LMFDB - Embedded newform 169.10.a.f.1.12

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			1.12
Root			$5.95885$ 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)

$f(q)$	$=$	$q+5.95885 q^{2} -250.658 q^{3} -476.492 q^{4} +841.807 q^{5} -1493.64 q^{6} +1268.09 q^{7} -5890.28 q^{8} +43146.7 q^{9} +5016.20 q^{10} -41521.0 q^{11} +119437. q^{12} +7556.36 q^{14} -211006. q^{15} +208865. q^{16} -310093. q^{17} +257105. q^{18} +713979. q^{19} -401114. q^{20} -317857. q^{21} -247418. q^{22} -1.16979e6 q^{23} +1.47645e6 q^{24} -1.24449e6 q^{25} -5.88137e6 q^{27} -604234. q^{28} -3.99892e6 q^{29} -1.25735e6 q^{30} -8.02230e6 q^{31} +4.26042e6 q^{32} +1.04076e7 q^{33} -1.84780e6 q^{34} +1.06749e6 q^{35} -2.05590e7 q^{36} +9.31295e6 q^{37} +4.25450e6 q^{38} -4.95848e6 q^{40} -3.10759e7 q^{41} -1.89406e6 q^{42} -2.70078e7 q^{43} +1.97844e7 q^{44} +3.63212e7 q^{45} -6.97060e6 q^{46} -9.72681e6 q^{47} -5.23537e7 q^{48} -3.87456e7 q^{49} -7.41571e6 q^{50} +7.77274e7 q^{51} +8.53737e6 q^{53} -3.50462e7 q^{54} -3.49527e7 q^{55} -7.46940e6 q^{56} -1.78965e8 q^{57} -2.38290e7 q^{58} +1.61549e8 q^{59} +1.00543e8 q^{60} -4.26305e7 q^{61} -4.78037e7 q^{62} +5.47138e7 q^{63} -8.15515e7 q^{64} +6.20174e7 q^{66} +1.07291e8 q^{67} +1.47757e8 q^{68} +2.93218e8 q^{69} +6.36099e6 q^{70} +1.58736e8 q^{71} -2.54146e8 q^{72} -7.49326e7 q^{73} +5.54945e7 q^{74} +3.11941e8 q^{75} -3.40205e8 q^{76} -5.26524e7 q^{77} +3.17665e8 q^{79} +1.75824e8 q^{80} +6.24959e8 q^{81} -1.85177e8 q^{82} +7.42376e8 q^{83} +1.51456e8 q^{84} -2.61038e8 q^{85} -1.60935e8 q^{86} +1.00236e9 q^{87} +2.44571e8 q^{88} +2.00141e8 q^{89} +2.16432e8 q^{90} +5.57395e8 q^{92} +2.01086e9 q^{93} -5.79606e7 q^{94} +6.01032e8 q^{95} -1.06791e9 q^{96} +3.37384e8 q^{97} -2.30879e8 q^{98} -1.79149e9 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 326 q^{3} + 5118 q^{4} + 129526 q^{9} + 88390 q^{10} + 427652 q^{12} + 473556 q^{14} + 1189618 q^{16} - 99312 q^{17} - 5073532 q^{22} + 6252378 q^{23} + 1529274 q^{25} + 18052718 q^{27} + 5424828 q^{29}+ \cdots + 9251202540 q^{95}+O(q^{100})$ 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

)

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

$2$	5.95885	0.263347	0.131673	−	0.991293i	$-0.457965\pi$
$2$	5.95885	0.263347	0.131673	+	0.991293i	$0.457965\pi$
$3$	−250.658	−1.78664	−0.893319	−	0.449422i	$-0.851630\pi$
$3$	−250.658	−1.78664	−0.893319	+	0.449422i	$0.851630\pi$
$4$	−476.492	−0.930649
$5$	841.807	0.602348	0.301174	−	0.953569i	$-0.402622\pi$
$5$	841.807	0.602348	0.301174	+	0.953569i	$0.402622\pi$
$6$	−1493.64	−0.470505
$7$	1268.09	0.199622	0.0998110	−	0.995006i	$-0.468176\pi$
$7$	1268.09	0.199622	0.0998110	+	0.995006i	$0.468176\pi$
$8$	−5890.28	−0.508430
$9$	43146.7	2.19208
$10$	5016.20	0.158626
$11$	−41521.0	−0.855069	−0.427534	−	0.903999i	$-0.640618\pi$
$11$	−41521.0	−0.855069	−0.427534	+	0.903999i	$0.640618\pi$
$12$	119437.	1.66273
$13$	0	0
$13$	0	0
$14$	7556.36	0.0525698
$15$	−211006.	−1.07618
$16$	208865.	0.796755
$17$	−310093.	−0.900475	−0.450238	−	0.892909i	$-0.648661\pi$
$17$	−310093.	−0.900475	−0.450238	+	0.892909i	$0.648661\pi$
$18$	257105.	0.577276
$19$	713979.	1.25688	0.628440	−	0.777858i	$-0.283694\pi$
$19$	713979.	1.25688	0.628440	+	0.777858i	$0.283694\pi$
$20$	−401114.	−0.560574
$21$	−317857.	−0.356652
$22$	−247418.	−0.225179
$23$	−1.16979e6	−0.871630	−0.435815	−	0.900036i	$-0.643540\pi$
$23$	−1.16979e6	−0.871630	−0.435815	+	0.900036i	$0.643540\pi$
$24$	1.47645e6	0.908380
$25$	−1.24449e6	−0.637177
$26$	0	0
$27$	−5.88137e6	−2.12981
$28$	−604234.	−0.185778
$29$	−3.99892e6	−1.04991	−0.524955	−	0.851130i	$-0.675918\pi$
$29$	−3.99892e6	−1.04991	−0.524955	+	0.851130i	$0.675918\pi$
$30$	−1.25735e6	−0.283408
$31$	−8.02230e6	−1.56017	−0.780084	−	0.625675i	$-0.784824\pi$
$31$	−8.02230e6	−1.56017	−0.780084	+	0.625675i	$0.784824\pi$
$32$	4.26042e6	0.718253
$33$	1.04076e7	1.52770
$34$	−1.84780e6	−0.237137
$35$	1.06749e6	0.120242
$36$	−2.05590e7	−2.04005
$37$	9.31295e6	0.816920	0.408460	−	0.912776i	$-0.366066\pi$
$37$	9.31295e6	0.816920	0.408460	+	0.912776i	$0.366066\pi$
$38$	4.25450e6	0.330995
$39$	0	0
$40$	−4.95848e6	−0.306252
$41$	−3.10759e7	−1.71750	−0.858750	−	0.512394i	$-0.828759\pi$
$41$	−3.10759e7	−1.71750	−0.858750	+	0.512394i	$0.828759\pi$
$42$	−1.89406e6	−0.0939232
$43$	−2.70078e7	−1.20470	−0.602352	−	0.798230i	$-0.705770\pi$
$43$	−2.70078e7	−1.20470	−0.602352	+	0.798230i	$0.705770\pi$
$44$	1.97844e7	0.795769
$45$	3.63212e7	1.32039
$46$	−6.97060e6	−0.229541
$47$	−9.72681e6	−0.290757	−0.145378	−	0.989376i	$-0.546440\pi$
$47$	−9.72681e6	−0.290757	−0.145378	+	0.989376i	$0.546440\pi$
$48$	−5.23537e7	−1.42351
$49$	−3.87456e7	−0.960151
$50$	−7.41571e6	−0.167798
$51$	7.77274e7	1.60882
$52$	0	0
$53$	8.53737e6	0.148622	0.0743110	−	0.997235i	$-0.476324\pi$
$53$	8.53737e6	0.148622	0.0743110	+	0.997235i	$0.476324\pi$
$54$	−3.50462e7	−0.560879
$55$	−3.49527e7	−0.515049
$56$	−7.46940e6	−0.101494
$57$	−1.78965e8	−2.24559
$58$	−2.38290e7	−0.276490
$59$	1.61549e8	1.73568	0.867842	−	0.496840i	$-0.165506\pi$
$59$	1.61549e8	1.73568	0.867842	+	0.496840i	$0.165506\pi$
$60$	1.00543e8	1.00154
$61$	−4.26305e7	−0.394218	−0.197109	−	0.980382i	$-0.563155\pi$
$61$	−4.26305e7	−0.394218	−0.197109	+	0.980382i	$0.563155\pi$
$62$	−4.78037e7	−0.410865
$63$	5.47138e7	0.437587
$64$	−8.15515e7	−0.607606
$65$	0	0
$66$	6.20174e7	0.402314
$67$	1.07291e8	0.650468	0.325234	−	0.945634i	$-0.394557\pi$
$67$	1.07291e8	0.650468	0.325234	+	0.945634i	$0.394557\pi$
$68$	1.47757e8	0.838026
$69$	2.93218e8	1.55729
$70$	6.36099e6	0.0316653
$71$	1.58736e8	0.741333	0.370666	−	0.928766i	$-0.379129\pi$
$71$	1.58736e8	0.741333	0.370666	+	0.928766i	$0.379129\pi$
$72$	−2.54146e8	−1.11452
$73$	−7.49326e7	−0.308829	−0.154414	−	0.988006i	$-0.549349\pi$
$73$	−7.49326e7	−0.308829	−0.154414	+	0.988006i	$0.549349\pi$
$74$	5.54945e7	0.215133
$75$	3.11941e8	1.13841
$76$	−3.40205e8	−1.16971
$77$	−5.26524e7	−0.170691
$78$	0	0
$79$	3.17665e8	0.917586	0.458793	−	0.888543i	$-0.348282\pi$
$79$	3.17665e8	0.917586	0.458793	+	0.888543i	$0.348282\pi$
$80$	1.75824e8	0.479924
$81$	6.24959e8	1.61313
$82$	−1.85177e8	−0.452298
$83$	7.42376e8	1.71701	0.858505	−	0.512806i	$-0.171394\pi$
$83$	7.42376e8	1.71701	0.858505	+	0.512806i	$0.171394\pi$
$84$	1.51456e8	0.331918
$85$	−2.61038e8	−0.542399
$86$	−1.60935e8	−0.317255
$87$	1.00236e9	1.87581
$88$	2.44571e8	0.434742
$89$	2.00141e8	0.338128	0.169064	−	0.985605i	$-0.445925\pi$
$89$	2.00141e8	0.338128	0.169064	+	0.985605i	$0.445925\pi$
$90$	2.16432e8	0.347721
$91$	0	0
$92$	5.57395e8	0.811181
$93$	2.01086e9	2.78746
$94$	−5.79606e7	−0.0765698
$95$	6.01032e8	0.757080
$96$	−1.06791e9	−1.28326
$97$	3.37384e8	0.386947	0.193474	−	0.981105i	$-0.438025\pi$
$97$	3.37384e8	0.386947	0.193474	+	0.981105i	$0.438025\pi$
$98$	−2.30879e8	−0.252853
$99$	−1.79149e9	−1.87438
$100$	5.92988e8	0.592988
$101$	−8.99494e8	−0.860106	−0.430053	−	0.902804i	$-0.641505\pi$
$101$	−8.99494e8	−0.860106	−0.430053	+	0.902804i	$0.641505\pi$
$102$	4.63166e8	0.423678
$103$	−1.30979e9	−1.14666	−0.573331	−	0.819324i	$-0.694349\pi$
$103$	−1.30979e9	−1.14666	−0.573331	+	0.819324i	$0.694349\pi$
$104$	0	0
$105$	−2.67574e8	−0.214829
$106$	5.08730e7	0.0391391
$107$	−6.26831e8	−0.462299	−0.231150	−	0.972918i	$-0.574249\pi$
$107$	−6.26831e8	−0.462299	−0.231150	+	0.972918i	$0.574249\pi$
$108$	2.80242e9	1.98211
$109$	−7.68123e8	−0.521208	−0.260604	−	0.965446i	$-0.583922\pi$
$109$	−7.68123e8	−0.521208	−0.260604	+	0.965446i	$0.583922\pi$
$110$	−2.08278e8	−0.135636
$111$	−2.33437e9	−1.45954
$112$	2.64859e8	0.159050
$113$	−1.42711e9	−0.823389	−0.411694	−	0.911322i	$-0.635063\pi$
$113$	−1.42711e9	−0.823389	−0.411694	+	0.911322i	$0.635063\pi$
$114$	−1.06643e9	−0.591369
$115$	−9.84736e8	−0.525025
$116$	1.90546e9	0.977097
$117$	0	0
$118$	9.62648e8	0.457087
$119$	−3.93225e8	−0.179755
$120$	1.24288e9	0.547161
$121$	−6.33951e8	−0.268857
$122$	−2.54029e8	−0.103816
$123$	7.78945e9	3.06855
$124$	3.82256e9	1.45197
$125$	−2.69177e9	−0.986150
$126$	3.26032e8	0.115237
$127$	−2.55295e9	−0.870815	−0.435408	−	0.900233i	$-0.643396\pi$
$127$	−2.55295e9	−0.870815	−0.435408	+	0.900233i	$0.643396\pi$
$128$	−2.66729e9	−0.878264
$129$	6.76972e9	2.15237
$130$	0	0
$131$	−1.50087e9	−0.445268	−0.222634	−	0.974902i	$-0.571465\pi$
$131$	−1.50087e9	−0.445268	−0.222634	+	0.974902i	$0.571465\pi$
$132$	−4.95914e9	−1.42175
$133$	9.05389e8	0.250901
$134$	6.39330e8	0.171298
$135$	−4.95097e9	−1.28289
$136$	1.82653e9	0.457828
$137$	5.49548e8	0.133279	0.0666397	−	0.997777i	$-0.478772\pi$
$137$	5.49548e8	0.133279	0.0666397	+	0.997777i	$0.478772\pi$
$138$	1.74724e9	0.410107
$139$	3.33033e9	0.756695	0.378347	−	0.925664i	$-0.376493\pi$
$139$	3.33033e9	0.756695	0.378347	+	0.925664i	$0.376493\pi$
$140$	−5.08649e8	−0.111903
$141$	2.43811e9	0.519478
$142$	9.45885e8	0.195228
$143$	0	0
$144$	9.01181e9	1.74655
$145$	−3.36632e9	−0.632411
$146$	−4.46512e8	−0.0813290
$147$	9.71190e9	1.71544
$148$	−4.43755e9	−0.760265
$149$	5.84923e9	0.972212	0.486106	−	0.873900i	$-0.338417\pi$
$149$	5.84923e9	0.972212	0.486106	+	0.873900i	$0.338417\pi$
$150$	1.85881e9	0.299795
$151$	−5.21852e9	−0.816867	−0.408433	−	0.912788i	$-0.633925\pi$
$151$	−5.21852e9	−0.816867	−0.408433	+	0.912788i	$0.633925\pi$
$152$	−4.20553e9	−0.639036
$153$	−1.33795e10	−1.97391
$154$	−3.13748e8	−0.0449508
$155$	−6.75323e9	−0.939764
$156$	0	0
$157$	−2.70457e9	−0.355262	−0.177631	−	0.984097i	$-0.556843\pi$
$157$	−2.70457e9	−0.355262	−0.177631	+	0.984097i	$0.556843\pi$
$158$	1.89292e9	0.241643
$159$	−2.13996e9	−0.265534
$160$	3.58645e9	0.432638
$161$	−1.48340e9	−0.173997
$162$	3.72404e9	0.424812
$163$	−6.07123e9	−0.673647	−0.336823	−	0.941568i	$-0.609353\pi$
$163$	−6.07123e9	−0.673647	−0.336823	+	0.941568i	$0.609353\pi$
$164$	1.48074e10	1.59839
$165$	8.76119e9	0.920206
$166$	4.42371e9	0.452169
$167$	3.39724e9	0.337988	0.168994	−	0.985617i	$-0.445948\pi$
$167$	3.39724e9	0.337988	0.168994	+	0.985617i	$0.445948\pi$
$168$	1.87227e9	0.181333
$169$	0	0
$170$	−1.55549e9	−0.142839
$171$	3.08058e10	2.75518
$172$	1.28690e10	1.12116
$173$	−3.31703e9	−0.281542	−0.140771	−	0.990042i	$-0.544958\pi$
$173$	−3.31703e9	−0.281542	−0.140771	+	0.990042i	$0.544958\pi$
$174$	5.97294e9	0.493988
$175$	−1.57812e9	−0.127195
$176$	−8.67227e9	−0.681281
$177$	−4.04937e10	−3.10104
$178$	1.19261e9	0.0890450
$179$	1.76717e10	1.28659	0.643295	−	0.765618i	$-0.277567\pi$
$179$	1.76717e10	1.28659	0.643295	+	0.765618i	$0.277567\pi$
$180$	−1.73067e10	−1.22882
$181$	6.42302e9	0.444821	0.222411	−	0.974953i	$-0.428607\pi$
$181$	6.42302e9	0.444821	0.222411	+	0.974953i	$0.428607\pi$
$182$	0	0
$183$	1.06857e10	0.704325
$184$	6.89039e9	0.443163
$185$	7.83971e9	0.492070
$186$	1.19824e10	0.734067
$187$	1.28754e10	0.769968
$188$	4.63475e9	0.270592
$189$	−7.45810e9	−0.425158
$190$	3.58146e9	0.199374
$191$	3.10908e10	1.69037	0.845185	−	0.534474i	$-0.179490\pi$
$191$	3.10908e10	1.69037	0.845185	+	0.534474i	$0.179490\pi$
$192$	2.04416e10	1.08557
$193$	1.18347e10	0.613971	0.306985	−	0.951714i	$-0.400680\pi$
$193$	1.18347e10	0.613971	0.306985	+	0.951714i	$0.400680\pi$
$194$	2.01042e9	0.101901
$195$	0	0
$196$	1.84620e10	0.893563
$197$	5.10133e9	0.241316	0.120658	−	0.992694i	$-0.461500\pi$
$197$	5.10133e9	0.241316	0.120658	+	0.992694i	$0.461500\pi$
$198$	−1.06753e10	−0.493611
$199$	−3.46014e9	−0.156406	−0.0782032	−	0.996937i	$-0.524918\pi$
$199$	−3.46014e9	−0.156406	−0.0782032	+	0.996937i	$0.524918\pi$
$200$	7.33037e9	0.323960
$201$	−2.68933e10	−1.16215
$202$	−5.35995e9	−0.226506
$203$	−5.07099e9	−0.209585
$204$	−3.70365e10	−1.49725
$205$	−2.61599e10	−1.03453
$206$	−7.80487e9	−0.301970
$207$	−5.04725e10	−1.91068
$208$	0	0
$209$	−2.96451e10	−1.07472
$210$	−1.59444e9	−0.0565745
$211$	1.60621e10	0.557869	0.278935	−	0.960310i	$-0.410019\pi$
$211$	1.60621e10	0.557869	0.278935	+	0.960310i	$0.410019\pi$
$212$	−4.06799e9	−0.138315
$213$	−3.97886e10	−1.32449
$214$	−3.73519e9	−0.121745
$215$	−2.27353e10	−0.725651
$216$	3.46429e10	1.08286
$217$	−1.01730e10	−0.311444
$218$	−4.57713e9	−0.137258
$219$	1.87825e10	0.551765
$220$	1.66547e10	0.479330
$221$	0	0
$222$	−1.39102e10	−0.384365
$223$	8.34952e9	0.226094	0.113047	−	0.993590i	$-0.463939\pi$
$223$	8.34952e9	0.226094	0.113047	+	0.993590i	$0.463939\pi$
$224$	5.40259e9	0.143379
$225$	−5.36954e10	−1.39674
$226$	−8.50395e9	−0.216837
$227$	−7.13717e8	−0.0178406	−0.00892031	−	0.999960i	$-0.502839\pi$
$227$	−7.13717e8	−0.0178406	−0.00892031	+	0.999960i	$0.502839\pi$
$228$	8.52753e10	2.08986
$229$	6.88093e10	1.65344	0.826718	−	0.562617i	$-0.190205\pi$
$229$	6.88093e10	1.65344	0.826718	+	0.562617i	$0.190205\pi$
$230$	−5.86790e9	−0.138263
$231$	1.31978e10	0.304962
$232$	2.35548e10	0.533806
$233$	1.62829e10	0.361936	0.180968	−	0.983489i	$-0.442077\pi$
$233$	1.62829e10	0.361936	0.180968	+	0.983489i	$0.442077\pi$
$234$	0	0
$235$	−8.18809e9	−0.175137
$236$	−7.69769e10	−1.61531
$237$	−7.96253e10	−1.63939
$238$	−2.34317e9	−0.0473378
$239$	9.39077e10	1.86170	0.930852	−	0.365397i	$-0.119067\pi$
$239$	9.39077e10	1.86170	0.930852	+	0.365397i	$0.119067\pi$
$240$	−4.40717e10	−0.857451
$241$	7.50295e10	1.43270	0.716350	−	0.697741i	$-0.245812\pi$
$241$	7.50295e10	1.43270	0.716350	+	0.697741i	$0.245812\pi$
$242$	−3.77762e9	−0.0708027
$243$	−4.08882e10	−0.752263
$244$	2.03131e10	0.366878
$245$	−3.26163e10	−0.578345
$246$	4.64162e10	0.808093
$247$	0	0
$248$	4.72536e10	0.793236
$249$	−1.86083e11	−3.06768
$250$	−1.60399e10	−0.259699
$251$	−3.76195e10	−0.598248	−0.299124	−	0.954214i	$-0.596694\pi$
$251$	−3.76195e10	−0.598248	−0.299124	+	0.954214i	$0.596694\pi$
$252$	−2.60707e10	−0.407240
$253$	4.85709e10	0.745304
$254$	−1.52127e10	−0.229326
$255$	6.54315e10	0.969072
$256$	2.58604e10	0.376318
$257$	−5.20095e10	−0.743676	−0.371838	−	0.928298i	$-0.621272\pi$
$257$	−5.20095e10	−0.743676	−0.371838	+	0.928298i	$0.621272\pi$
$258$	4.03398e10	0.566820
$259$	1.18096e10	0.163075
$260$	0	0
$261$	−1.72540e11	−2.30148
$262$	−8.94345e9	−0.117260
$263$	4.77077e10	0.614876	0.307438	−	0.951568i	$-0.400528\pi$
$263$	4.77077e10	0.614876	0.307438	+	0.951568i	$0.400528\pi$
$264$	−6.13037e10	−0.776728
$265$	7.18682e9	0.0895221
$266$	5.39508e9	0.0660740
$267$	−5.01671e10	−0.604113
$268$	−5.11232e10	−0.605357
$269$	−1.56389e11	−1.82105	−0.910524	−	0.413457i	$-0.864321\pi$
$269$	−1.56389e11	−1.82105	−0.910524	+	0.413457i	$0.864321\pi$
$270$	−2.95021e10	−0.337844
$271$	−2.01739e10	−0.227211	−0.113605	−	0.993526i	$-0.536240\pi$
$271$	−2.01739e10	−0.227211	−0.113605	+	0.993526i	$0.536240\pi$
$272$	−6.47674e10	−0.717458
$273$	0	0
$274$	3.27467e9	0.0350987
$275$	5.16724e10	0.544830
$276$	−1.39716e11	−1.44929
$277$	−1.00639e11	−1.02709	−0.513543	−	0.858064i	$-0.671667\pi$
$277$	−1.00639e11	−1.02709	−0.513543	+	0.858064i	$0.671667\pi$
$278$	1.98449e10	0.199273
$279$	−3.46136e11	−3.42001
$280$	−6.28779e9	−0.0611346
$281$	3.67033e9	0.0351178	0.0175589	−	0.999846i	$-0.494411\pi$
$281$	3.67033e9	0.0351178	0.0175589	+	0.999846i	$0.494411\pi$
$282$	1.45283e10	0.136803
$283$	1.39676e11	1.29445	0.647223	−	0.762301i	$-0.275930\pi$
$283$	1.39676e11	1.29445	0.647223	+	0.762301i	$0.275930\pi$
$284$	−7.56365e10	−0.689920
$285$	−1.50654e11	−1.35263
$286$	0	0
$287$	−3.94071e10	−0.342851
$288$	1.83823e11	1.57447
$289$	−2.24303e10	−0.189145
$290$	−2.00594e10	−0.166543
$291$	−8.45682e10	−0.691335
$292$	3.57048e10	0.287411
$293$	−7.26723e10	−0.576056	−0.288028	−	0.957622i	$-0.593000\pi$
$293$	−7.26723e10	−0.576056	−0.288028	+	0.957622i	$0.593000\pi$
$294$	5.78718e10	0.451756
$295$	1.35993e11	1.04549
$296$	−5.48559e10	−0.415346
$297$	2.44200e11	1.82114
$298$	3.48547e10	0.256029
$299$	0	0
$300$	−1.48637e11	−1.05946
$301$	−3.42482e10	−0.240486
$302$	−3.10964e10	−0.215119
$303$	2.25466e11	1.53670
$304$	1.49125e11	1.00143
$305$	−3.58867e10	−0.237456
$306$	−7.97263e10	−0.519823
$307$	−2.00120e11	−1.28579	−0.642893	−	0.765956i	$-0.722266\pi$
$307$	−2.00120e11	−1.28579	−0.642893	+	0.765956i	$0.722266\pi$
$308$	2.50884e10	0.158853
$309$	3.28311e11	2.04867
$310$	−4.02415e10	−0.247484
$311$	7.40889e10	0.449088	0.224544	−	0.974464i	$-0.427911\pi$
$311$	7.40889e10	0.449088	0.224544	+	0.974464i	$0.427911\pi$
$312$	0	0
$313$	2.85248e11	1.67986	0.839930	−	0.542694i	$-0.182596\pi$
$313$	2.85248e11	1.67986	0.839930	+	0.542694i	$0.182596\pi$
$314$	−1.61161e10	−0.0935571
$315$	4.60585e10	0.263580
$316$	−1.51365e11	−0.853950
$317$	3.13947e11	1.74618	0.873090	−	0.487559i	$-0.162112\pi$
$317$	3.13947e11	1.74618	0.873090	+	0.487559i	$0.162112\pi$
$318$	−1.27517e10	−0.0699274
$319$	1.66039e11	0.897746
$320$	−6.86506e10	−0.365990
$321$	1.57120e11	0.825962
$322$	−8.83934e9	−0.0458214
$323$	−2.21400e11	−1.13179
$324$	−2.97788e11	−1.50125
$325$	0	0
$326$	−3.61776e10	−0.177403
$327$	1.92536e11	0.931211
$328$	1.83046e11	0.873229
$329$	−1.23345e10	−0.0580415
$330$	5.22066e10	0.242333
$331$	2.76607e10	0.126659	0.0633296	−	0.997993i	$-0.479828\pi$
$331$	2.76607e10	0.126659	0.0633296	+	0.997993i	$0.479828\pi$
$332$	−3.53736e11	−1.59793
$333$	4.01823e11	1.79075
$334$	2.02436e10	0.0890081
$335$	9.03181e10	0.391808
$336$	−6.63891e10	−0.284165
$337$	2.23096e11	0.942232	0.471116	−	0.882071i	$-0.343851\pi$
$337$	2.23096e11	0.942232	0.471116	+	0.882071i	$0.343851\pi$
$338$	0	0
$339$	3.57718e11	1.47110
$340$	1.24383e11	0.504783
$341$	3.33094e11	1.33405
$342$	1.83567e11	0.725567
$343$	−1.00305e11	−0.391289
$344$	1.59083e11	0.612508
$345$	2.46833e11	0.938029
$346$	−1.97657e10	−0.0741430
$347$	4.59478e10	0.170130	0.0850652	−	0.996375i	$-0.472890\pi$
$347$	4.59478e10	0.170130	0.0850652	+	0.996375i	$0.472890\pi$
$348$	−4.77619e11	−1.74572
$349$	−8.20298e10	−0.295976	−0.147988	−	0.988989i	$-0.547280\pi$
$349$	−8.20298e10	−0.295976	−0.147988	+	0.988989i	$0.547280\pi$
$350$	−9.40378e9	−0.0334963
$351$	0	0
$352$	−1.76897e11	−0.614155
$353$	−2.20118e11	−0.754518	−0.377259	−	0.926108i	$-0.623133\pi$
$353$	−2.20118e11	−0.754518	−0.377259	+	0.926108i	$0.623133\pi$
$354$	−2.41296e11	−0.816649
$355$	1.33625e11	0.446540
$356$	−9.53657e10	−0.314679
$357$	9.85653e10	0.321157
$358$	1.05303e11	0.338819
$359$	3.75070e11	1.19175	0.595877	−	0.803075i	$-0.296804\pi$
$359$	3.75070e11	1.19175	0.595877	+	0.803075i	$0.296804\pi$
$360$	−2.13942e11	−0.671327
$361$	1.87078e11	0.579749
$362$	3.82738e10	0.117142
$363$	1.58905e11	0.480351
$364$	0	0
$365$	−6.30787e10	−0.186022
$366$	6.36745e10	0.185482
$367$	1.09206e10	0.0314230	0.0157115	−	0.999877i	$-0.494999\pi$
$367$	1.09206e10	0.0314230	0.0157115	+	0.999877i	$0.494999\pi$
$368$	−2.44328e11	−0.694476
$369$	−1.34082e12	−3.76490
$370$	4.67157e10	0.129585
$371$	1.08261e10	0.0296682
$372$	−9.58158e11	−2.59414
$373$	−3.75175e11	−1.00356	−0.501781	−	0.864995i	$-0.667321\pi$
$373$	−3.75175e11	−1.00356	−0.501781	+	0.864995i	$0.667321\pi$
$374$	7.67225e10	0.202769
$375$	6.74715e11	1.76189
$376$	5.72936e10	0.147829
$377$	0	0
$378$	−4.44417e10	−0.111964
$379$	−6.23413e11	−1.55203	−0.776014	−	0.630716i	$-0.782761\pi$
$379$	−6.23413e11	−1.55203	−0.776014	+	0.630716i	$0.782761\pi$
$380$	−2.86387e11	−0.704575
$381$	6.39919e11	1.55583
$382$	1.85265e11	0.445153
$383$	6.22449e11	1.47812	0.739059	−	0.673641i	$-0.235270\pi$
$383$	6.22449e11	1.47812	0.739059	+	0.673641i	$0.235270\pi$
$384$	6.68578e11	1.56914
$385$	−4.43231e10	−0.102815
$386$	7.05210e10	0.161687
$387$	−1.16529e12	−2.64081
$388$	−1.60761e11	−0.360112
$389$	5.65612e11	1.25241	0.626204	−	0.779659i	$-0.284608\pi$
$389$	5.65612e11	1.25241	0.626204	+	0.779659i	$0.284608\pi$
$390$	0	0
$391$	3.62743e11	0.784881
$392$	2.28222e11	0.488169
$393$	3.76205e11	0.795533
$394$	3.03981e10	0.0635497
$395$	2.67412e11	0.552706
$396$	8.53633e11	1.74439
$397$	−5.77427e11	−1.16665	−0.583324	−	0.812239i	$-0.698248\pi$
$397$	−5.77427e11	−1.16665	−0.583324	+	0.812239i	$0.698248\pi$
$398$	−2.06184e10	−0.0411891
$399$	−2.26943e11	−0.448270
$400$	−2.59929e11	−0.507674
$401$	−5.09487e11	−0.983973	−0.491986	−	0.870603i	$-0.663729\pi$
$401$	−5.09487e11	−0.983973	−0.491986	+	0.870603i	$0.663729\pi$
$402$	−1.60253e11	−0.306048
$403$	0	0
$404$	4.28602e11	0.800456
$405$	5.26094e11	0.971664
$406$	−3.02173e10	−0.0551936
$407$	−3.86683e11	−0.698523
$408$	−4.57836e11	−0.817974
$409$	−6.35433e10	−0.112283	−0.0561416	−	0.998423i	$-0.517880\pi$
$409$	−6.35433e10	−0.112283	−0.0561416	+	0.998423i	$0.517880\pi$
$410$	−1.55883e11	−0.272441
$411$	−1.37749e11	−0.238122
$412$	6.24106e11	1.06714
$413$	2.04859e11	0.346481
$414$	−3.00758e11	−0.503171
$415$	6.24937e11	1.03424
$416$	0	0
$417$	−8.34775e11	−1.35194
$418$	−1.76651e11	−0.283024
$419$	9.02911e11	1.43114	0.715569	−	0.698542i	$-0.246167\pi$
$419$	9.02911e11	1.43114	0.715569	+	0.698542i	$0.246167\pi$
$420$	1.27497e11	0.199930
$421$	1.03641e12	1.60791	0.803956	−	0.594689i	$-0.202725\pi$
$421$	1.03641e12	1.60791	0.803956	+	0.594689i	$0.202725\pi$
$422$	9.57119e10	0.146913
$423$	−4.19679e11	−0.637362
$424$	−5.02875e10	−0.0755638
$425$	3.85906e11	0.573762
$426$	−2.37094e11	−0.348801
$427$	−5.40593e10	−0.0786946
$428$	2.98680e11	0.430238
$429$	0	0
$430$	−1.35476e11	−0.191098
$431$	−3.10199e10	−0.0433005	−0.0216503	−	0.999766i	$-0.506892\pi$
$431$	−3.10199e10	−0.0433005	−0.0216503	+	0.999766i	$0.506892\pi$
$432$	−1.22841e12	−1.69694
$433$	6.70076e11	0.916069	0.458035	−	0.888934i	$-0.348554\pi$
$433$	6.70076e11	0.916069	0.458035	+	0.888934i	$0.348554\pi$
$434$	−6.06194e10	−0.0820177
$435$	8.43797e11	1.12989
$436$	3.66004e11	0.485062
$437$	−8.35205e11	−1.09554
$438$	1.11922e11	0.145306
$439$	−4.77633e11	−0.613767	−0.306884	−	0.951747i	$-0.599286\pi$
$439$	−4.77633e11	−0.613767	−0.306884	+	0.951747i	$0.599286\pi$
$440$	2.05881e11	0.261866
$441$	−1.67174e12	−2.10473
$442$	0	0
$443$	5.02360e11	0.619723	0.309862	−	0.950782i	$-0.399717\pi$
$443$	5.02360e11	0.619723	0.309862	+	0.950782i	$0.399717\pi$
$444$	1.11231e12	1.35832
$445$	1.68480e11	0.203671
$446$	4.97535e10	0.0595411
$447$	−1.46616e12	−1.73699
$448$	−1.03415e11	−0.121292
$449$	−4.72576e11	−0.548735	−0.274368	−	0.961625i	$-0.588469\pi$
$449$	−4.72576e11	−0.548735	−0.274368	+	0.961625i	$0.588469\pi$
$450$	−3.19963e11	−0.367827
$451$	1.29031e12	1.46858
$452$	6.80007e11	0.766286
$453$	1.30807e12	1.45945
$454$	−4.25294e9	−0.00469827
$455$	0	0
$456$	1.05415e12	1.14173
$457$	8.00021e11	0.857982	0.428991	−	0.903309i	$-0.358869\pi$
$457$	8.00021e11	0.857982	0.428991	+	0.903309i	$0.358869\pi$
$458$	4.10024e11	0.435427
$459$	1.82377e12	1.91784
$460$	4.69219e11	0.488613
$461$	−1.75335e12	−1.80807	−0.904034	−	0.427461i	$-0.859408\pi$
$461$	−1.75335e12	−1.80807	−0.904034	+	0.427461i	$0.859408\pi$
$462$	7.86435e10	0.0803108
$463$	4.08855e11	0.413481	0.206740	−	0.978396i	$-0.433714\pi$
$463$	4.08855e11	0.413481	0.206740	+	0.978396i	$0.433714\pi$
$464$	−8.35234e11	−0.836522
$465$	1.69275e12	1.67902
$466$	9.70277e10	0.0953145
$467$	9.38289e10	0.0912874	0.0456437	−	0.998958i	$-0.485466\pi$
$467$	9.38289e10	0.0912874	0.0456437	+	0.998958i	$0.485466\pi$
$468$	0	0
$469$	1.36054e11	0.129848
$470$	−4.87917e10	−0.0461217
$471$	6.77922e11	0.634726
$472$	−9.51570e11	−0.882474
$473$	1.12139e12	1.03011
$474$	−4.74476e11	−0.431729
$475$	−8.88537e11	−0.800856
$476$	1.87369e11	0.167288
$477$	3.68359e11	0.325791
$478$	5.59582e11	0.490273
$479$	−5.16728e11	−0.448490	−0.224245	−	0.974533i	$-0.571992\pi$
$479$	−5.16728e11	−0.448490	−0.224245	+	0.974533i	$0.571992\pi$
$480$	−8.98974e11	−0.772968
$481$	0	0
$482$	4.47090e11	0.377297
$483$	3.71826e11	0.310869
$484$	3.02073e11	0.250212
$485$	2.84012e11	0.233077
$486$	−2.43647e11	−0.198106
$487$	5.00815e11	0.403457	0.201728	−	0.979442i	$-0.435344\pi$
$487$	5.00815e11	0.403457	0.201728	+	0.979442i	$0.435344\pi$
$488$	2.51106e11	0.200432
$489$	1.52180e12	1.20356
$490$	−1.94356e11	−0.152305
$491$	4.95601e11	0.384827	0.192414	−	0.981314i	$-0.438368\pi$
$491$	4.95601e11	0.384827	0.192414	+	0.981314i	$0.438368\pi$
$492$	−3.71161e12	−2.85574
$493$	1.24004e12	0.945418
$494$	0	0
$495$	−1.50809e12	−1.12903
$496$	−1.67558e12	−1.24307
$497$	2.01292e11	0.147986
$498$	−1.10884e12	−0.807862
$499$	4.85674e11	0.350665	0.175332	−	0.984509i	$-0.443900\pi$
$499$	4.85674e11	0.350665	0.175332	+	0.984509i	$0.443900\pi$
$500$	1.28261e12	0.917759
$501$	−8.51546e11	−0.603863
$502$	−2.24169e11	−0.157547
$503$	1.17653e12	0.819494	0.409747	−	0.912199i	$-0.365617\pi$
$503$	1.17653e12	0.819494	0.409747	+	0.912199i	$0.365617\pi$
$504$	−3.22280e11	−0.222482
$505$	−7.57200e11	−0.518083
$506$	2.89427e11	0.196273
$507$	0	0
$508$	1.21646e12	0.810423
$509$	−1.59444e11	−0.105288	−0.0526439	−	0.998613i	$-0.516765\pi$
$509$	−1.59444e11	−0.105288	−0.0526439	+	0.998613i	$0.516765\pi$
$510$	3.89897e11	0.255202
$511$	−9.50212e10	−0.0616490
$512$	1.51975e12	0.977366
$513$	−4.19917e12	−2.67692
$514$	−3.09917e11	−0.195845
$515$	−1.10259e12	−0.690689
$516$	−3.22572e12	−2.00310
$517$	4.03867e11	0.248617
$518$	7.03720e10	0.0429453
$519$	8.31443e11	0.503013
$520$	0	0
$521$	−1.66196e12	−0.988211	−0.494105	−	0.869402i	$-0.664504\pi$
$521$	−1.66196e12	−0.988211	−0.494105	+	0.869402i	$0.664504\pi$
$522$	−1.02814e12	−0.606088
$523$	−3.12718e12	−1.82766	−0.913830	−	0.406096i	$-0.866890\pi$
$523$	−3.12718e12	−1.82766	−0.913830	+	0.406096i	$0.866890\pi$
$524$	7.15151e11	0.414388
$525$	3.95569e11	0.227251
$526$	2.84283e11	0.161925
$527$	2.48766e12	1.40489
$528$	2.17378e12	1.21720
$529$	−4.32746e11	−0.240261
$530$	4.28252e10	0.0235753
$531$	6.97031e12	3.80476
$532$	−4.31410e11	−0.233501
$533$	0	0
$534$	−2.98938e11	−0.159091
$535$	−5.27670e11	−0.278465
$536$	−6.31972e11	−0.330717
$537$	−4.42957e12	−2.29867
$538$	−9.31900e11	−0.479567
$539$	1.60876e12	0.820995
$540$	2.35910e12	1.19392
$541$	3.81175e11	0.191310	0.0956548	−	0.995415i	$-0.469506\pi$
$541$	3.81175e11	0.191310	0.0956548	+	0.995415i	$0.469506\pi$
$542$	−1.20213e11	−0.0598351
$543$	−1.60998e12	−0.794735
$544$	−1.32113e12	−0.646769
$545$	−6.46611e11	−0.313949
$546$	0	0
$547$	−5.62804e11	−0.268791	−0.134395	−	0.990928i	$-0.542909\pi$
$547$	−5.62804e11	−0.268791	−0.134395	+	0.990928i	$0.542909\pi$
$548$	−2.61855e11	−0.124036
$549$	−1.83936e12	−0.864156
$550$	3.07908e11	0.143479
$551$	−2.85515e12	−1.31961
$552$	−1.72713e12	−0.791772
$553$	4.02827e11	0.183170
$554$	−5.99693e11	−0.270480
$555$	−1.96509e12	−0.879151
$556$	−1.58688e12	−0.704217
$557$	2.46974e12	1.08718	0.543592	−	0.839349i	$-0.317064\pi$
$557$	2.46974e12	1.08718	0.543592	+	0.839349i	$0.317064\pi$
$558$	−2.06257e12	−0.900648
$559$	0	0
$560$	2.22960e11	0.0958034
$561$	−3.22732e12	−1.37565
$562$	2.18710e10	0.00924814
$563$	−3.89266e11	−0.163290	−0.0816449	−	0.996661i	$-0.526017\pi$
$563$	−3.89266e11	−0.163290	−0.0816449	+	0.996661i	$0.526017\pi$
$564$	−1.16174e12	−0.483451
$565$	−1.20135e12	−0.495966
$566$	8.32311e11	0.340888
$567$	7.92503e11	0.322016
$568$	−9.35000e11	−0.376916
$569$	−1.73577e12	−0.694205	−0.347102	−	0.937827i	$-0.612834\pi$
$569$	−1.73577e12	−0.694205	−0.347102	+	0.937827i	$0.612834\pi$
$570$	−8.97724e11	−0.356210
$571$	−6.09927e11	−0.240113	−0.120056	−	0.992767i	$-0.538308\pi$
$571$	−6.09927e11	−0.240113	−0.120056	+	0.992767i	$0.538308\pi$
$572$	0	0
$573$	−7.79317e12	−3.02008
$574$	−2.34821e11	−0.0902887
$575$	1.45579e12	0.555383
$576$	−3.51867e12	−1.33192
$577$	3.15162e12	1.18370	0.591852	−	0.806047i	$-0.298397\pi$
$577$	3.15162e12	1.18370	0.591852	+	0.806047i	$0.298397\pi$
$578$	−1.33659e11	−0.0498106
$579$	−2.96646e12	−1.09694
$580$	1.60403e12	0.588553
$581$	9.41399e11	0.342753
$582$	−5.03929e11	−0.182061
$583$	−3.54481e11	−0.127082
$584$	4.41374e11	0.157018
$585$	0	0
$586$	−4.33044e11	−0.151702
$587$	4.30912e11	0.149802	0.0749010	−	0.997191i	$-0.476136\pi$
$587$	4.30912e11	0.149802	0.0749010	+	0.997191i	$0.476136\pi$
$588$	−4.62764e12	−1.59647
$589$	−5.72775e12	−1.96095
$590$	8.10364e11	0.275325
$591$	−1.27869e12	−0.431144
$592$	1.94515e12	0.650885
$593$	1.36406e12	0.452987	0.226494	−	0.974013i	$-0.427274\pi$
$593$	1.36406e12	0.452987	0.226494	+	0.974013i	$0.427274\pi$
$594$	1.45515e12	0.479590
$595$	−3.31020e11	−0.108275
$596$	−2.78711e12	−0.904787
$597$	8.67312e11	0.279442
$598$	0	0
$599$	8.07677e11	0.256340	0.128170	−	0.991752i	$-0.459090\pi$
$599$	8.07677e11	0.256340	0.128170	+	0.991752i	$0.459090\pi$
$600$	−1.83742e12	−0.578799
$601$	5.46410e12	1.70838	0.854188	−	0.519964i	$-0.174055\pi$
$601$	5.46410e12	1.70838	0.854188	+	0.519964i	$0.174055\pi$
$602$	−2.04080e11	−0.0633311
$603$	4.62924e12	1.42588
$604$	2.48658e12	0.760216
$605$	−5.33665e11	−0.161946
$606$	1.34352e12	0.404684
$607$	−1.26439e12	−0.378035	−0.189017	−	0.981974i	$-0.560530\pi$
$607$	−1.26439e12	−0.378035	−0.189017	+	0.981974i	$0.560530\pi$
$608$	3.04185e12	0.902758
$609$	1.27109e12	0.374453
$610$	−2.13843e11	−0.0625333
$611$	0	0
$612$	6.37521e12	1.83702
$613$	−9.45976e11	−0.270588	−0.135294	−	0.990806i	$-0.543198\pi$
$613$	−9.45976e11	−0.270588	−0.135294	+	0.990806i	$0.543198\pi$
$614$	−1.19249e12	−0.338607
$615$	6.55721e12	1.84834
$616$	3.10137e11	0.0867842
$617$	−1.89715e12	−0.527008	−0.263504	−	0.964658i	$-0.584878\pi$
$617$	−1.89715e12	−0.527008	−0.263504	+	0.964658i	$0.584878\pi$
$618$	1.95636e12	0.539510
$619$	−3.25858e12	−0.892115	−0.446057	−	0.895004i	$-0.647172\pi$
$619$	−3.25858e12	−0.892115	−0.446057	+	0.895004i	$0.647172\pi$
$620$	3.21786e12	0.874590
$621$	6.87996e12	1.85641
$622$	4.41485e11	0.118266
$623$	2.53797e11	0.0674979
$624$	0	0
$625$	1.64686e11	0.0431716
$626$	1.69975e12	0.442386
$627$	7.43080e12	1.92014
$628$	1.28870e12	0.330624
$629$	−2.88788e12	−0.735616
$630$	2.74456e11	0.0694128
$631$	−2.46400e12	−0.618741	−0.309370	−	0.950942i	$-0.600118\pi$
$631$	−2.46400e12	−0.618741	−0.309370	+	0.950942i	$0.600118\pi$
$632$	−1.87113e12	−0.466528
$633$	−4.02611e12	−0.996711
$634$	1.87076e12	0.459851
$635$	−2.14909e12	−0.524534
$636$	1.01968e12	0.247119
$637$	0	0
$638$	9.89405e11	0.236418
$639$	6.84894e12	1.62506
$640$	−2.24534e12	−0.529020
$641$	1.69101e12	0.395625	0.197813	−	0.980240i	$-0.436616\pi$
$641$	1.69101e12	0.395625	0.197813	+	0.980240i	$0.436616\pi$
$642$	9.36258e11	0.217514
$643$	−2.23177e12	−0.514873	−0.257436	−	0.966295i	$-0.582878\pi$
$643$	−2.23177e12	−0.514873	−0.257436	+	0.966295i	$0.582878\pi$
$644$	7.06827e11	0.161930
$645$	5.69880e12	1.29648
$646$	−1.31929e12	−0.298053
$647$	6.95547e12	1.56048	0.780238	−	0.625483i	$-0.215098\pi$
$647$	6.95547e12	1.56048	0.780238	+	0.625483i	$0.215098\pi$
$648$	−3.68118e12	−0.820162
$649$	−6.70769e12	−1.48413
$650$	0	0
$651$	2.54995e12	0.556438
$652$	2.89289e12	0.626928
$653$	−6.69648e12	−1.44124	−0.720622	−	0.693329i	$-0.756143\pi$
$653$	−6.69648e12	−1.44124	−0.720622	+	0.693329i	$0.756143\pi$
$654$	1.14730e12	0.245231
$655$	−1.26344e12	−0.268206
$656$	−6.49066e12	−1.36843
$657$	−3.23309e12	−0.676977
$658$	−7.34992e10	−0.0152850
$659$	5.91884e12	1.22251	0.611255	−	0.791434i	$-0.290665\pi$
$659$	5.91884e12	1.22251	0.611255	+	0.791434i	$0.290665\pi$
$660$	−4.17464e12	−0.856389
$661$	8.01661e12	1.63337	0.816685	−	0.577084i	$-0.195810\pi$
$661$	8.01661e12	1.63337	0.816685	+	0.577084i	$0.195810\pi$
$662$	1.64826e11	0.0333553
$663$	0	0
$664$	−4.37280e12	−0.872979
$665$	7.62162e11	0.151130
$666$	2.39440e12	0.471589
$667$	4.67790e12	0.915134
$668$	−1.61876e12	−0.314548
$669$	−2.09288e12	−0.403949
$670$	5.38192e11	0.103181
$671$	1.77006e12	0.337083
$672$	−1.35420e12	−0.256167
$673$	−5.73165e12	−1.07699	−0.538496	−	0.842628i	$-0.681007\pi$
$673$	−5.73165e12	−1.07699	−0.538496	+	0.842628i	$0.681007\pi$
$674$	1.32940e12	0.248134
$675$	7.31928e12	1.35707
$676$	0	0
$677$	6.69302e12	1.22454	0.612271	−	0.790648i	$-0.290256\pi$
$677$	6.69302e12	1.22454	0.612271	+	0.790648i	$0.290256\pi$
$678$	2.13159e12	0.387409
$679$	4.27833e11	0.0772432
$680$	1.53759e12	0.275772
$681$	1.78899e11	0.0318747
$682$	1.98486e12	0.351318
$683$	−8.33919e12	−1.46633	−0.733163	−	0.680053i	$-0.761957\pi$
$683$	−8.33919e12	−1.46633	−0.733163	+	0.680053i	$0.761957\pi$
$684$	−1.46787e13	−2.56410
$685$	4.62613e11	0.0802805
$686$	−5.97701e11	−0.103045
$687$	−1.72476e13	−2.95409
$688$	−5.64097e12	−0.959855
$689$	0	0
$690$	1.47084e12	0.247027
$691$	5.09310e12	0.849827	0.424914	−	0.905234i	$-0.360304\pi$
$691$	5.09310e12	0.849827	0.424914	+	0.905234i	$0.360304\pi$
$692$	1.58054e12	0.262016
$693$	−2.27177e12	−0.374167
$694$	2.73796e11	0.0448033
$695$	2.80349e12	0.455793
$696$	−5.90421e12	−0.953718
$697$	9.63643e12	1.54657
$698$	−4.88803e11	−0.0779444
$699$	−4.08146e12	−0.646648
$700$	7.51961e11	0.118373
$701$	1.44378e12	0.225824	0.112912	−	0.993605i	$-0.463982\pi$
$701$	1.44378e12	0.225824	0.112912	+	0.993605i	$0.463982\pi$
$702$	0	0
$703$	6.64925e12	1.02677
$704$	3.38610e12	0.519545
$705$	2.05242e12	0.312906
$706$	−1.31165e12	−0.198700
$707$	−1.14064e12	−0.171696
$708$	1.92949e13	2.88598
$709$	1.08655e13	1.61488	0.807439	−	0.589951i	$-0.200853\pi$
$709$	1.08655e13	1.61488	0.807439	+	0.589951i	$0.200853\pi$
$710$	7.96253e11	0.117595
$711$	1.37062e13	2.01142
$712$	−1.17889e12	−0.171915
$713$	9.38440e12	1.35989
$714$	5.87336e11	0.0845755
$715$	0	0
$716$	−8.42043e12	−1.19736
$717$	−2.35388e13	−3.32619
$718$	2.23499e12	0.313845
$719$	9.35835e12	1.30593	0.652964	−	0.757389i	$-0.273525\pi$
$719$	9.35835e12	1.30593	0.652964	+	0.757389i	$0.273525\pi$
$720$	7.58620e12	1.05203
$721$	−1.66093e12	−0.228899
$722$	1.11477e12	0.152675
$723$	−1.88068e13	−2.55972
$724$	−3.06052e12	−0.413972
$725$	4.97661e12	0.668979
$726$	9.46894e11	0.126499
$727$	1.29034e13	1.71316	0.856582	−	0.516010i	$-0.172583\pi$
$727$	1.29034e13	1.71316	0.856582	+	0.516010i	$0.172583\pi$
$728$	0	0
$729$	−2.05208e12	−0.269105
$730$	−3.75877e11	−0.0489884
$731$	8.37492e12	1.08481
$732$	−5.09165e12	−0.655479
$733$	−9.05352e12	−1.15838	−0.579188	−	0.815194i	$-0.696630\pi$
$733$	−9.05352e12	−1.15838	−0.579188	+	0.815194i	$0.696630\pi$
$734$	6.50741e10	0.00827514
$735$	8.17554e12	1.03329
$736$	−4.98379e12	−0.626051
$737$	−4.45482e12	−0.556195
$738$	−7.98977e12	−0.991472
$739$	9.20185e12	1.13495	0.567473	−	0.823392i	$-0.307921\pi$
$739$	9.20185e12	1.13495	0.567473	+	0.823392i	$0.307921\pi$
$740$	−3.73556e12	−0.457944
$741$	0	0
$742$	6.45114e10	0.00781302
$743$	5.38869e12	0.648684	0.324342	−	0.945940i	$-0.394857\pi$
$743$	5.38869e12	0.648684	0.324342	+	0.945940i	$0.394857\pi$
$744$	−1.18445e13	−1.41723
$745$	4.92392e12	0.585610
$746$	−2.23561e12	−0.264284
$747$	3.20311e13	3.76382
$748$	−6.13502e12	−0.716570
$749$	−7.94877e11	−0.0922852
$750$	4.02053e12	0.463989
$751$	−1.07905e13	−1.23783	−0.618915	−	0.785458i	$-0.712427\pi$
$751$	−1.07905e13	−1.23783	−0.618915	+	0.785458i	$0.712427\pi$
$752$	−2.03159e12	−0.231662
$753$	9.42965e12	1.06885
$754$	0	0
$755$	−4.39299e12	−0.492038
$756$	3.55372e12	0.395672
$757$	−1.49917e13	−1.65928	−0.829638	−	0.558302i	$-0.811453\pi$
$757$	−1.49917e13	−1.65928	−0.829638	+	0.558302i	$0.811453\pi$
$758$	−3.71483e12	−0.408721
$759$	−1.21747e13	−1.33159
$760$	−3.54025e12	−0.384922
$761$	4.65403e12	0.503035	0.251517	−	0.967853i	$-0.419070\pi$
$761$	4.65403e12	0.503035	0.251517	+	0.967853i	$0.419070\pi$
$762$	3.81319e12	0.409723
$763$	−9.74048e11	−0.104045
$764$	−1.48145e13	−1.57314
$765$	−1.12629e13	−1.18898
$766$	3.70908e12	0.389257
$767$	0	0
$768$	−6.48212e12	−0.672345
$769$	−4.09205e12	−0.421961	−0.210980	−	0.977490i	$-0.567666\pi$
$769$	−4.09205e12	−0.421961	−0.210980	+	0.977490i	$0.567666\pi$
$770$	−2.64115e11	−0.0270760
$771$	1.30366e13	1.32868
$772$	−5.63912e12	−0.571391
$773$	−1.18223e13	−1.19095	−0.595476	−	0.803373i	$-0.703037\pi$
$773$	−1.18223e13	−1.19095	−0.595476	+	0.803373i	$0.703037\pi$
$774$	−6.94382e12	−0.695447
$775$	9.98365e12	0.994103
$776$	−1.98729e12	−0.196736
$777$	−2.96019e12	−0.291357
$778$	3.37040e12	0.329817
$779$	−2.21876e13	−2.15869
$780$	0	0
$781$	−6.59089e12	−0.633891
$782$	2.16153e12	0.206696
$783$	2.35191e13	2.23611
$784$	−8.09258e12	−0.765005
$785$	−2.27672e12	−0.213992
$786$	2.24175e12	0.209501
$787$	5.60653e12	0.520964	0.260482	−	0.965479i	$-0.416118\pi$
$787$	5.60653e12	0.520964	0.260482	+	0.965479i	$0.416118\pi$
$788$	−2.43074e12	−0.224580
$789$	−1.19583e13	−1.09856
$790$	1.59347e12	0.145553
$791$	−1.80970e12	−0.164367
$792$	1.05524e13	0.952989
$793$	0	0
$794$	−3.44081e12	−0.307233
$795$	−1.80144e12	−0.159944
$796$	1.64873e12	0.145559
$797$	2.35495e12	0.206737	0.103369	−	0.994643i	$-0.467038\pi$
$797$	2.35495e12	0.206737	0.103369	+	0.994643i	$0.467038\pi$
$798$	−1.35232e12	−0.118050
$799$	3.01621e12	0.261819
$800$	−5.30203e12	−0.457654
$801$	8.63543e12	0.741204
$802$	−3.03596e12	−0.259126
$803$	3.11128e12	0.264070
$804$	1.28145e13	1.08155
$805$	−1.24873e12	−0.104807
$806$	0	0
$807$	3.92003e13	3.25355
$808$	5.29827e12	0.437303
$809$	−1.67444e12	−0.137436	−0.0687182	−	0.997636i	$-0.521891\pi$
$809$	−1.67444e12	−0.137436	−0.0687182	+	0.997636i	$0.521891\pi$
$810$	3.13492e12	0.255884
$811$	−1.66227e13	−1.34930	−0.674649	−	0.738139i	$-0.735705\pi$
$811$	−1.66227e13	−1.34930	−0.674649	+	0.738139i	$0.735705\pi$
$812$	2.41629e12	0.195050
$813$	5.05677e12	0.405943
$814$	−2.30419e12	−0.183954
$815$	−5.11080e12	−0.405770
$816$	1.62345e13	1.28184
$817$	−1.92830e13	−1.51417
$818$	−3.78645e11	−0.0295694
$819$	0	0
$820$	1.24650e13	0.962787
$821$	9.85538e12	0.757058	0.378529	−	0.925589i	$-0.376430\pi$
$821$	9.85538e12	0.757058	0.378529	+	0.925589i	$0.376430\pi$
$822$	−8.20825e11	−0.0627086
$823$	8.78584e12	0.667550	0.333775	−	0.942653i	$-0.391677\pi$
$823$	8.78584e12	0.667550	0.333775	+	0.942653i	$0.391677\pi$
$824$	7.71505e12	0.582997
$825$	−1.29521e13	−0.973415
$826$	1.22072e12	0.0912446
$827$	−1.63242e13	−1.21355	−0.606776	−	0.794873i	$-0.707537\pi$
$827$	−1.63242e13	−1.21355	−0.606776	+	0.794873i	$0.707537\pi$
$828$	2.40497e13	1.77817
$829$	−6.63239e11	−0.0487725	−0.0243862	−	0.999703i	$-0.507763\pi$
$829$	−6.63239e11	−0.0487725	−0.0243862	+	0.999703i	$0.507763\pi$
$830$	3.72391e12	0.272363
$831$	2.52260e13	1.83503
$832$	0	0
$833$	1.20147e13	0.864592
$834$	−4.97430e12	−0.356029
$835$	2.85982e12	0.203587
$836$	1.41257e13	1.00019
$837$	4.71821e13	3.32287
$838$	5.38031e12	0.376886
$839$	−1.88038e13	−1.31013	−0.655067	−	0.755571i	$-0.727360\pi$
$839$	−1.88038e13	−1.31013	−0.655067	+	0.755571i	$0.727360\pi$
$840$	1.57609e12	0.109225
$841$	1.48425e12	0.102312
$842$	6.17582e12	0.423438
$843$	−9.19999e11	−0.0627427
$844$	−7.65348e12	−0.519180
$845$	0	0
$846$	−2.50081e12	−0.167847
$847$	−8.03907e11	−0.0536699
$848$	1.78316e12	0.118415
$849$	−3.50111e13	−2.31271
$850$	2.29956e12	0.151098
$851$	−1.08942e13	−0.712052
$852$	1.89589e13	1.23264
$853$	6.21462e12	0.401924	0.200962	−	0.979599i	$-0.435593\pi$
$853$	6.21462e12	0.401924	0.200962	+	0.979599i	$0.435593\pi$
$854$	−3.22131e11	−0.0207240
$855$	2.59325e13	1.65958
$856$	3.69221e12	0.235047
$857$	−1.74523e13	−1.10519	−0.552597	−	0.833448i	$-0.686363\pi$
$857$	−1.74523e13	−1.10519	−0.552597	+	0.833448i	$0.686363\pi$
$858$	0	0
$859$	−1.42322e13	−0.891871	−0.445936	−	0.895065i	$-0.647129\pi$
$859$	−1.42322e13	−0.891871	−0.445936	+	0.895065i	$0.647129\pi$
$860$	1.08332e13	0.675326
$861$	9.87771e12	0.612551
$862$	−1.84843e11	−0.0114030
$863$	−1.13528e12	−0.0696715	−0.0348358	−	0.999393i	$-0.511091\pi$
$863$	−1.13528e12	−0.0696715	−0.0348358	+	0.999393i	$0.511091\pi$
$864$	−2.50571e13	−1.52974
$865$	−2.79230e12	−0.169586
$866$	3.99288e12	0.241244
$867$	5.62233e12	0.337933
$868$	4.84735e12	0.289845
$869$	−1.31898e13	−0.784599
$870$	5.02806e12	0.297553
$871$	0	0
$872$	4.52446e12	0.264998
$873$	1.45570e13	0.848219
$874$	−4.97686e12	−0.288506
$875$	−3.41340e12	−0.196857
$876$	−8.94970e12	−0.513500
$877$	−4.64607e11	−0.0265209	−0.0132604	−	0.999912i	$-0.504221\pi$
$877$	−4.64607e11	−0.0265209	−0.0132604	+	0.999912i	$0.504221\pi$
$878$	−2.84614e12	−0.161634
$879$	1.82159e13	1.02920
$880$	−7.30038e12	−0.410368
$881$	2.48442e13	1.38942	0.694711	−	0.719289i	$-0.255532\pi$
$881$	2.48442e13	1.38942	0.694711	+	0.719289i	$0.255532\pi$
$882$	−9.96166e12	−0.554272
$883$	−2.41732e13	−1.33817	−0.669085	−	0.743185i	$-0.733314\pi$
$883$	−2.41732e13	−1.33817	−0.669085	+	0.743185i	$0.733314\pi$
$884$	0	0
$885$	−3.40879e13	−1.86791
$886$	2.99349e12	0.163202
$887$	−2.19116e12	−0.118855	−0.0594275	−	0.998233i	$-0.518928\pi$
$887$	−2.19116e12	−0.118855	−0.0594275	+	0.998233i	$0.518928\pi$
$888$	1.37501e13	0.742074
$889$	−3.23737e12	−0.173834
$890$	1.00395e12	0.0536360
$891$	−2.59489e13	−1.37933
$892$	−3.97848e12	−0.210414
$893$	−6.94474e12	−0.365447
$894$	−8.73663e12	−0.457431
$895$	1.48762e13	0.774975
$896$	−3.38236e12	−0.175321
$897$	0	0
$898$	−2.81601e12	−0.144508
$899$	3.20806e13	1.63804
$900$	2.55854e13	1.29988
$901$	−2.64738e12	−0.133830
$902$	7.68874e12	0.386746
$903$	8.58461e12	0.429661
$904$	8.40609e12	0.418635
$905$	5.40694e12	0.267937
$906$	7.79458e12	0.384340
$907$	−3.43961e13	−1.68763	−0.843813	−	0.536637i	$-0.819694\pi$
$907$	−3.43961e13	−1.68763	−0.843813	+	0.536637i	$0.819694\pi$
$908$	3.40081e11	0.0166033
$909$	−3.88101e13	−1.88542
$910$	0	0
$911$	−1.14361e13	−0.550104	−0.275052	−	0.961429i	$-0.588695\pi$
$911$	−1.14361e13	−0.550104	−0.275052	+	0.961429i	$0.588695\pi$
$912$	−3.73794e13	−1.78919
$913$	−3.08242e13	−1.46816
$914$	4.76721e12	0.225947
$915$	8.99530e12	0.424249
$916$	−3.27871e13	−1.53877
$917$	−1.90323e12	−0.0888853
$918$	1.08676e13	0.505057
$919$	−5.34901e12	−0.247374	−0.123687	−	0.992321i	$-0.539472\pi$
$919$	−5.34901e12	−0.247374	−0.123687	+	0.992321i	$0.539472\pi$
$920$	5.80037e12	0.266938
$921$	5.01618e13	2.29723
$922$	−1.04480e13	−0.476148
$923$	0	0
$924$	−6.28863e12	−0.283813
$925$	−1.15898e13	−0.520523
$926$	2.43631e12	0.108889
$927$	−5.65132e13	−2.51357
$928$	−1.70371e13	−0.754101
$929$	−1.85437e13	−0.816820	−0.408410	−	0.912799i	$-0.633917\pi$
$929$	−1.85437e13	−0.816820	−0.408410	+	0.912799i	$0.633917\pi$
$930$	1.00869e13	0.442164
$931$	−2.76635e13	−1.20680
$932$	−7.75869e12	−0.336835
$933$	−1.85710e13	−0.802358
$934$	5.59113e11	0.0240402
$935$	1.08386e13	0.463789
$936$	0	0
$937$	−9.05294e12	−0.383673	−0.191837	−	0.981427i	$-0.561444\pi$
$937$	−9.05294e12	−0.383673	−0.191837	+	0.981427i	$0.561444\pi$
$938$	8.10727e11	0.0341949
$939$	−7.14999e13	−3.00130
$940$	3.90156e12	0.162991
$941$	1.49307e13	0.620766	0.310383	−	0.950612i	$-0.399543\pi$
$941$	1.49307e13	0.620766	0.310383	+	0.950612i	$0.399543\pi$
$942$	4.03964e12	0.167153
$943$	3.63523e13	1.49703
$944$	3.37419e13	1.38292
$945$	−6.27828e12	−0.256093
$946$	6.68220e12	0.271275
$947$	−3.23761e13	−1.30812	−0.654062	−	0.756441i	$-0.726937\pi$
$947$	−3.23761e13	−1.30812	−0.654062	+	0.756441i	$0.726937\pi$
$948$	3.79408e13	1.52570
$949$	0	0
$950$	−5.29466e12	−0.210903
$951$	−7.86934e13	−3.11979
$952$	2.31621e12	0.0913926
$953$	−2.06348e13	−0.810370	−0.405185	−	0.914235i	$-0.632793\pi$
$953$	−2.06348e13	−0.810370	−0.405185	+	0.914235i	$0.632793\pi$
$954$	2.19500e12	0.0857959
$955$	2.61724e13	1.01819
$956$	−4.47463e13	−1.73259
$957$	−4.16192e13	−1.60395
$958$	−3.07911e12	−0.118108
$959$	6.96875e11	0.0266055
$960$	1.72079e13	0.653892
$961$	3.79177e13	1.43413
$962$	0	0
$963$	−2.70457e13	−1.01340
$964$	−3.57509e13	−1.33334
$965$	9.96249e12	0.369824
$966$	2.21566e12	0.0818663
$967$	8.19814e12	0.301506	0.150753	−	0.988571i	$-0.451830\pi$
$967$	8.19814e12	0.301506	0.150753	+	0.988571i	$0.451830\pi$
$968$	3.73415e12	0.136695
$969$	5.54957e13	2.02210
$970$	1.69239e12	0.0613800
$971$	1.60623e13	0.579859	0.289929	−	0.957048i	$-0.406368\pi$
$971$	1.60623e13	0.579859	0.289929	+	0.957048i	$0.406368\pi$
$972$	1.94829e13	0.700093
$973$	4.22315e12	0.151053
$974$	2.98428e12	0.106249
$975$	0	0
$976$	−8.90401e12	−0.314095
$977$	3.96308e13	1.39158	0.695789	−	0.718246i	$-0.255055\pi$
$977$	3.96308e13	1.39158	0.695789	+	0.718246i	$0.255055\pi$
$978$	9.06821e12	0.316954
$979$	−8.31007e12	−0.289123
$980$	1.55414e13	0.538236
$981$	−3.31419e13	−1.14253
$982$	2.95322e12	0.101343
$983$	6.58546e12	0.224955	0.112477	−	0.993654i	$-0.464121\pi$
$983$	6.58546e12	0.224955	0.112477	+	0.993654i	$0.464121\pi$
$984$	−4.58820e13	−1.56014
$985$	4.29433e12	0.145356
$986$	7.38921e12	0.248973
$987$	3.09174e12	0.103699
$988$	0	0
$989$	3.15934e13	1.05006
$990$	−8.98650e12	−0.297326
$991$	2.00271e12	0.0659608	0.0329804	−	0.999456i	$-0.489500\pi$
$991$	2.00271e12	0.0659608	0.0329804	+	0.999456i	$0.489500\pi$
$992$	−3.41784e13	−1.12059
$993$	−6.93338e12	−0.226294
$994$	1.19947e12	0.0389717
$995$	−2.91277e12	−0.0942110
$996$	8.86670e13	2.85493
$997$	6.23620e12	0.199890	0.0999452	−	0.994993i	$-0.468133\pi$
$997$	6.23620e12	0.199890	0.0999452	+	0.994993i	$0.468133\pi$
$998$	2.89406e12	0.0923464
$999$	−5.47729e13	−1.73989

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.1.12		20
13.6	odd	12		13.10.e.a.10.5	yes	20
13.11	odd	12		13.10.e.a.4.5	✓	20
13.12	even	2	inner	169.10.a.f.1.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.e.a.4.5	✓	20	13.11	odd	12
13.10.e.a.10.5	yes	20	13.6	odd	12
169.10.a.f.1.9		20	13.12	even	2	inner
169.10.a.f.1.12		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

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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.1.12

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