LMFDB - Embedded newform 273.2.p.e.265.6

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			265.6
Root			$1.27310 + 1.27310i$ of defining polynomial
Character	$\chi$	$=$	273.265
Dual form			273.2.p.e.34.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75588 - 1.75588i) q^{2} +1.00000i q^{3} -4.16620i q^{4} +(-2.27310 - 2.27310i) q^{5} +(1.75588 + 1.75588i) q^{6} +(-1.62270 - 2.08970i) q^{7} +(-3.80357 - 3.80357i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.75588 - 1.75588i) q^{2} +1.00000i q^{3} -4.16620i q^{4} +(-2.27310 - 2.27310i) q^{5} +(1.75588 + 1.75588i) q^{6} +(-1.62270 - 2.08970i) q^{7} +(-3.80357 - 3.80357i) q^{8} -1.00000 q^{9} -7.98257 q^{10} +(3.22478 + 3.22478i) q^{11} +4.16620 q^{12} +(3.60399 + 0.106106i) q^{13} +(-6.51851 - 0.819979i) q^{14} +(2.27310 - 2.27310i) q^{15} -5.02479 q^{16} +4.17939 q^{17} +(-1.75588 + 1.75588i) q^{18} +(-0.774590 - 0.774590i) q^{19} +(-9.47019 + 9.47019i) q^{20} +(2.08970 - 1.62270i) q^{21} +11.3246 q^{22} +3.94079i q^{23} +(3.80357 - 3.80357i) q^{24} +5.33399i q^{25} +(6.51447 - 6.14185i) q^{26} -1.00000i q^{27} +(-8.70608 + 6.76050i) q^{28} +3.61222 q^{29} -7.98257i q^{30} +(-4.54621 - 4.54621i) q^{31} +(-1.21577 + 1.21577i) q^{32} +(-3.22478 + 3.22478i) q^{33} +(7.33849 - 7.33849i) q^{34} +(-1.06152 + 8.43867i) q^{35} +4.16620i q^{36} +(-7.34938 - 7.34938i) q^{37} -2.72017 q^{38} +(-0.106106 + 3.60399i) q^{39} +17.2918i q^{40} +(6.60549 + 6.60549i) q^{41} +(0.819979 - 6.51851i) q^{42} +5.39841i q^{43} +(13.4351 - 13.4351i) q^{44} +(2.27310 + 2.27310i) q^{45} +(6.91953 + 6.91953i) q^{46} +(-7.77396 + 7.77396i) q^{47} -5.02479i q^{48} +(-1.73366 + 6.78192i) q^{49} +(9.36583 + 9.36583i) q^{50} +4.17939i q^{51} +(0.442060 - 15.0149i) q^{52} -0.429035 q^{53} +(-1.75588 - 1.75588i) q^{54} -14.6605i q^{55} +(-1.77623 + 14.1204i) q^{56} +(0.774590 - 0.774590i) q^{57} +(6.34261 - 6.34261i) q^{58} +(-1.29667 + 1.29667i) q^{59} +(-9.47019 - 9.47019i) q^{60} +3.25050i q^{61} -15.9651 q^{62} +(1.62270 + 2.08970i) q^{63} -5.78010i q^{64} +(-7.95105 - 8.43343i) q^{65} +11.3246i q^{66} +(1.90336 - 1.90336i) q^{67} -17.4122i q^{68} -3.94079 q^{69} +(12.9534 + 16.6811i) q^{70} +(-3.74459 + 3.74459i) q^{71} +(3.80357 + 3.80357i) q^{72} +(2.36752 - 2.36752i) q^{73} -25.8092 q^{74} -5.33399 q^{75} +(-3.22709 + 3.22709i) q^{76} +(1.50594 - 11.9717i) q^{77} +(6.14185 + 6.51447i) q^{78} +3.64288 q^{79} +(11.4219 + 11.4219i) q^{80} +1.00000 q^{81} +23.1968 q^{82} +(-0.336521 - 0.336521i) q^{83} +(-6.76050 - 8.70608i) q^{84} +(-9.50019 - 9.50019i) q^{85} +(9.47893 + 9.47893i) q^{86} +3.61222i q^{87} -24.5313i q^{88} +(11.2471 - 11.2471i) q^{89} +7.98257 q^{90} +(-5.62648 - 7.70342i) q^{91} +16.4181 q^{92} +(4.54621 - 4.54621i) q^{93} +27.3002i q^{94} +3.52145i q^{95} +(-1.21577 - 1.21577i) q^{96} +(0.459600 + 0.459600i) q^{97} +(8.86411 + 14.9523i) q^{98} +(-3.22478 - 3.22478i) 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 $

$2$	1.75588	−	1.75588i	1.24159	−	1.24159i	0.282250	−	0.959341i	$-0.408919\pi$
$2$	1.75588	−	1.75588i	1.24159	−	1.24159i	0.959341	−	0.282250i	$-0.0910809\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$		−	4.16620i		−	2.08310i
$5$	−2.27310	−	2.27310i	−1.01656	−	1.01656i	−0.999861	−	0.0167020i	$-0.994683\pi$
$5$	−2.27310	−	2.27310i	−1.01656	−	1.01656i	−0.0167020	−	0.999861i	$-0.505317\pi$
$6$	1.75588	+	1.75588i	0.716833	+	0.716833i
$7$	−1.62270	−	2.08970i	−0.613325	−	0.789831i
$7$	−1.62270	−	2.08970i	−0.613325	−	0.789831i
$8$	−3.80357	−	3.80357i	−1.34476	−	1.34476i
$9$	−1.00000			−0.333333
$10$	−7.98257			−2.52431
$11$	3.22478	+	3.22478i	0.972308	+	0.972308i	0.999627	−	0.0273189i	$-0.00869695\pi$
$11$	3.22478	+	3.22478i	0.972308	+	0.972308i	−0.0273189	+	0.999627i	$0.508697\pi$
$12$	4.16620			1.20268
$13$	3.60399	+	0.106106i	0.999567	+	0.0294286i
$13$	3.60399	+	0.106106i	0.999567	+	0.0294286i
$14$	−6.51851	−	0.819979i	−1.74215	−	0.219148i
$15$	2.27310	−	2.27310i	0.586913	−	0.586913i
$16$	−5.02479			−1.25620
$17$	4.17939			1.01365			0.506826	−	0.862049i	$-0.330819\pi$
$17$	4.17939			1.01365			0.506826	+	0.862049i	$0.330819\pi$
$18$	−1.75588	+	1.75588i	−0.413864	+	0.413864i
$19$	−0.774590	−	0.774590i	−0.177703	−	0.177703i	0.612651	−	0.790354i	$-0.290103\pi$
$19$	−0.774590	−	0.774590i	−0.177703	−	0.177703i	−0.790354	+	0.612651i	$0.790103\pi$
$20$	−9.47019	+	9.47019i	−2.11760	+	2.11760i
$21$	2.08970	−	1.62270i	0.456009	−	0.354103i
$22$	11.3246			2.41442
$23$			3.94079i			0.821711i	0.911701	+	0.410855i	$0.134770\pi$
$23$			3.94079i			0.821711i	−0.911701	+	0.410855i	$0.865230\pi$
$24$	3.80357	−	3.80357i	0.776400	−	0.776400i
$25$			5.33399i			1.06680i
$26$	6.51447	−	6.14185i	1.27759	−	1.20452i
$27$		−	1.00000i		−	0.192450i
$28$	−8.70608	+	6.76050i	−1.64529	+	1.27762i
$29$	3.61222			0.670773			0.335386	−	0.942081i	$-0.391133\pi$
$29$	3.61222			0.670773			0.335386	+	0.942081i	$0.391133\pi$
$30$		−	7.98257i		−	1.45741i
$31$	−4.54621	−	4.54621i	−0.816523	−	0.816523i	0.169080	−	0.985602i	$-0.445920\pi$
$31$	−4.54621	−	4.54621i	−0.816523	−	0.816523i	−0.985602	+	0.169080i	$0.945920\pi$
$32$	−1.21577	+	1.21577i	−0.214920	+	0.214920i
$33$	−3.22478	+	3.22478i	−0.561362	+	0.561362i
$34$	7.33849	−	7.33849i	1.25854	−	1.25854i
$35$	−1.06152	+	8.43867i	−0.179430	+	1.42640i
$36$			4.16620i			0.694366i
$37$	−7.34938	−	7.34938i	−1.20823	−	1.20823i	−0.971599	−	0.236632i	$-0.923957\pi$
$37$	−7.34938	−	7.34938i	−1.20823	−	1.20823i	−0.236632	−	0.971599i	$-0.576043\pi$
$38$	−2.72017			−0.441269
$39$	−0.106106	+	3.60399i	−0.0169906	+	0.577100i
$40$			17.2918i			2.73407i
$41$	6.60549	+	6.60549i	1.03160	+	1.03160i	0.999484	+	0.0321207i	$0.0102261\pi$
$41$	6.60549	+	6.60549i	1.03160	+	1.03160i	0.0321207	+	0.999484i	$0.489774\pi$
$42$	0.819979	−	6.51851i	0.126525	−	1.00583i
$43$			5.39841i			0.823249i	0.911353	+	0.411625i	$0.135039\pi$
$43$			5.39841i			0.823249i	−0.911353	+	0.411625i	$0.864961\pi$
$44$	13.4351	−	13.4351i	2.02541	−	2.02541i
$45$	2.27310	+	2.27310i	0.338854	+	0.338854i
$46$	6.91953	+	6.91953i	1.02023	+	1.02023i
$47$	−7.77396	+	7.77396i	−1.13395	+	1.13395i	−0.144434	+	0.989514i	$0.546136\pi$
$47$	−7.77396	+	7.77396i	−1.13395	+	1.13395i	−0.989514	+	0.144434i	$0.953864\pi$
$48$		−	5.02479i		−	0.725266i
$49$	−1.73366	+	6.78192i	−0.247666	+	0.968846i
$50$	9.36583	+	9.36583i	1.32453	+	1.32453i
$51$			4.17939i			0.585232i
$52$	0.442060	−	15.0149i	0.0613027	−	2.08220i
$53$	−0.429035			−0.0589325			−0.0294662	−	0.999566i	$-0.509381\pi$
$53$	−0.429035			−0.0589325			−0.0294662	+	0.999566i	$0.509381\pi$
$54$	−1.75588	−	1.75588i	−0.238944	−	0.238944i
$55$		−	14.6605i		−	1.97682i
$56$	−1.77623	+	14.1204i	−0.237359	+	1.88691i
$57$	0.774590	−	0.774590i	0.102597	−	0.102597i
$58$	6.34261	−	6.34261i	0.832826	−	0.832826i
$59$	−1.29667	+	1.29667i	−0.168812	+	0.168812i	−0.786457	−	0.617645i	$-0.788087\pi$
$59$	−1.29667	+	1.29667i	−0.168812	+	0.168812i	0.617645	+	0.786457i	$0.288087\pi$
$60$	−9.47019	−	9.47019i	−1.22260	−	1.22260i
$61$			3.25050i			0.416183i	0.978109	+	0.208092i	$0.0667252\pi$
$61$			3.25050i			0.416183i	−0.978109	+	0.208092i	$0.933275\pi$
$62$	−15.9651			−2.02757
$63$	1.62270	+	2.08970i	0.204442	+	0.263277i
$64$		−	5.78010i		−	0.722513i
$65$	−7.95105	−	8.43343i	−0.986206	−	1.04604i
$66$			11.3246i			1.39396i
$67$	1.90336	−	1.90336i	0.232532	−	0.232532i	−0.581217	−	0.813749i	$-0.697423\pi$
$67$	1.90336	−	1.90336i	0.232532	−	0.232532i	0.813749	+	0.581217i	$0.197423\pi$
$68$		−	17.4122i		−	2.11153i
$69$	−3.94079			−0.474415
$70$	12.9534	+	16.6811i	1.54822	+	1.99378i
$71$	−3.74459	+	3.74459i	−0.444401	+	0.444401i	−0.893488	−	0.449087i	$-0.851749\pi$
$71$	−3.74459	+	3.74459i	−0.444401	+	0.444401i	0.449087	+	0.893488i	$0.351749\pi$
$72$	3.80357	+	3.80357i	0.448255	+	0.448255i
$73$	2.36752	−	2.36752i	0.277097	−	0.277097i	−0.554852	−	0.831949i	$-0.687225\pi$
$73$	2.36752	−	2.36752i	0.277097	−	0.277097i	0.831949	+	0.554852i	$0.187225\pi$
$74$	−25.8092			−3.00026
$75$	−5.33399			−0.615916
$76$	−3.22709	+	3.22709i	−0.370173	+	0.370173i
$77$	1.50594	−	11.9717i	0.171618	−	1.36430i
$78$	6.14185	+	6.51447i	0.695427	+	0.737618i
$79$	3.64288			0.409856			0.204928	−	0.978777i	$-0.434304\pi$
$79$	3.64288			0.409856			0.204928	+	0.978777i	$0.434304\pi$
$80$	11.4219	+	11.4219i	1.27700	+	1.27700i
$81$	1.00000			0.111111
$82$	23.1968			2.56166
$83$	−0.336521	−	0.336521i	−0.0369379	−	0.0369379i	0.688397	−	0.725335i	$-0.258315\pi$
$83$	−0.336521	−	0.336521i	−0.0369379	−	0.0369379i	−0.725335	+	0.688397i	$0.758315\pi$
$84$	−6.76050	−	8.70608i	−0.737631	−	0.949911i
$85$	−9.50019	−	9.50019i	−1.03044	−	1.03044i
$86$	9.47893	+	9.47893i	1.02214	+	1.02214i
$87$			3.61222i			0.387271i
$88$		−	24.5313i		−	2.61505i
$89$	11.2471	−	11.2471i	1.19219	−	1.19219i	0.215737	−	0.976451i	$-0.430785\pi$
$89$	11.2471	−	11.2471i	1.19219	−	1.19219i	0.976451	−	0.215737i	$-0.0692154\pi$
$90$	7.98257			0.841437
$91$	−5.62648	−	7.70342i	−0.589815	−	0.807538i
$92$	16.4181			1.71170
$93$	4.54621	−	4.54621i	0.471420	−	0.471420i
$94$			27.3002i			2.81580i
$95$			3.52145i			0.361293i
$96$	−1.21577	−	1.21577i	−0.124084	−	0.124084i
$97$	0.459600	+	0.459600i	0.0466653	+	0.0466653i	0.730054	−	0.683389i	$-0.239495\pi$
$97$	0.459600	+	0.459600i	0.0466653	+	0.0466653i	−0.683389	+	0.730054i	$0.739495\pi$
$98$	8.86411	+	14.9523i	0.895411	+	1.51041i
$99$	−3.22478	−	3.22478i	−0.324103	−	0.324103i
$100$	22.2225			2.22225
$101$	−5.58367			−0.555596			−0.277798	−	0.960640i	$-0.589605\pi$
$101$	−5.58367			−0.555596			−0.277798	+	0.960640i	$0.589605\pi$
$102$	7.33849	+	7.33849i	0.726619	+	0.726619i
$103$	14.4248			1.42131			0.710657	−	0.703538i	$-0.248398\pi$
$103$	14.4248			1.42131			0.710657	+	0.703538i	$0.248398\pi$
$104$	−13.3044	−	14.1116i	−1.30461	−	1.38376i
$105$	−8.43867	−	1.06152i	−0.823530	−	0.103594i
$106$	−0.753332	+	0.753332i	−0.0731701	+	0.0731701i
$107$	0.723995			0.0699912			0.0349956	−	0.999387i	$-0.488858\pi$
$107$	0.723995			0.0699912			0.0349956	+	0.999387i	$0.488858\pi$
$108$	−4.16620			−0.400892
$109$	−3.82447	+	3.82447i	−0.366318	+	0.366318i	−0.866132	−	0.499815i	$-0.833401\pi$
$109$	−3.82447	+	3.82447i	−0.366318	+	0.366318i	0.499815	+	0.866132i	$0.333401\pi$
$110$	−25.7420	−	25.7420i	−2.45441	−	2.45441i
$111$	7.34938	−	7.34938i	0.697573	−	0.697573i
$112$	8.15375	+	10.5003i	0.770457	+	0.992184i
$113$	−18.2068			−1.71275			−0.856374	−	0.516357i	$-0.827288\pi$
$113$	−18.2068			−1.71275			−0.856374	+	0.516357i	$0.827288\pi$
$114$		−	2.72017i		−	0.254767i
$115$	8.95781	−	8.95781i	0.835320	−	0.835320i
$116$		−	15.0492i		−	1.39729i
$117$	−3.60399	−	0.106106i	−0.333189	−	0.00980954i
$118$			4.55357i			0.419190i
$119$	−6.78192	−	8.73366i	−0.621698	−	0.800613i
$120$	−17.2918			−1.57852
$121$			9.79842i			0.890765i
$122$	5.70747	+	5.70747i	0.516730	+	0.516730i
$123$	−6.60549	+	6.60549i	−0.595597	+	0.595597i
$124$	−18.9404	+	18.9404i	−1.70090	+	1.70090i
$125$	0.759200	−	0.759200i	0.0679049	−	0.0679049i
$126$	6.51851	+	0.819979i	0.580715	+	0.0730495i
$127$			4.35712i			0.386632i	0.981137	+	0.193316i	$0.0619242\pi$
$127$			4.35712i			0.386632i	−0.981137	+	0.193316i	$0.938076\pi$
$128$	−12.5807	−	12.5807i	−1.11199	−	1.11199i
$129$	−5.39841			−0.475303
$130$	−28.7691	−	0.847002i	−2.52322	−	0.0742870i
$131$			19.9916i			1.74668i	0.487115	+	0.873338i	$0.338049\pi$
$131$			19.9916i			1.74668i	−0.487115	+	0.873338i	$0.661951\pi$
$132$	13.4351	+	13.4351i	1.16937	+	1.16937i
$133$	−0.361727	+	2.87559i	−0.0313657	+	0.249345i
$134$		−	6.68411i		−	0.577419i
$135$	−2.27310	+	2.27310i	−0.195638	+	0.195638i
$136$	−15.8966	−	15.8966i	−1.36312	−	1.36312i
$137$	5.53907	+	5.53907i	0.473235	+	0.473235i	0.902960	−	0.429725i	$-0.141390\pi$
$137$	5.53907	+	5.53907i	0.473235	+	0.473235i	−0.429725	+	0.902960i	$0.641390\pi$
$138$	−6.91953	+	6.91953i	−0.589029	+	0.589029i
$139$			18.8236i			1.59659i	0.602265	+	0.798296i	$0.294265\pi$
$139$			18.8236i			1.59659i	−0.602265	+	0.798296i	$0.705735\pi$
$140$	35.1571	+	4.42250i	2.97132	+	0.373769i
$141$	−7.77396	−	7.77396i	−0.654686	−	0.654686i
$142$			13.1501i			1.10353i
$143$	11.2799	+	11.9642i	0.943273	+	1.00050i
$144$	5.02479			0.418733
$145$	−8.21095	−	8.21095i	−0.681883	−	0.681883i
$146$		−	8.31412i		−	0.688082i
$147$	−6.78192	−	1.73366i	−0.559363	−	0.142990i
$148$	−30.6190	+	30.6190i	−2.51686	+	2.51686i
$149$	0.387442	−	0.387442i	0.0317405	−	0.0317405i	−0.691058	−	0.722799i	$-0.742855\pi$
$149$	0.387442	−	0.387442i	0.0317405	−	0.0317405i	0.722799	+	0.691058i	$0.242855\pi$
$150$	−9.36583	+	9.36583i	−0.764716	+	0.764716i
$151$	2.85380	+	2.85380i	0.232239	+	0.232239i	0.813627	−	0.581387i	$-0.197490\pi$
$151$	2.85380	+	2.85380i	0.232239	+	0.232239i	−0.581387	+	0.813627i	$0.697490\pi$
$152$			5.89241i			0.477938i
$153$	−4.17939			−0.337884
$154$	−18.3765	−	23.6650i	−1.48082	−	1.90698i
$155$			20.6680i			1.66009i
$156$	15.0149	+	0.442060i	1.20216	+	0.0353931i
$157$		−	21.8189i		−	1.74134i	−0.491869	−	0.870669i	$-0.663686\pi$
$157$		−	21.8189i		−	1.74134i	0.491869	−	0.870669i	$-0.336314\pi$
$158$	6.39645	−	6.39645i	0.508874	−	0.508874i
$159$		−	0.429035i		−	0.0340247i
$160$	5.52714			0.436959
$161$	8.23504	−	6.39473i	0.649012	−	0.503975i
$162$	1.75588	−	1.75588i	0.137955	−	0.137955i
$163$	−15.2280	−	15.2280i	−1.19275	−	1.19275i	−0.976293	−	0.216455i	$-0.930551\pi$
$163$	−15.2280	−	15.2280i	−1.19275	−	1.19275i	−0.216455	−	0.976293i	$-0.569449\pi$
$164$	27.5198	−	27.5198i	2.14893	−	2.14893i
$165$	14.6605			1.14132
$166$	−1.18178			−0.0917236
$167$	−0.578070	+	0.578070i	−0.0447324	+	0.0447324i	−0.729119	−	0.684387i	$-0.760070\pi$
$167$	−0.578070	+	0.578070i	−0.0447324	+	0.0447324i	0.684387	+	0.729119i	$0.260070\pi$
$168$	−14.1204	−	1.77623i	−1.08941	−	0.137039i
$169$	12.9775	+	0.764813i	0.998268	+	0.0588318i
$170$	−33.3623			−2.55877
$171$	0.774590	+	0.774590i	0.0592344	+	0.0592344i
$172$	22.4908			1.71491
$173$	0.696157			0.0529279			0.0264639	−	0.999650i	$-0.491575\pi$
$173$	0.696157			0.0529279			0.0264639	+	0.999650i	$0.491575\pi$
$174$	6.34261	+	6.34261i	0.480832	+	0.480832i
$175$	11.1464	−	8.65550i	0.842590	−	0.654294i
$176$	−16.2038	−	16.2038i	−1.22141	−	1.22141i
$177$	−1.29667	−	1.29667i	−0.0974634	−	0.0974634i
$178$		−	39.4970i		−	2.96042i
$179$		−	0.801167i		−	0.0598820i	−0.999552	−	0.0299410i	$-0.990468\pi$
$179$		−	0.801167i		−	0.0598820i	0.999552	−	0.0299410i	$-0.00953194\pi$
$180$	9.47019	−	9.47019i	0.705866	−	0.705866i
$181$	−22.4677			−1.67001			−0.835005	−	0.550242i	$-0.814535\pi$
$181$	−22.4677			−1.67001			−0.835005	+	0.550242i	$0.814535\pi$
$182$	−23.4056	−	3.64685i	−1.73494	−	0.270323i
$183$	−3.25050			−0.240284
$184$	14.9890	−	14.9890i	1.10501	−	1.10501i
$185$			33.4118i			2.45648i
$186$		−	15.9651i		−	1.17062i
$187$	13.4776	+	13.4776i	0.985581	+	0.985581i
$188$	32.3878	+	32.3878i	2.36213	+	2.36213i
$189$	−2.08970	+	1.62270i	−0.152003	+	0.118034i
$190$	6.18322	+	6.18322i	0.448578	+	0.448578i
$191$	15.7270			1.13796			0.568982	−	0.822350i	$-0.307337\pi$
$191$	15.7270			1.13796			0.568982	+	0.822350i	$0.307337\pi$
$192$	5.78010			0.417143
$193$	6.55862	+	6.55862i	0.472100	+	0.472100i	0.902594	−	0.430494i	$-0.141661\pi$
$193$	6.55862	+	6.55862i	0.472100	+	0.472100i	−0.430494	+	0.902594i	$0.641661\pi$
$194$	1.61400			0.115879
$195$	8.43343	−	7.95105i	0.603930	−	0.569386i
$196$	28.2548	+	7.22276i	2.01820	+	0.515912i
$197$	−0.440789	+	0.440789i	−0.0314049	+	0.0314049i	−0.722635	−	0.691230i	$-0.757069\pi$
$197$	−0.440789	+	0.440789i	−0.0314049	+	0.0314049i	0.691230	+	0.722635i	$0.257069\pi$
$198$	−11.3246			−0.804806
$199$	−12.3117			−0.872750			−0.436375	−	0.899765i	$-0.643738\pi$
$199$	−12.3117			−0.872750			−0.436375	+	0.899765i	$0.643738\pi$
$200$	20.2882	−	20.2882i	1.43459	−	1.43459i
$201$	1.90336	+	1.90336i	0.134252	+	0.134252i
$202$	−9.80422	+	9.80422i	−0.689823	+	0.689823i
$203$	−5.86157	−	7.54845i	−0.411402	−	0.529797i
$204$	17.4122			1.21910
$205$		−	30.0299i		−	2.09738i
$206$	25.3281	−	25.3281i	1.76469	−	1.76469i
$207$		−	3.94079i		−	0.273904i
$208$	−18.1093	−	0.533163i	−1.25565	−	0.0369682i
$209$		−	4.99577i		−	0.345564i
$210$	−16.6811	+	12.9534i	−1.15111	+	0.893866i
$211$	−1.27815			−0.0879914			−0.0439957	−	0.999032i	$-0.514009\pi$
$211$	−1.27815			−0.0879914			−0.0439957	+	0.999032i	$0.514009\pi$
$212$			1.78744i			0.122762i
$213$	−3.74459	−	3.74459i	−0.256575	−	0.256575i
$214$	1.27125	−	1.27125i	0.0869005	−	0.0869005i
$215$	12.2711	−	12.2711i	0.836884	−	0.836884i
$216$	−3.80357	+	3.80357i	−0.258800	+	0.258800i
$217$	−2.12304	+	16.8773i	−0.144121	+	1.14571i
$218$			13.4306i			0.909633i
$219$	2.36752	+	2.36752i	0.159982	+	0.159982i
$220$	−61.0786			−4.11792
$221$	15.0625	+	0.443460i	1.01321	+	0.0298304i
$222$		−	25.8092i		−	1.73220i
$223$	−8.41160	−	8.41160i	−0.563283	−	0.563283i	0.366956	−	0.930238i	$-0.380400\pi$
$223$	−8.41160	−	8.41160i	−0.563283	−	0.563283i	−0.930238	+	0.366956i	$0.880400\pi$
$224$	4.51343	+	0.567754i	0.301566	+	0.0379347i
$225$		−	5.33399i		−	0.355600i
$226$	−31.9688	+	31.9688i	−2.12653	+	2.12653i
$227$	2.87572	+	2.87572i	0.190869	+	0.190869i	0.796071	−	0.605203i	$-0.206908\pi$
$227$	2.87572	+	2.87572i	0.190869	+	0.190869i	−0.605203	+	0.796071i	$0.706908\pi$
$228$	−3.22709	−	3.22709i	−0.213720	−	0.213720i
$229$	−3.18307	+	3.18307i	−0.210343	+	0.210343i	−0.804413	−	0.594070i	$-0.797520\pi$
$229$	−3.18307	+	3.18307i	−0.210343	+	0.210343i	0.594070	+	0.804413i	$0.297520\pi$
$230$		−	31.4576i		−	2.07425i
$231$	11.9717	+	1.50594i	0.787679	+	0.0990839i
$232$	−13.7393	−	13.7393i	−0.902032	−	0.902032i
$233$		−	17.7925i		−	1.16563i	−0.812607	−	0.582813i	$-0.801952\pi$
$233$		−	17.7925i		−	1.16563i	0.812607	−	0.582813i	$-0.198048\pi$
$234$	−6.51447	+	6.14185i	−0.425864	+	0.401505i
$235$	35.3420			2.30546
$236$	5.40216	+	5.40216i	0.351651	+	0.351651i
$237$			3.64288i			0.236631i
$238$	−27.2434	−	3.42701i	−1.76593	−	0.222140i
$239$	11.1681	−	11.1681i	0.722407	−	0.722407i	−0.246688	−	0.969095i	$-0.579342\pi$
$239$	11.1681	−	11.1681i	0.722407	−	0.722407i	0.969095	+	0.246688i	$0.0793424\pi$
$240$	−11.4219	+	11.4219i	−0.737278	+	0.737278i
$241$	5.05729	−	5.05729i	0.325768	−	0.325768i	−0.525206	−	0.850975i	$-0.676012\pi$
$241$	5.05729	−	5.05729i	0.325768	−	0.325768i	0.850975	+	0.525206i	$0.176012\pi$
$242$	17.2048	+	17.2048i	1.10597	+	1.10597i
$243$			1.00000i			0.0641500i
$244$	13.5422			0.866951
$245$	19.3568	−	11.4752i	1.23666	−	0.733125i
$246$			23.1968i			1.47898i
$247$	−2.70943	−	2.87380i	−0.172397	−	0.182856i
$248$			34.5836i			2.19606i
$249$	0.336521	−	0.336521i	0.0213261	−	0.0213261i
$250$		−	2.66612i		−	0.168620i
$251$	1.12847			0.0712284			0.0356142	−	0.999366i	$-0.488661\pi$
$251$	1.12847			0.0712284			0.0356142	+	0.999366i	$0.488661\pi$
$252$	8.70608	−	6.76050i	0.548432	−	0.425872i
$253$	−12.7082	+	12.7082i	−0.798956	+	0.798956i
$254$	7.65055	+	7.65055i	0.480038	+	0.480038i
$255$	9.50019	−	9.50019i	0.594925	−	0.594925i
$256$	−32.6200			−2.03875
$257$	−28.2971			−1.76512			−0.882562	−	0.470196i	$-0.844183\pi$
$257$	−28.2971			−1.76512			−0.882562	+	0.470196i	$0.844183\pi$
$258$	−9.47893	+	9.47893i	−0.590132	+	0.590132i
$259$	−3.43210	+	27.2839i	−0.213260	+	1.69534i
$260$	−35.1353	+	33.1256i	−2.17900	+	2.05436i
$261$	−3.61222			−0.223591
$262$	35.1028	+	35.1028i	2.16866	+	2.16866i
$263$	17.0950			1.05412			0.527061	−	0.849828i	$-0.323294\pi$
$263$	17.0950			1.05412			0.527061	+	0.849828i	$0.323294\pi$
$264$	24.5313			1.50980
$265$	0.975241	+	0.975241i	0.0599086	+	0.0599086i
$266$	4.41403	+	5.68432i	0.270641	+	0.348528i
$267$	11.2471	+	11.2471i	0.688310	+	0.688310i
$268$	−7.92975	−	7.92975i	−0.484387	−	0.484387i
$269$		−	4.65103i		−	0.283578i	−0.989897	−	0.141789i	$-0.954715\pi$
$269$		−	4.65103i		−	0.283578i	0.989897	−	0.141789i	$-0.0452855\pi$
$270$			7.98257i			0.485804i
$271$	9.51718	−	9.51718i	0.578128	−	0.578128i	−0.356259	−	0.934387i	$-0.615948\pi$
$271$	9.51718	−	9.51718i	0.578128	−	0.578128i	0.934387	+	0.356259i	$0.115948\pi$
$272$	−21.0006			−1.27335
$273$	7.70342	−	5.62648i	0.466232	−	0.340530i
$274$	19.4518			1.17513
$275$	−17.2010	+	17.2010i	−1.03726	+	1.03726i
$276$			16.4181i			0.988252i
$277$			18.5055i			1.11189i	0.831220	+	0.555943i	$0.187643\pi$
$277$			18.5055i			1.11189i	−0.831220	+	0.555943i	$0.812357\pi$
$278$	33.0518	+	33.0518i	1.98232	+	1.98232i
$279$	4.54621	+	4.54621i	0.272174	+	0.272174i
$280$	36.1346	−	28.0595i	2.15946	−	1.67688i
$281$	−14.2256	−	14.2256i	−0.848630	−	0.848630i	0.141332	−	0.989962i	$-0.454861\pi$
$281$	−14.2256	−	14.2256i	−0.848630	−	0.848630i	−0.989962	+	0.141332i	$0.954861\pi$
$282$	−27.3002			−1.62570
$283$	−6.56107			−0.390015			−0.195008	−	0.980802i	$-0.562473\pi$
$283$	−6.56107			−0.390015			−0.195008	+	0.980802i	$0.562473\pi$
$284$	15.6007	+	15.6007i	0.925731	+	0.925731i
$285$	−3.52145			−0.208592
$286$	40.8138	+	1.20162i	2.41337	+	0.0710530i
$287$	3.08471	−	24.5222i	0.182085	−	1.44750i
$288$	1.21577	−	1.21577i	0.0716399	−	0.0716399i
$289$	0.467318			0.0274893
$290$	−28.8348			−1.69324
$291$	−0.459600	+	0.459600i	−0.0269422	+	0.0269422i
$292$	−9.86353	−	9.86353i	−0.577220	−	0.577220i
$293$	−0.883923	+	0.883923i	−0.0516393	+	0.0516393i	−0.732455	−	0.680816i	$-0.761626\pi$
$293$	−0.883923	+	0.883923i	−0.0516393	+	0.0516393i	0.680816	+	0.732455i	$0.261626\pi$
$294$	−14.9523	+	8.86411i	−0.872035	+	0.516966i
$295$	5.89491			0.343215
$296$			55.9078i			3.24957i
$297$	3.22478	−	3.22478i	0.187121	−	0.187121i
$298$		−	1.36060i		−	0.0788175i
$299$	−0.418143	+	14.2025i	−0.0241818	+	0.821355i
$300$			22.2225i			1.28301i
$301$	11.2810	−	8.76002i	0.650228	−	0.504919i
$302$	10.0218			0.576693
$303$		−	5.58367i		−	0.320773i
$304$	3.89215	+	3.89215i	0.223230	+	0.223230i
$305$	7.38871	−	7.38871i	0.423076	−	0.423076i
$306$	−7.33849	+	7.33849i	−0.419514	+	0.419514i
$307$	−3.01480	+	3.01480i	−0.172064	+	0.172064i	−0.787885	−	0.615822i	$-0.788824\pi$
$307$	−3.01480	+	3.01480i	−0.172064	+	0.172064i	0.615822	+	0.787885i	$0.288824\pi$
$308$	−49.8763	−	6.27406i	−2.84197	−	0.357498i
$309$			14.4248i			0.820596i
$310$	36.2904	+	36.2904i	2.06116	+	2.06116i
$311$	−19.0648			−1.08107			−0.540533	−	0.841323i	$-0.681778\pi$
$311$	−19.0648			−1.08107			−0.540533	+	0.841323i	$0.681778\pi$
$312$	14.1116	−	13.3044i	0.798912	−	0.753215i
$313$		−	5.98295i		−	0.338176i	−0.985601	−	0.169088i	$-0.945918\pi$
$313$		−	5.98295i		−	0.338176i	0.985601	−	0.169088i	$-0.0540822\pi$
$314$	−38.3113	−	38.3113i	−2.16203	−	2.16203i
$315$	1.06152	−	8.43867i	0.0598098	−	0.475465i
$316$		−	15.1770i		−	0.853771i
$317$	−4.18438	+	4.18438i	−0.235018	+	0.235018i	−0.814783	−	0.579765i	$-0.803144\pi$
$317$	−4.18438	+	4.18438i	−0.235018	+	0.235018i	0.579765	+	0.814783i	$0.303144\pi$
$318$	−0.753332	−	0.753332i	−0.0422448	−	0.0422448i
$319$	11.6486	+	11.6486i	0.652198	+	0.652198i
$320$	−13.1388	+	13.1388i	−0.734479	+	0.734479i
$321$			0.723995i			0.0404095i
$322$	3.23136	−	25.6881i	0.180077	−	1.43154i
$323$	−3.23732	−	3.23732i	−0.180129	−	0.180129i
$324$		−	4.16620i		−	0.231455i
$325$	−0.565971	+	19.2237i	−0.0313944	+	1.06634i
$326$	−53.4769			−2.96181
$327$	−3.82447	−	3.82447i	−0.211494	−	0.211494i
$328$		−	50.2489i		−	2.77453i
$329$	28.8601	+	3.63037i	1.59111	+	0.200149i
$330$	25.7420	−	25.7420i	1.41705	−	1.41705i
$331$	−12.8296	+	12.8296i	−0.705179	+	0.705179i	−0.965517	−	0.260339i	$-0.916166\pi$
$331$	−12.8296	+	12.8296i	−0.705179	+	0.705179i	0.260339	+	0.965517i	$0.416166\pi$
$332$	−1.40201	+	1.40201i	−0.0769453	+	0.0769453i
$333$	7.34938	+	7.34938i	0.402744	+	0.402744i
$334$			2.03004i			0.111079i
$335$	−8.65304			−0.472766
$336$	−10.5003	+	8.15375i	−0.572838	+	0.444824i
$337$		−	24.2890i		−	1.32310i	−0.749899	−	0.661552i	$-0.769898\pi$
$337$		−	24.2890i		−	1.32310i	0.749899	−	0.661552i	$-0.230102\pi$
$338$	24.1298	−	21.4439i	1.31249	−	1.16640i
$339$		−	18.2068i		−	0.988855i
$340$	−39.5796	+	39.5796i	−2.14651	+	2.14651i
$341$		−	29.3210i		−	1.58782i
$342$	2.72017			0.147090
$343$	16.9854	−	7.38223i	0.917124	−	0.398603i
$344$	20.5332	−	20.5332i	1.10708	−	1.10708i
$345$	8.95781	+	8.95781i	0.482272	+	0.482272i
$346$	1.22237	−	1.22237i	0.0657148	−	0.0657148i
$347$	23.6977			1.27216			0.636080	−	0.771623i	$-0.280555\pi$
$347$	23.6977			1.27216			0.636080	+	0.771623i	$0.280555\pi$
$348$	15.0492			0.806723
$349$	−16.5957	+	16.5957i	−0.888347	+	0.888347i	−0.994364	−	0.106017i	$-0.966190\pi$
$349$	−16.5957	+	16.5957i	−0.888347	+	0.888347i	0.106017	+	0.994364i	$0.466190\pi$
$350$	4.37376	−	34.7697i	0.233787	−	1.85852i
$351$	0.106106	−	3.60399i	0.00566354	−	0.192367i
$352$	−7.84118			−0.417936
$353$	−6.69947	−	6.69947i	−0.356577	−	0.356577i	0.505973	−	0.862550i	$-0.331134\pi$
$353$	−6.69947	−	6.69947i	−0.356577	−	0.356577i	−0.862550	+	0.505973i	$0.831134\pi$
$354$	−4.55357			−0.242019
$355$	17.0237			0.903523
$356$	−46.8575	−	46.8575i	−2.48345	−	2.48345i
$357$	8.73366	−	6.78192i	0.462234	−	0.358937i
$358$	−1.40675	−	1.40675i	−0.0743490	−	0.0743490i
$359$	20.8627	+	20.8627i	1.10109	+	1.10109i	0.994279	+	0.106812i	$0.0340642\pi$
$359$	20.8627	+	20.8627i	1.10109	+	1.10109i	0.106812	+	0.994279i	$0.465936\pi$
$360$		−	17.2918i		−	0.911358i
$361$		−	17.8000i		−	0.936843i
$362$	−39.4505	+	39.4505i	−2.07347	+	2.07347i
$363$	−9.79842			−0.514284
$364$	−32.0940	+	23.4410i	−1.68218	+	1.22864i
$365$	−10.7632			−0.563372
$366$	−5.70747	+	5.70747i	−0.298334	+	0.298334i
$367$			0.958792i			0.0500485i	0.999687	+	0.0250243i	$0.00796630\pi$
$367$			0.958792i			0.0500485i	−0.999687	+	0.0250243i	$0.992034\pi$
$368$		−	19.8016i		−	1.03223i
$369$	−6.60549	−	6.60549i	−0.343868	−	0.343868i
$370$	58.6670	+	58.6670i	3.04995	+	3.04995i
$371$	0.696197	+	0.896553i	0.0361447	+	0.0465467i
$372$	−18.9404	−	18.9404i	−0.982013	−	0.982013i
$373$	0.340995			0.0176560			0.00882802	−	0.999961i	$-0.497190\pi$
$373$	0.340995			0.0176560			0.00882802	+	0.999961i	$0.497190\pi$
$374$	47.3300			2.44738
$375$	0.759200	+	0.759200i	0.0392049	+	0.0392049i
$376$	59.1376			3.04979
$377$	13.0184	+	0.383280i	0.670482	+	0.0197399i
$378$	−0.819979	+	6.51851i	−0.0421751	+	0.335276i
$379$	−17.4497	+	17.4497i	−0.896330	+	0.896330i	−0.995109	−	0.0987798i	$-0.968506\pi$
$379$	−17.4497	+	17.4497i	−0.896330	+	0.896330i	0.0987798	+	0.995109i	$0.468506\pi$
$380$	14.6710			0.752608
$381$	−4.35712			−0.223222
$382$	27.6146	−	27.6146i	1.41289	−	1.41289i
$383$	0.285743	+	0.285743i	0.0146008	+	0.0146008i	0.714369	−	0.699769i	$-0.246714\pi$
$383$	0.285743	+	0.285743i	0.0146008	+	0.0146008i	−0.699769	+	0.714369i	$0.746714\pi$
$384$	12.5807	−	12.5807i	0.642005	−	0.642005i
$385$	−30.6360	+	23.7897i	−1.56136	+	1.21243i
$386$	23.0322			1.17231
$387$		−	5.39841i		−	0.274416i
$388$	1.91478	−	1.91478i	0.0972084	−	0.0972084i
$389$			24.5975i			1.24714i	0.781766	+	0.623572i	$0.214319\pi$
$389$			24.5975i			1.24714i	−0.781766	+	0.623572i	$0.785681\pi$
$390$	0.847002	−	28.7691i	0.0428896	−	1.45678i
$391$			16.4701i			0.832928i
$392$	32.3896	−	19.2014i	1.63592	−	0.969817i
$393$	−19.9916			−1.00844
$394$			1.54794i			0.0779842i
$395$	−8.28065	−	8.28065i	−0.416645	−	0.416645i
$396$	−13.4351	+	13.4351i	−0.675137	+	0.675137i
$397$	13.7002	−	13.7002i	0.687593	−	0.687593i	−0.274106	−	0.961699i	$-0.588382\pi$
$397$	13.7002	−	13.7002i	0.687593	−	0.687593i	0.961699	+	0.274106i	$0.0883820\pi$
$398$	−21.6177	+	21.6177i	−1.08360	+	1.08360i
$399$	−2.87559	−	0.361727i	−0.143960	−	0.0181090i
$400$		−	26.8022i		−	1.34011i
$401$	−20.6555	−	20.6555i	−1.03149	−	1.03149i	−0.999488	−	0.0320001i	$-0.989812\pi$
$401$	−20.6555	−	20.6555i	−1.03149	−	1.03149i	−0.0320001	−	0.999488i	$-0.510188\pi$
$402$	6.68411			0.333373
$403$	−15.9021	−	16.8669i	−0.792140	−	0.840198i
$404$			23.2626i			1.15736i
$405$	−2.27310	−	2.27310i	−0.112951	−	0.112951i
$406$	−23.5463	−	2.96195i	−1.16858	−	0.146999i
$407$		−	47.4003i		−	2.34955i
$408$	15.8966	−	15.8966i	0.786999	−	0.786999i
$409$	13.1018	+	13.1018i	0.647845	+	0.647845i	0.952472	−	0.304627i	$-0.0985318\pi$
$409$	13.1018	+	13.1018i	0.647845	+	0.647845i	−0.304627	+	0.952472i	$0.598532\pi$
$410$	−52.7288	−	52.7288i	−2.60409	−	2.60409i
$411$	−5.53907	+	5.53907i	−0.273222	+	0.273222i
$412$		−	60.0964i		−	2.96074i
$413$	4.81374	+	0.605532i	0.236869	+	0.0297963i
$414$	−6.91953	−	6.91953i	−0.340076	−	0.340076i
$415$			1.52989i			0.0750995i
$416$	−4.51062	+	4.25262i	−0.221152	+	0.208502i
$417$	−18.8236			−0.921793
$418$	−8.77194	−	8.77194i	−0.429050	−	0.429050i
$419$		−	27.3048i		−	1.33392i	−0.745091	−	0.666962i	$-0.767594\pi$
$419$		−	27.3048i		−	1.33392i	0.745091	−	0.666962i	$-0.232406\pi$
$420$	−4.42250	+	35.1571i	−0.215796	+	1.71549i
$421$	0.649398	−	0.649398i	0.0316497	−	0.0316497i	−0.691105	−	0.722755i	$-0.742876\pi$
$421$	0.649398	−	0.649398i	0.0316497	−	0.0316497i	0.722755	+	0.691105i	$0.242876\pi$
$422$	−2.24427	+	2.24427i	−0.109249	+	0.109249i
$423$	7.77396	−	7.77396i	0.377983	−	0.377983i
$424$	1.63186	+	1.63186i	0.0792503	+	0.0792503i
$425$			22.2928i			1.08136i
$426$	−13.1501			−0.637123
$427$	6.79255	−	5.27460i	0.328714	−	0.255256i
$428$		−	3.01630i		−	0.145799i
$429$	−11.9642	+	11.2799i	−0.577639	+	0.544599i
$430$		−	43.0932i		−	2.07814i
$431$	−17.5655	+	17.5655i	−0.846102	+	0.846102i	−0.989644	−	0.143542i	$-0.954151\pi$
$431$	−17.5655	+	17.5655i	−0.846102	+	0.846102i	0.143542	+	0.989644i	$0.454151\pi$
$432$			5.02479i			0.241755i
$433$	27.3091			1.31239			0.656196	−	0.754590i	$-0.272164\pi$
$433$	27.3091			1.31239			0.656196	+	0.754590i	$0.272164\pi$
$434$	25.9067	+	33.3623i	1.24356	+	1.60144i
$435$	8.21095	−	8.21095i	0.393685	−	0.393685i
$436$	15.9335	+	15.9335i	0.763075	+	0.763075i
$437$	3.05249	−	3.05249i	0.146021	−	0.146021i
$438$	8.31412			0.397264
$439$	1.15280			0.0550201			0.0275100	−	0.999622i	$-0.491242\pi$
$439$	1.15280			0.0550201			0.0275100	+	0.999622i	$0.491242\pi$
$440$	−55.7623	+	55.7623i	−2.65836	+	2.65836i
$441$	1.73366	−	6.78192i	0.0825552	−	0.322949i
$442$	27.2265	−	25.6692i	1.29503	−	1.22096i
$443$	8.04614			0.382284			0.191142	−	0.981562i	$-0.438781\pi$
$443$	8.04614			0.382284			0.191142	+	0.981562i	$0.438781\pi$
$444$	−30.6190	−	30.6190i	−1.45311	−	1.45311i
$445$	−51.1316			−2.42387
$446$	−29.5395			−1.39873
$447$	0.387442	+	0.387442i	0.0183254	+	0.0183254i
$448$	−12.0787	+	9.37940i	−0.570663	+	0.443135i
$449$	9.18043	+	9.18043i	0.433251	+	0.433251i	0.889733	−	0.456482i	$-0.150891\pi$
$449$	9.18043	+	9.18043i	0.433251	+	0.433251i	−0.456482	+	0.889733i	$0.650891\pi$
$450$	−9.36583	−	9.36583i	−0.441509	−	0.441509i
$451$			42.6025i			2.00607i
$452$			75.8529i			3.56782i
$453$	−2.85380	+	2.85380i	−0.134083	+	0.134083i
$454$	10.0988			0.473961
$455$	−4.72110	+	30.3002i	−0.221329	+	1.42050i
$456$	−5.89241			−0.275938
$457$	25.8083	−	25.8083i	1.20726	−	1.20726i	0.235354	−	0.971910i	$-0.424375\pi$
$457$	25.8083	−	25.8083i	1.20726	−	1.20726i	0.971910	−	0.235354i	$-0.0756248\pi$
$458$			11.1781i			0.522320i
$459$		−	4.17939i		−	0.195077i
$460$	−37.3200	−	37.3200i	−1.74005	−	1.74005i
$461$	22.8970	+	22.8970i	1.06642	+	1.06642i	0.997631	+	0.0687888i	$0.0219135\pi$
$461$	22.8970	+	22.8970i	1.06642	+	1.06642i	0.0687888	+	0.997631i	$0.478087\pi$
$462$	23.6650	−	18.3765i	1.10100	−	0.854953i
$463$	6.51855	+	6.51855i	0.302943	+	0.302943i	0.842164	−	0.539221i	$-0.181281\pi$
$463$	6.51855	+	6.51855i	0.302943	+	0.302943i	−0.539221	+	0.842164i	$0.681281\pi$
$464$	−18.1507			−0.842624
$465$	−20.6680			−0.958455
$466$	−31.2414	−	31.2414i	−1.44723	−	1.44723i
$467$	−22.5573			−1.04383			−0.521914	−	0.852998i	$-0.674782\pi$
$467$	−22.5573			−1.04383			−0.521914	+	0.852998i	$0.674782\pi$
$468$	−0.442060	+	15.0149i	−0.0204342	+	0.694065i
$469$	−7.06602	−	0.888850i	−0.326278	−	0.0410433i
$470$	62.0562	−	62.0562i	2.86244	−	2.86244i
$471$	21.8189			1.00536
$472$	9.86391			0.454023
$473$	−17.4087	+	17.4087i	−0.800452	+	0.800452i
$474$	6.39645	+	6.39645i	0.293799	+	0.293799i
$475$	4.13166	−	4.13166i	0.189573	−	0.189573i
$476$	−36.3861	+	28.2548i	−1.66776	+	1.29506i
$477$	0.429035			0.0196442
$478$		−	39.2197i		−	1.79387i
$479$	−9.06086	+	9.06086i	−0.414001	+	0.414001i	−0.883130	−	0.469129i	$-0.844568\pi$
$479$	−9.06086	+	9.06086i	−0.414001	+	0.414001i	0.469129	+	0.883130i	$0.344568\pi$
$480$			5.52714i			0.252278i
$481$	−25.7073	−	27.2669i	−1.17215	−	1.24326i
$482$		−	17.7599i		−	0.808942i
$483$	6.39473	+	8.23504i	0.290970	+	0.374707i
$484$	40.8221			1.85555
$485$		−	2.08944i		−	0.0948764i
$486$	1.75588	+	1.75588i	0.0796481	+	0.0796481i
$487$	1.61762	−	1.61762i	0.0733015	−	0.0733015i	−0.669506	−	0.742807i	$-0.733494\pi$
$487$	1.61762	−	1.61762i	0.0733015	−	0.0733015i	0.742807	+	0.669506i	$0.233494\pi$
$488$	12.3635	−	12.3635i	0.559669	−	0.559669i
$489$	15.2280	−	15.2280i	0.688633	−	0.688633i
$490$	13.8391	−	54.1371i	0.625185	−	2.44567i
$491$		−	9.87760i		−	0.445770i	−0.974845	−	0.222885i	$-0.928453\pi$
$491$		−	9.87760i		−	0.445770i	0.974845	−	0.222885i	$-0.0715474\pi$
$492$	27.5198	+	27.5198i	1.24069	+	1.24069i
$493$	15.0969			0.679930
$494$	−9.80345	−	0.288627i	−0.441078	−	0.0129860i
$495$			14.6605i			0.658941i
$496$	22.8437	+	22.8437i	1.02571	+	1.02571i
$497$	13.9014	+	1.74869i	0.623564	+	0.0784396i
$498$		−	1.18178i		−	0.0529567i
$499$	−23.4077	+	23.4077i	−1.04787	+	1.04787i	−0.0490768	+	0.998795i	$0.515628\pi$
$499$	−23.4077	+	23.4077i	−1.04787	+	1.04787i	−0.998795	+	0.0490768i	$0.984372\pi$
$500$	−3.16297	−	3.16297i	−0.141453	−	0.141453i
$501$	−0.578070	−	0.578070i	−0.0258263	−	0.0258263i
$502$	1.98145	−	1.98145i	0.0884366	−	0.0884366i
$503$			5.15552i			0.229873i	0.993373	+	0.114937i	$0.0366665\pi$
$503$			5.15552i			0.229873i	−0.993373	+	0.114937i	$0.963334\pi$
$504$	1.77623	−	14.1204i	0.0791197	−	0.628971i
$505$	12.6923	+	12.6923i	0.564798	+	0.564798i
$506$			44.6279i			1.98395i
$507$	−0.764813	+	12.9775i	−0.0339665	+	0.576350i
$508$	18.1526			0.805391
$509$	4.51339	+	4.51339i	0.200053	+	0.200053i	0.800023	−	0.599970i	$-0.204821\pi$
$509$	4.51339	+	4.51339i	0.200053	+	0.200053i	−0.599970	+	0.800023i	$0.704821\pi$
$510$		−	33.3623i		−	1.47731i
$511$	−8.78917	−	1.10561i	−0.388810	−	0.0489093i
$512$	−32.1153	+	32.1153i	−1.41931	+	1.41931i
$513$	−0.774590	+	0.774590i	−0.0341990	+	0.0341990i
$514$	−49.6862	+	49.6862i	−2.19156	+	2.19156i
$515$	−32.7890	−	32.7890i	−1.44486	−	1.44486i
$516$			22.4908i			0.990103i
$517$	−50.1386			−2.20509
$518$	41.8807	+	53.9334i	1.84013	+	2.36970i
$519$			0.696157i			0.0305579i
$520$	−1.83477	+	62.3195i	−0.0804600	+	2.73289i
$521$		−	4.80886i		−	0.210680i	−0.994436	−	0.105340i	$-0.966407\pi$
$521$		−	4.80886i		−	0.210680i	0.994436	−	0.105340i	$-0.0335931\pi$
$522$	−6.34261	+	6.34261i	−0.277609	+	0.277609i
$523$		−	34.0474i		−	1.48879i	−0.667740	−	0.744395i	$-0.732738\pi$
$523$		−	34.0474i		−	1.48879i	0.667740	−	0.744395i	$-0.267262\pi$
$524$	83.2890			3.63850
$525$	8.65550	+	11.1464i	0.377757	+	0.486470i
$526$	30.0167	−	30.0167i	1.30879	−	1.30879i
$527$	−19.0004	−	19.0004i	−0.827669	−	0.827669i
$528$	16.2038	−	16.2038i	0.705182	−	0.705182i
$529$	7.47021			0.324792
$530$	3.42480			0.148764
$531$	1.29667	−	1.29667i	0.0562705	−	0.0562705i
$532$	11.9803	+	1.50702i	0.519410	+	0.0653378i
$533$	23.1052	+	24.5070i	1.00080	+	1.06152i
$534$	39.4970			1.70920
$535$	−1.64572	−	1.64572i	−0.0711505	−	0.0711505i
$536$	−14.4791			−0.625401
$537$	0.801167			0.0345729
$538$	−8.16662	−	8.16662i	−0.352088	−	0.352088i
$539$	−27.4609	+	16.2795i	−1.18282	+	0.701209i
$540$	9.47019	+	9.47019i	0.407532	+	0.407532i
$541$	13.3027	+	13.3027i	0.571929	+	0.571929i	0.932667	−	0.360738i	$-0.117475\pi$
$541$	13.3027	+	13.3027i	0.571929	+	0.571929i	−0.360738	+	0.932667i	$0.617475\pi$
$542$		−	33.4220i		−	1.43560i
$543$		−	22.4677i		−	0.964181i
$544$	−5.08118	+	5.08118i	−0.217854	+	0.217854i
$545$	17.3868			0.744769
$546$	3.64685	−	23.4056i	0.156071	−	1.00167i
$547$	−42.9461			−1.83624			−0.918122	−	0.396298i	$-0.870295\pi$
$547$	−42.9461			−1.83624			−0.918122	+	0.396298i	$0.870295\pi$
$548$	23.0768	−	23.0768i	0.985794	−	0.985794i
$549$		−	3.25050i		−	0.138728i
$550$			60.4055i			2.57570i
$551$	−2.79799	−	2.79799i	−0.119198	−	0.119198i
$552$	14.9890	+	14.9890i	0.637976	+	0.637976i
$553$	−5.91132	−	7.61252i	−0.251375	−	0.323717i
$554$	32.4933	+	32.4933i	1.38051	+	1.38051i
$555$	−33.4118			−1.41825
$556$	78.4226			3.32586
$557$	−21.0174	−	21.0174i	−0.890534	−	0.890534i	0.104039	−	0.994573i	$-0.466823\pi$
$557$	−21.0174	−	21.0174i	−0.890534	−	0.890534i	−0.994573	+	0.104039i	$0.966823\pi$
$558$	15.9651			0.675858
$559$	−0.572806	+	19.4558i	−0.0242271	+	0.822893i
$560$	5.33391	−	42.4025i	0.225399	−	1.79183i
$561$	−13.4776	+	13.4776i	−0.569026	+	0.569026i
$562$	−49.9569			−2.10730
$563$	−18.6622			−0.786518			−0.393259	−	0.919428i	$-0.628652\pi$
$563$	−18.6622			−0.786518			−0.393259	+	0.919428i	$0.628652\pi$
$564$	−32.3878	+	32.3878i	−1.36377	+	1.36377i
$565$	41.3858	+	41.3858i	1.74111	+	1.74111i
$566$	−11.5204	+	11.5204i	−0.484239	+	0.484239i
$567$	−1.62270	−	2.08970i	−0.0681472	−	0.0877590i
$568$	28.4856			1.19523
$569$			21.7954i			0.913711i	0.889541	+	0.456855i	$0.151024\pi$
$569$			21.7954i			0.913711i	−0.889541	+	0.456855i	$0.848976\pi$
$570$	−6.18322	+	6.18322i	−0.258987	+	0.258987i
$571$		−	0.292431i		−	0.0122378i	−0.999981	−	0.00611892i	$-0.998052\pi$
$571$		−	0.292431i		−	0.0122378i	0.999981	−	0.00611892i	$-0.00194773\pi$
$572$	49.8454	−	46.9943i	2.08414	−	1.96493i
$573$			15.7270i			0.657004i
$574$	−37.6416	−	48.4743i	−1.57113	−	2.02328i
$575$	−21.0201			−0.876600
$576$			5.78010i			0.240838i
$577$	−11.7221	−	11.7221i	−0.487999	−	0.487999i	0.419675	−	0.907674i	$-0.362144\pi$
$577$	−11.7221	−	11.7221i	−0.487999	−	0.487999i	−0.907674	+	0.419675i	$0.862144\pi$
$578$	0.820552	−	0.820552i	0.0341305	−	0.0341305i
$579$	−6.55862	+	6.55862i	−0.272567	+	0.272567i
$580$	−34.2084	+	34.2084i	−1.42043	+	1.42043i
$581$	−0.157152	+	1.24930i	−0.00651977	+	0.0518297i
$582$			1.61400i			0.0669025i
$583$	−1.38354	−	1.38354i	−0.0573005	−	0.0573005i
$584$	−18.0100			−0.745260
$585$	7.95105	+	8.43343i	0.328735	+	0.348679i
$586$			3.10412i			0.128230i
$587$	18.3164	+	18.3164i	0.756000	+	0.756000i	0.975592	−	0.219591i	$-0.0704724\pi$
$587$	18.3164	+	18.3164i	0.756000	+	0.756000i	−0.219591	+	0.975592i	$0.570472\pi$
$588$	−7.22276	+	28.2548i	−0.297862	+	1.16521i
$589$			7.04289i			0.290197i
$590$	10.3507	−	10.3507i	0.426133	−	0.426133i
$591$	−0.440789	−	0.440789i	−0.0181316	−	0.0181316i
$592$	36.9291	+	36.9291i	1.51778	+	1.51778i
$593$	21.2377	−	21.2377i	0.872129	−	0.872129i	−0.120575	−	0.992704i	$-0.538474\pi$
$593$	21.2377	−	21.2377i	0.872129	−	0.872129i	0.992704	+	0.120575i	$0.0384738\pi$
$594$		−	11.3246i		−	0.464655i
$595$	−4.43651	+	35.2685i	−0.181879	+	1.44587i
$596$	−1.61416	−	1.61416i	−0.0661186	−	0.0661186i
$597$		−	12.3117i		−	0.503883i
$598$	24.2037	+	25.6721i	0.989763	+	1.04981i
$599$	−3.95433			−0.161569			−0.0807847	−	0.996732i	$-0.525743\pi$
$599$	−3.95433			−0.161569			−0.0807847	+	0.996732i	$0.525743\pi$
$600$	20.2882	+	20.2882i	0.828262	+	0.828262i
$601$			8.53122i			0.347996i	0.984746	+	0.173998i	$0.0556686\pi$
$601$			8.53122i			0.347996i	−0.984746	+	0.173998i	$0.944331\pi$
$602$	4.42658	−	35.1896i	0.180414	−	1.43422i
$603$	−1.90336	+	1.90336i	−0.0775106	+	0.0775106i
$604$	11.8895	−	11.8895i	0.483777	−	0.483777i
$605$	22.2728	−	22.2728i	0.905519	−	0.905519i
$606$	−9.80422	−	9.80422i	−0.398269	−	0.398269i
$607$			4.46430i			0.181200i	0.995887	+	0.0906002i	$0.0288786\pi$
$607$			4.46430i			0.181200i	−0.995887	+	0.0906002i	$0.971121\pi$
$608$	1.88345			0.0763839
$609$	7.54845	−	5.86157i	0.305879	−	0.237523i
$610$		−	25.9473i		−	1.05058i
$611$	−28.8421	+	27.1924i	−1.16683	+	1.10009i
$612$			17.4122i			0.703845i
$613$	−5.06578	+	5.06578i	−0.204605	+	0.204605i	−0.801970	−	0.597365i	$-0.796214\pi$
$613$	−5.06578	+	5.06578i	−0.204605	+	0.204605i	0.597365	+	0.801970i	$0.296214\pi$
$614$			10.5872i			0.427266i
$615$	30.0299			1.21092
$616$	−51.2631	+	39.8071i	−2.06545	+	1.60387i
$617$	11.0059	−	11.0059i	0.443081	−	0.443081i	−0.449965	−	0.893046i	$-0.648564\pi$
$617$	11.0059	−	11.0059i	0.443081	−	0.443081i	0.893046	+	0.449965i	$0.148564\pi$
$618$	25.3281	+	25.3281i	1.01885	+	1.01885i
$619$	21.1306	−	21.1306i	0.849311	−	0.849311i	−0.140737	−	0.990047i	$-0.544947\pi$
$619$	21.1306	−	21.1306i	0.849311	−	0.849311i	0.990047	+	0.140737i	$0.0449470\pi$
$620$	86.1069			3.45813
$621$	3.94079			0.158138
$622$	−33.4754	+	33.4754i	−1.34224	+	1.34224i
$623$	−41.7537	−	5.25229i	−1.67283	−	0.210429i
$624$	0.533163	−	18.1093i	0.0213436	−	0.724952i
$625$	23.2185			0.928739
$626$	−10.5053	−	10.5053i	−0.419876	−	0.419876i
$627$	4.99577			0.199512
$628$	−90.9018			−3.62738
$629$	−30.7160	−	30.7160i	−1.22473	−	1.22473i
$630$	−12.9534	−	16.6811i	−0.516074	−	0.664593i
$631$	−18.3511	−	18.3511i	−0.730547	−	0.730547i	0.240181	−	0.970728i	$-0.422793\pi$
$631$	−18.3511	−	18.3511i	−0.730547	−	0.730547i	−0.970728	+	0.240181i	$0.922793\pi$
$632$	−13.8560	−	13.8560i	−0.551160	−	0.551160i
$633$		−	1.27815i		−	0.0508019i
$634$			14.6945i			0.583592i
$635$	9.90418	−	9.90418i	0.393035	−	0.393035i
$636$	−1.78744			−0.0708767
$637$	−6.96769	+	24.2580i	−0.276070	+	0.961138i
$638$	40.9071			1.61953
$639$	3.74459	−	3.74459i	0.148134	−	0.148134i
$640$			57.1943i			2.26081i
$641$		−	0.380630i		−	0.0150340i	−0.999972	−	0.00751698i	$-0.997607\pi$
$641$		−	0.380630i		−	0.0150340i	0.999972	−	0.00751698i	$-0.00239275\pi$
$642$	1.27125	+	1.27125i	0.0501720	+	0.0501720i
$643$	−23.7225	−	23.7225i	−0.935524	−	0.935524i	0.0625195	−	0.998044i	$-0.480086\pi$
$643$	−23.7225	−	23.7225i	−0.935524	−	0.935524i	−0.998044	+	0.0625195i	$0.980086\pi$
$644$	−26.6417	−	34.3088i	−1.04983	−	1.35196i
$645$	12.2711	+	12.2711i	0.483175	+	0.483175i
$646$	−11.3686			−0.447293
$647$	−15.5748			−0.612310			−0.306155	−	0.951982i	$-0.599042\pi$
$647$	−15.5748			−0.612310			−0.306155	+	0.951982i	$0.599042\pi$
$648$	−3.80357	−	3.80357i	−0.149418	−	0.149418i
$649$	−8.36292			−0.328274
$650$	32.7606	+	34.7481i	1.28498	+	1.36293i
$651$	−16.8773	−	2.12304i	−0.661475	−	0.0832084i
$652$	−63.4427	+	63.4427i	−2.48461	+	2.48461i
$653$	1.83334			0.0717443			0.0358722	−	0.999356i	$-0.488579\pi$
$653$	1.83334			0.0717443			0.0358722	+	0.999356i	$0.488579\pi$
$654$	−13.4306			−0.525177
$655$	45.4430	−	45.4430i	1.77560	−	1.77560i
$656$	−33.1912	−	33.1912i	−1.29590	−	1.29590i
$657$	−2.36752	+	2.36752i	−0.0923656	+	0.0923656i
$658$	57.0491	−	44.3002i	2.22401	−	1.72700i
$659$	−24.7339			−0.963495			−0.481748	−	0.876310i	$-0.659998\pi$
$659$	−24.7339			−0.963495			−0.481748	+	0.876310i	$0.659998\pi$
$660$		−	61.0786i		−	2.37748i
$661$	14.8957	−	14.8957i	0.579377	−	0.579377i	−0.355354	−	0.934732i	$-0.615640\pi$
$661$	14.8957	−	14.8957i	0.579377	−	0.579377i	0.934732	+	0.355354i	$0.115640\pi$
$662$			45.0544i			1.75109i
$663$	−0.443460	+	15.0625i	−0.0172226	+	0.584978i
$664$			2.55996i			0.0993457i
$665$	7.35875	−	5.71427i	0.285360	−	0.221590i
$666$	25.8092			1.00009
$667$			14.2350i			0.551181i
$668$	2.40835	+	2.40835i	0.0931820	+	0.0931820i
$669$	8.41160	−	8.41160i	0.325211	−	0.325211i
$670$	−15.1937	+	15.1937i	−0.586983	+	0.586983i
$671$	−10.4821	+	10.4821i	−0.404658	+	0.404658i
$672$	−0.567754	+	4.51343i	−0.0219016	+	0.174109i
$673$			15.2799i			0.588997i	0.955652	+	0.294499i	$0.0951527\pi$
$673$			15.2799i			0.588997i	−0.955652	+	0.294499i	$0.904847\pi$
$674$	−42.6484	−	42.6484i	−1.64275	−	1.64275i
$675$	5.33399			0.205305
$676$	3.18636	−	54.0667i	0.122552	−	2.07949i
$677$		−	23.9366i		−	0.919960i	−0.887929	−	0.459980i	$-0.847857\pi$
$677$		−	23.9366i		−	0.919960i	0.887929	−	0.459980i	$-0.152143\pi$
$678$	−31.9688	−	31.9688i	−1.22775	−	1.22775i
$679$	0.214629	−	1.70622i	0.00823672	−	0.0654787i
$680$			72.2692i			2.77140i
$681$	−2.87572	+	2.87572i	−0.110198	+	0.110198i
$682$	−51.4841	−	51.4841i	−1.97143	−	1.97143i
$683$	6.15176	+	6.15176i	0.235391	+	0.235391i	0.814938	−	0.579548i	$-0.196771\pi$
$683$	6.15176	+	6.15176i	0.235391	+	0.235391i	−0.579548	+	0.814938i	$0.696771\pi$
$684$	3.22709	−	3.22709i	0.123391	−	0.123391i
$685$		−	25.1817i		−	0.962145i
$686$	16.8619	−	42.7865i	0.643791	−	1.63359i
$687$	−3.18307	−	3.18307i	−0.121442	−	0.121442i
$688$		−	27.1259i		−	1.03416i
$689$	−1.54624	−	0.0455234i	−0.0589070	−	0.00173430i
$690$	31.4576			1.19757
$691$	5.18585	+	5.18585i	0.197279	+	0.197279i	0.798833	−	0.601553i	$-0.205451\pi$
$691$	5.18585	+	5.18585i	0.197279	+	0.197279i	−0.601553	+	0.798833i	$0.705451\pi$
$692$		−	2.90033i		−	0.110254i
$693$	−1.50594	+	11.9717i	−0.0572061	+	0.454766i
$694$	41.6102	−	41.6102i	1.57950	−	1.57950i
$695$	42.7879	−	42.7879i	1.62304	−	1.62304i
$696$	13.7393	−	13.7393i	0.520788	−	0.520788i
$697$	27.6069	+	27.6069i	1.04569	+	1.04569i
$698$			58.2799i			2.20593i
$699$	17.7925			0.672974
$700$	−36.0605	−	46.4382i	−1.36296	−	1.75520i
$701$		−	34.5225i		−	1.30390i	−0.758264	−	0.651948i	$-0.773952\pi$
$701$		−	34.5225i		−	1.30390i	0.758264	−	0.651948i	$-0.226048\pi$
$702$	−6.14185	−	6.51447i	−0.231809	−	0.245873i
$703$			11.3855i			0.429413i
$704$	18.6396	−	18.6396i	0.702505	−	0.702505i
$705$			35.3420i			1.33106i
$706$	−23.5269			−0.885446
$707$	9.06064	+	11.6682i	0.340761	+	0.438827i
$708$	−5.40216	+	5.40216i	−0.203026	+	0.203026i
$709$	−4.95440	−	4.95440i	−0.186066	−	0.186066i	0.607927	−	0.793993i	$-0.292001\pi$
$709$	−4.95440	−	4.95440i	−0.186066	−	0.186066i	−0.793993	+	0.607927i	$0.792001\pi$
$710$	29.8915	−	29.8915i	1.12181	−	1.12181i
$711$	−3.64288			−0.136619
$712$	−85.5581			−3.20643
$713$	17.9156	−	17.9156i	0.670945	−	0.670945i
$714$	3.42701	−	27.2434i	0.128253	−	1.01956i
$715$	1.55557	−	52.8363i	0.0581752	−	1.97597i
$716$	−3.33782			−0.124740
$717$	11.1681	+	11.1681i	0.417082	+	0.417082i
$718$	73.2646			2.73421
$719$	−10.1245			−0.377581			−0.188791	−	0.982017i	$-0.560457\pi$
$719$	−10.1245			−0.377581			−0.188791	+	0.982017i	$0.560457\pi$
$720$	−11.4219	−	11.4219i	−0.425668	−	0.425668i
$721$	−23.4071	−	30.1434i	−0.871727	−	1.12260i
$722$	−31.2546	−	31.2546i	−1.16318	−	1.16318i
$723$	5.05729	+	5.05729i	0.188082	+	0.188082i
$724$			93.6048i			3.47879i
$725$			19.2676i			0.715580i
$726$	−17.2048	+	17.2048i	−0.638530	+	0.638530i
$727$	35.4617			1.31520			0.657601	−	0.753367i	$-0.271571\pi$
$727$	35.4617			1.31520			0.657601	+	0.753367i	$0.271571\pi$
$728$	−7.89979	+	50.7012i	−0.292786	+	1.87911i
$729$	−1.00000			−0.0370370
$730$	−18.8989	+	18.8989i	−0.699478	+	0.699478i
$731$			22.5621i			0.834488i
$732$			13.5422i			0.500534i
$733$	9.46985	+	9.46985i	0.349777	+	0.349777i	0.860026	−	0.510249i	$-0.170447\pi$
$733$	9.46985	+	9.46985i	0.349777	+	0.349777i	−0.510249	+	0.860026i	$0.670447\pi$
$734$	1.68352	+	1.68352i	0.0621398	+	0.0621398i
$735$	11.4752	+	19.3568i	0.423270	+	0.713986i
$736$	−4.79109	−	4.79109i	−0.176602	−	0.176602i
$737$	12.2758			0.452185
$738$	−23.1968			−0.853888
$739$	−3.06141	−	3.06141i	−0.112616	−	0.112616i	0.648553	−	0.761169i	$-0.275374\pi$
$739$	−3.06141	−	3.06141i	−0.112616	−	0.112616i	−0.761169	+	0.648553i	$0.775374\pi$
$740$	139.200			5.11710
$741$	2.87380	−	2.70943i	0.105572	−	0.0995333i
$742$	2.79667	+	0.351799i	0.102669	+	0.0129150i
$743$	6.17880	−	6.17880i	0.226678	−	0.226678i	−0.584625	−	0.811303i	$-0.698758\pi$
$743$	6.17880	−	6.17880i	0.226678	−	0.226678i	0.811303	+	0.584625i	$0.198758\pi$
$744$	−34.5836			−1.26790
$745$	−1.76139			−0.0645325
$746$	0.598745	−	0.598745i	0.0219216	−	0.0219216i
$747$	0.336521	+	0.336521i	0.0123126	+	0.0123126i
$748$	56.1504	−	56.1504i	2.05306	−	2.05306i
$749$	−1.17483	−	1.51293i	−0.0429274	−	0.0552812i
$750$	2.66612			0.0973530
$751$			42.5093i			1.55119i	0.631232	+	0.775594i	$0.282549\pi$
$751$			42.5093i			1.55119i	−0.631232	+	0.775594i	$0.717451\pi$
$752$	39.0625	−	39.0625i	1.42446	−	1.42446i
$753$			1.12847i			0.0411237i
$754$	23.5317	−	22.1857i	0.856974	−	0.807956i
$755$		−	12.9740i		−	0.472172i
$756$	6.76050	+	8.70608i	0.245877	+	0.316637i
$757$	35.1636			1.27804			0.639022	−	0.769189i	$-0.279339\pi$
$757$	35.1636			1.27804			0.639022	+	0.769189i	$0.279339\pi$
$758$			61.2789i			2.22575i
$759$	−12.7082	−	12.7082i	−0.461277	−	0.461277i
$760$	13.3941	−	13.3941i	0.485854	−	0.485854i
$761$	−10.5424	+	10.5424i	−0.382161	+	0.382161i	−0.871880	−	0.489719i	$-0.837099\pi$
$761$	−10.5424	+	10.5424i	−0.382161	+	0.382161i	0.489719	+	0.871880i	$0.337099\pi$
$762$	−7.65055	+	7.65055i	−0.277150	+	0.277150i
$763$	14.1980	+	1.78599i	0.514001	+	0.0646573i
$764$		−	65.5216i		−	2.37049i
$765$	9.50019	+	9.50019i	0.343480	+	0.343480i
$766$	1.00346			0.0362564
$767$	−4.81075	+	4.53559i	−0.173706	+	0.163771i
$768$		−	32.6200i		−	1.17707i
$769$	19.7441	+	19.7441i	0.711991	+	0.711991i	0.966951	−	0.254961i	$-0.0820625\pi$
$769$	19.7441	+	19.7441i	0.711991	+	0.711991i	−0.254961	+	0.966951i	$0.582063\pi$
$770$	−12.0213	+	95.5647i	−0.433218	+	3.44391i
$771$		−	28.2971i		−	1.01909i
$772$	27.3245	−	27.3245i	0.983430	−	0.983430i
$773$	−30.5394	−	30.5394i	−1.09843	−	1.09843i	−0.994595	−	0.103831i	$-0.966890\pi$
$773$	−30.5394	−	30.5394i	−1.09843	−	1.09843i	−0.103831	−	0.994595i	$-0.533110\pi$
$774$	−9.47893	−	9.47893i	−0.340713	−	0.340713i
$775$	24.2494	−	24.2494i	0.871065	−	0.871065i
$776$		−	3.49624i		−	0.125508i
$777$	−27.2839	−	3.43210i	−0.978803	−	0.123126i
$778$	43.1902	+	43.1902i	1.54844	+	1.54844i
$779$		−	10.2331i		−	0.366639i
$780$	−33.1256	−	35.1353i	−1.18609	−	1.25805i
$781$	−24.1510			−0.864190
$782$	28.9194	+	28.9194i	1.03416	+	1.03416i
$783$		−	3.61222i		−	0.129090i
$784$	8.71128	−	34.0777i	0.311117	−	1.21706i
$785$	−49.5966	+	49.5966i	−1.77018	+	1.77018i
$786$	−35.1028	+	35.1028i	−1.25207	+	1.25207i
$787$	29.9108	−	29.9108i	1.06620	−	1.06620i	0.0685564	−	0.997647i	$-0.478161\pi$
$787$	29.9108	−	29.9108i	1.06620	−	1.06620i	0.997647	−	0.0685564i	$-0.0218393\pi$
$788$	1.83641	+	1.83641i	0.0654195	+	0.0654195i
$789$			17.0950i			0.608597i
$790$	−29.0796			−1.03460
$791$	29.5442	+	38.0466i	1.05047	+	1.35278i
$792$			24.5313i			0.871683i
$793$	−0.344898	+	11.7148i	−0.0122477	+	0.416003i
$794$		−	48.1117i		−	1.70742i
$795$	−0.975241	+	0.975241i	−0.0345882	+	0.0345882i
$796$			51.2928i			1.81802i
$797$	−45.4348			−1.60938			−0.804691	−	0.593694i	$-0.797669\pi$
$797$	−45.4348			−1.60938			−0.804691	+	0.593694i	$0.797669\pi$
$798$	−5.68432	+	4.41403i	−0.201223	+	0.156255i
$799$	−32.4904	+	32.4904i	−1.14943	+	1.14943i
$800$	−6.48491	−	6.48491i	−0.229276	−	0.229276i
$801$	−11.2471	+	11.2471i	−0.397396	+	0.397396i
$802$	−72.5371			−2.56137
$803$	15.2694			0.538847
$804$	7.92975	−	7.92975i	0.279661	−	0.279661i
$805$	−33.2550	−	4.18322i	−1.17208	−	0.147439i
$806$	−57.5382	−	1.69400i	−2.02670	−	0.0596687i
$807$	4.65103			0.163724
$808$	21.2379	+	21.2379i	0.747145	+	0.747145i
$809$	22.6070			0.794820			0.397410	−	0.917641i	$-0.369909\pi$
$809$	22.6070			0.794820			0.397410	+	0.917641i	$0.369909\pi$
$810$	−7.98257			−0.280479
$811$	−21.4603	−	21.4603i	−0.753572	−	0.753572i	0.221572	−	0.975144i	$-0.428881\pi$
$811$	−21.4603	−	21.4603i	−0.753572	−	0.753572i	−0.975144	+	0.221572i	$0.928881\pi$
$812$	−31.4483	+	24.4204i	−1.10362	+	0.856990i
$813$	9.51718	+	9.51718i	0.333782	+	0.333782i
$814$	−83.2290	−	83.2290i	−2.91717	−	2.91717i
$815$			69.2295i			2.42500i
$816$		−	21.0006i		−	0.735167i
$817$	4.18155	−	4.18155i	0.146294	−	0.146294i
$818$	46.0104			1.60872
$819$	5.62648	+	7.70342i	0.196605	+	0.269179i
$820$	−125.111			−4.36905
$821$	−14.9292	+	14.9292i	−0.521032	+	0.521032i	−0.917883	−	0.396851i	$-0.870103\pi$
$821$	−14.9292	+	14.9292i	−0.521032	+	0.521032i	0.396851	+	0.917883i	$0.370103\pi$
$822$			19.4518i			0.678460i
$823$		−	17.8395i		−	0.621847i	−0.950435	−	0.310924i	$-0.899362\pi$
$823$		−	17.8395i		−	0.621847i	0.950435	−	0.310924i	$-0.100638\pi$
$824$	−54.8656	−	54.8656i	−1.91133	−	1.91133i
$825$	−17.2010	−	17.2010i	−0.598860	−	0.598860i
$826$	9.51557	−	7.38909i	0.331089	−	0.257099i
$827$	−7.65905	−	7.65905i	−0.266331	−	0.266331i	0.561289	−	0.827620i	$-0.310306\pi$
$827$	−7.65905	−	7.65905i	−0.266331	−	0.266331i	−0.827620	+	0.561289i	$0.810306\pi$
$828$	−16.4181			−0.570568
$829$	41.4811			1.44070			0.720350	−	0.693611i	$-0.243981\pi$
$829$	41.4811			1.44070			0.720350	+	0.693611i	$0.243981\pi$
$830$	2.68630	+	2.68630i	0.0932428	+	0.0932428i
$831$	−18.5055			−0.641948
$832$	0.613306	−	20.8314i	0.0212626	−	0.722200i
$833$	−7.24564	+	28.3443i	−0.251047	+	0.982072i
$834$	−33.0518	+	33.0518i	−1.14449	+	1.14449i
$835$	2.62803			0.0909466
$836$	−20.8133			−0.719844
$837$	−4.54621	+	4.54621i	−0.157140	+	0.157140i
$838$	−47.9438	−	47.9438i	−1.65619	−	1.65619i
$839$	−36.9935	+	36.9935i	−1.27716	+	1.27716i	−0.334905	+	0.942252i	$0.608704\pi$
$839$	−36.9935	+	36.9935i	−1.27716	+	1.27716i	−0.942252	+	0.334905i	$0.891296\pi$
$840$	28.0595	+	36.1346i	0.968144	+	1.24676i
$841$	−15.9518			−0.550064
$842$		−	2.28052i		−	0.0785920i
$843$	14.2256	−	14.2256i	0.489957	−	0.489957i
$844$			5.32502i			0.183295i
$845$	−27.7607	−	31.2377i	−0.954996	−	1.07461i
$846$		−	27.3002i		−	0.938601i
$847$	20.4757	−	15.8999i	0.703554	−	0.546328i
$848$	2.15581			0.0740309
$849$		−	6.56107i		−	0.225175i
$850$	39.1435	+	39.1435i	1.34261	+	1.34261i
$851$	28.9623	−	28.9623i	0.992816	−	0.992816i
$852$	−15.6007	+	15.6007i	−0.534471	+	0.534471i
$853$	−28.9726	+	28.9726i	−0.992002	+	0.992002i	−0.999968	−	0.00796604i	$-0.997464\pi$
$853$	−28.9726	+	28.9726i	−0.992002	+	0.992002i	0.00796604	+	0.999968i	$0.497464\pi$
$854$	2.66534	−	21.1884i	0.0912060	−	0.725052i
$855$		−	3.52145i		−	0.120431i
$856$	−2.75376	−	2.75376i	−0.0941217	−	0.0941217i
$857$	33.3898			1.14057			0.570287	−	0.821446i	$-0.306832\pi$
$857$	33.3898			1.14057			0.570287	+	0.821446i	$0.306832\pi$
$858$	−1.20162	+	40.8138i	−0.0410225	+	1.39336i
$859$		−	2.81316i		−	0.0959838i	−0.998848	−	0.0479919i	$-0.984718\pi$
$859$		−	2.81316i		−	0.0959838i	0.998848	−	0.0479919i	$-0.0152822\pi$
$860$	−51.1239	−	51.1239i	−1.74331	−	1.74331i
$861$	24.5222	+	3.08471i	0.835716	+	0.105127i
$862$			61.6858i			2.10103i
$863$	16.9046	−	16.9046i	0.575440	−	0.575440i	−0.358203	−	0.933644i	$-0.616611\pi$
$863$	16.9046	−	16.9046i	0.575440	−	0.575440i	0.933644	+	0.358203i	$0.116611\pi$
$864$	1.21577	+	1.21577i	0.0413613	+	0.0413613i
$865$	−1.58244	−	1.58244i	−0.0538045	−	0.0538045i
$866$	47.9514	−	47.9514i	1.62945	−	1.62945i
$867$			0.467318i			0.0158710i
$868$	70.3143	+	8.84499i	2.38662	+	0.300219i
$869$	11.7475	+	11.7475i	0.398506	+	0.398506i
$870$		−	28.8348i		−	0.977592i
$871$	7.06163	−	6.65771i	0.239274	−	0.225588i
$872$	29.0932			0.985222
$873$	−0.459600	−	0.459600i	−0.0155551	−	0.0155551i
$874$		−	10.7196i		−	0.362596i
$875$	−2.81845	−	0.354540i	−0.0952811	−	0.0119856i
$876$	9.86353	−	9.86353i	0.333258	−	0.333258i
$877$	−15.4720	+	15.4720i	−0.522452	+	0.522452i	−0.918311	−	0.395860i	$-0.870447\pi$
$877$	−15.4720	+	15.4720i	−0.522452	+	0.522452i	0.395860	+	0.918311i	$0.370447\pi$
$878$	2.02417	−	2.02417i	0.0683124	−	0.0683124i
$879$	−0.883923	−	0.883923i	−0.0298140	−	0.0298140i
$880$			73.6660i			2.48328i
$881$	32.1869			1.08440			0.542202	−	0.840248i	$-0.317591\pi$
$881$	32.1869			1.08440			0.542202	+	0.840248i	$0.317591\pi$
$882$	−8.86411	−	14.9523i	−0.298470	−	0.503470i
$883$			40.9812i			1.37913i	0.724226	+	0.689563i	$0.242197\pi$
$883$			40.9812i			1.37913i	−0.724226	+	0.689563i	$0.757803\pi$
$884$	1.84754	−	62.7533i	0.0621396	−	2.11062i
$885$			5.89491i			0.198155i
$886$	14.1280	−	14.1280i	0.474640	−	0.474640i
$887$		−	14.9900i		−	0.503314i	−0.967816	−	0.251657i	$-0.919024\pi$
$887$		−	14.9900i		−	0.503314i	0.967816	−	0.251657i	$-0.0809755\pi$
$888$	−55.9078			−1.87614
$889$	9.10505	−	7.07032i	0.305374	−	0.237131i
$890$	−89.7806	+	89.7806i	−3.00945	+	3.00945i
$891$	3.22478	+	3.22478i	0.108034	+	0.108034i
$892$	−35.0444	+	35.0444i	−1.17337	+	1.17337i
$893$	12.0433			0.403013
$894$	1.36060			0.0455053
$895$	−1.82113	+	1.82113i	−0.0608738	+	0.0608738i
$896$	−5.87507	+	46.7045i	−0.196272	+	1.56029i
$897$	−14.2025	−	0.418143i	−0.474209	−	0.0139614i
$898$	32.2394			1.07584
$899$	−16.4219	−	16.4219i	−0.547701	−	0.547701i
$900$	−22.2225			−0.740748
$901$	−1.79311			−0.0597370
$902$	74.8047	+	74.8047i	2.49072	+	2.49072i
$903$	8.76002	+	11.2810i	0.291515	+	0.375409i
$904$	69.2506	+	69.2506i	2.30324	+	2.30324i
$905$	51.0714	+	51.0714i	1.69767	+	1.69767i
$906$			10.0218i			0.332954i
$907$		−	51.1729i		−	1.69917i	−0.527453	−	0.849584i	$-0.676853\pi$
$907$		−	51.1729i		−	1.69917i	0.527453	−	0.849584i	$-0.323147\pi$
$908$	11.9808	−	11.9808i	0.397598	−	0.397598i
$909$	5.58367			0.185199
$910$	44.9138	+	61.4931i	1.48888	+	2.03848i
$911$	45.1111			1.49460			0.747299	−	0.664488i	$-0.231350\pi$
$911$	45.1111			1.49460			0.747299	+	0.664488i	$0.231350\pi$
$912$	−3.89215	+	3.89215i	−0.128882	+	0.128882i
$913$		−	2.17041i		−	0.0718301i
$914$		−	90.6325i		−	2.99786i
$915$	7.38871	+	7.38871i	0.244263	+	0.244263i
$916$	13.2613	+	13.2613i	0.438165	+	0.438165i
$917$	41.7764	−	32.4405i	1.37958	−	1.07128i
$918$	−7.33849	−	7.33849i	−0.242206	−	0.242206i
$919$	32.8195			1.08262			0.541308	−	0.840825i	$-0.317929\pi$
$919$	32.8195			1.08262			0.541308	+	0.840825i	$0.317929\pi$
$920$	−68.1433			−2.24662
$921$	−3.01480	−	3.01480i	−0.0993410	−	0.0993410i
$922$	80.4086			2.64812
$923$	−13.8928	+	13.0981i	−0.457287	+	0.431131i
$924$	6.27406	−	49.8763i	0.206401	−	1.64081i
$925$	39.2016	−	39.2016i	1.28894	−	1.28894i
$926$	22.8915			0.752262
$927$	−14.4248			−0.473772
$928$	−4.39163	+	4.39163i	−0.144162	+	0.144162i
$929$	2.98532	+	2.98532i	0.0979452	+	0.0979452i	0.754381	−	0.656436i	$-0.227937\pi$
$929$	2.98532	+	2.98532i	0.0979452	+	0.0979452i	−0.656436	+	0.754381i	$0.727937\pi$
$930$	−36.2904	+	36.2904i	−1.19001	+	1.19001i
$931$	6.59608	−	3.91033i	0.216178	−	0.128156i
$932$	−74.1270			−2.42811
$933$		−	19.0648i		−	0.624154i
$934$	−39.6078	+	39.6078i	−1.29601	+	1.29601i
$935$		−	61.2720i		−	2.00381i
$936$	13.3044	+	14.1116i	0.434869	+	0.461252i
$937$		−	27.2131i		−	0.889014i	−0.895775	−	0.444507i	$-0.853379\pi$
$937$		−	27.2131i		−	0.889014i	0.895775	−	0.444507i	$-0.146621\pi$
$938$	−13.9678	+	10.8463i	−0.456063	+	0.354145i
$939$	5.98295			0.195246
$940$		−	147.242i		−	4.80250i
$941$	36.8328	+	36.8328i	1.20072	+	1.20072i	0.973949	+	0.226767i	$0.0728156\pi$
$941$	36.8328	+	36.8328i	1.20072	+	1.20072i	0.226767	+	0.973949i	$0.427184\pi$
$942$	38.3113	−	38.3113i	1.24825	−	1.24825i
$943$	−26.0308	+	26.0308i	−0.847680	+	0.847680i
$944$	6.51548	−	6.51548i	0.212061	−	0.212061i
$945$	8.43867	+	1.06152i	0.274510	+	0.0345312i
$946$			61.1349i			1.98767i
$947$	−5.92747	−	5.92747i	−0.192617	−	0.192617i	0.604209	−	0.796826i	$-0.293489\pi$
$947$	−5.92747	−	5.92747i	−0.192617	−	0.192617i	−0.796826	+	0.604209i	$0.793489\pi$
$948$	15.1770			0.492925
$949$	8.78371	−	8.28129i	0.285131	−	0.268822i
$950$		−	14.5094i		−	0.470746i
$951$	−4.18438	−	4.18438i	−0.135688	−	0.135688i
$952$	−7.42358	+	59.0146i	−0.240599	+	1.91267i
$953$			9.13478i			0.295905i	0.988994	+	0.147952i	$0.0472682\pi$
$953$			9.13478i			0.295905i	−0.988994	+	0.147952i	$0.952732\pi$
$954$	0.753332	−	0.753332i	0.0243900	−	0.0243900i
$955$	−35.7490	−	35.7490i	−1.15681	−	1.15681i
$956$	−46.5286	−	46.5286i	−1.50484	−	1.50484i
$957$	−11.6486	+	11.6486i	−0.376547	+	0.376547i
$958$			31.8195i			1.02804i
$959$	2.58670	−	20.5632i	0.0835288	−	0.664022i
$960$	−13.1388	−	13.1388i	−0.424052	−	0.424052i
$961$			10.3360i			0.333418i
$962$	−93.0161	−	2.73852i	−2.99896	−	0.0882935i
$963$	−0.723995			−0.0233304
$964$	−21.0696	−	21.0696i	−0.678607	−	0.678607i
$965$		−	29.8168i		−	0.959838i
$966$	25.6881	+	3.23136i	0.826500	+	0.103967i
$967$	23.6616	−	23.6616i	0.760907	−	0.760907i	−0.215580	−	0.976486i	$-0.569164\pi$
$967$	23.6616	−	23.6616i	0.760907	−	0.760907i	0.976486	+	0.215580i	$0.0691641\pi$
$968$	37.2689	−	37.2689i	1.19787	−	1.19787i
$969$	3.23732	−	3.23732i	0.103998	−	0.103998i
$970$	−3.66879	−	3.66879i	−0.117798	−	0.117798i
$971$		−	36.6944i		−	1.17758i	−0.808286	−	0.588789i	$-0.799605\pi$
$971$		−	36.6944i		−	1.17758i	0.808286	−	0.588789i	$-0.200395\pi$
$972$	4.16620			0.133631
$973$	39.3355	−	30.5451i	1.26104	−	0.979230i
$974$		−	5.68069i		−	0.182021i
$975$	−19.2237	−	0.565971i	−0.615650	−	0.0181256i
$976$		−	16.3331i		−	0.522809i
$977$	−4.94849	+	4.94849i	−0.158316	+	0.158316i	−0.781820	−	0.623504i	$-0.785709\pi$
$977$	−4.94849	+	4.94849i	−0.158316	+	0.158316i	0.623504	+	0.781820i	$0.285709\pi$
$978$		−	53.4769i		−	1.71000i
$979$	72.5388			2.31835
$980$	−47.8080	−	80.6441i	−1.52717	−	2.57608i
$981$	3.82447	−	3.82447i	0.122106	−	0.122106i
$982$	−17.3438	−	17.3438i	−0.553464	−	0.553464i
$983$	9.25132	−	9.25132i	0.295071	−	0.295071i	−0.544008	−	0.839080i	$-0.683094\pi$
$983$	9.25132	−	9.25132i	0.295071	−	0.295071i	0.839080	+	0.544008i	$0.183094\pi$
$984$	50.2489			1.60188
$985$	2.00392			0.0638501
$986$	26.5083	−	26.5083i	0.844195	−	0.844195i
$987$	−3.63037	+	28.8601i	−0.115556	+	0.918626i
$988$	−11.9728	+	11.2880i	−0.380906	+	0.359119i
$989$	−21.2740			−0.676473
$990$	25.7420	+	25.7420i	0.818136	+	0.818136i
$991$	−34.2453			−1.08784			−0.543918	−	0.839138i	$-0.683060\pi$
$991$	−34.2453			−1.08784			−0.543918	+	0.839138i	$0.683060\pi$
$992$	11.0543			0.350974
$993$	−12.8296	−	12.8296i	−0.407135	−	0.407135i
$994$	27.4797	−	21.3387i	0.871602	−	0.676822i
$995$	27.9857	+	27.9857i	0.887205	+	0.887205i
$996$	−1.40201	−	1.40201i	−0.0444244	−	0.0444244i
$997$			2.69156i			0.0852425i	0.999091	+	0.0426212i	$0.0135709\pi$
$997$			2.69156i			0.0852425i	−0.999091	+	0.0426212i	$0.986429\pi$
$998$			82.2019i			2.60206i
$999$	−7.34938	+	7.34938i	−0.232524	+	0.232524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.p.e.265.6	yes	12
3.2	odd	2		819.2.y.g.811.1		12
7.6	odd	2		273.2.p.f.265.6	yes	12
13.8	odd	4		273.2.p.f.34.6	yes	12
21.20	even	2		819.2.y.f.811.1		12
39.8	even	4		819.2.y.f.307.1		12
91.34	even	4	inner	273.2.p.e.34.6	✓	12
273.125	odd	4		819.2.y.g.307.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.e.34.6	✓	12	91.34	even	4	inner
273.2.p.e.265.6	yes	12	1.1	even	1	trivial
273.2.p.f.34.6	yes	12	13.8	odd	4
273.2.p.f.265.6	yes	12	7.6	odd	2
819.2.y.f.307.1		12	39.8	even	4
819.2.y.f.811.1		12	21.20	even	2
819.2.y.g.307.1		12	273.125	odd	4
819.2.y.g.811.1		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)

\(f(q)\)	\(=\)	\(q+(1.75588 - 1.75588i) q^{2} +1.00000i q^{3} -4.16620i q^{4} +(-2.27310 - 2.27310i) q^{5} +(1.75588 + 1.75588i) q^{6} +(-1.62270 - 2.08970i) q^{7} +(-3.80357 - 3.80357i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.75588 - 1.75588i) q^{2} +1.00000i q^{3} -4.16620i q^{4} +(-2.27310 - 2.27310i) q^{5} +(1.75588 + 1.75588i) q^{6} +(-1.62270 - 2.08970i) q^{7} +(-3.80357 - 3.80357i) q^{8} -1.00000 q^{9} -7.98257 q^{10} +(3.22478 + 3.22478i) q^{11} +4.16620 q^{12} +(3.60399 + 0.106106i) q^{13} +(-6.51851 - 0.819979i) q^{14} +(2.27310 - 2.27310i) q^{15} -5.02479 q^{16} +4.17939 q^{17} +(-1.75588 + 1.75588i) q^{18} +(-0.774590 - 0.774590i) q^{19} +(-9.47019 + 9.47019i) q^{20} +(2.08970 - 1.62270i) q^{21} +11.3246 q^{22} +3.94079i q^{23} +(3.80357 - 3.80357i) q^{24} +5.33399i q^{25} +(6.51447 - 6.14185i) q^{26} -1.00000i q^{27} +(-8.70608 + 6.76050i) q^{28} +3.61222 q^{29} -7.98257i q^{30} +(-4.54621 - 4.54621i) q^{31} +(-1.21577 + 1.21577i) q^{32} +(-3.22478 + 3.22478i) q^{33} +(7.33849 - 7.33849i) q^{34} +(-1.06152 + 8.43867i) q^{35} +4.16620i q^{36} +(-7.34938 - 7.34938i) q^{37} -2.72017 q^{38} +(-0.106106 + 3.60399i) q^{39} +17.2918i q^{40} +(6.60549 + 6.60549i) q^{41} +(0.819979 - 6.51851i) q^{42} +5.39841i q^{43} +(13.4351 - 13.4351i) q^{44} +(2.27310 + 2.27310i) q^{45} +(6.91953 + 6.91953i) q^{46} +(-7.77396 + 7.77396i) q^{47} -5.02479i q^{48} +(-1.73366 + 6.78192i) q^{49} +(9.36583 + 9.36583i) q^{50} +4.17939i q^{51} +(0.442060 - 15.0149i) q^{52} -0.429035 q^{53} +(-1.75588 - 1.75588i) q^{54} -14.6605i q^{55} +(-1.77623 + 14.1204i) q^{56} +(0.774590 - 0.774590i) q^{57} +(6.34261 - 6.34261i) q^{58} +(-1.29667 + 1.29667i) q^{59} +(-9.47019 - 9.47019i) q^{60} +3.25050i q^{61} -15.9651 q^{62} +(1.62270 + 2.08970i) q^{63} -5.78010i q^{64} +(-7.95105 - 8.43343i) q^{65} +11.3246i q^{66} +(1.90336 - 1.90336i) q^{67} -17.4122i q^{68} -3.94079 q^{69} +(12.9534 + 16.6811i) q^{70} +(-3.74459 + 3.74459i) q^{71} +(3.80357 + 3.80357i) q^{72} +(2.36752 - 2.36752i) q^{73} -25.8092 q^{74} -5.33399 q^{75} +(-3.22709 + 3.22709i) q^{76} +(1.50594 - 11.9717i) q^{77} +(6.14185 + 6.51447i) q^{78} +3.64288 q^{79} +(11.4219 + 11.4219i) q^{80} +1.00000 q^{81} +23.1968 q^{82} +(-0.336521 - 0.336521i) q^{83} +(-6.76050 - 8.70608i) q^{84} +(-9.50019 - 9.50019i) q^{85} +(9.47893 + 9.47893i) q^{86} +3.61222i q^{87} -24.5313i q^{88} +(11.2471 - 11.2471i) q^{89} +7.98257 q^{90} +(-5.62648 - 7.70342i) q^{91} +16.4181 q^{92} +(4.54621 - 4.54621i) q^{93} +27.3002i q^{94} +3.52145i q^{95} +(-1.21577 - 1.21577i) q^{96} +(0.459600 + 0.459600i) q^{97} +(8.86411 + 14.9523i) q^{98} +(-3.22478 - 3.22478i) 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

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Representations

Groups

Database

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