LMFDB - Embedded newform 273.2.p.e.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.e.34.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71968 - 1.71968i) q^{2} +1.00000i q^{3} -3.91457i q^{4} +(0.968182 + 0.968182i) q^{5} +(1.71968 + 1.71968i) q^{6} +(2.61416 + 0.407631i) q^{7} +(-3.29244 - 3.29244i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(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} +(2.61416 + 0.407631i) 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} +(-0.407631 + 2.61416i) 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} +(1.59570 - 10.2333i) 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} +(-2.61416 - 0.407631i) 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} +(8.70494 + 1.35738i) 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} +(10.2333 + 1.59570i) 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} +(-9.42690 + 1.46066i) 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} +(15.1313 - 7.80122i) q^{98} +(1.56169 + 1.56169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9	$ 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9} - 4 q^{11} + 28 q^{12} + 12 q^{15} - 36 q^{16} + 8 q^{17} - 8 q^{20} + 4 q^{21} + 32 q^{22} - 4 q^{26} - 28 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} - 12 q^{63} - 16 q^{65} - 32 q^{67} - 16 q^{69} + 52 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} + 12 q^{84} - 32 q^{85} - 4 q^{89} - 40 q^{91} + 112 q^{92} + 24 q^{93} + 20 q^{96} + 136 q^{98} + 4 q^{99}+O(q^{100}) $ 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9 - 4 * q^11 + 28 * q^12 + 12 * q^15 - 36 * q^16 + 8 * q^17 - 8 * q^20 + 4 * q^21 + 32 * q^22 - 4 * q^26 - 28 * 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 - 12 * q^63 - 16 * q^65 - 32 * q^67 - 16 * q^69 + 52 * 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 + 12 * q^84 - 32 * q^85 - 4 * q^89 - 40 * q^91 + 112 * q^92 + 24 * q^93 + 20 * q^96 + 136 * 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	0.889642	−	0.456658i	$-0.150954\pi$
$5$	0.968182	+	0.968182i	0.432984	+	0.432984i	−0.456658	+	0.889642i	$0.650954\pi$
$6$	1.71968	+	1.71968i	0.702055	+	0.702055i
$7$	2.61416	+	0.407631i	0.988060	+	0.154070i
$7$	2.61416	+	0.407631i	0.988060	+	0.154070i
$8$	−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	$-0.531521\pi$
$17$	−0.815262			−0.197730			−0.0988651	+	0.995101i	$0.531521\pi$
$18$	−1.71968	+	1.71968i	−0.405332	+	0.405332i
$19$	−3.54095	−	3.54095i	−0.812349	−	0.812349i	0.172637	−	0.984986i	$-0.444771\pi$
$19$	−3.54095	−	3.54095i	−0.812349	−	0.812349i	−0.984986	+	0.172637i	$0.944771\pi$
$20$	3.79002	−	3.79002i	0.847473	−	0.847473i
$21$	−0.407631	+	2.61416i	−0.0889524	+	0.570457i
$22$	−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
$28$	1.59570	−	10.2333i	0.301559	−	1.93392i
$29$	−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	0.859282	−	0.511501i	$-0.170910\pi$
$31$	1.93636	+	1.93636i	0.347781	+	0.347781i	−0.511501	+	0.859282i	$0.670910\pi$
$32$	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	0.894292	−	0.447485i	$-0.147680\pi$
$41$	2.86096	+	2.86096i	0.446807	+	0.446807i	−0.447485	+	0.894292i	$0.647680\pi$
$42$	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	$0.591650\pi$
$47$	−8.52020	+	8.52020i	−1.24280	+	1.24280i	−0.958835	+	0.283964i	$0.908350\pi$
$48$		−	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	−0.369920	−	0.929064i	$-0.620615\pi$
$59$	4.29487	−	4.29487i	0.559144	−	0.559144i	0.929064	+	0.369920i	$0.120615\pi$
$60$	3.79002	+	3.79002i	0.489289	+	0.489289i
$61$		−	14.1626i		−	1.81334i	−0.421842	−	0.906669i	$-0.638616\pi$
$61$		−	14.1626i		−	1.81334i	0.421842	−	0.906669i	$-0.361384\pi$
$62$	6.65983			0.845800
$63$	−2.61416	−	0.407631i	−0.329353	−	0.0513567i
$64$		−	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
$70$	8.70494	+	1.35738i	1.04044	+	0.162238i
$71$	−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	−0.0448186	−	0.998995i	$-0.514271\pi$
$73$	8.15249	−	8.15249i	0.954177	−	0.954177i	0.998995	+	0.0448186i	$0.0142710\pi$
$74$	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	0.171224	−	0.985232i	$-0.445228\pi$
$83$	−7.41597	−	7.41597i	−0.814008	−	0.814008i	−0.985232	+	0.171224i	$0.945228\pi$
$84$	10.2333	+	1.59570i	1.11655	+	0.174105i
$85$	−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	−0.703380	−	0.710814i	$-0.748327\pi$
$89$	0.0701292	−	0.0701292i	0.00743368	−	0.00743368i	0.710814	+	0.703380i	$0.248327\pi$
$90$	−3.32992			−0.351004
$91$	−9.42690	+	1.46066i	−0.988208	+	0.153119i
$92$	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	$0.0726408\pi$
$97$	11.8216	+	11.8216i	1.20031	+	1.20031i	0.226232	+	0.974073i	$0.427359\pi$
$98$	15.1313	−	7.80122i	1.52849	−	0.788042i
$99$	1.56169	+	1.56169i	0.156956	+	0.156956i
$100$	−12.2340			−1.22340
$101$	0.719293			0.0715723			0.0357861	−	0.999359i	$-0.488606\pi$
$101$	0.719293			0.0715723			0.0357861	+	0.999359i	$0.488606\pi$
$102$	−1.40199	−	1.40199i	−0.138817	−	0.138817i
$103$	6.38189			0.628826			0.314413	−	0.949286i	$-0.398192\pi$
$103$	6.38189			0.628826			0.314413	+	0.949286i	$0.398192\pi$
$104$	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
$112$	−9.13577	−	1.42456i	−0.863249	−	0.134608i
$113$	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
$119$	−2.13123	−	0.332326i	−0.195369	−	0.0304643i
$120$	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	$0.132215\pi$
$131$			9.23713i			0.807052i	−0.914968	+	0.403526i	$0.867785\pi$
$132$	−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	$-0.851234\pi$
$139$		−	10.6234i		−	0.901064i	0.892760	−	0.450532i	$-0.148766\pi$
$140$	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
$154$	−14.0412	−	2.18947i	−1.13147	−	0.176433i
$155$			3.74950i			0.301167i
$156$	−13.4482	+	4.28427i	−1.07672	+	0.343017i
$157$			0.836307i			0.0667446i	0.999443	+	0.0333723i	$0.0106247\pi$
$157$			0.836307i			0.0667446i	−0.999443	+	0.0333723i	$0.989375\pi$
$158$	−8.89900	+	8.89900i	−0.707966	+	0.707966i
$159$		−	3.01617i		−	0.239198i
$160$	1.11358			0.0880365
$161$	−2.63147	+	16.8758i	−0.207389	+	1.33000i
$162$	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	$0.662462\pi$
$167$	−17.5889	+	17.5889i	−1.36107	+	1.36107i	−0.872555	+	0.488517i	$0.837538\pi$
$168$	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	$-0.153708\pi$
$173$	23.2980			1.77132			0.885658	+	0.464338i	$0.153708\pi$
$174$	−10.9189	−	10.9189i	−0.827763	−	0.827763i
$175$	1.27395	−	8.16990i	0.0963015	−	0.617587i
$176$	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	$-0.356064\pi$
$181$	11.7567			0.873869			0.436934	+	0.899493i	$0.356064\pi$
$182$	−13.6994	+	18.7231i	−1.01546	+	1.38785i
$183$	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
$189$	0.407631	−	2.61416i	0.0296508	−	0.190152i
$190$	−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	$-0.580075\pi$
$199$	−7.02284			−0.497836			−0.248918	+	0.968525i	$0.580075\pi$
$200$	−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
$203$	−16.5984	−	2.58822i	−1.16498	−	0.181658i
$204$	−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
$210$	−1.35738	+	8.70494i	−0.0936680	+	0.600698i
$211$	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	0.717534	−	0.696524i	$-0.245271\pi$
$223$	0.313751	+	0.313751i	0.0210103	+	0.0210103i	−0.696524	+	0.717534i	$0.745271\pi$
$224$	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	0.405969	−	0.913887i	$-0.366934\pi$
$227$	−7.65255	−	7.65255i	−0.507918	−	0.507918i	−0.913887	+	0.405969i	$0.866934\pi$
$228$	−13.8613	−	13.8613i	−0.917986	−	0.917986i
$229$	−17.4766	+	17.4766i	−1.15489	+	1.15489i	−0.169325	+	0.985560i	$0.554159\pi$
$229$	−17.4766	+	17.4766i	−1.15489	+	1.15489i	−0.985560	+	0.169325i	$0.945841\pi$
$230$			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	−0.996618	−	0.0821690i	$-0.973815\pi$
$241$	−14.1961	+	14.1961i	−0.914449	+	0.914449i	0.0821690	+	0.996618i	$0.473815\pi$
$242$	−10.5282	−	10.5282i	−0.676781	−	0.676781i
$243$			1.00000i			0.0641500i
$244$	−55.4406			−3.54922
$245$	4.39210	+	8.51893i	0.280601	+	0.544255i
$246$			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	$-0.414715\pi$
$251$	8.38843			0.529473			0.264737	+	0.964321i	$0.414715\pi$
$252$	−1.59570	+	10.2333i	−0.100520	+	0.644638i
$253$	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	$-0.304943\pi$
$257$	18.4408			1.15030			0.575152	+	0.818047i	$0.304943\pi$
$258$	−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
$266$	−31.8367	−	4.96436i	−1.95203	−	0.304385i
$267$	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	$-0.788019\pi$
$269$		−	20.2658i		−	1.23563i	0.786325	−	0.617813i	$-0.211981\pi$
$270$		−	3.32992i		−	0.202652i
$271$	−11.4908	+	11.4908i	−0.698019	+	0.698019i	−0.963983	−	0.265964i	$-0.914310\pi$
$271$	−11.4908	+	11.4908i	−0.698019	+	0.698019i	0.265964	+	0.963983i	$0.414310\pi$
$272$	2.84912			0.172753
$273$	−1.46066	−	9.42690i	−0.0884032	−	0.570542i
$274$	−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
$280$	2.59880	−	16.6662i	0.155308	−	0.995997i
$281$	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	$-0.520734\pi$
$283$	−2.19005			−0.130185			−0.0650924	+	0.997879i	$0.520734\pi$
$284$	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	−0.895814	−	0.444428i	$-0.853407\pi$
$293$	−7.72648	+	7.72648i	−0.451386	+	0.451386i	0.444428	+	0.895814i	$0.353407\pi$
$294$	7.80122	+	15.1313i	0.454976	+	0.882473i
$295$	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
$301$	−0.577240	+	3.70187i	−0.0332715	+	0.213372i
$302$	−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	−0.374514	−	0.927221i	$-0.622190\pi$
$307$	9.68422	−	9.68422i	0.552708	−	0.552708i	0.927221	+	0.374514i	$0.122190\pi$
$308$	−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	$-0.506268\pi$
$311$	−0.694504			−0.0393817			−0.0196908	+	0.999806i	$0.506268\pi$
$312$	−7.70757	+	14.9144i	−0.436355	+	0.844359i
$313$		−	2.91031i		−	0.164500i	−0.996612	−	0.0822501i	$-0.973789\pi$
$313$		−	2.91031i		−	0.164500i	0.996612	−	0.0822501i	$-0.0262106\pi$
$314$	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
$336$	1.42456	−	9.13577i	0.0777160	−	0.498397i
$337$		−	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
$343$	16.5616	+	8.28932i	0.894243	+	0.447581i
$344$	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	−0.980838	−	0.194824i	$-0.937586\pi$
$349$	−14.6839	+	14.6839i	−0.786014	+	0.786014i	0.194824	+	0.980838i	$0.437586\pi$
$350$	−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	0.957130	−	0.289657i	$-0.0935413\pi$
$353$	12.5407	+	12.5407i	0.667473	+	0.667473i	−0.289657	+	0.957130i	$0.593541\pi$
$354$	14.7716			0.785099
$355$	−3.79839			−0.201598
$356$	−0.274526	−	0.274526i	−0.0145498	−	0.0145498i
$357$	0.332326	−	2.13123i	0.0175886	−	0.112796i
$358$	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
$364$	5.71786	+	36.9023i	0.299697	+	1.93420i
$365$	15.7862			0.826286
$366$	24.3551	−	24.3551i	1.27306	−	1.27306i
$367$			35.1154i			1.83301i	0.400027	+	0.916503i	$0.369001\pi$
$367$			35.1154i			1.83301i	−0.400027	+	0.916503i	$0.630999\pi$
$368$		−	22.5603i		−	1.17603i
$369$	−2.86096	−	2.86096i	−0.148936	−	0.148936i
$370$	18.1514	+	18.1514i	0.943648	+	0.943648i
$371$	−7.88474	−	1.22948i	−0.409356	−	0.0638316i
$372$	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	0.583742	−	0.811939i	$-0.301588\pi$
$383$	−4.46592	−	4.46592i	−0.228198	−	0.228198i	−0.811939	+	0.583742i	$0.801588\pi$
$384$	14.2708	−	14.2708i	0.728255	−	0.728255i
$385$	1.23268	−	7.90524i	0.0628231	−	0.402888i
$386$	−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
$392$	−14.9360	−	28.9699i	−0.754381	−	1.46320i
$393$	−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	−0.999979	−	0.00642876i	$-0.997954\pi$
$397$	−19.7964	+	19.7964i	−0.993551	+	0.993551i	0.00642876	+	0.999979i	$0.497954\pi$
$398$	−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	0.00841024	−	0.999965i	$-0.497323\pi$
$409$	−20.0529	−	20.0529i	−0.991554	−	0.991554i	−0.999965	+	0.00841024i	$0.997323\pi$
$410$	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	$0.0997935\pi$
$419$			12.6256i			0.616800i	−0.951257	+	0.308400i	$0.900207\pi$
$420$	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
$427$	5.77313	−	37.0234i	0.279381	−	1.79169i
$428$			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	$-0.345940\pi$
$433$	19.3653			0.930638			0.465319	+	0.885143i	$0.345940\pi$
$434$	17.4099	+	2.71476i	0.835701	+	0.130312i
$435$	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	$-0.549154\pi$
$439$	−6.44529			−0.307617			−0.153809	+	0.988101i	$0.549154\pi$
$440$	−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
$448$	3.65539	−	23.4422i	0.172701	−	1.10754i
$449$	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
$455$	−10.5411	−	7.71277i	−0.494176	−	0.361580i
$456$	−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	0.183936	−	0.982938i	$-0.441116\pi$
$461$	−17.1553	−	17.1553i	−0.799002	−	0.799002i	−0.982938	+	0.183936i	$0.941116\pi$
$462$	2.18947	−	14.0412i	0.101864	−	0.653257i
$463$	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	$-0.544820\pi$
$467$	−6.06557			−0.280681			−0.140341	+	0.990103i	$0.544820\pi$
$468$	−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
$476$	−1.30092	+	8.34284i	−0.0596273	+	0.382393i
$477$	3.01617			0.138101
$478$			27.9395i			1.27792i
$479$	−0.622849	+	0.622849i	−0.0284587	+	0.0284587i	−0.721193	−	0.692734i	$-0.756406\pi$
$479$	−0.622849	+	0.622849i	−0.0284587	+	0.0284587i	0.692734	+	0.721193i	$0.256406\pi$
$480$			1.11358i			0.0508279i
$481$	−24.6924	−	12.7608i	−1.12588	−	0.581841i
$482$			48.8253i			2.22393i
$483$	−16.8758	−	2.63147i	−0.767874	−	0.119736i
$484$	−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	$-0.724489\pi$
$503$		−	34.1550i		−	1.52290i	0.648226	−	0.761448i	$-0.275511\pi$
$504$	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	0.847809	−	0.530302i	$-0.177922\pi$
$509$	7.16328	+	7.16328i	0.317507	+	0.317507i	−0.530302	+	0.847809i	$0.677922\pi$
$510$		−	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
$518$	49.0102	+	7.64226i	2.15338	+	0.335781i
$519$			23.2980i			1.02267i
$520$	6.97747	+	21.9021i	0.305982	+	0.960472i
$521$		−	30.2128i		−	1.32365i	−0.749660	−	0.661823i	$-0.769783\pi$
$521$		−	30.2128i		−	1.32365i	0.749660	−	0.661823i	$-0.230217\pi$
$522$	10.9189	−	10.9189i	0.477909	−	0.477909i
$523$		−	10.9106i		−	0.477086i	−0.971132	−	0.238543i	$-0.923330\pi$
$523$		−	10.9106i		−	0.477086i	0.971132	−	0.238543i	$-0.0766698\pi$
$524$	36.1594			1.57963
$525$	8.16990	+	1.27395i	0.356564	+	0.0555997i
$526$	−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
$539$	−7.08454	−	13.7412i	−0.305153	−	0.591875i
$540$	−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
$546$	−18.7231	−	13.6994i	−0.801274	−	0.586278i
$547$	−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
$553$	−13.5278	−	2.10941i	−0.575260	−	0.0897014i
$554$	−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	$-0.641639\pi$
$563$	−20.4262			−0.860864			−0.430432	+	0.902623i	$0.641639\pi$
$564$	−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
$567$	2.61416	+	0.407631i	0.109784	+	0.0171189i
$568$	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
$574$	25.7230	+	4.01103i	1.07366	+	0.167417i
$575$	20.1751			0.841360
$576$			8.96739i			0.373641i
$577$	−12.8188	−	12.8188i	−0.533655	−	0.533655i	0.388003	−	0.921658i	$-0.373165\pi$
$577$	−12.8188	−	12.8188i	−0.533655	−	0.533655i	−0.921658	+	0.388003i	$0.873165\pi$
$578$	−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	0.280032	−	0.959991i	$-0.409655\pi$
$587$	−16.4741	−	16.4741i	−0.679958	−	0.679958i	−0.959991	+	0.280032i	$0.909655\pi$
$588$	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	−0.514043	−	0.857764i	$-0.671853\pi$
$593$	8.37016	−	8.37016i	0.343721	−	0.343721i	0.857764	+	0.514043i	$0.171853\pi$
$594$			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	$-0.826758\pi$
$601$		−	25.3871i		−	1.03556i	0.855513	−	0.517781i	$-0.173242\pi$
$602$	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	$0.0442582\pi$
$607$			6.82917i			0.277188i	−0.990349	+	0.138594i	$0.955742\pi$
$608$	−4.07273			−0.165171
$609$	2.58822	−	16.5984i	0.104880	−	0.672602i
$610$		−	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
$616$	−4.19190	+	26.8829i	−0.168897	+	1.08314i
$617$	−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	−0.908912	−	0.416988i	$-0.863086\pi$
$619$	−12.2389	+	12.2389i	−0.491924	+	0.491924i	0.416988	+	0.908912i	$0.363086\pi$
$620$	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
$630$	−8.70494	−	1.35738i	−0.346813	−	0.0540792i
$631$	−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
$637$	−25.2388	−	0.0242969i	−1.00000	−	0.000962678i
$638$	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	0.949930	−	0.312463i	$-0.101154\pi$
$643$	16.1645	+	16.1645i	0.637467	+	0.637467i	−0.312463	+	0.949930i	$0.601154\pi$
$644$	66.0614	+	10.3011i	2.60318	+	0.405919i
$645$	−1.37103	−	1.37103i	−0.0539841	−	0.0539841i
$646$	9.92873			0.390640
$647$	40.0087			1.57290			0.786452	−	0.617651i	$-0.211916\pi$
$647$	40.0087			1.57290			0.786452	+	0.617651i	$0.211916\pi$
$648$	−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
$658$	−11.9452	+	76.6053i	−0.465673	+	2.98639i
$659$	−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	−0.746102	−	0.665831i	$-0.768077\pi$
$661$	−2.06376	+	2.06376i	−0.0802710	+	0.0802710i	0.665831	+	0.746102i	$0.268077\pi$
$662$		−	28.8898i		−	1.12284i
$663$	0.892258	+	2.80078i	0.0346524	+	0.108773i
$664$			48.8333i			1.89510i
$665$	2.79495	−	17.9241i	0.108383	−	0.695069i
$666$	−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	$0.0360479\pi$
$677$			5.88065i			0.226012i	−0.993594	+	0.113006i	$0.963952\pi$
$678$	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	0.887587	−	0.460641i	$-0.152380\pi$
$691$	11.2231	+	11.2231i	0.426946	+	0.426946i	−0.460641	+	0.887587i	$0.652380\pi$
$692$		−	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
$700$	−31.9817	−	4.98696i	−1.20879	−	0.188490i
$701$			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
$707$	1.88035	+	0.293206i	0.0707177	+	0.0110271i
$708$	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	$-0.764700\pi$
$719$	−39.6312			−1.47799			−0.738996	+	0.673709i	$0.764700\pi$
$720$	3.38353	+	3.38353i	0.126097	+	0.126097i
$721$	16.6833	+	2.60146i	0.621318	+	0.0968833i
$722$	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	$-0.321141\pi$
$727$	28.7315			1.06559			0.532796	+	0.846244i	$0.321141\pi$
$728$	35.8467	+	26.2284i	1.32857	+	0.972089i
$729$	−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	0.681699	−	0.731633i	$-0.261242\pi$
$733$	−1.35193	−	1.35193i	−0.0499345	−	0.0499345i	−0.731633	+	0.681699i	$0.761242\pi$
$734$	60.3870	+	60.3870i	2.22893	+	2.22893i
$735$	−8.51893	+	4.39210i	−0.314226	+	0.162005i
$736$	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
$749$	−7.31242	−	1.14024i	−0.267190	−	0.0416635i
$750$	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
$756$	−10.2333	−	1.59570i	−0.372182	−	0.0580351i
$757$	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	$0.573125\pi$
$761$	−33.1432	+	33.1432i	−1.20144	+	1.20144i	−0.973728	+	0.227712i	$0.926875\pi$
$762$	−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	0.856395	−	0.516321i	$-0.172699\pi$
$769$	9.43052	+	9.43052i	0.340073	+	0.340073i	−0.516321	+	0.856395i	$0.672699\pi$
$770$	−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	0.873586	−	0.486669i	$-0.161788\pi$
$773$	10.7574	+	10.7574i	0.386917	+	0.386917i	−0.486669	+	0.873586i	$0.661788\pi$
$774$	−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	−0.384803	−	0.922999i	$-0.625730\pi$
$787$	15.0983	−	15.0983i	0.538196	−	0.538196i	0.922999	+	0.384803i	$0.125730\pi$
$788$	−38.8448	−	38.8448i	−1.38379	−	1.38379i
$789$		−	12.8900i		−	0.458897i
$790$	−17.2317			−0.613076
$791$	13.9539	+	2.17587i	0.496145	+	0.0773649i
$792$		−	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	$-0.518188\pi$
$797$	−3.22445			−0.114216			−0.0571080	+	0.998368i	$0.518188\pi$
$798$	4.96436	−	31.8367i	0.175737	−	1.12701i
$799$	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	0.281771	−	0.959482i	$-0.409078\pi$
$811$	−19.2999	−	19.2999i	−0.677711	−	0.677711i	−0.959482	+	0.281771i	$0.909078\pi$
$812$	−10.1318	+	64.9757i	−0.355556	+	2.28020i
$813$	−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
$819$	9.42690	−	1.46066i	0.329403	−	0.0510396i
$820$	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
$826$	6.02135	−	38.6152i	0.209509	−	1.34360i
$827$	−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	$-0.415175\pi$
$829$	15.1645			0.526684			0.263342	+	0.964703i	$0.415175\pi$
$830$	−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	−0.0935419	−	0.995615i	$-0.529819\pi$
$839$	26.1290	−	26.1290i	0.902073	−	0.902073i	0.995615	+	0.0935419i	$0.0298189\pi$
$840$	16.6662	+	2.59880i	0.575039	+	0.0896670i
$841$	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
$847$	2.49561	−	16.0045i	0.0857502	−	0.549921i
$848$	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	−0.983852	−	0.178982i	$-0.942719\pi$
$853$	−23.5072	+	23.5072i	−0.804870	+	0.804870i	0.178982	+	0.983852i	$0.442719\pi$
$854$	−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	$-0.434356\pi$
$857$	11.9890			0.409536			0.204768	+	0.978811i	$0.434356\pi$
$858$	5.87849	+	18.4524i	0.200688	+	0.629956i
$859$			1.16967i			0.0399085i	0.999801	+	0.0199542i	$0.00635205\pi$
$859$			1.16967i			0.0399085i	−0.999801	+	0.0199542i	$0.993648\pi$
$860$	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	$-0.549924\pi$
$881$	−9.27254			−0.312400			−0.156200	+	0.987725i	$0.549924\pi$
$882$	−15.1313	+	7.80122i	−0.509496	+	0.262681i
$883$		−	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	$-0.904427\pi$
$887$		−	17.6170i		−	0.591521i	0.955262	−	0.295760i	$-0.0955730\pi$
$888$	35.8943			1.20453
$889$	−5.37046	+	34.4411i	−0.180120	+	1.15512i
$890$	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
$903$	−3.70187	−	0.577240i	−0.123190	−	0.0192093i
$904$	−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
$910$	−31.3908	+	4.86388i	−1.04059	+	0.161236i
$911$	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
$917$	−3.76534	+	24.1473i	−0.124343	+	0.797415i
$918$	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	0.969354	−	0.245668i	$-0.0790073\pi$
$929$	22.0576	+	22.0576i	0.723686	+	0.723686i	−0.245668	+	0.969354i	$0.579007\pi$
$930$	−6.44793	+	6.44793i	−0.211436	+	0.211436i
$931$	−16.0633	−	31.1564i	−0.526454	−	1.02111i
$932$	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	$0.110927\pi$
$937$			20.9054i			0.682951i	−0.939891	+	0.341476i	$0.889073\pi$
$938$	−1.66419	+	10.6726i	−0.0543378	+	0.348471i
$939$	2.91031			0.0949743
$940$			64.5834i			2.10648i
$941$	3.82375	+	3.82375i	0.124651	+	0.124651i	0.766680	−	0.642029i	$-0.221907\pi$
$941$	3.82375	+	3.82375i	0.124651	+	0.124651i	−0.642029	+	0.766680i	$0.721907\pi$
$942$	−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	$-0.748162\pi$
$971$		−	44.3219i		−	1.42236i	0.703012	−	0.711178i	$-0.251838\pi$
$972$	3.91457			0.125560
$973$	4.33042	−	27.7712i	0.138827	−	0.890305i
$974$		−	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
$980$	33.3480	−	17.1932i	1.06526	−	0.549217i
$981$	−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	−0.997601	−	0.0692332i	$-0.977945\pi$
$983$	−29.1069	+	29.1069i	−0.928367	+	0.928367i	0.0692332	+	0.997601i	$0.477945\pi$
$984$	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
$994$	−2.75015	+	17.6369i	−0.0872295	+	0.559408i
$995$	−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	$0.291108\pi$
$997$			50.0333i			1.58457i	−0.610152	+	0.792284i	$0.708892\pi$
$998$			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.e.265.5	yes	12
3.2	odd	2		819.2.y.g.811.2		12
7.6	odd	2		273.2.p.f.265.5	yes	12
13.8	odd	4		273.2.p.f.34.5	yes	12
21.20	even	2		819.2.y.f.811.2		12
39.8	even	4		819.2.y.f.307.2		12
91.34	even	4	inner	273.2.p.e.34.5	✓	12
273.125	odd	4		819.2.y.g.307.2		12

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

\(f(q)\)	\(=\)	\(q+(1.71968 - 1.71968i) q^{2} +1.00000i q^{3} -3.91457i q^{4} +(0.968182 + 0.968182i) q^{5} +(1.71968 + 1.71968i) q^{6} +(2.61416 + 0.407631i) q^{7} +(-3.29244 - 3.29244i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(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} +(2.61416 + 0.407631i) 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} +(-0.407631 + 2.61416i) 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} +(1.59570 - 10.2333i) 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} +(-2.61416 - 0.407631i) 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} +(8.70494 + 1.35738i) 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} +(10.2333 + 1.59570i) 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} +(-9.42690 + 1.46066i) 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} +(15.1313 - 7.80122i) q^{98} +(1.56169 + 1.56169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9	\( 12 q - 12 q^{5} + 12 q^{7} - 12 q^{9} - 4 q^{11} + 28 q^{12} + 12 q^{15} - 36 q^{16} + 8 q^{17} - 8 q^{20} + 4 q^{21} + 32 q^{22} - 4 q^{26} - 28 q^{28} - 8 q^{29} - 24 q^{31} + 20 q^{32} + 4 q^{33} - 20 q^{35} - 4 q^{37} - 40 q^{38} - 16 q^{39} + 20 q^{41} + 8 q^{44} + 12 q^{45} + 20 q^{46} - 32 q^{47} + 20 q^{50} + 56 q^{52} - 16 q^{53} + 20 q^{56} - 8 q^{59} - 8 q^{60} - 12 q^{63} - 16 q^{65} - 32 q^{67} - 16 q^{69} + 52 q^{70} - 12 q^{71} + 32 q^{73} - 64 q^{74} - 4 q^{75} + 12 q^{77} + 16 q^{78} + 24 q^{79} + 4 q^{80} + 12 q^{81} + 12 q^{84} - 32 q^{85} - 4 q^{89} - 40 q^{91} + 112 q^{92} + 24 q^{93} + 20 q^{96} + 136 q^{98} + 4 q^{99}+O(q^{100}) \) 12 * q - 12 * q^5 + 12 * q^7 - 12 * q^9 - 4 * q^11 + 28 * q^12 + 12 * q^15 - 36 * q^16 + 8 * q^17 - 8 * q^20 + 4 * q^21 + 32 * q^22 - 4 * q^26 - 28 * 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 - 12 * q^63 - 16 * q^65 - 32 * q^67 - 16 * q^69 + 52 * 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 + 12 * q^84 - 32 * q^85 - 4 * q^89 - 40 * q^91 + 112 * q^92 + 24 * q^93 + 20 * q^96 + 136 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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