LMFDB - Embedded newform 160.6.o.a.47.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,6,Mod(47,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("160.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	160.o (of order $4$, degree $2$, not 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:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.12
Character	$\chi$	$=$	160.47
Dual form			160.6.o.a.143.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.45554 + 4.45554i) q^{3} +(-49.9881 - 25.0237i) q^{5} +(-169.279 + 169.279i) q^{7} +203.296i q^{9} +O(q^{10})$	\(q+(-4.45554 + 4.45554i) q^{3} +(-49.9881 - 25.0237i) q^{5} +(-169.279 + 169.279i) q^{7} +203.296i q^{9} +207.026 q^{11} +(249.136 + 249.136i) q^{13} +(334.219 - 111.230i) q^{15} +(-424.145 - 424.145i) q^{17} -2282.02i q^{19} -1508.46i q^{21} +(351.205 + 351.205i) q^{23} +(1872.62 + 2501.78i) q^{25} +(-1988.49 - 1988.49i) q^{27} -7256.22 q^{29} -7244.36i q^{31} +(-922.415 + 922.415i) q^{33} +(12697.9 - 4225.95i) q^{35} +(-266.347 + 266.347i) q^{37} -2220.08 q^{39} +16812.6 q^{41} +(4601.16 - 4601.16i) q^{43} +(5087.23 - 10162.4i) q^{45} +(-5614.39 + 5614.39i) q^{47} -40503.7i q^{49} +3779.59 q^{51} +(-937.132 - 937.132i) q^{53} +(-10348.9 - 5180.57i) q^{55} +(10167.6 + 10167.6i) q^{57} +16983.7i q^{59} -27237.2i q^{61} +(-34413.8 - 34413.8i) q^{63} +(-6219.54 - 18688.2i) q^{65} +(7571.99 + 7571.99i) q^{67} -3129.62 q^{69} +17125.0i q^{71} +(15977.8 - 15977.8i) q^{73} +(-19490.4 - 2803.23i) q^{75} +(-35045.2 + 35045.2i) q^{77} +72486.1 q^{79} -31681.3 q^{81} +(58657.5 - 58657.5i) q^{83} +(10588.5 + 31815.9i) q^{85} +(32330.4 - 32330.4i) q^{87} +34335.8i q^{89} -84347.1 q^{91} +(32277.6 + 32277.6i) q^{93} +(-57104.6 + 114074. i) q^{95} +(62650.0 + 62650.0i) q^{97} +42087.6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3}+O(q^{10}) $ 56 * q + 4 * q^3	$ 56 q + 4 q^{3} + 8 q^{11} - 408 q^{17} - 3120 q^{25} - 968 q^{27} - 976 q^{33} + 4780 q^{35} - 8 q^{41} - 1308 q^{43} - 20872 q^{51} + 968 q^{57} + 17680 q^{65} - 89252 q^{67} - 25184 q^{73} + 127740 q^{75} - 67792 q^{81} + 126444 q^{83} - 329432 q^{91} + 212576 q^{97}+O(q^{100}) $ 56 * q + 4 * q^3 + 8 * q^11 - 408 * q^17 - 3120 * q^25 - 968 * q^27 - 976 * q^33 + 4780 * q^35 - 8 * q^41 - 1308 * q^43 - 20872 * q^51 + 968 * q^57 + 17680 * q^65 - 89252 * q^67 - 25184 * q^73 + 127740 * q^75 - 67792 * q^81 + 126444 * q^83 - 329432 * q^91 + 212576 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−4.45554	+	4.45554i	−0.285823	+	0.285823i	−0.835426	−	0.549603i	$-0.814779\pi$
$3$	−4.45554	+	4.45554i	−0.285823	+	0.285823i	0.549603	+	0.835426i	$0.314779\pi$
$4$		0			0
$5$	−49.9881	−	25.0237i	−0.894215	−	0.447638i
$5$	−49.9881	−	25.0237i	−0.894215	−	0.447638i
$6$		0			0
$7$	−169.279	+	169.279i	−1.30574	+	1.30574i	−0.381287	+	0.924457i	$0.624519\pi$
$7$	−169.279	+	169.279i	−1.30574	+	1.30574i	−0.924457	+	0.381287i	$0.875481\pi$
$8$		0			0
$9$			203.296i			0.836610i
$10$		0			0
$11$	207.026			0.515874			0.257937	−	0.966162i	$-0.416957\pi$
$11$	207.026			0.515874			0.257937	+	0.966162i	$0.416957\pi$
$12$		0			0
$13$	249.136	+	249.136i	0.408864	+	0.408864i	0.881342	−	0.472478i	$-0.156640\pi$
$13$	249.136	+	249.136i	0.408864	+	0.408864i	−0.472478	+	0.881342i	$0.656640\pi$
$14$		0			0
$15$	334.219	−	111.230i	0.383533	−	0.127642i
$16$		0			0
$17$	−424.145	−	424.145i	−0.355952	−	0.355952i	0.506366	−	0.862318i	$-0.330988\pi$
$17$	−424.145	−	424.145i	−0.355952	−	0.355952i	−0.862318	+	0.506366i	$0.830988\pi$
$18$		0			0
$19$		−	2282.02i		−	1.45022i	−0.688631	−	0.725112i	$-0.741788\pi$
$19$		−	2282.02i		−	1.45022i	0.688631	−	0.725112i	$-0.258212\pi$
$20$		0			0
$21$		−	1508.46i		−	0.746424i
$22$		0			0
$23$	351.205	+	351.205i	0.138433	+	0.138433i	0.772928	−	0.634494i	$-0.218792\pi$
$23$	351.205	+	351.205i	0.138433	+	0.138433i	−0.634494	+	0.772928i	$0.718792\pi$
$24$		0			0
$25$	1872.62	+	2501.78i	0.599240	+	0.800569i
$26$		0			0
$27$	−1988.49	−	1988.49i	−0.524946	−	0.524946i
$28$		0			0
$29$	−7256.22			−1.60219			−0.801097	−	0.598534i	$-0.795750\pi$
$29$	−7256.22			−1.60219			−0.801097	+	0.598534i	$0.795750\pi$
$30$		0			0
$31$		−	7244.36i		−	1.35393i	−0.736016	−	0.676964i	$-0.763295\pi$
$31$		−	7244.36i		−	1.35393i	0.736016	−	0.676964i	$-0.236705\pi$
$32$		0			0
$33$	−922.415	+	922.415i	−0.147449	+	0.147449i
$34$		0			0
$35$	12697.9	−	4225.95i	1.75212	−	0.583114i
$36$		0			0
$37$	−266.347	+	266.347i	−0.0319848	+	0.0319848i	−0.722918	−	0.690933i	$-0.757200\pi$
$37$	−266.347	+	266.347i	−0.0319848	+	0.0319848i	0.690933	+	0.722918i	$0.257200\pi$
$38$		0			0
$39$	−2220.08			−0.233726
$40$		0			0
$41$	16812.6			1.56198			0.780990	−	0.624543i	$-0.214715\pi$
$41$	16812.6			1.56198			0.780990	+	0.624543i	$0.214715\pi$
$42$		0			0
$43$	4601.16	−	4601.16i	0.379486	−	0.379486i	−0.491431	−	0.870917i	$-0.663526\pi$
$43$	4601.16	−	4601.16i	0.379486	−	0.379486i	0.870917	+	0.491431i	$0.163526\pi$
$44$		0			0
$45$	5087.23	−	10162.4i	0.374499	−	0.748109i
$46$		0			0
$47$	−5614.39	+	5614.39i	−0.370730	+	0.370730i	−0.867743	−	0.497013i	$-0.834430\pi$
$47$	−5614.39	+	5614.39i	−0.370730	+	0.370730i	0.497013	+	0.867743i	$0.334430\pi$
$48$		0			0
$49$		−	40503.7i		−	2.40993i
$50$		0			0
$51$	3779.59			0.203479
$52$		0			0
$53$	−937.132	−	937.132i	−0.0458259	−	0.0458259i	0.683822	−	0.729648i	$-0.260316\pi$
$53$	−937.132	−	937.132i	−0.0458259	−	0.0458259i	−0.729648	+	0.683822i	$0.760316\pi$
$54$		0			0
$55$	−10348.9	−	5180.57i	−0.461302	−	0.230925i
$56$		0			0
$57$	10167.6	+	10167.6i	0.414508	+	0.414508i
$58$		0			0
$59$			16983.7i			0.635189i	0.948227	+	0.317595i	$0.102875\pi$
$59$			16983.7i			0.635189i	−0.948227	+	0.317595i	$0.897125\pi$
$60$		0			0
$61$		−	27237.2i		−	0.937212i	−0.883407	−	0.468606i	$-0.844756\pi$
$61$		−	27237.2i		−	0.937212i	0.883407	−	0.468606i	$-0.155244\pi$
$62$		0			0
$63$	−34413.8	−	34413.8i	−1.09240	−	1.09240i
$64$		0			0
$65$	−6219.54	−	18688.2i	−0.182589	−	0.548635i
$66$		0			0
$67$	7571.99	+	7571.99i	0.206074	+	0.206074i	0.802596	−	0.596523i	$-0.203451\pi$
$67$	7571.99	+	7571.99i	0.206074	+	0.206074i	−0.596523	+	0.802596i	$0.703451\pi$
$68$		0			0
$69$	−3129.62			−0.0791350
$70$		0			0
$71$			17125.0i			0.403167i	0.979471	+	0.201583i	$0.0646087\pi$
$71$			17125.0i			0.403167i	−0.979471	+	0.201583i	$0.935391\pi$
$72$		0			0
$73$	15977.8	−	15977.8i	0.350922	−	0.350922i	−0.509530	−	0.860453i	$-0.670181\pi$
$73$	15977.8	−	15977.8i	0.350922	−	0.350922i	0.860453	+	0.509530i	$0.170181\pi$
$74$		0			0
$75$	−19490.4	−	2803.23i	−0.400098	−	0.0575447i
$76$		0			0
$77$	−35045.2	+	35045.2i	−0.673599	+	0.673599i
$78$		0			0
$79$	72486.1			1.30673			0.653367	−	0.757041i	$-0.273356\pi$
$79$	72486.1			1.30673			0.653367	+	0.757041i	$0.273356\pi$
$80$		0			0
$81$	−31681.3			−0.536526
$82$		0			0
$83$	58657.5	−	58657.5i	0.934606	−	0.934606i	−0.0633833	−	0.997989i	$-0.520189\pi$
$83$	58657.5	−	58657.5i	0.934606	−	0.934606i	0.997989	+	0.0633833i	$0.0201891\pi$
$84$		0			0
$85$	10588.5	+	31815.9i	0.158960	+	0.477636i
$86$		0			0
$87$	32330.4	−	32330.4i	0.457944	−	0.457944i
$88$		0			0
$89$			34335.8i			0.459486i	0.973251	+	0.229743i	$0.0737886\pi$
$89$			34335.8i			0.459486i	−0.973251	+	0.229743i	$0.926211\pi$
$90$		0			0
$91$	−84347.1			−1.06774
$92$		0			0
$93$	32277.6	+	32277.6i	0.386984	+	0.386984i
$94$		0			0
$95$	−57104.6	+	114074.i	−0.649176	+	1.29681i
$96$		0			0
$97$	62650.0	+	62650.0i	0.676070	+	0.676070i	0.959109	−	0.283039i	$-0.0913425\pi$
$97$	62650.0	+	62650.0i	0.676070	+	0.676070i	−0.283039	+	0.959109i	$0.591342\pi$
$98$		0			0
$99$			42087.6i			0.431585i
$100$		0			0
$101$		−	79446.8i		−	0.774948i	−0.921881	−	0.387474i	$-0.873348\pi$
$101$		−	79446.8i		−	0.774948i	0.921881	−	0.387474i	$-0.126652\pi$
$102$		0			0
$103$	−15635.6	−	15635.6i	−0.145219	−	0.145219i	0.630760	−	0.775978i	$-0.282743\pi$
$103$	−15635.6	−	15635.6i	−0.145219	−	0.145219i	−0.775978	+	0.630760i	$0.782743\pi$
$104$		0			0
$105$	−37747.3	+	75405.1i	−0.334128	+	0.667463i
$106$		0			0
$107$	18399.8	+	18399.8i	0.155365	+	0.155365i	0.780509	−	0.625144i	$-0.214960\pi$
$107$	18399.8	+	18399.8i	0.155365	+	0.155365i	−0.625144	+	0.780509i	$0.714960\pi$
$108$		0			0
$109$	30952.5			0.249534			0.124767	−	0.992186i	$-0.460182\pi$
$109$	30952.5			0.249534			0.124767	+	0.992186i	$0.460182\pi$
$110$		0			0
$111$		−	2373.45i		−	0.0182840i
$112$		0			0
$113$	−125022.	+	125022.i	−0.921068	+	0.921068i	−0.997105	−	0.0760370i	$-0.975773\pi$
$113$	−125022.	+	125022.i	−0.921068	+	0.921068i	0.0760370	+	0.997105i	$0.475773\pi$
$114$		0			0
$115$	−8767.62	−	26344.5i	−0.0618211	−	0.185757i
$116$		0			0
$117$	−50648.5	+	50648.5i	−0.342060	+	0.342060i
$118$		0			0
$119$	143598.			0.929565
$120$		0			0
$121$	−118191.			−0.733874
$122$		0			0
$123$	−74909.4	+	74909.4i	−0.446451	+	0.446451i
$124$		0			0
$125$	−31005.1	−	171919.i	−0.177484	−	0.984124i
$126$		0			0
$127$	−5560.02	+	5560.02i	−0.0305892	+	0.0305892i	−0.722236	−	0.691647i	$-0.756886\pi$
$127$	−5560.02	+	5560.02i	−0.0305892	+	0.0305892i	0.691647	+	0.722236i	$0.256886\pi$
$128$		0			0
$129$			41001.3i			0.216932i
$130$		0			0
$131$	−207693.			−1.05741			−0.528705	−	0.848805i	$-0.677322\pi$
$131$	−207693.			−1.05741			−0.528705	+	0.848805i	$0.677322\pi$
$132$		0			0
$133$	386298.	+	386298.i	1.89362	+	1.89362i
$134$		0			0
$135$	49641.5	+	149161.i	0.234429	+	0.704400i
$136$		0			0
$137$	−254454.	−	254454.i	−1.15827	−	1.15827i	−0.984848	−	0.173418i	$-0.944519\pi$
$137$	−254454.	−	254454.i	−1.15827	−	1.15827i	−0.173418	−	0.984848i	$-0.555481\pi$
$138$		0			0
$139$		−	145526.i		−	0.638856i	−0.947610	−	0.319428i	$-0.896509\pi$
$139$		−	145526.i		−	0.638856i	0.947610	−	0.319428i	$-0.103491\pi$
$140$		0			0
$141$		−	50030.3i		−	0.211927i
$142$		0			0
$143$	51577.8	+	51577.8i	0.210922	+	0.210922i
$144$		0			0
$145$	362725.	+	181578.i	1.43271	+	0.717203i
$146$		0			0
$147$	180466.	+	180466.i	0.688815	+	0.688815i
$148$		0			0
$149$	−209820.			−0.774252			−0.387126	−	0.922027i	$-0.626532\pi$
$149$	−209820.			−0.774252			−0.387126	+	0.922027i	$0.626532\pi$
$150$		0			0
$151$		−	91400.1i		−	0.326215i	−0.986608	−	0.163108i	$-0.947848\pi$
$151$		−	91400.1i		−	0.326215i	0.986608	−	0.163108i	$-0.0521518\pi$
$152$		0			0
$153$	86227.0	−	86227.0i	0.297793	−	0.297793i
$154$		0			0
$155$	−181281.	+	362132.i	−0.606070	+	1.21070i
$156$		0			0
$157$	−239586.	+	239586.i	−0.775734	+	0.775734i	−0.979102	−	0.203368i	$-0.934811\pi$
$157$	−239586.	+	239586.i	−0.775734	+	0.775734i	0.203368	+	0.979102i	$0.434811\pi$
$158$		0			0
$159$	8350.87			0.0261962
$160$		0			0
$161$	−118903.			−0.361517
$162$		0			0
$163$	−235878.	+	235878.i	−0.695375	+	0.695375i	−0.963409	−	0.268034i	$-0.913626\pi$
$163$	−235878.	+	235878.i	−0.695375	+	0.695375i	0.268034	+	0.963409i	$0.413626\pi$
$164$		0			0
$165$	69192.0	−	23027.5i	0.197855	−	0.0658472i
$166$		0			0
$167$	−28120.6	+	28120.6i	−0.0780249	+	0.0780249i	−0.745042	−	0.667017i	$-0.767571\pi$
$167$	−28120.6	+	28120.6i	−0.0780249	+	0.0780249i	0.667017	+	0.745042i	$0.267571\pi$
$168$		0			0
$169$		−	247155.i		−	0.665660i
$170$		0			0
$171$	463926.			1.21327
$172$		0			0
$173$	−65641.2	−	65641.2i	−0.166748	−	0.166748i	0.618800	−	0.785548i	$-0.287619\pi$
$173$	−65641.2	−	65641.2i	−0.166748	−	0.166748i	−0.785548	+	0.618800i	$0.787619\pi$
$174$		0			0
$175$	−740495.	−	106503.i	−1.82779	−	0.262885i
$176$		0			0
$177$	−75671.8	−	75671.8i	−0.181552	−	0.181552i
$178$		0			0
$179$		−	377529.i		−	0.880679i	−0.897831	−	0.440340i	$-0.854858\pi$
$179$		−	377529.i		−	0.880679i	0.897831	−	0.440340i	$-0.145142\pi$
$180$		0			0
$181$		−	523723.i		−	1.18824i	−0.804376	−	0.594121i	$-0.797500\pi$
$181$		−	523723.i		−	1.18824i	0.804376	−	0.594121i	$-0.202500\pi$
$182$		0			0
$183$	121357.	+	121357.i	0.267877	+	0.267877i
$184$		0			0
$185$	19979.2	−	6649.20i	0.0429190	−	0.0142837i
$186$		0			0
$187$	−87809.1	−	87809.1i	−0.183626	−	0.183626i
$188$		0			0
$189$	673220.			1.37089
$190$		0			0
$191$		−	601520.i		−	1.19307i	−0.802586	−	0.596536i	$-0.796543\pi$
$191$		−	601520.i		−	1.19307i	0.802586	−	0.596536i	$-0.203457\pi$
$192$		0			0
$193$	423362.	−	423362.i	0.818123	−	0.818123i	−0.167713	−	0.985836i	$-0.553638\pi$
$193$	423362.	−	423362.i	0.818123	−	0.818123i	0.985836	+	0.167713i	$0.0536381\pi$
$194$		0			0
$195$	110977.	+	55554.6i	0.209001	+	0.104625i
$196$		0			0
$197$	164947.	−	164947.i	0.302815	−	0.302815i	−0.539299	−	0.842114i	$-0.681311\pi$
$197$	164947.	−	164947.i	0.302815	−	0.302815i	0.842114	+	0.539299i	$0.181311\pi$
$198$		0			0
$199$	609467.			1.09098			0.545491	−	0.838117i	$-0.316343\pi$
$199$	609467.			1.09098			0.545491	+	0.838117i	$0.316343\pi$
$200$		0			0
$201$	−67474.7			−0.117801
$202$		0			0
$203$	1.22832e6	−	1.22832e6i	2.09205	−	2.09205i
$204$		0			0
$205$	−840431.	−	420715.i	−1.39675	−	0.699202i
$206$		0			0
$207$	−71398.7	+	71398.7i	−0.115815	+	0.115815i
$208$		0			0
$209$		−	472437.i		−	0.748133i
$210$		0			0
$211$	−582093.			−0.900090			−0.450045	−	0.893006i	$-0.648592\pi$
$211$	−582093.			−0.900090			−0.450045	+	0.893006i	$0.648592\pi$
$212$		0			0
$213$	−76301.2	−	76301.2i	−0.115234	−	0.115234i
$214$		0			0
$215$	−345141.	+	114865.i	−0.509215	+	0.169470i
$216$		0			0
$217$	1.22632e6	+	1.22632e6i	1.76788	+	1.76788i
$218$		0			0
$219$			142380.i			0.200604i
$220$		0			0
$221$		−	211340.i		−	0.291072i
$222$		0			0
$223$	−27105.9	−	27105.9i	−0.0365007	−	0.0365007i	0.688621	−	0.725122i	$-0.258216\pi$
$223$	−27105.9	−	27105.9i	−0.0365007	−	0.0365007i	−0.725122	+	0.688621i	$0.758216\pi$
$224$		0			0
$225$	−508602.	+	380698.i	−0.669764	+	0.501330i
$226$		0			0
$227$	23392.5	+	23392.5i	0.0301309	+	0.0301309i	0.722012	−	0.691881i	$-0.243218\pi$
$227$	23392.5	+	23392.5i	0.0301309	+	0.0301309i	−0.691881	+	0.722012i	$0.743218\pi$
$228$		0			0
$229$	−637450.			−0.803262			−0.401631	−	0.915801i	$-0.631557\pi$
$229$	−637450.			−0.803262			−0.401631	+	0.915801i	$0.631557\pi$
$230$		0			0
$231$		−	312291.i		−	0.385061i
$232$		0			0
$233$	401694.	−	401694.i	0.484737	−	0.484737i	−0.421904	−	0.906641i	$-0.638638\pi$
$233$	401694.	−	401694.i	0.484737	−	0.484737i	0.906641	+	0.421904i	$0.138638\pi$
$234$		0			0
$235$	421146.	−	140160.i	0.497465	−	0.165559i
$236$		0			0
$237$	−322965.	+	322965.i	−0.373495	+	0.373495i
$238$		0			0
$239$	−797896.			−0.903548			−0.451774	−	0.892132i	$-0.649209\pi$
$239$	−797896.			−0.903548			−0.451774	+	0.892132i	$0.649209\pi$
$240$		0			0
$241$	−313970.			−0.348214			−0.174107	−	0.984727i	$-0.555704\pi$
$241$	−313970.			−0.348214			−0.174107	+	0.984727i	$0.555704\pi$
$242$		0			0
$243$	624361.	−	624361.i	0.678298	−	0.678298i
$244$		0			0
$245$	−1.01356e6	+	2.02471e6i	−1.07878	+	2.15500i
$246$		0			0
$247$	568534.	−	568534.i	0.592944	−	0.592944i
$248$		0			0
$249$			522703.i			0.534264i
$250$		0			0
$251$	−972796.			−0.974624			−0.487312	−	0.873228i	$-0.662023\pi$
$251$	−972796.			−0.974624			−0.487312	+	0.873228i	$0.662023\pi$
$252$		0			0
$253$	72708.6	+	72708.6i	0.0714142	+	0.0714142i
$254$		0			0
$255$	−188935.	−	94579.5i	−0.181954	−	0.0910849i
$256$		0			0
$257$	−736633.	−	736633.i	−0.695694	−	0.695694i	0.267785	−	0.963479i	$-0.413708\pi$
$257$	−736633.	−	736633.i	−0.695694	−	0.695694i	−0.963479	+	0.267785i	$0.913708\pi$
$258$		0			0
$259$		−	90174.1i		−	0.0835280i
$260$		0			0
$261$		−	1.47516e6i		−	1.34041i
$262$		0			0
$263$	1.10841e6	+	1.10841e6i	0.988125	+	0.988125i	0.999930	−	0.0118057i	$-0.00375796\pi$
$263$	1.10841e6	+	1.10841e6i	0.988125	+	0.988125i	−0.0118057	+	0.999930i	$0.503758\pi$
$264$		0			0
$265$	23394.9	+	70296.0i	0.0204648	+	0.0614916i
$266$		0			0
$267$	−152985.	−	152985.i	−0.131332	−	0.131332i
$268$		0			0
$269$	2.08719e6			1.75866			0.879328	−	0.476216i	$-0.157992\pi$
$269$	2.08719e6			1.75866			0.879328	+	0.476216i	$0.157992\pi$
$270$		0			0
$271$		−	869347.i		−	0.719068i	−0.933132	−	0.359534i	$-0.882936\pi$
$271$		−	869347.i		−	0.719068i	0.933132	−	0.359534i	$-0.117064\pi$
$272$		0			0
$273$	375812.	−	375812.i	0.305186	−	0.305186i
$274$		0			0
$275$	387682.	+	517934.i	0.309132	+	0.412993i
$276$		0			0
$277$	1.39022e6	−	1.39022e6i	1.08864	−	1.08864i	0.0929676	−	0.995669i	$-0.470365\pi$
$277$	1.39022e6	−	1.39022e6i	1.08864	−	1.08864i	0.995669	−	0.0929676i	$-0.0296353\pi$
$278$		0			0
$279$	1.47275e6			1.13271
$280$		0			0
$281$	−620023.			−0.468427			−0.234214	−	0.972185i	$-0.575252\pi$
$281$	−620023.			−0.468427			−0.234214	+	0.972185i	$0.575252\pi$
$282$		0			0
$283$	−1.76320e6	+	1.76320e6i	−1.30869	+	1.30869i	−0.386327	+	0.922362i	$0.626256\pi$
$283$	−1.76320e6	+	1.76320e6i	−1.30869	+	1.30869i	−0.922362	+	0.386327i	$0.873744\pi$
$284$		0			0
$285$	−253829.	−	762693.i	−0.185109	−	0.556209i
$286$		0			0
$287$	−2.84602e6	+	2.84602e6i	−2.03955	+	2.03955i
$288$		0			0
$289$		−	1.06006e6i		−	0.746596i
$290$		0			0
$291$	−558280.			−0.386473
$292$		0			0
$293$	729494.	+	729494.i	0.496424	+	0.496424i	0.910323	−	0.413899i	$-0.135833\pi$
$293$	729494.	+	729494.i	0.496424	+	0.496424i	−0.413899	+	0.910323i	$0.635833\pi$
$294$		0			0
$295$	424997.	−	848985.i	0.284335	−	0.567996i
$296$		0			0
$297$	−411670.	−	411670.i	−0.270806	−	0.270806i
$298$		0			0
$299$			174996.i			0.113201i
$300$		0			0
$301$			1.55776e6i			0.991023i
$302$		0			0
$303$	353979.	+	353979.i	0.221498	+	0.221498i
$304$		0			0
$305$	−681577.	+	1.36154e6i	−0.419532	+	0.838069i
$306$		0			0
$307$	907649.	+	907649.i	0.549632	+	0.549632i	0.926334	−	0.376702i	$-0.122942\pi$
$307$	907649.	+	907649.i	0.549632	+	0.549632i	−0.376702	+	0.926334i	$0.622942\pi$
$308$		0			0
$309$	139331.			0.0830138
$310$		0			0
$311$		−	1.31610e6i		−	0.771594i	−0.922584	−	0.385797i	$-0.873927\pi$
$311$		−	1.31610e6i		−	0.771594i	0.922584	−	0.385797i	$-0.126073\pi$
$312$		0			0
$313$	−896253.	+	896253.i	−0.517094	+	0.517094i	−0.916691	−	0.399597i	$-0.869150\pi$
$313$	−896253.	+	896253.i	−0.517094	+	0.517094i	0.399597	+	0.916691i	$0.369150\pi$
$314$		0			0
$315$	859119.	+	2.58144e6i	0.487839	+	1.46584i
$316$		0			0
$317$	−1.81983e6	+	1.81983e6i	−1.01715	+	1.01715i	−0.0172954	+	0.999850i	$0.505506\pi$
$317$	−1.81983e6	+	1.81983e6i	−1.01715	+	1.01715i	−0.999850	+	0.0172954i	$0.994494\pi$
$318$		0			0
$319$	−1.50223e6			−0.826530
$320$		0			0
$321$	−163963.			−0.0888141
$322$		0			0
$323$	−967906.	+	967906.i	−0.516210	+	0.516210i
$324$		0			0
$325$	−156745.	+	1.08982e6i	−0.0823164	+	0.572332i
$326$		0			0
$327$	−137910.	+	137910.i	−0.0713225	+	0.0713225i
$328$		0			0
$329$		−	1.90080e6i		−	0.968157i
$330$		0			0
$331$	−979058.			−0.491178			−0.245589	−	0.969374i	$-0.578981\pi$
$331$	−979058.			−0.491178			−0.245589	+	0.969374i	$0.578981\pi$
$332$		0			0
$333$	−54147.4	−	54147.4i	−0.0267588	−	0.0267588i
$334$		0			0
$335$	−189030.	−	567989.i	−0.0920277	−	0.276521i
$336$		0			0
$337$	2.59947e6	+	2.59947e6i	1.24684	+	1.24684i	0.957108	+	0.289731i	$0.0935659\pi$
$337$	2.59947e6	+	2.59947e6i	1.24684	+	1.24684i	0.289731	+	0.957108i	$0.406434\pi$
$338$		0			0
$339$		−	1.11409e6i		−	0.526525i
$340$		0			0
$341$		−	1.49977e6i		−	0.698457i
$342$		0			0
$343$	4.01136e6	+	4.01136e6i	1.84101	+	1.84101i
$344$		0			0
$345$	156444.	+	78314.8i	0.0707637	+	0.0354239i
$346$		0			0
$347$	−1.85742e6	−	1.85742e6i	−0.828107	−	0.828107i	0.159148	−	0.987255i	$-0.449125\pi$
$347$	−1.85742e6	−	1.85742e6i	−0.828107	−	0.828107i	−0.987255	+	0.159148i	$0.949125\pi$
$348$		0			0
$349$	3.47861e6			1.52877			0.764385	−	0.644760i	$-0.223043\pi$
$349$	3.47861e6			1.52877			0.764385	+	0.644760i	$0.223043\pi$
$350$		0			0
$351$		−	990812.i		−	0.429263i
$352$		0			0
$353$	−846494.	+	846494.i	−0.361566	+	0.361566i	−0.864389	−	0.502823i	$-0.832295\pi$
$353$	−846494.	+	846494.i	−0.361566	+	0.361566i	0.502823	+	0.864389i	$0.332295\pi$
$354$		0			0
$355$	428532.	−	856047.i	0.180473	−	0.360518i
$356$		0			0
$357$	−639805.	+	639805.i	−0.265691	+	0.265691i
$358$		0			0
$359$	2.26831e6			0.928892			0.464446	−	0.885601i	$-0.346253\pi$
$359$	2.26831e6			0.928892			0.464446	+	0.885601i	$0.346253\pi$
$360$		0			0
$361$	−2.73151e6			−1.10315
$362$		0			0
$363$	526606.	−	526606.i	0.209758	−	0.209758i
$364$		0			0
$365$	−1.19853e6	+	398877.i	−0.470886	+	0.156714i
$366$		0			0
$367$	936339.	−	936339.i	0.362884	−	0.362884i	−0.501990	−	0.864874i	$-0.667398\pi$
$367$	936339.	−	936339.i	0.362884	−	0.362884i	0.864874	+	0.501990i	$0.167398\pi$
$368$		0			0
$369$			3.41794e6i			1.30677i
$370$		0			0
$371$	317273.			0.119674
$372$		0			0
$373$	−529380.	−	529380.i	−0.197013	−	0.197013i	0.601705	−	0.798718i	$-0.294488\pi$
$373$	−529380.	−	529380.i	−0.197013	−	0.197013i	−0.798718	+	0.601705i	$0.794488\pi$
$374$		0			0
$375$	904139.	+	627850.i	0.332015	+	0.230557i
$376$		0			0
$377$	−1.80779e6	−	1.80779e6i	−0.655080	−	0.655080i
$378$		0			0
$379$		−	1.76855e6i		−	0.632439i	−0.948686	−	0.316220i	$-0.897586\pi$
$379$		−	1.76855e6i		−	0.632439i	0.948686	−	0.316220i	$-0.102414\pi$
$380$		0			0
$381$		−	49545.9i		−	0.0174862i
$382$		0			0
$383$	−2.62315e6	−	2.62315e6i	−0.913746	−	0.913746i	0.0828182	−	0.996565i	$-0.473608\pi$
$383$	−2.62315e6	−	2.62315e6i	−0.913746	−	0.913746i	−0.996565	+	0.0828182i	$0.973608\pi$
$384$		0			0
$385$	2.62880e6	−	874881.i	0.903871	−	0.300814i
$386$		0			0
$387$	935398.	+	935398.i	0.317482	+	0.317482i
$388$		0			0
$389$	−2.62506e6			−0.879561			−0.439780	−	0.898105i	$-0.644944\pi$
$389$	−2.62506e6			−0.879561			−0.439780	+	0.898105i	$0.644944\pi$
$390$		0			0
$391$		−	297923.i		−	0.0985514i
$392$		0			0
$393$	925386.	−	925386.i	0.302233	−	0.302233i
$394$		0			0
$395$	−3.62344e6	−	1.81387e6i	−1.16850	−	0.584944i
$396$		0			0
$397$	1.09332e6	−	1.09332e6i	0.348153	−	0.348153i	−0.511268	−	0.859421i	$-0.670824\pi$
$397$	1.09332e6	−	1.09332e6i	0.348153	−	0.348153i	0.859421	+	0.511268i	$0.170824\pi$
$398$		0			0
$399$	−3.44233e6			−1.08248
$400$		0			0
$401$	−3.31952e6			−1.03089			−0.515447	−	0.856922i	$-0.672374\pi$
$401$	−3.31952e6			−1.03089			−0.515447	+	0.856922i	$0.672374\pi$
$402$		0			0
$403$	1.80483e6	−	1.80483e6i	0.553573	−	0.553573i
$404$		0			0
$405$	1.58369e6	+	792786.i	0.479770	+	0.240170i
$406$		0			0
$407$	−55140.9	+	55140.9i	−0.0165001	+	0.0165001i
$408$		0			0
$409$			3.60316e6i			1.06506i	0.846410	+	0.532531i	$0.178759\pi$
$409$			3.60316e6i			1.06506i	−0.846410	+	0.532531i	$0.821241\pi$
$410$		0			0
$411$	2.26747e6			0.662119
$412$		0			0
$413$	−2.87499e6	−	2.87499e6i	−0.829395	−	0.829395i
$414$		0			0
$415$	−4.40001e6	+	1.46435e6i	−1.25410	+	0.417373i
$416$		0			0
$417$	648397.	+	648397.i	0.182600	+	0.182600i
$418$		0			0
$419$		−	1.60065e6i		−	0.445410i	−0.974886	−	0.222705i	$-0.928511\pi$
$419$		−	1.60065e6i		−	0.445410i	0.974886	−	0.222705i	$-0.0714887\pi$
$420$		0			0
$421$		−	387801.i		−	0.106636i	−0.998578	−	0.0533180i	$-0.983020\pi$
$421$		−	387801.i		−	0.106636i	0.998578	−	0.0533180i	$-0.0169797\pi$
$422$		0			0
$423$	−1.14138e6	−	1.14138e6i	−0.310156	−	0.310156i
$424$		0			0
$425$	266853.	−	1.85538e6i	0.0716637	−	0.498265i
$426$		0			0
$427$	4.61069e6	+	4.61069e6i	1.22376	+	1.22376i
$428$		0			0
$429$	−459614.			−0.120573
$430$		0			0
$431$			2.12752e6i			0.551673i	0.961205	+	0.275836i	$0.0889548\pi$
$431$			2.12752e6i			0.551673i	−0.961205	+	0.275836i	$0.911045\pi$
$432$		0			0
$433$	4.65162e6	−	4.65162e6i	1.19230	−	1.19230i	0.215877	−	0.976420i	$-0.430739\pi$
$433$	4.65162e6	−	4.65162e6i	1.19230	−	1.19230i	0.976420	−	0.215877i	$-0.0692612\pi$
$434$		0			0
$435$	−2.42516e6	+	807108.i	−0.614494	+	0.204507i
$436$		0			0
$437$	801456.	−	801456.i	0.200760	−	0.200760i
$438$		0			0
$439$	4.59779e6			1.13864			0.569321	−	0.822115i	$-0.307206\pi$
$439$	4.59779e6			1.13864			0.569321	+	0.822115i	$0.307206\pi$
$440$		0			0
$441$	8.23426e6			2.01617
$442$		0			0
$443$	1.69307e6	−	1.69307e6i	0.409889	−	0.409889i	−0.471811	−	0.881700i	$-0.656400\pi$
$443$	1.69307e6	−	1.69307e6i	0.409889	−	0.409889i	0.881700	+	0.471811i	$0.156400\pi$
$444$		0			0
$445$	859211.	−	1.71638e6i	0.205684	−	0.410879i
$446$		0			0
$447$	934865.	−	934865.i	0.221299	−	0.221299i
$448$		0			0
$449$		−	3.17626e6i		−	0.743533i	−0.928326	−	0.371766i	$-0.878752\pi$
$449$		−	3.17626e6i		−	0.743533i	0.928326	−	0.371766i	$-0.121248\pi$
$450$		0			0
$451$	3.48065e6			0.805785
$452$		0			0
$453$	407237.	+	407237.i	0.0932399	+	0.0932399i
$454$		0			0
$455$	4.21635e6	+	2.11068e6i	0.954792	+	0.477963i
$456$		0			0
$457$	−1.52765e6	−	1.52765e6i	−0.342163	−	0.342163i	0.515017	−	0.857180i	$-0.327786\pi$
$457$	−1.52765e6	−	1.52765e6i	−0.342163	−	0.342163i	−0.857180	+	0.515017i	$0.827786\pi$
$458$		0			0
$459$			1.68682e6i			0.373711i
$460$		0			0
$461$			2.42900e6i			0.532323i	0.963928	+	0.266161i	$0.0857554\pi$
$461$			2.42900e6i			0.532323i	−0.963928	+	0.266161i	$0.914245\pi$
$462$		0			0
$463$	−5.98030e6	−	5.98030e6i	−1.29649	−	1.29649i	−0.930693	−	0.365801i	$-0.880795\pi$
$463$	−5.98030e6	−	5.98030e6i	−1.29649	−	1.29649i	−0.365801	−	0.930693i	$-0.619205\pi$
$464$		0			0
$465$	−805790.	−	2.42120e6i	−0.172818	−	0.519276i
$466$		0			0
$467$	−3.69887e6	−	3.69887e6i	−0.784833	−	0.784833i	0.195809	−	0.980642i	$-0.437267\pi$
$467$	−3.69887e6	−	3.69887e6i	−0.784833	−	0.784833i	−0.980642	+	0.195809i	$0.937267\pi$
$468$		0			0
$469$	−2.56356e6			−0.538159
$470$		0			0
$471$		−	2.13498e6i		−	0.443446i
$472$		0			0
$473$	952560.	−	952560.i	0.195767	−	0.195767i
$474$		0			0
$475$	5.70911e6	−	4.27336e6i	1.16100	−	0.869032i
$476$		0			0
$477$	190515.	−	190515.i	0.0383384	−	0.0383384i
$478$		0			0
$479$	−5.88773e6			−1.17249			−0.586245	−	0.810134i	$-0.699394\pi$
$479$	−5.88773e6			−1.17249			−0.586245	+	0.810134i	$0.699394\pi$
$480$		0			0
$481$	−132714.			−0.0261549
$482$		0			0
$483$	529779.	−	529779.i	0.103330	−	0.103330i
$484$		0			0
$485$	−1.56402e6	−	4.69949e6i	−0.301917	−	0.907186i
$486$		0			0
$487$	4.54087e6	−	4.54087e6i	0.867594	−	0.867594i	−0.124612	−	0.992206i	$-0.539768\pi$
$487$	4.54087e6	−	4.54087e6i	0.867594	−	0.867594i	0.992206	+	0.124612i	$0.0397685\pi$
$488$		0			0
$489$		−	2.10193e6i		−	0.397509i
$490$		0			0
$491$	−2.71881e6			−0.508951			−0.254475	−	0.967079i	$-0.581903\pi$
$491$	−2.71881e6			−0.508951			−0.254475	+	0.967079i	$0.581903\pi$
$492$		0			0
$493$	3.07768e6	+	3.07768e6i	0.570305	+	0.570305i
$494$		0			0
$495$	1.05319e6	−	2.10388e6i	0.193194	−	0.385930i
$496$		0			0
$497$	−2.89890e6	−	2.89890e6i	−0.526433	−	0.526433i
$498$		0			0
$499$			1.02884e7i			1.84967i	0.380366	+	0.924836i	$0.375798\pi$
$499$			1.02884e7i			1.84967i	−0.380366	+	0.924836i	$0.624202\pi$
$500$		0			0
$501$		−	250585.i		−	0.0446027i
$502$		0			0
$503$	−2.13863e6	−	2.13863e6i	−0.376891	−	0.376891i	0.493088	−	0.869979i	$-0.335868\pi$
$503$	−2.13863e6	−	2.13863e6i	−0.376891	−	0.376891i	−0.869979	+	0.493088i	$0.835868\pi$
$504$		0			0
$505$	−1.98805e6	+	3.97139e6i	−0.346897	+	0.692970i
$506$		0			0
$507$	1.10121e6	+	1.10121e6i	0.190261	+	0.190261i
$508$		0			0
$509$	−7.79654e6			−1.33385			−0.666926	−	0.745124i	$-0.732390\pi$
$509$	−7.79654e6			−1.33385			−0.666926	+	0.745124i	$0.732390\pi$
$510$		0			0
$511$			5.40943e6i			0.916430i
$512$		0			0
$513$	−4.53778e6	+	4.53778e6i	−0.761289	+	0.761289i
$514$		0			0
$515$	390334.	+	1.17286e6i	0.0648513	+	0.194862i
$516$		0			0
$517$	−1.16233e6	+	1.16233e6i	−0.191250	+	0.191250i
$518$		0			0
$519$	584934.			0.0953210
$520$		0			0
$521$	9.36971e6			1.51228			0.756139	−	0.654411i	$-0.227083\pi$
$521$	9.36971e6			1.51228			0.756139	+	0.654411i	$0.227083\pi$
$522$		0			0
$523$	−5.04052e6	+	5.04052e6i	−0.805789	+	0.805789i	−0.983994	−	0.178204i	$-0.942971\pi$
$523$	−5.04052e6	+	5.04052e6i	−0.805789	+	0.805789i	0.178204	+	0.983994i	$0.442971\pi$
$524$		0			0
$525$	3.77383e6	−	2.82478e6i	0.597564	−	0.447287i
$526$		0			0
$527$	−3.07266e6	+	3.07266e6i	−0.481934	+	0.481934i
$528$		0			0
$529$		−	6.18965e6i		−	0.961672i
$530$		0			0
$531$	−3.45273e6			−0.531406
$532$		0			0
$533$	4.18864e6	+	4.18864e6i	0.638638	+	0.638638i
$534$		0			0
$535$	−459340.	−	1.38021e6i	−0.0693825	−	0.208478i
$536$		0			0
$537$	1.68210e6	+	1.68210e6i	0.251719	+	0.251719i
$538$		0			0
$539$		−	8.38534e6i		−	1.24322i
$540$		0			0
$541$		−	5.33336e6i		−	0.783443i	−0.920084	−	0.391721i	$-0.871880\pi$
$541$		−	5.33336e6i		−	0.783443i	0.920084	−	0.391721i	$-0.128120\pi$
$542$		0			0
$543$	2.33347e6	+	2.33347e6i	0.339627	+	0.339627i
$544$		0			0
$545$	−1.54726e6	−	774546.i	−0.223137	−	0.111701i
$546$		0			0
$547$	−4.38265e6	−	4.38265e6i	−0.626280	−	0.626280i	0.320850	−	0.947130i	$-0.396031\pi$
$547$	−4.38265e6	−	4.38265e6i	−0.626280	−	0.626280i	−0.947130	+	0.320850i	$0.896031\pi$
$548$		0			0
$549$	5.53722e6			0.784081
$550$		0			0
$551$			1.65588e7i			2.32354i
$552$		0			0
$553$	−1.22704e7	+	1.22704e7i	−1.70626	+	1.70626i
$554$		0			0
$555$	−59392.5	+	118644.i	−0.00818463	+	0.0163498i
$556$		0			0
$557$	−803306.	+	803306.i	−0.109709	+	0.109709i	−0.759830	−	0.650121i	$-0.774718\pi$
$557$	−803306.	+	803306.i	−0.109709	+	0.109709i	0.650121	+	0.759830i	$0.274718\pi$
$558$		0			0
$559$	2.29263e6			0.310316
$560$		0			0
$561$	782474.			0.104969
$562$		0			0
$563$	−804076.	+	804076.i	−0.106912	+	0.106912i	−0.758539	−	0.651627i	$-0.774087\pi$
$563$	−804076.	+	804076.i	−0.106912	+	0.106912i	0.651627	+	0.758539i	$0.274087\pi$
$564$		0			0
$565$	9.37816e6	−	3.12111e6i	1.23594	−	0.411327i
$566$		0			0
$567$	5.36299e6	−	5.36299e6i	0.700566	−	0.700566i
$568$		0			0
$569$			3.92427e6i			0.508134i	0.967187	+	0.254067i	$0.0817683\pi$
$569$			3.92427e6i			0.508134i	−0.967187	+	0.254067i	$0.918232\pi$
$570$		0			0
$571$	1.25466e7			1.61040			0.805201	−	0.593002i	$-0.202057\pi$
$571$	1.25466e7			1.61040			0.805201	+	0.593002i	$0.202057\pi$
$572$		0			0
$573$	2.68010e6	+	2.68010e6i	0.341008	+	0.341008i
$574$		0			0
$575$	−220962.	+	1.53631e6i	−0.0278707	+	0.193780i
$576$		0			0
$577$	−1.21454e6	−	1.21454e6i	−0.151870	−	0.151870i	0.627083	−	0.778953i	$-0.284249\pi$
$577$	−1.21454e6	−	1.21454e6i	−0.151870	−	0.151870i	−0.778953	+	0.627083i	$0.784249\pi$
$578$		0			0
$579$			3.77262e6i			0.467677i
$580$		0			0
$581$			1.98590e7i			2.44071i
$582$		0			0
$583$	−194011.	−	194011.i	−0.0236404	−	0.0236404i
$584$		0			0
$585$	3.79924e6	−	1.26441e6i	0.458994	−	0.152756i
$586$		0			0
$587$	−6.81043e6	−	6.81043e6i	−0.815791	−	0.815791i	0.169704	−	0.985495i	$-0.445719\pi$
$587$	−6.81043e6	−	6.81043e6i	−0.815791	−	0.815791i	−0.985495	+	0.169704i	$0.945719\pi$
$588$		0			0
$589$	−1.65318e7			−1.96350
$590$		0			0
$591$			1.46985e6i			0.173103i
$592$		0			0
$593$	−6.21457e6	+	6.21457e6i	−0.725729	+	0.725729i	−0.969766	−	0.244037i	$-0.921528\pi$
$593$	−6.21457e6	+	6.21457e6i	−0.725729	+	0.725729i	0.244037	+	0.969766i	$0.421528\pi$
$594$		0			0
$595$	−7.17817e6	−	3.59335e6i	−0.831230	−	0.416109i
$596$		0			0
$597$	−2.71551e6	+	2.71551e6i	−0.311828	+	0.311828i
$598$		0			0
$599$	6.64825e6			0.757078			0.378539	−	0.925585i	$-0.376427\pi$
$599$	6.64825e6			0.757078			0.378539	+	0.925585i	$0.376427\pi$
$600$		0			0
$601$	−7.82874e6			−0.884109			−0.442055	−	0.896988i	$-0.645750\pi$
$601$	−7.82874e6			−0.884109			−0.442055	+	0.896988i	$0.645750\pi$
$602$		0			0
$603$	−1.53936e6	+	1.53936e6i	−0.172403	+	0.172403i
$604$		0			0
$605$	5.90815e6	+	2.95758e6i	0.656241	+	0.328510i
$606$		0			0
$607$	−76234.2	+	76234.2i	−0.00839804	+	0.00839804i	−0.711293	−	0.702895i	$-0.751890\pi$
$607$	−76234.2	+	76234.2i	−0.00839804	+	0.00839804i	0.702895	+	0.711293i	$0.251890\pi$
$608$		0			0
$609$			1.09457e7i			1.19592i
$610$		0			0
$611$	−2.79750e6			−0.303156
$612$		0			0
$613$	−9.22892e6	−	9.22892e6i	−0.991973	−	0.991973i	0.00799526	−	0.999968i	$-0.497455\pi$
$613$	−9.22892e6	−	9.22892e6i	−0.991973	−	0.991973i	−0.999968	+	0.00799526i	$0.997455\pi$
$614$		0			0
$615$	5.61909e6	−	1.87007e6i	0.599071	−	0.199374i
$616$		0			0
$617$	−60556.8	−	60556.8i	−0.00640398	−	0.00640398i	0.703898	−	0.710302i	$-0.251441\pi$
$617$	−60556.8	−	60556.8i	−0.00640398	−	0.00640398i	−0.710302	+	0.703898i	$0.751441\pi$
$618$		0			0
$619$			1.44485e7i			1.51564i	0.652466	+	0.757818i	$0.273734\pi$
$619$			1.44485e7i			1.51564i	−0.652466	+	0.757818i	$0.726266\pi$
$620$		0			0
$621$		−	1.39674e6i		−	0.145340i
$622$		0			0
$623$	−5.81233e6	−	5.81233e6i	−0.599971	−	0.599971i
$624$		0			0
$625$	−2.75218e6	+	9.36979e6i	−0.281823	+	0.959466i
$626$		0			0
$627$	2.10497e6	+	2.10497e6i	0.213834	+	0.213834i
$628$		0			0
$629$	225940.			0.0227702
$630$		0			0
$631$			998279.i			0.0998110i	0.998754	+	0.0499055i	$0.0158920\pi$
$631$			998279.i			0.0998110i	−0.998754	+	0.0499055i	$0.984108\pi$
$632$		0			0
$633$	2.59354e6	−	2.59354e6i	0.257267	−	0.257267i
$634$		0			0
$635$	417068.	−	138803.i	0.0410461	−	0.0136604i
$636$		0			0
$637$	1.00910e7	−	1.00910e7i	0.985335	−	0.985335i
$638$		0			0
$639$	−3.48145e6			−0.337293
$640$		0			0
$641$	6.95063e6			0.668158			0.334079	−	0.942545i	$-0.391575\pi$
$641$	6.95063e6			0.668158			0.334079	+	0.942545i	$0.391575\pi$
$642$		0			0
$643$	2.82012e6	−	2.82012e6i	0.268993	−	0.268993i	−0.559702	−	0.828694i	$-0.689084\pi$
$643$	2.82012e6	−	2.82012e6i	0.268993	−	0.268993i	0.828694	+	0.559702i	$0.189084\pi$
$644$		0			0
$645$	1.02601e6	−	2.04958e6i	0.0971071	−	0.193984i
$646$		0			0
$647$	5.26200e6	−	5.26200e6i	0.494186	−	0.494186i	−0.415437	−	0.909622i	$-0.636371\pi$
$647$	5.26200e6	−	5.26200e6i	0.494186	−	0.494186i	0.909622	+	0.415437i	$0.136371\pi$
$648$		0			0
$649$			3.51608e6i			0.327678i
$650$		0			0
$651$	−1.09278e7			−1.01060
$652$		0			0
$653$	1.68361e6	+	1.68361e6i	0.154511	+	0.154511i	0.780129	−	0.625618i	$-0.215153\pi$
$653$	1.68361e6	+	1.68361e6i	0.154511	+	0.154511i	−0.625618	+	0.780129i	$0.715153\pi$
$654$		0			0
$655$	1.03822e7	+	5.19726e6i	0.945552	+	0.473338i
$656$		0			0
$657$	3.24824e6	+	3.24824e6i	0.293585	+	0.293585i
$658$		0			0
$659$			6.34724e6i			0.569339i	0.958626	+	0.284670i	$0.0918839\pi$
$659$			6.34724e6i			0.569339i	−0.958626	+	0.284670i	$0.908116\pi$
$660$		0			0
$661$			3.70354e6i			0.329696i	0.986319	+	0.164848i	$0.0527133\pi$
$661$			3.70354e6i			0.329696i	−0.986319	+	0.164848i	$0.947287\pi$
$662$		0			0
$663$	941634.	+	941634.i	0.0831952	+	0.0831952i
$664$		0			0
$665$	−9.64368e6	−	2.89769e7i	−0.845646	−	2.54096i
$666$		0			0
$667$	−2.54842e6	−	2.54842e6i	−0.221797	−	0.221797i
$668$		0			0
$669$	241543.			0.0208655
$670$		0			0
$671$		−	5.63882e6i		−	0.483483i
$672$		0			0
$673$	1.25751e7	−	1.25751e7i	1.07022	−	1.07022i	0.0728820	−	0.997341i	$-0.476780\pi$
$673$	1.25751e7	−	1.25751e7i	1.07022	−	1.07022i	0.997341	−	0.0728820i	$-0.0232197\pi$
$674$		0			0
$675$	1.25107e6	−	8.69847e6i	0.105687	−	0.734824i
$676$		0			0
$677$	1.12742e6	−	1.12742e6i	0.0945397	−	0.0945397i	−0.658255	−	0.752795i	$-0.728705\pi$
$677$	1.12742e6	−	1.12742e6i	0.0945397	−	0.0945397i	0.752795	+	0.658255i	$0.228705\pi$
$678$		0			0
$679$	−2.12106e7			−1.76555
$680$		0			0
$681$	−208453.			−0.0172242
$682$		0			0
$683$	−6.77294e6	+	6.77294e6i	−0.555553	+	0.555553i	−0.928038	−	0.372485i	$-0.878506\pi$
$683$	−6.77294e6	+	6.77294e6i	−0.555553	+	0.555553i	0.372485	+	0.928038i	$0.378506\pi$
$684$		0			0
$685$	6.35229e6	+	1.90871e7i	0.517254	+	1.55422i
$686$		0			0
$687$	2.84019e6	−	2.84019e6i	0.229591	−	0.229591i
$688$		0			0
$689$		−	466947.i		−	0.0374731i
$690$		0			0
$691$	1.88767e7			1.50394			0.751969	−	0.659198i	$-0.229104\pi$
$691$	1.88767e7			1.50394			0.751969	+	0.659198i	$0.229104\pi$
$692$		0			0
$693$	−7.12455e6	−	7.12455e6i	−0.563540	−	0.563540i
$694$		0			0
$695$	−3.64160e6	+	7.27457e6i	−0.285977	+	0.571275i
$696$		0			0
$697$	−7.13098e6	−	7.13098e6i	−0.555991	−	0.555991i
$698$		0			0
$699$			3.57953e6i			0.277098i
$700$		0			0
$701$			4.36760e6i			0.335697i	0.985813	+	0.167849i	$0.0536820\pi$
$701$			4.36760e6i			0.335697i	−0.985813	+	0.167849i	$0.946318\pi$
$702$		0			0
$703$	607810.	+	607810.i	0.0463852	+	0.0463852i
$704$		0			0
$705$	−1.25195e6	+	2.50092e6i	−0.0948664	+	0.189508i
$706$		0			0
$707$	1.34487e7	+	1.34487e7i	1.01188	+	1.01188i
$708$		0			0
$709$	2.34469e7			1.75174			0.875871	−	0.482545i	$-0.160287\pi$
$709$	2.34469e7			1.75174			0.875871	+	0.482545i	$0.160287\pi$
$710$		0			0
$711$			1.47362e7i			1.09323i
$712$		0			0
$713$	2.54426e6	−	2.54426e6i	0.187429	−	0.187429i
$714$		0			0
$715$	−1.28761e6	−	3.86894e6i	−0.0941929	−	0.283027i
$716$		0			0
$717$	3.55506e6	−	3.55506e6i	0.258255	−	0.258255i
$718$		0			0
$719$	3.10054e6			0.223674			0.111837	−	0.993727i	$-0.464327\pi$
$719$	3.10054e6			0.223674			0.111837	+	0.993727i	$0.464327\pi$
$720$		0			0
$721$	5.29357e6			0.379237
$722$		0			0
$723$	1.39891e6	−	1.39891e6i	0.0995276	−	0.0995276i
$724$		0			0
$725$	−1.35882e7	−	1.81535e7i	−0.960099	−	1.28267i
$726$		0			0
$727$	−1.31022e7	+	1.31022e7i	−0.919406	+	0.919406i	−0.996986	−	0.0775805i	$-0.975281\pi$
$727$	−1.31022e7	+	1.31022e7i	−0.919406	+	0.919406i	0.0775805	+	0.996986i	$0.475281\pi$
$728$		0			0
$729$		−	2.13483e6i		−	0.148780i
$730$		0			0
$731$	−3.90311e6			−0.270158
$732$		0			0
$733$	−1.58810e7	−	1.58810e7i	−1.09174	−	1.09174i	−0.995343	−	0.0963958i	$-0.969269\pi$
$733$	−1.58810e7	−	1.58810e7i	−1.09174	−	1.09174i	−0.0963958	−	0.995343i	$-0.530731\pi$
$734$		0			0
$735$	−4.50523e6	−	1.35371e7i	−0.307609	−	0.924289i
$736$		0			0
$737$	1.56760e6	+	1.56760e6i	0.106308	+	0.106308i
$738$		0			0
$739$		−	1.89695e7i		−	1.27774i	−0.769313	−	0.638872i	$-0.779401\pi$
$739$		−	1.89695e7i		−	1.27774i	0.769313	−	0.638872i	$-0.220599\pi$
$740$		0			0
$741$			5.06626e6i			0.338955i
$742$		0			0
$743$	−1.76147e7	−	1.76147e7i	−1.17058	−	1.17058i	−0.982071	−	0.188512i	$-0.939634\pi$
$743$	−1.76147e7	−	1.76147e7i	−1.17058	−	1.17058i	−0.188512	−	0.982071i	$-0.560366\pi$
$744$		0			0
$745$	1.04885e7	+	5.25049e6i	0.692347	+	0.346585i
$746$		0			0
$747$	1.19249e7	+	1.19249e7i	0.781901	+	0.781901i
$748$		0			0
$749$	−6.22941e6			−0.405735
$750$		0			0
$751$		−	4.68412e6i		−	0.303060i	−0.988453	−	0.151530i	$-0.951580\pi$
$751$		−	4.68412e6i		−	0.303060i	0.988453	−	0.151530i	$-0.0484200\pi$
$752$		0			0
$753$	4.33433e6	−	4.33433e6i	0.278570	−	0.278570i
$754$		0			0
$755$	−2.28717e6	+	4.56892e6i	−0.146026	+	0.291706i
$756$		0			0
$757$	−9.09156e6	+	9.09156e6i	−0.576632	+	0.576632i	−0.933974	−	0.357342i	$-0.883683\pi$
$757$	−9.09156e6	+	9.09156e6i	−0.576632	+	0.576632i	0.357342	+	0.933974i	$0.383683\pi$
$758$		0			0
$759$	−647913.			−0.0408237
$760$		0			0
$761$	−4.93887e6			−0.309148			−0.154574	−	0.987981i	$-0.549400\pi$
$761$	−4.93887e6			−0.309148			−0.154574	+	0.987981i	$0.549400\pi$
$762$		0			0
$763$	−5.23960e6	+	5.23960e6i	−0.325827	+	0.325827i
$764$		0			0
$765$	−6.46805e6	+	2.15260e6i	−0.399595	+	0.132987i
$766$		0			0
$767$	−4.23127e6	+	4.23127e6i	−0.259706	+	0.259706i
$768$		0			0
$769$			1.04569e6i			0.0637656i	0.999492	+	0.0318828i	$0.0101503\pi$
$769$			1.04569e6i			0.0637656i	−0.999492	+	0.0318828i	$0.989850\pi$
$770$		0			0
$771$	6.56420e6			0.397691
$772$		0			0
$773$	−4.05820e6	−	4.05820e6i	−0.244278	−	0.244278i	0.574339	−	0.818617i	$-0.305259\pi$
$773$	−4.05820e6	−	4.05820e6i	−0.244278	−	0.244278i	−0.818617	+	0.574339i	$0.805259\pi$
$774$		0			0
$775$	1.81238e7	−	1.35660e7i	1.08391	−	0.811328i
$776$		0			0
$777$	401775.	+	401775.i	0.0238743	+	0.0238743i
$778$		0			0
$779$		−	3.83667e7i		−	2.26522i
$780$		0			0
$781$			3.54532e6i			0.207983i
$782$		0			0
$783$	1.44289e7	+	1.44289e7i	0.841065	+	0.841065i
$784$		0			0
$785$	1.79718e7	−	5.98113e6i	1.04092	−	0.346425i
$786$		0			0
$787$	−1.09025e7	−	1.09025e7i	−0.627464	−	0.627464i	0.319966	−	0.947429i	$-0.396329\pi$
$787$	−1.09025e7	−	1.09025e7i	−0.627464	−	0.627464i	−0.947429	+	0.319966i	$0.896329\pi$
$788$		0			0
$789$	−9.87716e6			−0.564858
$790$		0			0
$791$		−	4.23273e7i		−	2.40536i
$792$		0			0
$793$	6.78578e6	−	6.78578e6i	0.383192	−	0.383192i
$794$		0			0
$795$	−417444.	−	208970.i	−0.0234251	−	0.0117264i
$796$		0			0
$797$	1.70728e7	−	1.70728e7i	0.952049	−	0.952049i	−0.0468526	−	0.998902i	$-0.514919\pi$
$797$	1.70728e7	−	1.70728e7i	0.952049	−	0.952049i	0.998902	+	0.0468526i	$0.0149191\pi$
$798$		0			0
$799$	4.76262e6			0.263924
$800$		0			0
$801$	−6.98034e6			−0.384411
$802$		0			0
$803$	3.30783e6	−	3.30783e6i	0.181032	−	0.181032i
$804$		0			0
$805$	5.94375e6	+	2.97540e6i	0.323274	+	0.161829i
$806$		0			0
$807$	−9.29957e6	+	9.29957e6i	−0.502665	+	0.502665i
$808$		0			0
$809$			1.78529e7i			0.959040i	0.877531	+	0.479520i	$0.159189\pi$
$809$			1.78529e7i			0.959040i	−0.877531	+	0.479520i	$0.840811\pi$
$810$		0			0
$811$	2.39804e7			1.28028			0.640139	−	0.768259i	$-0.278877\pi$
$811$	2.39804e7			1.28028			0.640139	+	0.768259i	$0.278877\pi$
$812$		0			0
$813$	3.87341e6	+	3.87341e6i	0.205526	+	0.205526i
$814$		0			0
$815$	1.76937e7	−	5.88856e6i	0.933091	−	0.310538i
$816$		0			0
$817$	−1.04999e7	−	1.04999e7i	−0.550340	−	0.550340i
$818$		0			0
$819$		−	1.71475e7i		−	0.893285i
$820$		0			0
$821$		−	1.28789e7i		−	0.666841i	−0.942778	−	0.333421i	$-0.891797\pi$
$821$		−	1.28789e7i		−	0.666841i	0.942778	−	0.333421i	$-0.108203\pi$
$822$		0			0
$823$	1.48554e7	+	1.48554e7i	0.764515	+	0.764515i	0.977135	−	0.212620i	$-0.0681997\pi$
$823$	1.48554e7	+	1.48554e7i	0.764515	+	0.764515i	−0.212620	+	0.977135i	$0.568200\pi$
$824$		0			0
$825$	−4.03501e6	−	580341.i	−0.206400	−	0.0296858i
$826$		0			0
$827$	−1.43004e7	−	1.43004e7i	−0.727084	−	0.727084i	0.242954	−	0.970038i	$-0.421884\pi$
$827$	−1.43004e7	−	1.43004e7i	−0.727084	−	0.727084i	−0.970038	+	0.242954i	$0.921884\pi$
$828$		0			0
$829$	1.83120e6			0.0925443			0.0462722	−	0.998929i	$-0.485266\pi$
$829$	1.83120e6			0.0925443			0.0462722	+	0.998929i	$0.485266\pi$
$830$		0			0
$831$			1.23883e7i			0.622316i
$832$		0			0
$833$	−1.71794e7	+	1.71794e7i	−0.857821	+	0.857821i
$834$		0			0
$835$	2.10938e6	−	702013.i	0.104698	−	0.0348441i
$836$		0			0
$837$	−1.44054e7	+	1.44054e7i	−0.710739	+	0.710739i
$838$		0			0
$839$	−2.93770e7			−1.44080			−0.720398	−	0.693561i	$-0.756041\pi$
$839$	−2.93770e7			−1.44080			−0.720398	+	0.693561i	$0.756041\pi$
$840$		0			0
$841$	3.21415e7			1.56703
$842$		0			0
$843$	2.76254e6	−	2.76254e6i	0.133887	−	0.133887i
$844$		0			0
$845$	−6.18474e6	+	1.23548e7i	−0.297975	+	0.595243i
$846$		0			0
$847$	2.00073e7	−	2.00073e7i	0.958251	−	0.958251i
$848$		0			0
$849$		−	1.57121e7i		−	0.748108i
$850$		0			0
$851$	−187085.			−0.00885555
$852$		0			0
$853$	−6.76720e6	−	6.76720e6i	−0.318446	−	0.318446i	0.529724	−	0.848170i	$-0.322296\pi$
$853$	−6.76720e6	−	6.76720e6i	−0.318446	−	0.318446i	−0.848170	+	0.529724i	$0.822296\pi$
$854$		0			0
$855$	−2.31908e7	−	1.16092e7i	−1.08493	−	0.543107i
$856$		0			0
$857$	2.35330e7	+	2.35330e7i	1.09452	+	1.09452i	0.995039	+	0.0994857i	$0.0317198\pi$
$857$	2.35330e7	+	2.35330e7i	1.09452	+	1.09452i	0.0994857	+	0.995039i	$0.468280\pi$
$858$		0			0
$859$			2.12302e7i			0.981681i	0.871250	+	0.490840i	$0.163310\pi$
$859$			2.12302e7i			0.981681i	−0.871250	+	0.490840i	$0.836690\pi$
$860$		0			0
$861$		−	2.53612e7i		−	1.16590i
$862$		0			0
$863$	1.84791e7	+	1.84791e7i	0.844605	+	0.844605i	0.989454	−	0.144849i	$-0.0462695\pi$
$863$	1.84791e7	+	1.84791e7i	0.844605	+	0.844605i	−0.144849	+	0.989454i	$0.546270\pi$
$864$		0			0
$865$	1.63869e6	+	4.92387e6i	0.0744658	+	0.223751i
$866$		0			0
$867$	4.72314e6	+	4.72314e6i	0.213395	+	0.213395i
$868$		0			0
$869$	1.50065e7			0.674110
$870$		0			0
$871$			3.77292e6i			0.168512i
$872$		0			0
$873$	−1.27365e7	+	1.27365e7i	−0.565607	+	0.565607i
$874$		0			0
$875$	3.43508e7	+	2.38538e7i	1.51676	+	1.05327i
$876$		0			0
$877$	−2.31623e7	+	2.31623e7i	−1.01691	+	1.01691i	−0.0170541	+	0.999855i	$0.505429\pi$
$877$	−2.31623e7	+	2.31623e7i	−1.01691	+	1.01691i	−0.999855	+	0.0170541i	$0.994571\pi$
$878$		0			0
$879$	−6.50059e6			−0.283779
$880$		0			0
$881$	−3.17232e7			−1.37701			−0.688505	−	0.725232i	$-0.741733\pi$
$881$	−3.17232e7			−1.37701			−0.688505	+	0.725232i	$0.741733\pi$
$882$		0			0
$883$	−991053.	+	991053.i	−0.0427755	+	0.0427755i	−0.728171	−	0.685395i	$-0.759629\pi$
$883$	−991053.	+	991053.i	−0.0427755	+	0.0427755i	0.685395	+	0.728171i	$0.259629\pi$
$884$		0			0
$885$	1.88910e6	+	5.67628e6i	0.0810768	+	0.243616i
$886$		0			0
$887$	−2.16096e7	+	2.16096e7i	−0.922228	+	0.922228i	−0.997187	−	0.0749584i	$-0.976118\pi$
$887$	−2.16096e7	+	2.16096e7i	−0.922228	+	0.922228i	0.0749584	+	0.997187i	$0.476118\pi$
$888$		0			0
$889$		−	1.88239e6i		−	0.0798832i
$890$		0			0
$891$	−6.55887e6			−0.276780
$892$		0			0
$893$	1.28121e7	+	1.28121e7i	0.537641	+	0.537641i
$894$		0			0
$895$	−9.44719e6	+	1.88720e7i	−0.394226	+	0.787516i
$896$		0			0
$897$	−779702.	−	779702.i	−0.0323555	−	0.0323555i
$898$		0			0
$899$			5.25666e7i			2.16926i
$900$		0			0
$901$			794959.i			0.0326237i
$902$		0			0
$903$	−6.94066e6	−	6.94066e6i	−0.283258	−	0.283258i
$904$		0			0
$905$	−1.31055e7	+	2.61799e7i	−0.531903	+	1.06254i
$906$		0			0
$907$	−3.16848e7	−	3.16848e7i	−1.27889	−	1.27889i	−0.941289	−	0.337601i	$-0.890385\pi$
$907$	−3.16848e7	−	3.16848e7i	−1.27889	−	1.27889i	−0.337601	−	0.941289i	$-0.609615\pi$
$908$		0			0
$909$	1.61512e7			0.648330
$910$		0			0
$911$			1.77379e7i			0.708121i	0.935223	+	0.354060i	$0.115199\pi$
$911$			1.77379e7i			0.708121i	−0.935223	+	0.354060i	$0.884801\pi$
$912$		0			0
$913$	1.21436e7	−	1.21436e7i	0.482139	−	0.482139i
$914$		0			0
$915$	−3.02959e6	−	9.10319e6i	−0.119628	−	0.359452i
$916$		0			0
$917$	3.51581e7	−	3.51581e7i	1.38071	−	1.38071i
$918$		0			0
$919$	−3.13742e6			−0.122542			−0.0612708	−	0.998121i	$-0.519515\pi$
$919$	−3.13742e6			−0.122542			−0.0612708	+	0.998121i	$0.519515\pi$
$920$		0			0
$921$	−8.08815e6			−0.314195
$922$		0			0
$923$	−4.26646e6	+	4.26646e6i	−0.164840	+	0.164840i
$924$		0			0
$925$	−1.16511e6	−	167574.i	−0.0447727	−	0.00643949i
$926$		0			0
$927$	3.17867e6	−	3.17867e6i	0.121491	−	0.121491i
$928$		0			0
$929$		−	3.33387e7i		−	1.26739i	−0.773584	−	0.633694i	$-0.781538\pi$
$929$		−	3.33387e7i		−	1.26739i	0.773584	−	0.633694i	$-0.218462\pi$
$930$		0			0
$931$	−9.24303e7			−3.49494
$932$		0			0
$933$	5.86395e6	+	5.86395e6i	0.220539	+	0.220539i
$934$		0			0
$935$	2.19210e6	+	6.58672e6i	0.0820033	+	0.246400i
$936$		0			0
$937$	−8.71957e6	−	8.71957e6i	−0.324449	−	0.324449i	0.526022	−	0.850471i	$-0.323683\pi$
$937$	−8.71957e6	−	8.71957e6i	−0.324449	−	0.324449i	−0.850471	+	0.526022i	$0.823683\pi$
$938$		0			0
$939$		−	7.98659e6i		−	0.295595i
$940$		0			0
$941$			3.11580e7i			1.14708i	0.819176	+	0.573542i	$0.194431\pi$
$941$			3.11580e7i			1.14708i	−0.819176	+	0.573542i	$0.805569\pi$
$942$		0			0
$943$	5.90468e6	+	5.90468e6i	0.216230	+	0.216230i
$944$		0			0
$945$	−3.36530e7	−	1.68465e7i	−1.22587	−	0.613663i
$946$		0			0
$947$	2.99596e7	+	2.99596e7i	1.08558	+	1.08558i	0.995978	+	0.0895993i	$0.0285586\pi$
$947$	2.99596e7	+	2.99596e7i	1.08558	+	1.08558i	0.0895993	+	0.995978i	$0.471441\pi$
$948$		0			0
$949$	7.96133e6			0.286959
$950$		0			0
$951$		−	1.62167e7i		−	0.581448i
$952$		0			0
$953$	1.16784e7	−	1.16784e7i	0.416534	−	0.416534i	−0.467473	−	0.884007i	$-0.654835\pi$
$953$	1.16784e7	−	1.16784e7i	0.416534	−	0.416534i	0.884007	+	0.467473i	$0.154835\pi$
$954$		0			0
$955$	−1.50523e7	+	3.00689e7i	−0.534065	+	1.06686i
$956$		0			0
$957$	6.69324e6	−	6.69324e6i	0.236242	−	0.236242i
$958$		0			0
$959$	8.61475e7			3.02480
$960$		0			0
$961$	−2.38516e7			−0.833123
$962$		0			0
$963$	−3.74062e6	+	3.74062e6i	−0.129980	+	0.129980i
$964$		0			0
$965$	−3.17572e7	+	1.05690e7i	−1.09780	+	0.365355i
$966$		0			0
$967$	6.11322e6	−	6.11322e6i	0.210234	−	0.210234i	−0.594133	−	0.804367i	$-0.702505\pi$
$967$	6.11322e6	−	6.11322e6i	0.210234	−	0.210234i	0.804367	+	0.594133i	$0.202505\pi$
$968$		0			0
$969$		−	8.62509e6i		−	0.295090i
$970$		0			0
$971$	3.60288e7			1.22631			0.613157	−	0.789961i	$-0.289899\pi$
$971$	3.60288e7			1.22631			0.613157	+	0.789961i	$0.289899\pi$
$972$		0			0
$973$	2.46345e7	+	2.46345e7i	0.834183	+	0.834183i
$974$		0			0
$975$	−4.15737e6	−	5.55414e6i	−0.140058	−	0.187114i
$976$		0			0
$977$	2.67594e7	+	2.67594e7i	0.896892	+	0.896892i	0.995160	−	0.0982680i	$-0.0313303\pi$
$977$	2.67594e7	+	2.67594e7i	0.896892	+	0.896892i	−0.0982680	+	0.995160i	$0.531330\pi$
$978$		0			0
$979$			7.10841e6i			0.237037i
$980$		0			0
$981$			6.29252e6i			0.208762i
$982$		0			0
$983$	1.14544e7	+	1.14544e7i	0.378084	+	0.378084i	0.870411	−	0.492326i	$-0.163853\pi$
$983$	1.14544e7	+	1.14544e7i	0.378084	+	0.378084i	−0.492326	+	0.870411i	$0.663853\pi$
$984$		0			0
$985$	−1.23730e7	+	4.11779e6i	−0.406334	+	0.135230i
$986$		0			0
$987$	8.46908e6	+	8.46908e6i	0.276722	+	0.276722i
$988$		0			0
$989$	3.23190e6			0.105067
$990$		0			0
$991$		−	4.84941e7i		−	1.56857i	−0.620399	−	0.784286i	$-0.713029\pi$
$991$		−	4.84941e7i		−	1.56857i	0.620399	−	0.784286i	$-0.286971\pi$
$992$		0			0
$993$	4.36224e6	−	4.36224e6i	0.140390	−	0.140390i
$994$		0			0
$995$	−3.04661e7	−	1.52511e7i	−0.975572	−	0.488365i
$996$		0			0
$997$	−8.47473e6	+	8.47473e6i	−0.270015	+	0.270015i	−0.829106	−	0.559091i	$-0.811150\pi$
$997$	−8.47473e6	+	8.47473e6i	−0.270015	+	0.270015i	0.559091	+	0.829106i	$0.311150\pi$
$998$		0			0
$999$	1.05926e6			0.0335806

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.o.a.47.12		56
4.3	odd	2		40.6.k.a.27.27	yes	56
5.3	odd	4	inner	160.6.o.a.143.11		56
8.3	odd	2	inner	160.6.o.a.47.11		56
8.5	even	2		40.6.k.a.27.13	yes	56
20.3	even	4		40.6.k.a.3.13	✓	56
40.3	even	4	inner	160.6.o.a.143.12		56
40.13	odd	4		40.6.k.a.3.27	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.13	✓	56	20.3	even	4
40.6.k.a.3.27	yes	56	40.13	odd	4
40.6.k.a.27.13	yes	56	8.5	even	2
40.6.k.a.27.27	yes	56	4.3	odd	2
160.6.o.a.47.11		56	8.3	odd	2	inner
160.6.o.a.47.12		56	1.1	even	1	trivial
160.6.o.a.143.11		56	5.3	odd	4	inner
160.6.o.a.143.12		56	40.3	even	4	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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.45554 + 4.45554i) q^{3} +(-49.9881 - 25.0237i) q^{5} +(-169.279 + 169.279i) q^{7} +203.296i q^{9} +O(q^{10})\)	\(q+(-4.45554 + 4.45554i) q^{3} +(-49.9881 - 25.0237i) q^{5} +(-169.279 + 169.279i) q^{7} +203.296i q^{9} +207.026 q^{11} +(249.136 + 249.136i) q^{13} +(334.219 - 111.230i) q^{15} +(-424.145 - 424.145i) q^{17} -2282.02i q^{19} -1508.46i q^{21} +(351.205 + 351.205i) q^{23} +(1872.62 + 2501.78i) q^{25} +(-1988.49 - 1988.49i) q^{27} -7256.22 q^{29} -7244.36i q^{31} +(-922.415 + 922.415i) q^{33} +(12697.9 - 4225.95i) q^{35} +(-266.347 + 266.347i) q^{37} -2220.08 q^{39} +16812.6 q^{41} +(4601.16 - 4601.16i) q^{43} +(5087.23 - 10162.4i) q^{45} +(-5614.39 + 5614.39i) q^{47} -40503.7i q^{49} +3779.59 q^{51} +(-937.132 - 937.132i) q^{53} +(-10348.9 - 5180.57i) q^{55} +(10167.6 + 10167.6i) q^{57} +16983.7i q^{59} -27237.2i q^{61} +(-34413.8 - 34413.8i) q^{63} +(-6219.54 - 18688.2i) q^{65} +(7571.99 + 7571.99i) q^{67} -3129.62 q^{69} +17125.0i q^{71} +(15977.8 - 15977.8i) q^{73} +(-19490.4 - 2803.23i) q^{75} +(-35045.2 + 35045.2i) q^{77} +72486.1 q^{79} -31681.3 q^{81} +(58657.5 - 58657.5i) q^{83} +(10588.5 + 31815.9i) q^{85} +(32330.4 - 32330.4i) q^{87} +34335.8i q^{89} -84347.1 q^{91} +(32277.6 + 32277.6i) q^{93} +(-57104.6 + 114074. i) q^{95} +(62650.0 + 62650.0i) q^{97} +42087.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3}+O(q^{10}) \) 56 * q + 4 * q^3	\( 56 q + 4 q^{3} + 8 q^{11} - 408 q^{17} - 3120 q^{25} - 968 q^{27} - 976 q^{33} + 4780 q^{35} - 8 q^{41} - 1308 q^{43} - 20872 q^{51} + 968 q^{57} + 17680 q^{65} - 89252 q^{67} - 25184 q^{73} + 127740 q^{75} - 67792 q^{81} + 126444 q^{83} - 329432 q^{91} + 212576 q^{97}+O(q^{100}) \) 56 * q + 4 * q^3 + 8 * q^11 - 408 * q^17 - 3120 * q^25 - 968 * q^27 - 976 * q^33 + 4780 * q^35 - 8 * q^41 - 1308 * q^43 - 20872 * q^51 + 968 * q^57 + 17680 * q^65 - 89252 * q^67 - 25184 * q^73 + 127740 * q^75 - 67792 * q^81 + 126444 * q^83 - 329432 * q^91 + 212576 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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