LMFDB - Embedded newform 1450.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(1,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.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:	$11.5783082931$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} -3.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} +2.00000 q^{18} -7.00000 q^{19} -4.00000 q^{21} +3.00000 q^{22} -6.00000 q^{23} +1.00000 q^{24} -4.00000 q^{26} +5.00000 q^{27} +4.00000 q^{28} -1.00000 q^{29} +2.00000 q^{31} -1.00000 q^{32} +3.00000 q^{33} +3.00000 q^{34} -2.00000 q^{36} +10.0000 q^{37} +7.00000 q^{38} -4.00000 q^{39} -9.00000 q^{41} +4.00000 q^{42} -8.00000 q^{43} -3.00000 q^{44} +6.00000 q^{46} +6.00000 q^{47} -1.00000 q^{48} +9.00000 q^{49} +3.00000 q^{51} +4.00000 q^{52} -12.0000 q^{53} -5.00000 q^{54} -4.00000 q^{56} +7.00000 q^{57} +1.00000 q^{58} +12.0000 q^{59} -10.0000 q^{61} -2.00000 q^{62} -8.00000 q^{63} +1.00000 q^{64} -3.00000 q^{66} -5.00000 q^{67} -3.00000 q^{68} +6.00000 q^{69} +6.00000 q^{71} +2.00000 q^{72} +7.00000 q^{73} -10.0000 q^{74} -7.00000 q^{76} -12.0000 q^{77} +4.00000 q^{78} -16.0000 q^{79} +1.00000 q^{81} +9.00000 q^{82} -9.00000 q^{83} -4.00000 q^{84} +8.00000 q^{86} +1.00000 q^{87} +3.00000 q^{88} -3.00000 q^{89} +16.0000 q^{91} -6.00000 q^{92} -2.00000 q^{93} -6.00000 q^{94} +1.00000 q^{96} -2.00000 q^{97} -9.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	−1.00000	−0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−4.00000	−1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	2.00000	0.471405
$19$	−7.00000	−1.60591	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000	−1.60591	−0.802955	+	0.596040i	$0.796740\pi$
$20$	0	0
$21$	−4.00000	−0.872872
$22$	3.00000	0.639602
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−4.00000	−0.784465
$27$	5.00000	0.962250
$28$	4.00000	0.755929
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000	−0.176777
$33$	3.00000	0.522233
$34$	3.00000	0.514496
$35$	0	0
$36$	−2.00000	−0.333333
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	7.00000	1.13555
$39$	−4.00000	−0.640513
$40$	0	0
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	4.00000	0.617213
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−3.00000	−0.452267
$45$	0	0
$46$	6.00000	0.884652
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	−1.00000	−0.144338
$49$	9.00000	1.28571
$50$	0	0
$51$	3.00000	0.420084
$52$	4.00000	0.554700
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	−4.00000	−0.534522
$57$	7.00000	0.927173
$58$	1.00000	0.131306
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−2.00000	−0.254000
$63$	−8.00000	−1.00791
$64$	1.00000	0.125000
$65$	0	0
$66$	−3.00000	−0.369274
$67$	−5.00000	−0.610847	−0.305424	−	0.952217i	$-0.598798\pi$
$67$	−5.00000	−0.610847	−0.305424	+	0.952217i	$0.598798\pi$
$68$	−3.00000	−0.363803
$69$	6.00000	0.722315
$70$	0	0
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	2.00000	0.235702
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	−10.0000	−1.16248
$75$	0	0
$76$	−7.00000	−0.802955
$77$	−12.0000	−1.36753
$78$	4.00000	0.452911
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	9.00000	0.993884
$83$	−9.00000	−0.987878	−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000	−0.987878	−0.493939	+	0.869496i	$0.664443\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	8.00000	0.862662
$87$	1.00000	0.107211
$88$	3.00000	0.319801
$89$	−3.00000	−0.317999	−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000	−0.317999	−0.159000	+	0.987279i	$0.550827\pi$
$90$	0	0
$91$	16.0000	1.67726
$92$	−6.00000	−0.625543
$93$	−2.00000	−0.207390
$94$	−6.00000	−0.618853
$95$	0	0
$96$	1.00000	0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−9.00000	−0.909137
$99$	6.00000	0.603023
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	−3.00000	−0.297044
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	12.0000	1.16554
$107$	−3.00000	−0.290021	−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000	−0.290021	−0.145010	+	0.989430i	$0.546322\pi$
$108$	5.00000	0.481125
$109$	−4.00000	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$110$	0	0
$111$	−10.0000	−0.949158
$112$	4.00000	0.377964
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	−7.00000	−0.655610
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	−8.00000	−0.739600
$118$	−12.0000	−1.10469
$119$	−12.0000	−1.10004
$120$	0	0
$121$	−2.00000	−0.181818
$122$	10.0000	0.905357
$123$	9.00000	0.811503
$124$	2.00000	0.179605
$125$	0	0
$126$	8.00000	0.712697
$127$	−20.0000	−1.77471	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000	−1.77471	−0.887357	+	0.461084i	$0.847461\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	0	0
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	3.00000	0.261116
$133$	−28.0000	−2.42791
$134$	5.00000	0.431934
$135$	0	0
$136$	3.00000	0.257248
$137$	21.0000	1.79415	0.897076	−	0.441877i	$-0.145687\pi$
$137$	21.0000	1.79415	0.897076	+	0.441877i	$0.145687\pi$
$138$	−6.00000	−0.510754
$139$	−13.0000	−1.10265	−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000	−1.10265	−0.551323	+	0.834292i	$0.685877\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	−6.00000	−0.503509
$143$	−12.0000	−1.00349
$144$	−2.00000	−0.166667
$145$	0	0
$146$	−7.00000	−0.579324
$147$	−9.00000	−0.742307
$148$	10.0000	0.821995
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	7.00000	0.567775
$153$	6.00000	0.485071
$154$	12.0000	0.966988
$155$	0	0
$156$	−4.00000	−0.320256
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	16.0000	1.27289
$159$	12.0000	0.951662
$160$	0	0
$161$	−24.0000	−1.89146
$162$	−1.00000	−0.0785674
$163$	−11.0000	−0.861586	−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000	−0.861586	−0.430793	+	0.902451i	$0.641766\pi$
$164$	−9.00000	−0.702782
$165$	0	0
$166$	9.00000	0.698535
$167$	−6.00000	−0.464294	−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000	−0.464294	−0.232147	+	0.972681i	$0.574575\pi$
$168$	4.00000	0.308607
$169$	3.00000	0.230769
$170$	0	0
$171$	14.0000	1.07061
$172$	−8.00000	−0.609994
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	−1.00000	−0.0758098
$175$	0	0
$176$	−3.00000	−0.226134
$177$	−12.0000	−0.901975
$178$	3.00000	0.224860
$179$	15.0000	1.12115	0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$180$	0	0
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	−16.0000	−1.18600
$183$	10.0000	0.739221
$184$	6.00000	0.442326
$185$	0	0
$186$	2.00000	0.146647
$187$	9.00000	0.658145
$188$	6.00000	0.437595
$189$	20.0000	1.45479
$190$	0	0
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	−1.00000	−0.0721688
$193$	25.0000	1.79954	0.899770	−	0.436365i	$-0.143734\pi$
$193$	25.0000	1.79954	0.899770	+	0.436365i	$0.143734\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	9.00000	0.642857
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	−6.00000	−0.426401
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	5.00000	0.352673
$202$	0	0
$203$	−4.00000	−0.280745
$204$	3.00000	0.210042
$205$	0	0
$206$	−4.00000	−0.278693
$207$	12.0000	0.834058
$208$	4.00000	0.277350
$209$	21.0000	1.45260
$210$	0	0
$211$	−13.0000	−0.894957	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000	−0.894957	−0.447478	+	0.894295i	$0.647678\pi$
$212$	−12.0000	−0.824163
$213$	−6.00000	−0.411113
$214$	3.00000	0.205076
$215$	0	0
$216$	−5.00000	−0.340207
$217$	8.00000	0.543075
$218$	4.00000	0.270914
$219$	−7.00000	−0.473016
$220$	0	0
$221$	−12.0000	−0.807207
$222$	10.0000	0.671156
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	−4.00000	−0.267261
$225$	0	0
$226$	9.00000	0.598671
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	7.00000	0.463586
$229$	−4.00000	−0.264327	−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000	−0.264327	−0.132164	+	0.991228i	$0.542192\pi$
$230$	0	0
$231$	12.0000	0.789542
$232$	1.00000	0.0656532
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	8.00000	0.522976
$235$	0	0
$236$	12.0000	0.781133
$237$	16.0000	1.03931
$238$	12.0000	0.777844
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	17.0000	1.09507	0.547533	−	0.836784i	$-0.315567\pi$
$241$	17.0000	1.09507	0.547533	+	0.836784i	$0.315567\pi$
$242$	2.00000	0.128565
$243$	−16.0000	−1.02640
$244$	−10.0000	−0.640184
$245$	0	0
$246$	−9.00000	−0.573819
$247$	−28.0000	−1.78160
$248$	−2.00000	−0.127000
$249$	9.00000	0.570352
$250$	0	0
$251$	−9.00000	−0.568075	−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000	−0.568075	−0.284037	+	0.958813i	$0.591674\pi$
$252$	−8.00000	−0.503953
$253$	18.0000	1.13165
$254$	20.0000	1.25491
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	−8.00000	−0.498058
$259$	40.0000	2.48548
$260$	0	0
$261$	2.00000	0.123797
$262$	12.0000	0.741362
$263$	18.0000	1.10993	0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000	1.10993	0.554964	+	0.831875i	$0.312732\pi$
$264$	−3.00000	−0.184637
$265$	0	0
$266$	28.0000	1.71679
$267$	3.00000	0.183597
$268$	−5.00000	−0.305424
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	−10.0000	−0.607457	−0.303728	−	0.952759i	$-0.598232\pi$
$271$	−10.0000	−0.607457	−0.303728	+	0.952759i	$0.598232\pi$
$272$	−3.00000	−0.181902
$273$	−16.0000	−0.968364
$274$	−21.0000	−1.26866
$275$	0	0
$276$	6.00000	0.361158
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	13.0000	0.779688
$279$	−4.00000	−0.239474
$280$	0	0
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	6.00000	0.357295
$283$	−29.0000	−1.72387	−0.861936	−	0.507018i	$-0.830748\pi$
$283$	−29.0000	−1.72387	−0.861936	+	0.507018i	$0.830748\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	12.0000	0.709575
$287$	−36.0000	−2.12501
$288$	2.00000	0.117851
$289$	−8.00000	−0.470588
$290$	0	0
$291$	2.00000	0.117242
$292$	7.00000	0.409644
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	9.00000	0.524891
$295$	0	0
$296$	−10.0000	−0.581238
$297$	−15.0000	−0.870388
$298$	18.0000	1.04271
$299$	−24.0000	−1.38796
$300$	0	0
$301$	−32.0000	−1.84445
$302$	4.00000	0.230174
$303$	0	0
$304$	−7.00000	−0.401478
$305$	0	0
$306$	−6.00000	−0.342997
$307$	−29.0000	−1.65512	−0.827559	−	0.561379i	$-0.810271\pi$
$307$	−29.0000	−1.65512	−0.827559	+	0.561379i	$0.810271\pi$
$308$	−12.0000	−0.683763
$309$	−4.00000	−0.227552
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	4.00000	0.226455
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	2.00000	0.112867
$315$	0	0
$316$	−16.0000	−0.900070
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	−12.0000	−0.672927
$319$	3.00000	0.167968
$320$	0	0
$321$	3.00000	0.167444
$322$	24.0000	1.33747
$323$	21.0000	1.16847
$324$	1.00000	0.0555556
$325$	0	0
$326$	11.0000	0.609234
$327$	4.00000	0.221201
$328$	9.00000	0.496942
$329$	24.0000	1.32316
$330$	0	0
$331$	17.0000	0.934405	0.467202	−	0.884150i	$-0.345262\pi$
$331$	17.0000	0.934405	0.467202	+	0.884150i	$0.345262\pi$
$332$	−9.00000	−0.493939
$333$	−20.0000	−1.09599
$334$	6.00000	0.328305
$335$	0	0
$336$	−4.00000	−0.218218
$337$	−5.00000	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$338$	−3.00000	−0.163178
$339$	9.00000	0.488813
$340$	0	0
$341$	−6.00000	−0.324918
$342$	−14.0000	−0.757033
$343$	8.00000	0.431959
$344$	8.00000	0.431331
$345$	0	0
$346$	−6.00000	−0.322562
$347$	9.00000	0.483145	0.241573	−	0.970383i	$-0.422337\pi$
$347$	9.00000	0.483145	0.241573	+	0.970383i	$0.422337\pi$
$348$	1.00000	0.0536056
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	0	0
$351$	20.0000	1.06752
$352$	3.00000	0.159901
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	12.0000	0.637793
$355$	0	0
$356$	−3.00000	−0.159000
$357$	12.0000	0.635107
$358$	−15.0000	−0.792775
$359$	6.00000	0.316668	0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000	0.316668	0.158334	+	0.987386i	$0.449388\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	−20.0000	−1.05118
$363$	2.00000	0.104973
$364$	16.0000	0.838628
$365$	0	0
$366$	−10.0000	−0.522708
$367$	10.0000	0.521996	0.260998	−	0.965339i	$-0.415948\pi$
$367$	10.0000	0.521996	0.260998	+	0.965339i	$0.415948\pi$
$368$	−6.00000	−0.312772
$369$	18.0000	0.937043
$370$	0	0
$371$	−48.0000	−2.49204
$372$	−2.00000	−0.103695
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	−9.00000	−0.465379
$375$	0	0
$376$	−6.00000	−0.309426
$377$	−4.00000	−0.206010
$378$	−20.0000	−1.02869
$379$	11.0000	0.565032	0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000	0.565032	0.282516	+	0.959263i	$0.408831\pi$
$380$	0	0
$381$	20.0000	1.02463
$382$	6.00000	0.306987
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−25.0000	−1.27247
$387$	16.0000	0.813326
$388$	−2.00000	−0.101535
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	18.0000	0.910299
$392$	−9.00000	−0.454569
$393$	12.0000	0.605320
$394$	12.0000	0.604551
$395$	0	0
$396$	6.00000	0.301511
$397$	16.0000	0.803017	0.401508	−	0.915855i	$-0.368486\pi$
$397$	16.0000	0.803017	0.401508	+	0.915855i	$0.368486\pi$
$398$	16.0000	0.802008
$399$	28.0000	1.40175
$400$	0	0
$401$	21.0000	1.04869	0.524345	−	0.851506i	$-0.324310\pi$
$401$	21.0000	1.04869	0.524345	+	0.851506i	$0.324310\pi$
$402$	−5.00000	−0.249377
$403$	8.00000	0.398508
$404$	0	0
$405$	0	0
$406$	4.00000	0.198517
$407$	−30.0000	−1.48704
$408$	−3.00000	−0.148522
$409$	23.0000	1.13728	0.568638	−	0.822588i	$-0.307470\pi$
$409$	23.0000	1.13728	0.568638	+	0.822588i	$0.307470\pi$
$410$	0	0
$411$	−21.0000	−1.03585
$412$	4.00000	0.197066
$413$	48.0000	2.36193
$414$	−12.0000	−0.589768
$415$	0	0
$416$	−4.00000	−0.196116
$417$	13.0000	0.636613
$418$	−21.0000	−1.02714
$419$	−21.0000	−1.02592	−0.512959	−	0.858413i	$-0.671451\pi$
$419$	−21.0000	−1.02592	−0.512959	+	0.858413i	$0.671451\pi$
$420$	0	0
$421$	−40.0000	−1.94948	−0.974740	−	0.223341i	$-0.928304\pi$
$421$	−40.0000	−1.94948	−0.974740	+	0.223341i	$0.928304\pi$
$422$	13.0000	0.632830
$423$	−12.0000	−0.583460
$424$	12.0000	0.582772
$425$	0	0
$426$	6.00000	0.290701
$427$	−40.0000	−1.93574
$428$	−3.00000	−0.145010
$429$	12.0000	0.579365
$430$	0	0
$431$	−30.0000	−1.44505	−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000	−1.44505	−0.722525	+	0.691345i	$0.757018\pi$
$432$	5.00000	0.240563
$433$	13.0000	0.624740	0.312370	−	0.949960i	$-0.398877\pi$
$433$	13.0000	0.624740	0.312370	+	0.949960i	$0.398877\pi$
$434$	−8.00000	−0.384012
$435$	0	0
$436$	−4.00000	−0.191565
$437$	42.0000	2.00913
$438$	7.00000	0.334473
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	0	0
$441$	−18.0000	−0.857143
$442$	12.0000	0.570782
$443$	−15.0000	−0.712672	−0.356336	−	0.934358i	$-0.615974\pi$
$443$	−15.0000	−0.712672	−0.356336	+	0.934358i	$0.615974\pi$
$444$	−10.0000	−0.474579
$445$	0	0
$446$	−16.0000	−0.757622
$447$	18.0000	0.851371
$448$	4.00000	0.188982
$449$	27.0000	1.27421	0.637104	−	0.770778i	$-0.280132\pi$
$449$	27.0000	1.27421	0.637104	+	0.770778i	$0.280132\pi$
$450$	0	0
$451$	27.0000	1.27138
$452$	−9.00000	−0.423324
$453$	4.00000	0.187936
$454$	−12.0000	−0.563188
$455$	0	0
$456$	−7.00000	−0.327805
$457$	19.0000	0.888783	0.444391	−	0.895833i	$-0.353420\pi$
$457$	19.0000	0.888783	0.444391	+	0.895833i	$0.353420\pi$
$458$	4.00000	0.186908
$459$	−15.0000	−0.700140
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	−12.0000	−0.558291
$463$	10.0000	0.464739	0.232370	−	0.972628i	$-0.425352\pi$
$463$	10.0000	0.464739	0.232370	+	0.972628i	$0.425352\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	−6.00000	−0.277945
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	−8.00000	−0.369800
$469$	−20.0000	−0.923514
$470$	0	0
$471$	2.00000	0.0921551
$472$	−12.0000	−0.552345
$473$	24.0000	1.10352
$474$	−16.0000	−0.734904
$475$	0	0
$476$	−12.0000	−0.550019
$477$	24.0000	1.09888
$478$	6.00000	0.274434
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	0	0
$481$	40.0000	1.82384
$482$	−17.0000	−0.774329
$483$	24.0000	1.09204
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	16.0000	0.725775
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	10.0000	0.452679
$489$	11.0000	0.497437
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	9.00000	0.405751
$493$	3.00000	0.135113
$494$	28.0000	1.25978
$495$	0	0
$496$	2.00000	0.0898027
$497$	24.0000	1.07655
$498$	−9.00000	−0.403300
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	0	0
$501$	6.00000	0.268060
$502$	9.00000	0.401690
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	8.00000	0.356348
$505$	0	0
$506$	−18.0000	−0.800198
$507$	−3.00000	−0.133235
$508$	−20.0000	−0.887357
$509$	24.0000	1.06378	0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000	1.06378	0.531891	+	0.846813i	$0.321482\pi$
$510$	0	0
$511$	28.0000	1.23865
$512$	−1.00000	−0.0441942
$513$	−35.0000	−1.54529
$514$	6.00000	0.264649
$515$	0	0
$516$	8.00000	0.352180
$517$	−18.0000	−0.791639
$518$	−40.0000	−1.75750
$519$	−6.00000	−0.263371
$520$	0	0
$521$	−27.0000	−1.18289	−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000	−1.18289	−0.591446	+	0.806345i	$0.701443\pi$
$522$	−2.00000	−0.0875376
$523$	−11.0000	−0.480996	−0.240498	−	0.970650i	$-0.577311\pi$
$523$	−11.0000	−0.480996	−0.240498	+	0.970650i	$0.577311\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−18.0000	−0.784837
$527$	−6.00000	−0.261364
$528$	3.00000	0.130558
$529$	13.0000	0.565217
$530$	0	0
$531$	−24.0000	−1.04151
$532$	−28.0000	−1.21395
$533$	−36.0000	−1.55933
$534$	−3.00000	−0.129823
$535$	0	0
$536$	5.00000	0.215967
$537$	−15.0000	−0.647298
$538$	6.00000	0.258678
$539$	−27.0000	−1.16297
$540$	0	0
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	10.0000	0.429537
$543$	−20.0000	−0.858282
$544$	3.00000	0.128624
$545$	0	0
$546$	16.0000	0.684737
$547$	−23.0000	−0.983409	−0.491704	−	0.870762i	$-0.663626\pi$
$547$	−23.0000	−0.983409	−0.491704	+	0.870762i	$0.663626\pi$
$548$	21.0000	0.897076
$549$	20.0000	0.853579
$550$	0	0
$551$	7.00000	0.298210
$552$	−6.00000	−0.255377
$553$	−64.0000	−2.72156
$554$	−10.0000	−0.424859
$555$	0	0
$556$	−13.0000	−0.551323
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	4.00000	0.169334
$559$	−32.0000	−1.35346
$560$	0	0
$561$	−9.00000	−0.379980
$562$	−30.0000	−1.26547
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	−6.00000	−0.252646
$565$	0	0
$566$	29.0000	1.21896
$567$	4.00000	0.167984
$568$	−6.00000	−0.251754
$569$	−33.0000	−1.38343	−0.691716	−	0.722170i	$-0.743145\pi$
$569$	−33.0000	−1.38343	−0.691716	+	0.722170i	$0.743145\pi$
$570$	0	0
$571$	44.0000	1.84134	0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000	1.84134	0.920671	+	0.390339i	$0.127642\pi$
$572$	−12.0000	−0.501745
$573$	6.00000	0.250654
$574$	36.0000	1.50261
$575$	0	0
$576$	−2.00000	−0.0833333
$577$	19.0000	0.790980	0.395490	−	0.918470i	$-0.370575\pi$
$577$	19.0000	0.790980	0.395490	+	0.918470i	$0.370575\pi$
$578$	8.00000	0.332756
$579$	−25.0000	−1.03896
$580$	0	0
$581$	−36.0000	−1.49353
$582$	−2.00000	−0.0829027
$583$	36.0000	1.49097
$584$	−7.00000	−0.289662
$585$	0	0
$586$	−24.0000	−0.991431
$587$	−33.0000	−1.36206	−0.681028	−	0.732257i	$-0.738467\pi$
$587$	−33.0000	−1.36206	−0.681028	+	0.732257i	$0.738467\pi$
$588$	−9.00000	−0.371154
$589$	−14.0000	−0.576860
$590$	0	0
$591$	12.0000	0.493614
$592$	10.0000	0.410997
$593$	−3.00000	−0.123195	−0.0615976	−	0.998101i	$-0.519620\pi$
$593$	−3.00000	−0.123195	−0.0615976	+	0.998101i	$0.519620\pi$
$594$	15.0000	0.615457
$595$	0	0
$596$	−18.0000	−0.737309
$597$	16.0000	0.654836
$598$	24.0000	0.981433
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	0	0
$601$	29.0000	1.18293	0.591467	−	0.806329i	$-0.298549\pi$
$601$	29.0000	1.18293	0.591467	+	0.806329i	$0.298549\pi$
$602$	32.0000	1.30422
$603$	10.0000	0.407231
$604$	−4.00000	−0.162758
$605$	0	0
$606$	0	0
$607$	28.0000	1.13648	0.568242	−	0.822861i	$-0.307624\pi$
$607$	28.0000	1.13648	0.568242	+	0.822861i	$0.307624\pi$
$608$	7.00000	0.283887
$609$	4.00000	0.162088
$610$	0	0
$611$	24.0000	0.970936
$612$	6.00000	0.242536
$613$	−20.0000	−0.807792	−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000	−0.807792	−0.403896	+	0.914805i	$0.632344\pi$
$614$	29.0000	1.17034
$615$	0	0
$616$	12.0000	0.483494
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	4.00000	0.160904
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	0	0
$621$	−30.0000	−1.20386
$622$	−18.0000	−0.721734
$623$	−12.0000	−0.480770
$624$	−4.00000	−0.160128
$625$	0	0
$626$	−10.0000	−0.399680
$627$	−21.0000	−0.838659
$628$	−2.00000	−0.0798087
$629$	−30.0000	−1.19618
$630$	0	0
$631$	2.00000	0.0796187	0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000	0.0796187	0.0398094	+	0.999207i	$0.487325\pi$
$632$	16.0000	0.636446
$633$	13.0000	0.516704
$634$	−6.00000	−0.238290
$635$	0	0
$636$	12.0000	0.475831
$637$	36.0000	1.42637
$638$	−3.00000	−0.118771
$639$	−12.0000	−0.474713
$640$	0	0
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	−3.00000	−0.118401
$643$	40.0000	1.57745	0.788723	−	0.614749i	$-0.210743\pi$
$643$	40.0000	1.57745	0.788723	+	0.614749i	$0.210743\pi$
$644$	−24.0000	−0.945732
$645$	0	0
$646$	−21.0000	−0.826234
$647$	−42.0000	−1.65119	−0.825595	−	0.564263i	$-0.809160\pi$
$647$	−42.0000	−1.65119	−0.825595	+	0.564263i	$0.809160\pi$
$648$	−1.00000	−0.0392837
$649$	−36.0000	−1.41312
$650$	0	0
$651$	−8.00000	−0.313545
$652$	−11.0000	−0.430793
$653$	36.0000	1.40879	0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000	1.40879	0.704394	+	0.709809i	$0.251219\pi$
$654$	−4.00000	−0.156412
$655$	0	0
$656$	−9.00000	−0.351391
$657$	−14.0000	−0.546192
$658$	−24.0000	−0.935617
$659$	−33.0000	−1.28550	−0.642749	−	0.766077i	$-0.722206\pi$
$659$	−33.0000	−1.28550	−0.642749	+	0.766077i	$0.722206\pi$
$660$	0	0
$661$	−28.0000	−1.08907	−0.544537	−	0.838737i	$-0.683295\pi$
$661$	−28.0000	−1.08907	−0.544537	+	0.838737i	$0.683295\pi$
$662$	−17.0000	−0.660724
$663$	12.0000	0.466041
$664$	9.00000	0.349268
$665$	0	0
$666$	20.0000	0.774984
$667$	6.00000	0.232321
$668$	−6.00000	−0.232147
$669$	−16.0000	−0.618596
$670$	0	0
$671$	30.0000	1.15814
$672$	4.00000	0.154303
$673$	−2.00000	−0.0770943	−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000	−0.0770943	−0.0385472	+	0.999257i	$0.512273\pi$
$674$	5.00000	0.192593
$675$	0	0
$676$	3.00000	0.115385
$677$	−36.0000	−1.38359	−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000	−1.38359	−0.691796	+	0.722093i	$0.743180\pi$
$678$	−9.00000	−0.345643
$679$	−8.00000	−0.307012
$680$	0	0
$681$	−12.0000	−0.459841
$682$	6.00000	0.229752
$683$	−3.00000	−0.114792	−0.0573959	−	0.998351i	$-0.518280\pi$
$683$	−3.00000	−0.114792	−0.0573959	+	0.998351i	$0.518280\pi$
$684$	14.0000	0.535303
$685$	0	0
$686$	−8.00000	−0.305441
$687$	4.00000	0.152610
$688$	−8.00000	−0.304997
$689$	−48.0000	−1.82865
$690$	0	0
$691$	−1.00000	−0.0380418	−0.0190209	−	0.999819i	$-0.506055\pi$
$691$	−1.00000	−0.0380418	−0.0190209	+	0.999819i	$0.506055\pi$
$692$	6.00000	0.228086
$693$	24.0000	0.911685
$694$	−9.00000	−0.341635
$695$	0	0
$696$	−1.00000	−0.0379049
$697$	27.0000	1.02270
$698$	−2.00000	−0.0757011
$699$	−6.00000	−0.226941
$700$	0	0
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	−20.0000	−0.754851
$703$	−70.0000	−2.64010
$704$	−3.00000	−0.113067
$705$	0	0
$706$	−18.0000	−0.677439
$707$	0	0
$708$	−12.0000	−0.450988
$709$	−46.0000	−1.72757	−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000	−1.72757	−0.863783	+	0.503864i	$0.831911\pi$
$710$	0	0
$711$	32.0000	1.20009
$712$	3.00000	0.112430
$713$	−12.0000	−0.449404
$714$	−12.0000	−0.449089
$715$	0	0
$716$	15.0000	0.560576
$717$	6.00000	0.224074
$718$	−6.00000	−0.223918
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	16.0000	0.595871
$722$	−30.0000	−1.11648
$723$	−17.0000	−0.632237
$724$	20.0000	0.743294
$725$	0	0
$726$	−2.00000	−0.0742270
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	−16.0000	−0.592999
$729$	13.0000	0.481481
$730$	0	0
$731$	24.0000	0.887672
$732$	10.0000	0.369611
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	−10.0000	−0.369107
$735$	0	0
$736$	6.00000	0.221163
$737$	15.0000	0.552532
$738$	−18.0000	−0.662589
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	0	0
$741$	28.0000	1.02861
$742$	48.0000	1.76214
$743$	18.0000	0.660356	0.330178	−	0.943919i	$-0.392891\pi$
$743$	18.0000	0.660356	0.330178	+	0.943919i	$0.392891\pi$
$744$	2.00000	0.0733236
$745$	0	0
$746$	14.0000	0.512576
$747$	18.0000	0.658586
$748$	9.00000	0.329073
$749$	−12.0000	−0.438470
$750$	0	0
$751$	26.0000	0.948753	0.474377	−	0.880322i	$-0.342673\pi$
$751$	26.0000	0.948753	0.474377	+	0.880322i	$0.342673\pi$
$752$	6.00000	0.218797
$753$	9.00000	0.327978
$754$	4.00000	0.145671
$755$	0	0
$756$	20.0000	0.727393
$757$	28.0000	1.01768	0.508839	−	0.860862i	$-0.330075\pi$
$757$	28.0000	1.01768	0.508839	+	0.860862i	$0.330075\pi$
$758$	−11.0000	−0.399538
$759$	−18.0000	−0.653359
$760$	0	0
$761$	−39.0000	−1.41375	−0.706874	−	0.707339i	$-0.749895\pi$
$761$	−39.0000	−1.41375	−0.706874	+	0.707339i	$0.749895\pi$
$762$	−20.0000	−0.724524
$763$	−16.0000	−0.579239
$764$	−6.00000	−0.217072
$765$	0	0
$766$	12.0000	0.433578
$767$	48.0000	1.73318
$768$	−1.00000	−0.0360844
$769$	23.0000	0.829401	0.414701	−	0.909958i	$-0.363886\pi$
$769$	23.0000	0.829401	0.414701	+	0.909958i	$0.363886\pi$
$770$	0	0
$771$	6.00000	0.216085
$772$	25.0000	0.899770
$773$	54.0000	1.94225	0.971123	−	0.238581i	$-0.0766824\pi$
$773$	54.0000	1.94225	0.971123	+	0.238581i	$0.0766824\pi$
$774$	−16.0000	−0.575108
$775$	0	0
$776$	2.00000	0.0717958
$777$	−40.0000	−1.43499
$778$	−6.00000	−0.215110
$779$	63.0000	2.25721
$780$	0	0
$781$	−18.0000	−0.644091
$782$	−18.0000	−0.643679
$783$	−5.00000	−0.178685
$784$	9.00000	0.321429
$785$	0	0
$786$	−12.0000	−0.428026
$787$	4.00000	0.142585	0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000	0.142585	0.0712923	+	0.997455i	$0.477288\pi$
$788$	−12.0000	−0.427482
$789$	−18.0000	−0.640817
$790$	0	0
$791$	−36.0000	−1.28001
$792$	−6.00000	−0.213201
$793$	−40.0000	−1.42044
$794$	−16.0000	−0.567819
$795$	0	0
$796$	−16.0000	−0.567105
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	−28.0000	−0.991189
$799$	−18.0000	−0.636794
$800$	0	0
$801$	6.00000	0.212000
$802$	−21.0000	−0.741536
$803$	−21.0000	−0.741074
$804$	5.00000	0.176336
$805$	0	0
$806$	−8.00000	−0.281788
$807$	6.00000	0.211210
$808$	0	0
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	0	0
$811$	44.0000	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$812$	−4.00000	−0.140372
$813$	10.0000	0.350715
$814$	30.0000	1.05150
$815$	0	0
$816$	3.00000	0.105021
$817$	56.0000	1.95919
$818$	−23.0000	−0.804176
$819$	−32.0000	−1.11817
$820$	0	0
$821$	−18.0000	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$822$	21.0000	0.732459
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	−48.0000	−1.67013
$827$	45.0000	1.56480	0.782402	−	0.622774i	$-0.213994\pi$
$827$	45.0000	1.56480	0.782402	+	0.622774i	$0.213994\pi$
$828$	12.0000	0.417029
$829$	−10.0000	−0.347314	−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000	−0.347314	−0.173657	+	0.984806i	$0.555558\pi$
$830$	0	0
$831$	−10.0000	−0.346896
$832$	4.00000	0.138675
$833$	−27.0000	−0.935495
$834$	−13.0000	−0.450153
$835$	0	0
$836$	21.0000	0.726300
$837$	10.0000	0.345651
$838$	21.0000	0.725433
$839$	−12.0000	−0.414286	−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000	−0.414286	−0.207143	+	0.978311i	$0.566417\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	40.0000	1.37849
$843$	−30.0000	−1.03325
$844$	−13.0000	−0.447478
$845$	0	0
$846$	12.0000	0.412568
$847$	−8.00000	−0.274883
$848$	−12.0000	−0.412082
$849$	29.0000	0.995277
$850$	0	0
$851$	−60.0000	−2.05677
$852$	−6.00000	−0.205557
$853$	28.0000	0.958702	0.479351	−	0.877623i	$-0.340872\pi$
$853$	28.0000	0.958702	0.479351	+	0.877623i	$0.340872\pi$
$854$	40.0000	1.36877
$855$	0	0
$856$	3.00000	0.102538
$857$	3.00000	0.102478	0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000	0.102478	0.0512390	+	0.998686i	$0.483683\pi$
$858$	−12.0000	−0.409673
$859$	41.0000	1.39890	0.699451	−	0.714681i	$-0.253428\pi$
$859$	41.0000	1.39890	0.699451	+	0.714681i	$0.253428\pi$
$860$	0	0
$861$	36.0000	1.22688
$862$	30.0000	1.02180
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	−13.0000	−0.441758
$867$	8.00000	0.271694
$868$	8.00000	0.271538
$869$	48.0000	1.62829
$870$	0	0
$871$	−20.0000	−0.677674
$872$	4.00000	0.135457
$873$	4.00000	0.135379
$874$	−42.0000	−1.42067
$875$	0	0
$876$	−7.00000	−0.236508
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	−8.00000	−0.269987
$879$	−24.0000	−0.809500
$880$	0	0
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	18.0000	0.606092
$883$	13.0000	0.437485	0.218742	−	0.975783i	$-0.429805\pi$
$883$	13.0000	0.437485	0.218742	+	0.975783i	$0.429805\pi$
$884$	−12.0000	−0.403604
$885$	0	0
$886$	15.0000	0.503935
$887$	−6.00000	−0.201460	−0.100730	−	0.994914i	$-0.532118\pi$
$887$	−6.00000	−0.201460	−0.100730	+	0.994914i	$0.532118\pi$
$888$	10.0000	0.335578
$889$	−80.0000	−2.68311
$890$	0	0
$891$	−3.00000	−0.100504
$892$	16.0000	0.535720
$893$	−42.0000	−1.40548
$894$	−18.0000	−0.602010
$895$	0	0
$896$	−4.00000	−0.133631
$897$	24.0000	0.801337
$898$	−27.0000	−0.901002
$899$	−2.00000	−0.0667037
$900$	0	0
$901$	36.0000	1.19933
$902$	−27.0000	−0.899002
$903$	32.0000	1.06489
$904$	9.00000	0.299336
$905$	0	0
$906$	−4.00000	−0.132891
$907$	−44.0000	−1.46100	−0.730498	−	0.682915i	$-0.760712\pi$
$907$	−44.0000	−1.46100	−0.730498	+	0.682915i	$0.760712\pi$
$908$	12.0000	0.398234
$909$	0	0
$910$	0	0
$911$	42.0000	1.39152	0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000	1.39152	0.695761	+	0.718273i	$0.255067\pi$
$912$	7.00000	0.231793
$913$	27.0000	0.893570
$914$	−19.0000	−0.628464
$915$	0	0
$916$	−4.00000	−0.132164
$917$	−48.0000	−1.58510
$918$	15.0000	0.495074
$919$	26.0000	0.857661	0.428830	−	0.903385i	$-0.358926\pi$
$919$	26.0000	0.857661	0.428830	+	0.903385i	$0.358926\pi$
$920$	0	0
$921$	29.0000	0.955582
$922$	0	0
$923$	24.0000	0.789970
$924$	12.0000	0.394771
$925$	0	0
$926$	−10.0000	−0.328620
$927$	−8.00000	−0.262754
$928$	1.00000	0.0328266
$929$	−30.0000	−0.984268	−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000	−0.984268	−0.492134	+	0.870519i	$0.663783\pi$
$930$	0	0
$931$	−63.0000	−2.06474
$932$	6.00000	0.196537
$933$	−18.0000	−0.589294
$934$	0	0
$935$	0	0
$936$	8.00000	0.261488
$937$	25.0000	0.816714	0.408357	−	0.912822i	$-0.366102\pi$
$937$	25.0000	0.816714	0.408357	+	0.912822i	$0.366102\pi$
$938$	20.0000	0.653023
$939$	−10.0000	−0.326338
$940$	0	0
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	−2.00000	−0.0651635
$943$	54.0000	1.75848
$944$	12.0000	0.390567
$945$	0	0
$946$	−24.0000	−0.780307
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	16.0000	0.519656
$949$	28.0000	0.908918
$950$	0	0
$951$	−6.00000	−0.194563
$952$	12.0000	0.388922
$953$	39.0000	1.26333	0.631667	−	0.775240i	$-0.282371\pi$
$953$	39.0000	1.26333	0.631667	+	0.775240i	$0.282371\pi$
$954$	−24.0000	−0.777029
$955$	0	0
$956$	−6.00000	−0.194054
$957$	−3.00000	−0.0969762
$958$	18.0000	0.581554
$959$	84.0000	2.71250
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−40.0000	−1.28965
$963$	6.00000	0.193347
$964$	17.0000	0.547533
$965$	0	0
$966$	−24.0000	−0.772187
$967$	−38.0000	−1.22200	−0.610999	−	0.791632i	$-0.709232\pi$
$967$	−38.0000	−1.22200	−0.610999	+	0.791632i	$0.709232\pi$
$968$	2.00000	0.0642824
$969$	−21.0000	−0.674617
$970$	0	0
$971$	−15.0000	−0.481373	−0.240686	−	0.970603i	$-0.577373\pi$
$971$	−15.0000	−0.481373	−0.240686	+	0.970603i	$0.577373\pi$
$972$	−16.0000	−0.513200
$973$	−52.0000	−1.66704
$974$	−16.0000	−0.512673
$975$	0	0
$976$	−10.0000	−0.320092
$977$	−57.0000	−1.82359	−0.911796	−	0.410644i	$-0.865304\pi$
$977$	−57.0000	−1.82359	−0.911796	+	0.410644i	$0.865304\pi$
$978$	−11.0000	−0.351741
$979$	9.00000	0.287641
$980$	0	0
$981$	8.00000	0.255420
$982$	−12.0000	−0.382935
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	−9.00000	−0.286910
$985$	0	0
$986$	−3.00000	−0.0955395
$987$	−24.0000	−0.763928
$988$	−28.0000	−0.890799
$989$	48.0000	1.52631
$990$	0	0
$991$	62.0000	1.96949	0.984747	−	0.173990i	$-0.0556660\pi$
$991$	62.0000	1.96949	0.984747	+	0.173990i	$0.0556660\pi$
$992$	−2.00000	−0.0635001
$993$	−17.0000	−0.539479
$994$	−24.0000	−0.761234
$995$	0	0
$996$	9.00000	0.285176
$997$	−8.00000	−0.253363	−0.126681	−	0.991943i	$-0.540433\pi$
$997$	−8.00000	−0.253363	−0.126681	+	0.991943i	$0.540433\pi$
$998$	4.00000	0.126618
$999$	50.0000	1.58193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.a.a.1.1	✓	1
5.2	odd	4		1450.2.b.e.349.1		2
5.3	odd	4		1450.2.b.e.349.2		2
5.4	even	2		1450.2.a.h.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1450.2.a.a.1.1	✓	1	1.1	even	1	trivial
1450.2.a.h.1.1	yes	1	5.4	even	2
1450.2.b.e.349.1		2	5.2	odd	4
1450.2.b.e.349.2		2	5.3	odd	4

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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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