LMFDB - Embedded newform 320.3.t.a.17.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(17,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("320.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.t (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:	$8.71936845953$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.20
Character	$\chi$	$=$	320.17
Dual form			320.3.t.a.113.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.94472 q^{3} +(3.69037 + 3.37360i) q^{5} +(3.22480 - 3.22480i) q^{7} +15.4503 q^{9} +O(q^{10})$	\(q+4.94472 q^{3} +(3.69037 + 3.37360i) q^{5} +(3.22480 - 3.22480i) q^{7} +15.4503 q^{9} +(7.67097 - 7.67097i) q^{11} -22.2152 q^{13} +(18.2478 + 16.6815i) q^{15} +(-3.76038 - 3.76038i) q^{17} +(-0.809445 + 0.809445i) q^{19} +(15.9458 - 15.9458i) q^{21} +(12.2839 + 12.2839i) q^{23} +(2.23764 + 24.8997i) q^{25} +31.8948 q^{27} +(-27.1574 + 27.1574i) q^{29} -25.5557 q^{31} +(37.9308 - 37.9308i) q^{33} +(22.7799 - 1.02151i) q^{35} +8.62466 q^{37} -109.848 q^{39} -73.4504i q^{41} -17.5521i q^{43} +(57.0172 + 52.1231i) q^{45} +(-17.4590 - 17.4590i) q^{47} +28.2013i q^{49} +(-18.5940 - 18.5940i) q^{51} +29.3309i q^{53} +(54.1875 - 2.42991i) q^{55} +(-4.00248 + 4.00248i) q^{57} +(72.6508 + 72.6508i) q^{59} +(19.7110 + 19.7110i) q^{61} +(49.8241 - 49.8241i) q^{63} +(-81.9821 - 74.9451i) q^{65} -14.0319i q^{67} +(60.7406 + 60.7406i) q^{69} -91.3292i q^{71} +(42.7665 + 42.7665i) q^{73} +(11.0645 + 123.122i) q^{75} -49.4747i q^{77} -46.7110i q^{79} +18.6585 q^{81} -82.9430 q^{83} +(-1.19117 - 26.5632i) q^{85} +(-134.286 + 134.286i) q^{87} -131.145 q^{89} +(-71.6395 + 71.6395i) q^{91} -126.366 q^{93} +(-5.71789 + 0.256406i) q^{95} +(-30.5363 - 30.5363i) q^{97} +(118.519 - 118.519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9	$ 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 32 q^{19} - 4 q^{21} + 40 q^{27} + 8 q^{31} - 4 q^{33} + 4 q^{35} - 4 q^{37} + 72 q^{39} - 70 q^{45} + 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} - 52 q^{85} + 36 q^{87} - 188 q^{91} - 40 q^{93} - 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 32 * q^19 - 4 * q^21 + 40 * q^27 + 8 * q^31 - 4 * q^33 + 4 * q^35 - 4 * q^37 + 72 * q^39 - 70 * q^45 + 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 - 52 * q^85 + 36 * q^87 - 188 * q^91 - 40 * q^93 - 380 * q^95 - 4 * q^97 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	4.94472			1.64824			0.824120	−	0.566415i	$-0.191670\pi$
$3$	4.94472			1.64824			0.824120	+	0.566415i	$0.191670\pi$
$4$		0			0
$5$	3.69037	+	3.37360i	0.738074	+	0.674720i
$5$	3.69037	+	3.37360i	0.738074	+	0.674720i
$6$		0			0
$7$	3.22480	−	3.22480i	0.460686	−	0.460686i	−0.438194	−	0.898880i	$-0.644382\pi$
$7$	3.22480	−	3.22480i	0.460686	−	0.460686i	0.898880	+	0.438194i	$0.144382\pi$
$8$		0			0
$9$	15.4503			1.71670
$10$		0			0
$11$	7.67097	−	7.67097i	0.697361	−	0.697361i	−0.266480	−	0.963841i	$-0.585861\pi$
$11$	7.67097	−	7.67097i	0.697361	−	0.697361i	0.963841	+	0.266480i	$0.0858605\pi$
$12$		0			0
$13$	−22.2152			−1.70886			−0.854429	−	0.519568i	$-0.826093\pi$
$13$	−22.2152			−1.70886			−0.854429	+	0.519568i	$0.826093\pi$
$14$		0			0
$15$	18.2478	+	16.6815i	1.21652	+	1.11210i
$16$		0			0
$17$	−3.76038	−	3.76038i	−0.221199	−	0.221199i	0.587804	−	0.809003i	$-0.299993\pi$
$17$	−3.76038	−	3.76038i	−0.221199	−	0.221199i	−0.809003	+	0.587804i	$0.799993\pi$
$18$		0			0
$19$	−0.809445	+	0.809445i	−0.0426024	+	0.0426024i	−0.728087	−	0.685485i	$-0.759590\pi$
$19$	−0.809445	+	0.809445i	−0.0426024	+	0.0426024i	0.685485	+	0.728087i	$0.259590\pi$
$20$		0			0
$21$	15.9458	−	15.9458i	0.759322	−	0.759322i
$22$		0			0
$23$	12.2839	+	12.2839i	0.534083	+	0.534083i	0.921785	−	0.387701i	$-0.126731\pi$
$23$	12.2839	+	12.2839i	0.534083	+	0.534083i	−0.387701	+	0.921785i	$0.626731\pi$
$24$		0			0
$25$	2.23764	+	24.8997i	0.0895055	+	0.995986i
$26$		0			0
$27$	31.8948			1.18129
$28$		0			0
$29$	−27.1574	+	27.1574i	−0.936464	+	0.936464i	−0.998099	−	0.0616350i	$-0.980369\pi$
$29$	−27.1574	+	27.1574i	−0.936464	+	0.936464i	0.0616350	+	0.998099i	$0.480369\pi$
$30$		0			0
$31$	−25.5557			−0.824379			−0.412189	−	0.911098i	$-0.635236\pi$
$31$	−25.5557			−0.824379			−0.412189	+	0.911098i	$0.635236\pi$
$32$		0			0
$33$	37.9308	−	37.9308i	1.14942	−	1.14942i
$34$		0			0
$35$	22.7799	−	1.02151i	0.650855	−	0.0291861i
$36$		0			0
$37$	8.62466			0.233099			0.116550	−	0.993185i	$-0.462817\pi$
$37$	8.62466			0.233099			0.116550	+	0.993185i	$0.462817\pi$
$38$		0			0
$39$	−109.848			−2.81661
$40$		0			0
$41$		−	73.4504i		−	1.79147i	−0.444585	−	0.895737i	$-0.646649\pi$
$41$		−	73.4504i		−	1.79147i	0.444585	−	0.895737i	$-0.353351\pi$
$42$		0			0
$43$		−	17.5521i		−	0.408188i	−0.978951	−	0.204094i	$-0.934575\pi$
$43$		−	17.5521i		−	0.408188i	0.978951	−	0.204094i	$-0.0654248\pi$
$44$		0			0
$45$	57.0172	+	52.1231i	1.26705	+	1.15829i
$46$		0			0
$47$	−17.4590	−	17.4590i	−0.371469	−	0.371469i	0.496543	−	0.868012i	$-0.334602\pi$
$47$	−17.4590	−	17.4590i	−0.371469	−	0.371469i	−0.868012	+	0.496543i	$0.834602\pi$
$48$		0			0
$49$			28.2013i			0.575536i
$50$		0			0
$51$	−18.5940	−	18.5940i	−0.364589	−	0.364589i
$52$		0			0
$53$			29.3309i			0.553413i	0.960954	+	0.276707i	$0.0892430\pi$
$53$			29.3309i			0.553413i	−0.960954	+	0.276707i	$0.910757\pi$
$54$		0			0
$55$	54.1875	−	2.42991i	0.985227	−	0.0441803i
$56$		0			0
$57$	−4.00248	+	4.00248i	−0.0702190	+	0.0702190i
$58$		0			0
$59$	72.6508	+	72.6508i	1.23137	+	1.23137i	0.963438	+	0.267931i	$0.0863398\pi$
$59$	72.6508	+	72.6508i	1.23137	+	1.23137i	0.267931	+	0.963438i	$0.413660\pi$
$60$		0			0
$61$	19.7110	+	19.7110i	0.323132	+	0.323132i	0.849967	−	0.526835i	$-0.176622\pi$
$61$	19.7110	+	19.7110i	0.323132	+	0.323132i	−0.526835	+	0.849967i	$0.676622\pi$
$62$		0			0
$63$	49.8241	−	49.8241i	0.790859	−	0.790859i
$64$		0			0
$65$	−81.9821	−	74.9451i	−1.26126	−	1.15300i
$66$		0			0
$67$		−	14.0319i		−	0.209431i	−0.994502	−	0.104716i	$-0.966607\pi$
$67$		−	14.0319i		−	0.209431i	0.994502	−	0.104716i	$-0.0333932\pi$
$68$		0			0
$69$	60.7406	+	60.7406i	0.880298	+	0.880298i
$70$		0			0
$71$		−	91.3292i		−	1.28633i	−0.765729	−	0.643163i	$-0.777622\pi$
$71$		−	91.3292i		−	1.28633i	0.765729	−	0.643163i	$-0.222378\pi$
$72$		0			0
$73$	42.7665	+	42.7665i	0.585843	+	0.585843i	0.936503	−	0.350660i	$-0.114043\pi$
$73$	42.7665	+	42.7665i	0.585843	+	0.585843i	−0.350660	+	0.936503i	$0.614043\pi$
$74$		0			0
$75$	11.0645	+	123.122i	0.147527	+	1.64163i
$76$		0			0
$77$		−	49.4747i		−	0.642529i
$78$		0			0
$79$		−	46.7110i		−	0.591278i	−0.955300	−	0.295639i	$-0.904467\pi$
$79$		−	46.7110i		−	0.591278i	0.955300	−	0.295639i	$-0.0955326\pi$
$80$		0			0
$81$	18.6585			0.230352
$82$		0			0
$83$	−82.9430			−0.999313			−0.499656	−	0.866224i	$-0.666540\pi$
$83$	−82.9430			−0.999313			−0.499656	+	0.866224i	$0.666540\pi$
$84$		0			0
$85$	−1.19117	−	26.5632i	−0.0140137	−	0.312508i
$86$		0			0
$87$	−134.286	+	134.286i	−1.54352	+	1.54352i
$88$		0			0
$89$	−131.145			−1.47354			−0.736768	−	0.676146i	$-0.763649\pi$
$89$	−131.145			−1.47354			−0.736768	+	0.676146i	$0.763649\pi$
$90$		0			0
$91$	−71.6395	+	71.6395i	−0.787247	+	0.787247i
$92$		0			0
$93$	−126.366			−1.35877
$94$		0			0
$95$	−5.71789	+	0.256406i	−0.0601884	+	0.00269901i
$96$		0			0
$97$	−30.5363	−	30.5363i	−0.314807	−	0.314807i	0.531962	−	0.846769i	$-0.321455\pi$
$97$	−30.5363	−	30.5363i	−0.314807	−	0.314807i	−0.846769	+	0.531962i	$0.821455\pi$
$98$		0			0
$99$	118.519	−	118.519i	1.19716	−	1.19716i
$100$		0			0
$101$	22.0905	−	22.0905i	0.218718	−	0.218718i	−0.589240	−	0.807958i	$-0.700573\pi$
$101$	22.0905	−	22.0905i	0.218718	−	0.218718i	0.807958	+	0.589240i	$0.200573\pi$
$102$		0			0
$103$	5.06551	+	5.06551i	0.0491797	+	0.0491797i	0.731269	−	0.682089i	$-0.238928\pi$
$103$	5.06551	+	5.06551i	0.0491797	+	0.0491797i	−0.682089	+	0.731269i	$0.738928\pi$
$104$		0			0
$105$	112.640	−	5.05110i	1.07276	−	0.0481057i
$106$		0			0
$107$	−54.6933			−0.511153			−0.255576	−	0.966789i	$-0.582265\pi$
$107$	−54.6933			−0.511153			−0.255576	+	0.966789i	$0.582265\pi$
$108$		0			0
$109$	81.8934	−	81.8934i	0.751316	−	0.751316i	−0.223409	−	0.974725i	$-0.571719\pi$
$109$	81.8934	−	81.8934i	0.751316	−	0.751316i	0.974725	+	0.223409i	$0.0717185\pi$
$110$		0			0
$111$	42.6466			0.384203
$112$		0			0
$113$	−19.1764	+	19.1764i	−0.169703	+	0.169703i	−0.786849	−	0.617146i	$-0.788289\pi$
$113$	−19.1764	+	19.1764i	−0.169703	+	0.169703i	0.617146	+	0.786849i	$0.288289\pi$
$114$		0			0
$115$	3.89115	+	86.7732i	0.0338361	+	0.754550i
$116$		0			0
$117$	−343.230			−2.93359
$118$		0			0
$119$	−24.2530			−0.203807
$120$		0			0
$121$			3.31247i			0.0273758i
$122$		0			0
$123$		−	363.192i		−	2.95278i
$124$		0			0
$125$	−75.7438	+	99.4378i	−0.605950	+	0.795502i
$126$		0			0
$127$	−100.021	−	100.021i	−0.787565	−	0.787565i	0.193529	−	0.981094i	$-0.438007\pi$
$127$	−100.021	−	100.021i	−0.787565	−	0.787565i	−0.981094	+	0.193529i	$0.938007\pi$
$128$		0			0
$129$		−	86.7901i		−	0.672792i
$130$		0			0
$131$	48.8021	+	48.8021i	0.372535	+	0.372535i	0.868400	−	0.495865i	$-0.165149\pi$
$131$	48.8021	+	48.8021i	0.372535	+	0.372535i	−0.495865	+	0.868400i	$0.665149\pi$
$132$		0			0
$133$			5.22060i			0.0392526i
$134$		0			0
$135$	117.704	+	107.600i	0.871879	+	0.797040i
$136$		0			0
$137$	−116.195	+	116.195i	−0.848135	+	0.848135i	−0.989900	−	0.141765i	$-0.954722\pi$
$137$	−116.195	+	116.195i	−0.848135	+	0.848135i	0.141765	+	0.989900i	$0.454722\pi$
$138$		0			0
$139$	−25.5977	−	25.5977i	−0.184156	−	0.184156i	0.609008	−	0.793164i	$-0.291568\pi$
$139$	−25.5977	−	25.5977i	−0.184156	−	0.184156i	−0.793164	+	0.609008i	$0.791568\pi$
$140$		0			0
$141$	−86.3301	−	86.3301i	−0.612270	−	0.612270i
$142$		0			0
$143$	−170.412	+	170.412i	−1.19169	+	1.19169i
$144$		0			0
$145$	−191.839	+	8.60260i	−1.32303	+	0.0593283i
$146$		0			0
$147$			139.448i			0.948623i
$148$		0			0
$149$	11.6294	+	11.6294i	0.0780497	+	0.0780497i	0.745054	−	0.667004i	$-0.232424\pi$
$149$	11.6294	+	11.6294i	0.0780497	+	0.0780497i	−0.667004	+	0.745054i	$0.732424\pi$
$150$		0			0
$151$		−	84.9872i		−	0.562829i	−0.959586	−	0.281414i	$-0.909196\pi$
$151$		−	84.9872i		−	0.562829i	0.959586	−	0.281414i	$-0.0908036\pi$
$152$		0			0
$153$	−58.0989	−	58.0989i	−0.379732	−	0.379732i
$154$		0			0
$155$	−94.3101	−	86.2149i	−0.608452	−	0.556225i
$156$		0			0
$157$			128.249i			0.816874i	0.912787	+	0.408437i	$0.133926\pi$
$157$			128.249i			0.816874i	−0.912787	+	0.408437i	$0.866074\pi$
$158$		0			0
$159$			145.033i			0.912158i
$160$		0			0
$161$	79.2265			0.492090
$162$		0			0
$163$	−82.0115			−0.503138			−0.251569	−	0.967839i	$-0.580947\pi$
$163$	−82.0115			−0.503138			−0.251569	+	0.967839i	$0.580947\pi$
$164$		0			0
$165$	267.942	−	12.0153i	1.62389	−	0.0728197i
$166$		0			0
$167$	131.169	−	131.169i	0.785444	−	0.785444i	−0.195299	−	0.980744i	$-0.562568\pi$
$167$	131.169	−	131.169i	0.785444	−	0.785444i	0.980744	+	0.195299i	$0.0625678\pi$
$168$		0			0
$169$	324.513			1.92020
$170$		0			0
$171$	−12.5061	+	12.5061i	−0.0731354	+	0.0731354i
$172$		0			0
$173$	58.5238			0.338288			0.169144	−	0.985591i	$-0.445900\pi$
$173$	58.5238			0.338288			0.169144	+	0.985591i	$0.445900\pi$
$174$		0			0
$175$	87.5124	+	73.0806i	0.500071	+	0.417603i
$176$		0			0
$177$	359.238	+	359.238i	2.02959	+	2.02959i
$178$		0			0
$179$	114.264	−	114.264i	0.638347	−	0.638347i	−0.311801	−	0.950147i	$-0.600932\pi$
$179$	114.264	−	114.264i	0.638347	−	0.638347i	0.950147	+	0.311801i	$0.100932\pi$
$180$		0			0
$181$	74.0068	−	74.0068i	0.408878	−	0.408878i	−0.472470	−	0.881347i	$-0.656637\pi$
$181$	74.0068	−	74.0068i	0.408878	−	0.408878i	0.881347	+	0.472470i	$0.156637\pi$
$182$		0			0
$183$	97.4656	+	97.4656i	0.532599	+	0.532599i
$184$		0			0
$185$	31.8282	+	29.0962i	0.172044	+	0.157277i
$186$		0			0
$187$	−57.6915			−0.308511
$188$		0			0
$189$	102.855	−	102.855i	0.544204	−	0.544204i
$190$		0			0
$191$	−92.5178			−0.484387			−0.242193	−	0.970228i	$-0.577867\pi$
$191$	−92.5178			−0.484387			−0.242193	+	0.970228i	$0.577867\pi$
$192$		0			0
$193$	52.8692	−	52.8692i	0.273934	−	0.273934i	−0.556748	−	0.830682i	$-0.687951\pi$
$193$	52.8692	−	52.8692i	0.273934	−	0.273934i	0.830682	+	0.556748i	$0.187951\pi$
$194$		0			0
$195$	−405.379	−	370.582i	−2.07887	−	1.90042i
$196$		0			0
$197$	−99.4134			−0.504637			−0.252318	−	0.967644i	$-0.581193\pi$
$197$	−99.4134			−0.504637			−0.252318	+	0.967644i	$0.581193\pi$
$198$		0			0
$199$	265.168			1.33250			0.666252	−	0.745727i	$-0.267898\pi$
$199$	265.168			1.33250			0.666252	+	0.745727i	$0.267898\pi$
$200$		0			0
$201$		−	69.3838i		−	0.345193i
$202$		0			0
$203$			175.155i			0.862832i
$204$		0			0
$205$	247.792	−	271.059i	1.20874	−	1.32224i
$206$		0			0
$207$	189.790	+	189.790i	0.916860	+	0.916860i
$208$		0			0
$209$			12.4185i			0.0594184i
$210$		0			0
$211$	226.573	+	226.573i	1.07380	+	1.07380i	0.997050	+	0.0767547i	$0.0244558\pi$
$211$	226.573	+	226.573i	1.07380	+	1.07380i	0.0767547	+	0.997050i	$0.475544\pi$
$212$		0			0
$213$		−	451.597i		−	2.12017i
$214$		0			0
$215$	59.2137	−	64.7736i	0.275413	−	0.301273i
$216$		0			0
$217$	−82.4122	+	82.4122i	−0.379780	+	0.379780i
$218$		0			0
$219$	211.469	+	211.469i	0.965610	+	0.965610i
$220$		0			0
$221$	83.5374	+	83.5374i	0.377997	+	0.377997i
$222$		0			0
$223$	238.888	−	238.888i	1.07125	−	1.07125i	0.0739871	−	0.997259i	$-0.476428\pi$
$223$	238.888	−	238.888i	1.07125	−	1.07125i	0.997259	−	0.0739871i	$-0.0235724\pi$
$224$		0			0
$225$	34.5721	+	384.707i	0.153654	+	1.70981i
$226$		0			0
$227$			442.991i			1.95150i	0.218884	+	0.975751i	$0.429758\pi$
$227$			442.991i			1.95150i	−0.218884	+	0.975751i	$0.570242\pi$
$228$		0			0
$229$	218.763	+	218.763i	0.955297	+	0.955297i	0.999043	−	0.0437454i	$-0.0139290\pi$
$229$	218.763	+	218.763i	0.955297	+	0.955297i	−0.0437454	+	0.999043i	$0.513929\pi$
$230$		0			0
$231$		−	244.639i		−	1.05904i
$232$		0			0
$233$	−181.998	−	181.998i	−0.781108	−	0.781108i	0.198910	−	0.980018i	$-0.436260\pi$
$233$	−181.998	−	181.998i	−0.781108	−	0.781108i	−0.980018	+	0.198910i	$0.936260\pi$
$234$		0			0
$235$	−5.53046	−	123.330i	−0.0235339	−	0.524809i
$236$		0			0
$237$		−	230.973i		−	0.974569i
$238$		0			0
$239$			41.3149i			0.172866i	0.996258	+	0.0864328i	$0.0275468\pi$
$239$			41.3149i			0.172866i	−0.996258	+	0.0864328i	$0.972453\pi$
$240$		0			0
$241$	223.654			0.928023			0.464012	−	0.885829i	$-0.346410\pi$
$241$	223.654			0.928023			0.464012	+	0.885829i	$0.346410\pi$
$242$		0			0
$243$	−194.792			−0.801614
$244$		0			0
$245$	−95.1399	+	104.073i	−0.388326	+	0.424788i
$246$		0			0
$247$	17.9819	−	17.9819i	0.0728014	−	0.0728014i
$248$		0			0
$249$	−410.130			−1.64711
$250$		0			0
$251$	329.376	−	329.376i	1.31226	−	1.31226i	0.392507	−	0.919749i	$-0.371608\pi$
$251$	329.376	−	329.376i	1.31226	−	1.31226i	0.919749	−	0.392507i	$-0.128392\pi$
$252$		0			0
$253$	188.459			0.744898
$254$		0			0
$255$	−5.88999	−	131.348i	−0.0230980	−	0.515089i
$256$		0			0
$257$	−102.275	−	102.275i	−0.397958	−	0.397958i	0.479555	−	0.877512i	$-0.340798\pi$
$257$	−102.275	−	102.275i	−0.397958	−	0.397958i	−0.877512	+	0.479555i	$0.840798\pi$
$258$		0			0
$259$	27.8128	−	27.8128i	0.107386	−	0.107386i
$260$		0			0
$261$	−419.590	+	419.590i	−1.60762	+	1.60762i
$262$		0			0
$263$	−149.290	−	149.290i	−0.567642	−	0.567642i	0.363826	−	0.931467i	$-0.381470\pi$
$263$	−149.290	−	149.290i	−0.567642	−	0.567642i	−0.931467	+	0.363826i	$0.881470\pi$
$264$		0			0
$265$	−98.9508	+	108.242i	−0.373399	+	0.408460i
$266$		0			0
$267$	−648.474			−2.42874
$268$		0			0
$269$	−169.168	+	169.168i	−0.628876	+	0.628876i	−0.947785	−	0.318909i	$-0.896684\pi$
$269$	−169.168	+	169.168i	−0.628876	+	0.628876i	0.318909	+	0.947785i	$0.396684\pi$
$270$		0			0
$271$	389.998			1.43911			0.719554	−	0.694437i	$-0.244346\pi$
$271$	389.998			1.43911			0.719554	+	0.694437i	$0.244346\pi$
$272$		0			0
$273$	−354.237	+	354.237i	−1.29757	+	1.29757i
$274$		0			0
$275$	208.169	+	173.840i	0.756979	+	0.632144i
$276$		0			0
$277$	290.668			1.04934			0.524671	−	0.851305i	$-0.324188\pi$
$277$	290.668			1.04934			0.524671	+	0.851305i	$0.324188\pi$
$278$		0			0
$279$	−394.843			−1.41521
$280$		0			0
$281$		−	235.390i		−	0.837688i	−0.908058	−	0.418844i	$-0.862435\pi$
$281$		−	235.390i		−	0.837688i	0.908058	−	0.418844i	$-0.137565\pi$
$282$		0			0
$283$			468.675i			1.65609i	0.560659	+	0.828047i	$0.310548\pi$
$283$			468.675i			1.65609i	−0.560659	+	0.828047i	$0.689452\pi$
$284$		0			0
$285$	−28.2734	+	1.26786i	−0.0992049	+	0.00444862i
$286$		0			0
$287$	−236.863	−	236.863i	−0.825307	−	0.825307i
$288$		0			0
$289$		−	260.719i		−	0.902142i
$290$		0			0
$291$	−150.993	−	150.993i	−0.518878	−	0.518878i
$292$		0			0
$293$		−	179.844i		−	0.613801i	−0.951742	−	0.306901i	$-0.900708\pi$
$293$		−	179.844i		−	0.613801i	0.951742	−	0.306901i	$-0.0992919\pi$
$294$		0			0
$295$	23.0134	+	513.203i	0.0780116	+	1.73967i
$296$		0			0
$297$	244.664	−	244.664i	0.823785	−	0.823785i
$298$		0			0
$299$	−272.889	−	272.889i	−0.912673	−	0.912673i
$300$		0			0
$301$	−56.6020	−	56.6020i	−0.188047	−	0.188047i
$302$		0			0
$303$	109.231	−	109.231i	0.360500	−	0.360500i
$304$		0			0
$305$	6.24382	+	139.238i	0.0204715	+	0.456519i
$306$		0			0
$307$		−	110.106i		−	0.358653i	−0.983790	−	0.179326i	$-0.942608\pi$
$307$		−	110.106i		−	0.358653i	0.983790	−	0.179326i	$-0.0573918\pi$
$308$		0			0
$309$	25.0475	+	25.0475i	0.0810599	+	0.0810599i
$310$		0			0
$311$			53.7610i			0.172865i	0.996258	+	0.0864325i	$0.0275467\pi$
$311$			53.7610i			0.172865i	−0.996258	+	0.0864325i	$0.972453\pi$
$312$		0			0
$313$	165.965	+	165.965i	0.530241	+	0.530241i	0.920644	−	0.390403i	$-0.127664\pi$
$313$	165.965	+	165.965i	0.530241	+	0.530241i	−0.390403	+	0.920644i	$0.627664\pi$
$314$		0			0
$315$	351.956	−	15.7827i	1.11732	−	0.0501037i
$316$		0			0
$317$		−	40.4315i		−	0.127544i	−0.997964	−	0.0637721i	$-0.979687\pi$
$317$		−	40.4315i		−	0.127544i	0.997964	−	0.0637721i	$-0.0203131\pi$
$318$		0			0
$319$			416.648i			1.30611i
$320$		0			0
$321$	−270.443			−0.842503
$322$		0			0
$323$	6.08764			0.0188472
$324$		0			0
$325$	−49.7094	−	553.150i	−0.152952	−	1.70200i
$326$		0			0
$327$	404.940	−	404.940i	1.23835	−	1.23835i
$328$		0			0
$329$	−112.604			−0.342261
$330$		0			0
$331$	107.944	−	107.944i	0.326116	−	0.326116i	−0.524992	−	0.851107i	$-0.675932\pi$
$331$	107.944	−	107.944i	0.326116	−	0.326116i	0.851107	+	0.524992i	$0.175932\pi$
$332$		0			0
$333$	133.253			0.400160
$334$		0			0
$335$	47.3380	−	51.7828i	0.141307	−	0.154576i
$336$		0			0
$337$	−119.972	−	119.972i	−0.356000	−	0.356000i	0.506336	−	0.862336i	$-0.330999\pi$
$337$	−119.972	−	119.972i	−0.356000	−	0.356000i	−0.862336	+	0.506336i	$0.830999\pi$
$338$		0			0
$339$	−94.8219	+	94.8219i	−0.279711	+	0.279711i
$340$		0			0
$341$	−196.037	+	196.037i	−0.574889	+	0.574889i
$342$		0			0
$343$	248.959	+	248.959i	0.725828	+	0.725828i
$344$		0			0
$345$	19.2406	+	429.070i	0.0557700	+	1.24368i
$346$		0			0
$347$	165.996			0.478375			0.239188	−	0.970973i	$-0.423119\pi$
$347$	165.996			0.478375			0.239188	+	0.970973i	$0.423119\pi$
$348$		0			0
$349$	−201.279	+	201.279i	−0.576730	+	0.576730i	−0.934001	−	0.357271i	$-0.883707\pi$
$349$	−201.279	+	201.279i	−0.576730	+	0.576730i	0.357271	+	0.934001i	$0.383707\pi$
$350$		0			0
$351$	−708.548			−2.01866
$352$		0			0
$353$	−5.16188	+	5.16188i	−0.0146229	+	0.0146229i	−0.714380	−	0.699758i	$-0.753291\pi$
$353$	−5.16188	+	5.16188i	−0.0146229	+	0.0146229i	0.699758	+	0.714380i	$0.253291\pi$
$354$		0			0
$355$	308.108	−	337.038i	0.867910	−	0.949403i
$356$		0			0
$357$	−119.924			−0.335922
$358$		0			0
$359$	−81.8547			−0.228008			−0.114004	−	0.993480i	$-0.536368\pi$
$359$	−81.8547			−0.228008			−0.114004	+	0.993480i	$0.536368\pi$
$360$		0			0
$361$			359.690i			0.996370i
$362$		0			0
$363$			16.3792i			0.0451218i
$364$		0			0
$365$	13.5471	+	302.102i	0.0371152	+	0.827676i
$366$		0			0
$367$	−120.769	−	120.769i	−0.329071	−	0.329071i	0.523162	−	0.852233i	$-0.324752\pi$
$367$	−120.769	−	120.769i	−0.329071	−	0.329071i	−0.852233	+	0.523162i	$0.824752\pi$
$368$		0			0
$369$		−	1134.83i		−	3.07542i
$370$		0			0
$371$	94.5864	+	94.5864i	0.254950	+	0.254950i
$372$		0			0
$373$			320.574i			0.859447i	0.902960	+	0.429724i	$0.141389\pi$
$373$			320.574i			0.859447i	−0.902960	+	0.429724i	$0.858611\pi$
$374$		0			0
$375$	−374.532	+	491.692i	−0.998752	+	1.31118i
$376$		0			0
$377$	603.307	−	603.307i	1.60028	−	1.60028i
$378$		0			0
$379$	3.16506	+	3.16506i	0.00835109	+	0.00835109i	0.711270	−	0.702919i	$-0.248120\pi$
$379$	3.16506	+	3.16506i	0.00835109	+	0.00835109i	−0.702919	+	0.711270i	$0.748120\pi$
$380$		0			0
$381$	−494.575	−	494.575i	−1.29810	−	1.29810i
$382$		0			0
$383$	−401.423	+	401.423i	−1.04810	+	1.04810i	−0.0493197	+	0.998783i	$0.515705\pi$
$383$	−401.423	+	401.423i	−1.04810	+	1.04810i	−0.998783	+	0.0493197i	$0.984295\pi$
$384$		0			0
$385$	166.908	−	182.580i	0.433527	−	0.474234i
$386$		0			0
$387$		−	271.184i		−	0.700735i
$388$		0			0
$389$	179.440	+	179.440i	0.461286	+	0.461286i	0.899077	−	0.437791i	$-0.144239\pi$
$389$	179.440	+	179.440i	0.461286	+	0.461286i	−0.437791	+	0.899077i	$0.644239\pi$
$390$		0			0
$391$		−	92.3844i		−	0.236277i
$392$		0			0
$393$	241.313	+	241.313i	0.614028	+	0.614028i
$394$		0			0
$395$	157.584	−	172.381i	0.398947	−	0.436407i
$396$		0			0
$397$			321.234i			0.809154i	0.914504	+	0.404577i	$0.132581\pi$
$397$			321.234i			0.809154i	−0.914504	+	0.404577i	$0.867419\pi$
$398$		0			0
$399$			25.8144i			0.0646978i
$400$		0			0
$401$	649.404			1.61946			0.809730	−	0.586802i	$-0.199613\pi$
$401$	649.404			1.61946			0.809730	+	0.586802i	$0.199613\pi$
$402$		0			0
$403$	567.725			1.40875
$404$		0			0
$405$	68.8569	+	62.9465i	0.170017	+	0.155423i
$406$		0			0
$407$	66.1595	−	66.1595i	0.162554	−	0.162554i
$408$		0			0
$409$	20.3455			0.0497444			0.0248722	−	0.999691i	$-0.492082\pi$
$409$	20.3455			0.0497444			0.0248722	+	0.999691i	$0.492082\pi$
$410$		0			0
$411$	−574.550	+	574.550i	−1.39793	+	1.39793i
$412$		0			0
$413$	468.569			1.13455
$414$		0			0
$415$	−306.090	−	279.816i	−0.737566	−	0.674256i
$416$		0			0
$417$	−126.573	−	126.573i	−0.303533	−	0.303533i
$418$		0			0
$419$	204.233	−	204.233i	0.487430	−	0.487430i	−0.420064	−	0.907494i	$-0.637992\pi$
$419$	204.233	−	204.233i	0.487430	−	0.487430i	0.907494	+	0.420064i	$0.137992\pi$
$420$		0			0
$421$	−74.3563	+	74.3563i	−0.176618	+	0.176618i	−0.789880	−	0.613262i	$-0.789857\pi$
$421$	−74.3563	+	74.3563i	−0.176618	+	0.176618i	0.613262	+	0.789880i	$0.289857\pi$
$422$		0			0
$423$	−269.747	−	269.747i	−0.637699	−	0.637699i
$424$		0			0
$425$	85.2178	−	102.047i	0.200513	−	0.240110i
$426$		0			0
$427$	127.128			0.297725
$428$		0			0
$429$	−842.639	+	842.639i	−1.96419	+	1.96419i
$430$		0			0
$431$	−30.9498			−0.0718092			−0.0359046	−	0.999355i	$-0.511431\pi$
$431$	−30.9498			−0.0718092			−0.0359046	+	0.999355i	$0.511431\pi$
$432$		0			0
$433$	−68.9194	+	68.9194i	−0.159167	+	0.159167i	−0.782198	−	0.623030i	$-0.785901\pi$
$433$	−68.9194	+	68.9194i	−0.159167	+	0.159167i	0.623030	+	0.782198i	$0.285901\pi$
$434$		0			0
$435$	−948.592	+	42.5375i	−2.18067	+	0.0977873i
$436$		0			0
$437$	−19.8863			−0.0455064
$438$		0			0
$439$	−755.005			−1.71983			−0.859914	−	0.510439i	$-0.829483\pi$
$439$	−755.005			−1.71983			−0.859914	+	0.510439i	$0.829483\pi$
$440$		0			0
$441$			435.718i			0.988022i
$442$		0			0
$443$		−	109.778i		−	0.247806i	−0.992294	−	0.123903i	$-0.960459\pi$
$443$		−	109.778i		−	0.247806i	0.992294	−	0.123903i	$-0.0395412\pi$
$444$		0			0
$445$	−483.972	−	442.430i	−1.08758	−	0.994224i
$446$		0			0
$447$	57.5042	+	57.5042i	0.128645	+	0.128645i
$448$		0			0
$449$			491.218i			1.09403i	0.837124	+	0.547013i	$0.184235\pi$
$449$			491.218i			1.09403i	−0.837124	+	0.547013i	$0.815765\pi$
$450$		0			0
$451$	−563.436	−	563.436i	−1.24930	−	1.24930i
$452$		0			0
$453$		−	420.238i		−	0.927678i
$454$		0			0
$455$	−506.059	+	22.6931i	−1.11222	+	0.0498749i
$456$		0			0
$457$	−468.944	+	468.944i	−1.02614	+	1.02614i	−0.0264867	+	0.999649i	$0.508432\pi$
$457$	−468.944	+	468.944i	−1.02614	+	1.02614i	−0.999649	+	0.0264867i	$0.991568\pi$
$458$		0			0
$459$	−119.937	−	119.937i	−0.261300	−	0.261300i
$460$		0			0
$461$	−78.6933	−	78.6933i	−0.170701	−	0.170701i	0.616586	−	0.787287i	$-0.288515\pi$
$461$	−78.6933	−	78.6933i	−0.170701	−	0.170701i	−0.787287	+	0.616586i	$0.788515\pi$
$462$		0			0
$463$	382.322	−	382.322i	0.825749	−	0.825749i	−0.161176	−	0.986926i	$-0.551529\pi$
$463$	382.322	−	382.322i	0.825749	−	0.825749i	0.986926	+	0.161176i	$0.0515288\pi$
$464$		0			0
$465$	−466.337	−	426.309i	−1.00288	−	0.916793i
$466$		0			0
$467$			374.594i			0.802129i	0.916050	+	0.401065i	$0.131360\pi$
$467$			374.594i			0.802129i	−0.916050	+	0.401065i	$0.868640\pi$
$468$		0			0
$469$	−45.2501	−	45.2501i	−0.0964820	−	0.0964820i
$470$		0			0
$471$			634.157i			1.34640i
$472$		0			0
$473$	−134.641	−	134.641i	−0.284654	−	0.284654i
$474$		0			0
$475$	−21.9661	−	18.3437i	−0.0462445	−	0.0386182i
$476$		0			0
$477$			453.171i			0.950043i
$478$		0			0
$479$		−	450.432i		−	0.940359i	−0.882571	−	0.470179i	$-0.844189\pi$
$479$		−	450.432i		−	0.940359i	0.882571	−	0.470179i	$-0.155811\pi$
$480$		0			0
$481$	−191.598			−0.398333
$482$		0			0
$483$	391.753			0.811082
$484$		0			0
$485$	−9.67290	−	215.707i	−0.0199441	−	0.444757i
$486$		0			0
$487$	292.281	−	292.281i	0.600166	−	0.600166i	−0.340190	−	0.940357i	$-0.610492\pi$
$487$	292.281	−	292.281i	0.600166	−	0.600166i	0.940357	+	0.340190i	$0.110492\pi$
$488$		0			0
$489$	−405.524			−0.829293
$490$		0			0
$491$	−434.376	+	434.376i	−0.884677	+	0.884677i	−0.994006	−	0.109329i	$-0.965130\pi$
$491$	−434.376	+	434.376i	−0.884677	+	0.884677i	0.109329	+	0.994006i	$0.465130\pi$
$492$		0			0
$493$	204.245			0.414289
$494$		0			0
$495$	837.212	−	37.5429i	1.69134	−	0.0758441i
$496$		0			0
$497$	−294.519	−	294.519i	−0.592593	−	0.592593i
$498$		0			0
$499$	−36.0616	+	36.0616i	−0.0722676	+	0.0722676i	−0.742317	−	0.670049i	$-0.766273\pi$
$499$	−36.0616	+	36.0616i	−0.0722676	+	0.0722676i	0.670049	+	0.742317i	$0.266273\pi$
$500$		0			0
$501$	648.595	−	648.595i	1.29460	−	1.29460i
$502$		0			0
$503$	−196.896	−	196.896i	−0.391444	−	0.391444i	0.483758	−	0.875202i	$-0.339271\pi$
$503$	−196.896	−	196.896i	−0.391444	−	0.391444i	−0.875202	+	0.483758i	$0.839271\pi$
$504$		0			0
$505$	156.047	−	6.99756i	0.309003	−	0.0138565i
$506$		0			0
$507$	1604.63			3.16494
$508$		0			0
$509$	459.143	−	459.143i	0.902049	−	0.902049i	−0.0935638	−	0.995613i	$-0.529826\pi$
$509$	459.143	−	459.143i	0.902049	−	0.902049i	0.995613	+	0.0935638i	$0.0298259\pi$
$510$		0			0
$511$	275.827			0.539780
$512$		0			0
$513$	−25.8171	+	25.8171i	−0.0503257	+	0.0503257i
$514$		0			0
$515$	1.60459	+	35.7826i	0.00311571	+	0.0694807i
$516$		0			0
$517$	−267.855			−0.518096
$518$		0			0
$519$	289.384			0.557580
$520$		0			0
$521$		−	726.368i		−	1.39418i	−0.716984	−	0.697090i	$-0.754478\pi$
$521$		−	726.368i		−	1.39418i	0.716984	−	0.697090i	$-0.245522\pi$
$522$		0			0
$523$			542.697i			1.03766i	0.854877	+	0.518831i	$0.173633\pi$
$523$			542.697i			1.03766i	−0.854877	+	0.518831i	$0.826367\pi$
$524$		0			0
$525$	432.725	+	361.363i	0.824237	+	0.688311i
$526$		0			0
$527$	96.0993	+	96.0993i	0.182352	+	0.182352i
$528$		0			0
$529$		−	227.211i		−	0.429510i
$530$		0			0
$531$	1122.47	+	1122.47i	2.11389	+	2.11389i
$532$		0			0
$533$			1631.71i			3.06137i
$534$		0			0
$535$	−201.839	−	184.513i	−0.377268	−	0.344885i
$536$		0			0
$537$	565.004	−	565.004i	1.05215	−	1.05215i
$538$		0			0
$539$	216.331	+	216.331i	0.401357	+	0.401357i
$540$		0			0
$541$	727.376	+	727.376i	1.34450	+	1.34450i	0.891519	+	0.452983i	$0.149640\pi$
$541$	727.376	+	727.376i	1.34450	+	1.34450i	0.452983	+	0.891519i	$0.350360\pi$
$542$		0			0
$543$	365.943	−	365.943i	0.673929	−	0.673929i
$544$		0			0
$545$	578.493	−	25.9412i	1.06145	−	0.0475985i
$546$		0			0
$547$		−	511.401i		−	0.934920i	−0.884014	−	0.467460i	$-0.845169\pi$
$547$		−	511.401i		−	0.934920i	0.884014	−	0.467460i	$-0.154831\pi$
$548$		0			0
$549$	304.541	+	304.541i	0.554720	+	0.554720i
$550$		0			0
$551$		−	43.9649i		−	0.0797911i
$552$		0			0
$553$	−150.634	−	150.634i	−0.272394	−	0.272394i
$554$		0			0
$555$	157.382	+	143.872i	0.283570	+	0.259230i
$556$		0			0
$557$		−	804.398i		−	1.44416i	−0.691809	−	0.722081i	$-0.743186\pi$
$557$		−	804.398i		−	1.44416i	0.691809	−	0.722081i	$-0.256814\pi$
$558$		0			0
$559$			389.922i			0.697535i
$560$		0			0
$561$	−285.269			−0.508500
$562$		0			0
$563$	−695.151			−1.23473			−0.617363	−	0.786678i	$-0.711799\pi$
$563$	−695.151			−1.23473			−0.617363	+	0.786678i	$0.711799\pi$
$564$		0			0
$565$	−135.461	+	6.07446i	−0.239755	+	0.0107513i
$566$		0			0
$567$	60.1701	−	60.1701i	0.106120	−	0.106120i
$568$		0			0
$569$	277.088			0.486974			0.243487	−	0.969904i	$-0.421709\pi$
$569$	277.088			0.486974			0.243487	+	0.969904i	$0.421709\pi$
$570$		0			0
$571$	569.098	−	569.098i	0.996669	−	0.996669i	−0.00332578	−	0.999994i	$-0.501059\pi$
$571$	569.098	−	569.098i	0.996669	−	0.996669i	0.999994	+	0.00332578i	$0.00105863\pi$
$572$		0			0
$573$	−457.475			−0.798386
$574$		0			0
$575$	−278.378	+	333.352i	−0.484136	+	0.579743i
$576$		0			0
$577$	687.894	+	687.894i	1.19219	+	1.19219i	0.976451	+	0.215740i	$0.0692163\pi$
$577$	687.894	+	687.894i	1.19219	+	1.19219i	0.215740	+	0.976451i	$0.430784\pi$
$578$		0			0
$579$	261.424	−	261.424i	0.451509	−	0.451509i
$580$		0			0
$581$	−267.475	+	267.475i	−0.460370	+	0.460370i
$582$		0			0
$583$	224.996	+	224.996i	0.385929	+	0.385929i
$584$		0			0
$585$	−1266.65	−	1157.92i	−2.16521	−	1.97935i
$586$		0			0
$587$	−78.2483			−0.133302			−0.0666510	−	0.997776i	$-0.521231\pi$
$587$	−78.2483			−0.133302			−0.0666510	+	0.997776i	$0.521231\pi$
$588$		0			0
$589$	20.6860	−	20.6860i	0.0351205	−	0.0351205i
$590$		0			0
$591$	−491.572			−0.831763
$592$		0			0
$593$	−296.118	+	296.118i	−0.499355	+	0.499355i	−0.911237	−	0.411882i	$-0.864872\pi$
$593$	−296.118	+	296.118i	−0.499355	+	0.499355i	0.411882	+	0.911237i	$0.364872\pi$
$594$		0			0
$595$	−89.5024	−	81.8199i	−0.150424	−	0.137512i
$596$		0			0
$597$	1311.18			2.19629
$598$		0			0
$599$	−48.2788			−0.0805990			−0.0402995	−	0.999188i	$-0.512831\pi$
$599$	−48.2788			−0.0805990			−0.0402995	+	0.999188i	$0.512831\pi$
$600$		0			0
$601$		−	592.230i		−	0.985408i	−0.870197	−	0.492704i	$-0.836008\pi$
$601$		−	592.230i		−	0.985408i	0.870197	−	0.492704i	$-0.163992\pi$
$602$		0			0
$603$		−	216.796i		−	0.359530i
$604$		0			0
$605$	−11.1749	+	12.2242i	−0.0184710	+	0.0202053i
$606$		0			0
$607$	289.382	+	289.382i	0.476741	+	0.476741i	0.904088	−	0.427346i	$-0.140552\pi$
$607$	289.382	+	289.382i	0.476741	+	0.476741i	−0.427346	+	0.904088i	$0.640552\pi$
$608$		0			0
$609$			866.092i			1.42215i
$610$		0			0
$611$	387.855	+	387.855i	0.634787	+	0.634787i
$612$		0			0
$613$		−	719.493i		−	1.17373i	−0.809687	−	0.586863i	$-0.800363\pi$
$613$		−	719.493i		−	1.17373i	0.809687	−	0.586863i	$-0.199637\pi$
$614$		0			0
$615$	1225.26	−	1340.31i	1.99230	−	2.17937i
$616$		0			0
$617$	−370.007	+	370.007i	−0.599687	+	0.599687i	−0.940229	−	0.340542i	$-0.889389\pi$
$617$	−370.007	+	370.007i	−0.599687	+	0.599687i	0.340542	+	0.940229i	$0.389389\pi$
$618$		0			0
$619$	524.739	+	524.739i	0.847721	+	0.847721i	0.989848	−	0.142127i	$-0.0453942\pi$
$619$	524.739	+	524.739i	0.847721	+	0.847721i	−0.142127	+	0.989848i	$0.545394\pi$
$620$		0			0
$621$	391.793	+	391.793i	0.630907	+	0.630907i
$622$		0			0
$623$	−422.916	+	422.916i	−0.678837	+	0.678837i
$624$		0			0
$625$	−614.986	+	111.433i	−0.983978	+	0.178292i
$626$		0			0
$627$			61.4058i			0.0979359i
$628$		0			0
$629$	−32.4320	−	32.4320i	−0.0515612	−	0.0515612i
$630$		0			0
$631$			481.853i			0.763634i	0.924238	+	0.381817i	$0.124702\pi$
$631$			481.853i			0.763634i	−0.924238	+	0.381817i	$0.875298\pi$
$632$		0			0
$633$	1120.34	+	1120.34i	1.76989	+	1.76989i
$634$		0			0
$635$	−31.6833	−	706.544i	−0.0498950	−	1.11267i
$636$		0			0
$637$		−	626.496i		−	0.983510i
$638$		0			0
$639$		−	1411.06i		−	2.20823i
$640$		0			0
$641$	602.798			0.940403			0.470202	−	0.882559i	$-0.344181\pi$
$641$	602.798			0.940403			0.470202	+	0.882559i	$0.344181\pi$
$642$		0			0
$643$	−1220.05			−1.89744			−0.948720	−	0.316118i	$-0.897621\pi$
$643$	−1220.05			−1.89744			−0.948720	+	0.316118i	$0.897621\pi$
$644$		0			0
$645$	292.795	−	320.288i	0.453946	−	0.496570i
$646$		0			0
$647$	−674.538	+	674.538i	−1.04256	+	1.04256i	−0.0435096	+	0.999053i	$0.513854\pi$
$647$	−674.538	+	674.538i	−1.04256	+	1.04256i	−0.999053	+	0.0435096i	$0.986146\pi$
$648$		0			0
$649$	1114.60			1.71742
$650$		0			0
$651$	−407.506	+	407.506i	−0.625969	+	0.625969i
$652$		0			0
$653$	−1069.12			−1.63724			−0.818620	−	0.574336i	$-0.805260\pi$
$653$	−1069.12			−1.63724			−0.818620	+	0.574336i	$0.805260\pi$
$654$		0			0
$655$	15.4589	+	344.737i	0.0236014	+	0.526315i
$656$		0			0
$657$	660.755	+	660.755i	1.00572	+	1.00572i
$658$		0			0
$659$	392.851	−	392.851i	0.596131	−	0.596131i	−0.343149	−	0.939281i	$-0.611494\pi$
$659$	392.851	−	392.851i	0.596131	−	0.596131i	0.939281	+	0.343149i	$0.111494\pi$
$660$		0			0
$661$	−251.961	+	251.961i	−0.381182	+	0.381182i	−0.871528	−	0.490346i	$-0.836871\pi$
$661$	−251.961	+	251.961i	−0.381182	+	0.381182i	0.490346	+	0.871528i	$0.336871\pi$
$662$		0			0
$663$	413.069	+	413.069i	0.623031	+	0.623031i
$664$		0			0
$665$	−17.6122	+	19.2659i	−0.0264845	+	0.0289713i
$666$		0			0
$667$	−667.200			−1.00030
$668$		0			0
$669$	1181.23	−	1181.23i	1.76567	−	1.76567i
$670$		0			0
$671$	302.406			0.450679
$672$		0			0
$673$	−54.2702	+	54.2702i	−0.0806392	+	0.0806392i	−0.746276	−	0.665637i	$-0.768160\pi$
$673$	−54.2702	+	54.2702i	−0.0806392	+	0.0806392i	0.665637	+	0.746276i	$0.268160\pi$
$674$		0			0
$675$	71.3690	+	794.170i	0.105732	+	1.17655i
$676$		0			0
$677$	−862.549			−1.27408			−0.637038	−	0.770832i	$-0.719841\pi$
$677$	−862.549			−1.27408			−0.637038	+	0.770832i	$0.719841\pi$
$678$		0			0
$679$	−196.947			−0.290054
$680$		0			0
$681$			2190.47i			3.21654i
$682$		0			0
$683$		−	887.581i		−	1.29953i	−0.760134	−	0.649766i	$-0.774867\pi$
$683$		−	887.581i		−	1.29953i	0.760134	−	0.649766i	$-0.225133\pi$
$684$		0			0
$685$	−820.794	+	36.8067i	−1.19824	+	0.0537323i
$686$		0			0
$687$	1081.72	+	1081.72i	1.57456	+	1.57456i
$688$		0			0
$689$		−	651.591i		−	0.945705i
$690$		0			0
$691$	−810.243	−	810.243i	−1.17257	−	1.17257i	−0.981596	−	0.190969i	$-0.938837\pi$
$691$	−810.243	−	810.243i	−1.17257	−	1.17257i	−0.190969	−	0.981596i	$-0.561163\pi$
$692$		0			0
$693$		−	764.398i		−	1.10303i
$694$		0			0
$695$	−8.10851	−	180.821i	−0.0116669	−	0.260174i
$696$		0			0
$697$	−276.202	+	276.202i	−0.396272	+	0.396272i
$698$		0			0
$699$	−899.930	−	899.930i	−1.28745	−	1.28745i
$700$		0			0
$701$	768.186	+	768.186i	1.09584	+	1.09584i	0.994891	+	0.100952i	$0.0321889\pi$
$701$	768.186	+	768.186i	1.09584	+	1.09584i	0.100952	+	0.994891i	$0.467811\pi$
$702$		0			0
$703$	−6.98119	+	6.98119i	−0.00993057	+	0.00993057i
$704$		0			0
$705$	−27.3466	−	609.833i	−0.0387895	−	0.865011i
$706$		0			0
$707$		−	142.475i		−	0.201521i
$708$		0			0
$709$	−587.694	−	587.694i	−0.828906	−	0.828906i	0.158459	−	0.987365i	$-0.449347\pi$
$709$	−587.694	−	587.694i	−0.828906	−	0.828906i	−0.987365	+	0.158459i	$0.949347\pi$
$710$		0			0
$711$		−	721.697i		−	1.01505i
$712$		0			0
$713$	−313.925	−	313.925i	−0.440287	−	0.440287i
$714$		0			0
$715$	−1203.78	+	53.9809i	−1.68361	+	0.0754978i
$716$		0			0
$717$			204.291i			0.284924i
$718$		0			0
$719$			735.293i			1.02266i	0.859384	+	0.511330i	$0.170847\pi$
$719$			735.293i			1.02266i	−0.859384	+	0.511330i	$0.829153\pi$
$720$		0			0
$721$	32.6705			0.0453128
$722$		0			0
$723$	1105.90			1.52961
$724$		0			0
$725$	−736.980	−	615.443i	−1.01652	−	0.848886i
$726$		0			0
$727$	282.639	−	282.639i	0.388775	−	0.388775i	−0.485475	−	0.874250i	$-0.661353\pi$
$727$	282.639	−	282.639i	0.388775	−	0.388775i	0.874250	+	0.485475i	$0.161353\pi$
$728$		0			0
$729$	−1131.12			−1.55160
$730$		0			0
$731$	−66.0025	+	66.0025i	−0.0902907	+	0.0902907i
$732$		0			0
$733$	−1241.78			−1.69410			−0.847050	−	0.531513i	$-0.821624\pi$
$733$	−1241.78			−1.69410			−0.847050	+	0.531513i	$0.821624\pi$
$734$		0			0
$735$	−470.440	+	514.613i	−0.640055	+	0.700153i
$736$		0			0
$737$	−107.638	−	107.638i	−0.146049	−	0.146049i
$738$		0			0
$739$	−682.480	+	682.480i	−0.923518	+	0.923518i	−0.997276	−	0.0737578i	$-0.976501\pi$
$739$	−682.480	+	682.480i	−0.923518	+	0.923518i	0.0737578	+	0.997276i	$0.476501\pi$
$740$		0			0
$741$	88.9157	−	88.9157i	0.119994	−	0.119994i
$742$		0			0
$743$	603.646	+	603.646i	0.812444	+	0.812444i	0.985000	−	0.172556i	$-0.0552025\pi$
$743$	603.646	+	603.646i	0.812444	+	0.812444i	−0.172556	+	0.985000i	$0.555203\pi$
$744$		0			0
$745$	3.68382	+	82.1497i	0.00494472	+	0.110268i
$746$		0			0
$747$	−1281.49			−1.71552
$748$		0			0
$749$	−176.375	+	176.375i	−0.235481	+	0.235481i
$750$		0			0
$751$	−849.499			−1.13116			−0.565578	−	0.824695i	$-0.691347\pi$
$751$	−849.499			−1.13116			−0.565578	+	0.824695i	$0.691347\pi$
$752$		0			0
$753$	1628.67	−	1628.67i	2.16291	−	2.16291i
$754$		0			0
$755$	286.713	−	313.634i	0.379752	−	0.415409i
$756$		0			0
$757$	410.039			0.541663			0.270832	−	0.962627i	$-0.412701\pi$
$757$	410.039			0.541663			0.270832	+	0.962627i	$0.412701\pi$
$758$		0			0
$759$	931.878			1.22777
$760$		0			0
$761$		−	582.295i		−	0.765171i	−0.923920	−	0.382585i	$-0.875034\pi$
$761$		−	582.295i		−	0.765171i	0.923920	−	0.382585i	$-0.124966\pi$
$762$		0			0
$763$		−	528.180i		−	0.692242i
$764$		0			0
$765$	−18.4039	−	410.409i	−0.0240573	−	0.536482i
$766$		0			0
$767$	−1613.95	−	1613.95i	−2.10423	−	2.10423i
$768$		0			0
$769$			1386.11i			1.80249i	0.433311	+	0.901245i	$0.357345\pi$
$769$			1386.11i			1.80249i	−0.433311	+	0.901245i	$0.642655\pi$
$770$		0			0
$771$	−505.722	−	505.722i	−0.655930	−	0.655930i
$772$		0			0
$773$			1124.50i			1.45473i	0.686253	+	0.727363i	$0.259254\pi$
$773$			1124.50i			1.45473i	−0.686253	+	0.727363i	$0.740746\pi$
$774$		0			0
$775$	−57.1845	−	636.329i	−0.0737864	−	0.821070i
$776$		0			0
$777$	137.527	−	137.527i	0.176997	−	0.176997i
$778$		0			0
$779$	59.4541	+	59.4541i	0.0763210	+	0.0763210i
$780$		0			0
$781$	−700.583	−	700.583i	−0.897033	−	0.897033i
$782$		0			0
$783$	−866.182	+	866.182i	−1.10623	+	1.10623i
$784$		0			0
$785$	−432.662	+	473.287i	−0.551161	+	0.602913i
$786$		0			0
$787$			785.121i			0.997612i	0.866714	+	0.498806i	$0.166228\pi$
$787$			785.121i			0.997612i	−0.866714	+	0.498806i	$0.833772\pi$
$788$		0			0
$789$	−738.196	−	738.196i	−0.935610	−	0.935610i
$790$		0			0
$791$			123.680i			0.156359i
$792$		0			0
$793$	−437.884	−	437.884i	−0.552186	−	0.552186i
$794$		0			0
$795$	−489.284	+	535.226i	−0.615452	+	0.673240i
$796$		0			0
$797$		−	58.6173i		−	0.0735474i	−0.999324	−	0.0367737i	$-0.988292\pi$
$797$		−	58.6173i		−	0.0735474i	0.999324	−	0.0367737i	$-0.0117081\pi$
$798$		0			0
$799$			131.305i			0.164337i
$800$		0			0
$801$	−2026.22			−2.52961
$802$		0			0
$803$	656.122			0.817088
$804$		0			0
$805$	292.375	+	267.278i	0.363198	+	0.332023i
$806$		0			0
$807$	−836.488	+	836.488i	−1.03654	+	1.03654i
$808$		0			0
$809$	361.896			0.447337			0.223669	−	0.974665i	$-0.428197\pi$
$809$	361.896			0.447337			0.223669	+	0.974665i	$0.428197\pi$
$810$		0			0
$811$	−88.5414	+	88.5414i	−0.109176	+	0.109176i	−0.759584	−	0.650409i	$-0.774598\pi$
$811$	−88.5414	+	88.5414i	−0.109176	+	0.109176i	0.650409	+	0.759584i	$0.274598\pi$
$812$		0			0
$813$	1928.43			2.37200
$814$		0			0
$815$	−302.653	−	276.674i	−0.371353	−	0.339477i
$816$		0			0
$817$	14.2074	+	14.2074i	0.0173898	+	0.0173898i
$818$		0			0
$819$	−1106.85	+	1106.85i	−1.35147	+	1.35147i
$820$		0			0
$821$	−74.7330	+	74.7330i	−0.0910268	+	0.0910268i	−0.751154	−	0.660127i	$-0.770502\pi$
$821$	−74.7330	+	74.7330i	−0.0910268	+	0.0910268i	0.660127	+	0.751154i	$0.270502\pi$
$822$		0			0
$823$	481.562	+	481.562i	0.585131	+	0.585131i	0.936309	−	0.351178i	$-0.114219\pi$
$823$	481.562	+	481.562i	0.585131	+	0.585131i	−0.351178	+	0.936309i	$0.614219\pi$
$824$		0			0
$825$	1029.34	+	859.589i	1.24768	+	1.04193i
$826$		0			0
$827$	1232.64			1.49049			0.745246	−	0.666789i	$-0.232332\pi$
$827$	1232.64			1.49049			0.745246	+	0.666789i	$0.232332\pi$
$828$		0			0
$829$	503.806	−	503.806i	0.607727	−	0.607727i	−0.334624	−	0.942352i	$-0.608609\pi$
$829$	503.806	−	503.806i	0.607727	−	0.607727i	0.942352	+	0.334624i	$0.108609\pi$
$830$		0			0
$831$	1437.27			1.72957
$832$		0			0
$833$	106.048	−	106.048i	0.127308	−	0.127308i
$834$		0			0
$835$	926.575	−	41.5502i	1.10967	−	0.0497607i
$836$		0			0
$837$	−815.096			−0.973830
$838$		0			0
$839$	949.352			1.13153			0.565764	−	0.824567i	$-0.308581\pi$
$839$	949.352			1.13153			0.565764	+	0.824567i	$0.308581\pi$
$840$		0			0
$841$		−	634.054i		−	0.753929i
$842$		0			0
$843$		−	1163.94i		−	1.38071i
$844$		0			0
$845$	1197.57	+	1094.78i	1.41725	+	1.29559i
$846$		0			0
$847$	10.6821	+	10.6821i	0.0126116	+	0.0126116i
$848$		0			0
$849$			2317.47i			2.72964i
$850$		0			0
$851$	105.945	+	105.945i	0.124494	+	0.124494i
$852$		0			0
$853$			331.721i			0.388887i	0.980914	+	0.194444i	$0.0622901\pi$
$853$			331.721i			0.388887i	−0.980914	+	0.194444i	$0.937710\pi$
$854$		0			0
$855$	−88.3430	+	3.96154i	−0.103325	+	0.00463338i
$856$		0			0
$857$	−207.103	+	207.103i	−0.241660	+	0.241660i	−0.817537	−	0.575876i	$-0.804661\pi$
$857$	−207.103	+	207.103i	−0.241660	+	0.241660i	0.575876	+	0.817537i	$0.304661\pi$
$858$		0			0
$859$	−315.715	−	315.715i	−0.367538	−	0.367538i	0.499041	−	0.866579i	$-0.333686\pi$
$859$	−315.715	−	315.715i	−0.367538	−	0.367538i	−0.866579	+	0.499041i	$0.833686\pi$
$860$		0			0
$861$	−1171.22	−	1171.22i	−1.36030	−	1.36030i
$862$		0			0
$863$	−278.969	+	278.969i	−0.323255	+	0.323255i	−0.850014	−	0.526760i	$-0.823407\pi$
$863$	−278.969	+	278.969i	−0.323255	+	0.323255i	0.526760	+	0.850014i	$0.323407\pi$
$864$		0			0
$865$	215.974	+	197.436i	0.249681	+	0.228250i
$866$		0			0
$867$		−	1289.18i		−	1.48695i
$868$		0			0
$869$	−358.318	−	358.318i	−0.412334	−	0.412334i
$870$		0			0
$871$			311.720i			0.357888i
$872$		0			0
$873$	−471.794	−	471.794i	−0.540428	−	0.540428i
$874$		0			0
$875$	76.4085	+	564.926i	0.0873240	+	0.645630i
$876$		0			0
$877$		−	1338.50i		−	1.52623i	−0.646263	−	0.763114i	$-0.723669\pi$
$877$		−	1338.50i		−	1.52623i	0.646263	−	0.763114i	$-0.276331\pi$
$878$		0			0
$879$		−	889.277i		−	1.01169i
$880$		0			0
$881$	−138.825			−0.157576			−0.0787881	−	0.996891i	$-0.525105\pi$
$881$	−138.825			−0.157576			−0.0787881	+	0.996891i	$0.525105\pi$
$882$		0			0
$883$	−212.516			−0.240675			−0.120337	−	0.992733i	$-0.538398\pi$
$883$	−212.516			−0.240675			−0.120337	+	0.992733i	$0.538398\pi$
$884$		0			0
$885$	113.795	+	2537.64i	0.128582	+	2.86740i
$886$		0			0
$887$	368.959	−	368.959i	0.415963	−	0.415963i	−0.467847	−	0.883810i	$-0.654970\pi$
$887$	368.959	−	368.959i	0.415963	−	0.415963i	0.883810	+	0.467847i	$0.154970\pi$
$888$		0			0
$889$	−645.095			−0.725641
$890$		0			0
$891$	143.129	−	143.129i	0.160639	−	0.160639i
$892$		0			0
$893$	28.2643			0.0316509
$894$		0			0
$895$	807.158	−	36.1951i	0.901852	−	0.0404415i
$896$		0			0
$897$	−1349.36	−	1349.36i	−1.50430	−	1.50430i
$898$		0			0
$899$	694.029	−	694.029i	0.772001	−	0.772001i
$900$		0			0
$901$	110.295	−	110.295i	0.122414	−	0.122414i
$902$		0			0
$903$	−279.881	−	279.881i	−0.309946	−	0.309946i
$904$		0			0
$905$	522.782	−	23.4430i	0.577660	−	0.0259038i
$906$		0			0
$907$	783.206			0.863513			0.431756	−	0.901990i	$-0.357894\pi$
$907$	783.206			0.863513			0.431756	+	0.901990i	$0.357894\pi$
$908$		0			0
$909$	341.304	−	341.304i	0.375472	−	0.375472i
$910$		0			0
$911$	1463.16			1.60610			0.803052	−	0.595909i	$-0.203208\pi$
$911$	1463.16			1.60610			0.803052	+	0.595909i	$0.203208\pi$
$912$		0			0
$913$	−636.253	+	636.253i	−0.696882	+	0.696882i
$914$		0			0
$915$	30.8740	+	688.494i	0.0337420	+	0.752453i
$916$		0			0
$917$	314.754			0.343244
$918$		0			0
$919$	−1217.73			−1.32506			−0.662529	−	0.749036i	$-0.730517\pi$
$919$	−1217.73			−1.32506			−0.662529	+	0.749036i	$0.730517\pi$
$920$		0			0
$921$		−	544.445i		−	0.591146i
$922$		0			0
$923$			2028.89i			2.19815i
$924$		0			0
$925$	19.2989	+	214.751i	0.0208636	+	0.232163i
$926$		0			0
$927$	78.2635	+	78.2635i	0.0844266	+	0.0844266i
$928$		0			0
$929$		−	169.265i		−	0.182201i	−0.995842	−	0.0911004i	$-0.970962\pi$
$929$		−	169.265i		−	0.182201i	0.995842	−	0.0911004i	$-0.0290384\pi$
$930$		0			0
$931$	−22.8274	−	22.8274i	−0.0245192	−	0.0245192i
$932$		0			0
$933$			265.833i			0.284923i
$934$		0			0
$935$	−212.903	−	194.628i	−0.227704	−	0.208159i
$936$		0			0
$937$	−457.486	+	457.486i	−0.488245	+	0.488245i	−0.907752	−	0.419507i	$-0.862203\pi$
$937$	−457.486	+	457.486i	−0.488245	+	0.488245i	0.419507	+	0.907752i	$0.362203\pi$
$938$		0			0
$939$	820.653	+	820.653i	0.873965	+	0.873965i
$940$		0			0
$941$	−206.539	−	206.539i	−0.219489	−	0.219489i	0.588794	−	0.808283i	$-0.299603\pi$
$941$	−206.539	−	206.539i	−0.219489	−	0.219489i	−0.808283	+	0.588794i	$0.799603\pi$
$942$		0			0
$943$	902.259	−	902.259i	0.956797	−	0.956797i
$944$		0			0
$945$	726.561	−	32.5810i	0.768848	−	0.0344772i
$946$		0			0
$947$		−	952.719i		−	1.00604i	−0.864275	−	0.503019i	$-0.832222\pi$
$947$		−	952.719i		−	1.00604i	0.864275	−	0.503019i	$-0.167778\pi$
$948$		0			0
$949$	−950.065	−	950.065i	−1.00112	−	1.00112i
$950$		0			0
$951$		−	199.923i		−	0.210224i
$952$		0			0
$953$	−830.106	−	830.106i	−0.871045	−	0.871045i	0.121542	−	0.992586i	$-0.461216\pi$
$953$	−830.106	−	830.106i	−0.871045	−	0.871045i	−0.992586	+	0.121542i	$0.961216\pi$
$954$		0			0
$955$	−341.425	−	312.118i	−0.357513	−	0.326825i
$956$		0			0
$957$			2060.21i			2.15278i
$958$		0			0
$959$			749.409i			0.781448i
$960$		0			0
$961$	−307.904			−0.320400
$962$		0			0
$963$	−845.027			−0.877494
$964$		0			0
$965$	373.467	−	16.7473i	0.387012	−	0.0173547i
$966$		0			0
$967$	−34.0691	+	34.0691i	−0.0352318	+	0.0352318i	−0.724503	−	0.689271i	$-0.757931\pi$
$967$	−34.0691	+	34.0691i	−0.0352318	+	0.0352318i	0.689271	+	0.724503i	$0.257931\pi$
$968$		0			0
$969$	30.1017			0.0310647
$970$		0			0
$971$	84.7430	−	84.7430i	0.0872739	−	0.0872739i	−0.662122	−	0.749396i	$-0.730344\pi$
$971$	84.7430	−	84.7430i	0.0872739	−	0.0872739i	0.749396	+	0.662122i	$0.230344\pi$
$972$		0			0
$973$	−165.095			−0.169676
$974$		0			0
$975$	−245.799	−	2735.17i	−0.252102	−	2.80530i
$976$		0			0
$977$	28.0540	+	28.0540i	0.0287145	+	0.0287145i	0.721318	−	0.692604i	$-0.243537\pi$
$977$	28.0540	+	28.0540i	0.0287145	+	0.0287145i	−0.692604	+	0.721318i	$0.743537\pi$
$978$		0			0
$979$	−1006.01	+	1006.01i	−1.02759	+	1.02759i
$980$		0			0
$981$	1265.28	−	1265.28i	1.28978	−	1.28978i
$982$		0			0
$983$	−359.158	−	359.158i	−0.365370	−	0.365370i	0.500416	−	0.865785i	$-0.333181\pi$
$983$	−359.158	−	359.158i	−0.365370	−	0.365370i	−0.865785	+	0.500416i	$0.833181\pi$
$984$		0			0
$985$	−366.872	−	335.381i	−0.372459	−	0.340489i
$986$		0			0
$987$	−556.795			−0.564129
$988$		0			0
$989$	215.608	−	215.608i	0.218006	−	0.218006i
$990$		0			0
$991$	−301.699			−0.304439			−0.152219	−	0.988347i	$-0.548642\pi$
$991$	−301.699			−0.304439			−0.152219	+	0.988347i	$0.548642\pi$
$992$		0			0
$993$	533.755	−	533.755i	0.537517	−	0.537517i
$994$		0			0
$995$	978.568	+	894.571i	0.983485	+	0.899067i
$996$		0			0
$997$	701.351			0.703461			0.351731	−	0.936101i	$-0.385593\pi$
$997$	701.351			0.703461			0.351731	+	0.936101i	$0.385593\pi$
$998$		0			0
$999$	275.082			0.275357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.t.a.17.20		44
4.3	odd	2		80.3.t.a.77.12	yes	44
5.3	odd	4		320.3.i.a.273.20		44
8.3	odd	2		640.3.t.b.417.20		44
8.5	even	2		640.3.t.a.417.3		44
16.3	odd	4		640.3.i.b.97.3		44
16.5	even	4		320.3.i.a.177.3		44
16.11	odd	4		80.3.i.a.37.1	yes	44
16.13	even	4		640.3.i.a.97.20		44
20.3	even	4		80.3.i.a.13.1	✓	44
20.7	even	4		400.3.i.b.93.22		44
20.19	odd	2		400.3.t.b.157.11		44
40.3	even	4		640.3.i.b.33.20		44
40.13	odd	4		640.3.i.a.33.3		44
80.3	even	4		640.3.t.b.353.20		44
80.13	odd	4		640.3.t.a.353.3		44
80.27	even	4		400.3.t.b.293.11		44
80.43	even	4		80.3.t.a.53.12	yes	44
80.53	odd	4	inner	320.3.t.a.113.20		44
80.59	odd	4		400.3.i.b.357.22		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.1	✓	44	20.3	even	4
80.3.i.a.37.1	yes	44	16.11	odd	4
80.3.t.a.53.12	yes	44	80.43	even	4
80.3.t.a.77.12	yes	44	4.3	odd	2
320.3.i.a.177.3		44	16.5	even	4
320.3.i.a.273.20		44	5.3	odd	4
320.3.t.a.17.20		44	1.1	even	1	trivial
320.3.t.a.113.20		44	80.53	odd	4	inner
400.3.i.b.93.22		44	20.7	even	4
400.3.i.b.357.22		44	80.59	odd	4
400.3.t.b.157.11		44	20.19	odd	2
400.3.t.b.293.11		44	80.27	even	4
640.3.i.a.33.3		44	40.13	odd	4
640.3.i.a.97.20		44	16.13	even	4
640.3.i.b.33.20		44	40.3	even	4
640.3.i.b.97.3		44	16.3	odd	4
640.3.t.a.353.3		44	80.13	odd	4
640.3.t.a.417.3		44	8.5	even	2
640.3.t.b.353.20		44	80.3	even	4
640.3.t.b.417.20		44	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+4.94472 q^{3} +(3.69037 + 3.37360i) q^{5} +(3.22480 - 3.22480i) q^{7} +15.4503 q^{9} +O(q^{10})\)	\(q+4.94472 q^{3} +(3.69037 + 3.37360i) q^{5} +(3.22480 - 3.22480i) q^{7} +15.4503 q^{9} +(7.67097 - 7.67097i) q^{11} -22.2152 q^{13} +(18.2478 + 16.6815i) q^{15} +(-3.76038 - 3.76038i) q^{17} +(-0.809445 + 0.809445i) q^{19} +(15.9458 - 15.9458i) q^{21} +(12.2839 + 12.2839i) q^{23} +(2.23764 + 24.8997i) q^{25} +31.8948 q^{27} +(-27.1574 + 27.1574i) q^{29} -25.5557 q^{31} +(37.9308 - 37.9308i) q^{33} +(22.7799 - 1.02151i) q^{35} +8.62466 q^{37} -109.848 q^{39} -73.4504i q^{41} -17.5521i q^{43} +(57.0172 + 52.1231i) q^{45} +(-17.4590 - 17.4590i) q^{47} +28.2013i q^{49} +(-18.5940 - 18.5940i) q^{51} +29.3309i q^{53} +(54.1875 - 2.42991i) q^{55} +(-4.00248 + 4.00248i) q^{57} +(72.6508 + 72.6508i) q^{59} +(19.7110 + 19.7110i) q^{61} +(49.8241 - 49.8241i) q^{63} +(-81.9821 - 74.9451i) q^{65} -14.0319i q^{67} +(60.7406 + 60.7406i) q^{69} -91.3292i q^{71} +(42.7665 + 42.7665i) q^{73} +(11.0645 + 123.122i) q^{75} -49.4747i q^{77} -46.7110i q^{79} +18.6585 q^{81} -82.9430 q^{83} +(-1.19117 - 26.5632i) q^{85} +(-134.286 + 134.286i) q^{87} -131.145 q^{89} +(-71.6395 + 71.6395i) q^{91} -126.366 q^{93} +(-5.71789 + 0.256406i) q^{95} +(-30.5363 - 30.5363i) q^{97} +(118.519 - 118.519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9	\( 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 32 q^{19} - 4 q^{21} + 40 q^{27} + 8 q^{31} - 4 q^{33} + 4 q^{35} - 4 q^{37} + 72 q^{39} - 70 q^{45} + 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} - 52 q^{85} + 36 q^{87} - 188 q^{91} - 40 q^{93} - 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 32 * q^19 - 4 * q^21 + 40 * q^27 + 8 * q^31 - 4 * q^33 + 4 * q^35 - 4 * q^37 + 72 * q^39 - 70 * q^45 + 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 - 52 * q^85 + 36 * q^87 - 188 * q^91 - 40 * q^93 - 380 * q^95 - 4 * q^97 - 92 * q^99

Introduction

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