LMFDB - Embedded newform 95.11.c.a.56.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,11,Mod(56,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.56"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	95.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$60.3589390040$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			56.4
Character	$\chi$	$=$	95.56
Dual form			95.11.c.a.56.65

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-59.4439i q^{2} +262.238i q^{3} -2509.58 q^{4} +1397.54 q^{5} +15588.5 q^{6} +13097.9 q^{7} +88308.7i q^{8} -9719.86 q^{9} -83075.4i q^{10} -257013. q^{11} -658108. i q^{12} -480775. i q^{13} -778594. i q^{14} +366489. i q^{15} +2.67961e6 q^{16} -2.30537e6 q^{17} +577787. i q^{18} +(2.04841e6 + 1.39107e6i) q^{19} -3.50724e6 q^{20} +3.43478e6i q^{21} +1.52778e7i q^{22} +1.00911e7 q^{23} -2.31579e7 q^{24} +1.95312e6 q^{25} -2.85791e7 q^{26} +1.29360e7i q^{27} -3.28704e7 q^{28} -2.35488e6i q^{29} +2.17855e7 q^{30} -1.61056e7i q^{31} -6.88582e7i q^{32} -6.73985e7i q^{33} +1.37040e8i q^{34} +1.83049e7 q^{35} +2.43928e7 q^{36} +8.27351e7i q^{37} +(8.26908e7 - 1.21766e8i) q^{38} +1.26077e8 q^{39} +1.23415e8i q^{40} +1.48154e8i q^{41} +2.04177e8 q^{42} -9.28064e7 q^{43} +6.44994e8 q^{44} -1.35839e7 q^{45} -5.99856e8i q^{46} +3.43656e8 q^{47} +7.02695e8i q^{48} -1.10919e8 q^{49} -1.16101e8i q^{50} -6.04555e8i q^{51} +1.20654e9i q^{52} +1.66273e8i q^{53} +7.68966e8 q^{54} -3.59186e8 q^{55} +1.15666e9i q^{56} +(-3.64792e8 + 5.37171e8i) q^{57} -1.39983e8 q^{58} -4.49521e8i q^{59} -9.19733e8i q^{60} +9.11025e8 q^{61} -9.57379e8 q^{62} -1.27310e8 q^{63} -1.34928e9 q^{64} -6.71903e8i q^{65} -4.00643e9 q^{66} +1.85954e9i q^{67} +5.78550e9 q^{68} +2.64628e9i q^{69} -1.08812e9i q^{70} -5.24579e8i q^{71} -8.58349e8i q^{72} +2.59195e9 q^{73} +4.91810e9 q^{74} +5.12184e8i q^{75} +(-5.14065e9 - 3.49101e9i) q^{76} -3.36634e9 q^{77} -7.49454e9i q^{78} -4.48832e9i q^{79} +3.74486e9 q^{80} -3.96626e9 q^{81} +8.80686e9 q^{82} +5.02264e9 q^{83} -8.61986e9i q^{84} -3.22185e9 q^{85} +5.51677e9i q^{86} +6.17539e8 q^{87} -2.26964e10i q^{88} -9.39863e8i q^{89} +8.07482e8i q^{90} -6.29716e9i q^{91} -2.53245e10 q^{92} +4.22350e9 q^{93} -2.04283e10i q^{94} +(2.86274e9 + 1.94408e9i) q^{95} +1.80572e10 q^{96} +6.09834e9i q^{97} +6.59346e9i q^{98} +2.49813e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 35644 q^{4} - 2044 q^{6} + 76620 q^{7} - 1353552 q^{9} - 418144 q^{11} + 21763300 q^{16} - 10023236 q^{17} + 518264 q^{19} + 4962204 q^{23} + 2604244 q^{24} + 132812500 q^{25} + 32178588 q^{26} - 109025284 q^{28}+ \cdots + 76070139768 q^{99}+O(q^{100}) $ 68 * q - 35644 * q^4 - 2044 * q^6 + 76620 * q^7 - 1353552 * q^9 - 418144 * q^11 + 21763300 * q^16 - 10023236 * q^17 + 518264 * q^19 + 4962204 * q^23 + 2604244 * q^24 + 132812500 * q^25 + 32178588 * q^26 - 109025284 * q^28 + 39875000 * q^30 + 39875000 * q^35 + 420547696 * q^36 - 504912596 * q^38 + 51693988 * q^39 + 343589380 * q^42 + 72617360 * q^43 - 846875584 * q^44 + 148625000 * q^45 + 426767656 * q^47 + 3802641528 * q^49 + 594603476 * q^54 - 361360620 * q^57 - 1963881788 * q^58 + 7470512872 * q^61 - 2514646024 * q^62 - 6611740944 * q^63 - 13094608884 * q^64 + 9558616040 * q^66 + 17177918780 * q^68 - 2447766556 * q^73 - 1842337832 * q^74 - 5604056776 * q^76 - 320485400 * q^77 - 821875000 * q^80 + 5162401956 * q^81 - 17137563304 * q^82 - 14922506320 * q^83 - 4799500000 * q^85 + 5085654996 * q^87 - 27413957236 * q^92 - 11067885256 * q^93 + 1613500000 * q^95 - 67563054044 * q^96 + 76070139768 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	59.4439i		−	1.85762i	−0.370553	−	0.928811i	$-0.620832\pi$
$2$		−	59.4439i		−	1.85762i	0.370553	−	0.928811i	$-0.379168\pi$
$3$			262.238i			1.07917i	0.841931	+	0.539585i	$0.181419\pi$
$3$			262.238i			1.07917i	−0.841931	+	0.539585i	$0.818581\pi$
$4$	−2509.58			−2.45076
$5$	1397.54			0.447214
$5$	1397.54			0.447214
$6$	15588.5			2.00469
$7$	13097.9			0.779315			0.389658	−	0.920960i	$-0.372593\pi$
$7$	13097.9			0.779315			0.389658	+	0.920960i	$0.372593\pi$
$8$			88308.7i			2.69497i
$9$	−9719.86			−0.164607
$10$		−	83075.4i		−	0.830754i
$11$	−257013.			−1.59585			−0.797923	−	0.602760i	$-0.794068\pi$
$11$	−257013.			−1.59585			−0.797923	+	0.602760i	$0.794068\pi$
$12$		−	658108.i		−	2.64479i
$13$		−	480775.i		−	1.29487i	−0.762123	−	0.647433i	$-0.775843\pi$
$13$		−	480775.i		−	1.29487i	0.762123	−	0.647433i	$-0.224157\pi$
$14$		−	778594.i		−	1.44767i
$15$			366489.i			0.482619i
$16$	2.67961e6			2.55547
$17$	−2.30537e6			−1.62366			−0.811831	−	0.583893i	$-0.801529\pi$
$17$	−2.30537e6			−1.62366			−0.811831	+	0.583893i	$0.801529\pi$
$18$			577787.i			0.305777i
$19$	2.04841e6	+	1.39107e6i	0.827273	+	0.561800i
$19$	2.04841e6	+	1.39107e6i	0.827273	+	0.561800i
$20$	−3.50724e6			−1.09601
$21$			3.43478e6i			0.841013i
$22$			1.52778e7i			2.96448i
$23$	1.00911e7			1.56784			0.783918	−	0.620865i	$-0.213218\pi$
$23$	1.00911e7			1.56784			0.783918	+	0.620865i	$0.213218\pi$
$24$	−2.31579e7			−2.90833
$25$	1.95312e6			0.200000
$26$	−2.85791e7			−2.40537
$27$			1.29360e7i			0.901531i
$28$	−3.28704e7			−1.90992
$29$		−	2.35488e6i		−	0.114810i	−0.998351	−	0.0574049i	$-0.981717\pi$
$29$		−	2.35488e6i		−	0.114810i	0.998351	−	0.0574049i	$-0.0182826\pi$
$30$	2.17855e7			0.896524
$31$		−	1.61056e7i		−	0.562559i	−0.959626	−	0.281280i	$-0.909241\pi$
$31$		−	1.61056e7i		−	0.562559i	0.959626	−	0.281280i	$-0.0907588\pi$
$32$		−	6.88582e7i		−	2.05213i
$33$		−	6.73985e7i		−	1.72219i
$34$			1.37040e8i			3.01615i
$35$	1.83049e7			0.348520
$36$	2.43928e7			0.403412
$37$			8.27351e7i			1.19311i	0.802571	+	0.596556i	$0.203465\pi$
$37$			8.27351e7i			1.19311i	−0.802571	+	0.596556i	$0.796535\pi$
$38$	8.26908e7	−	1.21766e8i	1.04361	−	1.53676i
$39$	1.26077e8			1.39738
$40$			1.23415e8i			1.20523i
$41$			1.48154e8i			1.27877i	0.768885	+	0.639387i	$0.220812\pi$
$41$			1.48154e8i			1.27877i	−0.768885	+	0.639387i	$0.779188\pi$
$42$	2.04177e8			1.56228
$43$	−9.28064e7			−0.631300			−0.315650	−	0.948876i	$-0.602222\pi$
$43$	−9.28064e7			−0.631300			−0.315650	+	0.948876i	$0.602222\pi$
$44$	6.44994e8			3.91104
$45$	−1.35839e7			−0.0736144
$46$		−	5.99856e8i		−	2.91245i
$47$	3.43656e8			1.49842			0.749212	−	0.662330i	$-0.230432\pi$
$47$	3.43656e8			1.49842			0.749212	+	0.662330i	$0.230432\pi$
$48$			7.02695e8i			2.75779i
$49$	−1.10919e8			−0.392668
$50$		−	1.16101e8i		−	0.371525i
$51$		−	6.04555e8i		−	1.75221i
$52$			1.20654e9i			3.17341i
$53$			1.66273e8i			0.397596i	0.980041	+	0.198798i	$0.0637037\pi$
$53$			1.66273e8i			0.397596i	−0.980041	+	0.198798i	$0.936296\pi$
$54$	7.68966e8			1.67470
$55$	−3.59186e8			−0.713684
$56$			1.15666e9i			2.10023i
$57$	−3.64792e8	+	5.37171e8i	−0.606278	+	0.892768i
$58$	−1.39983e8			−0.213273
$59$		−	4.49521e8i		−	0.628768i	−0.949296	−	0.314384i	$-0.898202\pi$
$59$		−	4.49521e8i		−	0.628768i	0.949296	−	0.314384i	$-0.101798\pi$
$60$		−	9.19733e8i		−	1.18278i
$61$	9.11025e8			1.07865			0.539326	−	0.842097i	$-0.318679\pi$
$61$	9.11025e8			1.07865			0.539326	+	0.842097i	$0.318679\pi$
$62$	−9.57379e8			−1.04502
$63$	−1.27310e8			−0.128281
$64$	−1.34928e9			−1.25662
$65$		−	6.71903e8i		−	0.579082i
$66$	−4.00643e9			−3.19918
$67$			1.85954e9i			1.37731i	0.725089	+	0.688656i	$0.241799\pi$
$67$			1.85954e9i			1.37731i	−0.725089	+	0.688656i	$0.758201\pi$
$68$	5.78550e9			3.97921
$69$			2.64628e9i			1.69196i
$70$		−	1.08812e9i		−	0.647419i
$71$		−	5.24579e8i		−	0.290750i	−0.989377	−	0.145375i	$-0.953561\pi$
$71$		−	5.24579e8i		−	0.290750i	0.989377	−	0.145375i	$-0.0464388\pi$
$72$		−	8.58349e8i		−	0.443610i
$73$	2.59195e9			1.25029			0.625146	−	0.780508i	$-0.285039\pi$
$73$	2.59195e9			1.25029			0.625146	+	0.780508i	$0.285039\pi$
$74$	4.91810e9			2.21635
$75$			5.12184e8i			0.215834i
$76$	−5.14065e9	−	3.49101e9i	−2.02745	−	1.37684i
$77$	−3.36634e9			−1.24367
$78$		−	7.49454e9i		−	2.59580i
$79$		−	4.48832e9i		−	1.45864i	−0.684173	−	0.729320i	$-0.739837\pi$
$79$		−	4.48832e9i		−	1.45864i	0.684173	−	0.729320i	$-0.260163\pi$
$80$	3.74486e9			1.14284
$81$	−3.96626e9			−1.13751
$82$	8.80686e9			2.37548
$83$	5.02264e9			1.27509			0.637546	−	0.770413i	$-0.279950\pi$
$83$	5.02264e9			1.27509			0.637546	+	0.770413i	$0.279950\pi$
$84$		−	8.61986e9i		−	2.06112i
$85$	−3.22185e9			−0.726123
$86$			5.51677e9i			1.17272i
$87$	6.17539e8			0.123899
$88$		−	2.26964e10i		−	4.30075i
$89$		−	9.39863e8i		−	0.168312i	−0.996453	−	0.0841559i	$-0.973181\pi$
$89$		−	9.39863e8i		−	0.168312i	0.996453	−	0.0841559i	$-0.0268194\pi$
$90$			8.07482e8i			0.136748i
$91$		−	6.29716e9i		−	1.00911i
$92$	−2.53245e10			−3.84239
$93$	4.22350e9			0.607097
$94$		−	2.04283e10i		−	2.78351i
$95$	2.86274e9	+	1.94408e9i	0.369968	+	0.251245i
$96$	1.80572e10			2.21460
$97$			6.09834e9i			0.710155i	0.934837	+	0.355077i	$0.115545\pi$
$97$			6.09834e9i			0.710155i	−0.934837	+	0.355077i	$0.884455\pi$
$98$			6.59346e9i			0.729429i
$99$	2.49813e9			0.262687
$100$	−4.90152e9			−0.490152
$101$	1.27170e10			1.20998			0.604991	−	0.796232i	$-0.293177\pi$
$101$	1.27170e10			1.20998			0.604991	+	0.796232i	$0.293177\pi$
$102$	−3.59371e10			−3.25494
$103$			1.93526e10i			1.66937i	0.550728	+	0.834685i	$0.314350\pi$
$103$			1.93526e10i			1.66937i	−0.550728	+	0.834685i	$0.685650\pi$
$104$	4.24566e10			3.48962
$105$			4.80025e9i			0.376112i
$106$	9.88390e9			0.738583
$107$			5.13896e9i			0.366401i	0.983076	+	0.183200i	$0.0586457\pi$
$107$			5.13896e9i			0.366401i	−0.983076	+	0.183200i	$0.941354\pi$
$108$		−	3.24639e10i		−	2.20944i
$109$			2.51223e10i			1.63278i	0.577502	+	0.816389i	$0.304028\pi$
$109$			2.51223e10i			1.63278i	−0.577502	+	0.816389i	$0.695972\pi$
$110$			2.13514e10i			1.32576i
$111$	−2.16963e10			−1.28757
$112$	3.50973e10			1.99152
$113$			7.95635e9i			0.431839i	0.976411	+	0.215919i	$0.0692749\pi$
$113$			7.95635e9i			0.431839i	−0.976411	+	0.215919i	$0.930725\pi$
$114$	3.19316e10	+	2.16847e10i	1.65843	+	1.12624i
$115$	1.41028e10			0.701157
$116$			5.90976e9i			0.281371i
$117$			4.67306e9i			0.213144i
$118$	−2.67213e10			−1.16801
$119$	−3.01956e10			−1.26534
$120$	−3.23642e10			−1.30064
$121$	4.01180e10			1.54672
$122$		−	5.41549e10i		−	2.00373i
$123$	−3.88516e10			−1.38001
$124$			4.04183e10i			1.37870i
$125$	2.72958e9			0.0894427
$126$			7.56782e9i			0.238297i
$127$			1.07829e10i			0.326375i	0.986595	+	0.163188i	$0.0521776\pi$
$127$			1.07829e10i			0.326375i	−0.986595	+	0.163188i	$0.947822\pi$
$128$			9.69595e9i			0.282189i
$129$		−	2.43374e10i		−	0.681279i
$130$	−3.99405e10			−1.07571
$131$	−4.37851e9			−0.113493			−0.0567466	−	0.998389i	$-0.518073\pi$
$131$	−4.37851e9			−0.113493			−0.0567466	+	0.998389i	$0.518073\pi$
$132$			1.69142e11i			4.22067i
$133$	2.68300e10	+	1.82202e10i	0.644706	+	0.437819i
$134$	1.10539e11			2.55852
$135$			1.80786e10i			0.403177i
$136$		−	2.03584e11i		−	4.37572i
$137$	1.50354e10			0.311539			0.155769	−	0.987793i	$-0.450214\pi$
$137$	1.50354e10			0.311539			0.155769	+	0.987793i	$0.450214\pi$
$138$	1.57305e11			3.14302
$139$	4.27580e10			0.824030			0.412015	−	0.911177i	$-0.364825\pi$
$139$	4.27580e10			0.824030			0.412015	+	0.911177i	$0.364825\pi$
$140$	−4.59377e10			−0.854140
$141$			9.01198e10i			1.61705i
$142$	−3.11831e10			−0.540103
$143$			1.23565e11i			2.06641i
$144$	−2.60454e10			−0.420648
$145$		−	3.29104e9i		−	0.0513445i
$146$		−	1.54075e11i		−	2.32257i
$147$		−	2.90872e10i		−	0.423755i
$148$		−	2.07630e11i		−	2.92403i
$149$	5.62686e10			0.766187			0.383094	−	0.923710i	$-0.374859\pi$
$149$	5.62686e10			0.766187			0.383094	+	0.923710i	$0.374859\pi$
$150$	3.04462e10			0.400938
$151$			3.77210e10i			0.480505i	0.970710	+	0.240253i	$0.0772303\pi$
$151$			3.77210e10i			0.480505i	−0.970710	+	0.240253i	$0.922770\pi$
$152$	−1.22844e11	+	1.80892e11i	−1.51403	+	2.22947i
$153$	2.24079e10			0.267266
$154$			2.00108e11i			2.31026i
$155$		−	2.25082e10i		−	0.251584i
$156$	−3.16401e11			−3.42464
$157$	4.56175e10			0.478226			0.239113	−	0.970992i	$-0.423143\pi$
$157$	4.56175e10			0.478226			0.239113	+	0.970992i	$0.423143\pi$
$158$	−2.66803e11			−2.70960
$159$	−4.36031e10			−0.429073
$160$		−	9.62322e10i		−	0.917742i
$161$	1.32173e11			1.22184
$162$			2.35770e11i			2.11307i
$163$	6.24608e10			0.542837			0.271419	−	0.962461i	$-0.412507\pi$
$163$	6.24608e10			0.542837			0.271419	+	0.962461i	$0.412507\pi$
$164$		−	3.71804e11i		−	3.13397i
$165$		−	9.41923e10i		−	0.770186i
$166$		−	2.98565e11i		−	2.36864i
$167$		−	1.96268e11i		−	1.51101i	−0.655141	−	0.755506i	$-0.727391\pi$
$167$		−	1.96268e11i		−	1.51101i	0.655141	−	0.755506i	$-0.272609\pi$
$168$	−3.03321e11			−2.26650
$169$	−9.32857e10			−0.676677
$170$			1.91519e11i			1.34886i
$171$	−1.99103e10	−	1.35210e10i	−0.136175	−	0.0924761i
$172$	2.32905e11			1.54716
$173$		−	2.38984e11i		−	1.54219i	−0.636719	−	0.771096i	$-0.719709\pi$
$173$		−	2.38984e11i		−	1.54219i	0.636719	−	0.771096i	$-0.280291\pi$
$174$		−	3.67090e10i		−	0.230158i
$175$	2.55819e10			0.155863
$176$	−6.88692e11			−4.07814
$177$	1.17882e11			0.678547
$178$	−5.58692e10			−0.312660
$179$			3.61356e11i			1.96639i	0.182553	+	0.983196i	$0.441564\pi$
$179$			3.61356e11i			1.96639i	−0.182553	+	0.983196i	$0.558436\pi$
$180$	3.40899e10			0.180411
$181$			2.17295e11i			1.11856i	0.828980	+	0.559278i	$0.188922\pi$
$181$			2.17295e11i			1.11856i	−0.828980	+	0.559278i	$0.811078\pi$
$182$	−3.74328e11			−1.87454
$183$			2.38905e11i			1.16405i
$184$			8.91134e11i			4.22527i
$185$			1.15626e11i			0.533576i
$186$		−	2.51061e11i		−	1.12776i
$187$	5.92508e11			2.59111
$188$	−8.62433e11			−3.67228
$189$			1.69435e11i			0.702577i
$190$	1.15564e11	−	1.70172e11i	0.466718	−	0.687260i
$191$	−2.02384e11			−0.796175			−0.398087	−	0.917348i	$-0.630326\pi$
$191$	−2.02384e11			−0.796175			−0.398087	+	0.917348i	$0.630326\pi$
$192$		−	3.53834e11i		−	1.35610i
$193$		−	4.66910e10i		−	0.174360i	−0.996193	−	0.0871800i	$-0.972214\pi$
$193$		−	4.66910e10i		−	0.174360i	0.996193	−	0.0871800i	$-0.0277855\pi$
$194$	3.62509e11			1.31920
$195$	1.76199e11			0.624927
$196$	2.78360e11			0.962335
$197$	−2.25267e11			−0.759219			−0.379609	−	0.925147i	$-0.623942\pi$
$197$	−2.25267e11			−0.759219			−0.379609	+	0.925147i	$0.623942\pi$
$198$		−	1.48498e11i		−	0.487973i
$199$	3.69923e11			1.18535			0.592674	−	0.805442i	$-0.298072\pi$
$199$	3.69923e11			1.18535			0.592674	+	0.805442i	$0.298072\pi$
$200$			1.72478e11i			0.538994i
$201$	−4.87643e11			−1.48635
$202$		−	7.55951e11i		−	2.24769i
$203$		−	3.08441e10i		−	0.0894729i
$204$			1.51718e12i			4.29424i
$205$			2.07052e11i			0.571886i
$206$	1.15039e12			3.10106
$207$	−9.80844e10			−0.258076
$208$		−	1.28829e12i		−	3.30899i
$209$	−5.26467e11	−	3.57523e11i	−1.32020	−	0.896546i
$210$	2.85346e11			0.698675
$211$		−	1.60082e11i		−	0.382764i	−0.981516	−	0.191382i	$-0.938703\pi$
$211$		−	1.60082e11i		−	0.382764i	0.981516	−	0.191382i	$-0.0612970\pi$
$212$		−	4.17275e11i		−	0.974412i
$213$	1.37565e11			0.313768
$214$	3.05480e11			0.680635
$215$	−1.29701e11			−0.282326
$216$	−1.14236e12			−2.42960
$217$		−	2.10950e11i		−	0.438411i
$218$	1.49337e12			3.03309
$219$			6.79707e11i			1.34928i
$220$	9.01406e11			1.74907
$221$			1.10836e12i			2.10242i
$222$			1.28971e12i			2.39182i
$223$		−	1.51101e11i		−	0.273995i	−0.990571	−	0.136997i	$-0.956255\pi$
$223$		−	1.51101e11i		−	0.273995i	0.990571	−	0.136997i	$-0.0437452\pi$
$224$		−	9.01901e11i		−	1.59926i
$225$	−1.89841e10			−0.0329213
$226$	4.72957e11			0.802194
$227$			3.98163e11i			0.660589i	0.943878	+	0.330294i	$0.107148\pi$
$227$			3.98163e11i			0.660589i	−0.943878	+	0.330294i	$0.892852\pi$
$228$	9.15476e11	−	1.34807e12i	1.48584	−	2.18796i
$229$	3.85348e10			0.0611894			0.0305947	−	0.999532i	$-0.490260\pi$
$229$	3.85348e10			0.0611894			0.0305947	+	0.999532i	$0.490260\pi$
$230$		−	8.38325e11i		−	1.30249i
$231$		−	8.82782e11i		−	1.34213i
$232$	2.07956e11			0.309408
$233$	−9.22953e11			−1.34400			−0.672001	−	0.740550i	$-0.734565\pi$
$233$	−9.22953e11			−1.34400			−0.672001	+	0.740550i	$0.734565\pi$
$234$	2.77785e11			0.395940
$235$	4.80274e11			0.670116
$236$			1.12811e12i			1.54096i
$237$	1.17701e12			1.57412
$238$			1.79494e12i			2.35053i
$239$	−1.15557e12			−1.48186			−0.740930	−	0.671582i	$-0.765615\pi$
$239$	−1.15557e12			−1.48186			−0.740930	+	0.671582i	$0.765615\pi$
$240$			9.82046e11i			1.23332i
$241$			5.05527e10i			0.0621812i	0.999517	+	0.0310906i	$0.00989804\pi$
$241$			5.05527e10i			0.0621812i	−0.999517	+	0.0310906i	$0.990102\pi$
$242$		−	2.38477e12i		−	2.87323i
$243$		−	2.76247e11i		−	0.326037i
$244$	−2.28629e12			−2.64352
$245$	−1.55014e11			−0.175606
$246$			2.30949e12i			2.56355i
$247$	6.68792e11	−	9.84823e11i	0.727456	−	1.07121i
$248$	1.42226e12			1.51608
$249$			1.31713e12i			1.37604i
$250$		−	1.62257e11i		−	0.166151i
$251$	−8.20305e11			−0.823392			−0.411696	−	0.911321i	$-0.635063\pi$
$251$	−8.20305e11			−0.823392			−0.411696	+	0.911321i	$0.635063\pi$
$252$	3.19495e11			0.314385
$253$	−2.59355e12			−2.50202
$254$	6.40978e11			0.606282
$255$		−	8.44892e11i		−	0.783610i
$256$	−8.05302e11			−0.732417
$257$			4.40672e11i			0.393052i	0.980499	+	0.196526i	$0.0629660\pi$
$257$			4.40672e11i			0.393052i	−0.980499	+	0.196526i	$0.937034\pi$
$258$	−1.44671e12			−1.26556
$259$			1.08366e12i			0.929810i
$260$			1.68619e12i			1.41919i
$261$			2.28891e10i			0.0188985i
$262$			2.60276e11i			0.210828i
$263$	−1.04393e12			−0.829649			−0.414824	−	0.909902i	$-0.636157\pi$
$263$	−1.04393e12			−0.829649			−0.414824	+	0.909902i	$0.636157\pi$
$264$	5.95187e12			4.64124
$265$			2.32373e11i			0.177810i
$266$	1.08308e12	−	1.59488e12i	0.813303	−	1.19762i
$267$	2.46468e11			0.181637
$268$		−	4.66667e12i		−	3.37546i
$269$			1.40263e12i			0.995824i	0.867228	+	0.497912i	$0.165900\pi$
$269$			1.40263e12i			0.995824i	−0.867228	+	0.497912i	$0.834100\pi$
$270$	1.07466e12			0.748950
$271$	3.66620e11			0.250824			0.125412	−	0.992105i	$-0.459975\pi$
$271$	3.66620e11			0.250824			0.125412	+	0.992105i	$0.459975\pi$
$272$	−6.17748e12			−4.14922
$273$	1.65136e12			1.08900
$274$		−	8.93763e11i		−	0.578721i
$275$	−5.01978e11			−0.319169
$276$		−	6.64105e12i		−	4.14659i
$277$	−1.33269e11			−0.0817206			−0.0408603	−	0.999165i	$-0.513010\pi$
$277$	−1.33269e11			−0.0817206			−0.0408603	+	0.999165i	$0.513010\pi$
$278$		−	2.54170e12i		−	1.53074i
$279$			1.56544e11i			0.0926010i
$280$			1.61649e12i			0.939251i
$281$		−	9.05856e11i		−	0.517044i	−0.966005	−	0.258522i	$-0.916764\pi$
$281$		−	9.05856e11i		−	0.517044i	0.966005	−	0.258522i	$-0.0832355\pi$
$282$	5.35707e12			3.00388
$283$	−2.13661e11			−0.117705			−0.0588524	−	0.998267i	$-0.518744\pi$
$283$	−2.13661e11			−0.117705			−0.0588524	+	0.998267i	$0.518744\pi$
$284$			1.31647e12i			0.712559i
$285$	−5.09813e11	+	7.50720e11i	−0.271136	+	0.399258i
$286$	7.34519e12			3.83860
$287$			1.94051e12i			0.996569i
$288$			6.69292e11i			0.337795i
$289$	3.29872e12			1.63628
$290$	−1.95633e11			−0.0953786
$291$	−1.59922e12			−0.766377
$292$	−6.50470e12			−3.06417
$293$		−	1.55492e12i		−	0.720061i	−0.932941	−	0.360030i	$-0.882766\pi$
$293$		−	1.55492e12i		−	0.720061i	0.932941	−	0.360030i	$-0.117234\pi$
$294$	−1.72906e12			−0.787177
$295$		−	6.28225e11i		−	0.281193i
$296$	−7.30623e12			−3.21540
$297$		−	3.32471e12i		−	1.43870i
$298$		−	3.34483e12i		−	1.42329i
$299$		−	4.85156e12i		−	2.03014i
$300$		−	1.28537e12i		−	0.528957i
$301$	−1.21557e12			−0.491981
$302$	2.24228e12			0.892597
$303$			3.33489e12i			1.30578i
$304$	5.48893e12	+	3.72753e12i	2.11407	+	1.43566i
$305$	1.27320e12			0.482387
$306$		−	1.33201e12i		−	0.496479i
$307$		−	1.35354e12i		−	0.496341i	−0.968716	−	0.248171i	$-0.920171\pi$
$307$		−	1.35354e12i		−	0.496341i	0.968716	−	0.248171i	$-0.0798294\pi$
$308$	8.44809e12			3.04793
$309$	−5.07498e12			−1.80153
$310$	−1.33798e12			−0.467348
$311$	2.07598e12			0.713543			0.356772	−	0.934192i	$-0.383877\pi$
$311$	2.07598e12			0.713543			0.356772	+	0.934192i	$0.383877\pi$
$312$			1.11337e13i			3.76589i
$313$	1.92478e12			0.640706			0.320353	−	0.947298i	$-0.396198\pi$
$313$	1.92478e12			0.640706			0.320353	+	0.947298i	$0.396198\pi$
$314$		−	2.71168e12i		−	0.888363i
$315$	−1.77922e11			−0.0573688
$316$			1.12638e13i			3.57478i
$317$		−	4.86195e11i		−	0.151885i	−0.997112	−	0.0759424i	$-0.975803\pi$
$317$		−	4.86195e11i		−	0.151885i	0.997112	−	0.0759424i	$-0.0241965\pi$
$318$			2.59194e12i			0.797056i
$319$			6.05233e11i			0.183219i
$320$	−1.88568e12			−0.561977
$321$	−1.34763e12			−0.395409
$322$		−	7.85689e12i		−	2.26971i
$323$	−4.72234e12	−	3.20693e12i	−1.34321	−	0.912173i
$324$	9.95364e12			2.78777
$325$		−	9.39013e11i		−	0.258973i
$326$		−	3.71292e12i		−	1.00839i
$327$	−6.58803e12			−1.76204
$328$	−1.30833e13			−3.44626
$329$	4.50119e12			1.16774
$330$	−5.59916e12			−1.43071
$331$		−	4.54318e12i		−	1.14346i	−0.820443	−	0.571728i	$-0.806273\pi$
$331$		−	4.54318e12i		−	1.14346i	0.820443	−	0.571728i	$-0.193727\pi$
$332$	−1.26047e13			−3.12495
$333$		−	8.04174e11i		−	0.196394i
$334$	−1.16670e13			−2.80689
$335$			2.59879e12i			0.615952i
$336$			9.20386e12i			2.14918i
$337$			4.54534e12i			1.04572i	0.852417	+	0.522862i	$0.175136\pi$
$337$			4.54534e12i			1.04572i	−0.852417	+	0.522862i	$0.824864\pi$
$338$			5.54527e12i			1.25701i
$339$	−2.08646e12			−0.466027
$340$	8.08549e12			1.77956
$341$			4.13934e12i			0.897757i
$342$	−8.03744e11	+	1.18354e12i	−0.171786	+	0.252961i
$343$	−5.15266e12			−1.08533
$344$		−	8.19561e12i		−	1.70133i
$345$			3.69829e12i			0.756668i
$346$	−1.42062e13			−2.86481
$347$	−1.47844e11			−0.0293871			−0.0146936	−	0.999892i	$-0.504677\pi$
$347$	−1.47844e11			−0.0293871			−0.0146936	+	0.999892i	$0.504677\pi$
$348$	−1.54976e12			−0.303647
$349$	6.03142e11			0.116491			0.0582455	−	0.998302i	$-0.481449\pi$
$349$	6.03142e11			0.116491			0.0582455	+	0.998302i	$0.481449\pi$
$350$		−	1.52069e12i		−	0.289535i
$351$	6.21929e12			1.16736
$352$			1.76974e13i			3.27489i
$353$	5.87718e12			1.07225			0.536125	−	0.844139i	$-0.319888\pi$
$353$	5.87718e12			1.07225			0.536125	+	0.844139i	$0.319888\pi$
$354$		−	7.00735e12i		−	1.26048i
$355$		−	7.33122e11i		−	0.130027i
$356$			2.35866e12i			0.412492i
$357$		−	7.91843e12i		−	1.36552i
$358$	2.14804e13			3.65281
$359$	−5.09133e12			−0.853806			−0.426903	−	0.904297i	$-0.640395\pi$
$359$	−5.09133e12			−0.853806			−0.426903	+	0.904297i	$0.640395\pi$
$360$		−	1.19958e12i		−	0.198388i
$361$	2.26090e12	+	5.69897e12i	0.368761	+	0.929524i
$362$	1.29169e13			2.07786
$363$			1.05205e13i			1.66918i
$364$			1.58032e13i			2.47308i
$365$	3.62235e12			0.559148
$366$	1.42015e13			2.16236
$367$	−9.15489e12			−1.37506			−0.687532	−	0.726154i	$-0.741306\pi$
$367$	−9.15489e12			−1.37506			−0.687532	+	0.726154i	$0.741306\pi$
$368$	2.70402e13			4.00656
$369$		−	1.44004e12i		−	0.210495i
$370$	6.87325e12			0.991183
$371$			2.17783e12i			0.309852i
$372$	−1.05992e13			−1.48785
$373$		−	5.60825e12i		−	0.776753i	−0.921501	−	0.388377i	$-0.873036\pi$
$373$		−	5.60825e12i		−	0.776753i	0.921501	−	0.388377i	$-0.126964\pi$
$374$		−	3.52210e13i		−	4.81331i
$375$			7.15799e11i			0.0965239i
$376$			3.03478e13i			4.03821i
$377$	−1.13217e12			−0.148663
$378$	1.00719e13			1.30512
$379$			1.48606e12i			0.190038i	0.995475	+	0.0950189i	$0.0302911\pi$
$379$			1.48606e12i			0.190038i	−0.995475	+	0.0950189i	$0.969709\pi$
$380$	−7.18427e12	−	4.87883e12i	−0.906703	−	0.615741i
$381$	−2.82769e12			−0.352214
$382$			1.20305e13i			1.47899i
$383$			8.88899e12i			1.07859i	0.842115	+	0.539297i	$0.181310\pi$
$383$			8.88899e12i			1.07859i	−0.842115	+	0.539297i	$0.818690\pi$
$384$	−2.54265e12			−0.304530
$385$	−4.70460e12			−0.556185
$386$	−2.77550e12			−0.323895
$387$	9.02065e11			0.103916
$388$		−	1.53043e13i		−	1.74042i
$389$	−7.90273e12			−0.887215			−0.443608	−	0.896221i	$-0.646302\pi$
$389$	−7.90273e12			−0.887215			−0.443608	+	0.896221i	$0.646302\pi$
$390$		−	1.04739e13i		−	1.16088i
$391$	−2.32638e13			−2.54563
$392$		−	9.79511e12i		−	1.05823i
$393$		−	1.14821e12i		−	0.122478i
$394$			1.33908e13i			1.41034i
$395$		−	6.27261e12i		−	0.652324i
$396$	−6.26925e12			−0.643783
$397$	1.18480e13			1.20142			0.600708	−	0.799469i	$-0.294886\pi$
$397$	1.18480e13			1.20142			0.600708	+	0.799469i	$0.294886\pi$
$398$		−	2.19897e13i		−	2.20193i
$399$	−4.77803e12	+	7.03584e12i	−0.472481	+	0.695747i
$400$	5.23361e12			0.511094
$401$		−	1.25986e13i		−	1.21507i	−0.794292	−	0.607536i	$-0.792158\pi$
$401$		−	1.25986e13i		−	1.21507i	0.794292	−	0.607536i	$-0.207842\pi$
$402$			2.89874e13i			2.76108i
$403$	−7.74316e12			−0.728438
$404$	−3.19144e13			−2.96538
$405$	−5.54301e12			−0.508711
$406$	−1.83349e12			−0.166207
$407$		−	2.12640e13i		−	1.90402i
$408$	5.33875e13			4.72214
$409$			6.20508e12i			0.542165i	0.962556	+	0.271082i	$0.0873816\pi$
$409$			6.20508e12i			0.542165i	−0.962556	+	0.271082i	$0.912618\pi$
$410$	1.23080e13			1.06235
$411$			3.94286e12i			0.336203i
$412$		−	4.85668e13i		−	4.09123i
$413$		−	5.88781e12i		−	0.490008i
$414$			5.83052e12i			0.479408i
$415$	7.01935e12			0.570238
$416$	−3.31053e13			−2.65724
$417$			1.12128e13i			0.889268i
$418$	−2.12526e13	+	3.12953e13i	−1.66544	+	2.45243i
$419$	7.02354e12			0.543859			0.271929	−	0.962317i	$-0.412338\pi$
$419$	7.02354e12			0.543859			0.271929	+	0.962317i	$0.412338\pi$
$420$		−	1.20466e13i		−	0.921762i
$421$			1.70425e13i			1.28861i	0.764767	+	0.644306i	$0.222854\pi$
$421$			1.70425e13i			1.28861i	−0.764767	+	0.644306i	$0.777146\pi$
$422$	−9.51592e12			−0.711031
$423$	−3.34029e12			−0.246651
$424$	−1.46833e13			−1.07151
$425$	−4.50267e12			−0.324732
$426$		−	8.17739e12i		−	0.582863i
$427$	1.19326e13			0.840609
$428$		−	1.28966e13i		−	0.897961i
$429$	−3.24035e13			−2.23000
$430$			7.70993e12i			0.524455i
$431$			5.47542e12i			0.368155i	0.982912	+	0.184078i	$0.0589298\pi$
$431$			5.47542e12i			0.368155i	−0.982912	+	0.184078i	$0.941070\pi$
$432$			3.46633e13i			2.30384i
$433$			9.97961e11i			0.0655653i	0.999463	+	0.0327827i	$0.0104369\pi$
$433$			9.97961e11i			0.0655653i	−0.999463	+	0.0327827i	$0.989563\pi$
$434$	−1.25397e13			−0.814402
$435$	8.63037e11			0.0554094
$436$		−	6.30465e13i		−	4.00155i
$437$	2.06708e13	+	1.40375e13i	1.29703	+	0.880810i
$438$	4.04045e13			2.50645
$439$			7.73022e12i			0.474099i	0.971498	+	0.237050i	$0.0761804\pi$
$439$			7.73022e12i			0.474099i	−0.971498	+	0.237050i	$0.923820\pi$
$440$		−	3.17192e13i		−	1.92336i
$441$	1.07812e12			0.0646358
$442$	6.58854e13			3.90551
$443$	−3.31553e13			−1.94327			−0.971637	−	0.236479i	$-0.924007\pi$
$443$	−3.31553e13			−1.94327			−0.971637	+	0.236479i	$0.924007\pi$
$444$	5.44486e13			3.15553
$445$		−	1.31350e12i		−	0.0752714i
$446$	−8.98202e12			−0.508979
$447$			1.47558e13i			0.826846i
$448$	−1.76729e13			−0.979302
$449$		−	2.13987e12i		−	0.117262i	−0.998280	−	0.0586309i	$-0.981326\pi$
$449$		−	2.13987e12i		−	0.117262i	0.998280	−	0.0586309i	$-0.0186735\pi$
$450$			1.12849e12i			0.0611554i
$451$		−	3.80774e13i		−	2.04073i
$452$		−	1.99671e13i		−	1.05833i
$453$	−9.89188e12			−0.518547
$454$	2.36684e13			1.22712
$455$		−	8.80055e12i		−	0.451287i
$456$	−4.74369e13	−	3.22143e13i	−2.40598	−	1.63390i
$457$	−4.90726e12			−0.246183			−0.123091	−	0.992395i	$-0.539281\pi$
$457$	−4.90726e12			−0.246183			−0.123091	+	0.992395i	$0.539281\pi$
$458$		−	2.29066e12i		−	0.113667i
$459$		−	2.98222e13i		−	1.46378i
$460$	−3.53921e13			−1.71837
$461$	−1.08774e13			−0.522422			−0.261211	−	0.965282i	$-0.584122\pi$
$461$	−1.08774e13			−0.522422			−0.261211	+	0.965282i	$0.584122\pi$
$462$	−5.24760e13			−2.49317
$463$	2.42119e13			1.13795			0.568976	−	0.822354i	$-0.307340\pi$
$463$	2.42119e13			1.13795			0.568976	+	0.822354i	$0.307340\pi$
$464$		−	6.31015e12i		−	0.293393i
$465$	5.90252e12			0.271502
$466$			5.48640e13i			2.49665i
$467$	1.68030e13			0.756486			0.378243	−	0.925706i	$-0.376528\pi$
$467$	1.68030e13			0.756486			0.378243	+	0.925706i	$0.376528\pi$
$468$		−	1.17274e13i		−	0.522364i
$469$			2.43562e13i			1.07336i
$470$		−	2.85494e13i		−	1.24482i
$471$			1.19626e13i			0.516086i
$472$	3.96966e13			1.69451
$473$	2.38524e13			1.00746
$474$		−	6.99660e13i		−	2.92412i
$475$	4.00080e12	+	2.71694e12i	0.165455	+	0.112360i
$476$	7.57782e13			3.10106
$477$		−	1.61615e12i		−	0.0654469i
$478$			6.86917e13i			2.75274i
$479$	−9.53778e12			−0.378242			−0.189121	−	0.981954i	$-0.560564\pi$
$479$	−9.53778e12			−0.378242			−0.189121	+	0.981954i	$0.560564\pi$
$480$	2.52358e13			0.990399
$481$	3.97769e13			1.54492
$482$	3.00505e12			0.115509
$483$			3.46608e13i			1.31857i
$484$	−1.00679e14			−3.79065
$485$			8.52269e12i			0.317591i
$486$	−1.64212e13			−0.605653
$487$		−	4.57912e13i		−	1.67162i	−0.549021	−	0.835809i	$-0.684999\pi$
$487$		−	4.57912e13i		−	1.67162i	0.549021	−	0.835809i	$-0.315001\pi$
$488$			8.04514e13i			2.90693i
$489$			1.63796e13i			0.585813i
$490$			9.21464e12i			0.326210i
$491$	1.58975e13			0.557084			0.278542	−	0.960424i	$-0.410149\pi$
$491$	1.58975e13			0.557084			0.278542	+	0.960424i	$0.410149\pi$
$492$	9.75013e13			3.38209
$493$			5.42886e12i			0.186412i
$494$	−5.85418e13	−	3.97556e13i	−1.98990	−	1.35134i
$495$	3.49124e12			0.117477
$496$		−	4.31566e13i		−	1.43760i
$497$		−	6.87091e12i		−	0.226586i
$498$	7.82952e13			2.55616
$499$	1.95575e13			0.632135			0.316067	−	0.948737i	$-0.397637\pi$
$499$	1.95575e13			0.632135			0.316067	+	0.948737i	$0.397637\pi$
$500$	−6.85009e12			−0.219203
$501$	5.14691e13			1.63064
$502$			4.87621e13i			1.52955i
$503$	−5.92819e13			−1.84112			−0.920561	−	0.390600i	$-0.872268\pi$
$503$	−5.92819e13			−1.84112			−0.920561	+	0.390600i	$0.872268\pi$
$504$		−	1.12426e13i		−	0.345712i
$505$	1.77726e13			0.541121
$506$			1.54171e14i			4.64782i
$507$		−	2.44631e13i		−	0.730249i
$508$		−	2.70605e13i		−	0.799867i
$509$		−	3.30097e12i		−	0.0966169i	−0.998832	−	0.0483084i	$-0.984617\pi$
$509$		−	3.30097e12i		−	0.0966169i	0.998832	−	0.0483084i	$-0.0153830\pi$
$510$	−5.02237e13			−1.45565
$511$	3.39492e13			0.974372
$512$			5.77989e13i			1.64274i
$513$	−1.79949e13	+	2.64982e13i	−0.506480	+	0.745812i
$514$	2.61953e13			0.730143
$515$			2.70460e13i			0.746565i
$516$			6.10766e13i			1.66965i
$517$	−8.83239e13			−2.39125
$518$	6.44170e13			1.72724
$519$	6.26708e13			1.66429
$520$	5.93349e13			1.56061
$521$			3.21190e13i			0.836708i	0.908284	+	0.418354i	$0.137393\pi$
$521$			3.21190e13i			0.836708i	−0.908284	+	0.418354i	$0.862607\pi$
$522$	1.36062e12			0.0351062
$523$		−	6.91588e13i		−	1.76742i	−0.468039	−	0.883708i	$-0.655039\pi$
$523$		−	6.91588e13i		−	1.76742i	0.468039	−	0.883708i	$-0.344961\pi$
$524$	1.09882e13			0.278145
$525$			6.70856e12i			0.168203i
$526$			6.20555e13i			1.54117i
$527$			3.71293e13i			0.913405i
$528$		−	1.80601e14i		−	4.40100i
$529$	6.04044e13			1.45811
$530$	1.38132e13			0.330304
$531$			4.36929e12i			0.103499i
$532$	−6.73320e13	−	4.57251e13i	−1.58002	−	1.07299i
$533$	7.12287e13			1.65584
$534$		−	1.46510e13i		−	0.337413i
$535$			7.18192e12i			0.163859i
$536$	−1.64214e14			−3.71181
$537$	−9.47613e13			−2.12207
$538$	8.33780e13			1.84987
$539$	2.85076e13			0.626637
$540$		−	4.53697e13i		−	0.988090i
$541$	−7.45917e12			−0.160955			−0.0804775	−	0.996756i	$-0.525645\pi$
$541$	−7.45917e12			−0.160955			−0.0804775	+	0.996756i	$0.525645\pi$
$542$		−	2.17933e13i		−	0.465937i
$543$	−5.69832e13			−1.20711
$544$			1.58743e14i			3.33197i
$545$			3.51095e13i			0.730201i
$546$		−	9.81631e13i		−	2.02295i
$547$			4.99021e13i			1.01902i	0.860465	+	0.509510i	$0.170173\pi$
$547$			4.99021e13i			1.01902i	−0.860465	+	0.509510i	$0.829827\pi$
$548$	−3.77325e13			−0.763507
$549$	−8.85504e12			−0.177553
$550$			2.98395e13i			0.592896i
$551$	3.27581e12	−	4.82376e12i	0.0645001	−	0.0949790i
$552$	−2.33689e14			−4.55978
$553$		−	5.87878e13i		−	1.13674i
$554$			7.92205e12i			0.151806i
$555$	−3.03215e13			−0.575819
$556$	−1.07305e14			−2.01950
$557$	−7.42251e13			−1.38444			−0.692221	−	0.721686i	$-0.743368\pi$
$557$	−7.42251e13			−1.38444			−0.692221	+	0.721686i	$0.743368\pi$
$558$	9.30560e12			0.172018
$559$			4.46189e13i			0.817448i
$560$	4.90500e13			0.890634
$561$			1.55378e14i			2.79625i
$562$	−5.38477e13			−0.960473
$563$		−	1.01205e13i		−	0.178921i	−0.995990	−	0.0894607i	$-0.971486\pi$
$563$		−	1.01205e13i		−	0.178921i	0.995990	−	0.0894607i	$-0.0285143\pi$
$564$		−	2.26163e14i		−	3.96301i
$565$			1.11193e13i			0.193124i
$566$			1.27009e13i			0.218651i
$567$	−5.19498e13			−0.886480
$568$	4.63249e13			0.783561
$569$			5.53259e13i			0.927614i	0.885936	+	0.463807i	$0.153517\pi$
$569$			5.53259e13i			0.927614i	−0.885936	+	0.463807i	$0.846483\pi$
$570$	4.46257e13	+	3.03053e13i	0.741670	+	0.503668i
$571$	−6.92313e13			−1.14057			−0.570285	−	0.821447i	$-0.693167\pi$
$571$	−6.92313e13			−1.14057			−0.570285	+	0.821447i	$0.693167\pi$
$572$		−	3.10096e14i		−	5.06427i
$573$		−	5.30727e13i		−	0.859207i
$574$	1.15352e14			1.85125
$575$	1.97092e13			0.313567
$576$	1.31149e13			0.206848
$577$	−6.76743e12			−0.105814			−0.0529072	−	0.998599i	$-0.516849\pi$
$577$	−6.76743e12			−0.105814			−0.0529072	+	0.998599i	$0.516849\pi$
$578$		−	1.96089e14i		−	3.03958i
$579$	1.22442e13			0.188164
$580$			8.25914e12i			0.125833i
$581$	6.57862e13			0.993698
$582$			9.50638e13i			1.42364i
$583$		−	4.27342e13i		−	0.634501i
$584$			2.28891e14i			3.36950i
$585$			6.53080e12i			0.0953207i
$586$	−9.24304e13			−1.33760
$587$	6.76963e13			0.971347			0.485673	−	0.874140i	$-0.338574\pi$
$587$	6.76963e13			0.971347			0.485673	+	0.874140i	$0.338574\pi$
$588$			7.29966e13i			1.03852i
$589$	2.24040e13	−	3.29908e13i	0.316046	−	0.465390i
$590$	−3.73442e13			−0.522351
$591$		−	5.90737e13i		−	0.819326i
$592$			2.21697e14i			3.04896i
$593$	−2.76940e12			−0.0377670			−0.0188835	−	0.999822i	$-0.506011\pi$
$593$	−2.76940e12			−0.0377670			−0.0188835	+	0.999822i	$0.506011\pi$
$594$	−1.97634e14			−2.67257
$595$	−4.21996e13			−0.565879
$596$	−1.41211e14			−1.87774
$597$			9.70079e13i			1.27919i
$598$	−2.88396e14			−3.77123
$599$		−	1.88803e13i		−	0.244836i	−0.992479	−	0.122418i	$-0.960935\pi$
$599$		−	1.88803e13i		−	0.244836i	0.992479	−	0.122418i	$-0.0390648\pi$
$600$	−4.52303e13			−0.581665
$601$		−	6.91622e13i		−	0.882056i	−0.897493	−	0.441028i	$-0.854614\pi$
$601$		−	6.91622e13i		−	0.882056i	0.897493	−	0.441028i	$-0.145386\pi$
$602$			7.22584e13i			0.913916i
$603$		−	1.80745e13i		−	0.226715i
$604$		−	9.46638e13i		−	1.17760i
$605$	5.60666e13			0.691716
$606$	1.98239e14			2.42564
$607$			8.87312e13i			1.07680i	0.842691	+	0.538398i	$0.180970\pi$
$607$			8.87312e13i			1.07680i	−0.842691	+	0.538398i	$0.819030\pi$
$608$	9.57867e13	−	1.41050e14i	1.15289	−	1.69767i
$609$	8.08850e12			0.0965565
$610$		−	7.56838e13i		−	0.896094i
$611$		−	1.65221e14i		−	1.94026i
$612$	−5.62343e13			−0.655004
$613$	1.17400e14			1.35633			0.678163	−	0.734911i	$-0.262776\pi$
$613$	1.17400e14			1.35633			0.678163	+	0.734911i	$0.262776\pi$
$614$	−8.04599e13			−0.922015
$615$	−5.42968e13			−0.617161
$616$		−	2.97277e14i		−	3.35164i
$617$	7.47260e13			0.835692			0.417846	−	0.908518i	$-0.362785\pi$
$617$	7.47260e13			0.835692			0.417846	+	0.908518i	$0.362785\pi$
$618$			3.01677e14i			3.34657i
$619$	1.43701e14			1.58128			0.790638	−	0.612284i	$-0.209749\pi$
$619$	1.43701e14			1.58128			0.790638	+	0.612284i	$0.209749\pi$
$620$			5.64862e13i			0.616573i
$621$			1.30539e14i			1.41345i
$622$		−	1.23404e14i		−	1.32549i
$623$		−	1.23103e13i		−	0.131168i
$624$	3.37838e14			3.57096
$625$	3.81470e12			0.0400000
$626$		−	1.14416e14i		−	1.19019i
$627$	9.37562e13	−	1.38060e14i	0.967526	−	1.42472i
$628$	−1.14481e14			−1.17202
$629$		−	1.90735e14i		−	1.93721i
$630$			1.05764e13i			0.106570i
$631$	4.72865e13			0.472705			0.236353	−	0.971667i	$-0.424048\pi$
$631$	4.72865e13			0.472705			0.236353	+	0.971667i	$0.424048\pi$
$632$	3.96358e14			3.93099
$633$	4.19797e13			0.413067
$634$	−2.89013e13			−0.282145
$635$			1.50696e13i			0.145959i
$636$	1.09425e14			1.05156
$637$			5.33270e13i			0.508452i
$638$	3.59775e13			0.340351
$639$			5.09884e12i			0.0478594i
$640$			1.35505e13i			0.126199i
$641$		−	2.35362e13i		−	0.217494i	−0.994069	−	0.108747i	$-0.965316\pi$
$641$		−	2.35362e13i		−	0.217494i	0.994069	−	0.108747i	$-0.0346838\pi$
$642$			8.01086e13i			0.734520i
$643$	2.13036e14			1.93820			0.969098	−	0.246677i	$-0.0793386\pi$
$643$	2.13036e14			1.93820			0.969098	+	0.246677i	$0.0793386\pi$
$644$	−3.31699e14			−2.99443
$645$		−	3.40125e13i		−	0.304677i
$646$	−1.90633e14	+	2.80714e14i	−1.69447	+	2.49518i
$647$	−2.01127e14			−1.77398			−0.886992	−	0.461786i	$-0.847209\pi$
$647$	−2.01127e14			−1.77398			−0.886992	+	0.461786i	$0.847209\pi$
$648$		−	3.50255e14i		−	3.06556i
$649$			1.15533e14i			1.00342i
$650$	−5.58186e13			−0.481074
$651$	5.53192e13			0.473120
$652$	−1.56750e14			−1.33036
$653$	5.64475e13			0.475422			0.237711	−	0.971336i	$-0.423603\pi$
$653$	5.64475e13			0.475422			0.237711	+	0.971336i	$0.423603\pi$
$654$			3.91618e14i			3.27321i
$655$	−6.11916e12			−0.0507557
$656$			3.96994e14i			3.26787i
$657$	−2.51934e13			−0.205807
$658$		−	2.67568e14i		−	2.16923i
$659$			6.32523e13i			0.508920i	0.967083	+	0.254460i	$0.0818977\pi$
$659$			6.32523e13i			0.508920i	−0.967083	+	0.254460i	$0.918102\pi$
$660$			2.36383e14i			1.88754i
$661$		−	2.11362e14i		−	1.67502i	−0.546422	−	0.837510i	$-0.684010\pi$
$661$		−	2.11362e14i		−	1.67502i	0.546422	−	0.837510i	$-0.315990\pi$
$662$	−2.70064e14			−2.12411
$663$	−2.90655e14			−2.26887
$664$			4.43543e14i			3.43633i
$665$	3.74960e13	+	2.54635e13i	0.288321	+	0.195799i
$666$	−4.78033e13			−0.364826
$667$		−	2.37634e13i		−	0.180003i
$668$			4.92551e14i			3.70313i
$669$	3.96244e13			0.295687
$670$	1.54482e14			1.14421
$671$	−2.34145e14			−1.72136
$672$	2.36513e14			1.72587
$673$		−	2.61390e13i		−	0.189327i	−0.995509	−	0.0946636i	$-0.969822\pi$
$673$		−	2.61390e13i		−	0.189327i	0.995509	−	0.0946636i	$-0.0301775\pi$
$674$	2.70193e14			1.94256
$675$			2.52656e13i			0.180306i
$676$	2.34108e14			1.65837
$677$		−	1.54762e14i		−	1.08823i	−0.839010	−	0.544115i	$-0.816865\pi$
$677$		−	1.54762e14i		−	1.08823i	0.839010	−	0.544115i	$-0.183135\pi$
$678$			1.24027e14i			0.865703i
$679$			7.98758e13i			0.553434i
$680$		−	2.84517e14i		−	1.95688i
$681$	−1.04413e14			−0.712887
$682$	2.46059e14			1.66769
$683$		−	1.74415e14i		−	1.17349i	−0.809771	−	0.586746i	$-0.800409\pi$
$683$		−	1.74415e14i		−	1.17349i	0.809771	−	0.586746i	$-0.199591\pi$
$684$	4.99664e13	+	3.39321e13i	0.333732	+	0.226637i
$685$	2.10126e13			0.139324
$686$			3.06294e14i			2.01613i
$687$			1.01053e13i			0.0660337i
$688$	−2.48685e14			−1.61327
$689$	7.99397e13			0.514833
$690$	2.19841e14			1.40560
$691$	2.28714e14			1.45179			0.725893	−	0.687808i	$-0.241427\pi$
$691$	2.28714e14			1.45179			0.725893	+	0.687808i	$0.241427\pi$
$692$			5.99750e14i			3.77955i
$693$	3.27203e13			0.204716
$694$			8.78845e12i			0.0545902i
$695$	5.97561e13			0.368517
$696$			5.45341e13i			0.333904i
$697$		−	3.41549e14i		−	2.07630i
$698$		−	3.58531e13i		−	0.216396i
$699$		−	2.42034e14i		−	1.45041i
$700$	−6.41999e13			−0.381983
$701$	−1.99743e14			−1.18000			−0.589999	−	0.807404i	$-0.700872\pi$
$701$	−1.99743e14			−1.18000			−0.589999	+	0.807404i	$0.700872\pi$
$702$		−	3.69699e14i		−	2.16852i
$703$	−1.15091e14	+	1.69475e14i	−0.670291	+	0.987029i
$704$	3.46783e14			2.00537
$705$			1.25946e14i			0.723168i
$706$		−	3.49363e14i		−	1.99183i
$707$	1.66567e14			0.942958
$708$	−2.95833e14			−1.66296
$709$	−4.30964e13			−0.240552			−0.120276	−	0.992740i	$-0.538378\pi$
$709$	−4.30964e13			−0.240552			−0.120276	+	0.992740i	$0.538378\pi$
$710$	−4.35796e13			−0.241542
$711$			4.36258e13i			0.240102i
$712$	8.29981e13			0.453595
$713$		−	1.62524e14i		−	0.882000i
$714$	−4.70703e14			−2.53662
$715$			1.72687e14i			0.924125i
$716$		−	9.06852e14i		−	4.81916i
$717$		−	3.03035e14i		−	1.59918i
$718$			3.02649e14i			1.58605i
$719$	3.33543e14			1.73583			0.867915	−	0.496713i	$-0.165460\pi$
$719$	3.33543e14			1.73583			0.867915	+	0.496713i	$0.165460\pi$
$720$	−3.63996e13			−0.188119
$721$			2.53479e14i			1.30096i
$722$	3.38769e14	−	1.34397e14i	1.72671	−	0.685019i
$723$	−1.32568e13			−0.0671040
$724$		−	5.45320e14i		−	2.74131i
$725$		−	4.59937e12i		−	0.0229619i
$726$	6.25379e14			3.10070
$727$	5.26018e13			0.259017			0.129509	−	0.991578i	$-0.458660\pi$
$727$	5.26018e13			0.259017			0.129509	+	0.991578i	$0.458660\pi$
$728$	5.56094e14			2.71951
$729$	−1.61761e14			−0.785663
$730$		−	2.15327e14i		−	1.03869i
$731$	2.13953e14			1.02502
$732$		−	5.99552e14i		−	2.85280i
$733$	−3.00849e14			−1.42177			−0.710884	−	0.703310i	$-0.751705\pi$
$733$	−3.00849e14			−1.42177			−0.710884	+	0.703310i	$0.751705\pi$
$734$			5.44203e14i			2.55435i
$735$		−	4.06506e13i		−	0.189509i
$736$		−	6.94857e14i		−	3.21741i
$737$		−	4.77926e14i		−	2.19798i
$738$	−8.56014e13			−0.391020
$739$	−3.13150e14			−1.42079			−0.710395	−	0.703804i	$-0.751484\pi$
$739$	−3.13150e14			−1.42079			−0.710395	+	0.703804i	$0.751484\pi$
$740$		−	2.90172e14i		−	1.30767i
$741$	2.58258e14	+	1.75383e14i	1.15601	+	0.785048i
$742$	1.29459e14			0.575589
$743$		−	1.56249e13i		−	0.0690038i	−0.999405	−	0.0345019i	$-0.989016\pi$
$743$		−	1.56249e13i		−	0.0690038i	0.999405	−	0.0345019i	$-0.0109845\pi$
$744$			3.72972e14i			1.63611i
$745$	7.86378e13			0.342649
$746$	−3.33376e14			−1.44291
$747$	−4.88193e13			−0.209889
$748$	−1.48695e15			−6.35020
$749$			6.73099e13i			0.285542i
$750$	4.25499e13			0.179305
$751$			4.51396e14i			1.88955i	0.327719	+	0.944775i	$0.393720\pi$
$751$			4.51396e14i			1.88955i	−0.327719	+	0.944775i	$0.606280\pi$
$752$	9.20863e14			3.82918
$753$		−	2.15115e14i		−	0.888579i
$754$			6.73004e13i			0.276160i
$755$			5.27167e13i			0.214888i
$756$		−	4.25210e14i		−	1.72185i
$757$	1.19935e14			0.482467			0.241233	−	0.970467i	$-0.422448\pi$
$757$	1.19935e14			0.482467			0.241233	+	0.970467i	$0.422448\pi$
$758$	8.83372e13			0.353018
$759$		−	6.80127e14i		−	2.70011i
$760$	−1.71679e14	+	2.52805e14i	−0.677096	+	0.997051i
$761$	1.87180e14			0.733390			0.366695	−	0.930341i	$-0.380489\pi$
$761$	1.87180e14			0.733390			0.366695	+	0.930341i	$0.380489\pi$
$762$			1.68089e14i			0.654281i
$763$			3.29051e14i			1.27245i
$764$	5.07898e14			1.95123
$765$	3.13159e13			0.119525
$766$	5.28396e14			2.00362
$767$	−2.16118e14			−0.814170
$768$		−	2.11181e14i		−	0.790403i
$769$	−2.12256e14			−0.789275			−0.394637	−	0.918837i	$-0.629130\pi$
$769$	−2.12256e14			−0.789275			−0.394637	+	0.918837i	$0.629130\pi$
$770$			2.79660e14i			1.03318i
$771$	−1.15561e14			−0.424170
$772$			1.17175e14i			0.427315i
$773$		−	1.66349e14i		−	0.602729i	−0.953509	−	0.301364i	$-0.902558\pi$
$773$		−	1.66349e14i		−	0.602729i	0.953509	−	0.301364i	$-0.0974420\pi$
$774$		−	5.36223e13i		−	0.193037i
$775$		−	3.14562e13i		−	0.112512i
$776$	−5.38537e14			−1.91384
$777$	−2.84177e14			−1.00342
$778$			4.69769e14i			1.64811i
$779$	−2.06093e14	+	3.03480e14i	−0.718416	+	1.05790i
$780$	−4.42184e14			−1.53155
$781$			1.34823e14i			0.463992i
$782$			1.38289e15i			4.72883i
$783$	3.04627e13			0.103505
$784$	−2.97219e14			−1.00345
$785$	6.37523e13			0.213869
$786$	−6.82543e13			−0.227519
$787$		−	2.93580e14i		−	0.972417i	−0.873843	−	0.486208i	$-0.838380\pi$
$787$		−	2.93580e14i		−	0.972417i	0.873843	−	0.486208i	$-0.161620\pi$
$788$	5.65326e14			1.86066
$789$		−	2.73759e14i		−	0.895331i
$790$	−3.72869e14			−1.21177
$791$			1.04212e14i			0.336539i
$792$			2.20606e14i			0.707933i
$793$		−	4.37998e14i		−	1.39671i
$794$		−	7.04293e14i		−	2.23178i
$795$	−6.09371e13			−0.191887
$796$	−9.28351e14			−2.90501
$797$			4.81601e14i			1.49760i	0.662797	+	0.748799i	$0.269369\pi$
$797$			4.81601e14i			1.49760i	−0.662797	+	0.748799i	$0.730631\pi$
$798$	4.18238e14	+	2.84025e14i	1.29244	+	0.877692i
$799$	−7.92253e14			−2.43293
$800$		−	1.34489e14i		−	0.410427i
$801$			9.13534e12i			0.0277053i
$802$	−7.48913e14			−2.25715
$803$	−6.66163e14			−1.99527
$804$	1.22378e15			3.64270
$805$	1.84718e14			0.546423
$806$			4.60284e14i			1.35316i
$807$	−3.67824e14			−1.07466
$808$			1.12303e15i			3.26086i
$809$	4.76554e14			1.37521			0.687606	−	0.726084i	$-0.258662\pi$
$809$	4.76554e14			1.37521			0.687606	+	0.726084i	$0.258662\pi$
$810$			3.29498e14i			0.944992i
$811$		−	2.15024e13i		−	0.0612890i	−0.999530	−	0.0306445i	$-0.990244\pi$
$811$		−	2.15024e13i		−	0.0612890i	0.999530	−	0.0306445i	$-0.00975597\pi$
$812$			7.74057e13i			0.219277i
$813$			9.61418e13i			0.270682i
$814$	−1.26401e15			−3.53696
$815$	8.72916e13			0.242764
$816$		−	1.61997e15i		−	4.47771i
$817$	−1.90105e14	−	1.29100e14i	−0.522257	−	0.354664i
$818$	3.68855e14			1.00714
$819$			6.12075e13i			0.166106i
$820$		−	5.19612e14i		−	1.40156i
$821$	1.25085e14			0.335343			0.167672	−	0.985843i	$-0.446375\pi$
$821$	1.25085e14			0.335343			0.167672	+	0.985843i	$0.446375\pi$
$822$	2.34379e14			0.624539
$823$	4.08897e14			1.08296			0.541482	−	0.840712i	$-0.317863\pi$
$823$	4.08897e14			1.08296			0.541482	+	0.840712i	$0.317863\pi$
$824$	−1.70900e15			−4.49890
$825$		−	1.31638e14i		−	0.344438i
$826$	−3.49994e14			−0.910250
$827$		−	4.34380e14i		−	1.12290i	−0.827509	−	0.561452i	$-0.810243\pi$
$827$		−	4.34380e14i		−	1.12290i	0.827509	−	0.561452i	$-0.189757\pi$
$828$	2.46151e14			0.632484
$829$		−	1.45668e14i		−	0.372043i	−0.982546	−	0.186021i	$-0.940441\pi$
$829$		−	1.45668e14i		−	0.372043i	0.982546	−	0.186021i	$-0.0595593\pi$
$830$		−	4.17258e14i		−	1.05929i
$831$		−	3.49483e13i		−	0.0881903i
$832$			6.48701e14i			1.62715i
$833$	2.55709e14			0.637560
$834$	6.66531e14			1.65192
$835$		−	2.74294e14i		−	0.675746i
$836$	1.32121e15	+	8.97233e14i	3.23550	+	2.19722i
$837$	2.08342e14			0.507164
$838$		−	4.17507e14i		−	1.01028i
$839$			4.33256e14i			1.04216i	0.853507	+	0.521081i	$0.174471\pi$
$839$			4.33256e14i			1.04216i	−0.853507	+	0.521081i	$0.825529\pi$
$840$	−4.23904e14			−1.01361
$841$	4.15162e14			0.986819
$842$	1.01307e15			2.39376
$843$	2.37550e14			0.557978
$844$			4.01740e14i			0.938064i
$845$	−1.30371e14			−0.302619
$846$			1.98560e14i			0.458184i
$847$	5.25464e14			1.20539
$848$			4.45545e14i			1.01604i
$849$		−	5.60302e13i		−	0.127023i
$850$			2.67656e14i			0.603230i
$851$			8.34891e14i			1.87060i
$852$	−3.45230e14			−0.768971
$853$	4.08862e14			0.905381			0.452691	−	0.891668i	$-0.350464\pi$
$853$	4.08862e14			0.905381			0.452691	+	0.891668i	$0.350464\pi$
$854$		−	7.09318e14i		−	1.56153i
$855$	−2.78254e13	−	1.88962e13i	−0.0608992	−	0.0413566i
$856$	−4.53815e14			−0.987439
$857$		−	2.80853e14i		−	0.607541i	−0.952745	−	0.303770i	$-0.901754\pi$
$857$		−	2.80853e14i		−	0.607541i	0.952745	−	0.303770i	$-0.0982456\pi$
$858$			1.92619e15i			4.14250i
$859$	3.11804e12			0.00666678			0.00333339	−	0.999994i	$-0.498939\pi$
$859$	3.11804e12			0.00666678			0.00333339	+	0.999994i	$0.498939\pi$
$860$	3.25495e14			0.691913
$861$	−5.08877e14			−1.07547
$862$	3.25480e14			0.683894
$863$			1.97761e14i			0.413130i	0.978433	+	0.206565i	$0.0662286\pi$
$863$			1.97761e14i			0.413130i	−0.978433	+	0.206565i	$0.933771\pi$
$864$	8.90748e14			1.85006
$865$		−	3.33991e14i		−	0.689690i
$866$	5.93227e13			0.121796
$867$			8.65051e14i			1.76582i
$868$			5.29396e14i			1.07444i
$869$			1.15355e15i			2.32776i
$870$		−	5.13023e13i		−	0.102930i
$871$	8.94021e14			1.78343
$872$	−2.21852e15			−4.40029
$873$		−	5.92750e13i		−	0.116896i
$874$	8.34444e14	−	1.22875e15i	1.63621	−	2.40939i
$875$	3.57518e13			0.0697041
$876$		−	1.70578e15i		−	3.30676i
$877$			3.77353e14i			0.727360i	0.931524	+	0.363680i	$0.118480\pi$
$877$			3.77353e14i			0.727360i	−0.931524	+	0.363680i	$0.881520\pi$
$878$	4.59515e14			0.880698
$879$	4.07759e14			0.777068
$880$	−9.62477e14			−1.82380
$881$	−9.90761e14			−1.86676			−0.933382	−	0.358885i	$-0.883157\pi$
$881$	−9.90761e14			−1.86676			−0.933382	+	0.358885i	$0.883157\pi$
$882$		−	6.40875e13i		−	0.120069i
$883$	5.10654e13			0.0951312			0.0475656	−	0.998868i	$-0.484854\pi$
$883$	5.10654e13			0.0951312			0.0475656	+	0.998868i	$0.484854\pi$
$884$		−	2.78152e15i		−	5.15254i
$885$	1.64745e14			0.303455
$886$			1.97088e15i			3.60987i
$887$		−	7.71062e14i		−	1.40434i	−0.712011	−	0.702169i	$-0.752215\pi$
$887$		−	7.71062e14i		−	1.40434i	0.712011	−	0.702169i	$-0.247785\pi$
$888$		−	1.91597e15i		−	3.46996i
$889$			1.41234e14i			0.254349i
$890$	−7.80795e13			−0.139826
$891$	1.01938e15			1.81529
$892$			3.79199e14i			0.671496i
$893$	7.03949e14	+	4.78051e14i	1.23961	+	0.841815i
$894$	8.77141e14			1.53597
$895$			5.05010e14i			0.879397i
$896$			1.26997e14i			0.219914i
$897$	1.27226e15			2.19086
$898$	−1.27203e14			−0.217828
$899$	−3.79267e13			−0.0645872
$900$	4.76421e13			0.0806824
$901$		−	3.83320e14i		−	0.645561i
$902$	−2.26347e15			−3.79090
$903$		−	3.18770e14i		−	0.530931i
$904$	−7.02615e14			−1.16379
$905$			3.03680e14i			0.500233i
$906$			5.88012e14i			0.963264i
$907$		−	1.60447e14i		−	0.261394i	−0.991422	−	0.130697i	$-0.958279\pi$
$907$		−	1.60447e14i		−	0.261394i	0.991422	−	0.130697i	$-0.0417215\pi$
$908$		−	9.99221e14i		−	1.61895i
$909$	−1.23608e14			−0.199171
$910$	−5.23139e14			−0.838321
$911$		−	5.42354e13i		−	0.0864353i	−0.999066	−	0.0432177i	$-0.986239\pi$
$911$		−	5.42354e13i		−	0.0864353i	0.999066	−	0.0432177i	$-0.0137609\pi$
$912$	−9.77500e14	+	1.43941e15i	−1.54933	+	2.28144i
$913$	−1.29088e15			−2.03485
$914$			2.91707e14i			0.457315i
$915$			3.33881e14i			0.520578i
$916$	−9.67063e13			−0.149961
$917$	−5.73495e13			−0.0884470
$918$	−1.77275e15			−2.71915
$919$	−2.42268e14			−0.369589			−0.184794	−	0.982777i	$-0.559162\pi$
$919$	−2.42268e14			−0.369589			−0.184794	+	0.982777i	$0.559162\pi$
$920$			1.24540e15i			1.88960i
$921$	3.54951e14			0.535636
$922$			6.46597e14i			0.970463i
$923$	−2.52204e14			−0.376482
$924$			2.21541e15i			3.28923i
$925$			1.61592e14i			0.238622i
$926$		−	1.43925e15i		−	2.11389i
$927$		−	1.88104e14i		−	0.274789i
$928$	−1.62153e14			−0.235605
$929$	−3.73940e14			−0.540409			−0.270205	−	0.962803i	$-0.587091\pi$
$929$	−3.73940e14			−0.540409			−0.270205	+	0.962803i	$0.587091\pi$
$930$		−	3.50869e14i		−	0.504348i
$931$	−2.27207e14	−	1.54296e14i	−0.324844	−	0.220601i
$932$	2.31623e15			3.29383
$933$			5.44400e14i			0.770034i
$934$		−	9.98833e14i		−	1.40527i
$935$	8.28055e14			1.15878
$936$	−4.12672e14			−0.574415
$937$	−8.79489e14			−1.21768			−0.608839	−	0.793294i	$-0.708364\pi$
$937$	−8.79489e14			−1.21768			−0.608839	+	0.793294i	$0.708364\pi$
$938$	1.44783e15			1.99390
$939$			5.04750e14i			0.691431i
$940$	−1.20529e15			−1.64229
$941$			1.35085e15i			1.83088i	0.402456	+	0.915439i	$0.368157\pi$
$941$			1.35085e15i			1.83088i	−0.402456	+	0.915439i	$0.631843\pi$
$942$	7.11106e14			0.958694
$943$			1.49504e15i			2.00491i
$944$		−	1.20454e15i		−	1.60680i
$945$			2.36792e14i			0.314202i
$946$		−	1.41788e15i		−	1.87147i
$947$	−5.97770e14			−0.784845			−0.392423	−	0.919785i	$-0.628363\pi$
$947$	−5.97770e14			−0.784845			−0.392423	+	0.919785i	$0.628363\pi$
$948$	−2.95380e15			−3.85779
$949$		−	1.24614e15i		−	1.61896i
$950$	1.61506e14	−	2.37823e14i	0.208723	−	0.307352i
$951$	1.27499e14			0.163909
$952$		−	2.66653e15i		−	3.41006i
$953$		−	1.25201e15i		−	1.59273i	−0.604814	−	0.796366i	$-0.706753\pi$
$953$		−	1.25201e15i		−	1.59273i	0.604814	−	0.796366i	$-0.293247\pi$
$954$	−9.60702e13			−0.121576
$955$	−2.82840e14			−0.356060
$956$	2.90000e15			3.63169
$957$	−1.58715e14			−0.197724
$958$			5.66963e14i			0.702631i
$959$	1.96933e14			0.242787
$960$		−	4.94498e14i		−	0.606468i
$961$	5.60238e14			0.683527
$962$		−	2.36450e15i		−	2.86988i
$963$		−	4.99500e13i		−	0.0603121i
$964$		−	1.26866e14i		−	0.152391i
$965$		−	6.52527e13i		−	0.0779762i
$966$	2.06038e15			2.44941
$967$	−3.41450e14			−0.403826			−0.201913	−	0.979403i	$-0.564716\pi$
$967$	−3.41450e14			−0.403826			−0.201913	+	0.979403i	$0.564716\pi$
$968$			3.54277e15i			4.16837i
$969$	8.40980e14	−	1.23838e15i	0.984390	−	1.44955i
$970$	5.06622e14			0.589964
$971$			1.35206e15i			1.56639i	0.621774	+	0.783197i	$0.286412\pi$
$971$			1.35206e15i			1.56639i	−0.621774	+	0.783197i	$0.713588\pi$
$972$			6.93264e14i			0.799038i
$973$	5.60042e14			0.642179
$974$	−2.72201e15			−3.10523
$975$	2.46245e14			0.279476
$976$	2.44119e15			2.75646
$977$		−	7.25298e14i		−	0.814786i	−0.913253	−	0.407393i	$-0.866438\pi$
$977$		−	7.25298e14i		−	0.814786i	0.913253	−	0.407393i	$-0.133562\pi$
$978$	9.73668e14			1.08822
$979$			2.41557e14i			0.268600i
$980$	3.89020e14			0.430370
$981$		−	2.44185e14i		−	0.268766i
$982$		−	9.45008e14i		−	1.03485i
$983$		−	1.08785e15i		−	1.18523i	−0.805486	−	0.592615i	$-0.798095\pi$
$983$		−	1.08785e15i		−	1.18523i	0.805486	−	0.592615i	$-0.201905\pi$
$984$		−	3.43094e15i		−	3.71910i
$985$	−3.14821e14			−0.339533
$986$	3.22713e14			0.346283
$987$			1.18038e15i			1.26019i
$988$	−1.67839e15	+	2.47149e15i	−1.78282	+	2.62527i
$989$	−9.36521e14			−0.989774
$990$		−	2.07533e14i		−	0.218228i
$991$			1.21165e15i			1.26768i	0.773466	+	0.633838i	$0.218521\pi$
$991$			1.21165e15i			1.26768i	−0.773466	+	0.633838i	$0.781479\pi$
$992$	−1.10900e15			−1.15445
$993$	1.19139e15			1.23398
$994$	−4.08434e14			−0.420911
$995$	5.16983e14			0.530104
$996$		−	3.30544e15i		−	3.37235i
$997$	−1.93560e14			−0.196489			−0.0982447	−	0.995162i	$-0.531323\pi$
$997$	−1.93560e14			−0.196489			−0.0982447	+	0.995162i	$0.531323\pi$
$998$		−	1.16257e15i		−	1.17427i
$999$	−1.07026e15			−1.07563

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.11.c.a.56.4	✓	68
19.18	odd	2	inner	95.11.c.a.56.65	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.11.c.a.56.4	✓	68	1.1	even	1	trivial
95.11.c.a.56.65	yes	68	19.18	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-59.4439i q^{2} +262.238i q^{3} -2509.58 q^{4} +1397.54 q^{5} +15588.5 q^{6} +13097.9 q^{7} +88308.7i q^{8} -9719.86 q^{9} -83075.4i q^{10} -257013. q^{11} -658108. i q^{12} -480775. i q^{13} -778594. i q^{14} +366489. i q^{15} +2.67961e6 q^{16} -2.30537e6 q^{17} +577787. i q^{18} +(2.04841e6 + 1.39107e6i) q^{19} -3.50724e6 q^{20} +3.43478e6i q^{21} +1.52778e7i q^{22} +1.00911e7 q^{23} -2.31579e7 q^{24} +1.95312e6 q^{25} -2.85791e7 q^{26} +1.29360e7i q^{27} -3.28704e7 q^{28} -2.35488e6i q^{29} +2.17855e7 q^{30} -1.61056e7i q^{31} -6.88582e7i q^{32} -6.73985e7i q^{33} +1.37040e8i q^{34} +1.83049e7 q^{35} +2.43928e7 q^{36} +8.27351e7i q^{37} +(8.26908e7 - 1.21766e8i) q^{38} +1.26077e8 q^{39} +1.23415e8i q^{40} +1.48154e8i q^{41} +2.04177e8 q^{42} -9.28064e7 q^{43} +6.44994e8 q^{44} -1.35839e7 q^{45} -5.99856e8i q^{46} +3.43656e8 q^{47} +7.02695e8i q^{48} -1.10919e8 q^{49} -1.16101e8i q^{50} -6.04555e8i q^{51} +1.20654e9i q^{52} +1.66273e8i q^{53} +7.68966e8 q^{54} -3.59186e8 q^{55} +1.15666e9i q^{56} +(-3.64792e8 + 5.37171e8i) q^{57} -1.39983e8 q^{58} -4.49521e8i q^{59} -9.19733e8i q^{60} +9.11025e8 q^{61} -9.57379e8 q^{62} -1.27310e8 q^{63} -1.34928e9 q^{64} -6.71903e8i q^{65} -4.00643e9 q^{66} +1.85954e9i q^{67} +5.78550e9 q^{68} +2.64628e9i q^{69} -1.08812e9i q^{70} -5.24579e8i q^{71} -8.58349e8i q^{72} +2.59195e9 q^{73} +4.91810e9 q^{74} +5.12184e8i q^{75} +(-5.14065e9 - 3.49101e9i) q^{76} -3.36634e9 q^{77} -7.49454e9i q^{78} -4.48832e9i q^{79} +3.74486e9 q^{80} -3.96626e9 q^{81} +8.80686e9 q^{82} +5.02264e9 q^{83} -8.61986e9i q^{84} -3.22185e9 q^{85} +5.51677e9i q^{86} +6.17539e8 q^{87} -2.26964e10i q^{88} -9.39863e8i q^{89} +8.07482e8i q^{90} -6.29716e9i q^{91} -2.53245e10 q^{92} +4.22350e9 q^{93} -2.04283e10i q^{94} +(2.86274e9 + 1.94408e9i) q^{95} +1.80572e10 q^{96} +6.09834e9i q^{97} +6.59346e9i q^{98} +2.49813e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 35644 q^{4} - 2044 q^{6} + 76620 q^{7} - 1353552 q^{9} - 418144 q^{11} + 21763300 q^{16} - 10023236 q^{17} + 518264 q^{19} + 4962204 q^{23} + 2604244 q^{24} + 132812500 q^{25} + 32178588 q^{26} - 109025284 q^{28}+ \cdots + 76070139768 q^{99}+O(q^{100}) \) 68 * q - 35644 * q^4 - 2044 * q^6 + 76620 * q^7 - 1353552 * q^9 - 418144 * q^11 + 21763300 * q^16 - 10023236 * q^17 + 518264 * q^19 + 4962204 * q^23 + 2604244 * q^24 + 132812500 * q^25 + 32178588 * q^26 - 109025284 * q^28 + 39875000 * q^30 + 39875000 * q^35 + 420547696 * q^36 - 504912596 * q^38 + 51693988 * q^39 + 343589380 * q^42 + 72617360 * q^43 - 846875584 * q^44 + 148625000 * q^45 + 426767656 * q^47 + 3802641528 * q^49 + 594603476 * q^54 - 361360620 * q^57 - 1963881788 * q^58 + 7470512872 * q^61 - 2514646024 * q^62 - 6611740944 * q^63 - 13094608884 * q^64 + 9558616040 * q^66 + 17177918780 * q^68 - 2447766556 * q^73 - 1842337832 * q^74 - 5604056776 * q^76 - 320485400 * q^77 - 821875000 * q^80 + 5162401956 * q^81 - 17137563304 * q^82 - 14922506320 * q^83 - 4799500000 * q^85 + 5085654996 * q^87 - 27413957236 * q^92 - 11067885256 * q^93 + 1613500000 * q^95 - 67563054044 * q^96 + 76070139768 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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