LMFDB - Embedded newform 6.19.b.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,19,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, 19, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 19 $
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:	$12.3231682626$
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} - 2x^{5} - 8797x^{4} + 1809980x^{3} + 107861490x^{2} - 7180095600x + 788142376800 $ x^6 - 2x^5 - 8797x^4 + 1809980x^3 + 107861490x^2 - 7180095600*x + 788142376800
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{31}\cdot 3^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.2
Root			$85.4804 + 88.2031i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.19.b.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-362.039i q^{2} +(-3612.02 - 19348.7i) q^{3} -131072. q^{4} +3.69488e6i q^{5} +(-7.00499e6 + 1.30769e6i) q^{6} +3.18077e7 q^{7} +4.74531e7i q^{8} +(-3.61327e8 + 1.39776e8i) q^{9} +O(q^{10})$	\(q-362.039i q^{2} +(-3612.02 - 19348.7i) q^{3} -131072. q^{4} +3.69488e6i q^{5} +(-7.00499e6 + 1.30769e6i) q^{6} +3.18077e7 q^{7} +4.74531e7i q^{8} +(-3.61327e8 + 1.39776e8i) q^{9} +1.33769e9 q^{10} -7.02311e8i q^{11} +(4.73435e8 + 2.53608e9i) q^{12} +8.10908e9 q^{13} -1.15156e10i q^{14} +(7.14912e10 - 1.33460e10i) q^{15} +1.71799e10 q^{16} +1.82909e11i q^{17} +(5.06044e10 + 1.30814e11i) q^{18} +2.50983e11 q^{19} -4.84295e11i q^{20} +(-1.14890e11 - 6.15439e11i) q^{21} -2.54264e11 q^{22} +9.32089e11i q^{23} +(9.18158e11 - 1.71402e11i) q^{24} -9.83742e12 q^{25} -2.93580e12i q^{26} +(4.00962e12 + 6.48635e12i) q^{27} -4.16910e12 q^{28} +8.17010e12i q^{29} +(-4.83176e12 - 2.58826e13i) q^{30} +2.87019e13 q^{31} -6.21978e12i q^{32} +(-1.35888e13 + 2.53676e12i) q^{33} +6.62202e13 q^{34} +1.17525e14i q^{35} +(4.73599e13 - 1.83207e13i) q^{36} +3.99953e13 q^{37} -9.08655e13i q^{38} +(-2.92902e13 - 1.56900e14i) q^{39} -1.75333e14 q^{40} +3.68995e14i q^{41} +(-2.22813e14 + 4.15947e13i) q^{42} -2.11773e14 q^{43} +9.20533e13i q^{44} +(-5.16456e14 - 1.33506e15i) q^{45} +3.37452e14 q^{46} +2.53857e14i q^{47} +(-6.20541e13 - 3.32409e14i) q^{48} -6.16685e14 q^{49} +3.56153e15i q^{50} +(3.53906e15 - 6.60673e14i) q^{51} -1.06287e15 q^{52} +2.48752e14i q^{53} +(2.34831e15 - 1.45164e15i) q^{54} +2.59495e15 q^{55} +1.50937e15i q^{56} +(-9.06556e14 - 4.85620e15i) q^{57} +2.95789e15 q^{58} -1.21495e14i q^{59} +(-9.37050e15 + 1.74928e15i) q^{60} +7.62514e14 q^{61} -1.03912e16i q^{62} +(-1.14930e16 + 4.44596e15i) q^{63} -2.25180e15 q^{64} +2.99621e16i q^{65} +(9.18406e14 + 4.91968e15i) q^{66} -4.78338e16 q^{67} -2.39743e16i q^{68} +(1.80347e16 - 3.36673e15i) q^{69} +4.25488e16 q^{70} -6.41967e16i q^{71} +(-6.63282e15 - 1.71461e16i) q^{72} +7.57613e16 q^{73} -1.44799e16i q^{74} +(3.55330e16 + 1.90342e17i) q^{75} -3.28968e16 q^{76} -2.23389e16i q^{77} +(-5.68040e16 + 1.06042e16i) q^{78} +1.35483e16 q^{79} +6.34775e16i q^{80} +(1.11020e17 - 1.01010e17i) q^{81} +1.33590e17 q^{82} -2.11746e17i q^{83} +(1.50589e16 + 8.06668e16i) q^{84} -6.75827e17 q^{85} +7.66699e16i q^{86} +(1.58081e17 - 2.95106e16i) q^{87} +3.33268e16 q^{88} -1.30497e17i q^{89} +(-4.83343e17 + 1.86977e17i) q^{90} +2.57931e17 q^{91} -1.22171e17i q^{92} +(-1.03672e17 - 5.55346e17i) q^{93} +9.19059e16 q^{94} +9.27351e17i q^{95} +(-1.20345e17 + 2.24660e16i) q^{96} +9.26791e17 q^{97} +2.23264e17i q^{98} +(9.81663e16 + 2.53764e17i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6258 q^{3} - 786432 q^{4} - 15753216 q^{6} + 28233804 q^{7} + 695971638 q^{9}+O(q^{10}) $ 6 * q - 6258 * q^3 - 786432 * q^4 - 15753216 * q^6 + 28233804 * q^7 + 695971638 * q^9	$ 6 q - 6258 q^{3} - 786432 q^{4} - 15753216 q^{6} + 28233804 q^{7} + 695971638 q^{9} - 434257920 q^{10} + 820248576 q^{12} + 29566196220 q^{13} + 119627095680 q^{15} + 103079215104 q^{16} + 315939373056 q^{18} - 438814047012 q^{19} + 2876527406172 q^{21} - 2844452929536 q^{22} + 2064805527552 q^{24} - 25696048717290 q^{25} + 11197265522814 q^{27} - 3700661157888 q^{28} + 13072787619840 q^{30} + 21775814927148 q^{31} - 962560003968 q^{33} + 99067611119616 q^{34} - 91222394535936 q^{36} + 638446564817436 q^{37} - 736541155104180 q^{39} + 56919054090240 q^{40} - 203954622480384 q^{42} - 16\!\cdots\!52 q^{43}+ \cdots + 76\!\cdots\!72 q^{99}+O(q^{100}) $ 6 * q - 6258 * q^3 - 786432 * q^4 - 15753216 * q^6 + 28233804 * q^7 + 695971638 * q^9 - 434257920 * q^10 + 820248576 * q^12 + 29566196220 * q^13 + 119627095680 * q^15 + 103079215104 * q^16 + 315939373056 * q^18 - 438814047012 * q^19 + 2876527406172 * q^21 - 2844452929536 * q^22 + 2064805527552 * q^24 - 25696048717290 * q^25 + 11197265522814 * q^27 - 3700661157888 * q^28 + 13072787619840 * q^30 + 21775814927148 * q^31 - 962560003968 * q^33 + 99067611119616 * q^34 - 91222394535936 * q^36 + 638446564817436 * q^37 - 736541155104180 * q^39 + 56919054090240 * q^40 - 203954622480384 * q^42 - 1688313718883652 * q^43 + 390590504075520 * q^45 + 1979247919104 * q^46 - 107511621353472 * q^48 - 895767896448270 * q^49 + 9636273526722048 * q^51 - 3875300470947840 * q^52 + 2993011804200960 * q^54 - 1259959207783680 * q^55 + 4023767318253996 * q^57 + 21251172660756480 * q^58 - 15679762684968960 * q^60 - 16279597277700036 * q^61 - 32525159214131028 * q^63 - 13510798882111488 * q^64 - 60047751762690048 * q^66 + 11153724314613276 * q^67 + 3612037794746112 * q^69 + 161904998736691200 * q^70 - 41410805505196032 * q^72 - 78910243347781140 * q^73 + 348225828845090910 * q^75 + 57516234769956864 * q^76 - 168903906208235520 * q^78 - 476518976428926228 * q^79 + 630680446106425062 * q^81 + 396536393269149696 * q^82 - 377032200181776384 * q^84 - 967978669078932480 * q^85 + 419256510981966720 * q^87 + 372828134380142592 * q^88 - 2046848246643179520 * q^90 - 1032060167365562760 * q^91 + 764294136047005116 * q^93 + 2566175766871080960 * q^94 - 270638190107295744 * q^96 + 834695417243310348 * q^97 + 761688154713814272 * 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 $

$2$		−	362.039i		−	0.707107i
$2$		−	362.039i		−	0.707107i
$3$	−3612.02	−	19348.7i	−0.183510	−	0.983018i
$3$	−3612.02	−	19348.7i	−0.183510	−	0.983018i
$4$	−131072.			−0.500000
$5$			3.69488e6i			1.89178i	0.324492	+	0.945889i	$0.394807\pi$
$5$			3.69488e6i			1.89178i	−0.324492	+	0.945889i	$0.605193\pi$
$6$	−7.00499e6	+	1.30769e6i	−0.695099	+	0.129761i
$7$	3.18077e7			0.788224			0.394112	−	0.919062i	$-0.371052\pi$
$7$	3.18077e7			0.788224			0.394112	+	0.919062i	$0.371052\pi$
$8$			4.74531e7i			0.353553i
$9$	−3.61327e8	+	1.39776e8i	−0.932648	+	0.360787i
$10$	1.33769e9			1.33769
$11$		−	7.02311e8i		−	0.297848i	−0.988849	−	0.148924i	$-0.952419\pi$
$11$		−	7.02311e8i		−	0.297848i	0.988849	−	0.148924i	$-0.0475810\pi$
$12$	4.73435e8	+	2.53608e9i	0.0917549	+	0.491509i
$13$	8.10908e9			0.764683			0.382342	−	0.924021i	$-0.375118\pi$
$13$	8.10908e9			0.764683			0.382342	+	0.924021i	$0.375118\pi$
$14$		−	1.15156e10i		−	0.557359i
$15$	7.14912e10	−	1.33460e10i	1.85965	−	0.347160i
$16$	1.71799e10			0.250000
$17$			1.82909e11i			1.54239i	0.636596	+	0.771197i	$0.280342\pi$
$17$			1.82909e11i			1.54239i	−0.636596	+	0.771197i	$0.719658\pi$
$18$	5.06044e10	+	1.30814e11i	0.255115	+	0.659482i
$19$	2.50983e11			0.777789			0.388894	−	0.921282i	$-0.372857\pi$
$19$	2.50983e11			0.777789			0.388894	+	0.921282i	$0.372857\pi$
$20$		−	4.84295e11i		−	0.945889i
$21$	−1.14890e11	−	6.15439e11i	−0.144647	−	0.774838i
$22$	−2.54264e11			−0.210611
$23$			9.32089e11i			0.517496i	0.965945	+	0.258748i	$0.0833099\pi$
$23$			9.32089e11i			0.517496i	−0.965945	+	0.258748i	$0.916690\pi$
$24$	9.18158e11	−	1.71402e11i	0.347549	−	0.0648805i
$25$	−9.83742e12			−2.57882
$26$		−	2.93580e12i		−	0.540713i
$27$	4.00962e12	+	6.48635e12i	0.525810	+	0.850602i
$28$	−4.16910e12			−0.394112
$29$			8.17010e12i			0.563178i	0.959535	+	0.281589i	$0.0908614\pi$
$29$			8.17010e12i			0.563178i	−0.959535	+	0.281589i	$0.909139\pi$
$30$	−4.83176e12	−	2.58826e13i	−0.245479	−	1.31497i
$31$	2.87019e13			1.08557			0.542783	−	0.839873i	$-0.317371\pi$
$31$	2.87019e13			1.08557			0.542783	+	0.839873i	$0.317371\pi$
$32$		−	6.21978e12i		−	0.176777i
$33$	−1.35888e13	+	2.53676e12i	−0.292790	+	0.0546581i
$34$	6.62202e13			1.09064
$35$			1.17525e14i			1.49114i
$36$	4.73599e13	−	1.83207e13i	0.466324	−	0.180393i
$37$	3.99953e13			0.307747			0.153874	−	0.988091i	$-0.450825\pi$
$37$	3.99953e13			0.307747			0.153874	+	0.988091i	$0.450825\pi$
$38$		−	9.08655e13i		−	0.549980i
$39$	−2.92902e13	−	1.56900e14i	−0.140327	−	0.751697i
$40$	−1.75333e14			−0.668844
$41$			3.68995e14i			1.12711i	0.826079	+	0.563554i	$0.190566\pi$
$41$			3.68995e14i			1.12711i	−0.826079	+	0.563554i	$0.809434\pi$
$42$	−2.22813e14	+	4.15947e13i	−0.547893	+	0.102281i
$43$	−2.11773e14			−0.421361			−0.210680	−	0.977555i	$-0.567568\pi$
$43$	−2.11773e14			−0.421361			−0.210680	+	0.977555i	$0.567568\pi$
$44$			9.20533e13i			0.148924i
$45$	−5.16456e14	−	1.33506e15i	−0.682528	−	1.76436i
$46$	3.37452e14			0.365925
$47$			2.53857e14i			0.226834i	0.993547	+	0.113417i	$0.0361796\pi$
$47$			2.53857e14i			0.226834i	−0.993547	+	0.113417i	$0.963820\pi$
$48$	−6.20541e13	−	3.32409e14i	−0.0458774	−	0.245754i
$49$	−6.16685e14			−0.378703
$50$			3.56153e15i			1.82350i
$51$	3.53906e15	−	6.60673e14i	1.51620	−	0.283044i
$52$	−1.06287e15			−0.382342
$53$			2.48752e14i			0.0753848i	0.999289	+	0.0376924i	$0.0120007\pi$
$53$			2.48752e14i			0.0753848i	−0.999289	+	0.0376924i	$0.987999\pi$
$54$	2.34831e15	−	1.45164e15i	0.601466	−	0.371804i
$55$	2.59495e15			0.563463
$56$			1.50937e15i			0.278679i
$57$	−9.06556e14	−	4.85620e15i	−0.142732	−	0.764580i
$58$	2.95789e15			0.398227
$59$		−	1.21495e14i		−	0.0140246i	−0.999975	−	0.00701231i	$-0.997768\pi$
$59$		−	1.21495e14i		−	0.0140246i	0.999975	−	0.00701231i	$-0.00223211\pi$
$60$	−9.37050e15	+	1.74928e15i	−0.929825	+	0.173580i
$61$	7.62514e14			0.0652047			0.0326024	−	0.999468i	$-0.489621\pi$
$61$	7.62514e14			0.0652047			0.0326024	+	0.999468i	$0.489621\pi$
$62$		−	1.03912e16i		−	0.767611i
$63$	−1.14930e16	+	4.44596e15i	−0.735136	+	0.284381i
$64$	−2.25180e15			−0.125000
$65$			2.99621e16i			1.44661i
$66$	9.18406e14	+	4.91968e15i	0.0386491	+	0.207034i
$67$	−4.78338e16			−1.75817			−0.879086	−	0.476663i	$-0.841846\pi$
$67$	−4.78338e16			−1.75817			−0.879086	+	0.476663i	$0.841846\pi$
$68$		−	2.39743e16i		−	0.771197i
$69$	1.80347e16	−	3.36673e15i	0.508707	−	0.0949655i
$70$	4.25488e16			1.05440
$71$		−	6.41967e16i		−	1.40019i	−0.714048	−	0.700096i	$-0.753140\pi$
$71$		−	6.41967e16i		−	1.40019i	0.714048	−	0.700096i	$-0.246860\pi$
$72$	−6.63282e15	−	1.71461e16i	−0.127557	−	0.329741i
$73$	7.57613e16			1.28689			0.643446	−	0.765492i	$-0.277504\pi$
$73$	7.57613e16			1.28689			0.643446	+	0.765492i	$0.277504\pi$
$74$		−	1.44799e16i		−	0.217610i
$75$	3.55330e16	+	1.90342e17i	0.473239	+	2.53503i
$76$	−3.28968e16			−0.388894
$77$		−	2.23389e16i		−	0.234771i
$78$	−5.68040e16	+	1.06042e16i	−0.531530	+	0.0992260i
$79$	1.35483e16			0.113042			0.0565209	−	0.998401i	$-0.481999\pi$
$79$	1.35483e16			0.113042			0.0565209	+	0.998401i	$0.481999\pi$
$80$			6.34775e16i			0.472944i
$81$	1.11020e17	−	1.01010e17i	0.739666	−	0.672974i
$82$	1.33590e17			0.796986
$83$		−	2.11746e17i		−	1.13269i	−0.824168	−	0.566346i	$-0.808357\pi$
$83$		−	2.11746e17i		−	1.13269i	0.824168	−	0.566346i	$-0.191643\pi$
$84$	1.50589e16	+	8.06668e16i	0.0723234	+	0.387419i
$85$	−6.75827e17			−2.91787
$86$			7.66699e16i			0.297947i
$87$	1.58081e17	−	2.95106e16i	0.553614	−	0.103349i
$88$	3.33268e16			0.105305
$89$		−	1.30497e17i		−	0.372470i	−0.982505	−	0.186235i	$-0.940371\pi$
$89$		−	1.30497e17i		−	0.372470i	0.982505	−	0.186235i	$-0.0596285\pi$
$90$	−4.83343e17	+	1.86977e17i	−1.24759	+	0.482620i
$91$	2.57931e17			0.602742
$92$		−	1.22171e17i		−	0.258748i
$93$	−1.03672e17	−	5.55346e17i	−0.199212	−	1.06713i
$94$	9.19059e16			0.160396
$95$			9.27351e17i			1.47140i
$96$	−1.20345e17	+	2.24660e16i	−0.173775	+	0.0324403i
$97$	9.26791e17			1.21909			0.609545	−	0.792751i	$-0.291352\pi$
$97$	9.26791e17			1.21909			0.609545	+	0.792751i	$0.291352\pi$
$98$			2.23264e17i			0.267783i
$99$	9.81663e16	+	2.53764e17i	0.107460	+	0.277788i
$100$	1.28941e18			1.28941
$101$		−	4.46291e16i		−	0.0408062i	−0.999792	−	0.0204031i	$-0.993505\pi$
$101$		−	4.46291e16i		−	0.0408062i	0.999792	−	0.0204031i	$-0.00649495\pi$
$102$	−2.39189e17	−	1.28128e18i	−0.200143	−	1.07212i
$103$	−1.64674e18			−1.26209			−0.631043	−	0.775747i	$-0.717373\pi$
$103$	−1.64674e18			−1.26209			−0.631043	+	0.775747i	$0.717373\pi$
$104$			3.84801e17i			0.270356i
$105$	2.27397e18	−	4.24505e17i	1.46582	−	0.273640i
$106$	9.00579e16			0.0533051
$107$			2.30785e18i			1.25532i	0.778488	+	0.627660i	$0.215987\pi$
$107$			2.30785e18i			1.25532i	−0.778488	+	0.627660i	$0.784013\pi$
$108$	−5.25548e17	−	8.50179e17i	−0.262905	−	0.425301i
$109$	−1.97197e18			−0.907951			−0.453975	−	0.891014i	$-0.649995\pi$
$109$	−1.97197e18			−0.907951			−0.453975	+	0.891014i	$0.649995\pi$
$110$		−	9.39473e17i		−	0.398428i
$111$	−1.44464e17	−	7.73860e17i	−0.0564746	−	0.302521i
$112$	5.46452e17			0.197056
$113$		−	1.28812e18i		−	0.428794i	−0.976747	−	0.214397i	$-0.931221\pi$
$113$		−	1.28812e18i		−	0.428794i	0.976747	−	0.214397i	$-0.0687787\pi$
$114$	−1.75813e18	+	3.28208e17i	−0.540640	+	0.100927i
$115$	−3.44395e18			−0.978986
$116$		−	1.07087e18i		−	0.281589i
$117$	−2.93003e18	+	1.13346e18i	−0.713180	+	0.275888i
$118$	−4.39860e16			−0.00991691
$119$			5.81792e18i			1.21575i
$120$	6.33309e17	+	3.39248e18i	0.122739	+	0.657486i
$121$	5.06668e18			0.911286
$122$		−	2.76059e17i		−	0.0461067i
$123$	7.13958e18	−	1.33282e18i	1.10797	−	0.206835i
$124$	−3.76202e18			−0.542783
$125$		−	2.22532e19i		−	2.98678i
$126$	1.60961e18	+	4.16090e18i	0.201088	+	0.519820i
$127$	2.56743e18			0.298721			0.149360	−	0.988783i	$-0.452279\pi$
$127$	2.56743e18			0.298721			0.149360	+	0.988783i	$0.452279\pi$
$128$			8.15239e17i			0.0883883i
$129$	7.64928e17	+	4.09754e18i	0.0773238	+	0.414205i
$130$	1.08474e19			1.02291
$131$			9.70264e18i			0.853981i	0.904256	+	0.426990i	$0.140426\pi$
$131$			9.70264e18i			0.853981i	−0.904256	+	0.426990i	$0.859574\pi$
$132$	1.78112e18	−	3.32499e17i	0.146395	−	0.0273290i
$133$	7.98318e18			0.613072
$134$			1.73177e19i			1.24322i
$135$	−2.39663e19	+	1.48150e19i	−1.60915	+	0.994715i
$136$	−8.67962e18			−0.545319
$137$		−	2.13367e19i		−	1.25500i	−0.778618	−	0.627498i	$-0.784079\pi$
$137$		−	2.13367e19i		−	1.25500i	0.778618	−	0.627498i	$-0.215921\pi$
$138$	−1.21888e18	−	6.52927e18i	−0.0671508	−	0.359710i
$139$	1.11915e19			0.577770			0.288885	−	0.957364i	$-0.406716\pi$
$139$	1.11915e19			0.577770			0.288885	+	0.957364i	$0.406716\pi$
$140$		−	1.54043e19i		−	0.745572i
$141$	4.91181e18	−	9.16936e17i	0.222982	−	0.0416262i
$142$	−2.32417e19			−0.990086
$143$		−	5.69509e18i		−	0.227760i
$144$	−6.20755e18	+	2.40134e18i	−0.233162	+	0.0901967i
$145$	−3.01875e19			−1.06541
$146$		−	2.74285e19i		−	0.909969i
$147$	2.22748e18	+	1.19321e19i	0.0694957	+	0.372272i
$148$	−5.24227e18			−0.153874
$149$			3.51402e19i			0.970796i	0.874293	+	0.485398i	$0.161325\pi$
$149$			3.51402e19i			0.970796i	−0.874293	+	0.485398i	$0.838675\pi$
$150$	6.89111e19	−	1.28643e19i	1.79253	−	0.334630i
$151$	−1.32025e19			−0.323491			−0.161746	−	0.986832i	$-0.551712\pi$
$151$	−1.32025e19			−0.323491			−0.161746	+	0.986832i	$0.551712\pi$
$152$			1.19099e19i			0.274990i
$153$	−2.55664e19	−	6.60901e19i	−0.556476	−	1.43851i
$154$	−8.08754e18			−0.166008
$155$			1.06050e20i			2.05365i
$156$	3.83912e18	+	2.05653e19i	0.0701634	+	0.375849i
$157$	6.77852e19			1.16960			0.584801	−	0.811177i	$-0.301173\pi$
$157$	6.77852e19			1.16960			0.584801	+	0.811177i	$0.301173\pi$
$158$		−	4.90499e18i		−	0.0799327i
$159$	4.81304e18	−	8.98498e17i	0.0741046	−	0.0138338i
$160$	2.29813e19			0.334422
$161$			2.96476e19i			0.407902i
$162$	−3.65695e19	−	4.01935e19i	−0.475865	−	0.523023i
$163$	1.40045e20			1.72416			0.862081	−	0.506770i	$-0.169161\pi$
$163$	1.40045e20			1.72416			0.862081	+	0.506770i	$0.169161\pi$
$164$		−	4.83649e19i		−	0.563554i
$165$	−9.37303e18	−	5.02091e19i	−0.103401	−	0.553894i
$166$	−7.66601e19			−0.800934
$167$		−	1.49329e20i		−	1.47808i	−0.673664	−	0.739038i	$-0.735280\pi$
$167$		−	1.49329e20i		−	1.47808i	0.673664	−	0.739038i	$-0.264720\pi$
$168$	2.92045e19	−	5.45189e18i	0.273947	−	0.0511404i
$169$	−4.66982e19			−0.415260
$170$			2.44676e20i			2.06324i
$171$	−9.06869e19	+	3.50814e19i	−0.725403	+	0.280616i
$172$	2.77575e19			0.210680
$173$			6.62161e19i			0.477033i	0.971138	+	0.238517i	$0.0766611\pi$
$173$			6.62161e19i			0.477033i	−0.971138	+	0.238517i	$0.923339\pi$
$174$	−1.06840e19	−	5.72315e19i	−0.0730785	−	0.391464i
$175$	−3.12906e20			−2.03269
$176$		−	1.20656e19i		−	0.0744621i
$177$	−2.35078e18	+	4.38844e17i	−0.0137865	+	0.00257366i
$178$	−4.72450e19			−0.263376
$179$		−	3.08840e20i		−	1.63703i	−0.574485	−	0.818515i	$-0.694798\pi$
$179$		−	3.08840e20i		−	1.63703i	0.574485	−	0.818515i	$-0.305202\pi$
$180$	6.76929e19	+	1.74989e20i	0.341264	+	0.882181i
$181$	2.66841e20			1.27981			0.639904	−	0.768455i	$-0.278974\pi$
$181$	2.66841e20			1.27981			0.639904	+	0.768455i	$0.278974\pi$
$182$		−	9.33810e19i		−	0.426203i
$183$	−2.75422e18	−	1.47537e19i	−0.0119657	−	0.0640974i
$184$	−4.42305e19			−0.182962
$185$			1.47778e20i			0.582189i
$186$	−2.01057e20	+	3.75333e19i	−0.754575	+	0.140864i
$187$	1.28459e20			0.459400
$188$		−	3.32735e19i		−	0.113417i
$189$	1.27537e20	+	2.06316e20i	0.414456	+	0.670465i
$190$	3.35737e20			1.04044
$191$			7.13917e19i			0.211032i	0.994418	+	0.105516i	$0.0336494\pi$
$191$			7.13917e19i			0.211032i	−0.994418	+	0.105516i	$0.966351\pi$
$192$	8.13355e18	+	4.35695e19i	0.0229387	+	0.122877i
$193$	−3.84509e20			−1.03488			−0.517441	−	0.855719i	$-0.673115\pi$
$193$	−3.84509e20			−1.03488			−0.517441	+	0.855719i	$0.673115\pi$
$194$		−	3.35534e20i		−	0.862027i
$195$	5.79728e20	−	1.08224e20i	1.42204	−	0.265467i
$196$	8.08301e19			0.189351
$197$		−	1.85603e20i		−	0.415325i	−0.978201	−	0.207663i	$-0.933414\pi$
$197$		−	1.85603e20i		−	0.415325i	0.978201	−	0.207663i	$-0.0665856\pi$
$198$	9.18723e19	−	3.55400e19i	0.196426	−	0.0759855i
$199$	2.31039e20			0.472071			0.236035	−	0.971744i	$-0.424152\pi$
$199$	2.31039e20			0.472071			0.236035	+	0.971744i	$0.424152\pi$
$200$		−	4.66816e20i		−	0.911751i
$201$	1.72777e20	+	9.25523e20i	0.322642	+	1.72831i
$202$	−1.61575e19			−0.0288543
$203$			2.59872e20i			0.443910i
$204$	−4.63872e20	+	8.65957e19i	−0.758101	+	0.141522i
$205$	−1.36339e21			−2.13224
$206$			5.96183e20i			0.892430i
$207$	−1.30284e20	−	3.36789e20i	−0.186706	−	0.482641i
$208$	1.39313e20			0.191171
$209$		−	1.76268e20i		−	0.231663i
$210$	−1.53687e20	−	8.23265e20i	−0.193492	−	1.03649i
$211$	2.14795e20			0.259108			0.129554	−	0.991572i	$-0.458645\pi$
$211$	2.14795e20			0.259108			0.129554	+	0.991572i	$0.458645\pi$
$212$		−	3.26044e19i		−	0.0376924i
$213$	−1.24213e21	+	2.31880e20i	−1.37641	+	0.256949i
$214$	8.35533e20			0.887645
$215$		−	7.82474e20i		−	0.797120i
$216$	−3.07798e20	+	1.90269e20i	−0.300733	+	0.185902i
$217$	9.12942e20			0.855669
$218$			7.13930e20i			0.642018i
$219$	−2.73652e20	−	1.46589e21i	−0.236157	−	1.26504i
$220$	−3.40126e20			−0.281731
$221$			1.48323e21i			1.17944i
$222$	−2.80167e20	+	5.23016e19i	−0.213915	+	0.0399336i
$223$	−3.18670e20			−0.233667			−0.116833	−	0.993152i	$-0.537274\pi$
$223$	−3.18670e20			−0.233667			−0.116833	+	0.993152i	$0.537274\pi$
$224$		−	1.97837e20i		−	0.139340i
$225$	3.55453e21	−	1.37504e21i	2.40513	−	0.930404i
$226$	−4.66348e20			−0.303203
$227$			6.91420e20i			0.432025i	0.976391	+	0.216013i	$0.0693052\pi$
$227$			6.91420e20i			0.432025i	−0.976391	+	0.216013i	$0.930695\pi$
$228$	1.18824e20	+	6.36512e20i	0.0713659	+	0.382290i
$229$	9.82621e20			0.567371			0.283685	−	0.958917i	$-0.408443\pi$
$229$	9.82621e20			0.567371			0.283685	+	0.958917i	$0.408443\pi$
$230$			1.24684e21i			0.692248i
$231$	−4.32229e20	+	8.06885e19i	−0.230784	+	0.0430828i
$232$	−3.87697e20			−0.199113
$233$			1.17159e21i			0.578856i	0.957200	+	0.289428i	$0.0934651\pi$
$233$			1.17159e21i			0.578856i	−0.957200	+	0.289428i	$0.906535\pi$
$234$	4.10355e20	+	1.06078e21i	0.195082	+	0.504295i
$235$	−9.37969e20			−0.429119
$236$			1.59246e19i			0.00701231i
$237$	−4.89366e19	−	2.62142e20i	−0.0207443	−	0.111122i
$238$	2.10631e21			0.859667
$239$		−	1.92312e21i		−	0.755832i	−0.925840	−	0.377916i	$-0.876641\pi$
$239$		−	1.92312e21i		−	0.755832i	0.925840	−	0.377916i	$-0.123359\pi$
$240$	1.22821e21	−	2.29282e20i	0.464913	−	0.0867899i
$241$	−1.72968e21			−0.630685			−0.315342	−	0.948978i	$-0.602119\pi$
$241$	−1.72968e21			−0.630685			−0.315342	+	0.948978i	$0.602119\pi$
$242$		−	1.83433e21i		−	0.644377i
$243$	−2.35542e21	−	1.78324e21i	−0.797282	−	0.603607i
$244$	−9.99442e19			−0.0326024
$245$		−	2.27858e21i		−	0.716421i
$246$	−4.82531e20	−	2.58481e21i	−0.146255	−	0.783451i
$247$	2.03524e21			0.594762
$248$			1.36200e21i			0.383805i
$249$	−4.09701e21	+	7.64830e20i	−1.11346	+	0.207860i
$250$	−8.05653e21			−2.11197
$251$			4.72980e21i			1.19613i	0.801447	+	0.598066i	$0.204064\pi$
$251$			4.72980e21i			1.19613i	−0.801447	+	0.598066i	$0.795936\pi$
$252$	1.50641e21	−	5.82740e20i	0.367568	−	0.142190i
$253$	6.54616e20			0.154135
$254$		−	9.29510e20i		−	0.211228i
$255$	2.44110e21	+	1.30764e22i	0.535457	+	2.86831i
$256$	2.95148e20			0.0625000
$257$		−	1.96395e21i		−	0.401543i	−0.979638	−	0.200771i	$-0.935655\pi$
$257$		−	1.96395e21i		−	0.401543i	0.979638	−	0.200771i	$-0.0643449\pi$
$258$	1.48347e21	−	2.76934e20i	0.292887	−	0.0546762i
$259$	1.27216e21			0.242574
$260$		−	3.92719e21i		−	0.723305i
$261$	−1.14199e21	−	2.95208e21i	−0.203187	−	0.525247i
$262$	3.51273e21			0.603856
$263$		−	7.44618e21i		−	1.23689i	−0.785827	−	0.618446i	$-0.787762\pi$
$263$		−	7.44618e21i		−	1.23689i	0.785827	−	0.618446i	$-0.212238\pi$
$264$	−1.20377e20	−	6.44833e20i	−0.0193246	−	0.103517i
$265$	−9.19108e20			−0.142611
$266$		−	2.89022e21i		−	0.433507i
$267$	−2.52495e21	+	4.71358e20i	−0.366144	+	0.0683518i
$268$	6.26967e21			0.879086
$269$			1.76444e21i			0.239241i	0.992820	+	0.119621i	$0.0381678\pi$
$269$			1.76444e21i			0.239241i	−0.992820	+	0.119621i	$0.961832\pi$
$270$	5.36362e21	+	8.67671e21i	0.703370	+	1.13784i
$271$	1.35817e22			1.72279			0.861394	−	0.507937i	$-0.169592\pi$
$271$	1.35817e22			1.72279			0.861394	+	0.507937i	$0.169592\pi$
$272$			3.14236e21i			0.385599i
$273$	−9.31653e20	−	4.99064e21i	−0.110609	−	0.592506i
$274$	−7.72472e21			−0.887417
$275$			6.90893e21i			0.768097i
$276$	−2.36385e21	+	4.41283e20i	−0.254354	+	0.0474828i
$277$	9.98253e21			1.03973			0.519867	−	0.854247i	$-0.325981\pi$
$277$	9.98253e21			1.03973			0.519867	+	0.854247i	$0.325981\pi$
$278$		−	4.05175e21i		−	0.408545i
$279$	−1.03708e22	+	4.01185e21i	−1.01245	+	0.391658i
$280$	−5.57695e21			−0.527199
$281$		−	1.38066e22i		−	1.26395i	−0.774988	−	0.631976i	$-0.782244\pi$
$281$		−	1.38066e22i		−	1.26395i	0.774988	−	0.631976i	$-0.217756\pi$
$282$	−3.31966e20	−	1.77826e21i	−0.0294342	−	0.157672i
$283$	−1.74078e22			−1.49509			−0.747543	−	0.664213i	$-0.768767\pi$
$283$	−1.74078e22			−1.49509			−0.747543	+	0.664213i	$0.768767\pi$
$284$			8.41439e21i			0.700096i
$285$	1.79431e22	−	3.34961e21i	1.44642	−	0.270017i
$286$	−2.06184e21			−0.161050
$287$			1.17369e22i			0.888413i
$288$	8.69377e20	+	2.24737e21i	0.0637787	+	0.164870i
$289$	−1.93927e22			−1.37898
$290$			1.09290e22i			0.753356i
$291$	−3.34759e21	−	1.79322e22i	−0.223715	−	1.19839i
$292$	−9.93019e21			−0.643446
$293$		−	9.25225e21i		−	0.581352i	−0.956822	−	0.290676i	$-0.906120\pi$
$293$		−	9.25225e21i		−	0.581352i	0.956822	−	0.290676i	$-0.0938801\pi$
$294$	4.31987e21	−	8.06434e20i	0.263236	−	0.0491409i
$295$	4.48910e20			0.0265315
$296$			1.89790e21i			0.108805i
$297$	4.55543e21	−	2.81600e21i	0.253350	−	0.156612i
$298$	1.27221e22			0.686456
$299$			7.55838e21i			0.395720i
$300$	−4.65738e21	−	2.49485e22i	−0.236619	−	1.26751i
$301$	−6.73600e21			−0.332127
$302$			4.77980e21i			0.228743i
$303$	−8.63517e20	+	1.61201e20i	−0.0401132	+	0.00748833i
$304$	4.31185e21			0.194447
$305$			2.81739e21i			0.123353i
$306$	−2.39272e22	+	9.25601e21i	−1.01718	+	0.393488i
$307$	3.43877e22			1.41957			0.709787	−	0.704416i	$-0.248791\pi$
$307$	3.43877e22			1.41957			0.709787	+	0.704416i	$0.248791\pi$
$308$			2.92800e21i			0.117386i
$309$	5.94805e21	+	3.18623e22i	0.231605	+	1.24065i
$310$	3.83942e22			1.45215
$311$			1.60564e22i			0.589934i	0.955507	+	0.294967i	$0.0953086\pi$
$311$			1.60564e22i			0.589934i	−0.955507	+	0.294967i	$0.904691\pi$
$312$	7.44542e21	−	1.38991e21i	0.265765	−	0.0496130i
$313$	2.72444e21			0.0944884			0.0472442	−	0.998883i	$-0.484956\pi$
$313$	2.72444e21			0.0944884			0.0472442	+	0.998883i	$0.484956\pi$
$314$		−	2.45409e22i		−	0.827033i
$315$	−1.64273e22	−	4.24651e22i	−0.537985	−	1.39071i
$316$	−1.77580e21			−0.0565209
$317$			2.47426e22i			0.765440i	0.923864	+	0.382720i	$0.125013\pi$
$317$			2.47426e22i			0.765440i	−0.923864	+	0.382720i	$0.874987\pi$
$318$	−3.25291e20	−	1.74251e21i	−0.00978201	−	0.0523999i
$319$	5.73795e21			0.167741
$320$		−	8.32012e21i		−	0.236472i
$321$	4.46541e22	−	8.33602e21i	1.23400	−	0.230363i
$322$	1.07336e22			0.288431
$323$			4.59071e22i			1.19966i
$324$	−1.45516e22	+	1.32396e22i	−0.369833	+	0.336487i
$325$	−7.97724e22			−1.97198
$326$		−	5.07016e22i		−	1.21917i
$327$	7.12281e21	+	3.81552e22i	0.166618	+	0.892532i
$328$	−1.75100e22			−0.398493
$329$			8.07459e21i			0.178796i
$330$	−1.81776e22	+	3.39340e21i	−0.391662	+	0.0731155i
$331$	−1.10986e22			−0.232711			−0.116356	−	0.993208i	$-0.537121\pi$
$331$	−1.10986e22			−0.232711			−0.116356	+	0.993208i	$0.537121\pi$
$332$			2.77539e22i			0.566346i
$333$	−1.44514e22	+	5.59040e21i	−0.287020	+	0.111031i
$334$	−5.40630e22			−1.04516
$335$		−	1.76740e23i		−	3.32607i
$336$	−1.97380e21	−	1.05732e22i	−0.0361617	−	0.193710i
$337$	4.70594e22			0.839415			0.419708	−	0.907659i	$-0.362133\pi$
$337$	4.70594e22			0.839415			0.419708	+	0.907659i	$0.362133\pi$
$338$			1.69066e22i			0.293633i
$339$	−2.49234e22	+	4.65270e21i	−0.421512	+	0.0786879i
$340$	8.85820e22			1.45893
$341$		−	2.01577e22i		−	0.323334i
$342$	1.27008e22	+	3.28322e22i	0.198425	+	0.512938i
$343$	−7.14114e22			−1.08673
$344$		−	1.00493e22i		−	0.148973i
$345$	1.24396e22	+	6.66362e22i	0.179654	+	0.962361i
$346$	2.39728e22			0.337313
$347$			2.23558e22i			0.306496i	0.988188	+	0.153248i	$0.0489733\pi$
$347$			2.23558e22i			0.306496i	−0.988188	+	0.153248i	$0.951027\pi$
$348$	−2.07200e22	+	3.86801e21i	−0.276807	+	0.0516743i
$349$	−9.63172e22			−1.25394			−0.626968	−	0.779045i	$-0.715704\pi$
$349$	−9.63172e22			−1.25394			−0.626968	+	0.779045i	$0.715704\pi$
$350$			1.13284e23i			1.43733i
$351$	3.25143e22	+	5.25983e22i	0.402078	+	0.650441i
$352$	−4.36822e21			−0.0526526
$353$		−	2.12429e22i		−	0.249599i	−0.992182	−	0.124799i	$-0.960171\pi$
$353$		−	2.12429e22i		−	0.249599i	0.992182	−	0.124799i	$-0.0398287\pi$
$354$	1.58878e20	+	8.51073e20i	0.00181985	+	0.00974850i
$355$	2.37199e23			2.64885
$356$			1.71045e22i			0.186235i
$357$	1.12569e23	−	2.10145e22i	1.19511	−	0.223102i
$358$	−1.11812e23			−1.15756
$359$		−	1.79251e23i		−	1.80972i	−0.425705	−	0.904862i	$-0.639974\pi$
$359$		−	1.79251e23i		−	1.80972i	0.425705	−	0.904862i	$-0.360026\pi$
$360$	6.33527e22	−	2.45075e22i	0.623796	−	0.241310i
$361$	−4.11350e22			−0.395045
$362$		−	9.66066e22i		−	0.904961i
$363$	−1.83010e22	−	9.80338e22i	−0.167230	−	0.895811i
$364$	−3.38075e22			−0.301371
$365$			2.79929e23i			2.43451i
$366$	−5.34140e21	+	9.97133e20i	−0.0453237	+	0.00846103i
$367$	2.02891e23			1.67984			0.839922	−	0.542706i	$-0.182600\pi$
$367$	2.02891e23			1.67984			0.839922	+	0.542706i	$0.182600\pi$
$368$			1.60132e22i			0.129374i
$369$	−5.15767e22	−	1.33328e23i	−0.406646	−	1.05120i
$370$	5.35013e22			0.411670
$371$			7.91223e21i			0.0594201i
$372$	1.35885e22	+	7.27904e22i	0.0996059	+	0.533565i
$373$	−1.15346e23			−0.825319			−0.412659	−	0.910885i	$-0.635400\pi$
$373$	−1.15346e23			−0.825319			−0.412659	+	0.910885i	$0.635400\pi$
$374$		−	4.65072e22i		−	0.324845i
$375$	−4.30572e23	+	8.03792e22i	−2.93606	+	0.548103i
$376$	−1.20463e22			−0.0801979
$377$			6.62520e22i			0.430652i
$378$	7.46943e22	−	4.61732e22i	0.474090	−	0.293065i
$379$	−1.01983e23			−0.632086			−0.316043	−	0.948745i	$-0.602354\pi$
$379$	−1.01983e23			−0.632086			−0.316043	+	0.948745i	$0.602354\pi$
$380$		−	1.21550e23i		−	0.735701i
$381$	−9.27363e21	−	4.96766e22i	−0.0548182	−	0.293648i
$382$	2.58466e22			0.149222
$383$			2.38227e23i			1.34339i	0.740828	+	0.671695i	$0.234433\pi$
$383$			2.38227e23i			1.34339i	−0.740828	+	0.671695i	$0.765567\pi$
$384$	1.57738e22	−	2.94466e21i	0.0868873	−	0.0162201i
$385$	8.25394e22			0.444135
$386$			1.39207e23i			0.731773i
$387$	7.65192e22	−	2.96008e22i	0.392981	−	0.152021i
$388$	−1.21476e23			−0.609545
$389$			8.49618e20i			0.00416560i	0.999998	+	0.00208280i	$0.000662976\pi$
$389$			8.49618e20i			0.00416560i	−0.999998	+	0.00208280i	$0.999337\pi$
$390$	−3.91811e22	−	2.09884e23i	−0.187714	−	1.00554i
$391$	−1.70488e23			−0.798182
$392$		−	2.92636e22i		−	0.133892i
$393$	1.87734e23	−	3.50461e22i	0.839478	−	0.156714i
$394$	−6.71954e22			−0.293679
$395$			5.00591e22i			0.213850i
$396$	−1.28669e22	−	3.32613e22i	−0.0537299	−	0.138894i
$397$	2.52796e23			1.03194			0.515971	−	0.856606i	$-0.327431\pi$
$397$	2.52796e23			1.03194			0.515971	+	0.856606i	$0.327431\pi$
$398$		−	8.36450e22i		−	0.333804i
$399$	−2.88354e22	−	1.54465e23i	−0.112505	−	0.602660i
$400$	−1.69006e23			−0.644705
$401$		−	2.33535e23i		−	0.871068i	−0.900172	−	0.435534i	$-0.856560\pi$
$401$		−	2.33535e23i		−	0.871068i	0.900172	−	0.435534i	$-0.143440\pi$
$402$	3.35075e23	−	6.25518e22i	1.22210	−	0.228142i
$403$	2.32746e23			0.830113
$404$			5.84963e21i			0.0204031i
$405$	3.73219e23	+	4.10205e23i	1.27312	+	1.39928i
$406$	9.40837e22			0.313892
$407$		−	2.80892e22i		−	0.0916620i
$408$	3.13510e22	+	1.67940e23i	0.100071	+	0.536058i
$409$	−4.91082e23			−1.53336			−0.766680	−	0.642029i	$-0.778093\pi$
$409$	−4.91082e23			−1.53336			−0.766680	+	0.642029i	$0.778093\pi$
$410$			4.93600e23i			1.50772i
$411$	−4.12839e23	+	7.70687e22i	−1.23368	+	0.230304i
$412$	2.15841e23			0.631043
$413$		−	3.86448e21i		−	0.0110545i
$414$	−1.21931e23	+	4.71678e22i	−0.341279	+	0.132021i
$415$	7.82374e23			2.14280
$416$		−	5.04367e22i		−	0.135178i
$417$	−4.04239e22	−	2.16541e23i	−0.106026	−	0.567958i
$418$	−6.38158e22			−0.163811
$419$			2.92094e23i			0.733832i	0.930254	+	0.366916i	$0.119586\pi$
$419$			2.92094e23i			0.733832i	−0.930254	+	0.366916i	$0.880414\pi$
$420$	−2.98054e23	+	5.56407e22i	−0.732911	+	0.136820i
$421$	−3.49420e23			−0.841026			−0.420513	−	0.907287i	$-0.638150\pi$
$421$	−3.49420e23			−0.841026			−0.420513	+	0.907287i	$0.638150\pi$
$422$		−	7.77640e22i		−	0.183217i
$423$	−3.54831e22	−	9.17253e22i	−0.0818387	−	0.211556i
$424$	−1.18041e22			−0.0266526
$425$		−	1.79936e24i		−	3.97756i
$426$	8.39496e22	+	4.49698e23i	0.181690	+	0.973272i
$427$	2.42538e22			0.0513959
$428$		−	3.02495e23i		−	0.627660i
$429$	−1.10193e23	+	2.05708e22i	−0.223892	+	0.0417961i
$430$	−2.83286e23			−0.563649
$431$			8.50240e23i			1.65671i	0.560205	+	0.828354i	$0.310723\pi$
$431$			8.50240e23i			1.65671i	−0.560205	+	0.828354i	$0.689277\pi$
$432$	6.88847e22	+	1.11435e23i	0.131452	+	0.212651i
$433$	−6.80853e23			−1.27251			−0.636257	−	0.771477i	$-0.719518\pi$
$433$	−6.80853e23			−1.27251			−0.636257	+	0.771477i	$0.719518\pi$
$434$		−	3.30520e23i		−	0.605049i
$435$	1.09038e23	+	5.84090e23i	0.195513	+	1.04731i
$436$	2.58470e23			0.453975
$437$			2.33938e23i			0.402502i
$438$	−5.30707e23	+	9.90725e22i	−0.894516	+	0.166988i
$439$	−6.56128e23			−1.08345			−0.541724	−	0.840556i	$-0.682228\pi$
$439$	−6.56128e23			−1.08345			−0.541724	+	0.840556i	$0.682228\pi$
$440$			1.23139e23i			0.199214i
$441$	2.22825e23	−	8.61979e22i	0.353197	−	0.136631i
$442$	5.36985e23			0.833992
$443$		−	9.77752e23i		−	1.48797i	−0.668194	−	0.743987i	$-0.732932\pi$
$443$		−	9.77752e23i		−	1.48797i	0.668194	−	0.743987i	$-0.267068\pi$
$444$	1.89352e22	+	1.01431e23i	0.0282373	+	0.151260i
$445$	4.82171e23			0.704629
$446$			1.15371e23i			0.165227i
$447$	6.79919e23	−	1.26927e23i	0.954310	−	0.178151i
$448$	−7.16245e22			−0.0985280
$449$			8.18355e23i			1.10338i	0.834050	+	0.551689i	$0.186017\pi$
$449$			8.18355e23i			1.10338i	−0.834050	+	0.551689i	$0.813983\pi$
$450$	−4.97817e23	−	1.28688e24i	−0.657895	−	1.70069i
$451$	2.59149e23			0.335707
$452$			1.68836e23i			0.214397i
$453$	4.76876e22	+	2.55451e23i	0.0593638	+	0.317998i
$454$	2.50321e23			0.305488
$455$			9.53024e23i			1.14025i
$456$	2.30442e23	−	4.30189e22i	0.270320	−	0.0504633i
$457$	9.22885e23			1.06146			0.530728	−	0.847542i	$-0.321919\pi$
$457$	9.22885e23			1.06146			0.530728	+	0.847542i	$0.321919\pi$
$458$		−	3.55747e23i		−	0.401192i
$459$	−1.18641e24	+	7.33396e23i	−1.31196	+	0.811006i
$460$	4.51406e23			0.489493
$461$			2.88458e23i			0.306743i	0.988169	+	0.153371i	$0.0490130\pi$
$461$			2.88458e23i			0.306743i	−0.988169	+	0.153371i	$0.950987\pi$
$462$	2.92124e22	+	1.56484e23i	0.0304641	+	0.163189i
$463$	1.02160e22			0.0104485			0.00522423	−	0.999986i	$-0.498337\pi$
$463$	1.02160e22			0.0104485			0.00522423	+	0.999986i	$0.498337\pi$
$464$			1.40361e23i			0.140794i
$465$	2.05194e24	−	3.83056e23i	2.01877	−	0.376864i
$466$	4.24159e23			0.409313
$467$		−	3.70628e23i		−	0.350822i	−0.984495	−	0.175411i	$-0.943875\pi$
$467$		−	3.70628e23i		−	0.350822i	0.984495	−	0.175411i	$-0.0561254\pi$
$468$	3.84045e23	−	1.48564e23i	0.356590	−	0.137944i
$469$	−1.52148e24			−1.38583
$470$			3.39581e23i			0.303433i
$471$	−2.44842e23	−	1.31156e24i	−0.214633	−	1.14974i
$472$	5.76533e21			0.00495845
$473$			1.48730e23i			0.125502i
$474$	−9.49054e22	+	1.77169e22i	−0.0785753	+	0.0146684i
$475$	−2.46902e24			−2.00578
$476$		−	7.62566e23i		−	0.607876i
$477$	−3.47696e22	−	8.98808e22i	−0.0271978	−	0.0703075i
$478$	−6.96243e23			−0.534454
$479$		−	6.56672e23i		−	0.494685i	−0.968928	−	0.247343i	$-0.920443\pi$
$479$		−	6.56672e23i		−	0.494685i	0.968928	−	0.247343i	$-0.0795573\pi$
$480$	−8.30090e22	−	4.44659e23i	−0.0613697	−	0.328743i
$481$	3.24325e23			0.235329
$482$			6.26211e23i			0.445961i
$483$	5.73643e23	−	1.07088e23i	0.400975	−	0.0748541i
$484$	−6.64099e23			−0.455643
$485$			3.42438e24i			2.30625i
$486$	−6.45604e23	+	8.52753e23i	−0.426815	+	0.563763i
$487$	2.28426e24			1.48247			0.741233	−	0.671248i	$-0.234242\pi$
$487$	2.28426e24			1.48247			0.741233	+	0.671248i	$0.234242\pi$
$488$			3.61837e22i			0.0230534i
$489$	−5.05845e23	−	2.70969e24i	−0.316401	−	1.69488i
$490$	−8.24932e23			−0.506586
$491$		−	2.05495e23i		−	0.123899i	−0.998079	−	0.0619496i	$-0.980268\pi$
$491$		−	2.05495e23i		−	0.123899i	0.998079	−	0.0619496i	$-0.0197318\pi$
$492$	−9.35799e23	+	1.74695e23i	−0.553984	+	0.103418i
$493$	−1.49439e24			−0.868642
$494$		−	7.36836e23i		−	0.420560i
$495$	−9.37626e23	+	3.62713e23i	−0.525512	+	0.203290i
$496$	4.93096e23			0.271391
$497$		−	2.04195e24i		−	1.10367i
$498$	2.76898e23	+	1.48328e24i	0.146979	+	0.787332i
$499$	2.98859e24			1.55798			0.778989	−	0.627037i	$-0.215733\pi$
$499$	2.98859e24			1.55798			0.778989	+	0.627037i	$0.215733\pi$
$500$			2.91677e24i			1.49339i
$501$	−2.88933e24	+	5.39381e23i	−1.45298	+	0.271241i
$502$	1.71237e24			0.845793
$503$		−	1.72827e24i		−	0.838494i	−0.907872	−	0.419247i	$-0.862294\pi$
$503$		−	1.72827e24i		−	0.838494i	0.907872	−	0.419247i	$-0.137706\pi$
$504$	−2.10975e23	−	5.45378e23i	−0.100544	−	0.259910i
$505$	1.64899e23			0.0771962
$506$		−	2.36996e23i		−	0.108990i
$507$	1.68675e23	+	9.03552e23i	0.0762043	+	0.408208i
$508$	−3.36519e23			−0.149360
$509$			1.92080e24i			0.837574i	0.908084	+	0.418787i	$0.137545\pi$
$509$			1.92080e24i			0.837574i	−0.908084	+	0.418787i	$0.862455\pi$
$510$	4.73417e24	−	8.83774e23i	2.02820	−	0.378625i
$511$	2.40979e24			1.01436
$512$		−	1.06855e23i		−	0.0441942i
$513$	1.00634e24	+	1.62796e24i	0.408969	+	0.661589i
$514$	−7.11025e23			−0.283934
$515$		−	6.08449e24i		−	2.38759i
$516$	−1.00261e23	−	5.37072e23i	−0.0386619	−	0.207103i
$517$	1.78286e23			0.0675621
$518$		−	4.60571e23i		−	0.171525i
$519$	1.28120e24	−	2.39174e23i	0.468932	−	0.0875402i
$520$	−1.42179e24			−0.511454
$521$		−	2.22359e24i		−	0.786166i	−0.919503	−	0.393083i	$-0.871408\pi$
$521$		−	2.22359e24i		−	0.786166i	0.919503	−	0.393083i	$-0.128592\pi$
$522$	−1.06877e24	+	4.13443e23i	−0.371405	+	0.143675i
$523$	−4.28781e23			−0.146461			−0.0732303	−	0.997315i	$-0.523331\pi$
$523$	−4.28781e23			−0.146461			−0.0732303	+	0.997315i	$0.523331\pi$
$524$		−	1.27174e24i		−	0.426990i
$525$	1.13022e24	+	6.05433e24i	0.373018	+	1.99817i
$526$	−2.69581e24			−0.874615
$527$			5.24985e24i			1.67437i
$528$	−2.33454e23	+	4.35813e22i	−0.0731976	+	0.0136645i
$529$	2.37536e24			0.732198
$530$			3.32753e23i			0.100841i
$531$	1.69821e22	+	4.38995e22i	0.00505990	+	0.0130800i
$532$	−1.04637e24			−0.306536
$533$			2.99221e24i			0.861880i
$534$	1.70650e23	+	9.14131e23i	0.0483320	+	0.258903i
$535$	−8.52724e24			−2.37479
$536$		−	2.26986e24i		−	0.621608i
$537$	−5.97567e24	+	1.11554e24i	−1.60923	+	0.300411i
$538$	6.38795e23			0.169169
$539$			4.33104e23i			0.112796i
$540$	3.14131e24	−	1.94184e24i	0.804575	−	0.497358i
$541$	3.73835e24			0.941683			0.470842	−	0.882218i	$-0.343950\pi$
$541$	3.73835e24			0.941683			0.470842	+	0.882218i	$0.343950\pi$
$542$		−	4.91712e24i		−	1.21820i
$543$	−9.63834e23	−	5.16303e24i	−0.234857	−	1.25807i
$544$	1.13765e24			0.272659
$545$		−	7.28619e24i		−	1.71764i
$546$	−1.80681e24	+	3.37294e23i	−0.418965	+	0.0782124i
$547$	−1.53228e24			−0.349503			−0.174752	−	0.984613i	$-0.555912\pi$
$547$	−1.53228e24			−0.349503			−0.174752	+	0.984613i	$0.555912\pi$
$548$			2.79665e24i			0.627498i
$549$	−2.75517e23	+	1.06581e23i	−0.0608131	+	0.0235250i
$550$	2.50130e24			0.543127
$551$			2.05055e24i			0.438033i
$552$	1.59762e23	+	8.55805e23i	0.0335754	+	0.179855i
$553$	4.30938e23			0.0891023
$554$		−	3.61406e24i		−	0.735204i
$555$	2.85932e24	−	5.33777e23i	0.572302	−	0.106837i
$556$	−1.46689e24			−0.288885
$557$			5.08097e24i			0.984578i	0.870432	+	0.492289i	$0.163840\pi$
$557$			5.08097e24i			0.984578i	−0.870432	+	0.492289i	$0.836160\pi$
$558$	1.45244e24	+	3.75463e24i	0.276944	+	0.715911i
$559$	−1.71728e24			−0.322207
$560$			2.01907e24i			0.372786i
$561$	−4.63997e23	−	2.48552e24i	−0.0843043	−	0.451598i
$562$	−4.99853e24			−0.893749
$563$			6.50158e24i			1.14405i	0.820238	+	0.572023i	$0.193841\pi$
$563$			6.50158e24i			1.14405i	−0.820238	+	0.572023i	$0.806159\pi$
$564$	−6.43800e23	+	1.20185e23i	−0.111491	+	0.0208131i
$565$	4.75943e24			0.811183
$566$			6.30230e24i			1.05719i
$567$	3.53128e24	−	3.21289e24i	0.583022	−	0.530455i
$568$	3.04634e24			0.495043
$569$			2.38767e24i			0.381913i	0.981598	+	0.190957i	$0.0611590\pi$
$569$			2.38767e24i			0.381913i	−0.981598	+	0.190957i	$0.938841\pi$
$570$	−1.21269e24	−	6.49608e24i	−0.190931	−	1.02277i
$571$	9.17508e24			1.42195			0.710976	−	0.703216i	$-0.248253\pi$
$571$	9.17508e24			1.42195			0.710976	+	0.703216i	$0.248253\pi$
$572$			7.46467e23i			0.113880i
$573$	1.38134e24	−	2.57869e23i	0.207448	−	0.0387264i
$574$	4.24920e24			0.628203
$575$		−	9.16935e24i		−	1.33453i
$576$	8.13636e23	−	3.14748e23i	0.116581	−	0.0450984i
$577$	−4.46121e24			−0.629318			−0.314659	−	0.949205i	$-0.601890\pi$
$577$	−4.46121e24			−0.629318			−0.314659	+	0.949205i	$0.601890\pi$
$578$			7.02091e24i			0.975087i
$579$	1.38886e24	+	7.43977e24i	0.189911	+	1.01731i
$580$	3.95674e24			0.532703
$581$		−	6.73514e24i		−	0.892815i
$582$	−6.49216e24	+	1.21196e24i	−0.847388	+	0.158190i
$583$	1.74701e23			0.0224532
$584$			3.59511e24i			0.454985i
$585$	−4.18798e24	−	1.08261e25i	−0.521918	−	1.34918i
$586$	−3.34967e24			−0.411078
$587$			5.98733e24i			0.723586i	0.932258	+	0.361793i	$0.117835\pi$
$587$			5.98733e24i			0.723586i	−0.932258	+	0.361793i	$0.882165\pi$
$588$	−2.91960e23	−	1.56396e24i	−0.0347478	−	0.186136i
$589$	7.20369e24			0.844340
$590$		−	1.62523e23i		−	0.0187606i
$591$	−3.59118e24	+	6.70401e23i	−0.408272	+	0.0762162i
$592$	6.87115e23			0.0769368
$593$		−	9.26339e24i		−	1.02159i	−0.859702	−	0.510796i	$-0.829351\pi$
$593$		−	9.26339e24i		−	1.02159i	0.859702	−	0.510796i	$-0.170649\pi$
$594$	−1.01950e24	−	1.64924e24i	−0.110741	−	0.179146i
$595$	−2.14965e25			−2.29993
$596$		−	4.60590e24i		−	0.485398i
$597$	−8.34517e23	−	4.47031e24i	−0.0866296	−	0.464054i
$598$	2.73643e24			0.279816
$599$			7.25144e24i			0.730437i	0.930922	+	0.365219i	$0.119006\pi$
$599$			7.25144e24i			0.730437i	−0.930922	+	0.365219i	$0.880994\pi$
$600$	−9.03231e24	+	1.68615e24i	−0.896267	+	0.167315i
$601$	−8.01360e23			−0.0783352			−0.0391676	−	0.999233i	$-0.512471\pi$
$601$	−8.01360e23			−0.0783352			−0.0391676	+	0.999233i	$0.512471\pi$
$602$			2.43869e24i			0.234849i
$603$	1.72836e25	−	6.68602e24i	1.63976	−	0.634325i
$604$	1.73047e24			0.161746
$605$			1.87207e25i			1.72395i
$606$	5.83611e22	+	3.12627e23i	0.00529505	+	0.0283643i
$607$	−1.52554e25			−1.36372			−0.681861	−	0.731482i	$-0.738829\pi$
$607$	−1.52554e25			−1.36372			−0.681861	+	0.731482i	$0.738829\pi$
$608$		−	1.56106e24i		−	0.137495i
$609$	5.02819e24	−	9.38663e23i	0.436372	−	0.0814618i
$610$	1.02001e24			0.0872236
$611$			2.05854e24i			0.173456i
$612$	3.35103e24	+	8.66256e24i	0.278238	+	0.719256i
$613$	−2.34840e25			−1.92145			−0.960723	−	0.277509i	$-0.910491\pi$
$613$	−2.34840e25			−1.92145			−0.960723	+	0.277509i	$0.910491\pi$
$614$		−	1.24497e25i		−	1.00379i
$615$	4.92460e24	+	2.63799e25i	0.391286	+	2.09603i
$616$	1.06005e24			0.0830042
$617$		−	2.25430e25i		−	1.73958i	−0.493421	−	0.869790i	$-0.664254\pi$
$617$		−	2.25430e25i		−	1.73958i	0.493421	−	0.869790i	$-0.335746\pi$
$618$	1.15354e25	−	2.15343e24i	0.877275	−	0.163770i
$619$	3.04763e24			0.228427			0.114213	−	0.993456i	$-0.463565\pi$
$619$	3.04763e24			0.228427			0.114213	+	0.993456i	$0.463565\pi$
$620$		−	1.39002e25i		−	1.02682i
$621$	−6.04585e24	+	3.73732e24i	−0.440183	+	0.272104i
$622$	5.81302e24			0.417146
$623$		−	4.15081e24i		−	0.293589i
$624$	−5.03202e23	−	2.69553e24i	−0.0350817	−	0.187924i
$625$	4.46961e25			3.07150
$626$		−	9.86353e23i		−	0.0668134i
$627$	−3.41056e24	+	6.36684e23i	−0.227729	+	0.0425124i
$628$	−8.88474e24			−0.584801
$629$			7.31552e24i			0.474667i
$630$	−1.53740e25	+	5.94731e24i	−0.983383	+	0.380413i
$631$	1.65170e25			1.04152			0.520760	−	0.853703i	$-0.325649\pi$
$631$	1.65170e25			1.04152			0.520760	+	0.853703i	$0.325649\pi$
$632$			6.42907e23i			0.0399663i
$633$	−7.75844e23	−	4.15601e24i	−0.0475489	−	0.254708i
$634$	8.95776e24			0.541248
$635$			9.48635e24i			0.565113i
$636$	−6.30855e23	+	1.17768e23i	−0.0370523	+	0.00691692i
$637$	−5.00075e24			−0.289588
$638$		−	2.07736e24i		−	0.118611i
$639$	8.97318e24	+	2.31960e25i	0.505171	+	1.30589i
$640$	−3.01221e24			−0.167211
$641$			1.10098e25i			0.602636i	0.953524	+	0.301318i	$0.0974266\pi$
$641$			1.10098e25i			0.602636i	−0.953524	+	0.301318i	$0.902573\pi$
$642$	−3.01796e24	−	1.61665e25i	−0.162892	−	0.872571i
$643$	1.18166e24			0.0628920			0.0314460	−	0.999505i	$-0.489989\pi$
$643$	1.18166e24			0.0628920			0.0314460	+	0.999505i	$0.489989\pi$
$644$		−	3.88597e24i		−	0.203951i
$645$	−1.51399e25	+	2.82632e24i	−0.783584	+	0.146279i
$646$	1.66201e25			0.848285
$647$		−	3.86630e25i		−	1.94606i	−0.230674	−	0.973031i	$-0.574093\pi$
$647$		−	3.86630e25i		−	1.94606i	0.230674	−	0.973031i	$-0.425907\pi$
$648$	4.79323e24	+	5.26824e24i	0.237932	+	0.261511i
$649$	−8.53274e22			−0.00417721
$650$			2.88807e25i			1.39440i
$651$	−3.29757e24	−	1.76643e25i	−0.157024	−	0.841138i
$652$	−1.83559e25			−0.862081
$653$		−	3.72586e25i		−	1.72587i	−0.505315	−	0.862935i	$-0.668624\pi$
$653$		−	3.72586e25i		−	1.72587i	0.505315	−	0.862935i	$-0.331376\pi$
$654$	1.38136e25	−	2.57873e24i	0.631115	−	0.117817i
$655$	−3.58501e25			−1.61554
$656$			6.33928e24i			0.281777i
$657$	−2.73746e25	+	1.05896e25i	−1.20022	+	0.464293i
$658$	2.92331e24			0.126428
$659$			1.32111e25i			0.563597i	0.959474	+	0.281799i	$0.0909310\pi$
$659$			1.32111e25i			0.563597i	−0.959474	+	0.281799i	$0.909069\pi$
$660$	1.22854e24	+	6.58100e24i	0.0517005	+	0.276947i
$661$	−1.10139e25			−0.457222			−0.228611	−	0.973518i	$-0.573418\pi$
$661$	−1.10139e25			−0.457222			−0.228611	+	0.973518i	$0.573418\pi$
$662$			4.01814e24i			0.164552i
$663$	2.86986e25	−	5.35745e24i	1.15941	−	0.216439i
$664$	1.00480e25			0.400467
$665$			2.94969e25i			1.15979i
$666$	2.02394e24	+	5.23197e24i	0.0785108	+	0.202954i
$667$	−7.61526e24			−0.291442
$668$			1.95729e25i			0.739038i
$669$	1.15104e24	+	6.16586e24i	0.0428802	+	0.229699i
$670$	−6.39867e25			−2.35189
$671$		−	5.35522e23i		−	0.0194211i
$672$	−3.82789e24	+	7.14591e23i	−0.136973	+	0.0255702i
$673$	2.97930e25			1.05191			0.525955	−	0.850513i	$-0.323708\pi$
$673$	2.97930e25			1.05191			0.525955	+	0.850513i	$0.323708\pi$
$674$		−	1.70373e25i		−	0.593556i
$675$	−3.94443e25	−	6.38089e25i	−1.35597	−	2.19355i
$676$	6.12083e24			0.207630
$677$			4.34240e24i			0.145356i	0.997355	+	0.0726778i	$0.0231545\pi$
$677$			4.34240e24i			0.145356i	−0.997355	+	0.0726778i	$0.976846\pi$
$678$	1.68446e24	+	9.02324e24i	0.0556408	+	0.298054i
$679$	2.94791e25			0.960917
$680$		−	3.20701e25i		−	1.03162i
$681$	1.33781e25	−	2.49742e24i	0.424689	−	0.0792809i
$682$	−7.29786e24			−0.228632
$683$			2.86178e24i			0.0884810i	0.999021	+	0.0442405i	$0.0140868\pi$
$683$			2.86178e24i			0.0884810i	−0.999021	+	0.0442405i	$0.985913\pi$
$684$	1.18865e25	−	4.59819e24i	0.362702	−	0.140308i
$685$	7.88366e25			2.37417
$686$			2.58537e25i			0.768432i
$687$	−3.54925e24	−	1.90125e25i	−0.104118	−	0.557736i
$688$	−3.63823e24			−0.105340
$689$			2.01715e24i			0.0576455i
$690$	2.41249e25	−	4.50363e24i	0.680492	−	0.127034i
$691$	−1.68395e25			−0.468842			−0.234421	−	0.972135i	$-0.575319\pi$
$691$	−1.68395e25			−0.468842			−0.234421	+	0.972135i	$0.575319\pi$
$692$		−	8.67907e24i		−	0.238517i
$693$	3.12244e24	+	8.07164e24i	0.0847024	+	0.218959i
$694$	8.09366e24			0.216725
$695$			4.13512e25i			1.09301i
$696$	1.40037e24	+	7.50144e24i	0.0365392	+	0.195732i
$697$	−6.74926e25			−1.73844
$698$			3.48706e25i			0.886666i
$699$	2.26687e25	−	4.23179e24i	0.569026	−	0.106226i
$700$	4.10132e25			1.01634
$701$			4.96096e25i			1.21368i	0.794825	+	0.606839i	$0.207563\pi$
$701$			4.96096e25i			1.21368i	−0.794825	+	0.606839i	$0.792437\pi$
$702$	1.90426e25	−	1.17714e25i	0.459931	−	0.284312i
$703$	1.00381e25			0.239362
$704$			1.58146e24i			0.0372310i
$705$	3.38797e24	+	1.81485e25i	0.0787476	+	0.421832i
$706$	−7.69076e24			−0.176493
$707$		−	1.41955e24i		−	0.0321644i
$708$	3.08121e23	−	5.75201e22i	0.00689323	−	0.00128683i
$709$	−1.44322e25			−0.318799			−0.159400	−	0.987214i	$-0.550956\pi$
$709$	−1.44322e25			−0.318799			−0.159400	+	0.987214i	$0.550956\pi$
$710$		−	8.58752e25i		−	1.87302i
$711$	−4.89535e24	+	1.89372e24i	−0.105428	+	0.0407840i
$712$	6.19250e24			0.131688
$713$			2.67527e25i			0.561775i
$714$	−7.60805e24	−	4.07545e25i	−0.157757	−	0.845068i
$715$	2.10427e25			0.430870
$716$			4.04803e25i			0.818515i
$717$	−3.72099e25	+	6.94635e24i	−0.742996	+	0.138702i
$718$	−6.48959e25			−1.27967
$719$		−	5.43271e25i		−	1.05793i	−0.848644	−	0.528965i	$-0.822580\pi$
$719$		−	5.43271e25i		−	1.05793i	0.848644	−	0.528965i	$-0.177420\pi$
$720$	−8.87264e24	−	2.29361e25i	−0.170632	−	0.441091i
$721$	−5.23789e25			−0.994807
$722$			1.48925e25i			0.279339i
$723$	6.24764e24	+	3.34671e25i	0.115737	+	0.619974i
$724$	−3.49753e25			−0.639904
$725$		−	8.03727e25i		−	1.45233i
$726$	−3.54920e25	+	6.62565e24i	−0.633434	+	0.118249i
$727$	6.60270e25			1.16389			0.581945	−	0.813228i	$-0.302292\pi$
$727$	6.60270e25			1.16389			0.581945	+	0.813228i	$0.302292\pi$
$728$			1.22396e25i			0.213101i
$729$	−2.59957e25	+	5.20155e25i	−0.447048	+	0.894510i
$730$	1.01345e26			1.72146
$731$		−	3.87352e25i		−	0.649904i
$732$	3.61001e23	+	1.93379e24i	0.00598285	+	0.0320487i
$733$	2.07863e25			0.340284			0.170142	−	0.985420i	$-0.445577\pi$
$733$	2.07863e25			0.340284			0.170142	+	0.985420i	$0.445577\pi$
$734$		−	7.34546e25i		−	1.18783i
$735$	−4.40876e25	+	8.23027e24i	−0.704255	+	0.131470i
$736$	5.79738e24			0.0914812
$737$			3.35942e25i			0.523669i
$738$	−4.82698e25	+	1.86728e25i	−0.743307	+	0.287542i
$739$	−2.13791e25			−0.325229			−0.162614	−	0.986690i	$-0.551993\pi$
$739$	−2.13791e25			−0.325229			−0.162614	+	0.986690i	$0.551993\pi$
$740$		−	1.93695e25i		−	0.291094i
$741$	−7.35133e24	−	3.93793e25i	−0.109145	−	0.584661i
$742$	2.86453e24			0.0420164
$743$		−	1.95124e25i		−	0.282756i	−0.989956	−	0.141378i	$-0.954847\pi$
$743$		−	1.95124e25i		−	0.282756i	0.989956	−	0.141378i	$-0.0451534\pi$
$744$	2.63529e25	−	4.91956e24i	0.377287	−	0.0704320i
$745$	−1.29839e26			−1.83653
$746$			4.17596e25i			0.583588i
$747$	2.95970e25	+	7.65094e25i	0.408660	+	1.05640i
$748$	−1.68374e25			−0.229700
$749$			7.34075e25i			0.989473i
$750$	2.91004e25	+	1.55884e26i	0.387567	+	2.07610i
$751$	8.83451e25			1.16258			0.581290	−	0.813696i	$-0.302548\pi$
$751$	8.83451e25			1.16258			0.581290	+	0.813696i	$0.302548\pi$
$752$			4.36122e24i			0.0567085i
$753$	9.15157e25	−	1.70841e25i	1.17582	−	0.219502i
$754$	2.39858e25			0.304517
$755$		−	4.87815e25i		−	0.611973i
$756$	−1.67165e25	−	2.70422e25i	−0.207228	−	0.335232i
$757$	4.11022e25			0.503504			0.251752	−	0.967792i	$-0.418993\pi$
$757$	4.11022e25			0.503504			0.251752	+	0.967792i	$0.418993\pi$
$758$			3.69219e25i			0.446953i
$759$	−2.36449e24	−	1.26660e25i	−0.0282853	−	0.151518i
$760$	−4.40057e25			−0.520219
$761$		−	9.29992e25i		−	1.08647i	−0.839581	−	0.543235i	$-0.817199\pi$
$761$		−	9.29992e25i		−	1.08647i	0.839581	−	0.543235i	$-0.182801\pi$
$762$	−1.79848e25	+	3.35741e24i	−0.207640	+	0.0387623i
$763$	−6.27239e25			−0.715668
$764$		−	9.35746e24i		−	0.105516i
$765$	2.44195e26	−	9.44646e25i	2.72134	−	1.05273i
$766$	8.62474e25			0.949920
$767$		−	9.85215e23i		−	0.0107244i
$768$	−1.06608e24	−	5.71074e24i	−0.0114694	−	0.0614386i
$769$	1.12638e26			1.19770			0.598850	−	0.800861i	$-0.295624\pi$
$769$	1.12638e26			1.19770			0.598850	+	0.800861i	$0.295624\pi$
$770$		−	2.98825e25i		−	0.314051i
$771$	−3.79999e25	+	7.09383e24i	−0.394724	+	0.0736871i
$772$	5.03984e25			0.517441
$773$		−	1.32815e26i		−	1.34782i	−0.738815	−	0.673908i	$-0.764614\pi$
$773$		−	1.32815e26i		−	1.34782i	0.738815	−	0.673908i	$-0.235386\pi$
$774$	−1.07166e25	−	2.77029e25i	−0.107495	−	0.277880i
$775$	−2.82353e26			−2.79948
$776$			4.39791e25i			0.431014i
$777$	−4.59507e24	−	2.46147e25i	−0.0445146	−	0.238454i
$778$	3.07594e23			0.00294552
$779$			9.26113e25i			0.876652i
$780$	−7.59861e25	+	1.41851e25i	−0.711022	+	0.132734i
$781$	−4.50861e25			−0.417045
$782$			6.17231e25i			0.564400i
$783$	−5.29941e25	+	3.27590e25i	−0.479040	+	0.296124i
$784$	−1.05946e25			−0.0946757
$785$			2.50458e26i			2.21263i
$786$	−1.26881e25	−	6.79669e25i	−0.110813	−	0.593601i
$787$	1.65188e26			1.42628			0.713140	−	0.701022i	$-0.247273\pi$
$787$	1.65188e26			1.42628			0.713140	+	0.701022i	$0.247273\pi$
$788$			2.43273e25i			0.207663i
$789$	−1.44074e26	+	2.68958e25i	−1.21589	+	0.226982i
$790$	1.81233e25			0.151215
$791$		−	4.09720e25i		−	0.337986i
$792$	−1.20419e25	+	4.65830e24i	−0.0982128	+	0.0379928i
$793$	6.18328e24			0.0498610
$794$		−	9.15218e25i		−	0.729692i
$795$	3.31984e24	+	1.77836e25i	0.0261706	+	0.140189i
$796$	−3.02827e25			−0.236035
$797$		−	1.75243e26i		−	1.35057i	−0.737557	−	0.675285i	$-0.764021\pi$
$797$		−	1.75243e26i		−	1.35057i	0.737557	−	0.675285i	$-0.235979\pi$
$798$	−5.59221e25	+	1.04395e25i	−0.426145	+	0.0795528i
$799$	−4.64327e25			−0.349867
$800$			6.11866e25i			0.455875i
$801$	1.82404e25	+	4.71521e25i	0.134382	+	0.347383i
$802$	−8.45486e25			−0.615938
$803$		−	5.32080e25i		−	0.383298i
$804$	−2.26462e25	−	1.21310e26i	−0.161321	−	0.864157i
$805$	−1.09544e26			−0.771661
$806$		−	8.42632e25i		−	0.586979i
$807$	3.41396e25	−	6.37319e24i	0.235178	−	0.0439031i
$808$	2.11779e24			0.0144272
$809$			1.81052e26i			1.21974i	0.792503	+	0.609869i	$0.208778\pi$
$809$			1.81052e26i			1.21974i	−0.792503	+	0.609869i	$0.791222\pi$
$810$	1.48510e26	−	1.35120e26i	0.989442	−	0.900230i
$811$	1.11663e26			0.735733			0.367867	−	0.929879i	$-0.380088\pi$
$811$	1.11663e26			0.735733			0.367867	+	0.929879i	$0.380088\pi$
$812$		−	3.40619e25i		−	0.221955i
$813$	−4.90576e25	−	2.62790e26i	−0.316148	−	1.69353i
$814$	−1.01694e25			−0.0648148
$815$			5.17448e26i			3.26173i
$816$	6.08007e25	−	1.13503e25i	0.379050	−	0.0707611i
$817$	−5.31513e25			−0.327730
$818$			1.77791e26i			1.08425i
$819$	−9.31975e25	+	3.60526e25i	−0.562146	+	0.217461i
$820$	1.78702e26			1.06612
$821$		−	2.31975e26i		−	1.36884i	−0.729088	−	0.684420i	$-0.760056\pi$
$821$		−	2.31975e26i		−	1.36884i	0.729088	−	0.684420i	$-0.239944\pi$
$822$	2.79019e25	+	1.49464e26i	0.162850	+	0.872347i
$823$	1.29059e26			0.745057			0.372528	−	0.928021i	$-0.378491\pi$
$823$	1.29059e26			0.745057			0.372528	+	0.928021i	$0.378491\pi$
$824$		−	7.81428e25i		−	0.446215i
$825$	1.33679e26	−	2.49552e25i	0.755054	−	0.140953i
$826$	−1.39909e24			−0.00781674
$827$			9.14427e25i			0.505358i	0.967550	+	0.252679i	$0.0813117\pi$
$827$			9.14427e25i			0.505358i	−0.967550	+	0.252679i	$0.918688\pi$
$828$	1.70766e25	+	4.41436e25i	0.0933528	+	0.241321i
$829$	−2.88476e26			−1.55998			−0.779989	−	0.625793i	$-0.784776\pi$
$829$	−2.88476e26			−1.55998			−0.779989	+	0.625793i	$0.784776\pi$
$830$		−	2.83250e26i		−	1.51519i
$831$	−3.60571e25	−	1.93149e26i	−0.190802	−	1.02208i
$832$	−1.82600e25			−0.0955854
$833$		−	1.12797e26i		−	0.584109i
$834$	−7.83963e25	+	1.46350e25i	−0.401607	+	0.0749720i
$835$	5.51754e26			2.79619
$836$			2.31038e25i			0.115832i
$837$	1.15084e26	+	1.86171e26i	0.570801	+	0.923384i
$838$	1.05749e26			0.518898
$839$			1.27722e26i			0.620021i	0.950733	+	0.310011i	$0.100333\pi$
$839$			1.27722e26i			0.620021i	−0.950733	+	0.310011i	$0.899667\pi$
$840$	2.01441e25	+	1.07907e26i	0.0967462	+	0.518246i
$841$	1.43707e26			0.682831
$842$			1.26504e26i			0.594695i
$843$	−2.67141e26	+	4.98699e25i	−1.24249	+	0.231948i
$844$	−2.81536e25			−0.129554
$845$		−	1.72544e26i		−	0.785579i
$846$	−3.32081e25	+	1.28463e25i	−0.149593	+	0.0578687i
$847$	1.61159e26			0.718298
$848$			4.27353e24i			0.0188462i
$849$	6.28774e25	+	3.36819e26i	0.274363	+	1.46970i
$850$	−6.51436e26			−2.81256
$851$			3.72792e25i			0.159258i
$852$	1.62808e26	−	3.03930e25i	0.688207	−	0.128475i
$853$	−3.33058e25			−0.139309			−0.0696545	−	0.997571i	$-0.522190\pi$
$853$	−3.33058e25			−0.139309			−0.0696545	+	0.997571i	$0.522190\pi$
$854$		−	8.78081e24i		−	0.0363424i
$855$	−1.29622e26	−	3.35077e26i	−0.530863	−	1.37230i
$856$	−1.09515e26			−0.443823
$857$		−	1.96913e26i		−	0.789672i	−0.918752	−	0.394836i	$-0.870801\pi$
$857$		−	1.96913e26i		−	0.789672i	0.918752	−	0.394836i	$-0.129199\pi$
$858$	7.44743e24	+	3.98941e25i	0.0295543	+	0.158315i
$859$	−4.72996e26			−1.85746			−0.928728	−	0.370761i	$-0.879097\pi$
$859$	−4.72996e26			−1.85746			−0.928728	+	0.370761i	$0.879097\pi$
$860$			1.02560e26i			0.398560i
$861$	2.27094e26	−	4.23938e25i	0.873326	−	0.163033i
$862$	3.07820e26			1.17147
$863$		−	4.83906e26i		−	1.82249i	−0.411870	−	0.911243i	$-0.635124\pi$
$863$		−	4.83906e26i		−	1.82249i	0.411870	−	0.911243i	$-0.364876\pi$
$864$	4.03436e25	−	2.49389e25i	0.150367	−	0.0929510i
$865$	−2.44660e26			−0.902440
$866$			2.46495e26i			0.899803i
$867$	7.00470e25	+	3.75225e26i	0.253056	+	1.35556i
$868$	−1.19661e26			−0.427834
$869$		−	9.51508e24i		−	0.0336693i
$870$	2.11463e26	−	3.94760e25i	0.740563	−	0.138248i
$871$	−3.87888e26			−1.34444
$872$		−	9.35762e25i		−	0.321009i
$873$	−3.34875e26	+	1.29543e26i	−1.13698	+	0.439832i
$874$	8.46947e25			0.284612
$875$		−	7.07823e26i		−	2.35425i
$876$	3.58681e25	+	1.92137e26i	0.118079	+	0.632518i
$877$	4.82462e26			1.57205			0.786026	−	0.618193i	$-0.212135\pi$
$877$	4.82462e26			1.57205			0.786026	+	0.618193i	$0.212135\pi$
$878$			2.37544e26i			0.766114i
$879$	−1.79019e26	+	3.34194e25i	−0.571479	+	0.106684i
$880$	4.45809e25			0.140866
$881$			3.32122e26i			1.03876i	0.854544	+	0.519379i	$0.173837\pi$
$881$			3.32122e26i			1.03876i	−0.854544	+	0.519379i	$0.826163\pi$
$882$	−3.12070e25	−	8.06713e25i	−0.0966127	−	0.249748i
$883$	−1.07959e25			−0.0330837			−0.0165418	−	0.999863i	$-0.505266\pi$
$883$	−1.07959e25			−0.0330837			−0.0165418	+	0.999863i	$0.505266\pi$
$884$		−	1.94409e26i		−	0.589721i
$885$	−1.62147e24	−	8.68584e24i	−0.00486878	−	0.0260809i
$886$	−3.53984e26			−1.05216
$887$			1.13579e24i			0.00334183i	0.999999	+	0.00167091i	$0.000531869\pi$
$887$			1.13579e24i			0.00334183i	−0.999999	+	0.00167091i	$0.999468\pi$
$888$	3.67221e25	−	6.85528e24i	0.106957	−	0.0199668i
$889$	8.16641e25			0.235459
$890$		−	1.74564e26i		−	0.498248i
$891$	−7.09403e25	−	7.79704e25i	−0.200444	−	0.220308i
$892$	4.17687e25			0.116833
$893$			6.37137e25i			0.176429i
$894$	−4.59526e25	−	2.46157e26i	−0.125971	−	0.674799i
$895$	1.14113e27			3.09690
$896$			2.59309e25i			0.0696698i
$897$	1.46245e26	−	2.73010e25i	0.389000	−	0.0726185i
$898$	2.96276e26			0.780206
$899$			2.34498e26i			0.611366i
$900$	−4.65899e26	+	1.80229e26i	−1.20257	+	0.465202i
$901$	−4.54991e25			−0.116273
$902$		−	9.38220e25i		−	0.237381i
$903$	2.43306e25	+	1.30333e26i	0.0609485	+	0.326486i
$904$	6.11251e25			0.151602
$905$			9.85943e26i			2.42111i
$906$	9.24831e25	−	1.72648e25i	0.224858	−	0.0419765i
$907$	3.78188e25			0.0910421			0.0455210	−	0.998963i	$-0.485505\pi$
$907$	3.78188e25			0.0910421			0.0455210	+	0.998963i	$0.485505\pi$
$908$		−	9.06258e25i		−	0.216013i
$909$	6.23809e24	+	1.61257e25i	0.0147223	+	0.0380578i
$910$	3.45031e26			0.806280
$911$			1.76798e26i			0.409083i	0.978858	+	0.204542i	$0.0655704\pi$
$911$			1.76798e26i			0.409083i	−0.978858	+	0.204542i	$0.934430\pi$
$912$	−1.55745e25	−	8.34289e25i	−0.0356830	−	0.191145i
$913$	−1.48711e26			−0.337370
$914$		−	3.34120e26i		−	0.750562i
$915$	5.45130e25	−	1.01765e25i	0.121258	−	0.0226364i
$916$	−1.28794e26			−0.283685
$917$			3.08618e26i			0.673128i
$918$	2.65518e26	+	4.29528e26i	0.573468	+	0.927699i
$919$	−6.28949e26			−1.34517			−0.672583	−	0.740022i	$-0.734815\pi$
$919$	−6.28949e26			−1.34517			−0.672583	+	0.740022i	$0.734815\pi$
$920$		−	1.63426e26i		−	0.346124i
$921$	−1.24209e26	−	6.65359e26i	−0.260506	−	1.39547i
$922$	1.04433e26			0.216900
$923$		−	5.20576e26i		−	1.07070i
$924$	5.66531e25	−	1.05760e25i	0.115392	−	0.0215414i
$925$	−3.93451e26			−0.793625
$926$		−	3.69859e24i		−	0.00738818i
$927$	5.95011e26	−	2.30175e26i	1.17708	−	0.455344i
$928$	5.08162e25			0.0995567
$929$		−	5.88758e26i		−	1.14234i	−0.820832	−	0.571170i	$-0.806490\pi$
$929$		−	5.88758e26i		−	1.14234i	0.820832	−	0.571170i	$-0.193510\pi$
$930$	−1.38681e26	−	7.42880e26i	−0.266483	−	1.42749i
$931$	−1.54777e26			−0.294551
$932$		−	1.53562e26i		−	0.289428i
$933$	3.10670e26	−	5.79959e25i	0.579916	−	0.108259i
$934$	−1.34182e26			−0.248068
$935$			4.74641e26i			0.869082i
$936$	−5.37861e25	−	1.39039e26i	−0.0975410	−	0.252147i
$937$	−7.68660e26			−1.38063			−0.690316	−	0.723508i	$-0.742528\pi$
$937$	−7.68660e26			−1.38063			−0.690316	+	0.723508i	$0.742528\pi$
$938$			5.50835e26i			0.979932i
$939$	−9.84074e24	−	5.27145e25i	−0.0173395	−	0.0928838i
$940$	1.22941e26			0.214560
$941$			9.90911e26i			1.71288i	0.516243	+	0.856442i	$0.327330\pi$
$941$			9.90911e26i			1.71288i	−0.516243	+	0.856442i	$0.672670\pi$
$942$	−4.74835e26	+	8.86422e25i	−0.812989	+	0.151769i
$943$	−3.43936e26			−0.583273
$944$		−	2.08727e24i		−	0.00350616i
$945$	−7.62311e26	+	4.71232e26i	−1.26837	+	0.784058i
$946$	5.38461e25			0.0887430
$947$		−	5.98010e26i		−	0.976244i	−0.872775	−	0.488122i	$-0.837682\pi$
$947$		−	5.98010e26i		−	0.976244i	0.872775	−	0.488122i	$-0.162318\pi$
$948$	6.41422e24	+	3.43594e25i	0.0103721	+	0.0555611i
$949$	6.14355e26			0.984064
$950$			8.93882e26i			1.41830i
$951$	4.78737e26	−	8.93707e25i	0.752441	−	0.140466i
$952$	−2.76079e26			−0.429833
$953$			6.89203e26i			1.06295i	0.847075	+	0.531473i	$0.178361\pi$
$953$			6.89203e26i			1.06295i	−0.847075	+	0.531473i	$0.821639\pi$
$954$	−3.25403e25	+	1.25879e25i	−0.0497149	+	0.0192318i
$955$	−2.63784e26			−0.399225
$956$			2.52067e26i			0.377916i
$957$	−2.07256e25	−	1.11022e26i	−0.0307822	−	0.164893i
$958$	−2.37741e26			−0.349795
$959$		−	6.78672e26i		−	0.989219i
$960$	−1.60984e26	+	3.00525e25i	−0.232456	+	0.0433950i
$961$	1.24748e26			0.178452
$962$		−	1.17418e26i		−	0.166403i
$963$	−3.22583e26	−	8.33890e26i	−0.452903	−	1.17077i
$964$	2.26713e26			0.315342
$965$		−	1.42072e27i		−	1.95777i
$966$	−3.87699e25	−	2.07681e26i	−0.0529298	−	0.283532i
$967$	2.57739e26			0.348612			0.174306	−	0.984692i	$-0.444232\pi$
$967$	2.57739e26			0.348612			0.174306	+	0.984692i	$0.444232\pi$
$968$			2.40430e26i			0.322188i
$969$	8.88244e26	−	1.65817e26i	1.17928	−	0.220149i
$970$	1.23976e27			1.63076
$971$			1.25582e27i			1.63665i	0.574756	+	0.818325i	$0.305097\pi$
$971$			1.25582e27i			1.63665i	−0.574756	+	0.818325i	$0.694903\pi$
$972$	3.08730e26	+	2.33733e26i	0.398641	+	0.301804i
$973$	3.55975e26			0.455412
$974$		−	8.26990e26i		−	1.04826i
$975$	2.88140e26	+	1.54350e27i	0.361878	+	1.93849i
$976$	1.30999e25			0.0163012
$977$		−	1.20250e27i		−	1.48264i	−0.671153	−	0.741319i	$-0.734201\pi$
$977$		−	1.20250e27i		−	1.48264i	0.671153	−	0.741319i	$-0.265799\pi$
$978$	−9.81012e26	+	1.83135e26i	−1.19846	+	0.223729i
$979$	−9.16495e25			−0.110939
$980$			2.98657e26i			0.358211i
$981$	7.12527e26	−	2.75635e26i	0.846799	−	0.327577i
$982$	−7.43972e25			−0.0876099
$983$		−	6.46717e26i		−	0.754627i	−0.926086	−	0.377314i	$-0.876848\pi$
$983$		−	6.46717e26i		−	0.754627i	0.926086	−	0.377314i	$-0.123152\pi$
$984$	6.32464e25	+	3.38796e26i	0.0731273	+	0.391726i
$985$	6.85779e26			0.785703
$986$			5.41026e26i			0.614223i
$987$	1.56233e26	−	2.91656e25i	0.175760	−	0.0328108i
$988$	−2.66763e26			−0.297381
$989$		−	1.97391e26i		−	0.218052i
$990$	1.31316e26	+	3.39457e26i	0.143748	+	0.371593i
$991$	−4.68254e25			−0.0507948			−0.0253974	−	0.999677i	$-0.508085\pi$
$991$	−4.68254e25			−0.0507948			−0.0253974	+	0.999677i	$0.508085\pi$
$992$		−	1.78520e26i		−	0.191903i
$993$	4.00885e25	+	2.14745e26i	0.0427048	+	0.228759i
$994$	−7.39265e26			−0.780409
$995$			8.53660e26i			0.893053i
$996$	5.37003e26	−	1.00248e26i	0.556728	−	0.103930i
$997$	−9.85361e26			−1.01237			−0.506185	−	0.862425i	$-0.668945\pi$
$997$	−9.85361e26			−1.01237			−0.506185	+	0.862425i	$0.668945\pi$
$998$		−	1.08199e27i		−	1.10166i
$999$	1.60366e26	+	2.59424e26i	0.161816	+	0.261770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.19.b.a.5.2	✓	6
3.2	odd	2	inner	6.19.b.a.5.5	yes	6
4.3	odd	2		48.19.e.d.17.4		6
12.11	even	2		48.19.e.d.17.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.19.b.a.5.2	✓	6	1.1	even	1	trivial
6.19.b.a.5.5	yes	6	3.2	odd	2	inner
48.19.e.d.17.3		6	12.11	even	2
48.19.e.d.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:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-362.039i q^{2} +(-3612.02 - 19348.7i) q^{3} -131072. q^{4} +3.69488e6i q^{5} +(-7.00499e6 + 1.30769e6i) q^{6} +3.18077e7 q^{7} +4.74531e7i q^{8} +(-3.61327e8 + 1.39776e8i) q^{9} +O(q^{10})\)	\(q-362.039i q^{2} +(-3612.02 - 19348.7i) q^{3} -131072. q^{4} +3.69488e6i q^{5} +(-7.00499e6 + 1.30769e6i) q^{6} +3.18077e7 q^{7} +4.74531e7i q^{8} +(-3.61327e8 + 1.39776e8i) q^{9} +1.33769e9 q^{10} -7.02311e8i q^{11} +(4.73435e8 + 2.53608e9i) q^{12} +8.10908e9 q^{13} -1.15156e10i q^{14} +(7.14912e10 - 1.33460e10i) q^{15} +1.71799e10 q^{16} +1.82909e11i q^{17} +(5.06044e10 + 1.30814e11i) q^{18} +2.50983e11 q^{19} -4.84295e11i q^{20} +(-1.14890e11 - 6.15439e11i) q^{21} -2.54264e11 q^{22} +9.32089e11i q^{23} +(9.18158e11 - 1.71402e11i) q^{24} -9.83742e12 q^{25} -2.93580e12i q^{26} +(4.00962e12 + 6.48635e12i) q^{27} -4.16910e12 q^{28} +8.17010e12i q^{29} +(-4.83176e12 - 2.58826e13i) q^{30} +2.87019e13 q^{31} -6.21978e12i q^{32} +(-1.35888e13 + 2.53676e12i) q^{33} +6.62202e13 q^{34} +1.17525e14i q^{35} +(4.73599e13 - 1.83207e13i) q^{36} +3.99953e13 q^{37} -9.08655e13i q^{38} +(-2.92902e13 - 1.56900e14i) q^{39} -1.75333e14 q^{40} +3.68995e14i q^{41} +(-2.22813e14 + 4.15947e13i) q^{42} -2.11773e14 q^{43} +9.20533e13i q^{44} +(-5.16456e14 - 1.33506e15i) q^{45} +3.37452e14 q^{46} +2.53857e14i q^{47} +(-6.20541e13 - 3.32409e14i) q^{48} -6.16685e14 q^{49} +3.56153e15i q^{50} +(3.53906e15 - 6.60673e14i) q^{51} -1.06287e15 q^{52} +2.48752e14i q^{53} +(2.34831e15 - 1.45164e15i) q^{54} +2.59495e15 q^{55} +1.50937e15i q^{56} +(-9.06556e14 - 4.85620e15i) q^{57} +2.95789e15 q^{58} -1.21495e14i q^{59} +(-9.37050e15 + 1.74928e15i) q^{60} +7.62514e14 q^{61} -1.03912e16i q^{62} +(-1.14930e16 + 4.44596e15i) q^{63} -2.25180e15 q^{64} +2.99621e16i q^{65} +(9.18406e14 + 4.91968e15i) q^{66} -4.78338e16 q^{67} -2.39743e16i q^{68} +(1.80347e16 - 3.36673e15i) q^{69} +4.25488e16 q^{70} -6.41967e16i q^{71} +(-6.63282e15 - 1.71461e16i) q^{72} +7.57613e16 q^{73} -1.44799e16i q^{74} +(3.55330e16 + 1.90342e17i) q^{75} -3.28968e16 q^{76} -2.23389e16i q^{77} +(-5.68040e16 + 1.06042e16i) q^{78} +1.35483e16 q^{79} +6.34775e16i q^{80} +(1.11020e17 - 1.01010e17i) q^{81} +1.33590e17 q^{82} -2.11746e17i q^{83} +(1.50589e16 + 8.06668e16i) q^{84} -6.75827e17 q^{85} +7.66699e16i q^{86} +(1.58081e17 - 2.95106e16i) q^{87} +3.33268e16 q^{88} -1.30497e17i q^{89} +(-4.83343e17 + 1.86977e17i) q^{90} +2.57931e17 q^{91} -1.22171e17i q^{92} +(-1.03672e17 - 5.55346e17i) q^{93} +9.19059e16 q^{94} +9.27351e17i q^{95} +(-1.20345e17 + 2.24660e16i) q^{96} +9.26791e17 q^{97} +2.23264e17i q^{98} +(9.81663e16 + 2.53764e17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6258 q^{3} - 786432 q^{4} - 15753216 q^{6} + 28233804 q^{7} + 695971638 q^{9}+O(q^{10}) \) 6 * q - 6258 * q^3 - 786432 * q^4 - 15753216 * q^6 + 28233804 * q^7 + 695971638 * q^9	\( 6 q - 6258 q^{3} - 786432 q^{4} - 15753216 q^{6} + 28233804 q^{7} + 695971638 q^{9} - 434257920 q^{10} + 820248576 q^{12} + 29566196220 q^{13} + 119627095680 q^{15} + 103079215104 q^{16} + 315939373056 q^{18} - 438814047012 q^{19} + 2876527406172 q^{21} - 2844452929536 q^{22} + 2064805527552 q^{24} - 25696048717290 q^{25} + 11197265522814 q^{27} - 3700661157888 q^{28} + 13072787619840 q^{30} + 21775814927148 q^{31} - 962560003968 q^{33} + 99067611119616 q^{34} - 91222394535936 q^{36} + 638446564817436 q^{37} - 736541155104180 q^{39} + 56919054090240 q^{40} - 203954622480384 q^{42} - 16\!\cdots\!52 q^{43}+ \cdots + 76\!\cdots\!72 q^{99}+O(q^{100}) \) 6 * q - 6258 * q^3 - 786432 * q^4 - 15753216 * q^6 + 28233804 * q^7 + 695971638 * q^9 - 434257920 * q^10 + 820248576 * q^12 + 29566196220 * q^13 + 119627095680 * q^15 + 103079215104 * q^16 + 315939373056 * q^18 - 438814047012 * q^19 + 2876527406172 * q^21 - 2844452929536 * q^22 + 2064805527552 * q^24 - 25696048717290 * q^25 + 11197265522814 * q^27 - 3700661157888 * q^28 + 13072787619840 * q^30 + 21775814927148 * q^31 - 962560003968 * q^33 + 99067611119616 * q^34 - 91222394535936 * q^36 + 638446564817436 * q^37 - 736541155104180 * q^39 + 56919054090240 * q^40 - 203954622480384 * q^42 - 1688313718883652 * q^43 + 390590504075520 * q^45 + 1979247919104 * q^46 - 107511621353472 * q^48 - 895767896448270 * q^49 + 9636273526722048 * q^51 - 3875300470947840 * q^52 + 2993011804200960 * q^54 - 1259959207783680 * q^55 + 4023767318253996 * q^57 + 21251172660756480 * q^58 - 15679762684968960 * q^60 - 16279597277700036 * q^61 - 32525159214131028 * q^63 - 13510798882111488 * q^64 - 60047751762690048 * q^66 + 11153724314613276 * q^67 + 3612037794746112 * q^69 + 161904998736691200 * q^70 - 41410805505196032 * q^72 - 78910243347781140 * q^73 + 348225828845090910 * q^75 + 57516234769956864 * q^76 - 168903906208235520 * q^78 - 476518976428926228 * q^79 + 630680446106425062 * q^81 + 396536393269149696 * q^82 - 377032200181776384 * q^84 - 967978669078932480 * q^85 + 419256510981966720 * q^87 + 372828134380142592 * q^88 - 2046848246643179520 * q^90 - 1032060167365562760 * q^91 + 764294136047005116 * q^93 + 2566175766871080960 * q^94 - 270638190107295744 * q^96 + 834695417243310348 * q^97 + 761688154713814272 * q^99

Introduction

L-functions

Modular forms

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