LMFDB - Embedded newform 162.6.c.e.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,6,Mod(55,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("162.55");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not 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:	$25.9821788097$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.109
Dual form			162.6.c.e.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(33.0000 - 57.1577i) q^{5} +(-88.0000 - 152.420i) q^{7} +64.0000 q^{8} +O(q^{10})$	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(33.0000 - 57.1577i) q^{5} +(-88.0000 - 152.420i) q^{7} +64.0000 q^{8} -264.000 q^{10} +(30.0000 + 51.9615i) q^{11} +(329.000 - 569.845i) q^{13} +(-352.000 + 609.682i) q^{14} +(-128.000 - 221.703i) q^{16} -414.000 q^{17} +956.000 q^{19} +(528.000 + 914.523i) q^{20} +(120.000 - 207.846i) q^{22} +(-300.000 + 519.615i) q^{23} +(-615.500 - 1066.08i) q^{25} -2632.00 q^{26} +2816.00 q^{28} +(-2787.00 - 4827.23i) q^{29} +(1796.00 - 3110.76i) q^{31} +(-512.000 + 886.810i) q^{32} +(828.000 + 1434.14i) q^{34} -11616.0 q^{35} -8458.00 q^{37} +(-1912.00 - 3311.68i) q^{38} +(2112.00 - 3658.09i) q^{40} +(-9597.00 + 16622.5i) q^{41} +(-6658.00 - 11532.0i) q^{43} -960.000 q^{44} +2400.00 q^{46} +(9840.00 + 17043.4i) q^{47} +(-7084.50 + 12270.7i) q^{49} +(-2462.00 + 4264.31i) q^{50} +(5264.00 + 9117.52i) q^{52} -31266.0 q^{53} +3960.00 q^{55} +(-5632.00 - 9754.91i) q^{56} +(-11148.0 + 19308.9i) q^{58} +(-13170.0 + 22811.1i) q^{59} +(15545.0 + 26924.7i) q^{61} -14368.0 q^{62} +4096.00 q^{64} +(-21714.0 - 37609.8i) q^{65} +(8402.00 - 14552.7i) q^{67} +(3312.00 - 5736.55i) q^{68} +(23232.0 + 40239.0i) q^{70} +6120.00 q^{71} -25558.0 q^{73} +(16916.0 + 29299.4i) q^{74} +(-7648.00 + 13246.7i) q^{76} +(5280.00 - 9145.23i) q^{77} +(-37204.0 - 64439.2i) q^{79} -16896.0 q^{80} +76776.0 q^{82} +(3234.00 + 5601.45i) q^{83} +(-13662.0 + 23663.3i) q^{85} +(-26632.0 + 46128.0i) q^{86} +(1920.00 + 3325.54i) q^{88} -32742.0 q^{89} -115808. q^{91} +(-4800.00 - 8313.84i) q^{92} +(39360.0 - 68173.5i) q^{94} +(31548.0 - 54642.7i) q^{95} +(-83041.0 - 143831. i) q^{97} +56676.0 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 16 q^{4} + 66 q^{5} - 176 q^{7} + 128 q^{8}+O(q^{10}) $ 2 * q - 4 * q^2 - 16 * q^4 + 66 * q^5 - 176 * q^7 + 128 * q^8	$ 2 q - 4 q^{2} - 16 q^{4} + 66 q^{5} - 176 q^{7} + 128 q^{8} - 528 q^{10} + 60 q^{11} + 658 q^{13} - 704 q^{14} - 256 q^{16} - 828 q^{17} + 1912 q^{19} + 1056 q^{20} + 240 q^{22} - 600 q^{23} - 1231 q^{25} - 5264 q^{26} + 5632 q^{28} - 5574 q^{29} + 3592 q^{31} - 1024 q^{32} + 1656 q^{34} - 23232 q^{35} - 16916 q^{37} - 3824 q^{38} + 4224 q^{40} - 19194 q^{41} - 13316 q^{43} - 1920 q^{44} + 4800 q^{46} + 19680 q^{47} - 14169 q^{49} - 4924 q^{50} + 10528 q^{52} - 62532 q^{53} + 7920 q^{55} - 11264 q^{56} - 22296 q^{58} - 26340 q^{59} + 31090 q^{61} - 28736 q^{62} + 8192 q^{64} - 43428 q^{65} + 16804 q^{67} + 6624 q^{68} + 46464 q^{70} + 12240 q^{71} - 51116 q^{73} + 33832 q^{74} - 15296 q^{76} + 10560 q^{77} - 74408 q^{79} - 33792 q^{80} + 153552 q^{82} + 6468 q^{83} - 27324 q^{85} - 53264 q^{86} + 3840 q^{88} - 65484 q^{89} - 231616 q^{91} - 9600 q^{92} + 78720 q^{94} + 63096 q^{95} - 166082 q^{97} + 113352 q^{98}+O(q^{100}) $ 2 * q - 4 * q^2 - 16 * q^4 + 66 * q^5 - 176 * q^7 + 128 * q^8 - 528 * q^10 + 60 * q^11 + 658 * q^13 - 704 * q^14 - 256 * q^16 - 828 * q^17 + 1912 * q^19 + 1056 * q^20 + 240 * q^22 - 600 * q^23 - 1231 * q^25 - 5264 * q^26 + 5632 * q^28 - 5574 * q^29 + 3592 * q^31 - 1024 * q^32 + 1656 * q^34 - 23232 * q^35 - 16916 * q^37 - 3824 * q^38 + 4224 * q^40 - 19194 * q^41 - 13316 * q^43 - 1920 * q^44 + 4800 * q^46 + 19680 * q^47 - 14169 * q^49 - 4924 * q^50 + 10528 * q^52 - 62532 * q^53 + 7920 * q^55 - 11264 * q^56 - 22296 * q^58 - 26340 * q^59 + 31090 * q^61 - 28736 * q^62 + 8192 * q^64 - 43428 * q^65 + 16804 * q^67 + 6624 * q^68 + 46464 * q^70 + 12240 * q^71 - 51116 * q^73 + 33832 * q^74 - 15296 * q^76 + 10560 * q^77 - 74408 * q^79 - 33792 * q^80 + 153552 * q^82 + 6468 * q^83 - 27324 * q^85 - 53264 * q^86 + 3840 * q^88 - 65484 * q^89 - 231616 * q^91 - 9600 * q^92 + 78720 * q^94 + 63096 * q^95 - 166082 * q^97 + 113352 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	33.0000	−	57.1577i	0.590322	−	1.02247i	−0.403867	−	0.914818i	$-0.632334\pi$
$5$	33.0000	−	57.1577i	0.590322	−	1.02247i	0.994189	−	0.107650i	$-0.0343325\pi$
$6$		0			0
$7$	−88.0000	−	152.420i	−0.678793	−	1.17570i	−0.975345	−	0.220688i	$-0.929170\pi$
$7$	−88.0000	−	152.420i	−0.678793	−	1.17570i	0.296551	−	0.955017i	$-0.404163\pi$
$8$	64.0000			0.353553
$9$		0			0
$10$	−264.000			−0.834841
$11$	30.0000	+	51.9615i	0.0747549	+	0.129479i	0.900980	−	0.433861i	$-0.142849\pi$
$11$	30.0000	+	51.9615i	0.0747549	+	0.129479i	−0.826225	+	0.563341i	$0.809516\pi$
$12$		0			0
$13$	329.000	−	569.845i	0.539930	−	0.935186i	−0.458977	−	0.888448i	$-0.651784\pi$
$13$	329.000	−	569.845i	0.539930	−	0.935186i	0.998907	−	0.0467382i	$-0.0148827\pi$
$14$	−352.000	+	609.682i	−0.479979	+	0.831349i
$15$		0			0
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−414.000			−0.347439			−0.173719	−	0.984795i	$-0.555579\pi$
$17$	−414.000			−0.347439			−0.173719	+	0.984795i	$0.555579\pi$
$18$		0			0
$19$	956.000			0.607539			0.303769	−	0.952746i	$-0.401755\pi$
$19$	956.000			0.607539			0.303769	+	0.952746i	$0.401755\pi$
$20$	528.000	+	914.523i	0.295161	+	0.511234i
$21$		0			0
$22$	120.000	−	207.846i	0.0528597	−	0.0915557i
$23$	−300.000	+	519.615i	−0.118250	+	0.204815i	−0.919074	−	0.394084i	$-0.871062\pi$
$23$	−300.000	+	519.615i	−0.118250	+	0.204815i	0.800824	+	0.598900i	$0.204395\pi$
$24$		0			0
$25$	−615.500	−	1066.08i	−0.196960	−	0.341145i
$26$	−2632.00			−0.763576
$27$		0			0
$28$	2816.00			0.678793
$29$	−2787.00	−	4827.23i	−0.615378	−	1.06587i	−0.990318	−	0.138817i	$-0.955670\pi$
$29$	−2787.00	−	4827.23i	−0.615378	−	1.06587i	0.374940	−	0.927049i	$-0.377663\pi$
$30$		0			0
$31$	1796.00	−	3110.76i	0.335662	−	0.581384i	−0.647950	−	0.761683i	$-0.724373\pi$
$31$	1796.00	−	3110.76i	0.335662	−	0.581384i	0.983612	+	0.180299i	$0.0577067\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$		0			0
$34$	828.000	+	1434.14i	0.122838	+	0.212762i
$35$	−11616.0			−1.60283
$36$		0			0
$37$	−8458.00			−1.01570			−0.507848	−	0.861447i	$-0.669559\pi$
$37$	−8458.00			−1.01570			−0.507848	+	0.861447i	$0.669559\pi$
$38$	−1912.00	−	3311.68i	−0.214797	−	0.372040i
$39$		0			0
$40$	2112.00	−	3658.09i	0.208710	−	0.361497i
$41$	−9597.00	+	16622.5i	−0.891612	+	1.54432i	−0.0536693	+	0.998559i	$0.517092\pi$
$41$	−9597.00	+	16622.5i	−0.891612	+	1.54432i	−0.837943	+	0.545758i	$0.816242\pi$
$42$		0			0
$43$	−6658.00	−	11532.0i	−0.549127	−	0.951116i	−0.998335	−	0.0576883i	$-0.981627\pi$
$43$	−6658.00	−	11532.0i	−0.549127	−	0.951116i	0.449208	−	0.893427i	$-0.351706\pi$
$44$	−960.000			−0.0747549
$45$		0			0
$46$	2400.00			0.167231
$47$	9840.00	+	17043.4i	0.649756	+	1.12541i	0.983181	+	0.182634i	$0.0584624\pi$
$47$	9840.00	+	17043.4i	0.649756	+	1.12541i	−0.333425	+	0.942777i	$0.608204\pi$
$48$		0			0
$49$	−7084.50	+	12270.7i	−0.421521	+	0.730095i
$50$	−2462.00	+	4264.31i	−0.139272	+	0.241226i
$51$		0			0
$52$	5264.00	+	9117.52i	0.269965	+	0.467593i
$53$	−31266.0			−1.52891			−0.764456	−	0.644676i	$-0.776992\pi$
$53$	−31266.0			−1.52891			−0.764456	+	0.644676i	$0.776992\pi$
$54$		0			0
$55$	3960.00			0.176518
$56$	−5632.00	−	9754.91i	−0.239990	−	0.415674i
$57$		0			0
$58$	−11148.0	+	19308.9i	−0.435138	+	0.753681i
$59$	−13170.0	+	22811.1i	−0.492556	+	0.853132i	−0.999963	−	0.00857419i	$-0.997271\pi$
$59$	−13170.0	+	22811.1i	−0.492556	+	0.853132i	0.507407	+	0.861706i	$0.330604\pi$
$60$		0			0
$61$	15545.0	+	26924.7i	0.534892	+	0.926460i	0.999169	+	0.0407699i	$0.0129811\pi$
$61$	15545.0	+	26924.7i	0.534892	+	0.926460i	−0.464277	+	0.885690i	$0.653686\pi$
$62$	−14368.0			−0.474698
$63$		0			0
$64$	4096.00			0.125000
$65$	−21714.0	−	37609.8i	−0.637465	−	1.10412i
$66$		0			0
$67$	8402.00	−	14552.7i	0.228663	−	0.396056i	−0.728749	−	0.684781i	$-0.759898\pi$
$67$	8402.00	−	14552.7i	0.228663	−	0.396056i	0.957412	+	0.288725i	$0.0932313\pi$
$68$	3312.00	−	5736.55i	0.0868596	−	0.150445i
$69$		0			0
$70$	23232.0	+	40239.0i	0.566685	+	0.981527i
$71$	6120.00			0.144081			0.0720403	−	0.997402i	$-0.477049\pi$
$71$	6120.00			0.144081			0.0720403	+	0.997402i	$0.477049\pi$
$72$		0			0
$73$	−25558.0			−0.561332			−0.280666	−	0.959806i	$-0.590555\pi$
$73$	−25558.0			−0.561332			−0.280666	+	0.959806i	$0.590555\pi$
$74$	16916.0	+	29299.4i	0.359102	+	0.621984i
$75$		0			0
$76$	−7648.00	+	13246.7i	−0.151885	+	0.263072i
$77$	5280.00	−	9145.23i	0.101486	−	0.175779i
$78$		0			0
$79$	−37204.0	−	64439.2i	−0.670690	−	1.16167i	−0.977709	−	0.209966i	$-0.932665\pi$
$79$	−37204.0	−	64439.2i	−0.670690	−	1.16167i	0.307019	−	0.951704i	$-0.400669\pi$
$80$	−16896.0			−0.295161
$81$		0			0
$82$	76776.0			1.26093
$83$	3234.00	+	5601.45i	0.0515282	+	0.0892494i	0.890639	−	0.454711i	$-0.150257\pi$
$83$	3234.00	+	5601.45i	0.0515282	+	0.0892494i	−0.839111	+	0.543960i	$0.816924\pi$
$84$		0			0
$85$	−13662.0	+	23663.3i	−0.205101	+	0.355245i
$86$	−26632.0	+	46128.0i	−0.388291	+	0.672540i
$87$		0			0
$88$	1920.00	+	3325.54i	0.0264298	+	0.0457778i
$89$	−32742.0			−0.438157			−0.219079	−	0.975707i	$-0.570305\pi$
$89$	−32742.0			−0.438157			−0.219079	+	0.975707i	$0.570305\pi$
$90$		0			0
$91$	−115808.			−1.46600
$92$	−4800.00	−	8313.84i	−0.0591251	−	0.102408i
$93$		0			0
$94$	39360.0	−	68173.5i	0.459447	−	0.795786i
$95$	31548.0	−	54642.7i	0.358643	−	0.621189i
$96$		0			0
$97$	−83041.0	−	143831.i	−0.896114	−	1.55211i	−0.832420	−	0.554145i	$-0.813045\pi$
$97$	−83041.0	−	143831.i	−0.896114	−	1.55211i	−0.0636941	−	0.997969i	$-0.520288\pi$
$98$	56676.0			0.596120
$99$		0			0
$100$	19696.0			0.196960
$101$	11001.0	+	19054.3i	0.107307	+	0.185861i	0.914678	−	0.404182i	$-0.132444\pi$
$101$	11001.0	+	19054.3i	0.107307	+	0.185861i	−0.807371	+	0.590044i	$0.799111\pi$
$102$		0			0
$103$	39632.0	−	68644.6i	0.368089	−	0.637549i	−0.621178	−	0.783670i	$-0.713345\pi$
$103$	39632.0	−	68644.6i	0.368089	−	0.637549i	0.989267	+	0.146121i	$0.0466788\pi$
$104$	21056.0	−	36470.1i	0.190894	−	0.330638i
$105$		0			0
$106$	62532.0	+	108309.i	0.540552	+	0.936264i
$107$	227988.			1.92510			0.962548	−	0.271110i	$-0.0873908\pi$
$107$	227988.			1.92510			0.962548	+	0.271110i	$0.0873908\pi$
$108$		0			0
$109$	−8530.00			−0.0687674			−0.0343837	−	0.999409i	$-0.510947\pi$
$109$	−8530.00			−0.0687674			−0.0343837	+	0.999409i	$0.510947\pi$
$110$	−7920.00	−	13717.8i	−0.0624085	−	0.108095i
$111$		0			0
$112$	−22528.0	+	39019.6i	−0.169698	+	0.293926i
$113$	97719.0	−	169254.i	0.719918	−	1.24693i	−0.241114	−	0.970497i	$-0.577513\pi$
$113$	97719.0	−	169254.i	0.719918	−	1.24693i	0.961032	−	0.276437i	$-0.0891539\pi$
$114$		0			0
$115$	19800.0	+	34294.6i	0.139611	+	0.241814i
$116$	89184.0			0.615378
$117$		0			0
$118$	105360.			0.696580
$119$	36432.0	+	63102.1i	0.235839	+	0.408485i
$120$		0			0
$121$	78725.5	−	136357.i	0.488823	−	0.846667i
$122$	62180.0	−	107699.i	0.378226	−	0.655106i
$123$		0			0
$124$	28736.0	+	49772.2i	0.167831	+	0.290692i
$125$	125004.			0.715565
$126$		0			0
$127$	173000.			0.951780			0.475890	−	0.879505i	$-0.342126\pi$
$127$	173000.			0.951780			0.475890	+	0.879505i	$0.342126\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−86856.0	+	150439.i	−0.450756	+	0.780732i
$131$	−75630.0	+	130995.i	−0.385049	+	0.666924i	−0.991776	−	0.127986i	$-0.959149\pi$
$131$	−75630.0	+	130995.i	−0.385049	+	0.666924i	0.606727	+	0.794910i	$0.292482\pi$
$132$		0			0
$133$	−84128.0	−	145714.i	−0.412393	−	0.714286i
$134$	−67216.0			−0.323378
$135$		0			0
$136$	−26496.0			−0.122838
$137$	64227.0	+	111244.i	0.292359	+	0.506380i	0.974367	−	0.224964i	$-0.0722265\pi$
$137$	64227.0	+	111244.i	0.292359	+	0.506380i	−0.682008	+	0.731345i	$0.738893\pi$
$138$		0			0
$139$	−77098.0	+	133538.i	−0.338459	+	0.586228i	−0.984143	−	0.177376i	$-0.943239\pi$
$139$	−77098.0	+	133538.i	−0.338459	+	0.586228i	0.645684	+	0.763605i	$0.276572\pi$
$140$	92928.0	−	160956.i	0.400707	−	0.694044i
$141$		0			0
$142$	−12240.0	−	21200.3i	−0.0509402	−	0.0882310i
$143$	39480.0			0.161450
$144$		0			0
$145$	−367884.			−1.45308
$146$	51116.0	+	88535.5i	0.198461	+	0.343744i
$147$		0			0
$148$	67664.0	−	117197.i	0.253924	−	0.439809i
$149$	−14727.0	+	25507.9i	−0.0543436	+	0.0941259i	−0.891917	−	0.452198i	$-0.850640\pi$
$149$	−14727.0	+	25507.9i	−0.0543436	+	0.0941259i	0.837574	+	0.546324i	$0.183973\pi$
$150$		0			0
$151$	101936.	+	176558.i	0.363819	+	0.630153i	0.988586	−	0.150658i	$-0.0481394\pi$
$151$	101936.	+	176558.i	0.363819	+	0.630153i	−0.624767	+	0.780811i	$0.714806\pi$
$152$	61184.0			0.214797
$153$		0			0
$154$	−42240.0			−0.143523
$155$	−118536.	−	205310.i	−0.396297	−	0.686407i
$156$		0			0
$157$	−68071.0	+	117902.i	−0.220401	+	0.381745i	−0.954930	−	0.296832i	$-0.904070\pi$
$157$	−68071.0	+	117902.i	−0.220401	+	0.381745i	0.734529	+	0.678577i	$0.237403\pi$
$158$	−148816.	+	257757.i	−0.474250	+	0.821424i
$159$		0			0
$160$	33792.0	+	58529.5i	0.104355	+	0.180748i
$161$	105600.			0.321070
$162$		0			0
$163$	−171124.			−0.504478			−0.252239	−	0.967665i	$-0.581167\pi$
$163$	−171124.			−0.504478			−0.252239	+	0.967665i	$0.581167\pi$
$164$	−153552.	−	265960.i	−0.445806	−	0.772159i
$165$		0			0
$166$	12936.0	−	22405.8i	0.0364359	−	0.0631089i
$167$	338100.	−	585606.i	0.938110	−	1.62486i	0.169119	−	0.985596i	$-0.445908\pi$
$167$	338100.	−	585606.i	0.938110	−	1.62486i	0.768991	−	0.639259i	$-0.220759\pi$
$168$		0			0
$169$	−30835.5	−	53408.7i	−0.0830490	−	0.143845i
$170$	109296.			0.290056
$171$		0			0
$172$	213056.			0.549127
$173$	−66579.0	−	115318.i	−0.169131	−	0.292943i	0.768984	−	0.639268i	$-0.220763\pi$
$173$	−66579.0	−	115318.i	−0.169131	−	0.292943i	−0.938114	+	0.346325i	$0.887429\pi$
$174$		0			0
$175$	−108328.	+	187630.i	−0.267390	+	0.463134i
$176$	7680.00	−	13302.2i	0.0186887	−	0.0323698i
$177$		0			0
$178$	65484.0	+	113422.i	0.154912	+	0.268316i
$179$	−693396.			−1.61752			−0.808758	−	0.588141i	$-0.799860\pi$
$179$	−693396.			−1.61752			−0.808758	+	0.588141i	$0.799860\pi$
$180$		0			0
$181$	377174.			0.855747			0.427873	−	0.903839i	$-0.359263\pi$
$181$	377174.			0.855747			0.427873	+	0.903839i	$0.359263\pi$
$182$	231616.	+	401171.i	0.518311	+	0.897740i
$183$		0			0
$184$	−19200.0	+	33255.4i	−0.0418077	+	0.0724131i
$185$	−279114.	+	483440.i	−0.599587	+	1.03852i
$186$		0			0
$187$	−12420.0	−	21512.1i	−0.0259727	−	0.0449861i
$188$	−314880.			−0.649756
$189$		0			0
$190$	−252384.			−0.507198
$191$	132672.	+	229795.i	0.263145	+	0.455781i	0.967076	−	0.254487i	$-0.0819068\pi$
$191$	132672.	+	229795.i	0.263145	+	0.455781i	−0.703931	+	0.710269i	$0.748573\pi$
$192$		0			0
$193$	−147649.	+	255736.i	−0.285323	+	0.494194i	−0.972688	−	0.232118i	$-0.925434\pi$
$193$	−147649.	+	255736.i	−0.285323	+	0.494194i	0.687364	+	0.726313i	$0.258768\pi$
$194$	−332164.	+	575325.i	−0.633648	+	1.09751i
$195$		0			0
$196$	−113352.	−	196331.i	−0.210760	−	0.365048i
$197$	201294.			0.369543			0.184772	−	0.982781i	$-0.440845\pi$
$197$	201294.			0.369543			0.184772	+	0.982781i	$0.440845\pi$
$198$		0			0
$199$	652448.			1.16792			0.583960	−	0.811782i	$-0.301502\pi$
$199$	652448.			1.16792			0.583960	+	0.811782i	$0.301502\pi$
$200$	−39392.0	−	68228.9i	−0.0696359	−	0.120613i
$201$		0			0
$202$	44004.0	−	76217.2i	0.0758776	−	0.131424i
$203$	−490512.	+	849592.i	−0.835429	+	1.44701i
$204$		0			0
$205$	633402.	+	1.09708e6i	1.05268	+	1.82329i
$206$	−317056.			−0.520557
$207$		0			0
$208$	−168448.			−0.269965
$209$	28680.0	+	49675.2i	0.0454165	+	0.0786636i
$210$		0			0
$211$	573530.	−	993383.i	0.886850	−	1.53607i	0.0432708	−	0.999063i	$-0.486222\pi$
$211$	573530.	−	993383.i	0.886850	−	1.53607i	0.843579	−	0.537005i	$-0.180444\pi$
$212$	250128.	−	433234.i	0.382228	−	0.662039i
$213$		0			0
$214$	−455976.	−	789774.i	−0.680624	−	1.17888i
$215$	−878856.			−1.29665
$216$		0			0
$217$	−632192.			−0.911380
$218$	17060.0	+	29548.8i	0.0243130	+	0.0421113i
$219$		0			0
$220$	−31680.0	+	54871.4i	−0.0441294	+	0.0764344i
$221$	−136206.	+	235916.i	−0.187593	+	0.324920i
$222$		0			0
$223$	−350980.	−	607915.i	−0.472629	−	0.818617i	0.526881	−	0.849939i	$-0.323362\pi$
$223$	−350980.	−	607915.i	−0.472629	−	0.818617i	−0.999509	+	0.0313222i	$0.990028\pi$
$224$	180224.			0.239990
$225$		0			0
$226$	−781752.			−1.01812
$227$	−618054.	−	1.07050e6i	−0.796089	−	1.37887i	−0.922145	−	0.386844i	$-0.873565\pi$
$227$	−618054.	−	1.07050e6i	−0.796089	−	1.37887i	0.126056	−	0.992023i	$-0.459768\pi$
$228$		0			0
$229$	−52915.0	+	91651.5i	−0.0666792	+	0.115492i	−0.897438	−	0.441141i	$-0.854574\pi$
$229$	−52915.0	+	91651.5i	−0.0666792	+	0.115492i	0.830758	+	0.556633i	$0.187907\pi$
$230$	79200.0	−	137178.i	0.0987201	−	0.170988i
$231$		0			0
$232$	−178368.	−	308942.i	−0.217569	−	0.376841i
$233$	−438678.			−0.529366			−0.264683	−	0.964335i	$-0.585267\pi$
$233$	−438678.			−0.529366			−0.264683	+	0.964335i	$0.585267\pi$
$234$		0			0
$235$	1.29888e6			1.53426
$236$	−210720.	−	364978.i	−0.246278	−	0.426566i
$237$		0			0
$238$	145728.	−	252408.i	0.166763	−	0.288843i
$239$	−14232.0	+	24650.5i	−0.0161165	+	0.0279146i	−0.873971	−	0.485978i	$-0.838464\pi$
$239$	−14232.0	+	24650.5i	−0.0161165	+	0.0279146i	0.857855	+	0.513892i	$0.171797\pi$
$240$		0			0
$241$	−446281.	−	772981.i	−0.494955	−	0.857287i	0.505028	−	0.863103i	$-0.331482\pi$
$241$	−446281.	−	772981.i	−0.494955	−	0.857287i	−0.999983	+	0.00581560i	$0.998149\pi$
$242$	−629804.			−0.691301
$243$		0			0
$244$	−497440.			−0.534892
$245$	467577.	+	809867.i	0.497666	+	0.861983i
$246$		0			0
$247$	314524.	−	544772.i	0.328028	−	0.568162i
$248$	114944.	−	199089.i	0.118674	−	0.205550i
$249$		0			0
$250$	−250008.	−	433027.i	−0.252990	−	0.438192i
$251$	−110124.			−0.110331			−0.0551655	−	0.998477i	$-0.517569\pi$
$251$	−110124.			−0.110331			−0.0551655	+	0.998477i	$0.517569\pi$
$252$		0			0
$253$	−36000.0			−0.0353591
$254$	−346000.	−	599290.i	−0.336505	−	0.582844i
$255$		0			0
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−70401.0	+	121938.i	−0.0664884	+	0.115161i	−0.897353	−	0.441313i	$-0.854513\pi$
$257$	−70401.0	+	121938.i	−0.0664884	+	0.115161i	0.830865	+	0.556474i	$0.187846\pi$
$258$		0			0
$259$	744304.	+	1.28917e6i	0.689447	+	1.19416i
$260$	694848.			0.637465
$261$		0			0
$262$	605040.			0.544541
$263$	469380.	+	812990.i	0.418442	+	0.724763i	0.995783	−	0.0917404i	$-0.0292430\pi$
$263$	469380.	+	812990.i	0.418442	+	0.724763i	−0.577341	+	0.816503i	$0.695910\pi$
$264$		0			0
$265$	−1.03178e6	+	1.78709e6i	−0.902551	+	1.56326i
$266$	−336512.	+	582856.i	−0.291606	+	0.505076i
$267$		0			0
$268$	134432.	+	232843.i	0.114331	+	0.198028i
$269$	−1.11451e6			−0.939078			−0.469539	−	0.882912i	$-0.655580\pi$
$269$	−1.11451e6			−0.939078			−0.469539	+	0.882912i	$0.655580\pi$
$270$		0			0
$271$	567704.			0.469568			0.234784	−	0.972048i	$-0.424562\pi$
$271$	567704.			0.469568			0.234784	+	0.972048i	$0.424562\pi$
$272$	52992.0	+	91784.8i	0.0434298	+	0.0752227i
$273$		0			0
$274$	256908.	−	444978.i	0.206729	−	0.358065i
$275$	36930.0	−	63964.6i	0.0294474	−	0.0510045i
$276$		0			0
$277$	606629.	+	1.05071e6i	0.475033	+	0.822781i	0.999591	−	0.0285934i	$-0.00910280\pi$
$277$	606629.	+	1.05071e6i	0.475033	+	0.822781i	−0.524558	+	0.851375i	$0.675769\pi$
$278$	616784.			0.478653
$279$		0			0
$280$	−743424.			−0.566685
$281$	−343869.	−	595599.i	−0.259793	−	0.449974i	0.706393	−	0.707819i	$-0.250321\pi$
$281$	−343869.	−	595599.i	−0.259793	−	0.449974i	−0.966186	+	0.257845i	$0.916988\pi$
$282$		0			0
$283$	415454.	−	719587.i	0.308359	−	0.534094i	−0.669644	−	0.742682i	$-0.733553\pi$
$283$	415454.	−	719587.i	0.308359	−	0.534094i	0.978004	+	0.208588i	$0.0668868\pi$
$284$	−48960.0	+	84801.2i	−0.0360202	+	0.0623887i
$285$		0			0
$286$	−78960.0	−	136763.i	−0.0570811	−	0.0988673i
$287$	3.37814e6			2.42088
$288$		0			0
$289$	−1.24846e6			−0.879286
$290$	735768.	+	1.27439e6i	0.513743	+	0.889829i
$291$		0			0
$292$	204464.	−	354142.i	0.140333	−	0.243064i
$293$	656313.	−	1.13677e6i	0.446624	−	0.773575i	−0.551540	−	0.834149i	$-0.685960\pi$
$293$	656313.	−	1.13677e6i	0.446624	−	0.773575i	0.998164	+	0.0605733i	$0.0192929\pi$
$294$		0			0
$295$	869220.	+	1.50553e6i	0.581533	+	1.00725i
$296$	−541312.			−0.359102
$297$		0			0
$298$	117816.			0.0768535
$299$	197400.	+	341907.i	0.127694	+	0.221172i
$300$		0			0
$301$	−1.17181e6	+	2.02963e6i	−0.745487	+	1.29122i
$302$	407744.	−	706233.i	0.257259	−	0.445585i
$303$		0			0
$304$	−122368.	−	211948.i	−0.0759423	−	0.131536i
$305$	2.05194e6			1.26303
$306$		0			0
$307$	1.69022e6			1.02352			0.511761	−	0.859128i	$-0.328993\pi$
$307$	1.69022e6			1.02352			0.511761	+	0.859128i	$0.328993\pi$
$308$	84480.0	+	146324.i	0.0507431	+	0.0878897i
$309$		0			0
$310$	−474144.	+	821241.i	−0.280224	+	0.485363i
$311$	751020.	−	1.30080e6i	0.440302	−	0.762625i	−0.557410	−	0.830238i	$-0.688205\pi$
$311$	751020.	−	1.30080e6i	0.440302	−	0.762625i	0.997712	+	0.0676123i	$0.0215381\pi$
$312$		0			0
$313$	−405421.	−	702210.i	−0.233908	−	0.405141i	0.725047	−	0.688700i	$-0.241818\pi$
$313$	−405421.	−	702210.i	−0.233908	−	0.405141i	−0.958955	+	0.283559i	$0.908485\pi$
$314$	544568.			0.311694
$315$		0			0
$316$	1.19053e6			0.670690
$317$	−451779.	−	782504.i	−0.252510	−	0.437359i	0.711707	−	0.702477i	$-0.247923\pi$
$317$	−451779.	−	782504.i	−0.252510	−	0.437359i	−0.964216	+	0.265117i	$0.914589\pi$
$318$		0			0
$319$	167220.	−	289634.i	0.0920050	−	0.159357i
$320$	135168.	−	234118.i	0.0737902	−	0.127808i
$321$		0			0
$322$	−211200.	−	365809.i	−0.113515	−	0.196614i
$323$	−395784.			−0.211082
$324$		0			0
$325$	−809998.			−0.425379
$326$	342248.	+	592791.i	0.178360	+	0.308928i
$327$		0			0
$328$	−614208.	+	1.06384e6i	−0.315232	+	0.545999i
$329$	1.73184e6	−	2.99963e6i	0.882100	−	1.52784i
$330$		0			0
$331$	−560986.	−	971656.i	−0.281438	−	0.487464i	0.690301	−	0.723522i	$-0.257478\pi$
$331$	−560986.	−	971656.i	−0.281438	−	0.487464i	−0.971739	+	0.236058i	$0.924145\pi$
$332$	−103488.			−0.0515282
$333$		0			0
$334$	−2.70480e6			−1.32669
$335$	−554532.	−	960478.i	−0.269969	−	0.467601i
$336$		0			0
$337$	1.37609e6	−	2.38345e6i	0.660041	−	1.14323i	−0.320563	−	0.947227i	$-0.603872\pi$
$337$	1.37609e6	−	2.38345e6i	0.660041	−	1.14323i	0.980604	−	0.195998i	$-0.0627946\pi$
$338$	−123342.	+	213635.i	−0.0587245	+	0.101714i
$339$		0			0
$340$	−218592.	−	378612.i	−0.102550	−	0.177622i
$341$	215520.			0.100369
$342$		0			0
$343$	−464288.			−0.213085
$344$	−426112.	−	738048.i	−0.194146	−	0.336270i
$345$		0			0
$346$	−266316.	+	461273.i	−0.119593	+	0.207142i
$347$	−958746.	+	1.66060e6i	−0.427445	+	0.740356i	−0.996645	−	0.0818428i	$-0.973919\pi$
$347$	−958746.	+	1.66060e6i	−0.427445	+	0.740356i	0.569201	+	0.822199i	$0.307253\pi$
$348$		0			0
$349$	−918295.	−	1.59053e6i	−0.403570	−	0.699003i	0.590584	−	0.806976i	$-0.298897\pi$
$349$	−918295.	−	1.59053e6i	−0.403570	−	0.699003i	−0.994154	+	0.107973i	$0.965564\pi$
$350$	866624.			0.378147
$351$		0			0
$352$	−61440.0			−0.0264298
$353$	311007.	+	538680.i	0.132841	+	0.230088i	0.924771	−	0.380525i	$-0.124257\pi$
$353$	311007.	+	538680.i	0.132841	+	0.230088i	−0.791929	+	0.610613i	$0.790923\pi$
$354$		0			0
$355$	201960.	−	349805.i	0.0850539	−	0.147318i
$356$	261936.	−	453686.i	0.109539	−	0.189728i
$357$		0			0
$358$	1.38679e6	+	2.40199e6i	0.571878	+	0.990523i
$359$	3.74062e6			1.53182			0.765909	−	0.642949i	$-0.222289\pi$
$359$	3.74062e6			1.53182			0.765909	+	0.642949i	$0.222289\pi$
$360$		0			0
$361$	−1.56216e6			−0.630897
$362$	−754348.	−	1.30657e6i	−0.302552	−	0.524036i
$363$		0			0
$364$	926464.	−	1.60468e6i	0.366501	−	0.634798i
$365$	−843414.	+	1.46084e6i	−0.331367	+	0.573944i
$366$		0			0
$367$	−8116.00	−	14057.3i	−0.00314541	−	0.00544801i	0.864448	−	0.502722i	$-0.167668\pi$
$367$	−8116.00	−	14057.3i	−0.00314541	−	0.00544801i	−0.867594	+	0.497274i	$0.834335\pi$
$368$	153600.			0.0591251
$369$		0			0
$370$	2.23291e6			0.847944
$371$	2.75141e6	+	4.76558e6i	1.03782	+	1.79755i
$372$		0			0
$373$	−146803.	+	254270.i	−0.0546340	+	0.0946288i	−0.892049	−	0.451939i	$-0.850733\pi$
$373$	−146803.	+	254270.i	−0.0546340	+	0.0946288i	0.837415	+	0.546568i	$0.184066\pi$
$374$	−49680.0	+	86048.3i	−0.0183655	+	0.0318100i
$375$		0			0
$376$	629760.	+	1.09078e6i	0.229724	+	0.397893i
$377$	−3.66769e6			−1.32904
$378$		0			0
$379$	3.18012e6			1.13722			0.568611	−	0.822607i	$-0.307481\pi$
$379$	3.18012e6			1.13722			0.568611	+	0.822607i	$0.307481\pi$
$380$	504768.	+	874284.i	0.179322	+	0.310594i
$381$		0			0
$382$	530688.	−	919179.i	0.186072	−	0.322286i
$383$	1.48992e6	−	2.58062e6i	0.518998	−	0.898932i	−0.480758	−	0.876853i	$-0.659638\pi$
$383$	1.48992e6	−	2.58062e6i	0.518998	−	0.898932i	0.999756	−	0.0220782i	$-0.00702828\pi$
$384$		0			0
$385$	−348480.	−	603585.i	−0.119819	−	0.207533i
$386$	1.18119e6			0.403508
$387$		0			0
$388$	2.65731e6			0.896114
$389$	−1.72989e6	−	2.99625e6i	−0.579620	−	1.00393i	−0.995523	−	0.0945228i	$-0.969867\pi$
$389$	−1.72989e6	−	2.99625e6i	−0.579620	−	1.00393i	0.415902	−	0.909409i	$-0.363466\pi$
$390$		0			0
$391$	124200.	−	215121.i	0.0410847	−	0.0711607i
$392$	−453408.	+	785326.i	−0.149030	+	0.258128i
$393$		0			0
$394$	−402588.	−	697303.i	−0.130653	−	0.226298i
$395$	−4.91093e6			−1.58369
$396$		0			0
$397$	−3.90416e6			−1.24323			−0.621615	−	0.783323i	$-0.713523\pi$
$397$	−3.90416e6			−1.24323			−0.621615	+	0.783323i	$0.713523\pi$
$398$	−1.30490e6	−	2.26015e6i	−0.412922	−	0.715202i
$399$		0			0
$400$	−157568.	+	272916.i	−0.0492400	+	0.0852862i
$401$	−2.72058e6	+	4.71218e6i	−0.844890	+	1.46339i	0.0408270	+	0.999166i	$0.487001\pi$
$401$	−2.72058e6	+	4.71218e6i	−0.844890	+	1.46339i	−0.885717	+	0.464226i	$0.846333\pi$
$402$		0			0
$403$	−1.18177e6	−	2.04688e6i	−0.362468	−	0.627813i
$404$	−352032.			−0.107307
$405$		0			0
$406$	3.92410e6			1.18148
$407$	−253740.	−	439491.i	−0.0759282	−	0.131511i
$408$		0			0
$409$	−984973.	+	1.70602e6i	−0.291150	+	0.504286i	−0.974082	−	0.226196i	$-0.927371\pi$
$409$	−984973.	+	1.70602e6i	−0.291150	+	0.504286i	0.682932	+	0.730482i	$0.260704\pi$
$410$	2.53361e6	−	4.38834e6i	0.744354	−	1.28926i
$411$		0			0
$412$	634112.	+	1.09831e6i	0.184045	+	0.318774i
$413$	4.63584e6			1.33738
$414$		0			0
$415$	426888.			0.121673
$416$	336896.	+	583521.i	0.0954471	+	0.165319i
$417$		0			0
$418$	114720.	−	198701.i	0.0321143	−	0.0556236i
$419$	−69510.0	+	120395.i	−0.0193425	+	0.0335022i	−0.875535	−	0.483155i	$-0.839491\pi$
$419$	−69510.0	+	120395.i	−0.0193425	+	0.0335022i	0.856192	+	0.516658i	$0.172824\pi$
$420$		0			0
$421$	−2.16372e6	−	3.74766e6i	−0.594970	−	1.03052i	−0.993551	−	0.113385i	$-0.963831\pi$
$421$	−2.16372e6	−	3.74766e6i	−0.594970	−	1.03052i	0.398581	−	0.917133i	$-0.369503\pi$
$422$	−4.58824e6			−1.25419
$423$		0			0
$424$	−2.00102e6			−0.540552
$425$	254817.	+	441356.i	0.0684315	+	0.118527i
$426$		0			0
$427$	2.73592e6	−	4.73875e6i	0.726162	−	1.25775i
$428$	−1.82390e6	+	3.15909e6i	−0.481274	+	0.833591i
$429$		0			0
$430$	1.75771e6	+	3.04445e6i	0.458434	+	0.794031i
$431$	−2.79936e6			−0.725881			−0.362941	−	0.931812i	$-0.618227\pi$
$431$	−2.79936e6			−0.725881			−0.362941	+	0.931812i	$0.618227\pi$
$432$		0			0
$433$	−5.90241e6			−1.51290			−0.756449	−	0.654052i	$-0.773068\pi$
$433$	−5.90241e6			−1.51290			−0.756449	+	0.654052i	$0.773068\pi$
$434$	1.26438e6	+	2.18998e6i	0.322222	+	0.558104i
$435$		0			0
$436$	68240.0	−	118195.i	0.0171919	−	0.0297772i
$437$	−286800.	+	496752.i	−0.0718415	+	0.124433i
$438$		0			0
$439$	223256.	+	386691.i	0.0552894	+	0.0957640i	0.892345	−	0.451353i	$-0.149059\pi$
$439$	223256.	+	386691.i	0.0552894	+	0.0957640i	−0.837056	+	0.547117i	$0.815725\pi$
$440$	253440.			0.0624085
$441$		0			0
$442$	1.08965e6			0.265296
$443$	−1.74763e6	−	3.02698e6i	−0.423096	−	0.732824i	0.573144	−	0.819454i	$-0.305723\pi$
$443$	−1.74763e6	−	3.02698e6i	−0.423096	−	0.732824i	−0.996241	+	0.0866303i	$0.972390\pi$
$444$		0			0
$445$	−1.08049e6	+	1.87146e6i	−0.258654	+	0.448002i
$446$	−1.40392e6	+	2.43166e6i	−0.334199	+	0.578850i
$447$		0			0
$448$	−360448.	−	624314.i	−0.0848492	−	0.146963i
$449$	−1.20613e6			−0.282343			−0.141171	−	0.989985i	$-0.545087\pi$
$449$	−1.20613e6			−0.282343			−0.141171	+	0.989985i	$0.545087\pi$
$450$		0			0
$451$	−1.15164e6			−0.266609
$452$	1.56350e6	+	2.70807e6i	0.359959	+	0.623467i
$453$		0			0
$454$	−2.47222e6	+	4.28200e6i	−0.562920	+	0.975006i
$455$	−3.82166e6	+	6.61932e6i	−0.865414	+	1.49894i
$456$		0			0
$457$	−116773.	−	202257.i	−0.0261548	−	0.0453015i	0.852652	−	0.522480i	$-0.174993\pi$
$457$	−116773.	−	202257.i	−0.0261548	−	0.0453015i	−0.878807	+	0.477178i	$0.841660\pi$
$458$	423320.			0.0942986
$459$		0			0
$460$	−633600.			−0.139611
$461$	872445.	+	1.51112e6i	0.191199	+	0.331166i	0.945648	−	0.325192i	$-0.105429\pi$
$461$	872445.	+	1.51112e6i	0.191199	+	0.331166i	−0.754449	+	0.656359i	$0.772096\pi$
$462$		0			0
$463$	1.45893e6	−	2.52694e6i	0.316288	−	0.547827i	−0.663423	−	0.748245i	$-0.730897\pi$
$463$	1.45893e6	−	2.52694e6i	0.316288	−	0.547827i	0.979710	+	0.200418i	$0.0642301\pi$
$464$	−713472.	+	1.23577e6i	−0.153845	+	0.266466i
$465$		0			0
$466$	877356.	+	1.51963e6i	0.187159	+	0.324169i
$467$	−5.31076e6			−1.12684			−0.563422	−	0.826169i	$-0.690516\pi$
$467$	−5.31076e6			−1.12684			−0.563422	+	0.826169i	$0.690516\pi$
$468$		0			0
$469$	−2.95750e6			−0.620859
$470$	−2.59776e6	−	4.49945e6i	−0.542443	−	0.939539i
$471$		0			0
$472$	−842880.	+	1.45991e6i	−0.174145	+	0.301628i
$473$	399480.	−	691920.i	0.0820998	−	0.142201i
$474$		0			0
$475$	−588418.	−	1.01917e6i	−0.119661	−	0.207259i
$476$	−1.16582e6			−0.235839
$477$		0			0
$478$	113856.			0.0227922
$479$	−1.17233e6	−	2.03053e6i	−0.233459	−	0.404363i	0.725365	−	0.688365i	$-0.241671\pi$
$479$	−1.17233e6	−	2.03053e6i	−0.233459	−	0.404363i	−0.958824	+	0.284002i	$0.908338\pi$
$480$		0			0
$481$	−2.78268e6	+	4.81975e6i	−0.548404	+	0.949864i
$482$	−1.78512e6	+	3.09193e6i	−0.349986	+	0.606194i
$483$		0			0
$484$	1.25961e6	+	2.18171e6i	0.244412	+	0.423333i
$485$	−1.09614e7			−2.11598
$486$		0			0
$487$	9.81531e6			1.87535			0.937674	−	0.347517i	$-0.112975\pi$
$487$	9.81531e6			1.87535			0.937674	+	0.347517i	$0.112975\pi$
$488$	994880.	+	1.72318e6i	0.189113	+	0.327553i
$489$		0			0
$490$	1.87031e6	−	3.23947e6i	0.351903	−	0.609514i
$491$	2.97260e6	−	5.14869e6i	0.556458	−	0.963814i	−0.441330	−	0.897345i	$-0.645493\pi$
$491$	2.97260e6	−	5.14869e6i	0.556458	−	0.963814i	0.997788	−	0.0664690i	$-0.0211733\pi$
$492$		0			0
$493$	1.15382e6	+	1.99847e6i	0.213806	+	0.370323i
$494$	−2.51619e6			−0.463902
$495$		0			0
$496$	−919552.			−0.167831
$497$	−538560.	−	932813.i	−0.0978010	−	0.169396i
$498$		0			0
$499$	−3.23916e6	+	5.61039e6i	−0.582346	+	1.00865i	0.412855	+	0.910797i	$0.364532\pi$
$499$	−3.23916e6	+	5.61039e6i	−0.582346	+	1.00865i	−0.995201	+	0.0978554i	$0.968802\pi$
$500$	−1.00003e6	+	1.73211e6i	−0.178891	+	0.309849i
$501$		0			0
$502$	220248.	+	381481.i	0.0390079	+	0.0675637i
$503$	4.71794e6			0.831444			0.415722	−	0.909492i	$-0.363529\pi$
$503$	4.71794e6			0.831444			0.415722	+	0.909492i	$0.363529\pi$
$504$		0			0
$505$	1.45213e6			0.253383
$506$	72000.0	+	124708.i	0.0125013	+	0.0216529i
$507$		0			0
$508$	−1.38400e6	+	2.39716e6i	−0.237945	+	0.412133i
$509$	953853.	−	1.65212e6i	0.163188	−	0.282649i	−0.772823	−	0.634622i	$-0.781156\pi$
$509$	953853.	−	1.65212e6i	0.163188	−	0.282649i	0.936010	+	0.351973i	$0.114489\pi$
$510$		0			0
$511$	2.24910e6	+	3.89556e6i	0.381028	+	0.659960i
$512$	262144.			0.0441942
$513$		0			0
$514$	563208.			0.0940288
$515$	−2.61571e6	−	4.53055e6i	−0.434582	−	0.752718i
$516$		0			0
$517$	−590400.	+	1.02260e6i	−0.0971449	+	0.168260i
$518$	2.97722e6	−	5.15669e6i	0.487513	−	0.844397i
$519$		0			0
$520$	−1.38970e6	−	2.40702e6i	−0.225378	−	0.390366i
$521$	8.01974e6			1.29439			0.647196	−	0.762324i	$-0.275941\pi$
$521$	8.01974e6			1.29439			0.647196	+	0.762324i	$0.275941\pi$
$522$		0			0
$523$	1.91162e6			0.305596			0.152798	−	0.988257i	$-0.451172\pi$
$523$	1.91162e6			0.305596			0.152798	+	0.988257i	$0.451172\pi$
$524$	−1.21008e6	−	2.09592e6i	−0.192524	−	0.333462i
$525$		0			0
$526$	1.87752e6	−	3.25196e6i	0.295883	−	0.512485i
$527$	−743544.	+	1.28786e6i	−0.116622	+	0.201995i
$528$		0			0
$529$	3.03817e6	+	5.26227e6i	0.472034	+	0.817587i
$530$	8.25422e6			1.27640
$531$		0			0
$532$	2.69210e6			0.412393
$533$	6.31483e6	+	1.09376e7i	0.962816	+	1.66765i
$534$		0			0
$535$	7.52360e6	−	1.30313e7i	1.13643	−	1.96835i
$536$	537728.	−	931372.i	0.0808445	−	0.140027i
$537$		0			0
$538$	2.22901e6	+	3.86076e6i	0.332014	+	0.575066i
$539$	−850140.			−0.126043
$540$		0			0
$541$	−1.19900e7			−1.76128			−0.880639	−	0.473788i	$-0.842886\pi$
$541$	−1.19900e7			−1.76128			−0.880639	+	0.473788i	$0.842886\pi$
$542$	−1.13541e6	−	1.96658e6i	−0.166017	−	0.287551i
$543$		0			0
$544$	211968.	−	367139.i	0.0307095	−	0.0531905i
$545$	−281490.	+	487555.i	−0.0405949	+	0.0703125i
$546$		0			0
$547$	−2.22905e6	−	3.86082e6i	−0.318530	−	0.551711i	0.661651	−	0.749812i	$-0.269856\pi$
$547$	−2.22905e6	−	3.86082e6i	−0.318530	−	0.551711i	−0.980182	+	0.198101i	$0.936523\pi$
$548$	−2.05526e6			−0.292359
$549$		0			0
$550$	−295440.			−0.0416450
$551$	−2.66437e6	−	4.61483e6i	−0.373866	−	0.647555i
$552$		0			0
$553$	−6.54790e6	+	1.13413e7i	−0.910520	+	1.57707i
$554$	2.42652e6	−	4.20285e6i	0.335899	−	0.581794i
$555$		0			0
$556$	−1.23357e6	−	2.13660e6i	−0.169230	−	0.293114i
$557$	9.02612e6			1.23272			0.616358	−	0.787466i	$-0.288607\pi$
$557$	9.02612e6			1.23272			0.616358	+	0.787466i	$0.288607\pi$
$558$		0			0
$559$	−8.76193e6			−1.18596
$560$	1.48685e6	+	2.57530e6i	0.200353	+	0.347022i
$561$		0			0
$562$	−1.37548e6	+	2.38239e6i	−0.183701	+	0.318180i
$563$	−3.42449e6	+	5.93140e6i	−0.455329	+	0.788653i	−0.998707	−	0.0508350i	$-0.983812\pi$
$563$	−3.42449e6	+	5.93140e6i	−0.455329	+	0.788653i	0.543378	+	0.839488i	$0.317145\pi$
$564$		0			0
$565$	−6.44945e6	−	1.11708e7i	−0.849967	−	1.47219i
$566$	−3.32363e6			−0.436086
$567$		0			0
$568$	391680.			0.0509402
$569$	2.73161e6	+	4.73129e6i	0.353703	+	0.612631i	0.986895	−	0.161364i	$-0.0515892\pi$
$569$	2.73161e6	+	4.73129e6i	0.353703	+	0.612631i	−0.633192	+	0.773994i	$0.718256\pi$
$570$		0			0
$571$	5.11619e6	−	8.86150e6i	0.656684	−	1.13741i	−0.324785	−	0.945788i	$-0.605292\pi$
$571$	5.11619e6	−	8.86150e6i	0.656684	−	1.13741i	0.981469	−	0.191622i	$-0.0613748\pi$
$572$	−315840.	+	547051.i	−0.0403624	+	0.0699097i
$573$		0			0
$574$	−6.75629e6	−	1.17022e7i	−0.855911	−	1.48248i
$575$	738600.			0.0931622
$576$		0			0
$577$	1.59437e7			1.99365			0.996825	−	0.0796186i	$-0.0253702\pi$
$577$	1.59437e7			1.99365			0.996825	+	0.0796186i	$0.0253702\pi$
$578$	2.49692e6	+	4.32480e6i	0.310875	+	0.538451i
$579$		0			0
$580$	2.94307e6	−	5.09755e6i	0.363271	−	0.629204i
$581$	569184.	−	985856.i	0.0699540	−	0.121164i
$582$		0			0
$583$	−937980.	−	1.62463e6i	−0.114294	−	0.197962i
$584$	−1.63571e6			−0.198461
$585$		0			0
$586$	−5.25050e6			−0.631622
$587$	4.73857e6	+	8.20744e6i	0.567612	+	0.983133i	0.996801	+	0.0799185i	$0.0254660\pi$
$587$	4.73857e6	+	8.20744e6i	0.567612	+	0.983133i	−0.429189	+	0.903215i	$0.641201\pi$
$588$		0			0
$589$	1.71698e6	−	2.97389e6i	0.203928	−	0.353213i
$590$	3.47688e6	−	6.02213e6i	0.411206	−	0.712230i
$591$		0			0
$592$	1.08262e6	+	1.87516e6i	0.126962	+	0.219904i
$593$	2.45349e6			0.286515			0.143258	−	0.989685i	$-0.454242\pi$
$593$	2.45349e6			0.286515			0.143258	+	0.989685i	$0.454242\pi$
$594$		0			0
$595$	4.80902e6			0.556884
$596$	−235632.	−	408127.i	−0.0271718	−	0.0470630i
$597$		0			0
$598$	789600.	−	1.36763e6i	0.0902930	−	0.156392i
$599$	4.64989e6	−	8.05385e6i	0.529512	−	0.917142i	−0.469895	−	0.882722i	$-0.655708\pi$
$599$	4.64989e6	−	8.05385e6i	0.529512	−	0.917142i	0.999407	−	0.0344196i	$-0.0109583\pi$
$600$		0			0
$601$	5.73085e6	+	9.92613e6i	0.647192	+	1.12097i	0.983791	+	0.179321i	$0.0573900\pi$
$601$	5.73085e6	+	9.92613e6i	0.647192	+	1.12097i	−0.336599	+	0.941648i	$0.609277\pi$
$602$	9.37446e6			1.05428
$603$		0			0
$604$	−3.26195e6			−0.363819
$605$	−5.19588e6	−	8.99953e6i	−0.577126	−	0.999612i
$606$		0			0
$607$	−5.63919e6	+	9.76736e6i	−0.621219	+	1.07598i	0.368040	+	0.929810i	$0.380029\pi$
$607$	−5.63919e6	+	9.76736e6i	−0.621219	+	1.07598i	−0.989259	+	0.146173i	$0.953304\pi$
$608$	−489472.	+	847790.i	−0.0536993	+	0.0930100i
$609$		0			0
$610$	−4.10388e6	−	7.10813e6i	−0.446550	−	0.773447i
$611$	1.29494e7			1.40329
$612$		0			0
$613$	93782.0			0.0100802			0.00504009	−	0.999987i	$-0.498396\pi$
$613$	93782.0			0.0100802			0.00504009	+	0.999987i	$0.498396\pi$
$614$	−3.38044e6	−	5.85509e6i	−0.361870	−	0.626777i
$615$		0			0
$616$	337920.	−	585295.i	0.0358808	−	0.0621474i
$617$	7.48208e6	−	1.29593e7i	0.791242	−	1.37047i	−0.133957	−	0.990987i	$-0.542768\pi$
$617$	7.48208e6	−	1.29593e7i	0.791242	−	1.37047i	0.925198	−	0.379484i	$-0.123898\pi$
$618$		0			0
$619$	2.53444e6	+	4.38978e6i	0.265861	+	0.460485i	0.967789	−	0.251763i	$-0.0810104\pi$
$619$	2.53444e6	+	4.38978e6i	0.265861	+	0.460485i	−0.701928	+	0.712248i	$0.747677\pi$
$620$	3.79315e6			0.396297
$621$		0			0
$622$	−6.00816e6			−0.622681
$623$	2.88130e6	+	4.99055e6i	0.297418	+	0.515144i
$624$		0			0
$625$	6.04857e6	−	1.04764e7i	0.619374	−	1.07279i
$626$	−1.62168e6	+	2.80884e6i	−0.165398	+	0.286478i
$627$		0			0
$628$	−1.08914e6	−	1.88644e6i	−0.110200	−	0.190873i
$629$	3.50161e6			0.352892
$630$		0			0
$631$	1.55919e7			1.55892			0.779462	−	0.626450i	$-0.215493\pi$
$631$	1.55919e7			1.55892			0.779462	+	0.626450i	$0.215493\pi$
$632$	−2.38106e6	−	4.12411e6i	−0.237125	−	0.410712i
$633$		0			0
$634$	−1.80712e6	+	3.13002e6i	−0.178551	+	0.309260i
$635$	5.70900e6	−	9.88828e6i	0.561857	−	0.973165i
$636$		0			0
$637$	4.66160e6	+	8.07413e6i	0.455184	+	0.788401i
$638$	−1.33776e6			−0.130115
$639$		0			0
$640$	−1.08134e6			−0.104355
$641$	−5.48506e6	−	9.50041e6i	−0.527274	−	0.913266i	−0.999495	−	0.0317855i	$-0.989881\pi$
$641$	−5.48506e6	−	9.50041e6i	−0.527274	−	0.913266i	0.472220	−	0.881481i	$-0.343453\pi$
$642$		0			0
$643$	1.41852e6	−	2.45695e6i	0.135303	−	0.234352i	−0.790410	−	0.612578i	$-0.790132\pi$
$643$	1.41852e6	−	2.45695e6i	0.135303	−	0.234352i	0.925713	+	0.378226i	$0.123466\pi$
$644$	−844800.	+	1.46324e6i	−0.0802674	+	0.139027i
$645$		0			0
$646$	791568.	+	1.37104e6i	0.0746289	+	0.129261i
$647$	−6.05686e6			−0.568835			−0.284418	−	0.958700i	$-0.591800\pi$
$647$	−6.05686e6			−0.568835			−0.284418	+	0.958700i	$0.591800\pi$
$648$		0			0
$649$	−1.58040e6			−0.147284
$650$	1.62000e6	+	2.80592e6i	0.150394	+	0.260490i
$651$		0			0
$652$	1.36899e6	−	2.37116e6i	0.126119	−	0.218445i
$653$	544461.	−	943034.i	0.0499671	−	0.0865455i	−0.839960	−	0.542648i	$-0.817422\pi$
$653$	544461.	−	943034.i	0.0499671	−	0.0865455i	0.889927	+	0.456103i	$0.150755\pi$
$654$		0			0
$655$	4.99158e6	+	8.64567e6i	0.454606	+	0.787400i
$656$	4.91366e6			0.445806
$657$		0			0
$658$	−1.38547e7			−1.24748
$659$	−3.70901e6	−	6.42420e6i	−0.332694	−	0.576243i	0.650345	−	0.759639i	$-0.274624\pi$
$659$	−3.70901e6	−	6.42420e6i	−0.332694	−	0.576243i	−0.983039	+	0.183396i	$0.941291\pi$
$660$		0			0
$661$	−383827.	+	664808.i	−0.0341690	+	0.0591824i	−0.882604	−	0.470117i	$-0.844212\pi$
$661$	−383827.	+	664808.i	−0.0341690	+	0.0591824i	0.848435	+	0.529299i	$0.177545\pi$
$662$	−2.24394e6	+	3.88663e6i	−0.199006	+	0.344689i
$663$		0			0
$664$	206976.	+	358493.i	0.0182180	+	0.0315544i
$665$	−1.11049e7			−0.973779
$666$		0			0
$667$	3.34440e6			0.291074
$668$	5.40960e6	+	9.36970e6i	0.469055	+	0.812428i
$669$		0			0
$670$	−2.21813e6	+	3.84191e6i	−0.190897	+	0.330644i
$671$	−932700.	+	1.61548e6i	−0.0799716	+	0.138515i
$672$		0			0
$673$	−711313.	−	1.23203e6i	−0.0605373	−	0.104854i	0.834168	−	0.551510i	$-0.185948\pi$
$673$	−711313.	−	1.23203e6i	−0.0605373	−	0.104854i	−0.894706	+	0.446656i	$0.852615\pi$
$674$	−1.10087e7			−0.933439
$675$		0			0
$676$	986736.			0.0830490
$677$	3.08115e6	+	5.33671e6i	0.258370	+	0.447509i	0.965805	−	0.259268i	$-0.0834814\pi$
$677$	3.08115e6	+	5.33671e6i	0.258370	+	0.447509i	−0.707436	+	0.706778i	$0.750148\pi$
$678$		0			0
$679$	−1.46152e7	+	2.53143e7i	−1.21655	+	2.10713i
$680$	−874368.	+	1.51445e6i	−0.0725140	+	0.125598i
$681$		0			0
$682$	−431040.	−	746583.i	−0.0354860	−	0.0614635i
$683$	1.50621e7			1.23548			0.617739	−	0.786383i	$-0.288049\pi$
$683$	1.50621e7			1.23548			0.617739	+	0.786383i	$0.288049\pi$
$684$		0			0
$685$	8.47796e6			0.690343
$686$	928576.	+	1.60834e6i	0.0753368	+	0.130487i
$687$		0			0
$688$	−1.70445e6	+	2.95219e6i	−0.137282	+	0.237779i
$689$	−1.02865e7	+	1.78168e7i	−0.825506	+	1.42982i
$690$		0			0
$691$	2.93818e6	+	5.08907e6i	0.234090	+	0.405456i	0.959008	−	0.283380i	$-0.0914556\pi$
$691$	2.93818e6	+	5.08907e6i	0.234090	+	0.405456i	−0.724918	+	0.688835i	$0.758122\pi$
$692$	2.13053e6			0.169131
$693$		0			0
$694$	7.66997e6			0.604498
$695$	5.08847e6	+	8.81349e6i	0.399600	+	0.692127i
$696$		0			0
$697$	3.97316e6	−	6.88171e6i	0.309780	−	0.536555i
$698$	−3.67318e6	+	6.36213e6i	−0.285367	+	0.494270i
$699$		0			0
$700$	−1.73325e6	−	3.00207e6i	−0.133695	−	0.231567i
$701$	3.60077e6			0.276758			0.138379	−	0.990379i	$-0.455811\pi$
$701$	3.60077e6			0.276758			0.138379	+	0.990379i	$0.455811\pi$
$702$		0			0
$703$	−8.08585e6			−0.617074
$704$	122880.	+	212834.i	0.00934436	+	0.0161849i
$705$		0			0
$706$	1.24403e6	−	2.15472e6i	0.0939330	−	0.162697i
$707$	1.93618e6	−	3.35356e6i	0.145679	−	0.252323i
$708$		0			0
$709$	−4.61258e6	−	7.98922e6i	−0.344610	−	0.596883i	0.640673	−	0.767814i	$-0.278656\pi$
$709$	−4.61258e6	−	7.98922e6i	−0.344610	−	0.596883i	−0.985283	+	0.170932i	$0.945322\pi$
$710$	−1.61568e6			−0.120284
$711$		0			0
$712$	−2.09549e6			−0.154912
$713$	1.07760e6	+	1.86646e6i	0.0793841	+	0.137497i
$714$		0			0
$715$	1.30284e6	−	2.25659e6i	0.0953073	−	0.165077i
$716$	5.54717e6	−	9.60798e6i	0.404379	−	0.700405i
$717$		0			0
$718$	−7.48123e6	−	1.29579e7i	−0.541579	−	0.938043i
$719$	−2.63923e7			−1.90395			−0.951975	−	0.306177i	$-0.900950\pi$
$719$	−2.63923e7			−1.90395			−0.951975	+	0.306177i	$0.900950\pi$
$720$		0			0
$721$	−1.39505e7			−0.999426
$722$	3.12433e6	+	5.41149e6i	0.223056	+	0.386344i
$723$		0			0
$724$	−3.01739e6	+	5.22628e6i	−0.213937	+	0.370549i
$725$	−3.43080e6	+	5.94231e6i	−0.242410	+	0.419866i
$726$		0			0
$727$	4.89742e6	+	8.48259e6i	0.343662	+	0.595240i	0.985110	−	0.171927i	$-0.0549992\pi$
$727$	4.89742e6	+	8.48259e6i	0.343662	+	0.595240i	−0.641448	+	0.767167i	$0.721666\pi$
$728$	−7.41171e6			−0.518311
$729$		0			0
$730$	6.74731e6			0.468623
$731$	2.75641e6	+	4.77425e6i	0.190788	+	0.330454i
$732$		0			0
$733$	−2.03792e6	+	3.52978e6i	−0.140096	+	0.242654i	−0.927533	−	0.373742i	$-0.878075\pi$
$733$	−2.03792e6	+	3.52978e6i	−0.140096	+	0.242654i	0.787436	+	0.616396i	$0.211408\pi$
$734$	−32464.0	+	56229.3i	−0.00222414	+	0.00385232i
$735$		0			0
$736$	−307200.	−	532086.i	−0.0209039	−	0.0362066i
$737$	1.00824e6			0.0683747
$738$		0			0
$739$	−1.65709e7			−1.11618			−0.558089	−	0.829781i	$-0.688465\pi$
$739$	−1.65709e7			−1.11618			−0.558089	+	0.829781i	$0.688465\pi$
$740$	−4.46582e6	−	7.73503e6i	−0.299794	−	0.519258i
$741$		0			0
$742$	1.10056e7	−	1.90623e7i	0.733846	−	1.27106i
$743$	−7.20707e6	+	1.24830e7i	−0.478946	+	0.829559i	−0.999709	−	0.0241427i	$-0.992314\pi$
$743$	−7.20707e6	+	1.24830e7i	−0.478946	+	0.829559i	0.520762	+	0.853702i	$0.325648\pi$
$744$		0			0
$745$	971982.	+	1.68352e6i	0.0641605	+	0.111129i
$746$	1.17442e6			0.0772641
$747$		0			0
$748$	397440.			0.0259727
$749$	−2.00629e7	−	3.47500e7i	−1.30674	−	2.26334i
$750$		0			0
$751$	−8.39722e6	+	1.45444e7i	−0.543295	+	0.941015i	0.455417	+	0.890278i	$0.349490\pi$
$751$	−8.39722e6	+	1.45444e7i	−0.543295	+	0.941015i	−0.998712	+	0.0507363i	$0.983843\pi$
$752$	2.51904e6	−	4.36311e6i	0.162439	−	0.281353i
$753$		0			0
$754$	7.33538e6	+	1.27053e7i	0.469888	+	0.813870i
$755$	1.34556e7			0.859081
$756$		0			0
$757$	1.32943e7			0.843188			0.421594	−	0.906785i	$-0.361471\pi$
$757$	1.32943e7			0.843188			0.421594	+	0.906785i	$0.361471\pi$
$758$	−6.36023e6	−	1.10162e7i	−0.402068	−	0.696403i
$759$		0			0
$760$	2.01907e6	−	3.49714e6i	0.126800	−	0.219623i
$761$	1.07393e6	−	1.86010e6i	0.0672225	−	0.116433i	−0.830455	−	0.557085i	$-0.811920\pi$
$761$	1.07393e6	−	1.86010e6i	0.0672225	−	0.116433i	0.897678	+	0.440653i	$0.145253\pi$
$762$		0			0
$763$	750640.	+	1.30015e6i	0.0466789	+	0.0808502i
$764$	−4.24550e6			−0.263145
$765$		0			0
$766$	−1.19194e7			−0.733975
$767$	8.66586e6	+	1.50097e7i	0.531892	+	0.921264i
$768$		0			0
$769$	6.55296e6	−	1.13501e7i	0.399596	−	0.692121i	−0.594080	−	0.804406i	$-0.702484\pi$
$769$	6.55296e6	−	1.13501e7i	0.399596	−	0.692121i	0.993676	+	0.112285i	$0.0358169\pi$
$770$	−1.39392e6	+	2.41434e6i	−0.0847249	+	0.146748i
$771$		0			0
$772$	−2.36238e6	−	4.09177e6i	−0.142662	−	0.247097i
$773$	−2.37154e7			−1.42752			−0.713759	−	0.700392i	$-0.753009\pi$
$773$	−2.37154e7			−1.42752			−0.713759	+	0.700392i	$0.753009\pi$
$774$		0			0
$775$	−4.42175e6			−0.264448
$776$	−5.31462e6	−	9.20520e6i	−0.316824	−	0.548755i
$777$		0			0
$778$	−6.91955e6	+	1.19850e7i	−0.409854	+	0.709887i
$779$	−9.17473e6	+	1.58911e7i	−0.541689	+	0.938232i
$780$		0			0
$781$	183600.	+	318005.i	0.0107707	+	0.0186554i
$782$	−993600.			−0.0581025
$783$		0			0
$784$	3.62726e6			0.210760
$785$	4.49269e6	+	7.78156e6i	0.260215	+	0.450705i
$786$		0			0
$787$	4.20024e6	−	7.27503e6i	0.241734	−	0.418695i	−0.719474	−	0.694519i	$-0.755617\pi$
$787$	4.20024e6	−	7.27503e6i	0.241734	−	0.418695i	0.961208	+	0.275824i	$0.0889506\pi$
$788$	−1.61035e6	+	2.78921e6i	−0.0923858	+	0.160017i
$789$		0			0
$790$	9.82186e6	+	1.70120e7i	0.559920	+	0.969810i
$791$	−3.43971e7			−1.95470
$792$		0			0
$793$	2.04572e7			1.15522
$794$	7.80832e6	+	1.35244e7i	0.439548	+	0.761320i
$795$		0			0
$796$	−5.21958e6	+	9.04058e6i	−0.291980	+	0.505724i
$797$	−2.70512e6	+	4.68540e6i	−0.150848	+	0.261277i	−0.931539	−	0.363640i	$-0.881534\pi$
$797$	−2.70512e6	+	4.68540e6i	−0.150848	+	0.261277i	0.780691	+	0.624917i	$0.214867\pi$
$798$		0			0
$799$	−4.07376e6	−	7.05596e6i	−0.225750	−	0.391011i
$800$	1.26054e6			0.0696359
$801$		0			0
$802$	2.17646e7			1.19485
$803$	−766740.	−	1.32803e6i	−0.0419623	−	0.0726808i
$804$		0			0
$805$	3.48480e6	−	6.03585e6i	0.189534	−	0.328283i
$806$	−4.72707e6	+	8.18753e6i	−0.256304	+	0.443931i
$807$		0			0
$808$	704064.	+	1.21947e6i	0.0379388	+	0.0657120i
$809$	−2.60777e7			−1.40087			−0.700436	−	0.713715i	$-0.747011\pi$
$809$	−2.60777e7			−1.40087			−0.700436	+	0.713715i	$0.747011\pi$
$810$		0			0
$811$	1.90021e7			1.01449			0.507247	−	0.861800i	$-0.330663\pi$
$811$	1.90021e7			1.01449			0.507247	+	0.861800i	$0.330663\pi$
$812$	−7.84819e6	−	1.35935e7i	−0.417714	−	0.723503i
$813$		0			0
$814$	−1.01496e6	+	1.75796e6i	−0.0536893	+	0.0929926i
$815$	−5.64709e6	+	9.78105e6i	−0.297804	+	0.515812i
$816$		0			0
$817$	−6.36505e6	−	1.10246e7i	−0.333616	−	0.577839i
$818$	7.87978e6			0.411748
$819$		0			0
$820$	−2.02689e7			−1.05268
$821$	1.55086e7	+	2.68618e7i	0.803001	+	1.39084i	0.917633	+	0.397430i	$0.130098\pi$
$821$	1.55086e7	+	2.68618e7i	0.803001	+	1.39084i	−0.114632	+	0.993408i	$0.536569\pi$
$822$		0			0
$823$	7.81448e6	−	1.35351e7i	0.402162	−	0.696564i	−0.591825	−	0.806066i	$-0.701592\pi$
$823$	7.81448e6	−	1.35351e7i	0.402162	−	0.696564i	0.993987	+	0.109502i	$0.0349257\pi$
$824$	2.53645e6	−	4.39326e6i	0.130139	−	0.225408i
$825$		0			0
$826$	−9.27168e6	−	1.60590e7i	−0.472834	−	0.818972i
$827$	1.58421e7			0.805467			0.402733	−	0.915317i	$-0.368060\pi$
$827$	1.58421e7			0.805467			0.402733	+	0.915317i	$0.368060\pi$
$828$		0			0
$829$	2.06176e6			0.104196			0.0520980	−	0.998642i	$-0.483409\pi$
$829$	2.06176e6			0.104196			0.0520980	+	0.998642i	$0.483409\pi$
$830$	−853776.	−	1.47878e6i	−0.0430179	−	0.0745091i
$831$		0			0
$832$	1.34758e6	−	2.33408e6i	0.0674913	−	0.116898i
$833$	2.93298e6	−	5.08008e6i	0.146453	−	0.253663i
$834$		0			0
$835$	−2.23146e7	−	3.86500e7i	−1.10757	−	1.91838i
$836$	−917760.			−0.0454165
$837$		0			0
$838$	556080.			0.0273544
$839$	−1.51950e7	−	2.63185e7i	−0.745240	−	1.29079i	−0.950083	−	0.311999i	$-0.899002\pi$
$839$	−1.51950e7	−	2.63185e7i	−0.745240	−	1.29079i	0.204843	−	0.978795i	$-0.434332\pi$
$840$		0			0
$841$	−5.27916e6	+	9.14378e6i	−0.257380	+	0.445796i
$842$	−8.65486e6	+	1.49907e7i	−0.420707	+	0.728686i
$843$		0			0
$844$	9.17648e6	+	1.58941e7i	0.443425	+	0.768034i
$845$	−4.07029e6			−0.196103
$846$		0			0
$847$	−2.77114e7			−1.32724
$848$	4.00205e6	+	6.93175e6i	0.191114	+	0.331019i
$849$		0			0
$850$	1.01927e6	−	1.76542e6i	0.0483884	−	0.0838111i
$851$	2.53740e6	−	4.39491e6i	0.120106	−	0.208030i
$852$		0			0
$853$	1.48869e7	+	2.57849e7i	0.700538	+	1.21337i	0.968278	+	0.249876i	$0.0803898\pi$
$853$	1.48869e7	+	2.57849e7i	0.700538	+	1.21337i	−0.267740	+	0.963491i	$0.586277\pi$
$854$	−2.18874e7			−1.02695
$855$		0			0
$856$	1.45912e7			0.680624
$857$	−4.32050e6	−	7.48333e6i	−0.200947	−	0.348051i	0.747887	−	0.663826i	$-0.231069\pi$
$857$	−4.32050e6	−	7.48333e6i	−0.200947	−	0.348051i	−0.948834	+	0.315776i	$0.897735\pi$
$858$		0			0
$859$	1.67831e7	−	2.90693e7i	0.776051	−	1.34416i	−0.158151	−	0.987415i	$-0.550553\pi$
$859$	1.67831e7	−	2.90693e7i	0.776051	−	1.34416i	0.934202	−	0.356745i	$-0.116114\pi$
$860$	7.03085e6	−	1.21778e7i	0.324162	−	0.561464i
$861$		0			0
$862$	5.59872e6	+	9.69727e6i	0.256638	+	0.444510i
$863$	3.90191e7			1.78341			0.891703	−	0.452621i	$-0.149511\pi$
$863$	3.90191e7			1.78341			0.891703	+	0.452621i	$0.149511\pi$
$864$		0			0
$865$	−8.78843e6			−0.399366
$866$	1.18048e7	+	2.04466e7i	0.534891	+	0.926458i
$867$		0			0
$868$	5.05754e6	−	8.75991e6i	0.227845	−	0.394639i
$869$	2.23224e6	−	3.86635e6i	0.100275	−	0.173681i
$870$		0			0
$871$	−5.52852e6	−	9.57567e6i	−0.246924	−	0.427685i
$872$	−545920.			−0.0243130
$873$		0			0
$874$	2.29440e6			0.101599
$875$	−1.10004e7	−	1.90532e7i	−0.485721	−	0.841293i
$876$		0			0
$877$	9.06909e6	−	1.57081e7i	0.398166	−	0.689645i	−0.595333	−	0.803479i	$-0.702980\pi$
$877$	9.06909e6	−	1.57081e7i	0.398166	−	0.689645i	0.993500	+	0.113834i	$0.0363133\pi$
$878$	893024.	−	1.54676e6i	0.0390955	−	0.0677154i
$879$		0			0
$880$	−506880.	−	877942.i	−0.0220647	−	0.0382172i
$881$	3.05312e7			1.32527			0.662634	−	0.748943i	$-0.269438\pi$
$881$	3.05312e7			1.32527			0.662634	+	0.748943i	$0.269438\pi$
$882$		0			0
$883$	−4.35533e7			−1.87983			−0.939916	−	0.341405i	$-0.889097\pi$
$883$	−4.35533e7			−1.87983			−0.939916	+	0.341405i	$0.889097\pi$
$884$	−2.17930e6	−	3.77465e6i	−0.0937963	−	0.162460i
$885$		0			0
$886$	−6.99050e6	+	1.21079e7i	−0.299174	+	0.518185i
$887$	6.70758e6	−	1.16179e7i	0.286257	−	0.495812i	−0.686656	−	0.726983i	$-0.740922\pi$
$887$	6.70758e6	−	1.16179e7i	0.286257	−	0.495812i	0.972913	+	0.231170i	$0.0742554\pi$
$888$		0			0
$889$	−1.52240e7	−	2.63687e7i	−0.646062	−	1.11901i
$890$	8.64389e6			0.365792
$891$		0			0
$892$	1.12314e7			0.472629
$893$	9.40704e6	+	1.62935e7i	0.394752	+	0.683731i
$894$		0			0
$895$	−2.28821e7	+	3.96329e7i	−0.954856	+	1.65386i
$896$	−1.44179e6	+	2.49726e6i	−0.0599974	+	0.103919i
$897$		0			0
$898$	2.41225e6	+	4.17814e6i	0.0998233	+	0.172899i
$899$	−2.00218e7			−0.826236
$900$		0			0
$901$	1.29441e7			0.531203
$902$	2.30328e6	+	3.98940e6i	0.0942606	+	0.163264i
$903$		0			0
$904$	6.25402e6	−	1.08323e7i	0.254529	−	0.440858i
$905$	1.24467e7	−	2.15584e7i	0.505166	−	0.874973i
$906$		0			0
$907$	−1.55408e6	−	2.69175e6i	−0.0627272	−	0.108647i	0.832956	−	0.553339i	$-0.186646\pi$
$907$	−1.55408e6	−	2.69175e6i	−0.0627272	−	0.108647i	−0.895684	+	0.444692i	$0.853313\pi$
$908$	1.97777e7			0.796089
$909$		0			0
$910$	3.05733e7			1.22388
$911$	−595176.	−	1.03088e6i	−0.0237602	−	0.0411538i	0.853901	−	0.520436i	$-0.174230\pi$
$911$	−595176.	−	1.03088e6i	−0.0237602	−	0.0411538i	−0.877661	+	0.479282i	$0.840897\pi$
$912$		0			0
$913$	−194040.	+	336087.i	−0.00770397	+	0.0133437i
$914$	−467092.	+	809027.i	−0.0184943	+	0.0320330i
$915$		0			0
$916$	−846640.	−	1.46642e6i	−0.0333396	−	0.0577458i
$917$	2.66218e7			1.04547
$918$		0			0
$919$	−4.71996e7			−1.84353			−0.921764	−	0.387752i	$-0.873252\pi$
$919$	−4.71996e7			−1.84353			−0.921764	+	0.387752i	$0.873252\pi$
$920$	1.26720e6	+	2.19485e6i	0.0493601	+	0.0854941i
$921$		0			0
$922$	3.48978e6	−	6.04448e6i	0.135198	−	0.234170i
$923$	2.01348e6	−	3.48745e6i	0.0777935	−	0.134742i
$924$		0			0
$925$	5.20590e6	+	9.01688e6i	0.200051	+	0.346499i
$926$	−1.16715e7			−0.447299
$927$		0			0
$928$	5.70778e6			0.217569
$929$	−667977.	−	1.15697e6i	−0.0253935	−	0.0439828i	0.853049	−	0.521830i	$-0.174751\pi$
$929$	−667977.	−	1.15697e6i	−0.0253935	−	0.0439828i	−0.878443	+	0.477847i	$0.841417\pi$
$930$		0			0
$931$	−6.77278e6	+	1.17308e7i	−0.256090	+	0.443561i
$932$	3.50942e6	−	6.07850e6i	0.132342	−	0.229222i
$933$		0			0
$934$	1.06215e7	+	1.83970e7i	0.398400	+	0.690049i
$935$	−1.63944e6			−0.0613291
$936$		0			0
$937$	1.47238e7			0.547861			0.273931	−	0.961749i	$-0.411676\pi$
$937$	1.47238e7			0.547861			0.273931	+	0.961749i	$0.411676\pi$
$938$	5.91501e6	+	1.02451e7i	0.219507	+	0.380197i
$939$		0			0
$940$	−1.03910e7	+	1.79978e7i	−0.383565	+	0.664355i
$941$	1.34598e7	−	2.33131e7i	0.495525	−	0.858274i	−0.504462	−	0.863434i	$-0.668309\pi$
$941$	1.34598e7	−	2.33131e7i	0.495525	−	0.858274i	0.999987	+	0.00516005i	$0.00164250\pi$
$942$		0			0
$943$	−5.75820e6	−	9.97349e6i	−0.210866	−	0.365231i
$944$	6.74304e6			0.246278
$945$		0			0
$946$	−3.19584e6			−0.116107
$947$	1.86580e6	+	3.23166e6i	0.0676068	+	0.117098i	0.897847	−	0.440307i	$-0.145130\pi$
$947$	1.86580e6	+	3.23166e6i	0.0676068	+	0.117098i	−0.830241	+	0.557405i	$0.811797\pi$
$948$		0			0
$949$	−8.40858e6	+	1.45641e7i	−0.303080	+	0.524950i
$950$	−2.35367e6	+	4.07668e6i	−0.0846130	+	0.146554i
$951$		0			0
$952$	2.33165e6	+	4.03853e6i	0.0833817	+	0.144421i
$953$	2.18735e7			0.780166			0.390083	−	0.920780i	$-0.372446\pi$
$953$	2.18735e7			0.780166			0.390083	+	0.920780i	$0.372446\pi$
$954$		0			0
$955$	1.75127e7			0.621362
$956$	−227712.	−	394409.i	−0.00805826	−	0.0139573i
$957$		0			0
$958$	−4.68931e6	+	8.12213e6i	−0.165080	+	0.285928i
$959$	1.13040e7	−	1.95790e7i	0.396902	−	0.687455i
$960$		0			0
$961$	7.86334e6	+	1.36197e7i	0.274662	+	0.475729i
$962$	2.22615e7			0.775561
$963$		0			0
$964$	1.42810e7			0.494955
$965$	9.74483e6	+	1.68785e7i	0.336865	+	0.583468i
$966$		0			0
$967$	−8.80125e6	+	1.52442e7i	−0.302676	+	0.524250i	−0.976741	−	0.214422i	$-0.931213\pi$
$967$	−8.80125e6	+	1.52442e7i	−0.302676	+	0.524250i	0.674065	+	0.738672i	$0.264547\pi$
$968$	5.03843e6	−	8.72682e6i	0.172825	−	0.299342i
$969$		0			0
$970$	2.19228e7	+	3.79714e7i	0.748113	+	1.29577i
$971$	1.67317e7			0.569497			0.284749	−	0.958602i	$-0.408090\pi$
$971$	1.67317e7			0.569497			0.284749	+	0.958602i	$0.408090\pi$
$972$		0			0
$973$	2.71385e7			0.918975
$974$	−1.96306e7	−	3.40012e7i	−0.663035	−	1.14841i
$975$		0			0
$976$	3.97952e6	−	6.89273e6i	0.133723	−	0.231615i
$977$	−2.77691e7	+	4.80975e7i	−0.930733	+	1.61208i	−0.148662	+	0.988888i	$0.547497\pi$
$977$	−2.77691e7	+	4.80975e7i	−0.930733	+	1.61208i	−0.782071	+	0.623189i	$0.785837\pi$
$978$		0			0
$979$	−982260.	−	1.70132e6i	−0.0327544	−	0.0567323i
$980$	−1.49625e7			−0.497666
$981$		0			0
$982$	−2.37808e7			−0.786951
$983$	1.93392e7	+	3.34965e7i	0.638344	+	1.10564i	0.985796	+	0.167947i	$0.0537137\pi$
$983$	1.93392e7	+	3.34965e7i	0.638344	+	1.10564i	−0.347452	+	0.937698i	$0.612953\pi$
$984$		0			0
$985$	6.64270e6	−	1.15055e7i	0.218149	−	0.377846i
$986$	4.61527e6	−	7.99389e6i	0.151184	−	0.261858i
$987$		0			0
$988$	5.03238e6	+	8.71634e6i	0.164014	+	0.284081i
$989$	7.98960e6			0.259737
$990$		0			0
$991$	9.58498e6			0.310033			0.155016	−	0.987912i	$-0.450457\pi$
$991$	9.58498e6			0.310033			0.155016	+	0.987912i	$0.450457\pi$
$992$	1.83910e6	+	3.18542e6i	0.0593372	+	0.102775i
$993$		0			0
$994$	−2.15424e6	+	3.73125e6i	−0.0691557	+	0.119781i
$995$	2.15308e7	−	3.72924e7i	0.689449	−	1.19416i
$996$		0			0
$997$	5.18252e6	+	8.97638e6i	0.165121	+	0.285998i	0.936698	−	0.350137i	$-0.113865\pi$
$997$	5.18252e6	+	8.97638e6i	0.165121	+	0.285998i	−0.771577	+	0.636136i	$0.780532\pi$
$998$	2.59133e7			0.823561
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.6.c.e.109.1		2
3.2	odd	2		162.6.c.h.109.1		2
9.2	odd	6		162.6.c.h.55.1		2
9.4	even	3		6.6.a.a.1.1	✓	1
9.5	odd	6		18.6.a.b.1.1		1
9.7	even	3	inner	162.6.c.e.55.1		2
36.23	even	6		144.6.a.j.1.1		1
36.31	odd	6		48.6.a.c.1.1		1
45.4	even	6		150.6.a.d.1.1		1
45.13	odd	12		150.6.c.b.49.1		2
45.14	odd	6		450.6.a.m.1.1		1
45.22	odd	12		150.6.c.b.49.2		2
45.23	even	12		450.6.c.j.199.2		2
45.32	even	12		450.6.c.j.199.1		2
63.4	even	3		294.6.e.g.79.1		2
63.13	odd	6		294.6.a.m.1.1		1
63.31	odd	6		294.6.e.a.79.1		2
63.40	odd	6		294.6.e.a.67.1		2
63.41	even	6		882.6.a.a.1.1		1
63.58	even	3		294.6.e.g.67.1		2
72.5	odd	6		576.6.a.j.1.1		1
72.13	even	6		192.6.a.o.1.1		1
72.59	even	6		576.6.a.i.1.1		1
72.67	odd	6		192.6.a.g.1.1		1
99.76	odd	6		726.6.a.a.1.1		1
117.103	even	6		1014.6.a.c.1.1		1
144.13	even	12		768.6.d.c.385.1		2
144.67	odd	12		768.6.d.p.385.2		2
144.85	even	12		768.6.d.c.385.2		2
144.139	odd	12		768.6.d.p.385.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.6.a.a.1.1	✓	1	9.4	even	3
18.6.a.b.1.1		1	9.5	odd	6
48.6.a.c.1.1		1	36.31	odd	6
144.6.a.j.1.1		1	36.23	even	6
150.6.a.d.1.1		1	45.4	even	6
150.6.c.b.49.1		2	45.13	odd	12
150.6.c.b.49.2		2	45.22	odd	12
162.6.c.e.55.1		2	9.7	even	3	inner
162.6.c.e.109.1		2	1.1	even	1	trivial
162.6.c.h.55.1		2	9.2	odd	6
162.6.c.h.109.1		2	3.2	odd	2
192.6.a.g.1.1		1	72.67	odd	6
192.6.a.o.1.1		1	72.13	even	6
294.6.a.m.1.1		1	63.13	odd	6
294.6.e.a.67.1		2	63.40	odd	6
294.6.e.a.79.1		2	63.31	odd	6
294.6.e.g.67.1		2	63.58	even	3
294.6.e.g.79.1		2	63.4	even	3
450.6.a.m.1.1		1	45.14	odd	6
450.6.c.j.199.1		2	45.32	even	12
450.6.c.j.199.2		2	45.23	even	12
576.6.a.i.1.1		1	72.59	even	6
576.6.a.j.1.1		1	72.5	odd	6
726.6.a.a.1.1		1	99.76	odd	6
768.6.d.c.385.1		2	144.13	even	12
768.6.d.c.385.2		2	144.85	even	12
768.6.d.p.385.1		2	144.139	odd	12
768.6.d.p.385.2		2	144.67	odd	12
882.6.a.a.1.1		1	63.41	even	6
1014.6.a.c.1.1		1	117.103	even	6

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(33.0000 - 57.1577i) q^{5} +(-88.0000 - 152.420i) q^{7} +64.0000 q^{8} +O(q^{10})\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(33.0000 - 57.1577i) q^{5} +(-88.0000 - 152.420i) q^{7} +64.0000 q^{8} -264.000 q^{10} +(30.0000 + 51.9615i) q^{11} +(329.000 - 569.845i) q^{13} +(-352.000 + 609.682i) q^{14} +(-128.000 - 221.703i) q^{16} -414.000 q^{17} +956.000 q^{19} +(528.000 + 914.523i) q^{20} +(120.000 - 207.846i) q^{22} +(-300.000 + 519.615i) q^{23} +(-615.500 - 1066.08i) q^{25} -2632.00 q^{26} +2816.00 q^{28} +(-2787.00 - 4827.23i) q^{29} +(1796.00 - 3110.76i) q^{31} +(-512.000 + 886.810i) q^{32} +(828.000 + 1434.14i) q^{34} -11616.0 q^{35} -8458.00 q^{37} +(-1912.00 - 3311.68i) q^{38} +(2112.00 - 3658.09i) q^{40} +(-9597.00 + 16622.5i) q^{41} +(-6658.00 - 11532.0i) q^{43} -960.000 q^{44} +2400.00 q^{46} +(9840.00 + 17043.4i) q^{47} +(-7084.50 + 12270.7i) q^{49} +(-2462.00 + 4264.31i) q^{50} +(5264.00 + 9117.52i) q^{52} -31266.0 q^{53} +3960.00 q^{55} +(-5632.00 - 9754.91i) q^{56} +(-11148.0 + 19308.9i) q^{58} +(-13170.0 + 22811.1i) q^{59} +(15545.0 + 26924.7i) q^{61} -14368.0 q^{62} +4096.00 q^{64} +(-21714.0 - 37609.8i) q^{65} +(8402.00 - 14552.7i) q^{67} +(3312.00 - 5736.55i) q^{68} +(23232.0 + 40239.0i) q^{70} +6120.00 q^{71} -25558.0 q^{73} +(16916.0 + 29299.4i) q^{74} +(-7648.00 + 13246.7i) q^{76} +(5280.00 - 9145.23i) q^{77} +(-37204.0 - 64439.2i) q^{79} -16896.0 q^{80} +76776.0 q^{82} +(3234.00 + 5601.45i) q^{83} +(-13662.0 + 23663.3i) q^{85} +(-26632.0 + 46128.0i) q^{86} +(1920.00 + 3325.54i) q^{88} -32742.0 q^{89} -115808. q^{91} +(-4800.00 - 8313.84i) q^{92} +(39360.0 - 68173.5i) q^{94} +(31548.0 - 54642.7i) q^{95} +(-83041.0 - 143831. i) q^{97} +56676.0 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 16 q^{4} + 66 q^{5} - 176 q^{7} + 128 q^{8}+O(q^{10}) \) 2 * q - 4 * q^2 - 16 * q^4 + 66 * q^5 - 176 * q^7 + 128 * q^8	\( 2 q - 4 q^{2} - 16 q^{4} + 66 q^{5} - 176 q^{7} + 128 q^{8} - 528 q^{10} + 60 q^{11} + 658 q^{13} - 704 q^{14} - 256 q^{16} - 828 q^{17} + 1912 q^{19} + 1056 q^{20} + 240 q^{22} - 600 q^{23} - 1231 q^{25} - 5264 q^{26} + 5632 q^{28} - 5574 q^{29} + 3592 q^{31} - 1024 q^{32} + 1656 q^{34} - 23232 q^{35} - 16916 q^{37} - 3824 q^{38} + 4224 q^{40} - 19194 q^{41} - 13316 q^{43} - 1920 q^{44} + 4800 q^{46} + 19680 q^{47} - 14169 q^{49} - 4924 q^{50} + 10528 q^{52} - 62532 q^{53} + 7920 q^{55} - 11264 q^{56} - 22296 q^{58} - 26340 q^{59} + 31090 q^{61} - 28736 q^{62} + 8192 q^{64} - 43428 q^{65} + 16804 q^{67} + 6624 q^{68} + 46464 q^{70} + 12240 q^{71} - 51116 q^{73} + 33832 q^{74} - 15296 q^{76} + 10560 q^{77} - 74408 q^{79} - 33792 q^{80} + 153552 q^{82} + 6468 q^{83} - 27324 q^{85} - 53264 q^{86} + 3840 q^{88} - 65484 q^{89} - 231616 q^{91} - 9600 q^{92} + 78720 q^{94} + 63096 q^{95} - 166082 q^{97} + 113352 q^{98}+O(q^{100}) \) 2 * q - 4 * q^2 - 16 * q^4 + 66 * q^5 - 176 * q^7 + 128 * q^8 - 528 * q^10 + 60 * q^11 + 658 * q^13 - 704 * q^14 - 256 * q^16 - 828 * q^17 + 1912 * q^19 + 1056 * q^20 + 240 * q^22 - 600 * q^23 - 1231 * q^25 - 5264 * q^26 + 5632 * q^28 - 5574 * q^29 + 3592 * q^31 - 1024 * q^32 + 1656 * q^34 - 23232 * q^35 - 16916 * q^37 - 3824 * q^38 + 4224 * q^40 - 19194 * q^41 - 13316 * q^43 - 1920 * q^44 + 4800 * q^46 + 19680 * q^47 - 14169 * q^49 - 4924 * q^50 + 10528 * q^52 - 62532 * q^53 + 7920 * q^55 - 11264 * q^56 - 22296 * q^58 - 26340 * q^59 + 31090 * q^61 - 28736 * q^62 + 8192 * q^64 - 43428 * q^65 + 16804 * q^67 + 6624 * q^68 + 46464 * q^70 + 12240 * q^71 - 51116 * q^73 + 33832 * q^74 - 15296 * q^76 + 10560 * q^77 - 74408 * q^79 - 33792 * q^80 + 153552 * q^82 + 6468 * q^83 - 27324 * q^85 - 53264 * q^86 + 3840 * q^88 - 65484 * q^89 - 231616 * q^91 - 9600 * q^92 + 78720 * q^94 + 63096 * q^95 - 166082 * q^97 + 113352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more