LMFDB - Embedded newform 960.4.f.d.769.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,4,Mod(769,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("960.769");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	960.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:	$56.6418336055$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			769.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	960.769
Dual form			960.4.f.d.769.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.00000i q^{3} +(-2.00000 + 11.0000i) q^{5} -2.00000i q^{7} -9.00000 q^{9} +O(q^{10})$	$q-3.00000i q^{3} +(-2.00000 + 11.0000i) q^{5} -2.00000i q^{7} -9.00000 q^{9} +70.0000 q^{11} -54.0000i q^{13} +(33.0000 + 6.00000i) q^{15} +22.0000i q^{17} -24.0000 q^{19} -6.00000 q^{21} +100.000i q^{23} +(-117.000 - 44.0000i) q^{25} +27.0000i q^{27} +216.000 q^{29} -208.000 q^{31} -210.000i q^{33} +(22.0000 + 4.00000i) q^{35} -254.000i q^{37} -162.000 q^{39} -206.000 q^{41} +292.000i q^{43} +(18.0000 - 99.0000i) q^{45} -320.000i q^{47} +339.000 q^{49} +66.0000 q^{51} +402.000i q^{53} +(-140.000 + 770.000i) q^{55} +72.0000i q^{57} +370.000 q^{59} +550.000 q^{61} +18.0000i q^{63} +(594.000 + 108.000i) q^{65} -728.000i q^{67} +300.000 q^{69} +540.000 q^{71} +604.000i q^{73} +(-132.000 + 351.000i) q^{75} -140.000i q^{77} +792.000 q^{79} +81.0000 q^{81} +404.000i q^{83} +(-242.000 - 44.0000i) q^{85} -648.000i q^{87} +938.000 q^{89} -108.000 q^{91} +624.000i q^{93} +(48.0000 - 264.000i) q^{95} -56.0000i q^{97} -630.000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{5} - 18 q^{9}+O(q^{10}) $ 2 * q - 4 * q^5 - 18 * q^9	$ 2 q - 4 q^{5} - 18 q^{9} + 140 q^{11} + 66 q^{15} - 48 q^{19} - 12 q^{21} - 234 q^{25} + 432 q^{29} - 416 q^{31} + 44 q^{35} - 324 q^{39} - 412 q^{41} + 36 q^{45} + 678 q^{49} + 132 q^{51} - 280 q^{55} + 740 q^{59} + 1100 q^{61} + 1188 q^{65} + 600 q^{69} + 1080 q^{71} - 264 q^{75} + 1584 q^{79} + 162 q^{81} - 484 q^{85} + 1876 q^{89} - 216 q^{91} + 96 q^{95} - 1260 q^{99}+O(q^{100}) $ 2 * q - 4 * q^5 - 18 * q^9 + 140 * q^11 + 66 * q^15 - 48 * q^19 - 12 * q^21 - 234 * q^25 + 432 * q^29 - 416 * q^31 + 44 * q^35 - 324 * q^39 - 412 * q^41 + 36 * q^45 + 678 * q^49 + 132 * q^51 - 280 * q^55 + 740 * q^59 + 1100 * q^61 + 1188 * q^65 + 600 * q^69 + 1080 * q^71 - 264 * q^75 + 1584 * q^79 + 162 * q^81 - 484 * q^85 + 1876 * q^89 - 216 * q^91 + 96 * q^95 - 1260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$-1$	$1$	$1$

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
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$		0			0
$5$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$5$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$6$		0			0
$7$		−	2.00000i		−	0.107990i	−0.998541	−	0.0539949i	$-0.982805\pi$
$7$		−	2.00000i		−	0.107990i	0.998541	−	0.0539949i	$-0.0171955\pi$
$8$		0			0
$9$	−9.00000			−0.333333
$10$		0			0
$11$	70.0000			1.91871			0.959354	−	0.282204i	$-0.0910657\pi$
$11$	70.0000			1.91871			0.959354	+	0.282204i	$0.0910657\pi$
$12$		0			0
$13$		−	54.0000i		−	1.15207i	−0.817425	−	0.576035i	$-0.804599\pi$
$13$		−	54.0000i		−	1.15207i	0.817425	−	0.576035i	$-0.195401\pi$
$14$		0			0
$15$	33.0000	+	6.00000i	0.568038	+	0.103280i
$16$		0			0
$17$			22.0000i			0.313870i	0.987609	+	0.156935i	$0.0501613\pi$
$17$			22.0000i			0.313870i	−0.987609	+	0.156935i	$0.949839\pi$
$18$		0			0
$19$	−24.0000			−0.289788			−0.144894	−	0.989447i	$-0.546284\pi$
$19$	−24.0000			−0.289788			−0.144894	+	0.989447i	$0.546284\pi$
$20$		0			0
$21$	−6.00000			−0.0623480
$22$		0			0
$23$			100.000i			0.906584i	0.891362	+	0.453292i	$0.149751\pi$
$23$			100.000i			0.906584i	−0.891362	+	0.453292i	$0.850249\pi$
$24$		0			0
$25$	−117.000	−	44.0000i	−0.936000	−	0.352000i
$26$		0			0
$27$			27.0000i			0.192450i
$28$		0			0
$29$	216.000			1.38311			0.691555	−	0.722324i	$-0.256926\pi$
$29$	216.000			1.38311			0.691555	+	0.722324i	$0.256926\pi$
$30$		0			0
$31$	−208.000			−1.20509			−0.602547	−	0.798084i	$-0.705847\pi$
$31$	−208.000			−1.20509			−0.602547	+	0.798084i	$0.705847\pi$
$32$		0			0
$33$		−	210.000i		−	1.10777i
$34$		0			0
$35$	22.0000	+	4.00000i	0.106248	+	0.0193178i
$36$		0			0
$37$		−	254.000i		−	1.12858i	−0.825578	−	0.564288i	$-0.809151\pi$
$37$		−	254.000i		−	1.12858i	0.825578	−	0.564288i	$-0.190849\pi$
$38$		0			0
$39$	−162.000			−0.665148
$40$		0			0
$41$	−206.000			−0.784678			−0.392339	−	0.919821i	$-0.628334\pi$
$41$	−206.000			−0.784678			−0.392339	+	0.919821i	$0.628334\pi$
$42$		0			0
$43$			292.000i			1.03557i	0.855510	+	0.517786i	$0.173244\pi$
$43$			292.000i			1.03557i	−0.855510	+	0.517786i	$0.826756\pi$
$44$		0			0
$45$	18.0000	−	99.0000i	0.0596285	−	0.327957i
$46$		0			0
$47$		−	320.000i		−	0.993123i	−0.868001	−	0.496562i	$-0.834596\pi$
$47$		−	320.000i		−	0.993123i	0.868001	−	0.496562i	$-0.165404\pi$
$48$		0			0
$49$	339.000			0.988338
$50$		0			0
$51$	66.0000			0.181213
$52$		0			0
$53$			402.000i			1.04187i	0.853597	+	0.520933i	$0.174416\pi$
$53$			402.000i			1.04187i	−0.853597	+	0.520933i	$0.825584\pi$
$54$		0			0
$55$	−140.000	+	770.000i	−0.343229	+	1.88776i
$56$		0			0
$57$			72.0000i			0.167309i
$58$		0			0
$59$	370.000			0.816439			0.408219	−	0.912884i	$-0.366150\pi$
$59$	370.000			0.816439			0.408219	+	0.912884i	$0.366150\pi$
$60$		0			0
$61$	550.000			1.15443			0.577215	−	0.816592i	$-0.304139\pi$
$61$	550.000			1.15443			0.577215	+	0.816592i	$0.304139\pi$
$62$		0			0
$63$			18.0000i			0.0359966i
$64$		0			0
$65$	594.000	+	108.000i	1.13349	+	0.206088i
$66$		0			0
$67$		−	728.000i		−	1.32745i	−0.747975	−	0.663727i	$-0.768974\pi$
$67$		−	728.000i		−	1.32745i	0.747975	−	0.663727i	$-0.231026\pi$
$68$		0			0
$69$	300.000			0.523417
$70$		0			0
$71$	540.000			0.902623			0.451311	−	0.892367i	$-0.350956\pi$
$71$	540.000			0.902623			0.451311	+	0.892367i	$0.350956\pi$
$72$		0			0
$73$			604.000i			0.968395i	0.874959	+	0.484198i	$0.160888\pi$
$73$			604.000i			0.968395i	−0.874959	+	0.484198i	$0.839112\pi$
$74$		0			0
$75$	−132.000	+	351.000i	−0.203227	+	0.540400i
$76$		0			0
$77$		−	140.000i		−	0.207201i
$78$		0			0
$79$	792.000			1.12794			0.563968	−	0.825797i	$-0.309274\pi$
$79$	792.000			1.12794			0.563968	+	0.825797i	$0.309274\pi$
$80$		0			0
$81$	81.0000			0.111111
$82$		0			0
$83$			404.000i			0.534274i	0.963659	+	0.267137i	$0.0860777\pi$
$83$			404.000i			0.534274i	−0.963659	+	0.267137i	$0.913922\pi$
$84$		0			0
$85$	−242.000	−	44.0000i	−0.308807	−	0.0561467i
$86$		0			0
$87$		−	648.000i		−	0.798539i
$88$		0			0
$89$	938.000			1.11717			0.558583	−	0.829449i	$-0.311345\pi$
$89$	938.000			1.11717			0.558583	+	0.829449i	$0.311345\pi$
$90$		0			0
$91$	−108.000			−0.124412
$92$		0			0
$93$			624.000i			0.695761i
$94$		0			0
$95$	48.0000	−	264.000i	0.0518389	−	0.285114i
$96$		0			0
$97$		−	56.0000i		−	0.0586179i	−0.999570	−	0.0293090i	$-0.990669\pi$
$97$		−	56.0000i		−	0.0586179i	0.999570	−	0.0293090i	$-0.00933067\pi$
$98$		0			0
$99$	−630.000			−0.639570
$100$		0			0
$101$	592.000			0.583230			0.291615	−	0.956536i	$-0.405807\pi$
$101$	592.000			0.583230			0.291615	+	0.956536i	$0.405807\pi$
$102$		0			0
$103$		−	62.0000i		−	0.0593111i	−0.999560	−	0.0296555i	$-0.990559\pi$
$103$		−	62.0000i		−	0.0593111i	0.999560	−	0.0296555i	$-0.00944104\pi$
$104$		0			0
$105$	12.0000	−	66.0000i	0.0111531	−	0.0613423i
$106$		0			0
$107$		−	84.0000i		−	0.0758933i	−0.999280	−	0.0379467i	$-0.987918\pi$
$107$		−	84.0000i		−	0.0758933i	0.999280	−	0.0379467i	$-0.0120817\pi$
$108$		0			0
$109$	370.000			0.325134			0.162567	−	0.986698i	$-0.448023\pi$
$109$	370.000			0.325134			0.162567	+	0.986698i	$0.448023\pi$
$110$		0			0
$111$	−762.000			−0.651584
$112$		0			0
$113$		−	1746.00i		−	1.45354i	−0.686882	−	0.726769i	$-0.741021\pi$
$113$		−	1746.00i		−	1.45354i	0.686882	−	0.726769i	$-0.258979\pi$
$114$		0			0
$115$	−1100.00	−	200.000i	−0.891961	−	0.162175i
$116$		0			0
$117$			486.000i			0.384023i
$118$		0			0
$119$	44.0000			0.0338947
$120$		0			0
$121$	3569.00			2.68144
$122$		0			0
$123$			618.000i			0.453034i
$124$		0			0
$125$	718.000	−	1199.00i	0.513759	−	0.857935i
$126$		0			0
$127$			1630.00i			1.13889i	0.822029	+	0.569445i	$0.192842\pi$
$127$			1630.00i			1.13889i	−0.822029	+	0.569445i	$0.807158\pi$
$128$		0			0
$129$	876.000			0.597888
$130$		0			0
$131$	−870.000			−0.580246			−0.290123	−	0.956989i	$-0.593696\pi$
$131$	−870.000			−0.580246			−0.290123	+	0.956989i	$0.593696\pi$
$132$		0			0
$133$			48.0000i			0.0312942i
$134$		0			0
$135$	−297.000	−	54.0000i	−0.189346	−	0.0344265i
$136$		0			0
$137$		−	918.000i		−	0.572482i	−0.958158	−	0.286241i	$-0.907594\pi$
$137$		−	918.000i		−	0.572482i	0.958158	−	0.286241i	$-0.0924058\pi$
$138$		0			0
$139$	596.000			0.363684			0.181842	−	0.983328i	$-0.441794\pi$
$139$	596.000			0.363684			0.181842	+	0.983328i	$0.441794\pi$
$140$		0			0
$141$	−960.000			−0.573380
$142$		0			0
$143$		−	3780.00i		−	2.21049i
$144$		0			0
$145$	−432.000	+	2376.00i	−0.247418	+	1.36080i
$146$		0			0
$147$		−	1017.00i		−	0.570617i
$148$		0			0
$149$	1076.00			0.591606			0.295803	−	0.955249i	$-0.404413\pi$
$149$	1076.00			0.591606			0.295803	+	0.955249i	$0.404413\pi$
$150$		0			0
$151$	32.0000			0.0172458			0.00862292	−	0.999963i	$-0.497255\pi$
$151$	32.0000			0.0172458			0.00862292	+	0.999963i	$0.497255\pi$
$152$		0			0
$153$		−	198.000i		−	0.104623i
$154$		0			0
$155$	416.000	−	2288.00i	0.215574	−	1.18566i
$156$		0			0
$157$		−	2554.00i		−	1.29829i	−0.760665	−	0.649145i	$-0.775127\pi$
$157$		−	2554.00i		−	1.29829i	0.760665	−	0.649145i	$-0.224873\pi$
$158$		0			0
$159$	1206.00			0.601522
$160$		0			0
$161$	200.000			0.0979019
$162$		0			0
$163$			752.000i			0.361357i	0.983542	+	0.180678i	$0.0578293\pi$
$163$			752.000i			0.361357i	−0.983542	+	0.180678i	$0.942171\pi$
$164$		0			0
$165$	2310.00	+	420.000i	1.08990	+	0.198163i
$166$		0			0
$167$			2700.00i			1.25109i	0.780188	+	0.625546i	$0.215124\pi$
$167$			2700.00i			1.25109i	−0.780188	+	0.625546i	$0.784876\pi$
$168$		0			0
$169$	−719.000			−0.327264
$170$		0			0
$171$	216.000			0.0965961
$172$		0			0
$173$			1334.00i			0.586255i	0.956073	+	0.293128i	$0.0946961\pi$
$173$			1334.00i			0.586255i	−0.956073	+	0.293128i	$0.905304\pi$
$174$		0			0
$175$	−88.0000	+	234.000i	−0.0380124	+	0.101078i
$176$		0			0
$177$		−	1110.00i		−	0.471371i
$178$		0			0
$179$	1714.00			0.715700			0.357850	−	0.933779i	$-0.383510\pi$
$179$	1714.00			0.715700			0.357850	+	0.933779i	$0.383510\pi$
$180$		0			0
$181$	4006.00			1.64510			0.822551	−	0.568691i	$-0.192550\pi$
$181$	4006.00			1.64510			0.822551	+	0.568691i	$0.192550\pi$
$182$		0			0
$183$		−	1650.00i		−	0.666511i
$184$		0			0
$185$	2794.00	+	508.000i	1.11037	+	0.201886i
$186$		0			0
$187$			1540.00i			0.602224i
$188$		0			0
$189$	54.0000			0.0207827
$190$		0			0
$191$	684.000			0.259123			0.129562	−	0.991571i	$-0.458643\pi$
$191$	684.000			0.259123			0.129562	+	0.991571i	$0.458643\pi$
$192$		0			0
$193$		−	4484.00i		−	1.67236i	−0.548455	−	0.836180i	$-0.684784\pi$
$193$		−	4484.00i		−	1.67236i	0.548455	−	0.836180i	$-0.315216\pi$
$194$		0			0
$195$	324.000	−	1782.00i	0.118985	−	0.654419i
$196$		0			0
$197$		−	1058.00i		−	0.382636i	−0.981528	−	0.191318i	$-0.938724\pi$
$197$		−	1058.00i		−	0.382636i	0.981528	−	0.191318i	$-0.0612762\pi$
$198$		0			0
$199$	−1128.00			−0.401818			−0.200909	−	0.979610i	$-0.564390\pi$
$199$	−1128.00			−0.401818			−0.200909	+	0.979610i	$0.564390\pi$
$200$		0			0
$201$	−2184.00			−0.766405
$202$		0			0
$203$		−	432.000i		−	0.149362i
$204$		0			0
$205$	412.000	−	2266.00i	0.140367	−	0.772021i
$206$		0			0
$207$		−	900.000i		−	0.302195i
$208$		0			0
$209$	−1680.00			−0.556019
$210$		0			0
$211$	780.000			0.254490			0.127245	−	0.991871i	$-0.459387\pi$
$211$	780.000			0.254490			0.127245	+	0.991871i	$0.459387\pi$
$212$		0			0
$213$		−	1620.00i		−	0.521129i
$214$		0			0
$215$	−3212.00	−	584.000i	−1.01887	−	0.185249i
$216$		0			0
$217$			416.000i			0.130138i
$218$		0			0
$219$	1812.00			0.559103
$220$		0			0
$221$	1188.00			0.361600
$222$		0			0
$223$			2570.00i			0.771749i	0.922551	+	0.385874i	$0.126100\pi$
$223$			2570.00i			0.771749i	−0.922551	+	0.385874i	$0.873900\pi$
$224$		0			0
$225$	1053.00	+	396.000i	0.312000	+	0.117333i
$226$		0			0
$227$			2836.00i			0.829216i	0.910000	+	0.414608i	$0.136081\pi$
$227$			2836.00i			0.829216i	−0.910000	+	0.414608i	$0.863919\pi$
$228$		0			0
$229$	−610.000			−0.176026			−0.0880130	−	0.996119i	$-0.528052\pi$
$229$	−610.000			−0.176026			−0.0880130	+	0.996119i	$0.528052\pi$
$230$		0			0
$231$	−420.000			−0.119628
$232$		0			0
$233$			3514.00i			0.988025i	0.869455	+	0.494012i	$0.164470\pi$
$233$			3514.00i			0.988025i	−0.869455	+	0.494012i	$0.835530\pi$
$234$		0			0
$235$	3520.00	+	640.000i	0.977104	+	0.177655i
$236$		0			0
$237$		−	2376.00i		−	0.651214i
$238$		0			0
$239$	−1844.00			−0.499073			−0.249536	−	0.968365i	$-0.580278\pi$
$239$	−1844.00			−0.499073			−0.249536	+	0.968365i	$0.580278\pi$
$240$		0			0
$241$	982.000			0.262474			0.131237	−	0.991351i	$-0.458105\pi$
$241$	982.000			0.262474			0.131237	+	0.991351i	$0.458105\pi$
$242$		0			0
$243$		−	243.000i		−	0.0641500i
$244$		0			0
$245$	−678.000	+	3729.00i	−0.176799	+	0.972396i
$246$		0			0
$247$			1296.00i			0.333856i
$248$		0			0
$249$	1212.00			0.308463
$250$		0			0
$251$	−3174.00			−0.798172			−0.399086	−	0.916914i	$-0.630672\pi$
$251$	−3174.00			−0.798172			−0.399086	+	0.916914i	$0.630672\pi$
$252$		0			0
$253$			7000.00i			1.73947i
$254$		0			0
$255$	−132.000	+	726.000i	−0.0324163	+	0.178290i
$256$		0			0
$257$			1194.00i			0.289804i	0.989446	+	0.144902i	$0.0462867\pi$
$257$			1194.00i			0.289804i	−0.989446	+	0.144902i	$0.953713\pi$
$258$		0			0
$259$	−508.000			−0.121875
$260$		0			0
$261$	−1944.00			−0.461037
$262$		0			0
$263$		−	140.000i		−	0.0328242i	−0.999865	−	0.0164121i	$-0.994776\pi$
$263$		−	140.000i		−	0.0328242i	0.999865	−	0.0164121i	$-0.00522437\pi$
$264$		0			0
$265$	−4422.00	−	804.000i	−1.02506	−	0.186375i
$266$		0			0
$267$		−	2814.00i		−	0.644996i
$268$		0			0
$269$	5256.00			1.19132			0.595658	−	0.803238i	$-0.296891\pi$
$269$	5256.00			1.19132			0.595658	+	0.803238i	$0.296891\pi$
$270$		0			0
$271$	−544.000			−0.121940			−0.0609698	−	0.998140i	$-0.519419\pi$
$271$	−544.000			−0.121940			−0.0609698	+	0.998140i	$0.519419\pi$
$272$		0			0
$273$			324.000i			0.0718292i
$274$		0			0
$275$	−8190.00	−	3080.00i	−1.79591	−	0.675385i
$276$		0			0
$277$			946.000i			0.205197i	0.994723	+	0.102599i	$0.0327157\pi$
$277$			946.000i			0.205197i	−0.994723	+	0.102599i	$0.967284\pi$
$278$		0			0
$279$	1872.00			0.401698
$280$		0			0
$281$	1278.00			0.271313			0.135657	−	0.990756i	$-0.456686\pi$
$281$	1278.00			0.271313			0.135657	+	0.990756i	$0.456686\pi$
$282$		0			0
$283$			7424.00i			1.55940i	0.626152	+	0.779701i	$0.284629\pi$
$283$			7424.00i			1.55940i	−0.626152	+	0.779701i	$0.715371\pi$
$284$		0			0
$285$	−792.000	−	144.000i	−0.164611	−	0.0299292i
$286$		0			0
$287$			412.000i			0.0847373i
$288$		0			0
$289$	4429.00			0.901486
$290$		0			0
$291$	−168.000			−0.0338431
$292$		0			0
$293$			1362.00i			0.271566i	0.990739	+	0.135783i	$0.0433550\pi$
$293$			1362.00i			0.271566i	−0.990739	+	0.135783i	$0.956645\pi$
$294$		0			0
$295$	−740.000	+	4070.00i	−0.146049	+	0.803270i
$296$		0			0
$297$			1890.00i			0.369256i
$298$		0			0
$299$	5400.00			1.04445
$300$		0			0
$301$	584.000			0.111831
$302$		0			0
$303$		−	1776.00i		−	0.336728i
$304$		0			0
$305$	−1100.00	+	6050.00i	−0.206511	+	1.13581i
$306$		0			0
$307$			7740.00i			1.43891i	0.694539	+	0.719455i	$0.255608\pi$
$307$			7740.00i			1.43891i	−0.694539	+	0.719455i	$0.744392\pi$
$308$		0			0
$309$	−186.000			−0.0342433
$310$		0			0
$311$	−4980.00			−0.908006			−0.454003	−	0.891000i	$-0.650004\pi$
$311$	−4980.00			−0.908006			−0.454003	+	0.891000i	$0.650004\pi$
$312$		0			0
$313$			604.000i			0.109074i	0.998512	+	0.0545369i	$0.0173683\pi$
$313$			604.000i			0.109074i	−0.998512	+	0.0545369i	$0.982632\pi$
$314$		0			0
$315$	−198.000	−	36.0000i	−0.0354160	−	0.00643927i
$316$		0			0
$317$		−	8566.00i		−	1.51771i	−0.651259	−	0.758856i	$-0.725759\pi$
$317$		−	8566.00i		−	1.51771i	0.651259	−	0.758856i	$-0.274241\pi$
$318$		0			0
$319$	15120.0			2.65379
$320$		0			0
$321$	−252.000			−0.0438170
$322$		0			0
$323$		−	528.000i		−	0.0909557i
$324$		0			0
$325$	−2376.00	+	6318.00i	−0.405529	+	1.07834i
$326$		0			0
$327$		−	1110.00i		−	0.187716i
$328$		0			0
$329$	−640.000			−0.107247
$330$		0			0
$331$	3472.00			0.576551			0.288275	−	0.957548i	$-0.406918\pi$
$331$	3472.00			0.576551			0.288275	+	0.957548i	$0.406918\pi$
$332$		0			0
$333$			2286.00i			0.376192i
$334$		0			0
$335$	8008.00	+	1456.00i	1.30604	+	0.237462i
$336$		0			0
$337$		−	5668.00i		−	0.916189i	−0.888904	−	0.458094i	$-0.848532\pi$
$337$		−	5668.00i		−	0.916189i	0.888904	−	0.458094i	$-0.151468\pi$
$338$		0			0
$339$	−5238.00			−0.839201
$340$		0			0
$341$	−14560.0			−2.31222
$342$		0			0
$343$		−	1364.00i		−	0.214720i
$344$		0			0
$345$	−600.000	+	3300.00i	−0.0936316	+	0.514974i
$346$		0			0
$347$		−	10836.0i		−	1.67639i	−0.545371	−	0.838194i	$-0.683611\pi$
$347$		−	10836.0i		−	1.67639i	0.545371	−	0.838194i	$-0.316389\pi$
$348$		0			0
$349$	−8990.00			−1.37886			−0.689432	−	0.724350i	$-0.742140\pi$
$349$	−8990.00			−1.37886			−0.689432	+	0.724350i	$0.742140\pi$
$350$		0			0
$351$	1458.00			0.221716
$352$		0			0
$353$		−	5078.00i		−	0.765651i	−0.923821	−	0.382825i	$-0.874951\pi$
$353$		−	5078.00i		−	0.765651i	0.923821	−	0.382825i	$-0.125049\pi$
$354$		0			0
$355$	−1080.00	+	5940.00i	−0.161466	+	0.888063i
$356$		0			0
$357$		−	132.000i		−	0.0195691i
$358$		0			0
$359$	−3696.00			−0.543363			−0.271682	−	0.962387i	$-0.587580\pi$
$359$	−3696.00			−0.543363			−0.271682	+	0.962387i	$0.587580\pi$
$360$		0			0
$361$	−6283.00			−0.916023
$362$		0			0
$363$		−	10707.0i		−	1.54813i
$364$		0			0
$365$	−6644.00	−	1208.00i	−0.952775	−	0.173232i
$366$		0			0
$367$			286.000i			0.0406787i	0.999793	+	0.0203393i	$0.00647466\pi$
$367$			286.000i			0.0406787i	−0.999793	+	0.0203393i	$0.993525\pi$
$368$		0			0
$369$	1854.00			0.261559
$370$		0			0
$371$	804.000			0.112511
$372$		0			0
$373$		−	8262.00i		−	1.14689i	−0.819244	−	0.573445i	$-0.805607\pi$
$373$		−	8262.00i		−	1.14689i	0.819244	−	0.573445i	$-0.194393\pi$
$374$		0			0
$375$	−3597.00	−	2154.00i	−0.495329	−	0.296619i
$376$		0			0
$377$		−	11664.0i		−	1.59344i
$378$		0			0
$379$	2956.00			0.400632			0.200316	−	0.979731i	$-0.435803\pi$
$379$	2956.00			0.400632			0.200316	+	0.979731i	$0.435803\pi$
$380$		0			0
$381$	4890.00			0.657539
$382$		0			0
$383$			5240.00i			0.699090i	0.936920	+	0.349545i	$0.113664\pi$
$383$			5240.00i			0.699090i	−0.936920	+	0.349545i	$0.886336\pi$
$384$		0			0
$385$	1540.00	+	280.000i	0.203859	+	0.0370653i
$386$		0			0
$387$		−	2628.00i		−	0.345191i
$388$		0			0
$389$	−884.000			−0.115220			−0.0576100	−	0.998339i	$-0.518348\pi$
$389$	−884.000			−0.115220			−0.0576100	+	0.998339i	$0.518348\pi$
$390$		0			0
$391$	−2200.00			−0.284549
$392$		0			0
$393$			2610.00i			0.335005i
$394$		0			0
$395$	−1584.00	+	8712.00i	−0.201771	+	1.10974i
$396$		0			0
$397$			3394.00i			0.429068i	0.976717	+	0.214534i	$0.0688233\pi$
$397$			3394.00i			0.429068i	−0.976717	+	0.214534i	$0.931177\pi$
$398$		0			0
$399$	144.000			0.0180677
$400$		0			0
$401$	−6826.00			−0.850060			−0.425030	−	0.905179i	$-0.639737\pi$
$401$	−6826.00			−0.850060			−0.425030	+	0.905179i	$0.639737\pi$
$402$		0			0
$403$			11232.0i			1.38835i
$404$		0			0
$405$	−162.000	+	891.000i	−0.0198762	+	0.109319i
$406$		0			0
$407$		−	17780.0i		−	2.16541i
$408$		0			0
$409$	−7814.00			−0.944688			−0.472344	−	0.881414i	$-0.656592\pi$
$409$	−7814.00			−0.944688			−0.472344	+	0.881414i	$0.656592\pi$
$410$		0			0
$411$	−2754.00			−0.330523
$412$		0			0
$413$		−	740.000i		−	0.0881671i
$414$		0			0
$415$	−4444.00	−	808.000i	−0.525656	−	0.0955739i
$416$		0			0
$417$		−	1788.00i		−	0.209973i
$418$		0			0
$419$	−8290.00			−0.966570			−0.483285	−	0.875463i	$-0.660557\pi$
$419$	−8290.00			−0.966570			−0.483285	+	0.875463i	$0.660557\pi$
$420$		0			0
$421$	−2110.00			−0.244264			−0.122132	−	0.992514i	$-0.538973\pi$
$421$	−2110.00			−0.244264			−0.122132	+	0.992514i	$0.538973\pi$
$422$		0			0
$423$			2880.00i			0.331041i
$424$		0			0
$425$	968.000	−	2574.00i	0.110482	−	0.293782i
$426$		0			0
$427$		−	1100.00i		−	0.124667i
$428$		0			0
$429$	−11340.0			−1.27622
$430$		0			0
$431$	12080.0			1.35005			0.675027	−	0.737793i	$-0.264132\pi$
$431$	12080.0			1.35005			0.675027	+	0.737793i	$0.264132\pi$
$432$		0			0
$433$			16492.0i			1.83038i	0.403022	+	0.915190i	$0.367960\pi$
$433$			16492.0i			1.83038i	−0.403022	+	0.915190i	$0.632040\pi$
$434$		0			0
$435$	7128.00	+	1296.00i	0.785658	+	0.142847i
$436$		0			0
$437$		−	2400.00i		−	0.262718i
$438$		0			0
$439$	−15048.0			−1.63600			−0.817998	−	0.575222i	$-0.804916\pi$
$439$	−15048.0			−1.63600			−0.817998	+	0.575222i	$0.804916\pi$
$440$		0			0
$441$	−3051.00			−0.329446
$442$		0			0
$443$		−	9876.00i		−	1.05919i	−0.848249	−	0.529597i	$-0.822343\pi$
$443$		−	9876.00i		−	1.05919i	0.848249	−	0.529597i	$-0.177657\pi$
$444$		0			0
$445$	−1876.00	+	10318.0i	−0.199845	+	1.09915i
$446$		0			0
$447$		−	3228.00i		−	0.341564i
$448$		0			0
$449$	−17166.0			−1.80426			−0.902131	−	0.431462i	$-0.857998\pi$
$449$	−17166.0			−1.80426			−0.902131	+	0.431462i	$0.857998\pi$
$450$		0			0
$451$	−14420.0			−1.50557
$452$		0			0
$453$		−	96.0000i		−	0.00995690i
$454$		0			0
$455$	216.000	−	1188.00i	0.0222555	−	0.122405i
$456$		0			0
$457$		−	14848.0i		−	1.51983i	−0.650025	−	0.759913i	$-0.725242\pi$
$457$		−	14848.0i		−	1.51983i	0.650025	−	0.759913i	$-0.274758\pi$
$458$		0			0
$459$	−594.000			−0.0604042
$460$		0			0
$461$	1260.00			0.127297			0.0636486	−	0.997972i	$-0.479726\pi$
$461$	1260.00			0.127297			0.0636486	+	0.997972i	$0.479726\pi$
$462$		0			0
$463$			11238.0i			1.12802i	0.825767	+	0.564011i	$0.190742\pi$
$463$			11238.0i			1.12802i	−0.825767	+	0.564011i	$0.809258\pi$
$464$		0			0
$465$	−6864.00	−	1248.00i	−0.684538	−	0.124462i
$466$		0			0
$467$		−	14772.0i		−	1.46374i	−0.681444	−	0.731870i	$-0.738648\pi$
$467$		−	14772.0i		−	1.46374i	0.681444	−	0.731870i	$-0.261352\pi$
$468$		0			0
$469$	−1456.00			−0.143351
$470$		0			0
$471$	−7662.00			−0.749568
$472$		0			0
$473$			20440.0i			1.98696i
$474$		0			0
$475$	2808.00	+	1056.00i	0.271242	+	0.102005i
$476$		0			0
$477$		−	3618.00i		−	0.347289i
$478$		0			0
$479$	−6116.00			−0.583397			−0.291699	−	0.956510i	$-0.594220\pi$
$479$	−6116.00			−0.583397			−0.291699	+	0.956510i	$0.594220\pi$
$480$		0			0
$481$	−13716.0			−1.30020
$482$		0			0
$483$		−	600.000i		−	0.0565237i
$484$		0			0
$485$	616.000	+	112.000i	0.0576724	+	0.0104859i
$486$		0			0
$487$			15906.0i			1.48002i	0.672596	+	0.740010i	$0.265179\pi$
$487$			15906.0i			1.48002i	−0.672596	+	0.740010i	$0.734821\pi$
$488$		0			0
$489$	2256.00			0.208630
$490$		0			0
$491$	18714.0			1.72006			0.860032	−	0.510241i	$-0.170444\pi$
$491$	18714.0			1.72006			0.860032	+	0.510241i	$0.170444\pi$
$492$		0			0
$493$			4752.00i			0.434116i
$494$		0			0
$495$	1260.00	−	6930.00i	0.114410	−	0.629253i
$496$		0			0
$497$		−	1080.00i		−	0.0974741i
$498$		0			0
$499$	4056.00			0.363871			0.181935	−	0.983310i	$-0.441764\pi$
$499$	4056.00			0.363871			0.181935	+	0.983310i	$0.441764\pi$
$500$		0			0
$501$	8100.00			0.722318
$502$		0			0
$503$		−	6288.00i		−	0.557392i	−0.960379	−	0.278696i	$-0.910098\pi$
$503$		−	6288.00i		−	0.557392i	0.960379	−	0.278696i	$-0.0899021\pi$
$504$		0			0
$505$	−1184.00	+	6512.00i	−0.104331	+	0.573822i
$506$		0			0
$507$			2157.00i			0.188946i
$508$		0			0
$509$	2856.00			0.248703			0.124352	−	0.992238i	$-0.460315\pi$
$509$	2856.00			0.248703			0.124352	+	0.992238i	$0.460315\pi$
$510$		0			0
$511$	1208.00			0.104577
$512$		0			0
$513$		−	648.000i		−	0.0557698i
$514$		0			0
$515$	682.000	+	124.000i	0.0583544	+	0.0106099i
$516$		0			0
$517$		−	22400.0i		−	1.90551i
$518$		0			0
$519$	4002.00			0.338475
$520$		0			0
$521$	17078.0			1.43609			0.718043	−	0.695999i	$-0.245038\pi$
$521$	17078.0			1.43609			0.718043	+	0.695999i	$0.245038\pi$
$522$		0			0
$523$		−	8560.00i		−	0.715684i	−0.933782	−	0.357842i	$-0.883513\pi$
$523$		−	8560.00i		−	0.715684i	0.933782	−	0.357842i	$-0.116487\pi$
$524$		0			0
$525$	702.000	+	264.000i	0.0583577	+	0.0219465i
$526$		0			0
$527$		−	4576.00i		−	0.378242i
$528$		0			0
$529$	2167.00			0.178105
$530$		0			0
$531$	−3330.00			−0.272146
$532$		0			0
$533$			11124.0i			0.904004i
$534$		0			0
$535$	924.000	+	168.000i	0.0746692	+	0.0135762i
$536$		0			0
$537$		−	5142.00i		−	0.413210i
$538$		0			0
$539$	23730.0			1.89633
$540$		0			0
$541$	−15970.0			−1.26914			−0.634569	−	0.772866i	$-0.718822\pi$
$541$	−15970.0			−1.26914			−0.634569	+	0.772866i	$0.718822\pi$
$542$		0			0
$543$		−	12018.0i		−	0.949801i
$544$		0			0
$545$	−740.000	+	4070.00i	−0.0581617	+	0.319889i
$546$		0			0
$547$			15524.0i			1.21345i	0.794911	+	0.606726i	$0.207518\pi$
$547$			15524.0i			1.21345i	−0.794911	+	0.606726i	$0.792482\pi$
$548$		0			0
$549$	−4950.00			−0.384810
$550$		0			0
$551$	−5184.00			−0.400809
$552$		0			0
$553$		−	1584.00i		−	0.121806i
$554$		0			0
$555$	1524.00	−	8382.00i	0.116559	−	0.641074i
$556$		0			0
$557$			6774.00i			0.515303i	0.966238	+	0.257651i	$0.0829486\pi$
$557$			6774.00i			0.515303i	−0.966238	+	0.257651i	$0.917051\pi$
$558$		0			0
$559$	15768.0			1.19305
$560$		0			0
$561$	4620.00			0.347694
$562$		0			0
$563$		−	10484.0i		−	0.784810i	−0.919793	−	0.392405i	$-0.871643\pi$
$563$		−	10484.0i		−	0.784810i	0.919793	−	0.392405i	$-0.128357\pi$
$564$		0			0
$565$	19206.0	+	3492.00i	1.43009	+	0.260017i
$566$		0			0
$567$		−	162.000i		−	0.0119989i
$568$		0			0
$569$	−23302.0			−1.71682			−0.858410	−	0.512964i	$-0.828547\pi$
$569$	−23302.0			−1.71682			−0.858410	+	0.512964i	$0.828547\pi$
$570$		0			0
$571$	21520.0			1.57720			0.788602	−	0.614903i	$-0.210805\pi$
$571$	21520.0			1.57720			0.788602	+	0.614903i	$0.210805\pi$
$572$		0			0
$573$		−	2052.00i		−	0.149605i
$574$		0			0
$575$	4400.00	−	11700.0i	0.319118	−	0.848563i
$576$		0			0
$577$		−	3856.00i		−	0.278210i	−0.990278	−	0.139105i	$-0.955577\pi$
$577$		−	3856.00i		−	0.278210i	0.990278	−	0.139105i	$-0.0444226\pi$
$578$		0			0
$579$	−13452.0			−0.965537
$580$		0			0
$581$	808.000			0.0576962
$582$		0			0
$583$			28140.0i			1.99904i
$584$		0			0
$585$	−5346.00	−	972.000i	−0.377829	−	0.0686962i
$586$		0			0
$587$			26796.0i			1.88414i	0.335418	+	0.942069i	$0.391122\pi$
$587$			26796.0i			1.88414i	−0.335418	+	0.942069i	$0.608878\pi$
$588$		0			0
$589$	4992.00			0.349222
$590$		0			0
$591$	−3174.00			−0.220915
$592$		0			0
$593$			9870.00i			0.683495i	0.939792	+	0.341747i	$0.111019\pi$
$593$			9870.00i			0.683495i	−0.939792	+	0.341747i	$0.888981\pi$
$594$		0			0
$595$	−88.0000	+	484.000i	−0.00606327	+	0.0333480i
$596$		0			0
$597$			3384.00i			0.231990i
$598$		0			0
$599$	−13296.0			−0.906945			−0.453472	−	0.891270i	$-0.649815\pi$
$599$	−13296.0			−0.906945			−0.453472	+	0.891270i	$0.649815\pi$
$600$		0			0
$601$	−9262.00			−0.628627			−0.314314	−	0.949319i	$-0.601774\pi$
$601$	−9262.00			−0.628627			−0.314314	+	0.949319i	$0.601774\pi$
$602$		0			0
$603$			6552.00i			0.442484i
$604$		0			0
$605$	−7138.00	+	39259.0i	−0.479671	+	2.63819i
$606$		0			0
$607$			5498.00i			0.367639i	0.982960	+	0.183820i	$0.0588462\pi$
$607$			5498.00i			0.367639i	−0.982960	+	0.183820i	$0.941154\pi$
$608$		0			0
$609$	−1296.00			−0.0862341
$610$		0			0
$611$	−17280.0			−1.14415
$612$		0			0
$613$		−	394.000i		−	0.0259600i	−0.999916	−	0.0129800i	$-0.995868\pi$
$613$		−	394.000i		−	0.0259600i	0.999916	−	0.0129800i	$-0.00413179\pi$
$614$		0			0
$615$	−6798.00	−	1236.00i	−0.445727	−	0.0810412i
$616$		0			0
$617$		−	7370.00i		−	0.480883i	−0.970664	−	0.240442i	$-0.922708\pi$
$617$		−	7370.00i		−	0.480883i	0.970664	−	0.240442i	$-0.0772923\pi$
$618$		0			0
$619$	−25316.0			−1.64384			−0.821919	−	0.569604i	$-0.807097\pi$
$619$	−25316.0			−1.64384			−0.821919	+	0.569604i	$0.807097\pi$
$620$		0			0
$621$	−2700.00			−0.174472
$622$		0			0
$623$		−	1876.00i		−	0.120643i
$624$		0			0
$625$	11753.0	+	10296.0i	0.752192	+	0.658944i
$626$		0			0
$627$			5040.00i			0.321018i
$628$		0			0
$629$	5588.00			0.354226
$630$		0			0
$631$	−2552.00			−0.161004			−0.0805020	−	0.996754i	$-0.525652\pi$
$631$	−2552.00			−0.161004			−0.0805020	+	0.996754i	$0.525652\pi$
$632$		0			0
$633$		−	2340.00i		−	0.146930i
$634$		0			0
$635$	−17930.0	−	3260.00i	−1.12052	−	0.203731i
$636$		0			0
$637$		−	18306.0i		−	1.13863i
$638$		0			0
$639$	−4860.00			−0.300874
$640$		0			0
$641$	8050.00			0.496031			0.248016	−	0.968756i	$-0.420222\pi$
$641$	8050.00			0.496031			0.248016	+	0.968756i	$0.420222\pi$
$642$		0			0
$643$		−	19368.0i		−	1.18787i	−0.804514	−	0.593934i	$-0.797574\pi$
$643$		−	19368.0i		−	1.18787i	0.804514	−	0.593934i	$-0.202426\pi$
$644$		0			0
$645$	−1752.00	+	9636.00i	−0.106953	+	0.588244i
$646$		0			0
$647$			9912.00i			0.602289i	0.953579	+	0.301144i	$0.0973686\pi$
$647$			9912.00i			0.602289i	−0.953579	+	0.301144i	$0.902631\pi$
$648$		0			0
$649$	25900.0			1.56651
$650$		0			0
$651$	1248.00			0.0751351
$652$		0			0
$653$		−	27986.0i		−	1.67715i	−0.544789	−	0.838573i	$-0.683390\pi$
$653$		−	27986.0i		−	1.67715i	0.544789	−	0.838573i	$-0.316610\pi$
$654$		0			0
$655$	1740.00	−	9570.00i	0.103798	−	0.570887i
$656$		0			0
$657$		−	5436.00i		−	0.322798i
$658$		0			0
$659$	−7562.00			−0.447001			−0.223501	−	0.974704i	$-0.571748\pi$
$659$	−7562.00			−0.447001			−0.223501	+	0.974704i	$0.571748\pi$
$660$		0			0
$661$	−20234.0			−1.19064			−0.595319	−	0.803490i	$-0.702974\pi$
$661$	−20234.0			−1.19064			−0.595319	+	0.803490i	$0.702974\pi$
$662$		0			0
$663$		−	3564.00i		−	0.208770i
$664$		0			0
$665$	−528.000	−	96.0000i	−0.0307894	−	0.00559808i
$666$		0			0
$667$			21600.0i			1.25391i
$668$		0			0
$669$	7710.00			0.445569
$670$		0			0
$671$	38500.0			2.21502
$672$		0			0
$673$			25332.0i			1.45093i	0.688258	+	0.725466i	$0.258376\pi$
$673$			25332.0i			1.45093i	−0.688258	+	0.725466i	$0.741624\pi$
$674$		0			0
$675$	1188.00	−	3159.00i	0.0677424	−	0.180133i
$676$		0			0
$677$		−	18358.0i		−	1.04218i	−0.853502	−	0.521090i	$-0.825526\pi$
$677$		−	18358.0i		−	1.04218i	0.853502	−	0.521090i	$-0.174474\pi$
$678$		0			0
$679$	−112.000			−0.00633014
$680$		0			0
$681$	8508.00			0.478748
$682$		0			0
$683$		−	124.000i		−	0.00694689i	−0.999994	−	0.00347345i	$-0.998894\pi$
$683$		−	124.000i		−	0.00694689i	0.999994	−	0.00347345i	$-0.00110563\pi$
$684$		0			0
$685$	10098.0	+	1836.00i	0.563248	+	0.102409i
$686$		0			0
$687$			1830.00i			0.101629i
$688$		0			0
$689$	21708.0			1.20030
$690$		0			0
$691$	−17456.0			−0.961009			−0.480505	−	0.876992i	$-0.659547\pi$
$691$	−17456.0			−0.961009			−0.480505	+	0.876992i	$0.659547\pi$
$692$		0			0
$693$			1260.00i			0.0690670i
$694$		0			0
$695$	−1192.00	+	6556.00i	−0.0650578	+	0.357818i
$696$		0			0
$697$		−	4532.00i		−	0.246287i
$698$		0			0
$699$	10542.0			0.570436
$700$		0			0
$701$	17816.0			0.959916			0.479958	−	0.877291i	$-0.340652\pi$
$701$	17816.0			0.959916			0.479958	+	0.877291i	$0.340652\pi$
$702$		0			0
$703$			6096.00i			0.327048i
$704$		0			0
$705$	1920.00	−	10560.0i	0.102569	−	0.564131i
$706$		0			0
$707$		−	1184.00i		−	0.0629829i
$708$		0			0
$709$	−14298.0			−0.757366			−0.378683	−	0.925526i	$-0.623623\pi$
$709$	−14298.0			−0.757366			−0.378683	+	0.925526i	$0.623623\pi$
$710$		0			0
$711$	−7128.00			−0.375979
$712$		0			0
$713$		−	20800.0i		−	1.09252i
$714$		0			0
$715$	41580.0	+	7560.00i	2.17483	+	0.395424i
$716$		0			0
$717$			5532.00i			0.288140i
$718$		0			0
$719$	−18440.0			−0.956462			−0.478231	−	0.878234i	$-0.658722\pi$
$719$	−18440.0			−0.956462			−0.478231	+	0.878234i	$0.658722\pi$
$720$		0			0
$721$	−124.000			−0.00640499
$722$		0			0
$723$		−	2946.00i		−	0.151539i
$724$		0			0
$725$	−25272.0	−	9504.00i	−1.29459	−	0.486855i
$726$		0			0
$727$			9666.00i			0.493112i	0.969129	+	0.246556i	$0.0792989\pi$
$727$			9666.00i			0.493112i	−0.969129	+	0.246556i	$0.920701\pi$
$728$		0			0
$729$	−729.000			−0.0370370
$730$		0			0
$731$	−6424.00			−0.325035
$732$		0			0
$733$			6094.00i			0.307076i	0.988143	+	0.153538i	$0.0490668\pi$
$733$			6094.00i			0.307076i	−0.988143	+	0.153538i	$0.950933\pi$
$734$		0			0
$735$	11187.0	+	2034.00i	0.561413	+	0.102075i
$736$		0			0
$737$		−	50960.0i		−	2.54700i
$738$		0			0
$739$	−9952.00			−0.495386			−0.247693	−	0.968839i	$-0.579672\pi$
$739$	−9952.00			−0.495386			−0.247693	+	0.968839i	$0.579672\pi$
$740$		0			0
$741$	3888.00			0.192752
$742$		0			0
$743$			2208.00i			0.109022i	0.998513	+	0.0545112i	$0.0173601\pi$
$743$			2208.00i			0.109022i	−0.998513	+	0.0545112i	$0.982640\pi$
$744$		0			0
$745$	−2152.00	+	11836.0i	−0.105830	+	0.582064i
$746$		0			0
$747$		−	3636.00i		−	0.178091i
$748$		0			0
$749$	−168.000			−0.00819571
$750$		0			0
$751$	9400.00			0.456739			0.228369	−	0.973575i	$-0.426661\pi$
$751$	9400.00			0.456739			0.228369	+	0.973575i	$0.426661\pi$
$752$		0			0
$753$			9522.00i			0.460825i
$754$		0			0
$755$	−64.0000	+	352.000i	−0.00308503	+	0.0169677i
$756$		0			0
$757$		−	22574.0i		−	1.08384i	−0.840430	−	0.541919i	$-0.817698\pi$
$757$		−	22574.0i		−	1.08384i	0.840430	−	0.541919i	$-0.182302\pi$
$758$		0			0
$759$	21000.0			1.00428
$760$		0			0
$761$	7278.00			0.346685			0.173343	−	0.984862i	$-0.444543\pi$
$761$	7278.00			0.346685			0.173343	+	0.984862i	$0.444543\pi$
$762$		0			0
$763$		−	740.000i		−	0.0351111i
$764$		0			0
$765$	2178.00	+	396.000i	0.102936	+	0.0187156i
$766$		0			0
$767$		−	19980.0i		−	0.940595i
$768$		0			0
$769$	16542.0			0.775708			0.387854	−	0.921721i	$-0.373216\pi$
$769$	16542.0			0.775708			0.387854	+	0.921721i	$0.373216\pi$
$770$		0			0
$771$	3582.00			0.167319
$772$		0			0
$773$			28926.0i			1.34592i	0.739679	+	0.672960i	$0.234977\pi$
$773$			28926.0i			1.34592i	−0.739679	+	0.672960i	$0.765023\pi$
$774$		0			0
$775$	24336.0	+	9152.00i	1.12797	+	0.424193i
$776$		0			0
$777$			1524.00i			0.0703645i
$778$		0			0
$779$	4944.00			0.227390
$780$		0			0
$781$	37800.0			1.73187
$782$		0			0
$783$			5832.00i			0.266180i
$784$		0			0
$785$	28094.0	+	5108.00i	1.27735	+	0.232245i
$786$		0			0
$787$		−	20608.0i		−	0.933413i	−0.884412	−	0.466706i	$-0.845440\pi$
$787$		−	20608.0i		−	0.933413i	0.884412	−	0.466706i	$-0.154560\pi$
$788$		0			0
$789$	−420.000			−0.0189511
$790$		0			0
$791$	−3492.00

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	960.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-3.00000i q^{3} +(-2.00000 + 11.0000i) q^{5} -2.00000i q^{7} -9.00000 q^{9} +O(q^{10})\)	\(q-3.00000i q^{3} +(-2.00000 + 11.0000i) q^{5} -2.00000i q^{7} -9.00000 q^{9} +70.0000 q^{11} -54.0000i q^{13} +(33.0000 + 6.00000i) q^{15} +22.0000i q^{17} -24.0000 q^{19} -6.00000 q^{21} +100.000i q^{23} +(-117.000 - 44.0000i) q^{25} +27.0000i q^{27} +216.000 q^{29} -208.000 q^{31} -210.000i q^{33} +(22.0000 + 4.00000i) q^{35} -254.000i q^{37} -162.000 q^{39} -206.000 q^{41} +292.000i q^{43} +(18.0000 - 99.0000i) q^{45} -320.000i q^{47} +339.000 q^{49} +66.0000 q^{51} +402.000i q^{53} +(-140.000 + 770.000i) q^{55} +72.0000i q^{57} +370.000 q^{59} +550.000 q^{61} +18.0000i q^{63} +(594.000 + 108.000i) q^{65} -728.000i q^{67} +300.000 q^{69} +540.000 q^{71} +604.000i q^{73} +(-132.000 + 351.000i) q^{75} -140.000i q^{77} +792.000 q^{79} +81.0000 q^{81} +404.000i q^{83} +(-242.000 - 44.0000i) q^{85} -648.000i q^{87} +938.000 q^{89} -108.000 q^{91} +624.000i q^{93} +(48.0000 - 264.000i) q^{95} -56.0000i q^{97} -630.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{5} - 18 q^{9}+O(q^{10}) \) 2 * q - 4 * q^5 - 18 * q^9	\( 2 q - 4 q^{5} - 18 q^{9} + 140 q^{11} + 66 q^{15} - 48 q^{19} - 12 q^{21} - 234 q^{25} + 432 q^{29} - 416 q^{31} + 44 q^{35} - 324 q^{39} - 412 q^{41} + 36 q^{45} + 678 q^{49} + 132 q^{51} - 280 q^{55} + 740 q^{59} + 1100 q^{61} + 1188 q^{65} + 600 q^{69} + 1080 q^{71} - 264 q^{75} + 1584 q^{79} + 162 q^{81} - 484 q^{85} + 1876 q^{89} - 216 q^{91} + 96 q^{95} - 1260 q^{99}+O(q^{100}) \) 2 * q - 4 * q^5 - 18 * q^9 + 140 * q^11 + 66 * q^15 - 48 * q^19 - 12 * q^21 - 234 * q^25 + 432 * q^29 - 416 * q^31 + 44 * q^35 - 324 * q^39 - 412 * q^41 + 36 * q^45 + 678 * q^49 + 132 * q^51 - 280 * q^55 + 740 * q^59 + 1100 * q^61 + 1188 * q^65 + 600 * q^69 + 1080 * q^71 - 264 * q^75 + 1584 * q^79 + 162 * q^81 - 484 * q^85 + 1876 * q^89 - 216 * q^91 + 96 * q^95 - 1260 * q^99

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