LMFDB - Embedded newform 4018.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{10} +2.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} -2.00000 q^{18} -1.00000 q^{20} +2.00000 q^{22} +4.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} -4.00000 q^{26} -5.00000 q^{27} -5.00000 q^{29} -1.00000 q^{30} -7.00000 q^{31} +1.00000 q^{32} +2.00000 q^{33} -3.00000 q^{34} -2.00000 q^{36} -2.00000 q^{37} -4.00000 q^{39} -1.00000 q^{40} -1.00000 q^{41} -1.00000 q^{43} +2.00000 q^{44} +2.00000 q^{45} +4.00000 q^{46} +2.00000 q^{47} +1.00000 q^{48} -4.00000 q^{50} -3.00000 q^{51} -4.00000 q^{52} -1.00000 q^{53} -5.00000 q^{54} -2.00000 q^{55} -5.00000 q^{58} -10.0000 q^{59} -1.00000 q^{60} +13.0000 q^{61} -7.00000 q^{62} +1.00000 q^{64} +4.00000 q^{65} +2.00000 q^{66} -2.00000 q^{67} -3.00000 q^{68} +4.00000 q^{69} -3.00000 q^{71} -2.00000 q^{72} -4.00000 q^{73} -2.00000 q^{74} -4.00000 q^{75} -4.00000 q^{78} -15.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -1.00000 q^{82} +6.00000 q^{83} +3.00000 q^{85} -1.00000 q^{86} -5.00000 q^{87} +2.00000 q^{88} +15.0000 q^{89} +2.00000 q^{90} +4.00000 q^{92} -7.00000 q^{93} +2.00000 q^{94} +1.00000 q^{96} +7.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)

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	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	−1.00000	−0.316228
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000	0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	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
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	2.00000	0.426401
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	1.00000	0.204124
$25$	−4.00000	−0.800000
$26$	−4.00000	−0.784465
$27$	−5.00000	−0.962250
$28$	0	0
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	−1.00000	−0.182574
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	1.00000	0.176777
$33$	2.00000	0.348155
$34$	−3.00000	−0.514496
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	0	0
$39$	−4.00000	−0.640513
$40$	−1.00000	−0.158114
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	2.00000	0.301511
$45$	2.00000	0.298142
$46$	4.00000	0.589768
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−4.00000	−0.565685
$51$	−3.00000	−0.420084
$52$	−4.00000	−0.554700
$53$	−1.00000	−0.137361	−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000	−0.137361	−0.0686803	+	0.997639i	$0.521879\pi$
$54$	−5.00000	−0.680414
$55$	−2.00000	−0.269680
$56$	0	0
$57$	0	0
$58$	−5.00000	−0.656532
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	−1.00000	−0.129099
$61$	13.0000	1.66448	0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000	1.66448	0.832240	+	0.554416i	$0.187058\pi$
$62$	−7.00000	−0.889001
$63$	0	0
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	2.00000	0.246183
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	−3.00000	−0.363803
$69$	4.00000	0.481543
$70$	0	0
$71$	−3.00000	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$72$	−2.00000	−0.235702
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	−2.00000	−0.232495
$75$	−4.00000	−0.461880
$76$	0	0
$77$	0	0
$78$	−4.00000	−0.452911
$79$	−15.0000	−1.68763	−0.843816	−	0.536633i	$-0.819696\pi$
$79$	−15.0000	−1.68763	−0.843816	+	0.536633i	$0.819696\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−1.00000	−0.110432
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	3.00000	0.325396
$86$	−1.00000	−0.107833
$87$	−5.00000	−0.536056
$88$	2.00000	0.213201
$89$	15.0000	1.59000	0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000	1.59000	0.794998	+	0.606612i	$0.207472\pi$
$90$	2.00000	0.210819
$91$	0	0
$92$	4.00000	0.417029
$93$	−7.00000	−0.725866
$94$	2.00000	0.206284
$95$	0	0
$96$	1.00000	0.102062
$97$	7.00000	0.710742	0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000	0.710742	0.355371	+	0.934725i	$0.384354\pi$
$98$	0	0
$99$	−4.00000	−0.402015
$100$	−4.00000	−0.400000
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	−3.00000	−0.297044
$103$	1.00000	0.0985329	0.0492665	−	0.998786i	$-0.484312\pi$
$103$	1.00000	0.0985329	0.0492665	+	0.998786i	$0.484312\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	−1.00000	−0.0971286
$107$	−17.0000	−1.64345	−0.821726	−	0.569883i	$-0.806989\pi$
$107$	−17.0000	−1.64345	−0.821726	+	0.569883i	$0.806989\pi$
$108$	−5.00000	−0.481125
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	−2.00000	−0.190693
$111$	−2.00000	−0.189832
$112$	0	0
$113$	9.00000	0.846649	0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000	0.846649	0.423324	+	0.905978i	$0.360863\pi$
$114$	0	0
$115$	−4.00000	−0.373002
$116$	−5.00000	−0.464238
$117$	8.00000	0.739600
$118$	−10.0000	−0.920575
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	−7.00000	−0.636364
$122$	13.0000	1.17696
$123$	−1.00000	−0.0901670
$124$	−7.00000	−0.628619
$125$	9.00000	0.804984
$126$	0	0
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	1.00000	0.0883883
$129$	−1.00000	−0.0880451
$130$	4.00000	0.350823
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	2.00000	0.174078
$133$	0	0
$134$	−2.00000	−0.172774
$135$	5.00000	0.430331
$136$	−3.00000	−0.257248
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	4.00000	0.340503
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	0	0
$141$	2.00000	0.168430
$142$	−3.00000	−0.251754
$143$	−8.00000	−0.668994
$144$	−2.00000	−0.166667
$145$	5.00000	0.415227
$146$	−4.00000	−0.331042
$147$	0	0
$148$	−2.00000	−0.164399
$149$	−5.00000	−0.409616	−0.204808	−	0.978802i	$-0.565657\pi$
$149$	−5.00000	−0.409616	−0.204808	+	0.978802i	$0.565657\pi$
$150$	−4.00000	−0.326599
$151$	7.00000	0.569652	0.284826	−	0.958579i	$-0.408064\pi$
$151$	7.00000	0.569652	0.284826	+	0.958579i	$0.408064\pi$
$152$	0	0
$153$	6.00000	0.485071
$154$	0	0
$155$	7.00000	0.562254
$156$	−4.00000	−0.320256
$157$	12.0000	0.957704	0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000	0.957704	0.478852	+	0.877896i	$0.341053\pi$
$158$	−15.0000	−1.19334
$159$	−1.00000	−0.0793052
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−1.00000	−0.0780869
$165$	−2.00000	−0.155700
$166$	6.00000	0.465690
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	3.00000	0.230089
$171$	0	0
$172$	−1.00000	−0.0762493
$173$	−9.00000	−0.684257	−0.342129	−	0.939653i	$-0.611148\pi$
$173$	−9.00000	−0.684257	−0.342129	+	0.939653i	$0.611148\pi$
$174$	−5.00000	−0.379049
$175$	0	0
$176$	2.00000	0.150756
$177$	−10.0000	−0.751646
$178$	15.0000	1.12430
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	2.00000	0.149071
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	13.0000	0.960988
$184$	4.00000	0.294884
$185$	2.00000	0.147043
$186$	−7.00000	−0.513265
$187$	−6.00000	−0.438763
$188$	2.00000	0.145865
$189$	0	0
$190$	0	0
$191$	17.0000	1.23008	0.615038	−	0.788497i	$-0.289140\pi$
$191$	17.0000	1.23008	0.615038	+	0.788497i	$0.289140\pi$
$192$	1.00000	0.0721688
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	7.00000	0.502571
$195$	4.00000	0.286446
$196$	0	0
$197$	28.0000	1.99492	0.997459	−	0.0712470i	$-0.0226979\pi$
$197$	28.0000	1.99492	0.997459	+	0.0712470i	$0.0226979\pi$
$198$	−4.00000	−0.284268
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	−4.00000	−0.282843
$201$	−2.00000	−0.141069
$202$	−2.00000	−0.140720
$203$	0	0
$204$	−3.00000	−0.210042
$205$	1.00000	0.0698430
$206$	1.00000	0.0696733
$207$	−8.00000	−0.556038
$208$	−4.00000	−0.277350
$209$	0	0
$210$	0	0
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	−1.00000	−0.0686803
$213$	−3.00000	−0.205557
$214$	−17.0000	−1.16210
$215$	1.00000	0.0681994
$216$	−5.00000	−0.340207
$217$	0	0
$218$	−10.0000	−0.677285
$219$	−4.00000	−0.270295
$220$	−2.00000	−0.134840
$221$	12.0000	0.807207
$222$	−2.00000	−0.134231
$223$	1.00000	0.0669650	0.0334825	−	0.999439i	$-0.489340\pi$
$223$	1.00000	0.0669650	0.0334825	+	0.999439i	$0.489340\pi$
$224$	0	0
$225$	8.00000	0.533333
$226$	9.00000	0.598671
$227$	−3.00000	−0.199117	−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000	−0.199117	−0.0995585	+	0.995032i	$0.531743\pi$
$228$	0	0
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	−5.00000	−0.328266
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	8.00000	0.522976
$235$	−2.00000	−0.130466
$236$	−10.0000	−0.650945
$237$	−15.0000	−0.974355
$238$	0	0
$239$	−20.0000	−1.29369	−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000	−1.29369	−0.646846	+	0.762620i	$0.723912\pi$
$240$	−1.00000	−0.0645497
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	−7.00000	−0.449977
$243$	16.0000	1.02640
$244$	13.0000	0.832240
$245$	0	0
$246$	−1.00000	−0.0637577
$247$	0	0
$248$	−7.00000	−0.444500
$249$	6.00000	0.380235
$250$	9.00000	0.569210
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	0	0
$253$	8.00000	0.502956
$254$	−2.00000	−0.125491
$255$	3.00000	0.187867
$256$	1.00000	0.0625000
$257$	17.0000	1.06043	0.530215	−	0.847863i	$-0.322111\pi$
$257$	17.0000	1.06043	0.530215	+	0.847863i	$0.322111\pi$
$258$	−1.00000	−0.0622573
$259$	0	0
$260$	4.00000	0.248069
$261$	10.0000	0.618984
$262$	−12.0000	−0.741362
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	2.00000	0.123091
$265$	1.00000	0.0614295
$266$	0	0
$267$	15.0000	0.917985
$268$	−2.00000	−0.122169
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	5.00000	0.304290
$271$	28.0000	1.70088	0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000	1.70088	0.850439	+	0.526073i	$0.176336\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	−12.0000	−0.724947
$275$	−8.00000	−0.482418
$276$	4.00000	0.240772
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	−10.0000	−0.599760
$279$	14.0000	0.838158
$280$	0	0
$281$	2.00000	0.119310	0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000	0.119310	0.0596550	+	0.998219i	$0.481000\pi$
$282$	2.00000	0.119098
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	−3.00000	−0.178017
$285$	0	0
$286$	−8.00000	−0.473050
$287$	0	0
$288$	−2.00000	−0.117851
$289$	−8.00000	−0.470588
$290$	5.00000	0.293610
$291$	7.00000	0.410347
$292$	−4.00000	−0.234082
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	10.0000	0.582223
$296$	−2.00000	−0.116248
$297$	−10.0000	−0.580259
$298$	−5.00000	−0.289642
$299$	−16.0000	−0.925304
$300$	−4.00000	−0.230940
$301$	0	0
$302$	7.00000	0.402805
$303$	−2.00000	−0.114897
$304$	0	0
$305$	−13.0000	−0.744378
$306$	6.00000	0.342997
$307$	12.0000	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$308$	0	0
$309$	1.00000	0.0568880
$310$	7.00000	0.397573
$311$	−22.0000	−1.24751	−0.623753	−	0.781622i	$-0.714393\pi$
$311$	−22.0000	−1.24751	−0.623753	+	0.781622i	$0.714393\pi$
$312$	−4.00000	−0.226455
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	12.0000	0.677199
$315$	0	0
$316$	−15.0000	−0.843816
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	−1.00000	−0.0560772
$319$	−10.0000	−0.559893
$320$	−1.00000	−0.0559017
$321$	−17.0000	−0.948847
$322$	0	0
$323$	0	0
$324$	1.00000	0.0555556
$325$	16.0000	0.887520
$326$	4.00000	0.221540
$327$	−10.0000	−0.553001
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	−2.00000	−0.110096
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	6.00000	0.329293
$333$	4.00000	0.219199
$334$	−8.00000	−0.437741
$335$	2.00000	0.109272
$336$	0	0
$337$	13.0000	0.708155	0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000	0.708155	0.354078	+	0.935216i	$0.384795\pi$
$338$	3.00000	0.163178
$339$	9.00000	0.488813
$340$	3.00000	0.162698
$341$	−14.0000	−0.758143
$342$	0	0
$343$	0	0
$344$	−1.00000	−0.0539164
$345$	−4.00000	−0.215353
$346$	−9.00000	−0.483843
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	−5.00000	−0.268028
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	0	0
$351$	20.0000	1.06752
$352$	2.00000	0.106600
$353$	−24.0000	−1.27739	−0.638696	−	0.769460i	$-0.720526\pi$
$353$	−24.0000	−1.27739	−0.638696	+	0.769460i	$0.720526\pi$
$354$	−10.0000	−0.531494
$355$	3.00000	0.159223
$356$	15.0000	0.794998
$357$	0	0
$358$	20.0000	1.05703
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	2.00000	0.105409
$361$	−19.0000	−1.00000
$362$	−2.00000	−0.105118
$363$	−7.00000	−0.367405
$364$	0	0
$365$	4.00000	0.209370
$366$	13.0000	0.679521
$367$	27.0000	1.40939	0.704694	−	0.709511i	$-0.251084\pi$
$367$	27.0000	1.40939	0.704694	+	0.709511i	$0.251084\pi$
$368$	4.00000	0.208514
$369$	2.00000	0.104116
$370$	2.00000	0.103975
$371$	0	0
$372$	−7.00000	−0.362933
$373$	34.0000	1.76045	0.880227	−	0.474554i	$-0.157390\pi$
$373$	34.0000	1.76045	0.880227	+	0.474554i	$0.157390\pi$
$374$	−6.00000	−0.310253
$375$	9.00000	0.464758
$376$	2.00000	0.103142
$377$	20.0000	1.03005
$378$	0	0
$379$	25.0000	1.28416	0.642082	−	0.766636i	$-0.278071\pi$
$379$	25.0000	1.28416	0.642082	+	0.766636i	$0.278071\pi$
$380$	0	0
$381$	−2.00000	−0.102463
$382$	17.0000	0.869796
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−16.0000	−0.814379
$387$	2.00000	0.101666
$388$	7.00000	0.355371
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	4.00000	0.202548
$391$	−12.0000	−0.606866
$392$	0	0
$393$	−12.0000	−0.605320
$394$	28.0000	1.41062
$395$	15.0000	0.754732
$396$	−4.00000	−0.201008
$397$	−8.00000	−0.401508	−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000	−0.401508	−0.200754	+	0.979642i	$0.564339\pi$
$398$	0	0
$399$	0	0
$400$	−4.00000	−0.200000
$401$	7.00000	0.349563	0.174782	−	0.984607i	$-0.444078\pi$
$401$	7.00000	0.349563	0.174782	+	0.984607i	$0.444078\pi$
$402$	−2.00000	−0.0997509
$403$	28.0000	1.39478
$404$	−2.00000	−0.0995037
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−4.00000	−0.198273
$408$	−3.00000	−0.148522
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	1.00000	0.0493865
$411$	−12.0000	−0.591916
$412$	1.00000	0.0492665
$413$	0	0
$414$	−8.00000	−0.393179
$415$	−6.00000	−0.294528
$416$	−4.00000	−0.196116
$417$	−10.0000	−0.489702
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−3.00000	−0.146211	−0.0731055	−	0.997324i	$-0.523291\pi$
$421$	−3.00000	−0.146211	−0.0731055	+	0.997324i	$0.523291\pi$
$422$	12.0000	0.584151
$423$	−4.00000	−0.194487
$424$	−1.00000	−0.0485643
$425$	12.0000	0.582086
$426$	−3.00000	−0.145350
$427$	0	0
$428$	−17.0000	−0.821726
$429$	−8.00000	−0.386244
$430$	1.00000	0.0482243
$431$	32.0000	1.54139	0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000	1.54139	0.770693	+	0.637207i	$0.219910\pi$
$432$	−5.00000	−0.240563
$433$	16.0000	0.768911	0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000	0.768911	0.384455	+	0.923144i	$0.374389\pi$
$434$	0	0
$435$	5.00000	0.239732
$436$	−10.0000	−0.478913
$437$	0	0
$438$	−4.00000	−0.191127
$439$	10.0000	0.477274	0.238637	−	0.971109i	$-0.423299\pi$
$439$	10.0000	0.477274	0.238637	+	0.971109i	$0.423299\pi$
$440$	−2.00000	−0.0953463
$441$	0	0
$442$	12.0000	0.570782
$443$	−21.0000	−0.997740	−0.498870	−	0.866677i	$-0.666252\pi$
$443$	−21.0000	−0.997740	−0.498870	+	0.866677i	$0.666252\pi$
$444$	−2.00000	−0.0949158
$445$	−15.0000	−0.711068
$446$	1.00000	0.0473514
$447$	−5.00000	−0.236492
$448$	0	0
$449$	−25.0000	−1.17982	−0.589911	−	0.807468i	$-0.700837\pi$
$449$	−25.0000	−1.17982	−0.589911	+	0.807468i	$0.700837\pi$
$450$	8.00000	0.377124
$451$	−2.00000	−0.0941763
$452$	9.00000	0.423324
$453$	7.00000	0.328889
$454$	−3.00000	−0.140797
$455$	0	0
$456$	0	0
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	0	0
$459$	15.0000	0.700140
$460$	−4.00000	−0.186501
$461$	−37.0000	−1.72326	−0.861631	−	0.507535i	$-0.830557\pi$
$461$	−37.0000	−1.72326	−0.861631	+	0.507535i	$0.830557\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−5.00000	−0.232119
$465$	7.00000	0.324617
$466$	14.0000	0.648537
$467$	−18.0000	−0.832941	−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000	−0.832941	−0.416470	+	0.909149i	$0.636733\pi$
$468$	8.00000	0.369800
$469$	0	0
$470$	−2.00000	−0.0922531
$471$	12.0000	0.552931
$472$	−10.0000	−0.460287
$473$	−2.00000	−0.0919601
$474$	−15.0000	−0.688973
$475$	0	0
$476$	0	0
$477$	2.00000	0.0915737
$478$	−20.0000	−0.914779
$479$	10.0000	0.456912	0.228456	−	0.973554i	$-0.426632\pi$
$479$	10.0000	0.456912	0.228456	+	0.973554i	$0.426632\pi$
$480$	−1.00000	−0.0456435
$481$	8.00000	0.364769
$482$	−22.0000	−1.00207
$483$	0	0
$484$	−7.00000	−0.318182
$485$	−7.00000	−0.317854
$486$	16.0000	0.725775
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	13.0000	0.588482
$489$	4.00000	0.180886
$490$	0	0
$491$	17.0000	0.767199	0.383600	−	0.923499i	$-0.374684\pi$
$491$	17.0000	0.767199	0.383600	+	0.923499i	$0.374684\pi$
$492$	−1.00000	−0.0450835
$493$	15.0000	0.675566
$494$	0	0
$495$	4.00000	0.179787
$496$	−7.00000	−0.314309
$497$	0	0
$498$	6.00000	0.268866
$499$	−30.0000	−1.34298	−0.671492	−	0.741012i	$-0.734346\pi$
$499$	−30.0000	−1.34298	−0.671492	+	0.741012i	$0.734346\pi$
$500$	9.00000	0.402492
$501$	−8.00000	−0.357414
$502$	−12.0000	−0.535586
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	0	0
$505$	2.00000	0.0889988
$506$	8.00000	0.355643
$507$	3.00000	0.133235
$508$	−2.00000	−0.0887357
$509$	20.0000	0.886484	0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000	0.886484	0.443242	+	0.896402i	$0.353828\pi$
$510$	3.00000	0.132842
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	17.0000	0.749838
$515$	−1.00000	−0.0440653
$516$	−1.00000	−0.0440225
$517$	4.00000	0.175920
$518$	0	0
$519$	−9.00000	−0.395056
$520$	4.00000	0.175412
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	10.0000	0.437688
$523$	36.0000	1.57417	0.787085	−	0.616844i	$-0.211589\pi$
$523$	36.0000	1.57417	0.787085	+	0.616844i	$0.211589\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−16.0000	−0.697633
$527$	21.0000	0.914774
$528$	2.00000	0.0870388
$529$	−7.00000	−0.304348
$530$	1.00000	0.0434372
$531$	20.0000	0.867926
$532$	0	0
$533$	4.00000	0.173259
$534$	15.0000	0.649113
$535$	17.0000	0.734974
$536$	−2.00000	−0.0863868
$537$	20.0000	0.863064
$538$	−10.0000	−0.431131
$539$	0	0
$540$	5.00000	0.215166
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	28.0000	1.20270
$543$	−2.00000	−0.0858282
$544$	−3.00000	−0.128624
$545$	10.0000	0.428353
$546$	0	0
$547$	−22.0000	−0.940652	−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000	−0.940652	−0.470326	+	0.882493i	$0.655864\pi$
$548$	−12.0000	−0.512615
$549$	−26.0000	−1.10965
$550$	−8.00000	−0.341121
$551$	0	0
$552$	4.00000	0.170251
$553$	0	0
$554$	−22.0000	−0.934690
$555$	2.00000	0.0848953
$556$	−10.0000	−0.424094
$557$	33.0000	1.39825	0.699127	−	0.714997i	$-0.253572\pi$
$557$	33.0000	1.39825	0.699127	+	0.714997i	$0.253572\pi$
$558$	14.0000	0.592667
$559$	4.00000	0.169182
$560$	0	0
$561$	−6.00000	−0.253320
$562$	2.00000	0.0843649
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	2.00000	0.0842152
$565$	−9.00000	−0.378633
$566$	−14.0000	−0.588464
$567$	0	0
$568$	−3.00000	−0.125877
$569$	15.0000	0.628833	0.314416	−	0.949285i	$-0.398191\pi$
$569$	15.0000	0.628833	0.314416	+	0.949285i	$0.398191\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	−8.00000	−0.334497
$573$	17.0000	0.710185
$574$	0	0
$575$	−16.0000	−0.667246
$576$	−2.00000	−0.0833333
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	−8.00000	−0.332756
$579$	−16.0000	−0.664937
$580$	5.00000	0.207614
$581$	0	0
$582$	7.00000	0.290159
$583$	−2.00000	−0.0828315
$584$	−4.00000	−0.165521
$585$	−8.00000	−0.330759
$586$	6.00000	0.247858
$587$	−33.0000	−1.36206	−0.681028	−	0.732257i	$-0.738467\pi$
$587$	−33.0000	−1.36206	−0.681028	+	0.732257i	$0.738467\pi$
$588$	0	0
$589$	0	0
$590$	10.0000	0.411693
$591$	28.0000	1.15177
$592$	−2.00000	−0.0821995
$593$	−19.0000	−0.780236	−0.390118	−	0.920765i	$-0.627566\pi$
$593$	−19.0000	−0.780236	−0.390118	+	0.920765i	$0.627566\pi$
$594$	−10.0000	−0.410305
$595$	0	0
$596$	−5.00000	−0.204808
$597$	0	0
$598$	−16.0000	−0.654289
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	−4.00000	−0.163299
$601$	13.0000	0.530281	0.265141	−	0.964210i	$-0.414582\pi$
$601$	13.0000	0.530281	0.265141	+	0.964210i	$0.414582\pi$
$602$	0	0
$603$	4.00000	0.162893
$604$	7.00000	0.284826
$605$	7.00000	0.284590
$606$	−2.00000	−0.0812444
$607$	−23.0000	−0.933541	−0.466771	−	0.884378i	$-0.654583\pi$
$607$	−23.0000	−0.933541	−0.466771	+	0.884378i	$0.654583\pi$
$608$	0	0
$609$	0	0
$610$	−13.0000	−0.526355
$611$	−8.00000	−0.323645
$612$	6.00000	0.242536
$613$	−36.0000	−1.45403	−0.727013	−	0.686624i	$-0.759092\pi$
$613$	−36.0000	−1.45403	−0.727013	+	0.686624i	$0.759092\pi$
$614$	12.0000	0.484281
$615$	1.00000	0.0403239
$616$	0	0
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	1.00000	0.0402259
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	7.00000	0.281127
$621$	−20.0000	−0.802572
$622$	−22.0000	−0.882120
$623$	0	0
$624$	−4.00000	−0.160128
$625$	11.0000	0.440000
$626$	26.0000	1.03917
$627$	0	0
$628$	12.0000	0.478852
$629$	6.00000	0.239236
$630$	0	0
$631$	42.0000	1.67199	0.835997	−	0.548734i	$-0.184890\pi$
$631$	42.0000	1.67199	0.835997	+	0.548734i	$0.184890\pi$
$632$	−15.0000	−0.596668
$633$	12.0000	0.476957
$634$	−2.00000	−0.0794301
$635$	2.00000	0.0793676
$636$	−1.00000	−0.0396526
$637$	0	0
$638$	−10.0000	−0.395904
$639$	6.00000	0.237356
$640$	−1.00000	−0.0395285
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	−17.0000	−0.670936
$643$	21.0000	0.828159	0.414080	−	0.910241i	$-0.364104\pi$
$643$	21.0000	0.828159	0.414080	+	0.910241i	$0.364104\pi$
$644$	0	0
$645$	1.00000	0.0393750
$646$	0	0
$647$	17.0000	0.668339	0.334169	−	0.942513i	$-0.391544\pi$
$647$	17.0000	0.668339	0.334169	+	0.942513i	$0.391544\pi$
$648$	1.00000	0.0392837
$649$	−20.0000	−0.785069
$650$	16.0000	0.627572
$651$	0	0
$652$	4.00000	0.156652
$653$	−21.0000	−0.821794	−0.410897	−	0.911682i	$-0.634784\pi$
$653$	−21.0000	−0.821794	−0.410897	+	0.911682i	$0.634784\pi$
$654$	−10.0000	−0.391031
$655$	12.0000	0.468879
$656$	−1.00000	−0.0390434
$657$	8.00000	0.312110
$658$	0	0
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	−2.00000	−0.0778499
$661$	18.0000	0.700119	0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000	0.700119	0.350059	+	0.936727i	$0.386161\pi$
$662$	12.0000	0.466393
$663$	12.0000	0.466041
$664$	6.00000	0.232845
$665$	0	0
$666$	4.00000	0.154997
$667$	−20.0000	−0.774403
$668$	−8.00000	−0.309529
$669$	1.00000	0.0386622
$670$	2.00000	0.0772667
$671$	26.0000	1.00372
$672$	0	0
$673$	34.0000	1.31060	0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000	1.31060	0.655302	+	0.755367i	$0.272541\pi$
$674$	13.0000	0.500741
$675$	20.0000	0.769800
$676$	3.00000	0.115385
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	9.00000	0.345643
$679$	0	0
$680$	3.00000	0.115045
$681$	−3.00000	−0.114960
$682$	−14.0000	−0.536088
$683$	−16.0000	−0.612223	−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000	−0.612223	−0.306111	+	0.951996i	$0.599028\pi$
$684$	0	0
$685$	12.0000	0.458496
$686$	0	0
$687$	0	0
$688$	−1.00000	−0.0381246
$689$	4.00000	0.152388
$690$	−4.00000	−0.152277
$691$	33.0000	1.25538	0.627690	−	0.778464i	$-0.284001\pi$
$691$	33.0000	1.25538	0.627690	+	0.778464i	$0.284001\pi$
$692$	−9.00000	−0.342129
$693$	0	0
$694$	−12.0000	−0.455514
$695$	10.0000	0.379322
$696$	−5.00000	−0.189525
$697$	3.00000	0.113633
$698$	−10.0000	−0.378506
$699$	14.0000	0.529529
$700$	0	0
$701$	−8.00000	−0.302156	−0.151078	−	0.988522i	$-0.548274\pi$
$701$	−8.00000	−0.302156	−0.151078	+	0.988522i	$0.548274\pi$
$702$	20.0000	0.754851
$703$	0	0
$704$	2.00000	0.0753778
$705$	−2.00000	−0.0753244
$706$	−24.0000	−0.903252
$707$	0	0
$708$	−10.0000	−0.375823
$709$	35.0000	1.31445	0.657226	−	0.753693i	$-0.271730\pi$
$709$	35.0000	1.31445	0.657226	+	0.753693i	$0.271730\pi$
$710$	3.00000	0.112588
$711$	30.0000	1.12509
$712$	15.0000	0.562149
$713$	−28.0000	−1.04861
$714$	0	0
$715$	8.00000	0.299183
$716$	20.0000	0.747435
$717$	−20.0000	−0.746914
$718$	20.0000	0.746393
$719$	−20.0000	−0.745874	−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000	−0.745874	−0.372937	+	0.927857i	$0.621649\pi$
$720$	2.00000	0.0745356
$721$	0	0
$722$	−19.0000	−0.707107
$723$	−22.0000	−0.818189
$724$	−2.00000	−0.0743294
$725$	20.0000	0.742781
$726$	−7.00000	−0.259794
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	4.00000	0.148047
$731$	3.00000	0.110959
$732$	13.0000	0.480494
$733$	21.0000	0.775653	0.387826	−	0.921732i	$-0.373226\pi$
$733$	21.0000	0.775653	0.387826	+	0.921732i	$0.373226\pi$
$734$	27.0000	0.996588
$735$	0	0
$736$	4.00000	0.147442
$737$	−4.00000	−0.147342
$738$	2.00000	0.0736210
$739$	15.0000	0.551784	0.275892	−	0.961189i	$-0.411027\pi$
$739$	15.0000	0.551784	0.275892	+	0.961189i	$0.411027\pi$
$740$	2.00000	0.0735215
$741$	0	0
$742$	0	0
$743$	−36.0000	−1.32071	−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000	−1.32071	−0.660356	+	0.750953i	$0.729595\pi$
$744$	−7.00000	−0.256632
$745$	5.00000	0.183186
$746$	34.0000	1.24483
$747$	−12.0000	−0.439057
$748$	−6.00000	−0.219382
$749$	0	0
$750$	9.00000	0.328634
$751$	32.0000	1.16770	0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000	1.16770	0.583848	+	0.811863i	$0.301546\pi$
$752$	2.00000	0.0729325
$753$	−12.0000	−0.437304
$754$	20.0000	0.728357
$755$	−7.00000	−0.254756
$756$	0	0
$757$	43.0000	1.56286	0.781431	−	0.623992i	$-0.214490\pi$
$757$	43.0000	1.56286	0.781431	+	0.623992i	$0.214490\pi$
$758$	25.0000	0.908041
$759$	8.00000	0.290382
$760$	0	0
$761$	−22.0000	−0.797499	−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000	−0.797499	−0.398750	+	0.917060i	$0.630556\pi$
$762$	−2.00000	−0.0724524
$763$	0	0
$764$	17.0000	0.615038
$765$	−6.00000	−0.216930
$766$	6.00000	0.216789
$767$	40.0000	1.44432
$768$	1.00000	0.0360844
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	0	0
$771$	17.0000	0.612240
$772$	−16.0000	−0.575853
$773$	−34.0000	−1.22290	−0.611448	−	0.791285i	$-0.709412\pi$
$773$	−34.0000	−1.22290	−0.611448	+	0.791285i	$0.709412\pi$
$774$	2.00000	0.0718885
$775$	28.0000	1.00579
$776$	7.00000	0.251285
$777$	0	0
$778$	30.0000	1.07555
$779$	0	0
$780$	4.00000	0.143223
$781$	−6.00000	−0.214697
$782$	−12.0000	−0.429119
$783$	25.0000	0.893427
$784$	0	0
$785$	−12.0000	−0.428298
$786$	−12.0000	−0.428026
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	28.0000	0.997459
$789$	−16.0000	−0.569615
$790$	15.0000	0.533676
$791$	0	0
$792$	−4.00000	−0.142134
$793$	−52.0000	−1.84657
$794$	−8.00000	−0.283909
$795$	1.00000	0.0354663
$796$	0	0
$797$	−43.0000	−1.52314	−0.761569	−	0.648084i	$-0.775571\pi$
$797$	−43.0000	−1.52314	−0.761569	+	0.648084i	$0.775571\pi$
$798$	0	0
$799$	−6.00000	−0.212265
$800$	−4.00000	−0.141421
$801$	−30.0000	−1.06000
$802$	7.00000	0.247179
$803$	−8.00000	−0.282314
$804$	−2.00000	−0.0705346
$805$	0	0
$806$	28.0000	0.986258
$807$	−10.0000	−0.352017
$808$	−2.00000	−0.0703598
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	−1.00000	−0.0351364
$811$	−12.0000	−0.421377	−0.210688	−	0.977553i	$-0.567571\pi$
$811$	−12.0000	−0.421377	−0.210688	+	0.977553i	$0.567571\pi$
$812$	0	0
$813$	28.0000	0.982003
$814$	−4.00000	−0.140200
$815$	−4.00000	−0.140114
$816$	−3.00000	−0.105021
$817$	0	0
$818$	10.0000	0.349642
$819$	0	0
$820$	1.00000	0.0349215
$821$	32.0000	1.11681	0.558404	−	0.829569i	$-0.311414\pi$
$821$	32.0000	1.11681	0.558404	+	0.829569i	$0.311414\pi$
$822$	−12.0000	−0.418548
$823$	49.0000	1.70803	0.854016	−	0.520246i	$-0.174160\pi$
$823$	49.0000	1.70803	0.854016	+	0.520246i	$0.174160\pi$
$824$	1.00000	0.0348367
$825$	−8.00000	−0.278524
$826$	0	0
$827$	−42.0000	−1.46048	−0.730242	−	0.683189i	$-0.760592\pi$
$827$	−42.0000	−1.46048	−0.730242	+	0.683189i	$0.760592\pi$
$828$	−8.00000	−0.278019
$829$	−45.0000	−1.56291	−0.781457	−	0.623959i	$-0.785523\pi$
$829$	−45.0000	−1.56291	−0.781457	+	0.623959i	$0.785523\pi$
$830$	−6.00000	−0.208263
$831$	−22.0000	−0.763172
$832$	−4.00000	−0.138675
$833$	0	0
$834$	−10.0000	−0.346272
$835$	8.00000	0.276851
$836$	0	0
$837$	35.0000	1.20978
$838$	0	0
$839$	−10.0000	−0.345238	−0.172619	−	0.984989i	$-0.555223\pi$
$839$	−10.0000	−0.345238	−0.172619	+	0.984989i	$0.555223\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−3.00000	−0.103387
$843$	2.00000	0.0688837
$844$	12.0000	0.413057
$845$	−3.00000	−0.103203
$846$	−4.00000	−0.137523
$847$	0	0
$848$	−1.00000	−0.0343401
$849$	−14.0000	−0.480479
$850$	12.0000	0.411597
$851$	−8.00000	−0.274236
$852$	−3.00000	−0.102778
$853$	11.0000	0.376633	0.188316	−	0.982108i	$-0.439697\pi$
$853$	11.0000	0.376633	0.188316	+	0.982108i	$0.439697\pi$
$854$	0	0
$855$	0	0
$856$	−17.0000	−0.581048
$857$	2.00000	0.0683187	0.0341593	−	0.999416i	$-0.489125\pi$
$857$	2.00000	0.0683187	0.0341593	+	0.999416i	$0.489125\pi$
$858$	−8.00000	−0.273115
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	1.00000	0.0340997
$861$	0	0
$862$	32.0000	1.08992
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	−5.00000	−0.170103
$865$	9.00000	0.306009
$866$	16.0000	0.543702
$867$	−8.00000	−0.271694
$868$	0	0
$869$	−30.0000	−1.01768
$870$	5.00000	0.169516
$871$	8.00000	0.271070
$872$	−10.0000	−0.338643
$873$	−14.0000	−0.473828
$874$	0	0
$875$	0	0
$876$	−4.00000	−0.135147
$877$	8.00000	0.270141	0.135070	−	0.990836i	$-0.456874\pi$
$877$	8.00000	0.270141	0.135070	+	0.990836i	$0.456874\pi$
$878$	10.0000	0.337484
$879$	6.00000	0.202375
$880$	−2.00000	−0.0674200
$881$	28.0000	0.943344	0.471672	−	0.881774i	$-0.343651\pi$
$881$	28.0000	0.943344	0.471672	+	0.881774i	$0.343651\pi$
$882$	0	0
$883$	−26.0000	−0.874970	−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000	−0.874970	−0.437485	+	0.899226i	$0.644131\pi$
$884$	12.0000	0.403604
$885$	10.0000	0.336146
$886$	−21.0000	−0.705509
$887$	−28.0000	−0.940148	−0.470074	−	0.882627i	$-0.655773\pi$
$887$	−28.0000	−0.940148	−0.470074	+	0.882627i	$0.655773\pi$
$888$	−2.00000	−0.0671156
$889$	0	0
$890$	−15.0000	−0.502801
$891$	2.00000	0.0670025
$892$	1.00000	0.0334825
$893$	0	0
$894$	−5.00000	−0.167225
$895$	−20.0000	−0.668526
$896$	0	0
$897$	−16.0000	−0.534224
$898$	−25.0000	−0.834261
$899$	35.0000	1.16732
$900$	8.00000	0.266667
$901$	3.00000	0.0999445
$902$	−2.00000	−0.0665927
$903$	0	0
$904$	9.00000	0.299336
$905$	2.00000	0.0664822
$906$	7.00000	0.232559
$907$	23.0000	0.763702	0.381851	−	0.924224i	$-0.375287\pi$
$907$	23.0000	0.763702	0.381851	+	0.924224i	$0.375287\pi$
$908$	−3.00000	−0.0995585
$909$	4.00000	0.132672
$910$	0	0
$911$	−38.0000	−1.25900	−0.629498	−	0.777002i	$-0.716739\pi$
$911$	−38.0000	−1.25900	−0.629498	+	0.777002i	$0.716739\pi$
$912$	0	0
$913$	12.0000	0.397142
$914$	−22.0000	−0.727695
$915$	−13.0000	−0.429767
$916$	0	0
$917$	0	0
$918$	15.0000	0.495074
$919$	−25.0000	−0.824674	−0.412337	−	0.911031i	$-0.635287\pi$
$919$	−25.0000	−0.824674	−0.412337	+	0.911031i	$0.635287\pi$
$920$	−4.00000	−0.131876
$921$	12.0000	0.395413
$922$	−37.0000	−1.21853
$923$	12.0000	0.394985
$924$	0	0
$925$	8.00000	0.263038
$926$	−16.0000	−0.525793
$927$	−2.00000	−0.0656886
$928$	−5.00000	−0.164133
$929$	−10.0000	−0.328089	−0.164045	−	0.986453i	$-0.552454\pi$
$929$	−10.0000	−0.328089	−0.164045	+	0.986453i	$0.552454\pi$
$930$	7.00000	0.229539
$931$	0	0
$932$	14.0000	0.458585
$933$	−22.0000	−0.720248
$934$	−18.0000	−0.588978
$935$	6.00000	0.196221
$936$	8.00000	0.261488
$937$	−33.0000	−1.07806	−0.539032	−	0.842286i	$-0.681210\pi$
$937$	−33.0000	−1.07806	−0.539032	+	0.842286i	$0.681210\pi$
$938$	0	0
$939$	26.0000	0.848478
$940$	−2.00000	−0.0652328
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	12.0000	0.390981
$943$	−4.00000	−0.130258
$944$	−10.0000	−0.325472
$945$	0	0
$946$	−2.00000	−0.0650256
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	−15.0000	−0.487177
$949$	16.0000	0.519382
$950$	0	0
$951$	−2.00000	−0.0648544
$952$	0	0
$953$	54.0000	1.74923	0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000	1.74923	0.874616	+	0.484817i	$0.161114\pi$
$954$	2.00000	0.0647524
$955$	−17.0000	−0.550107
$956$	−20.0000	−0.646846
$957$	−10.0000	−0.323254
$958$	10.0000	0.323085
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	18.0000	0.580645
$962$	8.00000	0.257930
$963$	34.0000	1.09563
$964$	−22.0000	−0.708572
$965$	16.0000	0.515058
$966$	0	0
$967$	13.0000	0.418052	0.209026	−	0.977910i	$-0.432971\pi$
$967$	13.0000	0.418052	0.209026	+	0.977910i	$0.432971\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	−7.00000	−0.224756
$971$	−47.0000	−1.50830	−0.754151	−	0.656701i	$-0.771951\pi$
$971$	−47.0000	−1.50830	−0.754151	+	0.656701i	$0.771951\pi$
$972$	16.0000	0.513200
$973$	0	0
$974$	−32.0000	−1.02535
$975$	16.0000	0.512410
$976$	13.0000	0.416120
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	4.00000	0.127906
$979$	30.0000	0.958804
$980$	0	0
$981$	20.0000	0.638551
$982$	17.0000	0.542492
$983$	1.00000	0.0318950	0.0159475	−	0.999873i	$-0.494924\pi$
$983$	1.00000	0.0318950	0.0159475	+	0.999873i	$0.494924\pi$
$984$	−1.00000	−0.0318788
$985$	−28.0000	−0.892154
$986$	15.0000	0.477697
$987$	0	0
$988$	0	0
$989$	−4.00000	−0.127193
$990$	4.00000	0.127128
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	−7.00000	−0.222250
$993$	12.0000	0.380808
$994$	0	0
$995$	0	0
$996$	6.00000	0.190117
$997$	−28.0000	−0.886769	−0.443384	−	0.896332i	$-0.646222\pi$
$997$	−28.0000	−0.886769	−0.443384	+	0.896332i	$0.646222\pi$
$998$	−30.0000	−0.949633
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.o.1.1		1
7.6	odd	2		574.2.a.i.1.1	✓	1
21.20	even	2		5166.2.a.h.1.1		1
28.27	even	2		4592.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.a.i.1.1	✓	1	7.6	odd	2
4018.2.a.o.1.1		1	1.1	even	1	trivial
4592.2.a.i.1.1		1	28.27	even	2
5166.2.a.h.1.1		1	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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