LMFDB - Embedded newform 230.6.b.a.139.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(139,230)]

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, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("230.139");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.b (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:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.5
Character	$\chi$	$=$	230.139
Dual form			230.6.b.a.139.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} -11.2210i q^{3} -16.0000 q^{4} +(-42.1119 + 36.7639i) q^{5} -44.8839 q^{6} +166.669i q^{7} +64.0000i q^{8} +117.090 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} -11.2210i q^{3} -16.0000 q^{4} +(-42.1119 + 36.7639i) q^{5} -44.8839 q^{6} +166.669i q^{7} +64.0000i q^{8} +117.090 q^{9} +(147.056 + 168.448i) q^{10} -290.245 q^{11} +179.536i q^{12} +151.623i q^{13} +666.676 q^{14} +(412.527 + 472.537i) q^{15} +256.000 q^{16} -1187.37i q^{17} -468.358i q^{18} -152.232 q^{19} +(673.791 - 588.223i) q^{20} +1870.19 q^{21} +1160.98i q^{22} -529.000i q^{23} +718.143 q^{24} +(421.828 - 3096.40i) q^{25} +606.493 q^{26} -4040.56i q^{27} -2666.70i q^{28} -6837.03 q^{29} +(1890.15 - 1650.11i) q^{30} +9466.03 q^{31} -1024.00i q^{32} +3256.84i q^{33} -4749.48 q^{34} +(-6127.40 - 7018.75i) q^{35} -1873.43 q^{36} -12749.8i q^{37} +608.929i q^{38} +1701.36 q^{39} +(-2352.89 - 2695.16i) q^{40} -3331.13 q^{41} -7480.76i q^{42} -8758.43i q^{43} +4643.92 q^{44} +(-4930.87 + 4304.67i) q^{45} -2116.00 q^{46} +25048.2i q^{47} -2872.57i q^{48} -10971.5 q^{49} +(-12385.6 - 1687.31i) q^{50} -13323.4 q^{51} -2425.97i q^{52} +4995.16i q^{53} -16162.2 q^{54} +(12222.8 - 10670.6i) q^{55} -10666.8 q^{56} +1708.19i q^{57} +27348.1i q^{58} +47516.4 q^{59} +(-6600.44 - 7560.59i) q^{60} +12260.3 q^{61} -37864.1i q^{62} +19515.2i q^{63} -4096.00 q^{64} +(-5574.27 - 6385.15i) q^{65} +13027.3 q^{66} -45206.8i q^{67} +18997.9i q^{68} -5935.90 q^{69} +(-28075.0 + 24509.6i) q^{70} -80170.2 q^{71} +7493.74i q^{72} -16936.9i q^{73} -50999.2 q^{74} +(-34744.6 - 4733.32i) q^{75} +2435.71 q^{76} -48374.9i q^{77} -6805.45i q^{78} -23136.2 q^{79} +(-10780.7 + 9411.56i) q^{80} -16886.2 q^{81} +13324.5i q^{82} -88743.6i q^{83} -29923.0 q^{84} +(43652.3 + 50002.4i) q^{85} -35033.7 q^{86} +76718.2i q^{87} -18575.7i q^{88} +24924.0 q^{89} +(17218.7 + 19723.5i) q^{90} -25270.9 q^{91} +8464.00i q^{92} -106218. i q^{93} +100193. q^{94} +(6410.79 - 5596.65i) q^{95} -11490.3 q^{96} -98206.3i q^{97} +43886.2i q^{98} -33984.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) $ 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9	$ 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) $ 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

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 $

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$		−	11.2210i		−	0.719826i	−0.932986	−	0.359913i	$-0.882806\pi$
$3$		−	11.2210i		−	0.719826i	0.932986	−	0.359913i	$-0.117194\pi$
$4$	−16.0000			−0.500000
$5$	−42.1119	+	36.7639i	−0.753321	+	0.657653i
$5$	−42.1119	+	36.7639i	−0.753321	+	0.657653i
$6$	−44.8839			−0.508994
$7$			166.669i			1.28561i	0.766029	+	0.642806i	$0.222230\pi$
$7$			166.669i			1.28561i	−0.766029	+	0.642806i	$0.777770\pi$
$8$			64.0000i			0.353553i
$9$	117.090			0.481850
$10$	147.056	+	168.448i	0.465031	+	0.532678i
$11$	−290.245			−0.723242			−0.361621	−	0.932325i	$-0.617776\pi$
$11$	−290.245			−0.723242			−0.361621	+	0.932325i	$0.617776\pi$
$12$			179.536i			0.359913i
$13$			151.623i			0.248833i	0.992230	+	0.124416i	$0.0397059\pi$
$13$			151.623i			0.248833i	−0.992230	+	0.124416i	$0.960294\pi$
$14$	666.676			0.909064
$15$	412.527	+	472.537i	0.473396	+	0.542260i
$16$	256.000			0.250000
$17$		−	1187.37i		−	0.996468i	−0.867043	−	0.498234i	$-0.833982\pi$
$17$		−	1187.37i		−	0.996468i	0.867043	−	0.498234i	$-0.166018\pi$
$18$		−	468.358i		−	0.340720i
$19$	−152.232			−0.0967436			−0.0483718	−	0.998829i	$-0.515403\pi$
$19$	−152.232			−0.0967436			−0.0483718	+	0.998829i	$0.515403\pi$
$20$	673.791	−	588.223i	0.376660	−	0.328827i
$21$	1870.19			0.925417
$22$			1160.98i			0.511409i
$23$		−	529.000i		−	0.208514i
$23$		−	529.000i		−	0.208514i
$24$	718.143			0.254497
$25$	421.828	−	3096.40i	0.134985	−	0.990848i
$26$	606.493			0.175951
$27$		−	4040.56i		−	1.06667i
$28$		−	2666.70i		−	0.642806i
$29$	−6837.03			−1.50964			−0.754818	−	0.655934i	$-0.772275\pi$
$29$	−6837.03			−1.50964			−0.754818	+	0.655934i	$0.772275\pi$
$30$	1890.15	−	1650.11i	0.383436	−	0.334741i
$31$	9466.03			1.76915			0.884573	−	0.466403i	$-0.154450\pi$
$31$	9466.03			1.76915			0.884573	+	0.466403i	$0.154450\pi$
$32$		−	1024.00i		−	0.176777i
$33$			3256.84i			0.520608i
$34$	−4749.48			−0.704609
$35$	−6127.40	−	7018.75i	−0.845486	−	0.968478i
$36$	−1873.43			−0.240925
$37$		−	12749.8i		−	1.53108i	−0.643386	−	0.765542i	$-0.722471\pi$
$37$		−	12749.8i		−	1.53108i	0.643386	−	0.765542i	$-0.277529\pi$
$38$			608.929i			0.0684081i
$39$	1701.36			0.179116
$40$	−2352.89	−	2695.16i	−0.232515	−	0.266339i
$41$	−3331.13			−0.309479			−0.154740	−	0.987955i	$-0.549454\pi$
$41$	−3331.13			−0.309479			−0.154740	+	0.987955i	$0.549454\pi$
$42$		−	7480.76i		−	0.654368i
$43$		−	8758.43i		−	0.722362i	−0.932496	−	0.361181i	$-0.882374\pi$
$43$		−	8758.43i		−	0.722362i	0.932496	−	0.361181i	$-0.117626\pi$
$44$	4643.92			0.361621
$45$	−4930.87	+	4304.67i	−0.362988	+	0.316890i
$46$	−2116.00			−0.147442
$47$			25048.2i			1.65398i	0.562213	+	0.826992i	$0.309950\pi$
$47$			25048.2i			1.65398i	−0.562213	+	0.826992i	$0.690050\pi$
$48$		−	2872.57i		−	0.179957i
$49$	−10971.5			−0.652796
$50$	−12385.6	−	1687.31i	−0.700635	−	0.0954488i
$51$	−13323.4			−0.717284
$52$		−	2425.97i		−	0.124416i
$53$			4995.16i			0.244264i	0.992514	+	0.122132i	$0.0389731\pi$
$53$			4995.16i			0.244264i	−0.992514	+	0.122132i	$0.961027\pi$
$54$	−16162.2			−0.754253
$55$	12222.8	−	10670.6i	0.544833	−	0.475642i
$56$	−10666.8			−0.454532
$57$			1708.19i			0.0696386i
$58$			27348.1i			1.06747i
$59$	47516.4			1.77711			0.888553	−	0.458774i	$-0.151711\pi$
$59$	47516.4			1.77711			0.888553	+	0.458774i	$0.151711\pi$
$60$	−6600.44	−	7560.59i	−0.236698	−	0.271130i
$61$	12260.3			0.421867			0.210934	−	0.977500i	$-0.432350\pi$
$61$	12260.3			0.421867			0.210934	+	0.977500i	$0.432350\pi$
$62$		−	37864.1i		−	1.25097i
$63$			19515.2i			0.619472i
$64$	−4096.00			−0.125000
$65$	−5574.27	−	6385.15i	−0.163646	−	0.187451i
$66$	13027.3			0.368126
$67$		−	45206.8i		−	1.23032i	−0.788404	−	0.615158i	$-0.789092\pi$
$67$		−	45206.8i		−	1.23032i	0.788404	−	0.615158i	$-0.210908\pi$
$68$			18997.9i			0.498234i
$69$	−5935.90			−0.150094
$70$	−28075.0	+	24509.6i	−0.684817	+	0.597849i
$71$	−80170.2			−1.88741			−0.943707	−	0.330783i	$-0.892687\pi$
$71$	−80170.2			−1.88741			−0.943707	+	0.330783i	$0.892687\pi$
$72$			7493.74i			0.170360i
$73$		−	16936.9i		−	0.371987i	−0.982551	−	0.185993i	$-0.940450\pi$
$73$		−	16936.9i		−	0.371987i	0.982551	−	0.185993i	$-0.0595503\pi$
$74$	−50999.2			−1.08264
$75$	−34744.6	−	4733.32i	−0.713238	−	0.0971657i
$76$	2435.71			0.0483718
$77$		−	48374.9i		−	0.929807i
$78$		−	6805.45i		−	0.126654i
$79$	−23136.2			−0.417085			−0.208543	−	0.978013i	$-0.566872\pi$
$79$	−23136.2			−0.417085			−0.208543	+	0.978013i	$0.566872\pi$
$80$	−10780.7	+	9411.56i	−0.188330	+	0.164413i
$81$	−16886.2			−0.285970
$82$			13324.5i			0.218835i
$83$		−	88743.6i		−	1.41397i	−0.707226	−	0.706987i	$-0.750054\pi$
$83$		−	88743.6i		−	1.41397i	0.707226	−	0.706987i	$-0.249946\pi$
$84$	−29923.0			−0.462708
$85$	43652.3	+	50002.4i	0.655330	+	0.750660i
$86$	−35033.7			−0.510787
$87$			76718.2i			1.08668i
$88$		−	18575.7i		−	0.255704i
$89$	24924.0			0.333535			0.166768	−	0.985996i	$-0.446667\pi$
$89$	24924.0			0.333535			0.166768	+	0.985996i	$0.446667\pi$
$90$	17218.7	+	19723.5i	0.224075	+	0.256671i
$91$	−25270.9			−0.319902
$92$			8464.00i			0.104257i
$93$		−	106218.i		−	1.27348i
$94$	100193.			1.16954
$95$	6410.79	−	5596.65i	0.0728790	−	0.0636237i
$96$	−11490.3			−0.127248
$97$		−	98206.3i		−	1.05977i	−0.848071	−	0.529883i	$-0.822236\pi$
$97$		−	98206.3i		−	1.05977i	0.848071	−	0.529883i	$-0.177764\pi$
$98$			43886.2i			0.461597i
$99$	−33984.7			−0.348494
$100$	−6749.25	+	49542.4i	−0.0674925	+	0.495424i
$101$	−51436.4			−0.501726			−0.250863	−	0.968023i	$-0.580714\pi$
$101$	−51436.4			−0.501726			−0.250863	+	0.968023i	$0.580714\pi$
$102$			53293.8i			0.507196i
$103$		−	25652.9i		−	0.238256i	−0.992879	−	0.119128i	$-0.961990\pi$
$103$		−	25652.9i		−	0.238256i	0.992879	−	0.119128i	$-0.0380099\pi$
$104$	−9703.89			−0.0879757
$105$	−78757.3	+	68755.5i	−0.697136	+	0.608603i
$106$	19980.6			0.172721
$107$		−	168639.i		−	1.42397i	−0.702196	−	0.711983i	$-0.747797\pi$
$107$		−	168639.i		−	1.42397i	0.702196	−	0.711983i	$-0.252203\pi$
$108$			64648.9i			0.533337i
$109$	88242.0			0.711392			0.355696	−	0.934602i	$-0.384244\pi$
$109$	88242.0			0.711392			0.355696	+	0.934602i	$0.384244\pi$
$110$	−42682.2	−	48891.1i	−0.336330	−	0.385255i
$111$	−143065.			−1.10211
$112$			42667.3i			0.321403i
$113$		−	89521.1i		−	0.659522i	−0.944064	−	0.329761i	$-0.893032\pi$
$113$		−	89521.1i		−	0.659522i	0.944064	−	0.329761i	$-0.106968\pi$
$114$	6832.78			0.0492419
$115$	19448.1	+	22277.2i	0.137130	+	0.157078i
$116$	109392.			0.754818
$117$			17753.5i			0.119900i
$118$		−	190066.i		−	1.25660i
$119$	197898.			1.28107
$120$	−30242.4	+	26401.7i	−0.191718	+	0.167371i
$121$	−76808.7			−0.476922
$122$		−	49041.1i		−	0.298305i
$123$			37378.5i			0.222771i
$124$	−151456.			−0.884573
$125$	96071.8	+	145903.i	0.549947	+	0.835200i
$126$	78060.8			0.438033
$127$		−	156874.i		−	0.863062i	−0.902098	−	0.431531i	$-0.857974\pi$
$127$		−	156874.i		−	0.863062i	0.902098	−	0.431531i	$-0.142026\pi$
$128$			16384.0i			0.0883883i
$129$	−98278.1			−0.519975
$130$	−25540.6	+	22297.1i	−0.132548	+	0.115715i
$131$	46490.2			0.236692			0.118346	−	0.992972i	$-0.462241\pi$
$131$	46490.2			0.236692			0.118346	+	0.992972i	$0.462241\pi$
$132$		−	52109.4i		−	0.260304i
$133$		−	25372.4i		−	0.124375i
$134$	−180827.			−0.869965
$135$	148547.	+	170156.i	0.701502	+	0.803548i
$136$	75991.6			0.352305
$137$			73633.9i			0.335179i	0.985857	+	0.167589i	$0.0535983\pi$
$137$			73633.9i			0.335179i	−0.985857	+	0.167589i	$0.946402\pi$
$138$			23743.6i			0.106133i
$139$	98634.2			0.433002			0.216501	−	0.976282i	$-0.430535\pi$
$139$	98634.2			0.433002			0.216501	+	0.976282i	$0.430535\pi$
$140$	98038.5	+	112300.i	0.422743	+	0.484239i
$141$	281065.			1.19058
$142$			320681.i			1.33460i
$143$		−	44007.9i		−	0.179966i
$144$	29974.9			0.120463
$145$	287920.	−	251356.i	1.13724	−	0.992817i
$146$	−67747.7			−0.263034
$147$			123111.i			0.469900i
$148$			203997.i			0.765542i
$149$	413358.			1.52532			0.762660	−	0.646800i	$-0.223893\pi$
$149$	413358.			1.52532			0.762660	+	0.646800i	$0.223893\pi$
$150$	−18933.3	+	138979.i	−0.0687066	+	0.504335i
$151$	−265942.			−0.949173			−0.474586	−	0.880209i	$-0.657402\pi$
$151$	−265942.			−0.949173			−0.474586	+	0.880209i	$0.657402\pi$
$152$		−	9742.86i		−	0.0342040i
$153$		−	139029.i		−	0.480148i
$154$	−193499.			−0.657473
$155$	−398633.	+	348008.i	−1.33273	+	1.16348i
$156$	−27221.8			−0.0895582
$157$			139087.i			0.450335i	0.974320	+	0.225168i	$0.0722930\pi$
$157$			139087.i			0.450335i	−0.974320	+	0.225168i	$0.927707\pi$
$158$			92545.0i			0.294924i
$159$	56050.6			0.175828
$160$	37646.3	+	43122.6i	0.116258	+	0.133170i
$161$	88167.9			0.268068
$162$			67545.0i			0.202211i
$163$		−	479057.i		−	1.41227i	−0.708076	−	0.706136i	$-0.750437\pi$
$163$		−	479057.i		−	1.41227i	0.708076	−	0.706136i	$-0.249563\pi$
$164$	53298.0			0.154740
$165$	−119734.	−	137152.i	−0.342380	−	0.392185i
$166$	−354974.			−0.999831
$167$		−	176308.i		−	0.489194i	−0.969625	−	0.244597i	$-0.921344\pi$
$167$		−	176308.i		−	0.489194i	0.969625	−	0.244597i	$-0.0786557\pi$
$168$			119692.i			0.327184i
$169$	348303.			0.938082
$170$	200010.	−	174609.i	0.530797	−	0.463388i
$171$	−17824.8			−0.0466160
$172$			140135.i			0.361181i
$173$			648002.i			1.64612i	0.567955	+	0.823059i	$0.307735\pi$
$173$			648002.i			1.64612i	−0.567955	+	0.823059i	$0.692265\pi$
$174$	306873.			0.768396
$175$	516074.	+	70305.7i	1.27384	+	0.173538i
$176$	−74302.8			−0.180810
$177$		−	533180.i		−	1.27921i
$178$		−	99695.8i		−	0.235845i
$179$	2097.95			0.00489399			0.00244700	−	0.999997i	$-0.499221\pi$
$179$	2097.95			0.00489399			0.00244700	+	0.999997i	$0.499221\pi$
$180$	78893.9	−	68874.8i	0.181494	−	0.158445i
$181$	449166.			1.01909			0.509543	−	0.860445i	$-0.329814\pi$
$181$	449166.			1.01909			0.509543	+	0.860445i	$0.329814\pi$
$182$			101084.i			0.226205i
$183$		−	137572.i		−	0.303671i
$184$	33856.0			0.0737210
$185$	468733.	+	536918.i	1.00692	+	1.15340i
$186$	−424872.			−0.900484
$187$			344628.i			0.720687i
$188$		−	400771.i		−	0.826992i
$189$	673436.			1.37133
$190$	−22386.6	−	25643.2i	−0.0449888	−	0.0515332i
$191$	−220170.			−0.436691			−0.218346	−	0.975872i	$-0.570066\pi$
$191$	−220170.			−0.436691			−0.218346	+	0.975872i	$0.570066\pi$
$192$			45961.1i			0.0899783i
$193$		−	80714.2i		−	0.155976i	−0.996954	−	0.0779878i	$-0.975150\pi$
$193$		−	80714.2i		−	0.155976i	0.996954	−	0.0779878i	$-0.0248495\pi$
$194$	−392825.			−0.749368
$195$	−71647.6	+	62548.7i	−0.134932	+	0.117796i
$196$	175545.			0.326398
$197$		−	199080.i		−	0.365479i	−0.983161	−	0.182740i	$-0.941503\pi$
$197$		−	199080.i		−	0.365479i	0.983161	−	0.182740i	$-0.0584965\pi$
$198$			135939.i			0.246423i
$199$	−146947.			−0.263044			−0.131522	−	0.991313i	$-0.541986\pi$
$199$	−146947.			−0.263044			−0.131522	+	0.991313i	$0.541986\pi$
$200$	198170.	+	26997.0i	0.350318	+	0.0477244i
$201$	−507265.			−0.885614
$202$			205746.i			0.354774i
$203$		−	1.13952e6i		−	1.94081i
$204$	213175.			0.358642
$205$	140280.	−	122465.i	0.233137	−	0.203530i
$206$	−102612.			−0.168473
$207$		−	61940.4i		−	0.100473i
$208$			38815.6i			0.0622082i
$209$	44184.7			0.0699690
$210$	275022.	+	315029.i	0.430347	+	0.492949i
$211$	1.06607e6			1.64847			0.824234	−	0.566250i	$-0.191606\pi$
$211$	1.06607e6			1.64847			0.824234	+	0.566250i	$0.191606\pi$
$212$		−	79922.5i		−	0.122132i
$213$			899588.i			1.35861i
$214$	−674558.			−1.00690
$215$	321994.	+	368834.i	0.475064	+	0.544170i
$216$	258596.			0.377126
$217$			1.57769e6i			2.27443i
$218$		−	352968.i		−	0.503030i
$219$	−190049.			−0.267766
$220$	−195565.	+	170729.i	−0.272417	+	0.237821i
$221$	180033.			0.247954
$222$			572261.i			0.779312i
$223$			649553.i			0.874686i	0.899295	+	0.437343i	$0.144080\pi$
$223$			649553.i			0.874686i	−0.899295	+	0.437343i	$0.855920\pi$
$224$	170669.			0.227266
$225$	49391.7	−	362556.i	0.0650426	−	0.477440i
$226$	−358084.			−0.466353
$227$		−	894576.i		−	1.15227i	−0.817356	−	0.576133i	$-0.804561\pi$
$227$		−	894576.i		−	1.15227i	0.817356	−	0.576133i	$-0.195439\pi$
$228$		−	27331.1i		−	0.0348193i
$229$	−1.29247e6			−1.62867			−0.814334	−	0.580397i	$-0.802897\pi$
$229$	−1.29247e6			−1.62867			−0.814334	+	0.580397i	$0.802897\pi$
$230$	89108.8	−	77792.5i	0.111071	−	0.0969656i
$231$	−542813.			−0.669300
$232$		−	437570.i		−	0.533737i
$233$			1.25898e6i			1.51924i	0.650365	+	0.759622i	$0.274616\pi$
$233$			1.25898e6i			1.51924i	−0.650365	+	0.759622i	$0.725384\pi$
$234$	71014.1			0.0847822
$235$	−920869.	−	1.05483e6i	−1.08775	−	1.24598i
$236$	−760262.			−0.888553
$237$			259611.i			0.300229i
$238$		−	791590.i		−	0.905853i
$239$	1.00810e6			1.14159			0.570793	−	0.821094i	$-0.306636\pi$
$239$	1.00810e6			1.14159			0.570793	+	0.821094i	$0.306636\pi$
$240$	105607.	+	120969.i	0.118349	+	0.135565i
$241$	−269725.			−0.299142			−0.149571	−	0.988751i	$-0.547789\pi$
$241$	−269725.			−0.299142			−0.149571	+	0.988751i	$0.547789\pi$
$242$			307235.i			0.337235i
$243$		−	792375.i		−	0.860826i
$244$	−196164.			−0.210934
$245$	462033.	−	403357.i	0.491765	−	0.429313i
$246$	149514.			0.157523
$247$		−	23081.9i		−	0.0240730i
$248$			605826.i			0.625487i
$249$	−995790.			−1.01782
$250$	583613.	−	384287.i	0.590575	−	0.388871i
$251$	−1.82724e6			−1.83068			−0.915339	−	0.402684i	$-0.868077\pi$
$251$	−1.82724e6			−1.83068			−0.915339	+	0.402684i	$0.868077\pi$
$252$		−	312243.i		−	0.309736i
$253$			153540.i			0.150806i
$254$	−627496.			−0.610277
$255$	561076.	−	489822.i	0.540345	−	0.471724i
$256$	65536.0			0.0625000
$257$			1.21502e6i			1.14749i	0.819032	+	0.573747i	$0.194511\pi$
$257$			1.21502e6i			1.14749i	−0.819032	+	0.573747i	$0.805489\pi$
$258$			393112.i			0.367678i
$259$	2.12500e6			1.96838
$260$	89188.3	+	102162.i	0.0818228	+	0.0937255i
$261$	−800545.			−0.727419
$262$		−	185961.i		−	0.167366i
$263$			207457.i			0.184944i	0.995715	+	0.0924719i	$0.0294768\pi$
$263$			207457.i			0.184944i	−0.995715	+	0.0924719i	$0.970523\pi$
$264$	−208437.			−0.184063
$265$	−183642.	−	210356.i	−0.160641	−	0.184009i
$266$	−101490.			−0.0879462
$267$		−	279671.i		−	0.240087i
$268$			723309.i			0.615158i
$269$	−1.85336e6			−1.56163			−0.780815	−	0.624763i	$-0.785196\pi$
$269$	−1.85336e6			−1.56163			−0.780815	+	0.624763i	$0.785196\pi$
$270$	680623.	−	594187.i	0.568194	−	0.496037i
$271$	60583.8			0.0501110			0.0250555	−	0.999686i	$-0.492024\pi$
$271$	60583.8			0.0501110			0.0250555	+	0.999686i	$0.492024\pi$
$272$		−	303966.i		−	0.249117i
$273$			283564.i			0.230274i
$274$	294536.			0.237007
$275$	−122434.	+	898715.i	−0.0976268	+	0.716622i
$276$	94974.4			0.0750471
$277$		−	539716.i		−	0.422635i	−0.977417	−	0.211318i	$-0.932225\pi$
$277$		−	539716.i		−	0.422635i	0.977417	−	0.211318i	$-0.0677754\pi$
$278$		−	394537.i		−	0.306179i
$279$	1.10837e6			0.852463
$280$	449200.	−	392154.i	0.342409	−	0.298924i
$281$	−1.09683e6			−0.828651			−0.414326	−	0.910129i	$-0.635983\pi$
$281$	−1.09683e6			−0.828651			−0.414326	+	0.910129i	$0.635983\pi$
$282$		−	1.12426e6i		−	0.841868i
$283$		−	1.50161e6i		−	1.11453i	−0.830334	−	0.557266i	$-0.811850\pi$
$283$		−	1.50161e6i		−	1.11453i	0.830334	−	0.557266i	$-0.188150\pi$
$284$	1.28272e6			0.943707
$285$	−62799.9	−	71935.3i	−0.0457980	−	0.0524602i
$286$	−176032.			−0.127255
$287$		−	555196.i		−	0.397870i
$288$		−	119900.i		−	0.0851799i
$289$	10012.4			0.00705172
$290$	−1.00542e6	−	1.15168e6i	−0.702028	−	0.804151i
$291$	−1.10197e6			−0.762847
$292$			270991.i			0.185993i
$293$		−	2.74350e6i		−	1.86696i	−0.358628	−	0.933481i	$-0.616755\pi$
$293$		−	2.74350e6i		−	1.86696i	0.358628	−	0.933481i	$-0.383245\pi$
$294$	492446.			0.332269
$295$	−2.00101e6	+	1.74689e6i	−1.33873	+	1.16872i
$296$	815987.			0.541320
$297$			1.17275e6i			0.771463i
$298$		−	1.65343e6i		−	1.07856i
$299$	80208.7			0.0518852
$300$	555914.	+	75733.2i	0.356619	+	0.0485829i
$301$	1.45976e6			0.928677
$302$			1.06377e6i			0.671166i
$303$			577167.i			0.361156i
$304$	−38971.4			−0.0241859
$305$	−516304.	+	450736.i	−0.317801	+	0.277442i
$306$	−556114.			−0.339516
$307$		−	15841.3i		−	0.00959277i	−0.999988	−	0.00479639i	$-0.998473\pi$
$307$		−	15841.3i		−	0.00959277i	0.999988	−	0.00479639i	$-0.00152674\pi$
$308$			773998.i			0.464904i
$309$	−287851.			−0.171503
$310$	1.39203e6	+	1.59453e6i	0.822707	+	0.942385i
$311$	−1.91441e6			−1.12237			−0.561183	−	0.827692i	$-0.689654\pi$
$311$	−1.91441e6			−1.12237			−0.561183	+	0.827692i	$0.689654\pi$
$312$			108887.i			0.0633272i
$313$		−	2.91834e6i		−	1.68374i	−0.539682	−	0.841869i	$-0.681456\pi$
$313$		−	2.91834e6i		−	1.68374i	0.539682	−	0.841869i	$-0.318544\pi$
$314$	556346.			0.318435
$315$	−717456.	−	821823.i	−0.407398	−	0.466661i
$316$	370180.			0.208543
$317$		−	1.10637e6i		−	0.618373i	−0.951001	−	0.309187i	$-0.899943\pi$
$317$		−	1.10637e6i		−	0.618373i	0.951001	−	0.309187i	$-0.100057\pi$
$318$		−	224202.i		−	0.124329i
$319$	1.98442e6			1.09183
$320$	172490.	−	150585.i	0.0941651	−	0.0822066i
$321$	−1.89230e6			−1.02501
$322$		−	352672.i		−	0.189553i
$323$			180756.i			0.0964019i
$324$	270180.			0.142985
$325$	469486.	+	63959.0i	0.246555	+	0.0335887i
$326$	−1.91623e6			−0.998627
$327$		−	990162.i		−	0.512079i
$328$		−	213192.i		−	0.109417i
$329$	−4.17475e6			−2.12638
$330$	−548606.	+	478936.i	−0.277317	+	0.242099i
$331$	−1.24948e6			−0.626841			−0.313421	−	0.949614i	$-0.601475\pi$
$331$	−1.24948e6			−0.626841			−0.313421	+	0.949614i	$0.601475\pi$
$332$			1.41990e6i			0.706987i
$333$		−	1.49287e6i		−	0.737753i
$334$	−705233.			−0.345913
$335$	1.66198e6	+	1.90375e6i	0.809121	+	0.926823i
$336$	478768.			0.231354
$337$			1.17428e6i			0.563243i	0.959526	+	0.281621i	$0.0908722\pi$
$337$			1.17428e6i			0.563243i	−0.959526	+	0.281621i	$0.909128\pi$
$338$		−	1.39321e6i		−	0.663324i
$339$	−1.00451e6			−0.474741
$340$	−698437.	−	800038.i	−0.327665	−	0.375330i
$341$	−2.74747e6			−1.27952
$342$			71299.2i			0.0329625i
$343$			972589.i			0.446369i
$344$	560539.			0.255394
$345$	249972.	−	218227.i	0.113069	−	0.0987099i
$346$	2.59201e6			1.16398
$347$			2.37200e6i			1.05752i	0.848770	+	0.528762i	$0.177344\pi$
$347$			2.37200e6i			1.05752i	−0.848770	+	0.528762i	$0.822656\pi$
$348$		−	1.22749e6i		−	0.543338i
$349$	610698.			0.268388			0.134194	−	0.990955i	$-0.457156\pi$
$349$	610698.			0.268388			0.134194	+	0.990955i	$0.457156\pi$
$350$	281223.	−	2.06429e6i	0.122710	−	0.900744i
$351$	612643.			0.265424
$352$			297211.i			0.127852i
$353$			2.20624e6i			0.942359i	0.882037	+	0.471179i	$0.156172\pi$
$353$			2.20624e6i			0.942359i	−0.882037	+	0.471179i	$0.843828\pi$
$354$	−2.13272e6			−0.904536
$355$	3.37612e6	−	2.94737e6i	1.42183	−	1.24126i
$356$	−398783.			−0.166768
$357$		−	2.22060e6i		−	0.922148i
$358$		−	8391.81i		−	0.00346057i
$359$	3.86544e6			1.58293			0.791466	−	0.611213i	$-0.209318\pi$
$359$	3.86544e6			1.58293			0.791466	+	0.611213i	$0.209318\pi$
$360$	−275499.	−	315576.i	−0.112038	−	0.128336i
$361$	−2.45292e6			−0.990641
$362$		−	1.79667e6i		−	0.720603i
$363$			861869.i			0.343301i
$364$	404334.			0.159951
$365$	622668.	+	713246.i	0.244638	+	0.280225i
$366$	−550289.			−0.214728
$367$		−	3.47556e6i		−	1.34698i	−0.739198	−	0.673488i	$-0.764795\pi$
$367$		−	3.47556e6i		−	1.34698i	0.739198	−	0.673488i	$-0.235205\pi$
$368$		−	135424.i		−	0.0521286i
$369$	−390040.			−0.149123
$370$	2.14767e6	−	1.87493e6i	0.815575	−	0.712001i
$371$	−832538.			−0.314029
$372$			1.69949e6i			0.636738i
$373$			2.66736e6i			0.992681i	0.868128	+	0.496341i	$0.165323\pi$
$373$			2.66736e6i			0.992681i	−0.868128	+	0.496341i	$0.834677\pi$
$374$	1.37851e6			0.509603
$375$	1.63718e6	−	1.07802e6i	0.601199	−	0.395866i
$376$	−1.60308e6			−0.584772
$377$		−	1.03665e6i		−	0.375647i
$378$		−	2.69374e6i		−	0.969676i
$379$	2.70623e6			0.967758			0.483879	−	0.875135i	$-0.339227\pi$
$379$	2.70623e6			0.967758			0.483879	+	0.875135i	$0.339227\pi$
$380$	−102573.	+	89546.4i	−0.0364395	+	0.0318119i
$381$	−1.76028e6			−0.621254
$382$			880679.i			0.308787i
$383$		−	430841.i		−	0.150079i	−0.997181	−	0.0750395i	$-0.976092\pi$
$383$		−	430841.i		−	0.150079i	0.997181	−	0.0750395i	$-0.0239083\pi$
$384$	183845.			0.0636242
$385$	1.77845e6	+	2.03716e6i	0.611491	+	0.700443i
$386$	−322857.			−0.110291
$387$		−	1.02552e6i		−	0.348070i
$388$			1.57130e6i			0.529883i
$389$	5.38624e6			1.80473			0.902364	−	0.430974i	$-0.141830\pi$
$389$	5.38624e6			1.80473			0.902364	+	0.430974i	$0.141830\pi$
$390$	250195.	+	286590.i	0.0832946	+	0.0954114i
$391$	−628118.			−0.207778
$392$		−	702179.i		−	0.230798i
$393$		−	521666.i		−	0.170377i
$394$	−796321.			−0.258433
$395$	974312.	−	850579.i	0.314199	−	0.274298i
$396$	543755.			0.174247
$397$			1.64277e6i			0.523119i	0.965187	+	0.261559i	$0.0842367\pi$
$397$			1.64277e6i			0.523119i	−0.965187	+	0.261559i	$0.915763\pi$
$398$			587789.i			0.186000i
$399$	−284703.			−0.0895282
$400$	107988.	−	792678.i	0.0337463	−	0.247712i
$401$	−3.96482e6			−1.23130			−0.615648	−	0.788021i	$-0.711106\pi$
$401$	−3.96482e6			−1.23130			−0.615648	+	0.788021i	$0.711106\pi$
$402$			2.02906e6i			0.626224i
$403$			1.43527e6i			0.440221i
$404$	822982.			0.250863
$405$	711112.	−	620804.i	0.215427	−	0.188069i
$406$	−4.55808e6			−1.37236
$407$			3.70057e6i			1.10734i
$408$		−	852700.i		−	0.253598i
$409$	3.14830e6			0.930612			0.465306	−	0.885150i	$-0.345944\pi$
$409$	3.14830e6			0.930612			0.465306	+	0.885150i	$0.345944\pi$
$410$	−489861.	−	561121.i	−0.143917	−	0.164853i
$411$	826245.			0.241270
$412$			410447.i			0.119128i
$413$			7.91951e6i			2.28467i
$414$	−247762.			−0.0710450
$415$	3.26256e6	+	3.73716e6i	0.929905	+	1.06518i
$416$	155262.			0.0439878
$417$		−	1.10677e6i		−	0.311686i
$418$		−	176739.i		−	0.0494756i
$419$	−5.53638e6			−1.54060			−0.770302	−	0.637680i	$-0.779894\pi$
$419$	−5.53638e6			−1.54060			−0.770302	+	0.637680i	$0.779894\pi$
$420$	1.26012e6	−	1.10009e6i	0.348568	−	0.304302i
$421$	−103687.			−0.0285115			−0.0142558	−	0.999898i	$-0.504538\pi$
$421$	−103687.			−0.0285115			−0.0142558	+	0.999898i	$0.504538\pi$
$422$		−	4.26429e6i		−	1.16564i
$423$			2.93288e6i			0.796973i
$424$	−319690.			−0.0863604
$425$	−3.67657e6	−	500866.i	−0.987348	−	0.134508i
$426$	3.59835e6			0.960682
$427$			2.04341e6i			0.542357i
$428$			2.69823e6i			0.711983i
$429$	−493812.			−0.129544
$430$	1.47534e6	−	1.28798e6i	0.384787	−	0.335921i
$431$	−3.26995e6			−0.847907			−0.423953	−	0.905684i	$-0.639358\pi$
$431$	−3.26995e6			−0.847907			−0.423953	+	0.905684i	$0.639358\pi$
$432$		−	1.03438e6i		−	0.266669i
$433$			294988.i			0.0756109i	0.999285	+	0.0378055i	$0.0120367\pi$
$433$			294988.i			0.0756109i	−0.999285	+	0.0378055i	$0.987963\pi$
$434$	6.31077e6			1.60827
$435$	−2.82046e6	−	3.23075e6i	−0.714656	−	0.818616i
$436$	−1.41187e6			−0.355696
$437$			80530.8i			0.0201724i
$438$			760195.i			0.189339i
$439$	1.18576e6			0.293655			0.146827	−	0.989162i	$-0.453094\pi$
$439$	1.18576e6			0.293655			0.146827	+	0.989162i	$0.453094\pi$
$440$	682915.	+	782258.i	0.168165	+	0.192628i
$441$	−1.28465e6			−0.314550
$442$		−	720131.i		−	0.175330i
$443$			5.37405e6i			1.30105i	0.759486	+	0.650523i	$0.225450\pi$
$443$			5.37405e6i			1.30105i	−0.759486	+	0.650523i	$0.774550\pi$
$444$	2.28904e6			0.551057
$445$	−1.04960e6	+	916302.i	−0.251259	+	0.219351i
$446$	2.59821e6			0.618496
$447$		−	4.63828e6i		−	1.09797i
$448$		−	682676.i		−	0.160701i
$449$	−2.35836e6			−0.552070			−0.276035	−	0.961148i	$-0.589021\pi$
$449$	−2.35836e6			−0.552070			−0.276035	+	0.961148i	$0.589021\pi$
$450$	−1.45022e6	−	197567.i	−0.337601	−	0.0459920i
$451$	966844.			0.223828
$452$			1.43234e6i			0.329761i
$453$			2.98413e6i			0.683239i
$454$	−3.57830e6			−0.814775
$455$	1.06421e6	−	929057.i	0.240989	−	0.210385i
$456$	−109324.			−0.0246210
$457$			7.04674e6i			1.57833i	0.614182	+	0.789164i	$0.289486\pi$
$457$			7.04674e6i			1.57833i	−0.614182	+	0.789164i	$0.710514\pi$
$458$			5.16989e6i			1.15164i
$459$	−4.79763e6			−1.06291
$460$	−311170.	−	356435.i	−0.0685651	−	0.0785391i
$461$	110933.			0.0243114			0.0121557	−	0.999926i	$-0.496131\pi$
$461$	110933.			0.0243114			0.0121557	+	0.999926i	$0.496131\pi$
$462$			2.17125e6i			0.473266i
$463$			3.70000e6i			0.802138i	0.916048	+	0.401069i	$0.131361\pi$
$463$			3.70000e6i			0.802138i	−0.916048	+	0.401069i	$0.868639\pi$
$464$	−1.75028e6			−0.377409
$465$	3.90499e6	+	4.47305e6i	0.837506	+	0.959337i
$466$	5.03590e6			1.07427
$467$		−	2.15388e6i		−	0.457013i	−0.973542	−	0.228507i	$-0.926616\pi$
$467$		−	2.15388e6i		−	0.457013i	0.973542	−	0.228507i	$-0.0733843\pi$
$468$		−	284056.i		−	0.0599501i
$469$	7.53457e6			1.58171
$470$	−4.21931e6	+	3.68348e6i	−0.881042	+	0.769154i
$471$	1.56069e6			0.324163
$472$			3.04105e6i			0.628302i
$473$			2.54209e6i			0.522442i
$474$	1.03845e6			0.212294
$475$	−64215.8	+	471372.i	−0.0130589	+	0.0958582i
$476$	−3.16636e6			−0.640535
$477$			584881.i			0.117699i
$478$		−	4.03240e6i		−	0.807224i
$479$	7.61668e6			1.51680			0.758398	−	0.651792i	$-0.225983\pi$
$479$	7.61668e6			1.51680			0.758398	+	0.651792i	$0.225983\pi$
$480$	483878.	−	422428.i	0.0958590	−	0.0836854i
$481$	1.93317e6			0.380984
$482$			1.07890e6i			0.211526i
$483$		−	989330.i		−	0.192963i
$484$	1.22894e6			0.238461
$485$	3.61045e6	+	4.13566e6i	0.696958	+	0.798344i
$486$	−3.16950e6			−0.608696
$487$		−	740776.i		−	0.141535i	−0.997493	−	0.0707676i	$-0.977455\pi$
$487$		−	740776.i		−	0.141535i	0.997493	−	0.0707676i	$-0.0225449\pi$
$488$			784658.i			0.149153i
$489$	−5.37549e6			−1.01659
$490$	−1.61343e6	−	1.84813e6i	−0.303570	−	0.347730i
$491$	−8.22711e6			−1.54008			−0.770041	−	0.637995i	$-0.779764\pi$
$491$	−8.22711e6			−1.54008			−0.770041	+	0.637995i	$0.779764\pi$
$492$		−	598056.i		−	0.111386i
$493$			8.11808e6i			1.50430i
$494$	−92327.8			−0.0170222
$495$	1.43116e6	−	1.24941e6i	0.262528	−	0.229188i
$496$	2.42330e6			0.442286
$497$		−	1.33619e7i		−	2.42648i
$498$			3.98316e6i			0.719705i
$499$	6.54399e6			1.17650			0.588249	−	0.808680i	$-0.299817\pi$
$499$	6.54399e6			1.17650			0.588249	+	0.808680i	$0.299817\pi$
$500$	−1.53715e6	−	2.33445e6i	−0.274973	−	0.417600i
$501$	−1.97835e6			−0.352135
$502$			7.30897e6i			1.29449i
$503$		−	7.80032e6i		−	1.37465i	−0.726349	−	0.687326i	$-0.758784\pi$
$503$		−	7.80032e6i		−	1.37465i	0.726349	−	0.687326i	$-0.241216\pi$
$504$	−1.24897e6			−0.219016
$505$	2.16608e6	−	1.89100e6i	0.377961	−	0.329962i
$506$	614159.			0.106636
$507$		−	3.90830e6i		−	0.675256i
$508$			2.50998e6i			0.431531i
$509$	−1.06233e7			−1.81745			−0.908726	−	0.417393i	$-0.862944\pi$
$509$	−1.06233e7			−1.81745			−0.908726	+	0.417393i	$0.862944\pi$
$510$	−1.95929e6	−	2.24430e6i	−0.333559	−	0.382081i
$511$	2.82286e6			0.478230
$512$		−	262144.i		−	0.0441942i
$513$			615103.i			0.103194i
$514$	4.86008e6			0.811401
$515$	943103.	+	1.08029e6i	0.156690	+	0.179483i
$516$	1.57245e6			0.259988
$517$		−	7.27011e6i		−	1.19623i
$518$		−	8.49998e6i		−	1.39185i
$519$	7.27122e6			1.18492
$520$	408650.	−	356753.i	0.0662739	−	0.0578575i
$521$	4.48778e6			0.724331			0.362166	−	0.932114i	$-0.382037\pi$
$521$	4.48778e6			0.724331			0.362166	+	0.932114i	$0.382037\pi$
$522$			3.20218e6i			0.514363i
$523$			6.88454e6i			1.10058i	0.834975	+	0.550289i	$0.185482\pi$
$523$			6.88454e6i			1.10058i	−0.834975	+	0.550289i	$0.814518\pi$
$524$	−743844.			−0.118346
$525$	788898.	−	5.79085e6i	0.124917	−	0.916947i
$526$	829830.			0.130775
$527$		−	1.12397e7i		−	1.76290i
$528$			833750.i			0.130152i
$529$	−279841.			−0.0434783
$530$	−841423.	+	734566.i	−0.130114	+	0.113590i
$531$	5.56368e6			0.856299
$532$			405958.i			0.0621874i
$533$		−	505076.i		−	0.0770086i
$534$	−1.11868e6			−0.169767
$535$	6.19985e6	+	7.10173e6i	0.936476	+	1.07270i
$536$	2.89324e6			0.434982
$537$		−	23541.1i		−	0.00352282i
$538$			7.41342e6i			1.10424i
$539$	3.18444e6			0.472129
$540$	−2.37675e6	−	2.72249e6i	−0.350751	−	0.401774i
$541$	−6.11124e6			−0.897710			−0.448855	−	0.893605i	$-0.648168\pi$
$541$	−6.11124e6			−0.897710			−0.448855	+	0.893605i	$0.648168\pi$
$542$		−	242335.i		−	0.0354339i
$543$		−	5.04009e6i		−	0.733565i
$544$	−1.21587e6			−0.176152
$545$	−3.71604e6	+	3.24412e6i	−0.535907	+	0.467849i
$546$	1.13426e6			0.162828
$547$		−	6.01214e6i		−	0.859134i	−0.903035	−	0.429567i	$-0.858666\pi$
$547$		−	6.01214e6i		−	0.859134i	0.903035	−	0.429567i	$-0.141334\pi$
$548$		−	1.17814e6i		−	0.167589i
$549$	1.43555e6			0.203277
$550$	3.59486e6	+	489734.i	0.506728	+	0.0690325i
$551$	1.04082e6			0.146048
$552$		−	379897.i		−	0.0530663i
$553$		−	3.85609e6i		−	0.536210i
$554$	−2.15886e6			−0.298848
$555$	6.02475e6	−	5.25964e6i	0.830246	−	0.724809i
$556$	−1.57815e6			−0.216501
$557$		−	6.14344e6i		−	0.839022i	−0.907750	−	0.419511i	$-0.862202\pi$
$557$		−	6.14344e6i		−	0.839022i	0.907750	−	0.419511i	$-0.137798\pi$
$558$		−	4.43349e6i		−	0.602782i
$559$	1.32798e6			0.179747
$560$	−1.56862e6	−	1.79680e6i	−0.211372	−	0.242119i
$561$	3.86706e6			0.518769
$562$			4.38730e6i			0.585945i
$563$		−	1.19614e7i		−	1.59042i	−0.606336	−	0.795208i	$-0.707361\pi$
$563$		−	1.19614e7i		−	1.59042i	0.606336	−	0.795208i	$-0.292639\pi$
$564$	−4.49704e6			−0.595291
$565$	3.29115e6	+	3.76991e6i	0.433737	+	0.496832i
$566$	−6.00646e6			−0.788093
$567$		−	2.81441e6i		−	0.367646i
$568$		−	5.13089e6i		−	0.667302i
$569$	−887647.			−0.114937			−0.0574685	−	0.998347i	$-0.518303\pi$
$569$	−887647.			−0.114937			−0.0574685	+	0.998347i	$0.518303\pi$
$570$	−287741.	+	251200.i	−0.0370950	+	0.0323841i
$571$	399120.			0.0512286			0.0256143	−	0.999672i	$-0.491846\pi$
$571$	399120.			0.0512286			0.0256143	+	0.999672i	$0.491846\pi$
$572$			704127.i			0.0899831i
$573$			2.47052e6i			0.314342i
$574$	−2.22078e6			−0.281337
$575$	−1.63800e6	−	223147.i	−0.206606	−	0.0281463i
$576$	−479599.			−0.0602313
$577$			6.25258e6i			0.781843i	0.920424	+	0.390922i	$0.127844\pi$
$577$			6.25258e6i			0.781843i	−0.920424	+	0.390922i	$0.872156\pi$
$578$		−	40049.8i		−	0.00498632i
$579$	−905693.			−0.112275
$580$	−4.60673e6	+	4.02170e6i	−0.568621	+	0.496409i
$581$	1.47908e7			1.81782
$582$			4.40788e6i			0.539414i
$583$		−	1.44982e6i		−	0.176662i
$584$	1.08396e6			0.131517
$585$	−652689.	−	747635.i	−0.0788527	−	0.0903233i
$586$	−1.09740e7			−1.32014
$587$		−	9.67070e6i		−	1.15841i	−0.815182	−	0.579205i	$-0.803363\pi$
$587$		−	9.67070e6i		−	1.15841i	0.815182	−	0.579205i	$-0.196637\pi$
$588$		−	1.96978e6i		−	0.234950i
$589$	−1.44103e6			−0.171154
$590$	6.98756e6	+	8.00403e6i	0.826409	+	0.946626i
$591$	−2.23388e6			−0.263082
$592$		−	3.26395e6i		−	0.382771i
$593$			3.46259e6i			0.404356i	0.979349	+	0.202178i	$0.0648020\pi$
$593$			3.46259e6i			0.404356i	−0.979349	+	0.202178i	$0.935198\pi$
$594$	4.69101e6			0.545507
$595$	−8.33385e6	+	7.27549e6i	−0.965057	+	0.842500i
$596$	−6.61373e6			−0.762660
$597$			1.64889e6i			0.189346i
$598$		−	320835.i		−	0.0366884i
$599$	−1.20015e7			−1.36668			−0.683341	−	0.730099i	$-0.739474\pi$
$599$	−1.20015e7			−1.36668			−0.683341	+	0.730099i	$0.739474\pi$
$600$	302933.	−	2.22366e6i	0.0343533	−	0.252168i
$601$	1.12147e7			1.26649			0.633247	−	0.773950i	$-0.281722\pi$
$601$	1.12147e7			1.26649			0.633247	+	0.773950i	$0.281722\pi$
$602$		−	5.83903e6i		−	0.656674i
$603$		−	5.29325e6i		−	0.592828i
$604$	4.25508e6			0.474586
$605$	3.23456e6	−	2.82379e6i	0.359275	−	0.313649i
$606$	2.30867e6			0.255376
$607$			8.20132e6i			0.903466i	0.892153	+	0.451733i	$0.149194\pi$
$607$			8.20132e6i			0.903466i	−0.892153	+	0.451733i	$0.850806\pi$
$608$			155886.i			0.0171020i
$609$	−1.27865e7			−1.39704
$610$	1.80294e6	+	2.06521e6i	0.196181	+	0.224719i
$611$	−3.79789e6			−0.411566
$612$			2.22446e6i			0.240074i
$613$		−	5.44849e6i		−	0.585632i	−0.956169	−	0.292816i	$-0.905408\pi$
$613$		−	5.44849e6i		−	0.585632i	0.956169	−	0.292816i	$-0.0945923\pi$
$614$	−63365.1			−0.00678311
$615$	−1.37418e6	−	1.57408e6i	−0.146506	−	0.167818i
$616$	3.09599e6			0.328737
$617$			1.05278e7i			1.11333i	0.830738	+	0.556664i	$0.187919\pi$
$617$			1.05278e7i			1.11333i	−0.830738	+	0.556664i	$0.812081\pi$
$618$			1.15140e6i			0.121271i
$619$	1.18253e6			0.124047			0.0620235	−	0.998075i	$-0.480245\pi$
$619$	1.18253e6			0.124047			0.0620235	+	0.998075i	$0.480245\pi$
$620$	6.37812e6	−	5.56813e6i	0.666367	−	0.581742i
$621$	−2.13746e6			−0.222417
$622$			7.65765e6i			0.793633i
$623$			4.15405e6i			0.428797i
$624$	435549.			0.0447791
$625$	−9.40975e6	−	2.61230e6i	−0.963558	−	0.267499i
$626$	−1.16733e7			−1.19058
$627$		−	495795.i		−	0.0503655i
$628$		−	2.22539e6i		−	0.225168i
$629$	−1.51387e7			−1.52568
$630$	−3.28729e6	+	2.86982e6i	−0.329979	+	0.288074i
$631$	3.03156e6			0.303105			0.151553	−	0.988449i	$-0.451573\pi$
$631$	3.03156e6			0.303105			0.151553	+	0.988449i	$0.451573\pi$
$632$		−	1.48072e6i		−	0.147462i
$633$		−	1.19624e7i		−	1.18661i
$634$	−4.42546e6			−0.437256
$635$	5.76731e6	+	6.60627e6i	0.567595	+	0.650162i
$636$	−896809.			−0.0879138
$637$		−	1.66354e6i		−	0.162437i
$638$		−	7.93766e6i		−	0.772042i
$639$	−9.38710e6			−0.909451
$640$	−602340.	−	689962.i	−0.0581289	−	0.0665848i
$641$	−942839.			−0.0906342			−0.0453171	−	0.998973i	$-0.514430\pi$
$641$	−942839.			−0.0906342			−0.0453171	+	0.998973i	$0.514430\pi$
$642$			7.56920e6i			0.724790i
$643$		−	1.13511e7i		−	1.08270i	−0.840796	−	0.541352i	$-0.817912\pi$
$643$		−	1.13511e7i		−	1.08270i	0.840796	−	0.541352i	$-0.182088\pi$
$644$	−1.41069e6			−0.134034
$645$	4.13868e6	−	3.61309e6i	0.391708	−	0.341963i
$646$	723023.			0.0681665
$647$		−	1.45738e7i		−	1.36871i	−0.729147	−	0.684357i	$-0.760083\pi$
$647$		−	1.45738e7i		−	1.36871i	0.729147	−	0.684357i	$-0.239917\pi$
$648$		−	1.08072e6i		−	0.101106i
$649$	−1.37914e7			−1.28528
$650$	255836.	−	1.87794e6i	0.0237508	−	0.174341i
$651$	1.77033e7			1.63720
$652$			7.66491e6i			0.706136i
$653$			1.15000e7i			1.05539i	0.849433	+	0.527697i	$0.176944\pi$
$653$			1.15000e7i			1.05539i	−0.849433	+	0.527697i	$0.823056\pi$
$654$	−3.96065e6			−0.362094
$655$	−1.95779e6	+	1.70916e6i	−0.178305	+	0.155661i
$656$	−852769.			−0.0773698
$657$		−	1.98314e6i		−	0.179242i
$658$			1.66990e7i			1.50358i
$659$	−4.34655e6			−0.389880			−0.194940	−	0.980815i	$-0.562451\pi$
$659$	−4.34655e6			−0.389880			−0.194940	+	0.980815i	$0.562451\pi$
$660$	1.91574e6	+	2.19443e6i	0.171190	+	0.196093i
$661$	−1.67589e7			−1.49191			−0.745953	−	0.665998i	$-0.768006\pi$
$661$	−1.67589e7			−1.49191			−0.745953	+	0.665998i	$0.768006\pi$
$662$			4.99790e6i			0.443244i
$663$		−	2.02014e6i		−	0.178484i
$664$	5.67959e6			0.499916
$665$	932788.	+	1.06848e6i	0.0817954	+	0.0936941i
$666$	−5.97148e6			−0.521670
$667$			3.61679e6i			0.314781i
$668$			2.82093e6i			0.244597i
$669$	7.28862e6			0.629622
$670$	7.61498e6	−	6.64792e6i	0.655363	−	0.572135i
$671$	−3.55849e6			−0.305112
$672$		−	1.91507e6i		−	0.163592i
$673$		−	541922.i		−	0.0461211i	−0.999734	−	0.0230605i	$-0.992659\pi$
$673$		−	541922.i		−	0.0461211i	0.999734	−	0.0230605i	$-0.00734105\pi$
$674$	4.69711e6			0.398273
$675$	−1.25112e7	−	1.70442e6i	−1.05691	−	0.143985i
$676$	−5.57285e6			−0.469041
$677$			872392.i			0.0731543i	0.999331	+	0.0365771i	$0.0116455\pi$
$677$			872392.i			0.0731543i	−0.999331	+	0.0365771i	$0.988355\pi$
$678$			4.01806e6i			0.335693i
$679$	1.63679e7			1.36245
$680$	−3.20015e6	+	2.79375e6i	−0.265398	+	0.231694i
$681$	−1.00380e7			−0.829431
$682$			1.09899e7i			0.904757i
$683$		−	2.34019e7i		−	1.91955i	−0.280766	−	0.959776i	$-0.590588\pi$
$683$		−	2.34019e7i		−	1.91955i	0.280766	−	0.959776i	$-0.409412\pi$
$684$	285197.			0.0233080
$685$	−2.70707e6	−	3.10087e6i	−0.220431	−	0.252497i
$686$	3.89036e6			0.315631
$687$			1.45028e7i			1.17236i
$688$		−	2.24216e6i		−	0.180591i
$689$	−757382.			−0.0607809
$690$	−872908.	−	999888.i	−0.0697984	−	0.0799519i
$691$	−1.22760e6			−0.0978051			−0.0489026	−	0.998804i	$-0.515572\pi$
$691$	−1.22760e6			−0.0978051			−0.0489026	+	0.998804i	$0.515572\pi$
$692$		−	1.03680e7i		−	0.823059i
$693$		−	5.66420e6i		−	0.448028i
$694$	9.48799e6			0.747783
$695$	−4.15367e6	+	3.62618e6i	−0.326190	+	0.284765i
$696$	−4.90996e6			−0.384198
$697$			3.95528e6i			0.308386i
$698$		−	2.44279e6i		−	0.189779i
$699$	1.41269e7			1.09359
$700$	−8.25718e6	−	1.12489e6i	−0.636922	−	0.0867691i
$701$	1.11754e7			0.858948			0.429474	−	0.903079i	$-0.358699\pi$
$701$	1.11754e7			0.858948			0.429474	+	0.903079i	$0.358699\pi$
$702$		−	2.45057e6i		−	0.187683i
$703$			1.94093e6i			0.148123i
$704$	1.18884e6			0.0904052
$705$	−1.18362e7	+	1.03331e7i	−0.896890	+	0.782989i
$706$	8.82496e6			0.666348
$707$		−	8.57285e6i		−	0.645025i
$708$			8.53089e6i			0.639604i
$709$	−1.99563e7			−1.49095			−0.745477	−	0.666532i	$-0.767778\pi$
$709$	−1.99563e7			−1.49095			−0.745477	+	0.666532i	$0.767778\pi$
$710$	−1.17895e7	−	1.35045e7i	−0.877706	−	1.00538i
$711$	−2.70901e6			−0.200973
$712$			1.59513e6i			0.117923i
$713$		−	5.00753e6i		−	0.368892i
$714$	−8.88242e6			−0.652057
$715$	1.61790e6	+	1.85326e6i	0.118355	+	0.135572i
$716$	−33567.2			−0.00244700
$717$		−	1.13119e7i		−	0.821744i
$718$		−	1.54617e7i		−	1.11930i
$719$	7.12486e6			0.513989			0.256994	−	0.966413i	$-0.417268\pi$
$719$	7.12486e6			0.513989			0.256994	+	0.966413i	$0.417268\pi$
$720$	−1.26230e6	+	1.10200e6i	−0.0907470	+	0.0792226i
$721$	4.27555e6			0.306305
$722$			9.81170e6i			0.700489i
$723$			3.02657e6i			0.215331i
$724$	−7.18666e6			−0.509543
$725$	−2.88405e6	+	2.11702e7i	−0.203778	+	1.49582i
$726$	3.44748e6			0.242750
$727$		−	1.35858e7i		−	0.953343i	−0.879082	−	0.476671i	$-0.841843\pi$
$727$		−	1.35858e7i		−	0.953343i	0.879082	−	0.476671i	$-0.158157\pi$
$728$		−	1.61734e6i		−	0.113103i
$729$	−1.29946e7			−0.905615
$730$	2.85299e6	−	2.49067e6i	0.198149	−	0.172985i
$731$	−1.03995e7			−0.719811
$732$			2.20116e6i			0.151835i
$733$		−	8.74825e6i		−	0.601397i	−0.953719	−	0.300698i	$-0.902780\pi$
$733$		−	8.74825e6i		−	0.601397i	0.953719	−	0.300698i	$-0.0972198\pi$
$734$	−1.39023e7			−0.952456
$735$	−4.52606e6	−	5.18446e6i	−0.309031	−	0.353985i
$736$	−541696.			−0.0368605
$737$			1.31211e7i			0.889816i
$738$			1.56016e6i			0.105446i
$739$	1.26219e6			0.0850186			0.0425093	−	0.999096i	$-0.486465\pi$
$739$	1.26219e6			0.0850186			0.0425093	+	0.999096i	$0.486465\pi$
$740$	−7.49972e6	−	8.59070e6i	−0.503461	−	0.576699i
$741$	−259002.			−0.0173284
$742$			3.33015e6i			0.222052i
$743$		−	1.86823e6i		−	0.124153i	−0.998071	−	0.0620767i	$-0.980228\pi$
$743$		−	1.86823e6i		−	0.124153i	0.998071	−	0.0620767i	$-0.0197723\pi$
$744$	6.79796e6			0.450242
$745$	−1.74073e7	+	1.51967e7i	−1.14906	+	1.00313i
$746$	1.06694e7			0.701932
$747$		−	1.03910e7i		−	0.681324i
$748$		−	5.51405e6i		−	0.360343i
$749$	2.81070e7			1.83067
$750$	−4.31208e6	−	6.54871e6i	−0.279920	−	0.425112i
$751$	1.29568e7			0.838296			0.419148	−	0.907918i	$-0.362329\pi$
$751$	1.29568e7			0.838296			0.419148	+	0.907918i	$0.362329\pi$
$752$			6.41233e6i			0.413496i
$753$			2.05035e7i			1.31777i
$754$	−4.14661e6			−0.265623
$755$	1.11993e7	−	9.77708e6i	0.715032	−	0.624226i
$756$	−1.07750e7			−0.685664
$757$			1.56707e7i			0.993915i	0.867775	+	0.496958i	$0.165550\pi$
$757$			1.56707e7i			0.993915i	−0.867775	+	0.496958i	$0.834450\pi$
$758$		−	1.08249e7i		−	0.684309i
$759$	1.72287e6			0.108554
$760$	358186.	+	410291.i	0.0224944	+	0.0257666i
$761$	−2.42696e6			−0.151915			−0.0759574	−	0.997111i	$-0.524201\pi$
$761$	−2.42696e6			−0.151915			−0.0759574	+	0.997111i	$0.524201\pi$
$762$			7.04112e6i			0.439293i
$763$			1.47072e7i			0.914574i
$764$	3.52272e6			0.218346
$765$	5.11124e6	+	5.85476e6i	0.315771	+	0.361706i
$766$	−1.72336e6			−0.106122
$767$			7.20459e6i			0.442202i
$768$		−	735378.i		−	0.0449891i
$769$	−5.06161e6			−0.308655			−0.154327	−	0.988020i	$-0.549321\pi$
$769$	−5.06161e6			−0.308655			−0.154327	+	0.988020i	$0.549321\pi$
$770$	8.14864e6	−	7.11380e6i	0.495288	−	0.432389i
$771$	1.36337e7			0.825997
$772$			1.29143e6i			0.0779878i
$773$		−	785817.i		−	0.0473013i	−0.999720	−	0.0236506i	$-0.992471\pi$
$773$		−	785817.i		−	0.0473013i	0.999720	−	0.0236506i	$-0.00752893\pi$
$774$	−4.10208e6			−0.246123
$775$	3.99304e6	−	2.93106e7i	0.238808	−	1.75295i
$776$	6.28520e6			0.374684
$777$		−	2.38445e7i		−	1.41689i
$778$		−	2.15450e7i		−	1.27614i
$779$	507105.			0.0299402
$780$	1.14636e6	−	1.00078e6i	0.0674660	−	0.0588982i
$781$	2.32690e7			1.36506
$782$			2.51247e6i			0.146921i
$783$			2.76254e7i			1.61029i
$784$	−2.80872e6			−0.163199
$785$	−5.11337e6	−	5.85720e6i	−0.296164	−	0.339247i
$786$	−2.08666e6			−0.120475
$787$			5.37837e6i			0.309538i	0.987951	+	0.154769i	$0.0494633\pi$
$787$			5.37837e6i			0.309538i	−0.987951	+	0.154769i	$0.950537\pi$
$788$			3.18529e6i			0.182740i
$789$	2.32788e6			0.133127
$790$	−3.40232e6	−	3.89725e6i	−0.193958	−	0.222172i
$791$	1.49204e7			0.847889
$792$		−	2.17502e6i		−	0.123211i
$793$			1.85894e6i			0.104974i
$794$	6.57107e6			0.369901
$795$	−2.36040e6	+	2.06064e6i	−0.132455	+	0.115634i
$796$	2.35115e6			0.131522
$797$		−	3.41647e6i		−	0.190516i	−0.995453	−	0.0952580i	$-0.969632\pi$
$797$		−	3.41647e6i		−	0.190516i	0.995453	−	0.0952580i	$-0.0303676\pi$
$798$			1.13881e6i			0.0633060i
$799$	2.97414e7			1.64814
$800$	−3.17071e6	−	431952.i	−0.175159	−	0.0238622i
$801$	2.91834e6			0.160714
$802$			1.58593e7i			0.870658i
$803$			4.91586e6i			0.269036i
$804$	8.11623e6			0.442807
$805$	−3.71292e6	+	3.24140e6i	−0.201942	+	0.176296i
$806$	5.74108e6			0.311283
$807$			2.07965e7i			1.12410i
$808$		−	3.29193e6i		−	0.177387i
$809$	2.54327e7			1.36622			0.683111	−	0.730315i	$-0.260627\pi$
$809$	2.54327e7			1.36622			0.683111	+	0.730315i	$0.260627\pi$
$810$	−2.48322e6	−	2.84445e6i	−0.132985	−	0.152330i
$811$	1.35849e7			0.725276			0.362638	−	0.931930i	$-0.381876\pi$
$811$	1.35849e7			0.725276			0.362638	+	0.931930i	$0.381876\pi$
$812$			1.82323e7i			0.970403i
$813$		−	679810.i		−	0.0360712i
$814$	1.48023e7			0.783010
$815$	1.76120e7	+	2.01740e7i	0.928785	+	1.06389i
$816$	−3.41080e6			−0.179321
$817$			1.33331e6i			0.0698839i
$818$		−	1.25932e7i		−	0.658042i
$819$	−2.95896e6			−0.154145
$820$	−2.24448e6	+	1.95944e6i	−0.116569	+	0.101765i
$821$	1.52990e7			0.792145			0.396073	−	0.918219i	$-0.370373\pi$
$821$	1.52990e7			0.792145			0.396073	+	0.918219i	$0.370373\pi$
$822$		−	3.30498e6i		−	0.170604i
$823$		−	5.67780e6i		−	0.292200i	−0.989270	−	0.146100i	$-0.953328\pi$
$823$		−	5.67780e6i		−	0.292200i	0.989270	−	0.146100i	$-0.0466722\pi$
$824$	1.64179e6			0.0842363
$825$	1.00845e7	+	1.37382e6i	0.515843	+	0.0702743i
$826$	3.16780e7			1.61550
$827$		−	7.35232e6i		−	0.373818i	−0.982377	−	0.186909i	$-0.940153\pi$
$827$		−	7.35232e6i		−	0.373818i	0.982377	−	0.186909i	$-0.0598470\pi$
$828$			991047.i			0.0502364i
$829$	−2.58137e7			−1.30456			−0.652280	−	0.757978i	$-0.726187\pi$
$829$	−2.58137e7			−1.30456			−0.652280	+	0.757978i	$0.726187\pi$
$830$	1.49487e7	−	1.30502e7i	0.753194	−	0.657542i
$831$	−6.05614e6			−0.304224
$832$		−	621049.i		−	0.0311041i
$833$			1.30273e7i			0.650490i
$834$	−4.42709e6			−0.220396
$835$	6.48178e6	+	7.42468e6i	0.321720	+	0.368520i
$836$	−706955.			−0.0349845
$837$		−	3.82480e7i		−	1.88710i
$838$			2.21455e7i			1.08937i
$839$	−9.02451e6			−0.442607			−0.221304	−	0.975205i	$-0.571031\pi$
$839$	−9.02451e6			−0.442607			−0.221304	+	0.975205i	$0.571031\pi$
$840$	−4.40035e6	−	5.04046e6i	−0.215174	−	0.246475i
$841$	2.62338e7			1.27900
$842$			414749.i			0.0201607i
$843$			1.23075e7i			0.596485i
$844$	−1.70571e7			−0.824234
$845$	−1.46677e7	+	1.28050e7i	−0.706677	+	0.616933i
$846$	1.17315e7			0.563545
$847$		−	1.28016e7i		−	0.613136i
$848$			1.27876e6i			0.0610660i
$849$	−1.68496e7			−0.802269
$850$	−2.00346e6	+	1.47063e7i	−0.0951117	+	0.698160i
$851$	−6.74464e6			−0.319253
$852$		−	1.43934e7i		−	0.679305i
$853$			948293.i			0.0446242i	0.999751	+	0.0223121i	$0.00710275\pi$
$853$			948293.i			0.0446242i	−0.999751	+	0.0223121i	$0.992897\pi$
$854$	8.17363e6			0.383504
$855$	750637.	−	655310.i	0.0351168	−	0.0306571i
$856$	1.07929e7			0.503448
$857$			1.46762e7i			0.682592i	0.939956	+	0.341296i	$0.110866\pi$
$857$			1.46762e7i			0.682592i	−0.939956	+	0.341296i	$0.889134\pi$
$858$			1.97525e6i			0.0916017i
$859$	3.08615e7			1.42703			0.713516	−	0.700638i	$-0.247101\pi$
$859$	3.08615e7			1.42703			0.713516	+	0.700638i	$0.247101\pi$
$860$	−5.15191e6	−	5.90135e6i	−0.237532	−	0.272085i
$861$	−6.22984e6			−0.286397
$862$			1.30798e7i			0.599560i
$863$		−	2.50437e7i		−	1.14465i	−0.820028	−	0.572324i	$-0.806042\pi$
$863$		−	2.50437e7i		−	1.14465i	0.820028	−	0.572324i	$-0.193958\pi$
$864$	−4.13753e6			−0.188563
$865$	−2.38231e7	−	2.72886e7i	−1.08258	−	1.24006i
$866$	1.17995e6			0.0534650
$867$		−	112349.i		−	0.00507602i
$868$		−	2.52431e7i		−	1.13722i
$869$	6.71518e6			0.301654
$870$	−1.29230e7	+	1.12818e7i	−0.578849	+	0.505338i
$871$	6.85440e6			0.306143
$872$			5.64749e6i			0.251515i
$873$		−	1.14989e7i		−	0.510648i
$874$	322123.			0.0142641
$875$	−2.43176e7	+	1.60122e7i	−1.07374	+	0.707018i
$876$	3.04078e6			0.133883
$877$			3.35264e7i			1.47193i	0.677018	+	0.735967i	$0.263272\pi$
$877$			3.35264e7i			1.47193i	−0.677018	+	0.735967i	$0.736728\pi$
$878$		−	4.74305e6i		−	0.207645i
$879$	−3.07847e7			−1.34389
$880$	3.12903e6	−	2.73166e6i	0.136208	−	0.118910i
$881$	8.23161e6			0.357310			0.178655	−	0.983912i	$-0.442825\pi$
$881$	8.23161e6			0.357310			0.178655	+	0.983912i	$0.442825\pi$
$882$			5.13862e6i			0.222420i
$883$			1.11787e7i			0.482492i	0.970464	+	0.241246i	$0.0775561\pi$
$883$			1.11787e7i			0.482492i	−0.970464	+	0.241246i	$0.922444\pi$
$884$	−2.88052e6			−0.123977
$885$	1.96018e7	+	2.24533e7i	0.841275	+	0.963654i
$886$	2.14962e7			0.919979
$887$			8.50824e6i			0.363104i	0.983381	+	0.181552i	$0.0581120\pi$
$887$			8.50824e6i			0.363104i	−0.983381	+	0.181552i	$0.941888\pi$
$888$		−	9.15617e6i		−	0.389656i
$889$	2.61460e7			1.10956
$890$	3.66521e6	+	4.19838e6i	0.155104	+	0.177667i
$891$	4.90115e6			0.206825
$892$		−	1.03928e7i		−	0.437343i
$893$		−	3.81314e6i		−	0.160012i
$894$	−1.85531e7			−0.776379
$895$	−88348.8	+	77129.0i	−0.00368675	+	0.00321855i
$896$	−2.73070e6			−0.113633
$897$		−	900020.i		−	0.0373483i
$898$			9.43344e6i			0.390372i
$899$	−6.47195e7			−2.67077
$900$	−790267.	+	5.80090e6i	−0.0325213	+	0.238720i
$901$	5.93109e6			0.243401
$902$		−	3.86737e6i		−	0.158270i
$903$		−	1.63799e7i		−	0.668486i
$904$	5.72935e6			0.233176
$905$	−1.89153e7	+	1.65131e7i	−0.767699	+	0.670205i
$906$	1.19365e7			0.483123
$907$			8.50276e6i			0.343196i	0.985167	+	0.171598i	$0.0548930\pi$
$907$			8.50276e6i			0.343196i	−0.985167	+	0.171598i	$0.945107\pi$
$908$			1.43132e7i			0.576133i
$909$	−6.02267e6			−0.241757
$910$	−3.71623e6	−	4.25682e6i	−0.148764	−	0.170405i
$911$	−3.06697e7			−1.22437			−0.612186	−	0.790714i	$-0.709710\pi$
$911$	−3.06697e7			−1.22437			−0.612186	+	0.790714i	$0.709710\pi$
$912$			437298.i			0.0174097i
$913$			2.57574e7i			1.02265i
$914$	2.81869e7			1.11605
$915$	5.05770e6	+	5.79343e6i	0.199710	+	0.228762i
$916$	2.06796e7			0.814334
$917$			7.74848e6i			0.304294i
$918$			1.91905e7i			0.751589i
$919$	8.08233e6			0.315681			0.157840	−	0.987465i	$-0.449547\pi$
$919$	8.08233e6			0.315681			0.157840	+	0.987465i	$0.449547\pi$
$920$	−1.42574e6	+	1.24468e6i	−0.0555356	+	0.0484828i
$921$	−177755.			−0.00690513
$922$		−	443733.i		−	0.0171907i
$923$		−	1.21557e7i		−	0.469650i
$924$	8.68501e6			0.334650
$925$	−3.94785e7	−	5.37822e6i	−1.51707	−	0.206673i
$926$	1.48000e7			0.567197
$927$		−	3.00369e6i		−	0.114804i
$928$			7.00112e6i			0.266869i
$929$	3.56711e7			1.35605			0.678027	−	0.735037i	$-0.262835\pi$
$929$	3.56711e7			1.35605			0.678027	+	0.735037i	$0.262835\pi$
$930$	1.78922e7	−	1.56200e7i	0.678354	−	0.592206i
$931$	1.67022e6			0.0631539
$932$		−	2.01436e7i		−	0.759622i
$933$			2.14816e7i			0.807909i
$934$	−8.61551e6			−0.323157
$935$	−1.26699e7	−	1.45130e7i	−0.473962	−	0.542909i
$936$	−1.13622e6			−0.0423911
$937$			6.31681e6i			0.235044i	0.993070	+	0.117522i	$0.0374951\pi$
$937$			6.31681e6i			0.235044i	−0.993070	+	0.117522i	$0.962505\pi$
$938$		−	3.01383e7i		−	1.11844i
$939$	−3.27466e7			−1.21200
$940$	1.47339e7	+	1.68772e7i	0.543874	+	0.622991i
$941$	−5.12084e7			−1.88524			−0.942621	−	0.333865i	$-0.891647\pi$
$941$	−5.12084e7			−1.88524			−0.942621	+	0.333865i	$0.891647\pi$
$942$		−	6.24275e6i		−	0.229218i
$943$			1.76217e6i			0.0645309i
$944$	1.21642e7			0.444277
$945$	−2.83597e7	+	2.47581e7i	−1.03305	+	0.901859i
$946$	1.01684e7			0.369422
$947$		−	3.35443e6i		−	0.121547i	−0.998152	−	0.0607734i	$-0.980643\pi$
$947$		−	3.35443e6i		−	0.121547i	0.998152	−	0.0607734i	$-0.0193567\pi$
$948$		−	4.15378e6i		−	0.150115i
$949$	2.56803e6			0.0925624
$950$	1.88549e6	+	256863.i	0.0677820	+	0.00923407i
$951$	−1.24145e7			−0.445121
$952$			1.26654e7i			0.452927i
$953$			1.49681e7i			0.533869i	0.963715	+	0.266935i	$0.0860108\pi$
$953$			1.49681e7i			0.533869i	−0.963715	+	0.266935i	$0.913989\pi$
$954$	2.33952e6			0.0832255
$955$	9.27178e6	−	8.09431e6i	0.328969	−	0.287191i
$956$	−1.61296e7			−0.570793
$957$		−	2.22671e7i		−	0.785929i
$958$		−	3.04667e7i		−	1.07254i
$959$	−1.22725e7			−0.430910
$960$	−1.68971e6	−	1.93551e6i	−0.0591745	−	0.0677825i
$961$	6.09765e7			2.12987
$962$		−	7.73267e6i		−	0.269396i
$963$		−	1.97459e7i		−	0.686139i
$964$	4.31559e6			0.149571
$965$	2.96737e6	+	3.39903e6i	0.102578	+	0.117500i
$966$	−3.95732e6			−0.136445
$967$		−	3.85976e7i		−	1.32738i	−0.748010	−	0.663688i	$-0.768990\pi$
$967$		−	3.85976e7i		−	1.32738i	0.748010	−	0.663688i	$-0.231010\pi$
$968$		−	4.91576e6i		−	0.168617i
$969$	2.02826e6			0.0693926
$970$	1.65426e7	−	1.44418e7i	0.564514	−	0.492824i
$971$	4.31685e6			0.146933			0.0734664	−	0.997298i	$-0.476594\pi$
$971$	4.31685e6			0.146933			0.0734664	+	0.997298i	$0.476594\pi$
$972$			1.26780e7i			0.430413i
$973$			1.64393e7i			0.556673i
$974$	−2.96310e6			−0.100081
$975$	717682.	−	5.26810e6i	0.0241780	−	0.177477i
$976$	3.13863e6			0.105467
$977$			4.55214e6i			0.152573i	0.997086	+	0.0762867i	$0.0243064\pi$
$977$			4.55214e6i			0.152573i	−0.997086	+	0.0762867i	$0.975694\pi$
$978$			2.15020e7i			0.718838i
$979$	−7.23406e6			−0.241227
$980$	−7.39253e6	+	6.45371e6i	−0.245883	+	0.214657i
$981$	1.03322e7			0.342785
$982$			3.29085e7i			1.08900i
$983$		−	4.80318e6i		−	0.158542i	−0.996853	−	0.0792712i	$-0.974741\pi$
$983$		−	4.80318e6i		−	0.158542i	0.996853	−	0.0792712i	$-0.0252593\pi$
$984$	−2.39222e6			−0.0787615
$985$	7.31897e6	+	8.38366e6i	0.240359	+	0.275323i
$986$	3.24723e7			1.06370
$987$			4.68448e7i			1.53062i
$988$			369311.i			0.0120365i
$989$	−4.63321e6			−0.150623
$990$	−4.99764e6	−	5.72464e6i	−0.162061	−	0.185635i
$991$	−2.01827e7			−0.652823			−0.326411	−	0.945228i	$-0.605839\pi$
$991$	−2.01827e7			−0.652823			−0.326411	+	0.945228i	$0.605839\pi$
$992$		−	9.69321e6i		−	0.312744i
$993$			1.40203e7i			0.451217i
$994$	−5.34475e7			−1.71578
$995$	6.18823e6	−	5.40235e6i	0.198157	−	0.172992i
$996$	1.59326e7			0.508908
$997$			3.27880e7i			1.04466i	0.852742	+	0.522332i	$0.174938\pi$
$997$			3.27880e7i			1.04466i	−0.852742	+	0.522332i	$0.825062\pi$
$998$		−	2.61760e7i		−	0.831910i
$999$	−5.15163e7			−1.63317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.b.a.139.5	✓	26
5.4	even	2	inner	230.6.b.a.139.22	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.b.a.139.5	✓	26	1.1	even	1	trivial
230.6.b.a.139.22	yes	26	5.4	even	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -11.2210i q^{3} -16.0000 q^{4} +(-42.1119 + 36.7639i) q^{5} -44.8839 q^{6} +166.669i q^{7} +64.0000i q^{8} +117.090 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} -11.2210i q^{3} -16.0000 q^{4} +(-42.1119 + 36.7639i) q^{5} -44.8839 q^{6} +166.669i q^{7} +64.0000i q^{8} +117.090 q^{9} +(147.056 + 168.448i) q^{10} -290.245 q^{11} +179.536i q^{12} +151.623i q^{13} +666.676 q^{14} +(412.527 + 472.537i) q^{15} +256.000 q^{16} -1187.37i q^{17} -468.358i q^{18} -152.232 q^{19} +(673.791 - 588.223i) q^{20} +1870.19 q^{21} +1160.98i q^{22} -529.000i q^{23} +718.143 q^{24} +(421.828 - 3096.40i) q^{25} +606.493 q^{26} -4040.56i q^{27} -2666.70i q^{28} -6837.03 q^{29} +(1890.15 - 1650.11i) q^{30} +9466.03 q^{31} -1024.00i q^{32} +3256.84i q^{33} -4749.48 q^{34} +(-6127.40 - 7018.75i) q^{35} -1873.43 q^{36} -12749.8i q^{37} +608.929i q^{38} +1701.36 q^{39} +(-2352.89 - 2695.16i) q^{40} -3331.13 q^{41} -7480.76i q^{42} -8758.43i q^{43} +4643.92 q^{44} +(-4930.87 + 4304.67i) q^{45} -2116.00 q^{46} +25048.2i q^{47} -2872.57i q^{48} -10971.5 q^{49} +(-12385.6 - 1687.31i) q^{50} -13323.4 q^{51} -2425.97i q^{52} +4995.16i q^{53} -16162.2 q^{54} +(12222.8 - 10670.6i) q^{55} -10666.8 q^{56} +1708.19i q^{57} +27348.1i q^{58} +47516.4 q^{59} +(-6600.44 - 7560.59i) q^{60} +12260.3 q^{61} -37864.1i q^{62} +19515.2i q^{63} -4096.00 q^{64} +(-5574.27 - 6385.15i) q^{65} +13027.3 q^{66} -45206.8i q^{67} +18997.9i q^{68} -5935.90 q^{69} +(-28075.0 + 24509.6i) q^{70} -80170.2 q^{71} +7493.74i q^{72} -16936.9i q^{73} -50999.2 q^{74} +(-34744.6 - 4733.32i) q^{75} +2435.71 q^{76} -48374.9i q^{77} -6805.45i q^{78} -23136.2 q^{79} +(-10780.7 + 9411.56i) q^{80} -16886.2 q^{81} +13324.5i q^{82} -88743.6i q^{83} -29923.0 q^{84} +(43652.3 + 50002.4i) q^{85} -35033.7 q^{86} +76718.2i q^{87} -18575.7i q^{88} +24924.0 q^{89} +(17218.7 + 19723.5i) q^{90} -25270.9 q^{91} +8464.00i q^{92} -106218. i q^{93} +100193. q^{94} +(6410.79 - 5596.65i) q^{95} -11490.3 q^{96} -98206.3i q^{97} +43886.2i q^{98} -33984.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) \) 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) \) 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

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