LMFDB - Embedded newform 230.6.b.a.139.1

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			139.1
Character	$\chi$	$=$	230.139
Dual form			230.6.b.a.139.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} -27.5301i q^{3} -16.0000 q^{4} +(28.4300 - 48.1325i) q^{5} -110.120 q^{6} -119.184i q^{7} +64.0000i q^{8} -514.906 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} -27.5301i q^{3} -16.0000 q^{4} +(28.4300 - 48.1325i) q^{5} -110.120 q^{6} -119.184i q^{7} +64.0000i q^{8} -514.906 q^{9} +(-192.530 - 113.720i) q^{10} -12.4715 q^{11} +440.482i q^{12} +426.025i q^{13} -476.737 q^{14} +(-1325.09 - 782.680i) q^{15} +256.000 q^{16} +1329.55i q^{17} +2059.63i q^{18} +674.564 q^{19} +(-454.879 + 770.120i) q^{20} -3281.15 q^{21} +49.8861i q^{22} -529.000i q^{23} +1761.93 q^{24} +(-1508.47 - 2736.81i) q^{25} +1704.10 q^{26} +7485.61i q^{27} +1906.95i q^{28} -2878.26 q^{29} +(-3130.72 + 5300.37i) q^{30} -7278.64 q^{31} -1024.00i q^{32} +343.342i q^{33} +5318.20 q^{34} +(-5736.63 - 3388.40i) q^{35} +8238.50 q^{36} -10791.6i q^{37} -2698.25i q^{38} +11728.5 q^{39} +(3080.48 + 1819.52i) q^{40} -12007.4 q^{41} +13124.6i q^{42} +8155.38i q^{43} +199.544 q^{44} +(-14638.8 + 24783.7i) q^{45} -2116.00 q^{46} +13652.4i q^{47} -7047.71i q^{48} +2602.14 q^{49} +(-10947.2 + 6033.90i) q^{50} +36602.7 q^{51} -6816.40i q^{52} -24791.4i q^{53} +29942.4 q^{54} +(-354.565 + 600.285i) q^{55} +7627.78 q^{56} -18570.8i q^{57} +11513.0i q^{58} +23331.4 q^{59} +(21201.5 + 12522.9i) q^{60} +23354.0 q^{61} +29114.6i q^{62} +61368.7i q^{63} -4096.00 q^{64} +(20505.6 + 12111.9i) q^{65} +1373.37 q^{66} -64725.1i q^{67} -21272.8i q^{68} -14563.4 q^{69} +(-13553.6 + 22946.5i) q^{70} +44846.8 q^{71} -32954.0i q^{72} +14714.9i q^{73} -43166.3 q^{74} +(-75344.7 + 41528.4i) q^{75} -10793.0 q^{76} +1486.41i q^{77} -46914.0i q^{78} +14233.2 q^{79} +(7278.07 - 12321.9i) q^{80} +80957.4 q^{81} +48029.4i q^{82} -85580.0i q^{83} +52498.4 q^{84} +(63994.6 + 37799.1i) q^{85} +32621.5 q^{86} +79238.8i q^{87} -798.177i q^{88} -89493.4 q^{89} +(99134.9 + 58555.1i) q^{90} +50775.4 q^{91} +8464.00i q^{92} +200382. i q^{93} +54609.7 q^{94} +(19177.8 - 32468.4i) q^{95} -28190.8 q^{96} -27676.0i q^{97} -10408.6i q^{98} +6421.66 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	27.5301i		−	1.76606i	−0.469320	−	0.883028i	$-0.655501\pi$
$3$		−	27.5301i		−	1.76606i	0.469320	−	0.883028i	$-0.344499\pi$
$4$	−16.0000			−0.500000
$5$	28.4300	−	48.1325i	0.508571	−	0.861020i
$5$	28.4300	−	48.1325i	0.508571	−	0.861020i
$6$	−110.120			−1.24879
$7$		−	119.184i		−	0.919334i	−0.888091	−	0.459667i	$-0.847969\pi$
$7$		−	119.184i		−	0.919334i	0.888091	−	0.459667i	$-0.152031\pi$
$8$			64.0000i			0.353553i
$9$	−514.906			−2.11896
$10$	−192.530	−	113.720i	−0.608833	−	0.359614i
$11$	−12.4715			−0.0310769			−0.0155384	−	0.999879i	$-0.504946\pi$
$11$	−12.4715			−0.0310769			−0.0155384	+	0.999879i	$0.504946\pi$
$12$			440.482i			0.883028i
$13$			426.025i			0.699160i	0.936906	+	0.349580i	$0.113676\pi$
$13$			426.025i			0.699160i	−0.936906	+	0.349580i	$0.886324\pi$
$14$	−476.737			−0.650067
$15$	−1325.09	−	782.680i	−1.52061	−	0.898165i
$16$	256.000			0.250000
$17$			1329.55i			1.11579i	0.829911	+	0.557895i	$0.188391\pi$
$17$			1329.55i			1.11579i	−0.829911	+	0.557895i	$0.811609\pi$
$18$			2059.63i			1.49833i
$19$	674.564			0.428686			0.214343	−	0.976758i	$-0.431239\pi$
$19$	674.564			0.428686			0.214343	+	0.976758i	$0.431239\pi$
$20$	−454.879	+	770.120i	−0.254285	+	0.430510i
$21$	−3281.15			−1.62360
$22$			49.8861i			0.0219747i
$23$		−	529.000i		−	0.208514i
$23$		−	529.000i		−	0.208514i
$24$	1761.93			0.624395
$25$	−1508.47	−	2736.81i	−0.482712	−	0.875779i
$26$	1704.10			0.494381
$27$			7485.61i			1.97614i
$28$			1906.95i			0.459667i
$29$	−2878.26			−0.635529			−0.317764	−	0.948170i	$-0.602932\pi$
$29$	−2878.26			−0.635529			−0.317764	+	0.948170i	$0.602932\pi$
$30$	−3130.72	+	5300.37i	−0.635098	+	1.07523i
$31$	−7278.64			−1.36034			−0.680168	−	0.733057i	$-0.738093\pi$
$31$	−7278.64			−1.36034			−0.680168	+	0.733057i	$0.738093\pi$
$32$		−	1024.00i		−	0.176777i
$33$			343.342i			0.0548836i
$34$	5318.20			0.788983
$35$	−5736.63	−	3388.40i	−0.791565	−	0.467546i
$36$	8238.50			1.05948
$37$		−	10791.6i		−	1.29593i	−0.761671	−	0.647964i	$-0.775621\pi$
$37$		−	10791.6i		−	1.29593i	0.761671	−	0.647964i	$-0.224379\pi$
$38$		−	2698.25i		−	0.303127i
$39$	11728.5			1.23476
$40$	3080.48	+	1819.52i	0.304417	+	0.179807i
$41$	−12007.4			−1.11555			−0.557773	−	0.829993i	$-0.688344\pi$
$41$	−12007.4			−1.11555			−0.557773	+	0.829993i	$0.688344\pi$
$42$			13124.6i			1.14806i
$43$			8155.38i			0.672625i	0.941750	+	0.336313i	$0.109180\pi$
$43$			8155.38i			0.672625i	−0.941750	+	0.336313i	$0.890820\pi$
$44$	199.544			0.0155384
$45$	−14638.8	+	24783.7i	−1.07764	+	1.82446i
$46$	−2116.00			−0.147442
$47$			13652.4i			0.901498i	0.892651	+	0.450749i	$0.148843\pi$
$47$			13652.4i			0.901498i	−0.892651	+	0.450749i	$0.851157\pi$
$48$		−	7047.71i		−	0.441514i
$49$	2602.14			0.154825
$50$	−10947.2	+	6033.90i	−0.619269	+	0.341329i
$51$	36602.7			1.97055
$52$		−	6816.40i		−	0.349580i
$53$		−	24791.4i		−	1.21230i	−0.795349	−	0.606152i	$-0.792712\pi$
$53$		−	24791.4i		−	1.21230i	0.795349	−	0.606152i	$-0.207288\pi$
$54$	29942.4			1.39734
$55$	−354.565	+	600.285i	−0.0158048	+	0.0267578i
$56$	7627.78			0.325034
$57$		−	18570.8i		−	0.757083i
$58$			11513.0i			0.449387i
$59$	23331.4			0.872590			0.436295	−	0.899804i	$-0.356290\pi$
$59$	23331.4			0.872590			0.436295	+	0.899804i	$0.356290\pi$
$60$	21201.5	+	12522.9i	0.760305	+	0.449082i
$61$	23354.0			0.803595			0.401798	−	0.915728i	$-0.368385\pi$
$61$	23354.0			0.803595			0.401798	+	0.915728i	$0.368385\pi$
$62$			29114.6i			0.961902i
$63$			61368.7i			1.94803i
$64$	−4096.00			−0.125000
$65$	20505.6	+	12111.9i	0.601991	+	0.355572i
$66$	1373.37			0.0388085
$67$		−	64725.1i		−	1.76151i	−0.473571	−	0.880756i	$-0.657035\pi$
$67$		−	64725.1i		−	1.76151i	0.473571	−	0.880756i	$-0.342965\pi$
$68$		−	21272.8i		−	0.557895i
$69$	−14563.4			−0.368248
$70$	−13553.6	+	22946.5i	−0.330605	+	0.559721i
$71$	44846.8			1.05581			0.527905	−	0.849304i	$-0.322978\pi$
$71$	44846.8			1.05581			0.527905	+	0.849304i	$0.322978\pi$
$72$		−	32954.0i		−	0.749164i
$73$			14714.9i			0.323185i	0.986858	+	0.161592i	$0.0516630\pi$
$73$			14714.9i			0.323185i	−0.986858	+	0.161592i	$0.948337\pi$
$74$	−43166.3			−0.916359
$75$	−75344.7	+	41528.4i	−1.54668	+	0.852496i
$76$	−10793.0			−0.214343
$77$			1486.41i			0.0285700i
$78$		−	46914.0i		−	0.873105i
$79$	14233.2			0.256587			0.128293	−	0.991736i	$-0.459050\pi$
$79$	14233.2			0.256587			0.128293	+	0.991736i	$0.459050\pi$
$80$	7278.07	−	12321.9i	0.127143	−	0.215255i
$81$	80957.4			1.37102
$82$			48029.4i			0.788811i
$83$		−	85580.0i		−	1.36357i	−0.731553	−	0.681784i	$-0.761204\pi$
$83$		−	85580.0i		−	1.36357i	0.731553	−	0.681784i	$-0.238796\pi$
$84$	52498.4			0.811798
$85$	63994.6	+	37799.1i	0.960718	+	0.567458i
$86$	32621.5			0.475618
$87$			79238.8i			1.12238i
$88$		−	798.177i		−	0.0109873i
$89$	−89493.4			−1.19761			−0.598806	−	0.800894i	$-0.704358\pi$
$89$	−89493.4			−1.19761			−0.598806	+	0.800894i	$0.704358\pi$
$90$	99134.9	+	58555.1i	1.29009	+	0.762006i
$91$	50775.4			0.642762
$92$			8464.00i			0.104257i
$93$			200382.i			2.40243i
$94$	54609.7			0.637456
$95$	19177.8	−	32468.4i	0.218017	−	0.369107i
$96$	−28190.8			−0.312198
$97$		−	27676.0i		−	0.298658i	−0.988788	−	0.149329i	$-0.952289\pi$
$97$		−	27676.0i		−	0.298658i	0.988788	−	0.149329i	$-0.0477113\pi$
$98$		−	10408.6i		−	0.109478i
$99$	6421.66			0.0658506
$100$	24135.6	+	43789.0i	0.241356	+	0.437890i
$101$	−102109.			−0.996000			−0.498000	−	0.867177i	$-0.665932\pi$
$101$	−102109.			−0.996000			−0.498000	+	0.867177i	$0.665932\pi$
$102$		−	146411.i		−	1.39339i
$103$			159357.i			1.48005i	0.672578	+	0.740026i	$0.265187\pi$
$103$			159357.i			1.48005i	−0.672578	+	0.740026i	$0.734813\pi$
$104$	−27265.6			−0.247190
$105$	−93283.0	+	157930.i	−0.825713	+	1.39795i
$106$	−99165.7			−0.857229
$107$		−	113612.i		−	0.959319i	−0.877455	−	0.479660i	$-0.840760\pi$
$107$		−	113612.i		−	0.959319i	0.877455	−	0.479660i	$-0.159240\pi$
$108$		−	119770.i		−	0.988070i
$109$	−98984.4			−0.797996			−0.398998	−	0.916952i	$-0.630642\pi$
$109$	−98984.4			−0.797996			−0.398998	+	0.916952i	$0.630642\pi$
$110$	2401.14	+	1418.26i	0.0189206	+	0.0111757i
$111$	−297093.			−2.28868
$112$		−	30511.1i		−	0.229834i
$113$			106983.i			0.788165i	0.919075	+	0.394083i	$0.128938\pi$
$113$			106983.i			0.788165i	−0.919075	+	0.394083i	$0.871062\pi$
$114$	−74283.2			−0.535339
$115$	−25462.1	−	15039.5i	−0.179535	−	0.106044i
$116$	46052.2			0.317764
$117$		−	219363.i		−	1.48149i
$118$		−	93325.5i		−	0.617014i
$119$	158461.			1.02578
$120$	50091.5	−	84805.9i	0.317549	−	0.537617i
$121$	−160895.			−0.999034
$122$		−	93416.2i		−	0.568228i
$123$			330564.i			1.97012i
$124$	116458.			0.680168
$125$	−174615.	−	5200.78i	−0.999557	−	0.0297710i
$126$	245475.			1.37746
$127$			189490.i			1.04250i	0.853404	+	0.521251i	$0.174534\pi$
$127$			189490.i			1.04250i	−0.853404	+	0.521251i	$0.825466\pi$
$128$			16384.0i			0.0883883i
$129$	224519.			1.18789
$130$	48447.5	−	82022.6i	0.251428	−	0.425672i
$131$	−174962.			−0.890767			−0.445384	−	0.895340i	$-0.646933\pi$
$131$	−174962.			−0.890767			−0.445384	+	0.895340i	$0.646933\pi$
$132$		−	5493.47i		−	0.0274418i
$133$		−	80397.3i		−	0.394105i
$134$	−258900.			−1.24558
$135$	360301.	+	212816.i	1.70150	+	1.00501i
$136$	−85091.3			−0.394492
$137$		−	281413.i		−	1.28098i	−0.767966	−	0.640491i	$-0.778731\pi$
$137$		−	281413.i		−	1.28098i	0.767966	−	0.640491i	$-0.221269\pi$
$138$			58253.7i			0.260391i
$139$	253153.			1.11134			0.555669	−	0.831403i	$-0.312462\pi$
$139$	253153.			1.11134			0.555669	+	0.831403i	$0.312462\pi$
$140$	91786.1	+	54214.4i	0.395783	+	0.233773i
$141$	375852.			1.59210
$142$		−	179387.i		−	0.746570i
$143$		−	5313.18i		−	0.0217277i
$144$	−131816.			−0.529739
$145$	−81828.9	+	138538.i	−0.323211	+	0.547203i
$146$	58859.7			0.228526
$147$		−	71637.3i		−	0.273430i
$148$			172665.i			0.647964i
$149$	280363.			1.03456			0.517280	−	0.855817i	$-0.326945\pi$
$149$	280363.			1.03456			0.517280	+	0.855817i	$0.326945\pi$
$150$	166114.	+	301379.i	0.602806	+	1.09367i
$151$	−497646.			−1.77614			−0.888071	−	0.459706i	$-0.847955\pi$
$151$	−497646.			−1.77614			−0.888071	+	0.459706i	$0.847955\pi$
$152$			43172.1i			0.151563i
$153$		−	684594.i		−	2.36431i
$154$	5945.63			0.0202021
$155$	−206931.	+	350339.i	−0.691827	+	1.17128i
$156$	−187656.			−0.617378
$157$		−	274270.i		−	0.888032i	−0.896019	−	0.444016i	$-0.853553\pi$
$157$		−	274270.i		−	0.888032i	0.896019	−	0.444016i	$-0.146447\pi$
$158$		−	56932.7i		−	0.181434i
$159$	−682510.			−2.14100
$160$	−49287.7	−	29112.3i	−0.152208	−	0.0899034i
$161$	−63048.4			−0.191694
$162$		−	323829.i		−	0.969457i
$163$		−	299063.i		−	0.881646i	−0.897594	−	0.440823i	$-0.854687\pi$
$163$		−	299063.i		−	0.881646i	0.897594	−	0.440823i	$-0.145313\pi$
$164$	192118.			0.557773
$165$	16525.9	+	9761.20i	0.0472559	+	0.0279122i
$166$	−342320.			−0.964188
$167$			613032.i			1.70095i	0.526015	+	0.850475i	$0.323686\pi$
$167$			613032.i			1.70095i	−0.526015	+	0.850475i	$0.676314\pi$
$168$		−	209994.i		−	0.574028i
$169$	189796.			0.511175
$170$	151196.	−	255978.i	0.401254	−	0.679331i
$171$	−347337.			−0.908366
$172$		−	130486.i		−	0.336313i
$173$		−	742336.i		−	1.88576i	−0.333140	−	0.942878i	$-0.608108\pi$
$173$		−	742336.i		−	1.88576i	0.333140	−	0.942878i	$-0.391892\pi$
$174$	316955.			0.793643
$175$	−326184.	+	179786.i	−0.805134	+	0.443773i
$176$	−3192.71			−0.00776922
$177$		−	642315.i		−	1.54104i
$178$			357974.i			0.846840i
$179$	137316.			0.320322			0.160161	−	0.987091i	$-0.448799\pi$
$179$	137316.			0.320322			0.160161	+	0.987091i	$0.448799\pi$
$180$	234220.	−	396540.i	0.538820	−	0.912232i
$181$	−455128.			−1.03261			−0.516306	−	0.856404i	$-0.672693\pi$
$181$	−455128.			−1.03261			−0.516306	+	0.856404i	$0.672693\pi$
$182$		−	203102.i		−	0.454501i
$183$		−	642939.i		−	1.41920i
$184$	33856.0			0.0737210
$185$	−519426.	−	306804.i	−1.11582	−	0.659071i
$186$	801527.			1.69877
$187$		−	16581.5i		−	0.0346753i
$188$		−	218439.i		−	0.450749i
$189$	892166.			1.81673
$190$	−129874.	−	76711.3i	−0.260998	−	0.154161i
$191$	37426.8			0.0742333			0.0371167	−	0.999311i	$-0.488183\pi$
$191$	37426.8			0.0742333			0.0371167	+	0.999311i	$0.488183\pi$
$192$			112763.i			0.220757i
$193$			385395.i			0.744754i	0.928082	+	0.372377i	$0.121457\pi$
$193$			385395.i			0.744754i	−0.928082	+	0.372377i	$0.878543\pi$
$194$	−110704.			−0.211183
$195$	333441.	−	564522.i	0.627961	−	1.06315i
$196$	−41634.3			−0.0774125
$197$		−	77950.8i		−	0.143105i	−0.997437	−	0.0715526i	$-0.977205\pi$
$197$		−	77950.8i		−	0.143105i	0.997437	−	0.0715526i	$-0.0227954\pi$
$198$		−	25686.7i		−	0.0465634i
$199$	−861933.			−1.54291			−0.771456	−	0.636283i	$-0.780471\pi$
$199$	−861933.			−1.54291			−0.771456	+	0.636283i	$0.780471\pi$
$200$	175156.	−	96542.4i	0.309635	−	0.170664i
$201$	−1.78189e6			−3.11093
$202$			408435.i			0.704278i
$203$			343043.i			0.584263i
$204$	−585643.			−0.985275
$205$	−341369.	+	577944.i	−0.567334	+	0.960509i
$206$	637427.			1.04656
$207$			272385.i			0.441833i
$208$			109062.i			0.174790i
$209$	−8412.83			−0.0133222
$210$	631720.	+	373132.i	0.988499	+	0.583867i
$211$	−169898.			−0.262713			−0.131357	−	0.991335i	$-0.541933\pi$
$211$	−169898.			−0.262713			−0.131357	+	0.991335i	$0.541933\pi$
$212$			396663.i			0.606152i
$213$		−	1.23464e6i		−	1.86462i
$214$	−454446.			−0.678341
$215$	392539.	+	231857.i	0.579144	+	0.342078i
$216$	−479079.			−0.698671
$217$			867498.i			1.25060i
$218$			395938.i			0.564268i
$219$	405103.			0.570762
$220$	5673.04	−	9604.56i	0.00790240	−	0.0133789i
$221$	−566422.			−0.780116
$222$			1.18837e6i			1.61834i
$223$			96991.9i			0.130609i	0.997865	+	0.0653045i	$0.0208019\pi$
$223$			96991.9i			0.130609i	−0.997865	+	0.0653045i	$0.979198\pi$
$224$	−122045.			−0.162517
$225$	776723.	+	1.40920e6i	1.02285	+	1.85574i
$226$	427931.			0.557317
$227$		−	158432.i		−	0.204069i	−0.994781	−	0.102034i	$-0.967465\pi$
$227$		−	158432.i		−	0.204069i	0.994781	−	0.102034i	$-0.0325352\pi$
$228$			297133.i			0.378542i
$229$	799344.			1.00727			0.503634	−	0.863917i	$-0.331996\pi$
$229$	799344.			1.00727			0.503634	+	0.863917i	$0.331996\pi$
$230$	−60157.8	+	101848.i	−0.0749847	+	0.126951i
$231$	40920.9			0.0504563
$232$		−	184209.i		−	0.224693i
$233$		−	129769.i		−	0.156596i	−0.996930	−	0.0782981i	$-0.975051\pi$
$233$		−	129769.i		−	0.156596i	0.996930	−	0.0782981i	$-0.0249486\pi$
$234$	−877452.			−1.04757
$235$	657125.	+	388138.i	0.776208	+	0.458476i
$236$	−373302.			−0.436295
$237$		−	391841.i		−	0.453147i
$238$		−	633846.i		−	0.725339i
$239$	875375.			0.991287			0.495644	−	0.868526i	$-0.334932\pi$
$239$	875375.			0.991287			0.495644	+	0.868526i	$0.334932\pi$
$240$	−339224.	−	200366.i	−0.380153	−	0.224541i
$241$	−558645.			−0.619574			−0.309787	−	0.950806i	$-0.600258\pi$
$241$	−558645.			−0.619574			−0.309787	+	0.950806i	$0.600258\pi$
$242$			643582.i			0.706424i
$243$		−	409761.i		−	0.445158i
$244$	−373665.			−0.401798
$245$	73978.8	−	125248.i	0.0787394	−	0.133307i
$246$	1.32226e6			1.39308
$247$			287381.i			0.299720i
$248$		−	465833.i		−	0.480951i
$249$	−2.35603e6			−2.40814
$250$	−20803.1	+	698462.i	−0.0210513	+	0.706793i
$251$	435186.			0.436005			0.218002	−	0.975948i	$-0.430046\pi$
$251$	435186.			0.436005			0.218002	+	0.975948i	$0.430046\pi$
$252$		−	981899.i		−	0.974014i
$253$			6597.43i			0.00647998i
$254$	757959.			0.737160
$255$	1.04061e6	−	1.76178e6i	1.00216	−	1.69668i
$256$	65536.0			0.0625000
$257$			609164.i			0.575310i	0.957734	+	0.287655i	$0.0928756\pi$
$257$			609164.i			0.575310i	−0.957734	+	0.287655i	$0.907124\pi$
$258$		−	898074.i		−	0.839968i
$259$	−1.28619e6			−1.19139
$260$	−328090.	−	193790.i	−0.300996	−	0.177786i
$261$	1.48204e6			1.34666
$262$			699846.i			0.629868i
$263$		−	482781.i		−	0.430389i	−0.976571	−	0.215194i	$-0.930961\pi$
$263$		−	482781.i		−	0.430389i	0.976571	−	0.215194i	$-0.0690385\pi$
$264$	−21973.9			−0.0194043
$265$	−1.19327e6	−	704819.i	−1.04382	−	0.616542i
$266$	−321589.			−0.278675
$267$			2.46376e6i			2.11505i
$268$			1.03560e6i			0.880756i
$269$	837773.			0.705904			0.352952	−	0.935641i	$-0.385178\pi$
$269$	837773.			0.705904			0.352952	+	0.935641i	$0.385178\pi$
$270$	851263.	−	1.44120e6i	0.710647	−	1.20314i
$271$	2.19016e6			1.81156			0.905780	−	0.423749i	$-0.139286\pi$
$271$	2.19016e6			1.81156			0.905780	+	0.423749i	$0.139286\pi$
$272$			340365.i			0.278948i
$273$		−	1.39785e6i		−	1.13515i
$274$	−1.12565e6			−0.905791
$275$	18813.0	+	34132.2i	0.0150012	+	0.0272165i
$276$	233015.			0.184124
$277$		−	1.88680e6i		−	1.47750i	−0.673981	−	0.738749i	$-0.735417\pi$
$277$		−	1.88680e6i		−	1.47750i	0.673981	−	0.738749i	$-0.264583\pi$
$278$		−	1.01261e6i		−	0.785835i
$279$	3.74782e6			2.88249
$280$	216858.	−	367144.i	0.165303	−	0.279861i
$281$	818314.			0.618236			0.309118	−	0.951024i	$-0.399966\pi$
$281$	818314.			0.618236			0.309118	+	0.951024i	$0.399966\pi$
$282$		−	1.50341e6i		−	1.12578i
$283$		−	91395.7i		−	0.0678359i	−0.999425	−	0.0339180i	$-0.989202\pi$
$283$		−	91395.7i		−	0.0678359i	0.999425	−	0.0339180i	$-0.0107985\pi$
$284$	−717549.			−0.527905
$285$	−893859.	−	527967.i	−0.651864	−	0.385030i
$286$	−21252.7			−0.0153638
$287$			1.43109e6i			1.02556i
$288$			527264.i			0.374582i
$289$	−347849.			−0.244989
$290$	554152.	+	327316.i	0.386931	+	0.228545i
$291$	−761923.			−0.527447
$292$		−	235439.i		−	0.161592i
$293$			1.13640e6i			0.773323i	0.922222	+	0.386662i	$0.126372\pi$
$293$			1.13640e6i			0.773323i	−0.922222	+	0.386662i	$0.873628\pi$
$294$	−286549.			−0.193344
$295$	663310.	−	1.12300e6i	0.443774	−	0.751318i
$296$	690661.			0.458180
$297$		−	93356.9i		−	0.0614123i
$298$		−	1.12145e6i		−	0.731544i
$299$	225367.			0.145785
$300$	1.20551e6	−	664455.i	0.773338	−	0.426248i
$301$	971992.			0.618367
$302$			1.99058e6i			1.25592i
$303$			2.81106e6i			1.75899i
$304$	172688.			0.107171
$305$	663955.	−	1.12409e6i	0.408685	−	0.691912i
$306$	−2.73838e6			−1.67182
$307$			1.22649e6i			0.742710i	0.928491	+	0.371355i	$0.121107\pi$
$307$			1.22649e6i			0.742710i	−0.928491	+	0.371355i	$0.878893\pi$
$308$		−	23782.5i		−	0.0142850i
$309$	4.38711e6			2.61386
$310$	1.40136e6	+	827726.i	0.828217	+	0.489195i
$311$	−2.34628e6			−1.37556			−0.687779	−	0.725920i	$-0.741414\pi$
$311$	−2.34628e6			−1.37556			−0.687779	+	0.725920i	$0.741414\pi$
$312$			750625.i			0.436552i
$313$			1.48268e6i			0.855435i	0.903912	+	0.427718i	$0.140682\pi$
$313$			1.48268e6i			0.855435i	−0.903912	+	0.427718i	$0.859318\pi$
$314$	−1.09708e6			−0.627934
$315$	2.95383e6	+	1.74471e6i	1.67729	+	0.990710i
$316$	−227731.			−0.128293
$317$			1.52424e6i			0.851935i	0.904738	+	0.425967i	$0.140066\pi$
$317$			1.52424e6i			0.851935i	−0.904738	+	0.425967i	$0.859934\pi$
$318$			2.73004e6i			1.51391i
$319$	35896.3			0.0197503
$320$	−116449.	+	197151.i	−0.0635713	+	0.107628i
$321$	−3.12774e6			−1.69421
$322$			252194.i			0.135548i
$323$			896867.i			0.478323i
$324$	−1.29532e6			−0.685510
$325$	1.16595e6	−	642648.i	0.612310	−	0.337493i
$326$	−1.19625e6			−0.623418
$327$			2.72505e6i			1.40931i
$328$		−	768471.i		−	0.394405i
$329$	1.62715e6			0.828778
$330$	39044.8	−	66103.7i	0.0197369	−	0.0334149i
$331$	−3.60947e6			−1.81081			−0.905406	−	0.424547i	$-0.860433\pi$
$331$	−3.60947e6			−1.81081			−0.905406	+	0.424547i	$0.860433\pi$
$332$			1.36928e6i			0.681784i
$333$			5.55666e6i			2.74601i
$334$	2.45213e6			1.20275
$335$	−3.11538e6	−	1.84013e6i	−1.51670	−	0.895853i
$336$	−839975.			−0.405899
$337$		−	785491.i		−	0.376762i	−0.982096	−	0.188381i	$-0.939676\pi$
$337$		−	785491.i		−	0.376762i	0.982096	−	0.188381i	$-0.0603239\pi$
$338$		−	759183.i		−	0.361455i
$339$	2.94524e6			1.39194
$340$	−1.02391e6	−	604785.i	−0.480359	−	0.283729i
$341$	90775.7			0.0422750
$342$			1.38935e6i			0.642312i
$343$		−	2.31326e6i		−	1.06167i
$344$	−521945.			−0.237809
$345$	−414038.	+	700974.i	−0.187280	+	0.317069i
$346$	−2.96934e6			−1.33343
$347$			316046.i			0.140905i	0.997515	+	0.0704526i	$0.0224443\pi$
$347$			316046.i			0.140905i	−0.997515	+	0.0704526i	$0.977556\pi$
$348$		−	1.26782e6i		−	0.561190i
$349$	−1.57295e6			−0.691277			−0.345639	−	0.938368i	$-0.612338\pi$
$349$	−1.57295e6			−0.691277			−0.345639	+	0.938368i	$0.612338\pi$
$350$	719145.	+	1.30474e6i	0.313795	+	0.569315i
$351$	−3.18906e6			−1.38164
$352$			12770.8i			0.00549367i
$353$			2.36881e6i			1.01180i	0.862593	+	0.505898i	$0.168839\pi$
$353$			2.36881e6i			1.01180i	−0.862593	+	0.505898i	$0.831161\pi$
$354$	−2.56926e6			−1.08968
$355$	1.27499e6	−	2.15859e6i	0.536954	−	0.909073i
$356$	1.43189e6			0.598806
$357$		−	4.36246e6i		−	1.81159i
$358$		−	549262.i		−	0.226502i
$359$	307390.			0.125879			0.0629396	−	0.998017i	$-0.479952\pi$
$359$	307390.			0.125879			0.0629396	+	0.998017i	$0.479952\pi$
$360$	−1.58616e6	−	936881.i	−0.645046	−	0.381003i
$361$	−2.02106e6			−0.816229
$362$			1.82051e6i			0.730166i
$363$			4.42947e6i			1.76435i
$364$	−812407.			−0.321381
$365$	708266.	+	418345.i	0.278269	+	0.164362i
$366$	−2.57176e6			−1.00352
$367$			4.42168e6i			1.71365i	0.515609	+	0.856824i	$0.327566\pi$
$367$			4.42168e6i			1.71365i	−0.515609	+	0.856824i	$0.672434\pi$
$368$		−	135424.i		−	0.0521286i
$369$	6.18267e6			2.36380
$370$	−1.22722e6	+	2.07770e6i	−0.466034	+	0.789004i
$371$	−2.95474e6			−1.11451
$372$		−	3.20611e6i		−	1.20121i
$373$		−	4.33271e6i		−	1.61246i	−0.591605	−	0.806228i	$-0.701505\pi$
$373$		−	4.33271e6i		−	1.61246i	0.591605	−	0.806228i	$-0.298495\pi$
$374$	−66326.1			−0.0245191
$375$	−143178.	+	4.80718e6i	−0.0525773	+	1.76527i
$376$	−873755.			−0.318728
$377$		−	1.22621e6i		−	0.444336i
$378$		−	3.56866e6i		−	1.28462i
$379$	1.03364e6			0.369635			0.184817	−	0.982773i	$-0.440831\pi$
$379$	1.03364e6			0.369635			0.184817	+	0.982773i	$0.440831\pi$
$380$	−306845.	+	519495.i	−0.109008	+	0.184554i
$381$	5.21667e6			1.84112
$382$		−	149707.i		−	0.0524909i
$383$		−	3.74814e6i		−	1.30563i	−0.757519	−	0.652813i	$-0.773589\pi$
$383$		−	3.74814e6i		−	1.30563i	0.757519	−	0.652813i	$-0.226411\pi$
$384$	451053.			0.156099
$385$	71544.5	+	42258.5i	0.0245994	+	0.0145299i
$386$	1.54158e6			0.526621
$387$		−	4.19926e6i		−	1.42526i
$388$			442816.i			0.149329i
$389$	2.54113e6			0.851439			0.425720	−	0.904855i	$-0.360021\pi$
$389$	2.54113e6			0.851439			0.425720	+	0.904855i	$0.360021\pi$
$390$	−2.25809e6	−	1.33376e6i	−0.751761	−	0.444035i
$391$	703333.			0.232658
$392$			166537.i			0.0547389i
$393$			4.81671e6i			1.57315i
$394$	−311803.			−0.101191
$395$	404649.	−	685079.i	0.130493	−	0.220926i
$396$	−102747.			−0.0329253
$397$		−	4.43637e6i		−	1.41270i	−0.707861	−	0.706352i	$-0.750340\pi$
$397$		−	4.43637e6i		−	1.41270i	0.707861	−	0.706352i	$-0.249660\pi$
$398$			3.44773e6i			1.09100i
$399$	−2.21335e6			−0.696012
$400$	−386169.	−	700623.i	−0.120678	−	0.218945i
$401$	−1.92946e6			−0.599204			−0.299602	−	0.954064i	$-0.596854\pi$
$401$	−1.92946e6			−0.599204			−0.299602	+	0.954064i	$0.596854\pi$
$402$			7.12755e6i			2.19976i
$403$		−	3.10088e6i		−	0.951092i
$404$	1.63374e6			0.498000
$405$	2.30161e6	−	3.89668e6i	0.697261	−	1.18048i
$406$	1.37217e6			0.413137
$407$			134587.i			0.0402734i
$408$			2.34257e6i			0.696695i
$409$	4.89363e6			1.44651			0.723257	−	0.690579i	$-0.242644\pi$
$409$	4.89363e6			1.44651			0.723257	+	0.690579i	$0.242644\pi$
$410$	2.31178e6	+	1.36548e6i	0.679182	+	0.401166i
$411$	−7.74733e6			−2.26229
$412$		−	2.54971e6i		−	0.740026i
$413$		−	2.78073e6i		−	0.802202i
$414$	1.08954e6			0.312423
$415$	−4.11918e6	−	2.43304e6i	−1.17406	−	0.693471i
$416$	436250.			0.123595
$417$		−	6.96933e6i		−	1.96269i
$418$			33651.3i			0.00942023i
$419$	−3.04435e6			−0.847149			−0.423575	−	0.905861i	$-0.639225\pi$
$419$	−3.04435e6			−0.847149			−0.423575	+	0.905861i	$0.639225\pi$
$420$	1.49253e6	−	2.52688e6i	0.412857	−	0.698975i
$421$	−4.07049e6			−1.11929			−0.559643	−	0.828734i	$-0.689062\pi$
$421$	−4.07049e6			−1.11929			−0.559643	+	0.828734i	$0.689062\pi$
$422$			679592.i			0.185766i
$423$		−	7.02972e6i		−	1.91024i
$424$	1.58665e6			0.428614
$425$	3.63873e6	−	2.00559e6i	0.977186	−	0.538605i
$426$	−4.93855e6			−1.31849
$427$		−	2.78343e6i		−	0.738773i
$428$			1.81779e6i			0.479660i
$429$	−146272.			−0.0383724
$430$	927429.	−	1.57016e6i	0.241885	−	0.409517i
$431$	2.34757e6			0.608730			0.304365	−	0.952555i	$-0.401556\pi$
$431$	2.34757e6			0.608730			0.304365	+	0.952555i	$0.401556\pi$
$432$			1.91632e6i			0.494035i
$433$		−	6.00453e6i		−	1.53907i	−0.638602	−	0.769537i	$-0.720487\pi$
$433$		−	6.00453e6i		−	1.53907i	0.638602	−	0.769537i	$-0.279513\pi$
$434$	3.46999e6			0.884309
$435$	3.81396e6	+	2.25276e6i	0.966392	+	0.570810i
$436$	1.58375e6			0.398998
$437$		−	356844.i		−	0.0893871i
$438$		−	1.62041e6i		−	0.403590i
$439$	−2.38265e6			−0.590063			−0.295031	−	0.955488i	$-0.595330\pi$
$439$	−2.38265e6			−0.590063			−0.295031	+	0.955488i	$0.595330\pi$
$440$	−38418.3	−	22692.1i	−0.00946032	−	0.00558784i
$441$	−1.33986e6			−0.328067
$442$			2.26569e6i			0.551626i
$443$		−	218347.i		−	0.0528614i	−0.999651	−	0.0264307i	$-0.991586\pi$
$443$		−	218347.i		−	0.0528614i	0.999651	−	0.0264307i	$-0.00841413\pi$
$444$	4.75349e6			1.14434
$445$	−2.54430e6	+	4.30754e6i	−0.609070	+	1.03117i
$446$	387968.			0.0923545
$447$		−	7.71843e6i		−	1.82709i
$448$			488178.i			0.114917i
$449$	−480857.			−0.112564			−0.0562821	−	0.998415i	$-0.517925\pi$
$449$	−480857.			−0.112564			−0.0562821	+	0.998415i	$0.517925\pi$
$450$	5.63680e6	−	3.10689e6i	1.31221	−	0.723261i
$451$	149750.			0.0346677
$452$		−	1.71172e6i		−	0.394083i
$453$			1.37002e7i			3.13677i
$454$	−633726.			−0.144299
$455$	1.44354e6	−	2.44395e6i	0.326890	−	0.553431i
$456$	1.18853e6			0.267669
$457$		−	6.78917e6i		−	1.52064i	−0.649549	−	0.760320i	$-0.725042\pi$
$457$		−	6.78917e6i		−	1.52064i	0.649549	−	0.760320i	$-0.274958\pi$
$458$		−	3.19738e6i		−	0.712246i
$459$	−9.95250e6			−2.20496
$460$	407393.	+	240631.i	0.0897676	+	0.0530222i
$461$	6.45382e6			1.41438			0.707188	−	0.707026i	$-0.249964\pi$
$461$	6.45382e6			1.41438			0.707188	+	0.707026i	$0.249964\pi$
$462$		−	163684.i		−	0.0356780i
$463$			3.45228e6i			0.748435i	0.927341	+	0.374217i	$0.122089\pi$
$463$			3.45228e6i			0.748435i	−0.927341	+	0.374217i	$0.877911\pi$
$464$	−736835.			−0.158882
$465$	9.64487e6	+	5.69684e6i	2.06854	+	1.22180i
$466$	−519076.			−0.110730
$467$		−	3.28944e6i		−	0.697959i	−0.937130	−	0.348979i	$-0.886528\pi$
$467$		−	3.28944e6i		−	0.697959i	0.937130	−	0.348979i	$-0.113472\pi$
$468$			3.50981e6i			0.740745i
$469$	−7.71420e6			−1.61942
$470$	1.55255e6	−	2.62850e6i	0.324191	−	0.548862i
$471$	−7.55067e6			−1.56832
$472$			1.49321e6i			0.308507i
$473$		−	101710.i		−	0.0209031i
$474$	−1.56736e6			−0.320423
$475$	−1.01756e6	−	1.84615e6i	−0.206932	−	0.375434i
$476$	−2.53538e6			−0.512892
$477$			1.27653e7i			2.56882i
$478$		−	3.50150e6i		−	0.700946i
$479$	5.62327e6			1.11982			0.559912	−	0.828552i	$-0.310835\pi$
$479$	5.62327e6			1.11982			0.559912	+	0.828552i	$0.310835\pi$
$480$	−801464.	+	1.35689e6i	−0.158775	+	0.268809i
$481$	4.59748e6			0.906061
$482$			2.23458e6i			0.438105i
$483$			1.73573e6i			0.338543i
$484$	2.57433e6			0.499517
$485$	−1.33211e6	−	786828.i	−0.257150	−	0.151889i
$486$	−1.63904e6			−0.314775
$487$		−	8.57126e6i		−	1.63766i	−0.574039	−	0.818828i	$-0.694624\pi$
$487$		−	8.57126e6i		−	1.63766i	0.574039	−	0.818828i	$-0.305376\pi$
$488$			1.49466e6i			0.284114i
$489$	−8.23325e6			−1.55704
$490$	−500991.	−	295915.i	−0.0942626	−	0.0556772i
$491$	−2.25124e6			−0.421423			−0.210712	−	0.977548i	$-0.567578\pi$
$491$	−2.25124e6			−0.421423			−0.210712	+	0.977548i	$0.567578\pi$
$492$		−	5.28902e6i		−	0.985060i
$493$		−	3.82680e6i		−	0.709117i
$494$	1.14952e6			0.211934
$495$	182568.	−	309091.i	0.0334897	−	0.0566987i
$496$	−1.86333e6			−0.340084
$497$		−	5.34503e6i		−	0.970642i
$498$			9.42410e6i			1.70281i
$499$	394737.			0.0709669			0.0354835	−	0.999370i	$-0.488703\pi$
$499$	394737.			0.0709669			0.0354835	+	0.999370i	$0.488703\pi$
$500$	2.79385e6	+	83212.5i	0.499778	+	0.0148855i
$501$	1.68768e7			3.00398
$502$		−	1.74075e6i		−	0.308302i
$503$		−	9.21417e6i		−	1.62381i	−0.583786	−	0.811907i	$-0.698429\pi$
$503$		−	9.21417e6i		−	1.62381i	0.583786	−	0.811907i	$-0.301571\pi$
$504$	−3.92760e6			−0.688732
$505$	−2.90295e6	+	4.91474e6i	−0.506536	+	0.857576i
$506$	26389.7			0.00458204
$507$		−	5.22510e6i		−	0.902764i
$508$		−	3.03184e6i		−	0.521251i
$509$	4.03944e6			0.691077			0.345539	−	0.938405i	$-0.387696\pi$
$509$	4.03944e6			0.691077			0.345539	+	0.938405i	$0.387696\pi$
$510$	−7.04711e6	−	4.16245e6i	−1.19974	−	0.708637i
$511$	1.75378e6			0.297115
$512$		−	262144.i		−	0.0441942i
$513$			5.04952e6i			0.847143i
$514$	2.43666e6			0.406805
$515$	7.67023e6	+	4.53050e6i	1.27436	+	0.752711i
$516$	−3.59230e6			−0.593947
$517$		−	170266.i		−	0.0280158i
$518$			5.14474e6i			0.842440i
$519$	−2.04366e7			−3.33035
$520$	−775160.	+	1.31236e6i	−0.125714	+	0.212836i
$521$	7.79838e6			1.25866			0.629332	−	0.777136i	$-0.283328\pi$
$521$	7.79838e6			1.25866			0.629332	+	0.777136i	$0.283328\pi$
$522$		−	5.92814e6i		−	0.952231i
$523$			4.48138e6i			0.716404i	0.933644	+	0.358202i	$0.116610\pi$
$523$			4.48138e6i			0.716404i	−0.933644	+	0.358202i	$0.883390\pi$
$524$	2.79938e6			0.445384
$525$	4.94953e6	+	8.97989e6i	0.783729	+	1.42191i
$526$	−1.93112e6			−0.304331
$527$		−	9.67732e6i		−	1.51785i
$528$			87895.6i			0.0137209i
$529$	−279841.			−0.0434783
$530$	−2.81928e6	+	4.77309e6i	−0.435961	+	0.738091i
$531$	−1.20135e7			−1.84898
$532$			1.28636e6i			0.197053i
$533$		−	5.11543e6i		−	0.779946i
$534$	9.85505e6			1.49557
$535$	−5.46841e6	−	3.22997e6i	−0.825993	−	0.487882i
$536$	4.14240e6			0.622788
$537$		−	3.78031e6i		−	0.565708i
$538$		−	3.35109e6i		−	0.499149i
$539$	−32452.7			−0.00481148
$540$	−5.76482e6	−	3.40505e6i	−0.850749	−	0.502504i
$541$	1.66628e6			0.244768			0.122384	−	0.992483i	$-0.460946\pi$
$541$	1.66628e6			0.244768			0.122384	+	0.992483i	$0.460946\pi$
$542$		−	8.76064e6i		−	1.28097i
$543$			1.25297e7i			1.82365i
$544$	1.36146e6			0.197246
$545$	−2.81412e6	+	4.76437e6i	−0.405837	+	0.687090i
$546$	−5.59141e6			−0.802675
$547$			1.26212e7i			1.80356i	0.432191	+	0.901782i	$0.357741\pi$
$547$			1.26212e7i			1.80356i	−0.432191	+	0.901782i	$0.642259\pi$
$548$			4.50261e6i			0.640491i
$549$	−1.20251e7			−1.70278
$550$	136529.	−	75251.9i	0.0192450	−	0.0106074i
$551$	−1.94157e6			−0.272442
$552$		−	932059.i		−	0.130195i
$553$		−	1.69637e6i		−	0.235889i
$554$	−7.54721e6			−1.04475
$555$	−8.44635e6	+	1.42998e7i	−1.16396	+	1.97060i
$556$	−4.05045e6			−0.555669
$557$			1.00483e7i			1.37232i	0.727451	+	0.686159i	$0.240705\pi$
$557$			1.00483e7i			1.37232i	−0.727451	+	0.686159i	$0.759295\pi$
$558$		−	1.49913e7i		−	2.03823i
$559$	−3.47440e6			−0.470273
$560$	−1.46858e6	−	867431.i	−0.197891	−	0.116887i
$561$	−456491.			−0.0612386
$562$		−	3.27326e6i		−	0.437159i
$563$			1.97170e6i			0.262162i	0.991372	+	0.131081i	$0.0418448\pi$
$563$			1.97170e6i			0.262162i	−0.991372	+	0.131081i	$0.958155\pi$
$564$	−6.01364e6			−0.796049
$565$	5.14934e6	+	3.04151e6i	0.678626	+	0.400838i
$566$	−365583.			−0.0479672
$567$		−	9.64883e6i		−	1.26043i
$568$			2.87020e6i			0.373285i
$569$	1.29603e7			1.67816			0.839082	−	0.544005i	$-0.183093\pi$
$569$	1.29603e7			1.67816			0.839082	+	0.544005i	$0.183093\pi$
$570$	−2.11187e6	+	3.57544e6i	−0.272258	+	0.460937i
$571$	4.42791e6			0.568340			0.284170	−	0.958774i	$-0.408282\pi$
$571$	4.42791e6			0.568340			0.284170	+	0.958774i	$0.408282\pi$
$572$			85010.8i			0.0108639i
$573$		−	1.03036e6i		−	0.131100i
$574$	5.72435e6			0.725181
$575$	−1.44777e6	+	797983.i	−0.182613	+	0.100652i
$576$	2.10906e6			0.264870
$577$		−	1.36598e7i		−	1.70807i	−0.520214	−	0.854036i	$-0.674148\pi$
$577$		−	1.36598e7i		−	1.70807i	0.520214	−	0.854036i	$-0.325852\pi$
$578$			1.39140e6i			0.173233i
$579$	1.06100e7			1.31528
$580$	1.30926e6	−	2.21661e6i	0.161606	−	0.273602i
$581$	−1.01998e7			−1.25357
$582$			3.04769e6i			0.372961i
$583$			309187.i			0.0376747i
$584$	−941755.			−0.114263
$585$	−1.05585e7	−	6.23648e6i	−1.27559	−	0.753442i
$586$	4.54559e6			0.546822
$587$			6.96174e6i			0.833917i	0.908926	+	0.416958i	$0.136904\pi$
$587$			6.96174e6i			0.833917i	−0.908926	+	0.416958i	$0.863096\pi$
$588$			1.14620e6i			0.136715i
$589$	−4.90990e6			−0.583156
$590$	−4.49199e6	−	2.65324e6i	−0.531262	−	0.313795i
$591$	−2.14599e6			−0.252732
$592$		−	2.76265e6i		−	0.323982i
$593$			7.33054e6i			0.856051i	0.903767	+	0.428025i	$0.140791\pi$
$593$			7.33054e6i			0.856051i	−0.903767	+	0.428025i	$0.859209\pi$
$594$	−373428.			−0.0434251
$595$	4.50505e6	−	7.62714e6i	0.521684	−	0.883221i
$596$	−4.48581e6			−0.517280
$597$			2.37291e7i			2.72487i
$598$		−	901469.i		−	0.103086i
$599$	−1.04959e7			−1.19523			−0.597615	−	0.801783i	$-0.703885\pi$
$599$	−1.04959e7			−1.19523			−0.597615	+	0.801783i	$0.703885\pi$
$600$	−2.65782e6	−	4.82206e6i	−0.301403	−	0.546833i
$601$	−5.50536e6			−0.621727			−0.310864	−	0.950455i	$-0.600618\pi$
$601$	−5.50536e6			−0.621727			−0.310864	+	0.950455i	$0.600618\pi$
$602$		−	3.88797e6i		−	0.437252i
$603$			3.33273e7i			3.73257i
$604$	7.96233e6			0.888071
$605$	−4.57425e6	+	7.74430e6i	−0.508079	+	0.860189i
$606$	1.12442e7			1.24379
$607$			5.85267e6i			0.644737i	0.946614	+	0.322368i	$0.104479\pi$
$607$			5.85267e6i			0.644737i	−0.946614	+	0.322368i	$0.895521\pi$
$608$		−	690753.i		−	0.0757816i
$609$	9.44401e6			1.03184
$610$	−4.49635e6	−	2.65582e6i	−0.489256	−	0.288984i
$611$	−5.81627e6			−0.630292
$612$			1.09535e7i			1.18216i
$613$			125210.i			0.0134582i	0.999977	+	0.00672909i	$0.00214195\pi$
$613$			125210.i			0.0134582i	−0.999977	+	0.00672909i	$0.997858\pi$
$614$	4.90597e6			0.525175
$615$	1.59109e7	+	9.39792e6i	1.69631	+	1.00194i
$616$	−95130.0			−0.0101010
$617$		−	5.83743e6i		−	0.617318i	−0.951173	−	0.308659i	$-0.900120\pi$
$617$		−	5.83743e6i		−	0.617318i	0.951173	−	0.308659i	$-0.0998802\pi$
$618$		−	1.75484e7i		−	1.84828i
$619$	3.32730e6			0.349032			0.174516	−	0.984654i	$-0.444164\pi$
$619$	3.32730e6			0.349032			0.174516	+	0.984654i	$0.444164\pi$
$620$	3.31090e6	−	5.60542e6i	0.345913	−	0.585638i
$621$	3.95989e6			0.412054
$622$			9.38512e6i			0.972667i
$623$			1.06662e7i			1.10101i
$624$	3.00250e6			0.308689
$625$	−5.21464e6	+	8.25682e6i	−0.533979	+	0.845498i
$626$	5.93073e6			0.604884
$627$			231606.i			0.0235278i
$628$			4.38832e6i			0.444016i
$629$	1.43480e7			1.44598
$630$	6.97884e6	−	1.18153e7i	0.700538	−	1.18602i
$631$	−6.85441e6			−0.685326			−0.342663	−	0.939458i	$-0.611329\pi$
$631$	−6.85441e6			−0.685326			−0.342663	+	0.939458i	$0.611329\pi$
$632$			910924.i			0.0907171i
$633$			4.67731e6i			0.463967i
$634$	6.09698e6			0.602409
$635$	9.12062e6	+	5.38719e6i	0.897615	+	0.530186i
$636$	1.09202e7			1.07050
$637$			1.10858e6i			0.108247i
$638$		−	143585.i		−	0.0139655i
$639$	−2.30919e7			−2.23721
$640$	788603.	+	465797.i	0.0761042	+	0.0449517i
$641$	1.07900e6			0.103723			0.0518617	−	0.998654i	$-0.483484\pi$
$641$	1.07900e6			0.103723			0.0518617	+	0.998654i	$0.483484\pi$
$642$			1.25110e7i			1.19799i
$643$		−	1.93747e7i		−	1.84802i	−0.382369	−	0.924010i	$-0.624892\pi$
$643$		−	1.93747e7i		−	1.84802i	0.382369	−	0.924010i	$-0.375108\pi$
$644$	1.00877e6			0.0958472
$645$	6.38305e6	−	1.08066e7i	0.604128	−	1.02280i
$646$	3.58747e6			0.338226
$647$		−	9.68077e6i		−	0.909179i	−0.890701	−	0.454589i	$-0.849786\pi$
$647$		−	9.68077e6i		−	0.909179i	0.890701	−	0.454589i	$-0.150214\pi$
$648$			5.18127e6i			0.484729i
$649$	−290978.			−0.0271174
$650$	−2.57059e6	−	4.66380e6i	−0.238643	−	0.432969i
$651$	2.38823e7			2.20863
$652$			4.78501e6i			0.440823i
$653$		−	1.23209e7i		−	1.13073i	−0.824841	−	0.565365i	$-0.808735\pi$
$653$		−	1.23209e7i		−	1.13073i	0.824841	−	0.565365i	$-0.191265\pi$
$654$	1.09002e7			0.996529
$655$	−4.97415e6	+	8.42133e6i	−0.453018	+	0.766969i
$656$	−3.07388e6			−0.278887
$657$		−	7.57681e6i		−	0.684814i
$658$		−	6.50861e6i		−	0.586035i
$659$	1.55477e7			1.39461			0.697303	−	0.716776i	$-0.254383\pi$
$659$	1.55477e7			1.39461			0.697303	+	0.716776i	$0.254383\pi$
$660$	−264415.	−	156179.i	−0.0236279	−	0.0139561i
$661$	7.54640e6			0.671794			0.335897	−	0.941899i	$-0.390961\pi$
$661$	7.54640e6			0.671794			0.335897	+	0.941899i	$0.390961\pi$
$662$			1.44379e7i			1.28044i
$663$			1.55937e7i			1.37773i
$664$	5.47712e6			0.482094
$665$	−3.86972e6	−	2.28569e6i	−0.339333	−	0.200430i
$666$	2.22266e7			1.94173
$667$			1.52260e6i			0.132517i
$668$		−	9.80851e6i		−	0.850475i
$669$	2.67020e6			0.230663
$670$	−7.36052e6	+	1.24615e7i	−0.633464	+	1.07247i
$671$	−291260.			−0.0249732
$672$			3.35990e6i			0.287014i
$673$		−	1.11899e7i		−	0.952332i	−0.879355	−	0.476166i	$-0.842026\pi$
$673$		−	1.11899e7i		−	0.952332i	0.879355	−	0.476166i	$-0.157974\pi$
$674$	−3.14196e6			−0.266411
$675$	2.04867e7	−	1.12919e7i	1.73066	−	0.953906i
$676$	−3.03673e6			−0.255588
$677$			1.85745e7i			1.55756i	0.627295	+	0.778781i	$0.284162\pi$
$677$			1.85745e7i			1.55756i	−0.627295	+	0.778781i	$0.715838\pi$
$678$		−	1.17810e7i		−	0.984253i
$679$	−3.29854e6			−0.274566
$680$	−2.41914e6	+	4.09566e6i	−0.200627	+	0.339665i
$681$	−4.36164e6			−0.360397
$682$		−	363103.i		−	0.0298929i
$683$		−	2.28740e7i		−	1.87625i	−0.346303	−	0.938123i	$-0.612563\pi$
$683$		−	2.28740e7i		−	1.87625i	0.346303	−	0.938123i	$-0.387437\pi$
$684$	5.55739e6			0.454183
$685$	−1.35451e7	−	8.00056e6i	−1.10295	−	0.651470i
$686$	−9.25305e6			−0.750714
$687$		−	2.20060e7i		−	1.77889i
$688$			2.08778e6i			0.168156i
$689$	1.05618e7			0.847595
$690$	2.80390e6	+	1.65615e6i	0.224202	+	0.132427i
$691$	−1.06900e7			−0.851696			−0.425848	−	0.904795i	$-0.640024\pi$
$691$	−1.06900e7			−0.851696			−0.425848	+	0.904795i	$0.640024\pi$
$692$			1.18774e7i			0.942878i
$693$		−	765360.i		−	0.0605387i
$694$	1.26418e6			0.0996350
$695$	7.19714e6	−	1.21849e7i	0.565194	−	0.956885i
$696$	−5.07129e6			−0.396821
$697$		−	1.59644e7i		−	1.24472i
$698$			6.29181e6i			0.488807i
$699$	−3.57255e6			−0.276558
$700$	5.21895e6	−	2.87658e6i	0.402567	−	0.221887i
$701$	−2.34648e6			−0.180352			−0.0901761	−	0.995926i	$-0.528743\pi$
$701$	−2.34648e6			−0.180352			−0.0901761	+	0.995926i	$0.528743\pi$
$702$			1.27562e7i			0.976966i
$703$		−	7.27961e6i		−	0.555546i
$704$	51083.3			0.00388461
$705$	1.06855e7	−	1.80907e7i	0.809694	−	1.37083i
$706$	9.47523e6			0.715448
$707$			1.21697e7i			0.915656i
$708$			1.02770e7i			0.770522i
$709$	−2.26822e7			−1.69461			−0.847305	−	0.531106i	$-0.821777\pi$
$709$	−2.26822e7			−1.69461			−0.847305	+	0.531106i	$0.821777\pi$
$710$	−8.63435e6	−	5.09997e6i	−0.642812	−	0.379684i
$711$	−7.32876e6			−0.543696
$712$		−	5.72758e6i		−	0.423420i
$713$			3.85040e6i			0.283649i
$714$	−1.74498e7			−1.28099
$715$	−255736.	−	151053.i	−0.0187080	−	0.0110501i
$716$	−2.19705e6			−0.160161
$717$		−	2.40992e7i		−	1.75067i
$718$		−	1.22956e6i		−	0.0890100i
$719$	2.71271e6			0.195696			0.0978478	−	0.995201i	$-0.468804\pi$
$719$	2.71271e6			0.195696			0.0978478	+	0.995201i	$0.468804\pi$
$720$	−3.74753e6	+	6.34464e6i	−0.269410	+	0.456116i
$721$	1.89928e7			1.36066
$722$			8.08425e6i			0.577161i
$723$			1.53796e7i			1.09420i
$724$	7.28204e6			0.516306
$725$	4.34178e6	+	7.87726e6i	0.306777	+	0.556583i
$726$	1.77179e7			1.24758
$727$			1.38203e7i			0.969800i	0.874570	+	0.484900i	$0.161144\pi$
$727$			1.38203e7i			0.969800i	−0.874570	+	0.484900i	$0.838856\pi$
$728$			3.24963e6i			0.227251i
$729$	8.39188e6			0.584845
$730$	1.67338e6	−	2.83306e6i	0.116222	−	0.196766i
$731$	−1.08430e7			−0.750509
$732$			1.02870e7i			0.709598i
$733$		−	1.38382e7i		−	0.951303i	−0.879634	−	0.475651i	$-0.842212\pi$
$733$		−	1.38382e7i		−	0.951303i	0.879634	−	0.475651i	$-0.157788\pi$
$734$	1.76867e7			1.21173
$735$	−3.44808e6	−	2.03664e6i	−0.235428	−	0.139058i
$736$	−541696.			−0.0368605
$737$			807220.i			0.0547423i
$738$		−	2.47307e7i		−	1.67146i
$739$	9.32302e6			0.627979			0.313990	−	0.949426i	$-0.398334\pi$
$739$	9.32302e6			0.627979			0.313990	+	0.949426i	$0.398334\pi$
$740$	8.31081e6	+	4.90887e6i	0.557910	+	0.329535i
$741$	7.91163e6			0.529322
$742$			1.18190e7i			0.788079i
$743$			2.77412e7i			1.84354i	0.387732	+	0.921772i	$0.373258\pi$
$743$			2.77412e7i			1.84354i	−0.387732	+	0.921772i	$0.626742\pi$
$744$	−1.28244e7			−0.849387
$745$	7.97071e6	−	1.34946e7i	0.526146	−	0.890776i
$746$	−1.73309e7			−1.14018
$747$			4.40657e7i			2.88934i
$748$			265304.i			0.0173377i
$749$	−1.35407e7			−0.881935
$750$	1.92287e7	+	572712.i	1.24824	+	0.0371778i
$751$	−1.08305e7			−0.700725			−0.350362	−	0.936614i	$-0.613942\pi$
$751$	−1.08305e7			−0.700725			−0.350362	+	0.936614i	$0.613942\pi$
$752$			3.49502e6i			0.225375i
$753$		−	1.19807e7i		−	0.770009i
$754$	−4.90485e6			−0.314193
$755$	−1.41480e7	+	2.39529e7i	−0.903294	+	1.52929i
$756$	−1.42747e7			−0.908367
$757$		−	2.53431e7i		−	1.60739i	−0.595043	−	0.803694i	$-0.702865\pi$
$757$		−	2.53431e7i		−	1.60739i	0.595043	−	0.803694i	$-0.297135\pi$
$758$		−	4.13458e6i		−	0.261371i
$759$	181628.			0.0114440
$760$	2.07798e6	+	1.22738e6i	0.130499	+	0.0770806i
$761$	1.67791e7			1.05029			0.525143	−	0.851014i	$-0.324012\pi$
$761$	1.67791e7			1.05029			0.525143	+	0.851014i	$0.324012\pi$
$762$		−	2.08667e7i		−	1.30187i
$763$			1.17974e7i			0.733624i
$764$	−598828.			−0.0371167
$765$	−3.29512e7	−	1.94630e7i	−2.03572	−	1.20242i
$766$	−1.49926e7			−0.923217
$767$			9.93975e6i			0.610080i
$768$		−	1.80421e6i		−	0.110379i
$769$	−2.98050e7			−1.81749			−0.908747	−	0.417347i	$-0.862960\pi$
$769$	−2.98050e7			−1.81749			−0.908747	+	0.417347i	$0.862960\pi$
$770$	169034.	−	286178.i	0.0102742	−	0.0173944i
$771$	1.67704e7			1.01603
$772$		−	6.16632e6i		−	0.372377i
$773$			9.90255e6i			0.596071i	0.954555	+	0.298036i	$0.0963314\pi$
$773$			9.90255e6i			0.596071i	−0.954555	+	0.298036i	$0.903669\pi$
$774$	−1.67970e7			−1.00781
$775$	1.09796e7	+	1.99203e7i	0.656650	+	1.19135i
$776$	1.77126e6			0.105591
$777$			3.54088e7i			2.10406i
$778$		−	1.01645e7i		−	0.602059i
$779$	−8.09973e6			−0.478219
$780$	−5.33506e6	+	9.03236e6i	−0.313980	+	0.531575i
$781$	−559308.			−0.0328113
$782$		−	2.81333e6i		−	0.164514i
$783$		−	2.15455e7i		−	1.25589i
$784$	666149.			0.0387062
$785$	−1.32013e7	−	7.79748e6i	−0.764614	−	0.451627i
$786$	1.92668e7			1.11238
$787$		−	1.64106e7i		−	0.944470i	−0.881473	−	0.472235i	$-0.843447\pi$
$787$		−	1.64106e7i		−	0.944470i	0.881473	−	0.472235i	$-0.156553\pi$
$788$			1.24721e6i			0.0715526i
$789$	−1.32910e7			−0.760091
$790$	−2.74031e6	−	1.61860e6i	−0.156219	−	0.0922721i
$791$	1.27506e7			0.724587
$792$			410986.i			0.0232817i
$793$			9.94941e6i			0.561842i
$794$	−1.77455e7			−0.998933
$795$	−1.94037e7	+	3.28509e7i	−1.08885	+	1.84344i
$796$	1.37909e7			0.771456
$797$			2.72909e7i			1.52185i	0.648840	+	0.760925i	$0.275254\pi$
$797$			2.72909e7i			1.52185i	−0.648840	+	0.760925i	$0.724746\pi$
$798$			8.85338e6i			0.492155i
$799$	−1.81516e7			−1.00588
$800$	−2.80249e6	+	1.54468e6i	−0.154817	+	0.0853322i
$801$	4.60807e7			2.53769
$802$			7.71784e6i			0.423701i
$803$		−	183517.i		−	0.0100436i
$804$	2.85102e7			1.55546
$805$	−1.79246e6	+	3.03468e6i	−0.0974901	+	0.165053i
$806$	−1.24035e7			−0.672524
$807$		−	2.30640e7i		−	1.24667i
$808$		−	6.53495e6i		−	0.352139i
$809$	−9.03260e6			−0.485223			−0.242611	−	0.970124i	$-0.578004\pi$
$809$	−9.03260e6			−0.485223			−0.242611	+	0.970124i	$0.578004\pi$
$810$	−1.55867e7	−	9.20646e6i	−0.834723	−	0.493038i
$811$	−3.22127e6			−0.171979			−0.0859894	−	0.996296i	$-0.527405\pi$
$811$	−3.22127e6			−0.171979			−0.0859894	+	0.996296i	$0.527405\pi$
$812$		−	5.48869e6i		−	0.292132i
$813$		−	6.02953e7i		−	3.19932i
$814$	538350.			0.0284776
$815$	−1.43947e7	−	8.50236e6i	−0.759115	−	0.448379i
$816$	9.37029e6			0.492637
$817$			5.50133e6i			0.288345i
$818$		−	1.95745e7i		−	1.02284i
$819$	−2.61446e7			−1.36198
$820$	5.46190e6	−	9.24711e6i	0.283667	−	0.480254i
$821$	−1.79822e7			−0.931076			−0.465538	−	0.885028i	$-0.654139\pi$
$821$	−1.79822e7			−0.931076			−0.465538	+	0.885028i	$0.654139\pi$
$822$			3.09893e7i			1.59968i
$823$		−	3.24068e7i		−	1.66777i	−0.551936	−	0.833886i	$-0.686111\pi$
$823$		−	3.24068e7i		−	1.66777i	0.551936	−	0.833886i	$-0.313889\pi$
$824$	−1.01988e7			−0.523278
$825$	939662.	−	517923.i	0.0480659	−	0.0264929i
$826$	−1.11229e7			−0.567242
$827$			1.69125e7i			0.859894i	0.902854	+	0.429947i	$0.141468\pi$
$827$			1.69125e7i			0.859894i	−0.902854	+	0.429947i	$0.858532\pi$
$828$		−	4.35817e6i		−	0.220916i
$829$	−1.33113e7			−0.672721			−0.336360	−	0.941733i	$-0.609196\pi$
$829$	−1.33113e7			−0.672721			−0.336360	+	0.941733i	$0.609196\pi$
$830$	−9.73214e6	+	1.64767e7i	−0.490358	+	0.830186i
$831$	−5.19438e7			−2.60935
$832$		−	1.74500e6i		−	0.0873950i
$833$			3.45968e6i			0.172752i
$834$	−2.78773e7			−1.38783
$835$	2.95067e7	+	1.74285e7i	1.46455	+	0.865053i
$836$	134605.			0.00666111
$837$		−	5.44851e7i		−	2.68821i
$838$			1.21774e7i			0.599025i
$839$	2.76782e7			1.35748			0.678739	−	0.734379i	$-0.262527\pi$
$839$	2.76782e7			1.35748			0.678739	+	0.734379i	$0.262527\pi$
$840$	−1.01075e7	−	5.97011e6i	−0.494250	−	0.291934i
$841$	−1.22268e7			−0.596103
$842$			1.62819e7i			0.791455i
$843$		−	2.25283e7i		−	1.09184i
$844$	2.71837e6			0.131357
$845$	5.39589e6	−	9.13534e6i	0.259969	−	0.440132i
$846$	−2.81189e7			−1.35074
$847$			1.91762e7i			0.918446i
$848$		−	6.34660e6i		−	0.303076i
$849$	−2.51613e6			−0.119802
$850$	−8.02238e6	−	1.45549e7i	−0.380851	−	0.690975i
$851$	−5.70875e6			−0.270220
$852$			1.97542e7i			0.932310i
$853$		−	3.42602e7i		−	1.61219i	−0.591784	−	0.806097i	$-0.701576\pi$
$853$		−	3.42602e7i		−	1.61219i	0.591784	−	0.806097i	$-0.298424\pi$
$854$	−1.11337e7			−0.522391
$855$	−9.87478e6	+	1.67182e7i	−0.461968	+	0.782122i
$856$	7.27114e6			0.339171
$857$		−	6.83240e6i		−	0.317776i	−0.987297	−	0.158888i	$-0.949209\pi$
$857$		−	6.83240e6i		−	0.317776i	0.987297	−	0.158888i	$-0.0507909\pi$
$858$			585089.i			0.0271334i
$859$	3.79158e7			1.75323			0.876613	−	0.481197i	$-0.159798\pi$
$859$	3.79158e7			1.75323			0.876613	+	0.481197i	$0.159798\pi$
$860$	−6.28062e6	−	3.70972e6i	−0.289572	−	0.171039i
$861$	3.93980e7			1.81120
$862$		−	9.39027e6i		−	0.430437i
$863$		−	9.04549e6i		−	0.413433i	−0.978401	−	0.206716i	$-0.933722\pi$
$863$		−	9.04549e6i		−	0.413433i	0.978401	−	0.206716i	$-0.0662778\pi$
$864$	7.66527e6			0.349336
$865$	−3.57305e7	−	2.11046e7i	−1.62367	−	0.959040i
$866$	−2.40181e7			−1.08829
$867$			9.57633e6i			0.432665i
$868$		−	1.38800e7i		−	0.625301i
$869$	−177509.			−0.00797392
$870$	9.01103e6	−	1.52559e7i	0.403623	−	0.683342i
$871$	2.75745e7			1.23158
$872$		−	6.33500e6i		−	0.282134i
$873$			1.42505e7i			0.632843i
$874$	−1.42738e6			−0.0632062
$875$	−619851.	+	2.08114e7i	−0.0273695	+	0.918927i
$876$	−6.48165e6			−0.285381
$877$		−	1.05102e6i		−	0.0461439i	−0.999734	−	0.0230719i	$-0.992655\pi$
$877$		−	1.05102e6i		−	0.0461439i	0.999734	−	0.0230719i	$-0.00734468\pi$
$878$			9.53059e6i			0.417237i
$879$	3.12851e7			1.36573
$880$	−90768.6	+	153673.i	−0.00395120	+	0.00668946i
$881$	1.98596e7			0.862048			0.431024	−	0.902340i	$-0.358152\pi$
$881$	1.98596e7			0.862048			0.431024	+	0.902340i	$0.358152\pi$
$882$			5.35944e6i			0.231979i
$883$			7.69285e6i			0.332036i	0.986123	+	0.166018i	$0.0530911\pi$
$883$			7.69285e6i			0.332036i	−0.986123	+	0.166018i	$0.946909\pi$
$884$	9.06275e6			0.390058
$885$	−3.09162e7	−	1.82610e7i	−1.32687	−	0.783729i
$886$	−873390.			−0.0373787
$887$		−	1.80584e7i		−	0.770672i	−0.922776	−	0.385336i	$-0.874085\pi$
$887$		−	1.80584e7i		−	0.770672i	0.922776	−	0.385336i	$-0.125915\pi$
$888$		−	1.90140e7i		−	0.809171i
$889$	2.25842e7			0.958407
$890$	1.72302e7	+	1.01772e7i	0.729146	+	0.430678i
$891$	−1.00966e6			−0.0426070
$892$		−	1.55187e6i		−	0.0653045i
$893$			9.20942e6i			0.386459i
$894$	−3.08737e7			−1.29195
$895$	3.90388e6	−	6.60934e6i	0.162907	−	0.275804i
$896$	1.95271e6			0.0812584
$897$		−	6.20438e6i		−	0.257465i
$898$			1.92343e6i			0.0795949i
$899$	2.09498e7			0.864532
$900$	−1.24276e7	−	2.25472e7i	−0.511423	−	0.927869i
$901$	3.29615e7			1.35268
$902$		−	599000.i		−	0.0245138i
$903$		−	2.67590e7i		−	1.09207i
$904$	−6.84689e6			−0.278658
$905$	−1.29393e7	+	2.19064e7i	−0.525156	+	0.889099i
$906$	5.48009e7			2.21803
$907$			2.55855e7i			1.03270i	0.856377	+	0.516352i	$0.172710\pi$
$907$			2.55855e7i			1.03270i	−0.856377	+	0.516352i	$0.827290\pi$
$908$			2.53490e6i			0.102034i
$909$	5.25764e7			2.11048
$910$	−9.77579e6	−	5.77417e6i	−0.391335	−	0.231146i
$911$	−1.20745e7			−0.482029			−0.241015	−	0.970521i	$-0.577480\pi$
$911$	−1.20745e7			−0.482029			−0.241015	+	0.970521i	$0.577480\pi$
$912$		−	4.75413e6i		−	0.189271i
$913$			1.06731e6i			0.0423755i
$914$	−2.71567e7			−1.07525
$915$	−3.09463e7	−	1.82787e7i	−1.22196	−	0.721761i
$916$	−1.27895e7			−0.503634
$917$			2.08526e7i			0.818913i
$918$			3.98100e7i			1.55914i
$919$	1.30549e7			0.509900			0.254950	−	0.966954i	$-0.417941\pi$
$919$	1.30549e7			0.509900			0.254950	+	0.966954i	$0.417941\pi$
$920$	962525.	−	1.62957e6i	0.0374923	−	0.0634753i
$921$	3.37655e7			1.31167
$922$		−	2.58153e7i		−	1.00011i
$923$			1.91059e7i			0.738180i
$924$	−654735.			−0.0252282
$925$	−2.95345e7	+	1.62788e7i	−1.13495	+	0.625560i
$926$	1.38091e7			0.529223
$927$		−	8.20538e7i		−	3.13617i
$928$			2.94734e6i			0.112347i
$929$	−4.48969e7			−1.70678			−0.853389	−	0.521275i	$-0.825457\pi$
$929$	−4.48969e7			−1.70678			−0.853389	+	0.521275i	$0.825457\pi$
$930$	2.27874e7	−	3.85795e7i	0.863947	−	1.46268i
$931$	1.75531e6			0.0663712
$932$			2.07630e6i			0.0782981i
$933$			6.45933e7i			2.42931i
$934$	−1.31578e7			−0.493531
$935$	−798110.	−	471412.i	−0.0298561	−	0.0176348i
$936$	1.40392e7			0.523786
$937$			2.57951e7i			0.959816i	0.877319	+	0.479908i	$0.159330\pi$
$937$			2.57951e7i			0.959816i	−0.877319	+	0.479908i	$0.840670\pi$
$938$			3.08568e7i			1.14510i
$939$	4.08184e7			1.51075
$940$	−1.05140e7	−	6.21020e6i	−0.388104	−	0.229238i
$941$	9.55779e6			0.351871			0.175935	−	0.984402i	$-0.443705\pi$
$941$	9.55779e6			0.351871			0.175935	+	0.984402i	$0.443705\pi$
$942$			3.02027e7i			1.10897i
$943$			6.35189e6i			0.232608i
$944$	5.97283e6			0.218147
$945$	2.53642e7	−	4.29422e7i	0.923937	−	1.56424i
$946$	−406840.			−0.0147807
$947$		−	3.30534e7i		−	1.19768i	−0.800868	−	0.598841i	$-0.795628\pi$
$947$		−	3.30534e7i		−	1.19768i	0.800868	−	0.598841i	$-0.204372\pi$
$948$			6.26946e6i			0.226573i
$949$	−6.26892e6			−0.225958
$950$	−7.38461e6	+	4.07025e6i	−0.265472	+	0.146323i
$951$	4.19626e7			1.50457
$952$			1.01415e7i			0.362670i
$953$		−	2.16346e7i		−	0.771645i	−0.922573	−	0.385822i	$-0.873918\pi$
$953$		−	2.16346e7i		−	0.771645i	0.922573	−	0.385822i	$-0.126082\pi$
$954$	5.10610e7			1.81643
$955$	1.06404e6	−	1.80144e6i	0.0377529	−	0.0639164i
$956$	−1.40060e7			−0.495644
$957$		−	988229.i		−	0.0348801i
$958$		−	2.24931e7i		−	0.791835i
$959$	−3.35400e7			−1.17765
$960$	5.42758e6	+	3.20586e6i	0.190076	+	0.112271i
$961$	2.43494e7			0.850512
$962$		−	1.83899e7i		−	0.640682i
$963$			5.84993e7i			2.03276i
$964$	8.93832e6			0.309787
$965$	1.85500e7	+	1.09568e7i	0.641248	+	0.378760i
$966$	6.94292e6			0.239386
$967$		−	4.94874e7i		−	1.70188i	−0.525265	−	0.850939i	$-0.676034\pi$
$967$		−	4.94874e7i		−	1.70188i	0.525265	−	0.850939i	$-0.323966\pi$
$968$		−	1.02973e7i		−	0.353212i
$969$	2.46908e7			0.844746
$970$	−3.14731e6	+	5.32846e6i	−0.107401	+	0.181833i
$971$	4.48432e7			1.52633			0.763166	−	0.646203i	$-0.223644\pi$
$971$	4.48432e7			1.52633			0.763166	+	0.646203i	$0.223644\pi$
$972$			6.55617e6i			0.222579i
$973$		−	3.01719e7i		−	1.02169i
$974$	−3.42851e7			−1.15800
$975$	−1.76922e7	−	3.20987e7i	−0.596031	−	1.08137i
$976$	5.97864e6			0.200899
$977$		−	3.97769e7i		−	1.33320i	−0.745417	−	0.666599i	$-0.767749\pi$
$977$		−	3.97769e7i		−	1.33320i	0.745417	−	0.666599i	$-0.232251\pi$
$978$			3.29330e7i			1.10099i
$979$	1.11612e6			0.0372181
$980$	−1.18366e6	+	2.00396e6i	−0.0393697	+	0.0666537i
$981$	5.09677e7			1.69092
$982$			9.00497e6i			0.297991i
$983$		−	4.82109e7i		−	1.59133i	−0.605735	−	0.795667i	$-0.707121\pi$
$983$		−	4.82109e7i		−	1.59133i	0.605735	−	0.795667i	$-0.292879\pi$
$984$	−2.11561e7			−0.696542
$985$	−3.75197e6	−	2.21614e6i	−0.123216	−	0.0727791i
$986$	−1.53072e7			−0.501422
$987$		−	4.47956e7i		−	1.46367i
$988$		−	4.59809e6i		−	0.149860i
$989$	4.31420e6			0.140252
$990$	−1.23636e6	−	730271.i	−0.0400920	−	0.0236808i
$991$	−3.97892e7			−1.28701			−0.643504	−	0.765443i	$-0.722520\pi$
$991$	−3.97892e7			−1.28701			−0.643504	+	0.765443i	$0.722520\pi$
$992$			7.45333e6i			0.240476i
$993$			9.93690e7i			3.19800i
$994$	−2.13801e7			−0.686347
$995$	−2.45047e7	+	4.14870e7i	−0.784679	+	1.32848i
$996$	3.76964e7			1.20407
$997$			2.50375e7i			0.797725i	0.917011	+	0.398862i	$0.130595\pi$
$997$			2.50375e7i			0.797725i	−0.917011	+	0.398862i	$0.869405\pi$
$998$		−	1.57895e6i		−	0.0501812i
$999$	8.07816e7			2.56094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.b.a.139.1	✓	26
5.4	even	2	inner	230.6.b.a.139.26	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.b.a.139.1	✓	26	1.1	even	1	trivial
230.6.b.a.139.26	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)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -27.5301i q^{3} -16.0000 q^{4} +(28.4300 - 48.1325i) q^{5} -110.120 q^{6} -119.184i q^{7} +64.0000i q^{8} -514.906 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} -27.5301i q^{3} -16.0000 q^{4} +(28.4300 - 48.1325i) q^{5} -110.120 q^{6} -119.184i q^{7} +64.0000i q^{8} -514.906 q^{9} +(-192.530 - 113.720i) q^{10} -12.4715 q^{11} +440.482i q^{12} +426.025i q^{13} -476.737 q^{14} +(-1325.09 - 782.680i) q^{15} +256.000 q^{16} +1329.55i q^{17} +2059.63i q^{18} +674.564 q^{19} +(-454.879 + 770.120i) q^{20} -3281.15 q^{21} +49.8861i q^{22} -529.000i q^{23} +1761.93 q^{24} +(-1508.47 - 2736.81i) q^{25} +1704.10 q^{26} +7485.61i q^{27} +1906.95i q^{28} -2878.26 q^{29} +(-3130.72 + 5300.37i) q^{30} -7278.64 q^{31} -1024.00i q^{32} +343.342i q^{33} +5318.20 q^{34} +(-5736.63 - 3388.40i) q^{35} +8238.50 q^{36} -10791.6i q^{37} -2698.25i q^{38} +11728.5 q^{39} +(3080.48 + 1819.52i) q^{40} -12007.4 q^{41} +13124.6i q^{42} +8155.38i q^{43} +199.544 q^{44} +(-14638.8 + 24783.7i) q^{45} -2116.00 q^{46} +13652.4i q^{47} -7047.71i q^{48} +2602.14 q^{49} +(-10947.2 + 6033.90i) q^{50} +36602.7 q^{51} -6816.40i q^{52} -24791.4i q^{53} +29942.4 q^{54} +(-354.565 + 600.285i) q^{55} +7627.78 q^{56} -18570.8i q^{57} +11513.0i q^{58} +23331.4 q^{59} +(21201.5 + 12522.9i) q^{60} +23354.0 q^{61} +29114.6i q^{62} +61368.7i q^{63} -4096.00 q^{64} +(20505.6 + 12111.9i) q^{65} +1373.37 q^{66} -64725.1i q^{67} -21272.8i q^{68} -14563.4 q^{69} +(-13553.6 + 22946.5i) q^{70} +44846.8 q^{71} -32954.0i q^{72} +14714.9i q^{73} -43166.3 q^{74} +(-75344.7 + 41528.4i) q^{75} -10793.0 q^{76} +1486.41i q^{77} -46914.0i q^{78} +14233.2 q^{79} +(7278.07 - 12321.9i) q^{80} +80957.4 q^{81} +48029.4i q^{82} -85580.0i q^{83} +52498.4 q^{84} +(63994.6 + 37799.1i) q^{85} +32621.5 q^{86} +79238.8i q^{87} -798.177i q^{88} -89493.4 q^{89} +(99134.9 + 58555.1i) q^{90} +50775.4 q^{91} +8464.00i q^{92} +200382. i q^{93} +54609.7 q^{94} +(19177.8 - 32468.4i) q^{95} -28190.8 q^{96} -27676.0i q^{97} -10408.6i q^{98} +6421.66 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) \) 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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