LMFDB - Embedded newform 630.6.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,6,Mod(1,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("630.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	630.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:	$101.041806482$
Analytic rank:	$1$
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	$\chi$	$=$	630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+4.00000 q^{2} +16.0000 q^{4} +25.0000 q^{5} +49.0000 q^{7} +64.0000 q^{8} +100.000 q^{10} -405.000 q^{11} -391.000 q^{13} +196.000 q^{14} +256.000 q^{16} -999.000 q^{17} +2342.00 q^{19} +400.000 q^{20} -1620.00 q^{22} -2430.00 q^{23} +625.000 q^{25} -1564.00 q^{26} +784.000 q^{28} -8259.00 q^{29} +4016.00 q^{31} +1024.00 q^{32} -3996.00 q^{34} +1225.00 q^{35} -7042.00 q^{37} +9368.00 q^{38} +1600.00 q^{40} -3336.00 q^{41} -23518.0 q^{43} -6480.00 q^{44} -9720.00 q^{46} -10317.0 q^{47} +2401.00 q^{49} +2500.00 q^{50} -6256.00 q^{52} -3084.00 q^{53} -10125.0 q^{55} +3136.00 q^{56} -33036.0 q^{58} +18816.0 q^{59} +21668.0 q^{61} +16064.0 q^{62} +4096.00 q^{64} -9775.00 q^{65} +52124.0 q^{67} -15984.0 q^{68} +4900.00 q^{70} +28560.0 q^{71} -70342.0 q^{73} -28168.0 q^{74} +37472.0 q^{76} -19845.0 q^{77} +58823.0 q^{79} +6400.00 q^{80} -13344.0 q^{82} -756.000 q^{83} -24975.0 q^{85} -94072.0 q^{86} -25920.0 q^{88} -135384. q^{89} -19159.0 q^{91} -38880.0 q^{92} -41268.0 q^{94} +58550.0 q^{95} +110435. q^{97} +9604.00 q^{98} +O(q^{100})\)

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	0	0
$3$	0	0
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	0	0
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	64.0000	0.353553
$9$	0	0
$10$	100.000	0.316228
$11$	−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	$0.603965\pi$
$14$	196.000	0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	−999.000	−0.838384	−0.419192	−	0.907898i	$-0.637687\pi$
$17$	−999.000	−0.838384	−0.419192	+	0.907898i	$0.637687\pi$
$18$	0	0
$19$	2342.00	1.48834	0.744171	−	0.667989i	$-0.232845\pi$
$19$	2342.00	1.48834	0.744171	+	0.667989i	$0.232845\pi$
$20$	400.000	0.223607
$21$	0	0
$22$	−1620.00	−0.713606
$23$	−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
$26$	−1564.00	−0.453736
$27$	0	0
$28$	784.000	0.188982
$29$	−8259.00	−1.82361	−0.911806	−	0.410621i	$-0.865312\pi$
$29$	−8259.00	−1.82361	−0.911806	+	0.410621i	$0.865312\pi$
$30$	0	0
$31$	4016.00	0.750567	0.375284	−	0.926910i	$-0.377545\pi$
$31$	4016.00	0.750567	0.375284	+	0.926910i	$0.377545\pi$
$32$	1024.00	0.176777
$33$	0	0
$34$	−3996.00	−0.592827
$35$	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	$0.638962\pi$
$38$	9368.00	1.05242
$39$	0	0
$40$	1600.00	0.158114
$41$	−3336.00	−0.309932	−0.154966	−	0.987920i	$-0.549527\pi$
$41$	−3336.00	−0.309932	−0.154966	+	0.987920i	$0.549527\pi$
$42$	0	0
$43$	−23518.0	−1.93968	−0.969838	−	0.243750i	$-0.921622\pi$
$43$	−23518.0	−1.93968	−0.969838	+	0.243750i	$0.921622\pi$
$44$	−6480.00	−0.504595
$45$	0	0
$46$	−9720.00	−0.677285
$47$	−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
$50$	2500.00	0.141421
$51$	0	0
$52$	−6256.00	−0.320840
$53$	−3084.00	−0.150808	−0.0754041	−	0.997153i	$-0.524025\pi$
$53$	−3084.00	−0.150808	−0.0754041	+	0.997153i	$0.524025\pi$
$54$	0	0
$55$	−10125.0	−0.451324
$56$	3136.00	0.133631
$57$	0	0
$58$	−33036.0	−1.28949
$59$	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	$0.378401\pi$
$62$	16064.0	0.530731
$63$	0	0
$64$	4096.00	0.125000
$65$	−9775.00	−0.286968
$66$	0	0
$67$	52124.0	1.41857	0.709285	−	0.704922i	$-0.249018\pi$
$67$	52124.0	1.41857	0.709285	+	0.704922i	$0.249018\pi$
$68$	−15984.0	−0.419192
$69$	0	0
$70$	4900.00	0.119523
$71$	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	$0.780975\pi$
$74$	−28168.0	−0.597966
$75$	0	0
$76$	37472.0	0.744171
$77$	−19845.0	−0.381438
$78$	0	0
$79$	58823.0	1.06042	0.530212	−	0.847865i	$-0.322112\pi$
$79$	58823.0	1.06042	0.530212	+	0.847865i	$0.322112\pi$
$80$	6400.00	0.111803
$81$	0	0
$82$	−13344.0	−0.219155
$83$	−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
$86$	−94072.0	−1.37156
$87$	0	0
$88$	−25920.0	−0.356803
$89$	−135384.	−1.81173	−0.905863	−	0.423572i	$-0.860776\pi$
$89$	−135384.	−1.81173	−0.905863	+	0.423572i	$0.860776\pi$
$90$	0	0
$91$	−19159.0	−0.242532
$92$	−38880.0	−0.478913
$93$	0	0
$94$	−41268.0	−0.481719
$95$	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	$0.296810\pi$
$98$	9604.00	0.101015
$99$	0	0
$100$	10000.0	0.100000
$101$	−33450.0	−0.326282	−0.163141	−	0.986603i	$-0.552162\pi$
$101$	−33450.0	−0.326282	−0.163141	+	0.986603i	$0.552162\pi$
$102$	0	0
$103$	−110311.	−1.02453	−0.512266	−	0.858827i	$-0.671194\pi$
$103$	−110311.	−1.02453	−0.512266	+	0.858827i	$0.671194\pi$
$104$	−25024.0	−0.226868
$105$	0	0
$106$	−12336.0	−0.106637
$107$	−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	$0.708592\pi$
$110$	−40500.0	−0.319134
$111$	0	0
$112$	12544.0	0.0944911
$113$	133686.	0.984895	0.492447	−	0.870342i	$-0.336102\pi$
$113$	133686.	0.984895	0.492447	+	0.870342i	$0.336102\pi$
$114$	0	0
$115$	−60750.0	−0.428353
$116$	−132144.	−0.911806
$117$	0	0
$118$	75264.0	0.497602
$119$	−48951.0	−0.316880
$120$	0	0
$121$	2974.00	0.0184662
$122$	86672.0	0.527205
$123$	0	0
$124$	64256.0	0.375284
$125$	15625.0	0.0894427
$126$	0	0
$127$	−283984.	−1.56237	−0.781186	−	0.624298i	$-0.785385\pi$
$127$	−283984.	−1.56237	−0.781186	+	0.624298i	$0.785385\pi$
$128$	16384.0	0.0883883
$129$	0	0
$130$	−39100.0	−0.202917
$131$	−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
$134$	208496.	1.00308
$135$	0	0
$136$	−63936.0	−0.296414
$137$	−39672.0	−0.180585	−0.0902927	−	0.995915i	$-0.528780\pi$
$137$	−39672.0	−0.180585	−0.0902927	+	0.995915i	$0.528780\pi$
$138$	0	0
$139$	−182626.	−0.801725	−0.400863	−	0.916138i	$-0.631290\pi$
$139$	−182626.	−0.801725	−0.400863	+	0.916138i	$0.631290\pi$
$140$	19600.0	0.0845154
$141$	0	0
$142$	114240.	0.475442
$143$	158355.	0.647577
$144$	0	0
$145$	−206475.	−0.815544
$146$	−281368.	−1.09243
$147$	0	0
$148$	−112672.	−0.422826
$149$	12078.0	0.0445686	0.0222843	−	0.999752i	$-0.492906\pi$
$149$	12078.0	0.0445686	0.0222843	+	0.999752i	$0.492906\pi$
$150$	0	0
$151$	−208417.	−0.743859	−0.371930	−	0.928261i	$-0.621304\pi$
$151$	−208417.	−0.743859	−0.371930	+	0.928261i	$0.621304\pi$
$152$	149888.	0.526209
$153$	0	0
$154$	−79380.0	−0.269718
$155$	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	$0.299351\pi$
$158$	235292.	0.749833
$159$	0	0
$160$	25600.0	0.0790569
$161$	−119070.	−0.362024
$162$	0	0
$163$	626.000	0.00184546	0.000922731	−	1.00000i	$-0.499706\pi$
$163$	626.000	0.00184546	0.000922731		1.00000i	$0.499706\pi$
$164$	−53376.0	−0.154966
$165$	0	0
$166$	−3024.00	−0.00851749
$167$	−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
$170$	−99900.0	−0.265120
$171$	0	0
$172$	−376288.	−0.969838
$173$	−643467.	−1.63460	−0.817299	−	0.576214i	$-0.804530\pi$
$173$	−643467.	−1.63460	−0.817299	+	0.576214i	$0.804530\pi$
$174$	0	0
$175$	30625.0	0.0755929
$176$	−103680.	−0.252298
$177$	0	0
$178$	−541536.	−1.28108
$179$	−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	$0.216024\pi$
$182$	−76636.0	−0.171496
$183$	0	0
$184$	−155520.	−0.338643
$185$	−176050.	−0.378187
$186$	0	0
$187$	404595.	0.846090
$188$	−165072.	−0.340627
$189$	0	0
$190$	234200.	0.470655
$191$	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	$0.455811\pi$
$194$	441740.	0.842679
$195$	0	0
$196$	38416.0	0.0714286
$197$	−348468.	−0.639731	−0.319865	−	0.947463i	$-0.603638\pi$
$197$	−348468.	−0.639731	−0.319865	+	0.947463i	$0.603638\pi$
$198$	0	0
$199$	754520.	1.35064	0.675318	−	0.737527i	$-0.264007\pi$
$199$	754520.	1.35064	0.675318	+	0.737527i	$0.264007\pi$
$200$	40000.0	0.0707107
$201$	0	0
$202$	−133800.	−0.230716
$203$	−404691.	−0.689261
$204$	0	0
$205$	−83400.0	−0.138606
$206$	−441244.	−0.724454
$207$	0	0
$208$	−100096.	−0.160420
$209$	−948510.	−1.50202
$210$	0	0
$211$	−590749.	−0.913475	−0.456738	−	0.889601i	$-0.650982\pi$
$211$	−590749.	−0.913475	−0.456738	+	0.889601i	$0.650982\pi$
$212$	−49344.0	−0.0754041
$213$	0	0
$214$	−141432.	−0.211112
$215$	−587950.	−0.867450
$216$	0	0
$217$	196784.	0.283688
$218$	−604732.	−0.861830
$219$	0	0
$220$	−162000.	−0.225662
$221$	390609.	0.537974
$222$	0	0
$223$	−396103.	−0.533391	−0.266696	−	0.963781i	$-0.585932\pi$
$223$	−396103.	−0.533391	−0.266696	+	0.963781i	$0.585932\pi$
$224$	50176.0	0.0668153
$225$	0	0
$226$	534744.	0.696426
$227$	−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	$0.353478\pi$
$230$	−243000.	−0.302891
$231$	0	0
$232$	−528576.	−0.644744
$233$	−534216.	−0.644655	−0.322327	−	0.946628i	$-0.604465\pi$
$233$	−534216.	−0.644655	−0.322327	+	0.946628i	$0.604465\pi$
$234$	0	0
$235$	−257925.	−0.304666
$236$	301056.	0.351858
$237$	0	0
$238$	−195804.	−0.224068
$239$	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	$0.677107\pi$
$242$	11896.0	0.0130576
$243$	0	0
$244$	346688.	0.372790
$245$	60025.0	0.0638877
$246$	0	0
$247$	−915722.	−0.955039
$248$	257024.	0.265366
$249$	0	0
$250$	62500.0	0.0632456
$251$	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
$254$	−1.13594e6	−1.10476
$255$	0	0
$256$	65536.0	0.0625000
$257$	1.08230e6	1.02215	0.511074	−	0.859537i	$-0.329248\pi$
$257$	1.08230e6	1.02215	0.511074	+	0.859537i	$0.329248\pi$
$258$	0	0
$259$	−345058.	−0.319626
$260$	−156400.	−0.143484
$261$	0	0
$262$	−1.04575e6	−0.941186
$263$	−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
$266$	459032.	0.397776
$267$	0	0
$268$	833984.	0.709285
$269$	633822.	0.534056	0.267028	−	0.963689i	$-0.413958\pi$
$269$	633822.	0.534056	0.267028	+	0.963689i	$0.413958\pi$
$270$	0	0
$271$	−278956.	−0.230734	−0.115367	−	0.993323i	$-0.536804\pi$
$271$	−278956.	−0.230734	−0.115367	+	0.993323i	$0.536804\pi$
$272$	−255744.	−0.209596
$273$	0	0
$274$	−158688.	−0.127693
$275$	−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	$0.175585\pi$
$278$	−730504.	−0.566905
$279$	0	0
$280$	78400.0	0.0597614
$281$	692901.	0.523486	0.261743	−	0.965138i	$-0.415703\pi$
$281$	692901.	0.523486	0.261743	+	0.965138i	$0.415703\pi$
$282$	0	0
$283$	1.04021e6	0.772065	0.386032	−	0.922485i	$-0.373845\pi$
$283$	1.04021e6	0.772065	0.386032	+	0.922485i	$0.373845\pi$
$284$	456960.	0.336188
$285$	0	0
$286$	633420.	0.457906
$287$	−163464.	−0.117143
$288$	0	0
$289$	−421856.	−0.297112
$290$	−825900.	−0.576677
$291$	0	0
$292$	−1.12547e6	−0.772463
$293$	1.08565e6	0.738789	0.369394	−	0.929273i	$-0.379565\pi$
$293$	1.08565e6	0.738789	0.369394	+	0.929273i	$0.379565\pi$
$294$	0	0
$295$	470400.	0.314711
$296$	−450688.	−0.298983
$297$	0	0
$298$	48312.0	0.0315148
$299$	950130.	0.614618
$300$	0	0
$301$	−1.15238e6	−0.733129
$302$	−833668.	−0.525988
$303$	0	0
$304$	599552.	0.372086
$305$	541700.	0.333434
$306$	0	0
$307$	1463.00	0.000885928 0	0.000442964	−	1.00000i	$-0.499859\pi$
$307$	1463.00	0.000885928 0	0.000442964		1.00000i	$0.499859\pi$
$308$	−317520.	−0.190719
$309$	0	0
$310$	401600.	0.237350
$311$	−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	$0.422903\pi$
$314$	1.45638e6	0.833584
$315$	0	0
$316$	941168.	0.530212
$317$	1.25851e6	0.703408	0.351704	−	0.936111i	$-0.385602\pi$
$317$	1.25851e6	0.703408	0.351704	+	0.936111i	$0.385602\pi$
$318$	0	0
$319$	3.34489e6	1.84037
$320$	102400.	0.0559017
$321$	0	0
$322$	−476280.	−0.255990
$323$	−2.33966e6	−1.24780
$324$	0	0
$325$	−244375.	−0.128336
$326$	2504.00	0.00130494
$327$	0	0
$328$	−213504.	−0.109578
$329$	−505533.	−0.257490
$330$	0	0
$331$	−2.30465e6	−1.15621	−0.578103	−	0.815964i	$-0.696207\pi$
$331$	−2.30465e6	−1.15621	−0.578103	+	0.815964i	$0.696207\pi$
$332$	−12096.0	−0.00602277
$333$	0	0
$334$	−1.78247e6	−0.874290
$335$	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	$0.440945\pi$
$338$	−873648.	−0.415953
$339$	0	0
$340$	−399600.	−0.187468
$341$	−1.62648e6	−0.757465
$342$	0	0
$343$	117649.	0.0539949
$344$	−1.50515e6	−0.685779
$345$	0	0
$346$	−2.57387e6	−1.15584
$347$	−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	$0.825919\pi$
$350$	122500.	0.0534522
$351$	0	0
$352$	−414720.	−0.178401
$353$	366453.	0.156524	0.0782621	−	0.996933i	$-0.475063\pi$
$353$	366453.	0.156524	0.0782621	+	0.996933i	$0.475063\pi$
$354$	0	0
$355$	714000.	0.300696
$356$	−2.16614e6	−0.905863
$357$	0	0
$358$	−980592.	−0.404372
$359$	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
$362$	2.74472e6	1.10085
$363$	0	0
$364$	−306544.	−0.121266
$365$	−1.75855e6	−0.690912
$366$	0	0
$367$	2.13740e6	0.828362	0.414181	−	0.910195i	$-0.364068\pi$
$367$	2.13740e6	0.828362	0.414181	+	0.910195i	$0.364068\pi$
$368$	−622080.	−0.239457
$369$	0	0
$370$	−704200.	−0.267419
$371$	−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	$0.512182\pi$
$374$	1.61838e6	0.598276
$375$	0	0
$376$	−660288.	−0.240860
$377$	3.22927e6	1.17018
$378$	0	0
$379$	3.50536e6	1.25353	0.626766	−	0.779208i	$-0.284378\pi$
$379$	3.50536e6	1.25353	0.626766	+	0.779208i	$0.284378\pi$
$380$	936800.	0.332804
$381$	0	0
$382$	2.10812e6	0.739159
$383$	−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
$386$	572864.	0.195697
$387$	0	0
$388$	1.76696e6	0.595864
$389$	1.20003e6	0.402084	0.201042	−	0.979583i	$-0.435567\pi$
$389$	1.20003e6	0.402084	0.201042	+	0.979583i	$0.435567\pi$
$390$	0	0
$391$	2.42757e6	0.803026
$392$	153664.	0.0505076
$393$	0	0
$394$	−1.39387e6	−0.452358
$395$	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	$0.748374\pi$
$398$	3.01808e6	0.955043
$399$	0	0
$400$	160000.	0.0500000
$401$	3.13278e6	0.972903	0.486451	−	0.873708i	$-0.338291\pi$
$401$	3.13278e6	0.972903	0.486451	+	0.873708i	$0.338291\pi$
$402$	0	0
$403$	−1.57026e6	−0.481624
$404$	−535200.	−0.163141
$405$	0	0
$406$	−1.61876e6	−0.487381
$407$	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	$0.459361\pi$
$410$	−333600.	−0.0980091
$411$	0	0
$412$	−1.76498e6	−0.512266
$413$	921984.	0.265980
$414$	0	0
$415$	−18900.0	−0.00538693
$416$	−400384.	−0.113434
$417$	0	0
$418$	−3.79404e6	−1.06209
$419$	−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	$0.0877159\pi$
$422$	−2.36300e6	−0.645925
$423$	0	0
$424$	−197376.	−0.0533187
$425$	−624375.	−0.167677
$426$	0	0
$427$	1.06173e6	0.281803
$428$	−565728.	−0.149279
$429$	0	0
$430$	−2.35180e6	−0.613379
$431$	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	$0.863485\pi$
$434$	787136.	0.200597
$435$	0	0
$436$	−2.41893e6	−0.609406
$437$	−5.69106e6	−1.42557
$438$	0	0
$439$	593258.	0.146920	0.0734602	−	0.997298i	$-0.476596\pi$
$439$	593258.	0.146920	0.0734602	+	0.997298i	$0.476596\pi$
$440$	−648000.	−0.159567
$441$	0	0
$442$	1.56244e6	0.380405
$443$	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
$446$	−1.58441e6	−0.377165
$447$	0	0
$448$	200704.	0.0472456
$449$	4.32930e6	1.01345	0.506724	−	0.862108i	$-0.330856\pi$
$449$	4.32930e6	1.01345	0.506724	+	0.862108i	$0.330856\pi$
$450$	0	0
$451$	1.35108e6	0.312781
$452$	2.13898e6	0.492447
$453$	0	0
$454$	−38148.0	−0.00868625
$455$	−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	$0.685596\pi$
$458$	2.82022e6	0.628232
$459$	0	0
$460$	−972000.	−0.214176
$461$	−7.02919e6	−1.54047	−0.770235	−	0.637761i	$-0.779861\pi$
$461$	−7.02919e6	−1.54047	−0.770235	+	0.637761i	$0.779861\pi$
$462$	0	0
$463$	2.88559e6	0.625579	0.312789	−	0.949823i	$-0.398737\pi$
$463$	2.88559e6	0.625579	0.312789	+	0.949823i	$0.398737\pi$
$464$	−2.11430e6	−0.455903
$465$	0	0
$466$	−2.13686e6	−0.455840
$467$	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
$470$	−1.03170e6	−0.215431
$471$	0	0
$472$	1.20422e6	0.248801
$473$	9.52479e6	1.95750
$474$	0	0
$475$	1.46375e6	0.297669
$476$	−783216.	−0.158440
$477$	0	0
$478$	3.60488e6	0.721642
$479$	−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
$482$	−3.80956e6	−0.746891
$483$	0	0
$484$	47584.0	0.00923310
$485$	2.76087e6	0.532957
$486$	0	0
$487$	1.91121e6	0.365162	0.182581	−	0.983191i	$-0.441555\pi$
$487$	1.91121e6	0.365162	0.182581	+	0.983191i	$0.441555\pi$
$488$	1.38675e6	0.263602
$489$	0	0
$490$	240100.	0.0451754
$491$	−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
$494$	−3.66289e6	−0.675315
$495$	0	0
$496$	1.02810e6	0.187642
$497$	1.39944e6	0.254134
$498$	0	0
$499$	7.09708e6	1.27593	0.637967	−	0.770063i	$-0.279775\pi$
$499$	7.09708e6	1.27593	0.637967	+	0.770063i	$0.279775\pi$
$500$	250000.	0.0447214
$501$	0	0
$502$	4.40095e6	0.779448
$503$	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
$506$	3.93660e6	0.683510
$507$	0	0
$508$	−4.54374e6	−0.781186
$509$	9.42509e6	1.61247	0.806234	−	0.591596i	$-0.201502\pi$
$509$	9.42509e6	1.61247	0.806234	+	0.591596i	$0.201502\pi$
$510$	0	0
$511$	−3.44676e6	−0.583927
$512$	262144.	0.0441942
$513$	0	0
$514$	4.32919e6	0.722768
$515$	−2.75778e6	−0.458185
$516$	0	0
$517$	4.17838e6	0.687515
$518$	−1.38023e6	−0.226010
$519$	0	0
$520$	−625600.	−0.101458
$521$	6.18917e6	0.998938	0.499469	−	0.866332i	$-0.333529\pi$
$521$	6.18917e6	0.998938	0.499469	+	0.866332i	$0.333529\pi$
$522$	0	0
$523$	−3.81497e6	−0.609870	−0.304935	−	0.952373i	$-0.598635\pi$
$523$	−3.81497e6	−0.609870	−0.304935	+	0.952373i	$0.598635\pi$
$524$	−4.18301e6	−0.665519
$525$	0	0
$526$	−331800.	−0.0522892
$527$	−4.01198e6	−0.629264
$528$	0	0
$529$	−531443.	−0.0825691
$530$	−308400.	−0.0476897
$531$	0	0
$532$	1.83613e6	0.281270
$533$	1.30438e6	0.198877
$534$	0	0
$535$	−883950.	−0.133519
$536$	3.33594e6	0.501540
$537$	0	0
$538$	2.53529e6	0.377634
$539$	−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	$0.346767\pi$
$542$	−1.11582e6	−0.163154
$543$	0	0
$544$	−1.02298e6	−0.148207
$545$	−3.77957e6	−0.545069
$546$	0	0
$547$	−8.48475e6	−1.21247	−0.606234	−	0.795286i	$-0.707321\pi$
$547$	−8.48475e6	−1.21247	−0.606234	+	0.795286i	$0.707321\pi$
$548$	−634752.	−0.0902927
$549$	0	0
$550$	−1.01250e6	−0.142721
$551$	−1.93426e7	−2.71416
$552$	0	0
$553$	2.88233e6	0.400802
$554$	8.70092e6	1.20446
$555$	0	0
$556$	−2.92202e6	−0.400863
$557$	−6.87794e6	−0.939335	−0.469668	−	0.882843i	$-0.655626\pi$
$557$	−6.87794e6	−0.939335	−0.469668	+	0.882843i	$0.655626\pi$
$558$	0	0
$559$	9.19554e6	1.24465
$560$	313600.	0.0422577
$561$	0	0
$562$	2.77160e6	0.370161
$563$	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
$566$	4.16083e6	0.545932
$567$	0	0
$568$	1.82784e6	0.237721
$569$	1.26751e7	1.64123	0.820614	−	0.571482i	$-0.193631\pi$
$569$	1.26751e7	1.64123	0.820614	+	0.571482i	$0.193631\pi$
$570$	0	0
$571$	−6.67155e6	−0.856321	−0.428160	−	0.903703i	$-0.640838\pi$
$571$	−6.67155e6	−0.856321	−0.428160	+	0.903703i	$0.640838\pi$
$572$	2.53368e6	0.323789
$573$	0	0
$574$	−653856.	−0.0828328
$575$	−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	$0.567474\pi$
$578$	−1.68742e6	−0.210090
$579$	0	0
$580$	−3.30360e6	−0.407772
$581$	−37044.0	−0.00455279
$582$	0	0
$583$	1.24902e6	0.152194
$584$	−4.50189e6	−0.546214
$585$	0	0
$586$	4.34260e6	0.522403
$587$	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
$590$	1.88160e6	0.222534
$591$	0	0
$592$	−1.80275e6	−0.211413
$593$	−1.40222e6	−0.163749	−0.0818747	−	0.996643i	$-0.526091\pi$
$593$	−1.40222e6	−0.163749	−0.0818747	+	0.996643i	$0.526091\pi$
$594$	0	0
$595$	−1.22378e6	−0.141713
$596$	193248.	0.0222843
$597$	0	0
$598$	3.80052e6	0.434600
$599$	−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	$0.532819\pi$
$602$	−4.60953e6	−0.518400
$603$	0	0
$604$	−3.33467e6	−0.371930
$605$	74350.0	0.00825834
$606$	0	0
$607$	−1.36917e7	−1.50830	−0.754148	−	0.656704i	$-0.771950\pi$
$607$	−1.36917e7	−1.50830	−0.754148	+	0.656704i	$0.771950\pi$
$608$	2.39821e6	0.263104
$609$	0	0
$610$	2.16680e6	0.235773
$611$	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	$0.294456\pi$
$614$	5852.00	0.000626446 0
$615$	0	0
$616$	−1.27008e6	−0.134859
$617$	1.37060e7	1.44944	0.724718	−	0.689045i	$-0.241970\pi$
$617$	1.37060e7	1.44944	0.724718	+	0.689045i	$0.241970\pi$
$618$	0	0
$619$	−7.93359e6	−0.832230	−0.416115	−	0.909312i	$-0.636609\pi$
$619$	−7.93359e6	−0.832230	−0.416115	+	0.909312i	$0.636609\pi$
$620$	1.60640e6	0.167832
$621$	0	0
$622$	−1.24791e7	−1.29332
$623$	−6.63382e6	−0.684768
$624$	0	0
$625$	390625.	0.0400000
$626$	3.32570e6	0.339193
$627$	0	0
$628$	5.82550e6	0.589433
$629$	7.03496e6	0.708981
$630$	0	0
$631$	−1.31143e7	−1.31121	−0.655604	−	0.755105i	$-0.727586\pi$
$631$	−1.31143e7	−1.31121	−0.655604	+	0.755105i	$0.727586\pi$
$632$	3.76467e6	0.374916
$633$	0	0
$634$	5.03402e6	0.497384
$635$	−7.09960e6	−0.698714
$636$	0	0
$637$	−938791.	−0.0916685
$638$	1.33796e7	1.30134
$639$	0	0
$640$	409600.	0.0395285
$641$	1.27270e7	1.22344	0.611719	−	0.791075i	$-0.290478\pi$
$641$	1.27270e7	1.22344	0.611719	+	0.791075i	$0.290478\pi$
$642$	0	0
$643$	1.88399e7	1.79701	0.898505	−	0.438964i	$-0.144655\pi$
$643$	1.88399e7	1.79701	0.898505	+	0.438964i	$0.144655\pi$
$644$	−1.90512e6	−0.181012
$645$	0	0
$646$	−9.35863e6	−0.882330
$647$	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
$650$	−977500.	−0.0907472
$651$	0	0
$652$	10016.0	0.000922731 0
$653$	−2.01024e7	−1.84486	−0.922432	−	0.386158i	$-0.873802\pi$
$653$	−2.01024e7	−1.84486	−0.922432	+	0.386158i	$0.873802\pi$
$654$	0	0
$655$	−6.53595e6	−0.595258
$656$	−854016.	−0.0774830
$657$	0	0
$658$	−2.02213e6	−0.182073
$659$	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	$0.503217\pi$
$662$	−9.21861e6	−0.817561
$663$	0	0
$664$	−48384.0	−0.00425874
$665$	2.86895e6	0.251576
$666$	0	0
$667$	2.00694e7	1.74670
$668$	−7.12987e6	−0.618216
$669$	0	0
$670$	5.21240e6	0.448591
$671$	−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	$0.192739\pi$
$674$	3.07666e6	0.260874
$675$	0	0
$676$	−3.49459e6	−0.294124
$677$	−3.35334e6	−0.281194	−0.140597	−	0.990067i	$-0.544902\pi$
$677$	−3.35334e6	−0.281194	−0.140597	+	0.990067i	$0.544902\pi$
$678$	0	0
$679$	5.41132e6	0.450431
$680$	−1.59840e6	−0.132560
$681$	0	0
$682$	−6.50592e6	−0.535609
$683$	−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
$686$	470596.	0.0381802
$687$	0	0
$688$	−6.02061e6	−0.484919
$689$	1.20584e6	0.0967705
$690$	0	0
$691$	1.35824e7	1.08213	0.541066	−	0.840980i	$-0.318021\pi$
$691$	1.35824e7	1.08213	0.541066	+	0.840980i	$0.318021\pi$
$692$	−1.02955e7	−0.817299
$693$	0	0
$694$	−1.52830e6	−0.120451
$695$	−4.56565e6	−0.358542
$696$	0	0
$697$	3.33266e6	0.259842
$698$	−1.55484e7	−1.20794
$699$	0	0
$700$	490000.	0.0377964
$701$	−2.05454e7	−1.57913	−0.789567	−	0.613664i	$-0.789695\pi$
$701$	−2.05454e7	−1.57913	−0.789567	+	0.613664i	$0.789695\pi$
$702$	0	0
$703$	−1.64924e7	−1.25862
$704$	−1.65888e6	−0.126149
$705$	0	0
$706$	1.46581e6	0.110679
$707$	−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	$0.0891040\pi$
$710$	2.85600e6	0.212624
$711$	0	0
$712$	−8.66458e6	−0.640542
$713$	−9.75888e6	−0.718913
$714$	0	0
$715$	3.95888e6	0.289605
$716$	−3.92237e6	−0.285934
$717$	0	0
$718$	1.25943e7	0.911726
$719$	−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
$722$	1.20355e7	0.859250
$723$	0	0
$724$	1.09789e7	0.778416
$725$	−5.16187e6	−0.364722
$726$	0	0
$727$	−1.90997e7	−1.34027	−0.670134	−	0.742240i	$-0.733763\pi$
$727$	−1.90997e7	−1.34027	−0.670134	+	0.742240i	$0.733763\pi$
$728$	−1.22618e6	−0.0857481
$729$	0	0
$730$	−7.03420e6	−0.488548
$731$	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	$0.525237\pi$
$734$	8.54959e6	0.585740
$735$	0	0
$736$	−2.48832e6	−0.169321
$737$	−2.11102e7	−1.43161
$738$	0	0
$739$	3.62955e6	0.244479	0.122240	−	0.992501i	$-0.460992\pi$
$739$	3.62955e6	0.244479	0.122240	+	0.992501i	$0.460992\pi$
$740$	−2.81680e6	−0.189094
$741$	0	0
$742$	−604464.	−0.0403052
$743$	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
$746$	−822496.	−0.0541111
$747$	0	0
$748$	6.47352e6	0.423045
$749$	−1.73254e6	−0.112844
$750$	0	0
$751$	−2.48272e7	−1.60630	−0.803152	−	0.595774i	$-0.796845\pi$
$751$	−2.48272e7	−1.60630	−0.803152	+	0.595774i	$0.796845\pi$
$752$	−2.64115e6	−0.170313
$753$	0	0
$754$	1.29171e7	0.827439
$755$	−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	$0.633491\pi$
$758$	1.40215e7	0.886380
$759$	0	0
$760$	3.74720e6	0.235328
$761$	−2.89560e7	−1.81250	−0.906249	−	0.422744i	$-0.861067\pi$
$761$	−2.89560e7	−1.81250	−0.906249	+	0.422744i	$0.861067\pi$
$762$	0	0
$763$	−7.40797e6	−0.460668
$764$	8.43250e6	0.522664
$765$	0	0
$766$	−4.51618e6	−0.278099
$767$	−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	$0.682739\pi$
$770$	−1.98450e6	−0.120621
$771$	0	0
$772$	2.29146e6	0.138378
$773$	−1.73536e7	−1.04458	−0.522290	−	0.852768i	$-0.674922\pi$
$773$	−1.73536e7	−1.04458	−0.522290	+	0.852768i	$0.674922\pi$
$774$	0	0
$775$	2.51000e6	0.150113
$776$	7.06784e6	0.421340
$777$	0	0
$778$	4.80011e6	0.284316
$779$	−7.81291e6	−0.461285
$780$	0	0
$781$	−1.15668e7	−0.678556
$782$	9.71028e6	0.567825
$783$	0	0
$784$	614656.	0.0357143
$785$	9.10235e6	0.527205
$786$	0	0
$787$	812177.	0.0467427	0.0233714	−	0.999727i	$-0.492560\pi$
$787$	812177.	0.0467427	0.0233714	+	0.999727i	$0.492560\pi$
$788$	−5.57549e6	−0.319865
$789$	0	0
$790$	5.88230e6	0.335335
$791$	6.55061e6	0.372255
$792$	0	0
$793$	−8.47219e6	−0.478424
$794$	−1.76735e7	−0.994879
$795$	0	0
$796$	1.20723e7	0.675318
$797$	8.58201e6	0.478568	0.239284	−	0.970950i	$-0.423087\pi$
$797$	8.58201e6	0.478568	0.239284	+	0.970950i	$0.423087\pi$
$798$	0	0
$799$	1.03067e7	0.571152
$800$	640000.	0.0353553
$801$	0	0
$802$	1.25311e7	0.687946
$803$	2.84885e7	1.55912
$804$	0	0
$805$	−2.97675e6	−0.161902
$806$	−6.28102e6	−0.340559
$807$	0	0
$808$	−2.14080e6	−0.115358
$809$	2.83000e6	0.152025	0.0760125	−	0.997107i	$-0.475781\pi$
$809$	2.83000e6	0.152025	0.0760125	+	0.997107i	$0.475781\pi$
$810$	0	0
$811$	−1.06484e7	−0.568504	−0.284252	−	0.958750i	$-0.591745\pi$
$811$	−1.06484e7	−0.568504	−0.284252	+	0.958750i	$0.591745\pi$
$812$	−6.47506e6	−0.344630
$813$	0	0
$814$	1.14080e7	0.603462
$815$	15650.0	0.000825316 0
$816$	0	0
$817$	−5.50792e7	−2.88690
$818$	3.44598e6	0.180065
$819$	0	0
$820$	−1.33440e6	−0.0693029
$821$	2.59970e7	1.34606	0.673032	−	0.739613i	$-0.264992\pi$
$821$	2.59970e7	1.34606	0.673032	+	0.739613i	$0.264992\pi$
$822$	0	0
$823$	−2.03099e7	−1.04522	−0.522611	−	0.852571i	$-0.675042\pi$
$823$	−2.03099e7	−1.04522	−0.522611	+	0.852571i	$0.675042\pi$
$824$	−7.05990e6	−0.362227
$825$	0	0
$826$	3.68794e6	0.188076
$827$	−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	$0.554238\pi$
$830$	−75600.0	−0.00380914
$831$	0	0
$832$	−1.60154e6	−0.0802100
$833$	−2.39860e6	−0.119769
$834$	0	0
$835$	−1.11404e7	−0.552950
$836$	−1.51762e7	−0.751011
$837$	0	0
$838$	−1.86318e7	−0.916527
$839$	−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
$842$	2.79958e7	1.36086
$843$	0	0
$844$	−9.45198e6	−0.456738
$845$	−5.46030e6	−0.263072
$846$	0	0
$847$	145726.	0.00697957
$848$	−789504.	−0.0377020
$849$	0	0
$850$	−2.49750e6	−0.118565
$851$	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	$0.427870\pi$
$854$	4.24693e6	0.199265
$855$	0	0
$856$	−2.26291e6	−0.105556
$857$	−3.51377e7	−1.63426	−0.817130	−	0.576453i	$-0.804436\pi$
$857$	−3.51377e7	−1.63426	−0.817130	+	0.576453i	$0.804436\pi$
$858$	0	0
$859$	−1.60428e7	−0.741816	−0.370908	−	0.928670i	$-0.620953\pi$
$859$	−1.60428e7	−0.741816	−0.370908	+	0.928670i	$0.620953\pi$
$860$	−9.40720e6	−0.433725
$861$	0	0
$862$	908364.	0.0416382
$863$	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
$866$	−2.83845e7	−1.28614
$867$	0	0
$868$	3.14854e6	0.141844
$869$	−2.38233e7	−1.07017
$870$	0	0
$871$	−2.03805e7	−0.910268
$872$	−9.67571e6	−0.430915
$873$	0	0
$874$	−2.27642e7	−1.00803
$875$	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	$0.317797\pi$
$878$	2.37303e6	0.103888
$879$	0	0
$880$	−2.59200e6	−0.112831
$881$	1.27792e7	0.554707	0.277353	−	0.960768i	$-0.410543\pi$
$881$	1.27792e7	0.554707	0.277353	+	0.960768i	$0.410543\pi$
$882$	0	0
$883$	−2.63417e7	−1.13695	−0.568476	−	0.822700i	$-0.692467\pi$
$883$	−2.63417e7	−1.13695	−0.568476	+	0.822700i	$0.692467\pi$
$884$	6.24974e6	0.268987
$885$	0	0
$886$	1.31077e7	0.560972
$887$	−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
$890$	−1.35384e7	−0.572918
$891$	0	0
$892$	−6.33765e6	−0.266696
$893$	−2.41624e7	−1.01394
$894$	0	0
$895$	−6.12870e6	−0.255747
$896$	802816.	0.0334077
$897$	0	0
$898$	1.73172e7	0.716616
$899$	−3.31681e7	−1.36874
$900$	0	0
$901$	3.08092e6	0.126435
$902$	5.40432e6	0.221169
$903$	0	0
$904$	8.55590e6	0.348213
$905$	1.71545e7	0.696236
$906$	0	0
$907$	−4.11852e7	−1.66235	−0.831177	−	0.556008i	$-0.812332\pi$
$907$	−4.11852e7	−1.66235	−0.831177	+	0.556008i	$0.812332\pi$
$908$	−152592.	−0.00614210
$909$	0	0
$910$	−1.91590e6	−0.0766954
$911$	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
$914$	−1.96655e7	−0.778646
$915$	0	0
$916$	1.12809e7	0.444227
$917$	−1.28105e7	−0.503085
$918$	0	0
$919$	1.59154e7	0.621624	0.310812	−	0.950471i	$-0.399399\pi$
$919$	1.59154e7	0.621624	0.310812	+	0.950471i	$0.399399\pi$
$920$	−3.88800e6	−0.151446
$921$	0	0
$922$	−2.81168e7	−1.08928
$923$	−1.11670e7	−0.431450
$924$	0	0
$925$	−4.40125e6	−0.169130
$926$	1.15424e7	0.442351
$927$	0	0
$928$	−8.45722e6	−0.322372
$929$	3.37148e7	1.28169	0.640843	−	0.767672i	$-0.278585\pi$
$929$	3.37148e7	1.28169	0.640843	+	0.767672i	$0.278585\pi$
$930$	0	0
$931$	5.62314e6	0.212620
$932$	−8.54746e6	−0.322327
$933$	0	0
$934$	2.40233e7	0.901085
$935$	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	$0.771056\pi$
$938$	1.02163e7	0.379129
$939$	0	0
$940$	−4.12680e6	−0.152333
$941$	−3.62378e7	−1.33410	−0.667048	−	0.745015i	$-0.732443\pi$
$941$	−3.62378e7	−1.33410	−0.667048	+	0.745015i	$0.732443\pi$
$942$	0	0
$943$	8.10648e6	0.296861
$944$	4.81690e6	0.175929
$945$	0	0
$946$	3.80992e7	1.38416
$947$	−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
$950$	5.85500e6	0.210483
$951$	0	0
$952$	−3.13286e6	−0.112034
$953$	−3.59497e7	−1.28222	−0.641110	−	0.767449i	$-0.721526\pi$
$953$	−3.59497e7	−1.28222	−0.641110	+	0.767449i	$0.721526\pi$
$954$	0	0
$955$	1.31758e7	0.467485
$956$	1.44195e7	0.510278
$957$	0	0
$958$	−3.76438e6	−0.132519
$959$	−1.94393e6	−0.0682549
$960$	0	0
$961$	−1.25009e7	−0.436649
$962$	1.10137e7	0.383703
$963$	0	0
$964$	−1.52382e7	−0.528132
$965$	3.58040e6	0.123769
$966$	0	0
$967$	1.19506e6	0.0410982	0.0205491	−	0.999789i	$-0.493459\pi$
$967$	1.19506e6	0.0410982	0.0205491	+	0.999789i	$0.493459\pi$
$968$	190336.	0.00652879
$969$	0	0
$970$	1.10435e7	0.376858
$971$	−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
$974$	7.64482e6	0.258208
$975$	0	0
$976$	5.54701e6	0.186395
$977$	−5.36858e7	−1.79938	−0.899690	−	0.436529i	$-0.856208\pi$
$977$	−5.36858e7	−1.79938	−0.899690	+	0.436529i	$0.856208\pi$
$978$	0	0
$979$	5.48305e7	1.82838
$980$	960400.	0.0319438
$981$	0	0
$982$	−1.58196e7	−0.523501
$983$	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
$986$	3.30030e7	1.08109
$987$	0	0
$988$	−1.46516e7	−0.477520
$989$	5.71487e7	1.85787
$990$	0	0
$991$	−1.97082e7	−0.637475	−0.318738	−	0.947843i	$-0.603259\pi$
$991$	−1.97082e7	−0.637475	−0.318738	+	0.947843i	$0.603259\pi$
$992$	4.11238e6	0.132683
$993$	0	0
$994$	5.59776e6	0.179700
$995$	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	$0.322642\pi$
$998$	2.83883e7	0.902222
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.6.a.n.1.1		1
3.2	odd	2		70.6.a.c.1.1	✓	1
12.11	even	2		560.6.a.d.1.1		1
15.2	even	4		350.6.c.e.99.1		2
15.8	even	4		350.6.c.e.99.2		2
15.14	odd	2		350.6.a.k.1.1		1
21.20	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	3.2	odd	2
350.6.a.k.1.1		1	15.14	odd	2
350.6.c.e.99.1		2	15.2	even	4
350.6.c.e.99.2		2	15.8	even	4
490.6.a.e.1.1		1	21.20	even	2
560.6.a.d.1.1		1	12.11	even	2
630.6.a.n.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	630.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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