LMFDB - Embedded newform 160.6.f.a.49.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,6,Mod(49,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("160.49");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	160.f (of order $2$, degree $1$, 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:	$28$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.7
Character	$\chi$	$=$	160.49
Dual form			160.6.f.a.49.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0077 q^{3} +(-19.1184 + 52.5308i) q^{5} +20.5525i q^{7} +13.2465 q^{9} +O(q^{10})$	$q-16.0077 q^{3} +(-19.1184 + 52.5308i) q^{5} +20.5525i q^{7} +13.2465 q^{9} +619.983i q^{11} +101.664 q^{13} +(306.042 - 840.897i) q^{15} +527.303i q^{17} +1703.28i q^{19} -328.998i q^{21} -1548.24i q^{23} +(-2393.97 - 2008.61i) q^{25} +3677.83 q^{27} -4308.41i q^{29} -201.464 q^{31} -9924.50i q^{33} +(-1079.64 - 392.932i) q^{35} -12439.1 q^{37} -1627.41 q^{39} -13917.3 q^{41} -16240.5 q^{43} +(-253.253 + 695.850i) q^{45} -29929.9i q^{47} +16384.6 q^{49} -8440.91i q^{51} +23517.7 q^{53} +(-32568.2 - 11853.1i) q^{55} -27265.5i q^{57} -13712.4i q^{59} +30368.5i q^{61} +272.249i q^{63} +(-1943.66 + 5340.50i) q^{65} -7812.39 q^{67} +24783.7i q^{69} -4047.41 q^{71} -49410.9i q^{73} +(38322.0 + 32153.3i) q^{75} -12742.2 q^{77} +68775.3 q^{79} -62092.4 q^{81} -7597.39 q^{83} +(-27699.6 - 10081.2i) q^{85} +68967.7i q^{87} +80012.0 q^{89} +2089.45i q^{91} +3224.97 q^{93} +(-89474.5 - 32564.0i) q^{95} +135262. i q^{97} +8212.61i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 1940 q^{9}+O(q^{10}) $ 28 * q + 1940 * q^9	$ 28 q + 1940 q^{9} + 488 q^{15} + 1556 q^{25} - 4368 q^{31} - 23360 q^{39} - 2480 q^{41} - 38420 q^{49} + 48776 q^{55} + 37200 q^{65} + 69232 q^{71} + 35984 q^{79} + 122596 q^{81} - 178744 q^{89} - 89416 q^{95}+O(q^{100}) $ 28 * q + 1940 * q^9 + 488 * q^15 + 1556 * q^25 - 4368 * q^31 - 23360 * q^39 - 2480 * q^41 - 38420 * q^49 + 48776 * q^55 + 37200 * q^65 + 69232 * q^71 + 35984 * q^79 + 122596 * q^81 - 178744 * q^89 - 89416 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−16.0077			−1.02689			−0.513447	−	0.858121i	$-0.671632\pi$
$3$	−16.0077			−1.02689			−0.513447	+	0.858121i	$0.671632\pi$
$4$		0			0
$5$	−19.1184	+	52.5308i	−0.342001	+	0.939700i
$5$	−19.1184	+	52.5308i	−0.342001	+	0.939700i
$6$		0			0
$7$			20.5525i			0.158533i	0.996853	+	0.0792664i	$0.0252578\pi$
$7$			20.5525i			0.158533i	−0.996853	+	0.0792664i	$0.974742\pi$
$8$		0			0
$9$	13.2465			0.0545124
$10$		0			0
$11$			619.983i			1.54489i	0.635080	+	0.772446i	$0.280967\pi$
$11$			619.983i			1.54489i	−0.635080	+	0.772446i	$0.719033\pi$
$12$		0			0
$13$	101.664			0.166844			0.0834218	−	0.996514i	$-0.473415\pi$
$13$	101.664			0.166844			0.0834218	+	0.996514i	$0.473415\pi$
$14$		0			0
$15$	306.042	−	840.897i	0.351199	−	0.964972i
$16$		0			0
$17$			527.303i			0.442525i	0.975214	+	0.221263i	$0.0710178\pi$
$17$			527.303i			0.442525i	−0.975214	+	0.221263i	$0.928982\pi$
$18$		0			0
$19$			1703.28i			1.08243i	0.840883	+	0.541216i	$0.182036\pi$
$19$			1703.28i			1.08243i	−0.840883	+	0.541216i	$0.817964\pi$
$20$		0			0
$21$		−	328.998i		−	0.162797i
$22$		0			0
$23$		−	1548.24i		−	0.610265i	−0.952310	−	0.305132i	$-0.901299\pi$
$23$		−	1548.24i		−	0.610265i	0.952310	−	0.305132i	$-0.0987007\pi$
$24$		0			0
$25$	−2393.97	−	2008.61i	−0.766070	−	0.642757i
$26$		0			0
$27$	3677.83			0.970916
$28$		0			0
$29$		−	4308.41i		−	0.951310i	−0.879632	−	0.475655i	$-0.842211\pi$
$29$		−	4308.41i		−	0.951310i	0.879632	−	0.475655i	$-0.157789\pi$
$30$		0			0
$31$	−201.464			−0.0376524			−0.0188262	−	0.999823i	$-0.505993\pi$
$31$	−201.464			−0.0376524			−0.0188262	+	0.999823i	$0.505993\pi$
$32$		0			0
$33$		−	9924.50i		−	1.58644i
$34$		0			0
$35$	−1079.64	−	392.932i	−0.148973	−	0.0542184i
$36$		0			0
$37$	−12439.1			−1.49377			−0.746886	−	0.664952i	$-0.768452\pi$
$37$	−12439.1			−1.49377			−0.746886	+	0.664952i	$0.768452\pi$
$38$		0			0
$39$	−1627.41			−0.171331
$40$		0			0
$41$	−13917.3			−1.29299			−0.646494	−	0.762919i	$-0.723765\pi$
$41$	−13917.3			−1.29299			−0.646494	+	0.762919i	$0.723765\pi$
$42$		0			0
$43$	−16240.5			−1.33946			−0.669728	−	0.742606i	$-0.733589\pi$
$43$	−16240.5			−1.33946			−0.669728	+	0.742606i	$0.733589\pi$
$44$		0			0
$45$	−253.253	+	695.850i	−0.0186433	+	0.0512253i
$46$		0			0
$47$		−	29929.9i		−	1.97633i	−0.153385	−	0.988167i	$-0.549017\pi$
$47$		−	29929.9i		−	1.97633i	0.153385	−	0.988167i	$-0.450983\pi$
$48$		0			0
$49$	16384.6			0.974867
$50$		0			0
$51$		−	8440.91i		−	0.454427i
$52$		0			0
$53$	23517.7			1.15002			0.575010	−	0.818147i	$-0.304998\pi$
$53$	23517.7			1.15002			0.575010	+	0.818147i	$0.304998\pi$
$54$		0			0
$55$	−32568.2	−	11853.1i	−1.45173	−	0.528355i
$56$		0			0
$57$		−	27265.5i		−	1.11154i
$58$		0			0
$59$		−	13712.4i		−	0.512843i	−0.966565	−	0.256422i	$-0.917456\pi$
$59$		−	13712.4i		−	0.512843i	0.966565	−	0.256422i	$-0.0825435\pi$
$60$		0			0
$61$			30368.5i			1.04496i	0.852653	+	0.522478i	$0.174992\pi$
$61$			30368.5i			1.04496i	−0.852653	+	0.522478i	$0.825008\pi$
$62$		0			0
$63$			272.249i			0.00864200i
$64$		0			0
$65$	−1943.66	+	5340.50i	−0.0570607	+	0.156783i
$66$		0			0
$67$	−7812.39			−0.212617			−0.106308	−	0.994333i	$-0.533903\pi$
$67$	−7812.39			−0.212617			−0.106308	+	0.994333i	$0.533903\pi$
$68$		0			0
$69$			24783.7i			0.626678i
$70$		0			0
$71$	−4047.41			−0.0952864			−0.0476432	−	0.998864i	$-0.515171\pi$
$71$	−4047.41			−0.0952864			−0.0476432	+	0.998864i	$0.515171\pi$
$72$		0			0
$73$		−	49410.9i		−	1.08521i	−0.839986	−	0.542607i	$-0.817437\pi$
$73$		−	49410.9i		−	1.08521i	0.839986	−	0.542607i	$-0.182563\pi$
$74$		0			0
$75$	38322.0	+	32153.3i	0.786674	+	0.660043i
$76$		0			0
$77$	−12742.2			−0.244916
$78$		0			0
$79$	68775.3			1.23984			0.619918	−	0.784666i	$-0.287166\pi$
$79$	68775.3			1.23984			0.619918	+	0.784666i	$0.287166\pi$
$80$		0			0
$81$	−62092.4			−1.05154
$82$		0			0
$83$	−7597.39			−0.121051			−0.0605256	−	0.998167i	$-0.519278\pi$
$83$	−7597.39			−0.121051			−0.0605256	+	0.998167i	$0.519278\pi$
$84$		0			0
$85$	−27699.6	−	10081.2i	−0.415841	−	0.151344i
$86$		0			0
$87$			68967.7i			0.976895i
$88$		0			0
$89$	80012.0			1.07073			0.535365	−	0.844621i	$-0.320174\pi$
$89$	80012.0			1.07073			0.535365	+	0.844621i	$0.320174\pi$
$90$		0			0
$91$			2089.45i			0.0264502i
$92$		0			0
$93$	3224.97			0.0386651
$94$		0			0
$95$	−89474.5	−	32564.0i	−1.01716	−	0.370193i
$96$		0			0
$97$			135262.i			1.45965i	0.683636	+	0.729823i	$0.260397\pi$
$97$			135262.i			1.45965i	−0.683636	+	0.729823i	$0.739603\pi$
$98$		0			0
$99$			8212.61i			0.0842157i
$100$		0			0
$101$		−	74276.1i		−	0.724512i	−0.932079	−	0.362256i	$-0.882007\pi$
$101$		−	74276.1i		−	0.724512i	0.932079	−	0.362256i	$-0.117993\pi$
$102$		0			0
$103$			34987.0i			0.324948i	0.986713	+	0.162474i	$0.0519473\pi$
$103$			34987.0i			0.324948i	−0.986713	+	0.162474i	$0.948053\pi$
$104$		0			0
$105$	17282.5	+	6289.93i	0.152980	+	0.0556766i
$106$		0			0
$107$	−118429.			−0.999995			−0.499998	−	0.866027i	$-0.666666\pi$
$107$	−118429.			−0.999995			−0.499998	+	0.866027i	$0.666666\pi$
$108$		0			0
$109$		−	188208.i		−	1.51730i	−0.651500	−	0.758649i	$-0.725860\pi$
$109$		−	188208.i		−	1.51730i	0.651500	−	0.758649i	$-0.274140\pi$
$110$		0			0
$111$	199121.			1.53395
$112$		0			0
$113$			219409.i			1.61644i	0.588884	+	0.808218i	$0.299567\pi$
$113$			219409.i			1.61644i	−0.588884	+	0.808218i	$0.700433\pi$
$114$		0			0
$115$	81330.2	+	29599.9i	0.573465	+	0.208711i
$116$		0			0
$117$	1346.70			0.00909505
$118$		0			0
$119$	−10837.4			−0.0701548
$120$		0			0
$121$	−223328.			−1.38669
$122$		0			0
$123$	222783.			1.32776
$124$		0			0
$125$	151283.	−	87355.6i	0.865995	−	0.500053i
$126$		0			0
$127$			178729.i			0.983301i	0.870793	+	0.491650i	$0.163606\pi$
$127$			178729.i			0.983301i	−0.870793	+	0.491650i	$0.836394\pi$
$128$		0			0
$129$	259973.			1.37548
$130$		0			0
$131$		−	182659.i		−	0.929957i	−0.885322	−	0.464979i	$-0.846062\pi$
$131$		−	182659.i		−	0.929957i	0.885322	−	0.464979i	$-0.153938\pi$
$132$		0			0
$133$	−35006.6			−0.171601
$134$		0			0
$135$	−70314.3	+	193199.i	−0.332054	+	0.912369i
$136$		0			0
$137$		−	107724.i		−	0.490357i	−0.969478	−	0.245178i	$-0.921153\pi$
$137$		−	107724.i		−	0.490357i	0.969478	−	0.245178i	$-0.0788465\pi$
$138$		0			0
$139$			174364.i			0.765455i	0.923861	+	0.382727i	$0.125015\pi$
$139$			174364.i			0.765455i	−0.923861	+	0.382727i	$0.874985\pi$
$140$		0			0
$141$			479108.i			2.02949i
$142$		0			0
$143$			63030.1i			0.257755i
$144$		0			0
$145$	226324.	+	82370.1i	0.893946	+	0.325349i
$146$		0			0
$147$	−262280.			−1.00109
$148$		0			0
$149$			208118.i			0.767971i	0.923339	+	0.383986i	$0.125449\pi$
$149$			208118.i			0.767971i	−0.923339	+	0.383986i	$0.874551\pi$
$150$		0			0
$151$	309204.			1.10358			0.551788	−	0.833985i	$-0.313946\pi$
$151$	309204.			1.10358			0.551788	+	0.833985i	$0.313946\pi$
$152$		0			0
$153$			6984.92i			0.0241231i
$154$		0			0
$155$	3851.68	−	10583.1i	0.0128772	−	0.0353820i
$156$		0			0
$157$	−432444.			−1.40017			−0.700085	−	0.714059i	$-0.746855\pi$
$157$	−432444.			−1.40017			−0.700085	+	0.714059i	$0.746855\pi$
$158$		0			0
$159$	−376464.			−1.18095
$160$		0			0
$161$	31820.1			0.0967470
$162$		0			0
$163$	131967.			0.389043			0.194521	−	0.980898i	$-0.437685\pi$
$163$	131967.			0.389043			0.194521	+	0.980898i	$0.437685\pi$
$164$		0			0
$165$	521342.	+	189741.i	1.49078	+	0.542565i
$166$		0			0
$167$		−	193263.i		−	0.536237i	−0.963386	−	0.268118i	$-0.913598\pi$
$167$		−	193263.i		−	0.536237i	0.963386	−	0.268118i	$-0.0864018\pi$
$168$		0			0
$169$	−360957.			−0.972163
$170$		0			0
$171$			22562.5i			0.0590060i
$172$		0			0
$173$	209492.			0.532172			0.266086	−	0.963949i	$-0.414269\pi$
$173$	209492.			0.532172			0.266086	+	0.963949i	$0.414269\pi$
$174$		0			0
$175$	41282.0	−	49202.0i	0.101898	−	0.121447i
$176$		0			0
$177$			219505.i			0.526636i
$178$		0			0
$179$		−	437147.i		−	1.01975i	−0.860248	−	0.509876i	$-0.829691\pi$
$179$		−	437147.i		−	1.01975i	0.860248	−	0.509876i	$-0.170309\pi$
$180$		0			0
$181$		−	559164.i		−	1.26865i	−0.773066	−	0.634326i	$-0.781278\pi$
$181$		−	559164.i		−	1.26865i	0.773066	−	0.634326i	$-0.218722\pi$
$182$		0			0
$183$		−	486129.i		−	1.07306i
$184$		0			0
$185$	237816.	−	653435.i	0.510872	−	1.40370i
$186$		0			0
$187$	−326919.			−0.683653
$188$		0			0
$189$			75588.4i			0.153922i
$190$		0			0
$191$	−330553.			−0.655627			−0.327814	−	0.944742i	$-0.606312\pi$
$191$	−330553.			−0.655627			−0.327814	+	0.944742i	$0.606312\pi$
$192$		0			0
$193$		−	407436.i		−	0.787347i	−0.919250	−	0.393673i	$-0.871204\pi$
$193$		−	407436.i		−	0.787347i	0.919250	−	0.393673i	$-0.128796\pi$
$194$		0			0
$195$	31113.6	−	85489.2i	0.0585954	−	0.161000i
$196$		0			0
$197$	−843885.			−1.54924			−0.774618	−	0.632429i	$-0.782058\pi$
$197$	−843885.			−1.54924			−0.774618	+	0.632429i	$0.782058\pi$
$198$		0			0
$199$	−245445.			−0.439362			−0.219681	−	0.975572i	$-0.570502\pi$
$199$	−245445.			−0.439362			−0.219681	+	0.975572i	$0.570502\pi$
$200$		0			0
$201$	125058.			0.218335
$202$		0			0
$203$	88548.5			0.150814
$204$		0			0
$205$	266076.	−	731085.i	0.442203	−	1.21502i
$206$		0			0
$207$		−	20508.8i		−	0.0332670i
$208$		0			0
$209$	−1.05600e6			−1.67224
$210$		0			0
$211$		−	73311.6i		−	0.113362i	−0.998392	−	0.0566809i	$-0.981948\pi$
$211$		−	73311.6i		−	0.113362i	0.998392	−	0.0566809i	$-0.0180518\pi$
$212$		0			0
$213$	64789.7			0.0978491
$214$		0			0
$215$	310493.	−	853127.i	0.458096	−	1.25869i
$216$		0			0
$217$		−	4140.58i		−	0.00596915i
$218$		0			0
$219$			790955.i			1.11440i
$220$		0			0
$221$			53607.9i			0.0738325i
$222$		0			0
$223$		−	382998.i		−	0.515744i	−0.966179	−	0.257872i	$-0.916979\pi$
$223$		−	382998.i		−	0.515744i	0.966179	−	0.257872i	$-0.0830212\pi$
$224$		0			0
$225$	−31711.7	−	26607.1i	−0.0417603	−	0.0350382i
$226$		0			0
$227$	−1.13601e6			−1.46324			−0.731622	−	0.681711i	$-0.761236\pi$
$227$	−1.13601e6			−1.46324			−0.731622	+	0.681711i	$0.761236\pi$
$228$		0			0
$229$		−	151374.i		−	0.190749i	−0.995441	−	0.0953743i	$-0.969595\pi$
$229$		−	151374.i		−	0.190749i	0.995441	−	0.0953743i	$-0.0304048\pi$
$230$		0			0
$231$	203973.			0.251503
$232$		0			0
$233$		−	684836.i		−	0.826412i	−0.910638	−	0.413206i	$-0.864409\pi$
$233$		−	684836.i		−	0.826412i	0.910638	−	0.413206i	$-0.135591\pi$
$234$		0			0
$235$	1.57224e6	+	572213.i	1.85716	+	0.675908i
$236$		0			0
$237$	−1.10093e6			−1.27318
$238$		0			0
$239$	−136612.			−0.154701			−0.0773505	−	0.997004i	$-0.524646\pi$
$239$	−136612.			−0.154701			−0.0773505	+	0.997004i	$0.524646\pi$
$240$		0			0
$241$	8903.12			0.00987415			0.00493707	−	0.999988i	$-0.498428\pi$
$241$	8903.12			0.00987415			0.00493707	+	0.999988i	$0.498428\pi$
$242$		0			0
$243$	100246.			0.108905
$244$		0			0
$245$	−313248.	+	860696.i	−0.333406	+	0.916082i
$246$		0			0
$247$			173162.i			0.180597i
$248$		0			0
$249$	121617.			0.124307
$250$		0			0
$251$			1.22945e6i			1.23176i	0.787840	+	0.615880i	$0.211200\pi$
$251$			1.22945e6i			1.23176i	−0.787840	+	0.615880i	$0.788800\pi$
$252$		0			0
$253$	959882.			0.942793
$254$		0			0
$255$	443408.	+	161377.i	0.427024	+	0.155414i
$256$		0			0
$257$		−	916382.i		−	0.865453i	−0.901525	−	0.432727i	$-0.857552\pi$
$257$		−	916382.i		−	0.865453i	0.901525	−	0.432727i	$-0.142448\pi$
$258$		0			0
$259$		−	255654.i		−	0.236812i
$260$		0			0
$261$		−	57071.4i		−	0.0518582i
$262$		0			0
$263$			820999.i			0.731903i	0.930634	+	0.365951i	$0.119256\pi$
$263$			820999.i			0.731903i	−0.930634	+	0.365951i	$0.880744\pi$
$264$		0			0
$265$	−449622.	+	1.23540e6i	−0.393308	+	1.08067i
$266$		0			0
$267$	−1.28081e6			−1.09953
$268$		0			0
$269$			475703.i			0.400825i	0.979712	+	0.200413i	$0.0642283\pi$
$269$			475703.i			0.400825i	−0.979712	+	0.200413i	$0.935772\pi$
$270$		0			0
$271$	−566034.			−0.468187			−0.234093	−	0.972214i	$-0.575212\pi$
$271$	−566034.			−0.468187			−0.234093	+	0.972214i	$0.575212\pi$
$272$		0			0
$273$		−	33447.3i		−	0.0271616i
$274$		0			0
$275$	1.24531e6	−	1.48422e6i	0.992990	−	1.18350i
$276$		0			0
$277$	124729.			0.0976713			0.0488357	−	0.998807i	$-0.484449\pi$
$277$	124729.			0.0976713			0.0488357	+	0.998807i	$0.484449\pi$
$278$		0			0
$279$	−2668.69			−0.00205252
$280$		0			0
$281$	1.46925e6			1.11002			0.555010	−	0.831844i	$-0.312714\pi$
$281$	1.46925e6			1.11002			0.555010	+	0.831844i	$0.312714\pi$
$282$		0			0
$283$	554357.			0.411456			0.205728	−	0.978609i	$-0.434044\pi$
$283$	554357.			0.411456			0.205728	+	0.978609i	$0.434044\pi$
$284$		0			0
$285$	1.43228e6	+	521275.i	1.04452	+	0.380149i
$286$		0			0
$287$		−	286034.i		−	0.204981i
$288$		0			0
$289$	1.14181e6			0.804172
$290$		0			0
$291$		−	2.16524e6i		−	1.49890i
$292$		0			0
$293$	1.42856e6			0.972144			0.486072	−	0.873919i	$-0.338429\pi$
$293$	1.42856e6			0.972144			0.486072	+	0.873919i	$0.338429\pi$
$294$		0			0
$295$	720325.	+	262160.i	0.481918	+	0.175393i
$296$		0			0
$297$			2.28019e6i			1.49996i
$298$		0			0
$299$		−	157400.i		−	0.101819i
$300$		0			0
$301$		−	333783.i		−	0.212348i
$302$		0			0
$303$			1.18899e6i			0.743997i
$304$		0			0
$305$	−1.59528e6	−	580598.i	−0.981945	−	0.357376i
$306$		0			0
$307$	−1.98189e6			−1.20015			−0.600073	−	0.799945i	$-0.704862\pi$
$307$	−1.98189e6			−1.20015			−0.600073	+	0.799945i	$0.704862\pi$
$308$		0			0
$309$		−	560061.i		−	0.333687i
$310$		0			0
$311$	−3.02125e6			−1.77127			−0.885635	−	0.464381i	$-0.846277\pi$
$311$	−3.02125e6			−1.77127			−0.885635	+	0.464381i	$0.846277\pi$
$312$		0			0
$313$			2.57822e6i			1.48751i	0.668455	+	0.743753i	$0.266956\pi$
$313$			2.57822e6i			1.48751i	−0.668455	+	0.743753i	$0.733044\pi$
$314$		0			0
$315$	−14301.4	−	5204.97i	−0.00812088	−	0.00295557i
$316$		0			0
$317$	−2.64595e6			−1.47888			−0.739442	−	0.673220i	$-0.764911\pi$
$317$	−2.64595e6			−1.47888			−0.739442	+	0.673220i	$0.764911\pi$
$318$		0			0
$319$	2.67114e6			1.46967
$320$		0			0
$321$	1.89577e6			1.02689
$322$		0			0
$323$	−898142.			−0.479004
$324$		0			0
$325$	−243381.	−	204204.i	−0.127814	−	0.107240i
$326$		0			0
$327$			3.01277e6i			1.55810i
$328$		0			0
$329$	615133.			0.313314
$330$		0			0
$331$			2.90430e6i			1.45704i	0.685026	+	0.728519i	$0.259791\pi$
$331$			2.90430e6i			1.45704i	−0.685026	+	0.728519i	$0.740209\pi$
$332$		0			0
$333$	−164775.			−0.0814291
$334$		0			0
$335$	149361.	−	410391.i	0.0727151	−	0.199796i
$336$		0			0
$337$			1.76207e6i			0.845177i	0.906322	+	0.422588i	$0.138878\pi$
$337$			1.76207e6i			0.845177i	−0.906322	+	0.422588i	$0.861122\pi$
$338$		0			0
$339$		−	3.51223e6i		−	1.65991i
$340$		0			0
$341$		−	124904.i		−	0.0581689i
$342$		0			0
$343$			682170.i			0.313081i
$344$		0			0
$345$	−1.30191e6	−	473827.i	−0.588889	−	0.214324i
$346$		0			0
$347$	1.83299e6			0.817214			0.408607	−	0.912710i	$-0.366015\pi$
$347$	1.83299e6			0.817214			0.408607	+	0.912710i	$0.366015\pi$
$348$		0			0
$349$			145377.i			0.0638900i	0.999490	+	0.0319450i	$0.0101701\pi$
$349$			145377.i			0.0638900i	−0.999490	+	0.0319450i	$0.989830\pi$
$350$		0			0
$351$	373903.			0.161991
$352$		0			0
$353$		−	2.82178e6i		−	1.20528i	−0.798015	−	0.602638i	$-0.794116\pi$
$353$		−	2.82178e6i		−	1.20528i	0.798015	−	0.602638i	$-0.205884\pi$
$354$		0			0
$355$	77380.1	−	212613.i	0.0325881	−	0.0895406i
$356$		0			0
$357$	173482.			0.0720415
$358$		0			0
$359$	2.95218e6			1.20894			0.604472	−	0.796626i	$-0.293384\pi$
$359$	2.95218e6			1.20894			0.604472	+	0.796626i	$0.293384\pi$
$360$		0			0
$361$	−425050.			−0.171661
$362$		0			0
$363$	3.57497e6			1.42399
$364$		0			0
$365$	2.59559e6	+	944660.i	1.01978	+	0.371145i
$366$		0			0
$367$			2.33961e6i			0.906731i	0.891325	+	0.453366i	$0.149777\pi$
$367$			2.33961e6i			0.906731i	−0.891325	+	0.453366i	$0.850223\pi$
$368$		0			0
$369$	−184355.			−0.0704838
$370$		0			0
$371$			483347.i			0.182316i
$372$		0			0
$373$	−1.56241e6			−0.581463			−0.290731	−	0.956805i	$-0.593899\pi$
$373$	−1.56241e6			−0.581463			−0.290731	+	0.956805i	$0.593899\pi$
$374$		0			0
$375$	−2.42169e6	+	1.39836e6i	−0.889286	+	0.513501i
$376$		0			0
$377$		−	438011.i		−	0.158720i
$378$		0			0
$379$			4.69434e6i			1.67871i	0.543580	+	0.839357i	$0.317068\pi$
$379$			4.69434e6i			1.67871i	−0.543580	+	0.839357i	$0.682932\pi$
$380$		0			0
$381$		−	2.86105e6i		−	1.00975i
$382$		0			0
$383$		−	4.36467e6i		−	1.52039i	−0.649696	−	0.760194i	$-0.725104\pi$
$383$		−	4.36467e6i		−	1.52039i	0.649696	−	0.760194i	$-0.274896\pi$
$384$		0			0
$385$	243611.	−	669358.i	0.0837616	−	0.230148i
$386$		0			0
$387$	−215130.			−0.0730169
$388$		0			0
$389$			455452.i			0.152605i	0.997085	+	0.0763024i	$0.0243114\pi$
$389$			455452.i			0.152605i	−0.997085	+	0.0763024i	$0.975689\pi$
$390$		0			0
$391$	816391.			0.270057
$392$		0			0
$393$			2.92395e6i			0.954968i
$394$		0			0
$395$	−1.31488e6	+	3.61282e6i	−0.424026	+	1.16507i
$396$		0			0
$397$	−1.41260e6			−0.449824			−0.224912	−	0.974379i	$-0.572210\pi$
$397$	−1.41260e6			−0.449824			−0.224912	+	0.974379i	$0.572210\pi$
$398$		0			0
$399$	560374.			0.176216
$400$		0			0
$401$	−3.45600e6			−1.07328			−0.536640	−	0.843811i	$-0.680307\pi$
$401$	−3.45600e6			−1.07328			−0.536640	+	0.843811i	$0.680307\pi$
$402$		0			0
$403$	−20481.7			−0.00628207
$404$		0			0
$405$	1.18711e6	−	3.26177e6i	0.359628	−	0.988132i
$406$		0			0
$407$		−	7.71203e6i		−	2.30772i
$408$		0			0
$409$	1.59180e6			0.470523			0.235262	−	0.971932i	$-0.424405\pi$
$409$	1.59180e6			0.470523			0.235262	+	0.971932i	$0.424405\pi$
$410$		0			0
$411$			1.72442e6i			0.503545i
$412$		0			0
$413$	281825.			0.0813025
$414$		0			0
$415$	145250.	−	399097.i	0.0413996	−	0.113752i
$416$		0			0
$417$		−	2.79117e6i		−	0.786041i
$418$		0			0
$419$		−	2.15084e6i		−	0.598513i	−0.954173	−	0.299256i	$-0.903261\pi$
$419$		−	2.15084e6i		−	0.598513i	0.954173	−	0.299256i	$-0.0967386\pi$
$420$		0			0
$421$			4.61854e6i			1.26999i	0.772517	+	0.634994i	$0.218997\pi$
$421$			4.61854e6i			1.26999i	−0.772517	+	0.634994i	$0.781003\pi$
$422$		0			0
$423$		−	396466.i		−	0.107735i
$424$		0			0
$425$	1.05915e6	−	1.26235e6i	0.284436	−	0.339005i
$426$		0			0
$427$	−624147.			−0.165660
$428$		0			0
$429$		−	1.00897e6i		−	0.264688i
$430$		0			0
$431$	−2.67275e6			−0.693051			−0.346525	−	0.938041i	$-0.612639\pi$
$431$	−2.67275e6			−0.693051			−0.346525	+	0.938041i	$0.612639\pi$
$432$		0			0
$433$			1.02544e6i			0.262840i	0.991327	+	0.131420i	$0.0419536\pi$
$433$			1.02544e6i			0.262840i	−0.991327	+	0.131420i	$0.958046\pi$
$434$		0			0
$435$	−3.62293e6	−	1.31856e6i	−0.917988	−	0.334099i
$436$		0			0
$437$	2.63708e6			0.660571
$438$		0			0
$439$	−4.60142e6			−1.13954			−0.569771	−	0.821803i	$-0.692968\pi$
$439$	−4.60142e6			−1.13954			−0.569771	+	0.821803i	$0.692968\pi$
$440$		0			0
$441$	217039.			0.0531423
$442$		0			0
$443$	−2.12572e6			−0.514631			−0.257315	−	0.966327i	$-0.582838\pi$
$443$	−2.12572e6			−0.514631			−0.257315	+	0.966327i	$0.582838\pi$
$444$		0			0
$445$	−1.52970e6	+	4.20309e6i	−0.366191	+	1.00616i
$446$		0			0
$447$		−	3.33150e6i		−	0.788625i
$448$		0			0
$449$	−1.97599e6			−0.462561			−0.231280	−	0.972887i	$-0.574291\pi$
$449$	−1.97599e6			−0.462561			−0.231280	+	0.972887i	$0.574291\pi$
$450$		0			0
$451$		−	8.62847e6i		−	1.99753i
$452$		0			0
$453$	−4.94964e6			−1.13326
$454$		0			0
$455$	−109761.	−	39947.1i	−0.0248552	−	0.00904600i
$456$		0			0
$457$		−	6.53536e6i		−	1.46379i	−0.681417	−	0.731895i	$-0.738636\pi$
$457$		−	6.53536e6i		−	1.46379i	0.681417	−	0.731895i	$-0.261364\pi$
$458$		0			0
$459$			1.93933e6i			0.429655i
$460$		0			0
$461$		−	1.38960e6i		−	0.304535i	−0.988339	−	0.152267i	$-0.951343\pi$
$461$		−	1.38960e6i		−	0.304535i	0.988339	−	0.152267i	$-0.0486575\pi$
$462$		0			0
$463$			2.88277e6i			0.624968i	0.949923	+	0.312484i	$0.101161\pi$
$463$			2.88277e6i			0.624968i	−0.949923	+	0.312484i	$0.898839\pi$
$464$		0			0
$465$	−61656.5	+	169410.i	−0.0132235	+	0.0363336i
$466$		0			0
$467$	−1.34330e6			−0.285024			−0.142512	−	0.989793i	$-0.545518\pi$
$467$	−1.34330e6			−0.285024			−0.142512	+	0.989793i	$0.545518\pi$
$468$		0			0
$469$		−	160564.i		−	0.0337067i
$470$		0			0
$471$	6.92244e6			1.43783
$472$		0			0
$473$		−	1.00688e7i		−	2.06932i
$474$		0			0
$475$	3.42122e6	−	4.07759e6i	0.695741	−	0.829220i
$476$		0			0
$477$	311527.			0.0626903
$478$		0			0
$479$	−6.70033e6			−1.33431			−0.667156	−	0.744918i	$-0.732488\pi$
$479$	−6.70033e6			−1.33431			−0.667156	+	0.744918i	$0.732488\pi$
$480$		0			0
$481$	−1.26461e6			−0.249226
$482$		0			0
$483$	−509367.			−0.0993490
$484$		0			0
$485$	−7.10544e6	−	2.58600e6i	−1.37163	−	0.499200i
$486$		0			0
$487$			7.10977e6i			1.35842i	0.733945	+	0.679209i	$0.237677\pi$
$487$			7.10977e6i			1.35842i	−0.733945	+	0.679209i	$0.762323\pi$
$488$		0			0
$489$	−2.11249e6			−0.399506
$490$		0			0
$491$			2.40729e6i			0.450634i	0.974285	+	0.225317i	$0.0723418\pi$
$491$			2.40729e6i			0.450634i	−0.974285	+	0.225317i	$0.927658\pi$
$492$		0			0
$493$	2.27184e6			0.420979
$494$		0			0
$495$	−431415.	−	157012.i	−0.0791375	−	0.0288019i
$496$		0			0
$497$		−	83184.2i		−	0.0151060i
$498$		0			0
$499$		−	5.17486e6i		−	0.930351i	−0.885218	−	0.465176i	$-0.845991\pi$
$499$		−	5.17486e6i		−	0.930351i	0.885218	−	0.465176i	$-0.154009\pi$
$500$		0			0
$501$			3.09369e6i			0.550658i
$502$		0			0
$503$		−	9.51641e6i		−	1.67708i	−0.544842	−	0.838539i	$-0.683410\pi$
$503$		−	9.51641e6i		−	1.67708i	0.544842	−	0.838539i	$-0.316590\pi$
$504$		0			0
$505$	3.90178e6	+	1.42004e6i	0.680824	+	0.247784i
$506$		0			0
$507$	5.77810e6			0.998309
$508$		0			0
$509$			977974.i			0.167314i	0.996495	+	0.0836571i	$0.0266601\pi$
$509$			977974.i			0.167314i	−0.996495	+	0.0836571i	$0.973340\pi$
$510$		0			0
$511$	1.01552e6			0.172042
$512$		0			0
$513$			6.26435e6i			1.05095i
$514$		0			0
$515$	−1.83789e6	−	668897.i	−0.305353	−	0.111132i
$516$		0			0
$517$	1.85560e7			3.05322
$518$		0			0
$519$	−3.35349e6			−0.546485
$520$		0			0
$521$	−6.38760e6			−1.03096			−0.515482	−	0.856900i	$-0.672387\pi$
$521$	−6.38760e6			−1.03096			−0.515482	+	0.856900i	$0.672387\pi$
$522$		0			0
$523$	−2.84665e6			−0.455072			−0.227536	−	0.973770i	$-0.573067\pi$
$523$	−2.84665e6			−0.455072			−0.227536	+	0.973770i	$0.573067\pi$
$524$		0			0
$525$	−660830.	+	787611.i	−0.104639	+	0.124714i
$526$		0			0
$527$		−	106233.i		−	0.0166621i
$528$		0			0
$529$	4.03930e6			0.627577
$530$		0			0
$531$		−	181642.i		−	0.0279563i
$532$		0			0
$533$	−1.41489e6			−0.215727
$534$		0			0
$535$	2.26418e6	−	6.22116e6i	0.342000	−	0.939695i
$536$		0			0
$537$			6.99771e6i			1.04718i
$538$		0			0
$539$			1.01582e7i			1.50606i
$540$		0			0
$541$			2.39581e6i			0.351933i	0.984396	+	0.175966i	$0.0563050\pi$
$541$			2.39581e6i			0.351933i	−0.984396	+	0.175966i	$0.943695\pi$
$542$		0			0
$543$			8.95092e6i			1.30277i
$544$		0			0
$545$	9.88669e6	+	3.59824e6i	1.42580	+	0.518918i
$546$		0			0
$547$	4.73593e6			0.676763			0.338382	−	0.941009i	$-0.390121\pi$
$547$	4.73593e6			0.676763			0.338382	+	0.941009i	$0.390121\pi$
$548$		0			0
$549$			402276.i			0.0569631i
$550$		0			0
$551$	7.33841e6			1.02973
$552$		0			0
$553$			1.41350e6i			0.196555i
$554$		0			0
$555$	−3.80689e6	+	1.04600e7i	−0.524611	+	1.44145i
$556$		0			0
$557$	−6.50430e6			−0.888306			−0.444153	−	0.895951i	$-0.646495\pi$
$557$	−6.50430e6			−0.888306			−0.444153	+	0.895951i	$0.646495\pi$
$558$		0			0
$559$	−1.65108e6			−0.223480
$560$		0			0
$561$	5.23322e6			0.702040
$562$		0			0
$563$	−7.39875e6			−0.983756			−0.491878	−	0.870664i	$-0.663689\pi$
$563$	−7.39875e6			−0.983756			−0.491878	+	0.870664i	$0.663689\pi$
$564$		0			0
$565$	−1.15257e7	−	4.19476e6i	−1.51896	−	0.552823i
$566$		0			0
$567$		−	1.27615e6i		−	0.166704i
$568$		0			0
$569$	−8.19657e6			−1.06133			−0.530666	−	0.847581i	$-0.678058\pi$
$569$	−8.19657e6			−1.06133			−0.530666	+	0.847581i	$0.678058\pi$
$570$		0			0
$571$			468744.i			0.0601653i	0.999547	+	0.0300826i	$0.00957704\pi$
$571$			468744.i			0.0601653i	−0.999547	+	0.0300826i	$0.990423\pi$
$572$		0			0
$573$	5.29139e6			0.673260
$574$		0			0
$575$	−3.10981e6	+	3.70644e6i	−0.392252	+	0.467506i
$576$		0			0
$577$			7.11469e6i			0.889645i	0.895619	+	0.444822i	$0.146733\pi$
$577$			7.11469e6i			0.889645i	−0.895619	+	0.444822i	$0.853267\pi$
$578$		0			0
$579$			6.52211e6i			0.808522i
$580$		0			0
$581$		−	156145.i		−	0.0191906i
$582$		0			0
$583$			1.45806e7i			1.77666i
$584$		0			0
$585$	−25746.7	+	70743.0i	−0.00311052	+	0.00854661i
$586$		0			0
$587$	1.51044e7			1.80929			0.904645	−	0.426166i	$-0.140136\pi$
$587$	1.51044e7			1.80929			0.904645	+	0.426166i	$0.140136\pi$
$588$		0			0
$589$		−	343149.i		−	0.0407562i
$590$		0			0
$591$	1.35087e7			1.59090
$592$		0			0
$593$			1.95268e6i			0.228031i	0.993479	+	0.114016i	$0.0363714\pi$
$593$			1.95268e6i			0.228031i	−0.993479	+	0.114016i	$0.963629\pi$
$594$		0			0
$595$	207194.	−	569297.i	0.0239930	−	0.0659244i
$596$		0			0
$597$	3.92902e6			0.451178
$598$		0			0
$599$	6.34911e6			0.723012			0.361506	−	0.932370i	$-0.382263\pi$
$599$	6.34911e6			0.723012			0.361506	+	0.932370i	$0.382263\pi$
$600$		0			0
$601$	−5.25950e6			−0.593961			−0.296981	−	0.954884i	$-0.595980\pi$
$601$	−5.25950e6			−0.593961			−0.296981	+	0.954884i	$0.595980\pi$
$602$		0			0
$603$	−103487.			−0.0115902
$604$		0			0
$605$	4.26968e6	−	1.17316e7i	0.474250	−	1.30307i
$606$		0			0
$607$		−	1.91612e6i		−	0.211081i	−0.994415	−	0.105541i	$-0.966343\pi$
$607$		−	1.91612e6i		−	0.211081i	0.994415	−	0.105541i	$-0.0336573\pi$
$608$		0			0
$609$	−1.41746e6			−0.154870
$610$		0			0
$611$		−	3.04280e6i		−	0.329739i
$612$		0			0
$613$	−3.26461e6			−0.350898			−0.175449	−	0.984489i	$-0.556138\pi$
$613$	−3.26461e6			−0.350898			−0.175449	+	0.984489i	$0.556138\pi$
$614$		0			0
$615$	−4.25927e6	+	1.17030e7i	−0.454096	+	1.24770i
$616$		0			0
$617$		−	6.30937e6i		−	0.667227i	−0.942710	−	0.333613i	$-0.891732\pi$
$617$		−	6.30937e6i		−	0.667227i	0.942710	−	0.333613i	$-0.108268\pi$
$618$		0			0
$619$		−	1.61077e7i		−	1.68969i	−0.535011	−	0.844845i	$-0.679692\pi$
$619$		−	1.61077e7i		−	1.68969i	0.535011	−	0.844845i	$-0.320308\pi$
$620$		0			0
$621$		−	5.69415e6i		−	0.592516i
$622$		0			0
$623$			1.64445e6i			0.169746i
$624$		0			0
$625$	1.69656e6	+	9.61713e6i	0.173728	+	0.984794i
$626$		0			0
$627$	1.69042e7			1.71722
$628$		0			0
$629$		−	6.55917e6i		−	0.661032i
$630$		0			0
$631$	−6.37953e6			−0.637845			−0.318923	−	0.947781i	$-0.603321\pi$
$631$	−6.37953e6			−0.637845			−0.318923	+	0.947781i	$0.603321\pi$
$632$		0			0
$633$			1.17355e6i			0.116411i
$634$		0			0
$635$	−9.38879e6	−	3.41703e6i	−0.924007	−	0.336290i
$636$		0			0
$637$	1.66573e6			0.162650
$638$		0			0
$639$	−53614.0			−0.00519429
$640$		0			0
$641$	−4.35064e6			−0.418224			−0.209112	−	0.977892i	$-0.567057\pi$
$641$	−4.35064e6			−0.418224			−0.209112	+	0.977892i	$0.567057\pi$
$642$		0			0
$643$	−5.59471e6			−0.533642			−0.266821	−	0.963746i	$-0.585973\pi$
$643$	−5.59471e6			−0.533642			−0.266821	+	0.963746i	$0.585973\pi$
$644$		0			0
$645$	−4.97028e6	+	1.36566e7i	−0.470416	+	1.29254i
$646$		0			0
$647$		−	5.34514e6i		−	0.501994i	−0.967988	−	0.250997i	$-0.919242\pi$
$647$		−	5.34514e6i		−	0.501994i	0.967988	−	0.250997i	$-0.0807584\pi$
$648$		0			0
$649$	8.50148e6			0.792287
$650$		0			0
$651$			66281.2i			0.00612968i
$652$		0			0
$653$	−5.04365e6			−0.462873			−0.231436	−	0.972850i	$-0.574343\pi$
$653$	−5.04365e6			−0.462873			−0.231436	+	0.972850i	$0.574343\pi$
$654$		0			0
$655$	9.59523e6	+	3.49216e6i	0.873880	+	0.318046i
$656$		0			0
$657$		−	654522.i		−	0.0591576i
$658$		0			0
$659$		−	7.04546e6i		−	0.631969i	−0.948764	−	0.315984i	$-0.897665\pi$
$659$		−	7.04546e6i		−	0.631969i	0.948764	−	0.315984i	$-0.102335\pi$
$660$		0			0
$661$		−	8.20765e6i		−	0.730660i	−0.930878	−	0.365330i	$-0.880956\pi$
$661$		−	8.20765e6i		−	0.730660i	0.930878	−	0.365330i	$-0.119044\pi$
$662$		0			0
$663$		−	858138.i		−	0.0758182i
$664$		0			0
$665$	669271.	−	1.83892e6i	0.0586878	−	0.161254i
$666$		0			0
$667$	−6.67045e6			−0.580551
$668$		0			0
$669$			6.13091e6i			0.529614i
$670$		0			0
$671$	−1.88279e7			−1.61434
$672$		0			0
$673$			6.23037e6i			0.530245i	0.964215	+	0.265122i	$0.0854124\pi$
$673$			6.23037e6i			0.530245i	−0.964215	+	0.265122i	$0.914588\pi$
$674$		0			0
$675$	−8.80460e6	−	7.38733e6i	−0.743790	−	0.624063i
$676$		0			0
$677$	1.39112e7			1.16652			0.583262	−	0.812284i	$-0.301776\pi$
$677$	1.39112e7			1.16652			0.583262	+	0.812284i	$0.301776\pi$
$678$		0			0
$679$	−2.77998e6			−0.231402
$680$		0			0
$681$	1.81849e7			1.50260
$682$		0			0
$683$	1.07327e6			0.0880350			0.0440175	−	0.999031i	$-0.485984\pi$
$683$	1.07327e6			0.0880350			0.0440175	+	0.999031i	$0.485984\pi$
$684$		0			0
$685$	5.65884e6	+	2.05952e6i	0.460788	+	0.167703i
$686$		0			0
$687$			2.42314e6i			0.195879i
$688$		0			0
$689$	2.39091e6			0.191873
$690$		0			0
$691$			4.51366e6i			0.359611i	0.983702	+	0.179806i	$0.0575469\pi$
$691$			4.51366e6i			0.359611i	−0.983702	+	0.179806i	$0.942453\pi$
$692$		0			0
$693$	−168790.			−0.0133510
$694$		0			0
$695$	−9.15948e6	−	3.33357e6i	−0.719298	−	0.261786i
$696$		0			0
$697$		−	7.33861e6i		−	0.572179i
$698$		0			0
$699$			1.09627e7i			0.848638i
$700$		0			0
$701$			2.00796e7i			1.54334i	0.636025	+	0.771668i	$0.280577\pi$
$701$			2.00796e7i			1.54334i	−0.636025	+	0.771668i	$0.719423\pi$
$702$		0			0
$703$		−	2.11872e7i		−	1.61691i
$704$		0			0
$705$	−2.51679e7	−	9.15981e6i	−1.90711	−	0.694086i
$706$		0			0
$707$	1.52656e6			0.114859
$708$		0			0
$709$			7.45228e6i			0.556767i	0.960470	+	0.278384i	$0.0897986\pi$
$709$			7.45228e6i			0.556767i	−0.960470	+	0.278384i	$0.910201\pi$
$710$		0			0
$711$	911032.			0.0675864
$712$		0			0
$713$			311914.i			0.0229779i
$714$		0			0
$715$	−3.31102e6	−	1.20504e6i	−0.242213	−	0.0881527i
$716$		0			0
$717$	2.18684e6			0.158862
$718$		0			0
$719$	2.33956e7			1.68776			0.843881	−	0.536531i	$-0.180265\pi$
$719$	2.33956e7			1.68776			0.843881	+	0.536531i	$0.180265\pi$
$720$		0			0
$721$	−719070.			−0.0515149
$722$		0			0
$723$	−142519.			−0.0101397
$724$		0			0
$725$	−8.65394e6	+	1.03142e7i	−0.611461	+	0.728770i
$726$		0			0
$727$			294804.i			0.0206870i	0.999947	+	0.0103435i	$0.00329250\pi$
$727$			294804.i			0.0206870i	−0.999947	+	0.0103435i	$0.996708\pi$
$728$		0			0
$729$	1.34838e7			0.939706
$730$		0			0
$731$		−	8.56367e6i		−	0.592743i
$732$		0			0
$733$	−1.28146e7			−0.880936			−0.440468	−	0.897768i	$-0.645187\pi$
$733$	−1.28146e7			−0.880936			−0.440468	+	0.897768i	$0.645187\pi$
$734$		0			0
$735$	5.01438e6	−	1.37778e7i	0.342373	−	0.940720i
$736$		0			0
$737$		−	4.84355e6i		−	0.328470i
$738$		0			0
$739$			1.38313e7i			0.931648i	0.884878	+	0.465824i	$0.154242\pi$
$739$			1.38313e7i			0.931648i	−0.884878	+	0.465824i	$0.845758\pi$
$740$		0			0
$741$		−	2.77193e6i		−	0.185454i
$742$		0			0
$743$			2.75909e6i			0.183355i	0.995789	+	0.0916776i	$0.0292229\pi$
$743$			2.75909e6i			0.183355i	−0.995789	+	0.0916776i	$0.970777\pi$
$744$		0			0
$745$	−1.09326e7	−	3.97890e6i	−0.721662	−	0.262647i
$746$		0			0
$747$	−100639.			−0.00659879
$748$		0			0
$749$		−	2.43401e6i		−	0.158532i
$750$		0			0
$751$	−2.08472e7			−1.34880			−0.674400	−	0.738366i	$-0.735598\pi$
$751$	−2.08472e7			−1.34880			−0.674400	+	0.738366i	$0.735598\pi$
$752$		0			0
$753$		−	1.96807e7i		−	1.26489i
$754$		0			0
$755$	−5.91149e6	+	1.62427e7i	−0.377424	+	1.03703i
$756$		0			0
$757$	2.19242e7			1.39054			0.695270	−	0.718748i	$-0.255285\pi$
$757$	2.19242e7			1.39054			0.695270	+	0.718748i	$0.255285\pi$
$758$		0			0
$759$	−1.53655e7			−0.968149
$760$		0			0
$761$	−8.04798e6			−0.503762			−0.251881	−	0.967758i	$-0.581049\pi$
$761$	−8.04798e6			−0.503762			−0.251881	+	0.967758i	$0.581049\pi$
$762$		0			0
$763$	3.86813e6			0.240542
$764$		0			0
$765$	−366924.	−	133541.i	−0.0226685	−	0.00825013i
$766$		0			0
$767$		−	1.39406e6i		−	0.0855646i
$768$		0			0
$769$	1.69276e6			0.103224			0.0516119	−	0.998667i	$-0.483564\pi$
$769$	1.69276e6			0.103224			0.0516119	+	0.998667i	$0.483564\pi$
$770$		0			0
$771$			1.46692e7i			0.888729i
$772$		0			0
$773$	−1.17341e7			−0.706320			−0.353160	−	0.935563i	$-0.614893\pi$
$773$	−1.17341e7			−0.706320			−0.353160	+	0.935563i	$0.614893\pi$
$774$		0			0
$775$	482299.	+	404663.i	0.0288444	+	0.0242013i
$776$		0			0
$777$			4.09244e6i			0.243181i
$778$		0			0
$779$		−	2.37049e7i		−	1.39957i
$780$		0			0
$781$		−	2.50932e6i		−	0.147207i
$782$		0			0
$783$		−	1.58456e7i		−	0.923642i
$784$		0			0
$785$	8.26766e6	−	2.27166e7i	0.478860	−	1.31574i
$786$		0			0
$787$	−4.79782e6			−0.276126			−0.138063	−	0.990423i	$-0.544088\pi$
$787$	−4.79782e6			−0.276126			−0.138063	+	0.990423i	$0.544088\pi$
$788$		0			0
$789$		−	1.31423e7i		−	0.751587i
$790$		0			0
$791$	−4.50940e6			−0.256258
$792$		0			0
$793$			3.08739e6i			0.174344i
$794$		0			0
$795$	7.19741e6	−	1.97760e7i	0.403886	−	1.10974i
$796$		0			0
$797$	−1.64953e7			−0.919845			−0.459922	−	0.887959i	$-0.652123\pi$
$797$	−1.64953e7			−0.919845			−0.459922	+	0.887959i	$0.652123\pi$
$798$		0			0
$799$	1.57821e7			0.874577
$800$		0			0
$801$	1.05988e6			0.0583680
$802$		0			0
$803$	3.06339e7			1.67654
$804$		0			0
$805$	−608352.	+	1.67154e6i	−0.0330876	+	0.0909131i
$806$		0			0
$807$		−	7.61491e6i		−	0.411605i
$808$		0			0
$809$	−1.68460e7			−0.904952			−0.452476	−	0.891777i	$-0.649459\pi$
$809$	−1.68460e7			−0.904952			−0.452476	+	0.891777i	$0.649459\pi$
$810$		0			0
$811$			1.09892e7i			0.586696i	0.956006	+	0.293348i	$0.0947695\pi$
$811$			1.09892e7i			0.586696i	−0.956006	+	0.293348i	$0.905231\pi$
$812$		0			0
$813$	9.06090e6			0.480778
$814$		0			0
$815$	−2.52301e6	+	6.93235e6i	−0.133053	+	0.365583i
$816$		0			0
$817$		−	2.76621e7i		−	1.44987i
$818$		0			0
$819$			27677.9i			0.00144186i
$820$		0			0
$821$		−	3.39298e7i		−	1.75680i	−0.477924	−	0.878401i	$-0.658610\pi$
$821$		−	3.39298e7i		−	1.75680i	0.477924	−	0.878401i	$-0.341390\pi$
$822$		0			0
$823$		−	1.59677e7i		−	0.821758i	−0.911690	−	0.410879i	$-0.865222\pi$
$823$		−	1.59677e7i		−	0.821758i	0.911690	−	0.410879i	$-0.134778\pi$
$824$		0			0
$825$	−1.99345e7	+	2.37590e7i	−1.01970	+	1.21533i
$826$		0			0
$827$	−1.35172e7			−0.687261			−0.343631	−	0.939105i	$-0.611657\pi$
$827$	−1.35172e7			−0.687261			−0.343631	+	0.939105i	$0.611657\pi$
$828$		0			0
$829$		−	1.89399e7i		−	0.957173i	−0.878040	−	0.478587i	$-0.841149\pi$
$829$		−	1.89399e7i		−	0.957173i	0.878040	−	0.478587i	$-0.158851\pi$
$830$		0			0
$831$	−1.99662e6			−0.100298
$832$		0			0
$833$			8.63965e6i			0.431403i
$834$		0			0
$835$	1.01522e7	+	3.69488e6i	0.503901	+	0.183394i
$836$		0			0
$837$	−740949.			−0.0365573
$838$		0			0
$839$	2.65584e7			1.30256			0.651279	−	0.758839i	$-0.274233\pi$
$839$	2.65584e7			1.30256			0.651279	+	0.758839i	$0.274233\pi$
$840$		0			0
$841$	1.94875e6			0.0950093
$842$		0			0
$843$	−2.35194e7			−1.13987
$844$		0			0
$845$	6.90094e6	−	1.89614e7i	0.332481	−	0.913541i
$846$		0			0
$847$		−	4.58995e6i		−	0.219836i
$848$		0			0
$849$	−8.87398e6			−0.422522
$850$		0			0
$851$			1.92587e7i			0.911596i
$852$		0			0
$853$	−3.19230e7			−1.50221			−0.751106	−	0.660182i	$-0.770479\pi$
$853$	−3.19230e7			−1.50221			−0.751106	+	0.660182i	$0.770479\pi$
$854$		0			0
$855$	−1.18522e6	−	431359.i	−0.0554479	−	0.0201801i
$856$		0			0
$857$			1.09419e7i			0.508910i	0.967085	+	0.254455i	$0.0818961\pi$
$857$			1.09419e7i			0.508910i	−0.967085	+	0.254455i	$0.918104\pi$
$858$		0			0
$859$			8.02039e6i			0.370862i	0.982657	+	0.185431i	$0.0593682\pi$
$859$			8.02039e6i			0.370862i	−0.982657	+	0.185431i	$0.940632\pi$
$860$		0			0
$861$			4.57875e6i			0.210494i
$862$		0			0
$863$			3.19608e7i			1.46080i	0.683019	+	0.730401i	$0.260667\pi$
$863$			3.19608e7i			1.46080i	−0.683019	+	0.730401i	$0.739333\pi$
$864$		0			0
$865$	−4.00516e6	+	1.10048e7i	−0.182003	+	0.500082i
$866$		0			0
$867$	−1.82777e7			−0.825799
$868$		0			0
$869$			4.26395e7i			1.91541i
$870$		0			0
$871$	−794241.			−0.0354737
$872$		0			0
$873$			1.79175e6i			0.0795687i
$874$		0			0
$875$	1.79537e6	+	3.10924e6i	0.0792748	+	0.137289i
$876$		0			0
$877$	−2.53762e7			−1.11411			−0.557053	−	0.830477i	$-0.688068\pi$
$877$	−2.53762e7			−1.11411			−0.557053	+	0.830477i	$0.688068\pi$
$878$		0			0
$879$	−2.28680e7			−0.998290
$880$		0			0
$881$	3.25533e7			1.41304			0.706522	−	0.707691i	$-0.250263\pi$
$881$	3.25533e7			1.41304			0.706522	+	0.707691i	$0.250263\pi$
$882$		0			0
$883$	−3.66593e6			−0.158227			−0.0791137	−	0.996866i	$-0.525209\pi$
$883$	−3.66593e6			−0.158227			−0.0791137	+	0.996866i	$0.525209\pi$
$884$		0			0
$885$	−1.15307e7	−	4.19658e6i	−0.494879	−	0.180110i
$886$		0			0
$887$			1.23711e7i			0.527957i	0.964529	+	0.263979i	$0.0850348\pi$
$887$			1.23711e7i			0.527957i	−0.964529	+	0.263979i	$0.914965\pi$
$888$		0			0
$889$	−3.67333e6			−0.155885
$890$		0			0
$891$		−	3.84963e7i		−	1.62452i
$892$		0			0
$893$	5.09788e7			2.13925
$894$		0			0
$895$	2.29637e7	+	8.35756e6i	0.958261	+	0.348756i
$896$		0			0
$897$			2.51962e6i			0.104557i
$898$		0			0
$899$			867989.i			0.0358191i
$900$		0			0
$901$			1.24010e7i			0.508912i
$902$		0			0
$903$			5.34310e6i			0.218059i
$904$		0			0
$905$	2.93733e7	+	1.06903e7i	1.19215	+	0.433880i
$906$		0			0
$907$	−1.12158e6			−0.0452702			−0.0226351	−	0.999744i	$-0.507206\pi$
$907$	−1.12158e6			−0.0452702			−0.0226351	+	0.999744i	$0.507206\pi$
$908$		0			0
$909$		−	983899.i		−	0.0394949i
$910$		0			0
$911$	−3.35511e7			−1.33940			−0.669700	−	0.742632i	$-0.733577\pi$
$911$	−3.35511e7			−1.33940			−0.669700	+	0.742632i	$0.733577\pi$
$912$		0			0
$913$		−	4.71025e6i		−	0.187011i
$914$		0			0
$915$	2.55368e7	+	9.29404e6i	1.00835	+	0.366988i
$916$		0			0
$917$	3.75410e6			0.147429
$918$		0			0
$919$	−1.22526e6			−0.0478562			−0.0239281	−	0.999714i	$-0.507617\pi$
$919$	−1.22526e6			−0.0478562			−0.0239281	+	0.999714i	$0.507617\pi$
$920$		0			0
$921$	3.17255e7			1.23242
$922$		0			0
$923$	−411476.			−0.0158979
$924$		0			0
$925$	2.97788e7	+	2.49853e7i	1.14433	+	0.960132i
$926$		0			0
$927$			463455.i			0.0177137i
$928$		0			0
$929$	−1.33528e7			−0.507615			−0.253808	−	0.967255i	$-0.581683\pi$
$929$	−1.33528e7			−0.507615			−0.253808	+	0.967255i	$0.581683\pi$
$930$		0			0
$931$			2.79075e7i			1.05523i
$932$		0			0
$933$	4.83632e7			1.81891
$934$		0			0
$935$	6.25018e6	−	1.71733e7i	0.233810	−	0.642429i
$936$		0			0
$937$			3.30748e7i			1.23069i	0.788258	+	0.615345i	$0.210983\pi$
$937$			3.30748e7i			1.23069i	−0.788258	+	0.615345i	$0.789017\pi$
$938$		0			0
$939$		−	4.12713e7i		−	1.52751i
$940$		0			0
$941$			7.79508e6i			0.286977i	0.989652	+	0.143488i	$0.0458320\pi$
$941$			7.79508e6i			0.286977i	−0.989652	+	0.143488i	$0.954168\pi$
$942$		0			0
$943$			2.15472e7i			0.789064i
$944$		0			0
$945$	−3.97072e6	−	1.44513e6i	−0.144641	−	0.0526415i
$946$		0			0
$947$	1.39656e7			0.506041			0.253021	−	0.967461i	$-0.418576\pi$
$947$	1.39656e7			0.506041			0.253021	+	0.967461i	$0.418576\pi$
$948$		0			0
$949$		−	5.02332e6i		−	0.181061i
$950$		0			0
$951$	4.23556e7			1.51866
$952$		0			0
$953$			3.59220e7i			1.28123i	0.767861	+	0.640616i	$0.221321\pi$
$953$			3.59220e7i			1.28123i	−0.767861	+	0.640616i	$0.778679\pi$
$954$		0			0
$955$	6.31965e6	−	1.73642e7i	0.224225	−	0.616093i
$956$		0			0
$957$	−4.27588e7			−1.50920
$958$		0			0
$959$	2.21400e6			0.0777377
$960$		0			0
$961$	−2.85886e7			−0.998582
$962$		0			0
$963$	−1.56877e6			−0.0545121
$964$		0			0
$965$	2.14029e7	+	7.78954e6i	0.739869	+	0.269273i
$966$		0			0
$967$			1.77704e7i			0.611127i	0.952172	+	0.305563i	$0.0988448\pi$
$967$			1.77704e7i			0.611127i	−0.952172	+	0.305563i	$0.901155\pi$
$968$		0			0
$969$	1.43772e7			0.491886
$970$		0			0
$971$		−	1.15077e7i		−	0.391690i	−0.980635	−	0.195845i	$-0.937255\pi$
$971$		−	1.15077e7i		−	0.391690i	0.980635	−	0.195845i	$-0.0627449\pi$
$972$		0			0
$973$	−3.58361e6			−0.121350
$974$		0			0
$975$	3.89597e6	+	3.26884e6i	0.131252	+	0.110124i
$976$		0			0
$977$			4.95837e7i			1.66189i	0.556354	+	0.830945i	$0.312200\pi$
$977$			4.95837e7i			1.66189i	−0.556354	+	0.830945i	$0.687800\pi$
$978$		0			0
$979$			4.96061e7i			1.65416i
$980$		0			0
$981$		−	2.49309e6i		−	0.0827115i
$982$		0			0
$983$			3.00805e7i			0.992890i	0.868068	+	0.496445i	$0.165362\pi$
$983$			3.00805e7i			0.992890i	−0.868068	+	0.496445i	$0.834638\pi$
$984$		0			0
$985$	1.61338e7	−	4.43300e7i	0.529841	−	1.45582i
$986$		0			0
$987$	−9.84687e6			−0.321740
$988$		0			0
$989$			2.51442e7i			0.817423i
$990$		0			0
$991$	1.83106e7			0.592270			0.296135	−	0.955146i	$-0.404302\pi$
$991$	1.83106e7			0.592270			0.296135	+	0.955146i	$0.404302\pi$
$992$		0			0
$993$		−	4.64911e7i		−	1.49622i
$994$		0			0
$995$	4.69253e6	−	1.28934e7i	0.150262	−	0.412868i
$996$		0			0
$997$	−3.42076e7			−1.08990			−0.544948	−	0.838470i	$-0.683450\pi$
$997$	−3.42076e7			−1.08990			−0.544948	+	0.838470i	$0.683450\pi$
$998$		0			0
$999$	−4.57488e7			−1.45033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.f.a.49.7		28
4.3	odd	2		40.6.f.a.29.28	yes	28
5.2	odd	4		800.6.d.e.401.16		28
5.3	odd	4		800.6.d.e.401.13		28
5.4	even	2	inner	160.6.f.a.49.22		28
8.3	odd	2		40.6.f.a.29.2	yes	28
8.5	even	2	inner	160.6.f.a.49.21		28
20.3	even	4		200.6.d.e.101.15		28
20.7	even	4		200.6.d.e.101.14		28
20.19	odd	2		40.6.f.a.29.1	✓	28
40.3	even	4		200.6.d.e.101.16		28
40.13	odd	4		800.6.d.e.401.14		28
40.19	odd	2		40.6.f.a.29.27	yes	28
40.27	even	4		200.6.d.e.101.13		28
40.29	even	2	inner	160.6.f.a.49.8		28
40.37	odd	4		800.6.d.e.401.15		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.f.a.29.1	✓	28	20.19	odd	2
40.6.f.a.29.2	yes	28	8.3	odd	2
40.6.f.a.29.27	yes	28	40.19	odd	2
40.6.f.a.29.28	yes	28	4.3	odd	2
160.6.f.a.49.7		28	1.1	even	1	trivial
160.6.f.a.49.8		28	40.29	even	2	inner
160.6.f.a.49.21		28	8.5	even	2	inner
160.6.f.a.49.22		28	5.4	even	2	inner
200.6.d.e.101.13		28	40.27	even	4
200.6.d.e.101.14		28	20.7	even	4
200.6.d.e.101.15		28	20.3	even	4
200.6.d.e.101.16		28	40.3	even	4
800.6.d.e.401.13		28	5.3	odd	4
800.6.d.e.401.14		28	40.13	odd	4
800.6.d.e.401.15		28	40.37	odd	4
800.6.d.e.401.16		28	5.2	odd	4

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.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-16.0077 q^{3} +(-19.1184 + 52.5308i) q^{5} +20.5525i q^{7} +13.2465 q^{9} +O(q^{10})\)	\(q-16.0077 q^{3} +(-19.1184 + 52.5308i) q^{5} +20.5525i q^{7} +13.2465 q^{9} +619.983i q^{11} +101.664 q^{13} +(306.042 - 840.897i) q^{15} +527.303i q^{17} +1703.28i q^{19} -328.998i q^{21} -1548.24i q^{23} +(-2393.97 - 2008.61i) q^{25} +3677.83 q^{27} -4308.41i q^{29} -201.464 q^{31} -9924.50i q^{33} +(-1079.64 - 392.932i) q^{35} -12439.1 q^{37} -1627.41 q^{39} -13917.3 q^{41} -16240.5 q^{43} +(-253.253 + 695.850i) q^{45} -29929.9i q^{47} +16384.6 q^{49} -8440.91i q^{51} +23517.7 q^{53} +(-32568.2 - 11853.1i) q^{55} -27265.5i q^{57} -13712.4i q^{59} +30368.5i q^{61} +272.249i q^{63} +(-1943.66 + 5340.50i) q^{65} -7812.39 q^{67} +24783.7i q^{69} -4047.41 q^{71} -49410.9i q^{73} +(38322.0 + 32153.3i) q^{75} -12742.2 q^{77} +68775.3 q^{79} -62092.4 q^{81} -7597.39 q^{83} +(-27699.6 - 10081.2i) q^{85} +68967.7i q^{87} +80012.0 q^{89} +2089.45i q^{91} +3224.97 q^{93} +(-89474.5 - 32564.0i) q^{95} +135262. i q^{97} +8212.61i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 1940 q^{9}+O(q^{10}) \) 28 * q + 1940 * q^9	\( 28 q + 1940 q^{9} + 488 q^{15} + 1556 q^{25} - 4368 q^{31} - 23360 q^{39} - 2480 q^{41} - 38420 q^{49} + 48776 q^{55} + 37200 q^{65} + 69232 q^{71} + 35984 q^{79} + 122596 q^{81} - 178744 q^{89} - 89416 q^{95}+O(q^{100}) \) 28 * q + 1940 * q^9 + 488 * q^15 + 1556 * q^25 - 4368 * q^31 - 23360 * q^39 - 2480 * q^41 - 38420 * q^49 + 48776 * q^55 + 37200 * q^65 + 69232 * q^71 + 35984 * q^79 + 122596 * q^81 - 178744 * q^89 - 89416 * q^95

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