LMFDB - Embedded newform 1280.3.e.k.639.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,3,Mod(639,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1280.639");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1280.e (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:	$34.8774738381$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 640)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			639.1
Character	$\chi$	$=$	1280.639
Dual form			1280.3.e.k.639.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.06912i q^{3} +(4.37877 + 2.41379i) q^{5} -13.1670 q^{7} -7.55776 q^{9} +O(q^{10})$	$q-4.06912i q^{3} +(4.37877 + 2.41379i) q^{5} -13.1670 q^{7} -7.55776 q^{9} +11.8660 q^{11} +18.9902 q^{13} +(9.82201 - 17.8177i) q^{15} -5.69141i q^{17} +4.21143 q^{19} +53.5780i q^{21} +3.23248 q^{23} +(13.3472 + 21.1389i) q^{25} -5.86867i q^{27} +25.9809i q^{29} +42.1333i q^{31} -48.2841i q^{33} +(-57.6551 - 31.7823i) q^{35} -12.4126 q^{37} -77.2733i q^{39} +16.7097 q^{41} -71.8532i q^{43} +(-33.0937 - 18.2428i) q^{45} +18.2144 q^{47} +124.369 q^{49} -23.1590 q^{51} +92.6160 q^{53} +(51.9584 + 28.6420i) q^{55} -17.1368i q^{57} +17.2071 q^{59} -56.4010i q^{61} +99.5127 q^{63} +(83.1535 + 45.8383i) q^{65} +31.8333i q^{67} -13.1534i q^{69} -94.3680i q^{71} -123.087i q^{73} +(86.0166 - 54.3115i) q^{75} -156.239 q^{77} -17.9809i q^{79} -91.9001 q^{81} +5.00127i q^{83} +(13.7379 - 24.9214i) q^{85} +105.720 q^{87} -90.1166 q^{89} -250.043 q^{91} +171.446 q^{93} +(18.4409 + 10.1655i) q^{95} -129.160i q^{97} -89.6802 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 72 q^{9}+O(q^{10}) $ 24 * q - 72 * q^9	$ 24 q - 72 q^{9} - 16 q^{11} + 48 q^{19} - 24 q^{25} - 112 q^{35} - 80 q^{41} + 168 q^{49} - 576 q^{51} + 496 q^{59} + 32 q^{65} + 224 q^{75} + 184 q^{81} - 144 q^{89} - 864 q^{91} + 368 q^{99}+O(q^{100}) $ 24 * q - 72 * q^9 - 16 * q^11 + 48 * q^19 - 24 * q^25 - 112 * q^35 - 80 * q^41 + 168 * q^49 - 576 * q^51 + 496 * q^59 + 32 * q^65 + 224 * q^75 + 184 * q^81 - 144 * q^89 - 864 * q^91 + 368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$-1$	$-1$	$-1$

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
$3$		−	4.06912i		−	1.35637i	−0.734889	−	0.678187i	$-0.762766\pi$
$3$		−	4.06912i		−	1.35637i	0.734889	−	0.678187i	$-0.237234\pi$
$4$		0			0
$5$	4.37877	+	2.41379i	0.875754	+	0.482758i
$5$	4.37877	+	2.41379i	0.875754	+	0.482758i
$6$		0			0
$7$	−13.1670			−1.88099			−0.940497	−	0.339801i	$-0.889640\pi$
$7$	−13.1670			−1.88099			−0.940497	+	0.339801i	$0.889640\pi$
$8$		0			0
$9$	−7.55776			−0.839751
$10$		0			0
$11$	11.8660			1.07873			0.539363	−	0.842073i	$-0.318665\pi$
$11$	11.8660			1.07873			0.539363	+	0.842073i	$0.318665\pi$
$12$		0			0
$13$	18.9902			1.46078			0.730391	−	0.683029i	$-0.239338\pi$
$13$	18.9902			1.46078			0.730391	+	0.683029i	$0.239338\pi$
$14$		0			0
$15$	9.82201	−	17.8177i	0.654800	−	1.18785i
$16$		0			0
$17$		−	5.69141i		−	0.334789i	−0.985890	−	0.167394i	$-0.946465\pi$
$17$		−	5.69141i		−	0.334789i	0.985890	−	0.167394i	$-0.0535353\pi$
$18$		0			0
$19$	4.21143			0.221654			0.110827	−	0.993840i	$-0.464650\pi$
$19$	4.21143			0.221654			0.110827	+	0.993840i	$0.464650\pi$
$20$		0			0
$21$			53.5780i			2.55133i
$22$		0			0
$23$	3.23248			0.140543			0.0702714	−	0.997528i	$-0.477613\pi$
$23$	3.23248			0.140543			0.0702714	+	0.997528i	$0.477613\pi$
$24$		0			0
$25$	13.3472	+	21.1389i	0.533890	+	0.845554i
$26$		0			0
$27$		−	5.86867i		−	0.217358i
$28$		0			0
$29$			25.9809i			0.895895i	0.894060	+	0.447947i	$0.147845\pi$
$29$			25.9809i			0.895895i	−0.894060	+	0.447947i	$0.852155\pi$
$30$		0			0
$31$			42.1333i			1.35914i	0.733611	+	0.679570i	$0.237834\pi$
$31$			42.1333i			1.35914i	−0.733611	+	0.679570i	$0.762166\pi$
$32$		0			0
$33$		−	48.2841i		−	1.46316i
$34$		0			0
$35$	−57.6551	−	31.7823i	−1.64729	−	0.908065i
$36$		0			0
$37$	−12.4126			−0.335476			−0.167738	−	0.985832i	$-0.553646\pi$
$37$	−12.4126			−0.335476			−0.167738	+	0.985832i	$0.553646\pi$
$38$		0			0
$39$		−	77.2733i		−	1.98137i
$40$		0			0
$41$	16.7097			0.407553			0.203776	−	0.979017i	$-0.434678\pi$
$41$	16.7097			0.407553			0.203776	+	0.979017i	$0.434678\pi$
$42$		0			0
$43$		−	71.8532i		−	1.67101i	−0.549486	−	0.835503i	$-0.685177\pi$
$43$		−	71.8532i		−	1.67101i	0.549486	−	0.835503i	$-0.314823\pi$
$44$		0			0
$45$	−33.0937	−	18.2428i	−0.735415	−	0.405396i
$46$		0			0
$47$	18.2144			0.387540			0.193770	−	0.981047i	$-0.437928\pi$
$47$	18.2144			0.387540			0.193770	+	0.981047i	$0.437928\pi$
$48$		0			0
$49$	124.369			2.53814
$50$		0			0
$51$	−23.1590			−0.454099
$52$		0			0
$53$	92.6160			1.74747			0.873736	−	0.486401i	$-0.161691\pi$
$53$	92.6160			1.74747			0.873736	+	0.486401i	$0.161691\pi$
$54$		0			0
$55$	51.9584	+	28.6420i	0.944698	+	0.520763i
$56$		0			0
$57$		−	17.1368i		−	0.300646i
$58$		0			0
$59$	17.2071			0.291646			0.145823	−	0.989311i	$-0.453417\pi$
$59$	17.2071			0.291646			0.145823	+	0.989311i	$0.453417\pi$
$60$		0			0
$61$		−	56.4010i		−	0.924606i	−0.886722	−	0.462303i	$-0.847023\pi$
$61$		−	56.4010i		−	0.924606i	0.886722	−	0.462303i	$-0.152977\pi$
$62$		0			0
$63$	99.5127			1.57957
$64$		0			0
$65$	83.1535	+	45.8383i	1.27929	+	0.705204i
$66$		0			0
$67$			31.8333i			0.475125i	0.971372	+	0.237562i	$0.0763484\pi$
$67$			31.8333i			0.475125i	−0.971372	+	0.237562i	$0.923652\pi$
$68$		0			0
$69$		−	13.1534i		−	0.190629i
$70$		0			0
$71$		−	94.3680i		−	1.32913i	−0.747232	−	0.664563i	$-0.768618\pi$
$71$		−	94.3680i		−	1.32913i	0.747232	−	0.664563i	$-0.231382\pi$
$72$		0			0
$73$		−	123.087i		−	1.68612i	−0.537821	−	0.843059i	$-0.680752\pi$
$73$		−	123.087i		−	1.68612i	0.537821	−	0.843059i	$-0.319248\pi$
$74$		0			0
$75$	86.0166	−	54.3115i	1.14689	−	0.724154i
$76$		0			0
$77$	−156.239			−2.02908
$78$		0			0
$79$		−	17.9809i		−	0.227607i	−0.993503	−	0.113803i	$-0.963697\pi$
$79$		−	17.9809i		−	0.227607i	0.993503	−	0.113803i	$-0.0363034\pi$
$80$		0			0
$81$	−91.9001			−1.13457
$82$		0			0
$83$			5.00127i			0.0602563i	0.999546	+	0.0301282i	$0.00959154\pi$
$83$			5.00127i			0.0602563i	−0.999546	+	0.0301282i	$0.990408\pi$
$84$		0			0
$85$	13.7379	−	24.9214i	0.161622	−	0.293192i
$86$		0			0
$87$	105.720			1.21517
$88$		0			0
$89$	−90.1166			−1.01255			−0.506273	−	0.862373i	$-0.668977\pi$
$89$	−90.1166			−1.01255			−0.506273	+	0.862373i	$0.668977\pi$
$90$		0			0
$91$	−250.043			−2.74772
$92$		0			0
$93$	171.446			1.84350
$94$		0			0
$95$	18.4409	+	10.1655i	0.194115	+	0.107005i
$96$		0			0
$97$		−	129.160i		−	1.33154i	−0.746155	−	0.665772i	$-0.768102\pi$
$97$		−	129.160i		−	1.33154i	0.746155	−	0.665772i	$-0.231898\pi$
$98$		0			0
$99$	−89.6802			−0.905860
$100$		0			0
$101$			92.3238i			0.914097i	0.889442	+	0.457049i	$0.151093\pi$
$101$			92.3238i			0.914097i	−0.889442	+	0.457049i	$0.848907\pi$
$102$		0			0
$103$	21.4411			0.208166			0.104083	−	0.994569i	$-0.466809\pi$
$103$	21.4411			0.208166			0.104083	+	0.994569i	$0.466809\pi$
$104$		0			0
$105$	−129.326	+	234.606i	−1.23168	+	2.23434i
$106$		0			0
$107$		−	69.2720i		−	0.647402i	−0.946160	−	0.323701i	$-0.895073\pi$
$107$		−	69.2720i		−	0.647402i	0.946160	−	0.323701i	$-0.104927\pi$
$108$		0			0
$109$		−	96.4476i		−	0.884840i	−0.896808	−	0.442420i	$-0.854120\pi$
$109$		−	96.4476i		−	0.884840i	0.896808	−	0.442420i	$-0.145880\pi$
$110$		0			0
$111$			50.5085i			0.455032i
$112$		0			0
$113$			141.121i			1.24885i	0.781083	+	0.624427i	$0.214667\pi$
$113$			141.121i			1.24885i	−0.781083	+	0.624427i	$0.785333\pi$
$114$		0			0
$115$	14.1543	+	7.80253i	0.123081	+	0.0678481i
$116$		0			0
$117$	−143.523			−1.22669
$118$		0			0
$119$			74.9385i			0.629735i
$120$		0			0
$121$	19.8015			0.163649
$122$		0			0
$123$		−	67.9936i		−	0.552794i
$124$		0			0
$125$	7.41973	+	124.780i	0.0593578	+	0.998237i
$126$		0			0
$127$	74.8485			0.589359			0.294679	−	0.955596i	$-0.404787\pi$
$127$	74.8485			0.589359			0.294679	+	0.955596i	$0.404787\pi$
$128$		0			0
$129$	−292.380			−2.26651
$130$		0			0
$131$	−77.6065			−0.592416			−0.296208	−	0.955123i	$-0.595722\pi$
$131$	−77.6065			−0.592416			−0.296208	+	0.955123i	$0.595722\pi$
$132$		0			0
$133$	−55.4518			−0.416931
$134$		0			0
$135$	14.1657	−	25.6975i	0.104931	−	0.190352i
$136$		0			0
$137$			68.6265i			0.500923i	0.968127	+	0.250462i	$0.0805824\pi$
$137$			68.6265i			0.500923i	−0.968127	+	0.250462i	$0.919418\pi$
$138$		0			0
$139$	187.749			1.35071			0.675357	−	0.737491i	$-0.263990\pi$
$139$	187.749			1.35071			0.675357	+	0.737491i	$0.263990\pi$
$140$		0			0
$141$		−	74.1166i		−	0.525649i
$142$		0			0
$143$	225.337			1.57578
$144$		0			0
$145$	−62.7125	+	113.765i	−0.432500	+	0.784583i
$146$		0			0
$147$		−	506.072i		−	3.44267i
$148$		0			0
$149$		−	18.2838i		−	0.122710i	−0.998116	−	0.0613550i	$-0.980458\pi$
$149$		−	18.2838i		−	0.122710i	0.998116	−	0.0613550i	$-0.0195422\pi$
$150$		0			0
$151$		−	93.1971i		−	0.617199i	−0.951192	−	0.308600i	$-0.900140\pi$
$151$		−	93.1971i		−	0.617199i	0.951192	−	0.308600i	$-0.0998603\pi$
$152$		0			0
$153$			43.0143i			0.281139i
$154$		0			0
$155$	−101.701	+	184.492i	−0.656135	+	1.19027i
$156$		0			0
$157$	−179.990			−1.14643			−0.573215	−	0.819405i	$-0.694304\pi$
$157$	−179.990			−1.14643			−0.573215	+	0.819405i	$0.694304\pi$
$158$		0			0
$159$		−	376.866i		−	2.37023i
$160$		0			0
$161$	−42.5620			−0.264360
$162$		0			0
$163$			13.0565i			0.0801012i	0.999198	+	0.0400506i	$0.0127519\pi$
$163$			13.0565i			0.0801012i	−0.999198	+	0.0400506i	$0.987248\pi$
$164$		0			0
$165$	116.548	−	211.425i	0.706350	−	1.28136i
$166$		0			0
$167$	184.301			1.10360			0.551801	−	0.833976i	$-0.313941\pi$
$167$	184.301			1.10360			0.551801	+	0.833976i	$0.313941\pi$
$168$		0			0
$169$	191.626			1.13388
$170$		0			0
$171$	−31.8290			−0.186134
$172$		0			0
$173$	188.458			1.08935			0.544676	−	0.838647i	$-0.316653\pi$
$173$	188.458			1.08935			0.544676	+	0.838647i	$0.316653\pi$
$174$		0			0
$175$	−175.743	−	278.334i	−1.00424	−	1.59048i
$176$		0			0
$177$		−	70.0178i		−	0.395581i
$178$		0			0
$179$	−15.9076			−0.0888693			−0.0444346	−	0.999012i	$-0.514149\pi$
$179$	−15.9076			−0.0888693			−0.0444346	+	0.999012i	$0.514149\pi$
$180$		0			0
$181$		−	283.761i		−	1.56774i	−0.620923	−	0.783871i	$-0.713242\pi$
$181$		−	283.761i		−	1.56774i	0.620923	−	0.783871i	$-0.286758\pi$
$182$		0			0
$183$	−229.503			−1.25411
$184$		0			0
$185$	−54.3520	−	29.9615i	−0.293795	−	0.161954i
$186$		0			0
$187$		−	67.5341i		−	0.361145i
$188$		0			0
$189$			77.2725i			0.408849i
$190$		0			0
$191$			139.652i			0.731164i	0.930779	+	0.365582i	$0.119130\pi$
$191$			139.652i			0.731164i	−0.930779	+	0.365582i	$0.880870\pi$
$192$		0			0
$193$			93.9188i			0.486626i	0.969948	+	0.243313i	$0.0782342\pi$
$193$			93.9188i			0.486626i	−0.969948	+	0.243313i	$0.921766\pi$
$194$		0			0
$195$	186.522	−	338.362i	0.956521	−	1.73519i
$196$		0			0
$197$	−173.027			−0.878312			−0.439156	−	0.898411i	$-0.644722\pi$
$197$	−173.027			−0.878312			−0.439156	+	0.898411i	$0.644722\pi$
$198$		0			0
$199$			128.021i			0.643322i	0.946855	+	0.321661i	$0.104241\pi$
$199$			128.021i			0.643322i	−0.946855	+	0.321661i	$0.895759\pi$
$200$		0			0
$201$	129.534			0.644447
$202$		0			0
$203$		−	342.090i		−	1.68517i
$204$		0			0
$205$	73.1677	+	40.3336i	0.356916	+	0.196749i
$206$		0			0
$207$	−24.4303			−0.118021
$208$		0			0
$209$	49.9728			0.239104
$210$		0			0
$211$	232.573			1.10224			0.551121	−	0.834425i	$-0.314200\pi$
$211$	232.573			1.10224			0.551121	+	0.834425i	$0.314200\pi$
$212$		0			0
$213$	−383.995			−1.80279
$214$		0			0
$215$	173.439	−	314.629i	0.806691	−	1.46339i
$216$		0			0
$217$		−	554.768i		−	2.55653i
$218$		0			0
$219$	−500.855			−2.28701
$220$		0			0
$221$		−	108.081i		−	0.489053i
$222$		0			0
$223$	−224.980			−1.00888			−0.504440	−	0.863447i	$-0.668301\pi$
$223$	−224.980			−1.00888			−0.504440	+	0.863447i	$0.668301\pi$
$224$		0			0
$225$	−100.875	−	159.762i	−0.448334	−	0.710055i
$226$		0			0
$227$			414.743i			1.82706i	0.406768	+	0.913531i	$0.366656\pi$
$227$			414.743i			1.82706i	−0.406768	+	0.913531i	$0.633344\pi$
$228$		0			0
$229$			5.32126i			0.0232370i	0.999933	+	0.0116185i	$0.00369836\pi$
$229$			5.32126i			0.0232370i	−0.999933	+	0.0116185i	$0.996302\pi$
$230$		0			0
$231$			635.755i			2.75219i
$232$		0			0
$233$		−	110.466i		−	0.474103i	−0.971497	−	0.237052i	$-0.923819\pi$
$233$		−	110.466i		−	0.474103i	0.971497	−	0.237052i	$-0.0761811\pi$
$234$		0			0
$235$	79.7566	+	43.9657i	0.339390	+	0.187088i
$236$		0			0
$237$	−73.1667			−0.308720
$238$		0			0
$239$			259.917i			1.08752i	0.839241	+	0.543760i	$0.183000\pi$
$239$			259.917i			1.08752i	−0.839241	+	0.543760i	$0.817000\pi$
$240$		0			0
$241$	289.960			1.20315			0.601577	−	0.798815i	$-0.294539\pi$
$241$	289.960			1.20315			0.601577	+	0.798815i	$0.294539\pi$
$242$		0			0
$243$			321.135i			1.32154i
$244$		0			0
$245$	544.583	+	300.200i	2.22279	+	1.22531i
$246$		0			0
$247$	79.9758			0.323789
$248$		0			0
$249$	20.3508			0.0817301
$250$		0			0
$251$	−46.7550			−0.186275			−0.0931374	−	0.995653i	$-0.529690\pi$
$251$	−46.7550			−0.186275			−0.0931374	+	0.995653i	$0.529690\pi$
$252$		0			0
$253$	38.3566			0.151607
$254$		0			0
$255$	−101.408	−	55.9010i	−0.397679	−	0.219220i
$256$		0			0
$257$		−	450.871i		−	1.75436i	−0.480161	−	0.877181i	$-0.659422\pi$
$257$		−	450.871i		−	1.75436i	0.480161	−	0.877181i	$-0.340578\pi$
$258$		0			0
$259$	163.437			0.631029
$260$		0			0
$261$		−	196.358i		−	0.752328i
$262$		0			0
$263$	251.947			0.957975			0.478987	−	0.877822i	$-0.341004\pi$
$263$	251.947			0.957975			0.478987	+	0.877822i	$0.341004\pi$
$264$		0			0
$265$	405.544	+	223.556i	1.53035	+	0.843606i
$266$		0			0
$267$			366.696i			1.37339i
$268$		0			0
$269$			264.303i			0.982539i	0.871008	+	0.491269i	$0.163467\pi$
$269$			264.303i			0.982539i	−0.871008	+	0.491269i	$0.836533\pi$
$270$		0			0
$271$		−	64.4675i		−	0.237888i	−0.992901	−	0.118944i	$-0.962049\pi$
$271$		−	64.4675i		−	0.237888i	0.992901	−	0.118944i	$-0.0379508\pi$
$272$		0			0
$273$			1017.45i			3.72694i
$274$		0			0
$275$	158.378	+	250.833i	0.575920	+	0.912121i
$276$		0			0
$277$	126.188			0.455552			0.227776	−	0.973714i	$-0.426855\pi$
$277$	126.188			0.455552			0.227776	+	0.973714i	$0.426855\pi$
$278$		0			0
$279$		−	318.433i		−	1.14134i
$280$		0			0
$281$	70.1393			0.249606			0.124803	−	0.992182i	$-0.460170\pi$
$281$	70.1393			0.249606			0.124803	+	0.992182i	$0.460170\pi$
$282$		0			0
$283$			186.941i			0.660569i	0.943881	+	0.330284i	$0.107145\pi$
$283$			186.941i			0.660569i	−0.943881	+	0.330284i	$0.892855\pi$
$284$		0			0
$285$	41.3647	−	75.0383i	0.145139	−	0.263292i
$286$		0			0
$287$	−220.015			−0.766604
$288$		0			0
$289$	256.608			0.887917
$290$		0			0
$291$	−525.567			−1.80607
$292$		0			0
$293$	−96.9707			−0.330958			−0.165479	−	0.986213i	$-0.552917\pi$
$293$	−96.9707			−0.330958			−0.165479	+	0.986213i	$0.552917\pi$
$294$		0			0
$295$	75.3460	+	41.5343i	0.255410	+	0.140794i
$296$		0			0
$297$		−	69.6375i		−	0.234470i
$298$		0			0
$299$	61.3854			0.205302
$300$		0			0
$301$			946.089i			3.14315i
$302$		0			0
$303$	375.677			1.23986
$304$		0			0
$305$	136.140	−	246.967i	0.446361	−	0.809728i
$306$		0			0
$307$		−	144.959i		−	0.472178i	−0.971731	−	0.236089i	$-0.924134\pi$
$307$		−	144.959i		−	0.472178i	0.971731	−	0.236089i	$-0.0758657\pi$
$308$		0			0
$309$		−	87.2465i		−	0.282351i
$310$		0			0
$311$			448.311i			1.44151i	0.693187	+	0.720757i	$0.256206\pi$
$311$			448.311i			1.44151i	−0.693187	+	0.720757i	$0.743794\pi$
$312$		0			0
$313$			11.4488i			0.0365777i	0.999833	+	0.0182888i	$0.00582184\pi$
$313$			11.4488i			0.0365777i	−0.999833	+	0.0182888i	$0.994178\pi$
$314$		0			0
$315$	435.743	+	240.203i	1.38331	+	0.762548i
$316$		0			0
$317$	−70.4744			−0.222317			−0.111158	−	0.993803i	$-0.535456\pi$
$317$	−70.4744			−0.222317			−0.111158	+	0.993803i	$0.535456\pi$
$318$		0			0
$319$			308.289i			0.966425i
$320$		0			0
$321$	−281.876			−0.878119
$322$		0			0
$323$		−	23.9690i		−	0.0742074i
$324$		0			0
$325$	253.466	+	401.430i	0.779896	+	1.23517i
$326$		0			0
$327$	−392.457			−1.20017
$328$		0			0
$329$	−239.828			−0.728961
$330$		0			0
$331$	−182.783			−0.552215			−0.276108	−	0.961127i	$-0.589045\pi$
$331$	−182.783			−0.552215			−0.276108	+	0.961127i	$0.589045\pi$
$332$		0			0
$333$	93.8116			0.281717
$334$		0			0
$335$	−76.8390	+	139.391i	−0.229370	+	0.416092i
$336$		0			0
$337$			5.55871i			0.0164947i	0.999966	+	0.00824734i	$0.00262524\pi$
$337$			5.55871i			0.0164947i	−0.999966	+	0.00824734i	$0.997375\pi$
$338$		0			0
$339$	574.237			1.69391
$340$		0			0
$341$			499.953i			1.46614i
$342$		0			0
$343$	−992.379			−2.89323
$344$		0			0
$345$	31.7495	−	57.5956i	0.0920274	−	0.166944i
$346$		0			0
$347$			147.085i			0.423876i	0.977283	+	0.211938i	$0.0679775\pi$
$347$			147.085i			0.423876i	−0.977283	+	0.211938i	$0.932023\pi$
$348$		0			0
$349$			103.671i			0.297052i	0.988908	+	0.148526i	$0.0474529\pi$
$349$			103.671i			0.297052i	−0.988908	+	0.148526i	$0.952547\pi$
$350$		0			0
$351$		−	111.447i		−	0.317513i
$352$		0			0
$353$		−	359.607i		−	1.01872i	−0.860554	−	0.509359i	$-0.829883\pi$
$353$		−	359.607i		−	1.01872i	0.860554	−	0.509359i	$-0.170117\pi$
$354$		0			0
$355$	227.784	−	413.216i	0.641646	−	1.16399i
$356$		0			0
$357$	304.934			0.854157
$358$		0			0
$359$		−	338.693i		−	0.943434i	−0.881750	−	0.471717i	$-0.843634\pi$
$359$		−	338.693i		−	0.943434i	0.881750	−	0.471717i	$-0.156366\pi$
$360$		0			0
$361$	−343.264			−0.950869
$362$		0			0
$363$		−	80.5748i		−	0.221969i
$364$		0			0
$365$	297.105	−	538.968i	0.813987	−	1.47662i
$366$		0			0
$367$	−576.010			−1.56951			−0.784755	−	0.619806i	$-0.787211\pi$
$367$	−576.010			−1.56951			−0.784755	+	0.619806i	$0.787211\pi$
$368$		0			0
$369$	−126.288			−0.342243
$370$		0			0
$371$	−1219.47			−3.28698
$372$		0			0
$373$	−277.303			−0.743441			−0.371720	−	0.928345i	$-0.621232\pi$
$373$	−277.303			−0.743441			−0.371720	+	0.928345i	$0.621232\pi$
$374$		0			0
$375$	507.743	−	30.1918i	1.35398	−	0.0805114i
$376$		0			0
$377$			493.382i			1.30871i
$378$		0			0
$379$	713.788			1.88335			0.941673	−	0.336529i	$-0.109253\pi$
$379$	713.788			1.88335			0.941673	+	0.336529i	$0.109253\pi$
$380$		0			0
$381$		−	304.568i		−	0.799391i
$382$		0			0
$383$	530.147			1.38420			0.692098	−	0.721804i	$-0.256687\pi$
$383$	530.147			1.38420			0.692098	+	0.721804i	$0.256687\pi$
$384$		0			0
$385$	−684.134	−	377.128i	−1.77697	−	0.979553i
$386$		0			0
$387$			543.049i			1.40323i
$388$		0			0
$389$			436.114i			1.12111i	0.828116	+	0.560557i	$0.189413\pi$
$389$			436.114i			1.12111i	−0.828116	+	0.560557i	$0.810587\pi$
$390$		0			0
$391$		−	18.3974i		−	0.0470521i
$392$		0			0
$393$			315.790i			0.803537i
$394$		0			0
$395$	43.4022	−	78.7344i	0.109879	−	0.199328i
$396$		0			0
$397$	358.849			0.903903			0.451951	−	0.892043i	$-0.350728\pi$
$397$	358.849			0.903903			0.451951	+	0.892043i	$0.350728\pi$
$398$		0			0
$399$			225.640i			0.565514i
$400$		0			0
$401$	755.221			1.88335			0.941673	−	0.336530i	$-0.109253\pi$
$401$	755.221			1.88335			0.941673	+	0.336530i	$0.109253\pi$
$402$		0			0
$403$			800.119i			1.98541i
$404$		0			0
$405$	−402.409	−	221.828i	−0.993604	−	0.547722i
$406$		0			0
$407$	−147.288			−0.361887
$408$		0			0
$409$	299.332			0.731864			0.365932	−	0.930642i	$-0.380750\pi$
$409$	299.332			0.731864			0.365932	+	0.930642i	$0.380750\pi$
$410$		0			0
$411$	279.249			0.679439
$412$		0			0
$413$	−226.565			−0.548584
$414$		0			0
$415$	−12.0720	+	21.8994i	−0.0290892	+	0.0527697i
$416$		0			0
$417$		−	763.975i		−	1.83207i
$418$		0			0
$419$	196.562			0.469122			0.234561	−	0.972101i	$-0.424635\pi$
$419$	196.562			0.469122			0.234561	+	0.972101i	$0.424635\pi$
$420$		0			0
$421$			79.5657i			0.188992i	0.995525	+	0.0944961i	$0.0301240\pi$
$421$			79.5657i			0.188992i	−0.995525	+	0.0944961i	$0.969876\pi$
$422$		0			0
$423$	−137.660			−0.325437
$424$		0			0
$425$	120.310	−	75.9646i	0.283082	−	0.178740i
$426$		0			0
$427$			742.630i			1.73918i
$428$		0			0
$429$		−	916.924i		−	2.13735i
$430$		0			0
$431$			548.958i			1.27369i	0.770994	+	0.636843i	$0.219760\pi$
$431$			548.958i			1.27369i	−0.770994	+	0.636843i	$0.780240\pi$
$432$		0			0
$433$			216.610i			0.500254i	0.968213	+	0.250127i	$0.0804724\pi$
$433$			216.610i			0.500254i	−0.968213	+	0.250127i	$0.919528\pi$
$434$		0			0
$435$	462.922	+	255.185i	1.06419	+	0.586632i
$436$		0			0
$437$	13.6134			0.0311519
$438$		0			0
$439$			390.262i			0.888980i	0.895784	+	0.444490i	$0.146615\pi$
$439$			390.262i			0.888980i	−0.895784	+	0.444490i	$0.853385\pi$
$440$		0			0
$441$	−939.949			−2.13140
$442$		0			0
$443$		−	439.009i		−	0.990990i	−0.868611	−	0.495495i	$-0.834987\pi$
$443$		−	439.009i		−	0.990990i	0.868611	−	0.495495i	$-0.165013\pi$
$444$		0			0
$445$	−394.600	−	217.523i	−0.886741	−	0.488815i
$446$		0			0
$447$	−74.3989			−0.166441
$448$		0			0
$449$	413.298			0.920487			0.460243	−	0.887793i	$-0.347762\pi$
$449$	413.298			0.920487			0.460243	+	0.887793i	$0.347762\pi$
$450$		0			0
$451$	198.277			0.439637
$452$		0			0
$453$	−379.230			−0.837153
$454$		0			0
$455$	−1094.88	−	603.551i	−2.40633	−	1.32648i
$456$		0			0
$457$			329.444i			0.720884i	0.932782	+	0.360442i	$0.117374\pi$
$457$			329.444i			0.720884i	−0.932782	+	0.360442i	$0.882626\pi$
$458$		0			0
$459$	−33.4010			−0.0727690
$460$		0			0
$461$		−	642.646i		−	1.39403i	−0.717058	−	0.697013i	$-0.754512\pi$
$461$		−	642.646i		−	1.39403i	0.717058	−	0.697013i	$-0.245488\pi$
$462$		0			0
$463$	−485.233			−1.04802			−0.524010	−	0.851712i	$-0.675564\pi$
$463$	−485.233			−1.04802			−0.524010	+	0.851712i	$0.675564\pi$
$464$		0			0
$465$	750.721	+	413.834i	1.61445	+	0.889965i
$466$		0			0
$467$		−	487.671i		−	1.04426i	−0.852865	−	0.522131i	$-0.825137\pi$
$467$		−	487.671i		−	1.04426i	0.852865	−	0.522131i	$-0.174863\pi$
$468$		0			0
$469$		−	419.148i		−	0.893707i
$470$		0			0
$471$			732.399i			1.55499i
$472$		0			0
$473$		−	852.609i		−	1.80256i
$474$		0			0
$475$	56.2110	+	89.0249i	0.118339	+	0.187421i
$476$		0			0
$477$	−699.969			−1.46744
$478$		0			0
$479$		−	435.030i		−	0.908206i	−0.890949	−	0.454103i	$-0.849960\pi$
$479$		−	435.030i		−	0.908206i	0.890949	−	0.454103i	$-0.150040\pi$
$480$		0			0
$481$	−235.718			−0.490058
$482$		0			0
$483$			173.190i			0.358571i
$484$		0			0
$485$	311.765	−	565.561i	0.642814	−	1.16611i
$486$		0			0
$487$	−468.360			−0.961725			−0.480862	−	0.876796i	$-0.659676\pi$
$487$	−468.360			−0.961725			−0.480862	+	0.876796i	$0.659676\pi$
$488$		0			0
$489$	53.1284			0.108647
$490$		0			0
$491$	1.11827			0.00227753			0.00113877	−	0.999999i	$-0.499638\pi$
$491$	1.11827			0.00227753			0.00113877	+	0.999999i	$0.499638\pi$
$492$		0			0
$493$	147.868			0.299935
$494$		0			0
$495$	−392.689	−	216.469i	−0.793311	−	0.437311i
$496$		0			0
$497$			1242.54i			2.50008i
$498$		0			0
$499$	−316.648			−0.634565			−0.317283	−	0.948331i	$-0.602770\pi$
$499$	−316.648			−0.634565			−0.317283	+	0.948331i	$0.602770\pi$
$500$		0			0
$501$		−	749.945i		−	1.49690i
$502$		0			0
$503$	−549.860			−1.09316			−0.546580	−	0.837407i	$-0.684071\pi$
$503$	−549.860			−1.09316			−0.546580	+	0.837407i	$0.684071\pi$
$504$		0			0
$505$	−222.850	+	404.265i	−0.441288	+	0.800524i
$506$		0			0
$507$		−	779.751i		−	1.53797i
$508$		0			0
$509$		−	412.523i		−	0.810457i	−0.914215	−	0.405229i	$-0.867192\pi$
$509$		−	412.523i		−	0.810457i	0.914215	−	0.405229i	$-0.132808\pi$
$510$		0			0
$511$			1620.68i			3.17158i
$512$		0			0
$513$		−	24.7155i		−	0.0481784i
$514$		0			0
$515$	93.8857	+	51.7543i	0.182302	+	0.100494i
$516$		0			0
$517$	216.132			0.418049
$518$		0			0
$519$		−	766.858i		−	1.47757i
$520$		0			0
$521$	−2.92054			−0.00560564			−0.00280282	−	0.999996i	$-0.500892\pi$
$521$	−2.92054			−0.00560564			−0.00280282	+	0.999996i	$0.500892\pi$
$522$		0			0
$523$			582.440i			1.11365i	0.830629	+	0.556826i	$0.187981\pi$
$523$			582.440i			1.11365i	−0.830629	+	0.556826i	$0.812019\pi$
$524$		0			0
$525$	−1132.58	+	715.118i	−2.15729	+	1.36213i
$526$		0			0
$527$	239.798			0.455024
$528$		0			0
$529$	−518.551			−0.980248
$530$		0			0
$531$	−130.047			−0.244910
$532$		0			0
$533$	317.319			0.595346
$534$		0			0
$535$	167.208	−	303.326i	0.312538	−	0.566964i
$536$		0			0
$537$			64.7300i			0.120540i
$538$		0			0
$539$	1475.76			2.73796
$540$		0			0
$541$			365.336i			0.675298i	0.941272	+	0.337649i	$0.109632\pi$
$541$			365.336i			0.675298i	−0.941272	+	0.337649i	$0.890368\pi$
$542$		0			0
$543$	−1154.66			−2.12645
$544$		0			0
$545$	232.804	−	422.322i	0.427164	−	0.774902i
$546$		0			0
$547$			552.196i			1.00950i	0.863266	+	0.504750i	$0.168415\pi$
$547$			552.196i			1.00950i	−0.863266	+	0.504750i	$0.831585\pi$
$548$		0			0
$549$			426.265i			0.776439i
$550$		0			0
$551$			109.417i			0.198579i
$552$		0			0
$553$			236.754i			0.428127i
$554$		0			0
$555$	−121.917	+	221.165i	−0.219670	+	0.398496i
$556$		0			0
$557$	−620.508			−1.11402			−0.557009	−	0.830507i	$-0.688051\pi$
$557$	−620.508			−1.11402			−0.557009	+	0.830507i	$0.688051\pi$
$558$		0			0
$559$		−	1364.50i		−	2.44097i
$560$		0			0
$561$	−274.805			−0.489848
$562$		0			0
$563$			146.535i			0.260276i	0.991496	+	0.130138i	$0.0415420\pi$
$563$			146.535i			0.260276i	−0.991496	+	0.130138i	$0.958458\pi$
$564$		0			0
$565$	−340.635	+	617.934i	−0.602894	+	1.09369i
$566$		0			0
$567$	1210.05			2.13412
$568$		0			0
$569$	−661.697			−1.16291			−0.581456	−	0.813578i	$-0.697517\pi$
$569$	−661.697			−1.16291			−0.581456	+	0.813578i	$0.697517\pi$
$570$		0			0
$571$	−489.577			−0.857403			−0.428701	−	0.903446i	$-0.641029\pi$
$571$	−489.577			−0.857403			−0.428701	+	0.903446i	$0.641029\pi$
$572$		0			0
$573$	568.262			0.991731
$574$		0			0
$575$	43.1447	+	68.3310i	0.0750343	+	0.118836i
$576$		0			0
$577$			483.716i			0.838330i	0.907910	+	0.419165i	$0.137677\pi$
$577$			483.716i			0.838330i	−0.907910	+	0.419165i	$0.862323\pi$
$578$		0			0
$579$	382.167			0.660047
$580$		0			0
$581$		−	65.8516i		−	0.113342i
$582$		0			0
$583$	1098.98			1.88504
$584$		0			0
$585$	−628.454	−	346.434i	−1.07428	−	0.592196i
$586$		0			0
$587$		−	247.881i		−	0.422285i	−0.977455	−	0.211142i	$-0.932282\pi$
$587$		−	247.881i		−	0.422285i	0.977455	−	0.211142i	$-0.0677184\pi$
$588$		0			0
$589$			177.442i			0.301259i
$590$		0			0
$591$			704.070i			1.19132i
$592$		0			0
$593$		−	1025.38i		−	1.72914i	−0.502515	−	0.864568i	$-0.667592\pi$
$593$		−	1025.38i		−	1.72914i	0.502515	−	0.864568i	$-0.332408\pi$
$594$		0			0
$595$	−180.886	+	328.138i	−0.304010	+	0.551493i
$596$		0			0
$597$	520.933			0.872585
$598$		0			0
$599$		−	473.830i		−	0.791035i	−0.918458	−	0.395518i	$-0.870565\pi$
$599$		−	473.830i		−	0.791035i	0.918458	−	0.395518i	$-0.129435\pi$
$600$		0			0
$601$	289.650			0.481947			0.240973	−	0.970532i	$-0.422533\pi$
$601$	289.650			0.481947			0.240973	+	0.970532i	$0.422533\pi$
$602$		0			0
$603$		−	240.589i		−	0.398986i
$604$		0			0
$605$	86.7063	+	47.7967i	0.143316	+	0.0790028i
$606$		0			0
$607$	534.039			0.879801			0.439900	−	0.898047i	$-0.355014\pi$
$607$	534.039			0.879801			0.439900	+	0.898047i	$0.355014\pi$
$608$		0			0
$609$	−1392.01			−2.28572
$610$		0			0
$611$	345.894			0.566112
$612$		0			0
$613$	387.688			0.632443			0.316222	−	0.948685i	$-0.397586\pi$
$613$	387.688			0.632443			0.316222	+	0.948685i	$0.397586\pi$
$614$		0			0
$615$	164.122	−	297.728i	0.266866	−	0.484111i
$616$		0			0
$617$			1106.63i			1.79357i	0.442464	+	0.896786i	$0.354104\pi$
$617$			1106.63i			1.79357i	−0.442464	+	0.896786i	$0.645896\pi$
$618$		0			0
$619$	−626.880			−1.01273			−0.506365	−	0.862319i	$-0.669011\pi$
$619$	−626.880			−1.01273			−0.506365	+	0.862319i	$0.669011\pi$
$620$		0			0
$621$		−	18.9704i		−	0.0305481i
$622$		0			0
$623$	1186.56			1.90459
$624$		0			0
$625$	−268.702	+	564.291i	−0.429924	+	0.902865i
$626$		0			0
$627$		−	203.345i		−	0.324315i
$628$		0			0
$629$			70.6453i			0.112314i
$630$		0			0
$631$			820.328i			1.30004i	0.759915	+	0.650022i	$0.225240\pi$
$631$			820.328i			1.30004i	−0.759915	+	0.650022i	$0.774760\pi$
$632$		0			0
$633$		−	946.369i		−	1.49505i
$634$		0			0
$635$	327.744	+	180.669i	0.516133	+	0.284518i
$636$		0			0
$637$	2361.79			3.70767
$638$		0			0
$639$			713.210i			1.11613i
$640$		0			0
$641$	−364.752			−0.569036			−0.284518	−	0.958671i	$-0.591834\pi$
$641$	−364.752			−0.569036			−0.284518	+	0.958671i	$0.591834\pi$
$642$		0			0
$643$		−	43.8885i		−	0.0682558i	−0.999417	−	0.0341279i	$-0.989135\pi$
$643$		−	43.8885i		−	0.0682558i	0.999417	−	0.0341279i	$-0.0108654\pi$
$644$		0			0
$645$	−1280.26	−	705.743i	−1.98490	−	1.09417i
$646$		0			0
$647$	−444.166			−0.686500			−0.343250	−	0.939244i	$-0.611528\pi$
$647$	−444.166			−0.686500			−0.343250	+	0.939244i	$0.611528\pi$
$648$		0			0
$649$	204.179			0.314606
$650$		0			0
$651$	−2257.42			−3.46762
$652$		0			0
$653$	−135.461			−0.207444			−0.103722	−	0.994606i	$-0.533075\pi$
$653$	−135.461			−0.207444			−0.103722	+	0.994606i	$0.533075\pi$
$654$		0			0
$655$	−339.821	−	187.326i	−0.518810	−	0.285993i
$656$		0			0
$657$			930.259i			1.41592i
$658$		0			0
$659$	−989.748			−1.50189			−0.750947	−	0.660362i	$-0.770403\pi$
$659$	−989.748			−1.50189			−0.750947	+	0.660362i	$0.770403\pi$
$660$		0			0
$661$			833.884i			1.26155i	0.775966	+	0.630774i	$0.217263\pi$
$661$			833.884i			1.26155i	−0.775966	+	0.630774i	$0.782737\pi$
$662$		0			0
$663$	−439.794			−0.663339
$664$		0			0
$665$	−242.811	−	133.849i	−0.365129	−	0.201277i
$666$		0			0
$667$			83.9830i			0.125911i
$668$		0			0
$669$			915.473i			1.36842i
$670$		0			0
$671$		−	669.253i		−	0.997397i
$672$		0			0
$673$		−	1059.89i		−	1.57488i	−0.616392	−	0.787440i	$-0.711406\pi$
$673$		−	1059.89i		−	1.57488i	0.616392	−	0.787440i	$-0.288594\pi$
$674$		0			0
$675$	124.057	−	78.3305i	0.183788	−	0.116045i
$676$		0			0
$677$	−350.919			−0.518345			−0.259172	−	0.965831i	$-0.583450\pi$
$677$	−350.919			−0.518345			−0.259172	+	0.965831i	$0.583450\pi$
$678$		0			0
$679$			1700.64i			2.50463i
$680$		0			0
$681$	1687.64			2.47818
$682$		0			0
$683$			156.363i			0.228936i	0.993427	+	0.114468i	$0.0365164\pi$
$683$			156.363i			0.228936i	−0.993427	+	0.114468i	$0.963484\pi$
$684$		0			0
$685$	−165.650	+	300.499i	−0.241825	+	0.438685i
$686$		0			0
$687$	21.6529			0.0315180
$688$		0			0
$689$	1758.79			2.55267
$690$		0			0
$691$	316.269			0.457698			0.228849	−	0.973462i	$-0.426504\pi$
$691$	316.269			0.457698			0.228849	+	0.973462i	$0.426504\pi$
$692$		0			0
$693$	1180.82			1.70392
$694$		0			0
$695$	822.110	+	453.187i	1.18289	+	0.652068i
$696$		0			0
$697$		−	95.1014i		−	0.136444i
$698$		0			0
$699$	−449.500			−0.643062
$700$		0			0
$701$		−	240.924i		−	0.343686i	−0.985124	−	0.171843i	$-0.945028\pi$
$701$		−	240.924i		−	0.343686i	0.985124	−	0.171843i	$-0.0549723\pi$
$702$		0			0
$703$	−52.2750			−0.0743598
$704$		0			0
$705$	178.902	−	324.539i	0.253761	−	0.460339i
$706$		0			0
$707$		−	1215.62i		−	1.71941i
$708$		0			0
$709$		−	3.26471i		−	0.00460467i	−0.999997	−	0.00230234i	$-0.999267\pi$
$709$		−	3.26471i		−	0.00460467i	0.999997	−	0.00230234i	$-0.000732857\pi$
$710$		0			0
$711$			135.896i			0.191133i
$712$		0			0
$713$			136.195i			0.191017i
$714$		0			0
$715$	986.698	+	543.916i	1.38000	+	0.760722i
$716$		0			0
$717$	1057.64			1.47508
$718$		0			0
$719$		−	482.939i		−	0.671681i	−0.941919	−	0.335841i	$-0.890980\pi$
$719$		−	482.939i		−	0.671681i	0.941919	−	0.335841i	$-0.109020\pi$
$720$		0			0
$721$	−282.314			−0.391559
$722$		0			0
$723$		−	1179.88i		−	1.63193i
$724$		0			0
$725$	−549.207	+	346.774i	−0.757528	+	0.478309i
$726$		0			0
$727$	−427.522			−0.588063			−0.294031	−	0.955796i	$-0.594997\pi$
$727$	−427.522			−0.588063			−0.294031	+	0.955796i	$0.594997\pi$
$728$		0			0
$729$	479.636			0.657937
$730$		0			0
$731$	−408.946			−0.559433
$732$		0			0
$733$	−233.644			−0.318751			−0.159375	−	0.987218i	$-0.550948\pi$
$733$	−233.644			−0.318751			−0.159375	+	0.987218i	$0.550948\pi$
$734$		0			0
$735$	1221.55	−	2215.97i	1.66197	−	3.01493i
$736$		0			0
$737$			377.734i			0.512529i
$738$		0			0
$739$	741.074			1.00281			0.501403	−	0.865214i	$-0.332817\pi$
$739$	741.074			1.00281			0.501403	+	0.865214i	$0.332817\pi$
$740$		0			0
$741$		−	325.431i		−	0.439179i
$742$		0			0
$743$	817.762			1.10062			0.550311	−	0.834960i	$-0.314509\pi$
$743$	817.762			1.10062			0.550311	+	0.834960i	$0.314509\pi$
$744$		0			0
$745$	44.1332	−	80.0605i	0.0592392	−	0.107464i
$746$		0			0
$747$		−	37.7984i		−	0.0506003i
$748$		0			0
$749$			912.101i			1.21776i
$750$		0			0
$751$		−	29.5547i		−	0.0393538i	−0.999806	−	0.0196769i	$-0.993736\pi$
$751$		−	29.5547i		−	0.0393538i	0.999806	−	0.0196769i	$-0.00626376\pi$
$752$		0			0
$753$			190.252i			0.252658i
$754$		0			0
$755$	224.958	−	408.089i	0.297958	−	0.540515i
$756$		0			0
$757$	−112.461			−0.148562			−0.0742808	−	0.997237i	$-0.523666\pi$
$757$	−112.461			−0.148562			−0.0742808	+	0.997237i	$0.523666\pi$
$758$		0			0
$759$		−	156.078i		−	0.205636i
$760$		0			0
$761$	1343.39			1.76530			0.882649	−	0.470032i	$-0.155758\pi$
$761$	1343.39			1.76530			0.882649	+	0.470032i	$0.155758\pi$
$762$		0			0
$763$			1269.92i			1.66438i
$764$		0			0
$765$	−103.827	+	188.349i	−0.135722	+	0.246208i
$766$		0			0
$767$	326.766			0.426031
$768$		0			0
$769$	177.946			0.231400			0.115700	−	0.993284i	$-0.463089\pi$
$769$	177.946			0.231400			0.115700	+	0.993284i	$0.463089\pi$
$770$		0			0
$771$	−1834.65			−2.37957
$772$		0			0
$773$	−402.852			−0.521153			−0.260577	−	0.965453i	$-0.583913\pi$
$773$	−402.852			−0.521153			−0.260577	+	0.965453i	$0.583913\pi$
$774$		0			0
$775$	−890.650	+	562.364i	−1.14923	+	0.725631i
$776$		0			0
$777$		−	665.043i		−	0.855912i
$778$		0			0
$779$	70.3716			0.0903358
$780$		0			0
$781$		−	1119.77i		−	1.43376i
$782$		0			0
$783$	152.474			0.194730
$784$		0			0
$785$	−788.133	−	434.457i	−1.00399	−	0.553448i
$786$		0			0
$787$			1297.35i			1.64848i	0.566242	+	0.824239i	$0.308397\pi$
$787$			1297.35i			1.64848i	−0.566242	+	0.824239i	$0.691603\pi$
$788$		0			0
$789$		−	1025.20i		−	1.29937i
$790$		0			0
$791$		−	1858.13i		−	2.34909i
$792$		0			0
$793$		−	1071.06i		−	1.35065i
$794$		0			0
$795$	909.675	−	1650.21i	1.14424	−	2.07573i
$796$		0			0
$797$	−1075.80			−1.34982			−0.674909	−	0.737901i	$-0.735817\pi$
$797$	−1075.80			−1.34982			−0.674909	+	0.737901i	$0.735817\pi$
$798$		0			0
$799$		−	103.665i		−	0.129744i
$800$		0			0
$801$	681.079			0.850286
$802$		0			0
$803$		−	1460.54i		−	1.81886i
$804$		0			0
$805$	−186.369	−	102.736i	−0.231514	−	0.127622i
$806$		0			0
$807$	1075.48			1.33269
$808$		0			0
$809$	427.397			0.528302			0.264151	−	0.964481i	$-0.414908\pi$
$809$	427.397			0.528302			0.264151	+	0.964481i	$0.414908\pi$
$810$		0			0
$811$	−248.240			−0.306092			−0.153046	−	0.988219i	$-0.548908\pi$
$811$	−248.240			−0.306092			−0.153046	+	0.988219i	$0.548908\pi$
$812$		0			0
$813$	−262.326			−0.322664
$814$		0			0
$815$	−31.5156	+	57.1713i	−0.0386695	+	0.0701489i
$816$		0			0
$817$		−	302.605i		−	0.370386i
$818$		0			0
$819$	1889.76			2.30740
$820$		0			0
$821$			1183.60i			1.44166i	0.693114	+	0.720828i	$0.256238\pi$
$821$			1183.60i			1.44166i	−0.693114	+	0.720828i	$0.743762\pi$
$822$		0			0
$823$	−563.390			−0.684556			−0.342278	−	0.939599i	$-0.611198\pi$
$823$	−563.390			−0.684556			−0.342278	+	0.939599i	$0.611198\pi$
$824$		0			0
$825$	1020.67	−	644.460i	1.23718	−	0.781163i
$826$		0			0
$827$		−	2.84338i		−	0.00343818i	−0.999999	−	0.00171909i	$-0.999453\pi$
$827$		−	2.84338i		−	0.00343818i	0.999999	−	0.00171909i	$-0.000547204\pi$
$828$		0			0
$829$			936.883i			1.13014i	0.825044	+	0.565068i	$0.191150\pi$
$829$			936.883i			1.13014i	−0.825044	+	0.565068i	$0.808850\pi$
$830$		0			0
$831$		−	513.474i		−	0.617899i
$832$		0			0
$833$		−	707.834i		−	0.849740i
$834$		0			0
$835$	807.013	+	444.865i	0.966483	+	0.532772i
$836$		0			0
$837$	247.267			0.295420
$838$		0			0
$839$		−	704.436i		−	0.839614i	−0.907613	−	0.419807i	$-0.862098\pi$
$839$		−	704.436i		−	0.839614i	0.907613	−	0.419807i	$-0.137902\pi$
$840$		0			0
$841$	165.990			0.197373
$842$		0			0
$843$		−	285.405i		−	0.338559i
$844$		0			0
$845$	839.088	+	462.546i	0.993003	+	0.547391i
$846$		0			0
$847$	−260.726			−0.307823
$848$		0			0
$849$	760.686			0.895979
$850$		0			0
$851$	−40.1236			−0.0471488
$852$		0			0
$853$	−1343.46			−1.57498			−0.787489	−	0.616329i	$-0.788619\pi$
$853$	−1343.46			−1.57498			−0.787489	+	0.616329i	$0.788619\pi$
$854$		0			0
$855$	−139.372	−	76.8285i	−0.163008	−	0.0898579i
$856$		0			0
$857$			1308.07i			1.52634i	0.646200	+	0.763168i	$0.276357\pi$
$857$			1308.07i			1.52634i	−0.646200	+	0.763168i	$0.723643\pi$
$858$		0			0
$859$	−1045.40			−1.21699			−0.608496	−	0.793557i	$-0.708227\pi$
$859$	−1045.40			−1.21699			−0.608496	+	0.793557i	$0.708227\pi$
$860$		0			0
$861$			895.270i			1.03980i
$862$		0			0
$863$	−1666.99			−1.93162			−0.965812	−	0.259244i	$-0.916527\pi$
$863$	−1666.99			−1.93162			−0.965812	+	0.259244i	$0.916527\pi$
$864$		0			0
$865$	825.213	+	454.898i	0.954004	+	0.525893i
$866$		0			0
$867$		−	1044.17i		−	1.20435i
$868$		0			0
$869$		−	213.362i		−	0.245525i
$870$		0			0
$871$			604.521i			0.694053i
$872$		0			0
$873$			976.159i			1.11817i
$874$		0			0
$875$	−97.6953	−	1642.97i	−0.111652	−	1.87768i
$876$		0			0
$877$	300.145			0.342240			0.171120	−	0.985250i	$-0.445261\pi$
$877$	300.145			0.342240			0.171120	+	0.985250i	$0.445261\pi$
$878$		0			0
$879$			394.586i			0.448903i
$880$		0			0
$881$	−1008.86			−1.14513			−0.572565	−	0.819859i	$-0.694052\pi$
$881$	−1008.86			−1.14513			−0.572565	+	0.819859i	$0.694052\pi$
$882$		0			0
$883$		−	1135.89i		−	1.28640i	−0.765700	−	0.643198i	$-0.777607\pi$
$883$		−	1135.89i		−	1.28640i	0.765700	−	0.643198i	$-0.222393\pi$
$884$		0			0
$885$	169.008	−	306.592i	0.190970	−	0.346432i
$886$		0			0
$887$	306.685			0.345756			0.172878	−	0.984943i	$-0.444693\pi$
$887$	306.685			0.345756			0.172878	+	0.984943i	$0.444693\pi$
$888$		0			0
$889$	−985.528			−1.10858
$890$		0			0
$891$	−1090.49			−1.22389
$892$		0			0
$893$	76.7087			0.0859000
$894$		0			0
$895$	−69.6557	−	38.3976i	−0.0778276	−	0.0429024i
$896$		0			0
$897$		−	249.785i		−	0.278467i
$898$		0			0
$899$	−1094.66			−1.21765
$900$		0			0
$901$		−	527.115i		−	0.585034i
$902$		0			0
$903$	3849.75			4.26329
$904$		0			0
$905$	684.940	−	1242.53i	0.756840	−	1.37296i
$906$		0			0
$907$		−	1041.79i		−	1.14862i	−0.818639	−	0.574308i	$-0.805271\pi$
$907$		−	1041.79i		−	1.14862i	0.818639	−	0.574308i	$-0.194729\pi$
$908$		0			0
$909$		−	697.761i		−	0.767614i
$910$		0			0
$911$			1385.25i			1.52058i	0.649581	+	0.760292i	$0.274944\pi$
$911$			1385.25i			1.52058i	−0.649581	+	0.760292i	$0.725056\pi$
$912$		0			0
$913$			59.3450i			0.0650000i
$914$		0			0
$915$	−1004.94	−	553.971i	−1.09829	−	0.605433i
$916$		0			0
$917$	1021.84			1.11433
$918$		0			0
$919$		−	1188.83i		−	1.29361i	−0.762654	−	0.646807i	$-0.776104\pi$
$919$		−	1188.83i		−	1.29361i	0.762654	−	0.646807i	$-0.223896\pi$
$920$		0			0
$921$	−589.855			−0.640450
$922$		0			0
$923$		−	1792.06i		−	1.94156i
$924$		0			0
$925$	−165.674	−	262.389i	−0.179107	−	0.283664i
$926$		0			0
$927$	−162.047			−0.174808
$928$		0			0
$929$	−1066.31			−1.14781			−0.573903	−	0.818923i	$-0.694571\pi$
$929$	−1066.31			−1.14781			−0.573903	+	0.818923i	$0.694571\pi$
$930$		0			0
$931$	523.771			0.562590
$932$		0			0
$933$	1824.23			1.95523
$934$		0			0
$935$	163.013	−	295.716i	0.174346	−	0.316274i
$936$		0			0
$937$		−	874.346i		−	0.933134i	−0.884486	−	0.466567i	$-0.845491\pi$
$937$		−	874.346i		−	0.933134i	0.884486	−	0.466567i	$-0.154509\pi$
$938$		0			0
$939$	46.5866			0.0496130
$940$		0			0
$941$		−	230.693i		−	0.245158i	−0.992459	−	0.122579i	$-0.960884\pi$
$941$		−	230.693i		−	0.245158i	0.992459	−	0.122579i	$-0.0391164\pi$
$942$		0			0
$943$	54.0137			0.0572786
$944$		0			0
$945$	−186.520	+	338.359i	−0.197375	+	0.358051i
$946$		0			0
$947$			793.091i			0.837477i	0.908107	+	0.418738i	$0.137528\pi$
$947$			793.091i			0.837477i	−0.908107	+	0.418738i	$0.862472\pi$
$948$		0			0
$949$		−	2337.44i		−	2.46305i
$950$		0			0
$951$			286.769i			0.301544i
$952$		0			0
$953$			1327.00i			1.39244i	0.717826	+	0.696222i	$0.245137\pi$
$953$			1327.00i			1.39244i	−0.717826	+	0.696222i	$0.754863\pi$
$954$		0			0
$955$	−337.091	+	611.505i	−0.352975	+	0.640319i
$956$		0			0
$957$	1254.47			1.31083
$958$		0			0
$959$		−	903.602i		−	0.942233i
$960$		0			0
$961$	−814.218			−0.847261
$962$		0			0
$963$			523.541i			0.543656i
$964$		0			0
$965$	−226.700	+	411.249i	−0.234922	+	0.426164i
$966$		0			0
$967$	−1550.46			−1.60337			−0.801685	−	0.597747i	$-0.796063\pi$
$967$	−1550.46			−1.60337			−0.801685	+	0.597747i	$0.796063\pi$
$968$		0			0
$969$	−97.5327			−0.100653
$970$		0			0
$971$	463.446			0.477287			0.238644	−	0.971107i	$-0.423297\pi$
$971$	463.446			0.477287			0.238644	+	0.971107i	$0.423297\pi$
$972$		0			0
$973$	−2472.09			−2.54069
$974$		0			0
$975$	1633.47	−	1031.39i	1.67535	−	1.05783i
$976$		0			0
$977$			1283.45i			1.31367i	0.754036	+	0.656833i	$0.228105\pi$
$977$			1283.45i			1.31367i	−0.754036	+	0.656833i	$0.771895\pi$
$978$		0			0
$979$	−1069.32			−1.09226
$980$		0			0
$981$			728.927i			0.743045i
$982$		0			0
$983$	−83.7435			−0.0851918			−0.0425959	−	0.999092i	$-0.513563\pi$
$983$	−83.7435			−0.0851918			−0.0425959	+	0.999092i	$0.513563\pi$
$984$		0			0
$985$	−757.647	−	417.652i	−0.769185	−	0.424012i
$986$		0			0
$987$			975.890i			0.988744i
$988$		0			0
$989$		−	232.264i		−	0.234848i
$990$		0			0
$991$			195.650i			0.197427i	0.995116	+	0.0987133i	$0.0314727\pi$
$991$			195.650i			0.197427i	−0.995116	+	0.0987133i	$0.968527\pi$
$992$		0			0
$993$			743.767i			0.749010i
$994$		0			0
$995$	−309.016	+	560.575i	−0.310569	+	0.563392i
$996$		0			0
$997$	975.919			0.978856			0.489428	−	0.872044i	$-0.337206\pi$
$997$	975.919			0.978856			0.489428	+	0.872044i	$0.337206\pi$
$998$		0			0
$999$			72.8456i			0.0729185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.3.e.k.639.1		24
4.3	odd	2		1280.3.e.l.639.24		24
5.4	even	2	inner	1280.3.e.k.639.24		24
8.3	odd	2	inner	1280.3.e.k.639.23		24
8.5	even	2		1280.3.e.l.639.2		24
16.3	odd	4		640.3.h.b.639.6	yes	24
16.5	even	4		640.3.h.a.639.6	yes	24
16.11	odd	4		640.3.h.a.639.19	yes	24
16.13	even	4		640.3.h.b.639.19	yes	24
20.19	odd	2		1280.3.e.l.639.1		24
40.19	odd	2	inner	1280.3.e.k.639.2		24
40.29	even	2		1280.3.e.l.639.23		24
80.19	odd	4		640.3.h.b.639.20	yes	24
80.29	even	4		640.3.h.b.639.5	yes	24
80.59	odd	4		640.3.h.a.639.5	✓	24
80.69	even	4		640.3.h.a.639.20	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.3.h.a.639.5	✓	24	80.59	odd	4
640.3.h.a.639.6	yes	24	16.5	even	4
640.3.h.a.639.19	yes	24	16.11	odd	4
640.3.h.a.639.20	yes	24	80.69	even	4
640.3.h.b.639.5	yes	24	80.29	even	4
640.3.h.b.639.6	yes	24	16.3	odd	4
640.3.h.b.639.19	yes	24	16.13	even	4
640.3.h.b.639.20	yes	24	80.19	odd	4
1280.3.e.k.639.1		24	1.1	even	1	trivial
1280.3.e.k.639.2		24	40.19	odd	2	inner
1280.3.e.k.639.23		24	8.3	odd	2	inner
1280.3.e.k.639.24		24	5.4	even	2	inner
1280.3.e.l.639.1		24	20.19	odd	2
1280.3.e.l.639.2		24	8.5	even	2
1280.3.e.l.639.23		24	40.29	even	2
1280.3.e.l.639.24		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1280.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4.06912i q^{3} +(4.37877 + 2.41379i) q^{5} -13.1670 q^{7} -7.55776 q^{9} +O(q^{10})\)	\(q-4.06912i q^{3} +(4.37877 + 2.41379i) q^{5} -13.1670 q^{7} -7.55776 q^{9} +11.8660 q^{11} +18.9902 q^{13} +(9.82201 - 17.8177i) q^{15} -5.69141i q^{17} +4.21143 q^{19} +53.5780i q^{21} +3.23248 q^{23} +(13.3472 + 21.1389i) q^{25} -5.86867i q^{27} +25.9809i q^{29} +42.1333i q^{31} -48.2841i q^{33} +(-57.6551 - 31.7823i) q^{35} -12.4126 q^{37} -77.2733i q^{39} +16.7097 q^{41} -71.8532i q^{43} +(-33.0937 - 18.2428i) q^{45} +18.2144 q^{47} +124.369 q^{49} -23.1590 q^{51} +92.6160 q^{53} +(51.9584 + 28.6420i) q^{55} -17.1368i q^{57} +17.2071 q^{59} -56.4010i q^{61} +99.5127 q^{63} +(83.1535 + 45.8383i) q^{65} +31.8333i q^{67} -13.1534i q^{69} -94.3680i q^{71} -123.087i q^{73} +(86.0166 - 54.3115i) q^{75} -156.239 q^{77} -17.9809i q^{79} -91.9001 q^{81} +5.00127i q^{83} +(13.7379 - 24.9214i) q^{85} +105.720 q^{87} -90.1166 q^{89} -250.043 q^{91} +171.446 q^{93} +(18.4409 + 10.1655i) q^{95} -129.160i q^{97} -89.6802 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 72 q^{9}+O(q^{10}) \) 24 * q - 72 * q^9	\( 24 q - 72 q^{9} - 16 q^{11} + 48 q^{19} - 24 q^{25} - 112 q^{35} - 80 q^{41} + 168 q^{49} - 576 q^{51} + 496 q^{59} + 32 q^{65} + 224 q^{75} + 184 q^{81} - 144 q^{89} - 864 q^{91} + 368 q^{99}+O(q^{100}) \) 24 * q - 72 * q^9 - 16 * q^11 + 48 * q^19 - 24 * q^25 - 112 * q^35 - 80 * q^41 + 168 * q^49 - 576 * q^51 + 496 * q^59 + 32 * q^65 + 224 * q^75 + 184 * q^81 - 144 * q^89 - 864 * q^91 + 368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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