LMFDB - Embedded newform 525.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(1,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("525.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.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:	$30.9760027530$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +3.00000 q^{3} -4.00000 q^{4} -6.00000 q^{6} -7.00000 q^{7} +24.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +3.00000 q^{3} -4.00000 q^{4} -6.00000 q^{6} -7.00000 q^{7} +24.0000 q^{8} +9.00000 q^{9} -21.0000 q^{11} -12.0000 q^{12} +24.0000 q^{13} +14.0000 q^{14} -16.0000 q^{16} -22.0000 q^{17} -18.0000 q^{18} +16.0000 q^{19} -21.0000 q^{21} +42.0000 q^{22} -25.0000 q^{23} +72.0000 q^{24} -48.0000 q^{26} +27.0000 q^{27} +28.0000 q^{28} +167.000 q^{29} +10.0000 q^{31} -160.000 q^{32} -63.0000 q^{33} +44.0000 q^{34} -36.0000 q^{36} -133.000 q^{37} -32.0000 q^{38} +72.0000 q^{39} -168.000 q^{41} +42.0000 q^{42} -97.0000 q^{43} +84.0000 q^{44} +50.0000 q^{46} -400.000 q^{47} -48.0000 q^{48} +49.0000 q^{49} -66.0000 q^{51} -96.0000 q^{52} -182.000 q^{53} -54.0000 q^{54} -168.000 q^{56} +48.0000 q^{57} -334.000 q^{58} +488.000 q^{59} +28.0000 q^{61} -20.0000 q^{62} -63.0000 q^{63} +448.000 q^{64} +126.000 q^{66} -967.000 q^{67} +88.0000 q^{68} -75.0000 q^{69} -285.000 q^{71} +216.000 q^{72} -838.000 q^{73} +266.000 q^{74} -64.0000 q^{76} +147.000 q^{77} -144.000 q^{78} -469.000 q^{79} +81.0000 q^{81} +336.000 q^{82} -406.000 q^{83} +84.0000 q^{84} +194.000 q^{86} +501.000 q^{87} -504.000 q^{88} +324.000 q^{89} -168.000 q^{91} +100.000 q^{92} +30.0000 q^{93} +800.000 q^{94} -480.000 q^{96} -114.000 q^{97} -98.0000 q^{98} -189.000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−2.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	24.0000	1.06066
$9$	9.00000	0.333333
$10$	0	0
$11$	−21.0000	−0.575613	−0.287806	−	0.957689i	$-0.592926\pi$
$11$	−21.0000	−0.575613	−0.287806	+	0.957689i	$0.592926\pi$
$12$	−12.0000	−0.288675
$13$	24.0000	0.512031	0.256015	−	0.966673i	$-0.417590\pi$
$13$	24.0000	0.512031	0.256015	+	0.966673i	$0.417590\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	−16.0000	−0.250000
$17$	−22.0000	−0.313870	−0.156935	−	0.987609i	$-0.550161\pi$
$17$	−22.0000	−0.313870	−0.156935	+	0.987609i	$0.550161\pi$
$18$	−18.0000	−0.235702
$19$	16.0000	0.193192	0.0965961	−	0.995324i	$-0.469204\pi$
$19$	16.0000	0.193192	0.0965961	+	0.995324i	$0.469204\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	42.0000	0.407020
$23$	−25.0000	−0.226646	−0.113323	−	0.993558i	$-0.536150\pi$
$23$	−25.0000	−0.226646	−0.113323	+	0.993558i	$0.536150\pi$
$24$	72.0000	0.612372
$25$	0	0
$26$	−48.0000	−0.362061
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	167.000	1.06935	0.534675	−	0.845058i	$-0.320434\pi$
$29$	167.000	1.06935	0.534675	+	0.845058i	$0.320434\pi$
$30$	0	0
$31$	10.0000	0.0579372	0.0289686	−	0.999580i	$-0.490778\pi$
$31$	10.0000	0.0579372	0.0289686	+	0.999580i	$0.490778\pi$
$32$	−160.000	−0.883883
$33$	−63.0000	−0.332330
$34$	44.0000	0.221939
$35$	0	0
$36$	−36.0000	−0.166667
$37$	−133.000	−0.590948	−0.295474	−	0.955351i	$-0.595478\pi$
$37$	−133.000	−0.590948	−0.295474	+	0.955351i	$0.595478\pi$
$38$	−32.0000	−0.136608
$39$	72.0000	0.295621
$40$	0	0
$41$	−168.000	−0.639932	−0.319966	−	0.947429i	$-0.603671\pi$
$41$	−168.000	−0.639932	−0.319966	+	0.947429i	$0.603671\pi$
$42$	42.0000	0.154303
$43$	−97.0000	−0.344008	−0.172004	−	0.985096i	$-0.555024\pi$
$43$	−97.0000	−0.344008	−0.172004	+	0.985096i	$0.555024\pi$
$44$	84.0000	0.287806
$45$	0	0
$46$	50.0000	0.160263
$47$	−400.000	−1.24140	−0.620702	−	0.784046i	$-0.713152\pi$
$47$	−400.000	−1.24140	−0.620702	+	0.784046i	$0.713152\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	0	0
$51$	−66.0000	−0.181213
$52$	−96.0000	−0.256015
$53$	−182.000	−0.471691	−0.235845	−	0.971791i	$-0.575786\pi$
$53$	−182.000	−0.471691	−0.235845	+	0.971791i	$0.575786\pi$
$54$	−54.0000	−0.136083
$55$	0	0
$56$	−168.000	−0.400892
$57$	48.0000	0.111540
$58$	−334.000	−0.756144
$59$	488.000	1.07682	0.538408	−	0.842684i	$-0.319026\pi$
$59$	488.000	1.07682	0.538408	+	0.842684i	$0.319026\pi$
$60$	0	0
$61$	28.0000	0.0587710	0.0293855	−	0.999568i	$-0.490645\pi$
$61$	28.0000	0.0587710	0.0293855	+	0.999568i	$0.490645\pi$
$62$	−20.0000	−0.0409678
$63$	−63.0000	−0.125988
$64$	448.000	0.875000
$65$	0	0
$66$	126.000	0.234993
$67$	−967.000	−1.76325	−0.881626	−	0.471949i	$-0.843551\pi$
$67$	−967.000	−1.76325	−0.881626	+	0.471949i	$0.843551\pi$
$68$	88.0000	0.156935
$69$	−75.0000	−0.130854
$70$	0	0
$71$	−285.000	−0.476384	−0.238192	−	0.971218i	$-0.576555\pi$
$71$	−285.000	−0.476384	−0.238192	+	0.971218i	$0.576555\pi$
$72$	216.000	0.353553
$73$	−838.000	−1.34357	−0.671784	−	0.740747i	$-0.734472\pi$
$73$	−838.000	−1.34357	−0.671784	+	0.740747i	$0.734472\pi$
$74$	266.000	0.417863
$75$	0	0
$76$	−64.0000	−0.0965961
$77$	147.000	0.217561
$78$	−144.000	−0.209036
$79$	−469.000	−0.667932	−0.333966	−	0.942585i	$-0.608387\pi$
$79$	−469.000	−0.667932	−0.333966	+	0.942585i	$0.608387\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	336.000	0.452500
$83$	−406.000	−0.536919	−0.268460	−	0.963291i	$-0.586515\pi$
$83$	−406.000	−0.536919	−0.268460	+	0.963291i	$0.586515\pi$
$84$	84.0000	0.109109
$85$	0	0
$86$	194.000	0.243251
$87$	501.000	0.617389
$88$	−504.000	−0.610529
$89$	324.000	0.385887	0.192943	−	0.981210i	$-0.438197\pi$
$89$	324.000	0.385887	0.192943	+	0.981210i	$0.438197\pi$
$90$	0	0
$91$	−168.000	−0.193530
$92$	100.000	0.113323
$93$	30.0000	0.0334501
$94$	800.000	0.877805
$95$	0	0
$96$	−480.000	−0.510310
$97$	−114.000	−0.119329	−0.0596647	−	0.998218i	$-0.519003\pi$
$97$	−114.000	−0.119329	−0.0596647	+	0.998218i	$0.519003\pi$
$98$	−98.0000	−0.101015
$99$	−189.000	−0.191871
$100$	0	0
$101$	34.0000	0.0334963	0.0167482	−	0.999860i	$-0.494669\pi$
$101$	34.0000	0.0334963	0.0167482	+	0.999860i	$0.494669\pi$
$102$	132.000	0.128137
$103$	−1976.00	−1.89030	−0.945151	−	0.326634i	$-0.894085\pi$
$103$	−1976.00	−1.89030	−0.945151	+	0.326634i	$0.894085\pi$
$104$	576.000	0.543091
$105$	0	0
$106$	364.000	0.333536
$107$	828.000	0.748091	0.374046	−	0.927410i	$-0.377970\pi$
$107$	828.000	0.748091	0.374046	+	0.927410i	$0.377970\pi$
$108$	−108.000	−0.0962250
$109$	−1467.00	−1.28911	−0.644556	−	0.764557i	$-0.722958\pi$
$109$	−1467.00	−1.28911	−0.644556	+	0.764557i	$0.722958\pi$
$110$	0	0
$111$	−399.000	−0.341184
$112$	112.000	0.0944911
$113$	783.000	0.651845	0.325922	−	0.945397i	$-0.394325\pi$
$113$	783.000	0.651845	0.325922	+	0.945397i	$0.394325\pi$
$114$	−96.0000	−0.0788704
$115$	0	0
$116$	−668.000	−0.534675
$117$	216.000	0.170677
$118$	−976.000	−0.761424
$119$	154.000	0.118632
$120$	0	0
$121$	−890.000	−0.668670
$122$	−56.0000	−0.0415574
$123$	−504.000	−0.369465
$124$	−40.0000	−0.0289686
$125$	0	0
$126$	126.000	0.0890871
$127$	−515.000	−0.359834	−0.179917	−	0.983682i	$-0.557583\pi$
$127$	−515.000	−0.359834	−0.179917	+	0.983682i	$0.557583\pi$
$128$	384.000	0.265165
$129$	−291.000	−0.198613
$130$	0	0
$131$	−1526.00	−1.01777	−0.508883	−	0.860836i	$-0.669941\pi$
$131$	−1526.00	−1.01777	−0.508883	+	0.860836i	$0.669941\pi$
$132$	252.000	0.166165
$133$	−112.000	−0.0730198
$134$	1934.00	1.24681
$135$	0	0
$136$	−528.000	−0.332909
$137$	−1822.00	−1.13623	−0.568117	−	0.822948i	$-0.692328\pi$
$137$	−1822.00	−1.13623	−0.568117	+	0.822948i	$0.692328\pi$
$138$	150.000	0.0925279
$139$	−3042.00	−1.85625	−0.928126	−	0.372266i	$-0.878581\pi$
$139$	−3042.00	−1.85625	−0.928126	+	0.372266i	$0.878581\pi$
$140$	0	0
$141$	−1200.00	−0.716725
$142$	570.000	0.336854
$143$	−504.000	−0.294731
$144$	−144.000	−0.0833333
$145$	0	0
$146$	1676.00	0.950046
$147$	147.000	0.0824786
$148$	532.000	0.295474
$149$	349.000	0.191887	0.0959436	−	0.995387i	$-0.469413\pi$
$149$	349.000	0.191887	0.0959436	+	0.995387i	$0.469413\pi$
$150$	0	0
$151$	−2167.00	−1.16787	−0.583934	−	0.811801i	$-0.698487\pi$
$151$	−2167.00	−1.16787	−0.583934	+	0.811801i	$0.698487\pi$
$152$	384.000	0.204911
$153$	−198.000	−0.104623
$154$	−294.000	−0.153839
$155$	0	0
$156$	−288.000	−0.147811
$157$	−1204.00	−0.612036	−0.306018	−	0.952026i	$-0.598997\pi$
$157$	−1204.00	−0.612036	−0.306018	+	0.952026i	$0.598997\pi$
$158$	938.000	0.472299
$159$	−546.000	−0.272331
$160$	0	0
$161$	175.000	0.0856642
$162$	−162.000	−0.0785674
$163$	3252.00	1.56268	0.781338	−	0.624108i	$-0.214537\pi$
$163$	3252.00	1.56268	0.781338	+	0.624108i	$0.214537\pi$
$164$	672.000	0.319966
$165$	0	0
$166$	812.000	0.379659
$167$	−1276.00	−0.591257	−0.295628	−	0.955303i	$-0.595529\pi$
$167$	−1276.00	−0.591257	−0.295628	+	0.955303i	$0.595529\pi$
$168$	−504.000	−0.231455
$169$	−1621.00	−0.737824
$170$	0	0
$171$	144.000	0.0643974
$172$	388.000	0.172004
$173$	1140.00	0.500998	0.250499	−	0.968117i	$-0.419405\pi$
$173$	1140.00	0.500998	0.250499	+	0.968117i	$0.419405\pi$
$174$	−1002.00	−0.436560
$175$	0	0
$176$	336.000	0.143903
$177$	1464.00	0.621700
$178$	−648.000	−0.272863
$179$	2724.00	1.13744	0.568719	−	0.822532i	$-0.307439\pi$
$179$	2724.00	1.13744	0.568719	+	0.822532i	$0.307439\pi$
$180$	0	0
$181$	4474.00	1.83729	0.918646	−	0.395082i	$-0.129284\pi$
$181$	4474.00	1.83729	0.918646	+	0.395082i	$0.129284\pi$
$182$	336.000	0.136846
$183$	84.0000	0.0339315
$184$	−600.000	−0.240394
$185$	0	0
$186$	−60.0000	−0.0236528
$187$	462.000	0.180667
$188$	1600.00	0.620702
$189$	−189.000	−0.0727393
$190$	0	0
$191$	3932.00	1.48958	0.744789	−	0.667300i	$-0.232550\pi$
$191$	3932.00	1.48958	0.744789	+	0.667300i	$0.232550\pi$
$192$	1344.00	0.505181
$193$	3441.00	1.28336	0.641680	−	0.766972i	$-0.278238\pi$
$193$	3441.00	1.28336	0.641680	+	0.766972i	$0.278238\pi$
$194$	228.000	0.0843786
$195$	0	0
$196$	−196.000	−0.0714286
$197$	−201.000	−0.0726937	−0.0363468	−	0.999339i	$-0.511572\pi$
$197$	−201.000	−0.0726937	−0.0363468	+	0.999339i	$0.511572\pi$
$198$	378.000	0.135673
$199$	−1384.00	−0.493011	−0.246505	−	0.969141i	$-0.579282\pi$
$199$	−1384.00	−0.493011	−0.246505	+	0.969141i	$0.579282\pi$
$200$	0	0
$201$	−2901.00	−1.01801
$202$	−68.0000	−0.0236855
$203$	−1169.00	−0.404176
$204$	264.000	0.0906064
$205$	0	0
$206$	3952.00	1.33665
$207$	−225.000	−0.0755487
$208$	−384.000	−0.128008
$209$	−336.000	−0.111204
$210$	0	0
$211$	3964.00	1.29333	0.646666	−	0.762773i	$-0.276163\pi$
$211$	3964.00	1.29333	0.646666	+	0.762773i	$0.276163\pi$
$212$	728.000	0.235845
$213$	−855.000	−0.275041
$214$	−1656.00	−0.528981
$215$	0	0
$216$	648.000	0.204124
$217$	−70.0000	−0.0218982
$218$	2934.00	0.911539
$219$	−2514.00	−0.775709
$220$	0	0
$221$	−528.000	−0.160711
$222$	798.000	0.241253
$223$	−762.000	−0.228822	−0.114411	−	0.993434i	$-0.536498\pi$
$223$	−762.000	−0.228822	−0.114411	+	0.993434i	$0.536498\pi$
$224$	1120.00	0.334077
$225$	0	0
$226$	−1566.00	−0.460924
$227$	−5764.00	−1.68533	−0.842665	−	0.538437i	$-0.819015\pi$
$227$	−5764.00	−1.68533	−0.842665	+	0.538437i	$0.819015\pi$
$228$	−192.000	−0.0557698
$229$	1510.00	0.435736	0.217868	−	0.975978i	$-0.430090\pi$
$229$	1510.00	0.435736	0.217868	+	0.975978i	$0.430090\pi$
$230$	0	0
$231$	441.000	0.125609
$232$	4008.00	1.13422
$233$	5937.00	1.66930	0.834648	−	0.550784i	$-0.185671\pi$
$233$	5937.00	1.66930	0.834648	+	0.550784i	$0.185671\pi$
$234$	−432.000	−0.120687
$235$	0	0
$236$	−1952.00	−0.538408
$237$	−1407.00	−0.385631
$238$	−308.000	−0.0838852
$239$	1456.00	0.394062	0.197031	−	0.980397i	$-0.436870\pi$
$239$	1456.00	0.394062	0.197031	+	0.980397i	$0.436870\pi$
$240$	0	0
$241$	−588.000	−0.157164	−0.0785818	−	0.996908i	$-0.525039\pi$
$241$	−588.000	−0.157164	−0.0785818	+	0.996908i	$0.525039\pi$
$242$	1780.00	0.472821
$243$	243.000	0.0641500
$244$	−112.000	−0.0293855
$245$	0	0
$246$	1008.00	0.261251
$247$	384.000	0.0989204
$248$	240.000	0.0614517
$249$	−1218.00	−0.309990
$250$	0	0
$251$	6510.00	1.63708	0.818541	−	0.574448i	$-0.194783\pi$
$251$	6510.00	1.63708	0.818541	+	0.574448i	$0.194783\pi$
$252$	252.000	0.0629941
$253$	525.000	0.130460
$254$	1030.00	0.254441
$255$	0	0
$256$	−4352.00	−1.06250
$257$	−2898.00	−0.703394	−0.351697	−	0.936114i	$-0.614395\pi$
$257$	−2898.00	−0.703394	−0.351697	+	0.936114i	$0.614395\pi$
$258$	582.000	0.140441
$259$	931.000	0.223357
$260$	0	0
$261$	1503.00	0.356450
$262$	3052.00	0.719669
$263$	2953.00	0.692357	0.346178	−	0.938169i	$-0.387479\pi$
$263$	2953.00	0.692357	0.346178	+	0.938169i	$0.387479\pi$
$264$	−1512.00	−0.352489
$265$	0	0
$266$	224.000	0.0516328
$267$	972.000	0.222792
$268$	3868.00	0.881626
$269$	3394.00	0.769278	0.384639	−	0.923067i	$-0.374326\pi$
$269$	3394.00	0.769278	0.384639	+	0.923067i	$0.374326\pi$
$270$	0	0
$271$	−1284.00	−0.287813	−0.143907	−	0.989591i	$-0.545967\pi$
$271$	−1284.00	−0.287813	−0.143907	+	0.989591i	$0.545967\pi$
$272$	352.000	0.0784674
$273$	−504.000	−0.111734
$274$	3644.00	0.803438
$275$	0	0
$276$	300.000	0.0654271
$277$	−3506.00	−0.760488	−0.380244	−	0.924886i	$-0.624160\pi$
$277$	−3506.00	−0.760488	−0.380244	+	0.924886i	$0.624160\pi$
$278$	6084.00	1.31257
$279$	90.0000	0.0193124
$280$	0	0
$281$	5823.00	1.23620	0.618098	−	0.786101i	$-0.287903\pi$
$281$	5823.00	1.23620	0.618098	+	0.786101i	$0.287903\pi$
$282$	2400.00	0.506801
$283$	−3830.00	−0.804487	−0.402244	−	0.915533i	$-0.631770\pi$
$283$	−3830.00	−0.804487	−0.402244	+	0.915533i	$0.631770\pi$
$284$	1140.00	0.238192
$285$	0	0
$286$	1008.00	0.208407
$287$	1176.00	0.241871
$288$	−1440.00	−0.294628
$289$	−4429.00	−0.901486
$290$	0	0
$291$	−342.000	−0.0688948
$292$	3352.00	0.671784
$293$	3572.00	0.712213	0.356107	−	0.934445i	$-0.384104\pi$
$293$	3572.00	0.712213	0.356107	+	0.934445i	$0.384104\pi$
$294$	−294.000	−0.0583212
$295$	0	0
$296$	−3192.00	−0.626795
$297$	−567.000	−0.110777
$298$	−698.000	−0.135685
$299$	−600.000	−0.116050
$300$	0	0
$301$	679.000	0.130023
$302$	4334.00	0.825807
$303$	102.000	0.0193391
$304$	−256.000	−0.0482980
$305$	0	0
$306$	396.000	0.0739798
$307$	7278.00	1.35302	0.676510	−	0.736433i	$-0.263491\pi$
$307$	7278.00	1.35302	0.676510	+	0.736433i	$0.263491\pi$
$308$	−588.000	−0.108781
$309$	−5928.00	−1.09137
$310$	0	0
$311$	3786.00	0.690303	0.345152	−	0.938547i	$-0.387827\pi$
$311$	3786.00	0.690303	0.345152	+	0.938547i	$0.387827\pi$
$312$	1728.00	0.313554
$313$	448.000	0.0809024	0.0404512	−	0.999182i	$-0.487120\pi$
$313$	448.000	0.0809024	0.0404512	+	0.999182i	$0.487120\pi$
$314$	2408.00	0.432775
$315$	0	0
$316$	1876.00	0.333966
$317$	−4081.00	−0.723066	−0.361533	−	0.932359i	$-0.617746\pi$
$317$	−4081.00	−0.723066	−0.361533	+	0.932359i	$0.617746\pi$
$318$	1092.00	0.192567
$319$	−3507.00	−0.615531
$320$	0	0
$321$	2484.00	0.431911
$322$	−350.000	−0.0605737
$323$	−352.000	−0.0606372
$324$	−324.000	−0.0555556
$325$	0	0
$326$	−6504.00	−1.10498
$327$	−4401.00	−0.744269
$328$	−4032.00	−0.678750
$329$	2800.00	0.469207
$330$	0	0
$331$	1071.00	0.177847	0.0889237	−	0.996038i	$-0.471657\pi$
$331$	1071.00	0.177847	0.0889237	+	0.996038i	$0.471657\pi$
$332$	1624.00	0.268460
$333$	−1197.00	−0.196983
$334$	2552.00	0.418082
$335$	0	0
$336$	336.000	0.0545545
$337$	2102.00	0.339772	0.169886	−	0.985464i	$-0.445660\pi$
$337$	2102.00	0.339772	0.169886	+	0.985464i	$0.445660\pi$
$338$	3242.00	0.521721
$339$	2349.00	0.376343
$340$	0	0
$341$	−210.000	−0.0333494
$342$	−288.000	−0.0455358
$343$	−343.000	−0.0539949
$344$	−2328.00	−0.364876
$345$	0	0
$346$	−2280.00	−0.354259
$347$	−11471.0	−1.77463	−0.887313	−	0.461167i	$-0.847431\pi$
$347$	−11471.0	−1.77463	−0.887313	+	0.461167i	$0.847431\pi$
$348$	−2004.00	−0.308694
$349$	−6448.00	−0.988979	−0.494489	−	0.869184i	$-0.664645\pi$
$349$	−6448.00	−0.988979	−0.494489	+	0.869184i	$0.664645\pi$
$350$	0	0
$351$	648.000	0.0985404
$352$	3360.00	0.508774
$353$	−10050.0	−1.51532	−0.757659	−	0.652650i	$-0.773657\pi$
$353$	−10050.0	−1.51532	−0.757659	+	0.652650i	$0.773657\pi$
$354$	−2928.00	−0.439609
$355$	0	0
$356$	−1296.00	−0.192943
$357$	462.000	0.0684920
$358$	−5448.00	−0.804290
$359$	−6597.00	−0.969851	−0.484925	−	0.874556i	$-0.661153\pi$
$359$	−6597.00	−0.969851	−0.484925	+	0.874556i	$0.661153\pi$
$360$	0	0
$361$	−6603.00	−0.962677
$362$	−8948.00	−1.29916
$363$	−2670.00	−0.386057
$364$	672.000	0.0967648
$365$	0	0
$366$	−168.000	−0.0239932
$367$	6500.00	0.924516	0.462258	−	0.886746i	$-0.347039\pi$
$367$	6500.00	0.924516	0.462258	+	0.886746i	$0.347039\pi$
$368$	400.000	0.0566615
$369$	−1512.00	−0.213311
$370$	0	0
$371$	1274.00	0.178282
$372$	−120.000	−0.0167250
$373$	8665.00	1.20283	0.601416	−	0.798936i	$-0.294603\pi$
$373$	8665.00	1.20283	0.601416	+	0.798936i	$0.294603\pi$
$374$	−924.000	−0.127751
$375$	0	0
$376$	−9600.00	−1.31671
$377$	4008.00	0.547540
$378$	378.000	0.0514344
$379$	−217.000	−0.0294104	−0.0147052	−	0.999892i	$-0.504681\pi$
$379$	−217.000	−0.0294104	−0.0147052	+	0.999892i	$0.504681\pi$
$380$	0	0
$381$	−1545.00	−0.207750
$382$	−7864.00	−1.05329
$383$	−4640.00	−0.619042	−0.309521	−	0.950893i	$-0.600169\pi$
$383$	−4640.00	−0.619042	−0.309521	+	0.950893i	$0.600169\pi$
$384$	1152.00	0.153093
$385$	0	0
$386$	−6882.00	−0.907473
$387$	−873.000	−0.114669
$388$	456.000	0.0596647
$389$	−3021.00	−0.393755	−0.196878	−	0.980428i	$-0.563080\pi$
$389$	−3021.00	−0.393755	−0.196878	+	0.980428i	$0.563080\pi$
$390$	0	0
$391$	550.000	0.0711373
$392$	1176.00	0.151523
$393$	−4578.00	−0.587607
$394$	402.000	0.0514022
$395$	0	0
$396$	756.000	0.0959354
$397$	−7826.00	−0.989359	−0.494680	−	0.869075i	$-0.664715\pi$
$397$	−7826.00	−0.989359	−0.494680	+	0.869075i	$0.664715\pi$
$398$	2768.00	0.348611
$399$	−336.000	−0.0421580
$400$	0	0
$401$	−3405.00	−0.424034	−0.212017	−	0.977266i	$-0.568003\pi$
$401$	−3405.00	−0.424034	−0.212017	+	0.977266i	$0.568003\pi$
$402$	5802.00	0.719844
$403$	240.000	0.0296656
$404$	−136.000	−0.0167482
$405$	0	0
$406$	2338.00	0.285796
$407$	2793.00	0.340157
$408$	−1584.00	−0.192205
$409$	4052.00	0.489874	0.244937	−	0.969539i	$-0.421233\pi$
$409$	4052.00	0.489874	0.244937	+	0.969539i	$0.421233\pi$
$410$	0	0
$411$	−5466.00	−0.656005
$412$	7904.00	0.945151
$413$	−3416.00	−0.406998
$414$	450.000	0.0534210
$415$	0	0
$416$	−3840.00	−0.452576
$417$	−9126.00	−1.07171
$418$	672.000	0.0786330
$419$	11322.0	1.32009	0.660043	−	0.751228i	$-0.270538\pi$
$419$	11322.0	1.32009	0.660043	+	0.751228i	$0.270538\pi$
$420$	0	0
$421$	−1757.00	−0.203399	−0.101699	−	0.994815i	$-0.532428\pi$
$421$	−1757.00	−0.203399	−0.101699	+	0.994815i	$0.532428\pi$
$422$	−7928.00	−0.914524
$423$	−3600.00	−0.413801
$424$	−4368.00	−0.500304
$425$	0	0
$426$	1710.00	0.194483
$427$	−196.000	−0.0222134
$428$	−3312.00	−0.374046
$429$	−1512.00	−0.170163
$430$	0	0
$431$	−9304.00	−1.03981	−0.519905	−	0.854224i	$-0.674033\pi$
$431$	−9304.00	−1.03981	−0.519905	+	0.854224i	$0.674033\pi$
$432$	−432.000	−0.0481125
$433$	−5752.00	−0.638391	−0.319196	−	0.947689i	$-0.603413\pi$
$433$	−5752.00	−0.638391	−0.319196	+	0.947689i	$0.603413\pi$
$434$	140.000	0.0154844
$435$	0	0
$436$	5868.00	0.644556
$437$	−400.000	−0.0437863
$438$	5028.00	0.548509
$439$	2344.00	0.254836	0.127418	−	0.991849i	$-0.459331\pi$
$439$	2344.00	0.254836	0.127418	+	0.991849i	$0.459331\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	1056.00	0.113640
$443$	−15132.0	−1.62290	−0.811448	−	0.584424i	$-0.801320\pi$
$443$	−15132.0	−1.62290	−0.811448	+	0.584424i	$0.801320\pi$
$444$	1596.00	0.170592
$445$	0	0
$446$	1524.00	0.161802
$447$	1047.00	0.110786
$448$	−3136.00	−0.330719
$449$	−5055.00	−0.531314	−0.265657	−	0.964068i	$-0.585589\pi$
$449$	−5055.00	−0.531314	−0.265657	+	0.964068i	$0.585589\pi$
$450$	0	0
$451$	3528.00	0.368353
$452$	−3132.00	−0.325922
$453$	−6501.00	−0.674268
$454$	11528.0	1.19171
$455$	0	0
$456$	1152.00	0.118306
$457$	−3795.00	−0.388452	−0.194226	−	0.980957i	$-0.562220\pi$
$457$	−3795.00	−0.388452	−0.194226	+	0.980957i	$0.562220\pi$
$458$	−3020.00	−0.308112
$459$	−594.000	−0.0604042
$460$	0	0
$461$	8300.00	0.838546	0.419273	−	0.907860i	$-0.362285\pi$
$461$	8300.00	0.838546	0.419273	+	0.907860i	$0.362285\pi$
$462$	−882.000	−0.0888189
$463$	−5052.00	−0.507098	−0.253549	−	0.967323i	$-0.581598\pi$
$463$	−5052.00	−0.507098	−0.253549	+	0.967323i	$0.581598\pi$
$464$	−2672.00	−0.267337
$465$	0	0
$466$	−11874.0	−1.18037
$467$	2482.00	0.245938	0.122969	−	0.992410i	$-0.460758\pi$
$467$	2482.00	0.245938	0.122969	+	0.992410i	$0.460758\pi$
$468$	−864.000	−0.0853385
$469$	6769.00	0.666446
$470$	0	0
$471$	−3612.00	−0.353359
$472$	11712.0	1.14214
$473$	2037.00	0.198016
$474$	2814.00	0.272682
$475$	0	0
$476$	−616.000	−0.0593158
$477$	−1638.00	−0.157230
$478$	−2912.00	−0.278644
$479$	14176.0	1.35223	0.676115	−	0.736796i	$-0.263662\pi$
$479$	14176.0	1.35223	0.676115	+	0.736796i	$0.263662\pi$
$480$	0	0
$481$	−3192.00	−0.302584
$482$	1176.00	0.111131
$483$	525.000	0.0494582
$484$	3560.00	0.334335
$485$	0	0
$486$	−486.000	−0.0453609
$487$	1039.00	0.0966768	0.0483384	−	0.998831i	$-0.484607\pi$
$487$	1039.00	0.0966768	0.0483384	+	0.998831i	$0.484607\pi$
$488$	672.000	0.0623361
$489$	9756.00	0.902212
$490$	0	0
$491$	9255.00	0.850656	0.425328	−	0.905039i	$-0.360159\pi$
$491$	9255.00	0.850656	0.425328	+	0.905039i	$0.360159\pi$
$492$	2016.00	0.184732
$493$	−3674.00	−0.335636
$494$	−768.000	−0.0699473
$495$	0	0
$496$	−160.000	−0.0144843
$497$	1995.00	0.180056
$498$	2436.00	0.219196
$499$	14396.0	1.29149	0.645745	−	0.763553i	$-0.276547\pi$
$499$	14396.0	1.29149	0.645745	+	0.763553i	$0.276547\pi$
$500$	0	0
$501$	−3828.00	−0.341362
$502$	−13020.0	−1.15759
$503$	−6998.00	−0.620329	−0.310164	−	0.950683i	$-0.600384\pi$
$503$	−6998.00	−0.620329	−0.310164	+	0.950683i	$0.600384\pi$
$504$	−1512.00	−0.133631
$505$	0	0
$506$	−1050.00	−0.0922494
$507$	−4863.00	−0.425983
$508$	2060.00	0.179917
$509$	−6400.00	−0.557318	−0.278659	−	0.960390i	$-0.589890\pi$
$509$	−6400.00	−0.557318	−0.278659	+	0.960390i	$0.589890\pi$
$510$	0	0
$511$	5866.00	0.507821
$512$	5632.00	0.486136
$513$	432.000	0.0371799
$514$	5796.00	0.497375
$515$	0	0
$516$	1164.00	0.0993067
$517$	8400.00	0.714568
$518$	−1862.00	−0.157937
$519$	3420.00	0.289251
$520$	0	0
$521$	15158.0	1.27463	0.637317	−	0.770602i	$-0.280044\pi$
$521$	15158.0	1.27463	0.637317	+	0.770602i	$0.280044\pi$
$522$	−3006.00	−0.252048
$523$	4120.00	0.344465	0.172232	−	0.985056i	$-0.444902\pi$
$523$	4120.00	0.344465	0.172232	+	0.985056i	$0.444902\pi$
$524$	6104.00	0.508883
$525$	0	0
$526$	−5906.00	−0.489570
$527$	−220.000	−0.0181847
$528$	1008.00	0.0830825
$529$	−11542.0	−0.948632
$530$	0	0
$531$	4392.00	0.358939
$532$	448.000	0.0365099
$533$	−4032.00	−0.327665
$534$	−1944.00	−0.157538
$535$	0	0
$536$	−23208.0	−1.87021
$537$	8172.00	0.656700
$538$	−6788.00	−0.543962
$539$	−1029.00	−0.0822304
$540$	0	0
$541$	3291.00	0.261536	0.130768	−	0.991413i	$-0.458256\pi$
$541$	3291.00	0.261536	0.130768	+	0.991413i	$0.458256\pi$
$542$	2568.00	0.203515
$543$	13422.0	1.06076
$544$	3520.00	0.277424
$545$	0	0
$546$	1008.00	0.0790081
$547$	−20547.0	−1.60608	−0.803040	−	0.595924i	$-0.796786\pi$
$547$	−20547.0	−1.60608	−0.803040	+	0.595924i	$0.796786\pi$
$548$	7288.00	0.568117
$549$	252.000	0.0195903
$550$	0	0
$551$	2672.00	0.206590
$552$	−1800.00	−0.138792
$553$	3283.00	0.252455
$554$	7012.00	0.537746
$555$	0	0
$556$	12168.0	0.928126
$557$	−3169.00	−0.241068	−0.120534	−	0.992709i	$-0.538461\pi$
$557$	−3169.00	−0.241068	−0.120534	+	0.992709i	$0.538461\pi$
$558$	−180.000	−0.0136559
$559$	−2328.00	−0.176143
$560$	0	0
$561$	1386.00	0.104308
$562$	−11646.0	−0.874123
$563$	−24878.0	−1.86231	−0.931157	−	0.364619i	$-0.881199\pi$
$563$	−24878.0	−1.86231	−0.931157	+	0.364619i	$0.881199\pi$
$564$	4800.00	0.358363
$565$	0	0
$566$	7660.00	0.568858
$567$	−567.000	−0.0419961
$568$	−6840.00	−0.505282
$569$	−1425.00	−0.104990	−0.0524948	−	0.998621i	$-0.516717\pi$
$569$	−1425.00	−0.104990	−0.0524948	+	0.998621i	$0.516717\pi$
$570$	0	0
$571$	−14649.0	−1.07363	−0.536814	−	0.843701i	$-0.680372\pi$
$571$	−14649.0	−1.07363	−0.536814	+	0.843701i	$0.680372\pi$
$572$	2016.00	0.147366
$573$	11796.0	0.860009
$574$	−2352.00	−0.171029
$575$	0	0
$576$	4032.00	0.291667
$577$	2108.00	0.152092	0.0760461	−	0.997104i	$-0.475770\pi$
$577$	2108.00	0.152092	0.0760461	+	0.997104i	$0.475770\pi$
$578$	8858.00	0.637447
$579$	10323.0	0.740949
$580$	0	0
$581$	2842.00	0.202936
$582$	684.000	0.0487160
$583$	3822.00	0.271511
$584$	−20112.0	−1.42507
$585$	0	0
$586$	−7144.00	−0.503611
$587$	24366.0	1.71328	0.856638	−	0.515919i	$-0.172549\pi$
$587$	24366.0	1.71328	0.856638	+	0.515919i	$0.172549\pi$
$588$	−588.000	−0.0412393
$589$	160.000	0.0111930
$590$	0	0
$591$	−603.000	−0.0419697
$592$	2128.00	0.147737
$593$	17892.0	1.23902	0.619508	−	0.784990i	$-0.287332\pi$
$593$	17892.0	1.23902	0.619508	+	0.784990i	$0.287332\pi$
$594$	1134.00	0.0783309
$595$	0	0
$596$	−1396.00	−0.0959436
$597$	−4152.00	−0.284640
$598$	1200.00	0.0820596
$599$	8077.00	0.550947	0.275474	−	0.961309i	$-0.411165\pi$
$599$	8077.00	0.550947	0.275474	+	0.961309i	$0.411165\pi$
$600$	0	0
$601$	−7836.00	−0.531842	−0.265921	−	0.963995i	$-0.585676\pi$
$601$	−7836.00	−0.531842	−0.265921	+	0.963995i	$0.585676\pi$
$602$	−1358.00	−0.0919401
$603$	−8703.00	−0.587751
$604$	8668.00	0.583934
$605$	0	0
$606$	−204.000	−0.0136748
$607$	−24092.0	−1.61098	−0.805489	−	0.592610i	$-0.798097\pi$
$607$	−24092.0	−1.61098	−0.805489	+	0.592610i	$0.798097\pi$
$608$	−2560.00	−0.170759
$609$	−3507.00	−0.233351
$610$	0	0
$611$	−9600.00	−0.635637
$612$	792.000	0.0523116
$613$	13647.0	0.899180	0.449590	−	0.893235i	$-0.351570\pi$
$613$	13647.0	0.899180	0.449590	+	0.893235i	$0.351570\pi$
$614$	−14556.0	−0.956730
$615$	0	0
$616$	3528.00	0.230758
$617$	12813.0	0.836032	0.418016	−	0.908440i	$-0.362726\pi$
$617$	12813.0	0.836032	0.418016	+	0.908440i	$0.362726\pi$
$618$	11856.0	0.771712
$619$	−300.000	−0.0194798	−0.00973992	−	0.999953i	$-0.503100\pi$
$619$	−300.000	−0.0194798	−0.00973992	+	0.999953i	$0.503100\pi$
$620$	0	0
$621$	−675.000	−0.0436181
$622$	−7572.00	−0.488118
$623$	−2268.00	−0.145852
$624$	−1152.00	−0.0739053
$625$	0	0
$626$	−896.000	−0.0572066
$627$	−1008.00	−0.0642036
$628$	4816.00	0.306018
$629$	2926.00	0.185481
$630$	0	0
$631$	24615.0	1.55294	0.776472	−	0.630152i	$-0.217007\pi$
$631$	24615.0	1.55294	0.776472	+	0.630152i	$0.217007\pi$
$632$	−11256.0	−0.708449
$633$	11892.0	0.746705
$634$	8162.00	0.511285
$635$	0	0
$636$	2184.00	0.136165
$637$	1176.00	0.0731473
$638$	7014.00	0.435246
$639$	−2565.00	−0.158795
$640$	0	0
$641$	−24117.0	−1.48606	−0.743030	−	0.669258i	$-0.766612\pi$
$641$	−24117.0	−1.48606	−0.743030	+	0.669258i	$0.766612\pi$
$642$	−4968.00	−0.305407
$643$	−14020.0	−0.859868	−0.429934	−	0.902860i	$-0.641463\pi$
$643$	−14020.0	−0.859868	−0.429934	+	0.902860i	$0.641463\pi$
$644$	−700.000	−0.0428321
$645$	0	0
$646$	704.000	0.0428769
$647$	2430.00	0.147656	0.0738278	−	0.997271i	$-0.476478\pi$
$647$	2430.00	0.147656	0.0738278	+	0.997271i	$0.476478\pi$
$648$	1944.00	0.117851
$649$	−10248.0	−0.619829
$650$	0	0
$651$	−210.000	−0.0126429
$652$	−13008.0	−0.781338
$653$	−27514.0	−1.64886	−0.824430	−	0.565963i	$-0.808504\pi$
$653$	−27514.0	−1.64886	−0.824430	+	0.565963i	$0.808504\pi$
$654$	8802.00	0.526277
$655$	0	0
$656$	2688.00	0.159983
$657$	−7542.00	−0.447856
$658$	−5600.00	−0.331779
$659$	−20772.0	−1.22786	−0.613932	−	0.789359i	$-0.710413\pi$
$659$	−20772.0	−1.22786	−0.613932	+	0.789359i	$0.710413\pi$
$660$	0	0
$661$	32132.0	1.89076	0.945378	−	0.325976i	$-0.105693\pi$
$661$	32132.0	1.89076	0.945378	+	0.325976i	$0.105693\pi$
$662$	−2142.00	−0.125757
$663$	−1584.00	−0.0927865
$664$	−9744.00	−0.569489
$665$	0	0
$666$	2394.00	0.139288
$667$	−4175.00	−0.242364
$668$	5104.00	0.295628
$669$	−2286.00	−0.132110
$670$	0	0
$671$	−588.000	−0.0338293
$672$	3360.00	0.192879
$673$	23542.0	1.34841	0.674203	−	0.738546i	$-0.264487\pi$
$673$	23542.0	1.34841	0.674203	+	0.738546i	$0.264487\pi$
$674$	−4204.00	−0.240255
$675$	0	0
$676$	6484.00	0.368912
$677$	30814.0	1.74930	0.874652	−	0.484752i	$-0.161090\pi$
$677$	30814.0	1.74930	0.874652	+	0.484752i	$0.161090\pi$
$678$	−4698.00	−0.266114
$679$	798.000	0.0451023
$680$	0	0
$681$	−17292.0	−0.973026
$682$	420.000	0.0235816
$683$	9009.00	0.504714	0.252357	−	0.967634i	$-0.418794\pi$
$683$	9009.00	0.504714	0.252357	+	0.967634i	$0.418794\pi$
$684$	−576.000	−0.0321987
$685$	0	0
$686$	686.000	0.0381802
$687$	4530.00	0.251572
$688$	1552.00	0.0860021
$689$	−4368.00	−0.241520
$690$	0	0
$691$	−25860.0	−1.42368	−0.711838	−	0.702343i	$-0.752137\pi$
$691$	−25860.0	−1.42368	−0.711838	+	0.702343i	$0.752137\pi$
$692$	−4560.00	−0.250499
$693$	1323.00	0.0725204
$694$	22942.0	1.25485
$695$	0	0
$696$	12024.0	0.654840
$697$	3696.00	0.200855
$698$	12896.0	0.699313
$699$	17811.0	0.963768
$700$	0	0
$701$	24170.0	1.30227	0.651133	−	0.758964i	$-0.274294\pi$
$701$	24170.0	1.30227	0.651133	+	0.758964i	$0.274294\pi$
$702$	−1296.00	−0.0696786
$703$	−2128.00	−0.114166
$704$	−9408.00	−0.503661
$705$	0	0
$706$	20100.0	1.07149
$707$	−238.000	−0.0126604
$708$	−5856.00	−0.310850
$709$	−8426.00	−0.446326	−0.223163	−	0.974781i	$-0.571638\pi$
$709$	−8426.00	−0.446326	−0.223163	+	0.974781i	$0.571638\pi$
$710$	0	0
$711$	−4221.00	−0.222644
$712$	7776.00	0.409295
$713$	−250.000	−0.0131312
$714$	−924.000	−0.0484311
$715$	0	0
$716$	−10896.0	−0.568719
$717$	4368.00	0.227512
$718$	13194.0	0.685788
$719$	−30752.0	−1.59507	−0.797536	−	0.603272i	$-0.793863\pi$
$719$	−30752.0	−1.59507	−0.797536	+	0.603272i	$0.793863\pi$
$720$	0	0
$721$	13832.0	0.714467
$722$	13206.0	0.680715
$723$	−1764.00	−0.0907384
$724$	−17896.0	−0.918646
$725$	0	0
$726$	5340.00	0.272983
$727$	11570.0	0.590244	0.295122	−	0.955460i	$-0.404640\pi$
$727$	11570.0	0.590244	0.295122	+	0.955460i	$0.404640\pi$
$728$	−4032.00	−0.205269
$729$	729.000	0.0370370
$730$	0	0
$731$	2134.00	0.107974
$732$	−336.000	−0.0169657
$733$	32836.0	1.65460	0.827302	−	0.561757i	$-0.189874\pi$
$733$	32836.0	1.65460	0.827302	+	0.561757i	$0.189874\pi$
$734$	−13000.0	−0.653731
$735$	0	0
$736$	4000.00	0.200329
$737$	20307.0	1.01495
$738$	3024.00	0.150833
$739$	−22351.0	−1.11258	−0.556289	−	0.830989i	$-0.687775\pi$
$739$	−22351.0	−1.11258	−0.556289	+	0.830989i	$0.687775\pi$
$740$	0	0
$741$	1152.00	0.0571117
$742$	−2548.00	−0.126065
$743$	−21720.0	−1.07245	−0.536224	−	0.844075i	$-0.680150\pi$
$743$	−21720.0	−1.07245	−0.536224	+	0.844075i	$0.680150\pi$
$744$	720.000	0.0354791
$745$	0	0
$746$	−17330.0	−0.850531
$747$	−3654.00	−0.178973
$748$	−1848.00	−0.0903337
$749$	−5796.00	−0.282752
$750$	0	0
$751$	−6352.00	−0.308639	−0.154319	−	0.988021i	$-0.549318\pi$
$751$	−6352.00	−0.308639	−0.154319	+	0.988021i	$0.549318\pi$
$752$	6400.00	0.310351
$753$	19530.0	0.945170
$754$	−8016.00	−0.387169
$755$	0	0
$756$	756.000	0.0363696
$757$	−7685.00	−0.368978	−0.184489	−	0.982835i	$-0.559063\pi$
$757$	−7685.00	−0.368978	−0.184489	+	0.982835i	$0.559063\pi$
$758$	434.000	0.0207963
$759$	1575.00	0.0753213
$760$	0	0
$761$	−12.0000	−0.000571616 0	−0.000285808	−	1.00000i	$-0.500091\pi$
$761$	−12.0000	−0.000571616 0	−0.000285808		1.00000i	$0.500091\pi$
$762$	3090.00	0.146901
$763$	10269.0	0.487238
$764$	−15728.0	−0.744789
$765$	0	0
$766$	9280.00	0.437728
$767$	11712.0	0.551364
$768$	−13056.0	−0.613435
$769$	−24832.0	−1.16445	−0.582227	−	0.813026i	$-0.697818\pi$
$769$	−24832.0	−1.16445	−0.582227	+	0.813026i	$0.697818\pi$
$770$	0	0
$771$	−8694.00	−0.406105
$772$	−13764.0	−0.641680
$773$	28242.0	1.31409	0.657047	−	0.753850i	$-0.271805\pi$
$773$	28242.0	1.31409	0.657047	+	0.753850i	$0.271805\pi$
$774$	1746.00	0.0810836
$775$	0	0
$776$	−2736.00	−0.126568
$777$	2793.00	0.128955
$778$	6042.00	0.278427
$779$	−2688.00	−0.123630
$780$	0	0
$781$	5985.00	0.274213
$782$	−1100.00	−0.0503017
$783$	4509.00	0.205796
$784$	−784.000	−0.0357143
$785$	0	0
$786$	9156.00	0.415501
$787$	12542.0	0.568074	0.284037	−	0.958813i	$-0.408326\pi$
$787$	12542.0	0.568074	0.284037	+	0.958813i	$0.408326\pi$
$788$	804.000	0.0363468
$789$	8859.00	0.399732
$790$	0	0
$791$	−5481.00	−0.246374
$792$	−4536.00	−0.203510
$793$	672.000	0.0300926
$794$	15652.0	0.699583
$795$	0	0
$796$	5536.00	0.246505
$797$	11058.0	0.491461	0.245731	−	0.969338i	$-0.420972\pi$
$797$	11058.0	0.491461	0.245731	+	0.969338i	$0.420972\pi$
$798$	672.000	0.0298102
$799$	8800.00	0.389639
$800$	0	0
$801$	2916.00	0.128629
$802$	6810.00	0.299837
$803$	17598.0	0.773375
$804$	11604.0	0.509007
$805$	0	0
$806$	−480.000	−0.0209768
$807$	10182.0	0.444143
$808$	816.000	0.0355282
$809$	−17307.0	−0.752141	−0.376070	−	0.926591i	$-0.622725\pi$
$809$	−17307.0	−0.752141	−0.376070	+	0.926591i	$0.622725\pi$
$810$	0	0
$811$	−2706.00	−0.117165	−0.0585823	−	0.998283i	$-0.518658\pi$
$811$	−2706.00	−0.117165	−0.0585823	+	0.998283i	$0.518658\pi$
$812$	4676.00	0.202088
$813$	−3852.00	−0.166169
$814$	−5586.00	−0.240527
$815$	0	0
$816$	1056.00	0.0453032
$817$	−1552.00	−0.0664597
$818$	−8104.00	−0.346393
$819$	−1512.00	−0.0645098
$820$	0	0
$821$	−38862.0	−1.65200	−0.826001	−	0.563669i	$-0.809389\pi$
$821$	−38862.0	−1.65200	−0.826001	+	0.563669i	$0.809389\pi$
$822$	10932.0	0.463865
$823$	27217.0	1.15276	0.576382	−	0.817180i	$-0.304464\pi$
$823$	27217.0	1.15276	0.576382	+	0.817180i	$0.304464\pi$
$824$	−47424.0	−2.00497
$825$	0	0
$826$	6832.00	0.287791
$827$	11301.0	0.475181	0.237590	−	0.971365i	$-0.423642\pi$
$827$	11301.0	0.475181	0.237590	+	0.971365i	$0.423642\pi$
$828$	900.000	0.0377744
$829$	6786.00	0.284303	0.142152	−	0.989845i	$-0.454598\pi$
$829$	6786.00	0.284303	0.142152	+	0.989845i	$0.454598\pi$
$830$	0	0
$831$	−10518.0	−0.439068
$832$	10752.0	0.448027
$833$	−1078.00	−0.0448385
$834$	18252.0	0.757812
$835$	0	0
$836$	1344.00	0.0556019
$837$	270.000	0.0111500
$838$	−22644.0	−0.933442
$839$	8358.00	0.343922	0.171961	−	0.985104i	$-0.444990\pi$
$839$	8358.00	0.343922	0.171961	+	0.985104i	$0.444990\pi$
$840$	0	0
$841$	3500.00	0.143507
$842$	3514.00	0.143825
$843$	17469.0	0.713718
$844$	−15856.0	−0.646666
$845$	0	0
$846$	7200.00	0.292602
$847$	6230.00	0.252734
$848$	2912.00	0.117923
$849$	−11490.0	−0.464471
$850$	0	0
$851$	3325.00	0.133936
$852$	3420.00	0.137520
$853$	−16500.0	−0.662309	−0.331154	−	0.943577i	$-0.607438\pi$
$853$	−16500.0	−0.662309	−0.331154	+	0.943577i	$0.607438\pi$
$854$	392.000	0.0157072
$855$	0	0
$856$	19872.0	0.793471
$857$	3372.00	0.134405	0.0672026	−	0.997739i	$-0.478593\pi$
$857$	3372.00	0.134405	0.0672026	+	0.997739i	$0.478593\pi$
$858$	3024.00	0.120324
$859$	39026.0	1.55012	0.775058	−	0.631890i	$-0.217721\pi$
$859$	39026.0	1.55012	0.775058	+	0.631890i	$0.217721\pi$
$860$	0	0
$861$	3528.00	0.139645
$862$	18608.0	0.735256
$863$	−41487.0	−1.63642	−0.818212	−	0.574917i	$-0.805034\pi$
$863$	−41487.0	−1.63642	−0.818212	+	0.574917i	$0.805034\pi$
$864$	−4320.00	−0.170103
$865$	0	0
$866$	11504.0	0.451411
$867$	−13287.0	−0.520473
$868$	280.000	0.0109491
$869$	9849.00	0.384470
$870$	0	0
$871$	−23208.0	−0.902839
$872$	−35208.0	−1.36731
$873$	−1026.00	−0.0397764
$874$	800.000	0.0309616
$875$	0	0
$876$	10056.0	0.387855
$877$	−158.000	−0.00608356	−0.00304178	−	0.999995i	$-0.500968\pi$
$877$	−158.000	−0.00608356	−0.00304178	+	0.999995i	$0.500968\pi$
$878$	−4688.00	−0.180196
$879$	10716.0	0.411196
$880$	0	0
$881$	36594.0	1.39941	0.699707	−	0.714430i	$-0.253314\pi$
$881$	36594.0	1.39941	0.699707	+	0.714430i	$0.253314\pi$
$882$	−882.000	−0.0336718
$883$	−17839.0	−0.679876	−0.339938	−	0.940448i	$-0.610406\pi$
$883$	−17839.0	−0.679876	−0.339938	+	0.940448i	$0.610406\pi$
$884$	2112.00	0.0803555
$885$	0	0
$886$	30264.0	1.14756
$887$	13996.0	0.529808	0.264904	−	0.964275i	$-0.414660\pi$
$887$	13996.0	0.529808	0.264904	+	0.964275i	$0.414660\pi$
$888$	−9576.00	−0.361880
$889$	3605.00	0.136004
$890$	0	0
$891$	−1701.00	−0.0639570
$892$	3048.00	0.114411
$893$	−6400.00	−0.239830
$894$	−2094.00	−0.0783376
$895$	0	0
$896$	−2688.00	−0.100223
$897$	−1800.00	−0.0670014
$898$	10110.0	0.375696
$899$	1670.00	0.0619551
$900$	0	0
$901$	4004.00	0.148049
$902$	−7056.00	−0.260465
$903$	2037.00	0.0750688
$904$	18792.0	0.691386
$905$	0	0
$906$	13002.0	0.476780
$907$	−31168.0	−1.14103	−0.570516	−	0.821286i	$-0.693257\pi$
$907$	−31168.0	−1.14103	−0.570516	+	0.821286i	$0.693257\pi$
$908$	23056.0	0.842665
$909$	306.000	0.0111654
$910$	0	0
$911$	1881.00	0.0684087	0.0342043	−	0.999415i	$-0.489110\pi$
$911$	1881.00	0.0684087	0.0342043	+	0.999415i	$0.489110\pi$
$912$	−768.000	−0.0278849
$913$	8526.00	0.309057
$914$	7590.00	0.274677
$915$	0	0
$916$	−6040.00	−0.217868
$917$	10682.0	0.384679
$918$	1188.00	0.0427122
$919$	42447.0	1.52361	0.761805	−	0.647807i	$-0.224314\pi$
$919$	42447.0	1.52361	0.761805	+	0.647807i	$0.224314\pi$
$920$	0	0
$921$	21834.0	0.781167
$922$	−16600.0	−0.592941
$923$	−6840.00	−0.243923
$924$	−1764.00	−0.0628045
$925$	0	0
$926$	10104.0	0.358572
$927$	−17784.0	−0.630101
$928$	−26720.0	−0.945180
$929$	7514.00	0.265367	0.132684	−	0.991158i	$-0.457641\pi$
$929$	7514.00	0.265367	0.132684	+	0.991158i	$0.457641\pi$
$930$	0	0
$931$	784.000	0.0275989
$932$	−23748.0	−0.834648
$933$	11358.0	0.398547
$934$	−4964.00	−0.173905
$935$	0	0
$936$	5184.00	0.181030
$937$	33284.0	1.16045	0.580225	−	0.814457i	$-0.302965\pi$
$937$	33284.0	1.16045	0.580225	+	0.814457i	$0.302965\pi$
$938$	−13538.0	−0.471249
$939$	1344.00	0.0467090
$940$	0	0
$941$	−10962.0	−0.379757	−0.189878	−	0.981808i	$-0.560809\pi$
$941$	−10962.0	−0.379757	−0.189878	+	0.981808i	$0.560809\pi$
$942$	7224.00	0.249863
$943$	4200.00	0.145038
$944$	−7808.00	−0.269204
$945$	0	0
$946$	−4074.00	−0.140018
$947$	−6172.00	−0.211788	−0.105894	−	0.994377i	$-0.533770\pi$
$947$	−6172.00	−0.211788	−0.105894	+	0.994377i	$0.533770\pi$
$948$	5628.00	0.192815
$949$	−20112.0	−0.687949
$950$	0	0
$951$	−12243.0	−0.417462
$952$	3696.00	0.125828
$953$	26263.0	0.892699	0.446349	−	0.894859i	$-0.352724\pi$
$953$	26263.0	0.892699	0.446349	+	0.894859i	$0.352724\pi$
$954$	3276.00	0.111179
$955$	0	0
$956$	−5824.00	−0.197031
$957$	−10521.0	−0.355377
$958$	−28352.0	−0.956171
$959$	12754.0	0.429456
$960$	0	0
$961$	−29691.0	−0.996643
$962$	6384.00	0.213959
$963$	7452.00	0.249364
$964$	2352.00	0.0785818
$965$	0	0
$966$	−1050.00	−0.0349723
$967$	−5920.00	−0.196871	−0.0984356	−	0.995143i	$-0.531384\pi$
$967$	−5920.00	−0.196871	−0.0984356	+	0.995143i	$0.531384\pi$
$968$	−21360.0	−0.709232
$969$	−1056.00	−0.0350089
$970$	0	0
$971$	13372.0	0.441944	0.220972	−	0.975280i	$-0.429077\pi$
$971$	13372.0	0.441944	0.220972	+	0.975280i	$0.429077\pi$
$972$	−972.000	−0.0320750
$973$	21294.0	0.701597
$974$	−2078.00	−0.0683608
$975$	0	0
$976$	−448.000	−0.0146928
$977$	−35155.0	−1.15119	−0.575593	−	0.817737i	$-0.695229\pi$
$977$	−35155.0	−1.15119	−0.575593	+	0.817737i	$0.695229\pi$
$978$	−19512.0	−0.637960
$979$	−6804.00	−0.222121
$980$	0	0
$981$	−13203.0	−0.429704
$982$	−18510.0	−0.601505
$983$	−1858.00	−0.0602859	−0.0301429	−	0.999546i	$-0.509596\pi$
$983$	−1858.00	−0.0602859	−0.0301429	+	0.999546i	$0.509596\pi$
$984$	−12096.0	−0.391876
$985$	0	0
$986$	7348.00	0.237331
$987$	8400.00	0.270897
$988$	−1536.00	−0.0494602
$989$	2425.00	0.0779682
$990$	0	0
$991$	−16401.0	−0.525726	−0.262863	−	0.964833i	$-0.584667\pi$
$991$	−16401.0	−0.525726	−0.262863	+	0.964833i	$0.584667\pi$
$992$	−1600.00	−0.0512097
$993$	3213.00	0.102680
$994$	−3990.00	−0.127319
$995$	0	0
$996$	4872.00	0.154995
$997$	−22952.0	−0.729084	−0.364542	−	0.931187i	$-0.618775\pi$
$997$	−22952.0	−0.729084	−0.364542	+	0.931187i	$0.618775\pi$
$998$	−28792.0	−0.913221
$999$	−3591.00	−0.113728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.d.1.1	✓	1
3.2	odd	2		1575.4.a.h.1.1		1
5.2	odd	4		525.4.d.e.274.1		2
5.3	odd	4		525.4.d.e.274.2		2
5.4	even	2		525.4.a.f.1.1	yes	1
15.14	odd	2		1575.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.d.1.1	✓	1	1.1	even	1	trivial
525.4.a.f.1.1	yes	1	5.4	even	2
525.4.d.e.274.1		2	5.2	odd	4
525.4.d.e.274.2		2	5.3	odd	4
1575.4.a.d.1.1		1	15.14	odd	2
1575.4.a.h.1.1		1	3.2	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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