LMFDB - Embedded newform 8.5.d.b.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,5,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	8.d (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:	$0.826959704671$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-15}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 4 $ x^2 - x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.1
Root			$0.500000 + 1.93649i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.5.d.b.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 3.87298i) q^{2} +6.00000 q^{3} +(-14.0000 + 7.74597i) q^{4} +30.9839i q^{5} +(-6.00000 - 23.2379i) q^{6} -61.9677i q^{7} +(44.0000 + 46.4758i) q^{8} -45.0000 q^{9} +O(q^{10})$	\(q+(-1.00000 - 3.87298i) q^{2} +6.00000 q^{3} +(-14.0000 + 7.74597i) q^{4} +30.9839i q^{5} +(-6.00000 - 23.2379i) q^{6} -61.9677i q^{7} +(44.0000 + 46.4758i) q^{8} -45.0000 q^{9} +(120.000 - 30.9839i) q^{10} -26.0000 q^{11} +(-84.0000 + 46.4758i) q^{12} -30.9839i q^{13} +(-240.000 + 61.9677i) q^{14} +185.903i q^{15} +(136.000 - 216.887i) q^{16} +226.000 q^{17} +(45.0000 + 174.284i) q^{18} +134.000 q^{19} +(-240.000 - 433.774i) q^{20} -371.806i q^{21} +(26.0000 + 100.698i) q^{22} +309.839i q^{23} +(264.000 + 278.855i) q^{24} -335.000 q^{25} +(-120.000 + 30.9839i) q^{26} -756.000 q^{27} +(480.000 + 867.548i) q^{28} +340.823i q^{29} +(720.000 - 185.903i) q^{30} -1239.35i q^{31} +(-976.000 - 309.839i) q^{32} -156.000 q^{33} +(-226.000 - 875.294i) q^{34} +1920.00 q^{35} +(630.000 - 348.569i) q^{36} +1766.08i q^{37} +(-134.000 - 518.980i) q^{38} -185.903i q^{39} +(-1440.00 + 1363.29i) q^{40} +994.000 q^{41} +(-1440.00 + 371.806i) q^{42} -1882.00 q^{43} +(364.000 - 201.395i) q^{44} -1394.27i q^{45} +(1200.00 - 309.839i) q^{46} +2106.90i q^{47} +(816.000 - 1301.32i) q^{48} -1439.00 q^{49} +(335.000 + 1297.45i) q^{50} +1356.00 q^{51} +(240.000 + 433.774i) q^{52} -3811.02i q^{53} +(756.000 + 2927.98i) q^{54} -805.581i q^{55} +(2880.00 - 2726.58i) q^{56} +804.000 q^{57} +(1320.00 - 340.823i) q^{58} -5018.00 q^{59} +(-1440.00 - 2602.64i) q^{60} +2075.92i q^{61} +(-4800.00 + 1239.35i) q^{62} +2788.55i q^{63} +(-224.000 + 4089.87i) q^{64} +960.000 q^{65} +(156.000 + 604.185i) q^{66} +8006.00 q^{67} +(-3164.00 + 1750.59i) q^{68} +1859.03i q^{69} +(-1920.00 - 7436.13i) q^{70} -557.710i q^{71} +(-1980.00 - 2091.41i) q^{72} +386.000 q^{73} +(6840.00 - 1766.08i) q^{74} -2010.00 q^{75} +(-1876.00 + 1037.96i) q^{76} +1611.16i q^{77} +(-720.000 + 185.903i) q^{78} -11030.3i q^{79} +(6720.00 + 4213.81i) q^{80} -891.000 q^{81} +(-994.000 - 3849.75i) q^{82} -2234.00 q^{83} +(2880.00 + 5205.29i) q^{84} +7002.35i q^{85} +(1882.00 + 7288.95i) q^{86} +2044.94i q^{87} +(-1144.00 - 1208.37i) q^{88} -10046.0 q^{89} +(-5400.00 + 1394.27i) q^{90} -1920.00 q^{91} +(-2400.00 - 4337.74i) q^{92} -7436.13i q^{93} +(8160.00 - 2106.90i) q^{94} +4151.84i q^{95} +(-5856.00 - 1859.03i) q^{96} +8738.00 q^{97} +(1439.00 + 5573.22i) q^{98} +1170.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 12 q^{3} - 28 q^{4} - 12 q^{6} + 88 q^{8} - 90 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 12 * q^3 - 28 * q^4 - 12 * q^6 + 88 * q^8 - 90 * q^9	$ 2 q - 2 q^{2} + 12 q^{3} - 28 q^{4} - 12 q^{6} + 88 q^{8} - 90 q^{9} + 240 q^{10} - 52 q^{11} - 168 q^{12} - 480 q^{14} + 272 q^{16} + 452 q^{17} + 90 q^{18} + 268 q^{19} - 480 q^{20} + 52 q^{22} + 528 q^{24} - 670 q^{25} - 240 q^{26} - 1512 q^{27} + 960 q^{28} + 1440 q^{30} - 1952 q^{32} - 312 q^{33} - 452 q^{34} + 3840 q^{35} + 1260 q^{36} - 268 q^{38} - 2880 q^{40} + 1988 q^{41} - 2880 q^{42} - 3764 q^{43} + 728 q^{44} + 2400 q^{46} + 1632 q^{48} - 2878 q^{49} + 670 q^{50} + 2712 q^{51} + 480 q^{52} + 1512 q^{54} + 5760 q^{56} + 1608 q^{57} + 2640 q^{58} - 10036 q^{59} - 2880 q^{60} - 9600 q^{62} - 448 q^{64} + 1920 q^{65} + 312 q^{66} + 16012 q^{67} - 6328 q^{68} - 3840 q^{70} - 3960 q^{72} + 772 q^{73} + 13680 q^{74} - 4020 q^{75} - 3752 q^{76} - 1440 q^{78} + 13440 q^{80} - 1782 q^{81} - 1988 q^{82} - 4468 q^{83} + 5760 q^{84} + 3764 q^{86} - 2288 q^{88} - 20092 q^{89} - 10800 q^{90} - 3840 q^{91} - 4800 q^{92} + 16320 q^{94} - 11712 q^{96} + 17476 q^{97} + 2878 q^{98} + 2340 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 12 * q^3 - 28 * q^4 - 12 * q^6 + 88 * q^8 - 90 * q^9 + 240 * q^10 - 52 * q^11 - 168 * q^12 - 480 * q^14 + 272 * q^16 + 452 * q^17 + 90 * q^18 + 268 * q^19 - 480 * q^20 + 52 * q^22 + 528 * q^24 - 670 * q^25 - 240 * q^26 - 1512 * q^27 + 960 * q^28 + 1440 * q^30 - 1952 * q^32 - 312 * q^33 - 452 * q^34 + 3840 * q^35 + 1260 * q^36 - 268 * q^38 - 2880 * q^40 + 1988 * q^41 - 2880 * q^42 - 3764 * q^43 + 728 * q^44 + 2400 * q^46 + 1632 * q^48 - 2878 * q^49 + 670 * q^50 + 2712 * q^51 + 480 * q^52 + 1512 * q^54 + 5760 * q^56 + 1608 * q^57 + 2640 * q^58 - 10036 * q^59 - 2880 * q^60 - 9600 * q^62 - 448 * q^64 + 1920 * q^65 + 312 * q^66 + 16012 * q^67 - 6328 * q^68 - 3840 * q^70 - 3960 * q^72 + 772 * q^73 + 13680 * q^74 - 4020 * q^75 - 3752 * q^76 - 1440 * q^78 + 13440 * q^80 - 1782 * q^81 - 1988 * q^82 - 4468 * q^83 + 5760 * q^84 + 3764 * q^86 - 2288 * q^88 - 20092 * q^89 - 10800 * q^90 - 3840 * q^91 - 4800 * q^92 + 16320 * q^94 - 11712 * q^96 + 17476 * q^97 + 2878 * q^98 + 2340 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−	3.87298i	−0.250000	−	0.968246i
$2$	−1.00000	−	3.87298i	−0.250000	−	0.968246i
$3$	6.00000			0.666667			0.333333	−	0.942809i	$-0.391827\pi$
$3$	6.00000			0.666667			0.333333	+	0.942809i	$0.391827\pi$
$4$	−14.0000	+	7.74597i	−0.875000	+	0.484123i
$5$			30.9839i			1.23935i	0.784857	+	0.619677i	$0.212737\pi$
$5$			30.9839i			1.23935i	−0.784857	+	0.619677i	$0.787263\pi$
$6$	−6.00000	−	23.2379i	−0.166667	−	0.645497i
$7$		−	61.9677i		−	1.26465i	−0.774704	−	0.632324i	$-0.782101\pi$
$7$		−	61.9677i		−	1.26465i	0.774704	−	0.632324i	$-0.217899\pi$
$8$	44.0000	+	46.4758i	0.687500	+	0.726184i
$9$	−45.0000			−0.555556
$10$	120.000	−	30.9839i	1.20000	−	0.309839i
$11$	−26.0000			−0.214876			−0.107438	−	0.994212i	$-0.534265\pi$
$11$	−26.0000			−0.214876			−0.107438	+	0.994212i	$0.534265\pi$
$12$	−84.0000	+	46.4758i	−0.583333	+	0.322749i
$13$		−	30.9839i		−	0.183336i	−0.995790	−	0.0916682i	$-0.970780\pi$
$13$		−	30.9839i		−	0.183336i	0.995790	−	0.0916682i	$-0.0292199\pi$
$14$	−240.000	+	61.9677i	−1.22449	+	0.316162i
$15$			185.903i			0.826236i
$16$	136.000	−	216.887i	0.531250	−	0.847215i
$17$	226.000			0.782007			0.391003	−	0.920389i	$-0.372128\pi$
$17$	226.000			0.782007			0.391003	+	0.920389i	$0.372128\pi$
$18$	45.0000	+	174.284i	0.138889	+	0.537914i
$19$	134.000			0.371191			0.185596	−	0.982626i	$-0.440579\pi$
$19$	134.000			0.371191			0.185596	+	0.982626i	$0.440579\pi$
$20$	−240.000	−	433.774i	−0.600000	−	1.08444i
$21$		−	371.806i		−	0.843098i
$22$	26.0000	+	100.698i	0.0537190	+	0.208053i
$23$			309.839i			0.585706i	0.956157	+	0.292853i	$0.0946047\pi$
$23$			309.839i			0.585706i	−0.956157	+	0.292853i	$0.905395\pi$
$24$	264.000	+	278.855i	0.458333	+	0.484123i
$25$	−335.000			−0.536000
$26$	−120.000	+	30.9839i	−0.177515	+	0.0458341i
$27$	−756.000			−1.03704
$28$	480.000	+	867.548i	0.612245	+	1.10657i
$29$			340.823i			0.405259i	0.979256	+	0.202629i	$0.0649487\pi$
$29$			340.823i			0.405259i	−0.979256	+	0.202629i	$0.935051\pi$
$30$	720.000	−	185.903i	0.800000	−	0.206559i
$31$		−	1239.35i		−	1.28965i	−0.764330	−	0.644826i	$-0.776930\pi$
$31$		−	1239.35i		−	1.28965i	0.764330	−	0.644826i	$-0.223070\pi$
$32$	−976.000	−	309.839i	−0.953125	−	0.302577i
$33$	−156.000			−0.143251
$34$	−226.000	−	875.294i	−0.195502	−	0.757175i
$35$	1920.00			1.56735
$36$	630.000	−	348.569i	0.486111	−	0.268957i
$37$			1766.08i			1.29005i	0.764161	+	0.645026i	$0.223153\pi$
$37$			1766.08i			1.29005i	−0.764161	+	0.645026i	$0.776847\pi$
$38$	−134.000	−	518.980i	−0.0927978	−	0.359404i
$39$		−	185.903i		−	0.122224i
$40$	−1440.00	+	1363.29i	−0.900000	+	0.852056i
$41$	994.000			0.591315			0.295657	−	0.955294i	$-0.404461\pi$
$41$	994.000			0.591315			0.295657	+	0.955294i	$0.404461\pi$
$42$	−1440.00	+	371.806i	−0.816327	+	0.210775i
$43$	−1882.00			−1.01785			−0.508924	−	0.860812i	$-0.669956\pi$
$43$	−1882.00			−1.01785			−0.508924	+	0.860812i	$0.669956\pi$
$44$	364.000	−	201.395i	0.188017	−	0.104026i
$45$		−	1394.27i		−	0.688530i
$46$	1200.00	−	309.839i	0.567108	−	0.146427i
$47$			2106.90i			0.953781i	0.878963	+	0.476891i	$0.158236\pi$
$47$			2106.90i			0.953781i	−0.878963	+	0.476891i	$0.841764\pi$
$48$	816.000	−	1301.32i	0.354167	−	0.564810i
$49$	−1439.00			−0.599334
$50$	335.000	+	1297.45i	0.134000	+	0.518980i
$51$	1356.00			0.521338
$52$	240.000	+	433.774i	0.0887574	+	0.160419i
$53$		−	3811.02i		−	1.35672i	−0.734731	−	0.678358i	$-0.762692\pi$
$53$		−	3811.02i		−	1.35672i	0.734731	−	0.678358i	$-0.237308\pi$
$54$	756.000	+	2927.98i	0.259259	+	1.00411i
$55$		−	805.581i		−	0.266308i
$56$	2880.00	−	2726.58i	0.918367	−	0.869445i
$57$	804.000			0.247461
$58$	1320.00	−	340.823i	0.392390	−	0.101315i
$59$	−5018.00			−1.44154			−0.720770	−	0.693174i	$-0.756212\pi$
$59$	−5018.00			−1.44154			−0.720770	+	0.693174i	$0.756212\pi$
$60$	−1440.00	−	2602.64i	−0.400000	−	0.722957i
$61$			2075.92i			0.557893i	0.960307	+	0.278946i	$0.0899852\pi$
$61$			2075.92i			0.557893i	−0.960307	+	0.278946i	$0.910015\pi$
$62$	−4800.00	+	1239.35i	−1.24870	+	0.322413i
$63$			2788.55i			0.702582i
$64$	−224.000	+	4089.87i	−0.0546875	+	0.998504i
$65$	960.000			0.227219
$66$	156.000	+	604.185i	0.0358127	+	0.138702i
$67$	8006.00			1.78347			0.891735	−	0.452557i	$-0.149488\pi$
$67$	8006.00			1.78347			0.891735	+	0.452557i	$0.149488\pi$
$68$	−3164.00	+	1750.59i	−0.684256	+	0.378587i
$69$			1859.03i			0.390471i
$70$	−1920.00	−	7436.13i	−0.391837	−	1.51758i
$71$		−	557.710i		−	0.110635i	−0.998469	−	0.0553174i	$-0.982383\pi$
$71$		−	557.710i		−	0.110635i	0.998469	−	0.0553174i	$-0.0176171\pi$
$72$	−1980.00	−	2091.41i	−0.381944	−	0.403436i
$73$	386.000			0.0724339			0.0362169	−	0.999344i	$-0.488469\pi$
$73$	386.000			0.0724339			0.0362169	+	0.999344i	$0.488469\pi$
$74$	6840.00	−	1766.08i	1.24909	−	0.322513i
$75$	−2010.00			−0.357333
$76$	−1876.00	+	1037.96i	−0.324792	+	0.179702i
$77$			1611.16i			0.271742i
$78$	−720.000	+	185.903i	−0.118343	+	0.0305561i
$79$		−	11030.3i		−	1.76739i	−0.468067	−	0.883693i	$-0.655049\pi$
$79$		−	11030.3i		−	1.76739i	0.468067	−	0.883693i	$-0.344951\pi$
$80$	6720.00	+	4213.81i	1.05000	+	0.658407i
$81$	−891.000			−0.135802
$82$	−994.000	−	3849.75i	−0.147829	−	0.572538i
$83$	−2234.00			−0.324285			−0.162143	−	0.986767i	$-0.551840\pi$
$83$	−2234.00			−0.324285			−0.162143	+	0.986767i	$0.551840\pi$
$84$	2880.00	+	5205.29i	0.408163	+	0.737711i
$85$			7002.35i			0.969184i
$86$	1882.00	+	7288.95i	0.254462	+	0.985527i
$87$			2044.94i			0.270172i
$88$	−1144.00	−	1208.37i	−0.147727	−	0.156040i
$89$	−10046.0			−1.26827			−0.634137	−	0.773221i	$-0.718645\pi$
$89$	−10046.0			−1.26827			−0.634137	+	0.773221i	$0.718645\pi$
$90$	−5400.00	+	1394.27i	−0.666667	+	0.172133i
$91$	−1920.00			−0.231856
$92$	−2400.00	−	4337.74i	−0.283554	−	0.512493i
$93$		−	7436.13i		−	0.859767i
$94$	8160.00	−	2106.90i	0.923495	−	0.238445i
$95$			4151.84i			0.460037i
$96$	−5856.00	−	1859.03i	−0.635417	−	0.201718i
$97$	8738.00			0.928685			0.464343	−	0.885656i	$-0.346291\pi$
$97$	8738.00			0.928685			0.464343	+	0.885656i	$0.346291\pi$
$98$	1439.00	+	5573.22i	0.149833	+	0.580302i
$99$	1170.00			0.119376
$100$	4690.00	−	2594.90i	0.469000	−	0.259490i
$101$		−	10627.5i		−	1.04181i	−0.853616	−	0.520903i	$-0.825595\pi$
$101$		−	10627.5i		−	1.04181i	0.853616	−	0.520903i	$-0.174405\pi$
$102$	−1356.00	−	5251.77i	−0.130334	−	0.504783i
$103$			10100.7i			0.952092i	0.879420	+	0.476046i	$0.157930\pi$
$103$			10100.7i			0.952092i	−0.879420	+	0.476046i	$0.842070\pi$
$104$	1440.00	−	1363.29i	0.133136	−	0.126044i
$105$	11520.0			1.04490
$106$	−14760.0	+	3811.02i	−1.31363	+	0.339179i
$107$	6886.00			0.601450			0.300725	−	0.953711i	$-0.402771\pi$
$107$	6886.00			0.601450			0.300725	+	0.953711i	$0.402771\pi$
$108$	10584.0	−	5855.95i	0.907407	−	0.502053i
$109$			1208.37i			0.101706i	0.998706	+	0.0508531i	$0.0161940\pi$
$109$			1208.37i			0.101706i	−0.998706	+	0.0508531i	$0.983806\pi$
$110$	−3120.00	+	805.581i	−0.257851	+	0.0665769i
$111$			10596.5i			0.860034i
$112$	−13440.0	−	8427.61i	−1.07143	−	0.671844i
$113$	−1214.00			−0.0950740			−0.0475370	−	0.998869i	$-0.515137\pi$
$113$	−1214.00			−0.0950740			−0.0475370	+	0.998869i	$0.515137\pi$
$114$	−804.000	−	3113.88i	−0.0618652	−	0.239603i
$115$	−9600.00			−0.725898
$116$	−2640.00	−	4771.52i	−0.196195	−	0.354601i
$117$			1394.27i			0.101854i
$118$	5018.00	+	19434.6i	0.360385	+	1.39576i
$119$		−	14004.7i		−	0.988963i
$120$	−8640.00	+	8179.74i	−0.600000	+	0.568038i
$121$	−13965.0			−0.953828
$122$	8040.00	−	2075.92i	0.540177	−	0.139473i
$123$	5964.00			0.394210
$124$	9600.00	+	17351.0i	0.624350	+	1.12844i
$125$			8985.32i			0.575061i
$126$	10800.0	−	2788.55i	0.680272	−	0.175646i
$127$		−	2974.45i		−	0.184416i	−0.995740	−	0.0922082i	$-0.970607\pi$
$127$		−	2974.45i		−	0.184416i	0.995740	−	0.0922082i	$-0.0293925\pi$
$128$	16064.0	−	3222.32i	0.980469	−	0.196675i
$129$	−11292.0			−0.678565
$130$	−960.000	−	3718.06i	−0.0568047	−	0.220004i
$131$	−14138.0			−0.823845			−0.411922	−	0.911219i	$-0.635143\pi$
$131$	−14138.0			−0.823845			−0.411922	+	0.911219i	$0.635143\pi$
$132$	2184.00	−	1208.37i	0.125344	−	0.0693509i
$133$		−	8303.68i		−	0.469426i
$134$	−8006.00	−	31007.1i	−0.445868	−	1.72684i
$135$		−	23423.8i		−	1.28526i
$136$	9944.00	+	10503.5i	0.537630	+	0.567881i
$137$	23266.0			1.23960			0.619799	−	0.784761i	$-0.287214\pi$
$137$	23266.0			1.23960			0.619799	+	0.784761i	$0.287214\pi$
$138$	7200.00	−	1859.03i	0.378072	−	0.0976177i
$139$	16934.0			0.876456			0.438228	−	0.898864i	$-0.355606\pi$
$139$	16934.0			0.876456			0.438228	+	0.898864i	$0.355606\pi$
$140$	−26880.0	+	14872.3i	−1.37143	+	0.758789i
$141$			12641.4i			0.635854i
$142$	−2160.00	+	557.710i	−0.107122	+	0.0276587i
$143$			805.581i			0.0393946i
$144$	−6120.00	+	9759.92i	−0.295139	+	0.470675i
$145$	−10560.0			−0.502259
$146$	−386.000	−	1494.97i	−0.0181085	−	0.0701338i
$147$	−8634.00			−0.399556
$148$	−13680.0	−	24725.1i	−0.624543	−	1.12880i
$149$			33121.8i			1.49190i	0.666000	+	0.745952i	$0.268005\pi$
$149$			33121.8i			1.49190i	−0.666000	+	0.745952i	$0.731995\pi$
$150$	2010.00	+	7784.70i	0.0893333	+	0.345987i
$151$			27079.9i			1.18766i	0.804590	+	0.593831i	$0.202385\pi$
$151$			27079.9i			1.18766i	−0.804590	+	0.593831i	$0.797615\pi$
$152$	5896.00	+	6227.76i	0.255194	+	0.269553i
$153$	−10170.0			−0.434448
$154$	6240.00	−	1611.16i	0.263114	−	0.0679356i
$155$	38400.0			1.59834
$156$	1440.00	+	2602.64i	0.0591716	+	0.106946i
$157$		−	29403.7i		−	1.19290i	−0.802652	−	0.596448i	$-0.796578\pi$
$157$		−	29403.7i		−	1.19290i	0.802652	−	0.596448i	$-0.203422\pi$
$158$	−42720.0	+	11030.3i	−1.71126	+	0.441847i
$159$		−	22866.1i		−	0.904477i
$160$	9600.00	−	30240.3i	0.375000	−	1.18126i
$161$	19200.0			0.740712
$162$	891.000	+	3450.83i	0.0339506	+	0.131490i
$163$	−37114.0			−1.39689			−0.698446	−	0.715663i	$-0.746125\pi$
$163$	−37114.0			−1.39689			−0.698446	+	0.715663i	$0.746125\pi$
$164$	−13916.0	+	7699.49i	−0.517400	+	0.286269i
$165$		−	4833.48i		−	0.177538i
$166$	2234.00	+	8652.24i	0.0810713	+	0.313988i
$167$			21502.8i			0.771014i	0.922705	+	0.385507i	$0.125973\pi$
$167$			21502.8i			0.771014i	−0.922705	+	0.385507i	$0.874027\pi$
$168$	17280.0	−	16359.5i	0.612245	−	0.579630i
$169$	27601.0			0.966388
$170$	27120.0	−	7002.35i	0.938408	−	0.242296i
$171$	−6030.00			−0.206217
$172$	26348.0	−	14577.9i	0.890617	−	0.492763i
$173$		−	26057.4i		−	0.870642i	−0.900275	−	0.435321i	$-0.856635\pi$
$173$		−	26057.4i		−	0.870642i	0.900275	−	0.435321i	$-0.143365\pi$
$174$	7920.00	−	2044.94i	0.261593	−	0.0675431i
$175$			20759.2i			0.677851i
$176$	−3536.00	+	5639.06i	−0.114153	+	0.182046i
$177$	−30108.0			−0.961027
$178$	10046.0	+	38908.0i	0.317069	+	1.22800i
$179$	−9146.00			−0.285447			−0.142723	−	0.989763i	$-0.545586\pi$
$179$	−9146.00			−0.285447			−0.142723	+	0.989763i	$0.545586\pi$
$180$	10800.0	+	19519.8i	0.333333	+	0.602464i
$181$		−	57351.1i		−	1.75059i	−0.483588	−	0.875296i	$-0.660667\pi$
$181$		−	57351.1i		−	1.75059i	0.483588	−	0.875296i	$-0.339333\pi$
$182$	1920.00	+	7436.13i	0.0579640	+	0.224494i
$183$			12455.5i			0.371929i
$184$	−14400.0	+	13632.9i	−0.425331	+	0.402673i
$185$	−54720.0			−1.59883
$186$	−28800.0	+	7436.13i	−0.832466	+	0.214942i
$187$	−5876.00			−0.168035
$188$	−16320.0	−	29496.6i	−0.461747	−	0.834559i
$189$			46847.6i			1.31149i
$190$	16080.0	−	4151.84i	0.445429	−	0.115009i
$191$		−	9419.10i		−	0.258192i	−0.991632	−	0.129096i	$-0.958792\pi$
$191$		−	9419.10i		−	0.258192i	0.991632	−	0.129096i	$-0.0412075\pi$
$192$	−1344.00	+	24539.2i	−0.0364583	+	0.665669i
$193$	45986.0			1.23456			0.617278	−	0.786745i	$-0.288235\pi$
$193$	45986.0			1.23456			0.617278	+	0.786745i	$0.288235\pi$
$194$	−8738.00	−	33842.1i	−0.232171	−	0.899196i
$195$	5760.00			0.151479
$196$	20146.0	−	11146.4i	0.524417	−	0.290151i
$197$			38203.1i			0.984388i	0.870486	+	0.492194i	$0.163805\pi$
$197$			38203.1i			0.984388i	−0.870486	+	0.492194i	$0.836195\pi$
$198$	−1170.00	−	4531.39i	−0.0298439	−	0.115585i
$199$		−	27327.8i		−	0.690078i	−0.938588	−	0.345039i	$-0.887866\pi$
$199$		−	27327.8i		−	0.690078i	0.938588	−	0.345039i	$-0.112134\pi$
$200$	−14740.0	−	15569.4i	−0.368500	−	0.389235i
$201$	48036.0			1.18898
$202$	−41160.0	+	10627.5i	−1.00872	+	0.260452i
$203$	21120.0			0.512509
$204$	−18984.0	+	10503.5i	−0.456171	+	0.252392i
$205$			30798.0i			0.732849i
$206$	39120.0	−	10100.7i	0.921859	−	0.238023i
$207$		−	13942.7i		−	0.325392i
$208$	−6720.00	−	4213.81i	−0.155325	−	0.0973975i
$209$	−3484.00			−0.0797601
$210$	−11520.0	−	44616.8i	−0.261224	−	1.01172i
$211$	49094.0			1.10272			0.551358	−	0.834269i	$-0.314110\pi$
$211$	49094.0			1.10272			0.551358	+	0.834269i	$0.314110\pi$
$212$	29520.0	+	53354.2i	0.656817	+	1.18713i
$213$		−	3346.26i		−	0.0737565i
$214$	−6886.00	−	26669.4i	−0.150362	−	0.582351i
$215$		−	58311.6i		−	1.26147i
$216$	−33264.0	−	35135.7i	−0.712963	−	0.753080i
$217$	−76800.0			−1.63095
$218$	4680.00	−	1208.37i	0.0984766	−	0.0254265i
$219$	2316.00			0.0482892
$220$	6240.00	+	11278.1i	0.128926	+	0.233019i
$221$		−	7002.35i		−	0.143370i
$222$	41040.0	−	10596.5i	0.832725	−	0.215009i
$223$			54779.5i			1.10156i	0.834650	+	0.550780i	$0.185670\pi$
$223$			54779.5i			1.10156i	−0.834650	+	0.550780i	$0.814330\pi$
$224$	−19200.0	+	60480.5i	−0.382653	+	1.20537i
$225$	15075.0			0.297778
$226$	1214.00	+	4701.80i	0.0237685	+	0.0920550i
$227$	−53882.0			−1.04566			−0.522832	−	0.852436i	$-0.675124\pi$
$227$	−53882.0			−1.04566			−0.522832	+	0.852436i	$0.675124\pi$
$228$	−11256.0	+	6227.76i	−0.216528	+	0.119801i
$229$			48861.6i			0.931743i	0.884852	+	0.465872i	$0.154259\pi$
$229$			48861.6i			0.931743i	−0.884852	+	0.465872i	$0.845741\pi$
$230$	9600.00	+	37180.6i	0.181474	+	0.702848i
$231$			9666.97i			0.181162i
$232$	−15840.0	+	14996.2i	−0.294293	+	0.278615i
$233$	25858.0			0.476303			0.238151	−	0.971228i	$-0.423459\pi$
$233$	25858.0			0.476303			0.238151	+	0.971228i	$0.423459\pi$
$234$	5400.00	−	1394.27i	0.0986193	−	0.0254634i
$235$	−65280.0			−1.18207
$236$	70252.0	−	38869.3i	1.26135	−	0.697882i
$237$		−	66181.5i		−	1.17826i
$238$	−54240.0	+	14004.7i	−0.957559	+	0.247241i
$239$		−	31107.8i		−	0.544595i	−0.962213	−	0.272297i	$-0.912217\pi$
$239$		−	31107.8i		−	0.544595i	0.962213	−	0.272297i	$-0.0877835\pi$
$240$	40320.0	+	25282.8i	0.700000	+	0.438938i
$241$	−25246.0			−0.434669			−0.217334	−	0.976097i	$-0.569736\pi$
$241$	−25246.0			−0.434669			−0.217334	+	0.976097i	$0.569736\pi$
$242$	13965.0	+	54086.2i	0.238457	+	0.923540i
$243$	55890.0			0.946502
$244$	−16080.0	−	29062.9i	−0.270089	−	0.488156i
$245$		−	44585.8i		−	0.742787i
$246$	−5964.00	−	23098.5i	−0.0985524	−	0.381692i
$247$		−	4151.84i		−	0.0680529i
$248$	57600.0	−	54531.6i	0.936524	−	0.886635i
$249$	−13404.0			−0.216190
$250$	34800.0	−	8985.32i	0.556800	−	0.143765i
$251$	−40346.0			−0.640403			−0.320201	−	0.947350i	$-0.603751\pi$
$251$	−40346.0			−0.640403			−0.320201	+	0.947350i	$0.603751\pi$
$252$	−21600.0	−	39039.7i	−0.340136	−	0.614759i
$253$		−	8055.81i		−	0.125854i
$254$	−11520.0	+	2974.45i	−0.178560	+	0.0461041i
$255$			42014.1i			0.646123i
$256$	−28544.0	−	58993.3i	−0.435547	−	0.900166i
$257$	4738.00			0.0717346			0.0358673	−	0.999357i	$-0.488581\pi$
$257$	4738.00			0.0717346			0.0358673	+	0.999357i	$0.488581\pi$
$258$	11292.0	+	43733.7i	0.169641	+	0.657018i
$259$	109440.			1.63146
$260$	−13440.0	+	7436.13i	−0.198817	+	0.110002i
$261$		−	15337.0i		−	0.225144i
$262$	14138.0	+	54756.2i	0.205961	+	0.797684i
$263$			114950.i			1.66187i	0.556367	+	0.830937i	$0.312195\pi$
$263$			114950.i			1.66187i	−0.556367	+	0.830937i	$0.687805\pi$
$264$	−6864.00	−	7250.22i	−0.0984848	−	0.104026i
$265$	118080.			1.68145
$266$	−32160.0	+	8303.68i	−0.454520	+	0.117356i
$267$	−60276.0			−0.845516
$268$	−112084.	+	62014.2i	−1.56054	+	0.863419i
$269$		−	1022.47i		−	0.0141301i	−0.999975	−	0.00706505i	$-0.997751\pi$
$269$		−	1022.47i		−	0.0141301i	0.999975	−	0.00706505i	$-0.00224889\pi$
$270$	−90720.0	+	23423.8i	−1.24444	+	0.321314i
$271$		−	32347.2i		−	0.440451i	−0.975449	−	0.220225i	$-0.929321\pi$
$271$		−	32347.2i		−	0.440451i	0.975449	−	0.220225i	$-0.0706793\pi$
$272$	30736.0	−	49016.5i	0.415441	−	0.662528i
$273$	−11520.0			−0.154571
$274$	−23266.0	−	90108.8i	−0.309899	−	1.20023i
$275$	8710.00			0.115174
$276$	−14400.0	−	26026.4i	−0.189036	−	0.341662i
$277$			27172.9i			0.354141i	0.984198	+	0.177070i	$0.0566620\pi$
$277$			27172.9i			0.354141i	−0.984198	+	0.177070i	$0.943338\pi$
$278$	−16934.0	−	65585.1i	−0.219114	−	0.848625i
$279$			55771.0i			0.716473i
$280$	84480.0	+	89233.5i	1.07755	+	1.13818i
$281$	−51518.0			−0.652449			−0.326224	−	0.945292i	$-0.605776\pi$
$281$	−51518.0			−0.652449			−0.326224	+	0.945292i	$0.605776\pi$
$282$	48960.0	−	12641.4i	0.615663	−	0.158964i
$283$	−54874.0			−0.685163			−0.342581	−	0.939488i	$-0.611301\pi$
$283$	−54874.0			−0.685163			−0.342581	+	0.939488i	$0.611301\pi$
$284$	4320.00	+	7807.93i	0.0535608	+	0.0968054i
$285$			24911.0i			0.306692i
$286$	3120.00	−	805.581i	0.0381437	−	0.00984865i
$287$		−	61595.9i		−	0.747805i
$288$	43920.0	+	13942.7i	0.529514	+	0.168098i
$289$	−32445.0			−0.388465
$290$	10560.0	+	40898.7i	0.125565	+	0.486310i
$291$	52428.0			0.619124
$292$	−5404.00	+	2989.94i	−0.0633796	+	0.0350669i
$293$		−	64663.3i		−	0.753222i	−0.926372	−	0.376611i	$-0.877089\pi$
$293$		−	64663.3i		−	0.753222i	0.926372	−	0.376611i	$-0.122911\pi$
$294$	8634.00	+	33439.3i	0.0998889	+	0.386868i
$295$		−	155477.i		−	1.78658i
$296$	−82080.0	+	77707.5i	−0.936815	+	0.886910i
$297$	19656.0			0.222834
$298$	128280.	−	33121.8i	1.44453	−	0.372976i
$299$	9600.00			0.107381
$300$	28140.0	−	15569.4i	0.312667	−	0.172993i
$301$			116623.i			1.28722i
$302$	104880.	−	27079.9i	1.14995	−	0.296916i
$303$		−	63764.8i		−	0.694538i
$304$	18224.0	−	29062.9i	0.197195	−	0.314479i
$305$	−64320.0			−0.691427
$306$	10170.0	+	39388.2i	0.108612	+	0.420653i
$307$	24326.0			0.258104			0.129052	−	0.991638i	$-0.458807\pi$
$307$	24326.0			0.258104			0.129052	+	0.991638i	$0.458807\pi$
$308$	−12480.0	−	22556.3i	−0.131557	−	0.237775i
$309$			60604.4i			0.634728i
$310$	−38400.0	−	148723.i	−0.399584	−	1.54758i
$311$			7002.35i			0.0723975i	0.999345	+	0.0361987i	$0.0115249\pi$
$311$			7002.35i			0.0723975i	−0.999345	+	0.0361987i	$0.988475\pi$
$312$	8640.00	−	8179.74i	0.0887574	−	0.0840292i
$313$	−83422.0			−0.851514			−0.425757	−	0.904837i	$-0.639992\pi$
$313$	−83422.0			−0.851514			−0.425757	+	0.904837i	$0.639992\pi$
$314$	−113880.	+	29403.7i	−1.15502	+	0.298224i
$315$	−86400.0			−0.870748
$316$	85440.0	+	154424.i	0.855632	+	1.54646i
$317$			7033.34i			0.0699911i	0.999387	+	0.0349956i	$0.0111417\pi$
$317$			7033.34i			0.0699911i	−0.999387	+	0.0349956i	$0.988858\pi$
$318$	−88560.0	+	22866.1i	−0.875756	+	0.226119i
$319$		−	8861.39i		−	0.0870804i
$320$	−126720.	−	6940.39i	−1.23750	−	0.0677772i
$321$	41316.0			0.400967
$322$	−19200.0	−	74361.3i	−0.185178	−	0.717191i
$323$	30284.0			0.290274
$324$	12474.0	−	6901.66i	0.118827	−	0.0657451i
$325$			10379.6i			0.0982684i
$326$	37114.0	+	143742.i	0.349223	+	1.35253i
$327$			7250.22i			0.0678041i
$328$	43736.0	+	46196.9i	0.406529	+	0.429403i
$329$	130560.			1.20620
$330$	−18720.0	+	4833.48i	−0.171901	+	0.0443846i
$331$	12134.0			0.110751			0.0553755	−	0.998466i	$-0.482364\pi$
$331$	12134.0			0.110751			0.0553755	+	0.998466i	$0.482364\pi$
$332$	31276.0	−	17304.5i	0.283749	−	0.156994i
$333$		−	79473.6i		−	0.716695i
$334$	83280.0	−	21502.8i	0.746531	−	0.192753i
$335$			248057.i			2.21035i
$336$	−80640.0	−	50565.7i	−0.714286	−	0.447896i
$337$	41666.0			0.366878			0.183439	−	0.983031i	$-0.441277\pi$
$337$	41666.0			0.366878			0.183439	+	0.983031i	$0.441277\pi$
$338$	−27601.0	−	106898.i	−0.241597	−	0.935701i
$339$	−7284.00			−0.0633827
$340$	−54240.0	−	98033.0i	−0.469204	−	0.848036i
$341$			32223.2i			0.277115i
$342$	6030.00	+	23354.1i	0.0515543	+	0.199669i
$343$		−	59613.0i		−	0.506702i
$344$	−82808.0	−	87467.5i	−0.699770	−	0.739145i
$345$	−57600.0			−0.483932
$346$	−100920.	+	26057.4i	−0.842995	+	0.217660i
$347$	135526.			1.12555			0.562774	−	0.826611i	$-0.309734\pi$
$347$	135526.			1.12555			0.562774	+	0.826611i	$0.309734\pi$
$348$	−15840.0	−	28629.1i	−0.130797	−	0.236401i
$349$		−	160775.i		−	1.31998i	−0.751273	−	0.659992i	$-0.770560\pi$
$349$		−	160775.i		−	1.31998i	0.751273	−	0.659992i	$-0.229440\pi$
$350$	80400.0	−	20759.2i	0.656327	−	0.169463i
$351$			23423.8i			0.190127i
$352$	25376.0	+	8055.81i	0.204804	+	0.0650165i
$353$	123778.			0.993331			0.496666	−	0.867942i	$-0.334558\pi$
$353$	123778.			0.993331			0.496666	+	0.867942i	$0.334558\pi$
$354$	30108.0	+	116608.i	0.240257	+	0.930510i
$355$	17280.0			0.137116
$356$	140644.	−	77816.0i	1.10974	−	0.614001i
$357$		−	84028.2i		−	0.659309i
$358$	9146.00	+	35422.3i	0.0713617	+	0.276383i
$359$			23981.5i			0.186075i	0.995663	+	0.0930374i	$0.0296576\pi$
$359$			23981.5i			0.186075i	−0.995663	+	0.0930374i	$0.970342\pi$
$360$	64800.0	−	61348.1i	0.500000	−	0.473365i
$361$	−112365.			−0.862217
$362$	−222120.	+	57351.1i	−1.69500	+	0.437648i
$363$	−83790.0			−0.635886
$364$	26880.0	−	14872.3i	0.202874	−	0.112247i
$365$			11959.8i			0.0897712i
$366$	48240.0	−	12455.5i	0.360118	−	0.0929821i
$367$			13509.0i			0.100297i	0.998742	+	0.0501487i	$0.0159695\pi$
$367$			13509.0i			0.100297i	−0.998742	+	0.0501487i	$0.984030\pi$
$368$	67200.0	+	42138.1i	0.496219	+	0.311157i
$369$	−44730.0			−0.328508
$370$	54720.0	+	211930.i	0.399708	+	1.54806i
$371$	−236160.			−1.71577
$372$	57600.0	+	104106.i	0.416233	+	0.752296i
$373$			120620.i			0.866967i	0.901162	+	0.433483i	$0.142716\pi$
$373$			120620.i			0.866967i	−0.901162	+	0.433483i	$0.857284\pi$
$374$	5876.00	+	22757.7i	0.0420086	+	0.162699i
$375$			53911.9i			0.383374i
$376$	−97920.0	+	92703.7i	−0.692621	+	0.655725i
$377$	10560.0			0.0742987
$378$	181440.	−	46847.6i	1.26984	−	0.327872i
$379$	−116506.			−0.811092			−0.405546	−	0.914075i	$-0.632919\pi$
$379$	−116506.			−0.811092			−0.405546	+	0.914075i	$0.632919\pi$
$380$	−32160.0	−	58125.7i	−0.222715	−	0.402533i
$381$		−	17846.7i		−	0.122944i
$382$	−36480.0	+	9419.10i	−0.249993	+	0.0645480i
$383$		−	173510.i		−	1.18284i	−0.806364	−	0.591420i	$-0.798568\pi$
$383$		−	173510.i		−	1.18284i	0.806364	−	0.591420i	$-0.201432\pi$
$384$	96384.0	−	19333.9i	0.653646	−	0.131117i
$385$	−49920.0			−0.336785
$386$	−45986.0	−	178103.i	−0.308639	−	1.19535i
$387$	84690.0			0.565471
$388$	−122332.	+	67684.3i	−0.812600	+	0.449598i
$389$		−	158606.i		−	1.04815i	−0.851674	−	0.524073i	$-0.824412\pi$
$389$		−	158606.i		−	1.04815i	0.851674	−	0.524073i	$-0.175588\pi$
$390$	−5760.00	−	22308.4i	−0.0378698	−	0.146669i
$391$			70023.5i			0.458026i
$392$	−63316.0	−	66878.7i	−0.412042	−	0.435227i
$393$	−84828.0			−0.549230
$394$	147960.	−	38203.1i	0.953129	−	0.246097i
$395$	341760.			2.19042
$396$	−16380.0	+	9062.78i	−0.104454	+	0.0577925i
$397$			138777.i			0.880513i	0.897872	+	0.440256i	$0.145112\pi$
$397$			138777.i			0.880513i	−0.897872	+	0.440256i	$0.854888\pi$
$398$	−105840.	+	27327.8i	−0.668165	+	0.172519i
$399$		−	49822.1i		−	0.312951i
$400$	−45560.0	+	72657.2i	−0.284750	+	0.454107i
$401$	58594.0			0.364388			0.182194	−	0.983263i	$-0.441680\pi$
$401$	58594.0			0.364388			0.182194	+	0.983263i	$0.441680\pi$
$402$	−48036.0	−	186043.i	−0.297245	−	1.15123i
$403$	−38400.0			−0.236440
$404$	82320.0	+	148785.i	0.504362	+	0.911581i
$405$		−	27606.6i		−	0.168307i
$406$	−21120.0	−	81797.4i	−0.128127	−	0.496235i
$407$		−	45918.1i		−	0.277201i
$408$	59664.0	+	63021.2i	0.358420	+	0.378587i
$409$	142754.			0.853378			0.426689	−	0.904398i	$-0.359680\pi$
$409$	142754.			0.853378			0.426689	+	0.904398i	$0.359680\pi$
$410$	119280.	−	30798.0i	0.709578	−	0.183212i
$411$	139596.			0.826398
$412$	−78240.0	−	141410.i	−0.460929	−	0.833080i
$413$			310954.i			1.82304i
$414$	−54000.0	+	13942.7i	−0.315060	+	0.0813481i
$415$		−	69218.0i		−	0.401904i
$416$	−9600.00	+	30240.3i	−0.0554734	+	0.174743i
$417$	101604.			0.584304
$418$	3484.00	+	13493.5i	0.0199400	+	0.0772274i
$419$	−283706.			−1.61600			−0.807998	−	0.589185i	$-0.799449\pi$
$419$	−283706.			−1.61600			−0.807998	+	0.589185i	$0.799449\pi$
$420$	−161280.	+	89233.5i	−0.914286	+	0.505859i
$421$			110829.i			0.625303i	0.949868	+	0.312651i	$0.101217\pi$
$421$			110829.i			0.625303i	−0.949868	+	0.312651i	$0.898783\pi$
$422$	−49094.0	−	190140.i	−0.275679	−	1.06770i
$423$		−	94810.6i		−	0.529879i
$424$	177120.	−	167685.i	0.985226	−	0.932742i
$425$	−75710.0			−0.419156
$426$	−12960.0	+	3346.26i	−0.0714144	+	0.0184391i
$427$	128640.			0.705538
$428$	−96404.0	+	53338.7i	−0.526269	+	0.291176i
$429$			4833.48i			0.0262631i
$430$	−225840.	+	58311.6i	−1.22142	+	0.315369i
$431$		−	165454.i		−	0.890681i	−0.895361	−	0.445341i	$-0.853083\pi$
$431$		−	165454.i		−	0.890681i	0.895361	−	0.445341i	$-0.146917\pi$
$432$	−102816.	+	163967.i	−0.550926	+	0.878593i
$433$	−110494.			−0.589336			−0.294668	−	0.955600i	$-0.595209\pi$
$433$	−110494.			−0.589336			−0.294668	+	0.955600i	$0.595209\pi$
$434$	76800.0	+	297445.i	0.407739	+	1.57916i
$435$	−63360.0			−0.334839
$436$	−9360.00	−	16917.2i	−0.0492383	−	0.0889929i
$437$			41518.4i			0.217409i
$438$	−2316.00	−	8969.83i	−0.0120723	−	0.0467559i
$439$			224137.i			1.16301i	0.813541	+	0.581507i	$0.197537\pi$
$439$			224137.i			1.16301i	−0.813541	+	0.581507i	$0.802463\pi$
$440$	37440.0	−	35445.5i	0.193388	−	0.183086i
$441$	64755.0			0.332963
$442$	−27120.0	+	7002.35i	−0.138818	+	0.0358426i
$443$	165286.			0.842226			0.421113	−	0.907008i	$-0.361640\pi$
$443$	165286.			0.842226			0.421113	+	0.907008i	$0.361640\pi$
$444$	−82080.0	−	148351.i	−0.416362	−	0.752530i
$445$		−	311264.i		−	1.57184i
$446$	212160.	−	54779.5i	1.06658	−	0.275390i
$447$			198731.i			0.994602i
$448$	253440.	+	13880.8i	1.26276	+	0.0691604i
$449$	−378206.			−1.87601			−0.938006	−	0.346618i	$-0.887330\pi$
$449$	−378206.			−1.87601			−0.938006	+	0.346618i	$0.887330\pi$
$450$	−15075.0	−	58385.2i	−0.0744444	−	0.288322i
$451$	−25844.0			−0.127059
$452$	16996.0	−	9403.60i	0.0831898	−	0.0460275i
$453$			162479.i			0.791775i
$454$	53882.0	+	208684.i	0.261416	+	1.01246i
$455$		−	59489.0i		−	0.287352i
$456$	35376.0	+	37366.5i	0.170129	+	0.179702i
$457$	165986.			0.794766			0.397383	−	0.917653i	$-0.369919\pi$
$457$	165986.			0.794766			0.397383	+	0.917653i	$0.369919\pi$
$458$	189240.	−	48861.6i	0.902157	−	0.232936i
$459$	−170856.			−0.810970
$460$	134400.	−	74361.3i	0.635161	−	0.351424i
$461$		−	361427.i		−	1.70066i	−0.526247	−	0.850332i	$-0.676401\pi$
$461$		−	361427.i		−	1.70066i	0.526247	−	0.850332i	$-0.323599\pi$
$462$	37440.0	−	9666.97i	0.175409	−	0.0452904i
$463$			5824.97i			0.0271726i	0.999908	+	0.0135863i	$0.00432479\pi$
$463$			5824.97i			0.0271726i	−0.999908	+	0.0135863i	$0.995675\pi$
$464$	73920.0	+	46351.9i	0.343341	+	0.215294i
$465$	230400.			1.06556
$466$	−25858.0	−	100148.i	−0.119076	−	0.461178i
$467$	−290042.			−1.32992			−0.664962	−	0.746877i	$-0.731552\pi$
$467$	−290042.			−1.32992			−0.664962	+	0.746877i	$0.731552\pi$
$468$	−10800.0	−	19519.8i	−0.0493097	−	0.0891219i
$469$		−	496114.i		−	2.25546i
$470$	65280.0	+	252828.i	0.295518	+	1.14454i
$471$		−	176422.i		−	0.795264i
$472$	−220792.	−	233216.i	−0.991059	−	1.04682i
$473$	48932.0			0.218711
$474$	−256320.	+	66181.5i	−1.14084	+	0.294564i
$475$	−44890.0			−0.198958
$476$	108480.	+	196066.i	0.478780	+	0.865343i
$477$			171496.i			0.753731i
$478$	−120480.	+	31107.8i	−0.527302	+	0.136149i
$479$			401799.i			1.75121i	0.483030	+	0.875604i	$0.339536\pi$
$479$			401799.i			1.75121i	−0.483030	+	0.875604i	$0.660464\pi$
$480$	57600.0	−	181442.i	0.250000	−	0.787507i
$481$	54720.0			0.236514
$482$	25246.0	+	97777.3i	0.108667	+	0.420866i
$483$	115200.			0.493808
$484$	195510.	−	108172.i	0.834600	−	0.461770i
$485$			270737.i			1.15097i
$486$	−55890.0	−	216461.i	−0.236626	−	0.916447i
$487$			258963.i			1.09189i	0.837820	+	0.545946i	$0.183830\pi$
$487$			258963.i			1.09189i	−0.837820	+	0.545946i	$0.816170\pi$
$488$	−96480.0	+	91340.4i	−0.405133	+	0.383551i
$489$	−222684.			−0.931261
$490$	−172680.	+	44585.8i	−0.719200	+	0.185697i
$491$	210982.			0.875150			0.437575	−	0.899182i	$-0.355837\pi$
$491$	210982.			0.875150			0.437575	+	0.899182i	$0.355837\pi$
$492$	−83496.0	+	46196.9i	−0.344934	+	0.190846i
$493$			77025.9i			0.316915i
$494$	−16080.0	+	4151.84i	−0.0658919	+	0.0170132i
$495$			36251.1i			0.147949i
$496$	−268800.	−	168552.i	−1.09261	−	0.685127i
$497$	−34560.0			−0.139914
$498$	13404.0	+	51913.5i	0.0540475	+	0.209325i
$499$	218822.			0.878800			0.439400	−	0.898292i	$-0.355191\pi$
$499$	218822.			0.878800			0.439400	+	0.898292i	$0.355191\pi$
$500$	−69600.0	−	125794.i	−0.278400	−	0.503178i
$501$			129017.i			0.514009i
$502$	40346.0	+	156259.i	0.160101	+	0.620067i
$503$		−	359351.i		−	1.42031i	−0.704046	−	0.710154i	$-0.748625\pi$
$503$		−	359351.i		−	1.42031i	0.704046	−	0.710154i	$-0.251375\pi$
$504$	−129600.	+	122696.i	−0.510204	+	0.483025i
$505$	329280.			1.29117
$506$	−31200.0	+	8055.81i	−0.121858	+	0.0314636i
$507$	165606.			0.644258
$508$	23040.0	+	41642.3i	0.0892802	+	0.161364i
$509$			30333.2i			0.117080i	0.998285	+	0.0585400i	$0.0186445\pi$
$509$			30333.2i			0.117080i	−0.998285	+	0.0585400i	$0.981355\pi$
$510$	162720.	−	42014.1i	0.625606	−	0.161531i
$511$		−	23919.5i		−	0.0916033i
$512$	−199936.	+	169544.i	−0.762695	+	0.646758i
$513$	−101304.			−0.384939
$514$	−4738.00	−	18350.2i	−0.0179337	−	0.0694567i
$515$	−312960.			−1.17998
$516$	158088.	−	87467.5i	0.593744	−	0.328509i
$517$		−	54779.5i		−	0.204945i
$518$	−109440.	−	423859.i	−0.407865	−	1.57965i
$519$		−	156345.i		−	0.580428i
$520$	42240.0	+	44616.8i	0.156213	+	0.165003i
$521$	−133406.			−0.491473			−0.245737	−	0.969337i	$-0.579030\pi$
$521$	−133406.			−0.491473			−0.245737	+	0.969337i	$0.579030\pi$
$522$	−59400.0	+	15337.0i	−0.217994	+	0.0562859i
$523$	−165274.			−0.604228			−0.302114	−	0.953272i	$-0.597692\pi$
$523$	−165274.			−0.604228			−0.302114	+	0.953272i	$0.597692\pi$
$524$	197932.	−	109512.i	0.720864	−	0.398842i
$525$			124555.i			0.451901i
$526$	445200.	−	114950.i	1.60910	−	0.415468i
$527$		−	280094.i		−	1.00852i
$528$	−21216.0	+	33834.4i	−0.0761019	+	0.121364i
$529$	183841.			0.656948
$530$	−118080.	−	457322.i	−0.420363	−	1.62806i
$531$	225810.			0.800855
$532$	64320.0	+	116251.i	0.227260	+	0.410748i
$533$		−	30798.0i		−	0.108410i
$534$	60276.0	+	233448.i	0.211379	+	0.818667i
$535$			213355.i			0.745410i
$536$	352264.	+	372085.i	1.22614	+	1.29513i
$537$	−54876.0			−0.190298
$538$	−3960.00	+	1022.47i	−0.0136814	+	0.00353252i
$539$	37414.0			0.128782
$540$	181440.	+	327933.i	0.622222	+	1.12460i
$541$			207561.i			0.709171i	0.935024	+	0.354586i	$0.115378\pi$
$541$			207561.i			0.709171i	−0.935024	+	0.354586i	$0.884622\pi$
$542$	−125280.	+	32347.2i	−0.426465	+	0.110113i
$543$		−	344107.i		−	1.16706i
$544$	−220576.	−	70023.5i	−0.745350	−	0.236617i
$545$	−37440.0			−0.126050
$546$	11520.0	+	44616.8i	0.0386427	+	0.149662i
$547$	−59194.0			−0.197835			−0.0989175	−	0.995096i	$-0.531538\pi$
$547$	−59194.0			−0.197835			−0.0989175	+	0.995096i	$0.531538\pi$
$548$	−325724.	+	180218.i	−1.08465	+	0.600117i
$549$		−	93416.4i		−	0.309940i
$550$	−8710.00	−	33733.7i	−0.0287934	−	0.111516i
$551$			45670.2i			0.150428i
$552$	−86400.0	+	81797.4i	−0.283554	+	0.268449i
$553$	−683520.			−2.23512
$554$	105240.	−	27172.9i	0.342895	−	0.0885351i
$555$	−328320.			−1.06589
$556$	−237076.	+	131170.i	−0.766899	+	0.424312i
$557$			80031.3i			0.257958i	0.991647	+	0.128979i	$0.0411700\pi$
$557$			80031.3i			0.257958i	−0.991647	+	0.128979i	$0.958830\pi$
$558$	216000.	−	55771.0i	0.693722	−	0.179118i
$559$			58311.6i			0.186609i
$560$	261120.	−	416423.i	0.832653	−	1.32788i
$561$	−35256.0			−0.112023
$562$	51518.0	+	199528.i	0.163112	+	0.631731i
$563$	212998.			0.671984			0.335992	−	0.941865i	$-0.390929\pi$
$563$	212998.			0.671984			0.335992	+	0.941865i	$0.390929\pi$
$564$	−97920.0	−	176980.i	−0.307832	−	0.556372i
$565$		−	37614.4i		−	0.117830i
$566$	54874.0	+	212526.i	0.171291	+	0.663406i
$567$			55213.3i			0.171742i
$568$	25920.0	−	24539.2i	0.0803412	−	0.0760614i
$569$	485794.			1.50047			0.750236	−	0.661171i	$-0.229940\pi$
$569$	485794.			1.50047			0.750236	+	0.661171i	$0.229940\pi$
$570$	96480.0	−	24911.0i	0.296953	−	0.0766729i
$571$	−295258.			−0.905585			−0.452793	−	0.891616i	$-0.649572\pi$
$571$	−295258.			−0.905585			−0.452793	+	0.891616i	$0.649572\pi$
$572$	−6240.00	−	11278.1i	−0.0190718	−	0.0344703i
$573$		−	56514.6i		−	0.172128i
$574$	−238560.	+	61595.9i	−0.724059	+	0.186951i
$575$		−	103796.i		−	0.313939i
$576$	10080.0	−	184044.i	0.0303819	−	0.554724i
$577$	−68734.0			−0.206452			−0.103226	−	0.994658i	$-0.532917\pi$
$577$	−68734.0			−0.206452			−0.103226	+	0.994658i	$0.532917\pi$
$578$	32445.0	+	125659.i	0.0971163	+	0.376130i
$579$	275916.			0.823038
$580$	147840.	−	81797.4i	0.439477	−	0.243155i
$581$			138436.i			0.410106i
$582$	−52428.0	−	203053.i	−0.154781	−	0.599464i
$583$			99086.4i			0.291526i
$584$	16984.0	+	17939.7i	0.0497983	+	0.0526003i
$585$	−43200.0			−0.126233
$586$	−250440.	+	64663.3i	−0.729304	+	0.188305i
$587$	133606.			0.387748			0.193874	−	0.981026i	$-0.437895\pi$
$587$	133606.			0.387748			0.193874	+	0.981026i	$0.437895\pi$
$588$	120876.	−	66878.7i	0.349611	−	0.193434i
$589$		−	166074.i		−	0.478707i
$590$	−602160.	+	155477.i	−1.72985	+	0.446645i
$591$			229219.i			0.656259i
$592$	383040.	+	240187.i	1.09295	+	0.685340i
$593$	670786.			1.90754			0.953772	−	0.300531i	$-0.0971638\pi$
$593$	670786.			1.90754			0.953772	+	0.300531i	$0.0971638\pi$
$594$	−19656.0	−	76127.4i	−0.0557086	−	0.215758i
$595$	433920.			1.22568
$596$	−256560.	−	463705.i	−0.722265	−	1.30542i
$597$		−	163967.i		−	0.460052i
$598$	−9600.00	−	37180.6i	−0.0268453	−	0.103972i
$599$			483658.i			1.34798i	0.738738	+	0.673992i	$0.235422\pi$
$599$			483658.i			1.34798i	−0.738738	+	0.673992i	$0.764578\pi$
$600$	−88440.0	−	93416.4i	−0.245667	−	0.259490i
$601$	226754.			0.627778			0.313889	−	0.949460i	$-0.398368\pi$
$601$	226754.			0.627778			0.313889	+	0.949460i	$0.398368\pi$
$602$	451680.	−	116623.i	1.24634	−	0.321805i
$603$	−360270.			−0.990817
$604$	−209760.	−	379119.i	−0.574975	−	1.03920i
$605$		−	432690.i		−	1.18213i
$606$	−246960.	+	63764.8i	−0.672483	+	0.173634i
$607$		−	136577.i		−	0.370681i	−0.982674	−	0.185340i	$-0.940661\pi$
$607$		−	136577.i		−	0.370681i	0.982674	−	0.185340i	$-0.0593387\pi$
$608$	−130784.	−	41518.4i	−0.353792	−	0.112314i
$609$	126720.			0.341673
$610$	64320.0	+	249110.i	0.172857	+	0.669471i
$611$	65280.0			0.174863
$612$	142380.	−	78776.5i	0.380142	−	0.210326i
$613$		−	23516.8i		−	0.0625830i	−0.999510	−	0.0312915i	$-0.990038\pi$
$613$		−	23516.8i		−	0.0625830i	0.999510	−	0.0312915i	$-0.00996202\pi$
$614$	−24326.0	−	94214.2i	−0.0645259	−	0.249908i
$615$			184788.i			0.488566i
$616$	−74880.0	+	70891.1i	−0.197335	+	0.186823i
$617$	−542462.			−1.42495			−0.712474	−	0.701699i	$-0.752425\pi$
$617$	−542462.			−1.42495			−0.712474	+	0.701699i	$0.752425\pi$
$618$	234720.	−	60604.4i	0.614573	−	0.158682i
$619$	−440218.			−1.14891			−0.574456	−	0.818536i	$-0.694786\pi$
$619$	−440218.			−1.14891			−0.574456	+	0.818536i	$0.694786\pi$
$620$	−537600.	+	297445.i	−1.39854	+	0.773791i
$621$		−	234238.i		−	0.607399i
$622$	27120.0	−	7002.35i	0.0700985	−	0.0180994i
$623$			622528.i			1.60392i
$624$	−40320.0	−	25282.8i	−0.103550	−	0.0649317i
$625$	−487775.			−1.24870
$626$	83422.0	+	323092.i	0.212879	+	0.824475i
$627$	−20904.0			−0.0531734
$628$	227760.	+	411652.i	0.577508	+	1.04378i
$629$			399134.i			1.00883i
$630$	86400.0	+	334626.i	0.217687	+	0.843098i
$631$		−	475354.i		−	1.19388i	−0.802288	−	0.596938i	$-0.796384\pi$
$631$		−	475354.i		−	1.19388i	0.802288	−	0.596938i	$-0.203616\pi$
$632$	512640.	−	485331.i	1.28345	−	1.21508i
$633$	294564.			0.735144
$634$	27240.0	−	7033.34i	0.0677686	−	0.0174978i
$635$	92160.0			0.228557
$636$	177120.	+	320125.i	0.437878	+	0.791418i
$637$			44585.8i			0.109880i
$638$	−34320.0	+	8861.39i	−0.0843152	+	0.0217701i
$639$			25096.9i			0.0614637i
$640$	99840.0	+	497725.i	0.243750	+	1.21515i
$641$	−373598.			−0.909261			−0.454630	−	0.890680i	$-0.650229\pi$
$641$	−373598.			−0.909261			−0.454630	+	0.890680i	$0.650229\pi$
$642$	−41316.0	−	160016.i	−0.100242	−	0.388234i
$643$	130118.			0.314714			0.157357	−	0.987542i	$-0.449703\pi$
$643$	130118.			0.314714			0.157357	+	0.987542i	$0.449703\pi$
$644$	−268800.	+	148723.i	−0.648123	+	0.358596i
$645$		−	349870.i		−	0.840983i
$646$	−30284.0	−	117289.i	−0.0725685	−	0.281057i
$647$		−	653450.i		−	1.56100i	−0.625154	−	0.780501i	$-0.714964\pi$
$647$		−	653450.i		−	1.56100i	0.625154	−	0.780501i	$-0.285036\pi$
$648$	−39204.0	−	41409.9i	−0.0933642	−	0.0986176i
$649$	130468.			0.309752
$650$	40200.0	−	10379.6i	0.0951479	−	0.0245671i
$651$	−460800.			−1.08730
$652$	519596.	−	287484.i	1.22228	−	0.676267i
$653$			241891.i			0.567275i	0.958932	+	0.283637i	$0.0915412\pi$
$653$			241891.i			0.567275i	−0.958932	+	0.283637i	$0.908459\pi$
$654$	28080.0	−	7250.22i	0.0656510	−	0.0169510i
$655$		−	438050.i		−	1.02104i
$656$	135184.	−	215586.i	0.314136	−	0.500971i
$657$	−17370.0			−0.0402410
$658$	−130560.	−	505657.i	−0.301549	−	1.16790i
$659$	232774.			0.535999			0.267999	−	0.963419i	$-0.413638\pi$
$659$	232774.			0.535999			0.267999	+	0.963419i	$0.413638\pi$
$660$	37440.0	+	67668.8i	0.0859504	+	0.155346i
$661$			594302.i			1.36020i	0.733118	+	0.680102i	$0.238064\pi$
$661$			594302.i			1.36020i	−0.733118	+	0.680102i	$0.761936\pi$
$662$	−12134.0	−	46994.8i	−0.0276878	−	0.107234i
$663$		−	42014.1i		−	0.0955803i
$664$	−98296.0	−	103827.i	−0.222946	−	0.235491i
$665$	257280.			0.581785
$666$	−307800.	+	79473.6i	−0.693937	+	0.179174i
$667$	−105600.			−0.237363
$668$	−166560.	−	301039.i	−0.373265	−	0.674637i
$669$			328677.i			0.734373i
$670$	960720.	−	248057.i	2.14016	−	0.552588i
$671$		−	53973.9i		−	0.119878i
$672$	−115200.	+	362883.i	−0.255102	+	0.803578i
$673$	108578.			0.239724			0.119862	−	0.992791i	$-0.461755\pi$
$673$	108578.			0.239724			0.119862	+	0.992791i	$0.461755\pi$
$674$	−41666.0	−	161372.i	−0.0917196	−	0.355228i
$675$	253260.			0.555852
$676$	−386414.	+	213796.i	−0.845589	+	0.467850i
$677$		−	550490.i		−	1.20108i	−0.799594	−	0.600541i	$-0.794952\pi$
$677$		−	550490.i		−	1.20108i	0.799594	−	0.600541i	$-0.205048\pi$
$678$	7284.00	+	28210.8i	0.0158457	+	0.0613700i
$679$		−	541474.i		−	1.17446i
$680$	−325440.	+	308104.i	−0.703806	+	0.666314i
$681$	−323292.			−0.697109
$682$	124800.	−	32223.2i	0.268316	−	0.0692788i
$683$	378406.			0.811179			0.405589	−	0.914055i	$-0.367066\pi$
$683$	378406.			0.811179			0.405589	+	0.914055i	$0.367066\pi$
$684$	84420.0	−	46708.2i	0.180440	−	0.0998345i
$685$			720871.i			1.53630i
$686$	−230880.	+	59613.0i	−0.490612	+	0.126675i
$687$			293169.i			0.621162i
$688$	−255952.	+	408181.i	−0.540731	+	0.862336i
$689$	−118080.			−0.248736
$690$	57600.0	+	223084.i	0.120983	+	0.468565i
$691$	396614.			0.830638			0.415319	−	0.909676i	$-0.363670\pi$
$691$	396614.			0.830638			0.415319	+	0.909676i	$0.363670\pi$
$692$	201840.	+	364804.i	0.421498	+	0.761811i
$693$		−	72502.2i		−	0.150968i
$694$	−135526.	−	524890.i	−0.281387	−	1.08981i
$695$			524681.i			1.08624i
$696$	−95040.0	+	89977.1i	−0.196195	+	0.185744i
$697$	224644.			0.462412
$698$	−622680.	+	160775.i	−1.27807	+	0.329996i
$699$	155148.			0.317535
$700$	−160800.	−	290629.i	−0.328163	−	0.593120i
$701$			32811.9i			0.0667722i	0.999443	+	0.0333861i	$0.0106291\pi$
$701$			32811.9i			0.0667722i	−0.999443	+	0.0333861i	$0.989371\pi$
$702$	90720.0	−	23423.8i	0.184089	−	0.0475317i
$703$			236655.i			0.478856i
$704$	5824.00	−	106337.i	0.0117510	−	0.214554i
$705$	−391680.			−0.788049
$706$	−123778.	−	479390.i	−0.248333	−	0.961789i
$707$	−658560.			−1.31752
$708$	421512.	−	233216.i	0.840898	−	0.465255i
$709$			78853.9i			0.156867i	0.996919	+	0.0784334i	$0.0249918\pi$
$709$			78853.9i			0.156867i	−0.996919	+	0.0784334i	$0.975008\pi$
$710$	−17280.0	−	66925.2i	−0.0342789	−	0.132762i
$711$			496362.i			0.981881i
$712$	−442024.	−	466896.i	−0.871939	−	0.921001i
$713$	384000.			0.755357
$714$	−325440.	+	84028.2i	−0.638373	+	0.164827i
$715$	−24960.0			−0.0488239
$716$	128044.	−	70844.6i	0.249766	−	0.138191i
$717$		−	186647.i		−	0.363063i
$718$	92880.0	−	23981.5i	0.180166	−	0.0465187i
$719$		−	444309.i		−	0.859463i	−0.902957	−	0.429731i	$-0.858608\pi$
$719$		−	444309.i		−	0.859463i	0.902957	−	0.429731i	$-0.141392\pi$
$720$	−302400.	−	189621.i	−0.583333	−	0.365782i
$721$	625920.			1.20406
$722$	112365.	+	435188.i	0.215554	+	0.834838i
$723$	−151476.			−0.289779
$724$	444240.	+	802916.i	0.847502	+	1.53177i
$725$		−	114176.i		−	0.217219i
$726$	83790.0	+	324517.i	0.158971	+	0.615694i
$727$		−	393805.i		−	0.745096i	−0.928013	−	0.372548i	$-0.878484\pi$
$727$		−	393805.i		−	0.745096i	0.928013	−	0.372548i	$-0.121516\pi$
$728$	−84480.0	−	89233.5i	−0.159401	−	0.168370i
$729$	407511.			0.766804
$730$	46320.0	−	11959.8i	0.0869206	−	0.0224428i
$731$	−425332.			−0.795964
$732$	−96480.0	−	174377.i	−0.180059	−	0.325437i
$733$		−	673372.i		−	1.25328i	−0.779310	−	0.626639i	$-0.784430\pi$
$733$		−	673372.i		−	1.25328i	0.779310	−	0.626639i	$-0.215570\pi$
$734$	52320.0	−	13509.0i	0.0971126	−	0.0250744i
$735$		−	267515.i		−	0.495191i
$736$	96000.0	−	302403.i	0.177221	−	0.558251i
$737$	−208156.			−0.383225
$738$	44730.0	+	173239.i	0.0821270	+	0.318077i
$739$	672902.			1.23215			0.616074	−	0.787688i	$-0.288722\pi$
$739$	672902.			1.23215			0.616074	+	0.787688i	$0.288722\pi$
$740$	766080.	−	423859.i	1.39898	−	0.774031i
$741$		−	24911.0i		−	0.0453686i
$742$	236160.	+	914644.i	0.428942	+	1.66129i
$743$			796347.i			1.44253i	0.692659	+	0.721265i	$0.256439\pi$
$743$			796347.i			1.44253i	−0.692659	+	0.721265i	$0.743561\pi$
$744$	345600.	−	327190.i	0.624350	−	0.591090i
$745$	−1.02624e6			−1.84900
$746$	467160.	−	120620.i	0.839437	−	0.216742i
$747$	100530.			0.180158
$748$	82264.0	−	45515.3i	0.147030	−	0.0813494i
$749$		−	426710.i		−	0.760622i
$750$	208800.	−	53911.9i	0.371200	−	0.0958434i
$751$			143393.i			0.254243i	0.991887	+	0.127122i	$0.0405738\pi$
$751$			143393.i			0.254243i	−0.991887	+	0.127122i	$0.959426\pi$
$752$	456960.	+	286539.i	0.808058	+	0.506696i
$753$	−242076.			−0.426935
$754$	−10560.0	−	40898.7i	−0.0185747	−	0.0719394i
$755$	−839040.			−1.47194
$756$	−362880.	−	655866.i	−0.634921	−	1.14755i
$757$			9574.01i			0.0167071i	0.999965	+	0.00835357i	$0.00265906\pi$
$757$			9574.01i			0.0167071i	−0.999965	+	0.00835357i	$0.997341\pi$
$758$	116506.	+	451226.i	0.202773	+	0.785336i
$759$		−	48334.8i		−	0.0839028i
$760$	−192960.	+	182681.i	−0.334072	+	0.316276i
$761$	−280286.			−0.483985			−0.241993	−	0.970278i	$-0.577801\pi$
$761$	−280286.			−0.483985			−0.241993	+	0.970278i	$0.577801\pi$
$762$	−69120.0	+	17846.7i	−0.119040	+	0.0307361i
$763$	74880.0			0.128622
$764$	72960.0	+	131867.i	0.124997	+	0.225918i
$765$		−	315106.i		−	0.538436i
$766$	−672000.	+	173510.i	−1.14528	+	0.295710i
$767$			155477.i			0.264287i
$768$	−171264.	−	353960.i	−0.290365	−	0.600111i
$769$	−149086.			−0.252107			−0.126053	−	0.992023i	$-0.540231\pi$
$769$	−149086.			−0.252107			−0.126053	+	0.992023i	$0.540231\pi$
$770$	49920.0	+	193339.i	0.0841963	+	0.326091i
$771$	28428.0			0.0478231
$772$	−643804.	+	356206.i	−1.08024	+	0.597677i
$773$		−	213138.i		−	0.356699i	−0.983967	−	0.178350i	$-0.942924\pi$
$773$		−	213138.i		−	0.356699i	0.983967	−	0.178350i	$-0.0570758\pi$
$774$	−84690.0	−	328003.i	−0.141368	−	0.547515i
$775$			415184.i			0.691253i
$776$	384472.	+	406106.i	0.638471	+	0.674397i
$777$	656640.			1.08764
$778$	−614280.	+	158606.i	−1.01486	+	0.262036i
$779$	133196.			0.219491
$780$	−80640.0	+	44616.8i	−0.132544	+	0.0733346i
$781$			14500.4i			0.0237727i
$782$	271200.	−	70023.5i	0.443482	−	0.114507i
$783$		−	257662.i		−	0.420268i
$784$	−195704.	+	312100.i	−0.318396	+	0.507764i
$785$	911040.			1.47842
$786$	84828.0	+	328537.i	0.137307	+	0.531790i
$787$	−916282.			−1.47938			−0.739690	−	0.672948i	$-0.765028\pi$
$787$	−916282.			−1.47938			−0.739690	+	0.672948i	$0.765028\pi$
$788$	−295920.	−	534844.i	−0.476565	−	0.861339i
$789$			689701.i			1.10792i
$790$	−341760.	−	1.32363e6i	−0.547605	−	2.12086i
$791$			75228.8i			0.120235i
$792$	51480.0	+	54376.7i	0.0820707	+	0.0866887i
$793$	64320.0			0.102282
$794$	537480.	−	138777.i	0.852553	−	0.220128i
$795$	708480.			1.12097
$796$	211680.	+	382589.i	0.334082	+	0.603818i
$797$			382062.i			0.601475i	0.953707	+	0.300737i	$0.0972327\pi$
$797$			382062.i			0.601475i	−0.953707	+	0.300737i	$0.902767\pi$
$798$	−192960.	+	49822.1i	−0.303013	+	0.0782377i
$799$			476160.i			0.745864i
$800$	326960.	+	103796.i	0.510875	+	0.162181i
$801$	452070.			0.704597
$802$	−58594.0	−	226934.i	−0.0910971	−	0.352817i
$803$	−10036.0			−0.0155643
$804$	−672504.	+	372085.i	−1.04036	+	0.575613i
$805$			594890.i			0.918005i
$806$	38400.0	+	148723.i	0.0591100	+	0.228932i
$807$		−	6134.81i		−	0.00942006i
$808$	493920.	−	467609.i	0.756543	−	0.716242i
$809$	−877598.			−1.34091			−0.670453	−	0.741952i	$-0.733900\pi$
$809$	−877598.			−1.34091			−0.670453	+	0.741952i	$0.733900\pi$
$810$	−106920.	+	27606.6i	−0.162963	+	0.0420769i
$811$	1.11498e6			1.69522			0.847610	−	0.530619i	$-0.178041\pi$
$811$	1.11498e6			1.69522			0.847610	+	0.530619i	$0.178041\pi$
$812$	−295680.	+	163595.i	−0.448446	+	0.248118i
$813$		−	194083.i		−	0.293634i
$814$	−177840.	+	45918.1i	−0.268399	+	0.0693003i
$815$		−	1.14994e6i		−	1.73124i
$816$	184416.	−	294099.i	0.276961	−	0.441685i
$817$	−252188.			−0.377816
$818$	−142754.	−	552884.i	−0.213345	−	0.826280i
$819$	86400.0			0.128809
$820$	−238560.	−	431171.i	−0.354789	−	0.641243i
$821$		−	1.28481e6i		−	1.90613i	−0.302770	−	0.953064i	$-0.597911\pi$
$821$		−	1.28481e6i		−	1.90613i	0.302770	−	0.953064i	$-0.402089\pi$
$822$	−139596.	−	540653.i	−0.206600	−	0.800157i
$823$		−	687036.i		−	1.01433i	−0.861848	−	0.507166i	$-0.830693\pi$
$823$		−	687036.i		−	1.01433i	0.861848	−	0.507166i	$-0.169307\pi$
$824$	−469440.	+	444433.i	−0.691394	+	0.654563i
$825$	52260.0			0.0767824
$826$	1.20432e6	−	310954.i	1.76515	−	0.455760i
$827$	935206.			1.36740			0.683701	−	0.729762i	$-0.260369\pi$
$827$	935206.			1.36740			0.683701	+	0.729762i	$0.260369\pi$
$828$	108000.	+	195198.i	0.157530	+	0.284718i
$829$			1.17203e6i			1.70541i	0.522394	+	0.852704i	$0.325039\pi$
$829$			1.17203e6i			1.70541i	−0.522394	+	0.852704i	$0.674961\pi$
$830$	−268080.	+	69218.0i	−0.389142	+	0.100476i
$831$			163037.i			0.236094i
$832$	126720.	+	6940.39i	0.183062	+	0.0100262i
$833$	−325214.			−0.468683
$834$	−101604.	−	393511.i	−0.146076	−	0.565750i
$835$	−666240.			−0.955560
$836$	48776.0	−	26986.9i	0.0697901	−	0.0386137i
$837$			936952.i			1.33742i
$838$	283706.	+	1.09879e6i	0.403999	+	1.56468i
$839$		−	1.26966e6i		−	1.80369i	−0.432057	−	0.901846i	$-0.642212\pi$
$839$		−	1.26966e6i		−	1.80369i	0.432057	−	0.901846i	$-0.357788\pi$
$840$	506880.	+	535401.i	0.718367	+	0.758789i
$841$	591121.			0.835765
$842$	429240.	−	110829.i	0.605447	−	0.156326i
$843$	−309108.			−0.434966
$844$	−687316.	+	380280.i	−0.964876	+	0.533850i
$845$			855186.i			1.19770i
$846$	−367200.	+	94810.6i	−0.513053	+	0.132470i
$847$			865379.i			1.20626i
$848$	−826560.	−	518298.i	−1.14943	−	0.720755i
$849$	−329244.			−0.456775
$850$	75710.0	+	293224.i	0.104789	+	0.405846i
$851$	−547200.			−0.755591
$852$	25920.0	+	46847.6i	0.0357072	+	0.0645369i
$853$		−	363967.i		−	0.500224i	−0.968217	−	0.250112i	$-0.919533\pi$
$853$		−	363967.i		−	0.500224i	0.968217	−	0.250112i	$-0.0804674\pi$
$854$	−128640.	−	498221.i	−0.176384	−	0.683134i
$855$		−	186833.i		−	0.255576i
$856$	302984.	+	320032.i	0.413497	+	0.436764i
$857$	−857054.			−1.16693			−0.583467	−	0.812137i	$-0.698304\pi$
$857$	−857054.			−1.16693			−0.583467	+	0.812137i	$0.698304\pi$
$858$	18720.0	−	4833.48i	0.0254291	−	0.00656577i
$859$	−867226.			−1.17529			−0.587646	−	0.809118i	$-0.699945\pi$
$859$	−867226.			−1.17529			−0.587646	+	0.809118i	$0.699945\pi$
$860$	451680.	+	816363.i	0.610708	+	1.10379i
$861$		−	369576.i		−	0.498536i
$862$	−640800.	+	165454.i	−0.862398	+	0.222670i
$863$			644712.i			0.865654i	0.901477	+	0.432827i	$0.142484\pi$
$863$			644712.i			0.865654i	−0.901477	+	0.432827i	$0.857516\pi$
$864$	737856.	+	234238.i	0.988426	+	0.313783i
$865$	807360.			1.07903
$866$	110494.	+	427941.i	0.147334	+	0.570622i
$867$	−194670.			−0.258977
$868$	1.07520e6	−	594890.i	1.42708	−	0.789582i
$869$			286787.i			0.379769i
$870$	63360.0	+	245392.i	0.0837099	+	0.324207i
$871$		−	248057.i		−	0.326975i
$872$	−56160.0	+	53168.3i	−0.0738574	+	0.0699230i
$873$	−393210.			−0.515936
$874$	160800.	−	41518.4i	0.210505	−	0.0543523i
$875$	556800.			0.727249
$876$	−32424.0	+	17939.7i	−0.0422531	+	0.0233779i
$877$		−	1.49395e6i		−	1.94239i	−0.238284	−	0.971195i	$-0.576585\pi$
$877$		−	1.49395e6i		−	1.94239i	0.238284	−	0.971195i	$-0.423415\pi$
$878$	868080.	−	224137.i	1.12608	−	0.290754i
$879$		−	387980.i		−	0.502148i
$880$	−174720.	−	109559.i	−0.225620	−	0.141476i
$881$	−529598.			−0.682330			−0.341165	−	0.940003i	$-0.610822\pi$
$881$	−529598.			−0.682330			−0.341165	+	0.940003i	$0.610822\pi$
$882$	−64755.0	−	250795.i	−0.0832408	−	0.322390i
$883$	−338554.			−0.434217			−0.217108	−	0.976148i	$-0.569662\pi$
$883$	−338554.			−0.434217			−0.217108	+	0.976148i	$0.569662\pi$
$884$	54240.0	+	98033.0i	0.0694089	+	0.125449i
$885$		−	932862.i		−	1.19105i
$886$	−165286.	−	640150.i	−0.210556	−	0.815482i
$887$			829438.i			1.05423i	0.849793	+	0.527117i	$0.176727\pi$
$887$			829438.i			1.05423i	−0.849793	+	0.527117i	$0.823273\pi$
$888$	−492480.	+	466245.i	−0.624543	+	0.591274i
$889$	−184320.			−0.233222
$890$	−1.20552e6	+	311264.i	−1.52193	+	0.392960i
$891$	23166.0			0.0291807
$892$	−424320.	−	766913.i	−0.533290	−	0.963865i
$893$			282325.i			0.354035i
$894$	769680.	−	198731.i	0.963020	−	0.248651i
$895$		−	283378.i		−	0.353770i
$896$	−199680.	−	995450.i	−0.248724	−	1.23995i
$897$	57600.0			0.0715876
$898$	378206.	+	1.46479e6i	0.469003	+	1.81644i
$899$	422400.			0.522642
$900$	−211050.	+	116770.i	−0.260556	+	0.144161i
$901$		−	861290.i		−	1.06096i
$902$	25844.0	+	100093.i	0.0317648	+	0.123025i
$903$			699740.i			0.858146i
$904$	−53416.0	−	56421.6i	−0.0653634	−	0.0690413i
$905$	1.77696e6			2.16960
$906$	629280.	−	162479.i	0.766633	−	0.197944i
$907$	1.09252e6			1.32805			0.664024	−	0.747711i	$-0.268847\pi$
$907$	1.09252e6			1.32805			0.664024	+	0.747711i	$0.268847\pi$
$908$	754348.	−	417368.i	0.914956	−	0.506230i
$909$			478236.i			0.578781i
$910$	−230400.	+	59489.0i	−0.278227	+	0.0718380i
$911$			1.05729e6i			1.27397i	0.770877	+	0.636984i	$0.219818\pi$
$911$			1.05729e6i			1.27397i	−0.770877	+	0.636984i	$0.780182\pi$
$912$	109344.	−	174377.i	0.131464	−	0.209652i
$913$	58084.0			0.0696811
$914$	−165986.	−	642861.i	−0.198691	−	0.769528i
$915$	−385920.			−0.460951
$916$	−378480.	−	684062.i	−0.451078	−	0.815276i
$917$			876100.i			1.04187i
$918$	170856.	+	661722.i	0.202743	+	0.785218i
$919$			548600.i			0.649569i	0.945788	+	0.324784i	$0.105292\pi$
$919$			548600.i			0.649569i	−0.945788	+	0.324784i	$0.894708\pi$
$920$	−422400.	−	446168.i	−0.499055	−	0.527136i
$921$	145956.			0.172069
$922$	−1.39980e6	+	361427.i	−1.64666	+	0.425166i
$923$	−17280.0			−0.0202834
$924$	−74880.0	−	135338.i	−0.0877045	−	0.158516i
$925$		−	591637.i		−	0.691468i
$926$	22560.0	−	5824.97i	0.0263098	−	0.00679315i
$927$		−	454533.i		−	0.528940i
$928$	105600.	−	332643.i	0.122622	−	0.386262i
$929$	500002.			0.579349			0.289675	−	0.957125i	$-0.406453\pi$
$929$	500002.			0.579349			0.289675	+	0.957125i	$0.406453\pi$
$930$	−230400.	−	892335.i	−0.266389	−	1.03172i
$931$	−192826.			−0.222467
$932$	−362012.	+	200295.i	−0.416765	+	0.230589i
$933$			42014.1i			0.0482650i
$934$	290042.	+	1.12333e6i	0.332481	+	1.28769i
$935$		−	182061.i		−	0.208254i
$936$	−64800.0	+	61348.1i	−0.0739645	+	0.0700244i
$937$	290306.			0.330656			0.165328	−	0.986239i	$-0.447132\pi$
$937$	290306.			0.330656			0.165328	+	0.986239i	$0.447132\pi$
$938$	−1.92144e6	+	496114.i	−2.18384	+	0.563865i
$939$	−500532.			−0.567676
$940$	913920.	−	505657.i	1.03431	−	0.572269i
$941$			40372.0i			0.0455933i	0.999740	+	0.0227966i	$0.00725702\pi$
$941$			40372.0i			0.0455933i	−0.999740	+	0.0227966i	$0.992743\pi$
$942$	−683280.	+	176422.i	−0.770011	+	0.198816i
$943$			307980.i			0.346337i
$944$	−682448.	+	1.08834e6i	−0.765818	+	1.22129i
$945$	−1.45152e6			−1.62540
$946$	−48932.0	−	189513.i	−0.0546778	−	0.211766i
$947$	136198.			0.151870			0.0759348	−	0.997113i	$-0.475806\pi$
$947$	136198.			0.151870			0.0759348	+	0.997113i	$0.475806\pi$
$948$	512640.	+	926542.i	0.570421	+	1.03098i
$949$		−	11959.8i		−	0.0132798i
$950$	44890.0	+	173858.i	0.0497396	+	0.192641i
$951$			42200.0i			0.0466607i
$952$	650880.	−	616207.i	0.718170	−	0.679912i
$953$	−2654.00			−0.00292223			−0.00146112	−	0.999999i	$-0.500465\pi$
$953$	−2654.00			−0.00292223			−0.00146112	+	0.999999i	$0.500465\pi$
$954$	664200.	−	171496.i	0.729797	−	0.188433i
$955$	291840.			0.319991
$956$	240960.	+	435509.i	0.263651	+	0.476520i
$957$		−	53168.3i		−	0.0580536i
$958$	1.55616e6	−	401799.i	1.69560	−	0.437802i
$959$		−	1.44174e6i		−	1.56765i
$960$	−760320.	−	41642.3i	−0.825000	−	0.0451848i
$961$	−612479.			−0.663200
$962$	−54720.0	−	211930.i	−0.0591284	−	0.229003i
$963$	−309870.			−0.334139
$964$	353444.	−	195555.i	0.380335	−	0.210433i
$965$			1.42482e6i			1.53005i
$966$	−115200.	−	446168.i	−0.123452	−	0.478128i
$967$			1.01770e6i			1.08834i	0.838975	+	0.544171i	$0.183156\pi$
$967$			1.01770e6i			1.08834i	−0.838975	+	0.544171i	$0.816844\pi$
$968$	−614460.	−	649035.i	−0.655757	−	0.692655i
$969$	181704.			0.193516
$970$	1.04856e6	−	270737.i	1.11442	−	0.287743i
$971$	−701786.			−0.744331			−0.372166	−	0.928166i	$-0.621385\pi$
$971$	−701786.			−0.744331			−0.372166	+	0.928166i	$0.621385\pi$
$972$	−782460.	+	432922.i	−0.828189	+	0.458223i
$973$		−	1.04936e6i		−	1.10841i
$974$	1.00296e6	−	258963.i	1.05722	−	0.272973i
$975$			62277.6i			0.0655122i
$976$	450240.	+	282325.i	0.472655	+	0.296381i
$977$	975586.			1.02206			0.511030	−	0.859563i	$-0.329264\pi$
$977$	975586.			1.02206			0.511030	+	0.859563i	$0.329264\pi$
$978$	222684.	+	862451.i	0.232815	+	0.901689i
$979$	261196.			0.272522
$980$	345360.	+	624201.i	0.359600	+	0.649939i
$981$		−	54376.7i		−	0.0565034i
$982$	−210982.	−	817130.i	−0.218787	−	0.847360i
$983$		−	582187.i		−	0.602498i	−0.953546	−	0.301249i	$-0.902597\pi$
$983$		−	582187.i		−	0.602498i	0.953546	−	0.301249i	$-0.0974035\pi$
$984$	262416.	+	277182.i	0.271019	+	0.286269i
$985$	−1.18368e6			−1.22001
$986$	298320.	−	77025.9i	0.306852	−	0.0792288i
$987$	783360.			0.804132
$988$	32160.0	+	58125.7i	0.0329460	+	0.0595463i
$989$		−	583116.i		−	0.596160i
$990$	140400.	−	36251.1i	0.143251	−	0.0369872i
$991$		−	988261.i		−	1.00629i	−0.864201	−	0.503147i	$-0.832176\pi$
$991$		−	988261.i		−	1.00629i	0.864201	−	0.503147i	$-0.167824\pi$
$992$	−384000.	+	1.20961e6i	−0.390219	+	1.22920i
$993$	72804.0			0.0738341
$994$	34560.0	+	133850.i	0.0349785	+	0.135471i
$995$	846720.			0.855251
$996$	187656.	−	103827.i	0.189166	−	0.104663i
$997$		−	408212.i		−	0.410673i	−0.978691	−	0.205336i	$-0.934171\pi$
$997$		−	408212.i		−	0.410673i	0.978691	−	0.205336i	$-0.0658288\pi$
$998$	−218822.	−	847494.i	−0.219700	−	0.850894i
$999$		−	1.33516e6i		−	1.33783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.5.d.b.3.1	✓	2
3.2	odd	2		72.5.b.b.19.2		2
4.3	odd	2		32.5.d.b.15.2		2
5.2	odd	4		200.5.e.c.99.3		4
5.3	odd	4		200.5.e.c.99.2		4
5.4	even	2		200.5.g.d.51.2		2
8.3	odd	2	inner	8.5.d.b.3.2	yes	2
8.5	even	2		32.5.d.b.15.1		2
12.11	even	2		288.5.b.b.271.1		2
16.3	odd	4		256.5.c.i.255.2		4
16.5	even	4		256.5.c.i.255.1		4
16.11	odd	4		256.5.c.i.255.3		4
16.13	even	4		256.5.c.i.255.4		4
20.3	even	4		800.5.e.c.399.2		4
20.7	even	4		800.5.e.c.399.3		4
20.19	odd	2		800.5.g.d.751.1		2
24.5	odd	2		288.5.b.b.271.2		2
24.11	even	2		72.5.b.b.19.1		2
40.3	even	4		200.5.e.c.99.4		4
40.13	odd	4		800.5.e.c.399.1		4
40.19	odd	2		200.5.g.d.51.1		2
40.27	even	4		200.5.e.c.99.1		4
40.29	even	2		800.5.g.d.751.2		2
40.37	odd	4		800.5.e.c.399.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.5.d.b.3.1	✓	2	1.1	even	1	trivial
8.5.d.b.3.2	yes	2	8.3	odd	2	inner
32.5.d.b.15.1		2	8.5	even	2
32.5.d.b.15.2		2	4.3	odd	2
72.5.b.b.19.1		2	24.11	even	2
72.5.b.b.19.2		2	3.2	odd	2
200.5.e.c.99.1		4	40.27	even	4
200.5.e.c.99.2		4	5.3	odd	4
200.5.e.c.99.3		4	5.2	odd	4
200.5.e.c.99.4		4	40.3	even	4
200.5.g.d.51.1		2	40.19	odd	2
200.5.g.d.51.2		2	5.4	even	2
256.5.c.i.255.1		4	16.5	even	4
256.5.c.i.255.2		4	16.3	odd	4
256.5.c.i.255.3		4	16.11	odd	4
256.5.c.i.255.4		4	16.13	even	4
288.5.b.b.271.1		2	12.11	even	2
288.5.b.b.271.2		2	24.5	odd	2
800.5.e.c.399.1		4	40.13	odd	4
800.5.e.c.399.2		4	20.3	even	4
800.5.e.c.399.3		4	20.7	even	4
800.5.e.c.399.4		4	40.37	odd	4
800.5.g.d.751.1		2	20.19	odd	2
800.5.g.d.751.2		2	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 3.87298i) q^{2} +6.00000 q^{3} +(-14.0000 + 7.74597i) q^{4} +30.9839i q^{5} +(-6.00000 - 23.2379i) q^{6} -61.9677i q^{7} +(44.0000 + 46.4758i) q^{8} -45.0000 q^{9} +O(q^{10})\)	\(q+(-1.00000 - 3.87298i) q^{2} +6.00000 q^{3} +(-14.0000 + 7.74597i) q^{4} +30.9839i q^{5} +(-6.00000 - 23.2379i) q^{6} -61.9677i q^{7} +(44.0000 + 46.4758i) q^{8} -45.0000 q^{9} +(120.000 - 30.9839i) q^{10} -26.0000 q^{11} +(-84.0000 + 46.4758i) q^{12} -30.9839i q^{13} +(-240.000 + 61.9677i) q^{14} +185.903i q^{15} +(136.000 - 216.887i) q^{16} +226.000 q^{17} +(45.0000 + 174.284i) q^{18} +134.000 q^{19} +(-240.000 - 433.774i) q^{20} -371.806i q^{21} +(26.0000 + 100.698i) q^{22} +309.839i q^{23} +(264.000 + 278.855i) q^{24} -335.000 q^{25} +(-120.000 + 30.9839i) q^{26} -756.000 q^{27} +(480.000 + 867.548i) q^{28} +340.823i q^{29} +(720.000 - 185.903i) q^{30} -1239.35i q^{31} +(-976.000 - 309.839i) q^{32} -156.000 q^{33} +(-226.000 - 875.294i) q^{34} +1920.00 q^{35} +(630.000 - 348.569i) q^{36} +1766.08i q^{37} +(-134.000 - 518.980i) q^{38} -185.903i q^{39} +(-1440.00 + 1363.29i) q^{40} +994.000 q^{41} +(-1440.00 + 371.806i) q^{42} -1882.00 q^{43} +(364.000 - 201.395i) q^{44} -1394.27i q^{45} +(1200.00 - 309.839i) q^{46} +2106.90i q^{47} +(816.000 - 1301.32i) q^{48} -1439.00 q^{49} +(335.000 + 1297.45i) q^{50} +1356.00 q^{51} +(240.000 + 433.774i) q^{52} -3811.02i q^{53} +(756.000 + 2927.98i) q^{54} -805.581i q^{55} +(2880.00 - 2726.58i) q^{56} +804.000 q^{57} +(1320.00 - 340.823i) q^{58} -5018.00 q^{59} +(-1440.00 - 2602.64i) q^{60} +2075.92i q^{61} +(-4800.00 + 1239.35i) q^{62} +2788.55i q^{63} +(-224.000 + 4089.87i) q^{64} +960.000 q^{65} +(156.000 + 604.185i) q^{66} +8006.00 q^{67} +(-3164.00 + 1750.59i) q^{68} +1859.03i q^{69} +(-1920.00 - 7436.13i) q^{70} -557.710i q^{71} +(-1980.00 - 2091.41i) q^{72} +386.000 q^{73} +(6840.00 - 1766.08i) q^{74} -2010.00 q^{75} +(-1876.00 + 1037.96i) q^{76} +1611.16i q^{77} +(-720.000 + 185.903i) q^{78} -11030.3i q^{79} +(6720.00 + 4213.81i) q^{80} -891.000 q^{81} +(-994.000 - 3849.75i) q^{82} -2234.00 q^{83} +(2880.00 + 5205.29i) q^{84} +7002.35i q^{85} +(1882.00 + 7288.95i) q^{86} +2044.94i q^{87} +(-1144.00 - 1208.37i) q^{88} -10046.0 q^{89} +(-5400.00 + 1394.27i) q^{90} -1920.00 q^{91} +(-2400.00 - 4337.74i) q^{92} -7436.13i q^{93} +(8160.00 - 2106.90i) q^{94} +4151.84i q^{95} +(-5856.00 - 1859.03i) q^{96} +8738.00 q^{97} +(1439.00 + 5573.22i) q^{98} +1170.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 12 q^{3} - 28 q^{4} - 12 q^{6} + 88 q^{8} - 90 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 12 * q^3 - 28 * q^4 - 12 * q^6 + 88 * q^8 - 90 * q^9	\( 2 q - 2 q^{2} + 12 q^{3} - 28 q^{4} - 12 q^{6} + 88 q^{8} - 90 q^{9} + 240 q^{10} - 52 q^{11} - 168 q^{12} - 480 q^{14} + 272 q^{16} + 452 q^{17} + 90 q^{18} + 268 q^{19} - 480 q^{20} + 52 q^{22} + 528 q^{24} - 670 q^{25} - 240 q^{26} - 1512 q^{27} + 960 q^{28} + 1440 q^{30} - 1952 q^{32} - 312 q^{33} - 452 q^{34} + 3840 q^{35} + 1260 q^{36} - 268 q^{38} - 2880 q^{40} + 1988 q^{41} - 2880 q^{42} - 3764 q^{43} + 728 q^{44} + 2400 q^{46} + 1632 q^{48} - 2878 q^{49} + 670 q^{50} + 2712 q^{51} + 480 q^{52} + 1512 q^{54} + 5760 q^{56} + 1608 q^{57} + 2640 q^{58} - 10036 q^{59} - 2880 q^{60} - 9600 q^{62} - 448 q^{64} + 1920 q^{65} + 312 q^{66} + 16012 q^{67} - 6328 q^{68} - 3840 q^{70} - 3960 q^{72} + 772 q^{73} + 13680 q^{74} - 4020 q^{75} - 3752 q^{76} - 1440 q^{78} + 13440 q^{80} - 1782 q^{81} - 1988 q^{82} - 4468 q^{83} + 5760 q^{84} + 3764 q^{86} - 2288 q^{88} - 20092 q^{89} - 10800 q^{90} - 3840 q^{91} - 4800 q^{92} + 16320 q^{94} - 11712 q^{96} + 17476 q^{97} + 2878 q^{98} + 2340 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 12 * q^3 - 28 * q^4 - 12 * q^6 + 88 * q^8 - 90 * q^9 + 240 * q^10 - 52 * q^11 - 168 * q^12 - 480 * q^14 + 272 * q^16 + 452 * q^17 + 90 * q^18 + 268 * q^19 - 480 * q^20 + 52 * q^22 + 528 * q^24 - 670 * q^25 - 240 * q^26 - 1512 * q^27 + 960 * q^28 + 1440 * q^30 - 1952 * q^32 - 312 * q^33 - 452 * q^34 + 3840 * q^35 + 1260 * q^36 - 268 * q^38 - 2880 * q^40 + 1988 * q^41 - 2880 * q^42 - 3764 * q^43 + 728 * q^44 + 2400 * q^46 + 1632 * q^48 - 2878 * q^49 + 670 * q^50 + 2712 * q^51 + 480 * q^52 + 1512 * q^54 + 5760 * q^56 + 1608 * q^57 + 2640 * q^58 - 10036 * q^59 - 2880 * q^60 - 9600 * q^62 - 448 * q^64 + 1920 * q^65 + 312 * q^66 + 16012 * q^67 - 6328 * q^68 - 3840 * q^70 - 3960 * q^72 + 772 * q^73 + 13680 * q^74 - 4020 * q^75 - 3752 * q^76 - 1440 * q^78 + 13440 * q^80 - 1782 * q^81 - 1988 * q^82 - 4468 * q^83 + 5760 * q^84 + 3764 * q^86 - 2288 * q^88 - 20092 * q^89 - 10800 * q^90 - 3840 * q^91 - 4800 * q^92 + 16320 * q^94 - 11712 * q^96 + 17476 * q^97 + 2878 * q^98 + 2340 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more