LMFDB - Embedded newform 80.5.p.c.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,5,Mod(17,80)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("80.17"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	80.p (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.26959704671$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	80.17
Dual form			80.5.p.c.33.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{3} +(-15.0000 - 20.0000i) q^{5} +(19.0000 + 19.0000i) q^{7} +79.0000i q^{9} -202.000 q^{11} +(-99.0000 + 99.0000i) q^{13} +(35.0000 + 5.00000i) q^{15} +(-239.000 - 239.000i) q^{17} -40.0000i q^{19} -38.0000 q^{21} +(-541.000 + 541.000i) q^{23} +(-175.000 + 600.000i) q^{25} +(-160.000 - 160.000i) q^{27} -200.000i q^{29} +758.000 q^{31} +(202.000 - 202.000i) q^{33} +(95.0000 - 665.000i) q^{35} +(141.000 + 141.000i) q^{37} -198.000i q^{39} +1042.00 q^{41} +(759.000 - 759.000i) q^{43} +(1580.00 - 1185.00i) q^{45} +(459.000 + 459.000i) q^{47} -1679.00i q^{49} +478.000 q^{51} +(-1819.00 + 1819.00i) q^{53} +(3030.00 + 4040.00i) q^{55} +(40.0000 + 40.0000i) q^{57} -4600.00i q^{59} +2082.00 q^{61} +(-1501.00 + 1501.00i) q^{63} +(3465.00 + 495.000i) q^{65} +(-5081.00 - 5081.00i) q^{67} -1082.00i q^{69} +3478.00 q^{71} +(-3479.00 + 3479.00i) q^{73} +(-425.000 - 775.000i) q^{75} +(-3838.00 - 3838.00i) q^{77} +7680.00i q^{79} -6079.00 q^{81} +(-6081.00 + 6081.00i) q^{83} +(-1195.00 + 8365.00i) q^{85} +(200.000 + 200.000i) q^{87} -5680.00i q^{89} -3762.00 q^{91} +(-758.000 + 758.000i) q^{93} +(-800.000 + 600.000i) q^{95} +(561.000 + 561.000i) q^{97} -15958.0i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 30 q^{5} + 38 q^{7} - 404 q^{11} - 198 q^{13} + 70 q^{15} - 478 q^{17} - 76 q^{21} - 1082 q^{23} - 350 q^{25} - 320 q^{27} + 1516 q^{31} + 404 q^{33} + 190 q^{35} + 282 q^{37} + 2084 q^{41}+ \cdots + 1122 q^{97}+O(q^{100}) $ 2 * q - 2 * q^3 - 30 * q^5 + 38 * q^7 - 404 * q^11 - 198 * q^13 + 70 * q^15 - 478 * q^17 - 76 * q^21 - 1082 * q^23 - 350 * q^25 - 320 * q^27 + 1516 * q^31 + 404 * q^33 + 190 * q^35 + 282 * q^37 + 2084 * q^41 + 1518 * q^43 + 3160 * q^45 + 918 * q^47 + 956 * q^51 - 3638 * q^53 + 6060 * q^55 + 80 * q^57 + 4164 * q^61 - 3002 * q^63 + 6930 * q^65 - 10162 * q^67 + 6956 * q^71 - 6958 * q^73 - 850 * q^75 - 7676 * q^77 - 12158 * q^81 - 12162 * q^83 - 2390 * q^85 + 400 * q^87 - 7524 * q^91 - 1516 * q^93 - 1600 * q^95 + 1122 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000	+	1.00000i	−0.111111	+	0.111111i	−0.760477	−	0.649365i	$-0.775035\pi$
$3$	−1.00000	+	1.00000i	−0.111111	+	0.111111i	0.649365	+	0.760477i	$0.275035\pi$
$4$		0			0
$5$	−15.0000	−	20.0000i	−0.600000	−	0.800000i
$5$	−15.0000	−	20.0000i	−0.600000	−	0.800000i
$6$		0			0
$7$	19.0000	+	19.0000i	0.387755	+	0.387755i	0.873886	−	0.486131i	$-0.161592\pi$
$7$	19.0000	+	19.0000i	0.387755	+	0.387755i	−0.486131	+	0.873886i	$0.661592\pi$
$8$		0			0
$9$			79.0000i			0.975309i
$10$		0			0
$11$	−202.000			−1.66942			−0.834711	−	0.550689i	$-0.814365\pi$
$11$	−202.000			−1.66942			−0.834711	+	0.550689i	$0.814365\pi$
$12$		0			0
$13$	−99.0000	+	99.0000i	−0.585799	+	0.585799i	−0.936491	−	0.350692i	$-0.885946\pi$
$13$	−99.0000	+	99.0000i	−0.585799	+	0.585799i	0.350692	+	0.936491i	$0.385946\pi$
$14$		0			0
$15$	35.0000	+	5.00000i	0.155556	+	0.0222222i
$16$		0			0
$17$	−239.000	−	239.000i	−0.826990	−	0.826990i	0.160110	−	0.987099i	$-0.448815\pi$
$17$	−239.000	−	239.000i	−0.826990	−	0.826990i	−0.987099	+	0.160110i	$0.948815\pi$
$18$		0			0
$19$		−	40.0000i		−	0.110803i	−0.998464	−	0.0554017i	$-0.982356\pi$
$19$		−	40.0000i		−	0.110803i	0.998464	−	0.0554017i	$-0.0176439\pi$
$20$		0			0
$21$	−38.0000			−0.0861678
$22$		0			0
$23$	−541.000	+	541.000i	−1.02268	+	1.02268i	−0.0229476	+	0.999737i	$0.507305\pi$
$23$	−541.000	+	541.000i	−1.02268	+	1.02268i	−0.999737	+	0.0229476i	$0.992695\pi$
$24$		0			0
$25$	−175.000	+	600.000i	−0.280000	+	0.960000i
$26$		0			0
$27$	−160.000	−	160.000i	−0.219479	−	0.219479i
$28$		0			0
$29$		−	200.000i		−	0.237812i	−0.992906	−	0.118906i	$-0.962061\pi$
$29$		−	200.000i		−	0.237812i	0.992906	−	0.118906i	$-0.0379387\pi$
$30$		0			0
$31$	758.000			0.788762			0.394381	−	0.918947i	$-0.370959\pi$
$31$	758.000			0.788762			0.394381	+	0.918947i	$0.370959\pi$
$32$		0			0
$33$	202.000	−	202.000i	0.185491	−	0.185491i
$34$		0			0
$35$	95.0000	−	665.000i	0.0775510	−	0.542857i
$36$		0			0
$37$	141.000	+	141.000i	0.102995	+	0.102995i	0.756726	−	0.653732i	$-0.226797\pi$
$37$	141.000	+	141.000i	0.102995	+	0.102995i	−0.653732	+	0.756726i	$0.726797\pi$
$38$		0			0
$39$		−	198.000i		−	0.130178i
$40$		0			0
$41$	1042.00			0.619869			0.309935	−	0.950758i	$-0.399693\pi$
$41$	1042.00			0.619869			0.309935	+	0.950758i	$0.399693\pi$
$42$		0			0
$43$	759.000	−	759.000i	0.410492	−	0.410492i	−0.471418	−	0.881910i	$-0.656258\pi$
$43$	759.000	−	759.000i	0.410492	−	0.410492i	0.881910	+	0.471418i	$0.156258\pi$
$44$		0			0
$45$	1580.00	−	1185.00i	0.780247	−	0.585185i
$46$		0			0
$47$	459.000	+	459.000i	0.207786	+	0.207786i	0.803326	−	0.595540i	$-0.203062\pi$
$47$	459.000	+	459.000i	0.207786	+	0.207786i	−0.595540	+	0.803326i	$0.703062\pi$
$48$		0			0
$49$		−	1679.00i		−	0.699292i
$50$		0			0
$51$	478.000			0.183775
$52$		0			0
$53$	−1819.00	+	1819.00i	−0.647561	+	0.647561i	−0.952403	−	0.304842i	$-0.901396\pi$
$53$	−1819.00	+	1819.00i	−0.647561	+	0.647561i	0.304842	+	0.952403i	$0.401396\pi$
$54$		0			0
$55$	3030.00	+	4040.00i	1.00165	+	1.33554i
$56$		0			0
$57$	40.0000	+	40.0000i	0.0123115	+	0.0123115i
$58$		0			0
$59$		−	4600.00i		−	1.32146i	−0.750624	−	0.660730i	$-0.770247\pi$
$59$		−	4600.00i		−	1.32146i	0.750624	−	0.660730i	$-0.229753\pi$
$60$		0			0
$61$	2082.00			0.559527			0.279764	−	0.960069i	$-0.409744\pi$
$61$	2082.00			0.559527			0.279764	+	0.960069i	$0.409744\pi$
$62$		0			0
$63$	−1501.00	+	1501.00i	−0.378181	+	0.378181i
$64$		0			0
$65$	3465.00	+	495.000i	0.820118	+	0.117160i
$66$		0			0
$67$	−5081.00	−	5081.00i	−1.13188	−	1.13188i	−0.989865	−	0.142013i	$-0.954642\pi$
$67$	−5081.00	−	5081.00i	−1.13188	−	1.13188i	−0.142013	−	0.989865i	$-0.545358\pi$
$68$		0			0
$69$		−	1082.00i		−	0.227263i
$70$		0			0
$71$	3478.00			0.689942			0.344971	−	0.938613i	$-0.387889\pi$
$71$	3478.00			0.689942			0.344971	+	0.938613i	$0.387889\pi$
$72$		0			0
$73$	−3479.00	+	3479.00i	−0.652843	+	0.652843i	−0.953677	−	0.300834i	$-0.902735\pi$
$73$	−3479.00	+	3479.00i	−0.652843	+	0.652843i	0.300834	+	0.953677i	$0.402735\pi$
$74$		0			0
$75$	−425.000	−	775.000i	−0.0755556	−	0.137778i
$76$		0			0
$77$	−3838.00	−	3838.00i	−0.647327	−	0.647327i
$78$		0			0
$79$			7680.00i			1.23057i	0.788304	+	0.615286i	$0.210959\pi$
$79$			7680.00i			1.23057i	−0.788304	+	0.615286i	$0.789041\pi$
$80$		0			0
$81$	−6079.00			−0.926536
$82$		0			0
$83$	−6081.00	+	6081.00i	−0.882712	+	0.882712i	−0.993809	−	0.111098i	$-0.964563\pi$
$83$	−6081.00	+	6081.00i	−0.882712	+	0.882712i	0.111098	+	0.993809i	$0.464563\pi$
$84$		0			0
$85$	−1195.00	+	8365.00i	−0.165398	+	1.15779i
$86$		0			0
$87$	200.000	+	200.000i	0.0264236	+	0.0264236i
$88$		0			0
$89$		−	5680.00i		−	0.717081i	−0.933514	−	0.358541i	$-0.883274\pi$
$89$		−	5680.00i		−	0.717081i	0.933514	−	0.358541i	$-0.116726\pi$
$90$		0			0
$91$	−3762.00			−0.454293
$92$		0			0
$93$	−758.000	+	758.000i	−0.0876402	+	0.0876402i
$94$		0			0
$95$	−800.000	+	600.000i	−0.0886427	+	0.0664820i
$96$		0			0
$97$	561.000	+	561.000i	0.0596238	+	0.0596238i	0.736290	−	0.676666i	$-0.236576\pi$
$97$	561.000	+	561.000i	0.0596238	+	0.0596238i	−0.676666	+	0.736290i	$0.736576\pi$
$98$		0			0
$99$		−	15958.0i		−	1.62820i
$100$		0			0
$101$	1682.00			0.164886			0.0824429	−	0.996596i	$-0.473728\pi$
$101$	1682.00			0.164886			0.0824429	+	0.996596i	$0.473728\pi$
$102$		0			0
$103$	−7021.00	+	7021.00i	−0.661797	+	0.661797i	−0.955803	−	0.294007i	$-0.905011\pi$
$103$	−7021.00	+	7021.00i	−0.661797	+	0.661797i	0.294007	+	0.955803i	$0.405011\pi$
$104$		0			0
$105$	570.000	+	760.000i	0.0517007	+	0.0689342i
$106$		0			0
$107$	2159.00	+	2159.00i	0.188575	+	0.188575i	0.795080	−	0.606505i	$-0.207429\pi$
$107$	2159.00	+	2159.00i	0.188575	+	0.188575i	−0.606505	+	0.795080i	$0.707429\pi$
$108$		0			0
$109$		−	280.000i		−	0.0235670i	−0.999931	−	0.0117835i	$-0.996249\pi$
$109$		−	280.000i		−	0.0235670i	0.999931	−	0.0117835i	$-0.00375090\pi$
$110$		0			0
$111$	−282.000			−0.0228878
$112$		0			0
$113$	−8479.00	+	8479.00i	−0.664030	+	0.664030i	−0.956327	−	0.292297i	$-0.905580\pi$
$113$	−8479.00	+	8479.00i	−0.664030	+	0.664030i	0.292297	+	0.956327i	$0.405580\pi$
$114$		0			0
$115$	18935.0	+	2705.00i	1.43176	+	0.204537i
$116$		0			0
$117$	−7821.00	−	7821.00i	−0.571335	−	0.571335i
$118$		0			0
$119$		−	9082.00i		−	0.641339i
$120$		0			0
$121$	26163.0			1.78697
$122$		0			0
$123$	−1042.00	+	1042.00i	−0.0688743	+	0.0688743i
$124$		0			0
$125$	14625.0	−	5500.00i	0.936000	−	0.352000i
$126$		0			0
$127$	−821.000	−	821.000i	−0.0509021	−	0.0509021i	0.681198	−	0.732100i	$-0.261459\pi$
$127$	−821.000	−	821.000i	−0.0509021	−	0.0509021i	−0.732100	+	0.681198i	$0.761459\pi$
$128$		0			0
$129$			1518.00i			0.0912205i
$130$		0			0
$131$	2198.00			0.128081			0.0640406	−	0.997947i	$-0.479601\pi$
$131$	2198.00			0.128081			0.0640406	+	0.997947i	$0.479601\pi$
$132$		0			0
$133$	760.000	−	760.000i	0.0429646	−	0.0429646i
$134$		0			0
$135$	−800.000	+	5600.00i	−0.0438957	+	0.307270i
$136$		0			0
$137$	−9399.00	−	9399.00i	−0.500773	−	0.500773i	0.410905	−	0.911678i	$-0.365213\pi$
$137$	−9399.00	−	9399.00i	−0.500773	−	0.500773i	−0.911678	+	0.410905i	$0.865213\pi$
$138$		0			0
$139$			13960.0i			0.722530i	0.932463	+	0.361265i	$0.117655\pi$
$139$			13960.0i			0.722530i	−0.932463	+	0.361265i	$0.882345\pi$
$140$		0			0
$141$	−918.000			−0.0461747
$142$		0			0
$143$	19998.0	−	19998.0i	0.977945	−	0.977945i
$144$		0			0
$145$	−4000.00	+	3000.00i	−0.190250	+	0.142687i
$146$		0			0
$147$	1679.00	+	1679.00i	0.0776991	+	0.0776991i
$148$		0			0
$149$		−	9000.00i		−	0.405387i	−0.979242	−	0.202694i	$-0.935030\pi$
$149$		−	9000.00i		−	0.405387i	0.979242	−	0.202694i	$-0.0649695\pi$
$150$		0			0
$151$	23798.0			1.04373			0.521863	−	0.853029i	$-0.325237\pi$
$151$	23798.0			1.04373			0.521863	+	0.853029i	$0.325237\pi$
$152$		0			0
$153$	18881.0	−	18881.0i	0.806570	−	0.806570i
$154$		0			0
$155$	−11370.0	−	15160.0i	−0.473257	−	0.631009i
$156$		0			0
$157$	29781.0	+	29781.0i	1.20820	+	1.20820i	0.971608	+	0.236595i	$0.0760314\pi$
$157$	29781.0	+	29781.0i	1.20820	+	1.20820i	0.236595	+	0.971608i	$0.423969\pi$
$158$		0			0
$159$		−	3638.00i		−	0.143903i
$160$		0			0
$161$	−20558.0			−0.793102
$162$		0			0
$163$	−12641.0	+	12641.0i	−0.475780	+	0.475780i	−0.903779	−	0.427999i	$-0.859219\pi$
$163$	−12641.0	+	12641.0i	−0.475780	+	0.475780i	0.427999	+	0.903779i	$0.359219\pi$
$164$		0			0
$165$	−7070.00	−	1010.00i	−0.259688	−	0.0370983i
$166$		0			0
$167$	−29981.0	−	29981.0i	−1.07501	−	1.07501i	−0.996948	−	0.0780632i	$-0.975126\pi$
$167$	−29981.0	−	29981.0i	−1.07501	−	1.07501i	−0.0780632	−	0.996948i	$-0.524874\pi$
$168$		0			0
$169$			8959.00i			0.313679i
$170$		0			0
$171$	3160.00			0.108067
$172$		0			0
$173$	−4739.00	+	4739.00i	−0.158341	+	0.158341i	−0.781831	−	0.623490i	$-0.785714\pi$
$173$	−4739.00	+	4739.00i	−0.158341	+	0.158341i	0.623490	+	0.781831i	$0.285714\pi$
$174$		0			0
$175$	−14725.0	+	8075.00i	−0.480816	+	0.263673i
$176$		0			0
$177$	4600.00	+	4600.00i	0.146829	+	0.146829i
$178$		0			0
$179$			32920.0i			1.02743i	0.857960	+	0.513717i	$0.171732\pi$
$179$			32920.0i			1.02743i	−0.857960	+	0.513717i	$0.828268\pi$
$180$		0			0
$181$	−40558.0			−1.23800			−0.618998	−	0.785392i	$-0.712461\pi$
$181$	−40558.0			−1.23800			−0.618998	+	0.785392i	$0.712461\pi$
$182$		0			0
$183$	−2082.00	+	2082.00i	−0.0621697	+	0.0621697i
$184$		0			0
$185$	705.000	−	4935.00i	0.0205990	−	0.144193i
$186$		0			0
$187$	48278.0	+	48278.0i	1.38059	+	1.38059i
$188$		0			0
$189$		−	6080.00i		−	0.170208i
$190$		0			0
$191$	−33002.0			−0.904635			−0.452318	−	0.891857i	$-0.649403\pi$
$191$	−33002.0			−0.904635			−0.452318	+	0.891857i	$0.649403\pi$
$192$		0			0
$193$	−23199.0	+	23199.0i	−0.622809	+	0.622809i	−0.946249	−	0.323440i	$-0.895161\pi$
$193$	−23199.0	+	23199.0i	−0.622809	+	0.622809i	0.323440	+	0.946249i	$0.395161\pi$
$194$		0			0
$195$	−3960.00	+	2970.00i	−0.104142	+	0.0781065i
$196$		0			0
$197$	−16899.0	−	16899.0i	−0.435440	−	0.435440i	0.455034	−	0.890474i	$-0.349627\pi$
$197$	−16899.0	−	16899.0i	−0.435440	−	0.435440i	−0.890474	+	0.455034i	$0.849627\pi$
$198$		0			0
$199$		−	14160.0i		−	0.357567i	−0.983888	−	0.178783i	$-0.942784\pi$
$199$		−	14160.0i		−	0.357567i	0.983888	−	0.178783i	$-0.0572161\pi$
$200$		0			0
$201$	10162.0			0.251528
$202$		0			0
$203$	3800.00	−	3800.00i	0.0922129	−	0.0922129i
$204$		0			0
$205$	−15630.0	−	20840.0i	−0.371921	−	0.495895i
$206$		0			0
$207$	−42739.0	−	42739.0i	−0.997433	−	0.997433i
$208$		0			0
$209$			8080.00i			0.184977i
$210$		0			0
$211$	−48842.0			−1.09706			−0.548528	−	0.836132i	$-0.684811\pi$
$211$	−48842.0			−1.09706			−0.548528	+	0.836132i	$0.684811\pi$
$212$		0			0
$213$	−3478.00	+	3478.00i	−0.0766603	+	0.0766603i
$214$		0			0
$215$	−26565.0	−	3795.00i	−0.574689	−	0.0820984i
$216$		0			0
$217$	14402.0	+	14402.0i	0.305846	+	0.305846i
$218$		0			0
$219$		−	6958.00i		−	0.145076i
$220$		0			0
$221$	47322.0			0.968899
$222$		0			0
$223$	35019.0	−	35019.0i	0.704197	−	0.704197i	−0.261112	−	0.965309i	$-0.584089\pi$
$223$	35019.0	−	35019.0i	0.704197	−	0.704197i	0.965309	+	0.261112i	$0.0840891\pi$
$224$		0			0
$225$	−47400.0	−	13825.0i	−0.936296	−	0.273086i
$226$		0			0
$227$	68599.0	+	68599.0i	1.33127	+	1.33127i	0.904235	+	0.427034i	$0.140442\pi$
$227$	68599.0	+	68599.0i	1.33127	+	1.33127i	0.427034	+	0.904235i	$0.359558\pi$
$228$		0			0
$229$			98760.0i			1.88326i	0.336651	+	0.941630i	$0.390706\pi$
$229$			98760.0i			1.88326i	−0.336651	+	0.941630i	$0.609294\pi$
$230$		0			0
$231$	7676.00			0.143850
$232$		0			0
$233$	53721.0	−	53721.0i	0.989537	−	0.989537i	−0.0104084	−	0.999946i	$-0.503313\pi$
$233$	53721.0	−	53721.0i	0.989537	−	0.989537i	0.999946	+	0.0104084i	$0.00331314\pi$
$234$		0			0
$235$	2295.00	−	16065.0i	0.0415573	−	0.290901i
$236$		0			0
$237$	−7680.00	−	7680.00i	−0.136730	−	0.136730i
$238$		0			0
$239$			45600.0i			0.798305i	0.916884	+	0.399153i	$0.130696\pi$
$239$			45600.0i			0.798305i	−0.916884	+	0.399153i	$0.869304\pi$
$240$		0			0
$241$	−57038.0			−0.982042			−0.491021	−	0.871148i	$-0.663376\pi$
$241$	−57038.0			−0.982042			−0.491021	+	0.871148i	$0.663376\pi$
$242$		0			0
$243$	19039.0	−	19039.0i	0.322427	−	0.322427i
$244$		0			0
$245$	−33580.0	+	25185.0i	−0.559434	+	0.419575i
$246$		0			0
$247$	3960.00	+	3960.00i	0.0649085	+	0.0649085i
$248$		0			0
$249$		−	12162.0i		−	0.196158i
$250$		0			0
$251$	−39402.0			−0.625419			−0.312709	−	0.949849i	$-0.601237\pi$
$251$	−39402.0			−0.625419			−0.312709	+	0.949849i	$0.601237\pi$
$252$		0			0
$253$	109282.	−	109282.i	1.70729	−	1.70729i
$254$		0			0
$255$	−7170.00	−	9560.00i	−0.110265	−	0.147020i
$256$		0			0
$257$	31121.0	+	31121.0i	0.471180	+	0.471180i	0.902297	−	0.431116i	$-0.141880\pi$
$257$	31121.0	+	31121.0i	0.471180	+	0.471180i	−0.431116	+	0.902297i	$0.641880\pi$
$258$		0			0
$259$			5358.00i			0.0798736i
$260$		0			0
$261$	15800.0			0.231940
$262$		0			0
$263$	60739.0	−	60739.0i	0.878125	−	0.878125i	−0.115216	−	0.993340i	$-0.536756\pi$
$263$	60739.0	−	60739.0i	0.878125	−	0.878125i	0.993340	+	0.115216i	$0.0367560\pi$
$264$		0			0
$265$	63665.0	+	9095.00i	0.906586	+	0.129512i
$266$		0			0
$267$	5680.00	+	5680.00i	0.0796757	+	0.0796757i
$268$		0			0
$269$		−	63800.0i		−	0.881690i	−0.897583	−	0.440845i	$-0.854679\pi$
$269$		−	63800.0i		−	0.881690i	0.897583	−	0.440845i	$-0.145321\pi$
$270$		0			0
$271$	113238.			1.54189			0.770945	−	0.636901i	$-0.219784\pi$
$271$	113238.			1.54189			0.770945	+	0.636901i	$0.219784\pi$
$272$		0			0
$273$	3762.00	−	3762.00i	0.0504770	−	0.0504770i
$274$		0			0
$275$	35350.0	−	121200.i	0.467438	−	1.60264i
$276$		0			0
$277$	−14739.0	−	14739.0i	−0.192092	−	0.192092i	0.604508	−	0.796599i	$-0.293370\pi$
$277$	−14739.0	−	14739.0i	−0.192092	−	0.192092i	−0.796599	+	0.604508i	$0.793370\pi$
$278$		0			0
$279$			59882.0i			0.769286i
$280$		0			0
$281$	−7278.00			−0.0921721			−0.0460860	−	0.998937i	$-0.514675\pi$
$281$	−7278.00			−0.0921721			−0.0460860	+	0.998937i	$0.514675\pi$
$282$		0			0
$283$	−58601.0	+	58601.0i	−0.731698	+	0.731698i	−0.970956	−	0.239258i	$-0.923096\pi$
$283$	−58601.0	+	58601.0i	−0.731698	+	0.731698i	0.239258	+	0.970956i	$0.423096\pi$
$284$		0			0
$285$	200.000	−	1400.00i	0.00246230	−	0.0172361i
$286$		0			0
$287$	19798.0	+	19798.0i	0.240357	+	0.240357i
$288$		0			0
$289$			30721.0i			0.367824i
$290$		0			0
$291$	−1122.00			−0.0132497
$292$		0			0
$293$	−95499.0	+	95499.0i	−1.11241	+	1.11241i	−0.119582	+	0.992824i	$0.538156\pi$
$293$	−95499.0	+	95499.0i	−1.11241	+	1.11241i	−0.992824	+	0.119582i	$0.961844\pi$
$294$		0			0
$295$	−92000.0	+	69000.0i	−1.05717	+	0.792876i
$296$		0			0
$297$	32320.0	+	32320.0i	0.366403	+	0.366403i
$298$		0			0
$299$		−	107118.i		−	1.19817i
$300$		0			0
$301$	28842.0			0.318341
$302$		0			0
$303$	−1682.00	+	1682.00i	−0.0183206	+	0.0183206i
$304$		0			0
$305$	−31230.0	−	41640.0i	−0.335716	−	0.447622i
$306$		0			0
$307$	−38601.0	−	38601.0i	−0.409564	−	0.409564i	0.472022	−	0.881587i	$-0.343524\pi$
$307$	−38601.0	−	38601.0i	−0.409564	−	0.409564i	−0.881587	+	0.472022i	$0.843524\pi$
$308$		0			0
$309$		−	14042.0i		−	0.147066i
$310$		0			0
$311$	−29162.0			−0.301506			−0.150753	−	0.988571i	$-0.548170\pi$
$311$	−29162.0			−0.301506			−0.150753	+	0.988571i	$0.548170\pi$
$312$		0			0
$313$	1881.00	−	1881.00i	0.0192000	−	0.0192000i	−0.697442	−	0.716642i	$-0.745678\pi$
$313$	1881.00	−	1881.00i	0.0192000	−	0.0192000i	0.716642	+	0.697442i	$0.245678\pi$
$314$		0			0
$315$	52535.0	+	7505.00i	0.529453	+	0.0756362i
$316$		0			0
$317$	83781.0	+	83781.0i	0.833733	+	0.833733i	0.988025	−	0.154292i	$-0.0493097\pi$
$317$	83781.0	+	83781.0i	0.833733	+	0.833733i	−0.154292	+	0.988025i	$0.549310\pi$
$318$		0			0
$319$			40400.0i			0.397009i
$320$		0			0
$321$	−4318.00			−0.0419056
$322$		0			0
$323$	−9560.00	+	9560.00i	−0.0916332	+	0.0916332i
$324$		0			0
$325$	−42075.0	−	76725.0i	−0.398343	−	0.726391i
$326$		0			0
$327$	280.000	+	280.000i	0.00261856	+	0.00261856i
$328$		0			0
$329$			17442.0i			0.161140i
$330$		0			0
$331$	−106282.			−0.970071			−0.485036	−	0.874494i	$-0.661193\pi$
$331$	−106282.			−0.970071			−0.485036	+	0.874494i	$0.661193\pi$
$332$		0			0
$333$	−11139.0	+	11139.0i	−0.100452	+	0.100452i
$334$		0			0
$335$	−25405.0	+	177835.i	−0.226376	+	1.58463i
$336$		0			0
$337$	−142479.	−	142479.i	−1.25456	−	1.25456i	−0.953654	−	0.300905i	$-0.902711\pi$
$337$	−142479.	−	142479.i	−1.25456	−	1.25456i	−0.300905	−	0.953654i	$-0.597289\pi$
$338$		0			0
$339$		−	16958.0i		−	0.147562i
$340$		0			0
$341$	−153116.			−1.31678
$342$		0			0
$343$	77520.0	−	77520.0i	0.658909	−	0.658909i
$344$		0			0
$345$	−21640.0	+	16230.0i	−0.181811	+	0.136358i
$346$		0			0
$347$	6479.00	+	6479.00i	0.0538083	+	0.0538083i	0.733499	−	0.679691i	$-0.237886\pi$
$347$	6479.00	+	6479.00i	0.0538083	+	0.0538083i	−0.679691	+	0.733499i	$0.737886\pi$
$348$		0			0
$349$			32920.0i			0.270277i	0.990827	+	0.135138i	$0.0431479\pi$
$349$			32920.0i			0.270277i	−0.990827	+	0.135138i	$0.956852\pi$
$350$		0			0
$351$	31680.0			0.257141
$352$		0			0
$353$	−53919.0	+	53919.0i	−0.432706	+	0.432706i	−0.889548	−	0.456842i	$-0.848980\pi$
$353$	−53919.0	+	53919.0i	−0.432706	+	0.432706i	0.456842	+	0.889548i	$0.348980\pi$
$354$		0			0
$355$	−52170.0	−	69560.0i	−0.413965	−	0.551954i
$356$		0			0
$357$	9082.00	+	9082.00i	0.0712599	+	0.0712599i
$358$		0			0
$359$			171760.i			1.33270i	0.745638	+	0.666351i	$0.232145\pi$
$359$			171760.i			1.33270i	−0.745638	+	0.666351i	$0.767855\pi$
$360$		0			0
$361$	128721.			0.987723
$362$		0			0
$363$	−26163.0	+	26163.0i	−0.198552	+	0.198552i
$364$		0			0
$365$	121765.	+	17395.0i	0.913980	+	0.130569i
$366$		0			0
$367$	−152261.	−	152261.i	−1.13046	−	1.13046i	−0.990100	−	0.140363i	$-0.955173\pi$
$367$	−152261.	−	152261.i	−1.13046	−	1.13046i	−0.140363	−	0.990100i	$-0.544827\pi$
$368$		0			0
$369$			82318.0i			0.604564i
$370$		0			0
$371$	−69122.0			−0.502190
$372$		0			0
$373$	−71339.0	+	71339.0i	−0.512754	+	0.512754i	−0.915369	−	0.402615i	$-0.868101\pi$
$373$	−71339.0	+	71339.0i	−0.512754	+	0.512754i	0.402615	+	0.915369i	$0.368101\pi$
$374$		0			0
$375$	−9125.00	+	20125.0i	−0.0648889	+	0.143111i
$376$		0			0
$377$	19800.0	+	19800.0i	0.139310	+	0.139310i
$378$		0			0
$379$		−	172600.i		−	1.20161i	−0.799397	−	0.600803i	$-0.794847\pi$
$379$		−	172600.i		−	1.20161i	0.799397	−	0.600803i	$-0.205153\pi$
$380$		0			0
$381$	1642.00			0.0113116
$382$		0			0
$383$	−158421.	+	158421.i	−1.07998	+	1.07998i	−0.0834683	+	0.996510i	$0.526600\pi$
$383$	−158421.	+	158421.i	−1.07998	+	1.07998i	−0.996510	+	0.0834683i	$0.973400\pi$
$384$		0			0
$385$	−19190.0	+	134330.i	−0.129465	+	0.906257i
$386$		0			0
$387$	59961.0	+	59961.0i	0.400357	+	0.400357i
$388$		0			0
$389$		−	146760.i		−	0.969859i	−0.874553	−	0.484929i	$-0.838845\pi$
$389$		−	146760.i		−	0.969859i	0.874553	−	0.484929i	$-0.161155\pi$
$390$		0			0
$391$	258598.			1.69150
$392$		0			0
$393$	−2198.00	+	2198.00i	−0.0142312	+	0.0142312i
$394$		0			0
$395$	153600.	−	115200.i	0.984458	−	0.738343i
$396$		0			0
$397$	−83579.0	−	83579.0i	−0.530293	−	0.530293i	0.390366	−	0.920660i	$-0.372348\pi$
$397$	−83579.0	−	83579.0i	−0.530293	−	0.530293i	−0.920660	+	0.390366i	$0.872348\pi$
$398$		0			0
$399$			1520.00i			0.00954768i
$400$		0			0
$401$	−42078.0			−0.261677			−0.130839	−	0.991404i	$-0.541767\pi$
$401$	−42078.0			−0.261677			−0.130839	+	0.991404i	$0.541767\pi$
$402$		0			0
$403$	−75042.0	+	75042.0i	−0.462056	+	0.462056i
$404$		0			0
$405$	91185.0	+	121580.i	0.555921	+	0.741228i
$406$		0			0
$407$	−28482.0	−	28482.0i	−0.171942	−	0.171942i
$408$		0			0
$409$		−	300960.i		−	1.79913i	−0.436789	−	0.899564i	$-0.643884\pi$
$409$		−	300960.i		−	1.79913i	0.436789	−	0.899564i	$-0.356116\pi$
$410$		0			0
$411$	18798.0			0.111283
$412$		0			0
$413$	87400.0	−	87400.0i	0.512403	−	0.512403i
$414$		0			0
$415$	212835.	+	30405.0i	1.23580	+	0.176542i
$416$		0			0
$417$	−13960.0	−	13960.0i	−0.0802811	−	0.0802811i
$418$		0			0
$419$		−	208680.i		−	1.18865i	−0.804226	−	0.594323i	$-0.797420\pi$
$419$		−	208680.i		−	1.18865i	0.804226	−	0.594323i	$-0.202580\pi$
$420$		0			0
$421$	86882.0			0.490191			0.245096	−	0.969499i	$-0.421181\pi$
$421$	86882.0			0.490191			0.245096	+	0.969499i	$0.421181\pi$
$422$		0			0
$423$	−36261.0	+	36261.0i	−0.202656	+	0.202656i
$424$		0			0
$425$	185225.	−	101575.i	1.02547	−	0.562353i
$426$		0			0
$427$	39558.0	+	39558.0i	0.216959	+	0.216959i
$428$		0			0
$429$			39996.0i			0.217321i
$430$		0			0
$431$	125078.			0.673328			0.336664	−	0.941625i	$-0.390701\pi$
$431$	125078.			0.673328			0.336664	+	0.941625i	$0.390701\pi$
$432$		0			0
$433$	5921.00	−	5921.00i	0.0315805	−	0.0315805i	−0.691140	−	0.722721i	$-0.742891\pi$
$433$	5921.00	−	5921.00i	0.0315805	−	0.0315805i	0.722721	+	0.691140i	$0.242891\pi$
$434$		0			0
$435$	1000.00	−	7000.00i	0.00528471	−	0.0369930i
$436$		0			0
$437$	21640.0	+	21640.0i	0.113317	+	0.113317i
$438$		0			0
$439$		−	55280.0i		−	0.286840i	−0.989662	−	0.143420i	$-0.954190\pi$
$439$		−	55280.0i		−	0.286840i	0.989662	−	0.143420i	$-0.0458099\pi$
$440$		0			0
$441$	132641.			0.682025
$442$		0			0
$443$	−63561.0	+	63561.0i	−0.323879	+	0.323879i	−0.850253	−	0.526374i	$-0.823551\pi$
$443$	−63561.0	+	63561.0i	−0.323879	+	0.323879i	0.526374	+	0.850253i	$0.323551\pi$
$444$		0			0
$445$	−113600.	+	85200.0i	−0.573665	+	0.430249i
$446$		0			0
$447$	9000.00	+	9000.00i	0.0450430	+	0.0450430i
$448$		0			0
$449$			204880.i			1.01626i	0.861279	+	0.508132i	$0.169664\pi$
$449$			204880.i			1.01626i	−0.861279	+	0.508132i	$0.830336\pi$
$450$		0			0
$451$	−210484.			−1.03482
$452$		0			0
$453$	−23798.0	+	23798.0i	−0.115970	+	0.115970i
$454$		0			0
$455$	56430.0	+	75240.0i	0.272576	+	0.363434i
$456$		0			0
$457$	−10599.0	−	10599.0i	−0.0507496	−	0.0507496i	0.681277	−	0.732026i	$-0.261425\pi$
$457$	−10599.0	−	10599.0i	−0.0507496	−	0.0507496i	−0.732026	+	0.681277i	$0.761425\pi$
$458$		0			0
$459$			76480.0i			0.363013i
$460$		0			0
$461$	224242.			1.05515			0.527576	−	0.849508i	$-0.323101\pi$
$461$	224242.			1.05515			0.527576	+	0.849508i	$0.323101\pi$
$462$		0			0
$463$	243499.	−	243499.i	1.13589	−	1.13589i	0.146707	−	0.989180i	$-0.453132\pi$
$463$	243499.	−	243499.i	1.13589	−	1.13589i	0.989180	−	0.146707i	$-0.0468675\pi$
$464$		0			0
$465$	26530.0	+	3790.00i	0.122696	+	0.0175280i
$466$		0			0
$467$	226919.	+	226919.i	1.04049	+	1.04049i	0.999145	+	0.0413430i	$0.0131637\pi$
$467$	226919.	+	226919.i	1.04049	+	1.04049i	0.0413430	+	0.999145i	$0.486836\pi$
$468$		0			0
$469$		−	193078.i		−	0.877783i
$470$		0			0
$471$	−59562.0			−0.268490
$472$		0			0
$473$	−153318.	+	153318.i	−0.685284	+	0.685284i
$474$		0			0
$475$	24000.0	+	7000.00i	0.106371	+	0.0310249i
$476$		0			0
$477$	−143701.	−	143701.i	−0.631572	−	0.631572i
$478$		0			0
$479$		−	334240.i		−	1.45676i	−0.685174	−	0.728379i	$-0.740274\pi$
$479$		−	334240.i		−	1.45676i	0.685174	−	0.728379i	$-0.259726\pi$
$480$		0			0
$481$	−27918.0			−0.120669
$482$		0			0
$483$	20558.0	−	20558.0i	0.0881225	−	0.0881225i
$484$		0			0
$485$	2805.00	−	19635.0i	0.0119248	−	0.0834733i
$486$		0			0
$487$	−278541.	−	278541.i	−1.17444	−	1.17444i	−0.981139	−	0.193302i	$-0.938080\pi$
$487$	−278541.	−	278541.i	−1.17444	−	1.17444i	−0.193302	−	0.981139i	$-0.561920\pi$
$488$		0			0
$489$		−	25282.0i		−	0.105729i
$490$		0			0
$491$	84118.0			0.348920			0.174460	−	0.984664i	$-0.444182\pi$
$491$	84118.0			0.348920			0.174460	+	0.984664i	$0.444182\pi$
$492$		0			0
$493$	−47800.0	+	47800.0i	−0.196668	+	0.196668i
$494$		0			0
$495$	−319160.	+	239370.i	−1.30256	+	0.976921i
$496$		0			0
$497$	66082.0	+	66082.0i	0.267529	+	0.267529i
$498$		0			0
$499$			166840.i			0.670037i	0.942211	+	0.335019i	$0.108743\pi$
$499$			166840.i			0.670037i	−0.942211	+	0.335019i	$0.891257\pi$
$500$		0			0
$501$	59962.0			0.238891
$502$		0			0
$503$	−190461.	+	190461.i	−0.752783	+	0.752783i	−0.974998	−	0.222214i	$-0.928672\pi$
$503$	−190461.	+	190461.i	−0.752783	+	0.752783i	0.222214	+	0.974998i	$0.428672\pi$
$504$		0			0
$505$	−25230.0	−	33640.0i	−0.0989315	−	0.131909i
$506$		0			0
$507$	−8959.00	−	8959.00i	−0.0348533	−	0.0348533i
$508$		0			0
$509$			223960.i			0.864440i	0.901768	+	0.432220i	$0.142270\pi$
$509$			223960.i			0.864440i	−0.901768	+	0.432220i	$0.857730\pi$
$510$		0			0
$511$	−132202.			−0.506286
$512$		0			0
$513$	−6400.00	+	6400.00i	−0.0243190	+	0.0243190i
$514$		0			0
$515$	245735.	+	35105.0i	0.926515	+	0.132359i
$516$		0			0
$517$	−92718.0	−	92718.0i	−0.346883	−	0.346883i
$518$		0			0
$519$		−	9478.00i		−	0.0351870i
$520$		0			0
$521$	−297918.			−1.09754			−0.548771	−	0.835973i	$-0.684904\pi$
$521$	−297918.			−1.09754			−0.548771	+	0.835973i	$0.684904\pi$
$522$		0			0
$523$	−200601.	+	200601.i	−0.733381	+	0.733381i	−0.971288	−	0.237907i	$-0.923539\pi$
$523$	−200601.	+	200601.i	−0.733381	+	0.733381i	0.237907	+	0.971288i	$0.423539\pi$
$524$		0			0
$525$	6650.00	−	22800.0i	0.0241270	−	0.0827211i
$526$		0			0
$527$	−181162.	−	181162.i	−0.652298	−	0.652298i
$528$		0			0
$529$		−	305521.i		−	1.09177i
$530$		0			0
$531$	363400.			1.28883
$532$		0			0
$533$	−103158.	+	103158.i	−0.363119	+	0.363119i
$534$		0			0
$535$	10795.0	−	75565.0i	0.0377151	−	0.264006i
$536$		0			0
$537$	−32920.0	−	32920.0i	−0.114159	−	0.114159i
$538$		0			0
$539$			339158.i			1.16741i
$540$		0			0
$541$	−288398.			−0.985366			−0.492683	−	0.870209i	$-0.663984\pi$
$541$	−288398.			−0.985366			−0.492683	+	0.870209i	$0.663984\pi$
$542$		0			0
$543$	40558.0	−	40558.0i	0.137555	−	0.137555i
$544$		0			0
$545$	−5600.00	+	4200.00i	−0.0188536	+	0.0141402i
$546$		0			0
$547$	−123081.	−	123081.i	−0.411355	−	0.411355i	0.470856	−	0.882210i	$-0.343945\pi$
$547$	−123081.	−	123081.i	−0.411355	−	0.411355i	−0.882210	+	0.470856i	$0.843945\pi$
$548$		0			0
$549$			164478.i			0.545712i
$550$		0			0
$551$	−8000.00			−0.0263504
$552$		0			0
$553$	−145920.	+	145920.i	−0.477161	+	0.477161i
$554$		0			0
$555$	4230.00	+	5640.00i	0.0137327	+	0.0183102i
$556$		0			0
$557$	162261.	+	162261.i	0.523002	+	0.523002i	0.918477	−	0.395474i	$-0.129420\pi$
$557$	162261.	+	162261.i	0.523002	+	0.523002i	−0.395474	+	0.918477i	$0.629420\pi$
$558$		0			0
$559$			150282.i			0.480932i
$560$		0			0
$561$	−96556.0			−0.306799
$562$		0			0
$563$	−264081.	+	264081.i	−0.833145	+	0.833145i	−0.987946	−	0.154801i	$-0.950526\pi$
$563$	−264081.	+	264081.i	−0.833145	+	0.833145i	0.154801	+	0.987946i	$0.450526\pi$
$564$		0			0
$565$	296765.	+	42395.0i	0.929642	+	0.132806i
$566$		0			0
$567$	−115501.	−	115501.i	−0.359269	−	0.359269i
$568$		0			0
$569$		−	8320.00i		−	0.0256980i	−0.999917	−	0.0128490i	$-0.995910\pi$
$569$		−	8320.00i		−	0.0256980i	0.999917	−	0.0128490i	$-0.00409007\pi$
$570$		0			0
$571$	−283082.			−0.868240			−0.434120	−	0.900855i	$-0.642941\pi$
$571$	−283082.			−0.868240			−0.434120	+	0.900855i	$0.642941\pi$
$572$		0			0
$573$	33002.0	−	33002.0i	0.100515	−	0.100515i
$574$		0			0
$575$	−229925.	−	419275.i	−0.695425	−	1.26813i
$576$		0			0
$577$	260401.	+	260401.i	0.782152	+	0.782152i	0.980194	−	0.198042i	$-0.0634582\pi$
$577$	260401.	+	260401.i	0.782152	+	0.782152i	−0.198042	+	0.980194i	$0.563458\pi$
$578$		0			0
$579$		−	46398.0i		−	0.138402i
$580$		0			0
$581$	−231078.			−0.684552
$582$		0			0
$583$	367438.	−	367438.i	1.08105	−	1.08105i
$584$		0			0
$585$	−39105.0	+	273735.i	−0.114267	+	0.799869i
$586$		0			0
$587$	281439.	+	281439.i	0.816786	+	0.816786i	0.985641	−	0.168855i	$-0.0540070\pi$
$587$	281439.	+	281439.i	0.816786	+	0.816786i	−0.168855	+	0.985641i	$0.554007\pi$
$588$		0			0
$589$		−	30320.0i		−	0.0873974i
$590$		0			0
$591$	33798.0			0.0967645
$592$		0			0
$593$	419761.	−	419761.i	1.19369	−	1.19369i	0.217671	−	0.976022i	$-0.430154\pi$
$593$	419761.	−	419761.i	1.19369	−	1.19369i	0.976022	−	0.217671i	$-0.0698460\pi$
$594$		0			0
$595$	−181640.	+	136230.i	−0.513071	+	0.384803i
$596$		0			0
$597$	14160.0	+	14160.0i	0.0397296	+	0.0397296i
$598$		0			0
$599$		−	136240.i		−	0.379709i	−0.981812	−	0.189855i	$-0.939198\pi$
$599$		−	136240.i		−	0.379709i	0.981812	−	0.189855i	$-0.0608016\pi$
$600$		0			0
$601$	234962.			0.650502			0.325251	−	0.945628i	$-0.394551\pi$
$601$	234962.			0.650502			0.325251	+	0.945628i	$0.394551\pi$
$602$		0			0
$603$	401399.	−	401399.i	1.10393	−	1.10393i
$604$		0			0
$605$	−392445.	−	523260.i	−1.07218	−	1.42957i
$606$		0			0
$607$	406779.	+	406779.i	1.10403	+	1.10403i	0.993919	+	0.110111i	$0.0351208\pi$
$607$	406779.	+	406779.i	1.10403	+	1.10403i	0.110111	+	0.993919i	$0.464879\pi$
$608$		0			0
$609$			7600.00i			0.0204917i
$610$		0			0
$611$	−90882.0			−0.243442
$612$		0			0
$613$	135621.	−	135621.i	0.360916	−	0.360916i	−0.503234	−	0.864150i	$-0.667857\pi$
$613$	135621.	−	135621.i	0.360916	−	0.360916i	0.864150	+	0.503234i	$0.167857\pi$
$614$		0			0
$615$	36470.0	+	5210.00i	0.0964241	+	0.0137749i
$616$		0			0
$617$	−151959.	−	151959.i	−0.399168	−	0.399168i	0.478771	−	0.877940i	$-0.341082\pi$
$617$	−151959.	−	151959.i	−0.399168	−	0.399168i	−0.877940	+	0.478771i	$0.841082\pi$
$618$		0			0
$619$			22440.0i			0.0585655i	0.999571	+	0.0292827i	$0.00932231\pi$
$619$			22440.0i			0.0585655i	−0.999571	+	0.0292827i	$0.990678\pi$
$620$		0			0
$621$	173120.			0.448915
$622$		0			0
$623$	107920.	−	107920.i	0.278052	−	0.278052i
$624$		0			0
$625$	−329375.	−	210000.i	−0.843200	−	0.537600i
$626$		0			0
$627$	−8080.00	−	8080.00i	−0.0205531	−	0.0205531i
$628$		0			0
$629$		−	67398.0i		−	0.170351i
$630$		0			0
$631$	199958.			0.502204			0.251102	−	0.967961i	$-0.419207\pi$
$631$	199958.			0.502204			0.251102	+	0.967961i	$0.419207\pi$
$632$		0			0
$633$	48842.0	−	48842.0i	0.121895	−	0.121895i
$634$		0			0
$635$	−4105.00	+	28735.0i	−0.0101804	+	0.0712629i
$636$		0			0
$637$	166221.	+	166221.i	0.409644	+	0.409644i
$638$		0			0
$639$			274762.i			0.672907i
$640$		0			0
$641$	448562.			1.09171			0.545854	−	0.837880i	$-0.316205\pi$
$641$	448562.			1.09171			0.545854	+	0.837880i	$0.316205\pi$
$642$		0			0
$643$	−73041.0	+	73041.0i	−0.176663	+	0.176663i	−0.789899	−	0.613237i	$-0.789867\pi$
$643$	−73041.0	+	73041.0i	−0.176663	+	0.176663i	0.613237	+	0.789899i	$0.289867\pi$
$644$		0			0
$645$	30360.0	−	22770.0i	0.0729764	−	0.0547323i
$646$		0			0
$647$	90259.0	+	90259.0i	0.215616	+	0.215616i	0.806648	−	0.591032i	$-0.201279\pi$
$647$	90259.0	+	90259.0i	0.215616	+	0.215616i	−0.591032	+	0.806648i	$0.701279\pi$
$648$		0			0
$649$			929200.i			2.20607i
$650$		0			0
$651$	−28804.0			−0.0679659
$652$		0			0
$653$	−56019.0	+	56019.0i	−0.131374	+	0.131374i	−0.769736	−	0.638362i	$-0.779612\pi$
$653$	−56019.0	+	56019.0i	−0.131374	+	0.131374i	0.638362	+	0.769736i	$0.279612\pi$
$654$		0			0
$655$	−32970.0	−	43960.0i	−0.0768487	−	0.102465i
$656$		0			0
$657$	−274841.	−	274841.i	−0.636723	−	0.636723i
$658$		0			0
$659$		−	438920.i		−	1.01068i	−0.862920	−	0.505341i	$-0.831367\pi$
$659$		−	438920.i		−	1.01068i	0.862920	−	0.505341i	$-0.168633\pi$
$660$		0			0
$661$	593762.			1.35897			0.679484	−	0.733690i	$-0.262204\pi$
$661$	593762.			1.35897			0.679484	+	0.733690i	$0.262204\pi$
$662$		0			0
$663$	−47322.0	+	47322.0i	−0.107655	+	0.107655i
$664$		0			0
$665$	−26600.0	−	3800.00i	−0.0601504	−	0.00859291i
$666$		0			0
$667$	108200.	+	108200.i	0.243207	+	0.243207i
$668$		0			0
$669$			70038.0i			0.156488i
$670$		0			0
$671$	−420564.			−0.934086
$672$		0			0
$673$	424561.	−	424561.i	0.937368	−	0.937368i	−0.0607833	−	0.998151i	$-0.519360\pi$
$673$	424561.	−	424561.i	0.937368	−	0.937368i	0.998151	+	0.0607833i	$0.0193599\pi$
$674$		0			0
$675$	124000.	−	68000.0i	0.272154	−	0.149246i
$676$		0			0
$677$	229021.	+	229021.i	0.499687	+	0.499687i	0.911340	−	0.411654i	$-0.135049\pi$
$677$	229021.	+	229021.i	0.499687	+	0.499687i	−0.411654	+	0.911340i	$0.635049\pi$
$678$		0			0
$679$			21318.0i			0.0462388i
$680$		0			0
$681$	−137198.			−0.295838
$682$		0			0
$683$	450999.	−	450999.i	0.966795	−	0.966795i	−0.0326716	−	0.999466i	$-0.510402\pi$
$683$	450999.	−	450999.i	0.966795	−	0.966795i	0.999466	+	0.0326716i	$0.0104016\pi$
$684$		0			0
$685$	−46995.0	+	328965.i	−0.100155	+	0.701082i
$686$		0			0
$687$	−98760.0	−	98760.0i	−0.209251	−	0.209251i
$688$		0			0
$689$		−	360162.i		−	0.758681i
$690$		0			0
$691$	432438.			0.905665			0.452833	−	0.891596i	$-0.350413\pi$
$691$	432438.			0.905665			0.452833	+	0.891596i	$0.350413\pi$
$692$		0			0
$693$	303202.	−	303202.i	0.631343	−	0.631343i
$694$		0			0
$695$	279200.	−	209400.i	0.578024	−	0.433518i
$696$		0			0
$697$	−249038.	−	249038.i	−0.512625	−	0.512625i
$698$		0			0
$699$			107442.i			0.219897i
$700$		0			0
$701$	−895838.			−1.82303			−0.911514	−	0.411269i	$-0.865086\pi$
$701$	−895838.			−1.82303			−0.911514	+	0.411269i	$0.865086\pi$
$702$		0			0
$703$	5640.00	−	5640.00i	0.0114122	−	0.0114122i
$704$		0			0
$705$	13770.0	+	18360.0i	0.0277048	+	0.0369398i
$706$		0			0
$707$	31958.0	+	31958.0i	0.0639353	+	0.0639353i
$708$		0			0
$709$			64360.0i			0.128033i	0.997949	+	0.0640167i	$0.0203911\pi$
$709$			64360.0i			0.128033i	−0.997949	+	0.0640167i	$0.979609\pi$
$710$		0			0
$711$	−606720.			−1.20019
$712$		0			0
$713$	−410078.	+	410078.i	−0.806654	+	0.806654i
$714$		0			0
$715$	−699930.	−	99990.0i	−1.36912	−	0.195589i
$716$		0			0
$717$	−45600.0	−	45600.0i	−0.0887006	−	0.0887006i
$718$		0			0
$719$			239840.i			0.463942i	0.972723	+	0.231971i	$0.0745175\pi$
$719$			239840.i			0.463942i	−0.972723	+	0.231971i	$0.925483\pi$
$720$		0			0
$721$	−266798.			−0.513230
$722$		0			0
$723$	57038.0	−	57038.0i	0.109116	−	0.109116i
$724$		0			0
$725$	120000.	+	35000.0i	0.228300	+	0.0665874i
$726$		0			0
$727$	438339.	+	438339.i	0.829357	+	0.829357i	0.987428	−	0.158071i	$-0.0505275\pi$
$727$	438339.	+	438339.i	0.829357	+	0.829357i	−0.158071	+	0.987428i	$0.550528\pi$
$728$		0			0
$729$		−	454321.i		−	0.854885i
$730$		0			0
$731$	−362802.			−0.678946
$732$		0			0
$733$	145261.	−	145261.i	0.270359	−	0.270359i	−0.558886	−	0.829245i	$-0.688771\pi$
$733$	145261.	−	145261.i	0.270359	−	0.270359i	0.829245	+	0.558886i	$0.188771\pi$
$734$		0			0
$735$	8395.00	−	58765.0i	0.0155398	−	0.108779i
$736$		0			0
$737$	1.02636e6	+	1.02636e6i	1.88958	+	1.88958i
$738$		0			0
$739$			738040.i			1.35142i	0.737167	+	0.675711i	$0.236163\pi$
$739$			738040.i			1.35142i	−0.737167	+	0.675711i	$0.763837\pi$
$740$		0			0
$741$	−7920.00			−0.0144241
$742$		0			0
$743$	−579101.	+	579101.i	−1.04900	+	1.04900i	−0.0502671	+	0.998736i	$0.516007\pi$
$743$	−579101.	+	579101.i	−1.04900	+	1.04900i	−0.998736	+	0.0502671i	$0.983993\pi$
$744$		0			0
$745$	−180000.	+	135000.i	−0.324310	+	0.243232i
$746$		0			0
$747$	−480399.	−	480399.i	−0.860916	−	0.860916i
$748$		0			0
$749$			82042.0i			0.146242i
$750$		0			0
$751$	495318.			0.878222			0.439111	−	0.898433i	$-0.355294\pi$
$751$	495318.			0.878222			0.439111	+	0.898433i	$0.355294\pi$
$752$		0			0
$753$	39402.0	−	39402.0i	0.0694910	−	0.0694910i
$754$		0			0
$755$	−356970.	−	475960.i	−0.626236	−	0.834981i
$756$		0			0
$757$	−536979.	−	536979.i	−0.937056	−	0.937056i	0.0610771	−	0.998133i	$-0.480546\pi$
$757$	−536979.	−	536979.i	−0.937056	−	0.937056i	−0.998133	+	0.0610771i	$0.980546\pi$
$758$		0			0
$759$			218564.i			0.379398i
$760$		0			0
$761$	−908798.			−1.56927			−0.784636	−	0.619957i	$-0.787150\pi$
$761$	−908798.			−1.56927			−0.784636	+	0.619957i	$0.787150\pi$
$762$		0			0
$763$	5320.00	−	5320.00i	0.00913824	−	0.00913824i
$764$		0			0
$765$	−660835.	−	94405.0i	−1.12920	−	0.161314i
$766$		0			0
$767$	455400.	+	455400.i	0.774109	+	0.774109i
$768$		0			0
$769$			1.02704e6i			1.73674i	0.495917	+	0.868370i	$0.334832\pi$
$769$			1.02704e6i			1.73674i	−0.495917	+	0.868370i	$0.665168\pi$
$770$		0			0
$771$	−62242.0			−0.104707
$772$		0			0
$773$	161061.	−	161061.i	0.269545	−	0.269545i	−0.559372	−	0.828917i	$-0.688958\pi$
$773$	161061.	−	161061.i	0.269545	−	0.269545i	0.828917	+	0.559372i	$0.188958\pi$
$774$		0			0
$775$	−132650.	+	454800.i	−0.220853	+	0.757211i
$776$		0			0
$777$	−5358.00	−	5358.00i	−0.00887484	−	0.00887484i
$778$		0			0
$779$		−	41680.0i		−	0.0686836i
$780$		0			0
$781$	−702556.			−1.15180
$782$		0			0
$783$	−32000.0	+	32000.0i	−0.0521947	+	0.0521947i
$784$		0			0
$785$	148905.	−	1.04234e6i	0.241641	−	1.69148i
$786$		0			0
$787$	−772201.	−	772201.i	−1.24675	−	1.24675i	−0.957145	−	0.289609i	$-0.906475\pi$
$787$	−772201.	−	772201.i	−1.24675	−	1.24675i	−0.289609	−	0.957145i	$-0.593525\pi$
$788$		0			0
$789$			121478.i			0.195139i
$790$		0			0
$791$	−322202.			−0.514962
$792$		0			0
$793$	−206118.	+	206118.i	−0.327770	+	0.327770i
$794$		0			0
$795$	−72760.0	+	54570.0i	−0.115122	+	0.0863415i
$796$		0			0
$797$	299781.	+	299781.i	0.471941	+	0.471941i	0.902542	−	0.430601i	$-0.141699\pi$
$797$	299781.	+	299781.i	0.471941	+	0.471941i	−0.430601	+	0.902542i	$0.641699\pi$
$798$		0			0
$799$		−	219402.i		−	0.343674i
$800$		0			0
$801$	448720.			0.699375
$802$		0			0
$803$	702758.	−	702758.i	1.08987	−	1.08987i
$804$		0			0
$805$	308370.	+	411160.i	0.475861	+	0.634482i
$806$		0			0
$807$	63800.0	+	63800.0i	0.0979656	+	0.0979656i
$808$		0			0
$809$		−	897040.i		−	1.37061i	−0.728255	−	0.685306i	$-0.759668\pi$
$809$		−	897040.i		−	1.37061i	0.728255	−	0.685306i	$-0.240332\pi$
$810$		0			0
$811$	115798.			0.176059			0.0880297	−	0.996118i	$-0.471943\pi$
$811$	115798.			0.176059			0.0880297	+	0.996118i	$0.471943\pi$
$812$		0			0
$813$	−113238.	+	113238.i	−0.171321	+	0.171321i
$814$		0			0
$815$	442435.	+	63205.0i	0.666092	+	0.0951560i
$816$		0			0
$817$	−30360.0	−	30360.0i	−0.0454839	−	0.0454839i
$818$		0			0
$819$		−	297198.i		−	0.443076i
$820$		0			0
$821$	1.24160e6			1.84203			0.921014	−	0.389530i	$-0.127363\pi$
$821$	1.24160e6			1.84203			0.921014	+	0.389530i	$0.127363\pi$
$822$		0			0
$823$	13219.0	−	13219.0i	0.0195164	−	0.0195164i	−0.697281	−	0.716798i	$-0.745607\pi$
$823$	13219.0	−	13219.0i	0.0195164	−	0.0195164i	0.716798	+	0.697281i	$0.245607\pi$
$824$		0			0
$825$	85850.0	+	156550.i	0.126134	+	0.230009i
$826$		0			0
$827$	−394641.	−	394641.i	−0.577020	−	0.577020i	0.357061	−	0.934081i	$-0.383779\pi$
$827$	−394641.	−	394641.i	−0.577020	−	0.577020i	−0.934081	+	0.357061i	$0.883779\pi$
$828$		0			0
$829$			694760.i			1.01094i	0.862844	+	0.505470i	$0.168681\pi$
$829$			694760.i			1.01094i	−0.862844	+	0.505470i	$0.831319\pi$
$830$		0			0
$831$	29478.0			0.0426870
$832$		0			0
$833$	−401281.	+	401281.i	−0.578307	+	0.578307i
$834$		0			0
$835$	−149905.	+	1.04934e6i	−0.215002	+	1.50502i
$836$		0			0
$837$	−121280.	−	121280.i	−0.173116	−	0.173116i
$838$		0			0
$839$		−	124400.i		−	0.176724i	−0.996088	−	0.0883622i	$-0.971837\pi$
$839$		−	124400.i		−	0.176724i	0.996088	−	0.0883622i	$-0.0281633\pi$
$840$		0			0
$841$	667281.			0.943445
$842$		0			0
$843$	7278.00	−	7278.00i	0.0102413	−	0.0102413i
$844$		0			0
$845$	179180.	−	134385.i	0.250944	−	0.188208i
$846$		0			0
$847$	497097.	+	497097.i	0.692906	+	0.692906i
$848$		0			0
$849$		−	117202.i		−	0.162600i
$850$		0			0
$851$	−152562.			−0.210663
$852$		0			0
$853$	−432299.	+	432299.i	−0.594136	+	0.594136i	−0.938746	−	0.344610i	$-0.888011\pi$
$853$	−432299.	+	432299.i	−0.594136	+	0.594136i	0.344610	+	0.938746i	$0.388011\pi$
$854$		0			0
$855$	−47400.0	−	63200.0i	−0.0648405	−	0.0864540i
$856$		0			0
$857$	−669159.	−	669159.i	−0.911103	−	0.911103i	0.0852557	−	0.996359i	$-0.472829\pi$
$857$	−669159.	−	669159.i	−0.911103	−	0.911103i	−0.996359	+	0.0852557i	$0.972829\pi$
$858$		0			0
$859$		−	370040.i		−	0.501490i	−0.968053	−	0.250745i	$-0.919324\pi$
$859$		−	370040.i		−	0.501490i	0.968053	−	0.250745i	$-0.0806756\pi$
$860$		0			0
$861$	−39596.0			−0.0534128
$862$		0			0
$863$	−490981.	+	490981.i	−0.659239	+	0.659239i	−0.955200	−	0.295961i	$-0.904360\pi$
$863$	−490981.	+	490981.i	−0.659239	+	0.659239i	0.295961	+	0.955200i	$0.404360\pi$
$864$		0			0
$865$	165865.	+	23695.0i	0.221678	+	0.0316683i
$866$		0			0
$867$	−30721.0	−	30721.0i	−0.0408693	−	0.0408693i
$868$		0			0
$869$		−	1.55136e6i		−	2.05434i
$870$		0			0
$871$	1.00604e6			1.32611
$872$		0			0
$873$	−44319.0	+	44319.0i	−0.0581516	+	0.0581516i
$874$		0			0
$875$	382375.	+	173375.i	0.499429	+	0.226449i
$876$		0			0
$877$	206181.	+	206181.i	0.268071	+	0.268071i	0.828322	−	0.560252i	$-0.189296\pi$
$877$	206181.	+	206181.i	0.268071	+	0.268071i	−0.560252	+	0.828322i	$0.689296\pi$
$878$		0			0
$879$		−	190998.i		−	0.247201i
$880$		0			0
$881$	−118478.			−0.152646			−0.0763231	−	0.997083i	$-0.524318\pi$
$881$	−118478.			−0.152646			−0.0763231	+	0.997083i	$0.524318\pi$
$882$		0			0
$883$	204719.	−	204719.i	0.262565	−	0.262565i	−0.563530	−	0.826095i	$-0.690557\pi$
$883$	204719.	−	204719.i	0.262565	−	0.262565i	0.826095	+	0.563530i	$0.190557\pi$
$884$		0			0
$885$	23000.0	−	161000.i	0.0293658	−	0.205560i
$886$		0			0
$887$	562179.	+	562179.i	0.714541	+	0.714541i	0.967482	−	0.252940i	$-0.0813977\pi$
$887$	562179.	+	562179.i	0.714541	+	0.714541i	−0.252940	+	0.967482i	$0.581398\pi$
$888$		0			0
$889$		−	31198.0i		−	0.0394751i
$890$		0			0
$891$	1.22796e6			1.54678
$892$		0			0
$893$	18360.0	−	18360.0i	0.0230234	−	0.0230234i
$894$		0			0
$895$	658400.	−	493800.i	0.821947	−	0.616460i
$896$		0			0
$897$	107118.	+	107118.i	0.133131	+	0.133131i
$898$		0			0
$899$		−	151600.i		−	0.187577i
$900$		0			0
$901$	869482.			1.07105
$902$		0			0
$903$	−28842.0	+	28842.0i	−0.0353712	+	0.0353712i
$904$		0			0
$905$	608370.	+	811160.i	0.742798	+	0.990397i
$906$		0			0
$907$	−492241.	−	492241.i	−0.598361	−	0.598361i	0.341515	−	0.939876i	$-0.389060\pi$
$907$	−492241.	−	492241.i	−0.598361	−	0.598361i	−0.939876	+	0.341515i	$0.889060\pi$
$908$		0			0
$909$			132878.i			0.160815i
$910$		0			0
$911$	−1.15284e6			−1.38910			−0.694549	−	0.719445i	$-0.744396\pi$
$911$	−1.15284e6			−1.38910			−0.694549	+	0.719445i	$0.744396\pi$
$912$		0			0
$913$	1.22836e6	−	1.22836e6i	1.47362	−	1.47362i
$914$		0			0
$915$	72870.0	+	10410.0i	0.0870375	+	0.0124339i
$916$		0			0
$917$	41762.0	+	41762.0i	0.0496641	+	0.0496641i
$918$		0			0
$919$		−	337520.i		−	0.399640i	−0.979833	−	0.199820i	$-0.935964\pi$
$919$		−	337520.i		−	0.399640i	0.979833	−	0.199820i	$-0.0640357\pi$
$920$		0			0
$921$	77202.0			0.0910142
$922$		0			0
$923$	−344322.	+	344322.i	−0.404167	+	0.404167i
$924$		0			0
$925$	−109275.	+	59925.0i	−0.127714	+	0.0700365i
$926$		0			0
$927$	−554659.	−	554659.i	−0.645456	−	0.645456i
$928$		0			0
$929$			760240.i			0.880885i	0.897781	+	0.440443i	$0.145178\pi$
$929$			760240.i			0.880885i	−0.897781	+	0.440443i	$0.854822\pi$
$930$		0			0
$931$	−67160.0			−0.0774839
$932$		0			0
$933$	29162.0	−	29162.0i	0.0335007	−	0.0335007i
$934$		0			0
$935$	241390.	−	1.68973e6i	0.276119	−	1.93283i
$936$		0			0
$937$	75721.0	+	75721.0i	0.0862456	+	0.0862456i	0.748913	−	0.662668i	$-0.230576\pi$
$937$	75721.0	+	75721.0i	0.0862456	+	0.0862456i	−0.662668	+	0.748913i	$0.730576\pi$
$938$		0			0
$939$			3762.00i			0.00426666i
$940$		0			0
$941$	−1.16552e6			−1.31625			−0.658127	−	0.752907i	$-0.728651\pi$
$941$	−1.16552e6			−1.31625			−0.658127	+	0.752907i	$0.728651\pi$
$942$		0			0
$943$	−563722.	+	563722.i	−0.633930	+	0.633930i
$944$		0			0
$945$	−121600.	+	91200.0i	−0.136166	+	0.102125i
$946$		0			0
$947$	331639.	+	331639.i	0.369799	+	0.369799i	0.867404	−	0.497605i	$-0.165787\pi$
$947$	331639.	+	331639.i	0.369799	+	0.369799i	−0.497605	+	0.867404i	$0.665787\pi$
$948$		0			0
$949$		−	688842.i		−	0.764869i
$950$		0			0
$951$	−167562.			−0.185274
$952$		0			0
$953$	−573639.	+	573639.i	−0.631616	+	0.631616i	−0.948473	−	0.316858i	$-0.897372\pi$
$953$	−573639.	+	573639.i	−0.631616	+	0.631616i	0.316858	+	0.948473i	$0.397372\pi$
$954$		0			0
$955$	495030.	+	660040.i	0.542781	+	0.723708i
$956$		0			0
$957$	−40400.0	−	40400.0i	−0.0441121	−	0.0441121i
$958$		0			0
$959$		−	357162.i		−	0.388354i
$960$		0			0
$961$	−348957.			−0.377855
$962$		0			0
$963$	−170561.	+	170561.i	−0.183919	+	0.183919i
$964$		0			0
$965$	811965.	+	115995.i	0.871932	+	0.124562i
$966$		0			0
$967$	49859.0	+	49859.0i	0.0533201	+	0.0533201i	0.733264	−	0.679944i	$-0.237996\pi$
$967$	49859.0	+	49859.0i	0.0533201	+	0.0533201i	−0.679944	+	0.733264i	$0.737996\pi$
$968$		0			0
$969$		−	19120.0i		−	0.0203629i
$970$		0			0
$971$	1.41132e6			1.49688			0.748439	−	0.663204i	$-0.230804\pi$
$971$	1.41132e6			1.49688			0.748439	+	0.663204i	$0.230804\pi$
$972$		0			0
$973$	−265240.	+	265240.i	−0.280165	+	0.280165i
$974$		0			0
$975$	118800.	+	34650.0i	0.124970	+	0.0364497i
$976$		0			0
$977$	−708639.	−	708639.i	−0.742397	−	0.742397i	0.230642	−	0.973039i	$-0.425917\pi$
$977$	−708639.	−	708639.i	−0.742397	−	0.742397i	−0.973039	+	0.230642i	$0.925917\pi$
$978$		0			0
$979$			1.14736e6i			1.19711i
$980$		0			0
$981$	22120.0			0.0229851
$982$		0			0
$983$	−234221.	+	234221.i	−0.242392	+	0.242392i	−0.817839	−	0.575447i	$-0.804828\pi$
$983$	−234221.	+	234221.i	−0.242392	+	0.242392i	0.575447	+	0.817839i	$0.304828\pi$
$984$		0			0
$985$	−84495.0	+	591465.i	−0.0870880	+	0.609616i
$986$		0			0
$987$	−17442.0	−	17442.0i	−0.0179045	−	0.0179045i
$988$		0			0
$989$			821238.i			0.839608i
$990$		0			0
$991$	−898762.			−0.915161			−0.457580	−	0.889168i	$-0.651284\pi$
$991$	−898762.			−0.915161			−0.457580	+	0.889168i	$0.651284\pi$
$992$		0			0
$993$	106282.	−	106282.i	0.107786	−	0.107786i
$994$		0			0
$995$	−283200.	+	212400.i	−0.286053	+	0.214540i
$996$		0			0
$997$	−223379.	−	223379.i	−0.224725	−	0.224725i	0.585760	−	0.810485i	$-0.300796\pi$
$997$	−223379.	−	223379.i	−0.224725	−	0.224725i	−0.810485	+	0.585760i	$0.800796\pi$
$998$		0			0
$999$		−	45120.0i		−	0.0452104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.5.p.c.17.1		2
4.3	odd	2		10.5.c.b.7.1	yes	2
5.2	odd	4		400.5.p.b.193.1		2
5.3	odd	4	inner	80.5.p.c.33.1		2
5.4	even	2		400.5.p.b.257.1		2
8.3	odd	2		320.5.p.d.257.1		2
8.5	even	2		320.5.p.g.257.1		2
12.11	even	2		90.5.g.a.37.1		2
20.3	even	4		10.5.c.b.3.1	✓	2
20.7	even	4		50.5.c.a.43.1		2
20.19	odd	2		50.5.c.a.7.1		2
40.3	even	4		320.5.p.d.193.1		2
40.13	odd	4		320.5.p.g.193.1		2
60.23	odd	4		90.5.g.a.73.1		2
60.47	odd	4		450.5.g.b.343.1		2
60.59	even	2		450.5.g.b.307.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.5.c.b.3.1	✓	2	20.3	even	4
10.5.c.b.7.1	yes	2	4.3	odd	2
50.5.c.a.7.1		2	20.19	odd	2
50.5.c.a.43.1		2	20.7	even	4
80.5.p.c.17.1		2	1.1	even	1	trivial
80.5.p.c.33.1		2	5.3	odd	4	inner
90.5.g.a.37.1		2	12.11	even	2
90.5.g.a.73.1		2	60.23	odd	4
320.5.p.d.193.1		2	40.3	even	4
320.5.p.d.257.1		2	8.3	odd	2
320.5.p.g.193.1		2	40.13	odd	4
320.5.p.g.257.1		2	8.5	even	2
400.5.p.b.193.1		2	5.2	odd	4
400.5.p.b.257.1		2	5.4	even	2
450.5.g.b.307.1		2	60.59	even	2
450.5.g.b.343.1		2	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	80.p (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{3} +(-15.0000 - 20.0000i) q^{5} +(19.0000 + 19.0000i) q^{7} +79.0000i q^{9} -202.000 q^{11} +(-99.0000 + 99.0000i) q^{13} +(35.0000 + 5.00000i) q^{15} +(-239.000 - 239.000i) q^{17} -40.0000i q^{19} -38.0000 q^{21} +(-541.000 + 541.000i) q^{23} +(-175.000 + 600.000i) q^{25} +(-160.000 - 160.000i) q^{27} -200.000i q^{29} +758.000 q^{31} +(202.000 - 202.000i) q^{33} +(95.0000 - 665.000i) q^{35} +(141.000 + 141.000i) q^{37} -198.000i q^{39} +1042.00 q^{41} +(759.000 - 759.000i) q^{43} +(1580.00 - 1185.00i) q^{45} +(459.000 + 459.000i) q^{47} -1679.00i q^{49} +478.000 q^{51} +(-1819.00 + 1819.00i) q^{53} +(3030.00 + 4040.00i) q^{55} +(40.0000 + 40.0000i) q^{57} -4600.00i q^{59} +2082.00 q^{61} +(-1501.00 + 1501.00i) q^{63} +(3465.00 + 495.000i) q^{65} +(-5081.00 - 5081.00i) q^{67} -1082.00i q^{69} +3478.00 q^{71} +(-3479.00 + 3479.00i) q^{73} +(-425.000 - 775.000i) q^{75} +(-3838.00 - 3838.00i) q^{77} +7680.00i q^{79} -6079.00 q^{81} +(-6081.00 + 6081.00i) q^{83} +(-1195.00 + 8365.00i) q^{85} +(200.000 + 200.000i) q^{87} -5680.00i q^{89} -3762.00 q^{91} +(-758.000 + 758.000i) q^{93} +(-800.000 + 600.000i) q^{95} +(561.000 + 561.000i) q^{97} -15958.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 30 q^{5} + 38 q^{7} - 404 q^{11} - 198 q^{13} + 70 q^{15} - 478 q^{17} - 76 q^{21} - 1082 q^{23} - 350 q^{25} - 320 q^{27} + 1516 q^{31} + 404 q^{33} + 190 q^{35} + 282 q^{37} + 2084 q^{41}+ \cdots + 1122 q^{97}+O(q^{100}) \) 2 * q - 2 * q^3 - 30 * q^5 + 38 * q^7 - 404 * q^11 - 198 * q^13 + 70 * q^15 - 478 * q^17 - 76 * q^21 - 1082 * q^23 - 350 * q^25 - 320 * q^27 + 1516 * q^31 + 404 * q^33 + 190 * q^35 + 282 * q^37 + 2084 * q^41 + 1518 * q^43 + 3160 * q^45 + 918 * q^47 + 956 * q^51 - 3638 * q^53 + 6060 * q^55 + 80 * q^57 + 4164 * q^61 - 3002 * q^63 + 6930 * q^65 - 10162 * q^67 + 6956 * q^71 - 6958 * q^73 - 850 * q^75 - 7676 * q^77 - 12158 * q^81 - 12162 * q^83 - 2390 * q^85 + 400 * q^87 - 7524 * q^91 - 1516 * q^93 - 1600 * q^95 + 1122 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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