LMFDB - Embedded newform 640.2.s.c.223.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(223,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 3]))

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

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

chi := DirichletCharacter("640.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.s (of order $4$, degree $2$, not 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.9
Root			$-0.480367 + 1.33013i$ of defining polynomial
Character	$\chi$	$=$	640.223
Dual form			640.2.s.c.287.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.85601 q^{3} +(1.71489 + 1.43498i) q^{5} +(0.458895 - 0.458895i) q^{7} +5.15678 q^{9} +O(q^{10})$	\(q+2.85601 q^{3} +(1.71489 + 1.43498i) q^{5} +(0.458895 - 0.458895i) q^{7} +5.15678 q^{9} +(-0.492763 - 0.492763i) q^{11} -4.52109i q^{13} +(4.89773 + 4.09831i) q^{15} +(-3.12823 + 3.12823i) q^{17} +(-4.04508 - 4.04508i) q^{19} +(1.31061 - 1.31061i) q^{21} +(1.80660 + 1.80660i) q^{23} +(0.881683 + 4.92165i) q^{25} +6.15978 q^{27} +(-3.83926 + 3.83926i) q^{29} -0.139949i q^{31} +(-1.40733 - 1.40733i) q^{33} +(1.44546 - 0.128450i) q^{35} +5.84330i q^{37} -12.9123i q^{39} +4.55648i q^{41} -7.49928i q^{43} +(8.84330 + 7.39986i) q^{45} +(-4.14073 - 4.14073i) q^{47} +6.57883i q^{49} +(-8.93426 + 8.93426i) q^{51} -2.75773 q^{53} +(-0.137930 - 1.55214i) q^{55} +(-11.5528 - 11.5528i) q^{57} +(3.62521 - 3.62521i) q^{59} +(-3.72781 - 3.72781i) q^{61} +(2.36642 - 2.36642i) q^{63} +(6.48766 - 7.75317i) q^{65} -3.32677i q^{67} +(5.15965 + 5.15965i) q^{69} -1.37056 q^{71} +(2.55028 - 2.55028i) q^{73} +(2.51809 + 14.0563i) q^{75} -0.452252 q^{77} -3.86426 q^{79} +2.12204 q^{81} +14.4698 q^{83} +(-9.85351 + 0.875628i) q^{85} +(-10.9650 + 10.9650i) q^{87} +3.35011 q^{89} +(-2.07470 - 2.07470i) q^{91} -0.399696i q^{93} +(-1.13226 - 12.7415i) q^{95} +(-4.95582 + 4.95582i) q^{97} +(-2.54107 - 2.54107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) $ 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9	$ 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9} - 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} + 2 q^{23} - 6 q^{25} - 24 q^{27} - 14 q^{29} - 8 q^{33} + 2 q^{35} + 14 q^{45} - 38 q^{47} + 8 q^{51} - 12 q^{53} + 6 q^{55} - 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} + 32 q^{69} - 24 q^{71} - 14 q^{73} + 16 q^{75} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} - 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) $ 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9 - 2 * q^11 + 20 * q^15 - 6 * q^17 - 2 * q^19 + 16 * q^21 + 2 * q^23 - 6 * q^25 - 24 * q^27 - 14 * q^29 - 8 * q^33 + 2 * q^35 + 14 * q^45 - 38 * q^47 + 8 * q^51 - 12 * q^53 + 6 * q^55 - 24 * q^57 + 10 * q^59 - 14 * q^61 + 6 * q^63 + 32 * q^69 - 24 * q^71 - 14 * q^73 + 16 * q^75 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 - 14 * q^85 - 24 * q^87 + 12 * q^89 - 34 * q^95 + 18 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.85601			1.64892			0.824458	−	0.565923i	$-0.191480\pi$
$3$	2.85601			1.64892			0.824458	+	0.565923i	$0.191480\pi$
$4$		0			0
$5$	1.71489	+	1.43498i	0.766921	+	0.641741i
$5$	1.71489	+	1.43498i	0.766921	+	0.641741i
$6$		0			0
$7$	0.458895	−	0.458895i	0.173446	−	0.173446i	−0.615046	−	0.788491i	$-0.710862\pi$
$7$	0.458895	−	0.458895i	0.173446	−	0.173446i	0.788491	+	0.615046i	$0.210862\pi$
$8$		0			0
$9$	5.15678			1.71893
$10$		0			0
$11$	−0.492763	−	0.492763i	−0.148574	−	0.148574i	0.628907	−	0.777481i	$-0.283503\pi$
$11$	−0.492763	−	0.492763i	−0.148574	−	0.148574i	−0.777481	+	0.628907i	$0.783503\pi$
$12$		0			0
$13$		−	4.52109i		−	1.25393i	−0.779049	−	0.626963i	$-0.784298\pi$
$13$		−	4.52109i		−	1.25393i	0.779049	−	0.626963i	$-0.215702\pi$
$14$		0			0
$15$	4.89773	+	4.09831i	1.26459	+	1.05818i
$16$		0			0
$17$	−3.12823	+	3.12823i	−0.758708	+	0.758708i	−0.976087	−	0.217379i	$-0.930249\pi$
$17$	−3.12823	+	3.12823i	−0.758708	+	0.758708i	0.217379	+	0.976087i	$0.430249\pi$
$18$		0			0
$19$	−4.04508	−	4.04508i	−0.928005	−	0.928005i	0.0695721	−	0.997577i	$-0.477837\pi$
$19$	−4.04508	−	4.04508i	−0.928005	−	0.928005i	−0.997577	+	0.0695721i	$0.977837\pi$
$20$		0			0
$21$	1.31061	−	1.31061i	0.285998	−	0.285998i
$22$		0			0
$23$	1.80660	+	1.80660i	0.376701	+	0.376701i	0.869911	−	0.493209i	$-0.164176\pi$
$23$	1.80660	+	1.80660i	0.376701	+	0.376701i	−0.493209	+	0.869911i	$0.664176\pi$
$24$		0			0
$25$	0.881683	+	4.92165i	0.176337	+	0.984330i
$26$		0			0
$27$	6.15978			1.18545
$28$		0			0
$29$	−3.83926	+	3.83926i	−0.712932	+	0.712932i	−0.967148	−	0.254215i	$-0.918183\pi$
$29$	−3.83926	+	3.83926i	−0.712932	+	0.712932i	0.254215	+	0.967148i	$0.418183\pi$
$30$		0			0
$31$		−	0.139949i		−	0.0251356i	−0.999921	−	0.0125678i	$-0.995999\pi$
$31$		−	0.139949i		−	0.0251356i	0.999921	−	0.0125678i	$-0.00400057\pi$
$32$		0			0
$33$	−1.40733	−	1.40733i	−0.244985	−	0.244985i
$34$		0			0
$35$	1.44546	−	0.128450i	0.244327	−	0.0217120i
$36$		0			0
$37$			5.84330i			0.960633i	0.877095	+	0.480317i	$0.159478\pi$
$37$			5.84330i			0.960633i	−0.877095	+	0.480317i	$0.840522\pi$
$38$		0			0
$39$		−	12.9123i		−	2.06762i
$40$		0			0
$41$			4.55648i			0.711602i	0.934562	+	0.355801i	$0.115792\pi$
$41$			4.55648i			0.711602i	−0.934562	+	0.355801i	$0.884208\pi$
$42$		0			0
$43$		−	7.49928i		−	1.14363i	−0.820383	−	0.571815i	$-0.806240\pi$
$43$		−	7.49928i		−	1.14363i	0.820383	−	0.571815i	$-0.193760\pi$
$44$		0			0
$45$	8.84330	+	7.39986i	1.31828	+	1.10311i
$46$		0			0
$47$	−4.14073	−	4.14073i	−0.603987	−	0.603987i	0.337381	−	0.941368i	$-0.390459\pi$
$47$	−4.14073	−	4.14073i	−0.603987	−	0.603987i	−0.941368	+	0.337381i	$0.890459\pi$
$48$		0			0
$49$			6.57883i			0.939833i
$50$		0			0
$51$	−8.93426	+	8.93426i	−1.25105	+	1.25105i
$52$		0			0
$53$	−2.75773			−0.378803			−0.189402	−	0.981900i	$-0.560655\pi$
$53$	−2.75773			−0.378803			−0.189402	+	0.981900i	$0.560655\pi$
$54$		0			0
$55$	−0.137930	−	1.55214i	−0.0185985	−	0.209290i
$56$		0			0
$57$	−11.5528	−	11.5528i	−1.53020	−	1.53020i
$58$		0			0
$59$	3.62521	−	3.62521i	0.471962	−	0.471962i	−0.430587	−	0.902549i	$-0.641694\pi$
$59$	3.62521	−	3.62521i	0.471962	−	0.471962i	0.902549	+	0.430587i	$0.141694\pi$
$60$		0			0
$61$	−3.72781	−	3.72781i	−0.477298	−	0.477298i	0.426969	−	0.904266i	$-0.359581\pi$
$61$	−3.72781	−	3.72781i	−0.477298	−	0.477298i	−0.904266	+	0.426969i	$0.859581\pi$
$62$		0			0
$63$	2.36642	−	2.36642i	0.298141	−	0.298141i
$64$		0			0
$65$	6.48766	−	7.75317i	0.804696	−	0.961662i
$66$		0			0
$67$		−	3.32677i		−	0.406430i	−0.979134	−	0.203215i	$-0.934861\pi$
$67$		−	3.32677i		−	0.406430i	0.979134	−	0.203215i	$-0.0651390\pi$
$68$		0			0
$69$	5.15965	+	5.15965i	0.621149	+	0.621149i
$70$		0			0
$71$	−1.37056			−0.162655			−0.0813275	−	0.996687i	$-0.525916\pi$
$71$	−1.37056			−0.162655			−0.0813275	+	0.996687i	$0.525916\pi$
$72$		0			0
$73$	2.55028	−	2.55028i	0.298488	−	0.298488i	−0.541933	−	0.840422i	$-0.682307\pi$
$73$	2.55028	−	2.55028i	0.298488	−	0.298488i	0.840422	+	0.541933i	$0.182307\pi$
$74$		0			0
$75$	2.51809	+	14.0563i	0.290764	+	1.62308i
$76$		0			0
$77$	−0.452252			−0.0515389
$78$		0			0
$79$	−3.86426			−0.434763			−0.217382	−	0.976087i	$-0.569752\pi$
$79$	−3.86426			−0.434763			−0.217382	+	0.976087i	$0.569752\pi$
$80$		0			0
$81$	2.12204			0.235782
$82$		0			0
$83$	14.4698			1.58827			0.794133	−	0.607744i	$-0.207925\pi$
$83$	14.4698			1.58827			0.794133	+	0.607744i	$0.207925\pi$
$84$		0			0
$85$	−9.85351	+	0.875628i	−1.06876	+	0.0949752i
$86$		0			0
$87$	−10.9650	+	10.9650i	−1.17557	+	1.17557i
$88$		0			0
$89$	3.35011			0.355111			0.177556	−	0.984111i	$-0.443181\pi$
$89$	3.35011			0.355111			0.177556	+	0.984111i	$0.443181\pi$
$90$		0			0
$91$	−2.07470	−	2.07470i	−0.217488	−	0.217488i
$92$		0			0
$93$		−	0.399696i		−	0.0414466i
$94$		0			0
$95$	−1.13226	−	12.7415i	−0.116168	−	1.30725i
$96$		0			0
$97$	−4.95582	+	4.95582i	−0.503187	+	0.503187i	−0.912427	−	0.409240i	$-0.865794\pi$
$97$	−4.95582	+	4.95582i	−0.503187	+	0.503187i	0.409240	+	0.912427i	$0.365794\pi$
$98$		0			0
$99$	−2.54107	−	2.54107i	−0.255387	−	0.255387i
$100$		0			0
$101$	1.84536	−	1.84536i	0.183621	−	0.183621i	−0.609311	−	0.792931i	$-0.708554\pi$
$101$	1.84536	−	1.84536i	0.183621	−	0.183621i	0.792931	+	0.609311i	$0.208554\pi$
$102$		0			0
$103$	11.6655	+	11.6655i	1.14944	+	1.14944i	0.986664	+	0.162773i	$0.0520437\pi$
$103$	11.6655	+	11.6655i	1.14944	+	1.14944i	0.162773	+	0.986664i	$0.447956\pi$
$104$		0			0
$105$	4.12823	−	0.366853i	0.402874	−	0.0358012i
$106$		0			0
$107$	−15.3106			−1.48013			−0.740067	−	0.672534i	$-0.765206\pi$
$107$	−15.3106			−1.48013			−0.740067	+	0.672534i	$0.765206\pi$
$108$		0			0
$109$	12.4798	−	12.4798i	1.19535	−	1.19535i	0.219803	−	0.975544i	$-0.429458\pi$
$109$	12.4798	−	12.4798i	1.19535	−	1.19535i	0.975544	−	0.219803i	$-0.0705416\pi$
$110$		0			0
$111$			16.6885i			1.58400i
$112$		0			0
$113$	2.53557	+	2.53557i	0.238526	+	0.238526i	0.816240	−	0.577713i	$-0.196055\pi$
$113$	2.53557	+	2.53557i	0.238526	+	0.238526i	−0.577713	+	0.816240i	$0.696055\pi$
$114$		0			0
$115$	0.505686	+	5.69053i	0.0471555	+	0.530645i
$116$		0			0
$117$		−	23.3143i		−	2.15541i
$118$		0			0
$119$			2.87106i			0.263189i
$120$		0			0
$121$		−	10.5144i		−	0.955852i
$122$		0			0
$123$			13.0133i			1.17337i
$124$		0			0
$125$	−5.55047	+	9.70527i	−0.496449	+	0.868066i
$126$		0			0
$127$	−0.615790	−	0.615790i	−0.0546426	−	0.0546426i	0.679257	−	0.733900i	$-0.262302\pi$
$127$	−0.615790	−	0.615790i	−0.0546426	−	0.0546426i	−0.733900	+	0.679257i	$0.762302\pi$
$128$		0			0
$129$		−	21.4180i		−	1.88575i
$130$		0			0
$131$	9.55413	−	9.55413i	0.834748	−	0.834748i	−0.153414	−	0.988162i	$-0.549027\pi$
$131$	9.55413	−	9.55413i	0.834748	−	0.834748i	0.988162	+	0.153414i	$0.0490268\pi$
$132$		0			0
$133$	−3.71253			−0.321917
$134$		0			0
$135$	10.5633	+	8.83914i	0.909147	+	0.760752i
$136$		0			0
$137$	3.70277	+	3.70277i	0.316349	+	0.316349i	0.847363	−	0.531014i	$-0.178189\pi$
$137$	3.70277	+	3.70277i	0.316349	+	0.316349i	−0.531014	+	0.847363i	$0.678189\pi$
$138$		0			0
$139$	−5.46761	+	5.46761i	−0.463756	+	0.463756i	−0.899885	−	0.436128i	$-0.856349\pi$
$139$	−5.46761	+	5.46761i	−0.463756	+	0.463756i	0.436128	+	0.899885i	$0.356349\pi$
$140$		0			0
$141$	−11.8260	−	11.8260i	−0.995925	−	0.995925i
$142$		0			0
$143$	−2.22783	+	2.22783i	−0.186300	+	0.186300i
$144$		0			0
$145$	−12.0931	+	1.07465i	−1.00428	+	0.0892450i
$146$		0			0
$147$			18.7892i			1.54971i
$148$		0			0
$149$	4.21561	+	4.21561i	0.345356	+	0.345356i	0.858376	−	0.513021i	$-0.171474\pi$
$149$	4.21561	+	4.21561i	0.345356	+	0.345356i	−0.513021	+	0.858376i	$0.671474\pi$
$150$		0			0
$151$	−12.4417			−1.01249			−0.506244	−	0.862390i	$-0.668966\pi$
$151$	−12.4417			−1.01249			−0.506244	+	0.862390i	$0.668966\pi$
$152$		0			0
$153$	−16.1316	+	16.1316i	−1.30416	+	1.30416i
$154$		0			0
$155$	0.200824	−	0.239997i	0.0161306	−	0.0192771i
$156$		0			0
$157$	−7.50500			−0.598964			−0.299482	−	0.954102i	$-0.596814\pi$
$157$	−7.50500			−0.598964			−0.299482	+	0.954102i	$0.596814\pi$
$158$		0			0
$159$	−7.87609			−0.624615
$160$		0			0
$161$	1.65807			0.130675
$162$		0			0
$163$	−23.7284			−1.85855			−0.929277	−	0.369383i	$-0.879569\pi$
$163$	−23.7284			−1.85855			−0.929277	+	0.369383i	$0.879569\pi$
$164$		0			0
$165$	−0.393929	−	4.43291i	−0.0306673	−	0.345102i
$166$		0			0
$167$	0.402976	−	0.402976i	0.0311832	−	0.0311832i	−0.691343	−	0.722526i	$-0.742981\pi$
$167$	0.402976	−	0.402976i	0.0311832	−	0.0311832i	0.722526	+	0.691343i	$0.242981\pi$
$168$		0			0
$169$	−7.44028			−0.572330
$170$		0			0
$171$	−20.8596	−	20.8596i	−1.59517	−	1.59517i
$172$		0			0
$173$			15.4500i			1.17464i	0.809355	+	0.587320i	$0.199817\pi$
$173$			15.4500i			1.17464i	−0.809355	+	0.587320i	$0.800183\pi$
$174$		0			0
$175$	2.66312	+	1.85392i	0.201313	+	0.140143i
$176$		0			0
$177$	10.3536	−	10.3536i	0.778225	−	0.778225i
$178$		0			0
$179$	−5.20444	−	5.20444i	−0.388998	−	0.388998i	0.485332	−	0.874330i	$-0.338699\pi$
$179$	−5.20444	−	5.20444i	−0.388998	−	0.388998i	−0.874330	+	0.485332i	$0.838699\pi$
$180$		0			0
$181$	9.08925	−	9.08925i	0.675599	−	0.675599i	−0.283402	−	0.959001i	$-0.591463\pi$
$181$	9.08925	−	9.08925i	0.675599	−	0.675599i	0.959001	+	0.283402i	$0.0914632\pi$
$182$		0			0
$183$	−10.6467	−	10.6467i	−0.787024	−	0.787024i
$184$		0			0
$185$	−8.38500	+	10.0206i	−0.616478	+	0.736730i
$186$		0			0
$187$	3.08295			0.225448
$188$		0			0
$189$	2.82669	−	2.82669i	0.205611	−	0.205611i
$190$		0			0
$191$		−	15.1075i		−	1.09314i	−0.837413	−	0.546571i	$-0.815933\pi$
$191$		−	15.1075i		−	1.09314i	0.837413	−	0.546571i	$-0.184067\pi$
$192$		0			0
$193$	4.19166	+	4.19166i	0.301722	+	0.301722i	0.841687	−	0.539965i	$-0.181563\pi$
$193$	4.19166	+	4.19166i	0.301722	+	0.301722i	−0.539965	+	0.841687i	$0.681563\pi$
$194$		0			0
$195$	18.5288	−	22.1431i	1.32688	−	1.58570i
$196$		0			0
$197$		−	4.03184i		−	0.287256i	−0.989632	−	0.143628i	$-0.954123\pi$
$197$		−	4.03184i		−	0.287256i	0.989632	−	0.143628i	$-0.0458769\pi$
$198$		0			0
$199$		−	5.43055i		−	0.384961i	−0.981301	−	0.192481i	$-0.938347\pi$
$199$		−	5.43055i		−	0.384961i	0.981301	−	0.192481i	$-0.0616533\pi$
$200$		0			0
$201$		−	9.50129i		−	0.670169i
$202$		0			0
$203$			3.52363i			0.247310i
$204$		0			0
$205$	−6.53844	+	7.81385i	−0.456664	+	0.545743i
$206$		0			0
$207$	9.31622	+	9.31622i	0.647522	+	0.647522i
$208$		0			0
$209$			3.98653i			0.275754i
$210$		0			0
$211$	3.23020	−	3.23020i	0.222376	−	0.222376i	−0.587122	−	0.809498i	$-0.699739\pi$
$211$	3.23020	−	3.23020i	0.222376	−	0.222376i	0.809498	+	0.587122i	$0.199739\pi$
$212$		0			0
$213$	−3.91432			−0.268205
$214$		0			0
$215$	10.7613	−	12.8604i	0.733914	−	0.877074i
$216$		0			0
$217$	−0.0642220	−	0.0642220i	−0.00435967	−	0.00435967i
$218$		0			0
$219$	7.28363	−	7.28363i	0.492182	−	0.492182i
$220$		0			0
$221$	14.1430	+	14.1430i	0.951363	+	0.951363i
$222$		0			0
$223$	−8.17319	+	8.17319i	−0.547317	+	0.547317i	−0.925664	−	0.378347i	$-0.876493\pi$
$223$	−8.17319	+	8.17319i	−0.547317	+	0.547317i	0.378347	+	0.925664i	$0.376493\pi$
$224$		0			0
$225$	4.54664	+	25.3799i	0.303110	+	1.69199i
$226$		0			0
$227$			1.54068i			0.102258i	0.998692	+	0.0511292i	$0.0162820\pi$
$227$			1.54068i			0.102258i	−0.998692	+	0.0511292i	$0.983718\pi$
$228$		0			0
$229$	−17.5646	−	17.5646i	−1.16070	−	1.16070i	−0.984322	−	0.176378i	$-0.943562\pi$
$229$	−17.5646	−	17.5646i	−1.16070	−	1.16070i	−0.176378	−	0.984322i	$-0.556438\pi$
$230$		0			0
$231$	−1.29164			−0.0849834
$232$		0			0
$233$	−9.99018	+	9.99018i	−0.654479	+	0.654479i	−0.954068	−	0.299590i	$-0.903150\pi$
$233$	−9.99018	+	9.99018i	−0.654479	+	0.654479i	0.299590	+	0.954068i	$0.403150\pi$
$234$		0			0
$235$	−1.15904	−	13.0427i	−0.0756072	−	0.850814i
$236$		0			0
$237$	−11.0364			−0.716889
$238$		0			0
$239$	26.2762			1.69967			0.849833	−	0.527052i	$-0.176703\pi$
$239$	26.2762			1.69967			0.849833	+	0.527052i	$0.176703\pi$
$240$		0			0
$241$	−0.113242			−0.00729456			−0.00364728	−	0.999993i	$-0.501161\pi$
$241$	−0.113242			−0.00729456			−0.00364728	+	0.999993i	$0.501161\pi$
$242$		0			0
$243$	−12.4188			−0.796665
$244$		0			0
$245$	−9.44047	+	11.2820i	−0.603130	+	0.720778i
$246$		0			0
$247$	−18.2882	+	18.2882i	−1.16365	+	1.16365i
$248$		0			0
$249$	41.3258			2.61892
$250$		0			0
$251$	19.2220	+	19.2220i	1.21328	+	1.21328i	0.969941	+	0.243339i	$0.0782427\pi$
$251$	19.2220	+	19.2220i	1.21328	+	1.21328i	0.243339	+	0.969941i	$0.421757\pi$
$252$		0			0
$253$		−	1.78045i		−	0.111936i
$254$		0			0
$255$	−28.1417	+	2.50080i	−1.76230	+	0.156606i
$256$		0			0
$257$	−0.757800	+	0.757800i	−0.0472703	+	0.0472703i	−0.730347	−	0.683077i	$-0.760642\pi$
$257$	−0.757800	+	0.757800i	−0.0472703	+	0.0472703i	0.683077	+	0.730347i	$0.260642\pi$
$258$		0			0
$259$	2.68146	+	2.68146i	0.166618	+	0.166618i
$260$		0			0
$261$	−19.7982	+	19.7982i	−1.22548	+	1.22548i
$262$		0			0
$263$	−5.73017	−	5.73017i	−0.353338	−	0.353338i	0.508012	−	0.861350i	$-0.330380\pi$
$263$	−5.73017	−	5.73017i	−0.353338	−	0.353338i	−0.861350	+	0.508012i	$0.830380\pi$
$264$		0			0
$265$	−4.72919	−	3.95728i	−0.290512	−	0.243094i
$266$		0			0
$267$	9.56795			0.585549
$268$		0			0
$269$	9.78879	−	9.78879i	0.596833	−	0.596833i	−0.342635	−	0.939468i	$-0.611320\pi$
$269$	9.78879	−	9.78879i	0.596833	−	0.596833i	0.939468	+	0.342635i	$0.111320\pi$
$270$		0			0
$271$		−	4.10159i		−	0.249154i	−0.992210	−	0.124577i	$-0.960243\pi$
$271$		−	4.10159i		−	0.249154i	0.992210	−	0.124577i	$-0.0397574\pi$
$272$		0			0
$273$	−5.92537	−	5.92537i	−0.358620	−	0.358620i
$274$		0			0
$275$	1.99075	−	2.85967i	0.120046	−	0.172444i
$276$		0			0
$277$			24.6755i			1.48261i	0.671169	+	0.741305i	$0.265793\pi$
$277$			24.6755i			1.48261i	−0.671169	+	0.741305i	$0.734207\pi$
$278$		0			0
$279$		−	0.721688i		−	0.0432063i
$280$		0			0
$281$		−	23.6688i		−	1.41196i	−0.708230	−	0.705981i	$-0.750506\pi$
$281$		−	23.6688i		−	1.41196i	0.708230	−	0.705981i	$-0.249494\pi$
$282$		0			0
$283$			13.0492i			0.775694i	0.921724	+	0.387847i	$0.126781\pi$
$283$			13.0492i			0.775694i	−0.921724	+	0.387847i	$0.873219\pi$
$284$		0			0
$285$	−3.23375	−	36.3897i	−0.191551	−	2.15554i
$286$		0			0
$287$	2.09094	+	2.09094i	0.123424	+	0.123424i
$288$		0			0
$289$		−	2.57168i		−	0.151275i
$290$		0			0
$291$	−14.1539	+	14.1539i	−0.829714	+	0.829714i
$292$		0			0
$293$	31.6731			1.85036			0.925181	−	0.379526i	$-0.123913\pi$
$293$	31.6731			1.85036			0.925181	+	0.379526i	$0.123913\pi$
$294$		0			0
$295$	11.4189	−	1.01474i	0.664835	−	0.0590802i
$296$		0			0
$297$	−3.03531	−	3.03531i	−0.176127	−	0.176127i
$298$		0			0
$299$	8.16779	−	8.16779i	0.472355	−	0.472355i
$300$		0			0
$301$	−3.44138	−	3.44138i	−0.198358	−	0.198358i
$302$		0			0
$303$	5.27037	−	5.27037i	0.302775	−	0.302775i
$304$		0			0
$305$	−1.04346	−	11.7421i	−0.0597482	−	0.672351i
$306$		0			0
$307$			27.3597i			1.56150i	0.624843	+	0.780751i	$0.285163\pi$
$307$			27.3597i			1.56150i	−0.624843	+	0.780751i	$0.714837\pi$
$308$		0			0
$309$	33.3168	+	33.3168i	1.89532	+	1.89532i
$310$		0			0
$311$	15.8076			0.896368			0.448184	−	0.893941i	$-0.352071\pi$
$311$	15.8076			0.896368			0.448184	+	0.893941i	$0.352071\pi$
$312$		0			0
$313$	13.8388	−	13.8388i	0.782217	−	0.782217i	−0.197988	−	0.980205i	$-0.563441\pi$
$313$	13.8388	−	13.8388i	0.782217	−	0.782217i	0.980205	+	0.197988i	$0.0634406\pi$
$314$		0			0
$315$	7.45390	−	0.662387i	0.419980	−	0.0373213i
$316$		0			0
$317$	35.0092			1.96631			0.983156	−	0.182766i	$-0.0585051\pi$
$317$	35.0092			1.96631			0.983156	+	0.182766i	$0.0585051\pi$
$318$		0			0
$319$	3.78369			0.211846
$320$		0			0
$321$	−43.7272			−2.44062
$322$		0			0
$323$	25.3079			1.40817
$324$		0			0
$325$	22.2512	−	3.98617i	1.23428	−	0.221113i
$326$		0			0
$327$	35.6424	−	35.6424i	1.97103	−	1.97103i
$328$		0			0
$329$	−3.80032			−0.209518
$330$		0			0
$331$	16.8212	+	16.8212i	0.924578	+	0.924578i	0.997349	−	0.0727709i	$-0.0231842\pi$
$331$	16.8212	+	16.8212i	0.924578	+	0.924578i	−0.0727709	+	0.997349i	$0.523184\pi$
$332$		0			0
$333$			30.1326i			1.65126i
$334$		0			0
$335$	4.77384	−	5.70504i	0.260823	−	0.311700i
$336$		0			0
$337$	14.4984	−	14.4984i	0.789777	−	0.789777i	−0.191680	−	0.981457i	$-0.561394\pi$
$337$	14.4984	−	14.4984i	0.789777	−	0.789777i	0.981457	+	0.191680i	$0.0613937\pi$
$338$		0			0
$339$	7.24160	+	7.24160i	0.393310	+	0.393310i
$340$		0			0
$341$	−0.0689618	+	0.0689618i	−0.00373449	+	0.00373449i
$342$		0			0
$343$	6.23125	+	6.23125i	0.336456	+	0.336456i
$344$		0			0
$345$	1.44424	+	16.2522i	0.0777555	+	0.874989i
$346$		0			0
$347$	−16.7705			−0.900286			−0.450143	−	0.892956i	$-0.648627\pi$
$347$	−16.7705			−0.900286			−0.450143	+	0.892956i	$0.648627\pi$
$348$		0			0
$349$	1.86337	−	1.86337i	0.0997439	−	0.0997439i	−0.655474	−	0.755218i	$-0.727531\pi$
$349$	1.86337	−	1.86337i	0.0997439	−	0.0997439i	0.755218	+	0.655474i	$0.227531\pi$
$350$		0			0
$351$		−	27.8489i		−	1.48647i
$352$		0			0
$353$	24.1362	+	24.1362i	1.28464	+	1.28464i	0.937998	+	0.346642i	$0.112678\pi$
$353$	24.1362	+	24.1362i	1.28464	+	1.28464i	0.346642	+	0.937998i	$0.387322\pi$
$354$		0			0
$355$	−2.35035	−	1.96672i	−0.124744	−	0.104382i
$356$		0			0
$357$			8.19976i			0.433978i
$358$		0			0
$359$			12.2500i			0.646532i	0.946308	+	0.323266i	$0.104781\pi$
$359$			12.2500i			0.646532i	−0.946308	+	0.323266i	$0.895219\pi$
$360$		0			0
$361$			13.7253i			0.722386i
$362$		0			0
$363$		−	30.0291i		−	1.57612i
$364$		0			0
$365$	8.03305	−	0.713853i	0.420469	−	0.0373648i
$366$		0			0
$367$	2.71307	+	2.71307i	0.141621	+	0.141621i	0.774363	−	0.632742i	$-0.218071\pi$
$367$	2.71307	+	2.71307i	0.141621	+	0.141621i	−0.632742	+	0.774363i	$0.718071\pi$
$368$		0			0
$369$			23.4967i			1.22319i
$370$		0			0
$371$	−1.26551	+	1.26551i	−0.0657018	+	0.0657018i
$372$		0			0
$373$	−16.4846			−0.853541			−0.426771	−	0.904360i	$-0.640349\pi$
$373$	−16.4846			−0.853541			−0.426771	+	0.904360i	$0.640349\pi$
$374$		0			0
$375$	−15.8522	+	27.7183i	−0.818603	+	1.43137i
$376$		0			0
$377$	17.3576	+	17.3576i	0.893964	+	0.893964i
$378$		0			0
$379$	13.7716	−	13.7716i	0.707401	−	0.707401i	−0.258587	−	0.965988i	$-0.583257\pi$
$379$	13.7716	−	13.7716i	0.707401	−	0.707401i	0.965988	+	0.258587i	$0.0832568\pi$
$380$		0			0
$381$	−1.75870	−	1.75870i	−0.0901011	−	0.0901011i
$382$		0			0
$383$	11.5530	−	11.5530i	0.590332	−	0.590332i	−0.347389	−	0.937721i	$-0.612932\pi$
$383$	11.5530	−	11.5530i	0.590332	−	0.590332i	0.937721	+	0.347389i	$0.112932\pi$
$384$		0			0
$385$	−0.775562	−	0.648972i	−0.0395263	−	0.0330747i
$386$		0			0
$387$		−	38.6722i		−	1.96582i
$388$		0			0
$389$	−15.7728	−	15.7728i	−0.799712	−	0.799712i	0.183338	−	0.983050i	$-0.441310\pi$
$389$	−15.7728	−	15.7728i	−0.799712	−	0.799712i	−0.983050	+	0.183338i	$0.941310\pi$
$390$		0			0
$391$	−11.3029			−0.571612
$392$		0			0
$393$	27.2867	−	27.2867i	1.37643	−	1.37643i
$394$		0			0
$395$	−6.62677	−	5.54512i	−0.333429	−	0.279006i
$396$		0			0
$397$	−29.9558			−1.50344			−0.751720	−	0.659483i	$-0.770775\pi$
$397$	−29.9558			−1.50344			−0.751720	+	0.659483i	$0.770775\pi$
$398$		0			0
$399$	−10.6030			−0.530815
$400$		0			0
$401$	19.9241			0.994963			0.497481	−	0.867475i	$-0.334258\pi$
$401$	19.9241			0.994963			0.497481	+	0.867475i	$0.334258\pi$
$402$		0			0
$403$	−0.632724			−0.0315182
$404$		0			0
$405$	3.63906	+	3.04508i	0.180826	+	0.151311i
$406$		0			0
$407$	2.87936	−	2.87936i	0.142725	−	0.142725i
$408$		0			0
$409$	−5.89856			−0.291665			−0.145832	−	0.989309i	$-0.546586\pi$
$409$	−5.89856			−0.291665			−0.145832	+	0.989309i	$0.546586\pi$
$410$		0			0
$411$	10.5751	+	10.5751i	0.521634	+	0.521634i
$412$		0			0
$413$		−	3.32717i		−	0.163720i
$414$		0			0
$415$	24.8141	+	20.7638i	1.21808	+	1.01926i
$416$		0			0
$417$	−15.6155	+	15.6155i	−0.764696	+	0.764696i
$418$		0			0
$419$	−8.24430	−	8.24430i	−0.402760	−	0.402760i	0.476444	−	0.879205i	$-0.341925\pi$
$419$	−8.24430	−	8.24430i	−0.402760	−	0.402760i	−0.879205	+	0.476444i	$0.841925\pi$
$420$		0			0
$421$	17.1776	−	17.1776i	0.837184	−	0.837184i	−0.151304	−	0.988487i	$-0.548347\pi$
$421$	17.1776	−	17.1776i	0.837184	−	0.837184i	0.988487	+	0.151304i	$0.0483471\pi$
$422$		0			0
$423$	−21.3528	−	21.3528i	−1.03821	−	1.03821i
$424$		0			0
$425$	−18.1542	−	12.6380i	−0.880607	−	0.613031i
$426$		0			0
$427$	−3.42135			−0.165571
$428$		0			0
$429$	−6.36269	+	6.36269i	−0.307194	+	0.307194i
$430$		0			0
$431$			32.1769i			1.54990i	0.632020	+	0.774952i	$0.282226\pi$
$431$			32.1769i			1.54990i	−0.632020	+	0.774952i	$0.717774\pi$
$432$		0			0
$433$	−20.3383	−	20.3383i	−0.977396	−	0.977396i	0.0223540	−	0.999750i	$-0.492884\pi$
$433$	−20.3383	−	20.3383i	−0.977396	−	0.977396i	−0.999750	+	0.0223540i	$0.992884\pi$
$434$		0			0
$435$	−34.5381	+	3.06921i	−1.65598	+	0.147158i
$436$		0			0
$437$		−	14.6156i		−	0.699161i
$438$		0			0
$439$		−	35.4180i		−	1.69041i	−0.534444	−	0.845204i	$-0.679479\pi$
$439$		−	35.4180i		−	1.69041i	0.534444	−	0.845204i	$-0.320521\pi$
$440$		0			0
$441$			33.9256i			1.61550i
$442$		0			0
$443$		−	3.03787i		−	0.144333i	−0.997393	−	0.0721667i	$-0.977009\pi$
$443$		−	3.03787i		−	0.144333i	0.997393	−	0.0721667i	$-0.0229913\pi$
$444$		0			0
$445$	5.74507	+	4.80733i	0.272342	+	0.227890i
$446$		0			0
$447$	12.0398	+	12.0398i	0.569463	+	0.569463i
$448$		0			0
$449$			8.65559i			0.408483i	0.978921	+	0.204241i	$0.0654727\pi$
$449$			8.65559i			0.408483i	−0.978921	+	0.204241i	$0.934527\pi$
$450$		0			0
$451$	2.24526	−	2.24526i	0.105725	−	0.105725i
$452$		0			0
$453$	−35.5335			−1.66951
$454$		0			0
$455$	−0.580733	−	6.53504i	−0.0272252	−	0.306367i
$456$		0			0
$457$	13.5575	+	13.5575i	0.634193	+	0.634193i	0.949117	−	0.314924i	$-0.101979\pi$
$457$	13.5575	+	13.5575i	0.634193	+	0.634193i	−0.314924	+	0.949117i	$0.601979\pi$
$458$		0			0
$459$	−19.2692	+	19.2692i	−0.899411	+	0.899411i
$460$		0			0
$461$	1.19682	+	1.19682i	0.0557416	+	0.0557416i	0.734428	−	0.678687i	$-0.237450\pi$
$461$	1.19682	+	1.19682i	0.0557416	+	0.0557416i	−0.678687	+	0.734428i	$0.737450\pi$
$462$		0			0
$463$	−21.1815	+	21.1815i	−0.984390	+	0.984390i	−0.999880	−	0.0154904i	$-0.995069\pi$
$463$	−21.1815	+	21.1815i	−0.984390	+	0.984390i	0.0154904	+	0.999880i	$0.495069\pi$
$464$		0			0
$465$	0.573555	−	0.685435i	0.0265980	−	0.0317863i
$466$		0			0
$467$		−	24.8448i		−	1.14968i	−0.818266	−	0.574840i	$-0.805064\pi$
$467$		−	24.8448i		−	1.14968i	0.818266	−	0.574840i	$-0.194936\pi$
$468$		0			0
$469$	−1.52664	−	1.52664i	−0.0704936	−	0.0704936i
$470$		0			0
$471$	−21.4343			−0.987642
$472$		0			0
$473$	−3.69537	+	3.69537i	−0.169913	+	0.169913i
$474$		0			0
$475$	16.3420	−	23.4749i	0.749822	−	1.07710i
$476$		0			0
$477$	−14.2210			−0.651135
$478$		0			0
$479$	−23.5766			−1.07724			−0.538621	−	0.842548i	$-0.681054\pi$
$479$	−23.5766			−1.07724			−0.538621	+	0.842548i	$0.681054\pi$
$480$		0			0
$481$	26.4181			1.20456
$482$		0			0
$483$	4.73547			0.215471
$484$		0			0
$485$	−15.6102	+	1.38719i	−0.708821	+	0.0629891i
$486$		0			0
$487$	2.63011	−	2.63011i	0.119182	−	0.119182i	−0.645001	−	0.764182i	$-0.723143\pi$
$487$	2.63011	−	2.63011i	0.119182	−	0.119182i	0.764182	+	0.645001i	$0.223143\pi$
$488$		0			0
$489$	−67.7686			−3.06460
$490$		0			0
$491$	−18.6899	−	18.6899i	−0.843465	−	0.843465i	0.145843	−	0.989308i	$-0.453411\pi$
$491$	−18.6899	−	18.6899i	−0.843465	−	0.843465i	−0.989308	+	0.145843i	$0.953411\pi$
$492$		0			0
$493$		−	24.0202i		−	1.08182i
$494$		0			0
$495$	−0.711274	−	8.00403i	−0.0319694	−	0.359754i
$496$		0			0
$497$	−0.628940	+	0.628940i	−0.0282118	+	0.0282118i
$498$		0			0
$499$	9.69342	+	9.69342i	0.433937	+	0.433937i	0.889965	−	0.456028i	$-0.150728\pi$
$499$	9.69342	+	9.69342i	0.433937	+	0.433937i	−0.456028	+	0.889965i	$0.650728\pi$
$500$		0			0
$501$	1.15090	−	1.15090i	0.0514185	−	0.0514185i
$502$		0			0
$503$	13.0434	+	13.0434i	0.581577	+	0.581577i	0.935336	−	0.353759i	$-0.115097\pi$
$503$	13.0434	+	13.0434i	0.581577	+	0.581577i	−0.353759	+	0.935336i	$0.615097\pi$
$504$		0			0
$505$	5.81265	−	0.516538i	0.258659	−	0.0229856i
$506$		0			0
$507$	−21.2495			−0.943724
$508$		0			0
$509$	−25.8539	+	25.8539i	−1.14595	+	1.14595i	−0.158611	+	0.987341i	$0.550702\pi$
$509$	−25.8539	+	25.8539i	−1.14595	+	1.14595i	−0.987341	+	0.158611i	$0.949298\pi$
$510$		0			0
$511$		−	2.34062i		−	0.103543i
$512$		0			0
$513$	−24.9168	−	24.9168i	−1.10010	−	1.10010i
$514$		0			0
$515$	3.26531	+	36.7448i	0.143887	+	1.61917i
$516$		0			0
$517$			4.08080i			0.179473i
$518$		0			0
$519$			44.1252i			1.93688i
$520$		0			0
$521$			25.0528i			1.09758i	0.835959	+	0.548792i	$0.184912\pi$
$521$			25.0528i			1.09758i	−0.835959	+	0.548792i	$0.815088\pi$
$522$		0			0
$523$			40.3434i			1.76410i	0.471160	+	0.882048i	$0.343835\pi$
$523$			40.3434i			1.76410i	−0.471160	+	0.882048i	$0.656165\pi$
$524$		0			0
$525$	7.60588	+	5.29481i	0.331948	+	0.231084i
$526$		0			0
$527$	0.437794	+	0.437794i	0.0190706	+	0.0190706i
$528$		0			0
$529$		−	16.4724i		−	0.716192i
$530$		0			0
$531$	18.6944	−	18.6944i	0.811267	−	0.811267i
$532$		0			0
$533$	20.6003			0.892296
$534$		0			0
$535$	−26.2560	−	21.9704i	−1.13515	−	0.949862i
$536$		0			0
$537$	−14.8639	−	14.8639i	−0.641425	−	0.641425i
$538$		0			0
$539$	3.24180	−	3.24180i	0.139634	−	0.139634i
$540$		0			0
$541$	24.7446	+	24.7446i	1.06385	+	1.06385i	0.997817	+	0.0660360i	$0.0210352\pi$
$541$	24.7446	+	24.7446i	1.06385	+	1.06385i	0.0660360	+	0.997817i	$0.478965\pi$
$542$		0			0
$543$	25.9590	−	25.9590i	1.11401	−	1.11401i
$544$		0			0
$545$	39.3097	−	3.49324i	1.68384	−	0.149634i
$546$		0			0
$547$		−	19.0254i		−	0.813465i	−0.913547	−	0.406733i	$-0.866668\pi$
$547$		−	19.0254i		−	0.813465i	0.913547	−	0.406733i	$-0.133332\pi$
$548$		0			0
$549$	−19.2235	−	19.2235i	−0.820440	−	0.820440i
$550$		0			0
$551$	31.0602			1.32321
$552$		0			0
$553$	−1.77329	+	1.77329i	−0.0754079	+	0.0754079i
$554$		0			0
$555$	−23.9476	+	28.6189i	−1.01652	+	1.21481i
$556$		0			0
$557$	−30.9517			−1.31146			−0.655732	−	0.754993i	$-0.727640\pi$
$557$	−30.9517			−1.31146			−0.655732	+	0.754993i	$0.727640\pi$
$558$		0			0
$559$	−33.9050			−1.43403
$560$		0			0
$561$	8.80494			0.371745
$562$		0			0
$563$	3.50238			0.147608			0.0738039	−	0.997273i	$-0.476486\pi$
$563$	3.50238			0.147608			0.0738039	+	0.997273i	$0.476486\pi$
$564$		0			0
$565$	0.709734	+	7.98670i	0.0298587	+	0.336003i
$566$		0			0
$567$	0.973793	−	0.973793i	0.0408955	−	0.0408955i
$568$		0			0
$569$	0.525780			0.0220418			0.0110209	−	0.999939i	$-0.496492\pi$
$569$	0.525780			0.0220418			0.0110209	+	0.999939i	$0.496492\pi$
$570$		0			0
$571$	−11.2487	−	11.2487i	−0.470743	−	0.470743i	0.431412	−	0.902155i	$-0.358016\pi$
$571$	−11.2487	−	11.2487i	−0.470743	−	0.470743i	−0.902155	+	0.431412i	$0.858016\pi$
$572$		0			0
$573$		−	43.1472i		−	1.80250i
$574$		0			0
$575$	−7.29859	+	10.4843i	−0.304372	+	0.437224i
$576$		0			0
$577$	−2.92884	+	2.92884i	−0.121929	+	0.121929i	−0.765438	−	0.643509i	$-0.777478\pi$
$577$	−2.92884	+	2.92884i	−0.121929	+	0.121929i	0.643509	+	0.765438i	$0.277478\pi$
$578$		0			0
$579$	11.9714	+	11.9714i	0.497515	+	0.497515i
$580$		0			0
$581$	6.64011	−	6.64011i	0.275478	−	0.275478i
$582$		0			0
$583$	1.35891	+	1.35891i	0.0562801	+	0.0562801i
$584$		0			0
$585$	33.4555	−	39.9814i	1.38321	−	1.65303i
$586$		0			0
$587$	23.1574			0.955809			0.477905	−	0.878412i	$-0.341396\pi$
$587$	23.1574			0.955809			0.477905	+	0.878412i	$0.341396\pi$
$588$		0			0
$589$	−0.566106	+	0.566106i	−0.0233260	+	0.0233260i
$590$		0			0
$591$		−	11.5150i		−	0.473662i
$592$		0			0
$593$	−13.9325	−	13.9325i	−0.572141	−	0.572141i	0.360585	−	0.932726i	$-0.382577\pi$
$593$	−13.9325	−	13.9325i	−0.572141	−	0.572141i	−0.932726	+	0.360585i	$0.882577\pi$
$594$		0			0
$595$	−4.11990	+	4.92354i	−0.168900	+	0.201846i
$596$		0			0
$597$		−	15.5097i		−	0.634769i
$598$		0			0
$599$			33.5311i			1.37004i	0.728523	+	0.685021i	$0.240207\pi$
$599$			33.5311i			1.37004i	−0.728523	+	0.685021i	$0.759793\pi$
$600$		0			0
$601$		−	19.4164i		−	0.792011i	−0.918248	−	0.396005i	$-0.870396\pi$
$601$		−	19.4164i		−	0.792011i	0.918248	−	0.396005i	$-0.129604\pi$
$602$		0			0
$603$		−	17.1554i		−	0.698623i
$604$		0			0
$605$	15.0879	−	18.0310i	0.613409	−	0.733063i
$606$		0			0
$607$	−9.51495	−	9.51495i	−0.386200	−	0.386200i	0.487130	−	0.873330i	$-0.338044\pi$
$607$	−9.51495	−	9.51495i	−0.386200	−	0.386200i	−0.873330	+	0.487130i	$0.838044\pi$
$608$		0			0
$609$			10.0635i			0.407794i
$610$		0			0
$611$	−18.7206	+	18.7206i	−0.757355	+	0.757355i
$612$		0			0
$613$	9.37947			0.378833			0.189417	−	0.981897i	$-0.439340\pi$
$613$	9.37947			0.378833			0.189417	+	0.981897i	$0.439340\pi$
$614$		0			0
$615$	−18.6738	+	22.3164i	−0.753002	+	0.899884i
$616$		0			0
$617$	3.54768	+	3.54768i	0.142824	+	0.142824i	0.774904	−	0.632079i	$-0.217798\pi$
$617$	3.54768	+	3.54768i	0.142824	+	0.142824i	−0.632079	+	0.774904i	$0.717798\pi$
$618$		0			0
$619$	−24.6158	+	24.6158i	−0.989392	+	0.989392i	−0.999944	−	0.0105527i	$-0.996641\pi$
$619$	−24.6158	+	24.6158i	−0.989392	+	0.989392i	0.0105527	+	0.999944i	$0.496641\pi$
$620$		0			0
$621$	11.1282	+	11.1282i	0.446561	+	0.446561i
$622$		0			0
$623$	1.53735	−	1.53735i	0.0615926	−	0.0615926i
$624$		0			0
$625$	−23.4453	+	8.67867i	−0.937811	+	0.347147i
$626$		0			0
$627$			11.3856i			0.454695i
$628$		0			0
$629$	−18.2792	−	18.2792i	−0.728840	−	0.728840i
$630$		0			0
$631$	28.8921			1.15018			0.575088	−	0.818092i	$-0.304968\pi$
$631$	28.8921			1.15018			0.575088	+	0.818092i	$0.304968\pi$
$632$		0			0
$633$	9.22547	−	9.22547i	0.366679	−	0.366679i
$634$		0			0
$635$	−0.172367	−	1.93966i	−0.00684016	−	0.0769729i
$636$		0			0
$637$	29.7435			1.17848
$638$		0			0
$639$	−7.06765			−0.279592
$640$		0			0
$641$	−16.6914			−0.659271			−0.329636	−	0.944108i	$-0.606926\pi$
$641$	−16.6914			−0.659271			−0.329636	+	0.944108i	$0.606926\pi$
$642$		0			0
$643$	−5.22468			−0.206041			−0.103021	−	0.994679i	$-0.532851\pi$
$643$	−5.22468			−0.206041			−0.103021	+	0.994679i	$0.532851\pi$
$644$		0			0
$645$	30.7343	−	36.7295i	1.21016	−	1.44622i
$646$		0			0
$647$	−21.6797	+	21.6797i	−0.852318	+	0.852318i	−0.990418	−	0.138100i	$-0.955900\pi$
$647$	−21.6797	+	21.6797i	−0.852318	+	0.852318i	0.138100	+	0.990418i	$0.455900\pi$
$648$		0			0
$649$	−3.57273			−0.140242
$650$		0			0
$651$	−0.183418	−	0.183418i	−0.00718874	−	0.00718874i
$652$		0			0
$653$		−	22.7642i		−	0.890833i	−0.895323	−	0.445417i	$-0.853056\pi$
$653$		−	22.7642i		−	0.890833i	0.895323	−	0.445417i	$-0.146944\pi$
$654$		0			0
$655$	30.0942	−	2.67431i	1.17588	−	0.104494i
$656$		0			0
$657$	13.1513	−	13.1513i	0.513079	−	0.513079i
$658$		0			0
$659$	1.66201	+	1.66201i	0.0647427	+	0.0647427i	0.738737	−	0.673994i	$-0.235423\pi$
$659$	1.66201	+	1.66201i	0.0647427	+	0.0647427i	−0.673994	+	0.738737i	$0.735423\pi$
$660$		0			0
$661$	5.62818	−	5.62818i	0.218911	−	0.218911i	−0.589129	−	0.808039i	$-0.700529\pi$
$661$	5.62818	−	5.62818i	0.218911	−	0.218911i	0.808039	+	0.589129i	$0.200529\pi$
$662$		0			0
$663$	40.3926	+	40.3926i	1.56872	+	1.56872i
$664$		0			0
$665$	−6.36657	−	5.32739i	−0.246885	−	0.206587i
$666$		0			0
$667$	−13.8720			−0.537125
$668$		0			0
$669$	−23.3427	+	23.3427i	−0.902481	+	0.902481i
$670$		0			0
$671$			3.67386i			0.141828i
$672$		0			0
$673$	0.278251	+	0.278251i	0.0107258	+	0.0107258i	0.712449	−	0.701724i	$-0.247586\pi$
$673$	0.278251	+	0.278251i	0.0107258	+	0.0107258i	−0.701724	+	0.712449i	$0.747586\pi$
$674$		0			0
$675$	5.43097	+	30.3163i	0.209038	+	1.16687i
$676$		0			0
$677$			26.3591i			1.01306i	0.862222	+	0.506531i	$0.169072\pi$
$677$			26.3591i			1.01306i	−0.862222	+	0.506531i	$0.830928\pi$
$678$		0			0
$679$			4.54840i			0.174551i
$680$		0			0
$681$			4.40019i			0.168616i
$682$		0			0
$683$		−	2.83023i		−	0.108296i	−0.998533	−	0.0541479i	$-0.982756\pi$
$683$		−	2.83023i		−	0.108296i	0.998533	−	0.0541479i	$-0.0172442\pi$
$684$		0			0
$685$	1.03645	+	11.6632i	0.0396006	+	0.445629i
$686$		0			0
$687$	−50.1646	−	50.1646i	−1.91390	−	1.91390i
$688$		0			0
$689$			12.4679i			0.474991i
$690$		0			0
$691$	22.1815	−	22.1815i	0.843825	−	0.843825i	−0.145529	−	0.989354i	$-0.546488\pi$
$691$	22.1815	−	22.1815i	0.843825	−	0.843825i	0.989354	+	0.145529i	$0.0464884\pi$
$692$		0			0
$693$	−2.33217			−0.0885917
$694$		0			0
$695$	−17.2222	+	1.53044i	−0.653276	+	0.0580531i
$696$		0			0
$697$	−14.2537	−	14.2537i	−0.539898	−	0.539898i
$698$		0			0
$699$	−28.5320	+	28.5320i	−1.07918	+	1.07918i
$700$		0			0
$701$	−16.2264	−	16.2264i	−0.612864	−	0.612864i	0.330828	−	0.943691i	$-0.392672\pi$
$701$	−16.2264	−	16.2264i	−0.612864	−	0.612864i	−0.943691	+	0.330828i	$0.892672\pi$
$702$		0			0
$703$	23.6366	−	23.6366i	0.891472	−	0.891472i
$704$		0			0
$705$	−3.31022	−	37.2502i	−0.124670	−	1.40292i
$706$		0			0
$707$		−	1.69365i		−	0.0636965i
$708$		0			0
$709$	25.3577	+	25.3577i	0.952329	+	0.952329i	0.998914	−	0.0465856i	$-0.0148340\pi$
$709$	25.3577	+	25.3577i	0.952329	+	0.952329i	−0.0465856	+	0.998914i	$0.514834\pi$
$710$		0			0
$711$	−19.9271			−0.747326
$712$		0			0
$713$	0.252832	−	0.252832i	0.00946863	−	0.00946863i
$714$		0			0
$715$	−7.01735	+	0.623594i	−0.262434	+	0.0233211i
$716$		0			0
$717$	75.0450			2.80261
$718$		0			0
$719$	41.3374			1.54163			0.770813	−	0.637061i	$-0.219850\pi$
$719$	41.3374			1.54163			0.770813	+	0.637061i	$0.219850\pi$
$720$		0			0
$721$	10.7065			0.398730
$722$		0			0
$723$	−0.323420			−0.0120281
$724$		0			0
$725$	−22.2805	−	15.5105i	−0.827477	−	0.576045i
$726$		0			0
$727$	23.4630	−	23.4630i	0.870193	−	0.870193i	−0.122300	−	0.992493i	$-0.539027\pi$
$727$	23.4630	−	23.4630i	0.870193	−	0.870193i	0.992493	+	0.122300i	$0.0390271\pi$
$728$		0			0
$729$	−41.8342			−1.54942
$730$		0			0
$731$	23.4595	+	23.4595i	0.867681	+	0.867681i
$732$		0			0
$733$			15.1628i			0.560051i	0.959993	+	0.280025i	$0.0903429\pi$
$733$			15.1628i			0.560051i	−0.959993	+	0.280025i	$0.909657\pi$
$734$		0			0
$735$	−26.9621	+	32.2214i	−0.994511	+	1.18850i
$736$		0			0
$737$	−1.63931	+	1.63931i	−0.0603848	+	0.0603848i
$738$		0			0
$739$	0.974343	+	0.974343i	0.0358418	+	0.0358418i	0.724801	−	0.688959i	$-0.241932\pi$
$739$	0.974343	+	0.974343i	0.0358418	+	0.0358418i	−0.688959	+	0.724801i	$0.741932\pi$
$740$		0			0
$741$	−52.2312	+	52.2312i	−1.91876	+	1.91876i
$742$		0			0
$743$	−29.0897	−	29.0897i	−1.06720	−	1.06720i	−0.997573	−	0.0696259i	$-0.977819\pi$
$743$	−29.0897	−	29.0897i	−1.06720	−	1.06720i	−0.0696259	−	0.997573i	$-0.522181\pi$
$744$		0			0
$745$	1.18000	+	13.2786i	0.0432317	+	0.486490i
$746$		0			0
$747$	74.6176			2.73011
$748$		0			0
$749$	−7.02596	+	7.02596i	−0.256723	+	0.256723i
$750$		0			0
$751$			7.77705i			0.283789i	0.989882	+	0.141894i	$0.0453193\pi$
$751$			7.77705i			0.283789i	−0.989882	+	0.141894i	$0.954681\pi$
$752$		0			0
$753$	54.8981	+	54.8981i	2.00060	+	2.00060i
$754$		0			0
$755$	−21.3361	−	17.8535i	−0.776498	−	0.649755i
$756$		0			0
$757$			1.42073i			0.0516372i	0.999667	+	0.0258186i	$0.00821923\pi$
$757$			1.42073i			0.0516372i	−0.999667	+	0.0258186i	$0.991781\pi$
$758$		0			0
$759$		−	5.08497i		−	0.184573i
$760$		0			0
$761$		−	26.6737i		−	0.966921i	−0.875366	−	0.483460i	$-0.839380\pi$
$761$		−	26.6737i		−	0.966921i	0.875366	−	0.483460i	$-0.160620\pi$
$762$		0			0
$763$		−	11.4538i		−	0.414656i
$764$		0			0
$765$	−50.8124	+	4.51542i	−1.83713	+	0.163255i
$766$		0			0
$767$	−16.3899	−	16.3899i	−0.591805	−	0.591805i
$768$		0			0
$769$		−	45.8210i		−	1.65235i	−0.563415	−	0.826174i	$-0.690513\pi$
$769$		−	45.8210i		−	1.65235i	0.563415	−	0.826174i	$-0.309487\pi$
$770$		0			0
$771$	−2.16428	+	2.16428i	−0.0779447	+	0.0779447i
$772$		0			0
$773$	18.5473			0.667101			0.333550	−	0.942732i	$-0.391753\pi$
$773$	18.5473			0.667101			0.333550	+	0.942732i	$0.391753\pi$
$774$		0			0
$775$	0.688782	−	0.123391i	0.0247418	−	0.00443233i
$776$		0			0
$777$	7.65827	+	7.65827i	0.274739	+	0.274739i
$778$		0			0
$779$	18.4313	−	18.4313i	0.660370	−	0.660370i
$780$		0			0
$781$	0.675359	+	0.675359i	0.0241662	+	0.0241662i
$782$		0			0
$783$	−23.6490	+	23.6490i	−0.845146	+	0.845146i
$784$		0			0
$785$	−12.8702	−	10.7695i	−0.459358	−	0.384380i
$786$		0			0
$787$			21.3016i			0.759319i	0.925126	+	0.379659i	$0.123959\pi$
$787$			21.3016i			0.759319i	−0.925126	+	0.379659i	$0.876041\pi$
$788$		0			0
$789$	−16.3654	−	16.3654i	−0.582624	−	0.582624i
$790$		0			0
$791$	2.32712			0.0827427
$792$		0			0
$793$	−16.8538	+	16.8538i	−0.598496	+	0.598496i
$794$		0			0
$795$	−13.5066	−	11.3020i	−0.479030	−	0.400841i
$796$		0			0
$797$	2.35457			0.0834033			0.0417016	−	0.999130i	$-0.486722\pi$
$797$	2.35457			0.0834033			0.0417016	+	0.999130i	$0.486722\pi$
$798$		0			0
$799$	25.9063			0.916500
$800$		0			0
$801$	17.2758			0.610410
$802$		0			0
$803$	−2.51337			−0.0886949
$804$		0			0
$805$	2.84341	+	2.37930i	0.100217	+	0.0838592i
$806$		0			0
$807$	27.9569	−	27.9569i	0.984128	−	0.984128i
$808$		0			0
$809$	23.9476			0.841952			0.420976	−	0.907072i	$-0.361688\pi$
$809$	23.9476			0.841952			0.420976	+	0.907072i	$0.361688\pi$
$810$		0			0
$811$	−1.33006	−	1.33006i	−0.0467048	−	0.0467048i	0.683369	−	0.730073i	$-0.260514\pi$
$811$	−1.33006	−	1.33006i	−0.0467048	−	0.0467048i	−0.730073	+	0.683369i	$0.760514\pi$
$812$		0			0
$813$		−	11.7142i		−	0.410834i
$814$		0			0
$815$	−40.6916	−	34.0498i	−1.42537	−	1.19271i
$816$		0			0
$817$	−30.3352	+	30.3352i	−1.06129	+	1.06129i
$818$		0			0
$819$	−10.6988	−	10.6988i	−0.373846	−	0.373846i
$820$		0			0
$821$	−36.4676	+	36.4676i	−1.27273	+	1.27273i	−0.328076	+	0.944651i	$0.606400\pi$
$821$	−36.4676	+	36.4676i	−1.27273	+	1.27273i	−0.944651	+	0.328076i	$0.893600\pi$
$822$		0			0
$823$	−26.3978	−	26.3978i	−0.920170	−	0.920170i	0.0768712	−	0.997041i	$-0.475507\pi$
$823$	−26.3978	−	26.3978i	−0.920170	−	0.920170i	−0.997041	+	0.0768712i	$0.975507\pi$
$824$		0			0
$825$	5.68559	−	8.16723i	0.197947	−	0.284346i
$826$		0			0
$827$	−1.99830			−0.0694878			−0.0347439	−	0.999396i	$-0.511062\pi$
$827$	−1.99830			−0.0694878			−0.0347439	+	0.999396i	$0.511062\pi$
$828$		0			0
$829$	−13.0376	+	13.0376i	−0.452813	+	0.452813i	−0.896287	−	0.443474i	$-0.853746\pi$
$829$	−13.0376	+	13.0376i	−0.452813	+	0.452813i	0.443474	+	0.896287i	$0.353746\pi$
$830$		0			0
$831$			70.4735i			2.44470i
$832$		0			0
$833$	−20.5801	−	20.5801i	−0.713059	−	0.713059i
$834$		0			0
$835$	1.26932	−	0.112797i	0.0439266	−	0.00390352i
$836$		0			0
$837$		−	0.862057i		−	0.0297971i
$838$		0			0
$839$		−	15.4102i		−	0.532018i	−0.963971	−	0.266009i	$-0.914295\pi$
$839$		−	15.4102i		−	0.532018i	0.963971	−	0.266009i	$-0.0857050\pi$
$840$		0			0
$841$		−	0.479815i		−	0.0165453i
$842$		0			0
$843$		−	67.5983i		−	2.32821i
$844$		0			0
$845$	−12.7593	−	10.6766i	−0.438932	−	0.367287i
$846$		0			0
$847$	−4.82499	−	4.82499i	−0.165789	−	0.165789i
$848$		0			0
$849$			37.2686i			1.27906i
$850$		0			0
$851$	−10.5565	+	10.5565i	−0.361872	+	0.361872i
$852$		0			0
$853$	−7.96419			−0.272689			−0.136344	−	0.990662i	$-0.543535\pi$
$853$	−7.96419			−0.272689			−0.136344	+	0.990662i	$0.543535\pi$
$854$		0			0
$855$	−5.83883	−	65.7049i	−0.199684	−	2.24706i
$856$		0			0
$857$	−5.35407	−	5.35407i	−0.182891	−	0.182891i	0.609723	−	0.792615i	$-0.291281\pi$
$857$	−5.35407	−	5.35407i	−0.182891	−	0.182891i	−0.792615	+	0.609723i	$0.791281\pi$
$858$		0			0
$859$	−35.0058	+	35.0058i	−1.19438	+	1.19438i	−0.218559	+	0.975824i	$0.570136\pi$
$859$	−35.0058	+	35.0058i	−1.19438	+	1.19438i	−0.975824	+	0.218559i	$0.929864\pi$
$860$		0			0
$861$	5.97175	+	5.97175i	0.203517	+	0.203517i
$862$		0			0
$863$	−36.7138	+	36.7138i	−1.24975	+	1.24975i	−0.293923	+	0.955829i	$0.594961\pi$
$863$	−36.7138	+	36.7138i	−1.24975	+	1.24975i	−0.955829	+	0.293923i	$0.905039\pi$
$864$		0			0
$865$	−22.1703	+	26.4950i	−0.753814	+	0.900856i
$866$		0			0
$867$		−	7.34475i		−	0.249441i
$868$		0			0
$869$	1.90416	+	1.90416i	0.0645943	+	0.0645943i
$870$		0			0
$871$	−15.0406			−0.509633
$872$		0			0
$873$	−25.5561	+	25.5561i	−0.864942	+	0.864942i
$874$		0			0
$875$	1.90662	+	7.00078i	0.0644555	+	0.236669i
$876$		0			0
$877$	14.3410			0.484262			0.242131	−	0.970244i	$-0.422154\pi$
$877$	14.3410			0.484262			0.242131	+	0.970244i	$0.422154\pi$
$878$		0			0
$879$	90.4586			3.05109
$880$		0			0
$881$	−13.6397			−0.459533			−0.229767	−	0.973246i	$-0.573796\pi$
$881$	−13.6397			−0.459533			−0.229767	+	0.973246i	$0.573796\pi$
$882$		0			0
$883$	6.12563			0.206144			0.103072	−	0.994674i	$-0.467133\pi$
$883$	6.12563			0.206144			0.103072	+	0.994674i	$0.467133\pi$
$884$		0			0
$885$	32.6125	−	2.89809i	1.09626	−	0.0974184i
$886$		0			0
$887$	−25.5187	+	25.5187i	−0.856834	+	0.856834i	−0.990964	−	0.134130i	$-0.957176\pi$
$887$	−25.5187	+	25.5187i	−0.856834	+	0.856834i	0.134130	+	0.990964i	$0.457176\pi$
$888$		0			0
$889$	−0.565166			−0.0189551
$890$		0			0
$891$	−1.04566	−	1.04566i	−0.0350310	−	0.0350310i
$892$		0			0
$893$			33.4992i			1.12101i
$894$		0			0
$895$	−1.45678	−	16.3933i	−0.0486948	−	0.547967i
$896$		0			0
$897$	23.3273	−	23.3273i	0.778875	−	0.778875i
$898$		0			0
$899$	0.537302	+	0.537302i	0.0179200	+	0.0179200i
$900$		0			0
$901$	8.62682	−	8.62682i	0.287401	−	0.287401i
$902$		0			0
$903$	−9.82861	−	9.82861i	−0.327076	−	0.327076i
$904$		0			0
$905$	28.6299	−	2.54418i	0.951691	−	0.0845715i
$906$		0			0
$907$	32.1815			1.06857			0.534284	−	0.845305i	$-0.320581\pi$
$907$	32.1815			1.06857			0.534284	+	0.845305i	$0.320581\pi$
$908$		0			0
$909$	9.51614	−	9.51614i	0.315630	−	0.315630i
$910$		0			0
$911$		−	38.6282i		−	1.27981i	−0.768455	−	0.639904i	$-0.778974\pi$
$911$		−	38.6282i		−	1.27981i	0.768455	−	0.639904i	$-0.221026\pi$
$912$		0			0
$913$	−7.13018	−	7.13018i	−0.235974	−	0.235974i
$914$		0			0
$915$	−2.98012	−	33.5356i	−0.0985198	−	1.10865i
$916$		0			0
$917$		−	8.76867i		−	0.289567i
$918$		0			0
$919$			19.1924i			0.633099i	0.948576	+	0.316550i	$0.102524\pi$
$919$			19.1924i			0.633099i	−0.948576	+	0.316550i	$0.897476\pi$
$920$		0			0
$921$			78.1395i			2.57479i
$922$		0			0
$923$			6.19641i			0.203957i
$924$		0			0
$925$	−28.7587	+	5.15194i	−0.945580	+	0.169395i
$926$		0			0
$927$	60.1564	+	60.1564i	1.97580	+	1.97580i
$928$		0			0
$929$			16.8576i			0.553081i	0.961002	+	0.276541i	$0.0891880\pi$
$929$			16.8576i			0.553081i	−0.961002	+	0.276541i	$0.910812\pi$
$930$		0			0
$931$	26.6119	−	26.6119i	0.872170	−	0.872170i
$932$		0			0
$933$	45.1467			1.47804
$934$		0			0
$935$	5.28692	+	4.42397i	0.172901	+	0.144679i
$936$		0			0
$937$	23.9511	+	23.9511i	0.782449	+	0.782449i	0.980243	−	0.197795i	$-0.0633779\pi$
$937$	23.9511	+	23.9511i	0.782449	+	0.782449i	−0.197795	+	0.980243i	$0.563378\pi$
$938$		0			0
$939$	39.5238	−	39.5238i	1.28981	−	1.28981i
$940$		0			0
$941$	−14.2496	−	14.2496i	−0.464525	−	0.464525i	0.435610	−	0.900135i	$-0.356533\pi$
$941$	−14.2496	−	14.2496i	−0.464525	−	0.464525i	−0.900135	+	0.435610i	$0.856533\pi$
$942$		0			0
$943$	−8.23171	+	8.23171i	−0.268061	+	0.268061i
$944$		0			0
$945$	8.90369	−	0.791222i	0.289637	−	0.0257385i
$946$		0			0
$947$		−	20.2943i		−	0.659477i	−0.944072	−	0.329738i	$-0.893039\pi$
$947$		−	20.2943i		−	0.659477i	0.944072	−	0.329738i	$-0.106961\pi$
$948$		0			0
$949$	−11.5301	−	11.5301i	−0.374282	−	0.374282i
$950$		0			0
$951$	99.9866			3.24229
$952$		0			0
$953$	10.9257	−	10.9257i	0.353919	−	0.353919i	−0.507647	−	0.861565i	$-0.669484\pi$
$953$	10.9257	−	10.9257i	0.353919	−	0.353919i	0.861565	+	0.507647i	$0.169484\pi$
$954$		0			0
$955$	21.6789	−	25.9077i	0.701514	−	0.838353i
$956$		0			0
$957$	10.8062			0.349316
$958$		0			0
$959$	3.39836			0.109739
$960$		0			0
$961$	30.9804			0.999368
$962$		0			0
$963$	−78.9535			−2.54424
$964$		0			0
$965$	1.17329	+	13.2032i	0.0377696	+	0.425025i
$966$		0			0
$967$	−10.7569	+	10.7569i	−0.345918	+	0.345918i	−0.858586	−	0.512669i	$-0.828657\pi$
$967$	−10.7569	+	10.7569i	−0.345918	+	0.345918i	0.512669	+	0.858586i	$0.328657\pi$
$968$		0			0
$969$	72.2796			2.32195
$970$		0			0
$971$	−18.7456	−	18.7456i	−0.601574	−	0.601574i	0.339156	−	0.940730i	$-0.389858\pi$
$971$	−18.7456	−	18.7456i	−0.601574	−	0.601574i	−0.940730	+	0.339156i	$0.889858\pi$
$972$		0			0
$973$			5.01811i			0.160873i
$974$		0			0
$975$	63.5497	−	11.3845i	2.03522	−	0.364597i
$976$		0			0
$977$	−26.3906	+	26.3906i	−0.844309	+	0.844309i	−0.989416	−	0.145107i	$-0.953647\pi$
$977$	−26.3906	+	26.3906i	−0.844309	+	0.844309i	0.145107	+	0.989416i	$0.453647\pi$
$978$		0			0
$979$	−1.65081	−	1.65081i	−0.0527602	−	0.0527602i
$980$		0			0
$981$	64.3556	−	64.3556i	2.05472	−	2.05472i
$982$		0			0
$983$	4.87875	+	4.87875i	0.155608	+	0.155608i	0.780617	−	0.625009i	$-0.214905\pi$
$983$	4.87875	+	4.87875i	0.155608	+	0.155608i	−0.625009	+	0.780617i	$0.714905\pi$
$984$		0			0
$985$	5.78559	−	6.91415i	0.184344	−	0.220303i
$986$		0			0
$987$	−10.8537			−0.345478
$988$		0			0
$989$	13.5482	−	13.5482i	0.430807	−	0.430807i
$990$		0			0
$991$		−	61.2103i		−	1.94441i	−0.234130	−	0.972205i	$-0.575224\pi$
$991$		−	61.2103i		−	1.94441i	0.234130	−	0.972205i	$-0.424776\pi$
$992$		0			0
$993$	48.0415	+	48.0415i	1.52455	+	1.52455i
$994$		0			0
$995$	7.79271	−	9.31279i	0.247046	−	0.295235i
$996$		0			0
$997$			39.1082i			1.23857i	0.785167	+	0.619284i	$0.212577\pi$
$997$			39.1082i			1.23857i	−0.785167	+	0.619284i	$0.787423\pi$
$998$		0			0
$999$			35.9935i			1.13878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.s.c.223.9		18
4.3	odd	2		640.2.s.d.223.1		18
5.2	odd	4		640.2.j.c.607.1		18
8.3	odd	2		80.2.s.b.3.1	yes	18
8.5	even	2		320.2.s.b.303.1		18
16.3	odd	4		320.2.j.b.143.1		18
16.5	even	4		640.2.j.d.543.1		18
16.11	odd	4		640.2.j.c.543.9		18
16.13	even	4		80.2.j.b.43.5	✓	18
20.7	even	4		640.2.j.d.607.9		18
24.11	even	2		720.2.z.g.163.9		18
40.3	even	4		400.2.j.d.307.5		18
40.13	odd	4		1600.2.j.d.1007.1		18
40.19	odd	2		400.2.s.d.243.9		18
40.27	even	4		80.2.j.b.67.5	yes	18
40.29	even	2		1600.2.s.d.943.9		18
40.37	odd	4		320.2.j.b.47.9		18
48.29	odd	4		720.2.bd.g.523.5		18
80.3	even	4		1600.2.s.d.207.9		18
80.13	odd	4		400.2.s.d.107.9		18
80.19	odd	4		1600.2.j.d.143.9		18
80.27	even	4	inner	640.2.s.c.287.9		18
80.29	even	4		400.2.j.d.43.5		18
80.37	odd	4		640.2.s.d.287.1		18
80.67	even	4		320.2.s.b.207.1		18
80.77	odd	4		80.2.s.b.27.1	yes	18
120.107	odd	4		720.2.bd.g.307.5		18
240.77	even	4		720.2.z.g.667.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.5	✓	18	16.13	even	4
80.2.j.b.67.5	yes	18	40.27	even	4
80.2.s.b.3.1	yes	18	8.3	odd	2
80.2.s.b.27.1	yes	18	80.77	odd	4
320.2.j.b.47.9		18	40.37	odd	4
320.2.j.b.143.1		18	16.3	odd	4
320.2.s.b.207.1		18	80.67	even	4
320.2.s.b.303.1		18	8.5	even	2
400.2.j.d.43.5		18	80.29	even	4
400.2.j.d.307.5		18	40.3	even	4
400.2.s.d.107.9		18	80.13	odd	4
400.2.s.d.243.9		18	40.19	odd	2
640.2.j.c.543.9		18	16.11	odd	4
640.2.j.c.607.1		18	5.2	odd	4
640.2.j.d.543.1		18	16.5	even	4
640.2.j.d.607.9		18	20.7	even	4
640.2.s.c.223.9		18	1.1	even	1	trivial
640.2.s.c.287.9		18	80.27	even	4	inner
640.2.s.d.223.1		18	4.3	odd	2
640.2.s.d.287.1		18	80.37	odd	4
720.2.z.g.163.9		18	24.11	even	2
720.2.z.g.667.9		18	240.77	even	4
720.2.bd.g.307.5		18	120.107	odd	4
720.2.bd.g.523.5		18	48.29	odd	4
1600.2.j.d.143.9		18	80.19	odd	4
1600.2.j.d.1007.1		18	40.13	odd	4
1600.2.s.d.207.9		18	80.3	even	4
1600.2.s.d.943.9		18	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.85601 q^{3} +(1.71489 + 1.43498i) q^{5} +(0.458895 - 0.458895i) q^{7} +5.15678 q^{9} +O(q^{10})\)	\(q+2.85601 q^{3} +(1.71489 + 1.43498i) q^{5} +(0.458895 - 0.458895i) q^{7} +5.15678 q^{9} +(-0.492763 - 0.492763i) q^{11} -4.52109i q^{13} +(4.89773 + 4.09831i) q^{15} +(-3.12823 + 3.12823i) q^{17} +(-4.04508 - 4.04508i) q^{19} +(1.31061 - 1.31061i) q^{21} +(1.80660 + 1.80660i) q^{23} +(0.881683 + 4.92165i) q^{25} +6.15978 q^{27} +(-3.83926 + 3.83926i) q^{29} -0.139949i q^{31} +(-1.40733 - 1.40733i) q^{33} +(1.44546 - 0.128450i) q^{35} +5.84330i q^{37} -12.9123i q^{39} +4.55648i q^{41} -7.49928i q^{43} +(8.84330 + 7.39986i) q^{45} +(-4.14073 - 4.14073i) q^{47} +6.57883i q^{49} +(-8.93426 + 8.93426i) q^{51} -2.75773 q^{53} +(-0.137930 - 1.55214i) q^{55} +(-11.5528 - 11.5528i) q^{57} +(3.62521 - 3.62521i) q^{59} +(-3.72781 - 3.72781i) q^{61} +(2.36642 - 2.36642i) q^{63} +(6.48766 - 7.75317i) q^{65} -3.32677i q^{67} +(5.15965 + 5.15965i) q^{69} -1.37056 q^{71} +(2.55028 - 2.55028i) q^{73} +(2.51809 + 14.0563i) q^{75} -0.452252 q^{77} -3.86426 q^{79} +2.12204 q^{81} +14.4698 q^{83} +(-9.85351 + 0.875628i) q^{85} +(-10.9650 + 10.9650i) q^{87} +3.35011 q^{89} +(-2.07470 - 2.07470i) q^{91} -0.399696i q^{93} +(-1.13226 - 12.7415i) q^{95} +(-4.95582 + 4.95582i) q^{97} +(-2.54107 - 2.54107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9	\( 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9} - 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} + 2 q^{23} - 6 q^{25} - 24 q^{27} - 14 q^{29} - 8 q^{33} + 2 q^{35} + 14 q^{45} - 38 q^{47} + 8 q^{51} - 12 q^{53} + 6 q^{55} - 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} + 32 q^{69} - 24 q^{71} - 14 q^{73} + 16 q^{75} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} - 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) \) 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9 - 2 * q^11 + 20 * q^15 - 6 * q^17 - 2 * q^19 + 16 * q^21 + 2 * q^23 - 6 * q^25 - 24 * q^27 - 14 * q^29 - 8 * q^33 + 2 * q^35 + 14 * q^45 - 38 * q^47 + 8 * q^51 - 12 * q^53 + 6 * q^55 - 24 * q^57 + 10 * q^59 - 14 * q^61 + 6 * q^63 + 32 * q^69 - 24 * q^71 - 14 * q^73 + 16 * q^75 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 - 14 * q^85 - 24 * q^87 + 12 * q^89 - 34 * q^95 + 18 * q^97 + 22 * q^99

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