LMFDB - Embedded newform 7098.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, 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("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.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:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -2.00000 q^{20} -1.00000 q^{21} +1.00000 q^{22} -6.00000 q^{23} -1.00000 q^{24} -1.00000 q^{25} -1.00000 q^{27} +1.00000 q^{28} +9.00000 q^{29} +2.00000 q^{30} -2.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -1.00000 q^{38} -2.00000 q^{40} -5.00000 q^{41} -1.00000 q^{42} -2.00000 q^{43} +1.00000 q^{44} -2.00000 q^{45} -6.00000 q^{46} +7.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} -1.00000 q^{53} -1.00000 q^{54} -2.00000 q^{55} +1.00000 q^{56} +1.00000 q^{57} +9.00000 q^{58} -10.0000 q^{59} +2.00000 q^{60} -11.0000 q^{61} -2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -1.00000 q^{66} -2.00000 q^{67} -1.00000 q^{68} +6.00000 q^{69} -2.00000 q^{70} +8.00000 q^{71} +1.00000 q^{72} -8.00000 q^{73} +2.00000 q^{74} +1.00000 q^{75} -1.00000 q^{76} +1.00000 q^{77} +11.0000 q^{79} -2.00000 q^{80} +1.00000 q^{81} -5.00000 q^{82} +12.0000 q^{83} -1.00000 q^{84} +2.00000 q^{85} -2.00000 q^{86} -9.00000 q^{87} +1.00000 q^{88} -11.0000 q^{89} -2.00000 q^{90} -6.00000 q^{92} +2.00000 q^{93} +7.00000 q^{94} +2.00000 q^{95} -1.00000 q^{96} +14.0000 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536	−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000	−0.242536	−0.121268	+	0.992620i	$0.538696\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−2.00000	−0.447214
$21$	−1.00000	−0.218218
$22$	1.00000	0.213201
$23$	−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
$25$	−1.00000	−0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	9.00000	1.67126	0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000	1.67126	0.835629	+	0.549294i	$0.185103\pi$
$30$	2.00000	0.365148
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	−2.00000	−0.338062
$36$	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
$39$	0	0
$40$	−2.00000	−0.316228
$41$	−5.00000	−0.780869	−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000	−0.780869	−0.390434	+	0.920631i	$0.627675\pi$
$42$	−1.00000	−0.154303
$43$	−2.00000	−0.304997	−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000	−0.304997	−0.152499	+	0.988304i	$0.548732\pi$
$44$	1.00000	0.150756
$45$	−2.00000	−0.298142
$46$	−6.00000	−0.884652
$47$	7.00000	1.02105	0.510527	−	0.859861i	$-0.329450\pi$
$47$	7.00000	1.02105	0.510527	+	0.859861i	$0.329450\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	0	0
$53$	−1.00000	−0.137361	−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000	−0.137361	−0.0686803	+	0.997639i	$0.521879\pi$
$54$	−1.00000	−0.136083
$55$	−2.00000	−0.269680
$56$	1.00000	0.133631
$57$	1.00000	0.132453
$58$	9.00000	1.18176
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	2.00000	0.258199
$61$	−11.0000	−1.40841	−0.704203	−	0.709999i	$-0.748695\pi$
$61$	−11.0000	−1.40841	−0.704203	+	0.709999i	$0.748695\pi$
$62$	−2.00000	−0.254000
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.00000	−0.123091
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	−1.00000	−0.121268
$69$	6.00000	0.722315
$70$	−2.00000	−0.239046
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	1.00000	0.117851
$73$	−8.00000	−0.936329	−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000	−0.936329	−0.468165	+	0.883641i	$0.655085\pi$
$74$	2.00000	0.232495
$75$	1.00000	0.115470
$76$	−1.00000	−0.114708
$77$	1.00000	0.113961
$78$	0	0
$79$	11.0000	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$80$	−2.00000	−0.223607
$81$	1.00000	0.111111
$82$	−5.00000	−0.552158
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	−1.00000	−0.109109
$85$	2.00000	0.216930
$86$	−2.00000	−0.215666
$87$	−9.00000	−0.964901
$88$	1.00000	0.106600
$89$	−11.0000	−1.16600	−0.582999	−	0.812473i	$-0.698121\pi$
$89$	−11.0000	−1.16600	−0.582999	+	0.812473i	$0.698121\pi$
$90$	−2.00000	−0.210819
$91$	0	0
$92$	−6.00000	−0.625543
$93$	2.00000	0.207390
$94$	7.00000	0.721995
$95$	2.00000	0.205196
$96$	−1.00000	−0.102062
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	1.00000	0.101015
$99$	1.00000	0.100504
$100$	−1.00000	−0.100000
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	1.00000	0.0990148
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	0	0
$105$	2.00000	0.195180
$106$	−1.00000	−0.0971286
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	−1.00000	−0.0962250
$109$	−16.0000	−1.53252	−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000	−1.53252	−0.766261	+	0.642529i	$0.777885\pi$
$110$	−2.00000	−0.190693
$111$	−2.00000	−0.189832
$112$	1.00000	0.0944911
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	1.00000	0.0936586
$115$	12.0000	1.11901
$116$	9.00000	0.835629
$117$	0	0
$118$	−10.0000	−0.920575
$119$	−1.00000	−0.0916698
$120$	2.00000	0.182574
$121$	−10.0000	−0.909091
$122$	−11.0000	−0.995893
$123$	5.00000	0.450835
$124$	−2.00000	−0.179605
$125$	12.0000	1.07331
$126$	1.00000	0.0890871
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	1.00000	0.0883883
$129$	2.00000	0.176090
$130$	0	0
$131$	−8.00000	−0.698963	−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000	−0.698963	−0.349482	+	0.936943i	$0.613642\pi$
$132$	−1.00000	−0.0870388
$133$	−1.00000	−0.0867110
$134$	−2.00000	−0.172774
$135$	2.00000	0.172133
$136$	−1.00000	−0.0857493
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	6.00000	0.510754
$139$	−9.00000	−0.763370	−0.381685	−	0.924292i	$-0.624656\pi$
$139$	−9.00000	−0.763370	−0.381685	+	0.924292i	$0.624656\pi$
$140$	−2.00000	−0.169031
$141$	−7.00000	−0.589506
$142$	8.00000	0.671345
$143$	0	0
$144$	1.00000	0.0833333
$145$	−18.0000	−1.49482
$146$	−8.00000	−0.662085
$147$	−1.00000	−0.0824786
$148$	2.00000	0.164399
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	1.00000	0.0816497
$151$	3.00000	0.244137	0.122068	−	0.992522i	$-0.461047\pi$
$151$	3.00000	0.244137	0.122068	+	0.992522i	$0.461047\pi$
$152$	−1.00000	−0.0811107
$153$	−1.00000	−0.0808452
$154$	1.00000	0.0805823
$155$	4.00000	0.321288
$156$	0	0
$157$	2.00000	0.159617	0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000	0.159617	0.0798087	+	0.996810i	$0.474569\pi$
$158$	11.0000	0.875113
$159$	1.00000	0.0793052
$160$	−2.00000	−0.158114
$161$	−6.00000	−0.472866
$162$	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	$0.524958\pi$
$164$	−5.00000	−0.390434
$165$	2.00000	0.155700
$166$	12.0000	0.931381
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	2.00000	0.153393
$171$	−1.00000	−0.0764719
$172$	−2.00000	−0.152499
$173$	8.00000	0.608229	0.304114	−	0.952636i	$-0.401639\pi$
$173$	8.00000	0.608229	0.304114	+	0.952636i	$0.401639\pi$
$174$	−9.00000	−0.682288
$175$	−1.00000	−0.0755929
$176$	1.00000	0.0753778
$177$	10.0000	0.751646
$178$	−11.0000	−0.824485
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	−2.00000	−0.149071
$181$	−19.0000	−1.41226	−0.706129	−	0.708083i	$-0.749560\pi$
$181$	−19.0000	−1.41226	−0.706129	+	0.708083i	$0.749560\pi$
$182$	0	0
$183$	11.0000	0.813143
$184$	−6.00000	−0.442326
$185$	−4.00000	−0.294086
$186$	2.00000	0.146647
$187$	−1.00000	−0.0731272
$188$	7.00000	0.510527
$189$	−1.00000	−0.0727393
$190$	2.00000	0.145095
$191$	4.00000	0.289430	0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000	0.289430	0.144715	+	0.989473i	$0.453773\pi$
$192$	−1.00000	−0.0721688
$193$	11.0000	0.791797	0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000	0.791797	0.395899	+	0.918294i	$0.370433\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	1.00000	0.0714286
$197$	−27.0000	−1.92367	−0.961835	−	0.273629i	$-0.911776\pi$
$197$	−27.0000	−1.92367	−0.961835	+	0.273629i	$0.911776\pi$
$198$	1.00000	0.0710669
$199$	10.0000	0.708881	0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000	0.708881	0.354441	+	0.935079i	$0.384671\pi$
$200$	−1.00000	−0.0707107
$201$	2.00000	0.141069
$202$	−2.00000	−0.140720
$203$	9.00000	0.631676
$204$	1.00000	0.0700140
$205$	10.0000	0.698430
$206$	−14.0000	−0.975426
$207$	−6.00000	−0.417029
$208$	0	0
$209$	−1.00000	−0.0691714
$210$	2.00000	0.138013
$211$	−6.00000	−0.413057	−0.206529	−	0.978441i	$-0.566217\pi$
$211$	−6.00000	−0.413057	−0.206529	+	0.978441i	$0.566217\pi$
$212$	−1.00000	−0.0686803
$213$	−8.00000	−0.548151
$214$	3.00000	0.205076
$215$	4.00000	0.272798
$216$	−1.00000	−0.0680414
$217$	−2.00000	−0.135769
$218$	−16.0000	−1.08366
$219$	8.00000	0.540590
$220$	−2.00000	−0.134840
$221$	0	0
$222$	−2.00000	−0.134231
$223$	−20.0000	−1.33930	−0.669650	−	0.742677i	$-0.733556\pi$
$223$	−20.0000	−1.33930	−0.669650	+	0.742677i	$0.733556\pi$
$224$	1.00000	0.0668153
$225$	−1.00000	−0.0666667
$226$	−6.00000	−0.399114
$227$	−2.00000	−0.132745	−0.0663723	−	0.997795i	$-0.521143\pi$
$227$	−2.00000	−0.132745	−0.0663723	+	0.997795i	$0.521143\pi$
$228$	1.00000	0.0662266
$229$	23.0000	1.51988	0.759941	−	0.649992i	$-0.225228\pi$
$229$	23.0000	1.51988	0.759941	+	0.649992i	$0.225228\pi$
$230$	12.0000	0.791257
$231$	−1.00000	−0.0657952
$232$	9.00000	0.590879
$233$	18.0000	1.17922	0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000	1.17922	0.589610	+	0.807688i	$0.299282\pi$
$234$	0	0
$235$	−14.0000	−0.913259
$236$	−10.0000	−0.650945
$237$	−11.0000	−0.714527
$238$	−1.00000	−0.0648204
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	2.00000	0.129099
$241$	−16.0000	−1.03065	−0.515325	−	0.856995i	$-0.672329\pi$
$241$	−16.0000	−1.03065	−0.515325	+	0.856995i	$0.672329\pi$
$242$	−10.0000	−0.642824
$243$	−1.00000	−0.0641500
$244$	−11.0000	−0.704203
$245$	−2.00000	−0.127775
$246$	5.00000	0.318788
$247$	0	0
$248$	−2.00000	−0.127000
$249$	−12.0000	−0.760469
$250$	12.0000	0.758947
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	1.00000	0.0629941
$253$	−6.00000	−0.377217
$254$	−12.0000	−0.752947
$255$	−2.00000	−0.125245
$256$	1.00000	0.0625000
$257$	−9.00000	−0.561405	−0.280702	−	0.959795i	$-0.590567\pi$
$257$	−9.00000	−0.561405	−0.280702	+	0.959795i	$0.590567\pi$
$258$	2.00000	0.124515
$259$	2.00000	0.124274
$260$	0	0
$261$	9.00000	0.557086
$262$	−8.00000	−0.494242
$263$	−28.0000	−1.72655	−0.863277	−	0.504730i	$-0.831592\pi$
$263$	−28.0000	−1.72655	−0.863277	+	0.504730i	$0.831592\pi$
$264$	−1.00000	−0.0615457
$265$	2.00000	0.122859
$266$	−1.00000	−0.0613139
$267$	11.0000	0.673189
$268$	−2.00000	−0.122169
$269$	16.0000	0.975537	0.487769	−	0.872973i	$-0.337811\pi$
$269$	16.0000	0.975537	0.487769	+	0.872973i	$0.337811\pi$
$270$	2.00000	0.121716
$271$	−2.00000	−0.121491	−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000	−0.121491	−0.0607457	+	0.998153i	$0.519348\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	10.0000	0.604122
$275$	−1.00000	−0.0603023
$276$	6.00000	0.361158
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−9.00000	−0.539784
$279$	−2.00000	−0.119737
$280$	−2.00000	−0.119523
$281$	20.0000	1.19310	0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000	1.19310	0.596550	+	0.802576i	$0.296538\pi$
$282$	−7.00000	−0.416844
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	8.00000	0.474713
$285$	−2.00000	−0.118470
$286$	0	0
$287$	−5.00000	−0.295141
$288$	1.00000	0.0589256
$289$	−16.0000	−0.941176
$290$	−18.0000	−1.05700
$291$	−14.0000	−0.820695
$292$	−8.00000	−0.468165
$293$	−20.0000	−1.16841	−0.584206	−	0.811605i	$-0.698594\pi$
$293$	−20.0000	−1.16841	−0.584206	+	0.811605i	$0.698594\pi$
$294$	−1.00000	−0.0583212
$295$	20.0000	1.16445
$296$	2.00000	0.116248
$297$	−1.00000	−0.0580259
$298$	−6.00000	−0.347571
$299$	0	0
$300$	1.00000	0.0577350
$301$	−2.00000	−0.115278
$302$	3.00000	0.172631
$303$	2.00000	0.114897
$304$	−1.00000	−0.0573539
$305$	22.0000	1.25972
$306$	−1.00000	−0.0571662
$307$	−19.0000	−1.08439	−0.542194	−	0.840254i	$-0.682406\pi$
$307$	−19.0000	−1.08439	−0.542194	+	0.840254i	$0.682406\pi$
$308$	1.00000	0.0569803
$309$	14.0000	0.796432
$310$	4.00000	0.227185
$311$	−15.0000	−0.850572	−0.425286	−	0.905059i	$-0.639826\pi$
$311$	−15.0000	−0.850572	−0.425286	+	0.905059i	$0.639826\pi$
$312$	0	0
$313$	−12.0000	−0.678280	−0.339140	−	0.940736i	$-0.610136\pi$
$313$	−12.0000	−0.678280	−0.339140	+	0.940736i	$0.610136\pi$
$314$	2.00000	0.112867
$315$	−2.00000	−0.112687
$316$	11.0000	0.618798
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	1.00000	0.0560772
$319$	9.00000	0.503903
$320$	−2.00000	−0.111803
$321$	−3.00000	−0.167444
$322$	−6.00000	−0.334367
$323$	1.00000	0.0556415
$324$	1.00000	0.0555556
$325$	0	0
$326$	−2.00000	−0.110770
$327$	16.0000	0.884802
$328$	−5.00000	−0.276079
$329$	7.00000	0.385922
$330$	2.00000	0.110096
$331$	−26.0000	−1.42909	−0.714545	−	0.699590i	$-0.753366\pi$
$331$	−26.0000	−1.42909	−0.714545	+	0.699590i	$0.753366\pi$
$332$	12.0000	0.658586
$333$	2.00000	0.109599
$334$	0	0
$335$	4.00000	0.218543
$336$	−1.00000	−0.0545545
$337$	−33.0000	−1.79762	−0.898812	−	0.438334i	$-0.855569\pi$
$337$	−33.0000	−1.79762	−0.898812	+	0.438334i	$0.855569\pi$
$338$	0	0
$339$	6.00000	0.325875
$340$	2.00000	0.108465
$341$	−2.00000	−0.108306
$342$	−1.00000	−0.0540738
$343$	1.00000	0.0539949
$344$	−2.00000	−0.107833
$345$	−12.0000	−0.646058
$346$	8.00000	0.430083
$347$	−3.00000	−0.161048	−0.0805242	−	0.996753i	$-0.525659\pi$
$347$	−3.00000	−0.161048	−0.0805242	+	0.996753i	$0.525659\pi$
$348$	−9.00000	−0.482451
$349$	6.00000	0.321173	0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000	0.321173	0.160586	+	0.987022i	$0.448662\pi$
$350$	−1.00000	−0.0534522
$351$	0	0
$352$	1.00000	0.0533002
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	10.0000	0.531494
$355$	−16.0000	−0.849192
$356$	−11.0000	−0.582999
$357$	1.00000	0.0529256
$358$	−12.0000	−0.634220
$359$	30.0000	1.58334	0.791670	−	0.610949i	$-0.209212\pi$
$359$	30.0000	1.58334	0.791670	+	0.610949i	$0.209212\pi$
$360$	−2.00000	−0.105409
$361$	−18.0000	−0.947368
$362$	−19.0000	−0.998618
$363$	10.0000	0.524864
$364$	0	0
$365$	16.0000	0.837478
$366$	11.0000	0.574979
$367$	−14.0000	−0.730794	−0.365397	−	0.930852i	$-0.619067\pi$
$367$	−14.0000	−0.730794	−0.365397	+	0.930852i	$0.619067\pi$
$368$	−6.00000	−0.312772
$369$	−5.00000	−0.260290
$370$	−4.00000	−0.207950
$371$	−1.00000	−0.0519174
$372$	2.00000	0.103695
$373$	0	0		−	1.00000i	$-0.5\pi$
$373$	0	0			1.00000i	$0.5\pi$
$374$	−1.00000	−0.0517088
$375$	−12.0000	−0.619677
$376$	7.00000	0.360997
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	2.00000	0.102598
$381$	12.0000	0.614779
$382$	4.00000	0.204658
$383$	−9.00000	−0.459879	−0.229939	−	0.973205i	$-0.573853\pi$
$383$	−9.00000	−0.459879	−0.229939	+	0.973205i	$0.573853\pi$
$384$	−1.00000	−0.0510310
$385$	−2.00000	−0.101929
$386$	11.0000	0.559885
$387$	−2.00000	−0.101666
$388$	14.0000	0.710742
$389$	22.0000	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$390$	0	0
$391$	6.00000	0.303433
$392$	1.00000	0.0505076
$393$	8.00000	0.403547
$394$	−27.0000	−1.36024
$395$	−22.0000	−1.10694
$396$	1.00000	0.0502519
$397$	21.0000	1.05396	0.526980	−	0.849878i	$-0.323324\pi$
$397$	21.0000	1.05396	0.526980	+	0.849878i	$0.323324\pi$
$398$	10.0000	0.501255
$399$	1.00000	0.0500626
$400$	−1.00000	−0.0500000
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	2.00000	0.0997509
$403$	0	0
$404$	−2.00000	−0.0995037
$405$	−2.00000	−0.0993808
$406$	9.00000	0.446663
$407$	2.00000	0.0991363
$408$	1.00000	0.0495074
$409$	−20.0000	−0.988936	−0.494468	−	0.869196i	$-0.664637\pi$
$409$	−20.0000	−0.988936	−0.494468	+	0.869196i	$0.664637\pi$
$410$	10.0000	0.493865
$411$	−10.0000	−0.493264
$412$	−14.0000	−0.689730
$413$	−10.0000	−0.492068
$414$	−6.00000	−0.294884
$415$	−24.0000	−1.17811
$416$	0	0
$417$	9.00000	0.440732
$418$	−1.00000	−0.0489116
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	2.00000	0.0975900
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	−6.00000	−0.292075
$423$	7.00000	0.340352
$424$	−1.00000	−0.0485643
$425$	1.00000	0.0485071
$426$	−8.00000	−0.387601
$427$	−11.0000	−0.532327
$428$	3.00000	0.145010
$429$	0	0
$430$	4.00000	0.192897
$431$	−28.0000	−1.34871	−0.674356	−	0.738406i	$-0.735579\pi$
$431$	−28.0000	−1.34871	−0.674356	+	0.738406i	$0.735579\pi$
$432$	−1.00000	−0.0481125
$433$	−18.0000	−0.865025	−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000	−0.865025	−0.432512	+	0.901628i	$0.642373\pi$
$434$	−2.00000	−0.0960031
$435$	18.0000	0.863034
$436$	−16.0000	−0.766261
$437$	6.00000	0.287019
$438$	8.00000	0.382255
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	−2.00000	−0.0953463
$441$	1.00000	0.0476190
$442$	0	0
$443$	35.0000	1.66290	0.831450	−	0.555599i	$-0.187511\pi$
$443$	35.0000	1.66290	0.831450	+	0.555599i	$0.187511\pi$
$444$	−2.00000	−0.0949158
$445$	22.0000	1.04290
$446$	−20.0000	−0.947027
$447$	6.00000	0.283790
$448$	1.00000	0.0472456
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	−1.00000	−0.0471405
$451$	−5.00000	−0.235441
$452$	−6.00000	−0.282216
$453$	−3.00000	−0.140952
$454$	−2.00000	−0.0938647
$455$	0	0
$456$	1.00000	0.0468293
$457$	6.00000	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$458$	23.0000	1.07472
$459$	1.00000	0.0466760
$460$	12.0000	0.559503
$461$	24.0000	1.11779	0.558896	−	0.829238i	$-0.311225\pi$
$461$	24.0000	1.11779	0.558896	+	0.829238i	$0.311225\pi$
$462$	−1.00000	−0.0465242
$463$	−1.00000	−0.0464739	−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000	−0.0464739	−0.0232370	+	0.999730i	$0.507397\pi$
$464$	9.00000	0.417815
$465$	−4.00000	−0.185496
$466$	18.0000	0.833834
$467$	8.00000	0.370196	0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000	0.370196	0.185098	+	0.982720i	$0.440740\pi$
$468$	0	0
$469$	−2.00000	−0.0923514
$470$	−14.0000	−0.645772
$471$	−2.00000	−0.0921551
$472$	−10.0000	−0.460287
$473$	−2.00000	−0.0919601
$474$	−11.0000	−0.505247
$475$	1.00000	0.0458831
$476$	−1.00000	−0.0458349
$477$	−1.00000	−0.0457869
$478$	12.0000	0.548867
$479$	−11.0000	−0.502603	−0.251301	−	0.967909i	$-0.580859\pi$
$479$	−11.0000	−0.502603	−0.251301	+	0.967909i	$0.580859\pi$
$480$	2.00000	0.0912871
$481$	0	0
$482$	−16.0000	−0.728780
$483$	6.00000	0.273009
$484$	−10.0000	−0.454545
$485$	−28.0000	−1.27141
$486$	−1.00000	−0.0453609
$487$	29.0000	1.31412	0.657058	−	0.753840i	$-0.271801\pi$
$487$	29.0000	1.31412	0.657058	+	0.753840i	$0.271801\pi$
$488$	−11.0000	−0.497947
$489$	2.00000	0.0904431
$490$	−2.00000	−0.0903508
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	5.00000	0.225417
$493$	−9.00000	−0.405340
$494$	0	0
$495$	−2.00000	−0.0898933
$496$	−2.00000	−0.0898027
$497$	8.00000	0.358849
$498$	−12.0000	−0.537733
$499$	30.0000	1.34298	0.671492	−	0.741012i	$-0.265654\pi$
$499$	30.0000	1.34298	0.671492	+	0.741012i	$0.265654\pi$
$500$	12.0000	0.536656
$501$	0	0
$502$	−8.00000	−0.357057
$503$	−8.00000	−0.356702	−0.178351	−	0.983967i	$-0.557076\pi$
$503$	−8.00000	−0.356702	−0.178351	+	0.983967i	$0.557076\pi$
$504$	1.00000	0.0445435
$505$	4.00000	0.177998
$506$	−6.00000	−0.266733
$507$	0	0
$508$	−12.0000	−0.532414
$509$	12.0000	0.531891	0.265945	−	0.963988i	$-0.414316\pi$
$509$	12.0000	0.531891	0.265945	+	0.963988i	$0.414316\pi$
$510$	−2.00000	−0.0885615
$511$	−8.00000	−0.353899
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−9.00000	−0.396973
$515$	28.0000	1.23383
$516$	2.00000	0.0880451
$517$	7.00000	0.307860
$518$	2.00000	0.0878750
$519$	−8.00000	−0.351161
$520$	0	0
$521$	19.0000	0.832405	0.416203	−	0.909272i	$-0.363361\pi$
$521$	19.0000	0.832405	0.416203	+	0.909272i	$0.363361\pi$
$522$	9.00000	0.393919
$523$	−11.0000	−0.480996	−0.240498	−	0.970650i	$-0.577311\pi$
$523$	−11.0000	−0.480996	−0.240498	+	0.970650i	$0.577311\pi$
$524$	−8.00000	−0.349482
$525$	1.00000	0.0436436
$526$	−28.0000	−1.22086
$527$	2.00000	0.0871214
$528$	−1.00000	−0.0435194
$529$	13.0000	0.565217
$530$	2.00000	0.0868744
$531$	−10.0000	−0.433963
$532$	−1.00000	−0.0433555
$533$	0	0
$534$	11.0000	0.476017
$535$	−6.00000	−0.259403
$536$	−2.00000	−0.0863868
$537$	12.0000	0.517838
$538$	16.0000	0.689809
$539$	1.00000	0.0430730
$540$	2.00000	0.0860663
$541$	16.0000	0.687894	0.343947	−	0.938989i	$-0.388236\pi$
$541$	16.0000	0.687894	0.343947	+	0.938989i	$0.388236\pi$
$542$	−2.00000	−0.0859074
$543$	19.0000	0.815368
$544$	−1.00000	−0.0428746
$545$	32.0000	1.37073
$546$	0	0
$547$	32.0000	1.36822	0.684111	−	0.729378i	$-0.260191\pi$
$547$	32.0000	1.36822	0.684111	+	0.729378i	$0.260191\pi$
$548$	10.0000	0.427179
$549$	−11.0000	−0.469469
$550$	−1.00000	−0.0426401
$551$	−9.00000	−0.383413
$552$	6.00000	0.255377
$553$	11.0000	0.467768
$554$	−2.00000	−0.0849719
$555$	4.00000	0.169791
$556$	−9.00000	−0.381685
$557$	3.00000	0.127114	0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000	0.127114	0.0635570	+	0.997978i	$0.479756\pi$
$558$	−2.00000	−0.0846668
$559$	0	0
$560$	−2.00000	−0.0845154
$561$	1.00000	0.0422200
$562$	20.0000	0.843649
$563$	34.0000	1.43293	0.716465	−	0.697623i	$-0.245759\pi$
$563$	34.0000	1.43293	0.716465	+	0.697623i	$0.245759\pi$
$564$	−7.00000	−0.294753
$565$	12.0000	0.504844
$566$	−28.0000	−1.17693
$567$	1.00000	0.0419961
$568$	8.00000	0.335673
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	−2.00000	−0.0837708
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	0	0
$573$	−4.00000	−0.167102
$574$	−5.00000	−0.208696
$575$	6.00000	0.250217
$576$	1.00000	0.0416667
$577$	−12.0000	−0.499567	−0.249783	−	0.968302i	$-0.580359\pi$
$577$	−12.0000	−0.499567	−0.249783	+	0.968302i	$0.580359\pi$
$578$	−16.0000	−0.665512
$579$	−11.0000	−0.457144
$580$	−18.0000	−0.747409
$581$	12.0000	0.497844
$582$	−14.0000	−0.580319
$583$	−1.00000	−0.0414158
$584$	−8.00000	−0.331042
$585$	0	0
$586$	−20.0000	−0.826192
$587$	26.0000	1.07313	0.536567	−	0.843857i	$-0.319721\pi$
$587$	26.0000	1.07313	0.536567	+	0.843857i	$0.319721\pi$
$588$	−1.00000	−0.0412393
$589$	2.00000	0.0824086
$590$	20.0000	0.823387
$591$	27.0000	1.11063
$592$	2.00000	0.0821995
$593$	3.00000	0.123195	0.0615976	−	0.998101i	$-0.480380\pi$
$593$	3.00000	0.123195	0.0615976	+	0.998101i	$0.480380\pi$
$594$	−1.00000	−0.0410305
$595$	2.00000	0.0819920
$596$	−6.00000	−0.245770
$597$	−10.0000	−0.409273
$598$	0	0
$599$	−30.0000	−1.22577	−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000	−1.22577	−0.612883	+	0.790173i	$0.709990\pi$
$600$	1.00000	0.0408248
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	−2.00000	−0.0815139
$603$	−2.00000	−0.0814463
$604$	3.00000	0.122068
$605$	20.0000	0.813116
$606$	2.00000	0.0812444
$607$	−46.0000	−1.86708	−0.933541	−	0.358470i	$-0.883298\pi$
$607$	−46.0000	−1.86708	−0.933541	+	0.358470i	$0.883298\pi$
$608$	−1.00000	−0.0405554
$609$	−9.00000	−0.364698
$610$	22.0000	0.890754
$611$	0	0
$612$	−1.00000	−0.0404226
$613$	−28.0000	−1.13091	−0.565455	−	0.824779i	$-0.691299\pi$
$613$	−28.0000	−1.13091	−0.565455	+	0.824779i	$0.691299\pi$
$614$	−19.0000	−0.766778
$615$	−10.0000	−0.403239
$616$	1.00000	0.0402911
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	14.0000	0.563163
$619$	−11.0000	−0.442127	−0.221064	−	0.975259i	$-0.570953\pi$
$619$	−11.0000	−0.442127	−0.221064	+	0.975259i	$0.570953\pi$
$620$	4.00000	0.160644
$621$	6.00000	0.240772
$622$	−15.0000	−0.601445
$623$	−11.0000	−0.440706
$624$	0	0
$625$	−19.0000	−0.760000
$626$	−12.0000	−0.479616
$627$	1.00000	0.0399362
$628$	2.00000	0.0798087
$629$	−2.00000	−0.0797452
$630$	−2.00000	−0.0796819
$631$	33.0000	1.31371	0.656855	−	0.754017i	$-0.271887\pi$
$631$	33.0000	1.31371	0.656855	+	0.754017i	$0.271887\pi$
$632$	11.0000	0.437557
$633$	6.00000	0.238479
$634$	−30.0000	−1.19145
$635$	24.0000	0.952411
$636$	1.00000	0.0396526
$637$	0	0
$638$	9.00000	0.356313
$639$	8.00000	0.316475
$640$	−2.00000	−0.0790569
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	−3.00000	−0.118401
$643$	43.0000	1.69575	0.847877	−	0.530193i	$-0.177880\pi$
$643$	43.0000	1.69575	0.847877	+	0.530193i	$0.177880\pi$
$644$	−6.00000	−0.236433
$645$	−4.00000	−0.157500
$646$	1.00000	0.0393445
$647$	39.0000	1.53325	0.766624	−	0.642096i	$-0.221935\pi$
$647$	39.0000	1.53325	0.766624	+	0.642096i	$0.221935\pi$
$648$	1.00000	0.0392837
$649$	−10.0000	−0.392534
$650$	0	0
$651$	2.00000	0.0783862
$652$	−2.00000	−0.0783260
$653$	−49.0000	−1.91752	−0.958759	−	0.284220i	$-0.908265\pi$
$653$	−49.0000	−1.91752	−0.958759	+	0.284220i	$0.908265\pi$
$654$	16.0000	0.625650
$655$	16.0000	0.625172
$656$	−5.00000	−0.195217
$657$	−8.00000	−0.312110
$658$	7.00000	0.272888
$659$	9.00000	0.350590	0.175295	−	0.984516i	$-0.443912\pi$
$659$	9.00000	0.350590	0.175295	+	0.984516i	$0.443912\pi$
$660$	2.00000	0.0778499
$661$	26.0000	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$662$	−26.0000	−1.01052
$663$	0	0
$664$	12.0000	0.465690
$665$	2.00000	0.0775567
$666$	2.00000	0.0774984
$667$	−54.0000	−2.09089
$668$	0	0
$669$	20.0000	0.773245
$670$	4.00000	0.154533
$671$	−11.0000	−0.424650
$672$	−1.00000	−0.0385758
$673$	−41.0000	−1.58043	−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000	−1.58043	−0.790217	+	0.612827i	$0.790032\pi$
$674$	−33.0000	−1.27111
$675$	1.00000	0.0384900
$676$	0	0
$677$	−4.00000	−0.153732	−0.0768662	−	0.997041i	$-0.524491\pi$
$677$	−4.00000	−0.153732	−0.0768662	+	0.997041i	$0.524491\pi$
$678$	6.00000	0.230429
$679$	14.0000	0.537271
$680$	2.00000	0.0766965
$681$	2.00000	0.0766402
$682$	−2.00000	−0.0765840
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	−1.00000	−0.0382360
$685$	−20.0000	−0.764161
$686$	1.00000	0.0381802
$687$	−23.0000	−0.877505
$688$	−2.00000	−0.0762493
$689$	0	0
$690$	−12.0000	−0.456832
$691$	32.0000	1.21734	0.608669	−	0.793424i	$-0.291704\pi$
$691$	32.0000	1.21734	0.608669	+	0.793424i	$0.291704\pi$
$692$	8.00000	0.304114
$693$	1.00000	0.0379869
$694$	−3.00000	−0.113878
$695$	18.0000	0.682779
$696$	−9.00000	−0.341144
$697$	5.00000	0.189389
$698$	6.00000	0.227103
$699$	−18.0000	−0.680823
$700$	−1.00000	−0.0377964
$701$	1.00000	0.0377695	0.0188847	−	0.999822i	$-0.493988\pi$
$701$	1.00000	0.0377695	0.0188847	+	0.999822i	$0.493988\pi$
$702$	0	0
$703$	−2.00000	−0.0754314
$704$	1.00000	0.0376889
$705$	14.0000	0.527271
$706$	−26.0000	−0.978523
$707$	−2.00000	−0.0752177
$708$	10.0000	0.375823
$709$	−24.0000	−0.901339	−0.450669	−	0.892691i	$-0.648815\pi$
$709$	−24.0000	−0.901339	−0.450669	+	0.892691i	$0.648815\pi$
$710$	−16.0000	−0.600469
$711$	11.0000	0.412532
$712$	−11.0000	−0.412242
$713$	12.0000	0.449404
$714$	1.00000	0.0374241
$715$	0	0
$716$	−12.0000	−0.448461
$717$	−12.0000	−0.448148
$718$	30.0000	1.11959
$719$	15.0000	0.559406	0.279703	−	0.960087i	$-0.409764\pi$
$719$	15.0000	0.559406	0.279703	+	0.960087i	$0.409764\pi$
$720$	−2.00000	−0.0745356
$721$	−14.0000	−0.521387
$722$	−18.0000	−0.669891
$723$	16.0000	0.595046
$724$	−19.0000	−0.706129
$725$	−9.00000	−0.334252
$726$	10.0000	0.371135
$727$	−52.0000	−1.92857	−0.964287	−	0.264861i	$-0.914674\pi$
$727$	−52.0000	−1.92857	−0.964287	+	0.264861i	$0.914674\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	16.0000	0.592187
$731$	2.00000	0.0739727
$732$	11.0000	0.406572
$733$	−43.0000	−1.58824	−0.794121	−	0.607760i	$-0.792068\pi$
$733$	−43.0000	−1.58824	−0.794121	+	0.607760i	$0.792068\pi$
$734$	−14.0000	−0.516749
$735$	2.00000	0.0737711
$736$	−6.00000	−0.221163
$737$	−2.00000	−0.0736709
$738$	−5.00000	−0.184053
$739$	38.0000	1.39785	0.698926	−	0.715194i	$-0.253662\pi$
$739$	38.0000	1.39785	0.698926	+	0.715194i	$0.253662\pi$
$740$	−4.00000	−0.147043
$741$	0	0
$742$	−1.00000	−0.0367112
$743$	42.0000	1.54083	0.770415	−	0.637542i	$-0.220049\pi$
$743$	42.0000	1.54083	0.770415	+	0.637542i	$0.220049\pi$
$744$	2.00000	0.0733236
$745$	12.0000	0.439646
$746$	0	0
$747$	12.0000	0.439057
$748$	−1.00000	−0.0365636
$749$	3.00000	0.109618
$750$	−12.0000	−0.438178
$751$	23.0000	0.839282	0.419641	−	0.907690i	$-0.362156\pi$
$751$	23.0000	0.839282	0.419641	+	0.907690i	$0.362156\pi$
$752$	7.00000	0.255264
$753$	8.00000	0.291536
$754$	0	0
$755$	−6.00000	−0.218362
$756$	−1.00000	−0.0363696
$757$	−36.0000	−1.30844	−0.654221	−	0.756303i	$-0.727003\pi$
$757$	−36.0000	−1.30844	−0.654221	+	0.756303i	$0.727003\pi$
$758$	0	0
$759$	6.00000	0.217786
$760$	2.00000	0.0725476
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	12.0000	0.434714
$763$	−16.0000	−0.579239
$764$	4.00000	0.144715
$765$	2.00000	0.0723102
$766$	−9.00000	−0.325183
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	46.0000	1.65880	0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000	1.65880	0.829401	+	0.558653i	$0.188682\pi$
$770$	−2.00000	−0.0720750
$771$	9.00000	0.324127
$772$	11.0000	0.395899
$773$	−54.0000	−1.94225	−0.971123	−	0.238581i	$-0.923318\pi$
$773$	−54.0000	−1.94225	−0.971123	+	0.238581i	$0.923318\pi$
$774$	−2.00000	−0.0718885
$775$	2.00000	0.0718421
$776$	14.0000	0.502571
$777$	−2.00000	−0.0717496
$778$	22.0000	0.788738
$779$	5.00000	0.179144
$780$	0	0
$781$	8.00000	0.286263
$782$	6.00000	0.214560
$783$	−9.00000	−0.321634
$784$	1.00000	0.0357143
$785$	−4.00000	−0.142766
$786$	8.00000	0.285351
$787$	29.0000	1.03374	0.516869	−	0.856064i	$-0.327097\pi$
$787$	29.0000	1.03374	0.516869	+	0.856064i	$0.327097\pi$
$788$	−27.0000	−0.961835
$789$	28.0000	0.996826
$790$	−22.0000	−0.782725
$791$	−6.00000	−0.213335
$792$	1.00000	0.0355335
$793$	0	0
$794$	21.0000	0.745262
$795$	−2.00000	−0.0709327
$796$	10.0000	0.354441
$797$	52.0000	1.84193	0.920967	−	0.389640i	$-0.127401\pi$
$797$	52.0000	1.84193	0.920967	+	0.389640i	$0.127401\pi$
$798$	1.00000	0.0353996
$799$	−7.00000	−0.247642
$800$	−1.00000	−0.0353553
$801$	−11.0000	−0.388666
$802$	−6.00000	−0.211867
$803$	−8.00000	−0.282314
$804$	2.00000	0.0705346
$805$	12.0000	0.422944
$806$	0	0
$807$	−16.0000	−0.563227
$808$	−2.00000	−0.0703598
$809$	−28.0000	−0.984428	−0.492214	−	0.870474i	$-0.663812\pi$
$809$	−28.0000	−0.984428	−0.492214	+	0.870474i	$0.663812\pi$
$810$	−2.00000	−0.0702728
$811$	36.0000	1.26413	0.632065	−	0.774915i	$-0.282207\pi$
$811$	36.0000	1.26413	0.632065	+	0.774915i	$0.282207\pi$
$812$	9.00000	0.315838
$813$	2.00000	0.0701431
$814$	2.00000	0.0701000
$815$	4.00000	0.140114
$816$	1.00000	0.0350070
$817$	2.00000	0.0699711
$818$	−20.0000	−0.699284
$819$	0	0
$820$	10.0000	0.349215
$821$	45.0000	1.57051	0.785255	−	0.619172i	$-0.212532\pi$
$821$	45.0000	1.57051	0.785255	+	0.619172i	$0.212532\pi$
$822$	−10.0000	−0.348790
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	−14.0000	−0.487713
$825$	1.00000	0.0348155
$826$	−10.0000	−0.347945
$827$	−16.0000	−0.556375	−0.278187	−	0.960527i	$-0.589734\pi$
$827$	−16.0000	−0.556375	−0.278187	+	0.960527i	$0.589734\pi$
$828$	−6.00000	−0.208514
$829$	19.0000	0.659897	0.329949	−	0.943999i	$-0.392969\pi$
$829$	19.0000	0.659897	0.329949	+	0.943999i	$0.392969\pi$
$830$	−24.0000	−0.833052
$831$	2.00000	0.0693792
$832$	0	0
$833$	−1.00000	−0.0346479
$834$	9.00000	0.311645
$835$	0	0
$836$	−1.00000	−0.0345857
$837$	2.00000	0.0691301
$838$	−20.0000	−0.690889
$839$	−8.00000	−0.276191	−0.138095	−	0.990419i	$-0.544098\pi$
$839$	−8.00000	−0.276191	−0.138095	+	0.990419i	$0.544098\pi$
$840$	2.00000	0.0690066
$841$	52.0000	1.79310
$842$	26.0000	0.896019
$843$	−20.0000	−0.688837
$844$	−6.00000	−0.206529
$845$	0	0
$846$	7.00000	0.240665
$847$	−10.0000	−0.343604
$848$	−1.00000	−0.0343401
$849$	28.0000	0.960958
$850$	1.00000	0.0342997
$851$	−12.0000	−0.411355
$852$	−8.00000	−0.274075
$853$	53.0000	1.81469	0.907343	−	0.420392i	$-0.138107\pi$
$853$	53.0000	1.81469	0.907343	+	0.420392i	$0.138107\pi$
$854$	−11.0000	−0.376412
$855$	2.00000	0.0683986
$856$	3.00000	0.102538
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	0	0
$859$	49.0000	1.67186	0.835929	−	0.548837i	$-0.184929\pi$
$859$	49.0000	1.67186	0.835929	+	0.548837i	$0.184929\pi$
$860$	4.00000	0.136399
$861$	5.00000	0.170400
$862$	−28.0000	−0.953684
$863$	50.0000	1.70202	0.851010	−	0.525150i	$-0.175991\pi$
$863$	50.0000	1.70202	0.851010	+	0.525150i	$0.175991\pi$
$864$	−1.00000	−0.0340207
$865$	−16.0000	−0.544016
$866$	−18.0000	−0.611665
$867$	16.0000	0.543388
$868$	−2.00000	−0.0678844
$869$	11.0000	0.373149
$870$	18.0000	0.610257
$871$	0	0
$872$	−16.0000	−0.541828
$873$	14.0000	0.473828
$874$	6.00000	0.202953
$875$	12.0000	0.405674
$876$	8.00000	0.270295
$877$	20.0000	0.675352	0.337676	−	0.941262i	$-0.390359\pi$
$877$	20.0000	0.675352	0.337676	+	0.941262i	$0.390359\pi$
$878$	−20.0000	−0.674967
$879$	20.0000	0.674583
$880$	−2.00000	−0.0674200
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	1.00000	0.0336718
$883$	46.0000	1.54802	0.774012	−	0.633171i	$-0.218247\pi$
$883$	46.0000	1.54802	0.774012	+	0.633171i	$0.218247\pi$
$884$	0	0
$885$	−20.0000	−0.672293
$886$	35.0000	1.17585
$887$	−21.0000	−0.705111	−0.352555	−	0.935791i	$-0.614687\pi$
$887$	−21.0000	−0.705111	−0.352555	+	0.935791i	$0.614687\pi$
$888$	−2.00000	−0.0671156
$889$	−12.0000	−0.402467
$890$	22.0000	0.737442
$891$	1.00000	0.0335013
$892$	−20.0000	−0.669650
$893$	−7.00000	−0.234246
$894$	6.00000	0.200670
$895$	24.0000	0.802232
$896$	1.00000	0.0334077
$897$	0	0
$898$	30.0000	1.00111
$899$	−18.0000	−0.600334
$900$	−1.00000	−0.0333333
$901$	1.00000	0.0333148
$902$	−5.00000	−0.166482
$903$	2.00000	0.0665558
$904$	−6.00000	−0.199557
$905$	38.0000	1.26316
$906$	−3.00000	−0.0996683
$907$	34.0000	1.12895	0.564476	−	0.825450i	$-0.309078\pi$
$907$	34.0000	1.12895	0.564476	+	0.825450i	$0.309078\pi$
$908$	−2.00000	−0.0663723
$909$	−2.00000	−0.0663358
$910$	0	0
$911$	40.0000	1.32526	0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000	1.32526	0.662630	+	0.748947i	$0.269440\pi$
$912$	1.00000	0.0331133
$913$	12.0000	0.397142
$914$	6.00000	0.198462
$915$	−22.0000	−0.727298
$916$	23.0000	0.759941
$917$	−8.00000	−0.264183
$918$	1.00000	0.0330049
$919$	29.0000	0.956622	0.478311	−	0.878191i	$-0.341249\pi$
$919$	29.0000	0.956622	0.478311	+	0.878191i	$0.341249\pi$
$920$	12.0000	0.395628
$921$	19.0000	0.626071
$922$	24.0000	0.790398
$923$	0	0
$924$	−1.00000	−0.0328976
$925$	−2.00000	−0.0657596
$926$	−1.00000	−0.0328620
$927$	−14.0000	−0.459820
$928$	9.00000	0.295439
$929$	−13.0000	−0.426516	−0.213258	−	0.976996i	$-0.568408\pi$
$929$	−13.0000	−0.426516	−0.213258	+	0.976996i	$0.568408\pi$
$930$	−4.00000	−0.131165
$931$	−1.00000	−0.0327737
$932$	18.0000	0.589610
$933$	15.0000	0.491078
$934$	8.00000	0.261768
$935$	2.00000	0.0654070
$936$	0	0
$937$	−4.00000	−0.130674	−0.0653372	−	0.997863i	$-0.520812\pi$
$937$	−4.00000	−0.130674	−0.0653372	+	0.997863i	$0.520812\pi$
$938$	−2.00000	−0.0653023
$939$	12.0000	0.391605
$940$	−14.0000	−0.456630
$941$	−32.0000	−1.04317	−0.521585	−	0.853199i	$-0.674659\pi$
$941$	−32.0000	−1.04317	−0.521585	+	0.853199i	$0.674659\pi$
$942$	−2.00000	−0.0651635
$943$	30.0000	0.976934
$944$	−10.0000	−0.325472
$945$	2.00000	0.0650600
$946$	−2.00000	−0.0650256
$947$	19.0000	0.617417	0.308709	−	0.951157i	$-0.400103\pi$
$947$	19.0000	0.617417	0.308709	+	0.951157i	$0.400103\pi$
$948$	−11.0000	−0.357263
$949$	0	0
$950$	1.00000	0.0324443
$951$	30.0000	0.972817
$952$	−1.00000	−0.0324102
$953$	−30.0000	−0.971795	−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000	−0.971795	−0.485898	+	0.874016i	$0.661507\pi$
$954$	−1.00000	−0.0323762
$955$	−8.00000	−0.258874
$956$	12.0000	0.388108
$957$	−9.00000	−0.290929
$958$	−11.0000	−0.355394
$959$	10.0000	0.322917
$960$	2.00000	0.0645497
$961$	−27.0000	−0.870968
$962$	0	0
$963$	3.00000	0.0966736
$964$	−16.0000	−0.515325
$965$	−22.0000	−0.708205
$966$	6.00000	0.193047
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	−10.0000	−0.321412
$969$	−1.00000	−0.0321246
$970$	−28.0000	−0.899026
$971$	−58.0000	−1.86131	−0.930654	−	0.365900i	$-0.880761\pi$
$971$	−58.0000	−1.86131	−0.930654	+	0.365900i	$0.880761\pi$
$972$	−1.00000	−0.0320750
$973$	−9.00000	−0.288527
$974$	29.0000	0.929220
$975$	0	0
$976$	−11.0000	−0.352101
$977$	−36.0000	−1.15174	−0.575871	−	0.817541i	$-0.695337\pi$
$977$	−36.0000	−1.15174	−0.575871	+	0.817541i	$0.695337\pi$
$978$	2.00000	0.0639529
$979$	−11.0000	−0.351562
$980$	−2.00000	−0.0638877
$981$	−16.0000	−0.510841
$982$	0	0
$983$	48.0000	1.53096	0.765481	−	0.643458i	$-0.222501\pi$
$983$	48.0000	1.53096	0.765481	+	0.643458i	$0.222501\pi$
$984$	5.00000	0.159394
$985$	54.0000	1.72058
$986$	−9.00000	−0.286618
$987$	−7.00000	−0.222812
$988$	0	0
$989$	12.0000	0.381578
$990$	−2.00000	−0.0635642
$991$	45.0000	1.42947	0.714736	−	0.699394i	$-0.246547\pi$
$991$	45.0000	1.42947	0.714736	+	0.699394i	$0.246547\pi$
$992$	−2.00000	−0.0635001
$993$	26.0000	0.825085
$994$	8.00000	0.253745
$995$	−20.0000	−0.634043
$996$	−12.0000	−0.380235
$997$	−35.0000	−1.10846	−0.554231	−	0.832363i	$-0.686987\pi$
$997$	−35.0000	−1.10846	−0.554231	+	0.832363i	$0.686987\pi$
$998$	30.0000	0.949633
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.r.1.1		1
13.4	even	6		546.2.l.g.211.1	✓	2
13.10	even	6		546.2.l.g.295.1	yes	2
13.12	even	2		7098.2.a.e.1.1		1
39.17	odd	6		1638.2.r.d.757.1		2
39.23	odd	6		1638.2.r.d.1387.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.g.211.1	✓	2	13.4	even	6
546.2.l.g.295.1	yes	2	13.10	even	6
1638.2.r.d.757.1		2	39.17	odd	6
1638.2.r.d.1387.1		2	39.23	odd	6
7098.2.a.e.1.1		1	13.12	even	2
7098.2.a.r.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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