LMFDB - Embedded newform 2450.4.a.z.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2450,4,Mod(1,2450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2450, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2450.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2450 = 2 \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2450.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:	$144.554679514$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 350)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -4.00000 q^{3} +4.00000 q^{4} -8.00000 q^{6} +8.00000 q^{8} -11.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -4.00000 q^{3} +4.00000 q^{4} -8.00000 q^{6} +8.00000 q^{8} -11.0000 q^{9} +30.0000 q^{11} -16.0000 q^{12} +4.00000 q^{13} +16.0000 q^{16} -9.00000 q^{17} -22.0000 q^{18} -88.0000 q^{19} +60.0000 q^{22} -33.0000 q^{23} -32.0000 q^{24} +8.00000 q^{26} +152.000 q^{27} +126.000 q^{29} +155.000 q^{31} +32.0000 q^{32} -120.000 q^{33} -18.0000 q^{34} -44.0000 q^{36} -116.000 q^{37} -176.000 q^{38} -16.0000 q^{39} -423.000 q^{41} +340.000 q^{43} +120.000 q^{44} -66.0000 q^{46} -339.000 q^{47} -64.0000 q^{48} +36.0000 q^{51} +16.0000 q^{52} +312.000 q^{53} +304.000 q^{54} +352.000 q^{57} +252.000 q^{58} -462.000 q^{59} +326.000 q^{61} +310.000 q^{62} +64.0000 q^{64} -240.000 q^{66} -704.000 q^{67} -36.0000 q^{68} +132.000 q^{69} +621.000 q^{71} -88.0000 q^{72} +250.000 q^{73} -232.000 q^{74} -352.000 q^{76} -32.0000 q^{78} -1105.00 q^{79} -311.000 q^{81} -846.000 q^{82} +198.000 q^{83} +680.000 q^{86} -504.000 q^{87} +240.000 q^{88} -873.000 q^{89} -132.000 q^{92} -620.000 q^{93} -678.000 q^{94} -128.000 q^{96} -905.000 q^{97} -330.000 q^{99} +O(q^{100})\)

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
$2$	2.00000	0.707107
$3$	−4.00000	−0.769800	−0.384900	−	0.922958i	$-0.625764\pi$
$3$	−4.00000	−0.769800	−0.384900	+	0.922958i	$0.625764\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−8.00000	−0.544331
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	−11.0000	−0.407407
$10$	0	0
$11$	30.0000	0.822304	0.411152	−	0.911567i	$-0.365127\pi$
$11$	30.0000	0.822304	0.411152	+	0.911567i	$0.365127\pi$
$12$	−16.0000	−0.384900
$13$	4.00000	0.0853385	0.0426692	−	0.999089i	$-0.486414\pi$
$13$	4.00000	0.0853385	0.0426692	+	0.999089i	$0.486414\pi$
$14$	0	0
$15$	0	0
$16$	16.0000	0.250000
$17$	−9.00000	−0.128401	−0.0642006	−	0.997937i	$-0.520450\pi$
$17$	−9.00000	−0.128401	−0.0642006	+	0.997937i	$0.520450\pi$
$18$	−22.0000	−0.288081
$19$	−88.0000	−1.06256	−0.531279	−	0.847197i	$-0.678288\pi$
$19$	−88.0000	−1.06256	−0.531279	+	0.847197i	$0.678288\pi$
$20$	0	0
$21$	0	0
$22$	60.0000	0.581456
$23$	−33.0000	−0.299173	−0.149586	−	0.988749i	$-0.547794\pi$
$23$	−33.0000	−0.299173	−0.149586	+	0.988749i	$0.547794\pi$
$24$	−32.0000	−0.272166
$25$	0	0
$26$	8.00000	0.0603434
$27$	152.000	1.08342
$28$	0	0
$29$	126.000	0.806814	0.403407	−	0.915021i	$-0.367826\pi$
$29$	126.000	0.806814	0.403407	+	0.915021i	$0.367826\pi$
$30$	0	0
$31$	155.000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	155.000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	32.0000	0.176777
$33$	−120.000	−0.633010
$34$	−18.0000	−0.0907934
$35$	0	0
$36$	−44.0000	−0.203704
$37$	−116.000	−0.515413	−0.257707	−	0.966223i	$-0.582967\pi$
$37$	−116.000	−0.515413	−0.257707	+	0.966223i	$0.582967\pi$
$38$	−176.000	−0.751341
$39$	−16.0000	−0.0656936
$40$	0	0
$41$	−423.000	−1.61126	−0.805628	−	0.592422i	$-0.798172\pi$
$41$	−423.000	−1.61126	−0.805628	+	0.592422i	$0.798172\pi$
$42$	0	0
$43$	340.000	1.20580	0.602901	−	0.797816i	$-0.294011\pi$
$43$	340.000	1.20580	0.602901	+	0.797816i	$0.294011\pi$
$44$	120.000	0.411152
$45$	0	0
$46$	−66.0000	−0.211547
$47$	−339.000	−1.05209	−0.526045	−	0.850457i	$-0.676326\pi$
$47$	−339.000	−1.05209	−0.526045	+	0.850457i	$0.676326\pi$
$48$	−64.0000	−0.192450
$49$	0	0
$50$	0	0
$51$	36.0000	0.0988433
$52$	16.0000	0.0426692
$53$	312.000	0.808613	0.404307	−	0.914624i	$-0.367513\pi$
$53$	312.000	0.808613	0.404307	+	0.914624i	$0.367513\pi$
$54$	304.000	0.766096
$55$	0	0
$56$	0	0
$57$	352.000	0.817957
$58$	252.000	0.570504
$59$	−462.000	−1.01945	−0.509723	−	0.860339i	$-0.670252\pi$
$59$	−462.000	−1.01945	−0.509723	+	0.860339i	$0.670252\pi$
$60$	0	0
$61$	326.000	0.684263	0.342131	−	0.939652i	$-0.388851\pi$
$61$	326.000	0.684263	0.342131	+	0.939652i	$0.388851\pi$
$62$	310.000	0.635001
$63$	0	0
$64$	64.0000	0.125000
$65$	0	0
$66$	−240.000	−0.447605
$67$	−704.000	−1.28369	−0.641845	−	0.766834i	$-0.721831\pi$
$67$	−704.000	−1.28369	−0.641845	+	0.766834i	$0.721831\pi$
$68$	−36.0000	−0.0642006
$69$	132.000	0.230303
$70$	0	0
$71$	621.000	1.03802	0.519008	−	0.854769i	$-0.326301\pi$
$71$	621.000	1.03802	0.519008	+	0.854769i	$0.326301\pi$
$72$	−88.0000	−0.144040
$73$	250.000	0.400826	0.200413	−	0.979712i	$-0.435772\pi$
$73$	250.000	0.400826	0.200413	+	0.979712i	$0.435772\pi$
$74$	−232.000	−0.364452
$75$	0	0
$76$	−352.000	−0.531279
$77$	0	0
$78$	−32.0000	−0.0464524
$79$	−1105.00	−1.57370	−0.786849	−	0.617145i	$-0.788289\pi$
$79$	−1105.00	−1.57370	−0.786849	+	0.617145i	$0.788289\pi$
$80$	0	0
$81$	−311.000	−0.426612
$82$	−846.000	−1.13933
$83$	198.000	0.261847	0.130924	−	0.991392i	$-0.458206\pi$
$83$	198.000	0.261847	0.130924	+	0.991392i	$0.458206\pi$
$84$	0	0
$85$	0	0
$86$	680.000	0.852631
$87$	−504.000	−0.621086
$88$	240.000	0.290728
$89$	−873.000	−1.03975	−0.519875	−	0.854242i	$-0.674022\pi$
$89$	−873.000	−1.03975	−0.519875	+	0.854242i	$0.674022\pi$
$90$	0	0
$91$	0	0
$92$	−132.000	−0.149586
$93$	−620.000	−0.691301
$94$	−678.000	−0.743940
$95$	0	0
$96$	−128.000	−0.136083
$97$	−905.000	−0.947308	−0.473654	−	0.880711i	$-0.657065\pi$
$97$	−905.000	−0.947308	−0.473654	+	0.880711i	$0.657065\pi$
$98$	0	0
$99$	−330.000	−0.335013
$100$	0	0
$101$	600.000	0.591111	0.295556	−	0.955326i	$-0.404495\pi$
$101$	600.000	0.591111	0.295556	+	0.955326i	$0.404495\pi$
$102$	72.0000	0.0698928
$103$	−293.000	−0.280293	−0.140146	−	0.990131i	$-0.544757\pi$
$103$	−293.000	−0.280293	−0.140146	+	0.990131i	$0.544757\pi$
$104$	32.0000	0.0301717
$105$	0	0
$106$	624.000	0.571776
$107$	1686.00	1.52329	0.761644	−	0.647996i	$-0.224393\pi$
$107$	1686.00	1.52329	0.761644	+	0.647996i	$0.224393\pi$
$108$	608.000	0.541711
$109$	1640.00	1.44113	0.720567	−	0.693386i	$-0.243882\pi$
$109$	1640.00	1.44113	0.720567	+	0.693386i	$0.243882\pi$
$110$	0	0
$111$	464.000	0.396765
$112$	0	0
$113$	1185.00	0.986508	0.493254	−	0.869885i	$-0.335807\pi$
$113$	1185.00	0.986508	0.493254	+	0.869885i	$0.335807\pi$
$114$	704.000	0.578383
$115$	0	0
$116$	504.000	0.403407
$117$	−44.0000	−0.0347675
$118$	−924.000	−0.720857
$119$	0	0
$120$	0	0
$121$	−431.000	−0.323817
$122$	652.000	0.483847
$123$	1692.00	1.24035
$124$	620.000	0.449013
$125$	0	0
$126$	0	0
$127$	−1976.00	−1.38064	−0.690321	−	0.723503i	$-0.742531\pi$
$127$	−1976.00	−1.38064	−0.690321	+	0.723503i	$0.742531\pi$
$128$	128.000	0.0883883
$129$	−1360.00	−0.928227
$130$	0	0
$131$	−1530.00	−1.02043	−0.510216	−	0.860046i	$-0.670435\pi$
$131$	−1530.00	−1.02043	−0.510216	+	0.860046i	$0.670435\pi$
$132$	−480.000	−0.316505
$133$	0	0
$134$	−1408.00	−0.907707
$135$	0	0
$136$	−72.0000	−0.0453967
$137$	1587.00	0.989683	0.494841	−	0.868983i	$-0.335226\pi$
$137$	1587.00	0.989683	0.494841	+	0.868983i	$0.335226\pi$
$138$	264.000	0.162849
$139$	−2242.00	−1.36809	−0.684043	−	0.729442i	$-0.739780\pi$
$139$	−2242.00	−1.36809	−0.684043	+	0.729442i	$0.739780\pi$
$140$	0	0
$141$	1356.00	0.809899
$142$	1242.00	0.733988
$143$	120.000	0.0701742
$144$	−176.000	−0.101852
$145$	0	0
$146$	500.000	0.283427
$147$	0	0
$148$	−464.000	−0.257707
$149$	−1470.00	−0.808236	−0.404118	−	0.914707i	$-0.632421\pi$
$149$	−1470.00	−0.808236	−0.404118	+	0.914707i	$0.632421\pi$
$150$	0	0
$151$	−664.000	−0.357851	−0.178926	−	0.983863i	$-0.557262\pi$
$151$	−664.000	−0.357851	−0.178926	+	0.983863i	$0.557262\pi$
$152$	−704.000	−0.375671
$153$	99.0000	0.0523116
$154$	0	0
$155$	0	0
$156$	−64.0000	−0.0328468
$157$	1966.00	0.999388	0.499694	−	0.866202i	$-0.333446\pi$
$157$	1966.00	0.999388	0.499694	+	0.866202i	$0.333446\pi$
$158$	−2210.00	−1.11277
$159$	−1248.00	−0.622471
$160$	0	0
$161$	0	0
$162$	−622.000	−0.301660
$163$	3016.00	1.44927	0.724636	−	0.689132i	$-0.242008\pi$
$163$	3016.00	1.44927	0.724636	+	0.689132i	$0.242008\pi$
$164$	−1692.00	−0.805628
$165$	0	0
$166$	396.000	0.185154
$167$	−1608.00	−0.745094	−0.372547	−	0.928013i	$-0.621516\pi$
$167$	−1608.00	−0.745094	−0.372547	+	0.928013i	$0.621516\pi$
$168$	0	0
$169$	−2181.00	−0.992717
$170$	0	0
$171$	968.000	0.432894
$172$	1360.00	0.602901
$173$	−2514.00	−1.10483	−0.552416	−	0.833569i	$-0.686294\pi$
$173$	−2514.00	−1.10483	−0.552416	+	0.833569i	$0.686294\pi$
$174$	−1008.00	−0.439174
$175$	0	0
$176$	480.000	0.205576
$177$	1848.00	0.784769
$178$	−1746.00	−0.735215
$179$	−1614.00	−0.673944	−0.336972	−	0.941515i	$-0.609403\pi$
$179$	−1614.00	−0.673944	−0.336972	+	0.941515i	$0.609403\pi$
$180$	0	0
$181$	−2770.00	−1.13753	−0.568764	−	0.822501i	$-0.692578\pi$
$181$	−2770.00	−1.13753	−0.568764	+	0.822501i	$0.692578\pi$
$182$	0	0
$183$	−1304.00	−0.526746
$184$	−264.000	−0.105774
$185$	0	0
$186$	−1240.00	−0.488824
$187$	−270.000	−0.105585
$188$	−1356.00	−0.526045
$189$	0	0
$190$	0	0
$191$	−4635.00	−1.75590	−0.877950	−	0.478753i	$-0.841089\pi$
$191$	−4635.00	−1.75590	−0.877950	+	0.478753i	$0.841089\pi$
$192$	−256.000	−0.0962250
$193$	475.000	0.177157	0.0885784	−	0.996069i	$-0.471768\pi$
$193$	475.000	0.177157	0.0885784	+	0.996069i	$0.471768\pi$
$194$	−1810.00	−0.669848
$195$	0	0
$196$	0	0
$197$	−4896.00	−1.77069	−0.885344	−	0.464936i	$-0.846077\pi$
$197$	−4896.00	−1.77069	−0.885344	+	0.464936i	$0.846077\pi$
$198$	−660.000	−0.236890
$199$	−2797.00	−0.996352	−0.498176	−	0.867076i	$-0.665997\pi$
$199$	−2797.00	−0.996352	−0.498176	+	0.867076i	$0.665997\pi$
$200$	0	0
$201$	2816.00	0.988186
$202$	1200.00	0.417979
$203$	0	0
$204$	144.000	0.0494217
$205$	0	0
$206$	−586.000	−0.198197
$207$	363.000	0.121885
$208$	64.0000	0.0213346
$209$	−2640.00	−0.873745
$210$	0	0
$211$	2612.00	0.852216	0.426108	−	0.904672i	$-0.359884\pi$
$211$	2612.00	0.852216	0.426108	+	0.904672i	$0.359884\pi$
$212$	1248.00	0.404307
$213$	−2484.00	−0.799065
$214$	3372.00	1.07713
$215$	0	0
$216$	1216.00	0.383048
$217$	0	0
$218$	3280.00	1.01904
$219$	−1000.00	−0.308556
$220$	0	0
$221$	−36.0000	−0.0109576
$222$	928.000	0.280555
$223$	−3629.00	−1.08976	−0.544879	−	0.838515i	$-0.683424\pi$
$223$	−3629.00	−1.08976	−0.544879	+	0.838515i	$0.683424\pi$
$224$	0	0
$225$	0	0
$226$	2370.00	0.697567
$227$	414.000	0.121049	0.0605245	−	0.998167i	$-0.480723\pi$
$227$	414.000	0.121049	0.0605245	+	0.998167i	$0.480723\pi$
$228$	1408.00	0.408978
$229$	−1570.00	−0.453050	−0.226525	−	0.974005i	$-0.572737\pi$
$229$	−1570.00	−0.453050	−0.226525	+	0.974005i	$0.572737\pi$
$230$	0	0
$231$	0	0
$232$	1008.00	0.285252
$233$	−5262.00	−1.47951	−0.739753	−	0.672878i	$-0.765058\pi$
$233$	−5262.00	−1.47951	−0.739753	+	0.672878i	$0.765058\pi$
$234$	−88.0000	−0.0245844
$235$	0	0
$236$	−1848.00	−0.509723
$237$	4420.00	1.21143
$238$	0	0
$239$	4305.00	1.16514	0.582568	−	0.812782i	$-0.302048\pi$
$239$	4305.00	1.16514	0.582568	+	0.812782i	$0.302048\pi$
$240$	0	0
$241$	−982.000	−0.262474	−0.131237	−	0.991351i	$-0.541895\pi$
$241$	−982.000	−0.262474	−0.131237	+	0.991351i	$0.541895\pi$
$242$	−862.000	−0.228973
$243$	−2860.00	−0.755017
$244$	1304.00	0.342131
$245$	0	0
$246$	3384.00	0.877057
$247$	−352.000	−0.0906770
$248$	1240.00	0.317500
$249$	−792.000	−0.201570
$250$	0	0
$251$	4080.00	1.02601	0.513003	−	0.858387i	$-0.328533\pi$
$251$	4080.00	1.02601	0.513003	+	0.858387i	$0.328533\pi$
$252$	0	0
$253$	−990.000	−0.246011
$254$	−3952.00	−0.976262
$255$	0	0
$256$	256.000	0.0625000
$257$	−846.000	−0.205339	−0.102669	−	0.994716i	$-0.532738\pi$
$257$	−846.000	−0.205339	−0.102669	+	0.994716i	$0.532738\pi$
$258$	−2720.00	−0.656356
$259$	0	0
$260$	0	0
$261$	−1386.00	−0.328702
$262$	−3060.00	−0.721555
$263$	3273.00	0.767383	0.383692	−	0.923461i	$-0.374653\pi$
$263$	3273.00	0.767383	0.383692	+	0.923461i	$0.374653\pi$
$264$	−960.000	−0.223803
$265$	0	0
$266$	0	0
$267$	3492.00	0.800400
$268$	−2816.00	−0.641845
$269$	−7140.00	−1.61834	−0.809170	−	0.587575i	$-0.800083\pi$
$269$	−7140.00	−1.61834	−0.809170	+	0.587575i	$0.800083\pi$
$270$	0	0
$271$	5681.00	1.27342	0.636709	−	0.771104i	$-0.280295\pi$
$271$	5681.00	1.27342	0.636709	+	0.771104i	$0.280295\pi$
$272$	−144.000	−0.0321003
$273$	0	0
$274$	3174.00	0.699812
$275$	0	0
$276$	528.000	0.115152
$277$	−2102.00	−0.455946	−0.227973	−	0.973667i	$-0.573210\pi$
$277$	−2102.00	−0.455946	−0.227973	+	0.973667i	$0.573210\pi$
$278$	−4484.00	−0.967383
$279$	−1705.00	−0.365863
$280$	0	0
$281$	−6297.00	−1.33682	−0.668412	−	0.743791i	$-0.733026\pi$
$281$	−6297.00	−1.33682	−0.668412	+	0.743791i	$0.733026\pi$
$282$	2712.00	0.572685
$283$	−8906.00	−1.87070	−0.935348	−	0.353730i	$-0.884913\pi$
$283$	−8906.00	−1.87070	−0.935348	+	0.353730i	$0.884913\pi$
$284$	2484.00	0.519008
$285$	0	0
$286$	240.000	0.0496206
$287$	0	0
$288$	−352.000	−0.0720201
$289$	−4832.00	−0.983513
$290$	0	0
$291$	3620.00	0.729238
$292$	1000.00	0.200413
$293$	4782.00	0.953472	0.476736	−	0.879046i	$-0.341820\pi$
$293$	4782.00	0.953472	0.476736	+	0.879046i	$0.341820\pi$
$294$	0	0
$295$	0	0
$296$	−928.000	−0.182226
$297$	4560.00	0.890902
$298$	−2940.00	−0.571509
$299$	−132.000	−0.0255310
$300$	0	0
$301$	0	0
$302$	−1328.00	−0.253039
$303$	−2400.00	−0.455038
$304$	−1408.00	−0.265639
$305$	0	0
$306$	198.000	0.0369899
$307$	9412.00	1.74974	0.874872	−	0.484355i	$-0.160946\pi$
$307$	9412.00	1.74974	0.874872	+	0.484355i	$0.160946\pi$
$308$	0	0
$309$	1172.00	0.215769
$310$	0	0
$311$	−7569.00	−1.38006	−0.690030	−	0.723781i	$-0.742403\pi$
$311$	−7569.00	−1.38006	−0.690030	+	0.723781i	$0.742403\pi$
$312$	−128.000	−0.0232262
$313$	8719.00	1.57453	0.787264	−	0.616617i	$-0.211497\pi$
$313$	8719.00	1.57453	0.787264	+	0.616617i	$0.211497\pi$
$314$	3932.00	0.706674
$315$	0	0
$316$	−4420.00	−0.786849
$317$	−3216.00	−0.569806	−0.284903	−	0.958556i	$-0.591961\pi$
$317$	−3216.00	−0.569806	−0.284903	+	0.958556i	$0.591961\pi$
$318$	−2496.00	−0.440153
$319$	3780.00	0.663446
$320$	0	0
$321$	−6744.00	−1.17263
$322$	0	0
$323$	792.000	0.136434
$324$	−1244.00	−0.213306
$325$	0	0
$326$	6032.00	1.02479
$327$	−6560.00	−1.10938
$328$	−3384.00	−0.569665
$329$	0	0
$330$	0	0
$331$	−4306.00	−0.715043	−0.357521	−	0.933905i	$-0.616378\pi$
$331$	−4306.00	−0.715043	−0.357521	+	0.933905i	$0.616378\pi$
$332$	792.000	0.130924
$333$	1276.00	0.209983
$334$	−3216.00	−0.526861
$335$	0	0
$336$	0	0
$337$	−3179.00	−0.513861	−0.256931	−	0.966430i	$-0.582711\pi$
$337$	−3179.00	−0.513861	−0.256931	+	0.966430i	$0.582711\pi$
$338$	−4362.00	−0.701957
$339$	−4740.00	−0.759414
$340$	0	0
$341$	4650.00	0.738450
$342$	1936.00	0.306102
$343$	0	0
$344$	2720.00	0.426316
$345$	0	0
$346$	−5028.00	−0.781234
$347$	−4818.00	−0.745371	−0.372686	−	0.927958i	$-0.621563\pi$
$347$	−4818.00	−0.745371	−0.372686	+	0.927958i	$0.621563\pi$
$348$	−2016.00	−0.310543
$349$	−9376.00	−1.43807	−0.719034	−	0.694975i	$-0.755415\pi$
$349$	−9376.00	−1.43807	−0.719034	+	0.694975i	$0.755415\pi$
$350$	0	0
$351$	608.000	0.0924577
$352$	960.000	0.145364
$353$	−10083.0	−1.52029	−0.760147	−	0.649751i	$-0.774873\pi$
$353$	−10083.0	−1.52029	−0.760147	+	0.649751i	$0.774873\pi$
$354$	3696.00	0.554916
$355$	0	0
$356$	−3492.00	−0.519875
$357$	0	0
$358$	−3228.00	−0.476551
$359$	−276.000	−0.0405758	−0.0202879	−	0.999794i	$-0.506458\pi$
$359$	−276.000	−0.0405758	−0.0202879	+	0.999794i	$0.506458\pi$
$360$	0	0
$361$	885.000	0.129028
$362$	−5540.00	−0.804353
$363$	1724.00	0.249274
$364$	0	0
$365$	0	0
$366$	−2608.00	−0.372465
$367$	6244.00	0.888104	0.444052	−	0.896001i	$-0.353541\pi$
$367$	6244.00	0.888104	0.444052	+	0.896001i	$0.353541\pi$
$368$	−528.000	−0.0747932
$369$	4653.00	0.656438
$370$	0	0
$371$	0	0
$372$	−2480.00	−0.345651
$373$	−416.000	−0.0577471	−0.0288735	−	0.999583i	$-0.509192\pi$
$373$	−416.000	−0.0577471	−0.0288735	+	0.999583i	$0.509192\pi$
$374$	−540.000	−0.0746597
$375$	0	0
$376$	−2712.00	−0.371970
$377$	504.000	0.0688523
$378$	0	0
$379$	12302.0	1.66731	0.833656	−	0.552284i	$-0.186244\pi$
$379$	12302.0	1.66731	0.833656	+	0.552284i	$0.186244\pi$
$380$	0	0
$381$	7904.00	1.06282
$382$	−9270.00	−1.24161
$383$	6393.00	0.852917	0.426458	−	0.904507i	$-0.359761\pi$
$383$	6393.00	0.852917	0.426458	+	0.904507i	$0.359761\pi$
$384$	−512.000	−0.0680414
$385$	0	0
$386$	950.000	0.125269
$387$	−3740.00	−0.491253
$388$	−3620.00	−0.473654
$389$	4068.00	0.530221	0.265110	−	0.964218i	$-0.414592\pi$
$389$	4068.00	0.530221	0.265110	+	0.964218i	$0.414592\pi$
$390$	0	0
$391$	297.000	0.0384142
$392$	0	0
$393$	6120.00	0.785530
$394$	−9792.00	−1.25207
$395$	0	0
$396$	−1320.00	−0.167506
$397$	14686.0	1.85660	0.928299	−	0.371835i	$-0.121271\pi$
$397$	14686.0	1.85660	0.928299	+	0.371835i	$0.121271\pi$
$398$	−5594.00	−0.704527
$399$	0	0
$400$	0	0
$401$	−3702.00	−0.461020	−0.230510	−	0.973070i	$-0.574039\pi$
$401$	−3702.00	−0.461020	−0.230510	+	0.973070i	$0.574039\pi$
$402$	5632.00	0.698753
$403$	620.000	0.0766362
$404$	2400.00	0.295556
$405$	0	0
$406$	0	0
$407$	−3480.00	−0.423826
$408$	288.000	0.0349464
$409$	−8443.00	−1.02073	−0.510366	−	0.859957i	$-0.670490\pi$
$409$	−8443.00	−1.02073	−0.510366	+	0.859957i	$0.670490\pi$
$410$	0	0
$411$	−6348.00	−0.761858
$412$	−1172.00	−0.140146
$413$	0	0
$414$	726.000	0.0861859
$415$	0	0
$416$	128.000	0.0150859
$417$	8968.00	1.05315
$418$	−5280.00	−0.617831
$419$	−13140.0	−1.53205	−0.766027	−	0.642808i	$-0.777769\pi$
$419$	−13140.0	−1.53205	−0.766027	+	0.642808i	$0.777769\pi$
$420$	0	0
$421$	−9604.00	−1.11181	−0.555903	−	0.831247i	$-0.687627\pi$
$421$	−9604.00	−1.11181	−0.555903	+	0.831247i	$0.687627\pi$
$422$	5224.00	0.602607
$423$	3729.00	0.428629
$424$	2496.00	0.285888
$425$	0	0
$426$	−4968.00	−0.565024
$427$	0	0
$428$	6744.00	0.761644
$429$	−480.000	−0.0540201
$430$	0	0
$431$	327.000	0.0365453	0.0182727	−	0.999833i	$-0.494183\pi$
$431$	327.000	0.0365453	0.0182727	+	0.999833i	$0.494183\pi$
$432$	2432.00	0.270856
$433$	5983.00	0.664029	0.332015	−	0.943274i	$-0.392272\pi$
$433$	5983.00	0.664029	0.332015	+	0.943274i	$0.392272\pi$
$434$	0	0
$435$	0	0
$436$	6560.00	0.720567
$437$	2904.00	0.317888
$438$	−2000.00	−0.218182
$439$	−14563.0	−1.58327	−0.791633	−	0.610996i	$-0.790769\pi$
$439$	−14563.0	−1.58327	−0.791633	+	0.610996i	$0.790769\pi$
$440$	0	0
$441$	0	0
$442$	−72.0000	−0.00774817
$443$	−15564.0	−1.66923	−0.834614	−	0.550835i	$-0.814309\pi$
$443$	−15564.0	−1.66923	−0.834614	+	0.550835i	$0.814309\pi$
$444$	1856.00	0.198383
$445$	0	0
$446$	−7258.00	−0.770575
$447$	5880.00	0.622180
$448$	0	0
$449$	4017.00	0.422214	0.211107	−	0.977463i	$-0.432293\pi$
$449$	4017.00	0.422214	0.211107	+	0.977463i	$0.432293\pi$
$450$	0	0
$451$	−12690.0	−1.32494
$452$	4740.00	0.493254
$453$	2656.00	0.275474
$454$	828.000	0.0855946
$455$	0	0
$456$	2816.00	0.289191
$457$	14974.0	1.53272	0.766361	−	0.642410i	$-0.222065\pi$
$457$	14974.0	1.53272	0.766361	+	0.642410i	$0.222065\pi$
$458$	−3140.00	−0.320355
$459$	−1368.00	−0.139113
$460$	0	0
$461$	8076.00	0.815915	0.407958	−	0.913001i	$-0.366241\pi$
$461$	8076.00	0.815915	0.407958	+	0.913001i	$0.366241\pi$
$462$	0	0
$463$	−14045.0	−1.40978	−0.704888	−	0.709318i	$-0.749003\pi$
$463$	−14045.0	−1.40978	−0.704888	+	0.709318i	$0.749003\pi$
$464$	2016.00	0.201704
$465$	0	0
$466$	−10524.0	−1.04617
$467$	7662.00	0.759219	0.379609	−	0.925147i	$-0.376058\pi$
$467$	7662.00	0.759219	0.379609	+	0.925147i	$0.376058\pi$
$468$	−176.000	−0.0173838
$469$	0	0
$470$	0	0
$471$	−7864.00	−0.769329
$472$	−3696.00	−0.360428
$473$	10200.0	0.991536
$474$	8840.00	0.856613
$475$	0	0
$476$	0	0
$477$	−3432.00	−0.329435
$478$	8610.00	0.823875
$479$	−6033.00	−0.575480	−0.287740	−	0.957709i	$-0.592904\pi$
$479$	−6033.00	−0.575480	−0.287740	+	0.957709i	$0.592904\pi$
$480$	0	0
$481$	−464.000	−0.0439846
$482$	−1964.00	−0.185597
$483$	0	0
$484$	−1724.00	−0.161908
$485$	0	0
$486$	−5720.00	−0.533878
$487$	−7337.00	−0.682692	−0.341346	−	0.939938i	$-0.610883\pi$
$487$	−7337.00	−0.682692	−0.341346	+	0.939938i	$0.610883\pi$
$488$	2608.00	0.241923
$489$	−12064.0	−1.11565
$490$	0	0
$491$	13032.0	1.19781	0.598906	−	0.800819i	$-0.295602\pi$
$491$	13032.0	1.19781	0.598906	+	0.800819i	$0.295602\pi$
$492$	6768.00	0.620173
$493$	−1134.00	−0.103596
$494$	−704.000	−0.0641183
$495$	0	0
$496$	2480.00	0.224507
$497$	0	0
$498$	−1584.00	−0.142532
$499$	−7786.00	−0.698495	−0.349248	−	0.937030i	$-0.613563\pi$
$499$	−7786.00	−0.698495	−0.349248	+	0.937030i	$0.613563\pi$
$500$	0	0
$501$	6432.00	0.573574
$502$	8160.00	0.725495
$503$	−12720.0	−1.12755	−0.563774	−	0.825929i	$-0.690651\pi$
$503$	−12720.0	−1.12755	−0.563774	+	0.825929i	$0.690651\pi$
$504$	0	0
$505$	0	0
$506$	−1980.00	−0.173956
$507$	8724.00	0.764194
$508$	−7904.00	−0.690321
$509$	5190.00	0.451950	0.225975	−	0.974133i	$-0.427443\pi$
$509$	5190.00	0.451950	0.225975	+	0.974133i	$0.427443\pi$
$510$	0	0
$511$	0	0
$512$	512.000	0.0441942
$513$	−13376.0	−1.15120
$514$	−1692.00	−0.145196
$515$	0	0
$516$	−5440.00	−0.464114
$517$	−10170.0	−0.865138
$518$	0	0
$519$	10056.0	0.850500
$520$	0	0
$521$	−18303.0	−1.53910	−0.769548	−	0.638589i	$-0.779518\pi$
$521$	−18303.0	−1.53910	−0.769548	+	0.638589i	$0.779518\pi$
$522$	−2772.00	−0.232427
$523$	8962.00	0.749294	0.374647	−	0.927167i	$-0.377764\pi$
$523$	8962.00	0.749294	0.374647	+	0.927167i	$0.377764\pi$
$524$	−6120.00	−0.510216
$525$	0	0
$526$	6546.00	0.542622
$527$	−1395.00	−0.115308
$528$	−1920.00	−0.158252
$529$	−11078.0	−0.910496
$530$	0	0
$531$	5082.00	0.415330
$532$	0	0
$533$	−1692.00	−0.137502
$534$	6984.00	0.565969
$535$	0	0
$536$	−5632.00	−0.453853
$537$	6456.00	0.518803
$538$	−14280.0	−1.14434
$539$	0	0
$540$	0	0
$541$	10340.0	0.821721	0.410861	−	0.911698i	$-0.365228\pi$
$541$	10340.0	0.821721	0.410861	+	0.911698i	$0.365228\pi$
$542$	11362.0	0.900442
$543$	11080.0	0.875669
$544$	−288.000	−0.0226983
$545$	0	0
$546$	0	0
$547$	−4196.00	−0.327985	−0.163993	−	0.986462i	$-0.552437\pi$
$547$	−4196.00	−0.327985	−0.163993	+	0.986462i	$0.552437\pi$
$548$	6348.00	0.494841
$549$	−3586.00	−0.278774
$550$	0	0
$551$	−11088.0	−0.857286
$552$	1056.00	0.0814245
$553$	0	0
$554$	−4204.00	−0.322402
$555$	0	0
$556$	−8968.00	−0.684043
$557$	−11178.0	−0.850318	−0.425159	−	0.905119i	$-0.639782\pi$
$557$	−11178.0	−0.850318	−0.425159	+	0.905119i	$0.639782\pi$
$558$	−3410.00	−0.258704
$559$	1360.00	0.102901
$560$	0	0
$561$	1080.00	0.0812792
$562$	−12594.0	−0.945277
$563$	15048.0	1.12646	0.563231	−	0.826300i	$-0.309558\pi$
$563$	15048.0	1.12646	0.563231	+	0.826300i	$0.309558\pi$
$564$	5424.00	0.404950
$565$	0	0
$566$	−17812.0	−1.32278
$567$	0	0
$568$	4968.00	0.366994
$569$	−7107.00	−0.523622	−0.261811	−	0.965119i	$-0.584320\pi$
$569$	−7107.00	−0.523622	−0.261811	+	0.965119i	$0.584320\pi$
$570$	0	0
$571$	−4060.00	−0.297558	−0.148779	−	0.988870i	$-0.547534\pi$
$571$	−4060.00	−0.297558	−0.148779	+	0.988870i	$0.547534\pi$
$572$	480.000	0.0350871
$573$	18540.0	1.35169
$574$	0	0
$575$	0	0
$576$	−704.000	−0.0509259
$577$	16558.0	1.19466	0.597330	−	0.801996i	$-0.296228\pi$
$577$	16558.0	1.19466	0.597330	+	0.801996i	$0.296228\pi$
$578$	−9664.00	−0.695449
$579$	−1900.00	−0.136375
$580$	0	0
$581$	0	0
$582$	7240.00	0.515649
$583$	9360.00	0.664926
$584$	2000.00	0.141713
$585$	0	0
$586$	9564.00	0.674207
$587$	9546.00	0.671219	0.335610	−	0.942001i	$-0.391058\pi$
$587$	9546.00	0.671219	0.335610	+	0.942001i	$0.391058\pi$
$588$	0	0
$589$	−13640.0	−0.954204
$590$	0	0
$591$	19584.0	1.36308
$592$	−1856.00	−0.128853
$593$	−11259.0	−0.779682	−0.389841	−	0.920882i	$-0.627470\pi$
$593$	−11259.0	−0.779682	−0.389841	+	0.920882i	$0.627470\pi$
$594$	9120.00	0.629963
$595$	0	0
$596$	−5880.00	−0.404118
$597$	11188.0	0.766992
$598$	−264.000	−0.0180531
$599$	−14181.0	−0.967312	−0.483656	−	0.875258i	$-0.660691\pi$
$599$	−14181.0	−0.967312	−0.483656	+	0.875258i	$0.660691\pi$
$600$	0	0
$601$	−3562.00	−0.241759	−0.120879	−	0.992667i	$-0.538571\pi$
$601$	−3562.00	−0.241759	−0.120879	+	0.992667i	$0.538571\pi$
$602$	0	0
$603$	7744.00	0.522985
$604$	−2656.00	−0.178926
$605$	0	0
$606$	−4800.00	−0.321760
$607$	18955.0	1.26748	0.633739	−	0.773547i	$-0.281519\pi$
$607$	18955.0	1.26748	0.633739	+	0.773547i	$0.281519\pi$
$608$	−2816.00	−0.187835
$609$	0	0
$610$	0	0
$611$	−1356.00	−0.0897838
$612$	396.000	0.0261558
$613$	3454.00	0.227579	0.113789	−	0.993505i	$-0.463701\pi$
$613$	3454.00	0.227579	0.113789	+	0.993505i	$0.463701\pi$
$614$	18824.0	1.23726
$615$	0	0
$616$	0	0
$617$	20745.0	1.35359	0.676793	−	0.736174i	$-0.263369\pi$
$617$	20745.0	1.35359	0.676793	+	0.736174i	$0.263369\pi$
$618$	2344.00	0.152572
$619$	17930.0	1.16424	0.582122	−	0.813101i	$-0.302222\pi$
$619$	17930.0	1.16424	0.582122	+	0.813101i	$0.302222\pi$
$620$	0	0
$621$	−5016.00	−0.324131
$622$	−15138.0	−0.975850
$623$	0	0
$624$	−256.000	−0.0164234
$625$	0	0
$626$	17438.0	1.11336
$627$	10560.0	0.672609
$628$	7864.00	0.499694
$629$	1044.00	0.0661797
$630$	0	0
$631$	−5689.00	−0.358915	−0.179458	−	0.983766i	$-0.557434\pi$
$631$	−5689.00	−0.358915	−0.179458	+	0.983766i	$0.557434\pi$
$632$	−8840.00	−0.556387
$633$	−10448.0	−0.656036
$634$	−6432.00	−0.402914
$635$	0	0
$636$	−4992.00	−0.311235
$637$	0	0
$638$	7560.00	0.469127
$639$	−6831.00	−0.422895
$640$	0	0
$641$	23205.0	1.42986	0.714932	−	0.699194i	$-0.246458\pi$
$641$	23205.0	1.42986	0.714932	+	0.699194i	$0.246458\pi$
$642$	−13488.0	−0.829173
$643$	18190.0	1.11562	0.557810	−	0.829969i	$-0.311642\pi$
$643$	18190.0	1.11562	0.557810	+	0.829969i	$0.311642\pi$
$644$	0	0
$645$	0	0
$646$	1584.00	0.0964731
$647$	−11388.0	−0.691976	−0.345988	−	0.938239i	$-0.612456\pi$
$647$	−11388.0	−0.691976	−0.345988	+	0.938239i	$0.612456\pi$
$648$	−2488.00	−0.150830
$649$	−13860.0	−0.838294
$650$	0	0
$651$	0	0
$652$	12064.0	0.724636
$653$	−23364.0	−1.40016	−0.700080	−	0.714065i	$-0.746852\pi$
$653$	−23364.0	−1.40016	−0.700080	+	0.714065i	$0.746852\pi$
$654$	−13120.0	−0.784454
$655$	0	0
$656$	−6768.00	−0.402814
$657$	−2750.00	−0.163299
$658$	0	0
$659$	7890.00	0.466390	0.233195	−	0.972430i	$-0.425082\pi$
$659$	7890.00	0.466390	0.233195	+	0.972430i	$0.425082\pi$
$660$	0	0
$661$	2774.00	0.163232	0.0816158	−	0.996664i	$-0.473992\pi$
$661$	2774.00	0.163232	0.0816158	+	0.996664i	$0.473992\pi$
$662$	−8612.00	−0.505612
$663$	144.000	0.00843514
$664$	1584.00	0.0925770
$665$	0	0
$666$	2552.00	0.148480
$667$	−4158.00	−0.241377
$668$	−6432.00	−0.372547
$669$	14516.0	0.838895
$670$	0	0
$671$	9780.00	0.562672
$672$	0	0
$673$	10075.0	0.577062	0.288531	−	0.957471i	$-0.406833\pi$
$673$	10075.0	0.577062	0.288531	+	0.957471i	$0.406833\pi$
$674$	−6358.00	−0.363355
$675$	0	0
$676$	−8724.00	−0.496359
$677$	−6414.00	−0.364121	−0.182061	−	0.983287i	$-0.558277\pi$
$677$	−6414.00	−0.364121	−0.182061	+	0.983287i	$0.558277\pi$
$678$	−9480.00	−0.536987
$679$	0	0
$680$	0	0
$681$	−1656.00	−0.0931836
$682$	9300.00	0.522163
$683$	13890.0	0.778164	0.389082	−	0.921203i	$-0.372792\pi$
$683$	13890.0	0.778164	0.389082	+	0.921203i	$0.372792\pi$
$684$	3872.00	0.216447
$685$	0	0
$686$	0	0
$687$	6280.00	0.348758
$688$	5440.00	0.301451
$689$	1248.00	0.0690058
$690$	0	0
$691$	−15730.0	−0.865988	−0.432994	−	0.901397i	$-0.642543\pi$
$691$	−15730.0	−0.865988	−0.432994	+	0.901397i	$0.642543\pi$
$692$	−10056.0	−0.552416
$693$	0	0
$694$	−9636.00	−0.527057
$695$	0	0
$696$	−4032.00	−0.219587
$697$	3807.00	0.206887
$698$	−18752.0	−1.01687
$699$	21048.0	1.13892
$700$	0	0
$701$	−12336.0	−0.664657	−0.332328	−	0.943164i	$-0.607834\pi$
$701$	−12336.0	−0.664657	−0.332328	+	0.943164i	$0.607834\pi$
$702$	1216.00	0.0653774
$703$	10208.0	0.547656
$704$	1920.00	0.102788
$705$	0	0
$706$	−20166.0	−1.07501
$707$	0	0
$708$	7392.00	0.392385
$709$	−22486.0	−1.19109	−0.595543	−	0.803324i	$-0.703063\pi$
$709$	−22486.0	−1.19109	−0.595543	+	0.803324i	$0.703063\pi$
$710$	0	0
$711$	12155.0	0.641137
$712$	−6984.00	−0.367607
$713$	−5115.00	−0.268665
$714$	0	0
$715$	0	0
$716$	−6456.00	−0.336972
$717$	−17220.0	−0.896921
$718$	−552.000	−0.0286914
$719$	7815.00	0.405355	0.202678	−	0.979246i	$-0.435036\pi$
$719$	7815.00	0.405355	0.202678	+	0.979246i	$0.435036\pi$
$720$	0	0
$721$	0	0
$722$	1770.00	0.0912363
$723$	3928.00	0.202052
$724$	−11080.0	−0.568764
$725$	0	0
$726$	3448.00	0.176263
$727$	20737.0	1.05790	0.528950	−	0.848653i	$-0.322586\pi$
$727$	20737.0	1.05790	0.528950	+	0.848653i	$0.322586\pi$
$728$	0	0
$729$	19837.0	1.00782
$730$	0	0
$731$	−3060.00	−0.154827
$732$	−5216.00	−0.263373
$733$	10102.0	0.509039	0.254520	−	0.967068i	$-0.418083\pi$
$733$	10102.0	0.509039	0.254520	+	0.967068i	$0.418083\pi$
$734$	12488.0	0.627984
$735$	0	0
$736$	−1056.00	−0.0528868
$737$	−21120.0	−1.05558
$738$	9306.00	0.464172
$739$	14612.0	0.727349	0.363675	−	0.931526i	$-0.381522\pi$
$739$	14612.0	0.727349	0.363675	+	0.931526i	$0.381522\pi$
$740$	0	0
$741$	1408.00	0.0698032
$742$	0	0
$743$	21981.0	1.08534	0.542668	−	0.839947i	$-0.317414\pi$
$743$	21981.0	1.08534	0.542668	+	0.839947i	$0.317414\pi$
$744$	−4960.00	−0.244412
$745$	0	0
$746$	−832.000	−0.0408334
$747$	−2178.00	−0.106679
$748$	−1080.00	−0.0527924
$749$	0	0
$750$	0	0
$751$	22184.0	1.07790	0.538952	−	0.842337i	$-0.318820\pi$
$751$	22184.0	1.07790	0.538952	+	0.842337i	$0.318820\pi$
$752$	−5424.00	−0.263023
$753$	−16320.0	−0.789819
$754$	1008.00	0.0486859
$755$	0	0
$756$	0	0
$757$	12148.0	0.583258	0.291629	−	0.956531i	$-0.405803\pi$
$757$	12148.0	0.583258	0.291629	+	0.956531i	$0.405803\pi$
$758$	24604.0	1.17897
$759$	3960.00	0.189379
$760$	0	0
$761$	29205.0	1.39117	0.695585	−	0.718444i	$-0.255145\pi$
$761$	29205.0	1.39117	0.695585	+	0.718444i	$0.255145\pi$
$762$	15808.0	0.751527
$763$	0	0
$764$	−18540.0	−0.877950
$765$	0	0
$766$	12786.0	0.603103
$767$	−1848.00	−0.0869979
$768$	−1024.00	−0.0481125
$769$	5906.00	0.276952	0.138476	−	0.990366i	$-0.455780\pi$
$769$	5906.00	0.276952	0.138476	+	0.990366i	$0.455780\pi$
$770$	0	0
$771$	3384.00	0.158070
$772$	1900.00	0.0885784
$773$	26136.0	1.21610	0.608051	−	0.793898i	$-0.291952\pi$
$773$	26136.0	1.21610	0.608051	+	0.793898i	$0.291952\pi$
$774$	−7480.00	−0.347368
$775$	0	0
$776$	−7240.00	−0.334924
$777$	0	0
$778$	8136.00	0.374923
$779$	37224.0	1.71205
$780$	0	0
$781$	18630.0	0.853564
$782$	594.000	0.0271629
$783$	19152.0	0.874121
$784$	0	0
$785$	0	0
$786$	12240.0	0.555453
$787$	2212.00	0.100190	0.0500948	−	0.998744i	$-0.484048\pi$
$787$	2212.00	0.100190	0.0500948	+	0.998744i	$0.484048\pi$
$788$	−19584.0	−0.885344
$789$	−13092.0	−0.590732
$790$	0	0
$791$	0	0
$792$	−2640.00	−0.118445
$793$	1304.00	0.0583939
$794$	29372.0	1.31281
$795$	0	0
$796$	−11188.0	−0.498176
$797$	24654.0	1.09572	0.547860	−	0.836570i	$-0.315442\pi$
$797$	24654.0	1.09572	0.547860	+	0.836570i	$0.315442\pi$
$798$	0	0
$799$	3051.00	0.135090
$800$	0	0
$801$	9603.00	0.423602
$802$	−7404.00	−0.325990
$803$	7500.00	0.329601
$804$	11264.0	0.494093
$805$	0	0
$806$	1240.00	0.0541900
$807$	28560.0	1.24580
$808$	4800.00	0.208989
$809$	−36870.0	−1.60232	−0.801162	−	0.598447i	$-0.795785\pi$
$809$	−36870.0	−1.60232	−0.801162	+	0.598447i	$0.795785\pi$
$810$	0	0
$811$	5096.00	0.220647	0.110324	−	0.993896i	$-0.464811\pi$
$811$	5096.00	0.220647	0.110324	+	0.993896i	$0.464811\pi$
$812$	0	0
$813$	−22724.0	−0.980277
$814$	−6960.00	−0.299690
$815$	0	0
$816$	576.000	0.0247108
$817$	−29920.0	−1.28123
$818$	−16886.0	−0.721767
$819$	0	0
$820$	0	0
$821$	12768.0	0.542760	0.271380	−	0.962472i	$-0.412520\pi$
$821$	12768.0	0.542760	0.271380	+	0.962472i	$0.412520\pi$
$822$	−12696.0	−0.538715
$823$	4300.00	0.182125	0.0910623	−	0.995845i	$-0.470974\pi$
$823$	4300.00	0.182125	0.0910623	+	0.995845i	$0.470974\pi$
$824$	−2344.00	−0.0990984
$825$	0	0
$826$	0	0
$827$	−1374.00	−0.0577735	−0.0288867	−	0.999583i	$-0.509196\pi$
$827$	−1374.00	−0.0577735	−0.0288867	+	0.999583i	$0.509196\pi$
$828$	1452.00	0.0609426
$829$	−32134.0	−1.34627	−0.673136	−	0.739518i	$-0.735053\pi$
$829$	−32134.0	−1.34627	−0.673136	+	0.739518i	$0.735053\pi$
$830$	0	0
$831$	8408.00	0.350987
$832$	256.000	0.0106673
$833$	0	0
$834$	17936.0	0.744692
$835$	0	0
$836$	−10560.0	−0.436872
$837$	23560.0	0.972942
$838$	−26280.0	−1.08333
$839$	−10227.0	−0.420829	−0.210414	−	0.977612i	$-0.567481\pi$
$839$	−10227.0	−0.420829	−0.210414	+	0.977612i	$0.567481\pi$
$840$	0	0
$841$	−8513.00	−0.349051
$842$	−19208.0	−0.786166
$843$	25188.0	1.02909
$844$	10448.0	0.426108
$845$	0	0
$846$	7458.00	0.303087
$847$	0	0
$848$	4992.00	0.202153
$849$	35624.0	1.44006
$850$	0	0
$851$	3828.00	0.154198
$852$	−9936.00	−0.399533
$853$	−9560.00	−0.383738	−0.191869	−	0.981421i	$-0.561455\pi$
$853$	−9560.00	−0.383738	−0.191869	+	0.981421i	$0.561455\pi$
$854$	0	0
$855$	0	0
$856$	13488.0	0.538563
$857$	−3558.00	−0.141819	−0.0709095	−	0.997483i	$-0.522590\pi$
$857$	−3558.00	−0.141819	−0.0709095	+	0.997483i	$0.522590\pi$
$858$	−960.000	−0.0381980
$859$	1550.00	0.0615661	0.0307831	−	0.999526i	$-0.490200\pi$
$859$	1550.00	0.0615661	0.0307831	+	0.999526i	$0.490200\pi$
$860$	0	0
$861$	0	0
$862$	654.000	0.0258414
$863$	15777.0	0.622312	0.311156	−	0.950359i	$-0.399284\pi$
$863$	15777.0	0.622312	0.311156	+	0.950359i	$0.399284\pi$
$864$	4864.00	0.191524
$865$	0	0
$866$	11966.0	0.469540
$867$	19328.0	0.757109
$868$	0	0
$869$	−33150.0	−1.29406
$870$	0	0
$871$	−2816.00	−0.109548
$872$	13120.0	0.509518
$873$	9955.00	0.385940
$874$	5808.00	0.224781
$875$	0	0
$876$	−4000.00	−0.154278
$877$	−20258.0	−0.780005	−0.390002	−	0.920814i	$-0.627526\pi$
$877$	−20258.0	−0.780005	−0.390002	+	0.920814i	$0.627526\pi$
$878$	−29126.0	−1.11954
$879$	−19128.0	−0.733983
$880$	0	0
$881$	43347.0	1.65766	0.828829	−	0.559501i	$-0.189007\pi$
$881$	43347.0	1.65766	0.828829	+	0.559501i	$0.189007\pi$
$882$	0	0
$883$	−1658.00	−0.0631893	−0.0315946	−	0.999501i	$-0.510059\pi$
$883$	−1658.00	−0.0631893	−0.0315946	+	0.999501i	$0.510059\pi$
$884$	−144.000	−0.00547878
$885$	0	0
$886$	−31128.0	−1.18032
$887$	14928.0	0.565088	0.282544	−	0.959254i	$-0.408822\pi$
$887$	14928.0	0.565088	0.282544	+	0.959254i	$0.408822\pi$
$888$	3712.00	0.140278
$889$	0	0
$890$	0	0
$891$	−9330.00	−0.350804
$892$	−14516.0	−0.544879
$893$	29832.0	1.11791
$894$	11760.0	0.439948
$895$	0	0
$896$	0	0
$897$	528.000	0.0196537
$898$	8034.00	0.298550
$899$	19530.0	0.724541
$900$	0	0
$901$	−2808.00	−0.103827
$902$	−25380.0	−0.936875
$903$	0	0
$904$	9480.00	0.348783
$905$	0	0
$906$	5312.00	0.194790
$907$	6370.00	0.233200	0.116600	−	0.993179i	$-0.462800\pi$
$907$	6370.00	0.233200	0.116600	+	0.993179i	$0.462800\pi$
$908$	1656.00	0.0605245
$909$	−6600.00	−0.240823
$910$	0	0
$911$	30273.0	1.10098	0.550488	−	0.834843i	$-0.314442\pi$
$911$	30273.0	1.10098	0.550488	+	0.834843i	$0.314442\pi$
$912$	5632.00	0.204489
$913$	5940.00	0.215318
$914$	29948.0	1.08380
$915$	0	0
$916$	−6280.00	−0.226525
$917$	0	0
$918$	−2736.00	−0.0983676
$919$	45389.0	1.62921	0.814606	−	0.580015i	$-0.196953\pi$
$919$	45389.0	1.62921	0.814606	+	0.580015i	$0.196953\pi$
$920$	0	0
$921$	−37648.0	−1.34695
$922$	16152.0	0.576939
$923$	2484.00	0.0885827
$924$	0	0
$925$	0	0
$926$	−28090.0	−0.996863
$927$	3223.00	0.114193
$928$	4032.00	0.142626
$929$	35298.0	1.24660	0.623299	−	0.781983i	$-0.285792\pi$
$929$	35298.0	1.24660	0.623299	+	0.781983i	$0.285792\pi$
$930$	0	0
$931$	0	0
$932$	−21048.0	−0.739753
$933$	30276.0	1.06237
$934$	15324.0	0.536849
$935$	0	0
$936$	−352.000	−0.0122922
$937$	−52382.0	−1.82630	−0.913151	−	0.407621i	$-0.866358\pi$
$937$	−52382.0	−1.82630	−0.913151	+	0.407621i	$0.866358\pi$
$938$	0	0
$939$	−34876.0	−1.21207
$940$	0	0
$941$	28944.0	1.00271	0.501354	−	0.865243i	$-0.332836\pi$
$941$	28944.0	1.00271	0.501354	+	0.865243i	$0.332836\pi$
$942$	−15728.0	−0.543998
$943$	13959.0	0.482044
$944$	−7392.00	−0.254861
$945$	0	0
$946$	20400.0	0.701122
$947$	−25776.0	−0.884485	−0.442243	−	0.896895i	$-0.645817\pi$
$947$	−25776.0	−0.884485	−0.442243	+	0.896895i	$0.645817\pi$
$948$	17680.0	0.605717
$949$	1000.00	0.0342059
$950$	0	0
$951$	12864.0	0.438637
$952$	0	0
$953$	−31062.0	−1.05582	−0.527910	−	0.849300i	$-0.677024\pi$
$953$	−31062.0	−1.05582	−0.527910	+	0.849300i	$0.677024\pi$
$954$	−6864.00	−0.232946
$955$	0	0
$956$	17220.0	0.582568
$957$	−15120.0	−0.510721
$958$	−12066.0	−0.406926
$959$	0	0
$960$	0	0
$961$	−5766.00	−0.193548
$962$	−928.000	−0.0311018
$963$	−18546.0	−0.620599
$964$	−3928.00	−0.131237
$965$	0	0
$966$	0	0
$967$	−44951.0	−1.49486	−0.747428	−	0.664342i	$-0.768712\pi$
$967$	−44951.0	−1.49486	−0.747428	+	0.664342i	$0.768712\pi$
$968$	−3448.00	−0.114486
$969$	−3168.00	−0.105027
$970$	0	0
$971$	46950.0	1.55170	0.775848	−	0.630920i	$-0.217322\pi$
$971$	46950.0	1.55170	0.775848	+	0.630920i	$0.217322\pi$
$972$	−11440.0	−0.377508
$973$	0	0
$974$	−14674.0	−0.482736
$975$	0	0
$976$	5216.00	0.171066
$977$	24867.0	0.814295	0.407147	−	0.913363i	$-0.366524\pi$
$977$	24867.0	0.814295	0.407147	+	0.913363i	$0.366524\pi$
$978$	−24128.0	−0.788884
$979$	−26190.0	−0.854991
$980$	0	0
$981$	−18040.0	−0.587128
$982$	26064.0	0.846981
$983$	−3720.00	−0.120701	−0.0603507	−	0.998177i	$-0.519222\pi$
$983$	−3720.00	−0.120701	−0.0603507	+	0.998177i	$0.519222\pi$
$984$	13536.0	0.438528
$985$	0	0
$986$	−2268.00	−0.0732534
$987$	0	0
$988$	−1408.00	−0.0453385
$989$	−11220.0	−0.360743
$990$	0	0
$991$	44939.0	1.44050	0.720249	−	0.693715i	$-0.244027\pi$
$991$	44939.0	1.44050	0.720249	+	0.693715i	$0.244027\pi$
$992$	4960.00	0.158750
$993$	17224.0	0.550440
$994$	0	0
$995$	0	0
$996$	−3168.00	−0.100785
$997$	−20132.0	−0.639505	−0.319753	−	0.947501i	$-0.603600\pi$
$997$	−20132.0	−0.639505	−0.319753	+	0.947501i	$0.603600\pi$
$998$	−15572.0	−0.493911
$999$	−17632.0	−0.558410

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2450.4.a.z.1.1		1
5.4	even	2		2450.4.a.p.1.1		1
7.2	even	3		350.4.e.c.151.1	yes	2
7.4	even	3		350.4.e.c.51.1	✓	2
7.6	odd	2		2450.4.a.bl.1.1		1
35.2	odd	12		350.4.j.c.249.2		4
35.4	even	6		350.4.e.f.51.1	yes	2
35.9	even	6		350.4.e.f.151.1	yes	2
35.18	odd	12		350.4.j.c.149.2		4
35.23	odd	12		350.4.j.c.249.1		4
35.32	odd	12		350.4.j.c.149.1		4
35.34	odd	2		2450.4.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.e.c.51.1	✓	2	7.4	even	3
350.4.e.c.151.1	yes	2	7.2	even	3
350.4.e.f.51.1	yes	2	35.4	even	6
350.4.e.f.151.1	yes	2	35.9	even	6
350.4.j.c.149.1		4	35.32	odd	12
350.4.j.c.149.2		4	35.18	odd	12
350.4.j.c.249.1		4	35.23	odd	12
350.4.j.c.249.2		4	35.2	odd	12
2450.4.a.f.1.1		1	35.34	odd	2
2450.4.a.p.1.1		1	5.4	even	2
2450.4.a.z.1.1		1	1.1	even	1	trivial
2450.4.a.bl.1.1		1	7.6	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:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2450.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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