LMFDB - Embedded newform 3822.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, 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("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.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:	$30.5188236525$
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	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.00000 q^{10} -5.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} -3.00000 q^{15} +1.00000 q^{16} +3.00000 q^{17} +1.00000 q^{18} +3.00000 q^{19} -3.00000 q^{20} -5.00000 q^{22} -3.00000 q^{23} +1.00000 q^{24} +4.00000 q^{25} +1.00000 q^{26} +1.00000 q^{27} -9.00000 q^{29} -3.00000 q^{30} +10.0000 q^{31} +1.00000 q^{32} -5.00000 q^{33} +3.00000 q^{34} +1.00000 q^{36} +1.00000 q^{37} +3.00000 q^{38} +1.00000 q^{39} -3.00000 q^{40} -4.00000 q^{41} -13.0000 q^{43} -5.00000 q^{44} -3.00000 q^{45} -3.00000 q^{46} -12.0000 q^{47} +1.00000 q^{48} +4.00000 q^{50} +3.00000 q^{51} +1.00000 q^{52} -10.0000 q^{53} +1.00000 q^{54} +15.0000 q^{55} +3.00000 q^{57} -9.00000 q^{58} +6.00000 q^{59} -3.00000 q^{60} -3.00000 q^{61} +10.0000 q^{62} +1.00000 q^{64} -3.00000 q^{65} -5.00000 q^{66} +3.00000 q^{68} -3.00000 q^{69} +6.00000 q^{71} +1.00000 q^{72} -9.00000 q^{73} +1.00000 q^{74} +4.00000 q^{75} +3.00000 q^{76} +1.00000 q^{78} -16.0000 q^{79} -3.00000 q^{80} +1.00000 q^{81} -4.00000 q^{82} -14.0000 q^{83} -9.00000 q^{85} -13.0000 q^{86} -9.00000 q^{87} -5.00000 q^{88} -4.00000 q^{89} -3.00000 q^{90} -3.00000 q^{92} +10.0000 q^{93} -12.0000 q^{94} -9.00000 q^{95} +1.00000 q^{96} -2.00000 q^{97} -5.00000 q^{99} +O(q^{100})\)

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
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.00000	−0.948683
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−3.00000	−0.774597
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	1.00000	0.235702
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	−3.00000	−0.670820
$21$	0	0
$22$	−5.00000	−1.06600
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	1.00000	0.204124
$25$	4.00000	0.800000
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	−9.00000	−1.67126	−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000	−1.67126	−0.835629	+	0.549294i	$0.814897\pi$
$30$	−3.00000	−0.547723
$31$	10.0000	1.79605	0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000	1.79605	0.898027	+	0.439941i	$0.145001\pi$
$32$	1.00000	0.176777
$33$	−5.00000	−0.870388
$34$	3.00000	0.514496
$35$	0	0
$36$	1.00000	0.166667
$37$	1.00000	0.164399	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	1.00000	0.164399	0.0821995	+	0.996616i	$0.473806\pi$
$38$	3.00000	0.486664
$39$	1.00000	0.160128
$40$	−3.00000	−0.474342
$41$	−4.00000	−0.624695	−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000	−0.624695	−0.312348	+	0.949968i	$0.601115\pi$
$42$	0	0
$43$	−13.0000	−1.98248	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−13.0000	−1.98248	−0.991241	+	0.132068i	$0.957838\pi$
$44$	−5.00000	−0.753778
$45$	−3.00000	−0.447214
$46$	−3.00000	−0.442326
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	4.00000	0.565685
$51$	3.00000	0.420084
$52$	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	$0.740986\pi$
$54$	1.00000	0.136083
$55$	15.0000	2.02260
$56$	0	0
$57$	3.00000	0.397360
$58$	−9.00000	−1.18176
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	−3.00000	−0.387298
$61$	−3.00000	−0.384111	−0.192055	−	0.981384i	$-0.561515\pi$
$61$	−3.00000	−0.384111	−0.192055	+	0.981384i	$0.561515\pi$
$62$	10.0000	1.27000
$63$	0	0
$64$	1.00000	0.125000
$65$	−3.00000	−0.372104
$66$	−5.00000	−0.615457
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	3.00000	0.363803
$69$	−3.00000	−0.361158
$70$	0	0
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	1.00000	0.117851
$73$	−9.00000	−1.05337	−0.526685	−	0.850060i	$-0.676565\pi$
$73$	−9.00000	−1.05337	−0.526685	+	0.850060i	$0.676565\pi$
$74$	1.00000	0.116248
$75$	4.00000	0.461880
$76$	3.00000	0.344124
$77$	0	0
$78$	1.00000	0.113228
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	−3.00000	−0.335410
$81$	1.00000	0.111111
$82$	−4.00000	−0.441726
$83$	−14.0000	−1.53670	−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000	−1.53670	−0.768350	+	0.640030i	$0.778922\pi$
$84$	0	0
$85$	−9.00000	−0.976187
$86$	−13.0000	−1.40183
$87$	−9.00000	−0.964901
$88$	−5.00000	−0.533002
$89$	−4.00000	−0.423999	−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000	−0.423999	−0.212000	+	0.977270i	$0.567998\pi$
$90$	−3.00000	−0.316228
$91$	0	0
$92$	−3.00000	−0.312772
$93$	10.0000	1.03695
$94$	−12.0000	−1.23771
$95$	−9.00000	−0.923381
$96$	1.00000	0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	0	0
$99$	−5.00000	−0.502519
$100$	4.00000	0.400000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	3.00000	0.297044
$103$	−19.0000	−1.87213	−0.936063	−	0.351833i	$-0.885559\pi$
$103$	−19.0000	−1.87213	−0.936063	+	0.351833i	$0.885559\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−10.0000	−0.971286
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	1.00000	0.0962250
$109$	15.0000	1.43674	0.718370	−	0.695662i	$-0.244889\pi$
$109$	15.0000	1.43674	0.718370	+	0.695662i	$0.244889\pi$
$110$	15.0000	1.43019
$111$	1.00000	0.0949158
$112$	0	0
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	3.00000	0.280976
$115$	9.00000	0.839254
$116$	−9.00000	−0.835629
$117$	1.00000	0.0924500
$118$	6.00000	0.552345
$119$	0	0
$120$	−3.00000	−0.273861
$121$	14.0000	1.27273
$122$	−3.00000	−0.271607
$123$	−4.00000	−0.360668
$124$	10.0000	0.898027
$125$	3.00000	0.268328
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	1.00000	0.0883883
$129$	−13.0000	−1.14459
$130$	−3.00000	−0.263117
$131$	7.00000	0.611593	0.305796	−	0.952097i	$-0.401077\pi$
$131$	7.00000	0.611593	0.305796	+	0.952097i	$0.401077\pi$
$132$	−5.00000	−0.435194
$133$	0	0
$134$	0	0
$135$	−3.00000	−0.258199
$136$	3.00000	0.257248
$137$	21.0000	1.79415	0.897076	−	0.441877i	$-0.145687\pi$
$137$	21.0000	1.79415	0.897076	+	0.441877i	$0.145687\pi$
$138$	−3.00000	−0.255377
$139$	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
$141$	−12.0000	−1.01058
$142$	6.00000	0.503509
$143$	−5.00000	−0.418121
$144$	1.00000	0.0833333
$145$	27.0000	2.24223
$146$	−9.00000	−0.744845
$147$	0	0
$148$	1.00000	0.0821995
$149$	−8.00000	−0.655386	−0.327693	−	0.944784i	$-0.606271\pi$
$149$	−8.00000	−0.655386	−0.327693	+	0.944784i	$0.606271\pi$
$150$	4.00000	0.326599
$151$	1.00000	0.0813788	0.0406894	−	0.999172i	$-0.487045\pi$
$151$	1.00000	0.0813788	0.0406894	+	0.999172i	$0.487045\pi$
$152$	3.00000	0.243332
$153$	3.00000	0.242536
$154$	0	0
$155$	−30.0000	−2.40966
$156$	1.00000	0.0800641
$157$	−7.00000	−0.558661	−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000	−0.558661	−0.279330	+	0.960195i	$0.590112\pi$
$158$	−16.0000	−1.27289
$159$	−10.0000	−0.793052
$160$	−3.00000	−0.237171
$161$	0	0
$162$	1.00000	0.0785674
$163$	−2.00000	−0.156652	−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	−2.00000	−0.156652	−0.0783260	+	0.996928i	$0.524958\pi$
$164$	−4.00000	−0.312348
$165$	15.0000	1.16775
$166$	−14.0000	−1.08661
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−9.00000	−0.690268
$171$	3.00000	0.229416
$172$	−13.0000	−0.991241
$173$	12.0000	0.912343	0.456172	−	0.889892i	$-0.349220\pi$
$173$	12.0000	0.912343	0.456172	+	0.889892i	$0.349220\pi$
$174$	−9.00000	−0.682288
$175$	0	0
$176$	−5.00000	−0.376889
$177$	6.00000	0.450988
$178$	−4.00000	−0.299813
$179$	22.0000	1.64436	0.822179	−	0.569230i	$-0.192758\pi$
$179$	22.0000	1.64436	0.822179	+	0.569230i	$0.192758\pi$
$180$	−3.00000	−0.223607
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	0	0
$183$	−3.00000	−0.221766
$184$	−3.00000	−0.221163
$185$	−3.00000	−0.220564
$186$	10.0000	0.733236
$187$	−15.0000	−1.09691
$188$	−12.0000	−0.875190
$189$	0	0
$190$	−9.00000	−0.652929
$191$	17.0000	1.23008	0.615038	−	0.788497i	$-0.289140\pi$
$191$	17.0000	1.23008	0.615038	+	0.788497i	$0.289140\pi$
$192$	1.00000	0.0721688
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	−2.00000	−0.143592
$195$	−3.00000	−0.214834
$196$	0	0
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	−5.00000	−0.355335
$199$	23.0000	1.63043	0.815213	−	0.579161i	$-0.196620\pi$
$199$	23.0000	1.63043	0.815213	+	0.579161i	$0.196620\pi$
$200$	4.00000	0.282843
$201$	0	0
$202$	2.00000	0.140720
$203$	0	0
$204$	3.00000	0.210042
$205$	12.0000	0.838116
$206$	−19.0000	−1.32379
$207$	−3.00000	−0.208514
$208$	1.00000	0.0693375
$209$	−15.0000	−1.03757
$210$	0	0
$211$	−7.00000	−0.481900	−0.240950	−	0.970538i	$-0.577459\pi$
$211$	−7.00000	−0.481900	−0.240950	+	0.970538i	$0.577459\pi$
$212$	−10.0000	−0.686803
$213$	6.00000	0.411113
$214$	−8.00000	−0.546869
$215$	39.0000	2.65978
$216$	1.00000	0.0680414
$217$	0	0
$218$	15.0000	1.01593
$219$	−9.00000	−0.608164
$220$	15.0000	1.01130
$221$	3.00000	0.201802
$222$	1.00000	0.0671156
$223$	14.0000	0.937509	0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000	0.937509	0.468755	+	0.883328i	$0.344703\pi$
$224$	0	0
$225$	4.00000	0.266667
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	3.00000	0.198680
$229$	−4.00000	−0.264327	−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000	−0.264327	−0.132164	+	0.991228i	$0.542192\pi$
$230$	9.00000	0.593442
$231$	0	0
$232$	−9.00000	−0.590879
$233$	−4.00000	−0.262049	−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000	−0.262049	−0.131024	+	0.991379i	$0.541827\pi$
$234$	1.00000	0.0653720
$235$	36.0000	2.34838
$236$	6.00000	0.390567
$237$	−16.0000	−1.03931
$238$	0	0
$239$	−14.0000	−0.905585	−0.452792	−	0.891616i	$-0.649572\pi$
$239$	−14.0000	−0.905585	−0.452792	+	0.891616i	$0.649572\pi$
$240$	−3.00000	−0.193649
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	14.0000	0.899954
$243$	1.00000	0.0641500
$244$	−3.00000	−0.192055
$245$	0	0
$246$	−4.00000	−0.255031
$247$	3.00000	0.190885
$248$	10.0000	0.635001
$249$	−14.0000	−0.887214
$250$	3.00000	0.189737
$251$	−5.00000	−0.315597	−0.157799	−	0.987471i	$-0.550440\pi$
$251$	−5.00000	−0.315597	−0.157799	+	0.987471i	$0.550440\pi$
$252$	0	0
$253$	15.0000	0.943042
$254$	0	0
$255$	−9.00000	−0.563602
$256$	1.00000	0.0625000
$257$	26.0000	1.62184	0.810918	−	0.585160i	$-0.198968\pi$
$257$	26.0000	1.62184	0.810918	+	0.585160i	$0.198968\pi$
$258$	−13.0000	−0.809345
$259$	0	0
$260$	−3.00000	−0.186052
$261$	−9.00000	−0.557086
$262$	7.00000	0.432461
$263$	−4.00000	−0.246651	−0.123325	−	0.992366i	$-0.539356\pi$
$263$	−4.00000	−0.246651	−0.123325	+	0.992366i	$0.539356\pi$
$264$	−5.00000	−0.307729
$265$	30.0000	1.84289
$266$	0	0
$267$	−4.00000	−0.244796
$268$	0	0
$269$	−12.0000	−0.731653	−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000	−0.731653	−0.365826	+	0.930683i	$0.619214\pi$
$270$	−3.00000	−0.182574
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	3.00000	0.181902
$273$	0	0
$274$	21.0000	1.26866
$275$	−20.0000	−1.20605
$276$	−3.00000	−0.180579
$277$	−32.0000	−1.92269	−0.961347	−	0.275340i	$-0.911209\pi$
$277$	−32.0000	−1.92269	−0.961347	+	0.275340i	$0.911209\pi$
$278$	4.00000	0.239904
$279$	10.0000	0.598684
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	−12.0000	−0.714590
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	6.00000	0.356034
$285$	−9.00000	−0.533114
$286$	−5.00000	−0.295656
$287$	0	0
$288$	1.00000	0.0589256
$289$	−8.00000	−0.470588
$290$	27.0000	1.58549
$291$	−2.00000	−0.117242
$292$	−9.00000	−0.526685
$293$	2.00000	0.116841	0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000	0.116841	0.0584206	+	0.998292i	$0.481394\pi$
$294$	0	0
$295$	−18.0000	−1.04800
$296$	1.00000	0.0581238
$297$	−5.00000	−0.290129
$298$	−8.00000	−0.463428
$299$	−3.00000	−0.173494
$300$	4.00000	0.230940
$301$	0	0
$302$	1.00000	0.0575435
$303$	2.00000	0.114897
$304$	3.00000	0.172062
$305$	9.00000	0.515339
$306$	3.00000	0.171499
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	0	0
$309$	−19.0000	−1.08087
$310$	−30.0000	−1.70389
$311$	2.00000	0.113410	0.0567048	−	0.998391i	$-0.481941\pi$
$311$	2.00000	0.113410	0.0567048	+	0.998391i	$0.481941\pi$
$312$	1.00000	0.0566139
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	−7.00000	−0.395033
$315$	0	0
$316$	−16.0000	−0.900070
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	−10.0000	−0.560772
$319$	45.0000	2.51952
$320$	−3.00000	−0.167705
$321$	−8.00000	−0.446516
$322$	0	0
$323$	9.00000	0.500773
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−2.00000	−0.110770
$327$	15.0000	0.829502
$328$	−4.00000	−0.220863
$329$	0	0
$330$	15.0000	0.825723
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	−14.0000	−0.768350
$333$	1.00000	0.0547997
$334$	−3.00000	−0.164153
$335$	0	0
$336$	0	0
$337$	7.00000	0.381314	0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000	0.381314	0.190657	+	0.981657i	$0.438938\pi$
$338$	1.00000	0.0543928
$339$	0	0
$340$	−9.00000	−0.488094
$341$	−50.0000	−2.70765
$342$	3.00000	0.162221
$343$	0	0
$344$	−13.0000	−0.700913
$345$	9.00000	0.484544
$346$	12.0000	0.645124
$347$	−6.00000	−0.322097	−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000	−0.322097	−0.161048	+	0.986947i	$0.551488\pi$
$348$	−9.00000	−0.482451
$349$	28.0000	1.49881	0.749403	−	0.662114i	$-0.230341\pi$
$349$	28.0000	1.49881	0.749403	+	0.662114i	$0.230341\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−5.00000	−0.266501
$353$	10.0000	0.532246	0.266123	−	0.963939i	$-0.414257\pi$
$353$	10.0000	0.532246	0.266123	+	0.963939i	$0.414257\pi$
$354$	6.00000	0.318896
$355$	−18.0000	−0.955341
$356$	−4.00000	−0.212000
$357$	0	0
$358$	22.0000	1.16274
$359$	−16.0000	−0.844448	−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000	−0.844448	−0.422224	+	0.906492i	$0.638750\pi$
$360$	−3.00000	−0.158114
$361$	−10.0000	−0.526316
$362$	−10.0000	−0.525588
$363$	14.0000	0.734809
$364$	0	0
$365$	27.0000	1.41324
$366$	−3.00000	−0.156813
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	−3.00000	−0.156386
$369$	−4.00000	−0.208232
$370$	−3.00000	−0.155963
$371$	0	0
$372$	10.0000	0.518476
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	−15.0000	−0.775632
$375$	3.00000	0.154919
$376$	−12.0000	−0.618853
$377$	−9.00000	−0.463524
$378$	0	0
$379$	−26.0000	−1.33553	−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000	−1.33553	−0.667765	+	0.744372i	$0.732749\pi$
$380$	−9.00000	−0.461690
$381$	0	0
$382$	17.0000	0.869796
$383$	9.00000	0.459879	0.229939	−	0.973205i	$-0.426147\pi$
$383$	9.00000	0.459879	0.229939	+	0.973205i	$0.426147\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	10.0000	0.508987
$387$	−13.0000	−0.660827
$388$	−2.00000	−0.101535
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	−3.00000	−0.151911
$391$	−9.00000	−0.455150
$392$	0	0
$393$	7.00000	0.353103
$394$	−22.0000	−1.10834
$395$	48.0000	2.41514
$396$	−5.00000	−0.251259
$397$	6.00000	0.301131	0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000	0.301131	0.150566	+	0.988600i	$0.451890\pi$
$398$	23.0000	1.15289
$399$	0	0
$400$	4.00000	0.200000
$401$	34.0000	1.69788	0.848939	−	0.528490i	$-0.177242\pi$
$401$	34.0000	1.69788	0.848939	+	0.528490i	$0.177242\pi$
$402$	0	0
$403$	10.0000	0.498135
$404$	2.00000	0.0995037
$405$	−3.00000	−0.149071
$406$	0	0
$407$	−5.00000	−0.247841
$408$	3.00000	0.148522
$409$	13.0000	0.642809	0.321404	−	0.946942i	$-0.395845\pi$
$409$	13.0000	0.642809	0.321404	+	0.946942i	$0.395845\pi$
$410$	12.0000	0.592638
$411$	21.0000	1.03585
$412$	−19.0000	−0.936063
$413$	0	0
$414$	−3.00000	−0.147442
$415$	42.0000	2.06170
$416$	1.00000	0.0490290
$417$	4.00000	0.195881
$418$	−15.0000	−0.733674
$419$	21.0000	1.02592	0.512959	−	0.858413i	$-0.328549\pi$
$419$	21.0000	1.02592	0.512959	+	0.858413i	$0.328549\pi$
$420$	0	0
$421$	30.0000	1.46211	0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000	1.46211	0.731055	+	0.682318i	$0.239028\pi$
$422$	−7.00000	−0.340755
$423$	−12.0000	−0.583460
$424$	−10.0000	−0.485643
$425$	12.0000	0.582086
$426$	6.00000	0.290701
$427$	0	0
$428$	−8.00000	−0.386695
$429$	−5.00000	−0.241402
$430$	39.0000	1.88075
$431$	−18.0000	−0.867029	−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000	−0.867029	−0.433515	+	0.901146i	$0.642727\pi$
$432$	1.00000	0.0481125
$433$	16.0000	0.768911	0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000	0.768911	0.384455	+	0.923144i	$0.374389\pi$
$434$	0	0
$435$	27.0000	1.29455
$436$	15.0000	0.718370
$437$	−9.00000	−0.430528
$438$	−9.00000	−0.430037
$439$	−23.0000	−1.09773	−0.548865	−	0.835911i	$-0.684940\pi$
$439$	−23.0000	−1.09773	−0.548865	+	0.835911i	$0.684940\pi$
$440$	15.0000	0.715097
$441$	0	0
$442$	3.00000	0.142695
$443$	30.0000	1.42534	0.712672	−	0.701498i	$-0.247485\pi$
$443$	30.0000	1.42534	0.712672	+	0.701498i	$0.247485\pi$
$444$	1.00000	0.0474579
$445$	12.0000	0.568855
$446$	14.0000	0.662919
$447$	−8.00000	−0.378387
$448$	0	0
$449$	5.00000	0.235965	0.117982	−	0.993016i	$-0.462357\pi$
$449$	5.00000	0.235965	0.117982	+	0.993016i	$0.462357\pi$
$450$	4.00000	0.188562
$451$	20.0000	0.941763
$452$	0	0
$453$	1.00000	0.0469841
$454$	0	0
$455$	0	0
$456$	3.00000	0.140488
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	−4.00000	−0.186908
$459$	3.00000	0.140028
$460$	9.00000	0.419627
$461$	−41.0000	−1.90956	−0.954780	−	0.297313i	$-0.903910\pi$
$461$	−41.0000	−1.90956	−0.954780	+	0.297313i	$0.903910\pi$
$462$	0	0
$463$	29.0000	1.34774	0.673872	−	0.738848i	$-0.264630\pi$
$463$	29.0000	1.34774	0.673872	+	0.738848i	$0.264630\pi$
$464$	−9.00000	−0.417815
$465$	−30.0000	−1.39122
$466$	−4.00000	−0.185296
$467$	23.0000	1.06431	0.532157	−	0.846646i	$-0.321382\pi$
$467$	23.0000	1.06431	0.532157	+	0.846646i	$0.321382\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	36.0000	1.66056
$471$	−7.00000	−0.322543
$472$	6.00000	0.276172
$473$	65.0000	2.98870
$474$	−16.0000	−0.734904
$475$	12.0000	0.550598
$476$	0	0
$477$	−10.0000	−0.457869
$478$	−14.0000	−0.640345
$479$	−5.00000	−0.228456	−0.114228	−	0.993455i	$-0.536439\pi$
$479$	−5.00000	−0.228456	−0.114228	+	0.993455i	$0.536439\pi$
$480$	−3.00000	−0.136931
$481$	1.00000	0.0455961
$482$	2.00000	0.0910975
$483$	0	0
$484$	14.0000	0.636364
$485$	6.00000	0.272446
$486$	1.00000	0.0453609
$487$	−24.0000	−1.08754	−0.543772	−	0.839233i	$-0.683004\pi$
$487$	−24.0000	−1.08754	−0.543772	+	0.839233i	$0.683004\pi$
$488$	−3.00000	−0.135804
$489$	−2.00000	−0.0904431
$490$	0	0
$491$	−2.00000	−0.0902587	−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−2.00000	−0.0902587	−0.0451294	+	0.998981i	$0.514370\pi$
$492$	−4.00000	−0.180334
$493$	−27.0000	−1.21602
$494$	3.00000	0.134976
$495$	15.0000	0.674200
$496$	10.0000	0.449013
$497$	0	0
$498$	−14.0000	−0.627355
$499$	−30.0000	−1.34298	−0.671492	−	0.741012i	$-0.734346\pi$
$499$	−30.0000	−1.34298	−0.671492	+	0.741012i	$0.734346\pi$
$500$	3.00000	0.134164
$501$	−3.00000	−0.134030
$502$	−5.00000	−0.223161
$503$	−40.0000	−1.78351	−0.891756	−	0.452517i	$-0.850526\pi$
$503$	−40.0000	−1.78351	−0.891756	+	0.452517i	$0.850526\pi$
$504$	0	0
$505$	−6.00000	−0.266996
$506$	15.0000	0.666831
$507$	1.00000	0.0444116
$508$	0	0
$509$	−17.0000	−0.753512	−0.376756	−	0.926313i	$-0.622960\pi$
$509$	−17.0000	−0.753512	−0.376756	+	0.926313i	$0.622960\pi$
$510$	−9.00000	−0.398527
$511$	0	0
$512$	1.00000	0.0441942
$513$	3.00000	0.132453
$514$	26.0000	1.14681
$515$	57.0000	2.51172
$516$	−13.0000	−0.572293
$517$	60.0000	2.63880
$518$	0	0
$519$	12.0000	0.526742
$520$	−3.00000	−0.131559
$521$	−7.00000	−0.306676	−0.153338	−	0.988174i	$-0.549002\pi$
$521$	−7.00000	−0.306676	−0.153338	+	0.988174i	$0.549002\pi$
$522$	−9.00000	−0.393919
$523$	−2.00000	−0.0874539	−0.0437269	−	0.999044i	$-0.513923\pi$
$523$	−2.00000	−0.0874539	−0.0437269	+	0.999044i	$0.513923\pi$
$524$	7.00000	0.305796
$525$	0	0
$526$	−4.00000	−0.174408
$527$	30.0000	1.30682
$528$	−5.00000	−0.217597
$529$	−14.0000	−0.608696
$530$	30.0000	1.30312
$531$	6.00000	0.260378
$532$	0	0
$533$	−4.00000	−0.173259
$534$	−4.00000	−0.173097
$535$	24.0000	1.03761
$536$	0	0
$537$	22.0000	0.949370
$538$	−12.0000	−0.517357
$539$	0	0
$540$	−3.00000	−0.129099
$541$	−13.0000	−0.558914	−0.279457	−	0.960158i	$-0.590154\pi$
$541$	−13.0000	−0.558914	−0.279457	+	0.960158i	$0.590154\pi$
$542$	20.0000	0.859074
$543$	−10.0000	−0.429141
$544$	3.00000	0.128624
$545$	−45.0000	−1.92759
$546$	0	0
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	21.0000	0.897076
$549$	−3.00000	−0.128037
$550$	−20.0000	−0.852803
$551$	−27.0000	−1.15024
$552$	−3.00000	−0.127688
$553$	0	0
$554$	−32.0000	−1.35955
$555$	−3.00000	−0.127343
$556$	4.00000	0.169638
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	10.0000	0.423334
$559$	−13.0000	−0.549841
$560$	0	0
$561$	−15.0000	−0.633300
$562$	6.00000	0.253095
$563$	−45.0000	−1.89652	−0.948262	−	0.317489i	$-0.897160\pi$
$563$	−45.0000	−1.89652	−0.948262	+	0.317489i	$0.897160\pi$
$564$	−12.0000	−0.505291
$565$	0	0
$566$	4.00000	0.168133
$567$	0	0
$568$	6.00000	0.251754
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	−9.00000	−0.376969
$571$	20.0000	0.836974	0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000	0.836974	0.418487	+	0.908223i	$0.362561\pi$
$572$	−5.00000	−0.209061
$573$	17.0000	0.710185
$574$	0	0
$575$	−12.0000	−0.500435
$576$	1.00000	0.0416667
$577$	10.0000	0.416305	0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000	0.416305	0.208153	+	0.978096i	$0.433255\pi$
$578$	−8.00000	−0.332756
$579$	10.0000	0.415586
$580$	27.0000	1.12111
$581$	0	0
$582$	−2.00000	−0.0829027
$583$	50.0000	2.07079
$584$	−9.00000	−0.372423
$585$	−3.00000	−0.124035
$586$	2.00000	0.0826192
$587$	−26.0000	−1.07313	−0.536567	−	0.843857i	$-0.680279\pi$
$587$	−26.0000	−1.07313	−0.536567	+	0.843857i	$0.680279\pi$
$588$	0	0
$589$	30.0000	1.23613
$590$	−18.0000	−0.741048
$591$	−22.0000	−0.904959
$592$	1.00000	0.0410997
$593$	36.0000	1.47834	0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000	1.47834	0.739171	+	0.673517i	$0.235217\pi$
$594$	−5.00000	−0.205152
$595$	0	0
$596$	−8.00000	−0.327693
$597$	23.0000	0.941327
$598$	−3.00000	−0.122679
$599$	11.0000	0.449448	0.224724	−	0.974422i	$-0.427852\pi$
$599$	11.0000	0.449448	0.224724	+	0.974422i	$0.427852\pi$
$600$	4.00000	0.163299
$601$	28.0000	1.14214	0.571072	−	0.820900i	$-0.306528\pi$
$601$	28.0000	1.14214	0.571072	+	0.820900i	$0.306528\pi$
$602$	0	0
$603$	0	0
$604$	1.00000	0.0406894
$605$	−42.0000	−1.70754
$606$	2.00000	0.0812444
$607$	−7.00000	−0.284121	−0.142061	−	0.989858i	$-0.545373\pi$
$607$	−7.00000	−0.284121	−0.142061	+	0.989858i	$0.545373\pi$
$608$	3.00000	0.121666
$609$	0	0
$610$	9.00000	0.364399
$611$	−12.0000	−0.485468
$612$	3.00000	0.121268
$613$	−9.00000	−0.363507	−0.181753	−	0.983344i	$-0.558177\pi$
$613$	−9.00000	−0.363507	−0.181753	+	0.983344i	$0.558177\pi$
$614$	4.00000	0.161427
$615$	12.0000	0.483887
$616$	0	0
$617$	19.0000	0.764911	0.382456	−	0.923974i	$-0.375078\pi$
$617$	19.0000	0.764911	0.382456	+	0.923974i	$0.375078\pi$
$618$	−19.0000	−0.764292
$619$	23.0000	0.924448	0.462224	−	0.886763i	$-0.347052\pi$
$619$	23.0000	0.924448	0.462224	+	0.886763i	$0.347052\pi$
$620$	−30.0000	−1.20483
$621$	−3.00000	−0.120386
$622$	2.00000	0.0801927
$623$	0	0
$624$	1.00000	0.0400320
$625$	−29.0000	−1.16000
$626$	−22.0000	−0.879297
$627$	−15.0000	−0.599042
$628$	−7.00000	−0.279330
$629$	3.00000	0.119618
$630$	0	0
$631$	41.0000	1.63218	0.816092	−	0.577922i	$-0.196136\pi$
$631$	41.0000	1.63218	0.816092	+	0.577922i	$0.196136\pi$
$632$	−16.0000	−0.636446
$633$	−7.00000	−0.278225
$634$	18.0000	0.714871
$635$	0	0
$636$	−10.0000	−0.396526
$637$	0	0
$638$	45.0000	1.78157
$639$	6.00000	0.237356
$640$	−3.00000	−0.118585
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	−8.00000	−0.315735
$643$	49.0000	1.93237	0.966186	−	0.257847i	$-0.0830131\pi$
$643$	49.0000	1.93237	0.966186	+	0.257847i	$0.0830131\pi$
$644$	0	0
$645$	39.0000	1.53562
$646$	9.00000	0.354100
$647$	40.0000	1.57256	0.786281	−	0.617869i	$-0.212004\pi$
$647$	40.0000	1.57256	0.786281	+	0.617869i	$0.212004\pi$
$648$	1.00000	0.0392837
$649$	−30.0000	−1.17760
$650$	4.00000	0.156893
$651$	0	0
$652$	−2.00000	−0.0783260
$653$	29.0000	1.13486	0.567429	−	0.823422i	$-0.307938\pi$
$653$	29.0000	1.13486	0.567429	+	0.823422i	$0.307938\pi$
$654$	15.0000	0.586546
$655$	−21.0000	−0.820538
$656$	−4.00000	−0.156174
$657$	−9.00000	−0.351123
$658$	0	0
$659$	38.0000	1.48027	0.740135	−	0.672458i	$-0.234762\pi$
$659$	38.0000	1.48027	0.740135	+	0.672458i	$0.234762\pi$
$660$	15.0000	0.583874
$661$	−38.0000	−1.47803	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	−38.0000	−1.47803	−0.739014	+	0.673690i	$0.764708\pi$
$662$	−4.00000	−0.155464
$663$	3.00000	0.116510
$664$	−14.0000	−0.543305
$665$	0	0
$666$	1.00000	0.0387492
$667$	27.0000	1.04544
$668$	−3.00000	−0.116073
$669$	14.0000	0.541271
$670$	0	0
$671$	15.0000	0.579069
$672$	0	0
$673$	−5.00000	−0.192736	−0.0963679	−	0.995346i	$-0.530723\pi$
$673$	−5.00000	−0.192736	−0.0963679	+	0.995346i	$0.530723\pi$
$674$	7.00000	0.269630
$675$	4.00000	0.153960
$676$	1.00000	0.0384615
$677$	−38.0000	−1.46046	−0.730229	−	0.683202i	$-0.760587\pi$
$677$	−38.0000	−1.46046	−0.730229	+	0.683202i	$0.760587\pi$
$678$	0	0
$679$	0	0
$680$	−9.00000	−0.345134
$681$	0	0
$682$	−50.0000	−1.91460
$683$	−15.0000	−0.573959	−0.286980	−	0.957937i	$-0.592651\pi$
$683$	−15.0000	−0.573959	−0.286980	+	0.957937i	$0.592651\pi$
$684$	3.00000	0.114708
$685$	−63.0000	−2.40711
$686$	0	0
$687$	−4.00000	−0.152610
$688$	−13.0000	−0.495620
$689$	−10.0000	−0.380970
$690$	9.00000	0.342624
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	12.0000	0.456172
$693$	0	0
$694$	−6.00000	−0.227757
$695$	−12.0000	−0.455186
$696$	−9.00000	−0.341144
$697$	−12.0000	−0.454532
$698$	28.0000	1.05982
$699$	−4.00000	−0.151294
$700$	0	0
$701$	−26.0000	−0.982006	−0.491003	−	0.871158i	$-0.663370\pi$
$701$	−26.0000	−0.982006	−0.491003	+	0.871158i	$0.663370\pi$
$702$	1.00000	0.0377426
$703$	3.00000	0.113147
$704$	−5.00000	−0.188445
$705$	36.0000	1.35584
$706$	10.0000	0.376355
$707$	0	0
$708$	6.00000	0.225494
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	−18.0000	−0.675528
$711$	−16.0000	−0.600047
$712$	−4.00000	−0.149906
$713$	−30.0000	−1.12351
$714$	0	0
$715$	15.0000	0.560968
$716$	22.0000	0.822179
$717$	−14.0000	−0.522840
$718$	−16.0000	−0.597115
$719$	−40.0000	−1.49175	−0.745874	−	0.666087i	$-0.767968\pi$
$719$	−40.0000	−1.49175	−0.745874	+	0.666087i	$0.767968\pi$
$720$	−3.00000	−0.111803
$721$	0	0
$722$	−10.0000	−0.372161
$723$	2.00000	0.0743808
$724$	−10.0000	−0.371647
$725$	−36.0000	−1.33701
$726$	14.0000	0.519589
$727$	−35.0000	−1.29808	−0.649039	−	0.760755i	$-0.724829\pi$
$727$	−35.0000	−1.29808	−0.649039	+	0.760755i	$0.724829\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	27.0000	0.999315
$731$	−39.0000	−1.44247
$732$	−3.00000	−0.110883
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	0	0
$735$	0	0
$736$	−3.00000	−0.110581
$737$	0	0
$738$	−4.00000	−0.147242
$739$	−2.00000	−0.0735712	−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000	−0.0735712	−0.0367856	+	0.999323i	$0.511712\pi$
$740$	−3.00000	−0.110282
$741$	3.00000	0.110208
$742$	0	0
$743$	−42.0000	−1.54083	−0.770415	−	0.637542i	$-0.779951\pi$
$743$	−42.0000	−1.54083	−0.770415	+	0.637542i	$0.779951\pi$
$744$	10.0000	0.366618
$745$	24.0000	0.879292
$746$	−14.0000	−0.512576
$747$	−14.0000	−0.512233
$748$	−15.0000	−0.548454
$749$	0	0
$750$	3.00000	0.109545
$751$	−14.0000	−0.510867	−0.255434	−	0.966827i	$-0.582218\pi$
$751$	−14.0000	−0.510867	−0.255434	+	0.966827i	$0.582218\pi$
$752$	−12.0000	−0.437595
$753$	−5.00000	−0.182210
$754$	−9.00000	−0.327761
$755$	−3.00000	−0.109181
$756$	0	0
$757$	−8.00000	−0.290765	−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000	−0.290765	−0.145382	+	0.989376i	$0.546441\pi$
$758$	−26.0000	−0.944363
$759$	15.0000	0.544466
$760$	−9.00000	−0.326464
$761$	−44.0000	−1.59500	−0.797499	−	0.603320i	$-0.793844\pi$
$761$	−44.0000	−1.59500	−0.797499	+	0.603320i	$0.793844\pi$
$762$	0	0
$763$	0	0
$764$	17.0000	0.615038
$765$	−9.00000	−0.325396
$766$	9.00000	0.325183
$767$	6.00000	0.216647
$768$	1.00000	0.0360844
$769$	−27.0000	−0.973645	−0.486822	−	0.873501i	$-0.661844\pi$
$769$	−27.0000	−0.973645	−0.486822	+	0.873501i	$0.661844\pi$
$770$	0	0
$771$	26.0000	0.936367
$772$	10.0000	0.359908
$773$	31.0000	1.11499	0.557496	−	0.830179i	$-0.311762\pi$
$773$	31.0000	1.11499	0.557496	+	0.830179i	$0.311762\pi$
$774$	−13.0000	−0.467275
$775$	40.0000	1.43684
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	−26.0000	−0.932145
$779$	−12.0000	−0.429945
$780$	−3.00000	−0.107417
$781$	−30.0000	−1.07348
$782$	−9.00000	−0.321839
$783$	−9.00000	−0.321634
$784$	0	0
$785$	21.0000	0.749522
$786$	7.00000	0.249682
$787$	−33.0000	−1.17632	−0.588161	−	0.808744i	$-0.700148\pi$
$787$	−33.0000	−1.17632	−0.588161	+	0.808744i	$0.700148\pi$
$788$	−22.0000	−0.783718
$789$	−4.00000	−0.142404
$790$	48.0000	1.70776
$791$	0	0
$792$	−5.00000	−0.177667
$793$	−3.00000	−0.106533
$794$	6.00000	0.212932
$795$	30.0000	1.06399
$796$	23.0000	0.815213
$797$	42.0000	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$798$	0	0
$799$	−36.0000	−1.27359
$800$	4.00000	0.141421
$801$	−4.00000	−0.141333
$802$	34.0000	1.20058
$803$	45.0000	1.58802
$804$	0	0
$805$	0	0
$806$	10.0000	0.352235
$807$	−12.0000	−0.422420
$808$	2.00000	0.0703598
$809$	−36.0000	−1.26569	−0.632846	−	0.774277i	$-0.718114\pi$
$809$	−36.0000	−1.26569	−0.632846	+	0.774277i	$0.718114\pi$
$810$	−3.00000	−0.105409
$811$	−9.00000	−0.316033	−0.158016	−	0.987436i	$-0.550510\pi$
$811$	−9.00000	−0.316033	−0.158016	+	0.987436i	$0.550510\pi$
$812$	0	0
$813$	20.0000	0.701431
$814$	−5.00000	−0.175250
$815$	6.00000	0.210171
$816$	3.00000	0.105021
$817$	−39.0000	−1.36444
$818$	13.0000	0.454534
$819$	0	0
$820$	12.0000	0.419058
$821$	32.0000	1.11681	0.558404	−	0.829569i	$-0.311414\pi$
$821$	32.0000	1.11681	0.558404	+	0.829569i	$0.311414\pi$
$822$	21.0000	0.732459
$823$	−18.0000	−0.627441	−0.313720	−	0.949515i	$-0.601575\pi$
$823$	−18.0000	−0.627441	−0.313720	+	0.949515i	$0.601575\pi$
$824$	−19.0000	−0.661896
$825$	−20.0000	−0.696311
$826$	0	0
$827$	15.0000	0.521601	0.260801	−	0.965393i	$-0.416014\pi$
$827$	15.0000	0.521601	0.260801	+	0.965393i	$0.416014\pi$
$828$	−3.00000	−0.104257
$829$	−11.0000	−0.382046	−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000	−0.382046	−0.191023	+	0.981586i	$0.561180\pi$
$830$	42.0000	1.45784
$831$	−32.0000	−1.11007
$832$	1.00000	0.0346688
$833$	0	0
$834$	4.00000	0.138509
$835$	9.00000	0.311458
$836$	−15.0000	−0.518786
$837$	10.0000	0.345651
$838$	21.0000	0.725433
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	52.0000	1.79310
$842$	30.0000	1.03387
$843$	6.00000	0.206651
$844$	−7.00000	−0.240950
$845$	−3.00000	−0.103203
$846$	−12.0000	−0.412568
$847$	0	0
$848$	−10.0000	−0.343401
$849$	4.00000	0.137280
$850$	12.0000	0.411597
$851$	−3.00000	−0.102839
$852$	6.00000	0.205557
$853$	−16.0000	−0.547830	−0.273915	−	0.961754i	$-0.588319\pi$
$853$	−16.0000	−0.547830	−0.273915	+	0.961754i	$0.588319\pi$
$854$	0	0
$855$	−9.00000	−0.307794
$856$	−8.00000	−0.273434
$857$	54.0000	1.84460	0.922302	−	0.386469i	$-0.126305\pi$
$857$	54.0000	1.84460	0.922302	+	0.386469i	$0.126305\pi$
$858$	−5.00000	−0.170697
$859$	−36.0000	−1.22830	−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000	−1.22830	−0.614152	+	0.789188i	$0.710502\pi$
$860$	39.0000	1.32989
$861$	0	0
$862$	−18.0000	−0.613082
$863$	−10.0000	−0.340404	−0.170202	−	0.985409i	$-0.554442\pi$
$863$	−10.0000	−0.340404	−0.170202	+	0.985409i	$0.554442\pi$
$864$	1.00000	0.0340207
$865$	−36.0000	−1.22404
$866$	16.0000	0.543702
$867$	−8.00000	−0.271694
$868$	0	0
$869$	80.0000	2.71381
$870$	27.0000	0.915386
$871$	0	0
$872$	15.0000	0.507964
$873$	−2.00000	−0.0676897
$874$	−9.00000	−0.304430
$875$	0	0
$876$	−9.00000	−0.304082
$877$	46.0000	1.55331	0.776655	−	0.629926i	$-0.216915\pi$
$877$	46.0000	1.55331	0.776655	+	0.629926i	$0.216915\pi$
$878$	−23.0000	−0.776212
$879$	2.00000	0.0674583
$880$	15.0000	0.505650
$881$	43.0000	1.44871	0.724353	−	0.689429i	$-0.242138\pi$
$881$	43.0000	1.44871	0.724353	+	0.689429i	$0.242138\pi$
$882$	0	0
$883$	−49.0000	−1.64898	−0.824491	−	0.565876i	$-0.808538\pi$
$883$	−49.0000	−1.64898	−0.824491	+	0.565876i	$0.808538\pi$
$884$	3.00000	0.100901
$885$	−18.0000	−0.605063
$886$	30.0000	1.00787
$887$	−44.0000	−1.47738	−0.738688	−	0.674048i	$-0.764554\pi$
$887$	−44.0000	−1.47738	−0.738688	+	0.674048i	$0.764554\pi$
$888$	1.00000	0.0335578
$889$	0	0
$890$	12.0000	0.402241
$891$	−5.00000	−0.167506
$892$	14.0000	0.468755
$893$	−36.0000	−1.20469
$894$	−8.00000	−0.267560
$895$	−66.0000	−2.20614
$896$	0	0
$897$	−3.00000	−0.100167
$898$	5.00000	0.166852
$899$	−90.0000	−3.00167
$900$	4.00000	0.133333
$901$	−30.0000	−0.999445
$902$	20.0000	0.665927
$903$	0	0
$904$	0	0
$905$	30.0000	0.997234
$906$	1.00000	0.0332228
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	0	0
$909$	2.00000	0.0663358
$910$	0	0
$911$	19.0000	0.629498	0.314749	−	0.949175i	$-0.398080\pi$
$911$	19.0000	0.629498	0.314749	+	0.949175i	$0.398080\pi$
$912$	3.00000	0.0993399
$913$	70.0000	2.31666
$914$	−18.0000	−0.595387
$915$	9.00000	0.297531
$916$	−4.00000	−0.132164
$917$	0	0
$918$	3.00000	0.0990148
$919$	−6.00000	−0.197922	−0.0989609	−	0.995091i	$-0.531552\pi$
$919$	−6.00000	−0.197922	−0.0989609	+	0.995091i	$0.531552\pi$
$920$	9.00000	0.296721
$921$	4.00000	0.131804
$922$	−41.0000	−1.35026
$923$	6.00000	0.197492
$924$	0	0
$925$	4.00000	0.131519
$926$	29.0000	0.952999
$927$	−19.0000	−0.624042
$928$	−9.00000	−0.295439
$929$	36.0000	1.18112	0.590561	−	0.806993i	$-0.298907\pi$
$929$	36.0000	1.18112	0.590561	+	0.806993i	$0.298907\pi$
$930$	−30.0000	−0.983739
$931$	0	0
$932$	−4.00000	−0.131024
$933$	2.00000	0.0654771
$934$	23.0000	0.752583
$935$	45.0000	1.47166
$936$	1.00000	0.0326860
$937$	8.00000	0.261349	0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000	0.261349	0.130674	+	0.991425i	$0.458286\pi$
$938$	0	0
$939$	−22.0000	−0.717943
$940$	36.0000	1.17419
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	−7.00000	−0.228072
$943$	12.0000	0.390774
$944$	6.00000	0.195283
$945$	0	0
$946$	65.0000	2.11333
$947$	−13.0000	−0.422443	−0.211222	−	0.977438i	$-0.567744\pi$
$947$	−13.0000	−0.422443	−0.211222	+	0.977438i	$0.567744\pi$
$948$	−16.0000	−0.519656
$949$	−9.00000	−0.292152
$950$	12.0000	0.389331
$951$	18.0000	0.583690
$952$	0	0
$953$	36.0000	1.16615	0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000	1.16615	0.583077	+	0.812417i	$0.301849\pi$
$954$	−10.0000	−0.323762
$955$	−51.0000	−1.65032
$956$	−14.0000	−0.452792
$957$	45.0000	1.45464
$958$	−5.00000	−0.161543
$959$	0	0
$960$	−3.00000	−0.0968246
$961$	69.0000	2.22581
$962$	1.00000	0.0322413
$963$	−8.00000	−0.257796
$964$	2.00000	0.0644157
$965$	−30.0000	−0.965734
$966$	0	0
$967$	23.0000	0.739630	0.369815	−	0.929105i	$-0.379421\pi$
$967$	23.0000	0.739630	0.369815	+	0.929105i	$0.379421\pi$
$968$	14.0000	0.449977
$969$	9.00000	0.289122
$970$	6.00000	0.192648
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−24.0000	−0.769010
$975$	4.00000	0.128103
$976$	−3.00000	−0.0960277
$977$	−9.00000	−0.287936	−0.143968	−	0.989582i	$-0.545986\pi$
$977$	−9.00000	−0.287936	−0.143968	+	0.989582i	$0.545986\pi$
$978$	−2.00000	−0.0639529
$979$	20.0000	0.639203
$980$	0	0
$981$	15.0000	0.478913
$982$	−2.00000	−0.0638226
$983$	−33.0000	−1.05254	−0.526268	−	0.850319i	$-0.676409\pi$
$983$	−33.0000	−1.05254	−0.526268	+	0.850319i	$0.676409\pi$
$984$	−4.00000	−0.127515
$985$	66.0000	2.10293
$986$	−27.0000	−0.859855
$987$	0	0
$988$	3.00000	0.0954427
$989$	39.0000	1.24013
$990$	15.0000	0.476731
$991$	22.0000	0.698853	0.349427	−	0.936964i	$-0.386376\pi$
$991$	22.0000	0.698853	0.349427	+	0.936964i	$0.386376\pi$
$992$	10.0000	0.317500
$993$	−4.00000	−0.126936
$994$	0	0
$995$	−69.0000	−2.18745
$996$	−14.0000	−0.443607
$997$	26.0000	0.823428	0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000	0.823428	0.411714	+	0.911313i	$0.364930\pi$
$998$	−30.0000	−0.949633
$999$	1.00000	0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bb.1.1	yes	1
7.6	odd	2		3822.2.a.y.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3822.2.a.y.1.1	✓	1	7.6	odd	2
3822.2.a.bb.1.1	yes	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:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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