LMFDB - Embedded newform 230.6.b.a.139.13

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			139.13
Character	$\chi$	$=$	230.139
Dual form			230.6.b.a.139.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} +24.8599i q^{3} -16.0000 q^{4} +(13.9210 - 54.1406i) q^{5} +99.4396 q^{6} +51.4359i q^{7} +64.0000i q^{8} -375.015 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} +24.8599i q^{3} -16.0000 q^{4} +(13.9210 - 54.1406i) q^{5} +99.4396 q^{6} +51.4359i q^{7} +64.0000i q^{8} -375.015 q^{9} +(-216.562 - 55.6841i) q^{10} +150.422 q^{11} -397.758i q^{12} -560.943i q^{13} +205.744 q^{14} +(1345.93 + 346.075i) q^{15} +256.000 q^{16} +1843.48i q^{17} +1500.06i q^{18} +2485.95 q^{19} +(-222.736 + 866.250i) q^{20} -1278.69 q^{21} -601.690i q^{22} -529.000i q^{23} -1591.03 q^{24} +(-2737.41 - 1507.39i) q^{25} -2243.77 q^{26} -3281.87i q^{27} -822.975i q^{28} +841.764 q^{29} +(1384.30 - 5383.72i) q^{30} +1658.14 q^{31} -1024.00i q^{32} +3739.49i q^{33} +7373.93 q^{34} +(2784.77 + 716.041i) q^{35} +6000.24 q^{36} +6023.45i q^{37} -9943.81i q^{38} +13945.0 q^{39} +(3465.00 + 890.946i) q^{40} -21358.7 q^{41} +5114.77i q^{42} +12665.3i q^{43} -2406.76 q^{44} +(-5220.59 + 20303.5i) q^{45} -2116.00 q^{46} +15417.0i q^{47} +6364.13i q^{48} +14161.3 q^{49} +(-6029.54 + 10949.6i) q^{50} -45828.8 q^{51} +8975.09i q^{52} +24158.0i q^{53} -13127.5 q^{54} +(2094.04 - 8143.96i) q^{55} -3291.90 q^{56} +61800.5i q^{57} -3367.06i q^{58} +14789.7 q^{59} +(-21534.9 - 5537.21i) q^{60} -16589.1 q^{61} -6632.54i q^{62} -19289.2i q^{63} -4096.00 q^{64} +(-30369.8 - 7808.90i) q^{65} +14958.0 q^{66} +43220.0i q^{67} -29495.7i q^{68} +13150.9 q^{69} +(2864.16 - 11139.1i) q^{70} +50914.4 q^{71} -24000.9i q^{72} +64277.4i q^{73} +24093.8 q^{74} +(37473.5 - 68051.7i) q^{75} -39775.2 q^{76} +7737.12i q^{77} -55780.0i q^{78} -105189. q^{79} +(3563.78 - 13860.0i) q^{80} -9541.54 q^{81} +85434.7i q^{82} +38980.8i q^{83} +20459.1 q^{84} +(99807.3 + 25663.2i) q^{85} +50661.4 q^{86} +20926.2i q^{87} +9627.04i q^{88} +104099. q^{89} +(81214.1 + 20882.4i) q^{90} +28852.6 q^{91} +8464.00i q^{92} +41221.1i q^{93} +61668.0 q^{94} +(34607.0 - 134591. i) q^{95} +25456.5 q^{96} -52850.5i q^{97} -56645.4i q^{98} -56410.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			24.8599i			1.59476i	0.603475	+	0.797382i	$0.293782\pi$
$3$			24.8599i			1.59476i	−0.603475	+	0.797382i	$0.706218\pi$
$4$	−16.0000			−0.500000
$5$	13.9210	−	54.1406i	0.249027	−	0.968497i
$5$	13.9210	−	54.1406i	0.249027	−	0.968497i
$6$	99.4396			1.12767
$7$			51.4359i			0.396754i	0.980126	+	0.198377i	$0.0635671\pi$
$7$			51.4359i			0.396754i	−0.980126	+	0.198377i	$0.936433\pi$
$8$			64.0000i			0.353553i
$9$	−375.015			−1.54327
$10$	−216.562	−	55.6841i	−0.684830	−	0.176089i
$11$	150.422			0.374827			0.187414	−	0.982281i	$-0.439990\pi$
$11$	150.422			0.374827			0.187414	+	0.982281i	$0.439990\pi$
$12$		−	397.758i		−	0.797382i
$13$		−	560.943i		−	0.920577i	−0.887769	−	0.460289i	$-0.847746\pi$
$13$		−	560.943i		−	0.920577i	0.887769	−	0.460289i	$-0.152254\pi$
$14$	205.744			0.280548
$15$	1345.93	+	346.075i	1.54452	+	0.397139i
$16$	256.000			0.250000
$17$			1843.48i			1.54710i	0.633738	+	0.773548i	$0.281520\pi$
$17$			1843.48i			1.54710i	−0.633738	+	0.773548i	$0.718480\pi$
$18$			1500.06i			1.09126i
$19$	2485.95			1.57982			0.789912	−	0.613220i	$-0.210126\pi$
$19$	2485.95			1.57982			0.789912	+	0.613220i	$0.210126\pi$
$20$	−222.736	+	866.250i	−0.124513	+	0.484248i
$21$	−1278.69			−0.632729
$22$		−	601.690i		−	0.265043i
$23$		−	529.000i		−	0.208514i
$23$		−	529.000i		−	0.208514i
$24$	−1591.03			−0.563834
$25$	−2737.41	−	1507.39i	−0.875971	−	0.482363i
$26$	−2243.77			−0.650947
$27$		−	3281.87i		−	0.866388i
$28$		−	822.975i		−	0.198377i
$29$	841.764			0.185864			0.0929320	−	0.995672i	$-0.470376\pi$
$29$	841.764			0.185864			0.0929320	+	0.995672i	$0.470376\pi$
$30$	1384.30	−	5383.72i	0.280820	−	1.09214i
$31$	1658.14			0.309896			0.154948	−	0.987923i	$-0.450479\pi$
$31$	1658.14			0.309896			0.154948	+	0.987923i	$0.450479\pi$
$32$		−	1024.00i		−	0.176777i
$33$			3739.49i			0.597761i
$34$	7373.93			1.09396
$35$	2784.77	+	716.041i	0.384255	+	0.0988025i
$36$	6000.24			0.771635
$37$			6023.45i			0.723338i	0.932307	+	0.361669i	$0.117793\pi$
$37$			6023.45i			0.723338i	−0.932307	+	0.361669i	$0.882207\pi$
$38$		−	9943.81i		−	1.11710i
$39$	13945.0			1.46810
$40$	3465.00	+	890.946i	0.342415	+	0.0880443i
$41$	−21358.7			−1.98433			−0.992167	−	0.124917i	$-0.960134\pi$
$41$	−21358.7			−1.98433			−0.992167	+	0.124917i	$0.960134\pi$
$42$			5114.77i			0.447407i
$43$			12665.3i			1.04459i	0.852765	+	0.522295i	$0.174924\pi$
$43$			12665.3i			1.04459i	−0.852765	+	0.522295i	$0.825076\pi$
$44$	−2406.76			−0.187414
$45$	−5220.59	+	20303.5i	−0.384316	+	1.49465i
$46$	−2116.00			−0.147442
$47$			15417.0i			1.01802i	0.860761	+	0.509009i	$0.169988\pi$
$47$			15417.0i			1.01802i	−0.860761	+	0.509009i	$0.830012\pi$
$48$			6364.13i			0.398691i
$49$	14161.3			0.842586
$50$	−6029.54	+	10949.6i	−0.341082	+	0.619405i
$51$	−45828.8			−2.46725
$52$			8975.09i			0.460289i
$53$			24158.0i			1.18133i	0.806917	+	0.590665i	$0.201135\pi$
$53$			24158.0i			1.18133i	−0.806917	+	0.590665i	$0.798865\pi$
$54$	−13127.5			−0.612629
$55$	2094.04	−	8143.96i	0.0933420	−	0.363019i
$56$	−3291.90			−0.140274
$57$			61800.5i			2.51945i
$58$		−	3367.06i		−	0.131426i
$59$	14789.7			0.553132			0.276566	−	0.960995i	$-0.410804\pi$
$59$	14789.7			0.553132			0.276566	+	0.960995i	$0.410804\pi$
$60$	−21534.9	−	5537.21i	−0.772261	−	0.198570i
$61$	−16589.1			−0.570820			−0.285410	−	0.958405i	$-0.592130\pi$
$61$	−16589.1			−0.570820			−0.285410	+	0.958405i	$0.592130\pi$
$62$		−	6632.54i		−	0.219129i
$63$		−	19289.2i		−	0.612299i
$64$	−4096.00			−0.125000
$65$	−30369.8	−	7808.90i	−0.891576	−	0.229249i
$66$	14958.0			0.422681
$67$			43220.0i			1.17625i	0.808772	+	0.588123i	$0.200133\pi$
$67$			43220.0i			1.17625i	−0.808772	+	0.588123i	$0.799867\pi$
$68$		−	29495.7i		−	0.773548i
$69$	13150.9			0.332531
$70$	2864.16	−	11139.1i	0.0698639	−	0.271709i
$71$	50914.4			1.19866			0.599328	−	0.800503i	$-0.295434\pi$
$71$	50914.4			1.19866			0.599328	+	0.800503i	$0.295434\pi$
$72$		−	24000.9i		−	0.545628i
$73$			64277.4i			1.41173i	0.708347	+	0.705864i	$0.249441\pi$
$73$			64277.4i			1.41173i	−0.708347	+	0.705864i	$0.750559\pi$
$74$	24093.8			0.511477
$75$	37473.5	−	68051.7i	0.769256	−	1.39697i
$76$	−39775.2			−0.789912
$77$			7737.12i			0.148714i
$78$		−	55780.0i		−	1.03811i
$79$	−105189.			−1.89629			−0.948144	−	0.317841i	$-0.897042\pi$
$79$	−105189.			−1.89629			−0.948144	+	0.317841i	$0.897042\pi$
$80$	3563.78	−	13860.0i	0.0622567	−	0.242124i
$81$	−9541.54			−0.161587
$82$			85434.7i			1.40314i
$83$			38980.8i			0.621092i	0.950558	+	0.310546i	$0.100512\pi$
$83$			38980.8i			0.621092i	−0.950558	+	0.310546i	$0.899488\pi$
$84$	20459.1			0.316365
$85$	99807.3	+	25663.2i	1.49836	+	0.385268i
$86$	50661.4			0.738637
$87$			20926.2i			0.296409i
$88$			9627.04i			0.132521i
$89$	104099.			1.39307			0.696535	−	0.717523i	$-0.254724\pi$
$89$	104099.			1.39307			0.696535	+	0.717523i	$0.254724\pi$
$90$	81214.1	+	20882.4i	1.05688	+	0.271752i
$91$	28852.6			0.365243
$92$			8464.00i			0.104257i
$93$			41221.1i			0.494210i
$94$	61668.0			0.719847
$95$	34607.0	−	134591.i	0.393419	−	1.53005i
$96$	25456.5			0.281917
$97$		−	52850.5i		−	0.570321i	−0.958480	−	0.285161i	$-0.907953\pi$
$97$		−	52850.5i		−	0.570321i	0.958480	−	0.285161i	$-0.0920469\pi$
$98$		−	56645.4i		−	0.595798i
$99$	−56410.6			−0.578460
$100$	43798.6	+	24118.2i	0.437986	+	0.241182i
$101$	137375.			1.34000			0.670000	−	0.742361i	$-0.266294\pi$
$101$	137375.			1.34000			0.670000	+	0.742361i	$0.266294\pi$
$102$			183315.i			1.74461i
$103$			32174.9i			0.298830i	0.988775	+	0.149415i	$0.0477390\pi$
$103$			32174.9i			0.298830i	−0.988775	+	0.149415i	$0.952261\pi$
$104$	35900.4			0.325473
$105$	−17800.7	+	69229.2i	−0.157567	+	0.612796i
$106$	96632.0			0.835326
$107$			87644.0i			0.740053i	0.929021	+	0.370027i	$0.120651\pi$
$107$			87644.0i			0.740053i	−0.929021	+	0.370027i	$0.879349\pi$
$108$			52510.0i			0.433194i
$109$	26559.7			0.214120			0.107060	−	0.994253i	$-0.465856\pi$
$109$	26559.7			0.214120			0.107060	+	0.994253i	$0.465856\pi$
$110$	−32575.9	−	8376.14i	−0.256693	−	0.0660028i
$111$	−149742.			−1.15355
$112$			13167.6i			0.0991886i
$113$		−	164500.i		−	1.21191i	−0.795500	−	0.605954i	$-0.792792\pi$
$113$		−	164500.i		−	1.21191i	0.795500	−	0.605954i	$-0.207208\pi$
$114$	247202.			1.78152
$115$	−28640.4	−	7364.22i	−0.201945	−	0.0519257i
$116$	−13468.2			−0.0929320
$117$			210362.i			1.42070i
$118$		−	59158.7i		−	0.391123i
$119$	−94821.3			−0.613817
$120$	−22148.8	+	86139.5i	−0.140410	+	0.546071i
$121$	−138424.			−0.859505
$122$			66356.6i			0.403631i
$123$		−	530975.i		−	3.16454i
$124$	−26530.2			−0.154948
$125$	−119718.	+	127221.i	−0.685308	+	0.728254i
$126$	−77156.9			−0.432961
$127$		−	144898.i		−	0.797171i	−0.917131	−	0.398586i	$-0.869501\pi$
$127$		−	144898.i		−	0.797171i	0.917131	−	0.398586i	$-0.130499\pi$
$128$			16384.0i			0.0883883i
$129$	−314859.			−1.66587
$130$	−31235.6	+	121479.i	−0.162103	+	0.630440i
$131$	205916.			1.04836			0.524181	−	0.851607i	$-0.324371\pi$
$131$	205916.			1.04836			0.524181	+	0.851607i	$0.324371\pi$
$132$		−	59831.8i		−	0.298880i
$133$			127867.i			0.626802i
$134$	172880.			0.831732
$135$	−177683.	−	45687.0i	−0.839094	−	0.215754i
$136$	−117983.			−0.546981
$137$		−	8634.46i		−	0.0393037i	−0.999807	−	0.0196519i	$-0.993744\pi$
$137$		−	8634.46i		−	0.0393037i	0.999807	−	0.0196519i	$-0.00625578\pi$
$138$		−	52603.6i		−	0.235135i
$139$	−225604.			−0.990396			−0.495198	−	0.868780i	$-0.664905\pi$
$139$	−225604.			−0.990396			−0.495198	+	0.868780i	$0.664905\pi$
$140$	−44556.4	−	11456.7i	−0.192128	−	0.0494012i
$141$	−383265.			−1.62350
$142$		−	203658.i		−	0.847578i
$143$		−	84378.4i		−	0.345057i
$144$	−96003.8			−0.385818
$145$	11718.2	−	45573.6i	0.0462851	−	0.180009i
$146$	257110.			0.998243
$147$			352050.i			1.34373i
$148$		−	96375.2i		−	0.361669i
$149$	238329.			0.879448			0.439724	−	0.898133i	$-0.355076\pi$
$149$	238329.			0.879448			0.439724	+	0.898133i	$0.355076\pi$
$150$	−272207.	−	149894.i	−0.987805	−	0.543946i
$151$	−129150.			−0.460948			−0.230474	−	0.973079i	$-0.574028\pi$
$151$	−129150.			−0.460948			−0.230474	+	0.973079i	$0.574028\pi$
$152$			159101.i			0.558552i
$153$		−	691334.i		−	2.38759i
$154$	30948.5			0.105157
$155$	23082.9	−	89772.4i	0.0771724	−	0.300133i
$156$	−223120.			−0.734052
$157$			391456.i			1.26746i	0.773555	+	0.633729i	$0.218477\pi$
$157$			391456.i			1.26746i	−0.773555	+	0.633729i	$0.781523\pi$
$158$			420758.i			1.34088i
$159$	−600565.			−1.88394
$160$	−55440.0	−	14255.1i	−0.171208	−	0.0440222i
$161$	27209.6			0.0827290
$162$			38166.2i			0.114259i
$163$		−	259135.i		−	0.763936i	−0.924176	−	0.381968i	$-0.875246\pi$
$163$		−	259135.i		−	0.763936i	0.924176	−	0.381968i	$-0.124754\pi$
$164$	341739.			0.992167
$165$	202458.	+	52057.5i	0.578929	+	0.148858i
$166$	155923.			0.439178
$167$		−	129777.i		−	0.360087i	−0.983659	−	0.180044i	$-0.942376\pi$
$167$		−	129777.i		−	0.360087i	0.983659	−	0.180044i	$-0.0576239\pi$
$168$		−	81836.3i		−	0.223704i
$169$	56636.0			0.152537
$170$	102653.	−	399229.i	0.272426	−	1.05950i
$171$	−932268.			−2.43810
$172$		−	202645.i		−	0.522295i
$173$		−	33100.8i		−	0.0840860i	−0.999116	−	0.0420430i	$-0.986613\pi$
$173$		−	33100.8i		−	0.0840860i	0.999116	−	0.0420430i	$-0.0133866\pi$
$174$	83704.7			0.209593
$175$	77533.8	−	140801.i	0.191380	−	0.347545i
$176$	38508.1			0.0937068
$177$			367670.i			0.882115i
$178$		−	416397.i		−	0.985049i
$179$	−597185.			−1.39308			−0.696541	−	0.717517i	$-0.745278\pi$
$179$	−597185.			−1.39308			−0.696541	+	0.717517i	$0.745278\pi$
$180$	83529.4	−	324856.i	0.192158	−	0.747326i
$181$	606068.			1.37507			0.687535	−	0.726152i	$-0.258693\pi$
$181$	606068.			1.37507			0.687535	+	0.726152i	$0.258693\pi$
$182$		−	115411.i		−	0.258266i
$183$		−	412405.i		−	0.910324i
$184$	33856.0			0.0737210
$185$	326113.	+	83852.6i	0.700550	+	0.180131i
$186$	164884.			0.349460
$187$			277301.i			0.579893i
$188$		−	246672.i		−	0.509009i
$189$	168806.			0.343743
$190$	−538364.	−	138428.i	−1.08191	−	0.278189i
$191$	−222926.			−0.442159			−0.221079	−	0.975256i	$-0.570958\pi$
$191$	−222926.			−0.442159			−0.221079	+	0.975256i	$0.570958\pi$
$192$		−	101826.i		−	0.199345i
$193$			386817.i			0.747502i	0.927529	+	0.373751i	$0.121929\pi$
$193$			386817.i			0.747502i	−0.927529	+	0.373751i	$0.878071\pi$
$194$	−211402.			−0.403278
$195$	194129.	−	754990.i	0.365597	−	1.42185i
$196$	−226581.			−0.421293
$197$		−	249852.i		−	0.458689i	−0.973345	−	0.229344i	$-0.926342\pi$
$197$		−	249852.i		−	0.458689i	0.973345	−	0.229344i	$-0.0736582\pi$
$198$			225643.i			0.409033i
$199$	1.05520e6			1.88888			0.944439	−	0.328687i	$-0.106606\pi$
$199$	1.05520e6			1.88888			0.944439	+	0.328687i	$0.106606\pi$
$200$	96472.7	−	175194.i	0.170541	−	0.309703i
$201$	−1.07445e6			−1.87583
$202$		−	549501.i		−	0.947524i
$203$			43296.9i			0.0737424i
$204$	733261.			1.23363
$205$	−297335.	+	1.15637e6i	−0.494153	+	1.92182i
$206$	128699.			0.211304
$207$			198383.i			0.321794i
$208$		−	143601.i		−	0.230144i
$209$	373943.			0.592161
$210$	276917.	+	71202.9i	0.433312	+	0.111416i
$211$	1.04565e6			1.61688			0.808441	−	0.588577i	$-0.200312\pi$
$211$	1.04565e6			1.61688			0.808441	+	0.588577i	$0.200312\pi$
$212$		−	386528.i		−	0.590665i
$213$			1.26573e6i			1.91157i
$214$	350576.			0.523297
$215$	685709.	+	176315.i	1.01168	+	0.260131i
$216$	210040.			0.306314
$217$			85287.7i			0.122952i
$218$		−	106239.i		−	0.151405i
$219$	−1.59793e6			−2.25137
$220$	−33504.6	+	130303.i	−0.0466710	+	0.181509i
$221$	1.03409e6			1.42422
$222$			598970.i			0.815685i
$223$		−	446559.i		−	0.601335i	−0.953729	−	0.300667i	$-0.902791\pi$
$223$		−	446559.i		−	0.601335i	0.953729	−	0.300667i	$-0.0972094\pi$
$224$	52670.4			0.0701369
$225$	1.02657e6	+	565292.i	1.35186	+	0.744417i
$226$	−657999.			−0.856948
$227$		−	315888.i		−	0.406882i	−0.979087	−	0.203441i	$-0.934787\pi$
$227$		−	315888.i		−	0.406882i	0.979087	−	0.203441i	$-0.0652125\pi$
$228$		−	988808.i		−	1.25972i
$229$	29948.6			0.0377388			0.0188694	−	0.999822i	$-0.493993\pi$
$229$	29948.6			0.0377388			0.0188694	+	0.999822i	$0.493993\pi$
$230$	−29456.9	+	114562.i	−0.0367170	+	0.142797i
$231$	−192344.			−0.237164
$232$			53872.9i			0.0657129i
$233$		−	31668.4i		−	0.0382152i	−0.999817	−	0.0191076i	$-0.993917\pi$
$233$		−	31668.4i		−	0.0382152i	0.999817	−	0.0191076i	$-0.00608250\pi$
$234$	841447.			1.00459
$235$	834685.	+	214620.i	0.985946	+	0.253514i
$236$	−236635.			−0.276566
$237$		−	2.61500e6i		−	3.02413i
$238$			379285.i			0.434034i
$239$	847531.			0.959756			0.479878	−	0.877335i	$-0.340681\pi$
$239$	847531.			0.959756			0.479878	+	0.877335i	$0.340681\pi$
$240$	344558.	+	88595.3i	0.386131	+	0.0992848i
$241$	−1.21512e6			−1.34764			−0.673822	−	0.738893i	$-0.735349\pi$
$241$	−1.21512e6			−1.34764			−0.673822	+	0.738893i	$0.735349\pi$
$242$			553696.i			0.607762i
$243$		−	1.03470e6i		−	1.12408i
$244$	265426.			0.285410
$245$	197140.	−	766704.i	0.209827	−	0.816042i
$246$	−2.12390e6			−2.23767
$247$		−	1.39448e6i		−	1.45435i
$248$			106121.i			0.109565i
$249$	−969060.			−0.990495
$250$	508883.	+	478873.i	0.514953	+	0.484586i
$251$	636548.			0.637745			0.318872	−	0.947798i	$-0.396696\pi$
$251$	636548.			0.637745			0.318872	+	0.947798i	$0.396696\pi$
$252$			308628.i			0.306150i
$253$		−	79573.5i		−	0.0781569i
$254$	−579590.			−0.563685
$255$	−637984.	+	2.48120e6i	−0.614412	+	2.38952i
$256$	65536.0			0.0625000
$257$		−	1.24371e6i		−	1.17459i	−0.809374	−	0.587294i	$-0.800193\pi$
$257$		−	1.24371e6i		−	1.17459i	0.809374	−	0.587294i	$-0.199807\pi$
$258$			1.25944e6i			1.17795i
$259$	−309822.			−0.286987
$260$	485917.	+	124942.i	0.445788	+	0.114624i
$261$	−315674.			−0.286838
$262$		−	823664.i		−	0.741305i
$263$		−	370582.i		−	0.330366i	−0.986263	−	0.165183i	$-0.947179\pi$
$263$		−	370582.i		−	0.330366i	0.986263	−	0.165183i	$-0.0528215\pi$
$264$	−239327.			−0.211340
$265$	1.30793e6	+	336304.i	1.14411	+	0.294183i
$266$	511469.			0.443216
$267$			2.58790e6i			2.22162i
$268$		−	691521.i		−	0.588123i
$269$	965294.			0.813353			0.406676	−	0.913572i	$-0.366688\pi$
$269$	965294.			0.813353			0.406676	+	0.913572i	$0.366688\pi$
$270$	−182748.	+	710730.i	−0.152561	+	0.593329i
$271$	−574398.			−0.475105			−0.237552	−	0.971375i	$-0.576345\pi$
$271$	−574398.			−0.475105			−0.237552	+	0.971375i	$0.576345\pi$
$272$			471932.i			0.386774i
$273$			717274.i			0.582476i
$274$	−34537.8			−0.0277919
$275$	−411768.	−	226745.i	−0.328338	−	0.180803i
$276$	−210414.			−0.166266
$277$			1.15117e6i			0.901444i	0.892664	+	0.450722i	$0.148833\pi$
$277$			1.15117e6i			0.901444i	−0.892664	+	0.450722i	$0.851167\pi$
$278$			902414.i			0.700316i
$279$	−621825.			−0.478253
$280$	−45826.6	+	178225.i	−0.0349320	+	0.135855i
$281$	−1.63828e6			−1.23772			−0.618860	−	0.785501i	$-0.712405\pi$
$281$	−1.63828e6			−1.23772			−0.618860	+	0.785501i	$0.712405\pi$
$282$			1.53306e6i			1.14799i
$283$			106275.i			0.0788794i	0.999222	+	0.0394397i	$0.0125573\pi$
$283$			106275.i			0.0788794i	−0.999222	+	0.0394397i	$0.987443\pi$
$284$	−814630.			−0.599328
$285$	3.34592e6	+	860327.i	2.44007	+	0.627410i
$286$	−337514.			−0.243992
$287$		−	1.09860e6i		−	0.787293i
$288$			384015.i			0.272814i
$289$	−1.97858e6			−1.39350
$290$	−182294.	−	46872.9i	−0.127285	−	0.0327285i
$291$	1.31386e6			0.909527
$292$		−	1.02844e6i		−	0.705864i
$293$			239515.i			0.162991i	0.996674	+	0.0814954i	$0.0259696\pi$
$293$			239515.i			0.162991i	−0.996674	+	0.0814954i	$0.974030\pi$
$294$	1.40820e6			0.950157
$295$	205888.	−	800722.i	0.137745	−	0.535707i
$296$	−385501.			−0.255738
$297$		−	493667.i		−	0.324746i
$298$		−	953314.i		−	0.621864i
$299$	−296739.			−0.191954
$300$	−599575.	+	1.08883e6i	−0.384628	+	0.698483i
$301$	−651454.			−0.414446
$302$			516599.i			0.325939i
$303$			3.41513e6i			2.13698i
$304$	636404.			0.394956
$305$	−230938.	+	898147.i	−0.142150	+	0.552838i
$306$	−2.76533e6			−1.68828
$307$		−	2.26499e6i		−	1.37157i	−0.727802	−	0.685787i	$-0.759458\pi$
$307$		−	2.26499e6i		−	1.37157i	0.727802	−	0.685787i	$-0.240542\pi$
$308$		−	123794.i		−	0.0743571i
$309$	−799864.			−0.476562
$310$	−359090.	−	92331.8i	−0.212226	−	0.0545691i
$311$	−815074.			−0.477855			−0.238927	−	0.971037i	$-0.576796\pi$
$311$	−815074.			−0.477855			−0.238927	+	0.971037i	$0.576796\pi$
$312$			892479.i			0.519053i
$313$		−	1.01630e6i		−	0.586355i	−0.956058	−	0.293178i	$-0.905287\pi$
$313$		−	1.01630e6i		−	0.586355i	0.956058	−	0.293178i	$-0.0947127\pi$
$314$	1.56582e6			0.896229
$315$	−1.04433e6	−	268526.i	−0.593010	−	0.152479i
$316$	1.68303e6			0.948144
$317$		−	212296.i		−	0.118657i	−0.998239	−	0.0593284i	$-0.981104\pi$
$317$		−	212296.i		−	0.118657i	0.998239	−	0.0593284i	$-0.0188959\pi$
$318$			2.40226e6i			1.33215i
$319$	126620.			0.0696669
$320$	−57020.5	+	221760.i	−0.0311284	+	0.121062i
$321$	−2.17882e6			−1.18021
$322$		−	108838.i		−	0.0584982i
$323$			4.58281e6i			2.44414i
$324$	152665.			0.0807934
$325$	−845557.	+	1.53553e6i	−0.444053	+	0.806399i
$326$	−1.03654e6			−0.540184
$327$			660271.i			0.341470i
$328$		−	1.36696e6i		−	0.701568i
$329$	−792988.			−0.403903
$330$	208230.	−	809832.i	0.105259	−	0.409365i
$331$	−2.40947e6			−1.20879			−0.604396	−	0.796684i	$-0.706585\pi$
$331$	−2.40947e6			−1.20879			−0.604396	+	0.796684i	$0.706585\pi$
$332$		−	623693.i		−	0.310546i
$333$		−	2.25888e6i		−	1.11631i
$334$	−519110.			−0.254620
$335$	2.33996e6	+	601667.i	1.13919	+	0.292917i
$336$	−327345.			−0.158182
$337$		−	2.03995e6i		−	0.978465i	−0.872153	−	0.489232i	$-0.837277\pi$
$337$		−	2.03995e6i		−	0.978465i	0.872153	−	0.489232i	$-0.162723\pi$
$338$		−	226544.i		−	0.107860i
$339$	4.08945e6			1.93270
$340$	−1.59692e6	−	410611.i	−0.749178	−	0.192634i
$341$	249421.			0.116157
$342$			3.72907e6i			1.72399i
$343$			1.59289e6i			0.731054i
$344$	−810582.			−0.369318
$345$	183074.	−	711997.i	0.0828092	−	0.322055i
$346$	−132403.			−0.0594578
$347$			863526.i			0.384992i	0.981298	+	0.192496i	$0.0616583\pi$
$347$			863526.i			0.384992i	−0.981298	+	0.192496i	$0.938342\pi$
$348$		−	334819.i		−	0.148205i
$349$	2.00160e6			0.879657			0.439828	−	0.898082i	$-0.355039\pi$
$349$	2.00160e6			0.879657			0.439828	+	0.898082i	$0.355039\pi$
$350$	−563205.	−	310135.i	−0.245752	−	0.135326i
$351$	−1.84094e6			−0.797577
$352$		−	154033.i		−	0.0662607i
$353$			2.16115e6i			0.923097i	0.887115	+	0.461549i	$0.152706\pi$
$353$			2.16115e6i			0.923097i	−0.887115	+	0.461549i	$0.847294\pi$
$354$	1.47068e6			0.623749
$355$	708781.	−	2.75654e6i	0.298498	−	1.16089i
$356$	−1.66559e6			−0.696535
$357$		−	2.35725e6i		−	0.978892i
$358$			2.38874e6i			0.985057i
$359$	3.12504e6			1.27973			0.639867	−	0.768486i	$-0.278990\pi$
$359$	3.12504e6			1.27973			0.639867	+	0.768486i	$0.278990\pi$
$360$	−1.29943e6	−	334118.i	−0.528439	−	0.135876i
$361$	3.70386e6			1.49584
$362$		−	2.42427e6i		−	0.972321i
$363$		−	3.44121e6i		−	1.37071i
$364$	−461642.			−0.182622
$365$	3.48002e6	+	894808.i	1.36725	+	0.351559i
$366$	−1.64962e6			−0.643696
$367$			2.07674e6i			0.804853i	0.915452	+	0.402426i	$0.131833\pi$
$367$			2.07674e6i			0.804853i	−0.915452	+	0.402426i	$0.868167\pi$
$368$		−	135424.i		−	0.0521286i
$369$	8.00982e6			3.06236
$370$	335410.	−	1.30445e6i	0.127372	−	0.495364i
$371$	−1.24259e6			−0.468698
$372$		−	659537.i		−	0.247105i
$373$		−	386893.i		−	0.143986i	−0.997405	−	0.0719928i	$-0.977064\pi$
$373$		−	386893.i		−	0.143986i	0.997405	−	0.0719928i	$-0.0229359\pi$
$374$	1.10921e6			0.410046
$375$	−3.16269e6	−	2.97619e6i	−1.16139	−	1.09290i
$376$	−986688.			−0.359923
$377$		−	472182.i		−	0.171102i
$378$		−	675225.i		−	0.243063i
$379$	−193130.			−0.0690641			−0.0345321	−	0.999404i	$-0.510994\pi$
$379$	−193130.			−0.0690641			−0.0345321	+	0.999404i	$0.510994\pi$
$380$	−553712.	+	2.15345e6i	−0.196709	+	0.765027i
$381$	3.60214e6			1.27130
$382$			891706.i			0.312653i
$383$			2.31170e6i			0.805256i	0.915364	+	0.402628i	$0.131903\pi$
$383$			2.31170e6i			0.805256i	−0.915364	+	0.402628i	$0.868097\pi$
$384$	−407305.			−0.140959
$385$	418892.	+	107709.i	0.144029	+	0.0370339i
$386$	1.54727e6			0.528564
$387$		−	4.74969e6i		−	1.61208i
$388$			845608.i			0.285161i
$389$	2.46955e6			0.827455			0.413728	−	0.910401i	$-0.364227\pi$
$389$	2.46955e6			0.827455			0.413728	+	0.910401i	$0.364227\pi$
$390$	−3.01996e6	−	776514.i	−1.00540	−	0.258516i
$391$	975203.			0.322592
$392$			906326.i			0.297899i
$393$			5.11905e6i			1.67189i
$394$	−999410.			−0.324342
$395$	−1.46434e6	+	5.69502e6i	−0.472227	+	1.83655i
$396$	902570.			0.289230
$397$			1.05340e6i			0.335443i	0.985834	+	0.167721i	$0.0536409\pi$
$397$			1.05340e6i			0.335443i	−0.985834	+	0.167721i	$0.946359\pi$
$398$		−	4.22082e6i		−	1.33564i
$399$	−3.17877e6			−0.999601
$400$	−700777.	−	385891.i	−0.218993	−	0.120591i
$401$	4.09231e6			1.27089			0.635445	−	0.772146i	$-0.280817\pi$
$401$	4.09231e6			1.27089			0.635445	+	0.772146i	$0.280817\pi$
$402$			4.29778e6i			1.32641i
$403$		−	930119.i		−	0.285283i
$404$	−2.19800e6			−0.670000
$405$	−132828.	+	516585.i	−0.0402395	+	0.156496i
$406$	173188.			0.0521437
$407$			906062.i			0.271127i
$408$		−	2.93304e6i		−	0.872305i
$409$	−866628.			−0.256168			−0.128084	−	0.991763i	$-0.540883\pi$
$409$	−866628.			−0.256168			−0.128084	+	0.991763i	$0.540883\pi$
$410$	4.62549e6	+	1.18934e6i	1.35893	+	0.349419i
$411$	214652.			0.0626801
$412$		−	514798.i		−	0.149415i
$413$			760721.i			0.219458i
$414$	793531.			0.227543
$415$	2.11045e6	+	542653.i	0.601525	+	0.154669i
$416$	−574406.			−0.162737
$417$		−	5.60848e6i		−	1.57945i
$418$		−	1.49577e6i		−	0.418721i
$419$	−2.09037e6			−0.581684			−0.290842	−	0.956771i	$-0.593935\pi$
$419$	−2.09037e6			−0.581684			−0.290842	+	0.956771i	$0.593935\pi$
$420$	284811.	−	1.10767e6i	0.0787833	−	0.306398i
$421$	−5.26367e6			−1.44738			−0.723692	−	0.690124i	$-0.757556\pi$
$421$	−5.26367e6			−1.44738			−0.723692	+	0.690124i	$0.757556\pi$
$422$		−	4.18258e6i		−	1.14331i
$423$		−	5.78160e6i		−	1.57108i
$424$	−1.54611e6			−0.417663
$425$	2.77884e6	−	5.04637e6i	0.746262	−	1.35521i
$426$	5.06291e6			1.35169
$427$		−	853279.i		−	0.226475i
$428$		−	1.40230e6i		−	0.370027i
$429$	2.09764e6			0.550285
$430$	705258.	−	2.74284e6i	0.183940	−	0.715367i
$431$	−3.26626e6			−0.846950			−0.423475	−	0.905908i	$-0.639190\pi$
$431$	−3.26626e6			−0.846950			−0.423475	+	0.905908i	$0.639190\pi$
$432$		−	840159.i		−	0.216597i
$433$		−	4.62534e6i		−	1.18556i	−0.805364	−	0.592780i	$-0.798030\pi$
$433$		−	4.62534e6i		−	1.18556i	0.805364	−	0.592780i	$-0.201970\pi$
$434$	341151.			0.0869405
$435$	1.13296e6	+	291314.i	0.287071	+	0.0738139i
$436$	−424955.			−0.107060
$437$		−	1.31507e6i		−	0.329416i
$438$			6.39172e6i			1.59196i
$439$	−6.05968e6			−1.50068			−0.750340	−	0.661052i	$-0.770110\pi$
$439$	−6.05968e6			−1.50068			−0.750340	+	0.661052i	$0.770110\pi$
$440$	521214.	+	134018.i	0.128347	+	0.0330014i
$441$	−5.31071e6			−1.30034
$442$		−	4.13636e6i		−	1.00708i
$443$			5.66304e6i			1.37101i	0.728069	+	0.685504i	$0.240418\pi$
$443$			5.66304e6i			1.37101i	−0.728069	+	0.685504i	$0.759582\pi$
$444$	2.39588e6			0.576776
$445$	1.44917e6	−	5.63600e6i	0.346912	−	1.34918i
$446$	−1.78623e6			−0.425208
$447$			5.92482e6i			1.40251i
$448$		−	210682.i		−	0.0495943i
$449$	−6.59197e6			−1.54312			−0.771559	−	0.636157i	$-0.780523\pi$
$449$	−6.59197e6			−1.54312			−0.771559	+	0.636157i	$0.780523\pi$
$450$	2.26117e6	−	4.10628e6i	0.526382	−	0.955910i
$451$	−3.21283e6			−0.743782
$452$			2.63200e6i			0.605954i
$453$		−	3.21065e6i		−	0.735102i
$454$	−1.26355e6			−0.287709
$455$	401658.	−	1.56210e6i	0.0909554	−	0.353737i
$456$	−3.95523e6			−0.890758
$457$			7.39715e6i			1.65681i	0.560127	+	0.828407i	$0.310753\pi$
$457$			7.39715e6i			1.65681i	−0.560127	+	0.828407i	$0.689247\pi$
$458$		−	119795.i		−	0.0266854i
$459$	6.05008e6			1.34038
$460$	458246.	+	117828.i	0.100973	+	0.0259629i
$461$	−2.28088e6			−0.499863			−0.249931	−	0.968264i	$-0.580408\pi$
$461$	−2.28088e6			−0.499863			−0.249931	+	0.968264i	$0.580408\pi$
$462$			769376.i			0.167700i
$463$		−	1.40559e6i		−	0.304724i	−0.988325	−	0.152362i	$-0.951312\pi$
$463$		−	1.40559e6i		−	0.304724i	0.988325	−	0.152362i	$-0.0486879\pi$
$464$	215492.			0.0464660
$465$	2.23173e6	+	573840.i	0.478641	+	0.123072i
$466$	−126673.			−0.0270222
$467$		−	3.79299e6i		−	0.804804i	−0.915463	−	0.402402i	$-0.868175\pi$
$467$		−	3.79299e6i		−	0.804804i	0.915463	−	0.402402i	$-0.131825\pi$
$468$		−	3.36579e6i		−	0.710350i
$469$	−2.22306e6			−0.466681
$470$	858482.	−	3.33874e6i	0.179261	−	0.697169i
$471$	−9.73156e6			−2.02130
$472$			946540.i			0.195562i
$473$			1.90515e6i			0.391541i
$474$	−1.04600e7			−2.13838
$475$	−6.80507e6	−	3.74729e6i	−1.38388	−	0.762049i
$476$	1.51714e6			0.306908
$477$		−	9.05960e6i		−	1.82311i
$478$		−	3.39013e6i		−	0.678650i
$479$	5.15546e6			1.02666			0.513332	−	0.858190i	$-0.328411\pi$
$479$	5.15546e6			1.02666			0.513332	+	0.858190i	$0.328411\pi$
$480$	354381.	−	1.37823e6i	0.0702049	−	0.273036i
$481$	3.37881e6			0.665888
$482$			4.86047e6i			0.952929i
$483$			676428.i			0.131933i
$484$	2.21479e6			0.429752
$485$	−2.86136e6	−	735733.i	−0.552354	−	0.142025i
$486$	−4.13879e6			−0.794845
$487$			8.96298e6i			1.71250i	0.516563	+	0.856249i	$0.327211\pi$
$487$			8.96298e6i			1.71250i	−0.516563	+	0.856249i	$0.672789\pi$
$488$		−	1.06171e6i		−	0.201815i
$489$	6.44207e6			1.21830
$490$	−3.06681e6	−	788562.i	−0.577029	−	0.148370i
$491$	3.02720e6			0.566680			0.283340	−	0.959020i	$-0.408558\pi$
$491$	3.02720e6			0.566680			0.283340	+	0.959020i	$0.408558\pi$
$492$			8.49560e6i			1.58227i
$493$			1.55178e6i			0.287549i
$494$	−5.57791e6			−1.02838
$495$	−785294.	+	3.05411e6i	−0.144052	+	0.560236i
$496$	424483.			0.0774739
$497$			2.61883e6i			0.475572i
$498$			3.87624e6i			0.700386i
$499$	−6.08665e6			−1.09428			−0.547138	−	0.837042i	$-0.684283\pi$
$499$	−6.08665e6			−1.09428			−0.547138	+	0.837042i	$0.684283\pi$
$500$	1.91549e6	−	2.03553e6i	0.342654	−	0.364127i
$501$	3.22625e6			0.574254
$502$		−	2.54619e6i		−	0.450954i
$503$			5.93859e6i			1.04656i	0.852161	+	0.523279i	$0.175291\pi$
$503$			5.93859e6i			1.04656i	−0.852161	+	0.523279i	$0.824709\pi$
$504$	1.23451e6			0.216480
$505$	1.91240e6	−	7.43758e6i	0.333696	−	1.29779i
$506$	−318294.			−0.0552652
$507$			1.40796e6i			0.243261i
$508$			2.31836e6i			0.398586i
$509$	5.47181e6			0.936131			0.468065	−	0.883694i	$-0.344951\pi$
$509$	5.47181e6			0.936131			0.468065	+	0.883694i	$0.344951\pi$
$510$	9.92480e6	+	2.55194e6i	1.68965	+	0.434455i
$511$	−3.30617e6			−0.560110
$512$		−	262144.i		−	0.0441942i
$513$		−	8.15858e6i		−	1.36874i
$514$	−4.97483e6			−0.830558
$515$	1.74197e6	+	447907.i	0.289415	+	0.0744166i
$516$	5.03775e6			0.832937
$517$			2.31906e6i			0.381580i
$518$			1.23929e6i			0.202931i
$519$	822883.			0.134097
$520$	499770.	−	1.94367e6i	0.0810516	−	0.315220i
$521$	−3.92881e6			−0.634114			−0.317057	−	0.948407i	$-0.602695\pi$
$521$	−3.92881e6			−0.634114			−0.317057	+	0.948407i	$0.602695\pi$
$522$			1.26270e6i			0.202825i
$523$		−	7.81452e6i		−	1.24925i	−0.780926	−	0.624623i	$-0.785253\pi$
$523$		−	7.81452e6i		−	1.24925i	0.780926	−	0.624623i	$-0.214747\pi$
$524$	−3.29465e6			−0.524181
$525$	3.50031e6	+	1.92748e6i	0.554253	+	0.305205i
$526$	−1.48233e6			−0.233604
$527$			3.05675e6i			0.479438i
$528$			957309.i			0.149440i
$529$	−279841.			−0.0434783
$530$	1.34522e6	−	5.23171e6i	0.208019	−	0.809011i
$531$	−5.54635e6			−0.853632
$532$		−	2.04588e6i		−	0.313401i
$533$			1.19810e7i			1.82673i
$534$	1.03516e7			1.57092
$535$	4.74510e6	+	1.22009e6i	0.716739	+	0.184293i
$536$	−2.76608e6			−0.415866
$537$		−	1.48460e7i		−	2.22164i
$538$		−	3.86118e6i		−	0.575127i
$539$	2.13018e6			0.315824
$540$	2.84292e6	+	730993.i	0.419547	+	0.107877i
$541$	−7.10890e6			−1.04426			−0.522131	−	0.852865i	$-0.674863\pi$
$541$	−7.10890e6			−1.04426			−0.522131	+	0.852865i	$0.674863\pi$
$542$			2.29759e6i			0.335950i
$543$			1.50668e7i			2.19291i
$544$	1.88773e6			0.273490
$545$	369738.	−	1.43796e6i	0.0533215	−	0.207374i
$546$	2.86909e6			0.411873
$547$		−	4.40862e6i		−	0.629991i	−0.949093	−	0.314995i	$-0.897997\pi$
$547$		−	4.40862e6i		−	0.629991i	0.949093	−	0.314995i	$-0.102003\pi$
$548$			138151.i			0.0196519i
$549$	6.22117e6			0.880930
$550$	−906979.	+	1.64707e6i	−0.127847	+	0.232170i
$551$	2.09258e6			0.293632
$552$			841657.i			0.117568i
$553$		−	5.41052e6i		−	0.752360i
$554$	4.60467e6			0.637417
$555$	−2.08457e6	+	8.10714e6i	−0.287266	+	1.11721i
$556$	3.60966e6			0.495198
$557$			3.44558e6i			0.470571i	0.971926	+	0.235285i	$0.0756025\pi$
$557$			3.44558e6i			0.470571i	−0.971926	+	0.235285i	$0.924398\pi$
$558$			2.48730e6i			0.338176i
$559$	7.10454e6			0.961626
$560$	712902.	+	183307.i	0.0960638	+	0.0247006i
$561$	−6.89368e6			−0.924792
$562$			6.55312e6i			0.875200i
$563$		−	1.37198e7i		−	1.82421i	−0.409954	−	0.912106i	$-0.634455\pi$
$563$		−	1.37198e7i		−	1.82421i	0.409954	−	0.912106i	$-0.365545\pi$
$564$	6.13224e6			0.811748
$565$	−8.90612e6	−	2.29001e6i	−1.17373	−	0.301797i
$566$	425098.			0.0557761
$567$		−	490778.i		−	0.0641103i
$568$			3.25852e6i			0.423789i
$569$	−3.97814e6			−0.515110			−0.257555	−	0.966264i	$-0.582917\pi$
$569$	−3.97814e6			−0.515110			−0.257555	+	0.966264i	$0.582917\pi$
$570$	3.44131e6	−	1.33837e7i	0.443646	−	1.72539i
$571$	−2.55842e6			−0.328383			−0.164192	−	0.986428i	$-0.552502\pi$
$571$	−2.55842e6			−0.328383			−0.164192	+	0.986428i	$0.552502\pi$
$572$			1.35005e6i			0.172529i
$573$		−	5.54193e6i		−	0.705139i
$574$	−4.39442e6			−0.556700
$575$	−797407.	+	1.44809e6i	−0.100580	+	0.182653i
$576$	1.53606e6			0.192909
$577$		−	8.40638e6i		−	1.05116i	−0.850744	−	0.525581i	$-0.823848\pi$
$577$		−	8.40638e6i		−	1.05116i	0.850744	−	0.525581i	$-0.176152\pi$
$578$			7.91430e6i			0.985356i
$579$	−9.61624e6			−1.19209
$580$	−187492.	+	729178.i	−0.0231426	+	0.0900043i
$581$	−2.00502e6			−0.246421
$582$		−	5.25543e6i		−	0.643133i
$583$			3.63391e6i			0.442795i
$584$	−4.11376e6			−0.499122
$585$	1.13891e7	+	2.92845e6i	1.37594	+	0.353793i
$586$	958058.			0.115252
$587$		−	4.41364e6i		−	0.528691i	−0.964428	−	0.264346i	$-0.914844\pi$
$587$		−	4.41364e6i		−	0.528691i	0.964428	−	0.264346i	$-0.0851560\pi$
$588$		−	5.63279e6i		−	0.671863i
$589$	4.12204e6			0.489581
$590$	−3.20289e6	−	823550.i	−0.378802	−	0.0974003i
$591$	6.21131e6			0.731500
$592$			1.54200e6i			0.180834i
$593$		−	1.44901e7i		−	1.69214i	−0.533075	−	0.846068i	$-0.678964\pi$
$593$		−	1.44901e7i		−	1.69214i	0.533075	−	0.846068i	$-0.321036\pi$
$594$	−1.97467e6			−0.229630
$595$	−1.32001e6	+	5.13368e6i	−0.152857	+	0.594479i
$596$	−3.81326e6			−0.439724
$597$			2.62323e7i			3.01231i
$598$			1.18696e6i			0.135732i
$599$	1.45845e7			1.66082			0.830411	−	0.557151i	$-0.188105\pi$
$599$	1.45845e7			1.66082			0.830411	+	0.557151i	$0.188105\pi$
$600$	4.35531e6	+	2.39830e6i	0.493902	+	0.271973i
$601$	8.24700e6			0.931343			0.465671	−	0.884958i	$-0.345813\pi$
$601$	8.24700e6			0.931343			0.465671	+	0.884958i	$0.345813\pi$
$602$			2.60582e6i			0.293057i
$603$		−	1.62082e7i		−	1.81527i
$604$	2.06640e6			0.230474
$605$	−1.92701e6	+	7.49436e6i	−0.214040	+	0.832427i
$606$	1.36605e7			1.51108
$607$			3.91781e6i			0.431590i	0.976439	+	0.215795i	$0.0692344\pi$
$607$			3.91781e6i			0.431590i	−0.976439	+	0.215795i	$0.930766\pi$
$608$		−	2.54561e6i		−	0.279276i
$609$	−1.07636e6			−0.117602
$610$	3.59259e6	+	923752.i	0.390915	+	0.100515i
$611$	8.64806e6			0.937164
$612$			1.10613e7i			1.19379i
$613$		−	8.36497e6i		−	0.899111i	−0.893253	−	0.449555i	$-0.851582\pi$
$613$		−	8.36497e6i		−	0.899111i	0.893253	−	0.449555i	$-0.148418\pi$
$614$	−9.05994e6			−0.969850
$615$	−2.87473e7	−	7.39172e6i	−3.06485	−	0.788057i
$616$	−495176.			−0.0525784
$617$			3.58718e6i			0.379350i	0.981847	+	0.189675i	$0.0607435\pi$
$617$			3.58718e6i			0.379350i	−0.981847	+	0.189675i	$0.939257\pi$
$618$			3.19945e6i			0.336981i
$619$	−1.66739e7			−1.74908			−0.874542	−	0.484950i	$-0.838838\pi$
$619$	−1.66739e7			−1.74908			−0.874542	+	0.484950i	$0.838838\pi$
$620$	−369327.	+	1.43636e6i	−0.0385862	+	0.150067i
$621$	−1.73611e6			−0.180654
$622$			3.26030e6i			0.337894i
$623$			5.35445e6i			0.552706i
$624$	3.56992e6			0.367026
$625$	5.22120e6	+	8.25267e6i	0.534651	+	0.845073i
$626$	−4.06520e6			−0.414616
$627$			9.29618e6i			0.944356i
$628$		−	6.26330e6i		−	0.633729i
$629$	−1.11041e7			−1.11907
$630$	−1.07410e6	+	4.17732e6i	−0.107819	+	0.419321i
$631$	953221.			0.0953060			0.0476530	−	0.998864i	$-0.484826\pi$
$631$	953221.			0.0953060			0.0476530	+	0.998864i	$0.484826\pi$
$632$		−	6.73212e6i		−	0.670439i
$633$			2.59946e7i			2.57854i
$634$	−849182.			−0.0839031
$635$	−7.84484e6	−	2.01712e6i	−0.772058	−	0.198517i
$636$	9.60905e6			0.941971
$637$		−	7.94371e6i		−	0.775666i
$638$		−	506481.i		−	0.0492619i
$639$	−1.90936e7			−1.84985
$640$	887040.	+	228082.i	0.0856038	+	0.0220111i
$641$	−7.03694e6			−0.676455			−0.338227	−	0.941064i	$-0.609827\pi$
$641$	−7.03694e6			−0.676455			−0.338227	+	0.941064i	$0.609827\pi$
$642$			8.71529e6i			0.834534i
$643$			1.04233e7i			0.994205i	0.867692	+	0.497103i	$0.165603\pi$
$643$			1.04233e7i			0.994205i	−0.867692	+	0.497103i	$0.834397\pi$
$644$	−435354.			−0.0413645
$645$	−4.38316e6	+	1.70467e7i	−0.414847	+	1.61339i
$646$	1.83312e7			1.72827
$647$		−	1.61695e7i		−	1.51857i	−0.650757	−	0.759286i	$-0.725548\pi$
$647$		−	1.61695e7i		−	1.51857i	0.650757	−	0.759286i	$-0.274452\pi$
$648$		−	610659.i		−	0.0571296i
$649$	2.22470e6			0.207329
$650$	6.14212e6	+	3.38223e6i	0.570210	+	0.313993i
$651$	−2.12024e6			−0.196080
$652$			4.14616e6i			0.381968i
$653$			6.75174e6i			0.619630i	0.950797	+	0.309815i	$0.100267\pi$
$653$			6.75174e6i			0.619630i	−0.950797	+	0.309815i	$0.899733\pi$
$654$	2.64108e6			0.241456
$655$	2.86656e6	−	1.11484e7i	0.261071	−	1.01534i
$656$	−5.46782e6			−0.496084
$657$		−	2.41050e7i		−	2.17868i
$658$			3.17195e6i			0.285602i
$659$	1.26940e7			1.13864			0.569319	−	0.822117i	$-0.307207\pi$
$659$	1.26940e7			1.13864			0.569319	+	0.822117i	$0.307207\pi$
$660$	−3.23933e6	−	832920.i	−0.289465	−	0.0744292i
$661$	−1.74828e7			−1.55635			−0.778175	−	0.628047i	$-0.783854\pi$
$661$	−1.74828e7			−1.55635			−0.778175	+	0.628047i	$0.783854\pi$
$662$			9.63788e6i			0.854745i
$663$			2.57074e7i			2.27130i
$664$	−2.49477e6			−0.219589
$665$	6.92281e6	+	1.78004e6i	0.607055	+	0.156091i
$666$	−9.03553e6			−0.789347
$667$		−	445293.i		−	0.0387553i
$668$			2.07644e6i			0.180044i
$669$	1.11014e7			0.958987
$670$	2.40667e6	−	9.35984e6i	0.207124	−	0.805529i
$671$	−2.49538e6			−0.213959
$672$			1.30938e6i			0.111852i
$673$			1.05180e7i			0.895151i	0.894246	+	0.447576i	$0.147712\pi$
$673$			1.05180e7i			0.895151i	−0.894246	+	0.447576i	$0.852288\pi$
$674$	−8.15981e6			−0.691879
$675$	−4.94705e6	+	8.98383e6i	−0.417914	+	0.758931i
$676$	−906175.			−0.0762686
$677$			2.14132e7i			1.79560i	0.440406	+	0.897799i	$0.354835\pi$
$677$			2.14132e7i			1.79560i	−0.440406	+	0.897799i	$0.645165\pi$
$678$		−	1.63578e7i		−	1.36663i
$679$	2.71841e6			0.226277
$680$	−1.64244e6	+	6.38767e6i	−0.136213	+	0.529749i
$681$	7.85294e6			0.648880
$682$		−	997683.i		−	0.0821356i
$683$			1.84067e6i			0.150981i	0.997147	+	0.0754907i	$0.0240523\pi$
$683$			1.84067e6i			0.150981i	−0.997147	+	0.0754907i	$0.975948\pi$
$684$	1.49163e7			1.21905
$685$	−467475.	−	120201.i	−0.0380655	−	0.00978768i
$686$	6.37154e6			0.516933
$687$			744520.i			0.0601845i
$688$			3.24233e6i			0.261147i
$689$	1.35513e7			1.08751
$690$	−2.84799e6	−	732296.i	−0.227727	−	0.0585550i
$691$	−1.50448e7			−1.19865			−0.599323	−	0.800507i	$-0.704563\pi$
$691$	−1.50448e7			−1.19865			−0.599323	+	0.800507i	$0.704563\pi$
$692$			529613.i			0.0420430i
$693$		−	2.90153e6i		−	0.229506i
$694$	3.45411e6			0.272231
$695$	−3.14063e6	+	1.22143e7i	−0.246635	+	0.959195i
$696$	−1.33927e6			−0.104796
$697$		−	3.93744e7i		−	3.06995i
$698$		−	8.00639e6i		−	0.622011i
$699$	787272.			0.0609442
$700$	−1.24054e6	+	2.25282e6i	−0.0956899	+	0.173773i
$701$	1.89568e7			1.45704			0.728519	−	0.685025i	$-0.240209\pi$
$701$	1.89568e7			1.45704			0.728519	+	0.685025i	$0.240209\pi$
$702$			7.36377e6i			0.563972i
$703$			1.49740e7i			1.14275i
$704$	−616130.			−0.0468534
$705$	−5.33544e6	+	2.07502e7i	−0.404294	+	1.57235i
$706$	8.64459e6			0.652728
$707$			7.06602e6i			0.531651i
$708$		−	5.88272e6i		−	0.441057i
$709$	6.28604e6			0.469636			0.234818	−	0.972039i	$-0.424551\pi$
$709$	6.28604e6			0.469636			0.234818	+	0.972039i	$0.424551\pi$
$710$	−1.10261e7	−	2.83512e6i	−0.820876	−	0.211070i
$711$	3.94476e7			2.92649
$712$			6.66235e6i			0.492524i
$713$		−	877153.i		−	0.0646177i
$714$	−9.42900e6			−0.692181
$715$	−4.56830e6	−	1.17463e6i	−0.334187	−	0.0859286i
$716$	9.55496e6			0.696541
$717$			2.10695e7i			1.53058i
$718$		−	1.25002e7i		−	0.904908i
$719$	−2.00076e7			−1.44336			−0.721678	−	0.692228i	$-0.756629\pi$
$719$	−2.00076e7			−1.44336			−0.721678	+	0.692228i	$0.756629\pi$
$720$	−1.33647e6	+	5.19770e6i	−0.0960790	+	0.373663i
$721$	−1.65494e6			−0.118562
$722$		−	1.48154e7i		−	1.05772i
$723$		−	3.02077e7i		−	2.14917i
$724$	−9.69708e6			−0.687535
$725$	−2.30425e6	−	1.26886e6i	−0.162812	−	0.0896540i
$726$	−1.37648e7			−0.969236
$727$		−	9.71960e6i		−	0.682044i	−0.940055	−	0.341022i	$-0.889227\pi$
$727$		−	9.71960e6i		−	0.682044i	0.940055	−	0.341022i	$-0.110773\pi$
$728$			1.84657e6i			0.129133i
$729$	2.34039e7			1.63106
$730$	3.57923e6	−	1.39201e7i	0.248589	−	0.966795i
$731$	−2.33484e7			−1.61608
$732$			6.59847e6i			0.455162i
$733$			1.31869e7i			0.906533i	0.891375	+	0.453267i	$0.149741\pi$
$733$			1.31869e7i			0.906533i	−0.891375	+	0.453267i	$0.850259\pi$
$734$	8.30695e6			0.569117
$735$	1.90602e7	+	4.90089e6i	1.30139	+	0.334624i
$736$	−541696.			−0.0368605
$737$			6.50126e6i			0.440889i
$738$		−	3.20393e7i		−	2.16542i
$739$	−1.36791e7			−0.921394			−0.460697	−	0.887557i	$-0.652401\pi$
$739$	−1.36791e7			−0.921394			−0.460697	+	0.887557i	$0.652401\pi$
$740$	−5.21781e6	−	1.34164e6i	−0.350275	−	0.0900653i
$741$	3.46666e7			2.31934
$742$			4.97036e6i			0.331419i
$743$			9.41077e6i			0.625393i	0.949853	+	0.312696i	$0.101232\pi$
$743$			9.41077e6i			0.625393i	−0.949853	+	0.312696i	$0.898768\pi$
$744$	−2.63815e6			−0.174730
$745$	3.31778e6	−	1.29033e7i	0.219006	−	0.851743i
$746$	−1.54757e6			−0.101813
$747$		−	1.46184e7i		−	0.958513i
$748$		−	4.43682e6i		−	0.289947i
$749$	−4.50805e6			−0.293619
$750$	−1.19047e7	+	1.26508e7i	−0.772800	+	0.821228i
$751$	2.49857e7			1.61656			0.808280	−	0.588799i	$-0.200399\pi$
$751$	2.49857e7			1.61656			0.808280	+	0.588799i	$0.200399\pi$
$752$			3.94675e6i			0.254504i
$753$			1.58245e7i			1.01705i
$754$	−1.88873e6			−0.120988
$755$	−1.79790e6	+	6.99225e6i	−0.114788	+	0.446426i
$756$	−2.70090e6			−0.171872
$757$		−	3.01345e7i		−	1.91128i	−0.294537	−	0.955640i	$-0.595165\pi$
$757$		−	3.01345e7i		−	1.91128i	0.294537	−	0.955640i	$-0.404835\pi$
$758$			772522.i			0.0488357i
$759$	1.97819e6			0.124642
$760$	8.61382e6	+	2.21485e6i	0.540956	+	0.139094i
$761$	1.01512e7			0.635412			0.317706	−	0.948189i	$-0.397087\pi$
$761$	1.01512e7			0.635412			0.317706	+	0.948189i	$0.397087\pi$
$762$		−	1.44086e7i		−	0.898945i
$763$			1.36612e6i			0.0849528i
$764$	3.56682e6			0.221079
$765$	−3.74292e7	−	9.62407e6i	−2.31237	−	0.594573i
$766$	9.24678e6			0.569402
$767$		−	8.29617e6i		−	0.509201i
$768$			1.62922e6i			0.0996727i
$769$	7.87137e6			0.479992			0.239996	−	0.970774i	$-0.422854\pi$
$769$	7.87137e6			0.479992			0.239996	+	0.970774i	$0.422854\pi$
$770$	430835.	−	1.67557e6i	0.0261869	−	0.101844i
$771$	3.09184e7			1.87319
$772$		−	6.18908e6i		−	0.373751i
$773$		−	2.85396e7i		−	1.71791i	−0.512054	−	0.858953i	$-0.671115\pi$
$773$		−	2.85396e7i		−	1.71791i	0.512054	−	0.858953i	$-0.328885\pi$
$774$	−1.89988e7			−1.13992
$775$	−4.53900e6	−	2.49945e6i	−0.271460	−	0.149482i
$776$	3.38243e6			0.201639
$777$		−	7.70214e6i		−	0.457677i
$778$		−	9.87821e6i		−	0.585099i
$779$	−5.30967e7			−3.13490
$780$	−3.10606e6	+	1.20798e7i	−0.182799	+	0.710926i
$781$	7.65867e6			0.449289
$782$		−	3.90081e6i		−	0.228107i
$783$		−	2.76256e6i		−	0.161030i
$784$	3.62530e6			0.210647
$785$	2.11937e7	+	5.44947e6i	1.22753	+	0.315631i
$786$	2.04762e7			1.18221
$787$		−	2.75146e7i		−	1.58353i	−0.610827	−	0.791764i	$-0.709163\pi$
$787$		−	2.75146e7i		−	1.58353i	0.610827	−	0.791764i	$-0.290837\pi$
$788$			3.99764e6i			0.229344i
$789$	9.21264e6			0.526856
$790$	2.27801e7	+	5.85738e6i	1.29864	+	0.333915i
$791$	8.46120e6			0.480829
$792$		−	3.61028e6i		−	0.204516i
$793$			9.30557e6i			0.525484i
$794$	4.21361e6			0.237194
$795$	−8.36049e6	+	3.25150e7i	−0.469152	+	1.82459i
$796$	−1.68833e7			−0.944439
$797$			7.10505e6i			0.396207i	0.980181	+	0.198103i	$0.0634781\pi$
$797$			7.10505e6i			0.396207i	−0.980181	+	0.198103i	$0.936522\pi$
$798$			1.27151e7i			0.706824i
$799$	−2.84210e7			−1.57497
$800$	−1.54356e6	+	2.80311e6i	−0.0852706	+	0.154851i
$801$	−3.90388e7			−2.14988
$802$		−	1.63693e7i		−	0.898655i
$803$			9.66877e6i			0.529154i
$804$	1.71911e7			0.937917
$805$	378786.	−	1.47314e6i	0.0206017	−	0.0801227i
$806$	−3.72048e6			−0.201726
$807$			2.39971e7i			1.29710i
$808$			8.79201e6i			0.473762i
$809$	1.46301e7			0.785918			0.392959	−	0.919556i	$-0.371451\pi$
$809$	1.46301e7			0.785918			0.392959	+	0.919556i	$0.371451\pi$
$810$	2.06634e6	+	531312.i	0.110660	+	0.0284536i
$811$	2.85186e7			1.52257			0.761284	−	0.648419i	$-0.224569\pi$
$811$	2.85186e7			1.52257			0.761284	+	0.648419i	$0.224569\pi$
$812$		−	692751.i		−	0.0368712i
$813$		−	1.42795e7i		−	0.757680i
$814$	3.62425e6			0.191715
$815$	−1.40297e7	−	3.60742e6i	−0.739869	−	0.190241i
$816$	−1.17322e7			−0.616813
$817$			3.14854e7i			1.65027i
$818$			3.46651e6i			0.181138i
$819$	−1.08202e7			−0.563669
$820$	4.75736e6	−	1.85020e7i	0.247076	−	0.960911i
$821$	4.37997e6			0.226784			0.113392	−	0.993550i	$-0.463828\pi$
$821$	4.37997e6			0.226784			0.113392	+	0.993550i	$0.463828\pi$
$822$		−	858607.i		−	0.0443215i
$823$		−	3.38668e7i		−	1.74291i	−0.490478	−	0.871454i	$-0.663178\pi$
$823$		−	3.38668e7i		−	1.74291i	0.490478	−	0.871454i	$-0.336822\pi$
$824$	−2.05919e6			−0.105652
$825$	5.63685e6	−	1.02365e7i	0.288338	−	0.523621i
$826$	3.04289e6			0.155180
$827$		−	3.09654e7i		−	1.57439i	−0.616704	−	0.787195i	$-0.711532\pi$
$827$		−	3.09654e7i		−	1.57439i	0.616704	−	0.787195i	$-0.288468\pi$
$828$		−	3.17412e6i		−	0.160897i
$829$	1.41016e7			0.712660			0.356330	−	0.934360i	$-0.384028\pi$
$829$	1.41016e7			0.712660			0.356330	+	0.934360i	$0.384028\pi$
$830$	2.17061e6	−	8.44178e6i	0.109367	−	0.425343i
$831$	−2.86179e7			−1.43759
$832$			2.29762e6i			0.115072i
$833$			2.61062e7i			1.30356i
$834$	−2.24339e7			−1.11684
$835$	−7.02623e6	−	1.80664e6i	−0.348743	−	0.0896715i
$836$	−5.98309e6			−0.296080
$837$		−	5.44179e6i		−	0.268490i
$838$			8.36146e6i			0.411313i
$839$	1.79728e7			0.881476			0.440738	−	0.897636i	$-0.354717\pi$
$839$	1.79728e7			0.881476			0.440738	+	0.897636i	$0.354717\pi$
$840$	−4.43067e6	−	1.13925e6i	−0.216656	−	0.0557082i
$841$	−1.98026e7			−0.965455
$842$			2.10547e7i			1.02345i
$843$		−	4.07275e7i		−	1.97387i
$844$	−1.67303e7			−0.808441
$845$	788431.	−	3.06631e6i	0.0379858	−	0.147732i
$846$	−2.31264e7			−1.11092
$847$		−	7.11997e6i		−	0.341012i
$848$			6.18445e6i			0.295333i
$849$	−2.64198e6			−0.125794
$850$	−2.01855e7	−	1.11154e7i	−0.958279	−	0.527687i
$851$	3.18641e6			0.150826
$852$		−	2.02516e7i		−	0.955787i
$853$		−	3.47203e7i		−	1.63385i	−0.576747	−	0.816923i	$-0.695678\pi$
$853$		−	3.47203e7i		−	1.63385i	0.576747	−	0.816923i	$-0.304322\pi$
$854$	−3.41311e6			−0.160142
$855$	−1.29781e7	+	5.04736e7i	−0.607151	+	2.36129i
$856$	−5.60922e6			−0.261648
$857$		−	8.43632e6i		−	0.392375i	−0.980566	−	0.196187i	$-0.937144\pi$
$857$		−	8.43632e6i		−	0.392375i	0.980566	−	0.196187i	$-0.0628561\pi$
$858$		−	8.39056e6i		−	0.389110i
$859$	2.64774e7			1.22431			0.612156	−	0.790737i	$-0.290302\pi$
$859$	2.64774e7			1.22431			0.612156	+	0.790737i	$0.290302\pi$
$860$	−1.09713e7	−	2.82103e6i	−0.505841	−	0.130066i
$861$	2.73112e7			1.25555
$862$			1.30650e7i			0.598884i
$863$			3.53738e7i			1.61679i	0.588639	+	0.808396i	$0.299664\pi$
$863$			3.53738e7i			1.61679i	−0.588639	+	0.808396i	$0.700336\pi$
$864$	−3.36064e6			−0.153157
$865$	−1.79210e6	−	460798.i	−0.0814370	−	0.0209397i
$866$	−1.85014e7			−0.838318
$867$		−	4.91872e7i		−	2.22231i
$868$		−	1.36460e6i		−	0.0614762i
$869$	−1.58228e7			−0.710780
$870$	1.16526e6	−	4.53182e6i	0.0521943	−	0.202990i
$871$	2.42440e7			1.08283
$872$			1.69982e6i			0.0757027i
$873$			1.98197e7i			0.880160i
$874$	−5.26027e6			−0.232932
$875$	−6.54372e6	−	6.15783e6i	−0.288938	−	0.271899i
$876$	2.55669e7			1.12569
$877$		−	2.47519e7i		−	1.08670i	−0.839506	−	0.543351i	$-0.817155\pi$
$877$		−	2.47519e7i		−	1.08670i	0.839506	−	0.543351i	$-0.182845\pi$
$878$			2.42387e7i			1.06114i
$879$	−5.95431e6			−0.259932
$880$	536073.	−	2.08485e6i	0.0233355	−	0.0907547i
$881$	−3.34450e7			−1.45175			−0.725873	−	0.687828i	$-0.758564\pi$
$881$	−3.34450e7			−1.45175			−0.725873	+	0.687828i	$0.758564\pi$
$882$			2.12428e7i			0.919478i
$883$		−	2.40148e7i		−	1.03652i	−0.855223	−	0.518260i	$-0.826580\pi$
$883$		−	2.40148e7i		−	1.03652i	0.855223	−	0.518260i	$-0.173420\pi$
$884$	−1.65454e7			−0.712110
$885$	1.99059e7	+	5.11835e6i	0.854325	+	0.219670i
$886$	2.26522e7			0.969449
$887$		−	1.59003e7i		−	0.678573i	−0.940683	−	0.339286i	$-0.889814\pi$
$887$		−	1.59003e7i		−	0.678573i	0.940683	−	0.339286i	$-0.110186\pi$
$888$		−	9.58351e6i		−	0.407842i
$889$	7.45294e6			0.316281
$890$	−2.25440e7	−	5.79668e6i	−0.954016	−	0.245304i
$891$	−1.43526e6			−0.0605671
$892$			7.14494e6i			0.300667i
$893$			3.83259e7i			1.60829i
$894$	2.36993e7			0.991726
$895$	−8.31343e6	+	3.23320e7i	−0.346915	+	1.34919i
$896$	−842727.			−0.0350685
$897$		−	7.37690e6i		−	0.306121i
$898$			2.63679e7i			1.09115i
$899$	1.39576e6			0.0575985
$900$	−1.64251e7	−	9.04467e6i	−0.675930	−	0.372209i
$901$	−4.45349e7			−1.82763
$902$			1.28513e7i			0.525934i
$903$		−	1.61951e7i		−	0.660943i
$904$	1.05280e7			0.428474
$905$	8.43708e6	−	3.28129e7i	0.342429	−	1.33175i
$906$	−1.28426e7			−0.519796
$907$		−	2.67551e6i		−	0.107991i	−0.998541	−	0.0539956i	$-0.982804\pi$
$907$		−	2.67551e6i		−	0.107991i	0.998541	−	0.0539956i	$-0.0171957\pi$
$908$			5.05421e6i			0.203441i
$909$	−5.15177e7			−2.06798
$910$	−6.24840e6	−	1.60663e6i	−0.250130	−	0.0643151i
$911$	1.46462e7			0.584693			0.292347	−	0.956312i	$-0.405564\pi$
$911$	1.46462e7			0.584693			0.292347	+	0.956312i	$0.405564\pi$
$912$			1.58209e7i			0.629861i
$913$			5.86359e6i			0.232802i
$914$	2.95886e7			1.17154
$915$	−2.23278e7	−	5.74110e6i	−0.881645	−	0.226695i
$916$	−479178.			−0.0188694
$917$			1.05915e7i			0.415942i
$918$		−	2.42003e7i		−	0.947795i
$919$	−1.47233e7			−0.575063			−0.287532	−	0.957771i	$-0.592835\pi$
$919$	−1.47233e7			−0.575063			−0.287532	+	0.957771i	$0.592835\pi$
$920$	471310.	−	1.83298e6i	0.0183585	−	0.0713985i
$921$	5.63073e7			2.18734
$922$			9.12353e6i			0.353456i
$923$		−	2.85601e7i		−	1.10346i
$924$	3.07751e6			0.118582
$925$	9.07966e6	−	1.64887e7i	0.348912	−	0.633623i
$926$	−5.62236e6			−0.215472
$927$		−	1.20660e7i		−	0.461175i
$928$		−	861966.i		−	0.0328564i
$929$	4.24468e7			1.61363			0.806817	−	0.590801i	$-0.201188\pi$
$929$	4.24468e7			1.61363			0.806817	+	0.590801i	$0.201188\pi$
$930$	2.29536e6	−	8.92694e6i	0.0870248	−	0.338450i
$931$	3.52044e7			1.33114
$932$			506694.i			0.0191076i
$933$		−	2.02627e7i		−	0.762065i
$934$	−1.51720e7			−0.569082
$935$	1.50133e7	+	3.86032e6i	0.561625	+	0.144409i
$936$	−1.34632e7			−0.502293
$937$			4.82096e7i			1.79384i	0.442191	+	0.896921i	$0.354201\pi$
$937$			4.82096e7i			1.79384i	−0.442191	+	0.896921i	$0.645799\pi$
$938$			8.89225e6i			0.329993i
$939$	2.52651e7			0.935098
$940$	−1.33550e7	−	3.43393e6i	−0.492973	−	0.126757i
$941$	−1.17955e7			−0.434253			−0.217126	−	0.976143i	$-0.569668\pi$
$941$	−1.17955e7			−0.434253			−0.217126	+	0.976143i	$0.569668\pi$
$942$			3.89262e7i			1.42927i
$943$			1.12987e7i			0.413762i
$944$	3.78616e6			0.138283
$945$	2.34996e6	−	9.13927e6i	0.0856013	−	0.332914i
$946$	7.62061e6			0.276861
$947$		−	3.68089e7i		−	1.33376i	−0.745164	−	0.666881i	$-0.767629\pi$
$947$		−	3.68089e7i		−	1.33376i	0.745164	−	0.666881i	$-0.232371\pi$
$948$			4.18400e7i			1.51207i
$949$	3.60560e7			1.29961
$950$	−1.49892e7	+	2.72203e7i	−0.538850	+	0.978551i
$951$	5.27765e6			0.189230
$952$		−	6.06857e6i		−	0.217017i
$953$		−	1.59382e7i		−	0.568471i	−0.958754	−	0.284236i	$-0.908260\pi$
$953$		−	1.59382e7i		−	0.568471i	0.958754	−	0.284236i	$-0.0917398\pi$
$954$	−3.62384e7			−1.28913
$955$	−3.10337e6	+	1.20694e7i	−0.110109	+	0.428229i
$956$	−1.35605e7			−0.479878
$957$			3.14777e6i			0.111102i
$958$		−	2.06218e7i		−	0.725962i
$959$	444121.			0.0155939
$960$	−5.51293e6	−	1.41752e6i	−0.193065	−	0.0496424i
$961$	−2.58797e7			−0.903965
$962$		−	1.35152e7i		−	0.470854i
$963$		−	3.28678e7i		−	1.14210i
$964$	1.94419e7			0.673822
$965$	2.09425e7	+	5.38489e6i	0.723953	+	0.186148i
$966$	2.70571e6			0.0932908
$967$		−	4.10102e7i		−	1.41035i	−0.709035	−	0.705173i	$-0.750869\pi$
$967$		−	4.10102e7i		−	1.41035i	0.709035	−	0.705173i	$-0.249131\pi$
$968$		−	8.85914e6i		−	0.303881i
$969$	−1.13928e8			−3.89782
$970$	−2.94293e6	+	1.14454e7i	−0.100427	+	0.390573i
$971$	−43774.0			−0.00148994			−0.000744969	−	1.00000i	$-0.500237\pi$
$971$	−43774.0			−0.00148994			−0.000744969		1.00000i	$0.500237\pi$
$972$			1.65551e7i			0.562040i
$973$		−	1.16041e7i		−	0.392944i
$974$	3.58519e7			1.21092
$975$	−3.81731e7	−	2.10205e7i	−1.28602	−	0.708159i
$976$	−4.24682e6			−0.142705
$977$		−	3.46632e6i		−	0.116180i	−0.998311	−	0.0580902i	$-0.981499\pi$
$977$		−	3.46632e6i		−	0.116180i	0.998311	−	0.0580902i	$-0.0185011\pi$
$978$		−	2.57683e7i		−	0.861466i
$979$	1.56589e7			0.522160
$980$	−3.15425e6	+	1.22673e7i	−0.104913	+	0.408021i
$981$	−9.96026e6			−0.330444
$982$		−	1.21088e7i		−	0.400703i
$983$		−	1.62849e7i		−	0.537529i	−0.963206	−	0.268764i	$-0.913385\pi$
$983$		−	1.62849e7i		−	0.537529i	0.963206	−	0.268764i	$-0.0866153\pi$
$984$	3.39824e7			1.11884
$985$	−1.35272e7	−	3.47820e6i	−0.444238	−	0.114226i
$986$	6.20711e6			0.203328
$987$		−	1.97136e7i		−	0.644129i
$988$			2.23116e7i			0.727175i
$989$	6.69997e6			0.217812
$990$	1.22164e7	+	3.14118e6i	0.396147	+	0.101860i
$991$	−1.88313e7			−0.609112			−0.304556	−	0.952494i	$-0.598508\pi$
$991$	−1.88313e7			−0.609112			−0.304556	+	0.952494i	$0.598508\pi$
$992$		−	1.69793e6i		−	0.0547824i
$993$		−	5.98992e7i		−	1.92774i
$994$	1.04753e7			0.336280
$995$	1.46895e7	−	5.71294e7i	0.470381	−	1.82937i
$996$	1.55050e7			0.495247
$997$			1.55218e7i			0.494544i	0.968946	+	0.247272i	$0.0795342\pi$
$997$			1.55218e7i			0.494544i	−0.968946	+	0.247272i	$0.920466\pi$
$998$			2.43466e7i			0.773770i
$999$	1.97682e7			0.626691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.b.a.139.13	✓	26
5.4	even	2	inner	230.6.b.a.139.14	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.b.a.139.13	✓	26	1.1	even	1	trivial
230.6.b.a.139.14	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)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} +24.8599i q^{3} -16.0000 q^{4} +(13.9210 - 54.1406i) q^{5} +99.4396 q^{6} +51.4359i q^{7} +64.0000i q^{8} -375.015 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} +24.8599i q^{3} -16.0000 q^{4} +(13.9210 - 54.1406i) q^{5} +99.4396 q^{6} +51.4359i q^{7} +64.0000i q^{8} -375.015 q^{9} +(-216.562 - 55.6841i) q^{10} +150.422 q^{11} -397.758i q^{12} -560.943i q^{13} +205.744 q^{14} +(1345.93 + 346.075i) q^{15} +256.000 q^{16} +1843.48i q^{17} +1500.06i q^{18} +2485.95 q^{19} +(-222.736 + 866.250i) q^{20} -1278.69 q^{21} -601.690i q^{22} -529.000i q^{23} -1591.03 q^{24} +(-2737.41 - 1507.39i) q^{25} -2243.77 q^{26} -3281.87i q^{27} -822.975i q^{28} +841.764 q^{29} +(1384.30 - 5383.72i) q^{30} +1658.14 q^{31} -1024.00i q^{32} +3739.49i q^{33} +7373.93 q^{34} +(2784.77 + 716.041i) q^{35} +6000.24 q^{36} +6023.45i q^{37} -9943.81i q^{38} +13945.0 q^{39} +(3465.00 + 890.946i) q^{40} -21358.7 q^{41} +5114.77i q^{42} +12665.3i q^{43} -2406.76 q^{44} +(-5220.59 + 20303.5i) q^{45} -2116.00 q^{46} +15417.0i q^{47} +6364.13i q^{48} +14161.3 q^{49} +(-6029.54 + 10949.6i) q^{50} -45828.8 q^{51} +8975.09i q^{52} +24158.0i q^{53} -13127.5 q^{54} +(2094.04 - 8143.96i) q^{55} -3291.90 q^{56} +61800.5i q^{57} -3367.06i q^{58} +14789.7 q^{59} +(-21534.9 - 5537.21i) q^{60} -16589.1 q^{61} -6632.54i q^{62} -19289.2i q^{63} -4096.00 q^{64} +(-30369.8 - 7808.90i) q^{65} +14958.0 q^{66} +43220.0i q^{67} -29495.7i q^{68} +13150.9 q^{69} +(2864.16 - 11139.1i) q^{70} +50914.4 q^{71} -24000.9i q^{72} +64277.4i q^{73} +24093.8 q^{74} +(37473.5 - 68051.7i) q^{75} -39775.2 q^{76} +7737.12i q^{77} -55780.0i q^{78} -105189. q^{79} +(3563.78 - 13860.0i) q^{80} -9541.54 q^{81} +85434.7i q^{82} +38980.8i q^{83} +20459.1 q^{84} +(99807.3 + 25663.2i) q^{85} +50661.4 q^{86} +20926.2i q^{87} +9627.04i q^{88} +104099. q^{89} +(81214.1 + 20882.4i) q^{90} +28852.6 q^{91} +8464.00i q^{92} +41221.1i q^{93} +61668.0 q^{94} +(34607.0 - 134591. i) q^{95} +25456.5 q^{96} -52850.5i q^{97} -56645.4i q^{98} -56410.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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