LMFDB - Embedded newform 273.2.i.e.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(79,273)]

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, 0]))

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

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

chi := DirichletCharacter("273.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 8x^{7} + 41x^{6} - 40x^{5} + 59x^{4} - 10x^{3} + 18x^{2} - 4x + 4 $ x^10 - x^9 + 7x^8 - 8x^7 + 41x^6 - 40x^5 + 59x^4 - 10x^3 + 18x^2 - 4x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.4
Root			$0.660865 + 1.14465i$ of defining polynomial
Character	$\chi$	$=$	273.79
Dual form			273.2.i.e.235.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.893230 - 1.54712i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.595718 - 1.03181i) q^{4} +(-1.71496 + 2.97040i) q^{5} +1.78646 q^{6} +(2.14626 + 1.54712i) q^{7} +1.44447 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.893230 - 1.54712i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.595718 - 1.03181i) q^{4} +(-1.71496 + 2.97040i) q^{5} +1.78646 q^{6} +(2.14626 + 1.54712i) q^{7} +1.44447 q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.06371 + 5.30650i) q^{10} +(-0.797511 - 1.38133i) q^{11} +(0.595718 - 1.03181i) q^{12} -1.00000 q^{13} +(4.31068 - 1.93858i) q^{14} -3.42992 q^{15} +(2.48168 - 4.29839i) q^{16} +(-0.0197437 - 0.0341971i) q^{17} +(0.893230 + 1.54712i) q^{18} +(1.82173 - 3.15533i) q^{19} +4.08653 q^{20} +(-0.266716 + 2.63227i) q^{21} -2.84944 q^{22} +(1.71118 - 2.96385i) q^{23} +(0.722233 + 1.25094i) q^{24} +(-3.38218 - 5.85810i) q^{25} +(-0.893230 + 1.54712i) q^{26} -1.00000 q^{27} +(0.317775 - 3.13619i) q^{28} -10.0028 q^{29} +(-3.06371 + 5.30650i) q^{30} +(3.07739 + 5.33020i) q^{31} +(-2.98895 - 5.17701i) q^{32} +(0.797511 - 1.38133i) q^{33} -0.0705426 q^{34} +(-8.27631 + 3.72199i) q^{35} +1.19144 q^{36} +(5.56513 - 9.63908i) q^{37} +(-3.25445 - 5.63687i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-2.47720 + 4.29064i) q^{40} -5.08793 q^{41} +(3.83420 + 2.76387i) q^{42} +2.91631 q^{43} +(-0.950184 + 1.64577i) q^{44} +(-1.71496 - 2.97040i) q^{45} +(-3.05695 - 5.29480i) q^{46} +(2.05432 - 3.55818i) q^{47} +4.96335 q^{48} +(2.21284 + 6.64103i) q^{49} -12.0842 q^{50} +(0.0197437 - 0.0341971i) q^{51} +(0.595718 + 1.03181i) q^{52} +(5.14558 + 8.91240i) q^{53} +(-0.893230 + 1.54712i) q^{54} +5.47080 q^{55} +(3.10019 + 2.23476i) q^{56} +3.64346 q^{57} +(-8.93483 + 15.4756i) q^{58} +(-4.59662 - 7.96158i) q^{59} +(2.04327 + 3.53904i) q^{60} +(0.980256 - 1.69785i) q^{61} +10.9953 q^{62} +(-2.41297 + 1.08515i) q^{63} -0.752565 q^{64} +(1.71496 - 2.97040i) q^{65} +(-1.42472 - 2.46769i) q^{66} +(-6.02844 - 10.4416i) q^{67} +(-0.0235234 + 0.0407437i) q^{68} +3.42236 q^{69} +(-1.63428 + 16.1290i) q^{70} +1.79825 q^{71} +(-0.722233 + 1.25094i) q^{72} +(3.35253 + 5.80675i) q^{73} +(-9.94187 - 17.2198i) q^{74} +(3.38218 - 5.85810i) q^{75} -4.34095 q^{76} +(0.425417 - 4.19853i) q^{77} -1.78646 q^{78} +(-7.31588 + 12.6715i) q^{79} +(8.51195 + 14.7431i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.54469 + 7.87163i) q^{82} -5.34655 q^{83} +(2.87491 - 1.29289i) q^{84} +0.135439 q^{85} +(2.60493 - 4.51187i) q^{86} +(-5.00142 - 8.66271i) q^{87} +(-1.15198 - 1.99528i) q^{88} +(6.23470 - 10.7988i) q^{89} -6.12741 q^{90} +(-2.14626 - 1.54712i) q^{91} -4.07753 q^{92} +(-3.07739 + 5.33020i) q^{93} +(-3.66996 - 6.35655i) q^{94} +(6.24839 + 10.8225i) q^{95} +(2.98895 - 5.17701i) q^{96} -12.5010 q^{97} +(12.2510 + 2.50843i) q^{98} +1.59502 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9} + 2 q^{10} + q^{11} + 6 q^{12} - 10 q^{13} + 23 q^{14} + 6 q^{15} + 13 q^{17} + 7 q^{19} - 26 q^{20} + 2 q^{21} - 38 q^{22} + 4 q^{23} + 3 q^{24} - 16 q^{25} - 10 q^{27} - 4 q^{28} - 24 q^{29} - 2 q^{30} + 6 q^{31} - 21 q^{32} - q^{33} - 14 q^{34} - 3 q^{35} + 12 q^{36} - 11 q^{37} + 14 q^{38} - 5 q^{39} + 11 q^{40} - 20 q^{41} - 2 q^{42} + 20 q^{43} + 29 q^{44} + 3 q^{45} - q^{46} - 4 q^{47} + 22 q^{49} - 58 q^{50} - 13 q^{51} + 6 q^{52} + 9 q^{53} + 24 q^{55} + 42 q^{56} + 14 q^{57} - 34 q^{58} + 7 q^{59} - 13 q^{60} + 23 q^{61} + 48 q^{62} - 2 q^{63} - 26 q^{64} - 3 q^{65} - 19 q^{66} - 25 q^{67} + 20 q^{68} + 8 q^{69} + 73 q^{70} - 54 q^{71} - 3 q^{72} + 18 q^{73} - 15 q^{74} + 16 q^{75} - 4 q^{76} + 27 q^{77} - 8 q^{79} + 41 q^{80} - 5 q^{81} + 26 q^{82} - 24 q^{83} - 5 q^{84} + 20 q^{85} + 19 q^{86} - 12 q^{87} + 36 q^{88} + 29 q^{89} - 4 q^{90} - 4 q^{91} - 100 q^{92} - 6 q^{93} - 2 q^{94} + 33 q^{95} + 21 q^{96} - 26 q^{97} + 15 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9 + 2 * q^10 + q^11 + 6 * q^12 - 10 * q^13 + 23 * q^14 + 6 * q^15 + 13 * q^17 + 7 * q^19 - 26 * q^20 + 2 * q^21 - 38 * q^22 + 4 * q^23 + 3 * q^24 - 16 * q^25 - 10 * q^27 - 4 * q^28 - 24 * q^29 - 2 * q^30 + 6 * q^31 - 21 * q^32 - q^33 - 14 * q^34 - 3 * q^35 + 12 * q^36 - 11 * q^37 + 14 * q^38 - 5 * q^39 + 11 * q^40 - 20 * q^41 - 2 * q^42 + 20 * q^43 + 29 * q^44 + 3 * q^45 - q^46 - 4 * q^47 + 22 * q^49 - 58 * q^50 - 13 * q^51 + 6 * q^52 + 9 * q^53 + 24 * q^55 + 42 * q^56 + 14 * q^57 - 34 * q^58 + 7 * q^59 - 13 * q^60 + 23 * q^61 + 48 * q^62 - 2 * q^63 - 26 * q^64 - 3 * q^65 - 19 * q^66 - 25 * q^67 + 20 * q^68 + 8 * q^69 + 73 * q^70 - 54 * q^71 - 3 * q^72 + 18 * q^73 - 15 * q^74 + 16 * q^75 - 4 * q^76 + 27 * q^77 - 8 * q^79 + 41 * q^80 - 5 * q^81 + 26 * q^82 - 24 * q^83 - 5 * q^84 + 20 * q^85 + 19 * q^86 - 12 * q^87 + 36 * q^88 + 29 * q^89 - 4 * q^90 - 4 * q^91 - 100 * q^92 - 6 * q^93 - 2 * q^94 + 33 * q^95 + 21 * q^96 - 26 * q^97 + 15 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.893230	−	1.54712i	0.631609	−	1.09398i	−0.355614	−	0.934633i	$-0.615728\pi$
$2$	0.893230	−	1.54712i	0.631609	−	1.09398i	0.987223	−	0.159346i	$-0.0509384\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.595718	−	1.03181i	−0.297859	−	0.515907i
$5$	−1.71496	+	2.97040i	−0.766954	+	1.32840i	0.172254	+	0.985053i	$0.444895\pi$
$5$	−1.71496	+	2.97040i	−0.766954	+	1.32840i	−0.939208	+	0.343350i	$0.888438\pi$
$6$	1.78646			0.729319
$7$	2.14626	+	1.54712i	0.811209	+	0.584756i
$7$	2.14626	+	1.54712i	0.811209	+	0.584756i
$8$	1.44447			0.510696
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	3.06371	+	5.30650i	0.968829	+	1.67806i
$11$	−0.797511	−	1.38133i	−0.240459	−	0.416487i	0.720386	−	0.693573i	$-0.243965\pi$
$11$	−0.797511	−	1.38133i	−0.240459	−	0.416487i	−0.960845	+	0.277086i	$0.910631\pi$
$12$	0.595718	−	1.03181i	0.171969	−	0.297859i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	4.31068	−	1.93858i	1.15208	−	0.518108i
$15$	−3.42992			−0.885602
$16$	2.48168	−	4.29839i	0.620419	−	1.07460i
$17$	−0.0197437	−	0.0341971i	−0.00478855	−	0.00829401i	0.863621	−	0.504141i	$-0.168191\pi$
$17$	−0.0197437	−	0.0341971i	−0.00478855	−	0.00829401i	−0.868410	+	0.495847i	$0.834858\pi$
$18$	0.893230	+	1.54712i	0.210536	+	0.364659i
$19$	1.82173	−	3.15533i	0.417934	−	0.723882i	−0.577798	−	0.816180i	$-0.696088\pi$
$19$	1.82173	−	3.15533i	0.417934	−	0.723882i	0.995731	+	0.0922976i	$0.0294211\pi$
$20$	4.08653			0.913777
$21$	−0.266716	+	2.63227i	−0.0582021	+	0.574409i
$22$	−2.84944			−0.607503
$23$	1.71118	−	2.96385i	0.356806	−	0.618006i	−0.630619	−	0.776092i	$-0.717199\pi$
$23$	1.71118	−	2.96385i	0.356806	−	0.618006i	0.987425	+	0.158086i	$0.0505324\pi$
$24$	0.722233	+	1.25094i	0.147425	+	0.255348i
$25$	−3.38218	−	5.85810i	−0.676436	−	1.17162i
$26$	−0.893230	+	1.54712i	−0.175177	+	0.303415i
$27$	−1.00000			−0.192450
$28$	0.317775	−	3.13619i	0.0600538	−	0.592684i
$29$	−10.0028			−1.85748			−0.928740	−	0.370731i	$-0.879107\pi$
$29$	−10.0028			−1.85748			−0.928740	+	0.370731i	$0.879107\pi$
$30$	−3.06371	+	5.30650i	−0.559354	+	0.968829i
$31$	3.07739	+	5.33020i	0.552716	+	0.957333i	0.998077	+	0.0619817i	$0.0197420\pi$
$31$	3.07739	+	5.33020i	0.552716	+	0.957333i	−0.445361	+	0.895351i	$0.646925\pi$
$32$	−2.98895	−	5.17701i	−0.528376	−	0.915175i
$33$	0.797511	−	1.38133i	0.138829	−	0.240459i
$34$	−0.0705426			−0.0120980
$35$	−8.27631	+	3.72199i	−1.39895	+	0.629132i
$36$	1.19144			0.198573
$37$	5.56513	−	9.63908i	0.914901	−	1.58466i	0.107855	−	0.994167i	$-0.465602\pi$
$37$	5.56513	−	9.63908i	0.914901	−	1.58466i	0.807046	−	0.590489i	$-0.201065\pi$
$38$	−3.25445	−	5.63687i	−0.527941	−	0.914421i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$	−2.47720	+	4.29064i	−0.391680	+	0.678409i
$41$	−5.08793			−0.794601			−0.397300	−	0.917689i	$-0.630053\pi$
$41$	−5.08793			−0.794601			−0.397300	+	0.917689i	$0.630053\pi$
$42$	3.83420	+	2.76387i	0.591630	+	0.426474i
$43$	2.91631			0.444732			0.222366	−	0.974963i	$-0.428622\pi$
$43$	2.91631			0.444732			0.222366	+	0.974963i	$0.428622\pi$
$44$	−0.950184	+	1.64577i	−0.143246	+	0.248109i
$45$	−1.71496	−	2.97040i	−0.255651	−	0.442801i
$46$	−3.05695	−	5.29480i	−0.450723	−	0.780676i
$47$	2.05432	−	3.55818i	0.299653	−	0.519015i	−0.676403	−	0.736531i	$-0.736462\pi$
$47$	2.05432	−	3.55818i	0.299653	−	0.519015i	0.976057	+	0.217517i	$0.0697957\pi$
$48$	4.96335			0.716398
$49$	2.21284	+	6.64103i	0.316121	+	0.948719i
$50$	−12.0842			−1.70897
$51$	0.0197437	−	0.0341971i	0.00276467	−	0.00478855i
$52$	0.595718	+	1.03181i	0.0826113	+	0.143087i
$53$	5.14558	+	8.91240i	0.706799	+	1.22421i	0.966038	+	0.258399i	$0.0831950\pi$
$53$	5.14558	+	8.91240i	0.706799	+	1.22421i	−0.259239	+	0.965813i	$0.583472\pi$
$54$	−0.893230	+	1.54712i	−0.121553	+	0.210536i
$55$	5.47080			0.737683
$56$	3.10019	+	2.23476i	0.414281	+	0.298632i
$57$	3.64346			0.482588
$58$	−8.93483	+	15.4756i	−1.17320	+	2.03204i
$59$	−4.59662	−	7.96158i	−0.598429	−	1.03651i	−0.993053	−	0.117666i	$-0.962459\pi$
$59$	−4.59662	−	7.96158i	−0.598429	−	1.03651i	0.394624	−	0.918842i	$-0.370875\pi$
$60$	2.04327	+	3.53904i	0.263785	+	0.456888i
$61$	0.980256	−	1.69785i	0.125509	−	0.217388i	−0.796423	−	0.604740i	$-0.793277\pi$
$61$	0.980256	−	1.69785i	0.125509	−	0.217388i	0.921932	+	0.387352i	$0.126610\pi$
$62$	10.9953			1.39640
$63$	−2.41297	+	1.08515i	−0.304006	+	0.136717i
$64$	−0.752565			−0.0940706
$65$	1.71496	−	2.97040i	0.212715	−	0.368433i
$66$	−1.42472	−	2.46769i	−0.175371	−	0.303752i
$67$	−6.02844	−	10.4416i	−0.736491	−	1.27564i	−0.954066	−	0.299596i	$-0.903148\pi$
$67$	−6.02844	−	10.4416i	−0.736491	−	1.27564i	0.217576	−	0.976043i	$-0.430185\pi$
$68$	−0.0235234	+	0.0407437i	−0.00285263	+	0.00494090i
$69$	3.42236			0.412004
$70$	−1.63428	+	16.1290i	−0.195333	+	1.92779i
$71$	1.79825			0.213413			0.106707	−	0.994291i	$-0.465969\pi$
$71$	1.79825			0.213413			0.106707	+	0.994291i	$0.465969\pi$
$72$	−0.722233	+	1.25094i	−0.0851159	+	0.147425i
$73$	3.35253	+	5.80675i	0.392384	+	0.679628i	0.992763	−	0.120087i	$-0.0383173\pi$
$73$	3.35253	+	5.80675i	0.392384	+	0.679628i	−0.600380	+	0.799715i	$0.704984\pi$
$74$	−9.94187	−	17.2198i	−1.15572	−	2.00176i
$75$	3.38218	−	5.85810i	0.390540	−	0.676436i
$76$	−4.34095			−0.497942
$77$	0.425417	−	4.19853i	0.0484808	−	0.478467i
$78$	−1.78646			−0.202277
$79$	−7.31588	+	12.6715i	−0.823101	+	1.42565i	0.0802617	+	0.996774i	$0.474424\pi$
$79$	−7.31588	+	12.6715i	−0.823101	+	1.42565i	−0.903362	+	0.428878i	$0.858909\pi$
$80$	8.51195	+	14.7431i	0.951665	+	1.64833i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.54469	+	7.87163i	−0.501877	+	0.869276i
$83$	−5.34655			−0.586860			−0.293430	−	0.955981i	$-0.594797\pi$
$83$	−5.34655			−0.586860			−0.293430	+	0.955981i	$0.594797\pi$
$84$	2.87491	−	1.29289i	0.313678	−	0.141066i
$85$	0.135439			0.0146904
$86$	2.60493	−	4.51187i	0.280897	−	0.486528i
$87$	−5.00142	−	8.66271i	−0.536208	−	0.928740i
$88$	−1.15198	−	1.99528i	−0.122801	−	0.212698i
$89$	6.23470	−	10.7988i	0.660877	−	1.14467i	−0.319508	−	0.947584i	$-0.603518\pi$
$89$	6.23470	−	10.7988i	0.660877	−	1.14467i	0.980385	−	0.197090i	$-0.0631490\pi$
$90$	−6.12741			−0.645886
$91$	−2.14626	−	1.54712i	−0.224989	−	0.162182i
$92$	−4.07753			−0.425112
$93$	−3.07739	+	5.33020i	−0.319111	+	0.552716i
$94$	−3.66996	−	6.35655i	−0.378527	−	0.655628i
$95$	6.24839	+	10.8225i	0.641071	+	1.11037i
$96$	2.98895	−	5.17701i	0.305058	−	0.528376i
$97$	−12.5010			−1.26929			−0.634643	−	0.772806i	$-0.718853\pi$
$97$	−12.5010			−1.26929			−0.634643	+	0.772806i	$0.718853\pi$
$98$	12.2510	+	2.50843i	1.23754	+	0.253390i
$99$	1.59502			0.160306
$100$	−4.02965	+	6.97956i	−0.402965	+	0.697956i
$101$	3.42561	+	5.93332i	0.340860	+	0.590388i	0.984593	−	0.174863i	$-0.0559483\pi$
$101$	3.42561	+	5.93332i	0.340860	+	0.590388i	−0.643732	+	0.765251i	$0.722615\pi$
$102$	−0.0352713	−	0.0610917i	−0.00349238	−	0.00604898i
$103$	−4.57125	+	7.91765i	−0.450419	+	0.780149i	−0.998412	−	0.0563342i	$-0.982059\pi$
$103$	−4.57125	+	7.91765i	−0.450419	+	0.780149i	0.547993	+	0.836483i	$0.315392\pi$
$104$	−1.44447			−0.141641
$105$	−7.36149	−	5.30650i	−0.718408	−	0.517861i
$106$	18.3847			1.78568
$107$	−6.83859	+	11.8448i	−0.661112	+	1.14508i	0.319212	+	0.947683i	$0.396582\pi$
$107$	−6.83859	+	11.8448i	−0.661112	+	1.14508i	−0.980324	+	0.197396i	$0.936752\pi$
$108$	0.595718	+	1.03181i	0.0573230	+	0.0992864i
$109$	−2.82217	−	4.88814i	−0.270315	−	0.468199i	0.698628	−	0.715485i	$-0.253794\pi$
$109$	−2.82217	−	4.88814i	−0.270315	−	0.468199i	−0.968942	+	0.247287i	$0.920461\pi$
$110$	4.88668	−	8.46398i	0.465927	−	0.807009i
$111$	11.1303			1.05644
$112$	11.9764	−	5.38600i	1.13167	−	0.508929i
$113$	−3.61852			−0.340402			−0.170201	−	0.985409i	$-0.554442\pi$
$113$	−3.61852			−0.340402			−0.170201	+	0.985409i	$0.554442\pi$
$114$	3.25445	−	5.63687i	0.304807	−	0.527941i
$115$	5.86921	+	10.1658i	0.547307	+	0.947964i
$116$	5.95888	+	10.3211i	0.553268	+	0.958288i
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$	−16.4233			−1.51189
$119$	0.0105319	−	0.103942i	0.000965458	−	0.00952832i
$120$	−4.95440			−0.452273
$121$	4.22795	−	7.32303i	0.384359	−	0.665730i
$122$	−1.75119	−	3.03315i	−0.158545	−	0.274608i
$123$	−2.54396	−	4.40627i	−0.229381	−	0.397300i
$124$	3.66652	−	6.35060i	0.329263	−	0.570301i
$125$	6.05160			0.541272
$126$	−0.476477	+	4.70245i	−0.0424479	+	0.418927i
$127$	12.6716			1.12442			0.562210	−	0.826995i	$-0.309951\pi$
$127$	12.6716			1.12442			0.562210	+	0.826995i	$0.309951\pi$
$128$	5.30568	−	9.18971i	0.468961	−	0.812264i
$129$	1.45815	+	2.52559i	0.128383	+	0.222366i
$130$	−3.06371	−	5.30650i	−0.268705	−	0.465410i
$131$	5.65548	−	9.79559i	0.494122	−	0.855844i	−0.505855	−	0.862618i	$-0.668823\pi$
$131$	5.65548	−	9.79559i	0.494122	−	0.855844i	0.999977	+	0.00677407i	$0.00215627\pi$
$132$	−1.90037			−0.165406
$133$	8.79158	−	3.95372i	0.762326	−	0.342831i
$134$	−21.5391			−1.86070
$135$	1.71496	−	2.97040i	0.147600	−	0.255651i
$136$	−0.0285191	−	0.0493965i	−0.00244549	−	0.00423572i
$137$	0.382339	+	0.662230i	0.0326654	+	0.0565781i	0.881896	−	0.471444i	$-0.156267\pi$
$137$	0.382339	+	0.662230i	0.0326654	+	0.0565781i	−0.849231	+	0.528022i	$0.822934\pi$
$138$	3.05695	−	5.29480i	0.260225	−	0.450723i
$139$	−0.894171			−0.0758426			−0.0379213	−	0.999281i	$-0.512074\pi$
$139$	−0.894171			−0.0758426			−0.0379213	+	0.999281i	$0.512074\pi$
$140$	8.77076	+	6.32236i	0.741264	+	0.534337i
$141$	4.10864			0.346010
$142$	1.60625	−	2.78211i	0.134794	−	0.233469i
$143$	0.797511	+	1.38133i	0.0666912	+	0.115513i
$144$	2.48168	+	4.29839i	0.206806	+	0.358199i
$145$	17.1545	−	29.7124i	1.42460	−	2.46748i
$146$	11.9783			0.991331
$147$	−4.64488	+	5.23690i	−0.383103	+	0.431932i
$148$	−13.2610			−1.09005
$149$	6.25587	−	10.8355i	0.512501	−	0.887677i	−0.487394	−	0.873182i	$-0.662053\pi$
$149$	6.25587	−	10.8355i	0.512501	−	0.887677i	0.999895	−	0.0144951i	$-0.00461411\pi$
$150$	−6.04212	−	10.4653i	−0.493337	−	0.854485i
$151$	0.916914	+	1.58814i	0.0746174	+	0.129241i	0.900920	−	0.433986i	$-0.142893\pi$
$151$	0.916914	+	1.58814i	0.0746174	+	0.129241i	−0.826302	+	0.563227i	$0.809560\pi$
$152$	2.63143	−	4.55776i	0.213437	−	0.369683i
$153$	0.0394874			0.00319237
$154$	−6.11564	−	4.40843i	−0.492812	−	0.355241i
$155$	−21.1104			−1.69563
$156$	−0.595718	+	1.03181i	−0.0476956	+	0.0826113i
$157$	−9.16243	−	15.8698i	−0.731241	−	1.26655i	−0.956353	−	0.292214i	$-0.905608\pi$
$157$	−9.16243	−	15.8698i	−0.731241	−	1.26655i	0.225112	−	0.974333i	$-0.427725\pi$
$158$	13.0695	+	22.6371i	1.03976	+	1.80091i
$159$	−5.14558	+	8.91240i	−0.408071	+	0.706799i
$160$	20.5037			1.62096
$161$	8.25807	−	3.71379i	0.650827	−	0.292688i
$162$	−1.78646			−0.140358
$163$	−7.38780	+	12.7960i	−0.578657	+	1.00226i	0.416977	+	0.908917i	$0.363090\pi$
$163$	−7.38780	+	12.7960i	−0.578657	+	1.00226i	−0.995634	+	0.0933461i	$0.970244\pi$
$164$	3.03097	+	5.24980i	0.236679	+	0.409940i
$165$	2.73540	+	4.73785i	0.212951	+	0.368841i
$166$	−4.77569	+	8.27175i	−0.370666	+	0.642012i
$167$	−6.61137			−0.511603			−0.255801	−	0.966729i	$-0.582339\pi$
$167$	−6.61137			−0.511603			−0.255801	+	0.966729i	$0.582339\pi$
$168$	−0.385261	+	3.80223i	−0.0297236	+	0.293348i
$169$	1.00000			0.0769231
$170$	0.120978	−	0.209540i	0.00927858	−	0.0160710i
$171$	1.82173	+	3.15533i	0.139311	+	0.241294i
$172$	−1.73730	−	3.00909i	−0.132468	−	0.229441i
$173$	0.362595	−	0.628033i	0.0275676	−	0.0477484i	−0.851912	−	0.523684i	$-0.824557\pi$
$173$	0.362595	−	0.628033i	0.0275676	−	0.0477484i	0.879480	+	0.475936i	$0.157891\pi$
$174$	−17.8697			−1.35470
$175$	1.80416	−	17.8056i	0.136382	−	1.34598i
$176$	−7.91666			−0.596741
$177$	4.59662	−	7.96158i	0.345503	−	0.598429i
$178$	−11.1380	−	19.2917i	−0.834832	−	1.44597i
$179$	9.39675	+	16.2756i	0.702346	+	1.21650i	0.967641	+	0.252332i	$0.0811974\pi$
$179$	9.39675	+	16.2756i	0.702346	+	1.21650i	−0.265295	+	0.964167i	$0.585469\pi$
$180$	−2.04327	+	3.53904i	−0.152296	+	0.263785i
$181$	−7.45429			−0.554073			−0.277036	−	0.960859i	$-0.589352\pi$
$181$	−7.45429			−0.554073			−0.277036	+	0.960859i	$0.589352\pi$
$182$	−4.31068	+	1.93858i	−0.319529	+	0.143697i
$183$	1.96051			0.144925
$184$	2.47174	−	4.28118i	0.182219	−	0.315613i
$185$	19.0879	+	33.0613i	1.40337	+	2.43071i
$186$	5.49764	+	9.52219i	0.403107	+	0.698201i
$187$	−0.0314916	+	0.0545451i	−0.00230290	+	0.00398874i
$188$	−4.89518			−0.357018
$189$	−2.14626	−	1.54712i	−0.156117	−	0.112536i
$190$	22.3250			1.61963
$191$	−10.1900	+	17.6495i	−0.737320	+	1.27708i	0.216378	+	0.976310i	$0.430576\pi$
$191$	−10.1900	+	17.6495i	−0.737320	+	1.27708i	−0.953698	+	0.300766i	$0.902758\pi$
$192$	−0.376282	−	0.651740i	−0.0271558	−	0.0470353i
$193$	5.15101	+	8.92181i	0.370778	+	0.642206i	0.989685	−	0.143258i	$-0.0457578\pi$
$193$	5.15101	+	8.92181i	0.370778	+	0.642206i	−0.618908	+	0.785464i	$0.712424\pi$
$194$	−11.1663	+	19.3406i	−0.801692	+	1.38857i
$195$	3.42992			0.245622
$196$	5.53408	−	6.23943i	0.395292	−	0.445674i
$197$	22.1453			1.57779			0.788895	−	0.614528i	$-0.210653\pi$
$197$	22.1453			1.57779			0.788895	+	0.614528i	$0.210653\pi$
$198$	1.42472	−	2.46769i	0.101251	−	0.175371i
$199$	7.31957	+	12.6779i	0.518871	+	0.898711i	0.999760	+	0.0219290i	$0.00698079\pi$
$199$	7.31957	+	12.6779i	0.518871	+	0.898711i	−0.480889	+	0.876782i	$0.659686\pi$
$200$	−4.88544	−	8.46183i	−0.345453	−	0.598341i
$201$	6.02844	−	10.4416i	0.425213	−	0.736491i
$202$	12.2394			0.861162
$203$	−21.4687	−	15.4756i	−1.50681	−	1.08617i
$204$	−0.0470468			−0.00329393
$205$	8.72559	−	15.1132i	0.609422	−	1.05555i
$206$	8.16636	+	14.1446i	0.568977	+	0.985498i
$207$	1.71118	+	2.96385i	0.118935	+	0.206002i
$208$	−2.48168	+	4.29839i	−0.172073	+	0.298040i
$209$	−5.81140			−0.401983
$210$	−14.7853	+	6.64919i	−1.02028	+	0.458838i
$211$	−16.5084			−1.13649			−0.568243	−	0.822861i	$-0.692377\pi$
$211$	−16.5084			−1.13649			−0.568243	+	0.822861i	$0.692377\pi$
$212$	6.13063	−	10.6186i	0.421053	−	0.729286i
$213$	0.899125	+	1.55733i	0.0616070	+	0.106707i
$214$	12.2169	+	21.1602i	0.835128	+	1.44648i
$215$	−5.00135	+	8.66259i	−0.341089	+	0.590784i
$216$	−1.44447			−0.0982834
$217$	−1.64158	+	16.2011i	−0.111438	+	1.09980i
$218$	−10.0834			−0.682932
$219$	−3.35253	+	5.80675i	−0.226543	+	0.392384i
$220$	−3.25906	−	5.64485i	−0.219726	−	0.380576i
$221$	0.0197437	+	0.0341971i	0.00132811	+	0.00230035i
$222$	9.94187	−	17.2198i	0.667255	−	1.15572i
$223$	−12.1251			−0.811958			−0.405979	−	0.913882i	$-0.633069\pi$
$223$	−12.1251			−0.811958			−0.405979	+	0.913882i	$0.633069\pi$
$224$	1.59440	−	15.7355i	0.106530	−	1.05137i
$225$	6.76436			0.450957
$226$	−3.23217	+	5.59828i	−0.215001	+	0.372392i
$227$	7.33168	+	12.6988i	0.486621	+	0.842852i	0.999882	−	0.0153807i	$-0.00489602\pi$
$227$	7.33168	+	12.6988i	0.486621	+	0.842852i	−0.513261	+	0.858233i	$0.671563\pi$
$228$	−2.17048	−	3.75938i	−0.143743	−	0.248971i
$229$	−6.68884	+	11.5854i	−0.442011	+	0.765586i	−0.997839	−	0.0657118i	$-0.979068\pi$
$229$	−6.68884	+	11.5854i	−0.442011	+	0.765586i	0.555827	+	0.831298i	$0.312402\pi$
$230$	20.9702			1.38274
$231$	3.84875	−	1.73085i	0.253229	−	0.113881i
$232$	−14.4488			−0.948607
$233$	−3.47177	+	6.01328i	−0.227443	+	0.393943i	−0.957050	−	0.289924i	$-0.906370\pi$
$233$	−3.47177	+	6.01328i	−0.227443	+	0.393943i	0.729607	+	0.683867i	$0.239703\pi$
$234$	−0.893230	−	1.54712i	−0.0583922	−	0.101138i
$235$	7.04615	+	12.2043i	0.459640	+	0.796120i
$236$	−5.47658	+	9.48572i	−0.356495	+	0.617468i
$237$	−14.6318			−0.950435
$238$	−0.151403	−	0.109138i	−0.00981398	−	0.00707436i
$239$	10.1854			0.658836			0.329418	−	0.944184i	$-0.393147\pi$
$239$	10.1854			0.658836			0.329418	+	0.944184i	$0.393147\pi$
$240$	−8.51195	+	14.7431i	−0.549444	+	0.951665i
$241$	4.87250	+	8.43942i	0.313865	+	0.543631i	0.979196	−	0.202918i	$-0.0650426\pi$
$241$	4.87250	+	8.43942i	0.313865	+	0.543631i	−0.665330	+	0.746549i	$0.731709\pi$
$242$	−7.55306	−	13.0823i	−0.485529	−	0.840961i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.33583			−0.149536
$245$	−23.5215	−	4.81608i	−1.50273	−	0.307688i
$246$	−9.08937			−0.579517
$247$	−1.82173	+	3.15533i	−0.115914	+	0.200769i
$248$	4.44519	+	7.69929i	0.282270	+	0.488906i
$249$	−2.67327	−	4.63025i	−0.169412	−	0.293430i
$250$	5.40547	−	9.36255i	0.341872	−	0.592139i
$251$	−25.5879			−1.61509			−0.807546	−	0.589805i	$-0.799205\pi$
$251$	−25.5879			−1.61509			−0.807546	+	0.589805i	$0.799205\pi$
$252$	2.55713	+	1.84329i	0.161084	+	0.116117i
$253$	−5.45874			−0.343188
$254$	11.3186	−	19.6044i	0.710193	−	1.23009i
$255$	0.0677193	+	0.117293i	0.00424075	+	0.00734519i
$256$	−10.2310	−	17.7205i	−0.639434	−	1.10753i
$257$	−5.78330	+	10.0170i	−0.360753	+	0.624842i	−0.988085	−	0.153910i	$-0.950813\pi$
$257$	−5.78330	+	10.0170i	−0.360753	+	0.624842i	0.627332	+	0.778752i	$0.284147\pi$
$258$	5.20986			0.324352
$259$	26.8570	−	12.0780i	1.66881	−	0.750493i
$260$	−4.08653			−0.253436
$261$	5.00142	−	8.66271i	0.309580	−	0.536208i
$262$	−10.1033	−	17.4994i	−0.624184	−	1.08112i
$263$	−2.14700	−	3.71871i	−0.132389	−	0.229305i	0.792208	−	0.610252i	$-0.208932\pi$
$263$	−2.14700	−	3.71871i	−0.132389	−	0.229305i	−0.924597	+	0.380946i	$0.875598\pi$
$264$	1.15198	−	1.99528i	0.0708993	−	0.122801i
$265$	−35.2978			−2.16833
$266$	1.73602	−	17.1332i	0.106442	−	1.05050i
$267$	12.4694			0.763115
$268$	−7.18250	+	12.4405i	−0.438741	+	0.759922i
$269$	3.40333	+	5.89473i	0.207504	+	0.359408i	0.950928	−	0.309413i	$-0.100133\pi$
$269$	3.40333	+	5.89473i	0.207504	+	0.359408i	−0.743423	+	0.668821i	$0.766799\pi$
$270$	−3.06371	−	5.30650i	−0.186451	−	0.322943i
$271$	5.33823	−	9.24609i	0.324274	−	0.561660i	−0.657091	−	0.753811i	$-0.728213\pi$
$271$	5.33823	−	9.24609i	0.324274	−	0.561660i	0.981365	+	0.192152i	$0.0615466\pi$
$272$	−0.195990			−0.0118836
$273$	0.266716	−	2.63227i	0.0161424	−	0.159312i
$274$	1.36606			0.0825270
$275$	−5.39465	+	9.34381i	−0.325310	+	0.563453i
$276$	−2.03876	−	3.53124i	−0.122719	−	0.212556i
$277$	−13.9118	−	24.0960i	−0.835880	−	1.44779i	−0.893312	−	0.449437i	$-0.851625\pi$
$277$	−13.9118	−	24.0960i	−0.835880	−	1.44779i	0.0574319	−	0.998349i	$-0.481709\pi$
$278$	−0.798700	+	1.38339i	−0.0479028	+	0.0829701i
$279$	−6.15479			−0.368478
$280$	−11.9548	+	5.37629i	−0.714438	+	0.321295i
$281$	27.3000			1.62858			0.814291	−	0.580458i	$-0.197126\pi$
$281$	27.3000			1.62858			0.814291	+	0.580458i	$0.197126\pi$
$282$	3.66996	−	6.35655i	0.218543	−	0.378527i
$283$	−7.92237	−	13.7220i	−0.470936	−	0.815685i	0.528511	−	0.848926i	$-0.322750\pi$
$283$	−7.92237	−	13.7220i	−0.470936	−	0.815685i	−0.999447	+	0.0332409i	$0.989417\pi$
$284$	−1.07125	−	1.85546i	−0.0635670	−	0.110101i
$285$	−6.24839	+	10.8225i	−0.370123	+	0.641071i
$286$	2.84944			0.168491
$287$	−10.9200	−	7.87163i	−0.644587	−	0.464648i
$288$	5.97790			0.352251
$289$	8.49922	−	14.7211i	0.499954	−	0.865946i
$290$	−30.6458	−	53.0800i	−1.79958	−	3.11697i
$291$	−6.25051	−	10.8262i	−0.366411	−	0.634643i
$292$	3.99432	−	6.91837i	0.233750	−	0.404867i
$293$	16.4408			0.960481			0.480240	−	0.877137i	$-0.340549\pi$
$293$	16.4408			0.960481			0.480240	+	0.877137i	$0.340549\pi$
$294$	3.95316	+	11.8639i	0.230553	+	0.691919i
$295$	31.5321			1.83587
$296$	8.03863	−	13.9233i	0.467236	−	0.809276i
$297$	0.797511	+	1.38133i	0.0462763	+	0.0801529i
$298$	−11.1759	−	19.3571i	−0.647400	−	1.12133i
$299$	−1.71118	+	2.96385i	−0.0989601	+	0.171404i
$300$	−8.05930			−0.465304
$301$	6.25914	+	4.51187i	0.360771	+	0.260060i
$302$	3.27606			0.188516
$303$	−3.42561	+	5.93332i	−0.196796	+	0.340860i
$304$	−9.04189	−	15.6610i	−0.518588	−	0.898221i
$305$	3.36220	+	5.82350i	0.192519	+	0.333453i
$306$	0.0352713	−	0.0610917i	0.00201633	−	0.00349238i
$307$	−24.0573			−1.37302			−0.686512	−	0.727119i	$-0.740859\pi$
$307$	−24.0573			−1.37302			−0.686512	+	0.727119i	$0.740859\pi$
$308$	−4.58554	+	2.06219i	−0.261285	+	0.117504i
$309$	−9.14251			−0.520099
$310$	−18.8565	+	32.6604i	−1.07098	+	1.85498i
$311$	17.0618	+	29.5519i	0.967487	+	1.67574i	0.702778	+	0.711409i	$0.251943\pi$
$311$	17.0618	+	29.5519i	0.967487	+	1.67574i	0.264709	+	0.964328i	$0.414724\pi$
$312$	−0.722233	−	1.25094i	−0.0408884	−	0.0708207i
$313$	−15.2959	+	26.4933i	−0.864575	+	1.49749i	0.00289390	+	0.999996i	$0.499079\pi$
$313$	−15.2959	+	26.4933i	−0.864575	+	1.49749i	−0.867469	+	0.497492i	$0.834254\pi$
$314$	−32.7366			−1.84743
$315$	0.914813	−	9.02849i	0.0515439	−	0.508698i
$316$	17.4328			0.980672
$317$	2.20908	−	3.82623i	0.124074	−	0.214903i	−0.797297	−	0.603588i	$-0.793737\pi$
$317$	2.20908	−	3.82623i	0.124074	−	0.214903i	0.921371	+	0.388685i	$0.127071\pi$
$318$	9.19236	+	15.9216i	0.515482	+	0.892841i
$319$	7.97738	+	13.8172i	0.446647	+	0.773616i
$320$	1.29062	−	2.23542i	0.0721478	−	0.124964i
$321$	−13.6772			−0.763386
$322$	1.63068	−	16.0935i	0.0908740	−	0.896855i
$323$	−0.143871			−0.00800519
$324$	−0.595718	+	1.03181i	−0.0330955	+	0.0573230i
$325$	3.38218	+	5.85810i	0.187609	+	0.324949i
$326$	13.1980	+	22.8596i	0.730970	+	1.26608i
$327$	2.82217	−	4.88814i	0.156066	−	0.270315i
$328$	−7.34933			−0.405799
$329$	9.91403	−	4.45851i	0.546578	−	0.245805i
$330$	9.77336			0.538006
$331$	−12.4337	+	21.5358i	−0.683418	+	1.18371i	0.290513	+	0.956871i	$0.406174\pi$
$331$	−12.4337	+	21.5358i	−0.683418	+	1.18371i	−0.973931	+	0.226844i	$0.927159\pi$
$332$	3.18504	+	5.51665i	0.174802	+	0.302765i
$333$	5.56513	+	9.63908i	0.304967	+	0.528218i
$334$	−5.90547	+	10.2286i	−0.323133	+	0.559683i
$335$	41.3541			2.25942
$336$	10.6526	+	7.67890i	0.581149	+	0.418918i
$337$	−10.1490			−0.552851			−0.276426	−	0.961035i	$-0.589150\pi$
$337$	−10.1490			−0.552851			−0.276426	+	0.961035i	$0.589150\pi$
$338$	0.893230	−	1.54712i	0.0485853	−	0.0841522i
$339$	−1.80926	−	3.13373i	−0.0982655	−	0.170201i
$340$	−0.0806833	−	0.139748i	−0.00437567	−	0.00757888i
$341$	4.90851	−	8.50179i	0.265811	−	0.460398i
$342$	6.50890			0.351961
$343$	−5.52513	+	17.6769i	−0.298329	+	0.954463i
$344$	4.21250			0.227123
$345$	−5.86921	+	10.1658i	−0.315988	+	0.547307i
$346$	−0.647761	−	1.12195i	−0.0348238	−	0.0603167i
$347$	0.148170	+	0.256638i	0.00795417	+	0.0137770i	0.869975	−	0.493096i	$-0.164135\pi$
$347$	0.148170	+	0.256638i	0.00795417	+	0.0137770i	−0.862021	+	0.506873i	$0.830801\pi$
$348$	−5.95888	+	10.3211i	−0.319429	+	0.553268i
$349$	28.7148			1.53707			0.768534	−	0.639809i	$-0.220987\pi$
$349$	28.7148			1.53707			0.768534	+	0.639809i	$0.220987\pi$
$350$	−25.9359	−	18.6958i	−1.38633	−	0.999331i
$351$	1.00000			0.0533761
$352$	−4.76744	+	8.25745i	−0.254105	+	0.440123i
$353$	−10.8041	−	18.7132i	−0.575042	−	0.996002i	−0.996037	−	0.0889393i	$-0.971652\pi$
$353$	−10.8041	−	18.7132i	−0.575042	−	0.996002i	0.420995	−	0.907063i	$-0.361681\pi$
$354$	−8.21167	−	14.2230i	−0.436445	−	0.755946i
$355$	−3.08393	+	5.34152i	−0.163678	+	0.283498i
$356$	−14.8565			−0.787394
$357$	0.0952821	−	0.0428499i	0.00504286	−	0.00226786i
$358$	33.5738			1.77443
$359$	−3.19945	+	5.54161i	−0.168860	+	0.292475i	−0.938019	−	0.346583i	$-0.887342\pi$
$359$	−3.19945	+	5.54161i	−0.168860	+	0.292475i	0.769159	+	0.639057i	$0.220675\pi$
$360$	−2.47720	−	4.29064i	−0.130560	−	0.226136i
$361$	2.86259	+	4.95816i	0.150663	+	0.260956i
$362$	−6.65839	+	11.5327i	−0.349957	+	0.606144i
$363$	8.45590			0.443820
$364$	−0.317775	+	3.13619i	−0.0166559	+	0.164381i
$365$	−22.9978			−1.20376
$366$	1.75119	−	3.03315i	0.0915361	−	0.158545i
$367$	−0.359462	−	0.622606i	−0.0187637	−	0.0324998i	0.856491	−	0.516162i	$-0.172640\pi$
$367$	−0.359462	−	0.622606i	−0.0187637	−	0.0324998i	−0.875255	+	0.483662i	$0.839306\pi$
$368$	−8.49319	−	14.7106i	−0.442738	−	0.766845i
$369$	2.54396	−	4.40627i	0.132433	−	0.229381i
$370$	68.1997			3.54553
$371$	−2.74481	+	27.0891i	−0.142504	+	1.40640i
$372$	7.33304			0.380201
$373$	4.94870	−	8.57139i	0.256234	−	0.443810i	−0.708996	−	0.705212i	$-0.750852\pi$
$373$	4.94870	−	8.57139i	0.256234	−	0.443810i	0.965230	+	0.261402i	$0.0841850\pi$
$374$	0.0562586	+	0.0974427i	0.00290906	+	0.00503864i
$375$	3.02580	+	5.24084i	0.156252	+	0.270636i
$376$	2.96739	−	5.13967i	0.153032	−	0.265058i
$377$	10.0028			0.515172
$378$	−4.31068	+	1.93858i	−0.221717	+	0.0997100i
$379$	3.64783			0.187376			0.0936882	−	0.995602i	$-0.470134\pi$
$379$	3.64783			0.187376			0.0936882	+	0.995602i	$0.470134\pi$
$380$	7.44456	−	12.8944i	0.381898	−	0.661467i
$381$	6.33578	+	10.9739i	0.324592	+	0.562210i
$382$	18.2040	+	31.5302i	0.931395	+	1.61322i
$383$	−7.85143	+	13.5991i	−0.401189	+	0.694880i	−0.993870	−	0.110558i	$-0.964736\pi$
$383$	−7.85143	+	13.5991i	−0.401189	+	0.694880i	0.592681	+	0.805438i	$0.298070\pi$
$384$	10.6114			0.541509
$385$	11.7417	+	8.46398i	0.598415	+	0.431364i
$386$	18.4041			0.936746
$387$	−1.45815	+	2.52559i	−0.0741221	+	0.128383i
$388$	7.44709	+	12.8987i	0.378068	+	0.654834i
$389$	−5.24131	−	9.07822i	−0.265745	−	0.460284i	0.702014	−	0.712164i	$-0.252285\pi$
$389$	−5.24131	−	9.07822i	−0.265745	−	0.460284i	−0.967759	+	0.251880i	$0.918951\pi$
$390$	3.06371	−	5.30650i	0.155137	−	0.268705i
$391$	−0.135140			−0.00683433
$392$	3.19638	+	9.59274i	0.161441	+	0.484507i
$393$	11.3110			0.570563
$394$	19.7809	−	34.2615i	0.996546	−	1.72607i
$395$	−25.0929	−	43.4621i	−1.26256	−	2.18682i
$396$	−0.950184	−	1.64577i	−0.0477486	−	0.0827029i
$397$	−13.1096	+	22.7065i	−0.657953	+	1.13961i	0.323191	+	0.946334i	$0.395244\pi$
$397$	−13.1096	+	22.7065i	−0.657953	+	1.13961i	−0.981145	+	0.193275i	$0.938089\pi$
$398$	26.1522			1.31089
$399$	7.81981	+	5.63687i	0.391480	+	0.282196i
$400$	−33.5739			−1.67869
$401$	14.9922	−	25.9673i	0.748676	−	1.29674i	−0.199782	−	0.979840i	$-0.564023\pi$
$401$	14.9922	−	25.9673i	0.748676	−	1.29674i	0.948458	−	0.316904i	$-0.102643\pi$
$402$	−10.7696	−	18.6534i	−0.537137	−	0.930348i
$403$	−3.07739	−	5.33020i	−0.153296	−	0.265516i
$404$	4.08139	−	7.06918i	0.203057	−	0.351705i
$405$	3.42992			0.170434
$406$	−43.1190	+	19.3913i	−2.13996	+	0.962376i
$407$	−17.7530			−0.879984
$408$	0.0285191	−	0.0493965i	0.00141191	−	0.00244549i
$409$	−8.06161	−	13.9631i	−0.398621	−	0.690432i	0.594935	−	0.803774i	$-0.297178\pi$
$409$	−8.06161	−	13.9631i	−0.398621	−	0.690432i	−0.993556	+	0.113342i	$0.963844\pi$
$410$	−15.5879	−	26.9991i	−0.769832	−	1.33339i
$411$	−0.382339	+	0.662230i	−0.0188594	+	0.0326654i
$412$	10.8927			0.536646
$413$	2.45198	−	24.1991i	0.120654	−	1.19076i
$414$	6.11391			0.300482
$415$	9.16912	−	15.8814i	0.450094	−	0.779586i
$416$	2.98895	+	5.17701i	0.146545	+	0.253824i
$417$	−0.447085	−	0.774374i	−0.0218939	−	0.0379213i
$418$	−5.19092	+	8.99093i	−0.253896	+	0.439761i
$419$	−6.10021			−0.298015			−0.149007	−	0.988836i	$-0.547608\pi$
$419$	−6.10021			−0.298015			−0.149007	+	0.988836i	$0.547608\pi$
$420$	−1.08994	+	10.7569i	−0.0531837	+	0.524882i
$421$	11.1161			0.541768			0.270884	−	0.962612i	$-0.412684\pi$
$421$	11.1161			0.541768			0.270884	+	0.962612i	$0.412684\pi$
$422$	−14.7458	+	25.5405i	−0.717814	+	1.24329i
$423$	2.05432	+	3.55818i	0.0998844	+	0.173005i
$424$	7.43261	+	12.8737i	0.360959	+	0.625200i
$425$	−0.133553	+	0.231321i	−0.00647829	+	0.0112207i
$426$	3.21250			0.155646
$427$	4.73066	−	2.12746i	0.228933	−	0.102955i
$428$	16.2955			0.787673
$429$	−0.797511	+	1.38133i	−0.0385042	+	0.0666912i
$430$	8.93470	+	15.4754i	0.430870	+	0.746288i
$431$	2.93016	+	5.07519i	0.141141	+	0.244464i	0.927927	−	0.372763i	$-0.121590\pi$
$431$	2.93016	+	5.07519i	0.141141	+	0.244464i	−0.786786	+	0.617227i	$0.788256\pi$
$432$	−2.48168	+	4.29839i	−0.119400	+	0.206806i
$433$	−32.1012			−1.54268			−0.771342	−	0.636421i	$-0.780414\pi$
$433$	−32.1012			−1.54268			−0.771342	+	0.636421i	$0.780414\pi$
$434$	23.5987	+	17.0110i	1.13277	+	0.816555i
$435$	34.3089			1.64499
$436$	−3.36243	+	5.82391i	−0.161031	+	0.278915i
$437$	−6.23462	−	10.7987i	−0.298242	−	0.516571i
$438$	5.98915	+	10.3735i	0.286173	+	0.495666i
$439$	14.5989	−	25.2861i	0.696769	−	1.20684i	−0.272811	−	0.962068i	$-0.587953\pi$
$439$	14.5989	−	25.2861i	0.696769	−	1.20684i	0.969581	−	0.244772i	$-0.0787132\pi$
$440$	7.90238			0.376731
$441$	−6.85773	−	1.40414i	−0.326558	−	0.0668637i
$442$	0.0705426			0.00335537
$443$	14.0758	−	24.3800i	0.668762	−	1.15833i	−0.309488	−	0.950903i	$-0.600158\pi$
$443$	14.0758	−	24.3800i	0.668762	−	1.15833i	0.978250	−	0.207427i	$-0.0665090\pi$
$444$	−6.63050	−	11.4844i	−0.314669	−	0.545024i
$445$	21.3845	+	37.0391i	1.01372	+	1.75582i
$446$	−10.8305	+	18.7590i	−0.512840	+	0.888265i
$447$	12.5117			0.591785
$448$	−1.61520	−	1.16431i	−0.0763109	−	0.0550084i
$449$	5.39643			0.254673			0.127337	−	0.991860i	$-0.459357\pi$
$449$	5.39643			0.254673			0.127337	+	0.991860i	$0.459357\pi$
$450$	6.04212	−	10.4653i	0.284828	−	0.493337i
$451$	4.05768	+	7.02810i	0.191069	+	0.330941i
$452$	2.15562	+	3.73364i	0.101392	+	0.175616i
$453$	−0.916914	+	1.58814i	−0.0430804	+	0.0746174i
$454$	26.1955			1.22942
$455$	8.27631	−	3.72199i	0.387999	−	0.174490i
$456$	5.26285			0.246456
$457$	−14.7540	+	25.5546i	−0.690161	+	1.19539i	0.281624	+	0.959525i	$0.409127\pi$
$457$	−14.7540	+	25.5546i	−0.690161	+	1.19539i	−0.971785	+	0.235869i	$0.924206\pi$
$458$	11.9493	+	20.6969i	0.558356	+	0.967102i
$459$	0.0197437	+	0.0341971i	0.000921557	+	0.00159618i
$460$	6.99280	−	12.1119i	0.326041	−	0.564719i
$461$	−17.6176			−0.820533			−0.410267	−	0.911966i	$-0.634564\pi$
$461$	−17.6176			−0.820533			−0.410267	+	0.911966i	$0.634564\pi$
$462$	0.759991	−	7.50051i	0.0353580	−	0.348955i
$463$	6.40031			0.297448			0.148724	−	0.988879i	$-0.452483\pi$
$463$	6.40031			0.297448			0.148724	+	0.988879i	$0.452483\pi$
$464$	−24.8238	+	42.9961i	−1.15242	+	1.99604i
$465$	−10.5552	−	18.2822i	−0.489487	−	0.847816i
$466$	6.20217	+	10.7425i	0.287310	+	0.497636i
$467$	7.71392	−	13.3609i	0.356958	−	0.618269i	−0.630493	−	0.776195i	$-0.717147\pi$
$467$	7.71392	−	13.3609i	0.356958	−	0.618269i	0.987451	+	0.157926i	$0.0504807\pi$
$468$	−1.19144			−0.0550742
$469$	3.21576	−	31.7370i	0.148490	−	1.46548i
$470$	25.1753			1.16125
$471$	9.16243	−	15.8698i	0.422182	−	0.731241i
$472$	−6.63965	−	11.5002i	−0.305615	−	0.529340i
$473$	−2.32579	−	4.02838i	−0.106940	−	0.185225i
$474$	−13.0695	+	22.6371i	−0.600303	+	1.03976i
$475$	−24.6457			−1.13082
$476$	−0.113523	+	0.0510530i	−0.00520330	+	0.00234001i
$477$	−10.2912			−0.471200
$478$	9.09786	−	15.7580i	0.416127	−	0.720752i
$479$	−11.5648	−	20.0309i	−0.528411	−	0.915235i	−0.999451	−	0.0331230i	$-0.989455\pi$
$479$	−11.5648	−	20.0309i	−0.528411	−	0.915235i	0.471040	−	0.882112i	$-0.343879\pi$
$480$	10.2519	+	17.7567i	0.467931	+	0.810480i
$481$	−5.56513	+	9.63908i	−0.253748	+	0.439504i
$482$	17.4091			0.792961
$483$	7.34527	+	5.29480i	0.334221	+	0.240922i
$484$	−10.0747			−0.457940
$485$	21.4387	−	37.1330i	0.973483	−	1.68612i
$486$	−0.893230	−	1.54712i	−0.0405177	−	0.0701788i
$487$	−3.90543	−	6.76440i	−0.176972	−	0.306524i	0.763870	−	0.645370i	$-0.223297\pi$
$487$	−3.90543	−	6.76440i	−0.176972	−	0.306524i	−0.940842	+	0.338846i	$0.889963\pi$
$488$	1.41595	−	2.45249i	0.0640969	−	0.111019i
$489$	−14.7756			−0.668176
$490$	−28.4611	+	32.0886i	−1.28574	+	1.44962i
$491$	−24.7444			−1.11670			−0.558350	−	0.829605i	$-0.688565\pi$
$491$	−24.7444			−1.11670			−0.558350	+	0.829605i	$0.688565\pi$
$492$	−3.03097	+	5.24980i	−0.136647	+	0.236679i
$493$	0.197493	+	0.342068i	0.00889464	+	0.0154060i
$494$	3.25445	+	5.63687i	0.146425	+	0.253615i
$495$	−2.73540	+	4.73785i	−0.122947	+	0.212951i
$496$	30.5484			1.37166
$497$	3.85951	+	2.78211i	0.173123	+	0.124795i
$498$	−9.55139			−0.428008
$499$	8.60258	−	14.9001i	0.385104	−	0.667020i	−0.606679	−	0.794947i	$-0.707499\pi$
$499$	8.60258	−	14.9001i	0.385104	−	0.667020i	0.991784	+	0.127926i	$0.0408321\pi$
$500$	−3.60505	−	6.24413i	−0.161223	−	0.279246i
$501$	−3.30568	−	5.72561i	−0.147687	−	0.255801i
$502$	−22.8558	+	39.5875i	−1.02011	+	1.76688i
$503$	31.0833			1.38593			0.692967	−	0.720969i	$-0.256303\pi$
$503$	31.0833			1.38593			0.692967	+	0.720969i	$0.256303\pi$
$504$	−3.48546	+	1.56747i	−0.155255	+	0.0698205i
$505$	−23.4991			−1.04570
$506$	−4.87591	+	8.44533i	−0.216761	+	0.375441i
$507$	0.500000	+	0.866025i	0.0222058	+	0.0384615i
$508$	−7.54869	−	13.0747i	−0.334919	−	0.580096i
$509$	9.34262	−	16.1819i	0.414104	−	0.717250i	−0.581230	−	0.813740i	$-0.697428\pi$
$509$	9.34262	−	16.1819i	0.414104	−	0.717250i	0.995334	+	0.0964899i	$0.0307615\pi$
$510$	0.241956			0.0107140
$511$	−1.78834	+	17.6495i	−0.0791116	+	0.780769i
$512$	−15.3316			−0.677569
$513$	−1.82173	+	3.15533i	−0.0804314	+	0.139311i
$514$	10.3316	+	17.8949i	0.455709	+	0.789311i
$515$	−15.6790	−	27.1569i	−0.690901	−	1.19668i
$516$	1.73730	−	3.00909i	0.0764802	−	0.132468i
$517$	−6.55337			−0.288217
$518$	5.30331	−	52.3394i	0.233014	−	2.29966i
$519$	0.725190			0.0318323
$520$	2.47720	−	4.29064i	0.108632	−	0.188157i
$521$	2.62718	+	4.55041i	0.115099	+	0.199357i	0.917819	−	0.396998i	$-0.129948\pi$
$521$	2.62718	+	4.55041i	0.115099	+	0.199357i	−0.802720	+	0.596356i	$0.796615\pi$
$522$	−8.93483	−	15.4756i	−0.391067	−	0.677348i
$523$	0.453417	−	0.785340i	0.0198265	−	0.0343405i	−0.855942	−	0.517072i	$-0.827022\pi$
$523$	0.453417	−	0.785340i	0.0198265	−	0.0343405i	0.875768	+	0.482731i	$0.160355\pi$
$524$	−13.4763			−0.588715
$525$	16.3222	−	7.34037i	0.712360	−	0.320360i
$526$	−7.67104			−0.334473
$527$	0.121518	−	0.210476i	0.00529342	−	0.00916847i
$528$	−3.95833	−	6.85603i	−0.172264	−	0.298370i
$529$	5.64372	+	9.77521i	0.245379	+	0.425009i
$530$	−31.5291	+	54.6100i	−1.36954	+	2.37211i
$531$	9.19324			0.398952
$532$	−9.31681	−	6.71597i	−0.403935	−	0.291174i
$533$	5.08793			0.220383
$534$	11.1380	−	19.2917i	0.481990	−	0.834832i
$535$	−23.4558	−	40.6267i	−1.01408	−	1.75645i
$536$	−8.70786	−	15.0825i	−0.376122	−	0.651463i
$537$	−9.39675	+	16.2756i	−0.405500	+	0.702346i
$538$	12.1598			0.524246
$539$	7.40869	−	8.35297i	0.319115	−	0.359788i
$540$	−4.08653			−0.175856
$541$	6.58021	−	11.3973i	0.282905	−	0.490006i	−0.689194	−	0.724577i	$-0.742035\pi$
$541$	6.58021	−	11.3973i	0.282905	−	0.490006i	0.972099	+	0.234571i	$0.0753685\pi$
$542$	−9.53653	−	16.5178i	−0.409629	−	0.709498i
$543$	−3.72714	−	6.45560i	−0.159947	−	0.277036i
$544$	−0.118026	+	0.204427i	−0.00506031	+	0.00876472i
$545$	19.3596			0.829275
$546$	−3.83420	−	2.76387i	−0.164089	−	0.118283i
$547$	2.77123			0.118489			0.0592446	−	0.998243i	$-0.481131\pi$
$547$	2.77123			0.118489			0.0592446	+	0.998243i	$0.481131\pi$
$548$	0.455532	−	0.789005i	0.0194594	−	0.0337046i
$549$	0.980256	+	1.69785i	0.0418363	+	0.0724626i
$550$	9.63732	+	16.6923i	0.410937	+	0.711763i
$551$	−18.2225	+	31.5623i	−0.776304	+	1.34460i
$552$	4.94348			0.210409
$553$	−35.3060	+	15.8777i	−1.50137	+	0.675189i
$554$	−49.7058			−2.11180
$555$	−19.0879	+	33.0613i	−0.810238	+	1.40337i
$556$	0.532674	+	0.922618i	0.0225904	+	0.0391277i
$557$	−6.56459	−	11.3702i	−0.278151	−	0.481771i	0.692775	−	0.721154i	$-0.256388\pi$
$557$	−6.56459	−	11.3702i	−0.278151	−	0.481771i	−0.970925	+	0.239383i	$0.923055\pi$
$558$	−5.49764	+	9.52219i	−0.232734	+	0.403107i
$559$	−2.91631			−0.123347
$560$	−4.54054	+	44.8116i	−0.191873	+	1.89363i
$561$	−0.0629833			−0.00265916
$562$	24.3852	−	42.2363i	1.02863	−	1.78163i
$563$	11.8737	+	20.5659i	0.500419	+	0.866751i	1.00000		0.000483665i	$0.000153955\pi$
$563$	11.8737	+	20.5659i	0.500419	+	0.866751i	−0.499581	+	0.866267i	$0.666513\pi$
$564$	−2.44759	−	4.23935i	−0.103062	−	0.178509i
$565$	6.20562	−	10.7484i	0.261072	−	0.452190i
$566$	−28.3060			−1.18979
$567$	0.266716	−	2.63227i	0.0112010	−	0.110545i
$568$	2.59751			0.108989
$569$	−15.6789	+	27.1566i	−0.657293	+	1.13846i	0.324021	+	0.946050i	$0.394965\pi$
$569$	−15.6789	+	27.1566i	−0.657293	+	1.13846i	−0.981314	+	0.192415i	$0.938368\pi$
$570$	11.1625	+	19.3340i	0.467546	+	0.809813i
$571$	−6.54230	−	11.3316i	−0.273787	−	0.474212i	0.696042	−	0.718001i	$-0.254943\pi$
$571$	−6.54230	−	11.3316i	−0.273787	−	0.474212i	−0.969828	+	0.243789i	$0.921610\pi$
$572$	0.950184	−	1.64577i	0.0397292	−	0.0688130i
$573$	−20.3799			−0.851383
$574$	−21.9324	+	9.86337i	−0.915441	+	0.411689i
$575$	−23.1501			−0.965425
$576$	0.376282	−	0.651740i	0.0156784	−	0.0271558i
$577$	−19.5049	−	33.7835i	−0.812000	−	1.40642i	−0.911462	−	0.411383i	$-0.865046\pi$
$577$	−19.5049	−	33.7835i	−0.812000	−	1.40642i	0.0994629	−	0.995041i	$-0.468288\pi$
$578$	−15.1835	−	26.2986i	−0.631551	−	1.09388i
$579$	−5.15101	+	8.92181i	−0.214069	+	0.370778i
$580$	−40.8769			−1.69732
$581$	−11.4751	−	8.27175i	−0.476066	−	0.343170i
$582$	−22.3326			−0.925714
$583$	8.20731	−	14.2155i	0.339912	−	0.588745i
$584$	4.84261	+	8.38764i	0.200388	+	0.347083i
$585$	1.71496	+	2.97040i	0.0709049	+	0.122811i
$586$	14.6854	−	25.4359i	0.606648	−	1.05075i
$587$	−9.86312			−0.407094			−0.203547	−	0.979065i	$-0.565247\pi$
$587$	−9.86312			−0.407094			−0.203547	+	0.979065i	$0.565247\pi$
$588$	8.17055	+	1.67294i	0.336948	+	0.0689909i
$589$	22.4247			0.923995
$590$	28.1654	−	48.7839i	1.15955	−	2.00840i
$591$	11.0727	+	19.1784i	0.455469	+	0.788895i
$592$	−27.6217	−	47.8422i	−1.13524	−	1.96630i
$593$	23.6448	−	40.9540i	0.970977	−	1.68178i	0.278357	−	0.960478i	$-0.410210\pi$
$593$	23.6448	−	40.9540i	0.970977	−	1.68178i	0.692620	−	0.721303i	$-0.256457\pi$
$594$	2.84944			0.116914
$595$	0.290686	+	0.209540i	0.0119170	+	0.00859029i
$596$	−14.9069			−0.610612
$597$	−7.31957	+	12.6779i	−0.299570	+	0.518871i
$598$	3.05695	+	5.29480i	0.125008	+	0.216521i
$599$	−7.21851	−	12.5028i	−0.294940	−	0.510852i	0.680031	−	0.733184i	$-0.261966\pi$
$599$	−7.21851	−	12.5028i	−0.294940	−	0.510852i	−0.974971	+	0.222332i	$0.928633\pi$
$600$	4.88544	−	8.46183i	0.199447	−	0.345453i
$601$	16.9536			0.691552			0.345776	−	0.938317i	$-0.387616\pi$
$601$	16.9536			0.691552			0.345776	+	0.938317i	$0.387616\pi$
$602$	12.5713	−	5.65350i	0.512366	−	0.230420i
$603$	12.0569			0.490994
$604$	1.09244	−	1.89217i	0.0444510	−	0.0769913i
$605$	14.5015	+	25.1174i	0.589571	+	1.02117i
$606$	6.11971	+	10.5996i	0.248596	+	0.430581i
$607$	15.5452	−	26.9251i	0.630962	−	1.09286i	−0.356394	−	0.934336i	$-0.615994\pi$
$607$	15.5452	−	26.9251i	0.630962	−	1.09286i	0.987355	−	0.158522i	$-0.0506729\pi$
$608$	−21.7802			−0.883305
$609$	2.66791	−	26.3302i	0.108109	−	1.06695i
$610$	12.0129			0.486387
$611$	−2.05432	+	3.55818i	−0.0831088	+	0.143949i
$612$	−0.0235234	−	0.0407437i	−0.000950876	−	0.00164697i
$613$	1.54240	+	2.67151i	0.0622969	+	0.107901i	0.895492	−	0.445078i	$-0.146824\pi$
$613$	1.54240	+	2.67151i	0.0622969	+	0.107901i	−0.833195	+	0.552980i	$0.813491\pi$
$614$	−21.4887	+	37.2195i	−0.867213	+	1.50206i
$615$	17.4512			0.703700
$616$	0.614501	−	6.06464i	0.0247589	−	0.244351i
$617$	−40.3163			−1.62307			−0.811537	−	0.584301i	$-0.801369\pi$
$617$	−40.3163			−1.62307			−0.811537	+	0.584301i	$0.801369\pi$
$618$	−8.16636	+	14.1446i	−0.328499	+	0.568977i
$619$	2.67578	+	4.63458i	0.107548	+	0.186279i	0.914777	−	0.403960i	$-0.132367\pi$
$619$	2.67578	+	4.63458i	0.107548	+	0.186279i	−0.807228	+	0.590240i	$0.799033\pi$
$620$	12.5759	+	21.7821i	0.505059	+	0.874789i
$621$	−1.71118	+	2.96385i	−0.0686673	+	0.118935i
$622$	60.9605			2.44429
$623$	30.0883	−	13.5312i	1.20546	−	0.542117i
$624$	−4.96335			−0.198693
$625$	6.53264	−	11.3149i	0.261305	−	0.452594i
$626$	27.3255	+	47.3291i	1.09215	+	1.89165i
$627$	−2.90570	−	5.03282i	−0.116043	−	0.200992i
$628$	−10.9165	+	18.9078i	−0.435614	+	0.754505i
$629$	−0.439505			−0.0175242
$630$	−13.1510	−	9.47984i	−0.523949	−	0.377686i
$631$	−8.84966			−0.352300			−0.176150	−	0.984363i	$-0.556364\pi$
$631$	−8.84966			−0.352300			−0.176150	+	0.984363i	$0.556364\pi$
$632$	−10.5675	+	18.3035i	−0.420354	+	0.728074i
$633$	−8.25420	−	14.2967i	−0.328075	−	0.568243i
$634$	−3.94643	−	6.83541i	−0.156733	−	0.271469i
$635$	−21.7312	+	37.6396i	−0.862378	+	1.49368i
$636$	12.2613			0.486191
$637$	−2.21284	−	6.64103i	−0.0876761	−	0.263127i
$638$	28.5025			1.12843
$639$	−0.899125	+	1.55733i	−0.0355688	+	0.0616070i
$640$	18.1981	+	31.5200i	0.719342	+	1.24594i
$641$	9.87131	+	17.0976i	0.389893	+	0.675315i	0.992435	−	0.122772i	$-0.0391785\pi$
$641$	9.87131	+	17.0976i	0.389893	+	0.675315i	−0.602541	+	0.798088i	$0.705845\pi$
$642$	−12.2169	+	21.1602i	−0.482161	+	0.835128i
$643$	17.4196			0.686962			0.343481	−	0.939160i	$-0.388394\pi$
$643$	17.4196			0.686962			0.343481	+	0.939160i	$0.388394\pi$
$644$	−8.75143	−	6.30842i	−0.344854	−	0.248587i
$645$	−10.0027			−0.393856
$646$	−0.128510	+	0.222585i	−0.00505615	+	0.00875750i
$647$	−21.2308	−	36.7728i	−0.834669	−	1.44569i	−0.894300	−	0.447468i	$-0.852326\pi$
$647$	−21.2308	−	36.7728i	−0.834669	−	1.44569i	0.0596315	−	0.998220i	$-0.481007\pi$
$648$	−0.722233	−	1.25094i	−0.0283720	−	0.0491417i
$649$	−7.33171	+	12.6989i	−0.287795	+	0.498475i
$650$	12.0842			0.473983
$651$	−14.8513	+	6.67889i	−0.582070	+	0.261767i
$652$	17.6042			0.689433
$653$	−2.64504	+	4.58135i	−0.103508	+	0.179282i	−0.913128	−	0.407673i	$-0.866340\pi$
$653$	−2.64504	+	4.58135i	−0.103508	+	0.179282i	0.809619	+	0.586955i	$0.199674\pi$
$654$	−5.04169	−	8.73246i	−0.197146	−	0.341466i
$655$	19.3979	+	33.5981i	0.757937	+	1.31279i
$656$	−12.6266	+	21.8699i	−0.492985	+	0.853876i
$657$	−6.70505			−0.261589
$658$	1.95767	−	19.3207i	0.0763179	−	0.753198i
$659$	44.9462			1.75086			0.875428	−	0.483348i	$-0.160579\pi$
$659$	44.9462			1.75086			0.875428	+	0.483348i	$0.160579\pi$
$660$	3.25906	−	5.64485i	0.126859	−	0.219726i
$661$	15.0885	+	26.1340i	0.586874	+	1.01650i	0.994639	+	0.103408i	$0.0329749\pi$
$661$	15.0885	+	26.1340i	0.586874	+	1.01650i	−0.407765	+	0.913087i	$0.633692\pi$
$662$	22.2123	+	38.4728i	0.863306	+	1.49529i
$663$	−0.0197437	+	0.0341971i	−0.000766782	+	0.00132811i
$664$	−7.72290			−0.299707
$665$	−3.33309	+	32.8949i	−0.129252	+	1.27561i
$666$	19.8837			0.770479
$667$	−17.1167	+	29.6469i	−0.662760	+	1.14793i
$668$	3.93851	+	6.82170i	0.152386	+	0.263940i
$669$	−6.06256	−	10.5007i	−0.234392	−	0.405979i
$670$	36.9387	−	63.9797i	1.42707	−	2.47175i
$671$	−3.12706			−0.120719
$672$	14.4245	−	6.48694i	0.556437	−	0.250239i
$673$	−32.0501			−1.23544			−0.617720	−	0.786398i	$-0.711944\pi$
$673$	−32.0501			−1.23544			−0.617720	+	0.786398i	$0.711944\pi$
$674$	−9.06539	+	15.7017i	−0.349186	+	0.604807i
$675$	3.38218	+	5.85810i	0.130180	+	0.225479i
$676$	−0.595718	−	1.03181i	−0.0229122	−	0.0396852i
$677$	−7.72182	+	13.3746i	−0.296774	+	0.514027i	−0.975396	−	0.220460i	$-0.929244\pi$
$677$	−7.72182	+	13.3746i	−0.296774	+	0.514027i	0.678622	+	0.734488i	$0.262577\pi$
$678$	−6.46434			−0.248261
$679$	−26.8304	−	19.3406i	−1.02966	−	0.742223i
$680$	0.195636			0.00750231
$681$	−7.33168	+	12.6988i	−0.280951	+	0.486621i
$682$	−8.76886	−	15.1881i	−0.335777	−	0.581583i
$683$	8.48899	+	14.7034i	0.324822	+	0.562609i	0.981476	−	0.191583i	$-0.0613622\pi$
$683$	8.48899	+	14.7034i	0.324822	+	0.562609i	−0.656654	+	0.754192i	$0.728029\pi$
$684$	2.17048	−	3.75938i	0.0829903	−	0.143743i
$685$	−2.62278			−0.100211
$686$	22.4131	+	24.3376i	0.855735	+	0.929213i
$687$	−13.3777			−0.510391
$688$	7.23732	−	12.5354i	0.275920	−	0.477908i
$689$	−5.14558	−	8.91240i	−0.196031	−	0.339535i
$690$	10.4851	+	18.1607i	0.399161	+	0.691368i
$691$	−9.79318	+	16.9623i	−0.372550	+	0.645276i	−0.989957	−	0.141368i	$-0.954850\pi$
$691$	−9.79318	+	16.9623i	−0.372550	+	0.645276i	0.617407	+	0.786644i	$0.288183\pi$
$692$	−0.864018			−0.0328450
$693$	3.42333	+	2.46769i	0.130042	+	0.0937398i
$694$	0.529399			0.0200957
$695$	1.53347	−	2.65604i	0.0581677	−	0.100749i
$696$	−7.22438	−	12.5130i	−0.273839	−	0.474304i
$697$	0.100455	+	0.173992i	0.00380499	+	0.00659043i
$698$	25.6489	−	44.4252i	0.970825	−	1.68152i
$699$	−6.94354			−0.262629
$700$	−19.4469	+	8.74559i	−0.735023	+	0.330552i
$701$	6.84859			0.258668			0.129334	−	0.991601i	$-0.458716\pi$
$701$	6.84859			0.258668			0.129334	+	0.991601i	$0.458716\pi$
$702$	0.893230	−	1.54712i	0.0337128	−	0.0583922i
$703$	−20.2763	−	35.1196i	−0.764736	−	1.32456i
$704$	0.600179	+	1.03954i	0.0226201	+	0.0391791i
$705$	−7.04615	+	12.2043i	−0.265373	+	0.459640i
$706$	−38.6020			−1.45281
$707$	−1.82733	+	18.0343i	−0.0687236	+	0.678248i
$708$	−10.9532			−0.411645
$709$	11.2003	−	19.3994i	0.420634	−	0.728560i	−0.575367	−	0.817895i	$-0.695141\pi$
$709$	11.2003	−	19.3994i	0.420634	−	0.728560i	0.996002	+	0.0893350i	$0.0284742\pi$
$710$	5.50931	+	9.54241i	0.206761	+	0.358120i
$711$	−7.31588	−	12.6715i	−0.274367	−	0.475217i
$712$	9.00581	−	15.5985i	0.337507	−	0.584579i
$713$	21.0639			0.788850
$714$	0.0188148	−	0.185688i	0.000704127	−	0.00694918i
$715$	−5.47080			−0.204596
$716$	11.1956	−	19.3914i	0.418401	−	0.724691i
$717$	5.09268	+	8.82078i	0.190190	+	0.329418i
$718$	5.71568	+	9.89985i	0.213307	+	0.369459i
$719$	26.2562	−	45.4770i	0.979191	−	1.69601i	0.313841	−	0.949475i	$-0.398384\pi$
$719$	26.2562	−	45.4770i	0.979191	−	1.69601i	0.665349	−	0.746532i	$-0.268283\pi$
$720$	−17.0239			−0.634443
$721$	−22.0606	+	9.92103i	−0.821581	+	0.369479i
$722$	10.2278			0.380640
$723$	−4.87250	+	8.43942i	−0.181210	+	0.313865i
$724$	4.44066	+	7.69145i	0.165036	+	0.285850i
$725$	33.8314	+	58.5977i	1.25647	+	2.17626i
$726$	7.55306	−	13.0823i	0.280320	−	0.485529i
$727$	22.4202			0.831519			0.415760	−	0.909475i	$-0.363516\pi$
$727$	22.4202			0.831519			0.415760	+	0.909475i	$0.363516\pi$
$728$	−3.10019	−	2.23476i	−0.114901	−	0.0828257i
$729$	1.00000			0.0370370
$730$	−20.5423	+	35.5803i	−0.760305	+	1.31689i
$731$	−0.0575787	−	0.0997292i	−0.00212962	−	0.00368862i
$732$	−1.16791	−	2.02289i	−0.0431673	−	0.0747680i
$733$	9.73500	−	16.8615i	0.359570	−	0.622794i	−0.628319	−	0.777956i	$-0.716257\pi$
$733$	9.73500	−	16.8615i	0.359570	−	0.622794i	0.987889	+	0.155162i	$0.0495900\pi$
$734$	−1.28433			−0.0474054
$735$	−7.58988	−	22.7782i	−0.279957	−	0.840187i
$736$	−20.4585			−0.754111
$737$	−9.61549	+	16.6545i	−0.354191	+	0.613477i
$738$	−4.54469	−	7.87163i	−0.167292	−	0.289759i
$739$	−3.05412	−	5.28988i	−0.112347	−	0.194591i	0.804369	−	0.594130i	$-0.202504\pi$
$739$	−3.05412	−	5.28988i	−0.112347	−	0.194591i	−0.916716	+	0.399539i	$0.869170\pi$
$740$	22.7421	−	39.3904i	0.836015	−	1.44802i
$741$	−3.64346			−0.133846
$742$	39.4584	+	28.4434i	1.44856	+	1.04419i
$743$	11.8031			0.433015			0.216507	−	0.976281i	$-0.430533\pi$
$743$	11.8031			0.433015			0.216507	+	0.976281i	$0.430533\pi$
$744$	−4.44519	+	7.69929i	−0.162969	+	0.282270i
$745$	21.4571	+	37.1648i	0.786128	+	1.36161i
$746$	−8.84065	−	15.3124i	−0.323679	−	0.560628i
$747$	2.67327	−	4.63025i	0.0978100	−	0.169412i
$748$	0.0750406			0.00274376
$749$	−33.0027	+	14.8419i	−1.20589	+	0.542310i
$750$	10.8109			0.394760
$751$	−0.240178	+	0.416001i	−0.00876423	+	0.0151801i	−0.870374	−	0.492391i	$-0.836123\pi$
$751$	−0.240178	+	0.416001i	−0.00876423	+	0.0151801i	0.861610	+	0.507571i	$0.169456\pi$
$752$	−10.1963	−	17.6605i	−0.371821	−	0.644013i
$753$	−12.7939	−	22.1597i	−0.466237	−	0.807546i
$754$	8.93483	−	15.4756i	0.325387	−	0.563588i
$755$	−6.28988			−0.228912
$756$	−0.317775	+	3.13619i	−0.0115574	+	0.114062i
$757$	−30.1679			−1.09647			−0.548235	−	0.836324i	$-0.684700\pi$
$757$	−30.1679			−1.09647			−0.548235	+	0.836324i	$0.684700\pi$
$758$	3.25835	−	5.64363i	0.118349	−	0.204986i
$759$	−2.72937	−	4.72741i	−0.0990699	−	0.171594i
$760$	9.02558	+	15.6328i	0.327392	+	0.567060i
$761$	17.3146	−	29.9898i	0.627654	−	1.08713i	−0.360367	−	0.932811i	$-0.617348\pi$
$761$	17.3146	−	29.9898i	0.627654	−	1.08713i	0.988021	−	0.154319i	$-0.0493182\pi$
$762$	22.6372			0.820061
$763$	1.50543	−	14.8574i	0.0545003	−	0.537875i
$764$	24.2814			0.878470
$765$	−0.0677193	+	0.117293i	−0.00244840	+	0.00424075i
$766$	14.0263	+	24.2942i	0.506789	+	0.877784i
$767$	4.59662	+	7.96158i	0.165974	+	0.287476i
$768$	10.2310	−	17.7205i	0.369178	−	0.639434i
$769$	4.33487			0.156320			0.0781598	−	0.996941i	$-0.475096\pi$
$769$	4.33487			0.156320			0.0781598	+	0.996941i	$0.475096\pi$
$770$	23.5829	−	10.6056i	0.849867	−	0.382199i
$771$	−11.5666			−0.416561
$772$	6.13710	−	10.6298i	0.220879	−	0.382574i
$773$	1.55712	+	2.69700i	0.0560055	+	0.0970045i	0.892669	−	0.450713i	$-0.148830\pi$
$773$	1.55712	+	2.69700i	0.0560055	+	0.0970045i	−0.836663	+	0.547717i	$0.815497\pi$
$774$	2.60493	+	4.51187i	0.0936323	+	0.162176i
$775$	20.8166	−	36.0554i	0.747754	−	1.29515i
$776$	−18.0573			−0.648219
$777$	23.8884	+	17.2198i	0.856991	+	0.617758i
$778$	−18.7268			−0.671388
$779$	−9.26883	+	16.0541i	−0.332090	+	0.575197i
$780$	−2.04327	−	3.53904i	−0.0731607	−	0.126718i
$781$	−1.43412	−	2.48398i	−0.0513170	−	0.0888837i
$782$	−0.120711	+	0.209078i	−0.00431662	+	0.00747661i
$783$	10.0028			0.357472
$784$	34.0373	+	6.96923i	1.21562	+	0.248901i
$785$	62.8528			2.24331
$786$	10.1033	−	17.4994i	0.360373	−	0.624184i
$787$	−7.63061	−	13.2166i	−0.272002	−	0.471121i	0.697372	−	0.716709i	$-0.254352\pi$
$787$	−7.63061	−	13.2166i	−0.272002	−	0.471121i	−0.969374	+	0.245588i	$0.921019\pi$
$788$	−13.1924	−	22.8499i	−0.469960	−	0.813994i
$789$	2.14700	−	3.71871i	0.0764351	−	0.132389i
$790$	−89.6548			−3.18978
$791$	−7.76627	−	5.59828i	−0.276137	−	0.199052i
$792$	2.30395			0.0818674
$793$	−0.980256	+	1.69785i	−0.0348099	+	0.0602926i
$794$	23.4198	+	40.5643i	0.831138	+	1.43957i
$795$	−17.6489	−	30.5688i	−0.625943	−	1.08416i
$796$	8.72081	−	15.1049i	0.309101	−	0.535379i
$797$	−15.7622			−0.558325			−0.279162	−	0.960244i	$-0.590057\pi$
$797$	−15.7622			−0.558325			−0.279162	+	0.960244i	$0.590057\pi$
$798$	15.7058	−	7.06315i	0.555979	−	0.250033i
$799$	−0.162239			−0.00573962
$800$	−20.2183	+	35.0191i	−0.714825	+	1.23811i
$801$	6.23470	+	10.7988i	0.220292	+	0.381558i
$802$	−26.7830	−	46.3895i	−0.945741	−	1.63807i
$803$	5.34735	−	9.26189i	0.188704	−	0.326845i
$804$	−14.3650			−0.506615
$805$	−3.13082	+	30.8987i	−0.110347	+	1.08904i
$806$	−10.9953			−0.387292
$807$	−3.40333	+	5.89473i	−0.119803	+	0.207504i
$808$	4.94817	+	8.57048i	0.174076	+	0.301508i
$809$	9.89087	+	17.1315i	0.347744	+	0.602311i	0.985848	−	0.167639i	$-0.0536143\pi$
$809$	9.89087	+	17.1315i	0.347744	+	0.602311i	−0.638104	+	0.769950i	$0.720281\pi$
$810$	3.06371	−	5.30650i	0.107648	−	0.186451i
$811$	14.8239			0.520537			0.260269	−	0.965536i	$-0.416189\pi$
$811$	14.8239			0.520537			0.260269	+	0.965536i	$0.416189\pi$
$812$	−3.17865	+	31.3708i	−0.111549	+	1.10090i
$813$	10.6765			0.374440
$814$	−15.8575	+	27.4660i	−0.555805	+	0.962683i
$815$	−25.3396	−	43.8894i	−0.887606	−	1.53738i
$816$	−0.0979949	−	0.169732i	−0.00343051	−	0.00594182i
$817$	5.31272	−	9.20191i	0.185869	−	0.321934i
$818$	−28.8035			−1.00709
$819$	2.41297	−	1.08515i	0.0843161	−	0.0379184i
$820$	−20.7920			−0.726088
$821$	−12.1535	+	21.0505i	−0.424160	+	0.734666i	−0.996342	−	0.0854608i	$-0.972764\pi$
$821$	−12.1535	+	21.0505i	−0.424160	+	0.734666i	0.572182	+	0.820127i	$0.306097\pi$
$822$	0.683032	+	1.18305i	0.0238235	+	0.0412635i
$823$	24.5528	+	42.5268i	0.855858	+	1.48239i	0.875846	+	0.482590i	$0.160304\pi$
$823$	24.5528	+	42.5268i	0.855858	+	1.48239i	−0.0199879	+	0.999800i	$0.506363\pi$
$824$	−6.60302	+	11.4368i	−0.230027	+	0.398418i
$825$	−10.7893			−0.375635
$826$	−35.2487	−	25.4089i	−1.22646	−	0.884088i
$827$	−49.5213			−1.72202			−0.861012	−	0.508585i	$-0.830169\pi$
$827$	−49.5213			−1.72202			−0.861012	+	0.508585i	$0.830169\pi$
$828$	2.03876	−	3.53124i	0.0708519	−	0.122719i
$829$	5.07080	+	8.78289i	0.176116	+	0.305042i	0.940547	−	0.339664i	$-0.110313\pi$
$829$	5.07080	+	8.78289i	0.176116	+	0.305042i	−0.764431	+	0.644706i	$0.776980\pi$
$830$	−16.3803	−	28.3714i	−0.568567	−	0.984787i
$831$	13.9118	−	24.0960i	0.482596	−	0.835880i
$832$	0.752565			0.0260905
$833$	0.183414	−	0.206791i	0.00635493	−	0.00716490i
$834$	−1.59740			−0.0553134
$835$	11.3382	−	19.6384i	0.392376	−	0.679615i
$836$	3.46196	+	5.99629i	0.119734	+	0.207386i
$837$	−3.07739	−	5.33020i	−0.106370	−	0.184239i
$838$	−5.44888	+	9.43775i	−0.188229	+	0.326021i
$839$	29.9487			1.03394			0.516972	−	0.856002i	$-0.327059\pi$
$839$	29.9487			1.03394			0.516972	+	0.856002i	$0.327059\pi$
$840$	−10.6334	−	7.66505i	−0.366888	−	0.264469i
$841$	71.0568			2.45023
$842$	9.92927	−	17.1980i	0.342185	−	0.592682i
$843$	13.6500	+	23.6425i	0.470131	+	0.814291i
$844$	9.83436	+	17.0336i	0.338513	+	0.586321i
$845$	−1.71496	+	2.97040i	−0.0589964	+	0.102185i
$846$	7.33991			0.252351
$847$	20.4039	−	9.17596i	0.701085	−	0.315290i
$848$	51.0786			1.75405
$849$	7.92237	−	13.7220i	0.271895	−	0.470936i
$850$	0.238588	+	0.413246i	0.00818349	+	0.0141742i
$851$	−19.0459	−	32.9884i	−0.652884	−	1.13083i
$852$	1.07125	−	1.85546i	0.0367004	−	0.0635670i
$853$	23.2279			0.795309			0.397655	−	0.917535i	$-0.369824\pi$
$853$	23.2279			0.795309			0.397655	+	0.917535i	$0.369824\pi$
$854$	0.934138	−	9.21921i	0.0319656	−	0.315475i
$855$	−12.4968			−0.427381
$856$	−9.87811	+	17.1094i	−0.337627	+	0.584787i
$857$	−3.20780	−	5.55608i	−0.109576	−	0.189792i	0.806022	−	0.591885i	$-0.201616\pi$
$857$	−3.20780	−	5.55608i	−0.109576	−	0.189792i	−0.915599	+	0.402093i	$0.868283\pi$
$858$	1.42472	+	2.46769i	0.0486392	+	0.0842455i
$859$	−9.58620	+	16.6038i	−0.327077	+	0.566514i	−0.981930	−	0.189242i	$-0.939397\pi$
$859$	−9.58620	+	16.6038i	−0.327077	+	0.566514i	0.654854	+	0.755756i	$0.272730\pi$
$860$	11.9176			0.406386
$861$	1.35703	−	13.3928i	0.0462474	−	0.456426i
$862$	10.4692			0.356584
$863$	−2.72637	+	4.72220i	−0.0928065	+	0.160746i	−0.908691	−	0.417469i	$-0.862917\pi$
$863$	−2.72637	+	4.72220i	−0.0928065	+	0.160746i	0.815885	+	0.578215i	$0.196250\pi$
$864$	2.98895	+	5.17701i	0.101686	+	0.176125i
$865$	1.24367	+	2.15410i	0.0422861	+	0.0732417i
$866$	−28.6737	+	49.6643i	−0.974372	+	1.68766i
$867$	16.9984			0.577297
$868$	17.6944	−	7.95748i	0.600588	−	0.270095i
$869$	23.3380			0.791687
$870$	30.6458	−	53.0800i	1.03899	−	1.79958i
$871$	6.02844	+	10.4416i	0.204266	+	0.353799i
$872$	−4.07652	−	7.06074i	−0.138048	−	0.239107i
$873$	6.25051	−	10.8262i	0.211548	−	0.366411i
$874$	−22.2758			−0.753490
$875$	12.9883	+	9.36255i	0.439084	+	0.316512i
$876$	7.98865			0.269911
$877$	−16.3083	+	28.2469i	−0.550693	+	0.953829i	0.447531	+	0.894268i	$0.352303\pi$
$877$	−16.3083	+	28.2469i	−0.550693	+	0.953829i	−0.998225	+	0.0595606i	$0.981030\pi$
$878$	−26.0804	−	45.1726i	−0.880171	−	1.52450i
$879$	8.22039	+	14.2381i	0.277267	+	0.480240i
$880$	13.5768	−	23.5156i	0.457672	−	0.792712i
$881$	−33.4768			−1.12786			−0.563931	−	0.825822i	$-0.690712\pi$
$881$	−33.4768			−1.12786			−0.563931	+	0.825822i	$0.690712\pi$
$882$	−8.29789	+	9.35550i	−0.279405	+	0.315016i
$883$	−10.1655			−0.342097			−0.171048	−	0.985263i	$-0.554715\pi$
$883$	−10.1655			−0.342097			−0.171048	+	0.985263i	$0.554715\pi$
$884$	0.0235234	−	0.0407437i	0.000791177	−	0.00137036i
$885$	15.7660	+	27.3076i	0.529969	+	0.917934i
$886$	−25.1459	−	43.5539i	−0.844792	−	1.46322i
$887$	−7.79677	+	13.5044i	−0.261790	+	0.453434i	−0.966718	−	0.255846i	$-0.917646\pi$
$887$	−7.79677	+	13.5044i	−0.261790	+	0.453434i	0.704928	+	0.709279i	$0.250979\pi$
$888$	16.0773			0.539518
$889$	27.1964	+	19.6044i	0.912139	+	0.657511i
$890$	76.4052			2.56111
$891$	−0.797511	+	1.38133i	−0.0267176	+	0.0462763i
$892$	7.22316	+	12.5109i	0.241849	+	0.418895i
$893$	−7.48483	−	12.9641i	−0.250470	−	0.433827i
$894$	11.1759	−	19.3571i	0.373776	−	0.647400i
$895$	−64.4602			−2.15467
$896$	25.6049	−	11.5150i	0.855401	−	0.384688i
$897$	−3.42236			−0.114269
$898$	4.82025	−	8.34893i	0.160854	−	0.278607i
$899$	−30.7827	−	53.3172i	−1.02666	−	1.77823i
$900$	−4.02965	−	6.97956i	−0.134322	−	0.232652i
$901$	0.203185	−	0.351928i	0.00676909	−	0.0117244i
$902$	14.4978			0.482722
$903$	−0.777824	+	7.67651i	−0.0258844	+	0.255458i
$904$	−5.22682			−0.173842
$905$	12.7838	−	22.1422i	0.424948	−	0.736032i
$906$	1.63803	+	2.83715i	0.0544199	+	0.0942580i
$907$	29.5913	+	51.2537i	0.982564	+	1.70185i	0.652297	+	0.757963i	$0.273805\pi$
$907$	29.5913	+	51.2537i	0.982564	+	1.70185i	0.330267	+	0.943888i	$0.392861\pi$
$908$	8.73524	−	15.1299i	0.289889	−	0.502102i
$909$	−6.85121			−0.227240
$910$	1.63428	−	16.1290i	0.0541758	−	0.534672i
$911$	1.45229			0.0481166			0.0240583	−	0.999711i	$-0.492341\pi$
$911$	1.45229			0.0481166			0.0240583	+	0.999711i	$0.492341\pi$
$912$	9.04189	−	15.6610i	0.299407	−	0.518588i
$913$	4.26393	+	7.38535i	0.141116	+	0.244419i
$914$	26.3573	+	45.6523i	0.871824	+	1.51004i
$915$	−3.36220	+	5.82350i	−0.111151	+	0.192519i
$916$	15.9387			0.526629
$917$	27.2931	−	12.2741i	0.901297	−	0.405328i
$918$	0.0705426			0.00232825
$919$	−19.2770	+	33.3888i	−0.635890	+	1.10139i	0.350436	+	0.936587i	$0.386033\pi$
$919$	−19.2770	+	33.3888i	−0.635890	+	1.10139i	−0.986326	+	0.164807i	$0.947300\pi$
$920$	8.47787	+	14.6841i	0.279507	+	0.484121i
$921$	−12.0287	−	20.8342i	−0.396358	−	0.686512i
$922$	−15.7366	+	27.2565i	−0.518256	+	0.897646i
$923$	−1.79825			−0.0591901
$924$	−4.07868	−	2.94010i	−0.134179	−	0.0967221i
$925$	−75.2890			−2.47549
$926$	5.71695	−	9.90204i	0.187871	−	0.325401i
$927$	−4.57125	−	7.91765i	−0.150140	−	0.260050i
$928$	29.8980	+	51.7848i	0.981449	+	1.69992i
$929$	21.3728	−	37.0188i	0.701220	−	1.21455i	−0.266819	−	0.963747i	$-0.585972\pi$
$929$	21.3728	−	37.0188i	0.701220	−	1.21455i	0.968038	−	0.250802i	$-0.0806942\pi$
$930$	−37.7129			−1.23666
$931$	24.9859	+	5.11592i	0.818878	+	0.167667i
$932$	8.27279			0.270984
$933$	−17.0618	+	29.5519i	−0.558579	+	0.967487i
$934$	−13.7806	−	23.8687i	−0.450915	−	0.781008i
$935$	−0.108014	−	0.187085i	−0.00353243	−	0.00611835i
$936$	0.722233	−	1.25094i	0.0236069	−	0.0408884i
$937$	47.2424			1.54334			0.771671	−	0.636022i	$-0.219421\pi$
$937$	47.2424			1.54334			0.771671	+	0.636022i	$0.219421\pi$
$938$	−46.2285	−	33.3236i	−1.50941	−	1.08805i
$939$	−30.5918			−0.998325
$940$	8.39504	−	14.5406i	0.273816	−	0.474264i
$941$	25.1450	+	43.5524i	0.819702	+	1.41977i	0.905902	+	0.423488i	$0.139195\pi$
$941$	25.1450	+	43.5524i	0.819702	+	1.41977i	−0.0861990	+	0.996278i	$0.527472\pi$
$942$	−16.3683	−	28.3507i	−0.533308	−	0.923717i
$943$	−8.70636	+	15.0799i	−0.283518	+	0.491068i
$944$	−45.6293			−1.48511
$945$	8.27631	−	3.72199i	0.269228	−	0.121076i
$946$	−8.30984			−0.270176
$947$	−10.5508	+	18.2745i	−0.342855	+	0.593842i	−0.984962	−	0.172773i	$-0.944727\pi$
$947$	−10.5508	+	18.2745i	−0.342855	+	0.593842i	0.642107	+	0.766615i	$0.278061\pi$
$948$	8.71641	+	15.0973i	0.283096	+	0.490336i
$949$	−3.35253	−	5.80675i	−0.108828	−	0.188495i
$950$	−22.0142	+	38.1298i	−0.714236	+	1.23709i
$951$	4.41815			0.143268
$952$	0.0152130	−	0.150140i	0.000493055	−	0.00486607i
$953$	−0.279996			−0.00906996			−0.00453498	−	0.999990i	$-0.501444\pi$
$953$	−0.279996			−0.00906996			−0.00453498	+	0.999990i	$0.501444\pi$
$954$	−9.19236	+	15.9216i	−0.297614	+	0.515482i
$955$	−34.9508	−	60.5365i	−1.13098	−	1.95891i
$956$	−6.06760	−	10.5094i	−0.196240	−	0.339898i
$957$	−7.97738	+	13.8172i	−0.257872	+	0.446647i
$958$	−41.3202			−1.33500
$959$	−0.203951	+	2.01284i	−0.00658593	+	0.0649980i
$960$	2.58124			0.0833091
$961$	−3.44071	+	5.95949i	−0.110991	+	0.192242i
$962$	9.94187	+	17.2198i	0.320539	+	0.555190i
$963$	−6.83859	−	11.8448i	−0.220371	−	0.381693i
$964$	5.80528	−	10.0550i	0.186975	−	0.323851i
$965$	−35.3351			−1.13748
$966$	14.7527	−	6.63453i	0.474660	−	0.213463i
$967$	23.5683			0.757905			0.378953	−	0.925416i	$-0.376284\pi$
$967$	23.5683			0.757905			0.378953	+	0.925416i	$0.376284\pi$
$968$	6.10713	−	10.5779i	0.196291	−	0.339985i
$969$	−0.0719354	−	0.124596i	−0.00231090	−	0.00400259i
$970$	−38.2994	−	66.3366i	−1.22972	−	2.12994i
$971$	0.706716	−	1.22407i	0.0226796	−	0.0392822i	−0.854463	−	0.519513i	$-0.826114\pi$
$971$	0.706716	−	1.22407i	0.0226796	−	0.0392822i	0.877142	+	0.480230i	$0.159447\pi$
$972$	−1.19144			−0.0382154
$973$	−1.91912	−	1.38339i	−0.0615242	−	0.0443494i
$974$	−13.9538			−0.447108
$975$	−3.38218	+	5.85810i	−0.108316	+	0.187609i
$976$	−4.86536	−	8.42705i	−0.155736	−	0.269743i
$977$	10.2263	+	17.7125i	0.327168	+	0.566671i	0.981949	−	0.189147i	$-0.0605724\pi$
$977$	10.2263	+	17.7125i	0.327168	+	0.566671i	−0.654781	+	0.755819i	$0.727239\pi$
$978$	−13.1980	+	22.8596i	−0.422025	+	0.730970i
$979$	−19.8890			−0.635655
$980$	9.04286	+	27.1388i	0.288864	+	0.866917i
$981$	5.64433			0.180210
$982$	−22.1025	+	38.2826i	−0.705318	+	1.22165i
$983$	−12.2003	−	21.1315i	−0.389129	−	0.673991i	0.603204	−	0.797587i	$-0.293891\pi$
$983$	−12.2003	−	21.1315i	−0.389129	−	0.673991i	−0.992333	+	0.123596i	$0.960557\pi$
$984$	−3.67467	−	6.36471i	−0.117144	−	0.202899i
$985$	−37.9784	+	65.7805i	−1.21009	+	2.09594i
$986$	0.705627			0.0224717
$987$	8.81820	+	6.35655i	0.280686	+	0.202331i
$988$	4.34095			0.138104
$989$	4.99032	−	8.64350i	0.158683	−	0.274847i
$990$	4.88668	+	8.46398i	0.155309	+	0.269003i
$991$	7.56596	+	13.1046i	0.240341	+	0.416282i	0.960811	−	0.277203i	$-0.0894075\pi$
$991$	7.56596	+	13.1046i	0.240341	+	0.416282i	−0.720471	+	0.693486i	$0.756074\pi$
$992$	18.3963	−	31.8634i	0.584085	−	1.01166i
$993$	−24.8674			−0.789143
$994$	7.75168	−	3.48606i	0.245868	−	0.110571i
$995$	−50.2111			−1.59180
$996$	−3.18504	+	5.51665i	−0.100922	+	0.174802i
$997$	27.0383	+	46.8316i	0.856310	+	1.48317i	0.875424	+	0.483356i	$0.160582\pi$
$997$	27.0383	+	46.8316i	0.856310	+	1.48317i	−0.0191139	+	0.999817i	$0.506085\pi$
$998$	−15.3682	−	26.6184i	−0.486471	−	0.842592i
$999$	−5.56513	+	9.63908i	−0.176073	+	0.304967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.i.e.79.4	✓	10
3.2	odd	2		819.2.j.g.352.2		10
7.2	even	3		1911.2.a.t.1.2		5
7.4	even	3	inner	273.2.i.e.235.4	yes	10
7.5	odd	6		1911.2.a.u.1.2		5
21.2	odd	6		5733.2.a.bq.1.4		5
21.5	even	6		5733.2.a.bp.1.4		5
21.11	odd	6		819.2.j.g.235.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.e.79.4	✓	10	1.1	even	1	trivial
273.2.i.e.235.4	yes	10	7.4	even	3	inner
819.2.j.g.235.2		10	21.11	odd	6
819.2.j.g.352.2		10	3.2	odd	2
1911.2.a.t.1.2		5	7.2	even	3
1911.2.a.u.1.2		5	7.5	odd	6
5733.2.a.bp.1.4		5	21.5	even	6
5733.2.a.bq.1.4		5	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.893230 - 1.54712i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.595718 - 1.03181i) q^{4} +(-1.71496 + 2.97040i) q^{5} +1.78646 q^{6} +(2.14626 + 1.54712i) q^{7} +1.44447 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.893230 - 1.54712i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.595718 - 1.03181i) q^{4} +(-1.71496 + 2.97040i) q^{5} +1.78646 q^{6} +(2.14626 + 1.54712i) q^{7} +1.44447 q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.06371 + 5.30650i) q^{10} +(-0.797511 - 1.38133i) q^{11} +(0.595718 - 1.03181i) q^{12} -1.00000 q^{13} +(4.31068 - 1.93858i) q^{14} -3.42992 q^{15} +(2.48168 - 4.29839i) q^{16} +(-0.0197437 - 0.0341971i) q^{17} +(0.893230 + 1.54712i) q^{18} +(1.82173 - 3.15533i) q^{19} +4.08653 q^{20} +(-0.266716 + 2.63227i) q^{21} -2.84944 q^{22} +(1.71118 - 2.96385i) q^{23} +(0.722233 + 1.25094i) q^{24} +(-3.38218 - 5.85810i) q^{25} +(-0.893230 + 1.54712i) q^{26} -1.00000 q^{27} +(0.317775 - 3.13619i) q^{28} -10.0028 q^{29} +(-3.06371 + 5.30650i) q^{30} +(3.07739 + 5.33020i) q^{31} +(-2.98895 - 5.17701i) q^{32} +(0.797511 - 1.38133i) q^{33} -0.0705426 q^{34} +(-8.27631 + 3.72199i) q^{35} +1.19144 q^{36} +(5.56513 - 9.63908i) q^{37} +(-3.25445 - 5.63687i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-2.47720 + 4.29064i) q^{40} -5.08793 q^{41} +(3.83420 + 2.76387i) q^{42} +2.91631 q^{43} +(-0.950184 + 1.64577i) q^{44} +(-1.71496 - 2.97040i) q^{45} +(-3.05695 - 5.29480i) q^{46} +(2.05432 - 3.55818i) q^{47} +4.96335 q^{48} +(2.21284 + 6.64103i) q^{49} -12.0842 q^{50} +(0.0197437 - 0.0341971i) q^{51} +(0.595718 + 1.03181i) q^{52} +(5.14558 + 8.91240i) q^{53} +(-0.893230 + 1.54712i) q^{54} +5.47080 q^{55} +(3.10019 + 2.23476i) q^{56} +3.64346 q^{57} +(-8.93483 + 15.4756i) q^{58} +(-4.59662 - 7.96158i) q^{59} +(2.04327 + 3.53904i) q^{60} +(0.980256 - 1.69785i) q^{61} +10.9953 q^{62} +(-2.41297 + 1.08515i) q^{63} -0.752565 q^{64} +(1.71496 - 2.97040i) q^{65} +(-1.42472 - 2.46769i) q^{66} +(-6.02844 - 10.4416i) q^{67} +(-0.0235234 + 0.0407437i) q^{68} +3.42236 q^{69} +(-1.63428 + 16.1290i) q^{70} +1.79825 q^{71} +(-0.722233 + 1.25094i) q^{72} +(3.35253 + 5.80675i) q^{73} +(-9.94187 - 17.2198i) q^{74} +(3.38218 - 5.85810i) q^{75} -4.34095 q^{76} +(0.425417 - 4.19853i) q^{77} -1.78646 q^{78} +(-7.31588 + 12.6715i) q^{79} +(8.51195 + 14.7431i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.54469 + 7.87163i) q^{82} -5.34655 q^{83} +(2.87491 - 1.29289i) q^{84} +0.135439 q^{85} +(2.60493 - 4.51187i) q^{86} +(-5.00142 - 8.66271i) q^{87} +(-1.15198 - 1.99528i) q^{88} +(6.23470 - 10.7988i) q^{89} -6.12741 q^{90} +(-2.14626 - 1.54712i) q^{91} -4.07753 q^{92} +(-3.07739 + 5.33020i) q^{93} +(-3.66996 - 6.35655i) q^{94} +(6.24839 + 10.8225i) q^{95} +(2.98895 - 5.17701i) q^{96} -12.5010 q^{97} +(12.2510 + 2.50843i) q^{98} +1.59502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9} + 2 q^{10} + q^{11} + 6 q^{12} - 10 q^{13} + 23 q^{14} + 6 q^{15} + 13 q^{17} + 7 q^{19} - 26 q^{20} + 2 q^{21} - 38 q^{22} + 4 q^{23} + 3 q^{24} - 16 q^{25} - 10 q^{27} - 4 q^{28} - 24 q^{29} - 2 q^{30} + 6 q^{31} - 21 q^{32} - q^{33} - 14 q^{34} - 3 q^{35} + 12 q^{36} - 11 q^{37} + 14 q^{38} - 5 q^{39} + 11 q^{40} - 20 q^{41} - 2 q^{42} + 20 q^{43} + 29 q^{44} + 3 q^{45} - q^{46} - 4 q^{47} + 22 q^{49} - 58 q^{50} - 13 q^{51} + 6 q^{52} + 9 q^{53} + 24 q^{55} + 42 q^{56} + 14 q^{57} - 34 q^{58} + 7 q^{59} - 13 q^{60} + 23 q^{61} + 48 q^{62} - 2 q^{63} - 26 q^{64} - 3 q^{65} - 19 q^{66} - 25 q^{67} + 20 q^{68} + 8 q^{69} + 73 q^{70} - 54 q^{71} - 3 q^{72} + 18 q^{73} - 15 q^{74} + 16 q^{75} - 4 q^{76} + 27 q^{77} - 8 q^{79} + 41 q^{80} - 5 q^{81} + 26 q^{82} - 24 q^{83} - 5 q^{84} + 20 q^{85} + 19 q^{86} - 12 q^{87} + 36 q^{88} + 29 q^{89} - 4 q^{90} - 4 q^{91} - 100 q^{92} - 6 q^{93} - 2 q^{94} + 33 q^{95} + 21 q^{96} - 26 q^{97} + 15 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9 + 2 * q^10 + q^11 + 6 * q^12 - 10 * q^13 + 23 * q^14 + 6 * q^15 + 13 * q^17 + 7 * q^19 - 26 * q^20 + 2 * q^21 - 38 * q^22 + 4 * q^23 + 3 * q^24 - 16 * q^25 - 10 * q^27 - 4 * q^28 - 24 * q^29 - 2 * q^30 + 6 * q^31 - 21 * q^32 - q^33 - 14 * q^34 - 3 * q^35 + 12 * q^36 - 11 * q^37 + 14 * q^38 - 5 * q^39 + 11 * q^40 - 20 * q^41 - 2 * q^42 + 20 * q^43 + 29 * q^44 + 3 * q^45 - q^46 - 4 * q^47 + 22 * q^49 - 58 * q^50 - 13 * q^51 + 6 * q^52 + 9 * q^53 + 24 * q^55 + 42 * q^56 + 14 * q^57 - 34 * q^58 + 7 * q^59 - 13 * q^60 + 23 * q^61 + 48 * q^62 - 2 * q^63 - 26 * q^64 - 3 * q^65 - 19 * q^66 - 25 * q^67 + 20 * q^68 + 8 * q^69 + 73 * q^70 - 54 * q^71 - 3 * q^72 + 18 * q^73 - 15 * q^74 + 16 * q^75 - 4 * q^76 + 27 * q^77 - 8 * q^79 + 41 * q^80 - 5 * q^81 + 26 * q^82 - 24 * q^83 - 5 * q^84 + 20 * q^85 + 19 * q^86 - 12 * q^87 + 36 * q^88 + 29 * q^89 - 4 * q^90 - 4 * q^91 - 100 * q^92 - 6 * q^93 - 2 * q^94 + 33 * q^95 + 21 * q^96 - 26 * q^97 + 15 * q^98 - 2 * q^99

Introduction

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