LMFDB - Embedded newform 273.2.p.f.265.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(34,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("273.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.p (of order $4$, 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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 60x^{8} - 8x^{7} + 80x^{5} + 320x^{4} + 160x^{3} + 32x^{2} - 32x + 16 $ x^12 + 60x^8 - 8x^7 + 80x^5 + 320x^4 + 160x^3 + 32x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			265.5
Root			$-1.96818 - 1.96818i$ of defining polynomial
Character	$\chi$	$=$	273.265
Dual form			273.2.p.f.34.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71968 - 1.71968i) q^{2} -1.00000i q^{3} -3.91457i q^{4} +(-0.968182 - 0.968182i) q^{5} +(-1.71968 - 1.71968i) q^{6} +(0.407631 + 2.61416i) q^{7} +(-3.29244 - 3.29244i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.71968 - 1.71968i) q^{2} -1.00000i q^{3} -3.91457i q^{4} +(-0.968182 - 0.968182i) q^{5} +(-1.71968 - 1.71968i) q^{6} +(0.407631 + 2.61416i) q^{7} +(-3.29244 - 3.29244i) q^{8} -1.00000 q^{9} -3.32992 q^{10} +(-1.56169 - 1.56169i) q^{11} -3.91457 q^{12} +(3.43543 - 1.09444i) q^{13} +(5.19650 + 3.79452i) q^{14} +(-0.968182 + 0.968182i) q^{15} -3.49472 q^{16} +0.815262 q^{17} +(-1.71968 + 1.71968i) q^{18} +(3.54095 + 3.54095i) q^{19} +(-3.79002 + 3.79002i) q^{20} +(2.61416 - 0.407631i) q^{21} -5.37121 q^{22} +6.45552i q^{23} +(-3.29244 + 3.29244i) q^{24} -3.12525i q^{25} +(4.02574 - 7.78992i) q^{26} +1.00000i q^{27} +(10.2333 - 1.59570i) q^{28} -6.34942 q^{29} +3.32992i q^{30} +(-1.93636 - 1.93636i) q^{31} +(0.575090 - 0.575090i) q^{32} +(-1.56169 + 1.56169i) q^{33} +(1.40199 - 1.40199i) q^{34} +(2.13632 - 2.92564i) q^{35} +3.91457i q^{36} +(5.45102 + 5.45102i) q^{37} +12.1786 q^{38} +(-1.09444 - 3.43543i) q^{39} +6.37536i q^{40} +(-2.86096 - 2.86096i) q^{41} +(3.79452 - 5.19650i) q^{42} +1.41608i q^{43} +(-6.11336 + 6.11336i) q^{44} +(0.968182 + 0.968182i) q^{45} +(11.1014 + 11.1014i) q^{46} +(8.52020 - 8.52020i) q^{47} +3.49472i q^{48} +(-6.66767 + 2.13123i) q^{49} +(-5.37442 - 5.37442i) q^{50} -0.815262i q^{51} +(-4.28427 - 13.4482i) q^{52} -3.01617 q^{53} +(1.71968 + 1.71968i) q^{54} +3.02401i q^{55} +(7.26487 - 9.94907i) q^{56} +(3.54095 - 3.54095i) q^{57} +(-10.9189 + 10.9189i) q^{58} +(-4.29487 + 4.29487i) q^{59} +(3.79002 + 3.79002i) q^{60} +14.1626i q^{61} -6.65983 q^{62} +(-0.407631 - 2.61416i) q^{63} -8.96739i q^{64} +(-4.38574 - 2.26650i) q^{65} +5.37121i q^{66} +(-1.18702 + 1.18702i) q^{67} -3.19140i q^{68} +6.45552 q^{69} +(-1.35738 - 8.70494i) q^{70} +(-1.96161 + 1.96161i) q^{71} +(3.29244 + 3.29244i) q^{72} +(-8.15249 + 8.15249i) q^{73} +18.7480 q^{74} -3.12525 q^{75} +(13.8613 - 13.8613i) q^{76} +(3.44592 - 4.71911i) q^{77} +(-7.78992 - 4.02574i) q^{78} -5.17481 q^{79} +(3.38353 + 3.38353i) q^{80} +1.00000 q^{81} -9.83985 q^{82} +(7.41597 + 7.41597i) q^{83} +(-1.59570 - 10.2333i) q^{84} +(-0.789322 - 0.789322i) q^{85} +(2.43520 + 2.43520i) q^{86} +6.34942i q^{87} +10.2836i q^{88} +(-0.0701292 + 0.0701292i) q^{89} +3.32992 q^{90} +(4.26144 + 8.53464i) q^{91} +25.2706 q^{92} +(-1.93636 + 1.93636i) q^{93} -29.3040i q^{94} -6.85656i q^{95} +(-0.575090 - 0.575090i) q^{96} +(-11.8216 - 11.8216i) q^{97} +(-7.80122 + 15.1313i) q^{98} +(1.56169 + 1.56169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9	$ 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9} - 4 q^{11} - 28 q^{12} + 12 q^{15} - 36 q^{16} - 8 q^{17} + 8 q^{20} + 12 q^{21} + 32 q^{22} + 4 q^{26} + 12 q^{28} - 8 q^{29} + 24 q^{31} + 20 q^{32} - 4 q^{33} - 20 q^{35} - 4 q^{37} + 40 q^{38} - 16 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 20 q^{46} + 32 q^{47} + 20 q^{50} - 56 q^{52} - 16 q^{53} - 20 q^{56} + 8 q^{59} - 8 q^{60} + 4 q^{63} - 16 q^{65} - 32 q^{67} + 16 q^{69} - 20 q^{70} - 12 q^{71} - 32 q^{73} - 64 q^{74} + 4 q^{75} - 12 q^{77} + 16 q^{78} + 24 q^{79} - 4 q^{80} + 12 q^{81} + 28 q^{84} - 32 q^{85} + 4 q^{89} + 32 q^{91} + 112 q^{92} + 24 q^{93} - 20 q^{96} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9 - 4 * q^11 - 28 * q^12 + 12 * q^15 - 36 * q^16 - 8 * q^17 + 8 * q^20 + 12 * q^21 + 32 * q^22 + 4 * q^26 + 12 * q^28 - 8 * q^29 + 24 * q^31 + 20 * q^32 - 4 * q^33 - 20 * q^35 - 4 * q^37 + 40 * q^38 - 16 * q^39 - 20 * q^41 + 8 * q^44 - 12 * q^45 + 20 * q^46 + 32 * q^47 + 20 * q^50 - 56 * q^52 - 16 * q^53 - 20 * q^56 + 8 * q^59 - 8 * q^60 + 4 * q^63 - 16 * q^65 - 32 * q^67 + 16 * q^69 - 20 * q^70 - 12 * q^71 - 32 * q^73 - 64 * q^74 + 4 * q^75 - 12 * q^77 + 16 * q^78 + 24 * q^79 - 4 * q^80 + 12 * q^81 + 28 * q^84 - 32 * q^85 + 4 * q^89 + 32 * q^91 + 112 * q^92 + 24 * q^93 - 20 * q^96 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.71968	−	1.71968i	1.21599	−	1.21599i	0.246972	−	0.969023i	$-0.420564\pi$
$2$	1.71968	−	1.71968i	1.21599	−	1.21599i	0.969023	−	0.246972i	$-0.0794355\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$		−	3.91457i		−	1.95729i
$5$	−0.968182	−	0.968182i	−0.432984	−	0.432984i	0.456658	−	0.889642i	$-0.349046\pi$
$5$	−0.968182	−	0.968182i	−0.432984	−	0.432984i	−0.889642	+	0.456658i	$0.849046\pi$
$6$	−1.71968	−	1.71968i	−0.702055	−	0.702055i
$7$	0.407631	+	2.61416i	0.154070	+	0.988060i
$7$	0.407631	+	2.61416i	0.154070	+	0.988060i
$8$	−3.29244	−	3.29244i	−1.16405	−	1.16405i
$9$	−1.00000			−0.333333
$10$	−3.32992			−1.05301
$11$	−1.56169	−	1.56169i	−0.470868	−	0.470868i	0.431327	−	0.902196i	$-0.358045\pi$
$11$	−1.56169	−	1.56169i	−0.470868	−	0.470868i	−0.902196	+	0.431327i	$0.858045\pi$
$12$	−3.91457			−1.13004
$13$	3.43543	−	1.09444i	0.952817	−	0.303544i
$13$	3.43543	−	1.09444i	0.952817	−	0.303544i
$14$	5.19650	+	3.79452i	1.38882	+	1.01413i
$15$	−0.968182	+	0.968182i	−0.249983	+	0.249983i
$16$	−3.49472			−0.873681
$17$	0.815262			0.197730			0.0988651	−	0.995101i	$-0.468479\pi$
$17$	0.815262			0.197730			0.0988651	+	0.995101i	$0.468479\pi$
$18$	−1.71968	+	1.71968i	−0.405332	+	0.405332i
$19$	3.54095	+	3.54095i	0.812349	+	0.812349i	0.984986	−	0.172637i	$-0.0552286\pi$
$19$	3.54095	+	3.54095i	0.812349	+	0.812349i	−0.172637	+	0.984986i	$0.555229\pi$
$20$	−3.79002	+	3.79002i	−0.847473	+	0.847473i
$21$	2.61416	−	0.407631i	0.570457	−	0.0889524i
$22$	−5.37121			−1.14515
$23$			6.45552i			1.34607i	0.739611	+	0.673034i	$0.235009\pi$
$23$			6.45552i			1.34607i	−0.739611	+	0.673034i	$0.764991\pi$
$24$	−3.29244	+	3.29244i	−0.672067	+	0.672067i
$25$		−	3.12525i		−	0.625050i
$26$	4.02574	−	7.78992i	0.789513	−	1.52773i
$27$			1.00000i			0.192450i
$28$	10.2333	−	1.59570i	1.93392	−	0.301559i
$29$	−6.34942			−1.17906			−0.589529	−	0.807747i	$-0.700687\pi$
$29$	−6.34942			−1.17906			−0.589529	+	0.807747i	$0.700687\pi$
$30$			3.32992i			0.607957i
$31$	−1.93636	−	1.93636i	−0.347781	−	0.347781i	0.511501	−	0.859282i	$-0.329090\pi$
$31$	−1.93636	−	1.93636i	−0.347781	−	0.347781i	−0.859282	+	0.511501i	$0.829090\pi$
$32$	0.575090	−	0.575090i	0.101663	−	0.101663i
$33$	−1.56169	+	1.56169i	−0.271856	+	0.271856i
$34$	1.40199	−	1.40199i	0.240439	−	0.240439i
$35$	2.13632	−	2.92564i	0.361104	−	0.494524i
$36$			3.91457i			0.652429i
$37$	5.45102	+	5.45102i	0.896142	+	0.896142i	0.995092	−	0.0989506i	$-0.0315486\pi$
$37$	5.45102	+	5.45102i	0.896142	+	0.896142i	−0.0989506	+	0.995092i	$0.531549\pi$
$38$	12.1786			1.97562
$39$	−1.09444	−	3.43543i	−0.175251	−	0.550109i
$40$			6.37536i			1.00803i
$41$	−2.86096	−	2.86096i	−0.446807	−	0.446807i	0.447485	−	0.894292i	$-0.352320\pi$
$41$	−2.86096	−	2.86096i	−0.446807	−	0.446807i	−0.894292	+	0.447485i	$0.852320\pi$
$42$	3.79452	−	5.19650i	0.585507	−	0.801838i
$43$			1.41608i			0.215951i	0.994154	+	0.107975i	$0.0344367\pi$
$43$			1.41608i			0.215951i	−0.994154	+	0.107975i	$0.965563\pi$
$44$	−6.11336	+	6.11336i	−0.921624	+	0.921624i
$45$	0.968182	+	0.968182i	0.144328	+	0.144328i
$46$	11.1014	+	11.1014i	1.63681	+	1.63681i
$47$	8.52020	−	8.52020i	1.24280	−	1.24280i	0.283964	−	0.958835i	$-0.408350\pi$
$47$	8.52020	−	8.52020i	1.24280	−	1.24280i	0.958835	−	0.283964i	$-0.0916497\pi$
$48$			3.49472i			0.504420i
$49$	−6.66767	+	2.13123i	−0.952525	+	0.304461i
$50$	−5.37442	−	5.37442i	−0.760057	−	0.760057i
$51$		−	0.815262i		−	0.114160i
$52$	−4.28427	−	13.4482i	−0.594122	−	1.86494i
$53$	−3.01617			−0.414302			−0.207151	−	0.978309i	$-0.566419\pi$
$53$	−3.01617			−0.414302			−0.207151	+	0.978309i	$0.566419\pi$
$54$	1.71968	+	1.71968i	0.234018	+	0.234018i
$55$			3.02401i			0.407757i
$56$	7.26487	−	9.94907i	0.970809	−	1.32950i
$57$	3.54095	−	3.54095i	0.469010	−	0.469010i
$58$	−10.9189	+	10.9189i	−1.43373	+	1.43373i
$59$	−4.29487	+	4.29487i	−0.559144	+	0.559144i	−0.929064	−	0.369920i	$-0.879385\pi$
$59$	−4.29487	+	4.29487i	−0.559144	+	0.559144i	0.369920	+	0.929064i	$0.379385\pi$
$60$	3.79002	+	3.79002i	0.489289	+	0.489289i
$61$			14.1626i			1.81334i	0.421842	+	0.906669i	$0.361384\pi$
$61$			14.1626i			1.81334i	−0.421842	+	0.906669i	$0.638616\pi$
$62$	−6.65983			−0.845800
$63$	−0.407631	−	2.61416i	−0.0513567	−	0.329353i
$64$		−	8.96739i		−	1.12092i
$65$	−4.38574	−	2.26650i	−0.543984	−	0.281125i
$66$			5.37121i			0.661151i
$67$	−1.18702	+	1.18702i	−0.145018	+	0.145018i	−0.775888	−	0.630870i	$-0.782698\pi$
$67$	−1.18702	+	1.18702i	−0.145018	+	0.145018i	0.630870	+	0.775888i	$0.282698\pi$
$68$		−	3.19140i		−	0.387014i
$69$	6.45552			0.777153
$70$	−1.35738	−	8.70494i	−0.162238	−	1.04044i
$71$	−1.96161	+	1.96161i	−0.232800	+	0.232800i	−0.813861	−	0.581060i	$-0.802638\pi$
$71$	−1.96161	+	1.96161i	−0.232800	+	0.232800i	0.581060	+	0.813861i	$0.302638\pi$
$72$	3.29244	+	3.29244i	0.388018	+	0.388018i
$73$	−8.15249	+	8.15249i	−0.954177	+	0.954177i	−0.998995	−	0.0448186i	$-0.985729\pi$
$73$	−8.15249	+	8.15249i	−0.954177	+	0.954177i	0.0448186	+	0.998995i	$0.485729\pi$
$74$	18.7480			2.17941
$75$	−3.12525			−0.360873
$76$	13.8613	−	13.8613i	1.59000	−	1.59000i
$77$	3.44592	−	4.71911i	0.392699	−	0.537793i
$78$	−7.78992	−	4.02574i	−0.882034	−	0.455826i
$79$	−5.17481			−0.582212			−0.291106	−	0.956691i	$-0.594023\pi$
$79$	−5.17481			−0.582212			−0.291106	+	0.956691i	$0.594023\pi$
$80$	3.38353	+	3.38353i	0.378290	+	0.378290i
$81$	1.00000			0.111111
$82$	−9.83985			−1.08663
$83$	7.41597	+	7.41597i	0.814008	+	0.814008i	0.985232	−	0.171224i	$-0.0547722\pi$
$83$	7.41597	+	7.41597i	0.814008	+	0.814008i	−0.171224	+	0.985232i	$0.554772\pi$
$84$	−1.59570	−	10.2333i	−0.174105	−	1.11655i
$85$	−0.789322	−	0.789322i	−0.0856140	−	0.0856140i
$86$	2.43520	+	2.43520i	0.262595	+	0.262595i
$87$			6.34942i			0.680730i
$88$			10.2836i			1.09623i
$89$	−0.0701292	+	0.0701292i	−0.00743368	+	0.00743368i	−0.710814	−	0.703380i	$-0.751673\pi$
$89$	−0.0701292	+	0.0701292i	−0.00743368	+	0.00743368i	0.703380	+	0.710814i	$0.251673\pi$
$90$	3.32992			0.351004
$91$	4.26144	+	8.53464i	0.446720	+	0.894674i
$92$	25.2706			2.63464
$93$	−1.93636	+	1.93636i	−0.200791	+	0.200791i
$94$		−	29.3040i		−	3.02247i
$95$		−	6.85656i		−	0.703468i
$96$	−0.575090	−	0.575090i	−0.0586949	−	0.0586949i
$97$	−11.8216	−	11.8216i	−1.20031	−	1.20031i	−0.974073	−	0.226232i	$-0.927359\pi$
$97$	−11.8216	−	11.8216i	−1.20031	−	1.20031i	−0.226232	−	0.974073i	$-0.572641\pi$
$98$	−7.80122	+	15.1313i	−0.788042	+	1.52849i
$99$	1.56169	+	1.56169i	0.156956	+	0.156956i
$100$	−12.2340			−1.22340
$101$	−0.719293			−0.0715723			−0.0357861	−	0.999359i	$-0.511394\pi$
$101$	−0.719293			−0.0715723			−0.0357861	+	0.999359i	$0.511394\pi$
$102$	−1.40199	−	1.40199i	−0.138817	−	0.138817i
$103$	−6.38189			−0.628826			−0.314413	−	0.949286i	$-0.601808\pi$
$103$	−6.38189			−0.628826			−0.314413	+	0.949286i	$0.601808\pi$
$104$	−14.9144	−	7.70757i	−1.46247	−	0.755789i
$105$	−2.92564	−	2.13632i	−0.285514	−	0.208484i
$106$	−5.18683	+	5.18683i	−0.503789	+	0.503789i
$107$	−2.79723			−0.270419			−0.135209	−	0.990817i	$-0.543171\pi$
$107$	−2.79723			−0.270419			−0.135209	+	0.990817i	$0.543171\pi$
$108$	3.91457			0.376680
$109$	9.58601	−	9.58601i	0.918173	−	0.918173i	−0.0787234	−	0.996896i	$-0.525084\pi$
$109$	9.58601	−	9.58601i	0.918173	−	0.918173i	0.996896	+	0.0787234i	$0.0250844\pi$
$110$	5.20031	+	5.20031i	0.495830	+	0.495830i
$111$	5.45102	−	5.45102i	0.517388	−	0.517388i
$112$	−1.42456	−	9.13577i	−0.134608	−	0.863249i
$113$	5.33783			0.502141			0.251070	−	0.967969i	$-0.419217\pi$
$113$	5.33783			0.502141			0.251070	+	0.967969i	$0.419217\pi$
$114$		−	12.1786i		−	1.14063i
$115$	6.25011	−	6.25011i	0.582826	−	0.582826i
$116$			24.8553i			2.30775i
$117$	−3.43543	+	1.09444i	−0.317606	+	0.101181i
$118$			14.7716i			1.35983i
$119$	0.332326	+	2.13123i	0.0304643	+	0.195369i
$120$	6.37536			0.581988
$121$		−	6.12223i		−	0.556566i
$122$	24.3551	+	24.3551i	2.20501	+	2.20501i
$123$	−2.86096	+	2.86096i	−0.257964	+	0.257964i
$124$	−7.58003	+	7.58003i	−0.680707	+	0.680707i
$125$	−7.86672	+	7.86672i	−0.703620	+	0.703620i
$126$	−5.19650	−	3.79452i	−0.462941	−	0.338042i
$127$			13.1748i			1.16908i	0.811367	+	0.584538i	$0.198724\pi$
$127$			13.1748i			1.16908i	−0.811367	+	0.584538i	$0.801276\pi$
$128$	−14.2708	−	14.2708i	−1.26137	−	1.26137i
$129$	1.41608			0.124679
$130$	−11.4397	+	3.64440i	−1.00333	+	0.319635i
$131$		−	9.23713i		−	0.807052i	−0.914968	−	0.403526i	$-0.867785\pi$
$131$		−	9.23713i		−	0.807052i	0.914968	−	0.403526i	$-0.132215\pi$
$132$	6.11336	+	6.11336i	0.532100	+	0.532100i
$133$	−7.81321	+	10.7000i	−0.677491	+	0.927808i
$134$			4.08259i			0.352682i
$135$	0.968182	−	0.968182i	0.0833278	−	0.0833278i
$136$	−2.68420	−	2.68420i	−0.230169	−	0.230169i
$137$	−15.1160	−	15.1160i	−1.29144	−	1.29144i	−0.933894	−	0.357551i	$-0.883612\pi$
$137$	−15.1160	−	15.1160i	−1.29144	−	1.29144i	−0.357551	−	0.933894i	$-0.616388\pi$
$138$	11.1014	−	11.1014i	0.945014	−	0.945014i
$139$			10.6234i			0.901064i	0.892760	+	0.450532i	$0.148766\pi$
$139$			10.6234i			0.901064i	−0.892760	+	0.450532i	$0.851234\pi$
$140$	−11.4526	−	8.36278i	−0.967925	−	0.706784i
$141$	−8.52020	−	8.52020i	−0.717530	−	0.717530i
$142$			6.74667i			0.566168i
$143$	−7.07428	−	3.65591i	−0.591581	−	0.305722i
$144$	3.49472			0.291227
$145$	6.14739	+	6.14739i	0.510513	+	0.510513i
$146$			28.0393i			2.32055i
$147$	2.13123	+	6.66767i	0.175781	+	0.549940i
$148$	21.3384	−	21.3384i	1.75401	−	1.75401i
$149$	−4.78773	+	4.78773i	−0.392226	+	0.392226i	−0.875480	−	0.483254i	$-0.839455\pi$
$149$	−4.78773	+	4.78773i	−0.392226	+	0.392226i	0.483254	+	0.875480i	$0.339455\pi$
$150$	−5.37442	+	5.37442i	−0.438819	+	0.438819i
$151$	−2.60195	−	2.60195i	−0.211743	−	0.211743i	0.593264	−	0.805008i	$-0.297839\pi$
$151$	−2.60195	−	2.60195i	−0.211743	−	0.211743i	−0.805008	+	0.593264i	$0.797839\pi$
$152$		−	23.3167i		−	1.89124i
$153$	−0.815262			−0.0659101
$154$	−2.18947	−	14.0412i	−0.176433	−	1.13147i
$155$			3.74950i			0.301167i
$156$	−13.4482	+	4.28427i	−1.07672	+	0.343017i
$157$		−	0.836307i		−	0.0667446i	−0.999443	−	0.0333723i	$-0.989375\pi$
$157$		−	0.836307i		−	0.0667446i	0.999443	−	0.0333723i	$-0.0106247\pi$
$158$	−8.89900	+	8.89900i	−0.707966	+	0.707966i
$159$			3.01617i			0.239198i
$160$	−1.11358			−0.0880365
$161$	−16.8758	+	2.63147i	−1.33000	+	0.207389i
$162$	1.71968	−	1.71968i	0.135111	−	0.135111i
$163$	4.55824	+	4.55824i	0.357029	+	0.357029i	0.862717	−	0.505688i	$-0.168761\pi$
$163$	4.55824	+	4.55824i	0.357029	+	0.357029i	−0.505688	+	0.862717i	$0.668761\pi$
$164$	−11.1994	+	11.1994i	−0.874529	+	0.874529i
$165$	3.02401			0.235419
$166$	25.5061			1.97966
$167$	17.5889	−	17.5889i	1.36107	−	1.36107i	0.488517	−	0.872555i	$-0.337538\pi$
$167$	17.5889	−	17.5889i	1.36107	−	1.36107i	0.872555	−	0.488517i	$-0.162462\pi$
$168$	−9.94907	−	7.26487i	−0.767588	−	0.560497i
$169$	10.6044	−	7.51977i	0.815722	−	0.578444i
$170$	−2.71476			−0.208212
$171$	−3.54095	−	3.54095i	−0.270783	−	0.270783i
$172$	5.54336			0.422677
$173$	−23.2980			−1.77132			−0.885658	−	0.464338i	$-0.846292\pi$
$173$	−23.2980			−1.77132			−0.885658	+	0.464338i	$0.846292\pi$
$174$	10.9189	+	10.9189i	0.827763	+	0.827763i
$175$	8.16990	−	1.27395i	0.617587	−	0.0963015i
$176$	5.45769	+	5.45769i	0.411389	+	0.411389i
$177$	4.29487	+	4.29487i	0.322822	+	0.322822i
$178$			0.241199i			0.0180786i
$179$			0.375015i			0.0280300i	0.999902	+	0.0140150i	$0.00446125\pi$
$179$			0.375015i			0.0280300i	−0.999902	+	0.0140150i	$0.995539\pi$
$180$	3.79002	−	3.79002i	0.282491	−	0.282491i
$181$	−11.7567			−0.873869			−0.436934	−	0.899493i	$-0.643936\pi$
$181$	−11.7567			−0.873869			−0.436934	+	0.899493i	$0.643936\pi$
$182$	22.0051	+	7.34853i	1.63113	+	0.544709i
$183$	14.1626			1.04693
$184$	21.2544	−	21.2544i	1.56690	−	1.56690i
$185$		−	10.5551i		−	0.776030i
$186$			6.65983i			0.488323i
$187$	−1.27319	−	1.27319i	−0.0931049	−	0.0931049i
$188$	−33.3529	−	33.3529i	−2.43251	−	2.43251i
$189$	−2.61416	+	0.407631i	−0.190152	+	0.0296508i
$190$	−11.7911	−	11.7911i	−0.855413	−	0.855413i
$191$	24.2210			1.75257			0.876286	−	0.481792i	$-0.160014\pi$
$191$	24.2210			1.75257			0.876286	+	0.481792i	$0.160014\pi$
$192$	−8.96739			−0.647165
$193$	−16.2804	−	16.2804i	−1.17189	−	1.17189i	−0.981759	−	0.190129i	$-0.939109\pi$
$193$	−16.2804	−	16.2804i	−1.17189	−	1.17189i	−0.190129	−	0.981759i	$-0.560891\pi$
$194$	−40.6588			−2.91913
$195$	−2.26650	+	4.38574i	−0.162308	+	0.314069i
$196$	8.34284	+	26.1011i	0.595917	+	1.86436i
$197$	9.92313	−	9.92313i	0.706994	−	0.706994i	−0.258908	−	0.965902i	$-0.583363\pi$
$197$	9.92313	−	9.92313i	0.706994	−	0.706994i	0.965902	+	0.258908i	$0.0833626\pi$
$198$	5.37121			0.381716
$199$	7.02284			0.497836			0.248918	−	0.968525i	$-0.419925\pi$
$199$	7.02284			0.497836			0.248918	+	0.968525i	$0.419925\pi$
$200$	−10.2897	+	10.2897i	−0.727592	+	0.727592i
$201$	1.18702	+	1.18702i	0.0837262	+	0.0837262i
$202$	−1.23695	+	1.23695i	−0.0870315	+	0.0870315i
$203$	−2.58822	−	16.5984i	−0.181658	−	1.16498i
$204$	−3.19140			−0.223443
$205$			5.53986i			0.386920i
$206$	−10.9748	+	10.9748i	−0.764649	+	0.764649i
$207$		−	6.45552i		−	0.448690i
$208$	−12.0059	+	3.82478i	−0.832459	+	0.265201i
$209$		−	11.0598i		−	0.765019i
$210$	−8.70494	+	1.35738i	−0.600698	+	0.0936680i
$211$	21.5808			1.48568			0.742842	−	0.669467i	$-0.233477\pi$
$211$	21.5808			1.48568			0.742842	+	0.669467i	$0.233477\pi$
$212$			11.8070i			0.810908i
$213$	1.96161	+	1.96161i	0.134407	+	0.134407i
$214$	−4.81034	+	4.81034i	−0.328828	+	0.328828i
$215$	1.37103	−	1.37103i	0.0935031	−	0.0935031i
$216$	3.29244	−	3.29244i	0.224022	−	0.224022i
$217$	4.27264	−	5.85129i	0.290046	−	0.397211i
$218$		−	32.9697i		−	2.23299i
$219$	8.15249	+	8.15249i	0.550894	+	0.550894i
$220$	11.8377			0.798097
$221$	2.80078	−	0.892258i	0.188401	−	0.0600198i
$222$		−	18.7480i		−	1.25828i
$223$	−0.313751	−	0.313751i	−0.0210103	−	0.0210103i	0.696524	−	0.717534i	$-0.254729\pi$
$223$	−0.313751	−	0.313751i	−0.0210103	−	0.0210103i	−0.717534	+	0.696524i	$0.754729\pi$
$224$	1.73780	+	1.26895i	0.116112	+	0.0847855i
$225$			3.12525i			0.208350i
$226$	9.17934	−	9.17934i	0.610600	−	0.610600i
$227$	7.65255	+	7.65255i	0.507918	+	0.507918i	0.913887	−	0.405969i	$-0.133066\pi$
$227$	7.65255	+	7.65255i	0.507918	+	0.507918i	−0.405969	+	0.913887i	$0.633066\pi$
$228$	−13.8613	−	13.8613i	−0.917986	−	0.917986i
$229$	17.4766	−	17.4766i	1.15489	−	1.15489i	0.169325	−	0.985560i	$-0.445841\pi$
$229$	17.4766	−	17.4766i	1.15489	−	1.15489i	0.985560	−	0.169325i	$-0.0541587\pi$
$230$		−	21.4963i		−	1.41743i
$231$	−4.71911	−	3.44592i	−0.310495	−	0.226725i
$232$	20.9051	+	20.9051i	1.37249	+	1.37249i
$233$			27.5842i			1.80710i	0.428481	+	0.903551i	$0.359049\pi$
$233$			27.5842i			1.80710i	−0.428481	+	0.903551i	$0.640951\pi$
$234$	−4.02574	+	7.78992i	−0.263171	+	0.509243i
$235$	−16.4982			−1.07622
$236$	16.8126	+	16.8126i	1.09440	+	1.09440i
$237$			5.17481i			0.336140i
$238$	4.23651	+	3.09353i	0.274612	+	0.200524i
$239$	−8.12347	+	8.12347i	−0.525463	+	0.525463i	−0.919216	−	0.393753i	$-0.871177\pi$
$239$	−8.12347	+	8.12347i	−0.525463	+	0.525463i	0.393753	+	0.919216i	$0.371177\pi$
$240$	3.38353	−	3.38353i	0.218406	−	0.218406i
$241$	14.1961	−	14.1961i	0.914449	−	0.914449i	−0.0821690	−	0.996618i	$-0.526185\pi$
$241$	14.1961	−	14.1961i	0.914449	−	0.914449i	0.996618	+	0.0821690i	$0.0261847\pi$
$242$	−10.5282	−	10.5282i	−0.676781	−	0.676781i
$243$		−	1.00000i		−	0.0641500i
$244$	55.4406			3.54922
$245$	8.51893	+	4.39210i	0.544255	+	0.280601i
$246$			9.83985i			0.627366i
$247$	16.0400	+	8.28932i	1.02060	+	0.527437i
$248$			12.7507i			0.809672i
$249$	7.41597	−	7.41597i	0.469968	−	0.469968i
$250$			27.0564i			1.71120i
$251$	−8.38843			−0.529473			−0.264737	−	0.964321i	$-0.585285\pi$
$251$	−8.38843			−0.529473			−0.264737	+	0.964321i	$0.585285\pi$
$252$	−10.2333	+	1.59570i	−0.644638	+	0.100520i
$253$	10.0815	−	10.0815i	0.633821	−	0.633821i
$254$	22.6564	+	22.6564i	1.42159	+	1.42159i
$255$	−0.789322	+	0.789322i	−0.0494293	+	0.0494293i
$256$	−31.1476			−1.94672
$257$	−18.4408			−1.15030			−0.575152	−	0.818047i	$-0.695057\pi$
$257$	−18.4408			−1.15030			−0.575152	+	0.818047i	$0.695057\pi$
$258$	2.43520	−	2.43520i	0.151609	−	0.151609i
$259$	−12.0278	+	16.4718i	−0.747373	+	1.02351i
$260$	−8.87239	+	17.1683i	−0.550242	+	1.06473i
$261$	6.34942			0.393019
$262$	−15.8849	−	15.8849i	−0.981370	−	0.981370i
$263$	−12.8900			−0.794833			−0.397416	−	0.917638i	$-0.630093\pi$
$263$	−12.8900			−0.794833			−0.397416	+	0.917638i	$0.630093\pi$
$264$	10.2836			0.632910
$265$	2.92020	+	2.92020i	0.179386	+	0.179386i
$266$	4.96436	+	31.8367i	0.304385	+	1.95203i
$267$	0.0701292	+	0.0701292i	0.00429184	+	0.00429184i
$268$	4.64669	+	4.64669i	0.283842	+	0.283842i
$269$			20.2658i			1.23563i	0.786325	+	0.617813i	$0.211981\pi$
$269$			20.2658i			1.23563i	−0.786325	+	0.617813i	$0.788019\pi$
$270$		−	3.32992i		−	0.202652i
$271$	11.4908	−	11.4908i	0.698019	−	0.698019i	−0.265964	−	0.963983i	$-0.585690\pi$
$271$	11.4908	−	11.4908i	0.698019	−	0.698019i	0.963983	+	0.265964i	$0.0856903\pi$
$272$	−2.84912			−0.172753
$273$	8.53464	−	4.26144i	0.516540	−	0.257914i
$274$	−51.9892			−3.14078
$275$	−4.88068	+	4.88068i	−0.294316	+	0.294316i
$276$		−	25.2706i		−	1.52111i
$277$		−	13.2761i		−	0.797683i	−0.917020	−	0.398841i	$-0.869412\pi$
$277$		−	13.2761i		−	0.797683i	0.917020	−	0.398841i	$-0.130588\pi$
$278$	18.2688	+	18.2688i	1.09569	+	1.09569i
$279$	1.93636	+	1.93636i	0.115927	+	0.115927i
$280$	−16.6662	+	2.59880i	−0.995997	+	0.155308i
$281$	15.5558	+	15.5558i	0.927978	+	0.927978i	0.997575	−	0.0695969i	$-0.0221713\pi$
$281$	15.5558	+	15.5558i	0.927978	+	0.927978i	−0.0695969	+	0.997575i	$0.522171\pi$
$282$	−29.3040			−1.74503
$283$	2.19005			0.130185			0.0650924	−	0.997879i	$-0.479266\pi$
$283$	2.19005			0.130185			0.0650924	+	0.997879i	$0.479266\pi$
$284$	7.67886	+	7.67886i	0.455657	+	0.455657i
$285$	−6.85656			−0.406148
$286$	−18.4524	+	5.87849i	−1.09112	+	0.347602i
$287$	6.31279	−	8.64523i	0.372632	−	0.510312i
$288$	−0.575090	+	0.575090i	−0.0338875	+	0.0338875i
$289$	−16.3353			−0.960903
$290$	21.1430			1.24156
$291$	−11.8216	+	11.8216i	−0.692997	+	0.692997i
$292$	31.9135	+	31.9135i	1.86760	+	1.86760i
$293$	7.72648	−	7.72648i	0.451386	−	0.451386i	−0.444428	−	0.895814i	$-0.646593\pi$
$293$	7.72648	−	7.72648i	0.451386	−	0.451386i	0.895814	+	0.444428i	$0.146593\pi$
$294$	15.1313	+	7.80122i	0.882473	+	0.454976i
$295$	8.31642			0.484201
$296$		−	35.8943i		−	2.08631i
$297$	1.56169	−	1.56169i	0.0906187	−	0.0906187i
$298$			16.4667i			0.953889i
$299$	7.06520	+	22.1775i	0.408591	+	1.28256i
$300$			12.2340i			0.706331i
$301$	−3.70187	+	0.577240i	−0.213372	+	0.0332715i
$302$	−8.94901			−0.514957
$303$			0.719293i			0.0413223i
$304$	−12.3746	−	12.3746i	−0.709734	−	0.709734i
$305$	13.7120	−	13.7120i	0.785147	−	0.785147i
$306$	−1.40199	+	1.40199i	−0.0801463	+	0.0801463i
$307$	−9.68422	+	9.68422i	−0.552708	+	0.552708i	−0.927221	−	0.374514i	$-0.877810\pi$
$307$	−9.68422	+	9.68422i	−0.552708	+	0.552708i	0.374514	+	0.927221i	$0.377810\pi$
$308$	−18.4733	−	13.4893i	−1.05261	−	0.768625i
$309$			6.38189i			0.363053i
$310$	6.44793	+	6.44793i	0.366218	+	0.366218i
$311$	0.694504			0.0393817			0.0196908	−	0.999806i	$-0.493732\pi$
$311$	0.694504			0.0393817			0.0196908	+	0.999806i	$0.493732\pi$
$312$	−7.70757	+	14.9144i	−0.436355	+	0.844359i
$313$			2.91031i			0.164500i	0.996612	+	0.0822501i	$0.0262106\pi$
$313$			2.91031i			0.164500i	−0.996612	+	0.0822501i	$0.973789\pi$
$314$	−1.43818	−	1.43818i	−0.0811610	−	0.0811610i
$315$	−2.13632	+	2.92564i	−0.120368	+	0.164841i
$316$			20.2572i			1.13955i
$317$	18.2225	−	18.2225i	1.02348	−	1.02348i	0.0237595	−	0.999718i	$-0.492436\pi$
$317$	18.2225	−	18.2225i	1.02348	−	1.02348i	0.999718	−	0.0237595i	$-0.00756361\pi$
$318$	5.18683	+	5.18683i	0.290863	+	0.290863i
$319$	9.91585	+	9.91585i	0.555181	+	0.555181i
$320$	−8.68206	+	8.68206i	−0.485342	+	0.485342i
$321$			2.79723i			0.156126i
$322$	−24.4956	+	33.5461i	−1.36508	+	1.86945i
$323$	2.88680	+	2.88680i	0.160626	+	0.160626i
$324$		−	3.91457i		−	0.217476i
$325$	−3.42041	−	10.7366i	−0.189730	−	0.595558i
$326$	15.6774			0.868290
$327$	−9.58601	−	9.58601i	−0.530107	−	0.530107i
$328$			18.8391i			1.04021i
$329$	25.7463	+	18.8001i	1.41944	+	1.03648i
$330$	5.20031	−	5.20031i	0.286268	−	0.286268i
$331$	8.39979	−	8.39979i	0.461694	−	0.461694i	−0.437516	−	0.899211i	$-0.644142\pi$
$331$	8.39979	−	8.39979i	0.461694	−	0.461694i	0.899211	+	0.437516i	$0.144142\pi$
$332$	29.0303	−	29.0303i	1.59325	−	1.59325i
$333$	−5.45102	−	5.45102i	−0.298714	−	0.298714i
$334$		−	60.4945i		−	3.31011i
$335$	2.29851			0.125581
$336$	−9.13577	+	1.42456i	−0.498397	+	0.0777160i
$337$		−	11.0835i		−	0.603758i	−0.953346	−	0.301879i	$-0.902386\pi$
$337$		−	11.0835i		−	0.603758i	0.953346	−	0.301879i	$-0.0976139\pi$
$338$	5.30455	−	31.1677i	0.288529	−	1.69530i
$339$		−	5.33783i		−	0.289911i
$340$	−3.08986	+	3.08986i	−0.167571	+	0.167571i
$341$			6.04801i			0.327518i
$342$	−12.1786			−0.658541
$343$	−8.28932	−	16.5616i	−0.447581	−	0.894243i
$344$	4.66237	−	4.66237i	0.251378	−	0.251378i
$345$	−6.25011	−	6.25011i	−0.336495	−	0.336495i
$346$	−40.0651	+	40.0651i	−2.15391	+	2.15391i
$347$	6.14617			0.329944			0.164972	−	0.986298i	$-0.447247\pi$
$347$	6.14617			0.329944			0.164972	+	0.986298i	$0.447247\pi$
$348$	24.8553			1.33238
$349$	14.6839	−	14.6839i	0.786014	−	0.786014i	−0.194824	−	0.980838i	$-0.562414\pi$
$349$	14.6839	−	14.6839i	0.786014	−	0.786014i	0.980838	+	0.194824i	$0.0624137\pi$
$350$	11.8588	−	16.2404i	0.633880	−	0.868084i
$351$	1.09444	+	3.43543i	0.0584170	+	0.183370i
$352$	−1.79623			−0.0957393
$353$	−12.5407	−	12.5407i	−0.667473	−	0.667473i	0.289657	−	0.957130i	$-0.406459\pi$
$353$	−12.5407	−	12.5407i	−0.667473	−	0.667473i	−0.957130	+	0.289657i	$0.906459\pi$
$354$	14.7716			0.785099
$355$	3.79839			0.201598
$356$	0.274526	+	0.274526i	0.0145498	+	0.0145498i
$357$	2.13123	−	0.332326i	0.112796	−	0.0175886i
$358$	0.644905	+	0.644905i	0.0340843	+	0.0340843i
$359$	6.37165	+	6.37165i	0.336283	+	0.336283i	0.854966	−	0.518683i	$-0.173578\pi$
$359$	6.37165	+	6.37165i	0.336283	+	0.336283i	−0.518683	+	0.854966i	$0.673578\pi$
$360$		−	6.37536i		−	0.336011i
$361$			6.07662i			0.319822i
$362$	−20.2177	+	20.2177i	−1.06262	+	1.06262i
$363$	−6.12223			−0.321334
$364$	33.4095	−	16.6817i	1.75113	−	0.874359i
$365$	15.7862			0.826286
$366$	24.3551	−	24.3551i	1.27306	−	1.27306i
$367$		−	35.1154i		−	1.83301i	−0.400027	−	0.916503i	$-0.630999\pi$
$367$		−	35.1154i		−	1.83301i	0.400027	−	0.916503i	$-0.369001\pi$
$368$		−	22.5603i		−	1.17603i
$369$	2.86096	+	2.86096i	0.148936	+	0.148936i
$370$	−18.1514	−	18.1514i	−0.943648	−	0.943648i
$371$	−1.22948	−	7.88474i	−0.0638316	−	0.409356i
$372$	7.58003	+	7.58003i	0.393006	+	0.393006i
$373$	3.00691			0.155692			0.0778459	−	0.996965i	$-0.475196\pi$
$373$	3.00691			0.155692			0.0778459	+	0.996965i	$0.475196\pi$
$374$	−4.37895			−0.226430
$375$	7.86672	+	7.86672i	0.406235	+	0.406235i
$376$	−56.1045			−2.89337
$377$	−21.8130	+	6.94908i	−1.12343	+	0.357896i
$378$	−3.79452	+	5.19650i	−0.195169	+	0.267279i
$379$	−23.8078	+	23.8078i	−1.22292	+	1.22292i	−0.256335	+	0.966588i	$0.582515\pi$
$379$	−23.8078	+	23.8078i	−1.22292	+	1.22292i	−0.966588	+	0.256335i	$0.917485\pi$
$380$	−26.8405			−1.37689
$381$	13.1748			0.674966
$382$	41.6523	−	41.6523i	2.13112	−	2.13112i
$383$	4.46592	+	4.46592i	0.228198	+	0.228198i	0.811939	−	0.583742i	$-0.198412\pi$
$383$	4.46592	+	4.46592i	0.228198	+	0.228198i	−0.583742	+	0.811939i	$0.698412\pi$
$384$	−14.2708	+	14.2708i	−0.728255	+	0.728255i
$385$	−7.90524	+	1.23268i	−0.402888	+	0.0628231i
$386$	−55.9940			−2.85002
$387$		−	1.41608i		−	0.0719835i
$388$	−46.2766	+	46.2766i	−2.34934	+	2.34934i
$389$		−	2.72745i		−	0.138287i	−0.997607	−	0.0691437i	$-0.977973\pi$
$389$		−	2.72745i		−	0.138287i	0.997607	−	0.0691437i	$-0.0220267\pi$
$390$	3.64440	+	11.4397i	0.184542	+	0.579272i
$391$			5.26294i			0.266158i
$392$	28.9699	+	14.9360i	1.46320	+	0.754381i
$393$	−9.23713			−0.465951
$394$		−	34.1292i		−	1.71940i
$395$	5.01016	+	5.01016i	0.252088	+	0.252088i
$396$	6.11336	−	6.11336i	0.307208	−	0.307208i
$397$	19.7964	−	19.7964i	0.993551	−	0.993551i	−0.00642876	−	0.999979i	$-0.502046\pi$
$397$	19.7964	−	19.7964i	0.993551	−	0.993551i	0.999979	+	0.00642876i	$0.00204635\pi$
$398$	12.0770	−	12.0770i	0.605366	−	0.605366i
$399$	10.7000	+	7.81321i	0.535670	+	0.391150i
$400$			10.9219i			0.546094i
$401$	−26.4312	−	26.4312i	−1.31991	−	1.31991i	−0.913841	−	0.406072i	$-0.866898\pi$
$401$	−26.4312	−	26.4312i	−1.31991	−	1.31991i	−0.406072	−	0.913841i	$-0.633102\pi$
$402$	4.08259			0.203621
$403$	−8.77148	−	4.53300i	−0.436939	−	0.225805i
$404$			2.81572i			0.140087i
$405$	−0.968182	−	0.968182i	−0.0481093	−	0.0481093i
$406$	−32.9948	−	24.0930i	−1.63750	−	1.19571i
$407$		−	17.0256i		−	0.843930i
$408$	−2.68420	+	2.68420i	−0.132888	+	0.132888i
$409$	20.0529	+	20.0529i	0.991554	+	0.991554i	0.999965	−	0.00841024i	$-0.00267709\pi$
$409$	20.0529	+	20.0529i	0.991554	+	0.991554i	−0.00841024	+	0.999965i	$0.502677\pi$
$410$	9.52676	+	9.52676i	0.470493	+	0.470493i
$411$	−15.1160	+	15.1160i	−0.745616	+	0.745616i
$412$			24.9824i			1.23079i
$413$	−12.9782	−	9.47675i	−0.638615	−	0.466320i
$414$	−11.1014	−	11.1014i	−0.545604	−	0.545604i
$415$		−	14.3600i		−	0.704905i
$416$	1.34628	−	2.60509i	0.0660068	−	0.127725i
$417$	10.6234			0.520229
$418$	−19.0192	−	19.0192i	−0.930259	−	0.930259i
$419$		−	12.6256i		−	0.616800i	−0.951257	−	0.308400i	$-0.900207\pi$
$419$		−	12.6256i		−	0.616800i	0.951257	−	0.308400i	$-0.0997935\pi$
$420$	−8.36278	+	11.4526i	−0.408062	+	0.558832i
$421$	−21.7733	+	21.7733i	−1.06116	+	1.06116i	−0.0631600	+	0.998003i	$0.520118\pi$
$421$	−21.7733	+	21.7733i	−1.06116	+	1.06116i	−0.998003	+	0.0631600i	$0.979882\pi$
$422$	37.1120	−	37.1120i	1.80658	−	1.80658i
$423$	−8.52020	+	8.52020i	−0.414266	+	0.414266i
$424$	9.93055	+	9.93055i	0.482270	+	0.482270i
$425$		−	2.54790i		−	0.123591i
$426$	6.74667			0.326877
$427$	−37.0234	+	5.77313i	−1.79169	+	0.279381i
$428$			10.9500i			0.529287i
$429$	−3.65591	+	7.07428i	−0.176509	+	0.341549i
$430$		−	4.71544i		−	0.227399i
$431$	−8.78099	+	8.78099i	−0.422965	+	0.422965i	−0.886223	−	0.463258i	$-0.846680\pi$
$431$	−8.78099	+	8.78099i	−0.422965	+	0.422965i	0.463258	+	0.886223i	$0.346680\pi$
$432$		−	3.49472i		−	0.168140i
$433$	−19.3653			−0.930638			−0.465319	−	0.885143i	$-0.654060\pi$
$433$	−19.3653			−0.930638			−0.465319	+	0.885143i	$0.654060\pi$
$434$	−2.71476	−	17.4099i	−0.130312	−	0.835701i
$435$	6.14739	−	6.14739i	0.294745	−	0.294745i
$436$	−37.5251	−	37.5251i	−1.79713	−	1.79713i
$437$	−22.8587	+	22.8587i	−1.09348	+	1.09348i
$438$	28.0393			1.33977
$439$	6.44529			0.307617			0.153809	−	0.988101i	$-0.450846\pi$
$439$	6.44529			0.307617			0.153809	+	0.988101i	$0.450846\pi$
$440$	9.95636	−	9.95636i	0.474651	−	0.474651i
$441$	6.66767	−	2.13123i	0.317508	−	0.101487i
$442$	3.28204	−	6.35083i	0.156111	−	0.302078i
$443$	−25.2134			−1.19793			−0.598963	−	0.800777i	$-0.704420\pi$
$443$	−25.2134			−1.19793			−0.598963	+	0.800777i	$0.704420\pi$
$444$	−21.3384	−	21.3384i	−1.01268	−	1.01268i
$445$	0.135796			0.00643733
$446$	−1.07910			−0.0510968
$447$	4.78773	+	4.78773i	0.226452	+	0.226452i
$448$	23.4422	−	3.65539i	1.10754	−	0.172701i
$449$	9.02024	+	9.02024i	0.425691	+	0.425691i	0.887158	−	0.461466i	$-0.152677\pi$
$449$	9.02024	+	9.02024i	0.425691	+	0.425691i	−0.461466	+	0.887158i	$0.652677\pi$
$450$	5.37442	+	5.37442i	0.253352	+	0.253352i
$451$			8.93589i			0.420775i
$452$		−	20.8953i		−	0.982833i
$453$	−2.60195	+	2.60195i	−0.122250	+	0.122250i
$454$	26.3198			1.23525
$455$	4.13724	−	12.3889i	0.193957	−	0.580802i
$456$	−23.3167			−1.09191
$457$	6.24609	−	6.24609i	0.292180	−	0.292180i	−0.545761	−	0.837941i	$-0.683759\pi$
$457$	6.24609	−	6.24609i	0.292180	−	0.292180i	0.837941	+	0.545761i	$0.183759\pi$
$458$		−	60.1081i		−	2.80867i
$459$			0.815262i			0.0380532i
$460$	−24.4665	−	24.4665i	−1.14076	−	1.14076i
$461$	17.1553	+	17.1553i	0.799002	+	0.799002i	0.982938	−	0.183936i	$-0.0588840\pi$
$461$	17.1553	+	17.1553i	0.799002	+	0.799002i	−0.183936	+	0.982938i	$0.558884\pi$
$462$	−14.0412	+	2.18947i	−0.653257	+	0.101864i
$463$	5.48181	+	5.48181i	0.254761	+	0.254761i	0.822919	−	0.568158i	$-0.192344\pi$
$463$	5.48181	+	5.48181i	0.254761	+	0.254761i	−0.568158	+	0.822919i	$0.692344\pi$
$464$	22.1895			1.03012
$465$	3.74950			0.173879
$466$	47.4359	+	47.4359i	2.19743	+	2.19743i
$467$	6.06557			0.280681			0.140341	−	0.990103i	$-0.455180\pi$
$467$	6.06557			0.280681			0.140341	+	0.990103i	$0.455180\pi$
$468$	4.28427	+	13.4482i	0.198041	+	0.621645i
$469$	−3.58694	−	2.61920i	−0.165630	−	0.120944i
$470$	−28.3716	+	28.3716i	−1.30868	+	1.30868i
$471$	−0.836307			−0.0385350
$472$	28.2812			1.30175
$473$	2.21149	−	2.21149i	0.101684	−	0.101684i
$474$	8.89900	+	8.89900i	0.408745	+	0.408745i
$475$	11.0663	−	11.0663i	0.507759	−	0.507759i
$476$	8.34284	−	1.30092i	0.382393	−	0.0596273i
$477$	3.01617			0.138101
$478$			27.9395i			1.27792i
$479$	0.622849	−	0.622849i	0.0284587	−	0.0284587i	−0.692734	−	0.721193i	$-0.743594\pi$
$479$	0.622849	−	0.622849i	0.0284587	−	0.0284587i	0.721193	+	0.692734i	$0.243594\pi$
$480$			1.11358i			0.0508279i
$481$	24.6924	+	12.7608i	1.12588	+	0.581841i
$482$		−	48.8253i		−	2.22393i
$483$	2.63147	+	16.8758i	0.119736	+	0.767874i
$484$	−23.9659			−1.08936
$485$			22.8910i			1.03943i
$486$	−1.71968	−	1.71968i	−0.0780061	−	0.0780061i
$487$	10.7371	−	10.7371i	0.486546	−	0.486546i	−0.420669	−	0.907214i	$-0.638205\pi$
$487$	10.7371	−	10.7371i	0.486546	−	0.486546i	0.907214	+	0.420669i	$0.138205\pi$
$488$	46.6296	−	46.6296i	2.11082	−	2.11082i
$489$	4.55824	−	4.55824i	0.206131	−	0.206131i
$490$	22.2028	−	7.09681i	1.00302	−	0.320601i
$491$		−	17.3812i		−	0.784400i	−0.919880	−	0.392200i	$-0.871714\pi$
$491$		−	17.3812i		−	0.784400i	0.919880	−	0.392200i	$-0.128286\pi$
$492$	11.1994	+	11.1994i	0.504909	+	0.504909i
$493$	−5.17645			−0.233135
$494$	41.8386	−	13.3287i	1.88241	−	0.599689i
$495$		−	3.02401i		−	0.135919i
$496$	6.76706	+	6.76706i	0.303850	+	0.303850i
$497$	−5.92758	−	4.32835i	−0.265888	−	0.194153i
$498$		−	25.5061i		−	1.14296i
$499$	−26.6474	+	26.6474i	−1.19290	+	1.19290i	−0.216650	+	0.976249i	$0.569513\pi$
$499$	−26.6474	+	26.6474i	−1.19290	+	1.19290i	−0.976249	+	0.216650i	$0.930487\pi$
$500$	30.7948	+	30.7948i	1.37719	+	1.37719i
$501$	−17.5889	−	17.5889i	−0.785815	−	0.785815i
$502$	−14.4254	+	14.4254i	−0.643837	+	0.643837i
$503$			34.1550i			1.52290i	0.648226	+	0.761448i	$0.275511\pi$
$503$			34.1550i			1.52290i	−0.648226	+	0.761448i	$0.724489\pi$
$504$	−7.26487	+	9.94907i	−0.323603	+	0.443167i
$505$	0.696406	+	0.696406i	0.0309896	+	0.0309896i
$506$		−	34.6740i		−	1.54145i
$507$	−7.51977	−	10.6044i	−0.333965	−	0.470957i
$508$	51.5737			2.28821
$509$	−7.16328	−	7.16328i	−0.317507	−	0.317507i	0.530302	−	0.847809i	$-0.322078\pi$
$509$	−7.16328	−	7.16328i	−0.317507	−	0.317507i	−0.847809	+	0.530302i	$0.822078\pi$
$510$			2.71476i			0.120211i
$511$	−24.6351	−	17.9887i	−1.08979	−	0.795773i
$512$	−25.0221	+	25.0221i	−1.10583	+	1.10583i
$513$	−3.54095	+	3.54095i	−0.156337	+	0.156337i
$514$	−31.7121	+	31.7121i	−1.39876	+	1.39876i
$515$	6.17883	+	6.17883i	0.272272	+	0.272272i
$516$		−	5.54336i		−	0.244033i
$517$	−26.6119			−1.17039
$518$	7.64226	+	49.0102i	0.335781	+	2.15338i
$519$			23.2980i			1.02267i
$520$	6.97747	+	21.9021i	0.305982	+	0.960472i
$521$			30.2128i			1.32365i	0.749660	+	0.661823i	$0.230217\pi$
$521$			30.2128i			1.32365i	−0.749660	+	0.661823i	$0.769783\pi$
$522$	10.9189	−	10.9189i	0.477909	−	0.477909i
$523$			10.9106i			0.477086i	0.971132	+	0.238543i	$0.0766698\pi$
$523$			10.9106i			0.477086i	−0.971132	+	0.238543i	$0.923330\pi$
$524$	−36.1594			−1.57963
$525$	−1.27395	−	8.16990i	−0.0555997	−	0.356564i
$526$	−22.1667	+	22.1667i	−0.966512	+	0.966512i
$527$	−1.57864	−	1.57864i	−0.0687668	−	0.0687668i
$528$	5.45769	−	5.45769i	0.237515	−	0.237515i
$529$	−18.6737			−0.811901
$530$	10.0436			0.436265
$531$	4.29487	−	4.29487i	0.186381	−	0.186381i
$532$	41.8859	+	30.5853i	1.81599	+	1.32604i
$533$	−12.9598	−	6.69748i	−0.561351	−	0.290100i
$534$	0.241199			0.0104377
$535$	2.70823	+	2.70823i	0.117087	+	0.117087i
$536$	7.81642			0.337618
$537$	0.375015			0.0161831
$538$	34.8506	+	34.8506i	1.50251	+	1.50251i
$539$	13.7412	+	7.08454i	0.591875	+	0.305153i
$540$	−3.79002	−	3.79002i	−0.163096	−	0.163096i
$541$	−11.2043	−	11.2043i	−0.481711	−	0.481711i	0.423967	−	0.905678i	$-0.360637\pi$
$541$	−11.2043	−	11.2043i	−0.481711	−	0.481711i	−0.905678	+	0.423967i	$0.860637\pi$
$542$		−	39.5210i		−	1.69757i
$543$			11.7567i			0.504528i
$544$	0.468849	−	0.468849i	0.0201018	−	0.0201018i
$545$	−18.5620			−0.795108
$546$	7.34853	−	22.0051i	0.314488	−	0.941732i
$547$	−23.5106			−1.00524			−0.502621	−	0.864507i	$-0.667631\pi$
$547$	−23.5106			−1.00524			−0.502621	+	0.864507i	$0.667631\pi$
$548$	−59.1726	+	59.1726i	−2.52773	+	2.52773i
$549$		−	14.1626i		−	0.604446i
$550$			16.7864i			0.715774i
$551$	−22.4830	−	22.4830i	−0.957807	−	0.957807i
$552$	−21.2544	−	21.2544i	−0.904648	−	0.904648i
$553$	−2.10941	−	13.5278i	−0.0897014	−	0.575260i
$554$	−22.8306	−	22.8306i	−0.969978	−	0.969978i
$555$	−10.5551			−0.448041
$556$	41.5860			1.76364
$557$	7.78928	+	7.78928i	0.330042	+	0.330042i	0.852602	−	0.522560i	$-0.175023\pi$
$557$	7.78928	+	7.78928i	0.330042	+	0.330042i	−0.522560	+	0.852602i	$0.675023\pi$
$558$	6.65983			0.281933
$559$	1.54982	+	4.86486i	0.0655505	+	0.205762i
$560$	−7.46585	+	10.2243i	−0.315490	+	0.432056i
$561$	−1.27319	+	1.27319i	−0.0537541	+	0.0537541i
$562$	53.5017			2.25683
$563$	20.4262			0.860864			0.430432	−	0.902623i	$-0.358361\pi$
$563$	20.4262			0.860864			0.430432	+	0.902623i	$0.358361\pi$
$564$	−33.3529	+	33.3529i	−1.40441	+	1.40441i
$565$	−5.16799	−	5.16799i	−0.217419	−	0.217419i
$566$	3.76617	−	3.76617i	0.158304	−	0.158304i
$567$	0.407631	+	2.61416i	0.0171189	+	0.109784i
$568$	12.9170			0.541984
$569$			25.0423i			1.04983i	0.851155	+	0.524914i	$0.175902\pi$
$569$			25.0423i			1.04983i	−0.851155	+	0.524914i	$0.824098\pi$
$570$	−11.7911	+	11.7911i	−0.493873	+	0.493873i
$571$			19.9789i			0.836090i	0.908426	+	0.418045i	$0.137285\pi$
$571$			19.9789i			0.836090i	−0.908426	+	0.418045i	$0.862715\pi$
$572$	−14.3113	+	27.6928i	−0.598386	+	1.15789i
$573$		−	24.2210i		−	1.01185i
$574$	−4.01103	−	25.7230i	−0.167417	−	1.07366i
$575$	20.1751			0.841360
$576$			8.96739i			0.373641i
$577$	12.8188	+	12.8188i	0.533655	+	0.533655i	0.921658	−	0.388003i	$-0.126835\pi$
$577$	12.8188	+	12.8188i	0.533655	+	0.533655i	−0.388003	+	0.921658i	$0.626835\pi$
$578$	−28.0915	+	28.0915i	−1.16845	+	1.16845i
$579$	−16.2804	+	16.2804i	−0.676590	+	0.676590i
$580$	24.0644	−	24.0644i	0.999220	−	0.999220i
$581$	−16.3636	+	22.4095i	−0.678874	+	0.929703i
$582$			40.6588i			1.68536i
$583$	4.71033	+	4.71033i	0.195082	+	0.195082i
$584$	53.6832			2.22143
$585$	4.38574	+	2.26650i	0.181328	+	0.0937083i
$586$		−	26.5741i		−	1.09777i
$587$	16.4741	+	16.4741i	0.679958	+	0.679958i	0.959991	−	0.280032i	$-0.0903452\pi$
$587$	16.4741	+	16.4741i	0.679958	+	0.679958i	−0.280032	+	0.959991i	$0.590345\pi$
$588$	26.1011	−	8.34284i	1.07639	−	0.344053i
$589$		−	13.7131i		−	0.565039i
$590$	14.3015	−	14.3015i	0.588785	−	0.588785i
$591$	−9.92313	−	9.92313i	−0.408183	−	0.408183i
$592$	−19.0498	−	19.0498i	−0.782942	−	0.782942i
$593$	−8.37016	+	8.37016i	−0.343721	+	0.343721i	−0.857764	−	0.514043i	$-0.828147\pi$
$593$	−8.37016	+	8.37016i	−0.343721	+	0.343721i	0.514043	+	0.857764i	$0.328147\pi$
$594$		−	5.37121i		−	0.220384i
$595$	1.74166	−	2.38517i	0.0714012	−	0.0977823i
$596$	18.7419	+	18.7419i	0.767698	+	0.767698i
$597$		−	7.02284i		−	0.287426i
$598$	50.2880	+	25.9883i	2.05643	+	1.06274i
$599$	−15.3914			−0.628875			−0.314437	−	0.949278i	$-0.601816\pi$
$599$	−15.3914			−0.628875			−0.314437	+	0.949278i	$0.601816\pi$
$600$	10.2897	+	10.2897i	0.420075	+	0.420075i
$601$			25.3871i			1.03556i	0.855513	+	0.517781i	$0.173242\pi$
$601$			25.3871i			1.03556i	−0.855513	+	0.517781i	$0.826758\pi$
$602$	−5.37335	+	7.35868i	−0.219001	+	0.299917i
$603$	1.18702	−	1.18702i	0.0483394	−	0.0483394i
$604$	−10.1855	+	10.1855i	−0.414442	+	0.414442i
$605$	−5.92743	+	5.92743i	−0.240984	+	0.240984i
$606$	1.23695	+	1.23695i	0.0502477	+	0.0502477i
$607$		−	6.82917i		−	0.277188i	−0.990349	−	0.138594i	$-0.955742\pi$
$607$		−	6.82917i		−	0.277188i	0.990349	−	0.138594i	$-0.0442582\pi$
$608$	4.07273			0.165171
$609$	−16.5984	+	2.58822i	−0.672602	+	0.104880i
$610$		−	47.1604i		−	1.90947i
$611$	19.9457	−	38.5954i	0.806917	−	1.56140i
$612$			3.19140i			0.129005i
$613$	9.93344	−	9.93344i	0.401208	−	0.401208i	−0.477451	−	0.878659i	$-0.658439\pi$
$613$	9.93344	−	9.93344i	0.401208	−	0.401208i	0.878659	+	0.477451i	$0.158439\pi$
$614$			33.3075i			1.34418i
$615$	5.53986			0.223389
$616$	−26.8829	+	4.19190i	−1.08314	+	0.168897i
$617$	−18.8786	+	18.8786i	−0.760025	+	0.760025i	−0.976327	−	0.216302i	$-0.930600\pi$
$617$	−18.8786	+	18.8786i	−0.760025	+	0.760025i	0.216302	+	0.976327i	$0.430600\pi$
$618$	10.9748	+	10.9748i	0.441470	+	0.441470i
$619$	12.2389	−	12.2389i	0.491924	−	0.491924i	−0.416988	−	0.908912i	$-0.636914\pi$
$619$	12.2389	−	12.2389i	0.491924	−	0.491924i	0.908912	+	0.416988i	$0.136914\pi$
$620$	14.6777			0.589470
$621$	−6.45552			−0.259051
$622$	1.19432	−	1.19432i	0.0478879	−	0.0478879i
$623$	−0.211916	−	0.154742i	−0.00849023	−	0.00619962i
$624$	3.82478	+	12.0059i	0.153114	+	0.480620i
$625$	−0.393427			−0.0157371
$626$	5.00478	+	5.00478i	0.200031	+	0.200031i
$627$	−11.0598			−0.441684
$628$	−3.27378			−0.130638
$629$	4.44401	+	4.44401i	0.177194	+	0.177194i
$630$	1.35738	+	8.70494i	0.0540792	+	0.346813i
$631$	−8.10028	−	8.10028i	−0.322467	−	0.322467i	0.527246	−	0.849713i	$-0.323225\pi$
$631$	−8.10028	−	8.10028i	−0.322467	−	0.322467i	−0.849713	+	0.527246i	$0.823225\pi$
$632$	17.0378	+	17.0378i	0.677726	+	0.677726i
$633$		−	21.5808i		−	0.857760i
$634$		−	62.6736i		−	2.48909i
$635$	12.7556	−	12.7556i	0.506191	−	0.506191i
$636$	11.8070			0.468178
$637$	−20.5738	+	14.6191i	−0.815165	+	0.579229i
$638$	34.1041			1.35019
$639$	1.96161	−	1.96161i	0.0776001	−	0.0776001i
$640$			27.6335i			1.09231i
$641$			11.2884i			0.445866i	0.974834	+	0.222933i	$0.0715631\pi$
$641$			11.2884i			0.445866i	−0.974834	+	0.222933i	$0.928437\pi$
$642$	4.81034	+	4.81034i	0.189849	+	0.189849i
$643$	−16.1645	−	16.1645i	−0.637467	−	0.637467i	0.312463	−	0.949930i	$-0.398846\pi$
$643$	−16.1645	−	16.1645i	−0.637467	−	0.637467i	−0.949930	+	0.312463i	$0.898846\pi$
$644$	10.3011	+	66.0614i	0.405919	+	2.60318i
$645$	−1.37103	−	1.37103i	−0.0539841	−	0.0539841i
$646$	9.92873			0.390640
$647$	−40.0087			−1.57290			−0.786452	−	0.617651i	$-0.788084\pi$
$647$	−40.0087			−1.57290			−0.786452	+	0.617651i	$0.788084\pi$
$648$	−3.29244	−	3.29244i	−0.129339	−	0.129339i
$649$	13.4145			0.526566
$650$	−24.3454	−	12.5814i	−0.954906	−	0.493485i
$651$	−5.85129	−	4.27264i	−0.229330	−	0.167458i
$652$	17.8435	−	17.8435i	0.698807	−	0.698807i
$653$	16.2041			0.634116			0.317058	−	0.948406i	$-0.397305\pi$
$653$	16.2041			0.634116			0.317058	+	0.948406i	$0.397305\pi$
$654$	−32.9697			−1.28922
$655$	−8.94322	+	8.94322i	−0.349440	+	0.349440i
$656$	9.99827	+	9.99827i	0.390367	+	0.390367i
$657$	8.15249	−	8.15249i	0.318059	−	0.318059i
$658$	76.6053	−	11.9452i	2.98639	−	0.465673i
$659$	−13.6034			−0.529912			−0.264956	−	0.964260i	$-0.585357\pi$
$659$	−13.6034			−0.529912			−0.264956	+	0.964260i	$0.585357\pi$
$660$		−	11.8377i		−	0.460781i
$661$	2.06376	−	2.06376i	0.0802710	−	0.0802710i	−0.665831	−	0.746102i	$-0.731923\pi$
$661$	2.06376	−	2.06376i	0.0802710	−	0.0802710i	0.746102	+	0.665831i	$0.231923\pi$
$662$		−	28.8898i		−	1.12284i
$663$	−0.892258	−	2.80078i	−0.0346524	−	0.108773i
$664$		−	48.8333i		−	1.89510i
$665$	17.9241	−	2.79495i	0.695069	−	0.108383i
$666$	−18.7480			−0.726469
$667$		−	40.9888i		−	1.58709i
$668$	−68.8531	−	68.8531i	−2.66400	−	2.66400i
$669$	−0.313751	+	0.313751i	−0.0121303	+	0.0121303i
$670$	3.95269	−	3.95269i	0.152706	−	0.152706i
$671$	22.1177	−	22.1177i	0.853844	−	0.853844i
$672$	1.26895	−	1.73780i	0.0489509	−	0.0670372i
$673$			27.1781i			1.04764i	0.851830	+	0.523819i	$0.175493\pi$
$673$			27.1781i			1.04764i	−0.851830	+	0.523819i	$0.824507\pi$
$674$	−19.0601	−	19.0601i	−0.734167	−	0.734167i
$675$	3.12525			0.120291
$676$	−29.4367	−	41.5116i	−1.13218	−	1.59660i
$677$		−	5.88065i		−	0.226012i	−0.993594	−	0.113006i	$-0.963952\pi$
$677$		−	5.88065i		−	0.226012i	0.993594	−	0.113006i	$-0.0360479\pi$
$678$	−9.17934	−	9.17934i	−0.352530	−	0.352530i
$679$	26.0848	−	35.7225i	1.00104	−	1.37090i
$680$			5.19759i			0.199319i
$681$	7.65255	−	7.65255i	0.293246	−	0.293246i
$682$	10.4006	+	10.4006i	0.398260	+	0.398260i
$683$	−6.28079	−	6.28079i	−0.240328	−	0.240328i	0.576658	−	0.816986i	$-0.304357\pi$
$683$	−6.28079	−	6.28079i	−0.240328	−	0.240328i	−0.816986	+	0.576658i	$0.804357\pi$
$684$	−13.8613	+	13.8613i	−0.530000	+	0.530000i
$685$			29.2700i			1.11835i
$686$	−42.7356	−	14.2257i	−1.63165	−	0.543138i
$687$	−17.4766	−	17.4766i	−0.666773	−	0.666773i
$688$		−	4.94882i		−	0.188672i
$689$	−10.3618	+	3.30102i	−0.394754	+	0.125759i
$690$	−21.4963			−0.818352
$691$	−11.2231	−	11.2231i	−0.426946	−	0.426946i	0.460641	−	0.887587i	$-0.347620\pi$
$691$	−11.2231	−	11.2231i	−0.426946	−	0.426946i	−0.887587	+	0.460641i	$0.847620\pi$
$692$			91.2018i			3.46697i
$693$	−3.44592	+	4.71911i	−0.130900	+	0.179264i
$694$	10.5694	−	10.5694i	0.401210	−	0.401210i
$695$	10.2854	−	10.2854i	0.390146	−	0.390146i
$696$	20.9051	−	20.9051i	0.792406	−	0.792406i
$697$	−2.33243	−	2.33243i	−0.0883472	−	0.0883472i
$698$		−	50.5033i		−	1.91158i
$699$	27.5842			1.04333
$700$	−4.98696	−	31.9817i	−0.188490	−	1.20879i
$701$			30.3617i			1.14674i	0.819295	+	0.573372i	$0.194365\pi$
$701$			30.3617i			1.14674i	−0.819295	+	0.573372i	$0.805635\pi$
$702$	7.78992	+	4.02574i	0.294011	+	0.151942i
$703$			38.6035i			1.45596i
$704$	−14.0043	+	14.0043i	−0.527807	+	0.527807i
$705$			16.4982i			0.621358i
$706$	−43.1318			−1.62329
$707$	−0.293206	−	1.88035i	−0.0110271	−	0.0707177i
$708$	16.8126	−	16.8126i	0.631855	−	0.631855i
$709$	19.6577	+	19.6577i	0.738259	+	0.738259i	0.972241	−	0.233982i	$-0.0751758\pi$
$709$	19.6577	+	19.6577i	0.738259	+	0.738259i	−0.233982	+	0.972241i	$0.575176\pi$
$710$	6.53200	−	6.53200i	0.245142	−	0.245142i
$711$	5.17481			0.194071
$712$	0.461793			0.0173064
$713$	12.5002	−	12.5002i	0.468137	−	0.468137i
$714$	3.09353	−	4.23651i	0.115772	−	0.158548i
$715$	3.30960	+	10.3888i	0.123772	+	0.388518i
$716$	1.46802			0.0548626
$717$	8.12347	+	8.12347i	0.303376	+	0.303376i
$718$	21.9144			0.817837
$719$	39.6312			1.47799			0.738996	−	0.673709i	$-0.235300\pi$
$719$	39.6312			1.47799			0.738996	+	0.673709i	$0.235300\pi$
$720$	−3.38353	−	3.38353i	−0.126097	−	0.126097i
$721$	−2.60146	−	16.6833i	−0.0968833	−	0.621318i
$722$	10.4498	+	10.4498i	0.388902	+	0.388902i
$723$	−14.1961	−	14.1961i	−0.527958	−	0.527958i
$724$			46.0225i			1.71041i
$725$			19.8435i			0.736970i
$726$	−10.5282	+	10.5282i	−0.390740	+	0.390740i
$727$	−28.7315			−1.06559			−0.532796	−	0.846244i	$-0.678859\pi$
$727$	−28.7315			−1.06559			−0.532796	+	0.846244i	$0.678859\pi$
$728$	14.0693	−	42.1304i	0.521442	−	1.56145i
$729$	−1.00000			−0.0370370
$730$	27.1471	−	27.1471i	1.00476	−	1.00476i
$731$			1.15448i			0.0426999i
$732$		−	55.4406i		−	2.04914i
$733$	1.35193	+	1.35193i	0.0499345	+	0.0499345i	0.731633	−	0.681699i	$-0.238758\pi$
$733$	1.35193	+	1.35193i	0.0499345	+	0.0499345i	−0.681699	+	0.731633i	$0.738758\pi$
$734$	−60.3870	−	60.3870i	−2.22893	−	2.22893i
$735$	4.39210	−	8.51893i	0.162005	−	0.314226i
$736$	3.71251	+	3.71251i	0.136845	+	0.136845i
$737$	3.70754			0.136569
$738$	9.83985			0.362210
$739$	−0.948546	−	0.948546i	−0.0348928	−	0.0348928i	0.689445	−	0.724338i	$-0.257854\pi$
$739$	−0.948546	−	0.948546i	−0.0348928	−	0.0348928i	−0.724338	+	0.689445i	$0.757854\pi$
$740$	−41.3189			−1.51891
$741$	8.28932	−	16.0400i	0.304516	−	0.589246i
$742$	−15.6735	−	11.4449i	−0.575393	−	0.420155i
$743$	19.4001	−	19.4001i	0.711721	−	0.711721i	−0.255174	−	0.966895i	$-0.582133\pi$
$743$	19.4001	−	19.4001i	0.711721	−	0.711721i	0.966895	+	0.255174i	$0.0821329\pi$
$744$	12.7507			0.467464
$745$	9.27078			0.339655
$746$	5.17091	−	5.17091i	0.189320	−	0.189320i
$747$	−7.41597	−	7.41597i	−0.271336	−	0.271336i
$748$	−4.98399	+	4.98399i	−0.182233	+	0.182233i
$749$	−1.14024	−	7.31242i	−0.0416635	−	0.267190i
$750$	27.0564			0.987960
$751$		−	42.2686i		−	1.54240i	−0.636591	−	0.771202i	$-0.719656\pi$
$751$		−	42.2686i		−	1.54240i	0.636591	−	0.771202i	$-0.280344\pi$
$752$	−29.7758	+	29.7758i	−1.08581	+	1.08581i
$753$			8.38843i			0.305691i
$754$	−25.5611	+	49.4615i	−0.930882	+	1.80128i
$755$			5.03831i			0.183363i
$756$	1.59570	+	10.2333i	0.0580351	+	0.372182i
$757$	46.6122			1.69415			0.847075	−	0.531474i	$-0.178362\pi$
$757$	46.6122			1.69415			0.847075	+	0.531474i	$0.178362\pi$
$758$			81.8833i			2.97414i
$759$	−10.0815	−	10.0815i	−0.365937	−	0.365937i
$760$	−22.5748	+	22.5748i	−0.818875	+	0.818875i
$761$	33.1432	−	33.1432i	1.20144	−	1.20144i	0.227712	−	0.973728i	$-0.426875\pi$
$761$	33.1432	−	33.1432i	1.20144	−	1.20144i	0.973728	−	0.227712i	$-0.0731246\pi$
$762$	22.6564	−	22.6564i	0.820755	−	0.820755i
$763$	28.9669	+	21.1518i	1.04867	+	0.765747i
$764$		−	94.8149i		−	3.43028i
$765$	0.789322	+	0.789322i	0.0285380	+	0.0285380i
$766$	15.3599			0.554975
$767$	−10.0542	+	19.4552i	−0.363037	+	0.702487i
$768$			31.1476i			1.12394i
$769$	−9.43052	−	9.43052i	−0.340073	−	0.340073i	0.516321	−	0.856395i	$-0.327301\pi$
$769$	−9.43052	−	9.43052i	−0.340073	−	0.340073i	−0.856395	+	0.516321i	$0.827301\pi$
$770$	−11.4746	+	15.7143i	−0.413517	+	0.566303i
$771$			18.4408i			0.664128i
$772$	−63.7307	+	63.7307i	−2.29372	+	2.29372i
$773$	−10.7574	−	10.7574i	−0.386917	−	0.386917i	0.486669	−	0.873586i	$-0.338212\pi$
$773$	−10.7574	−	10.7574i	−0.386917	−	0.386917i	−0.873586	+	0.486669i	$0.838212\pi$
$774$	−2.43520	−	2.43520i	−0.0875316	−	0.0875316i
$775$	−6.05162	+	6.05162i	−0.217380	+	0.217380i
$776$			77.8441i			2.79444i
$777$	16.4718	+	12.0278i	0.590924	+	0.431496i
$778$	−4.69034	−	4.69034i	−0.168157	−	0.168157i
$779$		−	20.2610i		−	0.725926i
$780$	17.1683	+	8.87239i	0.614724	+	0.317682i
$781$	6.12687			0.219237
$782$	9.05055	+	9.05055i	0.323647	+	0.323647i
$783$		−	6.34942i		−	0.226910i
$784$	23.3017	−	7.44805i	0.832203	−	0.266002i
$785$	−0.809697	+	0.809697i	−0.0288993	+	0.0288993i
$786$	−15.8849	+	15.8849i	−0.566594	+	0.566594i
$787$	−15.0983	+	15.0983i	−0.538196	+	0.538196i	−0.922999	−	0.384803i	$-0.874270\pi$
$787$	−15.0983	+	15.0983i	−0.538196	+	0.538196i	0.384803	+	0.922999i	$0.374270\pi$
$788$	−38.8448	−	38.8448i	−1.38379	−	1.38379i
$789$			12.8900i			0.458897i
$790$	17.2317			0.613076
$791$	2.17587	+	13.9539i	0.0773649	+	0.496145i
$792$		−	10.2836i		−	0.365411i
$793$	15.5002	+	48.6547i	0.550428	+	1.72778i
$794$		−	68.0866i		−	2.41630i
$795$	2.92020	−	2.92020i	0.103569	−	0.103569i
$796$		−	27.4914i		−	0.974408i
$797$	3.22445			0.114216			0.0571080	−	0.998368i	$-0.481812\pi$
$797$	3.22445			0.114216			0.0571080	+	0.998368i	$0.481812\pi$
$798$	31.8367	−	4.96436i	1.12701	−	0.175737i
$799$	6.94620	−	6.94620i	0.245739	−	0.245739i
$800$	−1.79730	−	1.79730i	−0.0635442	−	0.0635442i
$801$	0.0701292	−	0.0701292i	0.00247789	−	0.00247789i
$802$	−90.9063			−3.21001
$803$	25.4634			0.898583
$804$	4.64669	−	4.64669i	0.163876	−	0.163876i
$805$	18.8865	+	13.7911i	0.665663	+	0.486071i
$806$	−22.8794	+	7.28881i	−0.805893	+	0.256737i
$807$	20.2658			0.713389
$808$	2.36823	+	2.36823i	0.0833140	+	0.0833140i
$809$	−1.35576			−0.0476659			−0.0238330	−	0.999716i	$-0.507587\pi$
$809$	−1.35576			−0.0476659			−0.0238330	+	0.999716i	$0.507587\pi$
$810$	−3.32992			−0.117001
$811$	19.2999	+	19.2999i	0.677711	+	0.677711i	0.959482	−	0.281771i	$-0.0909217\pi$
$811$	19.2999	+	19.2999i	0.677711	+	0.677711i	−0.281771	+	0.959482i	$0.590922\pi$
$812$	−64.9757	+	10.1318i	−2.28020	+	0.355556i
$813$	−11.4908	−	11.4908i	−0.403001	−	0.403001i
$814$	−29.2786	−	29.2786i	−1.02621	−	1.02621i
$815$		−	8.82640i		−	0.309175i
$816$			2.84912i			0.0997391i
$817$	−5.01427	+	5.01427i	−0.175427	+	0.175427i
$818$	68.9691			2.41145
$819$	−4.26144	−	8.53464i	−0.148907	−	0.298225i
$820$	21.6862			0.757314
$821$	−15.1432	+	15.1432i	−0.528501	+	0.528501i	−0.920125	−	0.391624i	$-0.871913\pi$
$821$	−15.1432	+	15.1432i	−0.528501	+	0.528501i	0.391624	+	0.920125i	$0.371913\pi$
$822$			51.9892i			1.81333i
$823$			53.5942i			1.86818i	0.357042	+	0.934088i	$0.383785\pi$
$823$			53.5942i			1.86818i	−0.357042	+	0.934088i	$0.616215\pi$
$824$	21.0120	+	21.0120i	0.731988	+	0.731988i
$825$	4.88068	+	4.88068i	0.169924	+	0.169924i
$826$	−38.6152	+	6.02135i	−1.34360	+	0.209509i
$827$	−7.02585	−	7.02585i	−0.244313	−	0.244313i	0.574319	−	0.818632i	$-0.305267\pi$
$827$	−7.02585	−	7.02585i	−0.244313	−	0.244313i	−0.818632	+	0.574319i	$0.805267\pi$
$828$	−25.2706			−0.878214
$829$	−15.1645			−0.526684			−0.263342	−	0.964703i	$-0.584825\pi$
$829$	−15.1645			−0.526684			−0.263342	+	0.964703i	$0.584825\pi$
$830$	−24.6946	−	24.6946i	−0.857160	−	0.857160i
$831$	−13.2761			−0.460542
$832$	−9.81429	−	30.8068i	−0.340249	−	1.06804i
$833$	−5.43590	+	1.73751i	−0.188343	+	0.0602011i
$834$	18.2688	−	18.2688i	0.632596	−	0.632596i
$835$	−34.0585			−1.17864
$836$	−43.2942			−1.49736
$837$	1.93636	−	1.93636i	0.0669305	−	0.0669305i
$838$	−21.7119	−	21.7119i	−0.750025	−	0.750025i
$839$	−26.1290	+	26.1290i	−0.902073	+	0.902073i	−0.995615	−	0.0935419i	$-0.970181\pi$
$839$	−26.1290	+	26.1290i	−0.902073	+	0.902073i	0.0935419	+	0.995615i	$0.470181\pi$
$840$	2.59880	+	16.6662i	0.0896670	+	0.575039i
$841$	11.3152			0.390178
$842$			74.8859i			2.58074i
$843$	15.5558	−	15.5558i	0.535768	−	0.535768i
$844$		−	84.4796i		−	2.90791i
$845$	−17.5475	−	2.98647i	−0.603652	−	0.102738i
$846$			29.3040i			1.00749i
$847$	16.0045	−	2.49561i	0.549921	−	0.0857502i
$848$	10.5407			0.361968
$849$		−	2.19005i		−	0.0751622i
$850$	−4.38156	−	4.38156i	−0.150286	−	0.150286i
$851$	−35.1891	+	35.1891i	−1.20627	+	1.20627i
$852$	7.67886	−	7.67886i	0.263073	−	0.263073i
$853$	23.5072	−	23.5072i	0.804870	−	0.804870i	−0.178982	−	0.983852i	$-0.557281\pi$
$853$	23.5072	−	23.5072i	0.804870	−	0.804870i	0.983852	+	0.178982i	$0.0572805\pi$
$854$	−53.7403	+	73.5961i	−1.83896	+	2.51841i
$855$			6.85656i			0.234489i
$856$	9.20973	+	9.20973i	0.314782	+	0.314782i
$857$	−11.9890			−0.409536			−0.204768	−	0.978811i	$-0.565644\pi$
$857$	−11.9890			−0.409536			−0.204768	+	0.978811i	$0.565644\pi$
$858$	5.87849	+	18.4524i	0.200688	+	0.629956i
$859$		−	1.16967i		−	0.0399085i	−0.999801	−	0.0199542i	$-0.993648\pi$
$859$		−	1.16967i		−	0.0399085i	0.999801	−	0.0199542i	$-0.00635205\pi$
$860$	−5.36698	−	5.36698i	−0.183012	−	0.183012i
$861$	−8.64523	−	6.31279i	−0.294629	−	0.215139i
$862$			30.2009i			1.02865i
$863$	25.3127	−	25.3127i	0.861654	−	0.861654i	−0.129876	−	0.991530i	$-0.541458\pi$
$863$	25.3127	−	25.3127i	0.861654	−	0.861654i	0.991530	+	0.129876i	$0.0414579\pi$
$864$	0.575090	+	0.575090i	0.0195650	+	0.0195650i
$865$	22.5567	+	22.5567i	0.766952	+	0.766952i
$866$	−33.3021	+	33.3021i	−1.13165	+	1.13165i
$867$			16.3353i			0.554777i
$868$	−22.9053	−	16.7256i	−0.777456	−	0.567703i
$869$	8.08147	+	8.08147i	0.274145	+	0.274145i
$870$		−	21.1430i		−	0.716817i
$871$	−2.77881	+	5.37707i	−0.0941564	+	0.182195i
$872$	−63.1228			−2.13761
$873$	11.8216	+	11.8216i	0.400102	+	0.400102i
$874$			78.6189i			2.65933i
$875$	−23.7716	−	17.3581i	−0.803626	−	0.586812i
$876$	31.9135	−	31.9135i	1.07826	−	1.07826i
$877$	−24.0851	+	24.0851i	−0.813298	+	0.813298i	−0.985127	−	0.171829i	$-0.945032\pi$
$877$	−24.0851	+	24.0851i	−0.813298	+	0.813298i	0.171829	+	0.985127i	$0.445032\pi$
$878$	11.0838	−	11.0838i	0.374061	−	0.374061i
$879$	−7.72648	−	7.72648i	−0.260608	−	0.260608i
$880$		−	10.5681i		−	0.356249i
$881$	9.27254			0.312400			0.156200	−	0.987725i	$-0.450076\pi$
$881$	9.27254			0.312400			0.156200	+	0.987725i	$0.450076\pi$
$882$	7.80122	−	15.1313i	0.262681	−	0.509496i
$883$		−	8.71420i		−	0.293256i	−0.989192	−	0.146628i	$-0.953158\pi$
$883$		−	8.71420i		−	0.293256i	0.989192	−	0.146628i	$-0.0468420\pi$
$884$	−3.49281	−	10.9638i	−0.117476	−	0.368754i
$885$		−	8.31642i		−	0.279553i
$886$	−43.3589	+	43.3589i	−1.45667	+	1.45667i
$887$			17.6170i			0.591521i	0.955262	+	0.295760i	$0.0955730\pi$
$887$			17.6170i			0.591521i	−0.955262	+	0.295760i	$0.904427\pi$
$888$	−35.8943			−1.20453
$889$	−34.4411	+	5.37046i	−1.15512	+	0.180120i
$890$	0.233524	−	0.233524i	0.00782776	−	0.00782776i
$891$	−1.56169	−	1.56169i	−0.0523187	−	0.0523187i
$892$	−1.22820	+	1.22820i	−0.0411231	+	0.0411231i
$893$	60.3392			2.01917
$894$	16.4667			0.550728
$895$	0.363083	−	0.363083i	0.0121365	−	0.0121365i
$896$	31.4890	−	43.1234i	1.05197	−	1.44065i
$897$	22.1775	−	7.06520i	0.740485	−	0.235900i
$898$	31.0238			1.03528
$899$	12.2948	+	12.2948i	0.410054	+	0.410054i
$900$	12.2340			0.407800
$901$	−2.45897			−0.0819201
$902$	15.3668	+	15.3668i	0.511660	+	0.511660i
$903$	0.577240	+	3.70187i	0.0192093	+	0.123190i
$904$	−17.5745	−	17.5745i	−0.584519	−	0.584519i
$905$	11.3826	+	11.3826i	0.378371	+	0.378371i
$906$			8.94901i			0.297311i
$907$			2.47655i			0.0822325i	0.999154	+	0.0411163i	$0.0130914\pi$
$907$			2.47655i			0.0822325i	−0.999154	+	0.0411163i	$0.986909\pi$
$908$	29.9565	−	29.9565i	0.994140	−	0.994140i
$909$	0.719293			0.0238574
$910$	−14.1902	−	28.4197i	−0.470402	−	0.942102i
$911$	36.1943			1.19917			0.599586	−	0.800310i	$-0.295332\pi$
$911$	36.1943			1.19917			0.599586	+	0.800310i	$0.295332\pi$
$912$	−12.3746	+	12.3746i	−0.409765	+	0.409765i
$913$		−	23.1629i		−	0.766581i
$914$		−	21.4825i		−	0.710578i
$915$	−13.7120	−	13.7120i	−0.453305	−	0.453305i
$916$	−68.4133	−	68.4133i	−2.26044	−	2.26044i
$917$	24.1473	−	3.76534i	0.797415	−	0.124343i
$918$	1.40199	+	1.40199i	0.0462725	+	0.0462725i
$919$	39.4233			1.30045			0.650227	−	0.759740i	$-0.274674\pi$
$919$	39.4233			1.30045			0.650227	+	0.759740i	$0.274674\pi$
$920$	−41.1563			−1.35688
$921$	9.68422	+	9.68422i	0.319106	+	0.319106i
$922$	59.0031			1.94316
$923$	−4.59211	+	8.88585i	−0.151151	+	0.292481i
$924$	−13.4893	+	18.4733i	−0.443766	+	0.607727i
$925$	17.0358	−	17.0358i	0.560133	−	0.560133i
$926$	18.8539			0.619577
$927$	6.38189			0.209609
$928$	−3.65149	+	3.65149i	−0.119866	+	0.119866i
$929$	−22.0576	−	22.0576i	−0.723686	−	0.723686i	0.245668	−	0.969354i	$-0.420993\pi$
$929$	−22.0576	−	22.0576i	−0.723686	−	0.723686i	−0.969354	+	0.245668i	$0.920993\pi$
$930$	6.44793	−	6.44793i	0.211436	−	0.211436i
$931$	−31.1564	−	16.0633i	−1.02111	−	0.526454i
$932$	107.980			3.53701
$933$		−	0.694504i		−	0.0227370i
$934$	10.4308	−	10.4308i	0.341307	−	0.341307i
$935$			2.46536i			0.0806258i
$936$	14.9144	+	7.70757i	0.487491	+	0.251930i
$937$		−	20.9054i		−	0.682951i	−0.939891	−	0.341476i	$-0.889073\pi$
$937$		−	20.9054i		−	0.682951i	0.939891	−	0.341476i	$-0.110927\pi$
$938$	−10.6726	+	1.66419i	−0.348471	+	0.0543378i
$939$	2.91031			0.0949743
$940$			64.5834i			2.10648i
$941$	−3.82375	−	3.82375i	−0.124651	−	0.124651i	0.642029	−	0.766680i	$-0.278093\pi$
$941$	−3.82375	−	3.82375i	−0.124651	−	0.124651i	−0.766680	+	0.642029i	$0.778093\pi$
$942$	−1.43818	+	1.43818i	−0.0468583	+	0.0468583i
$943$	18.4690	−	18.4690i	0.601433	−	0.601433i
$944$	15.0094	−	15.0094i	0.488513	−	0.488513i
$945$	2.92564	+	2.13632i	0.0951712	+	0.0694945i
$946$		−	7.60608i		−	0.247295i
$947$	1.83357	+	1.83357i	0.0595829	+	0.0595829i	0.736270	−	0.676687i	$-0.236585\pi$
$947$	1.83357	+	1.83357i	0.0595829	+	0.0595829i	−0.676687	+	0.736270i	$0.736585\pi$
$948$	20.2572			0.657922
$949$	−19.0849	+	36.9298i	−0.619522	+	1.19879i
$950$		−	38.0610i		−	1.23486i
$951$	−18.2225	−	18.2225i	−0.590905	−	0.590905i
$952$	5.92278	−	8.11111i	0.191958	−	0.262882i
$953$		−	17.6702i		−	0.572393i	−0.958171	−	0.286197i	$-0.907609\pi$
$953$		−	17.6702i		−	0.572393i	0.958171	−	0.286197i	$-0.0923910\pi$
$954$	5.18683	−	5.18683i	0.167930	−	0.167930i
$955$	−23.4503	−	23.4503i	−0.758835	−	0.758835i
$956$	31.7999	+	31.7999i	1.02848	+	1.02848i
$957$	9.91585	−	9.91585i	0.320534	−	0.320534i
$958$		−	2.14220i		−	0.0692112i
$959$	33.3538	−	45.6773i	1.07705	−	1.47500i
$960$	8.68206	+	8.68206i	0.280212	+	0.280212i
$961$		−	23.5010i		−	0.758097i
$962$	64.4074	−	20.5186i	2.07658	−	0.661546i
$963$	2.79723			0.0901396
$964$	−55.5715	−	55.5715i	−1.78984	−	1.78984i
$965$			31.5247i			1.01482i
$966$	33.5461	+	24.4956i	1.07933	+	0.788132i
$967$	5.09632	−	5.09632i	0.163887	−	0.163887i	−0.620399	−	0.784286i	$-0.713029\pi$
$967$	5.09632	−	5.09632i	0.163887	−	0.163887i	0.784286	+	0.620399i	$0.213029\pi$
$968$	−20.1571	+	20.1571i	−0.647873	+	0.647873i
$969$	2.88680	−	2.88680i	0.0927374	−	0.0927374i
$970$	39.3651	+	39.3651i	1.26394	+	1.26394i
$971$			44.3219i			1.42236i	0.703012	+	0.711178i	$0.251838\pi$
$971$			44.3219i			1.42236i	−0.703012	+	0.711178i	$0.748162\pi$
$972$	−3.91457			−0.125560
$973$	−27.7712	+	4.33042i	−0.890305	+	0.138827i
$974$		−	36.9288i		−	1.18327i
$975$	−10.7366	+	3.42041i	−0.343846	+	0.109541i
$976$		−	49.4945i		−	1.58428i
$977$	36.8053	−	36.8053i	1.17750	−	1.17750i	0.197126	−	0.980378i	$-0.436839\pi$
$977$	36.8053	−	36.8053i	1.17750	−	1.17750i	0.980378	−	0.197126i	$-0.0631609\pi$
$978$		−	15.6774i		−	0.501308i
$979$	0.219041			0.00700057
$980$	17.1932	−	33.3480i	0.549217	−	1.06526i
$981$	−9.58601	+	9.58601i	−0.306058	+	0.306058i
$982$	−29.8899	−	29.8899i	−0.953827	−	0.953827i
$983$	29.1069	−	29.1069i	0.928367	−	0.928367i	−0.0692332	−	0.997601i	$-0.522055\pi$
$983$	29.1069	−	29.1069i	0.928367	−	0.928367i	0.997601	+	0.0692332i	$0.0220553\pi$
$984$	18.8391			0.600568
$985$	−19.2148			−0.612234
$986$	−8.90181	+	8.90181i	−0.283491	+	0.283491i
$987$	18.8001	−	25.7463i	0.598413	−	0.819513i
$988$	32.4491	−	62.7899i	1.03234	−	1.99761i
$989$	−9.14155			−0.290684
$990$	−5.20031	−	5.20031i	−0.165277	−	0.165277i
$991$	36.6164			1.16316			0.581579	−	0.813490i	$-0.302435\pi$
$991$	36.6164			1.16316			0.581579	+	0.813490i	$0.302435\pi$
$992$	−2.22717			−0.0707126
$993$	−8.39979	−	8.39979i	−0.266559	−	0.266559i
$994$	−17.6369	+	2.75015i	−0.559408	+	0.0872295i
$995$	−6.79939	−	6.79939i	−0.215555	−	0.215555i
$996$	−29.0303	−	29.0303i	−0.919861	−	0.919861i
$997$		−	50.0333i		−	1.58457i	−0.610152	−	0.792284i	$-0.708892\pi$
$997$		−	50.0333i		−	1.58457i	0.610152	−	0.792284i	$-0.291108\pi$
$998$			91.6496i			2.90112i
$999$	−5.45102	+	5.45102i	−0.172463	+	0.172463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.p.f.265.5	yes	12
3.2	odd	2		819.2.y.f.811.2		12
7.6	odd	2		273.2.p.e.265.5	yes	12
13.8	odd	4		273.2.p.e.34.5	✓	12
21.20	even	2		819.2.y.g.811.2		12
39.8	even	4		819.2.y.g.307.2		12
91.34	even	4	inner	273.2.p.f.34.5	yes	12
273.125	odd	4		819.2.y.f.307.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.e.34.5	✓	12	13.8	odd	4
273.2.p.e.265.5	yes	12	7.6	odd	2
273.2.p.f.34.5	yes	12	91.34	even	4	inner
273.2.p.f.265.5	yes	12	1.1	even	1	trivial
819.2.y.f.307.2		12	273.125	odd	4
819.2.y.f.811.2		12	3.2	odd	2
819.2.y.g.307.2		12	39.8	even	4
819.2.y.g.811.2		12	21.20	even	2

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.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71968 - 1.71968i) q^{2} -1.00000i q^{3} -3.91457i q^{4} +(-0.968182 - 0.968182i) q^{5} +(-1.71968 - 1.71968i) q^{6} +(0.407631 + 2.61416i) q^{7} +(-3.29244 - 3.29244i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.71968 - 1.71968i) q^{2} -1.00000i q^{3} -3.91457i q^{4} +(-0.968182 - 0.968182i) q^{5} +(-1.71968 - 1.71968i) q^{6} +(0.407631 + 2.61416i) q^{7} +(-3.29244 - 3.29244i) q^{8} -1.00000 q^{9} -3.32992 q^{10} +(-1.56169 - 1.56169i) q^{11} -3.91457 q^{12} +(3.43543 - 1.09444i) q^{13} +(5.19650 + 3.79452i) q^{14} +(-0.968182 + 0.968182i) q^{15} -3.49472 q^{16} +0.815262 q^{17} +(-1.71968 + 1.71968i) q^{18} +(3.54095 + 3.54095i) q^{19} +(-3.79002 + 3.79002i) q^{20} +(2.61416 - 0.407631i) q^{21} -5.37121 q^{22} +6.45552i q^{23} +(-3.29244 + 3.29244i) q^{24} -3.12525i q^{25} +(4.02574 - 7.78992i) q^{26} +1.00000i q^{27} +(10.2333 - 1.59570i) q^{28} -6.34942 q^{29} +3.32992i q^{30} +(-1.93636 - 1.93636i) q^{31} +(0.575090 - 0.575090i) q^{32} +(-1.56169 + 1.56169i) q^{33} +(1.40199 - 1.40199i) q^{34} +(2.13632 - 2.92564i) q^{35} +3.91457i q^{36} +(5.45102 + 5.45102i) q^{37} +12.1786 q^{38} +(-1.09444 - 3.43543i) q^{39} +6.37536i q^{40} +(-2.86096 - 2.86096i) q^{41} +(3.79452 - 5.19650i) q^{42} +1.41608i q^{43} +(-6.11336 + 6.11336i) q^{44} +(0.968182 + 0.968182i) q^{45} +(11.1014 + 11.1014i) q^{46} +(8.52020 - 8.52020i) q^{47} +3.49472i q^{48} +(-6.66767 + 2.13123i) q^{49} +(-5.37442 - 5.37442i) q^{50} -0.815262i q^{51} +(-4.28427 - 13.4482i) q^{52} -3.01617 q^{53} +(1.71968 + 1.71968i) q^{54} +3.02401i q^{55} +(7.26487 - 9.94907i) q^{56} +(3.54095 - 3.54095i) q^{57} +(-10.9189 + 10.9189i) q^{58} +(-4.29487 + 4.29487i) q^{59} +(3.79002 + 3.79002i) q^{60} +14.1626i q^{61} -6.65983 q^{62} +(-0.407631 - 2.61416i) q^{63} -8.96739i q^{64} +(-4.38574 - 2.26650i) q^{65} +5.37121i q^{66} +(-1.18702 + 1.18702i) q^{67} -3.19140i q^{68} +6.45552 q^{69} +(-1.35738 - 8.70494i) q^{70} +(-1.96161 + 1.96161i) q^{71} +(3.29244 + 3.29244i) q^{72} +(-8.15249 + 8.15249i) q^{73} +18.7480 q^{74} -3.12525 q^{75} +(13.8613 - 13.8613i) q^{76} +(3.44592 - 4.71911i) q^{77} +(-7.78992 - 4.02574i) q^{78} -5.17481 q^{79} +(3.38353 + 3.38353i) q^{80} +1.00000 q^{81} -9.83985 q^{82} +(7.41597 + 7.41597i) q^{83} +(-1.59570 - 10.2333i) q^{84} +(-0.789322 - 0.789322i) q^{85} +(2.43520 + 2.43520i) q^{86} +6.34942i q^{87} +10.2836i q^{88} +(-0.0701292 + 0.0701292i) q^{89} +3.32992 q^{90} +(4.26144 + 8.53464i) q^{91} +25.2706 q^{92} +(-1.93636 + 1.93636i) q^{93} -29.3040i q^{94} -6.85656i q^{95} +(-0.575090 - 0.575090i) q^{96} +(-11.8216 - 11.8216i) q^{97} +(-7.80122 + 15.1313i) q^{98} +(1.56169 + 1.56169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9	\( 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9} - 4 q^{11} - 28 q^{12} + 12 q^{15} - 36 q^{16} - 8 q^{17} + 8 q^{20} + 12 q^{21} + 32 q^{22} + 4 q^{26} + 12 q^{28} - 8 q^{29} + 24 q^{31} + 20 q^{32} - 4 q^{33} - 20 q^{35} - 4 q^{37} + 40 q^{38} - 16 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 20 q^{46} + 32 q^{47} + 20 q^{50} - 56 q^{52} - 16 q^{53} - 20 q^{56} + 8 q^{59} - 8 q^{60} + 4 q^{63} - 16 q^{65} - 32 q^{67} + 16 q^{69} - 20 q^{70} - 12 q^{71} - 32 q^{73} - 64 q^{74} + 4 q^{75} - 12 q^{77} + 16 q^{78} + 24 q^{79} - 4 q^{80} + 12 q^{81} + 28 q^{84} - 32 q^{85} + 4 q^{89} + 32 q^{91} + 112 q^{92} + 24 q^{93} - 20 q^{96} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 12 * q + 12 * q^5 - 4 * q^7 - 12 * q^9 - 4 * q^11 - 28 * q^12 + 12 * q^15 - 36 * q^16 - 8 * q^17 + 8 * q^20 + 12 * q^21 + 32 * q^22 + 4 * q^26 + 12 * q^28 - 8 * q^29 + 24 * q^31 + 20 * q^32 - 4 * q^33 - 20 * q^35 - 4 * q^37 + 40 * q^38 - 16 * q^39 - 20 * q^41 + 8 * q^44 - 12 * q^45 + 20 * q^46 + 32 * q^47 + 20 * q^50 - 56 * q^52 - 16 * q^53 - 20 * q^56 + 8 * q^59 - 8 * q^60 + 4 * q^63 - 16 * q^65 - 32 * q^67 + 16 * q^69 - 20 * q^70 - 12 * q^71 - 32 * q^73 - 64 * q^74 + 4 * q^75 - 12 * q^77 + 16 * q^78 + 24 * q^79 - 4 * q^80 + 12 * q^81 + 28 * q^84 - 32 * q^85 + 4 * q^89 + 32 * q^91 + 112 * q^92 + 24 * q^93 - 20 * q^96 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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