LMFDB - Embedded newform 230.5.c.a.229.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(229,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.229");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.c (of order $2$, degree $1$, 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:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.6
Character	$\chi$	$=$	230.229
Dual form			230.5.c.a.229.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843i q^{2} -13.4757i q^{3} -8.00000 q^{4} +(20.1787 + 14.7587i) q^{5} +38.1149 q^{6} +78.6574 q^{7} -22.6274i q^{8} -100.593 q^{9} +O(q^{10})$	\(q+2.82843i q^{2} -13.4757i q^{3} -8.00000 q^{4} +(20.1787 + 14.7587i) q^{5} +38.1149 q^{6} +78.6574 q^{7} -22.6274i q^{8} -100.593 q^{9} +(-41.7439 + 57.0741i) q^{10} +67.9692i q^{11} +107.805i q^{12} +229.153i q^{13} +222.477i q^{14} +(198.883 - 271.922i) q^{15} +64.0000 q^{16} +80.2906 q^{17} -284.521i q^{18} +377.665i q^{19} +(-161.430 - 118.069i) q^{20} -1059.96i q^{21} -192.246 q^{22} +(-481.515 - 219.052i) q^{23} -304.919 q^{24} +(189.363 + 595.623i) q^{25} -648.142 q^{26} +264.032i q^{27} -629.259 q^{28} +1489.97 q^{29} +(769.111 + 562.526i) q^{30} -1339.29 q^{31} +181.019i q^{32} +915.929 q^{33} +227.096i q^{34} +(1587.21 + 1160.88i) q^{35} +804.746 q^{36} +975.738 q^{37} -1068.20 q^{38} +3087.98 q^{39} +(333.951 - 456.593i) q^{40} +2823.50 q^{41} +2998.02 q^{42} -748.713 q^{43} -543.753i q^{44} +(-2029.85 - 1484.62i) q^{45} +(619.574 - 1361.93i) q^{46} +2124.13i q^{47} -862.442i q^{48} +3785.99 q^{49} +(-1684.68 + 535.598i) q^{50} -1081.97i q^{51} -1833.22i q^{52} +2437.98 q^{53} -746.796 q^{54} +(-1003.14 + 1371.53i) q^{55} -1779.81i q^{56} +5089.28 q^{57} +4214.28i q^{58} -4873.47 q^{59} +(-1591.06 + 2175.37i) q^{60} -4852.60i q^{61} -3788.08i q^{62} -7912.41 q^{63} -512.000 q^{64} +(-3381.99 + 4624.01i) q^{65} +2590.64i q^{66} +6915.37 q^{67} -642.325 q^{68} +(-2951.88 + 6488.73i) q^{69} +(-3283.46 + 4489.30i) q^{70} -1704.35 q^{71} +2276.17i q^{72} -1135.02i q^{73} +2759.80i q^{74} +(8026.41 - 2551.78i) q^{75} -3021.32i q^{76} +5346.28i q^{77} +8734.13i q^{78} -7424.39i q^{79} +(1291.44 + 944.556i) q^{80} -4590.05 q^{81} +7986.07i q^{82} +6146.88 q^{83} +8479.68i q^{84} +(1620.16 + 1184.98i) q^{85} -2117.68i q^{86} -20078.4i q^{87} +1537.97 q^{88} -8566.65i q^{89} +(4199.15 - 5741.27i) q^{90} +18024.6i q^{91} +(3852.12 + 1752.42i) q^{92} +18047.8i q^{93} -6007.95 q^{94} +(-5573.84 + 7620.80i) q^{95} +2439.35 q^{96} -921.872 q^{97} +10708.4i q^{98} -6837.24i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) $ 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9	$ 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49} - 3264 q^{50} + 10112 q^{54} + 12824 q^{55} + 7092 q^{59} - 24576 q^{64} + 14000 q^{69} - 6592 q^{70} - 12708 q^{71} + 24728 q^{75} - 13040 q^{81} - 15700 q^{85} - 9728 q^{94} - 46608 q^{95} - 4096 q^{96}+O(q^{100}) $ 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$			2.82843i			0.707107i
$2$			2.82843i			0.707107i
$3$		−	13.4757i		−	1.49730i	−0.662968	−	0.748648i	$-0.730704\pi$
$3$		−	13.4757i		−	1.49730i	0.662968	−	0.748648i	$-0.269296\pi$
$4$	−8.00000			−0.500000
$5$	20.1787	+	14.7587i	0.807149	+	0.590347i
$5$	20.1787	+	14.7587i	0.807149	+	0.590347i
$6$	38.1149			1.05875
$7$	78.6574			1.60525			0.802627	−	0.596481i	$-0.203435\pi$
$7$	78.6574			1.60525			0.802627	+	0.596481i	$0.203435\pi$
$8$		−	22.6274i		−	0.353553i
$9$	−100.593			−1.24189
$10$	−41.7439	+	57.0741i	−0.417439	+	0.570741i
$11$			67.9692i			0.561729i	0.959747	+	0.280864i	$0.0906211\pi$
$11$			67.9692i			0.561729i	−0.959747	+	0.280864i	$0.909379\pi$
$12$			107.805i			0.748648i
$13$			229.153i			1.35593i	0.735093	+	0.677966i	$0.237139\pi$
$13$			229.153i			1.35593i	−0.735093	+	0.677966i	$0.762861\pi$
$14$			222.477i			1.13509i
$15$	198.883	−	271.922i	0.883924	−	1.20854i
$16$	64.0000			0.250000
$17$	80.2906			0.277822			0.138911	−	0.990305i	$-0.455640\pi$
$17$	80.2906			0.277822			0.138911	+	0.990305i	$0.455640\pi$
$18$		−	284.521i		−	0.878151i
$19$			377.665i			1.04616i	0.852283	+	0.523081i	$0.175218\pi$
$19$			377.665i			1.04616i	−0.852283	+	0.523081i	$0.824782\pi$
$20$	−161.430	−	118.069i	−0.403575	−	0.295174i
$21$		−	1059.96i		−	2.40354i
$22$	−192.246			−0.397202
$23$	−481.515	−	219.052i	−0.910237	−	0.414088i
$23$	−481.515	−	219.052i	−0.910237	−	0.414088i
$24$	−304.919			−0.529374
$25$	189.363	+	595.623i	0.302980	+	0.952997i
$26$	−648.142			−0.958789
$27$			264.032i			0.362184i
$28$	−629.259			−0.802627
$29$	1489.97			1.77167			0.885835	−	0.464001i	$-0.153587\pi$
$29$	1489.97			1.77167			0.885835	+	0.464001i	$0.153587\pi$
$30$	769.111	+	562.526i	0.854567	+	0.625029i
$31$	−1339.29			−1.39364			−0.696821	−	0.717245i	$-0.745403\pi$
$31$	−1339.29			−1.39364			−0.696821	+	0.717245i	$0.745403\pi$
$32$			181.019i			0.176777i
$33$	915.929			0.841074
$34$			227.096i			0.196450i
$35$	1587.21	+	1160.88i	1.29568	+	0.947657i
$36$	804.746			0.620946
$37$	975.738			0.712738			0.356369	−	0.934345i	$-0.384015\pi$
$37$	975.738			0.712738			0.356369	+	0.934345i	$0.384015\pi$
$38$	−1068.20			−0.739749
$39$	3087.98			2.03023
$40$	333.951	−	456.593i	0.208719	−	0.285370i
$41$	2823.50			1.67966			0.839828	−	0.542853i	$-0.182656\pi$
$41$	2823.50			1.67966			0.839828	+	0.542853i	$0.182656\pi$
$42$	2998.02			1.69956
$43$	−748.713			−0.404929			−0.202464	−	0.979290i	$-0.564895\pi$
$43$	−748.713			−0.404929			−0.202464	+	0.979290i	$0.564895\pi$
$44$		−	543.753i		−	0.280864i
$45$	−2029.85	−	1484.62i	−1.00239	−	0.733148i
$46$	619.574	−	1361.93i	0.292804	−	0.643635i
$47$			2124.13i			0.961580i	0.876836	+	0.480790i	$0.159650\pi$
$47$			2124.13i			0.961580i	−0.876836	+	0.480790i	$0.840350\pi$
$48$		−	862.442i		−	0.374324i
$49$	3785.99			1.57684
$50$	−1684.68	+	535.598i	−0.673871	+	0.214239i
$51$		−	1081.97i		−	0.415982i
$52$		−	1833.22i		−	0.677966i
$53$	2437.98			0.867919			0.433959	−	0.900932i	$-0.357116\pi$
$53$	2437.98			0.867919			0.433959	+	0.900932i	$0.357116\pi$
$54$	−746.796			−0.256103
$55$	−1003.14	+	1371.53i	−0.331615	+	0.453399i
$56$		−	1779.81i		−	0.567543i
$57$	5089.28			1.56641
$58$			4214.28i			1.25276i
$59$	−4873.47			−1.40002			−0.700010	−	0.714133i	$-0.746821\pi$
$59$	−4873.47			−1.40002			−0.700010	+	0.714133i	$0.746821\pi$
$60$	−1591.06	+	2175.37i	−0.441962	+	0.604270i
$61$		−	4852.60i		−	1.30411i	−0.758171	−	0.652056i	$-0.773907\pi$
$61$		−	4852.60i		−	1.30411i	0.758171	−	0.652056i	$-0.226093\pi$
$62$		−	3788.08i		−	0.985454i
$63$	−7912.41			−1.99355
$64$	−512.000			−0.125000
$65$	−3381.99	+	4624.01i	−0.800471	+	1.09444i
$66$			2590.64i			0.594729i
$67$	6915.37			1.54052			0.770258	−	0.637733i	$-0.220128\pi$
$67$	6915.37			1.54052			0.770258	+	0.637733i	$0.220128\pi$
$68$	−642.325			−0.138911
$69$	−2951.88	+	6488.73i	−0.620012	+	1.36289i
$70$	−3283.46	+	4489.30i	−0.670095	+	0.916184i
$71$	−1704.35			−0.338098			−0.169049	−	0.985608i	$-0.554070\pi$
$71$	−1704.35			−0.338098			−0.169049	+	0.985608i	$0.554070\pi$
$72$			2276.17i			0.439075i
$73$		−	1135.02i		−	0.212988i	−0.994313	−	0.106494i	$-0.966037\pi$
$73$		−	1135.02i		−	0.212988i	0.994313	−	0.106494i	$-0.0339626\pi$
$74$			2759.80i			0.503982i
$75$	8026.41	−	2551.78i	1.42692	−	0.453651i
$76$		−	3021.32i		−	0.523081i
$77$			5346.28i			0.901717i
$78$			8734.13i			1.43559i
$79$		−	7424.39i		−	1.18962i	−0.803868	−	0.594808i	$-0.797228\pi$
$79$		−	7424.39i		−	1.18962i	0.803868	−	0.594808i	$-0.202772\pi$
$80$	1291.44	+	944.556i	0.201787	+	0.147587i
$81$	−4590.05			−0.699596
$82$			7986.07i			1.18770i
$83$	6146.88			0.892275			0.446138	−	0.894964i	$-0.352799\pi$
$83$	6146.88			0.892275			0.446138	+	0.894964i	$0.352799\pi$
$84$			8479.68i			1.20177i
$85$	1620.16	+	1184.98i	0.224244	+	0.164012i
$86$		−	2117.68i		−	0.286328i
$87$		−	20078.4i		−	2.65271i
$88$	1537.97			0.198601
$89$		−	8566.65i		−	1.08151i	−0.841180	−	0.540755i	$-0.818138\pi$
$89$		−	8566.65i		−	1.08151i	0.841180	−	0.540755i	$-0.181862\pi$
$90$	4199.15	−	5741.27i	0.518414	−	0.708799i
$91$			18024.6i			2.17662i
$92$	3852.12	+	1752.42i	0.455118	+	0.207044i
$93$			18047.8i			2.08669i
$94$	−6007.95			−0.679940
$95$	−5573.84	+	7620.80i	−0.617599	+	0.844410i
$96$	2439.35			0.264687
$97$	−921.872			−0.0979777			−0.0489889	−	0.998799i	$-0.515600\pi$
$97$	−921.872			−0.0979777			−0.0489889	+	0.998799i	$0.515600\pi$
$98$			10708.4i			1.11499i
$99$		−	6837.24i		−	0.697607i
$100$	−1514.90	−	4764.98i	−0.151490	−	0.476498i
$101$	−5940.51			−0.582346			−0.291173	−	0.956670i	$-0.594046\pi$
$101$	−5940.51			−0.582346			−0.291173	+	0.956670i	$0.594046\pi$
$102$	3060.27			0.294144
$103$	−18663.5			−1.75921			−0.879607	−	0.475702i	$-0.842194\pi$
$103$	−18663.5			−1.75921			−0.879607	+	0.475702i	$0.842194\pi$
$104$	5185.13			0.479395
$105$	15643.6	−	21388.7i	1.41892	−	1.94001i
$106$			6895.66i			0.613711i
$107$	−2500.06			−0.218365			−0.109183	−	0.994022i	$-0.534823\pi$
$107$	−2500.06			−0.218365			−0.109183	+	0.994022i	$0.534823\pi$
$108$		−	2112.26i		−	0.181092i
$109$		−	9372.32i		−	0.788849i	−0.918928	−	0.394425i	$-0.870944\pi$
$109$		−	9372.32i		−	0.788849i	0.918928	−	0.394425i	$-0.129056\pi$
$110$	−3879.28	−	2837.30i	−0.320601	−	0.234487i
$111$		−	13148.7i		−	1.06718i
$112$	5034.08			0.401313
$113$	−10686.0			−0.836869			−0.418435	−	0.908247i	$-0.637421\pi$
$113$	−10686.0			−0.836869			−0.418435	+	0.908247i	$0.637421\pi$
$114$			14394.7i			1.10762i
$115$	−6483.44	−	11526.7i	−0.490242	−	0.871587i
$116$	−11919.8			−0.885835
$117$		−	23051.2i		−	1.68392i
$118$		−	13784.3i		−	0.989964i
$119$	6315.46			0.445975
$120$	−6152.88	−	4500.21i	−0.427284	−	0.312514i
$121$	10021.2			0.684461
$122$	13725.2			0.922146
$123$		−	38048.5i		−	2.51494i
$124$	10714.3			0.696821
$125$	−4969.52	+	14813.7i	−0.318049	+	0.948074i
$126$		−	22379.7i		−	1.40965i
$127$		−	8603.37i		−	0.533410i	−0.963778	−	0.266705i	$-0.914065\pi$
$127$		−	8603.37i		−	0.533410i	0.963778	−	0.266705i	$-0.0859349\pi$
$128$		−	1448.15i		−	0.0883883i
$129$			10089.4i			0.606298i
$130$	−13078.7	−	9565.72i	−0.773886	−	0.566019i
$131$	−804.458			−0.0468771			−0.0234386	−	0.999725i	$-0.507461\pi$
$131$	−804.458			−0.0468771			−0.0234386	+	0.999725i	$0.507461\pi$
$132$	−7327.43			−0.420537
$133$			29706.1i			1.67936i
$134$			19559.6i			1.08931i
$135$	−3896.77	+	5327.84i	−0.213815	+	0.292337i
$136$		−	1816.77i		−	0.0982250i
$137$	−3987.93			−0.212474			−0.106237	−	0.994341i	$-0.533880\pi$
$137$	−3987.93			−0.212474			−0.106237	+	0.994341i	$0.533880\pi$
$138$	−18352.9	−	8349.16i	−0.963711	−	0.438414i
$139$	13382.5			0.692640			0.346320	−	0.938116i	$-0.387431\pi$
$139$	13382.5			0.692640			0.346320	+	0.938116i	$0.387431\pi$
$140$	−12697.7	−	9287.04i	−0.647840	−	0.473829i
$141$	28624.0			1.43977
$142$		−	4820.63i		−	0.239071i
$143$	−15575.3			−0.761666
$144$	−6437.97			−0.310473
$145$	30065.8	+	21990.1i	1.43000	+	1.04590i
$146$	3210.31			0.150606
$147$		−	51018.7i		−	2.36099i
$148$	−7805.90			−0.356369
$149$			10784.6i			0.485769i	0.970055	+	0.242884i	$0.0780935\pi$
$149$			10784.6i			0.485769i	−0.970055	+	0.242884i	$0.921906\pi$
$150$	7217.54	+	22702.1i	0.320779	+	1.00898i
$151$	−1140.06			−0.0500005			−0.0250003	−	0.999687i	$-0.507959\pi$
$151$	−1140.06			−0.0500005			−0.0250003	+	0.999687i	$0.507959\pi$
$152$	8545.58			0.369874
$153$	−8076.70			−0.345025
$154$	−15121.6			−0.637610
$155$	−27025.2	−	19766.2i	−1.12488	−	0.822733i
$156$	−24703.9			−1.01512
$157$	17206.4			0.698058			0.349029	−	0.937112i	$-0.386511\pi$
$157$	17206.4			0.698058			0.349029	+	0.937112i	$0.386511\pi$
$158$	20999.3			0.841185
$159$		−	32853.4i		−	1.29953i
$160$	−2671.61	+	3652.74i	−0.104360	+	0.142685i
$161$	−37874.8	−	17230.1i	−1.46116	−	0.664716i
$162$		−	12982.6i		−	0.494689i
$163$		−	29401.3i		−	1.10660i	−0.832982	−	0.553300i	$-0.813368\pi$
$163$		−	29401.3i		−	1.10660i	0.832982	−	0.553300i	$-0.186632\pi$
$164$	−22588.0			−0.839828
$165$	18482.3	+	13517.9i	0.678872	+	0.496526i
$166$			17386.0i			0.630934i
$167$			38742.0i			1.38915i	0.719420	+	0.694575i	$0.244408\pi$
$167$			38742.0i			1.38915i	−0.719420	+	0.694575i	$0.755592\pi$
$168$	−23984.2			−0.849779
$169$	−23949.9			−0.838554
$170$	−3351.64	+	4582.51i	−0.115974	+	0.158565i
$171$		−	37990.5i		−	1.29922i
$172$	5989.71			0.202464
$173$			4313.19i			0.144114i	0.997401	+	0.0720570i	$0.0229563\pi$
$173$			4313.19i			0.144114i	−0.997401	+	0.0720570i	$0.977044\pi$
$174$	56790.2			1.87575
$175$	14894.8	+	46850.2i	0.486360	+	1.52980i
$176$			4350.03i			0.140432i
$177$			65673.2i			2.09624i
$178$	24230.1			0.764744
$179$	−35650.2			−1.11264			−0.556322	−	0.830967i	$-0.687788\pi$
$179$	−35650.2			−1.11264			−0.556322	+	0.830967i	$0.687788\pi$
$180$	16238.8	+	11877.0i	0.501196	+	0.366574i
$181$		−	30803.5i		−	0.940248i	−0.882600	−	0.470124i	$-0.844209\pi$
$181$		−	30803.5i		−	0.940248i	0.882600	−	0.470124i	$-0.155791\pi$
$182$	−50981.2			−1.53910
$183$	−65392.0			−1.95264
$184$	−4956.59	+	10895.4i	−0.146402	+	0.321817i
$185$	19689.2	+	14400.6i	0.575286	+	0.420763i
$186$	−51046.9			−1.47551
$187$			5457.29i			0.156061i
$188$		−	16993.0i		−	0.480790i
$189$			20768.1i			0.581398i
$190$	−21554.9	−	15765.2i	−0.597088	−	0.436709i
$191$			68240.0i			1.87056i	0.353905	+	0.935282i	$0.384854\pi$
$191$			68240.0i			1.87056i	−0.353905	+	0.935282i	$0.615146\pi$
$192$			6899.54i			0.187162i
$193$		−	12814.1i		−	0.344011i	−0.985096	−	0.172006i	$-0.944975\pi$
$193$		−	12814.1i		−	0.344011i	0.985096	−	0.172006i	$-0.0550247\pi$
$194$		−	2607.45i		−	0.0692807i
$195$	62311.6	+	45574.5i	1.63870	+	1.19854i
$196$	−30287.9			−0.788420
$197$			67613.4i			1.74221i	0.491098	+	0.871104i	$0.336596\pi$
$197$			67613.4i			1.74221i	−0.491098	+	0.871104i	$0.663404\pi$
$198$	19338.6			0.493282
$199$			13588.2i			0.343127i	0.985173	+	0.171564i	$0.0548819\pi$
$199$			13588.2i			0.343127i	−0.985173	+	0.171564i	$0.945118\pi$
$200$	13477.4	−	4284.79i	0.336935	−	0.107120i
$201$		−	93189.2i		−	2.30661i
$202$		−	16802.3i		−	0.411781i
$203$	117198.			2.84398
$204$			8655.75i			0.207991i
$205$	56974.7	+	41671.2i	1.35573	+	0.991580i
$206$		−	52788.3i		−	1.24395i
$207$	48437.2	+	22035.2i	1.13042	+	0.514252i
$208$			14665.8i			0.338983i
$209$	−25669.6			−0.587660
$210$	60496.3	+	44246.8i	1.37180	+	1.00333i
$211$	−34724.2			−0.779950			−0.389975	−	0.920825i	$-0.627516\pi$
$211$	−34724.2			−0.779950			−0.389975	+	0.920825i	$0.627516\pi$
$212$	−19503.9			−0.433959
$213$			22967.3i			0.506232i
$214$		−	7071.25i		−	0.154408i
$215$	−15108.1	−	11050.0i	−0.326838	−	0.239049i
$216$	5974.37			0.128051
$217$	−105345.			−2.23715
$218$	26508.9			0.557801
$219$	−15295.1			−0.318907
$220$	8025.08	−	10972.3i	0.165808	−	0.226699i
$221$			18398.8i			0.376708i
$222$	37190.2			0.754609
$223$			21046.2i			0.423217i	0.977355	+	0.211608i	$0.0678702\pi$
$223$			21046.2i			0.423217i	−0.977355	+	0.211608i	$0.932130\pi$
$224$			14238.5i			0.283771i
$225$	−19048.6	−	59915.7i	−0.376269	−	1.18352i
$226$		−	30224.5i		−	0.591756i
$227$	−21261.6			−0.412615			−0.206307	−	0.978487i	$-0.566145\pi$
$227$	−21261.6			−0.412615			−0.206307	+	0.978487i	$0.566145\pi$
$228$	−40714.2			−0.783207
$229$			8226.29i			0.156867i	0.996919	+	0.0784337i	$0.0249919\pi$
$229$			8226.29i			0.156867i	−0.996919	+	0.0784337i	$0.975008\pi$
$230$	32602.5	−	18337.9i	0.616305	−	0.346653i
$231$	72044.6			1.35014
$232$		−	33714.3i		−	0.626380i
$233$		−	55103.9i		−	1.01501i	−0.861649	−	0.507505i	$-0.830568\pi$
$233$		−	55103.9i		−	1.01501i	0.861649	−	0.507505i	$-0.169432\pi$
$234$	65198.7			1.19071
$235$	−31349.4	+	42862.3i	−0.567666	+	0.776139i
$236$	38987.8			0.700010
$237$	−100049.			−1.78120
$238$			17862.8i			0.315352i
$239$	47334.7			0.828674			0.414337	−	0.910123i	$-0.364013\pi$
$239$	47334.7			0.828674			0.414337	+	0.910123i	$0.364013\pi$
$240$	12728.5	−	17403.0i	0.220981	−	0.302135i
$241$		−	82352.4i		−	1.41789i	−0.705264	−	0.708945i	$-0.749172\pi$
$241$		−	82352.4i		−	1.41789i	0.705264	−	0.708945i	$-0.250828\pi$
$242$			28344.2i			0.483987i
$243$			83240.5i			1.40969i
$244$			38820.8i			0.652056i
$245$	76396.5	+	55876.3i	1.27275	+	0.930883i
$246$	107617.			1.77833
$247$	−86542.9			−1.41853
$248$			30304.7i			0.492727i
$249$		−	82833.3i		−	1.33600i
$250$	−41899.4	−	14055.9i	−0.670390	−	0.224895i
$251$		−	109931.i		−	1.74490i	−0.488700	−	0.872452i	$-0.662529\pi$
$251$		−	109931.i		−	1.74490i	0.488700	−	0.872452i	$-0.337471\pi$
$252$	63299.3			0.996776
$253$	14888.8	−	32728.2i	0.232605	−	0.511306i
$254$	24334.0			0.377178
$255$	15968.4	−	21832.8i	0.245574	−	0.335760i
$256$	4096.00			0.0625000
$257$			85664.9i			1.29699i	0.761219	+	0.648495i	$0.224601\pi$
$257$			85664.9i			1.29699i	−0.761219	+	0.648495i	$0.775399\pi$
$258$	−28537.1			−0.428717
$259$	76749.0			1.14412
$260$	27055.9	−	36992.1i	0.400236	−	0.547220i
$261$	−149881.			−2.20022
$262$		−	2275.35i		−	0.0331471i
$263$	−2810.25			−0.0406287			−0.0203144	−	0.999794i	$-0.506467\pi$
$263$	−2810.25			−0.0406287			−0.0203144	+	0.999794i	$0.506467\pi$
$264$		−	20725.1i		−	0.297364i
$265$	49195.4	+	35981.4i	0.700540	+	0.512374i
$266$	−84021.7			−1.18748
$267$	−115441.			−1.61934
$268$	−55323.0			−0.770258
$269$	−98491.8			−1.36112			−0.680559	−	0.732693i	$-0.738263\pi$
$269$	−98491.8			−1.36112			−0.680559	+	0.732693i	$0.738263\pi$
$270$	−15069.4	−	11021.7i	−0.206713	−	0.151190i
$271$	73725.8			1.00388			0.501939	−	0.864903i	$-0.332620\pi$
$271$	73725.8			1.00388			0.501939	+	0.864903i	$0.332620\pi$
$272$	5138.60			0.0694556
$273$	242893.			3.25904
$274$		−	11279.6i		−	0.150242i
$275$	−40484.0	+	12870.8i	−0.535326	+	0.170193i
$276$	23615.0	−	51909.9i	0.310006	−	0.681447i
$277$		−	134224.i		−	1.74933i	−0.484729	−	0.874664i	$-0.661082\pi$
$277$		−	134224.i		−	1.74933i	0.484729	−	0.874664i	$-0.338918\pi$
$278$			37851.4i			0.489771i
$279$	134724.			1.73075
$280$	26267.7	−	35914.4i	0.335047	−	0.458092i
$281$			42871.7i			0.542947i	0.962446	+	0.271474i	$0.0875110\pi$
$281$			42871.7i			0.542947i	−0.962446	+	0.271474i	$0.912489\pi$
$282$			80961.0i			1.01807i
$283$	−76094.8			−0.950127			−0.475064	−	0.879951i	$-0.657575\pi$
$283$	−76094.8			−0.950127			−0.475064	+	0.879951i	$0.657575\pi$
$284$	13634.8			0.169049
$285$	102695.	+	75111.1i	1.26433	+	0.924729i
$286$		−	44053.6i		−	0.538579i
$287$	222089.			2.69627
$288$		−	18209.3i		−	0.219538i
$289$	−77074.4			−0.922815
$290$	−62197.3	+	85038.9i	−0.739563	+	1.01116i
$291$			12422.8i			0.146702i
$292$			9080.13i			0.106494i
$293$	82943.7			0.966158			0.483079	−	0.875577i	$-0.339518\pi$
$293$	82943.7			0.966158			0.483079	+	0.875577i	$0.339518\pi$
$294$	144303.			1.66948
$295$	−98340.5	−	71926.0i	−1.13003	−	0.826498i
$296$		−	22078.4i		−	0.251991i
$297$	−17946.1			−0.203449
$298$	−30503.3			−0.343490
$299$	50196.4	−	110341.i	0.561475	−	1.23422i
$300$	−64211.3	+	20414.3i	−0.713459	+	0.226825i
$301$	−58891.9			−0.650013
$302$		−	3224.58i		−	0.0353557i
$303$			80052.3i			0.871944i
$304$			24170.5i			0.261541i
$305$	71618.0	−	97919.3i	0.769879	−	1.05261i
$306$		−	22844.4i		−	0.243970i
$307$		−	10809.7i		−	0.114693i	−0.998354	−	0.0573464i	$-0.981736\pi$
$307$		−	10809.7i		−	0.114693i	0.998354	−	0.0573464i	$-0.0182639\pi$
$308$		−	42770.2i		−	0.450859i
$309$			251503.i			2.63406i
$310$	55907.1	−	76438.7i	0.581760	−	0.795408i
$311$	−115136.			−1.19040			−0.595199	−	0.803579i	$-0.702927\pi$
$311$	−115136.			−1.19040			−0.595199	+	0.803579i	$0.702927\pi$
$312$		−	69873.1i		−	0.717795i
$313$	111089.			1.13392			0.566962	−	0.823744i	$-0.308119\pi$
$313$	111089.			1.13392			0.566962	+	0.823744i	$0.308119\pi$
$314$			48667.2i			0.493602i
$315$	−159662.	−	116777.i	−1.60909	−	1.17689i
$316$			59395.1i			0.594808i
$317$			71652.6i			0.713039i	0.934288	+	0.356519i	$0.116037\pi$
$317$			71652.6i			0.713039i	−0.934288	+	0.356519i	$0.883963\pi$
$318$	92923.5			0.918907
$319$			101272.i			0.995197i
$320$	−10331.5	−	7556.45i	−0.100894	−	0.0737934i
$321$			33690.0i			0.326957i
$322$	48734.1	−	107126.i	0.470025	−	1.03320i
$323$			30323.0i			0.290647i
$324$	36720.4			0.349798
$325$	−136489.	+	43392.9i	−1.29220	+	0.410821i
$326$	83159.3			0.782485
$327$	−126298.			−1.18114
$328$		−	63888.5i		−	0.593848i
$329$			167079.i			1.54358i
$330$	−38234.4	+	52275.8i	−0.351097	+	0.480035i
$331$	−84835.5			−0.774322			−0.387161	−	0.922012i	$-0.626544\pi$
$331$	−84835.5			−0.774322			−0.387161	+	0.922012i	$0.626544\pi$
$332$	−49175.1			−0.446138
$333$	−98152.7			−0.885144
$334$	−109579.			−0.982278
$335$	139543.	+	102062.i	1.24343	+	0.909439i
$336$		−	67837.5i		−	0.600885i
$337$	29134.5			0.256535			0.128268	−	0.991740i	$-0.459058\pi$
$337$	29134.5			0.256535			0.128268	+	0.991740i	$0.459058\pi$
$338$		−	67740.6i		−	0.592947i
$339$			144001.i			1.25304i
$340$	−12961.3	−	9479.87i	−0.112122	−	0.0820058i
$341$		−	91030.4i		−	0.782849i
$342$	107453.			0.918689
$343$	108940.			0.925974
$344$			16941.4i			0.143164i
$345$	−155330.	+	87368.7i	−1.30502	+	0.734036i
$346$	−12199.5			−0.101904
$347$			147752.i			1.22708i	0.789662	+	0.613542i	$0.210256\pi$
$347$			147752.i			1.22708i	−0.789662	+	0.613542i	$0.789744\pi$
$348$			160627.i			1.32636i
$349$	−6408.38			−0.0526136			−0.0263068	−	0.999654i	$-0.508375\pi$
$349$	−6408.38			−0.0526136			−0.0263068	+	0.999654i	$0.508375\pi$
$350$	−132512.	+	42128.8i	−1.08173	+	0.343908i
$351$	−60503.7			−0.491098
$352$	−12303.7			−0.0993005
$353$		−	12380.9i		−	0.0993581i	−0.998765	−	0.0496790i	$-0.984180\pi$
$353$		−	12380.9i		−	0.0993581i	0.998765	−	0.0496790i	$-0.0158198\pi$
$354$	−185752.			−1.48227
$355$	−34391.7	−	25154.0i	−0.272896	−	0.199595i
$356$			68533.2i			0.540755i
$357$		−	85104.9i		−	0.667757i
$358$		−	100834.i		−	0.786758i
$359$		−	164179.i		−	1.27388i	−0.770912	−	0.636942i	$-0.780199\pi$
$359$		−	164179.i		−	1.27388i	0.770912	−	0.636942i	$-0.219801\pi$
$360$	−33593.2	+	45930.2i	−0.259207	+	0.354399i
$361$	−12309.7			−0.0944569
$362$	87125.4			0.664856
$363$		−	135042.i		−	1.02484i
$364$		−	144196.i		−	1.08831i
$365$	16751.3	−	22903.2i	0.125737	−	0.171914i
$366$		−	184956.i		−	1.38073i
$367$	−122351.			−0.908397			−0.454198	−	0.890901i	$-0.650074\pi$
$367$	−122351.			−0.908397			−0.454198	+	0.890901i	$0.650074\pi$
$368$	−30817.0	−	14019.4i	−0.227559	−	0.103522i
$369$	−284025.			−2.08595
$370$	−40731.1	+	55689.3i	−0.297524	+	0.406788i
$371$	191766.			1.39323
$372$		−	144382.i		−	1.04335i
$373$	−186135.			−1.33786			−0.668930	−	0.743326i	$-0.733247\pi$
$373$	−186135.			−1.33786			−0.668930	+	0.743326i	$0.733247\pi$
$374$	−15435.5			−0.110352
$375$	199624.	+	66967.5i	1.41955	+	0.476213i
$376$	48063.6			0.339970
$377$			341431.i			2.40226i
$378$	−58741.1			−0.411110
$379$		−	260261.i		−	1.81188i	−0.423403	−	0.905942i	$-0.639164\pi$
$379$		−	260261.i		−	1.81188i	0.423403	−	0.905942i	$-0.360836\pi$
$380$	44590.7	−	60966.4i	0.308800	−	0.422205i
$381$	−115936.			−0.798672
$382$	−193012.			−1.32269
$383$	87223.5			0.594615			0.297308	−	0.954782i	$-0.403911\pi$
$383$	87223.5			0.594615			0.297308	+	0.954782i	$0.403911\pi$
$384$	−19514.8			−0.132343
$385$	−78904.1	+	107881.i	−0.532326	+	0.727820i
$386$	36243.7			0.243253
$387$	75315.5			0.502878
$388$	7374.98			0.0489889
$389$			55040.4i			0.363733i	0.983323	+	0.181866i	$0.0582138\pi$
$389$			55040.4i			0.363733i	−0.983323	+	0.181866i	$0.941786\pi$
$390$	−128904.	+	176244.i	−0.847497	+	1.15874i
$391$	−38661.2	−	17587.9i	−0.252884	−	0.115043i
$392$		−	85667.2i		−	0.557497i
$393$			10840.6i			0.0701889i
$394$	−191239.			−1.23193
$395$	109574.	−	149815.i	0.702286	−	0.960197i
$396$			54697.9i			0.348803i
$397$		−	148622.i		−	0.942981i	−0.881871	−	0.471491i	$-0.843716\pi$
$397$		−	148622.i		−	0.942981i	0.881871	−	0.471491i	$-0.156284\pi$
$398$	−38433.2			−0.242628
$399$	400310.			2.51449
$400$	12119.2	+	38119.9i	0.0757450	+	0.238249i
$401$		−	46972.8i		−	0.292118i	−0.989276	−	0.146059i	$-0.953341\pi$
$401$		−	46972.8i		−	0.292118i	0.989276	−	0.146059i	$-0.0466589\pi$
$402$	263579.			1.63102
$403$		−	306902.i		−	1.88968i
$404$	47524.1			0.291173
$405$	−92621.3	−	67743.1i	−0.564678	−	0.413004i
$406$			331485.i			2.01100i
$407$			66320.1i			0.400365i
$408$	−24482.2			−0.147072
$409$	−166918.			−0.997829			−0.498914	−	0.866651i	$-0.666268\pi$
$409$	−166918.			−0.997829			−0.498914	+	0.866651i	$0.666268\pi$
$410$	−117864.	+	161149.i	−0.701153	+	0.958648i
$411$			53740.0i			0.318137i
$412$	149308.			0.879607
$413$	−383335.			−2.24739
$414$	−62325.0	+	137001.i	−0.363631	+	0.799325i
$415$	124036.	+	90719.9i	0.720199	+	0.526752i
$416$	−41481.1			−0.239697
$417$		−	180338.i		−	1.03709i
$418$		−	72604.5i		−	0.415538i
$419$			167816.i			0.955886i	0.878391	+	0.477943i	$0.158617\pi$
$419$			167816.i			0.955886i	−0.878391	+	0.477943i	$0.841383\pi$
$420$	−125149.	+	171109.i	−0.709461	+	0.970007i
$421$		−	74932.3i		−	0.422771i	−0.977403	−	0.211385i	$-0.932203\pi$
$421$		−	74932.3i		−	0.422771i	0.977403	−	0.211385i	$-0.0677975\pi$
$422$		−	98214.7i		−	0.551508i
$423$		−	213673.i		−	1.19418i
$424$		−	55165.3i		−	0.306856i
$425$	15204.0	+	47823.0i	0.0841746	+	0.264764i
$426$	−64961.2			−0.357960
$427$		−	381693.i		−	2.09343i
$428$	20000.5			0.109183
$429$			209888.i			1.14044i
$430$	31254.2	−	42732.1i	0.169033	−	0.231109i
$431$		−	243632.i		−	1.31153i	−0.754964	−	0.655767i	$-0.772346\pi$
$431$		−	243632.i		−	1.31153i	0.754964	−	0.655767i	$-0.227654\pi$
$432$			16898.1i			0.0905461i
$433$	146164.			0.779586			0.389793	−	0.920903i	$-0.372547\pi$
$433$	146164.			0.779586			0.389793	+	0.920903i	$0.372547\pi$
$434$		−	297961.i		−	1.58190i
$435$	296330.	−	405156.i	1.56602	−	2.14113i
$436$			74978.6i			0.394425i
$437$	82728.4	−	181851.i	0.433203	−	0.952256i
$438$		−	43261.0i		−	0.225501i
$439$	132110.			0.685501			0.342750	−	0.939426i	$-0.388641\pi$
$439$	132110.			0.685501			0.342750	+	0.939426i	$0.388641\pi$
$440$	31034.2	+	22698.4i	0.160301	+	0.117244i
$441$	−380845.			−1.95827
$442$	−52039.7			−0.266373
$443$		−	206261.i		−	1.05102i	−0.850789	−	0.525508i	$-0.823875\pi$
$443$		−	206261.i		−	1.05102i	0.850789	−	0.525508i	$-0.176125\pi$
$444$			105190.i			0.533589i
$445$	126432.	−	172864.i	0.638467	−	0.872941i
$446$	−59527.5			−0.299260
$447$	145329.			0.727339
$448$	−40272.6			−0.200657
$449$	233634.			1.15889			0.579447	−	0.815010i	$-0.303269\pi$
$449$	233634.			1.15889			0.579447	+	0.815010i	$0.303269\pi$
$450$	169467.	−	53877.6i	0.836875	−	0.266062i
$451$			191911.i			0.943511i
$452$	85487.8			0.418435
$453$			15363.1i			0.0748655i
$454$		−	60136.9i		−	0.291763i
$455$	−266019.	+	363713.i	−1.28496	+	1.75685i
$456$		−	115157.i		−	0.553811i
$457$	352986.			1.69015			0.845074	−	0.534649i	$-0.179556\pi$
$457$	352986.			1.69015			0.845074	+	0.534649i	$0.179556\pi$
$458$	−23267.5			−0.110922
$459$			21199.3i			0.100623i
$460$	51867.6	+	92213.9i	0.245121	+	0.435793i
$461$	−11192.8			−0.0526669			−0.0263334	−	0.999653i	$-0.508383\pi$
$461$	−11192.8			−0.0526669			−0.0263334	+	0.999653i	$0.508383\pi$
$462$			203773.i			0.954691i
$463$			120852.i			0.563759i	0.959450	+	0.281879i	$0.0909578\pi$
$463$			120852.i			0.563759i	−0.959450	+	0.281879i	$0.909042\pi$
$464$	95358.3			0.442917
$465$	−266362.	+	364182.i	−1.23187	+	1.68427i
$466$	155857.			0.717721
$467$	−203571.			−0.933429			−0.466715	−	0.884408i	$-0.654562\pi$
$467$	−203571.			−0.933429			−0.466715	+	0.884408i	$0.654562\pi$
$468$			184410.i			0.841961i
$469$	543946.			2.47292
$470$	−121233.	−	88669.4i	−0.548813	−	0.401401i
$471$		−	231868.i		−	1.04520i
$472$			110274.i			0.494982i
$473$		−	50889.4i		−	0.227460i
$474$		−	282980.i		−	1.25950i
$475$	−224946.	+	71515.6i	−0.996990	+	0.316967i
$476$	−50523.7			−0.222988
$477$	−245245.			−1.07786
$478$			133883.i			0.585961i
$479$		−	325797.i		−	1.41996i	−0.704222	−	0.709980i	$-0.748704\pi$
$479$		−	325797.i		−	1.41996i	0.704222	−	0.709980i	$-0.251296\pi$
$480$	49223.1	+	36001.7i	0.213642	+	0.156257i
$481$			223593.i			0.966424i
$482$	232928.			1.00260
$483$	−232187.	+	510387.i	−0.995276	+	2.18779i
$484$	−80169.5			−0.342230
$485$	−18602.2	−	13605.6i	−0.0790826	−	0.0578409i
$486$	−235440.			−0.996798
$487$			5022.90i			0.0211786i	0.999944	+	0.0105893i	$0.00337074\pi$
$487$			5022.90i			0.0211786i	−0.999944	+	0.0105893i	$0.996629\pi$
$488$	−109802.			−0.461073
$489$	−396201.			−1.65691
$490$	−158042.	+	216082.i	−0.658234	+	0.899967i
$491$	221213.			0.917587			0.458794	−	0.888543i	$-0.348282\pi$
$491$	221213.			0.917587			0.458794	+	0.888543i	$0.348282\pi$
$492$			304388.i			1.25747i
$493$	119631.			0.492209
$494$		−	244780.i		−	1.00305i
$495$	100909.	−	137967.i	0.411830	−	0.563073i
$496$	−85714.5			−0.348410
$497$	−134060.			−0.542733
$498$	234288.			0.944694
$499$	−303573.			−1.21916			−0.609581	−	0.792724i	$-0.708662\pi$
$499$	−303573.			−1.21916			−0.609581	+	0.792724i	$0.708662\pi$
$500$	39756.1	−	118509.i	0.159024	−	0.474037i
$501$	522074.			2.07997
$502$	310931.			1.23383
$503$	341324.			1.34906			0.674529	−	0.738249i	$-0.264347\pi$
$503$	341324.			1.34906			0.674529	+	0.738249i	$0.264347\pi$
$504$			179037.i			0.704827i
$505$	−119872.	−	87674.2i	−0.470040	−	0.343787i
$506$	92569.3	+	42111.9i	0.361548	+	0.164477i
$507$			322741.i			1.25556i
$508$			68827.0i			0.266705i
$509$	−150867.			−0.582318			−0.291159	−	0.956675i	$-0.594041\pi$
$509$	−150867.			−0.582318			−0.291159	+	0.956675i	$0.594041\pi$
$510$	61752.4	+	45165.6i	0.237418	+	0.173647i
$511$		−	89277.4i		−	0.341901i
$512$			11585.2i			0.0441942i
$513$	−99715.7			−0.378904
$514$	−242297.			−0.917110
$515$	−376606.	−	275449.i	−1.41995	−	1.03855i
$516$		−	80715.2i		−	0.303149i
$517$	−144375.			−0.540147
$518$			217079.i			0.809018i
$519$	58123.0			0.215781
$520$	104629.	+	76525.7i	0.386943	+	0.283009i
$521$		−	411255.i		−	1.51508i	−0.652788	−	0.757540i	$-0.726401\pi$
$521$		−	411255.i		−	1.51508i	0.652788	−	0.757540i	$-0.273599\pi$
$522$		−	423929.i		−	1.55579i
$523$	−37560.3			−0.137317			−0.0686587	−	0.997640i	$-0.521872\pi$
$523$	−37560.3			−0.137317			−0.0686587	+	0.997640i	$0.521872\pi$
$524$	6435.67			0.0234386
$525$	631337.	−	200717.i	2.29056	−	0.728224i
$526$		−	7948.58i		−	0.0287288i
$527$	−107532.			−0.387185
$528$	58619.5			0.210268
$529$	183873.	+	210954.i	0.657063	+	0.753836i
$530$	−101771.	+	139146.i	−0.362303	+	0.495357i
$531$	490238.			1.73867
$532$		−	237649.i		−	0.839679i
$533$			647013.i			2.27750i
$534$		−	326517.i		−	1.14505i
$535$	−50448.1	−	36897.7i	−0.176253	−	0.128911i
$536$		−	156477.i		−	0.544654i
$537$			480410.i			1.66596i
$538$		−	278577.i		−	0.962455i
$539$			257331.i			0.885756i
$540$	31174.2	−	42622.7i	0.106907	−	0.146168i
$541$	−294823.			−1.00732			−0.503659	−	0.863902i	$-0.668013\pi$
$541$	−294823.			−1.00732			−0.503659	+	0.863902i	$0.668013\pi$
$542$			208528.i			0.709849i
$543$	−415097.			−1.40783
$544$			14534.2i			0.0491125i
$545$	138323.	−	189122.i	0.465695	−	0.636719i
$546$			687004.i			2.30449i
$547$		−	486491.i		−	1.62593i	−0.582316	−	0.812963i	$-0.697853\pi$
$547$		−	486491.i		−	1.62593i	0.582316	−	0.812963i	$-0.302147\pi$
$548$	31903.5			0.106237
$549$			488139.i			1.61957i
$550$	−36404.2	−	114506.i	−0.120344	−	0.378532i
$551$			562711.i			1.85345i
$552$	146823.	+	66793.3i	0.481856	+	0.219207i
$553$		−	583983.i		−	1.90963i
$554$	379643.			1.23696
$555$	194058.	−	265324.i	0.630006	−	0.861372i
$556$	−107060.			−0.346320
$557$	−439683.			−1.41719			−0.708597	−	0.705613i	$-0.750672\pi$
$557$	−439683.			−1.41719			−0.708597	+	0.705613i	$0.750672\pi$
$558$			381056.i			1.22383i
$559$		−	171570.i		−	0.549056i
$560$	101581.	+	74296.3i	0.323920	+	0.236914i
$561$	73540.5			0.233669
$562$	−121259.			−0.383922
$563$	193996.			0.612033			0.306017	−	0.952026i	$-0.401004\pi$
$563$	193996.			0.612033			0.306017	+	0.952026i	$0.401004\pi$
$564$	−228992.			−0.719885
$565$	−215630.	−	157711.i	−0.675478	−	0.494043i
$566$		−	215228.i		−	0.671842i
$567$	−361041.			−1.12303
$568$			38565.1i			0.119536i
$569$			368901.i			1.13942i	0.821845	+	0.569711i	$0.192945\pi$
$569$			368901.i			1.13942i	−0.821845	+	0.569711i	$0.807055\pi$
$570$	−212446.	+	290466.i	−0.653882	+	0.894017i
$571$			77383.3i			0.237342i	0.992934	+	0.118671i	$0.0378634\pi$
$571$			77383.3i			0.237342i	−0.992934	+	0.118671i	$0.962137\pi$
$572$	124603.			0.380833
$573$	919579.			2.80078
$574$			628164.i			1.90655i
$575$	39291.7	−	328282.i	0.118841	−	0.992913i
$576$	51503.8			0.155237
$577$			332739.i			0.999429i	0.866190	+	0.499715i	$0.166562\pi$
$577$			332739.i			0.999429i	−0.866190	+	0.499715i	$0.833438\pi$
$578$		−	217999.i		−	0.652529i
$579$	−172678.			−0.515086
$580$	−240526.	−	175920.i	−0.715001	−	0.522950i
$581$	483498.			1.43233
$582$	−35137.1			−0.103734
$583$			165708.i			0.487535i
$584$	−25682.5			−0.0753028
$585$	340206.	−	465144.i	0.994099	−	1.35918i
$586$			234600.i			0.683177i
$587$		−	318035.i		−	0.922993i	−0.887142	−	0.461496i	$-0.847313\pi$
$587$		−	318035.i		−	0.922993i	0.887142	−	0.461496i	$-0.152687\pi$
$588$			408150.i			1.18050i
$589$		−	505803.i		−	1.45798i
$590$	203437.	−	278149.i	0.584422	−	0.799049i
$591$	911134.			2.60860
$592$	62447.2			0.178184
$593$			380812.i			1.08293i	0.840723	+	0.541465i	$0.182130\pi$
$593$			380812.i			1.08293i	−0.840723	+	0.541465i	$0.817870\pi$
$594$		−	50759.1i		−	0.143860i
$595$	127438.	+	93207.8i	0.359969	+	0.263280i
$596$		−	86276.4i		−	0.242884i
$597$	183110.			0.513763
$598$	312090.	+	141977.i	0.872725	+	0.397023i
$599$	176552.			0.492061			0.246030	−	0.969262i	$-0.420874\pi$
$599$	176552.			0.492061			0.246030	+	0.969262i	$0.420874\pi$
$600$	−57740.3	−	181617.i	−0.160390	−	0.504492i
$601$	−235642.			−0.652386			−0.326193	−	0.945303i	$-0.605766\pi$
$601$	−235642.			−0.652386			−0.326193	+	0.945303i	$0.605766\pi$
$602$		−	166571.i		−	0.459629i
$603$	−695640.			−1.91315
$604$	9120.50			0.0250003
$605$	202215.	+	147900.i	0.552462	+	0.404070i
$606$	−226422.			−0.616558
$607$			239145.i			0.649059i	0.945876	+	0.324530i	$0.105206\pi$
$607$			239145.i			0.649059i	−0.945876	+	0.324530i	$0.894794\pi$
$608$	−68364.6			−0.184937
$609$		−	1.57931e6i		−	4.25828i
$610$	276958.	+	202566.i	0.744310	+	0.544387i
$611$	−486750.			−1.30384
$612$	64613.6			0.172513
$613$	232706.			0.619280			0.309640	−	0.950854i	$-0.399791\pi$
$613$	232706.			0.619280			0.309640	+	0.950854i	$0.399791\pi$
$614$	30574.4			0.0811000
$615$	561546.	−	767771.i	1.48469	−	2.02993i
$616$	120973.			0.318805
$617$	−41374.8			−0.108684			−0.0543419	−	0.998522i	$-0.517306\pi$
$617$	−41374.8			−0.108684			−0.0543419	+	0.998522i	$0.517306\pi$
$618$	−711357.			−1.86256
$619$			261832.i			0.683347i	0.939819	+	0.341673i	$0.110994\pi$
$619$			261832.i			0.683347i	−0.939819	+	0.341673i	$0.889006\pi$
$620$	216201.	+	158129.i	0.562438	+	0.411366i
$621$	57836.9	−	127136.i	0.149976	−	0.329674i
$622$		−	325655.i		−	0.841738i
$623$		−	673830.i		−	1.73610i
$624$	197631.			0.507558
$625$	−318909.	+	225577.i	−0.816406	+	0.577478i
$626$			314208.i			0.801806i
$627$			345914.i			0.879900i
$628$	−137652.			−0.349029
$629$	78342.6			0.198014
$630$	330295.	−	451593.i	0.832186	−	1.13780i
$631$			608081.i			1.52722i	0.645675	+	0.763612i	$0.276576\pi$
$631$			608081.i			1.52722i	−0.645675	+	0.763612i	$0.723424\pi$
$632$	−167995.			−0.420592
$633$			467931.i			1.16782i
$634$	−202664.			−0.504195
$635$	126974.	−	173605.i	0.314897	−	0.430542i
$636$			262827.i			0.649765i
$637$			867570.i			2.13809i
$638$	−286441.			−0.703711
$639$	171446.			0.419881
$640$	21372.9	−	29221.9i	0.0521798	−	0.0713426i
$641$			200750.i			0.488585i	0.969702	+	0.244292i	$0.0785557\pi$
$641$			200750.i			0.488585i	−0.969702	+	0.244292i	$0.921444\pi$
$642$	−95289.7			−0.231194
$643$	257007.			0.621616			0.310808	−	0.950473i	$-0.399400\pi$
$643$	257007.			0.621616			0.310808	+	0.950473i	$0.399400\pi$
$644$	302998.	+	137841.i	0.730581	+	0.332358i
$645$	−148906.	+	203591.i	−0.357926	+	0.489373i
$646$	−85766.3			−0.205519
$647$			452974.i			1.08209i	0.840993	+	0.541046i	$0.181972\pi$
$647$			452974.i			1.08209i	−0.840993	+	0.541046i	$0.818028\pi$
$648$			103861.i			0.247344i
$649$		−	331246.i		−	0.786432i
$650$	−122734.	−	386048.i	−0.290494	−	0.913723i
$651$			1.41959e6i			3.34967i
$652$			235210.i			0.553300i
$653$		−	114734.i		−	0.269071i	−0.990909	−	0.134535i	$-0.957046\pi$
$653$		−	114734.i		−	0.269071i	0.990909	−	0.134535i	$-0.0429542\pi$
$654$		−	357225.i		−	0.835192i
$655$	−16233.0	−	11872.7i	−0.0378368	−	0.0276738i
$656$	180704.			0.419914
$657$			114175.i			0.264509i
$658$	−472570.			−1.09148
$659$		−	381641.i		−	0.878787i	−0.898295	−	0.439394i	$-0.855193\pi$
$659$		−	381641.i		−	0.878787i	0.898295	−	0.439394i	$-0.144807\pi$
$660$	−147858.	−	108143.i	−0.339436	−	0.248263i
$661$		−	828287.i		−	1.89574i	−0.318663	−	0.947868i	$-0.603234\pi$
$661$		−	828287.i		−	1.89574i	0.318663	−	0.947868i	$-0.396766\pi$
$662$		−	239951.i		−	0.547529i
$663$	247936.			0.564044
$664$		−	139088.i		−	0.315467i
$665$	−438424.	+	599432.i	−0.991404	+	1.35549i
$666$		−	277618.i		−	0.625891i
$667$	−717445.	−	326382.i	−1.61264	−	0.733627i
$668$		−	309936.i		−	0.694575i
$669$	283611.			0.633681
$670$	−288674.	+	394689.i	−0.643071	+	0.879235i
$671$	329827.			0.732557
$672$	191873.			0.424890
$673$		−	406762.i		−	0.898070i	−0.893514	−	0.449035i	$-0.851768\pi$
$673$		−	406762.i		−	0.898070i	0.893514	−	0.449035i	$-0.148232\pi$
$674$			82404.7i			0.181398i
$675$	−157264.	+	49997.8i	−0.345160	+	0.109735i
$676$	191599.			0.419277
$677$	206060.			0.449589			0.224795	−	0.974406i	$-0.427829\pi$
$677$	206060.			0.449589			0.224795	+	0.974406i	$0.427829\pi$
$678$	−407295.			−0.886033
$679$	−72512.1			−0.157279
$680$	26813.1	−	36660.1i	0.0579869	−	0.0792823i
$681$			286514.i			0.617806i
$682$	257473.			0.553557
$683$		−	69587.4i		−	0.149173i	−0.997215	−	0.0745863i	$-0.976236\pi$
$683$		−	69587.4i		−	0.149173i	0.997215	−	0.0745863i	$-0.0237636\pi$
$684$			303924.i			0.649611i
$685$	−80471.4	−	58856.6i	−0.171499	−	0.125434i
$686$			308129.i			0.654763i
$687$	110855.			0.234877
$688$	−47917.6			−0.101232
$689$			558670.i			1.17684i
$690$	−247116.	−	439340.i	−0.519042	−	0.922790i
$691$	383342.			0.802842			0.401421	−	0.915894i	$-0.368516\pi$
$691$	383342.			0.802842			0.401421	+	0.915894i	$0.368516\pi$
$692$		−	34505.5i		−	0.0720570i
$693$		−	537800.i		−	1.11984i
$694$	−417906.			−0.867679
$695$	270042.	+	197508.i	0.559064	+	0.408898i
$696$	−454322.			−0.937875
$697$	226701.			0.466646
$698$		−	18125.6i		−	0.0372034i
$699$	−742561.			−1.51977
$700$	−119158.	−	374801.i	−0.243180	−	0.764901i
$701$		−	452419.i		−	0.920672i	−0.887745	−	0.460336i	$-0.847729\pi$
$701$		−	452419.i		−	0.920672i	0.887745	−	0.460336i	$-0.152271\pi$
$702$		−	171130.i		−	0.347258i
$703$			368502.i			0.745640i
$704$		−	34800.2i		−	0.0702161i
$705$	577597.	+	422453.i	1.16211	+	0.849964i
$706$	35018.5			0.0702568
$707$	−467266.			−0.934813
$708$		−	525386.i		−	1.04812i
$709$			75384.0i			0.149964i	0.997185	+	0.0749819i	$0.0238899\pi$
$709$			75384.0i			0.149964i	−0.997185	+	0.0749819i	$0.976110\pi$
$710$	71146.2	−	97274.3i	0.141135	−	0.192966i
$711$			746844.i			1.47737i
$712$	−193841.			−0.382372
$713$	644889.	+	293375.i	1.26854	+	0.577090i
$714$	240713.			0.472175
$715$	−314290.	−	229871.i	−0.614778	−	0.449648i
$716$	285202.			0.556322
$717$		−	637866.i		−	1.24077i
$718$	464370.			0.900772
$719$	−853144.			−1.65031			−0.825153	−	0.564909i	$-0.808911\pi$
$719$	−853144.			−1.65031			−0.825153	+	0.564909i	$0.808911\pi$
$720$	−129910.	−	95016.0i	−0.250598	−	0.183287i
$721$	−1.46802e6			−2.82398
$722$		−	34817.1i		−	0.0667911i
$723$	−1.10975e6			−2.12300
$724$			246428.i			0.470124i
$725$	282145.	+	887463.i	0.536781	+	1.68840i
$726$	381957.			0.724671
$727$	−952918.			−1.80296			−0.901481	−	0.432818i	$-0.857519\pi$
$727$	−952918.			−1.80296			−0.901481	+	0.432818i	$0.857519\pi$
$728$	407849.			0.769550
$729$	749927.			1.41112
$730$	64780.0	+	47379.9i	0.121561	+	0.0889096i
$731$	−60114.7			−0.112498
$732$	523136.			0.976320
$733$	−803771.			−1.49598			−0.747988	−	0.663713i	$-0.768980\pi$
$733$	−803771.			−1.49598			−0.747988	+	0.663713i	$0.768980\pi$
$734$		−	346061.i		−	0.642333i
$735$	752969.	−	1.02949e6i	1.39381	−	1.90568i
$736$	39652.7	−	87163.6i	0.0732011	−	0.160909i
$737$			470032.i			0.865352i
$738$		−	803345.i		−	1.47499i
$739$	−665698.			−1.21896			−0.609479	−	0.792803i	$-0.708621\pi$
$739$	−665698.			−1.21896			−0.609479	+	0.792803i	$0.708621\pi$
$740$	−157513.	−	115205.i	−0.287643	−	0.210381i
$741$			1.16622e6i			2.12395i
$742$			542395.i			0.985162i
$743$	969220.			1.75568			0.877839	−	0.478956i	$-0.158985\pi$
$743$	969220.			1.75568			0.877839	+	0.478956i	$0.158985\pi$
$744$	408375.			0.737757
$745$	−159166.	+	217619.i	−0.286772	+	0.392088i
$746$		−	526469.i		−	0.946010i
$747$	−618335.			−1.10811
$748$		−	43658.3i		−	0.0780304i
$749$	−196649.			−0.350532
$750$	−189413.	+	564621.i	−0.336734	+	1.00377i
$751$			157812.i			0.279807i	0.990165	+	0.139904i	$0.0446793\pi$
$751$			157812.i			0.279807i	−0.990165	+	0.139904i	$0.955321\pi$
$752$			135944.i			0.240395i
$753$	−1.48139e6			−2.61264
$754$	−965714.			−1.69866
$755$	−23005.0	−	16825.8i	−0.0403579	−	0.0295177i
$756$		−	166145.i		−	0.290699i
$757$	37297.6			0.0650863			0.0325431	−	0.999470i	$-0.489639\pi$
$757$	37297.6			0.0650863			0.0325431	+	0.999470i	$0.489639\pi$
$758$	736128.			1.28119
$759$	−441034.	−	200637.i	−0.765576	−	0.348278i
$760$	172439.	+	126121.i	0.298544	+	0.218354i
$761$	−289646.			−0.500147			−0.250073	−	0.968227i	$-0.580455\pi$
$761$	−289646.			−0.500147			−0.250073	+	0.968227i	$0.580455\pi$
$762$		−	327917.i		−	0.564747i
$763$		−	737203.i		−	1.26630i
$764$		−	545920.i		−	0.935282i
$765$	−162978.	−	119201.i	−0.278487	−	0.203685i
$766$			246705.i			0.420456i
$767$		−	1.11677e6i		−	1.89833i
$768$		−	55196.3i		−	0.0935809i
$769$		−	12373.7i		−	0.0209241i	−0.999945	−	0.0104621i	$-0.996670\pi$
$769$		−	12373.7i		−	0.0209241i	0.999945	−	0.0104621i	$-0.00333024\pi$
$770$	−305134.	−	223174.i	−0.514647	−	0.376412i
$771$	1.15439e6			1.94198
$772$			102513.i			0.172006i
$773$	−215041.			−0.359884			−0.179942	−	0.983677i	$-0.557591\pi$
$773$	−215041.			−0.359884			−0.179942	+	0.983677i	$0.557591\pi$
$774$			213024.i			0.355588i
$775$	−253611.	−	797712.i	−0.422246	−	1.32814i
$776$			20859.6i			0.0346404i
$777$		−	1.03424e6i		−	1.71309i
$778$	−155678.			−0.257198
$779$			1.06634e6i			1.75719i
$780$	−498493.	−	364596.i	−0.819350	−	0.599271i
$781$		−	115843.i		−	0.189919i
$782$	49746.0	−	109350.i	0.0813476	−	0.178816i
$783$			393401.i			0.641671i
$784$	242304.			0.394210
$785$	347204.	+	253944.i	0.563437	+	0.412097i
$786$	−30661.9			−0.0496310
$787$	559223.			0.902892			0.451446	−	0.892298i	$-0.350908\pi$
$787$	559223.			0.902892			0.451446	+	0.892298i	$0.350908\pi$
$788$		−	540907.i		−	0.871104i
$789$			37869.9i			0.0608332i
$790$	423740.	+	309923.i	0.678962	+	0.496591i
$791$	−840532.			−1.34339
$792$	−154709.			−0.246641
$793$	1.11199e6			1.76829
$794$	420367.			0.666788
$795$	484873.	−	662941.i	0.767174	−	1.04892i
$796$		−	108705.i		−	0.171564i
$797$	327937.			0.516266			0.258133	−	0.966109i	$-0.416893\pi$
$797$	327937.			0.516266			0.258133	+	0.966109i	$0.416893\pi$
$798$			1.13225e6i			1.77802i
$799$			170548.i			0.267148i
$800$	−107819.	+	34278.3i	−0.168468	+	0.0535598i
$801$			861747.i			1.34312i
$802$	132859.			0.206558
$803$	77146.1			0.119642
$804$			745513.i			1.15330i
$805$	−509971.	−	906663.i	−0.786962	−	1.39912i
$806$	868049.			1.33621
$807$			1.32724e6i			2.03799i
$808$			134418.i			0.205890i
$809$	316932.			0.484250			0.242125	−	0.970245i	$-0.422156\pi$
$809$	316932.			0.484250			0.242125	+	0.970245i	$0.422156\pi$
$810$	191606.	−	261973.i	0.292038	−	0.399288i
$811$	613060.			0.932097			0.466048	−	0.884759i	$-0.345677\pi$
$811$	613060.			0.932097			0.466048	+	0.884759i	$0.345677\pi$
$812$	−937580.			−1.42199
$813$		−	993503.i		−	1.50310i
$814$	−187582.			−0.283101
$815$	433924.	−	593280.i	0.653279	−	0.893192i
$816$		−	69246.0i		−	0.103995i
$817$		−	282763.i		−	0.423621i
$818$		−	472115.i		−	0.705571i
$819$		−	1.81315e6i		−	2.70312i
$820$	−455797.	−	333369.i	−0.677867	−	0.495790i
$821$	−1.02986e6			−1.52790			−0.763948	−	0.645278i	$-0.776742\pi$
$821$	−1.02986e6			−1.52790			−0.763948	+	0.645278i	$0.776742\pi$
$822$	−152000.			−0.224957
$823$			697857.i			1.03031i	0.857098	+	0.515154i	$0.172265\pi$
$823$			697857.i			1.03031i	−0.857098	+	0.515154i	$0.827735\pi$
$824$			422307.i			0.621976i
$825$	173443.	+	545548.i	0.254829	+	0.801540i
$826$		−	1.08423e6i		−	1.58914i
$827$	−88464.0			−0.129347			−0.0646734	−	0.997906i	$-0.520601\pi$
$827$	−88464.0			−0.129347			−0.0646734	+	0.997906i	$0.520601\pi$
$828$	−387498.	−	176282.i	−0.565208	−	0.257126i
$829$	−390187.			−0.567759			−0.283879	−	0.958860i	$-0.591622\pi$
$829$	−390187.			−0.567759			−0.283879	+	0.958860i	$0.591622\pi$
$830$	−256595.	+	350828.i	−0.372470	+	0.509258i
$831$	−1.80876e6			−2.61926
$832$		−	117326.i		−	0.169492i
$833$	303980.			0.438081
$834$	510073.			0.733331
$835$	−571781.	+	781765.i	−0.820081	+	1.12125i
$836$	205357.			0.293830
$837$		−	353616.i		−	0.504755i
$838$	−474656.			−0.675913
$839$			382031.i			0.542719i	0.962478	+	0.271360i	$0.0874732\pi$
$839$			382031.i			0.542719i	−0.962478	+	0.271360i	$0.912527\pi$
$840$	−483970.	−	353975.i	−0.685899	−	0.501665i
$841$	1.51274e6			2.13881
$842$	211940.			0.298944
$843$	577724.			0.812953
$844$	277793.			0.389975
$845$	−483279.	−	353469.i	−0.676838	−	0.495038i
$846$	604359.			0.844412
$847$	788241.			1.09873
$848$	156031.			0.216980
$849$			1.02543e6i			1.42262i
$850$	−135264.	+	43003.5i	−0.187216	+	0.0595204i
$851$	−469833.	−	213738.i	−0.648760	−	0.295136i
$852$		−	183738.i		−	0.253116i
$853$		−	499538.i		−	0.686548i	−0.939235	−	0.343274i	$-0.888464\pi$
$853$		−	499538.i		−	0.686548i	0.939235	−	0.343274i	$-0.111536\pi$
$854$	1.07959e6			1.48028
$855$	560690.	−	766601.i	0.766992	−	1.04867i
$856$			56570.0i			0.0772038i
$857$			406696.i			0.553742i	0.960907	+	0.276871i	$0.0892975\pi$
$857$			406696.i			0.553742i	−0.960907	+	0.276871i	$0.910702\pi$
$858$	−593652.			−0.806412
$859$	444389.			0.602251			0.301125	−	0.953585i	$-0.402638\pi$
$859$	444389.			0.602251			0.301125	+	0.953585i	$0.402638\pi$
$860$	120865.	+	88400.2i	0.163419	+	0.119524i
$861$		−	2.99280e6i		−	4.03712i
$862$	689095.			0.927394
$863$			375941.i			0.504776i	0.967626	+	0.252388i	$0.0812158\pi$
$863$			375941.i			0.504776i	−0.967626	+	0.252388i	$0.918784\pi$
$864$	−47795.0			−0.0640257
$865$	−63656.9	+	87034.6i	−0.0850773	+	0.116321i
$866$			413413.i			0.551250i
$867$			1.03863e6i			1.38173i
$868$	842761.			1.11857
$869$	504630.			0.668241
$870$	1.14595e6	+	838149.i	1.51401	+	1.10734i
$871$			1.58468e6i			2.08884i
$872$	−212071.			−0.278900
$873$	92734.2			0.121678
$874$	514353.	+	233991.i	0.673347	+	0.306321i
$875$	−390889.	+	1.16520e6i	−0.510549	+	1.52190i
$876$	122361.			0.159453
$877$		−	5901.77i		−	0.00767331i	−0.999993	−	0.00383666i	$-0.998779\pi$
$877$		−	5901.77i		−	0.00767331i	0.999993	−	0.00383666i	$-0.00122125\pi$
$878$			373665.i			0.484722i
$879$		−	1.11772e6i		−	1.44662i
$880$	−64200.7	+	87778.0i	−0.0829038	+	0.113350i
$881$			274530.i			0.353702i	0.984238	+	0.176851i	$0.0565911\pi$
$881$			274530.i			0.353702i	−0.984238	+	0.176851i	$0.943409\pi$
$882$		−	1.07719e6i		−	1.38470i
$883$			498878.i			0.639842i	0.947444	+	0.319921i	$0.103656\pi$
$883$			498878.i			0.639842i	−0.947444	+	0.319921i	$0.896344\pi$
$884$		−	147191.i		−	0.188354i
$885$	−969250.	+	1.32520e6i	−1.23751	+	1.69198i
$886$	583393.			0.743180
$887$		−	522760.i		−	0.664439i	−0.943202	−	0.332219i	$-0.892203\pi$
$887$		−	522760.i		−	0.664439i	0.943202	−	0.332219i	$-0.107797\pi$
$888$	−297521.			−0.377305
$889$		−	676719.i		−	0.856258i
$890$	488933.	+	357605.i	0.617262	+	0.451464i
$891$		−	311982.i		−	0.392983i
$892$		−	168369.i		−	0.211608i
$893$	−802209.			−1.00597
$894$			411052.i			0.514306i
$895$	−719377.	−	526150.i	−0.898070	−	0.656847i
$896$		−	113908.i		−	0.141886i
$897$	−1.48691e6	−	676430.i	−1.84799	−	0.840694i
$898$			660817.i			0.819461i
$899$	−1.99551e6			−2.46907
$900$	152389.	+	479325.i	0.188134	+	0.591760i
$901$	195747.			0.241127
$902$	−542806.			−0.667163
$903$			793606.i			0.973262i
$904$			241796.i			0.295878i
$905$	454619.	−	621575.i	0.555073	−	0.758921i
$906$	−43453.4			−0.0529379
$907$	1.48998e6			1.81120			0.905602	−	0.424129i	$-0.139420\pi$
$907$	1.48998e6			1.81120			0.905602	+	0.424129i	$0.139420\pi$
$908$	170093.			0.206307
$909$	597576.			0.723211
$910$	−1.02874e6	−	752415.i	−1.24228	−	0.908604i
$911$		−	33800.6i		−	0.0407275i	−0.999793	−	0.0203638i	$-0.993518\pi$
$911$		−	33800.6i		−	0.0407275i	0.999793	−	0.0203638i	$-0.00648244\pi$
$912$	325714.			0.391604
$913$			417799.i			0.501216i
$914$			998395.i			1.19512i
$915$	−1.31953e6	−	965099.i	−1.57607	−	1.15274i
$916$		−	65810.3i		−	0.0784337i
$917$	−63276.6			−0.0752497
$918$	−59960.7			−0.0711511
$919$		−	384434.i		−	0.455188i	−0.973756	−	0.227594i	$-0.926914\pi$
$919$		−	384434.i		−	0.455188i	0.973756	−	0.227594i	$-0.0730859\pi$
$920$	−260820.	+	146704.i	−0.308152	+	0.173327i
$921$	−145667.			−0.171729
$922$		−	31658.1i		−	0.0372411i
$923$		−	390557.i		−	0.458438i
$924$	−576357.			−0.675068
$925$	184768.	+	581172.i	0.215945	+	0.679237i
$926$	−341822.			−0.398638
$927$	1.87742e6			2.18475
$928$			269714.i			0.313190i
$929$	−272424.			−0.315655			−0.157828	−	0.987467i	$-0.550449\pi$
$929$	−272424.			−0.315655			−0.157828	+	0.987467i	$0.550449\pi$
$930$	−1.03006e6	−	753385.i	−1.19096	−	0.871066i
$931$			1.42984e6i			1.64963i
$932$			440831.i			0.507505i
$933$			1.55154e6i			1.78238i
$934$		−	575785.i		−	0.660034i
$935$	−80542.4	+	110121.i	−0.0921300	+	0.125964i
$936$	−521589.			−0.595357
$937$	−218093.			−0.248406			−0.124203	−	0.992257i	$-0.539637\pi$
$937$	−218093.			−0.248406			−0.124203	+	0.992257i	$0.539637\pi$
$938$			1.53851e6i			1.74862i
$939$		−	1.49700e6i		−	1.69782i
$940$	250795.	−	342898.i	0.283833	−	0.388069i
$941$			244862.i			0.276530i	0.990395	+	0.138265i	$0.0441525\pi$
$941$			244862.i			0.276530i	−0.990395	+	0.138265i	$0.955847\pi$
$942$	655822.			0.739068
$943$	−1.35956e6	−	618495.i	−1.52888	−	0.695525i
$944$	−311902.			−0.350005
$945$	−306510.	+	419074.i	−0.343227	+	0.469275i
$946$	143937.			0.160839
$947$			376426.i			0.419739i	0.977729	+	0.209870i	$0.0673040\pi$
$947$			376426.i			0.419739i	−0.977729	+	0.209870i	$0.932696\pi$
$948$	800388.			0.890602
$949$	260092.			0.288798
$950$	−202277.	−	636243.i	−0.224129	−	0.704978i
$951$	965565.			1.06763
$952$		−	142902.i		−	0.157676i
$953$	1.54025e6			1.69591			0.847957	−	0.530064i	$-0.177832\pi$
$953$	1.54025e6			1.69591			0.847957	+	0.530064i	$0.177832\pi$
$954$		−	693657.i		−	0.762163i
$955$	−1.00713e6	+	1.37700e6i	−1.10428	+	1.50982i
$956$	−378678.			−0.414337
$957$	1.36471e6			1.49010
$958$	921493.			1.00406
$959$	−313681.			−0.341075
$960$	−101828.	+	139224.i	−0.110491	+	0.151068i
$961$	870176.			0.942237
$962$	−632416.			−0.683365
$963$	251490.			0.271186
$964$			658820.i			0.708945i
$965$	189119.	−	258572.i	0.203086	−	0.277668i
$966$	−1.44359e6	−	656724.i	−1.54700	−	0.703766i
$967$		−	979883.i		−	1.04790i	−0.851748	−	0.523951i	$-0.824457\pi$
$967$		−	979883.i		−	1.04790i	0.851748	−	0.523951i	$-0.175543\pi$
$968$		−	226754.i		−	0.241993i
$969$	408622.			0.435185
$970$	38482.5	−	52615.0i	0.0408997	−	0.0559199i
$971$		−	37065.4i		−	0.0393125i	−0.999807	−	0.0196562i	$-0.993743\pi$
$971$		−	37065.4i		−	0.0393125i	0.999807	−	0.0196562i	$-0.00625718\pi$
$972$		−	665924.i		−	0.704843i
$973$	1.05263e6			1.11186
$974$	−14206.9			−0.0149755
$975$	584748.	+	1.83927e6i	0.615120	+	1.93480i
$976$		−	310566.i		−	0.326028i
$977$	−1.62145e6			−1.69869			−0.849343	−	0.527841i	$-0.823002\pi$
$977$	−1.62145e6			−1.69869			−0.849343	+	0.527841i	$0.823002\pi$
$978$		−	1.12063e6i		−	1.17161i
$979$	582268.			0.607516
$980$	−611172.	−	447010.i	−0.636373	−	0.465442i
$981$			942792.i			0.979666i
$982$			625685.i			0.648832i
$983$	−168695.			−0.174580			−0.0872900	−	0.996183i	$-0.527821\pi$
$983$	−168695.			−0.174580			−0.0872900	+	0.996183i	$0.527821\pi$
$984$	−860940.			−0.889166
$985$	−997884.	+	1.36435e6i	−1.02851	+	1.40622i
$986$			338367.i			0.348044i
$987$	2.25149e6			2.31119
$988$	692343.			0.709263
$989$	360517.	+	164007.i	0.368581	+	0.167676i
$990$	390229.	+	285413.i	0.398153	+	0.291208i
$991$	1.00540e6			1.02374			0.511870	−	0.859063i	$-0.328953\pi$
$991$	1.00540e6			1.02374			0.511870	+	0.859063i	$0.328953\pi$
$992$		−	242437.i		−	0.246363i
$993$			1.14321e6i			1.15939i
$994$		−	379179.i		−	0.383770i
$995$	−200544.	+	274192.i	−0.202564	+	0.276955i
$996$			662666.i			0.668000i
$997$			1.06905e6i			1.07549i	0.843108	+	0.537744i	$0.180723\pi$
$997$			1.06905e6i			1.07549i	−0.843108	+	0.537744i	$0.819277\pi$
$998$		−	858633.i		−	0.862078i
$999$			257626.i			0.258142i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.c.a.229.6	yes	48
5.4	even	2	inner	230.5.c.a.229.43	yes	48
23.22	odd	2	inner	230.5.c.a.229.44	yes	48
115.114	odd	2	inner	230.5.c.a.229.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.c.a.229.5	✓	48	115.114	odd	2	inner
230.5.c.a.229.6	yes	48	1.1	even	1	trivial
230.5.c.a.229.43	yes	48	5.4	even	2	inner
230.5.c.a.229.44	yes	48	23.22	odd	2	inner

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843i q^{2} -13.4757i q^{3} -8.00000 q^{4} +(20.1787 + 14.7587i) q^{5} +38.1149 q^{6} +78.6574 q^{7} -22.6274i q^{8} -100.593 q^{9} +O(q^{10})\)	\(q+2.82843i q^{2} -13.4757i q^{3} -8.00000 q^{4} +(20.1787 + 14.7587i) q^{5} +38.1149 q^{6} +78.6574 q^{7} -22.6274i q^{8} -100.593 q^{9} +(-41.7439 + 57.0741i) q^{10} +67.9692i q^{11} +107.805i q^{12} +229.153i q^{13} +222.477i q^{14} +(198.883 - 271.922i) q^{15} +64.0000 q^{16} +80.2906 q^{17} -284.521i q^{18} +377.665i q^{19} +(-161.430 - 118.069i) q^{20} -1059.96i q^{21} -192.246 q^{22} +(-481.515 - 219.052i) q^{23} -304.919 q^{24} +(189.363 + 595.623i) q^{25} -648.142 q^{26} +264.032i q^{27} -629.259 q^{28} +1489.97 q^{29} +(769.111 + 562.526i) q^{30} -1339.29 q^{31} +181.019i q^{32} +915.929 q^{33} +227.096i q^{34} +(1587.21 + 1160.88i) q^{35} +804.746 q^{36} +975.738 q^{37} -1068.20 q^{38} +3087.98 q^{39} +(333.951 - 456.593i) q^{40} +2823.50 q^{41} +2998.02 q^{42} -748.713 q^{43} -543.753i q^{44} +(-2029.85 - 1484.62i) q^{45} +(619.574 - 1361.93i) q^{46} +2124.13i q^{47} -862.442i q^{48} +3785.99 q^{49} +(-1684.68 + 535.598i) q^{50} -1081.97i q^{51} -1833.22i q^{52} +2437.98 q^{53} -746.796 q^{54} +(-1003.14 + 1371.53i) q^{55} -1779.81i q^{56} +5089.28 q^{57} +4214.28i q^{58} -4873.47 q^{59} +(-1591.06 + 2175.37i) q^{60} -4852.60i q^{61} -3788.08i q^{62} -7912.41 q^{63} -512.000 q^{64} +(-3381.99 + 4624.01i) q^{65} +2590.64i q^{66} +6915.37 q^{67} -642.325 q^{68} +(-2951.88 + 6488.73i) q^{69} +(-3283.46 + 4489.30i) q^{70} -1704.35 q^{71} +2276.17i q^{72} -1135.02i q^{73} +2759.80i q^{74} +(8026.41 - 2551.78i) q^{75} -3021.32i q^{76} +5346.28i q^{77} +8734.13i q^{78} -7424.39i q^{79} +(1291.44 + 944.556i) q^{80} -4590.05 q^{81} +7986.07i q^{82} +6146.88 q^{83} +8479.68i q^{84} +(1620.16 + 1184.98i) q^{85} -2117.68i q^{86} -20078.4i q^{87} +1537.97 q^{88} -8566.65i q^{89} +(4199.15 - 5741.27i) q^{90} +18024.6i q^{91} +(3852.12 + 1752.42i) q^{92} +18047.8i q^{93} -6007.95 q^{94} +(-5573.84 + 7620.80i) q^{95} +2439.35 q^{96} -921.872 q^{97} +10708.4i q^{98} -6837.24i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) \) 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49} - 3264 q^{50} + 10112 q^{54} + 12824 q^{55} + 7092 q^{59} - 24576 q^{64} + 14000 q^{69} - 6592 q^{70} - 12708 q^{71} + 24728 q^{75} - 13040 q^{81} - 15700 q^{85} - 9728 q^{94} - 46608 q^{95} - 4096 q^{96}+O(q^{100}) \) 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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