LMFDB - Embedded newform 272.2.l.b.205.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [272,2,Mod(69,272)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(272, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("272.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (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:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.13
Character	$\chi$	$=$	272.205
Dual form			272.2.l.b.69.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25559 + 0.650757i) q^{2} +(1.55623 + 1.55623i) q^{3} +(1.15303 + 1.63417i) q^{4} +(-2.63792 + 2.63792i) q^{5} +(0.941264 + 2.96671i) q^{6} -4.77816i q^{7} +(0.384292 + 2.80220i) q^{8} +1.84368i q^{9} +(-5.02881 + 1.59551i) q^{10} +(2.76448 - 2.76448i) q^{11} +(-0.748763 + 4.33752i) q^{12} +(-0.583093 - 0.583093i) q^{13} +(3.10942 - 5.99943i) q^{14} -8.21041 q^{15} +(-1.34104 + 3.76850i) q^{16} -1.00000 q^{17} +(-1.19979 + 2.31492i) q^{18} +(2.09969 + 2.09969i) q^{19} +(-7.35243 - 1.26921i) q^{20} +(7.43590 - 7.43590i) q^{21} +(5.27006 - 1.67206i) q^{22} +3.45210i q^{23} +(-3.76281 + 4.95890i) q^{24} -8.91728i q^{25} +(-0.352677 - 1.11158i) q^{26} +(1.79949 - 1.79949i) q^{27} +(7.80834 - 5.50937i) q^{28} +(0.121933 + 0.121933i) q^{29} +(-10.3089 - 5.34298i) q^{30} -6.88358 q^{31} +(-4.13617 + 3.85902i) q^{32} +8.60430 q^{33} +(-1.25559 - 0.650757i) q^{34} +(12.6044 + 12.6044i) q^{35} +(-3.01289 + 2.12582i) q^{36} +(5.17091 - 5.17091i) q^{37} +(1.26997 + 4.00274i) q^{38} -1.81485i q^{39} +(-8.40572 - 6.37825i) q^{40} +0.314869i q^{41} +(14.1754 - 4.49751i) q^{42} +(0.241429 - 0.241429i) q^{43} +(7.70516 + 1.33010i) q^{44} +(-4.86349 - 4.86349i) q^{45} +(-2.24648 + 4.33444i) q^{46} +4.77851 q^{47} +(-7.95160 + 3.77769i) q^{48} -15.8308 q^{49} +(5.80298 - 11.1965i) q^{50} +(-1.55623 - 1.55623i) q^{51} +(0.280550 - 1.62520i) q^{52} +(-3.91747 + 3.91747i) q^{53} +(3.43046 - 1.08840i) q^{54} +14.5850i q^{55} +(13.3894 - 1.83621i) q^{56} +6.53517i q^{57} +(0.0737498 + 0.232448i) q^{58} +(-8.67212 + 8.67212i) q^{59} +(-9.46687 - 13.4172i) q^{60} +(-4.39926 - 4.39926i) q^{61} +(-8.64298 - 4.47954i) q^{62} +8.80941 q^{63} +(-7.70464 + 2.15372i) q^{64} +3.07631 q^{65} +(10.8035 + 5.59931i) q^{66} +(-6.77551 - 6.77551i) q^{67} +(-1.15303 - 1.63417i) q^{68} +(-5.37226 + 5.37226i) q^{69} +(7.62362 + 24.0284i) q^{70} -14.0089i q^{71} +(-5.16636 + 0.708511i) q^{72} -4.63937i q^{73} +(9.85757 - 3.12756i) q^{74} +(13.8773 - 13.8773i) q^{75} +(-1.01024 + 5.85225i) q^{76} +(-13.2091 - 13.2091i) q^{77} +(1.18103 - 2.27872i) q^{78} +4.68502 q^{79} +(-6.40348 - 13.4786i) q^{80} +11.1319 q^{81} +(-0.204903 + 0.395347i) q^{82} +(7.86768 + 7.86768i) q^{83} +(20.7254 + 3.57771i) q^{84} +(2.63792 - 2.63792i) q^{85} +(0.460249 - 0.146025i) q^{86} +0.379512i q^{87} +(8.80898 + 6.68425i) q^{88} -8.48789i q^{89} +(-2.94162 - 9.27152i) q^{90} +(-2.78611 + 2.78611i) q^{91} +(-5.64133 + 3.98039i) q^{92} +(-10.7124 - 10.7124i) q^{93} +(5.99987 + 3.10965i) q^{94} -11.0776 q^{95} +(-12.4423 - 0.431311i) q^{96} -6.89926 q^{97} +(-19.8771 - 10.3020i) q^{98} +(5.09682 + 5.09682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) $ 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	1.25559	+	0.650757i	0.887839	+	0.460154i
$2$	1.25559	+	0.650757i	0.887839	+	0.460154i
$3$	1.55623	+	1.55623i	0.898488	+	0.898488i	0.995302	−	0.0968146i	$-0.0308654\pi$
$3$	1.55623	+	1.55623i	0.898488	+	0.898488i	−0.0968146	+	0.995302i	$0.530865\pi$
$4$	1.15303	+	1.63417i	0.576516	+	0.817086i
$5$	−2.63792	+	2.63792i	−1.17972	+	1.17972i	−0.199899	+	0.979817i	$0.564061\pi$
$5$	−2.63792	+	2.63792i	−1.17972	+	1.17972i	−0.979817	+	0.199899i	$0.935939\pi$
$6$	0.941264	+	2.96671i	0.384269	+	1.21116i
$7$		−	4.77816i		−	1.80598i	−0.429667	−	0.902988i	$-0.641369\pi$
$7$		−	4.77816i		−	1.80598i	0.429667	−	0.902988i	$-0.358631\pi$
$8$	0.384292	+	2.80220i	0.135868	+	0.990727i
$9$			1.84368i			0.614561i
$10$	−5.02881	+	1.59551i	−1.59025	+	0.504546i
$11$	2.76448	−	2.76448i	0.833521	−	0.833521i	−0.154476	−	0.987997i	$-0.549369\pi$
$11$	2.76448	−	2.76448i	0.833521	−	0.833521i	0.987997	+	0.154476i	$0.0493688\pi$
$12$	−0.748763	+	4.33752i	−0.216149	+	1.25213i
$13$	−0.583093	−	0.583093i	−0.161721	−	0.161721i	0.621608	−	0.783329i	$-0.286480\pi$
$13$	−0.583093	−	0.583093i	−0.161721	−	0.161721i	−0.783329	+	0.621608i	$0.786480\pi$
$14$	3.10942	−	5.99943i	0.831027	−	1.60342i
$15$	−8.21041			−2.11992
$16$	−1.34104	+	3.76850i	−0.335259	+	0.942126i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	−1.19979	+	2.31492i	−0.282793	+	0.545631i
$19$	2.09969	+	2.09969i	0.481701	+	0.481701i	0.905675	−	0.423974i	$-0.139365\pi$
$19$	2.09969	+	2.09969i	0.481701	+	0.481701i	−0.423974	+	0.905675i	$0.639365\pi$
$20$	−7.35243	−	1.26921i	−1.64405	−	0.283804i
$21$	7.43590	−	7.43590i	1.62265	−	1.62265i
$22$	5.27006	−	1.67206i	1.12358	−	0.356484i
$23$			3.45210i			0.719814i	0.932988	+	0.359907i	$0.117192\pi$
$23$			3.45210i			0.719814i	−0.932988	+	0.359907i	$0.882808\pi$
$24$	−3.76281	+	4.95890i	−0.768081	+	1.01223i
$25$		−	8.91728i		−	1.78346i
$26$	−0.352677	−	1.11158i	−0.0691656	−	0.217999i
$27$	1.79949	−	1.79949i	0.346313	−	0.346313i
$28$	7.80834	−	5.50937i	1.47564	−	1.04117i
$29$	0.121933	+	0.121933i	0.0226424	+	0.0226424i	0.718337	−	0.695695i	$-0.244903\pi$
$29$	0.121933	+	0.121933i	0.0226424	+	0.0226424i	−0.695695	+	0.718337i	$0.744903\pi$
$30$	−10.3089	−	5.34298i	−1.88215	−	0.975490i
$31$	−6.88358			−1.23633			−0.618164	−	0.786049i	$-0.712123\pi$
$31$	−6.88358			−1.23633			−0.618164	+	0.786049i	$0.712123\pi$
$32$	−4.13617	+	3.85902i	−0.731179	+	0.682185i
$33$	8.60430			1.49782
$34$	−1.25559	−	0.650757i	−0.215333	−	0.111604i
$35$	12.6044	+	12.6044i	2.13054	+	2.13054i
$36$	−3.01289	+	2.12582i	−0.502149	+	0.354304i
$37$	5.17091	−	5.17091i	0.850093	−	0.850093i	−0.140051	−	0.990144i	$-0.544727\pi$
$37$	5.17091	−	5.17091i	0.850093	−	0.850093i	0.990144	+	0.140051i	$0.0447267\pi$
$38$	1.26997	+	4.00274i	0.206016	+	0.649330i
$39$		−	1.81485i		−	0.290609i
$40$	−8.40572	−	6.37825i	−1.32906	−	1.00849i
$41$			0.314869i			0.0491742i	0.999698	+	0.0245871i	$0.00782711\pi$
$41$			0.314869i			0.0491742i	−0.999698	+	0.0245871i	$0.992173\pi$
$42$	14.1754	−	4.49751i	2.18732	−	0.693981i
$43$	0.241429	−	0.241429i	0.0368176	−	0.0368176i	−0.688458	−	0.725276i	$-0.741712\pi$
$43$	0.241429	−	0.241429i	0.0368176	−	0.0368176i	0.725276	+	0.688458i	$0.241712\pi$
$44$	7.70516	+	1.33010i	1.16160	+	0.200520i
$45$	−4.86349	−	4.86349i	−0.725007	−	0.725007i
$46$	−2.24648	+	4.33444i	−0.331225	+	0.639079i
$47$	4.77851			0.697018			0.348509	−	0.937305i	$-0.386688\pi$
$47$	4.77851			0.697018			0.348509	+	0.937305i	$0.386688\pi$
$48$	−7.95160	+	3.77769i	−1.14771	+	0.545263i
$49$	−15.8308			−2.26155
$50$	5.80298	−	11.1965i	0.820665	−	1.58342i
$51$	−1.55623	−	1.55623i	−0.217915	−	0.217915i
$52$	0.280550	−	1.62520i	0.0389052	−	0.225375i
$53$	−3.91747	+	3.91747i	−0.538106	+	0.538106i	−0.922972	−	0.384867i	$-0.874247\pi$
$53$	−3.91747	+	3.91747i	−0.538106	+	0.538106i	0.384867	+	0.922972i	$0.374247\pi$
$54$	3.43046	−	1.08840i	0.466827	−	0.148113i
$55$			14.5850i			1.96663i
$56$	13.3894	−	1.83621i	1.78923	−	0.245373i
$57$			6.53517i			0.865605i
$58$	0.0737498	+	0.232448i	0.00968382	+	0.0305219i
$59$	−8.67212	+	8.67212i	−1.12901	+	1.12901i	−0.138676	+	0.990338i	$0.544285\pi$
$59$	−8.67212	+	8.67212i	−1.12901	+	1.12901i	−0.990338	+	0.138676i	$0.955715\pi$
$60$	−9.46687	−	13.4172i	−1.22217	−	1.73216i
$61$	−4.39926	−	4.39926i	−0.563268	−	0.563268i	0.366966	−	0.930234i	$-0.380396\pi$
$61$	−4.39926	−	4.39926i	−0.563268	−	0.563268i	−0.930234	+	0.366966i	$0.880396\pi$
$62$	−8.64298	−	4.47954i	−1.09766	−	0.568902i
$63$	8.80941			1.10988
$64$	−7.70464	+	2.15372i	−0.963080	+	0.269215i
$65$	3.07631			0.381569
$66$	10.8035	+	5.59931i	1.32982	+	0.689227i
$67$	−6.77551	−	6.77551i	−0.827760	−	0.827760i	0.159446	−	0.987207i	$-0.449029\pi$
$67$	−6.77551	−	6.77551i	−0.827760	−	0.827760i	−0.987207	+	0.159446i	$0.949029\pi$
$68$	−1.15303	−	1.63417i	−0.139826	−	0.198172i
$69$	−5.37226	+	5.37226i	−0.646744	+	0.646744i
$70$	7.62362	+	24.0284i	0.911197	+	2.87195i
$71$		−	14.0089i		−	1.66256i	−0.555857	−	0.831278i	$-0.687610\pi$
$71$		−	14.0089i		−	1.66256i	0.555857	−	0.831278i	$-0.312390\pi$
$72$	−5.16636	+	0.708511i	−0.608862	+	0.0834989i
$73$		−	4.63937i		−	0.542997i	−0.962439	−	0.271499i	$-0.912481\pi$
$73$		−	4.63937i		−	0.542997i	0.962439	−	0.271499i	$-0.0875192\pi$
$74$	9.85757	−	3.12756i	1.14592	−	0.363572i
$75$	13.8773	−	13.8773i	1.60241	−	1.60241i
$76$	−1.01024	+	5.85225i	−0.115883	+	0.671299i
$77$	−13.2091	−	13.2091i	−1.50532	−	1.50532i
$78$	1.18103	−	2.27872i	0.133725	−	0.258014i
$79$	4.68502			0.527106			0.263553	−	0.964645i	$-0.415106\pi$
$79$	4.68502			0.527106			0.263553	+	0.964645i	$0.415106\pi$
$80$	−6.40348	−	13.4786i	−0.715930	−	1.50695i
$81$	11.1319			1.23688
$82$	−0.204903	+	0.395347i	−0.0226277	+	0.0436588i
$83$	7.86768	+	7.86768i	0.863590	+	0.863590i	0.991753	−	0.128163i	$-0.0409082\pi$
$83$	7.86768	+	7.86768i	0.863590	+	0.863590i	−0.128163	+	0.991753i	$0.540908\pi$
$84$	20.7254	+	3.57771i	2.26132	+	0.390360i
$85$	2.63792	−	2.63792i	0.286123	−	0.286123i
$86$	0.460249	−	0.146025i	0.0496299	−	0.0157463i
$87$			0.379512i			0.0406879i
$88$	8.80898	+	6.68425i	0.939040	+	0.712543i
$89$		−	8.48789i		−	0.899715i	−0.893100	−	0.449857i	$-0.851475\pi$
$89$		−	8.48789i		−	0.899715i	0.893100	−	0.449857i	$-0.148525\pi$
$90$	−2.94162	−	9.27152i	−0.310074	−	0.977304i
$91$	−2.78611	+	2.78611i	−0.292064	+	0.292064i
$92$	−5.64133	+	3.98039i	−0.588150	+	0.414984i
$93$	−10.7124	−	10.7124i	−1.11083	−	1.11083i
$94$	5.99987	+	3.10965i	0.618840	+	0.320736i
$95$	−11.0776			−1.13654
$96$	−12.4423	−	0.431311i	−1.26989	−	0.0440205i
$97$	−6.89926			−0.700514			−0.350257	−	0.936654i	$-0.613906\pi$
$97$	−6.89926			−0.700514			−0.350257	+	0.936654i	$0.613906\pi$
$98$	−19.8771	−	10.3020i	−2.00789	−	1.04066i
$99$	5.09682	+	5.09682i	0.512249	+	0.512249i
$100$	14.5724	−	10.2819i	1.45724	−	1.02819i
$101$	−7.19545	+	7.19545i	−0.715974	+	0.715974i	−0.967778	−	0.251804i	$-0.918976\pi$
$101$	−7.19545	+	7.19545i	−0.715974	+	0.715974i	0.251804	+	0.967778i	$0.418976\pi$
$102$	−0.941264	−	2.96671i	−0.0931990	−	0.293748i
$103$			9.27087i			0.913486i	0.889599	+	0.456743i	$0.150984\pi$
$103$			9.27087i			0.913486i	−0.889599	+	0.456743i	$0.849016\pi$
$104$	1.40987	−	1.85802i	0.138249	−	0.182194i
$105$			39.2307i			3.82852i
$106$	−7.46807	+	2.36943i	−0.725363	+	0.230139i
$107$	4.88667	−	4.88667i	0.472412	−	0.472412i	−0.430283	−	0.902694i	$-0.641586\pi$
$107$	4.88667	−	4.88667i	0.472412	−	0.472412i	0.902694	+	0.430283i	$0.141586\pi$
$108$	5.01555	+	0.865808i	0.482622	+	0.0833124i
$109$	3.21108	+	3.21108i	0.307565	+	0.307565i	0.843964	−	0.536399i	$-0.180216\pi$
$109$	3.21108	+	3.21108i	0.307565	+	0.307565i	−0.536399	+	0.843964i	$0.680216\pi$
$110$	−9.49125	+	18.3128i	−0.904956	+	1.74605i
$111$	16.0942			1.52760
$112$	18.0065	+	6.40768i	1.70146	+	0.605469i
$113$	−7.67415			−0.721923			−0.360961	−	0.932581i	$-0.617551\pi$
$113$	−7.67415			−0.721923			−0.360961	+	0.932581i	$0.617551\pi$
$114$	−4.25281	+	8.20553i	−0.398312	+	0.768518i
$115$	−9.10639	−	9.10639i	−0.849175	−	0.849175i
$116$	−0.0586670	+	0.339853i	−0.00544709	+	0.0315545i
$117$	1.07504	−	1.07504i	0.0993874	−	0.0993874i
$118$	−16.5321	+	5.24522i	−1.52190	+	0.482862i
$119$			4.77816i			0.438013i
$120$	−3.15519	−	23.0072i	−0.288028	−	2.10026i
$121$		−	4.28466i		−	0.389515i
$122$	−2.66084	−	8.38654i	−0.240901	−	0.759281i
$123$	−0.490007	+	0.490007i	−0.0441825	+	0.0441825i
$124$	−7.93699	−	11.2490i	−0.712762	−	1.01019i
$125$	10.3335	+	10.3335i	0.924255	+	0.924255i
$126$	11.0610	+	5.73278i	0.985396	+	0.510717i
$127$	−7.78378			−0.690699			−0.345349	−	0.938474i	$-0.612240\pi$
$127$	−7.78378			−0.690699			−0.345349	+	0.938474i	$0.612240\pi$
$128$	−11.0754	−	2.30964i	−0.978941	−	0.204146i
$129$	0.751438			0.0661604
$130$	3.86260	+	2.00193i	0.338772	+	0.175581i
$131$	0.924387	+	0.924387i	0.0807641	+	0.0807641i	0.746335	−	0.665571i	$-0.231812\pi$
$131$	0.924387	+	0.924387i	0.0807641	+	0.0807641i	−0.665571	+	0.746335i	$0.731812\pi$
$132$	9.92103	+	14.0609i	0.863515	+	1.22385i
$133$	10.0326	−	10.0326i	0.869940	−	0.869940i
$134$	−4.09808	−	12.9165i	−0.354020	−	1.11582i
$135$			9.49385i			0.817100i
$136$	−0.384292	−	2.80220i	−0.0329527	−	0.240287i
$137$			14.4690i			1.23617i	0.786112	+	0.618083i	$0.212091\pi$
$137$			14.4690i			1.23617i	−0.786112	+	0.618083i	$0.787909\pi$
$138$	−10.2414	+	3.24934i	−0.871806	+	0.276602i
$139$	−14.6299	+	14.6299i	−1.24090	+	1.24090i	−0.281265	+	0.959630i	$0.590754\pi$
$139$	−14.6299	+	14.6299i	−1.24090	+	1.24090i	−0.959630	+	0.281265i	$0.909246\pi$
$140$	−6.06449	+	35.1311i	−0.512543	+	2.96912i
$141$	7.43645	+	7.43645i	0.626262	+	0.626262i
$142$	9.11641	−	17.5895i	0.765032	−	1.47608i
$143$	−3.22390			−0.269596
$144$	−6.94792	−	2.47244i	−0.578994	−	0.206037i
$145$	−0.643301			−0.0534233
$146$	3.01910	−	5.82516i	0.249863	−	0.482094i
$147$	−24.6364	−	24.6364i	−2.03197	−	2.03197i
$148$	14.4124	+	2.48793i	1.18469	+	0.204507i
$149$	12.9801	−	12.9801i	1.06337	−	1.06337i	0.0655188	−	0.997851i	$-0.479130\pi$
$149$	12.9801	−	12.9801i	1.06337	−	1.06337i	0.997851	−	0.0655188i	$-0.0208702\pi$
$150$	26.4550	−	8.39351i	2.16004	−	0.685327i
$151$			15.1409i			1.23215i	0.787689	+	0.616073i	$0.211277\pi$
$151$			15.1409i			1.23215i	−0.787689	+	0.616073i	$0.788723\pi$
$152$	−5.07685	+	6.69063i	−0.411787	+	0.542682i
$153$		−	1.84368i		−	0.149053i
$154$	−7.98936	−	25.1812i	−0.643801	−	2.02916i
$155$	18.1584	−	18.1584i	1.45851	−	1.45851i
$156$	2.96578	−	2.09258i	0.237452	−	0.167541i
$157$	15.3744	+	15.3744i	1.22701	+	1.22701i	0.965089	+	0.261923i	$0.0843565\pi$
$157$	15.3744	+	15.3744i	1.22701	+	1.22701i	0.261923	+	0.965089i	$0.415643\pi$
$158$	5.88249	+	3.04881i	0.467986	+	0.242550i
$159$	−12.1929			−0.966963
$160$	0.731105	−	21.0907i	0.0577989	−	1.66737i
$161$	16.4947			1.29997
$162$	13.9771	+	7.24415i	1.09815	+	0.569154i
$163$	4.51917	+	4.51917i	0.353968	+	0.353968i	0.861584	−	0.507615i	$-0.169473\pi$
$163$	4.51917	+	4.51917i	0.353968	+	0.353968i	−0.507615	+	0.861584i	$0.669473\pi$
$164$	−0.514550	+	0.363054i	−0.0401796	+	0.0283497i
$165$	−22.6975	+	22.6975i	−1.76700	+	1.76700i
$166$	4.75866	+	14.9986i	0.369344	+	1.16411i
$167$			10.8133i			0.836761i	0.908272	+	0.418380i	$0.137402\pi$
$167$			10.8133i			0.836761i	−0.908272	+	0.418380i	$0.862598\pi$
$168$	23.6944	+	17.9793i	1.82806	+	1.38713i
$169$		−	12.3200i		−	0.947693i
$170$	5.02881	−	1.59551i	0.385692	−	0.122370i
$171$	−3.87115	+	3.87115i	−0.296035	+	0.296035i
$172$	0.672913	+	0.116161i	0.0513091	+	0.00885722i
$173$	4.11948	+	4.11948i	0.313199	+	0.313199i	0.846147	−	0.532949i	$-0.178916\pi$
$173$	4.11948	+	4.11948i	0.313199	+	0.313199i	−0.532949	+	0.846147i	$0.678916\pi$
$174$	−0.246970	+	0.476512i	−0.0187227	+	0.0361243i
$175$	−42.6082			−3.22088
$176$	6.71068	+	14.1252i	0.505837	+	1.06473i
$177$	−26.9916			−2.02881
$178$	5.52355	−	10.6573i	0.414008	−	0.798802i
$179$	6.16384	+	6.16384i	0.460707	+	0.460707i	0.898887	−	0.438180i	$-0.144377\pi$
$179$	6.16384	+	6.16384i	0.460707	+	0.460707i	−0.438180	+	0.898887i	$0.644377\pi$
$180$	2.34002	−	13.5555i	0.174415	−	1.01037i
$181$	−0.315283	+	0.315283i	−0.0234348	+	0.0234348i	−0.718727	−	0.695292i	$-0.755275\pi$
$181$	−0.315283	+	0.315283i	−0.0234348	+	0.0234348i	0.695292	+	0.718727i	$0.255275\pi$
$182$	−5.31131	+	1.68515i	−0.393700	+	0.124911i
$183$		−	13.6925i		−	1.01218i
$184$	−9.67348	+	1.32661i	−0.713139	+	0.0977993i
$185$			27.2809i			2.00574i
$186$	−6.47926	−	20.4216i	−0.475083	−	1.49738i
$187$	−2.76448	+	2.76448i	−0.202159	+	0.202159i
$188$	5.50978	+	7.80891i	0.401842	+	0.569524i
$189$	−8.59827	−	8.59827i	−0.625432	−	0.625432i
$190$	−13.9090	−	7.20884i	−1.00906	−	0.522984i
$191$	−0.719005			−0.0520254			−0.0260127	−	0.999662i	$-0.508281\pi$
$191$	−0.719005			−0.0520254			−0.0260127	+	0.999662i	$0.508281\pi$
$192$	−15.3418	−	8.63848i	−1.10720	−	0.623429i
$193$	4.99424			0.359493			0.179747	−	0.983713i	$-0.442472\pi$
$193$	4.99424			0.359493			0.179747	+	0.983713i	$0.442472\pi$
$194$	−8.66267	−	4.48974i	−0.621944	−	0.322345i
$195$	4.78744	+	4.78744i	0.342835	+	0.342835i
$196$	−18.2534	−	25.8703i	−1.30382	−	1.84788i
$197$	−0.193878	+	0.193878i	−0.0138132	+	0.0138132i	−0.713980	−	0.700166i	$-0.753109\pi$
$197$	−0.193878	+	0.193878i	−0.0138132	+	0.0138132i	0.700166	+	0.713980i	$0.253109\pi$
$198$	3.08274	+	9.71632i	0.219081	+	0.690508i
$199$		−	10.5348i		−	0.746790i	−0.927673	−	0.373395i	$-0.878194\pi$
$199$		−	10.5348i		−	0.746790i	0.927673	−	0.373395i	$-0.121806\pi$
$200$	24.9880	−	3.42683i	1.76692	−	0.242314i
$201$		−	21.0885i		−	1.48747i
$202$	−13.7171	+	4.35208i	−0.965128	+	0.306211i
$203$	0.582617	−	0.582617i	0.0408917	−	0.0408917i
$204$	0.748763	−	4.33752i	0.0524239	−	0.303687i
$205$	−0.830600	−	0.830600i	−0.0580116	−	0.0580116i
$206$	−6.03308	+	11.6404i	−0.420345	+	0.811028i
$207$	−6.36458			−0.442369
$208$	2.97934	−	1.41544i	0.206580	−	0.0981432i
$209$	11.6091			0.803016
$210$	−25.5296	+	49.2578i	−1.76171	+	3.39911i
$211$	5.33443	+	5.33443i	0.367237	+	0.367237i	0.866469	−	0.499231i	$-0.166384\pi$
$211$	5.33443	+	5.33443i	0.367237	+	0.367237i	−0.499231	+	0.866469i	$0.666384\pi$
$212$	−10.9188	−	1.88485i	−0.749905	−	0.129452i
$213$	21.8011	−	21.8011i	1.49379	−	1.49379i
$214$	9.31570	−	2.95564i	0.636808	−	0.202043i
$215$			1.27374i			0.0868687i
$216$	5.73407	+	4.35101i	0.390154	+	0.296049i
$217$			32.8909i			2.23278i
$218$	1.94218	+	6.12144i	0.131541	+	0.414596i
$219$	7.21991	−	7.21991i	0.487876	−	0.487876i
$220$	−23.8343	+	16.8169i	−1.60691	+	1.13380i
$221$	0.583093	+	0.583093i	0.0392231	+	0.0392231i
$222$	20.2078	+	10.4734i	1.35626	+	0.702930i
$223$	21.8554			1.46355			0.731774	−	0.681547i	$-0.238693\pi$
$223$	21.8554			1.46355			0.731774	+	0.681547i	$0.238693\pi$
$224$	18.4390	+	19.7633i	1.23201	+	1.32049i
$225$	16.4406			1.09604
$226$	−9.63561	−	4.99400i	−0.640951	−	0.332196i
$227$	15.6094	+	15.6094i	1.03603	+	1.03603i	0.999326	+	0.0367057i	$0.0116864\pi$
$227$	15.6094	+	15.6094i	1.03603	+	1.03603i	0.0367057	+	0.999326i	$0.488314\pi$
$228$	−10.6796	+	7.53526i	−0.707274	+	0.499035i
$229$	8.72931	−	8.72931i	0.576849	−	0.576849i	−0.357184	−	0.934034i	$-0.616263\pi$
$229$	8.72931	−	8.72931i	0.576849	−	0.576849i	0.934034	+	0.357184i	$0.116263\pi$
$230$	−5.50788	−	17.3600i	−0.363179	−	1.14468i
$231$		−	41.1127i		−	2.70502i
$232$	−0.294823	+	0.388539i	−0.0193561	+	0.0255088i
$233$		−	19.9043i		−	1.30398i	−0.758229	−	0.651988i	$-0.773935\pi$
$233$		−	19.9043i		−	1.30398i	0.758229	−	0.651988i	$-0.226065\pi$
$234$	2.04940	−	0.650223i	0.133974	−	0.0425064i
$235$	−12.6054	+	12.6054i	−0.822283	+	0.822283i
$236$	−24.1710	−	4.17250i	−1.57340	−	0.271607i
$237$	7.29096	+	7.29096i	0.473599	+	0.473599i
$238$	−3.10942	+	5.99943i	−0.201554	+	0.388885i
$239$	1.25087			0.0809122			0.0404561	−	0.999181i	$-0.487119\pi$
$239$	1.25087			0.0809122			0.0404561	+	0.999181i	$0.487119\pi$
$240$	11.0105	−	30.9410i	0.710722	−	1.99723i
$241$	−3.78910			−0.244077			−0.122039	−	0.992525i	$-0.538943\pi$
$241$	−3.78910			−0.244077			−0.122039	+	0.992525i	$0.538943\pi$
$242$	2.78827	−	5.37979i	0.179237	−	0.345826i
$243$	11.9253	+	11.9253i	0.765005	+	0.765005i
$244$	2.11666	−	12.2616i	0.135505	−	0.784971i
$245$	41.7605	−	41.7605i	2.66798	−	2.66798i
$246$	−0.934125	+	0.296375i	−0.0595577	+	0.0188962i
$247$		−	2.44863i		−	0.155802i
$248$	−2.64530	−	19.2892i	−0.167977	−	1.22486i
$249$			24.4878i			1.55185i
$250$	6.25007	+	19.6992i	0.395289	+	1.24589i
$251$	5.20382	−	5.20382i	0.328463	−	0.328463i	−0.523539	−	0.852002i	$-0.675389\pi$
$251$	5.20382	−	5.20382i	0.328463	−	0.328463i	0.852002	+	0.523539i	$0.175389\pi$
$252$	10.1575	+	14.3961i	0.639864	+	0.906868i
$253$	9.54326	+	9.54326i	0.599980	+	0.599980i
$254$	−9.77327	−	5.06535i	−0.613229	−	0.317828i
$255$	8.21041			0.514156
$256$	−12.4032	−	10.1074i	−0.775203	−	0.631712i
$257$	−15.7652			−0.983407			−0.491703	−	0.870763i	$-0.663626\pi$
$257$	−15.7652			−0.983407			−0.491703	+	0.870763i	$0.663626\pi$
$258$	0.943501	+	0.489003i	0.0587398	+	0.0304440i
$259$	−24.7075	−	24.7075i	−1.53525	−	1.53525i
$260$	3.54708	+	5.02722i	0.219981	+	0.311775i
$261$	−0.224806	+	0.224806i	−0.0139152	+	0.0139152i
$262$	0.559104	+	1.76221i	0.0345415	+	0.108869i
$263$		−	3.27486i		−	0.201936i	−0.994890	−	0.100968i	$-0.967806\pi$
$263$		−	3.27486i		−	0.201936i	0.994890	−	0.100968i	$-0.0321940\pi$
$264$	3.30656	+	24.1110i	0.203505	+	1.48393i
$265$		−	20.6680i		−	1.26962i
$266$	19.1257	−	6.06811i	1.17267	−	0.372060i
$267$	13.2091	−	13.2091i	0.808383	−	0.808383i
$268$	3.25997	−	18.8847i	0.199134	−	1.15357i
$269$	−18.5744	−	18.5744i	−1.13250	−	1.13250i	−0.989760	−	0.142740i	$-0.954409\pi$
$269$	−18.5744	−	18.5744i	−1.13250	−	1.13250i	−0.142740	−	0.989760i	$-0.545591\pi$
$270$	−6.17818	+	11.9204i	−0.375992	+	0.725454i
$271$	21.6438			1.31477			0.657384	−	0.753556i	$-0.271663\pi$
$271$	21.6438			1.31477			0.657384	+	0.753556i	$0.271663\pi$
$272$	1.34104	−	3.76850i	0.0813122	−	0.228499i
$273$	−8.67165			−0.524832
$274$	−9.41577	+	18.1671i	−0.568828	+	1.09752i
$275$	−24.6516	−	24.6516i	−1.48655	−	1.48655i
$276$	−14.9736	−	2.58481i	−0.901303	−	0.155587i
$277$	−19.5133	+	19.5133i	−1.17244	+	1.17244i	−0.190811	+	0.981627i	$0.561112\pi$
$277$	−19.5133	+	19.5133i	−1.17244	+	1.17244i	−0.981627	+	0.190811i	$0.938888\pi$
$278$	−27.8898	+	8.84873i	−1.67272	+	0.530712i
$279$		−	12.6911i		−	0.759798i
$280$	−30.4763	+	40.1639i	−1.82131	+	2.40025i
$281$			10.4068i			0.620819i	0.950603	+	0.310410i	$0.100466\pi$
$281$			10.4068i			0.620819i	−0.950603	+	0.310410i	$0.899534\pi$
$282$	4.49784	+	14.1765i	0.267843	+	0.844197i
$283$	6.48739	−	6.48739i	0.385635	−	0.385635i	−0.487492	−	0.873127i	$-0.662088\pi$
$283$	6.48739	−	6.48739i	0.385635	−	0.385635i	0.873127	+	0.487492i	$0.162088\pi$
$284$	22.8930	−	16.1528i	1.35845	−	0.958490i
$285$	−17.2393	−	17.2393i	−1.02117	−	1.02117i
$286$	−4.04790	−	2.09797i	−0.239358	−	0.124056i
$287$	1.50449			0.0888075
$288$	−7.11481	−	7.62579i	−0.419244	−	0.449354i
$289$	1.00000			0.0588235
$290$	−0.807725	−	0.418632i	−0.0474312	−	0.0245829i
$291$	−10.7368	−	10.7368i	−0.629403	−	0.629403i
$292$	7.58153	−	5.34934i	0.443675	−	0.313047i
$293$	−12.5593	+	12.5593i	−0.733719	+	0.733719i	−0.971354	−	0.237635i	$-0.923628\pi$
$293$	−12.5593	+	12.5593i	−0.733719	+	0.733719i	0.237635	+	0.971354i	$0.423628\pi$
$294$	−14.9010	−	46.9655i	−0.869043	−	2.73908i
$295$		−	45.7528i		−	2.66383i
$296$	16.4771	+	12.5028i	0.957710	+	0.726710i
$297$		−	9.94931i		−	0.577318i
$298$	24.7446	−	7.85084i	1.43342	−	0.454787i
$299$	2.01290	−	2.01290i	0.116409	−	0.116409i
$300$	38.6789	+	6.67693i	2.23313	+	0.385493i
$301$	−1.15359	−	1.15359i	−0.0664917	−	0.0664917i
$302$	−9.85302	+	19.0108i	−0.566978	+	1.09395i
$303$	−22.3955			−1.28659
$304$	−10.7284	+	5.09692i	−0.615318	+	0.292329i
$305$	23.2098			1.32899
$306$	1.19979	−	2.31492i	0.0685873	−	0.132335i
$307$	−19.4580	−	19.4580i	−1.11053	−	1.11053i	−0.993079	−	0.117447i	$-0.962529\pi$
$307$	−19.4580	−	19.4580i	−1.11053	−	1.11053i	−0.117447	−	0.993079i	$-0.537471\pi$
$308$	6.35543	−	36.8165i	0.362134	−	2.09781i
$309$	−14.4276	+	14.4276i	−0.820756	+	0.820756i
$310$	34.6162	−	10.9829i	1.96607	−	0.623784i
$311$		−	15.7250i		−	0.891682i	−0.895112	−	0.445841i	$-0.852905\pi$
$311$		−	15.7250i		−	0.891682i	0.895112	−	0.445841i	$-0.147095\pi$
$312$	5.08557	−	0.697432i	0.287914	−	0.0394843i
$313$			14.5400i			0.821849i	0.911669	+	0.410925i	$0.134794\pi$
$313$			14.5400i			0.821849i	−0.911669	+	0.410925i	$0.865206\pi$
$314$	9.29902	+	29.3090i	0.524774	+	1.65400i
$315$	−23.2385	+	23.2385i	−1.30934	+	1.30934i
$316$	5.40198	+	7.65613i	0.303885	+	0.430691i
$317$	16.9554	+	16.9554i	0.952312	+	0.952312i	0.998914	−	0.0466013i	$-0.0148390\pi$
$317$	16.9554	+	16.9554i	0.952312	+	0.952312i	−0.0466013	+	0.998914i	$0.514839\pi$
$318$	−15.3094	−	7.93463i	−0.858507	−	0.444952i
$319$	0.674163			0.0377459
$320$	14.6429	−	26.0056i	0.818563	−	1.45376i
$321$	15.2095			0.848912
$322$	20.7107	+	10.7340i	1.15416	+	0.598185i
$323$	−2.09969	−	2.09969i	−0.116830	−	0.116830i
$324$	12.8354	+	18.1914i	0.713079	+	1.01063i
$325$	−5.19961	+	5.19961i	−0.288422	+	0.288422i
$326$	2.73336	+	8.61511i	0.151387	+	0.477147i
$327$			9.99433i			0.552688i
$328$	−0.882325	+	0.121001i	−0.0487183	+	0.00668118i
$329$		−	22.8325i		−	1.25880i
$330$	−43.2694	+	13.7283i	−2.38190	+	0.755717i
$331$	2.86846	−	2.86846i	0.157665	−	0.157665i	−0.623866	−	0.781531i	$-0.714439\pi$
$331$	2.86846	−	2.86846i	0.157665	−	0.157665i	0.781531	+	0.623866i	$0.214439\pi$
$332$	−3.78546	+	21.9288i	−0.207754	+	1.20350i
$333$	9.53352	+	9.53352i	0.522434	+	0.522434i
$334$	−7.03685	+	13.5772i	−0.385039	+	0.742909i
$335$	35.7466			1.95304
$336$	18.0504	+	37.9940i	0.984731	+	2.07274i
$337$	−9.35201			−0.509437			−0.254718	−	0.967015i	$-0.581983\pi$
$337$	−9.35201			−0.509437			−0.254718	+	0.967015i	$0.581983\pi$
$338$	8.01732	−	15.4689i	0.436085	−	0.841398i
$339$	−11.9427	−	11.9427i	−0.648639	−	0.648639i
$340$	7.35243	+	1.26921i	0.398741	+	0.0688326i
$341$	−19.0295	+	19.0295i	−1.03050	+	1.03050i
$342$	−7.37978	+	2.34142i	−0.399053	+	0.126609i
$343$			42.1951i			2.27832i
$344$	0.769313	+	0.583754i	0.0414786	+	0.0314739i
$345$		−	28.3432i		−	1.52595i
$346$	2.49162	+	7.85318i	0.133950	+	0.422190i
$347$	0.395832	−	0.395832i	0.0212494	−	0.0212494i	−0.696402	−	0.717652i	$-0.745217\pi$
$347$	0.395832	−	0.395832i	0.0212494	−	0.0212494i	0.717652	+	0.696402i	$0.245217\pi$
$348$	−0.620187	+	0.437589i	−0.0332455	+	0.0234572i
$349$	−15.1311	−	15.1311i	−0.809951	−	0.809951i	0.174675	−	0.984626i	$-0.444112\pi$
$349$	−15.1311	−	15.1311i	−0.809951	−	0.809951i	−0.984626	+	0.174675i	$0.944112\pi$
$350$	−53.4986	−	27.7276i	−2.85962	−	1.48210i
$351$	−2.09854			−0.112012
$352$	−0.766179	+	22.1025i	−0.0408375	+	1.17807i
$353$	−20.7584			−1.10486			−0.552429	−	0.833560i	$-0.686299\pi$
$353$	−20.7584			−1.10486			−0.552429	+	0.833560i	$0.686299\pi$
$354$	−33.8904	−	17.5649i	−1.80126	−	0.933566i
$355$	36.9545	+	36.9545i	1.96134	+	1.96134i
$356$	13.8707	−	9.78681i	0.735144	−	0.518700i
$357$	−7.43590	+	7.43590i	−0.393550	+	0.393550i
$358$	3.72812	+	11.7504i	0.197037	+	0.621030i
$359$			20.0560i			1.05851i	0.848461	+	0.529257i	$0.177529\pi$
$359$			20.0560i			1.05851i	−0.848461	+	0.529257i	$0.822471\pi$
$360$	11.7595	−	15.4975i	0.619779	−	0.816788i
$361$		−	10.1826i		−	0.535928i
$362$	−0.601041	+	0.190695i	−0.0315900	+	0.0100227i
$363$	6.66790	−	6.66790i	0.349974	−	0.349974i
$364$	−7.76547	−	1.34051i	−0.407021	−	0.0702619i
$365$	12.2383	+	12.2383i	0.640582	+	0.640582i
$366$	8.91048	−	17.1922i	0.465758	−	0.898651i
$367$	2.23827			0.116837			0.0584183	−	0.998292i	$-0.481394\pi$
$367$	2.23827			0.116837			0.0584183	+	0.998292i	$0.481394\pi$
$368$	−13.0093	−	4.62939i	−0.678155	−	0.241324i
$369$	−0.580518			−0.0302206
$370$	−17.7533	+	34.2538i	−0.922948	+	1.78077i
$371$	18.7183	+	18.7183i	0.971806	+	0.971806i
$372$	5.15417	−	29.8577i	0.267231	−	1.54805i
$373$	2.96908	−	2.96908i	0.153733	−	0.153733i	−0.626050	−	0.779783i	$-0.715329\pi$
$373$	2.96908	−	2.96908i	0.153733	−	0.153733i	0.779783	+	0.626050i	$0.215329\pi$
$374$	−5.27006	+	1.67206i	−0.272508	+	0.0864601i
$375$			32.1625i			1.66086i
$376$	1.83634	+	13.3903i	0.0947021	+	0.690555i
$377$		−	0.142197i		−	0.00732352i
$378$	−5.20055	−	16.3913i	−0.267488	−	0.843078i
$379$	11.5979	−	11.5979i	0.595743	−	0.595743i	−0.343434	−	0.939177i	$-0.611590\pi$
$379$	11.5979	−	11.5979i	0.595743	−	0.595743i	0.939177	+	0.343434i	$0.111590\pi$
$380$	−12.7729	−	18.1027i	−0.655233	−	0.928651i
$381$	−12.1133	−	12.1133i	−0.620585	−	0.620585i
$382$	−0.902779	−	0.467897i	−0.0461902	−	0.0239397i
$383$	32.0361			1.63697			0.818484	−	0.574529i	$-0.194815\pi$
$383$	32.0361			1.63697			0.818484	+	0.574529i	$0.194815\pi$
$384$	−13.6416	−	20.8302i	−0.696144	−	1.06299i
$385$	69.6893			3.55169
$386$	6.27074	+	3.25003i	0.319172	+	0.165422i
$387$	0.445119	+	0.445119i	0.0226267	+	0.0226267i
$388$	−7.95507	−	11.2746i	−0.403857	−	0.572380i
$389$	−12.9469	+	12.9469i	−0.656433	+	0.656433i	−0.954534	−	0.298101i	$-0.903647\pi$
$389$	−12.9469	+	12.9469i	−0.656433	+	0.656433i	0.298101	+	0.954534i	$0.403647\pi$
$390$	2.89562	+	9.12653i	0.146625	+	0.462140i
$391$		−	3.45210i		−	0.174580i
$392$	−6.08365	−	44.3611i	−0.307271	−	2.24058i
$393$			2.87711i			0.145131i
$394$	−0.369599	+	0.117264i	−0.0186201	+	0.00590769i
$395$	−12.3587	+	12.3587i	−0.621835	+	0.621835i
$396$	−2.45228	+	14.2059i	−0.123232	+	0.713871i
$397$	3.72601	+	3.72601i	0.187003	+	0.187003i	0.794399	−	0.607396i	$-0.207786\pi$
$397$	3.72601	+	3.72601i	0.187003	+	0.187003i	−0.607396	+	0.794399i	$0.707786\pi$
$398$	6.85557	−	13.2274i	0.343639	−	0.663029i
$399$	31.2261			1.56326
$400$	33.6048	+	11.9584i	1.68024	+	0.597919i
$401$	−14.2891			−0.713566			−0.356783	−	0.934187i	$-0.616126\pi$
$401$	−14.2891			−0.713566			−0.356783	+	0.934187i	$0.616126\pi$
$402$	13.7235	−	26.4785i	0.684464	−	1.32063i
$403$	4.01377	+	4.01377i	0.199940	+	0.199940i
$404$	−20.0552	−	3.46202i	−0.997783	−	0.172242i
$405$	−29.3651	+	29.3651i	−1.45916	+	1.45916i
$406$	1.11067	−	0.352388i	0.0551217	−	0.0174887i
$407$		−	28.5897i		−	1.41714i
$408$	3.76281	−	4.95890i	0.186287	−	0.245502i
$409$		−	30.2638i		−	1.49645i	−0.663446	−	0.748224i	$-0.730907\pi$
$409$		−	30.2638i		−	1.49645i	0.663446	−	0.748224i	$-0.269093\pi$
$410$	−0.502378	−	1.58341i	−0.0248107	−	0.0781992i
$411$	−22.5170	+	22.5170i	−1.11068	+	1.11068i
$412$	−15.1502	+	10.6896i	−0.746396	+	0.526639i
$413$	41.4368	+	41.4368i	2.03897	+	2.03897i
$414$	−7.99133	−	4.14179i	−0.392753	−	0.203558i
$415$	−41.5087			−2.03758
$416$	4.66195	+	0.161605i	0.228571	+	0.00792335i
$417$	−45.5350			−2.22986
$418$	14.5763	+	7.55468i	0.712949	+	0.369511i
$419$	8.86351	+	8.86351i	0.433011	+	0.433011i	0.889651	−	0.456640i	$-0.150947\pi$
$419$	8.86351	+	8.86351i	0.433011	+	0.433011i	−0.456640	+	0.889651i	$0.650947\pi$
$420$	−64.1097	+	45.2342i	−3.12823	+	2.20720i
$421$	12.8388	−	12.8388i	0.625724	−	0.625724i	−0.321265	−	0.946989i	$-0.604108\pi$
$421$	12.8388	−	12.8388i	0.625724	−	0.625724i	0.946989	+	0.321265i	$0.104108\pi$
$422$	3.22646	+	10.1693i	0.157062	+	0.495033i
$423$			8.81006i			0.428360i
$424$	−12.4830	−	9.47208i	−0.606227	−	0.460005i
$425$			8.91728i			0.432552i
$426$	41.5605	−	13.1861i	2.01361	−	0.638869i
$427$	−21.0204	+	21.0204i	−1.01725	+	1.01725i
$428$	13.6201	+	2.35117i	0.658354	+	0.113648i
$429$	−5.01711	−	5.01711i	−0.242228	−	0.242228i
$430$	−0.828898	+	1.59931i	−0.0399730	+	0.0771254i
$431$	−39.3781			−1.89678			−0.948389	−	0.317110i	$-0.897288\pi$
$431$	−39.3781			−1.89678			−0.948389	+	0.317110i	$0.897288\pi$
$432$	4.36821	+	9.19458i	0.210166	+	0.442374i
$433$	15.9330			0.765692			0.382846	−	0.923812i	$-0.374944\pi$
$433$	15.9330			0.765692			0.382846	+	0.923812i	$0.374944\pi$
$434$	−21.4039	+	41.2976i	−1.02742	+	1.98235i
$435$	−1.00112	−	1.00112i	−0.0480001	−	0.0480001i
$436$	−1.54498	+	8.94993i	−0.0739910	+	0.428624i
$437$	−7.24834	+	7.24834i	−0.346735	+	0.346735i
$438$	13.7637	−	4.36687i	0.657654	−	0.208657i
$439$			4.62738i			0.220853i	0.993884	+	0.110426i	$0.0352217\pi$
$439$			4.62738i			0.220853i	−0.993884	+	0.110426i	$0.964778\pi$
$440$	−40.8699	+	5.60487i	−1.94840	+	0.267202i
$441$		−	29.1870i		−	1.38986i
$442$	0.352677	+	1.11158i	0.0167751	+	0.0528725i
$443$	7.05770	−	7.05770i	0.335321	−	0.335321i	−0.519282	−	0.854603i	$-0.673800\pi$
$443$	7.05770	−	7.05770i	0.335321	−	0.335321i	0.854603	+	0.519282i	$0.173800\pi$
$444$	18.5572	+	26.3007i	0.880684	+	1.24818i
$445$	22.3904	+	22.3904i	1.06141	+	1.06141i
$446$	27.4416	+	14.2226i	1.29940	+	0.673458i
$447$	40.3999			1.91085
$448$	10.2908	+	36.8140i	0.486196	+	1.73930i
$449$	−8.34266			−0.393715			−0.196857	−	0.980432i	$-0.563074\pi$
$449$	−8.34266			−0.393715			−0.196857	+	0.980432i	$0.563074\pi$
$450$	20.6427	+	10.6988i	0.973108	+	0.504348i
$451$	0.870447	+	0.870447i	0.0409878	+	0.0409878i
$452$	−8.84853	−	12.5409i	−0.416200	−	0.589873i
$453$	−23.5626	+	23.5626i	−1.10707	+	1.10707i
$454$	9.44114	+	29.7570i	0.443095	+	1.39656i
$455$		−	14.6991i		−	0.689105i
$456$	−18.3129	+	2.51141i	−0.857578	+	0.117608i
$457$		−	33.3458i		−	1.55985i	−0.625872	−	0.779926i	$-0.715257\pi$
$457$		−	33.3458i		−	1.55985i	0.625872	−	0.779926i	$-0.284743\pi$
$458$	16.6411	−	5.27982i	0.777589	−	0.246710i
$459$	−1.79949	+	1.79949i	−0.0839931	+	0.0839931i
$460$	4.38145	−	25.3814i	0.204286	−	1.18341i
$461$	18.1105	+	18.1105i	0.843491	+	0.843491i	0.989311	−	0.145820i	$-0.0465820\pi$
$461$	18.1105	+	18.1105i	0.843491	+	0.843491i	−0.145820	+	0.989311i	$0.546582\pi$
$462$	26.7544	−	51.6209i	1.24473	−	2.40162i
$463$	12.8236			0.595965			0.297983	−	0.954571i	$-0.403686\pi$
$463$	12.8236			0.595965			0.297983	+	0.954571i	$0.403686\pi$
$464$	−0.623023	+	0.295989i	−0.0289231	+	0.0137410i
$465$	56.5170			2.62091
$466$	12.9529	−	24.9918i	0.600031	−	1.15772i
$467$	−3.65827	−	3.65827i	−0.169284	−	0.169284i	0.617380	−	0.786665i	$-0.288194\pi$
$467$	−3.65827	−	3.65827i	−0.169284	−	0.169284i	−0.786665	+	0.617380i	$0.788194\pi$
$468$	2.99635	+	0.517244i	0.138506	+	0.0239096i
$469$	−32.3745	+	32.3745i	−1.49491	+	1.49491i
$470$	−24.0302	+	7.62419i	−1.10843	+	0.351678i
$471$			47.8521i			2.20491i
$472$	−27.6336	−	20.9684i	−1.27194	−	0.965148i
$473$		−	1.33485i		−	0.0613765i
$474$	4.40984	+	13.8991i	0.202551	+	0.638408i
$475$	18.7235	−	18.7235i	0.859093	−	0.859093i
$476$	−7.80834	+	5.50937i	−0.357895	+	0.252522i
$477$	−7.22257	−	7.22257i	−0.330699	−	0.330699i
$478$	1.57059	+	0.814014i	0.0718370	+	0.0372321i
$479$	7.40604			0.338390			0.169195	−	0.985583i	$-0.445883\pi$
$479$	7.40604			0.338390			0.169195	+	0.985583i	$0.445883\pi$
$480$	33.9597	−	31.6842i	1.55004	−	1.44618i
$481$	−6.03025			−0.274956
$482$	−4.75757	−	2.46578i	−0.216701	−	0.112313i
$483$	25.6695	+	25.6695i	1.16800	+	1.16800i
$484$	7.00187	−	4.94035i	0.318267	−	0.224561i
$485$	18.1997	−	18.1997i	0.826407	−	0.826407i
$486$	7.21284	+	22.7337i	0.327181	+	1.03122i
$487$		−	20.8331i		−	0.944040i	−0.881588	−	0.472020i	$-0.843525\pi$
$487$		−	20.8331i		−	0.944040i	0.881588	−	0.472020i	$-0.156475\pi$
$488$	10.6370	−	14.0182i	0.481515	−	0.634574i
$489$			14.0657i			0.636073i
$490$	79.6102	−	25.2583i	3.59642	−	1.14105i
$491$	−26.9693	+	26.9693i	−1.21711	+	1.21711i	−0.248469	+	0.968640i	$0.579927\pi$
$491$	−26.9693	+	26.9693i	−1.21711	+	1.21711i	−0.968640	+	0.248469i	$0.920073\pi$
$492$	−1.36575	−	0.235762i	−0.0615728	−	0.0106290i
$493$	−0.121933	−	0.121933i	−0.00549160	−	0.00549160i
$494$	1.59346	−	3.07448i	0.0716931	−	0.138327i
$495$	−26.8900			−1.20862
$496$	9.23112	−	25.9408i	0.414490	−	1.16478i
$497$	−66.9370			−3.00253
$498$	−15.9356	+	30.7467i	−0.714090	+	1.37779i
$499$	−6.09344	−	6.09344i	−0.272780	−	0.272780i	0.557439	−	0.830218i	$-0.311784\pi$
$499$	−6.09344	−	6.09344i	−0.272780	−	0.272780i	−0.830218	+	0.557439i	$0.811784\pi$
$500$	−4.97185	+	28.8015i	−0.222348	+	1.28804i
$501$	−16.8280	+	16.8280i	−0.751819	+	0.751819i
$502$	9.92031	−	3.14747i	0.442765	−	0.140478i
$503$			23.3924i			1.04301i	0.853247	+	0.521507i	$0.174630\pi$
$503$			23.3924i			1.04301i	−0.853247	+	0.521507i	$0.825370\pi$
$504$	3.38538	+	24.6857i	0.150797	+	1.09959i
$505$		−	37.9621i		−	1.68929i
$506$	5.77212	+	18.1928i	0.256602	+	0.808769i
$507$	19.1727	−	19.1727i	0.851490	−	0.851490i
$508$	−8.97495	−	12.7200i	−0.398199	−	0.564360i
$509$	−16.5847	−	16.5847i	−0.735106	−	0.735106i	0.236521	−	0.971626i	$-0.423993\pi$
$509$	−16.5847	−	16.5847i	−0.735106	−	0.735106i	−0.971626	+	0.236521i	$0.923993\pi$
$510$	10.3089	+	5.34298i	0.456488	+	0.236591i
$511$	−22.1677			−0.980640
$512$	−8.99599	−	20.7623i	−0.397570	−	0.917572i
$513$	7.55674			0.333638
$514$	−19.7947	−	10.2593i	−0.873107	−	0.452519i
$515$	−24.4558	−	24.4558i	−1.07765	−	1.07765i
$516$	0.866432	+	1.22798i	0.0381425	+	0.0540587i
$517$	13.2101	−	13.2101i	0.580979	−	0.580979i
$518$	−14.9440	−	47.1011i	−0.656601	−	2.06950i
$519$			12.8217i			0.562810i
$520$	1.18220	+	8.62044i	0.0518429	+	0.378031i
$521$		−	28.7242i		−	1.25843i	−0.777232	−	0.629214i	$-0.783377\pi$
$521$		−	28.7242i		−	1.25843i	0.777232	−	0.629214i	$-0.216623\pi$
$522$	−0.428559	+	0.135971i	−0.0187575	+	0.00595129i
$523$	19.7496	−	19.7496i	0.863588	−	0.863588i	−0.128165	−	0.991753i	$-0.540909\pi$
$523$	19.7496	−	19.7496i	0.863588	−	0.863588i	0.991753	+	0.128165i	$0.0409088\pi$
$524$	−0.444760	+	2.57646i	−0.0194294	+	0.112553i
$525$	−66.3080	−	66.3080i	−2.89392	−	2.89392i
$526$	2.13113	−	4.11189i	0.0929219	−	0.179287i
$527$	6.88358			0.299853
$528$	−11.5387	+	32.4254i	−0.502156	+	1.41113i
$529$	11.0830			0.481868
$530$	13.4498	−	25.9506i	0.584223	−	1.12722i
$531$	−15.9886	−	15.9886i	−0.693847	−	0.693847i
$532$	27.9630	+	4.82711i	1.21235	+	0.209282i
$533$	0.183598	−	0.183598i	0.00795251	−	0.00795251i
$534$	25.1811	−	7.98935i	1.08969	−	0.345733i
$535$			25.7813i			1.11462i
$536$	16.3826	−	21.5901i	0.707619	−	0.932550i
$537$			19.1847i			0.827879i
$538$	−11.2345	−	35.4093i	−0.484353	−	1.52660i
$539$	−43.7639	+	43.7639i	−1.88505	+	1.88505i
$540$	−15.5146	+	10.9467i	−0.667641	+	0.471071i
$541$	15.9377	+	15.9377i	0.685216	+	0.685216i	0.961171	−	0.275954i	$-0.0889939\pi$
$541$	15.9377	+	15.9377i	0.685216	+	0.685216i	−0.275954	+	0.961171i	$0.588994\pi$
$542$	27.1758	+	14.0849i	1.16730	+	0.604996i
$543$	−0.981305			−0.0421118
$544$	4.13617	−	3.85902i	0.177337	−	0.165454i
$545$	−16.9412			−0.725679
$546$	−10.8881	−	5.64313i	−0.465966	−	0.241504i
$547$	−8.44858	−	8.44858i	−0.361235	−	0.361235i	0.503032	−	0.864268i	$-0.332218\pi$
$547$	−8.44858	−	8.44858i	−0.361235	−	0.361235i	−0.864268	+	0.503032i	$0.832218\pi$
$548$	−23.6448	+	16.6832i	−1.01005	+	0.712670i
$549$	8.11084	−	8.11084i	0.346162	−	0.346162i
$550$	−14.9102	−	46.9946i	−0.635774	−	2.00386i
$551$			0.512043i			0.0218138i
$552$	−17.1186	−	12.9896i	−0.728618	−	0.552875i
$553$		−	22.3858i		−	0.951941i
$554$	−37.1991	+	11.8023i	−1.58044	+	0.501434i
$555$	−42.4553	+	42.4553i	−1.80213	+	1.80213i
$556$	−40.7766	−	7.03905i	−1.72931	−	0.298522i
$557$	30.0579	+	30.0579i	1.27360	+	1.27360i	0.944188	+	0.329407i	$0.106849\pi$
$557$	30.0579	+	30.0579i	1.27360	+	1.27360i	0.329407	+	0.944188i	$0.393151\pi$
$558$	8.25884	−	15.9349i	0.349624	−	0.674578i
$559$	−0.281552			−0.0119084
$560$	−64.4028	+	30.5968i	−2.72151	+	1.29295i
$561$	−8.60430			−0.363274
$562$	−6.77231	+	13.0668i	−0.285673	+	0.551188i
$563$	−11.3635	−	11.3635i	−0.478916	−	0.478916i	0.425869	−	0.904785i	$-0.359968\pi$
$563$	−11.3635	−	11.3635i	−0.478916	−	0.478916i	−0.904785	+	0.425869i	$0.859968\pi$
$564$	−3.57797	+	20.7269i	−0.150660	+	0.872760i
$565$	20.2438	−	20.2438i	0.851663	−	0.851663i
$566$	12.3672	−	3.92381i	0.519833	−	0.164930i
$567$		−	53.1899i		−	2.23377i
$568$	39.2558	−	5.38352i	1.64714	−	0.225887i
$569$			9.15686i			0.383876i	0.981407	+	0.191938i	$0.0614772\pi$
$569$			9.15686i			0.383876i	−0.981407	+	0.191938i	$0.938523\pi$
$570$	−10.4270	−	32.8641i	−0.436738	−	1.37653i
$571$	7.65032	−	7.65032i	0.320156	−	0.320156i	−0.528671	−	0.848827i	$-0.677309\pi$
$571$	7.65032	−	7.65032i	0.320156	−	0.320156i	0.848827	+	0.528671i	$0.177309\pi$
$572$	−3.71725	−	5.26840i	−0.155426	−	0.220283i
$573$	−1.11894	−	1.11894i	−0.0467442	−	0.0467442i
$574$	1.88903	+	0.979059i	0.0788467	+	0.0408651i
$575$	30.7834			1.28376
$576$	−3.97078	−	14.2049i	−0.165449	−	0.591871i
$577$	−12.3643			−0.514734			−0.257367	−	0.966314i	$-0.582855\pi$
$577$	−12.3643			−0.514734			−0.257367	+	0.966314i	$0.582855\pi$
$578$	1.25559	+	0.650757i	0.0522258	+	0.0270679i
$579$	7.77217	+	7.77217i	0.323000	+	0.323000i
$580$	−0.741747	−	1.05126i	−0.0307994	−	0.0436514i
$581$	37.5930	−	37.5930i	1.55962	−	1.55962i
$582$	−6.49403	−	20.4681i	−0.269186	−	0.848431i
$583$			21.6595i			0.897045i
$584$	13.0004	−	1.78287i	0.537962	−	0.0737757i
$585$			5.67174i			0.234498i
$586$	−23.9423	+	7.59630i	−0.989049	+	0.313800i
$587$	13.6573	−	13.6573i	0.563695	−	0.563695i	−0.366660	−	0.930355i	$-0.619499\pi$
$587$	13.6573	−	13.6573i	0.563695	−	0.563695i	0.930355	+	0.366660i	$0.119499\pi$
$588$	11.8535	−	68.6665i	0.488832	−	2.83176i
$589$	−14.4534	−	14.4534i	−0.595540	−	0.595540i
$590$	29.7739	−	57.4469i	1.22577	−	2.36505i
$591$	−0.603435			−0.0248220
$592$	12.5522	+	26.4210i	0.515894	+	1.08590i
$593$	−9.55505			−0.392379			−0.196189	−	0.980566i	$-0.562857\pi$
$593$	−9.55505			−0.392379			−0.196189	+	0.980566i	$0.562857\pi$
$594$	6.47458	−	12.4923i	0.265655	−	0.512565i
$595$	−12.6044	−	12.6044i	−0.516731	−	0.516731i
$596$	36.1781	+	6.24524i	1.48191	+	0.255815i
$597$	16.3945	−	16.3945i	0.670981	−	0.670981i
$598$	3.83729	−	1.21748i	0.156919	−	0.0497863i
$599$		−	12.1444i		−	0.496208i	−0.968733	−	0.248104i	$-0.920193\pi$
$599$		−	12.1444i		−	0.496208i	0.968733	−	0.248104i	$-0.0798075\pi$
$600$	44.2199	+	33.5540i	1.80527	+	1.36984i
$601$		−	3.21274i		−	0.131050i	−0.997851	−	0.0655252i	$-0.979128\pi$
$601$		−	3.21274i		−	0.131050i	0.997851	−	0.0655252i	$-0.0208723\pi$
$602$	−0.697733	−	2.19914i	−0.0284375	−	0.0896304i
$603$	12.4919	−	12.4919i	0.508709	−	0.508709i
$604$	−24.7428	+	17.4579i	−1.00677	+	0.710352i
$605$	11.3026	+	11.3026i	0.459516	+	0.459516i
$606$	−28.1197	−	14.5740i	−1.14228	−	0.592029i
$607$	44.9542			1.82464			0.912318	−	0.409483i	$-0.134291\pi$
$607$	44.9542			1.82464			0.912318	+	0.409483i	$0.134291\pi$
$608$	−16.7874	−	0.581931i	−0.680819	−	0.0236004i
$609$	1.81337			0.0734814
$610$	29.1421	+	15.1040i	1.17993	+	0.611541i
$611$	−2.78632	−	2.78632i	−0.112722	−	0.112722i
$612$	3.01289	−	2.12582i	0.121789	−	0.0859313i
$613$	15.9353	−	15.9353i	0.643619	−	0.643619i	−0.307824	−	0.951443i	$-0.599601\pi$
$613$	15.9353	−	15.9353i	0.643619	−	0.643619i	0.951443	+	0.307824i	$0.0996009\pi$
$614$	−11.7689	−	37.0938i	−0.474955	−	1.49698i
$615$		−	2.58520i		−	0.104245i
$616$	31.9384	−	42.0907i	1.28684	−	1.69588i
$617$		−	0.599497i		−	0.0241348i	−0.999927	−	0.0120674i	$-0.996159\pi$
$617$		−	0.599497i		−	0.0241348i	0.999927	−	0.0120674i	$-0.00384127\pi$
$618$	−27.5040	+	8.72633i	−1.10637	+	0.351025i
$619$	−19.8870	+	19.8870i	−0.799328	+	0.799328i	−0.982989	−	0.183662i	$-0.941205\pi$
$619$	−19.8870	+	19.8870i	−0.799328	+	0.799328i	0.183662	+	0.982989i	$0.441205\pi$
$620$	50.6110	+	8.73671i	2.03259	+	0.350875i
$621$	6.21204	+	6.21204i	0.249280	+	0.249280i
$622$	10.2331	−	19.7442i	0.410312	−	0.791670i
$623$	−40.5565			−1.62486
$624$	6.83927	+	2.43378i	0.273790	+	0.0974291i
$625$	−9.93147			−0.397259
$626$	−9.46200	+	18.2563i	−0.378178	+	0.729670i
$627$	18.0663	+	18.0663i	0.721500	+	0.721500i
$628$	−7.39724	+	42.8516i	−0.295182	+	1.70997i
$629$	−5.17091	+	5.17091i	−0.206178	+	0.206178i
$630$	−44.3008	+	14.0555i	−1.76499	+	0.559986i
$631$		−	36.4278i		−	1.45017i	−0.688660	−	0.725084i	$-0.741801\pi$
$631$		−	36.4278i		−	1.45017i	0.688660	−	0.725084i	$-0.258199\pi$
$632$	1.80041	+	13.1284i	0.0716167	+	0.522219i
$633$			16.6032i			0.659917i
$634$	10.2553	+	32.3230i	0.407289	+	1.28371i
$635$	20.5330	−	20.5330i	0.814828	−	0.814828i
$636$	−14.0588	−	19.9254i	−0.557469	−	0.790092i
$637$	9.23085	+	9.23085i	0.365740	+	0.365740i
$638$	0.846475	+	0.438716i	0.0335123	+	0.0173689i
$639$	25.8280			1.02174
$640$	35.3088	−	23.1235i	1.39570	−	0.914037i
$641$	−4.64229			−0.183360			−0.0916798	−	0.995789i	$-0.529224\pi$
$641$	−4.64229			−0.183360			−0.0916798	+	0.995789i	$0.529224\pi$
$642$	19.0970	+	9.89769i	0.753698	+	0.390631i
$643$	1.23502	+	1.23502i	0.0487046	+	0.0487046i	0.731040	−	0.682335i	$-0.239035\pi$
$643$	1.23502	+	1.23502i	0.0487046	+	0.0487046i	−0.682335	+	0.731040i	$0.739035\pi$
$644$	19.0189	+	26.9552i	0.749451	+	1.06218i
$645$	−1.98223	+	1.98223i	−0.0780504	+	0.0780504i
$646$	−1.26997	−	4.00274i	−0.0499662	−	0.157486i
$647$			20.8044i			0.817904i	0.912556	+	0.408952i	$0.134106\pi$
$647$			20.8044i			0.817904i	−0.912556	+	0.408952i	$0.865894\pi$
$648$	4.27789	+	31.1938i	0.168051	+	1.22541i
$649$			47.9477i			1.88211i
$650$	−9.91227	+	3.14492i	−0.388791	+	0.123354i
$651$	−51.1856	+	51.1856i	−2.00612	+	2.00612i
$652$	−2.17435	+	12.5958i	−0.0851542	+	0.493291i
$653$	−11.7345	−	11.7345i	−0.459208	−	0.459208i	0.439188	−	0.898395i	$-0.355266\pi$
$653$	−11.7345	−	11.7345i	−0.459208	−	0.459208i	−0.898395	+	0.439188i	$0.855266\pi$
$654$	−6.50387	+	12.5488i	−0.254322	+	0.490698i
$655$	−4.87692			−0.190557
$656$	−1.18658	−	0.422250i	−0.0463283	−	0.0164861i
$657$	8.55352			0.333705
$658$	14.8584	−	28.6684i	0.579241	−	1.11761i
$659$	6.91417	+	6.91417i	0.269338	+	0.269338i	0.828833	−	0.559495i	$-0.189005\pi$
$659$	6.91417	+	6.91417i	0.269338	+	0.269338i	−0.559495	+	0.828833i	$0.689005\pi$
$660$	−63.2625	−	10.9207i	−2.46249	−	0.425087i
$661$	−6.46943	+	6.46943i	−0.251632	+	0.251632i	−0.821639	−	0.570008i	$-0.806940\pi$
$661$	−6.46943	+	6.46943i	−0.251632	+	0.251632i	0.570008	+	0.821639i	$0.306940\pi$
$662$	5.46829	−	1.73495i	0.212531	−	0.0674309i
$663$			1.81485i			0.0704830i
$664$	−19.0233	+	25.0703i	−0.738248	+	0.972916i
$665$			52.9307i			2.05256i
$666$	5.76623	+	18.1742i	0.223437	+	0.704237i
$667$	−0.420926	+	0.420926i	−0.0162983	+	0.0162983i
$668$	−17.6708	+	12.4681i	−0.683705	+	0.482406i
$669$	34.0120	+	34.0120i	1.31498	+	1.31498i
$670$	44.8831	+	23.2623i	1.73399	+	0.898701i
$671$	−24.3233			−0.938991
$672$	−2.06087	+	59.4515i	−0.0794999	+	2.29339i
$673$	−1.44866			−0.0558418			−0.0279209	−	0.999610i	$-0.508889\pi$
$673$	−1.44866			−0.0558418			−0.0279209	+	0.999610i	$0.508889\pi$
$674$	−11.7423	−	6.08589i	−0.452298	−	0.234420i
$675$	−16.0466	−	16.0466i	−0.617633	−	0.617633i
$676$	20.1330	−	14.2054i	0.774346	−	0.546360i
$677$	5.89064	−	5.89064i	0.226396	−	0.226396i	−0.584789	−	0.811185i	$-0.698823\pi$
$677$	5.89064	−	5.89064i	0.226396	−	0.226396i	0.811185	+	0.584789i	$0.198823\pi$
$678$	−7.22340	−	22.7670i	−0.277413	−	0.874361i
$679$			32.9658i			1.26511i
$680$	8.40572	+	6.37825i	0.322345	+	0.244595i
$681$			48.5835i			1.86172i
$682$	−36.2769	+	11.5097i	−1.38911	+	0.440731i
$683$	10.2200	−	10.2200i	0.391056	−	0.391056i	−0.484008	−	0.875064i	$-0.660819\pi$
$683$	10.2200	−	10.2200i	0.391056	−	0.391056i	0.875064	+	0.484008i	$0.160819\pi$
$684$	−10.7897	−	1.86257i	−0.412554	−	0.0712170i
$685$	−38.1680	−	38.1680i	−1.45832	−	1.45832i
$686$	−27.4587	+	52.9799i	−1.04838	+	2.02278i
$687$	27.1696			1.03658
$688$	0.586062	+	1.23359i	0.0223434	+	0.0470303i
$689$	4.56850			0.174046
$690$	18.4445	−	35.5876i	0.702171	−	1.35479i
$691$	17.4544	+	17.4544i	0.663997	+	0.663997i	0.956320	−	0.292323i	$-0.0944281\pi$
$691$	17.4544	+	17.4544i	0.663997	+	0.663997i	−0.292323	+	0.956320i	$0.594428\pi$
$692$	−1.98205	+	11.4818i	−0.0753462	+	0.436474i
$693$	24.3534	−	24.3534i	0.925109	−	0.925109i
$694$	0.754595	−	0.239414i	0.0286440	−	0.00908803i
$695$		−	77.1853i		−	2.92781i
$696$	−1.06347	+	0.145843i	−0.0403106	+	0.00552817i
$697$		−	0.314869i		−	0.0119265i
$698$	−9.15187	−	28.8452i	−0.346403	−	1.09181i
$699$	30.9757	−	30.9757i	1.17161	−	1.17161i
$700$	−49.1286	−	69.6291i	−1.85689	−	2.63173i
$701$	−21.3105	−	21.3105i	−0.804888	−	0.804888i	0.178967	−	0.983855i	$-0.442724\pi$
$701$	−21.3105	−	21.3105i	−0.804888	−	0.804888i	−0.983855	+	0.178967i	$0.942724\pi$
$702$	−2.63492	−	1.36564i	−0.0994486	−	0.0515428i
$703$	21.7146			0.818981
$704$	−15.3454	+	27.2532i	−0.578351	+	1.02714i
$705$	−39.2336			−1.47762
$706$	−26.0641	−	13.5087i	−0.980935	−	0.508405i
$707$	34.3810	+	34.3810i	1.29303	+	1.29303i
$708$	−31.1221	−	44.1088i	−1.16964	−	1.65771i
$709$	11.7773	−	11.7773i	0.442305	−	0.442305i	−0.450481	−	0.892786i	$-0.648748\pi$
$709$	11.7773	−	11.7773i	0.442305	−	0.442305i	0.892786	+	0.450481i	$0.148748\pi$
$710$	22.3515	+	70.4483i	0.838836	+	2.64388i
$711$			8.63769i			0.323939i
$712$	23.7848	−	3.26183i	0.891372	−	0.122242i
$713$		−	23.7628i		−	0.889925i
$714$	−14.1754	+	4.49751i	−0.530502	+	0.168315i
$715$	8.50439	−	8.50439i	0.318046	−	0.318046i
$716$	−2.96567	+	17.1799i	−0.110832	+	0.642042i
$717$	1.94664	+	1.94664i	0.0726987	+	0.0726987i
$718$	−13.0516	+	25.1822i	−0.487080	+	0.939790i
$719$	−17.8132			−0.664319			−0.332160	−	0.943223i	$-0.607777\pi$
$719$	−17.8132			−0.664319			−0.332160	+	0.943223i	$0.607777\pi$
$720$	24.8502	−	11.8060i	0.926112	−	0.439983i
$721$	44.2977			1.64973
$722$	6.62642	−	12.7853i	0.246610	−	0.475818i
$723$	−5.89670	−	5.89670i	−0.219300	−	0.219300i
$724$	−0.878759	−	0.151696i	−0.0326588	−	0.00563772i
$725$	1.08731	−	1.08731i	0.0403818	−	0.0403818i
$726$	12.7114	−	4.03300i	0.471763	−	0.149678i
$727$			24.6996i			0.916057i	0.888937	+	0.458029i	$0.151444\pi$
$727$			24.6996i			0.916057i	−0.888937	+	0.458029i	$0.848556\pi$
$728$	−8.87793	−	6.73657i	−0.329038	−	0.249674i
$729$			3.72114i			0.137820i
$730$	7.40218	+	23.3305i	0.273967	+	0.863500i
$731$	−0.241429	+	0.241429i	−0.00892959	+	0.00892959i
$732$	22.3759	−	15.7879i	0.827037	−	0.583537i
$733$	−5.62682	−	5.62682i	−0.207831	−	0.207831i	0.595514	−	0.803345i	$-0.296949\pi$
$733$	−5.62682	−	5.62682i	−0.207831	−	0.207831i	−0.803345	+	0.595514i	$0.796949\pi$
$734$	2.81036	+	1.45657i	0.103732	+	0.0537629i
$735$	129.978			4.79430
$736$	−13.3218	−	14.2785i	−0.491046	−	0.526313i
$737$	−37.4615			−1.37991
$738$	−0.728895	−	0.377776i	−0.0268310	−	0.0139061i
$739$	15.5991	+	15.5991i	0.573821	+	0.573821i	0.933194	−	0.359373i	$-0.117010\pi$
$739$	15.5991	+	15.5991i	0.573821	+	0.573821i	−0.359373	+	0.933194i	$0.617010\pi$
$740$	−44.5818	+	31.4558i	−1.63886	+	1.15634i
$741$	3.81062	−	3.81062i	0.139987	−	0.139987i
$742$	11.3215	+	35.6836i	0.415626	+	1.30999i
$743$		−	5.11385i		−	0.187609i	−0.995591	−	0.0938044i	$-0.970097\pi$
$743$		−	5.11385i		−	0.187609i	0.995591	−	0.0938044i	$-0.0299028\pi$
$744$	25.9016	−	34.1350i	0.949599	−	1.25145i
$745$			68.4809i			2.50895i
$746$	5.66011	−	1.79581i	0.207231	−	0.0657493i
$747$	−14.5055	+	14.5055i	−0.530728	+	0.530728i
$748$	−7.70516	−	1.33010i	−0.281729	−	0.0486333i
$749$	−23.3493	−	23.3493i	−0.853164	−	0.853164i
$750$	−20.9299	+	40.3830i	−0.764253	+	1.47458i
$751$	−6.54398			−0.238793			−0.119397	−	0.992847i	$-0.538096\pi$
$751$	−6.54398			−0.238793			−0.119397	+	0.992847i	$0.538096\pi$
$752$	−6.40816	+	18.0079i	−0.233681	+	0.656679i
$753$	16.1967			0.590239
$754$	0.0925356	−	0.178542i	0.00336995	−	0.00650210i
$755$	−39.9404	−	39.9404i	−1.45358	−	1.45358i
$756$	4.13697	−	23.9651i	0.150460	−	0.871603i
$757$	−14.3887	+	14.3887i	−0.522967	+	0.522967i	−0.918466	−	0.395500i	$-0.870571\pi$
$757$	−14.3887	+	14.3887i	−0.522967	+	0.522967i	0.395500	+	0.918466i	$0.370571\pi$
$758$	22.1096	−	7.01483i	0.803057	−	0.254790i
$759$			29.7030i			1.07815i
$760$	−4.25704	−	31.0417i	−0.154419	−	1.12600i
$761$		−	27.4548i		−	0.995237i	−0.867396	−	0.497619i	$-0.834208\pi$
$761$		−	27.4548i		−	0.995237i	0.867396	−	0.497619i	$-0.165792\pi$
$762$	−7.32659	−	23.0922i	−0.265414	−	0.836544i
$763$	15.3430	−	15.3430i	0.555456	−	0.555456i
$764$	−0.829036	−	1.17498i	−0.0299935	−	0.0425092i
$765$	4.86349	+	4.86349i	0.175840	+	0.175840i
$766$	40.2243	+	20.8477i	1.45336	+	0.753258i
$767$	10.1133			0.365170
$768$	−3.57287	−	35.0317i	−0.128925	−	1.26410i
$769$	30.0065			1.08206			0.541031	−	0.841003i	$-0.318034\pi$
$769$	30.0065			1.08206			0.541031	+	0.841003i	$0.318034\pi$
$770$	87.5014	+	45.3507i	3.15333	+	1.63433i
$771$	−24.5342	−	24.5342i	−0.883579	−	0.883579i
$772$	5.75852	+	8.16144i	0.207254	+	0.293737i
$773$	−11.1221	+	11.1221i	−0.400035	+	0.400035i	−0.878245	−	0.478210i	$-0.841286\pi$
$773$	−11.1221	+	11.1221i	−0.400035	+	0.400035i	0.478210	+	0.878245i	$0.341286\pi$
$774$	0.269225	+	0.848553i	0.00967708	+	0.0305006i
$775$			61.3828i			2.20494i
$776$	−2.65133	−	19.3331i	−0.0951771	−	0.694018i
$777$		−	76.9008i		−	2.75880i
$778$	−24.6813	+	7.83075i	−0.884867	+	0.280746i
$779$	−0.661126	+	0.661126i	−0.0236873	+	0.0236873i
$780$	−2.30343	+	13.3436i	−0.0824760	+	0.477776i
$781$	−38.7274	−	38.7274i	−1.38577	−	1.38577i
$782$	2.24648	−	4.33444i	0.0803340	−	0.154999i
$783$	0.438836			0.0156827
$784$	21.2297	−	59.6585i	0.758203	−	2.13066i
$785$	−81.1130			−2.89505
$786$	−1.87230	+	3.61248i	−0.0667827	+	0.128853i
$787$	24.7905	+	24.7905i	0.883685	+	0.883685i	0.993907	−	0.110222i	$-0.0351563\pi$
$787$	24.7905	+	24.7905i	0.883685	+	0.883685i	−0.110222	+	0.993907i	$0.535156\pi$
$788$	−0.540376	−	0.0932823i	−0.0192501	−	0.00332304i
$789$	5.09642	−	5.09642i	0.181437	−	0.181437i
$790$	−23.5601	+	7.47502i	−0.838230	+	0.265949i
$791$			36.6683i			1.30377i
$792$	−12.3236	+	16.2410i	−0.437901	+	0.577097i
$793$			5.13036i			0.182184i
$794$	2.25363	+	7.10308i	0.0799784	+	0.252079i
$795$	32.1640	−	32.1640i	1.14074	−	1.14074i
$796$	17.2156	−	12.1469i	0.610191	−	0.430536i
$797$	19.4849	+	19.4849i	0.690191	+	0.690191i	0.962274	−	0.272083i	$-0.0877124\pi$
$797$	19.4849	+	19.4849i	0.690191	+	0.690191i	−0.272083	+	0.962274i	$0.587712\pi$
$798$	39.2073	+	20.3206i	1.38792	+	0.719342i
$799$	−4.77851			−0.169052
$800$	34.4120	+	36.8834i	1.21665	+	1.30403i
$801$	15.6490			0.552929
$802$	−17.9414	−	9.29876i	−0.633532	−	0.328351i
$803$	−12.8254	−	12.8254i	−0.452600	−	0.452600i
$804$	34.4622	−	24.3157i	1.21539	−	0.857547i
$805$	−43.5118	+	43.5118i	−1.53359	+	1.53359i
$806$	2.42768	+	7.65165i	0.0855113	+	0.269518i
$807$		−	57.8119i		−	2.03508i
$808$	−22.9282	−	17.3979i	−0.806613	−	0.612057i
$809$			2.89446i			0.101764i	0.998705	+	0.0508818i	$0.0162032\pi$
$809$			2.89446i			0.101764i	−0.998705	+	0.0508818i	$0.983797\pi$
$810$	−55.9801	+	17.7611i	−1.96694	+	0.624061i
$811$	−13.7811	+	13.7811i	−0.483919	+	0.483919i	−0.906381	−	0.422462i	$-0.861166\pi$
$811$	−13.7811	+	13.7811i	−0.483919	+	0.483919i	0.422462	+	0.906381i	$0.361166\pi$
$812$	1.62387	+	0.280320i	0.0569867	+	0.00983731i
$813$	33.6827	+	33.6827i	1.18130	+	1.18130i
$814$	18.6050	−	35.8971i	0.652104	−	1.25819i
$815$	−23.8424			−0.835164
$816$	7.95160	−	3.77769i	0.278362	−	0.132246i
$817$	1.01385			0.0354702
$818$	19.6944	−	37.9990i	0.688597	−	1.32860i
$819$	−5.13671	−	5.13671i	−0.179491	−	0.179491i
$820$	0.399635	−	2.31505i	0.0139559	−	0.0808451i
$821$	−3.92174	+	3.92174i	−0.136870	+	0.136870i	−0.772222	−	0.635353i	$-0.780855\pi$
$821$	−3.92174	+	3.92174i	−0.136870	+	0.136870i	0.635353	+	0.772222i	$0.280855\pi$
$822$	−42.9253	+	13.6191i	−1.49719	+	0.475021i
$823$			51.5158i			1.79573i	0.440272	+	0.897864i	$0.354882\pi$
$823$			51.5158i			1.79573i	−0.440272	+	0.897864i	$0.645118\pi$
$824$	−25.9788	+	3.56272i	−0.905015	+	0.124113i
$825$		−	76.7270i		−	2.67129i
$826$	25.0625	+	78.9930i	0.872036	+	2.74852i
$827$	16.9304	−	16.9304i	0.588727	−	0.588727i	−0.348560	−	0.937287i	$-0.613329\pi$
$827$	16.9304	−	16.9304i	0.588727	−	0.588727i	0.937287	+	0.348560i	$0.113329\pi$
$828$	−7.33857	−	10.4008i	−0.255033	−	0.361454i
$829$	−18.1676	−	18.1676i	−0.630988	−	0.630988i	0.317328	−	0.948316i	$-0.397214\pi$
$829$	−18.1676	−	18.1676i	−0.630988	−	0.630988i	−0.948316	+	0.317328i	$0.897214\pi$
$830$	−52.1180	−	27.0120i	−1.80904	−	0.937601i
$831$	−60.7341			−2.10684
$832$	5.74835	+	3.23670i	0.199288	+	0.112212i
$833$	15.8308			0.548506
$834$	−57.1735	−	29.6322i	−1.97976	−	1.02608i
$835$	−28.5247	−	28.5247i	−0.987139	−	0.987139i
$836$	13.3856	+	18.9712i	0.462951	+	0.656133i
$837$	−12.3870	+	12.3870i	−0.428156	+	0.428156i
$838$	5.36098	+	16.8970i	0.185192	+	0.583696i
$839$		−	40.3540i		−	1.39318i	−0.717471	−	0.696588i	$-0.754701\pi$
$839$		−	40.3540i		−	1.39318i	0.717471	−	0.696588i	$-0.245299\pi$
$840$	−109.932	+	15.0760i	−3.79302	+	0.520172i
$841$		−	28.9703i		−	0.998975i
$842$	24.4752	−	7.76537i	0.843472	−	0.267612i
$843$	−16.1954	+	16.1954i	−0.557799	+	0.557799i
$844$	−2.56661	+	14.8681i	−0.0883463	+	0.511783i
$845$	32.4992	+	32.4992i	1.11801	+	1.11801i
$846$	−5.73320	+	11.0619i	−0.197112	+	0.380314i
$847$	−20.4728			−0.703454
$848$	−9.50953	−	20.0165i	−0.326559	−	0.687368i
$849$	20.1917			0.692977
$850$	−5.80298	+	11.1965i	−0.199040	+	0.384036i
$851$	17.8505	+	17.8505i	0.611909	+	0.611909i
$852$	60.7641	+	10.4894i	2.08174	+	0.359360i
$853$	−15.6080	+	15.6080i	−0.534409	+	0.534409i	−0.921881	−	0.387472i	$-0.873348\pi$
$853$	−15.6080	+	15.6080i	−0.534409	+	0.534409i	0.387472	+	0.921881i	$0.373348\pi$
$854$	−40.0722	+	12.7139i	−1.37124	+	0.435061i
$855$		−	20.4236i		−	0.698473i
$856$	15.5713	+	11.8155i	0.532217	+	0.403846i
$857$			52.1137i			1.78017i	0.455794	+	0.890085i	$0.349355\pi$
$857$			52.1137i			1.78017i	−0.455794	+	0.890085i	$0.650645\pi$
$858$	−3.03454	−	9.56437i	−0.103597	−	0.326522i
$859$	−0.838574	+	0.838574i	−0.0286118	+	0.0286118i	−0.721268	−	0.692656i	$-0.756440\pi$
$859$	−0.838574	+	0.838574i	−0.0286118	+	0.0286118i	0.692656	+	0.721268i	$0.256440\pi$
$860$	−2.08152	+	1.46867i	−0.0709792	+	0.0500812i
$861$	2.34133	+	2.34133i	0.0797924	+	0.0797924i
$862$	−49.4429	−	25.6256i	−1.68403	−	0.872810i
$863$	15.6048			0.531193			0.265597	−	0.964084i	$-0.414431\pi$
$863$	15.6048			0.531193			0.265597	+	0.964084i	$0.414431\pi$
$864$	−0.498732	+	14.3873i	−0.0169672	+	0.489466i
$865$	−21.7338			−0.738970
$866$	20.0054	+	10.3685i	0.679811	+	0.352337i
$867$	1.55623	+	1.55623i	0.0528522	+	0.0528522i
$868$	−53.7493	+	37.9242i	−1.82437	+	1.28723i
$869$	12.9516	−	12.9516i	0.439354	−	0.439354i
$870$	−0.605516	−	1.90849i	−0.0205289	−	0.0647039i
$871$			7.90151i			0.267732i
$872$	−7.76409	+	10.2321i	−0.262925	+	0.346502i
$873$		−	12.7200i		−	0.430508i
$874$	−13.8179	+	4.38406i	−0.467396	+	0.148293i
$875$	49.3750	−	49.3750i	1.66918	−	1.66918i
$876$	20.1234	+	3.47379i	0.679905	+	0.117368i
$877$	−8.45350	−	8.45350i	−0.285455	−	0.285455i	0.549825	−	0.835280i	$-0.314694\pi$
$877$	−8.45350	−	8.45350i	−0.285455	−	0.285455i	−0.835280	+	0.549825i	$0.814694\pi$
$878$	−3.01130	+	5.81011i	−0.101626	+	0.196082i
$879$	−39.0901			−1.31848
$880$	−54.9635	−	19.5589i	−1.85282	−	0.659332i
$881$	−25.9652			−0.874791			−0.437396	−	0.899269i	$-0.644099\pi$
$881$	−25.9652			−0.874791			−0.437396	+	0.899269i	$0.644099\pi$
$882$	18.9936	−	36.6470i	0.639549	−	1.23397i
$883$	13.7025	+	13.7025i	0.461126	+	0.461126i	0.899024	−	0.437899i	$-0.144277\pi$
$883$	13.7025	+	13.7025i	0.461126	+	0.461126i	−0.437899	+	0.899024i	$0.644277\pi$
$884$	−0.280550	+	1.62520i	−0.00943590	+	0.0546614i
$885$	71.2017	−	71.2017i	2.39342	−	2.39342i
$886$	13.4544	−	4.26876i	0.452011	−	0.143412i
$887$		−	18.4368i		−	0.619046i	−0.950892	−	0.309523i	$-0.899831\pi$
$887$		−	18.4368i		−	0.619046i	0.950892	−	0.309523i	$-0.100169\pi$
$888$	6.18487	+	45.0992i	0.207551	+	1.51343i
$889$			37.1922i			1.24739i
$890$	13.5426	+	42.6840i	0.453947	+	1.43077i
$891$	30.7738	−	30.7738i	1.03096	−	1.03096i
$892$	25.2000	+	35.7155i	0.843759	+	1.19585i
$893$	10.0334	+	10.0334i	0.335754	+	0.335754i
$894$	50.7259	+	26.2905i	1.69653	+	0.879286i
$895$	−32.5195			−1.08701
$896$	−11.0359	+	52.9203i	−0.368682	+	1.76794i
$897$	6.26505			0.209184
$898$	−10.4750	−	5.42904i	−0.349555	−	0.181170i
$899$	−0.839337	−	0.839337i	−0.0279935	−	0.0279935i
$900$	18.9566	+	26.8668i	0.631885	+	0.895560i
$901$	3.91747	−	3.91747i	0.130510	−	0.130510i
$902$	0.526479	+	1.65938i	0.0175298	+	0.0552512i
$903$		−	3.59049i		−	0.119484i
$904$	−2.94911	−	21.5045i	−0.0980859	−	0.715229i
$905$		−	1.66339i		−	0.0552929i
$906$	−44.9186	+	14.2516i	−1.49232	+	0.473476i
$907$	−7.22224	+	7.22224i	−0.239811	+	0.239811i	−0.816772	−	0.576961i	$-0.804238\pi$
$907$	−7.22224	+	7.22224i	−0.239811	+	0.239811i	0.576961	+	0.816772i	$0.304238\pi$
$908$	−7.51031	+	43.5066i	−0.249238	+	1.44382i
$909$	−13.2661	−	13.2661i	−0.440010	−	0.440010i
$910$	9.56554	−	18.4561i	0.317095	−	0.611814i
$911$	−45.3286			−1.50180			−0.750902	−	0.660414i	$-0.770381\pi$
$911$	−45.3286			−1.50180			−0.750902	+	0.660414i	$0.770381\pi$
$912$	−24.6278	−	8.76390i	−0.815509	−	0.290202i
$913$	43.5000			1.43964
$914$	21.7000	−	41.8688i	0.717773	−	1.38490i
$915$	36.1198	+	36.1198i	1.19408	+	1.19408i
$916$	24.3304	+	4.20002i	0.803898	+	0.138773i
$917$	4.41687	−	4.41687i	0.145858	−	0.145858i
$918$	−3.43046	+	1.08840i	−0.113222	+	0.0359226i
$919$		−	44.2704i		−	1.46035i	−0.683262	−	0.730174i	$-0.739439\pi$
$919$		−	44.2704i		−	1.46035i	0.683262	−	0.730174i	$-0.260561\pi$
$920$	22.0184	−	29.0174i	0.725925	−	0.956676i
$921$		−	60.5621i		−	1.99559i
$922$	10.9539	+	34.5250i	0.360748	+	1.13702i
$923$	−8.16852	+	8.16852i	−0.268870	+	0.268870i
$924$	67.1853	−	47.4043i	2.21023	−	1.55949i
$925$	−46.1105	−	46.1105i	−1.51610	−	1.51610i
$926$	16.1013	+	8.34507i	0.529121	+	0.274236i
$927$	−17.0925			−0.561392
$928$	−0.974881	−	0.0337940i	−0.0320020	−	0.00110934i
$929$	−38.5009			−1.26317			−0.631586	−	0.775306i	$-0.717596\pi$
$929$	−38.5009			−1.26317			−0.631586	+	0.775306i	$0.717596\pi$
$930$	70.9624	+	36.7788i	2.32695	+	1.20603i
$931$	−33.2398	−	33.2398i	−1.08939	−	1.08939i
$932$	32.5271	−	22.9503i	1.06546	−	0.751763i
$933$	24.4716	−	24.4716i	0.801166	−	0.801166i
$934$	−2.21266	−	6.97394i	−0.0724004	−	0.228194i
$935$		−	14.5850i		−	0.476979i
$936$	3.42560	+	2.59934i	0.111969	+	0.0849622i
$937$			22.7661i			0.743738i	0.928285	+	0.371869i	$0.121283\pi$
$937$			22.7661i			0.743738i	−0.928285	+	0.371869i	$0.878717\pi$
$938$	−61.7171	+	19.5813i	−2.01513	+	0.639352i
$939$	−22.6275	+	22.6275i	−0.738422	+	0.738422i
$940$	−35.1337	−	6.06494i	−1.14593	−	0.197817i
$941$	0.673191	+	0.673191i	0.0219454	+	0.0219454i	0.717994	−	0.696049i	$-0.245060\pi$
$941$	0.673191	+	0.673191i	0.0219454	+	0.0219454i	−0.696049	+	0.717994i	$0.745060\pi$
$942$	−31.1401	+	60.0828i	−1.01460	+	1.95760i
$943$	−1.08696			−0.0353963
$944$	−21.0513	−	44.3105i	−0.685161	−	1.44218i
$945$	45.3631			1.47566
$946$	0.868664	−	1.67603i	0.0282427	−	0.0544925i
$947$	31.0251	+	31.0251i	1.00818	+	1.00818i	0.999966	+	0.00821537i	$0.00261506\pi$
$947$	31.0251	+	31.0251i	1.00818	+	1.00818i	0.00821537	+	0.999966i	$0.497385\pi$
$948$	−3.50797	+	20.3214i	−0.113934	+	0.660008i
$949$	−2.70519	+	2.70519i	−0.0878141	+	0.0878141i
$950$	35.6935	−	11.3247i	1.15805	−	0.367421i
$951$			52.7730i			1.71128i
$952$	−13.3894	+	1.83621i	−0.433952	+	0.0595118i
$953$			7.81896i			0.253281i	0.991949	+	0.126640i	$0.0404194\pi$
$953$			7.81896i			0.253281i	−0.991949	+	0.126640i	$0.959581\pi$
$954$	−4.36848	−	13.7687i	−0.141435	−	0.445779i
$955$	1.89668	−	1.89668i	0.0613752	−	0.0613752i
$956$	1.44230	+	2.04414i	0.0466472	+	0.0661122i
$957$	1.04915	+	1.04915i	0.0339142	+	0.0339142i
$958$	9.29898	+	4.81953i	0.300436	+	0.155712i
$959$	69.1350			2.23249
$960$	63.2583	−	17.6830i	2.04165	−	0.570715i
$961$	16.3837			0.528506
$962$	−7.57155	−	3.92423i	−0.244116	−	0.126522i
$963$	9.00946	+	9.00946i	0.290326	+	0.290326i
$964$	−4.36895	−	6.19204i	−0.140714	−	0.199432i
$965$	−13.1744	+	13.1744i	−0.424100	+	0.424100i
$966$	15.5259	+	48.9351i	0.499537	+	1.57446i
$967$		−	9.01506i		−	0.289905i	−0.989439	−	0.144952i	$-0.953697\pi$
$967$		−	9.01506i		−	0.289905i	0.989439	−	0.144952i	$-0.0463029\pi$
$968$	12.0065	−	1.64656i	0.385903	−	0.0529224i
$969$		−	6.53517i		−	0.209940i
$970$	34.6951	−	11.0079i	1.11399	−	0.353441i
$971$	−26.1717	+	26.1717i	−0.839889	+	0.839889i	−0.988844	−	0.148955i	$-0.952409\pi$
$971$	−26.1717	+	26.1717i	−0.839889	+	0.839889i	0.148955	+	0.988844i	$0.452409\pi$
$972$	−5.73772	+	33.2381i	−0.184037	+	1.06611i
$973$	69.9042	+	69.9042i	2.24103	+	2.24103i
$974$	13.5573	−	26.1580i	0.434404	−	0.838155i
$975$	−16.1835			−0.518288
$976$	22.4782	−	10.6791i	0.719510	−	0.341829i
$977$	41.3479			1.32284			0.661418	−	0.750018i	$-0.269955\pi$
$977$	41.3479			1.32284			0.661418	+	0.750018i	$0.269955\pi$
$978$	−9.15334	+	17.6608i	−0.292692	+	0.564730i
$979$	−23.4646	−	23.4646i	−0.749931	−	0.749931i
$980$	116.395	+	20.0927i	3.71810	+	0.641836i
$981$	−5.92021	+	5.92021i	−0.189018	+	0.189018i
$982$	−51.4130	+	16.3121i	−1.64065	+	0.520539i
$983$		−	3.23290i		−	0.103113i	−0.998670	−	0.0515567i	$-0.983582\pi$
$983$		−	3.23290i		−	0.103113i	0.998670	−	0.0515567i	$-0.0164183\pi$
$984$	−1.56140	−	1.18479i	−0.0497757	−	0.0377698i
$985$		−	1.02287i		−	0.0325913i
$986$	−0.0737498	−	0.232448i	−0.00234867	−	0.00740264i
$987$	35.5326	−	35.5326i	1.13101	−	1.13101i
$988$	4.00148	−	2.82334i	0.127304	−	0.0898225i
$989$	0.833440	+	0.833440i	0.0265018	+	0.0265018i
$990$	−33.7629	−	17.4989i	−1.07306	−	0.556150i
$991$	26.1472			0.830592			0.415296	−	0.909686i	$-0.363678\pi$
$991$	26.1472			0.830592			0.415296	+	0.909686i	$0.363678\pi$
$992$	28.4717	−	26.5639i	0.903977	−	0.843405i
$993$	8.92795			0.283320
$994$	−84.0457	−	43.5597i	−2.66577	−	1.38163i
$995$	27.7899	+	27.7899i	0.880999	+	0.880999i
$996$	−40.0172	+	28.2352i	−1.26799	+	0.894666i
$997$	37.1931	−	37.1931i	1.17792	−	1.17792i	0.197644	−	0.980274i	$-0.436671\pi$
$997$	37.1931	−	37.1931i	1.17792	−	1.17792i	0.980274	−	0.197644i	$-0.0633291\pi$
$998$	−3.68554	−	11.6162i	−0.116664	−	0.367705i
$999$		−	18.6100i		−	0.588796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.b.205.13	yes	30
4.3	odd	2		1088.2.l.b.273.3		30
16.5	even	4	inner	272.2.l.b.69.13	✓	30
16.11	odd	4		1088.2.l.b.817.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.b.69.13	✓	30	16.5	even	4	inner
272.2.l.b.205.13	yes	30	1.1	even	1	trivial
1088.2.l.b.273.3		30	4.3	odd	2
1088.2.l.b.817.3		30	16.11	odd	4

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:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25559 + 0.650757i) q^{2} +(1.55623 + 1.55623i) q^{3} +(1.15303 + 1.63417i) q^{4} +(-2.63792 + 2.63792i) q^{5} +(0.941264 + 2.96671i) q^{6} -4.77816i q^{7} +(0.384292 + 2.80220i) q^{8} +1.84368i q^{9} +(-5.02881 + 1.59551i) q^{10} +(2.76448 - 2.76448i) q^{11} +(-0.748763 + 4.33752i) q^{12} +(-0.583093 - 0.583093i) q^{13} +(3.10942 - 5.99943i) q^{14} -8.21041 q^{15} +(-1.34104 + 3.76850i) q^{16} -1.00000 q^{17} +(-1.19979 + 2.31492i) q^{18} +(2.09969 + 2.09969i) q^{19} +(-7.35243 - 1.26921i) q^{20} +(7.43590 - 7.43590i) q^{21} +(5.27006 - 1.67206i) q^{22} +3.45210i q^{23} +(-3.76281 + 4.95890i) q^{24} -8.91728i q^{25} +(-0.352677 - 1.11158i) q^{26} +(1.79949 - 1.79949i) q^{27} +(7.80834 - 5.50937i) q^{28} +(0.121933 + 0.121933i) q^{29} +(-10.3089 - 5.34298i) q^{30} -6.88358 q^{31} +(-4.13617 + 3.85902i) q^{32} +8.60430 q^{33} +(-1.25559 - 0.650757i) q^{34} +(12.6044 + 12.6044i) q^{35} +(-3.01289 + 2.12582i) q^{36} +(5.17091 - 5.17091i) q^{37} +(1.26997 + 4.00274i) q^{38} -1.81485i q^{39} +(-8.40572 - 6.37825i) q^{40} +0.314869i q^{41} +(14.1754 - 4.49751i) q^{42} +(0.241429 - 0.241429i) q^{43} +(7.70516 + 1.33010i) q^{44} +(-4.86349 - 4.86349i) q^{45} +(-2.24648 + 4.33444i) q^{46} +4.77851 q^{47} +(-7.95160 + 3.77769i) q^{48} -15.8308 q^{49} +(5.80298 - 11.1965i) q^{50} +(-1.55623 - 1.55623i) q^{51} +(0.280550 - 1.62520i) q^{52} +(-3.91747 + 3.91747i) q^{53} +(3.43046 - 1.08840i) q^{54} +14.5850i q^{55} +(13.3894 - 1.83621i) q^{56} +6.53517i q^{57} +(0.0737498 + 0.232448i) q^{58} +(-8.67212 + 8.67212i) q^{59} +(-9.46687 - 13.4172i) q^{60} +(-4.39926 - 4.39926i) q^{61} +(-8.64298 - 4.47954i) q^{62} +8.80941 q^{63} +(-7.70464 + 2.15372i) q^{64} +3.07631 q^{65} +(10.8035 + 5.59931i) q^{66} +(-6.77551 - 6.77551i) q^{67} +(-1.15303 - 1.63417i) q^{68} +(-5.37226 + 5.37226i) q^{69} +(7.62362 + 24.0284i) q^{70} -14.0089i q^{71} +(-5.16636 + 0.708511i) q^{72} -4.63937i q^{73} +(9.85757 - 3.12756i) q^{74} +(13.8773 - 13.8773i) q^{75} +(-1.01024 + 5.85225i) q^{76} +(-13.2091 - 13.2091i) q^{77} +(1.18103 - 2.27872i) q^{78} +4.68502 q^{79} +(-6.40348 - 13.4786i) q^{80} +11.1319 q^{81} +(-0.204903 + 0.395347i) q^{82} +(7.86768 + 7.86768i) q^{83} +(20.7254 + 3.57771i) q^{84} +(2.63792 - 2.63792i) q^{85} +(0.460249 - 0.146025i) q^{86} +0.379512i q^{87} +(8.80898 + 6.68425i) q^{88} -8.48789i q^{89} +(-2.94162 - 9.27152i) q^{90} +(-2.78611 + 2.78611i) q^{91} +(-5.64133 + 3.98039i) q^{92} +(-10.7124 - 10.7124i) q^{93} +(5.99987 + 3.10965i) q^{94} -11.0776 q^{95} +(-12.4423 - 0.431311i) q^{96} -6.89926 q^{97} +(-19.8771 - 10.3020i) q^{98} +(5.09682 + 5.09682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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