LMFDB - Embedded newform 169.10.a.f.1.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [169,10,Mod(1,169)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("169.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(169, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

Level:	$N$	$=$	$169 = 13^{2}$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	169.a (trivial)

Newform invariants

comment:select newform

sage:traces = [20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$87.0410563117$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} - 7679 x^{18} + 24599364 x^{16} - 42662336000 x^{14} + 43527566862400 x^{12} + \cdots + 25\!\cdots\!36$ x^20 - 7679x^18 + 24599364x^16 - 42662336000x^14 + 43527566862400x^12 - 26625453181634304x^10 + 9550565219960082432x^8 - 1876223091685443895296x^6 + 172106193081772189679616x^4 - 4841822934658519419322368*x^2 + 25162285487879223389454336
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$2^{25}\cdot 3^{10}\cdot 13^{12}$
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$20.2564$ of defining polynomial
Character	$\chi$	$=$	169.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+20.2564 q^{2} -99.3079 q^{3} -101.676 q^{4} +1799.37 q^{5} -2011.63 q^{6} -1935.26 q^{7} -12430.9 q^{8} -9820.93 q^{9} +36448.7 q^{10} -53677.8 q^{11} +10097.3 q^{12} -39201.4 q^{14} -178691. q^{15} -199748. q^{16} +396185. q^{17} -198937. q^{18} +503022. q^{19} -182953. q^{20} +192186. q^{21} -1.08732e6 q^{22} -1.19761e6 q^{23} +1.23449e6 q^{24} +1.28459e6 q^{25} +2.92997e6 q^{27} +196770. q^{28} -4.89369e6 q^{29} -3.61965e6 q^{30} +2.72295e6 q^{31} +2.31845e6 q^{32} +5.33063e6 q^{33} +8.02531e6 q^{34} -3.48223e6 q^{35} +998558. q^{36} -6.11067e6 q^{37} +1.01894e7 q^{38} -2.23677e7 q^{40} +2.63954e7 q^{41} +3.89301e6 q^{42} +1.72494e7 q^{43} +5.45777e6 q^{44} -1.76714e7 q^{45} -2.42594e7 q^{46} -1.60235e7 q^{47} +1.98365e7 q^{48} -3.66084e7 q^{49} +2.60213e7 q^{50} -3.93444e7 q^{51} -4.91716e7 q^{53} +5.93509e7 q^{54} -9.65860e7 q^{55} +2.40570e7 q^{56} -4.99541e7 q^{57} -9.91287e7 q^{58} +4.85011e7 q^{59} +1.81687e7 q^{60} +1.31634e8 q^{61} +5.51574e7 q^{62} +1.90060e7 q^{63} +1.49234e8 q^{64} +1.07980e8 q^{66} +1.25404e8 q^{67} -4.02827e7 q^{68} +1.18932e8 q^{69} -7.05377e7 q^{70} +3.00073e8 q^{71} +1.22083e8 q^{72} +2.58604e8 q^{73} -1.23780e8 q^{74} -1.27570e8 q^{75} -5.11455e7 q^{76} +1.03880e8 q^{77} +8.39745e7 q^{79} -3.59419e8 q^{80} -9.76644e7 q^{81} +5.34677e8 q^{82} +3.52165e8 q^{83} -1.95408e7 q^{84} +7.12882e8 q^{85} +3.49411e8 q^{86} +4.85982e8 q^{87} +6.67264e8 q^{88} +1.14069e9 q^{89} -3.57961e8 q^{90} +1.21769e8 q^{92} -2.70411e8 q^{93} -3.24579e8 q^{94} +9.05120e8 q^{95} -2.30240e8 q^{96} -1.39071e9 q^{97} -7.41556e8 q^{98} +5.27166e8 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 326 q^{3} + 5118 q^{4} + 129526 q^{9} + 88390 q^{10} + 427652 q^{12} + 473556 q^{14} + 1189618 q^{16} - 99312 q^{17} - 5073532 q^{22} + 6252378 q^{23} + 1529274 q^{25} + 18052718 q^{27} + 5424828 q^{29}+ \cdots + 9251202540 q^{95}+O(q^{100})$ 20 * q + 326 * q^3 + 5118 * q^4 + 129526 * q^9 + 88390 * q^10 + 427652 * q^12 + 473556 * q^14 + 1189618 * q^16 - 99312 * q^17 - 5073532 * q^22 + 6252378 * q^23 + 1529274 * q^25 + 18052718 * q^27 + 5424828 * q^29 + 30045516 * q^30 - 15098160 * q^35 + 54078886 * q^36 + 39021096 * q^38 + 134360674 * q^40 + 121600068 * q^42 + 53242058 * q^43 + 82771076 * q^48 + 14055298 * q^49 + 10208934 * q^51 - 36429786 * q^53 - 131454160 * q^55 + 127272672 * q^56 + 536425792 * q^61 - 890759796 * q^62 - 343337066 * q^64 - 445758060 * q^66 + 336594090 * q^68 + 1083885582 * q^69 + 1083869262 * q^74 - 1218826882 * q^75 + 1470187374 * q^77 + 1556703616 * q^79 + 2139127516 * q^81 + 3719322754 * q^82 + 1288246146 * q^87 - 4109160928 * q^88 + 6489878934 * q^90 + 10148843820 * q^92 + 4894712828 * q^94 + 9251202540 * q^95

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

)

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

$2$	20.2564	0.895217	0.447608	−	0.894230i	$-0.352276\pi$
$2$	20.2564	0.895217	0.447608	+	0.894230i	$0.352276\pi$
$3$	−99.3079	−0.707845	−0.353923	−	0.935275i	$-0.615152\pi$
$3$	−99.3079	−0.707845	−0.353923	+	0.935275i	$0.615152\pi$
$4$	−101.676	−0.198587
$5$	1799.37	1.28752	0.643761	−	0.765227i	$-0.277373\pi$
$5$	1799.37	1.28752	0.643761	+	0.765227i	$0.277373\pi$
$6$	−2011.63	−0.633675
$7$	−1935.26	−0.304647	−0.152324	−	0.988331i	$-0.548676\pi$
$7$	−1935.26	−0.304647	−0.152324	+	0.988331i	$0.548676\pi$
$8$	−12430.9	−1.07300
$9$	−9820.93	−0.498955
$10$	36448.7	1.15261
$11$	−53677.8	−1.10542	−0.552711	−	0.833373i	$-0.686407\pi$
$11$	−53677.8	−1.10542	−0.552711	+	0.833373i	$0.686407\pi$
$12$	10097.3	0.140569
$13$	0	0
$13$	0	0
$14$	−39201.4	−0.272725
$15$	−178691.	−0.911366
$16$	−199748.	−0.761976
$17$	396185.	1.15048	0.575239	−	0.817985i	$-0.304909\pi$
$17$	396185.	1.15048	0.575239	+	0.817985i	$0.304909\pi$
$18$	−198937.	−0.446673
$19$	503022.	0.885515	0.442757	−	0.896641i	$-0.354000\pi$
$19$	503022.	0.885515	0.442757	+	0.896641i	$0.354000\pi$
$20$	−182953.	−0.255685
$21$	192186.	0.215643
$22$	−1.08732e6	−0.989592
$23$	−1.19761e6	−0.892362	−0.446181	−	0.894943i	$-0.647216\pi$
$23$	−1.19761e6	−0.892362	−0.446181	+	0.894943i	$0.647216\pi$
$24$	1.23449e6	0.759515
$25$	1.28459e6	0.657711
$26$	0	0
$27$	2.92997e6	1.06103
$28$	196770.	0.0604990
$29$	−4.89369e6	−1.28483	−0.642415	−	0.766357i	$-0.722067\pi$
$29$	−4.89369e6	−1.28483	−0.642415	+	0.766357i	$0.722067\pi$
$30$	−3.61965e6	−0.815870
$31$	2.72295e6	0.529557	0.264779	−	0.964309i	$-0.414701\pi$
$31$	2.72295e6	0.529557	0.264779	+	0.964309i	$0.414701\pi$
$32$	2.31845e6	0.390861
$33$	5.33063e6	0.782467
$34$	8.02531e6	1.02993
$35$	−3.48223e6	−0.392240
$36$	998558.	0.0990859
$37$	−6.11067e6	−0.536020	−0.268010	−	0.963416i	$-0.586366\pi$
$37$	−6.11067e6	−0.536020	−0.268010	+	0.963416i	$0.586366\pi$
$38$	1.01894e7	0.792728
$39$	0	0
$40$	−2.23677e7	−1.38150
$41$	2.63954e7	1.45882	0.729409	−	0.684078i	$-0.239795\pi$
$41$	2.63954e7	1.45882	0.729409	+	0.684078i	$0.239795\pi$
$42$	3.89301e6	0.193047
$43$	1.72494e7	0.769423	0.384712	−	0.923037i	$-0.374301\pi$
$43$	1.72494e7	0.769423	0.384712	+	0.923037i	$0.374301\pi$
$44$	5.45777e6	0.219522
$45$	−1.76714e7	−0.642415
$46$	−2.42594e7	−0.798858
$47$	−1.60235e7	−0.478979	−0.239489	−	0.970899i	$-0.576980\pi$
$47$	−1.60235e7	−0.478979	−0.239489	+	0.970899i	$0.576980\pi$
$48$	1.98365e7	0.539361
$49$	−3.66084e7	−0.907190
$50$	2.60213e7	0.588794
$51$	−3.93444e7	−0.814360
$52$	0	0
$53$	−4.91716e7	−0.855998	−0.427999	−	0.903779i	$-0.640781\pi$
$53$	−4.91716e7	−0.855998	−0.427999	+	0.903779i	$0.640781\pi$
$54$	5.93509e7	0.949850
$55$	−9.65860e7	−1.42325
$56$	2.40570e7	0.326885
$57$	−4.99541e7	−0.626807
$58$	−9.91287e7	−1.15020
$59$	4.85011e7	0.521096	0.260548	−	0.965461i	$-0.416097\pi$
$59$	4.85011e7	0.521096	0.260548	+	0.965461i	$0.416097\pi$
$60$	1.81687e7	0.180985
$61$	1.31634e8	1.21726	0.608631	−	0.793454i	$-0.291719\pi$
$61$	1.31634e8	1.21726	0.608631	+	0.793454i	$0.291719\pi$
$62$	5.51574e7	0.474068
$63$	1.90060e7	0.152005
$64$	1.49234e8	1.11188
$65$	0	0
$66$	1.07980e8	0.700478
$67$	1.25404e8	0.760285	0.380142	−	0.924928i	$-0.375875\pi$
$67$	1.25404e8	0.760285	0.380142	+	0.924928i	$0.375875\pi$
$68$	−4.02827e7	−0.228470
$69$	1.18932e8	0.631654
$70$	−7.05377e7	−0.351140
$71$	3.00073e8	1.40141	0.700704	−	0.713452i	$-0.252869\pi$
$71$	3.00073e8	1.40141	0.700704	+	0.713452i	$0.252869\pi$
$72$	1.22083e8	0.535376
$73$	2.58604e8	1.06581	0.532907	−	0.846174i	$-0.321099\pi$
$73$	2.58604e8	1.06581	0.532907	+	0.846174i	$0.321099\pi$
$74$	−1.23780e8	−0.479854
$75$	−1.27570e8	−0.465557
$76$	−5.11455e7	−0.175852
$77$	1.03880e8	0.336764
$78$	0	0
$79$	8.39745e7	0.242564	0.121282	−	0.992618i	$-0.461300\pi$
$79$	8.39745e7	0.242564	0.121282	+	0.992618i	$0.461300\pi$
$80$	−3.59419e8	−0.981061
$81$	−9.76644e7	−0.252089
$82$	5.34677e8	1.30596
$83$	3.52165e8	0.814506	0.407253	−	0.913315i	$-0.366487\pi$
$83$	3.52165e8	0.814506	0.407253	+	0.913315i	$0.366487\pi$
$84$	−1.95408e7	−0.0428239
$85$	7.12882e8	1.48126
$86$	3.49411e8	0.688801
$87$	4.85982e8	0.909460
$88$	6.67264e8	1.18611
$89$	1.14069e9	1.92714	0.963571	−	0.267451i	$-0.0861814\pi$
$89$	1.14069e9	1.92714	0.963571	+	0.267451i	$0.0861814\pi$
$90$	−3.57961e8	−0.575101
$91$	0	0
$92$	1.21769e8	0.177211
$93$	−2.70411e8	−0.374845
$94$	−3.24579e8	−0.428790
$95$	9.05120e8	1.14012
$96$	−2.30240e8	−0.276669
$97$	−1.39071e9	−1.59501	−0.797503	−	0.603315i	$-0.793846\pi$
$97$	−1.39071e9	−1.59501	−0.797503	+	0.603315i	$0.793846\pi$
$98$	−7.41556e8	−0.812132
$99$	5.27166e8	0.551555
$100$	−1.30613e8	−0.130613
$101$	−9.84869e8	−0.941743	−0.470871	−	0.882202i	$-0.656060\pi$
$101$	−9.84869e8	−0.941743	−0.470871	+	0.882202i	$0.656060\pi$
$102$	−7.96977e8	−0.729029
$103$	8.44246e8	0.739097	0.369548	−	0.929211i	$-0.379512\pi$
$103$	8.44246e8	0.739097	0.369548	+	0.929211i	$0.379512\pi$
$104$	0	0
$105$	3.45813e8	0.277645
$106$	−9.96042e8	−0.766304
$107$	2.58204e9	1.90430	0.952151	−	0.305628i	$-0.0988664\pi$
$107$	2.58204e9	1.90430	0.952151	+	0.305628i	$0.0988664\pi$
$108$	−2.97909e8	−0.210706
$109$	4.43075e8	0.300648	0.150324	−	0.988637i	$-0.451968\pi$
$109$	4.43075e8	0.300648	0.150324	+	0.988637i	$0.451968\pi$
$110$	−1.95649e9	−1.27412
$111$	6.06838e8	0.379419
$112$	3.86563e8	0.232134
$113$	2.18556e9	1.26098	0.630491	−	0.776197i	$-0.282854\pi$
$113$	2.18556e9	1.26098	0.630491	+	0.776197i	$0.282854\pi$
$114$	−1.01189e9	−0.561129
$115$	−2.15494e9	−1.14894
$116$	4.97573e8	0.255150
$117$	0	0
$118$	9.82460e8	0.466494
$119$	−7.66720e8	−0.350490
$120$	2.22129e9	0.977891
$121$	5.23361e8	0.221956
$122$	2.66644e9	1.08971
$123$	−2.62127e9	−1.03262
$124$	−2.76860e8	−0.105163
$125$	−1.20294e9	−0.440705
$126$	3.84994e8	0.136078
$127$	−4.65614e9	−1.58821	−0.794107	−	0.607778i	$-0.792061\pi$
$127$	−4.65614e9	−1.58821	−0.794107	+	0.607778i	$0.792061\pi$
$128$	1.83591e9	0.604514
$129$	−1.71300e9	−0.544633
$130$	0	0
$131$	5.42014e9	1.60801	0.804007	−	0.594619i	$-0.202697\pi$
$131$	5.42014e9	1.60801	0.804007	+	0.594619i	$0.202697\pi$
$132$	−5.42000e8	−0.155388
$133$	−9.73477e8	−0.269770
$134$	2.54025e9	0.680620
$135$	5.27210e9	1.36610
$136$	−4.92494e9	−1.23446
$137$	−3.41682e9	−0.828666	−0.414333	−	0.910125i	$-0.635985\pi$
$137$	−3.41682e9	−0.828666	−0.414333	+	0.910125i	$0.635985\pi$
$138$	2.40915e9	0.565468
$139$	−4.70867e9	−1.06987	−0.534936	−	0.844893i	$-0.679664\pi$
$139$	−4.70867e9	−1.06987	−0.534936	+	0.844893i	$0.679664\pi$
$140$	3.54061e8	0.0778937
$141$	1.59126e9	0.339043
$142$	6.07842e9	1.25456
$143$	0	0
$144$	1.96171e9	0.380192
$145$	−8.80554e9	−1.65424
$146$	5.23839e9	0.954135
$147$	3.63550e9	0.642150
$148$	6.21311e8	0.106447
$149$	−5.19976e9	−0.864262	−0.432131	−	0.901811i	$-0.642238\pi$
$149$	−5.19976e9	−0.864262	−0.432131	+	0.901811i	$0.642238\pi$
$150$	−2.58412e9	−0.416775
$151$	9.29610e9	1.45514	0.727570	−	0.686034i	$-0.240650\pi$
$151$	9.29610e9	1.45514	0.727570	+	0.686034i	$0.240650\pi$
$152$	−6.25302e9	−0.950153
$153$	−3.89091e9	−0.574037
$154$	2.10425e9	0.301476
$155$	4.89959e9	0.681816
$156$	0	0
$157$	−3.83536e9	−0.503800	−0.251900	−	0.967753i	$-0.581055\pi$
$157$	−3.83536e9	−0.503800	−0.251900	+	0.967753i	$0.581055\pi$
$158$	1.70103e9	0.217147
$159$	4.88313e9	0.605914
$160$	4.17173e9	0.503242
$161$	2.31769e9	0.271856
$162$	−1.97833e9	−0.225674
$163$	1.21061e10	1.34326	0.671632	−	0.740885i	$-0.265594\pi$
$163$	1.21061e10	1.34326	0.671632	+	0.740885i	$0.265594\pi$
$164$	−2.68379e9	−0.289702
$165$	9.59176e9	1.00744
$166$	7.13361e9	0.729160
$167$	−3.09065e9	−0.307486	−0.153743	−	0.988111i	$-0.549133\pi$
$167$	−3.09065e9	−0.307486	−0.153743	+	0.988111i	$0.549133\pi$
$168$	−2.38905e9	−0.231384
$169$	0	0
$170$	1.44405e10	1.32605
$171$	−4.94014e9	−0.441832
$172$	−1.75386e9	−0.152797
$173$	8.97038e9	0.761383	0.380692	−	0.924702i	$-0.375686\pi$
$173$	8.97038e9	0.761383	0.380692	+	0.924702i	$0.375686\pi$
$174$	9.84427e9	0.814164
$175$	−2.48601e9	−0.200370
$176$	1.07220e10	0.842305
$177$	−4.81654e9	−0.368855
$178$	2.31064e10	1.72521
$179$	−7.56223e9	−0.550569	−0.275284	−	0.961363i	$-0.588772\pi$
$179$	−7.56223e9	−0.550569	−0.275284	+	0.961363i	$0.588772\pi$
$180$	1.79677e9	0.127575
$181$	1.96786e9	0.136283	0.0681414	−	0.997676i	$-0.478293\pi$
$181$	1.96786e9	0.136283	0.0681414	+	0.997676i	$0.478293\pi$
$182$	0	0
$183$	−1.30723e10	−0.861633
$184$	1.48874e10	0.957500
$185$	−1.09953e10	−0.690137
$186$	−5.47757e9	−0.335567
$187$	−2.12664e10	−1.27176
$188$	1.62921e9	0.0951189
$189$	−5.67025e9	−0.323239
$190$	1.83345e10	1.02065
$191$	3.44779e9	0.187452	0.0937260	−	0.995598i	$-0.470122\pi$
$191$	3.44779e9	0.187452	0.0937260	+	0.995598i	$0.470122\pi$
$192$	−1.48201e10	−0.787040
$193$	8.02066e7	0.00416104	0.00208052	−	0.999998i	$-0.499338\pi$
$193$	8.02066e7	0.00416104	0.00208052	+	0.999998i	$0.499338\pi$
$194$	−2.81707e10	−1.42788
$195$	0	0
$196$	3.72221e9	0.180156
$197$	−1.78999e10	−0.846747	−0.423373	−	0.905955i	$-0.639154\pi$
$197$	−1.78999e10	−0.846747	−0.423373	+	0.905955i	$0.639154\pi$
$198$	1.06785e10	0.493762
$199$	1.17170e10	0.529635	0.264818	−	0.964299i	$-0.414688\pi$
$199$	1.17170e10	0.529635	0.264818	+	0.964299i	$0.414688\pi$
$200$	−1.59686e10	−0.705720
$201$	−1.24537e10	−0.538164
$202$	−1.99499e10	−0.843064
$203$	9.47054e9	0.391420
$204$	4.00040e9	0.161721
$205$	4.74950e10	1.87826
$206$	1.71014e10	0.661652
$207$	1.17617e10	0.445249
$208$	0	0
$209$	−2.70011e10	−0.978867
$210$	7.00495e9	0.248553
$211$	−4.53207e10	−1.57407	−0.787037	−	0.616905i	$-0.788386\pi$
$211$	−4.53207e10	−1.57407	−0.787037	+	0.616905i	$0.788386\pi$
$212$	4.99959e9	0.169990
$213$	−2.97996e10	−0.991980
$214$	5.23029e10	1.70476
$215$	3.10379e10	0.990649
$216$	−3.64222e10	−1.13848
$217$	−5.26962e9	−0.161328
$218$	8.97513e9	0.269145
$219$	−2.56814e10	−0.754432
$220$	9.82053e9	0.282639
$221$	0	0
$222$	1.22924e10	0.339662
$223$	7.30981e10	1.97940	0.989702	−	0.143145i	$-0.0457214\pi$
$223$	7.30981e10	1.97940	0.989702	+	0.143145i	$0.0457214\pi$
$224$	−4.48679e9	−0.119075
$225$	−1.26159e10	−0.328168
$226$	4.42716e10	1.12885
$227$	1.35949e10	0.339828	0.169914	−	0.985459i	$-0.445651\pi$
$227$	1.35949e10	0.339828	0.169914	+	0.985459i	$0.445651\pi$
$228$	5.07915e9	0.124476
$229$	−8.08453e8	−0.0194265	−0.00971327	−	0.999953i	$-0.503092\pi$
$229$	−8.08453e8	−0.0194265	−0.00971327	+	0.999953i	$0.503092\pi$
$230$	−4.36515e10	−1.02855
$231$	−1.03161e10	−0.238377
$232$	6.08330e10	1.37862
$233$	4.41310e10	0.980939	0.490469	−	0.871458i	$-0.336825\pi$
$233$	4.41310e10	0.980939	0.490469	+	0.871458i	$0.336825\pi$
$234$	0	0
$235$	−2.88321e10	−0.616695
$236$	−4.93142e9	−0.103483
$237$	−8.33934e9	−0.171697
$238$	−1.55310e10	−0.313765
$239$	1.97834e10	0.392202	0.196101	−	0.980584i	$-0.437172\pi$
$239$	1.97834e10	0.392202	0.196101	+	0.980584i	$0.437172\pi$
$240$	3.56931e10	0.694439
$241$	2.31372e10	0.441808	0.220904	−	0.975296i	$-0.429099\pi$
$241$	2.31372e10	0.441808	0.220904	+	0.975296i	$0.429099\pi$
$242$	1.06014e10	0.198699
$243$	−4.79718e10	−0.882588
$244$	−1.33841e10	−0.241732
$245$	−6.58719e10	−1.16803
$246$	−5.30977e10	−0.924416
$247$	0	0
$248$	−3.38488e10	−0.568212
$249$	−3.49728e10	−0.576544
$250$	−2.43672e10	−0.394526
$251$	−1.17864e11	−1.87434	−0.937170	−	0.348872i	$-0.886565\pi$
$251$	−1.17864e11	−1.87434	−0.937170	+	0.348872i	$0.886565\pi$
$252$	−1.93247e9	−0.0301863
$253$	6.42852e10	0.986436
$254$	−9.43168e10	−1.42180
$255$	−7.07949e10	−1.04851
$256$	−3.92189e10	−0.570710
$257$	−3.70538e10	−0.529826	−0.264913	−	0.964272i	$-0.585343\pi$
$257$	−3.70538e10	−0.529826	−0.264913	+	0.964272i	$0.585343\pi$
$258$	−3.46993e10	−0.487564
$259$	1.18257e10	0.163297
$260$	0	0
$261$	4.80606e10	0.641072
$262$	1.09793e11	1.43952
$263$	3.67802e10	0.474038	0.237019	−	0.971505i	$-0.423830\pi$
$263$	3.67802e10	0.474038	0.237019	+	0.971505i	$0.423830\pi$
$264$	−6.62646e10	−0.839583
$265$	−8.84777e10	−1.10212
$266$	−1.97192e10	−0.241502
$267$	−1.13280e11	−1.36412
$268$	−1.27507e10	−0.150983
$269$	−5.26657e9	−0.0613257	−0.0306629	−	0.999530i	$-0.509762\pi$
$269$	−5.26657e9	−0.0613257	−0.0306629	+	0.999530i	$0.509762\pi$
$270$	1.06794e11	1.22295
$271$	2.74908e9	0.0309617	0.0154809	−	0.999880i	$-0.495072\pi$
$271$	2.74908e9	0.0309617	0.0154809	+	0.999880i	$0.495072\pi$
$272$	−7.91371e10	−0.876637
$273$	0	0
$274$	−6.92126e10	−0.741836
$275$	−6.89541e10	−0.727047
$276$	−1.20926e10	−0.125438
$277$	8.27302e9	0.0844316	0.0422158	−	0.999109i	$-0.486558\pi$
$277$	8.27302e9	0.0844316	0.0422158	+	0.999109i	$0.486558\pi$
$278$	−9.53809e10	−0.957767
$279$	−2.67420e10	−0.264225
$280$	4.32873e10	0.420871
$281$	−1.96602e11	−1.88109	−0.940546	−	0.339666i	$-0.889686\pi$
$281$	−1.96602e11	−1.88109	−0.940546	+	0.339666i	$0.889686\pi$
$282$	3.22332e10	0.303517
$283$	−2.43028e10	−0.225225	−0.112613	−	0.993639i	$-0.535922\pi$
$283$	−2.43028e10	−0.225225	−0.112613	+	0.993639i	$0.535922\pi$
$284$	−3.05104e10	−0.278301
$285$	−8.98857e10	−0.807028
$286$	0	0
$287$	−5.10819e10	−0.444425
$288$	−2.27693e10	−0.195022
$289$	3.83750e10	0.323599
$290$	−1.78369e11	−1.48091
$291$	1.38108e11	1.12902
$292$	−2.62939e10	−0.211657
$293$	−1.21394e10	−0.0962262	−0.0481131	−	0.998842i	$-0.515321\pi$
$293$	−1.21394e10	−0.0962262	−0.0481131	+	0.998842i	$0.515321\pi$
$294$	7.36424e10	0.574864
$295$	8.72712e10	0.670922
$296$	7.59611e10	0.575147
$297$	−1.57275e11	−1.17288
$298$	−1.05329e11	−0.773702
$299$	0	0
$300$	1.29709e10	0.0924536
$301$	−3.33820e10	−0.234403
$302$	1.88306e11	1.30267
$303$	9.78053e10	0.666608
$304$	−1.00477e11	−0.674741
$305$	2.36858e11	1.56725
$306$	−7.88160e10	−0.513887
$307$	−1.40000e11	−0.899509	−0.449754	−	0.893152i	$-0.648489\pi$
$307$	−1.40000e11	−0.899509	−0.449754	+	0.893152i	$0.648489\pi$
$308$	−1.05622e10	−0.0668768
$309$	−8.38403e10	−0.523166
$310$	9.92483e10	0.610373
$311$	1.59754e11	0.968344	0.484172	−	0.874973i	$-0.339121\pi$
$311$	1.59754e11	0.968344	0.484172	+	0.874973i	$0.339121\pi$
$312$	0	0
$313$	2.71629e10	0.159965	0.0799827	−	0.996796i	$-0.474513\pi$
$313$	2.71629e10	0.159965	0.0799827	+	0.996796i	$0.474513\pi$
$314$	−7.76908e10	−0.451010
$315$	3.41988e10	0.195710
$316$	−8.53823e9	−0.0481699
$317$	−8.01897e10	−0.446018	−0.223009	−	0.974816i	$-0.571588\pi$
$317$	−8.01897e10	−0.446018	−0.223009	+	0.974816i	$0.571588\pi$
$318$	9.89148e10	0.542425
$319$	2.62683e11	1.42028
$320$	2.68527e11	1.43157
$321$	−2.56417e11	−1.34795
$322$	4.69481e10	0.243370
$323$	1.99290e11	1.01877
$324$	9.93017e9	0.0500615
$325$	0	0
$326$	2.45227e11	1.20251
$327$	−4.40009e10	−0.212812
$328$	−3.28119e11	−1.56530
$329$	3.10095e10	0.145920
$330$	1.94295e11	0.901880
$331$	−4.46025e10	−0.204237	−0.102118	−	0.994772i	$-0.532562\pi$
$331$	−4.46025e10	−0.204237	−0.102118	+	0.994772i	$0.532562\pi$
$332$	−3.58069e10	−0.161750
$333$	6.00125e10	0.267450
$334$	−6.26055e10	−0.275267
$335$	2.25648e11	0.978883
$336$	−3.83888e10	−0.164315
$337$	1.80607e11	0.762782	0.381391	−	0.924414i	$-0.375445\pi$
$337$	1.80607e11	0.762782	0.381391	+	0.924414i	$0.375445\pi$
$338$	0	0
$339$	−2.17043e11	−0.892580
$340$	−7.24834e10	−0.294160
$341$	−1.46162e11	−0.585384
$342$	−1.00070e11	−0.395535
$343$	1.48941e11	0.581020
$344$	−2.14425e11	−0.825587
$345$	2.14003e11	0.813268
$346$	1.81708e11	0.681603
$347$	8.40688e10	0.311281	0.155640	−	0.987814i	$-0.450256\pi$
$347$	8.40688e10	0.311281	0.155640	+	0.987814i	$0.450256\pi$
$348$	−4.94130e10	−0.180607
$349$	4.06721e10	0.146751	0.0733757	−	0.997304i	$-0.476623\pi$
$349$	4.06721e10	0.146751	0.0733757	+	0.997304i	$0.476623\pi$
$350$	−5.03578e10	−0.179374
$351$	0	0
$352$	−1.24449e11	−0.432066
$353$	3.72744e11	1.27769	0.638843	−	0.769337i	$-0.279413\pi$
$353$	3.72744e11	1.27769	0.638843	+	0.769337i	$0.279413\pi$
$354$	−9.75660e10	−0.330205
$355$	5.39941e11	1.80434
$356$	−1.15982e11	−0.382705
$357$	7.61414e10	0.248093
$358$	−1.53184e11	−0.492878
$359$	−1.65323e11	−0.525302	−0.262651	−	0.964891i	$-0.584597\pi$
$359$	−1.65323e11	−0.525302	−0.262651	+	0.964891i	$0.584597\pi$
$360$	2.19672e11	0.689308
$361$	−6.96566e10	−0.215864
$362$	3.98619e10	0.122003
$363$	−5.19739e10	−0.157111
$364$	0	0
$365$	4.65322e11	1.37226
$366$	−2.64798e11	−0.771348
$367$	5.04443e11	1.45149	0.725746	−	0.687963i	$-0.241495\pi$
$367$	5.04443e11	1.45149	0.725746	+	0.687963i	$0.241495\pi$
$368$	2.39220e11	0.679959
$369$	−2.59227e11	−0.727884
$370$	−2.22726e11	−0.617822
$371$	9.51596e10	0.260778
$372$	2.74944e10	0.0744392
$373$	5.76983e11	1.54338	0.771691	−	0.635998i	$-0.219411\pi$
$373$	5.76983e11	1.54338	0.771691	+	0.635998i	$0.219411\pi$
$374$	−4.30781e11	−1.13850
$375$	1.19461e11	0.311951
$376$	1.99186e11	0.513942
$377$	0	0
$378$	−1.14859e11	−0.289369
$379$	3.81859e11	0.950662	0.475331	−	0.879807i	$-0.342328\pi$
$379$	3.81859e11	0.950662	0.475331	+	0.879807i	$0.342328\pi$
$380$	−9.20295e10	−0.226413
$381$	4.62392e11	1.12421
$382$	6.98399e10	0.167810
$383$	−4.69117e11	−1.11400	−0.557002	−	0.830511i	$-0.688048\pi$
$383$	−4.69117e11	−1.11400	−0.557002	+	0.830511i	$0.688048\pi$
$384$	−1.82320e11	−0.427903
$385$	1.86919e11	0.433590
$386$	1.62470e9	0.00372504
$387$	−1.69405e11	−0.383908
$388$	1.41402e11	0.316747
$389$	1.41227e11	0.312713	0.156356	−	0.987701i	$-0.450025\pi$
$389$	1.41227e11	0.312713	0.156356	+	0.987701i	$0.450025\pi$
$390$	0	0
$391$	−4.74477e11	−1.02664
$392$	4.55075e11	0.973410
$393$	−5.38263e11	−1.13823
$394$	−3.62589e11	−0.758022
$395$	1.51101e11	0.312306
$396$	−5.36004e10	−0.109532
$397$	−4.08885e11	−0.826122	−0.413061	−	0.910703i	$-0.635540\pi$
$397$	−4.08885e11	−0.826122	−0.413061	+	0.910703i	$0.635540\pi$
$398$	2.37344e11	0.474138
$399$	9.66740e10	0.190955
$400$	−2.56594e11	−0.501160
$401$	−5.41734e11	−1.04625	−0.523126	−	0.852255i	$-0.675234\pi$
$401$	−5.41734e11	−1.04625	−0.523126	+	0.852255i	$0.675234\pi$
$402$	−2.52267e11	−0.481774
$403$	0	0
$404$	1.00138e11	0.187018
$405$	−1.75734e11	−0.324570
$406$	1.91840e11	0.350406
$407$	3.28007e11	0.592528
$408$	4.89086e11	0.873805
$409$	−9.14685e11	−1.61628	−0.808140	−	0.588990i	$-0.799526\pi$
$409$	−9.14685e11	−1.61628	−0.808140	+	0.588990i	$0.799526\pi$
$410$	9.62079e11	1.68145
$411$	3.39317e11	0.586568
$412$	−8.58399e10	−0.146775
$413$	−9.38620e10	−0.158750
$414$	2.38250e11	0.398594
$415$	6.33673e11	1.04869
$416$	0	0
$417$	4.67608e11	0.757303
$418$	−5.46947e11	−0.876298
$419$	3.73691e11	0.592311	0.296156	−	0.955140i	$-0.404295\pi$
$419$	3.73691e11	0.592311	0.296156	+	0.955140i	$0.404295\pi$
$420$	−3.51611e10	−0.0551367
$421$	4.33964e11	0.673262	0.336631	−	0.941637i	$-0.390713\pi$
$421$	4.33964e11	0.673262	0.336631	+	0.941637i	$0.390713\pi$
$422$	−9.18036e11	−1.40914
$423$	1.57365e11	0.238989
$424$	6.11247e11	0.918482
$425$	5.08936e11	0.756682
$426$	−6.03635e11	−0.888037
$427$	−2.54746e11	−0.370835
$428$	−2.62533e11	−0.378169
$429$	0	0
$430$	6.28718e11	0.886845
$431$	−8.45377e11	−1.18006	−0.590028	−	0.807383i	$-0.700883\pi$
$431$	−8.45377e11	−1.18006	−0.590028	+	0.807383i	$0.700883\pi$
$432$	−5.85255e11	−0.808479
$433$	−5.91980e11	−0.809303	−0.404652	−	0.914471i	$-0.632607\pi$
$433$	−5.91980e11	−0.809303	−0.404652	+	0.914471i	$0.632607\pi$
$434$	−1.06744e11	−0.144424
$435$	8.74460e11	1.17095
$436$	−4.50503e10	−0.0597047
$437$	−6.02426e11	−0.790200
$438$	−5.20214e11	−0.675380
$439$	1.26798e12	1.62938	0.814692	−	0.579894i	$-0.196906\pi$
$439$	1.26798e12	1.62938	0.814692	+	0.579894i	$0.196906\pi$
$440$	1.20065e12	1.52714
$441$	3.59528e11	0.452647
$442$	0	0
$443$	−1.96396e11	−0.242279	−0.121140	−	0.992635i	$-0.538655\pi$
$443$	−1.96396e11	−0.242279	−0.121140	+	0.992635i	$0.538655\pi$
$444$	−6.17011e10	−0.0753477
$445$	2.05252e12	2.48124
$446$	1.48071e12	1.77200
$447$	5.16378e11	0.611764
$448$	−2.88807e11	−0.338732
$449$	−2.80407e11	−0.325597	−0.162799	−	0.986659i	$-0.552052\pi$
$449$	−2.80407e11	−0.325597	−0.162799	+	0.986659i	$0.552052\pi$
$450$	−2.55553e11	−0.293782
$451$	−1.41685e12	−1.61261
$452$	−2.22220e11	−0.250414
$453$	−9.23177e11	−1.03001
$454$	2.75384e11	0.304219
$455$	0	0
$456$	6.20974e11	0.672561
$457$	−6.84356e11	−0.733938	−0.366969	−	0.930233i	$-0.619604\pi$
$457$	−6.84356e11	−0.733938	−0.366969	+	0.930233i	$0.619604\pi$
$458$	−1.63764e10	−0.0173910
$459$	1.16081e12	1.22069
$460$	2.19107e11	0.228163
$461$	1.74700e12	1.80152	0.900761	−	0.434315i	$-0.143009\pi$
$461$	1.74700e12	1.80152	0.900761	+	0.434315i	$0.143009\pi$
$462$	−2.08968e11	−0.213399
$463$	1.01806e12	1.02958	0.514788	−	0.857318i	$-0.327871\pi$
$463$	1.01806e12	1.02958	0.514788	+	0.857318i	$0.327871\pi$
$464$	9.77502e11	0.979010
$465$	−4.86568e11	−0.482620
$466$	8.93937e11	0.878153
$467$	−2.73806e11	−0.266389	−0.133195	−	0.991090i	$-0.542524\pi$
$467$	−2.73806e11	−0.266389	−0.133195	+	0.991090i	$0.542524\pi$
$468$	0	0
$469$	−2.42690e11	−0.231619
$470$	−5.84035e11	−0.552076
$471$	3.80882e11	0.356612
$472$	−6.02912e11	−0.559133
$473$	−9.25909e11	−0.850537
$474$	−1.68925e11	−0.153706
$475$	6.46178e11	0.582413
$476$	7.79574e10	0.0696027
$477$	4.82911e11	0.427105
$478$	4.00741e11	0.351106
$479$	−8.56952e11	−0.743784	−0.371892	−	0.928276i	$-0.621291\pi$
$479$	−8.56952e11	−0.743784	−0.371892	+	0.928276i	$0.621291\pi$
$480$	−4.14286e11	−0.356217
$481$	0	0
$482$	4.68677e11	0.395514
$483$	−2.30165e11	−0.192432
$484$	−5.32135e10	−0.0440775
$485$	−2.50239e12	−2.05360
$486$	−9.71739e11	−0.790108
$487$	−2.02529e12	−1.63157	−0.815787	−	0.578352i	$-0.803696\pi$
$487$	−2.02529e12	−1.63157	−0.815787	+	0.578352i	$0.803696\pi$
$488$	−1.63633e12	−1.30612
$489$	−1.20224e12	−0.950823
$490$	−1.33433e12	−1.04564
$491$	6.32049e11	0.490777	0.245388	−	0.969425i	$-0.421085\pi$
$491$	6.32049e11	0.490777	0.245388	+	0.969425i	$0.421085\pi$
$492$	2.66522e11	0.205064
$493$	−1.93881e12	−1.47817
$494$	0	0
$495$	9.48565e11	0.710139
$496$	−5.43904e11	−0.403510
$497$	−5.80719e11	−0.426935
$498$	−7.08424e11	−0.516132
$499$	2.07591e12	1.49884	0.749420	−	0.662094i	$-0.230332\pi$
$499$	2.07591e12	1.49884	0.749420	+	0.662094i	$0.230332\pi$
$500$	1.22310e11	0.0875181
$501$	3.06926e11	0.217653
$502$	−2.38750e12	−1.67794
$503$	8.87539e11	0.618204	0.309102	−	0.951029i	$-0.399972\pi$
$503$	8.87539e11	0.618204	0.309102	+	0.951029i	$0.399972\pi$
$504$	−2.36262e11	−0.163101
$505$	−1.77214e12	−1.21251
$506$	1.30219e12	0.883074
$507$	0	0
$508$	4.73420e11	0.315398
$509$	2.72435e11	0.179901	0.0899505	−	0.995946i	$-0.471329\pi$
$509$	2.72435e11	0.179901	0.0899505	+	0.995946i	$0.471329\pi$
$510$	−1.43405e12	−0.938640
$511$	−5.00464e11	−0.324697
$512$	−1.73442e12	−1.11542
$513$	1.47384e12	0.939556
$514$	−7.50577e11	−0.474309
$515$	1.51911e12	0.951603
$516$	1.74172e11	0.108157
$517$	8.60105e11	0.529473
$518$	2.39547e11	0.146186
$519$	−8.90830e11	−0.538941
$520$	0	0
$521$	−1.81355e12	−1.07835	−0.539174	−	0.842194i	$-0.681263\pi$
$521$	−1.81355e12	−1.07835	−0.539174	+	0.842194i	$0.681263\pi$
$522$	9.73537e11	0.573898
$523$	3.31885e12	1.93968	0.969840	−	0.243742i	$-0.0783749\pi$
$523$	3.31885e12	1.93968	0.969840	+	0.243742i	$0.0783749\pi$
$524$	−5.51101e11	−0.319331
$525$	2.46881e11	0.141831
$526$	7.45035e11	0.424366
$527$	1.07879e12	0.609244
$528$	−1.06478e12	−0.596222
$529$	−3.66876e11	−0.203690
$530$	−1.79224e12	−0.986633
$531$	−4.76326e11	−0.260003
$532$	9.89797e10	0.0535727
$533$	0	0
$534$	−2.29465e12	−1.22118
$535$	4.64603e12	2.45183
$536$	−1.55889e12	−0.815782
$537$	7.50990e11	0.389717
$538$	−1.06682e11	−0.0548998
$539$	1.96506e12	1.00283
$540$	−5.36048e11	−0.271289
$541$	−9.76068e11	−0.489883	−0.244942	−	0.969538i	$-0.578769\pi$
$541$	−9.76068e11	−0.489883	−0.244942	+	0.969538i	$0.578769\pi$
$542$	5.56866e10	0.0277175
$543$	−1.95424e11	−0.0964671
$544$	9.18535e11	0.449677
$545$	7.97254e11	0.387091
$546$	0	0
$547$	−3.95412e12	−1.88846	−0.944229	−	0.329291i	$-0.893190\pi$
$547$	−3.95412e12	−1.88846	−0.944229	+	0.329291i	$0.893190\pi$
$548$	3.47410e11	0.164562
$549$	−1.29277e12	−0.607359
$550$	−1.39676e12	−0.650865
$551$	−2.46163e12	−1.13774
$552$	−1.47844e12	−0.677762
$553$	−1.62512e11	−0.0738963
$554$	1.67582e11	0.0755846
$555$	1.09192e12	0.488510
$556$	4.78761e11	0.212462
$557$	8.83169e11	0.388772	0.194386	−	0.980925i	$-0.437729\pi$
$557$	8.83169e11	0.388772	0.194386	+	0.980925i	$0.437729\pi$
$558$	−5.41697e11	−0.236539
$559$	0	0
$560$	6.95568e11	0.298878
$561$	2.11192e12	0.900211
$562$	−3.98246e12	−1.68399
$563$	3.28351e11	0.137737	0.0688684	−	0.997626i	$-0.478061\pi$
$563$	3.28351e11	0.137737	0.0688684	+	0.997626i	$0.478061\pi$
$564$	−1.61794e11	−0.0673295
$565$	3.93261e12	1.62354
$566$	−4.92288e11	−0.201625
$567$	1.89006e11	0.0767982
$568$	−3.73018e12	−1.50370
$569$	3.01900e12	1.20742	0.603709	−	0.797204i	$-0.293689\pi$
$569$	3.01900e12	1.20742	0.603709	+	0.797204i	$0.293689\pi$
$570$	−1.82076e12	−0.722465
$571$	1.93373e12	0.761260	0.380630	−	0.924727i	$-0.375707\pi$
$571$	1.93373e12	0.761260	0.380630	+	0.924727i	$0.375707\pi$
$572$	0	0
$573$	−3.42393e11	−0.132687
$574$	−1.03474e12	−0.397857
$575$	−1.53844e12	−0.586916
$576$	−1.46562e12	−0.554779
$577$	−7.89015e11	−0.296343	−0.148171	−	0.988962i	$-0.547339\pi$
$577$	−7.89015e11	−0.296343	−0.148171	+	0.988962i	$0.547339\pi$
$578$	7.77340e11	0.289692
$579$	−7.96515e9	−0.00294537
$580$	8.95316e11	0.328511
$581$	−6.81529e11	−0.248137
$582$	2.79758e12	1.01072
$583$	2.63942e12	0.946238
$584$	−3.21468e12	−1.14361
$585$	0	0
$586$	−2.45901e11	−0.0861433
$587$	−1.02520e12	−0.356400	−0.178200	−	0.983994i	$-0.557027\pi$
$587$	−1.02520e12	−0.356400	−0.178200	+	0.983994i	$0.557027\pi$
$588$	−3.69645e11	−0.127523
$589$	1.36971e12	0.468931
$590$	1.76780e12	0.600620
$591$	1.77761e12	0.599366
$592$	1.22059e12	0.408435
$593$	−1.46514e12	−0.486558	−0.243279	−	0.969956i	$-0.578223\pi$
$593$	−1.46514e12	−0.486558	−0.243279	+	0.969956i	$0.578223\pi$
$594$	−3.18583e12	−1.04998
$595$	−1.37961e12	−0.451263
$596$	5.28694e11	0.171631
$597$	−1.16359e12	−0.374900
$598$	0	0
$599$	2.10151e12	0.666978	0.333489	−	0.942754i	$-0.391774\pi$
$599$	2.10151e12	0.666978	0.333489	+	0.942754i	$0.391774\pi$
$600$	1.58581e12	0.499541
$601$	−3.20560e12	−1.00225	−0.501123	−	0.865376i	$-0.667080\pi$
$601$	−3.20560e12	−1.00225	−0.501123	+	0.865376i	$0.667080\pi$
$602$	−6.76200e11	−0.209841
$603$	−1.23159e12	−0.379348
$604$	−9.45195e11	−0.288972
$605$	9.41717e11	0.285773
$606$	1.98119e12	0.596759
$607$	2.93741e12	0.878244	0.439122	−	0.898427i	$-0.355290\pi$
$607$	2.93741e12	0.878244	0.439122	+	0.898427i	$0.355290\pi$
$608$	1.16623e12	0.346113
$609$	−9.40500e11	−0.277065
$610$	4.79789e12	1.40303
$611$	0	0
$612$	3.95614e11	0.113996
$613$	2.34718e12	0.671390	0.335695	−	0.941971i	$-0.391029\pi$
$613$	2.34718e12	0.671390	0.335695	+	0.941971i	$0.391029\pi$
$614$	−2.83590e12	−0.805256
$615$	−4.71663e12	−1.32952
$616$	−1.29133e12	−0.361346
$617$	6.60966e12	1.83610	0.918048	−	0.396468i	$-0.129764\pi$
$617$	6.60966e12	1.83610	0.918048	+	0.396468i	$0.129764\pi$
$618$	−1.69831e12	−0.468347
$619$	5.28581e11	0.144712	0.0723559	−	0.997379i	$-0.476948\pi$
$619$	5.28581e11	0.144712	0.0723559	+	0.997379i	$0.476948\pi$
$620$	−4.98173e11	−0.135400
$621$	−3.50898e12	−0.946822
$622$	3.23605e12	0.866878
$623$	−2.20753e12	−0.587099
$624$	0	0
$625$	−4.67349e12	−1.22513
$626$	5.50223e11	0.143204
$627$	2.68143e12	0.692886
$628$	3.89966e11	0.100048
$629$	−2.42096e12	−0.616679
$630$	6.92746e11	0.175203
$631$	3.06685e12	0.770124	0.385062	−	0.922891i	$-0.374180\pi$
$631$	3.06685e12	0.770124	0.385062	+	0.922891i	$0.374180\pi$
$632$	−1.04388e12	−0.260270
$633$	4.50070e12	1.11420
$634$	−1.62436e12	−0.399283
$635$	−8.37809e12	−2.04486
$636$	−4.96499e11	−0.120327
$637$	0	0
$638$	5.32101e12	1.27146
$639$	−2.94700e12	−0.699240
$640$	3.30347e12	0.778325
$641$	6.09117e12	1.42508	0.712541	−	0.701630i	$-0.247544\pi$
$641$	6.09117e12	1.42508	0.712541	+	0.701630i	$0.247544\pi$
$642$	−5.19410e12	−1.20671
$643$	−9.51786e11	−0.219579	−0.109789	−	0.993955i	$-0.535018\pi$
$643$	−9.51786e11	−0.219579	−0.109789	+	0.993955i	$0.535018\pi$
$644$	−2.35654e11	−0.0539870
$645$	−3.08231e12	−0.701226
$646$	4.03691e12	0.912016
$647$	2.39734e12	0.537848	0.268924	−	0.963161i	$-0.413332\pi$
$647$	2.39734e12	0.537848	0.268924	+	0.963161i	$0.413332\pi$
$648$	1.21406e12	0.270490
$649$	−2.60343e12	−0.576030
$650$	0	0
$651$	5.23315e11	0.114195
$652$	−1.23091e12	−0.266755
$653$	7.79616e12	1.67792	0.838960	−	0.544193i	$-0.183164\pi$
$653$	7.79616e12	1.67792	0.838960	+	0.544193i	$0.183164\pi$
$654$	−8.91302e11	−0.190513
$655$	9.75282e12	2.07035
$656$	−5.27242e12	−1.11158
$657$	−2.53973e12	−0.531793
$658$	6.28143e11	0.130630
$659$	1.35009e11	0.0278855	0.0139427	−	0.999903i	$-0.495562\pi$
$659$	1.35009e11	0.0278855	0.0139427	+	0.999903i	$0.495562\pi$
$660$	−9.75256e11	−0.200065
$661$	1.05609e12	0.215176	0.107588	−	0.994196i	$-0.465687\pi$
$661$	1.05609e12	0.215176	0.107588	+	0.994196i	$0.465687\pi$
$662$	−9.03489e11	−0.182836
$663$	0	0
$664$	−4.37773e12	−0.873961
$665$	−1.75164e12	−0.347334
$666$	1.21564e12	0.239426
$667$	5.86074e12	1.14653
$668$	3.14246e11	0.0610627
$669$	−7.25922e12	−1.40111
$670$	4.57084e12	0.876312
$671$	−7.06583e12	−1.34559
$672$	4.45574e11	0.0842865
$673$	7.88255e12	1.48115	0.740574	−	0.671974i	$-0.234553\pi$
$673$	7.88255e12	1.48115	0.740574	+	0.671974i	$0.234553\pi$
$674$	3.65846e12	0.682855
$675$	3.76382e12	0.697850
$676$	0	0
$677$	4.65420e12	0.851523	0.425761	−	0.904835i	$-0.360006\pi$
$677$	4.65420e12	0.851523	0.425761	+	0.904835i	$0.360006\pi$
$678$	−4.39652e12	−0.799053
$679$	2.69137e12	0.485914
$680$	−8.86177e12	−1.58939
$681$	−1.35008e12	−0.240545
$682$	−2.96073e12	−0.524045
$683$	−3.75943e12	−0.661042	−0.330521	−	0.943799i	$-0.607225\pi$
$683$	−3.75943e12	−0.661042	−0.330521	+	0.943799i	$0.607225\pi$
$684$	5.02296e11	0.0877420
$685$	−6.14811e12	−1.06693
$686$	3.01702e12	0.520139
$687$	8.02858e10	0.0137510
$688$	−3.44552e12	−0.586282
$689$	0	0
$690$	4.33494e12	0.728052
$691$	−1.46171e12	−0.243899	−0.121949	−	0.992536i	$-0.538915\pi$
$691$	−1.46171e12	−0.243899	−0.121949	+	0.992536i	$0.538915\pi$
$692$	−9.12076e11	−0.151201
$693$	−1.02020e12	−0.168030
$694$	1.70293e12	0.278664
$695$	−8.47262e12	−1.37748
$696$	−6.04120e12	−0.975846
$697$	1.04575e13	1.67834
$698$	8.23872e11	0.131374
$699$	−4.38256e12	−0.694353
$700$	2.52769e11	0.0397908
$701$	−1.56446e12	−0.244700	−0.122350	−	0.992487i	$-0.539043\pi$
$701$	−1.56446e12	−0.244700	−0.122350	+	0.992487i	$0.539043\pi$
$702$	0	0
$703$	−3.07380e12	−0.474654
$704$	−8.01057e12	−1.22910
$705$	2.86326e12	0.436525
$706$	7.55047e12	1.14381
$707$	1.90597e12	0.286899
$708$	4.89729e11	0.0732498
$709$	−8.13253e10	−0.0120870	−0.00604349	−	0.999982i	$-0.501924\pi$
$709$	−8.13253e10	−0.0120870	−0.00604349	+	0.999982i	$0.501924\pi$
$710$	1.09373e13	1.61528
$711$	−8.24708e11	−0.121028
$712$	−1.41798e13	−2.06781
$713$	−3.26105e12	−0.472557
$714$	1.54235e12	0.222097
$715$	0	0
$716$	7.68901e11	0.109336
$717$	−1.96465e12	−0.277619
$718$	−3.34886e12	−0.470259
$719$	5.67153e12	0.791444	0.395722	−	0.918370i	$-0.370494\pi$
$719$	5.67153e12	0.791444	0.395722	+	0.918370i	$0.370494\pi$
$720$	3.52983e12	0.489505
$721$	−1.63383e12	−0.225164
$722$	−1.41099e12	−0.193245
$723$	−2.29771e12	−0.312732
$724$	−2.00085e11	−0.0270640
$725$	−6.28639e12	−0.845046
$726$	−1.05281e12	−0.140648
$727$	7.98313e12	1.05991	0.529954	−	0.848026i	$-0.322209\pi$
$727$	7.98313e12	1.05991	0.529954	+	0.848026i	$0.322209\pi$
$728$	0	0
$729$	6.68631e12	0.876825
$730$	9.42577e12	1.22847
$731$	6.83395e12	0.885204
$732$	1.32915e12	0.171109
$733$	9.62385e12	1.23135	0.615674	−	0.788001i	$-0.288884\pi$
$733$	9.62385e12	1.23135	0.615674	+	0.788001i	$0.288884\pi$
$734$	1.02182e13	1.29940
$735$	6.54160e12	0.826782
$736$	−2.77660e12	−0.348790
$737$	−6.73144e12	−0.840435
$738$	−5.25103e12	−0.651614
$739$	2.67570e12	0.330018	0.165009	−	0.986292i	$-0.447235\pi$
$739$	2.67570e12	0.330018	0.165009	+	0.986292i	$0.447235\pi$
$740$	1.11797e12	0.137052
$741$	0	0
$742$	1.92760e12	0.233452
$743$	−1.17772e13	−1.41773	−0.708865	−	0.705344i	$-0.750792\pi$
$743$	−1.17772e13	−1.41773	−0.708865	+	0.705344i	$0.750792\pi$
$744$	3.36145e12	0.402206
$745$	−9.35628e12	−1.11276
$746$	1.16876e13	1.38166
$747$	−3.45859e12	−0.406402
$748$	2.16229e12	0.252555
$749$	−4.99691e12	−0.580140
$750$	2.41986e12	0.279264
$751$	5.03731e12	0.577855	0.288927	−	0.957351i	$-0.406701\pi$
$751$	5.03731e12	0.577855	0.288927	+	0.957351i	$0.406701\pi$
$752$	3.20065e12	0.364971
$753$	1.17048e13	1.32674
$754$	0	0
$755$	1.67271e13	1.87352
$756$	5.76531e11	0.0641911
$757$	−6.66068e11	−0.0737203	−0.0368601	−	0.999320i	$-0.511736\pi$
$757$	−6.66068e11	−0.0737203	−0.0368601	+	0.999320i	$0.511736\pi$
$758$	7.73510e12	0.851049
$759$	−6.38404e12	−0.698244
$760$	−1.12515e13	−1.22334
$761$	9.59754e12	1.03736	0.518680	−	0.854969i	$-0.326424\pi$
$761$	9.59754e12	1.03736	0.518680	+	0.854969i	$0.326424\pi$
$762$	9.36641e12	1.00641
$763$	−8.57464e11	−0.0915916
$764$	−3.50559e11	−0.0372255
$765$	−7.00117e12	−0.739084
$766$	−9.50264e12	−0.997275
$767$	0	0
$768$	3.89475e12	0.403975
$769$	7.48650e12	0.771988	0.385994	−	0.922501i	$-0.373859\pi$
$769$	7.48650e12	0.771988	0.385994	+	0.922501i	$0.373859\pi$
$770$	3.78631e12	0.388157
$771$	3.67973e12	0.375035
$772$	−8.15512e9	−0.000826328 0
$773$	−2.93392e12	−0.295556	−0.147778	−	0.989021i	$-0.547212\pi$
$773$	−2.93392e12	−0.295556	−0.147778	+	0.989021i	$0.547212\pi$
$774$	−3.43154e12	−0.343681
$775$	3.49788e12	0.348295
$776$	1.72877e13	1.71143
$777$	−1.17439e12	−0.115589
$778$	2.86077e12	0.279946
$779$	1.32775e13	1.29180
$780$	0	0
$781$	−1.61073e13	−1.54915
$782$	−9.61121e12	−0.919068
$783$	−1.43384e13	−1.36324
$784$	7.31244e12	0.691257
$785$	−6.90122e12	−0.648653
$786$	−1.09033e13	−1.01896
$787$	−1.07787e13	−1.00157	−0.500784	−	0.865572i	$-0.666955\pi$
$787$	−1.07787e13	−1.00157	−0.500784	+	0.865572i	$0.666955\pi$
$788$	1.82000e12	0.168153
$789$	−3.65256e12	−0.335545
$790$	3.06077e12	0.279581
$791$	−4.22961e12	−0.384155
$792$	−6.55315e12	−0.591816
$793$	0	0
$794$	−8.28256e12	−0.739558
$795$	8.78654e12	0.780127
$796$	−1.19134e12	−0.105179
$797$	9.76856e11	0.0857567	0.0428784	−	0.999080i	$-0.486347\pi$
$797$	9.76856e11	0.0857567	0.0428784	+	0.999080i	$0.486347\pi$
$798$	1.95827e12	0.170946
$799$	−6.34827e12	−0.551054
$800$	2.97826e12	0.257073
$801$	−1.12027e13	−0.961558
$802$	−1.09736e13	−0.936623
$803$	−1.38813e13	−1.17817
$804$	1.26624e12	0.106872
$805$	4.17037e12	0.350020
$806$	0	0
$807$	5.23012e11	0.0434091
$808$	1.22428e13	1.01049
$809$	−5.80790e12	−0.476706	−0.238353	−	0.971179i	$-0.576608\pi$
$809$	−5.80790e12	−0.476706	−0.238353	+	0.971179i	$0.576608\pi$
$810$	−3.55974e12	−0.290560
$811$	−1.08989e13	−0.884685	−0.442342	−	0.896846i	$-0.645852\pi$
$811$	−1.08989e13	−0.884685	−0.442342	+	0.896846i	$0.645852\pi$
$812$	−9.62931e11	−0.0777308
$813$	−2.73005e11	−0.0219161
$814$	6.64426e12	0.530441
$815$	2.17834e13	1.72948
$816$	7.85894e12	0.620523
$817$	8.67681e12	0.681336
$818$	−1.85283e13	−1.44692
$819$	0	0
$820$	−4.82912e12	−0.372997
$821$	−6.54036e12	−0.502409	−0.251205	−	0.967934i	$-0.580827\pi$
$821$	−6.54036e12	−0.502409	−0.251205	+	0.967934i	$0.580827\pi$
$822$	6.87337e12	0.525105
$823$	1.64051e13	1.24646	0.623231	−	0.782038i	$-0.285820\pi$
$823$	1.64051e13	1.24646	0.623231	+	0.782038i	$0.285820\pi$
$824$	−1.04947e13	−0.793047
$825$	6.84769e12	0.514637
$826$	−1.90131e12	−0.142116
$827$	1.09682e13	0.815379	0.407690	−	0.913121i	$-0.366335\pi$
$827$	1.09682e13	0.815379	0.407690	+	0.913121i	$0.366335\pi$
$828$	−1.19589e12	−0.0884205
$829$	1.59259e13	1.17114	0.585571	−	0.810621i	$-0.300870\pi$
$829$	1.59259e13	1.17114	0.585571	+	0.810621i	$0.300870\pi$
$830$	1.28360e13	0.938809
$831$	−8.21576e11	−0.0597645
$832$	0	0
$833$	−1.45037e13	−1.04370
$834$	9.47208e12	0.677951
$835$	−5.56121e12	−0.395895
$836$	2.74538e12	0.194390
$837$	7.97819e12	0.561875
$838$	7.56966e12	0.530247
$839$	2.61649e11	0.0182301	0.00911506	−	0.999958i	$-0.497099\pi$
$839$	2.61649e11	0.0182301	0.00911506	+	0.999958i	$0.497099\pi$
$840$	−4.29877e12	−0.297912
$841$	9.44105e12	0.650786
$842$	8.79056e12	0.602715
$843$	1.95242e13	1.33152
$844$	4.60805e12	0.312591
$845$	0	0
$846$	3.18766e12	0.213947
$847$	−1.01284e12	−0.0676183
$848$	9.82190e12	0.652250
$849$	2.41346e12	0.159425
$850$	1.03092e13	0.677394
$851$	7.31821e12	0.478324
$852$	3.02992e12	0.196994
$853$	−1.54700e12	−0.100051	−0.0500254	−	0.998748i	$-0.515930\pi$
$853$	−1.54700e12	−0.100051	−0.0500254	+	0.998748i	$0.515930\pi$
$854$	−5.16024e12	−0.331978
$855$	−8.88913e12	−0.568868
$856$	−3.20971e13	−2.04331
$857$	−1.27687e13	−0.808598	−0.404299	−	0.914627i	$-0.632485\pi$
$857$	−1.27687e13	−0.808598	−0.404299	+	0.914627i	$0.632485\pi$
$858$	0	0
$859$	2.16957e13	1.35958	0.679791	−	0.733406i	$-0.262071\pi$
$859$	2.16957e13	1.35958	0.679791	+	0.733406i	$0.262071\pi$
$860$	−3.15583e12	−0.196730
$861$	5.07284e12	0.314584
$862$	−1.71243e13	−1.05641
$863$	−1.13113e13	−0.694167	−0.347083	−	0.937834i	$-0.612828\pi$
$863$	−1.13113e13	−0.694167	−0.347083	+	0.937834i	$0.612828\pi$
$864$	6.79299e12	0.414715
$865$	1.61410e13	0.980297
$866$	−1.19914e13	−0.724502
$867$	−3.81094e12	−0.229058
$868$	5.35796e11	0.0320376
$869$	−4.50757e12	−0.268135
$870$	1.77134e13	1.04825
$871$	0	0
$872$	−5.50783e12	−0.322594
$873$	1.36580e13	0.795836
$874$	−1.22030e13	−0.707400
$875$	2.32799e12	0.134259
$876$	2.61119e12	0.149820
$877$	7.02980e12	0.401277	0.200639	−	0.979665i	$-0.435698\pi$
$877$	7.02980e12	0.401277	0.200639	+	0.979665i	$0.435698\pi$
$878$	2.56848e13	1.45865
$879$	1.20554e12	0.0681133
$880$	1.92928e13	1.08449
$881$	1.37124e13	0.766871	0.383436	−	0.923568i	$-0.374741\pi$
$881$	1.37124e13	0.766871	0.383436	+	0.923568i	$0.374741\pi$
$882$	7.28277e12	0.405217
$883$	−1.34667e13	−0.745483	−0.372742	−	0.927935i	$-0.621582\pi$
$883$	−1.34667e13	−0.745483	−0.372742	+	0.927935i	$0.621582\pi$
$884$	0	0
$885$	−8.66672e12	−0.474909
$886$	−3.97829e12	−0.216893
$887$	−2.55342e13	−1.38505	−0.692527	−	0.721392i	$-0.743502\pi$
$887$	−2.55342e13	−1.38505	−0.692527	+	0.721392i	$0.743502\pi$
$888$	−7.54354e12	−0.407115
$889$	9.01082e12	0.483845
$890$	4.15768e13	2.22125
$891$	5.24241e12	0.278664
$892$	−7.43236e12	−0.393084
$893$	−8.06016e12	−0.424143
$894$	1.04600e13	0.547661
$895$	−1.36072e13	−0.708869
$896$	−3.55296e12	−0.184164
$897$	0	0
$898$	−5.68005e12	−0.291480
$899$	−1.33253e13	−0.680390
$900$	1.28274e12	0.0651699
$901$	−1.94811e13	−0.984807
$902$	−2.87003e13	−1.44363
$903$	3.31509e12	0.165921
$904$	−2.71684e13	−1.35303
$905$	3.54090e12	0.175467
$906$	−1.87003e13	−0.922085
$907$	−1.12761e13	−0.553255	−0.276627	−	0.960977i	$-0.589217\pi$
$907$	−1.12761e13	−0.553255	−0.276627	+	0.960977i	$0.589217\pi$
$908$	−1.38228e12	−0.0674853
$909$	9.67233e12	0.469887
$910$	0	0
$911$	4.27042e12	0.205418	0.102709	−	0.994711i	$-0.467249\pi$
$911$	4.27042e12	0.205418	0.102709	+	0.994711i	$0.467249\pi$
$912$	9.97821e12	0.477612
$913$	−1.89034e13	−0.900373
$914$	−1.38626e13	−0.657034
$915$	−2.35219e13	−1.10937
$916$	8.22007e10	0.00385785
$917$	−1.04894e13	−0.489877
$918$	2.35139e13	1.09278
$919$	−4.00984e13	−1.85442	−0.927209	−	0.374544i	$-0.877799\pi$
$919$	−4.00984e13	−1.85442	−0.927209	+	0.374544i	$0.877799\pi$
$920$	2.67879e13	1.23280
$921$	1.39031e13	0.636713
$922$	3.53881e13	1.61275
$923$	0	0
$924$	1.04891e12	0.0473384
$925$	−7.84971e12	−0.352546
$926$	2.06222e13	0.921693
$927$	−8.29128e12	−0.368776
$928$	−1.13458e13	−0.502190
$929$	7.00571e11	0.0308590	0.0154295	−	0.999881i	$-0.495088\pi$
$929$	7.00571e11	0.0308590	0.0154295	+	0.999881i	$0.495088\pi$
$930$	−9.85614e12	−0.432050
$931$	−1.84148e13	−0.803330
$932$	−4.48708e12	−0.194802
$933$	−1.58648e13	−0.685438
$934$	−5.54634e12	−0.238476
$935$	−3.82660e13	−1.63742
$936$	0	0
$937$	−4.14637e12	−0.175728	−0.0878638	−	0.996132i	$-0.528004\pi$
$937$	−4.14637e12	−0.175728	−0.0878638	+	0.996132i	$0.528004\pi$
$938$	−4.91603e12	−0.207349
$939$	−2.69749e12	−0.113231
$940$	2.93154e12	0.122468
$941$	2.16143e13	0.898643	0.449322	−	0.893370i	$-0.351666\pi$
$941$	2.16143e13	0.898643	0.449322	+	0.893370i	$0.351666\pi$
$942$	7.71531e12	0.319245
$943$	−3.16115e13	−1.30179
$944$	−9.68797e12	−0.397063
$945$	−1.02029e13	−0.416178
$946$	−1.87556e13	−0.761415
$947$	1.67051e13	0.674955	0.337477	−	0.941334i	$-0.390426\pi$
$947$	1.67051e13	0.674955	0.337477	+	0.941334i	$0.390426\pi$
$948$	8.47914e11	0.0340969
$949$	0	0
$950$	1.30893e13	0.521386
$951$	7.96348e12	0.315712
$952$	9.53103e12	0.376074
$953$	−1.43090e12	−0.0561941	−0.0280971	−	0.999605i	$-0.508945\pi$
$953$	−1.43090e12	−0.0561941	−0.0280971	+	0.999605i	$0.508945\pi$
$954$	9.78206e12	0.382351
$955$	6.20383e12	0.241348
$956$	−2.01151e12	−0.0778862
$957$	−2.60865e13	−1.00534
$958$	−1.73588e13	−0.665848
$959$	6.61242e12	0.252451
$960$	−2.66669e13	−1.01333
$961$	−1.90251e13	−0.719569
$962$	0	0
$963$	−2.53580e13	−0.950161
$964$	−2.35251e12	−0.0877373
$965$	1.44321e11	0.00535743
$966$	−4.66232e12	−0.172268
$967$	9.08218e12	0.334019	0.167009	−	0.985955i	$-0.446589\pi$
$967$	9.08218e12	0.334019	0.167009	+	0.985955i	$0.446589\pi$
$968$	−6.50584e12	−0.238158
$969$	−1.97911e13	−0.721128
$970$	−5.06895e13	−1.83842
$971$	2.46609e13	0.890271	0.445136	−	0.895463i	$-0.353155\pi$
$971$	2.46609e13	0.890271	0.445136	+	0.895463i	$0.353155\pi$
$972$	4.87761e12	0.175270
$973$	9.11248e12	0.325933
$974$	−4.10252e13	−1.46061
$975$	0	0
$976$	−2.62936e13	−0.927524
$977$	2.01448e12	0.0707354	0.0353677	−	0.999374i	$-0.488740\pi$
$977$	2.01448e12	0.0707354	0.0353677	+	0.999374i	$0.488740\pi$
$978$	−2.43530e13	−0.851193
$979$	−6.12299e13	−2.13030
$980$	6.69762e12	0.231955
$981$	−4.35141e12	−0.150010
$982$	1.28031e13	0.439352
$983$	−5.90624e12	−0.201753	−0.100876	−	0.994899i	$-0.532165\pi$
$983$	−5.90624e12	−0.201753	−0.100876	+	0.994899i	$0.532165\pi$
$984$	3.25848e13	1.10799
$985$	−3.22085e13	−1.09020
$986$	−3.92734e13	−1.32328
$987$	−3.07949e12	−0.103289
$988$	0	0
$989$	−2.06581e13	−0.686604
$990$	1.92145e13	0.635729
$991$	5.76104e13	1.89745	0.948723	−	0.316108i	$-0.102376\pi$
$991$	5.76104e13	1.89745	0.948723	+	0.316108i	$0.102376\pi$
$992$	6.31303e12	0.206983
$993$	4.42939e12	0.144568
$994$	−1.17633e13	−0.382200
$995$	2.10831e13	0.681917
$996$	3.55591e12	0.114494
$997$	−1.11789e13	−0.358320	−0.179160	−	0.983820i	$-0.557338\pi$
$997$	−1.11789e13	−0.358320	−0.179160	+	0.983820i	$0.557338\pi$
$998$	4.20505e13	1.34179
$999$	−1.79041e13	−0.568732

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.10.a.f.1.15		20
13.2	odd	12		13.10.e.a.4.8	✓	20
13.7	odd	12		13.10.e.a.10.8	yes	20
13.12	even	2	inner	169.10.a.f.1.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.e.a.4.8	✓	20	13.2	odd	12
13.10.e.a.10.8	yes	20	13.7	odd	12
169.10.a.f.1.6		20	13.12	even	2	inner
169.10.a.f.1.15		20	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 $\F_{q}$
Belyi maps

Introduction

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Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	169.10.a.f.1.15

Level	$169$
Weight	$10$
Character	169.1
Self dual	yes
Analytic conductor	$87.041$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$