LMFDB - Embedded newform 6.21.b.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,21,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	6.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:	$15.2108259062$
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} + 3396x^{4} + 2813589x^{2} + 548136050 $ x^6 + 3396x^4 + 2813589x^2 + 548136050
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{31}\cdot 3^{17} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.5
Root			$-47.5078i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.21.b.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+724.077i q^{2} +(25323.8 - 53343.1i) q^{3} -524288. q^{4} +6.05191e6i q^{5} +(3.86246e7 + 1.83364e7i) q^{6} +1.14251e8 q^{7} -3.79625e8i q^{8} +(-2.20420e9 - 2.70170e9i) q^{9} +O(q^{10})$	\(q+724.077i q^{2} +(25323.8 - 53343.1i) q^{3} -524288. q^{4} +6.05191e6i q^{5} +(3.86246e7 + 1.83364e7i) q^{6} +1.14251e8 q^{7} -3.79625e8i q^{8} +(-2.20420e9 - 2.70170e9i) q^{9} -4.38205e9 q^{10} -2.84306e10i q^{11} +(-1.32769e10 + 2.79672e10i) q^{12} +1.97422e11 q^{13} +8.27265e10i q^{14} +(3.22828e11 + 1.53257e11i) q^{15} +2.74878e11 q^{16} -2.02536e12i q^{17} +(1.95624e12 - 1.59601e12i) q^{18} +9.02206e12 q^{19} -3.17294e12i q^{20} +(2.89326e12 - 6.09451e12i) q^{21} +2.05860e13 q^{22} -1.39568e13i q^{23} +(-2.02504e13 - 9.61354e12i) q^{24} +5.87418e13 q^{25} +1.42949e14i q^{26} +(-1.99936e14 + 4.91616e13i) q^{27} -5.99004e13 q^{28} -1.81850e14i q^{29} +(-1.10970e14 + 2.33752e14i) q^{30} -9.52335e14 q^{31} +1.99033e14i q^{32} +(-1.51658e15 - 7.19970e14i) q^{33} +1.46652e15 q^{34} +6.91437e14i q^{35} +(1.15563e15 + 1.41647e15i) q^{36} +4.96554e15 q^{37} +6.53267e15i q^{38} +(4.99947e15 - 1.05311e16i) q^{39} +2.29746e15 q^{40} -2.06396e16i q^{41} +(4.41289e15 + 2.09495e15i) q^{42} -2.15327e16 q^{43} +1.49058e16i q^{44} +(1.63504e16 - 1.33396e16i) q^{45} +1.01058e16 q^{46} +7.74571e16i q^{47} +(6.96094e15 - 1.46629e16i) q^{48} -6.67390e16 q^{49} +4.25336e16i q^{50} +(-1.08039e17 - 5.12897e16i) q^{51} -1.03506e17 q^{52} +1.50500e17i q^{53} +(-3.55968e16 - 1.44769e17i) q^{54} +1.72060e17 q^{55} -4.33725e16i q^{56} +(2.28472e17 - 4.81265e17i) q^{57} +1.31673e17 q^{58} +7.95007e17i q^{59} +(-1.69255e17 - 8.03509e16i) q^{60} +1.04527e18 q^{61} -6.89564e17i q^{62} +(-2.51832e17 - 3.08672e17i) q^{63} -1.44115e17 q^{64} +1.19478e18i q^{65} +(5.21314e17 - 1.09812e18i) q^{66} -5.49957e17 q^{67} +1.06187e18i q^{68} +(-7.44499e17 - 3.53438e17i) q^{69} -5.00654e17 q^{70} +3.52780e16i q^{71} +(-1.02563e18 + 8.36769e17i) q^{72} -5.86016e18 q^{73} +3.59544e18i q^{74} +(1.48756e18 - 3.13347e18i) q^{75} -4.73016e18 q^{76} -3.24823e18i q^{77} +(7.62534e18 + 3.62000e18i) q^{78} +5.32011e18 q^{79} +1.66354e18i q^{80} +(-2.44069e18 + 1.19102e19i) q^{81} +1.49447e19 q^{82} -2.31602e19i q^{83} +(-1.51690e18 + 3.19528e18i) q^{84} +1.22573e19 q^{85} -1.55913e19i q^{86} +(-9.70043e18 - 4.60512e18i) q^{87} -1.07930e19 q^{88} -2.31315e19i q^{89} +(9.65891e18 + 1.18390e19i) q^{90} +2.25557e19 q^{91} +7.31737e18i q^{92} +(-2.41167e19 + 5.08005e19i) q^{93} -5.60849e19 q^{94} +5.46007e19i q^{95} +(1.06170e19 + 5.04026e18i) q^{96} +2.76998e19 q^{97} -4.83242e19i q^{98} +(-7.68110e19 + 6.26667e19i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9}+O(q^{10}) $ 6 * q + 18846 * q^3 - 3145728 * q^4 + 35057664 * q^6 - 566671812 * q^7 + 1944941382 * q^9	$ 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9} + 5360984064 q^{10} - 9880731648 q^{12} - 49898545620 q^{13} + 487708151328 q^{15} + 1649267441664 q^{16} - 3239129751552 q^{18} + 15927597287292 q^{19} - 20677554127188 q^{21} + 21184189636608 q^{22} - 18380312543232 q^{24} + 337510512308454 q^{25} - 10\!\cdots\!62 q^{27}+ \cdots - 22\!\cdots\!32 q^{99}+O(q^{100}) $ 6 * q + 18846 * q^3 - 3145728 * q^4 + 35057664 * q^6 - 566671812 * q^7 + 1944941382 * q^9 + 5360984064 * q^10 - 9880731648 * q^12 - 49898545620 * q^13 + 487708151328 * q^15 + 1649267441664 * q^16 - 3239129751552 * q^18 + 15927597287292 * q^19 - 20677554127188 * q^21 + 21184189636608 * q^22 - 18380312543232 * q^24 + 337510512308454 * q^25 - 1019514529044162 * q^27 + 297099230969856 * q^28 - 920809286295552 * q^30 + 1832545426397628 * q^31 - 3503562514347744 * q^33 + 2508713101983744 * q^34 - 1019709427286016 * q^36 + 424332326872812 * q^37 + 13854943345637340 * q^39 - 2810699612946432 * q^40 + 30169507188989952 * q^42 - 49488752333951556 * q^43 + 64297936569436992 * q^45 - 51218624034717696 * q^46 + 5180349034266624 * q^48 - 185965132589503470 * q^49 + 114461935953291648 * q^51 + 26161208686018560 * q^52 - 103567464750919680 * q^54 + 468503586680075712 * q^55 - 1250127589109383188 * q^57 + 330130684975472640 * q^58 - 255699531243454464 * q^60 + 3301830012872093484 * q^61 - 724019288731292484 * q^63 - 864691128455135232 * q^64 + 1110947414199017472 * q^66 - 2779226272508556228 * q^67 + 667934407322175168 * q^69 - 1866219302039371776 * q^70 + 1698236859181694976 * q^72 - 9149401536792501300 * q^73 + 9127347583517050878 * q^75 - 8350648126559748096 * q^76 + 19815256334884331520 * q^78 + 90056048403257148 * q^79 - 13310358127786728378 * q^81 - 19709381871486517248 * q^82 + 10840993498235142144 * q^84 + 78223886062534003968 * q^85 - 87334395308747540640 * q^87 - 11106616416197935104 * q^88 + 60406983770669457408 * q^90 + 132462766690215009720 * q^91 - 157075923546140581332 * q^93 - 106728395801434030080 * q^94 + 9636577302666018816 * q^96 + 92028905119987573836 * q^97 - 224342570810992842432 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$			724.077i			0.707107i
$2$			724.077i			0.707107i
$3$	25323.8	−	53343.1i	0.428860	−	0.903371i
$3$	25323.8	−	53343.1i	0.428860	−	0.903371i
$4$	−524288.			−0.500000
$5$			6.05191e6i			0.619716i	0.950783	+	0.309858i	$0.100281\pi$
$5$			6.05191e6i			0.619716i	−0.950783	+	0.309858i	$0.899719\pi$
$6$	3.86246e7	+	1.83364e7i	0.638780	+	0.303250i
$7$	1.14251e8			0.404464			0.202232	−	0.979338i	$-0.435181\pi$
$7$	1.14251e8			0.404464			0.202232	+	0.979338i	$0.435181\pi$
$8$		−	3.79625e8i		−	0.353553i
$9$	−2.20420e9	−	2.70170e9i	−0.632158	−	0.774840i
$10$	−4.38205e9			−0.438205
$11$		−	2.84306e10i		−	1.09612i	−0.836438	−	0.548062i	$-0.815366\pi$
$11$		−	2.84306e10i		−	1.09612i	0.836438	−	0.548062i	$-0.184634\pi$
$12$	−1.32769e10	+	2.79672e10i	−0.214430	+	0.451685i
$13$	1.97422e11			1.43206			0.716031	−	0.698068i	$-0.245957\pi$
$13$	1.97422e11			1.43206			0.716031	+	0.698068i	$0.245957\pi$
$14$			8.27265e10i			0.285999i
$15$	3.22828e11	+	1.53257e11i	0.559833	+	0.265771i
$16$	2.74878e11			0.250000
$17$		−	2.02536e12i		−	1.00465i	−0.864680	−	0.502323i	$-0.832479\pi$
$17$		−	2.02536e12i		−	1.00465i	0.864680	−	0.502323i	$-0.167521\pi$
$18$	1.95624e12	−	1.59601e12i	0.547894	−	0.447003i
$19$	9.02206e12			1.47153			0.735766	−	0.677236i	$-0.236822\pi$
$19$	9.02206e12			1.47153			0.735766	+	0.677236i	$0.236822\pi$
$20$		−	3.17294e12i		−	0.309858i
$21$	2.89326e12	−	6.09451e12i	0.173458	−	0.365381i
$22$	2.05860e13			0.775076
$23$		−	1.39568e13i		−	0.336905i	−0.985710	−	0.168452i	$-0.946123\pi$
$23$		−	1.39568e13i		−	0.336905i	0.985710	−	0.168452i	$-0.0538769\pi$
$24$	−2.02504e13	−	9.61354e12i	−0.319390	−	0.151625i
$25$	5.87418e13			0.615952
$26$			1.42949e14i			1.01262i
$27$	−1.99936e14	+	4.91616e13i	−0.971075	+	0.238775i
$28$	−5.99004e13			−0.202232
$29$		−	1.81850e14i		−	0.432247i	−0.976366	−	0.216124i	$-0.930659\pi$
$29$		−	1.81850e14i		−	0.432247i	0.976366	−	0.216124i	$-0.0693415\pi$
$30$	−1.10970e14	+	2.33752e14i	−0.187929	+	0.395862i
$31$	−9.52335e14			−1.16191			−0.580955	−	0.813935i	$-0.697321\pi$
$31$	−9.52335e14			−1.16191			−0.580955	+	0.813935i	$0.697321\pi$
$32$			1.99033e14i			0.176777i
$33$	−1.51658e15	−	7.19970e14i	−0.990206	−	0.470084i
$34$	1.46652e15			0.710392
$35$			6.91437e14i			0.250652i
$36$	1.15563e15	+	1.41647e15i	0.316079	+	0.387420i
$37$	4.96554e15			1.03264			0.516321	−	0.856395i	$-0.327301\pi$
$37$	4.96554e15			1.03264			0.516321	+	0.856395i	$0.327301\pi$
$38$			6.53267e15i			1.04053i
$39$	4.99947e15	−	1.05311e16i	0.614155	−	1.29368i
$40$	2.29746e15			0.219103
$41$		−	2.06396e16i		−	1.53767i	−0.639448	−	0.768834i	$-0.720837\pi$
$41$		−	2.06396e16i		−	1.53767i	0.639448	−	0.768834i	$-0.279163\pi$
$42$	4.41289e15	+	2.09495e15i	0.258363	+	0.122654i
$43$	−2.15327e16			−0.996353			−0.498176	−	0.867076i	$-0.665997\pi$
$43$	−2.15327e16			−0.996353			−0.498176	+	0.867076i	$0.665997\pi$
$44$			1.49058e16i			0.548062i
$45$	1.63504e16	−	1.33396e16i	0.480180	−	0.391758i
$46$	1.01058e16			0.238228
$47$			7.74571e16i			1.47259i	0.676659	+	0.736296i	$0.263427\pi$
$47$			7.74571e16i			1.47259i	−0.676659	+	0.736296i	$0.736573\pi$
$48$	6.96094e15	−	1.46629e16i	0.107215	−	0.225843i
$49$	−6.67390e16			−0.836409
$50$			4.25336e16i			0.435544i
$51$	−1.08039e17	−	5.12897e16i	−0.907567	−	0.430852i
$52$	−1.03506e17			−0.716031
$53$			1.50500e17i			0.860556i	0.902696	+	0.430278i	$0.141584\pi$
$53$			1.50500e17i			0.860556i	−0.902696	+	0.430278i	$0.858416\pi$
$54$	−3.55968e16	−	1.44769e17i	−0.168839	−	0.686654i
$55$	1.72060e17			0.679285
$56$		−	4.33725e16i		−	0.142999i
$57$	2.28472e17	−	4.81265e17i	0.631081	−	1.32934i
$58$	1.31673e17			0.305645
$59$			7.95007e17i			1.55543i	0.628616	+	0.777716i	$0.283622\pi$
$59$			7.95007e17i			1.55543i	−0.628616	+	0.777716i	$0.716378\pi$
$60$	−1.69255e17	−	8.03509e16i	−0.279917	−	0.132886i
$61$	1.04527e18			1.46531			0.732657	−	0.680598i	$-0.238280\pi$
$61$	1.04527e18			1.46531			0.732657	+	0.680598i	$0.238280\pi$
$62$		−	6.89564e17i		−	0.821595i
$63$	−2.51832e17	−	3.08672e17i	−0.255685	−	0.313394i
$64$	−1.44115e17			−0.125000
$65$			1.19478e18i			0.887472i
$66$	5.21314e17	−	1.09812e18i	0.332399	−	0.700181i
$67$	−5.49957e17			−0.301704			−0.150852	−	0.988556i	$-0.548202\pi$
$67$	−5.49957e17			−0.301704			−0.150852	+	0.988556i	$0.548202\pi$
$68$			1.06187e18i			0.502323i
$69$	−7.44499e17	−	3.53438e17i	−0.304350	−	0.144485i
$70$	−5.00654e17			−0.177238
$71$			3.52780e16i			0.0108373i	0.999985	+	0.00541865i	$0.00172482\pi$
$71$			3.52780e16i			0.0108373i	−0.999985	+	0.00541865i	$0.998275\pi$
$72$	−1.02563e18	+	8.36769e17i	−0.273947	+	0.223502i
$73$	−5.86016e18			−1.36358			−0.681791	−	0.731547i	$-0.738798\pi$
$73$	−5.86016e18			−1.36358			−0.681791	+	0.731547i	$0.738798\pi$
$74$			3.59544e18i			0.730188i
$75$	1.48756e18	−	3.13347e18i	0.264158	−	0.556433i
$76$	−4.73016e18			−0.735766
$77$		−	3.24823e18i		−	0.443342i
$78$	7.62534e18	+	3.62000e18i	0.914773	+	0.434273i
$79$	5.32011e18			0.561888			0.280944	−	0.959724i	$-0.409352\pi$
$79$	5.32011e18			0.561888			0.280944	+	0.959724i	$0.409352\pi$
$80$			1.66354e18i			0.154929i
$81$	−2.44069e18	+	1.19102e19i	−0.200753	+	0.979642i
$82$	1.49447e19			1.08730
$83$		−	2.31602e19i		−	1.49266i	−0.665576	−	0.746330i	$-0.731814\pi$
$83$		−	2.31602e19i		−	1.49266i	0.665576	−	0.746330i	$-0.268186\pi$
$84$	−1.51690e18	+	3.19528e18i	−0.0867292	+	0.182690i
$85$	1.22573e19			0.622595
$86$		−	1.55913e19i		−	0.704528i
$87$	−9.70043e18	−	4.60512e18i	−0.390480	−	0.185374i
$88$	−1.07930e19			−0.387538
$89$		−	2.31315e19i		−	0.741828i	−0.928667	−	0.370914i	$-0.879045\pi$
$89$		−	2.31315e19i		−	0.741828i	0.928667	−	0.370914i	$-0.120955\pi$
$90$	9.65891e18	+	1.18390e19i	0.277015	+	0.339539i
$91$	2.25557e19			0.579217
$92$			7.31737e18i			0.168452i
$93$	−2.41167e19	+	5.08005e19i	−0.498297	+	1.04964i
$94$	−5.60849e19			−1.04128
$95$			5.46007e19i			0.911931i
$96$	1.06170e19	+	5.04026e18i	0.159695	+	0.0758125i
$97$	2.76998e19			0.375629			0.187815	−	0.982205i	$-0.439860\pi$
$97$	2.76998e19			0.375629			0.187815	+	0.982205i	$0.439860\pi$
$98$		−	4.83242e19i		−	0.591431i
$99$	−7.68110e19	+	6.26667e19i	−0.849320	+	0.692923i
$100$	−3.07976e19			−0.307976
$101$		−	2.61381e19i		−	0.236625i	−0.992976	−	0.118313i	$-0.962252\pi$
$101$		−	2.61381e19i		−	0.236625i	0.992976	−	0.118313i	$-0.0377485\pi$
$102$	3.71377e19	−	7.82286e19i	0.304659	−	0.641747i
$103$	−6.85186e19			−0.509842			−0.254921	−	0.966962i	$-0.582050\pi$
$103$	−6.85186e19			−0.509842			−0.254921	+	0.966962i	$0.582050\pi$
$104$		−	7.49464e19i		−	0.506311i
$105$	3.68834e19	+	1.75098e19i	0.226432	+	0.107495i
$106$	−1.08974e20			−0.608505
$107$		−	8.87403e18i		−	0.0451111i	−0.999746	−	0.0225555i	$-0.992820\pi$
$107$		−	8.87403e18i		−	0.0451111i	0.999746	−	0.0225555i	$-0.00718026\pi$
$108$	1.04824e20	−	2.57749e19i	0.485537	−	0.119387i
$109$	3.76375e20			1.58985			0.794924	−	0.606709i	$-0.207510\pi$
$109$	3.76375e20			1.58985			0.794924	+	0.606709i	$0.207510\pi$
$110$			1.24584e20i			0.480327i
$111$	1.25746e20	−	2.64878e20i	0.442859	−	0.932858i
$112$	3.14051e19			0.101116
$113$			3.13328e20i			0.923027i	0.887133	+	0.461514i	$0.152693\pi$
$113$			3.13328e20i			0.923027i	−0.887133	+	0.461514i	$0.847307\pi$
$114$	3.48473e20	+	1.65432e20i	0.939984	+	0.446242i
$115$	8.44652e19			0.208785
$116$			9.53416e19i			0.216124i
$117$	−4.35157e20	−	5.33375e20i	−0.905290	−	1.10962i
$118$	−5.75647e20			−1.09986
$119$		−	2.31399e20i		−	0.406343i
$120$	5.81803e19	−	1.22554e20i	0.0939644	−	0.197931i
$121$	−1.35550e20			−0.201487
$122$			7.56857e20i			1.03613i
$123$	−1.10098e21	−	5.22672e20i	−1.38908	−	0.659445i
$124$	4.99298e20			0.580955
$125$			9.32655e20i			1.00143i
$126$	2.23502e20	−	1.82346e20i	0.221603	−	0.180796i
$127$	1.31747e20			0.120699			0.0603494	−	0.998177i	$-0.480779\pi$
$127$	1.31747e20			0.120699			0.0603494	+	0.998177i	$0.480779\pi$
$128$		−	1.04351e20i		−	0.0883883i
$129$	−5.45288e20	+	1.14862e21i	−0.427296	+	0.900076i
$130$	−8.65114e20			−0.627537
$131$		−	9.46406e20i		−	0.635864i	−0.948113	−	0.317932i	$-0.897012\pi$
$131$		−	9.46406e20i		−	0.635864i	0.948113	−	0.317932i	$-0.102988\pi$
$132$	7.95124e20	+	3.77472e20i	0.495103	+	0.235042i
$133$	1.03078e21			0.595181
$134$		−	3.98211e20i		−	0.213337i
$135$	−2.97522e20	−	1.20999e21i	−0.147973	−	0.601790i
$136$	−7.68877e20			−0.355196
$137$			1.21464e21i			0.521484i	0.965409	+	0.260742i	$0.0839672\pi$
$137$			1.21464e21i			0.521484i	−0.965409	+	0.260742i	$0.916033\pi$
$138$	2.55917e20	−	5.39075e20i	0.102166	−	0.215208i
$139$	2.40866e21			0.894598			0.447299	−	0.894384i	$-0.352386\pi$
$139$	2.40866e21			0.894598			0.447299	+	0.894384i	$0.352386\pi$
$140$		−	3.62512e20i		−	0.125326i
$141$	4.13181e21	+	1.96151e21i	1.33030	+	0.631537i
$142$	−2.55440e19			−0.00766313
$143$		−	5.61283e21i		−	1.56972i
$144$	−6.05885e20	−	7.42637e20i	−0.158039	−	0.193710i
$145$	1.10054e21			0.267871
$146$		−	4.24321e21i		−	0.964198i
$147$	−1.69008e21	+	3.56007e21i	−0.358703	+	0.755588i
$148$	−2.60338e21			−0.516321
$149$			7.21447e21i			1.33765i	0.743421	+	0.668824i	$0.233202\pi$
$149$			7.21447e21i			1.33765i	−0.743421	+	0.668824i	$0.766798\pi$
$150$	2.26888e21	+	1.07711e21i	0.393458	+	0.186788i
$151$	−8.19176e21			−1.32925			−0.664627	−	0.747176i	$-0.731409\pi$
$151$	−8.19176e21			−1.32925			−0.664627	+	0.747176i	$0.731409\pi$
$152$		−	3.42500e21i		−	0.520265i
$153$	−5.47191e21	+	4.46429e21i	−0.778439	+	0.635094i
$154$	2.35197e21			0.313490
$155$		−	5.76345e21i		−	0.720054i
$156$	−2.62116e21	+	5.52134e21i	−0.307077	+	0.646842i
$157$	2.87032e21			0.315453			0.157726	−	0.987483i	$-0.449584\pi$
$157$	2.87032e21			0.315453			0.157726	+	0.987483i	$0.449584\pi$
$158$			3.85217e21i			0.397315i
$159$	8.02817e21	+	3.81124e21i	0.777401	+	0.369058i
$160$	−1.20453e21			−0.109551
$161$		−	1.59458e21i		−	0.136266i
$162$	−8.62388e21	−	1.76725e21i	−0.692711	−	0.141954i
$163$	−1.49761e22			−1.13116			−0.565578	−	0.824695i	$-0.691347\pi$
$163$	−1.49761e22			−1.13116			−0.565578	+	0.824695i	$0.691347\pi$
$164$			1.08211e22i			0.768834i
$165$	4.35720e21	−	9.17820e21i	0.291318	−	0.613646i
$166$	1.67698e22			1.05547
$167$		−	2.33394e22i		−	1.38333i	−0.722221	−	0.691663i	$-0.756878\pi$
$167$		−	2.33394e22i		−	1.38333i	0.722221	−	0.691663i	$-0.243122\pi$
$168$	−2.31363e21	−	1.09836e21i	−0.129182	−	0.0613268i
$169$	1.99705e22			1.05080
$170$			8.87523e21i			0.440241i
$171$	−1.98864e22	−	2.43749e22i	−0.930240	−	1.14020i
$172$	1.12893e22			0.498176
$173$			1.25786e22i			0.523807i	0.965094	+	0.261904i	$0.0843503\pi$
$173$			1.25786e22i			0.523807i	−0.965094	+	0.261904i	$0.915650\pi$
$174$	3.33446e21	−	7.02386e21i	0.131079	−	0.276111i
$175$	6.71131e21			0.249130
$176$		−	7.81495e21i		−	0.274031i
$177$	4.24082e22	+	2.01326e22i	1.40513	+	0.667063i
$178$	1.67490e22			0.524551
$179$			4.18137e22i			1.23819i	0.785315	+	0.619097i	$0.212501\pi$
$179$			4.18137e22i			1.23819i	−0.785315	+	0.619097i	$0.787499\pi$
$180$	−8.57234e21	+	6.99380e21i	−0.240090	+	0.195879i
$181$	−4.88622e22			−1.29475			−0.647377	−	0.762170i	$-0.724134\pi$
$181$	−4.88622e22			−1.29475			−0.647377	+	0.762170i	$0.724134\pi$
$182$			1.63320e22i			0.409569i
$183$	2.64702e22	−	5.57581e22i	0.628415	−	1.32372i
$184$	−5.29834e21			−0.119114
$185$			3.00510e22i			0.639944i
$186$	−3.67835e22	−	1.74624e22i	−0.742205	−	0.352349i
$187$	−5.75822e22			−1.10122
$188$		−	4.06098e22i		−	0.736296i
$189$	−2.28428e22	+	5.61677e21i	−0.392764	+	0.0965758i
$190$	−3.95351e22			−0.644833
$191$		−	1.19022e22i		−	0.184201i	−0.995750	−	0.0921006i	$-0.970642\pi$
$191$		−	1.19022e22i		−	0.184201i	0.995750	−	0.0921006i	$-0.0293582\pi$
$192$	−3.64954e21	+	7.68756e21i	−0.0536075	+	0.112921i
$193$	−2.81464e22			−0.392509			−0.196255	−	0.980553i	$-0.562878\pi$
$193$	−2.81464e22			−0.392509			−0.196255	+	0.980553i	$0.562878\pi$
$194$			2.00568e22i			0.265610i
$195$	6.37334e22	+	3.02563e22i	0.801716	+	0.380601i
$196$	3.49904e22			0.418205
$197$			1.04332e23i			1.18510i	0.805532	+	0.592552i	$0.201879\pi$
$197$			1.04332e23i			1.18510i	−0.805532	+	0.592552i	$0.798121\pi$
$198$	−4.53755e22	−	5.56171e22i	−0.489971	−	0.600560i
$199$	8.17241e22			0.839111			0.419555	−	0.907730i	$-0.362186\pi$
$199$	8.17241e22			0.839111			0.419555	+	0.907730i	$0.362186\pi$
$200$		−	2.22999e22i		−	0.217772i
$201$	−1.39270e22	+	2.93364e22i	−0.129389	+	0.272550i
$202$	1.89260e22			0.167319
$203$		−	2.07765e22i		−	0.174828i
$204$	5.66436e22	+	2.68906e22i	0.453784	+	0.215426i
$205$	1.24909e23			0.952917
$206$		−	4.96127e22i		−	0.360513i
$207$	−3.77070e22	+	3.07635e22i	−0.261047	+	0.212977i
$208$	5.42670e22			0.358016
$209$		−	2.56503e23i		−	1.61298i
$210$	−1.26784e22	+	2.67064e22i	−0.0760104	+	0.160112i
$211$	−9.16044e21			−0.0523711			−0.0261855	−	0.999657i	$-0.508336\pi$
$211$	−9.16044e21			−0.0523711			−0.0261855	+	0.999657i	$0.508336\pi$
$212$		−	7.89056e22i		−	0.430278i
$213$	1.88184e21	+	8.93373e20i	0.00979010	+	0.00464769i
$214$	6.42548e21			0.0318983
$215$		−	1.30314e23i		−	0.617455i
$216$	1.86630e22	+	7.59006e22i	0.0844197	+	0.343327i
$217$	−1.08805e23			−0.469951
$218$			2.72525e23i			1.12419i
$219$	−1.48401e23	+	3.12599e23i	−0.584786	+	1.23182i
$220$	−9.02088e22			−0.339642
$221$		−	3.99850e23i		−	1.43872i
$222$	1.91792e23	+	9.10500e22i	0.659630	+	0.313149i
$223$	1.75904e23			0.578398			0.289199	−	0.957269i	$-0.406611\pi$
$223$	1.75904e23			0.578398			0.289199	+	0.957269i	$0.406611\pi$
$224$			2.27397e22i			0.0714997i
$225$	−1.29479e23	−	1.58703e23i	−0.389379	−	0.477264i
$226$	−2.26874e23			−0.652679
$227$			4.86738e23i			1.33979i	0.742456	+	0.669895i	$0.233661\pi$
$227$			4.86738e23i			1.33979i	−0.742456	+	0.669895i	$0.766339\pi$
$228$	−1.19785e23	+	2.52321e23i	−0.315541	+	0.664669i
$229$	−2.47734e23			−0.624643			−0.312321	−	0.949977i	$-0.601107\pi$
$229$	−2.47734e23			−0.624643			−0.312321	+	0.949977i	$0.601107\pi$
$230$			6.11593e22i			0.147633i
$231$	−1.73271e23	−	8.22573e22i	−0.400502	−	0.190132i
$232$	−6.90347e22			−0.152823
$233$			5.09443e22i			0.108028i	0.998540	+	0.0540140i	$0.0172016\pi$
$233$			5.09443e22i			0.108028i	−0.998540	+	0.0540140i	$0.982798\pi$
$234$	3.86205e23	−	3.15087e23i	0.784619	−	0.640136i
$235$	−4.68764e23			−0.912589
$236$		−	4.16813e23i		−	0.777716i
$237$	1.34725e23	−	2.83792e23i	0.240972	−	0.507594i
$238$	1.67551e23			0.287328
$239$			3.07834e23i			0.506219i	0.967438	+	0.253109i	$0.0814532\pi$
$239$			3.07834e23i			0.506219i	−0.967438	+	0.253109i	$0.918547\pi$
$240$	8.87383e22	+	4.21270e22i	0.139958	+	0.0664429i
$241$	7.98228e23			1.20769			0.603847	−	0.797100i	$-0.293634\pi$
$241$	7.98228e23			1.20769			0.603847	+	0.797100i	$0.293634\pi$
$242$		−	9.81488e22i		−	0.142473i
$243$	5.73518e23	+	4.31804e23i	0.798885	+	0.601484i
$244$	−5.48023e23			−0.732657
$245$		−	4.03898e23i		−	0.518336i
$246$	3.78455e23	−	7.97195e23i	0.466298	−	0.982231i
$247$	1.78115e24			2.10733
$248$			3.61530e23i			0.410797i
$249$	−1.23544e24	−	5.86503e23i	−1.34843	−	0.640142i
$250$	−6.75315e23			−0.708119
$251$			5.48885e23i			0.553024i	0.961010	+	0.276512i	$0.0891786\pi$
$251$			5.48885e23i			0.553024i	−0.961010	+	0.276512i	$0.910821\pi$
$252$	1.32032e23	+	1.61833e23i	0.127842	+	0.156697i
$253$	−3.96800e23			−0.369289
$254$			9.53948e22i			0.0853469i
$255$	3.10401e23	−	6.53843e23i	0.267006	−	0.562434i
$256$	7.55579e22			0.0625000
$257$			1.68105e24i			1.33737i	0.743548	+	0.668683i	$0.233141\pi$
$257$			1.68105e24i			1.33737i	−0.743548	+	0.668683i	$0.766859\pi$
$258$	−8.31689e23	−	3.94831e23i	−0.636450	−	0.302144i
$259$	5.67318e23			0.417666
$260$		−	6.26409e23i		−	0.443736i
$261$	−4.91303e23	+	4.00833e23i	−0.334922	+	0.273249i
$262$	6.85271e23			0.449624
$263$			9.52100e23i			0.601347i	0.953727	+	0.300673i	$0.0972114\pi$
$263$			9.52100e23i			0.601347i	−0.953727	+	0.300673i	$0.902789\pi$
$264$	−2.73319e23	+	5.75731e23i	−0.166200	+	0.350091i
$265$	−9.10815e23			−0.533300
$266$			7.46363e23i			0.420856i
$267$	−1.23390e24	−	5.85776e23i	−0.670145	−	0.318140i
$268$	2.88336e23			0.150852
$269$		−	5.56037e23i		−	0.280273i	−0.990132	−	0.140136i	$-0.955246\pi$
$269$		−	5.56037e23i		−	0.280273i	0.990132	−	0.140136i	$-0.0447541\pi$
$270$	8.76129e23	−	2.15429e23i	0.425530	−	0.104632i
$271$	−3.94134e24			−1.84481			−0.922403	−	0.386230i	$-0.873777\pi$
$271$	−3.94134e24			−1.84481			−0.922403	+	0.386230i	$0.873777\pi$
$272$		−	5.56726e23i		−	0.251161i
$273$	5.71194e23	−	1.20319e24i	0.248403	−	0.523248i
$274$	−8.79491e23			−0.368745
$275$		−	1.67007e24i		−	0.675160i
$276$	3.90332e23	+	1.85303e23i	0.152175	+	0.0722425i
$277$	8.74730e23			0.328910			0.164455	−	0.986385i	$-0.447414\pi$
$277$	8.74730e23			0.328910			0.164455	+	0.986385i	$0.447414\pi$
$278$			1.74406e24i			0.632577i
$279$	2.09913e24	+	2.57292e24i	0.734511	+	0.900295i
$280$	2.62487e23			0.0886190
$281$		−	3.89503e24i		−	1.26896i	−0.772939	−	0.634480i	$-0.781214\pi$
$281$		−	3.89503e24i		−	1.26896i	0.772939	−	0.634480i	$-0.218786\pi$
$282$	−1.42028e24	+	2.99175e24i	−0.446564	+	0.940662i
$283$	2.75034e24			0.834685			0.417343	−	0.908749i	$-0.362962\pi$
$283$	2.75034e24			0.834685			0.417343	+	0.908749i	$0.362962\pi$
$284$		−	1.84959e22i		−	0.00541865i
$285$	2.91257e24	+	1.38270e24i	0.823812	+	0.391091i
$286$	4.06412e24			1.10996
$287$		−	2.35809e24i		−	0.621931i
$288$	5.37727e23	−	4.38708e23i	0.136974	−	0.111751i
$289$	−3.78478e22			−0.00931241
$290$			7.96874e23i			0.189413i
$291$	7.01463e23	−	1.47759e24i	0.161092	−	0.339332i
$292$	3.07241e24			0.681791
$293$		−	1.74501e24i		−	0.374215i	−0.982339	−	0.187108i	$-0.940089\pi$
$293$		−	1.74501e24i		−	0.374215i	0.982339	−	0.187108i	$-0.0599113\pi$
$294$	−2.57776e24	−	1.22375e24i	−0.534281	−	0.253641i
$295$	−4.81131e24			−0.963925
$296$		−	1.88504e24i		−	0.365094i
$297$	1.39770e24	+	5.68430e24i	0.261727	+	1.06442i
$298$	−5.22383e24			−0.945860
$299$		−	2.75538e24i		−	0.482469i
$300$	−7.79912e23	+	1.64284e24i	−0.132079	+	0.278217i
$301$	−2.46013e24			−0.402988
$302$		−	5.93147e24i		−	0.939924i
$303$	−1.39429e24	−	6.61916e23i	−0.213760	−	0.101479i
$304$	2.47996e24			0.367883
$305$			6.32589e24i			0.908078i
$306$	−3.23249e24	−	3.96209e24i	−0.449080	−	0.550440i
$307$	−4.78787e24			−0.643812			−0.321906	−	0.946772i	$-0.604323\pi$
$307$	−4.78787e24			−0.643812			−0.321906	+	0.946772i	$0.604323\pi$
$308$			1.70301e24i			0.221671i
$309$	−1.73515e24	+	3.65500e24i	−0.218651	+	0.460577i
$310$	4.17318e24			0.509155
$311$			1.02735e25i			1.21371i	0.794812	+	0.606856i	$0.207570\pi$
$311$			1.02735e25i			1.21371i	−0.794812	+	0.606856i	$0.792430\pi$
$312$	−3.99787e24	−	1.89792e24i	−0.457386	−	0.217137i
$313$	8.14643e24			0.902660			0.451330	−	0.892357i	$-0.350950\pi$
$313$	8.14643e24			0.902660			0.451330	+	0.892357i	$0.350950\pi$
$314$			2.07834e24i			0.223059i
$315$	1.86805e24	−	1.52406e24i	0.194215	−	0.158452i
$316$	−2.78927e24			−0.280944
$317$			9.98989e24i			0.974918i	0.873146	+	0.487459i	$0.162076\pi$
$317$			9.98989e24i			0.974918i	−0.873146	+	0.487459i	$0.837924\pi$
$318$	−2.75963e24	+	5.81301e24i	−0.260964	+	0.549706i
$319$	−5.17010e24			−0.473797
$320$		−	8.72172e23i		−	0.0774645i
$321$	−4.73369e23	−	2.24724e23i	−0.0407520	−	0.0193463i
$322$	1.15460e24			0.0963544
$323$		−	1.82729e25i		−	1.47837i
$324$	1.27962e24	−	6.24435e24i	0.100377	−	0.489821i
$325$	1.15969e25			0.882083
$326$		−	1.08439e25i		−	0.799848i
$327$	9.53123e24	−	2.00770e25i	0.681823	−	1.43622i
$328$	−7.83531e24			−0.543648
$329$			8.84955e24i			0.595610i
$330$	6.64573e24	+	3.15495e24i	0.433913	+	0.205993i
$331$	1.08350e24			0.0686354			0.0343177	−	0.999411i	$-0.489074\pi$
$331$	1.08350e24			0.0686354			0.0343177	+	0.999411i	$0.489074\pi$
$332$			1.21426e25i			0.746330i
$333$	−1.09450e25	−	1.34154e25i	−0.652792	−	0.800132i
$334$	1.68995e25			0.978159
$335$		−	3.32829e24i		−	0.186970i
$336$	7.95295e23	−	1.67524e24i	0.0433646	−	0.0913452i
$337$	9.99666e23			0.0529122			0.0264561	−	0.999650i	$-0.491578\pi$
$337$	9.99666e23			0.0529122			0.0264561	+	0.999650i	$0.491578\pi$
$338$			1.44602e25i			0.743031i
$339$	1.67139e25	+	7.93464e24i	0.833836	+	0.395850i
$340$	−6.42635e24			−0.311297
$341$			2.70755e25i			1.27360i
$342$	1.76493e25	−	1.43993e25i	0.806244	−	0.657779i
$343$	−1.67413e25			−0.742761
$344$			8.17434e24i			0.352264i
$345$	2.13898e24	−	4.50564e24i	0.0895396	−	0.188610i
$346$	−9.10789e24			−0.370388
$347$		−	2.37469e25i		−	0.938234i	−0.883136	−	0.469117i	$-0.844572\pi$
$347$		−	2.37469e25i		−	0.938234i	0.883136	−	0.469117i	$-0.155428\pi$
$348$	5.08582e24	+	2.41441e24i	0.195240	+	0.0926869i
$349$	−1.90707e25			−0.711398			−0.355699	−	0.934601i	$-0.615757\pi$
$349$	−1.90707e25			−0.711398			−0.355699	+	0.934601i	$0.615757\pi$
$350$			4.85951e24i			0.176162i
$351$	−3.94717e25	+	9.70559e24i	−1.39064	+	0.341941i
$352$	5.65863e24			0.193769
$353$		−	1.35549e25i		−	0.451179i	−0.974222	−	0.225589i	$-0.927569\pi$
$353$		−	1.35549e25i		−	0.451179i	0.974222	−	0.225589i	$-0.0724308\pi$
$354$	−1.45775e25	+	3.07068e25i	−0.471684	+	0.993578i
$355$	−2.13500e23			−0.00671604
$356$			1.21275e25i			0.370914i
$357$	−1.23436e25	−	5.85990e24i	−0.367078	−	0.174264i
$358$	−3.02764e25			−0.875535
$359$			9.11815e24i			0.256426i	0.991747	+	0.128213i	$0.0409241\pi$
$359$			9.11815e24i			0.256426i	−0.991747	+	0.128213i	$0.959076\pi$
$360$	−5.06405e24	−	6.20704e24i	−0.138507	−	0.169769i
$361$	4.38075e25			1.16540
$362$		−	3.53800e25i		−	0.915529i
$363$	−3.43264e24	+	7.23067e24i	−0.0864096	+	0.182017i
$364$	−1.18257e25			−0.289609
$365$		−	3.54652e25i		−	0.845033i
$366$	4.03731e25	+	1.91665e25i	0.936013	+	0.444356i
$367$	3.59066e25			0.810053			0.405026	−	0.914305i	$-0.367262\pi$
$367$	3.59066e25			0.810053			0.405026	+	0.914305i	$0.367262\pi$
$368$		−	3.83641e24i		−	0.0842261i
$369$	−5.57620e25	+	4.54937e25i	−1.19145	+	0.972049i
$370$	−2.17593e25			−0.452509
$371$			1.71948e25i			0.348064i
$372$	1.26441e25	−	2.66341e25i	0.249149	−	0.524818i
$373$	5.06070e25			0.970782			0.485391	−	0.874297i	$-0.338677\pi$
$373$	5.06070e25			0.970782			0.485391	+	0.874297i	$0.338677\pi$
$374$		−	4.16940e25i		−	0.778677i
$375$	4.97508e25	+	2.36183e25i	0.904664	+	0.429474i
$376$	2.94047e25			0.520640
$377$		−	3.59011e25i		−	0.619005i
$378$	−4.06697e24	−	1.65400e25i	−0.0682894	−	0.277726i
$379$	−1.20670e25			−0.197336			−0.0986682	−	0.995120i	$-0.531458\pi$
$379$	−1.20670e25			−0.197336			−0.0986682	+	0.995120i	$0.531458\pi$
$380$		−	2.86265e25i		−	0.455966i
$381$	3.33632e24	−	7.02779e24i	0.0517629	−	0.109036i
$382$	8.61810e24			0.130250
$383$			1.07043e26i			1.57605i	0.615643	+	0.788025i	$0.288896\pi$
$383$			1.07043e26i			1.57605i	−0.615643	+	0.788025i	$0.711104\pi$
$384$	−5.56639e24	−	2.64255e24i	−0.0798475	−	0.0379062i
$385$	1.96580e25			0.274746
$386$		−	2.03802e25i		−	0.277546i
$387$	4.74622e25	+	5.81748e25i	0.629852	+	0.772014i
$388$	−1.45227e25			−0.187815
$389$		−	1.46981e26i		−	1.85253i	−0.376869	−	0.926266i	$-0.622999\pi$
$389$		−	1.46981e26i		−	1.85253i	0.376869	−	0.926266i	$-0.377001\pi$
$390$	−2.19079e25	+	4.61479e25i	−0.269126	+	0.566899i
$391$	−2.82675e25			−0.338470
$392$			2.53358e25i			0.295715i
$393$	−5.04843e25	−	2.39666e25i	−0.574421	−	0.272697i
$394$	−7.55446e25			−0.837995
$395$			3.21969e25i			0.348211i
$396$	4.02711e25	−	3.28554e25i	0.424660	−	0.346461i
$397$	4.92699e25			0.506613			0.253307	−	0.967386i	$-0.418482\pi$
$397$	4.92699e25			0.506613			0.253307	+	0.967386i	$0.418482\pi$
$398$			5.91746e25i			0.593341i
$399$	2.61032e25	−	5.49850e25i	0.255249	−	0.537669i
$400$	1.61468e25			0.153988
$401$			9.75912e25i			0.907751i	0.891065	+	0.453876i	$0.149959\pi$
$401$			9.75912e25i			0.907751i	−0.891065	+	0.453876i	$0.850041\pi$
$402$	−2.12418e25	−	1.00842e25i	−0.192722	−	0.0914916i
$403$	−1.88012e26			−1.66393
$404$			1.37039e25i			0.118313i
$405$	−7.20792e25	−	1.47708e25i	−0.607099	−	0.124410i
$406$	1.50438e25			0.123622
$407$		−	1.41173e26i		−	1.13190i
$408$	−1.94709e25	+	4.10143e25i	−0.152329	+	0.320874i
$409$	−2.10261e26			−1.60519			−0.802593	−	0.596527i	$-0.796547\pi$
$409$	−2.10261e26			−1.60519			−0.802593	+	0.596527i	$0.796547\pi$
$410$			9.04438e25i			0.673814i
$411$	6.47926e25	+	3.07592e25i	0.471093	+	0.223644i
$412$	3.59235e25			0.254921
$413$			9.08303e25i			0.629115i
$414$	−2.22752e25	−	2.73028e25i	−0.150597	−	0.184588i
$415$	1.40163e26			0.925025
$416$			3.92935e25i			0.253155i
$417$	6.09964e25	−	1.28486e26i	0.383658	−	0.808154i
$418$	1.85728e26			1.14055
$419$			2.25937e26i			1.35471i	0.735654	+	0.677357i	$0.236875\pi$
$419$			2.25937e26i			1.35471i	−0.735654	+	0.677357i	$0.763125\pi$
$420$	−1.93375e25	−	9.18017e24i	−0.113216	−	0.0537474i
$421$	−5.73225e23			−0.00327721			−0.00163860	−	0.999999i	$-0.500522\pi$
$421$	−5.73225e23			−0.00327721			−0.00163860	+	0.999999i	$0.500522\pi$
$422$		−	6.63287e24i		−	0.0370320i
$423$	2.09266e26	−	1.70731e26i	1.14102	−	0.930911i
$424$	5.71337e25			0.304252
$425$		−	1.18973e26i		−	0.618814i
$426$	−6.46871e23	+	1.36260e24i	−0.00328641	+	0.00692264i
$427$	1.19423e26			0.592666
$428$			4.65255e24i			0.0225555i
$429$	−2.99406e26	−	1.42138e26i	−1.41804	−	0.673190i
$430$	9.43572e25			0.436607
$431$			3.37322e25i			0.152501i	0.997089	+	0.0762503i	$0.0242948\pi$
$431$			3.37322e25i			0.152501i	−0.997089	+	0.0762503i	$0.975705\pi$
$432$	−5.49579e25	+	1.35135e25i	−0.242769	+	0.0596937i
$433$	2.64976e26			1.14374			0.571871	−	0.820343i	$-0.306218\pi$
$433$	2.64976e26			1.14374			0.571871	+	0.820343i	$0.306218\pi$
$434$		−	7.87834e25i		−	0.332305i
$435$	2.78698e25	−	5.87061e25i	0.114879	−	0.241986i
$436$	−1.97329e26			−0.794924
$437$		−	1.25919e26i		−	0.495766i
$438$	−2.26346e26	−	1.07454e26i	−0.871028	−	0.413506i
$439$	−3.82154e26			−1.43745			−0.718726	−	0.695293i	$-0.755275\pi$
$439$	−3.82154e26			−1.43745			−0.718726	+	0.695293i	$0.755275\pi$
$440$		−	6.53181e25i		−	0.240163i
$441$	1.47106e26	+	1.80309e26i	0.528743	+	0.648083i
$442$	2.89523e26			1.01733
$443$		−	8.71029e25i		−	0.299223i	−0.988745	−	0.149612i	$-0.952198\pi$
$443$		−	8.71029e25i		−	0.299223i	0.988745	−	0.149612i	$-0.0478023\pi$
$444$	−6.59273e25	+	1.38872e26i	−0.221429	+	0.466429i
$445$	1.39990e26			0.459722
$446$			1.27368e26i			0.408989i
$447$	3.84842e26	+	1.82698e26i	1.20839	+	0.573664i
$448$	−1.64653e25			−0.0505580
$449$			4.81674e26i			1.44640i	0.690636	+	0.723202i	$0.257331\pi$
$449$			4.81674e26i			1.44640i	−0.690636	+	0.723202i	$0.742669\pi$
$450$	1.14913e26	−	9.37525e25i	0.337477	−	0.275333i
$451$	−5.86796e26			−1.68547
$452$		−	1.64274e26i		−	0.461514i
$453$	−2.07446e26	+	4.36974e26i	−0.570064	+	1.20081i
$454$	−3.52436e26			−0.947375
$455$			1.36505e26i			0.358950i
$456$	−1.82700e26	−	8.67339e25i	−0.469992	−	0.223121i
$457$	4.94283e26			1.24398			0.621991	−	0.783025i	$-0.286324\pi$
$457$	4.94283e26			1.24398			0.621991	+	0.783025i	$0.286324\pi$
$458$		−	1.79379e26i		−	0.441689i
$459$	9.95700e25	+	4.04942e26i	0.239884	+	0.975586i
$460$	−4.42841e25			−0.104393
$461$		−	6.20823e26i		−	1.43205i	−0.698074	−	0.716026i	$-0.745959\pi$
$461$		−	6.20823e26i		−	1.43205i	0.698074	−	0.716026i	$-0.254041\pi$
$462$	5.95607e25	−	1.25461e26i	0.134443	−	0.283198i
$463$	−7.64108e26			−1.68789			−0.843946	−	0.536428i	$-0.819773\pi$
$463$	−7.64108e26			−1.68789			−0.843946	+	0.536428i	$0.819773\pi$
$464$		−	4.99864e25i		−	0.108062i
$465$	−3.07440e26	−	1.45952e26i	−0.650476	−	0.308803i
$466$	−3.68876e25			−0.0763874
$467$		−	3.13451e26i		−	0.635331i	−0.948203	−	0.317666i	$-0.897101\pi$
$467$		−	3.13451e26i		−	0.635331i	0.948203	−	0.317666i	$-0.102899\pi$
$468$	2.28148e26	+	2.79642e26i	0.452645	+	0.554810i
$469$	−6.28331e25			−0.122028
$470$		−	3.39421e26i		−	0.645298i
$471$	7.26874e25	−	1.53112e26i	0.135285	−	0.284971i
$472$	3.01805e26			0.549928
$473$			6.12187e26i			1.09213i
$474$	2.05487e26	+	9.75516e25i	0.358923	+	0.170393i
$475$	5.29972e26			0.906393
$476$			1.21320e26i			0.203171i
$477$	4.06607e26	−	3.31733e26i	0.666793	−	0.544007i
$478$	−2.22896e26			−0.357951
$479$		−	1.06999e27i		−	1.68277i	−0.540436	−	0.841385i	$-0.681741\pi$
$479$		−	1.06999e27i		−	1.68277i	0.540436	−	0.841385i	$-0.318259\pi$
$480$	−3.05032e25	+	6.42534e25i	−0.0469822	+	0.0989654i
$481$	9.80308e26			1.47881
$482$			5.77979e26i			0.853968i
$483$	−8.50597e25	−	4.03807e25i	−0.123098	−	0.0584389i
$484$	7.10673e25			0.100743
$485$			1.67637e26i			0.232783i
$486$	−3.12660e26	+	4.15271e26i	−0.425313	+	0.564897i
$487$	6.15533e26			0.820279			0.410140	−	0.912023i	$-0.365480\pi$
$487$	6.15533e26			0.820279			0.410140	+	0.912023i	$0.365480\pi$
$488$		−	3.96811e26i		−	0.518067i
$489$	−3.79251e26	+	7.98872e26i	−0.485108	+	1.02185i
$490$	2.92454e26			0.366519
$491$		−	8.23570e26i		−	1.01131i	−0.862735	−	0.505657i	$-0.831250\pi$
$491$		−	8.23570e26i		−	1.01131i	0.862735	−	0.505657i	$-0.168750\pi$
$492$	5.77231e26	+	2.74031e26i	0.694542	+	0.329722i
$493$	−3.68311e26			−0.434255
$494$			1.28969e27i			1.49010i
$495$	−3.79253e26	−	4.64853e26i	−0.429415	−	0.526337i
$496$	−2.61776e26			−0.290478
$497$			4.03055e24i			0.00438329i
$498$	4.24673e26	−	8.94552e26i	0.452649	−	0.953481i
$499$	−9.04798e26			−0.945249			−0.472625	−	0.881264i	$-0.656693\pi$
$499$	−9.04798e26			−0.945249			−0.472625	+	0.881264i	$0.656693\pi$
$500$		−	4.88980e26i		−	0.500716i
$501$	−1.24500e27	−	5.91041e26i	−1.24966	−	0.593253i
$502$	−3.97435e26			−0.391047
$503$			7.97659e26i			0.769374i	0.923047	+	0.384687i	$0.125691\pi$
$503$			7.97659e26i			0.769374i	−0.923047	+	0.384687i	$0.874309\pi$
$504$	−1.17180e26	+	9.56016e25i	−0.110802	+	0.0903982i
$505$	1.58186e26			0.146640
$506$		−	2.87314e26i		−	0.261127i
$507$	5.05728e26	−	1.06529e27i	0.450648	−	0.949266i
$508$	−6.90732e25			−0.0603494
$509$			1.98985e27i			1.70468i	0.522986	+	0.852341i	$0.324818\pi$
$509$			1.98985e27i			1.70468i	−0.522986	+	0.852341i	$0.675182\pi$
$510$	4.73433e26	+	2.24754e26i	0.397701	+	0.188802i
$511$	−6.69529e26			−0.551519
$512$			5.47097e25i			0.0441942i
$513$	−1.80383e27	+	4.43539e26i	−1.42897	+	0.351365i
$514$	−1.21721e27			−0.945660
$515$		−	4.14668e26i		−	0.315957i
$516$	2.85888e26	−	6.02208e26i	0.213648	−	0.450038i
$517$	2.20215e27			1.61414
$518$			4.10782e26i			0.295334i
$519$	6.70983e26	+	3.18538e26i	0.473192	+	0.224640i
$520$	4.53569e26			0.313769
$521$			1.04148e27i			0.706765i	0.935479	+	0.353383i	$0.114969\pi$
$521$			1.04148e27i			0.706765i	−0.935479	+	0.353383i	$0.885031\pi$
$522$	−2.90234e26	−	3.55741e26i	−0.193216	−	0.236826i
$523$	−1.09725e27			−0.716619			−0.358309	−	0.933603i	$-0.616647\pi$
$523$	−1.09725e27			−0.716619			−0.358309	+	0.933603i	$0.616647\pi$
$524$			4.96189e26i			0.317932i
$525$	1.69956e26	−	3.58002e26i	0.106842	−	0.225057i
$526$	−6.89394e26			−0.425216
$527$			1.92882e27i			1.16731i
$528$	−4.16874e26	−	1.97904e26i	−0.247551	−	0.117521i
$529$	1.52136e27			0.886495
$530$		−	6.59501e26i		−	0.377100i
$531$	2.14787e27	−	1.75235e27i	1.20521	−	0.983278i
$532$	−5.40425e26			−0.297590
$533$		−	4.07471e27i		−	2.20204i
$534$	4.24147e26	−	8.93443e26i	0.224959	−	0.473864i
$535$	5.37048e25			0.0279560
$536$			2.08777e26i			0.106668i
$537$	2.23047e27	+	1.05888e27i	1.11855	+	0.531012i
$538$	4.02614e26			0.198183
$539$			1.89743e27i			0.916808i
$540$	1.55987e26	+	6.34385e26i	0.0739863	+	0.300895i
$541$	−1.21596e27			−0.566168			−0.283084	−	0.959095i	$-0.591358\pi$
$541$	−1.21596e27			−0.566168			−0.283084	+	0.959095i	$0.591358\pi$
$542$		−	2.85383e27i		−	1.30447i
$543$	−1.23737e27	+	2.60646e27i	−0.555268	+	1.16964i
$544$	4.03113e26			0.177598
$545$			2.27779e27i			0.985254i
$546$	8.71202e26	+	4.13589e26i	0.369992	+	0.175648i
$547$	1.85958e27			0.775427			0.387713	−	0.921780i	$-0.373265\pi$
$547$	1.85958e27			0.775427			0.387713	+	0.921780i	$0.373265\pi$
$548$		−	6.36820e26i		−	0.260742i
$549$	−2.30398e27	−	2.82401e27i	−0.926309	−	1.13538i
$550$	1.20926e27			0.477410
$551$		−	1.64066e27i		−	0.636066i
$552$	−1.34174e26	+	2.82630e26i	−0.0510832	+	0.107604i
$553$	6.07828e26			0.227263
$554$			6.33372e26i			0.232574i
$555$	1.60302e27	+	7.61005e26i	0.578107	+	0.274447i
$556$	−1.26283e27			−0.447299
$557$		−	5.39648e27i		−	1.87741i	−0.344724	−	0.938704i	$-0.612028\pi$
$557$		−	5.39648e27i		−	1.87741i	0.344724	−	0.938704i	$-0.387972\pi$
$558$	−1.86299e27	+	1.51994e27i	−0.636604	+	0.519378i
$559$	−4.25102e27			−1.42684
$560$			1.90061e26i			0.0626631i
$561$	−1.45820e27	+	3.07162e27i	−0.472268	+	0.994806i
$562$	2.82030e27			0.897290
$563$			3.26074e27i			1.01914i	0.860431	+	0.509568i	$0.170195\pi$
$563$			3.26074e27i			1.01914i	−0.860431	+	0.509568i	$0.829805\pi$
$564$	−2.16626e27	−	1.02839e27i	−0.665149	−	0.315768i
$565$	−1.89623e27			−0.572015
$566$			1.99146e27i			0.590211i
$567$	−2.78851e26	+	1.36075e27i	−0.0811973	+	0.396229i
$568$	1.33924e25			0.00383156
$569$		−	2.40585e27i		−	0.676311i	−0.941090	−	0.338155i	$-0.890197\pi$
$569$		−	2.40585e27i		−	0.676311i	0.941090	−	0.338155i	$-0.109803\pi$
$570$	−1.00118e27	+	2.10893e27i	−0.276543	+	0.582523i
$571$	−9.09875e26			−0.246957			−0.123478	−	0.992347i	$-0.539405\pi$
$571$	−9.09875e26			−0.246957			−0.123478	+	0.992347i	$0.539405\pi$
$572$			2.94274e27i			0.784859i
$573$	−6.34899e26	−	3.01408e26i	−0.166402	−	0.0789966i
$574$	1.70744e27			0.439771
$575$		−	8.19847e26i		−	0.207517i
$576$	3.17658e26	+	3.89356e26i	0.0790197	+	0.0968550i
$577$	5.18337e26			0.126723			0.0633613	−	0.997991i	$-0.479818\pi$
$577$	5.18337e26			0.126723			0.0633613	+	0.997991i	$0.479818\pi$
$578$		−	2.74047e25i		−	0.00658487i
$579$	−7.12773e26	+	1.50142e27i	−0.168332	+	0.354581i
$580$	−5.76999e26			−0.133935
$581$		−	2.64607e27i		−	0.603727i
$582$	1.06989e27	+	5.07914e26i	0.239944	+	0.113910i
$583$	4.27882e27			0.943276
$584$			2.22466e27i			0.482099i
$585$	3.22794e27	−	2.63353e27i	0.687648	−	0.561022i
$586$	1.26352e27			0.264610
$587$		−	7.59093e27i		−	1.56284i	−0.624007	−	0.781419i	$-0.714496\pi$
$587$		−	7.59093e27i		−	1.56284i	0.624007	−	0.781419i	$-0.285504\pi$
$588$	8.86090e26	−	1.86650e27i	0.179351	−	0.377794i
$589$	−8.59202e27			−1.70979
$590$		−	3.48376e27i		−	0.681598i
$591$	5.56541e27	+	2.64209e27i	1.07059	+	0.508244i
$592$	1.36492e27			0.258160
$593$			4.78487e27i			0.889863i	0.895565	+	0.444932i	$0.146772\pi$
$593$			4.78487e27i			0.889863i	−0.895565	+	0.444932i	$0.853228\pi$
$594$	−4.11587e27	+	1.01204e27i	−0.752657	+	0.185069i
$595$	1.40041e27			0.251817
$596$		−	3.78246e27i		−	0.668824i
$597$	2.06956e27	−	4.35942e27i	0.359861	−	0.758028i
$598$	1.99511e27			0.341157
$599$			1.30817e27i			0.219987i	0.993932	+	0.109993i	$0.0350830\pi$
$599$			1.30817e27i			0.219987i	−0.993932	+	0.109993i	$0.964917\pi$
$600$	−1.18954e27	−	5.64717e26i	−0.196729	−	0.0933938i
$601$	5.77882e26			0.0939928			0.0469964	−	0.998895i	$-0.485035\pi$
$601$	5.77882e26			0.0939928			0.0469964	+	0.998895i	$0.485035\pi$
$602$		−	1.78132e27i		−	0.284956i
$603$	1.21221e27	+	1.48582e27i	0.190724	+	0.233772i
$604$	4.29484e27			0.664627
$605$		−	8.20337e26i		−	0.124864i
$606$	4.79279e26	−	1.00957e27i	0.0717566	−	0.151151i
$607$	3.69564e26			0.0544255			0.0272128	−	0.999630i	$-0.491337\pi$
$607$	3.69564e26			0.0544255			0.0272128	+	0.999630i	$0.491337\pi$
$608$			1.79569e27i			0.260132i
$609$	−1.10828e27	−	5.26139e26i	−0.157935	−	0.0749769i
$610$	−4.58043e27			−0.642108
$611$			1.52917e28i			2.10885i
$612$	2.86886e27	−	2.34057e27i	0.389220	−	0.317547i
$613$	5.40534e27			0.721471			0.360735	−	0.932668i	$-0.382526\pi$
$613$	5.40534e27			0.721471			0.360735	+	0.932668i	$0.382526\pi$
$614$		−	3.46679e27i		−	0.455244i
$615$	3.16317e27	−	6.66304e27i	0.408668	−	0.860837i
$616$	−1.23311e27			−0.156745
$617$			1.44324e28i			1.80504i	0.430645	+	0.902521i	$0.358286\pi$
$617$			1.44324e28i			1.80504i	−0.430645	+	0.902521i	$0.641714\pi$
$618$	−2.64650e27	−	1.25638e27i	−0.325677	−	0.154610i
$619$	−4.39354e27			−0.531996			−0.265998	−	0.963974i	$-0.585701\pi$
$619$	−4.39354e27			−0.531996			−0.265998	+	0.963974i	$0.585701\pi$
$620$			3.02171e27i			0.360027i
$621$	6.86138e26	+	2.79046e27i	0.0804444	+	0.327160i
$622$	−7.43883e27			−0.858224
$623$		−	2.64279e27i		−	0.300042i
$624$	1.37424e27	−	2.89477e27i	0.153539	−	0.323421i
$625$	−4.22924e25			−0.00465010
$626$			5.89865e27i			0.638277i
$627$	−1.36827e28	−	6.49561e27i	−1.45712	−	0.691743i
$628$	−1.50488e27			−0.157726
$629$		−	1.00570e28i		−	1.03744i
$630$	1.10354e27	+	1.35262e27i	0.112042	+	0.137331i
$631$	−2.36147e26			−0.0235988			−0.0117994	−	0.999930i	$-0.503756\pi$
$631$	−2.36147e26			−0.0235988			−0.0117994	+	0.999930i	$0.503756\pi$
$632$		−	2.01965e27i		−	0.198658i
$633$	−2.31977e26	+	4.88647e26i	−0.0224599	+	0.0473105i
$634$	−7.23345e27			−0.689371
$635$			7.97320e26i			0.0747989i
$636$	−4.20907e27	−	1.99819e27i	−0.388701	−	0.184529i
$637$	−1.31757e28			−1.19779
$638$		−	3.74355e27i		−	0.335025i
$639$	9.53106e25	−	7.77598e25i	0.00839717	−	0.00685088i
$640$	6.31520e26			0.0547756
$641$			1.02817e28i			0.877982i	0.898491	+	0.438991i	$0.144664\pi$
$641$			1.02817e28i			0.877982i	−0.898491	+	0.438991i	$0.855336\pi$
$642$	1.62717e26	−	3.42755e26i	0.0136799	−	0.0288160i
$643$	1.24429e28			1.02994			0.514969	−	0.857209i	$-0.327803\pi$
$643$	1.24429e28			1.02994			0.514969	+	0.857209i	$0.327803\pi$
$644$			8.36017e26i			0.0681328i
$645$	−6.95134e27	−	3.30003e27i	−0.557791	−	0.264802i
$646$	1.32310e28			1.04536
$647$			6.53765e26i			0.0508603i	0.999677	+	0.0254302i	$0.00809555\pi$
$647$			6.53765e26i			0.0508603i	−0.999677	+	0.0254302i	$0.991904\pi$
$648$	4.52139e27	+	9.26547e26i	0.346356	+	0.0709769i
$649$	2.26025e28			1.70494
$650$			8.39707e27i			0.623727i
$651$	−2.75536e27	+	5.80401e27i	−0.201543	+	0.424540i
$652$	7.85179e27			0.565578
$653$		−	1.56766e28i		−	1.11204i	−0.831169	−	0.556019i	$-0.812328\pi$
$653$		−	1.56766e28i		−	1.11204i	0.831169	−	0.556019i	$-0.187672\pi$
$654$	1.45373e28	+	6.90135e27i	1.01556	+	0.482122i
$655$	5.72756e27			0.394055
$656$		−	5.67337e27i		−	0.384417i
$657$	1.29170e28	+	1.58324e28i	0.861998	+	1.05656i
$658$	−6.40776e27			−0.421160
$659$		−	1.62234e28i		−	1.05024i	−0.851029	−	0.525119i	$-0.824021\pi$
$659$		−	1.62234e28i		−	1.05024i	0.851029	−	0.525119i	$-0.175979\pi$
$660$	−2.28443e27	+	4.81202e27i	−0.145659	+	0.306823i
$661$	−5.45854e27			−0.342817			−0.171408	−	0.985200i	$-0.554832\pi$
$661$	−5.45854e27			−0.342817			−0.171408	+	0.985200i	$0.554832\pi$
$662$			7.84537e26i			0.0485326i
$663$	−2.13293e28	−	1.01257e28i	−1.29969	−	0.617008i
$664$	−8.79218e27			−0.527735
$665$			6.23818e27i			0.368843i
$666$	9.71379e27	−	7.92506e27i	0.565778	−	0.461594i
$667$	−2.53804e27			−0.145626
$668$			1.22366e28i			0.691663i
$669$	4.45455e27	−	9.38327e27i	0.248052	−	0.522508i
$670$	2.40994e27			0.132208
$671$		−	2.97177e28i		−	1.60616i
$672$	1.21301e27	+	5.75855e26i	0.0645908	+	0.0306634i
$673$	5.33678e27			0.279981			0.139991	−	0.990153i	$-0.455293\pi$
$673$	5.33678e27			0.279981			0.139991	+	0.990153i	$0.455293\pi$
$674$			7.23835e26i			0.0374146i
$675$	−1.17446e28	+	2.88784e27i	−0.598136	+	0.147074i
$676$	−1.04703e28			−0.525402
$677$		−	1.17546e28i		−	0.581195i	−0.956845	−	0.290598i	$-0.906146\pi$
$677$		−	1.17546e28i		−	0.581195i	0.956845	−	0.290598i	$-0.0938541\pi$
$678$	−5.74530e27	+	1.21022e28i	−0.279908	+	0.589611i
$679$	3.16473e27			0.151928
$680$		−	4.65318e27i		−	0.220120i
$681$	2.59641e28	+	1.23260e28i	1.21033	+	0.574583i
$682$	−1.96047e28			−0.900569
$683$			9.10290e26i			0.0412071i	0.999788	+	0.0206036i	$0.00655878\pi$
$683$			9.10290e26i			0.0412071i	−0.999788	+	0.0206036i	$0.993441\pi$
$684$	1.04262e28	+	1.27795e28i	0.465120	+	0.570100i
$685$	−7.35088e27			−0.323172
$686$		−	1.21220e28i		−	0.525211i
$687$	−6.27357e27	+	1.32149e28i	−0.267884	+	0.564284i
$688$	−5.91885e27			−0.249088
$689$			2.97121e28i			1.23237i
$690$	3.26243e27	+	1.54878e27i	0.133368	+	0.0633141i
$691$	−2.65293e28			−1.06892			−0.534459	−	0.845194i	$-0.679485\pi$
$691$	−2.65293e28			−1.06892			−0.534459	+	0.845194i	$0.679485\pi$
$692$		−	6.59482e27i		−	0.261904i
$693$	−8.77573e27	+	7.15973e27i	−0.343519	+	0.280262i
$694$	1.71946e28			0.663432
$695$			1.45770e28i			0.554397i
$696$	−1.74822e27	+	3.68253e27i	−0.0655395	+	0.138055i
$697$	−4.18026e28			−1.54481
$698$		−	1.38087e28i		−	0.503034i
$699$	2.71753e27	+	1.29010e27i	0.0975894	+	0.0463289i
$700$	−3.51866e27			−0.124565
$701$			8.72923e27i			0.304646i	0.988331	+	0.152323i	$0.0486754\pi$
$701$			8.72923e27i			0.304646i	−0.988331	+	0.152323i	$0.951325\pi$
$702$	−7.02760e27	−	2.85806e28i	−0.241789	−	0.983331i
$703$	4.47994e28			1.51956
$704$			4.09728e27i			0.137015i
$705$	−1.18709e28	+	2.50053e28i	−0.391373	+	0.824406i
$706$	9.81479e27			0.319032
$707$		−	2.98631e27i		−	0.0957063i
$708$	−2.22341e28	−	1.05553e28i	−0.702566	−	0.333531i
$709$	2.73283e28			0.851434			0.425717	−	0.904856i	$-0.360022\pi$
$709$	2.73283e28			0.851434			0.425717	+	0.904856i	$0.360022\pi$
$710$		−	1.54590e26i		−	0.00474896i
$711$	−1.17266e28	−	1.43733e28i	−0.355202	−	0.435373i
$712$	−8.78128e27			−0.262276
$713$			1.32915e28i			0.391453i
$714$	4.24302e27	−	8.93769e27i	0.123223	−	0.259563i
$715$	3.39684e28			0.972779
$716$		−	2.19224e28i		−	0.619097i
$717$	1.64209e28	+	7.79553e27i	0.457303	+	0.217097i
$718$	−6.60224e27			−0.181321
$719$		−	3.15787e28i		−	0.855275i	−0.903950	−	0.427638i	$-0.859346\pi$
$719$		−	3.15787e28i		−	0.855275i	0.903950	−	0.427638i	$-0.140654\pi$
$720$	4.49438e27	−	3.66676e27i	0.120045	−	0.0979395i
$721$	−7.82831e27			−0.206213
$722$			3.17200e28i			0.824066i
$723$	2.02142e28	−	4.25800e28i	0.517932	−	1.09100i
$724$	2.56179e28			0.647377
$725$		−	1.06822e28i		−	0.266244i
$726$	−5.23556e27	−	2.48550e27i	−0.128706	−	0.0611008i
$727$	1.40235e28			0.340025			0.170013	−	0.985442i	$-0.445619\pi$
$727$	1.40235e28			0.340025			0.170013	+	0.985442i	$0.445619\pi$
$728$		−	8.56269e27i		−	0.204784i
$729$	3.75574e28	−	1.96583e28i	0.885973	−	0.463737i
$730$	2.56795e28			0.597528
$731$			4.36114e28i			1.00098i
$732$	−1.38780e28	+	2.92333e28i	−0.314207	+	0.661861i
$733$	−3.70597e28			−0.827679			−0.413840	−	0.910350i	$-0.635813\pi$
$733$	−3.70597e28			−0.827679			−0.413840	+	0.910350i	$0.635813\pi$
$734$			2.59991e28i			0.572794i
$735$	−2.15452e28	−	1.02282e28i	−0.468250	−	0.222294i
$736$	2.77786e27			0.0595569
$737$			1.56356e28i			0.330704i
$738$	−3.29410e28	−	4.03760e28i	−0.687342	−	0.842480i
$739$	2.40727e28			0.495542			0.247771	−	0.968819i	$-0.420302\pi$
$739$	2.40727e28			0.495542			0.247771	+	0.968819i	$0.420302\pi$
$740$		−	1.57554e28i		−	0.319972i
$741$	4.51055e28	−	9.50123e28i	0.903748	−	1.90370i
$742$	−1.24504e28			−0.246118
$743$			5.58377e28i			1.08903i	0.838751	+	0.544515i	$0.183286\pi$
$743$			5.58377e28i			1.08903i	−0.838751	+	0.544515i	$0.816714\pi$
$744$	1.92852e28	+	9.15531e27i	0.371102	+	0.176175i
$745$	−4.36613e28			−0.828961
$746$			3.66434e28i			0.686447i
$747$	−6.25718e28	+	5.10496e28i	−1.15657	+	0.943597i
$748$	3.01897e28			0.550608
$749$		−	1.01387e27i		−	0.0182458i
$750$	−1.71015e28	+	3.60234e28i	−0.303684	+	0.639694i
$751$	−5.86031e28			−1.02688			−0.513442	−	0.858124i	$-0.671630\pi$
$751$	−5.86031e28			−1.02688			−0.513442	+	0.858124i	$0.671630\pi$
$752$			2.12912e28i			0.368148i
$753$	2.92792e28	+	1.38998e28i	0.499586	+	0.237170i
$754$	2.59952e28			0.437703
$755$		−	4.95758e28i		−	0.823759i
$756$	1.19762e28	−	2.94480e27i	0.196382	−	0.0482879i
$757$	−1.00935e29			−1.63336			−0.816682	−	0.577087i	$-0.804189\pi$
$757$	−1.00935e29			−1.63336			−0.816682	+	0.577087i	$0.804189\pi$
$758$		−	8.73744e27i		−	0.139538i
$759$	−1.00485e28	+	2.11666e28i	−0.158373	+	0.333605i
$760$	2.07278e28			0.322416
$761$		−	6.12650e28i		−	0.940516i	−0.882529	−	0.470258i	$-0.844161\pi$
$761$		−	6.12650e28i		−	0.940516i	0.882529	−	0.470258i	$-0.155839\pi$
$762$	5.08866e27	+	2.41576e27i	0.0770999	+	0.0366019i
$763$	4.30012e28			0.643036
$764$			6.24017e27i			0.0921006i
$765$	−2.70175e28	−	3.31155e28i	−0.393578	−	0.482411i
$766$	−7.75074e28			−1.11444
$767$			1.56952e29i			2.22748i
$768$	1.91341e27	−	4.03049e27i	0.0268038	−	0.0564607i
$769$	−1.61313e28			−0.223052			−0.111526	−	0.993762i	$-0.535574\pi$
$769$	−1.61313e28			−0.223052			−0.111526	+	0.993762i	$0.535574\pi$
$770$			1.42339e28i			0.194275i
$771$	8.96726e28	+	4.25706e28i	1.20814	+	0.573543i
$772$	1.47568e28			0.196255
$773$		−	8.91516e28i		−	1.17040i	−0.810889	−	0.585200i	$-0.801016\pi$
$773$		−	8.91516e28i		−	1.17040i	0.810889	−	0.585200i	$-0.198984\pi$
$774$	−4.21230e28	+	3.43663e28i	−0.545896	+	0.445373i
$775$	−5.59419e28			−0.715682
$776$		−	1.05155e28i		−	0.132805i
$777$	1.43666e28	−	3.02625e28i	0.179120	−	0.377307i
$778$	1.06426e29			1.30994
$779$		−	1.86212e29i		−	2.26273i
$780$	−3.34146e28	−	1.58630e28i	−0.400858	−	0.190301i
$781$	1.00298e27			0.0118790
$782$		−	2.04679e28i		−	0.239334i
$783$	8.94003e27	+	3.63582e28i	0.103210	+	0.419745i
$784$	−1.83451e28			−0.209102
$785$			1.73709e28i			0.195491i
$786$	1.73536e28	−	3.65545e28i	0.192826	−	0.406177i
$787$	−1.09815e28			−0.120480			−0.0602399	−	0.998184i	$-0.519187\pi$
$787$	−1.09815e28			−0.120480			−0.0602399	+	0.998184i	$0.519187\pi$
$788$		−	5.47002e28i		−	0.592552i
$789$	5.07880e28	+	2.41108e28i	0.543239	+	0.257894i
$790$	−2.33130e28			−0.246222
$791$			3.57980e28i			0.373331i
$792$	2.37899e28	+	2.91594e28i	0.244985	+	0.300280i
$793$	2.06360e29			2.09842
$794$			3.56752e28i			0.358230i
$795$	−2.30653e28	+	4.85858e28i	−0.228711	+	0.481768i
$796$	−4.28470e28			−0.419555
$797$		−	1.04825e28i		−	0.101363i	−0.998715	−	0.0506815i	$-0.983861\pi$
$797$		−	1.04825e28i		−	0.101363i	0.998715	−	0.0506815i	$-0.0161393\pi$
$798$	3.98134e28	+	1.89007e28i	0.380189	+	0.180489i
$799$	1.56878e29			1.47943
$800$			1.16915e28i			0.108886i
$801$	−6.24942e28	+	5.09863e28i	−0.574797	+	0.468952i
$802$	−7.06636e28			−0.641877
$803$			1.66608e29i			1.49465i
$804$	7.30175e27	−	1.53807e28i	0.0646943	−	0.136275i
$805$	9.65023e27			0.0844460
$806$		−	1.36135e29i		−	1.17658i
$807$	−2.96607e28	−	1.40809e28i	−0.253190	−	0.120198i
$808$	−9.92269e27			−0.0836596
$809$		−	1.46596e29i		−	1.22078i	−0.792102	−	0.610389i	$-0.791013\pi$
$809$		−	1.46596e29i		−	1.22078i	0.792102	−	0.610389i	$-0.208987\pi$
$810$	1.06952e28	−	5.21909e28i	0.0879710	−	0.429284i
$811$	1.01091e29			0.821301			0.410651	−	0.911793i	$-0.365302\pi$
$811$	1.01091e29			0.821301			0.410651	+	0.911793i	$0.365302\pi$
$812$			1.08929e28i			0.0874142i
$813$	−9.98095e28	+	2.10243e29i	−0.791164	+	1.66654i
$814$	1.02221e29			0.800376
$815$		−	9.06340e28i		−	0.700995i
$816$	−2.96975e28	−	1.40984e28i	−0.226892	−	0.107713i
$817$	−1.94269e29			−1.46616
$818$		−	1.52245e29i		−	1.13504i
$819$	−4.97171e28	−	6.09386e28i	−0.366157	−	0.448801i
$820$	−6.54883e28			−0.476458
$821$			6.98301e28i			0.501893i	0.968001	+	0.250947i	$0.0807418\pi$
$821$			6.98301e28i			0.501893i	−0.968001	+	0.250947i	$0.919258\pi$
$822$	−2.22720e28	+	4.69148e28i	−0.158140	+	0.333113i
$823$	−4.33970e28			−0.304412			−0.152206	−	0.988349i	$-0.548638\pi$
$823$	−4.33970e28			−0.304412			−0.152206	+	0.988349i	$0.548638\pi$
$824$			2.60114e28i			0.180257i
$825$	−8.90866e28	−	4.22924e28i	−0.609920	−	0.289549i
$826$	−6.57682e28			−0.444852
$827$			2.54682e28i			0.170193i	0.996373	+	0.0850967i	$0.0271199\pi$
$827$			2.54682e28i			0.170193i	−0.996373	+	0.0850967i	$0.972880\pi$
$828$	1.97693e28	−	1.61289e28i	0.130524	−	0.106488i
$829$	−2.65122e29			−1.72942			−0.864709	−	0.502273i	$-0.832497\pi$
$829$	−2.65122e29			−1.72942			−0.864709	+	0.502273i	$0.832497\pi$
$830$			1.01489e29i			0.654091i
$831$	2.21515e28	−	4.66609e28i	0.141056	−	0.297127i
$832$	−2.84515e28			−0.179008
$833$			1.35170e29i			0.840295i
$834$	9.30336e28	+	4.41661e28i	0.571451	+	0.271287i
$835$	1.41248e29			0.857269
$836$			1.34481e29i			0.806490i
$837$	1.90406e29	−	4.68184e28i	1.12830	−	0.277435i
$838$	−1.63596e29			−0.957928
$839$			5.68363e27i			0.0328856i	0.999865	+	0.0164428i	$0.00523414\pi$
$839$			5.68363e27i			0.0328856i	−0.999865	+	0.0164428i	$0.994766\pi$
$840$	6.64715e27	−	1.40019e28i	0.0380052	−	0.0800558i
$841$	1.43925e29			0.813162
$842$		−	4.15059e26i		−	0.00231734i
$843$	−2.07773e29	−	9.86369e28i	−1.14634	−	0.544206i
$844$	4.80271e27			0.0261855
$845$			1.20860e29i			0.651200i
$846$	1.23622e29	+	1.51525e29i	0.658253	+	0.806825i
$847$	−1.54867e28			−0.0814940
$848$			4.13693e28i			0.215139i
$849$	6.96491e28	−	1.46712e29i	0.357963	−	0.754030i
$850$	8.61458e28			0.437567
$851$		−	6.93030e28i		−	0.347902i
$852$	−9.86627e26	−	4.68385e26i	−0.00489505	−	0.00232384i
$853$	3.80309e29			1.86486			0.932430	−	0.361349i	$-0.117684\pi$
$853$	3.80309e29			1.86486			0.932430	+	0.361349i	$0.117684\pi$
$854$			8.64717e28i			0.419078i
$855$	1.47515e29	−	1.20351e29i	0.706600	−	0.576484i
$856$	−3.36880e27			−0.0159492
$857$		−	2.85608e28i		−	0.133648i	−0.997765	−	0.0668240i	$-0.978713\pi$
$857$		−	2.85608e28i		−	0.133648i	0.997765	−	0.0668240i	$-0.0212866\pi$
$858$	1.02919e29	−	2.16793e29i	0.476017	−	1.00270i
$859$	−3.05517e29			−1.39670			−0.698351	−	0.715755i	$-0.746083\pi$
$859$	−3.05517e29			−1.39670			−0.698351	+	0.715755i	$0.746083\pi$
$860$			6.83219e28i			0.308728i
$861$	−1.25788e29	−	5.97158e28i	−0.561834	−	0.266721i
$862$	−2.44247e28			−0.107834
$863$		−	1.35950e29i		−	0.593296i	−0.954987	−	0.296648i	$-0.904131\pi$
$863$		−	1.35950e29i		−	0.593296i	0.954987	−	0.296648i	$-0.0958688\pi$
$864$	−9.78478e27	−	3.97938e28i	−0.0422099	−	0.171663i
$865$	−7.61246e28			−0.324612
$866$			1.91863e29i			0.808748i
$867$	−9.58449e26	+	2.01892e27i	−0.00399372	+	0.00841256i
$868$	5.70452e28			0.234975
$869$		−	1.51254e29i		−	0.615899i
$870$	4.25078e28	+	2.01799e28i	0.171110	+	0.0812317i
$871$	−1.08574e29			−0.432058
$872$		−	1.42881e29i		−	0.562096i
$873$	−6.10558e28	−	7.48365e28i	−0.237457	−	0.291052i
$874$	9.11750e28			0.350559
$875$			1.06557e29i			0.405042i
$876$	7.78051e28	−	1.63892e29i	0.292393	−	0.615910i
$877$	4.60178e29			1.70974			0.854870	−	0.518842i	$-0.173637\pi$
$877$	4.60178e29			1.70974			0.854870	+	0.518842i	$0.173637\pi$
$878$		−	2.76709e29i		−	1.01643i
$879$	−9.30843e28	−	4.41902e28i	−0.338055	−	0.160486i
$880$	4.72954e28			0.169821
$881$			1.92073e29i			0.681877i	0.940086	+	0.340939i	$0.110745\pi$
$881$			1.92073e29i			0.681877i	−0.940086	+	0.340939i	$0.889255\pi$
$882$	−1.30557e29	+	1.06516e29i	−0.458264	+	0.373877i
$883$	−8.65697e28			−0.300441			−0.150220	−	0.988653i	$-0.547998\pi$
$883$	−8.65697e28			−0.300441			−0.150220	+	0.988653i	$0.547998\pi$
$884$			2.09637e29i			0.719358i
$885$	−1.21841e29	+	2.56650e29i	−0.413389	+	0.870782i
$886$	6.30693e28			0.211583
$887$		−	2.82730e29i		−	0.937855i	−0.883237	−	0.468928i	$-0.844640\pi$
$887$		−	2.82730e29i		−	0.937855i	0.883237	−	0.468928i	$-0.155360\pi$
$888$	−1.00554e29	−	4.77364e28i	−0.329815	−	0.156574i
$889$	1.50522e28			0.0488182
$890$			1.01363e29i			0.325073i
$891$	3.38613e29	+	6.93903e28i	1.07381	+	0.220050i
$892$	−9.22243e28			−0.289199
$893$			6.98822e29i			2.16697i
$894$	−1.32287e29	+	2.78656e29i	−0.405642	+	0.854462i
$895$	−2.53053e29			−0.767328
$896$		−	1.19221e28i		−	0.0357499i
$897$	−1.46980e29	−	6.97765e28i	−0.435848	−	0.206912i
$898$	−3.48769e29			−1.02276
$899$			1.73182e29i			0.502233i
$900$	6.78841e28	+	8.32059e28i	0.194690	+	0.238632i
$901$	3.04817e29			0.864554
$902$		−	4.24886e29i		−	1.19181i
$903$	−6.22997e28	+	1.31231e29i	−0.172826	+	0.364048i
$904$	1.18947e29			0.326339
$905$		−	2.95710e29i		−	0.802379i
$906$	−3.16403e29	−	1.50207e29i	−0.849100	−	0.403096i
$907$	−4.27554e29			−1.13480			−0.567398	−	0.823444i	$-0.692050\pi$
$907$	−4.27554e29			−1.13480			−0.567398	+	0.823444i	$0.692050\pi$
$908$		−	2.55191e29i		−	0.669895i
$909$	−7.06174e28	+	5.76136e28i	−0.183347	+	0.149584i
$910$	−9.88401e28			−0.253816
$911$		−	2.34281e29i		−	0.595051i	−0.954714	−	0.297525i	$-0.903839\pi$
$911$		−	2.34281e29i		−	0.595051i	0.954714	−	0.297525i	$-0.0961613\pi$
$912$	6.28020e28	−	1.32289e29i	0.157770	−	0.332335i
$913$	−6.58458e29			−1.63614
$914$			3.57899e29i			0.879628i
$915$	3.37443e29	+	1.60195e29i	0.820331	+	0.389439i
$916$	1.29884e29			0.312321
$917$		−	1.08128e29i		−	0.257184i
$918$	−2.93209e29	+	7.20964e28i	−0.689843	+	0.169624i
$919$	6.61817e29			1.54022			0.770110	−	0.637911i	$-0.220201\pi$
$919$	6.61817e29			1.54022			0.770110	+	0.637911i	$0.220201\pi$
$920$		−	3.20651e28i		−	0.0738167i
$921$	−1.21247e29	+	2.55400e29i	−0.276105	+	0.581601i
$922$	4.49524e29			1.01261
$923$			6.96466e27i			0.0155197i
$924$	9.08437e28	+	4.31265e28i	0.200251	+	0.0950659i
$925$	2.91685e29			0.636058
$926$		−	5.53273e29i		−	1.19352i
$927$	1.51028e29	+	1.85117e29i	0.322301	+	0.395046i
$928$	3.61941e28			0.0764113
$929$		−	3.17087e29i		−	0.662248i	−0.943587	−	0.331124i	$-0.892572\pi$
$929$		−	3.17087e29i		−	0.662248i	0.943587	−	0.331124i	$-0.107428\pi$
$930$	1.05681e29	−	2.22611e29i	0.218356	−	0.459956i
$931$	−6.02123e29			−1.23080
$932$		−	2.67095e28i		−	0.0540140i
$933$	5.48023e29	+	2.60165e29i	1.09643	+	0.520513i
$934$	2.26962e29			0.449247
$935$		−	3.48482e29i		−	0.682440i
$936$	−2.02482e29	+	1.65197e29i	−0.392310	+	0.320068i
$937$	8.02259e29			1.53787			0.768934	−	0.639328i	$-0.220788\pi$
$937$	8.02259e29			1.53787			0.768934	+	0.639328i	$0.220788\pi$
$938$		−	4.54960e28i		−	0.0862869i
$939$	2.06298e29	−	4.34556e29i	0.387115	−	0.815437i
$940$	2.45767e29			0.456294
$941$			9.21432e29i			1.69265i	0.532667	+	0.846325i	$0.321190\pi$
$941$			9.21432e29i			1.69265i	−0.532667	+	0.846325i	$0.678810\pi$
$942$	1.10865e29	+	5.26313e28i	0.201505	+	0.0956611i
$943$	−2.88062e29			−0.518047
$944$			2.18530e29i			0.388858i
$945$	−3.39922e28	−	1.38243e29i	−0.0598495	−	0.243402i
$946$	−4.43271e29			−0.772249
$947$		−	7.20621e29i		−	1.24225i	−0.783713	−	0.621123i	$-0.786677\pi$
$947$		−	7.20621e29i		−	1.24225i	0.783713	−	0.621123i	$-0.213323\pi$
$948$	−7.06349e28	+	1.48789e29i	−0.120486	+	0.253797i
$949$	−1.15693e30			−1.95273
$950$			3.83741e29i			0.640917i
$951$	5.32892e29	+	2.52982e29i	0.880712	+	0.418103i
$952$	−8.78449e28			−0.143664
$953$		−	1.14502e30i		−	1.85303i	−0.376258	−	0.926515i	$-0.622789\pi$
$953$		−	1.14502e30i		−	1.85303i	0.376258	−	0.926515i	$-0.377211\pi$
$954$	2.40200e29	+	2.94415e29i	0.384671	+	0.471494i
$955$	7.20309e28			0.114152
$956$		−	1.61394e29i		−	0.253109i
$957$	−1.30926e29	+	2.75789e29i	−0.203192	+	0.428014i
$958$	7.74756e29			1.18990
$959$			1.38773e29i			0.210921i
$960$	−4.65244e28	−	2.20867e28i	−0.0699791	−	0.0332214i
$961$	2.35151e29			0.350036
$962$			7.09819e29i			1.04567i
$963$	−2.39750e28	+	1.95601e28i	−0.0349538	+	0.0285173i
$964$	−4.18502e29			−0.603847
$965$		−	1.70339e29i		−	0.243244i
$966$	2.92387e28	−	6.15898e28i	0.0413226	−	0.0870437i
$967$	−1.75377e29			−0.245305			−0.122653	−	0.992450i	$-0.539140\pi$
$967$	−1.75377e29			−0.245305			−0.122653	+	0.992450i	$0.539140\pi$
$968$			5.14582e28i			0.0712363i
$969$	−9.74734e29	−	4.62739e29i	−1.33551	−	0.634013i
$970$	−1.21382e29			−0.164603
$971$			1.35728e30i			1.82171i	0.412731	+	0.910853i	$0.364575\pi$
$971$			1.35728e30i			1.82171i	−0.412731	+	0.910853i	$0.635425\pi$
$972$	−3.00689e29	−	2.26390e29i	−0.399442	−	0.300742i
$973$	2.75192e29			0.361832
$974$			4.45693e29i			0.580025i
$975$	2.93678e29	−	6.18617e29i	0.378290	−	0.796848i
$976$	2.87322e29			0.366328
$977$		−	3.03730e29i		−	0.383303i	−0.981463	−	0.191651i	$-0.938616\pi$
$977$		−	3.03730e29i		−	0.383303i	0.981463	−	0.191651i	$-0.0613843\pi$
$978$	−5.78445e29	−	2.74607e29i	−0.722559	−	0.343023i
$979$	−6.57642e29			−0.813135
$980$			2.11759e29i			0.259168i
$981$	−8.29605e29	−	1.01685e30i	−1.00504	−	1.23188i
$982$	5.96329e29			0.715107
$983$			8.71880e29i			1.03496i	0.855697	+	0.517478i	$0.173129\pi$
$983$			8.71880e29i			1.03496i	−0.855697	+	0.517478i	$0.826871\pi$
$984$	−1.98419e29	+	4.17960e29i	−0.233149	+	0.491115i
$985$	−6.31410e29			−0.734427
$986$		−	2.66685e29i		−	0.307065i
$987$	4.72063e29	+	2.24104e29i	0.538057	+	0.255434i
$988$	−9.33837e29			−1.05366
$989$			3.00527e29i			0.335676i
$990$	3.36590e29	−	2.74609e29i	0.372176	−	0.303642i
$991$	−3.21138e29			−0.351524			−0.175762	−	0.984433i	$-0.556239\pi$
$991$	−3.21138e29			−0.351524			−0.175762	+	0.984433i	$0.556239\pi$
$992$		−	1.89546e29i		−	0.205399i
$993$	2.74383e28	−	5.77972e28i	0.0294350	−	0.0620032i
$994$	−2.91843e27			−0.00309946
$995$			4.94587e29i			0.520010i
$996$	6.47725e29	+	3.07496e29i	0.674213	+	0.320071i
$997$	1.70461e30			1.75661			0.878303	−	0.478104i	$-0.158676\pi$
$997$	1.70461e30			1.75661			0.878303	+	0.478104i	$0.158676\pi$
$998$		−	6.55144e29i		−	0.668392i
$999$	−9.92790e29	+	2.44114e29i	−1.00277	+	0.246569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.21.b.a.5.5	yes	6
3.2	odd	2	inner	6.21.b.a.5.2	✓	6
4.3	odd	2		48.21.e.b.17.4		6
12.11	even	2		48.21.e.b.17.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.21.b.a.5.2	✓	6	3.2	odd	2	inner
6.21.b.a.5.5	yes	6	1.1	even	1	trivial
48.21.e.b.17.3		6	12.11	even	2
48.21.e.b.17.4		6	4.3	odd	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+724.077i q^{2} +(25323.8 - 53343.1i) q^{3} -524288. q^{4} +6.05191e6i q^{5} +(3.86246e7 + 1.83364e7i) q^{6} +1.14251e8 q^{7} -3.79625e8i q^{8} +(-2.20420e9 - 2.70170e9i) q^{9} +O(q^{10})\)	\(q+724.077i q^{2} +(25323.8 - 53343.1i) q^{3} -524288. q^{4} +6.05191e6i q^{5} +(3.86246e7 + 1.83364e7i) q^{6} +1.14251e8 q^{7} -3.79625e8i q^{8} +(-2.20420e9 - 2.70170e9i) q^{9} -4.38205e9 q^{10} -2.84306e10i q^{11} +(-1.32769e10 + 2.79672e10i) q^{12} +1.97422e11 q^{13} +8.27265e10i q^{14} +(3.22828e11 + 1.53257e11i) q^{15} +2.74878e11 q^{16} -2.02536e12i q^{17} +(1.95624e12 - 1.59601e12i) q^{18} +9.02206e12 q^{19} -3.17294e12i q^{20} +(2.89326e12 - 6.09451e12i) q^{21} +2.05860e13 q^{22} -1.39568e13i q^{23} +(-2.02504e13 - 9.61354e12i) q^{24} +5.87418e13 q^{25} +1.42949e14i q^{26} +(-1.99936e14 + 4.91616e13i) q^{27} -5.99004e13 q^{28} -1.81850e14i q^{29} +(-1.10970e14 + 2.33752e14i) q^{30} -9.52335e14 q^{31} +1.99033e14i q^{32} +(-1.51658e15 - 7.19970e14i) q^{33} +1.46652e15 q^{34} +6.91437e14i q^{35} +(1.15563e15 + 1.41647e15i) q^{36} +4.96554e15 q^{37} +6.53267e15i q^{38} +(4.99947e15 - 1.05311e16i) q^{39} +2.29746e15 q^{40} -2.06396e16i q^{41} +(4.41289e15 + 2.09495e15i) q^{42} -2.15327e16 q^{43} +1.49058e16i q^{44} +(1.63504e16 - 1.33396e16i) q^{45} +1.01058e16 q^{46} +7.74571e16i q^{47} +(6.96094e15 - 1.46629e16i) q^{48} -6.67390e16 q^{49} +4.25336e16i q^{50} +(-1.08039e17 - 5.12897e16i) q^{51} -1.03506e17 q^{52} +1.50500e17i q^{53} +(-3.55968e16 - 1.44769e17i) q^{54} +1.72060e17 q^{55} -4.33725e16i q^{56} +(2.28472e17 - 4.81265e17i) q^{57} +1.31673e17 q^{58} +7.95007e17i q^{59} +(-1.69255e17 - 8.03509e16i) q^{60} +1.04527e18 q^{61} -6.89564e17i q^{62} +(-2.51832e17 - 3.08672e17i) q^{63} -1.44115e17 q^{64} +1.19478e18i q^{65} +(5.21314e17 - 1.09812e18i) q^{66} -5.49957e17 q^{67} +1.06187e18i q^{68} +(-7.44499e17 - 3.53438e17i) q^{69} -5.00654e17 q^{70} +3.52780e16i q^{71} +(-1.02563e18 + 8.36769e17i) q^{72} -5.86016e18 q^{73} +3.59544e18i q^{74} +(1.48756e18 - 3.13347e18i) q^{75} -4.73016e18 q^{76} -3.24823e18i q^{77} +(7.62534e18 + 3.62000e18i) q^{78} +5.32011e18 q^{79} +1.66354e18i q^{80} +(-2.44069e18 + 1.19102e19i) q^{81} +1.49447e19 q^{82} -2.31602e19i q^{83} +(-1.51690e18 + 3.19528e18i) q^{84} +1.22573e19 q^{85} -1.55913e19i q^{86} +(-9.70043e18 - 4.60512e18i) q^{87} -1.07930e19 q^{88} -2.31315e19i q^{89} +(9.65891e18 + 1.18390e19i) q^{90} +2.25557e19 q^{91} +7.31737e18i q^{92} +(-2.41167e19 + 5.08005e19i) q^{93} -5.60849e19 q^{94} +5.46007e19i q^{95} +(1.06170e19 + 5.04026e18i) q^{96} +2.76998e19 q^{97} -4.83242e19i q^{98} +(-7.68110e19 + 6.26667e19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9}+O(q^{10}) \) 6 * q + 18846 * q^3 - 3145728 * q^4 + 35057664 * q^6 - 566671812 * q^7 + 1944941382 * q^9	\( 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9} + 5360984064 q^{10} - 9880731648 q^{12} - 49898545620 q^{13} + 487708151328 q^{15} + 1649267441664 q^{16} - 3239129751552 q^{18} + 15927597287292 q^{19} - 20677554127188 q^{21} + 21184189636608 q^{22} - 18380312543232 q^{24} + 337510512308454 q^{25} - 10\!\cdots\!62 q^{27}+ \cdots - 22\!\cdots\!32 q^{99}+O(q^{100}) \) 6 * q + 18846 * q^3 - 3145728 * q^4 + 35057664 * q^6 - 566671812 * q^7 + 1944941382 * q^9 + 5360984064 * q^10 - 9880731648 * q^12 - 49898545620 * q^13 + 487708151328 * q^15 + 1649267441664 * q^16 - 3239129751552 * q^18 + 15927597287292 * q^19 - 20677554127188 * q^21 + 21184189636608 * q^22 - 18380312543232 * q^24 + 337510512308454 * q^25 - 1019514529044162 * q^27 + 297099230969856 * q^28 - 920809286295552 * q^30 + 1832545426397628 * q^31 - 3503562514347744 * q^33 + 2508713101983744 * q^34 - 1019709427286016 * q^36 + 424332326872812 * q^37 + 13854943345637340 * q^39 - 2810699612946432 * q^40 + 30169507188989952 * q^42 - 49488752333951556 * q^43 + 64297936569436992 * q^45 - 51218624034717696 * q^46 + 5180349034266624 * q^48 - 185965132589503470 * q^49 + 114461935953291648 * q^51 + 26161208686018560 * q^52 - 103567464750919680 * q^54 + 468503586680075712 * q^55 - 1250127589109383188 * q^57 + 330130684975472640 * q^58 - 255699531243454464 * q^60 + 3301830012872093484 * q^61 - 724019288731292484 * q^63 - 864691128455135232 * q^64 + 1110947414199017472 * q^66 - 2779226272508556228 * q^67 + 667934407322175168 * q^69 - 1866219302039371776 * q^70 + 1698236859181694976 * q^72 - 9149401536792501300 * q^73 + 9127347583517050878 * q^75 - 8350648126559748096 * q^76 + 19815256334884331520 * q^78 + 90056048403257148 * q^79 - 13310358127786728378 * q^81 - 19709381871486517248 * q^82 + 10840993498235142144 * q^84 + 78223886062534003968 * q^85 - 87334395308747540640 * q^87 - 11106616416197935104 * q^88 + 60406983770669457408 * q^90 + 132462766690215009720 * q^91 - 157075923546140581332 * q^93 - 106728395801434030080 * q^94 + 9636577302666018816 * q^96 + 92028905119987573836 * q^97 - 224342570810992842432 * q^99

Introduction

L-functions

Modular forms

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