LMFDB - Embedded newform 10.5.c.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,5,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	10.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.03369963084$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.5.c.b.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 + 2.00000i) q^{2} +(1.00000 - 1.00000i) q^{3} +8.00000i q^{4} +(-15.0000 - 20.0000i) q^{5} +4.00000 q^{6} +(-19.0000 - 19.0000i) q^{7} +(-16.0000 + 16.0000i) q^{8} +79.0000i q^{9} +(10.0000 - 70.0000i) q^{10} +202.000 q^{11} +(8.00000 + 8.00000i) q^{12} +(-99.0000 + 99.0000i) q^{13} -76.0000i q^{14} +(-35.0000 - 5.00000i) q^{15} -64.0000 q^{16} +(-239.000 - 239.000i) q^{17} +(-158.000 + 158.000i) q^{18} +40.0000i q^{19} +(160.000 - 120.000i) q^{20} -38.0000 q^{21} +(404.000 + 404.000i) q^{22} +(541.000 - 541.000i) q^{23} +32.0000i q^{24} +(-175.000 + 600.000i) q^{25} -396.000 q^{26} +(160.000 + 160.000i) q^{27} +(152.000 - 152.000i) q^{28} -200.000i q^{29} +(-60.0000 - 80.0000i) q^{30} -758.000 q^{31} +(-128.000 - 128.000i) q^{32} +(202.000 - 202.000i) q^{33} -956.000i q^{34} +(-95.0000 + 665.000i) q^{35} -632.000 q^{36} +(141.000 + 141.000i) q^{37} +(-80.0000 + 80.0000i) q^{38} +198.000i q^{39} +(560.000 + 80.0000i) q^{40} +1042.00 q^{41} +(-76.0000 - 76.0000i) q^{42} +(-759.000 + 759.000i) q^{43} +1616.00i q^{44} +(1580.00 - 1185.00i) q^{45} +2164.00 q^{46} +(-459.000 - 459.000i) q^{47} +(-64.0000 + 64.0000i) q^{48} -1679.00i q^{49} +(-1550.00 + 850.000i) q^{50} -478.000 q^{51} +(-792.000 - 792.000i) q^{52} +(-1819.00 + 1819.00i) q^{53} +640.000i q^{54} +(-3030.00 - 4040.00i) q^{55} +608.000 q^{56} +(40.0000 + 40.0000i) q^{57} +(400.000 - 400.000i) q^{58} +4600.00i q^{59} +(40.0000 - 280.000i) q^{60} +2082.00 q^{61} +(-1516.00 - 1516.00i) q^{62} +(1501.00 - 1501.00i) q^{63} -512.000i q^{64} +(3465.00 + 495.000i) q^{65} +808.000 q^{66} +(5081.00 + 5081.00i) q^{67} +(1912.00 - 1912.00i) q^{68} -1082.00i q^{69} +(-1520.00 + 1140.00i) q^{70} -3478.00 q^{71} +(-1264.00 - 1264.00i) q^{72} +(-3479.00 + 3479.00i) q^{73} +564.000i q^{74} +(425.000 + 775.000i) q^{75} -320.000 q^{76} +(-3838.00 - 3838.00i) q^{77} +(-396.000 + 396.000i) q^{78} -7680.00i q^{79} +(960.000 + 1280.00i) q^{80} -6079.00 q^{81} +(2084.00 + 2084.00i) q^{82} +(6081.00 - 6081.00i) q^{83} -304.000i q^{84} +(-1195.00 + 8365.00i) q^{85} -3036.00 q^{86} +(-200.000 - 200.000i) q^{87} +(-3232.00 + 3232.00i) q^{88} -5680.00i q^{89} +(5530.00 + 790.000i) q^{90} +3762.00 q^{91} +(4328.00 + 4328.00i) q^{92} +(-758.000 + 758.000i) q^{93} -1836.00i q^{94} +(800.000 - 600.000i) q^{95} -256.000 q^{96} +(561.000 + 561.000i) q^{97} +(3358.00 - 3358.00i) q^{98} +15958.0i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 2 q^{3} - 30 q^{5} + 8 q^{6} - 38 q^{7} - 32 q^{8} + 20 q^{10} + 404 q^{11} + 16 q^{12} - 198 q^{13} - 70 q^{15} - 128 q^{16} - 478 q^{17} - 316 q^{18} + 320 q^{20} - 76 q^{21} + 808 q^{22}+ \cdots + 6716 q^{98}+O(q^{100}) $ 2 * q + 4 * q^2 + 2 * q^3 - 30 * q^5 + 8 * q^6 - 38 * q^7 - 32 * q^8 + 20 * q^10 + 404 * q^11 + 16 * q^12 - 198 * q^13 - 70 * q^15 - 128 * q^16 - 478 * q^17 - 316 * q^18 + 320 * q^20 - 76 * q^21 + 808 * q^22 + 1082 * q^23 - 350 * q^25 - 792 * q^26 + 320 * q^27 + 304 * q^28 - 120 * q^30 - 1516 * q^31 - 256 * q^32 + 404 * q^33 - 190 * q^35 - 1264 * q^36 + 282 * q^37 - 160 * q^38 + 1120 * q^40 + 2084 * q^41 - 152 * q^42 - 1518 * q^43 + 3160 * q^45 + 4328 * q^46 - 918 * q^47 - 128 * q^48 - 3100 * q^50 - 956 * q^51 - 1584 * q^52 - 3638 * q^53 - 6060 * q^55 + 1216 * q^56 + 80 * q^57 + 800 * q^58 + 80 * q^60 + 4164 * q^61 - 3032 * q^62 + 3002 * q^63 + 6930 * q^65 + 1616 * q^66 + 10162 * q^67 + 3824 * q^68 - 3040 * q^70 - 6956 * q^71 - 2528 * q^72 - 6958 * q^73 + 850 * q^75 - 640 * q^76 - 7676 * q^77 - 792 * q^78 + 1920 * q^80 - 12158 * q^81 + 4168 * q^82 + 12162 * q^83 - 2390 * q^85 - 6072 * q^86 - 400 * q^87 - 6464 * q^88 + 11060 * q^90 + 7524 * q^91 + 8656 * q^92 - 1516 * q^93 + 1600 * q^95 - 512 * q^96 + 1122 * q^97 + 6716 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$	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	$0.224965\pi$
$4$			8.00000i			0.500000i
$5$	−15.0000	−	20.0000i	−0.600000	−	0.800000i
$5$	−15.0000	−	20.0000i	−0.600000	−	0.800000i
$6$	4.00000			0.111111
$7$	−19.0000	−	19.0000i	−0.387755	−	0.387755i	0.486131	−	0.873886i	$-0.338408\pi$
$7$	−19.0000	−	19.0000i	−0.387755	−	0.387755i	−0.873886	+	0.486131i	$0.838408\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$			79.0000i			0.975309i
$10$	10.0000	−	70.0000i	0.100000	−	0.700000i
$11$	202.000			1.66942			0.834711	−	0.550689i	$-0.185635\pi$
$11$	202.000			1.66942			0.834711	+	0.550689i	$0.185635\pi$
$12$	8.00000	+	8.00000i	0.0555556	+	0.0555556i
$13$	−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	$0.385946\pi$
$14$		−	76.0000i		−	0.387755i
$15$	−35.0000	−	5.00000i	−0.155556	−	0.0222222i
$16$	−64.0000			−0.250000
$17$	−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	$0.948815\pi$
$18$	−158.000	+	158.000i	−0.487654	+	0.487654i
$19$			40.0000i			0.110803i	0.998464	+	0.0554017i	$0.0176439\pi$
$19$			40.0000i			0.110803i	−0.998464	+	0.0554017i	$0.982356\pi$
$20$	160.000	−	120.000i	0.400000	−	0.300000i
$21$	−38.0000			−0.0861678
$22$	404.000	+	404.000i	0.834711	+	0.834711i
$23$	541.000	−	541.000i	1.02268	−	1.02268i	0.0229476	−	0.999737i	$-0.492695\pi$
$23$	541.000	−	541.000i	1.02268	−	1.02268i	0.999737	−	0.0229476i	$-0.00730510\pi$
$24$			32.0000i			0.0555556i
$25$	−175.000	+	600.000i	−0.280000	+	0.960000i
$26$	−396.000			−0.585799
$27$	160.000	+	160.000i	0.219479	+	0.219479i
$28$	152.000	−	152.000i	0.193878	−	0.193878i
$29$		−	200.000i		−	0.237812i	−0.992906	−	0.118906i	$-0.962061\pi$
$29$		−	200.000i		−	0.237812i	0.992906	−	0.118906i	$-0.0379387\pi$
$30$	−60.0000	−	80.0000i	−0.0666667	−	0.0888889i
$31$	−758.000			−0.788762			−0.394381	−	0.918947i	$-0.629041\pi$
$31$	−758.000			−0.788762			−0.394381	+	0.918947i	$0.629041\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	202.000	−	202.000i	0.185491	−	0.185491i
$34$		−	956.000i		−	0.826990i
$35$	−95.0000	+	665.000i	−0.0775510	+	0.542857i
$36$	−632.000			−0.487654
$37$	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	$0.726797\pi$
$38$	−80.0000	+	80.0000i	−0.0554017	+	0.0554017i
$39$			198.000i			0.130178i
$40$	560.000	+	80.0000i	0.350000	+	0.0500000i
$41$	1042.00			0.619869			0.309935	−	0.950758i	$-0.399693\pi$
$41$	1042.00			0.619869			0.309935	+	0.950758i	$0.399693\pi$
$42$	−76.0000	−	76.0000i	−0.0430839	−	0.0430839i
$43$	−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	$0.343742\pi$
$44$			1616.00i			0.834711i
$45$	1580.00	−	1185.00i	0.780247	−	0.585185i
$46$	2164.00			1.02268
$47$	−459.000	−	459.000i	−0.207786	−	0.207786i	0.595540	−	0.803326i	$-0.296938\pi$
$47$	−459.000	−	459.000i	−0.207786	−	0.207786i	−0.803326	+	0.595540i	$0.796938\pi$
$48$	−64.0000	+	64.0000i	−0.0277778	+	0.0277778i
$49$		−	1679.00i		−	0.699292i
$50$	−1550.00	+	850.000i	−0.620000	+	0.340000i
$51$	−478.000			−0.183775
$52$	−792.000	−	792.000i	−0.292899	−	0.292899i
$53$	−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	$0.401396\pi$
$54$			640.000i			0.219479i
$55$	−3030.00	−	4040.00i	−1.00165	−	1.33554i
$56$	608.000			0.193878
$57$	40.0000	+	40.0000i	0.0123115	+	0.0123115i
$58$	400.000	−	400.000i	0.118906	−	0.118906i
$59$			4600.00i			1.32146i	0.750624	+	0.660730i	$0.229753\pi$
$59$			4600.00i			1.32146i	−0.750624	+	0.660730i	$0.770247\pi$
$60$	40.0000	−	280.000i	0.0111111	−	0.0777778i
$61$	2082.00			0.559527			0.279764	−	0.960069i	$-0.409744\pi$
$61$	2082.00			0.559527			0.279764	+	0.960069i	$0.409744\pi$
$62$	−1516.00	−	1516.00i	−0.394381	−	0.394381i
$63$	1501.00	−	1501.00i	0.378181	−	0.378181i
$64$		−	512.000i		−	0.125000i
$65$	3465.00	+	495.000i	0.820118	+	0.117160i
$66$	808.000			0.185491
$67$	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	$0.454642\pi$
$68$	1912.00	−	1912.00i	0.413495	−	0.413495i
$69$		−	1082.00i		−	0.227263i
$70$	−1520.00	+	1140.00i	−0.310204	+	0.232653i
$71$	−3478.00			−0.689942			−0.344971	−	0.938613i	$-0.612111\pi$
$71$	−3478.00			−0.689942			−0.344971	+	0.938613i	$0.612111\pi$
$72$	−1264.00	−	1264.00i	−0.243827	−	0.243827i
$73$	−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	$0.402735\pi$
$74$			564.000i			0.102995i
$75$	425.000	+	775.000i	0.0755556	+	0.137778i
$76$	−320.000			−0.0554017
$77$	−3838.00	−	3838.00i	−0.647327	−	0.647327i
$78$	−396.000	+	396.000i	−0.0650888	+	0.0650888i
$79$		−	7680.00i		−	1.23057i	−0.788304	−	0.615286i	$-0.789041\pi$
$79$		−	7680.00i		−	1.23057i	0.788304	−	0.615286i	$-0.210959\pi$
$80$	960.000	+	1280.00i	0.150000	+	0.200000i
$81$	−6079.00			−0.926536
$82$	2084.00	+	2084.00i	0.309935	+	0.309935i
$83$	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	$0.0354367\pi$
$84$		−	304.000i		−	0.0430839i
$85$	−1195.00	+	8365.00i	−0.165398	+	1.15779i
$86$	−3036.00			−0.410492
$87$	−200.000	−	200.000i	−0.0264236	−	0.0264236i
$88$	−3232.00	+	3232.00i	−0.417355	+	0.417355i
$89$		−	5680.00i		−	0.717081i	−0.933514	−	0.358541i	$-0.883274\pi$
$89$		−	5680.00i		−	0.717081i	0.933514	−	0.358541i	$-0.116726\pi$
$90$	5530.00	+	790.000i	0.682716	+	0.0975309i
$91$	3762.00			0.454293
$92$	4328.00	+	4328.00i	0.511342	+	0.511342i
$93$	−758.000	+	758.000i	−0.0876402	+	0.0876402i
$94$		−	1836.00i		−	0.207786i
$95$	800.000	−	600.000i	0.0886427	−	0.0664820i
$96$	−256.000			−0.0277778
$97$	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	$0.736576\pi$
$98$	3358.00	−	3358.00i	0.349646	−	0.349646i
$99$			15958.0i			1.62820i
$100$	−4800.00	−	1400.00i	−0.480000	−	0.140000i
$101$	1682.00			0.164886			0.0824429	−	0.996596i	$-0.473728\pi$
$101$	1682.00			0.164886			0.0824429	+	0.996596i	$0.473728\pi$
$102$	−956.000	−	956.000i	−0.0918877	−	0.0918877i
$103$	7021.00	−	7021.00i	0.661797	−	0.661797i	−0.294007	−	0.955803i	$-0.594989\pi$
$103$	7021.00	−	7021.00i	0.661797	−	0.661797i	0.955803	+	0.294007i	$0.0949888\pi$
$104$		−	3168.00i		−	0.292899i
$105$	570.000	+	760.000i	0.0517007	+	0.0689342i
$106$	−7276.00			−0.647561
$107$	−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	$0.792571\pi$
$108$	−1280.00	+	1280.00i	−0.109739	+	0.109739i
$109$		−	280.000i		−	0.0235670i	−0.999931	−	0.0117835i	$-0.996249\pi$
$109$		−	280.000i		−	0.0235670i	0.999931	−	0.0117835i	$-0.00375090\pi$
$110$	2020.00	−	14140.0i	0.166942	−	1.16860i
$111$	282.000			0.0228878
$112$	1216.00	+	1216.00i	0.0969388	+	0.0969388i
$113$	−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	$0.405580\pi$
$114$			160.000i			0.0123115i
$115$	−18935.0	−	2705.00i	−1.43176	−	0.204537i
$116$	1600.00			0.118906
$117$	−7821.00	−	7821.00i	−0.571335	−	0.571335i
$118$	−9200.00	+	9200.00i	−0.660730	+	0.660730i
$119$			9082.00i			0.641339i
$120$	640.000	−	480.000i	0.0444444	−	0.0333333i
$121$	26163.0			1.78697
$122$	4164.00	+	4164.00i	0.279764	+	0.279764i
$123$	1042.00	−	1042.00i	0.0688743	−	0.0688743i
$124$		−	6064.00i		−	0.394381i
$125$	14625.0	−	5500.00i	0.936000	−	0.352000i
$126$	6004.00			0.378181
$127$	821.000	+	821.000i	0.0509021	+	0.0509021i	0.732100	−	0.681198i	$-0.238541\pi$
$127$	821.000	+	821.000i	0.0509021	+	0.0509021i	−0.681198	+	0.732100i	$0.738541\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$			1518.00i			0.0912205i
$130$	5940.00	+	7920.00i	0.351479	+	0.468639i
$131$	−2198.00			−0.128081			−0.0640406	−	0.997947i	$-0.520399\pi$
$131$	−2198.00			−0.128081			−0.0640406	+	0.997947i	$0.520399\pi$
$132$	1616.00	+	1616.00i	0.0927456	+	0.0927456i
$133$	760.000	−	760.000i	0.0429646	−	0.0429646i
$134$			20324.0i			1.13188i
$135$	800.000	−	5600.00i	0.0438957	−	0.307270i
$136$	7648.00			0.413495
$137$	−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	$0.865213\pi$
$138$	2164.00	−	2164.00i	0.113632	−	0.113632i
$139$		−	13960.0i		−	0.722530i	−0.932463	−	0.361265i	$-0.882345\pi$
$139$		−	13960.0i		−	0.722530i	0.932463	−	0.361265i	$-0.117655\pi$
$140$	−5320.00	−	760.000i	−0.271429	−	0.0387755i
$141$	−918.000			−0.0461747
$142$	−6956.00	−	6956.00i	−0.344971	−	0.344971i
$143$	−19998.0	+	19998.0i	−0.977945	+	0.977945i
$144$		−	5056.00i		−	0.243827i
$145$	−4000.00	+	3000.00i	−0.190250	+	0.142687i
$146$	−13916.0			−0.652843
$147$	−1679.00	−	1679.00i	−0.0776991	−	0.0776991i
$148$	−1128.00	+	1128.00i	−0.0514974	+	0.0514974i
$149$		−	9000.00i		−	0.405387i	−0.979242	−	0.202694i	$-0.935030\pi$
$149$		−	9000.00i		−	0.405387i	0.979242	−	0.202694i	$-0.0649695\pi$
$150$	−700.000	+	2400.00i	−0.0311111	+	0.106667i
$151$	−23798.0			−1.04373			−0.521863	−	0.853029i	$-0.674763\pi$
$151$	−23798.0			−1.04373			−0.521863	+	0.853029i	$0.674763\pi$
$152$	−640.000	−	640.000i	−0.0277008	−	0.0277008i
$153$	18881.0	−	18881.0i	0.806570	−	0.806570i
$154$		−	15352.0i		−	0.647327i
$155$	11370.0	+	15160.0i	0.473257	+	0.631009i
$156$	−1584.00			−0.0650888
$157$	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	$0.423969\pi$
$158$	15360.0	−	15360.0i	0.615286	−	0.615286i
$159$			3638.00i			0.143903i
$160$	−640.000	+	4480.00i	−0.0250000	+	0.175000i
$161$	−20558.0			−0.793102
$162$	−12158.0	−	12158.0i	−0.463268	−	0.463268i
$163$	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	$0.140781\pi$
$164$			8336.00i			0.309935i
$165$	−7070.00	−	1010.00i	−0.259688	−	0.0370983i
$166$	24324.0			0.882712
$167$	29981.0	+	29981.0i	1.07501	+	1.07501i	0.996948	+	0.0780632i	$0.0248736\pi$
$167$	29981.0	+	29981.0i	1.07501	+	1.07501i	0.0780632	+	0.996948i	$0.475126\pi$
$168$	608.000	−	608.000i	0.0215420	−	0.0215420i
$169$			8959.00i			0.313679i
$170$	−19120.0	+	14340.0i	−0.661592	+	0.496194i
$171$	−3160.00			−0.108067
$172$	−6072.00	−	6072.00i	−0.205246	−	0.205246i
$173$	−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	$0.285714\pi$
$174$		−	800.000i		−	0.0264236i
$175$	14725.0	−	8075.00i	0.480816	−	0.263673i
$176$	−12928.0			−0.417355
$177$	4600.00	+	4600.00i	0.146829	+	0.146829i
$178$	11360.0	−	11360.0i	0.358541	−	0.358541i
$179$		−	32920.0i		−	1.02743i	−0.857960	−	0.513717i	$-0.828268\pi$
$179$		−	32920.0i		−	1.02743i	0.857960	−	0.513717i	$-0.171732\pi$
$180$	9480.00	+	12640.0i	0.292593	+	0.390123i
$181$	−40558.0			−1.23800			−0.618998	−	0.785392i	$-0.712461\pi$
$181$	−40558.0			−1.23800			−0.618998	+	0.785392i	$0.712461\pi$
$182$	7524.00	+	7524.00i	0.227146	+	0.227146i
$183$	2082.00	−	2082.00i	0.0621697	−	0.0621697i
$184$			17312.0i			0.511342i
$185$	705.000	−	4935.00i	0.0205990	−	0.144193i
$186$	−3032.00			−0.0876402
$187$	−48278.0	−	48278.0i	−1.38059	−	1.38059i
$188$	3672.00	−	3672.00i	0.103893	−	0.103893i
$189$		−	6080.00i		−	0.170208i
$190$	2800.00	+	400.000i	0.0775623	+	0.0110803i
$191$	33002.0			0.904635			0.452318	−	0.891857i	$-0.350597\pi$
$191$	33002.0			0.904635			0.452318	+	0.891857i	$0.350597\pi$
$192$	−512.000	−	512.000i	−0.0138889	−	0.0138889i
$193$	−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	$0.395161\pi$
$194$			2244.00i			0.0596238i
$195$	3960.00	−	2970.00i	0.104142	−	0.0781065i
$196$	13432.0			0.349646
$197$	−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	$0.849627\pi$
$198$	−31916.0	+	31916.0i	−0.814101	+	0.814101i
$199$			14160.0i			0.357567i	0.983888	+	0.178783i	$0.0572161\pi$
$199$			14160.0i			0.357567i	−0.983888	+	0.178783i	$0.942784\pi$
$200$	−6800.00	−	12400.0i	−0.170000	−	0.310000i
$201$	10162.0			0.251528
$202$	3364.00	+	3364.00i	0.0824429	+	0.0824429i
$203$	−3800.00	+	3800.00i	−0.0922129	+	0.0922129i
$204$		−	3824.00i		−	0.0918877i
$205$	−15630.0	−	20840.0i	−0.371921	−	0.495895i
$206$	28084.0			0.661797
$207$	42739.0	+	42739.0i	0.997433	+	0.997433i
$208$	6336.00	−	6336.00i	0.146450	−	0.146450i
$209$			8080.00i			0.184977i
$210$	−380.000	+	2660.00i	−0.00861678	+	0.0603175i
$211$	48842.0			1.09706			0.548528	−	0.836132i	$-0.315189\pi$
$211$	48842.0			1.09706			0.548528	+	0.836132i	$0.315189\pi$
$212$	−14552.0	−	14552.0i	−0.323781	−	0.323781i
$213$	−3478.00	+	3478.00i	−0.0766603	+	0.0766603i
$214$		−	8636.00i		−	0.188575i
$215$	26565.0	+	3795.00i	0.574689	+	0.0820984i
$216$	−5120.00			−0.109739
$217$	14402.0	+	14402.0i	0.305846	+	0.305846i
$218$	560.000	−	560.000i	0.0117835	−	0.0117835i
$219$			6958.00i			0.145076i
$220$	32320.0	−	24240.0i	0.667769	−	0.500826i
$221$	47322.0			0.968899
$222$	564.000	+	564.000i	0.0114439	+	0.0114439i
$223$	−35019.0	+	35019.0i	−0.704197	+	0.704197i	−0.965309	−	0.261112i	$-0.915911\pi$
$223$	−35019.0	+	35019.0i	−0.704197	+	0.704197i	0.261112	+	0.965309i	$0.415911\pi$
$224$			4864.00i			0.0969388i
$225$	−47400.0	−	13825.0i	−0.936296	−	0.273086i
$226$	−33916.0			−0.664030
$227$	−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	$-0.640442\pi$
$228$	−320.000	+	320.000i	−0.00615574	+	0.00615574i
$229$			98760.0i			1.88326i	0.336651	+	0.941630i	$0.390706\pi$
$229$			98760.0i			1.88326i	−0.336651	+	0.941630i	$0.609294\pi$
$230$	−32460.0	−	43280.0i	−0.613611	−	0.818147i
$231$	−7676.00			−0.143850
$232$	3200.00	+	3200.00i	0.0594530	+	0.0594530i
$233$	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	$0.00331314\pi$
$234$		−	31284.0i		−	0.571335i
$235$	−2295.00	+	16065.0i	−0.0415573	+	0.290901i
$236$	−36800.0			−0.660730
$237$	−7680.00	−	7680.00i	−0.136730	−	0.136730i
$238$	−18164.0	+	18164.0i	−0.320669	+	0.320669i
$239$		−	45600.0i		−	0.798305i	−0.916884	−	0.399153i	$-0.869304\pi$
$239$		−	45600.0i		−	0.798305i	0.916884	−	0.399153i	$-0.130696\pi$
$240$	2240.00	+	320.000i	0.0388889	+	0.00555556i
$241$	−57038.0			−0.982042			−0.491021	−	0.871148i	$-0.663376\pi$
$241$	−57038.0			−0.982042			−0.491021	+	0.871148i	$0.663376\pi$
$242$	52326.0	+	52326.0i	0.893484	+	0.893484i
$243$	−19039.0	+	19039.0i	−0.322427	+	0.322427i
$244$			16656.0i			0.279764i
$245$	−33580.0	+	25185.0i	−0.559434	+	0.419575i
$246$	4168.00			0.0688743
$247$	−3960.00	−	3960.00i	−0.0649085	−	0.0649085i
$248$	12128.0	−	12128.0i	0.197190	−	0.197190i
$249$		−	12162.0i		−	0.196158i
$250$	40250.0	+	18250.0i	0.644000	+	0.292000i
$251$	39402.0			0.625419			0.312709	−	0.949849i	$-0.398763\pi$
$251$	39402.0			0.625419			0.312709	+	0.949849i	$0.398763\pi$
$252$	12008.0	+	12008.0i	0.189090	+	0.189090i
$253$	109282.	−	109282.i	1.70729	−	1.70729i
$254$			3284.00i			0.0509021i
$255$	7170.00	+	9560.00i	0.110265	+	0.147020i
$256$	4096.00			0.0625000
$257$	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	$0.641880\pi$
$258$	−3036.00	+	3036.00i	−0.0456102	+	0.0456102i
$259$		−	5358.00i		−	0.0798736i
$260$	−3960.00	+	27720.0i	−0.0585799	+	0.410059i
$261$	15800.0			0.231940
$262$	−4396.00	−	4396.00i	−0.0640406	−	0.0640406i
$263$	−60739.0	+	60739.0i	−0.878125	+	0.878125i	−0.993340	−	0.115216i	$-0.963244\pi$
$263$	−60739.0	+	60739.0i	−0.878125	+	0.878125i	0.115216	+	0.993340i	$0.463244\pi$
$264$			6464.00i			0.0927456i
$265$	63665.0	+	9095.00i	0.906586	+	0.129512i
$266$	3040.00			0.0429646
$267$	−5680.00	−	5680.00i	−0.0796757	−	0.0796757i
$268$	−40648.0	+	40648.0i	−0.565939	+	0.565939i
$269$		−	63800.0i		−	0.881690i	−0.897583	−	0.440845i	$-0.854679\pi$
$269$		−	63800.0i		−	0.881690i	0.897583	−	0.440845i	$-0.145321\pi$
$270$	12800.0	−	9600.00i	0.175583	−	0.131687i
$271$	−113238.			−1.54189			−0.770945	−	0.636901i	$-0.780216\pi$
$271$	−113238.			−1.54189			−0.770945	+	0.636901i	$0.780216\pi$
$272$	15296.0	+	15296.0i	0.206747	+	0.206747i
$273$	3762.00	−	3762.00i	0.0504770	−	0.0504770i
$274$		−	37596.0i		−	0.500773i
$275$	−35350.0	+	121200.i	−0.467438	+	1.60264i
$276$	8656.00			0.113632
$277$	−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	$0.793370\pi$
$278$	27920.0	−	27920.0i	0.361265	−	0.361265i
$279$		−	59882.0i		−	0.769286i
$280$	−9120.00	−	12160.0i	−0.116327	−	0.155102i
$281$	−7278.00			−0.0921721			−0.0460860	−	0.998937i	$-0.514675\pi$
$281$	−7278.00			−0.0921721			−0.0460860	+	0.998937i	$0.514675\pi$
$282$	−1836.00	−	1836.00i	−0.0230874	−	0.0230874i
$283$	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	$0.0769041\pi$
$284$		−	27824.0i		−	0.344971i
$285$	200.000	−	1400.00i	0.00246230	−	0.0172361i
$286$	−79992.0			−0.977945
$287$	−19798.0	−	19798.0i	−0.240357	−	0.240357i
$288$	10112.0	−	10112.0i	0.121914	−	0.121914i
$289$			30721.0i			0.367824i
$290$	−14000.0	−	2000.00i	−0.166468	−	0.0237812i
$291$	1122.00			0.0132497
$292$	−27832.0	−	27832.0i	−0.326421	−	0.326421i
$293$	−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	$0.961844\pi$
$294$		−	6716.00i		−	0.0776991i
$295$	92000.0	−	69000.0i	1.05717	−	0.792876i
$296$	−4512.00			−0.0514974
$297$	32320.0	+	32320.0i	0.366403	+	0.366403i
$298$	18000.0	−	18000.0i	0.202694	−	0.202694i
$299$			107118.i			1.19817i
$300$	−6200.00	+	3400.00i	−0.0688889	+	0.0377778i
$301$	28842.0			0.318341
$302$	−47596.0	−	47596.0i	−0.521863	−	0.521863i
$303$	1682.00	−	1682.00i	0.0183206	−	0.0183206i
$304$		−	2560.00i		−	0.0277008i
$305$	−31230.0	−	41640.0i	−0.335716	−	0.447622i
$306$	75524.0			0.806570
$307$	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	$0.656476\pi$
$308$	30704.0	−	30704.0i	0.323663	−	0.323663i
$309$		−	14042.0i		−	0.147066i
$310$	−7580.00	+	53060.0i	−0.0788762	+	0.552133i
$311$	29162.0			0.301506			0.150753	−	0.988571i	$-0.451830\pi$
$311$	29162.0			0.301506			0.150753	+	0.988571i	$0.451830\pi$
$312$	−3168.00	−	3168.00i	−0.0325444	−	0.0325444i
$313$	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	$0.245678\pi$
$314$			119124.i			1.20820i
$315$	−52535.0	−	7505.00i	−0.529453	−	0.0756362i
$316$	61440.0			0.615286
$317$	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	$0.549310\pi$
$318$	−7276.00	+	7276.00i	−0.0719513	+	0.0719513i
$319$		−	40400.0i		−	0.397009i
$320$	−10240.0	+	7680.00i	−0.100000	+	0.0750000i
$321$	−4318.00			−0.0419056
$322$	−41116.0	−	41116.0i	−0.396551	−	0.396551i
$323$	9560.00	−	9560.00i	0.0916332	−	0.0916332i
$324$		−	48632.0i		−	0.463268i
$325$	−42075.0	−	76725.0i	−0.398343	−	0.726391i
$326$	50564.0			0.475780
$327$	−280.000	−	280.000i	−0.00261856	−	0.00261856i
$328$	−16672.0	+	16672.0i	−0.154967	+	0.154967i
$329$			17442.0i			0.161140i
$330$	−12120.0	−	16160.0i	−0.111295	−	0.148393i
$331$	106282.			0.970071			0.485036	−	0.874494i	$-0.338807\pi$
$331$	106282.			0.970071			0.485036	+	0.874494i	$0.338807\pi$
$332$	48648.0	+	48648.0i	0.441356	+	0.441356i
$333$	−11139.0	+	11139.0i	−0.100452	+	0.100452i
$334$			119924.i			1.07501i
$335$	25405.0	−	177835.i	0.226376	−	1.58463i
$336$	2432.00			0.0215420
$337$	−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	$-0.597289\pi$
$338$	−17918.0	+	17918.0i	−0.156840	+	0.156840i
$339$			16958.0i			0.147562i
$340$	−66920.0	−	9560.00i	−0.578893	−	0.0826990i
$341$	−153116.			−1.31678
$342$	−6320.00	−	6320.00i	−0.0540337	−	0.0540337i
$343$	−77520.0	+	77520.0i	−0.658909	+	0.658909i
$344$		−	24288.0i		−	0.205246i
$345$	−21640.0	+	16230.0i	−0.181811	+	0.136358i
$346$	−18956.0			−0.158341
$347$	−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	$0.762114\pi$
$348$	1600.00	−	1600.00i	0.0132118	−	0.0132118i
$349$			32920.0i			0.270277i	0.990827	+	0.135138i	$0.0431479\pi$
$349$			32920.0i			0.270277i	−0.990827	+	0.135138i	$0.956852\pi$
$350$	45600.0	+	13300.0i	0.372245	+	0.108571i
$351$	−31680.0			−0.257141
$352$	−25856.0	−	25856.0i	−0.208678	−	0.208678i
$353$	−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	$0.348980\pi$
$354$			18400.0i			0.146829i
$355$	52170.0	+	69560.0i	0.413965	+	0.551954i
$356$	45440.0			0.358541
$357$	9082.00	+	9082.00i	0.0712599	+	0.0712599i
$358$	65840.0	−	65840.0i	0.513717	−	0.513717i
$359$		−	171760.i		−	1.33270i	−0.745638	−	0.666351i	$-0.767855\pi$
$359$		−	171760.i		−	1.33270i	0.745638	−	0.666351i	$-0.232145\pi$
$360$	−6320.00	+	44240.0i	−0.0487654	+	0.341358i
$361$	128721.			0.987723
$362$	−81116.0	−	81116.0i	−0.618998	−	0.618998i
$363$	26163.0	−	26163.0i	0.198552	−	0.198552i
$364$			30096.0i			0.227146i
$365$	121765.	+	17395.0i	0.913980	+	0.130569i
$366$	8328.00			0.0621697
$367$	152261.	+	152261.i	1.13046	+	1.13046i	0.990100	+	0.140363i	$0.0448271\pi$
$367$	152261.	+	152261.i	1.13046	+	1.13046i	0.140363	+	0.990100i	$0.455173\pi$
$368$	−34624.0	+	34624.0i	−0.255671	+	0.255671i
$369$			82318.0i			0.604564i
$370$	11280.0	−	8460.00i	0.0823959	−	0.0617969i
$371$	69122.0			0.502190
$372$	−6064.00	−	6064.00i	−0.0438201	−	0.0438201i
$373$	−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	$0.368101\pi$
$374$		−	193112.i		−	1.38059i
$375$	9125.00	−	20125.0i	0.0648889	−	0.143111i
$376$	14688.0			0.103893
$377$	19800.0	+	19800.0i	0.139310	+	0.139310i
$378$	12160.0	−	12160.0i	0.0851040	−	0.0851040i
$379$			172600.i			1.20161i	0.799397	+	0.600803i	$0.205153\pi$
$379$			172600.i			1.20161i	−0.799397	+	0.600803i	$0.794847\pi$
$380$	4800.00	+	6400.00i	0.0332410	+	0.0443213i
$381$	1642.00			0.0113116
$382$	66004.0	+	66004.0i	0.452318	+	0.452318i
$383$	158421.	−	158421.i	1.07998	−	1.07998i	0.0834683	−	0.996510i	$-0.473400\pi$
$383$	158421.	−	158421.i	1.07998	−	1.07998i	0.996510	−	0.0834683i	$-0.0265997\pi$
$384$		−	2048.00i		−	0.0138889i
$385$	−19190.0	+	134330.i	−0.129465	+	0.906257i
$386$	−92796.0			−0.622809
$387$	−59961.0	−	59961.0i	−0.400357	−	0.400357i
$388$	−4488.00	+	4488.00i	−0.0298119	+	0.0298119i
$389$		−	146760.i		−	0.969859i	−0.874553	−	0.484929i	$-0.838845\pi$
$389$		−	146760.i		−	0.969859i	0.874553	−	0.484929i	$-0.161155\pi$
$390$	13860.0	+	1980.00i	0.0911243	+	0.0130178i
$391$	−258598.			−1.69150
$392$	26864.0	+	26864.0i	0.174823	+	0.174823i
$393$	−2198.00	+	2198.00i	−0.0142312	+	0.0142312i
$394$		−	67596.0i		−	0.435440i
$395$	−153600.	+	115200.i	−0.984458	+	0.738343i
$396$	−127664.			−0.814101
$397$	−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	$0.872348\pi$
$398$	−28320.0	+	28320.0i	−0.178783	+	0.178783i
$399$		−	1520.00i		−	0.00954768i
$400$	11200.0	−	38400.0i	0.0700000	−	0.240000i
$401$	−42078.0			−0.261677			−0.130839	−	0.991404i	$-0.541767\pi$
$401$	−42078.0			−0.261677			−0.130839	+	0.991404i	$0.541767\pi$
$402$	20324.0	+	20324.0i	0.125764	+	0.125764i
$403$	75042.0	−	75042.0i	0.462056	−	0.462056i
$404$			13456.0i			0.0824429i
$405$	91185.0	+	121580.i	0.555921	+	0.741228i
$406$	−15200.0			−0.0922129
$407$	28482.0	+	28482.0i	0.171942	+	0.171942i
$408$	7648.00	−	7648.00i	0.0459439	−	0.0459439i
$409$		−	300960.i		−	1.79913i	−0.436789	−	0.899564i	$-0.643884\pi$
$409$		−	300960.i		−	1.79913i	0.436789	−	0.899564i	$-0.356116\pi$
$410$	10420.0	−	72940.0i	0.0619869	−	0.433908i
$411$	−18798.0			−0.111283
$412$	56168.0	+	56168.0i	0.330898	+	0.330898i
$413$	87400.0	−	87400.0i	0.512403	−	0.512403i
$414$			170956.i			0.997433i
$415$	−212835.	−	30405.0i	−1.23580	−	0.176542i
$416$	25344.0			0.146450
$417$	−13960.0	−	13960.0i	−0.0802811	−	0.0802811i
$418$	−16160.0	+	16160.0i	−0.0924887	+	0.0924887i
$419$			208680.i			1.18865i	0.804226	+	0.594323i	$0.202580\pi$
$419$			208680.i			1.18865i	−0.804226	+	0.594323i	$0.797420\pi$
$420$	−6080.00	+	4560.00i	−0.0344671	+	0.0258503i
$421$	86882.0			0.490191			0.245096	−	0.969499i	$-0.421181\pi$
$421$	86882.0			0.490191			0.245096	+	0.969499i	$0.421181\pi$
$422$	97684.0	+	97684.0i	0.548528	+	0.548528i
$423$	36261.0	−	36261.0i	0.202656	−	0.202656i
$424$		−	58208.0i		−	0.323781i
$425$	185225.	−	101575.i	1.02547	−	0.562353i
$426$	−13912.0			−0.0766603
$427$	−39558.0	−	39558.0i	−0.216959	−	0.216959i
$428$	17272.0	−	17272.0i	0.0942877	−	0.0942877i
$429$			39996.0i			0.217321i
$430$	45540.0	+	60720.0i	0.246295	+	0.328394i
$431$	−125078.			−0.673328			−0.336664	−	0.941625i	$-0.609299\pi$
$431$	−125078.			−0.673328			−0.336664	+	0.941625i	$0.609299\pi$
$432$	−10240.0	−	10240.0i	−0.0548697	−	0.0548697i
$433$	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	$0.242891\pi$
$434$			57608.0i			0.305846i
$435$	−1000.00	+	7000.00i	−0.00528471	+	0.0369930i
$436$	2240.00			0.0117835
$437$	21640.0	+	21640.0i	0.113317	+	0.113317i
$438$	−13916.0	+	13916.0i	−0.0725381	+	0.0725381i
$439$			55280.0i			0.286840i	0.989662	+	0.143420i	$0.0458099\pi$
$439$			55280.0i			0.286840i	−0.989662	+	0.143420i	$0.954190\pi$
$440$	113120.	+	16160.0i	0.584298	+	0.0834711i
$441$	132641.			0.682025
$442$	94644.0	+	94644.0i	0.484450	+	0.484450i
$443$	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	$0.176449\pi$
$444$			2256.00i			0.0114439i
$445$	−113600.	+	85200.0i	−0.573665	+	0.430249i
$446$	−140076.			−0.704197
$447$	−9000.00	−	9000.00i	−0.0450430	−	0.0450430i
$448$	−9728.00	+	9728.00i	−0.0484694	+	0.0484694i
$449$			204880.i			1.01626i	0.861279	+	0.508132i	$0.169664\pi$
$449$			204880.i			1.01626i	−0.861279	+	0.508132i	$0.830336\pi$
$450$	−67150.0	−	122450.i	−0.331605	−	0.604691i
$451$	210484.			1.03482
$452$	−67832.0	−	67832.0i	−0.332015	−	0.332015i
$453$	−23798.0	+	23798.0i	−0.115970	+	0.115970i
$454$		−	274396.i		−	1.33127i
$455$	−56430.0	−	75240.0i	−0.272576	−	0.363434i
$456$	−1280.00			−0.00615574
$457$	−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	$0.761425\pi$
$458$	−197520.	+	197520.i	−0.941630	+	0.941630i
$459$		−	76480.0i		−	0.363013i
$460$	21640.0	−	151480.i	0.102268	−	0.715879i
$461$	224242.			1.05515			0.527576	−	0.849508i	$-0.323101\pi$
$461$	224242.			1.05515			0.527576	+	0.849508i	$0.323101\pi$
$462$	−15352.0	−	15352.0i	−0.0719252	−	0.0719252i
$463$	−243499.	+	243499.i	−1.13589	+	1.13589i	−0.146707	+	0.989180i	$0.546868\pi$
$463$	−243499.	+	243499.i	−1.13589	+	1.13589i	−0.989180	+	0.146707i	$0.953132\pi$
$464$			12800.0i			0.0594530i
$465$	26530.0	+	3790.00i	0.122696	+	0.0175280i
$466$	214884.			0.989537
$467$	−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	$-0.513164\pi$
$468$	62568.0	−	62568.0i	0.285667	−	0.285667i
$469$		−	193078.i		−	0.877783i
$470$	−36720.0	+	27540.0i	−0.166229	+	0.124672i
$471$	59562.0			0.268490
$472$	−73600.0	−	73600.0i	−0.330365	−	0.330365i
$473$	−153318.	+	153318.i	−0.685284	+	0.685284i
$474$		−	30720.0i		−	0.136730i
$475$	−24000.0	−	7000.00i	−0.106371	−	0.0310249i
$476$	−72656.0			−0.320669
$477$	−143701.	−	143701.i	−0.631572	−	0.631572i
$478$	91200.0	−	91200.0i	0.399153	−	0.399153i
$479$			334240.i			1.45676i	0.685174	+	0.728379i	$0.259726\pi$
$479$			334240.i			1.45676i	−0.685174	+	0.728379i	$0.740274\pi$
$480$	3840.00	+	5120.00i	0.0166667	+	0.0222222i
$481$	−27918.0			−0.120669
$482$	−114076.	−	114076.i	−0.491021	−	0.491021i
$483$	−20558.0	+	20558.0i	−0.0881225	+	0.0881225i
$484$			209304.i			0.893484i
$485$	2805.00	−	19635.0i	0.0119248	−	0.0834733i
$486$	−76156.0			−0.322427
$487$	278541.	+	278541.i	1.17444	+	1.17444i	0.981139	+	0.193302i	$0.0619196\pi$
$487$	278541.	+	278541.i	1.17444	+	1.17444i	0.193302	+	0.981139i	$0.438080\pi$
$488$	−33312.0	+	33312.0i	−0.139882	+	0.139882i
$489$		−	25282.0i		−	0.105729i
$490$	−117530.	−	16790.0i	−0.489504	−	0.0699292i
$491$	−84118.0			−0.348920			−0.174460	−	0.984664i	$-0.555818\pi$
$491$	−84118.0			−0.348920			−0.174460	+	0.984664i	$0.555818\pi$
$492$	8336.00	+	8336.00i	0.0344372	+	0.0344372i
$493$	−47800.0	+	47800.0i	−0.196668	+	0.196668i
$494$		−	15840.0i		−	0.0649085i
$495$	319160.	−	239370.i	1.30256	−	0.976921i
$496$	48512.0			0.197190
$497$	66082.0	+	66082.0i	0.267529	+	0.267529i
$498$	24324.0	−	24324.0i	0.0980791	−	0.0980791i
$499$		−	166840.i		−	0.670037i	−0.942211	−	0.335019i	$-0.891257\pi$
$499$		−	166840.i		−	0.670037i	0.942211	−	0.335019i	$-0.108743\pi$
$500$	44000.0	+	117000.i	0.176000	+	0.468000i
$501$	59962.0			0.238891
$502$	78804.0	+	78804.0i	0.312709	+	0.312709i
$503$	190461.	−	190461.i	0.752783	−	0.752783i	−0.222214	−	0.974998i	$-0.571328\pi$
$503$	190461.	−	190461.i	0.752783	−	0.752783i	0.974998	+	0.222214i	$0.0713285\pi$
$504$			48032.0i			0.189090i
$505$	−25230.0	−	33640.0i	−0.0989315	−	0.131909i
$506$	437128.			1.70729
$507$	8959.00	+	8959.00i	0.0348533	+	0.0348533i
$508$	−6568.00	+	6568.00i	−0.0254511	+	0.0254511i
$509$			223960.i			0.864440i	0.901768	+	0.432220i	$0.142270\pi$
$509$			223960.i			0.864440i	−0.901768	+	0.432220i	$0.857730\pi$
$510$	−4780.00	+	33460.0i	−0.0183775	+	0.128643i
$511$	132202.			0.506286
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	−6400.00	+	6400.00i	−0.0243190	+	0.0243190i
$514$			124484.i			0.471180i
$515$	−245735.	−	35105.0i	−0.926515	−	0.132359i
$516$	−12144.0			−0.0456102
$517$	−92718.0	−	92718.0i	−0.346883	−	0.346883i
$518$	10716.0	−	10716.0i	0.0399368	−	0.0399368i
$519$			9478.00i			0.0351870i
$520$	−63360.0	+	47520.0i	−0.234320	+	0.175740i
$521$	−297918.			−1.09754			−0.548771	−	0.835973i	$-0.684904\pi$
$521$	−297918.			−1.09754			−0.548771	+	0.835973i	$0.684904\pi$
$522$	31600.0	+	31600.0i	0.115970	+	0.115970i
$523$	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	$0.0764613\pi$
$524$		−	17584.0i		−	0.0640406i
$525$	6650.00	−	22800.0i	0.0241270	−	0.0827211i
$526$	−242956.			−0.878125
$527$	181162.	+	181162.i	0.652298	+	0.652298i
$528$	−12928.0	+	12928.0i	−0.0463728	+	0.0463728i
$529$		−	305521.i		−	1.09177i
$530$	109140.	+	145520.i	0.388537	+	0.518049i
$531$	−363400.			−1.28883
$532$	6080.00	+	6080.00i	0.0214823	+	0.0214823i
$533$	−103158.	+	103158.i	−0.363119	+	0.363119i
$534$		−	22720.0i		−	0.0796757i
$535$	−10795.0	+	75565.0i	−0.0377151	+	0.264006i
$536$	−162592.			−0.565939
$537$	−32920.0	−	32920.0i	−0.114159	−	0.114159i
$538$	127600.	−	127600.i	0.440845	−	0.440845i
$539$		−	339158.i		−	1.16741i
$540$	44800.0	+	6400.00i	0.153635	+	0.0219479i
$541$	−288398.			−0.985366			−0.492683	−	0.870209i	$-0.663984\pi$
$541$	−288398.			−0.985366			−0.492683	+	0.870209i	$0.663984\pi$
$542$	−226476.	−	226476.i	−0.770945	−	0.770945i
$543$	−40558.0	+	40558.0i	−0.137555	+	0.137555i
$544$			61184.0i			0.206747i
$545$	−5600.00	+	4200.00i	−0.0188536	+	0.0141402i
$546$	15048.0			0.0504770
$547$	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	$0.656055\pi$
$548$	75192.0	−	75192.0i	0.250386	−	0.250386i
$549$			164478.i			0.545712i
$550$	−313100.	+	171700.i	−1.03504	+	0.567603i
$551$	8000.00			0.0263504
$552$	17312.0	+	17312.0i	0.0568158	+	0.0568158i
$553$	−145920.	+	145920.i	−0.477161	+	0.477161i
$554$		−	58956.0i		−	0.192092i
$555$	−4230.00	−	5640.00i	−0.0137327	−	0.0183102i
$556$	111680.			0.361265
$557$	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	$0.629420\pi$
$558$	119764.	−	119764.i	0.384643	−	0.384643i
$559$		−	150282.i		−	0.480932i
$560$	6080.00	−	42560.0i	0.0193878	−	0.135714i
$561$	−96556.0			−0.306799
$562$	−14556.0	−	14556.0i	−0.0460860	−	0.0460860i
$563$	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	$0.0494737\pi$
$564$		−	7344.00i		−	0.0230874i
$565$	296765.	+	42395.0i	0.929642	+	0.132806i
$566$	234404.			0.731698
$567$	115501.	+	115501.i	0.359269	+	0.359269i
$568$	55648.0	−	55648.0i	0.172486	−	0.172486i
$569$		−	8320.00i		−	0.0256980i	−0.999917	−	0.0128490i	$-0.995910\pi$
$569$		−	8320.00i		−	0.0256980i	0.999917	−	0.0128490i	$-0.00409007\pi$
$570$	3200.00	−	2400.00i	0.00984918	−	0.00738689i
$571$	283082.			0.868240			0.434120	−	0.900855i	$-0.357059\pi$
$571$	283082.			0.868240			0.434120	+	0.900855i	$0.357059\pi$
$572$	−159984.	−	159984.i	−0.488973	−	0.488973i
$573$	33002.0	−	33002.0i	0.100515	−	0.100515i
$574$		−	79192.0i		−	0.240357i
$575$	229925.	+	419275.i	0.695425	+	1.26813i
$576$	40448.0			0.121914
$577$	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	$0.563458\pi$
$578$	−61442.0	+	61442.0i	−0.183912	+	0.183912i
$579$			46398.0i			0.138402i
$580$	−24000.0	−	32000.0i	−0.0713436	−	0.0951249i
$581$	−231078.			−0.684552
$582$	2244.00	+	2244.00i	0.00662486	+	0.00662486i
$583$	−367438.	+	367438.i	−1.08105	+	1.08105i
$584$		−	111328.i		−	0.326421i
$585$	−39105.0	+	273735.i	−0.114267	+	0.799869i
$586$	−381996.			−1.11241
$587$	−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	$0.945993\pi$
$588$	13432.0	−	13432.0i	0.0388496	−	0.0388496i
$589$		−	30320.0i		−	0.0873974i
$590$	322000.	+	46000.0i	0.925022	+	0.132146i
$591$	−33798.0			−0.0967645
$592$	−9024.00	−	9024.00i	−0.0257487	−	0.0257487i
$593$	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	$-0.0698460\pi$
$594$			129280.i			0.366403i
$595$	181640.	−	136230.i	0.513071	−	0.384803i
$596$	72000.0			0.202694
$597$	14160.0	+	14160.0i	0.0397296	+	0.0397296i
$598$	−214236.	+	214236.i	−0.599087	+	0.599087i
$599$			136240.i			0.379709i	0.981812	+	0.189855i	$0.0608016\pi$
$599$			136240.i			0.379709i	−0.981812	+	0.189855i	$0.939198\pi$
$600$	−19200.0	−	5600.00i	−0.0533333	−	0.0155556i
$601$	234962.			0.650502			0.325251	−	0.945628i	$-0.394551\pi$
$601$	234962.			0.650502			0.325251	+	0.945628i	$0.394551\pi$
$602$	57684.0	+	57684.0i	0.159170	+	0.159170i
$603$	−401399.	+	401399.i	−1.10393	+	1.10393i
$604$		−	190384.i		−	0.521863i
$605$	−392445.	−	523260.i	−1.07218	−	1.42957i
$606$	6728.00			0.0183206
$607$	−406779.	−	406779.i	−1.10403	−	1.10403i	−0.993919	−	0.110111i	$-0.964879\pi$
$607$	−406779.	−	406779.i	−1.10403	−	1.10403i	−0.110111	−	0.993919i	$-0.535121\pi$
$608$	5120.00	−	5120.00i	0.0138504	−	0.0138504i
$609$			7600.00i			0.0204917i
$610$	20820.0	−	145740.i	0.0559527	−	0.391669i
$611$	90882.0			0.243442
$612$	151048.	+	151048.i	0.403285	+	0.403285i
$613$	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	$0.167857\pi$
$614$			154404.i			0.409564i
$615$	−36470.0	−	5210.00i	−0.0964241	−	0.0137749i
$616$	122816.			0.323663
$617$	−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	$0.841082\pi$
$618$	28084.0	−	28084.0i	0.0735330	−	0.0735330i
$619$		−	22440.0i		−	0.0585655i	−0.999571	−	0.0292827i	$-0.990678\pi$
$619$		−	22440.0i		−	0.0585655i	0.999571	−	0.0292827i	$-0.00932231\pi$
$620$	−121280.	+	90960.0i	−0.315505	+	0.236629i
$621$	173120.			0.448915
$622$	58324.0	+	58324.0i	0.150753	+	0.150753i
$623$	−107920.	+	107920.i	−0.278052	+	0.278052i
$624$		−	12672.0i		−	0.0325444i
$625$	−329375.	−	210000.i	−0.843200	−	0.537600i
$626$	7524.00			0.0192000
$627$	8080.00	+	8080.00i	0.0205531	+	0.0205531i
$628$	−238248.	+	238248.i	−0.604102	+	0.604102i
$629$		−	67398.0i		−	0.170351i
$630$	−90060.0	−	120080.i	−0.226909	−	0.302545i
$631$	−199958.			−0.502204			−0.251102	−	0.967961i	$-0.580793\pi$
$631$	−199958.			−0.502204			−0.251102	+	0.967961i	$0.580793\pi$
$632$	122880.	+	122880.i	0.307643	+	0.307643i
$633$	48842.0	−	48842.0i	0.121895	−	0.121895i
$634$			335124.i			0.833733i
$635$	4105.00	−	28735.0i	0.0101804	−	0.0712629i
$636$	−29104.0			−0.0719513
$637$	166221.	+	166221.i	0.409644	+	0.409644i
$638$	80800.0	−	80800.0i	0.198504	−	0.198504i
$639$		−	274762.i		−	0.672907i
$640$	−35840.0	−	5120.00i	−0.0875000	−	0.0125000i
$641$	448562.			1.09171			0.545854	−	0.837880i	$-0.316205\pi$
$641$	448562.			1.09171			0.545854	+	0.837880i	$0.316205\pi$
$642$	−8636.00	−	8636.00i	−0.0209528	−	0.0209528i
$643$	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	$0.210133\pi$
$644$		−	164464.i		−	0.396551i
$645$	30360.0	−	22770.0i	0.0729764	−	0.0547323i
$646$	38240.0			0.0916332
$647$	−90259.0	−	90259.0i	−0.215616	−	0.215616i	0.591032	−	0.806648i	$-0.298721\pi$
$647$	−90259.0	−	90259.0i	−0.215616	−	0.215616i	−0.806648	+	0.591032i	$0.798721\pi$
$648$	97264.0	−	97264.0i	0.231634	−	0.231634i
$649$			929200.i			2.20607i
$650$	69300.0	−	237600.i	0.164024	−	0.562367i
$651$	28804.0			0.0679659
$652$	101128.	+	101128.i	0.237890	+	0.237890i
$653$	−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	$0.279612\pi$
$654$		−	1120.00i		−	0.00261856i
$655$	32970.0	+	43960.0i	0.0768487	+	0.102465i
$656$	−66688.0			−0.154967
$657$	−274841.	−	274841.i	−0.636723	−	0.636723i
$658$	−34884.0	+	34884.0i	−0.0805702	+	0.0805702i
$659$			438920.i			1.01068i	0.862920	+	0.505341i	$0.168633\pi$
$659$			438920.i			1.01068i	−0.862920	+	0.505341i	$0.831367\pi$
$660$	8080.00	−	56560.0i	0.0185491	−	0.129844i
$661$	593762.			1.35897			0.679484	−	0.733690i	$-0.262204\pi$
$661$	593762.			1.35897			0.679484	+	0.733690i	$0.262204\pi$
$662$	212564.	+	212564.i	0.485036	+	0.485036i
$663$	47322.0	−	47322.0i	0.107655	−	0.107655i
$664$			194592.i			0.441356i
$665$	−26600.0	−	3800.00i	−0.0601504	−	0.00859291i
$666$	−44556.0			−0.100452
$667$	−108200.	−	108200.i	−0.243207	−	0.243207i
$668$	−239848.	+	239848.i	−0.537506	+	0.537506i
$669$			70038.0i			0.156488i
$670$	406480.	−	304860.i	0.905502	−	0.679127i
$671$	420564.			0.934086
$672$	4864.00	+	4864.00i	0.0107710	+	0.0107710i
$673$	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	$0.0193599\pi$
$674$		−	569916.i		−	1.25456i
$675$	−124000.	+	68000.0i	−0.272154	+	0.149246i
$676$	−71672.0			−0.156840
$677$	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	$0.635049\pi$
$678$	−33916.0	+	33916.0i	−0.0737811	+	0.0737811i
$679$		−	21318.0i		−	0.0462388i
$680$	−114720.	−	152960.i	−0.248097	−	0.330796i
$681$	−137198.			−0.295838
$682$	−306232.	−	306232.i	−0.658388	−	0.658388i
$683$	−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	$0.489598\pi$
$684$		−	25280.0i		−	0.0540337i
$685$	−46995.0	+	328965.i	−0.100155	+	0.701082i
$686$	−310080.			−0.658909
$687$	98760.0	+	98760.0i	0.209251	+	0.209251i
$688$	48576.0	−	48576.0i	0.102623	−	0.102623i
$689$		−	360162.i		−	0.758681i
$690$	−75740.0	−	10820.0i	−0.159084	−	0.0227263i
$691$	−432438.			−0.905665			−0.452833	−	0.891596i	$-0.649587\pi$
$691$	−432438.			−0.905665			−0.452833	+	0.891596i	$0.649587\pi$
$692$	−37912.0	−	37912.0i	−0.0791707	−	0.0791707i
$693$	303202.	−	303202.i	0.631343	−	0.631343i
$694$		−	25916.0i		−	0.0538083i
$695$	−279200.	+	209400.i	−0.578024	+	0.433518i
$696$	6400.00			0.0132118
$697$	−249038.	−	249038.i	−0.512625	−	0.512625i
$698$	−65840.0	+	65840.0i	−0.135138	+	0.135138i
$699$		−	107442.i		−	0.219897i
$700$	64600.0	+	117800.i	0.131837	+	0.240408i
$701$	−895838.			−1.82303			−0.911514	−	0.411269i	$-0.865086\pi$
$701$	−895838.			−1.82303			−0.911514	+	0.411269i	$0.865086\pi$
$702$	−63360.0	−	63360.0i	−0.128570	−	0.128570i
$703$	−5640.00	+	5640.00i	−0.0114122	+	0.0114122i
$704$		−	103424.i		−	0.208678i
$705$	13770.0	+	18360.0i	0.0277048	+	0.0369398i
$706$	−215676.			−0.432706
$707$	−31958.0	−	31958.0i	−0.0639353	−	0.0639353i
$708$	−36800.0	+	36800.0i	−0.0734144	+	0.0734144i
$709$			64360.0i			0.128033i	0.997949	+	0.0640167i	$0.0203911\pi$
$709$			64360.0i			0.128033i	−0.997949	+	0.0640167i	$0.979609\pi$
$710$	−34780.0	+	243460.i	−0.0689942	+	0.482960i
$711$	606720.			1.20019
$712$	90880.0	+	90880.0i	0.179270	+	0.179270i
$713$	−410078.	+	410078.i	−0.806654	+	0.806654i
$714$			36328.0i			0.0712599i
$715$	699930.	+	99990.0i	1.36912	+	0.195589i
$716$	263360.			0.513717
$717$	−45600.0	−	45600.0i	−0.0887006	−	0.0887006i
$718$	343520.	−	343520.i	0.666351	−	0.666351i
$719$		−	239840.i		−	0.463942i	−0.972723	−	0.231971i	$-0.925483\pi$
$719$		−	239840.i		−	0.463942i	0.972723	−	0.231971i	$-0.0745175\pi$
$720$	−101120.	+	75840.0i	−0.195062	+	0.146296i
$721$	−266798.			−0.513230
$722$	257442.	+	257442.i	0.493861	+	0.493861i
$723$	−57038.0	+	57038.0i	−0.109116	+	0.109116i
$724$		−	324464.i		−	0.618998i
$725$	120000.	+	35000.0i	0.228300	+	0.0665874i
$726$	104652.			0.198552
$727$	−438339.	−	438339.i	−0.829357	−	0.829357i	0.158071	−	0.987428i	$-0.449472\pi$
$727$	−438339.	−	438339.i	−0.829357	−	0.829357i	−0.987428	+	0.158071i	$0.949472\pi$
$728$	−60192.0	+	60192.0i	−0.113573	+	0.113573i
$729$		−	454321.i		−	0.854885i
$730$	208740.	+	278320.i	0.391706	+	0.522274i
$731$	362802.			0.678946
$732$	16656.0	+	16656.0i	0.0310848	+	0.0310848i
$733$	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	$0.188771\pi$
$734$			609044.i			1.13046i
$735$	−8395.00	+	58765.0i	−0.0155398	+	0.108779i
$736$	−138496.			−0.255671
$737$	1.02636e6	+	1.02636e6i	1.88958	+	1.88958i
$738$	−164636.	+	164636.i	−0.302282	+	0.302282i
$739$		−	738040.i		−	1.35142i	−0.737167	−	0.675711i	$-0.763837\pi$
$739$		−	738040.i		−	1.35142i	0.737167	−	0.675711i	$-0.236163\pi$
$740$	39480.0	+	5640.00i	0.0720964	+	0.0102995i
$741$	−7920.00			−0.0144241
$742$	138244.	+	138244.i	0.251095	+	0.251095i
$743$	579101.	−	579101.i	1.04900	−	1.04900i	0.0502671	−	0.998736i	$-0.483993\pi$
$743$	579101.	−	579101.i	1.04900	−	1.04900i	0.998736	−	0.0502671i	$-0.0160073\pi$
$744$		−	24256.0i		−	0.0438201i
$745$	−180000.	+	135000.i	−0.324310	+	0.243232i
$746$	−285356.			−0.512754
$747$	480399.	+	480399.i	0.860916	+	0.860916i
$748$	386224.	−	386224.i	0.690297	−	0.690297i
$749$			82042.0i			0.146242i
$750$	58500.0	−	22000.0i	0.104000	−	0.0391111i
$751$	−495318.			−0.878222			−0.439111	−	0.898433i	$-0.644706\pi$
$751$	−495318.			−0.878222			−0.439111	+	0.898433i	$0.644706\pi$
$752$	29376.0	+	29376.0i	0.0519466	+	0.0519466i
$753$	39402.0	−	39402.0i	0.0694910	−	0.0694910i
$754$			79200.0i			0.139310i
$755$	356970.	+	475960.i	0.626236	+	0.834981i
$756$	48640.0			0.0851040
$757$	−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	$0.980546\pi$
$758$	−345200.	+	345200.i	−0.600803	+	0.600803i
$759$		−	218564.i		−	0.379398i
$760$	−3200.00	+	22400.0i	−0.00554017	+	0.0387812i
$761$	−908798.			−1.56927			−0.784636	−	0.619957i	$-0.787150\pi$
$761$	−908798.			−1.56927			−0.784636	+	0.619957i	$0.787150\pi$
$762$	3284.00	+	3284.00i	0.00565579	+	0.00565579i
$763$	−5320.00	+	5320.00i	−0.00913824	+	0.00913824i
$764$			264016.i			0.452318i
$765$	−660835.	−	94405.0i	−1.12920	−	0.161314i
$766$	633684.			1.07998
$767$	−455400.	−	455400.i	−0.774109	−	0.77

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(1.00000 - 1.00000i) q^{3} +8.00000i q^{4} +(-15.0000 - 20.0000i) q^{5} +4.00000 q^{6} +(-19.0000 - 19.0000i) q^{7} +(-16.0000 + 16.0000i) q^{8} +79.0000i q^{9} +(10.0000 - 70.0000i) q^{10} +202.000 q^{11} +(8.00000 + 8.00000i) q^{12} +(-99.0000 + 99.0000i) q^{13} -76.0000i q^{14} +(-35.0000 - 5.00000i) q^{15} -64.0000 q^{16} +(-239.000 - 239.000i) q^{17} +(-158.000 + 158.000i) q^{18} +40.0000i q^{19} +(160.000 - 120.000i) q^{20} -38.0000 q^{21} +(404.000 + 404.000i) q^{22} +(541.000 - 541.000i) q^{23} +32.0000i q^{24} +(-175.000 + 600.000i) q^{25} -396.000 q^{26} +(160.000 + 160.000i) q^{27} +(152.000 - 152.000i) q^{28} -200.000i q^{29} +(-60.0000 - 80.0000i) q^{30} -758.000 q^{31} +(-128.000 - 128.000i) q^{32} +(202.000 - 202.000i) q^{33} -956.000i q^{34} +(-95.0000 + 665.000i) q^{35} -632.000 q^{36} +(141.000 + 141.000i) q^{37} +(-80.0000 + 80.0000i) q^{38} +198.000i q^{39} +(560.000 + 80.0000i) q^{40} +1042.00 q^{41} +(-76.0000 - 76.0000i) q^{42} +(-759.000 + 759.000i) q^{43} +1616.00i q^{44} +(1580.00 - 1185.00i) q^{45} +2164.00 q^{46} +(-459.000 - 459.000i) q^{47} +(-64.0000 + 64.0000i) q^{48} -1679.00i q^{49} +(-1550.00 + 850.000i) q^{50} -478.000 q^{51} +(-792.000 - 792.000i) q^{52} +(-1819.00 + 1819.00i) q^{53} +640.000i q^{54} +(-3030.00 - 4040.00i) q^{55} +608.000 q^{56} +(40.0000 + 40.0000i) q^{57} +(400.000 - 400.000i) q^{58} +4600.00i q^{59} +(40.0000 - 280.000i) q^{60} +2082.00 q^{61} +(-1516.00 - 1516.00i) q^{62} +(1501.00 - 1501.00i) q^{63} -512.000i q^{64} +(3465.00 + 495.000i) q^{65} +808.000 q^{66} +(5081.00 + 5081.00i) q^{67} +(1912.00 - 1912.00i) q^{68} -1082.00i q^{69} +(-1520.00 + 1140.00i) q^{70} -3478.00 q^{71} +(-1264.00 - 1264.00i) q^{72} +(-3479.00 + 3479.00i) q^{73} +564.000i q^{74} +(425.000 + 775.000i) q^{75} -320.000 q^{76} +(-3838.00 - 3838.00i) q^{77} +(-396.000 + 396.000i) q^{78} -7680.00i q^{79} +(960.000 + 1280.00i) q^{80} -6079.00 q^{81} +(2084.00 + 2084.00i) q^{82} +(6081.00 - 6081.00i) q^{83} -304.000i q^{84} +(-1195.00 + 8365.00i) q^{85} -3036.00 q^{86} +(-200.000 - 200.000i) q^{87} +(-3232.00 + 3232.00i) q^{88} -5680.00i q^{89} +(5530.00 + 790.000i) q^{90} +3762.00 q^{91} +(4328.00 + 4328.00i) q^{92} +(-758.000 + 758.000i) q^{93} -1836.00i q^{94} +(800.000 - 600.000i) q^{95} -256.000 q^{96} +(561.000 + 561.000i) q^{97} +(3358.00 - 3358.00i) q^{98} +15958.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 2 q^{3} - 30 q^{5} + 8 q^{6} - 38 q^{7} - 32 q^{8} + 20 q^{10} + 404 q^{11} + 16 q^{12} - 198 q^{13} - 70 q^{15} - 128 q^{16} - 478 q^{17} - 316 q^{18} + 320 q^{20} - 76 q^{21} + 808 q^{22}+ \cdots + 6716 q^{98}+O(q^{100}) \) 2 * q + 4 * q^2 + 2 * q^3 - 30 * q^5 + 8 * q^6 - 38 * q^7 - 32 * q^8 + 20 * q^10 + 404 * q^11 + 16 * q^12 - 198 * q^13 - 70 * q^15 - 128 * q^16 - 478 * q^17 - 316 * q^18 + 320 * q^20 - 76 * q^21 + 808 * q^22 + 1082 * q^23 - 350 * q^25 - 792 * q^26 + 320 * q^27 + 304 * q^28 - 120 * q^30 - 1516 * q^31 - 256 * q^32 + 404 * q^33 - 190 * q^35 - 1264 * q^36 + 282 * q^37 - 160 * q^38 + 1120 * q^40 + 2084 * q^41 - 152 * q^42 - 1518 * q^43 + 3160 * q^45 + 4328 * q^46 - 918 * q^47 - 128 * q^48 - 3100 * q^50 - 956 * q^51 - 1584 * q^52 - 3638 * q^53 - 6060 * q^55 + 1216 * q^56 + 80 * q^57 + 800 * q^58 + 80 * q^60 + 4164 * q^61 - 3032 * q^62 + 3002 * q^63 + 6930 * q^65 + 1616 * q^66 + 10162 * q^67 + 3824 * q^68 - 3040 * q^70 - 6956 * q^71 - 2528 * q^72 - 6958 * q^73 + 850 * q^75 - 640 * q^76 - 7676 * q^77 - 792 * q^78 + 1920 * q^80 - 12158 * q^81 + 4168 * q^82 + 12162 * q^83 - 2390 * q^85 - 6072 * q^86 - 400 * q^87 - 6464 * q^88 + 11060 * q^90 + 7524 * q^91 + 8656 * q^92 - 1516 * q^93 + 1600 * q^95 - 512 * q^96 + 1122 * q^97 + 6716 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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