LMFDB - Embedded newform 4650.2.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4650,2,Mod(1,4650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4650, 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("4650.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4650.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:	$37.1304369399$
Analytic rank:	$0$
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	$\chi$	$=$	4650.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +5.00000 q^{11} +1.00000 q^{12} +3.00000 q^{13} -3.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} +2.00000 q^{19} +3.00000 q^{21} -5.00000 q^{22} +4.00000 q^{23} -1.00000 q^{24} -3.00000 q^{26} +1.00000 q^{27} +3.00000 q^{28} +2.00000 q^{29} -1.00000 q^{31} -1.00000 q^{32} +5.00000 q^{33} -4.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} -2.00000 q^{38} +3.00000 q^{39} +3.00000 q^{41} -3.00000 q^{42} -5.00000 q^{43} +5.00000 q^{44} -4.00000 q^{46} +9.00000 q^{47} +1.00000 q^{48} +2.00000 q^{49} +4.00000 q^{51} +3.00000 q^{52} +1.00000 q^{53} -1.00000 q^{54} -3.00000 q^{56} +2.00000 q^{57} -2.00000 q^{58} -10.0000 q^{59} -9.00000 q^{61} +1.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} -5.00000 q^{66} +2.00000 q^{67} +4.00000 q^{68} +4.00000 q^{69} +3.00000 q^{71} -1.00000 q^{72} -6.00000 q^{73} +1.00000 q^{74} +2.00000 q^{76} +15.0000 q^{77} -3.00000 q^{78} -16.0000 q^{79} +1.00000 q^{81} -3.00000 q^{82} -3.00000 q^{83} +3.00000 q^{84} +5.00000 q^{86} +2.00000 q^{87} -5.00000 q^{88} -6.00000 q^{89} +9.00000 q^{91} +4.00000 q^{92} -1.00000 q^{93} -9.00000 q^{94} -1.00000 q^{96} +2.00000 q^{97} -2.00000 q^{98} +5.00000 q^{99} +O(q^{100})\)

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
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	1.00000	0.288675
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	−3.00000	−0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	−1.00000	−0.235702
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	3.00000	0.654654
$22$	−5.00000	−1.06600
$23$	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
$25$	0	0
$26$	−3.00000	−0.588348
$27$	1.00000	0.192450
$28$	3.00000	0.566947
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	5.00000	0.870388
$34$	−4.00000	−0.685994
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−2.00000	−0.324443
$39$	3.00000	0.480384
$40$	0	0
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	−3.00000	−0.462910
$43$	−5.00000	−0.762493	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000	−0.762493	−0.381246	+	0.924473i	$0.624505\pi$
$44$	5.00000	0.753778
$45$	0	0
$46$	−4.00000	−0.589768
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	1.00000	0.144338
$49$	2.00000	0.285714
$50$	0	0
$51$	4.00000	0.560112
$52$	3.00000	0.416025
$53$	1.00000	0.137361	0.0686803	−	0.997639i	$-0.478121\pi$
$53$	1.00000	0.137361	0.0686803	+	0.997639i	$0.478121\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−3.00000	−0.400892
$57$	2.00000	0.264906
$58$	−2.00000	−0.262613
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	0	0
$61$	−9.00000	−1.15233	−0.576166	−	0.817333i	$-0.695452\pi$
$61$	−9.00000	−1.15233	−0.576166	+	0.817333i	$0.695452\pi$
$62$	1.00000	0.127000
$63$	3.00000	0.377964
$64$	1.00000	0.125000
$65$	0	0
$66$	−5.00000	−0.615457
$67$	2.00000	0.244339	0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000	0.244339	0.122169	+	0.992509i	$0.461015\pi$
$68$	4.00000	0.485071
$69$	4.00000	0.481543
$70$	0	0
$71$	3.00000	0.356034	0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000	0.356034	0.178017	+	0.984027i	$0.443032\pi$
$72$	−1.00000	−0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	2.00000	0.229416
$77$	15.0000	1.70941
$78$	−3.00000	−0.339683
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−3.00000	−0.331295
$83$	−3.00000	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$84$	3.00000	0.327327
$85$	0	0
$86$	5.00000	0.539164
$87$	2.00000	0.214423
$88$	−5.00000	−0.533002
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	9.00000	0.943456
$92$	4.00000	0.417029
$93$	−1.00000	−0.103695
$94$	−9.00000	−0.928279
$95$	0	0
$96$	−1.00000	−0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−2.00000	−0.202031
$99$	5.00000	0.502519
$100$	0	0
$101$	−4.00000	−0.398015	−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000	−0.398015	−0.199007	+	0.979998i	$0.563772\pi$
$102$	−4.00000	−0.396059
$103$	−5.00000	−0.492665	−0.246332	−	0.969185i	$-0.579225\pi$
$103$	−5.00000	−0.492665	−0.246332	+	0.969185i	$0.579225\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	−1.00000	−0.0971286
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	1.00000	0.0962250
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	3.00000	0.283473
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	−2.00000	−0.187317
$115$	0	0
$116$	2.00000	0.185695
$117$	3.00000	0.277350
$118$	10.0000	0.920575
$119$	12.0000	1.10004
$120$	0	0
$121$	14.0000	1.27273
$122$	9.00000	0.814822
$123$	3.00000	0.270501
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	−3.00000	−0.267261
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	−1.00000	−0.0883883
$129$	−5.00000	−0.440225
$130$	0	0
$131$	−10.0000	−0.873704	−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000	−0.873704	−0.436852	+	0.899533i	$0.643907\pi$
$132$	5.00000	0.435194
$133$	6.00000	0.520266
$134$	−2.00000	−0.172774
$135$	0	0
$136$	−4.00000	−0.342997
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	−4.00000	−0.340503
$139$	−13.0000	−1.10265	−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000	−1.10265	−0.551323	+	0.834292i	$0.685877\pi$
$140$	0	0
$141$	9.00000	0.757937
$142$	−3.00000	−0.251754
$143$	15.0000	1.25436
$144$	1.00000	0.0833333
$145$	0	0
$146$	6.00000	0.496564
$147$	2.00000	0.164957
$148$	−1.00000	−0.0821995
$149$	−20.0000	−1.63846	−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−20.0000	−1.63846	−0.819232	+	0.573462i	$0.805600\pi$
$150$	0	0
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	−2.00000	−0.162221
$153$	4.00000	0.323381
$154$	−15.0000	−1.20873
$155$	0	0
$156$	3.00000	0.240192
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	16.0000	1.27289
$159$	1.00000	0.0793052
$160$	0	0
$161$	12.0000	0.945732
$162$	−1.00000	−0.0785674
$163$	6.00000	0.469956	0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000	0.469956	0.234978	+	0.972001i	$0.424498\pi$
$164$	3.00000	0.234261
$165$	0	0
$166$	3.00000	0.232845
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	−3.00000	−0.231455
$169$	−4.00000	−0.307692
$170$	0	0
$171$	2.00000	0.152944
$172$	−5.00000	−0.381246
$173$	26.0000	1.97674	0.988372	−	0.152057i	$-0.0485898\pi$
$173$	26.0000	1.97674	0.988372	+	0.152057i	$0.0485898\pi$
$174$	−2.00000	−0.151620
$175$	0	0
$176$	5.00000	0.376889
$177$	−10.0000	−0.751646
$178$	6.00000	0.449719
$179$	−1.00000	−0.0747435	−0.0373718	−	0.999301i	$-0.511899\pi$
$179$	−1.00000	−0.0747435	−0.0373718	+	0.999301i	$0.511899\pi$
$180$	0	0
$181$	3.00000	0.222988	0.111494	−	0.993765i	$-0.464436\pi$
$181$	3.00000	0.222988	0.111494	+	0.993765i	$0.464436\pi$
$182$	−9.00000	−0.667124
$183$	−9.00000	−0.665299
$184$	−4.00000	−0.294884
$185$	0	0
$186$	1.00000	0.0733236
$187$	20.0000	1.46254
$188$	9.00000	0.656392
$189$	3.00000	0.218218
$190$	0	0
$191$	−20.0000	−1.44715	−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000	−1.44715	−0.723575	+	0.690246i	$0.757502\pi$
$192$	1.00000	0.0721688
$193$	−11.0000	−0.791797	−0.395899	−	0.918294i	$-0.629567\pi$
$193$	−11.0000	−0.791797	−0.395899	+	0.918294i	$0.629567\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	2.00000	0.142857
$197$	13.0000	0.926212	0.463106	−	0.886303i	$-0.346735\pi$
$197$	13.0000	0.926212	0.463106	+	0.886303i	$0.346735\pi$
$198$	−5.00000	−0.355335
$199$	−26.0000	−1.84309	−0.921546	−	0.388270i	$-0.873073\pi$
$199$	−26.0000	−1.84309	−0.921546	+	0.388270i	$0.873073\pi$
$200$	0	0
$201$	2.00000	0.141069
$202$	4.00000	0.281439
$203$	6.00000	0.421117
$204$	4.00000	0.280056
$205$	0	0
$206$	5.00000	0.348367
$207$	4.00000	0.278019
$208$	3.00000	0.208013
$209$	10.0000	0.691714
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	1.00000	0.0686803
$213$	3.00000	0.205557
$214$	−8.00000	−0.546869
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−3.00000	−0.203653
$218$	6.00000	0.406371
$219$	−6.00000	−0.405442
$220$	0	0
$221$	12.0000	0.807207
$222$	1.00000	0.0671156
$223$	−10.0000	−0.669650	−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000	−0.669650	−0.334825	+	0.942280i	$0.608677\pi$
$224$	−3.00000	−0.200446
$225$	0	0
$226$	14.0000	0.931266
$227$	−8.00000	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$228$	2.00000	0.132453
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	0	0
$231$	15.0000	0.986928
$232$	−2.00000	−0.131306
$233$	5.00000	0.327561	0.163780	−	0.986497i	$-0.447631\pi$
$233$	5.00000	0.327561	0.163780	+	0.986497i	$0.447631\pi$
$234$	−3.00000	−0.196116
$235$	0	0
$236$	−10.0000	−0.650945
$237$	−16.0000	−1.03931
$238$	−12.0000	−0.777844
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−14.0000	−0.899954
$243$	1.00000	0.0641500
$244$	−9.00000	−0.576166
$245$	0	0
$246$	−3.00000	−0.191273
$247$	6.00000	0.381771
$248$	1.00000	0.0635001
$249$	−3.00000	−0.190117
$250$	0	0
$251$	5.00000	0.315597	0.157799	−	0.987471i	$-0.449560\pi$
$251$	5.00000	0.315597	0.157799	+	0.987471i	$0.449560\pi$
$252$	3.00000	0.188982
$253$	20.0000	1.25739
$254$	16.0000	1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	−7.00000	−0.436648	−0.218324	−	0.975876i	$-0.570059\pi$
$257$	−7.00000	−0.436648	−0.218324	+	0.975876i	$0.570059\pi$
$258$	5.00000	0.311286
$259$	−3.00000	−0.186411
$260$	0	0
$261$	2.00000	0.123797
$262$	10.0000	0.617802
$263$	−18.0000	−1.10993	−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000	−1.10993	−0.554964	+	0.831875i	$0.687268\pi$
$264$	−5.00000	−0.307729
$265$	0	0
$266$	−6.00000	−0.367884
$267$	−6.00000	−0.367194
$268$	2.00000	0.122169
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	4.00000	0.242536
$273$	9.00000	0.544705
$274$	−12.0000	−0.724947
$275$	0	0
$276$	4.00000	0.240772
$277$	18.0000	1.08152	0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000	1.08152	0.540758	+	0.841178i	$0.318138\pi$
$278$	13.0000	0.779688
$279$	−1.00000	−0.0598684
$280$	0	0
$281$	−5.00000	−0.298275	−0.149137	−	0.988816i	$-0.547650\pi$
$281$	−5.00000	−0.298275	−0.149137	+	0.988816i	$0.547650\pi$
$282$	−9.00000	−0.535942
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	3.00000	0.178017
$285$	0	0
$286$	−15.0000	−0.886969
$287$	9.00000	0.531253
$288$	−1.00000	−0.0589256
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	2.00000	0.117242
$292$	−6.00000	−0.351123
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	1.00000	0.0581238
$297$	5.00000	0.290129
$298$	20.0000	1.15857
$299$	12.0000	0.693978
$300$	0	0
$301$	−15.0000	−0.864586
$302$	−4.00000	−0.230174
$303$	−4.00000	−0.229794
$304$	2.00000	0.114708
$305$	0	0
$306$	−4.00000	−0.228665
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	15.0000	0.854704
$309$	−5.00000	−0.284440
$310$	0	0
$311$	11.0000	0.623753	0.311876	−	0.950123i	$-0.399043\pi$
$311$	11.0000	0.623753	0.311876	+	0.950123i	$0.399043\pi$
$312$	−3.00000	−0.169842
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	−6.00000	−0.338600
$315$	0	0
$316$	−16.0000	−0.900070
$317$	−20.0000	−1.12331	−0.561656	−	0.827371i	$-0.689836\pi$
$317$	−20.0000	−1.12331	−0.561656	+	0.827371i	$0.689836\pi$
$318$	−1.00000	−0.0560772
$319$	10.0000	0.559893
$320$	0	0
$321$	8.00000	0.446516
$322$	−12.0000	−0.668734
$323$	8.00000	0.445132
$324$	1.00000	0.0555556
$325$	0	0
$326$	−6.00000	−0.332309
$327$	−6.00000	−0.331801
$328$	−3.00000	−0.165647
$329$	27.0000	1.48856
$330$	0	0
$331$	−15.0000	−0.824475	−0.412237	−	0.911077i	$-0.635253\pi$
$331$	−15.0000	−0.824475	−0.412237	+	0.911077i	$0.635253\pi$
$332$	−3.00000	−0.164646
$333$	−1.00000	−0.0547997
$334$	0	0
$335$	0	0
$336$	3.00000	0.163663
$337$	22.0000	1.19842	0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000	1.19842	0.599208	+	0.800593i	$0.295482\pi$
$338$	4.00000	0.217571
$339$	−14.0000	−0.760376
$340$	0	0
$341$	−5.00000	−0.270765
$342$	−2.00000	−0.108148
$343$	−15.0000	−0.809924
$344$	5.00000	0.269582
$345$	0	0
$346$	−26.0000	−1.39777
$347$	−23.0000	−1.23470	−0.617352	−	0.786687i	$-0.711795\pi$
$347$	−23.0000	−1.23470	−0.617352	+	0.786687i	$0.711795\pi$
$348$	2.00000	0.107211
$349$	−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
$351$	3.00000	0.160128
$352$	−5.00000	−0.266501
$353$	−36.0000	−1.91609	−0.958043	−	0.286623i	$-0.907467\pi$
$353$	−36.0000	−1.91609	−0.958043	+	0.286623i	$0.907467\pi$
$354$	10.0000	0.531494
$355$	0	0
$356$	−6.00000	−0.317999
$357$	12.0000	0.635107
$358$	1.00000	0.0528516
$359$	28.0000	1.47778	0.738892	−	0.673824i	$-0.235349\pi$
$359$	28.0000	1.47778	0.738892	+	0.673824i	$0.235349\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−3.00000	−0.157676
$363$	14.0000	0.734809
$364$	9.00000	0.471728
$365$	0	0
$366$	9.00000	0.470438
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	4.00000	0.208514
$369$	3.00000	0.156174
$370$	0	0
$371$	3.00000	0.155752
$372$	−1.00000	−0.0518476
$373$	8.00000	0.414224	0.207112	−	0.978317i	$-0.433593\pi$
$373$	8.00000	0.414224	0.207112	+	0.978317i	$0.433593\pi$
$374$	−20.0000	−1.03418
$375$	0	0
$376$	−9.00000	−0.464140
$377$	6.00000	0.309016
$378$	−3.00000	−0.154303
$379$	−14.0000	−0.719132	−0.359566	−	0.933120i	$-0.617075\pi$
$379$	−14.0000	−0.719132	−0.359566	+	0.933120i	$0.617075\pi$
$380$	0	0
$381$	−16.0000	−0.819705
$382$	20.0000	1.02329
$383$	20.0000	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	11.0000	0.559885
$387$	−5.00000	−0.254164
$388$	2.00000	0.101535
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	16.0000	0.809155
$392$	−2.00000	−0.101015
$393$	−10.0000	−0.504433
$394$	−13.0000	−0.654931
$395$	0	0
$396$	5.00000	0.251259
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	26.0000	1.30326
$399$	6.00000	0.300376
$400$	0	0
$401$	32.0000	1.59800	0.799002	−	0.601329i	$-0.205362\pi$
$401$	32.0000	1.59800	0.799002	+	0.601329i	$0.205362\pi$
$402$	−2.00000	−0.0997509
$403$	−3.00000	−0.149441
$404$	−4.00000	−0.199007
$405$	0	0
$406$	−6.00000	−0.297775
$407$	−5.00000	−0.247841
$408$	−4.00000	−0.198030
$409$	30.0000	1.48340	0.741702	−	0.670729i	$-0.234019\pi$
$409$	30.0000	1.48340	0.741702	+	0.670729i	$0.234019\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	−5.00000	−0.246332
$413$	−30.0000	−1.47620
$414$	−4.00000	−0.196589
$415$	0	0
$416$	−3.00000	−0.147087
$417$	−13.0000	−0.636613
$418$	−10.0000	−0.489116
$419$	36.0000	1.75872	0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000	1.75872	0.879358	+	0.476162i	$0.157972\pi$
$420$	0	0
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	−20.0000	−0.973585
$423$	9.00000	0.437595
$424$	−1.00000	−0.0485643
$425$	0	0
$426$	−3.00000	−0.145350
$427$	−27.0000	−1.30662
$428$	8.00000	0.386695
$429$	15.0000	0.724207
$430$	0	0
$431$	−21.0000	−1.01153	−0.505767	−	0.862670i	$-0.668791\pi$
$431$	−21.0000	−1.01153	−0.505767	+	0.862670i	$0.668791\pi$
$432$	1.00000	0.0481125
$433$	28.0000	1.34559	0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000	1.34559	0.672797	+	0.739827i	$0.265093\pi$
$434$	3.00000	0.144005
$435$	0	0
$436$	−6.00000	−0.287348
$437$	8.00000	0.382692
$438$	6.00000	0.286691
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	−12.0000	−0.570782
$443$	−14.0000	−0.665160	−0.332580	−	0.943075i	$-0.607919\pi$
$443$	−14.0000	−0.665160	−0.332580	+	0.943075i	$0.607919\pi$
$444$	−1.00000	−0.0474579
$445$	0	0
$446$	10.0000	0.473514
$447$	−20.0000	−0.945968
$448$	3.00000	0.141737
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0	0
$451$	15.0000	0.706322
$452$	−14.0000	−0.658505
$453$	4.00000	0.187936
$454$	8.00000	0.375459
$455$	0	0
$456$	−2.00000	−0.0936586
$457$	28.0000	1.30978	0.654892	−	0.755722i	$-0.272714\pi$
$457$	28.0000	1.30978	0.654892	+	0.755722i	$0.272714\pi$
$458$	2.00000	0.0934539
$459$	4.00000	0.186704
$460$	0	0
$461$	1.00000	0.0465746	0.0232873	−	0.999729i	$-0.492587\pi$
$461$	1.00000	0.0465746	0.0232873	+	0.999729i	$0.492587\pi$
$462$	−15.0000	−0.697863
$463$	−12.0000	−0.557687	−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000	−0.557687	−0.278844	+	0.960337i	$0.589951\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	−5.00000	−0.231621
$467$	−26.0000	−1.20314	−0.601568	−	0.798821i	$-0.705457\pi$
$467$	−26.0000	−1.20314	−0.601568	+	0.798821i	$0.705457\pi$
$468$	3.00000	0.138675
$469$	6.00000	0.277054
$470$	0	0
$471$	6.00000	0.276465
$472$	10.0000	0.460287
$473$	−25.0000	−1.14950
$474$	16.0000	0.734904
$475$	0	0
$476$	12.0000	0.550019
$477$	1.00000	0.0457869
$478$	−6.00000	−0.274434
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	−3.00000	−0.136788
$482$	14.0000	0.637683
$483$	12.0000	0.546019
$484$	14.0000	0.636364
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	28.0000	1.26880	0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000	1.26880	0.634401	+	0.773004i	$0.281247\pi$
$488$	9.00000	0.407411
$489$	6.00000	0.271329
$490$	0	0
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	3.00000	0.135250
$493$	8.00000	0.360302
$494$	−6.00000	−0.269953
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	9.00000	0.403705
$498$	3.00000	0.134433
$499$	16.0000	0.716258	0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000	0.716258	0.358129	+	0.933672i	$0.383415\pi$
$500$	0	0
$501$	0	0
$502$	−5.00000	−0.223161
$503$	−23.0000	−1.02552	−0.512760	−	0.858532i	$-0.671377\pi$
$503$	−23.0000	−1.02552	−0.512760	+	0.858532i	$0.671377\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	−20.0000	−0.889108
$507$	−4.00000	−0.177646
$508$	−16.0000	−0.709885
$509$	−15.0000	−0.664863	−0.332432	−	0.943127i	$-0.607869\pi$
$509$	−15.0000	−0.664863	−0.332432	+	0.943127i	$0.607869\pi$
$510$	0	0
$511$	−18.0000	−0.796273
$512$	−1.00000	−0.0441942
$513$	2.00000	0.0883022
$514$	7.00000	0.308757
$515$	0	0
$516$	−5.00000	−0.220113
$517$	45.0000	1.97910
$518$	3.00000	0.131812
$519$	26.0000	1.14127
$520$	0	0
$521$	7.00000	0.306676	0.153338	−	0.988174i	$-0.450998\pi$
$521$	7.00000	0.306676	0.153338	+	0.988174i	$0.450998\pi$
$522$	−2.00000	−0.0875376
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	−10.0000	−0.436852
$525$	0	0
$526$	18.0000	0.784837
$527$	−4.00000	−0.174243
$528$	5.00000	0.217597
$529$	−7.00000	−0.304348
$530$	0	0
$531$	−10.0000	−0.433963
$532$	6.00000	0.260133
$533$	9.00000	0.389833
$534$	6.00000	0.259645
$535$	0	0
$536$	−2.00000	−0.0863868
$537$	−1.00000	−0.0431532
$538$	−6.00000	−0.258678
$539$	10.0000	0.430730
$540$	0	0
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	−16.0000	−0.687259
$543$	3.00000	0.128742
$544$	−4.00000	−0.171499
$545$	0	0
$546$	−9.00000	−0.385164
$547$	−28.0000	−1.19719	−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000	−1.19719	−0.598597	+	0.801050i	$0.704275\pi$
$548$	12.0000	0.512615
$549$	−9.00000	−0.384111
$550$	0	0
$551$	4.00000	0.170406
$552$	−4.00000	−0.170251
$553$	−48.0000	−2.04117
$554$	−18.0000	−0.764747
$555$	0	0
$556$	−13.0000	−0.551323
$557$	6.00000	0.254228	0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000	0.254228	0.127114	+	0.991888i	$0.459429\pi$
$558$	1.00000	0.0423334
$559$	−15.0000	−0.634432
$560$	0	0
$561$	20.0000	0.844401
$562$	5.00000	0.210912
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	9.00000	0.378968
$565$	0	0
$566$	0	0
$567$	3.00000	0.125988
$568$	−3.00000	−0.125877
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	0	0
$571$	37.0000	1.54840	0.774201	−	0.632940i	$-0.218152\pi$
$571$	37.0000	1.54840	0.774201	+	0.632940i	$0.218152\pi$
$572$	15.0000	0.627182
$573$	−20.0000	−0.835512
$574$	−9.00000	−0.375653
$575$	0	0
$576$	1.00000	0.0416667
$577$	42.0000	1.74848	0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000	1.74848	0.874241	+	0.485491i	$0.161359\pi$
$578$	1.00000	0.0415945
$579$	−11.0000	−0.457144
$580$	0	0
$581$	−9.00000	−0.373383
$582$	−2.00000	−0.0829027
$583$	5.00000	0.207079
$584$	6.00000	0.248282
$585$	0	0
$586$	−24.0000	−0.991431
$587$	23.0000	0.949312	0.474656	−	0.880172i	$-0.342573\pi$
$587$	23.0000	0.949312	0.474656	+	0.880172i	$0.342573\pi$
$588$	2.00000	0.0824786
$589$	−2.00000	−0.0824086
$590$	0	0
$591$	13.0000	0.534749
$592$	−1.00000	−0.0410997
$593$	−5.00000	−0.205325	−0.102663	−	0.994716i	$-0.532736\pi$
$593$	−5.00000	−0.205325	−0.102663	+	0.994716i	$0.532736\pi$
$594$	−5.00000	−0.205152
$595$	0	0
$596$	−20.0000	−0.819232
$597$	−26.0000	−1.06411
$598$	−12.0000	−0.490716
$599$	−19.0000	−0.776319	−0.388159	−	0.921592i	$-0.626889\pi$
$599$	−19.0000	−0.776319	−0.388159	+	0.921592i	$0.626889\pi$
$600$	0	0
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	15.0000	0.611354
$603$	2.00000	0.0814463
$604$	4.00000	0.162758
$605$	0	0
$606$	4.00000	0.162489
$607$	−45.0000	−1.82649	−0.913247	−	0.407407i	$-0.866433\pi$
$607$	−45.0000	−1.82649	−0.913247	+	0.407407i	$0.866433\pi$
$608$	−2.00000	−0.0811107
$609$	6.00000	0.243132
$610$	0	0
$611$	27.0000	1.09230
$612$	4.00000	0.161690
$613$	−10.0000	−0.403896	−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000	−0.403896	−0.201948	+	0.979396i	$0.564727\pi$
$614$	−16.0000	−0.645707
$615$	0	0
$616$	−15.0000	−0.604367
$617$	11.0000	0.442843	0.221422	−	0.975178i	$-0.428930\pi$
$617$	11.0000	0.442843	0.221422	+	0.975178i	$0.428930\pi$
$618$	5.00000	0.201129
$619$	−13.0000	−0.522514	−0.261257	−	0.965269i	$-0.584137\pi$
$619$	−13.0000	−0.522514	−0.261257	+	0.965269i	$0.584137\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	−11.0000	−0.441060
$623$	−18.0000	−0.721155
$624$	3.00000	0.120096
$625$	0	0
$626$	−22.0000	−0.879297
$627$	10.0000	0.399362
$628$	6.00000	0.239426
$629$	−4.00000	−0.159490
$630$	0	0
$631$	44.0000	1.75161	0.875806	−	0.482663i	$-0.160330\pi$
$631$	44.0000	1.75161	0.875806	+	0.482663i	$0.160330\pi$
$632$	16.0000	0.636446
$633$	20.0000	0.794929
$634$	20.0000	0.794301
$635$	0	0
$636$	1.00000	0.0396526
$637$	6.00000	0.237729
$638$	−10.0000	−0.395904
$639$	3.00000	0.118678
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	−8.00000	−0.315735
$643$	−7.00000	−0.276053	−0.138027	−	0.990429i	$-0.544076\pi$
$643$	−7.00000	−0.276053	−0.138027	+	0.990429i	$0.544076\pi$
$644$	12.0000	0.472866
$645$	0	0
$646$	−8.00000	−0.314756
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	−1.00000	−0.0392837
$649$	−50.0000	−1.96267
$650$	0	0
$651$	−3.00000	−0.117579
$652$	6.00000	0.234978
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	6.00000	0.234619
$655$	0	0
$656$	3.00000	0.117130
$657$	−6.00000	−0.234082
$658$	−27.0000	−1.05257
$659$	24.0000	0.934907	0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000	0.934907	0.467454	+	0.884018i	$0.345171\pi$
$660$	0	0
$661$	−16.0000	−0.622328	−0.311164	−	0.950356i	$-0.600719\pi$
$661$	−16.0000	−0.622328	−0.311164	+	0.950356i	$0.600719\pi$
$662$	15.0000	0.582992
$663$	12.0000	0.466041
$664$	3.00000	0.116423
$665$	0	0
$666$	1.00000	0.0387492
$667$	8.00000	0.309761
$668$	0	0
$669$	−10.0000	−0.386622
$670$	0	0
$671$	−45.0000	−1.73721
$672$	−3.00000	−0.115728
$673$	38.0000	1.46479	0.732396	−	0.680879i	$-0.238402\pi$
$673$	38.0000	1.46479	0.732396	+	0.680879i	$0.238402\pi$
$674$	−22.0000	−0.847408
$675$	0	0
$676$	−4.00000	−0.153846
$677$	21.0000	0.807096	0.403548	−	0.914959i	$-0.367777\pi$
$677$	21.0000	0.807096	0.403548	+	0.914959i	$0.367777\pi$
$678$	14.0000	0.537667
$679$	6.00000	0.230259
$680$	0	0
$681$	−8.00000	−0.306561
$682$	5.00000	0.191460
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	2.00000	0.0764719
$685$	0	0
$686$	15.0000	0.572703
$687$	−2.00000	−0.0763048
$688$	−5.00000	−0.190623
$689$	3.00000	0.114291
$690$	0	0
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	26.0000	0.988372
$693$	15.0000	0.569803
$694$	23.0000	0.873068
$695$	0	0
$696$	−2.00000	−0.0758098
$697$	12.0000	0.454532
$698$	26.0000	0.984115
$699$	5.00000	0.189117
$700$	0	0
$701$	40.0000	1.51078	0.755390	−	0.655276i	$-0.227448\pi$
$701$	40.0000	1.51078	0.755390	+	0.655276i	$0.227448\pi$
$702$	−3.00000	−0.113228
$703$	−2.00000	−0.0754314
$704$	5.00000	0.188445
$705$	0	0
$706$	36.0000	1.35488
$707$	−12.0000	−0.451306
$708$	−10.0000	−0.375823
$709$	−46.0000	−1.72757	−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000	−1.72757	−0.863783	+	0.503864i	$0.831911\pi$
$710$	0	0
$711$	−16.0000	−0.600047
$712$	6.00000	0.224860
$713$	−4.00000	−0.149801
$714$	−12.0000	−0.449089
$715$	0	0
$716$	−1.00000	−0.0373718
$717$	6.00000	0.224074
$718$	−28.0000	−1.04495
$719$	48.0000	1.79010	0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000	1.79010	0.895049	+	0.445968i	$0.147140\pi$
$720$	0	0
$721$	−15.0000	−0.558629
$722$	15.0000	0.558242
$723$	−14.0000	−0.520666
$724$	3.00000	0.111494
$725$	0	0
$726$	−14.0000	−0.519589
$727$	29.0000	1.07555	0.537775	−	0.843088i	$-0.319265\pi$
$727$	29.0000	1.07555	0.537775	+	0.843088i	$0.319265\pi$
$728$	−9.00000	−0.333562
$729$	1.00000	0.0370370
$730$	0	0
$731$	−20.0000	−0.739727
$732$	−9.00000	−0.332650
$733$	−20.0000	−0.738717	−0.369358	−	0.929287i	$-0.620423\pi$
$733$	−20.0000	−0.738717	−0.369358	+	0.929287i	$0.620423\pi$
$734$	16.0000	0.590571
$735$	0	0
$736$	−4.00000	−0.147442
$737$	10.0000	0.368355
$738$	−3.00000	−0.110432
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	0	0
$741$	6.00000	0.220416
$742$	−3.00000	−0.110133
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	1.00000	0.0366618
$745$	0	0
$746$	−8.00000	−0.292901
$747$	−3.00000	−0.109764
$748$	20.0000	0.731272
$749$	24.0000	0.876941
$750$	0	0
$751$	−33.0000	−1.20419	−0.602094	−	0.798426i	$-0.705667\pi$
$751$	−33.0000	−1.20419	−0.602094	+	0.798426i	$0.705667\pi$
$752$	9.00000	0.328196
$753$	5.00000	0.182210
$754$	−6.00000	−0.218507
$755$	0	0
$756$	3.00000	0.109109
$757$	−27.0000	−0.981332	−0.490666	−	0.871348i	$-0.663246\pi$
$757$	−27.0000	−0.981332	−0.490666	+	0.871348i	$0.663246\pi$
$758$	14.0000	0.508503
$759$	20.0000	0.725954
$760$	0	0
$761$	−14.0000	−0.507500	−0.253750	−	0.967270i	$-0.581664\pi$
$761$	−14.0000	−0.507500	−0.253750	+	0.967270i	$0.581664\pi$
$762$	16.0000	0.579619
$763$	−18.0000	−0.651644
$764$	−20.0000	−0.723575
$765$	0	0
$766$	−20.0000	−0.722629
$767$	−30.0000	−1.08324
$768$	1.00000	0.0360844
$769$	−5.00000	−0.180305	−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000	−0.180305	−0.0901523	+	0.995928i	$0.528735\pi$
$770$	0	0
$771$	−7.00000	−0.252099
$772$	−11.0000	−0.395899
$773$	−26.0000	−0.935155	−0.467578	−	0.883952i	$-0.654873\pi$
$773$	−26.0000	−0.935155	−0.467578	+	0.883952i	$0.654873\pi$
$774$	5.00000	0.179721
$775$	0	0
$776$	−2.00000	−0.0717958
$777$	−3.00000	−0.107624
$778$	−6.00000	−0.215110
$779$	6.00000	0.214972
$780$	0	0
$781$	15.0000	0.536742
$782$	−16.0000	−0.572159
$783$	2.00000	0.0714742
$784$	2.00000	0.0714286
$785$	0	0
$786$	10.0000	0.356688
$787$	5.00000	0.178231	0.0891154	−	0.996021i	$-0.471596\pi$
$787$	5.00000	0.178231	0.0891154	+	0.996021i	$0.471596\pi$
$788$	13.0000	0.463106
$789$	−18.0000	−0.640817
$790$	0	0
$791$	−42.0000	−1.49335
$792$	−5.00000	−0.177667
$793$	−27.0000	−0.958798
$794$	22.0000	0.780751
$795$	0	0
$796$	−26.0000	−0.921546
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	−6.00000	−0.212398
$799$	36.0000	1.27359
$800$	0	0
$801$	−6.00000	−0.212000
$802$	−32.0000	−1.12996
$803$	−30.0000	−1.05868
$804$	2.00000	0.0705346
$805$	0	0
$806$	3.00000	0.105670
$807$	6.00000	0.211210
$808$	4.00000	0.140720
$809$	26.0000	0.914111	0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000	0.914111	0.457056	+	0.889438i	$0.348904\pi$
$810$	0	0
$811$	−30.0000	−1.05344	−0.526721	−	0.850038i	$-0.676579\pi$
$811$	−30.0000	−1.05344	−0.526721	+	0.850038i	$0.676579\pi$
$812$	6.00000	0.210559
$813$	16.0000	0.561144
$814$	5.00000	0.175250
$815$	0	0
$816$	4.00000	0.140028
$817$	−10.0000	−0.349856
$818$	−30.0000	−1.04893
$819$	9.00000	0.314485
$820$	0	0
$821$	−25.0000	−0.872506	−0.436253	−	0.899824i	$-0.643695\pi$
$821$	−25.0000	−0.872506	−0.436253	+	0.899824i	$0.643695\pi$
$822$	−12.0000	−0.418548
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	5.00000	0.174183
$825$	0	0
$826$	30.0000	1.04383
$827$	−28.0000	−0.973655	−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000	−0.973655	−0.486828	+	0.873498i	$0.661846\pi$
$828$	4.00000	0.139010
$829$	−49.0000	−1.70184	−0.850920	−	0.525295i	$-0.823955\pi$
$829$	−49.0000	−1.70184	−0.850920	+	0.525295i	$0.823955\pi$
$830$	0	0
$831$	18.0000	0.624413
$832$	3.00000	0.104006
$833$	8.00000	0.277184
$834$	13.0000	0.450153
$835$	0	0
$836$	10.0000	0.345857
$837$	−1.00000	−0.0345651
$838$	−36.0000	−1.24360
$839$	7.00000	0.241667	0.120833	−	0.992673i	$-0.461443\pi$
$839$	7.00000	0.241667	0.120833	+	0.992673i	$0.461443\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−2.00000	−0.0689246
$843$	−5.00000	−0.172209
$844$	20.0000	0.688428
$845$	0	0
$846$	−9.00000	−0.309426
$847$	42.0000	1.44314
$848$	1.00000	0.0343401
$849$	0	0
$850$	0	0
$851$	−4.00000	−0.137118
$852$	3.00000	0.102778
$853$	14.0000	0.479351	0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000	0.479351	0.239675	+	0.970853i	$0.422959\pi$
$854$	27.0000	0.923921
$855$	0	0
$856$	−8.00000	−0.273434
$857$	−33.0000	−1.12726	−0.563629	−	0.826028i	$-0.690595\pi$
$857$	−33.0000	−1.12726	−0.563629	+	0.826028i	$0.690595\pi$
$858$	−15.0000	−0.512092
$859$	39.0000	1.33066	0.665331	−	0.746548i	$-0.268290\pi$
$859$	39.0000	1.33066	0.665331	+	0.746548i	$0.268290\pi$
$860$	0	0
$861$	9.00000	0.306719
$862$	21.0000	0.715263
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−28.0000	−0.951479
$867$	−1.00000	−0.0339618
$868$	−3.00000	−0.101827
$869$	−80.0000	−2.71381
$870$	0	0
$871$	6.00000	0.203302
$872$	6.00000	0.203186
$873$	2.00000	0.0676897
$874$	−8.00000	−0.270604
$875$	0	0
$876$	−6.00000	−0.202721
$877$	8.00000	0.270141	0.135070	−	0.990836i	$-0.456874\pi$
$877$	8.00000	0.270141	0.135070	+	0.990836i	$0.456874\pi$
$878$	8.00000	0.269987
$879$	24.0000	0.809500
$880$	0	0
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	−2.00000	−0.0673435
$883$	−31.0000	−1.04323	−0.521617	−	0.853180i	$-0.674671\pi$
$883$	−31.0000	−1.04323	−0.521617	+	0.853180i	$0.674671\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	14.0000	0.470339
$887$	−39.0000	−1.30949	−0.654746	−	0.755849i	$-0.727224\pi$
$887$	−39.0000	−1.30949	−0.654746	+	0.755849i	$0.727224\pi$
$888$	1.00000	0.0335578
$889$	−48.0000	−1.60987
$890$	0	0
$891$	5.00000	0.167506
$892$	−10.0000	−0.334825
$893$	18.0000	0.602347
$894$	20.0000	0.668900
$895$	0	0
$896$	−3.00000	−0.100223
$897$	12.0000	0.400668
$898$	6.00000	0.200223
$899$	−2.00000	−0.0667037
$900$	0	0
$901$	4.00000	0.133259
$902$	−15.0000	−0.499445
$903$	−15.0000	−0.499169
$904$	14.0000	0.465633
$905$	0	0
$906$	−4.00000	−0.132891
$907$	−16.0000	−0.531271	−0.265636	−	0.964073i	$-0.585582\pi$
$907$	−16.0000	−0.531271	−0.265636	+	0.964073i	$0.585582\pi$
$908$	−8.00000	−0.265489
$909$	−4.00000	−0.132672
$910$	0	0
$911$	6.00000	0.198789	0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000	0.198789	0.0993944	+	0.995048i	$0.468309\pi$
$912$	2.00000	0.0662266
$913$	−15.0000	−0.496428
$914$	−28.0000	−0.926158
$915$	0	0
$916$	−2.00000	−0.0660819
$917$	−30.0000	−0.990687
$918$	−4.00000	−0.132020
$919$	13.0000	0.428830	0.214415	−	0.976743i	$-0.431215\pi$
$919$	13.0000	0.428830	0.214415	+	0.976743i	$0.431215\pi$
$920$	0	0
$921$	16.0000	0.527218
$922$	−1.00000	−0.0329332
$923$	9.00000	0.296239
$924$	15.0000	0.493464
$925$	0	0
$926$	12.0000	0.394344
$927$	−5.00000	−0.164222
$928$	−2.00000	−0.0656532
$929$	54.0000	1.77168	0.885841	−	0.463988i	$-0.153582\pi$
$929$	54.0000	1.77168	0.885841	+	0.463988i	$0.153582\pi$
$930$	0	0
$931$	4.00000	0.131095
$932$	5.00000	0.163780
$933$	11.0000	0.360124
$934$	26.0000	0.850746
$935$	0	0
$936$	−3.00000	−0.0980581
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	−6.00000	−0.195907
$939$	22.0000	0.717943
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	−6.00000	−0.195491
$943$	12.0000	0.390774
$944$	−10.0000	−0.325472
$945$	0	0
$946$	25.0000	0.812820
$947$	−25.0000	−0.812391	−0.406195	−	0.913786i	$-0.633145\pi$
$947$	−25.0000	−0.812391	−0.406195	+	0.913786i	$0.633145\pi$
$948$	−16.0000	−0.519656
$949$	−18.0000	−0.584305
$950$	0	0
$951$	−20.0000	−0.648544
$952$	−12.0000	−0.388922
$953$	−60.0000	−1.94359	−0.971795	−	0.235826i	$-0.924220\pi$
$953$	−60.0000	−1.94359	−0.971795	+	0.235826i	$0.924220\pi$
$954$	−1.00000	−0.0323762
$955$	0	0
$956$	6.00000	0.194054
$957$	10.0000	0.323254
$958$	−24.0000	−0.775405
$959$	36.0000	1.16250
$960$	0	0
$961$	1.00000	0.0322581
$962$	3.00000	0.0967239
$963$	8.00000	0.257796
$964$	−14.0000	−0.450910
$965$	0	0
$966$	−12.0000	−0.386094
$967$	−22.0000	−0.707472	−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000	−0.707472	−0.353736	+	0.935345i	$0.615089\pi$
$968$	−14.0000	−0.449977
$969$	8.00000	0.256997
$970$	0	0
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	1.00000	0.0320750
$973$	−39.0000	−1.25028
$974$	−28.0000	−0.897178
$975$	0	0
$976$	−9.00000	−0.288083
$977$	−7.00000	−0.223950	−0.111975	−	0.993711i	$-0.535718\pi$
$977$	−7.00000	−0.223950	−0.111975	+	0.993711i	$0.535718\pi$
$978$	−6.00000	−0.191859
$979$	−30.0000	−0.958804
$980$	0	0
$981$	−6.00000	−0.191565
$982$	−20.0000	−0.638226
$983$	−26.0000	−0.829271	−0.414636	−	0.909988i	$-0.636091\pi$
$983$	−26.0000	−0.829271	−0.414636	+	0.909988i	$0.636091\pi$
$984$	−3.00000	−0.0956365
$985$	0	0
$986$	−8.00000	−0.254772
$987$	27.0000	0.859419
$988$	6.00000	0.190885
$989$	−20.0000	−0.635963
$990$	0	0
$991$	50.0000	1.58830	0.794151	−	0.607720i	$-0.207916\pi$
$991$	50.0000	1.58830	0.794151	+	0.607720i	$0.207916\pi$
$992$	1.00000	0.0317500
$993$	−15.0000	−0.476011
$994$	−9.00000	−0.285463
$995$	0	0
$996$	−3.00000	−0.0950586
$997$	28.0000	0.886769	0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000	0.886769	0.443384	+	0.896332i	$0.353778\pi$
$998$	−16.0000	−0.506471
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4650.2.a.v.1.1	✓	1
5.2	odd	4		4650.2.d.m.3349.1		2
5.3	odd	4		4650.2.d.m.3349.2		2
5.4	even	2		4650.2.a.y.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4650.2.a.v.1.1	✓	1	1.1	even	1	trivial
4650.2.a.y.1.1	yes	1	5.4	even	2
4650.2.d.m.3349.1		2	5.2	odd	4
4650.2.d.m.3349.2		2	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4650.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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