LMFDB - Embedded newform 3.25.b.b.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,25,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 25, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 25);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	3.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:	$10.9490145677$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 253102x^{4} + 17425276096x^{2} + 250659115499520 $ x^6 + 253102x^4 + 17425276096x^2 + 250659115499520
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{13}\cdot 3^{24}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.4
Root			$139.516i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.25.b.b.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2511.29i q^{2} +(-446105. + 288825. i) q^{3} +1.04706e7 q^{4} +3.68111e8i q^{5} +(-7.25325e8 - 1.12030e9i) q^{6} -8.30906e9 q^{7} +6.84273e10i q^{8} +(1.15589e11 - 2.57693e11i) q^{9} +O(q^{10})$	\(q+2511.29i q^{2} +(-446105. + 288825. i) q^{3} +1.04706e7 q^{4} +3.68111e8i q^{5} +(-7.25325e8 - 1.12030e9i) q^{6} -8.30906e9 q^{7} +6.84273e10i q^{8} +(1.15589e11 - 2.57693e11i) q^{9} -9.24434e11 q^{10} -3.87633e12i q^{11} +(-4.67100e12 + 3.02418e12i) q^{12} -3.48308e13 q^{13} -2.08665e13i q^{14} +(-1.06320e14 - 1.64216e14i) q^{15} +3.82721e12 q^{16} +2.61737e14i q^{17} +(6.47142e14 + 2.90279e14i) q^{18} +7.24444e14 q^{19} +3.85436e15i q^{20} +(3.70671e15 - 2.39987e15i) q^{21} +9.73460e15 q^{22} +1.12454e16i q^{23} +(-1.97635e16 - 3.05257e16i) q^{24} -7.59011e16 q^{25} -8.74702e16i q^{26} +(2.28632e16 + 1.48343e17i) q^{27} -8.70011e16 q^{28} -1.35463e17i q^{29} +(4.12394e17 - 2.67000e17i) q^{30} +2.21037e17 q^{31} +1.15763e18i q^{32} +(1.11958e18 + 1.72925e18i) q^{33} -6.57298e17 q^{34} -3.05866e18i q^{35} +(1.21029e18 - 2.69821e18i) q^{36} -1.03438e19 q^{37} +1.81929e18i q^{38} +(1.55382e19 - 1.00600e19i) q^{39} -2.51888e19 q^{40} +1.85510e19i q^{41} +(6.02676e18 + 9.30863e18i) q^{42} +2.09203e19 q^{43} -4.05877e19i q^{44} +(9.48595e19 + 4.25497e19i) q^{45} -2.82405e19 q^{46} +5.93575e19i q^{47} +(-1.70734e18 + 1.10540e18i) q^{48} -1.22541e20 q^{49} -1.90610e20i q^{50} +(-7.55963e19 - 1.16762e20i) q^{51} -3.64700e20 q^{52} +1.46669e20i q^{53} +(-3.72533e20 + 5.74162e19i) q^{54} +1.42692e21 q^{55} -5.68566e20i q^{56} +(-3.23178e20 + 2.09238e20i) q^{57} +3.40187e20 q^{58} +3.04315e21i q^{59} +(-1.11324e21 - 1.71945e21i) q^{60} +3.55521e21 q^{61} +5.55088e20i q^{62} +(-9.60439e20 + 2.14118e21i) q^{63} -2.84294e21 q^{64} -1.28216e22i q^{65} +(-4.34265e21 + 2.81160e21i) q^{66} -2.84438e21 q^{67} +2.74055e21i q^{68} +(-3.24796e21 - 5.01663e21i) q^{69} +7.68118e21 q^{70} +2.39541e22i q^{71} +(1.76332e22 + 7.90947e21i) q^{72} -1.66222e22 q^{73} -2.59763e22i q^{74} +(3.38599e22 - 2.19222e22i) q^{75} +7.58539e21 q^{76} +3.22087e22i q^{77} +(2.52636e22 + 3.90209e22i) q^{78} -6.08621e22 q^{79} +1.40884e21i q^{80} +(-5.30446e22 - 5.95731e22i) q^{81} -4.65869e22 q^{82} -7.63158e22i q^{83} +(3.88116e22 - 2.51281e22i) q^{84} -9.63483e22 q^{85} +5.25371e22i q^{86} +(3.91252e22 + 6.04307e22i) q^{87} +2.65247e23 q^{88} -1.24843e23i q^{89} +(-1.06855e23 + 2.38220e23i) q^{90} +2.89411e23 q^{91} +1.17747e23i q^{92} +(-9.86056e22 + 6.38411e22i) q^{93} -1.49064e23 q^{94} +2.66676e23i q^{95} +(-3.34353e23 - 5.16424e23i) q^{96} +9.42350e23 q^{97} -3.07736e23i q^{98} +(-9.98903e23 - 4.48063e23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 616842 q^{3} - 63346800 q^{4} - 2673890352 q^{6} + 1988064876 q^{7} - 791186949882 q^{9}+O(q^{10}) $ 6 * q - 616842 * q^3 - 63346800 * q^4 - 2673890352 * q^6 + 1988064876 * q^7 - 791186949882 * q^9	$ 6 q - 616842 q^{3} - 63346800 q^{4} - 2673890352 q^{6} + 1988064876 q^{7} - 791186949882 q^{9} + 2770823311200 q^{10} - 18492861842352 q^{12} - 73542438063924 q^{13} + 227151045057600 q^{15} - 433335898904448 q^{16} - 12\!\cdots\!40 q^{18}+ \cdots - 18\!\cdots\!20 q^{99}+O(q^{100}) $ 6 * q - 616842 * q^3 - 63346800 * q^4 - 2673890352 * q^6 + 1988064876 * q^7 - 791186949882 * q^9 + 2770823311200 * q^10 - 18492861842352 * q^12 - 73542438063924 * q^13 + 227151045057600 * q^15 - 433335898904448 * q^16 - 1227888881468640 * q^18 + 6095219493474156 * q^19 + 2706110098936524 * q^21 - 4132747004902560 * q^22 + 79223562819483264 * q^24 - 206274704562968250 * q^25 - 153687400093414602 * q^27 + 11425252275435936 * q^28 + 1679034252186079200 * q^30 - 1137843910975220628 * q^31 + 7067811391497299520 * q^33 - 15440589345121992576 * q^34 + 23041875850704576144 * q^36 - 14032623495718823604 * q^37 + 25380736596180392364 * q^39 - 121930725979226707200 * q^40 + 209343891033396594720 * q^42 - 114603298148542353684 * q^43 + 311304965429932790400 * q^45 - 346860905830754272704 * q^46 + 51162839242132733568 * q^48 + 107947782097205854482 * q^49 - 479022139696737883392 * q^51 - 124107229893322470624 * q^52 - 1113391638534691344528 * q^54 + 1679273232066520675200 * q^55 - 1140401446469855973684 * q^57 + 7395366373865537628960 * q^58 - 14436777252623118393600 * q^60 + 10013078414594836175052 * q^61 - 8325410033672205875604 * q^63 + 11741892494977734042624 * q^64 - 5418873997530695523360 * q^66 - 5445087092431082846484 * q^67 + 11943290073056639859072 * q^69 - 55632387081854182017600 * q^70 + 63773250138227244591360 * q^72 + 7228988839203443040396 * q^73 + 37723327374597984717750 * q^75 - 4244116415001816243552 * q^76 + 235720510135983845200800 * q^78 - 423484844106082827915924 * q^79 + 102726090691231740574086 * q^81 - 272255725325320387035840 * q^82 + 200996808333809534079264 * q^84 + 319008824808936798988800 * q^85 - 252430535429613815803200 * q^87 + 160152458683551892335360 * q^88 - 1246806301659161625597600 * q^90 + 1497033316223591396871768 * q^91 - 501165623869166897253684 * q^93 + 1979316836866080826257024 * q^94 - 1420600675222724601424896 * q^96 - 1411607470255832450422644 * q^97 - 1834460043482282449115520 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

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

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 $

$2$			2511.29i			0.613108i	0.951853	+	0.306554i	$0.0991760\pi$
$2$			2511.29i			0.613108i	−0.951853	+	0.306554i	$0.900824\pi$
$3$	−446105.	+	288825.i	−0.839425	+	0.543476i
$3$	−446105.	+	288825.i	−0.839425	+	0.543476i
$4$	1.04706e7			0.624098
$5$			3.68111e8i			1.50778i	0.656999	+	0.753892i	$0.271826\pi$
$5$			3.68111e8i			1.50778i	−0.656999	+	0.753892i	$0.728174\pi$
$6$	−7.25325e8	−	1.12030e9i	−0.333210	−	0.514658i
$7$	−8.30906e9			−0.600309			−0.300155	−	0.953891i	$-0.597038\pi$
$7$	−8.30906e9			−0.600309			−0.300155	+	0.953891i	$0.597038\pi$
$8$			6.84273e10i			0.995748i
$9$	1.15589e11	−	2.57693e11i	0.409268	−	0.912414i
$10$	−9.24434e11			−0.924434
$11$		−	3.87633e12i		−	1.23512i	−0.786524	−	0.617560i	$-0.788121\pi$
$11$		−	3.87633e12i		−	1.23512i	0.786524	−	0.617560i	$-0.211879\pi$
$12$	−4.67100e12	+	3.02418e12i	−0.523884	+	0.339182i
$13$	−3.48308e13			−1.49501			−0.747503	−	0.664259i	$-0.768747\pi$
$13$	−3.48308e13			−1.49501			−0.747503	+	0.664259i	$0.768747\pi$
$14$		−	2.08665e13i		−	0.368055i
$15$	−1.06320e14	−	1.64216e14i	−0.819444	−	1.26567i
$16$	3.82721e12			0.0135970
$17$			2.61737e14i			0.449240i	0.974446	+	0.224620i	$0.0721141\pi$
$17$			2.61737e14i			0.449240i	−0.974446	+	0.224620i	$0.927886\pi$
$18$	6.47142e14	+	2.90279e14i	0.559409	+	0.250926i
$19$	7.24444e14			0.327312			0.163656	−	0.986517i	$-0.447671\pi$
$19$	7.24444e14			0.327312			0.163656	+	0.986517i	$0.447671\pi$
$20$			3.85436e15i			0.941005i
$21$	3.70671e15	−	2.39987e15i	0.503915	−	0.326254i
$22$	9.73460e15			0.757262
$23$			1.12454e16i			0.513147i	0.966525	+	0.256573i	$0.0825935\pi$
$23$			1.12454e16i			0.513147i	−0.966525	+	0.256573i	$0.917406\pi$
$24$	−1.97635e16	−	3.05257e16i	−0.541165	−	0.835856i
$25$	−7.59011e16			−1.27341
$26$		−	8.74702e16i		−	0.916600i
$27$	2.28632e16	+	1.48343e17i	0.152325	+	0.988330i
$28$	−8.70011e16			−0.374652
$29$		−	1.35463e17i		−	0.382864i	−0.981506	−	0.191432i	$-0.938687\pi$
$29$		−	1.35463e17i		−	0.382864i	0.981506	−	0.191432i	$-0.0613132\pi$
$30$	4.12394e17	−	2.67000e17i	0.775993	−	0.502408i
$31$	2.21037e17			0.280624			0.140312	−	0.990107i	$-0.455189\pi$
$31$	2.21037e17			0.280624			0.140312	+	0.990107i	$0.455189\pi$
$32$			1.15763e18i			1.00408i
$33$	1.11958e18	+	1.72925e18i	0.671258	+	1.03679i
$34$	−6.57298e17			−0.275433
$35$		−	3.05866e18i		−	0.905136i
$36$	1.21029e18	−	2.69821e18i	0.255423	−	0.569436i
$37$	−1.03438e19			−1.57130			−0.785651	−	0.618670i	$-0.787672\pi$
$37$	−1.03438e19			−1.57130			−0.785651	+	0.618670i	$0.787672\pi$
$38$			1.81929e18i			0.200678i
$39$	1.55382e19	−	1.00600e19i	1.25494	−	0.812499i
$40$	−2.51888e19			−1.50137
$41$			1.85510e19i			0.822168i	0.911598	+	0.411084i	$0.134850\pi$
$41$			1.85510e19i			0.822168i	−0.911598	+	0.411084i	$0.865150\pi$
$42$	6.02676e18	+	9.30863e18i	0.200029	+	0.308954i
$43$	2.09203e19			0.523537			0.261768	−	0.965131i	$-0.415694\pi$
$43$	2.09203e19			0.523537			0.261768	+	0.965131i	$0.415694\pi$
$44$		−	4.05877e19i		−	0.770836i
$45$	9.48595e19	+	4.25497e19i	1.37572	+	0.617087i
$46$	−2.82405e19			−0.314614
$47$			5.93575e19i			0.510859i	0.966828	+	0.255430i	$0.0822169\pi$
$47$			5.93575e19i			0.510859i	−0.966828	+	0.255430i	$0.917783\pi$
$48$	−1.70734e18	+	1.10540e18i	−0.0114137	+	0.00738964i
$49$	−1.22541e20			−0.639629
$50$		−	1.90610e20i		−	0.780738i
$51$	−7.55963e19	−	1.16762e20i	−0.244151	−	0.377103i
$52$	−3.64700e20			−0.933030
$53$			1.46669e20i			0.298558i	0.988795	+	0.149279i	$0.0476953\pi$
$53$			1.46669e20i			0.298558i	−0.988795	+	0.149279i	$0.952305\pi$
$54$	−3.72533e20	+	5.74162e19i	−0.605953	+	0.0933920i
$55$	1.42692e21			1.86229
$56$		−	5.68566e20i		−	0.597757i
$57$	−3.23178e20	+	2.09238e20i	−0.274754	+	0.177886i
$58$	3.40187e20			0.234737
$59$			3.04315e21i			1.71041i	0.518294	+	0.855203i	$0.326567\pi$
$59$			3.04315e21i			1.71041i	−0.518294	+	0.855203i	$0.673433\pi$
$60$	−1.11324e21	−	1.71945e21i	−0.511413	−	0.789903i
$61$	3.55521e21			1.33939			0.669696	−	0.742636i	$-0.266425\pi$
$61$	3.55521e21			1.33939			0.669696	+	0.742636i	$0.266425\pi$
$62$			5.55088e20i			0.172053i
$63$	−9.60439e20	+	2.14118e21i	−0.245687	+	0.547731i
$64$	−2.84294e21			−0.602015
$65$		−	1.28216e22i		−	2.25414i
$66$	−4.34265e21	+	2.81160e21i	−0.635664	+	0.411554i
$67$	−2.84438e21			−0.347608			−0.173804	−	0.984780i	$-0.555606\pi$
$67$	−2.84438e21			−0.347608			−0.173804	+	0.984780i	$0.555606\pi$
$68$			2.74055e21i			0.280370i
$69$	−3.24796e21	−	5.01663e21i	−0.278883	−	0.430748i
$70$	7.68118e21			0.554947
$71$			2.39541e22i			1.45975i	0.683578	+	0.729877i	$0.260423\pi$
$71$			2.39541e22i			1.45975i	−0.683578	+	0.729877i	$0.739577\pi$
$72$	1.76332e22	+	7.90947e21i	0.908535	+	0.407528i
$73$	−1.66222e22			−0.725795			−0.362898	−	0.931829i	$-0.618213\pi$
$73$	−1.66222e22			−0.725795			−0.362898	+	0.931829i	$0.618213\pi$
$74$		−	2.59763e22i		−	0.963379i
$75$	3.38599e22	−	2.19222e22i	1.06893	−	0.692067i
$76$	7.58539e21			0.204275
$77$			3.22087e22i			0.741454i
$78$	2.52636e22	+	3.90209e22i	0.498150	+	0.769417i
$79$	−6.08621e22			−1.02996			−0.514982	−	0.857201i	$-0.672201\pi$
$79$	−6.08621e22			−1.02996			−0.514982	+	0.857201i	$0.672201\pi$
$80$			1.40884e21i			0.0205013i
$81$	−5.30446e22	−	5.95731e22i	−0.664999	−	0.746844i
$82$	−4.65869e22			−0.504078
$83$		−	7.63158e22i		−	0.713965i	−0.934111	−	0.356983i	$-0.883806\pi$
$83$		−	7.63158e22i		−	0.713965i	0.934111	−	0.356983i	$-0.116194\pi$
$84$	3.88116e22	−	2.51281e22i	0.314492	−	0.203614i
$85$	−9.63483e22			−0.677356
$86$			5.25371e22i			0.320985i
$87$	3.91252e22	+	6.04307e22i	0.208078	+	0.321386i
$88$	2.65247e23			1.22987
$89$		−	1.24843e23i		−	0.505457i	−0.967537	−	0.252729i	$-0.918672\pi$
$89$		−	1.24843e23i		−	0.505457i	0.967537	−	0.252729i	$-0.0813280\pi$
$90$	−1.06855e23	+	2.38220e23i	−0.378341	+	0.843467i
$91$	2.89411e23			0.897466
$92$			1.17747e23i			0.320254i
$93$	−9.86056e22	+	6.38411e22i	−0.235563	+	0.152512i
$94$	−1.49064e23			−0.313212
$95$			2.66676e23i			0.493515i
$96$	−3.34353e23	−	5.16424e23i	−0.545696	−	0.842853i
$97$	9.42350e23			1.35816			0.679081	−	0.734064i	$-0.262379\pi$
$97$	9.42350e23			1.35816			0.679081	+	0.734064i	$0.262379\pi$
$98$		−	3.07736e23i		−	0.392161i
$99$	−9.98903e23	−	4.48063e23i	−1.12694	−	0.505495i
$100$	−7.94733e23			−0.794733
$101$			7.50404e23i			0.665945i	0.942937	+	0.332973i	$0.108052\pi$
$101$			7.50404e23i			0.665945i	−0.942937	+	0.332973i	$0.891948\pi$
$102$	2.93224e23	−	1.89844e23i	0.231205	−	0.149691i
$103$	−3.47131e23			−0.243471			−0.121735	−	0.992563i	$-0.538846\pi$
$103$	−3.47131e23			−0.243471			−0.121735	+	0.992563i	$0.538846\pi$
$104$		−	2.38337e24i		−	1.48865i
$105$	8.83417e23	+	1.36448e24i	0.491920	+	0.759794i
$106$	−3.68330e23			−0.183049
$107$			1.70879e24i			0.758725i	0.925248	+	0.379362i	$0.123857\pi$
$107$			1.70879e24i			0.758725i	−0.925248	+	0.379362i	$0.876143\pi$
$108$	2.39392e23	+	1.55325e24i	0.0950660	+	0.616815i
$109$	1.33408e24			0.474311			0.237156	−	0.971472i	$-0.423785\pi$
$109$	1.33408e24			0.474311			0.237156	+	0.971472i	$0.423785\pi$
$110$			3.58342e24i			1.14179i
$111$	4.61442e24	−	2.98755e24i	1.31899	−	0.853965i
$112$	−3.18005e22			−0.00816240
$113$		−	5.07760e24i		−	1.17143i	−0.810516	−	0.585716i	$-0.800813\pi$
$113$		−	5.07760e24i		−	1.17143i	0.810516	−	0.585716i	$-0.199187\pi$
$114$	−5.25457e23	−	8.11594e23i	−0.109063	−	0.168454i
$115$	−4.13956e24			−0.773714
$116$		−	1.41838e24i		−	0.238945i
$117$	−4.02607e24	+	8.97564e24i	−0.611858	+	1.36406i
$118$	−7.64223e24			−1.04866
$119$		−	2.17479e24i		−	0.269683i
$120$	1.12369e25	−	7.27518e24i	1.26029	−	0.815959i
$121$	−5.17623e24			−0.525520
$122$			8.92817e24i			0.821192i
$123$	−5.35799e24	−	8.27568e24i	−0.446828	−	0.690148i
$124$	2.31440e24			0.175137
$125$		−	5.99892e24i		−	0.412242i
$126$	−5.37714e24	−	2.41194e24i	−0.335818	−	0.150633i
$127$	2.15191e25			1.22231			0.611153	−	0.791513i	$-0.290706\pi$
$127$	2.15191e25			1.22231			0.611153	+	0.791513i	$0.290706\pi$
$128$			1.22824e25i			0.634984i
$129$	−9.33267e24	+	6.04233e24i	−0.439470	+	0.284530i
$130$	3.21988e25			1.38203
$131$			1.23397e25i			0.483113i	0.970387	+	0.241556i	$0.0776579\pi$
$131$			1.23397e25i			0.483113i	−0.970387	+	0.241556i	$0.922342\pi$
$132$	1.17227e25	+	1.81064e25i	0.418931	+	0.647059i
$133$	−6.01945e24			−0.196488
$134$		−	7.14306e24i		−	0.213121i
$135$	−5.46067e25	+	8.41621e24i	−1.49019	+	0.229674i
$136$	−1.79100e25			−0.447330
$137$		−	6.62917e25i		−	1.51640i	−0.652025	−	0.758198i	$-0.726080\pi$
$137$		−	6.62917e25i		−	1.51640i	0.652025	−	0.758198i	$-0.273920\pi$
$138$	1.25982e25	−	8.15658e24i	0.264095	−	0.170985i
$139$	2.84244e25			0.546404			0.273202	−	0.961957i	$-0.411917\pi$
$139$	2.84244e25			0.546404			0.273202	+	0.961957i	$0.411917\pi$
$140$		−	3.20261e25i		−	0.564894i
$141$	−1.71439e25	−	2.64797e25i	−0.277640	−	0.428828i
$142$	−6.01558e25			−0.894988
$143$			1.35016e26i			1.84651i
$144$	4.42385e23	−	9.86245e23i	0.00556481	−	0.0124061i
$145$	4.98655e25			0.577277
$146$		−	4.17432e25i		−	0.444991i
$147$	5.46660e25	−	3.53929e25i	0.536920	−	0.347623i
$148$	−1.08306e26			−0.980647
$149$			1.02661e24i			0.00857376i	0.999991	+	0.00428688i	$0.00136456\pi$
$149$			1.02661e24i			0.00857376i	−0.999991	+	0.00428688i	$0.998635\pi$
$150$	5.50530e25	+	8.50320e25i	0.424312	+	0.655371i
$151$	1.66595e26			1.18560			0.592802	−	0.805348i	$-0.298022\pi$
$151$	1.66595e26			1.18560			0.592802	+	0.805348i	$0.298022\pi$
$152$			4.95717e25i			0.325920i
$153$	6.74478e25	+	3.02540e25i	0.409893	+	0.183860i
$154$	−8.08854e25			−0.454592
$155$			8.13661e25i			0.423120i
$156$	1.62694e26	−	1.05335e26i	0.783209	−	0.507080i
$157$	−1.37763e26			−0.614236			−0.307118	−	0.951671i	$-0.599365\pi$
$157$	−1.37763e26			−0.614236			−0.307118	+	0.951671i	$0.599365\pi$
$158$		−	1.52843e26i		−	0.631479i
$159$	−4.23619e25	−	6.54299e25i	−0.162259	−	0.250617i
$160$	−4.26137e26			−1.51394
$161$		−	9.34388e25i		−	0.308047i
$162$	1.49605e26	−	1.33211e26i	0.457896	−	0.407717i
$163$	−8.27258e24			−0.0235174			−0.0117587	−	0.999931i	$-0.503743\pi$
$163$	−8.27258e24			−0.0235174			−0.0117587	+	0.999931i	$0.503743\pi$
$164$			1.94240e26i			0.513113i
$165$	−6.36557e26	+	4.12131e26i	−1.56325	+	1.01211i
$166$	1.91651e26			0.437738
$167$		−	5.66343e26i		−	1.20360i	−0.798647	−	0.601800i	$-0.794450\pi$
$167$		−	5.66343e26i		−	1.20360i	0.798647	−	0.601800i	$-0.205550\pi$
$168$	1.64216e26	+	2.53640e26i	0.324867	+	0.501772i
$169$	6.70382e26			1.23504
$170$		−	2.41959e26i		−	0.415293i
$171$	8.37380e25	−	1.86684e26i	0.133958	−	0.298644i
$172$	2.19049e26			0.326739
$173$			1.17148e27i			1.62997i	0.579482	+	0.814985i	$0.303255\pi$
$173$			1.17148e27i			1.62997i	−0.579482	+	0.814985i	$0.696745\pi$
$174$	−1.51759e26	+	9.82547e25i	−0.197044	+	0.127574i
$175$	6.30667e26			0.764440
$176$		−	1.48356e25i		−	0.0167939i
$177$	−8.78939e26	−	1.35756e27i	−0.929564	−	1.43576i
$178$	3.13517e26			0.309900
$179$			6.53157e26i			0.603644i	0.953364	+	0.301822i	$0.0975948\pi$
$179$			6.53157e26i			0.603644i	−0.953364	+	0.301822i	$0.902405\pi$
$180$	9.93239e26	+	4.45523e26i	0.858586	+	0.385123i
$181$	−7.09180e26			−0.573606			−0.286803	−	0.957990i	$-0.592592\pi$
$181$	−7.09180e26			−0.573606			−0.286803	+	0.957990i	$0.592592\pi$
$182$			7.26795e26i			0.550244i
$183$	−1.58600e27	+	1.02684e27i	−1.12432	+	0.727927i
$184$	−7.69493e26			−0.510965
$185$		−	3.80767e27i		−	2.36918i
$186$	−1.60323e26	−	2.47627e26i	−0.0935065	−	0.144425i
$187$	1.01458e27			0.554865
$188$			6.21510e26i			0.318826i
$189$	−1.89972e26	−	1.23259e27i	−0.0914424	−	0.593304i
$190$	−6.69701e26			−0.302578
$191$		−	7.88629e26i		−	0.334559i	−0.985910	−	0.167279i	$-0.946502\pi$
$191$		−	7.88629e26i		−	0.334559i	0.985910	−	0.167279i	$-0.0534982\pi$
$192$	1.26825e27	−	8.21112e26i	0.505347	−	0.327181i
$193$	−1.97908e27			−0.740928			−0.370464	−	0.928847i	$-0.620801\pi$
$193$	−1.97908e27			−0.740928			−0.370464	+	0.928847i	$0.620801\pi$
$194$			2.36652e27i			0.832700i
$195$	3.70320e27	+	5.71977e27i	1.22507	+	1.89218i
$196$	−1.28308e27			−0.399191
$197$			4.04257e27i			1.18321i	0.806227	+	0.591606i	$0.201506\pi$
$197$			4.04257e27i			1.18321i	−0.806227	+	0.591606i	$0.798494\pi$
$198$	1.12522e27	−	2.50854e27i	0.309923	−	0.690937i
$199$	4.12378e27			1.06920			0.534599	−	0.845106i	$-0.320463\pi$
$199$	4.12378e27			1.06920			0.534599	+	0.845106i	$0.320463\pi$
$200$		−	5.19371e27i		−	1.26800i
$201$	1.26889e27	−	8.21528e26i	0.291791	−	0.188916i
$202$	−1.88448e27			−0.408296
$203$			1.12557e27i			0.229837i
$204$	−7.91541e26	−	1.22257e27i	−0.152374	−	0.235349i
$205$	−6.82882e27			−1.23965
$206$		−	8.71747e26i		−	0.149274i
$207$	2.89786e27	+	1.29985e27i	0.468202	+	0.210015i
$208$	−1.33305e26			−0.0203276
$209$		−	2.80819e27i		−	0.404269i
$210$	−3.42661e27	+	2.21852e27i	−0.465836	+	0.301600i
$211$	5.93408e27			0.762015			0.381008	−	0.924572i	$-0.375577\pi$
$211$	5.93408e27			0.762015			0.381008	+	0.924572i	$0.375577\pi$
$212$			1.53572e27i			0.186330i
$213$	−6.91856e27	−	1.06860e28i	−0.793342	−	1.22535i
$214$	−4.29128e27			−0.465180
$215$			7.70101e27i			0.789380i
$216$	−1.01507e28	+	1.56447e27i	−0.984128	+	0.151678i
$217$	−1.83661e27			−0.168461
$218$			3.35026e27i			0.290804i
$219$	7.41524e27	−	4.80091e27i	0.609251	−	0.394452i
$220$	1.49408e28			1.16225
$221$		−	9.11651e27i		−	0.671616i
$222$	7.50262e27	+	1.15882e28i	0.523573	+	0.808684i
$223$	1.59105e28			1.05202			0.526012	−	0.850477i	$-0.323687\pi$
$223$	1.59105e28			1.05202			0.526012	+	0.850477i	$0.323687\pi$
$224$		−	9.61882e27i		−	0.602761i
$225$	−8.77336e27	+	1.95592e28i	−0.521166	+	1.16188i
$226$	1.27513e28			0.718215
$227$			1.40593e28i			0.751026i	0.926817	+	0.375513i	$0.122533\pi$
$227$			1.40593e28i			0.751026i	−0.926817	+	0.375513i	$0.877467\pi$
$228$	−3.38388e27	+	2.19085e27i	−0.171473	+	0.111018i
$229$	−1.67156e28			−0.803706			−0.401853	−	0.915704i	$-0.631634\pi$
$229$	−1.67156e28			−0.803706			−0.401853	+	0.915704i	$0.631634\pi$
$230$		−	1.03956e28i		−	0.474370i
$231$	−9.30268e27	−	1.43684e28i	−0.402962	−	0.622395i
$232$	9.26937e27			0.381237
$233$		−	1.50356e28i		−	0.587286i	−0.955915	−	0.293643i	$-0.905132\pi$
$233$		−	1.50356e28i		−	0.587286i	0.955915	−	0.293643i	$-0.0948678\pi$
$234$	−2.25404e28	−	1.01106e28i	−0.836319	−	0.375135i
$235$	−2.18502e28			−0.770265
$236$			3.18637e28i			1.06746i
$237$	2.71509e28	−	1.75785e28i	0.864577	−	0.559761i
$238$	5.46153e27			0.165345
$239$			7.05496e27i			0.203104i	0.994830	+	0.101552i	$0.0323809\pi$
$239$			7.05496e27i			0.203104i	−0.994830	+	0.101552i	$0.967619\pi$
$240$	−4.06909e26	−	6.28490e26i	−0.0111420	−	0.0172093i
$241$	−7.67737e28			−1.99990			−0.999949	−	0.0100656i	$-0.996796\pi$
$241$	−7.67737e28			−1.99990			−0.999949	+	0.0100656i	$0.996796\pi$
$242$		−	1.29990e28i		−	0.322201i
$243$	4.08697e28	+	1.12552e28i	0.964109	+	0.265508i
$244$	3.72253e28			0.835912
$245$		−	4.51086e28i		−	0.964421i
$246$	2.07826e28	−	1.34555e28i	0.423135	−	0.273954i
$247$	−2.52329e28			−0.489333
$248$			1.51250e28i			0.279431i
$249$	2.20419e28	+	3.40448e28i	0.388023	+	0.599320i
$250$	1.50650e28			0.252749
$251$			5.81761e28i			0.930379i	0.885211	+	0.465189i	$0.154014\pi$
$251$			5.81761e28i			0.930379i	−0.885211	+	0.465189i	$0.845986\pi$
$252$	−1.00564e28	+	2.24195e28i	−0.153333	+	0.341838i
$253$	4.35910e28			0.633798
$254$			5.40408e28i			0.749406i
$255$	4.29815e28	−	2.78278e28i	0.568590	−	0.368127i
$256$	−7.85412e28			−0.991329
$257$			2.86017e28i			0.344505i	0.985053	+	0.172252i	$0.0551044\pi$
$257$			2.86017e28i			0.344505i	−0.985053	+	0.172252i	$0.944896\pi$
$258$	−1.51740e28	−	2.34370e28i	−0.174448	−	0.269443i
$259$	8.59473e28			0.943268
$260$		−	1.34250e29i		−	1.40681i
$261$	−3.49079e28	−	1.56581e28i	−0.349331	−	0.156694i
$262$	−3.09885e28			−0.296200
$263$		−	1.20689e29i		−	1.10204i	−0.834491	−	0.551022i	$-0.814238\pi$
$263$		−	1.20689e29i		−	1.10204i	0.834491	−	0.551022i	$-0.185762\pi$
$264$	−1.18328e29	+	7.66101e28i	−1.03238	+	0.668403i
$265$	−5.39907e28			−0.450161
$266$		−	1.51166e28i		−	0.120469i
$267$	3.60579e28	+	5.56931e28i	0.274704	+	0.424293i
$268$	−2.97824e28			−0.216941
$269$			3.95103e28i			0.275222i	0.990486	+	0.137611i	$0.0439424\pi$
$269$			3.95103e28i			0.275222i	−0.990486	+	0.137611i	$0.956058\pi$
$270$	−2.11356e28	−	1.37133e29i	−0.140815	−	0.913646i
$271$	4.81446e28			0.306843			0.153421	−	0.988161i	$-0.450971\pi$
$271$	4.81446e28			0.306843			0.153421	+	0.988161i	$0.450971\pi$
$272$			1.00172e27i			0.00610831i
$273$	−1.29108e29	+	8.35892e28i	−0.753355	+	0.487751i
$274$	1.66478e29			0.929714
$275$			2.94218e29i			1.57281i
$276$	−3.40082e28	−	5.25273e28i	−0.174050	−	0.268829i
$277$	1.28248e29			0.628484			0.314242	−	0.949343i	$-0.398250\pi$
$277$	1.28248e29			0.628484			0.314242	+	0.949343i	$0.398250\pi$
$278$			7.13819e28i			0.335005i
$279$	2.55495e28	−	5.69596e28i	0.114850	−	0.256045i
$280$	2.09296e29			0.901288
$281$		−	2.68050e29i		−	1.10596i	−0.833195	−	0.552980i	$-0.813491\pi$
$281$		−	2.68050e29i		−	1.10596i	0.833195	−	0.552980i	$-0.186509\pi$
$282$	6.64981e28	−	4.30535e28i	0.262918	−	0.170223i
$283$	5.05618e28			0.191595			0.0957977	−	0.995401i	$-0.469460\pi$
$283$	5.05618e28			0.191595			0.0957977	+	0.995401i	$0.469460\pi$
$284$			2.50815e29i			0.911030i
$285$	−7.70228e28	−	1.18965e29i	−0.268214	−	0.414269i
$286$	−3.39064e29			−1.13211
$287$		−	1.54141e29i		−	0.493555i
$288$	2.98313e29	+	1.33810e29i	0.916141	+	0.410940i
$289$	2.70942e29			0.798184
$290$			1.25227e29i			0.353933i
$291$	−4.20387e29	+	2.72175e29i	−1.14007	+	0.738128i
$292$	−1.74045e29			−0.452968
$293$		−	9.30833e28i		−	0.232520i	−0.993219	−	0.116260i	$-0.962909\pi$
$293$		−	9.30833e28i		−	0.232520i	0.993219	−	0.116260i	$-0.0370906\pi$
$294$	8.88819e28	+	1.37282e29i	0.213130	+	0.329190i
$295$	−1.12022e30			−2.57892
$296$		−	7.07799e29i		−	1.56462i
$297$	5.75027e29	−	8.86255e28i	1.22071	−	0.188140i
$298$	−2.57812e27			−0.00525664
$299$		−	3.91687e29i		−	0.767157i
$300$	3.54534e29	−	2.29539e29i	0.667118	−	0.431918i
$301$	−1.73828e29			−0.314284
$302$			4.18370e29i			0.726904i
$303$	−2.16736e29	−	3.34759e29i	−0.361925	−	0.559011i
$304$	2.77260e27			0.00445046
$305$			1.30871e30i			2.01951i
$306$	−7.59767e28	+	1.69381e29i	−0.112726	+	0.251309i
$307$	1.36422e30			1.94637			0.973184	−	0.230029i	$-0.0738822\pi$
$307$	1.36422e30			1.94637			0.973184	+	0.230029i	$0.0738822\pi$
$308$			3.37245e29i			0.462740i
$309$	1.54857e29	−	1.00260e29i	0.204375	−	0.132320i
$310$	−2.04334e29			−0.259418
$311$		−	1.43850e30i		−	1.75706i	−0.477690	−	0.878529i	$-0.658526\pi$
$311$		−	1.43850e30i		−	1.75706i	0.477690	−	0.878529i	$-0.341474\pi$
$312$	6.88379e29	+	1.06323e30i	0.809045	+	1.24961i
$313$	1.50996e29			0.170779			0.0853895	−	0.996348i	$-0.472787\pi$
$313$	1.50996e29			0.170779			0.0853895	+	0.996348i	$0.472787\pi$
$314$		−	3.45962e29i		−	0.376593i
$315$	−7.88193e29	−	3.53548e29i	−0.825859	−	0.370443i
$316$	−6.37265e29			−0.642799
$317$			1.97048e30i			1.91364i	0.290673	+	0.956822i	$0.406121\pi$
$317$			1.97048e30i			1.91364i	−0.290673	+	0.956822i	$0.593879\pi$
$318$	1.64314e29	−	1.06383e29i	0.153656	−	0.0994825i
$319$	−5.25100e29			−0.472883
$320$		−	1.04652e30i		−	0.907709i
$321$	−4.93543e29	−	7.62301e29i	−0.412349	−	0.636892i
$322$	2.34652e29			0.188866
$323$			1.89614e29i			0.147042i
$324$	−5.55411e29	−	6.23768e29i	−0.415025	−	0.466104i
$325$	2.64369e30			1.90375
$326$		−	2.07748e28i		−	0.0144187i
$327$	−5.95139e29	+	3.85316e29i	−0.398149	+	0.257777i
$328$	−1.26939e30			−0.818672
$329$		−	4.93205e29i		−	0.306674i
$330$	−1.03498e30	−	1.59858e30i	−0.620534	−	0.958444i
$331$	−1.75751e30			−1.01616			−0.508081	−	0.861309i	$-0.669645\pi$
$331$	−1.75751e30			−1.01616			−0.508081	+	0.861309i	$0.669645\pi$
$332$		−	7.99074e29i		−	0.445585i
$333$	−1.19563e30	+	2.66552e30i	−0.643084	+	1.43368i
$334$	1.42225e30			0.737937
$335$		−	1.04705e30i		−	0.524117i
$336$	1.41864e28	−	9.18480e27i	0.00685172	−	0.00443607i
$337$	3.21462e30			1.49820			0.749101	−	0.662456i	$-0.230486\pi$
$337$	3.21462e30			1.49820			0.749101	+	0.662456i	$0.230486\pi$
$338$			1.68352e30i			0.757214i
$339$	1.46654e30	+	2.26514e30i	0.636645	+	0.983329i
$340$	−1.00883e30			−0.422737
$341$		−	8.56813e29i		−	0.346604i
$342$	4.68818e29	+	2.10291e29i	0.183101	+	0.0821309i
$343$	2.61006e30			0.984285
$344$			1.43152e30i			0.521311i
$345$	1.84668e30	−	1.19561e30i	0.649475	−	0.420495i
$346$	−2.94192e30			−0.999348
$347$			1.03264e30i			0.338839i	0.985544	+	0.169419i	$0.0541893\pi$
$347$			1.03264e30i			0.338839i	−0.985544	+	0.169419i	$0.945811\pi$
$348$	4.09665e29	+	6.32748e29i	0.129861	+	0.200576i
$349$	−2.95287e30			−0.904356			−0.452178	−	0.891928i	$-0.649353\pi$
$349$	−2.95287e30			−0.904356			−0.452178	+	0.891928i	$0.649353\pi$
$350$			1.58379e30i			0.468684i
$351$	−7.96344e29	−	5.16690e30i	−0.227727	−	1.47756i
$352$	4.48736e30			1.24016
$353$		−	3.99773e30i		−	1.06787i	−0.845527	−	0.533933i	$-0.820713\pi$
$353$		−	3.99773e30i		−	1.06787i	0.845527	−	0.533933i	$-0.179287\pi$
$354$	3.40924e30	−	2.20727e30i	0.880274	−	0.569923i
$355$	−8.81777e30			−2.20099
$356$		−	1.30719e30i		−	0.315455i
$357$	6.28134e29	+	9.70184e29i	0.146566	+	0.226379i
$358$	−1.64027e30			−0.370099
$359$			7.15703e30i			1.56171i	0.624715	+	0.780853i	$0.285215\pi$
$359$			7.15703e30i			1.56171i	−0.624715	+	0.780853i	$0.714785\pi$
$360$	−2.91156e30	+	6.49098e30i	−0.614463	+	1.36987i
$361$	−4.37394e30			−0.892867
$362$		−	1.78096e30i		−	0.351682i
$363$	2.30914e30	−	1.49503e30i	0.441135	−	0.285608i
$364$	3.03031e30			0.560107
$365$		−	6.11882e30i		−	1.09434i
$366$	−2.57868e30	−	3.98290e30i	−0.446298	−	0.689329i
$367$	−1.49350e30			−0.250158			−0.125079	−	0.992147i	$-0.539918\pi$
$367$	−1.49350e30			−0.250158			−0.125079	+	0.992147i	$0.539918\pi$
$368$			4.30386e28i			0.00697725i
$369$	4.78045e30	+	2.14430e30i	0.750158	+	0.336487i
$370$	9.56217e30			1.45257
$371$		−	1.21868e30i		−	0.179227i
$372$	−1.03246e30	+	6.68456e29i	−0.147014	+	0.0951826i
$373$	−1.31814e30			−0.181742			−0.0908712	−	0.995863i	$-0.528965\pi$
$373$	−1.31814e30			−0.181742			−0.0908712	+	0.995863i	$0.528965\pi$
$374$			2.54791e30i			0.340192i
$375$	1.73264e30	+	2.67614e30i	0.224044	+	0.346046i
$376$	−4.06167e30			−0.508687
$377$			4.71828e30i			0.572385i
$378$	3.09540e30	−	4.77075e29i	0.363760	−	0.0560641i
$379$	1.51830e31			1.72857			0.864287	−	0.503000i	$-0.167770\pi$
$379$	1.51830e31			1.72857			0.864287	+	0.503000i	$0.167770\pi$
$380$			2.79227e30i			0.308002i
$381$	−9.59978e30	+	6.21527e30i	−1.02603	+	0.664294i
$382$	1.98048e30			0.205121
$383$			4.35082e28i			0.00436703i	0.999998	+	0.00218351i	$0.000695034\pi$
$383$			4.35082e28i			0.00436703i	−0.999998	+	0.00218351i	$0.999305\pi$
$384$	−3.54746e30	−	5.47923e30i	−0.345098	−	0.533021i
$385$	−1.18564e31			−1.11795
$386$		−	4.97005e30i		−	0.454269i
$387$	2.41817e30	−	5.39102e30i	0.214267	−	0.477683i
$388$	9.86700e30			0.847626
$389$			1.87100e30i			0.155840i	0.996960	+	0.0779199i	$0.0248278\pi$
$389$			1.87100e30i			0.155840i	−0.996960	+	0.0779199i	$0.975172\pi$
$390$	−1.43640e31	+	9.29982e30i	−1.16011	+	0.751102i
$391$	−2.94334e30			−0.230526
$392$		−	8.38514e30i		−	0.636909i
$393$	−3.56401e30	−	5.50479e30i	−0.262560	−	0.405537i
$394$	−1.01521e31			−0.725437
$395$		−	2.24040e31i		−	1.55296i
$396$	−1.04591e31	−	4.69150e30i	−0.703322	−	0.315478i
$397$	2.33254e31			1.52175			0.760873	−	0.648901i	$-0.224771\pi$
$397$	2.33254e31			1.52175			0.760873	+	0.648901i	$0.224771\pi$
$398$			1.03560e31i			0.655534i
$399$	2.68530e30	−	1.73857e30i	0.164937	−	0.106787i
$400$	−2.90490e29			−0.0173145
$401$			2.02792e31i			1.17306i	0.809929	+	0.586528i	$0.199506\pi$
$401$			2.02792e31i			1.17306i	−0.809929	+	0.586528i	$0.800494\pi$
$402$	2.06310e30	+	3.18655e30i	0.115826	+	0.178899i
$403$	−7.69889e30			−0.419534
$404$			7.85720e30i			0.415615i
$405$	2.19295e31	−	1.95263e31i	1.12608	−	1.00267i
$406$	−2.82664e30			−0.140915
$407$			4.00961e31i			1.94075i
$408$	7.98972e30	−	5.17285e30i	0.375500	−	0.243113i
$409$	−1.84468e31			−0.841863			−0.420932	−	0.907092i	$-0.638297\pi$
$409$	−1.84468e31			−0.841863			−0.420932	+	0.907092i	$0.638297\pi$
$410$		−	1.71492e31i		−	0.760040i
$411$	1.91467e31	+	2.95730e31i	0.824124	+	1.27290i
$412$	−3.63468e30			−0.151950
$413$		−	2.52857e31i		−	1.02677i
$414$	−3.26430e30	+	7.27738e30i	−0.128762	+	0.287059i
$415$	2.80927e31			1.07650
$416$		−	4.03212e31i		−	1.50111i
$417$	−1.26803e31	+	8.20969e30i	−0.458665	+	0.296957i
$418$	7.05218e30			0.247861
$419$			1.26954e31i			0.433590i	0.976217	+	0.216795i	$0.0695603\pi$
$419$			1.26954e31i			0.433590i	−0.976217	+	0.216795i	$0.930440\pi$
$420$	9.24994e30	+	1.42870e31i	0.307006	+	0.474186i
$421$	−3.70643e31			−1.19556			−0.597779	−	0.801661i	$-0.703950\pi$
$421$	−3.70643e31			−1.19556			−0.597779	+	0.801661i	$0.703950\pi$
$422$			1.49022e31i			0.467198i
$423$	1.52960e31	+	6.86110e30i	0.466115	+	0.209078i
$424$	−1.00362e31			−0.297289
$425$		−	1.98661e31i		−	0.572066i
$426$	2.68358e31	−	1.73745e31i	0.751275	−	0.486404i
$427$	−2.95405e31			−0.804049
$428$			1.78921e31i			0.473519i
$429$	−3.89960e31	−	6.02311e31i	−1.00353	−	1.55001i
$430$	−1.93395e31			−0.483975
$431$		−	1.77312e31i		−	0.431530i	−0.976445	−	0.215765i	$-0.930775\pi$
$431$		−	1.77312e31i		−	0.431530i	0.976445	−	0.215765i	$-0.0692246\pi$
$432$	8.75024e28	+	5.67741e29i	0.00207117	+	0.0134383i
$433$	−1.93980e31			−0.446584			−0.223292	−	0.974752i	$-0.571680\pi$
$433$	−1.93980e31			−0.446584			−0.223292	+	0.974752i	$0.571680\pi$
$434$		−	4.61226e30i		−	0.103285i
$435$	−2.22452e31	+	1.44024e31i	−0.484580	+	0.313736i
$436$	1.39686e31			0.296017
$437$			8.14668e30i			0.167959i
$438$	1.20565e31	+	1.86218e31i	0.241842	+	0.373537i
$439$	5.16945e31			1.00895			0.504476	−	0.863426i	$-0.331686\pi$
$439$	5.16945e31			1.00895			0.504476	+	0.863426i	$0.331686\pi$
$440$			9.76404e31i			1.85437i
$441$	−1.41644e31	+	3.15779e31i	−0.261779	+	0.583606i
$442$	2.28942e31			0.411773
$443$		−	6.85593e31i		−	1.20011i	−0.799958	−	0.600055i	$-0.795145\pi$
$443$		−	6.85593e31i		−	1.20011i	0.799958	−	0.600055i	$-0.204855\pi$
$444$	4.83159e31	−	3.12816e31i	0.823180	−	0.532958i
$445$	4.59561e31			0.762120
$446$			3.99559e31i			0.645005i
$447$	−2.96512e29	−	4.57977e29i	−0.00465963	−	0.00719703i
$448$	2.36221e31			0.361396
$449$		−	4.10228e31i		−	0.611039i	−0.952186	−	0.305519i	$-0.901170\pi$
$449$		−	4.10228e31i		−	0.611039i	0.952186	−	0.305519i	$-0.0988301\pi$
$450$	−4.91188e31	−	2.20325e31i	−0.712356	−	0.319531i
$451$	7.19098e31			1.01548
$452$		−	5.31657e31i		−	0.731089i
$453$	−7.43190e31	+	4.81170e31i	−0.995226	+	0.644347i
$454$	−3.53071e31			−0.460460
$455$			1.06535e32i			1.35318i
$456$	−1.43176e31	−	2.21142e31i	−0.177130	−	0.273585i
$457$	3.99710e31			0.481671			0.240835	−	0.970566i	$-0.422579\pi$
$457$	3.99710e31			0.481671			0.240835	+	0.970566i	$0.422579\pi$
$458$		−	4.19779e31i		−	0.492759i
$459$	−3.88269e31	+	5.98416e30i	−0.443997	+	0.0684307i
$460$	−4.33438e31			−0.482874
$461$			5.89356e31i			0.639685i	0.947471	+	0.319843i	$0.103630\pi$
$461$			5.89356e31i			0.639685i	−0.947471	+	0.319843i	$0.896370\pi$
$462$	3.60834e31	−	2.33617e31i	0.381595	−	0.247060i
$463$	−6.10063e31			−0.628641			−0.314321	−	0.949317i	$-0.601777\pi$
$463$	−6.10063e31			−0.628641			−0.314321	+	0.949317i	$0.601777\pi$
$464$		−	5.18446e29i		−	0.00520580i
$465$	−2.35006e31	−	3.62978e31i	−0.229955	−	0.355177i
$466$	3.77588e31			0.360070
$467$		−	1.42945e32i		−	1.32852i	−0.747503	−	0.664259i	$-0.768747\pi$
$467$		−	1.42945e32i		−	1.32852i	0.747503	−	0.664259i	$-0.231253\pi$
$468$	−4.21555e31	+	9.39806e31i	−0.381859	+	0.851310i
$469$	2.36341e31			0.208672
$470$		−	5.48721e31i		−	0.472256i
$471$	6.14566e31	−	3.97893e31i	0.515605	−	0.333823i
$472$	−2.08234e32			−1.70313
$473$		−	8.10942e31i		−	0.646631i
$474$	4.41448e31	+	6.81838e31i	0.343194	+	0.530079i
$475$	−5.49861e31			−0.416802
$476$		−	2.27714e31i		−	0.168309i
$477$	3.77957e31	+	1.69534e31i	0.272409	+	0.122190i
$478$	−1.77171e31			−0.124525
$479$			2.37636e32i			1.62887i	0.580256	+	0.814434i	$0.302953\pi$
$479$			2.37636e32i			1.62887i	−0.580256	+	0.814434i	$0.697047\pi$
$480$	1.90102e32	−	1.23079e32i	1.27084	−	0.822791i
$481$	3.60283e32			2.34911
$482$		−	1.92801e32i		−	1.22615i
$483$	2.69875e31	+	4.16835e31i	0.167416	+	0.258582i
$484$	−5.41984e31			−0.327976
$485$			3.46890e32i			2.04781i
$486$	−2.82651e31	+	1.02636e32i	−0.162785	+	0.591103i
$487$	−3.29449e32			−1.85115			−0.925573	−	0.378568i	$-0.876416\pi$
$487$	−3.29449e32			−1.85115			−0.925573	+	0.378568i	$0.876416\pi$
$488$			2.43273e32i			1.33370i
$489$	3.69044e30	−	2.38933e30i	0.0197411	−	0.0127811i
$490$	1.13281e32			0.591294
$491$		−	1.20947e32i		−	0.616053i	−0.951378	−	0.308027i	$-0.900331\pi$
$491$		−	1.20947e32i		−	0.616053i	0.951378	−	0.308027i	$-0.0996686\pi$
$492$	−5.61016e31	−	8.66516e31i	−0.278865	−	0.430720i
$493$	3.54557e31			0.171998
$494$		−	6.33673e31i		−	0.300014i
$495$	1.64937e32	−	3.67707e32i	0.762177	−	1.69918i
$496$	8.45955e29			0.00381564
$497$		−	1.99036e32i		−	0.876305i
$498$	−8.54965e31	+	5.53537e31i	−0.367448	+	0.237900i
$499$	−1.00770e32			−0.422789			−0.211395	−	0.977401i	$-0.567801\pi$
$499$	−1.00770e32			−0.422789			−0.211395	+	0.977401i	$0.567801\pi$
$500$		−	6.28124e31i		−	0.257280i
$501$	1.63574e32	+	2.52649e32i	0.654128	+	1.01033i
$502$	−1.46097e32			−0.570423
$503$		−	1.48102e32i		−	0.564607i	−0.959325	−	0.282304i	$-0.908901\pi$
$503$		−	1.48102e32i		−	0.564607i	0.959325	−	0.282304i	$-0.0910985\pi$
$504$	−1.46515e32	−	6.57202e31i	−0.545402	−	0.244643i
$505$	−2.76232e32			−1.00410
$506$			1.09470e32i			0.388586i
$507$	−2.99060e32	+	1.93623e32i	−1.03672	+	0.671215i
$508$	2.25319e32			0.762839
$509$		−	2.16830e32i		−	0.716978i	−0.933534	−	0.358489i	$-0.883292\pi$
$509$		−	2.16830e32i		−	0.716978i	0.933534	−	0.358489i	$-0.116708\pi$
$510$	6.98838e31	+	1.07939e32i	0.225702	+	0.348607i
$511$	1.38115e32			0.435702
$512$			8.82421e30i			0.0271917i
$513$	1.65631e31	+	1.07466e32i	0.0498579	+	0.323492i
$514$	−7.18273e31			−0.211219
$515$		−	1.27783e32i		−	0.367101i
$516$	−9.77189e31	+	6.32670e31i	−0.274272	+	0.177575i
$517$	2.30089e32			0.630972
$518$			2.15839e32i			0.578325i
$519$	−3.38352e32	−	5.22601e32i	−0.885850	−	1.36824i
$520$	8.77347e32			2.24456
$521$			4.79275e32i			1.19821i	0.800672	+	0.599104i	$0.204476\pi$
$521$			4.79275e32i			1.19821i	−0.800672	+	0.599104i	$0.795524\pi$
$522$	3.93220e31	−	8.76638e31i	0.0960705	−	0.214178i
$523$	−2.63835e32			−0.629958			−0.314979	−	0.949099i	$-0.601997\pi$
$523$	−2.63835e32			−0.629958			−0.314979	+	0.949099i	$0.601997\pi$
$524$			1.29204e32i			0.301510i
$525$	−2.81343e32	+	1.82153e32i	−0.641690	+	0.415455i
$526$	3.03085e32			0.675672
$527$			5.78536e31i			0.126067i
$528$	4.28488e30	+	6.61821e30i	0.00912708	+	0.0140972i
$529$	3.53791e32			0.736680
$530$		−	1.35586e32i		−	0.275998i
$531$	7.84197e32	+	3.51756e32i	1.56060	+	0.700014i
$532$	−6.30274e31			−0.122628
$533$		−	6.46145e32i		−	1.22915i
$534$	−1.39862e32	+	9.05518e31i	−0.260138	+	0.168423i
$535$	−6.29026e32			−1.14399
$536$		−	1.94633e32i		−	0.346130i
$537$	−1.88648e32	−	2.91376e32i	−0.328066	−	0.506714i
$538$	−9.92219e31			−0.168741
$539$			4.75009e32i			0.790018i
$540$	−5.71767e32	+	8.81230e31i	−0.930024	+	0.143339i
$541$	−3.78046e32			−0.601419			−0.300709	−	0.953716i	$-0.597223\pi$
$541$	−3.78046e32			−0.601419			−0.300709	+	0.953716i	$0.597223\pi$
$542$			1.20905e32i			0.188128i
$543$	3.16368e32	−	2.04829e32i	0.481499	−	0.311741i
$544$	−3.02995e32			−0.451075
$545$			4.91089e32i			0.715158i
$546$	−2.09917e32	−	3.24227e32i	−0.299044	−	0.461888i
$547$	−3.69487e32			−0.514934			−0.257467	−	0.966287i	$-0.582888\pi$
$547$	−3.69487e32			−0.514934			−0.257467	+	0.966287i	$0.582888\pi$
$548$		−	6.94116e32i		−	0.946380i
$549$	4.10945e32	−	9.16152e32i	0.548170	−	1.22208i
$550$	−7.38867e32			−0.964305
$551$		−	9.81355e31i		−	0.125316i
$552$	3.43275e32	−	2.22249e32i	0.428917	−	0.277697i
$553$	5.05707e32			0.618297
$554$			3.22069e32i			0.385329i
$555$	1.09975e33	+	1.69862e33i	1.28759	+	1.98875i
$556$	2.97621e32			0.341010
$557$			3.59246e32i			0.402837i	0.979505	+	0.201419i	$0.0645552\pi$
$557$			3.59246e32i			0.402837i	−0.979505	+	0.201419i	$0.935445\pi$
$558$	1.43042e32	+	6.41623e31i	0.156983	+	0.0704157i
$559$	−7.28672e32			−0.782691
$560$		−	1.17061e31i		−	0.0123071i
$561$	−4.52609e32	+	2.93037e32i	−0.465767	+	0.301556i
$562$	6.73151e32			0.678073
$563$		−	1.35875e33i		−	1.33980i	−0.742453	−	0.669898i	$-0.766338\pi$
$563$		−	1.35875e33i		−	1.33980i	0.742453	−	0.669898i	$-0.233662\pi$
$564$	−1.79508e32	−	2.77259e32i	−0.173274	−	0.267631i
$565$	1.86912e33			1.76627
$566$			1.26975e32i			0.117469i
$567$	4.40751e32	+	4.94996e32i	0.399205	+	0.448337i
$568$	−1.63911e33			−1.45355
$569$		−	1.73444e31i		−	0.0150596i	−0.999972	−	0.00752978i	$-0.997603\pi$
$569$		−	1.73444e31i		−	0.0150596i	0.999972	−	0.00752978i	$-0.00239683\pi$
$570$	2.98757e32	−	1.93427e32i	0.253992	−	0.164444i
$571$	−5.61122e32			−0.467115			−0.233558	−	0.972343i	$-0.575037\pi$
$571$	−5.61122e32			−0.467115			−0.233558	+	0.972343i	$0.575037\pi$
$572$			1.41370e33i			1.15240i
$573$	2.27776e32	+	3.51811e32i	0.181825	+	0.280837i
$574$	3.87093e32			0.302603
$575$		−	8.53540e32i		−	0.653446i
$576$	−3.28613e32	+	7.32604e32i	−0.246386	+	0.549287i
$577$	−1.03540e33			−0.760324			−0.380162	−	0.924920i	$-0.624132\pi$
$577$	−1.03540e33			−0.760324			−0.380162	+	0.924920i	$0.624132\pi$
$578$			6.80415e32i			0.489373i
$579$	8.82878e32	−	5.71609e32i	0.621953	−	0.402677i
$580$	5.22123e32			0.360277
$581$			6.34112e32i			0.428600i
$582$	−6.83510e32	−	1.05571e33i	−0.452552	−	0.698989i
$583$	5.68540e32			0.368755
$584$		−	1.13741e33i		−	0.722709i
$585$	−3.30403e33	−	1.48204e33i	−2.05671	−	0.922549i
$586$	2.33759e32			0.142560
$587$			5.66709e32i			0.338612i	0.985564	+	0.169306i	$0.0541527\pi$
$587$			5.66709e32i			0.338612i	−0.985564	+	0.169306i	$0.945847\pi$
$588$	5.72388e32	−	3.70586e32i	0.335091	−	0.216951i
$589$	1.60129e32			0.0918515
$590$		−	2.81319e33i		−	1.58116i
$591$	−1.16760e33	−	1.80341e33i	−0.643047	−	0.993217i
$592$	−3.95880e31			−0.0213650
$593$			1.33502e33i			0.706046i	0.935615	+	0.353023i	$0.114846\pi$
$593$			1.33502e33i			0.706046i	−0.935615	+	0.353023i	$0.885154\pi$
$594$	2.22564e32	+	1.44406e33i	0.115350	+	0.748425i
$595$	8.00564e32			0.406623
$596$			1.07493e31i			0.00535087i
$597$	−1.83964e33	+	1.19105e33i	−0.897512	+	0.581083i
$598$	9.83639e32			0.470350
$599$			3.46777e33i			1.62528i	0.582765	+	0.812640i	$0.301971\pi$
$599$			3.46777e33i			1.62528i	−0.582765	+	0.812640i	$0.698029\pi$
$600$	1.50007e33	+	2.31694e33i	0.689125	+	1.06439i
$601$	4.72137e32			0.212606			0.106303	−	0.994334i	$-0.466099\pi$
$601$	4.72137e32			0.212606			0.106303	+	0.994334i	$0.466099\pi$
$602$		−	4.36534e32i		−	0.192690i
$603$	−3.28780e32	+	7.32975e32i	−0.142265	+	0.317162i
$604$	1.74436e33			0.739934
$605$		−	1.90543e33i		−	0.792371i
$606$	8.40677e32	−	5.44286e32i	0.342734	−	0.221899i
$607$	3.27973e33			1.31091			0.655456	−	0.755233i	$-0.272476\pi$
$607$	3.27973e33			1.31091			0.655456	+	0.755233i	$0.272476\pi$
$608$			8.38639e32i			0.328649i
$609$	−3.25093e32	−	5.02122e32i	−0.124911	−	0.192931i
$610$	−3.28656e33			−1.23818
$611$		−	2.06747e33i		−	0.763737i
$612$	7.06221e32	+	3.16779e32i	0.255813	+	0.114746i
$613$	−4.43029e32			−0.157364			−0.0786822	−	0.996900i	$-0.525071\pi$
$613$	−4.43029e32			−0.157364			−0.0786822	+	0.996900i	$0.525071\pi$
$614$			3.42596e33i			1.19333i
$615$	3.04637e33	−	1.97234e33i	1.04059	−	0.673720i
$616$	−2.20395e33			−0.738301
$617$		−	3.96264e33i		−	1.30185i	−0.759140	−	0.650927i	$-0.774380\pi$
$617$		−	3.96264e33i		−	1.30185i	0.759140	−	0.650927i	$-0.225620\pi$
$618$	2.51783e32	+	3.88890e32i	0.0811267	+	0.125304i
$619$	−2.19510e33			−0.693693			−0.346846	−	0.937922i	$-0.612748\pi$
$619$	−2.19510e33			−0.693693			−0.346846	+	0.937922i	$0.612748\pi$
$620$			8.51955e32i			0.264068i
$621$	−1.66818e33	+	2.57107e32i	−0.507158	+	0.0781653i
$622$	3.61250e33			1.07727
$623$			1.03733e33i			0.303431i
$624$	5.94679e31	−	3.85018e31i	0.0170635	−	0.0110475i
$625$	−2.31579e33			−0.651838
$626$			3.79196e32i			0.104706i
$627$	8.11076e32	+	1.25275e33i	0.219711	+	0.339354i
$628$	−1.44246e33			−0.383344
$629$		−	2.70736e33i		−	0.705892i
$630$	8.87862e32	−	1.97938e33i	0.227122	−	0.506341i
$631$	−4.54010e33			−1.13950			−0.569748	−	0.821819i	$-0.692959\pi$
$631$	−4.54010e33			−1.13950			−0.569748	+	0.821819i	$0.692959\pi$
$632$		−	4.16463e33i		−	1.02558i
$633$	−2.64722e33	+	1.71391e33i	−0.639655	+	0.414137i
$634$	−4.94845e33			−1.17327
$635$			7.92143e33i			1.84297i
$636$	−4.43555e32	−	6.85093e32i	−0.101266	−	0.156410i
$637$	4.26819e33			0.956248
$638$		−	1.31868e33i		−	0.289929i
$639$	6.17280e33	+	2.76884e33i	1.33190	+	0.597431i
$640$	−4.52128e33			−0.957418
$641$		−	6.91601e33i		−	1.43734i	−0.695351	−	0.718670i	$-0.744751\pi$
$641$		−	6.91601e33i		−	1.43734i	0.695351	−	0.718670i	$-0.255249\pi$
$642$	1.91436e33	−	1.23943e33i	0.390484	−	0.252814i
$643$	3.18842e33			0.638327			0.319163	−	0.947700i	$-0.396598\pi$
$643$	3.18842e33			0.638327			0.319163	+	0.947700i	$0.396598\pi$
$644$		−	9.78363e32i		−	0.192252i
$645$	−2.22425e33	−	3.43546e33i	−0.429009	−	0.662625i
$646$	−4.76176e32			−0.0901524
$647$			7.84492e33i			1.45793i	0.684550	+	0.728966i	$0.259999\pi$
$647$			7.84492e33i			1.45793i	−0.684550	+	0.728966i	$0.740001\pi$
$648$	4.07642e33	−	3.62970e33i	0.743668	−	0.662172i
$649$	1.17963e34			2.11256
$650$			6.63909e33i			1.16721i
$651$	8.19320e32	−	5.30459e32i	0.141410	−	0.0915545i
$652$	−8.66191e31			−0.0146772
$653$			8.51699e33i			1.41686i	0.705779	+	0.708432i	$0.250597\pi$
$653$			8.51699e33i			1.41686i	−0.705779	+	0.708432i	$0.749403\pi$
$654$	−9.67640e32	−	1.49457e33i	−0.158045	−	0.244108i
$655$	−4.54238e33			−0.728429
$656$			7.09985e31i			0.0111790i
$657$	−1.92135e33	+	4.28342e33i	−0.297045	+	0.662226i
$658$	1.23858e33			0.188024
$659$		−	1.01641e34i		−	1.51511i	−0.652769	−	0.757557i	$-0.726393\pi$
$659$		−	1.01641e34i		−	1.51511i	0.652769	−	0.757557i	$-0.273607\pi$
$660$	−6.66515e33	+	4.31527e33i	−0.975624	+	0.631657i
$661$	−6.06911e32			−0.0872384			−0.0436192	−	0.999048i	$-0.513889\pi$
$661$	−6.06911e32			−0.0872384			−0.0436192	+	0.999048i	$0.513889\pi$
$662$		−	4.41363e33i		−	0.623017i
$663$	2.63308e33	+	4.06692e33i	0.365007	+	0.563771i
$664$	5.22208e33			0.710930
$665$		−	2.21583e33i		−	0.296262i
$666$	−6.69391e33	−	3.00259e33i	−0.879000	−	0.394280i
$667$	1.52334e33			0.196466
$668$		−	5.92997e33i		−	0.751165i
$669$	−7.09775e33	+	4.59536e33i	−0.883095	+	0.571750i
$670$	2.62944e33			0.321341
$671$		−	1.37812e34i		−	1.65431i
$672$	2.77816e33	+	4.29100e33i	0.327586	+	0.505973i
$673$	−1.05795e34			−1.22542			−0.612710	−	0.790308i	$-0.709921\pi$
$673$	−1.05795e34			−1.22542			−0.612710	+	0.790308i	$0.709921\pi$
$674$			8.07284e33i			0.918560i
$675$	−1.73534e33	−	1.12594e34i	−0.193973	−	1.25855i
$676$	7.01932e33			0.770788
$677$			1.68398e34i			1.81666i	0.418254	+	0.908330i	$0.362642\pi$
$677$			1.68398e34i			1.81666i	−0.418254	+	0.908330i	$0.637358\pi$
$678$	−5.68843e33	+	3.68291e33i	−0.602887	+	0.390332i
$679$	−7.83004e33			−0.815317
$680$		−	6.59286e33i		−	0.674476i
$681$	−4.06070e33	−	6.27194e33i	−0.408164	−	0.630430i
$682$	2.15171e33			0.212506
$683$		−	6.76012e33i		−	0.656004i	−0.944677	−	0.328002i	$-0.893625\pi$
$683$		−	6.76012e33i		−	0.656004i	0.944677	−	0.328002i	$-0.106375\pi$
$684$	8.76790e32	−	1.95470e33i	0.0836031	−	0.186383i
$685$	2.44027e34			2.28639
$686$			6.55462e33i			0.603473i
$687$	7.45693e33	−	4.82790e33i	0.674651	−	0.436795i
$688$	8.00666e31			0.00711853
$689$		−	5.10861e33i		−	0.446346i
$690$	3.00253e33	+	4.63755e33i	0.257809	+	0.398198i
$691$	−1.88650e34			−1.59191			−0.795957	−	0.605353i	$-0.793032\pi$
$691$	−1.88650e34			−1.59191			−0.795957	+	0.605353i	$0.793032\pi$
$692$			1.22661e34i			1.01726i
$693$	8.29994e33	+	3.72298e33i	0.676513	+	0.303453i
$694$	−2.59325e33			−0.207745
$695$			1.04633e34i			0.823858i
$696$	−4.13511e33	+	2.67723e33i	−0.320019	+	0.207193i
$697$	−4.85548e33			−0.369351
$698$		−	7.41552e33i		−	0.554468i
$699$	4.34266e33	+	6.70746e33i	0.319176	+	0.492983i
$700$	6.60348e33			0.477086
$701$			4.38316e33i			0.311294i	0.987813	+	0.155647i	$0.0497463\pi$
$701$			4.38316e33i			0.311294i	−0.987813	+	0.155647i	$0.950254\pi$
$702$	1.29756e34	−	1.99985e33i	0.905904	−	0.139622i
$703$	−7.49351e33			−0.514306
$704$			1.10202e34i			0.743561i
$705$	9.74746e33	−	6.31088e33i	0.646579	−	0.418620i
$706$	1.00395e34			0.654718
$707$		−	6.23515e33i		−	0.399773i
$708$	−9.20304e33	−	1.42145e34i	−0.580139	−	0.896053i
$709$	1.07367e34			0.665449			0.332724	−	0.943024i	$-0.392032\pi$
$709$	1.07367e34			0.665449			0.332724	+	0.943024i	$0.392032\pi$
$710$		−	2.21440e34i		−	1.34945i
$711$	−7.03501e33	+	1.56837e34i	−0.421531	+	0.939754i
$712$	8.54267e33			0.503308
$713$			2.48565e33i			0.144001i
$714$	−2.43641e33	+	1.57743e33i	−0.138795	+	0.0898609i
$715$	−4.97008e34			−2.78414
$716$			6.83896e33i			0.376733i
$717$	−2.03765e33	−	3.14725e33i	−0.110382	−	0.170491i
$718$	−1.79734e34			−0.957495
$719$		−	2.03907e34i		−	1.06828i	−0.845395	−	0.534142i	$-0.820635\pi$
$719$		−	2.03907e34i		−	1.06828i	0.845395	−	0.534142i	$-0.179365\pi$
$720$	3.63048e32	+	1.62847e32i	0.0187057	+	0.00839053i
$721$	2.88433e33			0.146158
$722$		−	1.09842e34i		−	0.547424i
$723$	3.42491e34	−	2.21742e34i	1.67876	−	1.08690i
$724$	−7.42556e33			−0.357986
$725$			1.02818e34i			0.487543i
$726$	3.75445e33	+	5.79893e33i	0.175108	+	0.270463i
$727$	−2.28961e34			−1.05038			−0.525192	−	0.850984i	$-0.676006\pi$
$727$	−2.28961e34			−1.05038			−0.525192	+	0.850984i	$0.676006\pi$
$728$			1.98036e34i			0.893650i
$729$	−2.14829e34	+	6.78320e33i	−0.953594	+	0.301096i
$730$	1.53661e34			0.670950
$731$			5.47563e33i			0.235194i
$732$	−1.66064e34	+	1.07516e34i	−0.701685	+	0.454298i
$733$	3.98718e34			1.65736			0.828682	−	0.559720i	$-0.189091\pi$
$733$	3.98718e34			1.65736			0.828682	+	0.559720i	$0.189091\pi$
$734$		−	3.75062e33i		−	0.153374i
$735$	1.30285e34	+	2.01232e34i	0.524140	+	0.809559i
$736$	−1.30180e34			−0.515243
$737$			1.10258e34i			0.429337i
$738$	−5.38495e33	+	1.20051e34i	−0.206303	+	0.459928i
$739$	3.89922e34			1.46975			0.734877	−	0.678201i	$-0.237240\pi$
$739$	3.89922e34			1.46975			0.734877	+	0.678201i	$0.237240\pi$
$740$		−	3.98687e34i		−	1.47860i
$741$	1.12565e34	−	7.28791e33i	0.410758	−	0.265941i
$742$	3.06047e33			0.109886
$743$			1.04111e34i			0.367815i	0.982944	+	0.183907i	$0.0588746\pi$
$743$			1.04111e34i			0.367815i	−0.982944	+	0.183907i	$0.941125\pi$
$744$	−4.36847e33	−	6.74731e33i	−0.151864	−	0.234561i
$745$	−3.77907e32			−0.0129274
$746$		−	3.31024e33i		−	0.111428i
$747$	−1.96660e34	−	8.82129e33i	−0.651432	−	0.292203i
$748$	1.06233e34			0.346290
$749$		−	1.41985e34i		−	0.455470i
$750$	−6.72058e33	+	4.35116e33i	−0.212164	+	0.137363i
$751$	5.18062e34			1.60954			0.804772	−	0.593585i	$-0.202288\pi$
$751$	5.18062e34			1.60954			0.804772	+	0.593585i	$0.202288\pi$
$752$			2.27174e32i			0.00694615i
$753$	−1.68027e34	−	2.59526e34i	−0.505638	−	0.780983i
$754$	−1.18490e34			−0.350934
$755$			6.13256e34i			1.78763i
$756$	−1.98913e33	−	1.29060e34i	−0.0570690	−	0.370280i
$757$	1.41190e33			0.0398706			0.0199353	−	0.999801i	$-0.493654\pi$
$757$	1.41190e33			0.0398706			0.0199353	+	0.999801i	$0.493654\pi$
$758$			3.81290e34i			1.05980i
$759$	−1.94462e34	+	1.25902e34i	−0.532025	+	0.344454i
$760$	−1.82479e34			−0.491417
$761$			3.79755e34i			1.00667i	0.864091	+	0.503335i	$0.167894\pi$
$761$			3.79755e34i			1.00667i	−0.864091	+	0.503335i	$0.832106\pi$
$762$	−1.56083e34	−	2.41079e34i	−0.407284	−	0.629070i
$763$	−1.10849e34			−0.284733
$764$		−	8.25745e33i		−	0.208798i
$765$	−1.11368e34	+	2.48283e34i	−0.277220	+	0.618030i
$766$	−1.09262e32			−0.00267746
$767$		−	1.05995e35i		−	2.55707i
$768$	3.50376e34	−	2.26847e34i	0.832146	−	0.538764i
$769$	−4.15614e34			−0.971795			−0.485897	−	0.874016i	$-0.661507\pi$
$769$	−4.15614e34			−0.971795			−0.485897	+	0.874016i	$0.661507\pi$
$770$		−	2.97748e34i		−	0.685425i
$771$	−8.26091e33	−	1.27594e34i	−0.187230	−	0.289186i
$772$	−2.07222e34			−0.462412
$773$		−	6.17444e34i		−	1.35657i	−0.734797	−	0.678287i	$-0.762723\pi$
$773$		−	6.17444e34i		−	1.35657i	0.734797	−	0.678287i	$-0.237277\pi$
$774$	1.35384e34	+	6.07273e33i	0.292871	+	0.131369i
$775$	−1.67769e34			−0.357349
$776$			6.44825e34i			1.35239i
$777$	−3.83415e34	+	2.48238e34i	−0.791802	+	0.512643i
$778$	−4.69862e33			−0.0955466
$779$			1.34391e34i			0.269105i
$780$	3.87749e34	+	5.98896e34i	0.764566	+	1.18091i
$781$	9.28541e34			1.80297
$782$		−	7.39159e33i		−	0.141337i
$783$	2.00950e34	−	3.09712e33i	0.378397	−	0.0583200i
$784$	−4.68990e32			−0.00869702
$785$		−	5.07120e34i		−	0.926135i
$786$	1.38241e34	−	8.95028e33i	0.248638	−	0.160978i
$787$	−2.90981e34			−0.515428			−0.257714	−	0.966221i	$-0.582969\pi$
$787$	−2.90981e34			−0.515428			−0.257714	+	0.966221i	$0.582969\pi$
$788$			4.23282e34i			0.738440i
$789$	3.48581e34	+	5.38400e34i	0.598934	+	0.925083i
$790$	5.62630e34			0.952134
$791$			4.21901e34i			0.703222i
$792$	3.06597e34	−	6.83522e34i	0.503346	−	1.12215i
$793$	−1.23831e35			−2.00240
$794$			5.85768e34i			0.932995i
$795$	2.40855e34	−	1.55939e34i	0.377877	−	0.244652i
$796$	4.31786e34			0.667285
$797$			4.28765e34i			0.652708i	0.945248	+	0.326354i	$0.105820\pi$
$797$			4.28765e34i			0.652708i	−0.945248	+	0.326354i	$0.894180\pi$
$798$	4.36605e33	+	6.74358e33i	0.0654718	+	0.101124i
$799$	−1.55361e34			−0.229498
$800$		−	8.78655e34i		−	1.27861i
$801$	−3.21712e34	−	1.44305e34i	−0.461186	−	0.206867i
$802$	−5.09270e34			−0.719210
$803$			6.44332e34i			0.896444i
$804$	1.32861e34	−	8.60192e33i	0.182106	−	0.117902i
$805$	3.43959e34			0.464468
$806$		−	1.93341e34i		−	0.257220i
$807$	−1.14116e34	−	1.76257e34i	−0.149576	−	0.231028i
$808$	−5.13481e34			−0.663114
$809$		−	1.25559e35i		−	1.59760i	−0.601600	−	0.798798i	$-0.705470\pi$
$809$		−	1.25559e35i		−	1.59760i	0.601600	−	0.798798i	$-0.294530\pi$
$810$	4.90363e34	+	5.50714e34i	0.614748	+	0.690408i
$811$	6.32414e34			0.781180			0.390590	−	0.920565i	$-0.372271\pi$
$811$	6.32414e34			0.781180			0.390590	+	0.920565i	$0.372271\pi$
$812$			1.17854e34i			0.143441i
$813$	−2.14775e34	+	1.39054e34i	−0.257571	+	0.166762i
$814$	−1.00693e35			−1.18989
$815$		−	3.04523e33i		−	0.0354592i
$816$	−2.89323e32	−	4.46874e32i	−0.00331972	−	0.00512747i
$817$	1.51556e34			0.171360
$818$		−	4.63253e34i		−	0.516153i
$819$	3.34528e34	−	7.45791e34i	0.367304	−	0.818861i
$820$	−7.15020e34			−0.773664
$821$			2.82235e34i			0.300949i	0.988614	+	0.150474i	$0.0480801\pi$
$821$			2.82235e34i			0.300949i	−0.988614	+	0.150474i	$0.951920\pi$
$822$	−7.42665e34	+	4.80830e34i	−0.780425	+	0.505277i
$823$	−1.40246e34			−0.145242			−0.0726208	−	0.997360i	$-0.523136\pi$
$823$	−1.40246e34			−0.145242			−0.0726208	+	0.997360i	$0.523136\pi$
$824$		−	2.37532e34i		−	0.242435i
$825$	−8.49777e34	−	1.31252e35i	−0.854786	−	1.32026i
$826$	6.34998e34			0.629523
$827$			1.64394e35i			1.60627i	0.595794	+	0.803137i	$0.296838\pi$
$827$			1.64394e35i			1.60627i	−0.595794	+	0.803137i	$0.703162\pi$
$828$	3.03424e34	+	1.36103e34i	0.292204	+	0.131070i
$829$	−4.85959e33			−0.0461260			−0.0230630	−	0.999734i	$-0.507342\pi$
$829$	−4.85959e33			−0.0461260			−0.0230630	+	0.999734i	$0.507342\pi$
$830$			7.05489e34i			0.660014i
$831$	−5.72122e34	+	3.70414e34i	−0.527565	+	0.341566i
$832$	9.90217e34			0.900017
$833$		−	3.20735e34i		−	0.287347i
$834$	−2.06169e34	−	3.18438e34i	−0.182067	−	0.281211i
$835$	2.08477e35			1.81477
$836$		−	2.94035e34i		−	0.252304i
$837$	5.05362e33	+	3.27893e34i	0.0427461	+	0.277349i
$838$	−3.18819e34			−0.265837
$839$		−	7.87973e34i		−	0.647691i	−0.946110	−	0.323846i	$-0.895024\pi$
$839$		−	7.87973e34i		−	0.647691i	0.946110	−	0.323846i	$-0.104976\pi$
$840$	−9.33677e34	+	6.04498e34i	−0.756563	+	0.489828i
$841$	1.06835e35			0.853415
$842$		−	9.30792e34i		−	0.733006i
$843$	7.74195e34	+	1.19578e35i	0.601062	+	0.928370i
$844$	6.21335e34			0.475573
$845$			2.46775e35i			1.86218i
$846$	−1.72302e34	+	3.84127e34i	−0.128188	+	0.285779i
$847$	4.30096e34			0.315475
$848$			5.61335e32i			0.00405950i
$849$	−2.25558e34	+	1.46035e34i	−0.160830	+	0.104127i
$850$	4.98897e34			0.350739
$851$		−	1.16320e35i		−	0.806309i
$852$	−7.24416e34	−	1.11890e35i	−0.495123	−	0.764742i
$853$	−1.44334e35			−0.972703			−0.486352	−	0.873763i	$-0.661673\pi$
$853$	−1.44334e35			−0.972703			−0.486352	+	0.873763i	$0.661673\pi$
$854$		−	7.41847e34i		−	0.492969i
$855$	6.87204e34	+	3.08249e34i	0.450290	+	0.201980i
$856$	−1.16928e35			−0.755499
$857$		−	2.13238e35i		−	1.35861i	−0.733855	−	0.679306i	$-0.762281\pi$
$857$		−	2.13238e35i		−	1.35861i	0.733855	−	0.679306i	$-0.237719\pi$
$858$	1.51258e35	−	9.79302e34i	0.950322	−	0.615275i
$859$	3.77793e34			0.234065			0.117032	−	0.993128i	$-0.462662\pi$
$859$	3.77793e34			0.234065			0.117032	+	0.993128i	$0.462662\pi$
$860$			8.06344e34i			0.492651i
$861$	4.45199e34	+	6.87631e34i	0.268235	+	0.414302i
$862$	4.45282e34			0.264575
$863$		−	3.76646e34i		−	0.220701i	−0.993893	−	0.110350i	$-0.964803\pi$
$863$		−	3.76646e34i		−	0.220701i	0.993893	−	0.110350i	$-0.0351973\pi$
$864$	−1.71726e35	+	2.64672e34i	−0.992367	+	0.152948i
$865$	−4.31233e35			−2.45764
$866$		−	4.87141e34i		−	0.273804i
$867$	−1.20869e35	+	7.82550e34i	−0.670015	+	0.433793i
$868$	−1.92304e34			−0.105136
$869$			2.35922e35i			1.27213i
$870$	−3.61687e34	−	5.58642e34i	−0.192354	−	0.297100i
$871$	9.90719e34			0.519676
$872$			9.12874e34i			0.472294i
$873$	1.08926e35	−	2.42837e35i	0.555852	−	1.23921i
$874$	−2.04587e34			−0.102977
$875$			4.98453e34i			0.247473i
$876$	7.76423e34	−	5.02686e34i	0.380232	−	0.246177i
$877$	1.03132e35			0.498196			0.249098	−	0.968478i	$-0.419866\pi$
$877$	1.03132e35			0.498196			0.249098	+	0.968478i	$0.419866\pi$
$878$			1.29820e35i			0.618596i
$879$	2.68848e34	+	4.15249e34i	0.126369	+	0.195183i
$880$	5.46113e33			0.0253216
$881$		−	1.21562e35i		−	0.556016i	−0.960579	−	0.278008i	$-0.910326\pi$
$881$		−	1.21562e35i		−	0.556016i	0.960579	−	0.278008i	$-0.0896742\pi$
$882$	−7.93012e34	−	3.55710e34i	−0.357814	−	0.160499i
$883$	−1.95912e35			−0.872033			−0.436017	−	0.899939i	$-0.643611\pi$
$883$	−1.95912e35			−0.872033			−0.436017	+	0.899939i	$0.643611\pi$
$884$		−	9.54556e34i		−	0.419155i
$885$	4.99734e35	−	3.23547e35i	2.16481	−	1.40158i
$886$	1.72172e35			0.735798
$887$		−	7.33356e34i		−	0.309194i	−0.987978	−	0.154597i	$-0.950592\pi$
$887$		−	7.33356e34i		−	0.309194i	0.987978	−	0.154597i	$-0.0494080\pi$
$888$	2.04430e35	+	3.15752e35i	0.850334	+	1.31338i
$889$	−1.78804e35			−0.733762
$890$			1.15409e35i			0.467262i
$891$	−2.30925e35	+	2.05619e35i	−0.922441	+	0.821354i
$892$	1.66593e35			0.656566
$893$			4.30012e34i			0.167210i
$894$	1.15011e33	−	7.44627e32i	0.00441256	−	0.00285686i
$895$	−2.40434e35			−0.910164
$896$		−	1.02055e35i		−	0.381187i
$897$	1.13129e35	+	1.74733e35i	0.416931	+	0.643971i
$898$	1.03020e35			0.374633
$899$		−	2.99423e34i		−	0.107441i
$900$	−9.18627e34	+	2.04797e35i	−0.325259	+	0.725125i
$901$	−3.83889e34			−0.134124
$902$			1.80586e35i			0.622596i
$903$	7.75456e34	−	5.02060e34i	0.263818	−	0.170806i
$904$	3.47446e35			1.16645
$905$		−	2.61057e35i		−	0.864873i
$906$	−1.20836e35	−	1.86637e35i	−0.395055	−	0.610181i
$907$	3.16824e34			0.102219			0.0511095	−	0.998693i	$-0.483724\pi$
$907$	3.16824e34			0.102219			0.0511095	+	0.998693i	$0.483724\pi$
$908$			1.47210e35i			0.468714i
$909$	1.93374e35	+	8.67387e34i	0.607618	+	0.272550i
$910$	−2.67541e35			−0.829648
$911$			1.58993e35i			0.486584i	0.969953	+	0.243292i	$0.0782273\pi$
$911$			1.58993e35i			0.486584i	−0.969953	+	0.243292i	$0.921773\pi$
$912$	−1.23687e33	+	8.00798e32i	−0.00373582	+	0.00241872i
$913$	−2.95825e35			−0.881832
$914$			1.00379e35i			0.295316i
$915$	−3.77989e35	−	5.83823e35i	−1.09756	−	1.69523i
$916$	−1.75023e35			−0.501592
$917$		−	1.02531e35i		−	0.290017i
$918$	−1.50280e34	−	9.75057e34i	−0.0419554	−	0.272218i
$919$	1.98151e35			0.546022			0.273011	−	0.962011i	$-0.411981\pi$
$919$	1.98151e35			0.546022			0.273011	+	0.962011i	$0.411981\pi$
$920$		−	2.83259e35i		−	0.770424i
$921$	−6.08586e35	+	3.94022e35i	−1.63383	+	1.05780i
$922$	−1.48004e35			−0.392196
$923$		−	8.34340e35i		−	2.18234i
$924$	−9.74050e34	−	1.50447e35i	−0.251488	−	0.388436i
$925$	7.85107e35			2.00091
$926$		−	1.53205e35i		−	0.385425i
$927$	−4.01246e34	+	8.94531e34i	−0.0996447	+	0.222146i
$928$	1.56816e35			0.384428
$929$			7.58963e35i			1.83667i	0.395799	+	0.918337i	$0.370468\pi$
$929$			7.58963e35i			1.83667i	−0.395799	+	0.918337i	$0.629532\pi$
$930$	9.11544e34	−	5.90169e34i	0.217762	−	0.140988i
$931$	−8.87740e34			−0.209358
$932$		−	1.57432e35i		−	0.366524i
$933$	4.15476e35	+	6.41723e35i	0.954918	+	1.47492i
$934$	3.58977e35			0.814525
$935$			3.73478e35i			0.836616i
$936$	−6.14178e35	−	2.75493e35i	−1.35826	−	0.609256i
$937$	5.59033e34			0.122057			0.0610285	−	0.998136i	$-0.480562\pi$
$937$	5.59033e34			0.122057			0.0610285	+	0.998136i	$0.480562\pi$
$938$			5.93521e34i			0.127939i
$939$	−6.73602e34	+	4.36116e34i	−0.143356	+	0.0928143i
$940$	−2.28785e35			−0.480721
$941$			5.80586e35i			1.20446i	0.798324	+	0.602228i	$0.205720\pi$
$941$			5.80586e35i			1.20446i	−0.798324	+	0.602228i	$0.794280\pi$
$942$	9.99226e34	+	1.54335e35i	0.204669	+	0.316122i
$943$	−2.08613e35			−0.421893
$944$			1.16468e34i			0.0232564i
$945$	4.53730e35	−	6.99307e34i	0.894574	−	0.137875i
$946$	2.03651e35			0.396455
$947$			8.32433e33i			0.0160011i	0.999968	+	0.00800054i	$0.00254668\pi$
$947$			8.32433e33i			0.0160011i	−0.999968	+	0.00800054i	$0.997453\pi$
$948$	2.84287e35	−	1.84058e35i	0.539581	−	0.349346i
$949$	5.78964e35			1.08507
$950$		−	1.38086e35i		−	0.255545i
$951$	−5.69125e35	−	8.79041e35i	−1.04002	−	1.60636i
$952$	1.48815e35			0.268536
$953$		−	4.25476e35i		−	0.758159i	−0.925364	−	0.379079i	$-0.876241\pi$
$953$		−	4.25476e35i		−	0.758159i	0.925364	−	0.379079i	$-0.123759\pi$
$954$	−4.25750e34	+	9.49159e34i	−0.0749159	+	0.167016i
$955$	2.90303e35			0.504442
$956$			7.38699e34i			0.126757i
$957$	2.34250e35	−	1.51662e35i	0.396950	−	0.257001i
$958$	−5.96773e35			−0.998673
$959$			5.50822e35i			0.910306i
$960$	3.02261e35	+	4.66856e35i	0.493318	+	0.761953i
$961$	−5.71555e35			−0.921250
$962$			9.04775e35i			1.44026i
$963$	4.40344e35	+	1.97518e35i	0.692271	+	0.310522i
$964$	−8.03869e35			−1.24813
$965$		−	7.28522e35i		−	1.11716i
$966$	−1.04679e35	+	6.77735e34i	−0.158539	+	0.102644i
$967$	8.69037e35			1.29993			0.649966	−	0.759964i	$-0.274783\pi$
$967$	8.69037e35			1.29993			0.649966	+	0.759964i	$0.274783\pi$
$968$		−	3.54196e35i		−	0.523286i
$969$	−5.47653e34	−	8.45877e34i	−0.0799135	−	0.123430i
$970$	−8.71141e35			−1.25553
$971$		−	1.21692e36i		−	1.73233i	−0.499754	−	0.866167i	$-0.666576\pi$
$971$		−	1.21692e36i		−	1.73233i	0.499754	−	0.866167i	$-0.333424\pi$
$972$	4.27931e35	+	1.17849e35i	0.601699	+	0.165703i
$973$	−2.36180e35			−0.328011
$974$		−	8.27343e35i		−	1.13495i
$975$	−1.17936e36	+	7.63566e35i	−1.59806	+	1.03464i
$976$	1.36066e34			0.0182117
$977$			2.55560e35i			0.337877i	0.985627	+	0.168938i	$0.0540339\pi$
$977$			2.55560e35i			0.337877i	−0.985627	+	0.168938i	$0.945966\pi$
$978$	6.00030e33	+	9.26776e33i	0.00783623	+	0.0121034i
$979$	−4.83934e35			−0.624300
$980$		−	4.72316e35i		−	0.601894i
$981$	1.54205e35	−	3.43782e35i	0.194120	−	0.432768i
$982$	3.03734e35			0.377707
$983$			1.04221e36i			1.28031i	0.768246	+	0.640154i	$0.221130\pi$
$983$			1.04221e36i			1.28031i	−0.768246	+	0.640154i	$0.778870\pi$
$984$	5.66282e35	−	3.66633e35i	0.687213	−	0.444928i
$985$	−1.48811e36			−1.78403
$986$			8.90397e34i			0.105453i
$987$	1.42450e35	+	2.20021e35i	0.166670	+	0.257429i
$988$	−2.64205e35			−0.305392
$989$			2.35258e35i			0.268651i
$990$	9.23420e35	+	4.14205e35i	1.04178	+	0.467297i
$991$	1.41937e36			1.58202			0.791011	−	0.611802i	$-0.209555\pi$
$991$	1.41937e36			1.58202			0.791011	+	0.611802i	$0.209555\pi$
$992$			2.55879e35i			0.281770i
$993$	7.84035e35	−	5.07614e35i	0.852991	−	0.552259i
$994$	4.99838e35			0.537270
$995$			1.51801e36i			1.61212i
$996$	2.30793e35	+	3.56471e35i	0.242164	+	0.374035i
$997$	2.54765e35			0.264118			0.132059	−	0.991242i	$-0.457841\pi$
$997$	2.54765e35			0.264118			0.132059	+	0.991242i	$0.457841\pi$
$998$		−	2.53062e35i		−	0.259216i
$999$	−2.36493e35	−	1.53443e36i	−0.239349	−	1.55297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.25.b.b.2.4	yes	6
3.2	odd	2	inner	3.25.b.b.2.3	✓	6
4.3	odd	2		48.25.e.b.17.5		6
12.11	even	2		48.25.e.b.17.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.25.b.b.2.3	✓	6	3.2	odd	2	inner
3.25.b.b.2.4	yes	6	1.1	even	1	trivial
48.25.e.b.17.5		6	4.3	odd	2
48.25.e.b.17.6		6	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2511.29i q^{2} +(-446105. + 288825. i) q^{3} +1.04706e7 q^{4} +3.68111e8i q^{5} +(-7.25325e8 - 1.12030e9i) q^{6} -8.30906e9 q^{7} +6.84273e10i q^{8} +(1.15589e11 - 2.57693e11i) q^{9} +O(q^{10})\)	\(q+2511.29i q^{2} +(-446105. + 288825. i) q^{3} +1.04706e7 q^{4} +3.68111e8i q^{5} +(-7.25325e8 - 1.12030e9i) q^{6} -8.30906e9 q^{7} +6.84273e10i q^{8} +(1.15589e11 - 2.57693e11i) q^{9} -9.24434e11 q^{10} -3.87633e12i q^{11} +(-4.67100e12 + 3.02418e12i) q^{12} -3.48308e13 q^{13} -2.08665e13i q^{14} +(-1.06320e14 - 1.64216e14i) q^{15} +3.82721e12 q^{16} +2.61737e14i q^{17} +(6.47142e14 + 2.90279e14i) q^{18} +7.24444e14 q^{19} +3.85436e15i q^{20} +(3.70671e15 - 2.39987e15i) q^{21} +9.73460e15 q^{22} +1.12454e16i q^{23} +(-1.97635e16 - 3.05257e16i) q^{24} -7.59011e16 q^{25} -8.74702e16i q^{26} +(2.28632e16 + 1.48343e17i) q^{27} -8.70011e16 q^{28} -1.35463e17i q^{29} +(4.12394e17 - 2.67000e17i) q^{30} +2.21037e17 q^{31} +1.15763e18i q^{32} +(1.11958e18 + 1.72925e18i) q^{33} -6.57298e17 q^{34} -3.05866e18i q^{35} +(1.21029e18 - 2.69821e18i) q^{36} -1.03438e19 q^{37} +1.81929e18i q^{38} +(1.55382e19 - 1.00600e19i) q^{39} -2.51888e19 q^{40} +1.85510e19i q^{41} +(6.02676e18 + 9.30863e18i) q^{42} +2.09203e19 q^{43} -4.05877e19i q^{44} +(9.48595e19 + 4.25497e19i) q^{45} -2.82405e19 q^{46} +5.93575e19i q^{47} +(-1.70734e18 + 1.10540e18i) q^{48} -1.22541e20 q^{49} -1.90610e20i q^{50} +(-7.55963e19 - 1.16762e20i) q^{51} -3.64700e20 q^{52} +1.46669e20i q^{53} +(-3.72533e20 + 5.74162e19i) q^{54} +1.42692e21 q^{55} -5.68566e20i q^{56} +(-3.23178e20 + 2.09238e20i) q^{57} +3.40187e20 q^{58} +3.04315e21i q^{59} +(-1.11324e21 - 1.71945e21i) q^{60} +3.55521e21 q^{61} +5.55088e20i q^{62} +(-9.60439e20 + 2.14118e21i) q^{63} -2.84294e21 q^{64} -1.28216e22i q^{65} +(-4.34265e21 + 2.81160e21i) q^{66} -2.84438e21 q^{67} +2.74055e21i q^{68} +(-3.24796e21 - 5.01663e21i) q^{69} +7.68118e21 q^{70} +2.39541e22i q^{71} +(1.76332e22 + 7.90947e21i) q^{72} -1.66222e22 q^{73} -2.59763e22i q^{74} +(3.38599e22 - 2.19222e22i) q^{75} +7.58539e21 q^{76} +3.22087e22i q^{77} +(2.52636e22 + 3.90209e22i) q^{78} -6.08621e22 q^{79} +1.40884e21i q^{80} +(-5.30446e22 - 5.95731e22i) q^{81} -4.65869e22 q^{82} -7.63158e22i q^{83} +(3.88116e22 - 2.51281e22i) q^{84} -9.63483e22 q^{85} +5.25371e22i q^{86} +(3.91252e22 + 6.04307e22i) q^{87} +2.65247e23 q^{88} -1.24843e23i q^{89} +(-1.06855e23 + 2.38220e23i) q^{90} +2.89411e23 q^{91} +1.17747e23i q^{92} +(-9.86056e22 + 6.38411e22i) q^{93} -1.49064e23 q^{94} +2.66676e23i q^{95} +(-3.34353e23 - 5.16424e23i) q^{96} +9.42350e23 q^{97} -3.07736e23i q^{98} +(-9.98903e23 - 4.48063e23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 616842 q^{3} - 63346800 q^{4} - 2673890352 q^{6} + 1988064876 q^{7} - 791186949882 q^{9}+O(q^{10}) \) 6 * q - 616842 * q^3 - 63346800 * q^4 - 2673890352 * q^6 + 1988064876 * q^7 - 791186949882 * q^9	\( 6 q - 616842 q^{3} - 63346800 q^{4} - 2673890352 q^{6} + 1988064876 q^{7} - 791186949882 q^{9} + 2770823311200 q^{10} - 18492861842352 q^{12} - 73542438063924 q^{13} + 227151045057600 q^{15} - 433335898904448 q^{16} - 12\!\cdots\!40 q^{18}+ \cdots - 18\!\cdots\!20 q^{99}+O(q^{100}) \) 6 * q - 616842 * q^3 - 63346800 * q^4 - 2673890352 * q^6 + 1988064876 * q^7 - 791186949882 * q^9 + 2770823311200 * q^10 - 18492861842352 * q^12 - 73542438063924 * q^13 + 227151045057600 * q^15 - 433335898904448 * q^16 - 1227888881468640 * q^18 + 6095219493474156 * q^19 + 2706110098936524 * q^21 - 4132747004902560 * q^22 + 79223562819483264 * q^24 - 206274704562968250 * q^25 - 153687400093414602 * q^27 + 11425252275435936 * q^28 + 1679034252186079200 * q^30 - 1137843910975220628 * q^31 + 7067811391497299520 * q^33 - 15440589345121992576 * q^34 + 23041875850704576144 * q^36 - 14032623495718823604 * q^37 + 25380736596180392364 * q^39 - 121930725979226707200 * q^40 + 209343891033396594720 * q^42 - 114603298148542353684 * q^43 + 311304965429932790400 * q^45 - 346860905830754272704 * q^46 + 51162839242132733568 * q^48 + 107947782097205854482 * q^49 - 479022139696737883392 * q^51 - 124107229893322470624 * q^52 - 1113391638534691344528 * q^54 + 1679273232066520675200 * q^55 - 1140401446469855973684 * q^57 + 7395366373865537628960 * q^58 - 14436777252623118393600 * q^60 + 10013078414594836175052 * q^61 - 8325410033672205875604 * q^63 + 11741892494977734042624 * q^64 - 5418873997530695523360 * q^66 - 5445087092431082846484 * q^67 + 11943290073056639859072 * q^69 - 55632387081854182017600 * q^70 + 63773250138227244591360 * q^72 + 7228988839203443040396 * q^73 + 37723327374597984717750 * q^75 - 4244116415001816243552 * q^76 + 235720510135983845200800 * q^78 - 423484844106082827915924 * q^79 + 102726090691231740574086 * q^81 - 272255725325320387035840 * q^82 + 200996808333809534079264 * q^84 + 319008824808936798988800 * q^85 - 252430535429613815803200 * q^87 + 160152458683551892335360 * q^88 - 1246806301659161625597600 * q^90 + 1497033316223591396871768 * q^91 - 501165623869166897253684 * q^93 + 1979316836866080826257024 * q^94 - 1420600675222724601424896 * q^96 - 1411607470255832450422644 * q^97 - 1834460043482282449115520 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more