LMFDB - Embedded newform 29.10.b.a.28.16

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			28.16
Character	$\chi$	$=$	29.28
Dual form			29.10.b.a.28.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+20.3455i q^{2} +80.4219i q^{3} +98.0611 q^{4} +535.165 q^{5} -1636.22 q^{6} -10636.4 q^{7} +12412.0i q^{8} +13215.3 q^{9} +O(q^{10})$	\(q+20.3455i q^{2} +80.4219i q^{3} +98.0611 q^{4} +535.165 q^{5} -1636.22 q^{6} -10636.4 q^{7} +12412.0i q^{8} +13215.3 q^{9} +10888.2i q^{10} +44107.9i q^{11} +7886.26i q^{12} -158803. q^{13} -216402. i q^{14} +43039.0i q^{15} -202321. q^{16} +140286. i q^{17} +268872. i q^{18} -877729. i q^{19} +52478.9 q^{20} -855397. i q^{21} -897397. q^{22} -330007. q^{23} -998196. q^{24} -1.66672e6 q^{25} -3.23093e6i q^{26} +2.64575e6i q^{27} -1.04301e6 q^{28} +(3.38158e6 - 1.75274e6i) q^{29} -875649. q^{30} -1.48548e6i q^{31} +2.23863e6i q^{32} -3.54724e6 q^{33} -2.85418e6 q^{34} -5.69221e6 q^{35} +1.29591e6 q^{36} +1.79573e7i q^{37} +1.78578e7 q^{38} -1.27713e7i q^{39} +6.64246e6i q^{40} +2.53309e7i q^{41} +1.74035e7 q^{42} -3.46744e7i q^{43} +4.32527e6i q^{44} +7.07238e6 q^{45} -6.71415e6i q^{46} +5.33798e7i q^{47} -1.62710e7i q^{48} +7.27788e7 q^{49} -3.39103e7i q^{50} -1.12820e7 q^{51} -1.55724e7 q^{52} +5.06370e7 q^{53} -5.38290e7 q^{54} +2.36050e7i q^{55} -1.32019e8i q^{56} +7.05887e7 q^{57} +(3.56603e7 + 6.87998e7i) q^{58} -1.38945e8 q^{59} +4.22045e6i q^{60} +1.55954e8i q^{61} +3.02228e7 q^{62} -1.40563e8 q^{63} -1.49134e8 q^{64} -8.49860e7 q^{65} -7.21704e7i q^{66} +5.38634e7 q^{67} +1.37566e7i q^{68} -2.65398e7i q^{69} -1.15811e8i q^{70} +4.97349e7 q^{71} +1.64028e8i q^{72} +8.08043e7i q^{73} -3.65350e8 q^{74} -1.34041e8i q^{75} -8.60711e7i q^{76} -4.69148e8i q^{77} +2.59838e8 q^{78} -1.32720e8i q^{79} -1.08275e8 q^{80} +4.73413e7 q^{81} -5.15369e8 q^{82} +5.96483e8 q^{83} -8.38812e7i q^{84} +7.50760e7i q^{85} +7.05468e8 q^{86} +(1.40958e8 + 2.71953e8i) q^{87} -5.47467e8 q^{88} +2.06855e8i q^{89} +1.43891e8i q^{90} +1.68909e9 q^{91} -3.23608e7 q^{92} +1.19465e8 q^{93} -1.08604e9 q^{94} -4.69730e8i q^{95} -1.80035e8 q^{96} +1.61759e9i q^{97} +1.48072e9i q^{98} +5.82900e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			20.3455i			0.899152i	0.893242	+	0.449576i	$0.148425\pi$
$2$			20.3455i			0.899152i	−0.893242	+	0.449576i	$0.851575\pi$
$3$			80.4219i			0.573230i	0.958046	+	0.286615i	$0.0925300\pi$
$3$			80.4219i			0.573230i	−0.958046	+	0.286615i	$0.907470\pi$
$4$	98.0611			0.191526
$5$	535.165			0.382933			0.191466	−	0.981499i	$-0.438676\pi$
$5$	535.165			0.382933			0.191466	+	0.981499i	$0.438676\pi$
$6$	−1636.22			−0.515421
$7$	−10636.4			−1.67437			−0.837187	−	0.546917i	$-0.815801\pi$
$7$	−10636.4			−1.67437			−0.837187	+	0.546917i	$0.815801\pi$
$8$			12412.0i			1.07136i
$9$	13215.3			0.671408
$10$			10888.2i			0.344315i
$11$			44107.9i			0.908342i	0.890914	+	0.454171i	$0.150065\pi$
$11$			44107.9i			0.908342i	−0.890914	+	0.454171i	$0.849935\pi$
$12$			7886.26i			0.109788i
$13$	−158803.			−1.54211			−0.771053	−	0.636771i	$-0.780270\pi$
$13$	−158803.			−1.54211			−0.771053	+	0.636771i	$0.780270\pi$
$14$		−	216402.i		−	1.50552i
$15$			43039.0i			0.219508i
$16$	−202321.			−0.771792
$17$			140286.i			0.407374i	0.979036	+	0.203687i	$0.0652925\pi$
$17$			140286.i			0.407374i	−0.979036	+	0.203687i	$0.934707\pi$
$18$			268872.i			0.603698i
$19$		−	877729.i		−	1.54515i	−0.634926	−	0.772573i	$-0.718970\pi$
$19$		−	877729.i		−	1.54515i	0.634926	−	0.772573i	$-0.281030\pi$
$20$	52478.9			0.0733415
$21$		−	855397.i		−	0.959801i
$22$	−897397.			−0.816738
$23$	−330007.			−0.245894			−0.122947	−	0.992413i	$-0.539234\pi$
$23$	−330007.			−0.245894			−0.122947	+	0.992413i	$0.539234\pi$
$24$	−998196.			−0.614137
$25$	−1.66672e6			−0.853362
$26$		−	3.23093e6i		−	1.38659i
$27$			2.64575e6i			0.958100i
$28$	−1.04301e6			−0.320685
$29$	3.38158e6	−	1.75274e6i	0.887827	−	0.460178i
$29$	3.38158e6	−	1.75274e6i	0.887827	−	0.460178i
$30$	−875649.			−0.197371
$31$		−	1.48548e6i		−	0.288895i	−0.989512	−	0.144447i	$-0.953860\pi$
$31$		−	1.48548e6i		−	0.288895i	0.989512	−	0.144447i	$-0.0461404\pi$
$32$			2.23863e6i			0.377404i
$33$	−3.54724e6			−0.520689
$34$	−2.85418e6			−0.366291
$35$	−5.69221e6			−0.641173
$36$	1.29591e6			0.128592
$37$			1.79573e7i			1.57519i	0.616193	+	0.787595i	$0.288674\pi$
$37$			1.79573e7i			1.57519i	−0.616193	+	0.787595i	$0.711326\pi$
$38$	1.78578e7			1.38932
$39$		−	1.27713e7i		−	0.883981i
$40$			6.64246e6i			0.410260i
$41$			2.53309e7i			1.39998i	0.714151	+	0.699992i	$0.246813\pi$
$41$			2.53309e7i			1.39998i	−0.714151	+	0.699992i	$0.753187\pi$
$42$	1.74035e7			0.863007
$43$		−	3.46744e7i		−	1.54668i	−0.633991	−	0.773341i	$-0.718584\pi$
$43$		−	3.46744e7i		−	1.54668i	0.633991	−	0.773341i	$-0.281416\pi$
$44$			4.32527e6i			0.173971i
$45$	7.07238e6			0.257104
$46$		−	6.71415e6i		−	0.221096i
$47$			5.33798e7i			1.59565i	0.602891	+	0.797823i	$0.294015\pi$
$47$			5.33798e7i			1.59565i	−0.602891	+	0.797823i	$0.705985\pi$
$48$		−	1.62710e7i		−	0.442414i
$49$	7.27788e7			1.80353
$50$		−	3.39103e7i		−	0.767303i
$51$	−1.12820e7			−0.233519
$52$	−1.55724e7			−0.295353
$53$	5.06370e7			0.881508			0.440754	−	0.897628i	$-0.354711\pi$
$53$	5.06370e7			0.881508			0.440754	+	0.897628i	$0.354711\pi$
$54$	−5.38290e7			−0.861478
$55$			2.36050e7i			0.347834i
$56$		−	1.32019e8i		−	1.79386i
$57$	7.05887e7			0.885723
$58$	3.56603e7	+	6.87998e7i	0.413770	+	0.798291i
$59$	−1.38945e8			−1.49282			−0.746411	−	0.665486i	$-0.768224\pi$
$59$	−1.38945e8			−1.49282			−0.746411	+	0.665486i	$0.768224\pi$
$60$			4.22045e6i			0.0420415i
$61$			1.55954e8i			1.44216i	0.692852	+	0.721080i	$0.256354\pi$
$61$			1.55954e8i			1.44216i	−0.692852	+	0.721080i	$0.743646\pi$
$62$	3.02228e7			0.259760
$63$	−1.40563e8			−1.12419
$64$	−1.49134e8			−1.11114
$65$	−8.49860e7			−0.590523
$66$		−	7.21704e7i		−	0.468178i
$67$	5.38634e7			0.326556			0.163278	−	0.986580i	$-0.447793\pi$
$67$	5.38634e7			0.326556			0.163278	+	0.986580i	$0.447793\pi$
$68$			1.37566e7i			0.0780226i
$69$		−	2.65398e7i		−	0.140954i
$70$		−	1.15811e8i		−	0.576512i
$71$	4.97349e7			0.232273			0.116137	−	0.993233i	$-0.462949\pi$
$71$	4.97349e7			0.232273			0.116137	+	0.993233i	$0.462949\pi$
$72$			1.64028e8i			0.719321i
$73$			8.08043e7i			0.333028i	0.986039	+	0.166514i	$0.0532512\pi$
$73$			8.08043e7i			0.333028i	−0.986039	+	0.166514i	$0.946749\pi$
$74$	−3.65350e8			−1.41634
$75$		−	1.34041e8i		−	0.489173i
$76$		−	8.60711e7i		−	0.295935i
$77$		−	4.69148e8i		−	1.52090i
$78$	2.59838e8			0.794834
$79$		−	1.32720e8i		−	0.383368i	−0.981457	−	0.191684i	$-0.938605\pi$
$79$		−	1.32720e8i		−	0.383368i	0.981457	−	0.191684i	$-0.0613948\pi$
$80$	−1.08275e8			−0.295545
$81$	4.73413e7			0.122196
$82$	−5.15369e8			−1.25880
$83$	5.96483e8			1.37958			0.689790	−	0.724009i	$-0.257703\pi$
$83$	5.96483e8			1.37958			0.689790	+	0.724009i	$0.257703\pi$
$84$		−	8.38812e7i		−	0.183826i
$85$			7.50760e7i			0.155997i
$86$	7.05468e8			1.39070
$87$	1.40958e8	+	2.71953e8i	0.263788	+	0.508929i
$88$	−5.47467e8			−0.973164
$89$			2.06855e8i			0.349470i	0.984615	+	0.174735i	$0.0559069\pi$
$89$			2.06855e8i			0.349470i	−0.984615	+	0.174735i	$0.944093\pi$
$90$			1.43891e8i			0.231176i
$91$	1.68909e9			2.58206
$92$	−3.23608e7			−0.0470950
$93$	1.19465e8			0.165603
$94$	−1.08604e9			−1.43473
$95$		−	4.69730e8i		−	0.591687i
$96$	−1.80035e8			−0.216339
$97$			1.61759e9i			1.85522i	0.373547	+	0.927611i	$0.378141\pi$
$97$			1.61759e9i			1.85522i	−0.373547	+	0.927611i	$0.621859\pi$
$98$			1.48072e9i			1.62164i
$99$			5.82900e8i			0.609868i
$100$	−1.63441e8			−0.163441
$101$		−	4.36489e8i		−	0.417376i	−0.977982	−	0.208688i	$-0.933081\pi$
$101$		−	4.36489e8i		−	0.417376i	0.977982	−	0.208688i	$-0.0669193\pi$
$102$		−	2.29539e8i		−	0.209969i
$103$	−3.54110e8			−0.310006			−0.155003	−	0.987914i	$-0.549539\pi$
$103$	−3.54110e8			−0.310006			−0.155003	+	0.987914i	$0.549539\pi$
$104$		−	1.97106e9i		−	1.65216i
$105$		−	4.57779e8i		−	0.367539i
$106$			1.03023e9i			0.792610i
$107$	1.79661e9			1.32504			0.662518	−	0.749046i	$-0.269488\pi$
$107$	1.79661e9			1.32504			0.662518	+	0.749046i	$0.269488\pi$
$108$			2.59445e8i			0.183501i
$109$	1.39982e9			0.949842			0.474921	−	0.880028i	$-0.342477\pi$
$109$	1.39982e9			0.949842			0.474921	+	0.880028i	$0.342477\pi$
$110$	−4.80255e8			−0.312756
$111$	−1.44416e9			−0.902946
$112$	2.15196e9			1.29227
$113$		−	7.48757e8i		−	0.432004i	−0.976393	−	0.216002i	$-0.930698\pi$
$113$		−	7.48757e8i		−	0.432004i	0.976393	−	0.216002i	$-0.0693018\pi$
$114$			1.43616e9i			0.796400i
$115$	−1.76608e8			−0.0941608
$116$	3.31601e8	−	1.71875e8i	0.170042	−	0.0881359i
$117$	−2.09864e9			−1.03538
$118$		−	2.82690e9i		−	1.34227i
$119$		−	1.49213e9i		−	0.682096i
$120$	−5.34199e8			−0.235173
$121$	4.12439e8			0.174915
$122$	−3.17297e9			−1.29672
$123$	−2.03716e9			−0.802512
$124$		−	1.45668e8i		−	0.0553307i
$125$	−1.93722e9			−0.709713
$126$		−	2.85982e9i		−	1.01082i
$127$		−	1.52234e9i		−	0.519273i	−0.965706	−	0.259637i	$-0.916397\pi$
$127$		−	1.52234e9i		−	0.519273i	0.965706	−	0.259637i	$-0.0836028\pi$
$128$		−	1.88803e9i		−	0.621676i
$129$	2.78858e9			0.886604
$130$		−	1.72908e9i		−	0.530970i
$131$			2.86615e9i			0.850310i	0.905120	+	0.425155i	$0.139780\pi$
$131$			2.86615e9i			0.850310i	−0.905120	+	0.425155i	$0.860220\pi$
$132$	−3.47847e8			−0.0997252
$133$			9.33586e9i			2.58715i
$134$			1.09588e9i			0.293623i
$135$			1.41591e9i			0.366888i
$136$	−1.74123e9			−0.436445
$137$		−	3.01939e9i		−	0.732279i	−0.930560	−	0.366139i	$-0.880679\pi$
$137$		−	3.01939e9i		−	0.732279i	0.930560	−	0.366139i	$-0.119321\pi$
$138$	5.39965e8			0.126739
$139$	1.02221e9			0.232261			0.116130	−	0.993234i	$-0.462951\pi$
$139$	1.02221e9			0.232261			0.116130	+	0.993234i	$0.462951\pi$
$140$	−5.58185e8			−0.122801
$141$	−4.29291e9			−0.914672
$142$			1.01188e9i			0.208849i
$143$		−	7.00448e9i		−	1.40076i
$144$	−2.67373e9			−0.518187
$145$	1.80970e9	−	9.38004e8i	0.339978	−	0.176217i
$146$	−1.64400e9			−0.299443
$147$			5.85301e9i			1.03384i
$148$			1.76091e9i			0.301689i
$149$	−7.62348e8			−0.126711			−0.0633556	−	0.997991i	$-0.520180\pi$
$149$	−7.62348e8			−0.126711			−0.0633556	+	0.997991i	$0.520180\pi$
$150$	2.72713e9			0.439841
$151$	−3.45856e9			−0.541377			−0.270688	−	0.962667i	$-0.587251\pi$
$151$	−3.45856e9			−0.541377			−0.270688	+	0.962667i	$0.587251\pi$
$152$	1.08944e10			1.65541
$153$			1.85392e9i			0.273514i
$154$	9.54505e9			1.36752
$155$		−	7.94977e8i		−	0.110627i
$156$		−	1.25236e9i		−	0.169305i
$157$		−	1.37283e8i		−	0.0180330i	−0.999959	−	0.00901651i	$-0.997130\pi$
$157$		−	1.37283e8i		−	0.0180330i	0.999959	−	0.00901651i	$-0.00287008\pi$
$158$	2.70026e9			0.344706
$159$			4.07232e9i			0.505307i
$160$			1.19803e9i			0.144520i
$161$	3.51008e9			0.411718
$162$			9.63182e8i			0.109873i
$163$		−	7.49335e9i		−	0.831442i	−0.909492	−	0.415721i	$-0.863529\pi$
$163$		−	7.49335e9i		−	0.831442i	0.909492	−	0.415721i	$-0.136471\pi$
$164$			2.48397e9i			0.268133i
$165$	−1.89836e9			−0.199389
$166$			1.21357e10i			1.24045i
$167$	−9.50829e9			−0.945972			−0.472986	−	0.881070i	$-0.656824\pi$
$167$	−9.50829e9			−0.945972			−0.472986	+	0.881070i	$0.656824\pi$
$168$	1.06172e10			1.02829
$169$	1.46140e10			1.37809
$170$	−1.52746e9			−0.140265
$171$		−	1.15995e10i		−	1.03742i
$172$		−	3.40021e9i		−	0.296229i
$173$	−1.59071e10			−1.35016			−0.675078	−	0.737747i	$-0.735890\pi$
$173$	−1.59071e10			−1.35016			−0.675078	+	0.737747i	$0.735890\pi$
$174$	−5.53301e9	+	2.86787e9i	−0.457604	+	0.237185i
$175$	1.77279e10			1.42885
$176$		−	8.92395e9i		−	0.701051i
$177$		−	1.11742e10i		−	0.855729i
$178$	−4.20856e9			−0.314227
$179$	1.90928e9			0.139005			0.0695024	−	0.997582i	$-0.477859\pi$
$179$	1.90928e9			0.139005			0.0695024	+	0.997582i	$0.477859\pi$
$180$	6.93525e8			0.0492420
$181$	7.14189e9			0.494606			0.247303	−	0.968938i	$-0.420456\pi$
$181$	7.14189e9			0.494606			0.247303	+	0.968938i	$0.420456\pi$
$182$			3.43654e10i			2.32167i
$183$	−1.25421e10			−0.826689
$184$		−	4.09604e9i		−	0.263441i
$185$			9.61012e9i			0.603192i
$186$			2.43058e9i			0.148902i
$187$	−6.18771e9			−0.370035
$188$			5.23449e9i			0.305607i
$189$		−	2.81411e10i		−	1.60422i
$190$	9.55688e9			0.532017
$191$		−	1.49830e9i		−	0.0814608i	−0.999170	−	0.0407304i	$-0.987032\pi$
$191$		−	1.49830e9i		−	0.0814608i	0.999170	−	0.0407304i	$-0.0129685\pi$
$192$		−	1.19936e10i		−	0.636936i
$193$			1.12301e10i			0.582607i	0.956631	+	0.291303i	$0.0940889\pi$
$193$			1.12301e10i			0.582607i	−0.956631	+	0.291303i	$0.905911\pi$
$194$	−3.29107e10			−1.66813
$195$		−	6.83473e9i		−	0.338505i
$196$	7.13677e9			0.345422
$197$	−3.05672e10			−1.44596			−0.722982	−	0.690867i	$-0.757229\pi$
$197$	−3.05672e10			−1.44596			−0.722982	+	0.690867i	$0.757229\pi$
$198$	−1.18594e10			−0.548364
$199$	−1.56663e10			−0.708153			−0.354076	−	0.935216i	$-0.615205\pi$
$199$	−1.56663e10			−0.708153			−0.354076	+	0.935216i	$0.615205\pi$
$200$		−	2.06874e10i		−	0.914261i
$201$			4.33180e9i			0.187191i
$202$	8.88058e9			0.375284
$203$	−3.59677e10	+	1.86428e10i	−1.48655	+	0.770510i
$204$	−1.10633e9			−0.0447249
$205$			1.35562e10i			0.536100i
$206$		−	7.20453e9i		−	0.278743i
$207$	−4.36114e9			−0.165095
$208$	3.21292e10			1.19019
$209$	3.87148e10			1.40352
$210$	9.31373e9			0.330474
$211$		−	3.93832e10i		−	1.36785i	−0.729550	−	0.683927i	$-0.760271\pi$
$211$		−	3.93832e10i		−	1.36785i	0.729550	−	0.683927i	$-0.239729\pi$
$212$	4.96552e9			0.168831
$213$			3.99978e9i			0.133146i
$214$			3.65530e10i			1.19141i
$215$		−	1.85565e10i		−	0.592275i
$216$	−3.28390e10			−1.02647
$217$			1.58001e10i			0.483718i
$218$			2.84799e10i			0.854053i
$219$	−6.49843e9			−0.190902
$220$			2.31473e9i			0.0666191i
$221$		−	2.22778e10i		−	0.628214i
$222$		−	2.93821e10i		−	0.811886i
$223$	3.45248e10			0.934886			0.467443	−	0.884023i	$-0.345175\pi$
$223$	3.45248e10			0.934886			0.467443	+	0.884023i	$0.345175\pi$
$224$		−	2.38109e10i		−	0.631915i
$225$	−2.20263e10			−0.572954
$226$	1.52338e10			0.388437
$227$	−4.70018e9			−0.117489			−0.0587447	−	0.998273i	$-0.518710\pi$
$227$	−4.70018e9			−0.117489			−0.0587447	+	0.998273i	$0.518710\pi$
$228$	6.92200e9			0.169639
$229$		−	3.48159e10i		−	0.836599i	−0.908309	−	0.418300i	$-0.862626\pi$
$229$		−	3.48159e10i		−	0.836599i	0.908309	−	0.418300i	$-0.137374\pi$
$230$		−	3.59318e9i		−	0.0846649i
$231$	3.77298e10			0.871827
$232$	2.17550e10	+	4.19721e10i	0.493018	+	0.951184i
$233$	1.84061e10			0.409128			0.204564	−	0.978853i	$-0.434422\pi$
$233$	1.84061e10			0.409128			0.204564	+	0.978853i	$0.434422\pi$
$234$		−	4.26978e10i		−	0.930966i
$235$			2.85670e10i			0.611026i
$236$	−1.36251e10			−0.285914
$237$	1.06736e10			0.219758
$238$	3.03581e10			0.613308
$239$	−3.94325e10			−0.781742			−0.390871	−	0.920445i	$-0.627826\pi$
$239$	−3.94325e10			−0.781742			−0.390871	+	0.920445i	$0.627826\pi$
$240$		−	8.70768e9i		−	0.169415i
$241$	2.81330e10			0.537204			0.268602	−	0.963251i	$-0.413438\pi$
$241$	2.81330e10			0.537204			0.268602	+	0.963251i	$0.413438\pi$
$242$			8.39128e9i			0.157275i
$243$			5.58835e10i			1.02815i
$244$			1.52931e10i			0.276211i
$245$	3.89487e10			0.690630
$246$		−	4.14470e10i		−	0.721580i
$247$			1.39386e11i			2.38278i
$248$	1.84378e10			0.309511
$249$			4.79703e10i			0.790816i
$250$		−	3.94136e10i		−	0.638140i
$251$			1.02466e11i			1.62948i	0.579830	+	0.814738i	$0.303119\pi$
$251$			1.02466e11i			1.62948i	−0.579830	+	0.814738i	$0.696881\pi$
$252$	−1.37838e10			−0.215311
$253$		−	1.45559e10i		−	0.223356i
$254$	3.09728e10			0.466905
$255$	−6.03776e9			−0.0894221
$256$	−3.79438e10			−0.552155
$257$	1.58190e10			0.226194			0.113097	−	0.993584i	$-0.463923\pi$
$257$	1.58190e10			0.226194			0.113097	+	0.993584i	$0.463923\pi$
$258$			5.67350e10i			0.797191i
$259$		−	1.91000e11i		−	2.63746i
$260$	−8.33382e9			−0.113100
$261$	4.46886e10	−	2.31630e10i	0.596094	−	0.308967i
$262$	−5.83131e10			−0.764558
$263$			2.83743e10i			0.365699i	0.983141	+	0.182850i	$0.0585322\pi$
$263$			2.83743e10i			0.365699i	−0.983141	+	0.182850i	$0.941468\pi$
$264$		−	4.40283e10i		−	0.557846i
$265$	2.70991e10			0.337558
$266$	−1.89943e11			−2.32624
$267$	−1.66356e10			−0.200327
$268$	5.28191e9			0.0625438
$269$			1.04744e10i			0.121968i	0.998139	+	0.0609838i	$0.0194238\pi$
$269$			1.04744e10i			0.121968i	−0.998139	+	0.0609838i	$0.980576\pi$
$270$	−2.88074e10			−0.329888
$271$			3.07175e9i			0.0345958i	0.999850	+	0.0172979i	$0.00550637\pi$
$271$			3.07175e9i			0.0345958i	−0.999850	+	0.0172979i	$0.994494\pi$
$272$		−	2.83827e10i		−	0.314408i
$273$			1.35840e11i			1.48011i
$274$	6.14309e10			0.658430
$275$		−	7.35157e10i		−	0.775145i
$276$		−	2.60252e9i		−	0.0269962i
$277$	−4.50980e10			−0.460255			−0.230127	−	0.973161i	$-0.573914\pi$
$277$	−4.50980e10			−0.460255			−0.230127	+	0.973161i	$0.573914\pi$
$278$			2.07975e10i			0.208838i
$279$		−	1.96311e10i		−	0.193966i
$280$		−	7.06517e10i		−	0.686928i
$281$	1.51749e11			1.45194			0.725968	−	0.687729i	$-0.241392\pi$
$281$	1.51749e11			1.45194			0.725968	+	0.687729i	$0.241392\pi$
$282$		−	8.73413e10i		−	0.822429i
$283$	−1.49268e11			−1.38334			−0.691670	−	0.722214i	$-0.743125\pi$
$283$	−1.49268e11			−1.38334			−0.691670	+	0.722214i	$0.743125\pi$
$284$	4.87706e9			0.0444863
$285$	3.77766e10			0.339173
$286$	1.42510e11			1.25950
$287$		−	2.69429e11i		−	2.34410i
$288$			2.95842e10i			0.253392i
$289$	9.89078e10			0.834046
$290$	1.90841e10	+	3.68193e10i	0.158446	+	0.305692i
$291$	−1.30090e11			−1.06347
$292$			7.92376e9i			0.0637835i
$293$		−	2.06197e11i		−	1.63448i	−0.576299	−	0.817239i	$-0.695504\pi$
$293$		−	2.06197e11i		−	1.63448i	0.576299	−	0.817239i	$-0.304496\pi$
$294$	−1.19082e11			−0.929575
$295$	−7.43583e10			−0.571650
$296$	−2.22886e11			−1.68760
$297$	−1.16698e11			−0.870283
$298$		−	1.55103e10i		−	0.113933i
$299$	5.24062e10			0.379194
$300$		−	1.31442e10i		−	0.0936891i
$301$			3.68810e11i			2.58972i
$302$		−	7.03661e10i		−	0.486780i
$303$	3.51033e10			0.239252
$304$			1.77583e11i			1.19253i
$305$			8.34613e10i			0.552250i
$306$	−3.77189e10			−0.245931
$307$		−	9.03945e10i		−	0.580790i	−0.956907	−	0.290395i	$-0.906213\pi$
$307$		−	9.03945e10i		−	0.580790i	0.956907	−	0.290395i	$-0.0937867\pi$
$308$		−	4.60052e10i		−	0.291292i
$309$		−	2.84782e10i		−	0.177705i
$310$	1.61742e10			0.0994707
$311$			4.39054e10i			0.266132i	0.991107	+	0.133066i	$0.0424821\pi$
$311$			4.39054e10i			0.266132i	−0.991107	+	0.133066i	$0.957518\pi$
$312$	1.58517e11			0.947065
$313$	1.81252e11			1.06741			0.533707	−	0.845669i	$-0.320799\pi$
$313$	1.81252e11			1.06741			0.533707	+	0.845669i	$0.320799\pi$
$314$	2.79309e9			0.0162144
$315$	−7.52244e10			−0.430488
$316$		−	1.30147e10i		−	0.0734247i
$317$			2.03586e11i			1.13235i	0.824284	+	0.566177i	$0.191578\pi$
$317$			2.03586e11i			1.13235i	−0.824284	+	0.566177i	$0.808422\pi$
$318$	−8.28533e10			−0.454347
$319$	7.73096e10	+	1.49154e11i	0.417999	+	0.806450i
$320$	−7.98114e10			−0.425490
$321$			1.44487e11i			0.759550i
$322$			7.14142e10i			0.370197i
$323$	1.23133e11			0.629452
$324$	4.64234e9			0.0234037
$325$	2.64681e11			1.31598
$326$	1.52456e11			0.747592
$327$			1.12576e11i			0.544478i
$328$	−3.14407e11			−1.49989
$329$		−	5.67768e11i		−	2.67171i
$330$		−	3.86231e10i		−	0.179281i
$331$			8.13614e10i			0.372557i	0.982497	+	0.186278i	$0.0596426\pi$
$331$			8.13614e10i			0.372557i	−0.982497	+	0.186278i	$0.940357\pi$
$332$	5.84918e10			0.264225
$333$			2.37311e11i			1.05760i
$334$		−	1.93451e11i		−	0.850573i
$335$	2.88258e10			0.125049
$336$			1.73065e11i			0.740767i
$337$		−	3.07171e11i		−	1.29731i	−0.761081	−	0.648657i	$-0.775331\pi$
$337$		−	3.07171e11i		−	1.29731i	0.761081	−	0.648657i	$-0.224669\pi$
$338$			2.97329e11i			1.23911i
$339$	6.02165e10			0.247638
$340$			7.36204e9i			0.0298774i
$341$	6.55215e10			0.262415
$342$	2.35997e11			0.932801
$343$	−3.44887e11			−1.34540
$344$	4.30378e11			1.65706
$345$		−	1.42032e10i		−	0.0539758i
$346$		−	3.23638e11i		−	1.21399i
$347$	−9.26712e10			−0.343133			−0.171566	−	0.985173i	$-0.554883\pi$
$347$	−9.26712e10			−0.343133			−0.171566	+	0.985173i	$0.554883\pi$
$348$	1.38225e10	+	2.66680e10i	0.0505221	+	0.0974729i
$349$	−7.76792e10			−0.280279			−0.140139	−	0.990132i	$-0.544755\pi$
$349$	−7.76792e10			−0.280279			−0.140139	+	0.990132i	$0.544755\pi$
$350$			3.60683e11i			1.28475i
$351$		−	4.20153e11i		−	1.47749i
$352$	−9.87411e10			−0.342812
$353$	5.23392e11			1.79408			0.897039	−	0.441952i	$-0.145714\pi$
$353$	5.23392e11			1.79408			0.897039	+	0.441952i	$0.145714\pi$
$354$	2.27344e11			0.769431
$355$	2.66164e10			0.0889450
$356$			2.02844e10i			0.0669325i
$357$	1.20000e11			0.390998
$358$			3.88451e10i			0.124986i
$359$		−	2.39340e11i		−	0.760483i	−0.924887	−	0.380242i	$-0.875841\pi$
$359$		−	2.39340e11i		−	0.760483i	0.924887	−	0.380242i	$-0.124159\pi$
$360$			8.77823e10i			0.275452i
$361$	−4.47721e11			−1.38747
$362$			1.45305e11i			0.444726i
$363$			3.31691e10i			0.100266i
$364$	1.65634e11			0.494531
$365$			4.32436e10i			0.127528i
$366$		−	2.55176e11i		−	0.743319i
$367$		−	7.91771e10i		−	0.227826i	−0.993491	−	0.113913i	$-0.963662\pi$
$367$		−	7.91771e10i		−	0.227826i	0.993491	−	0.113913i	$-0.0363384\pi$
$368$	6.67672e10			0.189779
$369$			3.34756e11i			0.939960i
$370$	−1.95522e11			−0.542362
$371$	−5.38594e11			−1.47597
$372$	1.17149e10			0.0317172
$373$	−6.23789e11			−1.66858			−0.834291	−	0.551324i	$-0.814123\pi$
$373$	−6.23789e11			−1.66858			−0.834291	+	0.551324i	$0.814123\pi$
$374$		−	1.25892e11i		−	0.332718i
$375$		−	1.55795e11i		−	0.406829i
$376$	−6.62550e11			−1.70952
$377$	−5.37005e11	+	2.78340e11i	−1.36912	+	0.709644i
$378$	5.72545e11			1.44244
$379$			9.29165e10i			0.231322i	0.993289	+	0.115661i	$0.0368986\pi$
$379$			9.29165e10i			0.231322i	−0.993289	+	0.115661i	$0.963101\pi$
$380$		−	4.60623e10i		−	0.113323i
$381$	1.22430e11			0.297663
$382$	3.04837e10			0.0732457
$383$	1.75973e11			0.417879			0.208940	−	0.977929i	$-0.432999\pi$
$383$	1.75973e11			0.417879			0.208940	+	0.977929i	$0.432999\pi$
$384$	1.51839e11			0.356363
$385$		−	2.51072e11i		−	0.582404i
$386$	−2.28482e11			−0.523852
$387$		−	4.58233e11i		−	1.03845i
$388$			1.58623e11i			0.355323i
$389$			4.78233e11i			1.05893i	0.848332	+	0.529464i	$0.177607\pi$
$389$			4.78233e11i			1.05893i	−0.848332	+	0.529464i	$0.822393\pi$
$390$	1.39056e11			0.304368
$391$		−	4.62953e10i		−	0.100171i
$392$			9.03330e11i			1.93223i
$393$	−2.30501e11			−0.487423
$394$		−	6.21904e11i		−	1.30014i
$395$		−	7.10273e10i		−	0.146804i
$396$			5.71599e10i			0.116805i
$397$	1.85757e11			0.375309			0.187654	−	0.982235i	$-0.439912\pi$
$397$	1.85757e11			0.375309			0.187654	+	0.982235i	$0.439912\pi$
$398$		−	3.18738e11i		−	0.636737i
$399$	−7.50807e11			−1.48303
$400$	3.37213e11			0.658619
$401$	1.25529e11			0.242435			0.121217	−	0.992626i	$-0.461320\pi$
$401$	1.25529e11			0.242435			0.121217	+	0.992626i	$0.461320\pi$
$402$	−8.81325e10			−0.168313
$403$			2.35899e11i			0.445506i
$404$		−	4.28026e10i		−	0.0799382i
$405$	2.53354e10			0.0467929
$406$	−3.79296e11	−	7.31781e11i	−0.692806	−	1.33664i
$407$	−7.92059e11			−1.43081
$408$		−	1.40033e11i		−	0.250183i
$409$		−	3.07828e11i		−	0.543943i	−0.962305	−	0.271972i	$-0.912324\pi$
$409$		−	3.07828e11i		−	0.543943i	0.962305	−	0.271972i	$-0.0876757\pi$
$410$	−2.75807e11			−0.482035
$411$	2.42825e11			0.419764
$412$	−3.47244e10			−0.0593741
$413$	1.47787e12			2.49954
$414$		−	8.87296e10i		−	0.148446i
$415$	3.19217e11			0.528287
$416$		−	3.55501e11i		−	0.581997i
$417$			8.22084e10i			0.133139i
$418$			7.87672e11i			1.26198i
$419$	−4.04000e11			−0.640352			−0.320176	−	0.947358i	$-0.603742\pi$
$419$	−4.04000e11			−0.640352			−0.320176	+	0.947358i	$0.603742\pi$
$420$		−	4.48903e10i		−	0.0703932i
$421$			7.55919e11i			1.17275i	0.810040	+	0.586375i	$0.199446\pi$
$421$			7.55919e11i			1.17275i	−0.810040	+	0.586375i	$0.800554\pi$
$422$	8.01270e11			1.22991
$423$			7.05431e11i			1.07133i
$424$			6.28506e11i			0.944415i
$425$		−	2.33818e11i		−	0.347638i
$426$	−8.13774e10			−0.119718
$427$		−	1.65879e12i		−	2.41471i
$428$	1.76178e11			0.253778
$429$	5.63314e11			0.802957
$430$	3.77541e11			0.532545
$431$	−4.56956e10			−0.0637862			−0.0318931	−	0.999491i	$-0.510154\pi$
$431$	−4.56956e10			−0.0637862			−0.0318931	+	0.999491i	$0.510154\pi$
$432$		−	5.35289e11i		−	0.739455i
$433$			3.79589e11i			0.518941i	0.965751	+	0.259471i	$0.0835481\pi$
$433$			3.79589e11i			0.518941i	−0.965751	+	0.259471i	$0.916452\pi$
$434$	−3.21461e11			−0.434936
$435$	7.54360e10	+	1.45540e11i	0.101013	+	0.194885i
$436$	1.37267e11			0.181919
$437$			2.89657e11i			0.379942i
$438$		−	1.32214e11i		−	0.171650i
$439$	−8.24841e11			−1.05994			−0.529968	−	0.848018i	$-0.677796\pi$
$439$	−8.24841e11			−1.05994			−0.529968	+	0.848018i	$0.677796\pi$
$440$	−2.92985e11			−0.372656
$441$	9.61795e11			1.21090
$442$	4.53254e11			0.564860
$443$			7.11667e8i			0.000877930i	1.00000		0.000438965i	$0.000139727\pi$
$443$			7.11667e8i			0.000877930i	−1.00000		0.000438965i	$0.999860\pi$
$444$	−1.41616e11			−0.172937
$445$			1.10701e11i			0.133824i
$446$			7.02423e11i			0.840605i
$447$		−	6.13095e10i		−	0.0726346i
$448$	1.58625e12			1.86046
$449$			1.24845e11i			0.144964i	0.997370	+	0.0724822i	$0.0230921\pi$
$449$			1.24845e11i			0.144964i	−0.997370	+	0.0724822i	$0.976908\pi$
$450$		−	4.48135e11i		−	0.515173i
$451$	−1.11729e12			−1.27166
$452$		−	7.34240e10i		−	0.0827399i
$453$		−	2.78144e11i		−	0.310333i
$454$		−	9.56275e10i		−	0.105641i
$455$	9.03942e11			0.988757
$456$			8.76146e11i			0.948931i
$457$	−8.62560e11			−0.925052			−0.462526	−	0.886606i	$-0.653057\pi$
$457$	−8.62560e11			−0.925052			−0.462526	+	0.886606i	$0.653057\pi$
$458$	7.08346e11			0.752230
$459$	−3.71160e11			−0.390305
$460$	−1.73184e10			−0.0180342
$461$			9.46653e11i			0.976195i	0.872789	+	0.488098i	$0.162309\pi$
$461$			9.46653e11i			0.976195i	−0.872789	+	0.488098i	$0.837691\pi$
$462$			7.67631e11i			0.783905i
$463$	5.82108e11			0.588694			0.294347	−	0.955699i	$-0.404898\pi$
$463$	5.82108e11			0.588694			0.294347	+	0.955699i	$0.404898\pi$
$464$	−6.84163e11	+	3.54615e11i	−0.685218	+	0.355162i
$465$	6.39336e10			0.0634148
$466$			3.74480e11i			0.367868i
$467$		−	1.55738e11i		−	0.151520i	−0.997126	−	0.0757600i	$-0.975862\pi$
$467$		−	1.55738e11i		−	0.151520i	0.997126	−	0.0757600i	$-0.0241383\pi$
$468$	−2.05795e11			−0.198302
$469$	−5.72911e11			−0.546776
$470$	−5.81210e11			−0.549405
$471$	1.10406e10			0.0103371
$472$		−	1.72458e12i		−	1.59935i
$473$	1.52942e12			1.40492
$474$			2.17160e11i			0.197596i
$475$			1.46293e12i			1.31857i
$476$		−	1.46320e11i		−	0.130639i
$477$	6.69184e11			0.591851
$478$		−	8.02273e11i		−	0.702905i
$479$		−	5.29436e11i		−	0.459520i	−0.973247	−	0.229760i	$-0.926206\pi$
$479$		−	5.29436e11i		−	0.459520i	0.973247	−	0.229760i	$-0.0737941\pi$
$480$	−9.63482e10			−0.0828434
$481$		−	2.85168e12i		−	2.42911i
$482$			5.72380e11i			0.483028i
$483$			2.82287e11i			0.236009i
$484$	4.04443e10			0.0335006
$485$			8.65678e11i			0.710426i
$486$	−1.13698e12			−0.924460
$487$	−6.90812e11			−0.556519			−0.278259	−	0.960506i	$-0.589757\pi$
$487$	−6.90812e11			−0.556519			−0.278259	+	0.960506i	$0.589757\pi$
$488$	−1.93570e12			−1.54508
$489$	6.02629e11			0.476607
$490$			7.92430e11i			0.620981i
$491$		−	9.33878e11i		−	0.725142i	−0.931956	−	0.362571i	$-0.881899\pi$
$491$		−	9.33878e11i		−	0.725142i	0.931956	−	0.362571i	$-0.118101\pi$
$492$	−1.99766e11			−0.153702
$493$	2.45884e11	+	4.74387e11i	0.187465	+	0.361678i
$494$	−2.83588e12			−2.14248
$495$			3.11948e11i			0.233538i
$496$			3.00544e11i			0.222967i
$497$	−5.28999e11			−0.388912
$498$	−9.75980e11			−0.711064
$499$	1.71340e12			1.23710			0.618551	−	0.785745i	$-0.287720\pi$
$499$	1.71340e12			1.23710			0.618551	+	0.785745i	$0.287720\pi$
$500$	−1.89966e11			−0.135928
$501$		−	7.64675e11i		−	0.542259i
$502$	−2.08472e12			−1.46515
$503$			6.70826e10i			0.0467255i	0.999727	+	0.0233627i	$0.00743727\pi$
$503$			6.70826e10i			0.0467255i	−0.999727	+	0.0233627i	$0.992563\pi$
$504$		−	1.74467e12i		−	1.20441i
$505$		−	2.33594e11i		−	0.159827i
$506$	2.96147e11			0.200831
$507$			1.17528e12i			0.789964i
$508$		−	1.49283e11i		−	0.0994541i
$509$	1.93076e12			1.27497			0.637484	−	0.770464i	$-0.279975\pi$
$509$	1.93076e12			1.27497			0.637484	+	0.770464i	$0.279975\pi$
$510$		−	1.22841e11i		−	0.0804040i
$511$		−	8.59464e11i		−	0.557614i
$512$		−	1.73866e12i		−	1.11815i
$513$	2.32225e12			1.48040
$514$			3.21846e11i			0.203383i
$515$	−1.89507e11			−0.118711
$516$	2.73451e11			0.169807
$517$	−2.35447e12			−1.44939
$518$	3.88600e12			2.37148
$519$		−	1.27928e12i		−	0.773949i
$520$		−	1.05484e12i		−	0.632665i
$521$	−6.66490e11			−0.396300			−0.198150	−	0.980172i	$-0.563493\pi$
$521$	−6.66490e11			−0.396300			−0.198150	+	0.980172i	$0.563493\pi$
$522$	4.71262e11	+	9.09212e11i	0.277808	+	0.535979i
$523$	−8.60903e11			−0.503149			−0.251575	−	0.967838i	$-0.580948\pi$
$523$	−8.60903e11			−0.503149			−0.251575	+	0.967838i	$0.580948\pi$
$524$			2.81058e11i			0.162856i
$525$			1.42571e12i			0.819058i
$526$	−5.77289e11			−0.328819
$527$	2.08392e11			0.117688
$528$	7.17681e11			0.401863
$529$	−1.69225e12			−0.939536
$530$			5.51345e11i			0.303516i
$531$	−1.83620e12			−1.00229
$532$			9.15485e11i			0.495506i
$533$		−	4.02263e12i		−	2.15892i
$534$		−	3.38460e11i		−	0.180124i
$535$	9.61484e11			0.507400
$536$			6.68552e11i			0.349859i
$537$			1.53548e11i			0.0796817i
$538$	−2.13107e11			−0.109668
$539$			3.21012e12i			1.63822i
$540$			1.38846e11i			0.0702685i
$541$		−	2.25301e11i		−	0.113078i	−0.998400	−	0.0565388i	$-0.981994\pi$
$541$		−	2.25301e11i		−	0.113078i	0.998400	−	0.0565388i	$-0.0180065\pi$
$542$	−6.24962e10			−0.0311069
$543$			5.74364e11i			0.283523i
$544$	−3.14047e11			−0.153745
$545$	7.49132e11			0.363726
$546$	−2.76373e12			−1.33085
$547$	3.83368e12			1.83094			0.915468	−	0.402390i	$-0.131821\pi$
$547$	3.83368e12			1.83094			0.915468	+	0.402390i	$0.131821\pi$
$548$		−	2.96085e11i		−	0.140250i
$549$			2.06099e12i			0.968277i
$550$	1.49571e12			0.696973
$551$	−1.53843e12	−	2.96811e12i	−0.711042	−	1.37182i
$552$	3.29411e11			0.151012
$553$			1.41166e12i			0.641901i
$554$		−	9.17541e11i		−	0.413839i
$555$	−7.72864e11			−0.345768
$556$	1.00240e11			0.0444839
$557$	1.62004e12			0.713145			0.356573	−	0.934268i	$-0.383945\pi$
$557$	1.62004e12			0.713145			0.356573	+	0.934268i	$0.383945\pi$
$558$	3.99404e11			0.174405
$559$			5.50641e12i			2.38515i
$560$	1.15165e12			0.494852
$561$		−	4.97628e11i		−	0.212115i
$562$			3.08741e12i			1.30551i
$563$		−	1.99631e11i		−	0.0837415i	−0.999123	−	0.0418708i	$-0.986668\pi$
$563$		−	1.99631e11i		−	0.0837415i	0.999123	−	0.0418708i	$-0.0133318\pi$
$564$	−4.20967e11			−0.175183
$565$		−	4.00708e11i		−	0.165429i
$566$		−	3.03694e12i		−	1.24383i
$567$	−5.03540e11			−0.204602
$568$			6.17309e11i			0.248849i
$569$			2.14233e12i			0.856803i	0.903588	+	0.428402i	$0.140923\pi$
$569$			2.14233e12i			0.856803i	−0.903588	+	0.428402i	$0.859077\pi$
$570$			7.68583e11i			0.304968i
$571$	4.43245e12			1.74494			0.872472	−	0.488664i	$-0.162515\pi$
$571$	4.43245e12			1.74494			0.872472	+	0.488664i	$0.162515\pi$
$572$		−	6.86867e11i		−	0.268282i
$573$	1.20496e11			0.0466958
$574$	5.48166e12			2.10770
$575$	5.50030e11			0.209837
$576$	−1.97086e12			−0.746025
$577$			1.88275e12i			0.707133i	0.935409	+	0.353567i	$0.115031\pi$
$577$			1.88275e12i			0.707133i	−0.935409	+	0.353567i	$0.884969\pi$
$578$			2.01233e12i			0.749934i
$579$	−9.03146e11			−0.333968
$580$	1.77461e11	−	9.19817e10i	0.0651145	−	0.0337501i
$581$	−6.34442e12			−2.30993
$582$		−	2.64674e12i		−	0.956220i
$583$			2.23349e12i			0.800711i
$584$	−1.00294e12			−0.356794
$585$	−1.12312e12			−0.396482
$586$	4.19519e12			1.46964
$587$	3.01626e12			1.04857			0.524285	−	0.851543i	$-0.324333\pi$
$587$	3.01626e12			1.04857			0.524285	+	0.851543i	$0.324333\pi$
$588$			5.73953e11i			0.198006i
$589$	−1.30385e12			−0.446384
$590$		−	1.51286e12i		−	0.514001i
$591$		−	2.45827e12i		−	0.828869i
$592$		−	3.63313e12i		−	1.21572i
$593$	9.19055e11			0.305208			0.152604	−	0.988287i	$-0.451234\pi$
$593$	9.19055e11			0.305208			0.152604	+	0.988287i	$0.451234\pi$
$594$		−	2.37428e12i		−	0.782517i
$595$		−	7.98537e11i		−	0.261197i
$596$	−7.47567e10			−0.0242684
$597$		−	1.25991e12i		−	0.405934i
$598$			1.06623e12i			0.340953i
$599$			3.71816e12i			1.18007i	0.807378	+	0.590035i	$0.200886\pi$
$599$			3.71816e12i			1.18007i	−0.807378	+	0.590035i	$0.799114\pi$
$600$	1.66372e12			0.524081
$601$		−	1.00197e11i		−	0.0313272i	−0.999877	−	0.0156636i	$-0.995014\pi$
$601$		−	1.00197e11i		−	0.0313272i	0.999877	−	0.0156636i	$-0.00498608\pi$
$602$	−7.50362e12			−2.32855
$603$	7.11822e11			0.219252
$604$	−3.39151e11			−0.103687
$605$	2.20723e11			0.0669805
$606$			7.14193e11i			0.215124i
$607$		−	2.51781e12i		−	0.752791i	−0.926459	−	0.376395i	$-0.877163\pi$
$607$		−	2.51781e12i		−	0.752791i	0.926459	−	0.376395i	$-0.122837\pi$
$608$	1.96491e12			0.583144
$609$	−1.49929e12	−	2.89259e12i	−0.441679	−	0.852137i
$610$	−1.69806e12			−0.496557
$611$		−	8.47689e12i		−	2.46066i
$612$			1.81798e11i			0.0523850i
$613$	−9.57162e11			−0.273787			−0.136894	−	0.990586i	$-0.543712\pi$
$613$	−9.57162e11			−0.273787			−0.136894	+	0.990586i	$0.543712\pi$
$614$	1.83912e12			0.522218
$615$	−1.09022e12			−0.307308
$616$	5.82306e12			1.62944
$617$		−	1.60480e12i		−	0.445796i	−0.974842	−	0.222898i	$-0.928448\pi$
$617$		−	1.60480e12i		−	0.445796i	0.974842	−	0.222898i	$-0.0715517\pi$
$618$	5.79402e11			0.159783
$619$			4.95111e12i			1.35548i	0.735300	+	0.677742i	$0.237041\pi$
$619$			4.95111e12i			1.35548i	−0.735300	+	0.677742i	$0.762959\pi$
$620$		−	7.79564e10i		−	0.0211880i
$621$		−	8.73114e11i		−	0.235591i
$622$	−8.93277e11			−0.239293
$623$		−	2.20018e12i		−	0.585144i
$624$			2.58389e12i			0.682250i
$625$	2.21859e12			0.581590
$626$			3.68766e12i			0.959767i
$627$			3.11352e12i			0.804540i
$628$		−	1.34621e10i		−	0.00345379i
$629$	−2.51915e12			−0.641692
$630$		−	1.53048e12i		−	0.387074i
$631$	−6.34685e12			−1.59377			−0.796885	−	0.604130i	$-0.793521\pi$
$631$	−6.34685e12			−1.59377			−0.796885	+	0.604130i	$0.793521\pi$
$632$	1.64732e12			0.410726
$633$	3.16727e12			0.784095
$634$	−4.14206e12			−1.01816
$635$		−	8.14705e11i		−	0.198847i
$636$			3.99336e11i			0.0967792i
$637$	−1.15575e13			−2.78123
$638$	−3.03462e12	+	1.57290e12i	−0.725122	+	0.375845i
$639$	6.57263e11			0.155950
$640$		−	1.01041e12i		−	0.238060i
$641$			1.71280e12i			0.400725i	0.979722	+	0.200363i	$0.0642120\pi$
$641$			1.71280e12i			0.400725i	−0.979722	+	0.200363i	$0.935788\pi$
$642$	−2.93966e12			−0.682951
$643$	−8.55386e11			−0.197339			−0.0986694	−	0.995120i	$-0.531459\pi$
$643$	−8.55386e11			−0.197339			−0.0986694	+	0.995120i	$0.531459\pi$
$644$	3.44202e11			0.0788546
$645$	1.49235e12			0.339510
$646$			2.50520e12i			0.565973i
$647$	−1.92841e12			−0.432642			−0.216321	−	0.976322i	$-0.569406\pi$
$647$	−1.92841e12			−0.432642			−0.216321	+	0.976322i	$0.569406\pi$
$648$			5.87600e11i			0.130916i
$649$		−	6.12856e12i		−	1.35599i
$650$			5.38507e12i			1.18326i
$651$	−1.27068e12			−0.277281
$652$		−	7.34806e11i		−	0.159242i
$653$		−	7.98270e12i		−	1.71807i	−0.511918	−	0.859035i	$-0.671065\pi$
$653$		−	7.98270e12i		−	1.71807i	0.511918	−	0.859035i	$-0.328935\pi$
$654$	−2.29041e12			−0.489568
$655$			1.53386e12i			0.325612i
$656$		−	5.12496e12i		−	1.08050i
$657$			1.06785e12i			0.223598i
$658$	1.15515e13			2.40227
$659$			5.35383e12i			1.10581i	0.833245	+	0.552904i	$0.186480\pi$
$659$			5.35383e12i			1.10581i	−0.833245	+	0.552904i	$0.813520\pi$
$660$	−1.86155e11			−0.0381881
$661$	4.06431e12			0.828095			0.414047	−	0.910255i	$-0.364115\pi$
$661$	4.06431e12			0.828095			0.414047	+	0.910255i	$0.364115\pi$
$662$	−1.65534e12			−0.334985
$663$	1.79163e12			0.360111
$664$			7.40355e12i			1.47803i
$665$			4.99622e12i			0.990705i
$666$	−4.82822e12			−0.950939
$667$	−1.11594e12	+	5.78415e11i	−0.218311	+	0.113155i
$668$	−9.32394e11			−0.181178
$669$			2.77655e12i			0.535905i
$670$			5.86475e11i			0.112438i
$671$	−6.87882e12			−1.30997
$672$	1.91491e12			0.362233
$673$	7.57103e12			1.42261			0.711307	−	0.702882i	$-0.248104\pi$
$673$	7.57103e12			1.42261			0.711307	+	0.702882i	$0.248104\pi$
$674$	6.24954e12			1.16648
$675$		−	4.40973e12i		−	0.817607i
$676$	1.43306e12			0.263940
$677$			8.91150e12i			1.63043i	0.579159	+	0.815214i	$0.303381\pi$
$677$			8.91150e12i			1.63043i	−0.579159	+	0.815214i	$0.696619\pi$
$678$			1.22513e12i			0.222664i
$679$		−	1.72053e13i		−	3.10634i
$680$	−9.31843e11			−0.167129
$681$		−	3.77998e11i		−	0.0673484i
$682$			1.33307e12i			0.235951i
$683$	1.07187e13			1.88473			0.942367	−	0.334580i	$-0.108595\pi$
$683$	1.07187e13			1.88473			0.942367	+	0.334580i	$0.108595\pi$
$684$		−	1.13746e12i		−	0.198693i
$685$		−	1.61587e12i		−	0.280414i
$686$		−	7.01689e12i		−	1.20972i
$687$	2.79996e12			0.479564
$688$			7.01535e12i			1.19372i
$689$	−8.04132e12			−1.35938
$690$	2.88970e11			0.0485324
$691$	−4.86749e12			−0.812183			−0.406091	−	0.913832i	$-0.633109\pi$
$691$	−4.86749e12			−0.812183			−0.406091	+	0.913832i	$0.633109\pi$
$692$	−1.55987e12			−0.258589
$693$		−	6.19994e12i		−	1.02115i
$694$		−	1.88544e12i		−	0.308529i
$695$	5.47053e11			0.0889402
$696$	−3.37548e12	+	1.74958e12i	−0.545247	+	0.282612i
$697$	−3.55356e12			−0.570317
$698$		−	1.58042e12i		−	0.252013i
$699$			1.48025e12i			0.234524i
$700$	1.73842e12			0.273661
$701$	6.00496e12			0.939245			0.469622	−	0.882867i	$-0.344390\pi$
$701$	6.00496e12			0.939245			0.469622	+	0.882867i	$0.344390\pi$
$702$	8.54822e12			1.32849
$703$	1.57616e13			2.43390
$704$		−	6.57800e12i		−	1.00929i
$705$	−2.29741e12			−0.350258
$706$			1.06487e13i			1.61315i
$707$			4.64266e12i			0.698843i
$708$		−	1.09575e12i		−	0.163894i
$709$	5.08153e12			0.755242			0.377621	−	0.925960i	$-0.376742\pi$
$709$	5.08153e12			0.755242			0.377621	+	0.925960i	$0.376742\pi$
$710$			5.41523e11i			0.0799751i
$711$		−	1.75394e12i		−	0.257396i
$712$	−2.56748e12			−0.374410
$713$			4.90219e11i			0.0710374i
$714$			2.44146e12i			0.351567i
$715$		−	3.74855e12i		−	0.536397i
$716$	1.87226e11			0.0266230
$717$		−	3.17123e12i		−	0.448118i
$718$	4.86948e12			0.683790
$719$	1.98825e12			0.277454			0.138727	−	0.990331i	$-0.455699\pi$
$719$	1.98825e12			0.277454			0.138727	+	0.990331i	$0.455699\pi$
$720$	−1.43089e12			−0.198431
$721$	3.76644e12			0.519066
$722$		−	9.10910e12i		−	1.24755i
$723$			2.26251e12i			0.307941i
$724$	7.00342e11			0.0947297
$725$	−5.63615e12	+	2.92133e12i	−0.757638	+	0.392699i
$726$	−6.74842e11			−0.0901545
$727$			1.11380e12i			0.147878i	0.997263	+	0.0739388i	$0.0235570\pi$
$727$			1.11380e12i			0.147878i	−0.997263	+	0.0739388i	$0.976443\pi$
$728$			2.09650e13i			2.76633i
$729$	−3.56244e12			−0.467168
$730$	−8.79812e11			−0.114667
$731$	4.86432e12			0.630078
$732$	−1.22990e12			−0.158332
$733$			9.38289e12i			1.20052i	0.799805	+	0.600259i	$0.204936\pi$
$733$			9.38289e12i			1.20052i	−0.799805	+	0.600259i	$0.795064\pi$
$734$	1.61090e12			0.204850
$735$			3.13233e12i			0.395889i
$736$		−	7.38762e11i		−	0.0928013i
$737$			2.37580e12i			0.296624i
$738$	−6.81077e12			−0.845167
$739$		−	2.75150e12i		−	0.339367i	−0.985499	−	0.169683i	$-0.945726\pi$
$739$		−	2.75150e12i		−	0.339367i	0.985499	−	0.169683i	$-0.0542745\pi$
$740$			9.42379e11i			0.115527i
$741$	−1.12097e13			−1.36588
$742$		−	1.09579e13i		−	1.32712i
$743$			1.35149e13i			1.62691i	0.581628	+	0.813455i	$0.302416\pi$
$743$			1.35149e13i			1.62691i	−0.581628	+	0.813455i	$0.697584\pi$
$744$			1.48280e12i			0.177421i
$745$	−4.07982e11			−0.0485219
$746$		−	1.26913e13i		−	1.50031i
$747$	7.88272e12			0.926261
$748$	−6.06774e11			−0.0708712
$749$	−1.91094e13			−2.21861
$750$	3.16972e12			0.365801
$751$			1.27467e13i			1.46224i	0.682248	+	0.731121i	$0.261002\pi$
$751$			1.27467e13i			1.46224i	−0.682248	+	0.731121i	$0.738998\pi$
$752$		−	1.07998e13i		−	1.23151i
$753$	−8.24051e12			−0.934064
$754$	−5.66297e12	−	1.09256e13i	−0.638077	−	1.23105i
$755$	−1.85090e12			−0.207311
$756$		−	2.75955e12i		−	0.307249i
$757$		−	9.73143e12i		−	1.07707i	−0.842602	−	0.538537i	$-0.818977\pi$
$757$		−	9.73143e12i		−	1.07707i	0.842602	−	0.538537i	$-0.181023\pi$
$758$	−1.89043e12			−0.207993
$759$	1.17061e12			0.128034
$760$	5.83028e12			0.633911
$761$	−1.06866e13			−1.15507			−0.577536	−	0.816366i	$-0.695986\pi$
$761$	−1.06866e13			−1.15507			−0.577536	+	0.816366i	$0.695986\pi$
$762$			2.49089e12i			0.267644i
$763$	−1.48890e13			−1.59039
$764$		−	1.46925e11i		−	0.0156018i
$765$			9.92154e11i			0.104738i
$766$			3.58025e12i			0.375737i
$767$	2.20649e13			2.30209
$768$		−	3.05151e12i		−	0.316511i
$769$		−	5.34569e12i		−	0.551233i	−0.961268	−	0.275617i	$-0.911118\pi$
$769$		−	5.34569e12i		−	0.551233i	0.961268	−	0.275617i	$-0.0888820\pi$
$770$	5.10818e12			0.523670
$771$			1.27220e12i			0.129661i
$772$			1.10124e12i			0.111584i
$773$			1.85162e12i			0.186528i	0.995641	+	0.0932642i	$0.0297301\pi$
$773$			1.85162e12i			0.186528i	−0.995641	+	0.0932642i	$0.970270\pi$
$774$	9.32298e12			0.933728
$775$			2.47589e12i			0.246532i
$776$	−2.00775e13			−1.98762
$777$	1.53606e13			1.51187
$778$	−9.72989e12			−0.952138
$779$	2.22337e13			2.16318
$780$		−	6.70221e11i		−	0.0648325i
$781$			2.19370e12i			0.210983i
$782$	9.41899e11			0.0900688
$783$	4.63730e12	+	8.94679e12i	0.440897	+	0.850627i
$784$	−1.47247e13			−1.39195
$785$		−	7.34691e10i		−	0.00690544i
$786$		−	4.68965e12i		−	0.438268i
$787$	−8.03534e12			−0.746651			−0.373326	−	0.927700i	$-0.621783\pi$
$787$	−8.03534e12			−0.746651			−0.373326	+	0.927700i	$0.621783\pi$
$788$	−2.99745e12			−0.276939
$789$	−2.28191e12			−0.209630
$790$	1.44508e12			0.131999
$791$			7.96406e12i			0.723336i
$792$	−7.23495e12			−0.653390
$793$		−	2.47661e13i		−	2.22396i
$794$			3.77932e12i			0.337459i
$795$			2.17936e12i			0.193498i
$796$	−1.53625e12			−0.135629
$797$		−	1.60473e13i		−	1.40877i	−0.709818	−	0.704385i	$-0.751223\pi$
$797$		−	1.60473e13i		−	1.40877i	0.709818	−	0.704385i	$-0.248777\pi$
$798$		−	1.52755e13i		−	1.33347i
$799$	−7.48843e12			−0.650025
$800$		−	3.73117e12i		−	0.322062i
$801$			2.73365e12i			0.234637i
$802$			2.55395e12i			0.217986i
$803$	−3.56411e12			−0.302504
$804$			4.24781e11i			0.0358519i
$805$	1.87847e12			0.157660
$806$	−4.79949e12			−0.400578
$807$	−8.42373e11			−0.0699155
$808$	5.41770e12			0.447161
$809$			1.66630e12i			0.136768i	0.997659	+	0.0683840i	$0.0217843\pi$
$809$			1.66630e12i			0.136768i	−0.997659	+	0.0683840i	$0.978216\pi$
$810$			5.15461e11i			0.0420740i
$811$	6.54035e12			0.530894			0.265447	−	0.964126i	$-0.414481\pi$
$811$	6.54035e12			0.530894			0.265447	+	0.964126i	$0.414481\pi$
$812$	−3.52703e12	+	1.82813e12i	−0.284713	+	0.147572i
$813$	−2.47036e11			−0.0198313
$814$		−	1.61148e13i		−	1.28652i
$815$		−	4.01018e12i		−	0.318386i
$816$	2.28259e12			0.180228
$817$	−3.04347e13			−2.38985
$818$	6.26291e12			0.489087
$819$	2.23219e13			1.73362
$820$			1.32934e12i			0.102677i
$821$	1.47748e13			1.13495			0.567477	−	0.823389i	$-0.307919\pi$
$821$	1.47748e13			1.13495			0.567477	+	0.823389i	$0.307919\pi$
$822$			4.94039e12i			0.377431i
$823$		−	1.48019e13i		−	1.12465i	−0.826916	−	0.562326i	$-0.809907\pi$
$823$		−	1.48019e13i		−	1.12465i	0.826916	−	0.562326i	$-0.190093\pi$
$824$		−	4.39520e12i		−	0.332129i
$825$	5.91227e12			0.444336
$826$			3.00679e13i			2.24747i
$827$			2.32185e13i			1.72607i	0.505140	+	0.863037i	$0.331441\pi$
$827$			2.32185e13i			1.72607i	−0.505140	+	0.863037i	$0.668559\pi$
$828$	−4.27659e11			−0.0316199
$829$			2.28319e13i			1.67898i	0.543372	+	0.839492i	$0.317147\pi$
$829$			2.28319e13i			1.67898i	−0.543372	+	0.839492i	$0.682853\pi$
$830$			6.49463e12i			0.475010i
$831$		−	3.62687e12i		−	0.263832i
$832$	2.36830e13			1.71349
$833$			1.02098e13i			0.734710i
$834$	−1.67257e12			−0.119712
$835$	−5.08851e12			−0.362244
$836$	3.79642e12			0.268810
$837$	3.93020e12			0.276790
$838$		−	8.21959e12i		−	0.575774i
$839$			7.47342e12i			0.520703i	0.965514	+	0.260352i	$0.0838385\pi$
$839$			7.47342e12i			0.520703i	−0.965514	+	0.260352i	$0.916161\pi$
$840$	5.68194e12			0.393768
$841$	8.36297e12	−	1.18540e13i	0.576472	−	0.817117i
$842$	−1.53795e13			−1.05448
$843$			1.22039e13i			0.832292i
$844$		−	3.86196e12i		−	0.261979i
$845$	7.82089e12			0.527717
$846$	−1.43523e13			−0.963288
$847$	−4.38686e12			−0.292872
$848$	−1.02449e13			−0.680341
$849$		−	1.20044e13i		−	0.792972i
$850$	4.75713e12			0.312579
$851$		−	5.92603e12i		−	0.387330i
$852$			3.92223e11i			0.0255008i
$853$			7.74707e12i			0.501034i	0.968112	+	0.250517i	$0.0806006\pi$
$853$			7.74707e12i			0.501034i	−0.968112	+	0.250517i	$0.919399\pi$
$854$	3.37489e13			2.17119
$855$		−	6.20763e12i		−	0.397263i
$856$			2.22995e13i			1.41959i
$857$	1.06335e13			0.673382			0.336691	−	0.941615i	$-0.390692\pi$
$857$	1.06335e13			0.673382			0.336691	+	0.941615i	$0.390692\pi$
$858$			1.14609e13i			0.721981i
$859$		−	2.71595e13i		−	1.70197i	−0.525186	−	0.850987i	$-0.676004\pi$
$859$		−	2.71595e13i		−	1.70197i	0.525186	−	0.850987i	$-0.323996\pi$
$860$		−	1.81967e12i		−	0.113436i
$861$	2.16680e13			1.34370
$862$		−	9.29699e11i		−	0.0573535i
$863$	−2.28650e13			−1.40321			−0.701605	−	0.712566i	$-0.747533\pi$
$863$	−2.28650e13			−1.40321			−0.701605	+	0.712566i	$0.747533\pi$
$864$	−5.92283e12			−0.361591
$865$	−8.51292e12			−0.517019
$866$	−7.72292e12			−0.466607
$867$			7.95435e12i			0.478100i
$868$			1.54938e12i			0.0926443i
$869$	5.85402e12			0.348229
$870$	−2.96107e12	+	1.53478e12i	−0.175232	+	0.0908260i
$871$	−8.55368e12			−0.503584
$872$			1.73745e13i			1.01763i
$873$			2.13770e13i			1.24561i
$874$	−5.89321e12			−0.341625
$875$	2.06050e13			1.18833
$876$	−6.37244e11			−0.0365626
$877$	−5.75255e12			−0.328369			−0.164185	−	0.986430i	$-0.552499\pi$
$877$	−5.75255e12			−0.328369			−0.164185	+	0.986430i	$0.552499\pi$
$878$		−	1.67818e13i		−	0.953044i
$879$	1.65828e13			0.936931
$880$		−	4.77578e12i		−	0.268456i
$881$		−	1.69119e13i		−	0.945805i	−0.881115	−	0.472903i	$-0.843206\pi$
$881$		−	1.69119e13i		−	0.945805i	0.881115	−	0.472903i	$-0.156794\pi$
$882$			1.95682e13i			1.08879i
$883$	−2.71114e13			−1.50082			−0.750410	−	0.660972i	$-0.770144\pi$
$883$	−2.71114e13			−1.50082			−0.750410	+	0.660972i	$0.770144\pi$
$884$		−	2.18459e12i		−	0.120319i
$885$		−	5.98004e12i		−	0.327687i
$886$	−1.44792e10			−0.000789393
$887$		−	2.32155e13i		−	1.25928i	−0.776887	−	0.629640i	$-0.783203\pi$
$887$		−	2.32155e13i		−	1.25928i	0.776887	−	0.629640i	$-0.216797\pi$
$888$		−	1.79249e13i		−	0.967383i
$889$			1.61922e13i			0.869457i
$890$	−2.25227e12			−0.120328
$891$			2.08813e12i			0.110996i
$892$	3.38554e12			0.179055
$893$	4.68530e13			2.46551
$894$	1.24737e12			0.0653096
$895$	1.02178e12			0.0532295
$896$			2.00818e13i			1.04092i
$897$			4.21460e12i			0.217366i
$898$	−2.54003e12			−0.130345
$899$	−2.60366e12	−	5.02327e12i	−0.132943	−	0.256488i
$900$	−2.15992e12			−0.109735
$901$			7.10365e12i			0.359104i
$902$		−	2.27319e13i		−	1.14342i
$903$	−2.96604e13			−1.48451
$904$	9.29357e12			0.462833
$905$	3.82209e12			0.189401
$906$	5.65898e12			0.279037
$907$			1.87021e13i			0.917610i	0.888537	+	0.458805i	$0.151722\pi$
$907$			1.87021e13i			0.917610i	−0.888537	+	0.458805i	$0.848278\pi$
$908$	−4.60905e11			−0.0225022
$909$		−	5.76834e12i		−	0.280229i
$910$			1.83911e13i			0.889043i
$911$		−	7.74807e12i		−	0.372701i	−0.982483	−	0.186351i	$-0.940334\pi$
$911$		−	7.74807e12i		−	0.372701i	0.982483	−	0.186351i	$-0.0596660\pi$
$912$	−1.42815e13			−0.683594
$913$			2.63096e13i			1.25313i
$914$		−	1.75492e13i		−	0.831762i
$915$	−6.71212e12			−0.316566
$916$		−	3.41408e12i		−	0.160230i
$917$		−	3.04854e13i		−	1.42374i
$918$		−	7.55144e12i		−	0.350944i
$919$	−1.28473e13			−0.594146			−0.297073	−	0.954855i	$-0.596010\pi$
$919$	−1.28473e13			−0.594146			−0.297073	+	0.954855i	$0.596010\pi$
$920$		−	2.19206e12i		−	0.100880i
$921$	7.26969e12			0.332926
$922$	−1.92601e13			−0.877748
$923$	−7.89807e12			−0.358190
$924$	3.69983e12			0.166977
$925$		−	2.99298e13i		−	1.34421i
$926$			1.18433e13i			0.529325i
$927$	−4.67967e12			−0.208140
$928$	3.92372e12	+	7.57008e12i	0.173673	+	0.335069i
$929$	−2.10384e13			−0.926707			−0.463353	−	0.886174i	$-0.653354\pi$
$929$	−2.10384e13			−0.926707			−0.463353	+	0.886174i	$0.653354\pi$
$930$			1.30076e12i			0.0570196i
$931$		−	6.38801e13i		−	2.78671i
$932$	1.80492e12			0.0783585
$933$	−3.53096e12			−0.152554
$934$	3.16857e12			0.136239
$935$	−3.31145e12			−0.141699
$936$		−	2.60483e13i		−	1.10927i
$937$	−2.93509e13			−1.24392			−0.621962	−	0.783047i	$-0.713664\pi$
$937$	−2.93509e13			−1.24392			−0.621962	+	0.783047i	$0.713664\pi$
$938$		−	1.16562e13i		−	0.491635i
$939$			1.45766e13i			0.611873i
$940$			2.80131e12i			0.117027i
$941$	−1.43965e12			−0.0598555			−0.0299277	−	0.999552i	$-0.509528\pi$
$941$	−1.43965e12			−0.0598555			−0.0299277	+	0.999552i	$0.509528\pi$
$942$			2.24626e11i			0.00929459i
$943$		−	8.35936e12i		−	0.344247i
$944$	2.81114e13			1.15215
$945$		−	1.50601e13i		−	0.614308i
$946$			3.11167e13i			1.26323i
$947$			3.80720e13i			1.53826i	0.639091	+	0.769131i	$0.279311\pi$
$947$			3.80720e13i			1.53826i	−0.639091	+	0.769131i	$0.720689\pi$
$948$	1.04667e12			0.0420892
$949$		−	1.28320e13i		−	0.513565i
$950$	−2.97641e13			−1.18559
$951$	−1.63728e13			−0.649099
$952$	1.85203e13			0.730773
$953$	−4.81983e13			−1.89284			−0.946420	−	0.322940i	$-0.895329\pi$
$953$	−4.81983e13			−1.89284			−0.946420	+	0.322940i	$0.895329\pi$
$954$			1.36149e13i			0.532164i
$955$		−	8.01838e11i		−	0.0311940i
$956$	−3.86679e12			−0.149724
$957$	−1.19953e13	+	6.21738e12i	−0.462281	+	0.239609i
$958$	1.07716e13			0.413178
$959$			3.21153e13i			1.22611i
$960$		−	6.41858e12i		−	0.243904i
$961$	2.42330e13			0.916540
$962$	5.80188e13			2.18414
$963$	2.37428e13			0.889639
$964$	2.75875e12			0.102888
$965$			6.00995e12i			0.223099i
$966$	−5.74326e12			−0.212208
$967$		−	2.22111e13i		−	0.816867i	−0.912788	−	0.408434i	$-0.866075\pi$
$967$		−	2.22111e13i		−	0.816867i	0.912788	−	0.408434i	$-0.133925\pi$
$968$			5.11919e12i			0.187397i
$969$			9.90258e12i			0.360821i
$970$	−1.76126e13			−0.638781
$971$			3.01586e13i			1.08874i	0.838845	+	0.544370i	$0.183231\pi$
$971$			3.01586e13i			1.08874i	−0.838845	+	0.544370i	$0.816769\pi$
$972$			5.48000e12i			0.196917i
$973$	−1.08727e13			−0.388891
$974$		−	1.40549e13i		−	0.500395i
$975$			2.12862e13i			0.754356i
$976$		−	3.15528e13i		−	1.11305i
$977$	−2.43069e13			−0.853501			−0.426750	−	0.904369i	$-0.640342\pi$
$977$	−2.43069e13			−0.853501			−0.426750	+	0.904369i	$0.640342\pi$
$978$			1.22608e13i			0.428542i
$979$	−9.12393e12			−0.317439
$980$	3.81935e12			0.132273
$981$	1.84990e13			0.637731
$982$	1.90002e13			0.652013
$983$		−	3.14903e13i		−	1.07569i	−0.843045	−	0.537843i	$-0.819239\pi$
$983$		−	3.14903e13i		−	1.07569i	0.843045	−	0.537843i	$-0.180761\pi$
$984$		−	2.52852e13i		−	0.859781i
$985$	−1.63585e13			−0.553707
$986$	−9.65163e12	+	5.00263e12i	−0.325203	+	0.168559i
$987$	4.56610e13			1.53150
$988$			1.36684e13i			0.456363i
$989$			1.14428e13i			0.380319i
$990$	−6.34673e12			−0.209987
$991$	−1.31881e13			−0.434361			−0.217180	−	0.976131i	$-0.569686\pi$
$991$	−1.31881e13			−0.434361			−0.217180	+	0.976131i	$0.569686\pi$
$992$	3.32544e12			0.109030
$993$	−6.54323e12			−0.213560
$994$		−	1.07627e13i		−	0.349691i
$995$	−8.38404e12			−0.271175
$996$			4.70402e12i			0.151462i
$997$			2.81582e13i			0.902561i	0.892382	+	0.451281i	$0.149033\pi$
$997$			2.81582e13i			0.902561i	−0.892382	+	0.451281i	$0.850967\pi$
$998$			3.48599e13i			1.11234i
$999$	−4.75104e13			−1.50919

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.b.a.28.16	yes	22
29.28	even	2	inner	29.10.b.a.28.7	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.b.a.28.7	✓	22	29.28	even	2	inner
29.10.b.a.28.16	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)

\(f(q)\)	\(=\)	\(q+20.3455i q^{2} +80.4219i q^{3} +98.0611 q^{4} +535.165 q^{5} -1636.22 q^{6} -10636.4 q^{7} +12412.0i q^{8} +13215.3 q^{9} +O(q^{10})\)	\(q+20.3455i q^{2} +80.4219i q^{3} +98.0611 q^{4} +535.165 q^{5} -1636.22 q^{6} -10636.4 q^{7} +12412.0i q^{8} +13215.3 q^{9} +10888.2i q^{10} +44107.9i q^{11} +7886.26i q^{12} -158803. q^{13} -216402. i q^{14} +43039.0i q^{15} -202321. q^{16} +140286. i q^{17} +268872. i q^{18} -877729. i q^{19} +52478.9 q^{20} -855397. i q^{21} -897397. q^{22} -330007. q^{23} -998196. q^{24} -1.66672e6 q^{25} -3.23093e6i q^{26} +2.64575e6i q^{27} -1.04301e6 q^{28} +(3.38158e6 - 1.75274e6i) q^{29} -875649. q^{30} -1.48548e6i q^{31} +2.23863e6i q^{32} -3.54724e6 q^{33} -2.85418e6 q^{34} -5.69221e6 q^{35} +1.29591e6 q^{36} +1.79573e7i q^{37} +1.78578e7 q^{38} -1.27713e7i q^{39} +6.64246e6i q^{40} +2.53309e7i q^{41} +1.74035e7 q^{42} -3.46744e7i q^{43} +4.32527e6i q^{44} +7.07238e6 q^{45} -6.71415e6i q^{46} +5.33798e7i q^{47} -1.62710e7i q^{48} +7.27788e7 q^{49} -3.39103e7i q^{50} -1.12820e7 q^{51} -1.55724e7 q^{52} +5.06370e7 q^{53} -5.38290e7 q^{54} +2.36050e7i q^{55} -1.32019e8i q^{56} +7.05887e7 q^{57} +(3.56603e7 + 6.87998e7i) q^{58} -1.38945e8 q^{59} +4.22045e6i q^{60} +1.55954e8i q^{61} +3.02228e7 q^{62} -1.40563e8 q^{63} -1.49134e8 q^{64} -8.49860e7 q^{65} -7.21704e7i q^{66} +5.38634e7 q^{67} +1.37566e7i q^{68} -2.65398e7i q^{69} -1.15811e8i q^{70} +4.97349e7 q^{71} +1.64028e8i q^{72} +8.08043e7i q^{73} -3.65350e8 q^{74} -1.34041e8i q^{75} -8.60711e7i q^{76} -4.69148e8i q^{77} +2.59838e8 q^{78} -1.32720e8i q^{79} -1.08275e8 q^{80} +4.73413e7 q^{81} -5.15369e8 q^{82} +5.96483e8 q^{83} -8.38812e7i q^{84} +7.50760e7i q^{85} +7.05468e8 q^{86} +(1.40958e8 + 2.71953e8i) q^{87} -5.47467e8 q^{88} +2.06855e8i q^{89} +1.43891e8i q^{90} +1.68909e9 q^{91} -3.23608e7 q^{92} +1.19465e8 q^{93} -1.08604e9 q^{94} -4.69730e8i q^{95} -1.80035e8 q^{96} +1.61759e9i q^{97} +1.48072e9i q^{98} +5.82900e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9}+O(q^{10}) \) 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

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