LMFDB - Embedded newform 273.2.i.d.235.3

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4868829729.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - x^{6} + 5x^{5} - 8x^{4} + 15x^{3} - 9x^{2} - 54x + 81 $ x^8 - 2x^7 - x^6 + 5x^5 - 8x^4 + 15x^3 - 9x^2 - 54x + 81
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			235.3
Root			$1.72192 + 0.187090i$ of defining polynomial
Character	$\chi$	$=$	273.235
Dual form			273.2.i.d.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.698934 + 1.21059i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.0229829 - 0.0398076i) q^{4} +(0.198934 + 0.344564i) q^{5} -1.39787 q^{6} +(1.69893 + 2.02821i) q^{7} +2.85999 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.698934 + 1.21059i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.0229829 - 0.0398076i) q^{4} +(0.198934 + 0.344564i) q^{5} -1.39787 q^{6} +(1.69893 + 2.02821i) q^{7} +2.85999 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.278083 + 0.481654i) q^{10} +(-0.824049 + 1.42729i) q^{11} +(0.0229829 + 0.0398076i) q^{12} -1.00000 q^{13} +(-1.26788 + 3.47429i) q^{14} -0.397868 q^{15} +(1.95298 + 3.38266i) q^{16} +(-2.10595 + 3.64761i) q^{17} +(0.698934 - 1.21059i) q^{18} +(-2.54597 - 4.40974i) q^{19} +0.0182883 q^{20} +(-2.60595 + 0.457216i) q^{21} -2.30382 q^{22} +(1.20808 + 2.09245i) q^{23} +(-1.42999 + 2.47682i) q^{24} +(2.42085 - 4.19304i) q^{25} +(-0.698934 - 1.21059i) q^{26} +1.00000 q^{27} +(0.119784 - 0.0210163i) q^{28} +1.48980 q^{29} +(-0.278083 - 0.481654i) q^{30} +(1.92999 - 3.34285i) q^{31} +(0.129985 - 0.225141i) q^{32} +(-0.824049 - 1.42729i) q^{33} -5.88767 q^{34} +(-0.360871 + 0.988870i) q^{35} -0.0459658 q^{36} +(-5.13274 - 8.89017i) q^{37} +(3.55892 - 6.16424i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.568949 + 0.985448i) q^{40} -4.65573 q^{41} +(-2.37488 - 2.83517i) q^{42} +8.47151 q^{43} +(0.0378781 + 0.0656068i) q^{44} +(0.198934 - 0.344564i) q^{45} +(-1.68873 + 2.92497i) q^{46} +(2.02680 + 3.51051i) q^{47} -3.90596 q^{48} +(-1.22725 + 6.89158i) q^{49} +6.76806 q^{50} +(-2.10595 - 3.64761i) q^{51} +(-0.0229829 + 0.0398076i) q^{52} +(4.66575 - 8.08132i) q^{53} +(0.698934 + 1.21059i) q^{54} -0.655725 q^{55} +(4.85893 + 5.80065i) q^{56} +5.09193 q^{57} +(1.04127 + 1.80353i) q^{58} +(0.827863 - 1.43390i) q^{59} +(-0.00914416 + 0.0158382i) q^{60} +(-5.50381 - 9.53288i) q^{61} +5.39575 q^{62} +(0.907012 - 2.48542i) q^{63} +8.17531 q^{64} +(-0.198934 - 0.344564i) q^{65} +(1.15191 - 1.99517i) q^{66} +(0.221917 - 0.384371i) q^{67} +(0.0968016 + 0.167665i) q^{68} -2.41616 q^{69} +(-1.44934 + 0.254288i) q^{70} -9.74766 q^{71} +(-1.42999 - 2.47682i) q^{72} +(-3.32786 + 5.76403i) q^{73} +(7.17489 - 12.4273i) q^{74} +(2.42085 + 4.19304i) q^{75} -0.234055 q^{76} +(-4.29485 + 0.753537i) q^{77} +1.39787 q^{78} +(-2.28190 - 3.95236i) q^{79} +(-0.777027 + 1.34585i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.25404 - 5.63617i) q^{82} +16.4234 q^{83} +(-0.0416916 + 0.114245i) q^{84} -1.67578 q^{85} +(5.92103 + 10.2555i) q^{86} +(-0.744900 + 1.29020i) q^{87} +(-2.35677 + 4.08205i) q^{88} +(-2.14915 - 3.72244i) q^{89} +0.556166 q^{90} +(-1.69893 - 2.02821i) q^{91} +0.111061 q^{92} +(1.92999 + 3.34285i) q^{93} +(-2.83319 + 4.90723i) q^{94} +(1.01296 - 1.75449i) q^{95} +(0.129985 + 0.225141i) q^{96} -8.26548 q^{97} +(-9.20063 + 3.33107i) q^{98} +1.64810 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 - 7 * q^4 - 3 * q^5 - 2 * q^6 + 9 * q^7 - 12 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9} - 14 q^{10} - 4 q^{11} - 7 q^{12} - 8 q^{13} + 16 q^{14} + 6 q^{15} - 9 q^{16} - 2 q^{17} + q^{18} - 6 q^{19} - 2 q^{20} - 6 q^{21} + 40 q^{22} + 4 q^{23} + 6 q^{24} + 3 q^{25} - q^{26} + 8 q^{27} - 20 q^{28} - 26 q^{29} - 14 q^{30} - 2 q^{31} + 18 q^{32} - 4 q^{33} + 13 q^{35} + 14 q^{36} + 5 q^{37} - 11 q^{38} + 4 q^{39} - 17 q^{40} + 16 q^{41} - 17 q^{42} + 32 q^{43} + 26 q^{44} - 3 q^{45} + 29 q^{46} - 15 q^{47} + 18 q^{48} - 21 q^{49} + 48 q^{50} - 2 q^{51} + 7 q^{52} + 2 q^{53} + q^{54} + 48 q^{55} - 35 q^{56} + 12 q^{57} - q^{58} - 20 q^{59} + q^{60} - 20 q^{61} - 44 q^{62} - 3 q^{63} + 40 q^{64} + 3 q^{65} - 20 q^{66} - 10 q^{67} - 13 q^{68} - 8 q^{69} - 31 q^{70} + 4 q^{71} + 6 q^{72} + 21 q^{74} + 3 q^{75} - 86 q^{76} + 3 q^{77} + 2 q^{78} - 6 q^{79} + 21 q^{80} - 4 q^{81} - 6 q^{82} + 32 q^{83} - 2 q^{84} + 4 q^{85} + 51 q^{86} + 13 q^{87} - 39 q^{88} - 51 q^{89} + 28 q^{90} - 9 q^{91} - 8 q^{92} - 2 q^{93} - 19 q^{94} - 17 q^{95} + 18 q^{96} + 26 q^{97} + 33 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - 7 * q^4 - 3 * q^5 - 2 * q^6 + 9 * q^7 - 12 * q^8 - 4 * q^9 - 14 * q^10 - 4 * q^11 - 7 * q^12 - 8 * q^13 + 16 * q^14 + 6 * q^15 - 9 * q^16 - 2 * q^17 + q^18 - 6 * q^19 - 2 * q^20 - 6 * q^21 + 40 * q^22 + 4 * q^23 + 6 * q^24 + 3 * q^25 - q^26 + 8 * q^27 - 20 * q^28 - 26 * q^29 - 14 * q^30 - 2 * q^31 + 18 * q^32 - 4 * q^33 + 13 * q^35 + 14 * q^36 + 5 * q^37 - 11 * q^38 + 4 * q^39 - 17 * q^40 + 16 * q^41 - 17 * q^42 + 32 * q^43 + 26 * q^44 - 3 * q^45 + 29 * q^46 - 15 * q^47 + 18 * q^48 - 21 * q^49 + 48 * q^50 - 2 * q^51 + 7 * q^52 + 2 * q^53 + q^54 + 48 * q^55 - 35 * q^56 + 12 * q^57 - q^58 - 20 * q^59 + q^60 - 20 * q^61 - 44 * q^62 - 3 * q^63 + 40 * q^64 + 3 * q^65 - 20 * q^66 - 10 * q^67 - 13 * q^68 - 8 * q^69 - 31 * q^70 + 4 * q^71 + 6 * q^72 + 21 * q^74 + 3 * q^75 - 86 * q^76 + 3 * q^77 + 2 * q^78 - 6 * q^79 + 21 * q^80 - 4 * q^81 - 6 * q^82 + 32 * q^83 - 2 * q^84 + 4 * q^85 + 51 * q^86 + 13 * q^87 - 39 * q^88 - 51 * q^89 + 28 * q^90 - 9 * q^91 - 8 * q^92 - 2 * q^93 - 19 * q^94 - 17 * q^95 + 18 * q^96 + 26 * q^97 + 33 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.698934	+	1.21059i	0.494221	+	0.856016i	0.999978	−	0.00666036i	$-0.00212007\pi$
$2$	0.698934	+	1.21059i	0.494221	+	0.856016i	−0.505757	+	0.862676i	$0.668787\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.0229829	−	0.0398076i	0.0114915	−	0.0199038i
$5$	0.198934	+	0.344564i	0.0889659	+	0.154094i	0.907074	−	0.420971i	$-0.138310\pi$
$5$	0.198934	+	0.344564i	0.0889659	+	0.154094i	−0.818108	+	0.575064i	$0.804977\pi$
$6$	−1.39787			−0.570677
$7$	1.69893	+	2.02821i	0.642137	+	0.766590i
$7$	1.69893	+	2.02821i	0.642137	+	0.766590i
$8$	2.85999			1.01116
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.278083	+	0.481654i	−0.0879376	+	0.152312i
$11$	−0.824049	+	1.42729i	−0.248460	+	0.430346i	−0.963099	−	0.269148i	$-0.913258\pi$
$11$	−0.824049	+	1.42729i	−0.248460	+	0.430346i	0.714639	+	0.699494i	$0.246591\pi$
$12$	0.0229829	+	0.0398076i	0.00663460	+	0.0114915i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−1.26788	+	3.47429i	−0.338856	+	0.928544i
$15$	−0.397868			−0.102729
$16$	1.95298	+	3.38266i	0.488244	+	0.845664i
$17$	−2.10595	+	3.64761i	−0.510767	+	0.884674i	0.489155	+	0.872197i	$0.337305\pi$
$17$	−2.10595	+	3.64761i	−0.510767	+	0.884674i	−0.999922	+	0.0124775i	$0.996028\pi$
$18$	0.698934	−	1.21059i	0.164740	−	0.285339i
$19$	−2.54597	−	4.40974i	−0.584085	−	1.01166i	−0.994989	−	0.0999857i	$-0.968120\pi$
$19$	−2.54597	−	4.40974i	−0.584085	−	1.01166i	0.410904	−	0.911679i	$-0.365213\pi$
$20$	0.0182883			0.00408939
$21$	−2.60595	+	0.457216i	−0.568664	+	0.0997728i
$22$	−2.30382			−0.491177
$23$	1.20808	+	2.09245i	0.251902	+	0.436307i	0.964049	−	0.265723i	$-0.0856107\pi$
$23$	1.20808	+	2.09245i	0.251902	+	0.436307i	−0.712148	+	0.702030i	$0.752277\pi$
$24$	−1.42999	+	2.47682i	−0.291896	+	0.505580i
$25$	2.42085	−	4.19304i	0.484170	−	0.838607i
$26$	−0.698934	−	1.21059i	−0.137072	−	0.237416i
$27$	1.00000			0.192450
$28$	0.119784	−	0.0210163i	0.0226371	−	0.00397171i
$29$	1.48980			0.276649			0.138324	−	0.990387i	$-0.455828\pi$
$29$	1.48980			0.276649			0.138324	+	0.990387i	$0.455828\pi$
$30$	−0.278083	−	0.481654i	−0.0507708	−	0.0879376i
$31$	1.92999	−	3.34285i	0.346637	−	0.600393i	−0.639013	−	0.769196i	$-0.720657\pi$
$31$	1.92999	−	3.34285i	0.346637	−	0.600393i	0.985650	+	0.168803i	$0.0539901\pi$
$32$	0.129985	−	0.225141i	0.0229783	−	0.0397996i
$33$	−0.824049	−	1.42729i	−0.143449	−	0.248460i
$34$	−5.88767			−1.00973
$35$	−0.360871	+	0.988870i	−0.0609983	+	0.167149i
$36$	−0.0459658			−0.00766097
$37$	−5.13274	−	8.89017i	−0.843818	−	1.46153i	−0.886644	−	0.462452i	$-0.846970\pi$
$37$	−5.13274	−	8.89017i	−0.843818	−	1.46153i	0.0428265	−	0.999083i	$-0.486364\pi$
$38$	3.55892	−	6.16424i	0.577334	−	0.999971i
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	0.568949	+	0.985448i	0.0899587	+	0.155813i
$41$	−4.65573			−0.727102			−0.363551	−	0.931574i	$-0.618436\pi$
$41$	−4.65573			−0.727102			−0.363551	+	0.931574i	$0.618436\pi$
$42$	−2.37488	−	2.83517i	−0.366453	−	0.437475i
$43$	8.47151			1.29189			0.645947	−	0.763383i	$-0.276463\pi$
$43$	8.47151			1.29189			0.645947	+	0.763383i	$0.276463\pi$
$44$	0.0378781	+	0.0656068i	0.00571034	+	0.00989060i
$45$	0.198934	−	0.344564i	0.0296553	−	0.0513645i
$46$	−1.68873	+	2.92497i	−0.248990	+	0.431264i
$47$	2.02680	+	3.51051i	0.295639	+	0.512061i	0.975133	−	0.221619i	$-0.0711342\pi$
$47$	2.02680	+	3.51051i	0.295639	+	0.512061i	−0.679495	+	0.733680i	$0.737801\pi$
$48$	−3.90596			−0.563776
$49$	−1.22725	+	6.89158i	−0.175321	+	0.984511i
$50$	6.76806			0.957148
$51$	−2.10595	−	3.64761i	−0.294891	−	0.510767i
$52$	−0.0229829	+	0.0398076i	−0.00318716	+	0.00552032i
$53$	4.66575	−	8.08132i	0.640890	−	1.11005i	−0.344344	−	0.938843i	$-0.611899\pi$
$53$	4.66575	−	8.08132i	0.640890	−	1.11005i	0.985234	−	0.171211i	$-0.0547679\pi$
$54$	0.698934	+	1.21059i	0.0951129	+	0.164740i
$55$	−0.655725			−0.0884179
$56$	4.85893	+	5.80065i	0.649302	+	0.775145i
$57$	5.09193			0.674443
$58$	1.04127	+	1.80353i	0.136726	+	0.236816i
$59$	0.827863	−	1.43390i	0.107779	−	0.186678i	−0.807091	−	0.590426i	$-0.798960\pi$
$59$	0.827863	−	1.43390i	0.107779	−	0.186678i	0.914870	+	0.403749i	$0.132293\pi$
$60$	−0.00914416	+	0.0158382i	−0.00118051	+	0.00204470i
$61$	−5.50381	−	9.53288i	−0.704691	−	1.22056i	−0.966803	−	0.255523i	$-0.917752\pi$
$61$	−5.50381	−	9.53288i	−0.704691	−	1.22056i	0.262112	−	0.965038i	$-0.415581\pi$
$62$	5.39575			0.685262
$63$	0.907012	−	2.48542i	0.114273	−	0.313134i
$64$	8.17531			1.02191
$65$	−0.198934	−	0.344564i	−0.0246747	−	0.0427378i
$66$	1.15191	−	1.99517i	0.141791	−	0.245588i
$67$	0.221917	−	0.384371i	0.0271114	−	0.0469584i	−0.852151	−	0.523295i	$-0.824702\pi$
$67$	0.221917	−	0.384371i	0.0271114	−	0.0469584i	0.879263	+	0.476337i	$0.158036\pi$
$68$	0.0968016	+	0.167665i	0.0117389	+	0.0203324i
$69$	−2.41616			−0.290871
$70$	−1.44934	+	0.254288i	−0.173229	+	0.0303933i
$71$	−9.74766			−1.15683			−0.578417	−	0.815741i	$-0.696329\pi$
$71$	−9.74766			−1.15683			−0.578417	+	0.815741i	$0.696329\pi$
$72$	−1.42999	−	2.47682i	−0.168527	−	0.291896i
$73$	−3.32786	+	5.76403i	−0.389497	+	0.674628i	−0.992382	−	0.123200i	$-0.960684\pi$
$73$	−3.32786	+	5.76403i	−0.389497	+	0.674628i	0.602885	+	0.797828i	$0.294018\pi$
$74$	7.17489	−	12.4273i	0.834065	−	1.44464i
$75$	2.42085	+	4.19304i	0.279536	+	0.484170i
$76$	−0.234055			−0.0268479
$77$	−4.29485	+	0.753537i	−0.489444	+	0.0858736i
$78$	1.39787			0.158277
$79$	−2.28190	−	3.95236i	−0.256733	−	0.444675i	0.708631	−	0.705579i	$-0.249313\pi$
$79$	−2.28190	−	3.95236i	−0.256733	−	0.444675i	−0.965365	+	0.260903i	$0.915980\pi$
$80$	−0.777027	+	1.34585i	−0.0868742	+	0.150471i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.25404	−	5.63617i	−0.359349	−	0.622411i
$83$	16.4234			1.80271			0.901353	−	0.433085i	$-0.142575\pi$
$83$	16.4234			1.80271			0.901353	+	0.433085i	$0.142575\pi$
$84$	−0.0416916	+	0.114245i	−0.00454892	+	0.0124651i
$85$	−1.67578			−0.181763
$86$	5.92103	+	10.2555i	0.638481	+	1.10588i
$87$	−0.744900	+	1.29020i	−0.0798616	+	0.138324i
$88$	−2.35677	+	4.08205i	−0.251233	+	0.435148i
$89$	−2.14915	−	3.72244i	−0.227810	−	0.394578i	0.729349	−	0.684142i	$-0.239823\pi$
$89$	−2.14915	−	3.72244i	−0.227810	−	0.394578i	−0.957159	+	0.289564i	$0.906490\pi$
$90$	0.556166			0.0586251
$91$	−1.69893	−	2.02821i	−0.178097	−	0.212614i
$92$	0.111061			0.0115789
$93$	1.92999	+	3.34285i	0.200131	+	0.346637i
$94$	−2.83319	+	4.90723i	−0.292222	+	0.506143i
$95$	1.01296	−	1.75449i	0.103927	−	0.180007i
$96$	0.129985	+	0.225141i	0.0132665	+	0.0229783i
$97$	−8.26548			−0.839233			−0.419616	−	0.907702i	$-0.637835\pi$
$97$	−8.26548			−0.839233			−0.419616	+	0.907702i	$0.637835\pi$
$98$	−9.20063	+	3.33107i	−0.929404	+	0.336488i
$99$	1.64810			0.165640
$100$	−0.111276	−	0.192736i	−0.0111276	−	0.0192736i
$101$	−8.25253	+	14.2938i	−0.821157	+	1.42229i	0.0836641	+	0.996494i	$0.473338\pi$
$101$	−8.25253	+	14.2938i	−0.821157	+	1.42229i	−0.904821	+	0.425792i	$0.859996\pi$
$102$	2.94383	−	5.09887i	0.291483	−	0.504863i
$103$	−2.57276	−	4.45615i	−0.253502	−	0.439078i	0.710986	−	0.703206i	$-0.248249\pi$
$103$	−2.57276	−	4.45615i	−0.253502	−	0.439078i	−0.964488	+	0.264128i	$0.914916\pi$
$104$	−2.85999			−0.280445
$105$	−0.675951	−	0.806958i	−0.0659661	−	0.0787510i
$106$	13.0442			1.26697
$107$	−4.44765	−	7.70355i	−0.429970	−	0.744730i	0.566900	−	0.823787i	$-0.308143\pi$
$107$	−4.44765	−	7.70355i	−0.429970	−	0.744730i	−0.996870	+	0.0790564i	$0.974809\pi$
$108$	0.0229829	−	0.0398076i	0.00221153	−	0.00383049i
$109$	−4.89681	+	8.48153i	−0.469029	+	0.812383i	−0.999373	−	0.0353998i	$-0.988730\pi$
$109$	−4.89681	+	8.48153i	−0.469029	+	0.812383i	0.530344	+	0.847783i	$0.322063\pi$
$110$	−0.458308	−	0.793813i	−0.0436980	−	0.0756871i
$111$	10.2655			0.974357
$112$	−3.54275	+	9.70795i	−0.334758	+	0.917315i
$113$	−12.4332			−1.16961			−0.584807	−	0.811172i	$-0.698830\pi$
$113$	−12.4332			−1.16961			−0.584807	+	0.811172i	$0.698830\pi$
$114$	3.55892	+	6.16424i	0.333324	+	0.577334i
$115$	−0.480655	+	0.832519i	−0.0448213	+	0.0776328i
$116$	0.0342399	−	0.0593053i	0.00317910	−	0.00550636i
$117$	0.500000	+	0.866025i	0.0462250	+	0.0800641i
$118$	2.31448			0.213066
$119$	−10.9760	+	1.92575i	−1.00616	+	0.176533i
$120$	−1.13790			−0.103875
$121$	4.14189	+	7.17396i	0.376535	+	0.652178i
$122$	7.69360	−	13.3257i	0.696546	−	1.20645i
$123$	2.32786	−	4.03198i	0.209896	−	0.363551i
$124$	−0.0887138	−	0.153657i	−0.00796674	−	0.0137988i
$125$	3.91570			0.350230
$126$	3.64277	−	0.639128i	0.324524	−	0.0569380i
$127$	9.23781			0.819723			0.409861	−	0.912148i	$-0.365577\pi$
$127$	9.23781			0.819723			0.409861	+	0.912148i	$0.365577\pi$
$128$	5.45403	+	9.44666i	0.482073	+	0.834975i
$129$	−4.23576	+	7.33654i	−0.372937	+	0.645947i
$130$	0.278083	−	0.481654i	0.0243895	−	0.0422439i
$131$	−7.33701	−	12.7081i	−0.641037	−	1.11031i	−0.985202	−	0.171400i	$-0.945171\pi$
$131$	−7.33701	−	12.7081i	−0.641037	−	1.11031i	0.344164	−	0.938909i	$-0.388162\pi$
$132$	−0.0757562			−0.00659373
$133$	4.61844	−	12.6556i	0.400470	−	1.09738i
$134$	0.620421			0.0535962
$135$	0.198934	+	0.344564i	0.0171215	+	0.0296553i
$136$	−6.02298	+	10.4321i	−0.516467	+	0.894546i
$137$	−2.37400	+	4.11189i	−0.202825	+	0.351303i	−0.949438	−	0.313956i	$-0.898346\pi$
$137$	−2.37400	+	4.11189i	−0.202825	+	0.351303i	0.746613	+	0.665259i	$0.231679\pi$
$138$	−1.68873	−	2.92497i	−0.143755	−	0.248990i
$139$	2.56379			0.217458			0.108729	−	0.994071i	$-0.465322\pi$
$139$	2.56379			0.217458			0.108729	+	0.994071i	$0.465322\pi$
$140$	0.0310707	+	0.0370925i	0.00262595	+	0.00313489i
$141$	−4.05359			−0.341374
$142$	−6.81297	−	11.8004i	−0.571732	−	0.990268i
$143$	0.824049	−	1.42729i	0.0689104	−	0.119356i
$144$	1.95298	−	3.38266i	0.162748	−	0.281888i
$145$	0.296372	+	0.513331i	0.0246123	+	0.0426298i
$146$	−9.30382			−0.769990
$147$	−5.35466	−	4.50862i	−0.441645	−	0.371864i
$148$	−0.471862			−0.0387868
$149$	4.30382	+	7.45444i	0.352583	+	0.610692i	0.986701	−	0.162545i	$-0.0519701\pi$
$149$	4.30382	+	7.45444i	0.352583	+	0.610692i	−0.634118	+	0.773236i	$0.718637\pi$
$150$	−3.38403	+	5.86131i	−0.276305	+	0.478574i
$151$	−3.86087	+	6.68722i	−0.314193	+	0.544199i	−0.979266	−	0.202580i	$-0.935067\pi$
$151$	−3.86087	+	6.68722i	−0.314193	+	0.544199i	0.665072	+	0.746779i	$0.268401\pi$
$152$	−7.28144	−	12.6118i	−0.590602	−	1.02295i
$153$	4.21189			0.340511
$154$	−3.91404	−	4.67263i	−0.315403	−	0.376531i
$155$	1.53577			0.123356
$156$	−0.0229829	−	0.0398076i	−0.00184011	−	0.00318716i
$157$	−6.22573	+	10.7833i	−0.496867	+	0.860600i	−0.999993	−	0.00361349i	$-0.998850\pi$
$157$	−6.22573	+	10.7833i	−0.496867	+	0.860600i	0.503126	+	0.864213i	$0.332183\pi$
$158$	3.18979	−	5.52488i	0.253766	−	0.439536i
$159$	4.66575	+	8.08132i	0.370018	+	0.640890i
$160$	0.103434			0.00817716
$161$	−2.19148	+	6.00517i	−0.172713	+	0.473274i
$162$	−1.39787			−0.109827
$163$	5.97550	+	10.3499i	0.468037	+	0.810664i	0.999333	−	0.0365222i	$-0.0116280\pi$
$163$	5.97550	+	10.3499i	0.468037	+	0.810664i	−0.531296	+	0.847187i	$0.678295\pi$
$164$	−0.107002	+	0.185333i	−0.00835547	+	0.0144721i
$165$	0.327863	−	0.567875i	0.0255241	−	0.0442090i
$166$	11.4789	+	19.8820i	0.890935	+	1.54314i
$167$	−3.09193			−0.239261			−0.119630	−	0.992818i	$-0.538171\pi$
$167$	−3.09193			−0.239261			−0.119630	+	0.992818i	$0.538171\pi$
$168$	−7.45298	+	1.30763i	−0.575010	+	0.100886i
$169$	1.00000			0.0769231
$170$	−1.17126	−	2.02868i	−0.0898313	−	0.155592i
$171$	−2.54597	+	4.40974i	−0.194695	+	0.337221i
$172$	0.194700	−	0.337230i	0.0148457	−	0.0257136i
$173$	3.05617	+	5.29344i	0.232356	+	0.402452i	0.958501	−	0.285089i	$-0.0920232\pi$
$173$	3.05617	+	5.29344i	0.232356	+	0.402452i	−0.726145	+	0.687542i	$0.758690\pi$
$174$	−2.08254			−0.157877
$175$	12.6172	−	2.21371i	0.953771	−	0.167340i
$176$	−6.43740			−0.485237
$177$	0.827863	+	1.43390i	0.0622260	+	0.107779i
$178$	3.00423	−	5.20349i	0.225177	−	0.390018i
$179$	−6.33168	+	10.9668i	−0.473252	+	0.819696i	−0.999531	−	0.0306157i	$-0.990253\pi$
$179$	−6.33168	+	10.9668i	−0.473252	+	0.819696i	0.526280	+	0.850312i	$0.323587\pi$
$180$	−0.00914416	−	0.0158382i	−0.000681566	−	0.00118051i
$181$	23.1255			1.71890			0.859451	−	0.511217i	$-0.170805\pi$
$181$	23.1255			1.71890			0.859451	+	0.511217i	$0.170805\pi$
$182$	1.26788	−	3.47429i	0.0939817	−	0.257532i
$183$	11.0076			0.813707
$184$	3.45509	+	5.98439i	0.254713	+	0.441175i
$185$	2.04215	−	3.53711i	0.150142	−	0.260054i
$186$	−2.69788	+	4.67286i	−0.197818	+	0.342631i
$187$	−3.47081	−	6.01161i	−0.253810	−	0.439613i
$188$	0.186327			0.0135893
$189$	1.69893	+	2.02821i	0.123579	+	0.147530i
$190$	2.83196			0.205452
$191$	10.7070	+	18.5451i	0.774733	+	1.34188i	0.934944	+	0.354794i	$0.115449\pi$
$191$	10.7070	+	18.5451i	0.774733	+	1.34188i	−0.160212	+	0.987083i	$0.551218\pi$
$192$	−4.08766	+	7.08003i	−0.295001	+	0.510957i
$193$	−7.36867	+	12.7629i	−0.530409	+	0.918695i	0.468962	+	0.883218i	$0.344628\pi$
$193$	−7.36867	+	12.7629i	−0.530409	+	0.918695i	−0.999371	+	0.0354764i	$0.988705\pi$
$194$	−5.77703	−	10.0061i	−0.414766	−	0.718396i
$195$	0.397868			0.0284919
$196$	0.246131	+	0.207242i	0.0175808	+	0.0148030i
$197$	−27.9672			−1.99258			−0.996289	−	0.0860669i	$-0.972570\pi$
$197$	−27.9672			−1.99258			−0.996289	+	0.0860669i	$0.972570\pi$
$198$	1.15191	+	1.99517i	0.0818628	+	0.141791i
$199$	6.02574	−	10.4369i	0.427153	−	0.739851i	−0.569465	−	0.822015i	$-0.692850\pi$
$199$	6.02574	−	10.4369i	0.427153	−	0.739851i	0.996619	+	0.0821639i	$0.0261831\pi$
$200$	6.92361	−	11.9920i	0.489573	−	0.847965i
$201$	0.221917	+	0.384371i	0.0156528	+	0.0271114i
$202$	−23.0719			−1.62333
$203$	2.53107	+	3.02162i	0.177646	+	0.212076i
$204$	−0.193603			−0.0135549
$205$	−0.926181	−	1.60419i	−0.0646873	−	0.112042i
$206$	3.59638	−	6.22912i	0.250572	−	0.434003i
$207$	1.20808	−	2.09245i	0.0839672	−	0.145436i
$208$	−1.95298	−	3.38266i	−0.135415	−	0.234545i
$209$	8.39200			0.580487
$210$	0.504450	−	1.38231i	0.0348103	−	0.0953884i
$211$	20.6451			1.42126			0.710632	−	0.703563i	$-0.248409\pi$
$211$	20.6451			1.42126			0.710632	+	0.703563i	$0.248409\pi$
$212$	−0.214465	−	0.371465i	−0.0147295	−	0.0255123i
$213$	4.87383	−	8.44172i	0.333949	−	0.578417i
$214$	6.21722	−	10.7685i	0.425001	−	0.736123i
$215$	1.68527	+	2.91897i	0.114934	+	0.199072i
$216$	2.85999			0.194598
$217$	10.0589	−	1.76485i	0.682844	−	0.119806i
$218$	−13.6902			−0.927217
$219$	−3.32786	−	5.76403i	−0.224876	−	0.389497i
$220$	−0.0150705	+	0.0261028i	−0.00101605	+	0.00175985i
$221$	2.10595	−	3.64761i	0.141661	−	0.245364i
$222$	7.17489	+	12.4273i	0.481547	+	0.834065i
$223$	16.3927			1.09774			0.548869	−	0.835908i	$-0.315059\pi$
$223$	16.3927			1.09774			0.548869	+	0.835908i	$0.315059\pi$
$224$	0.677468	−	0.118863i	0.0452652	−	0.00794184i
$225$	−4.84170			−0.322780
$226$	−8.68996	−	15.0515i	−0.578048	−	1.00121i
$227$	1.44383	−	2.50079i	0.0958306	−	0.165983i	−0.814124	−	0.580691i	$-0.802783\pi$
$227$	1.44383	−	2.50079i	0.0958306	−	0.165983i	0.909955	+	0.414707i	$0.136116\pi$
$228$	0.117027	−	0.202698i	0.00775033	−	0.0134240i
$229$	−3.34258	−	5.78952i	−0.220884	−	0.382582i	0.734193	−	0.678941i	$-0.237561\pi$
$229$	−3.34258	−	5.78952i	−0.220884	−	0.382582i	−0.955077	+	0.296359i	$0.904228\pi$
$230$	−1.34378			−0.0886066
$231$	1.49484	−	4.09622i	0.0983536	−	0.269512i
$232$	4.26081			0.279736
$233$	−10.5757	−	18.3176i	−0.692837	−	1.20003i	−0.970904	−	0.239467i	$-0.923027\pi$
$233$	−10.5757	−	18.3176i	−0.692837	−	1.20003i	0.278068	−	0.960561i	$-0.410306\pi$
$234$	−0.698934	+	1.21059i	−0.0456907	+	0.0791387i
$235$	−0.806397	+	1.39672i	−0.0526035	+	0.0911120i
$236$	−0.0380534	−	0.0659104i	−0.00247707	−	0.00429040i
$237$	4.56379			0.296450
$238$	−10.0028	−	11.9414i	−0.648382	−	0.774047i
$239$	−27.1702			−1.75749			−0.878746	−	0.477290i	$-0.841619\pi$
$239$	−27.1702			−1.75749			−0.878746	+	0.477290i	$0.841619\pi$
$240$	−0.777027	−	1.34585i	−0.0501569	−	0.0868742i
$241$	−3.70913	+	6.42441i	−0.238926	+	0.413833i	−0.960406	−	0.278603i	$-0.910129\pi$
$241$	−3.70913	+	6.42441i	−0.238926	+	0.413833i	0.721480	+	0.692435i	$0.243462\pi$
$242$	−5.78981	+	10.0282i	−0.372183	+	0.644640i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.505975			−0.0323917
$245$	−2.61873	+	0.948104i	−0.167304	+	0.0605721i
$246$	6.50809			0.414941
$247$	2.54597	+	4.40974i	0.161996	+	0.280585i
$248$	5.51977	−	9.56051i	0.350505	−	0.607093i
$249$	−8.21172	+	14.2231i	−0.520396	+	0.901353i
$250$	2.73681	+	4.74030i	0.173091	+	0.299803i
$251$	27.2454			1.71972			0.859858	−	0.510533i	$-0.170552\pi$
$251$	27.2454			1.71972			0.859858	+	0.510533i	$0.170552\pi$
$252$	−0.0780929	−	0.0932283i	−0.00491939	−	0.00587283i
$253$	−3.98206			−0.250350
$254$	6.45662	+	11.1832i	0.405124	+	0.701696i
$255$	0.837888	−	1.45126i	0.0524706	−	0.0908817i
$256$	0.551297	−	0.954874i	0.0344560	−	0.0596796i
$257$	−9.68358	−	16.7724i	−0.604045	−	1.04624i	−0.992202	−	0.124643i	$-0.960221\pi$
$257$	−9.68358	−	16.7724i	−0.604045	−	1.04624i	0.388157	−	0.921593i	$-0.373112\pi$
$258$	−11.8421			−0.737254
$259$	9.31092	−	25.5141i	0.578552	−	1.58537i
$260$	−0.0182883			−0.00113419
$261$	−0.744900	−	1.29020i	−0.0461081	−	0.0798616i
$262$	10.2562	−	17.7642i	0.633628	−	1.09748i
$263$	−3.92085	+	6.79111i	−0.241770	+	0.418758i	−0.961219	−	0.275788i	$-0.911061\pi$
$263$	−3.92085	+	6.79111i	−0.241770	+	0.418758i	0.719449	+	0.694546i	$0.244395\pi$
$264$	−2.35677	−	4.08205i	−0.145049	−	0.251233i
$265$	3.71270			0.228070
$266$	18.5487	−	3.25440i	1.13730	−	0.199540i
$267$	4.29831			0.263052
$268$	−0.0102006	−	0.0176679i	−0.000623100	−	0.00107924i
$269$	7.69167	−	13.3224i	0.468969	−	0.812278i	−0.530402	−	0.847746i	$-0.677959\pi$
$269$	7.69167	−	13.3224i	0.468969	−	0.812278i	0.999371	+	0.0354681i	$0.0112922\pi$
$270$	−0.278083	+	0.481654i	−0.0169236	+	0.0293125i
$271$	3.62875	+	6.28519i	0.220431	+	0.381798i	0.954939	−	0.296802i	$-0.0959203\pi$
$271$	3.62875	+	6.28519i	0.220431	+	0.381798i	−0.734508	+	0.678600i	$0.762587\pi$
$272$	−16.4515			−0.997516
$273$	2.60595	−	0.457216i	0.157719	−	0.0276720i
$274$	−6.63709			−0.400961
$275$	3.98980	+	6.91054i	0.240594	+	0.416721i
$276$	−0.0555303	+	0.0961813i	−0.00334253	+	0.00578944i
$277$	0.420851	−	0.728935i	0.0252865	−	0.0437974i	−0.853105	−	0.521739i	$-0.825284\pi$
$277$	0.420851	−	0.728935i	0.0252865	−	0.0437974i	0.878392	+	0.477941i	$0.158617\pi$
$278$	1.79192	+	3.10370i	0.107472	+	0.186148i
$279$	−3.85999			−0.231092
$280$	−1.03209	+	2.82816i	−0.0616790	+	0.169015i
$281$	−4.40090			−0.262536			−0.131268	−	0.991347i	$-0.541905\pi$
$281$	−4.40090			−0.262536			−0.131268	+	0.991347i	$0.541905\pi$
$282$	−2.83319	−	4.90723i	−0.168714	−	0.292222i
$283$	−4.52662	+	7.84034i	−0.269080	+	0.466060i	−0.968624	−	0.248529i	$-0.920053\pi$
$283$	−4.52662	+	7.84034i	−0.269080	+	0.466060i	0.699545	+	0.714589i	$0.253386\pi$
$284$	−0.224030	+	0.388031i	−0.0132937	+	0.0230254i
$285$	1.01296	+	1.75449i	0.0600024	+	0.103927i
$286$	2.30382			0.136228
$287$	−7.90977	−	9.44277i	−0.466899	−	0.557389i
$288$	−0.259970			−0.0153189
$289$	−0.370015	−	0.640885i	−0.0217656	−	0.0376991i
$290$	−0.414288	+	0.717568i	−0.0243278	+	0.0421371i
$291$	4.13274	−	7.15812i	0.242266	−	0.419616i
$292$	0.152968	+	0.264948i	0.00895178	+	0.0155049i
$293$	31.4667			1.83831			0.919153	−	0.393902i	$-0.128875\pi$
$293$	31.4667			1.83831			0.919153	+	0.393902i	$0.128875\pi$
$294$	1.71553	−	9.63352i	0.100052	−	0.561838i
$295$	0.658760			0.0383545
$296$	−14.6796	−	25.4258i	−0.853234	−	1.47784i
$297$	−0.824049	+	1.42729i	−0.0478162	+	0.0828200i
$298$	−6.01618	+	10.4203i	−0.348508	+	0.603633i
$299$	−1.20808	−	2.09245i	−0.0698650	−	0.121010i
$300$	0.222553			0.0128491
$301$	14.3925	+	17.1820i	0.829572	+	0.990353i
$302$	−10.7940			−0.621123
$303$	−8.25253	−	14.2938i	−0.474095	−	0.821157i
$304$	9.94443	−	17.2243i	0.570352	−	0.987879i
$305$	2.18979	−	3.79283i	0.125387	−	0.217177i
$306$	2.94383	+	5.09887i	0.168288	+	0.291483i
$307$	−12.8195			−0.731650			−0.365825	−	0.930684i	$-0.619213\pi$
$307$	−12.8195			−0.731650			−0.365825	+	0.930684i	$0.619213\pi$
$308$	−0.0687118	+	0.188286i	−0.00391522	+	0.0107286i
$309$	5.14552			0.292719
$310$	1.07340	+	1.85918i	0.0609649	+	0.105594i
$311$	−10.6355	+	18.4212i	−0.603084	+	1.04457i	0.389267	+	0.921125i	$0.372728\pi$
$311$	−10.6355	+	18.4212i	−0.603084	+	1.04457i	−0.992351	+	0.123447i	$0.960605\pi$
$312$	1.42999	−	2.47682i	0.0809575	−	0.140223i
$313$	−8.32804	−	14.4246i	−0.470729	−	0.815326i	0.528711	−	0.848802i	$-0.322676\pi$
$313$	−8.32804	−	14.4246i	−0.470729	−	0.815326i	−0.999440	+	0.0334762i	$0.989342\pi$
$314$	−17.4055			−0.982249
$315$	1.03682	−	0.181912i	0.0584183	−	0.0102496i
$316$	−0.209779			−0.0118010
$317$	−10.0587	−	17.4223i	−0.564956	−	0.978532i	−0.997054	−	0.0767052i	$-0.975560\pi$
$317$	−10.0587	−	17.4223i	−0.564956	−	0.978532i	0.432098	−	0.901827i	$-0.357773\pi$
$318$	−6.52210	+	11.2966i	−0.365741	+	0.633483i
$319$	−1.22767	+	2.12638i	−0.0687362	+	0.119055i
$320$	1.62635	+	2.81692i	0.0909156	+	0.157470i
$321$	8.89529			0.496487
$322$	−8.80149	+	1.54423i	−0.490488	+	0.0860567i
$323$	21.4467			1.19332
$324$	0.0229829	+	0.0398076i	0.00127683	+	0.00221153i
$325$	−2.42085	+	4.19304i	−0.134285	+	0.232588i
$326$	−8.35296	+	14.4677i	−0.462628	+	0.801294i
$327$	−4.89681	−	8.48153i	−0.270794	−	0.469029i
$328$	−13.3153			−0.735216
$329$	−3.67666	+	10.0749i	−0.202701	+	0.555447i
$330$	0.916617			0.0504581
$331$	−9.71846	−	16.8329i	−0.534175	−	0.925218i	−0.999203	−	0.0399221i	$-0.987289\pi$
$331$	−9.71846	−	16.8329i	−0.534175	−	0.925218i	0.465028	−	0.885296i	$-0.346044\pi$
$332$	0.377458	−	0.653777i	0.0207157	−	0.0358807i
$333$	−5.13274	+	8.89017i	−0.281273	+	0.487178i
$334$	−2.16106	−	3.74306i	−0.118248	−	0.204811i
$335$	0.176587			0.00964798
$336$	−6.63596	−	7.92209i	−0.362021	−	0.432185i
$337$	−1.95707			−0.106608			−0.0533042	−	0.998578i	$-0.516975\pi$
$337$	−1.95707			−0.106608			−0.0533042	+	0.998578i	$0.516975\pi$
$338$	0.698934	+	1.21059i	0.0380170	+	0.0658474i
$339$	6.21659	−	10.7674i	0.337639	−	0.584807i
$340$	−0.0385142	+	0.0667086i	−0.00208873	+	0.00361778i
$341$	3.18082	+	5.50934i	0.172251	+	0.298348i
$342$	−7.11785			−0.384889
$343$	−16.0626	+	9.21923i	−0.867297	+	0.497791i
$344$	24.2284			1.30631
$345$	−0.480655	−	0.832519i	−0.0258776	−	0.0448213i
$346$	−4.27212	+	7.39952i	−0.229670	+	0.397801i
$347$	2.24109	−	3.88168i	0.120308	−	0.208379i	−0.799581	−	0.600558i	$-0.794945\pi$
$347$	2.24109	−	3.88168i	0.120308	−	0.208379i	0.919889	+	0.392179i	$0.128279\pi$
$348$	0.0342399	+	0.0593053i	0.00183545	+	0.00317910i
$349$	−15.4411			−0.826546			−0.413273	−	0.910607i	$-0.635614\pi$
$349$	−15.4411			−0.826546			−0.413273	+	0.910607i	$0.635614\pi$
$350$	11.4985	+	13.7270i	0.614620	+	0.733740i
$351$	−1.00000			−0.0533761
$352$	0.214228	+	0.371054i	0.0114184	+	0.0197773i
$353$	16.2155	−	28.0861i	0.863066	−	1.49487i	−0.00588965	−	0.999983i	$-0.501875\pi$
$353$	16.2155	−	28.0861i	0.863066	−	1.49487i	0.868955	−	0.494891i	$-0.164792\pi$
$354$	−1.15724	+	2.00440i	−0.0615067	+	0.106533i
$355$	−1.93914	−	3.35869i	−0.102919	−	0.178261i
$356$	−0.197575			−0.0104715
$357$	3.82024	−	10.4683i	0.202188	−	0.554043i
$358$	−17.7017			−0.935563
$359$	16.1011	+	27.8879i	0.849782	+	1.47187i	0.881402	+	0.472366i	$0.156600\pi$
$359$	16.1011	+	27.8879i	0.849782	+	1.47187i	−0.0316201	+	0.999500i	$0.510067\pi$
$360$	0.568949	−	0.985448i	0.0299862	−	0.0519377i
$361$	−3.46388	+	5.99962i	−0.182310	+	0.315770i
$362$	16.1632	+	27.9954i	0.849518	+	1.47141i
$363$	−8.28377			−0.434785
$364$	−0.119784	+	0.0210163i	−0.00627841	+	0.00110156i
$365$	−2.64810			−0.138608
$366$	7.69360	+	13.3257i	0.402151	+	0.696546i
$367$	5.54110	−	9.59746i	0.289243	−	0.500983i	−0.684386	−	0.729120i	$-0.739930\pi$
$367$	5.54110	−	9.59746i	0.289243	−	0.500983i	0.973629	+	0.228136i	$0.0732632\pi$
$368$	−4.71870	+	8.17303i	−0.245979	+	0.426048i
$369$	2.32786	+	4.03198i	0.121184	+	0.209896i
$370$	5.70932			0.296813
$371$	24.3174	−	4.26651i	1.26250	−	0.221506i
$372$	0.177428			0.00919920
$373$	18.9868	+	32.8860i	0.983097	+	1.70277i	0.650103	+	0.759846i	$0.274726\pi$
$373$	18.9868	+	32.8860i	0.983097	+	1.70277i	0.332994	+	0.942929i	$0.391941\pi$
$374$	4.85173	−	8.40344i	0.250877	−	0.434531i
$375$	−1.95785	+	3.39109i	−0.101103	+	0.175115i
$376$	5.79662	+	10.0400i	0.298938	+	0.517775i
$377$	−1.48980			−0.0767286
$378$	−1.26788	+	3.47429i	−0.0652128	+	0.178698i
$379$	−21.3011			−1.09417			−0.547083	−	0.837078i	$-0.684262\pi$
$379$	−21.3011			−1.09417			−0.547083	+	0.837078i	$0.684262\pi$
$380$	−0.0465615	−	0.0806468i	−0.00238855	−	0.00413709i
$381$	−4.61890	+	8.00018i	−0.236634	+	0.409861i
$382$	−14.9670	+	25.9236i	−0.765778	+	1.32637i
$383$	9.81784	+	17.0050i	0.501668	+	0.868915i	0.999998	+	0.00192717i	$0.000613437\pi$
$383$	9.81784	+	17.0050i	0.501668	+	0.868915i	−0.498330	+	0.866987i	$0.666053\pi$
$384$	−10.9081			−0.556650
$385$	−1.11403	−	1.32995i	−0.0567764	−	0.0677803i
$386$	−20.6009			−1.04856
$387$	−4.23576	−	7.33654i	−0.215316	−	0.372937i
$388$	−0.189965	+	0.329029i	−0.00964401	+	0.0167039i
$389$	5.36913	−	9.29961i	0.272226	−	0.471509i	−0.697206	−	0.716871i	$-0.745574\pi$
$389$	5.36913	−	9.29961i	0.272226	−	0.471509i	0.969431	+	0.245362i	$0.0789069\pi$
$390$	0.278083	+	0.481654i	0.0140813	+	0.0243895i
$391$	−10.1766			−0.514652
$392$	−3.50992	+	19.7098i	−0.177277	+	0.995497i
$393$	14.6740			0.740206
$394$	−19.5472	−	33.8568i	−0.984774	−	1.70568i
$395$	0.907893	−	1.57252i	0.0456811	−	0.0791219i
$396$	0.0378781	−	0.0656068i	0.00190345	−	0.00329687i
$397$	9.38280	+	16.2515i	0.470909	+	0.815638i	0.999446	−	0.0332716i	$-0.0105926\pi$
$397$	9.38280	+	16.2515i	0.470909	+	0.815638i	−0.528537	+	0.848910i	$0.677259\pi$
$398$	16.8464			0.844432
$399$	8.65086	+	10.3275i	0.433084	+	0.517021i
$400$	18.9115			0.945573
$401$	11.4787	+	19.8817i	0.573220	+	0.992846i	0.996233	+	0.0867221i	$0.0276392\pi$
$401$	11.4787	+	19.8817i	0.573220	+	0.992846i	−0.423013	+	0.906124i	$0.639027\pi$
$402$	−0.310210	+	0.537300i	−0.0154719	+	0.0267981i
$403$	−1.92999	+	3.34285i	−0.0961399	+	0.166519i
$404$	0.379334	+	0.657026i	0.0188726	+	0.0326883i
$405$	−0.397868			−0.0197702
$406$	−1.88889	+	5.17600i	−0.0937441	+	0.256881i
$407$	16.9185			0.838620
$408$	−6.02298	−	10.4321i	−0.298182	−	0.516467i
$409$	−16.3076	+	28.2457i	−0.806361	+	1.39666i	0.109008	+	0.994041i	$0.465233\pi$
$409$	−16.3076	+	28.2457i	−0.806361	+	1.39666i	−0.915369	+	0.402617i	$0.868101\pi$
$410$	1.29468	−	2.24245i	0.0639396	−	0.110747i
$411$	−2.37400	−	4.11189i	−0.117101	−	0.202825i
$412$	−0.236518			−0.0116524
$413$	4.31473	−	0.757025i	0.212314	−	0.0372507i
$414$	3.37747			0.165993
$415$	3.26718	+	5.65892i	0.160379	+	0.277785i
$416$	−0.129985	+	0.225141i	−0.00637304	+	0.0110384i
$417$	−1.28190	+	2.22031i	−0.0627748	+	0.108729i
$418$	5.86546	+	10.1593i	0.286889	+	0.496906i
$419$	−19.7020			−0.962508			−0.481254	−	0.876581i	$-0.659818\pi$
$419$	−19.7020			−0.962508			−0.481254	+	0.876581i	$0.659818\pi$
$420$	−0.0476584	+	0.00836172i	−0.00232549	+	0.000408010i
$421$	−30.4204			−1.48260			−0.741300	−	0.671174i	$-0.765790\pi$
$421$	−30.4204			−1.48260			−0.741300	+	0.671174i	$0.765790\pi$
$422$	14.4295	+	24.9927i	0.702419	+	1.21662i
$423$	2.02680	−	3.51051i	0.0985462	−	0.170687i
$424$	13.3440	−	23.1125i	0.648042	−	1.12244i
$425$	10.1964	+	17.6606i	0.494596	+	0.856666i
$426$	13.6259			0.660179
$427$	9.98405	−	27.3586i	0.483162	−	1.32398i
$428$	−0.408880			−0.0197639
$429$	0.824049	+	1.42729i	0.0397855	+	0.0689104i
$430$	−2.35579	+	4.08034i	−0.113606	+	0.196771i
$431$	4.16194	−	7.20869i	0.200473	−	0.347230i	−0.748208	−	0.663465i	$-0.769085\pi$
$431$	4.16194	−	7.20869i	0.200473	−	0.347230i	0.948681	+	0.316234i	$0.102419\pi$
$432$	1.95298	+	3.38266i	0.0939627	+	0.162748i
$433$	−1.84078			−0.0884622			−0.0442311	−	0.999021i	$-0.514084\pi$
$433$	−1.84078			−0.0884622			−0.0442311	+	0.999021i	$0.514084\pi$
$434$	9.16703	+	10.9437i	0.440032	+	0.525315i
$435$	−0.592743			−0.0284199
$436$	0.225086	+	0.389861i	0.0107797	+	0.0186709i
$437$	6.15145	−	10.6546i	0.294264	−	0.509680i
$438$	4.65191	−	8.05735i	0.222277	−	0.384995i
$439$	6.83976	+	11.8468i	0.326444	+	0.565418i	0.981804	−	0.189899i	$-0.0608162\pi$
$439$	6.83976	+	11.8468i	0.326444	+	0.565418i	−0.655359	+	0.755317i	$0.727483\pi$
$440$	−1.87537			−0.0894046
$441$	6.58191	−	2.38296i	0.313424	−	0.113474i
$442$	5.88767			0.280048
$443$	−10.6172	−	18.3895i	−0.504439	−	0.873714i	−0.999987	−	0.00513322i	$-0.998366\pi$
$443$	−10.6172	−	18.3895i	−0.504439	−	0.873714i	0.495548	−	0.868581i	$-0.334967\pi$
$444$	0.235931	−	0.408644i	0.0111968	−	0.0193934i
$445$	0.855079	−	1.48104i	0.0405346	−	0.0702081i
$446$	11.4574	+	19.8448i	0.542525	+	0.939681i
$447$	−8.60765			−0.407128
$448$	13.8893	+	16.5812i	0.656209	+	0.783390i
$449$	−17.5876			−0.830010			−0.415005	−	0.909819i	$-0.636220\pi$
$449$	−17.5876			−0.830010			−0.415005	+	0.909819i	$0.636220\pi$
$450$	−3.38403	−	5.86131i	−0.159525	−	0.276305i
$451$	3.83655	−	6.64509i	0.180656	−	0.312905i
$452$	−0.285751	+	0.494935i	−0.0134406	+	0.0232798i
$453$	−3.86087	−	6.68722i	−0.181400	−	0.314193i
$454$	4.03658			0.189446
$455$	0.360871	−	0.988870i	0.0169179	−	0.0463589i
$456$	14.5629			0.681969
$457$	8.90062	+	15.4163i	0.416354	+	0.721146i	0.995570	−	0.0940285i	$-0.0299745\pi$
$457$	8.90062	+	15.4163i	0.416354	+	0.721146i	−0.579216	+	0.815174i	$0.696641\pi$
$458$	4.67249	−	8.09299i	0.218331	−	0.378160i
$459$	−2.10595	+	3.64761i	−0.0982971	+	0.170256i
$460$	0.0220937	+	0.0382675i	0.00103013	+	0.00178423i
$461$	−10.1629			−0.473333			−0.236667	−	0.971591i	$-0.576055\pi$
$461$	−10.1629			−0.473333			−0.236667	+	0.971591i	$0.576055\pi$
$462$	6.00364	−	1.05335i	0.279315	−	0.0490061i
$463$	−16.0408			−0.745480			−0.372740	−	0.927936i	$-0.621582\pi$
$463$	−16.0408			−0.745480			−0.372740	+	0.927936i	$0.621582\pi$
$464$	2.90955	+	5.03948i	0.135072	+	0.233952i
$465$	−0.767883	+	1.33001i	−0.0356097	+	0.0616778i
$466$	14.7834	−	25.6056i	0.684829	−	1.18616i
$467$	12.0130	+	20.8071i	0.555893	+	0.962836i	0.997833	+	0.0657910i	$0.0209571\pi$
$467$	12.0130	+	20.8071i	0.555893	+	0.962836i	−0.441940	+	0.897045i	$0.645710\pi$
$468$	0.0459658			0.00212477
$469$	1.15661	−	0.202928i	0.0534071	−	0.00937034i
$470$	−2.25447			−0.103991
$471$	−6.22573	−	10.7833i	−0.286867	−	0.496867i
$472$	2.36768	−	4.10094i	0.108981	−	0.188761i
$473$	−6.98094	+	12.0913i	−0.320984	+	0.555961i
$474$	3.18979	+	5.52488i	0.146512	+	0.253766i
$475$	−24.6536			−1.13119
$476$	−0.175600	+	0.481186i	−0.00804863	+	0.0220551i
$477$	−9.33150			−0.427260
$478$	−18.9901	−	32.8919i	−0.868589	−	1.50444i
$479$	−11.5038	+	19.9252i	−0.525623	+	0.910405i	0.473932	+	0.880561i	$0.342834\pi$
$479$	−11.5038	+	19.9252i	−0.525623	+	0.910405i	−0.999555	+	0.0298437i	$0.990499\pi$
$480$	−0.0517169	+	0.0895762i	−0.00236054	+	0.00408858i
$481$	5.13274	+	8.89017i	0.234033	+	0.405357i
$482$	−10.3698			−0.472330
$483$	−4.10489	−	4.90046i	−0.186779	−	0.222979i
$484$	0.380771			0.0173078
$485$	−1.64428	−	2.84798i	−0.0746631	−	0.129320i
$486$	0.698934	−	1.21059i	0.0317043	−	0.0549134i
$487$	5.03788	−	8.72586i	0.228288	−	0.395406i	−0.729013	−	0.684500i	$-0.760021\pi$
$487$	5.03788	−	8.72586i	0.228288	−	0.395406i	0.957301	+	0.289094i	$0.0933539\pi$
$488$	−15.7408	−	27.2640i	−0.712555	−	1.23418i
$489$	−11.9510			−0.540443
$490$	−2.97808	−	2.50754i	−0.134536	−	0.113279i
$491$	−12.5154			−0.564810			−0.282405	−	0.959295i	$-0.591132\pi$
$491$	−12.5154			−0.564810			−0.282405	+	0.959295i	$0.591132\pi$
$492$	−0.107002	−	0.185333i	−0.00482403	−	0.00835547i
$493$	−3.13744	+	5.43420i	−0.141303	+	0.244744i
$494$	−3.55892	+	6.16424i	−0.160124	+	0.277342i
$495$	0.327863	+	0.567875i	0.0147363	+	0.0255241i
$496$	15.0769			0.676975
$497$	−16.5606	−	19.7703i	−0.742846	−	0.886818i
$498$	−22.9578			−1.02876
$499$	−0.242603	−	0.420202i	−0.0108604	−	0.0188108i	0.860544	−	0.509376i	$-0.170124\pi$
$499$	−0.242603	−	0.420202i	−0.0108604	−	0.0188108i	−0.871405	+	0.490565i	$0.836790\pi$
$500$	0.0899941	−	0.155874i	0.00402466	−	0.00697091i
$501$	1.54597	−	2.67769i	0.0690687	−	0.119630i
$502$	19.0428	+	32.9830i	0.849920	+	1.47210i
$503$	−3.82645			−0.170613			−0.0853064	−	0.996355i	$-0.527187\pi$
$503$	−3.82645			−0.170613			−0.0853064	+	0.996355i	$0.527187\pi$
$504$	2.59404	−	7.10829i	0.115548	−	0.316628i
$505$	−6.56683			−0.292220
$506$	−2.78320	−	4.82064i	−0.123728	−	0.214304i
$507$	−0.500000	+	0.866025i	−0.0222058	+	0.0384615i
$508$	0.212312	−	0.367735i	0.00941981	−	0.0163156i
$509$	−12.3025	−	21.3085i	−0.545298	−	0.944484i	−0.998588	−	0.0531207i	$-0.983083\pi$
$509$	−12.3025	−	21.3085i	−0.545298	−	0.944484i	0.453290	−	0.891363i	$-0.350250\pi$
$510$	2.34251			0.103728
$511$	−17.3445	+	3.04311i	−0.767274	+	0.134619i
$512$	23.3574			1.03226
$513$	−2.54597	−	4.40974i	−0.112407	−	0.194695i
$514$	13.5364	−	23.4457i	0.597063	−	1.03414i
$515$	1.02362	−	1.77296i	0.0451060	−	0.0781260i
$516$	0.194700	+	0.337230i	0.00857119	+	0.0148457i
$517$	−6.68072			−0.293818
$518$	37.3948	−	6.56096i	1.64303	−	0.288272i
$519$	−6.11233			−0.268302
$520$	−0.568949	−	0.985448i	−0.0249501	−	0.0432148i
$521$	10.4825	−	18.1563i	0.459248	−	0.795441i	−0.539673	−	0.841874i	$-0.681452\pi$
$521$	10.4825	−	18.1563i	0.459248	−	0.795441i	0.998921	+	0.0464336i	$0.0147856\pi$
$522$	1.04127	−	1.80353i	0.0455752	−	0.0789386i
$523$	8.62805	+	14.9442i	0.377278	+	0.653465i	0.990665	−	0.136318i	$-0.0435267\pi$
$523$	8.62805	+	14.9442i	0.377278	+	0.653465i	−0.613387	+	0.789782i	$0.710193\pi$
$524$	−0.674503			−0.0294658
$525$	−4.39148	+	12.0337i	−0.191660	+	0.525193i
$526$	−10.9617			−0.477951
$527$	8.12893	+	14.0797i	0.354102	+	0.613322i
$528$	3.21870	−	5.57495i	0.140076	−	0.242619i
$529$	8.58109	−	14.8629i	0.373091	−	0.646213i
$530$	2.59493	+	4.49456i	0.112717	+	0.195231i
$531$	−1.65573			−0.0718523
$532$	−0.397644	−	0.474712i	−0.0172400	−	0.0205814i
$533$	4.65573			0.201662
$534$	3.00423	+	5.20349i	0.130006	+	0.225177i
$535$	1.76958	−	3.06499i	0.0765054	−	0.132511i
$536$	0.634680	−	1.09930i	0.0274140	−	0.0474824i
$537$	−6.33168	−	10.9668i	−0.273232	−	0.473252i
$538$	21.5039			0.927097
$539$	−8.82500	−	7.43064i	−0.380120	−	0.320060i
$540$	0.0182883			0.000787004
$541$	−22.4863	−	38.9475i	−0.966763	−	1.67448i	−0.704801	−	0.709405i	$-0.748964\pi$
$541$	−22.4863	−	38.9475i	−0.966763	−	1.67448i	−0.261963	−	0.965078i	$-0.584370\pi$
$542$	−5.07252	+	8.78586i	−0.217883	+	0.377385i
$543$	−11.5627	+	20.0272i	−0.496205	+	0.859451i
$544$	0.547483	+	0.948269i	0.0234731	+	0.0406567i
$545$	−3.89657			−0.166911
$546$	2.37488	+	2.83517i	0.101636	+	0.121334i
$547$	−1.43692			−0.0614384			−0.0307192	−	0.999528i	$-0.509780\pi$
$547$	−1.43692			−0.0614384			−0.0307192	+	0.999528i	$0.509780\pi$
$548$	0.109123	+	0.189007i	0.00466151	+	0.00807397i
$549$	−5.50381	+	9.53288i	−0.234897	+	0.406854i
$550$	−5.57721	+	9.66001i	−0.237813	+	0.411904i
$551$	−3.79298	−	6.56963i	−0.161586	−	0.279876i
$552$	−6.91018			−0.294117
$553$	4.13941	−	11.3430i	0.176026	−	0.482352i
$554$	1.17659			0.0499884
$555$	2.04215	+	3.53711i	0.0866845	+	0.150142i
$556$	0.0589235	−	0.102058i	0.00249891	−	0.00432824i
$557$	6.88936	−	11.9327i	0.291912	−	0.505606i	−0.682350	−	0.731025i	$-0.739042\pi$
$557$	6.88936	−	11.9327i	0.291912	−	0.505606i	0.974262	+	0.225420i	$0.0723754\pi$
$558$	−2.69788	−	4.67286i	−0.114210	−	0.197818i
$559$	−8.47151			−0.358307
$560$	−4.04978	+	0.710539i	−0.171134	+	0.0300257i
$561$	6.94161			0.293075
$562$	−3.07594	−	5.32768i	−0.129751	−	0.224735i
$563$	16.3116	−	28.2526i	0.687453	−	1.19070i	−0.285206	−	0.958466i	$-0.592062\pi$
$563$	16.3116	−	28.2526i	0.687453	−	1.19070i	0.972659	−	0.232237i	$-0.0746046\pi$
$564$	−0.0931634	+	0.161364i	−0.00392289	+	0.00679464i
$565$	−2.47338	−	4.28402i	−0.104056	−	0.180230i
$566$	−12.6552			−0.531939
$567$	−2.60595	+	0.457216i	−0.109439	+	0.0192013i
$568$	−27.8782			−1.16974
$569$	−16.6035	−	28.7582i	−0.696057	−	1.20561i	−0.969823	−	0.243810i	$-0.921603\pi$
$569$	−16.6035	−	28.7582i	−0.696057	−	1.20561i	0.273766	−	0.961796i	$-0.411731\pi$
$570$	−1.41598	+	2.45255i	−0.0593089	+	0.102726i
$571$	−2.69939	+	4.67549i	−0.112966	+	0.195663i	−0.916965	−	0.398968i	$-0.869368\pi$
$571$	−2.69939	+	4.67549i	−0.112966	+	0.195663i	0.803999	+	0.594631i	$0.202702\pi$
$572$	−0.0378781	−	0.0656068i	−0.00158376	−	0.00274316i
$573$	−21.4140			−0.894584
$574$	5.90291	−	16.1754i	0.246383	−	0.675146i
$575$	11.6983			0.487853
$576$	−4.08766	−	7.08003i	−0.170319	−	0.295001i
$577$	4.16575	−	7.21529i	0.173422	−	0.300377i	−0.766192	−	0.642612i	$-0.777851\pi$
$577$	4.16575	−	7.21529i	0.173422	−	0.300377i	0.939614	+	0.342236i	$0.111184\pi$
$578$	0.517232	−	0.895872i	0.0215140	−	0.0372634i
$579$	−7.36867	−	12.7629i	−0.306232	−	0.530409i
$580$	0.0272459			0.00113133
$581$	27.9023	+	33.3101i	1.15758	+	1.38194i
$582$	11.5541			0.478931
$583$	7.68961	+	13.3188i	0.318471	+	0.551608i
$584$	−9.51765	+	16.4851i	−0.393843	+	0.682157i
$585$	−0.198934	+	0.344564i	−0.00822490	+	0.0142459i
$586$	21.9932	+	38.0933i	0.908529	+	1.57362i
$587$	−35.5306			−1.46651			−0.733253	−	0.679956i	$-0.761999\pi$
$587$	−35.5306			−1.46651			−0.733253	+	0.679956i	$0.761999\pi$
$588$	−0.302543	+	0.109535i	−0.0124767	+	0.00451714i
$589$	−19.6548			−0.809862
$590$	0.460429	+	0.797487i	0.0189556	+	0.0328320i
$591$	13.9836	−	24.2203i	0.575208	−	0.996289i
$592$	20.0483	−	34.7246i	0.823978	−	1.42717i
$593$	−8.39077	−	14.5332i	−0.344568	−	0.596809i	0.640707	−	0.767785i	$-0.278641\pi$
$593$	−8.39077	−	14.5332i	−0.344568	−	0.596809i	−0.985275	+	0.170976i	$0.945308\pi$
$594$	−2.30382			−0.0945270
$595$	−2.84703	−	3.39882i	−0.116717	−	0.139338i
$596$	0.395658			0.0162068
$597$	6.02574	+	10.4369i	0.246617	+	0.427153i
$598$	1.68873	−	2.92497i	0.0690574	−	0.119611i
$599$	−9.95591	+	17.2441i	−0.406787	+	0.704577i	−0.994528	−	0.104473i	$-0.966684\pi$
$599$	−9.95591	+	17.2441i	−0.406787	+	0.704577i	0.587740	+	0.809050i	$0.300018\pi$
$600$	6.92361	+	11.9920i	0.282655	+	0.489573i
$601$	22.5906			0.921491			0.460746	−	0.887532i	$-0.347582\pi$
$601$	22.5906			0.921491			0.460746	+	0.887532i	$0.347582\pi$
$602$	−10.7409	+	29.4325i	−0.437766	+	1.19958i
$603$	−0.443834			−0.0180743
$604$	0.177468	+	0.307384i	0.00722108	+	0.0125073i
$605$	−1.64792	+	2.85429i	−0.0669976	+	0.116043i
$606$	11.5359	−	19.9808i	0.468616	−	0.811666i
$607$	−2.57792	−	4.46508i	−0.104634	−	0.181232i	0.808954	−	0.587871i	$-0.200034\pi$
$607$	−2.57792	−	4.46508i	−0.104634	−	0.181232i	−0.913589	+	0.406639i	$0.866701\pi$
$608$	−1.32375			−0.0536852
$609$	−3.88234	+	0.681161i	−0.157320	+	0.0276020i
$610$	6.12207			0.247875
$611$	−2.02680	−	3.51051i	−0.0819954	−	0.142020i
$612$	0.0968016	−	0.167665i	0.00391297	−	0.00677747i
$613$	10.3153	−	17.8666i	0.416630	−	0.721624i	−0.578968	−	0.815350i	$-0.696545\pi$
$613$	10.3153	−	17.8666i	0.416630	−	0.721624i	0.995598	+	0.0937264i	$0.0298779\pi$
$614$	−8.96001	−	15.5192i	−0.361597	−	0.626304i
$615$	1.85236			0.0746945
$616$	−12.2832	+	2.15511i	−0.494906	+	0.0868318i
$617$	−25.2999			−1.01854			−0.509269	−	0.860608i	$-0.670084\pi$
$617$	−25.2999			−1.01854			−0.509269	+	0.860608i	$0.670084\pi$
$618$	3.59638	+	6.22912i	0.144668	+	0.250572i
$619$	16.3908	−	28.3898i	0.658804	−	1.14108i	−0.322122	−	0.946698i	$-0.604396\pi$
$619$	16.3908	−	28.3898i	0.658804	−	1.14108i	0.980926	−	0.194383i	$-0.0622705\pi$
$620$	0.0352964	−	0.0611351i	0.00141754	−	0.00245525i
$621$	1.20808	+	2.09245i	0.0484785	+	0.0839672i
$622$	−29.7340			−1.19223
$623$	3.89862	−	10.6831i	0.156195	−	0.428010i
$624$	3.90596			0.156363
$625$	−11.3253	−	19.6160i	−0.453012	−	0.784639i
$626$	11.6415	−	20.1637i	0.465288	−	0.805902i
$627$	−4.19600	+	7.26769i	−0.167572	+	0.290243i
$628$	0.286171	+	0.495663i	0.0114195	+	0.0197791i
$629$	43.2371			1.72398
$630$	0.944890	+	1.12802i	0.0376453	+	0.0449414i
$631$	47.2229			1.87991			0.939957	−	0.341292i	$-0.110864\pi$
$631$	47.2229			1.87991			0.939957	+	0.341292i	$0.110864\pi$
$632$	−6.52620	−	11.3037i	−0.259598	−	0.449637i
$633$	−10.3225	+	17.8791i	−0.410284	+	0.710632i
$634$	14.0608	−	24.3540i	0.558426	−	0.967222i
$635$	1.83771	+	3.18301i	0.0729274	+	0.126314i
$636$	0.428930			0.0170082
$637$	1.22725	−	6.89158i	0.0486253	−	0.273054i
$638$	−3.43223			−0.135883
$639$	4.87383	+	8.44172i	0.192806	+	0.333949i
$640$	−2.16998	+	3.75852i	−0.0857762	+	0.148569i
$641$	−4.78084	+	8.28066i	−0.188832	+	0.327066i	−0.944861	−	0.327472i	$-0.893803\pi$
$641$	−4.78084	+	8.28066i	−0.188832	+	0.327066i	0.756029	+	0.654538i	$0.227137\pi$
$642$	6.21722	+	10.7685i	0.245374	+	0.425001i
$643$	1.83994			0.0725601			0.0362801	−	0.999342i	$-0.488449\pi$
$643$	1.83994			0.0725601			0.0362801	+	0.999342i	$0.488449\pi$
$644$	0.188685	+	0.225254i	0.00743522	+	0.00887625i
$645$	−3.37054			−0.132715
$646$	14.9898	+	25.9631i	0.589766	+	1.02150i
$647$	4.14154	−	7.17335i	0.162821	−	0.282013i	−0.773059	−	0.634335i	$-0.781274\pi$
$647$	4.14154	−	7.17335i	0.162821	−	0.282013i	0.935879	+	0.352321i	$0.114607\pi$
$648$	−1.42999	+	2.47682i	−0.0561755	+	0.0972988i
$649$	1.36440	+	2.36321i	0.0535573	+	0.0927640i
$650$	−6.76806			−0.265465
$651$	−3.50106	+	9.59371i	−0.137217	+	0.376007i
$652$	0.549338			0.0215137
$653$	−6.77170	−	11.7289i	−0.264997	−	0.458988i	0.702566	−	0.711619i	$-0.252038\pi$
$653$	−6.77170	−	11.7289i	−0.264997	−	0.458988i	−0.967563	+	0.252631i	$0.918704\pi$
$654$	6.84509	−	11.8561i	0.267664	−	0.463608i
$655$	2.91916	−	5.05613i	0.114061	−	0.197559i
$656$	−9.09253	−	15.7487i	−0.355004	−	0.614884i
$657$	6.65573			0.259665
$658$	−14.7663	+	2.59076i	−0.575650	+	0.100999i
$659$	−12.2357			−0.476635			−0.238317	−	0.971187i	$-0.576596\pi$
$659$	−12.2357			−0.476635			−0.238317	+	0.971187i	$0.576596\pi$
$660$	−0.0150705	−	0.0261028i	−0.000586618	−	0.00101605i
$661$	−16.9319	+	29.3269i	−0.658573	+	1.14068i	0.322412	+	0.946600i	$0.395506\pi$
$661$	−16.9319	+	29.3269i	−0.658573	+	1.14068i	−0.980985	+	0.194083i	$0.937827\pi$
$662$	13.5851	−	23.5301i	0.528001	−	0.914524i
$663$	2.10595	+	3.64761i	0.0817882	+	0.141661i
$664$	46.9708			1.82282
$665$	5.27943	−	0.926282i	0.204727	−	0.0359197i
$666$	−14.3498			−0.556043
$667$	1.79979	+	3.11733i	0.0696883	+	0.120704i
$668$	−0.0710616	+	0.123082i	−0.00274946	+	0.00476220i
$669$	−8.19636	+	14.1965i	−0.316890	+	0.548869i
$670$	0.123423	+	0.213774i	0.00476823	+	0.00825882i
$671$	18.1416			0.700351
$672$	−0.235796	+	0.646136i	−0.00909603	+	0.0249252i
$673$	25.1242			0.968467			0.484233	−	0.874939i	$-0.339099\pi$
$673$	25.1242			0.968467			0.484233	+	0.874939i	$0.339099\pi$
$674$	−1.36786	−	2.36921i	−0.0526881	−	0.0912584i
$675$	2.42085	−	4.19304i	0.0931786	−	0.161390i
$676$	0.0229829	−	0.0398076i	0.000883959	−	0.00153106i
$677$	11.3878	+	19.7243i	0.437670	+	0.758067i	0.997509	−	0.0705341i	$-0.0224704\pi$
$677$	11.3878	+	19.7243i	0.437670	+	0.758067i	−0.559839	+	0.828601i	$0.689137\pi$
$678$	17.3799			0.667472
$679$	−14.0425	−	16.7641i	−0.538902	−	0.643348i
$680$	−4.79270			−0.183792
$681$	1.44383	+	2.50079i	0.0553278	+	0.0958306i
$682$	−4.44637	+	7.70133i	−0.170260	+	0.294899i
$683$	9.01102	−	15.6075i	0.344797	−	0.597206i	−0.640520	−	0.767942i	$-0.721281\pi$
$683$	9.01102	−	15.6075i	0.344797	−	0.597206i	0.985317	+	0.170736i	$0.0546144\pi$
$684$	0.117027	+	0.202698i	0.00447466	+	0.00775033i
$685$	−1.88908			−0.0721780
$686$	−22.3874	−	13.0015i	−0.854753	−	0.496401i
$687$	6.68516			0.255055
$688$	16.5447	+	28.6562i	0.630760	+	1.09251i
$689$	−4.66575	+	8.08132i	−0.177751	+	0.307874i
$690$	0.671892	−	1.16375i	0.0255785	−	0.0443033i
$691$	−15.2612	−	26.4332i	−0.580564	−	1.00557i	−0.995413	−	0.0956756i	$-0.969499\pi$
$691$	−15.2612	−	26.4332i	−0.580564	−	1.00557i	0.414849	−	0.909890i	$-0.363834\pi$
$692$	0.280959			0.0106804
$693$	2.80001	+	3.34268i	0.106364	+	0.126978i
$694$	6.26548			0.237835
$695$	0.510025	+	0.883390i	0.0193464	+	0.0335089i
$696$	−2.13041	+	3.68997i	−0.0807528	+	0.139868i
$697$	9.80470	−	16.9822i	0.371380	−	0.643248i
$698$	−10.7923	−	18.6929i	−0.408496	−	0.707536i
$699$	21.1514			0.800019
$700$	0.201858	−	0.553138i	0.00762952	−	0.0209067i
$701$	20.4390			0.771972			0.385986	−	0.922505i	$-0.373861\pi$
$701$	20.4390			0.771972			0.385986	+	0.922505i	$0.373861\pi$
$702$	−0.698934	−	1.21059i	−0.0263796	−	0.0456907i
$703$	−26.1356	+	45.2681i	−0.985722	+	1.70732i
$704$	−6.73686	+	11.6686i	−0.253905	+	0.439776i
$705$	−0.806397	−	1.39672i	−0.0303707	−	0.0526035i
$706$	45.3343			1.70618
$707$	−43.0113	+	7.54638i	−1.61761	+	0.283811i
$708$	0.0761068			0.00286027
$709$	20.1675	+	34.9310i	0.757405	+	1.31186i	0.944170	+	0.329459i	$0.106866\pi$
$709$	20.1675	+	34.9310i	0.757405	+	1.31186i	−0.186766	+	0.982405i	$0.559800\pi$
$710$	2.71066	−	4.69500i	0.101729	−	0.176200i
$711$	−2.28190	+	3.95236i	−0.0855778	+	0.148225i
$712$	−6.14656	−	10.6462i	−0.230352	−	0.398981i
$713$	9.32634			0.349274
$714$	15.3429	−	2.69194i	0.574195	−	0.100743i
$715$	0.655725			0.0245227
$716$	0.291041	+	0.504098i	0.0108767	+	0.0188390i
$717$	13.5851	−	23.5301i	0.507344	−	0.878746i
$718$	−22.5072	+	38.9836i	−0.839960	+	1.45485i
$719$	26.2140	+	45.4040i	0.977618	+	1.69328i	0.671011	+	0.741447i	$0.265860\pi$
$719$	26.2140	+	45.4040i	0.977618	+	1.69328i	0.306606	+	0.951836i	$0.400806\pi$
$720$	1.55405			0.0579162
$721$	4.66705	−	12.7888i	0.173810	−	0.476280i
$722$	−9.68410			−0.360405
$723$	−3.70913	−	6.42441i	−0.137944	−	0.238926i
$724$	0.531491	−	0.920569i	0.0197527	−	0.0342127i
$725$	3.60658	−	6.24678i	0.133945	−	0.232000i
$726$	−5.78981	−	10.0282i	−0.214880	−	0.372183i
$727$	−20.8022			−0.771510			−0.385755	−	0.922601i	$-0.626059\pi$
$727$	−20.8022			−0.771510			−0.385755	+	0.922601i	$0.626059\pi$
$728$	−4.85893	−	5.80065i	−0.180084	−	0.214986i
$729$	1.00000			0.0370370
$730$	−1.85085	−	3.20576i	−0.0685029	−	0.118650i
$731$	−17.8405	+	30.9007i	−0.659856	+	1.14290i
$732$	0.252987	−	0.438187i	0.00935068	−	0.0161959i
$733$	15.3685	+	26.6190i	0.567648	+	0.983196i	0.996798	+	0.0799624i	$0.0254800\pi$
$733$	15.3685	+	26.6190i	0.567648	+	0.983196i	−0.429149	+	0.903233i	$0.641187\pi$
$734$	15.4914			0.571799
$735$	0.488282	−	2.74194i	0.0180106	−	0.101138i
$736$	0.628129			0.0231531
$737$	0.365741	+	0.633481i	0.0134722	+	0.0233346i
$738$	−3.25404	+	5.63617i	−0.119783	+	0.207470i
$739$	3.33718	−	5.78017i	0.122760	−	0.212627i	−0.798095	−	0.602532i	$-0.794159\pi$
$739$	3.33718	−	5.78017i	0.122760	−	0.212627i	0.920855	+	0.389905i	$0.127492\pi$
$740$	−0.0938693	−	0.162586i	−0.00345070	−	0.00597679i
$741$	−5.09193			−0.187057
$742$	22.1612	+	26.4563i	0.813565	+	0.971243i
$743$	−11.4509			−0.420092			−0.210046	−	0.977691i	$-0.567361\pi$
$743$	−11.4509			−0.420092			−0.210046	+	0.977691i	$0.567361\pi$
$744$	5.51977	+	9.56051i	0.202364	+	0.350505i
$745$	−1.71235	+	2.96588i	−0.0627357	+	0.108661i
$746$	−26.5410	+	45.9703i	−0.971735	+	1.68309i
$747$	−8.21172	−	14.2231i	−0.300451	−	0.520396i
$748$	−0.319077			−0.0116666
$749$	8.06814	−	22.1086i	0.294803	−	0.807830i
$750$	−5.47362			−0.199868
$751$	−0.850670	−	1.47340i	−0.0310414	−	0.0537653i	0.850087	−	0.526642i	$-0.176549\pi$
$751$	−0.850670	−	1.47340i	−0.0310414	−	0.0537653i	−0.881129	+	0.472876i	$0.843216\pi$
$752$	−7.91658	+	13.7119i	−0.288688	+	0.500022i
$753$	−13.6227	+	23.5952i	−0.496439	+	0.859858i
$754$	−1.04127	−	1.80353i	−0.0379209	−	0.0656809i
$755$	−3.07223			−0.111810
$756$	0.119784	−	0.0210163i	0.00435652	−	0.000764357i
$757$	42.4007			1.54108			0.770540	−	0.637392i	$-0.219987\pi$
$757$	42.4007			1.54108			0.770540	+	0.637392i	$0.219987\pi$
$758$	−14.8881	−	25.7869i	−0.540760	−	0.936623i
$759$	1.99103	−	3.44857i	0.0722699	−	0.125175i
$760$	2.89705	−	5.01783i	0.105087	−	0.182016i
$761$	−19.1842	−	33.2280i	−0.695428	−	1.20452i	−0.970036	−	0.242960i	$-0.921882\pi$
$761$	−19.1842	−	33.2280i	−0.695428	−	1.20452i	0.274609	−	0.961556i	$-0.411452\pi$
$762$	−12.9132			−0.467797
$763$	−25.5216	+	4.47780i	−0.923946	+	0.162107i
$764$	0.984315			0.0356113
$765$	0.837888	+	1.45126i	0.0302939	+	0.0524706i
$766$	−13.7240	+	23.7707i	−0.495870	+	0.858871i
$767$	−0.827863	+	1.43390i	−0.0298924	+	0.0517751i
$768$	0.551297	+	0.954874i	0.0198932	+	0.0344560i
$769$	−8.54466			−0.308128			−0.154064	−	0.988061i	$-0.549236\pi$
$769$	−8.54466			−0.308128			−0.154064	+	0.988061i	$0.549236\pi$
$770$	0.831382	−	2.27818i	0.0299609	−	0.0820999i
$771$	19.3672			0.697491
$772$	0.338707	+	0.586658i	0.0121903	+	0.0211143i
$773$	−7.68069	+	13.3033i	−0.276255	+	0.478488i	−0.970451	−	0.241298i	$-0.922427\pi$
$773$	−7.68069	+	13.3033i	−0.276255	+	0.478488i	0.694196	+	0.719786i	$0.255760\pi$
$774$	5.92103	−	10.2555i	0.212827	−	0.368627i
$775$	−9.34446	−	16.1851i	−0.335663	−	0.581385i
$776$	−23.6392			−0.848598
$777$	17.4404	+	20.8205i	0.625670	+	0.746932i
$778$	15.0107			0.538159
$779$	11.8533	+	20.5305i	0.424689	+	0.735583i
$780$	0.00914416	−	0.0158382i	0.000327414	−	0.000567097i
$781$	8.03255	−	13.9128i	0.287427	−	0.497838i
$782$	−7.11276	−	12.3197i	−0.254352	−	0.440550i
$783$	1.48980			0.0532411
$784$	−25.7086	+	9.30774i	−0.918165	+	0.332419i
$785$	−4.95403			−0.176817
$786$	10.2562	+	17.7642i	0.365825	+	0.633628i
$787$	15.2778	−	26.4619i	0.544595	−	0.943266i	−0.454037	−	0.890983i	$-0.650017\pi$
$787$	15.2778	−	26.4619i	0.544595	−	0.943266i	0.998632	−	0.0522835i	$-0.0166499\pi$
$788$	−0.642767	+	1.11331i	−0.0228976	+	0.0396599i
$789$	−3.92085	−	6.79111i	−0.139586	−	0.241770i
$790$	2.53823			0.0903061
$791$	−21.1231	−	25.2170i	−0.751052	−	0.896615i
$792$	4.71354			0.167488
$793$	5.50381	+	9.53288i	0.195446	+	0.338523i
$794$	−13.1159	+	22.7174i	−0.465466	+	0.806211i
$795$	−1.85635	+	3.21530i	−0.0658380	+	0.114035i
$796$	−0.276978	−	0.479740i	−0.00981723	−	0.0170039i
$797$	10.7114			0.379418			0.189709	−	0.981840i	$-0.439245\pi$
$797$	10.7114			0.379418			0.189709	+	0.981840i	$0.439245\pi$
$798$	−6.45597	+	17.6909i	−0.228539	+	0.626250i
$799$	−17.0733			−0.604010
$800$	−0.629349	−	1.09006i	−0.0222508	−	0.0385396i
$801$	−2.14915	+	3.72244i	−0.0759366	+	0.131526i
$802$	−16.0457	+	27.7920i	−0.566594	+	0.981370i
$803$	−5.48464	−	9.49968i	−0.193549	−	0.335236i
$804$	0.0204012			0.000719494
$805$	−2.50512	+	0.439527i	−0.0882940	+	0.0154913i
$806$	−5.39575			−0.190057
$807$	7.69167	+	13.3224i	0.270759	+	0.468969i
$808$	−23.6021	+	40.8801i	−0.830320	+	1.43816i
$809$	1.45901	−	2.52709i	0.0512962	−	0.0888476i	−0.839237	−	0.543766i	$-0.816998\pi$
$809$	1.45901	−	2.52709i	0.0512962	−	0.0888476i	0.890533	+	0.454918i	$0.150331\pi$
$810$	−0.278083	−	0.481654i	−0.00977085	−	0.0169236i
$811$	28.3281			0.994735			0.497367	−	0.867540i	$-0.334300\pi$
$811$	28.3281			0.994735			0.497367	+	0.867540i	$0.334300\pi$
$812$	0.178455	−	0.0313101i	0.00626254	−	0.00109877i
$813$	−7.25751			−0.254532
$814$	11.8249	+	20.4814i	0.414464	+	0.717872i
$815$	−2.37746	+	4.11788i	−0.0832787	+	0.144243i
$816$	8.22573	−	14.2474i	0.287958	−	0.498758i
$817$	−21.5682	−	37.3572i	−0.754575	−	1.30696i
$818$	−45.5918			−1.59408
$819$	−0.907012	+	2.48542i	−0.0316936	+	0.0868477i
$820$	−0.0851454			−0.00297341
$821$	−8.83443	−	15.3017i	−0.308324	−	0.534033i	0.669672	−	0.742657i	$-0.266435\pi$
$821$	−8.83443	−	15.3017i	−0.308324	−	0.534033i	−0.977996	+	0.208624i	$0.933101\pi$
$822$	3.31854	−	5.74789i	0.115747	−	0.200481i
$823$	−19.5306	+	33.8280i	−0.680794	+	1.17917i	0.293945	+	0.955822i	$0.405032\pi$
$823$	−19.5306	+	33.8280i	−0.680794	+	1.17917i	−0.974739	+	0.223348i	$0.928301\pi$
$824$	−7.35807	−	12.7446i	−0.256331	−	0.443978i
$825$	−7.97960			−0.277814
$826$	3.93216	+	4.69425i	0.136817	+	0.163334i
$827$	37.9766			1.32057			0.660287	−	0.751013i	$-0.270435\pi$
$827$	37.9766			1.32057			0.660287	+	0.751013i	$0.270435\pi$
$828$	−0.0555303	−	0.0961813i	−0.00192981	−	0.00334253i
$829$	28.0415	−	48.5692i	0.973920	−	1.68688i	0.290466	−	0.956885i	$-0.406190\pi$
$829$	28.0415	−	48.5692i	0.973920	−	1.68688i	0.683454	−	0.729994i	$-0.260477\pi$
$830$	−4.56708	+	7.91042i	−0.158526	+	0.274575i
$831$	0.420851	+	0.728935i	0.0145991	+	0.0252865i
$832$	−8.17531			−0.283428
$833$	−22.5532	−	18.9898i	−0.781424	−	0.657958i
$834$	−3.58384			−0.124098
$835$	−0.615090	−	1.06537i	−0.0212861	−	0.0368685i
$836$	0.192873	−	0.334065i	0.00667064	−	0.0115539i
$837$	1.92999	−	3.34285i	0.0667104	−	0.115546i
$838$	−13.7704	−	23.8511i	−0.475691	−	0.823922i
$839$	−30.1242			−1.04000			−0.520001	−	0.854165i	$-0.674069\pi$
$839$	−30.1242			−1.04000			−0.520001	+	0.854165i	$0.674069\pi$
$840$	−1.93321	−	2.30789i	−0.0667022	−	0.0796298i
$841$	−26.7805			−0.923465
$842$	−21.2618	−	36.8266i	−0.732732	−	1.26913i
$843$	2.20045	−	3.81129i	0.0757876	−	0.131268i
$844$	0.474484	−	0.821830i	0.0163324	−	0.0282886i
$845$	0.198934	+	0.344564i	0.00684353	+	0.0118533i
$846$	5.66639			0.194814
$847$	−7.51348	+	20.5887i	−0.258166	+	0.707435i
$848$	36.4484			1.25164
$849$	−4.52662	−	7.84034i	−0.155353	−	0.269080i
$850$	−14.2532	+	24.6872i	−0.488879	+	0.846764i
$851$	12.4015	−	21.4800i	0.425118	−	0.736326i
$852$	−0.224030	−	0.388031i	−0.00767513	−	0.0132937i
$853$	−43.6284			−1.49381			−0.746904	−	0.664932i	$-0.768461\pi$
$853$	−43.6284			−1.49381			−0.746904	+	0.664932i	$0.768461\pi$
$854$	40.0982	−	7.03528i	1.37213	−	0.240742i
$855$	−2.02592			−0.0692848
$856$	−12.7202	−	22.0321i	−0.434768	−	0.753041i
$857$	5.94723	−	10.3009i	0.203153	−	0.351872i	−0.746389	−	0.665509i	$-0.768214\pi$
$857$	5.94723	−	10.3009i	0.203153	−	0.351872i	0.949543	+	0.313637i	$0.101548\pi$
$858$	−1.15191	+	1.99517i	−0.0393256	+	0.0681140i
$859$	2.42227	+	4.19549i	0.0826466	+	0.143148i	0.904386	−	0.426715i	$-0.140329\pi$
$859$	2.42227	+	4.19549i	0.0826466	+	0.143148i	−0.821739	+	0.569864i	$0.806996\pi$
$860$	0.154930			0.00528306
$861$	12.1326	−	2.12867i	0.413477	−	0.0725450i
$862$	11.6357			0.396313
$863$	26.2994	+	45.5520i	0.895244	+	1.55061i	0.833503	+	0.552515i	$0.186332\pi$
$863$	26.2994	+	45.5520i	0.895244	+	1.55061i	0.0617407	+	0.998092i	$0.480335\pi$
$864$	0.129985	−	0.225141i	0.00442218	−	0.00765944i
$865$	−1.21595	+	2.10609i	−0.0413435	+	0.0716091i
$866$	−1.28658	−	2.22843i	−0.0437199	−	0.0757250i
$867$	0.740030			0.0251327
$868$	0.160929	−	0.440983i	0.00546229	−	0.0149679i
$869$	7.52158			0.255152
$870$	−0.414288	−	0.717568i	−0.0140457	−	0.0243278i
$871$	−0.221917	+	0.384371i	−0.00751936	+	0.0130239i
$872$	−14.0048	+	24.2571i	−0.474263	+	0.821448i
$873$	4.13274	+	7.15812i	0.139872	+	0.242266i
$874$	17.1978			0.581725
$875$	6.65251	+	7.94184i	0.224896	+	0.268483i
$876$	−0.305936			−0.0103366
$877$	2.85981	+	4.95334i	0.0965691	+	0.167263i	0.910262	−	0.414032i	$-0.135880\pi$
$877$	2.85981	+	4.95334i	0.0965691	+	0.167263i	−0.813693	+	0.581294i	$0.802546\pi$
$878$	−9.56108	+	16.5603i	−0.322671	+	0.558883i
$879$	−15.7334	+	27.2510i	−0.530673	+	0.919153i
$880$	−1.28062	−	2.21809i	−0.0431696	−	0.0747719i
$881$	45.1345			1.52062			0.760310	−	0.649560i	$-0.225047\pi$
$881$	45.1345			1.52062			0.760310	+	0.649560i	$0.225047\pi$
$882$	7.48510	+	6.30245i	0.252037	+	0.212215i
$883$	−39.5995			−1.33263			−0.666314	−	0.745671i	$-0.732129\pi$
$883$	−39.5995			−1.33263			−0.666314	+	0.745671i	$0.732129\pi$
$884$	−0.0968016	−	0.167665i	−0.00325579	−	0.00563919i
$885$	−0.329380	+	0.570502i	−0.0110720	+	0.0191772i
$886$	14.8415	−	25.7062i	0.498608	−	0.863615i
$887$	11.7253	+	20.3088i	0.393697	+	0.681904i	0.992934	−	0.118668i	$-0.0378625\pi$
$887$	11.7253	+	20.3088i	0.393697	+	0.681904i	−0.599237	+	0.800572i	$0.704529\pi$
$888$	29.3592			0.985230
$889$	15.6944	+	18.7362i	0.526374	+	0.628391i
$890$	2.39058			0.0801323
$891$	−0.824049	−	1.42729i	−0.0276067	−	0.0478162i
$892$	0.376753	−	0.652555i	0.0126146	−	0.0218491i
$893$	10.3203	−	17.8753i	0.345356	−	0.598174i
$894$	−6.01618	−	10.4203i	−0.201211	−	0.348508i
$895$	−5.03834			−0.168413
$896$	−9.89375	+	27.1112i	−0.330527	+	0.905721i
$897$	2.41616			0.0806731
$898$	−12.2926	−	21.2913i	−0.410208	−	0.710502i
$899$	2.87531	−	4.98017i	0.0958968	−	0.166098i
$900$	−0.111276	+	0.192736i	−0.00370921	+	0.00642455i
$901$	19.6516	+	34.0376i	0.654691	+	1.13396i
$902$	10.7260			0.357136
$903$	−22.0763	+	3.87331i	−0.734653	+	0.128896i
$904$	−35.5587			−1.18267
$905$	4.60044	+	7.96820i	0.152924	+	0.264872i
$906$	5.39699	−	9.34785i	0.179303	−	0.310562i
$907$	−13.1055	+	22.6994i	−0.435160	+	0.753720i	−0.997309	−	0.0733164i	$-0.976642\pi$
$907$	−13.1055	+	22.6994i	−0.435160	+	0.753720i	0.562148	+	0.827036i	$0.309975\pi$
$908$	−0.0663670	−	0.114951i	−0.00220247	−	0.00381479i
$909$	16.5051			0.547438
$910$	1.44934	−	0.254288i	0.0480451	−	0.00842958i
$911$	−4.65304			−0.154162			−0.0770811	−	0.997025i	$-0.524560\pi$
$911$	−4.65304			−0.154162			−0.0770811	+	0.997025i	$0.524560\pi$
$912$	9.94443	+	17.2243i	0.329293	+	0.570352i
$913$	−13.5337	+	23.4411i	−0.447901	+	0.775787i
$914$	−12.4419	+	21.5500i	−0.411541	+	0.712811i
$915$	2.18979	+	3.79283i	0.0723922	+	0.125387i
$916$	−0.307289			−0.0101531
$917$	13.3095	−	36.4711i	0.439519	−	1.20438i
$918$	−5.88767			−0.194322
$919$	22.0465	+	38.1857i	0.727247	+	1.25963i	0.958042	+	0.286626i	$0.0925338\pi$
$919$	22.0465	+	38.1857i	0.727247	+	1.25963i	−0.230796	+	0.973002i	$0.574133\pi$
$920$	−1.37467	+	2.38100i	−0.0453215	+	0.0784991i
$921$	6.40977	−	11.1020i	0.211209	−	0.365825i
$922$	−7.10319	−	12.3031i	−0.233931	−	0.405180i
$923$	9.74766			0.320848
$924$	−0.128705	−	0.153649i	−0.00423408	−	0.00505469i
$925$	−49.7024			−1.63421
$926$	−11.2115	−	19.4188i	−0.368432	−	0.638143i
$927$	−2.57276	+	4.45615i	−0.0845006	+	0.146359i
$928$	0.193652	−	0.335415i	0.00635693	−	0.0110105i
$929$	−20.6723	−	35.8055i	−0.678237	−	1.17474i	−0.975511	−	0.219949i	$-0.929411\pi$
$929$	−20.6723	−	35.8055i	−0.678237	−	1.17474i	0.297275	−	0.954792i	$-0.403922\pi$
$930$	−2.14680			−0.0703962
$931$	33.5146	−	12.1339i	1.09840	−	0.397672i
$932$	−0.972241			−0.0318468
$933$	−10.6355	−	18.4212i	−0.348191	−	0.603084i
$934$	−16.7925	+	29.0855i	−0.549468	+	0.951707i
$935$	1.38092	−	2.39183i	0.0451610	−	0.0782211i
$936$	1.42999	+	2.47682i	0.0467408	+	0.0809575i
$937$	56.2538			1.83773			0.918865	−	0.394571i	$-0.129107\pi$
$937$	56.2538			1.83773			0.918865	+	0.394571i	$0.129107\pi$
$938$	1.05405	+	1.25834i	0.0344161	+	0.0410863i
$939$	16.6561			0.543550
$940$	0.0370667	+	0.0642014i	0.00120898	+	0.00209402i
$941$	5.98493	−	10.3662i	0.195103	−	0.337929i	−0.751831	−	0.659356i	$-0.770829\pi$
$941$	5.98493	−	10.3662i	0.195103	−	0.337929i	0.946934	+	0.321427i	$0.104163\pi$
$942$	8.70275	−	15.0736i	0.283551	−	0.491124i
$943$	−5.62448	−	9.74188i	−0.183158	−	0.317239i
$944$	6.46719			0.210489
$945$	−0.360871	+	0.988870i	−0.0117391	+	0.0321679i
$946$	−19.5169			−0.634548
$947$	10.3238	+	17.8813i	0.335477	+	0.581064i	0.983576	−	0.180492i	$-0.0577691\pi$
$947$	10.3238	+	17.8813i	0.335477	+	0.581064i	−0.648099	+	0.761556i	$0.724436\pi$
$948$	0.104889	−	0.181674i	0.00340665	−	0.00590048i
$949$	3.32786	−	5.76403i	0.108027	−	0.187108i
$950$	−17.2312	−	29.8454i	−0.559055	−	0.968312i
$951$	20.1175			0.652355
$952$	−31.3911	+	5.50761i	−1.01739	+	0.178503i
$953$	58.7677			1.90367			0.951837	−	0.306606i	$-0.0991933\pi$
$953$	58.7677			1.90367			0.951837	+	0.306606i	$0.0991933\pi$
$954$	−6.52210	−	11.2966i	−0.211161	−	0.365741i
$955$	−4.25998	+	7.37850i	−0.137850	+	0.238763i
$956$	−0.624450	+	1.08158i	−0.0201962	+	0.0349808i
$957$	−1.22767	−	2.12638i	−0.0396849	−	0.0687362i
$958$	−32.1616			−1.03909
$959$	−12.3730	+	2.17087i	−0.399547	+	0.0701009i
$960$	−3.25269			−0.104980
$961$	8.05024	+	13.9434i	0.259685	+	0.449788i
$962$	−7.17489	+	12.4273i	−0.231328	+	0.400672i
$963$	−4.44765	+	7.70355i	−0.143323	+	0.248243i
$964$	0.170493	+	0.295303i	0.00549123	+	0.00951108i
$965$	−5.86351			−0.188753
$966$	3.06340	−	8.39443i	0.0985634	−	0.270086i
$967$	41.7729			1.34332			0.671662	−	0.740857i	$-0.265581\pi$
$967$	41.7729			1.34332			0.671662	+	0.740857i	$0.265581\pi$
$968$	11.8458	+	20.5174i	0.380737	+	0.659456i
$969$	−10.7233	+	18.5734i	−0.344483	+	0.596662i
$970$	2.29849	−	3.98111i	0.0738001	−	0.127826i
$971$	−23.0604	−	39.9419i	−0.740045	−	1.28180i	−0.952474	−	0.304619i	$-0.901471\pi$
$971$	−23.0604	−	39.9419i	−0.740045	−	1.28180i	0.212429	−	0.977176i	$-0.431863\pi$
$972$	−0.0459658			−0.00147436
$973$	4.35572	+	5.19990i	0.139638	+	0.166701i
$974$	14.0846			0.451299
$975$	−2.42085	−	4.19304i	−0.0775293	−	0.134285i
$976$	21.4977	−	37.2350i	0.688123	−	1.19186i
$977$	14.2373	−	24.6597i	0.455491	−	0.788933i	−0.543226	−	0.839587i	$-0.682797\pi$
$977$	14.2373	−	24.6597i	0.455491	−	0.788933i	0.998716	+	0.0506537i	$0.0161305\pi$
$978$	−8.35296	−	14.4677i	−0.267098	−	0.462628i
$979$	7.08404			0.226407
$980$	−0.0224443	+	0.126035i	−0.000716957	+	0.00402605i
$981$	9.79362			0.312686
$982$	−8.74741	−	15.1510i	−0.279141	−	0.483487i
$983$	4.30904	−	7.46348i	0.137437	−	0.238048i	−0.789089	−	0.614279i	$-0.789447\pi$
$983$	4.30904	−	7.46348i	0.137437	−	0.238048i	0.926526	+	0.376231i	$0.122780\pi$
$984$	6.65766	−	11.5314i	0.212239	−	0.367608i
$985$	−5.56362	−	9.63647i	−0.177272	−	0.307043i
$986$	−8.77144			−0.279340
$987$	−6.88679	−	8.22153i	−0.219209	−	0.261694i
$988$	0.234055			0.00744628
$989$	10.2342	+	17.7262i	0.325430	+	0.563661i
$990$	−0.458308	+	0.793813i	−0.0145660	+	0.0252290i
$991$	−5.53577	+	9.58823i	−0.175849	+	0.304580i	−0.940455	−	0.339919i	$-0.889601\pi$
$991$	−5.53577	+	9.58823i	−0.175849	+	0.304580i	0.764606	+	0.644499i	$0.222934\pi$
$992$	−0.501741	−	0.869041i	−0.0159303	−	0.0275921i
$993$	19.4369			0.616812
$994$	12.3589	−	33.8662i	0.392000	−	1.07417i
$995$	4.79489			0.152008
$996$	0.377458	+	0.653777i	0.0119602	+	0.0207157i
$997$	23.5341	−	40.7623i	0.745334	−	1.29096i	−0.204705	−	0.978824i	$-0.565623\pi$
$997$	23.5341	−	40.7623i	0.745334	−	1.29096i	0.950039	−	0.312132i	$-0.101043\pi$
$998$	0.339128	−	0.587386i	0.0107349	−	0.0185934i
$999$	−5.13274	−	8.89017i	−0.162393	−	0.281273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.i.d.235.3	yes	8
3.2	odd	2		819.2.j.f.235.2		8
7.2	even	3	inner	273.2.i.d.79.3	✓	8
7.3	odd	6		1911.2.a.q.1.2		4
7.4	even	3		1911.2.a.r.1.2		4
21.2	odd	6		819.2.j.f.352.2		8
21.11	odd	6		5733.2.a.bj.1.3		4
21.17	even	6		5733.2.a.bk.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.d.79.3	✓	8	7.2	even	3	inner
273.2.i.d.235.3	yes	8	1.1	even	1	trivial
819.2.j.f.235.2		8	3.2	odd	2
819.2.j.f.352.2		8	21.2	odd	6
1911.2.a.q.1.2		4	7.3	odd	6
1911.2.a.r.1.2		4	7.4	even	3
5733.2.a.bj.1.3		4	21.11	odd	6
5733.2.a.bk.1.3		4	21.17	even	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)

\(f(q)\)	\(=\)	\(q+(0.698934 + 1.21059i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.0229829 - 0.0398076i) q^{4} +(0.198934 + 0.344564i) q^{5} -1.39787 q^{6} +(1.69893 + 2.02821i) q^{7} +2.85999 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.698934 + 1.21059i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.0229829 - 0.0398076i) q^{4} +(0.198934 + 0.344564i) q^{5} -1.39787 q^{6} +(1.69893 + 2.02821i) q^{7} +2.85999 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.278083 + 0.481654i) q^{10} +(-0.824049 + 1.42729i) q^{11} +(0.0229829 + 0.0398076i) q^{12} -1.00000 q^{13} +(-1.26788 + 3.47429i) q^{14} -0.397868 q^{15} +(1.95298 + 3.38266i) q^{16} +(-2.10595 + 3.64761i) q^{17} +(0.698934 - 1.21059i) q^{18} +(-2.54597 - 4.40974i) q^{19} +0.0182883 q^{20} +(-2.60595 + 0.457216i) q^{21} -2.30382 q^{22} +(1.20808 + 2.09245i) q^{23} +(-1.42999 + 2.47682i) q^{24} +(2.42085 - 4.19304i) q^{25} +(-0.698934 - 1.21059i) q^{26} +1.00000 q^{27} +(0.119784 - 0.0210163i) q^{28} +1.48980 q^{29} +(-0.278083 - 0.481654i) q^{30} +(1.92999 - 3.34285i) q^{31} +(0.129985 - 0.225141i) q^{32} +(-0.824049 - 1.42729i) q^{33} -5.88767 q^{34} +(-0.360871 + 0.988870i) q^{35} -0.0459658 q^{36} +(-5.13274 - 8.89017i) q^{37} +(3.55892 - 6.16424i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.568949 + 0.985448i) q^{40} -4.65573 q^{41} +(-2.37488 - 2.83517i) q^{42} +8.47151 q^{43} +(0.0378781 + 0.0656068i) q^{44} +(0.198934 - 0.344564i) q^{45} +(-1.68873 + 2.92497i) q^{46} +(2.02680 + 3.51051i) q^{47} -3.90596 q^{48} +(-1.22725 + 6.89158i) q^{49} +6.76806 q^{50} +(-2.10595 - 3.64761i) q^{51} +(-0.0229829 + 0.0398076i) q^{52} +(4.66575 - 8.08132i) q^{53} +(0.698934 + 1.21059i) q^{54} -0.655725 q^{55} +(4.85893 + 5.80065i) q^{56} +5.09193 q^{57} +(1.04127 + 1.80353i) q^{58} +(0.827863 - 1.43390i) q^{59} +(-0.00914416 + 0.0158382i) q^{60} +(-5.50381 - 9.53288i) q^{61} +5.39575 q^{62} +(0.907012 - 2.48542i) q^{63} +8.17531 q^{64} +(-0.198934 - 0.344564i) q^{65} +(1.15191 - 1.99517i) q^{66} +(0.221917 - 0.384371i) q^{67} +(0.0968016 + 0.167665i) q^{68} -2.41616 q^{69} +(-1.44934 + 0.254288i) q^{70} -9.74766 q^{71} +(-1.42999 - 2.47682i) q^{72} +(-3.32786 + 5.76403i) q^{73} +(7.17489 - 12.4273i) q^{74} +(2.42085 + 4.19304i) q^{75} -0.234055 q^{76} +(-4.29485 + 0.753537i) q^{77} +1.39787 q^{78} +(-2.28190 - 3.95236i) q^{79} +(-0.777027 + 1.34585i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.25404 - 5.63617i) q^{82} +16.4234 q^{83} +(-0.0416916 + 0.114245i) q^{84} -1.67578 q^{85} +(5.92103 + 10.2555i) q^{86} +(-0.744900 + 1.29020i) q^{87} +(-2.35677 + 4.08205i) q^{88} +(-2.14915 - 3.72244i) q^{89} +0.556166 q^{90} +(-1.69893 - 2.02821i) q^{91} +0.111061 q^{92} +(1.92999 + 3.34285i) q^{93} +(-2.83319 + 4.90723i) q^{94} +(1.01296 - 1.75449i) q^{95} +(0.129985 + 0.225141i) q^{96} -8.26548 q^{97} +(-9.20063 + 3.33107i) q^{98} +1.64810 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 - 7 * q^4 - 3 * q^5 - 2 * q^6 + 9 * q^7 - 12 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9} - 14 q^{10} - 4 q^{11} - 7 q^{12} - 8 q^{13} + 16 q^{14} + 6 q^{15} - 9 q^{16} - 2 q^{17} + q^{18} - 6 q^{19} - 2 q^{20} - 6 q^{21} + 40 q^{22} + 4 q^{23} + 6 q^{24} + 3 q^{25} - q^{26} + 8 q^{27} - 20 q^{28} - 26 q^{29} - 14 q^{30} - 2 q^{31} + 18 q^{32} - 4 q^{33} + 13 q^{35} + 14 q^{36} + 5 q^{37} - 11 q^{38} + 4 q^{39} - 17 q^{40} + 16 q^{41} - 17 q^{42} + 32 q^{43} + 26 q^{44} - 3 q^{45} + 29 q^{46} - 15 q^{47} + 18 q^{48} - 21 q^{49} + 48 q^{50} - 2 q^{51} + 7 q^{52} + 2 q^{53} + q^{54} + 48 q^{55} - 35 q^{56} + 12 q^{57} - q^{58} - 20 q^{59} + q^{60} - 20 q^{61} - 44 q^{62} - 3 q^{63} + 40 q^{64} + 3 q^{65} - 20 q^{66} - 10 q^{67} - 13 q^{68} - 8 q^{69} - 31 q^{70} + 4 q^{71} + 6 q^{72} + 21 q^{74} + 3 q^{75} - 86 q^{76} + 3 q^{77} + 2 q^{78} - 6 q^{79} + 21 q^{80} - 4 q^{81} - 6 q^{82} + 32 q^{83} - 2 q^{84} + 4 q^{85} + 51 q^{86} + 13 q^{87} - 39 q^{88} - 51 q^{89} + 28 q^{90} - 9 q^{91} - 8 q^{92} - 2 q^{93} - 19 q^{94} - 17 q^{95} + 18 q^{96} + 26 q^{97} + 33 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - 7 * q^4 - 3 * q^5 - 2 * q^6 + 9 * q^7 - 12 * q^8 - 4 * q^9 - 14 * q^10 - 4 * q^11 - 7 * q^12 - 8 * q^13 + 16 * q^14 + 6 * q^15 - 9 * q^16 - 2 * q^17 + q^18 - 6 * q^19 - 2 * q^20 - 6 * q^21 + 40 * q^22 + 4 * q^23 + 6 * q^24 + 3 * q^25 - q^26 + 8 * q^27 - 20 * q^28 - 26 * q^29 - 14 * q^30 - 2 * q^31 + 18 * q^32 - 4 * q^33 + 13 * q^35 + 14 * q^36 + 5 * q^37 - 11 * q^38 + 4 * q^39 - 17 * q^40 + 16 * q^41 - 17 * q^42 + 32 * q^43 + 26 * q^44 - 3 * q^45 + 29 * q^46 - 15 * q^47 + 18 * q^48 - 21 * q^49 + 48 * q^50 - 2 * q^51 + 7 * q^52 + 2 * q^53 + q^54 + 48 * q^55 - 35 * q^56 + 12 * q^57 - q^58 - 20 * q^59 + q^60 - 20 * q^61 - 44 * q^62 - 3 * q^63 + 40 * q^64 + 3 * q^65 - 20 * q^66 - 10 * q^67 - 13 * q^68 - 8 * q^69 - 31 * q^70 + 4 * q^71 + 6 * q^72 + 21 * q^74 + 3 * q^75 - 86 * q^76 + 3 * q^77 + 2 * q^78 - 6 * q^79 + 21 * q^80 - 4 * q^81 - 6 * q^82 + 32 * q^83 - 2 * q^84 + 4 * q^85 + 51 * q^86 + 13 * q^87 - 39 * q^88 - 51 * q^89 + 28 * q^90 - 9 * q^91 - 8 * q^92 - 2 * q^93 - 19 * q^94 - 17 * q^95 + 18 * q^96 + 26 * q^97 + 33 * q^98 + 8 * q^99

Introduction

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