LMFDB - Embedded newform 29.10.b.a.28.5

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			28.5
Character	$\chi$	$=$	29.28
Dual form			29.10.b.a.28.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-27.8229i q^{2} -61.9183i q^{3} -262.115 q^{4} +1301.46 q^{5} -1722.75 q^{6} +8294.02 q^{7} -6952.53i q^{8} +15849.1 q^{9} +O(q^{10})$	\(q-27.8229i q^{2} -61.9183i q^{3} -262.115 q^{4} +1301.46 q^{5} -1722.75 q^{6} +8294.02 q^{7} -6952.53i q^{8} +15849.1 q^{9} -36210.3i q^{10} -3449.04i q^{11} +16229.7i q^{12} +76628.3 q^{13} -230764. i q^{14} -80583.9i q^{15} -327643. q^{16} +381375. i q^{17} -440969. i q^{18} +54085.5i q^{19} -341131. q^{20} -513552. i q^{21} -95962.4 q^{22} -2.27404e6 q^{23} -430489. q^{24} -259337. q^{25} -2.13202e6i q^{26} -2.20009e6i q^{27} -2.17399e6 q^{28} +(2.16069e6 - 3.13665e6i) q^{29} -2.24208e6 q^{30} +2.48288e6i q^{31} +5.55628e6i q^{32} -213559. q^{33} +1.06110e7 q^{34} +1.07943e7 q^{35} -4.15429e6 q^{36} -7.46415e6i q^{37} +1.50482e6 q^{38} -4.74469e6i q^{39} -9.04841e6i q^{40} +2.80841e7i q^{41} -1.42885e7 q^{42} -2.67503e7i q^{43} +904045. i q^{44} +2.06269e7 q^{45} +6.32704e7i q^{46} +5.19717e7i q^{47} +2.02871e7i q^{48} +2.84372e7 q^{49} +7.21551e6i q^{50} +2.36141e7 q^{51} -2.00854e7 q^{52} -3.40849e7 q^{53} -6.12129e7 q^{54} -4.48878e6i q^{55} -5.76644e7i q^{56} +3.34888e6 q^{57} +(-8.72708e7 - 6.01166e7i) q^{58} +7.09338e7 q^{59} +2.11223e7i q^{60} -1.40529e8i q^{61} +6.90810e7 q^{62} +1.31453e8 q^{63} -1.31611e7 q^{64} +9.97284e7 q^{65} +5.94183e6i q^{66} -3.74198e7 q^{67} -9.99640e7i q^{68} +1.40805e8i q^{69} -3.00329e8i q^{70} -3.17141e8 q^{71} -1.10192e8i q^{72} -2.89803e7i q^{73} -2.07674e8 q^{74} +1.60577e7i q^{75} -1.41766e7i q^{76} -2.86064e7i q^{77} -1.32011e8 q^{78} +3.43095e8i q^{79} -4.26413e8 q^{80} +1.75733e8 q^{81} +7.81383e8 q^{82} -4.04014e8 q^{83} +1.34610e8i q^{84} +4.96343e8i q^{85} -7.44270e8 q^{86} +(-1.94216e8 - 1.33786e8i) q^{87} -2.39796e7 q^{88} +6.56951e8i q^{89} -5.73902e8i q^{90} +6.35557e8 q^{91} +5.96060e8 q^{92} +1.53736e8 q^{93} +1.44601e9 q^{94} +7.03899e7i q^{95} +3.44035e8 q^{96} +7.43846e8i q^{97} -7.91205e8i q^{98} -5.46643e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	27.8229i		−	1.22961i	−0.788679	−	0.614806i	$-0.789234\pi$
$2$		−	27.8229i		−	1.22961i	0.788679	−	0.614806i	$-0.210766\pi$
$3$		−	61.9183i		−	0.441340i	−0.975349	−	0.220670i	$-0.929176\pi$
$3$		−	61.9183i		−	0.441340i	0.975349	−	0.220670i	$-0.0708244\pi$
$4$	−262.115			−0.511943
$5$	1301.46			0.931246			0.465623	−	0.884983i	$-0.345830\pi$
$5$	1301.46			0.931246			0.465623	+	0.884983i	$0.345830\pi$
$6$	−1722.75			−0.542677
$7$	8294.02			1.30564			0.652821	−	0.757512i	$-0.273585\pi$
$7$	8294.02			1.30564			0.652821	+	0.757512i	$0.273585\pi$
$8$		−	6952.53i		−	0.600120i
$9$	15849.1			0.805219
$10$		−	36210.3i		−	1.14507i
$11$		−	3449.04i		−	0.0710283i	−0.999369	−	0.0355141i	$-0.988693\pi$
$11$		−	3449.04i		−	0.0710283i	0.999369	−	0.0355141i	$-0.0113069\pi$
$12$			16229.7i			0.225941i
$13$	76628.3			0.744122			0.372061	−	0.928208i	$-0.378651\pi$
$13$	76628.3			0.744122			0.372061	+	0.928208i	$0.378651\pi$
$14$		−	230764.i		−	1.60543i
$15$		−	80583.9i		−	0.410996i
$16$	−327643.			−1.24986
$17$			381375.i			1.10747i	0.832693	+	0.553735i	$0.186798\pi$
$17$			381375.i			1.10747i	−0.832693	+	0.553735i	$0.813202\pi$
$18$		−	440969.i		−	0.990106i
$19$			54085.5i			0.0952116i	0.998866	+	0.0476058i	$0.0151591\pi$
$19$			54085.5i			0.0952116i	−0.998866	+	0.0476058i	$0.984841\pi$
$20$	−341131.			−0.476745
$21$		−	513552.i		−	0.576232i
$22$	−95962.4			−0.0873372
$23$	−2.27404e6			−1.69443			−0.847213	−	0.531253i	$-0.821721\pi$
$23$	−2.27404e6			−1.69443			−0.847213	+	0.531253i	$0.821721\pi$
$24$	−430489.			−0.264857
$25$	−259337.			−0.132780
$26$		−	2.13202e6i		−	0.914981i
$27$		−	2.20009e6i		−	0.796715i
$28$	−2.17399e6			−0.668414
$29$	2.16069e6	−	3.13665e6i	0.567284	−	0.823522i
$29$	2.16069e6	−	3.13665e6i	0.567284	−	0.823522i
$30$	−2.24208e6			−0.505365
$31$			2.48288e6i			0.482868i	0.970417	+	0.241434i	$0.0776177\pi$
$31$			2.48288e6i			0.482868i	−0.970417	+	0.241434i	$0.922382\pi$
$32$			5.55628e6i			0.936719i
$33$	−213559.			−0.0313476
$34$	1.06110e7			1.36176
$35$	1.07943e7			1.21587
$36$	−4.15429e6			−0.412227
$37$		−	7.46415e6i		−	0.654745i	−0.944895	−	0.327373i	$-0.893837\pi$
$37$		−	7.46415e6i		−	0.654745i	0.944895	−	0.327373i	$-0.106163\pi$
$38$	1.50482e6			0.117073
$39$		−	4.74469e6i		−	0.328411i
$40$		−	9.04841e6i		−	0.558859i
$41$			2.80841e7i			1.55215i	0.630640	+	0.776075i	$0.282792\pi$
$41$			2.80841e7i			1.55215i	−0.630640	+	0.776075i	$0.717208\pi$
$42$	−1.42885e7			−0.708541
$43$		−	2.67503e7i		−	1.19322i	−0.802532	−	0.596609i	$-0.796514\pi$
$43$		−	2.67503e7i		−	1.19322i	0.802532	−	0.596609i	$-0.203486\pi$
$44$			904045.i			0.0363625i
$45$	2.06269e7			0.749857
$46$			6.32704e7i			2.08348i
$47$			5.19717e7i			1.55356i	0.629775	+	0.776778i	$0.283147\pi$
$47$			5.19717e7i			1.55356i	−0.629775	+	0.776778i	$0.716853\pi$
$48$			2.02871e7i			0.551612i
$49$	2.84372e7			0.704700
$50$			7.21551e6i			0.163268i
$51$	2.36141e7			0.488771
$52$	−2.00854e7			−0.380948
$53$	−3.40849e7			−0.593364			−0.296682	−	0.954976i	$-0.595880\pi$
$53$	−3.40849e7			−0.593364			−0.296682	+	0.954976i	$0.595880\pi$
$54$	−6.12129e7			−0.979650
$55$		−	4.48878e6i		−	0.0661448i
$56$		−	5.76644e7i		−	0.783541i
$57$	3.34888e6			0.0420207
$58$	−8.72708e7	−	6.01166e7i	−1.01261	−	0.697539i
$59$	7.09338e7			0.762113			0.381056	−	0.924552i	$-0.375560\pi$
$59$	7.09338e7			0.762113			0.381056	+	0.924552i	$0.375560\pi$
$60$			2.11223e7i			0.210407i
$61$		−	1.40529e8i		−	1.29952i	−0.760140	−	0.649760i	$-0.774870\pi$
$61$		−	1.40529e8i		−	1.29952i	0.760140	−	0.649760i	$-0.225130\pi$
$62$	6.90810e7			0.593740
$63$	1.31453e8			1.05133
$64$	−1.31611e7			−0.0980578
$65$	9.97284e7			0.692961
$66$			5.94183e6i			0.0385454i
$67$	−3.74198e7			−0.226864			−0.113432	−	0.993546i	$-0.536184\pi$
$67$	−3.74198e7			−0.226864			−0.113432	+	0.993546i	$0.536184\pi$
$68$		−	9.99640e7i		−	0.566962i
$69$			1.40805e8i			0.747818i
$70$		−	3.00329e8i		−	1.49505i
$71$	−3.17141e8			−1.48112			−0.740558	−	0.671992i	$-0.765439\pi$
$71$	−3.17141e8			−1.48112			−0.740558	+	0.671992i	$0.765439\pi$
$72$		−	1.10192e8i		−	0.483228i
$73$		−	2.89803e7i		−	0.119440i	−0.998215	−	0.0597201i	$-0.980979\pi$
$73$		−	2.89803e7i		−	0.119440i	0.998215	−	0.0597201i	$-0.0190208\pi$
$74$	−2.07674e8			−0.805082
$75$			1.60577e7i			0.0586013i
$76$		−	1.41766e7i		−	0.0487429i
$77$		−	2.86064e7i		−	0.0927375i
$78$	−1.32011e8			−0.403818
$79$			3.43095e8i			0.991044i	0.868595	+	0.495522i	$0.165023\pi$
$79$			3.43095e8i			0.991044i	−0.868595	+	0.495522i	$0.834977\pi$
$80$	−4.26413e8			−1.16392
$81$	1.75733e8			0.453597
$82$	7.81383e8			1.90854
$83$	−4.04014e8			−0.934426			−0.467213	−	0.884145i	$-0.654742\pi$
$83$	−4.04014e8			−0.934426			−0.467213	+	0.884145i	$0.654742\pi$
$84$			1.34610e8i			0.294998i
$85$			4.96343e8i			1.03133i
$86$	−7.44270e8			−1.46719
$87$	−1.94216e8	−	1.33786e8i	−0.363453	−	0.250365i
$88$	−2.39796e7			−0.0426255
$89$			6.56951e8i			1.10989i	0.831889	+	0.554943i	$0.187260\pi$
$89$			6.56951e8i			1.10989i	−0.831889	+	0.554943i	$0.812740\pi$
$90$		−	5.73902e8i		−	0.922033i
$91$	6.35557e8			0.971557
$92$	5.96060e8			0.867450
$93$	1.53736e8			0.213109
$94$	1.44601e9			1.91027
$95$			7.03899e7i			0.0886654i
$96$	3.44035e8			0.413411
$97$			7.43846e8i			0.853120i	0.904459	+	0.426560i	$0.140275\pi$
$97$			7.43846e8i			0.853120i	−0.904459	+	0.426560i	$0.859725\pi$
$98$		−	7.91205e8i		−	0.866507i
$99$		−	5.46643e7i		−	0.0571933i
$100$	6.79761e7			0.0679761
$101$			1.45677e9i			1.39298i	0.717566	+	0.696491i	$0.245256\pi$
$101$			1.45677e9i			1.39298i	−0.717566	+	0.696491i	$0.754744\pi$
$102$		−	6.57012e8i		−	0.600998i
$103$	−1.02006e8			−0.0893015			−0.0446508	−	0.999003i	$-0.514218\pi$
$103$	−1.02006e8			−0.0893015			−0.0446508	+	0.999003i	$0.514218\pi$
$104$		−	5.32761e8i		−	0.446562i
$105$		−	6.68365e8i		−	0.536614i
$106$			9.48342e8i			0.729607i
$107$	7.36929e8			0.543499			0.271750	−	0.962368i	$-0.412398\pi$
$107$	7.36929e8			0.543499			0.271750	+	0.962368i	$0.412398\pi$
$108$			5.76676e8i			0.407873i
$109$	1.54526e9			1.04853			0.524267	−	0.851554i	$-0.324340\pi$
$109$	1.54526e9			1.04853			0.524267	+	0.851554i	$0.324340\pi$
$110$	−1.24891e8			−0.0813324
$111$	−4.62167e8			−0.288965
$112$	−2.71747e9			−1.63187
$113$		−	1.32576e9i		−	0.764913i	−0.923974	−	0.382456i	$-0.875078\pi$
$113$		−	1.32576e9i		−	0.764913i	0.923974	−	0.382456i	$-0.124922\pi$
$114$		−	9.31757e7i		−	0.0516691i
$115$	−2.95956e9			−1.57793
$116$	−5.66348e8	+	8.22163e8i	−0.290417	+	0.421597i
$117$	1.21449e9			0.599181
$118$		−	1.97359e9i		−	0.937102i
$119$			3.16313e9i			1.44596i
$120$	−5.60262e8			−0.246647
$121$	2.34605e9			0.994955
$122$	−3.90994e9			−1.59790
$123$	1.73892e9			0.685026
$124$		−	6.50801e8i		−	0.247201i
$125$	−2.87942e9			−1.05490
$126$		−	3.65741e9i		−	1.29272i
$127$		−	1.62593e9i		−	0.554606i	−0.960783	−	0.277303i	$-0.910559\pi$
$127$		−	1.62593e9i		−	0.554606i	0.960783	−	0.277303i	$-0.0894405\pi$
$128$			3.21099e9i			1.05729i
$129$	−1.65633e9			−0.526615
$130$		−	2.77473e9i		−	0.852072i
$131$		−	2.41278e8i		−	0.0715808i	−0.999359	−	0.0357904i	$-0.988605\pi$
$131$		−	2.41278e8i		−	0.0715808i	0.999359	−	0.0357904i	$-0.0113949\pi$
$132$	5.59769e7			0.0160482
$133$			4.48586e8i			0.124312i
$134$			1.04113e9i			0.278954i
$135$		−	2.86332e9i		−	0.741938i
$136$	2.65152e9			0.664614
$137$		−	6.88504e9i		−	1.66980i	−0.550402	−	0.834899i	$-0.685526\pi$
$137$		−	6.88504e9i		−	1.66980i	0.550402	−	0.834899i	$-0.314474\pi$
$138$	3.91759e9			0.919525
$139$	1.03249e9			0.234594			0.117297	−	0.993097i	$-0.462577\pi$
$139$	1.03249e9			0.234594			0.117297	+	0.993097i	$0.462577\pi$
$140$	−2.82935e9			−0.622458
$141$	3.21800e9			0.685646
$142$			8.82378e9i			1.82120i
$143$		−	2.64294e8i		−	0.0528537i
$144$	−5.19285e9			−1.00641
$145$	2.81204e9	−	4.08221e9i	0.528281	−	0.766902i
$146$	−8.06317e8			−0.146865
$147$		−	1.76078e9i		−	0.311012i
$148$			1.95647e9i			0.335193i
$149$	3.27647e9			0.544588			0.272294	−	0.962214i	$-0.412218\pi$
$149$	3.27647e9			0.544588			0.272294	+	0.962214i	$0.412218\pi$
$150$	4.46772e8			0.0720568
$151$	4.41149e9			0.690541			0.345270	−	0.938503i	$-0.387787\pi$
$151$	4.41149e9			0.690541			0.345270	+	0.938503i	$0.387787\pi$
$152$	3.76031e8			0.0571384
$153$			6.04446e9i			0.891756i
$154$	−7.95914e8			−0.114031
$155$			3.23136e9i			0.449669i
$156$			1.24366e9i			0.168128i
$157$		−	1.90401e9i		−	0.250104i	−0.992150	−	0.125052i	$-0.960090\pi$
$157$		−	1.90401e9i		−	0.250104i	0.992150	−	0.125052i	$-0.0399098\pi$
$158$	9.54591e9			1.21860
$159$			2.11048e9i			0.261875i
$160$			7.23125e9i			0.872316i
$161$	−1.88609e10			−2.21231
$162$		−	4.88940e9i		−	0.557748i
$163$			1.04650e10i			1.16116i	0.814202	+	0.580582i	$0.197175\pi$
$163$			1.04650e10i			1.16116i	−0.814202	+	0.580582i	$0.802825\pi$
$164$		−	7.36128e9i		−	0.794613i
$165$	−2.77937e8			−0.0291924
$166$			1.12408e10i			1.14898i
$167$	1.02595e10			1.02071			0.510355	−	0.859964i	$-0.329514\pi$
$167$	1.02595e10			1.02071			0.510355	+	0.859964i	$0.329514\pi$
$168$	−3.57048e9			−0.345808
$169$	−4.73260e9			−0.446282
$170$	1.38097e10			1.26813
$171$			8.57208e8i			0.0766662i
$172$			7.01164e9i			0.610860i
$173$	2.99888e8			0.0254537			0.0127269	−	0.999919i	$-0.495949\pi$
$173$	2.99888e8			0.0254537			0.0127269	+	0.999919i	$0.495949\pi$
$174$	−3.72232e9	+	5.40366e9i	−0.307852	+	0.446906i
$175$	−2.15094e9			−0.173364
$176$			1.13005e9i			0.0887752i
$177$		−	4.39210e9i		−	0.336351i
$178$	1.82783e10			1.36473
$179$	−2.37179e10			−1.72678			−0.863390	−	0.504537i	$-0.831663\pi$
$179$	−2.37179e10			−1.72678			−0.863390	+	0.504537i	$0.831663\pi$
$180$	−5.40663e9			−0.383884
$181$	3.44805e9			0.238792			0.119396	−	0.992847i	$-0.461904\pi$
$181$	3.44805e9			0.238792			0.119396	+	0.992847i	$0.461904\pi$
$182$		−	1.76830e10i		−	1.19464i
$183$	−8.70134e9			−0.573530
$184$			1.58103e10i			1.01686i
$185$		−	9.71426e9i		−	0.609729i
$186$		−	4.27738e9i		−	0.262041i
$187$	1.31538e9			0.0786617
$188$		−	1.36226e10i		−	0.795333i
$189$		−	1.82476e10i		−	1.04022i
$190$	1.95845e9			0.109024
$191$		−	1.47911e10i		−	0.804176i	−0.915601	−	0.402088i	$-0.868285\pi$
$191$		−	1.47911e10i		−	0.804176i	0.915601	−	0.402088i	$-0.131715\pi$
$192$			8.14912e8i			0.0432768i
$193$			2.26417e9i			0.117463i	0.998274	+	0.0587314i	$0.0187056\pi$
$193$			2.26417e9i			0.117463i	−0.998274	+	0.0587314i	$0.981294\pi$
$194$	2.06960e10			1.04901
$195$		−	6.17501e9i		−	0.305831i
$196$	−7.45381e9			−0.360766
$197$	4.21779e9			0.199520			0.0997601	−	0.995012i	$-0.468192\pi$
$197$	4.21779e9			0.199520			0.0997601	+	0.995012i	$0.468192\pi$
$198$	−1.52092e9			−0.0703255
$199$	−2.13515e10			−0.965138			−0.482569	−	0.875858i	$-0.660296\pi$
$199$	−2.13515e10			−0.965138			−0.482569	+	0.875858i	$0.660296\pi$
$200$			1.80305e9i			0.0796842i
$201$			2.31697e9i			0.100124i
$202$	4.05316e10			1.71283
$203$	1.79208e10	−	2.60154e10i	0.740670	−	1.07522i
$204$	−6.18960e9			−0.250223
$205$			3.65503e10i			1.44543i
$206$			2.83811e9i			0.109806i
$207$	−3.60415e10			−1.36438
$208$	−2.51067e10			−0.930046
$209$	1.86543e8			0.00676271
$210$	−1.85959e10			−0.659826
$211$		−	3.40025e10i		−	1.18097i	−0.807048	−	0.590486i	$-0.798936\pi$
$211$		−	3.40025e10i		−	1.18097i	0.807048	−	0.590486i	$-0.201064\pi$
$212$	8.93417e9			0.303769
$213$			1.96368e10i			0.653676i
$214$		−	2.05035e10i		−	0.668293i
$215$		−	3.48143e10i		−	1.11118i
$216$	−1.52962e10			−0.478125
$217$			2.05931e10i			0.630452i
$218$		−	4.29936e10i		−	1.28929i
$219$	−1.79441e9			−0.0527137
$220$			1.17658e9i			0.0338624i
$221$			2.92241e10i			0.824092i
$222$			1.28588e10i			0.355315i
$223$	3.15478e10			0.854275			0.427137	−	0.904187i	$-0.359522\pi$
$223$	3.15478e10			0.854275			0.427137	+	0.904187i	$0.359522\pi$
$224$			4.60839e10i			1.22302i
$225$	−4.11026e9			−0.106917
$226$	−3.68865e10			−0.940545
$227$	−1.66875e10			−0.417134			−0.208567	−	0.978008i	$-0.566880\pi$
$227$	−1.66875e10			−0.417134			−0.208567	+	0.978008i	$0.566880\pi$
$228$	−8.77792e8			−0.0215122
$229$			4.40393e10i			1.05823i	0.848550	+	0.529116i	$0.177476\pi$
$229$			4.40393e10i			1.05823i	−0.848550	+	0.529116i	$0.822524\pi$
$230$			8.23437e10i			1.94024i
$231$	−1.77126e9			−0.0409288
$232$	−2.18077e10	−	1.50222e10i	−0.494212	−	0.340439i
$233$	1.81461e10			0.403349			0.201674	−	0.979453i	$-0.435362\pi$
$233$	1.81461e10			0.403349			0.201674	+	0.979453i	$0.435362\pi$
$234$		−	3.37907e10i		−	0.736760i
$235$			6.76389e10i			1.44674i
$236$	−1.85928e10			−0.390159
$237$	2.12439e10			0.437387
$238$	8.80075e10			1.77797
$239$	5.82343e8			0.0115448			0.00577242	−	0.999983i	$-0.498163\pi$
$239$	5.82343e8			0.0115448			0.00577242	+	0.999983i	$0.498163\pi$
$240$			2.64027e10i			0.513687i
$241$	6.28520e10			1.20017			0.600085	−	0.799936i	$-0.295133\pi$
$241$	6.28520e10			1.20017			0.600085	+	0.799936i	$0.295133\pi$
$242$		−	6.52740e10i		−	1.22341i
$243$		−	5.41854e10i		−	0.996906i
$244$			3.68348e10i			0.665280i
$245$	3.70097e10			0.656249
$246$		−	4.83819e10i		−	0.842316i
$247$			4.14448e9i			0.0708490i
$248$	1.72623e10			0.289779
$249$			2.50158e10i			0.412399i
$250$			8.01139e10i			1.29711i
$251$		−	4.75308e10i		−	0.755864i	−0.925833	−	0.377932i	$-0.876635\pi$
$251$		−	4.75308e10i		−	0.755864i	0.925833	−	0.377932i	$-0.123365\pi$
$252$	−3.44558e10			−0.538220
$253$			7.84325e9i			0.120352i
$254$	−4.52380e10			−0.681949
$255$	3.07327e10			0.455166
$256$	8.26008e10			1.20200
$257$	7.44045e9			0.106390			0.0531949	−	0.998584i	$-0.483060\pi$
$257$	7.44045e9			0.106390			0.0531949	+	0.998584i	$0.483060\pi$
$258$			4.60839e10i			0.647532i
$259$		−	6.19078e10i		−	0.854863i
$260$	−2.61403e10			−0.354757
$261$	3.42450e10	−	4.97132e10i	0.456788	−	0.663116i
$262$	−6.71306e9			−0.0880166
$263$		−	1.32546e11i		−	1.70830i	−0.520023	−	0.854152i	$-0.674077\pi$
$263$		−	1.32546e11i		−	1.70830i	0.520023	−	0.854152i	$-0.325923\pi$
$264$			1.48477e9i			0.0188123i
$265$	−4.43600e10			−0.552568
$266$	1.24810e10			0.152856
$267$	4.06773e10			0.489837
$268$	9.80829e9			0.116141
$269$			1.63570e11i			1.90466i	0.305067	+	0.952331i	$0.401321\pi$
$269$			1.63570e11i			1.90466i	−0.305067	+	0.952331i	$0.598679\pi$
$270$	−7.96659e10			−0.912295
$271$			1.29205e11i			1.45518i	0.686011	+	0.727591i	$0.259360\pi$
$271$			1.29205e11i			1.45518i	−0.686011	+	0.727591i	$0.740640\pi$
$272$		−	1.24955e11i		−	1.38418i
$273$		−	3.93526e10i		−	0.428787i
$274$	−1.91562e11			−2.05320
$275$			8.94463e8i			0.00943116i
$276$		−	3.69070e10i		−	0.382840i
$277$	1.13400e11			1.15732			0.578662	−	0.815567i	$-0.303575\pi$
$277$	1.13400e11			1.15732			0.578662	+	0.815567i	$0.303575\pi$
$278$		−	2.87268e10i		−	0.288460i
$279$			3.93515e10i			0.388814i
$280$		−	7.50477e10i		−	0.729670i
$281$	−2.01423e11			−1.92722			−0.963611	−	0.267310i	$-0.913865\pi$
$281$	−2.01423e11			−1.92722			−0.963611	+	0.267310i	$0.913865\pi$
$282$		−	8.95342e10i		−	0.843078i
$283$	−9.91077e10			−0.918477			−0.459238	−	0.888313i	$-0.651878\pi$
$283$	−9.91077e10			−0.918477			−0.459238	+	0.888313i	$0.651878\pi$
$284$	8.31273e10			0.758248
$285$	4.35842e9			0.0391316
$286$	−7.35344e9			−0.0649895
$287$			2.32930e11i			2.02655i
$288$			8.80622e10i			0.754264i
$289$	−2.68588e10			−0.226489
$290$	−1.13579e11	−	7.82391e10i	−0.942991	−	0.649581i
$291$	4.60577e10			0.376516
$292$			7.59618e9i			0.0611466i
$293$			6.76058e10i			0.535895i	0.963434	+	0.267947i	$0.0863454\pi$
$293$			6.76058e10i			0.535895i	−0.963434	+	0.267947i	$0.913655\pi$
$294$	−4.89901e10			−0.382424
$295$	9.23172e10			0.709715
$296$	−5.18947e10			−0.392926
$297$	−7.58819e9			−0.0565893
$298$		−	9.11610e10i		−	0.669631i
$299$	−1.74256e11			−1.26086
$300$		−	4.20896e9i		−	0.0300006i
$301$		−	2.21867e11i		−	1.55792i
$302$		−	1.22741e11i		−	0.849096i
$303$	9.02008e10			0.614778
$304$		−	1.77207e10i		−	0.119001i
$305$		−	1.82893e11i		−	1.21017i
$306$	1.68174e11			1.09651
$307$		−	1.83816e11i		−	1.18103i	−0.807027	−	0.590514i	$-0.798925\pi$
$307$		−	1.83816e11i		−	1.18103i	0.807027	−	0.590514i	$-0.201075\pi$
$308$			7.49817e9i			0.0474763i
$309$			6.31605e9i			0.0394123i
$310$	8.99059e10			0.552918
$311$			1.94672e11i			1.18000i	0.807403	+	0.590000i	$0.200872\pi$
$311$			1.94672e11i			1.18000i	−0.807403	+	0.590000i	$0.799128\pi$
$312$	−3.29876e10			−0.197086
$313$	1.83670e11			1.08165			0.540827	−	0.841134i	$-0.318111\pi$
$313$	1.83670e11			1.08165			0.540827	+	0.841134i	$0.318111\pi$
$314$	−5.29752e10			−0.307531
$315$	1.71080e11			0.979045
$316$		−	8.99304e10i		−	0.507358i
$317$			2.57542e11i			1.43245i	0.697868	+	0.716227i	$0.254132\pi$
$317$			2.57542e11i			1.43245i	−0.697868	+	0.716227i	$0.745868\pi$
$318$	5.87197e10			0.322005
$319$	−1.08184e10	−	7.45230e9i	−0.0584934	−	0.0402932i
$320$	−1.71286e10			−0.0913160
$321$		−	4.56294e10i		−	0.239868i
$322$			5.24766e11i			2.72028i
$323$	−2.06269e10			−0.105444
$324$	−4.60622e10			−0.232216
$325$	−1.98725e10			−0.0988048
$326$	2.91166e11			1.42778
$327$		−	9.56798e10i		−	0.462760i
$328$	1.95256e11			0.931476
$329$			4.31055e11i			2.02839i
$330$			7.73303e9i			0.0358952i
$331$		−	2.34412e11i		−	1.07338i	−0.843778	−	0.536692i	$-0.819674\pi$
$331$		−	2.34412e11i		−	1.07338i	0.843778	−	0.536692i	$-0.180326\pi$
$332$	1.05898e11			0.478373
$333$		−	1.18300e11i		−	0.527213i
$334$		−	2.85449e11i		−	1.25508i
$335$	−4.87002e10			−0.211266
$336$			1.68261e11i			0.720208i
$337$			3.03832e11i			1.28321i	0.767033	+	0.641607i	$0.221732\pi$
$337$			3.03832e11i			1.28321i	−0.767033	+	0.641607i	$0.778268\pi$
$338$			1.31675e11i			0.548754i
$339$	−8.20888e10			−0.337587
$340$		−	1.30099e11i		−	0.527981i
$341$	8.56356e9			0.0342973
$342$	2.38500e10			0.0942696
$343$	−9.88351e10			−0.385556
$344$	−1.85982e11			−0.716074
$345$			1.83251e11i			0.696403i
$346$		−	8.34376e9i		−	0.0312982i
$347$	−5.33193e11			−1.97425			−0.987125	−	0.159950i	$-0.948867\pi$
$347$	−5.33193e11			−1.97425			−0.987125	+	0.159950i	$0.948867\pi$
$348$	5.09069e10	+	3.50673e10i	0.186067	+	0.128173i
$349$	−3.88581e11			−1.40206			−0.701031	−	0.713130i	$-0.747277\pi$
$349$	−3.88581e11			−1.40206			−0.701031	+	0.713130i	$0.747277\pi$
$350$			5.98456e10i			0.213170i
$351$		−	1.68589e11i		−	0.592853i
$352$	1.91638e10			0.0665335
$353$	5.03391e11			1.72552			0.862759	−	0.505616i	$-0.168735\pi$
$353$	5.03391e11			1.72552			0.862759	+	0.505616i	$0.168735\pi$
$354$	−1.22201e11			−0.413581
$355$	−4.12745e11			−1.37928
$356$		−	1.72197e11i		−	0.568198i
$357$	1.95856e11			0.638159
$358$			6.59900e11i			2.12327i
$359$		−	6.29937e10i		−	0.200157i	−0.994980	−	0.100079i	$-0.968091\pi$
$359$		−	6.29937e10i		−	0.200157i	0.994980	−	0.100079i	$-0.0319095\pi$
$360$		−	1.43409e11i		−	0.450004i
$361$	3.19762e11			0.990935
$362$		−	9.59347e10i		−	0.293621i
$363$		−	1.45264e11i		−	0.439113i
$364$	−1.66589e11			−0.497382
$365$		−	3.77166e10i		−	0.111228i
$366$			2.42097e11i			0.705219i
$367$		−	4.11486e11i		−	1.18402i	−0.805932	−	0.592008i	$-0.798335\pi$
$367$		−	4.11486e11i		−	1.18402i	0.805932	−	0.592008i	$-0.201665\pi$
$368$	7.45072e11			2.11779
$369$			4.45109e11i			1.24982i
$370$	−2.70279e11			−0.749730
$371$	−2.82701e11			−0.774720
$372$	−4.02965e10			−0.109100
$373$	3.36388e11			0.899809			0.449905	−	0.893077i	$-0.351458\pi$
$373$	3.36388e11			0.899809			0.449905	+	0.893077i	$0.351458\pi$
$374$		−	3.65976e10i		−	0.0967232i
$375$			1.78289e11i			0.465568i
$376$	3.61335e11			0.932320
$377$	1.65570e11	−	2.40356e11i	0.422129	−	0.612801i
$378$	−5.07701e11			−1.27907
$379$		−	7.23920e11i		−	1.80225i	−0.433562	−	0.901124i	$-0.642744\pi$
$379$		−	7.23920e11i		−	1.80225i	0.433562	−	0.901124i	$-0.357256\pi$
$380$		−	1.84503e10i		−	0.0453917i
$381$	−1.00675e11			−0.244770
$382$	−4.11532e11			−0.988823
$383$	−3.25910e10			−0.0773933			−0.0386967	−	0.999251i	$-0.512321\pi$
$383$	−3.25910e10			−0.0773933			−0.0386967	+	0.999251i	$0.512321\pi$
$384$	1.98819e11			0.466625
$385$		−	3.72300e10i		−	0.0863614i
$386$	6.29957e10			0.144434
$387$		−	4.23968e11i		−	0.960802i
$388$		−	1.94973e11i		−	0.436749i
$389$		−	5.47222e11i		−	1.21169i	−0.795584	−	0.605844i	$-0.792836\pi$
$389$		−	5.47222e11i		−	1.21169i	0.795584	−	0.605844i	$-0.207164\pi$
$390$	−1.71807e11			−0.376054
$391$		−	8.67261e11i		−	1.87653i
$392$		−	1.97710e11i		−	0.422904i
$393$	−1.49395e10			−0.0315915
$394$		−	1.17351e11i		−	0.245332i
$395$			4.46524e11i			0.922906i
$396$			1.43283e10i			0.0292797i
$397$	2.19816e11			0.444122			0.222061	−	0.975033i	$-0.428722\pi$
$397$	2.19816e11			0.444122			0.222061	+	0.975033i	$0.428722\pi$
$398$			5.94061e11i			1.18674i
$399$	2.77757e10			0.0548639
$400$	8.49698e10			0.165957
$401$	−7.97988e11			−1.54116			−0.770578	−	0.637345i	$-0.780032\pi$
$401$	−7.97988e11			−1.54116			−0.770578	+	0.637345i	$0.780032\pi$
$402$	6.44648e10			0.123113
$403$			1.90259e11i			0.359313i
$404$		−	3.81842e11i		−	0.713128i
$405$	2.28708e11			0.422410
$406$	−7.23826e11	−	4.98608e11i	−1.32211	−	0.910736i
$407$	−2.57442e10			−0.0465054
$408$		−	1.64178e11i		−	0.293321i
$409$			9.19938e11i			1.62556i	0.582569	+	0.812781i	$0.302048\pi$
$409$			9.19938e11i			1.62556i	−0.582569	+	0.812781i	$0.697952\pi$
$410$	1.01694e12			1.77732
$411$	−4.26310e11			−0.736949
$412$	2.67373e10			0.0457173
$413$	5.88326e11			0.995046
$414$			1.00278e12i			1.67766i
$415$	−5.25806e11			−0.870181
$416$			4.25768e11i			0.697033i
$417$		−	6.39297e10i		−	0.103536i
$418$		−	5.19018e9i		−	0.00831551i
$419$	9.93200e11			1.57425			0.787125	−	0.616793i	$-0.211569\pi$
$419$	9.93200e11			1.57425			0.787125	+	0.616793i	$0.211569\pi$
$420$			1.75188e11i			0.274716i
$421$			9.33549e10i			0.144833i	0.997374	+	0.0724165i	$0.0230711\pi$
$421$			9.33549e10i			0.144833i	−0.997374	+	0.0724165i	$0.976929\pi$
$422$	−9.46048e11			−1.45214
$423$			8.23707e11i			1.25095i
$424$			2.36977e11i			0.356089i
$425$		−	9.89045e10i		−	0.147050i
$426$	5.46353e11			0.803767
$427$		−	1.16555e12i		−	1.69671i
$428$	−1.93160e11			−0.278241
$429$	−1.63646e10			−0.0233265
$430$	−9.68635e11			−1.36632
$431$	5.44668e10			0.0760299			0.0380149	−	0.999277i	$-0.487897\pi$
$431$	5.44668e10			0.0760299			0.0380149	+	0.999277i	$0.487897\pi$
$432$			7.20843e11i			0.995780i
$433$		−	2.46574e10i		−	0.0337095i	−0.999858	−	0.0168547i	$-0.994635\pi$
$433$		−	2.46574e10i		−	0.0337095i	0.999858	−	0.0168547i	$-0.00536528\pi$
$434$	5.72959e11			0.775211
$435$	−2.52764e11	−	1.74117e11i	−0.338464	−	0.233152i
$436$	−4.05036e11			−0.536790
$437$		−	1.22993e11i		−	0.161329i
$438$			4.99258e10i			0.0648174i
$439$	−3.77301e11			−0.484839			−0.242419	−	0.970172i	$-0.577941\pi$
$439$	−3.77301e11			−0.484839			−0.242419	+	0.970172i	$0.577941\pi$
$440$	−3.12084e10			−0.0396948
$441$	4.50704e11			0.567438
$442$	8.13100e11			1.01331
$443$			6.63834e11i			0.818923i	0.912327	+	0.409461i	$0.134283\pi$
$443$			6.63834e11i			0.818923i	−0.912327	+	0.409461i	$0.865717\pi$
$444$	1.21141e11			0.147934
$445$			8.54993e11i			1.03358i
$446$		−	8.77753e11i		−	1.05043i
$447$		−	2.02873e11i		−	0.240348i
$448$	−1.09158e11			−0.128028
$449$			7.22697e11i			0.839166i	0.907717	+	0.419583i	$0.137824\pi$
$449$			7.22697e11i			0.839166i	−0.907717	+	0.419583i	$0.862176\pi$
$450$			1.14359e11i			0.131467i
$451$	9.68634e10			0.110247
$452$			3.47502e11i			0.391592i
$453$		−	2.73152e11i		−	0.304763i
$454$			4.64295e11i			0.512912i
$455$	8.27149e11			0.904758
$456$		−	2.32832e10i		−	0.0252174i
$457$	1.47862e11			0.158574			0.0792872	−	0.996852i	$-0.474736\pi$
$457$	1.47862e11			0.158574			0.0792872	+	0.996852i	$0.474736\pi$
$458$	1.22530e12			1.30121
$459$	8.39058e11			0.882338
$460$	7.75746e11			0.807810
$461$		−	7.20064e11i		−	0.742535i	−0.928526	−	0.371267i	$-0.878923\pi$
$461$		−	7.20064e11i		−	0.742535i	0.928526	−	0.371267i	$-0.121077\pi$
$462$			4.92816e10i			0.0503264i
$463$	−1.65614e12			−1.67487			−0.837437	−	0.546534i	$-0.815947\pi$
$463$	−1.65614e12			−1.67487			−0.837437	+	0.546534i	$0.815947\pi$
$464$	−7.07933e11	+	1.02770e12i	−0.709024	+	1.02929i
$465$	2.00080e11			0.198457
$466$		−	5.04876e11i		−	0.495962i
$467$			5.17300e11i			0.503288i	0.967820	+	0.251644i	$0.0809711\pi$
$467$			5.17300e11i			0.503288i	−0.967820	+	0.251644i	$0.919029\pi$
$468$	−3.18336e11			−0.306747
$469$	−3.10360e11			−0.296202
$470$	1.88191e12			1.77893
$471$	−1.17893e11			−0.110381
$472$		−	4.93169e11i		−	0.457359i
$473$	−9.22627e10			−0.0847523
$474$		−	5.91067e11i		−	0.537816i
$475$		−	1.40264e10i		−	0.0126422i
$476$		−	8.29104e11i		−	0.740249i
$477$	−5.40216e11			−0.477788
$478$		−	1.62025e10i		−	0.0141957i
$479$		−	2.05821e12i		−	1.78640i	−0.449656	−	0.893202i	$-0.648453\pi$
$479$		−	2.05821e12i		−	1.78640i	0.449656	−	0.893202i	$-0.351547\pi$
$480$	4.47747e11			0.384988
$481$		−	5.71965e11i		−	0.487210i
$482$		−	1.74873e12i		−	1.47574i
$483$			1.16784e12i			0.976382i
$484$	−6.14935e11			−0.509361
$485$			9.68083e11i			0.794465i
$486$	−1.50760e12			−1.22581
$487$	−5.82650e11			−0.469383			−0.234691	−	0.972070i	$-0.575408\pi$
$487$	−5.82650e11			−0.469383			−0.234691	+	0.972070i	$0.575408\pi$
$488$	−9.77035e11			−0.779867
$489$	6.47973e11			0.512468
$490$		−	1.02972e12i		−	0.806931i
$491$			1.61150e12i			1.25131i	0.780102	+	0.625653i	$0.215167\pi$
$491$			1.61150e12i			1.25131i	−0.780102	+	0.625653i	$0.784833\pi$
$492$	−4.55798e11			−0.350695
$493$	1.19624e12	+	8.24031e11i	0.912026	+	0.628250i
$494$	1.15312e11			0.0871168
$495$		−	7.11432e10i		−	0.0532611i
$496$		−	8.13498e11i		−	0.603516i
$497$	−2.63037e12			−1.93381
$498$	6.96014e11			0.507091
$499$	1.66255e12			1.20039			0.600194	−	0.799854i	$-0.295090\pi$
$499$	1.66255e12			1.20039			0.600194	+	0.799854i	$0.295090\pi$
$500$	7.54740e11			0.540048
$501$		−	6.35251e11i		−	0.450480i
$502$	−1.32245e12			−0.929418
$503$		−	2.19713e11i		−	0.153038i	−0.997068	−	0.0765191i	$-0.975619\pi$
$503$		−	2.19713e11i		−	0.153038i	0.997068	−	0.0765191i	$-0.0243806\pi$
$504$		−	9.13931e11i		−	0.630922i
$505$			1.89592e12i			1.29721i
$506$	2.18222e11			0.147986
$507$			2.93035e11i			0.196962i
$508$			4.26180e11i			0.283927i
$509$	−8.72380e11			−0.576071			−0.288035	−	0.957620i	$-0.593002\pi$
$509$	−8.72380e11			−0.576071			−0.288035	+	0.957620i	$0.593002\pi$
$510$		−	8.55073e11i		−	0.559677i
$511$		−	2.40363e11i		−	0.155946i
$512$		−	6.54166e11i		−	0.420700i
$513$	1.18993e11			0.0758565
$514$		−	2.07015e11i		−	0.130818i
$515$	−1.32757e11			−0.0831617
$516$	4.34149e11			0.269597
$517$	1.79253e11			0.110346
$518$	−1.72246e12			−1.05115
$519$		−	1.85685e10i		−	0.0112338i
$520$		−	6.93365e11i		−	0.415860i
$521$	−2.45268e12			−1.45838			−0.729190	−	0.684311i	$-0.760103\pi$
$521$	−2.45268e12			−1.45838			−0.729190	+	0.684311i	$0.760103\pi$
$522$	−1.38317e12	−	9.52796e11i	−0.815374	−	0.561672i
$523$	−1.08755e12			−0.635612			−0.317806	−	0.948156i	$-0.602946\pi$
$523$	−1.08755e12			−0.635612			−0.317806	+	0.948156i	$0.602946\pi$
$524$			6.32426e10i			0.0366453i
$525$			1.33183e11i			0.0765123i
$526$	−3.68781e12			−2.10055
$527$	−9.46908e11			−0.534762
$528$	6.99709e10			0.0391801
$529$	3.37010e12			1.87108
$530$			1.23423e12i			0.679443i
$531$	1.12424e12			0.613668
$532$		−	1.17581e11i		−	0.0636408i
$533$			2.15204e12i			1.15499i
$534$		−	1.13176e12i		−	0.602309i
$535$	9.59081e11			0.506132
$536$			2.60162e11i			0.136145i
$537$			1.46857e12i			0.762097i
$538$	4.55099e12			2.34199
$539$		−	9.80810e10i		−	0.0500536i
$540$			7.50519e11i			0.379830i
$541$		−	1.41922e12i		−	0.712297i	−0.934429	−	0.356149i	$-0.884090\pi$
$541$		−	1.41922e12i		−	0.712297i	0.934429	−	0.356149i	$-0.115910\pi$
$542$	3.59486e12			1.78931
$543$		−	2.13497e11i		−	0.105388i
$544$	−2.11902e12			−1.03739
$545$	2.01109e12			0.976443
$546$	−1.09490e12			−0.527241
$547$	1.29406e12			0.618031			0.309015	−	0.951057i	$-0.400001\pi$
$547$	1.29406e12			0.618031			0.309015	+	0.951057i	$0.400001\pi$
$548$			1.80467e12i			0.854843i
$549$		−	2.22727e12i		−	1.04640i
$550$	2.48866e10			0.0115967
$551$	1.69647e11	+	1.16862e11i	0.0784088	+	0.0540120i
$552$	9.78948e11			0.448780
$553$			2.84564e12i			1.29395i
$554$		−	3.15513e12i		−	1.42306i
$555$	−6.01490e11			−0.269098
$556$	−2.70630e11			−0.120099
$557$	3.07985e12			1.35575			0.677877	−	0.735176i	$-0.262900\pi$
$557$	3.07985e12			1.35575			0.677877	+	0.735176i	$0.262900\pi$
$558$	1.09487e12			0.478091
$559$		−	2.04983e12i		−	0.887900i
$560$	−3.53667e12			−1.51967
$561$		−	8.14459e10i		−	0.0347165i
$562$			5.60419e12i			2.36973i
$563$			4.43231e11i			0.185927i	0.995670	+	0.0929635i	$0.0296340\pi$
$563$			4.43231e11i			0.185927i	−0.995670	+	0.0929635i	$0.970366\pi$
$564$	−8.43486e11			−0.351012
$565$		−	1.72542e12i		−	0.712322i
$566$			2.75746e12i			1.12937i
$567$	1.45753e12			0.592235
$568$			2.20493e12i			0.888848i
$569$		−	2.22968e12i		−	0.891737i	−0.895099	−	0.445868i	$-0.852895\pi$
$569$		−	2.22968e12i		−	0.891737i	0.895099	−	0.445868i	$-0.147105\pi$
$570$		−	1.21264e11i		−	0.0481166i
$571$	5.43884e11			0.214113			0.107057	−	0.994253i	$-0.465857\pi$
$571$	5.43884e11			0.214113			0.107057	+	0.994253i	$0.465857\pi$
$572$			6.92755e10i			0.0270581i
$573$	−9.15841e11			−0.354915
$574$	6.48081e12			2.49187
$575$	5.89742e11			0.224987
$576$	−2.08592e11			−0.0789580
$577$		−	2.76459e12i		−	1.03834i	−0.854671	−	0.519171i	$-0.826241\pi$
$577$		−	2.76459e12i		−	1.03834i	0.854671	−	0.519171i	$-0.173759\pi$
$578$			7.47291e11i			0.278493i
$579$	1.40193e11			0.0518410
$580$	−7.37078e11	+	1.07001e12i	−0.270450	+	0.392610i
$581$	−3.35090e12			−1.22003
$582$		−	1.28146e12i		−	0.462968i
$583$			1.17560e11i			0.0421456i
$584$	−2.01487e11			−0.0716784
$585$	1.58061e12			0.557985
$586$	1.88099e12			0.658942
$587$	−1.75453e11			−0.0609942			−0.0304971	−	0.999535i	$-0.509709\pi$
$587$	−1.75453e11			−0.0609942			−0.0304971	+	0.999535i	$0.509709\pi$
$588$			4.61527e11i			0.159221i
$589$	−1.34288e11			−0.0459746
$590$		−	2.56854e12i		−	0.872673i
$591$		−	2.61158e11i		−	0.0880562i
$592$			2.44557e12i			0.818338i
$593$	−4.88984e12			−1.62386			−0.811931	−	0.583754i	$-0.801583\pi$
$593$	−4.88984e12			−1.62386			−0.811931	+	0.583754i	$0.801583\pi$
$594$			2.11126e11i			0.0695828i
$595$			4.11668e12i			1.34654i
$596$	−8.58812e11			−0.278798
$597$			1.32205e12i			0.425954i
$598$			4.84830e12i			1.55037i
$599$			2.00182e12i			0.635339i	0.948202	+	0.317669i	$0.102900\pi$
$599$			2.00182e12i			0.635339i	−0.948202	+	0.317669i	$0.897100\pi$
$600$	1.11642e11			0.0351678
$601$		−	8.75942e11i		−	0.273867i	−0.990580	−	0.136934i	$-0.956275\pi$
$601$		−	8.75942e11i		−	0.273867i	0.990580	−	0.136934i	$-0.0437247\pi$
$602$	−6.17299e12			−1.91563
$603$	−5.93071e11			−0.182675
$604$	−1.15632e12			−0.353518
$605$	3.05328e12			0.926548
$606$		−	2.50965e12i		−	0.755938i
$607$		−	6.01882e12i		−	1.79954i	−0.436361	−	0.899772i	$-0.643733\pi$
$607$		−	6.01882e12i		−	1.79954i	0.436361	−	0.899772i	$-0.356267\pi$
$608$	−3.00514e11			−0.0891865
$609$	−1.61083e12	−	1.10962e12i	−0.474540	−	0.326887i
$610$	−5.08861e12			−1.48804
$611$			3.98251e12i			1.15603i
$612$		−	1.58434e12i		−	0.456528i
$613$	1.54690e12			0.442475			0.221238	−	0.975220i	$-0.428990\pi$
$613$	1.54690e12			0.442475			0.221238	+	0.975220i	$0.428990\pi$
$614$	−5.11429e12			−1.45220
$615$	2.26313e12			0.637928
$616$	−1.98887e11			−0.0556536
$617$		−	4.86252e12i		−	1.35076i	−0.737470	−	0.675380i	$-0.763979\pi$
$617$		−	4.86252e12i		−	1.35076i	0.737470	−	0.675380i	$-0.236021\pi$
$618$	1.75731e11			0.0484618
$619$		−	6.11095e12i		−	1.67302i	−0.547952	−	0.836509i	$-0.684593\pi$
$619$		−	6.11095e12i		−	1.67302i	0.547952	−	0.836509i	$-0.315407\pi$
$620$		−	8.46988e11i		−	0.230205i
$621$			5.00309e12i			1.34998i
$622$	5.41634e12			1.45094
$623$			5.44877e12i			1.44911i
$624$			1.55456e12i			0.410467i
$625$	−3.24092e12			−0.849589
$626$		−	5.11023e12i		−	1.33001i
$627$		−	1.15504e10i		−	0.00298466i
$628$			4.99070e11i			0.128039i
$629$	2.84664e12			0.725111
$630$		−	4.75995e12i		−	1.20384i
$631$	−5.07192e12			−1.27362			−0.636810	−	0.771021i	$-0.719747\pi$
$631$	−5.07192e12			−1.27362			−0.636810	+	0.771021i	$0.719747\pi$
$632$	2.38538e12			0.594745
$633$	−2.10538e12			−0.521210
$634$	7.16556e12			1.76136
$635$		−	2.11607e12i		−	0.516474i
$636$		−	5.53189e11i		−	0.134065i
$637$	2.17909e12			0.524383
$638$	−2.07345e11	+	3.01001e11i	−0.0495450	+	0.0719241i
$639$	−5.02640e12			−1.19262
$640$			4.17897e12i			0.984599i
$641$		−	5.76556e12i		−	1.34890i	−0.738320	−	0.674451i	$-0.764380\pi$
$641$		−	5.76556e12i		−	1.34890i	0.738320	−	0.674451i	$-0.235620\pi$
$642$	−1.26954e12			−0.294944
$643$	4.39461e12			1.01384			0.506922	−	0.861992i	$-0.330783\pi$
$643$	4.39461e12			1.01384			0.506922	+	0.861992i	$0.330783\pi$
$644$	4.94373e12			1.13258
$645$	−2.15564e12			−0.490408
$646$			5.73899e11i			0.129655i
$647$	−1.68186e11			−0.0377330			−0.0188665	−	0.999822i	$-0.506006\pi$
$647$	−1.68186e11			−0.0377330			−0.0188665	+	0.999822i	$0.506006\pi$
$648$		−	1.22179e12i		−	0.272212i
$649$		−	2.44654e11i		−	0.0541316i
$650$			5.52912e11i			0.121492i
$651$	1.27509e12			0.278244
$652$		−	2.74303e12i		−	0.594451i
$653$		−	1.15108e12i		−	0.247740i	−0.992298	−	0.123870i	$-0.960469\pi$
$653$		−	1.15108e12i		−	0.247740i	0.992298	−	0.123870i	$-0.0395307\pi$
$654$	−2.66209e12			−0.569014
$655$		−	3.14013e11i		−	0.0666594i
$656$		−	9.20156e12i		−	1.93997i
$657$		−	4.59313e11i		−	0.0961755i
$658$	1.19932e13			2.49413
$659$		−	3.47403e12i		−	0.717546i	−0.933425	−	0.358773i	$-0.883195\pi$
$659$		−	3.47403e12i		−	0.717546i	0.933425	−	0.358773i	$-0.116805\pi$
$660$	7.28515e10			0.0149448
$661$	−5.09466e12			−1.03803			−0.519014	−	0.854766i	$-0.673701\pi$
$661$	−5.09466e12			−1.03803			−0.519014	+	0.854766i	$0.673701\pi$
$662$	−6.52204e12			−1.31984
$663$	1.80951e12			0.363705
$664$			2.80892e12i			0.560767i
$665$			5.83816e11i			0.115765i
$666$	−3.29146e12			−0.648268
$667$	−4.91348e12	+	7.13287e12i	−0.961221	+	1.39540i
$668$	−2.68917e12			−0.522546
$669$		−	1.95339e12i		−	0.377026i
$670$			1.35498e12i			0.259775i
$671$	−4.84691e11			−0.0923026
$672$	2.85344e12			0.539767
$673$	−1.71869e12			−0.322945			−0.161473	−	0.986877i	$-0.551624\pi$
$673$	−1.71869e12			−0.322945			−0.161473	+	0.986877i	$0.551624\pi$
$674$	8.45350e12			1.57785
$675$			5.70564e11i			0.105788i
$676$	1.24049e12			0.228471
$677$			1.61296e12i			0.295104i	0.989054	+	0.147552i	$0.0471394\pi$
$677$			1.61296e12i			0.295104i	−0.989054	+	0.147552i	$0.952861\pi$
$678$			2.28395e12i			0.415100i
$679$			6.16948e12i			1.11387i
$680$	3.45084e12			0.618920
$681$			1.03326e12i			0.184098i
$682$		−	2.38263e11i		−	0.0421723i
$683$	4.55771e12			0.801409			0.400704	−	0.916207i	$-0.368765\pi$
$683$	4.55771e12			0.801409			0.400704	+	0.916207i	$0.368765\pi$
$684$		−	2.24687e11i		−	0.0392487i
$685$		−	8.96058e12i		−	1.55499i
$686$			2.74988e12i			0.474084i
$687$	2.72684e12			0.467040
$688$			8.76453e12i			1.49135i
$689$	−2.61187e12			−0.441535
$690$	5.09858e12			0.856304
$691$	−1.14761e13			−1.91488			−0.957440	−	0.288633i	$-0.906799\pi$
$691$	−1.14761e13			−1.91488			−0.957440	+	0.288633i	$0.906799\pi$
$692$	−7.86051e10			−0.0130309
$693$		−	4.53387e11i		−	0.0746740i
$694$			1.48350e13i			2.42756i
$695$	1.34374e12			0.218465
$696$	−9.30151e11	+	1.35029e12i	−0.150249	+	0.218115i
$697$	−1.07106e13			−1.71896
$698$			1.08115e13i			1.72399i
$699$		−	1.12357e12i		−	0.178014i
$700$	5.63795e11			0.0887524
$701$	−1.98396e12			−0.310314			−0.155157	−	0.987890i	$-0.549588\pi$
$701$	−1.98396e12			−0.310314			−0.155157	+	0.987890i	$0.549588\pi$
$702$	−4.69064e12			−0.728979
$703$	4.03702e11			0.0623393
$704$			4.53932e10i			0.00696488i
$705$	4.18809e12			0.638506
$706$		−	1.40058e13i		−	2.12172i
$707$			1.20825e13i			1.81873i
$708$			1.15124e12i			0.172193i
$709$	4.83101e12			0.718009			0.359004	−	0.933336i	$-0.383116\pi$
$709$	4.83101e12			0.718009			0.359004	+	0.933336i	$0.383116\pi$
$710$			1.14838e13i			1.69598i
$711$			5.43776e12i			0.798007i
$712$	4.56747e12			0.666064
$713$		−	5.64617e12i		−	0.818184i
$714$		−	5.44927e12i		−	0.784688i
$715$		−	3.43967e11i		−	0.0492198i
$716$	6.21681e12			0.884013
$717$		−	3.60577e10i		−	0.00509520i
$718$	−1.75267e12			−0.246116
$719$	7.87793e12			1.09934			0.549670	−	0.835382i	$-0.314753\pi$
$719$	7.87793e12			1.09934			0.549670	+	0.835382i	$0.314753\pi$
$720$	−6.75827e12			−0.937215
$721$	−8.46041e11			−0.116596
$722$		−	8.89673e12i		−	1.21846i
$723$		−	3.89169e12i		−	0.529683i
$724$	−9.03785e11			−0.122248
$725$	−5.60345e11	+	8.13449e11i	−0.0753242	+	0.109348i
$726$	−4.04166e12			−0.539939
$727$		−	9.52425e12i		−	1.26452i	−0.774756	−	0.632261i	$-0.782127\pi$
$727$		−	9.52425e12i		−	1.26452i	0.774756	−	0.632261i	$-0.217873\pi$
$728$		−	4.41873e12i		−	0.583050i
$729$	1.03879e11			0.0136224
$730$	−1.04939e12			−0.136767
$731$	1.02019e13			1.32145
$732$	2.28075e12			0.293615
$733$			5.91593e12i			0.756929i	0.925616	+	0.378465i	$0.123548\pi$
$733$			5.91593e12i			0.756929i	−0.925616	+	0.378465i	$0.876452\pi$
$734$	−1.14487e13			−1.45588
$735$		−	2.29158e12i		−	0.289629i
$736$		−	1.26352e13i		−	1.58720i
$737$			1.29062e11i			0.0161137i
$738$	1.23842e13			1.53679
$739$			7.16023e12i			0.883135i	0.897228	+	0.441567i	$0.145577\pi$
$739$			7.16023e12i			0.883135i	−0.897228	+	0.441567i	$0.854423\pi$
$740$			2.54625e12i			0.312147i
$741$	2.56619e11			0.0312685
$742$			7.86557e12i			0.952605i
$743$			5.67927e12i			0.683665i	0.939761	+	0.341832i	$0.111047\pi$
$743$			5.67927e12i			0.683665i	−0.939761	+	0.341832i	$0.888953\pi$
$744$		−	1.06885e12i		−	0.127891i
$745$	4.26418e12			0.507145
$746$		−	9.35929e12i		−	1.10642i
$747$	−6.40327e12			−0.752417
$748$	−3.44780e11			−0.0402703
$749$	6.11211e12			0.709615
$750$	4.96052e12			0.572468
$751$			9.89674e12i			1.13530i	0.823268	+	0.567652i	$0.192148\pi$
$751$			9.89674e12i			1.13530i	−0.823268	+	0.567652i	$0.807852\pi$
$752$		−	1.70282e13i		−	1.94172i
$753$	−2.94303e12			−0.333593
$754$	−6.68741e12	−	4.60663e12i	−0.753507	−	0.519054i
$755$	5.74136e12			0.643063
$756$			4.78296e12i			0.532536i
$757$		−	1.41679e13i		−	1.56810i	−0.620698	−	0.784050i	$-0.713151\pi$
$757$		−	1.41679e13i		−	1.56810i	0.620698	−	0.784050i	$-0.286849\pi$
$758$	−2.01416e13			−2.21606
$759$	4.85641e11			0.0531162
$760$	4.89388e11			0.0532099
$761$	1.67696e13			1.81256			0.906279	−	0.422681i	$-0.138911\pi$
$761$	1.67696e13			1.81256			0.906279	+	0.422681i	$0.138911\pi$
$762$			2.80106e12i			0.300971i
$763$	1.28164e13			1.36901
$764$			3.87697e12i			0.411692i
$765$			7.86660e12i			0.830444i
$766$			9.06777e11i			0.0951637i
$767$	5.43554e12			0.567105
$768$		−	5.11450e12i		−	0.530490i
$769$			2.69623e12i			0.278028i	0.990290	+	0.139014i	$0.0443933\pi$
$769$			2.69623e12i			0.278028i	−0.990290	+	0.139014i	$0.955607\pi$
$770$	−1.03585e12			−0.106191
$771$		−	4.60700e11i		−	0.0469541i
$772$		−	5.93472e11i		−	0.0601343i
$773$		−	1.06661e13i		−	1.07448i	−0.843428	−	0.537242i	$-0.819466\pi$
$773$		−	1.06661e13i		−	1.07448i	0.843428	−	0.537242i	$-0.180534\pi$
$774$	−1.17960e13			−1.18141
$775$		−	6.43902e11i		−	0.0641154i
$776$	5.17161e12			0.511974
$777$	−3.83322e12			−0.377285
$778$	−1.52253e13			−1.48990
$779$	−1.51895e12			−0.147783
$780$			1.61856e12i			0.156568i
$781$			1.09383e12i			0.105201i
$782$	−2.41297e13			−2.30740
$783$	−6.90091e12	−	4.75370e12i	−0.656113	−	0.451964i
$784$	−9.31723e12			−0.880774
$785$		−	2.47799e12i		−	0.232909i
$786$			4.15661e11i			0.0388452i
$787$	8.57155e12			0.796477			0.398238	−	0.917282i	$-0.369622\pi$
$787$	8.57155e12			0.796477			0.398238	+	0.917282i	$0.369622\pi$
$788$	−1.10555e12			−0.102143
$789$	−8.20701e12			−0.753943
$790$	1.24236e13			1.13482
$791$		−	1.09959e13i		−	0.998702i
$792$	−3.80055e11			−0.0343228
$793$		−	1.07685e13i		−	0.967001i
$794$		−	6.11593e12i		−	0.546097i
$795$			2.74670e12i			0.243870i
$796$	5.59655e12			0.494096
$797$		−	7.23043e12i		−	0.634748i	−0.948300	−	0.317374i	$-0.897199\pi$
$797$		−	7.23043e12i		−	0.634748i	0.948300	−	0.317374i	$-0.102801\pi$
$798$		−	7.72801e11i		−	0.0674613i
$799$	−1.98207e13			−1.72052
$800$		−	1.44095e12i		−	0.124378i
$801$			1.04121e13i			0.893701i
$802$			2.22024e13i			1.89502i
$803$	−9.99543e10			−0.00848363
$804$		−	6.07312e11i		−	0.0512578i
$805$	−2.45467e13			−2.06021
$806$	5.29356e12			0.441815
$807$	1.01280e13			0.840603
$808$	1.01283e13			0.835956
$809$			5.63517e11i			0.0462528i	0.999733	+	0.0231264i	$0.00736202\pi$
$809$			5.63517e11i			0.0462528i	−0.999733	+	0.0231264i	$0.992638\pi$
$810$		−	6.36333e12i		−	0.519400i
$811$	−7.13154e11			−0.0578882			−0.0289441	−	0.999581i	$-0.509214\pi$
$811$	−7.13154e11			−0.0578882			−0.0289441	+	0.999581i	$0.509214\pi$
$812$	−4.69730e12	+	6.81904e12i	−0.379181	+	0.550454i
$813$	8.00015e12			0.642230
$814$			7.16278e11i			0.0571836i
$815$			1.36197e13i			1.08133i
$816$	−7.73698e12			−0.610894
$817$	1.44680e12			0.113608
$818$	2.55954e13			1.99881
$819$	1.00730e13			0.782316
$820$		−	9.58038e12i		−	0.739981i
$821$	−1.86371e13			−1.43164			−0.715819	−	0.698285i	$-0.753947\pi$
$821$	−1.86371e13			−1.43164			−0.715819	+	0.698285i	$0.753947\pi$
$822$			1.18612e13i			0.906161i
$823$			9.48577e12i			0.720731i	0.932811	+	0.360366i	$0.117348\pi$
$823$			9.48577e12i			0.720731i	−0.932811	+	0.360366i	$0.882652\pi$
$824$			7.09201e11i			0.0535916i
$825$	5.53836e10			0.00416235
$826$		−	1.63690e13i		−	1.22352i
$827$			2.79022e12i			0.207426i	0.994607	+	0.103713i	$0.0330724\pi$
$827$			2.79022e12i			0.207426i	−0.994607	+	0.103713i	$0.966928\pi$
$828$	9.44702e12			0.698487
$829$			1.27834e13i			0.940049i	0.882653	+	0.470025i	$0.155755\pi$
$829$			1.27834e13i			0.940049i	−0.882653	+	0.470025i	$0.844245\pi$
$830$			1.46295e13i			1.06998i
$831$		−	7.02155e12i		−	0.510773i
$832$	−1.00851e12			−0.0729670
$833$			1.08452e13i			0.780433i
$834$	−1.77871e12			−0.127309
$835$	1.33523e13			0.950532
$836$	−4.88958e10			−0.00346213
$837$	5.46256e12			0.384708
$838$		−	2.76337e13i		−	1.93572i
$839$			7.72707e12i			0.538377i	0.963088	+	0.269188i	$0.0867554\pi$
$839$			7.72707e12i			0.538377i	−0.963088	+	0.269188i	$0.913245\pi$
$840$	−4.64683e12			−0.322033
$841$	−5.17001e12	−	1.35546e13i	−0.356377	−	0.934342i
$842$	2.59741e12			0.178088
$843$			1.24718e13i			0.850560i
$844$			8.91256e12i			0.604591i
$845$	−6.15927e12			−0.415599
$846$	2.29179e13			1.53819
$847$	1.94582e13			1.29905
$848$	1.11677e13			0.741620
$849$			6.13658e12i			0.405361i
$850$	−2.75181e12			−0.180815
$851$			1.69738e13i			1.10942i
$852$		−	5.14710e12i		−	0.334645i
$853$		−	1.09039e13i		−	0.705201i	−0.935774	−	0.352600i	$-0.885298\pi$
$853$		−	1.09039e13i		−	0.705201i	0.935774	−	0.352600i	$-0.114702\pi$
$854$	−3.24291e13			−2.08629
$855$			1.11562e12i			0.0713951i
$856$		−	5.12353e12i		−	0.326165i
$857$	2.01416e13			1.27550			0.637750	−	0.770244i	$-0.279865\pi$
$857$	2.01416e13			1.27550			0.637750	+	0.770244i	$0.279865\pi$
$858$			4.55312e11i			0.0286825i
$859$		−	1.06310e13i		−	0.666199i	−0.942892	−	0.333100i	$-0.891905\pi$
$859$		−	1.06310e13i		−	0.666199i	0.942892	−	0.333100i	$-0.108095\pi$
$860$			9.12535e12i			0.568861i
$861$	1.44227e13			0.894398
$862$		−	1.51543e12i		−	0.0934872i
$863$	1.26120e13			0.773989			0.386995	−	0.922082i	$-0.373513\pi$
$863$	1.26120e13			0.773989			0.386995	+	0.922082i	$0.373513\pi$
$864$	1.22243e13			0.746298
$865$	3.90291e11			0.0237037
$866$	−6.86041e11			−0.0414495
$867$			1.66305e12i			0.0999586i
$868$		−	5.39775e12i		−	0.322756i
$869$	1.18335e12			0.0703921
$870$	−4.84443e12	+	7.03262e12i	−0.286686	+	0.416180i
$871$	−2.86741e12			−0.168814
$872$		−	1.07435e13i		−	0.629246i
$873$			1.17893e13i			0.686949i
$874$	−3.42201e12			−0.198372
$875$	−2.38820e13			−1.37732
$876$	4.70342e11			0.0269864
$877$	−1.86563e13			−1.06494			−0.532472	−	0.846448i	$-0.678737\pi$
$877$	−1.86563e13			−1.06494			−0.532472	+	0.846448i	$0.678737\pi$
$878$			1.04976e13i			0.596163i
$879$	4.18604e12			0.236512
$880$			1.47071e12i			0.0826716i
$881$			1.38263e13i			0.773241i	0.922239	+	0.386621i	$0.126358\pi$
$881$			1.38263e13i			0.773241i	−0.922239	+	0.386621i	$0.873642\pi$
$882$		−	1.25399e13i		−	0.697728i
$883$	−4.82881e10			−0.00267311			−0.00133655	−	0.999999i	$-0.500425\pi$
$883$	−4.82881e10			−0.00267311			−0.00133655	+	0.999999i	$0.500425\pi$
$884$		−	7.66008e12i		−	0.421889i
$885$		−	5.71613e12i		−	0.313225i
$886$	1.84698e13			1.00696
$887$		−	3.97505e12i		−	0.215619i	−0.994172	−	0.107809i	$-0.965616\pi$
$887$		−	3.97505e12i		−	0.215619i	0.994172	−	0.107809i	$-0.0343836\pi$
$888$			3.21323e12i			0.173414i
$889$		−	1.34855e13i		−	0.724116i
$890$	2.37884e13			1.27090
$891$		−	6.06109e11i		−	0.0322182i
$892$	−8.26916e12			−0.437340
$893$	−2.81092e12			−0.147917
$894$	−5.64453e12			−0.295535
$895$	−3.08678e13			−1.60806
$896$			2.66321e13i			1.38044i
$897$			1.07896e13i			0.556468i
$898$	2.01075e13			1.03185
$899$	7.78793e12	+	5.36473e12i	0.397652	+	0.273923i
$900$	1.07736e12			0.0547356
$901$		−	1.29991e13i		−	0.657132i
$902$		−	2.69502e12i		−	0.135560i
$903$	−1.37376e13			−0.687570
$904$	−9.21739e12			−0.459039
$905$	4.48748e12			0.222374
$906$	−7.59989e12			−0.374740
$907$		−	2.46562e12i		−	0.120974i	−0.998169	−	0.0604871i	$-0.980735\pi$
$907$		−	2.46562e12i		−	0.120974i	0.998169	−	0.0604871i	$-0.0192654\pi$
$908$	4.37405e12			0.213549
$909$			2.30886e13i			1.12166i
$910$		−	2.30137e13i		−	1.11250i
$911$		−	1.16213e13i		−	0.559011i	−0.960144	−	0.279505i	$-0.909830\pi$
$911$		−	1.16213e13i		−	0.559011i	0.960144	−	0.279505i	$-0.0901705\pi$
$912$	−1.09724e12			−0.0525199
$913$			1.39346e12i			0.0663707i
$914$		−	4.11395e12i		−	0.194985i
$915$	−1.13244e13			−0.534098
$916$		−	1.15434e13i		−	0.541755i
$917$		−	2.00116e12i		−	0.0934589i
$918$		−	2.33450e13i		−	1.08493i
$919$	1.25014e12			0.0578147			0.0289073	−	0.999582i	$-0.490797\pi$
$919$	1.25014e12			0.0578147			0.0289073	+	0.999582i	$0.490797\pi$
$920$			2.05764e13i			0.946946i
$921$	−1.13816e13			−0.521235
$922$	−2.00343e13			−0.913029
$923$	−2.43019e13			−1.10213
$924$	4.64274e11			0.0209532
$925$			1.93573e12i			0.0869374i
$926$			4.60786e13i			2.05944i
$927$	−1.61671e12			−0.0719073
$928$	1.74281e13	+	1.20054e13i	0.771408	+	0.531386i
$929$	−1.09147e12			−0.0480772			−0.0240386	−	0.999711i	$-0.507652\pi$
$929$	−1.09147e12			−0.0480772			−0.0240386	+	0.999711i	$0.507652\pi$
$930$		−	5.56682e12i		−	0.244025i
$931$			1.53804e12i			0.0670956i
$932$	−4.75635e12			−0.206492
$933$	1.20538e13			0.520781
$934$	1.43928e13			0.618848
$935$	1.71191e12			0.0732534
$936$		−	8.44379e12i		−	0.359581i
$937$	−3.10786e13			−1.31714			−0.658572	−	0.752518i	$-0.728839\pi$
$937$	−3.10786e13			−1.31714			−0.658572	+	0.752518i	$0.728839\pi$
$938$			8.63513e12i			0.364214i
$939$		−	1.13725e13i		−	0.477377i
$940$		−	1.77292e13i		−	0.740650i
$941$	−2.70205e13			−1.12341			−0.561707	−	0.827336i	$-0.689855\pi$
$941$	−2.70205e13			−1.12341			−0.561707	+	0.827336i	$0.689855\pi$
$942$			3.28013e12i			0.135726i
$943$		−	6.38644e13i		−	2.63000i
$944$	−2.32409e13			−0.952532
$945$		−	2.37484e13i		−	0.968705i
$946$			2.56702e12i			0.104212i
$947$		−	1.76628e13i		−	0.713650i	−0.934171	−	0.356825i	$-0.883859\pi$
$947$		−	1.76628e13i		−	0.713650i	0.934171	−	0.356825i	$-0.116141\pi$
$948$	−5.56834e12			−0.223918
$949$		−	2.22071e12i		−	0.0888781i
$950$	−3.90254e11			−0.0155450
$951$	1.59465e13			0.632199
$952$	2.19918e13			0.867748
$953$	4.22916e12			0.166087			0.0830437	−	0.996546i	$-0.473536\pi$
$953$	4.22916e12			0.166087			0.0830437	+	0.996546i	$0.473536\pi$
$954$			1.50304e13i			0.587493i
$955$		−	1.92500e13i		−	0.748886i
$956$	−1.52641e11			−0.00591031
$957$	−4.61433e11	+	6.69859e11i	−0.0177830	+	0.0258155i
$958$	−5.72654e13			−2.19658
$959$		−	5.71047e13i		−	2.18016i
$960$			1.06057e12i			0.0403014i
$961$	2.02749e13			0.766839
$962$	−1.59137e13			−0.599079
$963$	1.16797e13			0.437636
$964$	−1.64745e13			−0.614419
$965$			2.94671e12i			0.109387i
$966$	3.24926e13			1.20057
$967$			4.22628e13i			1.55432i	0.629305	+	0.777158i	$0.283340\pi$
$967$			4.22628e13i			1.55432i	−0.629305	+	0.777158i	$0.716660\pi$
$968$		−	1.63110e13i		−	0.597092i
$969$			1.27718e12i			0.0465366i
$970$	2.69349e13			0.976883
$971$		−	1.91175e10i		−	0.000690150i	−1.00000		0.000345075i	$-0.999890\pi$
$971$		−	1.91175e10i		−	0.000690150i	1.00000		0.000345075i	$-0.000109841\pi$
$972$			1.42028e13i			0.510359i
$973$	8.56346e12			0.306296
$974$			1.62110e13i			0.577159i
$975$			1.23047e12i			0.0436065i
$976$			4.60434e13i			1.62421i
$977$	4.89174e13			1.71766			0.858831	−	0.512260i	$-0.171191\pi$
$977$	4.89174e13			1.71766			0.858831	+	0.512260i	$0.171191\pi$
$978$		−	1.80285e13i		−	0.630137i
$979$	2.26585e12			0.0788332
$980$	−9.70081e12			−0.335962
$981$	2.44910e13			0.844299
$982$	4.48366e13			1.53862
$983$			1.90078e13i			0.649294i	0.945835	+	0.324647i	$0.105246\pi$
$983$			1.90078e13i			0.649294i	−0.945835	+	0.324647i	$0.894754\pi$
$984$		−	1.20899e13i		−	0.411098i
$985$	5.48927e12			0.185802
$986$	2.29270e13	−	3.32829e13i	0.772503	−	1.12144i
$987$	2.66902e13			0.895208
$988$		−	1.08633e12i		−	0.0362707i
$989$			6.08311e13i			2.02182i
$990$	−1.97941e12			−0.0654904
$991$	−2.13524e13			−0.703259			−0.351630	−	0.936139i	$-0.614372\pi$
$991$	−2.13524e13			−0.703259			−0.351630	+	0.936139i	$0.614372\pi$
$992$	−1.37956e13			−0.452311
$993$	−1.45144e13			−0.473727
$994$			7.31846e13i			2.37783i
$995$	−2.77880e13			−0.898781
$996$		−	6.55703e12i		−	0.211125i
$997$		−	2.56989e13i		−	0.823733i	−0.911244	−	0.411867i	$-0.864877\pi$
$997$		−	2.56989e13i		−	0.823733i	0.911244	−	0.411867i	$-0.135123\pi$
$998$		−	4.62569e13i		−	1.47601i
$999$	−1.64218e13			−0.521646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.b.a.28.5	✓	22
29.28	even	2	inner	29.10.b.a.28.18	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.b.a.28.5	✓	22	1.1	even	1	trivial
29.10.b.a.28.18	yes	22	29.28	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-27.8229i q^{2} -61.9183i q^{3} -262.115 q^{4} +1301.46 q^{5} -1722.75 q^{6} +8294.02 q^{7} -6952.53i q^{8} +15849.1 q^{9} +O(q^{10})\)	\(q-27.8229i q^{2} -61.9183i q^{3} -262.115 q^{4} +1301.46 q^{5} -1722.75 q^{6} +8294.02 q^{7} -6952.53i q^{8} +15849.1 q^{9} -36210.3i q^{10} -3449.04i q^{11} +16229.7i q^{12} +76628.3 q^{13} -230764. i q^{14} -80583.9i q^{15} -327643. q^{16} +381375. i q^{17} -440969. i q^{18} +54085.5i q^{19} -341131. q^{20} -513552. i q^{21} -95962.4 q^{22} -2.27404e6 q^{23} -430489. q^{24} -259337. q^{25} -2.13202e6i q^{26} -2.20009e6i q^{27} -2.17399e6 q^{28} +(2.16069e6 - 3.13665e6i) q^{29} -2.24208e6 q^{30} +2.48288e6i q^{31} +5.55628e6i q^{32} -213559. q^{33} +1.06110e7 q^{34} +1.07943e7 q^{35} -4.15429e6 q^{36} -7.46415e6i q^{37} +1.50482e6 q^{38} -4.74469e6i q^{39} -9.04841e6i q^{40} +2.80841e7i q^{41} -1.42885e7 q^{42} -2.67503e7i q^{43} +904045. i q^{44} +2.06269e7 q^{45} +6.32704e7i q^{46} +5.19717e7i q^{47} +2.02871e7i q^{48} +2.84372e7 q^{49} +7.21551e6i q^{50} +2.36141e7 q^{51} -2.00854e7 q^{52} -3.40849e7 q^{53} -6.12129e7 q^{54} -4.48878e6i q^{55} -5.76644e7i q^{56} +3.34888e6 q^{57} +(-8.72708e7 - 6.01166e7i) q^{58} +7.09338e7 q^{59} +2.11223e7i q^{60} -1.40529e8i q^{61} +6.90810e7 q^{62} +1.31453e8 q^{63} -1.31611e7 q^{64} +9.97284e7 q^{65} +5.94183e6i q^{66} -3.74198e7 q^{67} -9.99640e7i q^{68} +1.40805e8i q^{69} -3.00329e8i q^{70} -3.17141e8 q^{71} -1.10192e8i q^{72} -2.89803e7i q^{73} -2.07674e8 q^{74} +1.60577e7i q^{75} -1.41766e7i q^{76} -2.86064e7i q^{77} -1.32011e8 q^{78} +3.43095e8i q^{79} -4.26413e8 q^{80} +1.75733e8 q^{81} +7.81383e8 q^{82} -4.04014e8 q^{83} +1.34610e8i q^{84} +4.96343e8i q^{85} -7.44270e8 q^{86} +(-1.94216e8 - 1.33786e8i) q^{87} -2.39796e7 q^{88} +6.56951e8i q^{89} -5.73902e8i q^{90} +6.35557e8 q^{91} +5.96060e8 q^{92} +1.53736e8 q^{93} +1.44601e9 q^{94} +7.03899e7i q^{95} +3.44035e8 q^{96} +7.43846e8i q^{97} -7.91205e8i q^{98} -5.46643e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9}+O(q^{10}) \) 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

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Database

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