LMFDB - Embedded newform 416.2.w.a.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(225,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("416.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.w (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:	$3.32177672409$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	416.257
Dual form			416.2.w.a.225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 1.50000i) q^{3} +3.46410i q^{5} +(-2.59808 - 1.50000i) q^{7} +(4.33013 - 2.50000i) q^{11} +(-1.00000 - 3.46410i) q^{13} +(5.19615 - 3.00000i) q^{15} +(3.50000 - 6.06218i) q^{17} +(4.33013 + 2.50000i) q^{19} +5.19615i q^{21} +(-2.59808 - 4.50000i) q^{23} -7.00000 q^{25} -5.19615 q^{27} +(2.50000 + 4.33013i) q^{29} -2.00000i q^{31} +(-7.50000 - 4.33013i) q^{33} +(5.19615 - 9.00000i) q^{35} +(4.50000 - 2.59808i) q^{37} +(-4.33013 + 4.50000i) q^{39} +(-1.50000 + 0.866025i) q^{41} +(-2.59808 + 4.50000i) q^{43} -4.00000i q^{47} +(1.00000 + 1.73205i) q^{49} -12.1244 q^{51} +4.00000 q^{53} +(8.66025 + 15.0000i) q^{55} -8.66025i q^{57} +(-6.06218 - 3.50000i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(12.0000 - 3.46410i) q^{65} +(2.59808 - 1.50000i) q^{67} +(-4.50000 + 7.79423i) q^{69} +(6.06218 + 3.50000i) q^{71} +3.46410i q^{73} +(6.06218 + 10.5000i) q^{75} -15.0000 q^{77} +3.46410 q^{79} +(4.50000 + 7.79423i) q^{81} +14.0000i q^{83} +(21.0000 + 12.1244i) q^{85} +(4.33013 - 7.50000i) q^{87} +(1.50000 - 0.866025i) q^{89} +(-2.59808 + 10.5000i) q^{91} +(-3.00000 + 1.73205i) q^{93} +(-8.66025 + 15.0000i) q^{95} +(7.50000 + 4.33013i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{13} + 14 q^{17} - 28 q^{25} + 10 q^{29} - 30 q^{33} + 18 q^{37} - 6 q^{41} + 4 q^{49} + 16 q^{53} - 6 q^{61} + 48 q^{65} - 18 q^{69} - 60 q^{77} + 18 q^{81} + 84 q^{85} + 6 q^{89} - 12 q^{93}+ \cdots + 30 q^{97}+O(q^{100}) $ 4 * q - 4 * q^13 + 14 * q^17 - 28 * q^25 + 10 * q^29 - 30 * q^33 + 18 * q^37 - 6 * q^41 + 4 * q^49 + 16 * q^53 - 6 * q^61 + 48 * q^65 - 18 * q^69 - 60 * q^77 + 18 * q^81 + 84 * q^85 + 6 * q^89 - 12 * q^93 + 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i	−1.00000			$\pi$
$4$		0			0
$5$			3.46410i			1.54919i	0.632456	+	0.774597i	$0.282047\pi$
$5$			3.46410i			1.54919i	−0.632456	+	0.774597i	$0.717953\pi$
$6$		0			0
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.0791130	−	0.996866i	$-0.525209\pi$
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.902867	+	0.429919i	$0.858542\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.33013	−	2.50000i	1.30558	−	0.753778i	0.324227	−	0.945979i	$-0.394896\pi$
$11$	4.33013	−	2.50000i	1.30558	−	0.753778i	0.981356	+	0.192201i	$0.0615626\pi$
$12$		0			0
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$		0			0
$15$	5.19615	−	3.00000i	1.34164	−	0.774597i
$16$		0			0
$17$	3.50000	−	6.06218i	0.848875	−	1.47029i	−0.0333386	−	0.999444i	$-0.510614\pi$
$17$	3.50000	−	6.06218i	0.848875	−	1.47029i	0.882213	−	0.470850i	$-0.156053\pi$
$18$		0			0
$19$	4.33013	+	2.50000i	0.993399	+	0.573539i	0.906289	−	0.422659i	$-0.138903\pi$
$19$	4.33013	+	2.50000i	0.993399	+	0.573539i	0.0871106	+	0.996199i	$0.472237\pi$
$20$		0			0
$21$			5.19615i			1.13389i
$22$		0			0
$23$	−2.59808	−	4.50000i	−0.541736	−	0.938315i	−0.998805	−	0.0488832i	$-0.984434\pi$
$23$	−2.59808	−	4.50000i	−0.541736	−	0.938315i	0.457068	−	0.889432i	$-0.348900\pi$
$24$		0			0
$25$	−7.00000			−1.40000
$26$		0			0
$27$	−5.19615			−1.00000
$28$		0			0
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	0.999167	−	0.0408130i	$-0.0129948\pi$
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	−0.534928	+	0.844897i	$0.679661\pi$
$30$		0			0
$31$		−	2.00000i		−	0.359211i	−0.983739	−	0.179605i	$-0.942518\pi$
$31$		−	2.00000i		−	0.359211i	0.983739	−	0.179605i	$-0.0574821\pi$
$32$		0			0
$33$	−7.50000	−	4.33013i	−1.30558	−	0.753778i
$34$		0			0
$35$	5.19615	−	9.00000i	0.878310	−	1.52128i
$36$		0			0
$37$	4.50000	−	2.59808i	0.739795	−	0.427121i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	4.50000	−	2.59808i	0.739795	−	0.427121i	0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	−4.33013	+	4.50000i	−0.693375	+	0.720577i
$40$		0			0
$41$	−1.50000	+	0.866025i	−0.234261	+	0.135250i	−0.612536	−	0.790443i	$-0.709851\pi$
$41$	−1.50000	+	0.866025i	−0.234261	+	0.135250i	0.378275	+	0.925693i	$0.376517\pi$
$42$		0			0
$43$	−2.59808	+	4.50000i	−0.396203	+	0.686244i	−0.993254	−	0.115960i	$-0.963006\pi$
$43$	−2.59808	+	4.50000i	−0.396203	+	0.686244i	0.597051	+	0.802203i	$0.296339\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	4.00000i		−	0.583460i	−0.956501	−	0.291730i	$-0.905769\pi$
$47$		−	4.00000i		−	0.583460i	0.956501	−	0.291730i	$-0.0942309\pi$
$48$		0			0
$49$	1.00000	+	1.73205i	0.142857	+	0.247436i
$50$		0			0
$51$	−12.1244			−1.69775
$52$		0			0
$53$	4.00000			0.549442			0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000			0.549442			0.274721	+	0.961524i	$0.411414\pi$
$54$		0			0
$55$	8.66025	+	15.0000i	1.16775	+	2.02260i
$56$		0			0
$57$		−	8.66025i		−	1.14708i
$58$		0			0
$59$	−6.06218	−	3.50000i	−0.789228	−	0.455661i	0.0504625	−	0.998726i	$-0.483930\pi$
$59$	−6.06218	−	3.50000i	−0.789228	−	0.455661i	−0.839691	+	0.543065i	$0.817264\pi$
$60$		0			0
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	−0.945931	−	0.324367i	$-0.894849\pi$
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	0.753876	+	0.657017i	$0.228182\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	12.0000	−	3.46410i	1.48842	−	0.429669i
$66$		0			0
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	−0.332830	−	0.942987i	$-0.608004\pi$
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	0.650236	+	0.759733i	$0.274670\pi$
$68$		0			0
$69$	−4.50000	+	7.79423i	−0.541736	+	0.938315i
$70$		0			0
$71$	6.06218	+	3.50000i	0.719448	+	0.415374i	0.814550	−	0.580094i	$-0.196984\pi$
$71$	6.06218	+	3.50000i	0.719448	+	0.415374i	−0.0951014	+	0.995468i	$0.530318\pi$
$72$		0			0
$73$			3.46410i			0.405442i	0.979236	+	0.202721i	$0.0649785\pi$
$73$			3.46410i			0.405442i	−0.979236	+	0.202721i	$0.935021\pi$
$74$		0			0
$75$	6.06218	+	10.5000i	0.700000	+	1.21244i
$76$		0			0
$77$	−15.0000			−1.70941
$78$		0			0
$79$	3.46410			0.389742			0.194871	−	0.980829i	$-0.437571\pi$
$79$	3.46410			0.389742			0.194871	+	0.980829i	$0.437571\pi$
$80$		0			0
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$		0			0
$83$			14.0000i			1.53670i	0.640030	+	0.768350i	$0.278922\pi$
$83$			14.0000i			1.53670i	−0.640030	+	0.768350i	$0.721078\pi$
$84$		0			0
$85$	21.0000	+	12.1244i	2.27777	+	1.31507i
$86$		0			0
$87$	4.33013	−	7.50000i	0.464238	−	0.804084i
$88$		0			0
$89$	1.50000	−	0.866025i	0.159000	−	0.0917985i	−0.418389	−	0.908268i	$-0.637405\pi$
$89$	1.50000	−	0.866025i	0.159000	−	0.0917985i	0.577389	+	0.816469i	$0.304072\pi$
$90$		0			0
$91$	−2.59808	+	10.5000i	−0.272352	+	1.10070i
$92$		0			0
$93$	−3.00000	+	1.73205i	−0.311086	+	0.179605i
$94$		0			0
$95$	−8.66025	+	15.0000i	−0.888523	+	1.53897i
$96$		0			0
$97$	7.50000	+	4.33013i	0.761510	+	0.439658i	0.829837	−	0.558005i	$-0.188433\pi$
$97$	7.50000	+	4.33013i	0.761510	+	0.439658i	−0.0683279	+	0.997663i	$0.521766\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.50000	−	14.7224i	−0.845782	−	1.46494i	−0.884941	−	0.465704i	$-0.845801\pi$
$101$	−8.50000	−	14.7224i	−0.845782	−	1.46494i	0.0391591	−	0.999233i	$-0.487532\pi$
$102$		0			0
$103$	−6.92820			−0.682656			−0.341328	−	0.939944i	$-0.610877\pi$
$103$	−6.92820			−0.682656			−0.341328	+	0.939944i	$0.610877\pi$
$104$		0			0
$105$	−18.0000			−1.75662
$106$		0			0
$107$	−4.33013	−	7.50000i	−0.418609	−	0.725052i	0.577191	−	0.816609i	$-0.304149\pi$
$107$	−4.33013	−	7.50000i	−0.418609	−	0.725052i	−0.995800	+	0.0915571i	$0.970816\pi$
$108$		0			0
$109$		−	10.3923i		−	0.995402i	−0.867349	−	0.497701i	$-0.834178\pi$
$109$		−	10.3923i		−	0.995402i	0.867349	−	0.497701i	$-0.165822\pi$
$110$		0			0
$111$	−7.79423	−	4.50000i	−0.739795	−	0.427121i
$112$		0			0
$113$	−2.50000	+	4.33013i	−0.235180	+	0.407344i	−0.959325	−	0.282304i	$-0.908901\pi$
$113$	−2.50000	+	4.33013i	−0.235180	+	0.407344i	0.724145	+	0.689648i	$0.242235\pi$
$114$		0			0
$115$	15.5885	−	9.00000i	1.45363	−	0.839254i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−18.1865	+	10.5000i	−1.66716	+	0.962533i
$120$		0			0
$121$	7.00000	−	12.1244i	0.636364	−	1.10221i
$122$		0			0
$123$	2.59808	+	1.50000i	0.234261	+	0.135250i
$124$		0			0
$125$		−	6.92820i		−	0.619677i
$126$		0			0
$127$	9.52628	+	16.5000i	0.845321	+	1.46414i	0.885342	+	0.464939i	$0.153924\pi$
$127$	9.52628	+	16.5000i	0.845321	+	1.46414i	−0.0400219	+	0.999199i	$0.512743\pi$
$128$		0			0
$129$	9.00000			0.792406
$130$		0			0
$131$	−13.8564			−1.21064			−0.605320	−	0.795982i	$-0.706955\pi$
$131$	−13.8564			−1.21064			−0.605320	+	0.795982i	$0.706955\pi$
$132$		0			0
$133$	−7.50000	−	12.9904i	−0.650332	−	1.12641i
$134$		0			0
$135$		−	18.0000i		−	1.54919i
$136$		0			0
$137$	−4.50000	−	2.59808i	−0.384461	−	0.221969i	0.295296	−	0.955406i	$-0.404582\pi$
$137$	−4.50000	−	2.59808i	−0.384461	−	0.221969i	−0.679757	+	0.733437i	$0.737915\pi$
$138$		0			0
$139$	−4.33013	+	7.50000i	−0.367277	+	0.636142i	−0.989139	−	0.146985i	$-0.953043\pi$
$139$	−4.33013	+	7.50000i	−0.367277	+	0.636142i	0.621862	+	0.783127i	$0.286376\pi$
$140$		0			0
$141$	−6.00000	+	3.46410i	−0.505291	+	0.291730i
$142$		0			0
$143$	−12.9904	−	12.5000i	−1.08631	−	1.04530i
$144$		0			0
$145$	−15.0000	+	8.66025i	−1.24568	+	0.719195i
$146$		0			0
$147$	1.73205	−	3.00000i	0.142857	−	0.247436i
$148$		0			0
$149$	7.50000	+	4.33013i	0.614424	+	0.354738i	0.774695	−	0.632335i	$-0.217903\pi$
$149$	7.50000	+	4.33013i	0.614424	+	0.354738i	−0.160271	+	0.987073i	$0.551237\pi$
$150$		0			0
$151$		−	2.00000i		−	0.162758i	−0.996683	−	0.0813788i	$-0.974068\pi$
$151$		−	2.00000i		−	0.162758i	0.996683	−	0.0813788i	$-0.0259324\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.92820			0.556487
$156$		0			0
$157$	−8.00000			−0.638470			−0.319235	−	0.947676i	$-0.603426\pi$
$157$	−8.00000			−0.638470			−0.319235	+	0.947676i	$0.603426\pi$
$158$		0			0
$159$	−3.46410	−	6.00000i	−0.274721	−	0.475831i
$160$		0			0
$161$			15.5885i			1.22854i
$162$		0			0
$163$	16.4545	+	9.50000i	1.28881	+	0.744097i	0.978443	−	0.206518i	$-0.0662131\pi$
$163$	16.4545	+	9.50000i	1.28881	+	0.744097i	0.310372	+	0.950615i	$0.399546\pi$
$164$		0			0
$165$	15.0000	−	25.9808i	1.16775	−	2.02260i
$166$		0			0
$167$	16.4545	−	9.50000i	1.27329	−	0.735132i	0.297681	−	0.954665i	$-0.403787\pi$
$167$	16.4545	−	9.50000i	1.27329	−	0.735132i	0.975605	+	0.219533i	$0.0704535\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.50000	+	6.06218i	−0.266100	+	0.460899i	−0.967851	−	0.251523i	$-0.919068\pi$
$173$	−3.50000	+	6.06218i	−0.266100	+	0.460899i	0.701751	+	0.712422i	$0.252402\pi$
$174$		0			0
$175$	18.1865	+	10.5000i	1.37477	+	0.793725i
$176$		0			0
$177$			12.1244i			0.911322i
$178$		0			0
$179$	9.52628	+	16.5000i	0.712028	+	1.23327i	0.964095	+	0.265558i	$0.0855562\pi$
$179$	9.52628	+	16.5000i	0.712028	+	1.23327i	−0.252067	+	0.967710i	$0.581110\pi$
$180$		0			0
$181$	12.0000			0.891953			0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000			0.891953			0.445976	+	0.895045i	$0.352856\pi$
$182$		0			0
$183$	5.19615			0.384111
$184$		0			0
$185$	9.00000	+	15.5885i	0.661693	+	1.14609i
$186$		0			0
$187$		−	35.0000i		−	2.55945i
$188$		0			0
$189$	13.5000	+	7.79423i	0.981981	+	0.566947i
$190$		0			0
$191$	6.06218	−	10.5000i	0.438644	−	0.759753i	−0.558941	−	0.829207i	$-0.688792\pi$
$191$	6.06218	−	10.5000i	0.438644	−	0.759753i	0.997585	+	0.0694538i	$0.0221257\pi$
$192$		0			0
$193$	10.5000	−	6.06218i	0.755807	−	0.436365i	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	10.5000	−	6.06218i	0.755807	−	0.436365i	0.827788	+	0.561041i	$0.189599\pi$
$194$		0			0
$195$	−15.5885	−	15.0000i	−1.11631	−	1.07417i
$196$		0			0
$197$	1.50000	−	0.866025i	0.106871	−	0.0617018i	−0.445612	−	0.895226i	$-0.647014\pi$
$197$	1.50000	−	0.866025i	0.106871	−	0.0617018i	0.552483	+	0.833524i	$0.313681\pi$
$198$		0			0
$199$	0.866025	−	1.50000i	0.0613909	−	0.106332i	−0.833696	−	0.552223i	$-0.813780\pi$
$199$	0.866025	−	1.50000i	0.0613909	−	0.106332i	0.895087	+	0.445891i	$0.147113\pi$
$200$		0			0
$201$	−4.50000	−	2.59808i	−0.317406	−	0.183254i
$202$		0			0
$203$		−	15.0000i		−	1.05279i
$204$		0			0
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	25.0000			1.72929
$210$		0			0
$211$	2.59808	+	4.50000i	0.178859	+	0.309793i	0.941490	−	0.337041i	$-0.109426\pi$
$211$	2.59808	+	4.50000i	0.178859	+	0.309793i	−0.762631	+	0.646834i	$0.776093\pi$
$212$		0			0
$213$		−	12.1244i		−	0.830747i
$214$		0			0
$215$	−15.5885	−	9.00000i	−1.06312	−	0.613795i
$216$		0			0
$217$	−3.00000	+	5.19615i	−0.203653	+	0.352738i
$218$		0			0
$219$	5.19615	−	3.00000i	0.351123	−	0.202721i
$220$		0			0
$221$	−24.5000	−	6.06218i	−1.64805	−	0.407786i
$222$		0			0
$223$	−11.2583	+	6.50000i	−0.753914	+	0.435272i	−0.827106	−	0.562046i	$-0.810015\pi$
$223$	−11.2583	+	6.50000i	−0.753914	+	0.435272i	0.0731927	+	0.997318i	$0.476681\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.9186	−	11.5000i	−1.32204	−	0.763282i	−0.337989	−	0.941150i	$-0.609747\pi$
$227$	−19.9186	−	11.5000i	−1.32204	−	0.763282i	−0.984054	+	0.177868i	$0.943080\pi$
$228$		0			0
$229$			24.2487i			1.60240i	0.598397	+	0.801200i	$0.295805\pi$
$229$			24.2487i			1.60240i	−0.598397	+	0.801200i	$0.704195\pi$
$230$		0			0
$231$	12.9904	+	22.5000i	0.854704	+	1.48039i
$232$		0			0
$233$	−8.00000			−0.524097			−0.262049	−	0.965055i	$-0.584398\pi$
$233$	−8.00000			−0.524097			−0.262049	+	0.965055i	$0.584398\pi$
$234$		0			0
$235$	13.8564			0.903892
$236$		0			0
$237$	−3.00000	−	5.19615i	−0.194871	−	0.337526i
$238$		0			0
$239$			2.00000i			0.129369i	0.997906	+	0.0646846i	$0.0206041\pi$
$239$			2.00000i			0.129369i	−0.997906	+	0.0646846i	$0.979396\pi$
$240$		0			0
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	0.238597	−	0.971119i	$-0.423312\pi$
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	−0.721715	+	0.692191i	$0.756646\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.00000	+	3.46410i	−0.383326	+	0.221313i
$246$		0			0
$247$	4.33013	−	17.5000i	0.275519	−	1.11350i
$248$		0			0
$249$	21.0000	−	12.1244i	1.33082	−	0.768350i
$250$		0			0
$251$	7.79423	−	13.5000i	0.491967	−	0.852112i	−0.507990	−	0.861363i	$-0.669611\pi$
$251$	7.79423	−	13.5000i	0.491967	−	0.852112i	0.999957	+	0.00925060i	$0.00294460\pi$
$252$		0			0
$253$	−22.5000	−	12.9904i	−1.41456	−	0.816698i
$254$		0			0
$255$		−	42.0000i		−	2.63014i
$256$		0			0
$257$	11.5000	+	19.9186i	0.717350	+	1.24249i	0.962046	+	0.272887i	$0.0879786\pi$
$257$	11.5000	+	19.9186i	0.717350	+	1.24249i	−0.244696	+	0.969600i	$0.578688\pi$
$258$		0			0
$259$	−15.5885			−0.968620
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.866025	+	1.50000i	0.0534014	+	0.0924940i	0.891490	−	0.453040i	$-0.149660\pi$
$263$	0.866025	+	1.50000i	0.0534014	+	0.0924940i	−0.838089	+	0.545534i	$0.816327\pi$
$264$		0			0
$265$			13.8564i			0.851192i
$266$		0			0
$267$	−2.59808	−	1.50000i	−0.159000	−	0.0917985i
$268$		0			0
$269$	−0.500000	+	0.866025i	−0.0304855	+	0.0528025i	−0.880866	−	0.473366i	$-0.843039\pi$
$269$	−0.500000	+	0.866025i	−0.0304855	+	0.0528025i	0.850380	+	0.526169i	$0.176372\pi$
$270$		0			0
$271$	−7.79423	+	4.50000i	−0.473466	+	0.273356i	−0.717689	−	0.696363i	$-0.754800\pi$
$271$	−7.79423	+	4.50000i	−0.473466	+	0.273356i	0.244224	+	0.969719i	$0.421467\pi$
$272$		0			0
$273$	18.0000	−	5.19615i	1.08941	−	0.314485i
$274$		0			0
$275$	−30.3109	+	17.5000i	−1.82782	+	1.05529i
$276$		0			0
$277$	−4.50000	+	7.79423i	−0.270379	+	0.468310i	−0.968959	−	0.247222i	$-0.920482\pi$
$277$	−4.50000	+	7.79423i	−0.270379	+	0.468310i	0.698580	+	0.715532i	$0.253816\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	24.2487i		−	1.44656i	−0.690557	−	0.723278i	$-0.742634\pi$
$281$		−	24.2487i		−	1.44656i	0.690557	−	0.723278i	$-0.257366\pi$
$282$		0			0
$283$	16.4545	+	28.5000i	0.978117	+	1.69415i	0.669238	+	0.743048i	$0.266621\pi$
$283$	16.4545	+	28.5000i	0.978117	+	1.69415i	0.308879	+	0.951101i	$0.400046\pi$
$284$		0			0
$285$	30.0000			1.77705
$286$		0			0
$287$	5.19615			0.306719
$288$		0			0
$289$	−16.0000	−	27.7128i	−0.941176	−	1.63017i
$290$		0			0
$291$		−	15.0000i		−	0.879316i
$292$		0			0
$293$	−22.5000	−	12.9904i	−1.31446	−	0.758906i	−0.331632	−	0.943409i	$-0.607599\pi$
$293$	−22.5000	−	12.9904i	−1.31446	−	0.758906i	−0.982832	+	0.184503i	$0.940933\pi$
$294$		0			0
$295$	12.1244	−	21.0000i	0.705907	−	1.22267i
$296$		0			0
$297$	−22.5000	+	12.9904i	−1.30558	+	0.753778i
$298$		0			0
$299$	−12.9904	+	13.5000i	−0.751253	+	0.780725i
$300$		0			0
$301$	13.5000	−	7.79423i	0.778127	−	0.449252i
$302$		0			0
$303$	−14.7224	+	25.5000i	−0.845782	+	1.46494i
$304$		0			0
$305$	−9.00000	−	5.19615i	−0.515339	−	0.297531i
$306$		0			0
$307$			6.00000i			0.342438i	0.985233	+	0.171219i	$0.0547706\pi$
$307$			6.00000i			0.342438i	−0.985233	+	0.171219i	$0.945229\pi$
$308$		0			0
$309$	6.00000	+	10.3923i	0.341328	+	0.591198i
$310$		0			0
$311$	20.7846			1.17859			0.589294	−	0.807919i	$-0.299406\pi$
$311$	20.7846			1.17859			0.589294	+	0.807919i	$0.299406\pi$
$312$		0			0
$313$	12.0000			0.678280			0.339140	−	0.940736i	$-0.389864\pi$
$313$	12.0000			0.678280			0.339140	+	0.940736i	$0.389864\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	6.92820i		−	0.389127i	−0.980890	−	0.194563i	$-0.937671\pi$
$317$		−	6.92820i		−	0.389127i	0.980890	−	0.194563i	$-0.0623290\pi$
$318$		0			0
$319$	21.6506	+	12.5000i	1.21220	+	0.699866i
$320$		0			0
$321$	−7.50000	+	12.9904i	−0.418609	+	0.725052i
$322$		0			0
$323$	30.3109	−	17.5000i	1.68654	−	0.973726i
$324$		0			0
$325$	7.00000	+	24.2487i	0.388290	+	1.34508i
$326$		0			0
$327$	−15.5885	+	9.00000i	−0.862044	+	0.497701i
$328$		0			0
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$		0			0
$331$	12.9904	+	7.50000i	0.714016	+	0.412237i	0.812546	−	0.582897i	$-0.198081\pi$
$331$	12.9904	+	7.50000i	0.714016	+	0.412237i	−0.0985303	+	0.995134i	$0.531414\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.19615	+	9.00000i	0.283896	+	0.491723i
$336$		0			0
$337$	−28.0000			−1.52526			−0.762629	−	0.646837i	$-0.776092\pi$
$337$	−28.0000			−1.52526			−0.762629	+	0.646837i	$0.776092\pi$
$338$		0			0
$339$	8.66025			0.470360
$340$		0			0
$341$	−5.00000	−	8.66025i	−0.270765	−	0.468979i
$342$		0			0
$343$			15.0000i			0.809924i
$344$		0			0
$345$	−27.0000	−	15.5885i	−1.45363	−	0.839254i
$346$		0			0
$347$	7.79423	−	13.5000i	0.418416	−	0.724718i	−0.577364	−	0.816487i	$-0.695919\pi$
$347$	7.79423	−	13.5000i	0.418416	−	0.724718i	0.995780	+	0.0917687i	$0.0292521\pi$
$348$		0			0
$349$	−13.5000	+	7.79423i	−0.722638	+	0.417215i	−0.815723	−	0.578443i	$-0.803661\pi$
$349$	−13.5000	+	7.79423i	−0.722638	+	0.417215i	0.0930846	+	0.995658i	$0.470327\pi$
$350$		0			0
$351$	5.19615	+	18.0000i	0.277350	+	0.960769i
$352$		0			0
$353$	13.5000	−	7.79423i	0.718532	−	0.414845i	−0.0956798	−	0.995412i	$-0.530502\pi$
$353$	13.5000	−	7.79423i	0.718532	−	0.414845i	0.814212	+	0.580567i	$0.197169\pi$
$354$		0			0
$355$	−12.1244	+	21.0000i	−0.643494	+	1.11456i
$356$		0			0
$357$	31.5000	+	18.1865i	1.66716	+	0.962533i
$358$		0			0
$359$			22.0000i			1.16112i	0.814219	+	0.580558i	$0.197165\pi$
$359$			22.0000i			1.16112i	−0.814219	+	0.580558i	$0.802835\pi$
$360$		0			0
$361$	3.00000	+	5.19615i	0.157895	+	0.273482i
$362$		0			0
$363$	−24.2487			−1.27273
$364$		0			0
$365$	−12.0000			−0.628109
$366$		0			0
$367$	−6.06218	−	10.5000i	−0.316443	−	0.548096i	0.663300	−	0.748354i	$-0.269155\pi$
$367$	−6.06218	−	10.5000i	−0.316443	−	0.548096i	−0.979743	+	0.200258i	$0.935822\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−10.3923	−	6.00000i	−0.539542	−	0.311504i
$372$		0			0
$373$	1.50000	−	2.59808i	0.0776671	−	0.134523i	−0.824576	−	0.565751i	$-0.808586\pi$
$373$	1.50000	−	2.59808i	0.0776671	−	0.134523i	0.902243	+	0.431228i	$0.141920\pi$
$374$		0			0
$375$	−10.3923	+	6.00000i	−0.536656	+	0.309839i
$376$		0			0
$377$	12.5000	−	12.9904i	0.643783	−	0.669039i
$378$		0			0
$379$	−6.06218	+	3.50000i	−0.311393	+	0.179783i	−0.647550	−	0.762023i	$-0.724206\pi$
$379$	−6.06218	+	3.50000i	−0.311393	+	0.179783i	0.336157	+	0.941806i	$0.390873\pi$
$380$		0			0
$381$	16.5000	−	28.5788i	0.845321	−	1.46414i
$382$		0			0
$383$	−6.06218	−	3.50000i	−0.309763	−	0.178842i	0.337058	−	0.941484i	$-0.390568\pi$
$383$	−6.06218	−	3.50000i	−0.309763	−	0.178842i	−0.646820	+	0.762642i	$0.723902\pi$
$384$		0			0
$385$		−	51.9615i		−	2.64820i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	14.0000			0.709828			0.354914	−	0.934899i	$-0.384510\pi$
$389$	14.0000			0.709828			0.354914	+	0.934899i	$0.384510\pi$
$390$		0			0
$391$	−36.3731			−1.83947
$392$		0			0
$393$	12.0000	+	20.7846i	0.605320	+	1.04844i
$394$		0			0
$395$			12.0000i			0.603786i
$396$		0			0
$397$	28.5000	+	16.4545i	1.43037	+	0.825827i	0.997149	−	0.0754589i	$-0.0240422\pi$
$397$	28.5000	+	16.4545i	1.43037	+	0.825827i	0.433225	+	0.901286i	$0.357376\pi$
$398$		0			0
$399$	−12.9904	+	22.5000i	−0.650332	+	1.12641i
$400$		0			0
$401$	28.5000	−	16.4545i	1.42322	−	0.821698i	0.426649	−	0.904417i	$-0.359694\pi$
$401$	28.5000	−	16.4545i	1.42322	−	0.821698i	0.996573	+	0.0827195i	$0.0263606\pi$
$402$		0			0
$403$	−6.92820	+	2.00000i	−0.345118	+	0.0996271i
$404$		0			0
$405$	−27.0000	+	15.5885i	−1.34164	+	0.774597i
$406$		0			0
$407$	12.9904	−	22.5000i	0.643909	−	1.11528i
$408$		0			0
$409$	−13.5000	−	7.79423i	−0.667532	−	0.385400i	0.127609	−	0.991825i	$-0.459270\pi$
$409$	−13.5000	−	7.79423i	−0.667532	−	0.385400i	−0.795141	+	0.606425i	$0.792603\pi$
$410$		0			0
$411$			9.00000i			0.443937i
$412$		0			0
$413$	10.5000	+	18.1865i	0.516671	+	0.894901i
$414$		0			0
$415$	−48.4974			−2.38064
$416$		0			0
$417$	15.0000			0.734553
$418$		0			0
$419$	14.7224	+	25.5000i	0.719238	+	1.24576i	0.961302	+	0.275496i	$0.0888422\pi$
$419$	14.7224	+	25.5000i	0.719238	+	1.24576i	−0.242064	+	0.970260i	$0.577824\pi$
$420$		0			0
$421$			31.1769i			1.51947i	0.650233	+	0.759735i	$0.274671\pi$
$421$			31.1769i			1.51947i	−0.650233	+	0.759735i	$0.725329\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−24.5000	+	42.4352i	−1.18842	+	2.05841i
$426$		0			0
$427$	7.79423	−	4.50000i	0.377189	−	0.217770i
$428$		0			0
$429$	−7.50000	+	30.3109i	−0.362103	+	1.46342i
$430$		0			0
$431$	32.0429	−	18.5000i	1.54345	−	0.891114i	0.544837	−	0.838542i	$-0.316592\pi$
$431$	32.0429	−	18.5000i	1.54345	−	0.891114i	0.998617	−	0.0525716i	$-0.0167418\pi$
$432$		0			0
$433$	−16.5000	+	28.5788i	−0.792939	+	1.37341i	0.131200	+	0.991356i	$0.458117\pi$
$433$	−16.5000	+	28.5788i	−0.792939	+	1.37341i	−0.924139	+	0.382055i	$0.875216\pi$
$434$		0			0
$435$	25.9808	+	15.0000i	1.24568	+	0.719195i
$436$		0			0
$437$		−	25.9808i		−	1.24283i
$438$		0			0
$439$	2.59808	+	4.50000i	0.123999	+	0.214773i	0.921341	−	0.388755i	$-0.127095\pi$
$439$	2.59808	+	4.50000i	0.123999	+	0.214773i	−0.797342	+	0.603528i	$0.793761\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−13.8564			−0.658338			−0.329169	−	0.944271i	$-0.606769\pi$
$443$	−13.8564			−0.658338			−0.329169	+	0.944271i	$0.606769\pi$
$444$		0			0
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$		0			0
$447$		−	15.0000i		−	0.709476i
$448$		0			0
$449$	−7.50000	−	4.33013i	−0.353947	−	0.204351i	0.312475	−	0.949926i	$-0.398842\pi$
$449$	−7.50000	−	4.33013i	−0.353947	−	0.204351i	−0.666422	+	0.745575i	$0.732175\pi$
$450$		0			0
$451$	−4.33013	+	7.50000i	−0.203898	+	0.353161i
$452$		0			0
$453$	−3.00000	+	1.73205i	−0.140952	+	0.0813788i
$454$		0			0
$455$	−36.3731	−	9.00000i	−1.70520	−	0.421927i
$456$		0			0
$457$	31.5000	−	18.1865i	1.47351	−	0.850730i	0.473953	−	0.880550i	$-0.342827\pi$
$457$	31.5000	−	18.1865i	1.47351	−	0.850730i	0.999555	+	0.0298202i	$0.00949348\pi$
$458$		0			0
$459$	−18.1865	+	31.5000i	−0.848875	+	1.47029i
$460$		0			0
$461$	4.50000	+	2.59808i	0.209586	+	0.121004i	0.601119	−	0.799160i	$-0.294722\pi$
$461$	4.50000	+	2.59808i	0.209586	+	0.121004i	−0.391533	+	0.920164i	$0.628055\pi$
$462$		0			0
$463$			18.0000i			0.836531i	0.908325	+	0.418265i	$0.137362\pi$
$463$			18.0000i			0.836531i	−0.908325	+	0.418265i	$0.862638\pi$
$464$		0			0
$465$	−6.00000	−	10.3923i	−0.278243	−	0.481932i
$466$		0			0
$467$	38.1051			1.76329			0.881647	−	0.471909i	$-0.156435\pi$
$467$	38.1051			1.76329			0.881647	+	0.471909i	$0.156435\pi$
$468$		0			0
$469$	−9.00000			−0.415581
$470$		0			0
$471$	6.92820	+	12.0000i	0.319235	+	0.552931i
$472$		0			0
$473$			25.9808i			1.19460i
$474$		0			0
$475$	−30.3109	−	17.5000i	−1.39076	−	0.802955i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.7224	−	8.50000i	0.672685	−	0.388375i	−0.124408	−	0.992231i	$-0.539703\pi$
$479$	14.7224	−	8.50000i	0.672685	−	0.388375i	0.797093	+	0.603856i	$0.206370\pi$
$480$		0			0
$481$	−13.5000	−	12.9904i	−0.615547	−	0.592310i
$482$		0			0
$483$	23.3827	−	13.5000i	1.06395	−	0.614271i
$484$		0			0
$485$	−15.0000	+	25.9808i	−0.681115	+	1.17973i
$486$		0			0
$487$	19.9186	+	11.5000i	0.902597	+	0.521115i	0.878042	−	0.478584i	$-0.158850\pi$
$487$	19.9186	+	11.5000i	0.902597	+	0.521115i	0.0245553	+	0.999698i	$0.492183\pi$
$488$		0			0
$489$		−	32.9090i		−	1.48819i
$490$		0			0
$491$	−6.06218	−	10.5000i	−0.273582	−	0.473858i	0.696194	−	0.717853i	$-0.254875\pi$
$491$	−6.06218	−	10.5000i	−0.273582	−	0.473858i	−0.969776	+	0.243995i	$0.921542\pi$
$492$		0			0
$493$	35.0000			1.57632
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.5000	−	18.1865i	−0.470989	−	0.815778i
$498$		0			0
$499$			6.00000i			0.268597i	0.990941	+	0.134298i	$0.0428781\pi$
$499$			6.00000i			0.268597i	−0.990941	+	0.134298i	$0.957122\pi$
$500$		0			0
$501$	−28.5000	−	16.4545i	−1.27329	−	0.735132i
$502$		0			0
$503$	−4.33013	+	7.50000i	−0.193071	+	0.334408i	−0.946266	−	0.323388i	$-0.895178\pi$
$503$	−4.33013	+	7.50000i	−0.193071	+	0.334408i	0.753196	+	0.657797i	$0.228511\pi$
$504$		0			0
$505$	51.0000	−	29.4449i	2.26947	−	1.31028i
$506$		0			0
$507$	19.9186	+	10.5000i	0.884615	+	0.466321i
$508$		0			0
$509$	−19.5000	+	11.2583i	−0.864322	+	0.499017i	−0.865457	−	0.500983i	$-0.832972\pi$
$509$	−19.5000	+	11.2583i	−0.864322	+	0.499017i	0.00113503	+	0.999999i	$0.499639\pi$
$510$		0			0
$511$	5.19615	−	9.00000i	0.229864	−	0.398137i
$512$		0			0
$513$	−22.5000	−	12.9904i	−0.993399	−	0.573539i
$514$		0			0
$515$		−	24.0000i		−	1.05757i
$516$		0			0
$517$	−10.0000	−	17.3205i	−0.439799	−	0.761755i
$518$		0			0
$519$	12.1244			0.532200
$520$		0			0
$521$	4.00000			0.175243			0.0876216	−	0.996154i	$-0.472073\pi$
$521$	4.00000			0.175243			0.0876216	+	0.996154i	$0.472073\pi$
$522$		0			0
$523$	−6.06218	−	10.5000i	−0.265081	−	0.459133i	0.702504	−	0.711680i	$-0.252065\pi$
$523$	−6.06218	−	10.5000i	−0.265081	−	0.459133i	−0.967585	+	0.252547i	$0.918732\pi$
$524$		0			0
$525$		−	36.3731i		−	1.58745i
$526$		0			0
$527$	−12.1244	−	7.00000i	−0.528145	−	0.304925i
$528$		0			0
$529$	−2.00000	+	3.46410i	−0.0869565	+	0.150613i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.50000	+	4.33013i	0.194917	+	0.187559i
$534$		0			0
$535$	25.9808	−	15.0000i	1.12325	−	0.648507i
$536$		0			0
$537$	16.5000	−	28.5788i	0.712028	−	1.23327i
$538$		0			0
$539$	8.66025	+	5.00000i	0.373024	+	0.215365i
$540$		0			0
$541$			20.7846i			0.893600i	0.894634	+	0.446800i	$0.147436\pi$
$541$			20.7846i			0.893600i	−0.894634	+	0.446800i	$0.852564\pi$
$542$		0			0
$543$	−10.3923	−	18.0000i	−0.445976	−	0.772454i
$544$		0			0
$545$	36.0000			1.54207
$546$		0			0
$547$	6.92820			0.296229			0.148114	−	0.988970i	$-0.452680\pi$
$547$	6.92820			0.296229			0.148114	+	0.988970i	$0.452680\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			25.0000i			1.06504i
$552$		0			0
$553$	−9.00000	−	5.19615i	−0.382719	−	0.220963i
$554$		0			0
$555$	15.5885	−	27.0000i	0.661693	−	1.14609i
$556$		0			0
$557$	−34.5000	+	19.9186i	−1.46181	+	0.843978i	−0.999095	−	0.0425287i	$-0.986459\pi$
$557$	−34.5000	+	19.9186i	−1.46181	+	0.843978i	−0.462717	+	0.886506i	$0.653125\pi$
$558$		0			0
$559$	18.1865	+	4.50000i	0.769208	+	0.190330i
$560$		0			0
$561$	−52.5000	+	30.3109i	−2.21655	+	1.27973i
$562$		0			0
$563$	−4.33013	+	7.50000i	−0.182493	+	0.316087i	−0.942729	−	0.333560i	$-0.891750\pi$
$563$	−4.33013	+	7.50000i	−0.182493	+	0.316087i	0.760236	+	0.649647i	$0.225083\pi$
$564$		0			0
$565$	−15.0000	−	8.66025i	−0.631055	−	0.364340i
$566$		0			0
$567$		−	27.0000i		−	1.13389i
$568$		0			0
$569$	−15.5000	−	26.8468i	−0.649794	−	1.12548i	−0.983172	−	0.182683i	$-0.941522\pi$
$569$	−15.5000	−	26.8468i	−0.649794	−	1.12548i	0.333378	−	0.942793i	$-0.391811\pi$
$570$		0			0
$571$	−27.7128			−1.15975			−0.579873	−	0.814707i	$-0.696898\pi$
$571$	−27.7128			−1.15975			−0.579873	+	0.814707i	$0.696898\pi$
$572$		0			0
$573$	−21.0000			−0.877288
$574$		0			0
$575$	18.1865	+	31.5000i	0.758431	+	1.31364i
$576$		0			0
$577$			24.2487i			1.00949i	0.863269	+	0.504744i	$0.168413\pi$
$577$			24.2487i			1.00949i	−0.863269	+	0.504744i	$0.831587\pi$
$578$		0			0
$579$	−18.1865	−	10.5000i	−0.755807	−	0.436365i
$580$		0			0
$581$	21.0000	−	36.3731i	0.871227	−	1.50901i
$582$		0			0
$583$	17.3205	−	10.0000i	0.717342	−	0.414158i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	16.4545	−	9.50000i	0.679149	−	0.392107i	−0.120385	−	0.992727i	$-0.538413\pi$
$587$	16.4545	−	9.50000i	0.679149	−	0.392107i	0.799534	+	0.600620i	$0.205080\pi$
$588$		0			0
$589$	5.00000	−	8.66025i	0.206021	−	0.356840i
$590$		0			0
$591$	−2.59808	−	1.50000i	−0.106871	−	0.0617018i
$592$		0			0
$593$			38.1051i			1.56479i	0.622783	+	0.782395i	$0.286002\pi$
$593$			38.1051i			1.56479i	−0.622783	+	0.782395i	$0.713998\pi$
$594$		0			0
$595$	−36.3731	−	63.0000i	−1.49115	−	2.58275i
$596$		0			0
$597$	−3.00000			−0.122782
$598$		0			0
$599$	−17.3205			−0.707697			−0.353848	−	0.935303i	$-0.615127\pi$
$599$	−17.3205			−0.707697			−0.353848	+	0.935303i	$0.615127\pi$
$600$		0			0
$601$	19.5000	+	33.7750i	0.795422	+	1.37771i	0.922571	+	0.385827i	$0.126084\pi$
$601$	19.5000	+	33.7750i	0.795422	+	1.37771i	−0.127150	+	0.991884i	$0.540583\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	42.0000	+	24.2487i	1.70754	+	0.985850i
$606$		0			0
$607$	21.6506	−	37.5000i	0.878772	−	1.52208i	0.0260828	−	0.999660i	$-0.491697\pi$
$607$	21.6506	−	37.5000i	0.878772	−	1.52208i	0.852689	−	0.522418i	$-0.174970\pi$
$608$		0			0
$609$	−22.5000	+	12.9904i	−0.911746	+	0.526397i
$610$		0			0
$611$	−13.8564	+	4.00000i	−0.560570	+	0.161823i
$612$		0			0
$613$	34.5000	−	19.9186i	1.39344	−	0.804504i	0.399747	−	0.916625i	$-0.369098\pi$
$613$	34.5000	−	19.9186i	1.39344	−	0.804504i	0.993695	+	0.112121i	$0.0357645\pi$
$614$		0			0
$615$	−5.19615	+	9.00000i	−0.209529	+	0.362915i
$616$		0			0
$617$	−4.50000	−	2.59808i	−0.181163	−	0.104595i	0.406676	−	0.913573i	$-0.366688\pi$
$617$	−4.50000	−	2.59808i	−0.181163	−	0.104595i	−0.587839	+	0.808978i	$0.700021\pi$
$618$		0			0
$619$			6.00000i			0.241160i	0.992704	+	0.120580i	$0.0384755\pi$
$619$			6.00000i			0.241160i	−0.992704	+	0.120580i	$0.961525\pi$
$620$		0			0
$621$	13.5000	+	23.3827i	0.541736	+	0.938315i
$622$		0			0
$623$	−5.19615			−0.208179
$624$		0			0
$625$	−11.0000			−0.440000
$626$		0			0
$627$	−21.6506	−	37.5000i	−0.864643	−	1.49761i
$628$		0			0
$629$		−	36.3731i		−	1.45029i
$630$		0			0
$631$	−4.33013	−	2.50000i	−0.172380	−	0.0995234i	0.411328	−	0.911487i	$-0.365065\pi$
$631$	−4.33013	−	2.50000i	−0.172380	−	0.0995234i	−0.583707	+	0.811964i	$0.698398\pi$
$632$		0			0
$633$	4.50000	−	7.79423i	0.178859	−	0.309793i
$634$		0			0
$635$	−57.1577	+	33.0000i	−2.26823	+	1.30957i
$636$		0			0
$637$	5.00000	−	5.19615i	0.198107	−	0.205879i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.500000	+	0.866025i	−0.0197488	+	0.0342059i	−0.875731	−	0.482800i	$-0.839620\pi$
$641$	−0.500000	+	0.866025i	−0.0197488	+	0.0342059i	0.855982	+	0.517005i	$0.172953\pi$
$642$		0			0
$643$	−7.79423	−	4.50000i	−0.307374	−	0.177463i	0.338377	−	0.941011i	$-0.390122\pi$
$643$	−7.79423	−	4.50000i	−0.307374	−	0.177463i	−0.645751	+	0.763548i	$0.723456\pi$
$644$		0			0
$645$			31.1769i			1.22759i
$646$		0			0
$647$	−7.79423	−	13.5000i	−0.306423	−	0.530740i	0.671154	−	0.741318i	$-0.265799\pi$
$647$	−7.79423	−	13.5000i	−0.306423	−	0.530740i	−0.977577	+	0.210578i	$0.932465\pi$
$648$		0			0
$649$	−35.0000			−1.37387
$650$		0			0
$651$	10.3923			0.407307
$652$		0			0
$653$	−2.50000	−	4.33013i	−0.0978326	−	0.169451i	0.812955	−	0.582327i	$-0.197858\pi$
$653$	−2.50000	−	4.33013i	−0.0978326	−	0.169451i	−0.910787	+	0.412876i	$0.864524\pi$
$654$		0			0
$655$		−	48.0000i		−	1.87552i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	18.1865	−	31.5000i	0.708447	−	1.22707i	−0.256986	−	0.966415i	$-0.582730\pi$
$659$	18.1865	−	31.5000i	0.708447	−	1.22707i	0.965433	−	0.260651i	$-0.0839371\pi$
$660$		0			0
$661$	−1.50000	+	0.866025i	−0.0583432	+	0.0336845i	−0.528888	−	0.848692i	$-0.677391\pi$
$661$	−1.50000	+	0.866025i	−0.0583432	+	0.0336845i	0.470545	+	0.882376i	$0.344057\pi$
$662$		0			0
$663$	12.1244	+	42.0000i	0.470871	+	1.63114i
$664$		0			0
$665$	45.0000	−	25.9808i	1.74503	−	1.00749i
$666$		0			0
$667$	12.9904	−	22.5000i	0.502990	−	0.871203i
$668$		0			0
$669$	19.5000	+	11.2583i	0.753914	+	0.435272i
$670$		0			0
$671$			15.0000i			0.579069i
$672$		0			0
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	0.925832	+	0.377934i	$0.123365\pi$
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	−0.135615	+	0.990762i	$0.543301\pi$
$674$		0			0
$675$	36.3731			1.40000
$676$		0			0
$677$	−8.00000			−0.307465			−0.153732	−	0.988113i	$-0.549129\pi$
$677$	−8.00000			−0.307465			−0.153732	+	0.988113i	$0.549129\pi$
$678$		0			0
$679$	−12.9904	−	22.5000i	−0.498525	−	0.863471i
$680$		0			0
$681$			39.8372i			1.52656i
$682$		0			0
$683$	35.5070	+	20.5000i	1.35864	+	0.784411i	0.989440	−	0.144940i	$-0.0462988\pi$
$683$	35.5070	+	20.5000i	1.35864	+	0.784411i	0.369199	+	0.929350i	$0.379632\pi$
$684$		0			0
$685$	9.00000	−	15.5885i	0.343872	−	0.595604i
$686$		0			0
$687$	36.3731	−	21.0000i	1.38772	−	0.801200i
$688$		0			0
$689$	−4.00000	−	13.8564i	−0.152388	−	0.527887i
$690$		0			0
$691$	−12.9904	+	7.50000i	−0.494177	+	0.285313i	−0.726306	−	0.687372i	$-0.758764\pi$
$691$	−12.9904	+	7.50000i	−0.494177	+	0.285313i	0.232128	+	0.972685i	$0.425431\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−25.9808	−	15.0000i	−0.985506	−	0.568982i
$696$		0			0
$697$			12.1244i			0.459243i
$698$		0			0
$699$	6.92820	+	12.0000i	0.262049	+	0.453882i
$700$		0			0
$701$	8.00000			0.302156			0.151078	−	0.988522i	$-0.451726\pi$
$701$	8.00000			0.302156			0.151078	+	0.988522i	$0.451726\pi$
$702$		0			0
$703$	25.9808			0.979883
$704$		0			0
$705$	−12.0000	−	20.7846i	−0.451946	−	0.782794i
$706$		0			0
$707$			51.0000i			1.91805i
$708$		0			0
$709$	−1.50000	−	0.866025i	−0.0563337	−	0.0325243i	0.471569	−	0.881829i	$-0.343688\pi$
$709$	−1.50000	−	0.866025i	−0.0563337	−	0.0325243i	−0.527902	+	0.849305i	$0.677021\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9.00000	+	5.19615i	−0.337053	+	0.194597i
$714$		0			0
$715$	43.3013	−	45.0000i	1.61938	−	1.68290i
$716$		0			0
$717$	3.00000	−	1.73205i	0.112037	−	0.0646846i
$718$		0			0
$719$	6.06218	−	10.5000i	0.226081	−	0.391584i	−0.730562	−	0.682846i	$-0.760742\pi$
$719$	6.06218	−	10.5000i	0.226081	−	0.391584i	0.956643	+	0.291262i	$0.0940752\pi$
$720$		0			0
$721$	18.0000	+	10.3923i	0.670355	+	0.387030i
$722$		0			0
$723$			15.0000i			0.557856i
$724$		0			0
$725$	−17.5000	−	30.3109i	−0.649934	−	1.12572i
$726$		0			0
$727$	−41.5692			−1.54172			−0.770859	−	0.637006i	$-0.780172\pi$
$727$	−41.5692			−1.54172			−0.770859	+	0.637006i	$0.780172\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	18.1865	+	31.5000i	0.672653	+	1.16507i
$732$		0			0
$733$		−	48.4974i		−	1.79129i	−0.444766	−	0.895647i	$-0.646713\pi$
$733$		−	48.4974i		−	1.79129i	0.444766	−	0.895647i	$-0.353287\pi$
$734$		0			0
$735$	10.3923	+	6.00000i	0.383326	+	0.221313i
$736$		0			0
$737$	7.50000	−	12.9904i	0.276266	−	0.478507i
$738$		0			0
$739$	−18.1865	+	10.5000i	−0.669002	+	0.386249i	−0.795699	−	0.605693i	$-0.792896\pi$
$739$	−18.1865	+	10.5000i	−0.669002	+	0.386249i	0.126696	+	0.991942i	$0.459563\pi$
$740$		0			0
$741$	−30.0000	+	8.66025i	−1.10208	+	0.318142i
$742$		0			0
$743$	11.2583	−	6.50000i	0.413028	−	0.238462i	−0.279062	−	0.960273i	$-0.590023\pi$
$743$	11.2583	−	6.50000i	0.413028	−	0.238462i	0.692090	+	0.721811i	$0.256690\pi$
$744$		0			0
$745$	−15.0000	+	25.9808i	−0.549557	+	0.951861i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			25.9808i			0.949316i
$750$		0			0
$751$	−6.06218	−	10.5000i	−0.221212	−	0.383150i	0.733964	−	0.679188i	$-0.237668\pi$
$751$	−6.06218	−	10.5000i	−0.221212	−	0.383150i	−0.955176	+	0.296038i	$0.904335\pi$
$752$		0			0
$753$	−27.0000			−0.983935
$754$		0			0
$755$	6.92820			0.252143
$756$		0			0
$757$	−26.5000	−	45.8993i	−0.963159	−	1.66824i	−0.714482	−	0.699654i	$-0.753338\pi$
$757$	−26.5000	−	45.8993i	−0.963159	−	1.66824i	−0.248677	−	0.968587i	$-0.579996\pi$
$758$		0			0
$759$			45.0000i			1.63340i
$760$		0			0
$761$	40.5000	+	23.3827i	1.46812	+	0.847622i	0.999362	−	0.0357031i	$-0.0113671\pi$
$761$	40.5000	+	23.3827i	1.46812	+	0.847622i	0.468761	+	0.883325i	$0.344700\pi$
$762$		0			0
$763$	−15.5885	+	27.0000i	−0.564340	+	0.977466i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.06218	+	24.5000i	−0.218893	+	0.884644i
$768$		0			0
$769$	−25.5000	+	14.7224i	−0.919554	+	0.530904i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−25.5000	+	14.7224i	−0.919554	+	0.530904i	−0.0360609	+	0.999350i	$0.511481\pi$
$770$		0			0
$771$	19.9186	−	34.5000i	0.717350	−	1.24249i
$772$		0			0
$773$	−1.50000	−	0.866025i	−0.0539513	−	0.0311488i	0.472782	−	0.881180i	$-0.343250\pi$
$773$	−1.50000	−	0.866025i	−0.0539513	−	0.0311488i	−0.526733	+	0.850031i	$0.676583\pi$
$774$		0			0
$775$			14.0000i			0.502895i
$776$		0			0
$777$	13.5000	+	23.3827i	0.484310	+	0.838849i
$778$		0			0
$779$	−8.66025			−0.310286
$780$		0			0
$781$	35.0000			1.25240
$782$		0			0
$783$	−12.9904	−	22.5000i	−0.464238	−	0.804084i
$784$		0			0
$785$		−	27.7128i		−	0.989113i
$786$		0			0
$787$	−7.79423	−	4.50000i	−0.277834	−	0.160408i	0.354608	−	0.935015i	$-0.384614\pi$
$787$	−7.79423	−	4.50000i	−0.277834	−	0.160408i	−0.632443	+	0.774607i	$0.717948\pi$
$788$		0			0
$789$	1.50000	−	2.59808i	0.0534014	−	0.0924940i
$790$		0			0
$791$	12.9904	−	7.50000i	0.461885	−	0.266669i
$792$		0			0
$793$	10.5000	+	2.59808i	0.372866	+	0.0922604i
$794$		0			0
$795$	20.7846	−	12.0000i	0.737154	−	0.425596i
$796$		0			0
$797$	−9.50000	+	16.4545i	−0.336507	+	0.582848i	−0.983773	−	0.179417i	$-0.942579\pi$
$797$	−9.50000	+	16.4545i	−0.336507	+	0.582848i	0.647266	+	0.762264i	$0.275912\pi$
$798$		0			0
$799$	−24.2487	−	14.0000i	−0.857858	−	0.495284i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.66025	+	15.0000i	0.305614	+	0.529339i
$804$		0			0
$805$	−54.0000			−1.90325
$806$		0			0
$807$	1.73205			0.0609711
$808$		0			0
$809$	5.50000	+	9.52628i	0.193370	+	0.334926i	0.946365	−	0.323100i	$-0.104725\pi$
$809$	5.50000	+	9.52628i	0.193370	+	0.334926i	−0.752995	+	0.658026i	$0.771392\pi$
$810$		0			0
$811$		−	32.0000i		−	1.12367i	−0.827249	−	0.561836i	$-0.810095\pi$
$811$		−	32.0000i		−	1.12367i	0.827249	−	0.561836i	$-0.189905\pi$
$812$		0			0
$813$	13.5000	+	7.79423i	0.473466	+	0.273356i
$814$		0			0
$815$	−32.9090	+	57.0000i	−1.15275	+	1.99662i
$816$		0			0
$817$	−22.5000	+	12.9904i	−0.787175	+	0.454476i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−16.5000	+	9.52628i	−0.575854	+	0.332469i	−0.759484	−	0.650526i	$-0.774548\pi$
$821$	−16.5000	+	9.52628i	−0.575854	+	0.332469i	0.183630	+	0.982995i	$0.441215\pi$
$822$		0			0
$823$	4.33013	−	7.50000i	0.150939	−	0.261434i	−0.780634	−	0.624988i	$-0.785104\pi$
$823$	4.33013	−	7.50000i	0.150939	−	0.261434i	0.931573	+	0.363555i	$0.118437\pi$
$824$		0			0
$825$	52.5000	+	30.3109i	1.82782	+	1.05529i
$826$		0			0
$827$		−	22.0000i		−	0.765015i	−0.923952	−	0.382507i	$-0.875061\pi$
$827$		−	22.0000i		−	0.765015i	0.923952	−	0.382507i	$-0.124939\pi$
$828$		0			0
$829$	−17.5000	−	30.3109i	−0.607800	−	1.05274i	−0.991602	−	0.129325i	$-0.958719\pi$
$829$	−17.5000	−	30.3109i	−0.607800	−	1.05274i	0.383802	−	0.923415i	$-0.374614\pi$
$830$		0			0
$831$	15.5885			0.540758
$832$		0			0
$833$	14.0000			0.485071
$834$		0			0
$835$	32.9090	+	57.0000i	1.13886	+	1.97257i
$836$		0			0
$837$			10.3923i			0.359211i
$838$		0			0
$839$	9.52628	+	5.50000i	0.328884	+	0.189881i	0.655345	−	0.755329i	$-0.272523\pi$
$839$	9.52628	+	5.50000i	0.328884	+	0.189881i	−0.326462	+	0.945210i	$0.605856\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$		0			0
$843$	−36.3731	+	21.0000i	−1.25275	+	0.723278i
$844$		0			0
$845$	−24.0000	−	38.1051i	−0.825625	−	1.31086i
$846$		0			0
$847$	−36.3731	+	21.0000i	−1.24979	+	0.721569i
$848$		0			0
$849$	28.5000	−	49.3634i	0.978117	−	1.69415i
$850$		0			0
$851$	−23.3827	−	13.5000i	−0.801548	−	0.462774i
$852$		0			0
$853$			17.3205i			0.593043i	0.955026	+	0.296521i	$0.0958266\pi$
$853$			17.3205i			0.593043i	−0.955026	+	0.296521i	$0.904173\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−44.0000			−1.50301			−0.751506	−	0.659727i	$-0.770672\pi$
$857$	−44.0000			−1.50301			−0.751506	+	0.659727i	$0.770672\pi$
$858$		0			0
$859$	−41.5692			−1.41832			−0.709162	−	0.705046i	$-0.750926\pi$
$859$	−41.5692			−1.41832			−0.709162	+	0.705046i	$0.750926\pi$
$860$		0			0
$861$	−4.50000	−	7.79423i	−0.153360	−	0.265627i
$862$		0			0
$863$		−	2.00000i		−	0.0680808i	−0.999420	−	0.0340404i	$-0.989163\pi$
$863$		−	2.00000i		−	0.0680808i	0.999420	−	0.0340404i	$-0.0108375\pi$
$864$		0			0
$865$	−21.0000	−	12.1244i	−0.714021	−	0.412240i
$866$		0			0
$867$	−27.7128	+	48.0000i	−0.941176	+	1.63017i
$868$		0			0
$869$	15.0000	−	8.66025i	0.508840	−	0.293779i
$870$		0			0
$871$	−7.79423	−	7.50000i	−0.264097	−	0.254128i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−10.3923	+	18.0000i	−0.351324	+	0.608511i
$876$		0			0
$877$	7.50000	+	4.33013i	0.253257	+	0.146218i	0.621255	−	0.783609i	$-0.286623\pi$
$877$	7.50000	+	4.33013i	0.253257	+	0.146218i	−0.367998	+	0.929827i	$0.619957\pi$
$878$		0			0
$879$			45.0000i			1.51781i
$880$		0			0
$881$	−12.5000	−	21.6506i	−0.421136	−	0.729428i	0.574915	−	0.818213i	$-0.305035\pi$
$881$	−12.5000	−	21.6506i	−0.421136	−	0.729428i	−0.996051	+	0.0887846i	$0.971702\pi$
$882$		0			0
$883$	13.8564			0.466305			0.233153	−	0.972440i	$-0.425096\pi$
$883$	13.8564			0.466305			0.233153	+	0.972440i	$0.425096\pi$
$884$		0			0
$885$	−42.0000			−1.41181
$886$		0			0
$887$	−25.1147	−	43.5000i	−0.843270	−	1.46059i	−0.887115	−	0.461549i	$-0.847294\pi$
$887$	−25.1147	−	43.5000i	−0.843270	−	1.46059i	0.0438445	−	0.999038i	$-0.486039\pi$
$888$		0			0
$889$		−	57.1577i		−	1.91701i
$890$		0			0
$891$	38.9711	+	22.5000i	1.30558	+	0.753778i
$892$		0			0
$893$	10.0000	−	17.3205i	0.334637	−	0.579609i
$894$		0			0
$895$	−57.1577	+	33.0000i	−1.91057	+	1.10307i
$896$		0			0
$897$	31.5000	+	7.79423i	1.05175	+	0.260242i
$898$		0			0
$899$	8.66025	−	5.00000i	0.288836	−	0.166759i
$900$		0			0
$901$	14.0000	−	24.2487i	0.466408	−	0.807842i
$902$		0			0
$903$	−23.3827	−	13.5000i	−0.778127	−	0.449252i
$904$		0			0
$905$			41.5692i			1.38181i
$906$		0			0
$907$	−21.6506	−	37.5000i	−0.718898	−	1.24517i	−0.961437	−	0.275026i	$-0.911314\pi$
$907$	−21.6506	−	37.5000i	−0.718898	−	1.24517i	0.242539	−	0.970142i	$-0.422020\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	13.8564			0.459083			0.229542	−	0.973299i	$-0.426277\pi$
$911$	13.8564			0.459083			0.229542	+	0.973299i	$0.426277\pi$
$912$		0			0
$913$	35.0000	+	60.6218i	1.15833	+	2.00629i
$914$		0			0
$915$			18.0000i			0.595062i
$916$		0			0
$917$	36.0000	+	20.7846i	1.18882	+	0.686368i
$918$		0			0
$919$	−21.6506	+	37.5000i	−0.714189	+	1.23701i	0.249083	+	0.968482i	$0.419871\pi$
$919$	−21.6506	+	37.5000i	−0.714189	+	1.23701i	−0.963272	+	0.268529i	$0.913463\pi$
$920$		0			0
$921$	9.00000	−	5.19615i	0.296560	−	0.171219i
$922$		0			0
$923$	6.06218	−	24.5000i	0.199539	−	0.806427i
$924$		0			0
$925$	−31.5000	+	18.1865i	−1.03571	+	0.597970i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−37.5000	−	21.6506i	−1.23034	−	0.710334i	−0.263235	−	0.964732i	$-0.584790\pi$
$929$	−37.5000	−	21.6506i	−1.23034	−	0.710334i	−0.967100	+	0.254397i	$0.918123\pi$
$930$		0			0
$931$			10.0000i			0.327737i
$932$		0			0
$933$	−18.0000	−	31.1769i	−0.589294	−	1.02069i
$934$		0			0
$935$	121.244			3.96509
$936$		0			0
$937$	−24.0000			−0.784046			−0.392023	−	0.919955i	$-0.628225\pi$
$937$	−24.0000			−0.784046			−0.392023	+	0.919955i	$0.628225\pi$
$938$		0			0
$939$	−10.3923	−	18.0000i	−0.339140	−	0.587408i
$940$		0			0
$941$			20.7846i			0.677559i	0.940866	+	0.338779i	$0.110014\pi$
$941$			20.7846i			0.677559i	−0.940866	+	0.338779i	$0.889986\pi$
$942$		0			0
$943$	7.79423	+	4.50000i	0.253815	+	0.146540i
$944$		0			0
$945$	−27.0000	+	46.7654i	−0.878310	+	1.52128i
$946$		0			0
$947$	−26.8468	+	15.5000i	−0.872403	+	0.503682i	−0.868146	−	0.496309i	$-0.834688\pi$
$947$	−26.8468	+	15.5000i	−0.872403	+	0.503682i	−0.00425721	+	0.999991i	$0.501355\pi$
$948$		0			0
$949$	12.0000	−	3.46410i	0.389536	−	0.112449i
$950$		0			0
$951$	−10.3923	+	6.00000i	−0.336994	+	0.194563i
$952$		0			0
$953$	6.50000	−	11.2583i	0.210556	−	0.364693i	−0.741333	−	0.671137i	$-0.765806\pi$
$953$	6.50000	−	11.2583i	0.210556	−	0.364693i	0.951889	+	0.306444i	$0.0991394\pi$
$954$		0			0
$955$	36.3731	+	21.0000i	1.17700	+	0.679544i
$956$		0			0
$957$		−	43.3013i		−	1.39973i
$958$		0			0
$959$	7.79423	+	13.5000i	0.251689	+	0.435938i
$960$		0			0
$961$	27.0000			0.870968
$962$		0			0
$963$		0			0
$964$		0			0
$965$	21.0000	+	36.3731i	0.676014	+	1.17089i
$966$		0			0
$967$		−	2.00000i		−	0.0643157i	−0.999483	−	0.0321578i	$-0.989762\pi$
$967$		−	2.00000i		−	0.0643157i	0.999483	−	0.0321578i	$-0.0102379\pi$
$968$		0			0
$969$	−52.5000	−	30.3109i	−1.68654	−	0.973726i
$970$		0			0
$971$	−23.3827	+	40.5000i	−0.750386	+	1.29971i	0.197250	+	0.980353i	$0.436799\pi$
$971$	−23.3827	+	40.5000i	−0.750386	+	1.29971i	−0.947636	+	0.319354i	$0.896534\pi$
$972$		0			0
$973$	22.5000	−	12.9904i	0.721317	−	0.416452i
$974$		0			0
$975$	30.3109	−	31.5000i	0.970725	−	1.00881i
$976$		0			0
$977$	−22.5000	+	12.9904i	−0.719839	+	0.415599i	−0.814693	−	0.579892i	$-0.803095\pi$
$977$	−22.5000	+	12.9904i	−0.719839	+	0.415599i	0.0948546	+	0.995491i	$0.469761\pi$
$978$		0			0
$979$	4.33013	−	7.50000i	0.138391	−	0.239701i
$980$		0			0
$981$		0			0
$982$		0			0
$983$			14.0000i			0.446531i	0.974758	+	0.223265i	$0.0716716\pi$
$983$			14.0000i			0.446531i	−0.974758	+	0.223265i	$0.928328\pi$
$984$		0			0
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$		0			0
$987$	20.7846			0.661581
$988$		0			0
$989$	27.0000			0.858550
$990$		0			0
$991$	−14.7224	−	25.5000i	−0.467673	−	0.810034i	0.531644	−	0.846968i	$-0.321574\pi$
$991$	−14.7224	−	25.5000i	−0.467673	−	0.810034i	−0.999318	+	0.0369336i	$0.988241\pi$
$992$		0			0
$993$		−	25.9808i		−	0.824475i
$994$		0			0
$995$	5.19615	+	3.00000i	0.164729	+	0.0951064i
$996$		0			0
$997$	−9.50000	+	16.4545i	−0.300868	+	0.521119i	−0.976333	−	0.216274i	$-0.930610\pi$
$997$	−9.50000	+	16.4545i	−0.300868	+	0.521119i	0.675465	+	0.737392i	$0.263943\pi$
$998$		0			0
$999$	−23.3827	+	13.5000i	−0.739795	+	0.427121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.w.a.257.1	yes	4
4.3	odd	2	inner	416.2.w.a.257.2	yes	4
8.3	odd	2		832.2.w.e.257.1		4
8.5	even	2		832.2.w.e.257.2		4
13.2	odd	12		5408.2.a.u.1.2		2
13.4	even	6	inner	416.2.w.a.225.1	✓	4
13.11	odd	12		5408.2.a.z.1.2		2
52.11	even	12		5408.2.a.u.1.1		2
52.15	even	12		5408.2.a.z.1.1		2
52.43	odd	6	inner	416.2.w.a.225.2	yes	4
104.43	odd	6		832.2.w.e.641.1		4
104.69	even	6		832.2.w.e.641.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.w.a.225.1	✓	4	13.4	even	6	inner
416.2.w.a.225.2	yes	4	52.43	odd	6	inner
416.2.w.a.257.1	yes	4	1.1	even	1	trivial
416.2.w.a.257.2	yes	4	4.3	odd	2	inner
832.2.w.e.257.1		4	8.3	odd	2
832.2.w.e.257.2		4	8.5	even	2
832.2.w.e.641.1		4	104.43	odd	6
832.2.w.e.641.2		4	104.69	even	6
5408.2.a.u.1.1		2	52.11	even	12
5408.2.a.u.1.2		2	13.2	odd	12
5408.2.a.z.1.1		2	52.15	even	12
5408.2.a.z.1.2		2	13.11	odd	12

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 1.50000i) q^{3} +3.46410i q^{5} +(-2.59808 - 1.50000i) q^{7} +(4.33013 - 2.50000i) q^{11} +(-1.00000 - 3.46410i) q^{13} +(5.19615 - 3.00000i) q^{15} +(3.50000 - 6.06218i) q^{17} +(4.33013 + 2.50000i) q^{19} +5.19615i q^{21} +(-2.59808 - 4.50000i) q^{23} -7.00000 q^{25} -5.19615 q^{27} +(2.50000 + 4.33013i) q^{29} -2.00000i q^{31} +(-7.50000 - 4.33013i) q^{33} +(5.19615 - 9.00000i) q^{35} +(4.50000 - 2.59808i) q^{37} +(-4.33013 + 4.50000i) q^{39} +(-1.50000 + 0.866025i) q^{41} +(-2.59808 + 4.50000i) q^{43} -4.00000i q^{47} +(1.00000 + 1.73205i) q^{49} -12.1244 q^{51} +4.00000 q^{53} +(8.66025 + 15.0000i) q^{55} -8.66025i q^{57} +(-6.06218 - 3.50000i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(12.0000 - 3.46410i) q^{65} +(2.59808 - 1.50000i) q^{67} +(-4.50000 + 7.79423i) q^{69} +(6.06218 + 3.50000i) q^{71} +3.46410i q^{73} +(6.06218 + 10.5000i) q^{75} -15.0000 q^{77} +3.46410 q^{79} +(4.50000 + 7.79423i) q^{81} +14.0000i q^{83} +(21.0000 + 12.1244i) q^{85} +(4.33013 - 7.50000i) q^{87} +(1.50000 - 0.866025i) q^{89} +(-2.59808 + 10.5000i) q^{91} +(-3.00000 + 1.73205i) q^{93} +(-8.66025 + 15.0000i) q^{95} +(7.50000 + 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{13} + 14 q^{17} - 28 q^{25} + 10 q^{29} - 30 q^{33} + 18 q^{37} - 6 q^{41} + 4 q^{49} + 16 q^{53} - 6 q^{61} + 48 q^{65} - 18 q^{69} - 60 q^{77} + 18 q^{81} + 84 q^{85} + 6 q^{89} - 12 q^{93}+ \cdots + 30 q^{97}+O(q^{100}) \) 4 * q - 4 * q^13 + 14 * q^17 - 28 * q^25 + 10 * q^29 - 30 * q^33 + 18 * q^37 - 6 * q^41 + 4 * q^49 + 16 * q^53 - 6 * q^61 + 48 * q^65 - 18 * q^69 - 60 * q^77 + 18 * q^81 + 84 * q^85 + 6 * q^89 - 12 * q^93 + 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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