LMFDB - Embedded newform 798.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(1,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, 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("798.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.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:	$6.37206208130$
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	$\chi$	$=$	798.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{10} -6.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} -1.00000 q^{14} -4.00000 q^{15} +1.00000 q^{16} -4.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -4.00000 q^{20} -1.00000 q^{21} -6.00000 q^{22} +2.00000 q^{23} +1.00000 q^{24} +11.0000 q^{25} -4.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +2.00000 q^{29} -4.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} -6.00000 q^{33} -4.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -1.00000 q^{38} -4.00000 q^{39} -4.00000 q^{40} +6.00000 q^{41} -1.00000 q^{42} -6.00000 q^{44} -4.00000 q^{45} +2.00000 q^{46} -8.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +11.0000 q^{50} -4.00000 q^{51} -4.00000 q^{52} -14.0000 q^{53} +1.00000 q^{54} +24.0000 q^{55} -1.00000 q^{56} -1.00000 q^{57} +2.00000 q^{58} -4.00000 q^{59} -4.00000 q^{60} -10.0000 q^{61} +4.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} +16.0000 q^{65} -6.00000 q^{66} +10.0000 q^{67} -4.00000 q^{68} +2.00000 q^{69} +4.00000 q^{70} -4.00000 q^{71} +1.00000 q^{72} -14.0000 q^{73} +2.00000 q^{74} +11.0000 q^{75} -1.00000 q^{76} +6.00000 q^{77} -4.00000 q^{78} +2.00000 q^{79} -4.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -1.00000 q^{84} +16.0000 q^{85} +2.00000 q^{87} -6.00000 q^{88} +6.00000 q^{89} -4.00000 q^{90} +4.00000 q^{91} +2.00000 q^{92} +4.00000 q^{93} -8.00000 q^{94} +4.00000 q^{95} +1.00000 q^{96} +1.00000 q^{98} -6.00000 q^{99} +O(q^{100})\)

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
$5$	−4.00000	−1.78885	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−4.00000	−1.78885	−0.894427	+	0.447214i	$0.852416\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.00000	−1.26491
$11$	−6.00000	−1.80907	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000	−1.80907	−0.904534	+	0.426401i	$0.859781\pi$
$12$	1.00000	0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−1.00000	−0.267261
$15$	−4.00000	−1.03280
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−4.00000	−0.894427
$21$	−1.00000	−0.218218
$22$	−6.00000	−1.27920
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	1.00000	0.204124
$25$	11.0000	2.20000
$26$	−4.00000	−0.784465
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	−4.00000	−0.730297
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	1.00000	0.176777
$33$	−6.00000	−1.04447
$34$	−4.00000	−0.685994
$35$	4.00000	0.676123
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−1.00000	−0.162221
$39$	−4.00000	−0.640513
$40$	−4.00000	−0.632456
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	−1.00000	−0.154303
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	−6.00000	−0.904534
$45$	−4.00000	−0.596285
$46$	2.00000	0.294884
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	11.0000	1.55563
$51$	−4.00000	−0.560112
$52$	−4.00000	−0.554700
$53$	−14.0000	−1.92305	−0.961524	−	0.274721i	$-0.911414\pi$
$53$	−14.0000	−1.92305	−0.961524	+	0.274721i	$0.911414\pi$
$54$	1.00000	0.136083
$55$	24.0000	3.23616
$56$	−1.00000	−0.133631
$57$	−1.00000	−0.132453
$58$	2.00000	0.262613
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	−4.00000	−0.516398
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	4.00000	0.508001
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	16.0000	1.98456
$66$	−6.00000	−0.738549
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	−4.00000	−0.485071
$69$	2.00000	0.240772
$70$	4.00000	0.478091
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	1.00000	0.117851
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	2.00000	0.232495
$75$	11.0000	1.27017
$76$	−1.00000	−0.114708
$77$	6.00000	0.683763
$78$	−4.00000	−0.452911
$79$	2.00000	0.225018	0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000	0.225018	0.112509	+	0.993651i	$0.464111\pi$
$80$	−4.00000	−0.447214
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	−1.00000	−0.109109
$85$	16.0000	1.73544
$86$	0	0
$87$	2.00000	0.214423
$88$	−6.00000	−0.639602
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	−4.00000	−0.421637
$91$	4.00000	0.419314
$92$	2.00000	0.208514
$93$	4.00000	0.414781
$94$	−8.00000	−0.825137
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	1.00000	0.101015
$99$	−6.00000	−0.603023
$100$	11.0000	1.10000
$101$	4.00000	0.398015	0.199007	−	0.979998i	$-0.436228\pi$
$101$	4.00000	0.398015	0.199007	+	0.979998i	$0.436228\pi$
$102$	−4.00000	−0.396059
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	−4.00000	−0.392232
$105$	4.00000	0.390360
$106$	−14.0000	−1.35980
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	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	$0.592774\pi$
$110$	24.0000	2.28831
$111$	2.00000	0.189832
$112$	−1.00000	−0.0944911
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	−1.00000	−0.0936586
$115$	−8.00000	−0.746004
$116$	2.00000	0.185695
$117$	−4.00000	−0.369800
$118$	−4.00000	−0.368230
$119$	4.00000	0.366679
$120$	−4.00000	−0.365148
$121$	25.0000	2.27273
$122$	−10.0000	−0.905357
$123$	6.00000	0.541002
$124$	4.00000	0.359211
$125$	−24.0000	−2.14663
$126$	−1.00000	−0.0890871
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	16.0000	1.40329
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	−6.00000	−0.522233
$133$	1.00000	0.0867110
$134$	10.0000	0.863868
$135$	−4.00000	−0.344265
$136$	−4.00000	−0.342997
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	2.00000	0.170251
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	4.00000	0.338062
$141$	−8.00000	−0.673722
$142$	−4.00000	−0.335673
$143$	24.0000	2.00698
$144$	1.00000	0.0833333
$145$	−8.00000	−0.664364
$146$	−14.0000	−1.15865
$147$	1.00000	0.0824786
$148$	2.00000	0.164399
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	11.0000	0.898146
$151$	−14.0000	−1.13930	−0.569652	−	0.821886i	$-0.692922\pi$
$151$	−14.0000	−1.13930	−0.569652	+	0.821886i	$0.692922\pi$
$152$	−1.00000	−0.0811107
$153$	−4.00000	−0.323381
$154$	6.00000	0.483494
$155$	−16.0000	−1.28515
$156$	−4.00000	−0.320256
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	2.00000	0.159111
$159$	−14.0000	−1.11027
$160$	−4.00000	−0.316228
$161$	−2.00000	−0.157622
$162$	1.00000	0.0785674
$163$	−24.0000	−1.87983	−0.939913	−	0.341415i	$-0.889094\pi$
$163$	−24.0000	−1.87983	−0.939913	+	0.341415i	$0.889094\pi$
$164$	6.00000	0.468521
$165$	24.0000	1.86840
$166$	0	0
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	−1.00000	−0.0771517
$169$	3.00000	0.230769
$170$	16.0000	1.22714
$171$	−1.00000	−0.0764719
$172$	0	0
$173$	10.0000	0.760286	0.380143	−	0.924928i	$-0.375875\pi$
$173$	10.0000	0.760286	0.380143	+	0.924928i	$0.375875\pi$
$174$	2.00000	0.151620
$175$	−11.0000	−0.831522
$176$	−6.00000	−0.452267
$177$	−4.00000	−0.300658
$178$	6.00000	0.449719
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	−4.00000	−0.298142
$181$	16.0000	1.18927	0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000	1.18927	0.594635	+	0.803996i	$0.297296\pi$
$182$	4.00000	0.296500
$183$	−10.0000	−0.739221
$184$	2.00000	0.147442
$185$	−8.00000	−0.588172
$186$	4.00000	0.293294
$187$	24.0000	1.75505
$188$	−8.00000	−0.583460
$189$	−1.00000	−0.0727393
$190$	4.00000	0.290191
$191$	−14.0000	−1.01300	−0.506502	−	0.862239i	$-0.669062\pi$
$191$	−14.0000	−1.01300	−0.506502	+	0.862239i	$0.669062\pi$
$192$	1.00000	0.0721688
$193$	26.0000	1.87152	0.935760	−	0.352636i	$-0.114715\pi$
$193$	26.0000	1.87152	0.935760	+	0.352636i	$0.114715\pi$
$194$	0	0
$195$	16.0000	1.14578
$196$	1.00000	0.0714286
$197$	22.0000	1.56744	0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000	1.56744	0.783718	+	0.621117i	$0.213321\pi$
$198$	−6.00000	−0.426401
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	11.0000	0.777817
$201$	10.0000	0.705346
$202$	4.00000	0.281439
$203$	−2.00000	−0.140372
$204$	−4.00000	−0.280056
$205$	−24.0000	−1.67623
$206$	−4.00000	−0.278693
$207$	2.00000	0.139010
$208$	−4.00000	−0.277350
$209$	6.00000	0.415029
$210$	4.00000	0.276026
$211$	10.0000	0.688428	0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000	0.688428	0.344214	+	0.938891i	$0.388145\pi$
$212$	−14.0000	−0.961524
$213$	−4.00000	−0.274075
$214$	12.0000	0.820303
$215$	0	0
$216$	1.00000	0.0680414
$217$	−4.00000	−0.271538
$218$	−6.00000	−0.406371
$219$	−14.0000	−0.946032
$220$	24.0000	1.61808
$221$	16.0000	1.07628
$222$	2.00000	0.134231
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	−1.00000	−0.0668153
$225$	11.0000	0.733333
$226$	18.0000	1.19734
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	−1.00000	−0.0662266
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	−8.00000	−0.527504
$231$	6.00000	0.394771
$232$	2.00000	0.131306
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	−4.00000	−0.261488
$235$	32.0000	2.08745
$236$	−4.00000	−0.260378
$237$	2.00000	0.129914
$238$	4.00000	0.259281
$239$	−22.0000	−1.42306	−0.711531	−	0.702655i	$-0.751998\pi$
$239$	−22.0000	−1.42306	−0.711531	+	0.702655i	$0.751998\pi$
$240$	−4.00000	−0.258199
$241$	28.0000	1.80364	0.901819	−	0.432113i	$-0.142232\pi$
$241$	28.0000	1.80364	0.901819	+	0.432113i	$0.142232\pi$
$242$	25.0000	1.60706
$243$	1.00000	0.0641500
$244$	−10.0000	−0.640184
$245$	−4.00000	−0.255551
$246$	6.00000	0.382546
$247$	4.00000	0.254514
$248$	4.00000	0.254000
$249$	0	0
$250$	−24.0000	−1.51789
$251$	−20.0000	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$252$	−1.00000	−0.0629941
$253$	−12.0000	−0.754434
$254$	−2.00000	−0.125491
$255$	16.0000	1.00196
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	0	0
$259$	−2.00000	−0.124274
$260$	16.0000	0.992278
$261$	2.00000	0.123797
$262$	−20.0000	−1.23560
$263$	−2.00000	−0.123325	−0.0616626	−	0.998097i	$-0.519640\pi$
$263$	−2.00000	−0.123325	−0.0616626	+	0.998097i	$0.519640\pi$
$264$	−6.00000	−0.369274
$265$	56.0000	3.44005
$266$	1.00000	0.0613139
$267$	6.00000	0.367194
$268$	10.0000	0.610847
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	−4.00000	−0.243432
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	−4.00000	−0.242536
$273$	4.00000	0.242091
$274$	−18.0000	−1.08742
$275$	−66.0000	−3.97995
$276$	2.00000	0.120386
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	20.0000	1.19952
$279$	4.00000	0.239474
$280$	4.00000	0.239046
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	−8.00000	−0.476393
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	−4.00000	−0.237356
$285$	4.00000	0.236940
$286$	24.0000	1.41915
$287$	−6.00000	−0.354169
$288$	1.00000	0.0589256
$289$	−1.00000	−0.0588235
$290$	−8.00000	−0.469776
$291$	0	0
$292$	−14.0000	−0.819288
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	1.00000	0.0583212
$295$	16.0000	0.931556
$296$	2.00000	0.116248
$297$	−6.00000	−0.348155
$298$	−18.0000	−1.04271
$299$	−8.00000	−0.462652
$300$	11.0000	0.635085
$301$	0	0
$302$	−14.0000	−0.805609
$303$	4.00000	0.229794
$304$	−1.00000	−0.0573539
$305$	40.0000	2.29039
$306$	−4.00000	−0.228665
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	6.00000	0.341882
$309$	−4.00000	−0.227552
$310$	−16.0000	−0.908739
$311$	−4.00000	−0.226819	−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000	−0.226819	−0.113410	+	0.993548i	$0.536177\pi$
$312$	−4.00000	−0.226455
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	−22.0000	−1.24153
$315$	4.00000	0.225374
$316$	2.00000	0.112509
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	−14.0000	−0.785081
$319$	−12.0000	−0.671871
$320$	−4.00000	−0.223607
$321$	12.0000	0.669775
$322$	−2.00000	−0.111456
$323$	4.00000	0.222566
$324$	1.00000	0.0555556
$325$	−44.0000	−2.44068
$326$	−24.0000	−1.32924
$327$	−6.00000	−0.331801
$328$	6.00000	0.331295
$329$	8.00000	0.441054
$330$	24.0000	1.32116
$331$	−10.0000	−0.549650	−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000	−0.549650	−0.274825	+	0.961494i	$0.588620\pi$
$332$	0	0
$333$	2.00000	0.109599
$334$	8.00000	0.437741
$335$	−40.0000	−2.18543
$336$	−1.00000	−0.0545545
$337$	6.00000	0.326841	0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000	0.326841	0.163420	+	0.986557i	$0.447747\pi$
$338$	3.00000	0.163178
$339$	18.0000	0.977626
$340$	16.0000	0.867722
$341$	−24.0000	−1.29967
$342$	−1.00000	−0.0540738
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	−8.00000	−0.430706
$346$	10.0000	0.537603
$347$	6.00000	0.322097	0.161048	−	0.986947i	$-0.448512\pi$
$347$	6.00000	0.322097	0.161048	+	0.986947i	$0.448512\pi$
$348$	2.00000	0.107211
$349$	−30.0000	−1.60586	−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000	−1.60586	−0.802932	+	0.596071i	$0.796728\pi$
$350$	−11.0000	−0.587975
$351$	−4.00000	−0.213504
$352$	−6.00000	−0.319801
$353$	4.00000	0.212899	0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000	0.212899	0.106449	+	0.994318i	$0.466052\pi$
$354$	−4.00000	−0.212598
$355$	16.0000	0.849192
$356$	6.00000	0.317999
$357$	4.00000	0.211702
$358$	4.00000	0.211407
$359$	−34.0000	−1.79445	−0.897226	−	0.441572i	$-0.854421\pi$
$359$	−34.0000	−1.79445	−0.897226	+	0.441572i	$0.854421\pi$
$360$	−4.00000	−0.210819
$361$	1.00000	0.0526316
$362$	16.0000	0.840941
$363$	25.0000	1.31216
$364$	4.00000	0.209657
$365$	56.0000	2.93117
$366$	−10.0000	−0.522708
$367$	−32.0000	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$368$	2.00000	0.104257
$369$	6.00000	0.312348
$370$	−8.00000	−0.415900
$371$	14.0000	0.726844
$372$	4.00000	0.207390
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	24.0000	1.24101
$375$	−24.0000	−1.23935
$376$	−8.00000	−0.412568
$377$	−8.00000	−0.412021
$378$	−1.00000	−0.0514344
$379$	−34.0000	−1.74646	−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000	−1.74646	−0.873231	+	0.487306i	$0.837980\pi$
$380$	4.00000	0.205196
$381$	−2.00000	−0.102463
$382$	−14.0000	−0.716302
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	1.00000	0.0510310
$385$	−24.0000	−1.22315
$386$	26.0000	1.32337
$387$	0	0
$388$	0	0
$389$	34.0000	1.72387	0.861934	−	0.507020i	$-0.169253\pi$
$389$	34.0000	1.72387	0.861934	+	0.507020i	$0.169253\pi$
$390$	16.0000	0.810191
$391$	−8.00000	−0.404577
$392$	1.00000	0.0505076
$393$	−20.0000	−1.00887
$394$	22.0000	1.10834
$395$	−8.00000	−0.402524
$396$	−6.00000	−0.301511
$397$	10.0000	0.501886	0.250943	−	0.968002i	$-0.419259\pi$
$397$	10.0000	0.501886	0.250943	+	0.968002i	$0.419259\pi$
$398$	8.00000	0.401004
$399$	1.00000	0.0500626
$400$	11.0000	0.550000
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	10.0000	0.498755
$403$	−16.0000	−0.797017
$404$	4.00000	0.199007
$405$	−4.00000	−0.198762
$406$	−2.00000	−0.0992583
$407$	−12.0000	−0.594818
$408$	−4.00000	−0.198030
$409$	24.0000	1.18672	0.593362	−	0.804936i	$-0.297800\pi$
$409$	24.0000	1.18672	0.593362	+	0.804936i	$0.297800\pi$
$410$	−24.0000	−1.18528
$411$	−18.0000	−0.887875
$412$	−4.00000	−0.197066
$413$	4.00000	0.196827
$414$	2.00000	0.0982946
$415$	0	0
$416$	−4.00000	−0.196116
$417$	20.0000	0.979404
$418$	6.00000	0.293470
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	4.00000	0.195180
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	10.0000	0.486792
$423$	−8.00000	−0.388973
$424$	−14.0000	−0.679900
$425$	−44.0000	−2.13431
$426$	−4.00000	−0.193801
$427$	10.0000	0.483934
$428$	12.0000	0.580042
$429$	24.0000	1.15873
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	1.00000	0.0481125
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	−4.00000	−0.192006
$435$	−8.00000	−0.383571
$436$	−6.00000	−0.287348
$437$	−2.00000	−0.0956730
$438$	−14.0000	−0.668946
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	24.0000	1.14416
$441$	1.00000	0.0476190
$442$	16.0000	0.761042
$443$	18.0000	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$444$	2.00000	0.0949158
$445$	−24.0000	−1.13771
$446$	−16.0000	−0.757622
$447$	−18.0000	−0.851371
$448$	−1.00000	−0.0472456
$449$	−30.0000	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$450$	11.0000	0.518545
$451$	−36.0000	−1.69517
$452$	18.0000	0.846649
$453$	−14.0000	−0.657777
$454$	−20.0000	−0.938647
$455$	−16.0000	−0.750092
$456$	−1.00000	−0.0468293
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−2.00000	−0.0934539
$459$	−4.00000	−0.186704
$460$	−8.00000	−0.373002
$461$	36.0000	1.67669	0.838344	−	0.545142i	$-0.183524\pi$
$461$	36.0000	1.67669	0.838344	+	0.545142i	$0.183524\pi$
$462$	6.00000	0.279145
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	2.00000	0.0928477
$465$	−16.0000	−0.741982
$466$	6.00000	0.277945
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	−4.00000	−0.184900
$469$	−10.0000	−0.461757
$470$	32.0000	1.47605
$471$	−22.0000	−1.01371
$472$	−4.00000	−0.184115
$473$	0	0
$474$	2.00000	0.0918630
$475$	−11.0000	−0.504715
$476$	4.00000	0.183340
$477$	−14.0000	−0.641016
$478$	−22.0000	−1.00626
$479$	4.00000	0.182765	0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000	0.182765	0.0913823	+	0.995816i	$0.470871\pi$
$480$	−4.00000	−0.182574
$481$	−8.00000	−0.364769
$482$	28.0000	1.27537
$483$	−2.00000	−0.0910032
$484$	25.0000	1.13636
$485$	0	0
$486$	1.00000	0.0453609
$487$	−34.0000	−1.54069	−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000	−1.54069	−0.770344	+	0.637629i	$0.779915\pi$
$488$	−10.0000	−0.452679
$489$	−24.0000	−1.08532
$490$	−4.00000	−0.180702
$491$	30.0000	1.35388	0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000	1.35388	0.676941	+	0.736038i	$0.263305\pi$
$492$	6.00000	0.270501
$493$	−8.00000	−0.360302
$494$	4.00000	0.179969
$495$	24.0000	1.07872
$496$	4.00000	0.179605
$497$	4.00000	0.179425
$498$	0	0
$499$	24.0000	1.07439	0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000	1.07439	0.537194	+	0.843459i	$0.319484\pi$
$500$	−24.0000	−1.07331
$501$	8.00000	0.357414
$502$	−20.0000	−0.892644
$503$	28.0000	1.24846	0.624229	−	0.781241i	$-0.285413\pi$
$503$	28.0000	1.24846	0.624229	+	0.781241i	$0.285413\pi$
$504$	−1.00000	−0.0445435
$505$	−16.0000	−0.711991
$506$	−12.0000	−0.533465
$507$	3.00000	0.133235
$508$	−2.00000	−0.0887357
$509$	42.0000	1.86162	0.930809	−	0.365507i	$-0.119104\pi$
$509$	42.0000	1.86162	0.930809	+	0.365507i	$0.119104\pi$
$510$	16.0000	0.708492
$511$	14.0000	0.619324
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	−6.00000	−0.264649
$515$	16.0000	0.705044
$516$	0	0
$517$	48.0000	2.11104
$518$	−2.00000	−0.0878750
$519$	10.0000	0.438951
$520$	16.0000	0.701646
$521$	38.0000	1.66481	0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000	1.66481	0.832405	+	0.554168i	$0.186963\pi$
$522$	2.00000	0.0875376
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−20.0000	−0.873704
$525$	−11.0000	−0.480079
$526$	−2.00000	−0.0872041
$527$	−16.0000	−0.696971
$528$	−6.00000	−0.261116
$529$	−19.0000	−0.826087
$530$	56.0000	2.43248
$531$	−4.00000	−0.173585
$532$	1.00000	0.0433555
$533$	−24.0000	−1.03956
$534$	6.00000	0.259645
$535$	−48.0000	−2.07522
$536$	10.0000	0.431934
$537$	4.00000	0.172613
$538$	−6.00000	−0.258678
$539$	−6.00000	−0.258438
$540$	−4.00000	−0.172133
$541$	−14.0000	−0.601907	−0.300954	−	0.953639i	$-0.597305\pi$
$541$	−14.0000	−0.601907	−0.300954	+	0.953639i	$0.597305\pi$
$542$	8.00000	0.343629
$543$	16.0000	0.686626
$544$	−4.00000	−0.171499
$545$	24.0000	1.02805
$546$	4.00000	0.171184
$547$	10.0000	0.427569	0.213785	−	0.976881i	$-0.431421\pi$
$547$	10.0000	0.427569	0.213785	+	0.976881i	$0.431421\pi$
$548$	−18.0000	−0.768922
$549$	−10.0000	−0.426790
$550$	−66.0000	−2.81425
$551$	−2.00000	−0.0852029
$552$	2.00000	0.0851257
$553$	−2.00000	−0.0850487
$554$	−10.0000	−0.424859
$555$	−8.00000	−0.339581
$556$	20.0000	0.848189
$557$	−10.0000	−0.423714	−0.211857	−	0.977301i	$-0.567951\pi$
$557$	−10.0000	−0.423714	−0.211857	+	0.977301i	$0.567951\pi$
$558$	4.00000	0.169334
$559$	0	0
$560$	4.00000	0.169031
$561$	24.0000	1.01328
$562$	10.0000	0.421825
$563$	44.0000	1.85438	0.927189	−	0.374593i	$-0.122217\pi$
$563$	44.0000	1.85438	0.927189	+	0.374593i	$0.122217\pi$
$564$	−8.00000	−0.336861
$565$	−72.0000	−3.02906
$566$	−4.00000	−0.168133
$567$	−1.00000	−0.0419961
$568$	−4.00000	−0.167836
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	4.00000	0.167542
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	24.0000	1.00349
$573$	−14.0000	−0.584858
$574$	−6.00000	−0.250435
$575$	22.0000	0.917463
$576$	1.00000	0.0416667
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	−1.00000	−0.0415945
$579$	26.0000	1.08052
$580$	−8.00000	−0.332182
$581$	0	0
$582$	0	0
$583$	84.0000	3.47892
$584$	−14.0000	−0.579324
$585$	16.0000	0.661519
$586$	18.0000	0.743573
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	1.00000	0.0412393
$589$	−4.00000	−0.164817
$590$	16.0000	0.658710
$591$	22.0000	0.904959
$592$	2.00000	0.0821995
$593$	16.0000	0.657041	0.328521	−	0.944497i	$-0.393450\pi$
$593$	16.0000	0.657041	0.328521	+	0.944497i	$0.393450\pi$
$594$	−6.00000	−0.246183
$595$	−16.0000	−0.655936
$596$	−18.0000	−0.737309
$597$	8.00000	0.327418
$598$	−8.00000	−0.327144
$599$	−28.0000	−1.14405	−0.572024	−	0.820237i	$-0.693842\pi$
$599$	−28.0000	−1.14405	−0.572024	+	0.820237i	$0.693842\pi$
$600$	11.0000	0.449073
$601$	−8.00000	−0.326327	−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000	−0.326327	−0.163163	+	0.986599i	$0.552170\pi$
$602$	0	0
$603$	10.0000	0.407231
$604$	−14.0000	−0.569652
$605$	−100.000	−4.06558
$606$	4.00000	0.162489
$607$	−24.0000	−0.974130	−0.487065	−	0.873366i	$-0.661933\pi$
$607$	−24.0000	−0.974130	−0.487065	+	0.873366i	$0.661933\pi$
$608$	−1.00000	−0.0405554
$609$	−2.00000	−0.0810441
$610$	40.0000	1.61955
$611$	32.0000	1.29458
$612$	−4.00000	−0.161690
$613$	−34.0000	−1.37325	−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000	−1.37325	−0.686624	+	0.727013i	$0.740908\pi$
$614$	−8.00000	−0.322854
$615$	−24.0000	−0.967773
$616$	6.00000	0.241747
$617$	−2.00000	−0.0805170	−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000	−0.0805170	−0.0402585	+	0.999189i	$0.512818\pi$
$618$	−4.00000	−0.160904
$619$	12.0000	0.482321	0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000	0.482321	0.241160	+	0.970485i	$0.422472\pi$
$620$	−16.0000	−0.642575
$621$	2.00000	0.0802572
$622$	−4.00000	−0.160385
$623$	−6.00000	−0.240385
$624$	−4.00000	−0.160128
$625$	41.0000	1.64000
$626$	−14.0000	−0.559553
$627$	6.00000	0.239617
$628$	−22.0000	−0.877896
$629$	−8.00000	−0.318981
$630$	4.00000	0.159364
$631$	12.0000	0.477712	0.238856	−	0.971055i	$-0.423228\pi$
$631$	12.0000	0.477712	0.238856	+	0.971055i	$0.423228\pi$
$632$	2.00000	0.0795557
$633$	10.0000	0.397464
$634$	−18.0000	−0.714871
$635$	8.00000	0.317470
$636$	−14.0000	−0.555136
$637$	−4.00000	−0.158486
$638$	−12.0000	−0.475085
$639$	−4.00000	−0.158238
$640$	−4.00000	−0.158114
$641$	−22.0000	−0.868948	−0.434474	−	0.900684i	$-0.643066\pi$
$641$	−22.0000	−0.868948	−0.434474	+	0.900684i	$0.643066\pi$
$642$	12.0000	0.473602
$643$	−36.0000	−1.41970	−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000	−1.41970	−0.709851	+	0.704352i	$0.751238\pi$
$644$	−2.00000	−0.0788110
$645$	0	0
$646$	4.00000	0.157378
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	1.00000	0.0392837
$649$	24.0000	0.942082
$650$	−44.0000	−1.72582
$651$	−4.00000	−0.156772
$652$	−24.0000	−0.939913
$653$	−14.0000	−0.547862	−0.273931	−	0.961749i	$-0.588324\pi$
$653$	−14.0000	−0.547862	−0.273931	+	0.961749i	$0.588324\pi$
$654$	−6.00000	−0.234619
$655$	80.0000	3.12586
$656$	6.00000	0.234261
$657$	−14.0000	−0.546192
$658$	8.00000	0.311872
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	24.0000	0.934199
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	−10.0000	−0.388661
$663$	16.0000	0.621389
$664$	0	0
$665$	−4.00000	−0.155113
$666$	2.00000	0.0774984
$667$	4.00000	0.154881
$668$	8.00000	0.309529
$669$	−16.0000	−0.618596
$670$	−40.0000	−1.54533
$671$	60.0000	2.31627
$672$	−1.00000	−0.0385758
$673$	22.0000	0.848038	0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000	0.848038	0.424019	+	0.905653i	$0.360619\pi$
$674$	6.00000	0.231111
$675$	11.0000	0.423390
$676$	3.00000	0.115385
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	18.0000	0.691286
$679$	0	0
$680$	16.0000	0.613572
$681$	−20.0000	−0.766402
$682$	−24.0000	−0.919007
$683$	8.00000	0.306111	0.153056	−	0.988218i	$-0.451089\pi$
$683$	8.00000	0.306111	0.153056	+	0.988218i	$0.451089\pi$
$684$	−1.00000	−0.0382360
$685$	72.0000	2.75098
$686$	−1.00000	−0.0381802
$687$	−2.00000	−0.0763048
$688$	0	0
$689$	56.0000	2.13343
$690$	−8.00000	−0.304555
$691$	−4.00000	−0.152167	−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000	−0.152167	−0.0760836	+	0.997101i	$0.524242\pi$
$692$	10.0000	0.380143
$693$	6.00000	0.227921
$694$	6.00000	0.227757
$695$	−80.0000	−3.03457
$696$	2.00000	0.0758098
$697$	−24.0000	−0.909065
$698$	−30.0000	−1.13552
$699$	6.00000	0.226941
$700$	−11.0000	−0.415761
$701$	−6.00000	−0.226617	−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000	−0.226617	−0.113308	+	0.993560i	$0.536145\pi$
$702$	−4.00000	−0.150970
$703$	−2.00000	−0.0754314
$704$	−6.00000	−0.226134
$705$	32.0000	1.20519
$706$	4.00000	0.150542
$707$	−4.00000	−0.150435
$708$	−4.00000	−0.150329
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	16.0000	0.600469
$711$	2.00000	0.0750059
$712$	6.00000	0.224860
$713$	8.00000	0.299602
$714$	4.00000	0.149696
$715$	−96.0000	−3.59020
$716$	4.00000	0.149487
$717$	−22.0000	−0.821605
$718$	−34.0000	−1.26887
$719$	12.0000	0.447524	0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000	0.447524	0.223762	+	0.974644i	$0.428166\pi$
$720$	−4.00000	−0.149071
$721$	4.00000	0.148968
$722$	1.00000	0.0372161
$723$	28.0000	1.04133
$724$	16.0000	0.594635
$725$	22.0000	0.817059
$726$	25.0000	0.927837
$727$	−32.0000	−1.18681	−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000	−1.18681	−0.593407	+	0.804902i	$0.702218\pi$
$728$	4.00000	0.148250
$729$	1.00000	0.0370370
$730$	56.0000	2.07265
$731$	0	0
$732$	−10.0000	−0.369611
$733$	−30.0000	−1.10808	−0.554038	−	0.832492i	$-0.686914\pi$
$733$	−30.0000	−1.10808	−0.554038	+	0.832492i	$0.686914\pi$
$734$	−32.0000	−1.18114
$735$	−4.00000	−0.147542
$736$	2.00000	0.0737210
$737$	−60.0000	−2.21013
$738$	6.00000	0.220863
$739$	4.00000	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$740$	−8.00000	−0.294086
$741$	4.00000	0.146944
$742$	14.0000	0.513956
$743$	−32.0000	−1.17397	−0.586983	−	0.809599i	$-0.699684\pi$
$743$	−32.0000	−1.17397	−0.586983	+	0.809599i	$0.699684\pi$
$744$	4.00000	0.146647
$745$	72.0000	2.63788
$746$	14.0000	0.512576
$747$	0	0
$748$	24.0000	0.877527
$749$	−12.0000	−0.438470
$750$	−24.0000	−0.876356
$751$	22.0000	0.802791	0.401396	−	0.915905i	$-0.368525\pi$
$751$	22.0000	0.802791	0.401396	+	0.915905i	$0.368525\pi$
$752$	−8.00000	−0.291730
$753$	−20.0000	−0.728841
$754$	−8.00000	−0.291343
$755$	56.0000	2.03805
$756$	−1.00000	−0.0363696
$757$	46.0000	1.67190	0.835949	−	0.548807i	$-0.184918\pi$
$757$	46.0000	1.67190	0.835949	+	0.548807i	$0.184918\pi$
$758$	−34.0000	−1.23494
$759$	−12.0000	−0.435572
$760$	4.00000	0.145095
$761$	16.0000	0.580000	0.290000	−	0.957027i	$-0.406345\pi$
$761$	16.0000	0.580000	0.290000	+	0.957027i	$0.406345\pi$
$762$	−2.00000	−0.0724524
$763$	6.00000	0.217215
$764$	−14.0000	−0.506502
$765$	16.0000	0.578481
$766$	−24.0000	−0.867155
$767$	16.0000	0.577727
$768$	1.00000	0.0360844
$769$	18.0000	0.649097	0.324548	−	0.945869i	$-0.394788\pi$
$769$	18.0000	0.649097	0.324548	+	0.945869i	$0.394788\pi$
$770$	−24.0000	−0.864900
$771$	−6.00000	−0.216085
$772$	26.0000	0.935760
$773$	42.0000	1.51064	0.755318	−	0.655359i	$-0.227483\pi$
$773$	42.0000	1.51064	0.755318	+	0.655359i	$0.227483\pi$
$774$	0	0
$775$	44.0000	1.58053
$776$	0	0
$777$	−2.00000	−0.0717496
$778$	34.0000	1.21896
$779$	−6.00000	−0.214972
$780$	16.0000	0.572892
$781$	24.0000	0.858788
$782$	−8.00000	−0.286079
$783$	2.00000	0.0714742
$784$	1.00000	0.0357143
$785$	88.0000	3.14085
$786$	−20.0000	−0.713376
$787$	32.0000	1.14068	0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000	1.14068	0.570338	+	0.821410i	$0.306812\pi$
$788$	22.0000	0.783718
$789$	−2.00000	−0.0712019
$790$	−8.00000	−0.284627
$791$	−18.0000	−0.640006
$792$	−6.00000	−0.213201
$793$	40.0000	1.42044
$794$	10.0000	0.354887
$795$	56.0000	1.98612
$796$	8.00000	0.283552
$797$	2.00000	0.0708436	0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000	0.0708436	0.0354218	+	0.999372i	$0.488723\pi$
$798$	1.00000	0.0353996
$799$	32.0000	1.13208
$800$	11.0000	0.388909
$801$	6.00000	0.212000
$802$	30.0000	1.05934
$803$	84.0000	2.96430
$804$	10.0000	0.352673
$805$	8.00000	0.281963
$806$	−16.0000	−0.563576
$807$	−6.00000	−0.211210
$808$	4.00000	0.140720
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	−4.00000	−0.140546
$811$	−40.0000	−1.40459	−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000	−1.40459	−0.702295	+	0.711886i	$0.747841\pi$
$812$	−2.00000	−0.0701862
$813$	8.00000	0.280572
$814$	−12.0000	−0.420600
$815$	96.0000	3.36273
$816$	−4.00000	−0.140028
$817$	0	0
$818$	24.0000	0.839140
$819$	4.00000	0.139771
$820$	−24.0000	−0.838116
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	−18.0000	−0.627822
$823$	24.0000	0.836587	0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000	0.836587	0.418294	+	0.908312i	$0.362628\pi$
$824$	−4.00000	−0.139347
$825$	−66.0000	−2.29783
$826$	4.00000	0.139178
$827$	−28.0000	−0.973655	−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000	−0.973655	−0.486828	+	0.873498i	$0.661846\pi$
$828$	2.00000	0.0695048
$829$	−44.0000	−1.52818	−0.764092	−	0.645108i	$-0.776812\pi$
$829$	−44.0000	−1.52818	−0.764092	+	0.645108i	$0.776812\pi$
$830$	0	0
$831$	−10.0000	−0.346896
$832$	−4.00000	−0.138675
$833$	−4.00000	−0.138592
$834$	20.0000	0.692543
$835$	−32.0000	−1.10741
$836$	6.00000	0.207514
$837$	4.00000	0.138260
$838$	−12.0000	−0.414533
$839$	48.0000	1.65714	0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000	1.65714	0.828572	+	0.559883i	$0.189154\pi$
$840$	4.00000	0.138013
$841$	−25.0000	−0.862069
$842$	−2.00000	−0.0689246
$843$	10.0000	0.344418
$844$	10.0000	0.344214
$845$	−12.0000	−0.412813
$846$	−8.00000	−0.275046
$847$	−25.0000	−0.859010
$848$	−14.0000	−0.480762
$849$	−4.00000	−0.137280
$850$	−44.0000	−1.50919
$851$	4.00000	0.137118
$852$	−4.00000	−0.137038
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	10.0000	0.342193
$855$	4.00000	0.136797
$856$	12.0000	0.410152
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	24.0000	0.819346
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	0	0
$861$	−6.00000	−0.204479
$862$	12.0000	0.408722
$863$	48.0000	1.63394	0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000	1.63394	0.816970	+	0.576681i	$0.195652\pi$
$864$	1.00000	0.0340207
$865$	−40.0000	−1.36004
$866$	0	0
$867$	−1.00000	−0.0339618
$868$	−4.00000	−0.135769
$869$	−12.0000	−0.407072
$870$	−8.00000	−0.271225
$871$	−40.0000	−1.35535
$872$	−6.00000	−0.203186
$873$	0	0
$874$	−2.00000	−0.0676510
$875$	24.0000	0.811348
$876$	−14.0000	−0.473016
$877$	−54.0000	−1.82345	−0.911725	−	0.410801i	$-0.865249\pi$
$877$	−54.0000	−1.82345	−0.911725	+	0.410801i	$0.865249\pi$
$878$	20.0000	0.674967
$879$	18.0000	0.607125
$880$	24.0000	0.809040
$881$	12.0000	0.404290	0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000	0.404290	0.202145	+	0.979356i	$0.435209\pi$
$882$	1.00000	0.0336718
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	16.0000	0.538138
$885$	16.0000	0.537834
$886$	18.0000	0.604722
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	2.00000	0.0671156
$889$	2.00000	0.0670778
$890$	−24.0000	−0.804482
$891$	−6.00000	−0.201008
$892$	−16.0000	−0.535720
$893$	8.00000	0.267710
$894$	−18.0000	−0.602010
$895$	−16.0000	−0.534821
$896$	−1.00000	−0.0334077
$897$	−8.00000	−0.267112
$898$	−30.0000	−1.00111
$899$	8.00000	0.266815
$900$	11.0000	0.366667
$901$	56.0000	1.86563
$902$	−36.0000	−1.19867
$903$	0	0
$904$	18.0000	0.598671
$905$	−64.0000	−2.12743
$906$	−14.0000	−0.465119
$907$	−26.0000	−0.863316	−0.431658	−	0.902037i	$-0.642071\pi$
$907$	−26.0000	−0.863316	−0.431658	+	0.902037i	$0.642071\pi$
$908$	−20.0000	−0.663723
$909$	4.00000	0.132672
$910$	−16.0000	−0.530395
$911$	52.0000	1.72284	0.861418	−	0.507896i	$-0.169577\pi$
$911$	52.0000	1.72284	0.861418	+	0.507896i	$0.169577\pi$
$912$	−1.00000	−0.0331133
$913$	0	0
$914$	−10.0000	−0.330771
$915$	40.0000	1.32236
$916$	−2.00000	−0.0660819
$917$	20.0000	0.660458
$918$	−4.00000	−0.132020
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	−8.00000	−0.263752
$921$	−8.00000	−0.263609
$922$	36.0000	1.18560
$923$	16.0000	0.526646
$924$	6.00000	0.197386
$925$	22.0000	0.723356
$926$	0	0
$927$	−4.00000	−0.131377
$928$	2.00000	0.0656532
$929$	−52.0000	−1.70606	−0.853032	−	0.521858i	$-0.825239\pi$
$929$	−52.0000	−1.70606	−0.853032	+	0.521858i	$0.825239\pi$
$930$	−16.0000	−0.524661
$931$	−1.00000	−0.0327737
$932$	6.00000	0.196537
$933$	−4.00000	−0.130954
$934$	−8.00000	−0.261768
$935$	−96.0000	−3.13954
$936$	−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	$0.286847\pi$
$938$	−10.0000	−0.326512
$939$	−14.0000	−0.456873
$940$	32.0000	1.04372
$941$	2.00000	0.0651981	0.0325991	−	0.999469i	$-0.489622\pi$
$941$	2.00000	0.0651981	0.0325991	+	0.999469i	$0.489622\pi$
$942$	−22.0000	−0.716799
$943$	12.0000	0.390774
$944$	−4.00000	−0.130189
$945$	4.00000	0.130120
$946$	0	0
$947$	30.0000	0.974869	0.487435	−	0.873160i	$-0.337933\pi$
$947$	30.0000	0.974869	0.487435	+	0.873160i	$0.337933\pi$
$948$	2.00000	0.0649570
$949$	56.0000	1.81784
$950$	−11.0000	−0.356887
$951$	−18.0000	−0.583690
$952$	4.00000	0.129641
$953$	−22.0000	−0.712650	−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000	−0.712650	−0.356325	+	0.934362i	$0.615970\pi$
$954$	−14.0000	−0.453267
$955$	56.0000	1.81212
$956$	−22.0000	−0.711531
$957$	−12.0000	−0.387905
$958$	4.00000	0.129234
$959$	18.0000	0.581250
$960$	−4.00000	−0.129099
$961$	−15.0000	−0.483871
$962$	−8.00000	−0.257930
$963$	12.0000	0.386695
$964$	28.0000	0.901819
$965$	−104.000	−3.34788
$966$	−2.00000	−0.0643489
$967$	4.00000	0.128631	0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000	0.128631	0.0643157	+	0.997930i	$0.479514\pi$
$968$	25.0000	0.803530
$969$	4.00000	0.128499
$970$	0	0
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	1.00000	0.0320750
$973$	−20.0000	−0.641171
$974$	−34.0000	−1.08943
$975$	−44.0000	−1.40913
$976$	−10.0000	−0.320092
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	−24.0000	−0.767435
$979$	−36.0000	−1.15056
$980$	−4.00000	−0.127775
$981$	−6.00000	−0.191565
$982$	30.0000	0.957338
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	6.00000	0.191273
$985$	−88.0000	−2.80391
$986$	−8.00000	−0.254772
$987$	8.00000	0.254643
$988$	4.00000	0.127257
$989$	0	0
$990$	24.0000	0.762770
$991$	−30.0000	−0.952981	−0.476491	−	0.879180i	$-0.658091\pi$
$991$	−30.0000	−0.952981	−0.476491	+	0.879180i	$0.658091\pi$
$992$	4.00000	0.127000
$993$	−10.0000	−0.317340
$994$	4.00000	0.126872
$995$	−32.0000	−1.01447
$996$	0	0
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	24.0000	0.759707
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.a.h.1.1	✓	1
3.2	odd	2		2394.2.a.f.1.1		1
4.3	odd	2		6384.2.a.c.1.1		1
7.6	odd	2		5586.2.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.a.h.1.1	✓	1	1.1	even	1	trivial
2394.2.a.f.1.1		1	3.2	odd	2
5586.2.a.x.1.1		1	7.6	odd	2
6384.2.a.c.1.1		1	4.3	odd	2

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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