LMFDB - Embedded newform 570.2.k.a.77.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.13
Character	$\chi$	$=$	570.77
Dual form			570.2.k.a.533.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.518471 - 1.65263i) q^{3} -1.00000i q^{4} +(-2.11139 + 0.736229i) q^{5} +(-1.53520 - 0.801972i) q^{6} +(-2.44114 - 2.44114i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.46238 + 1.71368i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.518471 - 1.65263i) q^{3} -1.00000i q^{4} +(-2.11139 + 0.736229i) q^{5} +(-1.53520 - 0.801972i) q^{6} +(-2.44114 - 2.44114i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.46238 + 1.71368i) q^{9} +(-0.972386 + 2.01357i) q^{10} +5.62118i q^{11} +(-1.65263 + 0.518471i) q^{12} +(0.933851 - 0.933851i) q^{13} -3.45230 q^{14} +(2.31141 + 3.10763i) q^{15} -1.00000 q^{16} +(0.0532613 - 0.0532613i) q^{17} +(-0.529408 + 2.95292i) q^{18} +1.00000i q^{19} +(0.736229 + 2.11139i) q^{20} +(-2.76865 + 5.29997i) q^{21} +(3.97477 + 3.97477i) q^{22} +(-0.841693 - 0.841693i) q^{23} +(-0.801972 + 1.53520i) q^{24} +(3.91593 - 3.10893i) q^{25} -1.32067i q^{26} +(4.10875 + 3.18091i) q^{27} +(-2.44114 + 2.44114i) q^{28} -6.56484 q^{29} +(3.83184 + 0.563017i) q^{30} -5.11218 q^{31} +(-0.707107 + 0.707107i) q^{32} +(9.28973 - 2.91441i) q^{33} -0.0753229i q^{34} +(6.95144 + 3.35696i) q^{35} +(1.71368 + 2.46238i) q^{36} +(-5.88633 - 5.88633i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-2.02749 - 1.05914i) q^{39} +(2.01357 + 0.972386i) q^{40} -5.75913i q^{41} +(1.78991 + 5.70537i) q^{42} +(-7.57828 + 7.57828i) q^{43} +5.62118 q^{44} +(3.93738 - 5.43112i) q^{45} -1.19033 q^{46} +(2.64154 - 2.64154i) q^{47} +(0.518471 + 1.65263i) q^{48} +4.91834i q^{49} +(0.570637 - 4.96733i) q^{50} +(-0.115636 - 0.0604069i) q^{51} +(-0.933851 - 0.933851i) q^{52} +(-9.67459 - 9.67459i) q^{53} +(5.15457 - 0.656086i) q^{54} +(-4.13847 - 11.8685i) q^{55} +3.45230i q^{56} +(1.65263 - 0.518471i) q^{57} +(-4.64204 + 4.64204i) q^{58} -11.0697 q^{59} +(3.10763 - 2.31141i) q^{60} +9.82484 q^{61} +(-3.61486 + 3.61486i) q^{62} +(10.1943 + 1.82767i) q^{63} +1.00000i q^{64} +(-1.28420 + 2.65925i) q^{65} +(4.50803 - 8.62963i) q^{66} +(6.27631 + 6.27631i) q^{67} +(-0.0532613 - 0.0532613i) q^{68} +(-0.954615 + 1.82740i) q^{69} +(7.28914 - 2.54168i) q^{70} +2.29302i q^{71} +(2.95292 + 0.529408i) q^{72} +(-7.35442 + 7.35442i) q^{73} -8.32453 q^{74} +(-7.16821 - 4.85970i) q^{75} +1.00000 q^{76} +(13.7221 - 13.7221i) q^{77} +(-2.18257 + 0.684726i) q^{78} +3.41806i q^{79} +(2.11139 - 0.736229i) q^{80} +(3.12659 - 8.43946i) q^{81} +(-4.07232 - 4.07232i) q^{82} +(4.84479 + 4.84479i) q^{83} +(5.29997 + 2.76865i) q^{84} +(-0.0732429 + 0.151668i) q^{85} +10.7173i q^{86} +(3.40368 + 10.8493i) q^{87} +(3.97477 - 3.97477i) q^{88} +4.69409 q^{89} +(-1.05624 - 6.62453i) q^{90} -4.55933 q^{91} +(-0.841693 + 0.841693i) q^{92} +(2.65052 + 8.44855i) q^{93} -3.73570i q^{94} +(-0.736229 - 2.11139i) q^{95} +(1.53520 + 0.801972i) q^{96} +(-4.18214 - 4.18214i) q^{97} +(3.47779 + 3.47779i) q^{98} +(-9.63290 - 13.8415i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.518471	−	1.65263i	−0.299339	−	0.954147i
$3$	−0.518471	−	1.65263i	−0.299339	−	0.954147i
$4$		−	1.00000i		−	0.500000i
$5$	−2.11139	+	0.736229i	−0.944242	+	0.329251i
$5$	−2.11139	+	0.736229i	−0.944242	+	0.329251i
$6$	−1.53520	−	0.801972i	−0.626743	−	0.327404i
$7$	−2.44114	−	2.44114i	−0.922665	−	0.922665i	0.0745524	−	0.997217i	$-0.476247\pi$
$7$	−2.44114	−	2.44114i	−0.922665	−	0.922665i	−0.997217	+	0.0745524i	$0.976247\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.46238	+	1.71368i	−0.820792	+	0.571227i
$10$	−0.972386	+	2.01357i	−0.307495	+	0.636747i
$11$			5.62118i			1.69485i	0.530916	+	0.847424i	$0.321848\pi$
$11$			5.62118i			1.69485i	−0.530916	+	0.847424i	$0.678152\pi$
$12$	−1.65263	+	0.518471i	−0.477073	+	0.149670i
$13$	0.933851	−	0.933851i	0.259004	−	0.259004i	−0.565645	−	0.824649i	$-0.691373\pi$
$13$	0.933851	−	0.933851i	0.259004	−	0.259004i	0.824649	+	0.565645i	$0.191373\pi$
$14$	−3.45230			−0.922665
$15$	2.31141	+	3.10763i	0.596803	+	0.802388i
$16$	−1.00000			−0.250000
$17$	0.0532613	−	0.0532613i	0.0129178	−	0.0129178i	−0.700618	−	0.713536i	$-0.747092\pi$
$17$	0.0532613	−	0.0532613i	0.0129178	−	0.0129178i	0.713536	+	0.700618i	$0.247092\pi$
$18$	−0.529408	+	2.95292i	−0.124783	+	0.696010i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	0.736229	+	2.11139i	0.164626	+	0.472121i
$21$	−2.76865	+	5.29997i	−0.604168	+	1.15655i
$22$	3.97477	+	3.97477i	0.847424	+	0.847424i
$23$	−0.841693	−	0.841693i	−0.175505	−	0.175505i	0.613888	−	0.789393i	$-0.289605\pi$
$23$	−0.841693	−	0.841693i	−0.175505	−	0.175505i	−0.789393	+	0.613888i	$0.789605\pi$
$24$	−0.801972	+	1.53520i	−0.163702	+	0.313371i
$25$	3.91593	−	3.10893i	0.783187	−	0.621786i
$26$		−	1.32067i		−	0.259004i
$27$	4.10875	+	3.18091i	0.790730	+	0.612166i
$28$	−2.44114	+	2.44114i	−0.461332	+	0.461332i
$29$	−6.56484			−1.21906			−0.609530	−	0.792763i	$-0.708642\pi$
$29$	−6.56484			−1.21906			−0.609530	+	0.792763i	$0.708642\pi$
$30$	3.83184	+	0.563017i	0.699595	+	0.102792i
$31$	−5.11218			−0.918175			−0.459087	−	0.888391i	$-0.651824\pi$
$31$	−5.11218			−0.918175			−0.459087	+	0.888391i	$0.651824\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	9.28973	−	2.91441i	1.61713	−	0.507335i
$34$		−	0.0753229i		−	0.0129178i
$35$	6.95144	+	3.35696i	1.17501	+	0.567430i
$36$	1.71368	+	2.46238i	0.285614	+	0.410396i
$37$	−5.88633	−	5.88633i	−0.967707	−	0.967707i	0.0317880	−	0.999495i	$-0.489880\pi$
$37$	−5.88633	−	5.88633i	−0.967707	−	0.967707i	−0.999495	+	0.0317880i	$0.989880\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$	−2.02749	−	1.05914i	−0.324658	−	0.169598i
$40$	2.01357	+	0.972386i	0.318373	+	0.153748i
$41$		−	5.75913i		−	0.899426i	−0.893173	−	0.449713i	$-0.851526\pi$
$41$		−	5.75913i		−	0.899426i	0.893173	−	0.449713i	$-0.148474\pi$
$42$	1.78991	+	5.70537i	0.276190	+	0.880358i
$43$	−7.57828	+	7.57828i	−1.15568	+	1.15568i	−0.170282	+	0.985395i	$0.554468\pi$
$43$	−7.57828	+	7.57828i	−1.15568	+	1.15568i	−0.985395	+	0.170282i	$0.945532\pi$
$44$	5.62118			0.847424
$45$	3.93738	−	5.43112i	0.586949	−	0.809624i
$46$	−1.19033			−0.175505
$47$	2.64154	−	2.64154i	0.385308	−	0.385308i	−0.487702	−	0.873010i	$-0.662165\pi$
$47$	2.64154	−	2.64154i	0.385308	−	0.385308i	0.873010	+	0.487702i	$0.162165\pi$
$48$	0.518471	+	1.65263i	0.0748348	+	0.238537i
$49$			4.91834i			0.702620i
$50$	0.570637	−	4.96733i	0.0807003	−	0.702487i
$51$	−0.115636	−	0.0604069i	−0.0161922	−	0.00845865i
$52$	−0.933851	−	0.933851i	−0.129502	−	0.129502i
$53$	−9.67459	−	9.67459i	−1.32891	−	1.32891i	−0.906324	−	0.422583i	$-0.861124\pi$
$53$	−9.67459	−	9.67459i	−1.32891	−	1.32891i	−0.422583	−	0.906324i	$-0.638876\pi$
$54$	5.15457	−	0.656086i	0.701448	−	0.0892821i
$55$	−4.13847	−	11.8685i	−0.558031	−	1.60035i
$56$			3.45230i			0.461332i
$57$	1.65263	−	0.518471i	0.218896	−	0.0686731i
$58$	−4.64204	+	4.64204i	−0.609530	+	0.609530i
$59$	−11.0697			−1.44116			−0.720579	−	0.693373i	$-0.756124\pi$
$59$	−11.0697			−1.44116			−0.720579	+	0.693373i	$0.756124\pi$
$60$	3.10763	−	2.31141i	0.401194	−	0.298401i
$61$	9.82484			1.25794			0.628971	−	0.777429i	$-0.283476\pi$
$61$	9.82484			1.25794			0.628971	+	0.777429i	$0.283476\pi$
$62$	−3.61486	+	3.61486i	−0.459087	+	0.459087i
$63$	10.1943	+	1.82767i	1.28437	+	0.230265i
$64$			1.00000i			0.125000i
$65$	−1.28420	+	2.65925i	−0.159285	+	0.329840i
$66$	4.50803	−	8.62963i	0.554900	−	1.06223i
$67$	6.27631	+	6.27631i	0.766774	+	0.766774i	0.977537	−	0.210764i	$-0.0675950\pi$
$67$	6.27631	+	6.27631i	0.766774	+	0.766774i	−0.210764	+	0.977537i	$0.567595\pi$
$68$	−0.0532613	−	0.0532613i	−0.00645888	−	0.00645888i
$69$	−0.954615	+	1.82740i	−0.114922	+	0.219993i
$70$	7.28914	−	2.54168i	0.871219	−	0.303789i
$71$			2.29302i			0.272131i	0.990700	+	0.136066i	$0.0434458\pi$
$71$			2.29302i			0.272131i	−0.990700	+	0.136066i	$0.956554\pi$
$72$	2.95292	+	0.529408i	0.348005	+	0.0623913i
$73$	−7.35442	+	7.35442i	−0.860770	+	0.860770i	−0.991428	−	0.130658i	$-0.958291\pi$
$73$	−7.35442	+	7.35442i	−0.860770	+	0.860770i	0.130658	+	0.991428i	$0.458291\pi$
$74$	−8.32453			−0.967707
$75$	−7.16821	−	4.85970i	−0.827714	−	0.561150i
$76$	1.00000			0.114708
$77$	13.7221	−	13.7221i	1.56378	−	1.56378i
$78$	−2.18257	+	0.684726i	−0.247128	+	0.0775300i
$79$			3.41806i			0.384561i	0.981340	+	0.192281i	$0.0615884\pi$
$79$			3.41806i			0.384561i	−0.981340	+	0.192281i	$0.938412\pi$
$80$	2.11139	−	0.736229i	0.236061	−	0.0823129i
$81$	3.12659	−	8.43946i	0.347399	−	0.937717i
$82$	−4.07232	−	4.07232i	−0.449713	−	0.449713i
$83$	4.84479	+	4.84479i	0.531785	+	0.531785i	0.921103	−	0.389318i	$-0.127289\pi$
$83$	4.84479	+	4.84479i	0.531785	+	0.531785i	−0.389318	+	0.921103i	$0.627289\pi$
$84$	5.29997	+	2.76865i	0.578274	+	0.302084i
$85$	−0.0732429	+	0.151668i	−0.00794431	+	0.0164507i
$86$			10.7173i			1.15568i
$87$	3.40368	+	10.8493i	0.364912	+	1.16316i
$88$	3.97477	−	3.97477i	0.423712	−	0.423712i
$89$	4.69409			0.497572			0.248786	−	0.968558i	$-0.419968\pi$
$89$	4.69409			0.497572			0.248786	+	0.968558i	$0.419968\pi$
$90$	−1.05624	−	6.62453i	−0.111337	−	0.698286i
$91$	−4.55933			−0.477947
$92$	−0.841693	+	0.841693i	−0.0877526	+	0.0877526i
$93$	2.65052	+	8.44855i	0.274846	+	0.876073i
$94$		−	3.73570i		−	0.385308i
$95$	−0.736229	−	2.11139i	−0.0755355	−	0.216624i
$96$	1.53520	+	0.801972i	0.156686	+	0.0818509i
$97$	−4.18214	−	4.18214i	−0.424632	−	0.424632i	0.462163	−	0.886795i	$-0.347073\pi$
$97$	−4.18214	−	4.18214i	−0.424632	−	0.424632i	−0.886795	+	0.462163i	$0.847073\pi$
$98$	3.47779	+	3.47779i	0.351310	+	0.351310i
$99$	−9.63290	−	13.8415i	−0.968143	−	1.39112i
$100$	−3.10893	−	3.91593i	−0.310893	−	0.391593i
$101$		−	0.845280i		−	0.0841085i	−0.999115	−	0.0420543i	$-0.986610\pi$
$101$		−	0.845280i		−	0.0841085i	0.999115	−	0.0420543i	$-0.0133902\pi$
$102$	−0.124481	+	0.0390527i	−0.0123254	+	0.00386679i
$103$	1.72028	−	1.72028i	0.169505	−	0.169505i	−0.617257	−	0.786762i	$-0.711756\pi$
$103$	1.72028	−	1.72028i	0.169505	−	0.169505i	0.786762	+	0.617257i	$0.211756\pi$
$104$	−1.32067			−0.129502
$105$	1.94370	−	13.2286i	0.189686	−	1.29098i
$106$	−13.6819			−1.32891
$107$	6.17999	−	6.17999i	0.597442	−	0.597442i	−0.342189	−	0.939631i	$-0.611168\pi$
$107$	6.17999	−	6.17999i	0.597442	−	0.597442i	0.939631	+	0.342189i	$0.111168\pi$
$108$	3.18091	−	4.10875i	0.306083	−	0.395365i
$109$		−	13.7634i		−	1.31830i	−0.752012	−	0.659149i	$-0.770917\pi$
$109$		−	13.7634i		−	1.31830i	0.752012	−	0.659149i	$-0.229083\pi$
$110$	−11.3186	−	5.46595i	−1.07919	−	0.521158i
$111$	−6.67604	+	12.7798i	−0.633662	+	1.21301i
$112$	2.44114	+	2.44114i	0.230666	+	0.230666i
$113$	−13.5833	−	13.5833i	−1.27781	−	1.27781i	−0.941892	−	0.335915i	$-0.890955\pi$
$113$	−13.5833	−	13.5833i	−1.27781	−	1.27781i	−0.335915	−	0.941892i	$-0.609045\pi$
$114$	0.801972	−	1.53520i	0.0751116	−	0.143785i
$115$	2.39682	+	1.15746i	0.223505	+	0.107934i
$116$			6.56484i			0.609530i
$117$	−0.699170	+	3.89982i	−0.0646383	+	0.360538i
$118$	−7.82749	+	7.82749i	−0.720579	+	0.720579i
$119$	−0.260037			−0.0238375
$120$	0.563017	−	3.83184i	0.0513962	−	0.349798i
$121$	−20.5976			−1.87251
$122$	6.94721	−	6.94721i	0.628971	−	0.628971i
$123$	−9.51772	+	2.98594i	−0.858184	+	0.269233i
$124$			5.11218i			0.459087i
$125$	−5.97918	+	9.44719i	−0.534794	+	0.844982i
$126$	8.50085	−	5.91613i	0.757316	−	0.527051i
$127$	−4.84183	−	4.84183i	−0.429643	−	0.429643i	0.458864	−	0.888507i	$-0.348257\pi$
$127$	−4.84183	−	4.84183i	−0.429643	−	0.429643i	−0.888507	+	0.458864i	$0.848257\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	16.4532	+	8.59499i	1.44863	+	0.756746i
$130$	0.972312	+	2.78844i	0.0852774	+	0.244562i
$131$			0.132969i			0.0116176i	0.999983	+	0.00580880i	$0.00184901\pi$
$131$			0.132969i			0.0116176i	−0.999983	+	0.00580880i	$0.998151\pi$
$132$	−2.91441	−	9.28973i	−0.253667	−	0.808567i
$133$	2.44114	−	2.44114i	0.211674	−	0.211674i
$134$	8.87605			0.766774
$135$	−11.0171	−	3.69115i	−0.948197	−	0.317684i
$136$	−0.0753229			−0.00645888
$137$	11.8447	−	11.8447i	1.01196	−	1.01196i	0.0120322	−	0.999928i	$-0.496170\pi$
$137$	11.8447	−	11.8447i	1.01196	−	1.01196i	0.999928	−	0.0120322i	$-0.00383006\pi$
$138$	0.617153	+	1.96718i	0.0525356	+	0.167458i
$139$		−	11.4478i		−	0.970986i	−0.874241	−	0.485493i	$-0.838640\pi$
$139$		−	11.4478i		−	0.970986i	0.874241	−	0.485493i	$-0.161360\pi$
$140$	3.35696	−	6.95144i	0.283715	−	0.587504i
$141$	−5.73505	−	2.99593i	−0.482978	−	0.252303i
$142$	1.62141	+	1.62141i	0.136066	+	0.136066i
$143$	5.24934	+	5.24934i	0.438972	+	0.438972i
$144$	2.46238	−	1.71368i	0.205198	−	0.142807i
$145$	13.8609	−	4.83322i	1.15109	−	0.401377i
$146$			10.4007i			0.860770i
$147$	8.12820	−	2.55002i	0.670403	−	0.210322i
$148$	−5.88633	+	5.88633i	−0.483853	+	0.483853i
$149$	21.7749			1.78387			0.891934	−	0.452165i	$-0.149348\pi$
$149$	21.7749			1.78387			0.891934	+	0.452165i	$0.149348\pi$
$150$	−8.50502	+	1.63236i	−0.694432	+	0.133282i
$151$	−12.9880			−1.05694			−0.528472	−	0.848951i	$-0.677235\pi$
$151$	−12.9880			−1.05694			−0.528472	+	0.848951i	$0.677235\pi$
$152$	0.707107	−	0.707107i	0.0573539	−	0.0573539i
$153$	−0.0398765	+	0.222422i	−0.00322382	+	0.0179818i
$154$		−	19.4060i		−	1.56378i
$155$	10.7938	−	3.76373i	0.866979	−	0.302310i
$156$	−1.05914	+	2.02749i	−0.0847988	+	0.162329i
$157$	10.2762	+	10.2762i	0.820131	+	0.820131i	0.986127	−	0.165995i	$-0.0530837\pi$
$157$	10.2762	+	10.2762i	0.820131	+	0.820131i	−0.165995	+	0.986127i	$0.553084\pi$
$158$	2.41693	+	2.41693i	0.192281	+	0.192281i
$159$	−10.9725	+	21.0045i	−0.870178	+	1.66577i
$160$	0.972386	−	2.01357i	0.0768738	−	0.159187i
$161$			4.10938i			0.323865i
$162$	−3.75676	−	8.17843i	−0.295159	−	0.642558i
$163$	4.97451	−	4.97451i	0.389634	−	0.389634i	−0.484923	−	0.874557i	$-0.661152\pi$
$163$	4.97451	−	4.97451i	0.389634	−	0.389634i	0.874557	+	0.484923i	$0.161152\pi$
$164$	−5.75913			−0.449713
$165$	−17.4686	+	12.9928i	−1.35993	+	1.01149i
$166$	6.85157			0.531785
$167$	11.3116	−	11.3116i	0.875319	−	0.875319i	−0.117727	−	0.993046i	$-0.537561\pi$
$167$	11.3116	−	11.3116i	0.875319	−	0.875319i	0.993046	+	0.117727i	$0.0375607\pi$
$168$	5.70537	−	1.78991i	0.440179	−	0.138095i
$169$			11.2558i			0.865834i
$170$	0.0554549	+	0.159036i	0.00425319	+	0.0121975i
$171$	−1.71368	−	2.46238i	−0.131048	−	0.188303i
$172$	7.57828	+	7.57828i	0.577839	+	0.577839i
$173$	16.5624	+	16.5624i	1.25921	+	1.25921i	0.951468	+	0.307746i	$0.0995748\pi$
$173$	16.5624	+	16.5624i	1.25921	+	1.25921i	0.307746	+	0.951468i	$0.400425\pi$
$174$	10.0783	+	5.26482i	0.764037	+	0.399125i
$175$	−17.1487	−	1.97001i	−1.29632	−	0.148919i
$176$		−	5.62118i		−	0.423712i
$177$	5.73934	+	18.2942i	0.431395	+	1.37508i
$178$	3.31922	−	3.31922i	0.248786	−	0.248786i
$179$	−13.4740			−1.00710			−0.503549	−	0.863967i	$-0.667973\pi$
$179$	−13.4740			−1.00710			−0.503549	+	0.863967i	$0.667973\pi$
$180$	−5.43112	−	3.93738i	−0.404812	−	0.293475i
$181$	10.4967			0.780217			0.390108	−	0.920769i	$-0.372438\pi$
$181$	10.4967			0.780217			0.390108	+	0.920769i	$0.372438\pi$
$182$	−3.22393	+	3.22393i	−0.238974	+	0.238974i
$183$	−5.09389	−	16.2368i	−0.376551	−	1.20026i
$184$			1.19033i			0.0877526i
$185$	16.7620	+	8.09465i	1.23237	+	0.595131i
$186$	7.84822	+	4.09983i	0.575460	+	0.300614i
$187$	0.299391	+	0.299391i	0.0218937	+	0.0218937i
$188$	−2.64154	−	2.64154i	−0.192654	−	0.192654i
$189$	−2.26500	−	17.7951i	−0.164755	−	1.29440i
$190$	−2.01357	−	0.972386i	−0.146080	−	0.0705443i
$191$			16.2464i			1.17555i	0.809024	+	0.587775i	$0.199996\pi$
$191$			16.2464i			1.17555i	−0.809024	+	0.587775i	$0.800004\pi$
$192$	1.65263	−	0.518471i	0.119268	−	0.0374174i
$193$	−2.23569	+	2.23569i	−0.160928	+	0.160928i	−0.782978	−	0.622049i	$-0.786300\pi$
$193$	−2.23569	+	2.23569i	−0.160928	+	0.160928i	0.622049	+	0.782978i	$0.286300\pi$
$194$	−5.91443			−0.424632
$195$	5.06058	+	0.743558i	0.362396	+	0.0532473i
$196$	4.91834			0.351310
$197$	−5.51445	+	5.51445i	−0.392889	+	0.392889i	−0.875716	−	0.482827i	$-0.839610\pi$
$197$	−5.51445	+	5.51445i	−0.392889	+	0.392889i	0.482827	+	0.875716i	$0.339610\pi$
$198$	−16.5989	−	2.97589i	−1.17963	−	0.211488i
$199$		−	22.3312i		−	1.58302i	−0.611159	−	0.791508i	$-0.709297\pi$
$199$		−	22.3312i		−	1.58302i	0.611159	−	0.791508i	$-0.290703\pi$
$200$	−4.96733	−	0.570637i	−0.351243	−	0.0403501i
$201$	7.11834	−	13.6265i	0.502089	−	0.961140i
$202$	−0.597703	−	0.597703i	−0.0420543	−	0.0420543i
$203$	16.0257	+	16.0257i	1.12478	+	1.12478i
$204$	−0.0604069	+	0.115636i	−0.00422933	+	0.00809612i
$205$	4.24004	+	12.1598i	0.296137	+	0.849276i
$206$		−	2.43285i		−	0.169505i
$207$	3.51496	+	0.630172i	0.244307	+	0.0438000i
$208$	−0.933851	+	0.933851i	−0.0647509	+	0.0647509i
$209$	−5.62118			−0.388825
$210$	−7.97966	−	10.7285i	−0.550649	−	0.740335i
$211$	−4.91417			−0.338305			−0.169153	−	0.985590i	$-0.554103\pi$
$211$	−4.91417			−0.338305			−0.169153	+	0.985590i	$0.554103\pi$
$212$	−9.67459	+	9.67459i	−0.664454	+	0.664454i
$213$	3.78951	−	1.18886i	0.259653	−	0.0814595i
$214$		−	8.73982i		−	0.597442i
$215$	10.4214	−	21.5801i	0.710731	−	1.47175i
$216$	−0.656086	−	5.15457i	−0.0446410	−	0.350724i
$217$	12.4796	+	12.4796i	0.847167	+	0.847167i
$218$	−9.73222	−	9.73222i	−0.659149	−	0.659149i
$219$	15.9672	+	8.34109i	1.07896	+	0.563639i
$220$	−11.8685	+	4.13847i	−0.800174	+	0.279016i
$221$		−	0.0994763i		−	0.00669150i
$222$	4.31602	+	13.7574i	0.289673	+	0.923334i
$223$	−6.07075	+	6.07075i	−0.406527	+	0.406527i	−0.880526	−	0.473998i	$-0.842810\pi$
$223$	−6.07075	+	6.07075i	−0.406527	+	0.406527i	0.473998	+	0.880526i	$0.342810\pi$
$224$	3.45230			0.230666
$225$	−4.31479	+	14.3660i	−0.287652	+	0.957735i
$226$	−19.2097			−1.27781
$227$	−12.5348	+	12.5348i	−0.831965	+	0.831965i	−0.987785	−	0.155820i	$-0.950198\pi$
$227$	−12.5348	+	12.5348i	−0.831965	+	0.831965i	0.155820	+	0.987785i	$0.450198\pi$
$228$	−0.518471	−	1.65263i	−0.0343366	−	0.109448i
$229$			4.03489i			0.266633i	0.991073	+	0.133317i	$0.0425627\pi$
$229$			4.03489i			0.266633i	−0.991073	+	0.133317i	$0.957437\pi$
$230$	2.51326	−	0.876358i	0.165719	−	0.0577853i
$231$	−29.7920	−	15.5630i	−1.96017	−	1.02397i
$232$	4.64204	+	4.64204i	0.304765	+	0.304765i
$233$	−13.7826	−	13.7826i	−0.902931	−	0.902931i	0.0927575	−	0.995689i	$-0.470432\pi$
$233$	−13.7826	−	13.7826i	−0.902931	−	0.902931i	−0.995689	+	0.0927575i	$0.970432\pi$
$234$	2.26320	+	3.25198i	0.147950	+	0.212588i
$235$	−3.63254	+	7.52210i	−0.236961	+	0.490688i
$236$			11.0697i			0.720579i
$237$	5.64879	−	1.77216i	0.366928	−	0.115114i
$238$	−0.183874	+	0.183874i	−0.0119188	+	0.0119188i
$239$	−0.604284			−0.0390879			−0.0195439	−	0.999809i	$-0.506221\pi$
$239$	−0.604284			−0.0390879			−0.0195439	+	0.999809i	$0.506221\pi$
$240$	−2.31141	−	3.10763i	−0.149201	−	0.200597i
$241$	−1.64307			−0.105839			−0.0529196	−	0.998599i	$-0.516853\pi$
$241$	−1.64307			−0.105839			−0.0529196	+	0.998599i	$0.516853\pi$
$242$	−14.5647	+	14.5647i	−0.936255	+	0.936255i
$243$	−15.5684	−	0.791496i	−0.998710	−	0.0507745i
$244$		−	9.82484i		−	0.628971i
$245$	−3.62103	−	10.3845i	−0.231339	−	0.663444i
$246$	−4.61867	+	8.84143i	−0.294475	+	0.563709i
$247$	0.933851	+	0.933851i	0.0594195	+	0.0594195i
$248$	3.61486	+	3.61486i	0.229544	+	0.229544i
$249$	5.49477	−	10.5185i	0.348217	−	0.666585i
$250$	2.45225	+	10.9081i	0.155094	+	0.689888i
$251$		−	0.800477i		−	0.0505256i	−0.999681	−	0.0252628i	$-0.991958\pi$
$251$		−	0.800477i		−	0.0505256i	0.999681	−	0.0252628i	$-0.00804226\pi$
$252$	1.82767	−	10.1943i	0.115132	−	0.642183i
$253$	4.73131	−	4.73131i	0.297455	−	0.297455i
$254$	−6.84738			−0.429643
$255$	0.288625	+	0.0424081i	0.0180744	+	0.00265570i
$256$	1.00000			0.0625000
$257$	0.187825	−	0.187825i	0.0117162	−	0.0117162i	−0.701224	−	0.712941i	$-0.747363\pi$
$257$	0.187825	−	0.187825i	0.0117162	−	0.0117162i	0.712941	+	0.701224i	$0.247363\pi$
$258$	17.7118	−	5.55661i	1.10269	−	0.345940i
$259$			28.7387i			1.78574i
$260$	2.65925	+	1.28420i	0.164920	+	0.0796425i
$261$	16.1651	−	11.2500i	1.00059	−	0.696360i
$262$	0.0940236	+	0.0940236i	0.00580880	+	0.00580880i
$263$	0.0979650	+	0.0979650i	0.00604078	+	0.00604078i	0.710121	−	0.704080i	$-0.248640\pi$
$263$	0.0979650	+	0.0979650i	0.00604078	+	0.00604078i	−0.704080	+	0.710121i	$0.748640\pi$
$264$	−8.62963	−	4.50803i	−0.531117	−	0.277450i
$265$	27.5495	+	13.3041i	1.69235	+	0.817266i
$266$		−	3.45230i		−	0.211674i
$267$	−2.43375	−	7.75759i	−0.148943	−	0.474757i
$268$	6.27631	−	6.27631i	0.383387	−	0.383387i
$269$	−15.3546			−0.936185			−0.468093	−	0.883679i	$-0.655059\pi$
$269$	−15.3546			−0.936185			−0.468093	+	0.883679i	$0.655059\pi$
$270$	−10.4003	+	5.18019i	−0.632940	+	0.315257i
$271$	8.91573			0.541592			0.270796	−	0.962637i	$-0.412713\pi$
$271$	8.91573			0.541592			0.270796	+	0.962637i	$0.412713\pi$
$272$	−0.0532613	+	0.0532613i	−0.00322944	+	0.00322944i
$273$	2.36388	+	7.53488i	0.143068	+	0.456032i
$274$		−	16.7509i		−	1.01196i
$275$	17.4759	+	22.0122i	1.05383	+	1.32738i
$276$	1.82740	+	0.954615i	0.109997	+	0.0574611i
$277$	−5.23704	−	5.23704i	−0.314663	−	0.314663i	0.532050	−	0.846713i	$-0.321422\pi$
$277$	−5.23704	−	5.23704i	−0.314663	−	0.314663i	−0.846713	+	0.532050i	$0.821422\pi$
$278$	−8.09478	−	8.09478i	−0.485493	−	0.485493i
$279$	12.5881	−	8.76065i	0.753631	−	0.524486i
$280$	−2.54168	−	7.28914i	−0.151894	−	0.435610i
$281$		−	1.07688i		−	0.0642410i	−0.999484	−	0.0321205i	$-0.989774\pi$
$281$		−	1.07688i		−	0.0642410i	0.999484	−	0.0321205i	$-0.0102260\pi$
$282$	−6.17374	+	1.93685i	−0.367641	+	0.115338i
$283$	−13.3657	+	13.3657i	−0.794508	+	0.794508i	−0.982223	−	0.187715i	$-0.939892\pi$
$283$	−13.3657	+	13.3657i	−0.794508	+	0.794508i	0.187715	+	0.982223i	$0.439892\pi$
$284$	2.29302			0.136066
$285$	−3.10763	+	2.31141i	−0.184080	+	0.136916i
$286$	7.42369			0.438972
$287$	−14.0589	+	14.0589i	−0.829868	+	0.829868i
$288$	0.529408	−	2.95292i	0.0311956	−	0.174002i
$289$			16.9943i			0.999666i
$290$	6.38356	−	13.2188i	0.374855	−	0.776233i
$291$	−4.74321	+	9.07984i	−0.278052	+	0.532270i
$292$	7.35442	+	7.35442i	0.430385	+	0.430385i
$293$	−0.952778	−	0.952778i	−0.0556619	−	0.0556619i	0.678728	−	0.734390i	$-0.262532\pi$
$293$	−0.952778	−	0.952778i	−0.0556619	−	0.0556619i	−0.734390	+	0.678728i	$0.762532\pi$
$294$	3.94437	−	7.55064i	0.230041	−	0.440362i
$295$	23.3726	−	8.14987i	1.36080	−	0.474503i
$296$			8.32453i			0.483853i
$297$	−17.8804	+	23.0960i	−1.03753	+	1.34017i
$298$	15.3972	−	15.3972i	0.891934	−	0.891934i
$299$	−1.57203			−0.0909130
$300$	−4.85970	+	7.16821i	−0.280575	+	0.413857i
$301$	36.9993			2.13261
$302$	−9.18387	+	9.18387i	−0.528472	+	0.528472i
$303$	−1.39694	+	0.438253i	−0.0802519	+	0.0251770i
$304$		−	1.00000i		−	0.0573539i
$305$	−20.7441	+	7.23333i	−1.18780	+	0.414179i
$306$	0.129079	+	0.185473i	0.00737898	+	0.0106028i
$307$	12.7740	+	12.7740i	0.729052	+	0.729052i	0.970431	−	0.241379i	$-0.0775997\pi$
$307$	12.7740	+	12.7740i	0.729052	+	0.729052i	−0.241379	+	0.970431i	$0.577600\pi$
$308$	−13.7221	−	13.7221i	−0.781888	−	0.781888i
$309$	−3.73491	−	1.95108i	−0.212472	−	0.110993i
$310$	4.97101	−	10.2937i	0.282334	−	0.584645i
$311$		−	6.21244i		−	0.352275i	−0.984366	−	0.176138i	$-0.943640\pi$
$311$		−	6.21244i		−	0.352275i	0.984366	−	0.176138i	$-0.0563604\pi$
$312$	0.684726	+	2.18257i	0.0387650	+	0.123564i
$313$	−1.38773	+	1.38773i	−0.0784393	+	0.0784393i	−0.745238	−	0.666799i	$-0.767664\pi$
$313$	−1.38773	+	1.38773i	−0.0784393	+	0.0784393i	0.666799	+	0.745238i	$0.267664\pi$
$314$	14.5328			0.820131
$315$	−22.8698	+	3.64644i	−1.28857	+	0.205454i
$316$	3.41806			0.192281
$317$	−6.17490	+	6.17490i	−0.346817	+	0.346817i	−0.858922	−	0.512106i	$-0.828866\pi$
$317$	−6.17490	+	6.17490i	−0.346817	+	0.346817i	0.512106	+	0.858922i	$0.328866\pi$
$318$	7.09368	+	22.6112i	0.397794	+	1.26797i
$319$		−	36.9021i		−	2.06612i
$320$	−0.736229	−	2.11139i	−0.0411564	−	0.118030i
$321$	−13.4174	−	7.00910i	−0.748885	−	0.391210i
$322$	2.90577	+	2.90577i	0.161932	+	0.161932i
$323$	0.0532613	+	0.0532613i	0.00296354	+	0.00296354i
$324$	−8.43946	−	3.12659i	−0.468859	−	0.173700i
$325$	0.753621	−	6.56018i	0.0418034	−	0.363893i
$326$		−	7.03502i		−	0.389634i
$327$	−22.7459	+	7.13594i	−1.25785	+	0.394618i
$328$	−4.07232	+	4.07232i	−0.224856	+	0.224856i
$329$	−12.8967			−0.711021
$330$	−3.16482	+	21.5395i	−0.174218	+	1.18571i
$331$	9.52357			0.523463			0.261731	−	0.965141i	$-0.415707\pi$
$331$	9.52357			0.523463			0.261731	+	0.965141i	$0.415707\pi$
$332$	4.84479	−	4.84479i	0.265892	−	0.265892i
$333$	24.5817	+	4.40707i	1.34707	+	0.241506i
$334$		−	15.9970i		−	0.875319i
$335$	−17.8725	−	8.63094i	−0.976481	−	0.471559i
$336$	2.76865	−	5.29997i	0.151042	−	0.289137i
$337$	−16.6674	−	16.6674i	−0.907932	−	0.907932i	0.0881729	−	0.996105i	$-0.471897\pi$
$337$	−16.6674	−	16.6674i	−0.907932	−	0.907932i	−0.996105	+	0.0881729i	$0.971897\pi$
$338$	7.95908	+	7.95908i	0.432917	+	0.432917i
$339$	−15.4056	+	29.4907i	−0.836718	+	1.60171i
$340$	0.151668	+	0.0732429i	0.00822535	+	0.00397215i
$341$		−	28.7365i		−	1.55617i
$342$	−2.95292	−	0.529408i	−0.159676	−	0.0286271i
$343$	−5.08162	+	5.08162i	−0.274382	+	0.274382i
$344$	10.7173			0.577839
$345$	0.670179	−	4.56117i	0.0360812	−	0.245565i
$346$	23.4227			1.25921
$347$	7.59916	−	7.59916i	0.407944	−	0.407944i	−0.473077	−	0.881021i	$-0.656857\pi$
$347$	7.59916	−	7.59916i	0.407944	−	0.407944i	0.881021	+	0.473077i	$0.156857\pi$
$348$	10.8493	−	3.40368i	0.581581	−	0.182456i
$349$			9.65125i			0.516619i	0.966062	+	0.258310i	$0.0831655\pi$
$349$			9.65125i			0.516619i	−0.966062	+	0.258310i	$0.916835\pi$
$350$	−13.5190	+	10.7330i	−0.722619	+	0.573700i
$351$	6.80746	−	0.866471i	0.363355	−	0.0462488i
$352$	−3.97477	−	3.97477i	−0.211856	−	0.211856i
$353$	−1.80197	−	1.80197i	−0.0959090	−	0.0959090i	0.657524	−	0.753433i	$-0.271604\pi$
$353$	−1.80197	−	1.80197i	−0.0959090	−	0.0959090i	−0.753433	+	0.657524i	$0.771604\pi$
$354$	16.9943	+	8.87763i	0.903236	+	0.471841i
$355$	−1.68819	−	4.84145i	−0.0895996	−	0.256958i
$356$		−	4.69409i		−	0.248786i
$357$	0.134821	+	0.429745i	0.00713551	+	0.0227445i
$358$	−9.52759	+	9.52759i	−0.503549	+	0.503549i
$359$	−16.7534			−0.884209			−0.442104	−	0.896964i	$-0.645768\pi$
$359$	−16.7534			−0.884209			−0.442104	+	0.896964i	$0.645768\pi$
$360$	−6.62453	+	1.05624i	−0.349143	+	0.0556686i
$361$	−1.00000			−0.0526316
$362$	7.42232	−	7.42232i	0.390108	−	0.390108i
$363$	10.6793	+	34.0403i	0.560516	+	1.78665i
$364$			4.55933i			0.238974i
$365$	10.1135	−	20.9426i	0.529366	−	1.09619i
$366$	−15.0831	−	7.87925i	−0.788406	−	0.411855i
$367$	7.97950	+	7.97950i	0.416526	+	0.416526i	0.884005	−	0.467478i	$-0.154837\pi$
$367$	7.97950	+	7.97950i	0.416526	+	0.416526i	−0.467478	+	0.884005i	$0.654837\pi$
$368$	0.841693	+	0.841693i	0.0438763	+	0.0438763i
$369$	9.86932	+	14.1812i	0.513776	+	0.738241i
$370$	17.5763	−	6.12876i	0.913750	−	0.318619i
$371$			47.2341i			2.45227i
$372$	8.44855	−	2.65052i	0.438037	−	0.137423i
$373$	13.0474	−	13.0474i	0.675570	−	0.675570i	−0.283424	−	0.958995i	$-0.591470\pi$
$373$	13.0474	−	13.0474i	0.675570	−	0.675570i	0.958995	+	0.283424i	$0.0914704\pi$
$374$	0.423403			0.0218937
$375$	18.7127	+	4.98329i	0.966322	+	0.257336i
$376$	−3.73570			−0.192654
$377$	−6.13059	+	6.13059i	−0.315741	+	0.315741i
$378$	−14.1846	−	10.9814i	−0.729578	−	0.564824i
$379$			29.4531i			1.51290i	0.654050	+	0.756451i	$0.273069\pi$
$379$			29.4531i			1.51290i	−0.654050	+	0.756451i	$0.726931\pi$
$380$	−2.11139	+	0.736229i	−0.108312	+	0.0377677i
$381$	−5.49141	+	10.5121i	−0.281334	+	0.538551i
$382$	11.4880	+	11.4880i	0.587775	+	0.587775i
$383$	8.01839	+	8.01839i	0.409721	+	0.409721i	0.881641	−	0.471921i	$-0.156439\pi$
$383$	8.01839	+	8.01839i	0.409721	+	0.409721i	−0.471921	+	0.881641i	$0.656439\pi$
$384$	0.801972	−	1.53520i	0.0409255	−	0.0783429i
$385$	−18.8701	+	39.0753i	−0.961708	+	1.99146i
$386$			3.16174i			0.160928i
$387$	5.67383	−	31.6473i	0.288417	−	1.60873i
$388$	−4.18214	+	4.18214i	−0.212316	+	0.212316i
$389$	−23.1601			−1.17426			−0.587131	−	0.809492i	$-0.699743\pi$
$389$	−23.1601			−1.17426			−0.587131	+	0.809492i	$0.699743\pi$
$390$	4.10415	−	3.05260i	0.207821	−	0.154574i
$391$	−0.0896594			−0.00453427
$392$	3.47779	−	3.47779i	0.175655	−	0.175655i
$393$	0.219749	−	0.0689408i	0.0110849	−	0.00347760i
$394$			7.79862i			0.392889i
$395$	−2.51647	−	7.21685i	−0.126617	−	0.363119i
$396$	−13.8415	+	9.63290i	−0.695559	+	0.484072i
$397$	−16.3811	−	16.3811i	−0.822143	−	0.822143i	0.164272	−	0.986415i	$-0.447472\pi$
$397$	−16.3811	−	16.3811i	−0.822143	−	0.822143i	−0.986415	+	0.164272i	$0.947472\pi$
$398$	−15.7905	−	15.7905i	−0.791508	−	0.791508i
$399$	−5.29997	−	2.76865i	−0.265330	−	0.138606i
$400$	−3.91593	+	3.10893i	−0.195797	+	0.155447i
$401$		−	33.9549i		−	1.69563i	−0.530295	−	0.847813i	$-0.677919\pi$
$401$		−	33.9549i		−	1.69563i	0.530295	−	0.847813i	$-0.322081\pi$
$402$	−4.60197	−	14.6688i	−0.229525	−	0.731614i
$403$	−4.77402	+	4.77402i	−0.237811	+	0.237811i
$404$	−0.845280			−0.0420543
$405$	−0.388091	+	20.1209i	−0.0192844	+	0.999814i
$406$	22.6638			1.12478
$407$	33.0881	−	33.0881i	1.64012	−	1.64012i
$408$	0.0390527	+	0.124481i	0.00193340	+	0.00616272i
$409$			33.7198i			1.66734i	0.552266	+	0.833668i	$0.313763\pi$
$409$			33.7198i			1.66734i	−0.552266	+	0.833668i	$0.686237\pi$
$410$	11.5964	+	5.60010i	0.572706	+	0.276569i
$411$	−25.7160	−	13.4338i	−1.26848	−	0.662639i
$412$	−1.72028	−	1.72028i	−0.0847523	−	0.0847523i
$413$	27.0228	+	27.0228i	1.32971	+	1.32971i
$414$	2.93105	−	2.03985i	0.144053	−	0.100253i
$415$	−13.7961	−	6.66237i	−0.677225	−	0.327043i
$416$			1.32067i			0.0647509i
$417$	−18.9189	+	5.93532i	−0.926463	+	0.290654i
$418$	−3.97477	+	3.97477i	−0.194412	+	0.194412i
$419$	−1.26502			−0.0618005			−0.0309003	−	0.999522i	$-0.509837\pi$
$419$	−1.26502			−0.0618005			−0.0309003	+	0.999522i	$0.509837\pi$
$420$	−13.2286	−	1.94370i	−0.645492	−	0.0948430i
$421$	−4.67210			−0.227704			−0.113852	−	0.993498i	$-0.536319\pi$
$421$	−4.67210			−0.227704			−0.113852	+	0.993498i	$0.536319\pi$
$422$	−3.47484	+	3.47484i	−0.169153	+	0.169153i
$423$	−1.97771	+	11.0312i	−0.0961595	+	0.536356i
$424$			13.6819i			0.664454i
$425$	0.0429820	−	0.374154i	0.00208494	−	0.0181491i
$426$	1.83894	−	3.52024i	0.0890967	−	0.170556i
$427$	−23.9838	−	23.9838i	−1.16066	−	1.16066i
$428$	−6.17999	−	6.17999i	−0.298721	−	0.298721i
$429$	5.95360	−	11.3969i	0.287442	−	0.550245i
$430$	−7.89039	−	22.6284i	−0.380509	−	1.09124i
$431$			13.2679i			0.639093i	0.947571	+	0.319546i	$0.103531\pi$
$431$			13.2679i			0.639093i	−0.947571	+	0.319546i	$0.896469\pi$
$432$	−4.10875	−	3.18091i	−0.197682	−	0.153041i
$433$	27.9513	−	27.9513i	1.34326	−	1.34326i	0.450459	−	0.892797i	$-0.351260\pi$
$433$	27.9513	−	27.9513i	1.34326	−	1.34326i	0.892797	−	0.450459i	$-0.148740\pi$
$434$	17.6488			0.847167
$435$	−15.1740	−	20.4011i	−0.727539	−	0.978159i
$436$	−13.7634			−0.659149
$437$	0.841693	−	0.841693i	0.0402636	−	0.0402636i
$438$	17.1886	−	5.39247i	0.821301	−	0.257662i
$439$		−	6.40984i		−	0.305925i	−0.988232	−	0.152962i	$-0.951119\pi$
$439$		−	6.40984i		−	0.305925i	0.988232	−	0.152962i	$-0.0488813\pi$
$440$	−5.46595	+	11.3186i	−0.260579	+	0.539595i
$441$	−8.42847	−	12.1108i	−0.401356	−	0.576705i
$442$	−0.0703404	−	0.0703404i	−0.00334575	−	0.00334575i
$443$	19.7293	+	19.7293i	0.937366	+	0.937366i	0.998151	−	0.0607845i	$-0.0193602\pi$
$443$	19.7293	+	19.7293i	0.937366	+	0.937366i	−0.0607845	+	0.998151i	$0.519360\pi$
$444$	12.7798	+	6.67604i	0.606503	+	0.316831i
$445$	−9.91105	+	3.45592i	−0.469829	+	0.163826i
$446$			8.58534i			0.406527i
$447$	−11.2896	−	35.9859i	−0.533982	−	1.70207i
$448$	2.44114	−	2.44114i	0.115333	−	0.115333i
$449$	18.2109			0.859426			0.429713	−	0.902966i	$-0.358615\pi$
$449$	18.2109			0.859426			0.429713	+	0.902966i	$0.358615\pi$
$450$	7.10730	+	13.2093i	0.335041	+	0.622694i
$451$	32.3731			1.52439
$452$	−13.5833	+	13.5833i	−0.638904	+	0.638904i
$453$	6.73387	+	21.4643i	0.316385	+	1.00848i
$454$			17.7269i			0.831965i
$455$	9.62652	−	3.35671i	0.451298	−	0.157365i
$456$	−1.53520	−	0.801972i	−0.0718923	−	0.0375558i
$457$	−6.89858	−	6.89858i	−0.322702	−	0.322702i	0.527101	−	0.849803i	$-0.323279\pi$
$457$	−6.89858	−	6.89858i	−0.322702	−	0.322702i	−0.849803	+	0.527101i	$0.823279\pi$
$458$	2.85310	+	2.85310i	0.133317	+	0.133317i
$459$	0.388257	−	0.0494183i	0.0181223	−	0.00230665i
$460$	1.15746	−	2.39682i	0.0539670	−	0.111752i
$461$			14.4915i			0.674935i	0.941337	+	0.337467i	$0.109570\pi$
$461$			14.4915i			0.674935i	−0.941337	+	0.337467i	$0.890430\pi$
$462$	−32.0709	+	10.0614i	−1.49207	+	0.468100i
$463$	−19.3659	+	19.3659i	−0.900009	+	0.900009i	−0.995436	−	0.0954276i	$-0.969578\pi$
$463$	−19.3659	+	19.3659i	−0.900009	+	0.900009i	0.0954276	+	0.995436i	$0.469578\pi$
$464$	6.56484			0.304765
$465$	−11.8163	−	15.8868i	−0.547969	−	0.736732i
$466$	−19.4916			−0.902931
$467$	−1.06586	+	1.06586i	−0.0493219	+	0.0493219i	−0.731338	−	0.682016i	$-0.761104\pi$
$467$	−1.06586	+	1.06586i	−0.0493219	+	0.0493219i	0.682016	+	0.731338i	$0.261104\pi$
$468$	3.89982	+	0.699170i	0.180269	+	0.0323192i
$469$		−	30.6427i		−	1.41495i
$470$	2.75033	+	7.88752i	0.126863	+	0.363824i
$471$	11.6549	−	22.3107i	0.537028	−	1.02802i
$472$	7.82749	+	7.82749i	0.360290	+	0.360290i
$473$	−42.5989	−	42.5989i	−1.95870	−	1.95870i
$474$	2.74119	−	5.24740i	0.125907	−	0.241021i
$475$	3.10893	+	3.91593i	0.142648	+	0.179675i
$476$			0.260037i			0.0119188i
$477$	40.4016	+	7.24332i	1.84986	+	0.331649i
$478$	−0.427293	+	0.427293i	−0.0195439	+	0.0195439i
$479$	−10.1543			−0.463962			−0.231981	−	0.972720i	$-0.574521\pi$
$479$	−10.1543			−0.463962			−0.231981	+	0.972720i	$0.574521\pi$
$480$	−3.83184	−	0.563017i	−0.174899	−	0.0256981i
$481$	−10.9939			−0.501279
$482$	−1.16182	+	1.16182i	−0.0529196	+	0.0529196i
$483$	6.79129	−	2.13059i	0.309015	−	0.0969454i
$484$			20.5976i			0.936255i
$485$	11.9091	+	5.75111i	0.540766	+	0.261144i
$486$	−11.5682	+	10.4488i	−0.524742	+	0.473968i
$487$	−20.9045	−	20.9045i	−0.947275	−	0.947275i	0.0514027	−	0.998678i	$-0.483631\pi$
$487$	−20.9045	−	20.9045i	−0.947275	−	0.947275i	−0.998678	+	0.0514027i	$0.983631\pi$
$488$	−6.94721	−	6.94721i	−0.314485	−	0.314485i
$489$	−10.8002	−	5.64189i	−0.488400	−	0.255135i
$490$	−9.90343	−	4.78253i	−0.447391	−	0.216053i
$491$		−	1.07122i		−	0.0483436i	−0.999708	−	0.0241718i	$-0.992305\pi$
$491$		−	1.07122i		−	0.0483436i	0.999708	−	0.0241718i	$-0.00769487\pi$
$492$	2.98594	+	9.51772i	0.134617	+	0.429092i
$493$	−0.349652	+	0.349652i	−0.0157475	+	0.0157475i
$494$	1.32067			0.0594195
$495$	30.5293	+	22.1327i	1.37219	+	0.994790i
$496$	5.11218			0.229544
$497$	5.59758	−	5.59758i	0.251086	−	0.251086i
$498$	−3.55234	−	11.3231i	−0.159184	−	0.507401i
$499$		−	2.97605i		−	0.133226i	−0.997779	−	0.0666132i	$-0.978781\pi$
$499$		−	2.97605i		−	0.133226i	0.997779	−	0.0666132i	$-0.0212193\pi$
$500$	9.44719	+	5.97918i	0.422491	+	0.267397i
$501$	−24.5587	−	12.8292i	−1.09720	−	0.573166i
$502$	−0.566023	−	0.566023i	−0.0252628	−	0.0252628i
$503$	−22.6375	−	22.6375i	−1.00936	−	1.00936i	−0.999956	−	0.00940114i	$-0.997007\pi$
$503$	−22.6375	−	22.6375i	−1.00936	−	1.00936i	−0.00940114	−	0.999956i	$-0.502993\pi$
$504$	−5.91613	−	8.50085i	−0.263526	−	0.378658i
$505$	0.622320	+	1.78472i	0.0276929	+	0.0794188i
$506$		−	6.69108i		−	0.297455i
$507$	18.6018	−	5.83582i	0.826133	−	0.259178i
$508$	−4.84183	+	4.84183i	−0.214822	+	0.214822i
$509$	13.7670			0.610210			0.305105	−	0.952319i	$-0.401308\pi$
$509$	13.7670			0.610210			0.305105	+	0.952319i	$0.401308\pi$
$510$	0.234076	−	0.174102i	0.0103651	−	0.00770936i
$511$	35.9064			1.58840
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−3.18091	+	4.10875i	−0.140440	+	0.181406i
$514$		−	0.265624i		−	0.0117162i
$515$	−2.36567	+	4.89871i	−0.104244	+	0.215863i
$516$	8.59499	−	16.4532i	0.378373	−	0.724313i
$517$	14.8486	+	14.8486i	0.653039	+	0.653039i
$518$	20.3213	+	20.3213i	0.892869	+	0.892869i
$519$	18.7844	−	35.9586i	0.824543	−	1.57841i
$520$	2.78844	−	0.972312i	0.122281	−	0.0426387i
$521$			1.77371i			0.0777075i	0.999245	+	0.0388537i	$0.0123706\pi$
$521$			1.77371i			0.0777075i	−0.999245	+	0.0388537i	$0.987629\pi$
$522$	3.47548	−	19.3854i	0.152117	−	0.848478i
$523$	15.4539	−	15.4539i	0.675753	−	0.675753i	−0.283283	−	0.959036i	$-0.591424\pi$
$523$	15.4539	−	15.4539i	0.675753	−	0.675753i	0.959036	+	0.283283i	$0.0914237\pi$
$524$	0.132969			0.00580880
$525$	5.63540	+	29.3618i	0.245949	+	1.28146i
$526$	0.138543			0.00604078
$527$	−0.272282	+	0.272282i	−0.0118608	+	0.0118608i
$528$	−9.28973	+	2.91441i	−0.404284	+	0.126834i
$529$		−	21.5831i		−	0.938396i
$530$	28.8879	−	10.0730i	1.25481	−	0.437545i
$531$	27.2579	−	18.9700i	1.18289	−	0.823228i
$532$	−2.44114	−	2.44114i	−0.105837	−	0.105837i
$533$	−5.37818	−	5.37818i	−0.232955	−	0.232955i
$534$	−7.20637	−	3.76453i	−0.311850	−	0.162907i
$535$	−8.49848	+	17.5983i	−0.367421	+	0.760839i
$536$		−	8.87605i		−	0.383387i
$537$	6.98590	+	22.2676i	0.301464	+	0.960919i
$538$	−10.8573	+	10.8573i	−0.468093	+	0.468093i
$539$	−27.6469			−1.19084
$540$	−3.69115	+	11.0171i	−0.158842	+	0.474098i
$541$	11.0282			0.474141			0.237070	−	0.971492i	$-0.423813\pi$
$541$	11.0282			0.474141			0.237070	+	0.971492i	$0.423813\pi$
$542$	6.30438	−	6.30438i	0.270796	−	0.270796i
$543$	−5.44225	−	17.3472i	−0.233549	−	0.744441i
$544$			0.0753229i			0.00322944i
$545$	10.1330	+	29.0600i	0.434052	+	1.24479i
$546$	6.99948	+	3.65645i	0.299550	+	0.156482i
$547$	−8.33939	−	8.33939i	−0.356567	−	0.356567i	0.505979	−	0.862546i	$-0.331131\pi$
$547$	−8.33939	−	8.33939i	−0.356567	−	0.356567i	−0.862546	+	0.505979i	$0.831131\pi$
$548$	−11.8447	−	11.8447i	−0.505980	−	0.505980i
$549$	−24.1925	+	16.8366i	−1.03251	+	0.718570i
$550$	27.9222	+	3.20765i	1.19061	+	0.136775i
$551$		−	6.56484i		−	0.279672i
$552$	1.96718	−	0.617153i	0.0837288	−	0.0262678i
$553$	8.34396	−	8.34396i	0.354821	−	0.354821i
$554$	−7.40629			−0.314663
$555$	4.68685	−	31.8983i	0.198946	−	1.35401i
$556$	−11.4478			−0.485493
$557$	8.91400	−	8.91400i	0.377698	−	0.377698i	−0.492573	−	0.870271i	$-0.663943\pi$
$557$	8.91400	−	8.91400i	0.377698	−	0.377698i	0.870271	+	0.492573i	$0.163943\pi$
$558$	2.70643	−	15.0959i	0.114572	−	0.639058i
$559$			14.1540i			0.598650i
$560$	−6.95144	−	3.35696i	−0.293752	−	0.141858i
$561$	0.339558	−	0.650009i	0.0143361	−	0.0274434i
$562$	−0.761466	−	0.761466i	−0.0321205	−	0.0321205i
$563$	−17.4579	−	17.4579i	−0.735761	−	0.735761i	0.235993	−	0.971755i	$-0.424166\pi$
$563$	−17.4579	−	17.4579i	−0.735761	−	0.735761i	−0.971755	+	0.235993i	$0.924166\pi$
$564$	−2.99593	+	5.73505i	−0.126151	+	0.241489i
$565$	38.6800	+	18.6792i	1.62728	+	0.785840i
$566$			18.9019i			0.794508i
$567$	−28.2344	+	12.9694i	−1.18573	+	0.544665i
$568$	1.62141	−	1.62141i	0.0680328	−	0.0680328i
$569$	6.84928			0.287137			0.143568	−	0.989640i	$-0.454142\pi$
$569$	6.84928			0.287137			0.143568	+	0.989640i	$0.454142\pi$
$570$	−0.563017	+	3.83184i	−0.0235822	+	0.160498i
$571$	−30.2902			−1.26761			−0.633803	−	0.773495i	$-0.718507\pi$
$571$	−30.2902			−1.26761			−0.633803	+	0.773495i	$0.718507\pi$
$572$	5.24934	−	5.24934i	0.219486	−	0.219486i
$573$	26.8493	−	8.42329i	1.12165	−	0.351888i
$574$			19.8822i			0.829868i
$575$	−5.91278	−	0.679249i	−0.246580	−	0.0283266i
$576$	−1.71368	−	2.46238i	−0.0714034	−	0.102599i
$577$	−31.9328	−	31.9328i	−1.32938	−	1.32938i	−0.905910	−	0.423471i	$-0.860811\pi$
$577$	−31.9328	−	31.9328i	−1.32938	−	1.32938i	−0.423471	−	0.905910i	$-0.639189\pi$
$578$	12.0168	+	12.0168i	0.499833	+	0.499833i
$579$	4.85391	+	2.53563i	0.201722	+	0.105377i
$580$	−4.83322	−	13.8609i	−0.200689	−	0.575544i
$581$		−	23.6536i		−	0.981318i
$582$	3.06646	+	9.77437i	0.127109	+	0.405161i
$583$	54.3826	−	54.3826i	2.25230	−	2.25230i
$584$	10.4007			0.430385
$585$	−1.39494	−	8.74878i	−0.0576735	−	0.361718i
$586$	−1.34743			−0.0556619
$587$	27.2033	−	27.2033i	1.12280	−	1.12280i	0.131481	−	0.991319i	$-0.458027\pi$
$587$	27.2033	−	27.2033i	1.12280	−	1.12280i	0.991319	−	0.131481i	$-0.0419732\pi$
$588$	−2.55002	−	8.12820i	−0.105161	−	0.335201i
$589$		−	5.11218i		−	0.210644i
$590$	10.7641	−	22.2897i	0.443150	−	0.917653i
$591$	11.9724	+	6.25427i	0.492480	+	0.257266i
$592$	5.88633	+	5.88633i	0.241927	+	0.241927i
$593$	1.77591	+	1.77591i	0.0729280	+	0.0729280i	0.742630	−	0.669702i	$-0.233578\pi$
$593$	1.77591	+	1.77591i	0.0729280	+	0.0729280i	−0.669702	+	0.742630i	$0.733578\pi$
$594$	3.68798	+	28.9747i	0.151320	+	1.18885i
$595$	0.549039	−	0.191447i	0.0225084	−	0.00784855i
$596$		−	21.7749i		−	0.891934i
$597$	−36.9052	+	11.5781i	−1.51043	+	0.473858i
$598$	−1.11159	+	1.11159i	−0.0454565	+	0.0454565i
$599$	−4.67096			−0.190850			−0.0954252	−	0.995437i	$-0.530421\pi$
$599$	−4.67096			−0.190850			−0.0954252	+	0.995437i	$0.530421\pi$
$600$	1.63236	+	8.50502i	0.0666409	+	0.347216i
$601$	−46.7693			−1.90776			−0.953880	−	0.300187i	$-0.902951\pi$
$601$	−46.7693			−1.90776			−0.953880	+	0.300187i	$0.902951\pi$
$602$	26.1625	−	26.1625i	1.06630	−	1.06630i
$603$	−26.2102	−	4.69905i	−1.06736	−	0.191360i
$604$			12.9880i			0.528472i
$605$	43.4896	−	15.1646i	1.76810	−	0.616527i
$606$	−0.677891	+	1.29767i	−0.0275374	+	0.0527144i
$607$	−10.3777	−	10.3777i	−0.421219	−	0.421219i	0.464404	−	0.885623i	$-0.346268\pi$
$607$	−10.3777	−	10.3777i	−0.421219	−	0.421219i	−0.885623	+	0.464404i	$0.846268\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$	18.1757	−	34.7934i	0.736517	−	1.40990i
$610$	−9.55353	+	19.7830i	−0.386811	+	0.800990i
$611$		−	4.93361i		−	0.199593i
$612$	0.222422	+	0.0398765i	0.00899089	+	0.00161191i
$613$	−0.440870	+	0.440870i	−0.0178066	+	0.0178066i	−0.715954	−	0.698147i	$-0.754008\pi$
$613$	−0.440870	+	0.440870i	−0.0178066	+	0.0178066i	0.698147	+	0.715954i	$0.254008\pi$
$614$	18.0652			0.729052
$615$	17.8973	−	13.3117i	0.721688	−	0.536780i
$616$	−19.4060			−0.781888
$617$	−32.7653	+	32.7653i	−1.31908	+	1.31908i	−0.404577	+	0.914504i	$0.632581\pi$
$617$	−32.7653	+	32.7653i	−1.31908	+	1.31908i	−0.914504	+	0.404577i	$0.867419\pi$
$618$	−4.02060	+	1.26136i	−0.161732	+	0.0507394i
$619$			48.9217i			1.96633i	0.182725	+	0.983164i	$0.441508\pi$
$619$			48.9217i			1.96633i	−0.182725	+	0.983164i	$0.558492\pi$
$620$	−3.76373	−	10.7938i	−0.151155	−	0.433490i
$621$	−0.780962	−	6.13565i	−0.0313389	−	0.246215i
$622$	−4.39286	−	4.39286i	−0.176138	−	0.176138i
$623$	−11.4589	−	11.4589i	−0.459092	−	0.459092i
$624$	2.02749	+	1.05914i	0.0811644	+	0.0423994i
$625$	5.66909	−	24.3487i	0.226763	−	0.973950i
$626$			1.96255i			0.0784393i
$627$	2.91441	+	9.28973i	0.116391	+	0.370996i
$628$	10.2762	−	10.2762i	0.410066	−	0.410066i
$629$	−0.627027			−0.0250012
$630$	−13.5930	+	18.7498i	−0.541557	+	0.747011i
$631$	−2.96028			−0.117847			−0.0589235	−	0.998263i	$-0.518767\pi$
$631$	−2.96028			−0.117847			−0.0589235	+	0.998263i	$0.518767\pi$
$632$	2.41693	−	2.41693i	0.0961404	−	0.0961404i
$633$	2.54785	+	8.12130i	0.101268	+	0.322793i
$634$			8.73263i			0.346817i
$635$	13.7877	+	6.65830i	0.547148	+	0.264226i
$636$	21.0045	+	10.9725i	0.832883	+	0.435089i
$637$	4.59300	+	4.59300i	0.181981	+	0.181981i
$638$	−26.0937	−	26.0937i	−1.03306	−	1.03306i
$639$	−3.92950	−	5.64627i	−0.155449	−	0.223363i
$640$	−2.01357	−	0.972386i	−0.0795934	−	0.0384369i
$641$			33.7063i			1.33132i	0.746256	+	0.665659i	$0.231849\pi$
$641$			33.7063i			1.33132i	−0.746256	+	0.665659i	$0.768151\pi$
$642$	−14.4437	+	4.53134i	−0.570047	+	0.178838i
$643$	27.8461	−	27.8461i	1.09814	−	1.09814i	0.103516	−	0.994628i	$-0.466991\pi$
$643$	27.8461	−	27.8461i	1.09814	−	1.09814i	0.994628	−	0.103516i	$-0.0330093\pi$
$644$	4.10938			0.161932
$645$	−41.0670	−	6.03403i	−1.61701	−	0.237590i
$646$	0.0753229			0.00296354
$647$	−18.8461	+	18.8461i	−0.740918	+	0.740918i	−0.972755	−	0.231837i	$-0.925526\pi$
$647$	−18.8461	+	18.8461i	−0.740918	+	0.740918i	0.231837	+	0.972755i	$0.425526\pi$
$648$	−8.17843	+	3.75676i	−0.321279	+	0.147579i
$649$		−	62.2250i		−	2.44254i
$650$	−4.10586	−	5.17164i	−0.161045	−	0.202848i
$651$	14.1538	−	27.0944i	0.554732	−	1.06191i
$652$	−4.97451	−	4.97451i	−0.194817	−	0.194817i
$653$	−27.2344	−	27.2344i	−1.06577	−	1.06577i	−0.997679	−	0.0680864i	$-0.978311\pi$
$653$	−27.2344	−	27.2344i	−1.06577	−	1.06577i	−0.0680864	−	0.997679i	$-0.521689\pi$
$654$	−11.0379	+	21.1296i	−0.431616	+	0.826234i
$655$	−0.0978959	−	0.280750i	−0.00382511	−	0.0109698i
$656$			5.75913i			0.224856i
$657$	5.50622	−	30.7125i	0.214818	−	1.19821i
$658$	−9.11938	+	9.11938i	−0.355510	+	0.355510i
$659$	25.2158			0.982269			0.491135	−	0.871084i	$-0.336582\pi$
$659$	25.2158			0.982269			0.491135	+	0.871084i	$0.336582\pi$
$660$	12.9928	+	17.4686i	0.505745	+	0.679963i
$661$	4.05017			0.157533			0.0787666	−	0.996893i	$-0.474902\pi$
$661$	4.05017			0.157533			0.0787666	+	0.996893i	$0.474902\pi$
$662$	6.73418	−	6.73418i	0.261731	−	0.261731i
$663$	−0.164398	+	0.0515756i	−0.00638468	+	0.00200303i
$664$		−	6.85157i		−	0.265892i
$665$	−3.35696	+	6.95144i	−0.130177	+	0.269565i
$666$	20.4981	−	14.2656i	0.794286	−	0.552780i
$667$	5.52558	+	5.52558i	0.213951	+	0.213951i
$668$	−11.3116	−	11.3116i	−0.437660	−	0.437660i
$669$	13.1802	+	6.88520i	0.509576	+	0.266197i
$670$	−18.7408	+	6.53480i	−0.724020	+	0.252461i
$671$			55.2271i			2.13202i
$672$	−1.78991	−	5.70537i	−0.0690474	−	0.220089i
$673$	14.9688	−	14.9688i	0.577004	−	0.577004i	−0.357073	−	0.934077i	$-0.616225\pi$
$673$	14.9688	−	14.9688i	0.577004	−	0.577004i	0.934077	+	0.357073i	$0.116225\pi$
$674$	−23.5713			−0.907932
$675$	25.9788	−	0.317611i	0.999925	−	0.0122249i
$676$	11.2558			0.432917
$677$	−4.56460	+	4.56460i	−0.175432	+	0.175432i	−0.789361	−	0.613929i	$-0.789588\pi$
$677$	−4.56460	+	4.56460i	−0.175432	+	0.175432i	0.613929	+	0.789361i	$0.289588\pi$
$678$	9.95964	+	31.7465i	0.382498	+	1.21922i
$679$			20.4184i			0.783585i
$680$	0.159036	−	0.0554549i	0.00609875	−	0.00212660i
$681$	27.2144	+	14.2165i	1.04286	+	0.544777i
$682$	−20.3198	−	20.3198i	−0.778083	−	0.778083i
$683$	23.6277	+	23.6277i	0.904089	+	0.904089i	0.995787	−	0.0916982i	$-0.0292295\pi$
$683$	23.6277	+	23.6277i	0.904089	+	0.904089i	−0.0916982	+	0.995787i	$0.529230\pi$
$684$	−2.46238	+	1.71368i	−0.0941513	+	0.0655242i
$685$	−16.2884	+	33.7291i	−0.622346	+	1.28872i
$686$			7.18650i			0.274382i
$687$	6.66819	−	2.09197i	0.254407	−	0.0798138i
$688$	7.57828	−	7.57828i	0.288919	−	0.288919i
$689$	−18.0693			−0.688384
$690$	−2.75135	−	3.69912i	−0.104742	−	0.140823i
$691$	33.5858			1.27766			0.638831	−	0.769347i	$-0.279418\pi$
$691$	33.5858			1.27766			0.638831	+	0.769347i	$0.279418\pi$
$692$	16.5624	−	16.5624i	0.629607	−	0.629607i
$693$	−10.2737	+	57.3042i	−0.390264	+	2.17681i
$694$		−	10.7468i		−	0.407944i
$695$	8.42816	+	24.1707i	0.319698	+	0.916846i
$696$	5.26482	−	10.0783i	0.199562	−	0.382019i
$697$	−0.306739	−	0.306739i	−0.0116186	−	0.0116186i
$698$	6.82446	+	6.82446i	0.258310	+	0.258310i
$699$	−15.6317	+	29.9235i	−0.591246	+	1.13181i
$700$	−1.97001	+	17.1487i	−0.0744593	+	0.648160i
$701$		−	41.1049i		−	1.55251i	−0.630419	−	0.776255i	$-0.717117\pi$
$701$		−	41.1049i		−	1.55251i	0.630419	−	0.776255i	$-0.282883\pi$
$702$	4.20091	−	5.42629i	0.158553	−	0.204802i
$703$	5.88633	−	5.88633i	0.222007	−	0.222007i
$704$	−5.62118			−0.211856
$705$	14.3146	+	2.10327i	0.539120	+	0.0792136i
$706$	−2.54837			−0.0959090
$707$	−2.06345	+	2.06345i	−0.0776040	+	0.0776040i
$708$	18.2942	−	5.73934i	0.687538	−	0.215698i
$709$			12.7911i			0.480378i	0.970726	+	0.240189i	$0.0772095\pi$
$709$			12.7911i			0.480378i	−0.970726	+	0.240189i	$0.922791\pi$
$710$	−4.61715	−	2.22970i	−0.173279	−	0.0836791i
$711$	−5.85746	−	8.41654i	−0.219672	−	0.315645i
$712$	−3.31922	−	3.31922i	−0.124393	−	0.124393i
$713$	4.30289	+	4.30289i	0.161144	+	0.161144i
$714$	0.399209	+	0.208542i	0.0149400	+	0.00780450i
$715$	−14.9481	−	7.21869i	−0.559028	−	0.269964i
$716$			13.4740i			0.503549i
$717$	0.313304	+	0.998658i	0.0117005	+	0.0372956i
$718$	−11.8464	+	11.8464i	−0.442104	+	0.442104i
$719$	20.7582			0.774149			0.387075	−	0.922048i	$-0.373486\pi$
$719$	20.7582			0.774149			0.387075	+	0.922048i	$0.373486\pi$
$720$	−3.93738	+	5.43112i	−0.146737	+	0.202406i
$721$	−8.39891			−0.312792
$722$	−0.707107	+	0.707107i	−0.0263158	+	0.0263158i
$723$	0.851882	+	2.71538i	0.0316818	+	0.100986i
$724$		−	10.4967i		−	0.390108i
$725$	−25.7075	+	20.4096i	−0.954752	+	0.757995i
$726$	31.6215	+	16.5187i	1.17358	+	0.613067i
$727$	−7.71093	−	7.71093i	−0.285983	−	0.285983i	0.549507	−	0.835489i	$-0.314816\pi$
$727$	−7.71093	−	7.71093i	−0.285983	−	0.285983i	−0.835489	+	0.549507i	$0.814816\pi$
$728$	3.22393	+	3.22393i	0.119487	+	0.119487i
$729$	6.76368	+	26.1391i	0.250507	+	0.968115i
$730$	−7.65731	−	21.9600i	−0.283410	−	0.812775i
$731$			0.807259i			0.0298575i
$732$	−16.2368	+	5.09389i	−0.600131	+	0.188276i
$733$	21.6850	−	21.6850i	0.800954	−	0.800954i	−0.182291	−	0.983245i	$-0.558351\pi$
$733$	21.6850	−	21.6850i	0.800954	−	0.800954i	0.983245	+	0.182291i	$0.0583512\pi$
$734$	11.2847			0.416526
$735$	−15.2844	+	11.3683i	−0.563774	+	0.419326i
$736$	1.19033			0.0438763
$737$	−35.2803	+	35.2803i	−1.29956	+	1.29956i
$738$	17.0063	+	3.04893i	0.626009	+	0.112233i
$739$			9.14938i			0.336565i	0.985739	+	0.168283i	$0.0538221\pi$
$739$			9.14938i			0.336565i	−0.985739	+	0.168283i	$0.946178\pi$
$740$	8.09465	−	16.7620i	0.297565	−	0.616184i
$741$	1.05914	−	2.02749i	0.0389084	−	0.0744816i
$742$	33.3995	+	33.3995i	1.22614	+	1.22614i
$743$	−28.3515	−	28.3515i	−1.04012	−	1.04012i	−0.999161	−	0.0409557i	$-0.986960\pi$
$743$	−28.3515	−	28.3515i	−1.04012	−	1.04012i	−0.0409557	−	0.999161i	$-0.513040\pi$
$744$	4.09983	−	7.84822i	0.150307	−	0.287730i
$745$	−45.9753	+	16.0313i	−1.68440	+	0.587341i
$746$		−	18.4519i		−	0.675570i
$747$	−20.2321	−	3.62727i	−0.740255	−	0.132715i
$748$	0.299391	−	0.299391i	0.0109468	−	0.0109468i
$749$	−30.1725			−1.10248
$750$	16.7556	−	9.70820i	0.611829	−	0.354493i
$751$	19.6549			0.717219			0.358609	−	0.933488i	$-0.383251\pi$
$751$	19.6549			0.717219			0.358609	+	0.933488i	$0.383251\pi$
$752$	−2.64154	+	2.64154i	−0.0963271	+	0.0963271i
$753$	−1.32289	+	0.415024i	−0.0482089	+	0.0151243i
$754$			8.66996i			0.315741i
$755$	27.4226	−	9.56210i	0.998012	−	0.348001i
$756$	−17.7951	+	2.26500i	−0.647201	+	0.0823774i
$757$	−7.94564	−	7.94564i	−0.288789	−	0.288789i	0.547812	−	0.836601i	$-0.315461\pi$
$757$	−7.94564	−	7.94564i	−0.288789	−	0.288789i	−0.836601	+	0.547812i	$0.815461\pi$
$758$	20.8265	+	20.8265i	0.756451	+	0.756451i
$759$	−10.2721	−	5.36606i	−0.372855	−	0.194776i
$760$	−0.972386	+	2.01357i	−0.0352721	+	0.0730399i
$761$		−	8.05394i		−	0.291955i	−0.989288	−	0.145977i	$-0.953367\pi$
$761$		−	8.05394i		−	0.291955i	0.989288	−	0.145977i	$-0.0466327\pi$
$762$	3.55017	+	11.3162i	0.128609	+	0.409943i
$763$	−33.5985	+	33.5985i	−1.21635	+	1.21635i
$764$	16.2464			0.587775
$765$	−0.0795589	−	0.498979i	−0.00287646	−	0.0180406i
$766$	11.3397			0.409721
$767$	−10.3375	+	10.3375i	−0.373265	+	0.373265i
$768$	−0.518471	−	1.65263i	−0.0187087	−	0.0596342i
$769$			29.3869i			1.05972i	0.848086	+	0.529859i	$0.177755\pi$
$769$			29.3869i			1.05972i	−0.848086	+	0.529859i	$0.822245\pi$
$770$	14.2872	+	40.9735i	0.514876	+	1.47658i
$771$	−0.407787	−	0.213023i	−0.0146861	−	0.00767185i
$772$	2.23569	+	2.23569i	0.0804642	+	0.0804642i
$773$	7.89291	+	7.89291i	0.283888	+	0.283888i	0.834658	−	0.550769i	$-0.185666\pi$
$773$	7.89291	+	7.89291i	0.283888	+	0.283888i	−0.550769	+	0.834658i	$0.685666\pi$
$774$	−18.3661	−	26.3901i	−0.660154	−	0.948571i
$775$	−20.0190	+	15.8934i	−0.719102	+	0.570909i
$776$			5.91443i			0.212316i
$777$	47.4945	−	14.9002i	1.70386	−	0.534541i
$778$	−16.3766	+	16.3766i	−0.587131	+	0.587131i
$779$	5.75913			0.206342
$780$	0.743558	−	5.06058i	0.0266236	−	0.181198i
$781$	−12.8895			−0.461221
$782$	−0.0633988	+	0.0633988i	−0.00226713	+	0.00226713i
$783$	−26.9733	−	20.8821i	−0.963947	−	0.746267i
$784$		−	4.91834i		−	0.175655i
$785$	−29.2627	−	14.1315i	−1.04443	−	0.504373i
$786$	0.106638	−	0.204135i	0.00380364	−	0.00728125i
$787$	11.1698	+	11.1698i	0.398160	+	0.398160i	0.877583	−	0.479424i	$-0.159154\pi$
$787$	11.1698	+	11.1698i	0.398160	+	0.398160i	−0.479424	+	0.877583i	$0.659154\pi$
$788$	5.51445	+	5.51445i	0.196444	+	0.196444i
$789$	0.111108	−	0.212692i	0.00395555	−	0.00757203i
$790$	−6.88250	−	3.32367i	−0.244868	−	0.118251i
$791$			66.3174i			2.35798i
$792$	−2.97589	+	16.5989i	−0.105744	+	0.589815i
$793$	9.17494	−	9.17494i	0.325812	−	0.325812i
$794$	−23.1663			−0.822143
$795$	7.70317	−	52.4270i	0.273203	−	1.85939i
$796$	−22.3312			−0.791508
$797$	5.95116	−	5.95116i	0.210801	−	0.210801i	−0.593807	−	0.804608i	$-0.702376\pi$
$797$	5.95116	−	5.95116i	0.210801	−	0.210801i	0.804608	+	0.593807i	$0.202376\pi$
$798$	−5.70537	+	1.78991i	−0.201968	+	0.0633623i
$799$		−	0.281384i		−	0.00995465i
$800$	−0.570637	+	4.96733i	−0.0201751	+	0.175622i
$801$	−11.5586	+	8.04417i	−0.408403	+	0.284227i
$802$	−24.0097	−	24.0097i	−0.847813	−	0.847813i
$803$	−41.3405	−	41.3405i	−1.45887	−	1.45887i
$804$	−13.6265	−	7.11834i	−0.480570	−	0.251045i
$805$	−3.02545	−	8.67651i	−0.106633	−	0.305807i
$806$			6.75148i			0.237811i
$807$	7.96090	+	25.3754i	0.280237	+	0.893258i
$808$	−0.597703	+	0.597703i	−0.0210271	+	0.0210271i
$809$	43.0115			1.51220			0.756101	−	0.654455i	$-0.227102\pi$
$809$	43.0115			1.51220			0.756101	+	0.654455i	$0.227102\pi$
$810$	13.9532	+	14.5020i	0.490265	+	0.509549i
$811$	−4.06527			−0.142751			−0.0713755	−	0.997450i	$-0.522739\pi$
$811$	−4.06527			−0.142751			−0.0713755	+	0.997450i	$0.522739\pi$
$812$	16.0257	−	16.0257i	0.562392	−	0.562392i
$813$	−4.62255	−	14.7344i	−0.162120	−	0.516759i
$814$		−	46.7936i		−	1.64012i
$815$	−6.84075	+	14.1655i	−0.239621	+	0.496196i
$816$	0.115636	+	0.0604069i	0.00404806	+	0.00211466i
$817$	−7.57828	−	7.57828i	−0.265131	−	0.265131i
$818$	23.8435	+	23.8435i	0.833668	+	0.833668i
$819$	11.2268	−	7.81323i	0.392295	−	0.273016i
$820$	12.1598	−	4.24004i	0.424638	−	0.148069i
$821$			50.9029i			1.77652i	0.459336	+	0.888262i	$0.348087\pi$
$821$			50.9029i			1.77652i	−0.459336	+	0.888262i	$0.651913\pi$
$822$	−27.6831	+	8.68486i	−0.965558	+	0.302919i
$823$	1.05777	−	1.05777i	0.0368716	−	0.0368716i	−0.688431	−	0.725302i	$-0.741700\pi$
$823$	1.05777	−	1.05777i	0.0368716	−	0.0368716i	0.725302	+	0.688431i	$0.241700\pi$
$824$	−2.43285			−0.0847523
$825$	27.3173	−	40.2938i	0.951065	−	1.40285i
$826$	38.2160			1.32971
$827$	−18.7028	+	18.7028i	−0.650360	+	0.650360i	−0.953080	−	0.302720i	$-0.902105\pi$
$827$	−18.7028	+	18.7028i	−0.650360	+	0.650360i	0.302720	+	0.953080i	$0.402105\pi$
$828$	0.630172	−	3.51496i	0.0219000	−	0.122153i
$829$		−	16.8360i		−	0.584737i	−0.956306	−	0.292369i	$-0.905557\pi$
$829$		−	16.8360i		−	0.584737i	0.956306	−	0.292369i	$-0.0944434\pi$
$830$	−14.4663	+	5.04432i	−0.502134	+	0.175091i
$831$	−5.93964	+	11.3701i	−0.206044	+	0.394426i
$832$	0.933851	+	0.933851i	0.0323755	+	0.0323755i
$833$	0.261957	+	0.261957i	0.00907629	+	0.00907629i
$834$	−9.18078	+	17.5746i	−0.317904	+	0.608558i
$835$	−15.5553	+	32.2112i	−0.538313	+	1.11471i
$836$			5.62118i			0.194412i
$837$	−21.0047	−	16.2614i	−0.726028	−	0.562075i
$838$	−0.894508	+	0.894508i	−0.0309003	+	0.0309003i
$839$	−7.29360			−0.251803			−0.125901	−	0.992043i	$-0.540182\pi$
$839$	−7.29360			−0.251803			−0.125901	+	0.992043i	$0.540182\pi$
$840$	−10.7285	+	7.97966i	−0.370167	+	0.275325i
$841$	14.0971			0.486108
$842$	−3.30367	+	3.30367i	−0.113852	+	0.113852i
$843$	−1.77968	+	0.558328i	−0.0612953	+	0.0192298i
$844$			4.91417i			0.169153i
$845$	−8.28687	−	23.7655i	−0.285077	−	0.817557i
$846$	6.40180	+	9.19870i	0.220098	+	0.316258i
$847$	50.2817	+	50.2817i	1.72770	+	1.72770i
$848$	9.67459	+	9.67459i	0.332227	+	0.332227i
$849$	29.0183	+	15.1588i	0.995905	+	0.520250i
$850$	−0.234174	−	0.294960i	−0.00803209	−	0.0101170i
$851$			9.90897i			0.339675i
$852$	−1.18886	−	3.78951i	−0.0407297	−	0.129826i
$853$	−18.3610	+	18.3610i	−0.628669	+	0.628669i	−0.947733	−	0.319064i	$-0.896631\pi$
$853$	−18.3610	+	18.3610i	−0.628669	+	0.628669i	0.319064	+	0.947733i	$0.396631\pi$
$854$	−33.9182			−1.16066
$855$	5.43112	+	3.93738i	0.185740	+	0.134655i
$856$	−8.73982			−0.298721
$857$	−34.2645	+	34.2645i	−1.17045	+	1.17045i	−0.188352	+	0.982102i	$0.560315\pi$
$857$	−34.2645	+	34.2645i	−1.17045	+	1.17045i	−0.982102	+	0.188352i	$0.939685\pi$
$858$	−3.84897	−	12.2686i	−0.131402	−	0.418844i
$859$			15.3525i			0.523820i	0.965092	+	0.261910i	$0.0843524\pi$
$859$			15.3525i			0.523820i	−0.965092	+	0.261910i	$0.915648\pi$
$860$	−21.5801	−	10.4214i	−0.735874	−	0.355365i
$861$	30.5232	+	15.9450i	1.04023	+	0.543404i
$862$	9.38183	+	9.38183i	0.319546	+	0.319546i
$863$	−6.56803	−	6.56803i	−0.223578	−	0.223578i	0.586425	−	0.810003i	$-0.300535\pi$
$863$	−6.56803	−	6.56803i	−0.223578	−	0.223578i	−0.810003	+	0.586425i	$0.800535\pi$
$864$	−5.15457	+	0.656086i	−0.175362	+	0.0223205i
$865$	−47.1634	−	22.7759i	−1.60360	−	0.774405i
$866$		−	39.5292i		−	1.34326i
$867$	28.0853	−	8.81106i	0.953828	−	0.299239i
$868$	12.4796	−	12.4796i	0.423584	−	0.423584i
$869$	−19.2135			−0.651773
$870$	−25.1554	−	3.69612i	−0.852849	−	0.125310i
$871$	11.7223			0.397195
$872$	−9.73222	+	9.73222i	−0.329575	+	0.329575i
$873$	17.4648	+	3.13115i	0.591095	+	0.105973i
$874$		−	1.19033i		−	0.0402636i
$875$	37.6580	−	8.46590i	1.27307	−	0.286200i
$876$	8.34109	−	15.9672i	0.281819	−	0.539482i
$877$	−13.7736	−	13.7736i	−0.465103	−	0.465103i	0.435221	−	0.900324i	$-0.356670\pi$
$877$	−13.7736	−	13.7736i	−0.465103	−	0.465103i	−0.900324	+	0.435221i	$0.856670\pi$
$878$	−4.53244	−	4.53244i	−0.152962	−	0.152962i
$879$	−1.08060	+	2.06858i	−0.0364478	+	0.0697714i
$880$	4.13847	+	11.8685i	0.139508	+	0.400087i
$881$			13.2041i			0.444859i	0.974949	+	0.222429i	$0.0713986\pi$
$881$			13.2041i			0.444859i	−0.974949	+	0.222429i	$0.928601\pi$
$882$	−14.5235	−	2.60381i	−0.489031	−	0.0876748i
$883$	−34.9199	+	34.9199i	−1.17515	+	1.17515i	−0.194181	+	0.980966i	$0.562205\pi$
$883$	−34.9199	+	34.9199i	−1.17515	+	1.17515i	−0.980966	+	0.194181i	$0.937795\pi$
$884$	−0.0994763			−0.00334575
$885$	−25.5867	−	34.4007i	−0.860087	−	1.15637i
$886$	27.9014			0.937366
$887$	−5.21923	+	5.21923i	−0.175245	+	0.175245i	−0.789279	−	0.614035i	$-0.789546\pi$
$887$	−5.21923	+	5.21923i	−0.175245	+	0.175245i	0.614035	+	0.789279i	$0.289546\pi$
$888$	13.7574	−	4.31602i	0.461667	−	0.144836i
$889$			23.6392i			0.792833i
$890$	−4.56446	+	9.45188i	−0.153001	+	0.316828i
$891$	47.4397	+	17.5751i	1.58929	+	0.588789i
$892$	6.07075	+	6.07075i	0.203264	+	0.203264i
$893$	2.64154	+	2.64154i	0.0883958	+	0.0883958i
$894$	−33.4288	−	17.4629i	−1.11803	−	0.584045i
$895$	28.4490	−	9.91998i	0.950944	−	0.331588i
$896$		−	3.45230i		−	0.115333i
$897$	0.815053	+	2.59799i	0.0272138	+	0.0867443i
$898$	12.8771	−	12.8771i	0.429713	−	0.429713i
$899$	33.5606			1.11931
$900$	14.3660	+	4.31479i	0.478867	+	0.143826i
$901$	−1.03056			−0.0343330
$902$	22.8912	−	22.8912i	0.762195	−	0.762195i
$903$	−19.1831	−	61.1462i	−0.638372	−	2.03482i
$904$			19.2097i			0.638904i
$905$	−22.1627	+	7.72800i	−0.736714	+	0.256888i
$906$	19.9391	+	10.4160i	0.662433	+	0.346048i
$907$	−19.6088	−	19.6088i	−0.651100	−	0.651100i	0.302158	−	0.953258i	$-0.402293\pi$
$907$	−19.6088	−	19.6088i	−0.651100	−	0.651100i	−0.953258	+	0.302158i	$0.902293\pi$
$908$	12.5348	+	12.5348i	0.415983	+	0.415983i
$909$	1.44854	+	2.08140i	0.0480451	+	0.0690356i
$910$	4.43342	−	9.18053i	0.146967	−	0.304331i
$911$		−	49.5704i		−	1.64234i	−0.570683	−	0.821170i	$-0.693322\pi$
$911$		−	49.5704i		−	1.64234i	0.570683	−	0.821170i	$-0.306678\pi$
$912$	−1.65263	+	0.518471i	−0.0547241	+	0.0171683i
$913$	−27.2334	+	27.2334i	−0.901295	+	0.901295i
$914$	−9.75606			−0.322702
$915$	22.7092	+	30.5320i	0.750743	+	1.00936i
$916$	4.03489			0.133317
$917$	0.324597	−	0.324597i	0.0107191	−	0.0107191i
$918$	0.239595	−	0.309483i	0.00790781	−	0.0102145i
$919$		−	46.5841i		−	1.53667i	−0.640049	−	0.768334i	$-0.721086\pi$
$919$		−	46.5841i		−	1.53667i	0.640049	−	0.768334i	$-0.278914\pi$
$920$	−0.876358	−	2.51326i	−0.0288927	−	0.0828597i
$921$	14.4878	−	27.7337i	0.477389	−	0.913856i
$922$	10.2470	+	10.2470i	0.337467	+	0.337467i
$923$	2.14134	+	2.14134i	0.0704830	+	0.0704830i
$924$	−15.5630	+	29.7920i	−0.511986	+	0.980086i
$925$	−41.3507	−	4.75028i	−1.35960	−	0.156188i
$926$			27.3875i			0.900009i
$927$	−1.28797	+	7.18400i	−0.0423024	+	0.235954i
$928$	4.64204	−	4.64204i	0.152383	−	0.152383i
$929$	58.9237			1.93322			0.966611	−	0.256247i	$-0.0824859\pi$
$929$	58.9237			1.93322			0.966611	+	0.256247i	$0.0824859\pi$
$930$	−19.5891	−	2.87825i	−0.642351	−	0.0943814i
$931$	−4.91834			−0.161192
$932$	−13.7826	+	13.7826i	−0.451466	+	0.451466i
$933$	−10.2669	+	3.22097i	−0.336122	+	0.105450i
$934$			1.50735i			0.0493219i
$935$	−0.852552	−	0.411711i	−0.0278814	−	0.0134644i
$936$	3.25198	−	2.26320i	0.106294	−	0.0739750i
$937$	−8.63180	−	8.63180i	−0.281989	−	0.281989i	0.551913	−	0.833902i	$-0.313898\pi$
$937$	−8.63180	−	8.63180i	−0.281989	−	0.281989i	−0.833902	+	0.551913i	$0.813898\pi$
$938$	−21.6677	−	21.6677i	−0.707475	−	0.707475i
$939$	3.01291	+	1.57391i	0.0983226	+	0.0513627i
$940$	7.52210	+	3.63254i	0.245344	+	0.118481i
$941$		−	45.8679i		−	1.49525i	−0.664120	−	0.747626i	$-0.731194\pi$
$941$		−	45.8679i		−	1.49525i	0.664120	−	0.747626i	$-0.268806\pi$
$942$	−7.53481	−	24.0173i	−0.245497	−	0.782526i
$943$	−4.84742	+	4.84742i	−0.157854	+	0.157854i
$944$	11.0697			0.360290
$945$	17.8836	+	35.9048i	0.581752	+	1.16798i
$946$	−60.2439			−1.95870
$947$	−14.0103	+	14.0103i	−0.455272	+	0.455272i	−0.897100	−	0.441828i	$-0.854330\pi$
$947$	−14.0103	+	14.0103i	−0.455272	+	0.455272i	0.441828	+	0.897100i	$0.354330\pi$
$948$	−1.77216	−	5.64879i	−0.0575572	−	0.183464i
$949$			13.7359i			0.445885i
$950$	4.96733	+	0.570637i	0.161161	+	0.0185139i
$951$	13.4063	+	7.00332i	0.434730	+	0.227098i
$952$	0.183874	+	0.183874i	0.00595939	+	0.00595939i
$953$	8.61696	+	8.61696i	0.279131	+	0.279131i	0.832762	−	0.553631i	$-0.186758\pi$
$953$	8.61696	+	8.61696i	0.279131	+	0.279131i	−0.553631	+	0.832762i	$0.686758\pi$
$954$	33.6901	−	23.4465i	1.09076	−	0.759108i
$955$	−11.9611	−	34.3025i	−0.387052	−	1.11000i
$956$			0.604284i			0.0195439i
$957$	−60.9856	+	19.1327i	−1.97138	+	0.618471i
$958$	−7.18017	+	7.18017i	−0.231981	+	0.231981i
$959$	−57.8291			−1.86740
$960$	−3.10763	+	2.31141i	−0.100298	+	0.0746004i
$961$	−4.86561			−0.156955
$962$	−7.77387	+	7.77387i	−0.250640	+	0.250640i
$963$	−4.62693	+	25.8080i	−0.149101	+	0.831651i
$964$			1.64307i			0.0529196i
$965$	3.07443	−	6.36639i	0.0989695	−	0.204941i
$966$	3.29561	−	6.30873i	0.106035	−	0.202980i
$967$	19.4154	+	19.4154i	0.624358	+	0.624358i	0.946643	−	0.322285i	$-0.104451\pi$
$967$	19.4154	+	19.4154i	0.624358	+	0.624358i	−0.322285	+	0.946643i	$0.604451\pi$
$968$	14.5647	+	14.5647i	0.468128	+	0.468128i
$969$	0.0604069	−	0.115636i	0.00194055	−	0.00371476i
$970$	12.4877	−	4.35438i	0.400955	−	0.139811i
$971$			23.5075i			0.754391i	0.926134	+	0.377196i	$0.123112\pi$
$971$			23.5075i			0.754391i	−0.926134	+	0.377196i	$0.876888\pi$
$972$	−0.791496	+	15.5684i	−0.0253873	+	0.499355i
$973$	−27.9456	+	27.9456i	−0.895894	+	0.895894i
$974$	−29.5635			−0.947275
$975$	−11.2323	+	2.15580i	−0.359721	+	0.0690410i
$976$	−9.82484			−0.314485
$977$	1.74859	−	1.74859i	0.0559423	−	0.0559423i	−0.678582	−	0.734524i	$-0.737405\pi$
$977$	1.74859	−	1.74859i	0.0559423	−	0.0559423i	0.734524	+	0.678582i	$0.237405\pi$
$978$	−11.6263	+	3.64745i	−0.371768	+	0.116633i
$979$			26.3863i			0.843310i
$980$	−10.3845	+	3.62103i	−0.331722	+	0.115669i
$981$	23.5861	+	33.8908i	0.753048	+	1.08205i
$982$	−0.757468	−	0.757468i	−0.0241718	−	0.0241718i
$983$	17.3240	+	17.3240i	0.552548	+	0.552548i	0.927176	−	0.374627i	$-0.122229\pi$
$983$	17.3240	+	17.3240i	0.552548	+	0.552548i	−0.374627	+	0.927176i	$0.622229\pi$
$984$	8.84143	+	4.61867i	0.281854	+	0.147238i
$985$	7.58326	−	15.7031i	0.241623	−	0.500341i
$986$			0.494483i			0.0157475i
$987$	6.68658	+	21.3136i	0.212836	+	0.678418i
$988$	0.933851	−	0.933851i	0.0297098	−	0.0297098i
$989$	12.7572			0.405655
$990$	37.2376	−	5.93730i	1.18349	−	0.188700i
$991$	−13.0550			−0.414705			−0.207352	−	0.978266i	$-0.566485\pi$
$991$	−13.0550			−0.414705			−0.207352	+	0.978266i	$0.566485\pi$
$992$	3.61486	−	3.61486i	0.114772	−	0.114772i
$993$	−4.93769	−	15.7389i	−0.156693	−	0.499460i
$994$		−	7.91617i		−	0.251086i
$995$	16.4409	+	47.1498i	0.521210	+	1.49475i
$996$	−10.5185	−	5.49477i	−0.333292	−	0.174108i
$997$	−41.9934	−	41.9934i	−1.32994	−	1.32994i	−0.905414	−	0.424530i	$-0.860439\pi$
$997$	−41.9934	−	41.9934i	−1.32994	−	1.32994i	−0.424530	−	0.905414i	$-0.639561\pi$
$998$	−2.10439	−	2.10439i	−0.0666132	−	0.0666132i
$999$	−5.46161	−	42.9093i	−0.172798	−	1.35759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.a.77.13	yes	36
3.2	odd	2	inner	570.2.k.a.77.9	✓	36
5.3	odd	4	inner	570.2.k.a.533.9	yes	36
15.8	even	4	inner	570.2.k.a.533.13	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.a.77.9	✓	36	3.2	odd	2	inner
570.2.k.a.77.13	yes	36	1.1	even	1	trivial
570.2.k.a.533.9	yes	36	5.3	odd	4	inner
570.2.k.a.533.13	yes	36	15.8	even	4	inner

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.518471 - 1.65263i) q^{3} -1.00000i q^{4} +(-2.11139 + 0.736229i) q^{5} +(-1.53520 - 0.801972i) q^{6} +(-2.44114 - 2.44114i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.46238 + 1.71368i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.518471 - 1.65263i) q^{3} -1.00000i q^{4} +(-2.11139 + 0.736229i) q^{5} +(-1.53520 - 0.801972i) q^{6} +(-2.44114 - 2.44114i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.46238 + 1.71368i) q^{9} +(-0.972386 + 2.01357i) q^{10} +5.62118i q^{11} +(-1.65263 + 0.518471i) q^{12} +(0.933851 - 0.933851i) q^{13} -3.45230 q^{14} +(2.31141 + 3.10763i) q^{15} -1.00000 q^{16} +(0.0532613 - 0.0532613i) q^{17} +(-0.529408 + 2.95292i) q^{18} +1.00000i q^{19} +(0.736229 + 2.11139i) q^{20} +(-2.76865 + 5.29997i) q^{21} +(3.97477 + 3.97477i) q^{22} +(-0.841693 - 0.841693i) q^{23} +(-0.801972 + 1.53520i) q^{24} +(3.91593 - 3.10893i) q^{25} -1.32067i q^{26} +(4.10875 + 3.18091i) q^{27} +(-2.44114 + 2.44114i) q^{28} -6.56484 q^{29} +(3.83184 + 0.563017i) q^{30} -5.11218 q^{31} +(-0.707107 + 0.707107i) q^{32} +(9.28973 - 2.91441i) q^{33} -0.0753229i q^{34} +(6.95144 + 3.35696i) q^{35} +(1.71368 + 2.46238i) q^{36} +(-5.88633 - 5.88633i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-2.02749 - 1.05914i) q^{39} +(2.01357 + 0.972386i) q^{40} -5.75913i q^{41} +(1.78991 + 5.70537i) q^{42} +(-7.57828 + 7.57828i) q^{43} +5.62118 q^{44} +(3.93738 - 5.43112i) q^{45} -1.19033 q^{46} +(2.64154 - 2.64154i) q^{47} +(0.518471 + 1.65263i) q^{48} +4.91834i q^{49} +(0.570637 - 4.96733i) q^{50} +(-0.115636 - 0.0604069i) q^{51} +(-0.933851 - 0.933851i) q^{52} +(-9.67459 - 9.67459i) q^{53} +(5.15457 - 0.656086i) q^{54} +(-4.13847 - 11.8685i) q^{55} +3.45230i q^{56} +(1.65263 - 0.518471i) q^{57} +(-4.64204 + 4.64204i) q^{58} -11.0697 q^{59} +(3.10763 - 2.31141i) q^{60} +9.82484 q^{61} +(-3.61486 + 3.61486i) q^{62} +(10.1943 + 1.82767i) q^{63} +1.00000i q^{64} +(-1.28420 + 2.65925i) q^{65} +(4.50803 - 8.62963i) q^{66} +(6.27631 + 6.27631i) q^{67} +(-0.0532613 - 0.0532613i) q^{68} +(-0.954615 + 1.82740i) q^{69} +(7.28914 - 2.54168i) q^{70} +2.29302i q^{71} +(2.95292 + 0.529408i) q^{72} +(-7.35442 + 7.35442i) q^{73} -8.32453 q^{74} +(-7.16821 - 4.85970i) q^{75} +1.00000 q^{76} +(13.7221 - 13.7221i) q^{77} +(-2.18257 + 0.684726i) q^{78} +3.41806i q^{79} +(2.11139 - 0.736229i) q^{80} +(3.12659 - 8.43946i) q^{81} +(-4.07232 - 4.07232i) q^{82} +(4.84479 + 4.84479i) q^{83} +(5.29997 + 2.76865i) q^{84} +(-0.0732429 + 0.151668i) q^{85} +10.7173i q^{86} +(3.40368 + 10.8493i) q^{87} +(3.97477 - 3.97477i) q^{88} +4.69409 q^{89} +(-1.05624 - 6.62453i) q^{90} -4.55933 q^{91} +(-0.841693 + 0.841693i) q^{92} +(2.65052 + 8.44855i) q^{93} -3.73570i q^{94} +(-0.736229 - 2.11139i) q^{95} +(1.53520 + 0.801972i) q^{96} +(-4.18214 - 4.18214i) q^{97} +(3.47779 + 3.47779i) q^{98} +(-9.63290 - 13.8415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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