LMFDB - Embedded newform 273.2.bd.b.127.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(43,273)]

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, 0, 1]))

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

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

chi := DirichletCharacter("273.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bd (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} - 3 x^{12} + 32 x^{11} - 5 x^{10} - 44 x^{9} + 214 x^{8} + \cdots + 6561 $ x^16 - 4x^15 + 10x^14 - 8x^13 - 3x^12 + 32x^11 - 5x^10 - 44x^9 + 214x^8 - 132x^7 - 45x^6 + 864x^5 - 243x^4 - 1944x^3 + 7290x^2 - 8748*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.5
Root			$0.750089 - 1.56121i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.b.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.924500 - 0.533760i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.430200 + 0.745128i) q^{4} +0.994065i q^{5} +(0.924500 + 0.533760i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.05354i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.924500 - 0.533760i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.430200 + 0.745128i) q^{4} +0.994065i q^{5} +(0.924500 + 0.533760i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.05354i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.530592 + 0.919013i) q^{10} +(-0.215888 + 0.124643i) q^{11} -0.860399 q^{12} +(-3.56641 - 0.529854i) q^{13} +1.06752 q^{14} +(-0.860885 + 0.497032i) q^{15} +(0.769457 + 1.33274i) q^{16} +(3.10350 - 5.37541i) q^{17} +1.06752i q^{18} +(7.28287 + 4.20477i) q^{19} +(-0.740705 - 0.427646i) q^{20} +1.00000i q^{21} +(-0.133059 + 0.230465i) q^{22} +(-0.907804 - 1.57236i) q^{23} +(-2.64444 + 1.52677i) q^{24} +4.01184 q^{25} +(-3.57996 + 1.41376i) q^{26} -1.00000 q^{27} +(-0.745128 + 0.430200i) q^{28} +(-1.34505 - 2.32969i) q^{29} +(-0.530592 + 0.919013i) q^{30} -8.53282i q^{31} +(-3.86615 - 2.23212i) q^{32} +(-0.215888 - 0.124643i) q^{33} -6.62609i q^{34} +(-0.497032 + 0.860885i) q^{35} +(-0.430200 - 0.745128i) q^{36} +(-3.66498 + 2.11598i) q^{37} +8.97735 q^{38} +(-1.32434 - 3.35353i) q^{39} -3.03541 q^{40} +(5.57277 - 3.21744i) q^{41} +(0.533760 + 0.924500i) q^{42} +(-5.71391 + 9.89679i) q^{43} -0.214485i q^{44} +(-0.860885 - 0.497032i) q^{45} +(-1.67853 - 0.969100i) q^{46} -10.6030i q^{47} +(-0.769457 + 1.33274i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.70894 - 2.14136i) q^{50} +6.20699 q^{51} +(1.92908 - 2.42948i) q^{52} -0.601973 q^{53} +(-0.924500 + 0.533760i) q^{54} +(-0.123903 - 0.214607i) q^{55} +(-1.52677 + 2.64444i) q^{56} +8.40953i q^{57} +(-2.48699 - 1.43587i) q^{58} +(-7.71959 - 4.45691i) q^{59} -0.855293i q^{60} +(-2.87430 + 4.97843i) q^{61} +(-4.55448 - 7.88859i) q^{62} +(-0.866025 + 0.500000i) q^{63} -7.84351 q^{64} +(0.526710 - 3.54524i) q^{65} -0.266118 q^{66} +(5.73996 - 3.31397i) q^{67} +(2.67025 + 4.62500i) q^{68} +(0.907804 - 1.57236i) q^{69} +1.06118i q^{70} +(10.4088 + 6.00951i) q^{71} +(-2.64444 - 1.52677i) q^{72} +9.70387i q^{73} +(-2.25885 + 3.91244i) q^{74} +(2.00592 + 3.47435i) q^{75} +(-6.26618 + 3.61778i) q^{76} -0.249286 q^{77} +(-3.01433 - 2.39346i) q^{78} -5.63447 q^{79} +(-1.32483 + 0.764890i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.43468 - 5.94904i) q^{82} -16.5842i q^{83} +(-0.745128 - 0.430200i) q^{84} +(5.34351 + 3.08508i) q^{85} +12.1994i q^{86} +(1.34505 - 2.32969i) q^{87} +(-0.380602 - 0.659221i) q^{88} +(-8.47828 + 4.89494i) q^{89} -1.06118 q^{90} +(-2.82367 - 2.24207i) q^{91} +1.56215 q^{92} +(7.38964 - 4.26641i) q^{93} +(-5.65949 - 9.80252i) q^{94} +(-4.17981 + 7.23964i) q^{95} -4.46425i q^{96} +(2.10869 + 1.21745i) q^{97} +(0.924500 + 0.533760i) q^{98} -0.249286i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.924500	−	0.533760i	0.653720	−	0.377426i	−0.136160	−	0.990687i	$-0.543476\pi$
$2$	0.924500	−	0.533760i	0.653720	−	0.377426i	0.789880	+	0.613261i	$0.210143\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.430200	+	0.745128i	−0.215100	+	0.372564i
$5$			0.994065i			0.444559i	0.974983	+	0.222280i	$0.0713498\pi$
$5$			0.994065i			0.444559i	−0.974983	+	0.222280i	$0.928650\pi$
$6$	0.924500	+	0.533760i	0.377426	+	0.217907i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			3.05354i			1.07959i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.530592	+	0.919013i	0.167788	+	0.290617i
$11$	−0.215888	+	0.124643i	−0.0650927	+	0.0375813i	−0.532193	−	0.846623i	$-0.678632\pi$
$11$	−0.215888	+	0.124643i	−0.0650927	+	0.0375813i	0.467100	+	0.884204i	$0.345299\pi$
$12$	−0.860399			−0.248376
$13$	−3.56641	−	0.529854i	−0.989143	−	0.146955i
$13$	−3.56641	−	0.529854i	−0.989143	−	0.146955i
$14$	1.06752			0.285307
$15$	−0.860885	+	0.497032i	−0.222280	+	0.128333i
$16$	0.769457	+	1.33274i	0.192364	+	0.333185i
$17$	3.10350	−	5.37541i	0.752708	−	1.30373i	−0.193797	−	0.981042i	$-0.562080\pi$
$17$	3.10350	−	5.37541i	0.752708	−	1.30373i	0.946506	−	0.322688i	$-0.104586\pi$
$18$			1.06752i			0.251617i
$19$	7.28287	+	4.20477i	1.67081	+	0.964640i	0.967188	+	0.254060i	$0.0817661\pi$
$19$	7.28287	+	4.20477i	1.67081	+	0.964640i	0.703617	+	0.710580i	$0.251567\pi$
$20$	−0.740705	−	0.427646i	−0.165627	−	0.0956246i
$21$			1.00000i			0.218218i
$22$	−0.133059	+	0.230465i	−0.0283683	+	0.0491353i
$23$	−0.907804	−	1.57236i	−0.189290	−	0.327860i	0.755724	−	0.654891i	$-0.227285\pi$
$23$	−0.907804	−	1.57236i	−0.189290	−	0.327860i	−0.945014	+	0.327030i	$0.893952\pi$
$24$	−2.64444	+	1.52677i	−0.539794	+	0.311650i
$25$	4.01184			0.802367
$26$	−3.57996	+	1.41376i	−0.702088	+	0.277260i
$27$	−1.00000			−0.192450
$28$	−0.745128	+	0.430200i	−0.140816	+	0.0813001i
$29$	−1.34505	−	2.32969i	−0.249769	−	0.432612i	0.713693	−	0.700459i	$-0.247021\pi$
$29$	−1.34505	−	2.32969i	−0.249769	−	0.432612i	−0.963462	+	0.267847i	$0.913688\pi$
$30$	−0.530592	+	0.919013i	−0.0968725	+	0.167788i
$31$		−	8.53282i		−	1.53254i	−0.642519	−	0.766270i	$-0.722111\pi$
$31$		−	8.53282i		−	1.53254i	0.642519	−	0.766270i	$-0.277889\pi$
$32$	−3.86615	−	2.23212i	−0.683446	−	0.394588i
$33$	−0.215888	−	0.124643i	−0.0375813	−	0.0216976i
$34$		−	6.62609i		−	1.13637i
$35$	−0.497032	+	0.860885i	−0.0840138	+	0.145516i
$36$	−0.430200	−	0.745128i	−0.0716999	−	0.124188i
$37$	−3.66498	+	2.11598i	−0.602519	+	0.347864i	−0.770032	−	0.638006i	$-0.779760\pi$
$37$	−3.66498	+	2.11598i	−0.602519	+	0.347864i	0.167513	+	0.985870i	$0.446426\pi$
$38$	8.97735			1.45632
$39$	−1.32434	−	3.35353i	−0.212063	−	0.536994i
$40$	−3.03541			−0.479941
$41$	5.57277	−	3.21744i	0.870320	−	0.502479i	0.00286538	−	0.999996i	$-0.499088\pi$
$41$	5.57277	−	3.21744i	0.870320	−	0.502479i	0.867455	+	0.497516i	$0.165755\pi$
$42$	0.533760	+	0.924500i	0.0823610	+	0.142653i
$43$	−5.71391	+	9.89679i	−0.871364	+	1.50925i	−0.0107768	+	0.999942i	$0.503430\pi$
$43$	−5.71391	+	9.89679i	−0.871364	+	1.50925i	−0.860587	+	0.509304i	$0.829903\pi$
$44$		−	0.214485i		−	0.0323349i
$45$	−0.860885	−	0.497032i	−0.128333	−	0.0740932i
$46$	−1.67853	−	0.969100i	−0.247486	−	0.142886i
$47$		−	10.6030i		−	1.54661i	−0.634032	−	0.773307i	$-0.718601\pi$
$47$		−	10.6030i		−	1.54661i	0.634032	−	0.773307i	$-0.281399\pi$
$48$	−0.769457	+	1.33274i	−0.111062	+	0.192364i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	3.70894	−	2.14136i	0.524524	−	0.302834i
$51$	6.20699			0.869153
$52$	1.92908	−	2.42948i	0.267515	−	0.336909i
$53$	−0.601973			−0.0826873			−0.0413436	−	0.999145i	$-0.513164\pi$
$53$	−0.601973			−0.0826873			−0.0413436	+	0.999145i	$0.513164\pi$
$54$	−0.924500	+	0.533760i	−0.125809	+	0.0726356i
$55$	−0.123903	−	0.214607i	−0.0167071	−	0.0289375i
$56$	−1.52677	+	2.64444i	−0.204023	+	0.353378i
$57$			8.40953i			1.11387i
$58$	−2.48699	−	1.43587i	−0.326558	−	0.188538i
$59$	−7.71959	−	4.45691i	−1.00501	−	0.580240i	−0.0952798	−	0.995451i	$-0.530375\pi$
$59$	−7.71959	−	4.45691i	−1.00501	−	0.580240i	−0.909725	+	0.415211i	$0.863708\pi$
$60$		−	0.855293i		−	0.110418i
$61$	−2.87430	+	4.97843i	−0.368016	+	0.637422i	−0.989255	−	0.146199i	$-0.953296\pi$
$61$	−2.87430	+	4.97843i	−0.368016	+	0.637422i	0.621239	+	0.783621i	$0.286629\pi$
$62$	−4.55448	−	7.88859i	−0.578420	−	1.00185i
$63$	−0.866025	+	0.500000i	−0.109109	+	0.0629941i
$64$	−7.84351			−0.980438
$65$	0.526710	−	3.54524i	0.0653303	−	0.439733i
$66$	−0.266118			−0.0327568
$67$	5.73996	−	3.31397i	0.701248	−	0.404866i	−0.106564	−	0.994306i	$-0.533985\pi$
$67$	5.73996	−	3.31397i	0.701248	−	0.404866i	0.807812	+	0.589440i	$0.200652\pi$
$68$	2.67025	+	4.62500i	0.323815	+	0.560864i
$69$	0.907804	−	1.57236i	0.109287	−	0.189290i
$70$			1.06118i			0.126836i
$71$	10.4088	+	6.00951i	1.23529	+	0.713197i	0.968129	−	0.250453i	$-0.0805797\pi$
$71$	10.4088	+	6.00951i	1.23529	+	0.713197i	0.267165	+	0.963651i	$0.413913\pi$
$72$	−2.64444	−	1.52677i	−0.311650	−	0.179931i
$73$			9.70387i			1.13575i	0.823114	+	0.567876i	$0.192235\pi$
$73$			9.70387i			1.13575i	−0.823114	+	0.567876i	$0.807765\pi$
$74$	−2.25885	+	3.91244i	−0.262586	+	0.454812i
$75$	2.00592	+	3.47435i	0.231623	+	0.401184i
$76$	−6.26618	+	3.61778i	−0.718780	+	0.414988i
$77$	−0.249286			−0.0284088
$78$	−3.01433	−	2.39346i	−0.341305	−	0.271006i
$79$	−5.63447			−0.633928			−0.316964	−	0.948438i	$-0.602663\pi$
$79$	−5.63447			−0.633928			−0.316964	+	0.948438i	$0.602663\pi$
$80$	−1.32483	+	0.764890i	−0.148120	+	0.0855173i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.43468	−	5.94904i	0.379297	−	0.656962i
$83$		−	16.5842i		−	1.82035i	−0.414223	−	0.910175i	$-0.635947\pi$
$83$		−	16.5842i		−	1.82035i	0.414223	−	0.910175i	$-0.364053\pi$
$84$	−0.745128	−	0.430200i	−0.0813001	−	0.0469386i
$85$	5.34351	+	3.08508i	0.579585	+	0.334623i
$86$			12.1994i			1.31550i
$87$	1.34505	−	2.32969i	0.144204	−	0.249769i
$88$	−0.380602	−	0.659221i	−0.0405723	−	0.0702732i
$89$	−8.47828	+	4.89494i	−0.898696	+	0.518862i	−0.876777	−	0.480897i	$-0.840311\pi$
$89$	−8.47828	+	4.89494i	−0.898696	+	0.518862i	−0.0219191	+	0.999760i	$0.506978\pi$
$90$	−1.06118			−0.111859
$91$	−2.82367	−	2.24207i	−0.296001	−	0.235033i
$92$	1.56215			0.162865
$93$	7.38964	−	4.26641i	0.766270	−	0.442406i
$94$	−5.65949	−	9.80252i	−0.583732	−	1.01105i
$95$	−4.17981	+	7.23964i	−0.428840	+	0.742772i
$96$		−	4.46425i		−	0.455630i
$97$	2.10869	+	1.21745i	0.214105	+	0.123614i	0.603218	−	0.797577i	$-0.293885\pi$
$97$	2.10869	+	1.21745i	0.214105	+	0.123614i	−0.389113	+	0.921190i	$0.627218\pi$
$98$	0.924500	+	0.533760i	0.0933886	+	0.0539179i
$99$		−	0.249286i		−	0.0250542i
$100$	−1.72589	+	2.98933i	−0.172589	+	0.298933i
$101$	−2.58622	−	4.47946i	−0.257338	−	0.445723i	0.708190	−	0.706022i	$-0.249512\pi$
$101$	−2.58622	−	4.47946i	−0.257338	−	0.445723i	−0.965528	+	0.260299i	$0.916179\pi$
$102$	5.73837	−	3.31305i	0.568183	−	0.328040i
$103$	11.3681			1.12013			0.560064	−	0.828449i	$-0.310777\pi$
$103$	11.3681			1.12013			0.560064	+	0.828449i	$0.310777\pi$
$104$	1.61793	−	10.8901i	0.158651	−	1.06787i
$105$	−0.994065			−0.0970108
$106$	−0.556524	+	0.321309i	−0.0540544	+	0.0312083i
$107$	5.99438	+	10.3826i	0.579498	+	1.00372i	0.995537	+	0.0943734i	$0.0300848\pi$
$107$	5.99438	+	10.3826i	0.579498	+	1.00372i	−0.416039	+	0.909347i	$0.636582\pi$
$108$	0.430200	−	0.745128i	0.0413960	−	0.0716999i
$109$		−	6.30314i		−	0.603731i	−0.953350	−	0.301866i	$-0.902391\pi$
$109$		−	6.30314i		−	0.603731i	0.953350	−	0.301866i	$-0.0976094\pi$
$110$	−0.229097	−	0.132269i	−0.0218435	−	0.0126114i
$111$	−3.66498	−	2.11598i	−0.347864	−	0.200840i
$112$			1.53891i			0.145414i
$113$	−3.44378	+	5.96479i	−0.323963	+	0.561121i	−0.981302	−	0.192475i	$-0.938349\pi$
$113$	−3.44378	+	5.96479i	−0.323963	+	0.561121i	0.657339	+	0.753595i	$0.271682\pi$
$114$	4.48868	+	7.77462i	0.420403	+	0.728160i
$115$	1.56303	−	0.902416i	0.145753	−	0.0841508i
$116$	2.31455			0.214901
$117$	2.24207	−	2.82367i	0.207279	−	0.261049i
$118$	−9.51568			−0.875990
$119$	5.37541	−	3.10350i	0.492763	−	0.284497i
$120$	−1.51771	−	2.62874i	−0.138547	−	0.239970i
$121$	−5.46893	+	9.47246i	−0.497175	+	0.861133i
$122$			6.13674i			0.555594i
$123$	5.57277	+	3.21744i	0.502479	+	0.290107i
$124$	6.35804	+	3.67082i	0.570969	+	0.329649i
$125$			8.95835i			0.801259i
$126$	−0.533760	+	0.924500i	−0.0475512	+	0.0823610i
$127$	0.535395	+	0.927332i	0.0475087	+	0.0822874i	0.888802	−	0.458292i	$-0.151538\pi$
$127$	0.535395	+	0.927332i	0.0475087	+	0.0822874i	−0.841293	+	0.540579i	$0.818205\pi$
$128$	0.480982	−	0.277695i	0.0425132	−	0.0245450i
$129$	−11.4278			−1.00616
$130$	−1.40536	−	3.55871i	−0.123259	−	0.312120i
$131$	6.79609			0.593777			0.296889	−	0.954912i	$-0.404051\pi$
$131$	6.79609			0.593777			0.296889	+	0.954912i	$0.404051\pi$
$132$	0.185750	−	0.107243i	0.0161674	−	0.00933428i
$133$	4.20477	+	7.28287i	0.364600	+	0.631505i
$134$	3.53773	−	6.12753i	0.305613	−	0.529338i
$135$		−	0.994065i		−	0.0855555i
$136$	16.4140	+	9.47664i	1.40749	+	0.812615i
$137$	−16.1702	−	9.33585i	−1.38151	−	0.797615i	−0.389172	−	0.921165i	$-0.627239\pi$
$137$	−16.1702	−	9.33585i	−1.38151	−	0.797615i	−0.992338	+	0.123550i	$0.960572\pi$
$138$		−	1.93820i		−	0.164991i
$139$	3.10738	−	5.38214i	0.263564	−	0.456507i	−0.703622	−	0.710574i	$-0.748435\pi$
$139$	3.10738	−	5.38214i	0.263564	−	0.456507i	0.967187	+	0.254067i	$0.0817685\pi$
$140$	−0.427646	−	0.740705i	−0.0361427	−	0.0626010i
$141$	9.18251	−	5.30152i	0.773307	−	0.446469i
$142$	12.8305			1.07672
$143$	0.835987	−	0.330138i	0.0699087	−	0.0276075i
$144$	−1.53891			−0.128243
$145$	2.31586	−	1.33706i	0.192322	−	0.111037i
$146$	5.17954	+	8.97123i	0.428662	+	0.742464i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$		−	3.64117i		−	0.299302i
$149$	2.89242	+	1.66994i	0.236957	+	0.136807i	0.613777	−	0.789479i	$-0.289649\pi$
$149$	2.89242	+	1.66994i	0.236957	+	0.136807i	−0.376821	+	0.926286i	$0.622983\pi$
$150$	3.70894	+	2.14136i	0.302834	+	0.174841i
$151$		−	9.04809i		−	0.736324i	−0.929762	−	0.368162i	$-0.879987\pi$
$151$		−	9.04809i		−	0.736324i	0.929762	−	0.368162i	$-0.120013\pi$
$152$	−12.8394	+	22.2385i	−1.04141	+	1.80378i
$153$	3.10350	+	5.37541i	0.250903	+	0.434576i
$154$	−0.230465	+	0.133059i	−0.0185714	+	0.0107222i
$155$	8.48218			0.681305
$156$	3.06853	+	0.455886i	0.245679	+	0.0365001i
$157$	−12.0695			−0.963252			−0.481626	−	0.876377i	$-0.659954\pi$
$157$	−12.0695			−0.963252			−0.481626	+	0.876377i	$0.659954\pi$
$158$	−5.20907	+	3.00746i	−0.414411	+	0.239261i
$159$	−0.300986	−	0.521324i	−0.0238698	−	0.0413436i
$160$	2.21888	−	3.84321i	0.175418	−	0.303832i
$161$		−	1.81561i		−	0.143090i
$162$	−0.924500	−	0.533760i	−0.0726356	−	0.0419362i
$163$	−1.64381	−	0.949055i	−0.128753	−	0.0743358i	0.434240	−	0.900797i	$-0.357017\pi$
$163$	−1.64381	−	0.949055i	−0.128753	−	0.0743358i	−0.562993	+	0.826461i	$0.690350\pi$
$164$			5.53656i			0.432333i
$165$	0.123903	−	0.214607i	0.00964585	−	0.0167071i
$166$	−8.85198	−	15.3321i	−0.687047	−	1.19000i
$167$	11.8910	−	6.86525i	0.920150	−	0.531249i	0.0364674	−	0.999335i	$-0.488389\pi$
$167$	11.8910	−	6.86525i	0.920150	−	0.531249i	0.883683	+	0.468086i	$0.155056\pi$
$168$	−3.05354			−0.235585
$169$	12.4385	+	3.77935i	0.956808	+	0.290719i
$170$	6.58677			0.505182
$171$	−7.28287	+	4.20477i	−0.556935	+	0.321547i
$172$	−4.91625	−	8.51519i	−0.374860	−	0.649277i
$173$	−10.9284	+	18.9286i	−0.830872	+	1.43911i	0.0664761	+	0.997788i	$0.478824\pi$
$173$	−10.9284	+	18.9286i	−0.830872	+	1.43911i	−0.897348	+	0.441324i	$0.854509\pi$
$174$		−	2.87173i		−	0.217705i
$175$	3.47435	+	2.00592i	0.262636	+	0.151633i
$176$	−0.332233	−	0.191815i	−0.0250430	−	0.0144586i
$177$		−	8.91382i		−	0.670003i
$178$	−5.22545	+	9.05074i	−0.391664	+	0.678382i
$179$	3.73571	+	6.47043i	0.279220	+	0.483623i	0.971191	−	0.238302i	$-0.0765909\pi$
$179$	3.73571	+	6.47043i	0.279220	+	0.483623i	−0.691971	+	0.721925i	$0.743258\pi$
$180$	0.740705	−	0.427646i	0.0552089	−	0.0318749i
$181$	6.04007			0.448955			0.224477	−	0.974479i	$-0.427933\pi$
$181$	6.04007			0.448955			0.224477	+	0.974479i	$0.427933\pi$
$182$	−3.80721	−	0.565631i	−0.282209	−	0.0419273i
$183$	−5.74859			−0.424948
$184$	4.80127	−	2.77201i	0.353954	−	0.204356i
$185$	−2.10342	−	3.64322i	−0.154646	−	0.267855i
$186$	4.55448	−	7.88859i	0.333951	−	0.578420i
$187$			1.54732i			0.113151i
$188$	7.90062	+	4.56143i	0.576212	+	0.332676i
$189$	−0.866025	−	0.500000i	−0.0629941	−	0.0363696i
$190$			8.92407i			0.647420i
$191$	−6.24095	+	10.8096i	−0.451579	+	0.782158i	−0.998484	−	0.0550367i	$-0.982472\pi$
$191$	−6.24095	+	10.8096i	−0.451579	+	0.782158i	0.546905	+	0.837194i	$0.315806\pi$
$192$	−3.92175	−	6.79268i	−0.283028	−	0.490219i
$193$	4.97792	−	2.87400i	0.358318	−	0.206875i	−0.310025	−	0.950729i	$-0.600337\pi$
$193$	4.97792	−	2.87400i	0.358318	−	0.206875i	0.668343	+	0.743853i	$0.267004\pi$
$194$	2.59931			0.186620
$195$	3.33362	−	1.31648i	0.238726	−	0.0942748i
$196$	−0.860399			−0.0614571
$197$	−12.9690	+	7.48763i	−0.924000	+	0.533472i	−0.884909	−	0.465764i	$-0.845780\pi$
$197$	−12.9690	+	7.48763i	−0.924000	+	0.533472i	−0.0390912	+	0.999236i	$0.512446\pi$
$198$	−0.133059	−	0.230465i	−0.00945609	−	0.0163784i
$199$	−1.03719	+	1.79647i	−0.0735248	+	0.127349i	−0.900444	−	0.434972i	$-0.856758\pi$
$199$	−1.03719	+	1.79647i	−0.0735248	+	0.127349i	0.826919	+	0.562321i	$0.190091\pi$
$200$			12.2503i			0.866226i
$201$	5.73996	+	3.31397i	0.404866	+	0.233749i
$202$	−4.78192	−	2.76084i	−0.336455	−	0.194252i
$203$		−	2.69009i		−	0.188808i
$204$	−2.67025	+	4.62500i	−0.186955	+	0.323815i
$205$	3.19834	+	5.53969i	0.223382	+	0.386909i
$206$	10.5098	−	6.06782i	0.732250	−	0.422765i
$207$	1.81561			0.126194
$208$	−2.03804	−	5.16079i	−0.141313	−	0.357836i
$209$	−2.09638			−0.145010
$210$	−0.919013	+	0.530592i	−0.0634179	+	0.0366144i
$211$	−10.9283	−	18.9283i	−0.752333	−	1.30308i	−0.946689	−	0.322148i	$-0.895595\pi$
$211$	−10.9283	−	18.9283i	−0.752333	−	1.30308i	0.194356	−	0.980931i	$-0.437738\pi$
$212$	0.258968	−	0.448546i	0.0177860	−	0.0308063i
$213$			12.0190i			0.823529i
$214$	11.0836	+	6.39912i	0.757660	+	0.437435i
$215$	−9.83805	−	5.68000i	−0.670949	−	0.387373i
$216$		−	3.05354i		−	0.207767i
$217$	4.26641	−	7.38964i	0.289623	−	0.501641i
$218$	−3.36437	−	5.82725i	−0.227864	−	0.394671i
$219$	−8.40380	+	4.85193i	−0.567876	+	0.327863i
$220$	0.213212			0.0143748
$221$	−13.9165	+	17.5265i	−0.936126	+	1.17896i
$222$	−4.51770			−0.303208
$223$	−10.6138	+	6.12790i	−0.710755	+	0.410355i	−0.811341	−	0.584574i	$-0.801262\pi$
$223$	−10.6138	+	6.12790i	−0.710755	+	0.410355i	0.100585	+	0.994928i	$0.467928\pi$
$224$	−2.23212	−	3.86615i	−0.149140	−	0.258318i
$225$	−2.00592	+	3.47435i	−0.133728	+	0.231623i
$226$			7.35260i			0.489088i
$227$	−14.1397	−	8.16356i	−0.938485	−	0.541835i	−0.0490001	−	0.998799i	$-0.515603\pi$
$227$	−14.1397	−	8.16356i	−0.938485	−	0.541835i	−0.889485	+	0.456964i	$0.848937\pi$
$228$	−6.26618	−	3.61778i	−0.414988	−	0.239593i
$229$		−	3.88261i		−	0.256570i	−0.991737	−	0.128285i	$-0.959053\pi$
$229$		−	3.88261i		−	0.256570i	0.991737	−	0.128285i	$-0.0409472\pi$
$230$	0.963348	−	1.66857i	0.0635213	−	0.110022i
$231$	−0.124643	−	0.215888i	−0.00820090	−	0.0142044i
$232$	7.11379	−	4.10715i	0.467043	−	0.269647i
$233$	−18.6257			−1.22021			−0.610106	−	0.792320i	$-0.708873\pi$
$233$	−18.6257			−1.22021			−0.610106	+	0.792320i	$0.708873\pi$
$234$	0.565631	−	3.80721i	0.0369764	−	0.248885i
$235$	10.5401			0.687561
$236$	6.64193	−	3.83472i	0.432353	−	0.249619i
$237$	−2.81724	−	4.87960i	−0.182999	−	0.316964i
$238$	3.31305	−	5.73837i	0.214753	−	0.371963i
$239$		−	17.2578i		−	1.11631i	−0.829736	−	0.558156i	$-0.811509\pi$
$239$		−	17.2578i		−	1.11631i	0.829736	−	0.558156i	$-0.188491\pi$
$240$	−1.32483	−	0.764890i	−0.0855173	−	0.0493735i
$241$	13.2661	+	7.65919i	0.854545	+	0.493372i	0.862182	−	0.506599i	$-0.169097\pi$
$241$	13.2661	+	7.65919i	0.854545	+	0.493372i	−0.00763655	+	0.999971i	$0.502431\pi$
$242$			11.6764i			0.750587i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.47304	−	4.28344i	−0.158320	−	0.274219i
$245$	−0.860885	+	0.497032i	−0.0549999	+	0.0317542i
$246$	6.86936			0.437975
$247$	−23.7458	−	18.8548i	−1.51091	−	1.19970i
$248$	26.0553			1.65451
$249$	14.3623	−	8.29209i	0.910175	−	0.525490i
$250$	4.78161	+	8.28199i	0.302416	+	0.523799i
$251$	3.92011	−	6.78983i	0.247435	−	0.428570i	−0.715378	−	0.698737i	$-0.753746\pi$
$251$	3.92011	−	6.78983i	0.247435	−	0.428570i	0.962813	+	0.270167i	$0.0870789\pi$
$252$		−	0.860399i		−	0.0542001i
$253$	0.391968	+	0.226303i	0.0246428	+	0.0142275i
$254$	0.989946	+	0.571546i	0.0621148	+	0.0358620i
$255$			6.17015i			0.386390i
$256$	8.13995	−	14.0988i	0.508747	−	0.881176i
$257$	−3.44069	−	5.95945i	−0.214624	−	0.371740i	0.738532	−	0.674218i	$-0.235519\pi$
$257$	−3.44069	−	5.95945i	−0.214624	−	0.371740i	−0.953156	+	0.302478i	$0.902186\pi$
$258$	−10.5650	+	6.09972i	−0.657750	+	0.379752i
$259$	−4.23195			−0.262961
$260$	2.41507	+	1.91763i	0.149776	+	0.118926i
$261$	2.69009			0.166513
$262$	6.28299	−	3.62749i	0.388164	−	0.224107i
$263$	−12.1976	−	21.1269i	−0.752138	−	1.30274i	−0.946785	−	0.321867i	$-0.895690\pi$
$263$	−12.1976	−	21.1269i	−0.752138	−	1.30274i	0.194647	−	0.980873i	$-0.437644\pi$
$264$	0.380602	−	0.659221i	0.0234244	−	0.0405723i
$265$		−	0.598400i		−	0.0367594i
$266$	7.77462	+	4.48868i	0.476692	+	0.275218i
$267$	−8.47828	−	4.89494i	−0.518862	−	0.299565i
$268$			5.70267i			0.348346i
$269$	−7.46508	+	12.9299i	−0.455154	+	0.788350i	−0.998697	−	0.0510315i	$-0.983749\pi$
$269$	−7.46508	+	12.9299i	−0.455154	+	0.788350i	0.543543	+	0.839381i	$0.317082\pi$
$270$	−0.530592	−	0.919013i	−0.0322908	−	0.0559293i
$271$	−1.55659	+	0.898700i	−0.0945564	+	0.0545922i	−0.546533	−	0.837438i	$-0.684053\pi$
$271$	−1.55659	+	0.898700i	−0.0945564	+	0.0545922i	0.451976	+	0.892030i	$0.350719\pi$
$272$	9.55203			0.579177
$273$	0.529854	−	3.56641i	0.0320682	−	0.215849i
$274$	−19.9324			−1.20416
$275$	−0.866107	+	0.500047i	−0.0522282	+	0.0301540i
$276$	0.781074	+	1.35286i	0.0470152	+	0.0814326i
$277$	6.15944	−	10.6685i	0.370085	−	0.641005i	−0.619494	−	0.785002i	$-0.712662\pi$
$277$	6.15944	−	10.6685i	0.370085	−	0.641005i	0.989578	+	0.143996i	$0.0459953\pi$
$278$		−	6.63438i		−	0.397904i
$279$	7.38964	+	4.26641i	0.442406	+	0.255423i
$280$	−2.62874	−	1.51771i	−0.157098	−	0.0907003i
$281$			17.3105i			1.03266i	0.856390	+	0.516329i	$0.172702\pi$
$281$			17.3105i			1.03266i	−0.856390	+	0.516329i	$0.827298\pi$
$282$	5.65949	−	9.80252i	0.337018	−	0.583732i
$283$	−5.78080	−	10.0126i	−0.343633	−	0.595190i	0.641471	−	0.767147i	$-0.278324\pi$
$283$	−5.78080	−	10.0126i	−0.343633	−	0.595190i	−0.985104	+	0.171957i	$0.944991\pi$
$284$	−8.95570	+	5.17058i	−0.531423	+	0.306817i
$285$	−8.35962			−0.495181
$286$	0.596655	−	0.751429i	0.0352810	−	0.0444329i
$287$	6.43488			0.379839
$288$	3.86615	−	2.23212i	0.227815	−	0.131529i
$289$	−10.7634	−	18.6427i	−0.633140	−	1.09663i
$290$	1.42734	−	2.47223i	0.0838165	−	0.145174i
$291$			2.43491i			0.142737i
$292$	−7.23062	−	4.17460i	−0.423140	−	0.244300i
$293$	−2.28791	−	1.32092i	−0.133661	−	0.0771692i	0.431678	−	0.902028i	$-0.357922\pi$
$293$	−2.28791	−	1.32092i	−0.133661	−	0.0771692i	−0.565340	+	0.824858i	$0.691255\pi$
$294$			1.06752i			0.0622591i
$295$	4.43045	−	7.67377i	0.257951	−	0.446784i
$296$	−6.46121	−	11.1911i	−0.375550	−	0.650472i
$297$	0.215888	−	0.124643i	0.0125271	−	0.00723252i
$298$	3.56539			0.206538
$299$	2.40448	+	6.08869i	0.139054	+	0.352118i
$300$	−3.45178			−0.199289
$301$	−9.89679	+	5.71391i	−0.570441	+	0.329344i
$302$	−4.82951	−	8.36496i	−0.277907	−	0.481350i
$303$	2.58622	−	4.47946i	0.148574	−	0.257338i
$304$			12.9416i			0.742249i
$305$	−4.94888	−	2.85724i	−0.283372	−	0.163605i
$306$	5.73837	+	3.31305i	0.328040	+	0.189394i
$307$			18.9221i			1.07994i	0.841684	+	0.539971i	$0.181565\pi$
$307$			18.9221i			1.07994i	−0.841684	+	0.539971i	$0.818435\pi$
$308$	0.107243	−	0.185750i	0.00611072	−	0.0105841i
$309$	5.68403	+	9.84503i	0.323353	+	0.560064i
$310$	7.84177	−	4.52745i	0.445383	−	0.257142i
$311$	−16.9499			−0.961140			−0.480570	−	0.876956i	$-0.659570\pi$
$311$	−16.9499			−0.961140			−0.480570	+	0.876956i	$0.659570\pi$
$312$	10.2401	−	4.04391i	0.579732	−	0.228941i
$313$	−14.0214			−0.792537			−0.396268	−	0.918135i	$-0.629695\pi$
$313$	−14.0214			−0.792537			−0.396268	+	0.918135i	$0.629695\pi$
$314$	−11.1583	+	6.44223i	−0.629698	+	0.363556i
$315$	−0.497032	−	0.860885i	−0.0280046	−	0.0485054i
$316$	2.42395	−	4.19840i	0.136358	−	0.236179i
$317$		−	16.4256i		−	0.922554i	−0.887256	−	0.461277i	$-0.847392\pi$
$317$		−	16.4256i		−	0.922554i	0.887256	−	0.461277i	$-0.152608\pi$
$318$	−0.556524	−	0.321309i	−0.0312083	−	0.0180181i
$319$	0.580759	+	0.335301i	0.0325162	+	0.0187733i
$320$		−	7.79695i		−	0.435863i
$321$	−5.99438	+	10.3826i	−0.334573	+	0.579498i
$322$	−0.969100	−	1.67853i	−0.0540058	−	0.0935409i
$323$	45.2047	−	26.0990i	2.51526	−	1.45218i
$324$	0.860399			0.0478000
$325$	−14.3078	−	2.12569i	−0.793656	−	0.117912i
$326$	−2.02627			−0.112225
$327$	5.45868	−	3.15157i	0.301866	−	0.174282i
$328$	9.82456	+	17.0166i	0.542471	+	0.939587i
$329$	5.30152	−	9.18251i	0.292282	−	0.506248i
$330$		−	0.264538i		−	0.0145624i
$331$	3.84246	+	2.21845i	0.211201	+	0.121937i	0.601869	−	0.798595i	$-0.294423\pi$
$331$	3.84246	+	2.21845i	0.211201	+	0.121937i	−0.390668	+	0.920531i	$0.627756\pi$
$332$	12.3573	+	7.13451i	0.678197	+	0.391557i
$333$		−	4.23195i		−	0.231910i
$334$	7.32880	−	12.6939i	0.401014	−	0.694577i
$335$	3.29430	+	5.70589i	0.179987	+	0.311746i
$336$	−1.33274	+	0.769457i	−0.0727069	+	0.0419773i
$337$	−18.0752			−0.984618			−0.492309	−	0.870421i	$-0.663847\pi$
$337$	−18.0752			−0.984618			−0.492309	+	0.870421i	$0.663847\pi$
$338$	13.5167	−	3.14517i	0.735210	−	0.171075i
$339$	−6.88755			−0.374080
$340$	−4.59755	+	2.65440i	−0.249337	+	0.143955i
$341$	1.06356	+	1.84213i	0.0575948	+	0.0997571i
$342$	−4.48868	+	7.77462i	−0.242720	+	0.420403i
$343$			1.00000i			0.0539949i
$344$	−30.2202	−	17.4476i	−1.62936	−	0.940714i
$345$	1.56303	+	0.902416i	0.0841508	+	0.0485845i
$346$			23.3326i			1.25437i
$347$	−15.8920	+	27.5257i	−0.853126	+	1.47766i	0.0252467	+	0.999681i	$0.491963\pi$
$347$	−15.8920	+	27.5257i	−0.853126	+	1.47766i	−0.878373	+	0.477976i	$0.841370\pi$
$348$	1.15728	+	2.00446i	0.0620366	+	0.107450i
$349$	−4.41576	+	2.54944i	−0.236370	+	0.136468i	−0.613507	−	0.789689i	$-0.710242\pi$
$349$	−4.41576	+	2.54944i	−0.236370	+	0.136468i	0.377137	+	0.926157i	$0.376909\pi$
$350$	4.28272			0.228921
$351$	3.56641	+	0.529854i	0.190361	+	0.0282815i
$352$	1.11287			0.0593164
$353$	11.6546	−	6.72880i	0.620313	−	0.358138i	−0.156678	−	0.987650i	$-0.550078\pi$
$353$	11.6546	−	6.72880i	0.620313	−	0.358138i	0.776991	+	0.629512i	$0.216745\pi$
$354$	−4.75784	−	8.24082i	−0.252876	−	0.437995i
$355$	−5.97384	+	10.3470i	−0.317058	+	0.549161i
$356$		−	8.42320i		−	0.446429i
$357$	5.37541	+	3.10350i	0.284497	+	0.164254i
$358$	6.90732	+	3.98794i	0.365063	+	0.210769i
$359$		−	3.04253i		−	0.160578i	−0.996772	−	0.0802892i	$-0.974416\pi$
$359$		−	3.04253i		−	0.160578i	0.996772	−	0.0802892i	$-0.0255844\pi$
$360$	1.51771	−	2.62874i	0.0799901	−	0.138547i
$361$	25.8601	+	44.7911i	1.36106	+	2.35743i
$362$	5.58404	−	3.22395i	0.293491	−	0.169447i
$363$	−10.9379			−0.574089
$364$	2.88537	−	1.13946i	0.151235	−	0.0597238i
$365$	−9.64627			−0.504909
$366$	−5.31457	+	3.06837i	−0.277797	+	0.160386i
$367$	−6.44853	−	11.1692i	−0.336611	−	0.583027i	0.647182	−	0.762335i	$-0.275947\pi$
$367$	−6.44853	−	11.1692i	−0.336611	−	0.583027i	−0.983793	+	0.179309i	$0.942614\pi$
$368$	1.39703	−	2.41973i	0.0728254	−	0.126137i
$369$			6.43488i			0.334986i
$370$	−3.88922	−	2.24544i	−0.202191	−	0.116735i
$371$	−0.521324	−	0.300986i	−0.0270658	−	0.0156264i
$372$			7.34163i			0.380646i
$373$	2.55347	−	4.42274i	0.132214	−	0.229001i	−0.792316	−	0.610111i	$-0.791125\pi$
$373$	2.55347	−	4.42274i	0.132214	−	0.229001i	0.924530	+	0.381110i	$0.124458\pi$
$374$	0.825896	+	1.43049i	0.0427061	+	0.0739691i
$375$	−7.75816	+	4.47917i	−0.400629	+	0.231304i
$376$	32.3768			1.66971
$377$	3.56259	+	9.02130i	0.183483	+	0.464620i
$378$	−1.06752			−0.0549073
$379$	7.46265	−	4.30856i	0.383331	−	0.221316i	−0.295936	−	0.955208i	$-0.595631\pi$
$379$	7.46265	−	4.30856i	0.383331	−	0.221316i	0.679266	+	0.733892i	$0.262298\pi$
$380$	−3.59631	−	6.22899i	−0.184487	−	0.319540i
$381$	−0.535395	+	0.927332i	−0.0274291	+	0.0475087i
$382$			13.3247i			0.681750i
$383$	7.59826	+	4.38686i	0.388253	+	0.224158i	0.681403	−	0.731909i	$-0.261370\pi$
$383$	7.59826	+	4.38686i	0.388253	+	0.224158i	−0.293150	+	0.956066i	$0.594704\pi$
$384$	0.480982	+	0.277695i	0.0245450	+	0.0141711i
$385$		−	0.247806i		−	0.0126294i
$386$	3.06806	−	5.31403i	0.156160	−	0.270477i
$387$	−5.71391	−	9.89679i	−0.290455	−	0.503082i
$388$	−1.81432	+	1.04750i	−0.0921079	+	0.0531785i
$389$	28.8199			1.46123			0.730614	−	0.682791i	$-0.239234\pi$
$389$	28.8199			1.46123			0.730614	+	0.682791i	$0.239234\pi$
$390$	2.37925	−	2.99644i	0.120478	−	0.151730i
$391$	−11.2695			−0.569922
$392$	−2.64444	+	1.52677i	−0.133564	+	0.0771134i
$393$	3.39805	+	5.88559i	0.171409	+	0.296889i
$394$	−7.99320	+	13.8446i	−0.402692	+	0.697483i
$395$		−	5.60103i		−	0.281818i
$396$	0.185750	+	0.107243i	0.00933428	+	0.00538915i
$397$	−6.22008	−	3.59116i	−0.312177	−	0.180235i	0.335723	−	0.941961i	$-0.391019\pi$
$397$	−6.22008	−	3.59116i	−0.312177	−	0.180235i	−0.647900	+	0.761725i	$0.724353\pi$
$398$			2.21445i			0.111001i
$399$	−4.20477	+	7.28287i	−0.210502	+	0.364600i
$400$	3.08694	+	5.34673i	0.154347	+	0.267336i
$401$	−7.60538	+	4.39097i	−0.379795	+	0.219274i	−0.677729	−	0.735312i	$-0.737036\pi$
$401$	−7.60538	+	4.39097i	−0.379795	+	0.219274i	0.297934	+	0.954586i	$0.403702\pi$
$402$	7.07546			0.352892
$403$	−4.52115	+	30.4315i	−0.225215	+	1.51590i
$404$	4.45036			0.221414
$405$	0.860885	−	0.497032i	0.0427777	−	0.0246977i
$406$	−1.43587	−	2.48699i	−0.0712608	−	0.123427i
$407$	0.527483	−	0.913627i	0.0261464	−	0.0452868i
$408$			18.9533i			0.938327i
$409$	9.11938	+	5.26507i	0.450924	+	0.260341i	0.708220	−	0.705991i	$-0.249498\pi$
$409$	9.11938	+	5.26507i	0.450924	+	0.260341i	−0.257296	+	0.966333i	$0.582832\pi$
$410$	5.91373	+	3.41430i	0.292059	+	0.168620i
$411$		−	18.6717i		−	0.921007i
$412$	−4.89053	+	8.47065i	−0.240939	+	0.417319i
$413$	−4.45691	−	7.71959i	−0.219310	−	0.379856i
$414$	1.67853	−	0.969100i	0.0824953	−	0.0476287i
$415$	16.4858			0.809254
$416$	12.6056	+	10.0092i	0.618039	+	0.490739i
$417$	6.21476			0.304338
$418$	−1.93810	+	1.11896i	−0.0947957	+	0.0547303i
$419$	18.7428	+	32.4635i	0.915648	+	1.58595i	0.805950	+	0.591983i	$0.201655\pi$
$419$	18.7428	+	32.4635i	0.915648	+	1.58595i	0.109697	+	0.993965i	$0.465012\pi$
$420$	0.427646	−	0.740705i	0.0208670	−	0.0361427i
$421$			11.6873i			0.569602i	0.958587	+	0.284801i	$0.0919276\pi$
$421$			11.6873i			0.569602i	−0.958587	+	0.284801i	$0.908072\pi$
$422$	−20.2064	−	11.6662i	−0.983631	−	0.567900i
$423$	9.18251	+	5.30152i	0.446469	+	0.257769i
$424$		−	1.83814i		−	0.0892682i
$425$	12.4507	−	21.5653i	0.603948	−	1.04607i
$426$	6.41527	+	11.1116i	0.310821	+	0.538358i
$427$	−4.97843	+	2.87430i	−0.240923	+	0.139097i
$428$	−10.3151			−0.498600
$429$	0.703901	+	0.558917i	0.0339847	+	0.0269847i
$430$	−12.1270			−0.584818
$431$	8.16482	−	4.71396i	0.393286	−	0.227064i	−0.290297	−	0.956937i	$-0.593754\pi$
$431$	8.16482	−	4.71396i	0.393286	−	0.227064i	0.683583	+	0.729873i	$0.260421\pi$
$432$	−0.769457	−	1.33274i	−0.0370205	−	0.0641214i
$433$	−14.7784	+	25.5969i	−0.710204	+	1.23011i	0.254577	+	0.967053i	$0.418064\pi$
$433$	−14.7784	+	25.5969i	−0.710204	+	1.23011i	−0.964780	+	0.263056i	$0.915270\pi$
$434$		−	9.10896i		−	0.437244i
$435$	2.31586	+	1.33706i	0.111037	+	0.0641073i
$436$	4.69664	+	2.71161i	0.224928	+	0.129862i
$437$		−	15.2684i		−	0.730388i
$438$	−5.17954	+	8.97123i	−0.247488	+	0.428662i
$439$	1.98658	+	3.44086i	0.0948144	+	0.164223i	0.909531	−	0.415636i	$-0.136441\pi$
$439$	1.98658	+	3.44086i	0.0948144	+	0.164223i	−0.814717	+	0.579859i	$0.803108\pi$
$440$	0.655309	−	0.378343i	0.0312406	−	0.0180368i
$441$	−1.00000			−0.0476190
$442$	−3.51086	+	23.6313i	−0.166995	+	1.12403i
$443$	24.4103			1.15977			0.579885	−	0.814699i	$-0.303098\pi$
$443$	24.4103			1.15977			0.579885	+	0.814699i	$0.303098\pi$
$444$	3.15334	−	1.82058i	0.149651	−	0.0864011i
$445$	−4.86589	−	8.42796i	−0.230665	−	0.399524i
$446$	−6.54166	+	11.3305i	−0.309757	+	0.536514i
$447$			3.33988i			0.157971i
$448$	−6.79268	−	3.92175i	−0.320924	−	0.185285i
$449$	16.6491	+	9.61234i	0.785718	+	0.453634i	0.838453	−	0.544974i	$-0.183461\pi$
$449$	16.6491	+	9.61234i	0.785718	+	0.453634i	−0.0527352	+	0.998609i	$0.516794\pi$
$450$			4.28272i			0.201889i
$451$	−0.802062	+	1.38921i	−0.0377676	+	0.0654154i
$452$	−2.96302	−	5.13210i	−0.139369	−	0.241394i
$453$	7.83588	−	4.52405i	0.368162	−	0.212558i
$454$	−17.4295			−0.818009
$455$	2.22876	−	2.80691i	0.104486	−	0.131590i
$456$	−25.6788			−1.20252
$457$	20.1012	−	11.6054i	0.940295	−	0.542879i	0.0502420	−	0.998737i	$-0.484001\pi$
$457$	20.1012	−	11.6054i	0.940295	−	0.542879i	0.890053	+	0.455858i	$0.150667\pi$
$458$	−2.07238	−	3.58947i	−0.0968361	−	0.167725i
$459$	−3.10350	+	5.37541i	−0.144859	+	0.250903i
$460$			1.55288i			0.0724033i
$461$	11.7802	+	6.80131i	0.548660	+	0.316769i	0.748581	−	0.663043i	$-0.230735\pi$
$461$	11.7802	+	6.80131i	0.548660	+	0.316769i	−0.199922	+	0.979812i	$0.564069\pi$
$462$	−0.230465	−	0.133059i	−0.0107222	−	0.00619046i
$463$		−	13.6012i		−	0.632101i	−0.948742	−	0.316050i	$-0.897643\pi$
$463$		−	13.6012i		−	0.632101i	0.948742	−	0.316050i	$-0.102357\pi$
$464$	2.06991	−	3.58519i	0.0960932	−	0.166438i
$465$	4.24109	+	7.34578i	0.196676	+	0.340652i
$466$	−17.2195	+	9.94168i	−0.797678	+	0.460539i
$467$	9.00148			0.416539			0.208269	−	0.978072i	$-0.433217\pi$
$467$	9.00148			0.416539			0.208269	+	0.978072i	$0.433217\pi$
$468$	1.13946	+	2.88537i	0.0526714	+	0.133376i
$469$	6.62794			0.306050
$470$	9.74434	−	5.62590i	0.449473	−	0.259503i
$471$	−6.03476	−	10.4525i	−0.278067	−	0.481626i
$472$	13.6093	−	23.5720i	0.626420	−	1.08499i
$473$		−	2.84880i		−	0.130988i
$474$	−5.20907	−	3.00746i	−0.239261	−	0.138137i
$475$	29.2177	+	16.8688i	1.34060	+	0.773995i
$476$			5.34049i			0.244781i
$477$	0.300986	−	0.521324i	0.0137812	−	0.0238698i
$478$	−9.21151	−	15.9548i	−0.421325	−	0.729756i
$479$	20.6858	−	11.9429i	0.945157	−	0.545687i	0.0535838	−	0.998563i	$-0.482936\pi$
$479$	20.6858	−	11.9429i	0.945157	−	0.545687i	0.891573	+	0.452877i	$0.149602\pi$
$480$	4.43775			0.202555
$481$	14.1920	−	5.60452i	0.647098	−	0.255544i
$482$	16.3527			0.744845
$483$	1.57236	−	0.907804i	0.0715450	−	0.0413065i
$484$	−4.70546	−	8.15010i	−0.213885	−	0.370459i
$485$	−1.21023	+	2.09617i	−0.0549536	+	0.0951824i
$486$		−	1.06752i		−	0.0484237i
$487$	−17.8192	−	10.2879i	−0.807463	−	0.466189i	0.0386111	−	0.999254i	$-0.487707\pi$
$487$	−17.8192	−	10.2879i	−0.807463	−	0.466189i	−0.846074	+	0.533065i	$0.821040\pi$
$488$	−15.2018	−	8.77677i	−0.688153	−	0.397306i
$489$		−	1.89811i		−	0.0858355i
$490$	−0.530592	+	0.919013i	−0.0239697	+	0.0415168i
$491$	7.97149	+	13.8070i	0.359748	+	0.623103i	0.987919	−	0.154973i	$-0.0495292\pi$
$491$	7.97149	+	13.8070i	0.359748	+	0.623103i	−0.628170	+	0.778076i	$0.716196\pi$
$492$	−4.79480	+	2.76828i	−0.216166	+	0.124804i
$493$	−16.6974			−0.752012
$494$	−32.0169	−	4.75669i	−1.44051	−	0.214014i
$495$	0.247806			0.0111381
$496$	11.3720	−	6.56564i	0.510619	−	0.294806i
$497$	6.00951	+	10.4088i	0.269563	+	0.466897i
$498$	8.85198	−	15.3321i	0.396667	−	0.687047i
$499$		−	10.3975i		−	0.465454i	−0.972542	−	0.232727i	$-0.925235\pi$
$499$		−	10.3975i		−	0.465454i	0.972542	−	0.232727i	$-0.0747649\pi$
$500$	−6.67511	−	3.85388i	−0.298520	−	0.172351i
$501$	11.8910	+	6.86525i	0.531249	+	0.306717i
$502$		−	8.36960i		−	0.373553i
$503$	11.8034	−	20.4440i	0.526286	−	0.911553i	−0.473245	−	0.880931i	$-0.656918\pi$
$503$	11.8034	−	20.4440i	0.526286	−	0.911553i	0.999531	−	0.0306227i	$-0.00974903\pi$
$504$	−1.52677	−	2.64444i	−0.0680076	−	0.117793i
$505$	4.45287	−	2.57087i	0.198150	−	0.114402i
$506$	0.483166			0.0214793
$507$	2.94624	+	12.6617i	0.130847	+	0.562328i
$508$	−0.921308			−0.0408764
$509$	−32.5931	+	18.8177i	−1.44467	+	0.834078i	−0.998156	−	0.0607005i	$-0.980667\pi$
$509$	−32.5931	+	18.8177i	−1.44467	+	0.834078i	−0.446510	+	0.894779i	$0.647333\pi$
$510$	3.29338	+	5.70431i	0.145833	+	0.252591i
$511$	−4.85193	+	8.40380i	−0.214637	+	0.371762i
$512$		−	16.2684i		−	0.718967i
$513$	−7.28287	−	4.20477i	−0.321547	−	0.185645i
$514$	−6.36184	−	3.67301i	−0.280609	−	0.162009i
$515$			11.3006i			0.497963i
$516$	4.91625	−	8.51519i	0.216426	−	0.374860i
$517$	1.32160	+	2.28907i	0.0581237	+	0.100673i
$518$	−3.91244	+	2.25885i	−0.171903	+	0.0992481i
$519$	−21.8568			−0.959408
$520$	10.8255	+	1.60833i	0.474730	+	0.0705298i
$521$	12.3849			0.542592			0.271296	−	0.962496i	$-0.412548\pi$
$521$	12.3849			0.542592			0.271296	+	0.962496i	$0.412548\pi$
$522$	2.48699	−	1.43587i	0.108853	−	0.0628461i
$523$	−9.17568	−	15.8927i	−0.401225	−	0.694941i	0.592649	−	0.805460i	$-0.298082\pi$
$523$	−9.17568	−	15.8927i	−0.401225	−	0.694941i	−0.993874	+	0.110519i	$0.964749\pi$
$524$	−2.92368	+	5.06396i	−0.127721	+	0.221220i
$525$			4.01184i			0.175091i
$526$	−22.5534	−	13.0212i	−0.983375	−	0.567752i
$527$	−45.8674	−	26.4816i	−1.99802	−	1.15356i
$528$		−	0.383630i		−	0.0166953i
$529$	9.85178	−	17.0638i	0.428338	−	0.741904i
$530$	−0.319402	−	0.553221i	−0.0138739	−	0.0240304i
$531$	7.71959	−	4.45691i	0.335002	−	0.193413i
$532$	−7.23556			−0.313701
$533$	−21.5795	+	8.52194i	−0.934713	+	0.369126i
$534$	−10.4509			−0.452255
$535$	−10.3209	+	5.95880i	−0.446213	+	0.257621i
$536$	10.1193	+	17.5272i	0.437088	+	0.757059i
$537$	−3.73571	+	6.47043i	−0.161208	+	0.279220i
$538$			15.9383i			0.687147i
$539$	−0.215888	−	0.124643i	−0.00929895	−	0.00536875i
$540$	0.740705	+	0.427646i	0.0318749	+	0.0184030i
$541$		−	14.4935i		−	0.623126i	−0.950225	−	0.311563i	$-0.899147\pi$
$541$		−	14.4935i		−	0.623126i	0.950225	−	0.311563i	$-0.100853\pi$
$542$	−0.959381	+	1.66170i	−0.0412090	+	0.0713760i
$543$	3.02003	+	5.23085i	0.129602	+	0.224477i
$544$	−23.9972	+	13.8548i	−1.02887	+	0.594019i
$545$	6.26573			0.268394
$546$	−1.41376	−	3.57996i	−0.0605032	−	0.153208i
$547$	4.86021			0.207808			0.103904	−	0.994587i	$-0.466867\pi$
$547$	4.86021			0.207808			0.103904	+	0.994587i	$0.466867\pi$
$548$	13.9128	−	8.03256i	0.594325	−	0.343134i
$549$	−2.87430	−	4.97843i	−0.122672	−	0.212474i
$550$	−0.533811	+	0.924587i	−0.0227618	+	0.0394245i
$551$		−	22.6224i		−	0.963748i
$552$	4.80127	+	2.77201i	0.204356	+	0.117985i
$553$	−4.87960	−	2.81724i	−0.207502	−	0.119801i
$554$		−	13.1507i		−	0.558718i
$555$	2.10342	−	3.64322i	0.0892851	−	0.154646i
$556$	2.67359	+	4.63079i	0.113385	+	0.196389i
$557$	5.20395	−	3.00450i	0.220498	−	0.127305i	−0.385683	−	0.922632i	$-0.626034\pi$
$557$	5.20395	−	3.00450i	0.220498	−	0.127305i	0.606181	+	0.795327i	$0.292701\pi$
$558$	9.10896			0.385613
$559$	25.6220	−	32.2684i	1.08369	−	1.36481i
$560$	−1.52978			−0.0646450
$561$	−1.34001	+	0.773658i	−0.0565755	+	0.0326639i
$562$	9.23967	+	16.0036i	0.389752	+	0.675070i
$563$	21.2160	−	36.7472i	0.894149	−	1.54871i	0.0592944	−	0.998241i	$-0.481115\pi$
$563$	21.2160	−	36.7472i	0.894149	−	1.54871i	0.834854	−	0.550471i	$-0.185552\pi$
$564$			9.12286i			0.384142i
$565$	−5.92939	−	3.42334i	−0.249451	−	0.144021i
$566$	−10.6887	−	6.17113i	−0.449280	−	0.259392i
$567$		−	1.00000i		−	0.0419961i
$568$	−18.3502	+	31.7836i	−0.769959	+	1.33361i
$569$	11.0476	+	19.1349i	0.463138	+	0.802178i	0.999115	−	0.0420542i	$-0.0133902\pi$
$569$	11.0476	+	19.1349i	0.463138	+	0.802178i	−0.535978	+	0.844232i	$0.680057\pi$
$570$	−7.72847	+	4.46204i	−0.323710	+	0.186894i
$571$	−29.0504			−1.21572			−0.607861	−	0.794043i	$-0.707972\pi$
$571$	−29.0504			−1.21572			−0.607861	+	0.794043i	$0.707972\pi$
$572$	−0.113646	+	0.764942i	−0.00475178	+	0.0319838i
$573$	−12.4819			−0.521439
$574$	5.94904	−	3.43468i	0.248308	−	0.143361i
$575$	−3.64196	−	6.30806i	−0.151880	−	0.263064i
$576$	3.92175	−	6.79268i	0.163406	−	0.283028i
$577$		−	29.4874i		−	1.22758i	−0.789471	−	0.613788i	$-0.789645\pi$
$577$		−	29.4874i		−	1.22758i	0.789471	−	0.613788i	$-0.210355\pi$
$578$	−19.9015	−	11.4901i	−0.827793	−	0.477926i
$579$	4.97792	+	2.87400i	0.206875	+	0.119439i
$580$			2.30082i			0.0955362i
$581$	8.29209	−	14.3623i	0.344014	−	0.595850i
$582$	1.29966	+	2.25107i	0.0538725	+	0.0933099i
$583$	0.129959	−	0.0750316i	0.00538233	−	0.00310749i
$584$	−29.6311			−1.22614
$585$	2.80691	+	2.22876i	0.116052	+	0.0921480i
$586$	−2.82023			−0.116503
$587$	−33.4815	+	19.3305i	−1.38193	+	0.797857i	−0.992388	−	0.123152i	$-0.960700\pi$
$587$	−33.4815	+	19.3305i	−1.38193	+	0.797857i	−0.389541	+	0.921009i	$0.627366\pi$
$588$	−0.430200	−	0.745128i	−0.0177411	−	0.0307285i
$589$	35.8785	−	62.1434i	1.47835	−	2.56058i
$590$		−	9.45921i		−	0.389429i
$591$	−12.9690	−	7.48763i	−0.533472	−	0.308000i
$592$	−5.64009	−	3.25631i	−0.231806	−	0.133833i
$593$		−	34.9446i		−	1.43500i	−0.696556	−	0.717502i	$-0.745285\pi$
$593$		−	34.9446i		−	1.43500i	0.696556	−	0.717502i	$-0.254715\pi$
$594$	0.133059	−	0.230465i	0.00545947	−	0.00945609i
$595$	3.08508	+	5.34351i	0.126476	+	0.219062i
$596$	−2.48864	+	1.43682i	−0.101939	+	0.0588543i
$597$	−2.07439			−0.0848991
$598$	5.47284	+	4.34558i	0.223801	+	0.177704i
$599$	15.4209			0.630080			0.315040	−	0.949078i	$-0.397982\pi$
$599$	15.4209			0.630080			0.315040	+	0.949078i	$0.397982\pi$
$600$	−10.6091	+	6.12514i	−0.433113	+	0.250058i
$601$	6.34569	+	10.9911i	0.258846	+	0.448334i	0.965933	−	0.258792i	$-0.0833245\pi$
$601$	6.34569	+	10.9911i	0.258846	+	0.448334i	−0.707087	+	0.707126i	$0.749991\pi$
$602$	−6.09972	+	10.5650i	−0.248606	+	0.430598i
$603$			6.62794i			0.269910i
$604$	6.74199	+	3.89249i	0.274328	+	0.158383i
$605$	−9.41624	−	5.43647i	−0.382825	−	0.221024i
$606$		−	5.52168i		−	0.224303i
$607$	−9.58410	+	16.6002i	−0.389007	+	0.673780i	−0.992316	−	0.123728i	$-0.960515\pi$
$607$	−9.58410	+	16.6002i	−0.389007	+	0.673780i	0.603309	+	0.797507i	$0.293848\pi$
$608$	−18.7711	−	32.5125i	−0.761270	−	1.31856i
$609$	2.32969	−	1.34505i	0.0944038	−	0.0545040i
$610$	−6.10032			−0.246995
$611$	−5.61807	+	37.8148i	−0.227283	+	1.52982i
$612$	−5.34049			−0.215877
$613$	15.6414	−	9.03055i	0.631749	−	0.364740i	−0.149680	−	0.988734i	$-0.547824\pi$
$613$	15.6414	−	9.03055i	0.631749	−	0.364740i	0.781429	+	0.623994i	$0.214491\pi$
$614$	10.0999	+	17.4935i	0.407598	+	0.705980i
$615$	−3.19834	+	5.53969i	−0.128970	+	0.223382i
$616$		−	0.761203i		−	0.0306698i
$617$	−1.19682	−	0.690982i	−0.0481820	−	0.0278179i	0.475715	−	0.879599i	$-0.342189\pi$
$617$	−1.19682	−	0.690982i	−0.0481820	−	0.0278179i	−0.523898	+	0.851781i	$0.675523\pi$
$618$	10.5098	+	6.06782i	0.422765	+	0.244083i
$619$			17.0392i			0.684863i	0.939543	+	0.342432i	$0.111251\pi$
$619$			17.0392i			0.684863i	−0.939543	+	0.342432i	$0.888749\pi$
$620$	−3.64903	+	6.32030i	−0.146549	+	0.253830i
$621$	0.907804	+	1.57236i	0.0364289	+	0.0630968i
$622$	−15.6702	+	9.04718i	−0.628317	+	0.362759i
$623$	−9.78988			−0.392223
$624$	3.45035	−	4.34539i	0.138125	−	0.173955i
$625$	11.1540			0.446160
$626$	−12.9628	+	7.48407i	−0.518097	+	0.299124i
$627$	−1.04819	−	1.81552i	−0.0418606	−	0.0725048i
$628$	5.19230	−	8.99333i	0.207195	−	0.358873i
$629$			26.2677i			1.04736i
$630$	−0.919013	−	0.530592i	−0.0366144	−	0.0211393i
$631$	40.8243	+	23.5699i	1.62519	+	0.938303i	0.985501	+	0.169669i	$0.0542698\pi$
$631$	40.8243	+	23.5699i	1.62519	+	0.938303i	0.639688	+	0.768635i	$0.279064\pi$
$632$		−	17.2051i		−	0.684381i
$633$	10.9283	−	18.9283i	0.434360	−	0.752333i
$634$	−8.76733	−	15.1855i	−0.348195	−	0.603092i
$635$	−0.921828	+	0.532218i	−0.0365816	+	0.0211204i
$636$	0.517937			0.0205375
$637$	−1.32434	−	3.35353i	−0.0524721	−	0.132872i
$638$	0.715882			0.0283420
$639$	−10.4088	+	6.00951i	−0.411765	+	0.237732i
$640$	0.276047	+	0.478127i	0.0109117	+	0.0188996i
$641$	−15.6362	+	27.0826i	−0.617592	+	1.06970i	0.372332	+	0.928100i	$0.378558\pi$
$641$	−15.6362	+	27.0826i	−0.617592	+	1.06970i	−0.989924	+	0.141601i	$0.954775\pi$
$642$			12.7982i			0.505106i
$643$	13.1376	+	7.58497i	0.518095	+	0.299122i	0.736155	−	0.676813i	$-0.236640\pi$
$643$	13.1376	+	7.58497i	0.518095	+	0.299122i	−0.218060	+	0.975935i	$0.569973\pi$
$644$	1.35286	+	0.781074i	0.0533102	+	0.0307786i
$645$		−	11.3600i		−	0.447299i
$646$	27.8612	−	48.2570i	1.09618	−	1.89865i
$647$	3.09449	+	5.35981i	0.121657	+	0.210716i	0.920421	−	0.390928i	$-0.127846\pi$
$647$	3.09449	+	5.35981i	0.121657	+	0.210716i	−0.798764	+	0.601644i	$0.794513\pi$
$648$	2.64444	−	1.52677i	0.103883	−	0.0599771i
$649$	2.22209			0.0872246
$650$	−14.3622	+	5.67176i	−0.563332	+	0.222465i
$651$	8.53282			0.334428
$652$	1.41433	−	0.816567i	0.0553896	−	0.0319792i
$653$	13.8477	+	23.9849i	0.541901	+	0.938600i	0.998795	+	0.0490789i	$0.0156286\pi$
$653$	13.8477	+	23.9849i	0.541901	+	0.938600i	−0.456894	+	0.889521i	$0.651038\pi$
$654$	3.36437	−	5.82725i	0.131557	−	0.227864i
$655$			6.75576i			0.263969i
$656$	8.57601	+	4.95136i	0.334837	+	0.193318i
$657$	−8.40380	−	4.85193i	−0.327863	−	0.189292i
$658$		−	11.3190i		−	0.441260i
$659$	−12.7045	+	22.0048i	−0.494896	+	0.857185i	−0.999983	−	0.00588335i	$-0.998127\pi$
$659$	−12.7045	+	22.0048i	−0.494896	+	0.857185i	0.505086	+	0.863069i	$0.331461\pi$
$660$	0.106606	+	0.184647i	0.00414964	+	0.00718739i
$661$	6.35256	−	3.66765i	0.247086	−	0.142655i	−0.371343	−	0.928496i	$-0.621103\pi$
$661$	6.35256	−	3.66765i	0.247086	−	0.142655i	0.618429	+	0.785841i	$0.287769\pi$
$662$	4.73648			0.184088
$663$	−22.1367	−	3.28880i	−0.859716	−	0.127727i
$664$	50.6404			1.96523
$665$	−7.23964	+	4.17981i	−0.280741	+	0.162086i
$666$	−2.25885	−	3.91244i	−0.0875286	−	0.151604i
$667$	−2.44208	+	4.22980i	−0.0945577	+	0.163779i
$668$			11.8137i			0.457086i
$669$	−10.6138	−	6.12790i	−0.410355	−	0.236918i
$670$	6.09116	+	3.51673i	0.235322	+	0.135863i
$671$		−	1.43304i		−	0.0553220i
$672$	2.23212	−	3.86615i	0.0861061	−	0.149140i
$673$	−2.03837	−	3.53055i	−0.0785732	−	0.136093i	0.824061	−	0.566501i	$-0.191703\pi$
$673$	−2.03837	−	3.53055i	−0.0785732	−	0.136093i	−0.902635	+	0.430408i	$0.858370\pi$
$674$	−16.7105	+	9.64781i	−0.643665	+	0.371620i
$675$	−4.01184			−0.154416
$676$	−8.16714	+	7.64240i	−0.314121	+	0.293938i
$677$	7.12994			0.274026			0.137013	−	0.990569i	$-0.456250\pi$
$677$	7.12994			0.274026			0.137013	+	0.990569i	$0.456250\pi$
$678$	−6.36754	+	3.67630i	−0.244544	+	0.141188i
$679$	1.21745	+	2.10869i	0.0467216	+	0.0809241i
$680$	−9.42039	+	16.3166i	−0.361255	+	0.625713i
$681$		−	16.3271i		−	0.625657i
$682$	1.96651	+	1.13537i	0.0753017	+	0.0434755i
$683$	26.6854	+	15.4068i	1.02109	+	0.589525i	0.914419	−	0.404770i	$-0.132648\pi$
$683$	26.6854	+	15.4068i	1.02109	+	0.589525i	0.106668	+	0.994295i	$0.465982\pi$
$684$		−	7.23556i		−	0.276658i
$685$	9.28043	−	16.0742i	0.354587	−	0.614163i
$686$	0.533760	+	0.924500i	0.0203791	+	0.0352976i
$687$	3.36244	−	1.94131i	0.128285	−	0.0740654i
$688$	−17.5864			−0.670477
$689$	2.14688	+	0.318958i	0.0817896	+	0.0121513i
$690$	1.92670			0.0733481
$691$	−3.76220	+	2.17211i	−0.143121	+	0.0826309i	−0.569851	−	0.821748i	$-0.692999\pi$
$691$	−3.76220	+	2.17211i	−0.143121	+	0.0826309i	0.426730	+	0.904379i	$0.359666\pi$
$692$	−9.40280	−	16.2861i	−0.357441	−	0.619106i
$693$	0.124643	−	0.215888i	0.00473479	−	0.00820090i
$694$			33.9300i			1.28797i
$695$	5.35019	+	3.08894i	0.202944	+	0.117170i
$696$	7.11379	+	4.10715i	0.269647	+	0.155681i
$697$		−	39.9412i		−	1.51288i
$698$	−2.72158	+	4.71391i	−0.103013	+	0.178424i
$699$	−9.31287	−	16.1304i	−0.352245	−	0.610106i
$700$	−2.98933	+	1.72589i	−0.112986	+	0.0652325i
$701$	−28.8256			−1.08873			−0.544365	−	0.838849i	$-0.683229\pi$
$701$	−28.8256			−1.08873			−0.544365	+	0.838849i	$0.683229\pi$
$702$	3.57996	−	1.41376i	0.135117	−	0.0533588i
$703$	−35.5887			−1.34225
$704$	1.69332	−	0.977638i	0.0638193	−	0.0368461i
$705$	5.27006	+	9.12801i	0.198482	+	0.343781i
$706$	7.18314	−	12.4416i	0.270341	−	0.468244i
$707$		−	5.17244i		−	0.194529i
$708$	6.64193	+	3.83472i	0.249619	+	0.144118i
$709$	−3.96199	−	2.28745i	−0.148796	−	0.0859072i	0.423754	−	0.905777i	$-0.360712\pi$
$709$	−3.96199	−	2.28745i	−0.148796	−	0.0859072i	−0.572549	+	0.819870i	$0.694046\pi$
$710$			12.7544i			0.478664i
$711$	2.81724	−	4.87960i	0.105655	−	0.182999i
$712$	−14.9469	−	25.8887i	−0.560158	−	0.970221i
$713$	−13.4167	+	7.74613i	−0.502459	+	0.290095i
$714$	6.62609			0.247975
$715$	0.328179	+	0.831025i	0.0122732	+	0.0310786i
$716$	−6.42840			−0.240240
$717$	14.9457	−	8.62888i	0.558156	−	0.322252i
$718$	−1.62398	−	2.81282i	−0.0606064	−	0.104973i
$719$	9.72262	−	16.8401i	0.362593	−	0.628029i	−0.625794	−	0.779988i	$-0.715225\pi$
$719$	9.72262	−	16.8401i	0.362593	−	0.628029i	0.988387	+	0.151959i	$0.0485583\pi$
$720$		−	1.52978i		−	0.0570116i
$721$	9.84503	+	5.68403i	0.366648	+	0.211684i
$722$	47.8154	+	27.6062i	1.77951	+	1.02740i
$723$			15.3184i			0.569697i
$724$	−2.59843	+	4.50062i	−0.0965701	+	0.167264i
$725$	−5.39611	−	9.34633i	−0.200406	−	0.347114i
$726$	−10.1120	+	5.83819i	−0.375293	+	0.216676i
$727$	−30.2589			−1.12224			−0.561120	−	0.827734i	$-0.689630\pi$
$727$	−30.2589			−1.12224			−0.561120	+	0.827734i	$0.689630\pi$
$728$	6.84624	−	8.62218i	0.253739	−	0.319559i
$729$	1.00000			0.0370370
$730$	−8.91798	+	5.14880i	−0.330069	+	0.190566i
$731$	35.4662	+	61.4293i	1.31177	+	2.27204i
$732$	2.47304	−	4.28344i	0.0914063	−	0.158320i
$733$			31.9678i			1.18076i	0.807126	+	0.590379i	$0.201022\pi$
$733$			31.9678i			1.18076i	−0.807126	+	0.590379i	$0.798978\pi$
$734$	−11.9233	−	6.88394i	−0.440098	−	0.254091i
$735$	−0.860885	−	0.497032i	−0.0317542	−	0.0183333i
$736$			8.10533i			0.298766i
$737$	−0.826125	+	1.43089i	−0.0304307	+	0.0527076i
$738$	3.43468	+	5.94904i	0.126432	+	0.218987i
$739$	20.8353	−	12.0293i	0.766439	−	0.442504i	−0.0651639	−	0.997875i	$-0.520757\pi$
$739$	20.8353	−	12.0293i	0.766439	−	0.442504i	0.831603	+	0.555371i	$0.187424\pi$
$740$	3.61956			0.133058
$741$	4.45583	−	29.9918i	0.163689	−	1.10178i
$742$	−0.642618			−0.0235913
$743$	18.0539	−	10.4234i	0.662332	−	0.382398i	−0.130833	−	0.991404i	$-0.541765\pi$
$743$	18.0539	−	10.4234i	0.662332	−	0.382398i	0.793165	+	0.609007i	$0.208432\pi$
$744$	13.0276	+	22.5645i	0.477616	+	0.827256i
$745$	−1.66003	+	2.87526i	−0.0608188	+	0.105341i
$746$		−	5.45177i		−	0.199603i
$747$	14.3623	+	8.29209i	0.525490	+	0.303392i
$748$	−1.15295	−	0.665655i	−0.0421559	−	0.0243387i
$749$			11.9888i			0.438059i
$750$	−4.78161	+	8.28199i	−0.174600	+	0.302416i
$751$	16.3766	+	28.3652i	0.597592	+	1.03506i	0.993175	+	0.116630i	$0.0372091\pi$
$751$	16.3766	+	28.3652i	0.597592	+	1.03506i	−0.395583	+	0.918430i	$0.629458\pi$
$752$	14.1311	−	8.15859i	0.515308	−	0.297513i
$753$	7.84022			0.285714
$754$	8.10882	+	6.43862i	0.295306	+	0.234481i
$755$	8.99439			0.327339
$756$	0.745128	−	0.430200i	0.0271000	−	0.0156462i
$757$	17.6920	+	30.6435i	0.643028	+	1.11376i	0.984753	+	0.173958i	$0.0556556\pi$
$757$	17.6920	+	30.6435i	0.643028	+	1.11376i	−0.341725	+	0.939800i	$0.611011\pi$
$758$	4.59948	−	7.96653i	0.167061	−	0.289358i
$759$			0.452606i			0.0164285i
$760$	−22.1065	−	12.7632i	−0.801888	−	0.462970i
$761$	−11.8090	−	6.81792i	−0.428075	−	0.247149i	0.270451	−	0.962734i	$-0.412827\pi$
$761$	−11.8090	−	6.81792i	−0.428075	−	0.247149i	−0.698526	+	0.715584i	$0.746160\pi$
$762$			1.14309i			0.0414098i
$763$	3.15157	−	5.45868i	0.114094	−	0.197617i
$764$	−5.36971	−	9.30060i	−0.194269	−	0.336484i
$765$	−5.34351	+	3.08508i	−0.193195	+	0.111541i
$766$	9.36612			0.338412
$767$	25.1697	+	19.9854i	0.908825	+	0.721631i
$768$	16.2799			0.587450
$769$	−18.1442	+	10.4756i	−0.654298	+	0.377759i	−0.790101	−	0.612977i	$-0.789972\pi$
$769$	−18.1442	+	10.4756i	−0.654298	+	0.377759i	0.135803	+	0.990736i	$0.456639\pi$
$770$	−0.132269	−	0.229097i	−0.00476665	−	0.00825608i
$771$	3.44069	−	5.95945i	0.123913	−	0.214624i
$772$			4.94558i			0.177995i
$773$	−21.3133	−	12.3052i	−0.766586	−	0.442589i	0.0650693	−	0.997881i	$-0.479273\pi$
$773$	−21.3133	−	12.3052i	−0.766586	−	0.442589i	−0.831655	+	0.555292i	$0.812606\pi$
$774$	−10.5650	−	6.09972i	−0.379752	−	0.219250i
$775$		−	34.2323i		−	1.22966i
$776$	−3.71754	+	6.43896i	−0.133452	+	0.231145i
$777$	−2.11598	−	3.66498i	−0.0759102	−	0.131480i
$778$	26.6440	−	15.3829i	0.955234	−	0.551505i
$779$	54.1143			1.93885
$780$	−0.453181	+	3.05032i	−0.0162265	+	0.109219i
$781$	−2.99617			−0.107211
$782$	−10.4186	+	6.01520i	−0.372569	+	0.215103i
$783$	1.34505	+	2.32969i	0.0480680	+	0.0832563i
$784$	−0.769457	+	1.33274i	−0.0274806	+	0.0475978i
$785$		−	11.9979i		−	0.428223i
$786$	6.28299	+	3.62749i	0.224107	+	0.129388i
$787$	−8.75369	−	5.05395i	−0.312035	−	0.180154i	0.335802	−	0.941933i	$-0.390993\pi$
$787$	−8.75369	−	5.05395i	−0.312035	−	0.180154i	−0.647837	+	0.761779i	$0.724326\pi$
$788$		−	12.8847i		−	0.458999i
$789$	12.1976	−	21.1269i	0.434247	−	0.752138i
$790$	−2.98961	−	5.17815i	−0.106365	−	0.184230i
$791$	−5.96479	+	3.44378i	−0.212084	+	0.122447i
$792$	0.761203			0.0270482
$793$	12.8887	−	16.2321i	0.457693	−	0.576420i
$794$	−7.66728			−0.272102
$795$	0.518229	−	0.299200i	0.0183797	−	0.0106115i
$796$	−0.892401	−	1.54568i	−0.0316303	−	0.0547853i
$797$	−5.76790	+	9.99030i	−0.204310	+	0.353875i	−0.949913	−	0.312516i	$-0.898828\pi$
$797$	−5.76790	+	9.99030i	−0.204310	+	0.353875i	0.745603	+	0.666390i	$0.232162\pi$
$798$			8.97735i			0.317795i
$799$	−56.9958	−	32.9065i	−2.01637	−	1.16415i
$800$	−15.5104	−	8.95492i	−0.548374	−	0.316604i
$801$		−	9.78988i		−	0.345908i
$802$	−4.68745	+	8.11890i	−0.165520	+	0.286688i
$803$	−1.20952	−	2.09495i	−0.0426830	−	0.0739291i
$804$	−4.93866	+	2.85134i	−0.174173	+	0.100559i
$805$	1.80483			0.0636120
$806$	12.0633	+	30.5471i	0.424913	+	1.07598i
$807$	−14.9302			−0.525566
$808$	13.6782	−	7.89711i	0.481197	−	0.277819i
$809$	−13.4958	−	23.3754i	−0.474488	−	0.821837i	0.525085	−	0.851050i	$-0.324033\pi$
$809$	−13.4958	−	23.3754i	−0.474488	−	0.821837i	−0.999573	+	0.0292125i	$0.990700\pi$
$810$	0.530592	−	0.919013i	0.0186431	−	0.0322908i
$811$		−	28.7441i		−	1.00934i	−0.863311	−	0.504672i	$-0.831614\pi$
$811$		−	28.7441i		−	1.00934i	0.863311	−	0.504672i	$-0.168386\pi$
$812$	2.00446	+	1.15728i	0.0703429	+	0.0406125i
$813$	−1.55659	−	0.898700i	−0.0545922	−	0.0315188i
$814$		−	1.12620i		−	0.0394732i
$815$	0.943422	−	1.63406i	0.0330466	−	0.0572385i
$816$	4.77601	+	8.27230i	0.167194	+	0.289588i
$817$	−83.2274	+	48.0513i	−2.91176	+	1.68110i
$818$	11.2412			0.393038
$819$	3.35353	−	1.32434i	0.117182	−	0.0462760i
$820$	−5.50370			−0.192198
$821$	−25.7490	+	14.8662i	−0.898646	+	0.518834i	−0.876761	−	0.480927i	$-0.840300\pi$
$821$	−25.7490	+	14.8662i	−0.898646	+	0.518834i	−0.0218854	+	0.999760i	$0.506967\pi$
$822$	−9.96621	−	17.2620i	−0.347611	−	0.602081i
$823$	−23.8770	+	41.3561i	−0.832298	+	1.44158i	0.0639128	+	0.997955i	$0.479642\pi$
$823$	−23.8770	+	41.3561i	−0.832298	+	1.44158i	−0.896211	+	0.443628i	$0.853691\pi$
$824$			34.7128i			1.20928i
$825$	−0.866107	−	0.500047i	−0.0301540	−	0.0174094i
$826$	−8.24082	−	4.75784i	−0.286735	−	0.165546i
$827$			41.5782i			1.44581i	0.690945	+	0.722907i	$0.257195\pi$
$827$			41.5782i			1.44581i	−0.690945	+	0.722907i	$0.742805\pi$
$828$	−0.781074	+	1.35286i	−0.0271442	+	0.0470152i
$829$	28.4575	+	49.2899i	0.988371	+	1.71191i	0.625876	+	0.779922i	$0.284741\pi$
$829$	28.4575	+	49.2899i	0.988371	+	1.71191i	0.362494	+	0.931986i	$0.381925\pi$
$830$	15.2411	−	8.79944i	0.529026	−	0.305433i
$831$	12.3189			0.427337
$832$	27.9731	+	4.15592i	0.969794	+	0.144080i
$833$	6.20699			0.215060
$834$	5.74555	−	3.31719i	0.198952	−	0.114865i
$835$	6.82450	+	11.8204i	0.236172	+	0.409061i
$836$	0.901861	−	1.56207i	0.0311915	−	0.0540253i
$837$			8.53282i			0.294937i
$838$	34.6555	+	20.0084i	1.19715	+	0.691178i
$839$	−7.49855	−	4.32929i	−0.258879	−	0.149464i	0.364944	−	0.931029i	$-0.381088\pi$
$839$	−7.49855	−	4.32929i	−0.258879	−	0.149464i	−0.623823	+	0.781566i	$0.714421\pi$
$840$		−	3.03541i		−	0.104732i
$841$	10.8817	−	18.8477i	0.375231	−	0.649919i
$842$	6.23820	+	10.8049i	0.214982	+	0.372361i
$843$	−14.9913	+	8.65526i	−0.516329	+	0.298103i
$844$	18.8054			0.647307
$845$	−3.75692	+	12.3647i	−0.129242	+	0.425358i
$846$	11.3190			0.389154
$847$	−9.47246	+	5.46893i	−0.325478	+	0.187915i
$848$	−0.463192	−	0.802272i	−0.0159061	−	0.0275501i
$849$	5.78080	−	10.0126i	0.198397	−	0.343633i
$850$		−	26.5828i		−	0.911782i
$851$	6.65417	+	3.84178i	0.228102	+	0.131695i
$852$	−8.95570	−	5.17058i	−0.306817	−	0.177141i
$853$		−	46.7390i		−	1.60031i	−0.599790	−	0.800157i	$-0.704749\pi$
$853$		−	46.7390i		−	1.60031i	0.599790	−	0.800157i	$-0.295251\pi$
$854$	−3.06837	+	5.31457i	−0.104997	+	0.181861i
$855$	−4.17981	−	7.23964i	−0.142947	−	0.247591i
$856$	−31.7035	+	18.3040i	−1.08360	+	0.625619i
$857$	−49.1020			−1.67729			−0.838645	−	0.544678i	$-0.816652\pi$
$857$	−49.1020			−1.67729			−0.838645	+	0.544678i	$0.816652\pi$
$858$	0.949084	+	0.141004i	0.0324012	+	0.00481379i
$859$	45.8208			1.56338			0.781692	−	0.623665i	$-0.214357\pi$
$859$	45.8208			1.56338			0.781692	+	0.623665i	$0.214357\pi$
$860$	8.46465	−	4.88707i	0.288642	−	0.166648i
$861$	3.21744	+	5.57277i	0.109650	+	0.189919i
$862$	5.03225	−	8.71612i	0.171399	−	0.296872i
$863$			23.9377i			0.814849i	0.913239	+	0.407425i	$0.133573\pi$
$863$			23.9377i			0.814849i	−0.913239	+	0.407425i	$0.866427\pi$
$864$	3.86615	+	2.23212i	0.131529	+	0.0759384i
$865$	−18.8162	−	10.8635i	−0.639771	−	0.369372i
$866$			31.5525i			1.07220i
$867$	10.7634	−	18.6427i	0.365543	−	0.633140i
$868$	3.67082	+	6.35804i	0.124596	+	0.215806i
$869$	1.21641	−	0.702297i	0.0412640	−	0.0238238i
$870$	2.85469			0.0967829
$871$	−22.2270	+	8.77761i	−0.753132	+	0.297418i
$872$	19.2469			0.651781
$873$	−2.10869	+	1.21745i	−0.0713684	+	0.0412045i
$874$	−8.14968	−	14.1157i	−0.275667	−	0.477469i
$875$	−4.47917	+	7.75816i	−0.151424	+	0.262274i
$876$		−	8.34920i		−	0.282093i
$877$	34.2286	+	19.7619i	1.15582	+	0.667311i	0.950298	−	0.311343i	$-0.100779\pi$
$877$	34.2286	+	19.7619i	1.15582	+	0.667311i	0.205518	+	0.978653i	$0.434112\pi$
$878$	3.67319	+	2.12072i	0.123964	+	0.0715707i
$879$		−	2.64185i		−	0.0891074i
$880$	0.190676	−	0.330261i	0.00642770	−	0.0111331i
$881$	−5.01579	−	8.68761i	−0.168986	−	0.292693i	0.769077	−	0.639156i	$-0.220716\pi$
$881$	−5.01579	−	8.68761i	−0.168986	−	0.292693i	−0.938064	+	0.346463i	$0.887383\pi$
$882$	−0.924500	+	0.533760i	−0.0311295	+	0.0179726i
$883$	−12.3180			−0.414535			−0.207268	−	0.978284i	$-0.566457\pi$
$883$	−12.3180			−0.414535			−0.207268	+	0.978284i	$0.566457\pi$
$884$	−7.07260	−	17.9095i	−0.237877	−	0.602361i
$885$	8.86091			0.297856
$886$	22.5673	−	13.0293i	0.758165	−	0.437727i
$887$	19.9019	+	34.4711i	0.668241	+	1.15743i	0.978396	+	0.206741i	$0.0662859\pi$
$887$	19.9019	+	34.4711i	0.668241	+	1.15743i	−0.310154	+	0.950686i	$0.600381\pi$
$888$	6.46121	−	11.1911i	0.216824	−	0.375550i
$889$			1.07079i			0.0359132i
$890$	−8.99702	−	5.19443i	−0.301581	−	0.174118i
$891$	0.215888	+	0.124643i	0.00723252	+	0.00417570i
$892$		−	10.5449i		−	0.353069i
$893$	44.5834	−	77.2206i	1.49192	−	2.58409i
$894$	1.78270	+	3.08772i	0.0596223	+	0.103269i
$895$	−6.43203	+	3.71353i	−0.214999	+	0.124130i
$896$	0.555390			0.0185543
$897$	−4.07072	+	5.12668i	−0.135918	+	0.171175i
$898$	20.5227			0.684853
$899$	−19.8788	+	11.4770i	−0.662996	+	0.382781i
$900$	−1.72589	−	2.98933i	−0.0575297	−	0.0996443i
$901$	−1.86822	+	3.23585i	−0.0622394	+	0.107802i
$902$			1.71244i			0.0570179i
$903$	−9.89679	−	5.71391i	−0.329344	−	0.190147i
$904$	−18.2137	−	10.5157i	−0.605779	−	0.349747i
$905$			6.00422i			0.199587i
$906$	4.82951	−	8.36496i	0.160450	−	0.277907i
$907$	18.1135	+	31.3734i	0.601448	+	1.04174i	0.992602	+	0.121413i	$0.0387424\pi$
$907$	18.1135	+	31.3734i	0.601448	+	1.04174i	−0.391155	+	0.920325i	$0.627924\pi$
$908$	12.1658	−	7.02392i	0.403736	−	0.233097i
$909$	5.17244			0.171559
$910$	0.562273	−	3.78462i	0.0186392	−	0.125459i
$911$	−23.8182			−0.789134			−0.394567	−	0.918867i	$-0.629105\pi$
$911$	−23.8182			−0.789134			−0.394567	+	0.918867i	$0.629105\pi$
$912$	−11.2077	+	6.47078i	−0.371125	+	0.214269i
$913$	2.06710	+	3.58033i	0.0684111	+	0.118491i
$914$	12.3890	−	21.4585i	0.409793	−	0.709783i
$915$		−	5.71447i		−	0.188915i
$916$	2.89304	+	1.67030i	0.0955887	+	0.0551882i
$917$	5.88559	+	3.39805i	0.194359	+	0.112213i
$918$			6.62609i			0.218694i
$919$	−13.4621	+	23.3171i	−0.444074	+	0.769160i	−0.997987	−	0.0634152i	$-0.979801\pi$
$919$	−13.4621	+	23.3171i	−0.444074	+	0.769160i	0.553913	+	0.832575i	$0.313134\pi$
$920$	2.75556	+	4.77277i	0.0908481	+	0.157354i
$921$	−16.3870	+	9.46106i	−0.539971	+	0.311752i
$922$	14.5211			0.478227
$923$	−33.9377	−	26.9475i	−1.11707	−	0.886987i
$924$	0.214485			0.00705605
$925$	−14.7033	+	8.48895i	−0.483441	+	0.279115i
$926$	−7.25977	−	12.5743i	−0.238571	−	0.413217i
$927$	−5.68403	+	9.84503i	−0.186688	+	0.323353i
$928$			12.0092i			0.394223i
$929$	0.965721	+	0.557559i	0.0316843	+	0.0182929i	0.515758	−	0.856734i	$-0.327510\pi$
$929$	0.965721	+	0.557559i	0.0316843	+	0.0182929i	−0.484074	+	0.875027i	$0.660844\pi$
$930$	7.84177	+	4.52745i	0.257142	+	0.148461i
$931$			8.40953i			0.275611i
$932$	8.01278	−	13.8785i	0.262467	−	0.454607i
$933$	−8.47495	−	14.6790i	−0.277457	−	0.480570i
$934$	8.32187	−	4.80463i	0.272300	−	0.157212i
$935$	−1.53813			−0.0503023
$936$	8.62218	+	6.84624i	0.281825	+	0.223776i
$937$	23.7383			0.775496			0.387748	−	0.921765i	$-0.373253\pi$
$937$	23.7383			0.775496			0.387748	+	0.921765i	$0.373253\pi$
$938$	6.12753	−	3.53773i	0.200071	−	0.115511i
$939$	−7.01070	−	12.1429i	−0.228786	−	0.396268i
$940$	−4.53435	+	7.85373i	−0.147894	+	0.256160i
$941$			17.1820i			0.560117i	0.959983	+	0.280059i	$0.0903539\pi$
$941$			17.1820i			0.560117i	−0.959983	+	0.280059i	$0.909646\pi$
$942$	−11.1583	−	6.44223i	−0.363556	−	0.209899i
$943$	−10.1180	−	5.84161i	−0.329486	−	0.190229i
$944$		−	13.7176i		−	0.446470i
$945$	0.497032	−	0.860885i	0.0161685	−	0.0280046i
$946$	−1.52057	−	2.63371i	−0.0494381	−	0.0856294i
$947$	−31.2530	+	18.0439i	−1.01559	+	0.586349i	−0.912822	−	0.408357i	$-0.866102\pi$
$947$	−31.2530	+	18.0439i	−1.01559	+	0.586349i	−0.102764	+	0.994706i	$0.532769\pi$
$948$	4.84790			0.157452
$949$	5.14164	−	34.6079i	0.166905	−	1.12342i
$950$	36.0157			1.16850
$951$	14.2250	−	8.21280i	0.461277	−	0.266318i
$952$	9.47664	+	16.4140i	0.307140	+	0.531981i
$953$	17.1152	−	29.6443i	0.554414	−	0.960274i	−0.443534	−	0.896257i	$-0.646276\pi$
$953$	17.1152	−	29.6443i	0.554414	−	0.960274i	0.997949	−	0.0640167i	$-0.0203911\pi$
$954$		−	0.642618i		−	0.0208055i
$955$	−10.7455	−	6.20390i	−0.347715	−	0.200754i
$956$	12.8592	+	7.42429i	0.415898	+	0.240119i
$957$			0.670602i			0.0216775i
$958$	12.7493	−	22.0825i	0.411912	−	0.713453i
$959$	−9.33585	−	16.1702i	−0.301470	−	0.522162i
$960$	6.75236	−	3.89848i	0.217931	−	0.125823i
$961$	−41.8090			−1.34868
$962$	10.1290	−	12.7565i	0.326572	−	0.411286i
$963$	−11.9888			−0.386332
$964$	−11.4142	+	6.58996i	−0.367625	+	0.212248i
$965$	2.85694	+	4.94837i	0.0919682	+	0.159294i
$966$	0.969100	−	1.67853i	0.0311803	−	0.0540058i
$967$			20.2829i			0.652255i	0.945326	+	0.326127i	$0.105744\pi$
$967$			20.2829i			0.652255i	−0.945326	+	0.326127i	$0.894256\pi$
$968$	−28.9245	−	16.6996i	−0.929669	−	0.536744i
$969$	45.2047	+	26.0990i	1.45218	+	0.838419i
$970$			2.58389i			0.0829636i
$971$	21.2531	−	36.8114i	0.682044	−	1.18133i	−0.292312	−	0.956323i	$-0.594425\pi$
$971$	21.2531	−	36.8114i	0.682044	−	1.18133i	0.974356	−	0.225012i	$-0.0722421\pi$
$972$	0.430200	+	0.745128i	0.0137987	+	0.0239000i
$973$	5.38214	−	3.10738i	0.172543	−	0.0996180i
$974$	−21.9651			−0.703807
$975$	−5.31302	−	13.4538i	−0.170153	−	0.430866i
$976$	−8.84659			−0.283172
$977$	8.82051	−	5.09252i	0.282193	−	0.162924i	−0.352223	−	0.935916i	$-0.614574\pi$
$977$	8.82051	−	5.09252i	0.282193	−	0.162924i	0.634416	+	0.772992i	$0.281241\pi$
$978$	−1.01314	−	1.75480i	−0.0323965	−	0.0561124i
$979$	1.22024	−	2.11352i	0.0389990	−	0.0675483i
$980$		−	0.855293i		−	0.0273213i
$981$	5.45868	+	3.15157i	0.174282	+	0.100622i
$982$	14.7393	+	8.50973i	0.470350	+	0.271557i
$983$			35.9929i			1.14799i	0.818857	+	0.573997i	$0.194608\pi$
$983$			35.9929i			1.14799i	−0.818857	+	0.573997i	$0.805392\pi$
$984$	−9.82456	+	17.0166i	−0.313196	+	0.542471i
$985$	−7.44319	−	12.8920i	−0.237160	−	0.410773i
$986$	−15.4367	+	8.91240i	−0.491606	+	0.283829i
$987$	10.6030			0.337499
$988$	24.2646	−	9.58231i	0.771961	−	0.304854i
$989$	20.7485			0.659763
$990$	0.229097	−	0.132269i	0.00728118	−	0.00420379i
$991$	7.31676	+	12.6730i	0.232425	+	0.402571i	0.958521	−	0.285022i	$-0.0920008\pi$
$991$	7.31676	+	12.6730i	0.232425	+	0.402571i	−0.726096	+	0.687593i	$0.758667\pi$
$992$	−19.0463	+	32.9892i	−0.604721	+	1.04741i
$993$			4.43689i			0.140801i
$994$	11.1116	+	6.41527i	0.352438	+	0.203480i
$995$	−1.78581	−	1.03104i	−0.0566140	−	0.0326861i
$996$			14.2690i			0.452131i
$997$	30.2287	−	52.3577i	0.957353	−	1.65818i	0.228463	−	0.973553i	$-0.426630\pi$
$997$	30.2287	−	52.3577i	0.957353	−	1.65818i	0.728890	−	0.684631i	$-0.240037\pi$
$998$	−5.54975	−	9.61245i	−0.175674	−	0.304277i
$999$	3.66498	−	2.11598i	0.115955	−	0.0669465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bd.b.127.5	yes	16
3.2	odd	2		819.2.ct.c.127.4		16
13.2	odd	12		3549.2.a.ba.1.6		8
13.4	even	6	inner	273.2.bd.b.43.5	✓	16
13.11	odd	12		3549.2.a.bc.1.3		8
39.17	odd	6		819.2.ct.c.316.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.b.43.5	✓	16	13.4	even	6	inner
273.2.bd.b.127.5	yes	16	1.1	even	1	trivial
819.2.ct.c.127.4		16	3.2	odd	2
819.2.ct.c.316.4		16	39.17	odd	6
3549.2.a.ba.1.6		8	13.2	odd	12
3549.2.a.bc.1.3		8	13.11	odd	12

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.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.924500 - 0.533760i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.430200 + 0.745128i) q^{4} +0.994065i q^{5} +(0.924500 + 0.533760i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.05354i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.924500 - 0.533760i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.430200 + 0.745128i) q^{4} +0.994065i q^{5} +(0.924500 + 0.533760i) q^{6} +(0.866025 + 0.500000i) q^{7} +3.05354i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.530592 + 0.919013i) q^{10} +(-0.215888 + 0.124643i) q^{11} -0.860399 q^{12} +(-3.56641 - 0.529854i) q^{13} +1.06752 q^{14} +(-0.860885 + 0.497032i) q^{15} +(0.769457 + 1.33274i) q^{16} +(3.10350 - 5.37541i) q^{17} +1.06752i q^{18} +(7.28287 + 4.20477i) q^{19} +(-0.740705 - 0.427646i) q^{20} +1.00000i q^{21} +(-0.133059 + 0.230465i) q^{22} +(-0.907804 - 1.57236i) q^{23} +(-2.64444 + 1.52677i) q^{24} +4.01184 q^{25} +(-3.57996 + 1.41376i) q^{26} -1.00000 q^{27} +(-0.745128 + 0.430200i) q^{28} +(-1.34505 - 2.32969i) q^{29} +(-0.530592 + 0.919013i) q^{30} -8.53282i q^{31} +(-3.86615 - 2.23212i) q^{32} +(-0.215888 - 0.124643i) q^{33} -6.62609i q^{34} +(-0.497032 + 0.860885i) q^{35} +(-0.430200 - 0.745128i) q^{36} +(-3.66498 + 2.11598i) q^{37} +8.97735 q^{38} +(-1.32434 - 3.35353i) q^{39} -3.03541 q^{40} +(5.57277 - 3.21744i) q^{41} +(0.533760 + 0.924500i) q^{42} +(-5.71391 + 9.89679i) q^{43} -0.214485i q^{44} +(-0.860885 - 0.497032i) q^{45} +(-1.67853 - 0.969100i) q^{46} -10.6030i q^{47} +(-0.769457 + 1.33274i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.70894 - 2.14136i) q^{50} +6.20699 q^{51} +(1.92908 - 2.42948i) q^{52} -0.601973 q^{53} +(-0.924500 + 0.533760i) q^{54} +(-0.123903 - 0.214607i) q^{55} +(-1.52677 + 2.64444i) q^{56} +8.40953i q^{57} +(-2.48699 - 1.43587i) q^{58} +(-7.71959 - 4.45691i) q^{59} -0.855293i q^{60} +(-2.87430 + 4.97843i) q^{61} +(-4.55448 - 7.88859i) q^{62} +(-0.866025 + 0.500000i) q^{63} -7.84351 q^{64} +(0.526710 - 3.54524i) q^{65} -0.266118 q^{66} +(5.73996 - 3.31397i) q^{67} +(2.67025 + 4.62500i) q^{68} +(0.907804 - 1.57236i) q^{69} +1.06118i q^{70} +(10.4088 + 6.00951i) q^{71} +(-2.64444 - 1.52677i) q^{72} +9.70387i q^{73} +(-2.25885 + 3.91244i) q^{74} +(2.00592 + 3.47435i) q^{75} +(-6.26618 + 3.61778i) q^{76} -0.249286 q^{77} +(-3.01433 - 2.39346i) q^{78} -5.63447 q^{79} +(-1.32483 + 0.764890i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.43468 - 5.94904i) q^{82} -16.5842i q^{83} +(-0.745128 - 0.430200i) q^{84} +(5.34351 + 3.08508i) q^{85} +12.1994i q^{86} +(1.34505 - 2.32969i) q^{87} +(-0.380602 - 0.659221i) q^{88} +(-8.47828 + 4.89494i) q^{89} -1.06118 q^{90} +(-2.82367 - 2.24207i) q^{91} +1.56215 q^{92} +(7.38964 - 4.26641i) q^{93} +(-5.65949 - 9.80252i) q^{94} +(-4.17981 + 7.23964i) q^{95} -4.46425i q^{96} +(2.10869 + 1.21745i) q^{97} +(0.924500 + 0.533760i) q^{98} -0.249286i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more