LMFDB - Embedded newform 560.6.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,6,Mod(1,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("560.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	560.a (trivial)

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:	yes
Analytic conductor:	$89.8149390953$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	560.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+3.00000 q^{3} -25.0000 q^{5} -49.0000 q^{7} -234.000 q^{9} +O(q^{10})$

$q+3.00000 q^{3} -25.0000 q^{5} -49.0000 q^{7} -234.000 q^{9} -405.000 q^{11} -391.000 q^{13} -75.0000 q^{15} +999.000 q^{17} -2342.00 q^{19} -147.000 q^{21} -2430.00 q^{23} +625.000 q^{25} -1431.00 q^{27} +8259.00 q^{29} -4016.00 q^{31} -1215.00 q^{33} +1225.00 q^{35} -7042.00 q^{37} -1173.00 q^{39} +3336.00 q^{41} +23518.0 q^{43} +5850.00 q^{45} -10317.0 q^{47} +2401.00 q^{49} +2997.00 q^{51} +3084.00 q^{53} +10125.0 q^{55} -7026.00 q^{57} +18816.0 q^{59} +21668.0 q^{61} +11466.0 q^{63} +9775.00 q^{65} -52124.0 q^{67} -7290.00 q^{69} +28560.0 q^{71} -70342.0 q^{73} +1875.00 q^{75} +19845.0 q^{77} -58823.0 q^{79} +52569.0 q^{81} -756.000 q^{83} -24975.0 q^{85} +24777.0 q^{87} +135384. q^{89} +19159.0 q^{91} -12048.0 q^{93} +58550.0 q^{95} +110435. q^{97} +94770.0 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

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
$3$	3.00000	0.192450	0.0962250	−	0.995360i	$-0.469323\pi$
$3$	3.00000	0.192450	0.0962250	+	0.995360i	$0.469323\pi$
$4$	0	0
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	0	0
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	0	0
$9$	−234.000	−0.962963
$10$	0	0
$11$	−405.000	−1.00919	−0.504595	−	0.863356i	$-0.668358\pi$
$11$	−405.000	−1.00919	−0.504595	+	0.863356i	$0.668358\pi$
$12$	0	0
$13$	−391.000	−0.641680	−0.320840	−	0.947133i	$-0.603965\pi$
$13$	−391.000	−0.641680	−0.320840	+	0.947133i	$0.603965\pi$
$14$	0	0
$15$	−75.0000	−0.0860663
$16$	0	0
$17$	999.000	0.838384	0.419192	−	0.907898i	$-0.362313\pi$
$17$	999.000	0.838384	0.419192	+	0.907898i	$0.362313\pi$
$18$	0	0
$19$	−2342.00	−1.48834	−0.744171	−	0.667989i	$-0.767155\pi$
$19$	−2342.00	−1.48834	−0.744171	+	0.667989i	$0.767155\pi$
$20$	0	0
$21$	−147.000	−0.0727393
$22$	0	0
$23$	−2430.00	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$23$	−2430.00	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	0	0
$27$	−1431.00	−0.377772
$28$	0	0
$29$	8259.00	1.82361	0.911806	−	0.410621i	$-0.134688\pi$
$29$	8259.00	1.82361	0.911806	+	0.410621i	$0.134688\pi$
$30$	0	0
$31$	−4016.00	−0.750567	−0.375284	−	0.926910i	$-0.622455\pi$
$31$	−4016.00	−0.750567	−0.375284	+	0.926910i	$0.622455\pi$
$32$	0	0
$33$	−1215.00	−0.194219
$34$	0	0
$35$	1225.00	0.169031
$36$	0	0
$37$	−7042.00	−0.845652	−0.422826	−	0.906211i	$-0.638962\pi$
$37$	−7042.00	−0.845652	−0.422826	+	0.906211i	$0.638962\pi$
$38$	0	0
$39$	−1173.00	−0.123491
$40$	0	0
$41$	3336.00	0.309932	0.154966	−	0.987920i	$-0.450473\pi$
$41$	3336.00	0.309932	0.154966	+	0.987920i	$0.450473\pi$
$42$	0	0
$43$	23518.0	1.93968	0.969838	−	0.243750i	$-0.0783776\pi$
$43$	23518.0	1.93968	0.969838	+	0.243750i	$0.0783776\pi$
$44$	0	0
$45$	5850.00	0.430650
$46$	0	0
$47$	−10317.0	−0.681254	−0.340627	−	0.940199i	$-0.610639\pi$
$47$	−10317.0	−0.681254	−0.340627	+	0.940199i	$0.610639\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	0	0
$51$	2997.00	0.161347
$52$	0	0
$53$	3084.00	0.150808	0.0754041	−	0.997153i	$-0.475975\pi$
$53$	3084.00	0.150808	0.0754041	+	0.997153i	$0.475975\pi$
$54$	0	0
$55$	10125.0	0.451324
$56$	0	0
$57$	−7026.00	−0.286432
$58$	0	0
$59$	18816.0	0.703716	0.351858	−	0.936053i	$-0.385550\pi$
$59$	18816.0	0.703716	0.351858	+	0.936053i	$0.385550\pi$
$60$	0	0
$61$	21668.0	0.745580	0.372790	−	0.927916i	$-0.378401\pi$
$61$	21668.0	0.745580	0.372790	+	0.927916i	$0.378401\pi$
$62$	0	0
$63$	11466.0	0.363966
$64$	0	0
$65$	9775.00	0.286968
$66$	0	0
$67$	−52124.0	−1.41857	−0.709285	−	0.704922i	$-0.750982\pi$
$67$	−52124.0	−1.41857	−0.709285	+	0.704922i	$0.750982\pi$
$68$	0	0
$69$	−7290.00	−0.184334
$70$	0	0
$71$	28560.0	0.672376	0.336188	−	0.941795i	$-0.390862\pi$
$71$	28560.0	0.672376	0.336188	+	0.941795i	$0.390862\pi$
$72$	0	0
$73$	−70342.0	−1.54493	−0.772463	−	0.635060i	$-0.780975\pi$
$73$	−70342.0	−1.54493	−0.772463	+	0.635060i	$0.780975\pi$
$74$	0	0
$75$	1875.00	0.0384900
$76$	0	0
$77$	19845.0	0.381438
$78$	0	0
$79$	−58823.0	−1.06042	−0.530212	−	0.847865i	$-0.677888\pi$
$79$	−58823.0	−1.06042	−0.530212	+	0.847865i	$0.677888\pi$
$80$	0	0
$81$	52569.0	0.890261
$82$	0	0
$83$	−756.000	−0.0120455	−0.00602277	−	0.999982i	$-0.501917\pi$
$83$	−756.000	−0.0120455	−0.00602277	+	0.999982i	$0.501917\pi$
$84$	0	0
$85$	−24975.0	−0.374937
$86$	0	0
$87$	24777.0	0.350954
$88$	0	0
$89$	135384.	1.81173	0.905863	−	0.423572i	$-0.139224\pi$
$89$	135384.	1.81173	0.905863	+	0.423572i	$0.139224\pi$
$90$	0	0
$91$	19159.0	0.242532
$92$	0	0
$93$	−12048.0	−0.144447
$94$	0	0
$95$	58550.0	0.665607
$96$	0	0
$97$	110435.	1.19173	0.595864	−	0.803085i	$-0.296810\pi$
$97$	110435.	1.19173	0.595864	+	0.803085i	$0.296810\pi$
$98$	0	0
$99$	94770.0	0.971813
$100$	0	0
$101$	33450.0	0.326282	0.163141	−	0.986603i	$-0.447838\pi$
$101$	33450.0	0.326282	0.163141	+	0.986603i	$0.447838\pi$
$102$	0	0
$103$	110311.	1.02453	0.512266	−	0.858827i	$-0.328806\pi$
$103$	110311.	1.02453	0.512266	+	0.858827i	$0.328806\pi$
$104$	0	0
$105$	3675.00	0.0325300
$106$	0	0
$107$	−35358.0	−0.298558	−0.149279	−	0.988795i	$-0.547695\pi$
$107$	−35358.0	−0.298558	−0.149279	+	0.988795i	$0.547695\pi$
$108$	0	0
$109$	−151183.	−1.21881	−0.609406	−	0.792858i	$-0.708592\pi$
$109$	−151183.	−1.21881	−0.609406	+	0.792858i	$0.708592\pi$
$110$	0	0
$111$	−21126.0	−0.162746
$112$	0	0
$113$	−133686.	−0.984895	−0.492447	−	0.870342i	$-0.663898\pi$
$113$	−133686.	−0.984895	−0.492447	+	0.870342i	$0.663898\pi$
$114$	0	0
$115$	60750.0	0.428353
$116$	0	0
$117$	91494.0	0.617914
$118$	0	0
$119$	−48951.0	−0.316880
$120$	0	0
$121$	2974.00	0.0184662
$122$	0	0
$123$	10008.0	0.0596464
$124$	0	0
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	283984.	1.56237	0.781186	−	0.624298i	$-0.214615\pi$
$127$	283984.	1.56237	0.781186	+	0.624298i	$0.214615\pi$
$128$	0	0
$129$	70554.0	0.373291
$130$	0	0
$131$	−261438.	−1.33104	−0.665519	−	0.746381i	$-0.731790\pi$
$131$	−261438.	−1.33104	−0.665519	+	0.746381i	$0.731790\pi$
$132$	0	0
$133$	114758.	0.562541
$134$	0	0
$135$	35775.0	0.168945
$136$	0	0
$137$	39672.0	0.180585	0.0902927	−	0.995915i	$-0.471220\pi$
$137$	39672.0	0.180585	0.0902927	+	0.995915i	$0.471220\pi$
$138$	0	0
$139$	182626.	0.801725	0.400863	−	0.916138i	$-0.368710\pi$
$139$	182626.	0.801725	0.400863	+	0.916138i	$0.368710\pi$
$140$	0	0
$141$	−30951.0	−0.131107
$142$	0	0
$143$	158355.	0.647577
$144$	0	0
$145$	−206475.	−0.815544
$146$	0	0
$147$	7203.00	0.0274929
$148$	0	0
$149$	−12078.0	−0.0445686	−0.0222843	−	0.999752i	$-0.507094\pi$
$149$	−12078.0	−0.0445686	−0.0222843	+	0.999752i	$0.507094\pi$
$150$	0	0
$151$	208417.	0.743859	0.371930	−	0.928261i	$-0.378696\pi$
$151$	208417.	0.743859	0.371930	+	0.928261i	$0.378696\pi$
$152$	0	0
$153$	−233766.	−0.807333
$154$	0	0
$155$	100400.	0.335664
$156$	0	0
$157$	364094.	1.17887	0.589433	−	0.807817i	$-0.299351\pi$
$157$	364094.	1.17887	0.589433	+	0.807817i	$0.299351\pi$
$158$	0	0
$159$	9252.00	0.0290230
$160$	0	0
$161$	119070.	0.362024
$162$	0	0
$163$	−626.000	−0.00184546	−0.000922731	−	1.00000i	$-0.500294\pi$
$163$	−626.000	−0.00184546	−0.000922731		1.00000i	$0.500294\pi$
$164$	0	0
$165$	30375.0	0.0868573
$166$	0	0
$167$	−445617.	−1.23643	−0.618216	−	0.786008i	$-0.712144\pi$
$167$	−445617.	−1.23643	−0.618216	+	0.786008i	$0.712144\pi$
$168$	0	0
$169$	−218412.	−0.588247
$170$	0	0
$171$	548028.	1.43322
$172$	0	0
$173$	643467.	1.63460	0.817299	−	0.576214i	$-0.195470\pi$
$173$	643467.	1.63460	0.817299	+	0.576214i	$0.195470\pi$
$174$	0	0
$175$	−30625.0	−0.0755929
$176$	0	0
$177$	56448.0	0.135430
$178$	0	0
$179$	−245148.	−0.571868	−0.285934	−	0.958249i	$-0.592304\pi$
$179$	−245148.	−0.571868	−0.285934	+	0.958249i	$0.592304\pi$
$180$	0	0
$181$	686180.	1.55683	0.778416	−	0.627749i	$-0.216024\pi$
$181$	686180.	1.55683	0.778416	+	0.627749i	$0.216024\pi$
$182$	0	0
$183$	65004.0	0.143487
$184$	0	0
$185$	176050.	0.378187
$186$	0	0
$187$	−404595.	−0.846090
$188$	0	0
$189$	70119.0	0.142785
$190$	0	0
$191$	527031.	1.04533	0.522664	−	0.852539i	$-0.324938\pi$
$191$	527031.	1.04533	0.522664	+	0.852539i	$0.324938\pi$
$192$	0	0
$193$	143216.	0.276757	0.138378	−	0.990379i	$-0.455811\pi$
$193$	143216.	0.276757	0.138378	+	0.990379i	$0.455811\pi$
$194$	0	0
$195$	29325.0	0.0552270
$196$	0	0
$197$	348468.	0.639731	0.319865	−	0.947463i	$-0.396362\pi$
$197$	348468.	0.639731	0.319865	+	0.947463i	$0.396362\pi$
$198$	0	0
$199$	−754520.	−1.35064	−0.675318	−	0.737527i	$-0.735993\pi$
$199$	−754520.	−1.35064	−0.675318	+	0.737527i	$0.735993\pi$
$200$	0	0
$201$	−156372.	−0.273004
$202$	0	0
$203$	−404691.	−0.689261
$204$	0	0
$205$	−83400.0	−0.138606
$206$	0	0
$207$	568620.	0.922351
$208$	0	0
$209$	948510.	1.50202
$210$	0	0
$211$	590749.	0.913475	0.456738	−	0.889601i	$-0.349018\pi$
$211$	590749.	0.913475	0.456738	+	0.889601i	$0.349018\pi$
$212$	0	0
$213$	85680.0	0.129399
$214$	0	0
$215$	−587950.	−0.867450
$216$	0	0
$217$	196784.	0.283688
$218$	0	0
$219$	−211026.	−0.297321
$220$	0	0
$221$	−390609.	−0.537974
$222$	0	0
$223$	396103.	0.533391	0.266696	−	0.963781i	$-0.414068\pi$
$223$	396103.	0.533391	0.266696	+	0.963781i	$0.414068\pi$
$224$	0	0
$225$	−146250.	−0.192593
$226$	0	0
$227$	−9537.00	−0.0122842	−0.00614210	−	0.999981i	$-0.501955\pi$
$227$	−9537.00	−0.0122842	−0.00614210	+	0.999981i	$0.501955\pi$
$228$	0	0
$229$	705056.	0.888454	0.444227	−	0.895914i	$-0.353478\pi$
$229$	705056.	0.888454	0.444227	+	0.895914i	$0.353478\pi$
$230$	0	0
$231$	59535.0	0.0734078
$232$	0	0
$233$	534216.	0.644655	0.322327	−	0.946628i	$-0.395535\pi$
$233$	534216.	0.644655	0.322327	+	0.946628i	$0.395535\pi$
$234$	0	0
$235$	257925.	0.304666
$236$	0	0
$237$	−176469.	−0.204079
$238$	0	0
$239$	901221.	1.02056	0.510278	−	0.860010i	$-0.329543\pi$
$239$	901221.	1.02056	0.510278	+	0.860010i	$0.329543\pi$
$240$	0	0
$241$	−952390.	−1.05626	−0.528132	−	0.849162i	$-0.677107\pi$
$241$	−952390.	−1.05626	−0.528132	+	0.849162i	$0.677107\pi$
$242$	0	0
$243$	505440.	0.549103
$244$	0	0
$245$	−60025.0	−0.0638877
$246$	0	0
$247$	915722.	0.955039
$248$	0	0
$249$	−2268.00	−0.00231817
$250$	0	0
$251$	1.10024e6	1.10231	0.551153	−	0.834404i	$-0.314188\pi$
$251$	1.10024e6	1.10231	0.551153	+	0.834404i	$0.314188\pi$
$252$	0	0
$253$	984150.	0.966629
$254$	0	0
$255$	−74925.0	−0.0721566
$256$	0	0
$257$	−1.08230e6	−1.02215	−0.511074	−	0.859537i	$-0.670752\pi$
$257$	−1.08230e6	−1.02215	−0.511074	+	0.859537i	$0.670752\pi$
$258$	0	0
$259$	345058.	0.319626
$260$	0	0
$261$	−1.93261e6	−1.75607
$262$	0	0
$263$	−82950.0	−0.0739481	−0.0369740	−	0.999316i	$-0.511772\pi$
$263$	−82950.0	−0.0739481	−0.0369740	+	0.999316i	$0.511772\pi$
$264$	0	0
$265$	−77100.0	−0.0674434
$266$	0	0
$267$	406152.	0.348667
$268$	0	0
$269$	−633822.	−0.534056	−0.267028	−	0.963689i	$-0.586042\pi$
$269$	−633822.	−0.534056	−0.267028	+	0.963689i	$0.586042\pi$
$270$	0	0
$271$	278956.	0.230734	0.115367	−	0.993323i	$-0.463196\pi$
$271$	278956.	0.230734	0.115367	+	0.993323i	$0.463196\pi$
$272$	0	0
$273$	57477.0	0.0466753
$274$	0	0
$275$	−253125.	−0.201838
$276$	0	0
$277$	2.17523e6	1.70336	0.851679	−	0.524064i	$-0.175585\pi$
$277$	2.17523e6	1.70336	0.851679	+	0.524064i	$0.175585\pi$
$278$	0	0
$279$	939744.	0.722768
$280$	0	0
$281$	−692901.	−0.523486	−0.261743	−	0.965138i	$-0.584297\pi$
$281$	−692901.	−0.523486	−0.261743	+	0.965138i	$0.584297\pi$
$282$	0	0
$283$	−1.04021e6	−0.772065	−0.386032	−	0.922485i	$-0.626155\pi$
$283$	−1.04021e6	−0.772065	−0.386032	+	0.922485i	$0.626155\pi$
$284$	0	0
$285$	175650.	0.128096
$286$	0	0
$287$	−163464.	−0.117143
$288$	0	0
$289$	−421856.	−0.297112
$290$	0	0
$291$	331305.	0.229348
$292$	0	0
$293$	−1.08565e6	−0.738789	−0.369394	−	0.929273i	$-0.620435\pi$
$293$	−1.08565e6	−0.738789	−0.369394	+	0.929273i	$0.620435\pi$
$294$	0	0
$295$	−470400.	−0.314711
$296$	0	0
$297$	579555.	0.381244
$298$	0	0
$299$	950130.	0.614618
$300$	0	0
$301$	−1.15238e6	−0.733129
$302$	0	0
$303$	100350.	0.0627929
$304$	0	0
$305$	−541700.	−0.333434
$306$	0	0
$307$	−1463.00	−0.000885928 0	−0.000442964	−	1.00000i	$-0.500141\pi$
$307$	−1463.00	−0.000885928 0	−0.000442964		1.00000i	$0.500141\pi$
$308$	0	0
$309$	330933.	0.197171
$310$	0	0
$311$	−3.11977e6	−1.82903	−0.914515	−	0.404551i	$-0.867428\pi$
$311$	−3.11977e6	−1.82903	−0.914515	+	0.404551i	$0.867428\pi$
$312$	0	0
$313$	831425.	0.479692	0.239846	−	0.970811i	$-0.422903\pi$
$313$	831425.	0.479692	0.239846	+	0.970811i	$0.422903\pi$
$314$	0	0
$315$	−286650.	−0.162770
$316$	0	0
$317$	−1.25851e6	−0.703408	−0.351704	−	0.936111i	$-0.614398\pi$
$317$	−1.25851e6	−0.703408	−0.351704	+	0.936111i	$0.614398\pi$
$318$	0	0
$319$	−3.34489e6	−1.84037
$320$	0	0
$321$	−106074.	−0.0574575
$322$	0	0
$323$	−2.33966e6	−1.24780
$324$	0	0
$325$	−244375.	−0.128336
$326$	0	0
$327$	−453549.	−0.234560
$328$	0	0
$329$	505533.	0.257490
$330$	0	0
$331$	2.30465e6	1.15621	0.578103	−	0.815964i	$-0.303793\pi$
$331$	2.30465e6	1.15621	0.578103	+	0.815964i	$0.303793\pi$
$332$	0	0
$333$	1.64783e6	0.814332
$334$	0	0
$335$	1.30310e6	0.634404
$336$	0	0
$337$	769166.	0.368931	0.184466	−	0.982839i	$-0.440945\pi$
$337$	769166.	0.368931	0.184466	+	0.982839i	$0.440945\pi$
$338$	0	0
$339$	−401058.	−0.189543
$340$	0	0
$341$	1.62648e6	0.757465
$342$	0	0
$343$	−117649.	−0.0539949
$344$	0	0
$345$	182250.	0.0824365
$346$	0	0
$347$	−382074.	−0.170343	−0.0851714	−	0.996366i	$-0.527144\pi$
$347$	−382074.	−0.170343	−0.0851714	+	0.996366i	$0.527144\pi$
$348$	0	0
$349$	−3.88710e6	−1.70829	−0.854146	−	0.520034i	$-0.825919\pi$
$349$	−3.88710e6	−1.70829	−0.854146	+	0.520034i	$0.825919\pi$
$350$	0	0
$351$	559521.	0.242409
$352$	0	0
$353$	−366453.	−0.156524	−0.0782621	−	0.996933i	$-0.524937\pi$
$353$	−366453.	−0.156524	−0.0782621	+	0.996933i	$0.524937\pi$
$354$	0	0
$355$	−714000.	−0.300696
$356$	0	0
$357$	−146853.	−0.0609835
$358$	0	0
$359$	3.14858e6	1.28937	0.644687	−	0.764446i	$-0.276988\pi$
$359$	3.14858e6	1.28937	0.644687	+	0.764446i	$0.276988\pi$
$360$	0	0
$361$	3.00887e6	1.21516
$362$	0	0
$363$	8922.00	0.00355382
$364$	0	0
$365$	1.75855e6	0.690912
$366$	0	0
$367$	−2.13740e6	−0.828362	−0.414181	−	0.910195i	$-0.635932\pi$
$367$	−2.13740e6	−0.828362	−0.414181	+	0.910195i	$0.635932\pi$
$368$	0	0
$369$	−780624.	−0.298453
$370$	0	0
$371$	−151116.	−0.0570001
$372$	0	0
$373$	−205624.	−0.0765247	−0.0382624	−	0.999268i	$-0.512182\pi$
$373$	−205624.	−0.0765247	−0.0382624	+	0.999268i	$0.512182\pi$
$374$	0	0
$375$	−46875.0	−0.0172133
$376$	0	0
$377$	−3.22927e6	−1.17018
$378$	0	0
$379$	−3.50536e6	−1.25353	−0.626766	−	0.779208i	$-0.715622\pi$
$379$	−3.50536e6	−1.25353	−0.626766	+	0.779208i	$0.715622\pi$
$380$	0	0
$381$	851952.	0.300679
$382$	0	0
$383$	−1.12904e6	−0.393291	−0.196645	−	0.980475i	$-0.563005\pi$
$383$	−1.12904e6	−0.393291	−0.196645	+	0.980475i	$0.563005\pi$
$384$	0	0
$385$	−496125.	−0.170584
$386$	0	0
$387$	−5.50321e6	−1.86784
$388$	0	0
$389$	−1.20003e6	−0.402084	−0.201042	−	0.979583i	$-0.564433\pi$
$389$	−1.20003e6	−0.402084	−0.201042	+	0.979583i	$0.564433\pi$
$390$	0	0
$391$	−2.42757e6	−0.803026
$392$	0	0
$393$	−784314.	−0.256158
$394$	0	0
$395$	1.47058e6	0.474236
$396$	0	0
$397$	−4.41836e6	−1.40697	−0.703486	−	0.710709i	$-0.748374\pi$
$397$	−4.41836e6	−1.40697	−0.703486	+	0.710709i	$0.748374\pi$
$398$	0	0
$399$	344274.	0.108261
$400$	0	0
$401$	−3.13278e6	−0.972903	−0.486451	−	0.873708i	$-0.661709\pi$
$401$	−3.13278e6	−0.972903	−0.486451	+	0.873708i	$0.661709\pi$
$402$	0	0
$403$	1.57026e6	0.481624
$404$	0	0
$405$	−1.31422e6	−0.398137
$406$	0	0
$407$	2.85201e6	0.853424
$408$	0	0
$409$	861494.	0.254650	0.127325	−	0.991861i	$-0.459361\pi$
$409$	861494.	0.254650	0.127325	+	0.991861i	$0.459361\pi$
$410$	0	0
$411$	119016.	0.0347537
$412$	0	0
$413$	−921984.	−0.265980
$414$	0	0
$415$	18900.0	0.00538693
$416$	0	0
$417$	547878.	0.154292
$418$	0	0
$419$	−4.65796e6	−1.29617	−0.648083	−	0.761570i	$-0.724429\pi$
$419$	−4.65796e6	−1.29617	−0.648083	+	0.761570i	$0.724429\pi$
$420$	0	0
$421$	6.99894e6	1.92454	0.962271	−	0.272093i	$-0.0877159\pi$
$421$	6.99894e6	1.92454	0.962271	+	0.272093i	$0.0877159\pi$
$422$	0	0
$423$	2.41418e6	0.656022
$424$	0	0
$425$	624375.	0.167677
$426$	0	0
$427$	−1.06173e6	−0.281803
$428$	0	0
$429$	475065.	0.124626
$430$	0	0
$431$	227091.	0.0588853	0.0294426	−	0.999566i	$-0.490627\pi$
$431$	227091.	0.0588853	0.0294426	+	0.999566i	$0.490627\pi$
$432$	0	0
$433$	−7.09613e6	−1.81887	−0.909435	−	0.415846i	$-0.863485\pi$
$433$	−7.09613e6	−1.81887	−0.909435	+	0.415846i	$0.863485\pi$
$434$	0	0
$435$	−619425.	−0.156952
$436$	0	0
$437$	5.69106e6	1.42557
$438$	0	0
$439$	−593258.	−0.146920	−0.0734602	−	0.997298i	$-0.523404\pi$
$439$	−593258.	−0.146920	−0.0734602	+	0.997298i	$0.523404\pi$
$440$	0	0
$441$	−561834.	−0.137566
$442$	0	0
$443$	3.27692e6	0.793334	0.396667	−	0.917963i	$-0.370167\pi$
$443$	3.27692e6	0.793334	0.396667	+	0.917963i	$0.370167\pi$
$444$	0	0
$445$	−3.38460e6	−0.810228
$446$	0	0
$447$	−36234.0	−0.00857724
$448$	0	0
$449$	−4.32930e6	−1.01345	−0.506724	−	0.862108i	$-0.669144\pi$
$449$	−4.32930e6	−1.01345	−0.506724	+	0.862108i	$0.669144\pi$
$450$	0	0
$451$	−1.35108e6	−0.312781
$452$	0	0
$453$	625251.	0.143156
$454$	0	0
$455$	−478975.	−0.108464
$456$	0	0
$457$	−4.91638e6	−1.10117	−0.550586	−	0.834779i	$-0.685596\pi$
$457$	−4.91638e6	−1.10117	−0.550586	+	0.834779i	$0.685596\pi$
$458$	0	0
$459$	−1.42957e6	−0.316718
$460$	0	0
$461$	7.02919e6	1.54047	0.770235	−	0.637761i	$-0.220139\pi$
$461$	7.02919e6	1.54047	0.770235	+	0.637761i	$0.220139\pi$
$462$	0	0
$463$	−2.88559e6	−0.625579	−0.312789	−	0.949823i	$-0.601263\pi$
$463$	−2.88559e6	−0.625579	−0.312789	+	0.949823i	$0.601263\pi$
$464$	0	0
$465$	301200.	0.0645985
$466$	0	0
$467$	6.00583e6	1.27433	0.637163	−	0.770729i	$-0.280108\pi$
$467$	6.00583e6	1.27433	0.637163	+	0.770729i	$0.280108\pi$
$468$	0	0
$469$	2.55408e6	0.536169
$470$	0	0
$471$	1.09228e6	0.226873
$472$	0	0
$473$	−9.52479e6	−1.95750
$474$	0	0
$475$	−1.46375e6	−0.297669
$476$	0	0
$477$	−721656.	−0.145223
$478$	0	0
$479$	−941094.	−0.187411	−0.0937053	−	0.995600i	$-0.529871\pi$
$479$	−941094.	−0.187411	−0.0937053	+	0.995600i	$0.529871\pi$
$480$	0	0
$481$	2.75342e6	0.542638
$482$	0	0
$483$	357210.	0.0696716
$484$	0	0
$485$	−2.76087e6	−0.532957
$486$	0	0
$487$	−1.91121e6	−0.365162	−0.182581	−	0.983191i	$-0.558445\pi$
$487$	−1.91121e6	−0.365162	−0.182581	+	0.983191i	$0.558445\pi$
$488$	0	0
$489$	−1878.00	−0.000355160 0
$490$	0	0
$491$	−3.95490e6	−0.740342	−0.370171	−	0.928964i	$-0.620701\pi$
$491$	−3.95490e6	−0.740342	−0.370171	+	0.928964i	$0.620701\pi$
$492$	0	0
$493$	8.25074e6	1.52889
$494$	0	0
$495$	−2.36925e6	−0.434608
$496$	0	0
$497$	−1.39944e6	−0.254134
$498$	0	0
$499$	−7.09708e6	−1.27593	−0.637967	−	0.770063i	$-0.720225\pi$
$499$	−7.09708e6	−1.27593	−0.637967	+	0.770063i	$0.720225\pi$
$500$	0	0
$501$	−1.33685e6	−0.237952
$502$	0	0
$503$	9.15982e6	1.61424	0.807118	−	0.590390i	$-0.201026\pi$
$503$	9.15982e6	1.61424	0.807118	+	0.590390i	$0.201026\pi$
$504$	0	0
$505$	−836250.	−0.145918
$506$	0	0
$507$	−655236.	−0.113208
$508$	0	0
$509$	−9.42509e6	−1.61247	−0.806234	−	0.591596i	$-0.798498\pi$
$509$	−9.42509e6	−1.61247	−0.806234	+	0.591596i	$0.798498\pi$
$510$	0	0
$511$	3.44676e6	0.583927
$512$	0	0
$513$	3.35140e6	0.562255
$514$	0	0
$515$	−2.75778e6	−0.458185
$516$	0	0
$517$	4.17838e6	0.687515
$518$	0	0
$519$	1.93040e6	0.314579
$520$	0	0
$521$	−6.18917e6	−0.998938	−0.499469	−	0.866332i	$-0.666471\pi$
$521$	−6.18917e6	−0.998938	−0.499469	+	0.866332i	$0.666471\pi$
$522$	0	0
$523$	3.81497e6	0.609870	0.304935	−	0.952373i	$-0.401365\pi$
$523$	3.81497e6	0.609870	0.304935	+	0.952373i	$0.401365\pi$
$524$	0	0
$525$	−91875.0	−0.0145479
$526$	0	0
$527$	−4.01198e6	−0.629264
$528$	0	0
$529$	−531443.	−0.0825691
$530$	0	0
$531$	−4.40294e6	−0.677652
$532$	0	0
$533$	−1.30438e6	−0.198877
$534$	0	0
$535$	883950.	0.133519
$536$	0	0
$537$	−735444.	−0.110056
$538$	0	0
$539$	−972405.	−0.144170
$540$	0	0
$541$	6.30404e6	0.926032	0.463016	−	0.886350i	$-0.346767\pi$
$541$	6.30404e6	0.926032	0.463016	+	0.886350i	$0.346767\pi$
$542$	0	0
$543$	2.05854e6	0.299612
$544$	0	0
$545$	3.77957e6	0.545069
$546$	0	0
$547$	8.48475e6	1.21247	0.606234	−	0.795286i	$-0.292679\pi$
$547$	8.48475e6	1.21247	0.606234	+	0.795286i	$0.292679\pi$
$548$	0	0
$549$	−5.07031e6	−0.717966
$550$	0	0
$551$	−1.93426e7	−2.71416
$552$	0	0
$553$	2.88233e6	0.400802
$554$	0	0
$555$	528150.	0.0727821
$556$	0	0
$557$	6.87794e6	0.939335	0.469668	−	0.882843i	$-0.344374\pi$
$557$	6.87794e6	0.939335	0.469668	+	0.882843i	$0.344374\pi$
$558$	0	0
$559$	−9.19554e6	−1.24465
$560$	0	0
$561$	−1.21378e6	−0.162830
$562$	0	0
$563$	1.02257e7	1.35964	0.679820	−	0.733379i	$-0.262058\pi$
$563$	1.02257e7	1.35964	0.679820	+	0.733379i	$0.262058\pi$
$564$	0	0
$565$	3.34215e6	0.440458
$566$	0	0
$567$	−2.57588e6	−0.336487
$568$	0	0
$569$	−1.26751e7	−1.64123	−0.820614	−	0.571482i	$-0.806369\pi$
$569$	−1.26751e7	−1.64123	−0.820614	+	0.571482i	$0.806369\pi$
$570$	0	0
$571$	6.67155e6	0.856321	0.428160	−	0.903703i	$-0.359162\pi$
$571$	6.67155e6	0.856321	0.428160	+	0.903703i	$0.359162\pi$
$572$	0	0
$573$	1.58109e6	0.201174
$574$	0	0
$575$	−1.51875e6	−0.191565
$576$	0	0
$577$	−3.36511e6	−0.420784	−0.210392	−	0.977617i	$-0.567474\pi$
$577$	−3.36511e6	−0.420784	−0.210392	+	0.977617i	$0.567474\pi$
$578$	0	0
$579$	429648.	0.0532619
$580$	0	0
$581$	37044.0	0.00455279
$582$	0	0
$583$	−1.24902e6	−0.152194
$584$	0	0
$585$	−2.28735e6	−0.276339
$586$	0	0
$587$	1.10055e7	1.31830	0.659150	−	0.752012i	$-0.270916\pi$
$587$	1.10055e7	1.31830	0.659150	+	0.752012i	$0.270916\pi$
$588$	0	0
$589$	9.40547e6	1.11710
$590$	0	0
$591$	1.04540e6	0.123116
$592$	0	0
$593$	1.40222e6	0.163749	0.0818747	−	0.996643i	$-0.473909\pi$
$593$	1.40222e6	0.163749	0.0818747	+	0.996643i	$0.473909\pi$
$594$	0	0
$595$	1.22378e6	0.141713
$596$	0	0
$597$	−2.26356e6	−0.259930
$598$	0	0
$599$	−1.93034e6	−0.219820	−0.109910	−	0.993942i	$-0.535056\pi$
$599$	−1.93034e6	−0.219820	−0.109910	+	0.993942i	$0.535056\pi$
$600$	0	0
$601$	−1.82271e6	−0.205841	−0.102921	−	0.994690i	$-0.532819\pi$
$601$	−1.82271e6	−0.205841	−0.102921	+	0.994690i	$0.532819\pi$
$602$	0	0
$603$	1.21970e7	1.36603
$604$	0	0
$605$	−74350.0	−0.00825834
$606$	0	0
$607$	1.36917e7	1.50830	0.754148	−	0.656704i	$-0.228050\pi$
$607$	1.36917e7	1.50830	0.754148	+	0.656704i	$0.228050\pi$
$608$	0	0
$609$	−1.21407e6	−0.132648
$610$	0	0
$611$	4.03395e6	0.437147
$612$	0	0
$613$	1.11975e7	1.20357	0.601785	−	0.798658i	$-0.294456\pi$
$613$	1.11975e7	1.20357	0.601785	+	0.798658i	$0.294456\pi$
$614$	0	0
$615$	−250200.	−0.0266747
$616$	0	0
$617$	−1.37060e7	−1.44944	−0.724718	−	0.689045i	$-0.758030\pi$
$617$	−1.37060e7	−1.44944	−0.724718	+	0.689045i	$0.758030\pi$
$618$	0	0
$619$	7.93359e6	0.832230	0.416115	−	0.909312i	$-0.363391\pi$
$619$	7.93359e6	0.832230	0.416115	+	0.909312i	$0.363391\pi$
$620$	0	0
$621$	3.47733e6	0.361840
$622$	0	0
$623$	−6.63382e6	−0.684768
$624$	0	0
$625$	390625.	0.0400000
$626$	0	0
$627$	2.84553e6	0.289064
$628$	0	0
$629$	−7.03496e6	−0.708981
$630$	0	0
$631$	1.31143e7	1.31121	0.655604	−	0.755105i	$-0.272414\pi$
$631$	1.31143e7	1.31121	0.655604	+	0.755105i	$0.272414\pi$
$632$	0	0
$633$	1.77225e6	0.175798
$634$	0	0
$635$	−7.09960e6	−0.698714
$636$	0	0
$637$	−938791.	−0.0916685
$638$	0	0
$639$	−6.68304e6	−0.647473
$640$	0	0
$641$	−1.27270e7	−1.22344	−0.611719	−	0.791075i	$-0.709522\pi$
$641$	−1.27270e7	−1.22344	−0.611719	+	0.791075i	$0.709522\pi$
$642$	0	0
$643$	−1.88399e7	−1.79701	−0.898505	−	0.438964i	$-0.855345\pi$
$643$	−1.88399e7	−1.79701	−0.898505	+	0.438964i	$0.855345\pi$
$644$	0	0
$645$	−1.76385e6	−0.166941
$646$	0	0
$647$	944688.	0.0887213	0.0443606	−	0.999016i	$-0.485875\pi$
$647$	944688.	0.0887213	0.0443606	+	0.999016i	$0.485875\pi$
$648$	0	0
$649$	−7.62048e6	−0.710184
$650$	0	0
$651$	590352.	0.0545957
$652$	0	0
$653$	2.01024e7	1.84486	0.922432	−	0.386158i	$-0.126198\pi$
$653$	2.01024e7	1.84486	0.922432	+	0.386158i	$0.126198\pi$
$654$	0	0
$655$	6.53595e6	0.595258
$656$	0	0
$657$	1.64600e7	1.48771
$658$	0	0
$659$	1.97097e7	1.76793	0.883967	−	0.467549i	$-0.154863\pi$
$659$	1.97097e7	1.76793	0.883967	+	0.467549i	$0.154863\pi$
$660$	0	0
$661$	−227080.	−0.0202151	−0.0101075	−	0.999949i	$-0.503217\pi$
$661$	−227080.	−0.0202151	−0.0101075	+	0.999949i	$0.503217\pi$
$662$	0	0
$663$	−1.17183e6	−0.103533
$664$	0	0
$665$	−2.86895e6	−0.251576
$666$	0	0
$667$	−2.00694e7	−1.74670
$668$	0	0
$669$	1.18831e6	0.102651
$670$	0	0
$671$	−8.77554e6	−0.752433
$672$	0	0
$673$	1.93220e7	1.64443	0.822214	−	0.569178i	$-0.192739\pi$
$673$	1.93220e7	1.64443	0.822214	+	0.569178i	$0.192739\pi$
$674$	0	0
$675$	−894375.	−0.0755545
$676$	0	0
$677$	3.35334e6	0.281194	0.140597	−	0.990067i	$-0.455098\pi$
$677$	3.35334e6	0.281194	0.140597	+	0.990067i	$0.455098\pi$
$678$	0	0
$679$	−5.41132e6	−0.450431
$680$	0	0
$681$	−28611.0	−0.00236410
$682$	0	0
$683$	−1.60555e7	−1.31696	−0.658481	−	0.752598i	$-0.728801\pi$
$683$	−1.60555e7	−1.31696	−0.658481	+	0.752598i	$0.728801\pi$
$684$	0	0
$685$	−991800.	−0.0807603
$686$	0	0
$687$	2.11517e6	0.170983
$688$	0	0
$689$	−1.20584e6	−0.0967705
$690$	0	0
$691$	−1.35824e7	−1.08213	−0.541066	−	0.840980i	$-0.681979\pi$
$691$	−1.35824e7	−1.08213	−0.541066	+	0.840980i	$0.681979\pi$
$692$	0	0
$693$	−4.64373e6	−0.367311
$694$	0	0
$695$	−4.56565e6	−0.358542
$696$	0	0
$697$	3.33266e6	0.259842
$698$	0	0
$699$	1.60265e6	0.124064
$700$	0	0
$701$	2.05454e7	1.57913	0.789567	−	0.613664i	$-0.210305\pi$
$701$	2.05454e7	1.57913	0.789567	+	0.613664i	$0.210305\pi$
$702$	0	0
$703$	1.64924e7	1.25862
$704$	0	0
$705$	773775.	0.0586330
$706$	0	0
$707$	−1.63905e6	−0.123323
$708$	0	0
$709$	2.57278e7	1.92215	0.961075	−	0.276287i	$-0.0891040\pi$
$709$	2.57278e7	1.92215	0.961075	+	0.276287i	$0.0891040\pi$
$710$	0	0
$711$	1.37646e7	1.02115
$712$	0	0
$713$	9.75888e6	0.718913
$714$	0	0
$715$	−3.95888e6	−0.289605
$716$	0	0
$717$	2.70366e6	0.196406
$718$	0	0
$719$	−7.04806e6	−0.508449	−0.254225	−	0.967145i	$-0.581820\pi$
$719$	−7.04806e6	−0.508449	−0.254225	+	0.967145i	$0.581820\pi$
$720$	0	0
$721$	−5.40524e6	−0.387237
$722$	0	0
$723$	−2.85717e6	−0.203278
$724$	0	0
$725$	5.16187e6	0.364722
$726$	0	0
$727$	1.90997e7	1.34027	0.670134	−	0.742240i	$-0.266237\pi$
$727$	1.90997e7	1.34027	0.670134	+	0.742240i	$0.266237\pi$
$728$	0	0
$729$	−1.12579e7	−0.784586
$730$	0	0
$731$	2.34945e7	1.62619
$732$	0	0
$733$	−2.30424e6	−0.158404	−0.0792021	−	0.996859i	$-0.525237\pi$
$733$	−2.30424e6	−0.158404	−0.0792021	+	0.996859i	$0.525237\pi$
$734$	0	0
$735$	−180075.	−0.0122952
$736$	0	0
$737$	2.11102e7	1.43161
$738$	0	0
$739$	−3.62955e6	−0.244479	−0.122240	−	0.992501i	$-0.539008\pi$
$739$	−3.62955e6	−0.244479	−0.122240	+	0.992501i	$0.539008\pi$
$740$	0	0
$741$	2.74717e6	0.183797
$742$	0	0
$743$	9.73856e6	0.647177	0.323588	−	0.946198i	$-0.395111\pi$
$743$	9.73856e6	0.647177	0.323588	+	0.946198i	$0.395111\pi$
$744$	0	0
$745$	301950.	0.0199317
$746$	0	0
$747$	176904.	0.0115994
$748$	0	0
$749$	1.73254e6	0.112844
$750$	0	0
$751$	2.48272e7	1.60630	0.803152	−	0.595774i	$-0.203155\pi$
$751$	2.48272e7	1.60630	0.803152	+	0.595774i	$0.203155\pi$
$752$	0	0
$753$	3.30071e6	0.212139
$754$	0	0
$755$	−5.21043e6	−0.332664
$756$	0	0
$757$	−1.28400e7	−0.814376	−0.407188	−	0.913344i	$-0.633491\pi$
$757$	−1.28400e7	−0.814376	−0.407188	+	0.913344i	$0.633491\pi$
$758$	0	0
$759$	2.95245e6	0.186028
$760$	0	0
$761$	2.89560e7	1.81250	0.906249	−	0.422744i	$-0.138933\pi$
$761$	2.89560e7	1.81250	0.906249	+	0.422744i	$0.138933\pi$
$762$	0	0
$763$	7.40797e6	0.460668
$764$	0	0
$765$	5.84415e6	0.361050
$766$	0	0
$767$	−7.35706e6	−0.451560
$768$	0	0
$769$	−1.78116e7	−1.08614	−0.543071	−	0.839687i	$-0.682739\pi$
$769$	−1.78116e7	−1.08614	−0.543071	+	0.839687i	$0.682739\pi$
$770$	0	0
$771$	−3.24689e6	−0.196713
$772$	0	0
$773$	1.73536e7	1.04458	0.522290	−	0.852768i	$-0.325078\pi$
$773$	1.73536e7	1.04458	0.522290	+	0.852768i	$0.325078\pi$
$774$	0	0
$775$	−2.51000e6	−0.150113
$776$	0	0
$777$	1.03517e6	0.0615121
$778$	0	0
$779$	−7.81291e6	−0.461285
$780$	0	0
$781$	−1.15668e7	−0.678556
$782$	0	0
$783$	−1.18186e7	−0.688910
$784$	0	0
$785$	−9.10235e6	−0.527205
$786$	0	0
$787$	−812177.	−0.0467427	−0.0233714	−	0.999727i	$-0.507440\pi$
$787$	−812177.	−0.0467427	−0.0233714	+	0.999727i	$0.507440\pi$
$788$	0	0
$789$	−248850.	−0.0142313
$790$	0	0
$791$	6.55061e6	0.372255
$792$	0	0
$793$	−8.47219e6	−0.478424
$794$	0	0
$795$	−231300.	−0.0129795
$796$	0	0
$797$	−8.58201e6	−0.478568	−0.239284	−	0.970950i	$-0.576913\pi$
$797$	−8.58201e6	−0.478568	−0.239284	+	0.970950i	$0.576913\pi$
$798$	0	0
$799$	−1.03067e7	−0.571152
$800$	0	0
$801$	−3.16799e7	−1.74462
$802$	0	0
$803$	2.84885e7	1.55912
$804$	0	0
$805$	−2.97675e6	−0.161902
$806$	0	0
$807$	−1.90147e6	−0.102779
$808$	0	0
$809$	−2.83000e6	−0.152025	−0.0760125	−	0.997107i	$-0.524219\pi$
$809$	−2.83000e6	−0.152025	−0.0760125	+	0.997107i	$0.524219\pi$
$810$	0	0
$811$	1.06484e7	0.568504	0.284252	−	0.958750i	$-0.408255\pi$
$811$	1.06484e7	0.568504	0.284252	+	0.958750i	$0.408255\pi$
$812$	0	0
$813$	836868.	0.0444049
$814$	0	0
$815$	15650.0	0.000825316 0
$816$	0	0
$817$	−5.50792e7	−2.88690
$818$	0	0
$819$	−4.48321e6	−0.233549
$820$	0	0
$821$	−2.59970e7	−1.34606	−0.673032	−	0.739613i	$-0.735008\pi$
$821$	−2.59970e7	−1.34606	−0.673032	+	0.739613i	$0.735008\pi$
$822$	0	0
$823$	2.03099e7	1.04522	0.522611	−	0.852571i	$-0.324958\pi$
$823$	2.03099e7	1.04522	0.522611	+	0.852571i	$0.324958\pi$
$824$	0	0
$825$	−759375.	−0.0388438
$826$	0	0
$827$	−1.68001e6	−0.0854175	−0.0427088	−	0.999088i	$-0.513599\pi$
$827$	−1.68001e6	−0.0854175	−0.0427088	+	0.999088i	$0.513599\pi$
$828$	0	0
$829$	−6.71070e6	−0.339142	−0.169571	−	0.985518i	$-0.554238\pi$
$829$	−6.71070e6	−0.339142	−0.169571	+	0.985518i	$0.554238\pi$
$830$	0	0
$831$	6.52569e6	0.327811
$832$	0	0
$833$	2.39860e6	0.119769
$834$	0	0
$835$	1.11404e7	0.552950
$836$	0	0
$837$	5.74690e6	0.283543
$838$	0	0
$839$	−2.60856e7	−1.27937	−0.639686	−	0.768637i	$-0.720935\pi$
$839$	−2.60856e7	−1.27937	−0.639686	+	0.768637i	$0.720935\pi$
$840$	0	0
$841$	4.76999e7	2.32556
$842$	0	0
$843$	−2.07870e6	−0.100745
$844$	0	0
$845$	5.46030e6	0.263072
$846$	0	0
$847$	−145726.	−0.00697957
$848$	0	0
$849$	−3.12062e6	−0.148584
$850$	0	0
$851$	1.71121e7	0.809988
$852$	0	0
$853$	9.54873e6	0.449338	0.224669	−	0.974435i	$-0.427870\pi$
$853$	9.54873e6	0.449338	0.224669	+	0.974435i	$0.427870\pi$
$854$	0	0
$855$	−1.37007e7	−0.640955
$856$	0	0
$857$	3.51377e7	1.63426	0.817130	−	0.576453i	$-0.195564\pi$
$857$	3.51377e7	1.63426	0.817130	+	0.576453i	$0.195564\pi$
$858$	0	0
$859$	1.60428e7	0.741816	0.370908	−	0.928670i	$-0.379047\pi$
$859$	1.60428e7	0.741816	0.370908	+	0.928670i	$0.379047\pi$
$860$	0	0
$861$	−490392.	−0.0225442
$862$	0	0
$863$	2.77776e7	1.26960	0.634802	−	0.772675i	$-0.281082\pi$
$863$	2.77776e7	1.26960	0.634802	+	0.772675i	$0.281082\pi$
$864$	0	0
$865$	−1.60867e7	−0.731015
$866$	0	0
$867$	−1.26557e6	−0.0571792
$868$	0	0
$869$	2.38233e7	1.07017
$870$	0	0
$871$	2.03805e7	0.910268
$872$	0	0
$873$	−2.58418e7	−1.14759
$874$	0	0
$875$	765625.	0.0338062
$876$	0	0
$877$	2.46748e7	1.08332	0.541658	−	0.840599i	$-0.317797\pi$
$877$	2.46748e7	1.08332	0.541658	+	0.840599i	$0.317797\pi$
$878$	0	0
$879$	−3.25695e6	−0.142180
$880$	0	0
$881$	−1.27792e7	−0.554707	−0.277353	−	0.960768i	$-0.589457\pi$
$881$	−1.27792e7	−0.554707	−0.277353	+	0.960768i	$0.589457\pi$
$882$	0	0
$883$	2.63417e7	1.13695	0.568476	−	0.822700i	$-0.307533\pi$
$883$	2.63417e7	1.13695	0.568476	+	0.822700i	$0.307533\pi$
$884$	0	0
$885$	−1.41120e6	−0.0605662
$886$	0	0
$887$	−2.60037e7	−1.10975	−0.554877	−	0.831932i	$-0.687235\pi$
$887$	−2.60037e7	−1.10975	−0.554877	+	0.831932i	$0.687235\pi$
$888$	0	0
$889$	−1.39152e7	−0.590521
$890$	0	0
$891$	−2.12904e7	−0.898443
$892$	0	0
$893$	2.41624e7	1.01394
$894$	0	0
$895$	6.12870e6	0.255747
$896$	0	0
$897$	2.85039e6	0.118283
$898$	0	0
$899$	−3.31681e7	−1.36874
$900$	0	0
$901$	3.08092e6	0.126435
$902$	0	0
$903$	−3.45715e6	−0.141091
$904$	0	0
$905$	−1.71545e7	−0.696236
$906$	0	0
$907$	4.11852e7	1.66235	0.831177	−	0.556008i	$-0.187668\pi$
$907$	4.11852e7	1.66235	0.831177	+	0.556008i	$0.187668\pi$
$908$	0	0
$909$	−7.82730e6	−0.314197
$910$	0	0
$911$	7.92211e6	0.316261	0.158130	−	0.987418i	$-0.449453\pi$
$911$	7.92211e6	0.316261	0.158130	+	0.987418i	$0.449453\pi$
$912$	0	0
$913$	306180.	0.0121563
$914$	0	0
$915$	−1.62510e6	−0.0641693
$916$	0	0
$917$	1.28105e7	0.503085
$918$	0	0
$919$	−1.59154e7	−0.621624	−0.310812	−	0.950471i	$-0.600601\pi$
$919$	−1.59154e7	−0.621624	−0.310812	+	0.950471i	$0.600601\pi$
$920$	0	0
$921$	−4389.00	−0.000170497 0
$922$	0	0
$923$	−1.11670e7	−0.431450
$924$	0	0
$925$	−4.40125e6	−0.169130
$926$	0	0
$927$	−2.58128e7	−0.986587
$928$	0	0
$929$	−3.37148e7	−1.28169	−0.640843	−	0.767672i	$-0.721415\pi$
$929$	−3.37148e7	−1.28169	−0.640843	+	0.767672i	$0.721415\pi$
$930$	0	0
$931$	−5.62314e6	−0.212620
$932$	0	0
$933$	−9.35930e6	−0.351997
$934$	0	0
$935$	1.01149e7	0.378383
$936$	0	0
$937$	−4.04362e7	−1.50460	−0.752300	−	0.658820i	$-0.771056\pi$
$937$	−4.04362e7	−1.50460	−0.752300	+	0.658820i	$0.771056\pi$
$938$	0	0
$939$	2.49428e6	0.0923167
$940$	0	0
$941$	3.62378e7	1.33410	0.667048	−	0.745015i	$-0.267557\pi$
$941$	3.62378e7	1.33410	0.667048	+	0.745015i	$0.267557\pi$
$942$	0	0
$943$	−8.10648e6	−0.296861
$944$	0	0
$945$	−1.75298e6	−0.0638552
$946$	0	0
$947$	−2.94238e7	−1.06616	−0.533082	−	0.846064i	$-0.678966\pi$
$947$	−2.94238e7	−1.06616	−0.533082	+	0.846064i	$0.678966\pi$
$948$	0	0
$949$	2.75037e7	0.991348
$950$	0	0
$951$	−3.77552e6	−0.135371
$952$	0	0
$953$	3.59497e7	1.28222	0.641110	−	0.767449i	$-0.278474\pi$
$953$	3.59497e7	1.28222	0.641110	+	0.767449i	$0.278474\pi$
$954$	0	0
$955$	−1.31758e7	−0.467485
$956$	0	0
$957$	−1.00347e7	−0.354180
$958$	0	0
$959$	−1.94393e6	−0.0682549
$960$	0	0
$961$	−1.25009e7	−0.436649
$962$	0	0
$963$	8.27377e6	0.287500
$964$	0	0
$965$	−3.58040e6	−0.123769
$966$	0	0
$967$	−1.19506e6	−0.0410982	−0.0205491	−	0.999789i	$-0.506541\pi$
$967$	−1.19506e6	−0.0410982	−0.0205491	+	0.999789i	$0.506541\pi$
$968$	0	0
$969$	−7.01897e6	−0.240140
$970$	0	0
$971$	−3.26221e7	−1.11036	−0.555180	−	0.831730i	$-0.687351\pi$
$971$	−3.26221e7	−1.11036	−0.555180	+	0.831730i	$0.687351\pi$
$972$	0	0
$973$	−8.94867e6	−0.303024
$974$	0	0
$975$	−733125.	−0.0246983
$976$	0	0
$977$	5.36858e7	1.79938	0.899690	−	0.436529i	$-0.143792\pi$
$977$	5.36858e7	1.79938	0.899690	+	0.436529i	$0.143792\pi$
$978$	0	0
$979$	−5.48305e7	−1.82838
$980$	0	0
$981$	3.53768e7	1.17367
$982$	0	0
$983$	3.31124e7	1.09297	0.546484	−	0.837469i	$-0.315966\pi$
$983$	3.31124e7	1.09297	0.546484	+	0.837469i	$0.315966\pi$
$984$	0	0
$985$	−8.71170e6	−0.286096
$986$	0	0
$987$	1.51660e6	0.0495539
$988$	0	0
$989$	−5.71487e7	−1.85787
$990$	0	0
$991$	1.97082e7	0.637475	0.318738	−	0.947843i	$-0.396741\pi$
$991$	1.97082e7	0.637475	0.318738	+	0.947843i	$0.396741\pi$
$992$	0	0
$993$	6.91396e6	0.222512
$994$	0	0
$995$	1.88630e7	0.604022
$996$	0	0
$997$	3.31940e7	1.05760	0.528800	−	0.848747i	$-0.322642\pi$
$997$	3.31940e7	1.05760	0.528800	+	0.848747i	$0.322642\pi$
$998$	0	0
$999$	1.00771e7	0.319464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.6.a.d.1.1		1
4.3	odd	2		70.6.a.c.1.1	✓	1
12.11	even	2		630.6.a.n.1.1		1
20.3	even	4		350.6.c.e.99.2		2
20.7	even	4		350.6.c.e.99.1		2
20.19	odd	2		350.6.a.k.1.1		1
28.27	even	2		490.6.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.c.1.1	✓	1	4.3	odd	2
350.6.a.k.1.1		1	20.19	odd	2
350.6.c.e.99.1		2	20.7	even	4
350.6.c.e.99.2		2	20.3	even	4
490.6.a.e.1.1		1	28.27	even	2
560.6.a.d.1.1		1	1.1	even	1	trivial
630.6.a.n.1.1		1	12.11	even	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	560.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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