LMFDB - Embedded newform 1575.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1575,4,Mod(1,1575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1575, 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("1575.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1575.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:	$92.9280082590$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 525)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} -4.00000 q^{4} +7.00000 q^{7} +24.0000 q^{8} +O(q^{10})$

$q-2.00000 q^{2} -4.00000 q^{4} +7.00000 q^{7} +24.0000 q^{8} +21.0000 q^{11} -24.0000 q^{13} -14.0000 q^{14} -16.0000 q^{16} -22.0000 q^{17} +16.0000 q^{19} -42.0000 q^{22} -25.0000 q^{23} +48.0000 q^{26} -28.0000 q^{28} -167.000 q^{29} +10.0000 q^{31} -160.000 q^{32} +44.0000 q^{34} +133.000 q^{37} -32.0000 q^{38} +168.000 q^{41} +97.0000 q^{43} -84.0000 q^{44} +50.0000 q^{46} -400.000 q^{47} +49.0000 q^{49} +96.0000 q^{52} -182.000 q^{53} +168.000 q^{56} +334.000 q^{58} -488.000 q^{59} +28.0000 q^{61} -20.0000 q^{62} +448.000 q^{64} +967.000 q^{67} +88.0000 q^{68} +285.000 q^{71} +838.000 q^{73} -266.000 q^{74} -64.0000 q^{76} +147.000 q^{77} -469.000 q^{79} -336.000 q^{82} -406.000 q^{83} -194.000 q^{86} +504.000 q^{88} -324.000 q^{89} -168.000 q^{91} +100.000 q^{92} +800.000 q^{94} +114.000 q^{97} -98.0000 q^{98} +O(q^{100})$

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	$0.615027\pi$
$3$	0	0
$3$	0	0
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	24.0000	1.06066
$9$	0	0
$10$	0	0
$11$	21.0000	0.575613	0.287806	−	0.957689i	$-0.407074\pi$
$11$	21.0000	0.575613	0.287806	+	0.957689i	$0.407074\pi$
$12$	0	0
$13$	−24.0000	−0.512031	−0.256015	−	0.966673i	$-0.582410\pi$
$13$	−24.0000	−0.512031	−0.256015	+	0.966673i	$0.582410\pi$
$14$	−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	$0.550161\pi$
$18$	0	0
$19$	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
$21$	0	0
$22$	−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	$0.536150\pi$
$24$	0	0
$25$	0	0
$26$	48.0000	0.362061
$27$	0	0
$28$	−28.0000	−0.188982
$29$	−167.000	−1.06935	−0.534675	−	0.845058i	$-0.679566\pi$
$29$	−167.000	−1.06935	−0.534675	+	0.845058i	$0.679566\pi$
$30$	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
$33$	0	0
$34$	44.0000	0.221939
$35$	0	0
$36$	0	0
$37$	133.000	0.590948	0.295474	−	0.955351i	$-0.404522\pi$
$37$	133.000	0.590948	0.295474	+	0.955351i	$0.404522\pi$
$38$	−32.0000	−0.136608
$39$	0	0
$40$	0	0
$41$	168.000	0.639932	0.319966	−	0.947429i	$-0.396329\pi$
$41$	168.000	0.639932	0.319966	+	0.947429i	$0.396329\pi$
$42$	0	0
$43$	97.0000	0.344008	0.172004	−	0.985096i	$-0.444976\pi$
$43$	97.0000	0.344008	0.172004	+	0.985096i	$0.444976\pi$
$44$	−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	$0.713152\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	0	0
$51$	0	0
$52$	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	$0.575786\pi$
$54$	0	0
$55$	0	0
$56$	168.000	0.400892
$57$	0	0
$58$	334.000	0.756144
$59$	−488.000	−1.07682	−0.538408	−	0.842684i	$-0.680974\pi$
$59$	−488.000	−1.07682	−0.538408	+	0.842684i	$0.680974\pi$
$60$	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
$63$	0	0
$64$	448.000	0.875000
$65$	0	0
$66$	0	0
$67$	967.000	1.76325	0.881626	−	0.471949i	$-0.156449\pi$
$67$	967.000	1.76325	0.881626	+	0.471949i	$0.156449\pi$
$68$	88.0000	0.156935
$69$	0	0
$70$	0	0
$71$	285.000	0.476384	0.238192	−	0.971218i	$-0.423445\pi$
$71$	285.000	0.476384	0.238192	+	0.971218i	$0.423445\pi$
$72$	0	0
$73$	838.000	1.34357	0.671784	−	0.740747i	$-0.265528\pi$
$73$	838.000	1.34357	0.671784	+	0.740747i	$0.265528\pi$
$74$	−266.000	−0.417863
$75$	0	0
$76$	−64.0000	−0.0965961
$77$	147.000	0.217561
$78$	0	0
$79$	−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
$81$	0	0
$82$	−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	$0.586515\pi$
$84$	0	0
$85$	0	0
$86$	−194.000	−0.243251
$87$	0	0
$88$	504.000	0.610529
$89$	−324.000	−0.385887	−0.192943	−	0.981210i	$-0.561803\pi$
$89$	−324.000	−0.385887	−0.192943	+	0.981210i	$0.561803\pi$
$90$	0	0
$91$	−168.000	−0.193530
$92$	100.000	0.113323
$93$	0	0
$94$	800.000	0.877805
$95$	0	0
$96$	0	0
$97$	114.000	0.119329	0.0596647	−	0.998218i	$-0.480997\pi$
$97$	114.000	0.119329	0.0596647	+	0.998218i	$0.480997\pi$
$98$	−98.0000	−0.101015
$99$	0	0
$100$	0	0
$101$	−34.0000	−0.0334963	−0.0167482	−	0.999860i	$-0.505331\pi$
$101$	−34.0000	−0.0334963	−0.0167482	+	0.999860i	$0.505331\pi$
$102$	0	0
$103$	1976.00	1.89030	0.945151	−	0.326634i	$-0.105915\pi$
$103$	1976.00	1.89030	0.945151	+	0.326634i	$0.105915\pi$
$104$	−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	$0.377970\pi$
$108$	0	0
$109$	−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
$111$	0	0
$112$	−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	$0.394325\pi$
$114$	0	0
$115$	0	0
$116$	668.000	0.534675
$117$	0	0
$118$	976.000	0.761424
$119$	−154.000	−0.118632
$120$	0	0
$121$	−890.000	−0.668670
$122$	−56.0000	−0.0415574
$123$	0	0
$124$	−40.0000	−0.0289686
$125$	0	0
$126$	0	0
$127$	515.000	0.359834	0.179917	−	0.983682i	$-0.442417\pi$
$127$	515.000	0.359834	0.179917	+	0.983682i	$0.442417\pi$
$128$	384.000	0.265165
$129$	0	0
$130$	0	0
$131$	1526.00	1.01777	0.508883	−	0.860836i	$-0.330059\pi$
$131$	1526.00	1.01777	0.508883	+	0.860836i	$0.330059\pi$
$132$	0	0
$133$	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	$0.692328\pi$
$138$	0	0
$139$	−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
$141$	0	0
$142$	−570.000	−0.336854
$143$	−504.000	−0.294731
$144$	0	0
$145$	0	0
$146$	−1676.00	−0.950046
$147$	0	0
$148$	−532.000	−0.295474
$149$	−349.000	−0.191887	−0.0959436	−	0.995387i	$-0.530587\pi$
$149$	−349.000	−0.191887	−0.0959436	+	0.995387i	$0.530587\pi$
$150$	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
$153$	0	0
$154$	−294.000	−0.153839
$155$	0	0
$156$	0	0
$157$	1204.00	0.612036	0.306018	−	0.952026i	$-0.401003\pi$
$157$	1204.00	0.612036	0.306018	+	0.952026i	$0.401003\pi$
$158$	938.000	0.472299
$159$	0	0
$160$	0	0
$161$	−175.000	−0.0856642
$162$	0	0
$163$	−3252.00	−1.56268	−0.781338	−	0.624108i	$-0.785463\pi$
$163$	−3252.00	−1.56268	−0.781338	+	0.624108i	$0.785463\pi$
$164$	−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	$0.595529\pi$
$168$	0	0
$169$	−1621.00	−0.737824
$170$	0	0
$171$	0	0
$172$	−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	$0.419405\pi$
$174$	0	0
$175$	0	0
$176$	−336.000	−0.143903
$177$	0	0
$178$	648.000	0.272863
$179$	−2724.00	−1.13744	−0.568719	−	0.822532i	$-0.692561\pi$
$179$	−2724.00	−1.13744	−0.568719	+	0.822532i	$0.692561\pi$
$180$	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
$183$	0	0
$184$	−600.000	−0.240394
$185$	0	0
$186$	0	0
$187$	−462.000	−0.180667
$188$	1600.00	0.620702
$189$	0	0
$190$	0	0
$191$	−3932.00	−1.48958	−0.744789	−	0.667300i	$-0.767450\pi$
$191$	−3932.00	−1.48958	−0.744789	+	0.667300i	$0.767450\pi$
$192$	0	0
$193$	−3441.00	−1.28336	−0.641680	−	0.766972i	$-0.721762\pi$
$193$	−3441.00	−1.28336	−0.641680	+	0.766972i	$0.721762\pi$
$194$	−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	$0.511572\pi$
$198$	0	0
$199$	−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
$201$	0	0
$202$	68.0000	0.0236855
$203$	−1169.00	−0.404176
$204$	0	0
$205$	0	0
$206$	−3952.00	−1.33665
$207$	0	0
$208$	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
$213$	0	0
$214$	−1656.00	−0.528981
$215$	0	0
$216$	0	0
$217$	70.0000	0.0218982
$218$	2934.00	0.911539
$219$	0	0
$220$	0	0
$221$	528.000	0.160711
$222$	0	0
$223$	762.000	0.228822	0.114411	−	0.993434i	$-0.463502\pi$
$223$	762.000	0.228822	0.114411	+	0.993434i	$0.463502\pi$
$224$	−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	$0.819015\pi$
$228$	0	0
$229$	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
$231$	0	0
$232$	−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	$0.185671\pi$
$234$	0	0
$235$	0	0
$236$	1952.00	0.538408
$237$	0	0
$238$	308.000	0.0838852
$239$	−1456.00	−0.394062	−0.197031	−	0.980397i	$-0.563130\pi$
$239$	−1456.00	−0.394062	−0.197031	+	0.980397i	$0.563130\pi$
$240$	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
$243$	0	0
$244$	−112.000	−0.0293855
$245$	0	0
$246$	0	0
$247$	−384.000	−0.0989204
$248$	240.000	0.0614517
$249$	0	0
$250$	0	0
$251$	−6510.00	−1.63708	−0.818541	−	0.574448i	$-0.805217\pi$
$251$	−6510.00	−1.63708	−0.818541	+	0.574448i	$0.805217\pi$
$252$	0	0
$253$	−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	$0.614395\pi$
$258$	0	0
$259$	931.000	0.223357
$260$	0	0
$261$	0	0
$262$	−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	$0.387479\pi$
$264$	0	0
$265$	0	0
$266$	−224.000	−0.0516328
$267$	0	0
$268$	−3868.00	−0.881626
$269$	−3394.00	−0.769278	−0.384639	−	0.923067i	$-0.625674\pi$
$269$	−3394.00	−0.769278	−0.384639	+	0.923067i	$0.625674\pi$
$270$	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
$273$	0	0
$274$	3644.00	0.803438
$275$	0	0
$276$	0	0
$277$	3506.00	0.760488	0.380244	−	0.924886i	$-0.375840\pi$
$277$	3506.00	0.760488	0.380244	+	0.924886i	$0.375840\pi$
$278$	6084.00	1.31257
$279$	0	0
$280$	0	0
$281$	−5823.00	−1.23620	−0.618098	−	0.786101i	$-0.712097\pi$
$281$	−5823.00	−1.23620	−0.618098	+	0.786101i	$0.712097\pi$
$282$	0	0
$283$	3830.00	0.804487	0.402244	−	0.915533i	$-0.368230\pi$
$283$	3830.00	0.804487	0.402244	+	0.915533i	$0.368230\pi$
$284$	−1140.00	−0.238192
$285$	0	0
$286$	1008.00	0.208407
$287$	1176.00	0.241871
$288$	0	0
$289$	−4429.00	−0.901486
$290$	0	0
$291$	0	0
$292$	−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	$0.384104\pi$
$294$	0	0
$295$	0	0
$296$	3192.00	0.626795
$297$	0	0
$298$	698.000	0.135685
$299$	600.000	0.116050
$300$	0	0
$301$	679.000	0.130023
$302$	4334.00	0.825807
$303$	0	0
$304$	−256.000	−0.0482980
$305$	0	0
$306$	0	0
$307$	−7278.00	−1.35302	−0.676510	−	0.736433i	$-0.736509\pi$
$307$	−7278.00	−1.35302	−0.676510	+	0.736433i	$0.736509\pi$
$308$	−588.000	−0.108781
$309$	0	0
$310$	0	0
$311$	−3786.00	−0.690303	−0.345152	−	0.938547i	$-0.612173\pi$
$311$	−3786.00	−0.690303	−0.345152	+	0.938547i	$0.612173\pi$
$312$	0	0
$313$	−448.000	−0.0809024	−0.0404512	−	0.999182i	$-0.512880\pi$
$313$	−448.000	−0.0809024	−0.0404512	+	0.999182i	$0.512880\pi$
$314$	−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	$0.617746\pi$
$318$	0	0
$319$	−3507.00	−0.615531
$320$	0	0
$321$	0	0
$322$	350.000	0.0605737
$323$	−352.000	−0.0606372
$324$	0	0
$325$	0	0
$326$	6504.00	1.10498
$327$	0	0
$328$	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
$333$	0	0
$334$	2552.00	0.418082
$335$	0	0
$336$	0	0
$337$	−2102.00	−0.339772	−0.169886	−	0.985464i	$-0.554340\pi$
$337$	−2102.00	−0.339772	−0.169886	+	0.985464i	$0.554340\pi$
$338$	3242.00	0.521721
$339$	0	0
$340$	0	0
$341$	210.000	0.0333494
$342$	0	0
$343$	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	$0.847431\pi$
$348$	0	0
$349$	−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
$351$	0	0
$352$	−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	$0.773657\pi$
$354$	0	0
$355$	0	0
$356$	1296.00	0.192943
$357$	0	0
$358$	5448.00	0.804290
$359$	6597.00	0.969851	0.484925	−	0.874556i	$-0.338847\pi$
$359$	6597.00	0.969851	0.484925	+	0.874556i	$0.338847\pi$
$360$	0	0
$361$	−6603.00	−0.962677
$362$	−8948.00	−1.29916
$363$	0	0
$364$	672.000	0.0967648
$365$	0	0
$366$	0	0
$367$	−6500.00	−0.924516	−0.462258	−	0.886746i	$-0.652961\pi$
$367$	−6500.00	−0.924516	−0.462258	+	0.886746i	$0.652961\pi$
$368$	400.000	0.0566615
$369$	0	0
$370$	0	0
$371$	−1274.00	−0.178282
$372$	0	0
$373$	−8665.00	−1.20283	−0.601416	−	0.798936i	$-0.705397\pi$
$373$	−8665.00	−1.20283	−0.601416	+	0.798936i	$0.705397\pi$
$374$	924.000	0.127751
$375$	0	0
$376$	−9600.00	−1.31671
$377$	4008.00	0.547540
$378$	0	0
$379$	−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
$381$	0	0
$382$	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	$0.600169\pi$
$384$	0	0
$385$	0	0
$386$	6882.00	0.907473
$387$	0	0
$388$	−456.000	−0.0596647
$389$	3021.00	0.393755	0.196878	−	0.980428i	$-0.436920\pi$
$389$	3021.00	0.393755	0.196878	+	0.980428i	$0.436920\pi$
$390$	0	0
$391$	550.000	0.0711373
$392$	1176.00	0.151523
$393$	0	0
$394$	402.000	0.0514022
$395$	0	0
$396$	0	0
$397$	7826.00	0.989359	0.494680	−	0.869075i	$-0.335285\pi$
$397$	7826.00	0.989359	0.494680	+	0.869075i	$0.335285\pi$
$398$	2768.00	0.348611
$399$	0	0
$400$	0	0
$401$	3405.00	0.424034	0.212017	−	0.977266i	$-0.431997\pi$
$401$	3405.00	0.424034	0.212017	+	0.977266i	$0.431997\pi$
$402$	0	0
$403$	−240.000	−0.0296656
$404$	136.000	0.0167482
$405$	0	0
$406$	2338.00	0.285796
$407$	2793.00	0.340157
$408$	0	0
$409$	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
$411$	0	0
$412$	−7904.00	−0.945151
$413$	−3416.00	−0.406998
$414$	0	0
$415$	0	0
$416$	3840.00	0.452576
$417$	0	0
$418$	−672.000	−0.0786330
$419$	−11322.0	−1.32009	−0.660043	−	0.751228i	$-0.729462\pi$
$419$	−11322.0	−1.32009	−0.660043	+	0.751228i	$0.729462\pi$
$420$	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
$423$	0	0
$424$	−4368.00	−0.500304
$425$	0	0
$426$	0	0
$427$	196.000	0.0222134
$428$	−3312.00	−0.374046
$429$	0	0
$430$	0	0
$431$	9304.00	1.03981	0.519905	−	0.854224i	$-0.325967\pi$
$431$	9304.00	1.03981	0.519905	+	0.854224i	$0.325967\pi$
$432$	0	0
$433$	5752.00	0.638391	0.319196	−	0.947689i	$-0.396587\pi$
$433$	5752.00	0.638391	0.319196	+	0.947689i	$0.396587\pi$
$434$	−140.000	−0.0154844
$435$	0	0
$436$	5868.00	0.644556
$437$	−400.000	−0.0437863
$438$	0	0
$439$	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
$441$	0	0
$442$	−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	$0.801320\pi$
$444$	0	0
$445$	0	0
$446$	−1524.00	−0.161802
$447$	0	0
$448$	3136.00	0.330719
$449$	5055.00	0.531314	0.265657	−	0.964068i	$-0.414411\pi$
$449$	5055.00	0.531314	0.265657	+	0.964068i	$0.414411\pi$
$450$	0	0
$451$	3528.00	0.368353
$452$	−3132.00	−0.325922
$453$	0	0
$454$	11528.0	1.19171
$455$	0	0
$456$	0	0
$457$	3795.00	0.388452	0.194226	−	0.980957i	$-0.437780\pi$
$457$	3795.00	0.388452	0.194226	+	0.980957i	$0.437780\pi$
$458$	−3020.00	−0.308112
$459$	0	0
$460$	0	0
$461$	−8300.00	−0.838546	−0.419273	−	0.907860i	$-0.637715\pi$
$461$	−8300.00	−0.838546	−0.419273	+	0.907860i	$0.637715\pi$
$462$	0	0
$463$	5052.00	0.507098	0.253549	−	0.967323i	$-0.418402\pi$
$463$	5052.00	0.507098	0.253549	+	0.967323i	$0.418402\pi$
$464$	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	$0.460758\pi$
$468$	0	0
$469$	6769.00	0.666446
$470$	0	0
$471$	0	0
$472$	−11712.0	−1.14214
$473$	2037.00	0.198016
$474$	0	0
$475$	0	0
$476$	616.000	0.0593158
$477$	0	0
$478$	2912.00	0.278644
$479$	−14176.0	−1.35223	−0.676115	−	0.736796i	$-0.736338\pi$
$479$	−14176.0	−1.35223	−0.676115	+	0.736796i	$0.736338\pi$
$480$	0	0
$481$	−3192.00	−0.302584
$482$	1176.00	0.111131
$483$	0	0
$484$	3560.00	0.334335
$485$	0	0
$486$	0	0
$487$	−1039.00	−0.0966768	−0.0483384	−	0.998831i	$-0.515393\pi$
$487$	−1039.00	−0.0966768	−0.0483384	+	0.998831i	$0.515393\pi$
$488$	672.000	0.0623361
$489$	0	0
$490$	0	0
$491$	−9255.00	−0.850656	−0.425328	−	0.905039i	$-0.639841\pi$
$491$	−9255.00	−0.850656	−0.425328	+	0.905039i	$0.639841\pi$
$492$	0	0
$493$	3674.00	0.335636
$494$	768.000	0.0699473
$495$	0	0
$496$	−160.000	−0.0144843
$497$	1995.00	0.180056
$498$	0	0
$499$	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
$501$	0	0
$502$	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	$0.600384\pi$
$504$	0	0
$505$	0	0
$506$	1050.00	0.0922494
$507$	0	0
$508$	−2060.00	−0.179917
$509$	6400.00	0.557318	0.278659	−	0.960390i	$-0.410110\pi$
$509$	6400.00	0.557318	0.278659	+	0.960390i	$0.410110\pi$
$510$	0	0
$511$	5866.00	0.507821
$512$	5632.00	0.486136
$513$	0	0
$514$	5796.00	0.497375
$515$	0	0
$516$	0	0
$517$	−8400.00	−0.714568
$518$	−1862.00	−0.157937
$519$	0	0
$520$	0	0
$521$	−15158.0	−1.27463	−0.637317	−	0.770602i	$-0.719956\pi$
$521$	−15158.0	−1.27463	−0.637317	+	0.770602i	$0.719956\pi$
$522$	0	0
$523$	−4120.00	−0.344465	−0.172232	−	0.985056i	$-0.555098\pi$
$523$	−4120.00	−0.344465	−0.172232	+	0.985056i	$0.555098\pi$
$524$	−6104.00	−0.508883
$525$	0	0
$526$	−5906.00	−0.489570
$527$	−220.000	−0.0181847
$528$	0	0
$529$	−11542.0	−0.948632
$530$	0	0
$531$	0	0
$532$	−448.000	−0.0365099
$533$	−4032.00	−0.327665
$534$	0	0
$535$	0	0
$536$	23208.0	1.87021
$537$	0	0
$538$	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
$543$	0	0
$544$	3520.00	0.277424
$545$	0	0
$546$	0	0
$547$	20547.0	1.60608	0.803040	−	0.595924i	$-0.203214\pi$
$547$	20547.0	1.60608	0.803040	+	0.595924i	$0.203214\pi$
$548$	7288.00	0.568117
$549$	0	0
$550$	0	0
$551$	−2672.00	−0.206590
$552$	0	0
$553$	−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	$0.538461\pi$
$558$	0	0
$559$	−2328.00	−0.176143
$560$	0	0
$561$	0	0
$562$	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	$0.881199\pi$
$564$	0	0
$565$	0	0
$566$	−7660.00	−0.568858
$567$	0	0
$568$	6840.00	0.505282
$569$	1425.00	0.104990	0.0524948	−	0.998621i	$-0.483283\pi$
$569$	1425.00	0.104990	0.0524948	+	0.998621i	$0.483283\pi$
$570$	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
$573$	0	0
$574$	−2352.00	−0.171029
$575$	0	0
$576$	0	0
$577$	−2108.00	−0.152092	−0.0760461	−	0.997104i	$-0.524230\pi$
$577$	−2108.00	−0.152092	−0.0760461	+	0.997104i	$0.524230\pi$
$578$	8858.00	0.637447
$579$	0	0
$580$	0	0
$581$	−2842.00	−0.202936
$582$	0	0
$583$	−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	$0.172549\pi$
$588$	0	0
$589$	160.000	0.0111930
$590$	0	0
$591$	0	0
$592$	−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	$0.287332\pi$
$594$	0	0
$595$	0	0
$596$	1396.00	0.0959436
$597$	0	0
$598$	−1200.00	−0.0820596
$599$	−8077.00	−0.550947	−0.275474	−	0.961309i	$-0.588835\pi$
$599$	−8077.00	−0.550947	−0.275474	+	0.961309i	$0.588835\pi$
$600$	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
$603$	0	0
$604$	8668.00	0.583934
$605$	0	0
$606$	0	0
$607$	24092.0	1.61098	0.805489	−	0.592610i	$-0.201903\pi$
$607$	24092.0	1.61098	0.805489	+	0.592610i	$0.201903\pi$
$608$	−2560.00	−0.170759
$609$	0	0
$610$	0	0
$611$	9600.00	0.635637
$612$	0	0
$613$	−13647.0	−0.899180	−0.449590	−	0.893235i	$-0.648430\pi$
$613$	−13647.0	−0.899180	−0.449590	+	0.893235i	$0.648430\pi$
$614$	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	$0.362726\pi$
$618$	0	0
$619$	−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
$621$	0	0
$622$	7572.00	0.488118
$623$	−2268.00	−0.145852
$624$	0	0
$625$	0	0
$626$	896.000	0.0572066
$627$	0	0
$628$	−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
$633$	0	0
$634$	8162.00	0.511285
$635$	0	0
$636$	0	0
$637$	−1176.00	−0.0731473
$638$	7014.00	0.435246
$639$	0	0
$640$	0	0
$641$	24117.0	1.48606	0.743030	−	0.669258i	$-0.233388\pi$
$641$	24117.0	1.48606	0.743030	+	0.669258i	$0.233388\pi$
$642$	0	0
$643$	14020.0	0.859868	0.429934	−	0.902860i	$-0.358537\pi$
$643$	14020.0	0.859868	0.429934	+	0.902860i	$0.358537\pi$
$644$	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	$0.476478\pi$
$648$	0	0
$649$	−10248.0	−0.619829
$650$	0	0
$651$	0	0
$652$	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	$0.808504\pi$
$654$	0	0
$655$	0	0
$656$	−2688.00	−0.159983
$657$	0	0
$658$	5600.00	0.331779
$659$	20772.0	1.22786	0.613932	−	0.789359i	$-0.289587\pi$
$659$	20772.0	1.22786	0.613932	+	0.789359i	$0.289587\pi$
$660$	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
$663$	0	0
$664$	−9744.00	−0.569489
$665$	0	0
$666$	0	0
$667$	4175.00	0.242364
$668$	5104.00	0.295628
$669$	0	0
$670$	0	0
$671$	588.000	0.0338293
$672$	0	0
$673$	−23542.0	−1.34841	−0.674203	−	0.738546i	$-0.735513\pi$
$673$	−23542.0	−1.34841	−0.674203	+	0.738546i	$0.735513\pi$
$674$	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	$0.161090\pi$
$678$	0	0
$679$	798.000	0.0451023
$680$	0	0
$681$	0	0
$682$	−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	$0.418794\pi$
$684$	0	0
$685$	0	0
$686$	−686.000	−0.0381802
$687$	0	0
$688$	−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
$693$	0	0
$694$	22942.0	1.25485
$695$	0	0
$696$	0	0
$697$	−3696.00	−0.200855
$698$	12896.0	0.699313
$699$	0	0
$700$	0	0
$701$	−24170.0	−1.30227	−0.651133	−	0.758964i	$-0.725706\pi$
$701$	−24170.0	−1.30227	−0.651133	+	0.758964i	$0.725706\pi$
$702$	0	0
$703$	2128.00	0.114166
$704$	9408.00	0.503661
$705$	0	0
$706$	20100.0	1.07149
$707$	−238.000	−0.0126604
$708$	0	0
$709$	−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
$711$	0	0
$712$	−7776.00	−0.409295
$713$	−250.000	−0.0131312
$714$	0	0
$715$	0	0
$716$	10896.0	0.568719
$717$	0	0
$718$	−13194.0	−0.685788
$719$	30752.0	1.59507	0.797536	−	0.603272i	$-0.206137\pi$
$719$	30752.0	1.59507	0.797536	+	0.603272i	$0.206137\pi$
$720$	0	0
$721$	13832.0	0.714467
$722$	13206.0	0.680715
$723$	0	0
$724$	−17896.0	−0.918646
$725$	0	0
$726$	0	0
$727$	−11570.0	−0.590244	−0.295122	−	0.955460i	$-0.595360\pi$
$727$	−11570.0	−0.590244	−0.295122	+	0.955460i	$0.595360\pi$
$728$	−4032.00	−0.205269
$729$	0	0
$730$	0	0
$731$	−2134.00	−0.107974
$732$	0	0
$733$	−32836.0	−1.65460	−0.827302	−	0.561757i	$-0.810126\pi$
$733$	−32836.0	−1.65460	−0.827302	+	0.561757i	$0.810126\pi$
$734$	13000.0	0.653731
$735$	0	0
$736$	4000.00	0.200329
$737$	20307.0	1.01495
$738$	0	0
$739$	−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
$741$	0	0
$742$	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	$0.680150\pi$
$744$	0	0
$745$	0	0
$746$	17330.0	0.850531
$747$	0	0
$748$	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
$753$	0	0
$754$	−8016.00	−0.387169
$755$	0	0
$756$	0	0
$757$	7685.00	0.368978	0.184489	−	0.982835i	$-0.440937\pi$
$757$	7685.00	0.368978	0.184489	+	0.982835i	$0.440937\pi$
$758$	434.000	0.0207963
$759$	0	0
$760$	0	0
$761$	12.0000	0.000571616 0	0.000285808	−	1.00000i	$-0.499909\pi$
$761$	12.0000	0.000571616 0	0.000285808		1.00000i	$0.499909\pi$
$762$	0	0
$763$	−10269.0	−0.487238
$764$	15728.0	0.744789
$765$	0	0
$766$	9280.00	0.437728
$767$	11712.0	0.551364
$768$	0	0
$769$	−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
$771$	0	0
$772$	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	$0.271805\pi$
$774$	0	0
$775$	0	0
$776$	2736.00	0.126568
$777$	0	0
$778$	−6042.00	−0.278427
$779$	2688.00	0.123630
$780$	0	0
$781$	5985.00	0.274213
$782$	−1100.00	−0.0503017
$783$	0	0
$784$	−784.000	−0.0357143
$785$	0	0
$786$	0	0
$787$	−12542.0	−0.568074	−0.284037	−	0.958813i	$-0.591674\pi$
$787$	−12542.0	−0.568074	−0.284037	+	0.958813i	$0.591674\pi$
$788$	804.000	0.0363468
$789$	0	0
$790$	0	0
$791$	5481.00	0.246374
$792$	0	0
$793$	−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	$0.420972\pi$
$798$	0	0
$799$	8800.00	0.389639
$800$	0	0
$801$	0	0
$802$	−6810.00	−0.299837
$803$	17598.0	0.773375
$804$	0	0
$805$	0	0
$806$	480.000	0.0209768
$807$	0	0
$808$	−816.000	−0.0355282
$809$	17307.0	0.752141	0.376070	−	0.926591i	$-0.377275\pi$
$809$	17307.0	0.752141	0.376070	+	0.926591i	$0.377275\pi$
$810$	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
$813$	0	0
$814$	−5586.00	−0.240527
$815$	0	0
$816$	0	0
$817$	1552.00	0.0664597
$818$	−8104.00	−0.346393
$819$	0	0
$820$	0	0
$821$	38862.0	1.65200	0.826001	−	0.563669i	$-0.190611\pi$
$821$	38862.0	1.65200	0.826001	+	0.563669i	$0.190611\pi$
$822$	0	0
$823$	−27217.0	−1.15276	−0.576382	−	0.817180i	$-0.695536\pi$
$823$	−27217.0	−1.15276	−0.576382	+	0.817180i	$0.695536\pi$
$824$	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	$0.423642\pi$
$828$	0	0
$829$	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
$831$	0	0
$832$	−10752.0	−0.448027
$833$	−1078.00	−0.0448385
$834$	0	0
$835$	0	0
$836$	−1344.00	−0.0556019
$837$	0	0
$838$	22644.0	0.933442
$839$	−8358.00	−0.343922	−0.171961	−	0.985104i	$-0.555010\pi$
$839$	−8358.00	−0.343922	−0.171961	+	0.985104i	$0.555010\pi$
$840$	0	0
$841$	3500.00	0.143507
$842$	3514.00	0.143825
$843$	0	0
$844$	−15856.0	−0.646666
$845$	0	0
$846$	0	0
$847$	−6230.00	−0.252734
$848$	2912.00	0.117923
$849$	0	0
$850$	0	0
$851$	−3325.00	−0.133936
$852$	0	0
$853$	16500.0	0.662309	0.331154	−	0.943577i	$-0.392562\pi$
$853$	16500.0	0.662309	0.331154	+	0.943577i	$0.392562\pi$
$854$	−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	$0.478593\pi$
$858$	0	0
$859$	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
$861$	0	0
$862$	−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	$0.805034\pi$
$864$	0	0
$865$	0	0
$866$	−11504.0	−0.451411
$867$	0	0
$868$	−280.000	−0.0109491
$869$	−9849.00	−0.384470
$870$	0	0
$871$	−23208.0	−0.902839
$872$	−35208.0	−1.36731
$873$	0	0
$874$	800.000	0.0309616
$875$	0	0
$876$	0	0
$877$	158.000	0.00608356	0.00304178	−	0.999995i	$-0.499032\pi$
$877$	158.000	0.00608356	0.00304178	+	0.999995i	$0.499032\pi$
$878$	−4688.00	−0.180196
$879$	0	0
$880$	0	0
$881$	−36594.0	−1.39941	−0.699707	−	0.714430i	$-0.746686\pi$
$881$	−36594.0	−1.39941	−0.699707	+	0.714430i	$0.746686\pi$
$882$	0	0
$883$	17839.0	0.679876	0.339938	−	0.940448i	$-0.389594\pi$
$883$	17839.0	0.679876	0.339938	+	0.940448i	$0.389594\pi$
$884$	−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	$0.414660\pi$
$888$	0	0
$889$	3605.00	0.136004
$890$	0	0
$891$	0	0
$892$	−3048.00	−0.114411
$893$	−6400.00	−0.239830
$894$	0	0
$895$	0	0
$896$	2688.00	0.100223
$897$	0	0
$898$	−10110.0	−0.375696
$899$	−1670.00	−0.0619551
$900$	0	0
$901$	4004.00	0.148049
$902$	−7056.00	−0.260465
$903$	0	0
$904$	18792.0	0.691386
$905$	0	0
$906$	0	0
$907$	31168.0	1.14103	0.570516	−	0.821286i	$-0.306743\pi$
$907$	31168.0	1.14103	0.570516	+	0.821286i	$0.306743\pi$
$908$	23056.0	0.842665
$909$	0	0
$910$	0	0
$911$	−1881.00	−0.0684087	−0.0342043	−	0.999415i	$-0.510890\pi$
$911$	−1881.00	−0.0684087	−0.0342043	+	0.999415i	$0.510890\pi$
$912$	0	0
$913$	−8526.00	−0.309057
$914$	−7590.00	−0.274677
$915$	0	0
$916$	−6040.00	−0.217868
$917$	10682.0	0.384679
$918$	0	0
$919$	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
$921$	0	0
$922$	16600.0	0.592941
$923$	−6840.00	−0.243923
$924$	0	0
$925$	0	0
$926$	−10104.0	−0.358572
$927$	0	0
$928$	26720.0	0.945180
$929$	−7514.00	−0.265367	−0.132684	−	0.991158i	$-0.542359\pi$
$929$	−7514.00	−0.265367	−0.132684	+	0.991158i	$0.542359\pi$
$930$	0	0
$931$	784.000	0.0275989
$932$	−23748.0	−0.834648
$933$	0	0
$934$	−4964.00	−0.173905
$935$	0	0
$936$	0	0
$937$	−33284.0	−1.16045	−0.580225	−	0.814457i	$-0.697035\pi$
$937$	−33284.0	−1.16045	−0.580225	+	0.814457i	$0.697035\pi$
$938$	−13538.0	−0.471249
$939$	0	0
$940$	0	0
$941$	10962.0	0.379757	0.189878	−	0.981808i	$-0.439191\pi$
$941$	10962.0	0.379757	0.189878	+	0.981808i	$0.439191\pi$
$942$	0	0
$943$	−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	$0.533770\pi$
$948$	0	0
$949$	−20112.0	−0.687949
$950$	0	0
$951$	0	0
$952$	−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	$0.352724\pi$
$954$	0	0
$955$	0	0
$956$	5824.00	0.197031
$957$	0	0
$958$	28352.0	0.956171
$959$	−12754.0	−0.429456
$960$	0	0
$961$	−29691.0	−0.996643
$962$	6384.00	0.213959
$963$	0	0
$964$	2352.00	0.0785818
$965$	0	0
$966$	0	0
$967$	5920.00	0.196871	0.0984356	−	0.995143i	$-0.468616\pi$
$967$	5920.00	0.196871	0.0984356	+	0.995143i	$0.468616\pi$
$968$	−21360.0	−0.709232
$969$	0	0
$970$	0	0
$971$	−13372.0	−0.441944	−0.220972	−	0.975280i	$-0.570923\pi$
$971$	−13372.0	−0.441944	−0.220972	+	0.975280i	$0.570923\pi$
$972$	0	0
$973$	−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	$0.695229\pi$
$978$	0	0
$979$	−6804.00	−0.222121
$980$	0	0
$981$	0	0
$982$	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	$0.509596\pi$
$984$	0	0
$985$	0	0
$986$	−7348.00	−0.237331
$987$	0	0
$988$	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
$993$	0	0
$994$	−3990.00	−0.127319
$995$	0	0
$996$	0	0
$997$	22952.0	0.729084	0.364542	−	0.931187i	$-0.381225\pi$
$997$	22952.0	0.729084	0.364542	+	0.931187i	$0.381225\pi$
$998$	−28792.0	−0.913221
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.d.1.1	✓	1	15.14	odd	2
525.4.a.f.1.1	yes	1	3.2	odd	2
525.4.d.e.274.1		2	15.8	even	4
525.4.d.e.274.2		2	15.2	even	4
1575.4.a.d.1.1		1	1.1	even	1	trivial
1575.4.a.h.1.1		1	5.4	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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1575.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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