LMFDB - Embedded newform 6018.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
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	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} -3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} -3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} +2.00000 q^{11} +1.00000 q^{12} -2.00000 q^{13} -3.00000 q^{14} -2.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +1.00000 q^{19} -2.00000 q^{20} -3.00000 q^{21} +2.00000 q^{22} +3.00000 q^{23} +1.00000 q^{24} -1.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} -3.00000 q^{28} -4.00000 q^{29} -2.00000 q^{30} +2.00000 q^{31} +1.00000 q^{32} +2.00000 q^{33} +1.00000 q^{34} +6.00000 q^{35} +1.00000 q^{36} +4.00000 q^{37} +1.00000 q^{38} -2.00000 q^{39} -2.00000 q^{40} -11.0000 q^{41} -3.00000 q^{42} -6.00000 q^{43} +2.00000 q^{44} -2.00000 q^{45} +3.00000 q^{46} +1.00000 q^{48} +2.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} -2.00000 q^{52} +3.00000 q^{53} +1.00000 q^{54} -4.00000 q^{55} -3.00000 q^{56} +1.00000 q^{57} -4.00000 q^{58} +1.00000 q^{59} -2.00000 q^{60} +2.00000 q^{61} +2.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} +2.00000 q^{66} -6.00000 q^{67} +1.00000 q^{68} +3.00000 q^{69} +6.00000 q^{70} -6.00000 q^{71} +1.00000 q^{72} -11.0000 q^{73} +4.00000 q^{74} -1.00000 q^{75} +1.00000 q^{76} -6.00000 q^{77} -2.00000 q^{78} -8.00000 q^{79} -2.00000 q^{80} +1.00000 q^{81} -11.0000 q^{82} -11.0000 q^{83} -3.00000 q^{84} -2.00000 q^{85} -6.00000 q^{86} -4.00000 q^{87} +2.00000 q^{88} -9.00000 q^{89} -2.00000 q^{90} +6.00000 q^{91} +3.00000 q^{92} +2.00000 q^{93} -2.00000 q^{95} +1.00000 q^{96} +1.00000 q^{97} +2.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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
$3$	1.00000	0.577350
$4$	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	$0.647584\pi$
$6$	1.00000	0.408248
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	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
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−3.00000	−0.801784
$15$	−2.00000	−0.516398
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	−2.00000	−0.447214
$21$	−3.00000	−0.654654
$22$	2.00000	0.426401
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	1.00000	0.204124
$25$	−1.00000	−0.200000
$26$	−2.00000	−0.392232
$27$	1.00000	0.192450
$28$	−3.00000	−0.566947
$29$	−4.00000	−0.742781	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000	−0.742781	−0.371391	+	0.928477i	$0.621119\pi$
$30$	−2.00000	−0.365148
$31$	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
$33$	2.00000	0.348155
$34$	1.00000	0.171499
$35$	6.00000	1.01419
$36$	1.00000	0.166667
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	1.00000	0.162221
$39$	−2.00000	−0.320256
$40$	−2.00000	−0.316228
$41$	−11.0000	−1.71791	−0.858956	−	0.512050i	$-0.828886\pi$
$41$	−11.0000	−1.71791	−0.858956	+	0.512050i	$0.828886\pi$
$42$	−3.00000	−0.462910
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	2.00000	0.301511
$45$	−2.00000	−0.298142
$46$	3.00000	0.442326
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	2.00000	0.285714
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	−2.00000	−0.277350
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	1.00000	0.136083
$55$	−4.00000	−0.539360
$56$	−3.00000	−0.400892
$57$	1.00000	0.132453
$58$	−4.00000	−0.525226
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−2.00000	−0.258199
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	2.00000	0.254000
$63$	−3.00000	−0.377964
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	2.00000	0.246183
$67$	−6.00000	−0.733017	−0.366508	−	0.930415i	$-0.619447\pi$
$67$	−6.00000	−0.733017	−0.366508	+	0.930415i	$0.619447\pi$
$68$	1.00000	0.121268
$69$	3.00000	0.361158
$70$	6.00000	0.717137
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	1.00000	0.117851
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	4.00000	0.464991
$75$	−1.00000	−0.115470
$76$	1.00000	0.114708
$77$	−6.00000	−0.683763
$78$	−2.00000	−0.226455
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−2.00000	−0.223607
$81$	1.00000	0.111111
$82$	−11.0000	−1.21475
$83$	−11.0000	−1.20741	−0.603703	−	0.797209i	$-0.706309\pi$
$83$	−11.0000	−1.20741	−0.603703	+	0.797209i	$0.706309\pi$
$84$	−3.00000	−0.327327
$85$	−2.00000	−0.216930
$86$	−6.00000	−0.646997
$87$	−4.00000	−0.428845
$88$	2.00000	0.213201
$89$	−9.00000	−0.953998	−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000	−0.953998	−0.476999	+	0.878904i	$0.658275\pi$
$90$	−2.00000	−0.210819
$91$	6.00000	0.628971
$92$	3.00000	0.312772
$93$	2.00000	0.207390
$94$	0	0
$95$	−2.00000	−0.205196
$96$	1.00000	0.102062
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	2.00000	0.202031
$99$	2.00000	0.201008
$100$	−1.00000	−0.100000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	1.00000	0.0990148
$103$	−17.0000	−1.67506	−0.837530	−	0.546392i	$-0.816001\pi$
$103$	−17.0000	−1.67506	−0.837530	+	0.546392i	$0.816001\pi$
$104$	−2.00000	−0.196116
$105$	6.00000	0.585540
$106$	3.00000	0.291386
$107$	−13.0000	−1.25676	−0.628379	−	0.777908i	$-0.716281\pi$
$107$	−13.0000	−1.25676	−0.628379	+	0.777908i	$0.716281\pi$
$108$	1.00000	0.0962250
$109$	20.0000	1.91565	0.957826	−	0.287348i	$-0.0927736\pi$
$109$	20.0000	1.91565	0.957826	+	0.287348i	$0.0927736\pi$
$110$	−4.00000	−0.381385
$111$	4.00000	0.379663
$112$	−3.00000	−0.283473
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	1.00000	0.0936586
$115$	−6.00000	−0.559503
$116$	−4.00000	−0.371391
$117$	−2.00000	−0.184900
$118$	1.00000	0.0920575
$119$	−3.00000	−0.275010
$120$	−2.00000	−0.182574
$121$	−7.00000	−0.636364
$122$	2.00000	0.181071
$123$	−11.0000	−0.991837
$124$	2.00000	0.179605
$125$	12.0000	1.07331
$126$	−3.00000	−0.267261
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	1.00000	0.0883883
$129$	−6.00000	−0.528271
$130$	4.00000	0.350823
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	2.00000	0.174078
$133$	−3.00000	−0.260133
$134$	−6.00000	−0.518321
$135$	−2.00000	−0.172133
$136$	1.00000	0.0857493
$137$	−8.00000	−0.683486	−0.341743	−	0.939793i	$-0.611017\pi$
$137$	−8.00000	−0.683486	−0.341743	+	0.939793i	$0.611017\pi$
$138$	3.00000	0.255377
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	6.00000	0.507093
$141$	0	0
$142$	−6.00000	−0.503509
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	8.00000	0.664364
$146$	−11.0000	−0.910366
$147$	2.00000	0.164957
$148$	4.00000	0.328798
$149$	−4.00000	−0.327693	−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000	−0.327693	−0.163846	+	0.986486i	$0.552390\pi$
$150$	−1.00000	−0.0816497
$151$	−15.0000	−1.22068	−0.610341	−	0.792139i	$-0.708968\pi$
$151$	−15.0000	−1.22068	−0.610341	+	0.792139i	$0.708968\pi$
$152$	1.00000	0.0811107
$153$	1.00000	0.0808452
$154$	−6.00000	−0.483494
$155$	−4.00000	−0.321288
$156$	−2.00000	−0.160128
$157$	−17.0000	−1.35675	−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000	−1.35675	−0.678374	+	0.734717i	$0.737315\pi$
$158$	−8.00000	−0.636446
$159$	3.00000	0.237915
$160$	−2.00000	−0.158114
$161$	−9.00000	−0.709299
$162$	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	$0.449930\pi$
$164$	−11.0000	−0.858956
$165$	−4.00000	−0.311400
$166$	−11.0000	−0.853766
$167$	4.00000	0.309529	0.154765	−	0.987951i	$-0.450538\pi$
$167$	4.00000	0.309529	0.154765	+	0.987951i	$0.450538\pi$
$168$	−3.00000	−0.231455
$169$	−9.00000	−0.692308
$170$	−2.00000	−0.153393
$171$	1.00000	0.0764719
$172$	−6.00000	−0.457496
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	−4.00000	−0.303239
$175$	3.00000	0.226779
$176$	2.00000	0.150756
$177$	1.00000	0.0751646
$178$	−9.00000	−0.674579
$179$	15.0000	1.12115	0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$180$	−2.00000	−0.149071
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	6.00000	0.444750
$183$	2.00000	0.147844
$184$	3.00000	0.221163
$185$	−8.00000	−0.588172
$186$	2.00000	0.146647
$187$	2.00000	0.146254
$188$	0	0
$189$	−3.00000	−0.218218
$190$	−2.00000	−0.145095
$191$	−10.0000	−0.723575	−0.361787	−	0.932261i	$-0.617833\pi$
$191$	−10.0000	−0.723575	−0.361787	+	0.932261i	$0.617833\pi$
$192$	1.00000	0.0721688
$193$	−12.0000	−0.863779	−0.431889	−	0.901927i	$-0.642153\pi$
$193$	−12.0000	−0.863779	−0.431889	+	0.901927i	$0.642153\pi$
$194$	1.00000	0.0717958
$195$	4.00000	0.286446
$196$	2.00000	0.142857
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	2.00000	0.142134
$199$	9.00000	0.637993	0.318997	−	0.947756i	$-0.396654\pi$
$199$	9.00000	0.637993	0.318997	+	0.947756i	$0.396654\pi$
$200$	−1.00000	−0.0707107
$201$	−6.00000	−0.423207
$202$	14.0000	0.985037
$203$	12.0000	0.842235
$204$	1.00000	0.0700140
$205$	22.0000	1.53655
$206$	−17.0000	−1.18445
$207$	3.00000	0.208514
$208$	−2.00000	−0.138675
$209$	2.00000	0.138343
$210$	6.00000	0.414039
$211$	−16.0000	−1.10149	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000	−1.10149	−0.550743	+	0.834675i	$0.685655\pi$
$212$	3.00000	0.206041
$213$	−6.00000	−0.411113
$214$	−13.0000	−0.888662
$215$	12.0000	0.818393
$216$	1.00000	0.0680414
$217$	−6.00000	−0.407307
$218$	20.0000	1.35457
$219$	−11.0000	−0.743311
$220$	−4.00000	−0.269680
$221$	−2.00000	−0.134535
$222$	4.00000	0.268462
$223$	28.0000	1.87502	0.937509	−	0.347960i	$-0.113126\pi$
$223$	28.0000	1.87502	0.937509	+	0.347960i	$0.113126\pi$
$224$	−3.00000	−0.200446
$225$	−1.00000	−0.0666667
$226$	2.00000	0.133038
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	1.00000	0.0662266
$229$	1.00000	0.0660819	0.0330409	−	0.999454i	$-0.489481\pi$
$229$	1.00000	0.0660819	0.0330409	+	0.999454i	$0.489481\pi$
$230$	−6.00000	−0.395628
$231$	−6.00000	−0.394771
$232$	−4.00000	−0.262613
$233$	−22.0000	−1.44127	−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000	−1.44127	−0.720634	+	0.693316i	$0.756149\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	1.00000	0.0650945
$237$	−8.00000	−0.519656
$238$	−3.00000	−0.194461
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	−2.00000	−0.129099
$241$	20.0000	1.28831	0.644157	−	0.764894i	$-0.277208\pi$
$241$	20.0000	1.28831	0.644157	+	0.764894i	$0.277208\pi$
$242$	−7.00000	−0.449977
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	−4.00000	−0.255551
$246$	−11.0000	−0.701334
$247$	−2.00000	−0.127257
$248$	2.00000	0.127000
$249$	−11.0000	−0.697097
$250$	12.0000	0.758947
$251$	−14.0000	−0.883672	−0.441836	−	0.897096i	$-0.645673\pi$
$251$	−14.0000	−0.883672	−0.441836	+	0.897096i	$0.645673\pi$
$252$	−3.00000	−0.188982
$253$	6.00000	0.377217
$254$	−12.0000	−0.752947
$255$	−2.00000	−0.125245
$256$	1.00000	0.0625000
$257$	14.0000	0.873296	0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000	0.873296	0.436648	+	0.899632i	$0.356166\pi$
$258$	−6.00000	−0.373544
$259$	−12.0000	−0.745644
$260$	4.00000	0.248069
$261$	−4.00000	−0.247594
$262$	6.00000	0.370681
$263$	−11.0000	−0.678289	−0.339145	−	0.940734i	$-0.610138\pi$
$263$	−11.0000	−0.678289	−0.339145	+	0.940734i	$0.610138\pi$
$264$	2.00000	0.123091
$265$	−6.00000	−0.368577
$266$	−3.00000	−0.183942
$267$	−9.00000	−0.550791
$268$	−6.00000	−0.366508
$269$	−3.00000	−0.182913	−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000	−0.182913	−0.0914566	+	0.995809i	$0.529152\pi$
$270$	−2.00000	−0.121716
$271$	28.0000	1.70088	0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000	1.70088	0.850439	+	0.526073i	$0.176336\pi$
$272$	1.00000	0.0606339
$273$	6.00000	0.363137
$274$	−8.00000	−0.483298
$275$	−2.00000	−0.120605
$276$	3.00000	0.180579
$277$	−3.00000	−0.180253	−0.0901263	−	0.995930i	$-0.528727\pi$
$277$	−3.00000	−0.180253	−0.0901263	+	0.995930i	$0.528727\pi$
$278$	−4.00000	−0.239904
$279$	2.00000	0.119737
$280$	6.00000	0.358569
$281$	−30.0000	−1.78965	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000	−1.78965	−0.894825	+	0.446417i	$0.852700\pi$
$282$	0	0
$283$	−15.0000	−0.891657	−0.445829	−	0.895118i	$-0.647091\pi$
$283$	−15.0000	−0.891657	−0.445829	+	0.895118i	$0.647091\pi$
$284$	−6.00000	−0.356034
$285$	−2.00000	−0.118470
$286$	−4.00000	−0.236525
$287$	33.0000	1.94793
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	8.00000	0.469776
$291$	1.00000	0.0586210
$292$	−11.0000	−0.643726
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	2.00000	0.116642
$295$	−2.00000	−0.116445
$296$	4.00000	0.232495
$297$	2.00000	0.116052
$298$	−4.00000	−0.231714
$299$	−6.00000	−0.346989
$300$	−1.00000	−0.0577350
$301$	18.0000	1.03750
$302$	−15.0000	−0.863153
$303$	14.0000	0.804279
$304$	1.00000	0.0573539
$305$	−4.00000	−0.229039
$306$	1.00000	0.0571662
$307$	−21.0000	−1.19853	−0.599267	−	0.800549i	$-0.704541\pi$
$307$	−21.0000	−1.19853	−0.599267	+	0.800549i	$0.704541\pi$
$308$	−6.00000	−0.341882
$309$	−17.0000	−0.967096
$310$	−4.00000	−0.227185
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	−2.00000	−0.113228
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	−17.0000	−0.959366
$315$	6.00000	0.338062
$316$	−8.00000	−0.450035
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	3.00000	0.168232
$319$	−8.00000	−0.447914
$320$	−2.00000	−0.111803
$321$	−13.0000	−0.725589
$322$	−9.00000	−0.501550
$323$	1.00000	0.0556415
$324$	1.00000	0.0555556
$325$	2.00000	0.110940
$326$	4.00000	0.221540
$327$	20.0000	1.10600
$328$	−11.0000	−0.607373
$329$	0	0
$330$	−4.00000	−0.220193
$331$	13.0000	0.714545	0.357272	−	0.934000i	$-0.383707\pi$
$331$	13.0000	0.714545	0.357272	+	0.934000i	$0.383707\pi$
$332$	−11.0000	−0.603703
$333$	4.00000	0.219199
$334$	4.00000	0.218870
$335$	12.0000	0.655630
$336$	−3.00000	−0.163663
$337$	19.0000	1.03500	0.517498	−	0.855684i	$-0.326864\pi$
$337$	19.0000	1.03500	0.517498	+	0.855684i	$0.326864\pi$
$338$	−9.00000	−0.489535
$339$	2.00000	0.108625
$340$	−2.00000	−0.108465
$341$	4.00000	0.216612
$342$	1.00000	0.0540738
$343$	15.0000	0.809924
$344$	−6.00000	−0.323498
$345$	−6.00000	−0.323029
$346$	18.0000	0.967686
$347$	4.00000	0.214731	0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000	0.214731	0.107366	+	0.994220i	$0.465758\pi$
$348$	−4.00000	−0.214423
$349$	11.0000	0.588817	0.294408	−	0.955680i	$-0.404877\pi$
$349$	11.0000	0.588817	0.294408	+	0.955680i	$0.404877\pi$
$350$	3.00000	0.160357
$351$	−2.00000	−0.106752
$352$	2.00000	0.106600
$353$	21.0000	1.11772	0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000	1.11772	0.558859	+	0.829263i	$0.311239\pi$
$354$	1.00000	0.0531494
$355$	12.0000	0.636894
$356$	−9.00000	−0.476999
$357$	−3.00000	−0.158777
$358$	15.0000	0.792775
$359$	9.00000	0.475002	0.237501	−	0.971387i	$-0.423672\pi$
$359$	9.00000	0.475002	0.237501	+	0.971387i	$0.423672\pi$
$360$	−2.00000	−0.105409
$361$	−18.0000	−0.947368
$362$	14.0000	0.735824
$363$	−7.00000	−0.367405
$364$	6.00000	0.314485
$365$	22.0000	1.15153
$366$	2.00000	0.104542
$367$	24.0000	1.25279	0.626395	−	0.779506i	$-0.284530\pi$
$367$	24.0000	1.25279	0.626395	+	0.779506i	$0.284530\pi$
$368$	3.00000	0.156386
$369$	−11.0000	−0.572637
$370$	−8.00000	−0.415900
$371$	−9.00000	−0.467257
$372$	2.00000	0.103695
$373$	−24.0000	−1.24267	−0.621336	−	0.783544i	$-0.713410\pi$
$373$	−24.0000	−1.24267	−0.621336	+	0.783544i	$0.713410\pi$
$374$	2.00000	0.103418
$375$	12.0000	0.619677
$376$	0	0
$377$	8.00000	0.412021
$378$	−3.00000	−0.154303
$379$	2.00000	0.102733	0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000	0.102733	0.0513665	+	0.998680i	$0.483642\pi$
$380$	−2.00000	−0.102598
$381$	−12.0000	−0.614779
$382$	−10.0000	−0.511645
$383$	−13.0000	−0.664269	−0.332134	−	0.943232i	$-0.607769\pi$
$383$	−13.0000	−0.664269	−0.332134	+	0.943232i	$0.607769\pi$
$384$	1.00000	0.0510310
$385$	12.0000	0.611577
$386$	−12.0000	−0.610784
$387$	−6.00000	−0.304997
$388$	1.00000	0.0507673
$389$	−14.0000	−0.709828	−0.354914	−	0.934899i	$-0.615490\pi$
$389$	−14.0000	−0.709828	−0.354914	+	0.934899i	$0.615490\pi$
$390$	4.00000	0.202548
$391$	3.00000	0.151717
$392$	2.00000	0.101015
$393$	6.00000	0.302660
$394$	−22.0000	−1.10834
$395$	16.0000	0.805047
$396$	2.00000	0.100504
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	9.00000	0.451129
$399$	−3.00000	−0.150188
$400$	−1.00000	−0.0500000
$401$	22.0000	1.09863	0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000	1.09863	0.549314	+	0.835616i	$0.314889\pi$
$402$	−6.00000	−0.299253
$403$	−4.00000	−0.199254
$404$	14.0000	0.696526
$405$	−2.00000	−0.0993808
$406$	12.0000	0.595550
$407$	8.00000	0.396545
$408$	1.00000	0.0495074
$409$	38.0000	1.87898	0.939490	−	0.342578i	$-0.111300\pi$
$409$	38.0000	1.87898	0.939490	+	0.342578i	$0.111300\pi$
$410$	22.0000	1.08650
$411$	−8.00000	−0.394611
$412$	−17.0000	−0.837530
$413$	−3.00000	−0.147620
$414$	3.00000	0.147442
$415$	22.0000	1.07994
$416$	−2.00000	−0.0980581
$417$	−4.00000	−0.195881
$418$	2.00000	0.0978232
$419$	−38.0000	−1.85642	−0.928211	−	0.372055i	$-0.878653\pi$
$419$	−38.0000	−1.85642	−0.928211	+	0.372055i	$0.878653\pi$
$420$	6.00000	0.292770
$421$	1.00000	0.0487370	0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000	0.0487370	0.0243685	+	0.999703i	$0.492242\pi$
$422$	−16.0000	−0.778868
$423$	0	0
$424$	3.00000	0.145693
$425$	−1.00000	−0.0485071
$426$	−6.00000	−0.290701
$427$	−6.00000	−0.290360
$428$	−13.0000	−0.628379
$429$	−4.00000	−0.193122
$430$	12.0000	0.578691
$431$	−23.0000	−1.10787	−0.553936	−	0.832560i	$-0.686875\pi$
$431$	−23.0000	−1.10787	−0.553936	+	0.832560i	$0.686875\pi$
$432$	1.00000	0.0481125
$433$	1.00000	0.0480569	0.0240285	−	0.999711i	$-0.492351\pi$
$433$	1.00000	0.0480569	0.0240285	+	0.999711i	$0.492351\pi$
$434$	−6.00000	−0.288009
$435$	8.00000	0.383571
$436$	20.0000	0.957826
$437$	3.00000	0.143509
$438$	−11.0000	−0.525600
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	−4.00000	−0.190693
$441$	2.00000	0.0952381
$442$	−2.00000	−0.0951303
$443$	35.0000	1.66290	0.831450	−	0.555599i	$-0.187511\pi$
$443$	35.0000	1.66290	0.831450	+	0.555599i	$0.187511\pi$
$444$	4.00000	0.189832
$445$	18.0000	0.853282
$446$	28.0000	1.32584
$447$	−4.00000	−0.189194
$448$	−3.00000	−0.141737
$449$	−25.0000	−1.17982	−0.589911	−	0.807468i	$-0.700837\pi$
$449$	−25.0000	−1.17982	−0.589911	+	0.807468i	$0.700837\pi$
$450$	−1.00000	−0.0471405
$451$	−22.0000	−1.03594
$452$	2.00000	0.0940721
$453$	−15.0000	−0.704761
$454$	4.00000	0.187729
$455$	−12.0000	−0.562569
$456$	1.00000	0.0468293
$457$	34.0000	1.59045	0.795226	−	0.606313i	$-0.207352\pi$
$457$	34.0000	1.59045	0.795226	+	0.606313i	$0.207352\pi$
$458$	1.00000	0.0467269
$459$	1.00000	0.0466760
$460$	−6.00000	−0.279751
$461$	−27.0000	−1.25752	−0.628758	−	0.777601i	$-0.716436\pi$
$461$	−27.0000	−1.25752	−0.628758	+	0.777601i	$0.716436\pi$
$462$	−6.00000	−0.279145
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−4.00000	−0.185695
$465$	−4.00000	−0.185496
$466$	−22.0000	−1.01913
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	−2.00000	−0.0924500
$469$	18.0000	0.831163
$470$	0	0
$471$	−17.0000	−0.783319
$472$	1.00000	0.0460287
$473$	−12.0000	−0.551761
$474$	−8.00000	−0.367452
$475$	−1.00000	−0.0458831
$476$	−3.00000	−0.137505
$477$	3.00000	0.137361
$478$	12.0000	0.548867
$479$	6.00000	0.274147	0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000	0.274147	0.137073	+	0.990561i	$0.456230\pi$
$480$	−2.00000	−0.0912871
$481$	−8.00000	−0.364769
$482$	20.0000	0.910975
$483$	−9.00000	−0.409514
$484$	−7.00000	−0.318182
$485$	−2.00000	−0.0908153
$486$	1.00000	0.0453609
$487$	11.0000	0.498458	0.249229	−	0.968445i	$-0.419823\pi$
$487$	11.0000	0.498458	0.249229	+	0.968445i	$0.419823\pi$
$488$	2.00000	0.0905357
$489$	4.00000	0.180886
$490$	−4.00000	−0.180702
$491$	−6.00000	−0.270776	−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000	−0.270776	−0.135388	+	0.990793i	$0.543228\pi$
$492$	−11.0000	−0.495918
$493$	−4.00000	−0.180151
$494$	−2.00000	−0.0899843
$495$	−4.00000	−0.179787
$496$	2.00000	0.0898027
$497$	18.0000	0.807410
$498$	−11.0000	−0.492922
$499$	22.0000	0.984855	0.492428	−	0.870353i	$-0.336110\pi$
$499$	22.0000	0.984855	0.492428	+	0.870353i	$0.336110\pi$
$500$	12.0000	0.536656
$501$	4.00000	0.178707
$502$	−14.0000	−0.624851
$503$	21.0000	0.936344	0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000	0.936344	0.468172	+	0.883637i	$0.344913\pi$
$504$	−3.00000	−0.133631
$505$	−28.0000	−1.24598
$506$	6.00000	0.266733
$507$	−9.00000	−0.399704
$508$	−12.0000	−0.532414
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	−2.00000	−0.0885615
$511$	33.0000	1.45983
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	14.0000	0.617514
$515$	34.0000	1.49822
$516$	−6.00000	−0.264135
$517$	0	0
$518$	−12.0000	−0.527250
$519$	18.0000	0.790112
$520$	4.00000	0.175412
$521$	−7.00000	−0.306676	−0.153338	−	0.988174i	$-0.549002\pi$
$521$	−7.00000	−0.306676	−0.153338	+	0.988174i	$0.549002\pi$
$522$	−4.00000	−0.175075
$523$	44.0000	1.92399	0.961993	−	0.273075i	$-0.0880406\pi$
$523$	44.0000	1.92399	0.961993	+	0.273075i	$0.0880406\pi$
$524$	6.00000	0.262111
$525$	3.00000	0.130931
$526$	−11.0000	−0.479623
$527$	2.00000	0.0871214
$528$	2.00000	0.0870388
$529$	−14.0000	−0.608696
$530$	−6.00000	−0.260623
$531$	1.00000	0.0433963
$532$	−3.00000	−0.130066
$533$	22.0000	0.952926
$534$	−9.00000	−0.389468
$535$	26.0000	1.12408
$536$	−6.00000	−0.259161
$537$	15.0000	0.647298
$538$	−3.00000	−0.129339
$539$	4.00000	0.172292
$540$	−2.00000	−0.0860663
$541$	32.0000	1.37579	0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000	1.37579	0.687894	+	0.725811i	$0.258536\pi$
$542$	28.0000	1.20270
$543$	14.0000	0.600798
$544$	1.00000	0.0428746
$545$	−40.0000	−1.71341
$546$	6.00000	0.256776
$547$	30.0000	1.28271	0.641354	−	0.767245i	$-0.278373\pi$
$547$	30.0000	1.28271	0.641354	+	0.767245i	$0.278373\pi$
$548$	−8.00000	−0.341743
$549$	2.00000	0.0853579
$550$	−2.00000	−0.0852803
$551$	−4.00000	−0.170406
$552$	3.00000	0.127688
$553$	24.0000	1.02058
$554$	−3.00000	−0.127458
$555$	−8.00000	−0.339581
$556$	−4.00000	−0.169638
$557$	14.0000	0.593199	0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000	0.593199	0.296600	+	0.955002i	$0.404147\pi$
$558$	2.00000	0.0846668
$559$	12.0000	0.507546
$560$	6.00000	0.253546
$561$	2.00000	0.0844401
$562$	−30.0000	−1.26547
$563$	−15.0000	−0.632175	−0.316087	−	0.948730i	$-0.602369\pi$
$563$	−15.0000	−0.632175	−0.316087	+	0.948730i	$0.602369\pi$
$564$	0	0
$565$	−4.00000	−0.168281
$566$	−15.0000	−0.630497
$567$	−3.00000	−0.125988
$568$	−6.00000	−0.251754
$569$	−21.0000	−0.880366	−0.440183	−	0.897908i	$-0.645086\pi$
$569$	−21.0000	−0.880366	−0.440183	+	0.897908i	$0.645086\pi$
$570$	−2.00000	−0.0837708
$571$	25.0000	1.04622	0.523109	−	0.852266i	$-0.324772\pi$
$571$	25.0000	1.04622	0.523109	+	0.852266i	$0.324772\pi$
$572$	−4.00000	−0.167248
$573$	−10.0000	−0.417756
$574$	33.0000	1.37739
$575$	−3.00000	−0.125109
$576$	1.00000	0.0416667
$577$	−34.0000	−1.41544	−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000	−1.41544	−0.707719	+	0.706494i	$0.750276\pi$
$578$	1.00000	0.0415945
$579$	−12.0000	−0.498703
$580$	8.00000	0.332182
$581$	33.0000	1.36907
$582$	1.00000	0.0414513
$583$	6.00000	0.248495
$584$	−11.0000	−0.455183
$585$	4.00000	0.165380
$586$	−14.0000	−0.578335
$587$	−17.0000	−0.701665	−0.350833	−	0.936438i	$-0.614101\pi$
$587$	−17.0000	−0.701665	−0.350833	+	0.936438i	$0.614101\pi$
$588$	2.00000	0.0824786
$589$	2.00000	0.0824086
$590$	−2.00000	−0.0823387
$591$	−22.0000	−0.904959
$592$	4.00000	0.164399
$593$	−44.0000	−1.80686	−0.903432	−	0.428732i	$-0.858960\pi$
$593$	−44.0000	−1.80686	−0.903432	+	0.428732i	$0.858960\pi$
$594$	2.00000	0.0820610
$595$	6.00000	0.245976
$596$	−4.00000	−0.163846
$597$	9.00000	0.368345
$598$	−6.00000	−0.245358
$599$	7.00000	0.286012	0.143006	−	0.989722i	$-0.454323\pi$
$599$	7.00000	0.286012	0.143006	+	0.989722i	$0.454323\pi$
$600$	−1.00000	−0.0408248
$601$	21.0000	0.856608	0.428304	−	0.903635i	$-0.359111\pi$
$601$	21.0000	0.856608	0.428304	+	0.903635i	$0.359111\pi$
$602$	18.0000	0.733625
$603$	−6.00000	−0.244339
$604$	−15.0000	−0.610341
$605$	14.0000	0.569181
$606$	14.0000	0.568711
$607$	27.0000	1.09590	0.547948	−	0.836512i	$-0.315409\pi$
$607$	27.0000	1.09590	0.547948	+	0.836512i	$0.315409\pi$
$608$	1.00000	0.0405554
$609$	12.0000	0.486265
$610$	−4.00000	−0.161955
$611$	0	0
$612$	1.00000	0.0404226
$613$	29.0000	1.17130	0.585649	−	0.810564i	$-0.300840\pi$
$613$	29.0000	1.17130	0.585649	+	0.810564i	$0.300840\pi$
$614$	−21.0000	−0.847491
$615$	22.0000	0.887126
$616$	−6.00000	−0.241747
$617$	−27.0000	−1.08698	−0.543490	−	0.839416i	$-0.682897\pi$
$617$	−27.0000	−1.08698	−0.543490	+	0.839416i	$0.682897\pi$
$618$	−17.0000	−0.683840
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	−4.00000	−0.160644
$621$	3.00000	0.120386
$622$	−6.00000	−0.240578
$623$	27.0000	1.08173
$624$	−2.00000	−0.0800641
$625$	−19.0000	−0.760000
$626$	22.0000	0.879297
$627$	2.00000	0.0798723
$628$	−17.0000	−0.678374
$629$	4.00000	0.159490
$630$	6.00000	0.239046
$631$	36.0000	1.43314	0.716569	−	0.697517i	$-0.245712\pi$
$631$	36.0000	1.43314	0.716569	+	0.697517i	$0.245712\pi$
$632$	−8.00000	−0.318223
$633$	−16.0000	−0.635943
$634$	−12.0000	−0.476581
$635$	24.0000	0.952411
$636$	3.00000	0.118958
$637$	−4.00000	−0.158486
$638$	−8.00000	−0.316723
$639$	−6.00000	−0.237356
$640$	−2.00000	−0.0790569
$641$	41.0000	1.61940	0.809701	−	0.586842i	$-0.199629\pi$
$641$	41.0000	1.61940	0.809701	+	0.586842i	$0.199629\pi$
$642$	−13.0000	−0.513069
$643$	−34.0000	−1.34083	−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000	−1.34083	−0.670415	+	0.741987i	$0.733884\pi$
$644$	−9.00000	−0.354650
$645$	12.0000	0.472500
$646$	1.00000	0.0393445
$647$	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
$649$	2.00000	0.0785069
$650$	2.00000	0.0784465
$651$	−6.00000	−0.235159
$652$	4.00000	0.156652
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	20.0000	0.782062
$655$	−12.0000	−0.468879
$656$	−11.0000	−0.429478
$657$	−11.0000	−0.429151
$658$	0	0
$659$	−27.0000	−1.05177	−0.525885	−	0.850555i	$-0.676266\pi$
$659$	−27.0000	−1.05177	−0.525885	+	0.850555i	$0.676266\pi$
$660$	−4.00000	−0.155700
$661$	48.0000	1.86698	0.933492	−	0.358599i	$-0.116745\pi$
$661$	48.0000	1.86698	0.933492	+	0.358599i	$0.116745\pi$
$662$	13.0000	0.505259
$663$	−2.00000	−0.0776736
$664$	−11.0000	−0.426883
$665$	6.00000	0.232670
$666$	4.00000	0.154997
$667$	−12.0000	−0.464642
$668$	4.00000	0.154765
$669$	28.0000	1.08254
$670$	12.0000	0.463600
$671$	4.00000	0.154418
$672$	−3.00000	−0.115728
$673$	5.00000	0.192736	0.0963679	−	0.995346i	$-0.469277\pi$
$673$	5.00000	0.192736	0.0963679	+	0.995346i	$0.469277\pi$
$674$	19.0000	0.731853
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	−8.00000	−0.307465	−0.153732	−	0.988113i	$-0.549129\pi$
$677$	−8.00000	−0.307465	−0.153732	+	0.988113i	$0.549129\pi$
$678$	2.00000	0.0768095
$679$	−3.00000	−0.115129
$680$	−2.00000	−0.0766965
$681$	4.00000	0.153280
$682$	4.00000	0.153168
$683$	16.0000	0.612223	0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000	0.612223	0.306111	+	0.951996i	$0.400972\pi$
$684$	1.00000	0.0382360
$685$	16.0000	0.611329
$686$	15.0000	0.572703
$687$	1.00000	0.0381524
$688$	−6.00000	−0.228748
$689$	−6.00000	−0.228582
$690$	−6.00000	−0.228416
$691$	35.0000	1.33146	0.665731	−	0.746191i	$-0.268120\pi$
$691$	35.0000	1.33146	0.665731	+	0.746191i	$0.268120\pi$
$692$	18.0000	0.684257
$693$	−6.00000	−0.227921
$694$	4.00000	0.151838
$695$	8.00000	0.303457
$696$	−4.00000	−0.151620
$697$	−11.0000	−0.416655
$698$	11.0000	0.416356
$699$	−22.0000	−0.832116
$700$	3.00000	0.113389
$701$	−20.0000	−0.755390	−0.377695	−	0.925930i	$-0.623283\pi$
$701$	−20.0000	−0.755390	−0.377695	+	0.925930i	$0.623283\pi$
$702$	−2.00000	−0.0754851
$703$	4.00000	0.150863
$704$	2.00000	0.0753778
$705$	0	0
$706$	21.0000	0.790345
$707$	−42.0000	−1.57957
$708$	1.00000	0.0375823
$709$	−14.0000	−0.525781	−0.262891	−	0.964826i	$-0.584676\pi$
$709$	−14.0000	−0.525781	−0.262891	+	0.964826i	$0.584676\pi$
$710$	12.0000	0.450352
$711$	−8.00000	−0.300023
$712$	−9.00000	−0.337289
$713$	6.00000	0.224702
$714$	−3.00000	−0.112272
$715$	8.00000	0.299183
$716$	15.0000	0.560576
$717$	12.0000	0.448148
$718$	9.00000	0.335877
$719$	16.0000	0.596699	0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000	0.596699	0.298350	+	0.954457i	$0.403564\pi$
$720$	−2.00000	−0.0745356
$721$	51.0000	1.89934
$722$	−18.0000	−0.669891
$723$	20.0000	0.743808
$724$	14.0000	0.520306
$725$	4.00000	0.148556
$726$	−7.00000	−0.259794
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	6.00000	0.222375
$729$	1.00000	0.0370370
$730$	22.0000	0.814257
$731$	−6.00000	−0.221918
$732$	2.00000	0.0739221
$733$	28.0000	1.03420	0.517102	−	0.855924i	$-0.327011\pi$
$733$	28.0000	1.03420	0.517102	+	0.855924i	$0.327011\pi$
$734$	24.0000	0.885856
$735$	−4.00000	−0.147542
$736$	3.00000	0.110581
$737$	−12.0000	−0.442026
$738$	−11.0000	−0.404916
$739$	4.00000	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$740$	−8.00000	−0.294086
$741$	−2.00000	−0.0734718
$742$	−9.00000	−0.330400
$743$	8.00000	0.293492	0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000	0.293492	0.146746	+	0.989174i	$0.453120\pi$
$744$	2.00000	0.0733236
$745$	8.00000	0.293097
$746$	−24.0000	−0.878702
$747$	−11.0000	−0.402469
$748$	2.00000	0.0731272
$749$	39.0000	1.42503
$750$	12.0000	0.438178
$751$	2.00000	0.0729810	0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000	0.0729810	0.0364905	+	0.999334i	$0.488382\pi$
$752$	0	0
$753$	−14.0000	−0.510188
$754$	8.00000	0.291343
$755$	30.0000	1.09181
$756$	−3.00000	−0.109109
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	2.00000	0.0726433
$759$	6.00000	0.217786
$760$	−2.00000	−0.0725476
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	−12.0000	−0.434714
$763$	−60.0000	−2.17215
$764$	−10.0000	−0.361787
$765$	−2.00000	−0.0723102
$766$	−13.0000	−0.469709
$767$	−2.00000	−0.0722158
$768$	1.00000	0.0360844
$769$	−54.0000	−1.94729	−0.973645	−	0.228069i	$-0.926759\pi$
$769$	−54.0000	−1.94729	−0.973645	+	0.228069i	$0.926759\pi$
$770$	12.0000	0.432450
$771$	14.0000	0.504198
$772$	−12.0000	−0.431889
$773$	−46.0000	−1.65451	−0.827253	−	0.561830i	$-0.810097\pi$
$773$	−46.0000	−1.65451	−0.827253	+	0.561830i	$0.810097\pi$
$774$	−6.00000	−0.215666
$775$	−2.00000	−0.0718421
$776$	1.00000	0.0358979
$777$	−12.0000	−0.430498
$778$	−14.0000	−0.501924
$779$	−11.0000	−0.394116
$780$	4.00000	0.143223
$781$	−12.0000	−0.429394
$782$	3.00000	0.107280
$783$	−4.00000	−0.142948
$784$	2.00000	0.0714286
$785$	34.0000	1.21351
$786$	6.00000	0.214013
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	−22.0000	−0.783718
$789$	−11.0000	−0.391610
$790$	16.0000	0.569254
$791$	−6.00000	−0.213335
$792$	2.00000	0.0710669
$793$	−4.00000	−0.142044
$794$	22.0000	0.780751
$795$	−6.00000	−0.212798
$796$	9.00000	0.318997
$797$	−4.00000	−0.141687	−0.0708436	−	0.997487i	$-0.522569\pi$
$797$	−4.00000	−0.141687	−0.0708436	+	0.997487i	$0.522569\pi$
$798$	−3.00000	−0.106199
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	−9.00000	−0.317999
$802$	22.0000	0.776847
$803$	−22.0000	−0.776363
$804$	−6.00000	−0.211604
$805$	18.0000	0.634417
$806$	−4.00000	−0.140894
$807$	−3.00000	−0.105605
$808$	14.0000	0.492518
$809$	2.00000	0.0703163	0.0351581	−	0.999382i	$-0.488807\pi$
$809$	2.00000	0.0703163	0.0351581	+	0.999382i	$0.488807\pi$
$810$	−2.00000	−0.0702728
$811$	13.0000	0.456492	0.228246	−	0.973604i	$-0.426701\pi$
$811$	13.0000	0.456492	0.228246	+	0.973604i	$0.426701\pi$
$812$	12.0000	0.421117
$813$	28.0000	0.982003
$814$	8.00000	0.280400
$815$	−8.00000	−0.280228
$816$	1.00000	0.0350070
$817$	−6.00000	−0.209913
$818$	38.0000	1.32864
$819$	6.00000	0.209657
$820$	22.0000	0.768273
$821$	−13.0000	−0.453703	−0.226852	−	0.973929i	$-0.572843\pi$
$821$	−13.0000	−0.453703	−0.226852	+	0.973929i	$0.572843\pi$
$822$	−8.00000	−0.279032
$823$	2.00000	0.0697156	0.0348578	−	0.999392i	$-0.488902\pi$
$823$	2.00000	0.0697156	0.0348578	+	0.999392i	$0.488902\pi$
$824$	−17.0000	−0.592223
$825$	−2.00000	−0.0696311
$826$	−3.00000	−0.104383
$827$	1.00000	0.0347734	0.0173867	−	0.999849i	$-0.494465\pi$
$827$	1.00000	0.0347734	0.0173867	+	0.999849i	$0.494465\pi$
$828$	3.00000	0.104257
$829$	−22.0000	−0.764092	−0.382046	−	0.924143i	$-0.624780\pi$
$829$	−22.0000	−0.764092	−0.382046	+	0.924143i	$0.624780\pi$
$830$	22.0000	0.763631
$831$	−3.00000	−0.104069
$832$	−2.00000	−0.0693375
$833$	2.00000	0.0692959
$834$	−4.00000	−0.138509
$835$	−8.00000	−0.276851
$836$	2.00000	0.0691714
$837$	2.00000	0.0691301
$838$	−38.0000	−1.31269
$839$	−24.0000	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$840$	6.00000	0.207020
$841$	−13.0000	−0.448276
$842$	1.00000	0.0344623
$843$	−30.0000	−1.03325
$844$	−16.0000	−0.550743
$845$	18.0000	0.619219
$846$	0	0
$847$	21.0000	0.721569
$848$	3.00000	0.103020
$849$	−15.0000	−0.514799
$850$	−1.00000	−0.0342997
$851$	12.0000	0.411355
$852$	−6.00000	−0.205557
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	−6.00000	−0.205316
$855$	−2.00000	−0.0683986
$856$	−13.0000	−0.444331
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	−4.00000	−0.136558
$859$	−30.0000	−1.02359	−0.511793	−	0.859109i	$-0.671019\pi$
$859$	−30.0000	−1.02359	−0.511793	+	0.859109i	$0.671019\pi$
$860$	12.0000	0.409197
$861$	33.0000	1.12464
$862$	−23.0000	−0.783383
$863$	40.0000	1.36162	0.680808	−	0.732462i	$-0.261629\pi$
$863$	40.0000	1.36162	0.680808	+	0.732462i	$0.261629\pi$
$864$	1.00000	0.0340207
$865$	−36.0000	−1.22404
$866$	1.00000	0.0339814
$867$	1.00000	0.0339618
$868$	−6.00000	−0.203653
$869$	−16.0000	−0.542763
$870$	8.00000	0.271225
$871$	12.0000	0.406604
$872$	20.0000	0.677285
$873$	1.00000	0.0338449
$874$	3.00000	0.101477
$875$	−36.0000	−1.21702
$876$	−11.0000	−0.371656
$877$	−11.0000	−0.371444	−0.185722	−	0.982602i	$-0.559462\pi$
$877$	−11.0000	−0.371444	−0.185722	+	0.982602i	$0.559462\pi$
$878$	−32.0000	−1.07995
$879$	−14.0000	−0.472208
$880$	−4.00000	−0.134840
$881$	−4.00000	−0.134763	−0.0673817	−	0.997727i	$-0.521465\pi$
$881$	−4.00000	−0.134763	−0.0673817	+	0.997727i	$0.521465\pi$
$882$	2.00000	0.0673435
$883$	−9.00000	−0.302874	−0.151437	−	0.988467i	$-0.548390\pi$
$883$	−9.00000	−0.302874	−0.151437	+	0.988467i	$0.548390\pi$
$884$	−2.00000	−0.0672673
$885$	−2.00000	−0.0672293
$886$	35.0000	1.17585
$887$	−3.00000	−0.100730	−0.0503651	−	0.998731i	$-0.516038\pi$
$887$	−3.00000	−0.100730	−0.0503651	+	0.998731i	$0.516038\pi$
$888$	4.00000	0.134231
$889$	36.0000	1.20740
$890$	18.0000	0.603361
$891$	2.00000	0.0670025
$892$	28.0000	0.937509
$893$	0	0
$894$	−4.00000	−0.133780
$895$	−30.0000	−1.00279
$896$	−3.00000	−0.100223
$897$	−6.00000	−0.200334
$898$	−25.0000	−0.834261
$899$	−8.00000	−0.266815
$900$	−1.00000	−0.0333333
$901$	3.00000	0.0999445
$902$	−22.0000	−0.732520
$903$	18.0000	0.599002
$904$	2.00000	0.0665190
$905$	−28.0000	−0.930751
$906$	−15.0000	−0.498342
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	4.00000	0.132745
$909$	14.0000	0.464351
$910$	−12.0000	−0.397796
$911$	−52.0000	−1.72284	−0.861418	−	0.507896i	$-0.830423\pi$
$911$	−52.0000	−1.72284	−0.861418	+	0.507896i	$0.830423\pi$
$912$	1.00000	0.0331133
$913$	−22.0000	−0.728094
$914$	34.0000	1.12462
$915$	−4.00000	−0.132236
$916$	1.00000	0.0330409
$917$	−18.0000	−0.594412
$918$	1.00000	0.0330049
$919$	−24.0000	−0.791687	−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000	−0.791687	−0.395843	+	0.918318i	$0.629548\pi$
$920$	−6.00000	−0.197814
$921$	−21.0000	−0.691974
$922$	−27.0000	−0.889198
$923$	12.0000	0.394985
$924$	−6.00000	−0.197386
$925$	−4.00000	−0.131519
$926$	−16.0000	−0.525793
$927$	−17.0000	−0.558353
$928$	−4.00000	−0.131306
$929$	2.00000	0.0656179	0.0328089	−	0.999462i	$-0.489555\pi$
$929$	2.00000	0.0656179	0.0328089	+	0.999462i	$0.489555\pi$
$930$	−4.00000	−0.131165
$931$	2.00000	0.0655474
$932$	−22.0000	−0.720634
$933$	−6.00000	−0.196431
$934$	0	0
$935$	−4.00000	−0.130814
$936$	−2.00000	−0.0653720
$937$	56.0000	1.82944	0.914720	−	0.404088i	$-0.132411\pi$
$937$	56.0000	1.82944	0.914720	+	0.404088i	$0.132411\pi$
$938$	18.0000	0.587721
$939$	22.0000	0.717943
$940$	0	0
$941$	17.0000	0.554184	0.277092	−	0.960843i	$-0.410629\pi$
$941$	17.0000	0.554184	0.277092	+	0.960843i	$0.410629\pi$
$942$	−17.0000	−0.553890
$943$	−33.0000	−1.07463
$944$	1.00000	0.0325472
$945$	6.00000	0.195180
$946$	−12.0000	−0.390154
$947$	−31.0000	−1.00736	−0.503682	−	0.863889i	$-0.668022\pi$
$947$	−31.0000	−1.00736	−0.503682	+	0.863889i	$0.668022\pi$
$948$	−8.00000	−0.259828
$949$	22.0000	0.714150
$950$	−1.00000	−0.0324443
$951$	−12.0000	−0.389127
$952$	−3.00000	−0.0972306
$953$	−30.0000	−0.971795	−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000	−0.971795	−0.485898	+	0.874016i	$0.661507\pi$
$954$	3.00000	0.0971286
$955$	20.0000	0.647185
$956$	12.0000	0.388108
$957$	−8.00000	−0.258603
$958$	6.00000	0.193851
$959$	24.0000	0.775000
$960$	−2.00000	−0.0645497
$961$	−27.0000	−0.870968
$962$	−8.00000	−0.257930
$963$	−13.0000	−0.418919
$964$	20.0000	0.644157
$965$	24.0000	0.772587
$966$	−9.00000	−0.289570
$967$	7.00000	0.225105	0.112552	−	0.993646i	$-0.464097\pi$
$967$	7.00000	0.225105	0.112552	+	0.993646i	$0.464097\pi$
$968$	−7.00000	−0.224989
$969$	1.00000	0.0321246
$970$	−2.00000	−0.0642161
$971$	50.0000	1.60458	0.802288	−	0.596937i	$-0.203616\pi$
$971$	50.0000	1.60458	0.802288	+	0.596937i	$0.203616\pi$
$972$	1.00000	0.0320750
$973$	12.0000	0.384702
$974$	11.0000	0.352463
$975$	2.00000	0.0640513
$976$	2.00000	0.0640184
$977$	2.00000	0.0639857	0.0319928	−	0.999488i	$-0.489815\pi$
$977$	2.00000	0.0639857	0.0319928	+	0.999488i	$0.489815\pi$
$978$	4.00000	0.127906
$979$	−18.0000	−0.575282
$980$	−4.00000	−0.127775
$981$	20.0000	0.638551
$982$	−6.00000	−0.191468
$983$	51.0000	1.62665	0.813324	−	0.581811i	$-0.197656\pi$
$983$	51.0000	1.62665	0.813324	+	0.581811i	$0.197656\pi$
$984$	−11.0000	−0.350667
$985$	44.0000	1.40196
$986$	−4.00000	−0.127386
$987$	0	0
$988$	−2.00000	−0.0636285
$989$	−18.0000	−0.572367
$990$	−4.00000	−0.127128
$991$	20.0000	0.635321	0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000	0.635321	0.317660	+	0.948205i	$0.397103\pi$
$992$	2.00000	0.0635001
$993$	13.0000	0.412543
$994$	18.0000	0.570925
$995$	−18.0000	−0.570638
$996$	−11.0000	−0.348548
$997$	7.00000	0.221692	0.110846	−	0.993838i	$-0.464644\pi$
$997$	7.00000	0.221692	0.110846	+	0.993838i	$0.464644\pi$
$998$	22.0000	0.696398
$999$	4.00000	0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.k.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.k.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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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