LMFDB - Embedded newform 320.5.p.g.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,5,Mod(193,320)]

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, 0, 3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("320.193");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	320.p (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:	$33.0783881868$
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			257.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	320.257
Dual form			320.5.p.g.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{3} +(15.0000 + 20.0000i) q^{5} +(19.0000 + 19.0000i) q^{7} +79.0000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{3} +(15.0000 + 20.0000i) q^{5} +(19.0000 + 19.0000i) q^{7} +79.0000i q^{9} +202.000 q^{11} +(99.0000 - 99.0000i) q^{13} +(35.0000 + 5.00000i) q^{15} +(-239.000 - 239.000i) q^{17} +40.0000i q^{19} +38.0000 q^{21} +(-541.000 + 541.000i) q^{23} +(-175.000 + 600.000i) q^{25} +(160.000 + 160.000i) q^{27} +200.000i q^{29} +758.000 q^{31} +(202.000 - 202.000i) q^{33} +(-95.0000 + 665.000i) q^{35} +(-141.000 - 141.000i) q^{37} -198.000i q^{39} +1042.00 q^{41} +(-759.000 + 759.000i) q^{43} +(-1580.00 + 1185.00i) q^{45} +(459.000 + 459.000i) q^{47} -1679.00i q^{49} -478.000 q^{51} +(1819.00 - 1819.00i) q^{53} +(3030.00 + 4040.00i) q^{55} +(40.0000 + 40.0000i) q^{57} +4600.00i q^{59} -2082.00 q^{61} +(-1501.00 + 1501.00i) q^{63} +(3465.00 + 495.000i) q^{65} +(5081.00 + 5081.00i) q^{67} +1082.00i q^{69} +3478.00 q^{71} +(-3479.00 + 3479.00i) q^{73} +(425.000 + 775.000i) q^{75} +(3838.00 + 3838.00i) q^{77} +7680.00i q^{79} -6079.00 q^{81} +(6081.00 - 6081.00i) q^{83} +(1195.00 - 8365.00i) q^{85} +(200.000 + 200.000i) q^{87} -5680.00i q^{89} +3762.00 q^{91} +(758.000 - 758.000i) q^{93} +(-800.000 + 600.000i) q^{95} +(561.000 + 561.000i) q^{97} +15958.0i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 30 q^{5} + 38 q^{7}+O(q^{10}) $ 2 * q + 2 * q^3 + 30 * q^5 + 38 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.649365	−	0.760477i	$-0.724965\pi$
$3$	1.00000	−	1.00000i	0.111111	−	0.111111i	0.760477	+	0.649365i	$0.224965\pi$
$4$		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	$-0.185635\pi$
$11$	202.000			1.66942			0.834711	+	0.550689i	$0.185635\pi$
$12$		0			0
$13$	99.0000	−	99.0000i	0.585799	−	0.585799i	−0.350692	−	0.936491i	$-0.614054\pi$
$13$	99.0000	−	99.0000i	0.585799	−	0.585799i	0.936491	+	0.350692i	$0.114054\pi$
$14$		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	$0.0176439\pi$
$19$			40.0000i			0.110803i	−0.998464	+	0.0554017i	$0.982356\pi$
$20$		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	$0.0379387\pi$
$29$			200.000i			0.237812i	−0.992906	+	0.118906i	$0.962061\pi$
$30$		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	0.653732	−	0.756726i	$-0.273203\pi$
$37$	−141.000	−	141.000i	−0.102995	−	0.102995i	−0.756726	+	0.653732i	$0.773203\pi$
$38$		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	−0.881910	−	0.471418i	$-0.843742\pi$
$43$	−759.000	+	759.000i	−0.410492	+	0.410492i	0.471418	+	0.881910i	$0.343742\pi$
$44$		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	−0.304842	−	0.952403i	$-0.598604\pi$
$53$	1819.00	−	1819.00i	0.647561	−	0.647561i	0.952403	+	0.304842i	$0.0986035\pi$
$54$		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	$0.229753\pi$
$59$			4600.00i			1.32146i	−0.750624	+	0.660730i	$0.770247\pi$
$60$		0			0
$61$	−2082.00			−0.559527			−0.279764	−	0.960069i	$-0.590256\pi$
$61$	−2082.00			−0.559527			−0.279764	+	0.960069i	$0.590256\pi$
$62$		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	$0.0453575\pi$
$67$	5081.00	+	5081.00i	1.13188	+	1.13188i	0.142013	+	0.989865i	$0.454642\pi$
$68$		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	−0.111098	−	0.993809i	$-0.535437\pi$
$83$	6081.00	−	6081.00i	0.882712	−	0.882712i	0.993809	+	0.111098i	$0.0354367\pi$
$84$		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	$-0.526272\pi$
$101$	−1682.00			−0.164886			−0.0824429	+	0.996596i	$0.526272\pi$
$102$		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	0.606505	−	0.795080i	$-0.292571\pi$
$107$	−2159.00	−	2159.00i	−0.188575	−	0.188575i	−0.795080	+	0.606505i	$0.792571\pi$
$108$		0			0
$109$			280.000i			0.0235670i	0.999931	+	0.0117835i	$0.00375090\pi$
$109$			280.000i			0.0235670i	−0.999931	+	0.0117835i	$0.996249\pi$
$110$		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	$-0.520399\pi$
$131$	−2198.00			−0.128081			−0.0640406	+	0.997947i	$0.520399\pi$
$132$		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	$-0.882345\pi$
$139$		−	13960.0i		−	0.722530i	0.932463	−	0.361265i	$-0.117655\pi$
$140$		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	$0.0649695\pi$
$149$			9000.00i			0.405387i	−0.979242	+	0.202694i	$0.935030\pi$
$150$		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	$-0.923969\pi$
$157$	−29781.0	−	29781.0i	−1.20820	−	1.20820i	−0.236595	−	0.971608i	$-0.576031\pi$
$158$		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	−0.427999	−	0.903779i	$-0.640781\pi$
$163$	12641.0	−	12641.0i	0.475780	−	0.475780i	0.903779	+	0.427999i	$0.140781\pi$
$164$		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	−0.623490	−	0.781831i	$-0.714286\pi$
$173$	4739.00	−	4739.00i	0.158341	−	0.158341i	0.781831	+	0.623490i	$0.214286\pi$
$174$		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	$-0.828268\pi$
$179$		−	32920.0i		−	1.02743i	0.857960	−	0.513717i	$-0.171732\pi$
$180$		0			0
$181$	40558.0			1.23800			0.618998	−	0.785392i	$-0.287539\pi$
$181$	40558.0			1.23800			0.618998	+	0.785392i	$0.287539\pi$
$182$		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	0.890474	−	0.455034i	$-0.150373\pi$
$197$	16899.0	+	16899.0i	0.435440	+	0.435440i	−0.455034	+	0.890474i	$0.650373\pi$
$198$		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	$-0.315189\pi$
$211$	48842.0			1.09706			0.548528	+	0.836132i	$0.315189\pi$
$212$		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	$-0.859558\pi$
$227$	−68599.0	−	68599.0i	−1.33127	−	1.33127i	−0.427034	−	0.904235i	$-0.640442\pi$
$228$		0			0
$229$		−	98760.0i		−	1.88326i	−0.336651	−	0.941630i	$-0.609294\pi$
$229$		−	98760.0i		−	1.88326i	0.336651	−	0.941630i	$-0.390706\pi$
$230$		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	$-0.398763\pi$
$251$	39402.0			0.625419			0.312709	+	0.949849i	$0.398763\pi$
$252$		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	$0.145321\pi$
$269$			63800.0i			0.881690i	−0.897583	+	0.440845i	$0.854679\pi$
$270$		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	0.796599	−	0.604508i	$-0.206630\pi$
$277$	14739.0	+	14739.0i	0.192092	+	0.192092i	−0.604508	+	0.796599i	$0.706630\pi$
$278$		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	−0.239258	−	0.970956i	$-0.576904\pi$
$283$	58601.0	−	58601.0i	0.731698	−	0.731698i	0.970956	+	0.239258i	$0.0769041\pi$
$284$		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	$-0.461844\pi$
$293$	95499.0	−	95499.0i	1.11241	−	1.11241i	0.992824	−	0.119582i	$-0.0381556\pi$
$294$		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	0.881587	−	0.472022i	$-0.156476\pi$
$307$	38601.0	+	38601.0i	0.409564	+	0.409564i	−0.472022	+	0.881587i	$0.656476\pi$
$308$		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	0.154292	−	0.988025i	$-0.450690\pi$
$317$	−83781.0	−	83781.0i	−0.833733	−	0.833733i	−0.988025	+	0.154292i	$0.950690\pi$
$318$		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	$-0.338807\pi$
$331$	106282.			0.970071			0.485036	+	0.874494i	$0.338807\pi$
$332$		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	0.679691	−	0.733499i	$-0.262114\pi$
$347$	−6479.00	−	6479.00i	−0.0538083	−	0.0538083i	−0.733499	+	0.679691i	$0.762114\pi$
$348$		0			0
$349$		−	32920.0i		−	0.270277i	−0.990827	−	0.135138i	$-0.956852\pi$
$349$		−	32920.0i		−	0.270277i	0.990827	−	0.135138i	$-0.0431479\pi$
$350$		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	−0.402615	−	0.915369i	$-0.631899\pi$
$373$	71339.0	−	71339.0i	0.512754	−	0.512754i	0.915369	+	0.402615i	$0.131899\pi$
$374$		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	$0.205153\pi$
$379$			172600.i			1.20161i	−0.799397	+	0.600803i	$0.794847\pi$
$380$		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	$0.161155\pi$
$389$			146760.i			0.969859i	−0.874553	+	0.484929i	$0.838845\pi$
$390$		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	0.920660	−	0.390366i	$-0.127652\pi$
$397$	83579.0	+	83579.0i	0.530293	+	0.530293i	−0.390366	+	0.920660i	$0.627652\pi$
$398$		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	$0.202580\pi$
$419$			208680.i			1.18865i	−0.804226	+	0.594323i	$0.797420\pi$
$420$		0			0
$421$	−86882.0			−0.490191			−0.245096	−	0.969499i	$-0.578819\pi$
$421$	−86882.0			−0.490191			−0.245096	+	0.969499i	$0.578819\pi$
$422$		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	−0.526374	−	0.850253i	$-0.676449\pi$
$443$	63561.0	−	63561.0i	0.323879	−	0.323879i	0.850253	+	0.526374i	$0.176449\pi$
$444$		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	$-0.676899\pi$
$461$	−224242.			−1.05515			−0.527576	+	0.849508i	$0.676899\pi$
$462$		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	$-0.986836\pi$
$467$	−226919.	−	226919.i	−1.04049	−	1.04049i	−0.0413430	−	0.999145i	$-0.513164\pi$
$468$		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	$-0.555818\pi$
$491$	−84118.0			−0.348920			−0.174460	+	0.984664i	$0.555818\pi$
$492$		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	$-0.891257\pi$
$499$		−	166840.i		−	0.670037i	0.942211	−	0.335019i	$-0.108743\pi$
$500$		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	$-0.857730\pi$
$509$		−	223960.i		−	0.864440i	0.901768	−	0.432220i	$-0.142270\pi$
$510$		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	−0.237907	−	0.971288i	$-0.576461\pi$
$523$	200601.	−	200601.i	0.733381	−	0.733381i	0.971288	+	0.237907i	$0.0764613\pi$
$524$		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	$-0.336016\pi$
$541$	288398.			0.985366			0.492683	+	0.870209i	$0.336016\pi$
$542$		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	0.882210	−	0.470856i	$-0.156055\pi$
$547$	123081.	+	123081.i	0.411355	+	0.411355i	−0.470856	+	0.882210i	$0.656055\pi$
$548$		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	0.395474	−	0.918477i	$-0.370580\pi$
$557$	−162261.	−	162261.i	−0.523002	−	0.523002i	−0.918477	+	0.395474i	$0.870580\pi$
$558$		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	−0.154801	−	0.987946i	$-0.549474\pi$
$563$	264081.	−	264081.i	0.833145	−	0.833145i	0.987946	+	0.154801i	$0.0494737\pi$
$564$		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	$-0.357059\pi$
$571$	283082.			0.868240			0.434120	+	0.900855i	$0.357059\pi$
$572$		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	0.168855	−	0.985641i	$-0.445993\pi$
$587$	−281439.	−	281439.i	−0.816786	−	0.816786i	−0.985641	+	0.168855i	$0.945993\pi$
$588$		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	−0.864150	−	0.503234i	$-0.832143\pi$
$613$	−135621.	+	135621.i	−0.360916	+	0.360916i	0.503234	+	0.864150i	$0.332143\pi$
$614$		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	$-0.990678\pi$
$619$		−	22440.0i		−	0.0585655i	0.999571	−	0.0292827i	$-0.00932231\pi$
$620$		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	−0.613237	−	0.789899i	$-0.710133\pi$
$643$	73041.0	−	73041.0i	0.176663	−	0.176663i	0.789899	+	0.613237i	$0.210133\pi$
$644$		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	−0.638362	−	0.769736i	$-0.720388\pi$
$653$	56019.0	−	56019.0i	0.131374	−	0.131374i	0.769736	+	0.638362i	$0.220388\pi$
$654$		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	$0.168633\pi$
$659$			438920.i			1.01068i	−0.862920	+	0.505341i	$0.831367\pi$
$660$		0			0
$661$	−593762.			−1.35897			−0.679484	−	0.733690i	$-0.737796\pi$
$661$	−593762.			−1.35897			−0.679484	+	0.733690i	$0.737796\pi$
$662$		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	0.411654	−	0.911340i	$-0.364951\pi$
$677$	−229021.	−	229021.i	−0.499687	−	0.499687i	−0.911340	+	0.411654i	$0.864951\pi$
$678$		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	−0.999466	−	0.0326716i	$-0.989598\pi$
$683$	−450999.	+	450999.i	−0.966795	+	0.966795i	0.0326716	+	0.999466i	$0.489598\pi$
$684$		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	$-0.649587\pi$
$691$	−432438.			−0.905665			−0.452833	+	0.891596i	$0.649587\pi$
$692$		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	$-0.134914\pi$
$701$	895838.			1.82303			0.911514	+	0.411269i	$0.134914\pi$
$702$		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	$-0.979609\pi$
$709$		−	64360.0i		−	0.128033i	0.997949	−	0.0640167i	$-0.0203911\pi$
$710$		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	−0.829245	−	0.558886i	$-0.811229\pi$
$733$	−145261.	+	145261.i	−0.270359	+	0.270359i	0.558886	+	0.829245i	$0.311229\pi$
$734$		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	$-0.763837\pi$
$739$		−	738040.i		−	1.35142i	0.737167	−	0.675711i	$-0.236163\pi$
$740$		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	0.998133	−	0.0610771i	$-0.0194535\pi$
$757$	536979.	+	536979.i	0.937056	+	0.937056i	−0.0610771	+	0.998133i	$0.519454\pi$
$758$		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	−0.828917	−	0.559372i	$-0.811042\pi$
$773$	−161061.	+	161061.i	−0.269545	+	0.269545i	0.559372	+	0.828917i	$0.311042\pi$
$774$		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	$0.0935254\pi$
$787$	772201.	+	772201.i	1.24675	+	1.24675i	0.289609	+	0.957145i	$0.406475\pi$
$788$		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	0.430601	−	0.902542i	$-0.358301\pi$
$797$	−299781.	−	299781.i	−0.471941	−	0.471941i	−0.902542	+	0.430601i	$0.858301\pi$
$798$		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	$-0.528057\pi$
$811$	−115798.			−0.176059			−0.0880297	+	0.996118i	$0.528057\pi$
$812$		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	$-0.872637\pi$
$821$	−1.24160e6			−1.84203			−0.921014	+	0.389530i	$0.872637\pi$
$822$		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	0.934081	−	0.357061i	$-0.116221\pi$
$827$	394641.	+	394641.i	0.577020	+	0.577020i	−0.357061	+	0.934081i	$0.616221\pi$
$828$		0			0
$829$		−	694760.i		−	1.01094i	−0.862844	−	0.505470i	$-0.831319\pi$
$829$		−	694760.i		−	1.01094i	0.862844	−	0.505470i	$-0.168681\pi$
$830$		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	−0.344610	−	0.938746i	$-0.611989\pi$
$853$	432299.	−	432299.i	0.594136	−	0.594136i	0.938746	+	0.344610i	$0.111989\pi$
$854$		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	$0.0806756\pi$
$859$			370040.i			0.501490i	−0.968053	+	0.250745i	$0.919324\pi$
$860$		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	0.560252	−	0.828322i	$-0.310704\pi$
$877$	−206181.	−	206181.i	−0.268071	−	0.268071i	−0.828322	+	0.560252i	$0.810704\pi$
$878$		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	−0.826095	−	0.563530i	$-0.809443\pi$
$883$	−204719.	+	204719.i	−0.262565	+	0.262565i	0.563530	+	0.826095i	$0.309443\pi$
$884$		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	0.939876	−	0.341515i	$-0.110940\pi$
$907$	492241.	+	492241.i	0.598361	+	0.598361i	−0.341515	+	0.939876i	$0.610940\pi$
$908$		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	$-0.271349\pi$
$941$	1.16552e6			1.31625			0.658127	+	0.752907i	$0.271349\pi$
$942$		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	0.497605	−	0.867404i	$-0.334213\pi$
$947$	−331639.	−	331639.i	−0.369799	−	0.369799i	−0.867404	+	0.497605i	$0.834213\pi$
$948$		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	$-0.769196\pi$
$971$	−1.41132e6			−1.49688			−0.748439	+	0.663204i	$0.769196\pi$
$972$		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	0.810485	−	0.585760i	$-0.199204\pi$
$997$	223379.	+	223379.i	0.224725	+	0.224725i	−0.585760	+	0.810485i	$0.699204\pi$
$998$		0			0
$999$		−	45120.0i		−	0.0452104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.5.p.g.257.1		2
4.3	odd	2		320.5.p.d.257.1		2
5.3	odd	4	inner	320.5.p.g.193.1		2
8.3	odd	2		10.5.c.b.7.1	yes	2
8.5	even	2		80.5.p.c.17.1		2
20.3	even	4		320.5.p.d.193.1		2
24.11	even	2		90.5.g.a.37.1		2
40.3	even	4		10.5.c.b.3.1	✓	2
40.13	odd	4		80.5.p.c.33.1		2
40.19	odd	2		50.5.c.a.7.1		2
40.27	even	4		50.5.c.a.43.1		2
40.29	even	2		400.5.p.b.257.1		2
40.37	odd	4		400.5.p.b.193.1		2
120.59	even	2		450.5.g.b.307.1		2
120.83	odd	4		90.5.g.a.73.1		2
120.107	odd	4		450.5.g.b.343.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.5.c.b.3.1	✓	2	40.3	even	4
10.5.c.b.7.1	yes	2	8.3	odd	2
50.5.c.a.7.1		2	40.19	odd	2
50.5.c.a.43.1		2	40.27	even	4
80.5.p.c.17.1		2	8.5	even	2
80.5.p.c.33.1		2	40.13	odd	4
90.5.g.a.37.1		2	24.11	even	2
90.5.g.a.73.1		2	120.83	odd	4
320.5.p.d.193.1		2	20.3	even	4
320.5.p.d.257.1		2	4.3	odd	2
320.5.p.g.193.1		2	5.3	odd	4	inner
320.5.p.g.257.1		2	1.1	even	1	trivial
400.5.p.b.193.1		2	40.37	odd	4
400.5.p.b.257.1		2	40.29	even	2
450.5.g.b.307.1		2	120.59	even	2
450.5.g.b.343.1		2	120.107	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{3} +(15.0000 + 20.0000i) q^{5} +(19.0000 + 19.0000i) q^{7} +79.0000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{3} +(15.0000 + 20.0000i) q^{5} +(19.0000 + 19.0000i) q^{7} +79.0000i q^{9} +202.000 q^{11} +(99.0000 - 99.0000i) q^{13} +(35.0000 + 5.00000i) q^{15} +(-239.000 - 239.000i) q^{17} +40.0000i q^{19} +38.0000 q^{21} +(-541.000 + 541.000i) q^{23} +(-175.000 + 600.000i) q^{25} +(160.000 + 160.000i) q^{27} +200.000i q^{29} +758.000 q^{31} +(202.000 - 202.000i) q^{33} +(-95.0000 + 665.000i) q^{35} +(-141.000 - 141.000i) q^{37} -198.000i q^{39} +1042.00 q^{41} +(-759.000 + 759.000i) q^{43} +(-1580.00 + 1185.00i) q^{45} +(459.000 + 459.000i) q^{47} -1679.00i q^{49} -478.000 q^{51} +(1819.00 - 1819.00i) q^{53} +(3030.00 + 4040.00i) q^{55} +(40.0000 + 40.0000i) q^{57} +4600.00i q^{59} -2082.00 q^{61} +(-1501.00 + 1501.00i) q^{63} +(3465.00 + 495.000i) q^{65} +(5081.00 + 5081.00i) q^{67} +1082.00i q^{69} +3478.00 q^{71} +(-3479.00 + 3479.00i) q^{73} +(425.000 + 775.000i) q^{75} +(3838.00 + 3838.00i) q^{77} +7680.00i q^{79} -6079.00 q^{81} +(6081.00 - 6081.00i) q^{83} +(1195.00 - 8365.00i) q^{85} +(200.000 + 200.000i) q^{87} -5680.00i q^{89} +3762.00 q^{91} +(758.000 - 758.000i) q^{93} +(-800.000 + 600.000i) q^{95} +(561.000 + 561.000i) q^{97} +15958.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 30 q^{5} + 38 q^{7}+O(q^{10}) \) 2 * q + 2 * q^3 + 30 * q^5 + 38 * q^7	\( 2 q + 2 q^{3} + 30 q^{5} + 38 q^{7} + 404 q^{11} + 198 q^{13} + 70 q^{15} - 478 q^{17} + 76 q^{21} - 1082 q^{23} - 350 q^{25} + 320 q^{27} + 1516 q^{31} + 404 q^{33} - 190 q^{35} - 282 q^{37} + 2084 q^{41} - 1518 q^{43} - 3160 q^{45} + 918 q^{47} - 956 q^{51} + 3638 q^{53} + 6060 q^{55} + 80 q^{57} - 4164 q^{61} - 3002 q^{63} + 6930 q^{65} + 10162 q^{67} + 6956 q^{71} - 6958 q^{73} + 850 q^{75} + 7676 q^{77} - 12158 q^{81} + 12162 q^{83} + 2390 q^{85} + 400 q^{87} + 7524 q^{91} + 1516 q^{93} - 1600 q^{95} + 1122 q^{97}+O(q^{100}) \) 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

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