LMFDB - Embedded newform 570.2.k.a.77.9

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			77.9
Character	$\chi$	$=$	570.77
Dual form			570.2.k.a.533.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.65263 + 0.518471i) q^{3} -1.00000i q^{4} +(2.11139 - 0.736229i) q^{5} +(-1.53520 + 0.801972i) q^{6} +(-2.44114 - 2.44114i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.46238 + 1.71368i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.65263 + 0.518471i) 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} +(0.518471 - 1.65263i) q^{12} +(0.933851 - 0.933851i) q^{13} +3.45230 q^{14} +(3.87106 - 0.122020i) q^{15} -1.00000 q^{16} +(-0.0532613 + 0.0532613i) q^{17} +(-2.95292 + 0.529408i) 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} +(3.18091 + 4.10875i) q^{27} +(-2.44114 + 2.44114i) q^{28} +6.56484 q^{29} +(-2.65097 + 2.82353i) q^{30} -5.11218 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.91441 - 9.28973i) 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} +(5.70537 + 1.78991i) q^{42} +(-7.57828 + 7.57828i) q^{43} -5.62118 q^{44} +(6.46070 + 1.80538i) q^{45} -1.19033 q^{46} +(-2.64154 + 2.64154i) q^{47} +(-1.65263 - 0.518471i) 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} +(-0.518471 + 1.65263i) q^{57} +(-4.64204 + 4.64204i) q^{58} +11.0697 q^{59} +(-0.122020 - 3.87106i) q^{60} +9.82484 q^{61} +(3.61486 - 3.61486i) q^{62} +(-1.82767 - 10.1943i) 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} +(0.529408 + 2.95292i) q^{72} +(-7.35442 + 7.35442i) q^{73} +8.32453 q^{74} +(8.08348 - 3.10762i) q^{75} +1.00000 q^{76} +(-13.7221 + 13.7221i) q^{77} +(-0.684726 + 2.18257i) 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} +(10.8493 + 3.40368i) q^{87} +(3.97477 - 3.97477i) q^{88} -4.69409 q^{89} +(-5.84500 + 3.29181i) q^{90} -4.55933 q^{91} +(0.841693 - 0.841693i) q^{92} +(-8.44855 - 2.65052i) 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
$3$	1.65263	+	0.518471i	0.954147	+	0.299339i
$3$	1.65263	+	0.518471i	0.954147	+	0.299339i
$4$		−	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	$-0.678152\pi$
$11$		−	5.62118i		−	1.69485i	0.530916	−	0.847424i	$-0.321848\pi$
$12$	0.518471	−	1.65263i	0.149670	−	0.477073i
$13$	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
$15$	3.87106	−	0.122020i	0.999504	−	0.0315055i
$16$	−1.00000			−0.250000
$17$	−0.0532613	+	0.0532613i	−0.0129178	+	0.0129178i	−0.713536	−	0.700618i	$-0.752908\pi$
$17$	−0.0532613	+	0.0532613i	−0.0129178	+	0.0129178i	0.700618	+	0.713536i	$0.252908\pi$
$18$	−2.95292	+	0.529408i	−0.696010	+	0.124783i
$19$			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	0.789393	−	0.613888i	$-0.210395\pi$
$23$	0.841693	+	0.841693i	0.175505	+	0.175505i	−0.613888	+	0.789393i	$0.710395\pi$
$24$	0.801972	+	1.53520i	0.163702	+	0.313371i
$25$	3.91593	−	3.10893i	0.783187	−	0.621786i
$26$			1.32067i			0.259004i
$27$	3.18091	+	4.10875i	0.612166	+	0.790730i
$28$	−2.44114	+	2.44114i	−0.461332	+	0.461332i
$29$	6.56484			1.21906			0.609530	−	0.792763i	$-0.291358\pi$
$29$	6.56484			1.21906			0.609530	+	0.792763i	$0.291358\pi$
$30$	−2.65097	+	2.82353i	−0.483999	+	0.515505i
$31$	−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
$33$	2.91441	−	9.28973i	0.507335	−	1.61713i
$34$		−	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	$0.148474\pi$
$41$			5.75913i			0.899426i	−0.893173	+	0.449713i	$0.851526\pi$
$42$	5.70537	+	1.78991i	0.880358	+	0.276190i
$43$	−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
$45$	6.46070	+	1.80538i	0.963104	+	0.269130i
$46$	−1.19033			−0.175505
$47$	−2.64154	+	2.64154i	−0.385308	+	0.385308i	−0.873010	−	0.487702i	$-0.837835\pi$
$47$	−2.64154	+	2.64154i	−0.385308	+	0.385308i	0.487702	+	0.873010i	$0.337835\pi$
$48$	−1.65263	−	0.518471i	−0.238537	−	0.0748348i
$49$			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	$0.138876\pi$
$53$	9.67459	+	9.67459i	1.32891	+	1.32891i	0.422583	+	0.906324i	$0.361124\pi$
$54$	−5.15457	−	0.656086i	−0.701448	−	0.0892821i
$55$	−4.13847	−	11.8685i	−0.558031	−	1.60035i
$56$		−	3.45230i		−	0.461332i
$57$	−0.518471	+	1.65263i	−0.0686731	+	0.218896i
$58$	−4.64204	+	4.64204i	−0.609530	+	0.609530i
$59$	11.0697			1.44116			0.720579	−	0.693373i	$-0.243876\pi$
$59$	11.0697			1.44116			0.720579	+	0.693373i	$0.243876\pi$
$60$	−0.122020	−	3.87106i	−0.0157528	−	0.499752i
$61$	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
$63$	−1.82767	−	10.1943i	−0.230265	−	1.28437i
$64$			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	$-0.956554\pi$
$71$		−	2.29302i		−	0.272131i	0.990700	−	0.136066i	$-0.0434458\pi$
$72$	0.529408	+	2.95292i	0.0623913	+	0.348005i
$73$	−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
$75$	8.08348	−	3.10762i	0.933400	−	0.358837i
$76$	1.00000			0.114708
$77$	−13.7221	+	13.7221i	−1.56378	+	1.56378i
$78$	−0.684726	+	2.18257i	−0.0775300	+	0.247128i
$79$			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	0.389318	−	0.921103i	$-0.372711\pi$
$83$	−4.84479	−	4.84479i	−0.531785	−	0.531785i	−0.921103	+	0.389318i	$0.872711\pi$
$84$	−5.29997	+	2.76865i	−0.578274	+	0.302084i
$85$	−0.0732429	+	0.151668i	−0.00794431	+	0.0164507i
$86$		−	10.7173i		−	1.15568i
$87$	10.8493	+	3.40368i	1.16316	+	0.364912i
$88$	3.97477	−	3.97477i	0.423712	−	0.423712i
$89$	−4.69409			−0.497572			−0.248786	−	0.968558i	$-0.580032\pi$
$89$	−4.69409			−0.497572			−0.248786	+	0.968558i	$0.580032\pi$
$90$	−5.84500	+	3.29181i	−0.616117	+	0.346987i
$91$	−4.55933			−0.477947
$92$	0.841693	−	0.841693i	0.0877526	−	0.0877526i
$93$	−8.44855	−	2.65052i	−0.876073	−	0.274846i
$94$		−	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	$0.0133902\pi$
$101$			0.845280i			0.0841085i	−0.999115	+	0.0420543i	$0.986610\pi$
$102$	0.0390527	−	0.124481i	0.00386679	−	0.0123254i
$103$	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
$105$	−9.74768	−	9.15194i	−0.951276	−	0.893138i
$106$	−13.6819			−1.32891
$107$	−6.17999	+	6.17999i	−0.597442	+	0.597442i	−0.939631	−	0.342189i	$-0.888832\pi$
$107$	−6.17999	+	6.17999i	−0.597442	+	0.597442i	0.342189	+	0.939631i	$0.388832\pi$
$108$	4.10875	−	3.18091i	0.395365	−	0.306083i
$109$		−	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	$0.109045\pi$
$113$	13.5833	+	13.5833i	1.27781	+	1.27781i	0.335915	+	0.941892i	$0.390955\pi$
$114$	−0.801972	−	1.53520i	−0.0751116	−	0.143785i
$115$	2.39682	+	1.15746i	0.223505	+	0.107934i
$116$		−	6.56484i		−	0.609530i
$117$	3.89982	−	0.699170i	0.360538	−	0.0646383i
$118$	−7.82749	+	7.82749i	−0.720579	+	0.720579i
$119$	0.260037			0.0238375
$120$	2.82353	+	2.65097i	0.257752	+	0.242000i
$121$	−20.5976			−1.87251
$122$	−6.94721	+	6.94721i	−0.628971	+	0.628971i
$123$	−2.98594	+	9.51772i	−0.269233	+	0.858184i
$124$			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	$-0.998151\pi$
$131$		−	0.132969i		−	0.0116176i	0.999983	−	0.00580880i	$-0.00184901\pi$
$132$	−9.28973	−	2.91441i	−0.808567	−	0.253667i
$133$	2.44114	−	2.44114i	0.211674	−	0.211674i
$134$	−8.87605			−0.766774
$135$	9.74111	+	6.33330i	0.838381	+	0.545084i
$136$	−0.0753229			−0.00645888
$137$	−11.8447	+	11.8447i	−1.01196	+	1.01196i	−0.0120322	+	0.999928i	$0.503830\pi$
$137$	−11.8447	+	11.8447i	−1.01196	+	1.01196i	−0.999928	+	0.0120322i	$0.996170\pi$
$138$	−1.96718	−	0.617153i	−0.167458	−	0.0525356i
$139$		−	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
$147$	−2.55002	+	8.12820i	−0.210322	+	0.670403i
$148$	−5.88633	+	5.88633i	−0.483853	+	0.483853i
$149$	−21.7749			−1.78387			−0.891934	−	0.452165i	$-0.850652\pi$
$149$	−21.7749			−1.78387			−0.891934	+	0.452165i	$0.850652\pi$
$150$	−3.51847	+	7.91330i	−0.287282	+	0.646119i
$151$	−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
$153$	−0.222422	+	0.0398765i	−0.0179818	+	0.00322382i
$154$		−	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
$162$	−8.17843	−	3.75676i	−0.642558	−	0.295159i
$163$	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
$165$	−0.685899	−	21.7599i	−0.0533971	−	1.69401i
$166$	6.85157			0.531785
$167$	−11.3116	+	11.3116i	−0.875319	+	0.875319i	−0.993046	−	0.117727i	$-0.962439\pi$
$167$	−11.3116	+	11.3116i	−0.875319	+	0.875319i	0.117727	+	0.993046i	$0.462439\pi$
$168$	1.78991	−	5.70537i	0.138095	−	0.440179i
$169$			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	$-0.900425\pi$
$173$	−16.5624	−	16.5624i	−1.25921	−	1.25921i	−0.307746	−	0.951468i	$-0.599575\pi$
$174$	−10.0783	+	5.26482i	−0.764037	+	0.399125i
$175$	−17.1487	−	1.97001i	−1.29632	−	0.148919i
$176$			5.62118i			0.423712i
$177$	18.2942	+	5.73934i	1.37508	+	0.431395i
$178$	3.31922	−	3.31922i	0.248786	−	0.248786i
$179$	13.4740			1.00710			0.503549	−	0.863967i	$-0.332027\pi$
$179$	13.4740			1.00710			0.503549	+	0.863967i	$0.332027\pi$
$180$	1.80538	−	6.46070i	0.134565	−	0.481552i
$181$	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
$183$	16.2368	+	5.09389i	1.20026	+	0.376551i
$184$			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	$-0.800004\pi$
$191$		−	16.2464i		−	1.17555i	0.809024	−	0.587775i	$-0.199996\pi$
$192$	−0.518471	+	1.65263i	−0.0374174	+	0.119268i
$193$	−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
$195$	3.50105	−	3.72894i	0.250715	−	0.267035i
$196$	4.91834			0.351310
$197$	5.51445	−	5.51445i	0.392889	−	0.392889i	−0.482827	−	0.875716i	$-0.660390\pi$
$197$	5.51445	−	5.51445i	0.392889	−	0.392889i	0.875716	+	0.482827i	$0.160390\pi$
$198$	2.97589	+	16.5989i	0.211488	+	1.17963i
$199$		−	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
$207$	0.630172	+	3.51496i	0.0438000	+	0.244307i
$208$	−0.933851	+	0.933851i	−0.0647509	+	0.0647509i
$209$	5.62118			0.388825
$210$	13.3640	−	0.421251i	0.922207	−	0.0290691i
$211$	−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
$213$	1.18886	−	3.78951i	0.0814595	−	0.259653i
$214$		−	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
$222$	13.7574	+	4.31602i	0.923334	+	0.289673i
$223$	−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
$225$	14.9702	−	0.944697i	0.998015	−	0.0629798i
$226$	−19.2097			−1.27781
$227$	12.5348	−	12.5348i	0.831965	−	0.831965i	−0.155820	−	0.987785i	$-0.549802\pi$
$227$	12.5348	−	12.5348i	0.831965	−	0.831965i	0.987785	+	0.155820i	$0.0498021\pi$
$228$	1.65263	+	0.518471i	0.109448	+	0.0343366i
$229$			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	0.995689	−	0.0927575i	$-0.0295681\pi$
$233$	13.7826	+	13.7826i	0.902931	+	0.902931i	−0.0927575	+	0.995689i	$0.529568\pi$
$234$	−2.26320	+	3.25198i	−0.147950	+	0.212588i
$235$	−3.63254	+	7.52210i	−0.236961	+	0.490688i
$236$		−	11.0697i		−	0.720579i
$237$	−1.77216	+	5.64879i	−0.115114	+	0.366928i
$238$	−0.183874	+	0.183874i	−0.0119188	+	0.0119188i
$239$	0.604284			0.0390879			0.0195439	−	0.999809i	$-0.493779\pi$
$239$	0.604284			0.0390879			0.0195439	+	0.999809i	$0.493779\pi$
$240$	−3.87106	+	0.122020i	−0.249876	+	0.00787639i
$241$	−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
$243$	0.791496	+	15.5684i	0.0507745	+	0.998710i
$244$		−	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	$0.00804226\pi$
$251$			0.800477i			0.0505256i	−0.999681	+	0.0252628i	$0.991958\pi$
$252$	−10.1943	+	1.82767i	−0.642183	+	0.115132i
$253$	4.73131	−	4.73131i	0.297455	−	0.297455i
$254$	6.84738			0.429643
$255$	−0.199679	+	0.212677i	−0.0125044	+	0.0133183i
$256$	1.00000			0.0625000
$257$	−0.187825	+	0.187825i	−0.0117162	+	0.0117162i	−0.712941	−	0.701224i	$-0.752637\pi$
$257$	−0.187825	+	0.187825i	−0.0117162	+	0.0117162i	0.701224	+	0.712941i	$0.252637\pi$
$258$	5.55661	−	17.7118i	0.345940	−	1.10269i
$259$			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	0.704080	−	0.710121i	$-0.251360\pi$
$263$	−0.0979650	−	0.0979650i	−0.00604078	−	0.00604078i	−0.710121	+	0.704080i	$0.751360\pi$
$264$	8.62963	−	4.50803i	0.531117	−	0.277450i
$265$	27.5495	+	13.3041i	1.69235	+	0.817266i
$266$			3.45230i			0.211674i
$267$	−7.75759	−	2.43375i	−0.474757	−	0.148943i
$268$	6.27631	−	6.27631i	0.383387	−	0.383387i
$269$	15.3546			0.936185			0.468093	−	0.883679i	$-0.344941\pi$
$269$	15.3546			0.936185			0.468093	+	0.883679i	$0.344941\pi$
$270$	−11.3663	+	2.40969i	−0.691733	+	0.146649i
$271$	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
$273$	−7.53488	−	2.36388i	−0.456032	−	0.143068i
$274$		−	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	$0.0102260\pi$
$281$			1.07688i			0.0642410i	−0.999484	+	0.0321205i	$0.989774\pi$
$282$	1.93685	−	6.17374i	0.115338	−	0.367641i
$283$	−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
$285$	0.122020	+	3.87106i	0.00722787	+	0.229302i
$286$	7.42369			0.438972
$287$	14.0589	−	14.0589i	0.829868	−	0.829868i
$288$	2.95292	−	0.529408i	0.174002	−	0.0311956i
$289$			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	0.734390	−	0.678728i	$-0.237468\pi$
$293$	0.952778	+	0.952778i	0.0556619	+	0.0556619i	−0.678728	+	0.734390i	$0.737468\pi$
$294$	−3.94437	−	7.55064i	−0.230041	−	0.440362i
$295$	23.3726	−	8.14987i	1.36080	−	0.474503i
$296$		−	8.32453i		−	0.483853i
$297$	23.0960	−	17.8804i	1.34017	−	1.03753i
$298$	15.3972	−	15.3972i	0.891934	−	0.891934i
$299$	1.57203			0.0909130
$300$	−3.10762	−	8.08348i	−0.179418	−	0.466700i
$301$	36.9993			2.13261
$302$	9.18387	−	9.18387i	0.528472	−	0.528472i
$303$	−0.438253	+	1.39694i	−0.0251770	+	0.0802519i
$304$		−	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	$0.0563604\pi$
$311$			6.21244i			0.352275i	−0.984366	+	0.176138i	$0.943640\pi$
$312$	2.18257	+	0.684726i	0.123564	+	0.0387650i
$313$	−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
$315$	−11.3643	−	20.1787i	−0.640306	−	1.13694i
$316$	3.41806			0.192281
$317$	6.17490	−	6.17490i	0.346817	−	0.346817i	−0.512106	−	0.858922i	$-0.671134\pi$
$317$	6.17490	−	6.17490i	0.346817	−	0.346817i	0.858922	+	0.512106i	$0.171134\pi$
$318$	−22.6112	−	7.09368i	−1.26797	−	0.397794i
$319$		−	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
$327$	7.13594	−	22.7459i	0.394618	−	1.25785i
$328$	−4.07232	+	4.07232i	−0.224856	+	0.224856i
$329$	12.8967			0.711021
$330$	15.8716	+	14.9016i	0.873702	+	0.820305i
$331$	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
$333$	−4.40707	−	24.5817i	−0.241506	−	1.34707i
$334$		−	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
$342$	−0.529408	−	2.95292i	−0.0286271	−	0.159676i
$343$	−5.08162	+	5.08162i	−0.274382	+	0.274382i
$344$	−10.7173			−0.577839
$345$	3.36095	+	3.15554i	0.180947	+	0.169889i
$346$	23.4227			1.25921
$347$	−7.59916	+	7.59916i	−0.407944	+	0.407944i	−0.881021	−	0.473077i	$-0.843143\pi$
$347$	−7.59916	+	7.59916i	−0.407944	+	0.407944i	0.473077	+	0.881021i	$0.343143\pi$
$348$	3.40368	−	10.8493i	0.182456	−	0.581581i
$349$			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	0.753433	−	0.657524i	$-0.228396\pi$
$353$	1.80197	+	1.80197i	0.0959090	+	0.0959090i	−0.657524	+	0.753433i	$0.728396\pi$
$354$	−16.9943	+	8.87763i	−0.903236	+	0.471841i
$355$	−1.68819	−	4.84145i	−0.0895996	−	0.256958i
$356$			4.69409i			0.248786i
$357$	0.429745	+	0.134821i	0.0227445	+	0.00713551i
$358$	−9.52759	+	9.52759i	−0.503549	+	0.503549i
$359$	16.7534			0.884209			0.442104	−	0.896964i	$-0.354232\pi$
$359$	16.7534			0.884209			0.442104	+	0.896964i	$0.354232\pi$
$360$	3.29181	+	5.84500i	0.173494	+	0.308058i
$361$	−1.00000			−0.0526316
$362$	−7.42232	+	7.42232i	−0.390108	+	0.390108i
$363$	−34.0403	−	10.6793i	−1.78665	−	0.560516i
$364$			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
$372$	−2.65052	+	8.44855i	−0.137423	+	0.438037i
$373$	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
$375$	14.7795	−	12.5127i	0.763208	−	0.646152i
$376$	−3.73570			−0.192654
$377$	6.13059	−	6.13059i	0.315741	−	0.315741i
$378$	10.9814	+	14.1846i	0.564824	+	0.729578i
$379$			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	0.471921	−	0.881641i	$-0.343561\pi$
$383$	−8.01839	−	8.01839i	−0.409721	−	0.409721i	−0.881641	+	0.471921i	$0.843561\pi$
$384$	−0.801972	−	1.53520i	−0.0409255	−	0.0783429i
$385$	−18.8701	+	39.0753i	−0.961708	+	1.99146i
$386$		−	3.16174i		−	0.160928i
$387$	−31.6473	+	5.67383i	−1.60873	+	0.288417i
$388$	−4.18214	+	4.18214i	−0.212316	+	0.212316i
$389$	23.1601			1.17426			0.587131	−	0.809492i	$-0.300257\pi$
$389$	23.1601			1.17426			0.587131	+	0.809492i	$0.300257\pi$
$390$	0.161148	+	5.11238i	0.00816006	+	0.258875i
$391$	−0.0896594			−0.00453427
$392$	−3.47779	+	3.47779i	−0.175655	+	0.175655i
$393$	0.0689408	−	0.219749i	0.00347760	−	0.0110849i
$394$			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	$0.322081\pi$
$401$			33.9549i			1.69563i	−0.530295	+	0.847813i	$0.677919\pi$
$402$	−14.6688	−	4.60197i	−0.731614	−	0.229525i
$403$	−4.77402	+	4.77402i	−0.237811	+	0.237811i
$404$	0.845280			0.0420543
$405$	12.8148	+	15.5171i	0.636774	+	0.771050i
$406$	22.6638			1.12478
$407$	−33.0881	+	33.0881i	−1.64012	+	1.64012i
$408$	−0.124481	−	0.0390527i	−0.00616272	−	0.00193340i
$409$			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
$417$	5.93532	−	18.9189i	0.290654	−	0.926463i
$418$	−3.97477	+	3.97477i	−0.194412	+	0.194412i
$419$	1.26502			0.0618005			0.0309003	−	0.999522i	$-0.490163\pi$
$419$	1.26502			0.0618005			0.0309003	+	0.999522i	$0.490163\pi$
$420$	−9.15194	+	9.74768i	−0.446569	+	0.475638i
$421$	−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
$423$	−11.0312	+	1.97771i	−0.536356	+	0.0961595i
$424$			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	$-0.896469\pi$
$431$		−	13.2679i		−	0.639093i	0.947571	−	0.319546i	$-0.103531\pi$
$432$	−3.18091	−	4.10875i	−0.153041	−	0.197682i
$433$	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
$435$	25.4129	−	0.801045i	1.21845	−	0.0384072i
$436$	−13.7634			−0.659149
$437$	−0.841693	+	0.841693i	−0.0402636	+	0.0402636i
$438$	5.39247	−	17.1886i	0.257662	−	0.821301i
$439$		−	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	0.0607845	−	0.998151i	$-0.480640\pi$
$443$	−19.7293	−	19.7293i	−0.937366	−	0.937366i	−0.998151	+	0.0607845i	$0.980640\pi$
$444$	−12.7798	+	6.67604i	−0.606503	+	0.316831i
$445$	−9.91105	+	3.45592i	−0.469829	+	0.163826i
$446$		−	8.58534i		−	0.406527i
$447$	−35.9859	−	11.2896i	−1.70207	−	0.533982i
$448$	2.44114	−	2.44114i	0.115333	−	0.115333i
$449$	−18.2109			−0.859426			−0.429713	−	0.902966i	$-0.641385\pi$
$449$	−18.2109			−0.859426			−0.429713	+	0.902966i	$0.641385\pi$
$450$	−9.91754	+	11.2535i	−0.467517	+	0.530497i
$451$	32.3731			1.52439
$452$	13.5833	−	13.5833i	0.638904	−	0.638904i
$453$	−21.4643	−	6.73387i	−1.00848	−	0.316385i
$454$			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	$-0.890430\pi$
$461$		−	14.4915i		−	0.674935i	0.941337	−	0.337467i	$-0.109570\pi$
$462$	10.0614	−	32.0709i	0.468100	−	1.49207i
$463$	−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
$465$	−19.7896	+	0.623791i	−0.917719	+	0.0289276i
$466$	−19.4916			−0.902931
$467$	1.06586	−	1.06586i	0.0493219	−	0.0493219i	−0.682016	−	0.731338i	$-0.738896\pi$
$467$	1.06586	−	1.06586i	0.0493219	−	0.0493219i	0.731338	+	0.682016i	$0.238896\pi$
$468$	−0.699170	−	3.89982i	−0.0323192	−	0.180269i
$469$		−	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
$477$	7.24332	+	40.4016i	0.331649	+	1.84986i
$478$	−0.427293	+	0.427293i	−0.0195439	+	0.0195439i
$479$	10.1543			0.463962			0.231981	−	0.972720i	$-0.425479\pi$
$479$	10.1543			0.463962			0.231981	+	0.972720i	$0.425479\pi$
$480$	2.65097	−	2.82353i	0.121000	−	0.128876i
$481$	−10.9939			−0.501279
$482$	1.16182	−	1.16182i	0.0529196	−	0.0529196i
$483$	2.13059	−	6.79129i	0.0969454	−	0.309015i
$484$			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	$0.00769487\pi$
$491$			1.07122i			0.0483436i	−0.999708	+	0.0241718i	$0.992305\pi$
$492$	9.51772	+	2.98594i	0.429092	+	0.134617i
$493$	−0.349652	+	0.349652i	−0.0157475	+	0.0157475i
$494$	−1.32067			−0.0594195
$495$	10.1483	−	36.3167i	0.456134	−	1.63232i
$496$	5.11218			0.229544
$497$	−5.59758	+	5.59758i	−0.251086	+	0.251086i
$498$	11.3231	+	3.55234i	0.507401	+	0.159184i
$499$		−	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	$0.00299252\pi$
$503$	22.6375	+	22.6375i	1.00936	+	1.00936i	0.00940114	+	0.999956i	$0.497007\pi$
$504$	5.91613	−	8.50085i	0.263526	−	0.378658i
$505$	0.622320	+	1.78472i	0.0276929	+	0.0794188i
$506$			6.69108i			0.297455i
$507$	−5.83582	+	18.6018i	−0.259178	+	0.826133i
$508$	−4.84183	+	4.84183i	−0.214822	+	0.214822i
$509$	−13.7670			−0.610210			−0.305105	−	0.952319i	$-0.598692\pi$
$509$	−13.7670			−0.610210			−0.305105	+	0.952319i	$0.598692\pi$
$510$	−0.00919093	−	0.291579i	−0.000406981	−	0.0129114i
$511$	35.9064			1.58840
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−4.10875	+	3.18091i	−0.181406	+	0.140440i
$514$		−	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	$-0.987629\pi$
$521$		−	1.77371i		−	0.0777075i	0.999245	−	0.0388537i	$-0.0123706\pi$
$522$	−19.3854	+	3.47548i	−0.848478	+	0.152117i
$523$	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
$525$	−27.3191	−	12.1468i	−1.19230	−	0.530129i
$526$	0.138543			0.00604078
$527$	0.272282	−	0.272282i	0.0118608	−	0.0118608i
$528$	−2.91441	+	9.28973i	−0.126834	+	0.404284i
$529$		−	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
$537$	22.2676	+	6.98590i	0.960919	+	0.301464i
$538$	−10.8573	+	10.8573i	−0.468093	+	0.468093i
$539$	27.6469			1.19084
$540$	6.33330	−	9.74111i	0.272542	−	0.419191i
$541$	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
$543$	17.3472	+	5.44225i	0.744441	+	0.233549i
$544$			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
$552$	−0.617153	+	1.96718i	−0.0262678	+	0.0837288i
$553$	8.34396	−	8.34396i	0.354821	−	0.354821i
$554$	7.40629			0.314663
$555$	−23.5046	−	22.0681i	−0.997714	−	0.936738i
$556$	−11.4478			−0.485493
$557$	−8.91400	+	8.91400i	−0.377698	+	0.377698i	−0.870271	−	0.492573i	$-0.836057\pi$
$557$	−8.91400	+	8.91400i	−0.377698	+	0.377698i	0.492573	+	0.870271i	$0.336057\pi$
$558$	15.0959	−	2.70643i	0.639058	−	0.114572i
$559$			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	0.971755	−	0.235993i	$-0.0758344\pi$
$563$	17.4579	+	17.4579i	0.735761	+	0.735761i	−0.235993	+	0.971755i	$0.575834\pi$
$564$	2.99593	+	5.73505i	0.126151	+	0.241489i
$565$	38.6800	+	18.6792i	1.62728	+	0.785840i
$566$		−	18.9019i		−	0.794508i
$567$	12.9694	−	28.2344i	0.544665	−	1.18573i
$568$	1.62141	−	1.62141i	0.0680328	−	0.0680328i
$569$	−6.84928			−0.287137			−0.143568	−	0.989640i	$-0.545858\pi$
$569$	−6.84928			−0.287137			−0.143568	+	0.989640i	$0.545858\pi$
$570$	−2.82353	−	2.65097i	−0.118265	−	0.111037i
$571$	−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
$573$	8.42329	−	26.8493i	0.351888	−	1.12165i
$574$			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
$582$	9.77437	+	3.06646i	0.405161	+	0.127109i
$583$	54.3826	−	54.3826i	2.25230	−	2.25230i
$584$	−10.4007			−0.430385
$585$	7.71929	−	4.34738i	0.319153	−	0.179742i
$586$	−1.34743			−0.0556619
$587$	−27.2033	+	27.2033i	−1.12280	+	1.12280i	−0.131481	+	0.991319i	$0.541973\pi$
$587$	−27.2033	+	27.2033i	−1.12280	+	1.12280i	−0.991319	+	0.131481i	$0.958027\pi$
$588$	8.12820	+	2.55002i	0.335201	+	0.105161i
$589$		−	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	0.669702	−	0.742630i	$-0.266422\pi$
$593$	−1.77591	−	1.77591i	−0.0729280	−	0.0729280i	−0.742630	+	0.669702i	$0.766422\pi$
$594$	−3.68798	+	28.9747i	−0.151320	+	1.18885i
$595$	0.549039	−	0.191447i	0.0225084	−	0.00784855i
$596$			21.7749i			0.891934i
$597$	11.5781	−	36.9052i	0.473858	−	1.51043i
$598$	−1.11159	+	1.11159i	−0.0454565	+	0.0454565i
$599$	4.67096			0.190850			0.0954252	−	0.995437i	$-0.469579\pi$
$599$	4.67096			0.190850			0.0954252	+	0.995437i	$0.469579\pi$
$600$	7.91330	+	3.51847i	0.323059	+	0.143641i
$601$	−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
$603$	4.69905	+	26.2102i	0.191360	+	1.06736i
$604$			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
$612$	0.0398765	+	0.222422i	0.00161191	+	0.00899089i
$613$	−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
$615$	0.702732	+	22.2940i	0.0283369	+	0.898979i
$616$	−19.4060			−0.781888
$617$	32.7653	−	32.7653i	1.31908	−	1.31908i	0.404577	−	0.914504i	$-0.367419\pi$
$617$	32.7653	−	32.7653i	1.31908	−	1.31908i	0.914504	−	0.404577i	$-0.132581\pi$
$618$	−1.26136	+	4.02060i	−0.0507394	+	0.161732i
$619$			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
$627$	9.28973	+	2.91441i	0.370996	+	0.116391i
$628$	10.2762	−	10.2762i	0.410066	−	0.410066i
$629$	0.627027			0.0250012
$630$	22.3042	+	6.23269i	0.888622	+	0.248316i
$631$	−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
$633$	−8.12130	−	2.54785i	−0.322793	−	0.101268i
$634$			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	$-0.768151\pi$
$641$		−	33.7063i		−	1.33132i	0.746256	−	0.665659i	$-0.231849\pi$
$642$	4.53134	−	14.4437i	0.178838	−	0.570047i
$643$	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
$645$	−28.4113	+	30.2607i	−1.11869	+	1.19151i
$646$	0.0753229			0.00296354
$647$	18.8461	−	18.8461i	0.740918	−	0.740918i	−0.231837	−	0.972755i	$-0.574474\pi$
$647$	18.8461	−	18.8461i	0.740918	−	0.740918i	0.972755	+	0.231837i	$0.0744736\pi$
$648$	−3.75676	+	8.17843i	−0.147579	+	0.321279i
$649$		−	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	$0.0216894\pi$
$653$	27.2344	+	27.2344i	1.06577	+	1.06577i	0.0680864	+	0.997679i	$0.478311\pi$
$654$	11.0379	+	21.1296i	0.431616	+	0.826234i
$655$	−0.0978959	−	0.280750i	−0.00382511	−	0.0109698i
$656$		−	5.75913i		−	0.224856i
$657$	−30.7125	+	5.50622i	−1.19821	+	0.214818i
$658$	−9.11938	+	9.11938i	−0.355510	+	0.355510i
$659$	−25.2158			−0.982269			−0.491135	−	0.871084i	$-0.663418\pi$
$659$	−25.2158			−0.982269			−0.491135	+	0.871084i	$0.663418\pi$
$660$	−21.7599	+	0.685899i	−0.847003	+	0.0266986i
$661$	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
$663$	−0.0515756	+	0.164398i	−0.00200303	+	0.00638468i
$664$		−	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
$672$	−5.70537	−	1.78991i	−0.220089	−	0.0690474i
$673$	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
$675$	25.2300	+	6.20039i	0.971105	+	0.238653i
$676$	11.2558			0.432917
$677$	4.56460	−	4.56460i	0.175432	−	0.175432i	−0.613929	−	0.789361i	$-0.710412\pi$
$677$	4.56460	−	4.56460i	0.175432	−	0.175432i	0.789361	+	0.613929i	$0.210412\pi$
$678$	−31.7465	−	9.95964i	−1.21922	−	0.382498i
$679$			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	0.0916982	−	0.995787i	$-0.470770\pi$
$683$	−23.6277	−	23.6277i	−0.904089	−	0.904089i	−0.995787	+	0.0916982i	$0.970770\pi$
$684$	2.46238	+	1.71368i	0.0941513	+	0.0655242i
$685$	−16.2884	+	33.7291i	−0.622346	+	1.28872i
$686$		−	7.18650i		−	0.274382i
$687$	−2.09197	+	6.66819i	−0.0798138	+	0.254407i
$688$	7.57828	−	7.57828i	0.288919	−	0.288919i
$689$	18.0693			0.688384
$690$	−4.60785	+	0.145245i	−0.175418	+	0.00552939i
$691$	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
$693$	−57.3042	+	10.2737i	−2.17681	+	0.390264i
$694$		−	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	$0.282883\pi$
$701$			41.1049i			1.55251i	−0.630419	+	0.776255i	$0.717117\pi$
$702$	−5.42629	+	4.20091i	−0.204802	+	0.158553i
$703$	5.88633	−	5.88633i	0.222007	−	0.222007i
$704$	5.62118			0.211856
$705$	−9.90324	+	10.5479i	−0.372978	+	0.397256i
$706$	−2.54837			−0.0959090
$707$	2.06345	−	2.06345i	0.0776040	−	0.0776040i
$708$	5.73934	−	18.2942i	0.215698	−	0.687538i
$709$			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
$717$	0.998658	+	0.313304i	0.0372956	+	0.0117005i
$718$	−11.8464	+	11.8464i	−0.442104	+	0.442104i
$719$	−20.7582			−0.774149			−0.387075	−	0.922048i	$-0.626514\pi$
$719$	−20.7582			−0.774149			−0.387075	+	0.922048i	$0.626514\pi$
$720$	−6.46070	−	1.80538i	−0.240776	−	0.0672824i
$721$	−8.39891			−0.312792
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$	−2.71538	−	0.851882i	−0.100986	−	0.0316818i
$724$		−	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
$732$	5.09389	−	16.2368i	0.188276	−	0.600131i
$733$	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
$735$	0.600138	+	19.0392i	0.0221364	+	0.702272i
$736$	1.19033			0.0438763
$737$	35.2803	−	35.2803i	1.29956	−	1.29956i
$738$	−3.04893	−	17.0063i	−0.112233	−	0.626009i
$739$			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	$0.0130403\pi$
$743$	28.3515	+	28.3515i	1.04012	+	1.04012i	0.0409557	+	0.999161i	$0.486960\pi$
$744$	−4.09983	−	7.84822i	−0.150307	−	0.287730i
$745$	−45.9753	+	16.0313i	−1.68440	+	0.587341i
$746$			18.4519i			0.675570i
$747$	−3.62727	−	20.2321i	−0.132715	−	0.740255i
$748$	0.299391	−	0.299391i	0.0109468	−	0.0109468i
$749$	30.1725			1.10248
$750$	−1.60286	+	19.2985i	−0.0585280	+	0.704680i
$751$	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
$753$	−0.415024	+	1.32289i	−0.0151243	+	0.0482089i
$754$			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	$0.0466327\pi$
$761$			8.05394i			0.291955i	−0.989288	+	0.145977i	$0.953367\pi$
$762$	11.3162	+	3.55017i	0.409943	+	0.128609i
$763$	−33.5985	+	33.5985i	−1.21635	+	1.21635i
$764$	−16.2464			−0.587775
$765$	−0.440262	+	0.247949i	−0.0159177	+	0.00896460i
$766$	11.3397			0.409721
$767$	10.3375	−	10.3375i	0.373265	−	0.373265i
$768$	1.65263	+	0.518471i	0.0596342	+	0.0187087i
$769$			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	0.550769	−	0.834658i	$-0.314334\pi$
$773$	−7.89291	−	7.89291i	−0.283888	−	0.283888i	−0.834658	+	0.550769i	$0.814334\pi$
$774$	18.3661	−	26.3901i	0.660154	−	0.948571i
$775$	−20.0190	+	15.8934i	−0.719102	+	0.570909i
$776$		−	5.91443i		−	0.212316i
$777$	−14.9002	+	47.4945i	−0.534541	+	1.70386i
$778$	−16.3766	+	16.3766i	−0.587131	+	0.587131i
$779$	−5.75913			−0.206342
$780$	−3.72894	−	3.50105i	−0.133518	−	0.125358i
$781$	−12.8895			−0.461221
$782$	0.0633988	−	0.0633988i	0.00226713	−	0.00226713i
$783$	20.8821	+	26.9733i	0.746267	+	0.963947i
$784$		−	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
$792$	16.5989	−	2.97589i	0.589815	−	0.105744i
$793$	9.17494	−	9.17494i	0.325812	−	0.325812i
$794$	23.1663			0.822143
$795$	38.6314	+	36.2704i	1.37012	+	1.28638i
$796$	−22.3312			−0.791508
$797$	−5.95116	+	5.95116i	−0.210801	+	0.210801i	−0.804608	−	0.593807i	$-0.797624\pi$
$797$	−5.95116	+	5.95116i	−0.210801	+	0.210801i	0.593807	+	0.804608i	$0.297624\pi$
$798$	−1.78991	+	5.70537i	−0.0633623	+	0.201968i
$799$		−	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
$807$	25.3754	+	7.96090i	0.893258	+	0.280237i
$808$	−0.597703	+	0.597703i	−0.0210271	+	0.0210271i
$809$	−43.0115			−1.51220			−0.756101	−	0.654455i	$-0.772898\pi$
$809$	−43.0115			−1.51220			−0.756101	+	0.654455i	$0.772898\pi$
$810$	−20.0337	−	1.91079i	−0.703912	−	0.0671382i
$811$	−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
$813$	14.7344	+	4.62255i	0.516759	+	0.162120i
$814$		−	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	$-0.651913\pi$
$821$		−	50.9029i		−	1.77652i	0.459336	−	0.888262i	$-0.348087\pi$
$822$	8.68486	−	27.6831i	0.302919	−	0.965558i
$823$	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
$825$	−17.4685	−	45.4387i	−0.608174	−	1.58197i
$826$	38.2160			1.32971
$827$	18.7028	−	18.7028i	0.650360	−	0.650360i	−0.302720	−	0.953080i	$-0.597895\pi$
$827$	18.7028	−	18.7028i	0.650360	−	0.650360i	0.953080	+	0.302720i	$0.0978945\pi$
$828$	3.51496	−	0.630172i	0.122153	−	0.0219000i
$829$		−	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
$837$	−16.2614	−	21.0047i	−0.562075	−	0.726028i
$838$	−0.894508	+	0.894508i	−0.0309003	+	0.0309003i
$839$	7.29360			0.251803			0.125901	−	0.992043i	$-0.459818\pi$
$839$	7.29360			0.251803			0.125901	+	0.992043i	$0.459818\pi$
$840$	−0.421251	−	13.3640i	−0.0145345	−	0.461103i
$841$	14.0971			0.486108
$842$	3.30367	−	3.30367i	0.113852	−	0.113852i
$843$	−0.558328	+	1.77968i	−0.0192298	+	0.0612953i
$844$			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
$852$	−3.78951	−	1.18886i	−0.129826	−	0.0407297i
$853$	−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
$855$	−1.80538	+	6.46070i	−0.0617426	+	0.220951i
$856$	−8.73982			−0.298721
$857$	34.2645	−	34.2645i	1.17045	−	1.17045i	0.188352	−	0.982102i	$-0.439685\pi$
$857$	34.2645	−	34.2645i	1.17045	−	1.17045i	0.982102	−	0.188352i	$-0.0603146\pi$
$858$	12.2686	+	3.84897i	0.418844	+	0.131402i
$859$			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	0.810003	−	0.586425i	$-0.199465\pi$
$863$	6.56803	+	6.56803i	0.223578	+	0.223578i	−0.586425	+	0.810003i	$0.699465\pi$
$864$	5.15457	+	0.656086i	0.175362	+	0.0223205i
$865$	−47.1634	−	22.7759i	−1.60360	−	0.774405i
$866$			39.5292i			1.34326i
$867$	−8.81106	+	28.0853i	−0.299239	+	0.953828i
$868$	12.4796	−	12.4796i	0.423584	−	0.423584i
$869$	19.2135			0.651773
$870$	−17.4032	+	18.5361i	−0.590024	+	0.628431i
$871$	11.7223			0.397195
$872$	9.73222	−	9.73222i	0.329575	−	0.329575i
$873$	−3.13115	−	17.4648i	−0.105973	−	0.591095i
$874$		−	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	$-0.928601\pi$
$881$		−	13.2041i		−	0.444859i	0.974949	−	0.222429i	$-0.0713986\pi$
$882$	−2.60381	−	14.5235i	−0.0876748	−	0.489031i
$883$	−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
$885$	42.8517	−	1.35074i	1.44044	−	0.0454045i
$886$	27.9014			0.937366
$887$	5.21923	−	5.21923i	0.175245	−	0.175245i	−0.614035	−	0.789279i	$-0.710454\pi$
$887$	5.21923	−	5.21923i	0.175245	−	0.175245i	0.789279	+	0.614035i	$0.210454\pi$
$888$	4.31602	−	13.7574i	0.144836	−	0.461667i
$889$			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
$897$	2.59799	+	0.815053i	0.0867443	+	0.0272138i
$898$	12.8771	−	12.8771i	0.429713	−	0.429713i
$899$	−33.5606			−1.11931
$900$	−0.944697	−	14.9702i	−0.0314899	−	0.499007i
$901$	−1.03056			−0.0343330
$902$	−22.8912	+	22.8912i	−0.762195	+	0.762195i
$903$	61.1462	+	19.1831i	2.03482	+	0.638372i
$904$			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	$0.306678\pi$
$911$			49.5704i			1.64234i	−0.570683	+	0.821170i	$0.693322\pi$
$912$	0.518471	−	1.65263i	0.0171683	−	0.0547241i
$913$	−27.2334	+	27.2334i	−0.901295	+	0.901295i
$914$	9.75606			0.322702
$915$	38.0325	−	1.19883i	1.25732	−	0.0396321i
$916$	4.03489			0.133317
$917$	−0.324597	+	0.324597i	−0.0107191	+	0.0107191i
$918$	0.309483	−	0.239595i	0.0102145	−	0.00790781i
$919$		−	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
$927$	7.18400	−	1.28797i	0.235954	−	0.0423024i
$928$	4.64204	−	4.64204i	0.152383	−	0.152383i
$929$	−58.9237			−1.93322			−0.966611	−	0.256247i	$-0.917514\pi$
$929$	−58.9237			−1.93322			−0.966611	+	0.256247i	$0.917514\pi$
$930$	13.5522	−	14.4344i	0.444396	−	0.473323i
$931$	−4.91834			−0.161192
$932$	13.7826	−	13.7826i	0.451466	−	0.451466i
$933$	−3.22097	+	10.2669i	−0.105450	+	0.336122i
$934$			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	$0.268806\pi$
$941$			45.8679i			1.49525i	−0.664120	+	0.747626i	$0.731194\pi$
$942$	−24.0173	−	7.53481i	−0.782526	−	0.245497i
$943$	−4.84742	+	4.84742i	−0.157854	+	0.157854i
$944$	−11.0697			−0.360290
$945$	−8.31895	−	39.2399i	−0.270615	−	1.27647i
$946$	−60.2439			−1.95870
$947$	14.0103	−	14.0103i	0.455272	−	0.455272i	−0.441828	−	0.897100i	$-0.645670\pi$
$947$	14.0103	−	14.0103i	0.455272	−	0.455272i	0.897100	+	0.441828i	$0.145670\pi$
$948$	5.64879	+	1.77216i	0.183464	+	0.0575572i
$949$			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	0.553631	−	0.832762i	$-0.313242\pi$
$953$	−8.61696	−	8.61696i	−0.279131	−	0.279131i	−0.832762	+	0.553631i	$0.813242\pi$
$954$	−33.6901	−	23.4465i	−1.09076	−	0.759108i
$955$	−11.9611	−	34.3025i	−0.387052	−	1.11000i
$956$		−	0.604284i		−	0.0195439i
$957$	19.1327	−	60.9856i	0.618471	−	1.97138i
$958$	−7.18017	+	7.18017i	−0.231981	+	0.231981i
$959$	57.8291			1.86740
$960$	0.122020	+	3.87106i	0.00393819	+	0.124938i
$961$	−4.86561			−0.156955
$962$	7.77387	−	7.77387i	0.250640	−	0.250640i
$963$	−25.8080	+	4.62693i	−0.831651	+	0.149101i
$964$			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	$-0.876888\pi$
$971$		−	23.5075i		−	0.754391i	0.926134	−	0.377196i	$-0.123112\pi$
$972$	15.5684	−	0.791496i	0.499355	−	0.0253873i
$973$	−27.9456	+	27.9456i	−0.895894	+	0.895894i
$974$	29.5635			0.947275
$975$	4.64672	−	10.4508i	0.148814	−	0.334694i
$976$	−9.82484			−0.314485
$977$	−1.74859	+	1.74859i	−0.0559423	+	0.0559423i	−0.734524	−	0.678582i	$-0.762595\pi$
$977$	−1.74859	+	1.74859i	−0.0559423	+	0.0559423i	0.678582	+	0.734524i	$0.262595\pi$
$978$	−3.64745	+	11.6263i	−0.116633	+	0.371768i
$979$			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	0.374627	−	0.927176i	$-0.377771\pi$
$983$	−17.3240	−	17.3240i	−0.552548	−	0.552548i	−0.927176	+	0.374627i	$0.877771\pi$
$984$	−8.84143	+	4.61867i	−0.281854	+	0.147238i
$985$	7.58326	−	15.7031i	0.241623	−	0.500341i
$986$		−	0.494483i		−	0.0157475i
$987$	21.3136	+	6.68658i	0.678418	+	0.212836i
$988$	0.933851	−	0.933851i	0.0297098	−	0.0297098i
$989$	−12.7572			−0.405655
$990$	18.5038	+	32.8558i	0.588091	+	1.04422i
$991$	−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
$993$	15.7389	+	4.93769i	0.499460	+	0.156693i
$994$		−	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.77.9	✓	36
3.2	odd	2	inner	570.2.k.a.77.13	yes	36
5.3	odd	4	inner	570.2.k.a.533.13	yes	36
15.8	even	4	inner	570.2.k.a.533.9	yes	36

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.65263 + 0.518471i) q^{3} -1.00000i q^{4} +(2.11139 - 0.736229i) q^{5} +(-1.53520 + 0.801972i) q^{6} +(-2.44114 - 2.44114i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.46238 + 1.71368i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.65263 + 0.518471i) 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} +(0.518471 - 1.65263i) q^{12} +(0.933851 - 0.933851i) q^{13} +3.45230 q^{14} +(3.87106 - 0.122020i) q^{15} -1.00000 q^{16} +(-0.0532613 + 0.0532613i) q^{17} +(-2.95292 + 0.529408i) 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} +(3.18091 + 4.10875i) q^{27} +(-2.44114 + 2.44114i) q^{28} +6.56484 q^{29} +(-2.65097 + 2.82353i) q^{30} -5.11218 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.91441 - 9.28973i) 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} +(5.70537 + 1.78991i) q^{42} +(-7.57828 + 7.57828i) q^{43} -5.62118 q^{44} +(6.46070 + 1.80538i) q^{45} -1.19033 q^{46} +(-2.64154 + 2.64154i) q^{47} +(-1.65263 - 0.518471i) 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} +(-0.518471 + 1.65263i) q^{57} +(-4.64204 + 4.64204i) q^{58} +11.0697 q^{59} +(-0.122020 - 3.87106i) q^{60} +9.82484 q^{61} +(3.61486 - 3.61486i) q^{62} +(-1.82767 - 10.1943i) 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} +(0.529408 + 2.95292i) q^{72} +(-7.35442 + 7.35442i) q^{73} +8.32453 q^{74} +(8.08348 - 3.10762i) q^{75} +1.00000 q^{76} +(-13.7221 + 13.7221i) q^{77} +(-0.684726 + 2.18257i) 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} +(10.8493 + 3.40368i) q^{87} +(3.97477 - 3.97477i) q^{88} -4.69409 q^{89} +(-5.84500 + 3.29181i) q^{90} -4.55933 q^{91} +(0.841693 - 0.841693i) q^{92} +(-8.44855 - 2.65052i) 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

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