229
$928$	−4.18533	−	7.24920i	−0.137390	−	0.237967i
$929$	−8.33555	−	14.4376i	−0.273480	−	0.473682i	0.696270	−	0.717780i	$-0.254842\pi$
$929$	−8.33555	−	14.4376i	−0.273480	−	0.473682i	−0.969751	+	0.244098i	$0.921508\pi$
$930$	−6.74088	+	11.6755i	−0.221042	+	0.382856i
$931$	−28.9739	+	20.4938i	−0.949581	+	0.671657i
$932$	14.9590	−	25.9098i	0.490000	−	0.848704i
$933$	30.4275			0.996153
$934$	4.24898	−	7.35945i	0.139031	−	0.240808i
$935$	16.5217	+	28.6164i	0.540316	+	0.935855i
$936$	−9.34388	−	3.32405i	−0.305414	−	0.108650i
$937$	−2.55078			−0.0833303			−0.0416651	−	0.999132i	$-0.513266\pi$
$937$	−2.55078			−0.0833303			−0.0416651	+	0.999132i	$0.513266\pi$
$938$	−9.21733	−	28.9930i	−0.300957	−	0.946656i
$939$	13.6859	+	23.7047i	0.446623	+	0.773574i
$940$	−2.13765	−	3.70251i	−0.0697223	−	0.120763i
$941$	17.3944	+	30.1280i	0.567041	+	0.982144i	0.996857	+	0.0792275i	$0.0252453\pi$
$941$	17.3944	+	30.1280i	0.567041	+	0.982144i	−0.429815	+	0.902917i	$0.641421\pi$
$942$	0.547937			0.0178527
$943$	−5.61634	−	9.72778i	−0.182893	−	0.316780i
$944$	−3.99095			−0.129894
$945$	−2.09772	−	6.59834i	−0.0682387	−	0.214644i
$946$	0.168393	+	0.291665i	0.00547493	+	0.00948285i
$947$	14.9857			0.486969			0.243485	−	0.969905i	$-0.421709\pi$
$947$	14.9857			0.486969			0.243485	+	0.969905i	$0.421709\pi$
$948$	4.03288	+	6.98516i	0.130982	+	0.226867i
$949$	−22.1982	−	7.89694i	−0.720585	−	0.256345i
$950$	3.89483	−	6.74604i	0.126365	−	0.218870i
$951$	6.18424	+	10.7114i	0.200538	+	0.347342i
$952$	33.4994	−	36.7332i	1.08572	−	1.19053i
$953$	−6.40858	+	11.1000i	−0.207594	+	0.359564i	−0.950956	−	0.309326i	$-0.899897\pi$
$953$	−6.40858	+	11.1000i	−0.207594	+	0.359564i	0.743362	+	0.668889i	$0.233230\pi$
$954$	−1.11344	+	1.92853i	−0.0360489	+	0.0624386i
$955$	−4.78810			−0.154939
$956$	14.7266			0.476291
$957$	1.33913	−	2.31945i	0.0432880	−	0.0749771i
$958$	−5.28177	+	9.14829i	−0.170646	+	0.295568i
$959$	−18.8208	+	20.6376i	−0.607755	+	0.666423i
$960$	5.41559	+	9.38008i	0.174787	+	0.302741i
$961$	−3.70488	+	6.41704i	−0.119512	+	0.207001i
$962$	−17.9773	+	15.3092i	−0.579612	+	0.493588i
$963$	−3.60694	−	6.24740i	−0.116232	−	0.201320i
$964$	−25.4554			−0.819862
$965$	−4.13413	−	7.16052i	−0.133082	−	0.230505i
$966$	−0.848134	−	2.66780i	−0.0272883	−	0.0858350i
$967$	17.8560			0.574209			0.287105	−	0.957899i	$-0.407307\pi$
$967$	17.8560			0.574209			0.287105	+	0.957899i	$0.407307\pi$
$968$	10.4298	+	18.0649i	0.335225	+	0.580627i
$969$	−34.6338			−1.11260
$970$	−13.2308	−	22.9165i	−0.424816	−	0.735803i
$971$	−17.6534	−	30.5765i	−0.566523	−	0.981247i	−0.996906	−	0.0786007i	$-0.974955\pi$
$971$	−17.6534	−	30.5765i	−0.566523	−	0.981247i	0.430383	−	0.902646i	$-0.358379\pi$
$972$	−0.654511	−	1.13365i	−0.0209934	−	0.0363617i
$973$	7.33855	+	23.0834i	0.235263	+	0.740018i
$974$	−17.0256			−0.545537
$975$	−5.07388	+	4.32084i	−0.162494	+	0.138378i
$976$	1.44606	+	2.50465i	0.0462872	+	0.0801718i
$977$	−9.55272	+	16.5458i	−0.305618	+	0.529347i	−0.977399	−	0.211404i	$-0.932197\pi$
$977$	−9.55272	+	16.5458i	−0.305618	+	0.529347i	0.671780	+	0.740750i	$0.265530\pi$
$978$	15.1164			0.483368
$979$	−14.0060	+	24.2591i	−0.447634	+	0.775325i
$980$	−21.7807	−	10.0307i	−0.695758	−	0.320417i
$981$	4.34979	−	7.53406i	0.138878	−	0.240544i
$982$	8.24682	+	14.2839i	0.263167	+	0.455818i
$983$	−18.4765	−	32.0022i	−0.589308	−	1.02071i	−0.994323	−	0.106402i	$-0.966067\pi$
$983$	−18.4765	−	32.0022i	−0.589308	−	1.02071i	0.405015	−	0.914310i	$-0.367266\pi$
$984$	24.2737			0.773816
$985$	−29.1839			−0.929877
$986$	−4.11406	−	7.12576i	−0.131018	−	0.226930i
$987$	−3.22540	−	0.707011i	−0.102666	−	0.0225044i
$988$	22.5445	+	8.02012i	0.717236	+	0.255154i
$989$	−0.139503	+	0.241626i	−0.00443593	+	0.00768326i
$990$	−2.01041	+	3.48212i	−0.0638949	+	0.110669i
$991$	−27.9186	+	48.3564i	−0.886863	+	1.53609i	−0.0433004	+	0.999062i	$0.513787\pi$
$991$	−27.9186	+	48.3564i	−0.886863	+	1.53609i	−0.843563	+	0.537030i	$0.819546\pi$
$992$	17.9013	+	31.0059i	0.568367	+	0.984440i
$993$	12.4062			0.393699
$994$	2.38322	+	7.49640i	0.0755911	+	0.237771i
$995$	−27.1503	+	47.0257i	−0.860722	+	1.49081i
$996$	5.67944	−	9.83708i	0.179960	−	0.311700i
$997$	−22.8782			−0.724560			−0.362280	−	0.932069i	$-0.618002\pi$
$997$	−22.8782			−0.724560			−0.362280	+	0.932069i	$0.618002\pi$
$998$	11.5892	−	20.0731i	0.366850	−	0.635402i
$999$	−7.87843			−0.249263

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.b.16.3	yes	16
3.2	odd	2		819.2.s.e.289.6		16
7.4	even	3		273.2.j.b.172.6	yes	16
13.9	even	3		273.2.j.b.100.6	✓	16
21.11	odd	6		819.2.n.e.172.3		16
39.35	odd	6		819.2.n.e.100.3		16
91.74	even	3	inner	273.2.l.b.256.3	yes	16
273.74	odd	6		819.2.s.e.802.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.6	✓	16	13.9	even	3
273.2.j.b.172.6	yes	16	7.4	even	3
273.2.l.b.16.3	yes	16	1.1	even	1	trivial
273.2.l.b.256.3	yes	16	91.74	even	3	inner
819.2.n.e.100.3		16	39.35	odd	6
819.2.n.e.172.3		16	21.11	odd	6
819.2.s.e.289.6		16	3.2	odd	2
819.2.s.e.802.6		16	273.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.831251 q^{2} +(0.500000 - 0.866025i) q^{3} -1.30902 q^{4} +(-1.30847 + 2.26634i) q^{5} +(-0.415625 + 0.719884i) q^{6} +(1.78280 - 1.95490i) q^{7} +2.75063 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-0.831251 q^{2} +(0.500000 - 0.866025i) q^{3} -1.30902 q^{4} +(-1.30847 + 2.26634i) q^{5} +(-0.415625 + 0.719884i) q^{6} +(1.78280 - 1.95490i) q^{7} +2.75063 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.08767 - 1.88389i) q^{10} +(0.924183 - 1.60073i) q^{11} +(-0.654511 + 1.13365i) q^{12} +(2.74506 - 2.33765i) q^{13} +(-1.48195 + 1.62501i) q^{14} +(1.30847 + 2.26634i) q^{15} +0.331582 q^{16} +6.83128 q^{17} +(0.415625 + 0.719884i) q^{18} +(-2.53494 - 4.39065i) q^{19} +(1.71281 - 2.96668i) q^{20} +(-0.801591 - 2.52140i) q^{21} +(-0.768228 + 1.33061i) q^{22} -1.27286 q^{23} +(1.37531 - 2.38211i) q^{24} +(-0.924183 - 1.60073i) q^{25} +(-2.28184 + 1.94318i) q^{26} -1.00000 q^{27} +(-2.33372 + 2.55900i) q^{28} +(0.724496 + 1.25486i) q^{29} +(-1.08767 - 1.88389i) q^{30} +(-3.09878 - 5.36725i) q^{31} -5.77688 q^{32} +(-0.924183 - 1.60073i) q^{33} -5.67851 q^{34} +(2.09772 + 6.59834i) q^{35} +(0.654511 + 1.13365i) q^{36} +7.87843 q^{37} +(2.10717 + 3.64973i) q^{38} +(-0.651934 - 3.54612i) q^{39} +(-3.59911 + 6.23384i) q^{40} +(4.41239 + 7.64248i) q^{41} +(0.666324 + 2.09592i) q^{42} +(0.109598 - 0.189830i) q^{43} +(-1.20978 + 2.09539i) q^{44} +2.61694 q^{45} +1.05806 q^{46} +(0.624016 - 1.08083i) q^{47} +(0.165791 - 0.287158i) q^{48} +(-0.643251 - 6.97038i) q^{49} +(0.768228 + 1.33061i) q^{50} +(3.41564 - 5.91607i) q^{51} +(-3.59335 + 3.06004i) q^{52} +(1.33947 + 2.32004i) q^{53} +0.831251 q^{54} +(2.41853 + 4.18902i) q^{55} +(4.90382 - 5.37720i) q^{56} -5.06988 q^{57} +(-0.602238 - 1.04311i) q^{58} -12.0361 q^{59} +(-1.71281 - 2.96668i) q^{60} +(4.36109 + 7.55363i) q^{61} +(2.57586 + 4.46153i) q^{62} +(-2.58439 - 0.566501i) q^{63} +4.13888 q^{64} +(1.70607 + 9.27998i) q^{65} +(0.768228 + 1.33061i) q^{66} +(-6.91656 + 11.9798i) q^{67} -8.94230 q^{68} +(-0.636428 + 1.10233i) q^{69} +(-1.74373 - 5.48488i) q^{70} +(1.78833 - 3.09749i) q^{71} +(-1.37531 - 2.38211i) q^{72} +(-3.26733 - 5.65918i) q^{73} -6.54896 q^{74} -1.84837 q^{75} +(3.31829 + 5.74745i) q^{76} +(-1.48163 - 4.66047i) q^{77} +(0.541921 + 2.94772i) q^{78} +(3.08084 - 5.33616i) q^{79} +(-0.433865 + 0.751475i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.66780 - 6.35282i) q^{82} -8.67738 q^{83} +(1.04930 + 3.30057i) q^{84} +(-8.93852 + 15.4820i) q^{85} +(-0.0911037 + 0.157796i) q^{86} +1.44899 q^{87} +(2.54208 - 4.40302i) q^{88} -15.1550 q^{89} -2.17533 q^{90} +(0.324029 - 9.53389i) q^{91} +1.66620 q^{92} -6.19756 q^{93} +(-0.518714 + 0.898438i) q^{94} +13.2676 q^{95} +(-2.88844 + 5.00293i) q^{96} +(6.08221 - 10.5347i) q^{97} +(0.534703 + 5.79414i) q^{98} -1.84837 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Introduction

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