LMFDB - Embedded newform 1950.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,4,Mod(1,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, 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("1950.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1950.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:	$115.053724511$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{6} -8.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{6} -8.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +12.0000 q^{11} +12.0000 q^{12} -13.0000 q^{13} +16.0000 q^{14} +16.0000 q^{16} +42.0000 q^{17} -18.0000 q^{18} -52.0000 q^{19} -24.0000 q^{21} -24.0000 q^{22} -132.000 q^{23} -24.0000 q^{24} +26.0000 q^{26} +27.0000 q^{27} -32.0000 q^{28} +282.000 q^{29} +116.000 q^{31} -32.0000 q^{32} +36.0000 q^{33} -84.0000 q^{34} +36.0000 q^{36} -398.000 q^{37} +104.000 q^{38} -39.0000 q^{39} +174.000 q^{41} +48.0000 q^{42} +76.0000 q^{43} +48.0000 q^{44} +264.000 q^{46} -456.000 q^{47} +48.0000 q^{48} -279.000 q^{49} +126.000 q^{51} -52.0000 q^{52} -150.000 q^{53} -54.0000 q^{54} +64.0000 q^{56} -156.000 q^{57} -564.000 q^{58} -156.000 q^{59} +230.000 q^{61} -232.000 q^{62} -72.0000 q^{63} +64.0000 q^{64} -72.0000 q^{66} +592.000 q^{67} +168.000 q^{68} -396.000 q^{69} +408.000 q^{71} -72.0000 q^{72} +730.000 q^{73} +796.000 q^{74} -208.000 q^{76} -96.0000 q^{77} +78.0000 q^{78} +728.000 q^{79} +81.0000 q^{81} -348.000 q^{82} -36.0000 q^{83} -96.0000 q^{84} -152.000 q^{86} +846.000 q^{87} -96.0000 q^{88} -1482.00 q^{89} +104.000 q^{91} -528.000 q^{92} +348.000 q^{93} +912.000 q^{94} -96.0000 q^{96} -1742.00 q^{97} +558.000 q^{98} +108.000 q^{99} +O(q^{100})\)

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
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−6.00000	−0.408248
$7$	−8.00000	−0.431959	−0.215980	−	0.976398i	$-0.569295\pi$
$7$	−8.00000	−0.431959	−0.215980	+	0.976398i	$0.569295\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	0	0
$11$	12.0000	0.328921	0.164461	−	0.986384i	$-0.447412\pi$
$11$	12.0000	0.328921	0.164461	+	0.986384i	$0.447412\pi$
$12$	12.0000	0.288675
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	16.0000	0.305441
$15$	0	0
$16$	16.0000	0.250000
$17$	42.0000	0.599206	0.299603	−	0.954064i	$-0.403146\pi$
$17$	42.0000	0.599206	0.299603	+	0.954064i	$0.403146\pi$
$18$	−18.0000	−0.235702
$19$	−52.0000	−0.627875	−0.313937	−	0.949444i	$-0.601648\pi$
$19$	−52.0000	−0.627875	−0.313937	+	0.949444i	$0.601648\pi$
$20$	0	0
$21$	−24.0000	−0.249392
$22$	−24.0000	−0.232583
$23$	−132.000	−1.19669	−0.598346	−	0.801238i	$-0.704175\pi$
$23$	−132.000	−1.19669	−0.598346	+	0.801238i	$0.704175\pi$
$24$	−24.0000	−0.204124
$25$	0	0
$26$	26.0000	0.196116
$27$	27.0000	0.192450
$28$	−32.0000	−0.215980
$29$	282.000	1.80573	0.902864	−	0.429927i	$-0.141461\pi$
$29$	282.000	1.80573	0.902864	+	0.429927i	$0.141461\pi$
$30$	0	0
$31$	116.000	0.672071	0.336036	−	0.941849i	$-0.390914\pi$
$31$	116.000	0.672071	0.336036	+	0.941849i	$0.390914\pi$
$32$	−32.0000	−0.176777
$33$	36.0000	0.189903
$34$	−84.0000	−0.423702
$35$	0	0
$36$	36.0000	0.166667
$37$	−398.000	−1.76840	−0.884200	−	0.467109i	$-0.845296\pi$
$37$	−398.000	−1.76840	−0.884200	+	0.467109i	$0.845296\pi$
$38$	104.000	0.443974
$39$	−39.0000	−0.160128
$40$	0	0
$41$	174.000	0.662786	0.331393	−	0.943493i	$-0.392481\pi$
$41$	174.000	0.662786	0.331393	+	0.943493i	$0.392481\pi$
$42$	48.0000	0.176347
$43$	76.0000	0.269532	0.134766	−	0.990877i	$-0.456972\pi$
$43$	76.0000	0.269532	0.134766	+	0.990877i	$0.456972\pi$
$44$	48.0000	0.164461
$45$	0	0
$46$	264.000	0.846189
$47$	−456.000	−1.41520	−0.707600	−	0.706613i	$-0.750222\pi$
$47$	−456.000	−1.41520	−0.707600	+	0.706613i	$0.750222\pi$
$48$	48.0000	0.144338
$49$	−279.000	−0.813411
$50$	0	0
$51$	126.000	0.345952
$52$	−52.0000	−0.138675
$53$	−150.000	−0.388756	−0.194378	−	0.980927i	$-0.562269\pi$
$53$	−150.000	−0.388756	−0.194378	+	0.980927i	$0.562269\pi$
$54$	−54.0000	−0.136083
$55$	0	0
$56$	64.0000	0.152721
$57$	−156.000	−0.362504
$58$	−564.000	−1.27684
$59$	−156.000	−0.344228	−0.172114	−	0.985077i	$-0.555060\pi$
$59$	−156.000	−0.344228	−0.172114	+	0.985077i	$0.555060\pi$
$60$	0	0
$61$	230.000	0.482762	0.241381	−	0.970430i	$-0.422400\pi$
$61$	230.000	0.482762	0.241381	+	0.970430i	$0.422400\pi$
$62$	−232.000	−0.475226
$63$	−72.0000	−0.143986
$64$	64.0000	0.125000
$65$	0	0
$66$	−72.0000	−0.134282
$67$	592.000	1.07947	0.539734	−	0.841836i	$-0.318525\pi$
$67$	592.000	1.07947	0.539734	+	0.841836i	$0.318525\pi$
$68$	168.000	0.299603
$69$	−396.000	−0.690910
$70$	0	0
$71$	408.000	0.681982	0.340991	−	0.940067i	$-0.389238\pi$
$71$	408.000	0.681982	0.340991	+	0.940067i	$0.389238\pi$
$72$	−72.0000	−0.117851
$73$	730.000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	730.000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	796.000	1.25045
$75$	0	0
$76$	−208.000	−0.313937
$77$	−96.0000	−0.142081
$78$	78.0000	0.113228
$79$	728.000	1.03679	0.518395	−	0.855141i	$-0.326530\pi$
$79$	728.000	1.03679	0.518395	+	0.855141i	$0.326530\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−348.000	−0.468661
$83$	−36.0000	−0.0476086	−0.0238043	−	0.999717i	$-0.507578\pi$
$83$	−36.0000	−0.0476086	−0.0238043	+	0.999717i	$0.507578\pi$
$84$	−96.0000	−0.124696
$85$	0	0
$86$	−152.000	−0.190588
$87$	846.000	1.04254
$88$	−96.0000	−0.116291
$89$	−1482.00	−1.76508	−0.882538	−	0.470242i	$-0.844167\pi$
$89$	−1482.00	−1.76508	−0.882538	+	0.470242i	$0.844167\pi$
$90$	0	0
$91$	104.000	0.119804
$92$	−528.000	−0.598346
$93$	348.000	0.388021
$94$	912.000	1.00070
$95$	0	0
$96$	−96.0000	−0.102062
$97$	−1742.00	−1.82344	−0.911718	−	0.410816i	$-0.865244\pi$
$97$	−1742.00	−1.82344	−0.911718	+	0.410816i	$0.865244\pi$
$98$	558.000	0.575168
$99$	108.000	0.109640
$100$	0	0
$101$	−534.000	−0.526089	−0.263044	−	0.964784i	$-0.584727\pi$
$101$	−534.000	−0.526089	−0.263044	+	0.964784i	$0.584727\pi$
$102$	−252.000	−0.244625
$103$	−248.000	−0.237244	−0.118622	−	0.992939i	$-0.537848\pi$
$103$	−248.000	−0.237244	−0.118622	+	0.992939i	$0.537848\pi$
$104$	104.000	0.0980581
$105$	0	0
$106$	300.000	0.274892
$107$	−1044.00	−0.943246	−0.471623	−	0.881800i	$-0.656332\pi$
$107$	−1044.00	−0.943246	−0.471623	+	0.881800i	$0.656332\pi$
$108$	108.000	0.0962250
$109$	−1342.00	−1.17927	−0.589634	−	0.807670i	$-0.700728\pi$
$109$	−1342.00	−1.17927	−0.589634	+	0.807670i	$0.700728\pi$
$110$	0	0
$111$	−1194.00	−1.02099
$112$	−128.000	−0.107990
$113$	186.000	0.154844	0.0774222	−	0.996998i	$-0.475331\pi$
$113$	186.000	0.154844	0.0774222	+	0.996998i	$0.475331\pi$
$114$	312.000	0.256329
$115$	0	0
$116$	1128.00	0.902864
$117$	−117.000	−0.0924500
$118$	312.000	0.243406
$119$	−336.000	−0.258833
$120$	0	0
$121$	−1187.00	−0.891811
$122$	−460.000	−0.341364
$123$	522.000	0.382660
$124$	464.000	0.336036
$125$	0	0
$126$	144.000	0.101814
$127$	1096.00	0.765782	0.382891	−	0.923794i	$-0.374929\pi$
$127$	1096.00	0.765782	0.382891	+	0.923794i	$0.374929\pi$
$128$	−128.000	−0.0883883
$129$	228.000	0.155615
$130$	0	0
$131$	−1200.00	−0.800340	−0.400170	−	0.916441i	$-0.631049\pi$
$131$	−1200.00	−0.800340	−0.400170	+	0.916441i	$0.631049\pi$
$132$	144.000	0.0949514
$133$	416.000	0.271216
$134$	−1184.00	−0.763299
$135$	0	0
$136$	−336.000	−0.211851
$137$	−534.000	−0.333012	−0.166506	−	0.986040i	$-0.553249\pi$
$137$	−534.000	−0.333012	−0.166506	+	0.986040i	$0.553249\pi$
$138$	792.000	0.488547
$139$	−1756.00	−1.07153	−0.535763	−	0.844369i	$-0.679976\pi$
$139$	−1756.00	−1.07153	−0.535763	+	0.844369i	$0.679976\pi$
$140$	0	0
$141$	−1368.00	−0.817067
$142$	−816.000	−0.482234
$143$	−156.000	−0.0912264
$144$	144.000	0.0833333
$145$	0	0
$146$	−1460.00	−0.827606
$147$	−837.000	−0.469623
$148$	−1592.00	−0.884200
$149$	690.000	0.379376	0.189688	−	0.981844i	$-0.439252\pi$
$149$	690.000	0.379376	0.189688	+	0.981844i	$0.439252\pi$
$150$	0	0
$151$	308.000	0.165991	0.0829956	−	0.996550i	$-0.473551\pi$
$151$	308.000	0.165991	0.0829956	+	0.996550i	$0.473551\pi$
$152$	416.000	0.221987
$153$	378.000	0.199735
$154$	192.000	0.100466
$155$	0	0
$156$	−156.000	−0.0800641
$157$	490.000	0.249084	0.124542	−	0.992214i	$-0.460254\pi$
$157$	490.000	0.249084	0.124542	+	0.992214i	$0.460254\pi$
$158$	−1456.00	−0.733121
$159$	−450.000	−0.224449
$160$	0	0
$161$	1056.00	0.516922
$162$	−162.000	−0.0785674
$163$	952.000	0.457463	0.228731	−	0.973490i	$-0.426542\pi$
$163$	952.000	0.457463	0.228731	+	0.973490i	$0.426542\pi$
$164$	696.000	0.331393
$165$	0	0
$166$	72.0000	0.0336644
$167$	−3480.00	−1.61252	−0.806259	−	0.591563i	$-0.798511\pi$
$167$	−3480.00	−1.61252	−0.806259	+	0.591563i	$0.798511\pi$
$168$	192.000	0.0881733
$169$	169.000	0.0769231
$170$	0	0
$171$	−468.000	−0.209292
$172$	304.000	0.134766
$173$	1530.00	0.672392	0.336196	−	0.941792i	$-0.390860\pi$
$173$	1530.00	0.672392	0.336196	+	0.941792i	$0.390860\pi$
$174$	−1692.00	−0.737185
$175$	0	0
$176$	192.000	0.0822304
$177$	−468.000	−0.198740
$178$	2964.00	1.24810
$179$	2280.00	0.952040	0.476020	−	0.879434i	$-0.342079\pi$
$179$	2280.00	0.952040	0.476020	+	0.879434i	$0.342079\pi$
$180$	0	0
$181$	−2554.00	−1.04882	−0.524412	−	0.851464i	$-0.675715\pi$
$181$	−2554.00	−1.04882	−0.524412	+	0.851464i	$0.675715\pi$
$182$	−208.000	−0.0847142
$183$	690.000	0.278723
$184$	1056.00	0.423094
$185$	0	0
$186$	−696.000	−0.274372
$187$	504.000	0.197092
$188$	−1824.00	−0.707600
$189$	−216.000	−0.0831306
$190$	0	0
$191$	360.000	0.136381	0.0681903	−	0.997672i	$-0.478278\pi$
$191$	360.000	0.136381	0.0681903	+	0.997672i	$0.478278\pi$
$192$	192.000	0.0721688
$193$	2242.00	0.836180	0.418090	−	0.908406i	$-0.362700\pi$
$193$	2242.00	0.836180	0.418090	+	0.908406i	$0.362700\pi$
$194$	3484.00	1.28936
$195$	0	0
$196$	−1116.00	−0.406706
$197$	318.000	0.115008	0.0575040	−	0.998345i	$-0.481686\pi$
$197$	318.000	0.115008	0.0575040	+	0.998345i	$0.481686\pi$
$198$	−216.000	−0.0775275
$199$	4376.00	1.55883	0.779413	−	0.626510i	$-0.215517\pi$
$199$	4376.00	1.55883	0.779413	+	0.626510i	$0.215517\pi$
$200$	0	0
$201$	1776.00	0.623231
$202$	1068.00	0.372001
$203$	−2256.00	−0.780001
$204$	504.000	0.172976
$205$	0	0
$206$	496.000	0.167757
$207$	−1188.00	−0.398897
$208$	−208.000	−0.0693375
$209$	−624.000	−0.206521
$210$	0	0
$211$	1532.00	0.499845	0.249922	−	0.968266i	$-0.419595\pi$
$211$	1532.00	0.499845	0.249922	+	0.968266i	$0.419595\pi$
$212$	−600.000	−0.194378
$213$	1224.00	0.393742
$214$	2088.00	0.666975
$215$	0	0
$216$	−216.000	−0.0680414
$217$	−928.000	−0.290308
$218$	2684.00	0.833869
$219$	2190.00	0.675737
$220$	0	0
$221$	−546.000	−0.166190
$222$	2388.00	0.721946
$223$	5848.00	1.75610	0.878052	−	0.478566i	$-0.158843\pi$
$223$	5848.00	1.75610	0.878052	+	0.478566i	$0.158843\pi$
$224$	256.000	0.0763604
$225$	0	0
$226$	−372.000	−0.109491
$227$	−4884.00	−1.42803	−0.714014	−	0.700131i	$-0.753125\pi$
$227$	−4884.00	−1.42803	−0.714014	+	0.700131i	$0.753125\pi$
$228$	−624.000	−0.181252
$229$	−5254.00	−1.51613	−0.758066	−	0.652178i	$-0.773855\pi$
$229$	−5254.00	−1.51613	−0.758066	+	0.652178i	$0.773855\pi$
$230$	0	0
$231$	−288.000	−0.0820303
$232$	−2256.00	−0.638421
$233$	−2358.00	−0.662994	−0.331497	−	0.943456i	$-0.607554\pi$
$233$	−2358.00	−0.662994	−0.331497	+	0.943456i	$0.607554\pi$
$234$	234.000	0.0653720
$235$	0	0
$236$	−624.000	−0.172114
$237$	2184.00	0.598591
$238$	672.000	0.183022
$239$	−2328.00	−0.630066	−0.315033	−	0.949081i	$-0.602016\pi$
$239$	−2328.00	−0.630066	−0.315033	+	0.949081i	$0.602016\pi$
$240$	0	0
$241$	−3670.00	−0.980936	−0.490468	−	0.871459i	$-0.663174\pi$
$241$	−3670.00	−0.980936	−0.490468	+	0.871459i	$0.663174\pi$
$242$	2374.00	0.630605
$243$	243.000	0.0641500
$244$	920.000	0.241381
$245$	0	0
$246$	−1044.00	−0.270581
$247$	676.000	0.174141
$248$	−928.000	−0.237613
$249$	−108.000	−0.0274868
$250$	0	0
$251$	−6312.00	−1.58729	−0.793645	−	0.608381i	$-0.791819\pi$
$251$	−6312.00	−1.58729	−0.793645	+	0.608381i	$0.791819\pi$
$252$	−288.000	−0.0719932
$253$	−1584.00	−0.393617
$254$	−2192.00	−0.541489
$255$	0	0
$256$	256.000	0.0625000
$257$	−6006.00	−1.45776	−0.728879	−	0.684642i	$-0.759958\pi$
$257$	−6006.00	−1.45776	−0.728879	+	0.684642i	$0.759958\pi$
$258$	−456.000	−0.110036
$259$	3184.00	0.763877
$260$	0	0
$261$	2538.00	0.601909
$262$	2400.00	0.565926
$263$	−5220.00	−1.22387	−0.611937	−	0.790906i	$-0.709610\pi$
$263$	−5220.00	−1.22387	−0.611937	+	0.790906i	$0.709610\pi$
$264$	−288.000	−0.0671408
$265$	0	0
$266$	−832.000	−0.191779
$267$	−4446.00	−1.01907
$268$	2368.00	0.539734
$269$	−126.000	−0.0285589	−0.0142795	−	0.999898i	$-0.504545\pi$
$269$	−126.000	−0.0285589	−0.0142795	+	0.999898i	$0.504545\pi$
$270$	0	0
$271$	−3244.00	−0.727155	−0.363577	−	0.931564i	$-0.618445\pi$
$271$	−3244.00	−0.727155	−0.363577	+	0.931564i	$0.618445\pi$
$272$	672.000	0.149801
$273$	312.000	0.0691689
$274$	1068.00	0.235475
$275$	0	0
$276$	−1584.00	−0.345455
$277$	7666.00	1.66284	0.831418	−	0.555648i	$-0.187530\pi$
$277$	7666.00	1.66284	0.831418	+	0.555648i	$0.187530\pi$
$278$	3512.00	0.757683
$279$	1044.00	0.224024
$280$	0	0
$281$	−1458.00	−0.309527	−0.154763	−	0.987952i	$-0.549462\pi$
$281$	−1458.00	−0.309527	−0.154763	+	0.987952i	$0.549462\pi$
$282$	2736.00	0.577753
$283$	−188.000	−0.0394892	−0.0197446	−	0.999805i	$-0.506285\pi$
$283$	−188.000	−0.0394892	−0.0197446	+	0.999805i	$0.506285\pi$
$284$	1632.00	0.340991
$285$	0	0
$286$	312.000	0.0645068
$287$	−1392.00	−0.286297
$288$	−288.000	−0.0589256
$289$	−3149.00	−0.640953
$290$	0	0
$291$	−5226.00	−1.05276
$292$	2920.00	0.585206
$293$	−3738.00	−0.745312	−0.372656	−	0.927970i	$-0.621553\pi$
$293$	−3738.00	−0.745312	−0.372656	+	0.927970i	$0.621553\pi$
$294$	1674.00	0.332074
$295$	0	0
$296$	3184.00	0.625224
$297$	324.000	0.0633010
$298$	−1380.00	−0.268259
$299$	1716.00	0.331902
$300$	0	0
$301$	−608.000	−0.116427
$302$	−616.000	−0.117374
$303$	−1602.00	−0.303738
$304$	−832.000	−0.156969
$305$	0	0
$306$	−756.000	−0.141234
$307$	−8216.00	−1.52740	−0.763700	−	0.645571i	$-0.776619\pi$
$307$	−8216.00	−1.52740	−0.763700	+	0.645571i	$0.776619\pi$
$308$	−384.000	−0.0710404
$309$	−744.000	−0.136973
$310$	0	0
$311$	6288.00	1.14649	0.573247	−	0.819382i	$-0.305683\pi$
$311$	6288.00	1.14649	0.573247	+	0.819382i	$0.305683\pi$
$312$	312.000	0.0566139
$313$	2446.00	0.441713	0.220856	−	0.975306i	$-0.429115\pi$
$313$	2446.00	0.441713	0.220856	+	0.975306i	$0.429115\pi$
$314$	−980.000	−0.176129
$315$	0	0
$316$	2912.00	0.518395
$317$	5430.00	0.962079	0.481040	−	0.876699i	$-0.340259\pi$
$317$	5430.00	0.962079	0.481040	+	0.876699i	$0.340259\pi$
$318$	900.000	0.158709
$319$	3384.00	0.593942
$320$	0	0
$321$	−3132.00	−0.544583
$322$	−2112.00	−0.365519
$323$	−2184.00	−0.376226
$324$	324.000	0.0555556
$325$	0	0
$326$	−1904.00	−0.323475
$327$	−4026.00	−0.680851
$328$	−1392.00	−0.234330
$329$	3648.00	0.611309
$330$	0	0
$331$	1628.00	0.270341	0.135171	−	0.990822i	$-0.456842\pi$
$331$	1628.00	0.270341	0.135171	+	0.990822i	$0.456842\pi$
$332$	−144.000	−0.0238043
$333$	−3582.00	−0.589467
$334$	6960.00	1.14022
$335$	0	0
$336$	−384.000	−0.0623480
$337$	−5546.00	−0.896468	−0.448234	−	0.893916i	$-0.647947\pi$
$337$	−5546.00	−0.896468	−0.448234	+	0.893916i	$0.647947\pi$
$338$	−338.000	−0.0543928
$339$	558.000	0.0893994
$340$	0	0
$341$	1392.00	0.221059
$342$	936.000	0.147991
$343$	4976.00	0.783320
$344$	−608.000	−0.0952941
$345$	0	0
$346$	−3060.00	−0.475453
$347$	−2772.00	−0.428844	−0.214422	−	0.976741i	$-0.568787\pi$
$347$	−2772.00	−0.428844	−0.214422	+	0.976741i	$0.568787\pi$
$348$	3384.00	0.521269
$349$	10538.0	1.61629	0.808146	−	0.588982i	$-0.200471\pi$
$349$	10538.0	1.61629	0.808146	+	0.588982i	$0.200471\pi$
$350$	0	0
$351$	−351.000	−0.0533761
$352$	−384.000	−0.0581456
$353$	−942.000	−0.142033	−0.0710164	−	0.997475i	$-0.522624\pi$
$353$	−942.000	−0.142033	−0.0710164	+	0.997475i	$0.522624\pi$
$354$	936.000	0.140531
$355$	0	0
$356$	−5928.00	−0.882538
$357$	−1008.00	−0.149437
$358$	−4560.00	−0.673194
$359$	6000.00	0.882083	0.441042	−	0.897487i	$-0.354609\pi$
$359$	6000.00	0.882083	0.441042	+	0.897487i	$0.354609\pi$
$360$	0	0
$361$	−4155.00	−0.605773
$362$	5108.00	0.741631
$363$	−3561.00	−0.514887
$364$	416.000	0.0599020
$365$	0	0
$366$	−1380.00	−0.197087
$367$	−8264.00	−1.17541	−0.587707	−	0.809073i	$-0.699969\pi$
$367$	−8264.00	−1.17541	−0.587707	+	0.809073i	$0.699969\pi$
$368$	−2112.00	−0.299173
$369$	1566.00	0.220929
$370$	0	0
$371$	1200.00	0.167927
$372$	1392.00	0.194010
$373$	−2654.00	−0.368415	−0.184208	−	0.982887i	$-0.558972\pi$
$373$	−2654.00	−0.368415	−0.184208	+	0.982887i	$0.558972\pi$
$374$	−1008.00	−0.139365
$375$	0	0
$376$	3648.00	0.500349
$377$	−3666.00	−0.500819
$378$	432.000	0.0587822
$379$	−3076.00	−0.416896	−0.208448	−	0.978033i	$-0.566841\pi$
$379$	−3076.00	−0.416896	−0.208448	+	0.978033i	$0.566841\pi$
$380$	0	0
$381$	3288.00	0.442124
$382$	−720.000	−0.0964356
$383$	−12864.0	−1.71624	−0.858120	−	0.513450i	$-0.828367\pi$
$383$	−12864.0	−1.71624	−0.858120	+	0.513450i	$0.828367\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	−4484.00	−0.591268
$387$	684.000	0.0898441
$388$	−6968.00	−0.911718
$389$	−10974.0	−1.43034	−0.715172	−	0.698948i	$-0.753652\pi$
$389$	−10974.0	−1.43034	−0.715172	+	0.698948i	$0.753652\pi$
$390$	0	0
$391$	−5544.00	−0.717064
$392$	2232.00	0.287584
$393$	−3600.00	−0.462076
$394$	−636.000	−0.0813229
$395$	0	0
$396$	432.000	0.0548202
$397$	−8582.00	−1.08493	−0.542466	−	0.840078i	$-0.682509\pi$
$397$	−8582.00	−1.08493	−0.542466	+	0.840078i	$0.682509\pi$
$398$	−8752.00	−1.10226
$399$	1248.00	0.156587
$400$	0	0
$401$	2142.00	0.266749	0.133375	−	0.991066i	$-0.457419\pi$
$401$	2142.00	0.266749	0.133375	+	0.991066i	$0.457419\pi$
$402$	−3552.00	−0.440691
$403$	−1508.00	−0.186399
$404$	−2136.00	−0.263044
$405$	0	0
$406$	4512.00	0.551544
$407$	−4776.00	−0.581665
$408$	−1008.00	−0.122312
$409$	6122.00	0.740131	0.370065	−	0.929006i	$-0.379335\pi$
$409$	6122.00	0.740131	0.370065	+	0.929006i	$0.379335\pi$
$410$	0	0
$411$	−1602.00	−0.192265
$412$	−992.000	−0.118622
$413$	1248.00	0.148693
$414$	2376.00	0.282063
$415$	0	0
$416$	416.000	0.0490290
$417$	−5268.00	−0.618645
$418$	1248.00	0.146033
$419$	−13056.0	−1.52226	−0.761130	−	0.648599i	$-0.775355\pi$
$419$	−13056.0	−1.52226	−0.761130	+	0.648599i	$0.775355\pi$
$420$	0	0
$421$	−7582.00	−0.877729	−0.438865	−	0.898553i	$-0.644619\pi$
$421$	−7582.00	−0.877729	−0.438865	+	0.898553i	$0.644619\pi$
$422$	−3064.00	−0.353444
$423$	−4104.00	−0.471734
$424$	1200.00	0.137446
$425$	0	0
$426$	−2448.00	−0.278418
$427$	−1840.00	−0.208534
$428$	−4176.00	−0.471623
$429$	−468.000	−0.0526696
$430$	0	0
$431$	−3888.00	−0.434521	−0.217260	−	0.976114i	$-0.569712\pi$
$431$	−3888.00	−0.434521	−0.217260	+	0.976114i	$0.569712\pi$
$432$	432.000	0.0481125
$433$	2710.00	0.300772	0.150386	−	0.988627i	$-0.451948\pi$
$433$	2710.00	0.300772	0.150386	+	0.988627i	$0.451948\pi$
$434$	1856.00	0.205278
$435$	0	0
$436$	−5368.00	−0.589634
$437$	6864.00	0.751372
$438$	−4380.00	−0.477818
$439$	6008.00	0.653180	0.326590	−	0.945166i	$-0.394100\pi$
$439$	6008.00	0.653180	0.326590	+	0.945166i	$0.394100\pi$
$440$	0	0
$441$	−2511.00	−0.271137
$442$	1092.00	0.117514
$443$	−13884.0	−1.48905	−0.744525	−	0.667595i	$-0.767324\pi$
$443$	−13884.0	−1.48905	−0.744525	+	0.667595i	$0.767324\pi$
$444$	−4776.00	−0.510493
$445$	0	0
$446$	−11696.0	−1.24175
$447$	2070.00	0.219033
$448$	−512.000	−0.0539949
$449$	−8706.00	−0.915059	−0.457530	−	0.889194i	$-0.651266\pi$
$449$	−8706.00	−0.915059	−0.457530	+	0.889194i	$0.651266\pi$
$450$	0	0
$451$	2088.00	0.218005
$452$	744.000	0.0774222
$453$	924.000	0.0958351
$454$	9768.00	1.00977
$455$	0	0
$456$	1248.00	0.128164
$457$	−5078.00	−0.519779	−0.259889	−	0.965638i	$-0.583686\pi$
$457$	−5078.00	−0.519779	−0.259889	+	0.965638i	$0.583686\pi$
$458$	10508.0	1.07207
$459$	1134.00	0.115317
$460$	0	0
$461$	−14934.0	−1.50878	−0.754388	−	0.656429i	$-0.772066\pi$
$461$	−14934.0	−1.50878	−0.754388	+	0.656429i	$0.772066\pi$
$462$	576.000	0.0580042
$463$	3448.00	0.346095	0.173048	−	0.984913i	$-0.444639\pi$
$463$	3448.00	0.346095	0.173048	+	0.984913i	$0.444639\pi$
$464$	4512.00	0.451432
$465$	0	0
$466$	4716.00	0.468808
$467$	10332.0	1.02379	0.511893	−	0.859049i	$-0.328944\pi$
$467$	10332.0	1.02379	0.511893	+	0.859049i	$0.328944\pi$
$468$	−468.000	−0.0462250
$469$	−4736.00	−0.466286
$470$	0	0
$471$	1470.00	0.143809
$472$	1248.00	0.121703
$473$	912.000	0.0886550
$474$	−4368.00	−0.423268
$475$	0	0
$476$	−1344.00	−0.129416
$477$	−1350.00	−0.129585
$478$	4656.00	0.445524
$479$	−2328.00	−0.222065	−0.111032	−	0.993817i	$-0.535416\pi$
$479$	−2328.00	−0.222065	−0.111032	+	0.993817i	$0.535416\pi$
$480$	0	0
$481$	5174.00	0.490466
$482$	7340.00	0.693626
$483$	3168.00	0.298445
$484$	−4748.00	−0.445905
$485$	0	0
$486$	−486.000	−0.0453609
$487$	−13160.0	−1.22451	−0.612255	−	0.790660i	$-0.709737\pi$
$487$	−13160.0	−1.22451	−0.612255	+	0.790660i	$0.709737\pi$
$488$	−1840.00	−0.170682
$489$	2856.00	0.264116
$490$	0	0
$491$	8688.00	0.798542	0.399271	−	0.916833i	$-0.369263\pi$
$491$	8688.00	0.798542	0.399271	+	0.916833i	$0.369263\pi$
$492$	2088.00	0.191330
$493$	11844.0	1.08200
$494$	−1352.00	−0.123136
$495$	0	0
$496$	1856.00	0.168018
$497$	−3264.00	−0.294588
$498$	216.000	0.0194361
$499$	−15460.0	−1.38694	−0.693472	−	0.720484i	$-0.743920\pi$
$499$	−15460.0	−1.38694	−0.693472	+	0.720484i	$0.743920\pi$
$500$	0	0
$501$	−10440.0	−0.930988
$502$	12624.0	1.12238
$503$	7116.00	0.630789	0.315394	−	0.948961i	$-0.397863\pi$
$503$	7116.00	0.630789	0.315394	+	0.948961i	$0.397863\pi$
$504$	576.000	0.0509069
$505$	0	0
$506$	3168.00	0.278330
$507$	507.000	0.0444116
$508$	4384.00	0.382891
$509$	−14694.0	−1.27957	−0.639784	−	0.768555i	$-0.720976\pi$
$509$	−14694.0	−1.27957	−0.639784	+	0.768555i	$0.720976\pi$
$510$	0	0
$511$	−5840.00	−0.505570
$512$	−512.000	−0.0441942
$513$	−1404.00	−0.120835
$514$	12012.0	1.03079
$515$	0	0
$516$	912.000	0.0778073
$517$	−5472.00	−0.465490
$518$	−6368.00	−0.540143
$519$	4590.00	0.388205
$520$	0	0
$521$	−13782.0	−1.15893	−0.579463	−	0.814999i	$-0.696738\pi$
$521$	−13782.0	−1.15893	−0.579463	+	0.814999i	$0.696738\pi$
$522$	−5076.00	−0.425614
$523$	5596.00	0.467870	0.233935	−	0.972252i	$-0.424840\pi$
$523$	5596.00	0.467870	0.233935	+	0.972252i	$0.424840\pi$
$524$	−4800.00	−0.400170
$525$	0	0
$526$	10440.0	0.865410
$527$	4872.00	0.402709
$528$	576.000	0.0474757
$529$	5257.00	0.432070
$530$	0	0
$531$	−1404.00	−0.114743
$532$	1664.00	0.135608
$533$	−2262.00	−0.183824
$534$	8892.00	0.720589
$535$	0	0
$536$	−4736.00	−0.381649
$537$	6840.00	0.549661
$538$	252.000	0.0201942
$539$	−3348.00	−0.267548
$540$	0	0
$541$	7322.00	0.581881	0.290940	−	0.956741i	$-0.406032\pi$
$541$	7322.00	0.581881	0.290940	+	0.956741i	$0.406032\pi$
$542$	6488.00	0.514176
$543$	−7662.00	−0.605539
$544$	−1344.00	−0.105926
$545$	0	0
$546$	−624.000	−0.0489098
$547$	15652.0	1.22346	0.611729	−	0.791068i	$-0.290474\pi$
$547$	15652.0	1.22346	0.611729	+	0.791068i	$0.290474\pi$
$548$	−2136.00	−0.166506
$549$	2070.00	0.160921
$550$	0	0
$551$	−14664.0	−1.13377
$552$	3168.00	0.244274
$553$	−5824.00	−0.447851
$554$	−15332.0	−1.17580
$555$	0	0
$556$	−7024.00	−0.535763
$557$	−13458.0	−1.02376	−0.511879	−	0.859057i	$-0.671051\pi$
$557$	−13458.0	−1.02376	−0.511879	+	0.859057i	$0.671051\pi$
$558$	−2088.00	−0.158409
$559$	−988.000	−0.0747548
$560$	0	0
$561$	1512.00	0.113791
$562$	2916.00	0.218868
$563$	18108.0	1.35553	0.677763	−	0.735280i	$-0.262950\pi$
$563$	18108.0	1.35553	0.677763	+	0.735280i	$0.262950\pi$
$564$	−5472.00	−0.408533
$565$	0	0
$566$	376.000	0.0279231
$567$	−648.000	−0.0479955
$568$	−3264.00	−0.241117
$569$	−20118.0	−1.48223	−0.741116	−	0.671377i	$-0.765703\pi$
$569$	−20118.0	−1.48223	−0.741116	+	0.671377i	$0.765703\pi$
$570$	0	0
$571$	−4156.00	−0.304594	−0.152297	−	0.988335i	$-0.548667\pi$
$571$	−4156.00	−0.304594	−0.152297	+	0.988335i	$0.548667\pi$
$572$	−624.000	−0.0456132
$573$	1080.00	0.0787393
$574$	2784.00	0.202442
$575$	0	0
$576$	576.000	0.0416667
$577$	7378.00	0.532323	0.266161	−	0.963929i	$-0.414245\pi$
$577$	7378.00	0.532323	0.266161	+	0.963929i	$0.414245\pi$
$578$	6298.00	0.453222
$579$	6726.00	0.482769
$580$	0	0
$581$	288.000	0.0205650
$582$	10452.0	0.744415
$583$	−1800.00	−0.127870
$584$	−5840.00	−0.413803
$585$	0	0
$586$	7476.00	0.527015
$587$	−6372.00	−0.448042	−0.224021	−	0.974584i	$-0.571918\pi$
$587$	−6372.00	−0.448042	−0.224021	+	0.974584i	$0.571918\pi$
$588$	−3348.00	−0.234812
$589$	−6032.00	−0.421977
$590$	0	0
$591$	954.000	0.0663999
$592$	−6368.00	−0.442100
$593$	−2382.00	−0.164953	−0.0824764	−	0.996593i	$-0.526283\pi$
$593$	−2382.00	−0.164953	−0.0824764	+	0.996593i	$0.526283\pi$
$594$	−648.000	−0.0447605
$595$	0	0
$596$	2760.00	0.189688
$597$	13128.0	0.899989
$598$	−3432.00	−0.234690
$599$	10536.0	0.718680	0.359340	−	0.933207i	$-0.383002\pi$
$599$	10536.0	0.718680	0.359340	+	0.933207i	$0.383002\pi$
$600$	0	0
$601$	13610.0	0.923733	0.461866	−	0.886949i	$-0.347180\pi$
$601$	13610.0	0.923733	0.461866	+	0.886949i	$0.347180\pi$
$602$	1216.00	0.0823263
$603$	5328.00	0.359822
$604$	1232.00	0.0829956
$605$	0	0
$606$	3204.00	0.214775
$607$	−13736.0	−0.918496	−0.459248	−	0.888308i	$-0.651881\pi$
$607$	−13736.0	−0.918496	−0.459248	+	0.888308i	$0.651881\pi$
$608$	1664.00	0.110994
$609$	−6768.00	−0.450334
$610$	0	0
$611$	5928.00	0.392506
$612$	1512.00	0.0998676
$613$	10882.0	0.716998	0.358499	−	0.933530i	$-0.383289\pi$
$613$	10882.0	0.716998	0.358499	+	0.933530i	$0.383289\pi$
$614$	16432.0	1.08004
$615$	0	0
$616$	768.000	0.0502331
$617$	−4902.00	−0.319849	−0.159925	−	0.987129i	$-0.551125\pi$
$617$	−4902.00	−0.319849	−0.159925	+	0.987129i	$0.551125\pi$
$618$	1488.00	0.0968546
$619$	−20692.0	−1.34359	−0.671795	−	0.740737i	$-0.734476\pi$
$619$	−20692.0	−1.34359	−0.671795	+	0.740737i	$0.734476\pi$
$620$	0	0
$621$	−3564.00	−0.230303
$622$	−12576.0	−0.810694
$623$	11856.0	0.762441
$624$	−624.000	−0.0400320
$625$	0	0
$626$	−4892.00	−0.312338
$627$	−1872.00	−0.119235
$628$	1960.00	0.124542
$629$	−16716.0	−1.05964
$630$	0	0
$631$	14348.0	0.905206	0.452603	−	0.891712i	$-0.350496\pi$
$631$	14348.0	0.905206	0.452603	+	0.891712i	$0.350496\pi$
$632$	−5824.00	−0.366561
$633$	4596.00	0.288585
$634$	−10860.0	−0.680293
$635$	0	0
$636$	−1800.00	−0.112224
$637$	3627.00	0.225600
$638$	−6768.00	−0.419981
$639$	3672.00	0.227327
$640$	0	0
$641$	−1182.00	−0.0728334	−0.0364167	−	0.999337i	$-0.511594\pi$
$641$	−1182.00	−0.0728334	−0.0364167	+	0.999337i	$0.511594\pi$
$642$	6264.00	0.385078
$643$	26080.0	1.59953	0.799763	−	0.600316i	$-0.204959\pi$
$643$	26080.0	1.59953	0.799763	+	0.600316i	$0.204959\pi$
$644$	4224.00	0.258461
$645$	0	0
$646$	4368.00	0.266032
$647$	21852.0	1.32781	0.663903	−	0.747819i	$-0.268899\pi$
$647$	21852.0	1.32781	0.663903	+	0.747819i	$0.268899\pi$
$648$	−648.000	−0.0392837
$649$	−1872.00	−0.113224
$650$	0	0
$651$	−2784.00	−0.167609
$652$	3808.00	0.228731
$653$	12018.0	0.720215	0.360108	−	0.932911i	$-0.382740\pi$
$653$	12018.0	0.720215	0.360108	+	0.932911i	$0.382740\pi$
$654$	8052.00	0.481434
$655$	0	0
$656$	2784.00	0.165697
$657$	6570.00	0.390137
$658$	−7296.00	−0.432261
$659$	23400.0	1.38321	0.691604	−	0.722277i	$-0.256904\pi$
$659$	23400.0	1.38321	0.691604	+	0.722277i	$0.256904\pi$
$660$	0	0
$661$	11354.0	0.668108	0.334054	−	0.942554i	$-0.391583\pi$
$661$	11354.0	0.668108	0.334054	+	0.942554i	$0.391583\pi$
$662$	−3256.00	−0.191160
$663$	−1638.00	−0.0959497
$664$	288.000	0.0168322
$665$	0	0
$666$	7164.00	0.416816
$667$	−37224.0	−2.16090
$668$	−13920.0	−0.806259
$669$	17544.0	1.01389
$670$	0	0
$671$	2760.00	0.158791
$672$	768.000	0.0440867
$673$	23374.0	1.33878	0.669392	−	0.742909i	$-0.266555\pi$
$673$	23374.0	1.33878	0.669392	+	0.742909i	$0.266555\pi$
$674$	11092.0	0.633899
$675$	0	0
$676$	676.000	0.0384615
$677$	22866.0	1.29810	0.649049	−	0.760747i	$-0.275167\pi$
$677$	22866.0	1.29810	0.649049	+	0.760747i	$0.275167\pi$
$678$	−1116.00	−0.0632149
$679$	13936.0	0.787650
$680$	0	0
$681$	−14652.0	−0.824473
$682$	−2784.00	−0.156312
$683$	13164.0	0.737491	0.368746	−	0.929530i	$-0.379787\pi$
$683$	13164.0	0.737491	0.368746	+	0.929530i	$0.379787\pi$
$684$	−1872.00	−0.104646
$685$	0	0
$686$	−9952.00	−0.553891
$687$	−15762.0	−0.875339
$688$	1216.00	0.0673831
$689$	1950.00	0.107822
$690$	0	0
$691$	17012.0	0.936566	0.468283	−	0.883579i	$-0.344873\pi$
$691$	17012.0	0.936566	0.468283	+	0.883579i	$0.344873\pi$
$692$	6120.00	0.336196
$693$	−864.000	−0.0473602
$694$	5544.00	0.303238
$695$	0	0
$696$	−6768.00	−0.368592
$697$	7308.00	0.397145
$698$	−21076.0	−1.14289
$699$	−7074.00	−0.382780
$700$	0	0
$701$	−17910.0	−0.964981	−0.482490	−	0.875901i	$-0.660268\pi$
$701$	−17910.0	−0.964981	−0.482490	+	0.875901i	$0.660268\pi$
$702$	702.000	0.0377426
$703$	20696.0	1.11033
$704$	768.000	0.0411152
$705$	0	0
$706$	1884.00	0.100432
$707$	4272.00	0.227249
$708$	−1872.00	−0.0993702
$709$	−10918.0	−0.578327	−0.289164	−	0.957280i	$-0.593377\pi$
$709$	−10918.0	−0.578327	−0.289164	+	0.957280i	$0.593377\pi$
$710$	0	0
$711$	6552.00	0.345597
$712$	11856.0	0.624048
$713$	−15312.0	−0.804262
$714$	2016.00	0.105668
$715$	0	0
$716$	9120.00	0.476020
$717$	−6984.00	−0.363769
$718$	−12000.0	−0.623727
$719$	−26064.0	−1.35191	−0.675955	−	0.736943i	$-0.736269\pi$
$719$	−26064.0	−1.35191	−0.675955	+	0.736943i	$0.736269\pi$
$720$	0	0
$721$	1984.00	0.102480
$722$	8310.00	0.428347
$723$	−11010.0	−0.566343
$724$	−10216.0	−0.524412
$725$	0	0
$726$	7122.00	0.364080
$727$	−1688.00	−0.0861134	−0.0430567	−	0.999073i	$-0.513710\pi$
$727$	−1688.00	−0.0861134	−0.0430567	+	0.999073i	$0.513710\pi$
$728$	−832.000	−0.0423571
$729$	729.000	0.0370370
$730$	0	0
$731$	3192.00	0.161505
$732$	2760.00	0.139361
$733$	20626.0	1.03934	0.519672	−	0.854366i	$-0.326054\pi$
$733$	20626.0	1.03934	0.519672	+	0.854366i	$0.326054\pi$
$734$	16528.0	0.831144
$735$	0	0
$736$	4224.00	0.211547
$737$	7104.00	0.355060
$738$	−3132.00	−0.156220
$739$	16292.0	0.810976	0.405488	−	0.914100i	$-0.367102\pi$
$739$	16292.0	0.810976	0.405488	+	0.914100i	$0.367102\pi$
$740$	0	0
$741$	2028.00	0.100540
$742$	−2400.00	−0.118742
$743$	−24048.0	−1.18740	−0.593698	−	0.804688i	$-0.702333\pi$
$743$	−24048.0	−1.18740	−0.593698	+	0.804688i	$0.702333\pi$
$744$	−2784.00	−0.137186
$745$	0	0
$746$	5308.00	0.260509
$747$	−324.000	−0.0158695
$748$	2016.00	0.0985458
$749$	8352.00	0.407444
$750$	0	0
$751$	15248.0	0.740889	0.370444	−	0.928855i	$-0.379205\pi$
$751$	15248.0	0.740889	0.370444	+	0.928855i	$0.379205\pi$
$752$	−7296.00	−0.353800
$753$	−18936.0	−0.916423
$754$	7332.00	0.354132
$755$	0	0
$756$	−864.000	−0.0415653
$757$	−4286.00	−0.205782	−0.102891	−	0.994693i	$-0.532809\pi$
$757$	−4286.00	−0.205782	−0.102891	+	0.994693i	$0.532809\pi$
$758$	6152.00	0.294790
$759$	−4752.00	−0.227255
$760$	0	0
$761$	21294.0	1.01433	0.507166	−	0.861848i	$-0.330693\pi$
$761$	21294.0	1.01433	0.507166	+	0.861848i	$0.330693\pi$
$762$	−6576.00	−0.312629
$763$	10736.0	0.509396
$764$	1440.00	0.0681903
$765$	0	0
$766$	25728.0	1.21356
$767$	2028.00	0.0954718
$768$	768.000	0.0360844
$769$	−7198.00	−0.337538	−0.168769	−	0.985656i	$-0.553979\pi$
$769$	−7198.00	−0.337538	−0.168769	+	0.985656i	$0.553979\pi$
$770$	0	0
$771$	−18018.0	−0.841637
$772$	8968.00	0.418090
$773$	−11322.0	−0.526810	−0.263405	−	0.964685i	$-0.584846\pi$
$773$	−11322.0	−0.526810	−0.263405	+	0.964685i	$0.584846\pi$
$774$	−1368.00	−0.0635294
$775$	0	0
$776$	13936.0	0.644682
$777$	9552.00	0.441025
$778$	21948.0	1.01141
$779$	−9048.00	−0.416147
$780$	0	0
$781$	4896.00	0.224318
$782$	11088.0	0.507041
$783$	7614.00	0.347512
$784$	−4464.00	−0.203353
$785$	0	0
$786$	7200.00	0.326737
$787$	−13424.0	−0.608023	−0.304011	−	0.952668i	$-0.598326\pi$
$787$	−13424.0	−0.608023	−0.304011	+	0.952668i	$0.598326\pi$
$788$	1272.00	0.0575040
$789$	−15660.0	−0.706604
$790$	0	0
$791$	−1488.00	−0.0668865
$792$	−864.000	−0.0387638
$793$	−2990.00	−0.133894
$794$	17164.0	0.767163
$795$	0	0
$796$	17504.0	0.779413
$797$	23202.0	1.03119	0.515594	−	0.856833i	$-0.327571\pi$
$797$	23202.0	1.03119	0.515594	+	0.856833i	$0.327571\pi$
$798$	−2496.00	−0.110724
$799$	−19152.0	−0.847996
$800$	0	0
$801$	−13338.0	−0.588358
$802$	−4284.00	−0.188620
$803$	8760.00	0.384973
$804$	7104.00	0.311615
$805$	0	0
$806$	3016.00	0.131804
$807$	−378.000	−0.0164885
$808$	4272.00	0.186001
$809$	−38814.0	−1.68681	−0.843404	−	0.537280i	$-0.819452\pi$
$809$	−38814.0	−1.68681	−0.843404	+	0.537280i	$0.819452\pi$
$810$	0	0
$811$	−9292.00	−0.402326	−0.201163	−	0.979558i	$-0.564472\pi$
$811$	−9292.00	−0.402326	−0.201163	+	0.979558i	$0.564472\pi$
$812$	−9024.00	−0.390000
$813$	−9732.00	−0.419823
$814$	9552.00	0.411299
$815$	0	0
$816$	2016.00	0.0864879
$817$	−3952.00	−0.169233
$818$	−12244.0	−0.523351
$819$	936.000	0.0399347
$820$	0	0
$821$	40338.0	1.71475	0.857373	−	0.514696i	$-0.172095\pi$
$821$	40338.0	1.71475	0.857373	+	0.514696i	$0.172095\pi$
$822$	3204.00	0.135952
$823$	33352.0	1.41261	0.706305	−	0.707908i	$-0.250361\pi$
$823$	33352.0	1.41261	0.706305	+	0.707908i	$0.250361\pi$
$824$	1984.00	0.0838785
$825$	0	0
$826$	−2496.00	−0.105142
$827$	−35076.0	−1.47486	−0.737432	−	0.675422i	$-0.763962\pi$
$827$	−35076.0	−1.47486	−0.737432	+	0.675422i	$0.763962\pi$
$828$	−4752.00	−0.199449
$829$	32678.0	1.36906	0.684532	−	0.728983i	$-0.260007\pi$
$829$	32678.0	1.36906	0.684532	+	0.728983i	$0.260007\pi$
$830$	0	0
$831$	22998.0	0.960038
$832$	−832.000	−0.0346688
$833$	−11718.0	−0.487401
$834$	10536.0	0.437448
$835$	0	0
$836$	−2496.00	−0.103261
$837$	3132.00	0.129340
$838$	26112.0	1.07640
$839$	11424.0	0.470084	0.235042	−	0.971985i	$-0.424477\pi$
$839$	11424.0	0.470084	0.235042	+	0.971985i	$0.424477\pi$
$840$	0	0
$841$	55135.0	2.26065
$842$	15164.0	0.620648
$843$	−4374.00	−0.178705
$844$	6128.00	0.249922
$845$	0	0
$846$	8208.00	0.333566
$847$	9496.00	0.385226
$848$	−2400.00	−0.0971891
$849$	−564.000	−0.0227991
$850$	0	0
$851$	52536.0	2.11623
$852$	4896.00	0.196871
$853$	−15374.0	−0.617111	−0.308556	−	0.951206i	$-0.599846\pi$
$853$	−15374.0	−0.617111	−0.308556	+	0.951206i	$0.599846\pi$
$854$	3680.00	0.147456
$855$	0	0
$856$	8352.00	0.333488
$857$	17010.0	0.678005	0.339003	−	0.940785i	$-0.389910\pi$
$857$	17010.0	0.678005	0.339003	+	0.940785i	$0.389910\pi$
$858$	936.000	0.0372430
$859$	−19516.0	−0.775177	−0.387589	−	0.921832i	$-0.626692\pi$
$859$	−19516.0	−0.775177	−0.387589	+	0.921832i	$0.626692\pi$
$860$	0	0
$861$	−4176.00	−0.165293
$862$	7776.00	0.307252
$863$	672.000	0.0265065	0.0132533	−	0.999912i	$-0.495781\pi$
$863$	672.000	0.0265065	0.0132533	+	0.999912i	$0.495781\pi$
$864$	−864.000	−0.0340207
$865$	0	0
$866$	−5420.00	−0.212678
$867$	−9447.00	−0.370054
$868$	−3712.00	−0.145154
$869$	8736.00	0.341022
$870$	0	0
$871$	−7696.00	−0.299390
$872$	10736.0	0.416934
$873$	−15678.0	−0.607812
$874$	−13728.0	−0.531300
$875$	0	0
$876$	8760.00	0.337869
$877$	−35390.0	−1.36264	−0.681320	−	0.731986i	$-0.738594\pi$
$877$	−35390.0	−1.36264	−0.681320	+	0.731986i	$0.738594\pi$
$878$	−12016.0	−0.461868
$879$	−11214.0	−0.430306
$880$	0	0
$881$	−10206.0	−0.390294	−0.195147	−	0.980774i	$-0.562518\pi$
$881$	−10206.0	−0.390294	−0.195147	+	0.980774i	$0.562518\pi$
$882$	5022.00	0.191723
$883$	−21884.0	−0.834038	−0.417019	−	0.908898i	$-0.636925\pi$
$883$	−21884.0	−0.834038	−0.417019	+	0.908898i	$0.636925\pi$
$884$	−2184.00	−0.0830949
$885$	0	0
$886$	27768.0	1.05292
$887$	−9588.00	−0.362946	−0.181473	−	0.983396i	$-0.558087\pi$
$887$	−9588.00	−0.362946	−0.181473	+	0.983396i	$0.558087\pi$
$888$	9552.00	0.360973
$889$	−8768.00	−0.330787
$890$	0	0
$891$	972.000	0.0365468
$892$	23392.0	0.878052
$893$	23712.0	0.888569
$894$	−4140.00	−0.154880
$895$	0	0
$896$	1024.00	0.0381802
$897$	5148.00	0.191624
$898$	17412.0	0.647045
$899$	32712.0	1.21358
$900$	0	0
$901$	−6300.00	−0.232945
$902$	−4176.00	−0.154153
$903$	−1824.00	−0.0672192
$904$	−1488.00	−0.0547457
$905$	0	0
$906$	−1848.00	−0.0677657
$907$	27124.0	0.992985	0.496493	−	0.868041i	$-0.334621\pi$
$907$	27124.0	0.992985	0.496493	+	0.868041i	$0.334621\pi$
$908$	−19536.0	−0.714014
$909$	−4806.00	−0.175363
$910$	0	0
$911$	3168.00	0.115215	0.0576073	−	0.998339i	$-0.481653\pi$
$911$	3168.00	0.115215	0.0576073	+	0.998339i	$0.481653\pi$
$912$	−2496.00	−0.0906259
$913$	−432.000	−0.0156595
$914$	10156.0	0.367539
$915$	0	0
$916$	−21016.0	−0.758066
$917$	9600.00	0.345714
$918$	−2268.00	−0.0815416
$919$	19784.0	0.710135	0.355067	−	0.934841i	$-0.384458\pi$
$919$	19784.0	0.710135	0.355067	+	0.934841i	$0.384458\pi$
$920$	0	0
$921$	−24648.0	−0.881845
$922$	29868.0	1.06687
$923$	−5304.00	−0.189148
$924$	−1152.00	−0.0410152
$925$	0	0
$926$	−6896.00	−0.244726
$927$	−2232.00	−0.0790814
$928$	−9024.00	−0.319210
$929$	32454.0	1.14616	0.573079	−	0.819500i	$-0.305749\pi$
$929$	32454.0	1.14616	0.573079	+	0.819500i	$0.305749\pi$
$930$	0	0
$931$	14508.0	0.510720
$932$	−9432.00	−0.331497
$933$	18864.0	0.661929
$934$	−20664.0	−0.723926
$935$	0	0
$936$	936.000	0.0326860
$937$	34198.0	1.19232	0.596158	−	0.802867i	$-0.296693\pi$
$937$	34198.0	1.19232	0.596158	+	0.802867i	$0.296693\pi$
$938$	9472.00	0.329714
$939$	7338.00	0.255023
$940$	0	0
$941$	6090.00	0.210976	0.105488	−	0.994421i	$-0.466360\pi$
$941$	6090.00	0.210976	0.105488	+	0.994421i	$0.466360\pi$
$942$	−2940.00	−0.101688
$943$	−22968.0	−0.793151
$944$	−2496.00	−0.0860571
$945$	0	0
$946$	−1824.00	−0.0626885
$947$	−12324.0	−0.422889	−0.211445	−	0.977390i	$-0.567817\pi$
$947$	−12324.0	−0.422889	−0.211445	+	0.977390i	$0.567817\pi$
$948$	8736.00	0.299295
$949$	−9490.00	−0.324614
$950$	0	0
$951$	16290.0	0.555457
$952$	2688.00	0.0915111
$953$	5034.00	0.171109	0.0855547	−	0.996333i	$-0.472734\pi$
$953$	5034.00	0.171109	0.0855547	+	0.996333i	$0.472734\pi$
$954$	2700.00	0.0916307
$955$	0	0
$956$	−9312.00	−0.315033
$957$	10152.0	0.342913
$958$	4656.00	0.157024
$959$	4272.00	0.143848
$960$	0	0
$961$	−16335.0	−0.548320
$962$	−10348.0	−0.346812
$963$	−9396.00	−0.314415
$964$	−14680.0	−0.490468
$965$	0	0
$966$	−6336.00	−0.211033
$967$	21256.0	0.706874	0.353437	−	0.935458i	$-0.385013\pi$
$967$	21256.0	0.706874	0.353437	+	0.935458i	$0.385013\pi$
$968$	9496.00	0.315303
$969$	−6552.00	−0.217214
$970$	0	0
$971$	11832.0	0.391047	0.195524	−	0.980699i	$-0.437359\pi$
$971$	11832.0	0.391047	0.195524	+	0.980699i	$0.437359\pi$
$972$	972.000	0.0320750
$973$	14048.0	0.462855
$974$	26320.0	0.865860
$975$	0	0
$976$	3680.00	0.120691
$977$	34386.0	1.12600	0.563002	−	0.826456i	$-0.309646\pi$
$977$	34386.0	1.12600	0.563002	+	0.826456i	$0.309646\pi$
$978$	−5712.00	−0.186758
$979$	−17784.0	−0.580571
$980$	0	0
$981$	−12078.0	−0.393090
$982$	−17376.0	−0.564654
$983$	−10752.0	−0.348866	−0.174433	−	0.984669i	$-0.555809\pi$
$983$	−10752.0	−0.348866	−0.174433	+	0.984669i	$0.555809\pi$
$984$	−4176.00	−0.135291
$985$	0	0
$986$	−23688.0	−0.765091
$987$	10944.0	0.352940
$988$	2704.00	0.0870705
$989$	−10032.0	−0.322547
$990$	0	0
$991$	32672.0	1.04729	0.523643	−	0.851938i	$-0.324573\pi$
$991$	32672.0	1.04729	0.523643	+	0.851938i	$0.324573\pi$
$992$	−3712.00	−0.118807
$993$	4884.00	0.156082
$994$	6528.00	0.208305
$995$	0	0
$996$	−432.000	−0.0137434
$997$	34.0000	0.00108003	0.000540015	−	1.00000i	$-0.499828\pi$
$997$	34.0000	0.00108003	0.000540015		1.00000i	$0.499828\pi$
$998$	30920.0	0.980717
$999$	−10746.0	−0.340329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.4.a.e.1.1		1
5.4	even	2		390.4.a.i.1.1	✓	1
15.14	odd	2		1170.4.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.4.a.i.1.1	✓	1	5.4	even	2
1170.4.a.g.1.1		1	15.14	odd	2
1950.4.a.e.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1950.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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