LMFDB - Embedded newform 315.2.bb.a.89.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(89,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("315.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bb (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12745506816.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 $ x^8 - 8x^6 + 55x^4 - 72*x^2 + 81
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			89.4
Root			$1.00781 - 0.581861i$ of defining polynomial
Character	$\chi$	$=$	315.89
Dual form			315.2.bb.a.269.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{4} +(2.23256 - 0.125246i) q^{5} +(-1.32288 + 2.29129i) q^{7} +(2.44949 - 1.41421i) q^{11} -2.64575 q^{13} +(-2.00000 + 3.46410i) q^{16} +(-3.24037 + 1.87083i) q^{17} +(1.50000 + 0.866025i) q^{19} +(2.44949 + 3.74166i) q^{20} +(3.24037 - 5.61249i) q^{23} +(4.96863 - 0.559237i) q^{25} -5.29150 q^{28} -1.41421i q^{29} +(4.50000 - 2.59808i) q^{31} +(-2.66642 + 5.28112i) q^{35} +(3.96863 + 2.29129i) q^{37} -4.89898 q^{41} +4.58258i q^{43} +(4.89898 + 2.82843i) q^{44} +(3.24037 + 1.87083i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(-2.64575 - 4.58258i) q^{52} +(-6.48074 - 11.2250i) q^{53} +(5.29150 - 3.46410i) q^{55} +(-3.67423 - 6.36396i) q^{59} +(-9.00000 - 5.19615i) q^{61} -8.00000 q^{64} +(-5.90679 + 0.331369i) q^{65} +(11.9059 - 6.87386i) q^{67} +(-6.48074 - 3.74166i) q^{68} +11.3137i q^{71} +(-6.61438 - 11.4564i) q^{73} +3.46410i q^{76} +7.48331i q^{77} +(3.50000 - 6.06218i) q^{79} +(-4.03125 + 7.98430i) q^{80} -14.9666i q^{83} +(-7.00000 + 4.58258i) q^{85} +(-8.57321 + 14.8492i) q^{89} +(3.50000 - 6.06218i) q^{91} +12.9615 q^{92} +(3.45730 + 1.74558i) q^{95} +5.29150 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 16 q^{16} + 12 q^{19} + 8 q^{25} + 36 q^{31} - 28 q^{49} - 72 q^{61} - 64 q^{64} + 28 q^{79} - 56 q^{85} + 28 q^{91}+O(q^{100}) $ 8 * q + 8 * q^4 - 16 * q^16 + 12 * q^19 + 8 * q^25 + 36 * q^31 - 28 * q^49 - 72 * q^61 - 64 * q^64 + 28 * q^79 - 56 * q^85 + 28 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	2.23256	−	0.125246i	0.998430	−	0.0560116i
$5$	2.23256	−	0.125246i	0.998430	−	0.0560116i
$6$		0			0
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.44949	−	1.41421i	0.738549	−	0.426401i	−0.0829925	−	0.996550i	$-0.526448\pi$
$11$	2.44949	−	1.41421i	0.738549	−	0.426401i	0.821541	+	0.570149i	$0.193114\pi$
$12$		0			0
$13$	−2.64575			−0.733799			−0.366900	−	0.930261i	$-0.619581\pi$
$13$	−2.64575			−0.733799			−0.366900	+	0.930261i	$0.619581\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−3.24037	+	1.87083i	−0.785905	+	0.453743i	−0.838519	−	0.544872i	$-0.816578\pi$
$17$	−3.24037	+	1.87083i	−0.785905	+	0.453743i	0.0526138	+	0.998615i	$0.483245\pi$
$18$		0			0
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$	2.44949	+	3.74166i	0.547723	+	0.836660i
$21$		0			0
$22$		0			0
$23$	3.24037	−	5.61249i	0.675664	−	1.17028i	−0.300610	−	0.953747i	$-0.597190\pi$
$23$	3.24037	−	5.61249i	0.675664	−	1.17028i	0.976274	−	0.216537i	$-0.0694763\pi$
$24$		0			0
$25$	4.96863	−	0.559237i	0.993725	−	0.111847i
$26$		0			0
$27$		0			0
$28$	−5.29150			−1.00000
$29$		−	1.41421i		−	0.262613i	−0.991342	−	0.131306i	$-0.958083\pi$
$29$		−	1.41421i		−	0.262613i	0.991342	−	0.131306i	$-0.0419172\pi$
$30$		0			0
$31$	4.50000	−	2.59808i	0.808224	−	0.466628i	−0.0381148	−	0.999273i	$-0.512135\pi$
$31$	4.50000	−	2.59808i	0.808224	−	0.466628i	0.846339	+	0.532645i	$0.178802\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.66642	+	5.28112i	−0.450708	+	0.892672i
$36$		0			0
$37$	3.96863	+	2.29129i	0.652438	+	0.376685i	0.789390	−	0.613892i	$-0.210397\pi$
$37$	3.96863	+	2.29129i	0.652438	+	0.376685i	−0.136951	+	0.990578i	$0.543730\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.89898			−0.765092			−0.382546	−	0.923936i	$-0.624953\pi$
$41$	−4.89898			−0.765092			−0.382546	+	0.923936i	$0.624953\pi$
$42$		0			0
$43$			4.58258i			0.698836i	0.936967	+	0.349418i	$0.113621\pi$
$43$			4.58258i			0.698836i	−0.936967	+	0.349418i	$0.886379\pi$
$44$	4.89898	+	2.82843i	0.738549	+	0.426401i
$45$		0			0
$46$		0			0
$47$	3.24037	+	1.87083i	0.472657	+	0.272888i	0.717351	−	0.696712i	$-0.245354\pi$
$47$	3.24037	+	1.87083i	0.472657	+	0.272888i	−0.244695	+	0.969600i	$0.578688\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$		0			0
$51$		0			0
$52$	−2.64575	−	4.58258i	−0.366900	−	0.635489i
$53$	−6.48074	−	11.2250i	−0.890198	−	1.54187i	−0.839637	−	0.543148i	$-0.817232\pi$
$53$	−6.48074	−	11.2250i	−0.890198	−	1.54187i	−0.0505609	−	0.998721i	$-0.516101\pi$
$54$		0			0
$55$	5.29150	−	3.46410i	0.713506	−	0.467099i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.67423	−	6.36396i	−0.478345	−	0.828517i	0.521347	−	0.853345i	$-0.325430\pi$
$59$	−3.67423	−	6.36396i	−0.478345	−	0.828517i	−0.999692	+	0.0248275i	$0.992096\pi$
$60$		0			0
$61$	−9.00000	−	5.19615i	−1.15233	−	0.665299i	−0.202878	−	0.979204i	$-0.565029\pi$
$61$	−9.00000	−	5.19615i	−1.15233	−	0.665299i	−0.949454	+	0.313905i	$0.898363\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−5.90679	+	0.331369i	−0.732647	+	0.0411013i
$66$		0			0
$67$	11.9059	−	6.87386i	1.45453	−	0.839776i	0.455801	−	0.890082i	$-0.349353\pi$
$67$	11.9059	−	6.87386i	1.45453	−	0.839776i	0.998734	+	0.0503056i	$0.0160195\pi$
$68$	−6.48074	−	3.74166i	−0.785905	−	0.453743i
$69$		0			0
$70$		0			0
$71$			11.3137i			1.34269i	0.741145	+	0.671345i	$0.234283\pi$
$71$			11.3137i			1.34269i	−0.741145	+	0.671345i	$0.765717\pi$
$72$		0			0
$73$	−6.61438	−	11.4564i	−0.774154	−	1.34087i	−0.935269	−	0.353939i	$-0.884842\pi$
$73$	−6.61438	−	11.4564i	−0.774154	−	1.34087i	0.161114	−	0.986936i	$-0.448491\pi$
$74$		0			0
$75$		0			0
$76$			3.46410i			0.397360i
$77$			7.48331i			0.852803i
$78$		0			0
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	−0.599164	−	0.800626i	$-0.704500\pi$
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	0.992945	+	0.118578i	$0.0378336\pi$
$80$	−4.03125	+	7.98430i	−0.450708	+	0.892672i
$81$		0			0
$82$		0			0
$83$		−	14.9666i		−	1.64280i	−0.570352	−	0.821401i	$-0.693193\pi$
$83$		−	14.9666i		−	1.64280i	0.570352	−	0.821401i	$-0.306807\pi$
$84$		0			0
$85$	−7.00000	+	4.58258i	−0.759257	+	0.497050i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−8.57321	+	14.8492i	−0.908759	+	1.57402i	−0.0929683	+	0.995669i	$0.529636\pi$
$89$	−8.57321	+	14.8492i	−0.908759	+	1.57402i	−0.815791	+	0.578347i	$0.803698\pi$
$90$		0			0
$91$	3.50000	−	6.06218i	0.366900	−	0.635489i
$92$	12.9615			1.35133
$93$		0			0
$94$		0			0
$95$	3.45730	+	1.74558i	0.354712	+	0.179093i
$96$		0			0
$97$	5.29150			0.537271			0.268635	−	0.963242i	$-0.413427\pi$
$97$	5.29150			0.537271			0.268635	+	0.963242i	$0.413427\pi$
$98$		0			0
$99$		0			0
$100$	5.93725	+	8.04668i	0.593725	+	0.804668i
$101$	−4.89898	−	8.48528i	−0.487467	−	0.844317i	0.512429	−	0.858729i	$-0.328746\pi$
$101$	−4.89898	−	8.48528i	−0.487467	−	0.844317i	−0.999896	+	0.0144123i	$0.995412\pi$
$102$		0			0
$103$	−6.61438	+	11.4564i	−0.651734	+	1.12884i	0.330968	+	0.943642i	$0.392625\pi$
$103$	−6.61438	+	11.4564i	−0.651734	+	1.12884i	−0.982702	+	0.185194i	$0.940708\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.24037	+	5.61249i	−0.313258	+	0.542580i	−0.979066	−	0.203544i	$-0.934754\pi$
$107$	−3.24037	+	5.61249i	−0.313258	+	0.542580i	0.665807	+	0.746124i	$0.268087\pi$
$108$		0			0
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	0.983531	−	0.180741i	$-0.0578495\pi$
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	−0.648292	+	0.761392i	$0.724516\pi$
$110$		0			0
$111$		0			0
$112$	−5.29150	−	9.16515i	−0.500000	−	0.866025i
$113$	6.48074			0.609657			0.304828	−	0.952407i	$-0.401401\pi$
$113$	6.48074			0.609657			0.304828	+	0.952407i	$0.401401\pi$
$114$		0			0
$115$	6.53137	−	12.9360i	0.609054	−	1.20629i
$116$	2.44949	−	1.41421i	0.227429	−	0.131306i
$117$		0			0
$118$		0			0
$119$		−	9.89949i		−	0.907485i
$120$		0			0
$121$	−1.50000	+	2.59808i	−0.136364	+	0.236189i
$122$		0			0
$123$		0			0
$124$	9.00000	+	5.19615i	0.808224	+	0.466628i
$125$	11.0227	−	1.87083i	0.985901	−	0.167332i
$126$		0			0
$127$			13.7477i			1.21991i	0.792435	+	0.609957i	$0.208813\pi$
$127$			13.7477i			1.21991i	−0.792435	+	0.609957i	$0.791187\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.57321	−	14.8492i	0.749045	−	1.29738i	−0.199236	−	0.979952i	$-0.563846\pi$
$131$	8.57321	−	14.8492i	0.749045	−	1.29738i	0.948281	−	0.317433i	$-0.102821\pi$
$132$		0			0
$133$	−3.96863	+	2.29129i	−0.344124	+	0.198680i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.24037	−	5.61249i	−0.276844	−	0.479507i	0.693755	−	0.720211i	$-0.255955\pi$
$137$	−3.24037	−	5.61249i	−0.276844	−	0.479507i	−0.970599	+	0.240704i	$0.922622\pi$
$138$		0			0
$139$			8.66025i			0.734553i	0.930112	+	0.367277i	$0.119710\pi$
$139$			8.66025i			0.734553i	−0.930112	+	0.367277i	$0.880290\pi$
$140$	−11.8136	+	0.662739i	−0.998430	+	0.0560116i
$141$		0			0
$142$		0			0
$143$	−6.48074	+	3.74166i	−0.541947	+	0.312893i
$144$		0			0
$145$	−0.177124	−	3.15731i	−0.0147094	−	0.262201i
$146$		0			0
$147$		0			0
$148$			9.16515i			0.753371i
$149$	12.2474	+	7.07107i	1.00335	+	0.579284i	0.909238	−	0.416277i	$-0.136665\pi$
$149$	12.2474	+	7.07107i	1.00335	+	0.579284i	0.0941123	+	0.995562i	$0.469999\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	9.72111	−	6.36396i	0.780818	−	0.511166i
$156$		0			0
$157$	−2.64575	−	4.58258i	−0.211154	−	0.365729i	0.740922	−	0.671591i	$-0.234389\pi$
$157$	−2.64575	−	4.58258i	−0.211154	−	0.365729i	−0.952076	+	0.305862i	$0.901055\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.57321	+	14.8492i	0.675664	+	1.17028i
$162$		0			0
$163$	−7.93725	−	4.58258i	−0.621694	−	0.358935i	0.155834	−	0.987783i	$-0.450193\pi$
$163$	−7.93725	−	4.58258i	−0.621694	−	0.358935i	−0.777528	+	0.628848i	$0.783527\pi$
$164$	−4.89898	−	8.48528i	−0.382546	−	0.662589i
$165$		0			0
$166$		0			0
$167$			7.48331i			0.579076i	0.957166	+	0.289538i	$0.0935017\pi$
$167$			7.48331i			0.579076i	−0.957166	+	0.289538i	$0.906498\pi$
$168$		0			0
$169$	−6.00000			−0.461538
$170$		0			0
$171$		0			0
$172$	−7.93725	+	4.58258i	−0.605210	+	0.349418i
$173$	12.9615	+	7.48331i	0.985443	+	0.568946i	0.903909	−	0.427725i	$-0.140685\pi$
$173$	12.9615	+	7.48331i	0.985443	+	0.568946i	0.0815341	+	0.996671i	$0.474018\pi$
$174$		0			0
$175$	−5.29150	+	12.1244i	−0.400000	+	0.916515i
$176$			11.3137i			0.852803i
$177$		0			0
$178$		0			0
$179$	6.12372	−	3.53553i	0.457709	−	0.264258i	−0.253372	−	0.967369i	$-0.581540\pi$
$179$	6.12372	−	3.53553i	0.457709	−	0.264258i	0.711080	+	0.703111i	$0.248206\pi$
$180$		0			0
$181$			15.5885i			1.15868i	0.815086	+	0.579340i	$0.196690\pi$
$181$			15.5885i			1.15868i	−0.815086	+	0.579340i	$0.803310\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	9.14716	+	4.61838i	0.672513	+	0.339550i
$186$		0			0
$187$	−5.29150	+	9.16515i	−0.386953	+	0.670222i
$188$			7.48331i			0.545777i
$189$		0			0
$190$		0			0
$191$	−13.4722	−	7.77817i	−0.974814	−	0.562809i	−0.0741134	−	0.997250i	$-0.523613\pi$
$191$	−13.4722	−	7.77817i	−0.974814	−	0.562809i	−0.900700	+	0.434441i	$0.856946\pi$
$192$		0			0
$193$	11.9059	−	6.87386i	0.857004	−	0.494792i	−0.00600382	−	0.999982i	$-0.501911\pi$
$193$	11.9059	−	6.87386i	0.857004	−	0.494792i	0.863008	+	0.505190i	$0.168578\pi$
$194$		0			0
$195$		0			0
$196$	7.00000	−	12.1244i	0.500000	−	0.866025i
$197$	−19.4422			−1.38520			−0.692600	−	0.721321i	$-0.743535\pi$
$197$	−19.4422			−1.38520			−0.692600	+	0.721321i	$0.743535\pi$
$198$		0			0
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	−0.272026	−	0.962290i	$-0.587694\pi$
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	0.697355	+	0.716726i	$0.254360\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.24037	+	1.87083i	0.227429	+	0.131306i
$204$		0			0
$205$	−10.9373	+	0.613577i	−0.763891	+	0.0428541i
$206$		0			0
$207$		0			0
$208$	5.29150	−	9.16515i	0.366900	−	0.635489i
$209$	4.89898			0.338869
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	12.9615	−	22.4499i	0.890198	−	1.54187i
$213$		0			0
$214$		0			0
$215$	0.573948	+	10.2309i	0.0391430	+	0.697739i
$216$		0			0
$217$			13.7477i			0.933257i
$218$		0			0
$219$		0			0
$220$	11.2915	+	5.70105i	0.761273	+	0.384365i
$221$	8.57321	−	4.94975i	0.576697	−	0.332956i
$222$		0			0
$223$	5.29150			0.354345			0.177173	−	0.984180i	$-0.443305\pi$
$223$	5.29150			0.354345			0.177173	+	0.984180i	$0.443305\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.9615	+	7.48331i	−0.860284	+	0.496685i	−0.864107	−	0.503308i	$-0.832116\pi$
$227$	−12.9615	+	7.48331i	−0.860284	+	0.496685i	0.00382356	+	0.999993i	$0.498783\pi$
$228$		0			0
$229$	−1.50000	−	0.866025i	−0.0991228	−	0.0572286i	0.449619	−	0.893220i	$-0.351560\pi$
$229$	−1.50000	−	0.866025i	−0.0991228	−	0.0572286i	−0.548742	+	0.835992i	$0.684893\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.24037	+	5.61249i	−0.212284	+	0.367686i	−0.952429	−	0.304761i	$-0.901423\pi$
$233$	−3.24037	+	5.61249i	−0.212284	+	0.367686i	0.740145	+	0.672447i	$0.234757\pi$
$234$		0			0
$235$	7.46863	+	3.77089i	0.487200	+	0.245986i
$236$	7.34847	−	12.7279i	0.478345	−	0.828517i
$237$		0			0
$238$		0			0
$239$		−	18.3848i		−	1.18921i	−0.804017	−	0.594606i	$-0.797308\pi$
$239$		−	18.3848i		−	1.18921i	0.804017	−	0.594606i	$-0.202692\pi$
$240$		0			0
$241$	−15.0000	+	8.66025i	−0.966235	+	0.557856i	−0.898086	−	0.439819i	$-0.855043\pi$
$241$	−15.0000	+	8.66025i	−0.966235	+	0.557856i	−0.0681486	+	0.997675i	$0.521709\pi$
$242$		0			0
$243$		0			0
$244$		−	20.7846i		−	1.33060i
$245$	−8.57321	−	13.0958i	−0.547723	−	0.836660i
$246$		0			0
$247$	−3.96863	−	2.29129i	−0.252518	−	0.145791i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−22.0454			−1.39149			−0.695747	−	0.718287i	$-0.744926\pi$
$251$	−22.0454			−1.39149			−0.695747	+	0.718287i	$0.744926\pi$
$252$		0			0
$253$		−	18.3303i		−	1.15242i
$254$		0			0
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−6.48074	−	3.74166i	−0.404257	−	0.233398i	0.284062	−	0.958806i	$-0.408318\pi$
$257$	−6.48074	−	3.74166i	−0.404257	−	0.233398i	−0.688319	+	0.725408i	$0.741651\pi$
$258$		0			0
$259$	−10.5000	+	6.06218i	−0.652438	+	0.376685i
$260$	−6.48074	−	9.89949i	−0.401918	−	0.613941i
$261$		0			0
$262$		0			0
$263$	6.48074	+	11.2250i	0.399620	+	0.692161i	0.993679	−	0.112260i	$-0.0358089\pi$
$263$	6.48074	+	11.2250i	0.399620	+	0.692161i	−0.594059	+	0.804421i	$0.702476\pi$
$264$		0			0
$265$	−15.8745	−	24.2487i	−0.975163	−	1.48959i
$266$		0			0
$267$		0			0
$268$	23.8118	+	13.7477i	1.45453	+	0.839776i
$269$	8.57321	+	14.8492i	0.522718	+	0.905374i	0.999651	+	0.0264343i	$0.00841529\pi$
$269$	8.57321	+	14.8492i	0.522718	+	0.905374i	−0.476932	+	0.878940i	$0.658251\pi$
$270$		0			0
$271$	−12.0000	−	6.92820i	−0.728948	−	0.420858i	0.0890891	−	0.996024i	$-0.471604\pi$
$271$	−12.0000	−	6.92820i	−0.728948	−	0.420858i	−0.818037	+	0.575165i	$0.804938\pi$
$272$		−	14.9666i		−	0.907485i
$273$		0			0
$274$		0			0
$275$	11.3797	−	8.39655i	0.686223	−	0.506331i
$276$		0			0
$277$	−3.96863	+	2.29129i	−0.238452	+	0.137670i	−0.614465	−	0.788944i	$-0.710628\pi$
$277$	−3.96863	+	2.29129i	−0.238452	+	0.137670i	0.376013	+	0.926614i	$0.377295\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			28.2843i			1.68730i	0.536895	+	0.843649i	$0.319597\pi$
$281$			28.2843i			1.68730i	−0.536895	+	0.843649i	$0.680403\pi$
$282$		0			0
$283$	9.26013	+	16.0390i	0.550458	+	0.953420i	0.998241	+	0.0592787i	$0.0188801\pi$
$283$	9.26013	+	16.0390i	0.550458	+	0.953420i	−0.447784	+	0.894142i	$0.647787\pi$
$284$	−19.5959	+	11.3137i	−1.16280	+	0.671345i
$285$		0			0
$286$		0			0
$287$	6.48074	−	11.2250i	0.382546	−	0.662589i
$288$		0			0
$289$	−1.50000	+	2.59808i	−0.0882353	+	0.152828i
$290$		0			0
$291$		0			0
$292$	13.2288	−	22.9129i	0.774154	−	1.34087i
$293$			29.9333i			1.74872i	0.485278	+	0.874360i	$0.338718\pi$
$293$			29.9333i			1.74872i	−0.485278	+	0.874360i	$0.661282\pi$
$294$		0			0
$295$	−9.00000	−	13.7477i	−0.524000	−	0.800424i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−8.57321	+	14.8492i	−0.495802	+	0.858754i
$300$		0			0
$301$	−10.5000	−	6.06218i	−0.605210	−	0.349418i
$302$		0			0
$303$		0			0
$304$	−6.00000	+	3.46410i	−0.344124	+	0.198680i
$305$	−20.7438	−	10.4735i	−1.18779	−	0.599711i
$306$		0			0
$307$	−2.64575			−0.151001			−0.0755005	−	0.997146i	$-0.524055\pi$
$307$	−2.64575			−0.151001			−0.0755005	+	0.997146i	$0.524055\pi$
$308$	−12.9615	+	7.48331i	−0.738549	+	0.426401i
$309$		0			0
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	9.26013	−	16.0390i	0.523413	−	0.906579i	−0.476215	−	0.879329i	$-0.657992\pi$
$313$	9.26013	−	16.0390i	0.523413	−	0.906579i	0.999629	−	0.0272499i	$-0.00867500\pi$
$314$		0			0
$315$		0			0
$316$	14.0000			0.787562
$317$	−9.72111	+	16.8375i	−0.545992	+	0.945686i	0.452552	+	0.891738i	$0.350514\pi$
$317$	−9.72111	+	16.8375i	−0.545992	+	0.945686i	−0.998544	+	0.0539477i	$0.982820\pi$
$318$		0			0
$319$	−2.00000	−	3.46410i	−0.111979	−	0.193952i
$320$	−17.8605	+	1.00197i	−0.998430	+	0.0560116i
$321$		0			0
$322$		0			0
$323$	−6.48074			−0.360598
$324$		0			0
$325$	−13.1458	+	1.47960i	−0.729195	+	0.0820736i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−8.57321	+	4.94975i	−0.472657	+	0.272888i
$330$		0			0
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	−0.753660	−	0.657264i	$-0.771714\pi$
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	0.946038	+	0.324057i	$0.105047\pi$
$332$	25.9230	−	14.9666i	1.42271	−	0.821401i
$333$		0			0
$334$		0			0
$335$	25.7196	−	16.8375i	1.40521	−	0.919929i
$336$		0			0
$337$		−	32.0780i		−	1.74740i	−0.486464	−	0.873701i	$-0.661713\pi$
$337$		−	32.0780i		−	1.74740i	0.486464	−	0.873701i	$-0.338287\pi$
$338$		0			0
$339$		0			0
$340$	−14.9373	−	7.54178i	−0.810086	−	0.409010i
$341$	7.34847	−	12.7279i	0.397942	−	0.689256i
$342$		0			0
$343$	18.5203			1.00000
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$		0			0
$349$		−	3.46410i		−	0.185429i	−0.995693	−	0.0927146i	$-0.970446\pi$
$349$		−	3.46410i		−	0.185429i	0.995693	−	0.0927146i	$-0.0295544\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.48074	−	3.74166i	0.344935	−	0.199148i	−0.317517	−	0.948253i	$-0.602849\pi$
$353$	6.48074	−	3.74166i	0.344935	−	0.199148i	0.662452	+	0.749104i	$0.269516\pi$
$354$		0			0
$355$	1.41699	+	25.2585i	0.0752063	+	1.34058i
$356$	−34.2929			−1.81752
$357$		0			0
$358$		0			0
$359$	−13.4722	−	7.77817i	−0.711035	−	0.410516i	0.100409	−	0.994946i	$-0.467985\pi$
$359$	−13.4722	−	7.77817i	−0.711035	−	0.410516i	−0.811444	+	0.584430i	$0.801318\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$		0			0
$363$		0			0
$364$	14.0000			0.733799
$365$	−16.2019	−	24.7487i	−0.848044	−	1.29541i
$366$		0			0
$367$	9.26013	+	16.0390i	0.483375	+	0.837230i	0.999818	−	0.0190919i	$-0.00607750\pi$
$367$	9.26013	+	16.0390i	0.483375	+	0.837230i	−0.516443	+	0.856322i	$0.672744\pi$
$368$	12.9615	+	22.4499i	0.675664	+	1.17028i
$369$		0			0
$370$		0			0
$371$	34.2929			1.78040
$372$		0			0
$373$	−3.96863	−	2.29129i	−0.205488	−	0.118638i	0.393725	−	0.919228i	$-0.371186\pi$
$373$	−3.96863	−	2.29129i	−0.205488	−	0.118638i	−0.599213	+	0.800590i	$0.704520\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			3.74166i			0.192705i
$378$		0			0
$379$	5.00000			0.256833			0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000			0.256833			0.128416	+	0.991720i	$0.459011\pi$
$380$	0.433864	+	7.73381i	0.0222568	+	0.396736i
$381$		0			0
$382$		0			0
$383$	−6.48074	−	3.74166i	−0.331150	−	0.191190i	0.325201	−	0.945645i	$-0.394568\pi$
$383$	−6.48074	−	3.74166i	−0.331150	−	0.191190i	−0.656352	+	0.754455i	$0.727901\pi$
$384$		0			0
$385$	0.937254	+	16.7069i	0.0477669	+	0.851464i
$386$		0			0
$387$		0			0
$388$	5.29150	+	9.16515i	0.268635	+	0.465290i
$389$	2.44949	−	1.41421i	0.124194	−	0.0717035i	−0.436616	−	0.899648i	$-0.643823\pi$
$389$	2.44949	−	1.41421i	0.124194	−	0.0717035i	0.560810	+	0.827945i	$0.310490\pi$
$390$		0			0
$391$			24.2487i			1.22631i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7.05469	−	13.9725i	0.354960	−	0.703034i
$396$		0			0
$397$	−14.5516	+	25.2042i	−0.730325	+	1.26496i	0.226419	+	0.974030i	$0.427298\pi$
$397$	−14.5516	+	25.2042i	−0.730325	+	1.26496i	−0.956744	+	0.290931i	$0.906035\pi$
$398$		0			0
$399$		0			0
$400$	−8.00000	+	18.3303i	−0.400000	+	0.916515i
$401$	4.89898	+	2.82843i	0.244643	+	0.141245i	0.617309	−	0.786721i	$-0.288223\pi$
$401$	4.89898	+	2.82843i	0.244643	+	0.141245i	−0.372666	+	0.927966i	$0.621556\pi$
$402$		0			0
$403$	−11.9059	+	6.87386i	−0.593074	+	0.342412i
$404$	9.79796	−	16.9706i	0.487467	−	0.844317i
$405$		0			0
$406$		0			0
$407$	12.9615			0.642477
$408$		0			0
$409$	−4.50000	+	2.59808i	−0.222511	+	0.128467i	−0.607112	−	0.794616i	$-0.707672\pi$
$409$	−4.50000	+	2.59808i	−0.222511	+	0.128467i	0.384602	+	0.923083i	$0.374339\pi$
$410$		0			0
$411$		0			0
$412$	−26.4575			−1.30347
$413$	19.4422			0.956689
$414$		0			0
$415$	−1.87451	−	33.4139i	−0.0920160	−	1.64022i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.1464			0.837658			0.418829	−	0.908065i	$-0.362441\pi$
$419$	17.1464			0.837658			0.418829	+	0.908065i	$0.362441\pi$
$420$		0			0
$421$	35.0000			1.70580			0.852898	−	0.522078i	$-0.174843\pi$
$421$	35.0000			1.70580			0.852898	+	0.522078i	$0.174843\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−15.0540	+	11.1076i	−0.730224	+	0.538797i
$426$		0			0
$427$	23.8118	−	13.7477i	1.15233	−	0.665299i
$428$	−12.9615			−0.626517
$429$		0			0
$430$		0			0
$431$	6.12372	−	3.53553i	0.294969	−	0.170301i	−0.345211	−	0.938525i	$-0.612193\pi$
$431$	6.12372	−	3.53553i	0.294969	−	0.170301i	0.640181	+	0.768224i	$0.278859\pi$
$432$		0			0
$433$	13.2288			0.635733			0.317867	−	0.948135i	$-0.397034\pi$
$433$	13.2288			0.635733			0.317867	+	0.948135i	$0.397034\pi$
$434$		0			0
$435$		0			0
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	9.72111	−	5.61249i	0.465024	−	0.268482i
$438$		0			0
$439$	9.00000	+	5.19615i	0.429547	+	0.247999i	0.699153	−	0.714972i	$-0.253560\pi$
$439$	9.00000	+	5.19615i	0.429547	+	0.247999i	−0.269607	+	0.962970i	$0.586894\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.4422	+	33.6749i	−0.923728	+	1.59994i	−0.130133	+	0.991496i	$0.541541\pi$
$443$	−19.4422	+	33.6749i	−0.923728	+	1.59994i	−0.793594	+	0.608447i	$0.791793\pi$
$444$		0			0
$445$	−17.2804	+	34.2255i	−0.819169	+	1.62245i
$446$		0			0
$447$		0			0
$448$	10.5830	−	18.3303i	0.500000	−	0.866025i
$449$		−	18.3848i		−	0.867631i	−0.901002	−	0.433816i	$-0.857167\pi$
$449$		−	18.3848i		−	0.867631i	0.901002	−	0.433816i	$-0.142833\pi$
$450$		0			0
$451$	−12.0000	+	6.92820i	−0.565058	+	0.326236i
$452$	6.48074	+	11.2250i	0.304828	+	0.527978i
$453$		0			0
$454$		0			0
$455$	7.05469	−	13.9725i	0.330729	−	0.655042i
$456$		0			0
$457$	−11.9059	−	6.87386i	−0.556934	−	0.321546i	0.194980	−	0.980807i	$-0.437536\pi$
$457$	−11.9059	−	6.87386i	−0.556934	−	0.321546i	−0.751914	+	0.659261i	$0.770869\pi$
$458$		0			0
$459$		0			0
$460$	28.9373	−	1.62337i	1.34921	−	0.0756901i
$461$	−17.1464			−0.798589			−0.399294	−	0.916823i	$-0.630745\pi$
$461$	−17.1464			−0.798589			−0.399294	+	0.916823i	$0.630745\pi$
$462$		0			0
$463$		−	4.58258i		−	0.212970i	−0.994314	−	0.106485i	$-0.966040\pi$
$463$		−	4.58258i		−	0.212970i	0.994314	−	0.106485i	$-0.0339597\pi$
$464$	4.89898	+	2.82843i	0.227429	+	0.131306i
$465$		0			0
$466$		0			0
$467$	3.24037	+	1.87083i	0.149946	+	0.0865716i	0.573096	−	0.819488i	$-0.305742\pi$
$467$	3.24037	+	1.87083i	0.149946	+	0.0865716i	−0.423150	+	0.906060i	$0.639076\pi$
$468$		0			0
$469$			36.3731i			1.67955i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	6.48074	+	11.2250i	0.297985	+	0.516125i
$474$		0			0
$475$	7.93725	+	3.46410i	0.364186	+	0.158944i
$476$	17.1464	−	9.89949i	0.785905	−	0.453743i
$477$		0			0
$478$		0			0
$479$	17.1464	+	29.6985i	0.783440	+	1.35696i	0.929926	+	0.367746i	$0.119870\pi$
$479$	17.1464	+	29.6985i	0.783440	+	1.35696i	−0.146486	+	0.989213i	$0.546796\pi$
$480$		0			0
$481$	−10.5000	−	6.06218i	−0.478759	−	0.276412i
$482$		0			0
$483$		0			0
$484$	−6.00000			−0.272727
$485$	11.8136	−	0.662739i	0.536427	−	0.0300934i
$486$		0			0
$487$	−19.8431	+	11.4564i	−0.899178	+	0.519141i	−0.876933	−	0.480612i	$-0.840415\pi$
$487$	−19.8431	+	11.4564i	−0.899178	+	0.519141i	−0.0222448	+	0.999753i	$0.507081\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			11.3137i			0.510581i	0.966864	+	0.255290i	$0.0821710\pi$
$491$			11.3137i			0.510581i	−0.966864	+	0.255290i	$0.917829\pi$
$492$		0			0
$493$	2.64575	+	4.58258i	0.119159	+	0.206389i
$494$		0			0
$495$		0			0
$496$			20.7846i			0.933257i
$497$	−25.9230	−	14.9666i	−1.16280	−	0.671345i
$498$		0			0
$499$	6.50000	−	11.2583i	0.290980	−	0.503992i	−0.683062	−	0.730361i	$-0.739352\pi$
$499$	6.50000	−	11.2583i	0.290980	−	0.503992i	0.974042	+	0.226369i	$0.0726854\pi$
$500$	14.2631	+	17.2211i	0.637864	+	0.770149i
$501$		0			0
$502$		0			0
$503$		−	3.74166i		−	0.166832i	−0.996515	−	0.0834161i	$-0.973417\pi$
$503$		−	3.74166i		−	0.166832i	0.996515	−	0.0834161i	$-0.0265831\pi$
$504$		0			0
$505$	−12.0000	−	18.3303i	−0.533993	−	0.815688i
$506$		0			0
$507$		0			0
$508$	−23.8118	+	13.7477i	−1.05648	+	0.609957i
$509$	8.57321	−	14.8492i	0.380001	−	0.658181i	−0.611061	−	0.791584i	$-0.709257\pi$
$509$	8.57321	−	14.8492i	0.380001	−	0.658181i	0.991062	+	0.133402i	$0.0425903\pi$
$510$		0			0
$511$	35.0000			1.54831
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−13.3321	+	26.4056i	−0.587483	+	1.16357i
$516$		0			0
$517$	10.5830			0.465440
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.1464	−	29.6985i	−0.751199	−	1.30111i	−0.947242	−	0.320519i	$-0.896143\pi$
$521$	−17.1464	−	29.6985i	−0.751199	−	1.30111i	0.196043	−	0.980595i	$-0.437191\pi$
$522$		0			0
$523$	−6.61438	+	11.4564i	−0.289227	+	0.500955i	−0.973625	−	0.228153i	$-0.926731\pi$
$523$	−6.61438	+	11.4564i	−0.289227	+	0.500955i	0.684399	+	0.729108i	$0.260065\pi$
$524$	34.2929			1.49809
$525$		0			0
$526$		0			0
$527$	−9.72111	+	16.8375i	−0.423458	+	0.733451i
$528$		0			0
$529$	−9.50000	−	16.4545i	−0.413043	−	0.715412i
$530$		0			0
$531$		0			0
$532$	−7.93725	−	4.58258i	−0.344124	−	0.198680i
$533$	12.9615			0.561424
$534$		0			0
$535$	−6.53137	+	12.9360i	−0.282376	+	0.559274i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−17.1464	−	9.89949i	−0.738549	−	0.426401i
$540$		0			0
$541$	3.50000	−	6.06218i	0.150477	−	0.260633i	−0.780926	−	0.624623i	$-0.785252\pi$
$541$	3.50000	−	6.06218i	0.150477	−	0.260633i	0.931403	+	0.363990i	$0.118586\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.57321	+	13.0958i	0.367236	+	0.560962i
$546$		0			0
$547$			18.3303i			0.783747i	0.920019	+	0.391874i	$0.128173\pi$
$547$			18.3303i			0.783747i	−0.920019	+	0.391874i	$0.871827\pi$
$548$	6.48074	−	11.2250i	0.276844	−	0.479507i
$549$		0			0
$550$		0			0
$551$	1.22474	−	2.12132i	0.0521759	−	0.0903713i
$552$		0			0
$553$	9.26013	+	16.0390i	0.393781	+	0.682048i
$554$		0			0
$555$		0			0
$556$	−15.0000	+	8.66025i	−0.636142	+	0.367277i
$557$	3.24037	+	5.61249i	0.137299	+	0.237809i	0.926473	−	0.376360i	$-0.122825\pi$
$557$	3.24037	+	5.61249i	0.137299	+	0.237809i	−0.789174	+	0.614169i	$0.789491\pi$
$558$		0			0
$559$		−	12.1244i		−	0.512806i
$560$	−12.9615	−	19.7990i	−0.547723	−	0.836660i
$561$		0			0
$562$		0			0
$563$	16.2019	−	9.35414i	0.682827	−	0.394230i	−0.118093	−	0.993003i	$-0.537678\pi$
$563$	16.2019	−	9.35414i	0.682827	−	0.394230i	0.800919	+	0.598772i	$0.204345\pi$
$564$		0			0
$565$	14.4686	−	0.811686i	0.608700	−	0.0341479i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−39.1918	−	22.6274i	−1.64301	−	0.948591i	−0.979756	−	0.200194i	$-0.935843\pi$
$569$	−39.1918	−	22.6274i	−1.64301	−	0.948591i	−0.663251	−	0.748397i	$-0.730824\pi$
$570$		0			0
$571$	−8.50000	−	14.7224i	−0.355714	−	0.616115i	0.631526	−	0.775355i	$-0.282429\pi$
$571$	−8.50000	−	14.7224i	−0.355714	−	0.616115i	−0.987240	+	0.159240i	$0.949096\pi$
$572$	−12.9615	−	7.48331i	−0.541947	−	0.312893i
$573$		0			0
$574$		0			0
$575$	12.9615	−	29.6985i	0.540531	−	1.23851i
$576$		0			0
$577$	17.1974	+	29.7867i	0.715936	+	1.24004i	0.962597	+	0.270936i	$0.0873333\pi$
$577$	17.1974	+	29.7867i	0.715936	+	1.24004i	−0.246661	+	0.969102i	$0.579333\pi$
$578$		0			0
$579$		0			0
$580$	5.29150	−	3.46410i	0.219718	−	0.143839i
$581$	34.2929	+	19.7990i	1.42271	+	0.821401i
$582$		0			0
$583$	−31.7490	−	18.3303i	−1.31491	−	0.759164i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	26.1916i		−	1.08104i	−0.841330	−	0.540522i	$-0.818227\pi$
$587$		−	26.1916i		−	1.08104i	0.841330	−	0.540522i	$-0.181773\pi$
$588$		0			0
$589$	9.00000			0.370839
$590$		0			0
$591$		0			0
$592$	−15.8745	+	9.16515i	−0.652438	+	0.376685i
$593$	12.9615	+	7.48331i	0.532264	+	0.307303i	0.741938	−	0.670468i	$-0.233907\pi$
$593$	12.9615	+	7.48331i	0.532264	+	0.307303i	−0.209674	+	0.977771i	$0.567240\pi$
$594$		0			0
$595$	−1.23987	−	22.1012i	−0.0508297	−	0.906061i
$596$			28.2843i			1.15857i
$597$		0			0
$598$		0			0
$599$	2.44949	−	1.41421i	0.100083	−	0.0577832i	−0.449123	−	0.893470i	$-0.648263\pi$
$599$	2.44949	−	1.41421i	0.100083	−	0.0577832i	0.549206	+	0.835687i	$0.314930\pi$
$600$		0			0
$601$		−	8.66025i		−	0.353259i	−0.984277	−	0.176630i	$-0.943481\pi$
$601$		−	8.66025i		−	0.353259i	0.984277	−	0.176630i	$-0.0565195\pi$
$602$		0			0
$603$		0			0
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	−3.02344	+	5.98822i	−0.122920	+	0.243456i
$606$		0			0
$607$	17.1974	−	29.7867i	0.698020	−	1.20901i	−0.271132	−	0.962542i	$-0.587398\pi$
$607$	17.1974	−	29.7867i	0.698020	−	1.20901i	0.969152	−	0.246464i	$-0.0792688\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.57321	−	4.94975i	−0.346835	−	0.200245i
$612$		0			0
$613$	15.8745	−	9.16515i	0.641165	−	0.370177i	−0.143898	−	0.989593i	$-0.545964\pi$
$613$	15.8745	−	9.16515i	0.641165	−	0.370177i	0.785063	+	0.619416i	$0.212630\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−32.4037			−1.30452			−0.652262	−	0.757994i	$-0.726180\pi$
$617$	−32.4037			−1.30452			−0.652262	+	0.757994i	$0.726180\pi$
$618$		0			0
$619$	25.5000	−	14.7224i	1.02493	−	0.591744i	0.109403	−	0.993997i	$-0.465106\pi$
$619$	25.5000	−	14.7224i	1.02493	−	0.591744i	0.915529	+	0.402253i	$0.131773\pi$
$620$	20.7438	+	10.4735i	0.833092	+	0.420626i
$621$		0			0
$622$		0			0
$623$	−22.6826	−	39.2874i	−0.908759	−	1.57402i
$624$		0			0
$625$	24.3745	−	5.55728i	0.974980	−	0.222291i
$626$		0			0
$627$		0			0
$628$	5.29150	−	9.16515i	0.211154	−	0.365729i
$629$	−17.1464			−0.683673
$630$		0			0
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.72185	+	30.6926i	0.0683294	+	1.21800i
$636$		0			0
$637$	9.26013	+	16.0390i	0.366900	+	0.635489i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−23.2702	+	13.4350i	−0.919116	+	0.530652i	−0.883353	−	0.468709i	$-0.844719\pi$
$641$	−23.2702	+	13.4350i	−0.919116	+	0.530652i	−0.0357629	+	0.999360i	$0.511386\pi$
$642$		0			0
$643$	−2.64575			−0.104338			−0.0521691	−	0.998638i	$-0.516613\pi$
$643$	−2.64575			−0.104338			−0.0521691	+	0.998638i	$0.516613\pi$
$644$	−17.1464	+	29.6985i	−0.675664	+	1.17028i
$645$		0			0
$646$		0			0
$647$	−12.9615	+	7.48331i	−0.509568	+	0.294199i	−0.732656	−	0.680599i	$-0.761720\pi$
$647$	−12.9615	+	7.48331i	−0.509568	+	0.294199i	0.223088	+	0.974798i	$0.428386\pi$
$648$		0			0
$649$	−18.0000	−	10.3923i	−0.706562	−	0.407934i
$650$		0			0
$651$		0			0
$652$		−	18.3303i		−	0.717870i
$653$	12.9615	−	22.4499i	0.507222	−	0.878534i	−0.492743	−	0.870175i	$-0.664006\pi$
$653$	12.9615	−	22.4499i	0.507222	−	0.878534i	0.999965	−	0.00835938i	$-0.00266090\pi$
$654$		0			0
$655$	17.2804	−	34.2255i	0.675201	−	1.33730i
$656$	9.79796	−	16.9706i	0.382546	−	0.662589i
$657$		0			0
$658$		0			0
$659$			28.2843i			1.10180i	0.834572	+	0.550899i	$0.185715\pi$
$659$			28.2843i			1.10180i	−0.834572	+	0.550899i	$0.814285\pi$
$660$		0			0
$661$	−4.50000	+	2.59808i	−0.175030	+	0.101053i	−0.584955	−	0.811065i	$-0.698888\pi$
$661$	−4.50000	+	2.59808i	−0.175030	+	0.101053i	0.409926	+	0.912119i	$0.365555\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.57321	+	5.61249i	−0.332455	+	0.217643i
$666$		0			0
$667$	−7.93725	−	4.58258i	−0.307332	−	0.177438i
$668$	−12.9615	+	7.48331i	−0.501495	+	0.289538i
$669$		0			0
$670$		0			0
$671$	−29.3939			−1.13474
$672$		0			0
$673$		−	22.9129i		−	0.883227i	−0.897206	−	0.441613i	$-0.854406\pi$
$673$		−	22.9129i		−	0.883227i	0.897206	−	0.441613i	$-0.145594\pi$
$674$		0			0
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	3.24037	+	1.87083i	0.124538	+	0.0719018i	0.560975	−	0.827833i	$-0.310427\pi$
$677$	3.24037	+	1.87083i	0.124538	+	0.0719018i	−0.436437	+	0.899735i	$0.643760\pi$
$678$		0			0
$679$	−7.00000	+	12.1244i	−0.268635	+	0.465290i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−16.2019	−	28.0624i	−0.619947	−	1.07378i	−0.989495	−	0.144568i	$-0.953821\pi$
$683$	−16.2019	−	28.0624i	−0.619947	−	1.07378i	0.369548	−	0.929212i	$-0.379512\pi$
$684$		0			0
$685$	−7.93725	−	12.1244i	−0.303267	−	0.463248i
$686$		0			0
$687$		0			0
$688$	−15.8745	−	9.16515i	−0.605210	−	0.349418i
$689$	17.1464	+	29.6985i	0.653227	+	1.13142i
$690$		0			0
$691$	−40.5000	−	23.3827i	−1.54069	−	0.889519i	−0.998795	−	0.0490747i	$-0.984373\pi$
$691$	−40.5000	−	23.3827i	−1.54069	−	0.889519i	−0.541897	−	0.840445i	$-0.682294\pi$
$692$			29.9333i			1.13789i
$693$		0			0
$694$		0			0
$695$	1.08466	+	19.3345i	0.0411435	+	0.733400i
$696$		0			0
$697$	15.8745	−	9.16515i	0.601290	−	0.347155i
$698$		0			0
$699$		0			0
$700$	−26.2915	+	2.95920i	−0.993725	+	0.111847i
$701$		−	1.41421i		−	0.0534141i	−0.999643	−	0.0267071i	$-0.991498\pi$
$701$		−	1.41421i		−	0.0534141i	0.999643	−	0.0267071i	$-0.00850213\pi$
$702$		0			0
$703$	3.96863	+	6.87386i	0.149680	+	0.259253i
$704$	−19.5959	+	11.3137i	−0.738549	+	0.426401i
$705$		0			0
$706$		0			0
$707$	25.9230			0.974933
$708$		0			0
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	−0.931309	−	0.364229i	$-0.881333\pi$
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	0.781086	+	0.624423i	$0.214666\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	33.6749i		−	1.26114i
$714$		0			0
$715$	−14.0000	+	9.16515i	−0.523570	+	0.342757i
$716$	12.2474	+	7.07107i	0.457709	+	0.264258i
$717$		0			0
$718$		0			0
$719$	−1.22474	+	2.12132i	−0.0456753	+	0.0791119i	−0.887959	−	0.459922i	$-0.847877\pi$
$719$	−1.22474	+	2.12132i	−0.0456753	+	0.0791119i	0.842284	+	0.539034i	$0.181211\pi$
$720$		0			0
$721$	−17.5000	−	30.3109i	−0.651734	−	1.12884i
$722$		0			0
$723$		0			0
$724$	−27.0000	+	15.5885i	−1.00345	+	0.579340i
$725$	−0.790881	−	7.02670i	−0.0293726	−	0.260965i
$726$		0			0
$727$	29.1033			1.07938			0.539690	−	0.841864i	$-0.318541\pi$
$727$	29.1033			1.07938			0.539690	+	0.841864i	$0.318541\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.57321	−	14.8492i	−0.317092	−	0.549219i
$732$		0			0
$733$	−6.61438	+	11.4564i	−0.244308	+	0.423153i	−0.961937	−	0.273272i	$-0.911894\pi$
$733$	−6.61438	+	11.4564i	−0.244308	+	0.423153i	0.717629	+	0.696426i	$0.245227\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.4422	−	33.6749i	0.716163	−	1.24043i
$738$		0			0
$739$	−8.50000	−	14.7224i	−0.312678	−	0.541573i	0.666264	−	0.745716i	$-0.267893\pi$
$739$	−8.50000	−	14.7224i	−0.312678	−	0.541573i	−0.978941	+	0.204143i	$0.934559\pi$
$740$	1.14790	+	20.4617i	0.0421975	+	0.752188i
$741$		0			0
$742$		0			0
$743$	−51.8459			−1.90204			−0.951021	−	0.309125i	$-0.899964\pi$
$743$	−51.8459			−1.90204			−0.951021	+	0.309125i	$0.899964\pi$
$744$		0			0
$745$	28.2288	+	14.2526i	1.03422	+	0.522176i
$746$		0			0
$747$		0			0
$748$	−21.1660			−0.773906
$749$	−8.57321	−	14.8492i	−0.313258	−	0.542580i
$750$		0			0
$751$	3.50000	−	6.06218i	0.127717	−	0.221212i	−0.795075	−	0.606511i	$-0.792568\pi$
$751$	3.50000	−	6.06218i	0.127717	−	0.221212i	0.922792	+	0.385299i	$0.125902\pi$
$752$	−12.9615	+	7.48331i	−0.472657	+	0.272888i
$753$		0			0
$754$		0			0
$755$	12.2474	+	18.7083i	0.445730	+	0.680864i
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	8.57321	−	14.8492i	0.310779	−	0.538285i	−0.667752	−	0.744383i	$-0.732744\pi$
$761$	8.57321	−	14.8492i	0.310779	−	0.538285i	0.978531	+	0.206099i	$0.0660768\pi$
$762$		0			0
$763$	−18.5203			−0.670478
$764$		−	31.1127i		−	1.12562i
$765$		0			0
$766$		0			0
$767$	9.72111	+	16.8375i	0.351009	+	0.607965i
$768$		0			0
$769$		−	32.9090i		−	1.18673i	−0.804934	−	0.593364i	$-0.797800\pi$
$769$		−	32.9090i		−	1.18673i	0.804934	−	0.593364i	$-0.202200\pi$
$770$		0			0
$771$		0			0
$772$	23.8118	+	13.7477i	0.857004	+	0.494792i
$773$	25.9230	−	14.9666i	0.932384	−	0.538312i	0.0448193	−	0.998995i	$-0.485729\pi$
$773$	25.9230	−	14.9666i	0.932384	−	0.538312i	0.887565	+	0.460683i	$0.152395\pi$
$774$		0			0
$775$	20.9059	−	15.4254i	0.750961	−	0.554098i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.34847	−	4.24264i	−0.263286	−	0.152008i
$780$		0			0
$781$	16.0000	+	27.7128i	0.572525	+	0.991642i
$782$		0			0
$783$		0			0
$784$	28.0000			1.00000
$785$	−6.48074	−	9.89949i	−0.231308	−	0.353328i
$786$		0			0
$787$	−26.4575	−	45.8258i	−0.943108	−	1.63351i	−0.759495	−	0.650513i	$-0.774554\pi$
$787$	−26.4575	−	45.8258i	−0.943108	−	1.63351i	−0.183614	−	0.982998i	$-0.558780\pi$
$788$	−19.4422	−	33.6749i	−0.692600	−	1.19962i
$789$		0			0
$790$		0			0
$791$	−8.57321	+	14.8492i	−0.304828	+	0.527978i
$792$		0			0
$793$	23.8118	+	13.7477i	0.845580	+	0.488196i
$794$		0			0
$795$		0			0
$796$	12.0000	+	6.92820i	0.425329	+	0.245564i
$797$			41.1582i			1.45790i	0.684567	+	0.728950i	$0.259991\pi$
$797$			41.1582i			1.45790i	−0.684567	+	0.728950i	$0.740009\pi$
$798$		0			0
$799$	−14.0000			−0.495284
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−32.4037	−	18.7083i	−1.14350	−	0.660201i
$804$		0			0
$805$	21.0000	+	32.0780i	0.740153	+	1.13060i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	28.1691	−	16.2635i	0.990374	−	0.571793i	0.0849879	−	0.996382i	$-0.472915\pi$
$809$	28.1691	−	16.2635i	0.990374	−	0.571793i	0.905386	+	0.424589i	$0.139582\pi$
$810$		0			0
$811$			20.7846i			0.729846i	0.931038	+	0.364923i	$0.118905\pi$
$811$			20.7846i			0.729846i	−0.931038	+	0.364923i	$0.881095\pi$
$812$			7.48331i			0.262613i
$813$		0			0
$814$		0			0
$815$	−18.2943	−	9.23676i	−0.640822	−	0.323549i
$816$		0			0
$817$	−3.96863	+	6.87386i	−0.138845	+	0.240486i
$818$		0			0
$819$		0			0
$820$	−12.0000	−	18.3303i	−0.419058	−	0.640122i
$821$	4.89898	+	2.82843i	0.170976	+	0.0987128i	0.583046	−	0.812439i	$-0.301861\pi$
$821$	4.89898	+	2.82843i	0.170976	+	0.0987128i	−0.412070	+	0.911152i	$0.635194\pi$
$822$		0			0
$823$	−23.8118	+	13.7477i	−0.830026	+	0.479216i	−0.853862	−	0.520500i	$-0.825745\pi$
$823$	−23.8118	+	13.7477i	−0.830026	+	0.479216i	0.0238357	+	0.999716i	$0.492412\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	19.4422			0.676072			0.338036	−	0.941133i	$-0.390237\pi$
$827$	19.4422			0.676072			0.338036	+	0.941133i	$0.390237\pi$
$828$		0			0
$829$	37.5000	−	21.6506i	1.30243	−	0.751958i	0.321609	−	0.946873i	$-0.395776\pi$
$829$	37.5000	−	21.6506i	1.30243	−	0.751958i	0.980820	+	0.194915i	$0.0624431\pi$
$830$		0			0
$831$		0			0
$832$	21.1660			0.733799
$833$	22.6826	+	13.0958i	0.785905	+	0.453743i
$834$		0			0
$835$	0.937254	+	16.7069i	0.0324350	+	0.578167i
$836$	4.89898	+	8.48528i	0.169435	+	0.293470i
$837$		0			0
$838$		0			0
$839$	12.2474			0.422829			0.211414	−	0.977397i	$-0.432193\pi$
$839$	12.2474			0.422829			0.211414	+	0.977397i	$0.432193\pi$
$840$		0			0
$841$	27.0000			0.931034
$842$		0			0
$843$		0			0
$844$	14.0000	+	24.2487i	0.481900	+	0.834675i
$845$	−13.3953	+	0.751475i	−0.460814	+	0.0258515i
$846$		0			0
$847$	−3.96863	−	6.87386i	−0.136364	−	0.236189i
$848$	51.8459			1.78040
$849$		0			0
$850$		0			0
$851$	25.7196	−	14.8492i	0.881658	−	0.509025i
$852$		0			0
$853$	−50.2693			−1.72119			−0.860594	−	0.509292i	$-0.829907\pi$
$853$	−50.2693			−1.72119			−0.860594	+	0.509292i	$0.829907\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.2019	−	9.35414i	0.553445	−	0.319531i	−0.197065	−	0.980390i	$-0.563141\pi$
$857$	16.2019	−	9.35414i	0.553445	−	0.319531i	0.750510	+	0.660859i	$0.229808\pi$
$858$		0			0
$859$	12.0000	+	6.92820i	0.409435	+	0.236387i	0.690547	−	0.723288i	$-0.257370\pi$
$859$	12.0000	+	6.92820i	0.409435	+	0.236387i	−0.281112	+	0.959675i	$0.590703\pi$
$860$	−17.1464	+	11.2250i	−0.584688	+	0.382768i
$861$		0			0
$862$		0			0
$863$	16.2019	−	28.0624i	0.551517	−	0.955256i	−0.446648	−	0.894710i	$-0.647382\pi$
$863$	16.2019	−	28.0624i	0.551517	−	0.955256i	0.998165	−	0.0605464i	$-0.0192843\pi$
$864$		0			0
$865$	29.8745	+	15.0836i	1.01576	+	0.512856i
$866$		0			0
$867$		0			0
$868$	−23.8118	+	13.7477i	−0.808224	+	0.466628i
$869$		−	19.7990i		−	0.671635i
$870$		0			0
$871$	−31.5000	+	18.1865i	−1.06734	+	0.616227i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−10.2951	+	27.7311i	−0.348037	+	0.937481i
$876$		0			0
$877$	7.93725	+	4.58258i	0.268022	+	0.154743i	0.627988	−	0.778223i	$-0.283879\pi$
$877$	7.93725	+	4.58258i	0.268022	+	0.154743i	−0.359966	+	0.932965i	$0.617212\pi$
$878$		0			0
$879$		0			0
$880$	1.41699	+	25.2585i	0.0477669	+	0.851464i
$881$	−29.3939			−0.990305			−0.495152	−	0.868806i	$-0.664888\pi$
$881$	−29.3939			−0.990305			−0.495152	+	0.868806i	$0.664888\pi$
$882$		0			0
$883$			41.2432i			1.38794i	0.720002	+	0.693972i	$0.244141\pi$
$883$			41.2432i			1.38794i	−0.720002	+	0.693972i	$0.755859\pi$
$884$	17.1464	+	9.89949i	0.576697	+	0.332956i
$885$		0			0
$886$		0			0
$887$	32.4037	+	18.7083i	1.08801	+	0.628163i	0.933046	−	0.359757i	$-0.117141\pi$
$887$	32.4037	+	18.7083i	1.08801	+	0.628163i	0.154964	+	0.987920i	$0.450474\pi$
$888$		0			0
$889$	−31.5000	−	18.1865i	−1.05648	−	0.609957i
$890$		0			0
$891$		0			0
$892$	5.29150	+	9.16515i	0.177173	+	0.306872i
$893$	3.24037	+	5.61249i	0.108435	+	0.187815i
$894$		0			0
$895$	13.2288	−	8.66025i	0.442189	−	0.289480i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.67423	−	6.36396i	−0.122543	−	0.212250i
$900$		0			0
$901$	42.0000	+	24.2487i	1.39922	+	0.807842i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.95239	+	34.8021i	0.0648996	+	1.15686i
$906$		0			0
$907$	19.8431	−	11.4564i	0.658880	−	0.380405i	−0.132970	−	0.991120i	$-0.542451\pi$
$907$	19.8431	−	11.4564i	0.658880	−	0.380405i	0.791850	+	0.610715i	$0.209118\pi$
$908$	−25.9230	−	14.9666i	−0.860284	−	0.496685i
$909$		0			0
$910$		0			0
$911$			41.0122i			1.35879i	0.733771	+	0.679397i	$0.237759\pi$
$911$			41.0122i			1.35879i	−0.733771	+	0.679397i	$0.762241\pi$
$912$		0			0
$913$	−21.1660	−	36.6606i	−0.700493	−	1.21329i
$914$		0			0
$915$		0			0
$916$		−	3.46410i		−	0.114457i
$917$	22.6826	+	39.2874i	0.749045	+	1.29738i
$918$		0			0
$919$	−17.5000	+	30.3109i	−0.577272	+	0.999864i	0.418519	+	0.908208i	$0.362549\pi$
$919$	−17.5000	+	30.3109i	−0.577272	+	0.999864i	−0.995791	+	0.0916559i	$0.970784\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	29.9333i		−	0.985265i
$924$		0			0
$925$	21.0000	+	9.16515i	0.690476	+	0.301348i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$929$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$930$		0			0
$931$		−	12.1244i		−	0.397360i
$932$	−12.9615			−0.424567
$933$		0			0
$934$		0			0
$935$	−10.6657	+	21.1245i	−0.348805	+	0.690844i
$936$		0			0
$937$	−50.2693			−1.64223			−0.821113	−	0.570766i	$-0.806646\pi$
$937$	−50.2693			−1.64223			−0.821113	+	0.570766i	$0.806646\pi$
$938$		0			0
$939$		0			0
$940$	0.937254	+	16.7069i	0.0305699	+	0.544920i
$941$	−3.67423	−	6.36396i	−0.119777	−	0.207459i	0.799902	−	0.600130i	$-0.204885\pi$
$941$	−3.67423	−	6.36396i	−0.119777	−	0.207459i	−0.919679	+	0.392671i	$0.871551\pi$
$942$		0			0
$943$	−15.8745	+	27.4955i	−0.516945	+	0.895375i
$944$	29.3939			0.956689
$945$		0			0
$946$		0			0
$947$	−19.4422	+	33.6749i	−0.631787	+	1.09429i	0.355399	+	0.934715i	$0.384345\pi$
$947$	−19.4422	+	33.6749i	−0.631787	+	1.09429i	−0.987186	+	0.159573i	$0.948988\pi$
$948$		0			0
$949$	17.5000	+	30.3109i	0.568074	+	0.983933i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$	−31.0516	−	15.6779i	−1.00481	−	0.507325i
$956$	31.8434	−	18.3848i	1.02989	−	0.594606i
$957$		0			0
$958$		0			0
$959$	17.1464			0.553687
$960$		0			0
$961$	−2.00000	+	3.46410i	−0.0645161	+	0.111745i
$962$		0			0
$963$		0			0
$964$	−30.0000	−	17.3205i	−0.966235	−	0.557856i
$965$	25.7196	−	16.8375i	0.827945	−	0.542017i
$966$		0			0
$967$		−	4.58258i		−	0.147366i	−0.997282	−	0.0736828i	$-0.976525\pi$
$967$		−	4.58258i		−	0.147366i	0.997282	−	0.0736828i	$-0.0234753\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.79796	−	16.9706i	0.314431	−	0.544611i	−0.664885	−	0.746946i	$-0.731519\pi$
$971$	9.79796	−	16.9706i	0.314431	−	0.544611i	0.979316	+	0.202334i	$0.0648528\pi$
$972$		0			0
$973$	−19.8431	−	11.4564i	−0.636142	−	0.367277i
$974$		0			0
$975$		0			0
$976$	36.0000	−	20.7846i	1.15233	−	0.665299i
$977$	−19.4422	−	33.6749i	−0.622012	−	1.07736i	−0.989111	−	0.147174i	$-0.952982\pi$
$977$	−19.4422	−	33.6749i	−0.622012	−	1.07736i	0.367099	−	0.930182i	$-0.380351\pi$
$978$		0			0
$979$			48.4974i			1.54998i
$980$	14.1094	−	27.9450i	0.450708	−	0.892672i
$981$		0			0
$982$		0			0
$983$	−42.1248	+	24.3208i	−1.34357	+	0.775712i	−0.987330	−	0.158681i	$-0.949276\pi$
$983$	−42.1248	+	24.3208i	−1.34357	+	0.775712i	−0.356243	+	0.934393i	$0.615942\pi$
$984$		0			0
$985$	−43.4059	+	2.43506i	−1.38303	+	0.0775874i
$986$		0			0
$987$		0			0
$988$		−	9.16515i		−	0.291582i
$989$	25.7196	+	14.8492i	0.817837	+	0.472178i
$990$		0			0
$991$	3.50000	+	6.06218i	0.111181	+	0.192571i	0.916247	−	0.400614i	$-0.131203\pi$
$991$	3.50000	+	6.06218i	0.111181	+	0.192571i	−0.805066	+	0.593186i	$0.797870\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	12.9615	−	8.48528i	0.410907	−	0.269002i
$996$		0			0
$997$	1.32288	+	2.29129i	0.0418959	+	0.0725658i	0.886213	−	0.463278i	$-0.153327\pi$
$997$	1.32288	+	2.29129i	0.0418959	+	0.0725658i	−0.844317	+	0.535844i	$0.819994\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bb.a.89.4	yes	8
3.2	odd	2	inner	315.2.bb.a.89.1	✓	8
5.2	odd	4		1575.2.bk.d.26.2		8
5.3	odd	4		1575.2.bk.d.26.4		8
5.4	even	2	inner	315.2.bb.a.89.2	yes	8
7.2	even	3		2205.2.g.a.2204.2		8
7.3	odd	6	inner	315.2.bb.a.269.3	yes	8
7.5	odd	6		2205.2.g.a.2204.8		8
15.2	even	4		1575.2.bk.d.26.1		8
15.8	even	4		1575.2.bk.d.26.3		8
15.14	odd	2	inner	315.2.bb.a.89.3	yes	8
21.2	odd	6		2205.2.g.a.2204.7		8
21.5	even	6		2205.2.g.a.2204.1		8
21.17	even	6	inner	315.2.bb.a.269.2	yes	8
35.3	even	12		1575.2.bk.d.1151.3		8
35.9	even	6		2205.2.g.a.2204.4		8
35.17	even	12		1575.2.bk.d.1151.1		8
35.19	odd	6		2205.2.g.a.2204.6		8
35.24	odd	6	inner	315.2.bb.a.269.1	yes	8
105.17	odd	12		1575.2.bk.d.1151.2		8
105.38	odd	12		1575.2.bk.d.1151.4		8
105.44	odd	6		2205.2.g.a.2204.5		8
105.59	even	6	inner	315.2.bb.a.269.4	yes	8
105.89	even	6		2205.2.g.a.2204.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bb.a.89.1	✓	8	3.2	odd	2	inner
315.2.bb.a.89.2	yes	8	5.4	even	2	inner
315.2.bb.a.89.3	yes	8	15.14	odd	2	inner
315.2.bb.a.89.4	yes	8	1.1	even	1	trivial
315.2.bb.a.269.1	yes	8	35.24	odd	6	inner
315.2.bb.a.269.2	yes	8	21.17	even	6	inner
315.2.bb.a.269.3	yes	8	7.3	odd	6	inner
315.2.bb.a.269.4	yes	8	105.59	even	6	inner
1575.2.bk.d.26.1		8	15.2	even	4
1575.2.bk.d.26.2		8	5.2	odd	4
1575.2.bk.d.26.3		8	15.8	even	4
1575.2.bk.d.26.4		8	5.3	odd	4
1575.2.bk.d.1151.1		8	35.17	even	12
1575.2.bk.d.1151.2		8	105.17	odd	12
1575.2.bk.d.1151.3		8	35.3	even	12
1575.2.bk.d.1151.4		8	105.38	odd	12
2205.2.g.a.2204.1		8	21.5	even	6
2205.2.g.a.2204.2		8	7.2	even	3
2205.2.g.a.2204.3		8	105.89	even	6
2205.2.g.a.2204.4		8	35.9	even	6
2205.2.g.a.2204.5		8	105.44	odd	6
2205.2.g.a.2204.6		8	35.19	odd	6
2205.2.g.a.2204.7		8	21.2	odd	6
2205.2.g.a.2204.8		8	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{4} +(2.23256 - 0.125246i) q^{5} +(-1.32288 + 2.29129i) q^{7} +(2.44949 - 1.41421i) q^{11} -2.64575 q^{13} +(-2.00000 + 3.46410i) q^{16} +(-3.24037 + 1.87083i) q^{17} +(1.50000 + 0.866025i) q^{19} +(2.44949 + 3.74166i) q^{20} +(3.24037 - 5.61249i) q^{23} +(4.96863 - 0.559237i) q^{25} -5.29150 q^{28} -1.41421i q^{29} +(4.50000 - 2.59808i) q^{31} +(-2.66642 + 5.28112i) q^{35} +(3.96863 + 2.29129i) q^{37} -4.89898 q^{41} +4.58258i q^{43} +(4.89898 + 2.82843i) q^{44} +(3.24037 + 1.87083i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(-2.64575 - 4.58258i) q^{52} +(-6.48074 - 11.2250i) q^{53} +(5.29150 - 3.46410i) q^{55} +(-3.67423 - 6.36396i) q^{59} +(-9.00000 - 5.19615i) q^{61} -8.00000 q^{64} +(-5.90679 + 0.331369i) q^{65} +(11.9059 - 6.87386i) q^{67} +(-6.48074 - 3.74166i) q^{68} +11.3137i q^{71} +(-6.61438 - 11.4564i) q^{73} +3.46410i q^{76} +7.48331i q^{77} +(3.50000 - 6.06218i) q^{79} +(-4.03125 + 7.98430i) q^{80} -14.9666i q^{83} +(-7.00000 + 4.58258i) q^{85} +(-8.57321 + 14.8492i) q^{89} +(3.50000 - 6.06218i) q^{91} +12.9615 q^{92} +(3.45730 + 1.74558i) q^{95} +5.29150 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 16 q^{16} + 12 q^{19} + 8 q^{25} + 36 q^{31} - 28 q^{49} - 72 q^{61} - 64 q^{64} + 28 q^{79} - 56 q^{85} + 28 q^{91}+O(q^{100}) \) 8 * q + 8 * q^4 - 16 * q^16 + 12 * q^19 + 8 * q^25 + 36 * q^31 - 28 * q^49 - 72 * q^61 - 64 * q^64 + 28 * q^79 - 56 * q^85 + 28 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more