LMFDB - Embedded newform 29.10.b.a.28.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,10,Mod(28,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("29.28");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	29.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$14.9360392488$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			28.12
Character	$\chi$	$=$	29.28
Dual form			29.10.b.a.28.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.67374i q^{2} +77.6458i q^{3} +467.461 q^{4} -531.517 q^{5} -518.188 q^{6} +5986.73 q^{7} +6536.67i q^{8} +13654.1 q^{9} +O(q^{10})$	\(q+6.67374i q^{2} +77.6458i q^{3} +467.461 q^{4} -531.517 q^{5} -518.188 q^{6} +5986.73 q^{7} +6536.67i q^{8} +13654.1 q^{9} -3547.20i q^{10} -35675.4i q^{11} +36296.4i q^{12} -39313.0 q^{13} +39953.9i q^{14} -41270.0i q^{15} +195716. q^{16} +656546. i q^{17} +91124.1i q^{18} +367464. i q^{19} -248464. q^{20} +464844. i q^{21} +238089. q^{22} +1.94156e6 q^{23} -507545. q^{24} -1.67061e6 q^{25} -262365. i q^{26} +2.58849e6i q^{27} +2.79856e6 q^{28} +(-1.14619e6 + 3.63227e6i) q^{29} +275426. q^{30} -674359. i q^{31} +4.65293e6i q^{32} +2.77005e6 q^{33} -4.38162e6 q^{34} -3.18205e6 q^{35} +6.38278e6 q^{36} -2.24196e7i q^{37} -2.45236e6 q^{38} -3.05249e6i q^{39} -3.47435e6i q^{40} +1.38767e7i q^{41} -3.10225e6 q^{42} -2.78011e7i q^{43} -1.66769e7i q^{44} -7.25740e6 q^{45} +1.29574e7i q^{46} -3.13351e7i q^{47} +1.51965e7i q^{48} -4.51271e6 q^{49} -1.11492e7i q^{50} -5.09781e7 q^{51} -1.83773e7 q^{52} +7.62713e7 q^{53} -1.72749e7 q^{54} +1.89621e7i q^{55} +3.91332e7i q^{56} -2.85320e7 q^{57} +(-2.42408e7 - 7.64935e6i) q^{58} -1.45282e6 q^{59} -1.92921e7i q^{60} -6.58800e7i q^{61} +4.50050e6 q^{62} +8.17435e7 q^{63} +6.91542e7 q^{64} +2.08955e7 q^{65} +1.84866e7i q^{66} +1.66618e8 q^{67} +3.06910e8i q^{68} +1.50754e8i q^{69} -2.12361e7i q^{70} -1.87382e8 q^{71} +8.92525e7i q^{72} +2.99303e8i q^{73} +1.49623e8 q^{74} -1.29716e8i q^{75} +1.71775e8i q^{76} -2.13579e8i q^{77} +2.03715e7 q^{78} -3.49735e8i q^{79} -1.04026e8 q^{80} +6.77690e7 q^{81} -9.26097e7 q^{82} -6.55911e8 q^{83} +2.17297e8i q^{84} -3.48965e8i q^{85} +1.85537e8 q^{86} +(-2.82031e8 - 8.89965e7i) q^{87} +2.33199e8 q^{88} -1.20605e8i q^{89} -4.84340e7i q^{90} -2.35356e8 q^{91} +9.07602e8 q^{92} +5.23612e7 q^{93} +2.09122e8 q^{94} -1.95313e8i q^{95} -3.61281e8 q^{96} -6.52780e8i q^{97} -3.01167e7i q^{98} -4.87117e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9}+O(q^{10}) $ 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9	$ 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9} - 244222 q^{13} + 1246804 q^{16} - 1658748 q^{20} + 822328 q^{22} - 874956 q^{23} + 8668172 q^{24} + 5307748 q^{25} - 620352 q^{28} - 2425374 q^{29} - 8942448 q^{30} + 10134274 q^{33} - 37785784 q^{34} - 20790348 q^{35} + 34550680 q^{36} - 30663552 q^{38} + 56872008 q^{42} - 43877176 q^{45} - 131743922 q^{49} - 6194732 q^{51} + 342496580 q^{52} + 34886610 q^{53} + 116488784 q^{54} - 308361676 q^{57} + 342193888 q^{58} + 175799052 q^{59} - 484313328 q^{62} - 190643424 q^{63} - 419498924 q^{64} - 149739966 q^{65} - 508277640 q^{67} + 263144256 q^{71} + 435201408 q^{74} + 1065897336 q^{78} + 2990464236 q^{80} - 129895134 q^{81} - 527065064 q^{82} + 1555989756 q^{83} - 3422424120 q^{86} + 2176720604 q^{87} - 387386068 q^{88} - 1493579244 q^{91} - 1262849472 q^{92} + 2042413382 q^{93} + 166226488 q^{94} - 6686432820 q^{96}+O(q^{100}) $ 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9 - 244222 * q^13 + 1246804 * q^16 - 1658748 * q^20 + 822328 * q^22 - 874956 * q^23 + 8668172 * q^24 + 5307748 * q^25 - 620352 * q^28 - 2425374 * q^29 - 8942448 * q^30 + 10134274 * q^33 - 37785784 * q^34 - 20790348 * q^35 + 34550680 * q^36 - 30663552 * q^38 + 56872008 * q^42 - 43877176 * q^45 - 131743922 * q^49 - 6194732 * q^51 + 342496580 * q^52 + 34886610 * q^53 + 116488784 * q^54 - 308361676 * q^57 + 342193888 * q^58 + 175799052 * q^59 - 484313328 * q^62 - 190643424 * q^63 - 419498924 * q^64 - 149739966 * q^65 - 508277640 * q^67 + 263144256 * q^71 + 435201408 * q^74 + 1065897336 * q^78 + 2990464236 * q^80 - 129895134 * q^81 - 527065064 * q^82 + 1555989756 * q^83 - 3422424120 * q^86 + 2176720604 * q^87 - 387386068 * q^88 - 1493579244 * q^91 - 1262849472 * q^92 + 2042413382 * q^93 + 166226488 * q^94 - 6686432820 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			6.67374i			0.294940i	0.989067	+	0.147470i	$0.0471130\pi$
$2$			6.67374i			0.294940i	−0.989067	+	0.147470i	$0.952887\pi$
$3$			77.6458i			0.553442i	0.960950	+	0.276721i	$0.0892478\pi$
$3$			77.6458i			0.553442i	−0.960950	+	0.276721i	$0.910752\pi$
$4$	467.461			0.913010
$5$	−531.517			−0.380322			−0.190161	−	0.981753i	$-0.560901\pi$
$5$	−531.517			−0.380322			−0.190161	+	0.981753i	$0.560901\pi$
$6$	−518.188			−0.163232
$7$	5986.73			0.942428			0.471214	−	0.882019i	$-0.343816\pi$
$7$	5986.73			0.942428			0.471214	+	0.882019i	$0.343816\pi$
$8$			6536.67i			0.564224i
$9$	13654.1			0.693702
$10$		−	3547.20i		−	0.112172i
$11$		−	35675.4i		−	0.734687i	−0.930085	−	0.367343i	$-0.880267\pi$
$11$		−	35675.4i		−	0.734687i	0.930085	−	0.367343i	$-0.119733\pi$
$12$			36296.4i			0.505298i
$13$	−39313.0			−0.381761			−0.190881	−	0.981613i	$-0.561134\pi$
$13$	−39313.0			−0.381761			−0.190881	+	0.981613i	$0.561134\pi$
$14$			39953.9i			0.277960i
$15$		−	41270.0i		−	0.210487i
$16$	195716.			0.746598
$17$			656546.i			1.90654i	0.302124	+	0.953269i	$0.402304\pi$
$17$			656546.i			1.90654i	−0.302124	+	0.953269i	$0.597696\pi$
$18$			91124.1i			0.204601i
$19$			367464.i			0.646880i	0.946249	+	0.323440i	$0.104839\pi$
$19$			367464.i			0.646880i	−0.946249	+	0.323440i	$0.895161\pi$
$20$	−248464.			−0.347238
$21$			464844.i			0.521580i
$22$	238089.			0.216689
$23$	1.94156e6			1.44669			0.723343	−	0.690488i	$-0.242604\pi$
$23$	1.94156e6			1.44669			0.723343	+	0.690488i	$0.242604\pi$
$24$	−507545.			−0.312265
$25$	−1.67061e6			−0.855355
$26$		−	262365.i		−	0.112597i
$27$			2.58849e6i			0.937366i
$28$	2.79856e6			0.860446
$29$	−1.14619e6	+	3.63227e6i	−0.300929	+	0.953647i
$29$	−1.14619e6	+	3.63227e6i	−0.300929	+	0.953647i
$30$	275426.			0.0620810
$31$		−	674359.i		−	0.131149i	−0.997848	−	0.0655743i	$-0.979112\pi$
$31$		−	674359.i		−	0.131149i	0.997848	−	0.0655743i	$-0.0208879\pi$
$32$			4.65293e6i			0.784426i
$33$	2.77005e6			0.406607
$34$	−4.38162e6			−0.562315
$35$	−3.18205e6			−0.358427
$36$	6.38278e6			0.633357
$37$		−	2.24196e7i		−	1.96662i	−0.181940	−	0.983310i	$-0.558238\pi$
$37$		−	2.24196e7i		−	1.96662i	0.181940	−	0.983310i	$-0.441762\pi$
$38$	−2.45236e6			−0.190791
$39$		−	3.05249e6i		−	0.211283i
$40$		−	3.47435e6i		−	0.214587i
$41$			1.38767e7i			0.766937i	0.923554	+	0.383469i	$0.125271\pi$
$41$			1.38767e7i			0.766937i	−0.923554	+	0.383469i	$0.874729\pi$
$42$	−3.10225e6			−0.153835
$43$		−	2.78011e7i		−	1.24009i	−0.784566	−	0.620045i	$-0.787114\pi$
$43$		−	2.78011e7i		−	1.24009i	0.784566	−	0.620045i	$-0.212886\pi$
$44$		−	1.66769e7i		−	0.670777i
$45$	−7.25740e6			−0.263830
$46$			1.29574e7i			0.426686i
$47$		−	3.13351e7i		−	0.936677i	−0.883549	−	0.468339i	$-0.844853\pi$
$47$		−	3.13351e7i		−	0.936677i	0.883549	−	0.468339i	$-0.155147\pi$
$48$			1.51965e7i			0.413199i
$49$	−4.51271e6			−0.111829
$50$		−	1.11492e7i		−	0.252279i
$51$	−5.09781e7			−1.05516
$52$	−1.83773e7			−0.348552
$53$	7.62713e7			1.32776			0.663880	−	0.747839i	$-0.268908\pi$
$53$	7.62713e7			1.32776			0.663880	+	0.747839i	$0.268908\pi$
$54$	−1.72749e7			−0.276467
$55$			1.89621e7i			0.279418i
$56$			3.91332e7i			0.531741i
$57$	−2.85320e7			−0.358011
$58$	−2.42408e7	−	7.64935e6i	−0.281269	−	0.0887561i
$59$	−1.45282e6			−0.0156091			−0.00780453	−	0.999970i	$-0.502484\pi$
$59$	−1.45282e6			−0.0156091			−0.00780453	+	0.999970i	$0.502484\pi$
$60$		−	1.92921e7i		−	0.192176i
$61$		−	6.58800e7i		−	0.609213i	−0.952478	−	0.304607i	$-0.901475\pi$
$61$		−	6.58800e7i		−	0.609213i	0.952478	−	0.304607i	$-0.0985250\pi$
$62$	4.50050e6			0.0386810
$63$	8.17435e7			0.653764
$64$	6.91542e7			0.515239
$65$	2.08955e7			0.145192
$66$			1.84866e7i			0.119925i
$67$	1.66618e8			1.01015			0.505074	−	0.863076i	$-0.331465\pi$
$67$	1.66618e8			1.01015			0.505074	+	0.863076i	$0.331465\pi$
$68$			3.06910e8i			1.74069i
$69$			1.50754e8i			0.800658i
$70$		−	2.12361e7i		−	0.105714i
$71$	−1.87382e8			−0.875115			−0.437558	−	0.899190i	$-0.644156\pi$
$71$	−1.87382e8			−0.875115			−0.437558	+	0.899190i	$0.644156\pi$
$72$			8.92525e7i			0.391403i
$73$			2.99303e8i			1.23355i	0.787138	+	0.616777i	$0.211562\pi$
$73$			2.99303e8i			1.23355i	−0.787138	+	0.616777i	$0.788438\pi$
$74$	1.49623e8			0.580035
$75$		−	1.29716e8i		−	0.473389i
$76$			1.71775e8i			0.590608i
$77$		−	2.13579e8i		−	0.692390i
$78$	2.03715e7			0.0623158
$79$		−	3.49735e8i		−	1.01022i	−0.863054	−	0.505111i	$-0.831452\pi$
$79$		−	3.49735e8i		−	1.01022i	0.863054	−	0.505111i	$-0.168548\pi$
$80$	−1.04026e8			−0.283948
$81$	6.77690e7			0.174924
$82$	−9.26097e7			−0.226201
$83$	−6.55911e8			−1.51703			−0.758514	−	0.651657i	$-0.774074\pi$
$83$	−6.55911e8			−1.51703			−0.758514	+	0.651657i	$0.774074\pi$
$84$			2.17297e8i			0.476207i
$85$		−	3.48965e8i		−	0.725099i
$86$	1.85537e8			0.365753
$87$	−2.82031e8	−	8.89965e7i	−0.527788	−	0.166547i
$88$	2.33199e8			0.414528
$89$		−	1.20605e8i		−	0.203756i	−0.994797	−	0.101878i	$-0.967515\pi$
$89$		−	1.20605e8i		−	0.203756i	0.994797	−	0.101878i	$-0.0324851\pi$
$90$		−	4.84340e7i		−	0.0778142i
$91$	−2.35356e8			−0.359782
$92$	9.07602e8			1.32084
$93$	5.23612e7			0.0725832
$94$	2.09122e8			0.276264
$95$		−	1.95313e8i		−	0.246023i
$96$	−3.61281e8			−0.434134
$97$		−	6.52780e8i		−	0.748676i	−0.927292	−	0.374338i	$-0.877870\pi$
$97$		−	6.52780e8i		−	0.748676i	0.927292	−	0.374338i	$-0.122130\pi$
$98$		−	3.01167e7i		−	0.0329830i
$99$		−	4.87117e8i		−	0.509654i
$100$	−7.80948e8			−0.780948
$101$		−	5.96162e8i		−	0.570057i	−0.958519	−	0.285029i	$-0.907997\pi$
$101$		−	5.96162e8i		−	0.570057i	0.958519	−	0.285029i	$-0.0920031\pi$
$102$		−	3.40214e8i		−	0.311209i
$103$	1.42147e9			1.24443			0.622214	−	0.782848i	$-0.286234\pi$
$103$	1.42147e9			1.24443			0.622214	+	0.782848i	$0.286234\pi$
$104$		−	2.56976e8i		−	0.215399i
$105$		−	2.47072e8i		−	0.198368i
$106$			5.09015e8i			0.391610i
$107$	−1.62881e9			−1.20128			−0.600639	−	0.799520i	$-0.705087\pi$
$107$	−1.62881e9			−1.20128			−0.600639	+	0.799520i	$0.705087\pi$
$108$			1.21002e9i			0.855825i
$109$	−1.71786e9			−1.16565			−0.582826	−	0.812597i	$-0.698053\pi$
$109$	−1.71786e9			−1.16565			−0.582826	+	0.812597i	$0.698053\pi$
$110$	−1.26548e8			−0.0824116
$111$	1.74079e9			1.08841
$112$	1.17170e9			0.703615
$113$		−	1.91764e9i		−	1.10640i	−0.833047	−	0.553202i	$-0.813406\pi$
$113$		−	1.91764e9i		−	1.10640i	0.833047	−	0.553202i	$-0.186594\pi$
$114$		−	1.90415e8i		−	0.105592i
$115$	−1.03197e9			−0.550208
$116$	−5.35798e8	+	1.69795e9i	−0.274751	+	0.870689i
$117$	−5.36785e8			−0.264828
$118$		−	9.69572e6i		−	0.00460374i
$119$			3.93056e9i			1.79677i
$120$	2.69769e8			0.118762
$121$	1.08521e9			0.460235
$122$	4.39666e8			0.179682
$123$	−1.07747e9			−0.424455
$124$		−	3.15237e8i		−	0.119740i
$125$	1.92608e9			0.705633
$126$			5.45535e8i			0.192821i
$127$			9.00363e8i			0.307115i	0.988140	+	0.153557i	$0.0490730\pi$
$127$			9.00363e8i			0.307115i	−0.988140	+	0.153557i	$0.950927\pi$
$128$			2.84382e9i			0.936391i
$129$	2.15864e9			0.686319
$130$			1.39451e8i			0.0428231i
$131$		−	9.72351e8i		−	0.288471i	−0.989543	−	0.144236i	$-0.953928\pi$
$131$		−	9.72351e8i		−	0.288471i	0.989543	−	0.144236i	$-0.0460723\pi$
$132$	1.29489e9			0.371236
$133$			2.19991e9i			0.609638i
$134$			1.11196e9i			0.297933i
$135$		−	1.37582e9i		−	0.356501i
$136$	−4.29163e9			−1.07571
$137$		−	8.22848e7i		−	0.0199562i	−0.999950	−	0.00997809i	$-0.996824\pi$
$137$		−	8.22848e7i		−	0.0199562i	0.999950	−	0.00997809i	$-0.00317618\pi$
$138$	−1.00609e9			−0.236146
$139$	4.49972e9			1.02239			0.511197	−	0.859463i	$-0.329202\pi$
$139$	4.49972e9			1.02239			0.511197	+	0.859463i	$0.329202\pi$
$140$	−1.48748e9			−0.327247
$141$	2.43304e9			0.518397
$142$		−	1.25054e9i		−	0.258107i
$143$			1.40251e9i			0.280475i
$144$	2.67233e9			0.517916
$145$	6.09217e8	−	1.93061e9i	0.114450	−	0.362693i
$146$	−1.99747e9			−0.363825
$147$		−	3.50393e8i		−	0.0618910i
$148$		−	1.04803e10i		−	1.79554i
$149$	−4.61124e9			−0.766443			−0.383221	−	0.923657i	$-0.625185\pi$
$149$	−4.61124e9			−0.766443			−0.383221	+	0.923657i	$0.625185\pi$
$150$	8.65692e8			0.139622
$151$	−8.48355e9			−1.32795			−0.663975	−	0.747755i	$-0.731132\pi$
$151$	−8.48355e9			−1.32795			−0.663975	+	0.747755i	$0.731132\pi$
$152$	−2.40199e9			−0.364985
$153$			8.96457e9i			1.32257i
$154$	1.42537e9			0.204214
$155$			3.58433e8i			0.0498788i
$156$		−	1.42692e9i		−	0.192903i
$157$		−	1.10744e10i		−	1.45470i	−0.686268	−	0.727349i	$-0.740752\pi$
$157$		−	1.10744e10i		−	1.45470i	0.686268	−	0.727349i	$-0.259248\pi$
$158$	2.33404e9			0.297955
$159$			5.92215e9i			0.734839i
$160$		−	2.47311e9i		−	0.298335i
$161$	1.16236e10			1.36340
$162$			4.52273e8i			0.0515921i
$163$		−	1.14130e10i		−	1.26635i	−0.774007	−	0.633177i	$-0.781750\pi$
$163$		−	1.14130e10i		−	1.26635i	0.774007	−	0.633177i	$-0.218250\pi$
$164$			6.48683e9i			0.700221i
$165$	−1.47233e9			−0.154642
$166$		−	4.37738e9i		−	0.447433i
$167$	−7.50314e9			−0.746481			−0.373241	−	0.927735i	$-0.621753\pi$
$167$	−7.50314e9			−0.746481			−0.373241	+	0.927735i	$0.621753\pi$
$168$	−3.03853e9			−0.294288
$169$	−9.05898e9			−0.854259
$170$	2.32890e9			0.213861
$171$			5.01740e9i			0.448742i
$172$		−	1.29959e10i		−	1.13222i
$173$	1.32608e10			1.12554			0.562772	−	0.826612i	$-0.309735\pi$
$173$	1.32608e10			1.12554			0.562772	+	0.826612i	$0.309735\pi$
$174$	5.93940e8	−	1.88220e9i	0.0491214	−	0.155666i
$175$	−1.00015e10			−0.806110
$176$		−	6.98226e9i		−	0.548516i
$177$		−	1.12805e8i		−	0.00863872i
$178$	8.04885e8			0.0600957
$179$	6.16964e9			0.449181			0.224591	−	0.974453i	$-0.427896\pi$
$179$	6.16964e9			0.449181			0.224591	+	0.974453i	$0.427896\pi$
$180$	−3.39255e9			−0.240880
$181$	−1.81565e10			−1.25741			−0.628706	−	0.777643i	$-0.716415\pi$
$181$	−1.81565e10			−1.25741			−0.628706	+	0.777643i	$0.716415\pi$
$182$		−	1.57071e9i		−	0.106114i
$183$	5.11530e9			0.337164
$184$			1.26913e10i			0.816255i
$185$			1.19164e10i			0.747950i
$186$			3.49445e8i			0.0214077i
$187$	2.34226e10			1.40071
$188$		−	1.46479e10i		−	0.855196i
$189$			1.54966e10i			0.883400i
$190$	1.30347e9			0.0725621
$191$			2.35317e10i			1.27939i	0.768628	+	0.639696i	$0.220940\pi$
$191$			2.35317e10i			1.27939i	−0.768628	+	0.639696i	$0.779060\pi$
$192$			5.36953e9i			0.285155i
$193$			7.75957e9i			0.402559i	0.979534	+	0.201280i	$0.0645100\pi$
$193$			7.75957e9i			0.402559i	−0.979534	+	0.201280i	$0.935490\pi$
$194$	4.35648e9			0.220815
$195$			1.62245e9i			0.0803555i
$196$	−2.10952e9			−0.102101
$197$	−1.60842e10			−0.760854			−0.380427	−	0.924811i	$-0.624223\pi$
$197$	−1.60842e10			−0.760854			−0.380427	+	0.924811i	$0.624223\pi$
$198$	3.25089e9			0.150317
$199$	2.22934e10			1.00772			0.503858	−	0.863786i	$-0.331913\pi$
$199$	2.22934e10			1.00772			0.503858	+	0.863786i	$0.331913\pi$
$200$		−	1.09203e10i		−	0.482612i
$201$			1.29372e10i			0.559058i
$202$	3.97863e9			0.168133
$203$	−6.86190e9	+	2.17454e10i	−0.283604	+	0.898743i
$204$	−2.38303e10			−0.963370
$205$		−	7.37571e9i		−	0.291683i
$206$			9.48650e9i			0.367032i
$207$	2.65103e10			1.00357
$208$	−7.69420e9			−0.285022
$209$	1.31094e10			0.475254
$210$	1.64890e9			0.0585069
$211$		−	2.72088e9i		−	0.0945013i	−0.998883	−	0.0472507i	$-0.984954\pi$
$211$		−	2.72088e9i		−	0.0945013i	0.998883	−	0.0472507i	$-0.0150460\pi$
$212$	3.56539e10			1.21226
$213$		−	1.45494e10i		−	0.484326i
$214$		−	1.08703e10i		−	0.354305i
$215$			1.47767e10i			0.471634i
$216$	−1.69201e10			−0.528884
$217$		−	4.03720e9i		−	0.123598i
$218$		−	1.14646e10i		−	0.343798i
$219$	−2.32396e10			−0.682701
$220$			8.86405e9i			0.255111i
$221$		−	2.58108e10i		−	0.727842i
$222$			1.16176e10i			0.321016i
$223$	−1.79701e10			−0.486607			−0.243303	−	0.969950i	$-0.578231\pi$
$223$	−1.79701e10			−0.486607			−0.243303	+	0.969950i	$0.578231\pi$
$224$			2.78558e10i			0.739265i
$225$	−2.28108e10			−0.593361
$226$	1.27978e10			0.326323
$227$	−2.54851e10			−0.637045			−0.318522	−	0.947915i	$-0.603187\pi$
$227$	−2.54851e10			−0.637045			−0.318522	+	0.947915i	$0.603187\pi$
$228$	−1.33376e10			−0.326867
$229$		−	7.92518e10i		−	1.90436i	−0.305536	−	0.952180i	$-0.598836\pi$
$229$		−	7.92518e10i		−	1.90436i	0.305536	−	0.952180i	$-0.401164\pi$
$230$		−	6.88710e9i		−	0.162278i
$231$	1.65835e10			0.383198
$232$	−2.37430e10	−	7.49224e9i	−0.538070	−	0.169791i
$233$	2.67518e10			0.594636			0.297318	−	0.954779i	$-0.403908\pi$
$233$	2.67518e10			0.594636			0.297318	+	0.954779i	$0.403908\pi$
$234$		−	3.58237e9i		−	0.0781085i
$235$			1.66551e10i			0.356240i
$236$	−6.79136e8			−0.0142512
$237$	2.71554e10			0.559099
$238$	−2.62316e10			−0.529941
$239$	2.16718e10			0.429639			0.214819	−	0.976654i	$-0.431084\pi$
$239$	2.16718e10			0.429639			0.214819	+	0.976654i	$0.431084\pi$
$240$		−	8.07721e9i		−	0.157149i
$241$	−4.50784e10			−0.860779			−0.430390	−	0.902643i	$-0.641624\pi$
$241$	−4.50784e10			−0.860779			−0.430390	+	0.902643i	$0.641624\pi$
$242$			7.24241e9i			0.135742i
$243$			5.62112e10i			1.03418i
$244$		−	3.07963e10i		−	0.556218i
$245$	2.39858e9			0.0425312
$246$		−	7.19075e9i		−	0.125189i
$247$		−	1.44461e10i		−	0.246954i
$248$	4.40806e9			0.0739972
$249$		−	5.09287e10i		−	0.839587i
$250$			1.28541e10i			0.208120i
$251$		−	2.98852e10i		−	0.475253i	−0.971357	−	0.237626i	$-0.923631\pi$
$251$		−	2.98852e10i		−	0.475253i	0.971357	−	0.237626i	$-0.0763694\pi$
$252$	3.82119e10			0.596893
$253$		−	6.92659e10i		−	1.06286i
$254$	−6.00879e9			−0.0905806
$255$	2.70957e10			0.401300
$256$	1.64280e10			0.239059
$257$	−4.74121e10			−0.677938			−0.338969	−	0.940798i	$-0.610078\pi$
$257$	−4.74121e10			−0.677938			−0.338969	+	0.940798i	$0.610078\pi$
$258$			1.44062e10i			0.202423i
$259$		−	1.34220e11i		−	1.85340i
$260$	9.76786e9			0.132562
$261$	−1.56502e10	+	4.95955e10i	−0.208755	+	0.661546i
$262$	6.48922e9			0.0850818
$263$		−	4.76220e10i		−	0.613771i	−0.951746	−	0.306886i	$-0.900713\pi$
$263$		−	4.76220e10i		−	0.613771i	0.951746	−	0.306886i	$-0.0992869\pi$
$264$			1.81069e10i			0.229417i
$265$	−4.05395e10			−0.504977
$266$	−1.46816e10			−0.179807
$267$	9.36445e9			0.112767
$268$	7.78874e10			0.922275
$269$			1.07090e11i			1.24699i	0.781827	+	0.623495i	$0.214288\pi$
$269$			1.07090e11i			1.24699i	−0.781827	+	0.623495i	$0.785712\pi$
$270$	9.18190e9			0.105147
$271$			8.11543e10i			0.914007i	0.889465	+	0.457004i	$0.151077\pi$
$271$			8.11543e10i			0.914007i	−0.889465	+	0.457004i	$0.848923\pi$
$272$			1.28497e11i			1.42342i
$273$		−	1.82744e10i		−	0.199119i
$274$	5.49148e8			0.00588588
$275$			5.95999e10i			0.628418i
$276$			7.04715e10i			0.731009i
$277$	1.85325e10			0.189136			0.0945680	−	0.995518i	$-0.469853\pi$
$277$	1.85325e10			0.189136			0.0945680	+	0.995518i	$0.469853\pi$
$278$			3.00299e10i			0.301545i
$279$		−	9.20779e9i		−	0.0909780i
$280$		−	2.08000e10i		−	0.202233i
$281$	3.91971e10			0.375038			0.187519	−	0.982261i	$-0.439955\pi$
$281$	3.91971e10			0.375038			0.187519	+	0.982261i	$0.439955\pi$
$282$			1.62374e10i			0.152896i
$283$	9.09678e10			0.843041			0.421520	−	0.906819i	$-0.361497\pi$
$283$	9.09678e10			0.843041			0.421520	+	0.906819i	$0.361497\pi$
$284$	−8.75938e10			−0.798989
$285$	1.51653e10			0.136160
$286$	−9.35999e9			−0.0827233
$287$			8.30762e10i			0.722783i
$288$			6.35317e10i			0.544157i
$289$	−3.12465e11			−2.63488
$290$	1.28844e10	+	4.06576e9i	0.106973	+	0.0337560i
$291$	5.06856e10			0.414349
$292$			1.39912e11i			1.12625i
$293$		−	1.65979e11i		−	1.31568i	−0.753158	−	0.657839i	$-0.771471\pi$
$293$		−	1.65979e11i		−	1.31568i	0.753158	−	0.657839i	$-0.228529\pi$
$294$	2.33843e9			0.0182542
$295$	7.72197e8			0.00593648
$296$	1.46550e11			1.10961
$297$	9.23455e10			0.688671
$298$		−	3.07742e10i		−	0.226055i
$299$	−7.63285e10			−0.552289
$300$		−	6.06373e10i		−	0.432209i
$301$		−	1.66437e11i		−	1.16870i
$302$		−	5.66170e10i		−	0.391666i
$303$	4.62895e10			0.315494
$304$			7.19186e10i			0.482959i
$305$			3.50163e10i			0.231697i
$306$	−5.98272e10			−0.390079
$307$			1.07124e11i			0.688275i	0.938919	+	0.344138i	$0.111829\pi$
$307$			1.07124e11i			0.688275i	−0.938919	+	0.344138i	$0.888171\pi$
$308$		−	9.98400e10i		−	0.632159i
$309$			1.10371e11i			0.688719i
$310$	−2.39209e9			−0.0147113
$311$			3.51421e10i			0.213013i	0.994312	+	0.106506i	$0.0339665\pi$
$311$			3.51421e10i			0.213013i	−0.994312	+	0.106506i	$0.966034\pi$
$312$	1.99531e10			0.119211
$313$	2.07262e11			1.22059			0.610296	−	0.792174i	$-0.291051\pi$
$313$	2.07262e11			1.22059			0.610296	+	0.792174i	$0.291051\pi$
$314$	7.39078e10			0.429049
$315$	−4.34481e10			−0.248641
$316$		−	1.63487e11i		−	0.922343i
$317$			5.13274e8i			0.00285484i	0.999999	+	0.00142742i	$0.000454362\pi$
$317$			5.13274e8i			0.00285484i	−0.999999	+	0.00142742i	$0.999546\pi$
$318$	−3.95229e10			−0.216734
$319$	1.29583e11	+	4.08907e10i	0.700632	+	0.221089i
$320$	−3.67566e10			−0.195957
$321$		−	1.26470e11i		−	0.664838i
$322$			7.75726e10i			0.402121i
$323$	−2.41257e11			−1.23330
$324$	3.16794e10			0.159707
$325$	6.56770e10			0.326541
$326$	7.61674e10			0.373499
$327$		−	1.33385e11i		−	0.645121i
$328$	−9.07076e10			−0.432724
$329$		−	1.87594e11i		−	0.882751i
$330$		−	9.82593e9i		−	0.0456101i
$331$			3.38724e11i			1.55103i	0.631328	+	0.775516i	$0.282510\pi$
$331$			3.38724e11i			1.55103i	−0.631328	+	0.775516i	$0.717490\pi$
$332$	−3.06613e11			−1.38506
$333$		−	3.06120e11i		−	1.36425i
$334$		−	5.00740e10i		−	0.220168i
$335$	−8.85602e10			−0.384182
$336$			9.09775e10i			0.389410i
$337$		−	1.43175e11i		−	0.604690i	−0.953199	−	0.302345i	$-0.902231\pi$
$337$		−	1.43175e11i		−	0.604690i	0.953199	−	0.302345i	$-0.0977695\pi$
$338$		−	6.04573e10i		−	0.251955i
$339$	1.48897e11			0.612331
$340$		−	1.63128e11i		−	0.662023i
$341$	−2.40581e10			−0.0963532
$342$	−3.34848e10			−0.132352
$343$	−2.68602e11			−1.04782
$344$	1.81726e11			0.699689
$345$		−	8.01281e10i		−	0.304508i
$346$			8.84991e10i			0.331968i
$347$	8.43217e10			0.312217			0.156108	−	0.987740i	$-0.450105\pi$
$347$	8.43217e10			0.312217			0.156108	+	0.987740i	$0.450105\pi$
$348$	−1.31838e11	−	4.16024e10i	−0.481876	−	0.152059i
$349$	6.86877e10			0.247836			0.123918	−	0.992292i	$-0.460454\pi$
$349$	6.86877e10			0.247836			0.123918	+	0.992292i	$0.460454\pi$
$350$		−	6.67475e10i		−	0.237755i
$351$		−	1.01761e11i		−	0.357850i
$352$	1.65995e11			0.576307
$353$	−3.90153e11			−1.33736			−0.668680	−	0.743550i	$-0.733140\pi$
$353$	−3.90153e11			−1.33736			−0.668680	+	0.743550i	$0.733140\pi$
$354$	7.52832e8			0.00254791
$355$	9.95967e10			0.332826
$356$		−	5.63781e10i		−	0.186031i
$357$	−3.05192e11			−0.994411
$358$			4.11746e10i			0.132482i
$359$			2.62586e11i			0.834346i	0.908827	+	0.417173i	$0.136979\pi$
$359$			2.62586e11i			0.834346i	−0.908827	+	0.417173i	$0.863021\pi$
$360$		−	4.74392e10i		−	0.148859i
$361$	1.87658e11			0.581546
$362$		−	1.21172e11i		−	0.370862i
$363$			8.42620e10i			0.254714i
$364$	−1.10020e11			−0.328485
$365$		−	1.59085e11i		−	0.469148i
$366$			3.41382e10i			0.0994433i
$367$			4.49192e11i			1.29251i	0.763120	+	0.646256i	$0.223666\pi$
$367$			4.49192e11i			1.29251i	−0.763120	+	0.646256i	$0.776334\pi$
$368$	3.79994e11			1.08009
$369$			1.89475e11i			0.532026i
$370$	−7.95269e10			−0.220601
$371$	4.56616e11			1.25132
$372$	2.44768e10			0.0662692
$373$	1.51488e11			0.405218			0.202609	−	0.979260i	$-0.435058\pi$
$373$	1.51488e11			0.405218			0.202609	+	0.979260i	$0.435058\pi$
$374$			1.56316e11i			0.413125i
$375$			1.49552e11i			0.390527i
$376$	2.04827e11			0.528496
$377$	4.50601e10	−	1.42796e11i	0.114883	−	0.364065i
$378$	−1.03420e11			−0.260550
$379$			6.03931e11i			1.50353i	0.659434	+	0.751763i	$0.270796\pi$
$379$			6.03931e11i			1.50353i	−0.659434	+	0.751763i	$0.729204\pi$
$380$		−	9.13014e10i		−	0.224622i
$381$	−6.99094e10			−0.169970
$382$	−1.57044e11			−0.377344
$383$	3.78128e11			0.897933			0.448966	−	0.893549i	$-0.351792\pi$
$383$	3.78128e11			0.897933			0.448966	+	0.893549i	$0.351792\pi$
$384$	−2.20811e11			−0.518238
$385$			1.13521e11i			0.263331i
$386$	−5.17853e10			−0.118731
$387$		−	3.79599e11i		−	0.860253i
$388$		−	3.05149e11i		−	0.683549i
$389$			1.25281e10i			0.0277404i	0.999904	+	0.0138702i	$0.00441516\pi$
$389$			1.25281e10i			0.0277404i	−0.999904	+	0.0138702i	$0.995585\pi$
$390$	−1.08278e10			−0.0237001
$391$			1.27472e12i			2.75816i
$392$		−	2.94981e10i		−	0.0630967i
$393$	7.54990e10			0.159652
$394$		−	1.07342e11i		−	0.224407i
$395$			1.85890e11i			0.384210i
$396$		−	2.27708e11i		−	0.465319i
$397$	5.12338e11			1.03514			0.517570	−	0.855641i	$-0.326837\pi$
$397$	5.12338e11			1.03514			0.517570	+	0.855641i	$0.326837\pi$
$398$			1.48781e11i			0.297216i
$399$	−1.70814e11			−0.337399
$400$	−3.26966e11			−0.638606
$401$	−8.92964e10			−0.172458			−0.0862292	−	0.996275i	$-0.527482\pi$
$401$	−8.92964e10			−0.172458			−0.0862292	+	0.996275i	$0.527482\pi$
$402$	−8.63393e10			−0.164889
$403$			2.65111e10i			0.0500674i
$404$		−	2.78683e11i		−	0.520468i
$405$	−3.60204e10			−0.0665274
$406$	−1.45123e11	−	4.57946e10i	−0.265076	−	0.0836463i
$407$	−7.99830e11			−1.44485
$408$		−	3.33227e11i		−	0.595346i
$409$		−	2.89865e11i		−	0.512201i	−0.966650	−	0.256101i	$-0.917562\pi$
$409$		−	2.89865e11i		−	0.512201i	0.966650	−	0.256101i	$-0.0824378\pi$
$410$	4.92236e10			0.0860292
$411$	6.38907e9			0.0110446
$412$	6.64481e11			1.13617
$413$	−8.69762e9			−0.0147104
$414$			1.76923e11i			0.295993i
$415$	3.48628e11			0.576960
$416$		−	1.82921e11i		−	0.299463i
$417$			3.49384e11i			0.565836i
$418$			8.74890e10i			0.140172i
$419$	2.33955e10			0.0370825			0.0185413	−	0.999828i	$-0.494098\pi$
$419$	2.33955e10			0.0370825			0.0185413	+	0.999828i	$0.494098\pi$
$420$		−	1.15497e11i		−	0.181112i
$421$			5.89286e11i			0.914233i	0.889407	+	0.457117i	$0.151118\pi$
$421$			5.89286e11i			0.914233i	−0.889407	+	0.457117i	$0.848882\pi$
$422$	1.81584e10			0.0278723
$423$		−	4.27853e11i		−	0.649775i
$424$			4.98560e11i			0.749154i
$425$		−	1.09684e12i		−	1.63077i
$426$	9.70991e10			0.142847
$427$		−	3.94405e11i		−	0.574139i
$428$	−7.61406e11			−1.09678
$429$	−1.08899e11			−0.155227
$430$	−9.86161e10			−0.139104
$431$	8.06791e11			1.12619			0.563097	−	0.826391i	$-0.309610\pi$
$431$	8.06791e11			1.12619			0.563097	+	0.826391i	$0.309610\pi$
$432$			5.06609e11i			0.699835i
$433$		−	3.66445e11i		−	0.500972i	−0.968120	−	0.250486i	$-0.919410\pi$
$433$		−	3.66445e11i		−	0.500972i	0.968120	−	0.250486i	$-0.0805905\pi$
$434$	2.69433e10			0.0364541
$435$	1.49904e11	+	4.73032e10i	0.200730	+	0.0633415i
$436$	−8.03034e11			−1.06425
$437$			7.13452e11i			0.935833i
$438$		−	1.55095e11i		−	0.201356i
$439$	−8.04770e11			−1.03414			−0.517072	−	0.855942i	$-0.672978\pi$
$439$	−8.04770e11			−1.03414			−0.517072	+	0.855942i	$0.672978\pi$
$440$	−1.23949e11			−0.157654
$441$	−6.16172e10			−0.0775761
$442$	1.72255e11			0.214670
$443$		−	8.31309e11i		−	1.02552i	−0.858531	−	0.512762i	$-0.828622\pi$
$443$		−	8.31309e11i		−	1.02552i	0.858531	−	0.512762i	$-0.171378\pi$
$444$	8.13751e11			0.993730
$445$			6.41035e10i			0.0774928i
$446$		−	1.19928e11i		−	0.143520i
$447$		−	3.58044e11i		−	0.424182i
$448$	4.14007e11			0.485576
$449$		−	1.07916e12i		−	1.25307i	−0.779392	−	0.626537i	$-0.784472\pi$
$449$		−	1.07916e12i		−	1.25307i	0.779392	−	0.626537i	$-0.215528\pi$
$450$		−	1.52233e11i		−	0.175006i
$451$	4.95058e11			0.563459
$452$		−	8.96421e11i		−	1.01016i
$453$		−	6.58712e11i		−	0.734943i
$454$		−	1.70081e11i		−	0.187890i
$455$	1.25096e11			0.136833
$456$		−	1.86505e11i		−	0.201998i
$457$	−1.19185e12			−1.27820			−0.639098	−	0.769126i	$-0.720692\pi$
$457$	−1.19185e12			−1.27820			−0.639098	+	0.769126i	$0.720692\pi$
$458$	5.28906e11			0.561673
$459$	−1.69946e12			−1.78712
$460$	−4.82406e11			−0.502345
$461$		−	3.15098e11i		−	0.324931i	−0.986714	−	0.162466i	$-0.948055\pi$
$461$		−	3.15098e11i		−	0.324931i	0.986714	−	0.162466i	$-0.0519446\pi$
$462$			1.10674e11i			0.113020i
$463$	4.58970e11			0.464162			0.232081	−	0.972696i	$-0.425447\pi$
$463$	4.58970e11			0.464162			0.232081	+	0.972696i	$0.425447\pi$
$464$	−2.24327e11	+	7.10894e11i	−0.224673	+	0.711990i
$465$	−2.78308e10			−0.0276050
$466$			1.78534e11i			0.175382i
$467$			1.05886e12i			1.03018i	0.857137	+	0.515089i	$0.172241\pi$
$467$			1.05886e12i			1.03018i	−0.857137	+	0.515089i	$0.827759\pi$
$468$	−2.50926e11			−0.241791
$469$	9.97495e11			0.951991
$470$	−1.11152e11			−0.105069
$471$	8.59882e11			0.805091
$472$		−	9.49658e9i		−	0.00880701i
$473$	−9.91815e11			−0.911078
$474$			1.81228e11i			0.164901i
$475$		−	6.13891e11i		−	0.553312i
$476$			1.83739e12i			1.64047i
$477$	1.04142e12			0.921070
$478$			1.44632e11i			0.126718i
$479$		−	7.34282e11i		−	0.637313i	−0.947870	−	0.318657i	$-0.896768\pi$
$479$		−	7.34282e11i		−	0.637313i	0.947870	−	0.318657i	$-0.103232\pi$
$480$	1.92027e11			0.165111
$481$			8.81383e11i			0.750779i
$482$		−	3.00841e11i		−	0.253879i
$483$			9.02521e11i			0.754562i
$484$	5.07294e11			0.420199
$485$			3.46964e11i			0.284738i
$486$	−3.75139e11			−0.305020
$487$	1.31652e12			1.06059			0.530293	−	0.847814i	$-0.322082\pi$
$487$	1.31652e12			1.06059			0.530293	+	0.847814i	$0.322082\pi$
$488$	4.30636e11			0.343733
$489$	8.86171e11			0.700854
$490$			1.60075e10i			0.0125442i
$491$			1.82828e12i			1.41963i	0.704387	+	0.709816i	$0.251222\pi$
$491$			1.82828e12i			1.41963i	−0.704387	+	0.709816i	$0.748778\pi$
$492$	−5.03675e11			−0.387532
$493$	−2.38476e12	−	7.52524e11i	−1.81816	−	0.573733i
$494$	9.64097e10			0.0728366
$495$			2.58911e11i			0.193833i
$496$		−	1.31983e11i		−	0.0979153i
$497$	−1.12180e12			−0.824733
$498$	3.39885e11			0.247628
$499$	4.34353e11			0.313610			0.156805	−	0.987630i	$-0.449881\pi$
$499$	4.34353e11			0.313610			0.156805	+	0.987630i	$0.449881\pi$
$500$	9.00367e11			0.644250
$501$		−	5.82587e11i		−	0.413134i
$502$	1.99446e11			0.140171
$503$		−	1.24120e12i		−	0.864543i	−0.901744	−	0.432271i	$-0.857712\pi$
$503$		−	1.24120e12i		−	0.864543i	0.901744	−	0.432271i	$-0.142288\pi$
$504$			5.34330e11i			0.368869i
$505$			3.16870e11i			0.216806i
$506$	4.62262e11			0.313481
$507$		−	7.03392e11i		−	0.472783i
$508$			4.20885e11i			0.280399i
$509$	2.46498e12			1.62774			0.813868	−	0.581050i	$-0.197358\pi$
$509$	2.46498e12			1.62774			0.813868	+	0.581050i	$0.197358\pi$
$510$			1.80830e11i			0.118360i
$511$			1.79184e12i			1.16254i
$512$			1.56567e12i			1.00690i
$513$	−9.51176e11			−0.606363
$514$		−	3.16416e11i		−	0.199951i
$515$	−7.55534e11			−0.473284
$516$	1.00908e12			0.626616
$517$	−1.11789e12			−0.688165
$518$	8.95750e11			0.546642
$519$			1.02965e12i			0.622923i
$520$			1.36587e11i			0.0819210i
$521$	−2.93550e12			−1.74547			−0.872735	−	0.488194i	$-0.837656\pi$
$521$	−2.93550e12			−1.74547			−0.872735	+	0.488194i	$0.837656\pi$
$522$	−3.30988e11	−	1.04445e11i	−0.195117	−	0.0615703i
$523$	−1.81865e12			−1.06290			−0.531450	−	0.847090i	$-0.678353\pi$
$523$	−1.81865e12			−1.06290			−0.531450	+	0.847090i	$0.678353\pi$
$524$		−	4.54537e11i		−	0.263377i
$525$		−	7.76576e11i		−	0.446136i
$526$	3.17817e11			0.181026
$527$	4.42748e11			0.250040
$528$	5.42143e11			0.303572
$529$	1.96849e12			1.09290
$530$		−	2.70550e11i		−	0.148938i
$531$	−1.98370e10			−0.0108280
$532$			1.02837e12i			0.556606i
$533$		−	5.45536e11i		−	0.292787i
$534$			6.24959e10i			0.0332595i
$535$	8.65740e11			0.456873
$536$			1.08913e12i			0.569949i
$537$			4.79047e11i			0.248596i
$538$	−7.14690e11			−0.367788
$539$			1.60993e11i			0.0821595i
$540$		−	6.43145e11i		−	0.325489i
$541$		−	2.84716e12i		−	1.42897i	−0.699649	−	0.714487i	$-0.746660\pi$
$541$		−	2.84716e12i		−	1.42897i	0.699649	−	0.714487i	$-0.253340\pi$
$542$	−5.41603e11			−0.269578
$543$		−	1.40977e12i		−	0.695905i
$544$	−3.05487e12			−1.49554
$545$	9.13073e11			0.443324
$546$	1.21959e11			0.0587282
$547$	1.33074e12			0.635550			0.317775	−	0.948166i	$-0.397064\pi$
$547$	1.33074e12			0.635550			0.317775	+	0.948166i	$0.397064\pi$
$548$		−	3.84650e10i		−	0.0182202i
$549$		−	8.99534e11i		−	0.422612i
$550$	−3.97754e11			−0.185346
$551$	−1.33473e12	−	4.21182e11i	−0.616895	−	0.194665i
$552$	−9.85427e11			−0.451750
$553$		−	2.09377e12i		−	0.952061i
$554$			1.23681e11i			0.0557838i
$555$	−9.25258e11			−0.413947
$556$	2.10344e12			0.933456
$557$	2.59107e12			1.14059			0.570297	−	0.821439i	$-0.306828\pi$
$557$	2.59107e12			1.14059			0.570297	+	0.821439i	$0.306828\pi$
$558$	6.14504e10			0.0268331
$559$			1.09294e12i			0.473418i
$560$	−6.22778e11			−0.267600
$561$			1.81867e12i			0.775211i
$562$			2.61591e11i			0.110614i
$563$		−	3.38257e12i		−	1.41893i	−0.704743	−	0.709463i	$-0.748938\pi$
$563$		−	3.38257e12i		−	1.41893i	0.704743	−	0.709463i	$-0.251062\pi$
$564$	1.13735e12			0.473302
$565$			1.01926e12i			0.420790i
$566$			6.07095e11i			0.248647i
$567$	4.05715e11			0.164853
$568$		−	1.22485e12i		−	0.493761i
$569$		−	1.07559e12i		−	0.430172i	−0.976595	−	0.215086i	$-0.930997\pi$
$569$		−	1.07559e12i		−	0.430172i	0.976595	−	0.215086i	$-0.0690032\pi$
$570$			1.01209e11i			0.0401589i
$571$	2.97890e12			1.17272			0.586359	−	0.810051i	$-0.300561\pi$
$571$	2.97890e12			1.17272			0.586359	+	0.810051i	$0.300561\pi$
$572$			6.55619e11i			0.256076i
$573$	−1.82714e12			−0.708069
$574$	−5.54429e11			−0.213178
$575$	−3.24359e12			−1.23743
$576$	9.44240e11			0.357422
$577$		−	6.08721e11i		−	0.228627i	−0.993445	−	0.114313i	$-0.963533\pi$
$577$		−	6.08721e11i		−	0.228627i	0.993445	−	0.114313i	$-0.0364668\pi$
$578$		−	2.08531e12i		−	0.777134i
$579$	−6.02498e11			−0.222793
$580$	2.84785e11	−	9.02487e11i	0.104494	−	0.331143i
$581$	−3.92676e12			−1.42969
$582$			3.38263e11i			0.122208i
$583$		−	2.72101e12i		−	0.975488i
$584$	−1.95644e12			−0.696000
$585$	2.85310e11			0.100720
$586$	1.10770e12			0.388047
$587$	4.95878e12			1.72387			0.861933	−	0.507022i	$-0.169254\pi$
$587$	4.95878e12			1.72387			0.861933	+	0.507022i	$0.169254\pi$
$588$		−	1.63795e11i		−	0.0565071i
$589$	2.47803e11			0.0848374
$590$			5.15344e9i			0.00175091i
$591$		−	1.24887e12i		−	0.421089i
$592$		−	4.38788e12i		−	1.46827i
$593$	2.06051e11			0.0684273			0.0342137	−	0.999415i	$-0.489107\pi$
$593$	2.06051e11			0.0684273			0.0342137	+	0.999415i	$0.489107\pi$
$594$			6.16289e11i			0.203117i
$595$		−	2.08916e12i		−	0.683354i
$596$	−2.15558e12			−0.699770
$597$			1.73099e12i			0.557713i
$598$		−	5.09396e11i		−	0.162892i
$599$			4.58074e12i			1.45383i	0.686725	+	0.726917i	$0.259048\pi$
$599$			4.58074e12i			1.45383i	−0.686725	+	0.726917i	$0.740952\pi$
$600$	8.47912e11			0.267098
$601$			5.94548e12i			1.85888i	0.368973	+	0.929440i	$0.379710\pi$
$601$			5.94548e12i			1.85888i	−0.368973	+	0.929440i	$0.620290\pi$
$602$	1.11076e12			0.344696
$603$	2.27502e12			0.700741
$604$	−3.96573e12			−1.21243
$605$	−5.76808e11			−0.175038
$606$			3.08924e11i			0.0930518i
$607$			2.39134e11i			0.0714977i	0.999361	+	0.0357488i	$0.0113816\pi$
$607$			2.39134e11i			0.0714977i	−0.999361	+	0.0357488i	$0.988618\pi$
$608$	−1.70979e12			−0.507429
$609$	−1.68844e12	−	5.32798e11i	−0.497402	−	0.156958i
$610$	−2.33690e11			−0.0683369
$611$			1.23188e12i			0.357587i
$612$			4.19059e12i			1.20752i
$613$	−1.53752e12			−0.439793			−0.219896	−	0.975523i	$-0.570572\pi$
$613$	−1.53752e12			−0.439793			−0.219896	+	0.975523i	$0.570572\pi$
$614$	−7.14914e11			−0.203000
$615$	5.72693e11			0.161430
$616$	1.39610e12			0.390663
$617$			6.28135e12i			1.74490i	0.488706	+	0.872449i	$0.337469\pi$
$617$			6.28135e12i			1.74490i	−0.488706	+	0.872449i	$0.662531\pi$
$618$	−7.36587e11			−0.203131
$619$		−	2.27826e12i		−	0.623728i	−0.950127	−	0.311864i	$-0.899047\pi$
$619$		−	2.27826e12i		−	0.623728i	0.950127	−	0.311864i	$-0.100953\pi$
$620$			1.67554e11i			0.0455398i
$621$			5.02569e12i			1.35608i
$622$	−2.34529e11			−0.0628261
$623$		−	7.22028e11i		−	0.192025i
$624$		−	5.97422e11i		−	0.157743i
$625$	2.23918e12			0.586987
$626$			1.38321e12i			0.360002i
$627$			1.01789e12i			0.263026i
$628$		−	5.17686e12i		−	1.32815i
$629$	1.47195e13			3.74943
$630$		−	2.89961e11i		−	0.0733343i
$631$	−5.53759e12			−1.39056			−0.695278	−	0.718741i	$-0.744719\pi$
$631$	−5.53759e12			−1.39056			−0.695278	+	0.718741i	$0.744719\pi$
$632$	2.28610e12			0.569991
$633$	2.11265e11			0.0523010
$634$	−3.42545e9			−0.000842008
$635$		−	4.78558e11i		−	0.116803i
$636$			2.76837e12i			0.670915i
$637$	1.77409e11			0.0426920
$638$	−2.72894e11	+	8.64803e11i	−0.0652080	+	0.206645i
$639$	−2.55854e12			−0.607069
$640$		−	1.51154e12i		−	0.356130i
$641$			3.85767e12i			0.902534i	0.892389	+	0.451267i	$0.149028\pi$
$641$			3.85767e12i			0.902534i	−0.892389	+	0.451267i	$0.850972\pi$
$642$	8.44030e11			0.196088
$643$	−5.47180e12			−1.26235			−0.631177	−	0.775639i	$-0.717428\pi$
$643$	−5.47180e12			−1.26235			−0.631177	+	0.775639i	$0.717428\pi$
$644$	5.43356e12			1.24480
$645$	−1.14735e12			−0.261022
$646$		−	1.61009e12i		−	0.363750i
$647$	−1.51750e12			−0.340454			−0.170227	−	0.985405i	$-0.554450\pi$
$647$	−1.51750e12			−0.340454			−0.170227	+	0.985405i	$0.554450\pi$
$648$			4.42984e11i			0.0986962i
$649$			5.18299e10i			0.0114678i
$650$			4.38311e11i			0.0963102i
$651$	3.13472e11			0.0684044
$652$		−	5.33513e12i		−	1.15619i
$653$		−	3.36780e12i		−	0.724831i	−0.932017	−	0.362415i	$-0.881952\pi$
$653$		−	3.36780e12i		−	0.724831i	0.932017	−	0.362415i	$-0.118048\pi$
$654$	8.90175e11			0.190272
$655$			5.16821e11i			0.109712i
$656$			2.71590e12i			0.572593i
$657$			4.08672e12i			0.855718i
$658$	1.25196e12			0.260359
$659$		−	3.07004e12i		−	0.634104i	−0.948408	−	0.317052i	$-0.897307\pi$
$659$		−	3.07004e12i		−	0.634104i	0.948408	−	0.317052i	$-0.102693\pi$
$660$	−6.88256e11			−0.141189
$661$	5.43059e12			1.10647			0.553236	−	0.833024i	$-0.313393\pi$
$661$	5.43059e12			1.10647			0.553236	+	0.833024i	$0.313393\pi$
$662$	−2.26056e12			−0.457462
$663$	2.00410e12			0.402818
$664$		−	4.28747e12i		−	0.855943i
$665$		−	1.16929e12i		−	0.231859i
$666$	2.04297e12			0.402372
$667$	−2.22538e12	+	7.05226e12i	−0.435350	+	1.37963i
$668$	−3.50743e12			−0.681545
$669$		−	1.39530e12i		−	0.269309i
$670$		−	5.91028e11i		−	0.113311i
$671$	−2.35030e12			−0.447581
$672$	−2.16289e12			−0.409140
$673$	6.36684e12			1.19634			0.598172	−	0.801368i	$-0.295894\pi$
$673$	6.36684e12			1.19634			0.598172	+	0.801368i	$0.295894\pi$
$674$	9.55513e11			0.178348
$675$		−	4.32437e12i		−	0.801781i
$676$	−4.23472e12			−0.779947
$677$			9.54705e12i			1.74671i	0.487086	+	0.873354i	$0.338060\pi$
$677$			9.54705e12i			1.74671i	−0.487086	+	0.873354i	$0.661940\pi$
$678$			9.93697e11i			0.180601i
$679$		−	3.90802e12i		−	0.705574i
$680$	2.28107e12			0.409118
$681$		−	1.97881e12i		−	0.352568i
$682$		−	1.60557e11i		−	0.0284184i
$683$	−9.58395e12			−1.68520			−0.842600	−	0.538541i	$-0.818976\pi$
$683$	−9.58395e12			−1.68520			−0.842600	+	0.538541i	$0.818976\pi$
$684$			2.34544e12i			0.409706i
$685$			4.37358e10i			0.00758978i
$686$		−	1.79258e12i		−	0.309044i
$687$	6.15357e12			1.05395
$688$		−	5.44112e12i		−	0.925849i
$689$	−2.99846e12			−0.506887
$690$	5.34754e11			0.0898117
$691$	−2.27332e12			−0.379323			−0.189661	−	0.981850i	$-0.560739\pi$
$691$	−2.27332e12			−0.379323			−0.189661	+	0.981850i	$0.560739\pi$
$692$	6.19891e12			1.02763
$693$		−	2.91624e12i		−	0.480312i
$694$			5.62741e11i			0.0920854i
$695$	−2.39167e12			−0.388840
$696$	5.81741e11	−	1.84354e12i	0.0939697	−	0.297791i
$697$	−9.11072e12			−1.46219
$698$			4.58403e11i			0.0730968i
$699$			2.07716e12i			0.329096i
$700$	−4.67532e12			−0.735987
$701$	−8.32935e12			−1.30281			−0.651403	−	0.758732i	$-0.725819\pi$
$701$	−8.32935e12			−1.30281			−0.651403	+	0.758732i	$0.725819\pi$
$702$	6.79129e11			0.105544
$703$	8.23840e12			1.27217
$704$		−	2.46711e12i		−	0.378539i
$705$	−1.29320e12			−0.197158
$706$		−	2.60378e12i		−	0.394442i
$707$		−	3.56906e12i		−	0.537238i
$708$		−	5.27320e10i		−	0.00788723i
$709$	−1.69349e12			−0.251695			−0.125848	−	0.992050i	$-0.540165\pi$
$709$	−1.69349e12			−0.251695			−0.125848	+	0.992050i	$0.540165\pi$
$710$			6.64682e11i			0.0981638i
$711$		−	4.77532e12i		−	0.700793i
$712$	7.88353e11			0.114964
$713$		−	1.30931e12i		−	0.189731i
$714$		−	2.03677e12i		−	0.293292i
$715$		−	7.45458e11i		−	0.106671i
$716$	2.88407e12			0.410107
$717$			1.68272e12i			0.237780i
$718$	−1.75243e12			−0.246082
$719$	−2.27690e12			−0.317734			−0.158867	−	0.987300i	$-0.550784\pi$
$719$	−2.27690e12			−0.317734			−0.158867	+	0.987300i	$0.550784\pi$
$720$	−1.42039e12			−0.196975
$721$	8.50994e12			1.17278
$722$			1.25238e12i			0.171521i
$723$		−	3.50015e12i		−	0.476391i
$724$	−8.48745e12			−1.14803
$725$	1.91484e12	−	6.06813e12i	0.257401	−	0.815706i
$726$	−5.62343e11			−0.0751253
$727$		−	1.40727e13i		−	1.86841i	−0.356741	−	0.934203i	$-0.616112\pi$
$727$		−	1.40727e13i		−	1.86841i	0.356741	−	0.934203i	$-0.383888\pi$
$728$		−	1.53845e12i		−	0.202998i
$729$	−3.03066e12			−0.397433
$730$	1.06169e12			0.138371
$731$	1.82527e13			2.36428
$732$	2.39121e12			0.307834
$733$			1.22229e13i			1.56389i	0.623346	+	0.781946i	$0.285773\pi$
$733$			1.22229e13i			1.56389i	−0.623346	+	0.781946i	$0.714227\pi$
$734$	−2.99779e12			−0.381214
$735$			1.86240e11i			0.0235386i
$736$			9.03393e12i			1.13482i
$737$		−	5.94416e12i		−	0.742142i
$738$	−1.26450e12			−0.156916
$739$			2.08367e12i			0.256997i	0.991710	+	0.128499i	$0.0410158\pi$
$739$			2.08367e12i			0.256997i	−0.991710	+	0.128499i	$0.958984\pi$
$740$			5.57045e12i			0.682886i
$741$	1.12168e12			0.136675
$742$			3.04733e12i			0.369065i
$743$		−	3.72702e12i		−	0.448654i	−0.974514	−	0.224327i	$-0.927982\pi$
$743$		−	3.72702e12i		−	0.448654i	0.974514	−	0.224327i	$-0.0720184\pi$
$744$			3.42268e11i			0.0409532i
$745$	2.45095e12			0.291495
$746$			1.01099e12i			0.119515i
$747$	−8.95589e12			−1.05236
$748$	1.09491e13			1.27886
$749$	−9.75124e12			−1.13212
$750$	−9.98070e11			−0.115182
$751$			1.63988e13i			1.88119i	0.339525	+	0.940597i	$0.389734\pi$
$751$			1.63988e13i			1.88119i	−0.339525	+	0.940597i	$0.610266\pi$
$752$		−	6.13277e12i		−	0.699321i
$753$	2.32046e12			0.263025
$754$	9.52981e11	+	3.00719e11i	0.107377	+	0.0338836i
$755$	4.50915e12			0.505049
$756$			7.24405e12i			0.806553i
$757$		−	3.56614e12i		−	0.394699i	−0.980333	−	0.197350i	$-0.936767\pi$
$757$		−	3.56614e12i		−	0.394699i	0.980333	−	0.197350i	$-0.0632334\pi$
$758$	−4.03048e12			−0.443450
$759$	5.37820e12			0.588233
$760$	1.27670e12			0.138812
$761$	1.20541e13			1.30287			0.651437	−	0.758703i	$-0.274167\pi$
$761$	1.20541e13			1.30287			0.651437	+	0.758703i	$0.274167\pi$
$762$		−	4.66557e11i		−	0.0501311i
$763$	−1.02844e13			−1.09854
$764$			1.10002e13i			1.16810i
$765$		−	4.76482e12i		−	0.503002i
$766$			2.52353e12i			0.264837i
$767$	5.71147e10			0.00595893
$768$			1.27557e12i			0.132306i
$769$			1.46799e13i			1.51375i	0.653560	+	0.756875i	$0.273275\pi$
$769$			1.46799e13i			1.51375i	−0.653560	+	0.756875i	$0.726725\pi$
$770$	−7.57609e11			−0.0776670
$771$		−	3.68135e12i		−	0.375200i
$772$			3.62730e12i			0.367541i
$773$		−	1.21332e12i		−	0.122227i	−0.998131	−	0.0611133i	$-0.980535\pi$
$773$		−	1.21332e12i		−	0.122227i	0.998131	−	0.0611133i	$-0.0194651\pi$
$774$	2.53335e12			0.253723
$775$			1.12659e12i			0.112179i
$776$	4.26701e12			0.422421
$777$	1.04216e13			1.02575
$778$	−8.36094e10			−0.00818176
$779$	−5.09920e12			−0.496116
$780$			7.58433e11i			0.0733654i
$781$			6.68494e12i			0.642936i
$782$	−8.50716e12			−0.813494
$783$	−9.40209e12	−	2.96689e12i	−0.893916	−	0.282081i
$784$	−8.83211e11			−0.0834915
$785$			5.88624e12i			0.553254i
$786$			5.03861e11i			0.0470879i
$787$	−1.40861e13			−1.30889			−0.654445	−	0.756109i	$-0.727098\pi$
$787$	−1.40861e13			−1.30889			−0.654445	+	0.756109i	$0.727098\pi$
$788$	−7.51874e12			−0.694667
$789$	3.69765e12			0.339687
$790$	−1.24058e12			−0.113319
$791$		−	1.14804e13i		−	1.04271i
$792$	3.18412e12			0.287559
$793$			2.58994e12i			0.232574i
$794$			3.41921e12i			0.305305i
$795$		−	3.14772e12i		−	0.279476i
$796$	1.04213e13			0.920055
$797$			2.55452e12i			0.224258i	0.993694	+	0.112129i	$0.0357669\pi$
$797$			2.55452e12i			0.224258i	−0.993694	+	0.112129i	$0.964233\pi$
$798$		−	1.13996e12i		−	0.0995127i
$799$	2.05729e13			1.78581
$800$		−	7.77326e12i		−	0.670962i
$801$		−	1.64675e12i		−	0.141346i
$802$		−	5.95941e11i		−	0.0508649i
$803$	1.06778e13			0.906276
$804$			6.04763e12i			0.510426i
$805$	−6.17812e12			−0.518531
$806$	−1.76928e11			−0.0147669
$807$	−8.31508e12			−0.690137
$808$	3.89692e12			0.321640
$809$		−	1.45130e13i		−	1.19122i	−0.803276	−	0.595608i	$-0.796911\pi$
$809$		−	1.45130e13i		−	1.19122i	0.803276	−	0.595608i	$-0.203089\pi$
$810$		−	2.40391e11i		−	0.0196216i
$811$	−7.15755e12			−0.580992			−0.290496	−	0.956876i	$-0.593820\pi$
$811$	−7.15755e12			−0.580992			−0.290496	+	0.956876i	$0.593820\pi$
$812$	−3.20767e12	+	1.01651e13i	−0.258933	+	0.820562i
$813$	−6.30129e12			−0.505850
$814$		−	5.33785e12i		−	0.426144i
$815$			6.06620e12i			0.481623i
$816$	−9.97723e12			−0.787779
$817$	1.02159e13			0.802190
$818$	1.93448e12			0.151069
$819$	−3.21359e12			−0.249582
$820$		−	3.44786e12i		−	0.266310i
$821$	−1.16566e12			−0.0895422			−0.0447711	−	0.998997i	$-0.514256\pi$
$821$	−1.16566e12			−0.0895422			−0.0447711	+	0.998997i	$0.514256\pi$
$822$			4.26390e10i			0.00325750i
$823$		−	2.91814e12i		−	0.221721i	−0.993836	−	0.110860i	$-0.964639\pi$
$823$		−	2.91814e12i		−	0.221721i	0.993836	−	0.110860i	$-0.0353606\pi$
$824$			9.29166e12i			0.702136i
$825$	−4.62768e12			−0.347793
$826$		−	5.80456e10i		−	0.00433870i
$827$		−	1.32461e13i		−	0.984718i	−0.870392	−	0.492359i	$-0.836135\pi$
$827$		−	1.32461e13i		−	0.984718i	0.870392	−	0.492359i	$-0.163865\pi$
$828$	1.23925e13			0.916269
$829$			3.74763e12i			0.275588i	0.990461	+	0.137794i	$0.0440012\pi$
$829$			3.74763e12i			0.275588i	−0.990461	+	0.137794i	$0.955999\pi$
$830$			2.32665e12i			0.170169i
$831$			1.43897e12i			0.104676i
$832$	−2.71866e12			−0.196698
$833$		−	2.96281e12i		−	0.213207i
$834$	−2.33170e12			−0.166888
$835$	3.98805e12			0.283904
$836$	6.12816e12			0.433912
$837$	1.74557e12			0.122934
$838$			1.56136e11i			0.0109371i
$839$			1.41572e13i			0.986393i	0.869918	+	0.493196i	$0.164172\pi$
$839$			1.41572e13i			0.986393i	−0.869918	+	0.493196i	$0.835828\pi$
$840$	1.61503e12			0.111924
$841$	−1.18797e13	−	8.32652e12i	−0.818883	−	0.573960i
$842$	−3.93274e12			−0.269644
$843$			3.04349e12i			0.207562i
$844$		−	1.27190e12i		−	0.0862807i
$845$	4.81500e12			0.324894
$846$	2.85538e12			0.191645
$847$	6.49686e12			0.433739
$848$	1.49275e13			0.991303
$849$			7.06327e12i			0.466574i
$850$	7.32000e12			0.480979
$851$		−	4.35289e13i		−	2.84508i
$852$		−	6.80129e12i		−	0.442194i
$853$		−	3.10228e12i		−	0.200636i	−0.994955	−	0.100318i	$-0.968014\pi$
$853$		−	3.10228e12i		−	0.200636i	0.994955	−	0.100318i	$-0.0319861\pi$
$854$	2.63216e12			0.169337
$855$		−	2.66683e12i		−	0.170667i
$856$		−	1.06470e13i		−	0.677790i
$857$	−2.27008e13			−1.43756			−0.718781	−	0.695236i	$-0.755300\pi$
$857$	−2.27008e13			−1.43756			−0.718781	+	0.695236i	$0.755300\pi$
$858$		−	7.26764e11i		−	0.0457826i
$859$		−	1.88797e11i		−	0.0118311i	−0.999983	−	0.00591557i	$-0.998117\pi$
$859$		−	1.88797e11i		−	0.0118311i	0.999983	−	0.00591557i	$-0.00188300\pi$
$860$			6.90755e12i			0.430607i
$861$	−6.45052e12			−0.400019
$862$			5.38431e12i			0.332160i
$863$	−2.78527e13			−1.70930			−0.854652	−	0.519201i	$-0.826230\pi$
$863$	−2.78527e13			−1.70930			−0.854652	+	0.519201i	$0.826230\pi$
$864$	−1.20441e13			−0.735294
$865$	−7.04834e12			−0.428069
$866$	2.44556e12			0.147757
$867$		−	2.42616e13i		−	1.45826i
$868$		−	1.88724e12i		−	0.112846i
$869$	−1.24769e13			−0.742197
$870$	−3.15689e11	+	1.00042e12i	−0.0186820	+	0.0592033i
$871$	−6.55025e12			−0.385635
$872$		−	1.12291e13i		−	0.657689i
$873$		−	8.91314e12i		−	0.519358i
$874$	−4.76139e12			−0.276015
$875$	1.15309e13			0.665009
$876$	−1.08636e13			−0.623313
$877$	1.65972e13			0.947410			0.473705	−	0.880684i	$-0.342916\pi$
$877$	1.65972e13			0.947410			0.473705	+	0.880684i	$0.342916\pi$
$878$		−	5.37082e12i		−	0.305011i
$879$	1.28876e13			0.728152
$880$			3.71119e12i			0.208613i
$881$		−	1.08832e13i		−	0.608648i	−0.952569	−	0.304324i	$-0.901569\pi$
$881$		−	1.08832e13i		−	0.608648i	0.952569	−	0.304324i	$-0.0984306\pi$
$882$		−	4.11217e11i		−	0.0228803i
$883$	1.58732e13			0.878699			0.439349	−	0.898316i	$-0.355209\pi$
$883$	1.58732e13			0.878699			0.439349	+	0.898316i	$0.355209\pi$
$884$		−	1.20656e13i		−	0.664527i
$885$			5.99578e10i			0.00328550i
$886$	5.54794e12			0.302468
$887$			2.54827e13i			1.38226i	0.722732	+	0.691129i	$0.242886\pi$
$887$			2.54827e13i			1.38226i	−0.722732	+	0.691129i	$0.757114\pi$
$888$			1.13790e13i			0.614107i
$889$			5.39023e12i			0.289434i
$890$	−4.27810e11			−0.0228558
$891$		−	2.41769e12i		−	0.128514i
$892$	−8.40032e12			−0.444277
$893$	1.15145e13			0.605918
$894$	2.38949e12			0.125108
$895$	−3.27927e12			−0.170834
$896$			1.70252e13i			0.882481i
$897$		−	5.92658e12i		−	0.305660i
$898$	7.20202e12			0.369582
$899$	2.44946e12	+	7.72941e11i	0.125069	+	0.0394664i
$900$	−1.06632e13			−0.541745
$901$			5.00757e13i			2.53143i
$902$			3.30389e12i			0.166187i
$903$	1.29232e13			0.646806
$904$	1.25350e13			0.624260
$905$	9.65047e12			0.478222
$906$	4.39607e12			0.216764
$907$			9.53219e12i			0.467692i	0.972274	+	0.233846i	$0.0751311\pi$
$907$			9.53219e12i			0.467692i	−0.972274	+	0.233846i	$0.924869\pi$
$908$	−1.19133e13			−0.581628
$909$		−	8.14008e12i		−	0.395450i
$910$			8.34857e11i			0.0403577i
$911$			2.60296e13i			1.25209i	0.779787	+	0.626045i	$0.215327\pi$
$911$			2.60296e13i			1.25209i	−0.779787	+	0.626045i	$0.784673\pi$
$912$	−5.58418e12			−0.267290
$913$			2.33999e13i			1.11454i
$914$		−	7.95407e12i		−	0.376991i
$915$	−2.71887e12			−0.128231
$916$		−	3.70471e13i		−	1.73870i
$917$		−	5.82120e12i		−	0.271863i
$918$		−	1.13418e13i		−	0.527095i
$919$	−6.62368e12			−0.306323			−0.153162	−	0.988201i	$-0.548945\pi$
$919$	−6.62368e12			−0.306323			−0.153162	+	0.988201i	$0.548945\pi$
$920$		−	6.74564e12i		−	0.310440i
$921$	−8.31769e12			−0.380921
$922$	2.10288e12			0.0958353
$923$	7.36656e12			0.334085
$924$	7.75215e12			0.349863
$925$			3.74545e13i			1.68216i
$926$			3.06305e12i			0.136900i
$927$	1.94089e13			0.863261
$928$	−1.69007e13	−	5.33313e12i	−0.748065	−	0.236057i
$929$	−2.88196e13			−1.26946			−0.634728	−	0.772736i	$-0.718888\pi$
$929$	−2.88196e13			−1.26946			−0.634728	+	0.772736i	$0.718888\pi$
$930$		−	1.85736e11i		−	0.00814184i
$931$		−	1.65826e12i		−	0.0723401i
$932$	1.25054e13			0.542908
$933$	−2.72863e12			−0.117890
$934$	−7.06655e12			−0.303841
$935$	−1.24495e13			−0.532721
$936$		−	3.50879e12i		−	0.149422i
$937$	3.11480e13			1.32009			0.660043	−	0.751228i	$-0.270538\pi$
$937$	3.11480e13			1.32009			0.660043	+	0.751228i	$0.270538\pi$
$938$			6.65702e12i			0.280781i
$939$			1.60930e13i			0.675527i
$940$			7.78562e12i			0.325250i
$941$	1.23726e12			0.0514408			0.0257204	−	0.999669i	$-0.491812\pi$
$941$	1.23726e12			0.0514408			0.0257204	+	0.999669i	$0.491812\pi$
$942$			5.73863e12i			0.237454i
$943$			2.69424e13i			1.10952i
$944$	−2.84340e11			−0.0116537
$945$		−	8.23669e12i		−	0.335977i
$946$		−	6.61912e12i		−	0.268714i
$947$		−	1.04229e13i		−	0.421128i	−0.977580	−	0.210564i	$-0.932470\pi$
$947$		−	1.04229e13i		−	0.421128i	0.977580	−	0.210564i	$-0.0675300\pi$
$948$	1.26941e13			0.510463
$949$		−	1.17665e13i		−	0.470923i
$950$	4.09695e12			0.163194
$951$	−3.98535e10			−0.00157999
$952$	−2.56928e13			−1.01378
$953$	1.34711e13			0.529037			0.264518	−	0.964381i	$-0.414787\pi$
$953$	1.34711e13			0.529037			0.264518	+	0.964381i	$0.414787\pi$
$954$			6.95016e12i			0.271661i
$955$		−	1.25075e13i		−	0.486581i
$956$	1.01307e13			0.392265
$957$	−3.17499e12	+	1.00616e13i	−0.122360	+	0.387759i
$958$	4.90040e12			0.187969
$959$		−	4.92617e11i		−	0.0188073i
$960$		−	2.85400e12i		−	0.108451i
$961$	2.59849e13			0.982800
$962$	−5.88212e12			−0.221435
$963$	−2.22400e13			−0.833329
$964$	−2.10724e13			−0.785900
$965$		−	4.12434e12i		−	0.153102i
$966$	−6.02319e12			−0.222551
$967$			2.71772e13i			0.999505i	0.866168	+	0.499752i	$0.166576\pi$
$967$			2.71772e13i			0.999505i	−0.866168	+	0.499752i	$0.833424\pi$
$968$			7.09366e12i			0.259676i
$969$		−	1.87326e13i		−	0.682561i
$970$	−2.31554e12			−0.0839809
$971$			4.18693e12i			0.151150i	0.997140	+	0.0755752i	$0.0240793\pi$
$971$			4.18693e12i			0.151150i	−0.997140	+	0.0755752i	$0.975921\pi$
$972$			2.62766e13i			0.944213i
$973$	2.69386e13			0.963533
$974$			8.78609e12i			0.312810i
$975$			5.09954e12i			0.180722i
$976$		−	1.28938e13i		−	0.454837i
$977$	8.55777e12			0.300494			0.150247	−	0.988649i	$-0.451993\pi$
$977$	8.55777e12			0.300494			0.150247	+	0.988649i	$0.451993\pi$
$978$			5.91407e12i			0.206710i
$979$	−4.30263e12			−0.149697
$980$	1.12124e12			0.0388314
$981$	−2.34559e13			−0.808615
$982$	−1.22015e13			−0.418707
$983$			1.22060e12i			0.0416949i	0.999783	+	0.0208475i	$0.00663644\pi$
$983$			1.22060e12i			0.0416949i	−0.999783	+	0.0208475i	$0.993364\pi$
$984$		−	7.04306e12i		−	0.239488i
$985$	8.54902e12			0.289370
$986$	5.02215e12	−	1.59152e13i	0.169217	−	0.536250i
$987$	1.45659e13			0.488552
$988$		−	6.75301e12i		−	0.225471i
$989$		−	5.39773e13i		−	1.79402i
$990$	−1.72790e12			−0.0571691
$991$	−4.08383e12			−0.134504			−0.0672521	−	0.997736i	$-0.521423\pi$
$991$	−4.08383e12			−0.134504			−0.0672521	+	0.997736i	$0.521423\pi$
$992$	3.13775e12			0.102876
$993$	−2.63005e13			−0.858406
$994$		−	7.48663e12i		−	0.243247i
$995$	−1.18493e13			−0.383257
$996$		−	2.38072e13i		−	0.766551i
$997$		−	8.69095e12i		−	0.278573i	−0.990252	−	0.139287i	$-0.955519\pi$
$997$		−	8.69095e12i		−	0.278573i	0.990252	−	0.139287i	$-0.0444809\pi$
$998$			2.89876e12i			0.0924964i
$999$	5.80329e13			1.84344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.b.a.28.12	yes	22
29.28	even	2	inner	29.10.b.a.28.11	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.b.a.28.11	✓	22	29.28	even	2	inner
29.10.b.a.28.12	yes	22	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	29.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+6.67374i q^{2} +77.6458i q^{3} +467.461 q^{4} -531.517 q^{5} -518.188 q^{6} +5986.73 q^{7} +6536.67i q^{8} +13654.1 q^{9} +O(q^{10})\)	\(q+6.67374i q^{2} +77.6458i q^{3} +467.461 q^{4} -531.517 q^{5} -518.188 q^{6} +5986.73 q^{7} +6536.67i q^{8} +13654.1 q^{9} -3547.20i q^{10} -35675.4i q^{11} +36296.4i q^{12} -39313.0 q^{13} +39953.9i q^{14} -41270.0i q^{15} +195716. q^{16} +656546. i q^{17} +91124.1i q^{18} +367464. i q^{19} -248464. q^{20} +464844. i q^{21} +238089. q^{22} +1.94156e6 q^{23} -507545. q^{24} -1.67061e6 q^{25} -262365. i q^{26} +2.58849e6i q^{27} +2.79856e6 q^{28} +(-1.14619e6 + 3.63227e6i) q^{29} +275426. q^{30} -674359. i q^{31} +4.65293e6i q^{32} +2.77005e6 q^{33} -4.38162e6 q^{34} -3.18205e6 q^{35} +6.38278e6 q^{36} -2.24196e7i q^{37} -2.45236e6 q^{38} -3.05249e6i q^{39} -3.47435e6i q^{40} +1.38767e7i q^{41} -3.10225e6 q^{42} -2.78011e7i q^{43} -1.66769e7i q^{44} -7.25740e6 q^{45} +1.29574e7i q^{46} -3.13351e7i q^{47} +1.51965e7i q^{48} -4.51271e6 q^{49} -1.11492e7i q^{50} -5.09781e7 q^{51} -1.83773e7 q^{52} +7.62713e7 q^{53} -1.72749e7 q^{54} +1.89621e7i q^{55} +3.91332e7i q^{56} -2.85320e7 q^{57} +(-2.42408e7 - 7.64935e6i) q^{58} -1.45282e6 q^{59} -1.92921e7i q^{60} -6.58800e7i q^{61} +4.50050e6 q^{62} +8.17435e7 q^{63} +6.91542e7 q^{64} +2.08955e7 q^{65} +1.84866e7i q^{66} +1.66618e8 q^{67} +3.06910e8i q^{68} +1.50754e8i q^{69} -2.12361e7i q^{70} -1.87382e8 q^{71} +8.92525e7i q^{72} +2.99303e8i q^{73} +1.49623e8 q^{74} -1.29716e8i q^{75} +1.71775e8i q^{76} -2.13579e8i q^{77} +2.03715e7 q^{78} -3.49735e8i q^{79} -1.04026e8 q^{80} +6.77690e7 q^{81} -9.26097e7 q^{82} -6.55911e8 q^{83} +2.17297e8i q^{84} -3.48965e8i q^{85} +1.85537e8 q^{86} +(-2.82031e8 - 8.89965e7i) q^{87} +2.33199e8 q^{88} -1.20605e8i q^{89} -4.84340e7i q^{90} -2.35356e8 q^{91} +9.07602e8 q^{92} +5.23612e7 q^{93} +2.09122e8 q^{94} -1.95313e8i q^{95} -3.61281e8 q^{96} -6.52780e8i q^{97} -3.01167e7i q^{98} -4.87117e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9}+O(q^{10}) \) 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9	\( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9} - 244222 q^{13} + 1246804 q^{16} - 1658748 q^{20} + 822328 q^{22} - 874956 q^{23} + 8668172 q^{24} + 5307748 q^{25} - 620352 q^{28} - 2425374 q^{29} - 8942448 q^{30} + 10134274 q^{33} - 37785784 q^{34} - 20790348 q^{35} + 34550680 q^{36} - 30663552 q^{38} + 56872008 q^{42} - 43877176 q^{45} - 131743922 q^{49} - 6194732 q^{51} + 342496580 q^{52} + 34886610 q^{53} + 116488784 q^{54} - 308361676 q^{57} + 342193888 q^{58} + 175799052 q^{59} - 484313328 q^{62} - 190643424 q^{63} - 419498924 q^{64} - 149739966 q^{65} - 508277640 q^{67} + 263144256 q^{71} + 435201408 q^{74} + 1065897336 q^{78} + 2990464236 q^{80} - 129895134 q^{81} - 527065064 q^{82} + 1555989756 q^{83} - 3422424120 q^{86} + 2176720604 q^{87} - 387386068 q^{88} - 1493579244 q^{91} - 1262849472 q^{92} + 2042413382 q^{93} + 166226488 q^{94} - 6686432820 q^{96}+O(q^{100}) \) 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9 - 244222 * q^13 + 1246804 * q^16 - 1658748 * q^20 + 822328 * q^22 - 874956 * q^23 + 8668172 * q^24 + 5307748 * q^25 - 620352 * q^28 - 2425374 * q^29 - 8942448 * q^30 + 10134274 * q^33 - 37785784 * q^34 - 20790348 * q^35 + 34550680 * q^36 - 30663552 * q^38 + 56872008 * q^42 - 43877176 * q^45 - 131743922 * q^49 - 6194732 * q^51 + 342496580 * q^52 + 34886610 * q^53 + 116488784 * q^54 - 308361676 * q^57 + 342193888 * q^58 + 175799052 * q^59 - 484313328 * q^62 - 190643424 * q^63 - 419498924 * q^64 - 149739966 * q^65 - 508277640 * q^67 + 263144256 * q^71 + 435201408 * q^74 + 1065897336 * q^78 + 2990464236 * q^80 - 129895134 * q^81 - 527065064 * q^82 + 1555989756 * q^83 - 3422424120 * q^86 + 2176720604 * q^87 - 387386068 * q^88 - 1493579244 * q^91 - 1262849472 * q^92 + 2042413382 * q^93 + 166226488 * q^94 - 6686432820 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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