LMFDB - Embedded newform 1575.4.a.k.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
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)

$f(q)$

$=$

$q+4.00000 q^{2} +8.00000 q^{4} +7.00000 q^{7} +O(q^{10})$

$q+4.00000 q^{2} +8.00000 q^{4} +7.00000 q^{7} -62.0000 q^{11} +62.0000 q^{13} +28.0000 q^{14} -64.0000 q^{16} +84.0000 q^{17} +100.000 q^{19} -248.000 q^{22} -42.0000 q^{23} +248.000 q^{26} +56.0000 q^{28} +10.0000 q^{29} -48.0000 q^{31} -256.000 q^{32} +336.000 q^{34} +246.000 q^{37} +400.000 q^{38} +248.000 q^{41} -68.0000 q^{43} -496.000 q^{44} -168.000 q^{46} +324.000 q^{47} +49.0000 q^{49} +496.000 q^{52} +258.000 q^{53} +40.0000 q^{58} -120.000 q^{59} +622.000 q^{61} -192.000 q^{62} -512.000 q^{64} -904.000 q^{67} +672.000 q^{68} +678.000 q^{71} +642.000 q^{73} +984.000 q^{74} +800.000 q^{76} -434.000 q^{77} +740.000 q^{79} +992.000 q^{82} +468.000 q^{83} -272.000 q^{86} -200.000 q^{89} +434.000 q^{91} -336.000 q^{92} +1296.00 q^{94} +1266.00 q^{97} +196.000 q^{98} +O(q^{100})$

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 $

$2$	4.00000	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$2$	4.00000	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$3$	0	0
$3$	0	0
$4$	8.00000	1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	0	0
$9$	0	0
$10$	0	0
$11$	−62.0000	−1.69943	−0.849714	−	0.527244i	$-0.823225\pi$
$11$	−62.0000	−1.69943	−0.849714	+	0.527244i	$0.823225\pi$
$12$	0	0
$13$	62.0000	1.32275	0.661373	−	0.750057i	$-0.269974\pi$
$13$	62.0000	1.32275	0.661373	+	0.750057i	$0.269974\pi$
$14$	28.0000	0.534522
$15$	0	0
$16$	−64.0000	−1.00000
$17$	84.0000	1.19841	0.599206	−	0.800595i	$-0.295483\pi$
$17$	84.0000	1.19841	0.599206	+	0.800595i	$0.295483\pi$
$18$	0	0
$19$	100.000	1.20745	0.603726	−	0.797192i	$-0.293682\pi$
$19$	100.000	1.20745	0.603726	+	0.797192i	$0.293682\pi$
$20$	0	0
$21$	0	0
$22$	−248.000	−2.40335
$23$	−42.0000	−0.380765	−0.190383	−	0.981710i	$-0.560973\pi$
$23$	−42.0000	−0.380765	−0.190383	+	0.981710i	$0.560973\pi$
$24$	0	0
$25$	0	0
$26$	248.000	1.87065
$27$	0	0
$28$	56.0000	0.377964
$29$	10.0000	0.0640329	0.0320164	−	0.999487i	$-0.489807\pi$
$29$	10.0000	0.0640329	0.0320164	+	0.999487i	$0.489807\pi$
$30$	0	0
$31$	−48.0000	−0.278099	−0.139049	−	0.990285i	$-0.544405\pi$
$31$	−48.0000	−0.278099	−0.139049	+	0.990285i	$0.544405\pi$
$32$	−256.000	−1.41421
$33$	0	0
$34$	336.000	1.69481
$35$	0	0
$36$	0	0
$37$	246.000	1.09303	0.546516	−	0.837449i	$-0.315954\pi$
$37$	246.000	1.09303	0.546516	+	0.837449i	$0.315954\pi$
$38$	400.000	1.70759
$39$	0	0
$40$	0	0
$41$	248.000	0.944661	0.472330	−	0.881422i	$-0.343413\pi$
$41$	248.000	0.944661	0.472330	+	0.881422i	$0.343413\pi$
$42$	0	0
$43$	−68.0000	−0.241161	−0.120580	−	0.992704i	$-0.538476\pi$
$43$	−68.0000	−0.241161	−0.120580	+	0.992704i	$0.538476\pi$
$44$	−496.000	−1.69943
$45$	0	0
$46$	−168.000	−0.538484
$47$	324.000	1.00554	0.502769	−	0.864421i	$-0.332315\pi$
$47$	324.000	1.00554	0.502769	+	0.864421i	$0.332315\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	0	0
$51$	0	0
$52$	496.000	1.32275
$53$	258.000	0.668661	0.334330	−	0.942456i	$-0.391490\pi$
$53$	258.000	0.668661	0.334330	+	0.942456i	$0.391490\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	40.0000	0.0905562
$59$	−120.000	−0.264791	−0.132396	−	0.991197i	$-0.542267\pi$
$59$	−120.000	−0.264791	−0.132396	+	0.991197i	$0.542267\pi$
$60$	0	0
$61$	622.000	1.30556	0.652778	−	0.757549i	$-0.273603\pi$
$61$	622.000	1.30556	0.652778	+	0.757549i	$0.273603\pi$
$62$	−192.000	−0.393291
$63$	0	0
$64$	−512.000	−1.00000
$65$	0	0
$66$	0	0
$67$	−904.000	−1.64838	−0.824188	−	0.566316i	$-0.808368\pi$
$67$	−904.000	−1.64838	−0.824188	+	0.566316i	$0.808368\pi$
$68$	672.000	1.19841
$69$	0	0
$70$	0	0
$71$	678.000	1.13329	0.566646	−	0.823961i	$-0.308241\pi$
$71$	678.000	1.13329	0.566646	+	0.823961i	$0.308241\pi$
$72$	0	0
$73$	642.000	1.02932	0.514660	−	0.857394i	$-0.327918\pi$
$73$	642.000	1.02932	0.514660	+	0.857394i	$0.327918\pi$
$74$	984.000	1.54578
$75$	0	0
$76$	800.000	1.20745
$77$	−434.000	−0.642323
$78$	0	0
$79$	740.000	1.05388	0.526940	−	0.849903i	$-0.323339\pi$
$79$	740.000	1.05388	0.526940	+	0.849903i	$0.323339\pi$
$80$	0	0
$81$	0	0
$82$	992.000	1.33595
$83$	468.000	0.618912	0.309456	−	0.950914i	$-0.399853\pi$
$83$	468.000	0.618912	0.309456	+	0.950914i	$0.399853\pi$
$84$	0	0
$85$	0	0
$86$	−272.000	−0.341052
$87$	0	0
$88$	0	0
$89$	−200.000	−0.238202	−0.119101	−	0.992882i	$-0.538001\pi$
$89$	−200.000	−0.238202	−0.119101	+	0.992882i	$0.538001\pi$
$90$	0	0
$91$	434.000	0.499951
$92$	−336.000	−0.380765
$93$	0	0
$94$	1296.00	1.42204
$95$	0	0
$96$	0	0
$97$	1266.00	1.32518	0.662592	−	0.748981i	$-0.269456\pi$
$97$	1266.00	1.32518	0.662592	+	0.748981i	$0.269456\pi$
$98$	196.000	0.202031
$99$	0	0
$100$	0	0
$101$	−232.000	−0.228563	−0.114281	−	0.993448i	$-0.536457\pi$
$101$	−232.000	−0.228563	−0.114281	+	0.993448i	$0.536457\pi$
$102$	0	0
$103$	1792.00	1.71428	0.857141	−	0.515082i	$-0.172239\pi$
$103$	1792.00	1.71428	0.857141	+	0.515082i	$0.172239\pi$
$104$	0	0
$105$	0	0
$106$	1032.00	0.945629
$107$	−1906.00	−1.72206	−0.861028	−	0.508558i	$-0.830179\pi$
$107$	−1906.00	−1.72206	−0.861028	+	0.508558i	$0.830179\pi$
$108$	0	0
$109$	−90.0000	−0.0790866	−0.0395433	−	0.999218i	$-0.512590\pi$
$109$	−90.0000	−0.0790866	−0.0395433	+	0.999218i	$0.512590\pi$
$110$	0	0
$111$	0	0
$112$	−448.000	−0.377964
$113$	458.000	0.381283	0.190642	−	0.981660i	$-0.438943\pi$
$113$	458.000	0.381283	0.190642	+	0.981660i	$0.438943\pi$
$114$	0	0
$115$	0	0
$116$	80.0000	0.0640329
$117$	0	0
$118$	−480.000	−0.374471
$119$	588.000	0.452957
$120$	0	0
$121$	2513.00	1.88805
$122$	2488.00	1.84634
$123$	0	0
$124$	−384.000	−0.278099
$125$	0	0
$126$	0	0
$127$	−804.000	−0.561760	−0.280880	−	0.959743i	$-0.590626\pi$
$127$	−804.000	−0.561760	−0.280880	+	0.959743i	$0.590626\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	−812.000	−0.541563	−0.270782	−	0.962641i	$-0.587282\pi$
$131$	−812.000	−0.541563	−0.270782	+	0.962641i	$0.587282\pi$
$132$	0	0
$133$	700.000	0.456374
$134$	−3616.00	−2.33116
$135$	0	0
$136$	0	0
$137$	414.000	0.258178	0.129089	−	0.991633i	$-0.458795\pi$
$137$	414.000	0.258178	0.129089	+	0.991633i	$0.458795\pi$
$138$	0	0
$139$	−1620.00	−0.988537	−0.494268	−	0.869309i	$-0.664564\pi$
$139$	−1620.00	−0.988537	−0.494268	+	0.869309i	$0.664564\pi$
$140$	0	0
$141$	0	0
$142$	2712.00	1.60272
$143$	−3844.00	−2.24791
$144$	0	0
$145$	0	0
$146$	2568.00	1.45568
$147$	0	0
$148$	1968.00	1.09303
$149$	−2370.00	−1.30307	−0.651537	−	0.758617i	$-0.725875\pi$
$149$	−2370.00	−1.30307	−0.651537	+	0.758617i	$0.725875\pi$
$150$	0	0
$151$	−568.000	−0.306114	−0.153057	−	0.988217i	$-0.548912\pi$
$151$	−568.000	−0.306114	−0.153057	+	0.988217i	$0.548912\pi$
$152$	0	0
$153$	0	0
$154$	−1736.00	−0.908382
$155$	0	0
$156$	0	0
$157$	266.000	0.135217	0.0676086	−	0.997712i	$-0.478463\pi$
$157$	266.000	0.135217	0.0676086	+	0.997712i	$0.478463\pi$
$158$	2960.00	1.49041
$159$	0	0
$160$	0	0
$161$	−294.000	−0.143916
$162$	0	0
$163$	272.000	0.130704	0.0653518	−	0.997862i	$-0.479183\pi$
$163$	272.000	0.130704	0.0653518	+	0.997862i	$0.479183\pi$
$164$	1984.00	0.944661
$165$	0	0
$166$	1872.00	0.875273
$167$	−1876.00	−0.869277	−0.434638	−	0.900605i	$-0.643124\pi$
$167$	−1876.00	−0.869277	−0.434638	+	0.900605i	$0.643124\pi$
$168$	0	0
$169$	1647.00	0.749659
$170$	0	0
$171$	0	0
$172$	−544.000	−0.241161
$173$	−152.000	−0.0667997	−0.0333998	−	0.999442i	$-0.510633\pi$
$173$	−152.000	−0.0667997	−0.0333998	+	0.999442i	$0.510633\pi$
$174$	0	0
$175$	0	0
$176$	3968.00	1.69943
$177$	0	0
$178$	−800.000	−0.336868
$179$	−610.000	−0.254713	−0.127356	−	0.991857i	$-0.540649\pi$
$179$	−610.000	−0.254713	−0.127356	+	0.991857i	$0.540649\pi$
$180$	0	0
$181$	1042.00	0.427907	0.213954	−	0.976844i	$-0.431366\pi$
$181$	1042.00	0.427907	0.213954	+	0.976844i	$0.431366\pi$
$182$	1736.00	0.707038
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−5208.00	−2.03661
$188$	2592.00	1.00554
$189$	0	0
$190$	0	0
$191$	2038.00	0.772065	0.386033	−	0.922485i	$-0.373845\pi$
$191$	2038.00	0.772065	0.386033	+	0.922485i	$0.373845\pi$
$192$	0	0
$193$	2602.00	0.970446	0.485223	−	0.874390i	$-0.338738\pi$
$193$	2602.00	0.970446	0.485223	+	0.874390i	$0.338738\pi$
$194$	5064.00	1.87409
$195$	0	0
$196$	392.000	0.142857
$197$	2354.00	0.851348	0.425674	−	0.904877i	$-0.360037\pi$
$197$	2354.00	0.851348	0.425674	+	0.904877i	$0.360037\pi$
$198$	0	0
$199$	1680.00	0.598452	0.299226	−	0.954182i	$-0.403271\pi$
$199$	1680.00	0.598452	0.299226	+	0.954182i	$0.403271\pi$
$200$	0	0
$201$	0	0
$202$	−928.000	−0.323237
$203$	70.0000	0.0242022
$204$	0	0
$205$	0	0
$206$	7168.00	2.42436
$207$	0	0
$208$	−3968.00	−1.32275
$209$	−6200.00	−2.05198
$210$	0	0
$211$	−668.000	−0.217948	−0.108974	−	0.994045i	$-0.534757\pi$
$211$	−668.000	−0.217948	−0.108974	+	0.994045i	$0.534757\pi$
$212$	2064.00	0.668661
$213$	0	0
$214$	−7624.00	−2.43535
$215$	0	0
$216$	0	0
$217$	−336.000	−0.105111
$218$	−360.000	−0.111845
$219$	0	0
$220$	0	0
$221$	5208.00	1.58519
$222$	0	0
$223$	1832.00	0.550134	0.275067	−	0.961425i	$-0.411300\pi$
$223$	1832.00	0.550134	0.275067	+	0.961425i	$0.411300\pi$
$224$	−1792.00	−0.534522
$225$	0	0
$226$	1832.00	0.539216
$227$	4944.00	1.44557	0.722786	−	0.691072i	$-0.242861\pi$
$227$	4944.00	1.44557	0.722786	+	0.691072i	$0.242861\pi$
$228$	0	0
$229$	−5470.00	−1.57846	−0.789231	−	0.614096i	$-0.789521\pi$
$229$	−5470.00	−1.57846	−0.789231	+	0.614096i	$0.789521\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−2802.00	−0.787833	−0.393917	−	0.919146i	$-0.628880\pi$
$233$	−2802.00	−0.787833	−0.393917	+	0.919146i	$0.628880\pi$
$234$	0	0
$235$	0	0
$236$	−960.000	−0.264791
$237$	0	0
$238$	2352.00	0.640578
$239$	1170.00	0.316657	0.158328	−	0.987386i	$-0.449390\pi$
$239$	1170.00	0.316657	0.158328	+	0.987386i	$0.449390\pi$
$240$	0	0
$241$	−2338.00	−0.624912	−0.312456	−	0.949932i	$-0.601152\pi$
$241$	−2338.00	−0.624912	−0.312456	+	0.949932i	$0.601152\pi$
$242$	10052.0	2.67011
$243$	0	0
$244$	4976.00	1.30556
$245$	0	0
$246$	0	0
$247$	6200.00	1.59715
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−2792.00	−0.702109	−0.351055	−	0.936355i	$-0.614177\pi$
$251$	−2792.00	−0.702109	−0.351055	+	0.936355i	$0.614177\pi$
$252$	0	0
$253$	2604.00	0.647083
$254$	−3216.00	−0.794448
$255$	0	0
$256$	4096.00	1.00000
$257$	7024.00	1.70484	0.852422	−	0.522854i	$-0.175133\pi$
$257$	7024.00	1.70484	0.852422	+	0.522854i	$0.175133\pi$
$258$	0	0
$259$	1722.00	0.413127
$260$	0	0
$261$	0	0
$262$	−3248.00	−0.765886
$263$	2438.00	0.571610	0.285805	−	0.958288i	$-0.407739\pi$
$263$	2438.00	0.571610	0.285805	+	0.958288i	$0.407739\pi$
$264$	0	0
$265$	0	0
$266$	2800.00	0.645410
$267$	0	0
$268$	−7232.00	−1.64838
$269$	6780.00	1.53674	0.768372	−	0.640004i	$-0.221067\pi$
$269$	6780.00	1.53674	0.768372	+	0.640004i	$0.221067\pi$
$270$	0	0
$271$	−1928.00	−0.432168	−0.216084	−	0.976375i	$-0.569329\pi$
$271$	−1928.00	−0.432168	−0.216084	+	0.976375i	$0.569329\pi$
$272$	−5376.00	−1.19841
$273$	0	0
$274$	1656.00	0.365119
$275$	0	0
$276$	0	0
$277$	−5554.00	−1.20472	−0.602360	−	0.798224i	$-0.705773\pi$
$277$	−5554.00	−1.20472	−0.602360	+	0.798224i	$0.705773\pi$
$278$	−6480.00	−1.39800
$279$	0	0
$280$	0	0
$281$	−1942.00	−0.412278	−0.206139	−	0.978523i	$-0.566090\pi$
$281$	−1942.00	−0.412278	−0.206139	+	0.978523i	$0.566090\pi$
$282$	0	0
$283$	−4828.00	−1.01412	−0.507058	−	0.861912i	$-0.669267\pi$
$283$	−4828.00	−1.01412	−0.507058	+	0.861912i	$0.669267\pi$
$284$	5424.00	1.13329
$285$	0	0
$286$	−15376.0	−3.17903
$287$	1736.00	0.357048
$288$	0	0
$289$	2143.00	0.436190
$290$	0	0
$291$	0	0
$292$	5136.00	1.02932
$293$	−6152.00	−1.22663	−0.613317	−	0.789837i	$-0.710165\pi$
$293$	−6152.00	−1.22663	−0.613317	+	0.789837i	$0.710165\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	−9480.00	−1.84282
$299$	−2604.00	−0.503656
$300$	0	0
$301$	−476.000	−0.0911501
$302$	−2272.00	−0.432910
$303$	0	0
$304$	−6400.00	−1.20745
$305$	0	0
$306$	0	0
$307$	−5884.00	−1.09387	−0.546934	−	0.837176i	$-0.684205\pi$
$307$	−5884.00	−1.09387	−0.546934	+	0.837176i	$0.684205\pi$
$308$	−3472.00	−0.642323
$309$	0	0
$310$	0	0
$311$	−9132.00	−1.66504	−0.832521	−	0.553993i	$-0.813103\pi$
$311$	−9132.00	−1.66504	−0.832521	+	0.553993i	$0.813103\pi$
$312$	0	0
$313$	9382.00	1.69426	0.847128	−	0.531389i	$-0.178330\pi$
$313$	9382.00	1.69426	0.847128	+	0.531389i	$0.178330\pi$
$314$	1064.00	0.191226
$315$	0	0
$316$	5920.00	1.05388
$317$	3114.00	0.551734	0.275867	−	0.961196i	$-0.411035\pi$
$317$	3114.00	0.551734	0.275867	+	0.961196i	$0.411035\pi$
$318$	0	0
$319$	−620.000	−0.108819
$320$	0	0
$321$	0	0
$322$	−1176.00	−0.203528
$323$	8400.00	1.44702
$324$	0	0
$325$	0	0
$326$	1088.00	0.184843
$327$	0	0
$328$	0	0
$329$	2268.00	0.380057
$330$	0	0
$331$	1532.00	0.254400	0.127200	−	0.991877i	$-0.459401\pi$
$331$	1532.00	0.254400	0.127200	+	0.991877i	$0.459401\pi$
$332$	3744.00	0.618912
$333$	0	0
$334$	−7504.00	−1.22934
$335$	0	0
$336$	0	0
$337$	4166.00	0.673402	0.336701	−	0.941612i	$-0.390689\pi$
$337$	4166.00	0.673402	0.336701	+	0.941612i	$0.390689\pi$
$338$	6588.00	1.06018
$339$	0	0
$340$	0	0
$341$	2976.00	0.472608
$342$	0	0
$343$	343.000	0.0539949
$344$	0	0
$345$	0	0
$346$	−608.000	−0.0944690
$347$	−11366.0	−1.75838	−0.879191	−	0.476469i	$-0.841917\pi$
$347$	−11366.0	−1.75838	−0.879191	+	0.476469i	$0.841917\pi$
$348$	0	0
$349$	9310.00	1.42795	0.713973	−	0.700174i	$-0.246894\pi$
$349$	9310.00	1.42795	0.713973	+	0.700174i	$0.246894\pi$
$350$	0	0
$351$	0	0
$352$	15872.0	2.40335
$353$	−8572.00	−1.29247	−0.646234	−	0.763139i	$-0.723657\pi$
$353$	−8572.00	−1.29247	−0.646234	+	0.763139i	$0.723657\pi$
$354$	0	0
$355$	0	0
$356$	−1600.00	−0.238202
$357$	0	0
$358$	−2440.00	−0.360218
$359$	4790.00	0.704196	0.352098	−	0.935963i	$-0.385468\pi$
$359$	4790.00	0.704196	0.352098	+	0.935963i	$0.385468\pi$
$360$	0	0
$361$	3141.00	0.457938
$362$	4168.00	0.605153
$363$	0	0
$364$	3472.00	0.499951
$365$	0	0
$366$	0	0
$367$	−5424.00	−0.771473	−0.385736	−	0.922609i	$-0.626053\pi$
$367$	−5424.00	−0.771473	−0.385736	+	0.922609i	$0.626053\pi$
$368$	2688.00	0.380765
$369$	0	0
$370$	0	0
$371$	1806.00	0.252730
$372$	0	0
$373$	−1838.00	−0.255142	−0.127571	−	0.991829i	$-0.540718\pi$
$373$	−1838.00	−0.255142	−0.127571	+	0.991829i	$0.540718\pi$
$374$	−20832.0	−2.88021
$375$	0	0
$376$	0	0
$377$	620.000	0.0846993
$378$	0	0
$379$	−4260.00	−0.577365	−0.288683	−	0.957425i	$-0.593217\pi$
$379$	−4260.00	−0.577365	−0.288683	+	0.957425i	$0.593217\pi$
$380$	0	0
$381$	0	0
$382$	8152.00	1.09187
$383$	9048.00	1.20713	0.603566	−	0.797313i	$-0.293746\pi$
$383$	9048.00	1.20713	0.603566	+	0.797313i	$0.293746\pi$
$384$	0	0
$385$	0	0
$386$	10408.0	1.37242
$387$	0	0
$388$	10128.0	1.32518
$389$	11490.0	1.49760	0.748800	−	0.662796i	$-0.230631\pi$
$389$	11490.0	1.49760	0.748800	+	0.662796i	$0.230631\pi$
$390$	0	0
$391$	−3528.00	−0.456314
$392$	0	0
$393$	0	0
$394$	9416.00	1.20399
$395$	0	0
$396$	0	0
$397$	1866.00	0.235899	0.117949	−	0.993020i	$-0.462368\pi$
$397$	1866.00	0.235899	0.117949	+	0.993020i	$0.462368\pi$
$398$	6720.00	0.846340
$399$	0	0
$400$	0	0
$401$	−13662.0	−1.70137	−0.850683	−	0.525679i	$-0.823811\pi$
$401$	−13662.0	−1.70137	−0.850683	+	0.525679i	$0.823811\pi$
$402$	0	0
$403$	−2976.00	−0.367854
$404$	−1856.00	−0.228563
$405$	0	0
$406$	280.000	0.0342270
$407$	−15252.0	−1.85753
$408$	0	0
$409$	−13210.0	−1.59705	−0.798524	−	0.601963i	$-0.794385\pi$
$409$	−13210.0	−1.59705	−0.798524	+	0.601963i	$0.794385\pi$
$410$	0	0
$411$	0	0
$412$	14336.0	1.71428
$413$	−840.000	−0.100082
$414$	0	0
$415$	0	0
$416$	−15872.0	−1.87065
$417$	0	0
$418$	−24800.0	−2.90193
$419$	−6960.00	−0.811499	−0.405750	−	0.913984i	$-0.632990\pi$
$419$	−6960.00	−0.811499	−0.405750	+	0.913984i	$0.632990\pi$
$420$	0	0
$421$	8162.00	0.944873	0.472437	−	0.881365i	$-0.343375\pi$
$421$	8162.00	0.944873	0.472437	+	0.881365i	$0.343375\pi$
$422$	−2672.00	−0.308225
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	4354.00	0.493454
$428$	−15248.0	−1.72206
$429$	0	0
$430$	0	0
$431$	−16602.0	−1.85543	−0.927715	−	0.373290i	$-0.878230\pi$
$431$	−16602.0	−1.85543	−0.927715	+	0.373290i	$0.878230\pi$
$432$	0	0
$433$	−7738.00	−0.858810	−0.429405	−	0.903112i	$-0.641277\pi$
$433$	−7738.00	−0.858810	−0.429405	+	0.903112i	$0.641277\pi$
$434$	−1344.00	−0.148650
$435$	0	0
$436$	−720.000	−0.0790866
$437$	−4200.00	−0.459756
$438$	0	0
$439$	−840.000	−0.0913235	−0.0456617	−	0.998957i	$-0.514540\pi$
$439$	−840.000	−0.0913235	−0.0456617	+	0.998957i	$0.514540\pi$
$440$	0	0
$441$	0	0
$442$	20832.0	2.24180
$443$	6618.00	0.709776	0.354888	−	0.934909i	$-0.384519\pi$
$443$	6618.00	0.709776	0.354888	+	0.934909i	$0.384519\pi$
$444$	0	0
$445$	0	0
$446$	7328.00	0.778006
$447$	0	0
$448$	−3584.00	−0.377964
$449$	−3090.00	−0.324780	−0.162390	−	0.986727i	$-0.551920\pi$
$449$	−3090.00	−0.324780	−0.162390	+	0.986727i	$0.551920\pi$
$450$	0	0
$451$	−15376.0	−1.60538
$452$	3664.00	0.381283
$453$	0	0
$454$	19776.0	2.04435
$455$	0	0
$456$	0	0
$457$	−5914.00	−0.605351	−0.302675	−	0.953094i	$-0.597880\pi$
$457$	−5914.00	−0.605351	−0.302675	+	0.953094i	$0.597880\pi$
$458$	−21880.0	−2.23228
$459$	0	0
$460$	0	0
$461$	15968.0	1.61324	0.806620	−	0.591070i	$-0.201294\pi$
$461$	15968.0	1.61324	0.806620	+	0.591070i	$0.201294\pi$
$462$	0	0
$463$	1172.00	0.117640	0.0588202	−	0.998269i	$-0.481266\pi$
$463$	1172.00	0.117640	0.0588202	+	0.998269i	$0.481266\pi$
$464$	−640.000	−0.0640329
$465$	0	0
$466$	−11208.0	−1.11416
$467$	5304.00	0.525567	0.262784	−	0.964855i	$-0.415359\pi$
$467$	5304.00	0.525567	0.262784	+	0.964855i	$0.415359\pi$
$468$	0	0
$469$	−6328.00	−0.623027
$470$	0	0
$471$	0	0
$472$	0	0
$473$	4216.00	0.409835
$474$	0	0
$475$	0	0
$476$	4704.00	0.452957
$477$	0	0
$478$	4680.00	0.447821
$479$	−5740.00	−0.547531	−0.273765	−	0.961796i	$-0.588269\pi$
$479$	−5740.00	−0.547531	−0.273765	+	0.961796i	$0.588269\pi$
$480$	0	0
$481$	15252.0	1.44580
$482$	−9352.00	−0.883759
$483$	0	0
$484$	20104.0	1.88805
$485$	0	0
$486$	0	0
$487$	−8944.00	−0.832220	−0.416110	−	0.909314i	$-0.636607\pi$
$487$	−8944.00	−0.832220	−0.416110	+	0.909314i	$0.636607\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	5558.00	0.510853	0.255427	−	0.966828i	$-0.417784\pi$
$491$	5558.00	0.510853	0.255427	+	0.966828i	$0.417784\pi$
$492$	0	0
$493$	840.000	0.0767377
$494$	24800.0	2.25871
$495$	0	0
$496$	3072.00	0.278099
$497$	4746.00	0.428344
$498$	0	0
$499$	−19820.0	−1.77809	−0.889043	−	0.457823i	$-0.848629\pi$
$499$	−19820.0	−1.77809	−0.889043	+	0.457823i	$0.848629\pi$
$500$	0	0
$501$	0	0
$502$	−11168.0	−0.992933
$503$	1848.00	0.163814	0.0819068	−	0.996640i	$-0.473899\pi$
$503$	1848.00	0.163814	0.0819068	+	0.996640i	$0.473899\pi$
$504$	0	0
$505$	0	0
$506$	10416.0	0.915114
$507$	0	0
$508$	−6432.00	−0.561760
$509$	−340.000	−0.0296075	−0.0148038	−	0.999890i	$-0.504712\pi$
$509$	−340.000	−0.0296075	−0.0148038	+	0.999890i	$0.504712\pi$
$510$	0	0
$511$	4494.00	0.389047
$512$	16384.0	1.41421
$513$	0	0
$514$	28096.0	2.41101
$515$	0	0
$516$	0	0
$517$	−20088.0	−1.70884
$518$	6888.00	0.584250
$519$	0	0
$520$	0	0
$521$	−10212.0	−0.858725	−0.429363	−	0.903132i	$-0.641262\pi$
$521$	−10212.0	−0.858725	−0.429363	+	0.903132i	$0.641262\pi$
$522$	0	0
$523$	9332.00	0.780229	0.390115	−	0.920766i	$-0.372435\pi$
$523$	9332.00	0.780229	0.390115	+	0.920766i	$0.372435\pi$
$524$	−6496.00	−0.541563
$525$	0	0
$526$	9752.00	0.808379
$527$	−4032.00	−0.333276
$528$	0	0
$529$	−10403.0	−0.855018
$530$	0	0
$531$	0	0
$532$	5600.00	0.456374
$533$	15376.0	1.24955
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	27120.0	2.17328
$539$	−3038.00	−0.242775
$540$	0	0
$541$	−8998.00	−0.715073	−0.357536	−	0.933899i	$-0.616383\pi$
$541$	−8998.00	−0.715073	−0.357536	+	0.933899i	$0.616383\pi$
$542$	−7712.00	−0.611179
$543$	0	0
$544$	−21504.0	−1.69481
$545$	0	0
$546$	0	0
$547$	3416.00	0.267016	0.133508	−	0.991048i	$-0.457376\pi$
$547$	3416.00	0.267016	0.133508	+	0.991048i	$0.457376\pi$
$548$	3312.00	0.258178
$549$	0	0
$550$	0	0
$551$	1000.00	0.0773166
$552$	0	0
$553$	5180.00	0.398329
$554$	−22216.0	−1.70373
$555$	0	0
$556$	−12960.0	−0.988537
$557$	−526.000	−0.0400132	−0.0200066	−	0.999800i	$-0.506369\pi$
$557$	−526.000	−0.0400132	−0.0200066	+	0.999800i	$0.506369\pi$
$558$	0	0
$559$	−4216.00	−0.318994
$560$	0	0
$561$	0	0
$562$	−7768.00	−0.583049
$563$	−6712.00	−0.502446	−0.251223	−	0.967929i	$-0.580833\pi$
$563$	−6712.00	−0.502446	−0.251223	+	0.967929i	$0.580833\pi$
$564$	0	0
$565$	0	0
$566$	−19312.0	−1.43418
$567$	0	0
$568$	0	0
$569$	−4190.00	−0.308706	−0.154353	−	0.988016i	$-0.549329\pi$
$569$	−4190.00	−0.308706	−0.154353	+	0.988016i	$0.549329\pi$
$570$	0	0
$571$	3032.00	0.222216	0.111108	−	0.993808i	$-0.464560\pi$
$571$	3032.00	0.222216	0.111108	+	0.993808i	$0.464560\pi$
$572$	−30752.0	−2.24791
$573$	0	0
$574$	6944.00	0.504942
$575$	0	0
$576$	0	0
$577$	−5434.00	−0.392063	−0.196032	−	0.980598i	$-0.562805\pi$
$577$	−5434.00	−0.392063	−0.196032	+	0.980598i	$0.562805\pi$
$578$	8572.00	0.616865
$579$	0	0
$580$	0	0
$581$	3276.00	0.233927
$582$	0	0
$583$	−15996.0	−1.13634
$584$	0	0
$585$	0	0
$586$	−24608.0	−1.73472
$587$	464.000	0.0326258	0.0163129	−	0.999867i	$-0.494807\pi$
$587$	464.000	0.0326258	0.0163129	+	0.999867i	$0.494807\pi$
$588$	0	0
$589$	−4800.00	−0.335790
$590$	0	0
$591$	0	0
$592$	−15744.0	−1.09303
$593$	11748.0	0.813546	0.406773	−	0.913529i	$-0.366654\pi$
$593$	11748.0	0.813546	0.406773	+	0.913529i	$0.366654\pi$
$594$	0	0
$595$	0	0
$596$	−18960.0	−1.30307
$597$	0	0
$598$	−10416.0	−0.712277
$599$	−7650.00	−0.521821	−0.260910	−	0.965363i	$-0.584023\pi$
$599$	−7650.00	−0.521821	−0.260910	+	0.965363i	$0.584023\pi$
$600$	0	0
$601$	−22878.0	−1.55277	−0.776384	−	0.630261i	$-0.782948\pi$
$601$	−22878.0	−1.55277	−0.776384	+	0.630261i	$0.782948\pi$
$602$	−1904.00	−0.128906
$603$	0	0
$604$	−4544.00	−0.306114
$605$	0	0
$606$	0	0
$607$	−704.000	−0.0470749	−0.0235375	−	0.999723i	$-0.507493\pi$
$607$	−704.000	−0.0470749	−0.0235375	+	0.999723i	$0.507493\pi$
$608$	−25600.0	−1.70759
$609$	0	0
$610$	0	0
$611$	20088.0	1.33007
$612$	0	0
$613$	−24958.0	−1.64444	−0.822222	−	0.569167i	$-0.807266\pi$
$613$	−24958.0	−1.64444	−0.822222	+	0.569167i	$0.807266\pi$
$614$	−23536.0	−1.54696
$615$	0	0
$616$	0	0
$617$	−8826.00	−0.575886	−0.287943	−	0.957648i	$-0.592971\pi$
$617$	−8826.00	−0.575886	−0.287943	+	0.957648i	$0.592971\pi$
$618$	0	0
$619$	21220.0	1.37787	0.688937	−	0.724821i	$-0.258078\pi$
$619$	21220.0	1.37787	0.688937	+	0.724821i	$0.258078\pi$
$620$	0	0
$621$	0	0
$622$	−36528.0	−2.35473
$623$	−1400.00	−0.0900318
$624$	0	0
$625$	0	0
$626$	37528.0	2.39604
$627$	0	0
$628$	2128.00	0.135217
$629$	20664.0	1.30990
$630$	0	0
$631$	−3268.00	−0.206176	−0.103088	−	0.994672i	$-0.532872\pi$
$631$	−3268.00	−0.206176	−0.103088	+	0.994672i	$0.532872\pi$
$632$	0	0
$633$	0	0
$634$	12456.0	0.780270
$635$	0	0
$636$	0	0
$637$	3038.00	0.188964
$638$	−2480.00	−0.153894
$639$	0	0
$640$	0	0
$641$	−13062.0	−0.804864	−0.402432	−	0.915450i	$-0.631835\pi$
$641$	−13062.0	−0.804864	−0.402432	+	0.915450i	$0.631835\pi$
$642$	0	0
$643$	28012.0	1.71802	0.859009	−	0.511961i	$-0.171081\pi$
$643$	28012.0	1.71802	0.859009	+	0.511961i	$0.171081\pi$
$644$	−2352.00	−0.143916
$645$	0	0
$646$	33600.0	2.04640
$647$	3844.00	0.233575	0.116788	−	0.993157i	$-0.462740\pi$
$647$	3844.00	0.233575	0.116788	+	0.993157i	$0.462740\pi$
$648$	0	0
$649$	7440.00	0.449993
$650$	0	0
$651$	0	0
$652$	2176.00	0.130704
$653$	−28482.0	−1.70687	−0.853436	−	0.521198i	$-0.825485\pi$
$653$	−28482.0	−1.70687	−0.853436	+	0.521198i	$0.825485\pi$
$654$	0	0
$655$	0	0
$656$	−15872.0	−0.944661
$657$	0	0
$658$	9072.00	0.537482
$659$	9330.00	0.551510	0.275755	−	0.961228i	$-0.411072\pi$
$659$	9330.00	0.551510	0.275755	+	0.961228i	$0.411072\pi$
$660$	0	0
$661$	8782.00	0.516763	0.258381	−	0.966043i	$-0.416811\pi$
$661$	8782.00	0.516763	0.258381	+	0.966043i	$0.416811\pi$
$662$	6128.00	0.359776
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−420.000	−0.0243815
$668$	−15008.0	−0.869277
$669$	0	0
$670$	0	0
$671$	−38564.0	−2.21870
$672$	0	0
$673$	10562.0	0.604956	0.302478	−	0.953156i	$-0.402186\pi$
$673$	10562.0	0.604956	0.302478	+	0.953156i	$0.402186\pi$
$674$	16664.0	0.952334
$675$	0	0
$676$	13176.0	0.749659
$677$	−26016.0	−1.47692	−0.738461	−	0.674296i	$-0.764447\pi$
$677$	−26016.0	−1.47692	−0.738461	+	0.674296i	$0.764447\pi$
$678$	0	0
$679$	8862.00	0.500872
$680$	0	0
$681$	0	0
$682$	11904.0	0.668369
$683$	8898.00	0.498496	0.249248	−	0.968440i	$-0.419817\pi$
$683$	8898.00	0.498496	0.249248	+	0.968440i	$0.419817\pi$
$684$	0	0
$685$	0	0
$686$	1372.00	0.0763604
$687$	0	0
$688$	4352.00	0.241161
$689$	15996.0	0.884469
$690$	0	0
$691$	30572.0	1.68309	0.841544	−	0.540189i	$-0.181647\pi$
$691$	30572.0	1.68309	0.841544	+	0.540189i	$0.181647\pi$
$692$	−1216.00	−0.0667997
$693$	0	0
$694$	−45464.0	−2.48673
$695$	0	0
$696$	0	0
$697$	20832.0	1.13209
$698$	37240.0	2.01942
$699$	0	0
$700$	0	0
$701$	30618.0	1.64968	0.824840	−	0.565366i	$-0.191265\pi$
$701$	30618.0	1.64968	0.824840	+	0.565366i	$0.191265\pi$
$702$	0	0
$703$	24600.0	1.31978
$704$	31744.0	1.69943
$705$	0	0
$706$	−34288.0	−1.82783
$707$	−1624.00	−0.0863887
$708$	0	0
$709$	−8130.00	−0.430647	−0.215323	−	0.976543i	$-0.569081\pi$
$709$	−8130.00	−0.430647	−0.215323	+	0.976543i	$0.569081\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	2016.00	0.105890
$714$	0	0
$715$	0	0
$716$	−4880.00	−0.254713
$717$	0	0
$718$	19160.0	0.995884
$719$	27840.0	1.44403	0.722014	−	0.691878i	$-0.243216\pi$
$719$	27840.0	1.44403	0.722014	+	0.691878i	$0.243216\pi$
$720$	0	0
$721$	12544.0	0.647938
$722$	12564.0	0.647623
$723$	0	0
$724$	8336.00	0.427907
$725$	0	0
$726$	0	0
$727$	−14624.0	−0.746044	−0.373022	−	0.927822i	$-0.621678\pi$
$727$	−14624.0	−0.746044	−0.373022	+	0.927822i	$0.621678\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	−5712.00	−0.289010
$732$	0	0
$733$	20862.0	1.05124	0.525618	−	0.850721i	$-0.323834\pi$
$733$	20862.0	1.05124	0.525618	+	0.850721i	$0.323834\pi$
$734$	−21696.0	−1.09103
$735$	0	0
$736$	10752.0	0.538484
$737$	56048.0	2.80130
$738$	0	0
$739$	−13920.0	−0.692903	−0.346452	−	0.938068i	$-0.612614\pi$
$739$	−13920.0	−0.692903	−0.346452	+	0.938068i	$0.612614\pi$
$740$	0	0
$741$	0	0
$742$	7224.00	0.357414
$743$	25578.0	1.26294	0.631471	−	0.775400i	$-0.282452\pi$
$743$	25578.0	1.26294	0.631471	+	0.775400i	$0.282452\pi$
$744$	0	0
$745$	0	0
$746$	−7352.00	−0.360826
$747$	0	0
$748$	−41664.0	−2.03661
$749$	−13342.0	−0.650876
$750$	0	0
$751$	33472.0	1.62638	0.813189	−	0.581999i	$-0.197729\pi$
$751$	33472.0	1.62638	0.813189	+	0.581999i	$0.197729\pi$
$752$	−20736.0	−1.00554
$753$	0	0
$754$	2480.00	0.119783
$755$	0	0
$756$	0	0
$757$	−25934.0	−1.24516	−0.622581	−	0.782556i	$-0.713916\pi$
$757$	−25934.0	−1.24516	−0.622581	+	0.782556i	$0.713916\pi$
$758$	−17040.0	−0.816518
$759$	0	0
$760$	0	0
$761$	−26952.0	−1.28385	−0.641925	−	0.766768i	$-0.721864\pi$
$761$	−26952.0	−1.28385	−0.641925	+	0.766768i	$0.721864\pi$
$762$	0	0
$763$	−630.000	−0.0298919
$764$	16304.0	0.772065
$765$	0	0
$766$	36192.0	1.70714
$767$	−7440.00	−0.350251
$768$	0	0
$769$	23450.0	1.09965	0.549824	−	0.835281i	$-0.314695\pi$
$769$	23450.0	1.09965	0.549824	+	0.835281i	$0.314695\pi$
$770$	0	0
$771$	0	0
$772$	20816.0	0.970446
$773$	39568.0	1.84109	0.920545	−	0.390637i	$-0.127745\pi$
$773$	39568.0	1.84109	0.920545	+	0.390637i	$0.127745\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	45960.0	2.11793
$779$	24800.0	1.14063
$780$	0	0
$781$	−42036.0	−1.92595
$782$	−14112.0	−0.645325
$783$	0	0
$784$	−3136.00	−0.142857
$785$	0	0
$786$	0	0
$787$	12356.0	0.559649	0.279825	−	0.960051i	$-0.409724\pi$
$787$	12356.0	0.559649	0.279825	+	0.960051i	$0.409724\pi$
$788$	18832.0	0.851348
$789$	0	0
$790$	0	0
$791$	3206.00	0.144112
$792$	0	0
$793$	38564.0	1.72692
$794$	7464.00	0.333611
$795$	0	0
$796$	13440.0	0.598452
$797$	−21736.0	−0.966033	−0.483017	−	0.875611i	$-0.660459\pi$
$797$	−21736.0	−0.966033	−0.483017	+	0.875611i	$0.660459\pi$
$798$	0	0
$799$	27216.0	1.20505
$800$	0	0
$801$	0	0
$802$	−54648.0	−2.40609
$803$	−39804.0	−1.74926
$804$	0	0
$805$	0	0
$806$	−11904.0	−0.520224
$807$	0	0
$808$	0	0
$809$	38310.0	1.66490	0.832452	−	0.554097i	$-0.186936\pi$
$809$	38310.0	1.66490	0.832452	+	0.554097i	$0.186936\pi$
$810$	0	0
$811$	2132.00	0.0923115	0.0461558	−	0.998934i	$-0.485303\pi$
$811$	2132.00	0.0923115	0.0461558	+	0.998934i	$0.485303\pi$
$812$	560.000	0.0242022
$813$	0	0
$814$	−61008.0	−2.62694
$815$	0	0
$816$	0	0
$817$	−6800.00	−0.291190
$818$	−52840.0	−2.25857
$819$	0	0
$820$	0	0
$821$	−5002.00	−0.212632	−0.106316	−	0.994332i	$-0.533906\pi$
$821$	−5002.00	−0.212632	−0.106316	+	0.994332i	$0.533906\pi$
$822$	0	0
$823$	3612.00	0.152985	0.0764923	−	0.997070i	$-0.475628\pi$
$823$	3612.00	0.152985	0.0764923	+	0.997070i	$0.475628\pi$
$824$	0	0
$825$	0	0
$826$	−3360.00	−0.141537
$827$	−27666.0	−1.16329	−0.581645	−	0.813443i	$-0.697591\pi$
$827$	−27666.0	−1.16329	−0.581645	+	0.813443i	$0.697591\pi$
$828$	0	0
$829$	12890.0	0.540034	0.270017	−	0.962856i	$-0.412971\pi$
$829$	12890.0	0.540034	0.270017	+	0.962856i	$0.412971\pi$
$830$	0	0
$831$	0	0
$832$	−31744.0	−1.32275
$833$	4116.00	0.171202
$834$	0	0
$835$	0	0
$836$	−49600.0	−2.05198
$837$	0	0
$838$	−27840.0	−1.14763
$839$	9340.00	0.384330	0.192165	−	0.981363i	$-0.438449\pi$
$839$	9340.00	0.384330	0.192165	+	0.981363i	$0.438449\pi$
$840$	0	0
$841$	−24289.0	−0.995900
$842$	32648.0	1.33625
$843$	0	0
$844$	−5344.00	−0.217948
$845$	0	0
$846$	0	0
$847$	17591.0	0.713617
$848$	−16512.0	−0.668661
$849$	0	0
$850$	0	0
$851$	−10332.0	−0.416188
$852$	0	0
$853$	33082.0	1.32791	0.663954	−	0.747773i	$-0.268877\pi$
$853$	33082.0	1.32791	0.663954	+	0.747773i	$0.268877\pi$
$854$	17416.0	0.697849
$855$	0	0
$856$	0	0
$857$	7544.00	0.300698	0.150349	−	0.988633i	$-0.451960\pi$
$857$	7544.00	0.300698	0.150349	+	0.988633i	$0.451960\pi$
$858$	0	0
$859$	8180.00	0.324910	0.162455	−	0.986716i	$-0.448059\pi$
$859$	8180.00	0.324910	0.162455	+	0.986716i	$0.448059\pi$
$860$	0	0
$861$	0	0
$862$	−66408.0	−2.62397
$863$	10518.0	0.414875	0.207437	−	0.978248i	$-0.433488\pi$
$863$	10518.0	0.414875	0.207437	+	0.978248i	$0.433488\pi$
$864$	0	0
$865$	0	0
$866$	−30952.0	−1.21454
$867$	0	0
$868$	−2688.00	−0.105111
$869$	−45880.0	−1.79099
$870$	0	0
$871$	−56048.0	−2.18038
$872$	0	0
$873$	0	0
$874$	−16800.0	−0.650193
$875$	0	0
$876$	0	0
$877$	−14134.0	−0.544209	−0.272104	−	0.962268i	$-0.587720\pi$
$877$	−14134.0	−0.544209	−0.272104	+	0.962268i	$0.587720\pi$
$878$	−3360.00	−0.129151
$879$	0	0
$880$	0	0
$881$	−6492.00	−0.248265	−0.124132	−	0.992266i	$-0.539615\pi$
$881$	−6492.00	−0.248265	−0.124132	+	0.992266i	$0.539615\pi$
$882$	0	0
$883$	−38228.0	−1.45694	−0.728468	−	0.685080i	$-0.759767\pi$
$883$	−38228.0	−1.45694	−0.728468	+	0.685080i	$0.759767\pi$
$884$	41664.0	1.58519
$885$	0	0
$886$	26472.0	1.00377
$887$	−43076.0	−1.63061	−0.815305	−	0.579032i	$-0.803431\pi$
$887$	−43076.0	−1.63061	−0.815305	+	0.579032i	$0.803431\pi$
$888$	0	0
$889$	−5628.00	−0.212325
$890$	0	0
$891$	0	0
$892$	14656.0	0.550134
$893$	32400.0	1.21414
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−12360.0	−0.459308
$899$	−480.000	−0.0178074
$900$	0	0
$901$	21672.0	0.801331
$902$	−61504.0	−2.27035
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	32236.0	1.18013	0.590065	−	0.807355i	$-0.299102\pi$
$907$	32236.0	1.18013	0.590065	+	0.807355i	$0.299102\pi$
$908$	39552.0	1.44557
$909$	0	0
$910$	0	0
$911$	46518.0	1.69178	0.845889	−	0.533359i	$-0.179070\pi$
$911$	46518.0	1.69178	0.845889	+	0.533359i	$0.179070\pi$
$912$	0	0
$913$	−29016.0	−1.05180
$914$	−23656.0	−0.856095
$915$	0	0
$916$	−43760.0	−1.57846
$917$	−5684.00	−0.204692
$918$	0	0
$919$	17840.0	0.640356	0.320178	−	0.947357i	$-0.396257\pi$
$919$	17840.0	0.640356	0.320178	+	0.947357i	$0.396257\pi$
$920$	0	0
$921$	0	0
$922$	63872.0	2.28147
$923$	42036.0	1.49906
$924$	0	0
$925$	0	0
$926$	4688.00	0.166369
$927$	0	0
$928$	−2560.00	−0.0905562
$929$	−7000.00	−0.247215	−0.123607	−	0.992331i	$-0.539446\pi$
$929$	−7000.00	−0.247215	−0.123607	+	0.992331i	$0.539446\pi$
$930$	0	0
$931$	4900.00	0.172493
$932$	−22416.0	−0.787833
$933$	0	0
$934$	21216.0	0.743264
$935$	0	0
$936$	0	0
$937$	−36114.0	−1.25912	−0.629559	−	0.776953i	$-0.716764\pi$
$937$	−36114.0	−1.25912	−0.629559	+	0.776953i	$0.716764\pi$
$938$	−25312.0	−0.881094
$939$	0	0
$940$	0	0
$941$	4748.00	0.164485	0.0822425	−	0.996612i	$-0.473792\pi$
$941$	4748.00	0.164485	0.0822425	+	0.996612i	$0.473792\pi$
$942$	0	0
$943$	−10416.0	−0.359694
$944$	7680.00	0.264791
$945$	0	0
$946$	16864.0	0.579594
$947$	42694.0	1.46501	0.732507	−	0.680759i	$-0.238350\pi$
$947$	42694.0	1.46501	0.732507	+	0.680759i	$0.238350\pi$
$948$	0	0
$949$	39804.0	1.36153
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−16742.0	−0.569073	−0.284537	−	0.958665i	$-0.591840\pi$
$953$	−16742.0	−0.569073	−0.284537	+	0.958665i	$0.591840\pi$
$954$	0	0
$955$	0	0
$956$	9360.00	0.316657
$957$	0	0
$958$	−22960.0	−0.774326
$959$	2898.00	0.0975822
$960$	0	0
$961$	−27487.0	−0.922661
$962$	61008.0	2.04467
$963$	0	0
$964$	−18704.0	−0.624912
$965$	0	0
$966$	0	0
$967$	9956.00	0.331089	0.165545	−	0.986202i	$-0.447062\pi$
$967$	9956.00	0.331089	0.165545	+	0.986202i	$0.447062\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	26388.0	0.872123	0.436061	−	0.899917i	$-0.356373\pi$
$971$	26388.0	0.872123	0.436061	+	0.899917i	$0.356373\pi$
$972$	0	0
$973$	−11340.0	−0.373632
$974$	−35776.0	−1.17694
$975$	0	0
$976$	−39808.0	−1.30556
$977$	−786.000	−0.0257383	−0.0128692	−	0.999917i	$-0.504096\pi$
$977$	−786.000	−0.0257383	−0.0128692	+	0.999917i	$0.504096\pi$
$978$	0	0
$979$	12400.0	0.404807
$980$	0	0
$981$	0	0
$982$	22232.0	0.722456
$983$	51888.0	1.68359	0.841796	−	0.539796i	$-0.181499\pi$
$983$	51888.0	1.68359	0.841796	+	0.539796i	$0.181499\pi$
$984$	0	0
$985$	0	0
$986$	3360.00	0.108524
$987$	0	0
$988$	49600.0	1.59715
$989$	2856.00	0.0918256
$990$	0	0
$991$	−51928.0	−1.66453	−0.832264	−	0.554379i	$-0.812956\pi$
$991$	−51928.0	−1.66453	−0.832264	+	0.554379i	$0.812956\pi$
$992$	12288.0	0.393291
$993$	0	0
$994$	18984.0	0.605771
$995$	0	0
$996$	0	0
$997$	386.000	0.0122615	0.00613076	−	0.999981i	$-0.498049\pi$
$997$	386.000	0.0122615	0.00613076	+	0.999981i	$0.498049\pi$
$998$	−79280.0	−2.51459
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.4.a.k.1.1		1
3.2	odd	2		525.4.a.b.1.1		1
5.4	even	2		63.4.a.a.1.1		1
15.2	even	4		525.4.d.b.274.1		2
15.8	even	4		525.4.d.b.274.2		2
15.14	odd	2		21.4.a.b.1.1	✓	1
20.19	odd	2		1008.4.a.m.1.1		1
35.4	even	6		441.4.e.m.226.1		2
35.9	even	6		441.4.e.m.361.1		2
35.19	odd	6		441.4.e.n.361.1		2
35.24	odd	6		441.4.e.n.226.1		2
35.34	odd	2		441.4.a.b.1.1		1
60.59	even	2		336.4.a.h.1.1		1
105.44	odd	6		147.4.e.c.67.1		2
105.59	even	6		147.4.e.b.79.1		2
105.74	odd	6		147.4.e.c.79.1		2
105.89	even	6		147.4.e.b.67.1		2
105.104	even	2		147.4.a.g.1.1		1
120.29	odd	2		1344.4.a.w.1.1		1
120.59	even	2		1344.4.a.i.1.1		1
420.419	odd	2		2352.4.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.b.1.1	✓	1	15.14	odd	2
63.4.a.a.1.1		1	5.4	even	2
147.4.a.g.1.1		1	105.104	even	2
147.4.e.b.67.1		2	105.89	even	6
147.4.e.b.79.1		2	105.59	even	6
147.4.e.c.67.1		2	105.44	odd	6
147.4.e.c.79.1		2	105.74	odd	6
336.4.a.h.1.1		1	60.59	even	2
441.4.a.b.1.1		1	35.34	odd	2
441.4.e.m.226.1		2	35.4	even	6
441.4.e.m.361.1		2	35.9	even	6
441.4.e.n.226.1		2	35.24	odd	6
441.4.e.n.361.1		2	35.19	odd	6
525.4.a.b.1.1		1	3.2	odd	2
525.4.d.b.274.1		2	15.2	even	4
525.4.d.b.274.2		2	15.8	even	4
1008.4.a.m.1.1		1	20.19	odd	2
1344.4.a.i.1.1		1	120.59	even	2
1344.4.a.w.1.1		1	120.29	odd	2
1575.4.a.k.1.1		1	1.1	even	1	trivial
2352.4.a.l.1.1		1	420.419	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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1575.a (trivial)

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