LMFDB - Embedded newform 169.14.a.c.1.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [169,14,Mod(1,169)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(169, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 14, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("169.1"); S:= CuspForms(chi, 14); N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	169.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14,-65] 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:	$181.220269929$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5 x^{13} - 83806 x^{12} + 371578 x^{11} + 2652253571 x^{10} - 14037350343 x^{9} + \cdots - 28\!\cdots\!92 $ x^14 - 5x^13 - 83806x^12 + 371578x^11 + 2652253571x^10 - 14037350343x^9 - 39644654446336x^8 + 300703569393724x^7 + 284900696882506007x^6 - 3278532385091665539x^5 - 859708854051254655478x^4 + 13773050954326302049834x^3 + 573293034250775539851589x^2 - 9544933594873872878261137*x - 28754672412840977519710092
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{24}\cdot 3^{3}\cdot 5\cdot 13^{6} $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$27.4573$ 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)

$f(q)$	$=$	\(q+22.4573 q^{2} +2284.08 q^{3} -7687.67 q^{4} -17999.0 q^{5} +51294.3 q^{6} +563042. q^{7} -356614. q^{8} +3.62272e6 q^{9} -404209. q^{10} -6.98942e6 q^{11} -1.75593e7 q^{12} +1.26444e7 q^{14} -4.11113e7 q^{15} +5.49688e7 q^{16} -3.79357e7 q^{17} +8.13565e7 q^{18} -6.56105e7 q^{19} +1.38370e8 q^{20} +1.28604e9 q^{21} -1.56963e8 q^{22} -9.97845e8 q^{23} -8.14537e8 q^{24} -8.96739e8 q^{25} +4.63303e9 q^{27} -4.32848e9 q^{28} -3.48340e9 q^{29} -9.23248e8 q^{30} -2.61380e9 q^{31} +4.15583e9 q^{32} -1.59644e10 q^{33} -8.51932e8 q^{34} -1.01342e10 q^{35} -2.78503e10 q^{36} -8.62981e8 q^{37} -1.47343e9 q^{38} +6.41870e9 q^{40} -1.77509e9 q^{41} +2.88809e10 q^{42} +6.99718e8 q^{43} +5.37324e10 q^{44} -6.52054e10 q^{45} -2.24089e10 q^{46} -4.91139e10 q^{47} +1.25553e11 q^{48} +2.20128e11 q^{49} -2.01383e10 q^{50} -8.66483e10 q^{51} +3.91615e10 q^{53} +1.04045e11 q^{54} +1.25803e11 q^{55} -2.00789e11 q^{56} -1.49860e11 q^{57} -7.82278e10 q^{58} +2.32206e11 q^{59} +3.16050e11 q^{60} +3.05574e10 q^{61} -5.86988e10 q^{62} +2.03975e12 q^{63} -3.56976e11 q^{64} -3.58518e11 q^{66} -8.74899e11 q^{67} +2.91637e11 q^{68} -2.27916e12 q^{69} -2.27587e11 q^{70} +9.60262e11 q^{71} -1.29191e12 q^{72} -8.68862e11 q^{73} -1.93802e10 q^{74} -2.04823e12 q^{75} +5.04392e11 q^{76} -3.93534e12 q^{77} -7.23289e11 q^{79} -9.89384e11 q^{80} +4.80645e12 q^{81} -3.98637e10 q^{82} +2.62815e12 q^{83} -9.88663e12 q^{84} +6.82804e11 q^{85} +1.57138e10 q^{86} -7.95639e12 q^{87} +2.49253e12 q^{88} +4.90223e12 q^{89} -1.46434e12 q^{90} +7.67110e12 q^{92} -5.97014e12 q^{93} -1.10296e12 q^{94} +1.18092e12 q^{95} +9.49228e12 q^{96} -6.50670e12 q^{97} +4.94347e12 q^{98} -2.53207e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 65 q^{2} - 728 q^{3} + 53249 q^{4} - 20930 q^{5} + 143910 q^{6} - 173992 q^{7} - 1308489 q^{8} + 5231838 q^{9} - 2769243 q^{10} + 10986144 q^{11} - 22602732 q^{12} - 11865878 q^{14} - 75354448 q^{15}+ \cdots - 16619904586272 q^{99}+O(q^{100}) $ 14 * q - 65 * q^2 - 728 * q^3 + 53249 * q^4 - 20930 * q^5 + 143910 * q^6 - 173992 * q^7 - 1308489 * q^8 + 5231838 * q^9 - 2769243 * q^10 + 10986144 * q^11 - 22602732 * q^12 - 11865878 * q^14 - 75354448 * q^15 + 273433217 * q^16 - 255934950 * q^17 + 175342921 * q^18 - 266623552 * q^19 - 225433091 * q^20 + 1257937928 * q^21 - 77223114 * q^22 - 1914406544 * q^23 - 680727216 * q^24 + 2612939384 * q^25 + 1775226160 * q^27 - 3680076400 * q^28 - 6211296126 * q^29 - 5703660004 * q^30 - 3498837472 * q^31 + 2312486527 * q^32 + 5621901584 * q^33 + 11686861797 * q^34 - 23009265024 * q^35 - 23496114839 * q^36 + 19577630774 * q^37 + 25824361822 * q^38 - 55850293929 * q^40 - 6039692074 * q^41 - 143590583874 * q^42 - 16878499784 * q^43 + 244775923496 * q^44 - 148673926778 * q^45 + 177583142490 * q^46 - 184702457472 * q^47 - 92920518608 * q^48 + 195653684766 * q^49 - 753661423970 * q^50 + 308584639568 * q^51 - 143775384550 * q^53 + 365361720282 * q^54 - 855926433792 * q^55 - 192505368988 * q^56 + 962256719424 * q^57 - 660641292207 * q^58 + 637655529992 * q^59 - 1277628531192 * q^60 - 1530666437030 * q^61 - 1907899186036 * q^62 - 832654573712 * q^63 + 316116140225 * q^64 - 135426824550 * q^66 - 1120398677944 * q^67 - 4085795015901 * q^68 - 1473200404976 * q^69 + 4688842372344 * q^70 + 1506585643472 * q^71 + 3521118562923 * q^72 + 426256990718 * q^73 - 4665118313621 * q^74 - 2605103918408 * q^75 - 6106356745372 * q^76 + 1427057517512 * q^77 - 3516338331392 * q^79 + 5983641421745 * q^80 - 2512348302642 * q^81 + 8600700659175 * q^82 - 1016970123936 * q^83 - 4374201207844 * q^84 + 2527554975426 * q^85 + 3773647528794 * q^86 + 1118899666832 * q^87 + 5943200108772 * q^88 + 5229645042596 * q^89 + 2110232695965 * q^90 + 1915125894160 * q^92 - 1283055655752 * q^93 + 32271602536104 * q^94 - 8980600417472 * q^95 - 25846279484896 * q^96 + 3129146550452 * q^97 - 5503659823363 * q^98 - 16619904586272 * q^99

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 $

$2$	22.4573	0.248120	0.124060	−	0.992275i	$-0.460408\pi$
$2$	22.4573	0.248120	0.124060	+	0.992275i	$0.460408\pi$
$3$	2284.08	1.80894	0.904470	−	0.426538i	$-0.140267\pi$
$3$	2284.08	1.80894	0.904470	+	0.426538i	$0.140267\pi$
$4$	−7687.67	−0.938436
$5$	−17999.0	−0.515162	−0.257581	−	0.966257i	$-0.582925\pi$
$5$	−17999.0	−0.515162	−0.257581	+	0.966257i	$0.582925\pi$
$6$	51294.3	0.448835
$7$	563042.	1.80886	0.904428	−	0.426627i	$-0.140298\pi$
$7$	563042.	1.80886	0.904428	+	0.426627i	$0.140298\pi$
$8$	−356614.	−0.480965
$9$	3.62272e6	2.27226
$10$	−404209.	−0.127822
$11$	−6.98942e6	−1.18957	−0.594783	−	0.803886i	$-0.702762\pi$
$11$	−6.98942e6	−1.18957	−0.594783	+	0.803886i	$0.702762\pi$
$12$	−1.75593e7	−1.69757
$13$	0	0
$13$	0	0
$14$	1.26444e7	0.448814
$15$	−4.11113e7	−0.931896
$16$	5.49688e7	0.819099
$17$	−3.79357e7	−0.381180	−0.190590	−	0.981670i	$-0.561040\pi$
$17$	−3.79357e7	−0.381180	−0.190590	+	0.981670i	$0.561040\pi$
$18$	8.13565e7	0.563794
$19$	−6.56105e7	−0.319944	−0.159972	−	0.987122i	$-0.551140\pi$
$19$	−6.56105e7	−0.319944	−0.159972	+	0.987122i	$0.551140\pi$
$20$	1.38370e8	0.483446
$21$	1.28604e9	3.27211
$22$	−1.56963e8	−0.295156
$23$	−9.97845e8	−1.40550	−0.702752	−	0.711435i	$-0.748046\pi$
$23$	−9.97845e8	−1.40550	−0.702752	+	0.711435i	$0.748046\pi$
$24$	−8.14537e8	−0.870037
$25$	−8.96739e8	−0.734608
$26$	0	0
$27$	4.63303e9	2.30145
$28$	−4.32848e9	−1.69750
$29$	−3.48340e9	−1.08747	−0.543734	−	0.839257i	$-0.682990\pi$
$29$	−3.48340e9	−1.08747	−0.543734	+	0.839257i	$0.682990\pi$
$30$	−9.23248e8	−0.231222
$31$	−2.61380e9	−0.528958	−0.264479	−	0.964391i	$-0.585200\pi$
$31$	−2.61380e9	−0.528958	−0.264479	+	0.964391i	$0.585200\pi$
$32$	4.15583e9	0.684201
$33$	−1.59644e10	−2.15185
$34$	−8.51932e8	−0.0945784
$35$	−1.01342e10	−0.931853
$36$	−2.78503e10	−2.13237
$37$	−8.62981e8	−0.0552955	−0.0276477	−	0.999618i	$-0.508802\pi$
$37$	−8.62981e8	−0.0552955	−0.0276477	+	0.999618i	$0.508802\pi$
$38$	−1.47343e9	−0.0793847
$39$	0	0
$40$	6.41870e9	0.247775
$41$	−1.77509e9	−0.0583613	−0.0291807	−	0.999574i	$-0.509290\pi$
$41$	−1.77509e9	−0.0583613	−0.0291807	+	0.999574i	$0.509290\pi$
$42$	2.88809e10	0.811877
$43$	6.99718e8	0.0168802	0.00844011	−	0.999964i	$-0.497313\pi$
$43$	6.99718e8	0.0168802	0.00844011	+	0.999964i	$0.497313\pi$
$44$	5.37324e10	1.11633
$45$	−6.52054e10	−1.17058
$46$	−2.24089e10	−0.348734
$47$	−4.91139e10	−0.664612	−0.332306	−	0.943172i	$-0.607827\pi$
$47$	−4.91139e10	−0.664612	−0.332306	+	0.943172i	$0.607827\pi$
$48$	1.25553e11	1.48170
$49$	2.20128e11	2.27196
$50$	−2.01383e10	−0.182271
$51$	−8.66483e10	−0.689531
$52$	0	0
$53$	3.91615e10	0.242698	0.121349	−	0.992610i	$-0.461278\pi$
$53$	3.91615e10	0.242698	0.121349	+	0.992610i	$0.461278\pi$
$54$	1.04045e11	0.571036
$55$	1.25803e11	0.612819
$56$	−2.00789e11	−0.869997
$57$	−1.49860e11	−0.578760
$58$	−7.82278e10	−0.269823
$59$	2.32206e11	0.716697	0.358349	−	0.933588i	$-0.383340\pi$
$59$	2.32206e11	0.716697	0.358349	+	0.933588i	$0.383340\pi$
$60$	3.16050e11	0.874525
$61$	3.05574e10	0.0759403	0.0379701	−	0.999279i	$-0.487911\pi$
$61$	3.05574e10	0.0759403	0.0379701	+	0.999279i	$0.487911\pi$
$62$	−5.86988e10	−0.131245
$63$	2.03975e12	4.11019
$64$	−3.56976e11	−0.649335
$65$	0	0
$66$	−3.58518e11	−0.533919
$67$	−8.74899e11	−1.18160	−0.590802	−	0.806817i	$-0.701188\pi$
$67$	−8.74899e11	−1.18160	−0.590802	+	0.806817i	$0.701188\pi$
$68$	2.91637e11	0.357713
$69$	−2.27916e12	−2.54247
$70$	−2.27587e11	−0.231212
$71$	9.60262e11	0.889632	0.444816	−	0.895622i	$-0.353269\pi$
$71$	9.60262e11	0.889632	0.444816	+	0.895622i	$0.353269\pi$
$72$	−1.29191e12	−1.09288
$73$	−8.68862e11	−0.671974	−0.335987	−	0.941867i	$-0.609070\pi$
$73$	−8.68862e11	−0.671974	−0.335987	+	0.941867i	$0.609070\pi$
$74$	−1.93802e10	−0.0137199
$75$	−2.04823e12	−1.32886
$76$	5.04392e11	0.300248
$77$	−3.93534e12	−2.15175
$78$	0	0
$79$	−7.23289e11	−0.334762	−0.167381	−	0.985892i	$-0.553531\pi$
$79$	−7.23289e11	−0.334762	−0.167381	+	0.985892i	$0.553531\pi$
$80$	−9.89384e11	−0.421968
$81$	4.80645e12	1.89091
$82$	−3.98637e10	−0.0144806
$83$	2.62815e12	0.882353	0.441176	−	0.897420i	$-0.354561\pi$
$83$	2.62815e12	0.882353	0.441176	+	0.897420i	$0.354561\pi$
$84$	−9.88663e12	−3.07067
$85$	6.82804e11	0.196369
$86$	1.57138e10	0.00418833
$87$	−7.95639e12	−1.96717
$88$	2.49253e12	0.572141
$89$	4.90223e12	1.04558	0.522792	−	0.852460i	$-0.324891\pi$
$89$	4.90223e12	1.04558	0.522792	+	0.852460i	$0.324891\pi$
$90$	−1.46434e12	−0.290445
$91$	0	0
$92$	7.67110e12	1.31898
$93$	−5.97014e12	−0.956853
$94$	−1.10296e12	−0.164904
$95$	1.18092e12	0.164823
$96$	9.49228e12	1.23768
$97$	−6.50670e12	−0.793130	−0.396565	−	0.918007i	$-0.629798\pi$
$97$	−6.50670e12	−0.793130	−0.396565	+	0.918007i	$0.629798\pi$
$98$	4.94347e12	0.563719
$99$	−2.53207e13	−2.70301
$100$	6.89383e12	0.689383
$101$	−7.33753e12	−0.687798	−0.343899	−	0.939007i	$-0.611748\pi$
$101$	−7.33753e12	−0.687798	−0.343899	+	0.939007i	$0.611748\pi$
$102$	−1.94588e12	−0.171087
$103$	−1.44084e13	−1.18898	−0.594489	−	0.804103i	$-0.702646\pi$
$103$	−1.44084e13	−1.18898	−0.594489	+	0.804103i	$0.702646\pi$
$104$	0	0
$105$	−2.31474e13	−1.68567
$106$	8.79461e11	0.0602183
$107$	−2.66271e13	−1.71526	−0.857628	−	0.514271i	$-0.828063\pi$
$107$	−2.66271e13	−1.71526	−0.857628	+	0.514271i	$0.828063\pi$
$108$	−3.56172e13	−2.15976
$109$	−6.54899e12	−0.374026	−0.187013	−	0.982357i	$-0.559881\pi$
$109$	−6.54899e12	−0.374026	−0.187013	+	0.982357i	$0.559881\pi$
$110$	2.82519e12	0.152053
$111$	−1.97112e12	−0.100026
$112$	3.09498e13	1.48163
$113$	−2.94436e13	−1.33040	−0.665198	−	0.746667i	$-0.731653\pi$
$113$	−2.94436e13	−1.33040	−0.665198	+	0.746667i	$0.731653\pi$
$114$	−3.36545e12	−0.143602
$115$	1.79602e13	0.724062
$116$	2.67793e13	1.02052
$117$	0	0
$118$	5.21472e12	0.177827
$119$	−2.13594e13	−0.689499
$120$	1.46609e13	0.448210
$121$	1.43293e13	0.415070
$122$	6.86236e11	0.0188423
$123$	−4.05445e12	−0.105572
$124$	2.00940e13	0.496393
$125$	3.81119e13	0.893604
$126$	4.58071e13	1.01982
$127$	3.00703e13	0.635935	0.317968	−	0.948102i	$-0.397000\pi$
$127$	3.00703e13	0.635935	0.317968	+	0.948102i	$0.397000\pi$
$128$	−4.20613e13	−0.845314
$129$	1.59822e12	0.0305353
$130$	0	0
$131$	3.69868e12	0.0639416	0.0319708	−	0.999489i	$-0.489822\pi$
$131$	3.69868e12	0.0639416	0.0319708	+	0.999489i	$0.489822\pi$
$132$	1.22729e14	2.01938
$133$	−3.69415e13	−0.578733
$134$	−1.96479e13	−0.293180
$135$	−8.33900e13	−1.18562
$136$	1.35284e13	0.183334
$137$	1.60146e13	0.206934	0.103467	−	0.994633i	$-0.467006\pi$
$137$	1.60146e13	0.206934	0.103467	+	0.994633i	$0.467006\pi$
$138$	−5.11838e13	−0.630839
$139$	−9.87981e11	−0.0116186	−0.00580928	−	0.999983i	$-0.501849\pi$
$139$	−9.87981e11	−0.0116186	−0.00580928	+	0.999983i	$0.501849\pi$
$140$	7.79084e13	0.874485
$141$	−1.12180e14	−1.20224
$142$	2.15649e13	0.220736
$143$	0	0
$144$	1.99137e14	1.86121
$145$	6.26978e13	0.560222
$146$	−1.95123e13	−0.166730
$147$	5.02790e14	4.10983
$148$	6.63431e12	0.0518913
$149$	1.28340e14	0.960842	0.480421	−	0.877038i	$-0.340484\pi$
$149$	1.28340e14	0.960842	0.480421	+	0.877038i	$0.340484\pi$
$150$	−4.59976e13	−0.329718
$151$	3.79463e13	0.260507	0.130253	−	0.991481i	$-0.458421\pi$
$151$	3.79463e13	0.260507	0.130253	+	0.991481i	$0.458421\pi$
$152$	2.33976e13	0.153882
$153$	−1.37430e14	−0.866140
$154$	−8.83771e13	−0.533894
$155$	4.70458e13	0.272499
$156$	0	0
$157$	−2.24267e14	−1.19513	−0.597567	−	0.801819i	$-0.703866\pi$
$157$	−2.24267e14	−1.19513	−0.597567	+	0.801819i	$0.703866\pi$
$158$	−1.62431e13	−0.0830612
$159$	8.94482e13	0.439026
$160$	−7.48009e13	−0.352474
$161$	−5.61829e14	−2.54235
$162$	1.07940e14	0.469174
$163$	−1.58288e12	−0.00661042	−0.00330521	−	0.999995i	$-0.501052\pi$
$163$	−1.58288e12	−0.00661042	−0.00330521	+	0.999995i	$0.501052\pi$
$164$	1.36463e13	0.0547684
$165$	2.87344e14	1.10855
$166$	5.90211e13	0.218930
$167$	−3.83958e14	−1.36970	−0.684852	−	0.728682i	$-0.740133\pi$
$167$	−3.83958e14	−1.36970	−0.684852	+	0.728682i	$0.740133\pi$
$168$	−4.58619e14	−1.57377
$169$	0	0
$170$	1.53339e13	0.0487232
$171$	−2.37688e14	−0.726998
$172$	−5.37920e12	−0.0158410
$173$	−6.48567e14	−1.83931	−0.919655	−	0.392728i	$-0.871532\pi$
$173$	−6.48567e14	−1.83931	−0.919655	+	0.392728i	$0.871532\pi$
$174$	−1.78679e14	−0.488094
$175$	−5.04902e14	−1.32880
$176$	−3.84200e14	−0.974373
$177$	5.30379e14	1.29646
$178$	1.10091e14	0.259430
$179$	−2.94991e14	−0.670293	−0.335147	−	0.942166i	$-0.608786\pi$
$179$	−2.94991e14	−0.670293	−0.335147	+	0.942166i	$0.608786\pi$
$180$	5.01277e14	1.09852
$181$	3.58502e14	0.757846	0.378923	−	0.925428i	$-0.376294\pi$
$181$	3.58502e14	0.757846	0.378923	+	0.925428i	$0.376294\pi$
$182$	0	0
$183$	6.97956e13	0.137371
$184$	3.55846e14	0.675999
$185$	1.55328e13	0.0284861
$186$	−1.34073e14	−0.237415
$187$	2.65148e14	0.453439
$188$	3.77571e14	0.623696
$189$	2.60859e15	4.16298
$190$	2.65203e13	0.0408960
$191$	−5.71145e14	−0.851196	−0.425598	−	0.904912i	$-0.639936\pi$
$191$	−5.71145e14	−0.851196	−0.425598	+	0.904912i	$0.639936\pi$
$192$	−8.15363e14	−1.17461
$193$	9.65742e14	1.34505	0.672525	−	0.740074i	$-0.265210\pi$
$193$	9.65742e14	1.34505	0.672525	+	0.740074i	$0.265210\pi$
$194$	−1.46123e14	−0.196792
$195$	0	0
$196$	−1.69227e15	−2.13209
$197$	8.80676e14	1.07346	0.536730	−	0.843754i	$-0.319660\pi$
$197$	8.80676e14	1.07346	0.536730	+	0.843754i	$0.319660\pi$
$198$	−5.68635e14	−0.670671
$199$	−6.69730e14	−0.764460	−0.382230	−	0.924067i	$-0.624844\pi$
$199$	−6.69730e14	−0.764460	−0.382230	+	0.924067i	$0.624844\pi$
$200$	3.19790e14	0.353321
$201$	−1.99834e15	−2.13745
$202$	−1.64781e14	−0.170657
$203$	−1.96130e15	−1.96707
$204$	6.66123e14	0.647081
$205$	3.19498e13	0.0300655
$206$	−3.23574e14	−0.295010
$207$	−3.61491e15	−3.19367
$208$	0	0
$209$	4.58579e14	0.380595
$210$	−5.19828e14	−0.418248
$211$	−3.94506e14	−0.307764	−0.153882	−	0.988089i	$-0.549178\pi$
$211$	−3.94506e14	−0.307764	−0.153882	+	0.988089i	$0.549178\pi$
$212$	−3.01061e14	−0.227757
$213$	2.19332e15	1.60929
$214$	−5.97972e14	−0.425590
$215$	−1.25942e13	−0.00869604
$216$	−1.65221e15	−1.10692
$217$	−1.47168e15	−0.956808
$218$	−1.47073e14	−0.0928035
$219$	−1.98456e15	−1.21556
$220$	−9.67130e14	−0.575092
$221$	0	0
$222$	−4.42660e13	−0.0248185
$223$	1.25180e15	0.681639	0.340820	−	0.940129i	$-0.389295\pi$
$223$	1.25180e15	0.681639	0.340820	+	0.940129i	$0.389295\pi$
$224$	2.33991e15	1.23762
$225$	−3.24863e15	−1.66922
$226$	−6.61223e14	−0.330098
$227$	−9.93356e14	−0.481878	−0.240939	−	0.970540i	$-0.577455\pi$
$227$	−9.93356e14	−0.481878	−0.240939	+	0.970540i	$0.577455\pi$
$228$	1.15207e15	0.543130
$229$	3.21076e15	1.47122	0.735610	−	0.677406i	$-0.236896\pi$
$229$	3.21076e15	1.47122	0.735610	+	0.677406i	$0.236896\pi$
$230$	4.03338e14	0.179654
$231$	−8.98865e15	−3.89239
$232$	1.24223e15	0.523035
$233$	−2.86663e15	−1.17370	−0.586852	−	0.809694i	$-0.699633\pi$
$233$	−2.86663e15	−1.17370	−0.586852	+	0.809694i	$0.699633\pi$
$234$	0	0
$235$	8.84001e14	0.342382
$236$	−1.78513e15	−0.672575
$237$	−1.65205e15	−0.605564
$238$	−4.79674e14	−0.171079
$239$	−1.30135e15	−0.451656	−0.225828	−	0.974167i	$-0.572509\pi$
$239$	−1.30135e15	−0.451656	−0.225828	+	0.974167i	$0.572509\pi$
$240$	−2.25984e15	−0.763315
$241$	3.70381e15	1.21769	0.608847	−	0.793287i	$-0.291632\pi$
$241$	3.70381e15	1.21769	0.608847	+	0.793287i	$0.291632\pi$
$242$	3.21798e14	0.102987
$243$	3.59179e15	1.11910
$244$	−2.34915e14	−0.0712651
$245$	−3.96208e15	−1.17043
$246$	−9.10520e13	−0.0261946
$247$	0	0
$248$	9.32118e14	0.254410
$249$	6.00291e15	1.59612
$250$	8.55889e14	0.221721
$251$	7.03934e14	0.177686	0.0888429	−	0.996046i	$-0.471683\pi$
$251$	7.03934e14	0.177686	0.0888429	+	0.996046i	$0.471683\pi$
$252$	−1.56809e16	−3.85716
$253$	6.97436e15	1.67194
$254$	6.75296e14	0.157788
$255$	1.55958e15	0.355220
$256$	1.97976e15	0.439595
$257$	6.73444e15	1.45793	0.728965	−	0.684551i	$-0.240002\pi$
$257$	6.73444e15	1.45793	0.728965	+	0.684551i	$0.240002\pi$
$258$	3.58916e13	0.00757643
$259$	−4.85895e14	−0.100022
$260$	0	0
$261$	−1.26194e16	−2.47101
$262$	8.30623e13	0.0158652
$263$	−1.05856e16	−1.97244	−0.986218	−	0.165449i	$-0.947093\pi$
$263$	−1.05856e16	−1.97244	−0.986218	+	0.165449i	$0.947093\pi$
$264$	5.69315e15	1.03497
$265$	−7.04869e14	−0.125029
$266$	−8.29605e14	−0.143595
$267$	1.11971e16	1.89140
$268$	6.72593e15	1.10886
$269$	9.26365e15	1.49071	0.745354	−	0.666669i	$-0.232281\pi$
$269$	9.26365e15	1.49071	0.745354	+	0.666669i	$0.232281\pi$
$270$	−1.87271e15	−0.294176
$271$	2.06693e15	0.316975	0.158487	−	0.987361i	$-0.449338\pi$
$271$	2.06693e15	0.316975	0.158487	+	0.987361i	$0.449338\pi$
$272$	−2.08528e15	−0.312224
$273$	0	0
$274$	3.59645e14	0.0513446
$275$	6.26769e15	0.873866
$276$	1.75214e16	2.38595
$277$	1.01472e16	1.34967	0.674833	−	0.737970i	$-0.264216\pi$
$277$	1.01472e16	1.34967	0.674833	+	0.737970i	$0.264216\pi$
$278$	−2.21874e13	−0.00288280
$279$	−9.46906e15	−1.20193
$280$	3.61400e15	0.448189
$281$	−9.99465e15	−1.21109	−0.605545	−	0.795811i	$-0.707045\pi$
$281$	−9.99465e15	−1.21109	−0.605545	+	0.795811i	$0.707045\pi$
$282$	−2.51926e15	−0.298301
$283$	−2.14952e14	−0.0248731	−0.0124365	−	0.999923i	$-0.503959\pi$
$283$	−2.14952e14	−0.0248731	−0.0124365	+	0.999923i	$0.503959\pi$
$284$	−7.38218e15	−0.834863
$285$	2.69733e15	0.298155
$286$	0	0
$287$	−9.99450e14	−0.105567
$288$	1.50554e16	1.55468
$289$	−8.46546e15	−0.854702
$290$	1.40802e15	0.139003
$291$	−1.48618e16	−1.43472
$292$	6.67953e15	0.630605
$293$	−5.38906e15	−0.497592	−0.248796	−	0.968556i	$-0.580035\pi$
$293$	−5.38906e15	−0.497592	−0.248796	+	0.968556i	$0.580035\pi$
$294$	1.12913e16	1.01973
$295$	−4.17948e15	−0.369215
$296$	3.07751e14	0.0265952
$297$	−3.23822e16	−2.73772
$298$	2.88217e15	0.238405
$299$	0	0
$300$	1.57461e16	1.24705
$301$	3.93971e14	0.0305339
$302$	8.52171e14	0.0646371
$303$	−1.67595e16	−1.24419
$304$	−3.60653e15	−0.262066
$305$	−5.50002e14	−0.0391215
$306$	−3.08631e15	−0.214907
$307$	−8.55076e15	−0.582915	−0.291458	−	0.956584i	$-0.594140\pi$
$307$	−8.55076e15	−0.582915	−0.291458	+	0.956584i	$0.594140\pi$
$308$	3.02536e16	2.01928
$309$	−3.29100e16	−2.15079
$310$	1.05652e15	0.0676125
$311$	−2.68661e16	−1.68369	−0.841846	−	0.539719i	$-0.818531\pi$
$311$	−2.68661e16	−1.68369	−0.841846	+	0.539719i	$0.818531\pi$
$312$	0	0
$313$	1.98404e16	1.19265	0.596325	−	0.802743i	$-0.296627\pi$
$313$	1.98404e16	1.19265	0.596325	+	0.802743i	$0.296627\pi$
$314$	−5.03642e15	−0.296537
$315$	−3.67134e16	−2.11741
$316$	5.56041e15	0.314153
$317$	5.96403e15	0.330107	0.165053	−	0.986285i	$-0.447220\pi$
$317$	5.96403e15	0.330107	0.165053	+	0.986285i	$0.447220\pi$
$318$	2.00876e15	0.108931
$319$	2.43470e16	1.29362
$320$	6.42521e15	0.334513
$321$	−6.08185e16	−3.10279
$322$	−1.26172e16	−0.630810
$323$	2.48898e15	0.121956
$324$	−3.69504e16	−1.77450
$325$	0	0
$326$	−3.55472e13	−0.00164018
$327$	−1.49584e16	−0.676591
$328$	6.33022e14	0.0280698
$329$	−2.76532e16	−1.20219
$330$	6.45297e15	0.275055
$331$	−3.64400e16	−1.52299	−0.761495	−	0.648171i	$-0.775534\pi$
$331$	−3.64400e16	−1.52299	−0.761495	+	0.648171i	$0.775534\pi$
$332$	−2.02043e16	−0.828032
$333$	−3.12634e15	−0.125646
$334$	−8.62266e15	−0.339852
$335$	1.57473e16	0.608717
$336$	7.06919e16	2.68018
$337$	2.45702e16	0.913723	0.456861	−	0.889538i	$-0.348974\pi$
$337$	2.45702e16	0.913723	0.456861	+	0.889538i	$0.348974\pi$
$338$	0	0
$339$	−6.72516e16	−2.40660
$340$	−5.24917e15	−0.184280
$341$	1.82689e16	0.629231
$342$	−5.33784e15	−0.180383
$343$	6.93886e16	2.30079
$344$	−2.49529e14	−0.00811880
$345$	4.10227e16	1.30978
$346$	−1.45650e16	−0.456370
$347$	2.75785e16	0.848065	0.424033	−	0.905647i	$-0.360614\pi$
$347$	2.75785e16	0.848065	0.424033	+	0.905647i	$0.360614\pi$
$348$	6.11661e16	1.84606
$349$	−1.26995e16	−0.376202	−0.188101	−	0.982150i	$-0.560233\pi$
$349$	−1.26995e16	−0.376202	−0.188101	+	0.982150i	$0.560233\pi$
$350$	−1.13387e16	−0.329702
$351$	0	0
$352$	−2.90469e16	−0.813902
$353$	1.96015e15	0.0539205	0.0269603	−	0.999637i	$-0.491417\pi$
$353$	1.96015e15	0.0539205	0.0269603	+	0.999637i	$0.491417\pi$
$354$	1.19109e16	0.321679
$355$	−1.72838e16	−0.458305
$356$	−3.76867e16	−0.981213
$357$	−4.87866e16	−1.24726
$358$	−6.62471e15	−0.166313
$359$	−7.65438e16	−1.88710	−0.943552	−	0.331223i	$-0.892539\pi$
$359$	−7.65438e16	−1.88710	−0.943552	+	0.331223i	$0.892539\pi$
$360$	2.32532e16	0.563010
$361$	−3.77483e16	−0.897636
$362$	8.05099e15	0.188037
$363$	3.27294e16	0.750836
$364$	0	0
$365$	1.56387e16	0.346175
$366$	1.56742e15	0.0340846
$367$	7.32195e16	1.56422	0.782109	−	0.623142i	$-0.214144\pi$
$367$	7.32195e16	1.56422	0.782109	+	0.623142i	$0.214144\pi$
$368$	−5.48503e16	−1.15125
$369$	−6.43065e15	−0.132612
$370$	3.48824e14	0.00706799
$371$	2.20496e16	0.439006
$372$	4.58964e16	0.897945
$373$	−4.05086e16	−0.778825	−0.389413	−	0.921063i	$-0.627322\pi$
$373$	−4.05086e16	−0.778825	−0.389413	+	0.921063i	$0.627322\pi$
$374$	5.95451e15	0.112507
$375$	8.70507e16	1.61648
$376$	1.75147e16	0.319655
$377$	0	0
$378$	5.85819e16	1.03292
$379$	−1.46494e16	−0.253901	−0.126950	−	0.991909i	$-0.540519\pi$
$379$	−1.46494e16	−0.253901	−0.126950	+	0.991909i	$0.540519\pi$
$380$	−9.07855e15	−0.154676
$381$	6.86830e16	1.15037
$382$	−1.28264e16	−0.211199
$383$	−3.91996e16	−0.634585	−0.317292	−	0.948328i	$-0.602774\pi$
$383$	−3.91996e16	−0.634585	−0.317292	+	0.948328i	$0.602774\pi$
$384$	−9.60716e16	−1.52912
$385$	7.08323e16	1.10850
$386$	2.16879e16	0.333734
$387$	2.53488e15	0.0383563
$388$	5.00213e16	0.744302
$389$	1.62572e16	0.237888	0.118944	−	0.992901i	$-0.462049\pi$
$389$	1.62572e16	0.237888	0.118944	+	0.992901i	$0.462049\pi$
$390$	0	0
$391$	3.78539e16	0.535749
$392$	−7.85007e16	−1.09273
$393$	8.44810e15	0.115666
$394$	1.97776e16	0.266347
$395$	1.30185e16	0.172456
$396$	1.94657e17	2.53660
$397$	−1.38532e17	−1.77587	−0.887933	−	0.459972i	$-0.847859\pi$
$397$	−1.38532e17	−1.77587	−0.887933	+	0.459972i	$0.847859\pi$
$398$	−1.50403e16	−0.189678
$399$	−8.43774e16	−1.04689
$400$	−4.92927e16	−0.601717
$401$	−1.60746e17	−1.93064	−0.965320	−	0.261068i	$-0.915925\pi$
$401$	−1.60746e17	−1.93064	−0.965320	+	0.261068i	$0.915925\pi$
$402$	−4.48774e16	−0.530345
$403$	0	0
$404$	5.64085e16	0.645455
$405$	−8.65114e16	−0.974127
$406$	−4.40456e16	−0.488071
$407$	6.03174e15	0.0657777
$408$	3.09000e16	0.331641
$409$	1.78081e17	1.88112	0.940560	−	0.339629i	$-0.110301\pi$
$409$	1.78081e17	1.88112	0.940560	+	0.339629i	$0.110301\pi$
$410$	7.17507e14	0.00745987
$411$	3.65787e16	0.374332
$412$	1.10767e17	1.11578
$413$	1.30742e17	1.29640
$414$	−8.11811e16	−0.792415
$415$	−4.73041e16	−0.454554
$416$	0	0
$417$	−2.25663e15	−0.0210173
$418$	1.02984e16	0.0944334
$419$	−1.16067e17	−1.04789	−0.523945	−	0.851752i	$-0.675540\pi$
$419$	−1.16067e17	−1.04789	−0.523945	+	0.851752i	$0.675540\pi$
$420$	1.77949e17	1.58189
$421$	8.56586e16	0.749786	0.374893	−	0.927068i	$-0.377679\pi$
$421$	8.56586e16	0.749786	0.374893	+	0.927068i	$0.377679\pi$
$422$	−8.85954e15	−0.0763625
$423$	−1.77926e17	−1.51017
$424$	−1.39656e16	−0.116729
$425$	3.40184e16	0.280018
$426$	4.92560e16	0.399298
$427$	1.72051e16	0.137365
$428$	2.04700e17	1.60966
$429$	0	0
$430$	−2.82832e14	−0.00215767
$431$	1.96830e17	1.47907	0.739537	−	0.673115i	$-0.235044\pi$
$431$	1.96830e17	1.47907	0.739537	+	0.673115i	$0.235044\pi$
$432$	2.54672e17	1.88511
$433$	1.74834e17	1.27483	0.637417	−	0.770519i	$-0.280003\pi$
$433$	1.74834e17	1.27483	0.637417	+	0.770519i	$0.280003\pi$
$434$	−3.30499e16	−0.237404
$435$	1.43207e17	1.01341
$436$	5.03465e16	0.351000
$437$	6.54691e16	0.449683
$438$	−4.45677e16	−0.301605
$439$	1.19887e17	0.799377	0.399689	−	0.916651i	$-0.369118\pi$
$439$	1.19887e17	0.799377	0.399689	+	0.916651i	$0.369118\pi$
$440$	−4.48630e16	−0.294745
$441$	7.97461e17	5.16248
$442$	0	0
$443$	1.17204e17	0.736745	0.368372	−	0.929678i	$-0.379915\pi$
$443$	1.17204e17	0.736745	0.368372	+	0.929678i	$0.379915\pi$
$444$	1.51533e16	0.0938682
$445$	−8.82353e16	−0.538645
$446$	2.81121e16	0.169129
$447$	2.93140e17	1.73811
$448$	−2.00992e17	−1.17455
$449$	1.80445e17	1.03930	0.519652	−	0.854378i	$-0.326062\pi$
$449$	1.80445e17	1.03930	0.519652	+	0.854378i	$0.326062\pi$
$450$	−7.29555e16	−0.414168
$451$	1.24068e16	0.0694247
$452$	2.26352e17	1.24849
$453$	8.66726e16	0.471241
$454$	−2.23081e16	−0.119564
$455$	0	0
$456$	5.34422e16	0.278364
$457$	2.28310e17	1.17238	0.586191	−	0.810173i	$-0.300627\pi$
$457$	2.28310e17	1.17238	0.586191	+	0.810173i	$0.300627\pi$
$458$	7.21050e16	0.365039
$459$	−1.75757e17	−0.877264
$460$	−1.38072e17	−0.679486
$461$	7.32739e16	0.355544	0.177772	−	0.984072i	$-0.443111\pi$
$461$	7.32739e16	0.355544	0.177772	+	0.984072i	$0.443111\pi$
$462$	−2.01861e17	−0.965782
$463$	−1.35914e17	−0.641190	−0.320595	−	0.947216i	$-0.603883\pi$
$463$	−1.35914e17	−0.641190	−0.320595	+	0.947216i	$0.603883\pi$
$464$	−1.91479e17	−0.890745
$465$	1.07457e17	0.492934
$466$	−6.43768e16	−0.291220
$467$	−1.92016e17	−0.856600	−0.428300	−	0.903637i	$-0.640887\pi$
$467$	−1.92016e17	−0.856600	−0.428300	+	0.903637i	$0.640887\pi$
$468$	0	0
$469$	−4.92605e17	−2.13735
$470$	1.98523e16	0.0849521
$471$	−5.12244e17	−2.16193
$472$	−8.28081e16	−0.344707
$473$	−4.89063e15	−0.0200802
$474$	−3.71006e16	−0.150253
$475$	5.88354e16	0.235034
$476$	1.64204e17	0.647051
$477$	1.41871e17	0.551474
$478$	−2.92248e16	−0.112065
$479$	1.95441e17	0.739323	0.369662	−	0.929166i	$-0.379474\pi$
$479$	1.95441e17	0.739323	0.369662	+	0.929166i	$0.379474\pi$
$480$	−1.70852e17	−0.637604
$481$	0	0
$482$	8.31776e16	0.302135
$483$	−1.28327e18	−4.59896
$484$	−1.10159e17	−0.389516
$485$	1.17114e17	0.408590
$486$	8.06619e16	0.277672
$487$	4.86993e17	1.65419	0.827094	−	0.562064i	$-0.189993\pi$
$487$	4.86993e17	1.65419	0.827094	+	0.562064i	$0.189993\pi$
$488$	−1.08972e16	−0.0365246
$489$	−3.61544e15	−0.0119578
$490$	−8.89776e16	−0.290406
$491$	−5.90247e16	−0.190110	−0.0950549	−	0.995472i	$-0.530303\pi$
$491$	−5.90247e16	−0.190110	−0.0950549	+	0.995472i	$0.530303\pi$
$492$	3.11693e16	0.0990727
$493$	1.32145e17	0.414521
$494$	0	0
$495$	4.55748e17	1.39249
$496$	−1.43677e17	−0.433269
$497$	5.40668e17	1.60922
$498$	1.34809e17	0.396030
$499$	4.34707e17	1.26050	0.630250	−	0.776392i	$-0.282952\pi$
$499$	4.34707e17	1.26050	0.630250	+	0.776392i	$0.282952\pi$
$500$	−2.92991e17	−0.838590
$501$	−8.76993e17	−2.47771
$502$	1.58084e16	0.0440875
$503$	−6.61219e17	−1.82035	−0.910173	−	0.414229i	$-0.864051\pi$
$503$	−6.61219e17	−1.82035	−0.910173	+	0.414229i	$0.864051\pi$
$504$	−7.27402e17	−1.97686
$505$	1.32068e17	0.354327
$506$	1.56625e17	0.414843
$507$	0	0
$508$	−2.31170e17	−0.596785
$509$	5.88159e17	1.49909	0.749547	−	0.661951i	$-0.230271\pi$
$509$	5.88159e17	1.49909	0.749547	+	0.661951i	$0.230271\pi$
$510$	3.50240e16	0.0881373
$511$	−4.89206e17	−1.21550
$512$	3.89026e17	0.954386
$513$	−3.03975e17	−0.736335
$514$	1.51237e17	0.361742
$515$	2.59337e17	0.612516
$516$	−1.22866e16	−0.0286554
$517$	3.43278e17	0.790600
$518$	−1.09119e16	−0.0248174
$519$	−1.48138e18	−3.32720
$520$	0	0
$521$	5.46350e17	1.19681	0.598405	−	0.801193i	$-0.295801\pi$
$521$	5.46350e17	1.19681	0.598405	+	0.801193i	$0.295801\pi$
$522$	−2.83397e17	−0.613109
$523$	4.55097e17	0.972397	0.486198	−	0.873849i	$-0.338383\pi$
$523$	4.55097e17	0.972397	0.486198	+	0.873849i	$0.338383\pi$
$524$	−2.84342e16	−0.0600051
$525$	−1.15324e18	−2.40372
$526$	−2.37724e17	−0.489402
$527$	9.91561e16	0.201628
$528$	−8.77546e17	−1.76258
$529$	4.91658e17	0.975442
$530$	−1.58294e16	−0.0310222
$531$	8.41218e17	1.62852
$532$	2.83994e17	0.543104
$533$	0	0
$534$	2.51457e17	0.469294
$535$	4.79261e17	0.883634
$536$	3.12001e17	0.568310
$537$	−6.73785e17	−1.21252
$538$	2.08036e17	0.369875
$539$	−1.53857e18	−2.70265
$540$	6.41075e17	1.11263
$541$	−1.13354e18	−1.94381	−0.971904	−	0.235377i	$-0.924367\pi$
$541$	−1.13354e18	−1.94381	−0.971904	+	0.235377i	$0.924367\pi$
$542$	4.64176e16	0.0786479
$543$	8.18850e17	1.37090
$544$	−1.57654e17	−0.260803
$545$	1.17875e17	0.192684
$546$	0	0
$547$	−2.31128e17	−0.368922	−0.184461	−	0.982840i	$-0.559054\pi$
$547$	−2.31128e17	−0.368922	−0.184461	+	0.982840i	$0.559054\pi$
$548$	−1.23115e17	−0.194195
$549$	1.10701e17	0.172556
$550$	1.40755e17	0.216824
$551$	2.28548e17	0.347930
$552$	8.12782e17	1.22284
$553$	−4.07242e17	−0.605535
$554$	2.27878e17	0.334880
$555$	3.54782e16	0.0515297
$556$	7.59527e15	0.0109033
$557$	7.29742e17	1.03541	0.517703	−	0.855560i	$-0.326787\pi$
$557$	7.29742e17	1.03541	0.517703	+	0.855560i	$0.326787\pi$
$558$	−2.12649e17	−0.298223
$559$	0	0
$560$	−5.57065e17	−0.763280
$561$	6.05621e17	0.820243
$562$	−2.24453e17	−0.300496
$563$	1.01773e18	1.34688	0.673441	−	0.739241i	$-0.264816\pi$
$563$	1.01773e18	1.34688	0.673441	+	0.739241i	$0.264816\pi$
$564$	8.62404e17	1.12823
$565$	5.29955e17	0.685369
$566$	−4.82723e15	−0.00617151
$567$	2.70624e18	3.42039
$568$	−3.42443e17	−0.427882
$569$	−6.60459e17	−0.815861	−0.407931	−	0.913013i	$-0.633749\pi$
$569$	−6.60459e17	−0.815861	−0.407931	+	0.913013i	$0.633749\pi$
$570$	6.05747e16	0.0739783
$571$	−3.91758e16	−0.0473024	−0.0236512	−	0.999720i	$-0.507529\pi$
$571$	−3.91758e16	−0.0473024	−0.0236512	+	0.999720i	$0.507529\pi$
$572$	0	0
$573$	−1.30454e18	−1.53976
$574$	−2.24449e16	−0.0261934
$575$	8.94806e17	1.03250
$576$	−1.29322e18	−1.47546
$577$	−1.66029e18	−1.87302	−0.936508	−	0.350645i	$-0.885962\pi$
$577$	−1.66029e18	−1.87302	−0.936508	+	0.350645i	$0.885962\pi$
$578$	−1.90111e17	−0.212069
$579$	2.20584e18	2.43311
$580$	−4.82000e17	−0.525733
$581$	1.47976e18	1.59605
$582$	−3.33757e17	−0.355984
$583$	−2.73716e17	−0.288706
$584$	3.09849e17	0.323196
$585$	0	0
$586$	−1.21024e17	−0.123463
$587$	1.25872e17	0.126994	0.0634969	−	0.997982i	$-0.479775\pi$
$587$	1.25872e17	0.126994	0.0634969	+	0.997982i	$0.479775\pi$
$588$	−3.86529e18	−3.85682
$589$	1.71492e17	0.169237
$590$	−9.38599e16	−0.0916098
$591$	2.01154e18	1.94182
$592$	−4.74370e16	−0.0452925
$593$	8.66609e17	0.818404	0.409202	−	0.912444i	$-0.365807\pi$
$593$	8.66609e17	0.818404	0.409202	+	0.912444i	$0.365807\pi$
$594$	−7.27217e17	−0.679285
$595$	3.84448e17	0.355203
$596$	−9.86638e17	−0.901689
$597$	−1.52972e18	−1.38286
$598$	0	0
$599$	5.85295e17	0.517727	0.258863	−	0.965914i	$-0.416652\pi$
$599$	5.85295e17	0.517727	0.258863	+	0.965914i	$0.416652\pi$
$600$	7.30427e17	0.639137
$601$	8.85402e16	0.0766402	0.0383201	−	0.999266i	$-0.487799\pi$
$601$	8.85402e16	0.0766402	0.0383201	+	0.999266i	$0.487799\pi$
$602$	8.84752e15	0.00757608
$603$	−3.16951e18	−2.68491
$604$	−2.91719e17	−0.244469
$605$	−2.57914e17	−0.213828
$606$	−3.76374e17	−0.308708
$607$	1.67753e18	1.36127	0.680634	−	0.732624i	$-0.261704\pi$
$607$	1.67753e18	1.36127	0.680634	+	0.732624i	$0.261704\pi$
$608$	−2.72666e17	−0.218906
$609$	−4.47978e18	−3.55832
$610$	−1.23516e16	−0.00970684
$611$	0	0
$612$	1.05652e18	0.812817
$613$	−2.30593e17	−0.175531	−0.0877654	−	0.996141i	$-0.527973\pi$
$613$	−2.30593e17	−0.175531	−0.0877654	+	0.996141i	$0.527973\pi$
$614$	−1.92027e17	−0.144633
$615$	7.29762e16	0.0543867
$616$	1.40340e18	1.03492
$617$	−2.01416e18	−1.46974	−0.734870	−	0.678208i	$-0.762757\pi$
$617$	−2.01416e18	−1.46974	−0.734870	+	0.678208i	$0.762757\pi$
$618$	−7.39070e17	−0.533655
$619$	−1.59377e18	−1.13877	−0.569387	−	0.822070i	$-0.692819\pi$
$619$	−1.59377e18	−1.13877	−0.569387	+	0.822070i	$0.692819\pi$
$620$	−3.61672e17	−0.255723
$621$	−4.62305e18	−3.23469
$622$	−6.03340e17	−0.417758
$623$	2.76016e18	1.89131
$624$	0	0
$625$	4.08676e17	0.274258
$626$	4.45562e17	0.295921
$627$	1.04743e18	0.688474
$628$	1.72409e18	1.12156
$629$	3.27377e16	0.0210775
$630$	−8.24483e17	−0.525374
$631$	1.97321e18	1.24446	0.622232	−	0.782833i	$-0.286226\pi$
$631$	1.97321e18	1.24446	0.622232	+	0.782833i	$0.286226\pi$
$632$	2.57935e17	0.161009
$633$	−9.01086e17	−0.556727
$634$	1.33936e17	0.0819063
$635$	−5.41235e17	−0.327610
$636$	−6.87648e17	−0.411998
$637$	0	0
$638$	5.46767e17	0.320973
$639$	3.47876e18	2.02148
$640$	7.57062e17	0.435473
$641$	1.84756e18	1.05201	0.526007	−	0.850481i	$-0.323689\pi$
$641$	1.84756e18	1.05201	0.526007	+	0.850481i	$0.323689\pi$
$642$	−1.36582e18	−0.769866
$643$	−1.87154e17	−0.104431	−0.0522153	−	0.998636i	$-0.516628\pi$
$643$	−1.87154e17	−0.104431	−0.0522153	+	0.998636i	$0.516628\pi$
$644$	4.31916e18	2.38584
$645$	−2.87663e16	−0.0157306
$646$	5.58956e16	0.0302598
$647$	1.99668e18	1.07011	0.535057	−	0.844816i	$-0.320290\pi$
$647$	1.99668e18	1.07011	0.535057	+	0.844816i	$0.320290\pi$
$648$	−1.71405e18	−0.909464
$649$	−1.62299e18	−0.852560
$650$	0	0
$651$	−3.36144e18	−1.73081
$652$	1.21687e16	0.00620346
$653$	9.77373e16	0.0493315	0.0246658	−	0.999696i	$-0.492148\pi$
$653$	9.77373e16	0.0493315	0.0246658	+	0.999696i	$0.492148\pi$
$654$	−3.35926e17	−0.167876
$655$	−6.65726e16	−0.0329402
$656$	−9.75745e16	−0.0478037
$657$	−3.14764e18	−1.52690
$658$	−6.21016e17	−0.298287
$659$	−1.76709e18	−0.840432	−0.420216	−	0.907424i	$-0.638046\pi$
$659$	−1.76709e18	−0.840432	−0.420216	+	0.907424i	$0.638046\pi$
$660$	−2.20901e18	−1.04031
$661$	−2.10933e17	−0.0983636	−0.0491818	−	0.998790i	$-0.515661\pi$
$661$	−2.10933e17	−0.0983636	−0.0491818	+	0.998790i	$0.515661\pi$
$662$	−8.18345e17	−0.377885
$663$	0	0
$664$	−9.37235e17	−0.424381
$665$	6.64910e17	0.298141
$666$	−7.02091e16	−0.0311753
$667$	3.47590e18	1.52844
$668$	2.95174e18	1.28538
$669$	2.85922e18	1.23304
$670$	3.53642e17	0.151035
$671$	−2.13578e17	−0.0903360
$672$	5.34456e18	2.23878
$673$	2.57489e18	1.06822	0.534111	−	0.845415i	$-0.320647\pi$
$673$	2.57489e18	1.06822	0.534111	+	0.845415i	$0.320647\pi$
$674$	5.51780e17	0.226713
$675$	−4.15462e18	−1.69066
$676$	0	0
$677$	−1.54014e18	−0.614801	−0.307401	−	0.951580i	$-0.599459\pi$
$677$	−1.54014e18	−0.614801	−0.307401	+	0.951580i	$0.599459\pi$
$678$	−1.51029e18	−0.597127
$679$	−3.66355e18	−1.43466
$680$	−2.43498e17	−0.0944468
$681$	−2.26891e18	−0.871688
$682$	4.10271e17	0.156125
$683$	1.70025e18	0.640882	0.320441	−	0.947268i	$-0.396169\pi$
$683$	1.70025e18	0.640882	0.320441	+	0.947268i	$0.396169\pi$
$684$	1.82727e18	0.682241
$685$	−2.88247e17	−0.106605
$686$	1.55828e18	0.570872
$687$	7.33365e18	2.66135
$688$	3.84627e16	0.0138266
$689$	0	0
$690$	9.21258e17	0.324984
$691$	−2.53772e18	−0.886821	−0.443411	−	0.896319i	$-0.646232\pi$
$691$	−2.53772e18	−0.886821	−0.443411	+	0.896319i	$0.646232\pi$
$692$	4.98597e18	1.72608
$693$	−1.42566e19	−4.88935
$694$	6.19339e17	0.210422
$695$	1.77827e16	0.00598544
$696$	2.83736e18	0.946139
$697$	6.73392e16	0.0222461
$698$	−2.85196e17	−0.0933433
$699$	−6.54763e18	−2.12316
$700$	3.88152e18	1.24699
$701$	−6.08102e17	−0.193557	−0.0967786	−	0.995306i	$-0.530854\pi$
$701$	−6.08102e17	−0.193557	−0.0967786	+	0.995306i	$0.530854\pi$
$702$	0	0
$703$	5.66205e16	0.0176915
$704$	2.49505e18	0.772427
$705$	2.01913e18	0.619349
$706$	4.40197e16	0.0133788
$707$	−4.13134e18	−1.24413
$708$	−4.07738e18	−1.21665
$709$	−1.31120e17	−0.0387676	−0.0193838	−	0.999812i	$-0.506170\pi$
$709$	−1.31120e17	−0.0387676	−0.0193838	+	0.999812i	$0.506170\pi$
$710$	−3.88147e17	−0.113715
$711$	−2.62027e18	−0.760666
$712$	−1.74821e18	−0.502889
$713$	2.60816e18	0.743452
$714$	−1.09562e18	−0.309471
$715$	0	0
$716$	2.26780e18	0.629027
$717$	−2.97239e18	−0.817018
$718$	−1.71897e18	−0.468229
$719$	−1.65987e18	−0.448060	−0.224030	−	0.974582i	$-0.571921\pi$
$719$	−1.65987e18	−0.448060	−0.224030	+	0.974582i	$0.571921\pi$
$720$	−3.58426e18	−0.958823
$721$	−8.11255e18	−2.15069
$722$	−8.47723e17	−0.222722
$723$	8.45982e18	2.20274
$724$	−2.75605e18	−0.711191
$725$	3.12370e18	0.798864
$726$	7.35013e17	0.186298
$727$	−4.82210e17	−0.121133	−0.0605666	−	0.998164i	$-0.519291\pi$
$727$	−4.82210e17	−0.121133	−0.0605666	+	0.998164i	$0.519291\pi$
$728$	0	0
$729$	5.40923e17	0.133477
$730$	3.51202e17	0.0858931
$731$	−2.65443e16	−0.00643440
$732$	−5.36566e17	−0.128914
$733$	8.09696e18	1.92817	0.964086	−	0.265589i	$-0.0855663\pi$
$733$	8.09696e18	1.92817	0.964086	+	0.265589i	$0.0855663\pi$
$734$	1.64431e18	0.388114
$735$	−9.04973e18	−2.11723
$736$	−4.14688e18	−0.961647
$737$	6.11504e18	1.40560
$738$	−1.44415e17	−0.0329038
$739$	−3.32783e18	−0.751575	−0.375787	−	0.926706i	$-0.622628\pi$
$739$	−3.32783e18	−0.751575	−0.375787	+	0.926706i	$0.622628\pi$
$740$	−1.19411e17	−0.0267324
$741$	0	0
$742$	4.95174e17	0.108926
$743$	5.92753e18	1.29255	0.646273	−	0.763106i	$-0.276327\pi$
$743$	5.92753e18	1.29255	0.646273	+	0.763106i	$0.276327\pi$
$744$	2.12904e18	0.460213
$745$	−2.31000e18	−0.494989
$746$	−9.09714e17	−0.193242
$747$	9.52104e18	2.00494
$748$	−2.03837e18	−0.425523
$749$	−1.49922e19	−3.10265
$750$	1.95492e18	0.401080
$751$	4.59644e18	0.934893	0.467447	−	0.884021i	$-0.345174\pi$
$751$	4.59644e18	0.934893	0.467447	+	0.884021i	$0.345174\pi$
$752$	−2.69973e18	−0.544383
$753$	1.60784e18	0.321423
$754$	0	0
$755$	−6.82996e17	−0.134203
$756$	−2.00540e19	−3.90669
$757$	3.48373e18	0.672855	0.336428	−	0.941709i	$-0.390781\pi$
$757$	3.48373e18	0.672855	0.336428	+	0.941709i	$0.390781\pi$
$758$	−3.28985e17	−0.0629980
$759$	1.59300e19	3.02444
$760$	−4.21134e17	−0.0792742
$761$	2.55323e18	0.476530	0.238265	−	0.971200i	$-0.423421\pi$
$761$	2.55323e18	0.476530	0.238265	+	0.971200i	$0.423421\pi$
$762$	1.54243e18	0.285430
$763$	−3.68736e18	−0.676559
$764$	4.39078e18	0.798793
$765$	2.47361e18	0.446202
$766$	−8.80317e17	−0.157453
$767$	0	0
$768$	4.52194e18	0.795202
$769$	8.61810e18	1.50276	0.751381	−	0.659869i	$-0.229388\pi$
$769$	8.61810e18	1.50276	0.751381	+	0.659869i	$0.229388\pi$
$770$	1.59070e18	0.275042
$771$	1.53820e19	2.63731
$772$	−7.42431e18	−1.26224
$773$	−1.02044e19	−1.72037	−0.860183	−	0.509986i	$-0.829650\pi$
$773$	−1.02044e19	−1.72037	−0.860183	+	0.509986i	$0.829650\pi$
$774$	5.69266e16	0.00951698
$775$	2.34389e18	0.388577
$776$	2.32038e18	0.381468
$777$	−1.10982e18	−0.180933
$778$	3.65092e17	0.0590249
$779$	1.16464e17	0.0186724
$780$	0	0
$781$	−6.71168e18	−1.05828
$782$	8.50096e17	0.132930
$783$	−1.61387e19	−2.50275
$784$	1.21002e19	1.86096
$785$	4.03658e18	0.615687
$786$	1.89721e17	0.0286992
$787$	−3.89958e18	−0.585036	−0.292518	−	0.956260i	$-0.594493\pi$
$787$	−3.89958e18	−0.585036	−0.292518	+	0.956260i	$0.594493\pi$
$788$	−6.77035e18	−1.00737
$789$	−2.41784e19	−3.56802
$790$	2.92360e17	0.0427899
$791$	−1.65780e19	−2.40649
$792$	9.02973e18	1.30005
$793$	0	0
$794$	−3.11104e18	−0.440629
$795$	−1.60998e18	−0.226169
$796$	5.14866e18	0.717397
$797$	−1.04786e17	−0.0144819	−0.00724093	−	0.999974i	$-0.502305\pi$
$797$	−1.04786e17	−0.0144819	−0.00724093	+	0.999974i	$0.502305\pi$
$798$	−1.89489e18	−0.259756
$799$	1.86317e18	0.253336
$800$	−3.72670e18	−0.502619
$801$	1.77594e19	2.37584
$802$	−3.60992e18	−0.479031
$803$	6.07285e18	0.799358
$804$	1.53626e19	2.00586
$805$	1.01124e19	1.30972
$806$	0	0
$807$	2.11590e19	2.69660
$808$	2.61667e18	0.330807
$809$	−6.69922e18	−0.840154	−0.420077	−	0.907488i	$-0.637997\pi$
$809$	−6.69922e18	−0.840154	−0.420077	+	0.907488i	$0.637997\pi$
$810$	−1.94281e18	−0.241701
$811$	−6.00687e18	−0.741332	−0.370666	−	0.928766i	$-0.620871\pi$
$811$	−6.00687e18	−0.741332	−0.370666	+	0.928766i	$0.620871\pi$
$812$	1.50779e19	1.84597
$813$	4.72104e18	0.573389
$814$	1.35456e17	0.0163208
$815$	2.84903e16	0.00340543
$816$	−4.76295e18	−0.564794
$817$	−4.59088e16	−0.00540073
$818$	3.99922e18	0.466744
$819$	0	0
$820$	−2.45620e17	−0.0282146
$821$	−3.67403e18	−0.418708	−0.209354	−	0.977840i	$-0.567136\pi$
$821$	−3.67403e18	−0.418708	−0.209354	+	0.977840i	$0.567136\pi$
$822$	8.21459e17	0.0928793
$823$	−2.94489e18	−0.330347	−0.165173	−	0.986265i	$-0.552818\pi$
$823$	−2.94489e18	−0.330347	−0.165173	+	0.986265i	$0.552818\pi$
$824$	5.13825e18	0.571858
$825$	1.43159e19	1.58077
$826$	2.93611e18	0.321664
$827$	−6.74405e18	−0.733053	−0.366526	−	0.930408i	$-0.619453\pi$
$827$	−6.74405e18	−0.733053	−0.366526	+	0.930408i	$0.619453\pi$
$828$	2.77903e19	2.99706
$829$	1.20906e19	1.29373	0.646864	−	0.762605i	$-0.276080\pi$
$829$	1.20906e19	1.29373	0.646864	+	0.762605i	$0.276080\pi$
$830$	−1.06232e18	−0.112784
$831$	2.31770e19	2.44146
$832$	0	0
$833$	−8.35069e18	−0.866024
$834$	−5.06779e16	−0.00521481
$835$	6.91087e18	0.705619
$836$	−3.52541e18	−0.357165
$837$	−1.21098e19	−1.21737
$838$	−2.60654e18	−0.260003
$839$	−1.55156e19	−1.53574	−0.767868	−	0.640608i	$-0.778683\pi$
$839$	−1.55156e19	−1.53574	−0.767868	+	0.640608i	$0.778683\pi$
$840$	8.25469e18	0.810747
$841$	1.87347e18	0.182588
$842$	1.92366e18	0.186037
$843$	−2.28286e19	−2.19079
$844$	3.03283e18	0.288817
$845$	0	0
$846$	−3.99573e18	−0.374704
$847$	8.06802e18	0.750801
$848$	2.15266e18	0.198794
$849$	−4.90968e17	−0.0449939
$850$	7.63960e17	0.0694781
$851$	8.61121e17	0.0777180
$852$	−1.68615e19	−1.51022
$853$	8.08095e18	0.718280	0.359140	−	0.933284i	$-0.383070\pi$
$853$	8.08095e18	0.718280	0.359140	+	0.933284i	$0.383070\pi$
$854$	3.86380e17	0.0340830
$855$	4.27815e18	0.374521
$856$	9.49559e18	0.824979
$857$	−9.56317e18	−0.824568	−0.412284	−	0.911055i	$-0.635269\pi$
$857$	−9.56317e18	−0.824568	−0.412284	+	0.911055i	$0.635269\pi$
$858$	0	0
$859$	5.20067e18	0.441676	0.220838	−	0.975311i	$-0.429121\pi$
$859$	5.20067e18	0.441676	0.220838	+	0.975311i	$0.429121\pi$
$860$	9.68203e16	0.00816068
$861$	−2.28283e18	−0.190965
$862$	4.42028e18	0.366989
$863$	4.34228e18	0.357806	0.178903	−	0.983867i	$-0.442745\pi$
$863$	4.34228e18	0.357806	0.178903	+	0.983867i	$0.442745\pi$
$864$	1.92541e19	1.57465
$865$	1.16736e19	0.947542
$866$	3.92629e18	0.316312
$867$	−1.93358e19	−1.54610
$868$	1.13138e19	0.897903
$869$	5.05537e18	0.398221
$870$	3.21604e18	0.251447
$871$	0	0
$872$	2.33546e18	0.179894
$873$	−2.35719e19	−1.80220
$874$	1.47026e18	0.111576
$875$	2.14586e19	1.61640
$876$	1.52566e19	1.14073
$877$	−1.11368e19	−0.826536	−0.413268	−	0.910610i	$-0.635613\pi$
$877$	−1.11368e19	−0.826536	−0.413268	+	0.910610i	$0.635613\pi$
$878$	2.69233e18	0.198342
$879$	−1.23091e19	−0.900115
$880$	6.91522e18	0.501960
$881$	1.36399e18	0.0982806	0.0491403	−	0.998792i	$-0.484352\pi$
$881$	1.36399e18	0.0982806	0.0491403	+	0.998792i	$0.484352\pi$
$882$	1.79088e19	1.28092
$883$	2.56255e19	1.81940	0.909700	−	0.415265i	$-0.136311\pi$
$883$	2.56255e19	1.81940	0.909700	+	0.415265i	$0.136311\pi$
$884$	0	0
$885$	−9.54629e18	−0.667888
$886$	2.63208e18	0.182801
$887$	−6.51789e18	−0.449369	−0.224685	−	0.974432i	$-0.572135\pi$
$887$	−6.51789e18	−0.449369	−0.224685	+	0.974432i	$0.572135\pi$
$888$	7.02930e17	0.0481092
$889$	1.69308e19	1.15031
$890$	−1.98153e18	−0.133649
$891$	−3.35943e19	−2.24937
$892$	−9.62345e18	−0.639675
$893$	3.22238e18	0.212639
$894$	6.58313e18	0.431259
$895$	5.30955e18	0.345309
$896$	−2.36823e19	−1.52905
$897$	0	0
$898$	4.05229e18	0.257872
$899$	9.10491e18	0.575225
$900$	2.49744e19	1.56646
$901$	−1.48562e18	−0.0925116
$902$	2.78624e17	0.0172257
$903$	8.99863e17	0.0552339
$904$	1.05000e19	0.639874
$905$	−6.45269e18	−0.390413
$906$	1.94643e18	0.116925
$907$	1.12237e19	0.669405	0.334702	−	0.942324i	$-0.391364\pi$
$907$	1.12237e19	0.669405	0.334702	+	0.942324i	$0.391364\pi$
$908$	7.63659e18	0.452212
$909$	−2.65818e19	−1.56286
$910$	0	0
$911$	−7.22046e18	−0.418500	−0.209250	−	0.977862i	$-0.567102\pi$
$911$	−7.22046e18	−0.418500	−0.209250	+	0.977862i	$0.567102\pi$
$912$	−8.23762e18	−0.474062
$913$	−1.83692e19	−1.04962
$914$	5.12722e18	0.290892
$915$	−1.25625e18	−0.0707685
$916$	−2.46833e19	−1.38065
$917$	2.08251e18	0.115661
$918$	−3.94703e18	−0.217667
$919$	2.06326e18	0.112980	0.0564902	−	0.998403i	$-0.482009\pi$
$919$	2.06326e18	0.112980	0.0564902	+	0.998403i	$0.482009\pi$
$920$	−6.40487e18	−0.348249
$921$	−1.95307e19	−1.05446
$922$	1.64553e18	0.0882177
$923$	0	0
$924$	6.91018e19	3.65276
$925$	7.73868e17	0.0406205
$926$	−3.05225e18	−0.159092
$927$	−5.21976e19	−2.70167
$928$	−1.44764e19	−0.744047
$929$	3.01912e18	0.154091	0.0770457	−	0.997028i	$-0.475451\pi$
$929$	3.01912e18	0.154091	0.0770457	+	0.997028i	$0.475451\pi$
$930$	2.41318e18	0.122307
$931$	−1.44427e19	−0.726900
$932$	2.20377e19	1.10145
$933$	−6.13645e19	−3.04570
$934$	−4.31216e18	−0.212540
$935$	−4.77241e18	−0.233594
$936$	0	0
$937$	−1.50446e19	−0.726229	−0.363114	−	0.931745i	$-0.618287\pi$
$937$	−1.50446e19	−0.726229	−0.363114	+	0.931745i	$0.618287\pi$
$938$	−1.10626e19	−0.530320
$939$	4.53172e19	2.15743
$940$	−6.79591e18	−0.321304
$941$	4.24474e18	0.199305	0.0996526	−	0.995022i	$-0.468227\pi$
$941$	4.24474e18	0.199305	0.0996526	+	0.995022i	$0.468227\pi$
$942$	−1.15036e19	−0.536418
$943$	1.77126e18	0.0820271
$944$	1.27641e19	0.587046
$945$	−4.69521e19	−2.14461
$946$	−1.09830e17	−0.00498229
$947$	3.99930e19	1.80181	0.900906	−	0.434015i	$-0.142904\pi$
$947$	3.99930e19	1.80181	0.900906	+	0.434015i	$0.142904\pi$
$948$	1.27004e19	0.568283
$949$	0	0
$950$	1.32128e18	0.0583167
$951$	1.36224e19	0.597144
$952$	7.61706e18	0.331625
$953$	1.66145e19	0.718427	0.359214	−	0.933255i	$-0.383045\pi$
$953$	1.66145e19	0.718427	0.359214	+	0.933255i	$0.383045\pi$
$954$	3.18604e18	0.136832
$955$	1.02800e19	0.438504
$956$	1.00043e19	0.423850
$957$	5.56106e19	2.34007
$958$	4.38907e18	0.183441
$959$	9.01690e18	0.374314
$960$	1.46757e19	0.605113
$961$	−1.75856e19	−0.720204
$962$	0	0
$963$	−9.64624e19	−3.89751
$964$	−2.84737e19	−1.14273
$965$	−1.73824e19	−0.692919
$966$	−2.88187e19	−1.14110
$967$	3.07638e19	1.20995	0.604976	−	0.796244i	$-0.293183\pi$
$967$	3.07638e19	1.20995	0.604976	+	0.796244i	$0.293183\pi$
$968$	−5.11004e18	−0.199634
$969$	5.68503e18	0.220612
$970$	2.63006e18	0.101380
$971$	−2.54238e19	−0.973454	−0.486727	−	0.873554i	$-0.661809\pi$
$971$	−2.54238e19	−0.973454	−0.486727	+	0.873554i	$0.661809\pi$
$972$	−2.76125e19	−1.05021
$973$	−5.56275e17	−0.0210163
$974$	1.09365e19	0.410437
$975$	0	0
$976$	1.67970e18	0.0622026
$977$	2.79025e18	0.102643	0.0513214	−	0.998682i	$-0.483657\pi$
$977$	2.79025e18	0.102643	0.0513214	+	0.998682i	$0.483657\pi$
$978$	−8.11929e16	−0.00296698
$979$	−3.42638e19	−1.24379
$980$	3.04592e19	1.09837
$981$	−2.37252e19	−0.849886
$982$	−1.32554e18	−0.0471701
$983$	−3.74867e19	−1.32519	−0.662596	−	0.748977i	$-0.730545\pi$
$983$	−3.74867e19	−1.32519	−0.662596	+	0.748977i	$0.730545\pi$
$984$	1.44588e18	0.0507765
$985$	−1.58513e19	−0.553005
$986$	2.96762e18	0.102851
$987$	−6.31622e19	−2.17468
$988$	0	0
$989$	−6.98210e17	−0.0237252
$990$	1.02349e19	0.345504
$991$	−5.01476e18	−0.168179	−0.0840895	−	0.996458i	$-0.526798\pi$
$991$	−5.01476e18	−0.168179	−0.0840895	+	0.996458i	$0.526798\pi$
$992$	−1.08625e19	−0.361913
$993$	−8.32321e19	−2.75500
$994$	1.21419e19	0.399279
$995$	1.20545e19	0.393820
$996$	−4.61484e19	−1.49786
$997$	3.25426e19	1.04938	0.524691	−	0.851293i	$-0.324181\pi$
$997$	3.25426e19	1.04938	0.524691	+	0.851293i	$0.324181\pi$
$998$	9.76234e18	0.312756
$999$	−3.99822e18	−0.127260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.14.a.c.1.9		14
13.4	even	6		13.14.c.a.3.9	✓	28
13.10	even	6		13.14.c.a.9.9	yes	28
13.12	even	2		169.14.a.e.1.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.14.c.a.3.9	✓	28	13.4	even	6
13.14.c.a.9.9	yes	28	13.10	even	6
169.14.a.c.1.9		14	1.1	even	1	trivial
169.14.a.e.1.6		14	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	169.a (trivial)

\(f(q)\)	\(=\)	\(q+22.4573 q^{2} +2284.08 q^{3} -7687.67 q^{4} -17999.0 q^{5} +51294.3 q^{6} +563042. q^{7} -356614. q^{8} +3.62272e6 q^{9} -404209. q^{10} -6.98942e6 q^{11} -1.75593e7 q^{12} +1.26444e7 q^{14} -4.11113e7 q^{15} +5.49688e7 q^{16} -3.79357e7 q^{17} +8.13565e7 q^{18} -6.56105e7 q^{19} +1.38370e8 q^{20} +1.28604e9 q^{21} -1.56963e8 q^{22} -9.97845e8 q^{23} -8.14537e8 q^{24} -8.96739e8 q^{25} +4.63303e9 q^{27} -4.32848e9 q^{28} -3.48340e9 q^{29} -9.23248e8 q^{30} -2.61380e9 q^{31} +4.15583e9 q^{32} -1.59644e10 q^{33} -8.51932e8 q^{34} -1.01342e10 q^{35} -2.78503e10 q^{36} -8.62981e8 q^{37} -1.47343e9 q^{38} +6.41870e9 q^{40} -1.77509e9 q^{41} +2.88809e10 q^{42} +6.99718e8 q^{43} +5.37324e10 q^{44} -6.52054e10 q^{45} -2.24089e10 q^{46} -4.91139e10 q^{47} +1.25553e11 q^{48} +2.20128e11 q^{49} -2.01383e10 q^{50} -8.66483e10 q^{51} +3.91615e10 q^{53} +1.04045e11 q^{54} +1.25803e11 q^{55} -2.00789e11 q^{56} -1.49860e11 q^{57} -7.82278e10 q^{58} +2.32206e11 q^{59} +3.16050e11 q^{60} +3.05574e10 q^{61} -5.86988e10 q^{62} +2.03975e12 q^{63} -3.56976e11 q^{64} -3.58518e11 q^{66} -8.74899e11 q^{67} +2.91637e11 q^{68} -2.27916e12 q^{69} -2.27587e11 q^{70} +9.60262e11 q^{71} -1.29191e12 q^{72} -8.68862e11 q^{73} -1.93802e10 q^{74} -2.04823e12 q^{75} +5.04392e11 q^{76} -3.93534e12 q^{77} -7.23289e11 q^{79} -9.89384e11 q^{80} +4.80645e12 q^{81} -3.98637e10 q^{82} +2.62815e12 q^{83} -9.88663e12 q^{84} +6.82804e11 q^{85} +1.57138e10 q^{86} -7.95639e12 q^{87} +2.49253e12 q^{88} +4.90223e12 q^{89} -1.46434e12 q^{90} +7.67110e12 q^{92} -5.97014e12 q^{93} -1.10296e12 q^{94} +1.18092e12 q^{95} +9.49228e12 q^{96} -6.50670e12 q^{97} +4.94347e12 q^{98} -2.53207e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 65 q^{2} - 728 q^{3} + 53249 q^{4} - 20930 q^{5} + 143910 q^{6} - 173992 q^{7} - 1308489 q^{8} + 5231838 q^{9} - 2769243 q^{10} + 10986144 q^{11} - 22602732 q^{12} - 11865878 q^{14} - 75354448 q^{15}+ \cdots - 16619904586272 q^{99}+O(q^{100}) \) 14 * q - 65 * q^2 - 728 * q^3 + 53249 * q^4 - 20930 * q^5 + 143910 * q^6 - 173992 * q^7 - 1308489 * q^8 + 5231838 * q^9 - 2769243 * q^10 + 10986144 * q^11 - 22602732 * q^12 - 11865878 * q^14 - 75354448 * q^15 + 273433217 * q^16 - 255934950 * q^17 + 175342921 * q^18 - 266623552 * q^19 - 225433091 * q^20 + 1257937928 * q^21 - 77223114 * q^22 - 1914406544 * q^23 - 680727216 * q^24 + 2612939384 * q^25 + 1775226160 * q^27 - 3680076400 * q^28 - 6211296126 * q^29 - 5703660004 * q^30 - 3498837472 * q^31 + 2312486527 * q^32 + 5621901584 * q^33 + 11686861797 * q^34 - 23009265024 * q^35 - 23496114839 * q^36 + 19577630774 * q^37 + 25824361822 * q^38 - 55850293929 * q^40 - 6039692074 * q^41 - 143590583874 * q^42 - 16878499784 * q^43 + 244775923496 * q^44 - 148673926778 * q^45 + 177583142490 * q^46 - 184702457472 * q^47 - 92920518608 * q^48 + 195653684766 * q^49 - 753661423970 * q^50 + 308584639568 * q^51 - 143775384550 * q^53 + 365361720282 * q^54 - 855926433792 * q^55 - 192505368988 * q^56 + 962256719424 * q^57 - 660641292207 * q^58 + 637655529992 * q^59 - 1277628531192 * q^60 - 1530666437030 * q^61 - 1907899186036 * q^62 - 832654573712 * q^63 + 316116140225 * q^64 - 135426824550 * q^66 - 1120398677944 * q^67 - 4085795015901 * q^68 - 1473200404976 * q^69 + 4688842372344 * q^70 + 1506585643472 * q^71 + 3521118562923 * q^72 + 426256990718 * q^73 - 4665118313621 * q^74 - 2605103918408 * q^75 - 6106356745372 * q^76 + 1427057517512 * q^77 - 3516338331392 * q^79 + 5983641421745 * q^80 - 2512348302642 * q^81 + 8600700659175 * q^82 - 1016970123936 * q^83 - 4374201207844 * q^84 + 2527554975426 * q^85 + 3773647528794 * q^86 + 1118899666832 * q^87 + 5943200108772 * q^88 + 5229645042596 * q^89 + 2110232695965 * q^90 + 1915125894160 * q^92 - 1283055655752 * q^93 + 32271602536104 * q^94 - 8980600417472 * q^95 - 25846279484896 * q^96 + 3129146550452 * q^97 - 5503659823363 * q^98 - 16619904586272 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more