LMFDB - Embedded newform 4650.2.a.bn.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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} +1.00000 q^{18} -2.00000 q^{21} +2.00000 q^{22} -6.00000 q^{23} +1.00000 q^{24} +4.00000 q^{26} +1.00000 q^{27} -2.00000 q^{28} -5.00000 q^{29} +1.00000 q^{31} +1.00000 q^{32} +2.00000 q^{33} +3.00000 q^{34} +1.00000 q^{36} +8.00000 q^{37} +4.00000 q^{39} +12.0000 q^{41} -2.00000 q^{42} -1.00000 q^{43} +2.00000 q^{44} -6.00000 q^{46} +3.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} +3.00000 q^{51} +4.00000 q^{52} +14.0000 q^{53} +1.00000 q^{54} -2.00000 q^{56} -5.00000 q^{58} -8.00000 q^{61} +1.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +2.00000 q^{66} -2.00000 q^{67} +3.00000 q^{68} -6.00000 q^{69} +7.00000 q^{71} +1.00000 q^{72} +14.0000 q^{73} +8.00000 q^{74} -4.00000 q^{77} +4.00000 q^{78} -5.00000 q^{79} +1.00000 q^{81} +12.0000 q^{82} +4.00000 q^{83} -2.00000 q^{84} -1.00000 q^{86} -5.00000 q^{87} +2.00000 q^{88} -5.00000 q^{89} -8.00000 q^{91} -6.00000 q^{92} +1.00000 q^{93} +3.00000 q^{94} +1.00000 q^{96} -7.00000 q^{97} -3.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000	0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	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
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	−2.00000	−0.436436
$22$	2.00000	0.426401
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	4.00000	0.784465
$27$	1.00000	0.192450
$28$	−2.00000	−0.377964
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	2.00000	0.348155
$34$	3.00000	0.514496
$35$	0	0
$36$	1.00000	0.166667
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	0	0
$39$	4.00000	0.640513
$40$	0	0
$41$	12.0000	1.87409	0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000	1.87409	0.937043	+	0.349215i	$0.113552\pi$
$42$	−2.00000	−0.308607
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−6.00000	−0.884652
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	1.00000	0.144338
$49$	−3.00000	−0.428571
$50$	0	0
$51$	3.00000	0.420084
$52$	4.00000	0.554700
$53$	14.0000	1.92305	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	14.0000	1.92305	0.961524	+	0.274721i	$0.0885855\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−2.00000	−0.267261
$57$	0	0
$58$	−5.00000	−0.656532
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	1.00000	0.127000
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	2.00000	0.246183
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	3.00000	0.363803
$69$	−6.00000	−0.722315
$70$	0	0
$71$	7.00000	0.830747	0.415374	−	0.909651i	$-0.363651\pi$
$71$	7.00000	0.830747	0.415374	+	0.909651i	$0.363651\pi$
$72$	1.00000	0.117851
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	0	0
$77$	−4.00000	−0.455842
$78$	4.00000	0.452911
$79$	−5.00000	−0.562544	−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000	−0.562544	−0.281272	+	0.959628i	$0.590756\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	12.0000	1.32518
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	−1.00000	−0.107833
$87$	−5.00000	−0.536056
$88$	2.00000	0.213201
$89$	−5.00000	−0.529999	−0.264999	−	0.964249i	$-0.585372\pi$
$89$	−5.00000	−0.529999	−0.264999	+	0.964249i	$0.585372\pi$
$90$	0	0
$91$	−8.00000	−0.838628
$92$	−6.00000	−0.625543
$93$	1.00000	0.103695
$94$	3.00000	0.309426
$95$	0	0
$96$	1.00000	0.102062
$97$	−7.00000	−0.710742	−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000	−0.710742	−0.355371	+	0.934725i	$0.615646\pi$
$98$	−3.00000	−0.303046
$99$	2.00000	0.201008
$100$	0	0
$101$	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
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	4.00000	0.392232
$105$	0	0
$106$	14.0000	1.35980
$107$	−17.0000	−1.64345	−0.821726	−	0.569883i	$-0.806989\pi$
$107$	−17.0000	−1.64345	−0.821726	+	0.569883i	$0.806989\pi$
$108$	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	$0.244889\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	−2.00000	−0.188982
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	0	0
$116$	−5.00000	−0.464238
$117$	4.00000	0.369800
$118$	0	0
$119$	−6.00000	−0.550019
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−8.00000	−0.724286
$123$	12.0000	1.08200
$124$	1.00000	0.0898027
$125$	0	0
$126$	−2.00000	−0.178174
$127$	3.00000	0.266207	0.133103	−	0.991102i	$-0.457506\pi$
$127$	3.00000	0.266207	0.133103	+	0.991102i	$0.457506\pi$
$128$	1.00000	0.0883883
$129$	−1.00000	−0.0880451
$130$	0	0
$131$	−13.0000	−1.13582	−0.567908	−	0.823092i	$-0.692247\pi$
$131$	−13.0000	−1.13582	−0.567908	+	0.823092i	$0.692247\pi$
$132$	2.00000	0.174078
$133$	0	0
$134$	−2.00000	−0.172774
$135$	0	0
$136$	3.00000	0.257248
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	−6.00000	−0.510754
$139$	−15.0000	−1.27228	−0.636142	−	0.771572i	$-0.719471\pi$
$139$	−15.0000	−1.27228	−0.636142	+	0.771572i	$0.719471\pi$
$140$	0	0
$141$	3.00000	0.252646
$142$	7.00000	0.587427
$143$	8.00000	0.668994
$144$	1.00000	0.0833333
$145$	0	0
$146$	14.0000	1.15865
$147$	−3.00000	−0.247436
$148$	8.00000	0.657596
$149$	20.0000	1.63846	0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000	1.63846	0.819232	+	0.573462i	$0.194400\pi$
$150$	0	0
$151$	17.0000	1.38344	0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000	1.38344	0.691720	+	0.722166i	$0.256853\pi$
$152$	0	0
$153$	3.00000	0.242536
$154$	−4.00000	−0.322329
$155$	0	0
$156$	4.00000	0.320256
$157$	3.00000	0.239426	0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000	0.239426	0.119713	+	0.992809i	$0.461803\pi$
$158$	−5.00000	−0.397779
$159$	14.0000	1.11027
$160$	0	0
$161$	12.0000	0.945732
$162$	1.00000	0.0785674
$163$	24.0000	1.87983	0.939913	−	0.341415i	$-0.110906\pi$
$163$	24.0000	1.87983	0.939913	+	0.341415i	$0.110906\pi$
$164$	12.0000	0.937043
$165$	0	0
$166$	4.00000	0.310460
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	−2.00000	−0.154303
$169$	3.00000	0.230769
$170$	0	0
$171$	0	0
$172$	−1.00000	−0.0762493
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	−5.00000	−0.379049
$175$	0	0
$176$	2.00000	0.150756
$177$	0	0
$178$	−5.00000	−0.374766
$179$	−10.0000	−0.747435	−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000	−0.747435	−0.373718	+	0.927543i	$0.621917\pi$
$180$	0	0
$181$	12.0000	0.891953	0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000	0.891953	0.445976	+	0.895045i	$0.352856\pi$
$182$	−8.00000	−0.592999
$183$	−8.00000	−0.591377
$184$	−6.00000	−0.442326
$185$	0	0
$186$	1.00000	0.0733236
$187$	6.00000	0.438763
$188$	3.00000	0.218797
$189$	−2.00000	−0.145479
$190$	0	0
$191$	17.0000	1.23008	0.615038	−	0.788497i	$-0.289140\pi$
$191$	17.0000	1.23008	0.615038	+	0.788497i	$0.289140\pi$
$192$	1.00000	0.0721688
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−7.00000	−0.502571
$195$	0	0
$196$	−3.00000	−0.214286
$197$	13.0000	0.926212	0.463106	−	0.886303i	$-0.346735\pi$
$197$	13.0000	0.926212	0.463106	+	0.886303i	$0.346735\pi$
$198$	2.00000	0.142134
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	−2.00000	−0.141069
$202$	2.00000	0.140720
$203$	10.0000	0.701862
$204$	3.00000	0.210042
$205$	0	0
$206$	4.00000	0.278693
$207$	−6.00000	−0.417029
$208$	4.00000	0.277350
$209$	0	0
$210$	0	0
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	14.0000	0.961524
$213$	7.00000	0.479632
$214$	−17.0000	−1.16210
$215$	0	0
$216$	1.00000	0.0680414
$217$	−2.00000	−0.135769
$218$	15.0000	1.01593
$219$	14.0000	0.946032
$220$	0	0
$221$	12.0000	0.807207
$222$	8.00000	0.536925
$223$	−1.00000	−0.0669650	−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000	−0.0669650	−0.0334825	+	0.999439i	$0.510660\pi$
$224$	−2.00000	−0.133631
$225$	0	0
$226$	−6.00000	−0.399114
$227$	13.0000	0.862840	0.431420	−	0.902151i	$-0.358013\pi$
$227$	13.0000	0.862840	0.431420	+	0.902151i	$0.358013\pi$
$228$	0	0
$229$	−20.0000	−1.32164	−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000	−1.32164	−0.660819	+	0.750546i	$0.729791\pi$
$230$	0	0
$231$	−4.00000	−0.263181
$232$	−5.00000	−0.328266
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	4.00000	0.261488
$235$	0	0
$236$	0	0
$237$	−5.00000	−0.324785
$238$	−6.00000	−0.388922
$239$	−10.0000	−0.646846	−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000	−0.646846	−0.323423	+	0.946254i	$0.604834\pi$
$240$	0	0
$241$	−8.00000	−0.515325	−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000	−0.515325	−0.257663	+	0.966235i	$0.582952\pi$
$242$	−7.00000	−0.449977
$243$	1.00000	0.0641500
$244$	−8.00000	−0.512148
$245$	0	0
$246$	12.0000	0.765092
$247$	0	0
$248$	1.00000	0.0635001
$249$	4.00000	0.253490
$250$	0	0
$251$	2.00000	0.126239	0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000	0.126239	0.0631194	+	0.998006i	$0.479895\pi$
$252$	−2.00000	−0.125988
$253$	−12.0000	−0.754434
$254$	3.00000	0.188237
$255$	0	0
$256$	1.00000	0.0625000
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	−1.00000	−0.0622573
$259$	−16.0000	−0.994192
$260$	0	0
$261$	−5.00000	−0.309492
$262$	−13.0000	−0.803143
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	2.00000	0.123091
$265$	0	0
$266$	0	0
$267$	−5.00000	−0.305995
$268$	−2.00000	−0.122169
$269$	−15.0000	−0.914566	−0.457283	−	0.889321i	$-0.651177\pi$
$269$	−15.0000	−0.914566	−0.457283	+	0.889321i	$0.651177\pi$
$270$	0	0
$271$	−3.00000	−0.182237	−0.0911185	−	0.995840i	$-0.529044\pi$
$271$	−3.00000	−0.182237	−0.0911185	+	0.995840i	$0.529044\pi$
$272$	3.00000	0.181902
$273$	−8.00000	−0.484182
$274$	3.00000	0.181237
$275$	0	0
$276$	−6.00000	−0.361158
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	−15.0000	−0.899640
$279$	1.00000	0.0598684
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	3.00000	0.178647
$283$	−26.0000	−1.54554	−0.772770	−	0.634686i	$-0.781129\pi$
$283$	−26.0000	−1.54554	−0.772770	+	0.634686i	$0.781129\pi$
$284$	7.00000	0.415374
$285$	0	0
$286$	8.00000	0.473050
$287$	−24.0000	−1.41668
$288$	1.00000	0.0589256
$289$	−8.00000	−0.470588
$290$	0	0
$291$	−7.00000	−0.410347
$292$	14.0000	0.819288
$293$	34.0000	1.98630	0.993151	−	0.116841i	$-0.0372769\pi$
$293$	34.0000	1.98630	0.993151	+	0.116841i	$0.0372769\pi$
$294$	−3.00000	−0.174964
$295$	0	0
$296$	8.00000	0.464991
$297$	2.00000	0.116052
$298$	20.0000	1.15857
$299$	−24.0000	−1.38796
$300$	0	0
$301$	2.00000	0.115278
$302$	17.0000	0.978240
$303$	2.00000	0.114897
$304$	0	0
$305$	0	0
$306$	3.00000	0.171499
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	−4.00000	−0.227921
$309$	4.00000	0.227552
$310$	0	0
$311$	−3.00000	−0.170114	−0.0850572	−	0.996376i	$-0.527107\pi$
$311$	−3.00000	−0.170114	−0.0850572	+	0.996376i	$0.527107\pi$
$312$	4.00000	0.226455
$313$	4.00000	0.226093	0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000	0.226093	0.113047	+	0.993590i	$0.463939\pi$
$314$	3.00000	0.169300
$315$	0	0
$316$	−5.00000	−0.281272
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	14.0000	0.785081
$319$	−10.0000	−0.559893
$320$	0	0
$321$	−17.0000	−0.948847
$322$	12.0000	0.668734
$323$	0	0
$324$	1.00000	0.0555556
$325$	0	0
$326$	24.0000	1.32924
$327$	15.0000	0.829502
$328$	12.0000	0.662589
$329$	−6.00000	−0.330791
$330$	0	0
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	4.00000	0.219529
$333$	8.00000	0.438397
$334$	−12.0000	−0.656611
$335$	0	0
$336$	−2.00000	−0.109109
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	3.00000	0.163178
$339$	−6.00000	−0.325875
$340$	0	0
$341$	2.00000	0.108306
$342$	0	0
$343$	20.0000	1.07990
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	−6.00000	−0.322562
$347$	−22.0000	−1.18102	−0.590511	−	0.807030i	$-0.701074\pi$
$347$	−22.0000	−1.18102	−0.590511	+	0.807030i	$0.701074\pi$
$348$	−5.00000	−0.268028
$349$	−25.0000	−1.33822	−0.669110	−	0.743164i	$-0.733324\pi$
$349$	−25.0000	−1.33822	−0.669110	+	0.743164i	$0.733324\pi$
$350$	0	0
$351$	4.00000	0.213504
$352$	2.00000	0.106600
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	0	0
$355$	0	0
$356$	−5.00000	−0.264999
$357$	−6.00000	−0.317554
$358$	−10.0000	−0.528516
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	12.0000	0.630706
$363$	−7.00000	−0.367405
$364$	−8.00000	−0.419314
$365$	0	0
$366$	−8.00000	−0.418167
$367$	−27.0000	−1.40939	−0.704694	−	0.709511i	$-0.748916\pi$
$367$	−27.0000	−1.40939	−0.704694	+	0.709511i	$0.748916\pi$
$368$	−6.00000	−0.312772
$369$	12.0000	0.624695
$370$	0	0
$371$	−28.0000	−1.45369
$372$	1.00000	0.0518476
$373$	−21.0000	−1.08734	−0.543669	−	0.839299i	$-0.682965\pi$
$373$	−21.0000	−1.08734	−0.543669	+	0.839299i	$0.682965\pi$
$374$	6.00000	0.310253
$375$	0	0
$376$	3.00000	0.154713
$377$	−20.0000	−1.03005
$378$	−2.00000	−0.102869
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	3.00000	0.153695
$382$	17.0000	0.869796
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	14.0000	0.712581
$387$	−1.00000	−0.0508329
$388$	−7.00000	−0.355371
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	0	0
$391$	−18.0000	−0.910299
$392$	−3.00000	−0.151523
$393$	−13.0000	−0.655763
$394$	13.0000	0.654931
$395$	0	0
$396$	2.00000	0.100504
$397$	18.0000	0.903394	0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000	0.903394	0.451697	+	0.892171i	$0.350819\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	2.00000	0.0998752	0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000	0.0998752	0.0499376	+	0.998752i	$0.484098\pi$
$402$	−2.00000	−0.0997509
$403$	4.00000	0.199254
$404$	2.00000	0.0995037
$405$	0	0
$406$	10.0000	0.496292
$407$	16.0000	0.793091
$408$	3.00000	0.148522
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	3.00000	0.147979
$412$	4.00000	0.197066
$413$	0	0
$414$	−6.00000	−0.294884
$415$	0	0
$416$	4.00000	0.196116
$417$	−15.0000	−0.734553
$418$	0	0
$419$	−15.0000	−0.732798	−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000	−0.732798	−0.366399	+	0.930458i	$0.619409\pi$
$420$	0	0
$421$	−3.00000	−0.146211	−0.0731055	−	0.997324i	$-0.523291\pi$
$421$	−3.00000	−0.146211	−0.0731055	+	0.997324i	$0.523291\pi$
$422$	−8.00000	−0.389434
$423$	3.00000	0.145865
$424$	14.0000	0.679900
$425$	0	0
$426$	7.00000	0.339151
$427$	16.0000	0.774294
$428$	−17.0000	−0.821726
$429$	8.00000	0.386244
$430$	0	0
$431$	32.0000	1.54139	0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000	1.54139	0.770693	+	0.637207i	$0.219910\pi$
$432$	1.00000	0.0481125
$433$	−26.0000	−1.24948	−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000	−1.24948	−0.624740	+	0.780833i	$0.714795\pi$
$434$	−2.00000	−0.0960031
$435$	0	0
$436$	15.0000	0.718370
$437$	0	0
$438$	14.0000	0.668946
$439$	−30.0000	−1.43182	−0.715911	−	0.698192i	$-0.753988\pi$
$439$	−30.0000	−1.43182	−0.715911	+	0.698192i	$0.753988\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	12.0000	0.570782
$443$	39.0000	1.85295	0.926473	−	0.376361i	$-0.122825\pi$
$443$	39.0000	1.85295	0.926473	+	0.376361i	$0.122825\pi$
$444$	8.00000	0.379663
$445$	0	0
$446$	−1.00000	−0.0473514
$447$	20.0000	0.945968
$448$	−2.00000	−0.0944911
$449$	−25.0000	−1.17982	−0.589911	−	0.807468i	$-0.700837\pi$
$449$	−25.0000	−1.17982	−0.589911	+	0.807468i	$0.700837\pi$
$450$	0	0
$451$	24.0000	1.13012
$452$	−6.00000	−0.282216
$453$	17.0000	0.798730
$454$	13.0000	0.610120
$455$	0	0
$456$	0	0
$457$	−32.0000	−1.49690	−0.748448	−	0.663193i	$-0.769201\pi$
$457$	−32.0000	−1.49690	−0.748448	+	0.663193i	$0.769201\pi$
$458$	−20.0000	−0.934539
$459$	3.00000	0.140028
$460$	0	0
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	−4.00000	−0.186097
$463$	−21.0000	−0.975953	−0.487976	−	0.872857i	$-0.662265\pi$
$463$	−21.0000	−0.975953	−0.487976	+	0.872857i	$0.662265\pi$
$464$	−5.00000	−0.232119
$465$	0	0
$466$	−6.00000	−0.277945
$467$	3.00000	0.138823	0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000	0.138823	0.0694117	+	0.997588i	$0.477888\pi$
$468$	4.00000	0.184900
$469$	4.00000	0.184703
$470$	0	0
$471$	3.00000	0.138233
$472$	0	0
$473$	−2.00000	−0.0919601
$474$	−5.00000	−0.229658
$475$	0	0
$476$	−6.00000	−0.275010
$477$	14.0000	0.641016
$478$	−10.0000	−0.457389
$479$	−35.0000	−1.59919	−0.799595	−	0.600539i	$-0.794953\pi$
$479$	−35.0000	−1.59919	−0.799595	+	0.600539i	$0.794953\pi$
$480$	0	0
$481$	32.0000	1.45907
$482$	−8.00000	−0.364390
$483$	12.0000	0.546019
$484$	−7.00000	−0.318182
$485$	0	0
$486$	1.00000	0.0453609
$487$	13.0000	0.589086	0.294543	−	0.955638i	$-0.404833\pi$
$487$	13.0000	0.589086	0.294543	+	0.955638i	$0.404833\pi$
$488$	−8.00000	−0.362143
$489$	24.0000	1.08532
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	12.0000	0.541002
$493$	−15.0000	−0.675566
$494$	0	0
$495$	0	0
$496$	1.00000	0.0449013
$497$	−14.0000	−0.627986
$498$	4.00000	0.179244
$499$	−25.0000	−1.11915	−0.559577	−	0.828778i	$-0.689036\pi$
$499$	−25.0000	−1.11915	−0.559577	+	0.828778i	$0.689036\pi$
$500$	0	0
$501$	−12.0000	−0.536120
$502$	2.00000	0.0892644
$503$	−21.0000	−0.936344	−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000	−0.936344	−0.468172	+	0.883637i	$0.655087\pi$
$504$	−2.00000	−0.0890871
$505$	0	0
$506$	−12.0000	−0.533465
$507$	3.00000	0.133235
$508$	3.00000	0.133103
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	0	0
$511$	−28.0000	−1.23865
$512$	1.00000	0.0441942
$513$	0	0
$514$	−22.0000	−0.970378
$515$	0	0
$516$	−1.00000	−0.0440225
$517$	6.00000	0.263880
$518$	−16.0000	−0.703000
$519$	−6.00000	−0.263371
$520$	0	0
$521$	12.0000	0.525730	0.262865	−	0.964833i	$-0.415333\pi$
$521$	12.0000	0.525730	0.262865	+	0.964833i	$0.415333\pi$
$522$	−5.00000	−0.218844
$523$	−21.0000	−0.918266	−0.459133	−	0.888368i	$-0.651840\pi$
$523$	−21.0000	−0.918266	−0.459133	+	0.888368i	$0.651840\pi$
$524$	−13.0000	−0.567908
$525$	0	0
$526$	24.0000	1.04645
$527$	3.00000	0.130682
$528$	2.00000	0.0870388
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	0	0
$533$	48.0000	2.07911
$534$	−5.00000	−0.216371
$535$	0	0
$536$	−2.00000	−0.0863868
$537$	−10.0000	−0.431532
$538$	−15.0000	−0.646696
$539$	−6.00000	−0.258438
$540$	0	0
$541$	−33.0000	−1.41878	−0.709390	−	0.704816i	$-0.751030\pi$
$541$	−33.0000	−1.41878	−0.709390	+	0.704816i	$0.751030\pi$
$542$	−3.00000	−0.128861
$543$	12.0000	0.514969
$544$	3.00000	0.128624
$545$	0	0
$546$	−8.00000	−0.342368
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	3.00000	0.128154
$549$	−8.00000	−0.341432
$550$	0	0
$551$	0	0
$552$	−6.00000	−0.255377
$553$	10.0000	0.425243
$554$	8.00000	0.339887
$555$	0	0
$556$	−15.0000	−0.636142
$557$	3.00000	0.127114	0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000	0.127114	0.0635570	+	0.997978i	$0.479756\pi$
$558$	1.00000	0.0423334
$559$	−4.00000	−0.169182
$560$	0	0
$561$	6.00000	0.253320
$562$	−18.0000	−0.759284
$563$	−11.0000	−0.463595	−0.231797	−	0.972764i	$-0.574461\pi$
$563$	−11.0000	−0.463595	−0.231797	+	0.972764i	$0.574461\pi$
$564$	3.00000	0.126323
$565$	0	0
$566$	−26.0000	−1.09286
$567$	−2.00000	−0.0839921
$568$	7.00000	0.293713
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	0	0
$571$	−28.0000	−1.17176	−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000	−1.17176	−0.585882	+	0.810397i	$0.699252\pi$
$572$	8.00000	0.334497
$573$	17.0000	0.710185
$574$	−24.0000	−1.00174
$575$	0	0
$576$	1.00000	0.0416667
$577$	−27.0000	−1.12402	−0.562012	−	0.827129i	$-0.689973\pi$
$577$	−27.0000	−1.12402	−0.562012	+	0.827129i	$0.689973\pi$
$578$	−8.00000	−0.332756
$579$	14.0000	0.581820
$580$	0	0
$581$	−8.00000	−0.331896
$582$	−7.00000	−0.290159
$583$	28.0000	1.15964
$584$	14.0000	0.579324
$585$	0	0
$586$	34.0000	1.40453
$587$	18.0000	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$588$	−3.00000	−0.123718
$589$	0	0
$590$	0	0
$591$	13.0000	0.534749
$592$	8.00000	0.328798
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	2.00000	0.0820610
$595$	0	0
$596$	20.0000	0.819232
$597$	0	0
$598$	−24.0000	−0.981433
$599$	−45.0000	−1.83865	−0.919325	−	0.393499i	$-0.871265\pi$
$599$	−45.0000	−1.83865	−0.919325	+	0.393499i	$0.871265\pi$
$600$	0	0
$601$	−38.0000	−1.55005	−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000	−1.55005	−0.775026	+	0.631929i	$0.782263\pi$
$602$	2.00000	0.0815139
$603$	−2.00000	−0.0814463
$604$	17.0000	0.691720
$605$	0	0
$606$	2.00000	0.0812444
$607$	28.0000	1.13648	0.568242	−	0.822861i	$-0.307624\pi$
$607$	28.0000	1.13648	0.568242	+	0.822861i	$0.307624\pi$
$608$	0	0
$609$	10.0000	0.405220
$610$	0	0
$611$	12.0000	0.485468
$612$	3.00000	0.121268
$613$	−36.0000	−1.45403	−0.727013	−	0.686624i	$-0.759092\pi$
$613$	−36.0000	−1.45403	−0.727013	+	0.686624i	$0.759092\pi$
$614$	28.0000	1.12999
$615$	0	0
$616$	−4.00000	−0.161165
$617$	28.0000	1.12724	0.563619	−	0.826035i	$-0.309409\pi$
$617$	28.0000	1.12724	0.563619	+	0.826035i	$0.309409\pi$
$618$	4.00000	0.160904
$619$	25.0000	1.00483	0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000	1.00483	0.502417	+	0.864625i	$0.332444\pi$
$620$	0	0
$621$	−6.00000	−0.240772
$622$	−3.00000	−0.120289
$623$	10.0000	0.400642
$624$	4.00000	0.160128
$625$	0	0
$626$	4.00000	0.159872
$627$	0	0
$628$	3.00000	0.119713
$629$	24.0000	0.956943
$630$	0	0
$631$	−23.0000	−0.915616	−0.457808	−	0.889051i	$-0.651365\pi$
$631$	−23.0000	−0.915616	−0.457808	+	0.889051i	$0.651365\pi$
$632$	−5.00000	−0.198889
$633$	−8.00000	−0.317971
$634$	−2.00000	−0.0794301
$635$	0	0
$636$	14.0000	0.555136
$637$	−12.0000	−0.475457
$638$	−10.0000	−0.395904
$639$	7.00000	0.276916
$640$	0	0
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	−17.0000	−0.670936
$643$	−1.00000	−0.0394362	−0.0197181	−	0.999806i	$-0.506277\pi$
$643$	−1.00000	−0.0394362	−0.0197181	+	0.999806i	$0.506277\pi$
$644$	12.0000	0.472866
$645$	0	0
$646$	0	0
$647$	28.0000	1.10079	0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000	1.10079	0.550397	+	0.834903i	$0.314476\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	24.0000	0.939913
$653$	4.00000	0.156532	0.0782660	−	0.996933i	$-0.475062\pi$
$653$	4.00000	0.156532	0.0782660	+	0.996933i	$0.475062\pi$
$654$	15.0000	0.586546
$655$	0	0
$656$	12.0000	0.468521
$657$	14.0000	0.546192
$658$	−6.00000	−0.233904
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	0	0
$661$	−3.00000	−0.116686	−0.0583432	−	0.998297i	$-0.518582\pi$
$661$	−3.00000	−0.116686	−0.0583432	+	0.998297i	$0.518582\pi$
$662$	−28.0000	−1.08825
$663$	12.0000	0.466041
$664$	4.00000	0.155230
$665$	0	0
$666$	8.00000	0.309994
$667$	30.0000	1.16160
$668$	−12.0000	−0.464294
$669$	−1.00000	−0.0386622
$670$	0	0
$671$	−16.0000	−0.617673
$672$	−2.00000	−0.0771517
$673$	−26.0000	−1.00223	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501113	+	0.865382i	$0.667076\pi$
$674$	−2.00000	−0.0770371
$675$	0	0
$676$	3.00000	0.115385
$677$	−17.0000	−0.653363	−0.326682	−	0.945134i	$-0.605930\pi$
$677$	−17.0000	−0.653363	−0.326682	+	0.945134i	$0.605930\pi$
$678$	−6.00000	−0.230429
$679$	14.0000	0.537271
$680$	0	0
$681$	13.0000	0.498161
$682$	2.00000	0.0765840
$683$	−31.0000	−1.18618	−0.593091	−	0.805135i	$-0.702093\pi$
$683$	−31.0000	−1.18618	−0.593091	+	0.805135i	$0.702093\pi$
$684$	0	0
$685$	0	0
$686$	20.0000	0.763604
$687$	−20.0000	−0.763048
$688$	−1.00000	−0.0381246
$689$	56.0000	2.13343
$690$	0	0
$691$	2.00000	0.0760836	0.0380418	−	0.999276i	$-0.487888\pi$
$691$	2.00000	0.0760836	0.0380418	+	0.999276i	$0.487888\pi$
$692$	−6.00000	−0.228086
$693$	−4.00000	−0.151947
$694$	−22.0000	−0.835109
$695$	0	0
$696$	−5.00000	−0.189525
$697$	36.0000	1.36360
$698$	−25.0000	−0.946264
$699$	−6.00000	−0.226941
$700$	0	0
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	4.00000	0.150970
$703$	0	0
$704$	2.00000	0.0753778
$705$	0	0
$706$	14.0000	0.526897
$707$	−4.00000	−0.150435
$708$	0	0
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	−5.00000	−0.187515
$712$	−5.00000	−0.187383
$713$	−6.00000	−0.224702
$714$	−6.00000	−0.224544
$715$	0	0
$716$	−10.0000	−0.373718
$717$	−10.0000	−0.373457
$718$	0	0
$719$	−10.0000	−0.372937	−0.186469	−	0.982461i	$-0.559704\pi$
$719$	−10.0000	−0.372937	−0.186469	+	0.982461i	$0.559704\pi$
$720$	0	0
$721$	−8.00000	−0.297936
$722$	−19.0000	−0.707107
$723$	−8.00000	−0.297523
$724$	12.0000	0.445976
$725$	0	0
$726$	−7.00000	−0.259794
$727$	18.0000	0.667583	0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000	0.667583	0.333792	+	0.942647i	$0.391672\pi$
$728$	−8.00000	−0.296500
$729$	1.00000	0.0370370
$730$	0	0
$731$	−3.00000	−0.110959
$732$	−8.00000	−0.295689
$733$	−1.00000	−0.0369358	−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000	−0.0369358	−0.0184679	+	0.999829i	$0.505879\pi$
$734$	−27.0000	−0.996588
$735$	0	0
$736$	−6.00000	−0.221163
$737$	−4.00000	−0.147342
$738$	12.0000	0.441726
$739$	25.0000	0.919640	0.459820	−	0.888012i	$-0.347914\pi$
$739$	25.0000	0.919640	0.459820	+	0.888012i	$0.347914\pi$
$740$	0	0
$741$	0	0
$742$	−28.0000	−1.02791
$743$	−26.0000	−0.953847	−0.476924	−	0.878945i	$-0.658248\pi$
$743$	−26.0000	−0.953847	−0.476924	+	0.878945i	$0.658248\pi$
$744$	1.00000	0.0366618
$745$	0	0
$746$	−21.0000	−0.768865
$747$	4.00000	0.146352
$748$	6.00000	0.219382
$749$	34.0000	1.24233
$750$	0	0
$751$	−8.00000	−0.291924	−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000	−0.291924	−0.145962	+	0.989290i	$0.546628\pi$
$752$	3.00000	0.109399
$753$	2.00000	0.0728841
$754$	−20.0000	−0.728357
$755$	0	0
$756$	−2.00000	−0.0727393
$757$	−42.0000	−1.52652	−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000	−1.52652	−0.763258	+	0.646094i	$0.776401\pi$
$758$	−20.0000	−0.726433
$759$	−12.0000	−0.435572
$760$	0	0
$761$	−33.0000	−1.19625	−0.598125	−	0.801403i	$-0.704087\pi$
$761$	−33.0000	−1.19625	−0.598125	+	0.801403i	$0.704087\pi$
$762$	3.00000	0.108679
$763$	−30.0000	−1.08607
$764$	17.0000	0.615038
$765$	0	0
$766$	−6.00000	−0.216789
$767$	0	0
$768$	1.00000	0.0360844
$769$	−15.0000	−0.540914	−0.270457	−	0.962732i	$-0.587175\pi$
$769$	−15.0000	−0.540914	−0.270457	+	0.962732i	$0.587175\pi$
$770$	0	0
$771$	−22.0000	−0.792311
$772$	14.0000	0.503871
$773$	−21.0000	−0.755318	−0.377659	−	0.925945i	$-0.623271\pi$
$773$	−21.0000	−0.755318	−0.377659	+	0.925945i	$0.623271\pi$
$774$	−1.00000	−0.0359443
$775$	0	0
$776$	−7.00000	−0.251285
$777$	−16.0000	−0.573997
$778$	30.0000	1.07555
$779$	0	0
$780$	0	0
$781$	14.0000	0.500959
$782$	−18.0000	−0.643679
$783$	−5.00000	−0.178685
$784$	−3.00000	−0.107143
$785$	0	0
$786$	−13.0000	−0.463695
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	13.0000	0.463106
$789$	24.0000	0.854423
$790$	0	0
$791$	12.0000	0.426671
$792$	2.00000	0.0710669
$793$	−32.0000	−1.13635
$794$	18.0000	0.638796
$795$	0	0
$796$	0	0
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	0	0
$799$	9.00000	0.318397
$800$	0	0
$801$	−5.00000	−0.176666
$802$	2.00000	0.0706225
$803$	28.0000	0.988099
$804$	−2.00000	−0.0705346
$805$	0	0
$806$	4.00000	0.140894
$807$	−15.0000	−0.528025
$808$	2.00000	0.0703598
$809$	5.00000	0.175791	0.0878953	−	0.996130i	$-0.471986\pi$
$809$	5.00000	0.175791	0.0878953	+	0.996130i	$0.471986\pi$
$810$	0	0
$811$	32.0000	1.12367	0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000	1.12367	0.561836	+	0.827249i	$0.310095\pi$
$812$	10.0000	0.350931
$813$	−3.00000	−0.105215
$814$	16.0000	0.560800
$815$	0	0
$816$	3.00000	0.105021
$817$	0	0
$818$	0	0
$819$	−8.00000	−0.279543
$820$	0	0
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	3.00000	0.104637
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	0	0
$827$	−2.00000	−0.0695468	−0.0347734	−	0.999395i	$-0.511071\pi$
$827$	−2.00000	−0.0695468	−0.0347734	+	0.999395i	$0.511071\pi$
$828$	−6.00000	−0.208514
$829$	−40.0000	−1.38926	−0.694629	−	0.719368i	$-0.744431\pi$
$829$	−40.0000	−1.38926	−0.694629	+	0.719368i	$0.744431\pi$
$830$	0	0
$831$	8.00000	0.277517
$832$	4.00000	0.138675
$833$	−9.00000	−0.311832
$834$	−15.0000	−0.519408
$835$	0	0
$836$	0	0
$837$	1.00000	0.0345651
$838$	−15.0000	−0.518166
$839$	5.00000	0.172619	0.0863096	−	0.996268i	$-0.472493\pi$
$839$	5.00000	0.172619	0.0863096	+	0.996268i	$0.472493\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−3.00000	−0.103387
$843$	−18.0000	−0.619953
$844$	−8.00000	−0.275371
$845$	0	0
$846$	3.00000	0.103142
$847$	14.0000	0.481046
$848$	14.0000	0.480762
$849$	−26.0000	−0.892318
$850$	0	0
$851$	−48.0000	−1.64542
$852$	7.00000	0.239816
$853$	9.00000	0.308154	0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000	0.308154	0.154077	+	0.988059i	$0.450760\pi$
$854$	16.0000	0.547509
$855$	0	0
$856$	−17.0000	−0.581048
$857$	−12.0000	−0.409912	−0.204956	−	0.978771i	$-0.565705\pi$
$857$	−12.0000	−0.409912	−0.204956	+	0.978771i	$0.565705\pi$
$858$	8.00000	0.273115
$859$	25.0000	0.852989	0.426494	−	0.904490i	$-0.359748\pi$
$859$	25.0000	0.852989	0.426494	+	0.904490i	$0.359748\pi$
$860$	0	0
$861$	−24.0000	−0.817918
$862$	32.0000	1.08992
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−26.0000	−0.883516
$867$	−8.00000	−0.271694
$868$	−2.00000	−0.0678844
$869$	−10.0000	−0.339227
$870$	0	0
$871$	−8.00000	−0.271070
$872$	15.0000	0.507964
$873$	−7.00000	−0.236914
$874$	0	0
$875$	0	0
$876$	14.0000	0.473016
$877$	−27.0000	−0.911725	−0.455863	−	0.890050i	$-0.650669\pi$
$877$	−27.0000	−0.911725	−0.455863	+	0.890050i	$0.650669\pi$
$878$	−30.0000	−1.01245
$879$	34.0000	1.14679
$880$	0	0
$881$	7.00000	0.235836	0.117918	−	0.993023i	$-0.462378\pi$
$881$	7.00000	0.235836	0.117918	+	0.993023i	$0.462378\pi$
$882$	−3.00000	−0.101015
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	39.0000	1.31023
$887$	−27.0000	−0.906571	−0.453286	−	0.891365i	$-0.649748\pi$
$887$	−27.0000	−0.906571	−0.453286	+	0.891365i	$0.649748\pi$
$888$	8.00000	0.268462
$889$	−6.00000	−0.201234
$890$	0	0
$891$	2.00000	0.0670025
$892$	−1.00000	−0.0334825
$893$	0	0
$894$	20.0000	0.668900
$895$	0	0
$896$	−2.00000	−0.0668153
$897$	−24.0000	−0.801337
$898$	−25.0000	−0.834261
$899$	−5.00000	−0.166759
$900$	0	0
$901$	42.0000	1.39922
$902$	24.0000	0.799113
$903$	2.00000	0.0665558
$904$	−6.00000	−0.199557
$905$	0	0
$906$	17.0000	0.564787
$907$	8.00000	0.265636	0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000	0.265636	0.132818	+	0.991140i	$0.457597\pi$
$908$	13.0000	0.431420
$909$	2.00000	0.0663358
$910$	0	0
$911$	32.0000	1.06021	0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000	1.06021	0.530104	+	0.847933i	$0.322153\pi$
$912$	0	0
$913$	8.00000	0.264761
$914$	−32.0000	−1.05847
$915$	0	0
$916$	−20.0000	−0.660819
$917$	26.0000	0.858596
$918$	3.00000	0.0990148
$919$	30.0000	0.989609	0.494804	−	0.869004i	$-0.335240\pi$
$919$	30.0000	0.989609	0.494804	+	0.869004i	$0.335240\pi$
$920$	0	0
$921$	28.0000	0.922631
$922$	−18.0000	−0.592798
$923$	28.0000	0.921631
$924$	−4.00000	−0.131590
$925$	0	0
$926$	−21.0000	−0.690103
$927$	4.00000	0.131377
$928$	−5.00000	−0.164133
$929$	−30.0000	−0.984268	−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000	−0.984268	−0.492134	+	0.870519i	$0.663783\pi$
$930$	0	0
$931$	0	0
$932$	−6.00000	−0.196537
$933$	−3.00000	−0.0982156
$934$	3.00000	0.0981630
$935$	0	0
$936$	4.00000	0.130744
$937$	38.0000	1.24141	0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000	1.24141	0.620703	+	0.784046i	$0.286847\pi$
$938$	4.00000	0.130605
$939$	4.00000	0.130535
$940$	0	0
$941$	−3.00000	−0.0977972	−0.0488986	−	0.998804i	$-0.515571\pi$
$941$	−3.00000	−0.0977972	−0.0488986	+	0.998804i	$0.515571\pi$
$942$	3.00000	0.0977453
$943$	−72.0000	−2.34464
$944$	0	0
$945$	0	0
$946$	−2.00000	−0.0650256
$947$	−32.0000	−1.03986	−0.519930	−	0.854209i	$-0.674042\pi$
$947$	−32.0000	−1.03986	−0.519930	+	0.854209i	$0.674042\pi$
$948$	−5.00000	−0.162392
$949$	56.0000	1.81784
$950$	0	0
$951$	−2.00000	−0.0648544
$952$	−6.00000	−0.194461
$953$	14.0000	0.453504	0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000	0.453504	0.226752	+	0.973952i	$0.427189\pi$
$954$	14.0000	0.453267
$955$	0	0
$956$	−10.0000	−0.323423
$957$	−10.0000	−0.323254
$958$	−35.0000	−1.13080
$959$	−6.00000	−0.193750
$960$	0	0
$961$	1.00000	0.0322581
$962$	32.0000	1.03172
$963$	−17.0000	−0.547817
$964$	−8.00000	−0.257663
$965$	0	0
$966$	12.0000	0.386094
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	0	0
$971$	−3.00000	−0.0962746	−0.0481373	−	0.998841i	$-0.515328\pi$
$971$	−3.00000	−0.0962746	−0.0481373	+	0.998841i	$0.515328\pi$
$972$	1.00000	0.0320750
$973$	30.0000	0.961756
$974$	13.0000	0.416547
$975$	0	0
$976$	−8.00000	−0.256074
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	24.0000	0.767435
$979$	−10.0000	−0.319601
$980$	0	0
$981$	15.0000	0.478913
$982$	12.0000	0.382935
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	12.0000	0.382546
$985$	0	0
$986$	−15.0000	−0.477697
$987$	−6.00000	−0.190982
$988$	0	0
$989$	6.00000	0.190789
$990$	0	0
$991$	−13.0000	−0.412959	−0.206479	−	0.978451i	$-0.566201\pi$
$991$	−13.0000	−0.412959	−0.206479	+	0.978451i	$0.566201\pi$
$992$	1.00000	0.0317500
$993$	−28.0000	−0.888553
$994$	−14.0000	−0.444053
$995$	0	0
$996$	4.00000	0.126745
$997$	18.0000	0.570066	0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000	0.570066	0.285033	+	0.958518i	$0.407995\pi$
$998$	−25.0000	−0.791361
$999$	8.00000	0.253109

Twists

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

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

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