LMFDB - Embedded newform 735.2.i.b.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(226,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("735.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.i (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:	$5.86900454856$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	735.361
Dual form			735.2.i.b.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{12} +6.00000 q^{13} +1.00000 q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-4.00000 - 6.92820i) q^{19} +1.00000 q^{20} +(-4.00000 - 6.92820i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.00000 - 5.19615i) q^{26} -1.00000 q^{27} -2.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-2.50000 + 4.33013i) q^{32} -2.00000 q^{34} -1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-4.00000 + 6.92820i) q^{38} +(3.00000 - 5.19615i) q^{39} +(-1.50000 - 2.59808i) q^{40} +6.00000 q^{41} +4.00000 q^{43} +(0.500000 - 0.866025i) q^{45} +(-4.00000 + 6.92820i) q^{46} +(4.00000 + 6.92820i) q^{47} +1.00000 q^{48} +1.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(3.00000 - 5.19615i) q^{52} +(-5.00000 + 8.66025i) q^{53} +(0.500000 + 0.866025i) q^{54} -8.00000 q^{57} +(1.00000 + 1.73205i) q^{58} +(2.00000 - 3.46410i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-1.00000 - 1.73205i) q^{61} -4.00000 q^{62} +7.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(-1.00000 - 1.73205i) q^{68} -8.00000 q^{69} -12.0000 q^{71} +(1.50000 + 2.59808i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(1.00000 - 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} -8.00000 q^{76} -6.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +4.00000 q^{83} +2.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(-1.00000 + 1.73205i) q^{87} +(-3.00000 - 5.19615i) q^{89} -1.00000 q^{90} -8.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(4.00000 - 6.92820i) q^{94} +(4.00000 - 6.92820i) q^{95} +(2.50000 + 4.33013i) q^{96} +18.0000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} + q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 + q^4 + q^5 - 2 * q^6 - 6 * q^8 - q^9	$ 2 q - q^{2} + q^{3} + q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - q^{9} + q^{10} - q^{12} + 12 q^{13} + 2 q^{15} + q^{16} + 2 q^{17} - q^{18} - 8 q^{19} + 2 q^{20} - 8 q^{23} - 3 q^{24} - q^{25} - 6 q^{26} - 2 q^{27} - 4 q^{29} - q^{30} + 4 q^{31} - 5 q^{32} - 4 q^{34} - 2 q^{36} + 2 q^{37} - 8 q^{38} + 6 q^{39} - 3 q^{40} + 12 q^{41} + 8 q^{43} + q^{45} - 8 q^{46} + 8 q^{47} + 2 q^{48} + 2 q^{50} - 2 q^{51} + 6 q^{52} - 10 q^{53} + q^{54} - 16 q^{57} + 2 q^{58} + 4 q^{59} + q^{60} - 2 q^{61} - 8 q^{62} + 14 q^{64} + 6 q^{65} - 4 q^{67} - 2 q^{68} - 16 q^{69} - 24 q^{71} + 3 q^{72} - 2 q^{73} + 2 q^{74} + q^{75} - 16 q^{76} - 12 q^{78} - 8 q^{79} - q^{80} - q^{81} - 6 q^{82} + 8 q^{83} + 4 q^{85} - 4 q^{86} - 2 q^{87} - 6 q^{89} - 2 q^{90} - 16 q^{92} - 4 q^{93} + 8 q^{94} + 8 q^{95} + 5 q^{96} + 36 q^{97}+O(q^{100}) $ 2 * q - q^2 + q^3 + q^4 + q^5 - 2 * q^6 - 6 * q^8 - q^9 + q^10 - q^12 + 12 * q^13 + 2 * q^15 + q^16 + 2 * q^17 - q^18 - 8 * q^19 + 2 * q^20 - 8 * q^23 - 3 * q^24 - q^25 - 6 * q^26 - 2 * q^27 - 4 * q^29 - q^30 + 4 * q^31 - 5 * q^32 - 4 * q^34 - 2 * q^36 + 2 * q^37 - 8 * q^38 + 6 * q^39 - 3 * q^40 + 12 * q^41 + 8 * q^43 + q^45 - 8 * q^46 + 8 * q^47 + 2 * q^48 + 2 * q^50 - 2 * q^51 + 6 * q^52 - 10 * q^53 + q^54 - 16 * q^57 + 2 * q^58 + 4 * q^59 + q^60 - 2 * q^61 - 8 * q^62 + 14 * q^64 + 6 * q^65 - 4 * q^67 - 2 * q^68 - 16 * q^69 - 24 * q^71 + 3 * q^72 - 2 * q^73 + 2 * q^74 + q^75 - 16 * q^76 - 12 * q^78 - 8 * q^79 - q^80 - q^81 - 6 * q^82 + 8 * q^83 + 4 * q^85 - 4 * q^86 - 2 * q^87 - 6 * q^89 - 2 * q^90 - 16 * q^92 - 4 * q^93 + 8 * q^94 + 8 * q^95 + 5 * q^96 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	−3.00000			−1.06066
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	6.00000			1.66410			0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000			1.66410			0.832050	+	0.554700i	$0.187167\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.114708	−	0.993399i	$-0.536593\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$		0			0
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−3.00000	−	5.19615i	−0.588348	−	1.01905i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$		0			0
$34$	−2.00000			−0.342997
$35$		0			0
$36$	−1.00000			−0.166667
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	−4.00000	+	6.92820i	−0.648886	+	1.12390i
$39$	3.00000	−	5.19615i	0.480384	−	0.832050i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	−4.00000	+	6.92820i	−0.589768	+	1.02151i
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$	1.00000			0.141421
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	3.00000	−	5.19615i	0.416025	−	0.720577i
$53$	−5.00000	+	8.66025i	−0.686803	+	1.18958i	0.286064	+	0.958211i	$0.407653\pi$
$53$	−5.00000	+	8.66025i	−0.686803	+	1.18958i	−0.972867	+	0.231367i	$0.925680\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$		0			0
$57$	−8.00000			−1.05963
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	7.00000			0.875000
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$	−8.00000			−0.963087
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−8.00000			−0.917663
$77$		0			0
$78$	−6.00000			−0.679366
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$	−1.00000	+	1.73205i	−0.107211	+	0.185695i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	−8.00000			−0.834058
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$	4.00000	−	6.92820i	0.412568	−	0.714590i
$95$	4.00000	−	6.92820i	0.410391	−	0.710819i
$96$	2.50000	+	4.33013i	0.255155	+	0.441942i
$97$	18.0000			1.82762			0.913812	−	0.406138i	$-0.133125\pi$
$97$	18.0000			1.82762			0.913812	+	0.406138i	$0.133125\pi$
$98$		0			0
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$	−1.00000	+	1.73205i	−0.0990148	+	0.171499i
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	−18.0000			−1.76505
$105$		0			0
$106$	10.0000			0.971286
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	−0.00790932	−	0.999969i	$-0.502518\pi$
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	0.869953	−	0.493135i	$-0.164149\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	4.00000	+	6.92820i	0.374634	+	0.648886i
$115$	4.00000	−	6.92820i	0.373002	−	0.646058i
$116$	−1.00000	+	1.73205i	−0.0928477	+	0.160817i
$117$	−3.00000	−	5.19615i	−0.277350	−	0.480384i
$118$	−4.00000			−0.368230
$119$		0			0
$120$	−3.00000			−0.273861
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−1.00000	+	1.73205i	−0.0905357	+	0.156813i
$123$	3.00000	−	5.19615i	0.270501	−	0.468521i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$	3.00000	−	5.19615i	0.263117	−	0.455733i
$131$	10.0000	+	17.3205i	0.873704	+	1.51330i	0.858137	+	0.513421i	$0.171622\pi$
$131$	10.0000	+	17.3205i	0.873704	+	1.51330i	0.0155672	+	0.999879i	$0.495045\pi$
$132$		0			0
$133$		0			0
$134$	4.00000			0.345547
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	5.00000	−	8.66025i	0.427179	−	0.739895i	−0.569442	−	0.822031i	$-0.692841\pi$
$137$	5.00000	−	8.66025i	0.427179	−	0.739895i	0.996621	+	0.0821359i	$0.0261741\pi$
$138$	4.00000	+	6.92820i	0.340503	+	0.589768i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	8.00000			0.673722
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$		0			0
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−1.00000	−	1.73205i	−0.0830455	−	0.143839i
$146$	2.00000			0.165521
$147$		0			0
$148$	2.00000			0.164399
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	−0.996207	−	0.0870170i	$-0.972267\pi$
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	0.422744	−	0.906249i	$-0.361067\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$	12.0000	+	20.7846i	0.973329	+	1.68585i
$153$	−2.00000			−0.161690
$154$		0			0
$155$	4.00000			0.321288
$156$	−3.00000	−	5.19615i	−0.240192	−	0.416025i
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$	5.00000	+	8.66025i	0.396526	+	0.686803i
$160$	−5.00000			−0.395285
$161$		0			0
$162$	1.00000			0.0785674
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	0.529454	−	0.848339i	$-0.322397\pi$
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	−0.999410	+	0.0343508i	$0.989064\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$		0			0
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	23.0000			1.76923
$170$	−1.00000	−	1.73205i	−0.0766965	−	0.132842i
$171$	−4.00000	+	6.92820i	−0.305888	+	0.529813i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	2.00000			0.151620
$175$		0			0
$176$		0			0
$177$	−2.00000	−	3.46410i	−0.150329	−	0.260378i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.0655145	−	0.997852i	$-0.479131\pi$
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.831408	−	0.555663i	$-0.187536\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	−2.00000			−0.147844
$184$	12.0000	+	20.7846i	0.884652	+	1.53226i
$185$	−1.00000	+	1.73205i	−0.0735215	+	0.127343i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$		0			0
$188$	8.00000			0.583460
$189$		0			0
$190$	−8.00000			−0.580381
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$	3.50000	−	6.06218i	0.252591	−	0.437500i
$193$	−9.00000	+	15.5885i	−0.647834	+	1.12208i	0.335805	+	0.941932i	$0.390992\pi$
$193$	−9.00000	+	15.5885i	−0.647834	+	1.12208i	−0.983639	+	0.180150i	$0.942342\pi$
$194$	−9.00000	−	15.5885i	−0.646162	−	1.11919i
$195$	6.00000			0.429669
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$	1.50000	−	2.59808i	0.106066	−	0.183712i
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$	10.0000			0.703598
$203$		0			0
$204$	−2.00000			−0.140028
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$	−4.00000	+	6.92820i	−0.278019	+	0.481543i
$208$	3.00000	+	5.19615i	0.208013	+	0.360288i
$209$		0			0
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	5.00000	+	8.66025i	0.343401	+	0.594789i
$213$	−6.00000	+	10.3923i	−0.411113	+	0.712069i
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	2.00000	+	3.46410i	0.136399	+	0.236250i
$216$	3.00000			0.204124
$217$		0			0
$218$	−18.0000			−1.21911
$219$	1.00000	+	1.73205i	0.0675737	+	0.117041i
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$	−1.00000	−	1.73205i	−0.0671156	−	0.116248i
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	−3.00000	−	5.19615i	−0.199557	−	0.345643i
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$	−4.00000	+	6.92820i	−0.264906	+	0.458831i
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$	6.00000			0.393919
$233$	9.00000	+	15.5885i	0.589610	+	1.02123i	0.994283	+	0.106773i	$0.0340517\pi$
$233$	9.00000	+	15.5885i	0.589610	+	1.02123i	−0.404674	+	0.914461i	$0.632615\pi$
$234$	−3.00000	+	5.19615i	−0.196116	+	0.339683i
$235$	−4.00000	+	6.92820i	−0.260931	+	0.451946i
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$	−8.00000			−0.519656
$238$		0			0
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−3.00000	+	5.19615i	−0.193247	+	0.334714i	−0.946324	−	0.323218i	$-0.895235\pi$
$241$	−3.00000	+	5.19615i	−0.193247	+	0.334714i	0.753077	+	0.657932i	$0.228569\pi$
$242$	5.50000	−	9.52628i	0.353553	−	0.612372i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	−6.00000			−0.382546
$247$	−24.0000	−	41.5692i	−1.52708	−	2.64499i
$248$	−6.00000	+	10.3923i	−0.381000	+	0.659912i
$249$	2.00000	−	3.46410i	0.126745	−	0.219529i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$		0			0
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$	1.00000	−	1.73205i	0.0626224	−	0.108465i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$	−4.00000			−0.249029
$259$		0			0
$260$	6.00000			0.372104
$261$	1.00000	+	1.73205i	0.0618984	+	0.107211i
$262$	10.0000	−	17.3205i	0.617802	−	1.07006i
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	−0.999970	−	0.00771799i	$-0.997543\pi$
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	0.506669	+	0.862141i	$0.330877\pi$
$264$		0			0
$265$	−10.0000			−0.614295
$266$		0			0
$267$	−6.00000			−0.367194
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	−0.569789	−	0.821791i	$-0.692975\pi$
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	0.996586	+	0.0825561i	$0.0263084\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	0.988692	−	0.149963i	$-0.0479155\pi$
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	−0.624218	+	0.781251i	$0.714582\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	−10.0000			−0.604122
$275$		0			0
$276$	−4.00000	+	6.92820i	−0.240772	+	0.417029i
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	−0.995997	−	0.0893846i	$-0.971510\pi$
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	0.575408	+	0.817867i	$0.304843\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	−4.00000	−	6.92820i	−0.238197	−	0.412568i
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$	−4.00000	−	6.92820i	−0.236940	−	0.410391i
$286$		0			0
$287$		0			0
$288$	5.00000			0.294628
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−1.00000	+	1.73205i	−0.0587220	+	0.101710i
$291$	9.00000	−	15.5885i	0.527589	−	0.913812i
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$		0			0
$295$	4.00000			0.232889
$296$	−3.00000	−	5.19615i	−0.174371	−	0.302020i
$297$		0			0
$298$	−7.00000	+	12.1244i	−0.405499	+	0.702345i
$299$	−24.0000	−	41.5692i	−1.38796	−	2.40401i
$300$	1.00000			0.0577350
$301$		0			0
$302$	8.00000			0.460348
$303$	5.00000	+	8.66025i	0.287242	+	0.497519i
$304$	4.00000	−	6.92820i	0.229416	−	0.397360i
$305$	1.00000	−	1.73205i	0.0572598	−	0.0991769i
$306$	1.00000	+	1.73205i	0.0571662	+	0.0990148i
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$	−9.00000	+	15.5885i	−0.509525	+	0.882523i
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	0.689412	−	0.724370i	$-0.257869\pi$
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	−0.972028	+	0.234863i	$0.924536\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	−8.00000			−0.450035
$317$	−1.00000	−	1.73205i	−0.0561656	−	0.0972817i	0.836576	−	0.547852i	$-0.184554\pi$
$317$	−1.00000	−	1.73205i	−0.0561656	−	0.0972817i	−0.892741	+	0.450570i	$0.851221\pi$
$318$	5.00000	−	8.66025i	0.280386	−	0.485643i
$319$		0			0
$320$	3.50000	+	6.06218i	0.195656	+	0.338886i
$321$	12.0000			0.669775
$322$		0			0
$323$	−16.0000			−0.890264
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−3.00000	+	5.19615i	−0.166410	+	0.288231i
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$	−9.00000	−	15.5885i	−0.497701	−	0.862044i
$328$	−18.0000			−0.993884
$329$		0			0
$330$		0			0
$331$	6.00000	+	10.3923i	0.329790	+	0.571213i	0.982470	−	0.186421i	$-0.0596888\pi$
$331$	6.00000	+	10.3923i	0.329790	+	0.571213i	−0.652680	+	0.757634i	$0.726355\pi$
$332$	2.00000	−	3.46410i	0.109764	−	0.190117i
$333$	1.00000	−	1.73205i	0.0547997	−	0.0949158i
$334$	4.00000	+	6.92820i	0.218870	+	0.379094i
$335$	−4.00000			−0.218543
$336$		0			0
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	−11.5000	−	19.9186i	−0.625518	−	1.08343i
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$	1.00000	−	1.73205i	0.0542326	−	0.0939336i
$341$		0			0
$342$	8.00000			0.432590
$343$		0			0
$344$	−12.0000			−0.646997
$345$	−4.00000	−	6.92820i	−0.215353	−	0.373002i
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	10.0000	−	17.3205i	0.536828	−	0.929814i	−0.462244	−	0.886753i	$-0.652956\pi$
$347$	10.0000	−	17.3205i	0.536828	−	0.929814i	0.999072	−	0.0430610i	$-0.0137110\pi$
$348$	1.00000	+	1.73205i	0.0536056	+	0.0928477i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	−6.00000			−0.320256
$352$		0			0
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$	−2.00000	+	3.46410i	−0.106299	+	0.184115i
$355$	−6.00000	−	10.3923i	−0.318447	−	0.551566i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−24.0000			−1.26844
$359$	18.0000	+	31.1769i	0.950004	+	1.64545i	0.745409	+	0.666608i	$0.232254\pi$
$359$	18.0000	+	31.1769i	0.950004	+	1.64545i	0.204595	+	0.978847i	$0.434412\pi$
$360$	−1.50000	+	2.59808i	−0.0790569	+	0.136931i
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$	11.0000			0.577350
$364$		0			0
$365$	−2.00000			−0.104685
$366$	1.00000	+	1.73205i	0.0522708	+	0.0905357i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	4.00000	−	6.92820i	0.208514	−	0.361158i
$369$	−3.00000	−	5.19615i	−0.156174	−	0.270501i
$370$	2.00000			0.103975
$371$		0			0
$372$	−4.00000			−0.207390
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	−12.0000	−	20.7846i	−0.618853	−	1.07188i
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$	−4.00000	−	6.92820i	−0.205196	−	0.355409i
$381$	4.00000	−	6.92820i	0.204926	−	0.354943i
$382$	−2.00000	+	3.46410i	−0.102329	+	0.177239i
$383$	−16.0000	−	27.7128i	−0.817562	−	1.41606i	−0.907474	−	0.420109i	$-0.861992\pi$
$383$	−16.0000	−	27.7128i	−0.817562	−	1.41606i	0.0899119	−	0.995950i	$-0.471341\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	18.0000			0.916176
$387$	−2.00000	−	3.46410i	−0.101666	−	0.176090i
$388$	9.00000	−	15.5885i	0.456906	−	0.791384i
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$	−3.00000	−	5.19615i	−0.151911	−	0.263117i
$391$	−16.0000			−0.809155
$392$		0			0
$393$	20.0000			1.00887
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$	4.00000	−	6.92820i	0.201262	−	0.348596i
$396$		0			0
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	−0.998125	−	0.0612128i	$-0.980503\pi$
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	0.446051	−	0.895008i	$-0.352830\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$	2.00000	−	3.46410i	0.0997509	−	0.172774i
$403$	12.0000	−	20.7846i	0.597763	−	1.03536i
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$		0			0
$408$	3.00000	+	5.19615i	0.148522	+	0.257248i
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	0.454759	+	0.890614i	$0.349725\pi$
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	−0.998674	+	0.0514740i	$0.983608\pi$
$410$	3.00000	−	5.19615i	0.148159	−	0.256620i
$411$	−5.00000	−	8.66025i	−0.246632	−	0.427179i
$412$	8.00000			0.394132
$413$		0			0
$414$	8.00000			0.393179
$415$	2.00000	+	3.46410i	0.0981761	+	0.170046i
$416$	−15.0000	+	25.9808i	−0.735436	+	1.27381i
$417$		0			0
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$	10.0000	+	17.3205i	0.486792	+	0.843149i
$423$	4.00000	−	6.92820i	0.194487	−	0.336861i
$424$	15.0000	−	25.9808i	0.728464	−	1.26174i
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$	12.0000			0.581402
$427$		0			0
$428$	12.0000			0.580042
$429$		0			0
$430$	2.00000	−	3.46410i	0.0964486	−	0.167054i
$431$	−14.0000	+	24.2487i	−0.674356	+	1.16802i	0.302300	+	0.953213i	$0.402245\pi$
$431$	−14.0000	+	24.2487i	−0.674356	+	1.16802i	−0.976657	+	0.214807i	$0.931088\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$	−2.00000			−0.0958927
$436$	−9.00000	−	15.5885i	−0.431022	−	0.746552i
$437$	−32.0000	+	55.4256i	−1.53077	+	2.65137i
$438$	1.00000	−	1.73205i	0.0477818	−	0.0827606i
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$		0			0
$442$	−12.0000			−0.570782
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$	1.00000	−	1.73205i	0.0474579	−	0.0821995i
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$	−12.0000	−	20.7846i	−0.568216	−	0.984180i
$447$	−14.0000			−0.662177
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	−0.500000	−	0.866025i	−0.0235702	−	0.0408248i
$451$		0			0
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$	4.00000	+	6.92820i	0.187936	+	0.325515i
$454$	4.00000			0.187729
$455$		0			0
$456$	24.0000			1.12390
$457$	−9.00000	−	15.5885i	−0.421002	−	0.729197i	0.575036	−	0.818128i	$-0.304988\pi$
$457$	−9.00000	−	15.5885i	−0.421002	−	0.729197i	−0.996038	+	0.0889312i	$0.971655\pi$
$458$	11.0000	−	19.0526i	0.513996	−	0.890268i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	−4.00000	−	6.92820i	−0.186501	−	0.323029i
$461$	2.00000			0.0931493			0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000			0.0931493			0.0465746	+	0.998915i	$0.485169\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	−1.00000	−	1.73205i	−0.0464238	−	0.0804084i
$465$	2.00000	−	3.46410i	0.0927478	−	0.160644i
$466$	9.00000	−	15.5885i	0.416917	−	0.722121i
$467$	14.0000	+	24.2487i	0.647843	+	1.12210i	0.983637	+	0.180161i	$0.0576619\pi$
$467$	14.0000	+	24.2487i	0.647843	+	1.12210i	−0.335794	+	0.941935i	$0.609005\pi$
$468$	−6.00000			−0.277350
$469$		0			0
$470$	8.00000			0.369012
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$		0			0
$474$	4.00000	+	6.92820i	0.183726	+	0.318223i
$475$	8.00000			0.367065
$476$		0			0
$477$	10.0000			0.457869
$478$	2.00000	+	3.46410i	0.0914779	+	0.158444i
$479$	16.0000	−	27.7128i	0.731059	−	1.26623i	−0.225372	−	0.974273i	$-0.572360\pi$
$479$	16.0000	−	27.7128i	0.731059	−	1.26623i	0.956431	−	0.291958i	$-0.0943068\pi$
$480$	−2.50000	+	4.33013i	−0.114109	+	0.197642i
$481$	6.00000	+	10.3923i	0.273576	+	0.473848i
$482$	6.00000			0.273293
$483$		0			0
$484$	11.0000			0.500000
$485$	9.00000	+	15.5885i	0.408669	+	0.707835i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	3.00000	+	5.19615i	0.135804	+	0.235219i
$489$	−12.0000			−0.542659
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	−3.00000	−	5.19615i	−0.135250	−	0.234261i
$493$	−2.00000	+	3.46410i	−0.0900755	+	0.156015i
$494$	−24.0000	+	41.5692i	−1.07981	+	1.87029i
$495$		0			0
$496$	4.00000			0.179605
$497$		0			0
$498$	−4.00000			−0.179244
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	0.550572	−	0.834788i	$-0.314410\pi$
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	−0.998233	+	0.0594153i	$0.981076\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−4.00000	+	6.92820i	−0.178707	+	0.309529i
$502$	−6.00000	−	10.3923i	−0.267793	−	0.463831i
$503$	8.00000			0.356702			0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000			0.356702			0.178351	+	0.983967i	$0.442924\pi$
$504$		0			0
$505$	−10.0000			−0.444994
$506$		0			0
$507$	11.5000	−	19.9186i	0.510733	−	0.884615i
$508$	4.00000	−	6.92820i	0.177471	−	0.307389i
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	0.843012	−	0.537895i	$-0.180780\pi$
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	−0.887336	+	0.461123i	$0.847447\pi$
$510$	−2.00000			−0.0885615
$511$		0			0
$512$	−11.0000			−0.486136
$513$	4.00000	+	6.92820i	0.176604	+	0.305888i
$514$	−3.00000	+	5.19615i	−0.132324	+	0.229192i
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$	−2.00000	−	3.46410i	−0.0880451	−	0.152499i
$517$		0			0
$518$		0			0
$519$	6.00000			0.263371
$520$	−9.00000	−	15.5885i	−0.394676	−	0.683599i
$521$	5.00000	−	8.66025i	0.219054	−	0.379413i	−0.735465	−	0.677563i	$-0.763036\pi$
$521$	5.00000	−	8.66025i	0.219054	−	0.379413i	0.954519	+	0.298150i	$0.0963696\pi$
$522$	1.00000	−	1.73205i	0.0437688	−	0.0758098i
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$	20.0000			0.873704
$525$		0			0
$526$	16.0000			0.697633
$527$	−4.00000	−	6.92820i	−0.174243	−	0.301797i
$528$		0			0
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	5.00000	+	8.66025i	0.217186	+	0.376177i
$531$	−4.00000			−0.173585
$532$		0			0
$533$	36.0000			1.55933
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$	−12.0000	−	20.7846i	−0.517838	−	0.896922i
$538$	−14.0000			−0.603583
$539$		0			0
$540$	−1.00000			−0.0430331
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	0.992036	−	0.125952i	$-0.0401986\pi$
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	−0.605096	+	0.796152i	$0.706865\pi$
$542$	6.00000	−	10.3923i	0.257722	−	0.446388i
$543$	1.00000	−	1.73205i	0.0429141	−	0.0743294i
$544$	5.00000	+	8.66025i	0.214373	+	0.371305i
$545$	18.0000			0.771035
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−5.00000	−	8.66025i	−0.213589	−	0.369948i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$	8.00000	+	13.8564i	0.340811	+	0.590303i
$552$	24.0000			1.02151
$553$		0			0
$554$	14.0000			0.594803
$555$	1.00000	+	1.73205i	0.0424476	+	0.0735215i
$556$		0			0
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	−0.886433	−	0.462856i	$-0.846825\pi$
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	0.844062	+	0.536246i	$0.180158\pi$
$558$	2.00000	+	3.46410i	0.0846668	+	0.146647i
$559$	24.0000			1.01509
$560$		0			0
$561$		0			0
$562$	−9.00000	−	15.5885i	−0.379642	−	0.657559i
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$	4.00000	−	6.92820i	0.168430	−	0.291730i
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$	4.00000			0.168133
$567$		0			0
$568$	36.0000			1.51053
$569$	−21.0000	−	36.3731i	−0.880366	−	1.52484i	−0.850935	−	0.525271i	$-0.823964\pi$
$569$	−21.0000	−	36.3731i	−0.880366	−	1.52484i	−0.0294311	−	0.999567i	$-0.509370\pi$
$570$	−4.00000	+	6.92820i	−0.167542	+	0.290191i
$571$	18.0000	−	31.1769i	0.753277	−	1.30471i	−0.192950	−	0.981209i	$-0.561806\pi$
$571$	18.0000	−	31.1769i	0.753277	−	1.30471i	0.946227	−	0.323505i	$-0.104861\pi$
$572$		0			0
$573$	−4.00000			−0.167102
$574$		0			0
$575$	8.00000			0.333623
$576$	−3.50000	−	6.06218i	−0.145833	−	0.252591i
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	−0.886090	−	0.463513i	$-0.846589\pi$
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	0.844459	+	0.535620i	$0.179922\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$	9.00000	+	15.5885i	0.374027	+	0.647834i
$580$	−2.00000			−0.0830455
$581$		0			0
$582$	−18.0000			−0.746124
$583$		0			0
$584$	3.00000	−	5.19615i	0.124141	−	0.215018i
$585$	3.00000	−	5.19615i	0.124035	−	0.214834i
$586$	7.00000	+	12.1244i	0.289167	+	0.500853i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	−32.0000			−1.31854
$590$	−2.00000	−	3.46410i	−0.0823387	−	0.142615i
$591$	9.00000	−	15.5885i	0.370211	−	0.641223i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	−15.0000	−	25.9808i	−0.615976	−	1.06690i	−0.990212	−	0.139569i	$-0.955428\pi$
$593$	−15.0000	−	25.9808i	−0.615976	−	1.06690i	0.374236	−	0.927333i	$-0.377905\pi$
$594$		0			0
$595$		0			0
$596$	−14.0000			−0.573462
$597$	2.00000	+	3.46410i	0.0818546	+	0.141776i
$598$	−24.0000	+	41.5692i	−0.981433	+	1.69989i
$599$	2.00000	−	3.46410i	0.0817178	−	0.141539i	−0.822270	−	0.569097i	$-0.807293\pi$
$599$	2.00000	−	3.46410i	0.0817178	−	0.141539i	0.903988	+	0.427558i	$0.140626\pi$
$600$	−1.50000	−	2.59808i	−0.0612372	−	0.106066i
$601$	−18.0000			−0.734235			−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000			−0.734235			−0.367118	+	0.930175i	$0.619655\pi$
$602$		0			0
$603$	4.00000			0.162893
$604$	4.00000	+	6.92820i	0.162758	+	0.281905i
$605$	−5.50000	+	9.52628i	−0.223607	+	0.387298i
$606$	5.00000	−	8.66025i	0.203111	−	0.351799i
$607$	4.00000	+	6.92820i	0.162355	+	0.281207i	0.935713	−	0.352763i	$-0.114758\pi$
$607$	4.00000	+	6.92820i	0.162355	+	0.281207i	−0.773358	+	0.633970i	$0.781424\pi$
$608$	40.0000			1.62221
$609$		0			0
$610$	−2.00000			−0.0809776
$611$	24.0000	+	41.5692i	0.970936	+	1.68171i
$612$	−1.00000	+	1.73205i	−0.0404226	+	0.0700140i
$613$	9.00000	−	15.5885i	0.363507	−	0.629612i	−0.625029	−	0.780602i	$-0.714913\pi$
$613$	9.00000	−	15.5885i	0.363507	−	0.629612i	0.988535	+	0.150990i	$0.0482461\pi$
$614$	6.00000	+	10.3923i	0.242140	+	0.419399i
$615$	6.00000			0.241943
$616$		0			0
$617$	30.0000			1.20775			0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000			1.20775			0.603877	+	0.797077i	$0.293622\pi$
$618$	−4.00000	−	6.92820i	−0.160904	−	0.278693i
$619$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$619$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$620$	2.00000	−	3.46410i	0.0803219	−	0.139122i
$621$	4.00000	+	6.92820i	0.160514	+	0.278019i
$622$	−24.0000			−0.962312
$623$		0			0
$624$	6.00000			0.240192
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−5.00000	+	8.66025i	−0.199840	+	0.346133i
$627$		0			0
$628$	7.00000	+	12.1244i	0.279330	+	0.483814i
$629$	4.00000			0.159490
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$	12.0000	+	20.7846i	0.477334	+	0.826767i
$633$	−10.0000	+	17.3205i	−0.397464	+	0.688428i
$634$	−1.00000	+	1.73205i	−0.0397151	+	0.0687885i
$635$	4.00000	+	6.92820i	0.158735	+	0.274937i
$636$	10.0000			0.396526
$637$		0			0
$638$		0			0
$639$	6.00000	+	10.3923i	0.237356	+	0.411113i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	−0.800678	−	0.599095i	$-0.795527\pi$
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	0.919171	+	0.393860i	$0.128860\pi$
$642$	−6.00000	−	10.3923i	−0.236801	−	0.410152i
$643$	−28.0000			−1.10421			−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000			−1.10421			−0.552106	+	0.833774i	$0.686176\pi$
$644$		0			0
$645$	4.00000			0.157500
$646$	8.00000	+	13.8564i	0.314756	+	0.545173i
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	−0.527710	−	0.849425i	$-0.676949\pi$
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	0.999478	+	0.0322975i	$0.0102824\pi$
$648$	1.50000	−	2.59808i	0.0589256	−	0.102062i
$649$		0			0
$650$	6.00000			0.235339
$651$		0			0
$652$	−12.0000			−0.469956
$653$	11.0000	+	19.0526i	0.430463	+	0.745584i	0.996913	−	0.0785119i	$-0.0250169\pi$
$653$	11.0000	+	19.0526i	0.430463	+	0.745584i	−0.566450	+	0.824096i	$0.691684\pi$
$654$	−9.00000	+	15.5885i	−0.351928	+	0.609557i
$655$	−10.0000	+	17.3205i	−0.390732	+	0.676768i
$656$	3.00000	+	5.19615i	0.117130	+	0.202876i
$657$	2.00000			0.0780274
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	19.0000	−	32.9090i	0.739014	−	1.28001i	−0.213925	−	0.976850i	$-0.568625\pi$
$661$	19.0000	−	32.9090i	0.739014	−	1.28001i	0.952940	−	0.303160i	$-0.0980418\pi$
$662$	6.00000	−	10.3923i	0.233197	−	0.403908i
$663$	−6.00000	−	10.3923i	−0.233021	−	0.403604i
$664$	−12.0000			−0.465690
$665$		0			0
$666$	−2.00000			−0.0774984
$667$	8.00000	+	13.8564i	0.309761	+	0.536522i
$668$	−4.00000	+	6.92820i	−0.154765	+	0.268060i
$669$	12.0000	−	20.7846i	0.463947	−	0.803579i
$670$	2.00000	+	3.46410i	0.0772667	+	0.133830i
$671$		0			0
$672$		0			0
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$	7.00000	+	12.1244i	0.269630	+	0.467013i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	11.5000	−	19.9186i	0.442308	−	0.766099i
$677$	23.0000	+	39.8372i	0.883962	+	1.53107i	0.846899	+	0.531754i	$0.178467\pi$
$677$	23.0000	+	39.8372i	0.883962	+	1.53107i	0.0370628	+	0.999313i	$0.488200\pi$
$678$	−6.00000			−0.230429
$679$		0			0
$680$	−6.00000			−0.230089
$681$	2.00000	+	3.46410i	0.0766402	+	0.132745i
$682$		0			0
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	4.00000	+	6.92820i	0.152944	+	0.264906i
$685$	10.0000			0.382080
$686$		0			0
$687$	22.0000			0.839352
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−30.0000	+	51.9615i	−1.14291	+	1.97958i
$690$	−4.00000	+	6.92820i	−0.152277	+	0.263752i
$691$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−20.0000			−0.759190
$695$		0			0
$696$	3.00000	−	5.19615i	0.113715	−	0.196960i
$697$	6.00000	−	10.3923i	0.227266	−	0.393637i
$698$	7.00000	+	12.1244i	0.264954	+	0.458914i
$699$	18.0000			0.680823
$700$		0			0
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$	3.00000	+	5.19615i	0.113228	+	0.196116i
$703$	8.00000	−	13.8564i	0.301726	−	0.522604i
$704$		0			0
$705$	4.00000	+	6.92820i	0.150649	+	0.260931i
$706$	−18.0000			−0.677439
$707$		0			0
$708$	−4.00000			−0.150329
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	0.999908	−	0.0135434i	$-0.00431112\pi$
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	−0.511683	+	0.859174i	$0.670978\pi$
$710$	−6.00000	+	10.3923i	−0.225176	+	0.390016i
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$	9.00000	+	15.5885i	0.337289	+	0.584202i
$713$	−32.0000			−1.19841
$714$		0			0
$715$		0			0
$716$	−12.0000	−	20.7846i	−0.448461	−	0.776757i
$717$	−2.00000	+	3.46410i	−0.0746914	+	0.129369i
$718$	18.0000	−	31.1769i	0.671754	−	1.16351i
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	0.930923	−	0.365216i	$-0.119005\pi$
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	−0.781748	+	0.623595i	$0.785672\pi$
$720$	1.00000			0.0372678
$721$		0			0
$722$	45.0000			1.67473
$723$	3.00000	+	5.19615i	0.111571	+	0.193247i
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$	1.00000	−	1.73205i	0.0371391	−	0.0643268i
$726$	−5.50000	−	9.52628i	−0.204124	−	0.353553i
$727$	−16.0000			−0.593407			−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000			−0.593407			−0.296704	+	0.954970i	$0.595887\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	1.00000	+	1.73205i	0.0370117	+	0.0641061i
$731$	4.00000	−	6.92820i	0.147945	−	0.256249i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	13.0000	+	22.5167i	0.480166	+	0.831672i	0.999741	−	0.0227529i	$-0.00724310\pi$
$733$	13.0000	+	22.5167i	0.480166	+	0.831672i	−0.519575	+	0.854425i	$0.673910\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$	40.0000			1.47442
$737$		0			0
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	−0.989230	−	0.146369i	$-0.953241\pi$
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	0.621374	+	0.783514i	$0.286575\pi$
$740$	1.00000	+	1.73205i	0.0367607	+	0.0636715i
$741$	−48.0000			−1.76332
$742$		0			0
$743$	−48.0000			−1.76095			−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000			−1.76095			−0.880475	+	0.474093i	$0.842776\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$	7.00000	−	12.1244i	0.256460	−	0.444202i
$746$	5.00000	−	8.66025i	0.183063	−	0.317074i
$747$	−2.00000	−	3.46410i	−0.0731762	−	0.126745i
$748$		0			0
$749$		0			0
$750$	1.00000			0.0365148
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	0.783769	−	0.621052i	$-0.213294\pi$
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	−0.929731	+	0.368238i	$0.879961\pi$
$752$	−4.00000	+	6.92820i	−0.145865	+	0.252646i
$753$	6.00000	−	10.3923i	0.218652	−	0.378717i
$754$	6.00000	+	10.3923i	0.218507	+	0.378465i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	2.00000	+	3.46410i	0.0726433	+	0.125822i
$759$		0			0
$760$	−12.0000	+	20.7846i	−0.435286	+	0.753937i
$761$	−27.0000	−	46.7654i	−0.978749	−	1.69524i	−0.666962	−	0.745091i	$-0.732406\pi$
$761$	−27.0000	−	46.7654i	−0.978749	−	1.69524i	−0.311787	−	0.950152i	$-0.600927\pi$
$762$	−8.00000			−0.289809
$763$		0			0
$764$	−4.00000			−0.144715
$765$	−1.00000	−	1.73205i	−0.0361551	−	0.0626224i
$766$	−16.0000	+	27.7128i	−0.578103	+	1.00130i
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$	−8.50000	−	14.7224i	−0.306717	−	0.531250i
$769$	−26.0000			−0.937584			−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000			−0.937584			−0.468792	+	0.883309i	$0.655311\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$	9.00000	+	15.5885i	0.323917	+	0.561041i
$773$	15.0000	−	25.9808i	0.539513	−	0.934463i	−0.459418	−	0.888220i	$-0.651942\pi$
$773$	15.0000	−	25.9808i	0.539513	−	0.934463i	0.998930	−	0.0462427i	$-0.0147248\pi$
$774$	−2.00000	+	3.46410i	−0.0718885	+	0.124515i
$775$	2.00000	+	3.46410i	0.0718421	+	0.124434i
$776$	−54.0000			−1.93849
$777$		0			0
$778$	30.0000			1.07555
$779$	−24.0000	−	41.5692i	−0.859889	−	1.48937i
$780$	3.00000	−	5.19615i	0.107417	−	0.186052i
$781$		0			0
$782$	8.00000	+	13.8564i	0.286079	+	0.495504i
$783$	2.00000			0.0714742
$784$		0			0
$785$	−14.0000			−0.499681
$786$	−10.0000	−	17.3205i	−0.356688	−	0.617802i
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$	8.00000	+	13.8564i	0.284808	+	0.493301i
$790$	−8.00000			−0.284627
$791$		0			0
$792$		0			0
$793$	−6.00000	−	10.3923i	−0.213066	−	0.369042i
$794$	−11.0000	+	19.0526i	−0.390375	+	0.676150i
$795$	−5.00000	+	8.66025i	−0.177332	+	0.307148i
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	−54.0000			−1.91278			−0.956389	−	0.292096i	$-0.905647\pi$
$797$	−54.0000			−1.91278			−0.956389	+	0.292096i	$0.905647\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$	−2.50000	−	4.33013i	−0.0883883	−	0.153093i
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$		0			0
$804$	4.00000			0.141069
$805$		0			0
$806$	−24.0000			−0.845364
$807$	−7.00000	−	12.1244i	−0.246412	−	0.426798i
$808$	15.0000	−	25.9808i	0.527698	−	0.914000i
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	−0.979739	−	0.200279i	$-0.935815\pi$
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	0.663316	+	0.748340i	$0.269149\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	12.0000			0.420858
$814$		0			0
$815$	6.00000	−	10.3923i	0.210171	−	0.364027i
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$	−16.0000	−	27.7128i	−0.559769	−	0.969549i
$818$	22.0000			0.769212
$819$		0			0
$820$	6.00000			0.209529
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	0.955636	+	0.294549i	$0.0951694\pi$
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	−0.222731	+	0.974880i	$0.571497\pi$
$822$	−5.00000	+	8.66025i	−0.174395	+	0.302061i
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	−12.0000	−	20.7846i	−0.418040	−	0.724066i
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	4.00000	+	6.92820i	0.139010	+	0.240772i
$829$	−21.0000	+	36.3731i	−0.729360	+	1.26329i	0.227794	+	0.973709i	$0.426849\pi$
$829$	−21.0000	+	36.3731i	−0.729360	+	1.26329i	−0.957154	+	0.289579i	$0.906485\pi$
$830$	2.00000	−	3.46410i	0.0694210	−	0.120241i
$831$	7.00000	+	12.1244i	0.242827	+	0.420589i
$832$	42.0000			1.45609
$833$		0			0
$834$		0			0
$835$	−4.00000	−	6.92820i	−0.138426	−	0.239760i
$836$		0			0
$837$	−2.00000	+	3.46410i	−0.0691301	+	0.119737i
$838$	−6.00000	−	10.3923i	−0.207267	−	0.358996i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	13.0000	+	22.5167i	0.448010	+	0.775975i
$843$	9.00000	−	15.5885i	0.309976	−	0.536895i
$844$	−10.0000	+	17.3205i	−0.344214	+	0.596196i
$845$	11.5000	+	19.9186i	0.395612	+	0.685220i
$846$	−8.00000			−0.275046
$847$		0			0
$848$	−10.0000			−0.343401
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$	1.00000	−	1.73205i	0.0342997	−	0.0594089i
$851$	8.00000	−	13.8564i	0.274236	−	0.474991i
$852$	6.00000	+	10.3923i	0.205557	+	0.356034i
$853$	30.0000			1.02718			0.513590	−	0.858036i	$-0.328315\pi$
$853$	30.0000			1.02718			0.513590	+	0.858036i	$0.328315\pi$
$854$		0			0
$855$	−8.00000			−0.273594
$856$	−18.0000	−	31.1769i	−0.615227	−	1.06561i
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	−0.974249	−	0.225475i	$-0.927607\pi$
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	0.291858	−	0.956462i	$-0.405727\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$	28.0000			0.953684
$863$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$863$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$	−3.00000	+	5.19615i	−0.102003	+	0.176674i
$866$	−1.00000	−	1.73205i	−0.0339814	−	0.0588575i
$867$	13.0000			0.441503
$868$		0			0
$869$		0			0
$870$	1.00000	+	1.73205i	0.0339032	+	0.0587220i
$871$	−12.0000	+	20.7846i	−0.406604	+	0.704260i
$872$	−27.0000	+	46.7654i	−0.914335	+	1.58368i
$873$	−9.00000	−	15.5885i	−0.304604	−	0.527589i
$874$	64.0000			2.16483
$875$		0			0
$876$	2.00000			0.0675737
$877$	29.0000	+	50.2295i	0.979260	+	1.69613i	0.665092	+	0.746762i	$0.268392\pi$
$877$	29.0000	+	50.2295i	0.979260	+	1.69613i	0.314169	+	0.949367i	$0.398274\pi$
$878$	14.0000	−	24.2487i	0.472477	−	0.818354i
$879$	−7.00000	+	12.1244i	−0.236104	+	0.408944i
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$	2.00000	−	3.46410i	0.0672293	−	0.116445i
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	8.00000	+	13.8564i	0.268614	+	0.465253i	0.968504	−	0.248998i	$-0.0801012\pi$
$887$	8.00000	+	13.8564i	0.268614	+	0.465253i	−0.699890	+	0.714250i	$0.746768\pi$
$888$	−6.00000			−0.201347
$889$		0			0
$890$	−6.00000			−0.201120
$891$		0			0
$892$	12.0000	−	20.7846i	0.401790	−	0.695920i
$893$	32.0000	−	55.4256i	1.07084	−	1.85475i
$894$	7.00000	+	12.1244i	0.234115	+	0.405499i
$895$	24.0000			0.802232
$896$		0			0
$897$	−48.0000			−1.60267
$898$	15.0000	+	25.9808i	0.500556	+	0.866989i
$899$	−4.00000	+	6.92820i	−0.133407	+	0.231069i
$900$	0.500000	−	0.866025i	0.0166667	−	0.0288675i
$901$	10.0000	+	17.3205i	0.333148	+	0.577030i
$902$		0			0
$903$		0			0
$904$	−18.0000			−0.598671
$905$	1.00000	+	1.73205i	0.0332411	+	0.0575753i
$906$	4.00000	−	6.92820i	0.132891	−	0.230174i
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	−0.999195	−	0.0401089i	$-0.987230\pi$
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	0.534333	+	0.845274i	$0.320563\pi$
$908$	2.00000	+	3.46410i	0.0663723	+	0.114960i
$909$	10.0000			0.331679
$910$		0			0
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$	−4.00000	−	6.92820i	−0.132453	−	0.229416i
$913$		0			0
$914$	−9.00000	+	15.5885i	−0.297694	+	0.515620i
$915$	−1.00000	−	1.73205i	−0.0330590	−	0.0572598i
$916$	22.0000			0.726900
$917$		0			0
$918$	2.00000			0.0660098
$919$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$919$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$920$	−12.0000	+	20.7846i	−0.395628	+	0.685248i
$921$	−6.00000	+	10.3923i	−0.197707	+	0.342438i
$922$	−1.00000	−	1.73205i	−0.0329332	−	0.0570421i
$923$	−72.0000			−2.36991
$924$		0			0
$925$	−2.00000			−0.0657596
$926$	12.0000	+	20.7846i	0.394344	+	0.683025i
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$	5.00000	−	8.66025i	0.164133	−	0.284287i
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$	−4.00000			−0.131165
$931$		0			0
$932$	18.0000			0.589610
$933$	−12.0000	−	20.7846i	−0.392862	−	0.680458i
$934$	14.0000	−	24.2487i	0.458094	−	0.793442i
$935$		0			0
$936$	9.00000	+	15.5885i	0.294174	+	0.509525i
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		0			0
$939$	−10.0000			−0.326338
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	−0.974609	−	0.223912i	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$	7.00000	−	12.1244i	0.228072	−	0.395033i
$943$	−24.0000	−	41.5692i	−0.781548	−	1.35368i
$944$	4.00000			0.130189
$945$		0			0
$946$		0			0
$947$	−10.0000	−	17.3205i	−0.324956	−	0.562841i	0.656547	−	0.754285i	$-0.272016\pi$
$947$	−10.0000	−	17.3205i	−0.324956	−	0.562841i	−0.981504	+	0.191444i	$0.938683\pi$
$948$	−4.00000	+	6.92820i	−0.129914	+	0.225018i
$949$	−6.00000	+	10.3923i	−0.194768	+	0.337348i
$950$	−4.00000	−	6.92820i	−0.129777	−	0.224781i
$951$	−2.00000			−0.0648544
$952$		0			0
$953$	−2.00000			−0.0647864			−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000			−0.0647864			−0.0323932	+	0.999475i	$0.510313\pi$
$954$	−5.00000	−	8.66025i	−0.161881	−	0.280386i
$955$	2.00000	−	3.46410i	0.0647185	−	0.112096i
$956$	−2.00000	+	3.46410i	−0.0646846	+	0.112037i
$957$		0			0
$958$	−32.0000			−1.03387
$959$		0			0
$960$	7.00000			0.225924
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	6.00000	−	10.3923i	0.193448	−	0.335061i
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	3.00000	+	5.19615i	0.0966235	+	0.167357i
$965$	−18.0000			−0.579441
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	−16.5000	−	28.5788i	−0.530330	−	0.918559i
$969$	−8.00000	+	13.8564i	−0.256997	+	0.445132i
$970$	9.00000	−	15.5885i	0.288973	−	0.500515i
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	0.980677	−	0.195633i	$-0.0626762\pi$
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	−0.659762	+	0.751475i	$0.729343\pi$
$972$	1.00000			0.0320750
$973$		0			0
$974$	−16.0000			−0.512673
$975$	3.00000	+	5.19615i	0.0960769	+	0.166410i
$976$	1.00000	−	1.73205i	0.0320092	−	0.0554416i
$977$	5.00000	−	8.66025i	0.159964	−	0.277066i	−0.774891	−	0.632094i	$-0.782195\pi$
$977$	5.00000	−	8.66025i	0.159964	−	0.277066i	0.934856	+	0.355028i	$0.115529\pi$
$978$	6.00000	+	10.3923i	0.191859	+	0.332309i
$979$		0			0
$980$		0			0
$981$	−18.0000			−0.574696
$982$		0			0
$983$	−8.00000	+	13.8564i	−0.255160	+	0.441951i	−0.964939	−	0.262474i	$-0.915462\pi$
$983$	−8.00000	+	13.8564i	−0.255160	+	0.441951i	0.709779	+	0.704425i	$0.248795\pi$
$984$	−9.00000	+	15.5885i	−0.286910	+	0.496942i
$985$	9.00000	+	15.5885i	0.286764	+	0.496690i
$986$	4.00000			0.127386
$987$		0			0
$988$	−48.0000			−1.52708
$989$	−16.0000	−	27.7128i	−0.508770	−	0.881216i
$990$		0			0
$991$	12.0000	−	20.7846i	0.381193	−	0.660245i	−0.610040	−	0.792370i	$-0.708847\pi$
$991$	12.0000	−	20.7846i	0.381193	−	0.660245i	0.991233	+	0.132125i	$0.0421802\pi$
$992$	10.0000	+	17.3205i	0.317500	+	0.549927i
$993$	12.0000			0.380808
$994$		0			0
$995$	−4.00000			−0.126809
$996$	−2.00000	−	3.46410i	−0.0633724	−	0.109764i
$997$	1.00000	−	1.73205i	0.0316703	−	0.0548546i	−0.849756	−	0.527176i	$-0.823251\pi$
$997$	1.00000	−	1.73205i	0.0316703	−	0.0548546i	0.881426	+	0.472322i	$0.156584\pi$
$998$	−10.0000	+	17.3205i	−0.316544	+	0.548271i
$999$	−1.00000	−	1.73205i	−0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.i.b.361.1		2
7.2	even	3	inner	735.2.i.b.226.1		2
7.3	odd	6		105.2.a.a.1.1	✓	1
7.4	even	3		735.2.a.f.1.1		1
7.5	odd	6		735.2.i.a.226.1		2
7.6	odd	2		735.2.i.a.361.1		2
21.11	odd	6		2205.2.a.b.1.1		1
21.17	even	6		315.2.a.a.1.1		1
28.3	even	6		1680.2.a.f.1.1		1
35.3	even	12		525.2.d.b.274.1		2
35.4	even	6		3675.2.a.f.1.1		1
35.17	even	12		525.2.d.b.274.2		2
35.24	odd	6		525.2.a.a.1.1		1
56.3	even	6		6720.2.a.bk.1.1		1
56.45	odd	6		6720.2.a.p.1.1		1
84.59	odd	6		5040.2.a.d.1.1		1
105.17	odd	12		1575.2.d.b.1324.1		2
105.38	odd	12		1575.2.d.b.1324.2		2
105.59	even	6		1575.2.a.h.1.1		1
140.59	even	6		8400.2.a.co.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.a.a.1.1	✓	1	7.3	odd	6
315.2.a.a.1.1		1	21.17	even	6
525.2.a.a.1.1		1	35.24	odd	6
525.2.d.b.274.1		2	35.3	even	12
525.2.d.b.274.2		2	35.17	even	12
735.2.a.f.1.1		1	7.4	even	3
735.2.i.a.226.1		2	7.5	odd	6
735.2.i.a.361.1		2	7.6	odd	2
735.2.i.b.226.1		2	7.2	even	3	inner
735.2.i.b.361.1		2	1.1	even	1	trivial
1575.2.a.h.1.1		1	105.59	even	6
1575.2.d.b.1324.1		2	105.17	odd	12
1575.2.d.b.1324.2		2	105.38	odd	12
1680.2.a.f.1.1		1	28.3	even	6
2205.2.a.b.1.1		1	21.11	odd	6
3675.2.a.f.1.1		1	35.4	even	6
5040.2.a.d.1.1		1	84.59	odd	6
6720.2.a.p.1.1		1	56.45	odd	6
6720.2.a.bk.1.1		1	56.3	even	6
8400.2.a.co.1.1		1	140.59	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{12} +6.00000 q^{13} +1.00000 q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-4.00000 - 6.92820i) q^{19} +1.00000 q^{20} +(-4.00000 - 6.92820i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.00000 - 5.19615i) q^{26} -1.00000 q^{27} -2.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-2.50000 + 4.33013i) q^{32} -2.00000 q^{34} -1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-4.00000 + 6.92820i) q^{38} +(3.00000 - 5.19615i) q^{39} +(-1.50000 - 2.59808i) q^{40} +6.00000 q^{41} +4.00000 q^{43} +(0.500000 - 0.866025i) q^{45} +(-4.00000 + 6.92820i) q^{46} +(4.00000 + 6.92820i) q^{47} +1.00000 q^{48} +1.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(3.00000 - 5.19615i) q^{52} +(-5.00000 + 8.66025i) q^{53} +(0.500000 + 0.866025i) q^{54} -8.00000 q^{57} +(1.00000 + 1.73205i) q^{58} +(2.00000 - 3.46410i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-1.00000 - 1.73205i) q^{61} -4.00000 q^{62} +7.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(-1.00000 - 1.73205i) q^{68} -8.00000 q^{69} -12.0000 q^{71} +(1.50000 + 2.59808i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(1.00000 - 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} -8.00000 q^{76} -6.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +4.00000 q^{83} +2.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(-1.00000 + 1.73205i) q^{87} +(-3.00000 - 5.19615i) q^{89} -1.00000 q^{90} -8.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(4.00000 - 6.92820i) q^{94} +(4.00000 - 6.92820i) q^{95} +(2.50000 + 4.33013i) q^{96} +18.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} + q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 + q^4 + q^5 - 2 * q^6 - 6 * q^8 - q^9	\( 2 q - q^{2} + q^{3} + q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - q^{9} + q^{10} - q^{12} + 12 q^{13} + 2 q^{15} + q^{16} + 2 q^{17} - q^{18} - 8 q^{19} + 2 q^{20} - 8 q^{23} - 3 q^{24} - q^{25} - 6 q^{26} - 2 q^{27} - 4 q^{29} - q^{30} + 4 q^{31} - 5 q^{32} - 4 q^{34} - 2 q^{36} + 2 q^{37} - 8 q^{38} + 6 q^{39} - 3 q^{40} + 12 q^{41} + 8 q^{43} + q^{45} - 8 q^{46} + 8 q^{47} + 2 q^{48} + 2 q^{50} - 2 q^{51} + 6 q^{52} - 10 q^{53} + q^{54} - 16 q^{57} + 2 q^{58} + 4 q^{59} + q^{60} - 2 q^{61} - 8 q^{62} + 14 q^{64} + 6 q^{65} - 4 q^{67} - 2 q^{68} - 16 q^{69} - 24 q^{71} + 3 q^{72} - 2 q^{73} + 2 q^{74} + q^{75} - 16 q^{76} - 12 q^{78} - 8 q^{79} - q^{80} - q^{81} - 6 q^{82} + 8 q^{83} + 4 q^{85} - 4 q^{86} - 2 q^{87} - 6 q^{89} - 2 q^{90} - 16 q^{92} - 4 q^{93} + 8 q^{94} + 8 q^{95} + 5 q^{96} + 36 q^{97}+O(q^{100}) \) 2 * q - q^2 + q^3 + q^4 + q^5 - 2 * q^6 - 6 * q^8 - q^9 + q^10 - q^12 + 12 * q^13 + 2 * q^15 + q^16 + 2 * q^17 - q^18 - 8 * q^19 + 2 * q^20 - 8 * q^23 - 3 * q^24 - q^25 - 6 * q^26 - 2 * q^27 - 4 * q^29 - q^30 + 4 * q^31 - 5 * q^32 - 4 * q^34 - 2 * q^36 + 2 * q^37 - 8 * q^38 + 6 * q^39 - 3 * q^40 + 12 * q^41 + 8 * q^43 + q^45 - 8 * q^46 + 8 * q^47 + 2 * q^48 + 2 * q^50 - 2 * q^51 + 6 * q^52 - 10 * q^53 + q^54 - 16 * q^57 + 2 * q^58 + 4 * q^59 + q^60 - 2 * q^61 - 8 * q^62 + 14 * q^64 + 6 * q^65 - 4 * q^67 - 2 * q^68 - 16 * q^69 - 24 * q^71 + 3 * q^72 - 2 * q^73 + 2 * q^74 + q^75 - 16 * q^76 - 12 * q^78 - 8 * q^79 - q^80 - q^81 - 6 * q^82 + 8 * q^83 + 4 * q^85 - 4 * q^86 - 2 * q^87 - 6 * q^89 - 2 * q^90 - 16 * q^92 - 4 * q^93 + 8 * q^94 + 8 * q^95 + 5 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more