LMFDB - Embedded newform 169.14.a.e.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			$-28.9774$ 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)

$f(q)$	$=$	\(q+33.9774 q^{2} -1595.69 q^{3} -7037.54 q^{4} -28205.3 q^{5} -54217.3 q^{6} -354344. q^{7} -517460. q^{8} +951897. q^{9} -958341. q^{10} -4.97041e6 q^{11} +1.12297e7 q^{12} -1.20397e7 q^{14} +4.50068e7 q^{15} +4.00696e7 q^{16} -1.07108e8 q^{17} +3.23430e7 q^{18} -3.23912e8 q^{19} +1.98496e8 q^{20} +5.65422e8 q^{21} -1.68882e8 q^{22} -5.25984e8 q^{23} +8.25705e8 q^{24} -4.25166e8 q^{25} +1.02511e9 q^{27} +2.49371e9 q^{28} -1.20291e9 q^{29} +1.52921e9 q^{30} +3.17736e9 q^{31} +5.60049e9 q^{32} +7.93123e9 q^{33} -3.63924e9 q^{34} +9.99436e9 q^{35} -6.69901e9 q^{36} +1.84885e10 q^{37} -1.10057e10 q^{38} +1.45951e10 q^{40} +2.17511e10 q^{41} +1.92116e10 q^{42} +5.15859e10 q^{43} +3.49795e10 q^{44} -2.68485e10 q^{45} -1.78716e10 q^{46} +1.84645e10 q^{47} -6.39385e10 q^{48} +2.86705e10 q^{49} -1.44461e10 q^{50} +1.70910e11 q^{51} -1.97464e11 q^{53} +3.48306e10 q^{54} +1.40192e11 q^{55} +1.83359e11 q^{56} +5.16862e11 q^{57} -4.08719e10 q^{58} +1.45498e11 q^{59} -3.16737e11 q^{60} +6.36102e11 q^{61} +1.07958e11 q^{62} -3.37299e11 q^{63} -1.37960e11 q^{64} +2.69482e11 q^{66} -6.61973e11 q^{67} +7.53774e11 q^{68} +8.39307e11 q^{69} +3.39582e11 q^{70} -1.75593e12 q^{71} -4.92569e11 q^{72} -1.33173e12 q^{73} +6.28192e11 q^{74} +6.78433e11 q^{75} +2.27954e12 q^{76} +1.76123e12 q^{77} +1.34409e12 q^{79} -1.13017e12 q^{80} -3.15339e12 q^{81} +7.39045e11 q^{82} +2.49195e12 q^{83} -3.97918e12 q^{84} +3.02100e12 q^{85} +1.75276e12 q^{86} +1.91948e12 q^{87} +2.57199e12 q^{88} +6.50805e12 q^{89} -9.12242e11 q^{90} +3.70163e12 q^{92} -5.07007e12 q^{93} +6.27374e11 q^{94} +9.13602e12 q^{95} -8.93664e12 q^{96} +6.79919e11 q^{97} +9.74148e11 q^{98} -4.73132e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	33.9774	0.375401	0.187700	−	0.982226i	$-0.439897\pi$
$2$	33.9774	0.375401	0.187700	+	0.982226i	$0.439897\pi$
$3$	−1595.69	−1.26375	−0.631873	−	0.775072i	$-0.717714\pi$
$3$	−1595.69	−1.26375	−0.631873	+	0.775072i	$0.717714\pi$
$4$	−7037.54	−0.859074
$5$	−28205.3	−0.807282	−0.403641	−	0.914918i	$-0.632255\pi$
$5$	−28205.3	−0.807282	−0.403641	+	0.914918i	$0.632255\pi$
$6$	−54217.3	−0.474411
$7$	−354344.	−1.13838	−0.569190	−	0.822206i	$-0.692743\pi$
$7$	−354344.	−1.13838	−0.569190	+	0.822206i	$0.692743\pi$
$8$	−517460.	−0.697898
$9$	951897.	0.597054
$10$	−958341.	−0.303054
$11$	−4.97041e6	−0.845941	−0.422970	−	0.906144i	$-0.639013\pi$
$11$	−4.97041e6	−0.845941	−0.422970	+	0.906144i	$0.639013\pi$
$12$	1.12297e7	1.08565
$13$	0	0
$13$	0	0
$14$	−1.20397e7	−0.427349
$15$	4.50068e7	1.02020
$16$	4.00696e7	0.597083
$17$	−1.07108e8	−1.07622	−0.538112	−	0.842874i	$-0.680862\pi$
$17$	−1.07108e8	−1.07622	−0.538112	+	0.842874i	$0.680862\pi$
$18$	3.23430e7	0.224135
$19$	−3.23912e8	−1.57953	−0.789766	−	0.613408i	$-0.789798\pi$
$19$	−3.23912e8	−1.57953	−0.789766	+	0.613408i	$0.789798\pi$
$20$	1.98496e8	0.693515
$21$	5.65422e8	1.43862
$22$	−1.68882e8	−0.317567
$23$	−5.25984e8	−0.740870	−0.370435	−	0.928858i	$-0.620791\pi$
$23$	−5.25984e8	−0.740870	−0.370435	+	0.928858i	$0.620791\pi$
$24$	8.25705e8	0.881966
$25$	−4.25166e8	−0.348296
$26$	0	0
$27$	1.02511e9	0.509221
$28$	2.49371e9	0.977953
$29$	−1.20291e9	−0.375533	−0.187766	−	0.982214i	$-0.560125\pi$
$29$	−1.20291e9	−0.375533	−0.187766	+	0.982214i	$0.560125\pi$
$30$	1.52921e9	0.382983
$31$	3.17736e9	0.643006	0.321503	−	0.946909i	$-0.395812\pi$
$31$	3.17736e9	0.643006	0.321503	+	0.946909i	$0.395812\pi$
$32$	5.60049e9	0.922043
$33$	7.93123e9	1.06905
$34$	−3.63924e9	−0.404015
$35$	9.99436e9	0.918994
$36$	−6.69901e9	−0.512914
$37$	1.84885e10	1.18465	0.592326	−	0.805698i	$-0.298210\pi$
$37$	1.84885e10	1.18465	0.592326	+	0.805698i	$0.298210\pi$
$38$	−1.10057e10	−0.592958
$39$	0	0
$40$	1.45951e10	0.563400
$41$	2.17511e10	0.715131	0.357566	−	0.933888i	$-0.383607\pi$
$41$	2.17511e10	0.715131	0.357566	+	0.933888i	$0.383607\pi$
$42$	1.92116e10	0.540061
$43$	5.15859e10	1.24448	0.622238	−	0.782828i	$-0.286224\pi$
$43$	5.15859e10	1.24448	0.622238	+	0.782828i	$0.286224\pi$
$44$	3.49795e10	0.726726
$45$	−2.68485e10	−0.481991
$46$	−1.78716e10	−0.278123
$47$	1.84645e10	0.249862	0.124931	−	0.992165i	$-0.460129\pi$
$47$	1.84645e10	0.249862	0.124931	+	0.992165i	$0.460129\pi$
$48$	−6.39385e10	−0.754561
$49$	2.86705e10	0.295910
$50$	−1.44461e10	−0.130751
$51$	1.70910e11	1.36007
$52$	0	0
$53$	−1.97464e11	−1.22376	−0.611878	−	0.790952i	$-0.709586\pi$
$53$	−1.97464e11	−1.22376	−0.611878	+	0.790952i	$0.709586\pi$
$54$	3.48306e10	0.191162
$55$	1.40192e11	0.682912
$56$	1.83359e11	0.794473
$57$	5.16862e11	1.99613
$58$	−4.08719e10	−0.140975
$59$	1.45498e11	0.449076	0.224538	−	0.974465i	$-0.427913\pi$
$59$	1.45498e11	0.449076	0.224538	+	0.974465i	$0.427913\pi$
$60$	−3.16737e11	−0.876427
$61$	6.36102e11	1.58082	0.790411	−	0.612577i	$-0.209867\pi$
$61$	6.36102e11	1.58082	0.790411	+	0.612577i	$0.209867\pi$
$62$	1.07958e11	0.241385
$63$	−3.37299e11	−0.679675
$64$	−1.37960e11	−0.250947
$65$	0	0
$66$	2.69482e11	0.401324
$67$	−6.61973e11	−0.894034	−0.447017	−	0.894526i	$-0.647514\pi$
$67$	−6.61973e11	−0.894034	−0.447017	+	0.894526i	$0.647514\pi$
$68$	7.53774e11	0.924556
$69$	8.39307e11	0.936271
$70$	3.39582e11	0.344991
$71$	−1.75593e12	−1.62678	−0.813390	−	0.581719i	$-0.802380\pi$
$71$	−1.75593e12	−1.62678	−0.813390	+	0.581719i	$0.802380\pi$
$72$	−4.92569e11	−0.416683
$73$	−1.33173e12	−1.02995	−0.514975	−	0.857205i	$-0.672199\pi$
$73$	−1.33173e12	−1.02995	−0.514975	+	0.857205i	$0.672199\pi$
$74$	6.28192e11	0.444719
$75$	6.78433e11	0.440158
$76$	2.27954e12	1.35694
$77$	1.76123e12	0.963002
$78$	0	0
$79$	1.34409e12	0.622088	0.311044	−	0.950396i	$-0.399321\pi$
$79$	1.34409e12	0.622088	0.311044	+	0.950396i	$0.399321\pi$
$80$	−1.13017e12	−0.482014
$81$	−3.15339e12	−1.24058
$82$	7.39045e11	0.268461
$83$	2.49195e12	0.836628	0.418314	−	0.908302i	$-0.362621\pi$
$83$	2.49195e12	0.836628	0.418314	+	0.908302i	$0.362621\pi$
$84$	−3.97918e12	−1.23588
$85$	3.02100e12	0.868815
$86$	1.75276e12	0.467177
$87$	1.91948e12	0.474578
$88$	2.57199e12	0.590380
$89$	6.50805e12	1.38808	0.694042	−	0.719934i	$-0.255828\pi$
$89$	6.50805e12	1.38808	0.694042	+	0.719934i	$0.255828\pi$
$90$	−9.12242e11	−0.180940
$91$	0	0
$92$	3.70163e12	0.636462
$93$	−5.07007e12	−0.812596
$94$	6.27374e11	0.0937985
$95$	9.13602e12	1.27513
$96$	−8.93664e12	−1.16523
$97$	6.79919e11	0.0828783	0.0414391	−	0.999141i	$-0.486806\pi$
$97$	6.79919e11	0.0828783	0.0414391	+	0.999141i	$0.486806\pi$
$98$	9.74148e11	0.111085
$99$	−4.73132e12	−0.505072
$100$	2.99212e12	0.299212
$101$	−1.76959e13	−1.65876	−0.829380	−	0.558685i	$-0.811306\pi$
$101$	−1.76959e13	−1.65876	−0.829380	+	0.558685i	$0.811306\pi$
$102$	5.80709e12	0.510573
$103$	2.04628e13	1.68859	0.844293	−	0.535882i	$-0.180021\pi$
$103$	2.04628e13	1.68859	0.844293	+	0.535882i	$0.180021\pi$
$104$	0	0
$105$	−1.59479e13	−1.16137
$106$	−6.70931e12	−0.459399
$107$	−7.36001e12	−0.474115	−0.237058	−	0.971496i	$-0.576183\pi$
$107$	−7.36001e12	−0.474115	−0.237058	+	0.971496i	$0.576183\pi$
$108$	−7.21426e12	−0.437459
$109$	−3.07635e12	−0.175697	−0.0878483	−	0.996134i	$-0.527999\pi$
$109$	−3.07635e12	−0.175697	−0.0878483	+	0.996134i	$0.527999\pi$
$110$	4.76335e12	0.256366
$111$	−2.95019e13	−1.49710
$112$	−1.41984e13	−0.679708
$113$	−3.09845e12	−0.140002	−0.0700010	−	0.997547i	$-0.522300\pi$
$113$	−3.09845e12	−0.140002	−0.0700010	+	0.997547i	$0.522300\pi$
$114$	1.75616e13	0.749348
$115$	1.48355e13	0.598091
$116$	8.46556e12	0.322611
$117$	0	0
$118$	4.94366e12	0.168584
$119$	3.79529e13	1.22515
$120$	−2.32892e13	−0.711995
$121$	−9.81772e12	−0.284384
$122$	2.16131e13	0.593442
$123$	−3.47079e13	−0.903744
$124$	−2.23608e13	−0.552390
$125$	4.64222e13	1.08845
$126$	−1.14605e13	−0.255150
$127$	−4.52905e13	−0.957818	−0.478909	−	0.877865i	$-0.658968\pi$
$127$	−4.52905e13	−0.957818	−0.478909	+	0.877865i	$0.658968\pi$
$128$	−5.05667e13	−1.01625
$129$	−8.23150e13	−1.57270
$130$	0	0
$131$	−9.41327e13	−1.62734	−0.813668	−	0.581330i	$-0.802532\pi$
$131$	−9.41327e13	−1.62734	−0.813668	+	0.581330i	$0.802532\pi$
$132$	−5.58163e13	−0.918397
$133$	1.14776e14	1.79811
$134$	−2.24921e13	−0.335621
$135$	−2.89135e13	−0.411085
$136$	5.54239e13	0.751094
$137$	2.42650e13	0.313542	0.156771	−	0.987635i	$-0.449892\pi$
$137$	2.42650e13	0.313542	0.156771	+	0.987635i	$0.449892\pi$
$138$	2.85175e13	0.351477
$139$	7.46609e12	0.0878005	0.0439002	−	0.999036i	$-0.486022\pi$
$139$	7.46609e12	0.0878005	0.0439002	+	0.999036i	$0.486022\pi$
$140$	−7.03356e13	−0.789484
$141$	−2.94635e13	−0.315762
$142$	−5.96620e13	−0.610694
$143$	0	0
$144$	3.81421e13	0.356491
$145$	3.39285e13	0.303161
$146$	−4.52486e13	−0.386644
$147$	−4.57491e13	−0.373956
$148$	−1.30114e14	−1.01770
$149$	1.12298e14	0.840739	0.420369	−	0.907353i	$-0.361900\pi$
$149$	1.12298e14	0.840739	0.420369	+	0.907353i	$0.361900\pi$
$150$	2.30514e13	0.165236
$151$	3.36374e12	0.0230926	0.0115463	−	0.999933i	$-0.496325\pi$
$151$	3.36374e12	0.0230926	0.0115463	+	0.999933i	$0.496325\pi$
$152$	1.67612e14	1.10235
$153$	−1.01955e14	−0.642563
$154$	5.98422e13	0.361512
$155$	−8.96181e13	−0.519087
$156$	0	0
$157$	1.62804e14	0.867597	0.433799	−	0.901010i	$-0.357173\pi$
$157$	1.62804e14	0.867597	0.433799	+	0.901010i	$0.357173\pi$
$158$	4.56686e13	0.233532
$159$	3.15091e14	1.54652
$160$	−1.57963e14	−0.744349
$161$	1.86379e14	0.843392
$162$	−1.07144e14	−0.465715
$163$	−1.41843e14	−0.592362	−0.296181	−	0.955132i	$-0.595713\pi$
$163$	−1.41843e14	−0.592362	−0.296181	+	0.955132i	$0.595713\pi$
$164$	−1.53074e14	−0.614351
$165$	−2.23702e14	−0.863028
$166$	8.46701e13	0.314071
$167$	−4.39748e14	−1.56873	−0.784363	−	0.620302i	$-0.787010\pi$
$167$	−4.39748e14	−1.56873	−0.784363	+	0.620302i	$0.787010\pi$
$168$	−2.92583e14	−1.00401
$169$	0	0
$170$	1.02646e14	0.326154
$171$	−3.08331e14	−0.943066
$172$	−3.63038e14	−1.06910
$173$	−2.09177e14	−0.593219	−0.296609	−	0.954999i	$-0.595856\pi$
$173$	−2.09177e14	−0.593219	−0.296609	+	0.954999i	$0.595856\pi$
$174$	6.52188e13	0.178157
$175$	1.50655e14	0.396494
$176$	−1.99162e14	−0.505097
$177$	−2.32170e14	−0.567519
$178$	2.21127e14	0.521088
$179$	−3.37836e14	−0.767647	−0.383824	−	0.923406i	$-0.625393\pi$
$179$	−3.37836e14	−0.767647	−0.383824	+	0.923406i	$0.625393\pi$
$180$	1.88947e14	0.414066
$181$	6.90056e13	0.145873	0.0729363	−	0.997337i	$-0.476763\pi$
$181$	6.90056e13	0.145873	0.0729363	+	0.997337i	$0.476763\pi$
$182$	0	0
$183$	−1.01502e15	−1.99776
$184$	2.72176e14	0.517052
$185$	−5.21473e14	−0.956348
$186$	−1.72268e14	−0.305049
$187$	5.32369e14	0.910421
$188$	−1.29944e14	−0.214650
$189$	−3.63242e14	−0.579688
$190$	3.10418e14	0.478684
$191$	1.11773e15	1.66579	0.832893	−	0.553434i	$-0.186683\pi$
$191$	1.11773e15	1.66579	0.832893	+	0.553434i	$0.186683\pi$
$192$	2.20140e14	0.317133
$193$	1.28086e15	1.78394	0.891968	−	0.452099i	$-0.149324\pi$
$193$	1.28086e15	1.78394	0.891968	+	0.452099i	$0.149324\pi$
$194$	2.31019e13	0.0311126
$195$	0	0
$196$	−2.01769e14	−0.254209
$197$	−1.36897e15	−1.66864	−0.834319	−	0.551281i	$-0.814139\pi$
$197$	−1.36897e15	−1.66864	−0.834319	+	0.551281i	$0.814139\pi$
$198$	−1.60758e14	−0.189605
$199$	8.59136e14	0.980657	0.490328	−	0.871538i	$-0.336877\pi$
$199$	8.59136e14	0.980657	0.490328	+	0.871538i	$0.336877\pi$
$200$	2.20007e14	0.243075
$201$	1.05630e15	1.12983
$202$	−6.01261e14	−0.622700
$203$	4.26245e14	0.427499
$204$	−1.20279e15	−1.16840
$205$	−6.13495e14	−0.577312
$206$	6.95273e14	0.633896
$207$	−5.00683e14	−0.442339
$208$	0	0
$209$	1.60998e15	1.33619
$210$	−5.41867e14	−0.435981
$211$	6.29982e14	0.491465	0.245732	−	0.969338i	$-0.420972\pi$
$211$	6.29982e14	0.491465	0.245732	+	0.969338i	$0.420972\pi$
$212$	1.38966e15	1.05130
$213$	2.80192e15	2.05584
$214$	−2.50074e14	−0.177983
$215$	−1.45499e15	−1.00464
$216$	−5.30454e14	−0.355385
$217$	−1.12588e15	−0.731985
$218$	−1.04526e14	−0.0659566
$219$	2.12502e15	1.30160
$220$	−9.86605e14	−0.586672
$221$	0	0
$222$	−1.00240e15	−0.562012
$223$	4.18442e14	0.227852	0.113926	−	0.993489i	$-0.463657\pi$
$223$	4.18442e14	0.227852	0.113926	+	0.993489i	$0.463657\pi$
$224$	−1.98450e15	−1.04964
$225$	−4.04715e14	−0.207952
$226$	−1.05277e14	−0.0525569
$227$	3.83748e14	0.186156	0.0930782	−	0.995659i	$-0.470329\pi$
$227$	3.83748e14	0.186156	0.0930782	+	0.995659i	$0.470329\pi$
$228$	−3.63744e15	−1.71482
$229$	9.04228e13	0.0414331	0.0207165	−	0.999785i	$-0.493405\pi$
$229$	9.04228e13	0.0414331	0.0207165	+	0.999785i	$0.493405\pi$
$230$	5.04073e14	0.224524
$231$	−2.81038e15	−1.21699
$232$	6.22460e14	0.262084
$233$	−3.15966e15	−1.29368	−0.646839	−	0.762626i	$-0.723910\pi$
$233$	−3.15966e15	−1.29368	−0.646839	+	0.762626i	$0.723910\pi$
$234$	0	0
$235$	−5.20795e14	−0.201709
$236$	−1.02395e15	−0.385790
$237$	−2.14474e15	−0.786161
$238$	1.28954e15	0.459923
$239$	1.59971e15	0.555206	0.277603	−	0.960696i	$-0.410460\pi$
$239$	1.59971e15	0.555206	0.277603	+	0.960696i	$0.410460\pi$
$240$	1.80340e15	0.609143
$241$	3.18694e15	1.04776	0.523882	−	0.851791i	$-0.324483\pi$
$241$	3.18694e15	1.04776	0.523882	+	0.851791i	$0.324483\pi$
$242$	−3.33581e14	−0.106758
$243$	3.39747e15	1.05856
$244$	−4.47659e15	−1.35804
$245$	−8.08658e14	−0.238883
$246$	−1.17929e15	−0.339266
$247$	0	0
$248$	−1.64415e15	−0.448752
$249$	−3.97638e15	−1.05729
$250$	1.57730e15	0.408607
$251$	−6.77483e15	−1.71009	−0.855045	−	0.518553i	$-0.826471\pi$
$251$	−6.77483e15	−1.71009	−0.855045	+	0.518553i	$0.826471\pi$
$252$	2.37375e15	0.583891
$253$	2.61436e15	0.626732
$254$	−1.53885e15	−0.359565
$255$	−4.82057e15	−1.09796
$256$	−5.87961e14	−0.130554
$257$	5.50919e15	1.19268	0.596338	−	0.802734i	$-0.296622\pi$
$257$	5.50919e15	1.19268	0.596338	+	0.802734i	$0.296622\pi$
$258$	−2.79685e15	−0.590393
$259$	−6.55129e15	−1.34859
$260$	0	0
$261$	−1.14505e15	−0.224213
$262$	−3.19838e15	−0.610903
$263$	6.68617e15	1.24585	0.622924	−	0.782283i	$-0.285945\pi$
$263$	6.68617e15	1.24585	0.622924	+	0.782283i	$0.285945\pi$
$264$	−4.10409e15	−0.746091
$265$	5.56952e15	0.987915
$266$	3.89980e15	0.675012
$267$	−1.03848e16	−1.75419
$268$	4.65866e15	0.768041
$269$	9.99864e15	1.60898	0.804491	−	0.593965i	$-0.202438\pi$
$269$	9.99864e15	1.60898	0.804491	+	0.593965i	$0.202438\pi$
$270$	−9.82407e14	−0.154322
$271$	−8.44069e15	−1.29443	−0.647213	−	0.762309i	$-0.724066\pi$
$271$	−8.44069e15	−1.29443	−0.647213	+	0.762309i	$0.724066\pi$
$272$	−4.29175e15	−0.642595
$273$	0	0
$274$	8.24460e14	0.117704
$275$	2.11325e15	0.294638
$276$	−5.90665e15	−0.804327
$277$	−1.41348e16	−1.88006	−0.940028	−	0.341098i	$-0.889201\pi$
$277$	−1.41348e16	−1.88006	−0.940028	+	0.341098i	$0.889201\pi$
$278$	2.53678e14	0.0329604
$279$	3.02452e15	0.383909
$280$	−5.17168e15	−0.641364
$281$	6.65234e15	0.806089	0.403045	−	0.915180i	$-0.367952\pi$
$281$	6.65234e15	0.806089	0.403045	+	0.915180i	$0.367952\pi$
$282$	−1.00109e15	−0.118537
$283$	−1.04456e16	−1.20871	−0.604353	−	0.796716i	$-0.706568\pi$
$283$	−1.04456e16	−1.20871	−0.604353	+	0.796716i	$0.706568\pi$
$284$	1.23574e16	1.39752
$285$	−1.45782e16	−1.61144
$286$	0	0
$287$	−7.70736e15	−0.814092
$288$	5.33109e15	0.550510
$289$	1.56747e15	0.158257
$290$	1.15280e15	0.113807
$291$	−1.08494e15	−0.104737
$292$	9.37207e15	0.884804
$293$	−6.42375e15	−0.593129	−0.296564	−	0.955013i	$-0.595841\pi$
$293$	−6.42375e15	−0.593129	−0.296564	+	0.955013i	$0.595841\pi$
$294$	−1.55444e15	−0.140383
$295$	−4.10382e15	−0.362531
$296$	−9.56707e15	−0.826766
$297$	−5.09523e15	−0.430771
$298$	3.81559e15	0.315614
$299$	0	0
$300$	−4.77450e15	−0.378129
$301$	−1.82791e16	−1.41669
$302$	1.14291e14	0.00866898
$303$	2.82371e16	2.09625
$304$	−1.29790e16	−0.943112
$305$	−1.79414e16	−1.27617
$306$	−3.46418e15	−0.241219
$307$	−1.06113e16	−0.723384	−0.361692	−	0.932298i	$-0.617801\pi$
$307$	−1.06113e16	−0.723384	−0.361692	+	0.932298i	$0.617801\pi$
$308$	−1.23947e16	−0.827291
$309$	−3.26522e16	−2.13394
$310$	−3.04499e15	−0.194866
$311$	−2.79778e16	−1.75336	−0.876680	−	0.481075i	$-0.840247\pi$
$311$	−2.79778e16	−1.75336	−0.876680	+	0.481075i	$0.840247\pi$
$312$	0	0
$313$	8.49575e14	0.0510697	0.0255349	−	0.999674i	$-0.491871\pi$
$313$	8.49575e14	0.0510697	0.0255349	+	0.999674i	$0.491871\pi$
$314$	5.53167e15	0.325697
$315$	9.51360e15	0.548689
$316$	−9.45907e15	−0.534419
$317$	2.39229e16	1.32412	0.662062	−	0.749449i	$-0.269681\pi$
$317$	2.39229e16	1.32412	0.662062	+	0.749449i	$0.269681\pi$
$318$	1.07060e16	0.580563
$319$	5.97898e15	0.317679
$320$	3.89119e15	0.202585
$321$	1.17443e16	0.599161
$322$	6.33268e15	0.316610
$323$	3.46934e16	1.69993
$324$	2.21921e16	1.06575
$325$	0	0
$326$	−4.81944e15	−0.222373
$327$	4.90889e15	0.222036
$328$	−1.12553e16	−0.499089
$329$	−6.54277e15	−0.284438
$330$	−7.60082e15	−0.323981
$331$	1.97999e16	0.827527	0.413763	−	0.910385i	$-0.364214\pi$
$331$	1.97999e16	0.827527	0.413763	+	0.910385i	$0.364214\pi$
$332$	−1.75372e16	−0.718726
$333$	1.75992e16	0.707301
$334$	−1.49415e16	−0.588901
$335$	1.86711e16	0.721737
$336$	2.26562e16	0.858978
$337$	3.87319e16	1.44037	0.720185	−	0.693782i	$-0.244057\pi$
$337$	3.87319e16	1.44037	0.720185	+	0.693782i	$0.244057\pi$
$338$	0	0
$339$	4.94416e15	0.176927
$340$	−2.12604e16	−0.746377
$341$	−1.57928e16	−0.543945
$342$	−1.04763e16	−0.354028
$343$	2.41728e16	0.801522
$344$	−2.66937e16	−0.868517
$345$	−2.36729e16	−0.755835
$346$	−7.10730e15	−0.222695
$347$	3.48412e16	1.07140	0.535699	−	0.844409i	$-0.320048\pi$
$347$	3.48412e16	1.07140	0.535699	+	0.844409i	$0.320048\pi$
$348$	−1.35084e16	−0.407698
$349$	4.99162e15	0.147869	0.0739343	−	0.997263i	$-0.476444\pi$
$349$	4.99162e15	0.147869	0.0739343	+	0.997263i	$0.476444\pi$
$350$	5.11887e15	0.148844
$351$	0	0
$352$	−2.78367e16	−0.779994
$353$	−9.16167e15	−0.252022	−0.126011	−	0.992029i	$-0.540217\pi$
$353$	−9.16167e15	−0.252022	−0.126011	+	0.992029i	$0.540217\pi$
$354$	−7.88854e15	−0.213047
$355$	4.95266e16	1.31327
$356$	−4.58006e16	−1.19247
$357$	−6.05610e16	−1.54828
$358$	−1.14788e16	−0.288175
$359$	−5.08836e16	−1.25448	−0.627240	−	0.778826i	$-0.715816\pi$
$359$	−5.08836e16	−1.25448	−0.627240	+	0.778826i	$0.715816\pi$
$360$	1.38930e16	0.336380
$361$	6.28660e16	1.49492
$362$	2.34463e15	0.0547607
$363$	1.56660e16	0.359390
$364$	0	0
$365$	3.75617e16	0.831460
$366$	−3.44878e16	−0.749960
$367$	−4.51196e15	−0.0963908	−0.0481954	−	0.998838i	$-0.515347\pi$
$367$	−4.51196e15	−0.0963908	−0.0481954	+	0.998838i	$0.515347\pi$
$368$	−2.10760e16	−0.442361
$369$	2.07048e16	0.426972
$370$	−1.77183e16	−0.359014
$371$	6.99701e16	1.39310
$372$	3.56808e16	0.698080
$373$	3.55313e16	0.683130	0.341565	−	0.939858i	$-0.389043\pi$
$373$	3.55313e16	0.683130	0.341565	+	0.939858i	$0.389043\pi$
$374$	1.80885e16	0.341773
$375$	−7.40753e16	−1.37553
$376$	−9.55462e15	−0.174378
$377$	0	0
$378$	−1.23420e16	−0.217615
$379$	7.75963e16	1.34489	0.672444	−	0.740148i	$-0.265245\pi$
$379$	7.75963e16	1.34489	0.672444	+	0.740148i	$0.265245\pi$
$380$	−6.42951e16	−1.09543
$381$	7.22695e16	1.21044
$382$	3.79775e16	0.625337
$383$	3.28839e16	0.532343	0.266172	−	0.963926i	$-0.414241\pi$
$383$	3.28839e16	0.532343	0.266172	+	0.963926i	$0.414241\pi$
$384$	8.06887e16	1.28428
$385$	−4.96761e16	−0.777414
$386$	4.35203e16	0.669691
$387$	4.91045e16	0.743019
$388$	−4.78495e15	−0.0711986
$389$	4.57248e16	0.669082	0.334541	−	0.942381i	$-0.391419\pi$
$389$	4.57248e16	0.669082	0.334541	+	0.942381i	$0.391419\pi$
$390$	0	0
$391$	5.63370e16	0.797342
$392$	−1.48358e16	−0.206515
$393$	1.50206e17	2.05654
$394$	−4.65139e16	−0.626408
$395$	−3.79103e16	−0.502200
$396$	3.32968e16	0.433895
$397$	9.69224e16	1.24247	0.621235	−	0.783624i	$-0.286631\pi$
$397$	9.69224e16	1.24247	0.621235	+	0.783624i	$0.286631\pi$
$398$	2.91912e16	0.368139
$399$	−1.83147e17	−2.27235
$400$	−1.70362e16	−0.207962
$401$	1.06253e16	0.127615	0.0638076	−	0.997962i	$-0.479676\pi$
$401$	1.06253e16	0.127615	0.0638076	+	0.997962i	$0.479676\pi$
$402$	3.58904e16	0.424140
$403$	0	0
$404$	1.24536e17	1.42500
$405$	8.89422e16	1.00150
$406$	1.44827e16	0.160484
$407$	−9.18956e16	−1.00215
$408$	−8.84393e16	−0.949192
$409$	−2.85315e16	−0.301386	−0.150693	−	0.988581i	$-0.548151\pi$
$409$	−2.85315e16	−0.301386	−0.150693	+	0.988581i	$0.548151\pi$
$410$	−2.08450e16	−0.216724
$411$	−3.87193e16	−0.396237
$412$	−1.44008e17	−1.45062
$413$	−5.15565e16	−0.511220
$414$	−1.70119e16	−0.166055
$415$	−7.02862e16	−0.675395
$416$	0	0
$417$	−1.19135e16	−0.110957
$418$	5.47028e16	0.501607
$419$	7.81789e16	0.705827	0.352914	−	0.935656i	$-0.385191\pi$
$419$	7.81789e16	0.705827	0.352914	+	0.935656i	$0.385191\pi$
$420$	1.12234e17	0.997707
$421$	6.34549e15	0.0555433	0.0277716	−	0.999614i	$-0.491159\pi$
$421$	6.34549e15	0.0555433	0.0277716	+	0.999614i	$0.491159\pi$
$422$	2.14052e16	0.184496
$423$	1.75763e16	0.149181
$424$	1.02180e17	0.854057
$425$	4.55386e16	0.374845
$426$	9.52020e16	0.771763
$427$	−2.25399e17	−1.79958
$428$	5.17963e16	0.407300
$429$	0	0
$430$	−4.94369e16	−0.377143
$431$	1.34700e16	0.101220	0.0506100	−	0.998718i	$-0.483883\pi$
$431$	1.34700e16	0.101220	0.0506100	+	0.998718i	$0.483883\pi$
$432$	4.10758e16	0.304047
$433$	9.56660e15	0.0697568	0.0348784	−	0.999392i	$-0.488896\pi$
$433$	9.56660e15	0.0697568	0.0348784	+	0.999392i	$0.488896\pi$
$434$	−3.82543e16	−0.274788
$435$	−5.41393e16	−0.383118
$436$	2.16499e16	0.150936
$437$	1.70373e17	1.17023
$438$	7.22026e16	0.488620
$439$	2.06703e17	1.37824	0.689122	−	0.724645i	$-0.257996\pi$
$439$	2.06703e17	1.37824	0.689122	+	0.724645i	$0.257996\pi$
$440$	−7.25436e16	−0.476603
$441$	2.72913e16	0.176675
$442$	0	0
$443$	−1.91066e16	−0.120104	−0.0600522	−	0.998195i	$-0.519127\pi$
$443$	−1.91066e16	−0.120104	−0.0600522	+	0.998195i	$0.519127\pi$
$444$	2.07621e17	1.28612
$445$	−1.83561e17	−1.12058
$446$	1.42176e16	0.0855359
$447$	−1.79193e17	−1.06248
$448$	4.88851e16	0.285673
$449$	2.36332e17	1.36120	0.680600	−	0.732655i	$-0.261719\pi$
$449$	2.36332e17	1.36120	0.680600	+	0.732655i	$0.261719\pi$
$450$	−1.37512e16	−0.0780652
$451$	−1.08112e17	−0.604959
$452$	2.18055e16	0.120272
$453$	−5.36748e15	−0.0291832
$454$	1.30388e16	0.0698832
$455$	0	0
$456$	−2.67456e17	−1.39309
$457$	1.64178e17	0.843064	0.421532	−	0.906814i	$-0.361493\pi$
$457$	1.64178e17	0.843064	0.421532	+	0.906814i	$0.361493\pi$
$458$	3.07233e15	0.0155540
$459$	−1.09797e17	−0.548036
$460$	−1.04406e17	−0.513804
$461$	2.38359e17	1.15658	0.578291	−	0.815831i	$-0.303720\pi$
$461$	2.38359e17	1.15658	0.578291	+	0.815831i	$0.303720\pi$
$462$	−9.54894e16	−0.456859
$463$	4.47197e16	0.210971	0.105485	−	0.994421i	$-0.466360\pi$
$463$	4.47197e16	0.210971	0.105485	+	0.994421i	$0.466360\pi$
$464$	−4.82003e16	−0.224224
$465$	1.43003e17	0.655994
$466$	−1.07357e17	−0.485648
$467$	2.83964e17	1.26678	0.633392	−	0.773831i	$-0.281662\pi$
$467$	2.83964e17	1.26678	0.633392	+	0.773831i	$0.281662\pi$
$468$	0	0
$469$	2.34566e17	1.01775
$470$	−1.76953e16	−0.0757218
$471$	−2.59785e17	−1.09642
$472$	−7.52896e16	−0.313409
$473$	−2.56403e17	−1.05275
$474$	−7.28728e16	−0.295125
$475$	1.37717e17	0.550145
$476$	−2.67095e17	−1.05250
$477$	−1.87965e17	−0.730648
$478$	5.43539e16	0.208425
$479$	4.29868e16	0.162613	0.0813064	−	0.996689i	$-0.474091\pi$
$479$	4.29868e16	0.162613	0.0813064	+	0.996689i	$0.474091\pi$
$480$	2.52060e17	0.940668
$481$	0	0
$482$	1.08284e17	0.393331
$483$	−2.97403e17	−1.06583
$484$	6.90926e16	0.244307
$485$	−1.91773e16	−0.0669061
$486$	1.15437e17	0.397383
$487$	−3.73286e17	−1.26795	−0.633977	−	0.773352i	$-0.718579\pi$
$487$	−3.73286e17	−1.26795	−0.633977	+	0.773352i	$0.718579\pi$
$488$	−3.29157e17	−1.10325
$489$	2.26337e17	0.748595
$490$	−2.74761e16	−0.0896769
$491$	−3.06371e17	−0.986776	−0.493388	−	0.869809i	$-0.664242\pi$
$491$	−3.06371e17	−0.986776	−0.493388	+	0.869809i	$0.664242\pi$
$492$	2.44258e17	0.776384
$493$	1.28841e17	0.404157
$494$	0	0
$495$	1.33448e17	0.407736
$496$	1.27315e17	0.383928
$497$	6.22204e17	1.85189
$498$	−1.35107e17	−0.396906
$499$	−2.26621e17	−0.657122	−0.328561	−	0.944483i	$-0.606564\pi$
$499$	−2.26621e17	−0.657122	−0.328561	+	0.944483i	$0.606564\pi$
$500$	−3.26698e17	−0.935064
$501$	7.01701e17	1.98247
$502$	−2.30191e17	−0.641969
$503$	2.43483e17	0.670310	0.335155	−	0.942163i	$-0.391211\pi$
$503$	2.43483e17	0.670310	0.335155	+	0.942163i	$0.391211\pi$
$504$	1.74539e17	0.474344
$505$	4.99117e17	1.33909
$506$	8.88291e16	0.235276
$507$	0	0
$508$	3.18733e17	0.822836
$509$	−2.46104e17	−0.627267	−0.313634	−	0.949544i	$-0.601546\pi$
$509$	−2.46104e17	−0.627267	−0.313634	+	0.949544i	$0.601546\pi$
$510$	−1.63790e17	−0.412176
$511$	4.71889e17	1.17248
$512$	3.94265e17	0.967239
$513$	−3.32046e17	−0.804332
$514$	1.87188e17	0.447731
$515$	−5.77159e17	−1.36316
$516$	5.79295e17	1.35107
$517$	−9.17760e16	−0.211369
$518$	−2.22596e17	−0.506260
$519$	3.33782e17	0.749678
$520$	0	0
$521$	−6.84199e16	−0.149878	−0.0749389	−	0.997188i	$-0.523876\pi$
$521$	−6.84199e16	−0.149878	−0.0749389	+	0.997188i	$0.523876\pi$
$522$	−3.89059e16	−0.0841699
$523$	−7.79936e17	−1.66647	−0.833236	−	0.552917i	$-0.813515\pi$
$523$	−7.79936e17	−1.66647	−0.833236	+	0.552917i	$0.813515\pi$
$524$	6.62462e17	1.39800
$525$	−2.40398e17	−0.501068
$526$	2.27179e17	0.467692
$527$	−3.40319e17	−0.692018
$528$	3.17801e17	0.638314
$529$	−2.27377e17	−0.451112
$530$	1.89238e17	0.370864
$531$	1.38500e17	0.268123
$532$	−8.07742e17	−1.54471
$533$	0	0
$534$	−3.52849e17	−0.658523
$535$	2.07591e17	0.382744
$536$	3.42544e17	0.623944
$537$	5.39081e17	0.970111
$538$	3.39728e17	0.604013
$539$	−1.42504e17	−0.250323
$540$	2.03480e17	0.353153
$541$	2.29126e17	0.392910	0.196455	−	0.980513i	$-0.437057\pi$
$541$	2.29126e17	0.392910	0.196455	+	0.980513i	$0.437057\pi$
$542$	−2.86793e17	−0.485929
$543$	−1.10111e17	−0.184346
$544$	−5.99855e17	−0.992325
$545$	8.67692e16	0.141837
$546$	0	0
$547$	2.50993e16	0.0400631	0.0200316	−	0.999799i	$-0.493623\pi$
$547$	2.50993e16	0.0400631	0.0200316	+	0.999799i	$0.493623\pi$
$548$	−1.70765e17	−0.269356
$549$	6.05504e17	0.943836
$550$	7.18028e16	0.110607
$551$	3.89639e17	0.593166
$552$	−4.34308e17	−0.653422
$553$	−4.76269e17	−0.708172
$554$	−4.80263e17	−0.705774
$555$	8.32109e17	1.20858
$556$	−5.25428e16	−0.0754271
$557$	9.34157e17	1.32544	0.662721	−	0.748866i	$-0.269401\pi$
$557$	9.34157e17	1.32544	0.662721	+	0.748866i	$0.269401\pi$
$558$	1.02765e17	0.144120
$559$	0	0
$560$	4.00469e17	0.548715
$561$	−8.49495e17	−1.15054
$562$	2.26029e17	0.302607
$563$	−1.27798e18	−1.69130	−0.845650	−	0.533737i	$-0.820787\pi$
$563$	−1.27798e18	−1.69130	−0.845650	+	0.533737i	$0.820787\pi$
$564$	2.07351e17	0.271263
$565$	8.73926e16	0.113021
$566$	−3.54914e17	−0.453749
$567$	1.11738e18	1.41225
$568$	9.08625e17	1.13533
$569$	−2.67064e17	−0.329903	−0.164951	−	0.986302i	$-0.552747\pi$
$569$	−2.67064e17	−0.329903	−0.164951	+	0.986302i	$0.552747\pi$
$570$	−4.95331e17	−0.604935
$571$	−6.71054e17	−0.810257	−0.405129	−	0.914260i	$-0.632773\pi$
$571$	−6.71054e17	−0.810257	−0.405129	+	0.914260i	$0.632773\pi$
$572$	0	0
$573$	−1.78355e18	−2.10513
$574$	−2.61876e17	−0.305611
$575$	2.23631e17	0.258042
$576$	−1.31323e17	−0.149829
$577$	1.55405e18	1.75316	0.876579	−	0.481258i	$-0.159820\pi$
$577$	1.55405e18	1.75316	0.876579	+	0.481258i	$0.159820\pi$
$578$	5.32585e16	0.0594098
$579$	−2.04385e18	−2.25444
$580$	−2.38773e17	−0.260438
$581$	−8.83009e17	−0.952401
$582$	−3.68634e16	−0.0393184
$583$	9.81477e17	1.03522
$584$	6.89115e17	0.718800
$585$	0	0
$586$	−2.18262e17	−0.222661
$587$	1.40353e18	1.41603	0.708016	−	0.706197i	$-0.249591\pi$
$587$	1.40353e18	1.41603	0.708016	+	0.706197i	$0.249591\pi$
$588$	3.21961e17	0.321256
$589$	−1.02918e18	−1.01565
$590$	−1.39437e17	−0.136094
$591$	2.18444e18	2.10874
$592$	7.40827e17	0.707336
$593$	−1.73606e18	−1.63949	−0.819744	−	0.572731i	$-0.805884\pi$
$593$	−1.73606e18	−1.63949	−0.819744	+	0.572731i	$0.805884\pi$
$594$	−1.73123e17	−0.161712
$595$	−1.07047e18	−0.989043
$596$	−7.90301e17	−0.722257
$597$	−1.37091e18	−1.23930
$598$	0	0
$599$	8.77681e16	0.0776358	0.0388179	−	0.999246i	$-0.487641\pi$
$599$	8.77681e16	0.0776358	0.0388179	+	0.999246i	$0.487641\pi$
$600$	−3.51062e17	−0.307185
$601$	−1.45598e18	−1.26029	−0.630145	−	0.776477i	$-0.717005\pi$
$601$	−1.45598e18	−1.26029	−0.630145	+	0.776477i	$0.717005\pi$
$602$	−6.21078e17	−0.531825
$603$	−6.30130e17	−0.533786
$604$	−2.36725e16	−0.0198383
$605$	2.76911e17	0.229578
$606$	9.59424e17	0.786935
$607$	−1.40576e18	−1.14073	−0.570367	−	0.821390i	$-0.693199\pi$
$607$	−1.40576e18	−1.14073	−0.570367	+	0.821390i	$0.693199\pi$
$608$	−1.81407e18	−1.45640
$609$	−6.80155e17	−0.540251
$610$	−6.09603e17	−0.479075
$611$	0	0
$612$	7.17515e17	0.552010
$613$	−2.71406e17	−0.206598	−0.103299	−	0.994650i	$-0.532940\pi$
$613$	−2.71406e17	−0.206598	−0.103299	+	0.994650i	$0.532940\pi$
$614$	−3.60544e17	−0.271559
$615$	9.78946e17	0.729576
$616$	−9.11368e17	−0.672077
$617$	2.34922e18	1.71424	0.857118	−	0.515121i	$-0.172253\pi$
$617$	2.34922e18	1.71424	0.857118	+	0.515121i	$0.172253\pi$
$618$	−1.10944e18	−0.801084
$619$	1.31985e18	0.943054	0.471527	−	0.881852i	$-0.343703\pi$
$619$	1.31985e18	0.943054	0.471527	+	0.881852i	$0.343703\pi$
$620$	6.30691e17	0.445934
$621$	−5.39193e17	−0.377267
$622$	−9.50613e17	−0.658212
$623$	−2.30609e18	−1.58017
$624$	0	0
$625$	−7.90348e17	−0.530393
$626$	2.88664e16	0.0191716
$627$	−2.56902e18	−1.68861
$628$	−1.14574e18	−0.745330
$629$	−1.98026e18	−1.27495
$630$	3.23247e17	0.205978
$631$	−4.99011e17	−0.314716	−0.157358	−	0.987542i	$-0.550298\pi$
$631$	−4.99011e17	−0.314716	−0.157358	+	0.987542i	$0.550298\pi$
$632$	−6.95512e17	−0.434154
$633$	−1.00526e18	−0.621087
$634$	8.12838e17	0.497077
$635$	1.27743e18	0.773229
$636$	−2.21746e18	−1.32857
$637$	0	0
$638$	2.03150e17	0.119257
$639$	−1.67147e18	−0.971275
$640$	1.42625e18	0.820399
$641$	−1.66121e18	−0.945905	−0.472953	−	0.881088i	$-0.656812\pi$
$641$	−1.66121e18	−0.945905	−0.472953	+	0.881088i	$0.656812\pi$
$642$	3.99040e17	0.224926
$643$	−2.39626e17	−0.133710	−0.0668548	−	0.997763i	$-0.521296\pi$
$643$	−2.39626e17	−0.133710	−0.0668548	+	0.997763i	$0.521296\pi$
$644$	−1.31165e18	−0.724536
$645$	2.32172e18	1.26961
$646$	1.17879e18	0.638155
$647$	−6.81737e17	−0.365375	−0.182688	−	0.983171i	$-0.558480\pi$
$647$	−6.81737e17	−0.365375	−0.182688	+	0.983171i	$0.558480\pi$
$648$	1.63175e18	0.865799
$649$	−7.23187e17	−0.379892
$650$	0	0
$651$	1.79655e18	0.925044
$652$	9.98223e17	0.508883
$653$	3.90793e17	0.197247	0.0986235	−	0.995125i	$-0.468556\pi$
$653$	3.90793e17	0.197247	0.0986235	+	0.995125i	$0.468556\pi$
$654$	1.66791e17	0.0833524
$655$	2.65504e18	1.31372
$656$	8.71556e17	0.426993
$657$	−1.26767e18	−0.614936
$658$	−2.22306e17	−0.106778
$659$	−8.58969e17	−0.408528	−0.204264	−	0.978916i	$-0.565480\pi$
$659$	−8.58969e17	−0.408528	−0.204264	+	0.978916i	$0.565480\pi$
$660$	1.57431e18	0.741405
$661$	−2.46793e17	−0.115086	−0.0575431	−	0.998343i	$-0.518327\pi$
$661$	−2.46793e17	−0.115086	−0.0575431	+	0.998343i	$0.518327\pi$
$662$	6.72750e17	0.310654
$663$	0	0
$664$	−1.28949e18	−0.583881
$665$	−3.23729e18	−1.45158
$666$	5.97974e17	0.265522
$667$	6.32715e17	0.278221
$668$	3.09475e18	1.34765
$669$	−6.67702e17	−0.287947
$670$	6.34396e17	0.270941
$671$	−3.16169e18	−1.33728
$672$	3.16664e18	1.32647
$673$	−3.06116e18	−1.26995	−0.634976	−	0.772532i	$-0.718990\pi$
$673$	−3.06116e18	−1.26995	−0.634976	+	0.772532i	$0.718990\pi$
$674$	1.31601e18	0.540716
$675$	−4.35843e17	−0.177360
$676$	0	0
$677$	1.84266e18	0.735561	0.367780	−	0.929913i	$-0.380118\pi$
$677$	1.84266e18	0.735561	0.367780	+	0.929913i	$0.380118\pi$
$678$	1.67990e17	0.0664186
$679$	−2.40925e17	−0.0943470
$680$	−1.56325e18	−0.606344
$681$	−6.12342e17	−0.235254
$682$	−5.36597e17	−0.204197
$683$	−2.50777e17	−0.0945265	−0.0472633	−	0.998882i	$-0.515050\pi$
$683$	−2.50777e17	−0.0945265	−0.0472633	+	0.998882i	$0.515050\pi$
$684$	2.16989e18	0.810164
$685$	−6.84399e17	−0.253117
$686$	8.21329e17	0.300892
$687$	−1.44287e17	−0.0523609
$688$	2.06702e18	0.743055
$689$	0	0
$690$	−8.04343e17	−0.283741
$691$	−1.91505e15	−0.000669227 0	−0.000334614	−	1.00000i	$-0.500107\pi$
$691$	−1.91505e15	−0.000669227 0	−0.000334614		1.00000i	$0.500107\pi$
$692$	1.47209e18	0.509619
$693$	1.67651e18	0.574964
$694$	1.18381e18	0.402204
$695$	−2.10583e17	−0.0708797
$696$	−9.93253e17	−0.331207
$697$	−2.32971e18	−0.769641
$698$	1.69602e17	0.0555100
$699$	5.04183e18	1.63488
$700$	−1.06024e18	−0.340618
$701$	−4.81575e17	−0.153284	−0.0766421	−	0.997059i	$-0.524420\pi$
$701$	−4.81575e17	−0.153284	−0.0766421	+	0.997059i	$0.524420\pi$
$702$	0	0
$703$	−5.98865e18	−1.87120
$704$	6.85716e17	0.212286
$705$	8.31026e17	0.254909
$706$	−3.11290e17	−0.0946093
$707$	6.27043e18	1.88830
$708$	1.63391e18	0.487541
$709$	8.72197e17	0.257878	0.128939	−	0.991653i	$-0.458843\pi$
$709$	8.72197e17	0.257878	0.128939	+	0.991653i	$0.458843\pi$
$710$	1.68278e18	0.493002
$711$	1.27943e18	0.371420
$712$	−3.36766e18	−0.968741
$713$	−1.67124e18	−0.476384
$714$	−2.05771e18	−0.581226
$715$	0	0
$716$	2.37754e18	0.659466
$717$	−2.55263e18	−0.701639
$718$	−1.72889e18	−0.470933
$719$	6.02638e18	1.62674	0.813371	−	0.581745i	$-0.197630\pi$
$719$	6.02638e18	1.62674	0.813371	+	0.581745i	$0.197630\pi$
$720$	−1.07581e18	−0.287788
$721$	−7.25087e18	−1.92225
$722$	2.13602e18	0.561195
$723$	−5.08536e18	−1.32411
$724$	−4.85630e17	−0.125315
$725$	5.11439e17	0.130797
$726$	5.32291e17	0.134915
$727$	1.62464e18	0.408116	0.204058	−	0.978959i	$-0.434587\pi$
$727$	1.62464e18	0.408116	0.204058	+	0.978959i	$0.434587\pi$
$728$	0	0
$729$	−3.93775e17	−0.0971670
$730$	1.27625e18	0.312131
$731$	−5.52525e18	−1.33933
$732$	7.14324e18	1.71622
$733$	−7.33094e16	−0.0174576	−0.00872878	−	0.999962i	$-0.502778\pi$
$733$	−7.33094e16	−0.0174576	−0.00872878	+	0.999962i	$0.502778\pi$
$734$	−1.53305e17	−0.0361852
$735$	1.29037e18	0.301888
$736$	−2.94577e18	−0.683114
$737$	3.29028e18	0.756299
$738$	7.03495e17	0.160286
$739$	3.97098e18	0.896828	0.448414	−	0.893826i	$-0.351989\pi$
$739$	3.97098e18	0.896828	0.448414	+	0.893826i	$0.351989\pi$
$740$	3.66989e18	0.821574
$741$	0	0
$742$	2.37740e18	0.522971
$743$	5.29093e18	1.15373	0.576866	−	0.816839i	$-0.304275\pi$
$743$	5.29093e18	1.15373	0.576866	+	0.816839i	$0.304275\pi$
$744$	2.62356e18	0.567109
$745$	−3.16739e18	−0.678713
$746$	1.20726e18	0.256448
$747$	2.37208e18	0.499512
$748$	−3.74657e18	−0.782119
$749$	2.60797e18	0.539724
$750$	−2.51689e18	−0.516375
$751$	−1.90639e17	−0.0387750	−0.0193875	−	0.999812i	$-0.506172\pi$
$751$	−1.90639e17	−0.0387750	−0.0193875	+	0.999812i	$0.506172\pi$
$752$	7.39863e17	0.149188
$753$	1.08105e19	2.16112
$754$	0	0
$755$	−9.48753e16	−0.0186422
$756$	2.55633e18	0.497995
$757$	9.42837e18	1.82101	0.910507	−	0.413493i	$-0.135692\pi$
$757$	9.42837e18	1.82101	0.910507	+	0.413493i	$0.135692\pi$
$758$	2.63652e18	0.504872
$759$	−4.17170e18	−0.792030
$760$	−4.72753e18	−0.889909
$761$	2.31758e18	0.432548	0.216274	−	0.976333i	$-0.430610\pi$
$761$	2.31758e18	0.432548	0.216274	+	0.976333i	$0.430610\pi$
$762$	2.45553e18	0.454399
$763$	1.09008e18	0.200010
$764$	−7.86605e18	−1.43103
$765$	2.87568e18	0.518730
$766$	1.11731e18	0.199842
$767$	0	0
$768$	9.38203e17	0.164987
$769$	−4.69894e18	−0.819368	−0.409684	−	0.912228i	$-0.634361\pi$
$769$	−4.69894e18	−0.819368	−0.409684	+	0.912228i	$0.634361\pi$
$770$	−1.68786e18	−0.291842
$771$	−8.79094e18	−1.50724
$772$	−9.01410e18	−1.53253
$773$	2.06429e16	0.00348020	0.00174010	−	0.999998i	$-0.499446\pi$
$773$	2.06429e16	0.00348020	0.00174010	+	0.999998i	$0.499446\pi$
$774$	1.66844e18	0.278930
$775$	−1.35091e18	−0.223957
$776$	−3.51831e17	−0.0578406
$777$	1.04538e19	1.70427
$778$	1.55361e18	0.251174
$779$	−7.04544e18	−1.12957
$780$	0	0
$781$	8.72771e18	1.37616
$782$	1.91418e18	0.299323
$783$	−1.23312e18	−0.191229
$784$	1.14881e18	0.176683
$785$	−4.59194e18	−0.700395
$786$	5.10362e18	0.772026
$787$	7.25388e18	1.08827	0.544133	−	0.838999i	$-0.316859\pi$
$787$	7.25388e18	1.08827	0.544133	+	0.838999i	$0.316859\pi$
$788$	9.63415e18	1.43348
$789$	−1.06690e19	−1.57443
$790$	−1.28809e18	−0.188526
$791$	1.09792e18	0.159376
$792$	2.44827e18	0.352489
$793$	0	0
$794$	3.29317e18	0.466424
$795$	−8.88722e18	−1.24847
$796$	−6.04620e18	−0.842457
$797$	−7.12000e18	−0.984014	−0.492007	−	0.870591i	$-0.663737\pi$
$797$	−7.12000e18	−0.984014	−0.492007	+	0.870591i	$0.663737\pi$
$798$	−6.22286e18	−0.853043
$799$	−1.97768e18	−0.268908
$800$	−2.38114e18	−0.321144
$801$	6.19499e18	0.828761
$802$	3.61020e17	0.0479069
$803$	6.61923e18	0.871277
$804$	−7.43376e18	−0.970609
$805$	−5.25688e18	−0.680855
$806$	0	0
$807$	−1.59547e19	−2.03334
$808$	9.15692e18	1.15765
$809$	−2.66124e18	−0.333748	−0.166874	−	0.985978i	$-0.553367\pi$
$809$	−2.66124e18	−0.333748	−0.166874	+	0.985978i	$0.553367\pi$
$810$	3.02202e18	0.375963
$811$	−1.00968e19	−1.24609	−0.623044	−	0.782187i	$-0.714104\pi$
$811$	−1.00968e19	−1.24609	−0.623044	+	0.782187i	$0.714104\pi$
$812$	−2.99972e18	−0.367254
$813$	1.34687e19	1.63583
$814$	−3.12237e18	−0.376206
$815$	4.00071e18	0.478203
$816$	6.84830e18	0.812076
$817$	−1.67093e19	−1.96569
$818$	−9.69426e17	−0.113141
$819$	0	0
$820$	4.31749e18	0.495954
$821$	9.92737e18	1.13137	0.565684	−	0.824622i	$-0.308612\pi$
$821$	9.92737e18	1.13137	0.565684	+	0.824622i	$0.308612\pi$
$822$	−1.31558e18	−0.148748
$823$	−4.52749e18	−0.507877	−0.253938	−	0.967220i	$-0.581726\pi$
$823$	−4.52749e18	−0.507877	−0.253938	+	0.967220i	$0.581726\pi$
$824$	−1.05887e19	−1.17846
$825$	−3.37209e18	−0.372348
$826$	−1.75175e18	−0.191912
$827$	−1.50983e19	−1.64113	−0.820564	−	0.571555i	$-0.806340\pi$
$827$	−1.50983e19	−1.64113	−0.820564	+	0.571555i	$0.806340\pi$
$828$	3.52357e18	0.380002
$829$	−1.32631e19	−1.41919	−0.709597	−	0.704608i	$-0.751123\pi$
$829$	−1.32631e19	−1.41919	−0.709597	+	0.704608i	$0.751123\pi$
$830$	−2.38814e18	−0.253544
$831$	2.25547e19	2.37591
$832$	0	0
$833$	−3.07083e18	−0.318466
$834$	−4.04791e17	−0.0416535
$835$	1.24032e19	1.26640
$836$	−1.13303e19	−1.14789
$837$	3.25714e18	0.327432
$838$	2.65632e18	0.264968
$839$	7.44149e18	0.736558	0.368279	−	0.929715i	$-0.379947\pi$
$839$	7.44149e18	0.736558	0.368279	+	0.929715i	$0.379947\pi$
$840$	8.25239e18	0.810521
$841$	−8.81362e18	−0.858975
$842$	2.15603e17	0.0208510
$843$	−1.06151e19	−1.01869
$844$	−4.43352e18	−0.422205
$845$	0	0
$846$	5.97196e17	0.0560027
$847$	3.47885e18	0.323738
$848$	−7.91229e18	−0.730684
$849$	1.66679e19	1.52750
$850$	1.54728e18	0.140717
$851$	−9.72467e18	−0.877673
$852$	−1.97186e19	−1.76612
$853$	−2.21083e18	−0.196511	−0.0982554	−	0.995161i	$-0.531326\pi$
$853$	−2.21083e18	−0.196511	−0.0982554	+	0.995161i	$0.531326\pi$
$854$	−7.65847e18	−0.675563
$855$	8.69655e18	0.761320
$856$	3.80851e18	0.330884
$857$	−4.25774e18	−0.367117	−0.183558	−	0.983009i	$-0.558762\pi$
$857$	−4.25774e18	−0.367117	−0.183558	+	0.983009i	$0.558762\pi$
$858$	0	0
$859$	5.49014e18	0.466260	0.233130	−	0.972446i	$-0.425103\pi$
$859$	5.49014e18	0.466260	0.233130	+	0.972446i	$0.425103\pi$
$860$	1.02396e19	0.863062
$861$	1.22985e19	1.02881
$862$	4.57676e17	0.0379980
$863$	1.00892e19	0.831352	0.415676	−	0.909513i	$-0.363545\pi$
$863$	1.00892e19	0.831352	0.415676	+	0.909513i	$0.363545\pi$
$864$	5.74113e18	0.469524
$865$	5.89990e18	0.478895
$866$	3.25048e17	0.0261868
$867$	−2.50119e18	−0.199997
$868$	7.92339e18	0.628830
$869$	−6.68067e18	−0.526249
$870$	−1.83951e18	−0.143823
$871$	0	0
$872$	1.59189e18	0.122618
$873$	6.47212e17	0.0494828
$874$	5.78882e18	0.439305
$875$	−1.64494e19	−1.23908
$876$	−1.49549e19	−1.11817
$877$	1.32246e18	0.0981489	0.0490745	−	0.998795i	$-0.484373\pi$
$877$	1.32246e18	0.0981489	0.0490745	+	0.998795i	$0.484373\pi$
$878$	7.02321e18	0.517394
$879$	1.02503e19	0.749564
$880$	5.61742e18	0.407755
$881$	2.18433e19	1.57389	0.786947	−	0.617021i	$-0.211661\pi$
$881$	2.18433e19	1.57389	0.786947	+	0.617021i	$0.211661\pi$
$882$	9.27289e17	0.0663238
$883$	1.53200e19	1.08772	0.543858	−	0.839177i	$-0.316963\pi$
$883$	1.53200e19	1.08772	0.543858	+	0.839177i	$0.316963\pi$
$884$	0	0
$885$	6.54842e18	0.458147
$886$	−6.49193e17	−0.0450873
$887$	6.60099e18	0.455098	0.227549	−	0.973767i	$-0.426929\pi$
$887$	6.60099e18	0.455098	0.227549	+	0.973767i	$0.426929\pi$
$888$	1.52661e19	1.04482
$889$	1.60484e19	1.09036
$890$	−6.23693e18	−0.420665
$891$	1.56736e19	1.04946
$892$	−2.94480e18	−0.195742
$893$	−5.98086e18	−0.394665
$894$	−6.08850e18	−0.398856
$895$	9.52876e18	0.619707
$896$	1.79180e19	1.15688
$897$	0	0
$898$	8.02996e18	0.510996
$899$	−3.82209e18	−0.241470
$900$	2.84819e18	0.178646
$901$	2.11499e19	1.31703
$902$	−3.67336e18	−0.227102
$903$	2.91678e19	1.79033
$904$	1.60332e18	0.0977072
$905$	−1.94632e18	−0.117760
$906$	−1.82373e17	−0.0109554
$907$	−1.69955e19	−1.01365	−0.506824	−	0.862050i	$-0.669181\pi$
$907$	−1.69955e19	−1.01365	−0.506824	+	0.862050i	$0.669181\pi$
$908$	−2.70064e18	−0.159922
$909$	−1.68447e19	−0.990370
$910$	0	0
$911$	−1.07698e19	−0.624223	−0.312112	−	0.950045i	$-0.601036\pi$
$911$	−1.07698e19	−0.624223	−0.312112	+	0.950045i	$0.601036\pi$
$912$	2.07104e19	1.19185
$913$	−1.23860e19	−0.707738
$914$	5.57835e18	0.316487
$915$	2.86289e19	1.61275
$916$	−6.36354e17	−0.0355941
$917$	3.33553e19	1.85253
$918$	−3.73063e18	−0.205733
$919$	2.38881e18	0.130807	0.0654035	−	0.997859i	$-0.479167\pi$
$919$	2.38881e18	0.130807	0.0654035	+	0.997859i	$0.479167\pi$
$920$	−7.67679e18	−0.417406
$921$	1.69323e19	0.914174
$922$	8.09883e18	0.434181
$923$	0	0
$924$	1.97782e19	1.04549
$925$	−7.86070e18	−0.412610
$926$	1.51946e18	0.0791985
$927$	1.94785e19	1.00818
$928$	−6.73692e18	−0.346258
$929$	−2.62065e19	−1.33754	−0.668771	−	0.743468i	$-0.733180\pi$
$929$	−2.62065e19	−1.33754	−0.668771	+	0.743468i	$0.733180\pi$
$930$	4.85886e18	0.246261
$931$	−9.28671e18	−0.467400
$932$	2.22362e19	1.11137
$933$	4.46438e19	2.21580
$934$	9.64834e18	0.475552
$935$	−1.50156e19	−0.734966
$936$	0	0
$937$	−1.48285e19	−0.715799	−0.357899	−	0.933760i	$-0.616507\pi$
$937$	−1.48285e19	−0.715799	−0.357899	+	0.933760i	$0.616507\pi$
$938$	7.96994e18	0.382064
$939$	−1.35566e18	−0.0645392
$940$	3.66511e18	0.173283
$941$	1.63127e19	0.765938	0.382969	−	0.923761i	$-0.374902\pi$
$941$	1.63127e19	0.765938	0.382969	+	0.923761i	$0.374902\pi$
$942$	−8.82681e18	−0.411598
$943$	−1.14407e19	−0.529819
$944$	5.83006e18	0.268136
$945$	1.02453e19	0.467971
$946$	−8.71192e18	−0.395204
$947$	1.32279e19	0.595958	0.297979	−	0.954572i	$-0.403687\pi$
$947$	1.32279e19	0.595958	0.297979	+	0.954572i	$0.403687\pi$
$948$	1.50937e19	0.675370
$949$	0	0
$950$	4.67925e18	0.206525
$951$	−3.81735e19	−1.67336
$952$	−1.96391e19	−0.855031
$953$	−1.23625e19	−0.534566	−0.267283	−	0.963618i	$-0.586126\pi$
$953$	−1.23625e19	−0.534566	−0.267283	+	0.963618i	$0.586126\pi$
$954$	−6.38657e18	−0.274286
$955$	−3.15258e19	−1.34476
$956$	−1.12580e19	−0.476963
$957$	−9.54059e18	−0.401465
$958$	1.46058e18	0.0610449
$959$	−8.59813e18	−0.356930
$960$	−6.20912e18	−0.256016
$961$	−1.43220e19	−0.586544
$962$	0	0
$963$	−7.00597e18	−0.283072
$964$	−2.24282e19	−0.900107
$965$	−3.61270e19	−1.44014
$966$	−1.01050e19	−0.400115
$967$	2.63801e18	0.103754	0.0518770	−	0.998653i	$-0.483480\pi$
$967$	2.63801e18	0.103754	0.0518770	+	0.998653i	$0.483480\pi$
$968$	5.08028e18	0.198471
$969$	−5.53599e19	−2.14828
$970$	−6.51594e17	−0.0251166
$971$	−3.26457e19	−1.24997	−0.624986	−	0.780636i	$-0.714895\pi$
$971$	−3.26457e19	−1.24997	−0.624986	+	0.780636i	$0.714895\pi$
$972$	−2.39098e19	−0.909379
$973$	−2.64556e18	−0.0999503
$974$	−1.26833e19	−0.475991
$975$	0	0
$976$	2.54883e19	0.943882
$977$	−7.67549e18	−0.282352	−0.141176	−	0.989984i	$-0.545088\pi$
$977$	−7.67549e18	−0.282352	−0.141176	+	0.989984i	$0.545088\pi$
$978$	7.69033e18	0.281023
$979$	−3.23477e19	−1.17424
$980$	5.69096e18	0.205218
$981$	−2.92837e18	−0.104900
$982$	−1.04097e19	−0.370436
$983$	−5.57748e18	−0.197170	−0.0985848	−	0.995129i	$-0.531432\pi$
$983$	−5.57748e18	−0.197170	−0.0985848	+	0.995129i	$0.531432\pi$
$984$	1.79600e19	0.630721
$985$	3.86121e19	1.34706
$986$	4.37770e18	0.151721
$987$	1.04402e19	0.359458
$988$	0	0
$989$	−2.71334e19	−0.921994
$990$	4.53422e18	0.153064
$991$	−1.13219e19	−0.379701	−0.189850	−	0.981813i	$-0.560800\pi$
$991$	−1.13219e19	−0.379701	−0.189850	+	0.981813i	$0.560800\pi$
$992$	1.77948e19	0.592879
$993$	−3.15945e19	−1.04578
$994$	2.11409e19	0.695203
$995$	−2.42322e19	−0.791666
$996$	2.79839e19	0.908287
$997$	−4.27955e19	−1.38000	−0.690001	−	0.723809i	$-0.742390\pi$
$997$	−4.27955e19	−1.38000	−0.690001	+	0.723809i	$0.742390\pi$
$998$	−7.69998e18	−0.246684
$999$	1.89528e19	0.603250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.14.a.e.1.9		14
13.3	even	3		13.14.c.a.9.6	yes	28
13.9	even	3		13.14.c.a.3.6	✓	28
13.12	even	2		169.14.a.c.1.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.14.c.a.3.6	✓	28	13.9	even	3
13.14.c.a.9.6	yes	28	13.3	even	3
169.14.a.c.1.6		14	13.12	even	2
169.14.a.e.1.9		14	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

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

\(f(q)\)	\(=\)	\(q+33.9774 q^{2} -1595.69 q^{3} -7037.54 q^{4} -28205.3 q^{5} -54217.3 q^{6} -354344. q^{7} -517460. q^{8} +951897. q^{9} -958341. q^{10} -4.97041e6 q^{11} +1.12297e7 q^{12} -1.20397e7 q^{14} +4.50068e7 q^{15} +4.00696e7 q^{16} -1.07108e8 q^{17} +3.23430e7 q^{18} -3.23912e8 q^{19} +1.98496e8 q^{20} +5.65422e8 q^{21} -1.68882e8 q^{22} -5.25984e8 q^{23} +8.25705e8 q^{24} -4.25166e8 q^{25} +1.02511e9 q^{27} +2.49371e9 q^{28} -1.20291e9 q^{29} +1.52921e9 q^{30} +3.17736e9 q^{31} +5.60049e9 q^{32} +7.93123e9 q^{33} -3.63924e9 q^{34} +9.99436e9 q^{35} -6.69901e9 q^{36} +1.84885e10 q^{37} -1.10057e10 q^{38} +1.45951e10 q^{40} +2.17511e10 q^{41} +1.92116e10 q^{42} +5.15859e10 q^{43} +3.49795e10 q^{44} -2.68485e10 q^{45} -1.78716e10 q^{46} +1.84645e10 q^{47} -6.39385e10 q^{48} +2.86705e10 q^{49} -1.44461e10 q^{50} +1.70910e11 q^{51} -1.97464e11 q^{53} +3.48306e10 q^{54} +1.40192e11 q^{55} +1.83359e11 q^{56} +5.16862e11 q^{57} -4.08719e10 q^{58} +1.45498e11 q^{59} -3.16737e11 q^{60} +6.36102e11 q^{61} +1.07958e11 q^{62} -3.37299e11 q^{63} -1.37960e11 q^{64} +2.69482e11 q^{66} -6.61973e11 q^{67} +7.53774e11 q^{68} +8.39307e11 q^{69} +3.39582e11 q^{70} -1.75593e12 q^{71} -4.92569e11 q^{72} -1.33173e12 q^{73} +6.28192e11 q^{74} +6.78433e11 q^{75} +2.27954e12 q^{76} +1.76123e12 q^{77} +1.34409e12 q^{79} -1.13017e12 q^{80} -3.15339e12 q^{81} +7.39045e11 q^{82} +2.49195e12 q^{83} -3.97918e12 q^{84} +3.02100e12 q^{85} +1.75276e12 q^{86} +1.91948e12 q^{87} +2.57199e12 q^{88} +6.50805e12 q^{89} -9.12242e11 q^{90} +3.70163e12 q^{92} -5.07007e12 q^{93} +6.27374e11 q^{94} +9.13602e12 q^{95} -8.93664e12 q^{96} +6.79919e11 q^{97} +9.74148e11 q^{98} -4.73132e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 65 q^{2} - 728 q^{3} + 53249 q^{4} + 20930 q^{5} - 143910 q^{6} + 173992 q^{7} + 1308489 q^{8} + 5231838 q^{9} - 2769243 q^{10} - 10986144 q^{11} - 22602732 q^{12} - 11865878 q^{14} + 75354448 q^{15}+ \cdots + 16619904586272 q^{99}+O(q^{100}) \) 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

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