LMFDB - Embedded newform 1170.2.bs.a.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(361,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1170.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bs (of order $6$, degree $2$, 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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.361
Dual form			1170.2.bs.a.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-1.50000 - 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-1.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-2.59808 + 1.50000i) q^{11} +(3.50000 + 0.866025i) q^{13} +1.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.50000 + 2.59808i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(1.50000 - 2.59808i) q^{22} +(-1.73205 - 3.00000i) q^{23} -1.00000 q^{25} +(-3.46410 + 1.00000i) q^{26} +(-1.50000 + 0.866025i) q^{28} +(3.46410 + 6.00000i) q^{29} -10.3923i q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.866025 + 1.50000i) q^{35} +(7.50000 - 4.33013i) q^{37} -5.19615 q^{38} +1.00000 q^{40} +(5.19615 - 3.00000i) q^{41} +(5.00000 - 8.66025i) q^{43} +3.00000i q^{44} +(3.00000 + 1.73205i) q^{46} -9.00000i q^{47} +(-2.00000 - 3.46410i) q^{49} +(0.866025 - 0.500000i) q^{50} +(2.50000 - 2.59808i) q^{52} -12.1244 q^{53} +(1.50000 + 2.59808i) q^{55} +(0.866025 - 1.50000i) q^{56} +(-6.00000 - 3.46410i) q^{58} +(-10.3923 - 6.00000i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(5.19615 + 9.00000i) q^{62} -1.00000 q^{64} +(0.866025 - 3.50000i) q^{65} -1.73205i q^{70} +(5.19615 + 3.00000i) q^{71} -6.92820i q^{73} +(-4.33013 + 7.50000i) q^{74} +(4.50000 - 2.59808i) q^{76} +5.19615 q^{77} +10.0000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-3.00000 + 5.19615i) q^{82} -12.0000i q^{83} +10.0000i q^{86} +(-1.50000 - 2.59808i) q^{88} +(12.9904 - 7.50000i) q^{89} +(-4.50000 - 4.33013i) q^{91} -3.46410 q^{92} +(4.50000 + 7.79423i) q^{94} +(2.59808 - 4.50000i) q^{95} +(-6.00000 - 3.46410i) q^{97} +(3.46410 + 2.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 6 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 - 6 * q^7	$ 4 q + 2 q^{4} - 6 q^{7} + 2 q^{10} + 14 q^{13} - 2 q^{16} + 18 q^{19} + 6 q^{22} - 4 q^{25} - 6 q^{28} + 30 q^{37} + 4 q^{40} + 20 q^{43} + 12 q^{46} - 8 q^{49} + 10 q^{52} + 6 q^{55} - 24 q^{58} - 20 q^{61} - 4 q^{64} + 18 q^{76} + 40 q^{79} - 12 q^{82} - 6 q^{88} - 18 q^{91} + 18 q^{94} - 24 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 6 * q^7 + 2 * q^10 + 14 * q^13 - 2 * q^16 + 18 * q^19 + 6 * q^22 - 4 * q^25 - 6 * q^28 + 30 * q^37 + 4 * q^40 + 20 * q^43 + 12 * q^46 - 8 * q^49 + 10 * q^52 + 6 * q^55 - 24 * q^58 - 20 * q^61 - 4 * q^64 + 18 * q^76 + 40 * q^79 - 12 * q^82 - 6 * q^88 - 18 * q^91 + 18 * q^94 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−1.50000	−	0.866025i	−0.566947	−	0.327327i	0.188982	−	0.981981i	$-0.439481\pi$
$7$	−1.50000	−	0.866025i	−0.566947	−	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	−0.837616	−	0.546259i	$-0.816051\pi$
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$12$		0			0
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$	1.73205			0.462910
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	4.50000	+	2.59808i	1.03237	+	0.596040i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	4.50000	+	2.59808i	1.03237	+	0.596040i	0.114708	+	0.993399i	$0.463407\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$		0			0
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	−1.73205	−	3.00000i	−0.361158	−	0.625543i	0.626994	−	0.779024i	$-0.284285\pi$
$23$	−1.73205	−	3.00000i	−0.361158	−	0.625543i	−0.988152	+	0.153481i	$0.950952\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−3.46410	+	1.00000i	−0.679366	+	0.196116i
$27$		0			0
$28$	−1.50000	+	0.866025i	−0.283473	+	0.163663i
$29$	3.46410	+	6.00000i	0.643268	+	1.11417i	0.984699	+	0.174265i	$0.0557550\pi$
$29$	3.46410	+	6.00000i	0.643268	+	1.11417i	−0.341431	+	0.939907i	$0.610912\pi$
$30$		0			0
$31$		−	10.3923i		−	1.86651i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$		−	10.3923i		−	1.86651i	0.359211	−	0.933257i	$-0.383046\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		0			0
$35$	−0.866025	+	1.50000i	−0.146385	+	0.253546i
$36$		0			0
$37$	7.50000	−	4.33013i	1.23299	−	0.711868i	0.265340	−	0.964155i	$-0.414516\pi$
$37$	7.50000	−	4.33013i	1.23299	−	0.711868i	0.967653	+	0.252286i	$0.0811825\pi$
$38$	−5.19615			−0.842927
$39$		0			0
$40$	1.00000			0.158114
$41$	5.19615	−	3.00000i	0.811503	−	0.468521i	−0.0359748	−	0.999353i	$-0.511454\pi$
$41$	5.19615	−	3.00000i	0.811503	−	0.468521i	0.847477	+	0.530831i	$0.178120\pi$
$42$		0			0
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	−0.179069	−	0.983836i	$-0.557309\pi$
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	0.941562	−	0.336840i	$-0.109358\pi$
$44$			3.00000i			0.452267i
$45$		0			0
$46$	3.00000	+	1.73205i	0.442326	+	0.255377i
$47$		−	9.00000i		−	1.31278i	−0.754420	−	0.656392i	$-0.772082\pi$
$47$		−	9.00000i		−	1.31278i	0.754420	−	0.656392i	$-0.227918\pi$
$48$		0			0
$49$	−2.00000	−	3.46410i	−0.285714	−	0.494872i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		0			0
$52$	2.50000	−	2.59808i	0.346688	−	0.360288i
$53$	−12.1244			−1.66541			−0.832704	−	0.553718i	$-0.813209\pi$
$53$	−12.1244			−1.66541			−0.832704	+	0.553718i	$0.813209\pi$
$54$		0			0
$55$	1.50000	+	2.59808i	0.202260	+	0.350325i
$56$	0.866025	−	1.50000i	0.115728	−	0.200446i
$57$		0			0
$58$	−6.00000	−	3.46410i	−0.787839	−	0.454859i
$59$	−10.3923	−	6.00000i	−1.35296	−	0.781133i	−0.364299	−	0.931282i	$-0.618692\pi$
$59$	−10.3923	−	6.00000i	−1.35296	−	0.781133i	−0.988663	+	0.150148i	$0.952025\pi$
$60$		0			0
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$	5.19615	+	9.00000i	0.659912	+	1.14300i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.866025	−	3.50000i	0.107417	−	0.434122i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$		0			0
$70$		−	1.73205i		−	0.207020i
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	0.775571	−	0.631260i	$-0.217462\pi$
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	−0.158901	+	0.987294i	$0.550795\pi$
$72$		0			0
$73$		−	6.92820i		−	0.810885i	−0.914121	−	0.405442i	$-0.867117\pi$
$73$		−	6.92820i		−	0.810885i	0.914121	−	0.405442i	$-0.132883\pi$
$74$	−4.33013	+	7.50000i	−0.503367	+	0.871857i
$75$		0			0
$76$	4.50000	−	2.59808i	0.516185	−	0.298020i
$77$	5.19615			0.592157
$78$		0			0
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$		0			0
$82$	−3.00000	+	5.19615i	−0.331295	+	0.573819i
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$		0			0
$85$		0			0
$86$			10.0000i			1.07833i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	12.9904	−	7.50000i	1.37698	−	0.794998i	0.385183	−	0.922840i	$-0.374138\pi$
$89$	12.9904	−	7.50000i	1.37698	−	0.794998i	0.991795	+	0.127842i	$0.0408050\pi$
$90$		0			0
$91$	−4.50000	−	4.33013i	−0.471728	−	0.453921i
$92$	−3.46410			−0.361158
$93$		0			0
$94$	4.50000	+	7.79423i	0.464140	+	0.803913i
$95$	2.59808	−	4.50000i	0.266557	−	0.461690i
$96$		0			0
$97$	−6.00000	−	3.46410i	−0.609208	−	0.351726i	0.163448	−	0.986552i	$-0.447739\pi$
$97$	−6.00000	−	3.46410i	−0.609208	−	0.351726i	−0.772655	+	0.634826i	$0.781072\pi$
$98$	3.46410	+	2.00000i	0.349927	+	0.202031i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	6.92820	+	12.0000i	0.689382	+	1.19404i	0.972038	+	0.234823i	$0.0754512\pi$
$101$	6.92820	+	12.0000i	0.689382	+	1.19404i	−0.282656	+	0.959221i	$0.591216\pi$
$102$		0			0
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	−0.866025	+	3.50000i	−0.0849208	+	0.343203i
$105$		0			0
$106$	10.5000	−	6.06218i	1.01985	−	0.588811i
$107$	−1.73205	−	3.00000i	−0.167444	−	0.290021i	0.770077	−	0.637951i	$-0.220218\pi$
$107$	−1.73205	−	3.00000i	−0.167444	−	0.290021i	−0.937520	+	0.347930i	$0.886885\pi$
$108$		0			0
$109$			10.3923i			0.995402i	0.867349	+	0.497701i	$0.165822\pi$
$109$			10.3923i			0.995402i	−0.867349	+	0.497701i	$0.834178\pi$
$110$	−2.59808	−	1.50000i	−0.247717	−	0.143019i
$111$		0			0
$112$			1.73205i			0.163663i
$113$	6.92820	−	12.0000i	0.651751	−	1.12887i	−0.330947	−	0.943649i	$-0.607368\pi$
$113$	6.92820	−	12.0000i	0.651751	−	1.12887i	0.982698	−	0.185216i	$-0.0592984\pi$
$114$		0			0
$115$	−3.00000	+	1.73205i	−0.279751	+	0.161515i
$116$	6.92820			0.643268
$117$		0			0
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$		−	10.0000i		−	0.905357i
$123$		0			0
$124$	−9.00000	−	5.19615i	−0.808224	−	0.466628i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	5.50000	+	9.52628i	0.488046	+	0.845321i	0.999905	−	0.0137486i	$-0.00437646\pi$
$127$	5.50000	+	9.52628i	0.488046	+	0.845321i	−0.511859	+	0.859069i	$0.671043\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	1.00000	+	3.46410i	0.0877058	+	0.303822i
$131$	12.1244			1.05931			0.529655	−	0.848213i	$-0.322321\pi$
$131$	12.1244			1.05931			0.529655	+	0.848213i	$0.322321\pi$
$132$		0			0
$133$	−4.50000	−	7.79423i	−0.390199	−	0.675845i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.873247	−	0.487278i	$-0.162010\pi$
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.0146279	+	0.999893i	$0.495344\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$	0.866025	+	1.50000i	0.0731925	+	0.126773i
$141$		0			0
$142$	−6.00000			−0.503509
$143$	−10.3923	+	3.00000i	−0.869048	+	0.250873i
$144$		0			0
$145$	6.00000	−	3.46410i	0.498273	−	0.287678i
$146$	3.46410	+	6.00000i	0.286691	+	0.496564i
$147$		0			0
$148$		−	8.66025i		−	0.711868i
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	0.697507	−	0.716578i	$-0.254293\pi$
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	−0.271821	+	0.962348i	$0.587626\pi$
$150$		0			0
$151$		−	10.3923i		−	0.845714i	−0.906196	−	0.422857i	$-0.861027\pi$
$151$		−	10.3923i		−	0.845714i	0.906196	−	0.422857i	$-0.138973\pi$
$152$	−2.59808	+	4.50000i	−0.210732	+	0.364998i
$153$		0			0
$154$	−4.50000	+	2.59808i	−0.362620	+	0.209359i
$155$	−10.3923			−0.834730
$156$		0			0
$157$	11.0000			0.877896			0.438948	−	0.898513i	$-0.355351\pi$
$157$	11.0000			0.877896			0.438948	+	0.898513i	$0.355351\pi$
$158$	−8.66025	+	5.00000i	−0.688973	+	0.397779i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$			6.00000i			0.472866i
$162$		0			0
$163$	−6.00000	−	3.46410i	−0.469956	−	0.271329i	0.246265	−	0.969202i	$-0.420797\pi$
$163$	−6.00000	−	3.46410i	−0.469956	−	0.271329i	−0.716221	+	0.697873i	$0.754130\pi$
$164$		−	6.00000i		−	0.468521i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	−2.59808	+	1.50000i	−0.201045	+	0.116073i	−0.597143	−	0.802135i	$-0.703697\pi$
$167$	−2.59808	+	1.50000i	−0.201045	+	0.116073i	0.396098	+	0.918208i	$0.370364\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$		0			0
$171$		0			0
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	2.59808	−	4.50000i	0.197528	−	0.342129i	−0.750198	−	0.661213i	$-0.770042\pi$
$173$	2.59808	−	4.50000i	0.197528	−	0.342129i	0.947726	+	0.319084i	$0.103375\pi$
$174$		0			0
$175$	1.50000	+	0.866025i	0.113389	+	0.0654654i
$176$	2.59808	+	1.50000i	0.195837	+	0.113067i
$177$		0			0
$178$	−7.50000	+	12.9904i	−0.562149	+	0.973670i
$179$	1.73205	+	3.00000i	0.129460	+	0.224231i	0.923467	−	0.383677i	$-0.125342\pi$
$179$	1.73205	+	3.00000i	0.129460	+	0.224231i	−0.794008	+	0.607908i	$0.792009\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	6.06218	+	1.50000i	0.449359	+	0.111187i
$183$		0			0
$184$	3.00000	−	1.73205i	0.221163	−	0.127688i
$185$	−4.33013	−	7.50000i	−0.318357	−	0.551411i
$186$		0			0
$187$		0			0
$188$	−7.79423	−	4.50000i	−0.568453	−	0.328196i
$189$		0			0
$190$			5.19615i			0.376969i
$191$	8.66025	−	15.0000i	0.626634	−	1.08536i	−0.361588	−	0.932338i	$-0.617765\pi$
$191$	8.66025	−	15.0000i	0.626634	−	1.08536i	0.988222	−	0.153024i	$-0.0489012\pi$
$192$		0			0
$193$	−6.00000	+	3.46410i	−0.431889	+	0.249351i	−0.700151	−	0.713995i	$-0.746884\pi$
$193$	−6.00000	+	3.46410i	−0.431889	+	0.249351i	0.268262	+	0.963346i	$0.413551\pi$
$194$	6.92820			0.497416
$195$		0			0
$196$	−4.00000			−0.285714
$197$	−2.59808	+	1.50000i	−0.185105	+	0.106871i	−0.589689	−	0.807630i	$-0.700750\pi$
$197$	−2.59808	+	1.50000i	−0.185105	+	0.106871i	0.404584	+	0.914501i	$0.367416\pi$
$198$		0			0
$199$	−11.0000	+	19.0526i	−0.779769	+	1.35060i	0.152305	+	0.988334i	$0.451330\pi$
$199$	−11.0000	+	19.0526i	−0.779769	+	1.35060i	−0.932075	+	0.362267i	$0.882003\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	−12.0000	−	6.92820i	−0.844317	−	0.487467i
$203$		−	12.0000i		−	0.842235i
$204$		0			0
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	0.866025	−	0.500000i	0.0603388	−	0.0348367i
$207$		0			0
$208$	−1.00000	−	3.46410i	−0.0693375	−	0.240192i
$209$	−15.5885			−1.07828
$210$		0			0
$211$	5.50000	+	9.52628i	0.378636	+	0.655816i	0.990864	−	0.134865i	$-0.0430600\pi$
$211$	5.50000	+	9.52628i	0.378636	+	0.655816i	−0.612228	+	0.790681i	$0.709727\pi$
$212$	−6.06218	+	10.5000i	−0.416352	+	0.721143i
$213$		0			0
$214$	3.00000	+	1.73205i	0.205076	+	0.118401i
$215$	−8.66025	−	5.00000i	−0.590624	−	0.340997i
$216$		0			0
$217$	−9.00000	+	15.5885i	−0.610960	+	1.05821i
$218$	−5.19615	−	9.00000i	−0.351928	−	0.609557i
$219$		0			0
$220$	3.00000			0.202260
$221$		0			0
$222$		0			0
$223$	−10.5000	+	6.06218i	−0.703132	+	0.405953i	−0.808513	−	0.588478i	$-0.799727\pi$
$223$	−10.5000	+	6.06218i	−0.703132	+	0.405953i	0.105381	+	0.994432i	$0.466394\pi$
$224$	−0.866025	−	1.50000i	−0.0578638	−	0.100223i
$225$		0			0
$226$			13.8564i			0.921714i
$227$	20.7846	+	12.0000i	1.37952	+	0.796468i	0.992102	−	0.125435i	$-0.0400326\pi$
$227$	20.7846	+	12.0000i	1.37952	+	0.796468i	0.387421	+	0.921903i	$0.373366\pi$
$228$		0			0
$229$		−	3.46410i		−	0.228914i	−0.993428	−	0.114457i	$-0.963487\pi$
$229$		−	3.46410i		−	0.228914i	0.993428	−	0.114457i	$-0.0365129\pi$
$230$	1.73205	−	3.00000i	0.114208	−	0.197814i
$231$		0			0
$232$	−6.00000	+	3.46410i	−0.393919	+	0.227429i
$233$	−3.46410			−0.226941			−0.113470	−	0.993541i	$-0.536197\pi$
$233$	−3.46410			−0.226941			−0.113470	+	0.993541i	$0.536197\pi$
$234$		0			0
$235$	−9.00000			−0.587095
$236$	−10.3923	+	6.00000i	−0.676481	+	0.390567i
$237$		0			0
$238$		0			0
$239$			6.00000i			0.388108i	0.980991	+	0.194054i	$0.0621637\pi$
$239$			6.00000i			0.388108i	−0.980991	+	0.194054i	$0.937836\pi$
$240$		0			0
$241$	−25.5000	−	14.7224i	−1.64260	−	0.948355i	−0.979905	−	0.199465i	$-0.936079\pi$
$241$	−25.5000	−	14.7224i	−1.64260	−	0.948355i	−0.662695	−	0.748890i	$-0.730587\pi$
$242$		−	2.00000i		−	0.128565i
$243$		0			0
$244$	5.00000	+	8.66025i	0.320092	+	0.554416i
$245$	−3.46410	+	2.00000i	−0.221313	+	0.127775i
$246$		0			0
$247$	13.5000	+	12.9904i	0.858984	+	0.826558i
$248$	10.3923			0.659912
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−2.59808	+	4.50000i	−0.163989	+	0.284037i	−0.936296	−	0.351212i	$-0.885770\pi$
$251$	−2.59808	+	4.50000i	−0.163989	+	0.284037i	0.772307	+	0.635250i	$0.219103\pi$
$252$		0			0
$253$	9.00000	+	5.19615i	0.565825	+	0.326679i
$254$	−9.52628	−	5.50000i	−0.597732	−	0.345101i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.92820	+	12.0000i	0.432169	+	0.748539i	0.997060	−	0.0766265i	$-0.0244149\pi$
$257$	6.92820	+	12.0000i	0.432169	+	0.748539i	−0.564890	+	0.825166i	$0.691082\pi$
$258$		0			0
$259$	−15.0000			−0.932055
$260$	−2.59808	−	2.50000i	−0.161126	−	0.155043i
$261$		0			0
$262$	−10.5000	+	6.06218i	−0.648692	+	0.374523i
$263$	−7.79423	−	13.5000i	−0.480613	−	0.832446i	0.519140	−	0.854689i	$-0.326252\pi$
$263$	−7.79423	−	13.5000i	−0.480613	−	0.832446i	−0.999753	+	0.0222436i	$0.992919\pi$
$264$		0			0
$265$			12.1244i			0.744793i
$266$	7.79423	+	4.50000i	0.477895	+	0.275913i
$267$		0			0
$268$		0			0
$269$	3.46410	−	6.00000i	0.211210	−	0.365826i	−0.740883	−	0.671634i	$-0.765593\pi$
$269$	3.46410	−	6.00000i	0.211210	−	0.365826i	0.952093	+	0.305807i	$0.0989263\pi$
$270$		0			0
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$		0			0
$273$		0			0
$274$	−12.0000			−0.724947
$275$	2.59808	−	1.50000i	0.156670	−	0.0904534i
$276$		0			0
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	−0.425684	−	0.904872i	$-0.639967\pi$
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	0.996484	−	0.0837823i	$-0.0267000\pi$
$278$		−	5.00000i		−	0.299880i
$279$		0			0
$280$	−1.50000	−	0.866025i	−0.0896421	−	0.0517549i
$281$			18.0000i			1.07379i	0.843649	+	0.536895i	$0.180403\pi$
$281$			18.0000i			1.07379i	−0.843649	+	0.536895i	$0.819597\pi$
$282$		0			0
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$		0			0
$286$	7.50000	−	7.79423i	0.443484	−	0.460882i
$287$	−10.3923			−0.613438
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−3.46410	+	6.00000i	−0.203419	+	0.352332i
$291$		0			0
$292$	−6.00000	−	3.46410i	−0.351123	−	0.202721i
$293$	−28.5788	−	16.5000i	−1.66959	−	0.963940i	−0.967856	−	0.251505i	$-0.919075\pi$
$293$	−28.5788	−	16.5000i	−1.66959	−	0.963940i	−0.701737	−	0.712436i	$-0.747592\pi$
$294$		0			0
$295$	−6.00000	+	10.3923i	−0.349334	+	0.605063i
$296$	4.33013	+	7.50000i	0.251684	+	0.435929i
$297$		0			0
$298$	−6.00000			−0.347571
$299$	−3.46410	−	12.0000i	−0.200334	−	0.693978i
$300$		0			0
$301$	−15.0000	+	8.66025i	−0.864586	+	0.499169i
$302$	5.19615	+	9.00000i	0.299005	+	0.517892i
$303$		0			0
$304$		−	5.19615i		−	0.298020i
$305$	8.66025	+	5.00000i	0.495885	+	0.286299i
$306$		0			0
$307$		−	10.3923i		−	0.593120i	−0.955014	−	0.296560i	$-0.904160\pi$
$307$		−	10.3923i		−	0.593120i	0.955014	−	0.296560i	$-0.0958395\pi$
$308$	2.59808	−	4.50000i	0.148039	−	0.256411i
$309$		0			0
$310$	9.00000	−	5.19615i	0.511166	−	0.295122i
$311$	−27.7128			−1.57145			−0.785725	−	0.618576i	$-0.787710\pi$
$311$	−27.7128			−1.57145			−0.785725	+	0.618576i	$0.787710\pi$
$312$		0			0
$313$	−2.00000			−0.113047			−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000			−0.113047			−0.0565233	+	0.998401i	$0.518002\pi$
$314$	−9.52628	+	5.50000i	−0.537599	+	0.310383i
$315$		0			0
$316$	5.00000	−	8.66025i	0.281272	−	0.487177i
$317$			9.00000i			0.505490i	0.967533	+	0.252745i	$0.0813334\pi$
$317$			9.00000i			0.505490i	−0.967533	+	0.252745i	$0.918667\pi$
$318$		0			0
$319$	−18.0000	−	10.3923i	−1.00781	−	0.581857i
$320$			1.00000i			0.0559017i
$321$		0			0
$322$	−3.00000	−	5.19615i	−0.167183	−	0.289570i
$323$		0			0
$324$		0			0
$325$	−3.50000	−	0.866025i	−0.194145	−	0.0480384i
$326$	6.92820			0.383718
$327$		0			0
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	−7.79423	+	13.5000i	−0.429710	+	0.744279i
$330$		0			0
$331$	−15.0000	−	8.66025i	−0.824475	−	0.476011i	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	−15.0000	−	8.66025i	−0.824475	−	0.476011i	−0.851957	+	0.523612i	$0.824584\pi$
$332$	−10.3923	−	6.00000i	−0.570352	−	0.329293i
$333$		0			0
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$		0			0
$336$		0			0
$337$	−26.0000			−1.41631			−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000			−1.41631			−0.708155	+	0.706057i	$0.750472\pi$
$338$	−12.9904	+	0.500000i	−0.706584	+	0.0271964i
$339$		0			0
$340$		0			0
$341$	15.5885	+	27.0000i	0.844162	+	1.46213i
$342$		0			0
$343$			19.0526i			1.02874i
$344$	8.66025	+	5.00000i	0.466930	+	0.269582i
$345$		0			0
$346$			5.19615i			0.279347i
$347$	3.46410	−	6.00000i	0.185963	−	0.322097i	−0.757938	−	0.652327i	$-0.773793\pi$
$347$	3.46410	−	6.00000i	0.185963	−	0.322097i	0.943901	+	0.330230i	$0.107126\pi$
$348$		0			0
$349$	12.0000	−	6.92820i	0.642345	−	0.370858i	−0.143172	−	0.989698i	$-0.545730\pi$
$349$	12.0000	−	6.92820i	0.642345	−	0.370858i	0.785517	+	0.618840i	$0.212397\pi$
$350$	−1.73205			−0.0925820
$351$		0			0
$352$	−3.00000			−0.159901
$353$	−10.3923	+	6.00000i	−0.553127	+	0.319348i	−0.750382	−	0.661004i	$-0.770130\pi$
$353$	−10.3923	+	6.00000i	−0.553127	+	0.319348i	0.197256	+	0.980352i	$0.436797\pi$
$354$		0			0
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$		−	15.0000i		−	0.794998i
$357$		0			0
$358$	−3.00000	−	1.73205i	−0.158555	−	0.0915417i
$359$			6.00000i			0.316668i	0.987386	+	0.158334i	$0.0506123\pi$
$359$			6.00000i			0.316668i	−0.987386	+	0.158334i	$0.949388\pi$
$360$		0			0
$361$	4.00000	+	6.92820i	0.210526	+	0.364642i
$362$	8.66025	−	5.00000i	0.455173	−	0.262794i
$363$		0			0
$364$	−6.00000	+	1.73205i	−0.314485	+	0.0907841i
$365$	−6.92820			−0.362639
$366$		0			0
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	0.995697	−	0.0926670i	$-0.0295392\pi$
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	−0.578101	+	0.815966i	$0.696206\pi$
$368$	−1.73205	+	3.00000i	−0.0902894	+	0.156386i
$369$		0			0
$370$	7.50000	+	4.33013i	0.389906	+	0.225113i
$371$	18.1865	+	10.5000i	0.944198	+	0.545133i
$372$		0			0
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	0.427051	+	0.904227i	$0.359552\pi$
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	−0.996610	+	0.0822766i	$0.973781\pi$
$374$		0			0
$375$		0			0
$376$	9.00000			0.464140
$377$	6.92820	+	24.0000i	0.356821	+	1.23606i
$378$		0			0
$379$	22.5000	−	12.9904i	1.15575	−	0.667271i	0.205466	−	0.978664i	$-0.434129\pi$
$379$	22.5000	−	12.9904i	1.15575	−	0.667271i	0.950281	+	0.311393i	$0.100796\pi$
$380$	−2.59808	−	4.50000i	−0.133278	−	0.230845i
$381$		0			0
$382$			17.3205i			0.886194i
$383$	−31.1769	−	18.0000i	−1.59307	−	0.919757i	−0.992777	−	0.119974i	$-0.961719\pi$
$383$	−31.1769	−	18.0000i	−1.59307	−	0.919757i	−0.600289	−	0.799783i	$-0.704948\pi$
$384$		0			0
$385$		−	5.19615i		−	0.264820i
$386$	3.46410	−	6.00000i	0.176318	−	0.305392i
$387$		0			0
$388$	−6.00000	+	3.46410i	−0.304604	+	0.175863i
$389$	27.7128			1.40510			0.702548	−	0.711637i	$-0.252046\pi$
$389$	27.7128			1.40510			0.702548	+	0.711637i	$0.252046\pi$
$390$		0			0
$391$		0			0
$392$	3.46410	−	2.00000i	0.174964	−	0.101015i
$393$		0			0
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$		−	10.0000i		−	0.503155i
$396$		0			0
$397$	16.5000	+	9.52628i	0.828111	+	0.478110i	0.853206	−	0.521575i	$-0.174655\pi$
$397$	16.5000	+	9.52628i	0.828111	+	0.478110i	−0.0250943	+	0.999685i	$0.507989\pi$
$398$		−	22.0000i		−	1.10276i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	28.5788	−	16.5000i	1.42716	−	0.823971i	0.430263	−	0.902703i	$-0.358421\pi$
$401$	28.5788	−	16.5000i	1.42716	−	0.823971i	0.996896	+	0.0787327i	$0.0250874\pi$
$402$		0			0
$403$	9.00000	−	36.3731i	0.448322	−	1.81187i
$404$	13.8564			0.689382
$405$		0			0
$406$	6.00000	+	10.3923i	0.297775	+	0.515761i
$407$	−12.9904	+	22.5000i	−0.643909	+	1.11528i
$408$		0			0
$409$	1.50000	+	0.866025i	0.0741702	+	0.0428222i	0.536626	−	0.843820i	$-0.319698\pi$
$409$	1.50000	+	0.866025i	0.0741702	+	0.0428222i	−0.462456	+	0.886642i	$0.653032\pi$
$410$	5.19615	+	3.00000i	0.256620	+	0.148159i
$411$		0			0
$412$	−0.500000	+	0.866025i	−0.0246332	+	0.0426660i
$413$	10.3923	+	18.0000i	0.511372	+	0.885722i
$414$		0			0
$415$	−12.0000			−0.589057
$416$	2.59808	+	2.50000i	0.127381	+	0.122573i
$417$		0			0
$418$	13.5000	−	7.79423i	0.660307	−	0.381228i
$419$	−12.1244	−	21.0000i	−0.592314	−	1.02592i	−0.993920	−	0.110105i	$-0.964881\pi$
$419$	−12.1244	−	21.0000i	−0.592314	−	1.02592i	0.401606	−	0.915812i	$-0.368452\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	−9.52628	−	5.50000i	−0.463732	−	0.267736i
$423$		0			0
$424$		−	12.1244i		−	0.588811i
$425$		0			0
$426$		0			0
$427$	15.0000	−	8.66025i	0.725901	−	0.419099i
$428$	−3.46410			−0.167444
$429$		0			0
$430$	10.0000			0.482243
$431$	−10.3923	+	6.00000i	−0.500580	+	0.289010i	−0.728953	−	0.684564i	$-0.759993\pi$
$431$	−10.3923	+	6.00000i	−0.500580	+	0.289010i	0.228373	+	0.973574i	$0.426659\pi$
$432$		0			0
$433$	−2.00000	+	3.46410i	−0.0961139	+	0.166474i	−0.910073	−	0.414448i	$-0.863975\pi$
$433$	−2.00000	+	3.46410i	−0.0961139	+	0.166474i	0.813959	+	0.580922i	$0.197308\pi$
$434$		−	18.0000i		−	0.864028i
$435$		0			0
$436$	9.00000	+	5.19615i	0.431022	+	0.248851i
$437$		−	18.0000i		−	0.861057i
$438$		0			0
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	0.649218	−	0.760602i	$-0.275096\pi$
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	−0.983310	+	0.181938i	$0.941763\pi$
$440$	−2.59808	+	1.50000i	−0.123858	+	0.0715097i
$441$		0			0
$442$		0			0
$443$	−10.3923			−0.493753			−0.246877	−	0.969047i	$-0.579404\pi$
$443$	−10.3923			−0.493753			−0.246877	+	0.969047i	$0.579404\pi$
$444$		0			0
$445$	−7.50000	−	12.9904i	−0.355534	−	0.615803i
$446$	6.06218	−	10.5000i	0.287052	−	0.497189i
$447$		0			0
$448$	1.50000	+	0.866025i	0.0708683	+	0.0409159i
$449$	28.5788	+	16.5000i	1.34872	+	0.778683i	0.988068	−	0.154018i	$-0.0492213\pi$
$449$	28.5788	+	16.5000i	1.34872	+	0.778683i	0.360651	+	0.932701i	$0.382555\pi$
$450$		0			0
$451$	−9.00000	+	15.5885i	−0.423793	+	0.734032i
$452$	−6.92820	−	12.0000i	−0.325875	−	0.564433i
$453$		0			0
$454$	−24.0000			−1.12638
$455$	−4.33013	+	4.50000i	−0.202999	+	0.210963i
$456$		0			0
$457$	33.0000	−	19.0526i	1.54367	−	0.891241i	0.545073	−	0.838389i	$-0.316502\pi$
$457$	33.0000	−	19.0526i	1.54367	−	0.891241i	0.998602	−	0.0528522i	$-0.0168312\pi$
$458$	1.73205	+	3.00000i	0.0809334	+	0.140181i
$459$		0			0
$460$			3.46410i			0.161515i
$461$	10.3923	+	6.00000i	0.484018	+	0.279448i	0.722089	−	0.691800i	$-0.243182\pi$
$461$	10.3923	+	6.00000i	0.484018	+	0.279448i	−0.238071	+	0.971248i	$0.576515\pi$
$462$		0			0
$463$		−	24.2487i		−	1.12693i	−0.826139	−	0.563467i	$-0.809467\pi$
$463$		−	24.2487i		−	1.12693i	0.826139	−	0.563467i	$-0.190533\pi$
$464$	3.46410	−	6.00000i	0.160817	−	0.278543i
$465$		0			0
$466$	3.00000	−	1.73205i	0.138972	−	0.0802357i
$467$	−34.6410			−1.60300			−0.801498	−	0.597998i	$-0.795963\pi$
$467$	−34.6410			−1.60300			−0.801498	+	0.597998i	$0.795963\pi$
$468$		0			0
$469$		0			0
$470$	7.79423	−	4.50000i	0.359521	−	0.207570i
$471$		0			0
$472$	6.00000	−	10.3923i	0.276172	−	0.478345i
$473$			30.0000i			1.37940i
$474$		0			0
$475$	−4.50000	−	2.59808i	−0.206474	−	0.119208i
$476$		0			0
$477$		0			0
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$479$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$480$		0			0
$481$	30.0000	−	8.66025i	1.36788	−	0.394874i
$482$	29.4449			1.34118
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−3.46410	+	6.00000i	−0.157297	+	0.272446i
$486$		0			0
$487$	1.50000	+	0.866025i	0.0679715	+	0.0392434i	0.533601	−	0.845737i	$-0.320839\pi$
$487$	1.50000	+	0.866025i	0.0679715	+	0.0392434i	−0.465629	+	0.884980i	$0.654172\pi$
$488$	−8.66025	−	5.00000i	−0.392031	−	0.226339i
$489$		0			0
$490$	2.00000	−	3.46410i	0.0903508	−	0.156492i
$491$	6.06218	+	10.5000i	0.273582	+	0.473858i	0.969776	−	0.243995i	$-0.0784581\pi$
$491$	6.06218	+	10.5000i	0.273582	+	0.473858i	−0.696194	+	0.717853i	$0.745125\pi$
$492$		0			0
$493$		0			0
$494$	−18.1865	−	4.50000i	−0.818251	−	0.202465i
$495$		0			0
$496$	−9.00000	+	5.19615i	−0.404112	+	0.233314i
$497$	−5.19615	−	9.00000i	−0.233079	−	0.403705i
$498$		0			0
$499$			24.2487i			1.08552i	0.839887	+	0.542761i	$0.182621\pi$
$499$			24.2487i			1.08552i	−0.839887	+	0.542761i	$0.817379\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$		0			0
$502$		−	5.19615i		−	0.231916i
$503$	9.52628	−	16.5000i	0.424756	−	0.735699i	−0.571642	−	0.820503i	$-0.693693\pi$
$503$	9.52628	−	16.5000i	0.424756	−	0.735699i	0.996398	+	0.0848047i	$0.0270266\pi$
$504$		0			0
$505$	12.0000	−	6.92820i	0.533993	−	0.308301i
$506$	−10.3923			−0.461994
$507$		0			0
$508$	11.0000			0.488046
$509$	−5.19615	+	3.00000i	−0.230315	+	0.132973i	−0.610718	−	0.791849i	$-0.709119\pi$
$509$	−5.19615	+	3.00000i	−0.230315	+	0.132973i	0.380402	+	0.924821i	$0.375786\pi$
$510$		0			0
$511$	−6.00000	+	10.3923i	−0.265424	+	0.459728i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−12.0000	−	6.92820i	−0.529297	−	0.305590i
$515$			1.00000i			0.0440653i
$516$		0			0
$517$	13.5000	+	23.3827i	0.593729	+	1.02837i
$518$	12.9904	−	7.50000i	0.570765	−	0.329531i
$519$		0			0
$520$	3.50000	+	0.866025i	0.153485	+	0.0379777i
$521$	−12.1244			−0.531178			−0.265589	−	0.964086i	$-0.585566\pi$
$521$	−12.1244			−0.531178			−0.265589	+	0.964086i	$0.585566\pi$
$522$		0			0
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	0.950958	+	0.309320i	$0.100101\pi$
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	−0.207600	+	0.978214i	$0.566565\pi$
$524$	6.06218	−	10.5000i	0.264827	−	0.458695i
$525$		0			0
$526$	13.5000	+	7.79423i	0.588628	+	0.339845i
$527$		0			0
$528$		0			0
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	−6.06218	−	10.5000i	−0.263324	−	0.456091i
$531$		0			0
$532$	−9.00000			−0.390199
$533$	20.7846	−	6.00000i	0.900281	−	0.259889i
$534$		0			0
$535$	−3.00000	+	1.73205i	−0.129701	+	0.0748831i
$536$		0			0
$537$		0			0
$538$			6.92820i			0.298696i
$539$	10.3923	+	6.00000i	0.447628	+	0.258438i
$540$		0			0
$541$			3.46410i			0.148933i	0.997224	+	0.0744667i	$0.0237254\pi$
$541$			3.46410i			0.148933i	−0.997224	+	0.0744667i	$0.976275\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	10.3923			0.445157
$546$		0			0
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$	10.3923	−	6.00000i	0.443937	−	0.256307i
$549$		0			0
$550$	−1.50000	+	2.59808i	−0.0639602	+	0.110782i
$551$			36.0000i			1.53365i
$552$		0			0
$553$	−15.0000	−	8.66025i	−0.637865	−	0.368271i
$554$			19.0000i			0.807233i
$555$		0			0
$556$	2.50000	+	4.33013i	0.106024	+	0.183638i
$557$	−7.79423	+	4.50000i	−0.330252	+	0.190671i	−0.655953	−	0.754802i	$-0.727733\pi$
$557$	−7.79423	+	4.50000i	−0.330252	+	0.190671i	0.325701	+	0.945473i	$0.394400\pi$
$558$		0			0
$559$	25.0000	−	25.9808i	1.05739	−	1.09887i
$560$	1.73205			0.0731925
$561$		0			0
$562$	−9.00000	−	15.5885i	−0.379642	−	0.657559i
$563$	6.92820	−	12.0000i	0.291989	−	0.505740i	−0.682291	−	0.731081i	$-0.739016\pi$
$563$	6.92820	−	12.0000i	0.291989	−	0.505740i	0.974280	+	0.225341i	$0.0723496\pi$
$564$		0			0
$565$	−12.0000	−	6.92820i	−0.504844	−	0.291472i
$566$	−12.1244	−	7.00000i	−0.509625	−	0.294232i
$567$		0			0
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	9.52628	+	16.5000i	0.399362	+	0.691716i	0.993647	−	0.112539i	$-0.0358982\pi$
$569$	9.52628	+	16.5000i	0.399362	+	0.691716i	−0.594285	+	0.804255i	$0.702565\pi$
$570$		0			0
$571$	−5.00000			−0.209243			−0.104622	−	0.994512i	$-0.533363\pi$
$571$	−5.00000			−0.209243			−0.104622	+	0.994512i	$0.533363\pi$
$572$	−2.59808	+	10.5000i	−0.108631	+	0.439027i
$573$		0			0
$574$	9.00000	−	5.19615i	0.375653	−	0.216883i
$575$	1.73205	+	3.00000i	0.0722315	+	0.125109i
$576$		0			0
$577$			10.3923i			0.432637i	0.976323	+	0.216319i	$0.0694050\pi$
$577$			10.3923i			0.432637i	−0.976323	+	0.216319i	$0.930595\pi$
$578$	−14.7224	−	8.50000i	−0.612372	−	0.353553i
$579$		0			0
$580$		−	6.92820i		−	0.287678i
$581$	−10.3923	+	18.0000i	−0.431145	+	0.746766i
$582$		0			0
$583$	31.5000	−	18.1865i	1.30460	−	0.753209i
$584$	6.92820			0.286691
$585$		0			0
$586$	33.0000			1.36322
$587$	36.3731	−	21.0000i	1.50128	−	0.866763i	0.501278	−	0.865286i	$-0.332863\pi$
$587$	36.3731	−	21.0000i	1.50128	−	0.866763i	0.999999	−	0.00147660i	$-0.000470017\pi$
$588$		0			0
$589$	27.0000	−	46.7654i	1.11252	−	1.92693i
$590$		−	12.0000i		−	0.494032i
$591$		0			0
$592$	−7.50000	−	4.33013i	−0.308248	−	0.177967i
$593$		−	36.0000i		−	1.47834i	−0.673517	−	0.739171i	$-0.735217\pi$
$593$		−	36.0000i		−	1.47834i	0.673517	−	0.739171i	$-0.264783\pi$
$594$		0			0
$595$		0			0
$596$	5.19615	−	3.00000i	0.212843	−	0.122885i
$597$		0			0
$598$	9.00000	+	8.66025i	0.368037	+	0.354144i
$599$	−24.2487			−0.990775			−0.495388	−	0.868672i	$-0.664974\pi$
$599$	−24.2487			−0.990775			−0.495388	+	0.868672i	$0.664974\pi$
$600$		0			0
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	−0.945558	−	0.325455i	$-0.894483\pi$
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	0.190927	−	0.981604i	$-0.438851\pi$
$602$	8.66025	−	15.0000i	0.352966	−	0.611354i
$603$		0			0
$604$	−9.00000	−	5.19615i	−0.366205	−	0.211428i
$605$	1.73205	+	1.00000i	0.0704179	+	0.0406558i
$606$		0			0
$607$	−5.50000	+	9.52628i	−0.223238	+	0.386660i	−0.955789	−	0.294052i	$-0.904996\pi$
$607$	−5.50000	+	9.52628i	−0.223238	+	0.386660i	0.732551	+	0.680712i	$0.238329\pi$
$608$	2.59808	+	4.50000i	0.105366	+	0.182499i
$609$		0			0
$610$	−10.0000			−0.404888
$611$	7.79423	−	31.5000i	0.315321	−	1.27435i
$612$		0			0
$613$	−19.5000	+	11.2583i	−0.787598	+	0.454720i	−0.839116	−	0.543952i	$-0.816927\pi$
$613$	−19.5000	+	11.2583i	−0.787598	+	0.454720i	0.0515185	+	0.998672i	$0.483594\pi$
$614$	5.19615	+	9.00000i	0.209700	+	0.363210i
$615$		0			0
$616$			5.19615i			0.209359i
$617$	5.19615	+	3.00000i	0.209189	+	0.120775i	0.600935	−	0.799298i	$-0.294795\pi$
$617$	5.19615	+	3.00000i	0.209189	+	0.120775i	−0.391745	+	0.920074i	$0.628129\pi$
$618$		0			0
$619$		−	12.1244i		−	0.487319i	−0.969861	−	0.243659i	$-0.921652\pi$
$619$		−	12.1244i		−	0.487319i	0.969861	−	0.243659i	$-0.0783479\pi$
$620$	−5.19615	+	9.00000i	−0.208683	+	0.361449i
$621$		0			0
$622$	24.0000	−	13.8564i	0.962312	−	0.555591i
$623$	−25.9808			−1.04090
$624$		0			0
$625$	1.00000			0.0400000
$626$	1.73205	−	1.00000i	0.0692267	−	0.0399680i
$627$		0			0
$628$	5.50000	−	9.52628i	0.219474	−	0.380140i
$629$		0			0
$630$		0			0
$631$	−36.0000	−	20.7846i	−1.43314	−	0.827422i	−0.435779	−	0.900054i	$-0.643527\pi$
$631$	−36.0000	−	20.7846i	−1.43314	−	0.827422i	−0.997359	+	0.0726317i	$0.976860\pi$
$632$			10.0000i			0.397779i
$633$		0			0
$634$	−4.50000	−	7.79423i	−0.178718	−	0.309548i
$635$	9.52628	−	5.50000i	0.378039	−	0.218261i
$636$		0			0
$637$	−4.00000	−	13.8564i	−0.158486	−	0.549011i
$638$	20.7846			0.822871
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	6.06218	−	10.5000i	0.239442	−	0.414725i	−0.721113	−	0.692818i	$-0.756369\pi$
$641$	6.06218	−	10.5000i	0.239442	−	0.414725i	0.960554	+	0.278093i	$0.0897023\pi$
$642$		0			0
$643$	−6.00000	−	3.46410i	−0.236617	−	0.136611i	0.377004	−	0.926212i	$-0.376954\pi$
$643$	−6.00000	−	3.46410i	−0.236617	−	0.136611i	−0.613621	+	0.789601i	$0.710288\pi$
$644$	5.19615	+	3.00000i	0.204757	+	0.118217i
$645$		0			0
$646$		0			0
$647$	18.1865	+	31.5000i	0.714986	+	1.23839i	0.962965	+	0.269627i	$0.0869005\pi$
$647$	18.1865	+	31.5000i	0.714986	+	1.23839i	−0.247978	+	0.968766i	$0.579766\pi$
$648$		0			0
$649$	36.0000			1.41312
$650$	3.46410	−	1.00000i	0.135873	−	0.0392232i
$651$		0			0
$652$	−6.00000	+	3.46410i	−0.234978	+	0.135665i
$653$	23.3827	+	40.5000i	0.915035	+	1.58489i	0.806850	+	0.590757i	$0.201171\pi$
$653$	23.3827	+	40.5000i	0.915035	+	1.58489i	0.108185	+	0.994131i	$0.465496\pi$
$654$		0			0
$655$		−	12.1244i		−	0.473738i
$656$	−5.19615	−	3.00000i	−0.202876	−	0.117130i
$657$		0			0
$658$		−	15.5885i		−	0.607701i
$659$	−12.1244	+	21.0000i	−0.472298	+	0.818044i	−0.999498	−	0.0316976i	$-0.989909\pi$
$659$	−12.1244	+	21.0000i	−0.472298	+	0.818044i	0.527200	+	0.849741i	$0.323242\pi$
$660$		0			0
$661$	9.00000	−	5.19615i	0.350059	−	0.202107i	−0.314652	−	0.949207i	$-0.601888\pi$
$661$	9.00000	−	5.19615i	0.350059	−	0.202107i	0.664711	+	0.747100i	$0.268554\pi$
$662$	17.3205			0.673181
$663$		0			0
$664$	12.0000			0.465690
$665$	−7.79423	+	4.50000i	−0.302247	+	0.174503i
$666$		0			0
$667$	12.0000	−	20.7846i	0.464642	−	0.804783i
$668$			3.00000i			0.116073i
$669$		0			0
$670$		0			0
$671$		−	30.0000i		−	1.15814i
$672$		0			0
$673$	20.0000	+	34.6410i	0.770943	+	1.33531i	0.937046	+	0.349205i	$0.113548\pi$
$673$	20.0000	+	34.6410i	0.770943	+	1.33531i	−0.166103	+	0.986108i	$0.553118\pi$
$674$	22.5167	−	13.0000i	0.867309	−	0.500741i
$675$		0			0
$676$	11.0000	−	6.92820i	0.423077	−	0.266469i
$677$	27.7128			1.06509			0.532545	−	0.846402i	$-0.321236\pi$
$677$	27.7128			1.06509			0.532545	+	0.846402i	$0.321236\pi$
$678$		0			0
$679$	6.00000	+	10.3923i	0.230259	+	0.398820i
$680$		0			0
$681$		0			0
$682$	−27.0000	−	15.5885i	−1.03388	−	0.596913i
$683$	25.9808	+	15.0000i	0.994126	+	0.573959i	0.906505	−	0.422195i	$-0.138740\pi$
$683$	25.9808	+	15.0000i	0.994126	+	0.573959i	0.0876211	+	0.996154i	$0.472074\pi$
$684$		0			0
$685$	6.00000	−	10.3923i	0.229248	−	0.397070i
$686$	−9.52628	−	16.5000i	−0.363715	−	0.629973i
$687$		0			0
$688$	−10.0000			−0.381246
$689$	−42.4352	−	10.5000i	−1.61665	−	0.400018i
$690$		0			0
$691$	25.5000	−	14.7224i	0.970066	−	0.560068i	0.0708094	−	0.997490i	$-0.477442\pi$
$691$	25.5000	−	14.7224i	0.970066	−	0.560068i	0.899256	+	0.437422i	$0.144108\pi$
$692$	−2.59808	−	4.50000i	−0.0987640	−	0.171064i
$693$		0			0
$694$			6.92820i			0.262991i
$695$	4.33013	+	2.50000i	0.164251	+	0.0948304i
$696$		0			0
$697$		0			0
$698$	−6.92820	+	12.0000i	−0.262236	+	0.454207i
$699$		0			0
$700$	1.50000	−	0.866025i	0.0566947	−	0.0327327i
$701$	−13.8564			−0.523349			−0.261675	−	0.965156i	$-0.584275\pi$
$701$	−13.8564			−0.523349			−0.261675	+	0.965156i	$0.584275\pi$
$702$		0			0
$703$	45.0000			1.69721
$704$	2.59808	−	1.50000i	0.0979187	−	0.0565334i
$705$		0			0
$706$	6.00000	−	10.3923i	0.225813	−	0.391120i
$707$		−	24.0000i		−	0.902613i
$708$		0			0
$709$	−42.0000	−	24.2487i	−1.57734	−	0.910679i	−0.995228	−	0.0975728i	$-0.968892\pi$
$709$	−42.0000	−	24.2487i	−1.57734	−	0.910679i	−0.582115	−	0.813107i	$-0.697775\pi$
$710$			6.00000i			0.225176i
$711$		0			0
$712$	7.50000	+	12.9904i	0.281074	+	0.486835i
$713$	−31.1769	+	18.0000i	−1.16758	+	0.674105i
$714$		0			0
$715$	3.00000	+	10.3923i	0.112194	+	0.388650i
$716$	3.46410			0.129460
$717$		0			0
$718$	−3.00000	−	5.19615i	−0.111959	−	0.193919i
$719$	−6.92820	+	12.0000i	−0.258378	+	0.447524i	−0.965808	−	0.259260i	$-0.916521\pi$
$719$	−6.92820	+	12.0000i	−0.258378	+	0.447524i	0.707429	+	0.706784i	$0.249855\pi$
$720$		0			0
$721$	1.50000	+	0.866025i	0.0558629	+	0.0322525i
$722$	−6.92820	−	4.00000i	−0.257841	−	0.148865i
$723$		0			0
$724$	−5.00000	+	8.66025i	−0.185824	+	0.321856i
$725$	−3.46410	−	6.00000i	−0.128654	−	0.222834i
$726$		0			0
$727$	37.0000			1.37225			0.686127	−	0.727482i	$-0.259309\pi$
$727$	37.0000			1.37225			0.686127	+	0.727482i	$0.259309\pi$
$728$	4.33013	−	4.50000i	0.160485	−	0.166781i
$729$		0			0
$730$	6.00000	−	3.46410i	0.222070	−	0.128212i
$731$		0			0
$732$		0			0
$733$			29.4449i			1.08757i	0.839224	+	0.543785i	$0.183009\pi$
$733$			29.4449i			1.08757i	−0.839224	+	0.543785i	$0.816991\pi$
$734$	−13.8564	−	8.00000i	−0.511449	−	0.295285i
$735$		0			0
$736$		−	3.46410i		−	0.127688i
$737$		0			0
$738$		0			0
$739$	−40.5000	+	23.3827i	−1.48982	+	0.860146i	−0.999932	−	0.0116414i	$-0.996294\pi$
$739$	−40.5000	+	23.3827i	−1.48982	+	0.860146i	−0.489884	+	0.871787i	$0.662961\pi$
$740$	−8.66025			−0.318357
$741$		0			0
$742$	−21.0000			−0.770934
$743$	−20.7846	+	12.0000i	−0.762513	+	0.440237i	−0.830197	−	0.557470i	$-0.811772\pi$
$743$	−20.7846	+	12.0000i	−0.762513	+	0.440237i	0.0676840	+	0.997707i	$0.478439\pi$
$744$		0			0
$745$	3.00000	−	5.19615i	0.109911	−	0.190372i
$746$		−	22.0000i		−	0.805477i
$747$		0			0
$748$		0			0
$749$			6.00000i			0.219235i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	−7.79423	+	4.50000i	−0.284226	+	0.164098i
$753$		0			0
$754$	−18.0000	−	17.3205i	−0.655521	−	0.630776i
$755$	−10.3923			−0.378215
$756$		0			0
$757$	14.5000	+	25.1147i	0.527011	+	0.912811i	0.999505	+	0.0314762i	$0.0100208\pi$
$757$	14.5000	+	25.1147i	0.527011	+	0.912811i	−0.472493	+	0.881334i	$0.656646\pi$
$758$	−12.9904	+	22.5000i	−0.471832	+	0.817237i
$759$		0			0
$760$	4.50000	+	2.59808i	0.163232	+	0.0942421i
$761$	18.1865	+	10.5000i	0.659261	+	0.380625i	0.791995	−	0.610527i	$-0.209042\pi$
$761$	18.1865	+	10.5000i	0.659261	+	0.380625i	−0.132734	+	0.991152i	$0.542376\pi$
$762$		0			0
$763$	9.00000	−	15.5885i	0.325822	−	0.564340i
$764$	−8.66025	−	15.0000i	−0.313317	−	0.542681i
$765$		0			0
$766$	36.0000			1.30073
$767$	−31.1769	−	30.0000i	−1.12573	−	1.08324i
$768$		0			0
$769$	−6.00000	+	3.46410i	−0.216366	+	0.124919i	−0.604266	−	0.796782i	$-0.706534\pi$
$769$	−6.00000	+	3.46410i	−0.216366	+	0.124919i	0.387901	+	0.921701i	$0.373200\pi$
$770$	2.59808	+	4.50000i	0.0936282	+	0.162169i
$771$		0			0
$772$			6.92820i			0.249351i
$773$	33.7750	+	19.5000i	1.21480	+	0.701366i	0.963802	−	0.266621i	$-0.0859071\pi$
$773$	33.7750	+	19.5000i	1.21480	+	0.701366i	0.251000	+	0.967987i	$0.419240\pi$
$774$		0			0
$775$			10.3923i			0.373303i
$776$	3.46410	−	6.00000i	0.124354	−	0.215387i
$777$		0			0
$778$	−24.0000	+	13.8564i	−0.860442	+	0.496776i
$779$	31.1769			1.11703
$780$		0			0
$781$	−18.0000			−0.644091
$782$		0			0
$783$		0			0
$784$	−2.00000	+	3.46410i	−0.0714286	+	0.123718i
$785$		−	11.0000i		−	0.392607i
$786$		0			0
$787$	−24.0000	−	13.8564i	−0.855508	−	0.493928i	0.00699773	−	0.999976i	$-0.497773\pi$
$787$	−24.0000	−	13.8564i	−0.855508	−	0.493928i	−0.862505	+	0.506048i	$0.831106\pi$
$788$			3.00000i			0.106871i
$789$		0			0
$790$	5.00000	+	8.66025i	0.177892	+	0.308118i
$791$	−20.7846	+	12.0000i	−0.739016	+	0.426671i
$792$		0			0
$793$	−25.0000	+	25.9808i	−0.887776	+	0.922604i
$794$	−19.0526			−0.676150
$795$		0			0
$796$	11.0000	+	19.0526i	0.389885	+	0.675300i
$797$	−6.92820	+	12.0000i	−0.245410	+	0.425062i	−0.962247	−	0.272179i	$-0.912256\pi$
$797$	−6.92820	+	12.0000i	−0.245410	+	0.425062i	0.716837	+	0.697241i	$0.245589\pi$
$798$		0			0
$799$		0			0
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$		0			0
$802$	−16.5000	+	28.5788i	−0.582635	+	1.00915i
$803$	10.3923	+	18.0000i	0.366736	+	0.635206i
$804$		0			0
$805$	6.00000			0.211472
$806$	10.3923	+	36.0000i	0.366053	+	1.26805i
$807$		0			0
$808$	−12.0000	+	6.92820i	−0.422159	+	0.243733i
$809$	−10.3923	−	18.0000i	−0.365374	−	0.632846i	0.623462	−	0.781854i	$-0.285726\pi$
$809$	−10.3923	−	18.0000i	−0.365374	−	0.632846i	−0.988836	+	0.149007i	$0.952392\pi$
$810$		0			0
$811$			29.4449i			1.03395i	0.856001	+	0.516975i	$0.172942\pi$
$811$			29.4449i			1.03395i	−0.856001	+	0.516975i	$0.827058\pi$
$812$	−10.3923	−	6.00000i	−0.364698	−	0.210559i
$813$		0			0
$814$		−	25.9808i		−	0.910625i
$815$	−3.46410	+	6.00000i	−0.121342	+	0.210171i
$816$		0			0
$817$	45.0000	−	25.9808i	1.57435	−	0.908952i
$818$	−1.73205			−0.0605597
$819$		0			0
$820$	−6.00000			−0.209529
$821$	−15.5885	+	9.00000i	−0.544041	+	0.314102i	−0.746715	−	0.665144i	$-0.768370\pi$
$821$	−15.5885	+	9.00000i	−0.544041	+	0.314102i	0.202674	+	0.979246i	$0.435037\pi$
$822$		0			0
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	−0.730215	−	0.683217i	$-0.760580\pi$
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	0.956791	+	0.290776i	$0.0939136\pi$
$824$		−	1.00000i		−	0.0348367i
$825$		0			0
$826$	−18.0000	−	10.3923i	−0.626300	−	0.361595i
$827$		−	6.00000i		−	0.208640i	−0.994544	−	0.104320i	$-0.966733\pi$
$827$		−	6.00000i		−	0.208640i	0.994544	−	0.104320i	$-0.0332667\pi$
$828$		0			0
$829$	−8.00000	−	13.8564i	−0.277851	−	0.481253i	0.692999	−	0.720938i	$-0.256289\pi$
$829$	−8.00000	−	13.8564i	−0.277851	−	0.481253i	−0.970851	+	0.239686i	$0.922956\pi$
$830$	10.3923	−	6.00000i	0.360722	−	0.208263i
$831$		0			0
$832$	−3.50000	−	0.866025i	−0.121341	−	0.0300240i
$833$		0			0
$834$		0			0
$835$	1.50000	+	2.59808i	0.0519096	+	0.0899101i
$836$	−7.79423	+	13.5000i	−0.269569	+	0.466907i
$837$		0			0
$838$	21.0000	+	12.1244i	0.725433	+	0.418829i
$839$	−36.3731	−	21.0000i	−1.25574	−	0.725001i	−0.283495	−	0.958974i	$-0.591494\pi$
$839$	−36.3731	−	21.0000i	−1.25574	−	0.725001i	−0.972243	+	0.233973i	$0.924827\pi$
$840$		0			0
$841$	−9.50000	+	16.4545i	−0.327586	+	0.567396i
$842$		0			0
$843$		0			0
$844$	11.0000			0.378636
$845$	6.06218	−	11.5000i	0.208545	−	0.395612i
$846$		0			0
$847$	3.00000	−	1.73205i	0.103081	−	0.0595140i
$848$	6.06218	+	10.5000i	0.208176	+	0.360571i
$849$		0			0
$850$		0			0
$851$	−25.9808	−	15.0000i	−0.890609	−	0.514193i
$852$		0			0
$853$		−	13.8564i		−	0.474434i	−0.971457	−	0.237217i	$-0.923765\pi$
$853$		−	13.8564i		−	0.474434i	0.971457	−	0.237217i	$-0.0762353\pi$
$854$	−8.66025	+	15.0000i	−0.296348	+	0.513289i
$855$		0			0
$856$	3.00000	−	1.73205i	0.102538	−	0.0592003i
$857$	3.46410			0.118331			0.0591657	−	0.998248i	$-0.481156\pi$
$857$	3.46410			0.118331			0.0591657	+	0.998248i	$0.481156\pi$
$858$		0			0
$859$	31.0000			1.05771			0.528853	−	0.848713i	$-0.322622\pi$
$859$	31.0000			1.05771			0.528853	+	0.848713i	$0.322622\pi$
$860$	−8.66025	+	5.00000i	−0.295312	+	0.170499i
$861$		0			0
$862$	6.00000	−	10.3923i	0.204361	−	0.353963i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$		0			0
$865$	−4.50000	−	2.59808i	−0.153005	−	0.0883372i
$866$		−	4.00000i		−	0.135926i
$867$		0			0
$868$	9.00000	+	15.5885i	0.305480	+	0.529107i
$869$	−25.9808	+	15.0000i	−0.881337	+	0.508840i
$870$		0			0
$871$		0			0
$872$	−10.3923			−0.351928
$873$		0			0
$874$	9.00000	+	15.5885i	0.304430	+	0.527287i
$875$	0.866025	−	1.50000i	0.0292770	−	0.0507093i
$876$		0			0
$877$	−36.0000	−	20.7846i	−1.21563	−	0.701846i	−0.251653	−	0.967818i	$-0.580974\pi$
$877$	−36.0000	−	20.7846i	−1.21563	−	0.701846i	−0.963981	+	0.265971i	$0.914307\pi$
$878$	12.1244	+	7.00000i	0.409177	+	0.236239i
$879$		0			0
$880$	1.50000	−	2.59808i	0.0505650	−	0.0875811i
$881$	−16.4545	−	28.5000i	−0.554366	−	0.960189i	−0.997953	−	0.0639581i	$-0.979628\pi$
$881$	−16.4545	−	28.5000i	−0.554366	−	0.960189i	0.443587	−	0.896231i	$-0.353706\pi$
$882$		0			0
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$		0			0
$885$		0			0
$886$	9.00000	−	5.19615i	0.302361	−	0.174568i
$887$	−12.9904	−	22.5000i	−0.436174	−	0.755476i	0.561216	−	0.827669i	$-0.310334\pi$
$887$	−12.9904	−	22.5000i	−0.436174	−	0.755476i	−0.997391	+	0.0721931i	$0.977000\pi$
$888$		0			0
$889$		−	19.0526i		−	0.639002i
$890$	12.9904	+	7.50000i	0.435439	+	0.251401i
$891$		0			0
$892$			12.1244i			0.405953i
$893$	23.3827	−	40.5000i	0.782472	−	1.35528i
$894$		0			0
$895$	3.00000	−	1.73205i	0.100279	−	0.0578961i
$896$	−1.73205			−0.0578638
$897$		0			0
$898$	−33.0000			−1.10122
$899$	62.3538	−	36.0000i	2.07962	−	1.20067i
$900$		0			0
$901$		0			0
$902$		−	18.0000i		−	0.599334i
$903$		0			0
$904$	12.0000	+	6.92820i	0.399114	+	0.230429i
$905$			10.0000i			0.332411i
$906$		0			0
$907$	13.0000	+	22.5167i	0.431658	+	0.747653i	0.997016	−	0.0771920i	$-0.0245954\pi$
$907$	13.0000	+	22.5167i	0.431658	+	0.747653i	−0.565358	+	0.824845i	$0.691262\pi$
$908$	20.7846	−	12.0000i	0.689761	−	0.398234i
$909$		0			0
$910$	1.50000	−	6.06218i	0.0497245	−	0.200959i
$911$	−34.6410			−1.14771			−0.573854	−	0.818958i	$-0.694552\pi$
$911$	−34.6410			−1.14771			−0.573854	+	0.818958i	$0.694552\pi$
$912$		0			0
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$	−19.0526	+	33.0000i	−0.630203	+	1.09154i
$915$		0			0
$916$	−3.00000	−	1.73205i	−0.0991228	−	0.0572286i
$917$	−18.1865	−	10.5000i	−0.600572	−	0.346741i
$918$		0			0
$919$	−23.0000	+	39.8372i	−0.758700	+	1.31411i	0.184814	+	0.982774i	$0.440832\pi$
$919$	−23.0000	+	39.8372i	−0.758700	+	1.31411i	−0.943514	+	0.331333i	$0.892502\pi$
$920$	−1.73205	−	3.00000i	−0.0571040	−	0.0989071i
$921$		0			0
$922$	−12.0000			−0.395199
$923$	15.5885	+	15.0000i	0.513100	+	0.493731i
$924$		0			0
$925$	−7.50000	+	4.33013i	−0.246598	+	0.142374i
$926$	12.1244	+	21.0000i	0.398431	+	0.690103i
$927$		0			0
$928$			6.92820i			0.227429i
$929$	36.3731	+	21.0000i	1.19336	+	0.688988i	0.959067	−	0.283178i	$-0.0913887\pi$
$929$	36.3731	+	21.0000i	1.19336	+	0.688988i	0.234294	+	0.972166i	$0.424722\pi$
$930$		0			0
$931$		−	20.7846i		−	0.681188i
$932$	−1.73205	+	3.00000i	−0.0567352	+	0.0982683i
$933$		0			0
$934$	30.0000	−	17.3205i	0.981630	−	0.566744i
$935$		0			0
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$		0			0
$939$		0			0
$940$	−4.50000	+	7.79423i	−0.146774	+	0.254220i
$941$		−	12.0000i		−	0.391189i	−0.980685	−	0.195594i	$-0.937336\pi$
$941$		−	12.0000i		−	0.391189i	0.980685	−	0.195594i	$-0.0626636\pi$
$942$		0			0
$943$	−18.0000	−	10.3923i	−0.586161	−	0.338420i
$944$			12.0000i			0.390567i
$945$		0			0
$946$	−15.0000	−	25.9808i	−0.487692	−	0.844707i
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	−0.731417	−	0.681930i	$-0.761141\pi$
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	0.224860	+	0.974391i	$0.427807\pi$
$948$		0			0
$949$	6.00000	−	24.2487i	0.194768	−	0.787146i
$950$	5.19615			0.168585
$951$		0			0
$952$		0			0
$953$	15.5885	−	27.0000i	0.504960	−	0.874616i	−0.495024	−	0.868879i	$-0.664841\pi$
$953$	15.5885	−	27.0000i	0.504960	−	0.874616i	0.999984	−	0.00573642i	$-0.00182597\pi$
$954$		0			0
$955$	−15.0000	−	8.66025i	−0.485389	−	0.280239i
$956$	5.19615	+	3.00000i	0.168056	+	0.0970269i
$957$		0			0
$958$		0			0
$959$	−10.3923	−	18.0000i	−0.335585	−	0.581250i
$960$		0			0
$961$	−77.0000			−2.48387
$962$	−21.6506	+	22.5000i	−0.698044	+	0.725429i
$963$		0			0
$964$	−25.5000	+	14.7224i	−0.821300	+	0.474178i
$965$	3.46410	+	6.00000i	0.111513	+	0.193147i
$966$		0			0
$967$			19.0526i			0.612689i	0.951921	+	0.306344i	$0.0991059\pi$
$967$			19.0526i			0.612689i	−0.951921	+	0.306344i	$0.900894\pi$
$968$	−1.73205	−	1.00000i	−0.0556702	−	0.0321412i
$969$		0			0
$970$		−	6.92820i		−	0.222451i
$971$	23.3827	−	40.5000i	0.750386	−	1.29971i	−0.197250	−	0.980353i	$-0.563201\pi$
$971$	23.3827	−	40.5000i	0.750386	−	1.29971i	0.947636	−	0.319354i	$-0.103466\pi$
$972$		0			0
$973$	7.50000	−	4.33013i	0.240439	−	0.138817i
$974$	−1.73205			−0.0554985
$975$		0			0
$976$	10.0000			0.320092
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$	−22.5000	+	38.9711i	−0.719103	+	1.24552i
$980$			4.00000i			0.127775i
$981$		0			0
$982$	−10.5000	−	6.06218i	−0.335068	−	0.193452i
$983$			51.0000i			1.62665i	0.581811	+	0.813324i	$0.302344\pi$
$983$			51.0000i			1.62665i	−0.581811	+	0.813324i	$0.697656\pi$
$984$		0			0
$985$	1.50000	+	2.59808i	0.0477940	+	0.0827816i
$986$		0			0
$987$		0			0
$988$	18.0000	−	5.19615i	0.572656	−	0.165312i
$989$	−34.6410			−1.10152
$990$		0			0
$991$	11.0000	+	19.0526i	0.349427	+	0.605224i	0.986148	−	0.165870i	$-0.0530431\pi$
$991$	11.0000	+	19.0526i	0.349427	+	0.605224i	−0.636721	+	0.771094i	$0.719710\pi$
$992$	5.19615	−	9.00000i	0.164978	−	0.285750i
$993$		0			0
$994$	9.00000	+	5.19615i	0.285463	+	0.164812i
$995$	19.0526	+	11.0000i	0.604007	+	0.348723i
$996$		0			0
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	0.0512480	+	0.998686i	$0.483680\pi$
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	−0.890511	+	0.454961i	$0.849653\pi$
$998$	−12.1244	−	21.0000i	−0.383790	−	0.664743i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.a.361.1	✓	4
3.2	odd	2	inner	1170.2.bs.a.361.2	yes	4
13.4	even	6	inner	1170.2.bs.a.901.1	yes	4
39.17	odd	6	inner	1170.2.bs.a.901.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.bs.a.361.1	✓	4	1.1	even	1	trivial
1170.2.bs.a.361.2	yes	4	3.2	odd	2	inner
1170.2.bs.a.901.1	yes	4	13.4	even	6	inner
1170.2.bs.a.901.2	yes	4	39.17	odd	6	inner

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-1.50000 - 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-1.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-2.59808 + 1.50000i) q^{11} +(3.50000 + 0.866025i) q^{13} +1.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.50000 + 2.59808i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(1.50000 - 2.59808i) q^{22} +(-1.73205 - 3.00000i) q^{23} -1.00000 q^{25} +(-3.46410 + 1.00000i) q^{26} +(-1.50000 + 0.866025i) q^{28} +(3.46410 + 6.00000i) q^{29} -10.3923i q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.866025 + 1.50000i) q^{35} +(7.50000 - 4.33013i) q^{37} -5.19615 q^{38} +1.00000 q^{40} +(5.19615 - 3.00000i) q^{41} +(5.00000 - 8.66025i) q^{43} +3.00000i q^{44} +(3.00000 + 1.73205i) q^{46} -9.00000i q^{47} +(-2.00000 - 3.46410i) q^{49} +(0.866025 - 0.500000i) q^{50} +(2.50000 - 2.59808i) q^{52} -12.1244 q^{53} +(1.50000 + 2.59808i) q^{55} +(0.866025 - 1.50000i) q^{56} +(-6.00000 - 3.46410i) q^{58} +(-10.3923 - 6.00000i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(5.19615 + 9.00000i) q^{62} -1.00000 q^{64} +(0.866025 - 3.50000i) q^{65} -1.73205i q^{70} +(5.19615 + 3.00000i) q^{71} -6.92820i q^{73} +(-4.33013 + 7.50000i) q^{74} +(4.50000 - 2.59808i) q^{76} +5.19615 q^{77} +10.0000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-3.00000 + 5.19615i) q^{82} -12.0000i q^{83} +10.0000i q^{86} +(-1.50000 - 2.59808i) q^{88} +(12.9904 - 7.50000i) q^{89} +(-4.50000 - 4.33013i) q^{91} -3.46410 q^{92} +(4.50000 + 7.79423i) q^{94} +(2.59808 - 4.50000i) q^{95} +(-6.00000 - 3.46410i) q^{97} +(3.46410 + 2.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 6 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 - 6 * q^7	\( 4 q + 2 q^{4} - 6 q^{7} + 2 q^{10} + 14 q^{13} - 2 q^{16} + 18 q^{19} + 6 q^{22} - 4 q^{25} - 6 q^{28} + 30 q^{37} + 4 q^{40} + 20 q^{43} + 12 q^{46} - 8 q^{49} + 10 q^{52} + 6 q^{55} - 24 q^{58} - 20 q^{61} - 4 q^{64} + 18 q^{76} + 40 q^{79} - 12 q^{82} - 6 q^{88} - 18 q^{91} + 18 q^{94} - 24 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 6 * q^7 + 2 * q^10 + 14 * q^13 - 2 * q^16 + 18 * q^19 + 6 * q^22 - 4 * q^25 - 6 * q^28 + 30 * q^37 + 4 * q^40 + 20 * q^43 + 12 * q^46 - 8 * q^49 + 10 * q^52 + 6 * q^55 - 24 * q^58 - 20 * q^61 - 4 * q^64 + 18 * q^76 + 40 * q^79 - 12 * q^82 - 6 * q^88 - 18 * q^91 + 18 * q^94 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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