LMFDB - Embedded newform 169.10.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,10,Mod(1,169)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("169.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$87.0410563117$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 1438x^{3} - 4164x^{2} + 396957x - 59580 $ x^5 - 1438x^3 - 4164x^2 + 396957*x - 59580
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$35.1685$ 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)

$f(q)$	$=$	$q-38.1685 q^{2} +47.8784 q^{3} +944.833 q^{4} +109.762 q^{5} -1827.45 q^{6} -5947.44 q^{7} -16520.6 q^{8} -17390.7 q^{9} +O(q^{10})$	\(q-38.1685 q^{2} +47.8784 q^{3} +944.833 q^{4} +109.762 q^{5} -1827.45 q^{6} -5947.44 q^{7} -16520.6 q^{8} -17390.7 q^{9} -4189.45 q^{10} +25205.7 q^{11} +45237.1 q^{12} +227005. q^{14} +5255.24 q^{15} +146811. q^{16} +109318. q^{17} +663775. q^{18} +904609. q^{19} +103707. q^{20} -284754. q^{21} -962062. q^{22} -435749. q^{23} -790979. q^{24} -1.94108e6 q^{25} -1.77503e6 q^{27} -5.61934e6 q^{28} +6.44791e6 q^{29} -200584. q^{30} -6.62308e6 q^{31} +2.85499e6 q^{32} +1.20681e6 q^{33} -4.17250e6 q^{34} -652804. q^{35} -1.64313e7 q^{36} -4.14357e6 q^{37} -3.45275e7 q^{38} -1.81333e6 q^{40} -1.49568e7 q^{41} +1.08686e7 q^{42} +4.01789e7 q^{43} +2.38151e7 q^{44} -1.90884e6 q^{45} +1.66319e7 q^{46} -6.30151e6 q^{47} +7.02907e6 q^{48} -4.98153e6 q^{49} +7.40880e7 q^{50} +5.23397e6 q^{51} +1.53111e7 q^{53} +6.77501e7 q^{54} +2.76663e6 q^{55} +9.82552e7 q^{56} +4.33112e7 q^{57} -2.46107e8 q^{58} +1.52760e8 q^{59} +4.96532e6 q^{60} +8.66321e7 q^{61} +2.52793e8 q^{62} +1.03430e8 q^{63} -1.84138e8 q^{64} -4.60620e7 q^{66} +1.01034e8 q^{67} +1.03287e8 q^{68} -2.08630e7 q^{69} +2.49165e7 q^{70} -4.13122e8 q^{71} +2.87304e8 q^{72} +3.14453e8 q^{73} +1.58154e8 q^{74} -9.29357e7 q^{75} +8.54704e8 q^{76} -1.49909e8 q^{77} -2.00580e8 q^{79} +1.61143e7 q^{80} +2.57315e8 q^{81} +5.70879e8 q^{82} -6.34578e7 q^{83} -2.69045e8 q^{84} +1.19990e7 q^{85} -1.53357e9 q^{86} +3.08715e8 q^{87} -4.16412e8 q^{88} -3.47074e7 q^{89} +7.28574e7 q^{90} -4.11710e8 q^{92} -3.17102e8 q^{93} +2.40519e8 q^{94} +9.92918e7 q^{95} +1.36692e8 q^{96} +1.25403e9 q^{97} +1.90137e8 q^{98} -4.38343e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 15 q^{2} + 161 q^{3} + 361 q^{4} - 1803 q^{5} - 5693 q^{6} - 10099 q^{7} - 23151 q^{8} + 61060 q^{9}+O(q^{10}) $ 5 * q - 15 * q^2 + 161 * q^3 + 361 * q^4 - 1803 * q^5 - 5693 * q^6 - 10099 * q^7 - 23151 * q^8 + 61060 * q^9	\( 5 q - 15 q^{2} + 161 q^{3} + 361 q^{4} - 1803 q^{5} - 5693 q^{6} - 10099 q^{7} - 23151 q^{8} + 61060 q^{9} + 84505 q^{10} - 121746 q^{11} + 113389 q^{12} + 8475 q^{14} - 105973 q^{15} - 322463 q^{16} - 495669 q^{17} + 656228 q^{18} + 840738 q^{19} + 1595607 q^{20} + 1599467 q^{21} - 2023594 q^{22} - 592152 q^{23} + 2295657 q^{24} + 1670362 q^{25} + 6847883 q^{27} - 2587955 q^{28} + 10678182 q^{29} + 5491201 q^{30} - 12885296 q^{31} - 3282927 q^{32} - 17278298 q^{33} + 9934079 q^{34} + 8380731 q^{35} - 20483302 q^{36} - 7171823 q^{37} - 25568814 q^{38} - 54359445 q^{40} - 9294012 q^{41} - 69520457 q^{42} + 12831975 q^{43} + 41479074 q^{44} - 26135198 q^{45} + 59319696 q^{46} - 43354215 q^{47} - 86874671 q^{48} + 25249488 q^{49} + 16270770 q^{50} + 16905901 q^{51} + 93231780 q^{53} - 58983719 q^{54} + 99448846 q^{55} + 199599225 q^{56} - 90173382 q^{57} - 151020970 q^{58} - 246496182 q^{59} - 90097913 q^{60} - 132232612 q^{61} + 158135724 q^{62} + 416955202 q^{63} + 91019105 q^{64} - 323733130 q^{66} + 369388534 q^{67} + 238172073 q^{68} - 579986760 q^{69} + 144857425 q^{70} - 212150457 q^{71} + 415774278 q^{72} + 252729806 q^{73} + 192105957 q^{74} - 752457788 q^{75} + 953775990 q^{76} + 449666118 q^{77} - 1247271728 q^{79} - 900649725 q^{80} - 317713115 q^{81} + 169559388 q^{82} - 1696894296 q^{83} - 1247983739 q^{84} + 775363765 q^{85} - 3291621459 q^{86} - 614530466 q^{87} - 220227222 q^{88} + 753854382 q^{89} + 2296265882 q^{90} + 13876128 q^{92} + 892784668 q^{93} + 272071215 q^{94} + 1442632962 q^{95} - 930612847 q^{96} - 3824606 q^{97} - 1570614816 q^{98} - 3016199848 q^{99}+O(q^{100}) \) 5 * q - 15 * q^2 + 161 * q^3 + 361 * q^4 - 1803 * q^5 - 5693 * q^6 - 10099 * q^7 - 23151 * q^8 + 61060 * q^9 + 84505 * q^10 - 121746 * q^11 + 113389 * q^12 + 8475 * q^14 - 105973 * q^15 - 322463 * q^16 - 495669 * q^17 + 656228 * q^18 + 840738 * q^19 + 1595607 * q^20 + 1599467 * q^21 - 2023594 * q^22 - 592152 * q^23 + 2295657 * q^24 + 1670362 * q^25 + 6847883 * q^27 - 2587955 * q^28 + 10678182 * q^29 + 5491201 * q^30 - 12885296 * q^31 - 3282927 * q^32 - 17278298 * q^33 + 9934079 * q^34 + 8380731 * q^35 - 20483302 * q^36 - 7171823 * q^37 - 25568814 * q^38 - 54359445 * q^40 - 9294012 * q^41 - 69520457 * q^42 + 12831975 * q^43 + 41479074 * q^44 - 26135198 * q^45 + 59319696 * q^46 - 43354215 * q^47 - 86874671 * q^48 + 25249488 * q^49 + 16270770 * q^50 + 16905901 * q^51 + 93231780 * q^53 - 58983719 * q^54 + 99448846 * q^55 + 199599225 * q^56 - 90173382 * q^57 - 151020970 * q^58 - 246496182 * q^59 - 90097913 * q^60 - 132232612 * q^61 + 158135724 * q^62 + 416955202 * q^63 + 91019105 * q^64 - 323733130 * q^66 + 369388534 * q^67 + 238172073 * q^68 - 579986760 * q^69 + 144857425 * q^70 - 212150457 * q^71 + 415774278 * q^72 + 252729806 * q^73 + 192105957 * q^74 - 752457788 * q^75 + 953775990 * q^76 + 449666118 * q^77 - 1247271728 * q^79 - 900649725 * q^80 - 317713115 * q^81 + 169559388 * q^82 - 1696894296 * q^83 - 1247983739 * q^84 + 775363765 * q^85 - 3291621459 * q^86 - 614530466 * q^87 - 220227222 * q^88 + 753854382 * q^89 + 2296265882 * q^90 + 13876128 * q^92 + 892784668 * q^93 + 272071215 * q^94 + 1442632962 * q^95 - 930612847 * q^96 - 3824606 * q^97 - 1570614816 * q^98 - 3016199848 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−38.1685	−1.68682	−0.843412	−	0.537267i	$-0.819457\pi$
$2$	−38.1685	−1.68682	−0.843412	+	0.537267i	$0.819457\pi$
$3$	47.8784	0.341267	0.170633	−	0.985335i	$-0.445419\pi$
$3$	47.8784	0.341267	0.170633	+	0.985335i	$0.445419\pi$
$4$	944.833	1.84538
$5$	109.762	0.0785394	0.0392697	−	0.999229i	$-0.487497\pi$
$5$	109.762	0.0785394	0.0392697	+	0.999229i	$0.487497\pi$
$6$	−1827.45	−0.575657
$7$	−5947.44	−0.936244	−0.468122	−	0.883664i	$-0.655069\pi$
$7$	−5947.44	−0.936244	−0.468122	+	0.883664i	$0.655069\pi$
$8$	−16520.6	−1.42600
$9$	−17390.7	−0.883537
$10$	−4189.45	−0.132482
$11$	25205.7	0.519076	0.259538	−	0.965733i	$-0.416430\pi$
$11$	25205.7	0.519076	0.259538	+	0.965733i	$0.416430\pi$
$12$	45237.1	0.629766
$13$	0	0
$13$	0	0
$14$	227005.	1.57928
$15$	5255.24	0.0268029
$16$	146811.	0.560039
$17$	109318.	0.317447	0.158724	−	0.987323i	$-0.449262\pi$
$17$	109318.	0.317447	0.158724	+	0.987323i	$0.449262\pi$
$18$	663775.	1.49037
$19$	904609.	1.59246	0.796232	−	0.604992i	$-0.206824\pi$
$19$	904609.	1.59246	0.796232	+	0.604992i	$0.206824\pi$
$20$	103707.	0.144935
$21$	−284754.	−0.319509
$22$	−962062.	−0.875590
$23$	−435749.	−0.324684	−0.162342	−	0.986735i	$-0.551905\pi$
$23$	−435749.	−0.324684	−0.162342	+	0.986735i	$0.551905\pi$
$24$	−790979.	−0.486647
$25$	−1.94108e6	−0.993832
$26$	0	0
$27$	−1.77503e6	−0.642789
$28$	−5.61934e6	−1.72772
$29$	6.44791e6	1.69289	0.846443	−	0.532479i	$-0.178740\pi$
$29$	6.44791e6	1.69289	0.846443	+	0.532479i	$0.178740\pi$
$30$	−200584.	−0.0452118
$31$	−6.62308e6	−1.28805	−0.644024	−	0.765005i	$-0.722736\pi$
$31$	−6.62308e6	−1.28805	−0.644024	+	0.765005i	$0.722736\pi$
$32$	2.85499e6	0.481315
$33$	1.20681e6	0.177143
$34$	−4.17250e6	−0.535477
$35$	−652804.	−0.0735320
$36$	−1.64313e7	−1.63046
$37$	−4.14357e6	−0.363469	−0.181734	−	0.983348i	$-0.558171\pi$
$37$	−4.14357e6	−0.363469	−0.181734	+	0.983348i	$0.558171\pi$
$38$	−3.45275e7	−2.68621
$39$	0	0
$40$	−1.81333e6	−0.111997
$41$	−1.49568e7	−0.826632	−0.413316	−	0.910588i	$-0.635630\pi$
$41$	−1.49568e7	−0.826632	−0.413316	+	0.910588i	$0.635630\pi$
$42$	1.08686e7	0.538956
$43$	4.01789e7	1.79221	0.896107	−	0.443838i	$-0.146384\pi$
$43$	4.01789e7	1.79221	0.896107	+	0.443838i	$0.146384\pi$
$44$	2.38151e7	0.957891
$45$	−1.90884e6	−0.0693925
$46$	1.66319e7	0.547685
$47$	−6.30151e6	−0.188367	−0.0941834	−	0.995555i	$-0.530024\pi$
$47$	−6.30151e6	−0.188367	−0.0941834	+	0.995555i	$0.530024\pi$
$48$	7.02907e6	0.191123
$49$	−4.98153e6	−0.123447
$50$	7.40880e7	1.67642
$51$	5.23397e6	0.108334
$52$	0	0
$53$	1.53111e7	0.266542	0.133271	−	0.991080i	$-0.457452\pi$
$53$	1.53111e7	0.266542	0.133271	+	0.991080i	$0.457452\pi$
$54$	6.77501e7	1.08427
$55$	2.76663e6	0.0407679
$56$	9.82552e7	1.33509
$57$	4.33112e7	0.543455
$58$	−2.46107e8	−2.85560
$59$	1.52760e8	1.64126	0.820629	−	0.571462i	$-0.193624\pi$
$59$	1.52760e8	1.64126	0.820629	+	0.571462i	$0.193624\pi$
$60$	4.96532e6	0.0494614
$61$	8.66321e7	0.801114	0.400557	−	0.916272i	$-0.368817\pi$
$61$	8.66321e7	0.801114	0.400557	+	0.916272i	$0.368817\pi$
$62$	2.52793e8	2.17271
$63$	1.03430e8	0.827206
$64$	−1.84138e8	−1.37193
$65$	0	0
$66$	−4.60620e7	−0.298810
$67$	1.01034e8	0.612537	0.306268	−	0.951945i	$-0.400920\pi$
$67$	1.01034e8	0.612537	0.306268	+	0.951945i	$0.400920\pi$
$68$	1.03287e8	0.585809
$69$	−2.08630e7	−0.110804
$70$	2.49165e7	0.124036
$71$	−4.13122e8	−1.92937	−0.964685	−	0.263406i	$-0.915154\pi$
$71$	−4.13122e8	−1.92937	−0.964685	+	0.263406i	$0.915154\pi$
$72$	2.87304e8	1.25993
$73$	3.14453e8	1.29599	0.647997	−	0.761643i	$-0.275607\pi$
$73$	3.14453e8	1.29599	0.647997	+	0.761643i	$0.275607\pi$
$74$	1.58154e8	0.613108
$75$	−9.29357e7	−0.339162
$76$	8.54704e8	2.93870
$77$	−1.49909e8	−0.485982
$78$	0	0
$79$	−2.00580e8	−0.579383	−0.289692	−	0.957120i	$-0.593553\pi$
$79$	−2.00580e8	−0.579383	−0.289692	+	0.957120i	$0.593553\pi$
$80$	1.61143e7	0.0439851
$81$	2.57315e8	0.664175
$82$	5.70879e8	1.39438
$83$	−6.34578e7	−0.146769	−0.0733843	−	0.997304i	$-0.523380\pi$
$83$	−6.34578e7	−0.146769	−0.0733843	+	0.997304i	$0.523380\pi$
$84$	−2.69045e8	−0.589614
$85$	1.19990e7	0.0249321
$86$	−1.53357e9	−3.02315
$87$	3.08715e8	0.577726
$88$	−4.16412e8	−0.740204
$89$	−3.47074e7	−0.0586364	−0.0293182	−	0.999570i	$-0.509334\pi$
$89$	−3.47074e7	−0.0586364	−0.0293182	+	0.999570i	$0.509334\pi$
$90$	7.28574e7	0.117053
$91$	0	0
$92$	−4.11710e8	−0.599164
$93$	−3.17102e8	−0.439568
$94$	2.40519e8	0.317742
$95$	9.92918e7	0.125071
$96$	1.36692e8	0.164257
$97$	1.25403e9	1.43825	0.719127	−	0.694879i	$-0.244542\pi$
$97$	1.25403e9	1.43825	0.719127	+	0.694879i	$0.244542\pi$
$98$	1.90137e8	0.208233
$99$	−4.38343e8	−0.458623
$100$	−1.83399e9	−1.83399
$101$	−9.06459e8	−0.866766	−0.433383	−	0.901210i	$-0.642680\pi$
$101$	−9.06459e8	−0.866766	−0.433383	+	0.901210i	$0.642680\pi$
$102$	−1.99773e8	−0.182741
$103$	−4.17013e8	−0.365075	−0.182537	−	0.983199i	$-0.558431\pi$
$103$	−4.17013e8	−0.365075	−0.182537	+	0.983199i	$0.558431\pi$
$104$	0	0
$105$	−3.12552e7	−0.0250940
$106$	−5.84402e8	−0.449610
$107$	6.71636e8	0.495344	0.247672	−	0.968844i	$-0.420334\pi$
$107$	6.71636e8	0.495344	0.247672	+	0.968844i	$0.420334\pi$
$108$	−1.67710e9	−1.18619
$109$	−1.66748e9	−1.13147	−0.565734	−	0.824588i	$-0.691407\pi$
$109$	−1.66748e9	−1.13147	−0.565734	+	0.824588i	$0.691407\pi$
$110$	−1.05598e8	−0.0687683
$111$	−1.98387e8	−0.124040
$112$	−8.73149e8	−0.524333
$113$	−1.84580e9	−1.06496	−0.532478	−	0.846444i	$-0.678739\pi$
$113$	−1.84580e9	−1.06496	−0.532478	+	0.846444i	$0.678739\pi$
$114$	−1.65312e9	−0.916713
$115$	−4.78287e7	−0.0255005
$116$	6.09219e9	3.12401
$117$	0	0
$118$	−5.83063e9	−2.76851
$119$	−6.50162e8	−0.297208
$120$	−8.68195e7	−0.0382210
$121$	−1.72262e9	−0.730560
$122$	−3.30661e9	−1.35134
$123$	−7.16109e8	−0.282102
$124$	−6.25770e9	−2.37694
$125$	−4.27436e8	−0.156594
$126$	−3.94776e9	−1.39535
$127$	1.87922e9	0.641006	0.320503	−	0.947248i	$-0.396148\pi$
$127$	1.87922e9	0.641006	0.320503	+	0.947248i	$0.396148\pi$
$128$	5.56650e9	1.83290
$129$	1.92370e9	0.611623
$130$	0	0
$131$	3.46045e9	1.02663	0.513313	−	0.858201i	$-0.328418\pi$
$131$	3.46045e9	1.02663	0.513313	+	0.858201i	$0.328418\pi$
$132$	1.14023e9	0.326896
$133$	−5.38011e9	−1.49093
$134$	−3.85632e9	−1.03324
$135$	−1.94831e8	−0.0504842
$136$	−1.80600e9	−0.452680
$137$	−5.04786e9	−1.22424	−0.612118	−	0.790766i	$-0.709682\pi$
$137$	−5.04786e9	−1.22424	−0.612118	+	0.790766i	$0.709682\pi$
$138$	7.96307e8	0.186907
$139$	3.59716e9	0.817322	0.408661	−	0.912686i	$-0.365996\pi$
$139$	3.59716e9	0.817322	0.408661	+	0.912686i	$0.365996\pi$
$140$	−6.16791e8	−0.135694
$141$	−3.01706e8	−0.0642833
$142$	1.57682e10	3.25451
$143$	0	0
$144$	−2.55314e9	−0.494815
$145$	7.07736e8	0.132958
$146$	−1.20022e10	−2.18611
$147$	−2.38508e8	−0.0421283
$148$	−3.91498e9	−0.670736
$149$	−1.27561e9	−0.212022	−0.106011	−	0.994365i	$-0.533808\pi$
$149$	−1.27561e9	−0.212022	−0.106011	+	0.994365i	$0.533808\pi$
$150$	3.54721e9	0.572106
$151$	−4.35273e9	−0.681342	−0.340671	−	0.940183i	$-0.610654\pi$
$151$	−4.35273e9	−0.681342	−0.340671	+	0.940183i	$0.610654\pi$
$152$	−1.49447e10	−2.27086
$153$	−1.90111e9	−0.280476
$154$	5.72181e9	0.819766
$155$	−7.26963e8	−0.101163
$156$	0	0
$157$	−1.41002e10	−1.85215	−0.926075	−	0.377339i	$-0.876839\pi$
$157$	−1.41002e10	−1.85215	−0.926075	+	0.377339i	$0.876839\pi$
$158$	7.65584e9	0.977318
$159$	7.33072e8	0.0909619
$160$	3.13370e8	0.0378022
$161$	2.59159e9	0.303983
$162$	−9.82132e9	−1.12035
$163$	−7.24812e8	−0.0804231	−0.0402116	−	0.999191i	$-0.512803\pi$
$163$	−7.24812e8	−0.0804231	−0.0402116	+	0.999191i	$0.512803\pi$
$164$	−1.41317e10	−1.52545
$165$	1.32462e8	0.0139127
$166$	2.42209e9	0.247573
$167$	8.33031e8	0.0828776	0.0414388	−	0.999141i	$-0.486806\pi$
$167$	8.33031e8	0.0828776	0.0414388	+	0.999141i	$0.486806\pi$
$168$	4.70430e9	0.455621
$169$	0	0
$170$	−4.57983e8	−0.0420561
$171$	−1.57317e10	−1.40700
$172$	3.79623e10	3.30731
$173$	5.77955e8	0.0490553	0.0245277	−	0.999699i	$-0.492192\pi$
$173$	5.77955e8	0.0490553	0.0245277	+	0.999699i	$0.492192\pi$
$174$	−1.17832e10	−0.974522
$175$	1.15444e10	0.930469
$176$	3.70046e9	0.290703
$177$	7.31392e9	0.560106
$178$	1.32473e9	0.0989094
$179$	−1.56569e10	−1.13990	−0.569952	−	0.821678i	$-0.693038\pi$
$179$	−1.56569e10	−1.13990	−0.569952	+	0.821678i	$0.693038\pi$
$180$	−1.80353e9	−0.128055
$181$	−2.18552e10	−1.51356	−0.756781	−	0.653668i	$-0.773229\pi$
$181$	−2.18552e10	−1.51356	−0.756781	+	0.653668i	$0.773229\pi$
$182$	0	0
$183$	4.14780e9	0.273394
$184$	7.19882e9	0.463000
$185$	−4.54807e8	−0.0285466
$186$	1.21033e10	0.741474
$187$	2.75543e9	0.164779
$188$	−5.95388e9	−0.347608
$189$	1.05569e10	0.601807
$190$	−3.78982e9	−0.210973
$191$	1.67784e10	0.912222	0.456111	−	0.889923i	$-0.349242\pi$
$191$	1.67784e10	0.912222	0.456111	+	0.889923i	$0.349242\pi$
$192$	−8.81622e9	−0.468195
$193$	2.70036e10	1.40092	0.700462	−	0.713690i	$-0.252977\pi$
$193$	2.70036e10	1.40092	0.700462	+	0.713690i	$0.252977\pi$
$194$	−4.78645e10	−2.42608
$195$	0	0
$196$	−4.70671e9	−0.227806
$197$	−1.58277e10	−0.748720	−0.374360	−	0.927283i	$-0.622138\pi$
$197$	−1.58277e10	−0.748720	−0.374360	+	0.927283i	$0.622138\pi$
$198$	1.67309e10	0.773616
$199$	8.80397e9	0.397960	0.198980	−	0.980004i	$-0.436237\pi$
$199$	8.80397e9	0.397960	0.198980	+	0.980004i	$0.436237\pi$
$200$	3.20677e10	1.41721
$201$	4.83736e9	0.209038
$202$	3.45982e10	1.46208
$203$	−3.83485e10	−1.58495
$204$	4.94523e9	0.199917
$205$	−1.64169e9	−0.0649232
$206$	1.59167e10	0.615817
$207$	7.57796e9	0.286870
$208$	0	0
$209$	2.28013e10	0.826610
$210$	1.19296e9	0.0423292
$211$	−1.82054e10	−0.632308	−0.316154	−	0.948708i	$-0.602392\pi$
$211$	−1.82054e10	−0.632308	−0.316154	+	0.948708i	$0.602392\pi$
$212$	1.44665e10	0.491870
$213$	−1.97796e10	−0.658430
$214$	−2.56353e10	−0.835558
$215$	4.41012e9	0.140759
$216$	2.93245e10	0.916618
$217$	3.93904e10	1.20593
$218$	6.36453e10	1.90859
$219$	1.50555e10	0.442280
$220$	2.61400e9	0.0752322
$221$	0	0
$222$	7.57215e9	0.209233
$223$	−1.53511e10	−0.415688	−0.207844	−	0.978162i	$-0.566645\pi$
$223$	−1.53511e10	−0.415688	−0.207844	+	0.978162i	$0.566645\pi$
$224$	−1.69799e10	−0.450628
$225$	3.37566e10	0.878087
$226$	7.04514e10	1.79639
$227$	−4.20620e10	−1.05141	−0.525707	−	0.850666i	$-0.676199\pi$
$227$	−4.20620e10	−1.05141	−0.525707	+	0.850666i	$0.676199\pi$
$228$	4.09219e10	1.00288
$229$	6.68760e10	1.60698	0.803490	−	0.595318i	$-0.202974\pi$
$229$	6.68760e10	1.60698	0.803490	+	0.595318i	$0.202974\pi$
$230$	1.82555e9	0.0430148
$231$	−7.17741e9	−0.165849
$232$	−1.06523e11	−2.41406
$233$	−5.19268e10	−1.15422	−0.577112	−	0.816665i	$-0.695820\pi$
$233$	−5.19268e10	−1.15422	−0.577112	+	0.816665i	$0.695820\pi$
$234$	0	0
$235$	−6.91668e8	−0.0147942
$236$	1.44333e11	3.02874
$237$	−9.60345e9	−0.197724
$238$	2.48157e10	0.501338
$239$	−7.45881e10	−1.47870	−0.739348	−	0.673323i	$-0.764866\pi$
$239$	−7.45881e10	−1.47870	−0.739348	+	0.673323i	$0.764866\pi$
$240$	7.71525e8	0.0150107
$241$	−5.74852e10	−1.09769	−0.548845	−	0.835924i	$-0.684932\pi$
$241$	−5.74852e10	−1.09769	−0.548845	+	0.835924i	$0.684932\pi$
$242$	6.57499e10	1.23233
$243$	4.72577e10	0.869449
$244$	8.18528e10	1.47836
$245$	−5.46784e8	−0.00969545
$246$	2.73328e10	0.475857
$247$	0	0
$248$	1.09417e11	1.83676
$249$	−3.03826e9	−0.0500873
$250$	1.63146e10	0.264147
$251$	−1.07873e11	−1.71546	−0.857732	−	0.514097i	$-0.828127\pi$
$251$	−1.07873e11	−1.71546	−0.857732	+	0.514097i	$0.828127\pi$
$252$	9.77240e10	1.52651
$253$	−1.09833e10	−0.168536
$254$	−7.17272e10	−1.08126
$255$	5.74492e8	0.00850850
$256$	−1.18186e11	−1.71984
$257$	−6.64074e10	−0.949550	−0.474775	−	0.880107i	$-0.657470\pi$
$257$	−6.64074e10	−0.949550	−0.474775	+	0.880107i	$0.657470\pi$
$258$	−7.34247e10	−1.03170
$259$	2.46436e10	0.340295
$260$	0	0
$261$	−1.12133e11	−1.49573
$262$	−1.32080e11	−1.73174
$263$	−8.15356e10	−1.05086	−0.525432	−	0.850836i	$-0.676096\pi$
$263$	−8.15356e10	−1.05086	−0.525432	+	0.850836i	$0.676096\pi$
$264$	−1.99371e10	−0.252607
$265$	1.68058e9	0.0209340
$266$	2.05351e11	2.51494
$267$	−1.66174e9	−0.0200107
$268$	9.54605e10	1.13036
$269$	1.00568e11	1.17105	0.585523	−	0.810656i	$-0.300889\pi$
$269$	1.00568e11	1.17105	0.585523	+	0.810656i	$0.300889\pi$
$270$	7.43640e9	0.0851580
$271$	2.98757e10	0.336477	0.168239	−	0.985746i	$-0.446192\pi$
$271$	2.98757e10	0.336477	0.168239	+	0.985746i	$0.446192\pi$
$272$	1.60491e10	0.177783
$273$	0	0
$274$	1.92669e11	2.06507
$275$	−4.89261e10	−0.515874
$276$	−1.97120e10	−0.204475
$277$	−3.17195e10	−0.323718	−0.161859	−	0.986814i	$-0.551749\pi$
$277$	−3.17195e10	−0.323718	−0.161859	+	0.986814i	$0.551749\pi$
$278$	−1.37298e11	−1.37868
$279$	1.15180e11	1.13804
$280$	1.07847e10	0.104857
$281$	−9.86953e10	−0.944318	−0.472159	−	0.881513i	$-0.656525\pi$
$281$	−9.86953e10	−0.944318	−0.472159	+	0.881513i	$0.656525\pi$
$282$	1.15157e10	0.108435
$283$	−1.06164e11	−0.983871	−0.491935	−	0.870632i	$-0.663710\pi$
$283$	−1.06164e11	−0.983871	−0.491935	+	0.870632i	$0.663710\pi$
$284$	−3.90331e11	−3.56042
$285$	4.75393e9	0.0426826
$286$	0	0
$287$	8.89549e10	0.773929
$288$	−4.96501e10	−0.425260
$289$	−1.06637e11	−0.899227
$290$	−2.70132e10	−0.224277
$291$	6.00410e10	0.490828
$292$	2.97106e11	2.39160
$293$	−2.26355e11	−1.79426	−0.897132	−	0.441763i	$-0.854353\pi$
$293$	−2.26355e11	−1.79426	−0.897132	+	0.441763i	$0.854353\pi$
$294$	9.10348e9	0.0710631
$295$	1.67673e10	0.128903
$296$	6.84541e10	0.518307
$297$	−4.47407e10	−0.333656
$298$	4.86881e10	0.357643
$299$	0	0
$300$	−8.78087e10	−0.625881
$301$	−2.38962e11	−1.67795
$302$	1.66137e11	1.14930
$303$	−4.33998e10	−0.295798
$304$	1.32806e11	0.891841
$305$	9.50892e9	0.0629190
$306$	7.25625e10	0.473114
$307$	2.23009e10	0.143285	0.0716424	−	0.997430i	$-0.477176\pi$
$307$	2.23009e10	0.143285	0.0716424	+	0.997430i	$0.477176\pi$
$308$	−1.41639e11	−0.896820
$309$	−1.99659e10	−0.124588
$310$	2.77471e10	0.170643
$311$	−2.71805e11	−1.64754	−0.823770	−	0.566925i	$-0.808133\pi$
$311$	−2.71805e11	−1.64754	−0.823770	+	0.566925i	$0.808133\pi$
$312$	0	0
$313$	−7.90775e10	−0.465697	−0.232849	−	0.972513i	$-0.574805\pi$
$313$	−7.90775e10	−0.465697	−0.232849	+	0.972513i	$0.574805\pi$
$314$	5.38183e11	3.12425
$315$	1.13527e10	0.0649683
$316$	−1.89515e11	−1.06918
$317$	−2.03032e11	−1.12927	−0.564636	−	0.825340i	$-0.690983\pi$
$317$	−2.03032e11	−1.12927	−0.564636	+	0.825340i	$0.690983\pi$
$318$	−2.79802e10	−0.153437
$319$	1.62524e11	0.878736
$320$	−2.02114e10	−0.107751
$321$	3.21568e10	0.169044
$322$	−9.89171e10	−0.512767
$323$	9.88899e10	0.505523
$324$	2.43120e11	1.22565
$325$	0	0
$326$	2.76650e10	0.135660
$327$	−7.98365e10	−0.386132
$328$	2.47095e11	1.17878
$329$	3.74779e10	0.176357
$330$	−5.05586e9	−0.0234683
$331$	−3.24137e11	−1.48424	−0.742118	−	0.670270i	$-0.766178\pi$
$331$	−3.24137e11	−1.48424	−0.742118	+	0.670270i	$0.766178\pi$
$332$	−5.99570e10	−0.270844
$333$	7.20594e10	0.321138
$334$	−3.17955e10	−0.139800
$335$	1.10897e10	0.0481083
$336$	−4.18050e10	−0.178937
$337$	2.68510e11	1.13403	0.567017	−	0.823706i	$-0.308097\pi$
$337$	2.68510e11	1.13403	0.567017	+	0.823706i	$0.308097\pi$
$338$	0	0
$339$	−8.83739e10	−0.363434
$340$	1.13370e10	0.0460091
$341$	−1.66939e11	−0.668595
$342$	6.00457e11	2.37336
$343$	2.69628e11	1.05182
$344$	−6.63778e11	−2.55570
$345$	−2.28996e9	−0.00870247
$346$	−2.20597e10	−0.0827478
$347$	2.74715e11	1.01719	0.508593	−	0.861007i	$-0.330166\pi$
$347$	2.74715e11	1.01719	0.508593	+	0.861007i	$0.330166\pi$
$348$	2.91684e11	1.06612
$349$	3.54006e11	1.27731	0.638655	−	0.769494i	$-0.279491\pi$
$349$	3.54006e11	1.27731	0.638655	+	0.769494i	$0.279491\pi$
$350$	−4.40634e11	−1.56954
$351$	0	0
$352$	7.19619e10	0.249839
$353$	2.25650e11	0.773481	0.386741	−	0.922189i	$-0.373601\pi$
$353$	2.25650e11	0.773481	0.386741	+	0.922189i	$0.373601\pi$
$354$	−2.79161e11	−0.944801
$355$	−4.53451e10	−0.151532
$356$	−3.27927e10	−0.108206
$357$	−3.11287e10	−0.101427
$358$	5.97602e11	1.92282
$359$	−3.39022e10	−0.107722	−0.0538608	−	0.998548i	$-0.517153\pi$
$359$	−3.39022e10	−0.107722	−0.0538608	+	0.998548i	$0.517153\pi$
$360$	3.15351e10	0.0989538
$361$	4.95629e11	1.53594
$362$	8.34178e11	2.55312
$363$	−8.24764e10	−0.249316
$364$	0	0
$365$	3.45150e10	0.101787
$366$	−1.58315e11	−0.461167
$367$	−7.74387e10	−0.222823	−0.111412	−	0.993774i	$-0.535537\pi$
$367$	−7.74387e10	−0.222823	−0.111412	+	0.993774i	$0.535537\pi$
$368$	−6.39726e10	−0.181836
$369$	2.60109e11	0.730360
$370$	1.73593e10	0.0481531
$371$	−9.10620e10	−0.249548
$372$	−2.99609e11	−0.811169
$373$	6.50821e11	1.74089	0.870446	−	0.492264i	$-0.163831\pi$
$373$	6.50821e11	1.74089	0.870446	+	0.492264i	$0.163831\pi$
$374$	−1.05171e11	−0.277954
$375$	−2.04649e10	−0.0534404
$376$	1.04105e11	0.268612
$377$	0	0
$378$	−4.02940e11	−1.01514
$379$	−1.93989e11	−0.482948	−0.241474	−	0.970407i	$-0.577631\pi$
$379$	−1.93989e11	−0.482948	−0.241474	+	0.970407i	$0.577631\pi$
$380$	9.38141e10	0.230803
$381$	8.99743e10	0.218754
$382$	−6.40406e11	−1.53876
$383$	−4.44645e11	−1.05589	−0.527946	−	0.849278i	$-0.677037\pi$
$383$	−4.44645e11	−1.05589	−0.527946	+	0.849278i	$0.677037\pi$
$384$	2.66515e11	0.625506
$385$	−1.64544e10	−0.0381687
$386$	−1.03069e12	−2.36311
$387$	−6.98737e11	−1.58349
$388$	1.18485e12	2.65412
$389$	−1.69623e11	−0.375589	−0.187794	−	0.982208i	$-0.560134\pi$
$389$	−1.69623e11	−0.375589	−0.187794	+	0.982208i	$0.560134\pi$
$390$	0	0
$391$	−4.76352e10	−0.103070
$392$	8.22978e10	0.176036
$393$	1.65681e11	0.350353
$394$	6.04119e11	1.26296
$395$	−2.20161e10	−0.0455044
$396$	−4.14161e11	−0.846332
$397$	−2.94468e11	−0.594951	−0.297476	−	0.954729i	$-0.596145\pi$
$397$	−2.94468e11	−0.594951	−0.297476	+	0.954729i	$0.596145\pi$
$398$	−3.36034e11	−0.671289
$399$	−2.57591e11	−0.508806
$400$	−2.84971e11	−0.556584
$401$	−4.43362e11	−0.856265	−0.428133	−	0.903716i	$-0.640828\pi$
$401$	−4.43362e11	−0.856265	−0.428133	+	0.903716i	$0.640828\pi$
$402$	−1.84635e11	−0.352611
$403$	0	0
$404$	−8.56452e11	−1.59951
$405$	2.82434e10	0.0521639
$406$	1.46371e12	2.67354
$407$	−1.04441e11	−0.188668
$408$	−8.64682e10	−0.154485
$409$	1.01253e11	0.178918	0.0894592	−	0.995990i	$-0.471486\pi$
$409$	1.01253e11	0.178918	0.0894592	+	0.995990i	$0.471486\pi$
$410$	6.26610e10	0.109514
$411$	−2.41684e11	−0.417791
$412$	−3.94007e11	−0.673700
$413$	−9.08533e11	−1.53662
$414$	−2.89239e11	−0.483900
$415$	−6.96526e9	−0.0115271
$416$	0	0
$417$	1.72226e11	0.278925
$418$	−8.70289e11	−1.39435
$419$	7.93982e10	0.125848	0.0629242	−	0.998018i	$-0.479957\pi$
$419$	7.93982e10	0.125848	0.0629242	+	0.998018i	$0.479957\pi$
$420$	−2.95310e10	−0.0463080
$421$	6.06765e11	0.941350	0.470675	−	0.882307i	$-0.344010\pi$
$421$	6.06765e11	0.941350	0.470675	+	0.882307i	$0.344010\pi$
$422$	6.94871e11	1.06659
$423$	1.09587e11	0.166429
$424$	−2.52949e11	−0.380089
$425$	−2.12195e11	−0.315489
$426$	7.54958e11	1.11066
$427$	−5.15239e11	−0.750038
$428$	6.34583e11	0.914096
$429$	0	0
$430$	−1.68328e11	−0.237436
$431$	2.72544e11	0.380442	0.190221	−	0.981741i	$-0.439080\pi$
$431$	2.72544e11	0.380442	0.190221	+	0.981741i	$0.439080\pi$
$432$	−2.60593e11	−0.359987
$433$	−1.15522e12	−1.57931	−0.789655	−	0.613551i	$-0.789740\pi$
$433$	−1.15522e12	−1.57931	−0.789655	+	0.613551i	$0.789740\pi$
$434$	−1.50347e12	−2.03419
$435$	3.38853e10	0.0453742
$436$	−1.57549e12	−2.08799
$437$	−3.94182e11	−0.517047
$438$	−5.74646e11	−0.746048
$439$	1.78053e11	0.228801	0.114401	−	0.993435i	$-0.463505\pi$
$439$	1.78053e11	0.228801	0.114401	+	0.993435i	$0.463505\pi$
$440$	−4.57063e10	−0.0581351
$441$	8.66321e10	0.109070
$442$	0	0
$443$	−6.55260e10	−0.0808345	−0.0404173	−	0.999183i	$-0.512869\pi$
$443$	−6.55260e10	−0.0808345	−0.0404173	+	0.999183i	$0.512869\pi$
$444$	−1.87443e11	−0.228900
$445$	−3.80956e9	−0.00460527
$446$	5.85928e11	0.701192
$447$	−6.10742e10	−0.0723559
$448$	1.09515e12	1.28446
$449$	7.98150e11	0.926779	0.463390	−	0.886155i	$-0.346633\pi$
$449$	7.98150e11	0.926779	0.463390	+	0.886155i	$0.346633\pi$
$450$	−1.28844e12	−1.48118
$451$	−3.76997e11	−0.429085
$452$	−1.74397e12	−1.96525
$453$	−2.08402e11	−0.232519
$454$	1.60544e12	1.77355
$455$	0	0
$456$	−7.15526e11	−0.774968
$457$	8.92736e11	0.957415	0.478708	−	0.877974i	$-0.341105\pi$
$457$	8.92736e11	0.957415	0.478708	+	0.877974i	$0.341105\pi$
$458$	−2.55256e12	−2.71069
$459$	−1.94042e11	−0.204051
$460$	−4.51901e10	−0.0470580
$461$	−2.32490e11	−0.239745	−0.119872	−	0.992789i	$-0.538249\pi$
$461$	−2.32490e11	−0.239745	−0.119872	+	0.992789i	$0.538249\pi$
$462$	2.73951e11	0.279759
$463$	1.54421e12	1.56168	0.780841	−	0.624730i	$-0.214791\pi$
$463$	1.54421e12	1.56168	0.780841	+	0.624730i	$0.214791\pi$
$464$	9.46622e11	0.948082
$465$	−3.48058e10	−0.0345234
$466$	1.98197e12	1.94697
$467$	1.63317e12	1.58893	0.794465	−	0.607310i	$-0.207751\pi$
$467$	1.63317e12	1.58893	0.794465	+	0.607310i	$0.207751\pi$
$468$	0	0
$469$	−6.00895e11	−0.573484
$470$	2.63999e10	0.0249553
$471$	−6.75094e11	−0.632077
$472$	−2.52369e12	−2.34044
$473$	1.01274e12	0.930295
$474$	3.66549e11	0.333526
$475$	−1.75592e12	−1.58264
$476$	−6.14295e11	−0.548461
$477$	−2.66271e11	−0.235500
$478$	2.84692e12	2.49430
$479$	−1.54414e12	−1.34022	−0.670112	−	0.742260i	$-0.733754\pi$
$479$	−1.54414e12	−1.34022	−0.670112	+	0.742260i	$0.733754\pi$
$480$	1.50036e10	0.0129006
$481$	0	0
$482$	2.19412e12	1.85161
$483$	1.24081e11	0.103739
$484$	−1.62759e12	−1.34816
$485$	1.37645e11	0.112960
$486$	−1.80375e12	−1.46661
$487$	−2.55439e11	−0.205782	−0.102891	−	0.994693i	$-0.532809\pi$
$487$	−2.55439e11	−0.205782	−0.102891	+	0.994693i	$0.532809\pi$
$488$	−1.43121e12	−1.14239
$489$	−3.47028e10	−0.0274457
$490$	2.08699e10	0.0163545
$491$	1.58407e12	1.23000	0.615002	−	0.788526i	$-0.289155\pi$
$491$	1.58407e12	1.23000	0.615002	+	0.788526i	$0.289155\pi$
$492$	−6.76603e11	−0.520584
$493$	7.04872e11	0.537402
$494$	0	0
$495$	−4.81135e10	−0.0360200
$496$	−9.72340e11	−0.721357
$497$	2.45702e12	1.80636
$498$	1.15966e11	0.0844884
$499$	6.29948e11	0.454833	0.227417	−	0.973798i	$-0.426972\pi$
$499$	6.29948e11	0.454833	0.227417	+	0.973798i	$0.426972\pi$
$500$	−4.03856e11	−0.288976
$501$	3.98842e10	0.0282834
$502$	4.11736e12	2.89369
$503$	5.49263e11	0.382582	0.191291	−	0.981533i	$-0.438733\pi$
$503$	5.49263e11	0.382582	0.191291	+	0.981533i	$0.438733\pi$
$504$	−1.70872e12	−1.17960
$505$	−9.94949e10	−0.0680753
$506$	4.19217e11	0.284290
$507$	0	0
$508$	1.77555e12	1.18290
$509$	−1.36923e11	−0.0904165	−0.0452083	−	0.998978i	$-0.514395\pi$
$509$	−1.36923e11	−0.0904165	−0.0452083	+	0.998978i	$0.514395\pi$
$510$	−2.19275e10	−0.0143523
$511$	−1.87019e12	−1.21337
$512$	1.66095e12	1.06817
$513$	−1.60570e12	−1.02362
$514$	2.53467e12	1.60172
$515$	−4.57722e10	−0.0286727
$516$	1.81758e12	1.12867
$517$	−1.58834e11	−0.0977767
$518$	−9.40610e11	−0.574018
$519$	2.76715e10	0.0167410
$520$	0	0
$521$	−1.66627e12	−0.990779	−0.495389	−	0.868671i	$-0.664975\pi$
$521$	−1.66627e12	−0.990779	−0.495389	+	0.868671i	$0.664975\pi$
$522$	4.27996e12	2.52303
$523$	1.97187e12	1.15244	0.576222	−	0.817293i	$-0.304526\pi$
$523$	1.97187e12	1.15244	0.576222	+	0.817293i	$0.304526\pi$
$524$	3.26955e12	1.89451
$525$	5.52730e11	0.317538
$526$	3.11209e12	1.77262
$527$	−7.24021e11	−0.408887
$528$	1.77172e11	0.0992072
$529$	−1.61128e12	−0.894580
$530$	−6.41452e10	−0.0353121
$531$	−2.65660e12	−1.45011
$532$	−5.08330e12	−2.75134
$533$	0	0
$534$	6.34260e10	0.0337545
$535$	7.37202e10	0.0389040
$536$	−1.66914e12	−0.873479
$537$	−7.49629e11	−0.389011
$538$	−3.83852e12	−1.97535
$539$	−1.25563e11	−0.0640784
$540$	−1.84083e11	−0.0931624
$541$	−1.54916e12	−0.777513	−0.388756	−	0.921341i	$-0.627095\pi$
$541$	−1.54916e12	−0.777513	−0.388756	+	0.921341i	$0.627095\pi$
$542$	−1.14031e12	−0.567578
$543$	−1.04639e12	−0.516529
$544$	3.12101e11	0.152792
$545$	−1.83027e11	−0.0888648
$546$	0	0
$547$	1.98052e12	0.945879	0.472939	−	0.881095i	$-0.343193\pi$
$547$	1.98052e12	0.945879	0.472939	+	0.881095i	$0.343193\pi$
$548$	−4.76939e12	−2.25918
$549$	−1.50659e12	−0.707814
$550$	1.86744e12	0.870189
$551$	5.83283e12	2.69586
$552$	3.44668e11	0.158007
$553$	1.19294e12	0.542444
$554$	1.21068e12	0.546056
$555$	−2.17754e10	−0.00974200
$556$	3.39871e12	1.50827
$557$	−8.86577e11	−0.390273	−0.195136	−	0.980776i	$-0.562515\pi$
$557$	−8.86577e11	−0.390273	−0.195136	+	0.980776i	$0.562515\pi$
$558$	−4.39623e12	−1.91967
$559$	0	0
$560$	−9.58387e10	−0.0411808
$561$	1.31926e11	0.0562336
$562$	3.76705e12	1.59290
$563$	3.89786e12	1.63508	0.817539	−	0.575873i	$-0.195338\pi$
$563$	3.89786e12	1.63508	0.817539	+	0.575873i	$0.195338\pi$
$564$	−2.85062e11	−0.118627
$565$	−2.02599e11	−0.0836410
$566$	4.05212e12	1.65962
$567$	−1.53037e12	−0.621830
$568$	6.82501e12	2.75129
$569$	−2.26590e12	−0.906223	−0.453112	−	0.891454i	$-0.649686\pi$
$569$	−2.26590e12	−0.906223	−0.453112	+	0.891454i	$0.649686\pi$
$570$	−1.81450e11	−0.0719981
$571$	−3.09546e12	−1.21860	−0.609302	−	0.792938i	$-0.708550\pi$
$571$	−3.09546e12	−1.21860	−0.609302	+	0.792938i	$0.708550\pi$
$572$	0	0
$573$	8.03323e11	0.311311
$574$	−3.39527e12	−1.30548
$575$	8.45822e11	0.322681
$576$	3.20228e12	1.21215
$577$	3.23415e12	1.21470	0.607350	−	0.794434i	$-0.292233\pi$
$577$	3.23415e12	1.21470	0.607350	+	0.794434i	$0.292233\pi$
$578$	4.07019e12	1.51684
$579$	1.29289e12	0.478089
$580$	6.68692e11	0.245358
$581$	3.77411e11	0.137411
$582$	−2.29167e12	−0.827941
$583$	3.85927e11	0.138356
$584$	−5.19495e12	−1.84809
$585$	0	0
$586$	8.63964e12	3.02661
$587$	8.78491e11	0.305398	0.152699	−	0.988273i	$-0.451204\pi$
$587$	8.78491e11	0.305398	0.152699	+	0.988273i	$0.451204\pi$
$588$	−2.25350e11	−0.0777427
$589$	−5.99129e12	−2.05117
$590$	−6.39983e11	−0.217437
$591$	−7.57805e11	−0.255513
$592$	−6.08321e11	−0.203556
$593$	1.91730e12	0.636712	0.318356	−	0.947971i	$-0.396869\pi$
$593$	1.91730e12	0.636712	0.318356	+	0.947971i	$0.396869\pi$
$594$	1.70769e12	0.562819
$595$	−7.13632e10	−0.0233425
$596$	−1.20524e12	−0.391260
$597$	4.21520e11	0.135811
$598$	0	0
$599$	−5.10464e12	−1.62011	−0.810054	−	0.586355i	$-0.800562\pi$
$599$	−5.10464e12	−1.62011	−0.810054	+	0.586355i	$0.800562\pi$
$600$	1.53535e12	0.483645
$601$	3.00419e12	0.939273	0.469636	−	0.882860i	$-0.344385\pi$
$601$	3.00419e12	0.939273	0.469636	+	0.882860i	$0.344385\pi$
$602$	9.12080e12	2.83041
$603$	−1.75705e12	−0.541199
$604$	−4.11260e12	−1.25733
$605$	−1.89079e11	−0.0573778
$606$	1.65650e12	0.498960
$607$	1.18434e12	0.354101	0.177051	−	0.984202i	$-0.443344\pi$
$607$	1.18434e12	0.354101	0.177051	+	0.984202i	$0.443344\pi$
$608$	2.58265e12	0.766477
$609$	−1.83607e12	−0.540892
$610$	−3.62941e11	−0.106133
$611$	0	0
$612$	−1.79623e12	−0.517584
$613$	−6.42597e11	−0.183809	−0.0919045	−	0.995768i	$-0.529295\pi$
$613$	−6.42597e11	−0.183809	−0.0919045	+	0.995768i	$0.529295\pi$
$614$	−8.51193e11	−0.241696
$615$	−7.86017e10	−0.0221561
$616$	2.47659e12	0.693011
$617$	−5.05474e12	−1.40416	−0.702078	−	0.712100i	$-0.747744\pi$
$617$	−5.05474e12	−1.40416	−0.702078	+	0.712100i	$0.747744\pi$
$618$	7.62068e11	0.210158
$619$	3.09492e11	0.0847308	0.0423654	−	0.999102i	$-0.486511\pi$
$619$	3.09492e11	0.0847308	0.0423654	+	0.999102i	$0.486511\pi$
$620$	−6.86859e11	−0.186683
$621$	7.73466e11	0.208703
$622$	1.03744e13	2.77911
$623$	2.06421e11	0.0548980
$624$	0	0
$625$	3.74425e12	0.981533
$626$	3.01827e12	0.785549
$627$	1.09169e12	0.282094
$628$	−1.33223e13	−3.41792
$629$	−4.52966e11	−0.115382
$630$	−4.33315e11	−0.109590
$631$	7.94237e11	0.199443	0.0997214	−	0.995015i	$-0.468205\pi$
$631$	7.94237e11	0.199443	0.0997214	+	0.995015i	$0.468205\pi$
$632$	3.31370e12	0.826202
$633$	−8.71644e11	−0.215786
$634$	7.74944e12	1.90488
$635$	2.06268e11	0.0503442
$636$	6.92631e11	0.167859
$637$	0	0
$638$	−6.20328e12	−1.48227
$639$	7.18446e12	1.70467
$640$	6.10991e11	0.143954
$641$	2.30298e12	0.538802	0.269401	−	0.963028i	$-0.413174\pi$
$641$	2.30298e12	0.538802	0.269401	+	0.963028i	$0.413174\pi$
$642$	−1.22738e12	−0.285148
$643$	2.54593e12	0.587350	0.293675	−	0.955905i	$-0.405122\pi$
$643$	2.54593e12	0.587350	0.293675	+	0.955905i	$0.405122\pi$
$644$	2.44862e12	0.560964
$645$	2.11149e11	0.0480365
$646$	−3.77448e12	−0.852728
$647$	−2.74568e11	−0.0616001	−0.0308000	−	0.999526i	$-0.509806\pi$
$647$	−2.74568e11	−0.0616001	−0.0308000	+	0.999526i	$0.509806\pi$
$648$	−4.25099e12	−0.947115
$649$	3.85043e12	0.851937
$650$	0	0
$651$	1.88595e12	0.411543
$652$	−6.84826e11	−0.148411
$653$	−6.05719e12	−1.30365	−0.651826	−	0.758369i	$-0.725997\pi$
$653$	−6.05719e12	−1.30365	−0.651826	+	0.758369i	$0.725997\pi$
$654$	3.04724e12	0.651338
$655$	3.79827e11	0.0806306
$656$	−2.19582e12	−0.462946
$657$	−5.46855e12	−1.14506
$658$	−1.43047e12	−0.297484
$659$	4.97718e12	1.02801	0.514007	−	0.857786i	$-0.328160\pi$
$659$	4.97718e12	1.02801	0.514007	+	0.857786i	$0.328160\pi$
$660$	1.25154e11	0.0256742
$661$	−1.79834e12	−0.366409	−0.183204	−	0.983075i	$-0.558647\pi$
$661$	−1.79834e12	−0.366409	−0.183204	+	0.983075i	$0.558647\pi$
$662$	1.23718e13	2.50364
$663$	0	0
$664$	1.04836e12	0.209292
$665$	−5.90532e11	−0.117097
$666$	−2.75040e12	−0.541703
$667$	−2.80967e12	−0.549653
$668$	7.87076e11	0.152940
$669$	−7.34986e11	−0.141860
$670$	−4.23278e11	−0.0811502
$671$	2.18362e12	0.415839
$672$	−8.12969e11	−0.153784
$673$	1.37693e12	0.258728	0.129364	−	0.991597i	$-0.458706\pi$
$673$	1.37693e12	0.258728	0.129364	+	0.991597i	$0.458706\pi$
$674$	−1.02486e13	−1.91292
$675$	3.44547e12	0.638824
$676$	0	0
$677$	6.49642e11	0.118857	0.0594285	−	0.998233i	$-0.481072\pi$
$677$	6.49642e11	0.118857	0.0594285	+	0.998233i	$0.481072\pi$
$678$	3.37310e12	0.613049
$679$	−7.45828e12	−1.34656
$680$	−1.98230e11	−0.0355532
$681$	−2.01386e12	−0.358813
$682$	6.37181e12	1.12780
$683$	1.10011e12	0.193438	0.0967190	−	0.995312i	$-0.469165\pi$
$683$	1.10011e12	0.193438	0.0967190	+	0.995312i	$0.469165\pi$
$684$	−1.48639e13	−2.59645
$685$	−5.54064e11	−0.0961507
$686$	−1.02913e13	−1.77424
$687$	3.20192e12	0.548409
$688$	5.89869e12	1.00371
$689$	0	0
$690$	8.74044e10	0.0146795
$691$	−7.72289e12	−1.28863	−0.644315	−	0.764760i	$-0.722858\pi$
$691$	−7.72289e12	−1.28863	−0.644315	+	0.764760i	$0.722858\pi$
$692$	5.46071e11	0.0905256
$693$	2.60702e12	0.429383
$694$	−1.04855e13	−1.71581
$695$	3.94832e11	0.0641920
$696$	−5.10016e12	−0.823838
$697$	−1.63505e12	−0.262412
$698$	−1.35119e13	−2.15460
$699$	−2.48617e12	−0.393898
$700$	1.09076e13	1.71707
$701$	1.40436e12	0.219658	0.109829	−	0.993950i	$-0.464970\pi$
$701$	1.40436e12	0.219658	0.109829	+	0.993950i	$0.464970\pi$
$702$	0	0
$703$	−3.74831e12	−0.578810
$704$	−4.64131e12	−0.712137
$705$	−3.31159e10	−0.00504877
$706$	−8.61273e12	−1.30473
$707$	5.39111e12	0.811505
$708$	6.91043e12	1.03361
$709$	−5.19764e12	−0.772499	−0.386250	−	0.922394i	$-0.626230\pi$
$709$	−5.19764e12	−0.772499	−0.386250	+	0.922394i	$0.626230\pi$
$710$	1.73075e12	0.255607
$711$	3.48822e12	0.511907
$712$	5.73387e11	0.0836157
$713$	2.88600e12	0.418209
$714$	1.18814e12	0.171090
$715$	0	0
$716$	−1.47932e13	−2.10355
$717$	−3.57116e12	−0.504630
$718$	1.29400e12	0.181707
$719$	−1.27042e13	−1.77284	−0.886418	−	0.462886i	$-0.846814\pi$
$719$	−1.27042e13	−1.77284	−0.886418	+	0.462886i	$0.846814\pi$
$720$	−2.80238e11	−0.0388625
$721$	2.48016e12	0.341799
$722$	−1.89174e13	−2.59086
$723$	−2.75230e12	−0.374605
$724$	−2.06495e13	−2.79309
$725$	−1.25159e13	−1.68244
$726$	3.14800e12	0.420552
$727$	9.91998e11	0.131706	0.0658531	−	0.997829i	$-0.479023\pi$
$727$	9.91998e11	0.131706	0.0658531	+	0.997829i	$0.479023\pi$
$728$	0	0
$729$	−2.80211e12	−0.367461
$730$	−1.31739e12	−0.171696
$731$	4.39227e12	0.568933
$732$	3.91898e12	0.504514
$733$	−5.54849e12	−0.709916	−0.354958	−	0.934882i	$-0.615505\pi$
$733$	−5.54849e12	−0.709916	−0.354958	+	0.934882i	$0.615505\pi$
$734$	2.95572e12	0.375864
$735$	−2.61791e10	−0.00330873
$736$	−1.24406e12	−0.156275
$737$	2.54663e12	0.317953
$738$	−9.92797e12	−1.23199
$739$	−8.78597e12	−1.08365	−0.541826	−	0.840491i	$-0.682267\pi$
$739$	−8.78597e12	−1.08365	−0.541826	+	0.840491i	$0.682267\pi$
$740$	−4.29717e11	−0.0526792
$741$	0	0
$742$	3.47570e12	0.420944
$743$	−4.04326e12	−0.486724	−0.243362	−	0.969936i	$-0.578250\pi$
$743$	−4.04326e12	−0.486724	−0.243362	+	0.969936i	$0.578250\pi$
$744$	5.23871e12	0.626825
$745$	−1.40014e11	−0.0166521
$746$	−2.48408e13	−2.93658
$747$	1.10357e12	0.129676
$748$	2.60342e12	0.304080
$749$	−3.99451e12	−0.463763
$750$	7.81116e11	0.0901446
$751$	−2.52936e11	−0.0290156	−0.0145078	−	0.999895i	$-0.504618\pi$
$751$	−2.52936e11	−0.0290156	−0.0145078	+	0.999895i	$0.504618\pi$
$752$	−9.25130e11	−0.105493
$753$	−5.16479e12	−0.585431
$754$	0	0
$755$	−4.77765e11	−0.0535122
$756$	9.97448e12	1.11056
$757$	9.99638e12	1.10640	0.553199	−	0.833049i	$-0.313407\pi$
$757$	9.99638e12	1.10640	0.553199	+	0.833049i	$0.313407\pi$
$758$	7.40426e12	0.814649
$759$	−5.25864e11	−0.0575156
$760$	−1.64036e12	−0.178352
$761$	2.98848e12	0.323013	0.161507	−	0.986872i	$-0.448365\pi$
$761$	2.98848e12	0.323013	0.161507	+	0.986872i	$0.448365\pi$
$762$	−3.43418e12	−0.369000
$763$	9.91726e12	1.05933
$764$	1.58528e13	1.68339
$765$	−2.08670e11	−0.0220284
$766$	1.69714e13	1.78110
$767$	0	0
$768$	−5.65858e12	−0.586924
$769$	−1.54887e13	−1.59715	−0.798576	−	0.601894i	$-0.794413\pi$
$769$	−1.54887e13	−1.59715	−0.798576	+	0.601894i	$0.794413\pi$
$770$	6.28038e11	0.0643839
$771$	−3.17948e12	−0.324050
$772$	2.55139e13	2.58523
$773$	−1.07589e13	−1.08383	−0.541915	−	0.840434i	$-0.682300\pi$
$773$	−1.07589e13	−1.08383	−0.541915	+	0.840434i	$0.682300\pi$
$774$	2.66697e13	2.67106
$775$	1.28559e13	1.28010
$776$	−2.07173e13	−2.05095
$777$	1.17990e12	0.116131
$778$	6.47427e12	0.633552
$779$	−1.35301e13	−1.31638
$780$	0	0
$781$	−1.04130e13	−1.00149
$782$	1.81816e12	0.173861
$783$	−1.14452e13	−1.08817
$784$	−7.31343e11	−0.0691351
$785$	−1.54767e12	−0.145467
$786$	−6.32379e12	−0.590985
$787$	−1.29304e13	−1.20151	−0.600755	−	0.799433i	$-0.705133\pi$
$787$	−1.29304e13	−1.20151	−0.600755	+	0.799433i	$0.705133\pi$
$788$	−1.49545e13	−1.38167
$789$	−3.90379e12	−0.358625
$790$	8.40321e11	0.0767579
$791$	1.09778e13	0.997059
$792$	7.24168e12	0.653997
$793$	0	0
$794$	1.12394e13	1.00358
$795$	8.04635e10	0.00714409
$796$	8.31828e12	0.734387
$797$	1.24713e13	1.09484	0.547418	−	0.836859i	$-0.315611\pi$
$797$	1.24713e13	1.09484	0.547418	+	0.836859i	$0.315611\pi$
$798$	9.83185e12	0.858267
$799$	−6.88868e11	−0.0597965
$800$	−5.54175e12	−0.478346
$801$	6.03585e11	0.0518075
$802$	1.69224e13	1.44437
$803$	7.92600e12	0.672719
$804$	4.57049e12	0.385755
$805$	2.84459e11	0.0238747
$806$	0	0
$807$	4.81502e12	0.399639
$808$	1.49752e13	1.23601
$809$	−2.40763e13	−1.97616	−0.988079	−	0.153948i	$-0.950801\pi$
$809$	−2.40763e13	−1.97616	−0.988079	+	0.153948i	$0.950801\pi$
$810$	−1.07801e12	−0.0879913
$811$	−1.14686e13	−0.930928	−0.465464	−	0.885067i	$-0.654112\pi$
$811$	−1.14686e13	−0.930928	−0.465464	+	0.885067i	$0.654112\pi$
$812$	−3.62330e13	−2.92484
$813$	1.43040e12	0.114829
$814$	3.98637e12	0.318249
$815$	−7.95569e10	−0.00631638
$816$	7.68403e11	0.0606713
$817$	3.63462e13	2.85403
$818$	−3.86469e12	−0.301804
$819$	0	0
$820$	−1.55113e12	−0.119808
$821$	2.50113e13	1.92129	0.960643	−	0.277786i	$-0.0896005\pi$
$821$	2.50113e13	1.92129	0.960643	+	0.277786i	$0.0896005\pi$
$822$	9.22470e12	0.704740
$823$	1.29351e13	0.982808	0.491404	−	0.870932i	$-0.336484\pi$
$823$	1.29351e13	0.982808	0.491404	+	0.870932i	$0.336484\pi$
$824$	6.88929e12	0.520597
$825$	−2.34250e12	−0.176051
$826$	3.46773e13	2.59200
$827$	−1.00464e13	−0.746851	−0.373425	−	0.927660i	$-0.621817\pi$
$827$	−1.00464e13	−0.746851	−0.373425	+	0.927660i	$0.621817\pi$
$828$	7.15990e12	0.529384
$829$	8.77304e12	0.645141	0.322570	−	0.946545i	$-0.395453\pi$
$829$	8.77304e12	0.645141	0.322570	+	0.946545i	$0.395453\pi$
$830$	2.65853e11	0.0194442
$831$	−1.51868e12	−0.110474
$832$	0	0
$833$	−5.44571e11	−0.0391879
$834$	−6.57361e12	−0.470497
$835$	9.14353e10	0.00650916
$836$	2.15434e13	1.52541
$837$	1.17561e13	0.827943
$838$	−3.03051e12	−0.212284
$839$	1.54259e13	1.07478	0.537392	−	0.843332i	$-0.319410\pi$
$839$	1.54259e13	1.07478	0.537392	+	0.843332i	$0.319410\pi$
$840$	5.16354e11	0.0357842
$841$	2.70683e13	1.86586
$842$	−2.31593e13	−1.58789
$843$	−4.72537e12	−0.322264
$844$	−1.72010e13	−1.16685
$845$	0	0
$846$	−4.18279e12	−0.280737
$847$	1.02452e13	0.683983
$848$	2.24784e12	0.149274
$849$	−5.08296e12	−0.335762
$850$	8.09914e12	0.532174
$851$	1.80556e12	0.118012
$852$	−1.86884e13	−1.21505
$853$	1.84928e12	0.119600	0.0598002	−	0.998210i	$-0.480954\pi$
$853$	1.84928e12	0.119600	0.0598002	+	0.998210i	$0.480954\pi$
$854$	1.96659e13	1.26518
$855$	−1.72675e12	−0.110505
$856$	−1.10958e13	−0.706361
$857$	−2.34715e13	−1.48637	−0.743185	−	0.669086i	$-0.766686\pi$
$857$	−2.34715e13	−1.48637	−0.743185	+	0.669086i	$0.766686\pi$
$858$	0	0
$859$	1.25121e12	0.0784079	0.0392039	−	0.999231i	$-0.487518\pi$
$859$	1.25121e12	0.0784079	0.0392039	+	0.999231i	$0.487518\pi$
$860$	4.16683e12	0.259754
$861$	4.25902e12	0.264116
$862$	−1.04026e13	−0.641739
$863$	−2.38217e13	−1.46192	−0.730961	−	0.682419i	$-0.760928\pi$
$863$	−2.38217e13	−1.46192	−0.730961	+	0.682419i	$0.760928\pi$
$864$	−5.06768e12	−0.309384
$865$	6.34375e10	0.00385278
$866$	4.40928e13	2.66402
$867$	−5.10563e12	−0.306876
$868$	3.72173e13	2.22539
$869$	−5.05575e12	−0.300744
$870$	−1.29335e12	−0.0765383
$871$	0	0
$872$	2.75478e13	1.61348
$873$	−2.18084e13	−1.27075
$874$	1.50453e13	0.872168
$875$	2.54215e12	0.146611
$876$	1.42249e13	0.816173
$877$	1.35717e13	0.774707	0.387353	−	0.921931i	$-0.373389\pi$
$877$	1.35717e13	0.774707	0.387353	+	0.921931i	$0.373389\pi$
$878$	−6.79601e12	−0.385948
$879$	−1.08375e13	−0.612323
$880$	4.06171e11	0.0228316
$881$	2.38436e12	0.133346	0.0666730	−	0.997775i	$-0.478762\pi$
$881$	2.38436e12	0.133346	0.0666730	+	0.997775i	$0.478762\pi$
$882$	−3.30662e12	−0.183982
$883$	−5.99779e11	−0.0332023	−0.0166011	−	0.999862i	$-0.505285\pi$
$883$	−5.99779e11	−0.0332023	−0.0166011	+	0.999862i	$0.505285\pi$
$884$	0	0
$885$	8.02792e11	0.0439904
$886$	2.50103e12	0.136354
$887$	1.02483e13	0.555897	0.277949	−	0.960596i	$-0.410346\pi$
$887$	1.02483e13	0.555897	0.277949	+	0.960596i	$0.410346\pi$
$888$	3.27747e12	0.176881
$889$	−1.11766e13	−0.600138
$890$	1.45405e11	0.00776828
$891$	6.48579e12	0.344757
$892$	−1.45042e13	−0.767101
$893$	−5.70040e12	−0.299967
$894$	2.33111e12	0.122052
$895$	−1.71854e12	−0.0895274
$896$	−3.31065e13	−1.71604
$897$	0	0
$898$	−3.04642e13	−1.56331
$899$	−4.27050e13	−2.18052
$900$	3.18944e13	1.62040
$901$	1.67378e12	0.0846130
$902$	1.43894e13	0.723791
$903$	−1.14411e13	−0.572628
$904$	3.04937e13	1.51863
$905$	−2.39887e12	−0.118874
$906$	7.95437e12	0.392219
$907$	−2.43855e13	−1.19646	−0.598231	−	0.801323i	$-0.704130\pi$
$907$	−2.43855e13	−1.19646	−0.598231	+	0.801323i	$0.704130\pi$
$908$	−3.97416e13	−1.94026
$909$	1.57639e13	0.765820
$910$	0	0
$911$	2.90386e13	1.39683	0.698415	−	0.715693i	$-0.253889\pi$
$911$	2.90386e13	1.39683	0.698415	+	0.715693i	$0.253889\pi$
$912$	6.35855e12	0.304356
$913$	−1.59949e12	−0.0761841
$914$	−3.40744e13	−1.61499
$915$	4.55272e11	0.0214722
$916$	6.31867e13	2.96549
$917$	−2.05809e13	−0.961173
$918$	7.40630e12	0.344199
$919$	−1.41793e13	−0.655746	−0.327873	−	0.944722i	$-0.606332\pi$
$919$	−1.41793e13	−0.655746	−0.327873	+	0.944722i	$0.606332\pi$
$920$	7.90158e11	0.0363638
$921$	1.06773e12	0.0488984
$922$	8.87378e12	0.404408
$923$	0	0
$924$	−6.78146e12	−0.306055
$925$	8.04299e12	0.361226
$926$	−5.89402e13	−2.63428
$927$	7.25212e12	0.322557
$928$	1.84087e13	0.814812
$929$	3.56246e13	1.56920	0.784601	−	0.620001i	$-0.212868\pi$
$929$	3.56246e13	1.56920	0.784601	+	0.620001i	$0.212868\pi$
$930$	1.32849e12	0.0582349
$931$	−4.50634e12	−0.196585
$932$	−4.90621e13	−2.12998
$933$	−1.30136e13	−0.562250
$934$	−6.23355e13	−2.68025
$935$	3.02442e11	0.0129417
$936$	0	0
$937$	9.35575e12	0.396506	0.198253	−	0.980151i	$-0.436473\pi$
$937$	9.35575e12	0.396506	0.198253	+	0.980151i	$0.436473\pi$
$938$	2.29353e13	0.967366
$939$	−3.78610e12	−0.158927
$940$	−6.53510e11	−0.0273009
$941$	−1.23413e13	−0.513106	−0.256553	−	0.966530i	$-0.582587\pi$
$941$	−1.23413e13	−0.513106	−0.256553	+	0.966530i	$0.582587\pi$
$942$	2.57673e13	1.06620
$943$	6.51742e12	0.268394
$944$	2.24269e13	0.919168
$945$	1.15875e12	0.0472656
$946$	−3.86546e13	−1.56924
$947$	−2.93722e12	−0.118676	−0.0593379	−	0.998238i	$-0.518899\pi$
$947$	−2.93722e12	−0.118676	−0.0593379	+	0.998238i	$0.518899\pi$
$948$	−9.07366e12	−0.364876
$949$	0	0
$950$	6.70206e13	2.66964
$951$	−9.72086e12	−0.385383
$952$	1.07411e13	0.423819
$953$	−3.90544e12	−0.153374	−0.0766870	−	0.997055i	$-0.524434\pi$
$953$	−3.90544e12	−0.153374	−0.0766870	+	0.997055i	$0.524434\pi$
$954$	1.01631e13	0.397247
$955$	1.84163e12	0.0716454
$956$	−7.04733e13	−2.72875
$957$	7.78137e12	0.299883
$958$	5.89375e13	2.26072
$959$	3.00219e13	1.14618
$960$	−9.67687e11	−0.0367718
$961$	1.74255e13	0.659069
$962$	0	0
$963$	−1.16802e13	−0.437655
$964$	−5.43139e13	−2.02565
$965$	2.96398e12	0.110028
$966$	−4.73599e12	−0.174990
$967$	1.06697e13	0.392405	0.196203	−	0.980563i	$-0.437139\pi$
$967$	1.06697e13	0.392405	0.196203	+	0.980563i	$0.437139\pi$
$968$	2.84587e13	1.04178
$969$	4.73469e12	0.172518
$970$	−5.25371e12	−0.190543
$971$	−3.10264e12	−0.112007	−0.0560034	−	0.998431i	$-0.517836\pi$
$971$	−3.10264e12	−0.112007	−0.0560034	+	0.998431i	$0.517836\pi$
$972$	4.46506e13	1.60446
$973$	−2.13939e13	−0.765213
$974$	9.74972e12	0.347118
$975$	0	0
$976$	1.27185e13	0.448655
$977$	4.66167e13	1.63688	0.818438	−	0.574594i	$-0.194840\pi$
$977$	4.66167e13	1.63688	0.818438	+	0.574594i	$0.194840\pi$
$978$	1.32455e12	0.0462961
$979$	−8.74824e11	−0.0304368
$980$	−5.16619e11	−0.0178918
$981$	2.89986e13	0.999694
$982$	−6.04614e13	−2.07480
$983$	3.22316e13	1.10101	0.550505	−	0.834832i	$-0.314435\pi$
$983$	3.22316e13	1.10101	0.550505	+	0.834832i	$0.314435\pi$
$984$	1.18305e13	0.402278
$985$	−1.73728e12	−0.0588040
$986$	−2.69039e13	−0.906502
$987$	1.79438e12	0.0601849
$988$	0	0
$989$	−1.75079e13	−0.581903
$990$	1.83642e12	0.0607594
$991$	−2.25008e13	−0.741081	−0.370540	−	0.928816i	$-0.620828\pi$
$991$	−2.25008e13	−0.741081	−0.370540	+	0.928816i	$0.620828\pi$
$992$	−1.89088e13	−0.619957
$993$	−1.55192e13	−0.506520
$994$	−9.37807e13	−3.04701
$995$	9.66342e11	0.0312556
$996$	−2.87064e12	−0.0924299
$997$	−3.13756e13	−1.00569	−0.502844	−	0.864377i	$-0.667713\pi$
$997$	−3.13756e13	−1.00569	−0.502844	+	0.864377i	$0.667713\pi$
$998$	−2.40442e13	−0.767224
$999$	7.35495e12	0.233633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.10.a.b.1.1		5
13.12	even	2		13.10.a.b.1.5	✓	5
39.38	odd	2		117.10.a.e.1.1		5
52.51	odd	2		208.10.a.h.1.3		5
65.64	even	2		325.10.a.b.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.b.1.5	✓	5	13.12	even	2
117.10.a.e.1.1		5	39.38	odd	2
169.10.a.b.1.1		5	1.1	even	1	trivial
208.10.a.h.1.3		5	52.51	odd	2
325.10.a.b.1.1		5	65.64	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-38.1685 q^{2} +47.8784 q^{3} +944.833 q^{4} +109.762 q^{5} -1827.45 q^{6} -5947.44 q^{7} -16520.6 q^{8} -17390.7 q^{9} +O(q^{10})\)	\(q-38.1685 q^{2} +47.8784 q^{3} +944.833 q^{4} +109.762 q^{5} -1827.45 q^{6} -5947.44 q^{7} -16520.6 q^{8} -17390.7 q^{9} -4189.45 q^{10} +25205.7 q^{11} +45237.1 q^{12} +227005. q^{14} +5255.24 q^{15} +146811. q^{16} +109318. q^{17} +663775. q^{18} +904609. q^{19} +103707. q^{20} -284754. q^{21} -962062. q^{22} -435749. q^{23} -790979. q^{24} -1.94108e6 q^{25} -1.77503e6 q^{27} -5.61934e6 q^{28} +6.44791e6 q^{29} -200584. q^{30} -6.62308e6 q^{31} +2.85499e6 q^{32} +1.20681e6 q^{33} -4.17250e6 q^{34} -652804. q^{35} -1.64313e7 q^{36} -4.14357e6 q^{37} -3.45275e7 q^{38} -1.81333e6 q^{40} -1.49568e7 q^{41} +1.08686e7 q^{42} +4.01789e7 q^{43} +2.38151e7 q^{44} -1.90884e6 q^{45} +1.66319e7 q^{46} -6.30151e6 q^{47} +7.02907e6 q^{48} -4.98153e6 q^{49} +7.40880e7 q^{50} +5.23397e6 q^{51} +1.53111e7 q^{53} +6.77501e7 q^{54} +2.76663e6 q^{55} +9.82552e7 q^{56} +4.33112e7 q^{57} -2.46107e8 q^{58} +1.52760e8 q^{59} +4.96532e6 q^{60} +8.66321e7 q^{61} +2.52793e8 q^{62} +1.03430e8 q^{63} -1.84138e8 q^{64} -4.60620e7 q^{66} +1.01034e8 q^{67} +1.03287e8 q^{68} -2.08630e7 q^{69} +2.49165e7 q^{70} -4.13122e8 q^{71} +2.87304e8 q^{72} +3.14453e8 q^{73} +1.58154e8 q^{74} -9.29357e7 q^{75} +8.54704e8 q^{76} -1.49909e8 q^{77} -2.00580e8 q^{79} +1.61143e7 q^{80} +2.57315e8 q^{81} +5.70879e8 q^{82} -6.34578e7 q^{83} -2.69045e8 q^{84} +1.19990e7 q^{85} -1.53357e9 q^{86} +3.08715e8 q^{87} -4.16412e8 q^{88} -3.47074e7 q^{89} +7.28574e7 q^{90} -4.11710e8 q^{92} -3.17102e8 q^{93} +2.40519e8 q^{94} +9.92918e7 q^{95} +1.36692e8 q^{96} +1.25403e9 q^{97} +1.90137e8 q^{98} -4.38343e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 15 q^{2} + 161 q^{3} + 361 q^{4} - 1803 q^{5} - 5693 q^{6} - 10099 q^{7} - 23151 q^{8} + 61060 q^{9}+O(q^{10}) \) 5 * q - 15 * q^2 + 161 * q^3 + 361 * q^4 - 1803 * q^5 - 5693 * q^6 - 10099 * q^7 - 23151 * q^8 + 61060 * q^9	\( 5 q - 15 q^{2} + 161 q^{3} + 361 q^{4} - 1803 q^{5} - 5693 q^{6} - 10099 q^{7} - 23151 q^{8} + 61060 q^{9} + 84505 q^{10} - 121746 q^{11} + 113389 q^{12} + 8475 q^{14} - 105973 q^{15} - 322463 q^{16} - 495669 q^{17} + 656228 q^{18} + 840738 q^{19} + 1595607 q^{20} + 1599467 q^{21} - 2023594 q^{22} - 592152 q^{23} + 2295657 q^{24} + 1670362 q^{25} + 6847883 q^{27} - 2587955 q^{28} + 10678182 q^{29} + 5491201 q^{30} - 12885296 q^{31} - 3282927 q^{32} - 17278298 q^{33} + 9934079 q^{34} + 8380731 q^{35} - 20483302 q^{36} - 7171823 q^{37} - 25568814 q^{38} - 54359445 q^{40} - 9294012 q^{41} - 69520457 q^{42} + 12831975 q^{43} + 41479074 q^{44} - 26135198 q^{45} + 59319696 q^{46} - 43354215 q^{47} - 86874671 q^{48} + 25249488 q^{49} + 16270770 q^{50} + 16905901 q^{51} + 93231780 q^{53} - 58983719 q^{54} + 99448846 q^{55} + 199599225 q^{56} - 90173382 q^{57} - 151020970 q^{58} - 246496182 q^{59} - 90097913 q^{60} - 132232612 q^{61} + 158135724 q^{62} + 416955202 q^{63} + 91019105 q^{64} - 323733130 q^{66} + 369388534 q^{67} + 238172073 q^{68} - 579986760 q^{69} + 144857425 q^{70} - 212150457 q^{71} + 415774278 q^{72} + 252729806 q^{73} + 192105957 q^{74} - 752457788 q^{75} + 953775990 q^{76} + 449666118 q^{77} - 1247271728 q^{79} - 900649725 q^{80} - 317713115 q^{81} + 169559388 q^{82} - 1696894296 q^{83} - 1247983739 q^{84} + 775363765 q^{85} - 3291621459 q^{86} - 614530466 q^{87} - 220227222 q^{88} + 753854382 q^{89} + 2296265882 q^{90} + 13876128 q^{92} + 892784668 q^{93} + 272071215 q^{94} + 1442632962 q^{95} - 930612847 q^{96} - 3824606 q^{97} - 1570614816 q^{98} - 3016199848 q^{99}+O(q^{100}) \) 5 * q - 15 * q^2 + 161 * q^3 + 361 * q^4 - 1803 * q^5 - 5693 * q^6 - 10099 * q^7 - 23151 * q^8 + 61060 * q^9 + 84505 * q^10 - 121746 * q^11 + 113389 * q^12 + 8475 * q^14 - 105973 * q^15 - 322463 * q^16 - 495669 * q^17 + 656228 * q^18 + 840738 * q^19 + 1595607 * q^20 + 1599467 * q^21 - 2023594 * q^22 - 592152 * q^23 + 2295657 * q^24 + 1670362 * q^25 + 6847883 * q^27 - 2587955 * q^28 + 10678182 * q^29 + 5491201 * q^30 - 12885296 * q^31 - 3282927 * q^32 - 17278298 * q^33 + 9934079 * q^34 + 8380731 * q^35 - 20483302 * q^36 - 7171823 * q^37 - 25568814 * q^38 - 54359445 * q^40 - 9294012 * q^41 - 69520457 * q^42 + 12831975 * q^43 + 41479074 * q^44 - 26135198 * q^45 + 59319696 * q^46 - 43354215 * q^47 - 86874671 * q^48 + 25249488 * q^49 + 16270770 * q^50 + 16905901 * q^51 + 93231780 * q^53 - 58983719 * q^54 + 99448846 * q^55 + 199599225 * q^56 - 90173382 * q^57 - 151020970 * q^58 - 246496182 * q^59 - 90097913 * q^60 - 132232612 * q^61 + 158135724 * q^62 + 416955202 * q^63 + 91019105 * q^64 - 323733130 * q^66 + 369388534 * q^67 + 238172073 * q^68 - 579986760 * q^69 + 144857425 * q^70 - 212150457 * q^71 + 415774278 * q^72 + 252729806 * q^73 + 192105957 * q^74 - 752457788 * q^75 + 953775990 * q^76 + 449666118 * q^77 - 1247271728 * q^79 - 900649725 * q^80 - 317713115 * q^81 + 169559388 * q^82 - 1696894296 * q^83 - 1247983739 * q^84 + 775363765 * q^85 - 3291621459 * q^86 - 614530466 * q^87 - 220227222 * q^88 + 753854382 * q^89 + 2296265882 * q^90 + 13876128 * q^92 + 892784668 * q^93 + 272071215 * q^94 + 1442632962 * q^95 - 930612847 * q^96 - 3824606 * q^97 - 1570614816 * q^98 - 3016199848 * q^99

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