LMFDB - Embedded newform 7098.2.a.s.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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} +1.00000 q^{21} +1.00000 q^{22} -3.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{27} -1.00000 q^{28} +9.00000 q^{29} +1.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} -9.00000 q^{37} +1.00000 q^{38} -1.00000 q^{40} -8.00000 q^{41} +1.00000 q^{42} -7.00000 q^{43} +1.00000 q^{44} -1.00000 q^{45} -3.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.00000 q^{50} +1.00000 q^{51} -10.0000 q^{53} -1.00000 q^{54} -1.00000 q^{55} -1.00000 q^{56} -1.00000 q^{57} +9.00000 q^{58} -6.00000 q^{59} +1.00000 q^{60} +11.0000 q^{61} +4.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.00000 q^{66} +12.0000 q^{67} -1.00000 q^{68} +3.00000 q^{69} +1.00000 q^{70} -6.00000 q^{71} +1.00000 q^{72} +11.0000 q^{73} -9.00000 q^{74} +4.00000 q^{75} +1.00000 q^{76} -1.00000 q^{77} -12.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -8.00000 q^{82} -6.00000 q^{83} +1.00000 q^{84} +1.00000 q^{85} -7.00000 q^{86} -9.00000 q^{87} +1.00000 q^{88} +12.0000 q^{89} -1.00000 q^{90} -3.00000 q^{92} -4.00000 q^{93} +8.00000 q^{94} -1.00000 q^{95} -1.00000 q^{96} +2.00000 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	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
$15$	1.00000	0.258199
$16$	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	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	−1.00000	−0.223607
$21$	1.00000	0.218218
$22$	1.00000	0.213201
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	−1.00000	−0.204124
$25$	−4.00000	−0.800000
$26$	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	$0.185103\pi$
$30$	1.00000	0.182574
$31$	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
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−9.00000	−1.47959	−0.739795	−	0.672832i	$-0.765078\pi$
$37$	−9.00000	−1.47959	−0.739795	+	0.672832i	$0.765078\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	1.00000	0.154303
$43$	−7.00000	−1.06749	−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000	−1.06749	−0.533745	+	0.845645i	$0.679216\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	−3.00000	−0.442326
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.00000	−0.565685
$51$	1.00000	0.140028
$52$	0	0
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	−1.00000	−0.133631
$57$	−1.00000	−0.132453
$58$	9.00000	1.18176
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	1.00000	0.129099
$61$	11.0000	1.40841	0.704203	−	0.709999i	$-0.251305\pi$
$61$	11.0000	1.40841	0.704203	+	0.709999i	$0.251305\pi$
$62$	4.00000	0.508001
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.00000	−0.123091
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	−1.00000	−0.121268
$69$	3.00000	0.361158
$70$	1.00000	0.119523
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	1.00000	0.117851
$73$	11.0000	1.28745	0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000	1.28745	0.643726	+	0.765256i	$0.277388\pi$
$74$	−9.00000	−1.04623
$75$	4.00000	0.461880
$76$	1.00000	0.114708
$77$	−1.00000	−0.113961
$78$	0	0
$79$	−12.0000	−1.35011	−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000	−1.35011	−0.675053	+	0.737769i	$0.735879\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−8.00000	−0.883452
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	1.00000	0.109109
$85$	1.00000	0.108465
$86$	−7.00000	−0.754829
$87$	−9.00000	−0.964901
$88$	1.00000	0.106600
$89$	12.0000	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−3.00000	−0.312772
$93$	−4.00000	−0.414781
$94$	8.00000	0.825137
$95$	−1.00000	−0.102598
$96$	−1.00000	−0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	1.00000	0.101015
$99$	1.00000	0.100504
$100$	−4.00000	−0.400000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	1.00000	0.0990148
$103$	5.00000	0.492665	0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000	0.492665	0.246332	+	0.969185i	$0.420775\pi$
$104$	0	0
$105$	−1.00000	−0.0975900
$106$	−10.0000	−0.971286
$107$	−2.00000	−0.193347	−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000	−0.193347	−0.0966736	+	0.995316i	$0.530820\pi$
$108$	−1.00000	−0.0962250
$109$	−7.00000	−0.670478	−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000	−0.670478	−0.335239	+	0.942133i	$0.608817\pi$
$110$	−1.00000	−0.0953463
$111$	9.00000	0.854242
$112$	−1.00000	−0.0944911
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	−1.00000	−0.0936586
$115$	3.00000	0.279751
$116$	9.00000	0.835629
$117$	0	0
$118$	−6.00000	−0.552345
$119$	1.00000	0.0916698
$120$	1.00000	0.0912871
$121$	−10.0000	−0.909091
$122$	11.0000	0.995893
$123$	8.00000	0.721336
$124$	4.00000	0.359211
$125$	9.00000	0.804984
$126$	−1.00000	−0.0890871
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	1.00000	0.0883883
$129$	7.00000	0.616316
$130$	0	0
$131$	−3.00000	−0.262111	−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000	−0.262111	−0.131056	+	0.991375i	$0.541837\pi$
$132$	−1.00000	−0.0870388
$133$	−1.00000	−0.0867110
$134$	12.0000	1.03664
$135$	1.00000	0.0860663
$136$	−1.00000	−0.0857493
$137$	−15.0000	−1.28154	−0.640768	−	0.767734i	$-0.721384\pi$
$137$	−15.0000	−1.28154	−0.640768	+	0.767734i	$0.721384\pi$
$138$	3.00000	0.255377
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	1.00000	0.0845154
$141$	−8.00000	−0.673722
$142$	−6.00000	−0.503509
$143$	0	0
$144$	1.00000	0.0833333
$145$	−9.00000	−0.747409
$146$	11.0000	0.910366
$147$	−1.00000	−0.0824786
$148$	−9.00000	−0.739795
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	4.00000	0.326599
$151$	1.00000	0.0813788	0.0406894	−	0.999172i	$-0.487045\pi$
$151$	1.00000	0.0813788	0.0406894	+	0.999172i	$0.487045\pi$
$152$	1.00000	0.0811107
$153$	−1.00000	−0.0808452
$154$	−1.00000	−0.0805823
$155$	−4.00000	−0.321288
$156$	0	0
$157$	−21.0000	−1.67598	−0.837991	−	0.545684i	$-0.816270\pi$
$157$	−21.0000	−1.67598	−0.837991	+	0.545684i	$0.816270\pi$
$158$	−12.0000	−0.954669
$159$	10.0000	0.793052
$160$	−1.00000	−0.0790569
$161$	3.00000	0.236433
$162$	1.00000	0.0785674
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	−8.00000	−0.624695
$165$	1.00000	0.0778499
$166$	−6.00000	−0.465690
$167$	−11.0000	−0.851206	−0.425603	−	0.904910i	$-0.639938\pi$
$167$	−11.0000	−0.851206	−0.425603	+	0.904910i	$0.639938\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	1.00000	0.0766965
$171$	1.00000	0.0764719
$172$	−7.00000	−0.533745
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	−9.00000	−0.682288
$175$	4.00000	0.302372
$176$	1.00000	0.0753778
$177$	6.00000	0.450988
$178$	12.0000	0.899438
$179$	18.0000	1.34538	0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000	1.34538	0.672692	+	0.739923i	$0.265138\pi$
$180$	−1.00000	−0.0745356
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	0	0
$183$	−11.0000	−0.813143
$184$	−3.00000	−0.221163
$185$	9.00000	0.661693
$186$	−4.00000	−0.293294
$187$	−1.00000	−0.0731272
$188$	8.00000	0.583460
$189$	1.00000	0.0727393
$190$	−1.00000	−0.0725476
$191$	−11.0000	−0.795932	−0.397966	−	0.917400i	$-0.630284\pi$
$191$	−11.0000	−0.795932	−0.397966	+	0.917400i	$0.630284\pi$
$192$	−1.00000	−0.0721688
$193$	−12.0000	−0.863779	−0.431889	−	0.901927i	$-0.642153\pi$
$193$	−12.0000	−0.863779	−0.431889	+	0.901927i	$0.642153\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	1.00000	0.0714286
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	1.00000	0.0710669
$199$	−5.00000	−0.354441	−0.177220	−	0.984171i	$-0.556711\pi$
$199$	−5.00000	−0.354441	−0.177220	+	0.984171i	$0.556711\pi$
$200$	−4.00000	−0.282843
$201$	−12.0000	−0.846415
$202$	2.00000	0.140720
$203$	−9.00000	−0.631676
$204$	1.00000	0.0700140
$205$	8.00000	0.558744
$206$	5.00000	0.348367
$207$	−3.00000	−0.208514
$208$	0	0
$209$	1.00000	0.0691714
$210$	−1.00000	−0.0690066
$211$	−5.00000	−0.344214	−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000	−0.344214	−0.172107	+	0.985078i	$0.555058\pi$
$212$	−10.0000	−0.686803
$213$	6.00000	0.411113
$214$	−2.00000	−0.136717
$215$	7.00000	0.477396
$216$	−1.00000	−0.0680414
$217$	−4.00000	−0.271538
$218$	−7.00000	−0.474100
$219$	−11.0000	−0.743311
$220$	−1.00000	−0.0674200
$221$	0	0
$222$	9.00000	0.604040
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	−1.00000	−0.0668153
$225$	−4.00000	−0.266667
$226$	−2.00000	−0.133038
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	−1.00000	−0.0662266
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	3.00000	0.197814
$231$	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
$235$	−8.00000	−0.521862
$236$	−6.00000	−0.390567
$237$	12.0000	0.779484
$238$	1.00000	0.0648204
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	1.00000	0.0645497
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	−10.0000	−0.642824
$243$	−1.00000	−0.0641500
$244$	11.0000	0.704203
$245$	−1.00000	−0.0638877
$246$	8.00000	0.510061
$247$	0	0
$248$	4.00000	0.254000
$249$	6.00000	0.380235
$250$	9.00000	0.569210
$251$	−11.0000	−0.694314	−0.347157	−	0.937807i	$-0.612853\pi$
$251$	−11.0000	−0.694314	−0.347157	+	0.937807i	$0.612853\pi$
$252$	−1.00000	−0.0629941
$253$	−3.00000	−0.188608
$254$	−16.0000	−1.00393
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	7.00000	0.435801
$259$	9.00000	0.559233
$260$	0	0
$261$	9.00000	0.557086
$262$	−3.00000	−0.185341
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	−1.00000	−0.0615457
$265$	10.0000	0.614295
$266$	−1.00000	−0.0613139
$267$	−12.0000	−0.734388
$268$	12.0000	0.733017
$269$	−20.0000	−1.21942	−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−20.0000	−1.21942	−0.609711	+	0.792624i	$0.708714\pi$
$270$	1.00000	0.0608581
$271$	−4.00000	−0.242983	−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000	−0.242983	−0.121491	+	0.992592i	$0.538768\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−15.0000	−0.906183
$275$	−4.00000	−0.241209
$276$	3.00000	0.180579
$277$	−16.0000	−0.961347	−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000	−0.961347	−0.480673	+	0.876900i	$0.659608\pi$
$278$	−12.0000	−0.719712
$279$	4.00000	0.239474
$280$	1.00000	0.0597614
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	−8.00000	−0.476393
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−6.00000	−0.356034
$285$	1.00000	0.0592349
$286$	0	0
$287$	8.00000	0.472225
$288$	1.00000	0.0589256
$289$	−16.0000	−0.941176
$290$	−9.00000	−0.528498
$291$	−2.00000	−0.117242
$292$	11.0000	0.643726
$293$	−26.0000	−1.51894	−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000	−1.51894	−0.759468	+	0.650545i	$0.774541\pi$
$294$	−1.00000	−0.0583212
$295$	6.00000	0.349334
$296$	−9.00000	−0.523114
$297$	−1.00000	−0.0580259
$298$	−6.00000	−0.347571
$299$	0	0
$300$	4.00000	0.230940
$301$	7.00000	0.403473
$302$	1.00000	0.0575435
$303$	−2.00000	−0.114897
$304$	1.00000	0.0573539
$305$	−11.0000	−0.629858
$306$	−1.00000	−0.0571662
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	−1.00000	−0.0569803
$309$	−5.00000	−0.284440
$310$	−4.00000	−0.227185
$311$	−8.00000	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$312$	0	0
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	−21.0000	−1.18510
$315$	1.00000	0.0563436
$316$	−12.0000	−0.675053
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	10.0000	0.560772
$319$	9.00000	0.503903
$320$	−1.00000	−0.0559017
$321$	2.00000	0.111629
$322$	3.00000	0.167183
$323$	−1.00000	−0.0556415
$324$	1.00000	0.0555556
$325$	0	0
$326$	−20.0000	−1.10770
$327$	7.00000	0.387101
$328$	−8.00000	−0.441726
$329$	−8.00000	−0.441054
$330$	1.00000	0.0550482
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	−6.00000	−0.329293
$333$	−9.00000	−0.493197
$334$	−11.0000	−0.601893
$335$	−12.0000	−0.655630
$336$	1.00000	0.0545545
$337$	−17.0000	−0.926049	−0.463025	−	0.886345i	$-0.653236\pi$
$337$	−17.0000	−0.926049	−0.463025	+	0.886345i	$0.653236\pi$
$338$	0	0
$339$	2.00000	0.108625
$340$	1.00000	0.0542326
$341$	4.00000	0.216612
$342$	1.00000	0.0540738
$343$	−1.00000	−0.0539949
$344$	−7.00000	−0.377415
$345$	−3.00000	−0.161515
$346$	−14.0000	−0.752645
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	−9.00000	−0.482451
$349$	−4.00000	−0.214115	−0.107058	−	0.994253i	$-0.534143\pi$
$349$	−4.00000	−0.214115	−0.107058	+	0.994253i	$0.534143\pi$
$350$	4.00000	0.213809
$351$	0	0
$352$	1.00000	0.0533002
$353$	16.0000	0.851594	0.425797	−	0.904819i	$-0.359994\pi$
$353$	16.0000	0.851594	0.425797	+	0.904819i	$0.359994\pi$
$354$	6.00000	0.318896
$355$	6.00000	0.318447
$356$	12.0000	0.635999
$357$	−1.00000	−0.0529256
$358$	18.0000	0.951330
$359$	30.0000	1.58334	0.791670	−	0.610949i	$-0.209212\pi$
$359$	30.0000	1.58334	0.791670	+	0.610949i	$0.209212\pi$
$360$	−1.00000	−0.0527046
$361$	−18.0000	−0.947368
$362$	2.00000	0.105118
$363$	10.0000	0.524864
$364$	0	0
$365$	−11.0000	−0.575766
$366$	−11.0000	−0.574979
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	−3.00000	−0.156386
$369$	−8.00000	−0.416463
$370$	9.00000	0.467888
$371$	10.0000	0.519174
$372$	−4.00000	−0.207390
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	−1.00000	−0.0517088
$375$	−9.00000	−0.464758
$376$	8.00000	0.412568
$377$	0	0
$378$	1.00000	0.0514344
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	−1.00000	−0.0512989
$381$	16.0000	0.819705
$382$	−11.0000	−0.562809
$383$	−35.0000	−1.78842	−0.894208	−	0.447651i	$-0.852261\pi$
$383$	−35.0000	−1.78842	−0.894208	+	0.447651i	$0.852261\pi$
$384$	−1.00000	−0.0510310
$385$	1.00000	0.0509647
$386$	−12.0000	−0.610784
$387$	−7.00000	−0.355830
$388$	2.00000	0.101535
$389$	−2.00000	−0.101404	−0.0507020	−	0.998714i	$-0.516146\pi$
$389$	−2.00000	−0.101404	−0.0507020	+	0.998714i	$0.516146\pi$
$390$	0	0
$391$	3.00000	0.151717
$392$	1.00000	0.0505076
$393$	3.00000	0.151330
$394$	2.00000	0.100759
$395$	12.0000	0.603786
$396$	1.00000	0.0502519
$397$	4.00000	0.200754	0.100377	−	0.994949i	$-0.467995\pi$
$397$	4.00000	0.200754	0.100377	+	0.994949i	$0.467995\pi$
$398$	−5.00000	−0.250627
$399$	1.00000	0.0500626
$400$	−4.00000	−0.200000
$401$	14.0000	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$402$	−12.0000	−0.598506
$403$	0	0
$404$	2.00000	0.0995037
$405$	−1.00000	−0.0496904
$406$	−9.00000	−0.446663
$407$	−9.00000	−0.446113
$408$	1.00000	0.0495074
$409$	−27.0000	−1.33506	−0.667532	−	0.744581i	$-0.732649\pi$
$409$	−27.0000	−1.33506	−0.667532	+	0.744581i	$0.732649\pi$
$410$	8.00000	0.395092
$411$	15.0000	0.739895
$412$	5.00000	0.246332
$413$	6.00000	0.295241
$414$	−3.00000	−0.147442
$415$	6.00000	0.294528
$416$	0	0
$417$	12.0000	0.587643
$418$	1.00000	0.0489116
$419$	23.0000	1.12362	0.561812	−	0.827265i	$-0.310105\pi$
$419$	23.0000	1.12362	0.561812	+	0.827265i	$0.310105\pi$
$420$	−1.00000	−0.0487950
$421$	−22.0000	−1.07221	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000	−1.07221	−0.536107	+	0.844150i	$0.680106\pi$
$422$	−5.00000	−0.243396
$423$	8.00000	0.388973
$424$	−10.0000	−0.485643
$425$	4.00000	0.194029
$426$	6.00000	0.290701
$427$	−11.0000	−0.532327
$428$	−2.00000	−0.0966736
$429$	0	0
$430$	7.00000	0.337570
$431$	18.0000	0.867029	0.433515	−	0.901146i	$-0.357273\pi$
$431$	18.0000	0.867029	0.433515	+	0.901146i	$0.357273\pi$
$432$	−1.00000	−0.0481125
$433$	−4.00000	−0.192228	−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000	−0.192228	−0.0961139	+	0.995370i	$0.530641\pi$
$434$	−4.00000	−0.192006
$435$	9.00000	0.431517
$436$	−7.00000	−0.335239
$437$	−3.00000	−0.143509
$438$	−11.0000	−0.525600
$439$	33.0000	1.57500	0.787502	−	0.616312i	$-0.211374\pi$
$439$	33.0000	1.57500	0.787502	+	0.616312i	$0.211374\pi$
$440$	−1.00000	−0.0476731
$441$	1.00000	0.0476190
$442$	0	0
$443$	−6.00000	−0.285069	−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000	−0.285069	−0.142534	+	0.989790i	$0.545525\pi$
$444$	9.00000	0.427121
$445$	−12.0000	−0.568855
$446$	8.00000	0.378811
$447$	6.00000	0.283790
$448$	−1.00000	−0.0472456
$449$	−15.0000	−0.707894	−0.353947	−	0.935266i	$-0.615161\pi$
$449$	−15.0000	−0.707894	−0.353947	+	0.935266i	$0.615161\pi$
$450$	−4.00000	−0.188562
$451$	−8.00000	−0.376705
$452$	−2.00000	−0.0940721
$453$	−1.00000	−0.0469841
$454$	12.0000	0.563188
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	−4.00000	−0.187112	−0.0935561	−	0.995614i	$-0.529823\pi$
$457$	−4.00000	−0.187112	−0.0935561	+	0.995614i	$0.529823\pi$
$458$	2.00000	0.0934539
$459$	1.00000	0.0466760
$460$	3.00000	0.139876
$461$	−3.00000	−0.139724	−0.0698620	−	0.997557i	$-0.522256\pi$
$461$	−3.00000	−0.139724	−0.0698620	+	0.997557i	$0.522256\pi$
$462$	1.00000	0.0465242
$463$	29.0000	1.34774	0.673872	−	0.738848i	$-0.264630\pi$
$463$	29.0000	1.34774	0.673872	+	0.738848i	$0.264630\pi$
$464$	9.00000	0.417815
$465$	4.00000	0.185496
$466$	18.0000	0.833834
$467$	37.0000	1.71216	0.856078	−	0.516847i	$-0.172894\pi$
$467$	37.0000	1.71216	0.856078	+	0.516847i	$0.172894\pi$
$468$	0	0
$469$	−12.0000	−0.554109
$470$	−8.00000	−0.369012
$471$	21.0000	0.967629
$472$	−6.00000	−0.276172
$473$	−7.00000	−0.321860
$474$	12.0000	0.551178
$475$	−4.00000	−0.183533
$476$	1.00000	0.0458349
$477$	−10.0000	−0.457869
$478$	8.00000	0.365911
$479$	39.0000	1.78196	0.890978	−	0.454047i	$-0.150020\pi$
$479$	39.0000	1.78196	0.890978	+	0.454047i	$0.150020\pi$
$480$	1.00000	0.0456435
$481$	0	0
$482$	10.0000	0.455488
$483$	−3.00000	−0.136505
$484$	−10.0000	−0.454545
$485$	−2.00000	−0.0908153
$486$	−1.00000	−0.0453609
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	11.0000	0.497947
$489$	20.0000	0.904431
$490$	−1.00000	−0.0451754
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	8.00000	0.360668
$493$	−9.00000	−0.405340
$494$	0	0
$495$	−1.00000	−0.0449467
$496$	4.00000	0.179605
$497$	6.00000	0.269137
$498$	6.00000	0.268866
$499$	10.0000	0.447661	0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000	0.447661	0.223831	+	0.974628i	$0.428144\pi$
$500$	9.00000	0.402492
$501$	11.0000	0.491444
$502$	−11.0000	−0.490954
$503$	−38.0000	−1.69434	−0.847168	−	0.531325i	$-0.821694\pi$
$503$	−38.0000	−1.69434	−0.847168	+	0.531325i	$0.821694\pi$
$504$	−1.00000	−0.0445435
$505$	−2.00000	−0.0889988
$506$	−3.00000	−0.133366
$507$	0	0
$508$	−16.0000	−0.709885
$509$	37.0000	1.64000	0.819998	−	0.572366i	$-0.193974\pi$
$509$	37.0000	1.64000	0.819998	+	0.572366i	$0.193974\pi$
$510$	−1.00000	−0.0442807
$511$	−11.0000	−0.486611
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	−14.0000	−0.617514
$515$	−5.00000	−0.220326
$516$	7.00000	0.308158
$517$	8.00000	0.351840
$518$	9.00000	0.395437
$519$	14.0000	0.614532
$520$	0	0
$521$	−31.0000	−1.35813	−0.679067	−	0.734076i	$-0.737616\pi$
$521$	−31.0000	−1.35813	−0.679067	+	0.734076i	$0.737616\pi$
$522$	9.00000	0.393919
$523$	−36.0000	−1.57417	−0.787085	−	0.616844i	$-0.788411\pi$
$523$	−36.0000	−1.57417	−0.787085	+	0.616844i	$0.788411\pi$
$524$	−3.00000	−0.131056
$525$	−4.00000	−0.174574
$526$	16.0000	0.697633
$527$	−4.00000	−0.174243
$528$	−1.00000	−0.0435194
$529$	−14.0000	−0.608696
$530$	10.0000	0.434372
$531$	−6.00000	−0.260378
$532$	−1.00000	−0.0433555
$533$	0	0
$534$	−12.0000	−0.519291
$535$	2.00000	0.0864675
$536$	12.0000	0.518321
$537$	−18.0000	−0.776757
$538$	−20.0000	−0.862261
$539$	1.00000	0.0430730
$540$	1.00000	0.0430331
$541$	41.0000	1.76273	0.881364	−	0.472438i	$-0.156626\pi$
$541$	41.0000	1.76273	0.881364	+	0.472438i	$0.156626\pi$
$542$	−4.00000	−0.171815
$543$	−2.00000	−0.0858282
$544$	−1.00000	−0.0428746
$545$	7.00000	0.299847
$546$	0	0
$547$	−28.0000	−1.19719	−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000	−1.19719	−0.598597	+	0.801050i	$0.704275\pi$
$548$	−15.0000	−0.640768
$549$	11.0000	0.469469
$550$	−4.00000	−0.170561
$551$	9.00000	0.383413
$552$	3.00000	0.127688
$553$	12.0000	0.510292
$554$	−16.0000	−0.679775
$555$	−9.00000	−0.382029
$556$	−12.0000	−0.508913
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	4.00000	0.169334
$559$	0	0
$560$	1.00000	0.0422577
$561$	1.00000	0.0422200
$562$	−22.0000	−0.928014
$563$	−11.0000	−0.463595	−0.231797	−	0.972764i	$-0.574461\pi$
$563$	−11.0000	−0.463595	−0.231797	+	0.972764i	$0.574461\pi$
$564$	−8.00000	−0.336861
$565$	2.00000	0.0841406
$566$	14.0000	0.588464
$567$	−1.00000	−0.0419961
$568$	−6.00000	−0.251754
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	1.00000	0.0418854
$571$	−32.0000	−1.33916	−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000	−1.33916	−0.669579	+	0.742741i	$0.733526\pi$
$572$	0	0
$573$	11.0000	0.459532
$574$	8.00000	0.333914
$575$	12.0000	0.500435
$576$	1.00000	0.0416667
$577$	18.0000	0.749350	0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000	0.749350	0.374675	+	0.927156i	$0.377754\pi$
$578$	−16.0000	−0.665512
$579$	12.0000	0.498703
$580$	−9.00000	−0.373705
$581$	6.00000	0.248922
$582$	−2.00000	−0.0829027
$583$	−10.0000	−0.414158
$584$	11.0000	0.455183
$585$	0	0
$586$	−26.0000	−1.07405
$587$	16.0000	0.660391	0.330195	−	0.943913i	$-0.392885\pi$
$587$	16.0000	0.660391	0.330195	+	0.943913i	$0.392885\pi$
$588$	−1.00000	−0.0412393
$589$	4.00000	0.164817
$590$	6.00000	0.247016
$591$	−2.00000	−0.0822690
$592$	−9.00000	−0.369898
$593$	−28.0000	−1.14982	−0.574911	−	0.818216i	$-0.694963\pi$
$593$	−28.0000	−1.14982	−0.574911	+	0.818216i	$0.694963\pi$
$594$	−1.00000	−0.0410305
$595$	−1.00000	−0.0409960
$596$	−6.00000	−0.245770
$597$	5.00000	0.204636
$598$	0	0
$599$	39.0000	1.59350	0.796748	−	0.604311i	$-0.206552\pi$
$599$	39.0000	1.59350	0.796748	+	0.604311i	$0.206552\pi$
$600$	4.00000	0.163299
$601$	−16.0000	−0.652654	−0.326327	−	0.945257i	$-0.605811\pi$
$601$	−16.0000	−0.652654	−0.326327	+	0.945257i	$0.605811\pi$
$602$	7.00000	0.285299
$603$	12.0000	0.488678
$604$	1.00000	0.0406894
$605$	10.0000	0.406558
$606$	−2.00000	−0.0812444
$607$	1.00000	0.0405887	0.0202944	−	0.999794i	$-0.493540\pi$
$607$	1.00000	0.0405887	0.0202944	+	0.999794i	$0.493540\pi$
$608$	1.00000	0.0405554
$609$	9.00000	0.364698
$610$	−11.0000	−0.445377
$611$	0	0
$612$	−1.00000	−0.0404226
$613$	17.0000	0.686624	0.343312	−	0.939222i	$-0.388451\pi$
$613$	17.0000	0.686624	0.343312	+	0.939222i	$0.388451\pi$
$614$	−8.00000	−0.322854
$615$	−8.00000	−0.322591
$616$	−1.00000	−0.0402911
$617$	19.0000	0.764911	0.382456	−	0.923974i	$-0.375078\pi$
$617$	19.0000	0.764911	0.382456	+	0.923974i	$0.375078\pi$
$618$	−5.00000	−0.201129
$619$	21.0000	0.844061	0.422031	−	0.906582i	$-0.361317\pi$
$619$	21.0000	0.844061	0.422031	+	0.906582i	$0.361317\pi$
$620$	−4.00000	−0.160644
$621$	3.00000	0.120386
$622$	−8.00000	−0.320771
$623$	−12.0000	−0.480770
$624$	0	0
$625$	11.0000	0.440000
$626$	−14.0000	−0.559553
$627$	−1.00000	−0.0399362
$628$	−21.0000	−0.837991
$629$	9.00000	0.358854
$630$	1.00000	0.0398410
$631$	29.0000	1.15447	0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000	1.15447	0.577236	+	0.816577i	$0.304131\pi$
$632$	−12.0000	−0.477334
$633$	5.00000	0.198732
$634$	12.0000	0.476581
$635$	16.0000	0.634941
$636$	10.0000	0.396526
$637$	0	0
$638$	9.00000	0.356313
$639$	−6.00000	−0.237356
$640$	−1.00000	−0.0395285
$641$	44.0000	1.73790	0.868948	−	0.494904i	$-0.164797\pi$
$641$	44.0000	1.73790	0.868948	+	0.494904i	$0.164797\pi$
$642$	2.00000	0.0789337
$643$	19.0000	0.749287	0.374643	−	0.927169i	$-0.377765\pi$
$643$	19.0000	0.749287	0.374643	+	0.927169i	$0.377765\pi$
$644$	3.00000	0.118217
$645$	−7.00000	−0.275625
$646$	−1.00000	−0.0393445
$647$	−42.0000	−1.65119	−0.825595	−	0.564263i	$-0.809160\pi$
$647$	−42.0000	−1.65119	−0.825595	+	0.564263i	$0.809160\pi$
$648$	1.00000	0.0392837
$649$	−6.00000	−0.235521
$650$	0	0
$651$	4.00000	0.156772
$652$	−20.0000	−0.783260
$653$	−13.0000	−0.508729	−0.254365	−	0.967108i	$-0.581866\pi$
$653$	−13.0000	−0.508729	−0.254365	+	0.967108i	$0.581866\pi$
$654$	7.00000	0.273722
$655$	3.00000	0.117220
$656$	−8.00000	−0.312348
$657$	11.0000	0.429151
$658$	−8.00000	−0.311872
$659$	−30.0000	−1.16863	−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000	−1.16863	−0.584317	+	0.811525i	$0.698638\pi$
$660$	1.00000	0.0389249
$661$	26.0000	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$662$	8.00000	0.310929
$663$	0	0
$664$	−6.00000	−0.232845
$665$	1.00000	0.0387783
$666$	−9.00000	−0.348743
$667$	−27.0000	−1.04544
$668$	−11.0000	−0.425603
$669$	−8.00000	−0.309298
$670$	−12.0000	−0.463600
$671$	11.0000	0.424650
$672$	1.00000	0.0385758
$673$	−29.0000	−1.11787	−0.558934	−	0.829212i	$-0.688789\pi$
$673$	−29.0000	−1.11787	−0.558934	+	0.829212i	$0.688789\pi$
$674$	−17.0000	−0.654816
$675$	4.00000	0.153960
$676$	0	0
$677$	32.0000	1.22986	0.614930	−	0.788582i	$-0.289184\pi$
$677$	32.0000	1.22986	0.614930	+	0.788582i	$0.289184\pi$
$678$	2.00000	0.0768095
$679$	−2.00000	−0.0767530
$680$	1.00000	0.0383482
$681$	−12.0000	−0.459841
$682$	4.00000	0.153168
$683$	19.0000	0.727015	0.363507	−	0.931591i	$-0.381579\pi$
$683$	19.0000	0.727015	0.363507	+	0.931591i	$0.381579\pi$
$684$	1.00000	0.0382360
$685$	15.0000	0.573121
$686$	−1.00000	−0.0381802
$687$	−2.00000	−0.0763048
$688$	−7.00000	−0.266872
$689$	0	0
$690$	−3.00000	−0.114208
$691$	40.0000	1.52167	0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000	1.52167	0.760836	+	0.648944i	$0.224789\pi$
$692$	−14.0000	−0.532200
$693$	−1.00000	−0.0379869
$694$	0	0
$695$	12.0000	0.455186
$696$	−9.00000	−0.341144
$697$	8.00000	0.303022
$698$	−4.00000	−0.151402
$699$	−18.0000	−0.680823
$700$	4.00000	0.151186
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	0	0
$703$	−9.00000	−0.339441
$704$	1.00000	0.0376889
$705$	8.00000	0.301297
$706$	16.0000	0.602168
$707$	−2.00000	−0.0752177
$708$	6.00000	0.225494
$709$	−14.0000	−0.525781	−0.262891	−	0.964826i	$-0.584676\pi$
$709$	−14.0000	−0.525781	−0.262891	+	0.964826i	$0.584676\pi$
$710$	6.00000	0.225176
$711$	−12.0000	−0.450035
$712$	12.0000	0.449719
$713$	−12.0000	−0.449404
$714$	−1.00000	−0.0374241
$715$	0	0
$716$	18.0000	0.672692
$717$	−8.00000	−0.298765
$718$	30.0000	1.11959
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	−1.00000	−0.0372678
$721$	−5.00000	−0.186210
$722$	−18.0000	−0.669891
$723$	−10.0000	−0.371904
$724$	2.00000	0.0743294
$725$	−36.0000	−1.33701
$726$	10.0000	0.371135
$727$	−23.0000	−0.853023	−0.426511	−	0.904482i	$-0.640258\pi$
$727$	−23.0000	−0.853023	−0.426511	+	0.904482i	$0.640258\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−11.0000	−0.407128
$731$	7.00000	0.258904
$732$	−11.0000	−0.406572
$733$	40.0000	1.47743	0.738717	−	0.674016i	$-0.235432\pi$
$733$	40.0000	1.47743	0.738717	+	0.674016i	$0.235432\pi$
$734$	−8.00000	−0.295285
$735$	1.00000	0.0368856
$736$	−3.00000	−0.110581
$737$	12.0000	0.442026
$738$	−8.00000	−0.294484
$739$	8.00000	0.294285	0.147142	−	0.989115i	$-0.452992\pi$
$739$	8.00000	0.294285	0.147142	+	0.989115i	$0.452992\pi$
$740$	9.00000	0.330847
$741$	0	0
$742$	10.0000	0.367112
$743$	36.0000	1.32071	0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000	1.32071	0.660356	+	0.750953i	$0.270405\pi$
$744$	−4.00000	−0.146647
$745$	6.00000	0.219823
$746$	−14.0000	−0.512576
$747$	−6.00000	−0.219529
$748$	−1.00000	−0.0365636
$749$	2.00000	0.0730784
$750$	−9.00000	−0.328634
$751$	−20.0000	−0.729810	−0.364905	−	0.931045i	$-0.618899\pi$
$751$	−20.0000	−0.729810	−0.364905	+	0.931045i	$0.618899\pi$
$752$	8.00000	0.291730
$753$	11.0000	0.400862
$754$	0	0
$755$	−1.00000	−0.0363937
$756$	1.00000	0.0363696
$757$	38.0000	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$758$	−16.0000	−0.581146
$759$	3.00000	0.108893
$760$	−1.00000	−0.0362738
$761$	−42.0000	−1.52250	−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000	−1.52250	−0.761249	+	0.648459i	$0.775414\pi$
$762$	16.0000	0.579619
$763$	7.00000	0.253417
$764$	−11.0000	−0.397966
$765$	1.00000	0.0361551
$766$	−35.0000	−1.26460
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−31.0000	−1.11789	−0.558944	−	0.829205i	$-0.688793\pi$
$769$	−31.0000	−1.11789	−0.558944	+	0.829205i	$0.688793\pi$
$770$	1.00000	0.0360375
$771$	14.0000	0.504198
$772$	−12.0000	−0.431889
$773$	−19.0000	−0.683383	−0.341691	−	0.939812i	$-0.611000\pi$
$773$	−19.0000	−0.683383	−0.341691	+	0.939812i	$0.611000\pi$
$774$	−7.00000	−0.251610
$775$	−16.0000	−0.574737
$776$	2.00000	0.0717958
$777$	−9.00000	−0.322873
$778$	−2.00000	−0.0717035
$779$	−8.00000	−0.286630
$780$	0	0
$781$	−6.00000	−0.214697
$782$	3.00000	0.107280
$783$	−9.00000	−0.321634
$784$	1.00000	0.0357143
$785$	21.0000	0.749522
$786$	3.00000	0.107006
$787$	53.0000	1.88925	0.944623	−	0.328158i	$-0.106428\pi$
$787$	53.0000	1.88925	0.944623	+	0.328158i	$0.106428\pi$
$788$	2.00000	0.0712470
$789$	−16.0000	−0.569615
$790$	12.0000	0.426941
$791$	2.00000	0.0711118
$792$	1.00000	0.0355335
$793$	0	0
$794$	4.00000	0.141955
$795$	−10.0000	−0.354663
$796$	−5.00000	−0.177220
$797$	−2.00000	−0.0708436	−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000	−0.0708436	−0.0354218	+	0.999372i	$0.511277\pi$
$798$	1.00000	0.0353996
$799$	−8.00000	−0.283020
$800$	−4.00000	−0.141421
$801$	12.0000	0.423999
$802$	14.0000	0.494357
$803$	11.0000	0.388182
$804$	−12.0000	−0.423207
$805$	−3.00000	−0.105736
$806$	0	0
$807$	20.0000	0.704033
$808$	2.00000	0.0703598
$809$	−4.00000	−0.140633	−0.0703163	−	0.997525i	$-0.522401\pi$
$809$	−4.00000	−0.140633	−0.0703163	+	0.997525i	$0.522401\pi$
$810$	−1.00000	−0.0351364
$811$	21.0000	0.737410	0.368705	−	0.929547i	$-0.379801\pi$
$811$	21.0000	0.737410	0.368705	+	0.929547i	$0.379801\pi$
$812$	−9.00000	−0.315838
$813$	4.00000	0.140286
$814$	−9.00000	−0.315450
$815$	20.0000	0.700569
$816$	1.00000	0.0350070
$817$	−7.00000	−0.244899
$818$	−27.0000	−0.944033
$819$	0	0
$820$	8.00000	0.279372
$821$	−36.0000	−1.25641	−0.628204	−	0.778048i	$-0.716210\pi$
$821$	−36.0000	−1.25641	−0.628204	+	0.778048i	$0.716210\pi$
$822$	15.0000	0.523185
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	5.00000	0.174183
$825$	4.00000	0.139262
$826$	6.00000	0.208767
$827$	−3.00000	−0.104320	−0.0521601	−	0.998639i	$-0.516611\pi$
$827$	−3.00000	−0.104320	−0.0521601	+	0.998639i	$0.516611\pi$
$828$	−3.00000	−0.104257
$829$	−25.0000	−0.868286	−0.434143	−	0.900844i	$-0.642949\pi$
$829$	−25.0000	−0.868286	−0.434143	+	0.900844i	$0.642949\pi$
$830$	6.00000	0.208263
$831$	16.0000	0.555034
$832$	0	0
$833$	−1.00000	−0.0346479
$834$	12.0000	0.415526
$835$	11.0000	0.380671
$836$	1.00000	0.0345857
$837$	−4.00000	−0.138260
$838$	23.0000	0.794522
$839$	52.0000	1.79524	0.897620	−	0.440771i	$-0.145295\pi$
$839$	52.0000	1.79524	0.897620	+	0.440771i	$0.145295\pi$
$840$	−1.00000	−0.0345033
$841$	52.0000	1.79310
$842$	−22.0000	−0.758170
$843$	22.0000	0.757720
$844$	−5.00000	−0.172107
$845$	0	0
$846$	8.00000	0.275046
$847$	10.0000	0.343604
$848$	−10.0000	−0.343401
$849$	−14.0000	−0.480479
$850$	4.00000	0.137199
$851$	27.0000	0.925548
$852$	6.00000	0.205557
$853$	−56.0000	−1.91740	−0.958702	−	0.284413i	$-0.908201\pi$
$853$	−56.0000	−1.91740	−0.958702	+	0.284413i	$0.908201\pi$
$854$	−11.0000	−0.376412
$855$	−1.00000	−0.0341993
$856$	−2.00000	−0.0683586
$857$	22.0000	0.751506	0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000	0.751506	0.375753	+	0.926720i	$0.377384\pi$
$858$	0	0
$859$	10.0000	0.341196	0.170598	−	0.985341i	$-0.445430\pi$
$859$	10.0000	0.341196	0.170598	+	0.985341i	$0.445430\pi$
$860$	7.00000	0.238698
$861$	−8.00000	−0.272639
$862$	18.0000	0.613082
$863$	−48.0000	−1.63394	−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000	−1.63394	−0.816970	+	0.576681i	$0.804348\pi$
$864$	−1.00000	−0.0340207
$865$	14.0000	0.476014
$866$	−4.00000	−0.135926
$867$	16.0000	0.543388
$868$	−4.00000	−0.135769
$869$	−12.0000	−0.407072
$870$	9.00000	0.305129
$871$	0	0
$872$	−7.00000	−0.237050
$873$	2.00000	0.0676897
$874$	−3.00000	−0.101477
$875$	−9.00000	−0.304256
$876$	−11.0000	−0.371656
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	33.0000	1.11370
$879$	26.0000	0.876958
$880$	−1.00000	−0.0337100
$881$	59.0000	1.98776	0.993880	−	0.110463i	$-0.0352333\pi$
$881$	59.0000	1.98776	0.993880	+	0.110463i	$0.0352333\pi$
$882$	1.00000	0.0336718
$883$	−31.0000	−1.04323	−0.521617	−	0.853180i	$-0.674671\pi$
$883$	−31.0000	−1.04323	−0.521617	+	0.853180i	$0.674671\pi$
$884$	0	0
$885$	−6.00000	−0.201688
$886$	−6.00000	−0.201574
$887$	2.00000	0.0671534	0.0335767	−	0.999436i	$-0.489310\pi$
$887$	2.00000	0.0671534	0.0335767	+	0.999436i	$0.489310\pi$
$888$	9.00000	0.302020
$889$	16.0000	0.536623
$890$	−12.0000	−0.402241
$891$	1.00000	0.0335013
$892$	8.00000	0.267860
$893$	8.00000	0.267710
$894$	6.00000	0.200670
$895$	−18.0000	−0.601674
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−15.0000	−0.500556
$899$	36.0000	1.20067
$900$	−4.00000	−0.133333
$901$	10.0000	0.333148
$902$	−8.00000	−0.266371
$903$	−7.00000	−0.232945
$904$	−2.00000	−0.0665190
$905$	−2.00000	−0.0664822
$906$	−1.00000	−0.0332228
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	12.0000	0.398234
$909$	2.00000	0.0663358
$910$	0	0
$911$	−29.0000	−0.960813	−0.480406	−	0.877046i	$-0.659511\pi$
$911$	−29.0000	−0.960813	−0.480406	+	0.877046i	$0.659511\pi$
$912$	−1.00000	−0.0331133
$913$	−6.00000	−0.198571
$914$	−4.00000	−0.132308
$915$	11.0000	0.363649
$916$	2.00000	0.0660819
$917$	3.00000	0.0990687
$918$	1.00000	0.0330049
$919$	34.0000	1.12156	0.560778	−	0.827966i	$-0.310502\pi$
$919$	34.0000	1.12156	0.560778	+	0.827966i	$0.310502\pi$
$920$	3.00000	0.0989071
$921$	8.00000	0.263609
$922$	−3.00000	−0.0987997
$923$	0	0
$924$	1.00000	0.0328976
$925$	36.0000	1.18367
$926$	29.0000	0.952999
$927$	5.00000	0.164222
$928$	9.00000	0.295439
$929$	26.0000	0.853032	0.426516	−	0.904480i	$-0.359741\pi$
$929$	26.0000	0.853032	0.426516	+	0.904480i	$0.359741\pi$
$930$	4.00000	0.131165
$931$	1.00000	0.0327737
$932$	18.0000	0.589610
$933$	8.00000	0.261908
$934$	37.0000	1.21068
$935$	1.00000	0.0327035
$936$	0	0
$937$	−20.0000	−0.653372	−0.326686	−	0.945133i	$-0.605932\pi$
$937$	−20.0000	−0.653372	−0.326686	+	0.945133i	$0.605932\pi$
$938$	−12.0000	−0.391814
$939$	14.0000	0.456873
$940$	−8.00000	−0.260931
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	21.0000	0.684217
$943$	24.0000	0.781548
$944$	−6.00000	−0.195283
$945$	−1.00000	−0.0325300
$946$	−7.00000	−0.227590
$947$	−35.0000	−1.13735	−0.568674	−	0.822563i	$-0.692543\pi$
$947$	−35.0000	−1.13735	−0.568674	+	0.822563i	$0.692543\pi$
$948$	12.0000	0.389742
$949$	0	0
$950$	−4.00000	−0.129777
$951$	−12.0000	−0.389127
$952$	1.00000	0.0324102
$953$	42.0000	1.36051	0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000	1.36051	0.680257	+	0.732974i	$0.261868\pi$
$954$	−10.0000	−0.323762
$955$	11.0000	0.355952
$956$	8.00000	0.258738
$957$	−9.00000	−0.290929
$958$	39.0000	1.26003
$959$	15.0000	0.484375
$960$	1.00000	0.0322749
$961$	−15.0000	−0.483871
$962$	0	0
$963$	−2.00000	−0.0644491
$964$	10.0000	0.322078
$965$	12.0000	0.386294
$966$	−3.00000	−0.0965234
$967$	−9.00000	−0.289420	−0.144710	−	0.989474i	$-0.546225\pi$
$967$	−9.00000	−0.289420	−0.144710	+	0.989474i	$0.546225\pi$
$968$	−10.0000	−0.321412
$969$	1.00000	0.0321246
$970$	−2.00000	−0.0642161
$971$	−4.00000	−0.128366	−0.0641831	−	0.997938i	$-0.520444\pi$
$971$	−4.00000	−0.128366	−0.0641831	+	0.997938i	$0.520444\pi$
$972$	−1.00000	−0.0320750
$973$	12.0000	0.384702
$974$	−32.0000	−1.02535
$975$	0	0
$976$	11.0000	0.352101
$977$	39.0000	1.24772	0.623860	−	0.781536i	$-0.285563\pi$
$977$	39.0000	1.24772	0.623860	+	0.781536i	$0.285563\pi$
$978$	20.0000	0.639529
$979$	12.0000	0.383522
$980$	−1.00000	−0.0319438
$981$	−7.00000	−0.223493
$982$	−12.0000	−0.382935
$983$	−9.00000	−0.287055	−0.143528	−	0.989646i	$-0.545845\pi$
$983$	−9.00000	−0.287055	−0.143528	+	0.989646i	$0.545845\pi$
$984$	8.00000	0.255031
$985$	−2.00000	−0.0637253
$986$	−9.00000	−0.286618
$987$	8.00000	0.254643
$988$	0	0
$989$	21.0000	0.667761
$990$	−1.00000	−0.0317821
$991$	−12.0000	−0.381193	−0.190596	−	0.981669i	$-0.561042\pi$
$991$	−12.0000	−0.381193	−0.190596	+	0.981669i	$0.561042\pi$
$992$	4.00000	0.127000
$993$	−8.00000	−0.253872
$994$	6.00000	0.190308
$995$	5.00000	0.158511
$996$	6.00000	0.190117
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	10.0000	0.316544
$999$	9.00000	0.284747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.s.1.1		1
13.5	odd	4		546.2.c.a.337.1	✓	2
13.8	odd	4		546.2.c.a.337.2	yes	2
13.12	even	2		7098.2.a.d.1.1		1
39.5	even	4		1638.2.c.f.883.2		2
39.8	even	4		1638.2.c.f.883.1		2
52.31	even	4		4368.2.h.k.337.2		2
52.47	even	4		4368.2.h.k.337.1		2
91.34	even	4		3822.2.c.e.883.2		2
91.83	even	4		3822.2.c.e.883.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.c.a.337.1	✓	2	13.5	odd	4
546.2.c.a.337.2	yes	2	13.8	odd	4
1638.2.c.f.883.1		2	39.8	even	4
1638.2.c.f.883.2		2	39.5	even	4
3822.2.c.e.883.1		2	91.83	even	4
3822.2.c.e.883.2		2	91.34	even	4
4368.2.h.k.337.1		2	52.47	even	4
4368.2.h.k.337.2		2	52.31	even	4
7098.2.a.d.1.1		1	13.12	even	2
7098.2.a.s.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

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