LMFDB - Embedded newform 4018.2.a.r.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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -4.00000 q^{11} +2.00000 q^{12} +1.00000 q^{13} -4.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} -6.00000 q^{19} -2.00000 q^{20} -4.00000 q^{22} -2.00000 q^{23} +2.00000 q^{24} -1.00000 q^{25} +1.00000 q^{26} -4.00000 q^{27} -5.00000 q^{29} -4.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} -8.00000 q^{33} +1.00000 q^{36} -2.00000 q^{37} -6.00000 q^{38} +2.00000 q^{39} -2.00000 q^{40} +1.00000 q^{41} -1.00000 q^{43} -4.00000 q^{44} -2.00000 q^{45} -2.00000 q^{46} -8.00000 q^{47} +2.00000 q^{48} -1.00000 q^{50} +1.00000 q^{52} -10.0000 q^{53} -4.00000 q^{54} +8.00000 q^{55} -12.0000 q^{57} -5.00000 q^{58} +1.00000 q^{59} -4.00000 q^{60} +14.0000 q^{61} +4.00000 q^{62} +1.00000 q^{64} -2.00000 q^{65} -8.00000 q^{66} +10.0000 q^{67} -4.00000 q^{69} -15.0000 q^{71} +1.00000 q^{72} +7.00000 q^{73} -2.00000 q^{74} -2.00000 q^{75} -6.00000 q^{76} +2.00000 q^{78} -2.00000 q^{80} -11.0000 q^{81} +1.00000 q^{82} +9.00000 q^{83} -1.00000 q^{86} -10.0000 q^{87} -4.00000 q^{88} -2.00000 q^{90} -2.00000 q^{92} +8.00000 q^{93} -8.00000 q^{94} +12.0000 q^{95} +2.00000 q^{96} -4.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)

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
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	2.00000	0.816497
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	2.00000	0.577350
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	0	0
$15$	−4.00000	−1.03280
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	1.00000	0.235702
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	−4.00000	−0.852803
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	2.00000	0.408248
$25$	−1.00000	−0.200000
$26$	1.00000	0.196116
$27$	−4.00000	−0.769800
$28$	0	0
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	−4.00000	−0.730297
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	1.00000	0.176777
$33$	−8.00000	−1.39262
$34$	0	0
$35$	0	0
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−6.00000	−0.973329
$39$	2.00000	0.320256
$40$	−2.00000	−0.316228
$41$	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	$0.524294\pi$
$44$	−4.00000	−0.603023
$45$	−2.00000	−0.298142
$46$	−2.00000	−0.294884
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	2.00000	0.288675
$49$	0	0
$50$	−1.00000	−0.141421
$51$	0	0
$52$	1.00000	0.138675
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	−4.00000	−0.544331
$55$	8.00000	1.07872
$56$	0	0
$57$	−12.0000	−1.58944
$58$	−5.00000	−0.656532
$59$	1.00000	0.130189	0.0650945	−	0.997879i	$-0.479265\pi$
$59$	1.00000	0.130189	0.0650945	+	0.997879i	$0.479265\pi$
$60$	−4.00000	−0.516398
$61$	14.0000	1.79252	0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000	1.79252	0.896258	+	0.443533i	$0.146275\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	−8.00000	−0.984732
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	0	0
$69$	−4.00000	−0.481543
$70$	0	0
$71$	−15.0000	−1.78017	−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000	−1.78017	−0.890086	+	0.455792i	$0.849356\pi$
$72$	1.00000	0.117851
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	−2.00000	−0.232495
$75$	−2.00000	−0.230940
$76$	−6.00000	−0.688247
$77$	0	0
$78$	2.00000	0.226455
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−2.00000	−0.223607
$81$	−11.0000	−1.22222
$82$	1.00000	0.110432
$83$	9.00000	0.987878	0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000	0.987878	0.493939	+	0.869496i	$0.335557\pi$
$84$	0	0
$85$	0	0
$86$	−1.00000	−0.107833
$87$	−10.0000	−1.07211
$88$	−4.00000	−0.426401
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	−2.00000	−0.210819
$91$	0	0
$92$	−2.00000	−0.208514
$93$	8.00000	0.829561
$94$	−8.00000	−0.825137
$95$	12.0000	1.23117
$96$	2.00000	0.204124
$97$	−4.00000	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$98$	0	0
$99$	−4.00000	−0.402015
$100$	−1.00000	−0.100000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	−10.0000	−0.985329	−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000	−0.985329	−0.492665	+	0.870219i	$0.663977\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−10.0000	−0.971286
$107$	13.0000	1.25676	0.628379	−	0.777908i	$-0.283719\pi$
$107$	13.0000	1.25676	0.628379	+	0.777908i	$0.283719\pi$
$108$	−4.00000	−0.384900
$109$	−7.00000	−0.670478	−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000	−0.670478	−0.335239	+	0.942133i	$0.608817\pi$
$110$	8.00000	0.762770
$111$	−4.00000	−0.379663
$112$	0	0
$113$	−3.00000	−0.282216	−0.141108	−	0.989994i	$-0.545067\pi$
$113$	−3.00000	−0.282216	−0.141108	+	0.989994i	$0.545067\pi$
$114$	−12.0000	−1.12390
$115$	4.00000	0.373002
$116$	−5.00000	−0.464238
$117$	1.00000	0.0924500
$118$	1.00000	0.0920575
$119$	0	0
$120$	−4.00000	−0.365148
$121$	5.00000	0.454545
$122$	14.0000	1.26750
$123$	2.00000	0.180334
$124$	4.00000	0.359211
$125$	12.0000	1.07331
$126$	0	0
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	1.00000	0.0883883
$129$	−2.00000	−0.176090
$130$	−2.00000	−0.175412
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	−8.00000	−0.696311
$133$	0	0
$134$	10.0000	0.863868
$135$	8.00000	0.688530
$136$	0	0
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	−4.00000	−0.340503
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	−16.0000	−1.34744
$142$	−15.0000	−1.25877
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	10.0000	0.830455
$146$	7.00000	0.579324
$147$	0	0
$148$	−2.00000	−0.164399
$149$	1.00000	0.0819232	0.0409616	−	0.999161i	$-0.486958\pi$
$149$	1.00000	0.0819232	0.0409616	+	0.999161i	$0.486958\pi$
$150$	−2.00000	−0.163299
$151$	19.0000	1.54620	0.773099	−	0.634285i	$-0.218706\pi$
$151$	19.0000	1.54620	0.773099	+	0.634285i	$0.218706\pi$
$152$	−6.00000	−0.486664
$153$	0	0
$154$	0	0
$155$	−8.00000	−0.642575
$156$	2.00000	0.160128
$157$	−15.0000	−1.19713	−0.598565	−	0.801074i	$-0.704262\pi$
$157$	−15.0000	−1.19713	−0.598565	+	0.801074i	$0.704262\pi$
$158$	0	0
$159$	−20.0000	−1.58610
$160$	−2.00000	−0.158114
$161$	0	0
$162$	−11.0000	−0.864242
$163$	−23.0000	−1.80150	−0.900750	−	0.434339i	$-0.856982\pi$
$163$	−23.0000	−1.80150	−0.900750	+	0.434339i	$0.856982\pi$
$164$	1.00000	0.0780869
$165$	16.0000	1.24560
$166$	9.00000	0.698535
$167$	5.00000	0.386912	0.193456	−	0.981109i	$-0.438030\pi$
$167$	5.00000	0.386912	0.193456	+	0.981109i	$0.438030\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−6.00000	−0.458831
$172$	−1.00000	−0.0762493
$173$	24.0000	1.82469	0.912343	−	0.409426i	$-0.134271\pi$
$173$	24.0000	1.82469	0.912343	+	0.409426i	$0.134271\pi$
$174$	−10.0000	−0.758098
$175$	0	0
$176$	−4.00000	−0.301511
$177$	2.00000	0.150329
$178$	0	0
$179$	−10.0000	−0.747435	−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000	−0.747435	−0.373718	+	0.927543i	$0.621917\pi$
$180$	−2.00000	−0.149071
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	0	0
$183$	28.0000	2.06982
$184$	−2.00000	−0.147442
$185$	4.00000	0.294086
$186$	8.00000	0.586588
$187$	0	0
$188$	−8.00000	−0.583460
$189$	0	0
$190$	12.0000	0.870572
$191$	5.00000	0.361787	0.180894	−	0.983503i	$-0.442101\pi$
$191$	5.00000	0.361787	0.180894	+	0.983503i	$0.442101\pi$
$192$	2.00000	0.144338
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−4.00000	−0.287183
$195$	−4.00000	−0.286446
$196$	0	0
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	−4.00000	−0.284268
$199$	−3.00000	−0.212664	−0.106332	−	0.994331i	$-0.533911\pi$
$199$	−3.00000	−0.212664	−0.106332	+	0.994331i	$0.533911\pi$
$200$	−1.00000	−0.0707107
$201$	20.0000	1.41069
$202$	−10.0000	−0.703598
$203$	0	0
$204$	0	0
$205$	−2.00000	−0.139686
$206$	−10.0000	−0.696733
$207$	−2.00000	−0.139010
$208$	1.00000	0.0693375
$209$	24.0000	1.66011
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	−10.0000	−0.686803
$213$	−30.0000	−2.05557
$214$	13.0000	0.888662
$215$	2.00000	0.136399
$216$	−4.00000	−0.272166
$217$	0	0
$218$	−7.00000	−0.474100
$219$	14.0000	0.946032
$220$	8.00000	0.539360
$221$	0	0
$222$	−4.00000	−0.268462
$223$	26.0000	1.74109	0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000	1.74109	0.870544	+	0.492090i	$0.163767\pi$
$224$	0	0
$225$	−1.00000	−0.0666667
$226$	−3.00000	−0.199557
$227$	−18.0000	−1.19470	−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000	−1.19470	−0.597351	+	0.801980i	$0.703780\pi$
$228$	−12.0000	−0.794719
$229$	−21.0000	−1.38772	−0.693860	−	0.720110i	$-0.744091\pi$
$229$	−21.0000	−1.38772	−0.693860	+	0.720110i	$0.744091\pi$
$230$	4.00000	0.263752
$231$	0	0
$232$	−5.00000	−0.328266
$233$	−16.0000	−1.04819	−0.524097	−	0.851658i	$-0.675597\pi$
$233$	−16.0000	−1.04819	−0.524097	+	0.851658i	$0.675597\pi$
$234$	1.00000	0.0653720
$235$	16.0000	1.04372
$236$	1.00000	0.0650945
$237$	0	0
$238$	0	0
$239$	16.0000	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$240$	−4.00000	−0.258199
$241$	−5.00000	−0.322078	−0.161039	−	0.986948i	$-0.551485\pi$
$241$	−5.00000	−0.322078	−0.161039	+	0.986948i	$0.551485\pi$
$242$	5.00000	0.321412
$243$	−10.0000	−0.641500
$244$	14.0000	0.896258
$245$	0	0
$246$	2.00000	0.127515
$247$	−6.00000	−0.381771
$248$	4.00000	0.254000
$249$	18.0000	1.14070
$250$	12.0000	0.758947
$251$	−9.00000	−0.568075	−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000	−0.568075	−0.284037	+	0.958813i	$0.591674\pi$
$252$	0	0
$253$	8.00000	0.502956
$254$	4.00000	0.250982
$255$	0	0
$256$	1.00000	0.0625000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	−2.00000	−0.124515
$259$	0	0
$260$	−2.00000	−0.124035
$261$	−5.00000	−0.309492
$262$	12.0000	0.741362
$263$	−31.0000	−1.91154	−0.955771	−	0.294112i	$-0.904976\pi$
$263$	−31.0000	−1.91154	−0.955771	+	0.294112i	$0.904976\pi$
$264$	−8.00000	−0.492366
$265$	20.0000	1.22859
$266$	0	0
$267$	0	0
$268$	10.0000	0.610847
$269$	16.0000	0.975537	0.487769	−	0.872973i	$-0.337811\pi$
$269$	16.0000	0.975537	0.487769	+	0.872973i	$0.337811\pi$
$270$	8.00000	0.486864
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	0	0
$273$	0	0
$274$	−18.0000	−1.08742
$275$	4.00000	0.241209
$276$	−4.00000	−0.240772
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	4.00000	0.239904
$279$	4.00000	0.239474
$280$	0	0
$281$	14.0000	0.835170	0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000	0.835170	0.417585	+	0.908638i	$0.362877\pi$
$282$	−16.0000	−0.952786
$283$	−1.00000	−0.0594438	−0.0297219	−	0.999558i	$-0.509462\pi$
$283$	−1.00000	−0.0594438	−0.0297219	+	0.999558i	$0.509462\pi$
$284$	−15.0000	−0.890086
$285$	24.0000	1.42164
$286$	−4.00000	−0.236525
$287$	0	0
$288$	1.00000	0.0589256
$289$	−17.0000	−1.00000
$290$	10.0000	0.587220
$291$	−8.00000	−0.468968
$292$	7.00000	0.409644
$293$	3.00000	0.175262	0.0876309	−	0.996153i	$-0.472070\pi$
$293$	3.00000	0.175262	0.0876309	+	0.996153i	$0.472070\pi$
$294$	0	0
$295$	−2.00000	−0.116445
$296$	−2.00000	−0.116248
$297$	16.0000	0.928414
$298$	1.00000	0.0579284
$299$	−2.00000	−0.115663
$300$	−2.00000	−0.115470
$301$	0	0
$302$	19.0000	1.09333
$303$	−20.0000	−1.14897
$304$	−6.00000	−0.344124
$305$	−28.0000	−1.60328
$306$	0	0
$307$	9.00000	0.513657	0.256829	−	0.966457i	$-0.417322\pi$
$307$	9.00000	0.513657	0.256829	+	0.966457i	$0.417322\pi$
$308$	0	0
$309$	−20.0000	−1.13776
$310$	−8.00000	−0.454369
$311$	13.0000	0.737162	0.368581	−	0.929596i	$-0.379844\pi$
$311$	13.0000	0.737162	0.368581	+	0.929596i	$0.379844\pi$
$312$	2.00000	0.113228
$313$	16.0000	0.904373	0.452187	−	0.891923i	$-0.350644\pi$
$313$	16.0000	0.904373	0.452187	+	0.891923i	$0.350644\pi$
$314$	−15.0000	−0.846499
$315$	0	0
$316$	0	0
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	−20.0000	−1.12154
$319$	20.0000	1.11979
$320$	−2.00000	−0.111803
$321$	26.0000	1.45118
$322$	0	0
$323$	0	0
$324$	−11.0000	−0.611111
$325$	−1.00000	−0.0554700
$326$	−23.0000	−1.27385
$327$	−14.0000	−0.774202
$328$	1.00000	0.0552158
$329$	0	0
$330$	16.0000	0.880771
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	9.00000	0.493939
$333$	−2.00000	−0.109599
$334$	5.00000	0.273588
$335$	−20.0000	−1.09272
$336$	0	0
$337$	31.0000	1.68868	0.844339	−	0.535810i	$-0.179994\pi$
$337$	31.0000	1.68868	0.844339	+	0.535810i	$0.179994\pi$
$338$	−12.0000	−0.652714
$339$	−6.00000	−0.325875
$340$	0	0
$341$	−16.0000	−0.866449
$342$	−6.00000	−0.324443
$343$	0	0
$344$	−1.00000	−0.0539164
$345$	8.00000	0.430706
$346$	24.0000	1.29025
$347$	−24.0000	−1.28839	−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000	−1.28839	−0.644194	+	0.764862i	$0.722807\pi$
$348$	−10.0000	−0.536056
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	−4.00000	−0.213201
$353$	21.0000	1.11772	0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000	1.11772	0.558859	+	0.829263i	$0.311239\pi$
$354$	2.00000	0.106299
$355$	30.0000	1.59223
$356$	0	0
$357$	0	0
$358$	−10.0000	−0.528516
$359$	14.0000	0.738892	0.369446	−	0.929252i	$-0.379548\pi$
$359$	14.0000	0.738892	0.369446	+	0.929252i	$0.379548\pi$
$360$	−2.00000	−0.105409
$361$	17.0000	0.894737
$362$	2.00000	0.105118
$363$	10.0000	0.524864
$364$	0	0
$365$	−14.0000	−0.732793
$366$	28.0000	1.46358
$367$	−18.0000	−0.939592	−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000	−0.939592	−0.469796	+	0.882775i	$0.655673\pi$
$368$	−2.00000	−0.104257
$369$	1.00000	0.0520579
$370$	4.00000	0.207950
$371$	0	0
$372$	8.00000	0.414781
$373$	16.0000	0.828449	0.414224	−	0.910175i	$-0.364053\pi$
$373$	16.0000	0.828449	0.414224	+	0.910175i	$0.364053\pi$
$374$	0	0
$375$	24.0000	1.23935
$376$	−8.00000	−0.412568
$377$	−5.00000	−0.257513
$378$	0	0
$379$	−29.0000	−1.48963	−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000	−1.48963	−0.744815	+	0.667271i	$0.767462\pi$
$380$	12.0000	0.615587
$381$	8.00000	0.409852
$382$	5.00000	0.255822
$383$	−15.0000	−0.766464	−0.383232	−	0.923652i	$-0.625189\pi$
$383$	−15.0000	−0.766464	−0.383232	+	0.923652i	$0.625189\pi$
$384$	2.00000	0.102062
$385$	0	0
$386$	−10.0000	−0.508987
$387$	−1.00000	−0.0508329
$388$	−4.00000	−0.203069
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	−4.00000	−0.202548
$391$	0	0
$392$	0	0
$393$	24.0000	1.21064
$394$	−2.00000	−0.100759
$395$	0	0
$396$	−4.00000	−0.201008
$397$	26.0000	1.30490	0.652451	−	0.757831i	$-0.273741\pi$
$397$	26.0000	1.30490	0.652451	+	0.757831i	$0.273741\pi$
$398$	−3.00000	−0.150376
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	25.0000	1.24844	0.624220	−	0.781248i	$-0.285417\pi$
$401$	25.0000	1.24844	0.624220	+	0.781248i	$0.285417\pi$
$402$	20.0000	0.997509
$403$	4.00000	0.199254
$404$	−10.0000	−0.497519
$405$	22.0000	1.09319
$406$	0	0
$407$	8.00000	0.396545
$408$	0	0
$409$	35.0000	1.73064	0.865319	−	0.501221i	$-0.167116\pi$
$409$	35.0000	1.73064	0.865319	+	0.501221i	$0.167116\pi$
$410$	−2.00000	−0.0987730
$411$	−36.0000	−1.77575
$412$	−10.0000	−0.492665
$413$	0	0
$414$	−2.00000	−0.0982946
$415$	−18.0000	−0.883585
$416$	1.00000	0.0490290
$417$	8.00000	0.391762
$418$	24.0000	1.17388
$419$	−33.0000	−1.61216	−0.806078	−	0.591810i	$-0.798414\pi$
$419$	−33.0000	−1.61216	−0.806078	+	0.591810i	$0.798414\pi$
$420$	0	0
$421$	−30.0000	−1.46211	−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000	−1.46211	−0.731055	+	0.682318i	$0.760972\pi$
$422$	0	0
$423$	−8.00000	−0.388973
$424$	−10.0000	−0.485643
$425$	0	0
$426$	−30.0000	−1.45350
$427$	0	0
$428$	13.0000	0.628379
$429$	−8.00000	−0.386244
$430$	2.00000	0.0964486
$431$	26.0000	1.25238	0.626188	−	0.779672i	$-0.284614\pi$
$431$	26.0000	1.25238	0.626188	+	0.779672i	$0.284614\pi$
$432$	−4.00000	−0.192450
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	0	0
$435$	20.0000	0.958927
$436$	−7.00000	−0.335239
$437$	12.0000	0.574038
$438$	14.0000	0.668946
$439$	−7.00000	−0.334092	−0.167046	−	0.985949i	$-0.553423\pi$
$439$	−7.00000	−0.334092	−0.167046	+	0.985949i	$0.553423\pi$
$440$	8.00000	0.381385
$441$	0	0
$442$	0	0
$443$	−15.0000	−0.712672	−0.356336	−	0.934358i	$-0.615974\pi$
$443$	−15.0000	−0.712672	−0.356336	+	0.934358i	$0.615974\pi$
$444$	−4.00000	−0.189832
$445$	0	0
$446$	26.0000	1.23114
$447$	2.00000	0.0945968
$448$	0	0
$449$	11.0000	0.519122	0.259561	−	0.965727i	$-0.416422\pi$
$449$	11.0000	0.519122	0.259561	+	0.965727i	$0.416422\pi$
$450$	−1.00000	−0.0471405
$451$	−4.00000	−0.188353
$452$	−3.00000	−0.141108
$453$	38.0000	1.78540
$454$	−18.0000	−0.844782
$455$	0	0
$456$	−12.0000	−0.561951
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	−21.0000	−0.981266
$459$	0	0
$460$	4.00000	0.186501
$461$	−20.0000	−0.931493	−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000	−0.931493	−0.465746	+	0.884918i	$0.654214\pi$
$462$	0	0
$463$	−7.00000	−0.325318	−0.162659	−	0.986682i	$-0.552007\pi$
$463$	−7.00000	−0.325318	−0.162659	+	0.986682i	$0.552007\pi$
$464$	−5.00000	−0.232119
$465$	−16.0000	−0.741982
$466$	−16.0000	−0.741186
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	16.0000	0.738025
$471$	−30.0000	−1.38233
$472$	1.00000	0.0460287
$473$	4.00000	0.183920
$474$	0	0
$475$	6.00000	0.275299
$476$	0	0
$477$	−10.0000	−0.457869
$478$	16.0000	0.731823
$479$	−7.00000	−0.319838	−0.159919	−	0.987130i	$-0.551123\pi$
$479$	−7.00000	−0.319838	−0.159919	+	0.987130i	$0.551123\pi$
$480$	−4.00000	−0.182574
$481$	−2.00000	−0.0911922
$482$	−5.00000	−0.227744
$483$	0	0
$484$	5.00000	0.227273
$485$	8.00000	0.363261
$486$	−10.0000	−0.453609
$487$	22.0000	0.996915	0.498458	−	0.866914i	$-0.333900\pi$
$487$	22.0000	0.996915	0.498458	+	0.866914i	$0.333900\pi$
$488$	14.0000	0.633750
$489$	−46.0000	−2.08019
$490$	0	0
$491$	−13.0000	−0.586682	−0.293341	−	0.956008i	$-0.594767\pi$
$491$	−13.0000	−0.586682	−0.293341	+	0.956008i	$0.594767\pi$
$492$	2.00000	0.0901670
$493$	0	0
$494$	−6.00000	−0.269953
$495$	8.00000	0.359573
$496$	4.00000	0.179605
$497$	0	0
$498$	18.0000	0.806599
$499$	36.0000	1.61158	0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000	1.61158	0.805791	+	0.592200i	$0.201741\pi$
$500$	12.0000	0.536656
$501$	10.0000	0.446767
$502$	−9.00000	−0.401690
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	0	0
$505$	20.0000	0.889988
$506$	8.00000	0.355643
$507$	−24.0000	−1.06588
$508$	4.00000	0.177471
$509$	19.0000	0.842160	0.421080	−	0.907023i	$-0.361651\pi$
$509$	19.0000	0.842160	0.421080	+	0.907023i	$0.361651\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	24.0000	1.05963
$514$	−2.00000	−0.0882162
$515$	20.0000	0.881305
$516$	−2.00000	−0.0880451
$517$	32.0000	1.40736
$518$	0	0
$519$	48.0000	2.10697
$520$	−2.00000	−0.0877058
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	−5.00000	−0.218844
$523$	−36.0000	−1.57417	−0.787085	−	0.616844i	$-0.788411\pi$
$523$	−36.0000	−1.57417	−0.787085	+	0.616844i	$0.788411\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	−31.0000	−1.35166
$527$	0	0
$528$	−8.00000	−0.348155
$529$	−19.0000	−0.826087
$530$	20.0000	0.868744
$531$	1.00000	0.0433963
$532$	0	0
$533$	1.00000	0.0433148
$534$	0	0
$535$	−26.0000	−1.12408
$536$	10.0000	0.431934
$537$	−20.0000	−0.863064
$538$	16.0000	0.689809
$539$	0	0
$540$	8.00000	0.344265
$541$	8.00000	0.343947	0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000	0.343947	0.171973	+	0.985102i	$0.444986\pi$
$542$	20.0000	0.859074
$543$	4.00000	0.171656
$544$	0	0
$545$	14.0000	0.599694
$546$	0	0
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	−18.0000	−0.768922
$549$	14.0000	0.597505
$550$	4.00000	0.170561
$551$	30.0000	1.27804
$552$	−4.00000	−0.170251
$553$	0	0
$554$	8.00000	0.339887
$555$	8.00000	0.339581
$556$	4.00000	0.169638
$557$	27.0000	1.14403	0.572013	−	0.820244i	$-0.306163\pi$
$557$	27.0000	1.14403	0.572013	+	0.820244i	$0.306163\pi$
$558$	4.00000	0.169334
$559$	−1.00000	−0.0422955
$560$	0	0
$561$	0	0
$562$	14.0000	0.590554
$563$	16.0000	0.674320	0.337160	−	0.941447i	$-0.390534\pi$
$563$	16.0000	0.674320	0.337160	+	0.941447i	$0.390534\pi$
$564$	−16.0000	−0.673722
$565$	6.00000	0.252422
$566$	−1.00000	−0.0420331
$567$	0	0
$568$	−15.0000	−0.629386
$569$	−3.00000	−0.125767	−0.0628833	−	0.998021i	$-0.520030\pi$
$569$	−3.00000	−0.125767	−0.0628833	+	0.998021i	$0.520030\pi$
$570$	24.0000	1.00525
$571$	−42.0000	−1.75765	−0.878823	−	0.477149i	$-0.841670\pi$
$571$	−42.0000	−1.75765	−0.878823	+	0.477149i	$0.841670\pi$
$572$	−4.00000	−0.167248
$573$	10.0000	0.417756
$574$	0	0
$575$	2.00000	0.0834058
$576$	1.00000	0.0416667
$577$	6.00000	0.249783	0.124892	−	0.992170i	$-0.460142\pi$
$577$	6.00000	0.249783	0.124892	+	0.992170i	$0.460142\pi$
$578$	−17.0000	−0.707107
$579$	−20.0000	−0.831172
$580$	10.0000	0.415227
$581$	0	0
$582$	−8.00000	−0.331611
$583$	40.0000	1.65663
$584$	7.00000	0.289662
$585$	−2.00000	−0.0826898
$586$	3.00000	0.123929
$587$	18.0000	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$588$	0	0
$589$	−24.0000	−0.988903
$590$	−2.00000	−0.0823387
$591$	−4.00000	−0.164538
$592$	−2.00000	−0.0821995
$593$	−38.0000	−1.56047	−0.780236	−	0.625485i	$-0.784901\pi$
$593$	−38.0000	−1.56047	−0.780236	+	0.625485i	$0.784901\pi$
$594$	16.0000	0.656488
$595$	0	0
$596$	1.00000	0.0409616
$597$	−6.00000	−0.245564
$598$	−2.00000	−0.0817861
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	−2.00000	−0.0816497
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	0	0
$603$	10.0000	0.407231
$604$	19.0000	0.773099
$605$	−10.0000	−0.406558
$606$	−20.0000	−0.812444
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	−6.00000	−0.243332
$609$	0	0
$610$	−28.0000	−1.13369
$611$	−8.00000	−0.323645
$612$	0	0
$613$	−6.00000	−0.242338	−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000	−0.242338	−0.121169	+	0.992632i	$0.538664\pi$
$614$	9.00000	0.363210
$615$	−4.00000	−0.161296
$616$	0	0
$617$	−3.00000	−0.120775	−0.0603877	−	0.998175i	$-0.519234\pi$
$617$	−3.00000	−0.120775	−0.0603877	+	0.998175i	$0.519234\pi$
$618$	−20.0000	−0.804518
$619$	−29.0000	−1.16561	−0.582804	−	0.812613i	$-0.698045\pi$
$619$	−29.0000	−1.16561	−0.582804	+	0.812613i	$0.698045\pi$
$620$	−8.00000	−0.321288
$621$	8.00000	0.321029
$622$	13.0000	0.521253
$623$	0	0
$624$	2.00000	0.0800641
$625$	−19.0000	−0.760000
$626$	16.0000	0.639489
$627$	48.0000	1.91694
$628$	−15.0000	−0.598565
$629$	0	0
$630$	0	0
$631$	30.0000	1.19428	0.597141	−	0.802137i	$-0.296303\pi$
$631$	30.0000	1.19428	0.597141	+	0.802137i	$0.296303\pi$
$632$	0	0
$633$	0	0
$634$	−2.00000	−0.0794301
$635$	−8.00000	−0.317470
$636$	−20.0000	−0.793052
$637$	0	0
$638$	20.0000	0.791808
$639$	−15.0000	−0.593391
$640$	−2.00000	−0.0790569
$641$	−6.00000	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$642$	26.0000	1.02614
$643$	24.0000	0.946468	0.473234	−	0.880937i	$-0.343087\pi$
$643$	24.0000	0.946468	0.473234	+	0.880937i	$0.343087\pi$
$644$	0	0
$645$	4.00000	0.157500
$646$	0	0
$647$	34.0000	1.33668	0.668339	−	0.743857i	$-0.267006\pi$
$647$	34.0000	1.33668	0.668339	+	0.743857i	$0.267006\pi$
$648$	−11.0000	−0.432121
$649$	−4.00000	−0.157014
$650$	−1.00000	−0.0392232
$651$	0	0
$652$	−23.0000	−0.900750
$653$	15.0000	0.586995	0.293498	−	0.955960i	$-0.405181\pi$
$653$	15.0000	0.586995	0.293498	+	0.955960i	$0.405181\pi$
$654$	−14.0000	−0.547443
$655$	−24.0000	−0.937758
$656$	1.00000	0.0390434
$657$	7.00000	0.273096
$658$	0	0
$659$	22.0000	0.856998	0.428499	−	0.903542i	$-0.359042\pi$
$659$	22.0000	0.856998	0.428499	+	0.903542i	$0.359042\pi$
$660$	16.0000	0.622799
$661$	−18.0000	−0.700119	−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000	−0.700119	−0.350059	+	0.936727i	$0.613839\pi$
$662$	12.0000	0.466393
$663$	0	0
$664$	9.00000	0.349268
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	10.0000	0.387202
$668$	5.00000	0.193456
$669$	52.0000	2.01044
$670$	−20.0000	−0.772667
$671$	−56.0000	−2.16186
$672$	0	0
$673$	40.0000	1.54189	0.770943	−	0.636904i	$-0.219785\pi$
$673$	40.0000	1.54189	0.770943	+	0.636904i	$0.219785\pi$
$674$	31.0000	1.19408
$675$	4.00000	0.153960
$676$	−12.0000	−0.461538
$677$	12.0000	0.461197	0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000	0.461197	0.230599	+	0.973049i	$0.425932\pi$
$678$	−6.00000	−0.230429
$679$	0	0
$680$	0	0
$681$	−36.0000	−1.37952
$682$	−16.0000	−0.612672
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	−6.00000	−0.229416
$685$	36.0000	1.37549
$686$	0	0
$687$	−42.0000	−1.60240
$688$	−1.00000	−0.0381246
$689$	−10.0000	−0.380970
$690$	8.00000	0.304555
$691$	−30.0000	−1.14125	−0.570627	−	0.821209i	$-0.693300\pi$
$691$	−30.0000	−1.14125	−0.570627	+	0.821209i	$0.693300\pi$
$692$	24.0000	0.912343
$693$	0	0
$694$	−24.0000	−0.911028
$695$	−8.00000	−0.303457
$696$	−10.0000	−0.379049
$697$	0	0
$698$	−26.0000	−0.984115
$699$	−32.0000	−1.21035
$700$	0	0
$701$	−44.0000	−1.66186	−0.830929	−	0.556379i	$-0.812190\pi$
$701$	−44.0000	−1.66186	−0.830929	+	0.556379i	$0.812190\pi$
$702$	−4.00000	−0.150970
$703$	12.0000	0.452589
$704$	−4.00000	−0.150756
$705$	32.0000	1.20519
$706$	21.0000	0.790345
$707$	0	0
$708$	2.00000	0.0751646
$709$	35.0000	1.31445	0.657226	−	0.753693i	$-0.271730\pi$
$709$	35.0000	1.31445	0.657226	+	0.753693i	$0.271730\pi$
$710$	30.0000	1.12588
$711$	0	0
$712$	0	0
$713$	−8.00000	−0.299602
$714$	0	0
$715$	8.00000	0.299183
$716$	−10.0000	−0.373718
$717$	32.0000	1.19506
$718$	14.0000	0.522475
$719$	−31.0000	−1.15610	−0.578052	−	0.816000i	$-0.696187\pi$
$719$	−31.0000	−1.15610	−0.578052	+	0.816000i	$0.696187\pi$
$720$	−2.00000	−0.0745356
$721$	0	0
$722$	17.0000	0.632674
$723$	−10.0000	−0.371904
$724$	2.00000	0.0743294
$725$	5.00000	0.185695
$726$	10.0000	0.371135
$727$	−43.0000	−1.59478	−0.797391	−	0.603463i	$-0.793787\pi$
$727$	−43.0000	−1.59478	−0.797391	+	0.603463i	$0.793787\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	−14.0000	−0.518163
$731$	0	0
$732$	28.0000	1.03491
$733$	−42.0000	−1.55131	−0.775653	−	0.631160i	$-0.782579\pi$
$733$	−42.0000	−1.55131	−0.775653	+	0.631160i	$0.782579\pi$
$734$	−18.0000	−0.664392
$735$	0	0
$736$	−2.00000	−0.0737210
$737$	−40.0000	−1.47342
$738$	1.00000	0.0368105
$739$	−15.0000	−0.551784	−0.275892	−	0.961189i	$-0.588973\pi$
$739$	−15.0000	−0.551784	−0.275892	+	0.961189i	$0.588973\pi$
$740$	4.00000	0.147043
$741$	−12.0000	−0.440831
$742$	0	0
$743$	−36.0000	−1.32071	−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000	−1.32071	−0.660356	+	0.750953i	$0.729595\pi$
$744$	8.00000	0.293294
$745$	−2.00000	−0.0732743
$746$	16.0000	0.585802
$747$	9.00000	0.329293
$748$	0	0
$749$	0	0
$750$	24.0000	0.876356
$751$	5.00000	0.182453	0.0912263	−	0.995830i	$-0.470921\pi$
$751$	5.00000	0.182453	0.0912263	+	0.995830i	$0.470921\pi$
$752$	−8.00000	−0.291730
$753$	−18.0000	−0.655956
$754$	−5.00000	−0.182089
$755$	−38.0000	−1.38296
$756$	0	0
$757$	31.0000	1.12671	0.563357	−	0.826214i	$-0.309510\pi$
$757$	31.0000	1.12671	0.563357	+	0.826214i	$0.309510\pi$
$758$	−29.0000	−1.05333
$759$	16.0000	0.580763
$760$	12.0000	0.435286
$761$	−50.0000	−1.81250	−0.906249	−	0.422744i	$-0.861067\pi$
$761$	−50.0000	−1.81250	−0.906249	+	0.422744i	$0.861067\pi$
$762$	8.00000	0.289809
$763$	0	0
$764$	5.00000	0.180894
$765$	0	0
$766$	−15.0000	−0.541972
$767$	1.00000	0.0361079
$768$	2.00000	0.0721688
$769$	−34.0000	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$770$	0	0
$771$	−4.00000	−0.144056
$772$	−10.0000	−0.359908
$773$	−14.0000	−0.503545	−0.251773	−	0.967786i	$-0.581013\pi$
$773$	−14.0000	−0.503545	−0.251773	+	0.967786i	$0.581013\pi$
$774$	−1.00000	−0.0359443
$775$	−4.00000	−0.143684
$776$	−4.00000	−0.143592
$777$	0	0
$778$	0	0
$779$	−6.00000	−0.214972
$780$	−4.00000	−0.143223
$781$	60.0000	2.14697
$782$	0	0
$783$	20.0000	0.714742
$784$	0	0
$785$	30.0000	1.07075
$786$	24.0000	0.856052
$787$	40.0000	1.42585	0.712923	−	0.701242i	$-0.247371\pi$
$787$	40.0000	1.42585	0.712923	+	0.701242i	$0.247371\pi$
$788$	−2.00000	−0.0712470
$789$	−62.0000	−2.20726
$790$	0	0
$791$	0	0
$792$	−4.00000	−0.142134
$793$	14.0000	0.497155
$794$	26.0000	0.922705
$795$	40.0000	1.41865
$796$	−3.00000	−0.106332
$797$	−14.0000	−0.495905	−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−14.0000	−0.495905	−0.247953	+	0.968772i	$0.579758\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	25.0000	0.882781
$803$	−28.0000	−0.988099
$804$	20.0000	0.705346
$805$	0	0
$806$	4.00000	0.140894
$807$	32.0000	1.12645
$808$	−10.0000	−0.351799
$809$	−50.0000	−1.75791	−0.878953	−	0.476908i	$-0.841757\pi$
$809$	−50.0000	−1.75791	−0.878953	+	0.476908i	$0.841757\pi$
$810$	22.0000	0.773001
$811$	33.0000	1.15879	0.579393	−	0.815048i	$-0.303290\pi$
$811$	33.0000	1.15879	0.579393	+	0.815048i	$0.303290\pi$
$812$	0	0
$813$	40.0000	1.40286
$814$	8.00000	0.280400
$815$	46.0000	1.61131
$816$	0	0
$817$	6.00000	0.209913
$818$	35.0000	1.22375
$819$	0	0
$820$	−2.00000	−0.0698430
$821$	−52.0000	−1.81481	−0.907406	−	0.420255i	$-0.861941\pi$
$821$	−52.0000	−1.81481	−0.907406	+	0.420255i	$0.861941\pi$
$822$	−36.0000	−1.25564
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	−10.0000	−0.348367
$825$	8.00000	0.278524
$826$	0	0
$827$	−54.0000	−1.87776	−0.938882	−	0.344239i	$-0.888137\pi$
$827$	−54.0000	−1.87776	−0.938882	+	0.344239i	$0.888137\pi$
$828$	−2.00000	−0.0695048
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	−18.0000	−0.624789
$831$	16.0000	0.555034
$832$	1.00000	0.0346688
$833$	0	0
$834$	8.00000	0.277017
$835$	−10.0000	−0.346064
$836$	24.0000	0.830057
$837$	−16.0000	−0.553041
$838$	−33.0000	−1.13997
$839$	−29.0000	−1.00119	−0.500596	−	0.865681i	$-0.666886\pi$
$839$	−29.0000	−1.00119	−0.500596	+	0.865681i	$0.666886\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−30.0000	−1.03387
$843$	28.0000	0.964371
$844$	0	0
$845$	24.0000	0.825625
$846$	−8.00000	−0.275046
$847$	0	0
$848$	−10.0000	−0.343401
$849$	−2.00000	−0.0686398
$850$	0	0
$851$	4.00000	0.137118
$852$	−30.0000	−1.02778
$853$	−38.0000	−1.30110	−0.650548	−	0.759465i	$-0.725461\pi$
$853$	−38.0000	−1.30110	−0.650548	+	0.759465i	$0.725461\pi$
$854$	0	0
$855$	12.0000	0.410391
$856$	13.0000	0.444331
$857$	−53.0000	−1.81045	−0.905223	−	0.424937i	$-0.860296\pi$
$857$	−53.0000	−1.81045	−0.905223	+	0.424937i	$0.860296\pi$
$858$	−8.00000	−0.273115
$859$	−13.0000	−0.443554	−0.221777	−	0.975097i	$-0.571186\pi$
$859$	−13.0000	−0.443554	−0.221777	+	0.975097i	$0.571186\pi$
$860$	2.00000	0.0681994
$861$	0	0
$862$	26.0000	0.885564
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	−4.00000	−0.136083
$865$	−48.0000	−1.63205
$866$	2.00000	0.0679628
$867$	−34.0000	−1.15470
$868$	0	0
$869$	0	0
$870$	20.0000	0.678064
$871$	10.0000	0.338837
$872$	−7.00000	−0.237050
$873$	−4.00000	−0.135379
$874$	12.0000	0.405906
$875$	0	0
$876$	14.0000	0.473016
$877$	−52.0000	−1.75592	−0.877958	−	0.478738i	$-0.841094\pi$
$877$	−52.0000	−1.75592	−0.877958	+	0.478738i	$0.841094\pi$
$878$	−7.00000	−0.236239
$879$	6.00000	0.202375
$880$	8.00000	0.269680
$881$	−7.00000	−0.235836	−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000	−0.235836	−0.117918	+	0.993023i	$0.537622\pi$
$882$	0	0
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	0	0
$885$	−4.00000	−0.134459
$886$	−15.0000	−0.503935
$887$	13.0000	0.436497	0.218249	−	0.975893i	$-0.429966\pi$
$887$	13.0000	0.436497	0.218249	+	0.975893i	$0.429966\pi$
$888$	−4.00000	−0.134231
$889$	0	0
$890$	0	0
$891$	44.0000	1.47406
$892$	26.0000	0.870544
$893$	48.0000	1.60626
$894$	2.00000	0.0668900
$895$	20.0000	0.668526
$896$	0	0
$897$	−4.00000	−0.133556
$898$	11.0000	0.367075
$899$	−20.0000	−0.667037
$900$	−1.00000	−0.0333333
$901$	0	0
$902$	−4.00000	−0.133185
$903$	0	0
$904$	−3.00000	−0.0997785
$905$	−4.00000	−0.132964
$906$	38.0000	1.26247
$907$	23.0000	0.763702	0.381851	−	0.924224i	$-0.375287\pi$
$907$	23.0000	0.763702	0.381851	+	0.924224i	$0.375287\pi$
$908$	−18.0000	−0.597351
$909$	−10.0000	−0.331679
$910$	0	0
$911$	40.0000	1.32526	0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000	1.32526	0.662630	+	0.748947i	$0.269440\pi$
$912$	−12.0000	−0.397360
$913$	−36.0000	−1.19143
$914$	26.0000	0.860004
$915$	−56.0000	−1.85130
$916$	−21.0000	−0.693860
$917$	0	0
$918$	0	0
$919$	23.0000	0.758700	0.379350	−	0.925253i	$-0.376148\pi$
$919$	23.0000	0.758700	0.379350	+	0.925253i	$0.376148\pi$
$920$	4.00000	0.131876
$921$	18.0000	0.593120
$922$	−20.0000	−0.658665
$923$	−15.0000	−0.493731
$924$	0	0
$925$	2.00000	0.0657596
$926$	−7.00000	−0.230034
$927$	−10.0000	−0.328443
$928$	−5.00000	−0.164133
$929$	−38.0000	−1.24674	−0.623370	−	0.781927i	$-0.714237\pi$
$929$	−38.0000	−1.24674	−0.623370	+	0.781927i	$0.714237\pi$
$930$	−16.0000	−0.524661
$931$	0	0
$932$	−16.0000	−0.524097
$933$	26.0000	0.851202
$934$	−12.0000	−0.392652
$935$	0	0
$936$	1.00000	0.0326860
$937$	30.0000	0.980057	0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000	0.980057	0.490029	+	0.871706i	$0.336986\pi$
$938$	0	0
$939$	32.0000	1.04428
$940$	16.0000	0.521862
$941$	36.0000	1.17357	0.586783	−	0.809744i	$-0.300394\pi$
$941$	36.0000	1.17357	0.586783	+	0.809744i	$0.300394\pi$
$942$	−30.0000	−0.977453
$943$	−2.00000	−0.0651290
$944$	1.00000	0.0325472
$945$	0	0
$946$	4.00000	0.130051
$947$	45.0000	1.46230	0.731152	−	0.682215i	$-0.238983\pi$
$947$	45.0000	1.46230	0.731152	+	0.682215i	$0.238983\pi$
$948$	0	0
$949$	7.00000	0.227230
$950$	6.00000	0.194666
$951$	−4.00000	−0.129709
$952$	0	0
$953$	−9.00000	−0.291539	−0.145769	−	0.989319i	$-0.546566\pi$
$953$	−9.00000	−0.291539	−0.145769	+	0.989319i	$0.546566\pi$
$954$	−10.0000	−0.323762
$955$	−10.0000	−0.323592
$956$	16.0000	0.517477
$957$	40.0000	1.29302
$958$	−7.00000	−0.226160
$959$	0	0
$960$	−4.00000	−0.129099
$961$	−15.0000	−0.483871
$962$	−2.00000	−0.0644826
$963$	13.0000	0.418919
$964$	−5.00000	−0.161039
$965$	20.0000	0.643823
$966$	0	0
$967$	31.0000	0.996893	0.498446	−	0.866921i	$-0.333904\pi$
$967$	31.0000	0.996893	0.498446	+	0.866921i	$0.333904\pi$
$968$	5.00000	0.160706
$969$	0	0
$970$	8.00000	0.256865
$971$	2.00000	0.0641831	0.0320915	−	0.999485i	$-0.489783\pi$
$971$	2.00000	0.0641831	0.0320915	+	0.999485i	$0.489783\pi$
$972$	−10.0000	−0.320750
$973$	0	0
$974$	22.0000	0.704925
$975$	−2.00000	−0.0640513
$976$	14.0000	0.448129
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	−46.0000	−1.47092
$979$	0	0
$980$	0	0
$981$	−7.00000	−0.223493
$982$	−13.0000	−0.414847
$983$	44.0000	1.40338	0.701691	−	0.712481i	$-0.252429\pi$
$983$	44.0000	1.40338	0.701691	+	0.712481i	$0.252429\pi$
$984$	2.00000	0.0637577
$985$	4.00000	0.127451
$986$	0	0
$987$	0	0
$988$	−6.00000	−0.190885
$989$	2.00000	0.0635963
$990$	8.00000	0.254257
$991$	−19.0000	−0.603555	−0.301777	−	0.953378i	$-0.597580\pi$
$991$	−19.0000	−0.603555	−0.301777	+	0.953378i	$0.597580\pi$
$992$	4.00000	0.127000
$993$	24.0000	0.761617
$994$	0	0
$995$	6.00000	0.190213
$996$	18.0000	0.570352
$997$	−35.0000	−1.10846	−0.554231	−	0.832363i	$-0.686987\pi$
$997$	−35.0000	−1.10846	−0.554231	+	0.832363i	$0.686987\pi$
$998$	36.0000	1.13956
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.r.1.1		1
7.2	even	3		574.2.e.a.165.1	✓	2
7.4	even	3		574.2.e.a.247.1	yes	2
7.6	odd	2		4018.2.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.a.165.1	✓	2	7.2	even	3
574.2.e.a.247.1	yes	2	7.4	even	3
4018.2.a.l.1.1		1	7.6	odd	2
4018.2.a.r.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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
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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