LMFDB - Embedded newform 1288.2.q.b.737.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1288,2,Mod(737,1288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1288, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1288.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1288 = 2^{3} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1288.q (of order $3$, 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:	$10.2847317803$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			737.5
Character	$\chi$	$=$	1288.737
Dual form			1288.2.q.b.921.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.426141 - 0.738098i) q^{3} +(-0.627198 + 1.08634i) q^{5} +(0.127177 - 2.64269i) q^{7} +(1.13681 - 1.96901i) q^{9} +O(q^{10})$	\(q+(-0.426141 - 0.738098i) q^{3} +(-0.627198 + 1.08634i) q^{5} +(0.127177 - 2.64269i) q^{7} +(1.13681 - 1.96901i) q^{9} +(-2.84658 - 4.93041i) q^{11} -1.56428 q^{13} +1.06910 q^{15} +(1.83376 + 3.17616i) q^{17} +(-2.55621 + 4.42748i) q^{19} +(-2.00476 + 1.03229i) q^{21} +(0.500000 - 0.866025i) q^{23} +(1.71324 + 2.96743i) q^{25} -4.49461 q^{27} -3.12094 q^{29} +(-0.706969 - 1.22451i) q^{31} +(-2.42609 + 4.20211i) q^{33} +(2.79110 + 1.79565i) q^{35} +(-0.653491 + 1.13188i) q^{37} +(0.666603 + 1.15459i) q^{39} -2.24298 q^{41} -5.84516 q^{43} +(1.42601 + 2.46992i) q^{45} +(-2.30705 + 3.99593i) q^{47} +(-6.96765 - 0.672180i) q^{49} +(1.56288 - 2.70698i) q^{51} +(-4.29745 - 7.44340i) q^{53} +7.14147 q^{55} +4.35722 q^{57} +(-6.45000 - 11.1717i) q^{59} +(-2.52419 + 4.37203i) q^{61} +(-5.05891 - 3.25465i) q^{63} +(0.981112 - 1.69934i) q^{65} +(-6.39808 - 11.0818i) q^{67} -0.852282 q^{69} +12.6302 q^{71} +(-4.73419 - 8.19986i) q^{73} +(1.46017 - 2.52909i) q^{75} +(-13.3916 + 6.89559i) q^{77} +(-3.15976 + 5.47287i) q^{79} +(-1.49508 - 2.58956i) q^{81} +11.3499 q^{83} -4.60051 q^{85} +(1.32996 + 2.30356i) q^{87} +(-0.884380 + 1.53179i) q^{89} +(-0.198940 + 4.13390i) q^{91} +(-0.602537 + 1.04362i) q^{93} +(-3.20650 - 5.55381i) q^{95} -6.92877 q^{97} -12.9440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} - 9 q^{5} - q^{7} - 11 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 - 9 * q^5 - q^7 - 11 * q^9	$ 22 q + 2 q^{3} - 9 q^{5} - q^{7} - 11 q^{9} + 30 q^{13} - 4 q^{15} - 5 q^{17} + 3 q^{21} + 11 q^{23} - 22 q^{25} - 10 q^{27} + 10 q^{29} - 6 q^{31} - 14 q^{33} + 25 q^{35} + q^{37} - 11 q^{39} + 40 q^{41} - 14 q^{43} - 41 q^{45} + 3 q^{47} + 9 q^{49} + 13 q^{51} - 19 q^{53} - 6 q^{55} - 10 q^{57} - 7 q^{59} - 39 q^{61} + 81 q^{63} - 5 q^{65} - 7 q^{67} + 4 q^{69} - 38 q^{71} + 5 q^{73} - 16 q^{75} - 17 q^{77} - 11 q^{79} - 43 q^{81} + 66 q^{83} - 26 q^{85} + 30 q^{87} - 34 q^{89} + 8 q^{91} + 12 q^{93} - 37 q^{95} + 34 q^{97} - 98 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 - 9 * q^5 - q^7 - 11 * q^9 + 30 * q^13 - 4 * q^15 - 5 * q^17 + 3 * q^21 + 11 * q^23 - 22 * q^25 - 10 * q^27 + 10 * q^29 - 6 * q^31 - 14 * q^33 + 25 * q^35 + q^37 - 11 * q^39 + 40 * q^41 - 14 * q^43 - 41 * q^45 + 3 * q^47 + 9 * q^49 + 13 * q^51 - 19 * q^53 - 6 * q^55 - 10 * q^57 - 7 * q^59 - 39 * q^61 + 81 * q^63 - 5 * q^65 - 7 * q^67 + 4 * q^69 - 38 * q^71 + 5 * q^73 - 16 * q^75 - 17 * q^77 - 11 * q^79 - 43 * q^81 + 66 * q^83 - 26 * q^85 + 30 * q^87 - 34 * q^89 + 8 * q^91 + 12 * q^93 - 37 * q^95 + 34 * q^97 - 98 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1288\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$645$	$967$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.426141	−	0.738098i	−0.246033	−	0.426141i	0.716389	−	0.697701i	$-0.245794\pi$
$3$	−0.426141	−	0.738098i	−0.246033	−	0.426141i	−0.962421	+	0.271560i	$0.912460\pi$
$4$		0			0
$5$	−0.627198	+	1.08634i	−0.280492	+	0.485826i	−0.971506	−	0.237015i	$-0.923831\pi$
$5$	−0.627198	+	1.08634i	−0.280492	+	0.485826i	0.691014	+	0.722841i	$0.257164\pi$
$6$		0			0
$7$	0.127177	−	2.64269i	0.0480684	−	0.998844i
$7$	0.127177	−	2.64269i	0.0480684	−	0.998844i
$8$		0			0
$9$	1.13681	−	1.96901i	0.378936	−	0.656336i
$10$		0			0
$11$	−2.84658	−	4.93041i	−0.858275	−	1.48658i	−0.873573	−	0.486693i	$-0.838203\pi$
$11$	−2.84658	−	4.93041i	−0.858275	−	1.48658i	0.0152980	−	0.999883i	$-0.495130\pi$
$12$		0			0
$13$	−1.56428			−0.433852			−0.216926	−	0.976188i	$-0.569603\pi$
$13$	−1.56428			−0.433852			−0.216926	+	0.976188i	$0.569603\pi$
$14$		0			0
$15$	1.06910			0.276040
$16$		0			0
$17$	1.83376	+	3.17616i	0.444751	+	0.770331i	0.998035	−	0.0626615i	$-0.0199589\pi$
$17$	1.83376	+	3.17616i	0.444751	+	0.770331i	−0.553284	+	0.832993i	$0.686626\pi$
$18$		0			0
$19$	−2.55621	+	4.42748i	−0.586434	+	1.01573i	0.408261	+	0.912865i	$0.366135\pi$
$19$	−2.55621	+	4.42748i	−0.586434	+	1.01573i	−0.994695	+	0.102868i	$0.967198\pi$
$20$		0			0
$21$	−2.00476	+	1.03229i	−0.437475	+	0.225264i
$22$		0			0
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$		0			0
$25$	1.71324	+	2.96743i	0.342649	+	0.593485i
$26$		0			0
$27$	−4.49461			−0.864988
$28$		0			0
$29$	−3.12094			−0.579544			−0.289772	−	0.957096i	$-0.593579\pi$
$29$	−3.12094			−0.579544			−0.289772	+	0.957096i	$0.593579\pi$
$30$		0			0
$31$	−0.706969	−	1.22451i	−0.126975	−	0.219928i	0.795528	−	0.605917i	$-0.207194\pi$
$31$	−0.706969	−	1.22451i	−0.126975	−	0.219928i	−0.922503	+	0.385989i	$0.873860\pi$
$32$		0			0
$33$	−2.42609	+	4.20211i	−0.422327	+	0.731493i
$34$		0			0
$35$	2.79110	+	1.79565i	0.471781	+	0.303520i
$36$		0			0
$37$	−0.653491	+	1.13188i	−0.107433	+	0.186080i	−0.914730	−	0.404066i	$-0.867597\pi$
$37$	−0.653491	+	1.13188i	−0.107433	+	0.186080i	0.807296	+	0.590146i	$0.200930\pi$
$38$		0			0
$39$	0.666603	+	1.15459i	0.106742	+	0.184882i
$40$		0			0
$41$	−2.24298			−0.350295			−0.175148	−	0.984542i	$-0.556040\pi$
$41$	−2.24298			−0.350295			−0.175148	+	0.984542i	$0.556040\pi$
$42$		0			0
$43$	−5.84516			−0.891378			−0.445689	−	0.895188i	$-0.647041\pi$
$43$	−5.84516			−0.891378			−0.445689	+	0.895188i	$0.647041\pi$
$44$		0			0
$45$	1.42601	+	2.46992i	0.212577	+	0.368193i
$46$		0			0
$47$	−2.30705	+	3.99593i	−0.336518	+	0.582866i	−0.983775	−	0.179406i	$-0.942583\pi$
$47$	−2.30705	+	3.99593i	−0.336518	+	0.582866i	0.647257	+	0.762271i	$0.275916\pi$
$48$		0			0
$49$	−6.96765	−	0.672180i	−0.995379	−	0.0960258i
$50$		0			0
$51$	1.56288	−	2.70698i	0.218847	−	0.379053i
$52$		0			0
$53$	−4.29745	−	7.44340i	−0.590300	−	1.02243i	−0.994192	−	0.107623i	$-0.965676\pi$
$53$	−4.29745	−	7.44340i	−0.590300	−	1.02243i	0.403892	−	0.914807i	$-0.367657\pi$
$54$		0			0
$55$	7.14147			0.962956
$56$		0			0
$57$	4.35722			0.577128
$58$		0			0
$59$	−6.45000	−	11.1717i	−0.839719	−	1.45444i	−0.890130	−	0.455707i	$-0.849386\pi$
$59$	−6.45000	−	11.1717i	−0.839719	−	1.45444i	0.0504108	−	0.998729i	$-0.483947\pi$
$60$		0			0
$61$	−2.52419	+	4.37203i	−0.323189	+	0.559781i	−0.981144	−	0.193277i	$-0.938088\pi$
$61$	−2.52419	+	4.37203i	−0.323189	+	0.559781i	0.657955	+	0.753057i	$0.271422\pi$
$62$		0			0
$63$	−5.05891	−	3.25465i	−0.637363	−	0.410047i
$64$		0			0
$65$	0.981112	−	1.69934i	0.121692	−	0.210777i
$66$		0			0
$67$	−6.39808	−	11.0818i	−0.781650	−	1.35386i	−0.930980	−	0.365070i	$-0.881045\pi$
$67$	−6.39808	−	11.0818i	−0.781650	−	1.35386i	0.149330	−	0.988787i	$-0.452288\pi$
$68$		0			0
$69$	−0.852282			−0.102603
$70$		0			0
$71$	12.6302			1.49893			0.749463	−	0.662047i	$-0.230312\pi$
$71$	12.6302			1.49893			0.749463	+	0.662047i	$0.230312\pi$
$72$		0			0
$73$	−4.73419	−	8.19986i	−0.554095	−	0.959721i	−0.997973	−	0.0636337i	$-0.979731\pi$
$73$	−4.73419	−	8.19986i	−0.554095	−	0.959721i	0.443878	−	0.896087i	$-0.353602\pi$
$74$		0			0
$75$	1.46017	−	2.52909i	0.168606	−	0.292034i
$76$		0			0
$77$	−13.3916	+	6.89559i	−1.52611	+	0.785826i
$78$		0			0
$79$	−3.15976	+	5.47287i	−0.355501	+	0.615746i	−0.987204	−	0.159465i	$-0.949023\pi$
$79$	−3.15976	+	5.47287i	−0.355501	+	0.615746i	0.631702	+	0.775211i	$0.282357\pi$
$80$		0			0
$81$	−1.49508	−	2.58956i	−0.166121	−	0.287729i
$82$		0			0
$83$	11.3499			1.24581			0.622906	−	0.782297i	$-0.285952\pi$
$83$	11.3499			1.24581			0.622906	+	0.782297i	$0.285952\pi$
$84$		0			0
$85$	−4.60051			−0.498996
$86$		0			0
$87$	1.32996	+	2.30356i	0.142587	+	0.246967i
$88$		0			0
$89$	−0.884380	+	1.53179i	−0.0937441	+	0.162370i	−0.909084	−	0.416613i	$-0.863217\pi$
$89$	−0.884380	+	1.53179i	−0.0937441	+	0.162370i	0.815340	+	0.578983i	$0.196550\pi$
$90$		0			0
$91$	−0.198940	+	4.13390i	−0.0208546	+	0.433351i
$92$		0			0
$93$	−0.602537	+	1.04362i	−0.0624802	+	0.108219i
$94$		0			0
$95$	−3.20650	−	5.55381i	−0.328980	−	0.569809i
$96$		0			0
$97$	−6.92877			−0.703510			−0.351755	−	0.936092i	$-0.614415\pi$
$97$	−6.92877			−0.703510			−0.351755	+	0.936092i	$0.614415\pi$
$98$		0			0
$99$	−12.9440			−1.30092
$100$		0			0
$101$	6.34377	+	10.9877i	0.631228	+	1.09332i	0.987301	+	0.158861i	$0.0507823\pi$
$101$	6.34377	+	10.9877i	0.631228	+	1.09332i	−0.356073	+	0.934458i	$0.615884\pi$
$102$		0			0
$103$	−3.82041	+	6.61715i	−0.376437	+	0.652007i	−0.990541	−	0.137217i	$-0.956184\pi$
$103$	−3.82041	+	6.61715i	−0.376437	+	0.652007i	0.614104	+	0.789225i	$0.289517\pi$
$104$		0			0
$105$	0.135965	−	2.82530i	0.0132688	−	0.275721i
$106$		0			0
$107$	−2.69770	+	4.67255i	−0.260796	+	0.451713i	−0.966454	−	0.256841i	$-0.917318\pi$
$107$	−2.69770	+	4.67255i	−0.260796	+	0.451713i	0.705657	+	0.708553i	$0.250652\pi$
$108$		0			0
$109$	2.23594	+	3.87276i	0.214164	+	0.370943i	0.953014	−	0.302927i	$-0.0979640\pi$
$109$	2.23594	+	3.87276i	0.214164	+	0.370943i	−0.738850	+	0.673870i	$0.764631\pi$
$110$		0			0
$111$	1.11392			0.105728
$112$		0			0
$113$	−2.08084			−0.195749			−0.0978745	−	0.995199i	$-0.531204\pi$
$113$	−2.08084			−0.195749			−0.0978745	+	0.995199i	$0.531204\pi$
$114$		0			0
$115$	0.627198	+	1.08634i	0.0584865	+	0.101302i
$116$		0			0
$117$	−1.77828	+	3.08007i	−0.164402	+	0.284753i
$118$		0			0
$119$	8.62682	−	4.44212i	0.790819	−	0.407208i
$120$		0			0
$121$	−10.7060	+	18.5433i	−0.973272	+	1.68576i
$122$		0			0
$123$	0.955828	+	1.65554i	0.0861841	+	0.149275i
$124$		0			0
$125$	−10.5702			−0.945424
$126$		0			0
$127$	−8.74889			−0.776339			−0.388169	−	0.921588i	$-0.626892\pi$
$127$	−8.74889			−0.776339			−0.388169	+	0.921588i	$0.626892\pi$
$128$		0			0
$129$	2.49086	+	4.31430i	0.219308	+	0.379853i
$130$		0			0
$131$	9.38413	−	16.2538i	0.819895	−	1.42010i	−0.0858638	−	0.996307i	$-0.527365\pi$
$131$	9.38413	−	16.2538i	0.819895	−	1.42010i	0.905759	−	0.423793i	$-0.139302\pi$
$132$		0			0
$133$	11.3754	+	7.31834i	0.986370	+	0.634581i
$134$		0			0
$135$	2.81901	−	4.88267i	0.242622	−	0.420233i
$136$		0			0
$137$	3.71111	+	6.42782i	0.317061	+	0.549166i	0.979873	−	0.199619i	$-0.0639706\pi$
$137$	3.71111	+	6.42782i	0.317061	+	0.549166i	−0.662812	+	0.748786i	$0.730637\pi$
$138$		0			0
$139$	7.40666			0.628225			0.314112	−	0.949386i	$-0.398293\pi$
$139$	7.40666			0.628225			0.314112	+	0.949386i	$0.398293\pi$
$140$		0			0
$141$	3.93251			0.331178
$142$		0			0
$143$	4.45283	+	7.71253i	0.372365	+	0.644955i
$144$		0			0
$145$	1.95745	−	3.39040i	0.162557	−	0.281557i
$146$		0			0
$147$	2.47307	+	5.42925i	0.203975	+	0.447797i
$148$		0			0
$149$	4.23834	−	7.34102i	0.347218	−	0.601399i	−0.638536	−	0.769592i	$-0.720460\pi$
$149$	4.23834	−	7.34102i	0.347218	−	0.601399i	0.985754	+	0.168192i	$0.0537930\pi$
$150$		0			0
$151$	−5.24900	−	9.09154i	−0.427158	−	0.739859i	0.569462	−	0.822018i	$-0.307152\pi$
$151$	−5.24900	−	9.09154i	−0.427158	−	0.739859i	−0.996619	+	0.0821593i	$0.973818\pi$
$152$		0			0
$153$	8.33851			0.674128
$154$		0			0
$155$	1.77364			0.142462
$156$		0			0
$157$	−5.06169	−	8.76711i	−0.403967	−	0.699692i	0.590233	−	0.807233i	$-0.299036\pi$
$157$	−5.06169	−	8.76711i	−0.403967	−	0.699692i	−0.994201	+	0.107541i	$0.965702\pi$
$158$		0			0
$159$	−3.66264	+	6.34388i	−0.290466	+	0.503102i
$160$		0			0
$161$	−2.22505	−	1.43149i	−0.175359	−	0.112817i
$162$		0			0
$163$	−2.36789	+	4.10131i	−0.185468	+	0.321239i	−0.943734	−	0.330706i	$-0.892713\pi$
$163$	−2.36789	+	4.10131i	−0.185468	+	0.321239i	0.758266	+	0.651945i	$0.226047\pi$
$164$		0			0
$165$	−3.04327	−	5.27111i	−0.236919	−	0.410355i
$166$		0			0
$167$	20.1367			1.55822			0.779110	−	0.626887i	$-0.215671\pi$
$167$	20.1367			1.55822			0.779110	+	0.626887i	$0.215671\pi$
$168$		0			0
$169$	−10.5530			−0.811772
$170$		0			0
$171$	5.81183	+	10.0664i	0.444442	+	0.769795i
$172$		0			0
$173$	1.65218	−	2.86166i	0.125613	−	0.217568i	−0.796359	−	0.604824i	$-0.793244\pi$
$173$	1.65218	−	2.86166i	0.125613	−	0.217568i	0.921972	+	0.387256i	$0.126577\pi$
$174$		0			0
$175$	8.05988	−	4.15019i	0.609270	−	0.313725i
$176$		0			0
$177$	−5.49722	+	9.52147i	−0.413197	+	0.715678i
$178$		0			0
$179$	−8.24984	−	14.2891i	−0.616622	−	1.06802i	−0.990098	−	0.140381i	$-0.955167\pi$
$179$	−8.24984	−	14.2891i	−0.616622	−	1.06802i	0.373476	−	0.927640i	$-0.378166\pi$
$180$		0			0
$181$	11.8233			0.878820			0.439410	−	0.898287i	$-0.355188\pi$
$181$	11.8233			0.878820			0.439410	+	0.898287i	$0.355188\pi$
$182$		0			0
$183$	4.30265			0.318061
$184$		0			0
$185$	−0.819737	−	1.41983i	−0.0602682	−	0.104388i
$186$		0			0
$187$	10.4398	−	18.0823i	0.763437	−	1.32231i
$188$		0			0
$189$	−0.571612	+	11.8779i	−0.0415786	+	0.863988i
$190$		0			0
$191$	6.00592	−	10.4026i	0.434573	−	0.752703i	−0.562687	−	0.826670i	$-0.690232\pi$
$191$	6.00592	−	10.4026i	0.434573	−	0.752703i	0.997261	+	0.0739666i	$0.0235658\pi$
$192$		0			0
$193$	−2.90758	−	5.03608i	−0.209292	−	0.362505i	0.742200	−	0.670179i	$-0.233783\pi$
$193$	−2.90758	−	5.03608i	−0.209292	−	0.362505i	−0.951492	+	0.307674i	$0.900449\pi$
$194$		0			0
$195$	−1.67237			−0.119761
$196$		0			0
$197$	10.5460			0.751371			0.375686	−	0.926747i	$-0.377407\pi$
$197$	10.5460			0.751371			0.375686	+	0.926747i	$0.377407\pi$
$198$		0			0
$199$	4.06241	+	7.03630i	0.287977	+	0.498790i	0.973327	−	0.229424i	$-0.0736841\pi$
$199$	4.06241	+	7.03630i	0.287977	+	0.498790i	−0.685350	+	0.728214i	$0.740351\pi$
$200$		0			0
$201$	−5.45297	+	9.44483i	−0.384623	+	0.666187i
$202$		0			0
$203$	−0.396912	+	8.24768i	−0.0278578	+	0.578874i
$204$		0			0
$205$	1.40680	−	2.43664i	0.0982549	−	0.170182i
$206$		0			0
$207$	−1.13681	−	1.96901i	−0.0790136	−	0.136856i
$208$		0			0
$209$	29.1057			2.01329
$210$		0			0
$211$	−20.3208			−1.39894			−0.699470	−	0.714662i	$-0.746581\pi$
$211$	−20.3208			−1.39894			−0.699470	+	0.714662i	$0.746581\pi$
$212$		0			0
$213$	−5.38223	−	9.32230i	−0.368785	−	0.638754i
$214$		0			0
$215$	3.66607	−	6.34982i	0.250024	−	0.433054i
$216$		0			0
$217$	−3.32590	+	1.71257i	−0.225777	+	0.116257i
$218$		0			0
$219$	−4.03487	+	6.98859i	−0.272651	+	0.472245i
$220$		0			0
$221$	−2.86850	−	4.96839i	−0.192956	−	0.334210i
$222$		0			0
$223$	16.9855			1.13743			0.568716	−	0.822534i	$-0.307440\pi$
$223$	16.9855			1.13743			0.568716	+	0.822534i	$0.307440\pi$
$224$		0			0
$225$	7.79052			0.519368
$226$		0			0
$227$	7.02668	+	12.1706i	0.466377	+	0.807789i	0.999263	−	0.0383983i	$-0.0122255\pi$
$227$	7.02668	+	12.1706i	0.466377	+	0.807789i	−0.532885	+	0.846188i	$0.678892\pi$
$228$		0			0
$229$	−0.443559	+	0.768267i	−0.0293112	+	0.0507685i	−0.880309	−	0.474401i	$-0.842665\pi$
$229$	−0.443559	+	0.768267i	−0.0293112	+	0.0507685i	0.850998	+	0.525169i	$0.175998\pi$
$230$		0			0
$231$	10.7963	+	6.94581i	0.710346	+	0.457001i
$232$		0			0
$233$	7.79778	−	13.5061i	0.510849	−	0.884817i	−0.489071	−	0.872244i	$-0.662664\pi$
$233$	7.79778	−	13.5061i	0.510849	−	0.884817i	0.999921	−	0.0125735i	$-0.00400239\pi$
$234$		0			0
$235$	−2.89395	−	5.01248i	−0.188781	−	0.326978i
$236$		0			0
$237$	5.38602			0.349860
$238$		0			0
$239$	−6.73697			−0.435778			−0.217889	−	0.975974i	$-0.569917\pi$
$239$	−6.73697			−0.435778			−0.217889	+	0.975974i	$0.569917\pi$
$240$		0			0
$241$	−11.5443	−	19.9954i	−0.743635	−	1.28801i	−0.950830	−	0.309714i	$-0.899767\pi$
$241$	−11.5443	−	19.9954i	−0.743635	−	1.28801i	0.207195	−	0.978300i	$-0.433567\pi$
$242$		0			0
$243$	−8.01615	+	13.8844i	−0.514236	+	0.890683i
$244$		0			0
$245$	5.10031	−	7.14764i	0.325847	−	0.456646i
$246$		0			0
$247$	3.99861	−	6.92580i	0.254426	−	0.440678i
$248$		0			0
$249$	−4.83666	−	8.37733i	−0.306511	−	0.530892i
$250$		0			0
$251$	−27.6053			−1.74243			−0.871215	−	0.490901i	$-0.836668\pi$
$251$	−27.6053			−1.74243			−0.871215	+	0.490901i	$0.836668\pi$
$252$		0			0
$253$	−5.69315			−0.357925
$254$		0			0
$255$	1.96047	+	3.39563i	0.122769	+	0.212643i
$256$		0			0
$257$	−5.09383	+	8.82277i	−0.317744	+	0.550349i	−0.980017	−	0.198914i	$-0.936259\pi$
$257$	−5.09383	+	8.82277i	−0.317744	+	0.550349i	0.662273	+	0.749263i	$0.269592\pi$
$258$		0			0
$259$	2.90810	+	1.87093i	0.180701	+	0.116254i
$260$		0			0
$261$	−3.54791	+	6.14515i	−0.219610	+	0.380375i
$262$		0			0
$263$	−6.84676	−	11.8589i	−0.422189	−	0.731253i	0.573964	−	0.818880i	$-0.305405\pi$
$263$	−6.84676	−	11.8589i	−0.422189	−	0.731253i	−0.996153	+	0.0876275i	$0.972071\pi$
$264$		0			0
$265$	10.7814			0.662297
$266$		0			0
$267$	1.50748			0.0922565
$268$		0			0
$269$	−11.1466	−	19.3065i	−0.679621	−	1.17714i	−0.975095	−	0.221787i	$-0.928811\pi$
$269$	−11.1466	−	19.3065i	−0.679621	−	1.17714i	0.295474	−	0.955351i	$-0.404522\pi$
$270$		0			0
$271$	2.80208	−	4.85334i	0.170214	−	0.294819i	−0.768281	−	0.640113i	$-0.778887\pi$
$271$	2.80208	−	4.85334i	0.170214	−	0.294819i	0.938495	+	0.345294i	$0.112221\pi$
$272$		0			0
$273$	3.13600	−	1.61479i	0.189800	−	0.0977315i
$274$		0			0
$275$	9.75376	−	16.8940i	0.588174	−	1.01875i
$276$		0			0
$277$	10.3287	+	17.8899i	0.620592	+	1.07490i	0.989376	+	0.145382i	$0.0464411\pi$
$277$	10.3287	+	17.8899i	0.620592	+	1.07490i	−0.368783	+	0.929515i	$0.620226\pi$
$278$		0			0
$279$	−3.21475			−0.192462
$280$		0			0
$281$	28.5499			1.70314			0.851572	−	0.524238i	$-0.175650\pi$
$281$	28.5499			1.70314			0.851572	+	0.524238i	$0.175650\pi$
$282$		0			0
$283$	4.44954	+	7.70683i	0.264498	+	0.458124i	0.967432	−	0.253131i	$-0.0814605\pi$
$283$	4.44954	+	7.70683i	0.264498	+	0.458124i	−0.702934	+	0.711255i	$0.748127\pi$
$284$		0			0
$285$	−2.73284	+	4.73342i	−0.161879	+	0.280383i
$286$		0			0
$287$	−0.285256	+	5.92752i	−0.0168382	+	0.349890i
$288$		0			0
$289$	1.77468	−	3.07384i	0.104393	−	0.180814i
$290$		0			0
$291$	2.95263	+	5.11411i	0.173086	+	0.299794i
$292$		0			0
$293$	7.85210			0.458725			0.229362	−	0.973341i	$-0.426336\pi$
$293$	7.85210			0.458725			0.229362	+	0.973341i	$0.426336\pi$
$294$		0			0
$295$	16.1817			0.942136
$296$		0			0
$297$	12.7942	+	22.1603i	0.742397	+	1.28587i
$298$		0			0
$299$	−0.782138	+	1.35470i	−0.0452322	+	0.0783445i
$300$		0			0
$301$	−0.743371	+	15.4470i	−0.0428472	+	0.890348i
$302$		0			0
$303$	5.40668	−	9.36464i	0.310606	−	0.537985i
$304$		0			0
$305$	−3.16634	−	5.48425i	−0.181304	−	0.314027i
$306$		0			0
$307$	11.7088			0.668258			0.334129	−	0.942527i	$-0.391558\pi$
$307$	11.7088			0.668258			0.334129	+	0.942527i	$0.391558\pi$
$308$		0			0
$309$	6.51214			0.370463
$310$		0			0
$311$	−15.7746	−	27.3224i	−0.894497	−	1.54931i	−0.834427	−	0.551119i	$-0.814201\pi$
$311$	−15.7746	−	27.3224i	−0.894497	−	1.54931i	−0.0600700	−	0.998194i	$-0.519132\pi$
$312$		0			0
$313$	7.24248	−	12.5443i	0.409369	−	0.709048i	−0.585450	−	0.810708i	$-0.699082\pi$
$313$	7.24248	−	12.5443i	0.409369	−	0.709048i	0.994819	+	0.101661i	$0.0324156\pi$
$314$		0			0
$315$	6.70859	−	3.45438i	0.377986	−	0.194632i
$316$		0			0
$317$	10.1286	−	17.5432i	0.568877	−	0.985324i	−0.427800	−	0.903873i	$-0.640711\pi$
$317$	10.1286	−	17.5432i	0.568877	−	0.985324i	0.996677	−	0.0814508i	$-0.0259554\pi$
$318$		0			0
$319$	8.88399	+	15.3875i	0.497408	+	0.861536i
$320$		0			0
$321$	4.59840			0.256658
$322$		0			0
$323$	−18.7498			−1.04327
$324$		0			0
$325$	−2.67999	−	4.64188i	−0.148659	−	0.257485i
$326$		0			0
$327$	1.90565	−	3.30068i	0.105383	−	0.182528i
$328$		0			0
$329$	10.2666	+	6.60501i	0.566016	+	0.364146i
$330$		0			0
$331$	2.49700	−	4.32493i	0.137247	−	0.237719i	−0.789206	−	0.614128i	$-0.789508\pi$
$331$	2.49700	−	4.32493i	0.137247	−	0.237719i	0.926454	+	0.376409i	$0.122841\pi$
$332$		0			0
$333$	1.48579	+	2.57346i	0.0814206	+	0.141025i
$334$		0			0
$335$	16.0515			0.876985
$336$		0			0
$337$	−13.8245			−0.753070			−0.376535	−	0.926402i	$-0.622885\pi$
$337$	−13.8245			−0.753070			−0.376535	+	0.926402i	$0.622885\pi$
$338$		0			0
$339$	0.886731	+	1.53586i	0.0481606	+	0.0834167i
$340$		0			0
$341$	−4.02488	+	6.97130i	−0.217959	+	0.377517i
$342$		0			0
$343$	−2.66249	+	18.3279i	−0.143761	+	0.989612i
$344$		0			0
$345$	0.534550	−	0.925868i	0.0287792	−	0.0498470i
$346$		0			0
$347$	7.68590	+	13.3124i	0.412601	+	0.714645i	0.995173	−	0.0981334i	$-0.0312872\pi$
$347$	7.68590	+	13.3124i	0.412601	+	0.714645i	−0.582573	+	0.812779i	$0.697954\pi$
$348$		0			0
$349$	33.3719			1.78636			0.893178	−	0.449703i	$-0.148470\pi$
$349$	33.3719			1.78636			0.893178	+	0.449703i	$0.148470\pi$
$350$		0			0
$351$	7.03081			0.375277
$352$		0			0
$353$	−2.15824	−	3.73818i	−0.114871	−	0.198963i	0.802857	−	0.596172i	$-0.203312\pi$
$353$	−2.15824	−	3.73818i	−0.114871	−	0.198963i	−0.917728	+	0.397209i	$0.869979\pi$
$354$		0			0
$355$	−7.92162	+	13.7206i	−0.420436	+	0.728216i
$356$		0			0
$357$	−6.95496	−	4.47447i	−0.368096	−	0.236814i
$358$		0			0
$359$	6.78257	−	11.7478i	0.357970	−	0.620023i	−0.629651	−	0.776878i	$-0.716802\pi$
$359$	6.78257	−	11.7478i	0.357970	−	0.620023i	0.987622	+	0.156855i	$0.0501356\pi$
$360$		0			0
$361$	−3.56838	−	6.18062i	−0.187809	−	0.325296i
$362$		0			0
$363$	18.2491			0.957827
$364$		0			0
$365$	11.8771			0.621676
$366$		0			0
$367$	6.53018	+	11.3106i	0.340872	+	0.590408i	0.984595	−	0.174851i	$-0.0559443\pi$
$367$	6.53018	+	11.3106i	0.340872	+	0.590408i	−0.643723	+	0.765259i	$0.722611\pi$
$368$		0			0
$369$	−2.54984	+	4.41646i	−0.132739	+	0.229911i
$370$		0			0
$371$	−20.2172	+	10.4102i	−1.04962	+	0.540471i
$372$		0			0
$373$	−1.52173	+	2.63572i	−0.0787922	+	0.136472i	−0.902729	−	0.430209i	$-0.858440\pi$
$373$	−1.52173	+	2.63572i	−0.0787922	+	0.136472i	0.823937	+	0.566682i	$0.191773\pi$
$374$		0			0
$375$	4.50438	+	7.80181i	0.232605	+	0.402884i
$376$		0			0
$377$	4.88201			0.251436
$378$		0			0
$379$	−17.4799			−0.897882			−0.448941	−	0.893561i	$-0.648199\pi$
$379$	−17.4799			−0.897882			−0.448941	+	0.893561i	$0.648199\pi$
$380$		0			0
$381$	3.72826	+	6.45754i	0.191005	+	0.330830i
$382$		0			0
$383$	−12.0764	+	20.9169i	−0.617074	+	1.06880i	0.372943	+	0.927854i	$0.378349\pi$
$383$	−12.0764	+	20.9169i	−0.617074	+	1.06880i	−0.990017	+	0.140949i	$0.954985\pi$
$384$		0			0
$385$	0.908232	−	18.8727i	0.0462878	−	0.961843i
$386$		0			0
$387$	−6.64482	+	11.5092i	−0.337775	+	0.585044i
$388$		0			0
$389$	4.28544	+	7.42261i	0.217281	+	0.376341i	0.953976	−	0.299884i	$-0.0969480\pi$
$389$	4.28544	+	7.42261i	0.217281	+	0.376341i	−0.736695	+	0.676225i	$0.763615\pi$
$390$		0			0
$391$	3.66751			0.185474
$392$		0			0
$393$	−15.9959			−0.806884
$394$		0			0
$395$	−3.96360	−	6.86515i	−0.199430	−	0.345423i
$396$		0			0
$397$	−14.5100	+	25.1321i	−0.728238	+	1.26135i	0.229389	+	0.973335i	$0.426327\pi$
$397$	−14.5100	+	25.1321i	−0.728238	+	1.26135i	−0.957627	+	0.288011i	$0.907006\pi$
$398$		0			0
$399$	0.554139	−	11.5148i	0.0277416	−	0.576461i
$400$		0			0
$401$	−7.70681	+	13.3486i	−0.384860	+	0.666596i	−0.991750	−	0.128189i	$-0.959083\pi$
$401$	−7.70681	+	13.3486i	−0.384860	+	0.666596i	0.606890	+	0.794786i	$0.292417\pi$
$402$		0			0
$403$	1.10589	+	1.91547i	0.0550885	+	0.0954161i
$404$		0			0
$405$	3.75086			0.186382
$406$		0			0
$407$	7.44085			0.368829
$408$		0			0
$409$	−15.0471	−	26.0623i	−0.744031	−	1.28870i	−0.950646	−	0.310277i	$-0.899578\pi$
$409$	−15.0471	−	26.0623i	−0.744031	−	1.28870i	0.206615	−	0.978422i	$-0.433755\pi$
$410$		0			0
$411$	3.16291	−	5.47832i	0.156015	−	0.270226i
$412$		0			0
$413$	−30.3438	+	15.6246i	−1.49312	+	0.768836i
$414$		0			0
$415$	−7.11863	+	12.3298i	−0.349440	+	0.605248i
$416$		0			0
$417$	−3.15628	−	5.46684i	−0.154564	−	0.267712i
$418$		0			0
$419$	−10.0662			−0.491765			−0.245883	−	0.969300i	$-0.579078\pi$
$419$	−10.0662			−0.491765			−0.245883	+	0.969300i	$0.579078\pi$
$420$		0			0
$421$	−7.32442			−0.356970			−0.178485	−	0.983943i	$-0.557120\pi$
$421$	−7.32442			−0.356970			−0.178485	+	0.983943i	$0.557120\pi$
$422$		0			0
$423$	5.24534	+	9.08520i	0.255037	+	0.441737i
$424$		0			0
$425$	−6.28334	+	10.8831i	−0.304787	+	0.527906i
$426$		0			0
$427$	11.2329	+	7.22668i	0.543598	+	0.349724i
$428$		0			0
$429$	3.79507	−	6.57326i	0.183228	−	0.317360i
$430$		0			0
$431$	−18.0899	−	31.3326i	−0.871360	−	1.50924i	−0.860591	−	0.509297i	$-0.829905\pi$
$431$	−18.0899	−	31.3326i	−0.871360	−	1.50924i	−0.0107692	−	0.999942i	$-0.503428\pi$
$432$		0			0
$433$	10.8417			0.521017			0.260508	−	0.965472i	$-0.416110\pi$
$433$	10.8417			0.521017			0.260508	+	0.965472i	$0.416110\pi$
$434$		0			0
$435$	−3.33660			−0.159977
$436$		0			0
$437$	2.55621	+	4.42748i	0.122280	+	0.211795i
$438$		0			0
$439$	−0.875306	+	1.51607i	−0.0417761	+	0.0723583i	−0.886157	−	0.463384i	$-0.846635\pi$
$439$	−0.875306	+	1.51607i	−0.0417761	+	0.0723583i	0.844381	+	0.535743i	$0.179968\pi$
$440$		0			0
$441$	−9.24441	+	12.9552i	−0.440210	+	0.616915i
$442$		0			0
$443$	16.8149	−	29.1242i	0.798898	−	1.38373i	−0.121437	−	0.992599i	$-0.538750\pi$
$443$	16.8149	−	29.1242i	0.798898	−	1.38373i	0.920335	−	0.391132i	$-0.127916\pi$
$444$		0			0
$445$	−1.10936	−	1.92147i	−0.0525889	−	0.0910866i
$446$		0			0
$447$	−7.22452			−0.341708
$448$		0			0
$449$	17.9122			0.845331			0.422666	−	0.906286i	$-0.361094\pi$
$449$	17.9122			0.845331			0.422666	+	0.906286i	$0.361094\pi$
$450$		0			0
$451$	6.38483	+	11.0588i	0.300650	+	0.520741i
$452$		0			0
$453$	−4.47363	+	7.74855i	−0.210189	+	0.364059i
$454$		0			0
$455$	−4.36605	−	2.80889i	−0.204683	−	0.131683i
$456$		0			0
$457$	13.8300	−	23.9543i	0.646940	−	1.12053i	−0.336909	−	0.941537i	$-0.609382\pi$
$457$	13.8300	−	23.9543i	0.646940	−	1.12053i	0.983850	−	0.178997i	$-0.0572851\pi$
$458$		0			0
$459$	−8.24201	−	14.2756i	−0.384704	−	0.666327i
$460$		0			0
$461$	22.2048			1.03418			0.517091	−	0.855930i	$-0.327015\pi$
$461$	22.2048			1.03418			0.517091	+	0.855930i	$0.327015\pi$
$462$		0			0
$463$	40.9791			1.90446			0.952230	−	0.305382i	$-0.0987840\pi$
$463$	40.9791			1.90446			0.952230	+	0.305382i	$0.0987840\pi$
$464$		0			0
$465$	−0.755820	−	1.30912i	−0.0350503	−	0.0607089i
$466$		0			0
$467$	−3.90099	+	6.75672i	−0.180516	+	0.312664i	−0.942057	−	0.335454i	$-0.891110\pi$
$467$	−3.90099	+	6.75672i	−0.180516	+	0.312664i	0.761540	+	0.648118i	$0.224444\pi$
$468$		0			0
$469$	−30.0995	+	15.4988i	−1.38987	+	0.715669i
$470$		0			0
$471$	−4.31399	+	7.47205i	−0.198778	+	0.344294i
$472$		0			0
$473$	16.6387	+	28.8191i	0.765048	+	1.32510i
$474$		0			0
$475$	−17.5176			−0.803764
$476$		0			0
$477$	−19.5415			−0.894743
$478$		0			0
$479$	8.94757	+	15.4977i	0.408825	+	0.708106i	0.994758	−	0.102253i	$-0.0326053\pi$
$479$	8.94757	+	15.4977i	0.408825	+	0.708106i	−0.585933	+	0.810359i	$0.699272\pi$
$480$		0			0
$481$	1.02224	−	1.77057i	0.0466102	−	0.0807312i
$482$		0			0
$483$	−0.108391	+	2.25232i	−0.00493195	+	0.102484i
$484$		0			0
$485$	4.34571	−	7.52699i	0.197329	−	0.341783i
$486$		0			0
$487$	16.7868	+	29.0755i	0.760681	+	1.31754i	0.942500	+	0.334206i	$0.108468\pi$
$487$	16.7868	+	29.0755i	0.760681	+	1.31754i	−0.181820	+	0.983332i	$0.558199\pi$
$488$		0			0
$489$	4.03622			0.182524
$490$		0			0
$491$	−28.5841			−1.28998			−0.644992	−	0.764190i	$-0.723139\pi$
$491$	−28.5841			−1.28998			−0.644992	+	0.764190i	$0.723139\pi$
$492$		0			0
$493$	−5.72304	−	9.91259i	−0.257753	−	0.446441i
$494$		0			0
$495$	8.11848	−	14.0616i	0.364898	−	0.632023i
$496$		0			0
$497$	1.60627	−	33.3777i	0.0720510	−	1.49719i
$498$		0			0
$499$	−21.1948	+	36.7105i	−0.948809	+	1.64339i	−0.200871	+	0.979618i	$0.564377\pi$
$499$	−21.1948	+	36.7105i	−0.948809	+	1.64339i	−0.747938	+	0.663769i	$0.768956\pi$
$500$		0			0
$501$	−8.58106	−	14.8628i	−0.383373	−	0.664022i
$502$		0			0
$503$	−10.2991			−0.459216			−0.229608	−	0.973283i	$-0.573744\pi$
$503$	−10.2991			−0.459216			−0.229608	+	0.973283i	$0.573744\pi$
$504$		0			0
$505$	−15.9152			−0.708217
$506$		0			0
$507$	4.49708	+	7.78918i	0.199722	+	0.345930i
$508$		0			0
$509$	1.87806	−	3.25289i	0.0832434	−	0.144182i	−0.821398	−	0.570355i	$-0.806805\pi$
$509$	1.87806	−	3.25289i	0.0832434	−	0.144182i	0.904641	+	0.426174i	$0.140139\pi$
$510$		0			0
$511$	−22.2718	+	11.4682i	−0.985246	+	0.507322i
$512$		0			0
$513$	11.4891	−	19.8998i	0.507258	−	0.878597i
$514$		0			0
$515$	−4.79231	−	8.30053i	−0.211175	−	0.365765i
$516$		0			0
$517$	26.2688			1.15530
$518$		0			0
$519$	−2.81625			−0.123619
$520$		0			0
$521$	−9.69222	−	16.7874i	−0.424624	−	0.735470i	0.571761	−	0.820420i	$-0.306260\pi$
$521$	−9.69222	−	16.7874i	−0.424624	−	0.735470i	−0.996385	+	0.0849500i	$0.972927\pi$
$522$		0			0
$523$	2.20687	−	3.82242i	0.0964998	−	0.167143i	−0.813734	−	0.581238i	$-0.802569\pi$
$523$	2.20687	−	3.82242i	0.0964998	−	0.167143i	0.910234	+	0.414095i	$0.135902\pi$
$524$		0			0
$525$	−6.49790	−	4.18042i	−0.283591	−	0.182448i
$526$		0			0
$527$	2.59281	−	4.49089i	0.112945	−	0.195626i
$528$		0			0
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	−29.3296			−1.27280
$532$		0			0
$533$	3.50865			0.151976
$534$		0			0
$535$	−3.38399	−	5.86123i	−0.146302	−	0.253403i
$536$		0			0
$537$	−7.03119	+	12.1784i	−0.303418	+	0.525536i
$538$		0			0
$539$	16.5198	+	36.2668i	0.711559	+	1.56212i
$540$		0			0
$541$	14.2536	−	24.6879i	0.612809	−	1.06142i	−0.377956	−	0.925824i	$-0.623373\pi$
$541$	14.2536	−	24.6879i	0.612809	−	1.06142i	0.990765	−	0.135592i	$-0.0432937\pi$
$542$		0			0
$543$	−5.03840	−	8.72676i	−0.216218	−	0.374501i
$544$		0			0
$545$	−5.60951			−0.240285
$546$		0			0
$547$	5.98857			0.256053			0.128026	−	0.991771i	$-0.459136\pi$
$547$	5.98857			0.256053			0.128026	+	0.991771i	$0.459136\pi$
$548$		0			0
$549$	5.73904	+	9.94030i	0.244936	+	0.424242i
$550$		0			0
$551$	7.97776	−	13.8179i	0.339864	−	0.588662i
$552$		0			0
$553$	14.0613	+	9.04631i	0.597946	+	0.384688i
$554$		0			0
$555$	−0.698647	+	1.21009i	−0.0296559	+	0.0513656i
$556$		0			0
$557$	10.4933	+	18.1750i	0.444617	+	0.770100i	0.998025	−	0.0628103i	$-0.0200063\pi$
$557$	10.4933	+	18.1750i	0.444617	+	0.770100i	−0.553408	+	0.832910i	$0.686673\pi$
$558$		0			0
$559$	9.14345			0.386727
$560$		0			0
$561$	−17.7954			−0.751322
$562$		0			0
$563$	−21.0767	−	36.5060i	−0.888279	−	1.53854i	−0.841909	−	0.539620i	$-0.818568\pi$
$563$	−21.0767	−	36.5060i	−0.888279	−	1.53854i	−0.0463700	−	0.998924i	$-0.514765\pi$
$564$		0			0
$565$	1.30510	−	2.26050i	0.0549059	−	0.0950999i
$566$		0			0
$567$	−7.03356	+	3.62172i	−0.295382	+	0.152098i
$568$		0			0
$569$	13.6008	−	23.5573i	0.570176	−	0.987574i	−0.426371	−	0.904548i	$-0.640208\pi$
$569$	13.6008	−	23.5573i	0.570176	−	0.987574i	0.996547	−	0.0830258i	$-0.0264584\pi$
$570$		0			0
$571$	−19.7911	−	34.2793i	−0.828233	−	1.43454i	−0.899423	−	0.437079i	$-0.856013\pi$
$571$	−19.7911	−	34.2793i	−0.828233	−	1.43454i	0.0711896	−	0.997463i	$-0.477320\pi$
$572$		0			0
$573$	−10.2375			−0.427677
$574$		0			0
$575$	3.42649			0.142894
$576$		0			0
$577$	−10.8725	−	18.8317i	−0.452629	−	0.783976i	0.545920	−	0.837837i	$-0.316180\pi$
$577$	−10.8725	−	18.8317i	−0.452629	−	0.783976i	−0.998548	+	0.0538617i	$0.982847\pi$
$578$		0			0
$579$	−2.47808	+	4.29216i	−0.102985	+	0.178376i
$580$		0			0
$581$	1.44345	−	29.9943i	0.0598843	−	1.24437i
$582$		0			0
$583$	−24.4660	+	42.3764i	−1.01328	+	1.75505i
$584$		0			0
$585$	−2.23067	−	3.86363i	−0.0922269	−	0.159742i
$586$		0			0
$587$	−11.8644			−0.489695			−0.244848	−	0.969562i	$-0.578738\pi$
$587$	−11.8644			−0.489695			−0.244848	+	0.969562i	$0.578738\pi$
$588$		0			0
$589$	7.22863			0.297851
$590$		0			0
$591$	−4.49409	−	7.78398i	−0.184862	−	0.320190i
$592$		0			0
$593$	12.2299	−	21.1828i	0.502222	−	0.869875i	−0.497774	−	0.867307i	$-0.665849\pi$
$593$	12.2299	−	21.1828i	0.502222	−	0.869875i	0.999997	−	0.00256809i	$-0.000817451\pi$
$594$		0			0
$595$	−0.585080	+	12.1577i	−0.0239859	+	0.498419i
$596$		0			0
$597$	3.46232	−	5.99692i	0.141703	−	0.245437i
$598$		0			0
$599$	−19.9660	−	34.5822i	−0.815789	−	1.41299i	−0.908760	−	0.417320i	$-0.862970\pi$
$599$	−19.9660	−	34.5822i	−0.815789	−	1.41299i	0.0929705	−	0.995669i	$-0.470364\pi$
$600$		0			0
$601$	3.52664			0.143855			0.0719273	−	0.997410i	$-0.477085\pi$
$601$	3.52664			0.143855			0.0719273	+	0.997410i	$0.477085\pi$
$602$		0			0
$603$	−29.0936			−1.18478
$604$		0			0
$605$	−13.4296	−	23.2607i	−0.545989	−	0.945681i
$606$		0			0
$607$	6.12530	−	10.6093i	0.248618	−	0.430619i	−0.714524	−	0.699610i	$-0.753357\pi$
$607$	6.12530	−	10.6093i	0.248618	−	0.430619i	0.963143	+	0.268991i	$0.0866902\pi$
$608$		0			0
$609$	6.25674	−	3.22172i	0.253536	−	0.130551i
$610$		0			0
$611$	3.60886	−	6.25074i	0.145999	−	0.252878i
$612$		0			0
$613$	3.99849	+	6.92559i	0.161498	+	0.279722i	0.935406	−	0.353576i	$-0.115034\pi$
$613$	3.99849	+	6.92559i	0.161498	+	0.279722i	−0.773908	+	0.633298i	$0.781701\pi$
$614$		0			0
$615$	−2.39797			−0.0966957
$616$		0			0
$617$	2.29366			0.0923394			0.0461697	−	0.998934i	$-0.485299\pi$
$617$	2.29366			0.0923394			0.0461697	+	0.998934i	$0.485299\pi$
$618$		0			0
$619$	22.1341	+	38.3374i	0.889644	+	1.54091i	0.840297	+	0.542127i	$0.182381\pi$
$619$	22.1341	+	38.3374i	0.889644	+	1.54091i	0.0493471	+	0.998782i	$0.484286\pi$
$620$		0			0
$621$	−2.24730	+	3.89245i	−0.0901812	+	0.156198i
$622$		0			0
$623$	3.93558	+	2.53195i	0.157676	+	0.101441i
$624$		0			0
$625$	−1.93664	+	3.35436i	−0.0774656	+	0.134174i
$626$		0			0
$627$	−12.4032	−	21.4829i	−0.495334	−	0.857944i
$628$		0			0
$629$	−4.79337			−0.191124
$630$		0			0
$631$	−25.6202			−1.01993			−0.509963	−	0.860196i	$-0.670341\pi$
$631$	−25.6202			−1.01993			−0.509963	+	0.860196i	$0.670341\pi$
$632$		0			0
$633$	8.65952	+	14.9987i	0.344185	+	0.596146i
$634$		0			0
$635$	5.48729	−	9.50426i	0.217756	−	0.377165i
$636$		0			0
$637$	10.8993	+	1.05148i	0.431847	+	0.0416610i
$638$		0			0
$639$	14.3581	−	24.8689i	0.567996	−	0.983799i
$640$		0			0
$641$	−13.3242	−	23.0782i	−0.526275	−	0.911536i	−0.999531	−	0.0306107i	$-0.990255\pi$
$641$	−13.3242	−	23.0782i	−0.526275	−	0.911536i	0.473256	−	0.880925i	$-0.343079\pi$
$642$		0			0
$643$	−26.0623			−1.02780			−0.513899	−	0.857851i	$-0.671799\pi$
$643$	−26.0623			−1.02780			−0.513899	+	0.857851i	$0.671799\pi$
$644$		0			0
$645$	−6.24906			−0.246056
$646$		0			0
$647$	13.1707	+	22.8124i	0.517795	+	0.896848i	0.999786	+	0.0206717i	$0.00658049\pi$
$647$	13.1707	+	22.8124i	0.517795	+	0.896848i	−0.481991	+	0.876176i	$0.660086\pi$
$648$		0			0
$649$	−36.7209	+	63.6024i	−1.44142	+	2.49661i
$650$		0			0
$651$	2.68135	+	1.72505i	0.105090	+	0.0676098i
$652$		0			0
$653$	18.9371	−	32.8001i	0.741067	−	1.28357i	−0.210943	−	0.977498i	$-0.567653\pi$
$653$	18.9371	−	32.8001i	0.741067	−	1.28357i	0.952010	−	0.306068i	$-0.0990133\pi$
$654$		0			0
$655$	11.7714	+	20.3887i	0.459947	+	0.796652i
$656$		0			0
$657$	−21.5275			−0.839866
$658$		0			0
$659$	−26.3762			−1.02747			−0.513735	−	0.857949i	$-0.671738\pi$
$659$	−26.3762			−1.02747			−0.513735	+	0.857949i	$0.671738\pi$
$660$		0			0
$661$	−3.54030	−	6.13198i	−0.137702	−	0.238506i	0.788925	−	0.614490i	$-0.210638\pi$
$661$	−3.54030	−	6.13198i	−0.137702	−	0.238506i	−0.926626	+	0.375984i	$0.877305\pi$
$662$		0			0
$663$	−2.44477	+	4.23447i	−0.0949471	+	0.164453i
$664$		0			0
$665$	−15.0848	+	7.76747i	−0.584964	+	0.301209i
$666$		0			0
$667$	−1.56047	+	2.70281i	−0.0604216	+	0.104653i
$668$		0			0
$669$	−7.23822	−	12.5370i	−0.279846	−	0.484707i
$670$		0			0
$671$	28.7412			1.10954
$672$		0			0
$673$	48.1412			1.85571			0.927854	−	0.372945i	$-0.121652\pi$
$673$	48.1412			1.85571			0.927854	+	0.372945i	$0.121652\pi$
$674$		0			0
$675$	−7.70036	−	13.3374i	−0.296387	−	0.513358i
$676$		0			0
$677$	11.6415	−	20.1637i	0.447420	−	0.774955i	−0.550797	−	0.834639i	$-0.685676\pi$
$677$	11.6415	−	20.1637i	0.447420	−	0.774955i	0.998217	+	0.0596847i	$0.0190095\pi$
$678$		0			0
$679$	−0.881181	+	18.3106i	−0.0338166	+	0.702697i
$680$		0			0
$681$	5.98872	−	10.3728i	0.229488	−	0.397485i
$682$		0			0
$683$	11.5043	+	19.9261i	0.440201	+	0.762451i	0.997704	−	0.0677240i	$-0.0215737\pi$
$683$	11.5043	+	19.9261i	0.440201	+	0.762451i	−0.557503	+	0.830175i	$0.688240\pi$
$684$		0			0
$685$	−9.31040			−0.355732
$686$		0			0
$687$	0.756075			0.0288461
$688$		0			0
$689$	6.72240	+	11.6435i	0.256103	+	0.443584i
$690$		0			0
$691$	−7.01994	+	12.1589i	−0.267051	+	0.462546i	−0.968099	−	0.250568i	$-0.919383\pi$
$691$	−7.01994	+	12.1589i	−0.267051	+	0.462546i	0.701048	+	0.713114i	$0.252716\pi$
$692$		0			0
$693$	−1.64619	+	34.2071i	−0.0625334	+	1.29942i
$694$		0			0
$695$	−4.64544	+	8.04615i	−0.176212	+	0.305208i
$696$		0			0
$697$	−4.11308	−	7.12407i	−0.155794	−	0.269843i
$698$		0			0
$699$	−13.2918			−0.502743
$700$		0			0
$701$	−47.3589			−1.78872			−0.894360	−	0.447348i	$-0.852369\pi$
$701$	−47.3589			−1.78872			−0.894360	+	0.447348i	$0.852369\pi$
$702$		0			0
$703$	−3.34091	−	5.78663i	−0.126005	−	0.218247i
$704$		0			0
$705$	−2.46647	+	4.27204i	−0.0928925	+	0.160895i
$706$		0			0
$707$	29.8440	−	15.3672i	1.12240	−	0.577945i
$708$		0			0
$709$	0.892303	−	1.54551i	0.0335111	−	0.0580430i	−0.848783	−	0.528741i	$-0.822664\pi$
$709$	0.892303	−	1.54551i	0.0335111	−	0.0580430i	0.882295	+	0.470698i	$0.155998\pi$
$710$		0			0
$711$	7.18409	+	12.4432i	0.269424	+	0.466657i
$712$		0			0
$713$	−1.41394			−0.0529524
$714$		0			0
$715$	−11.1712			−0.417781
$716$		0			0
$717$	2.87090	+	4.97254i	0.107216	+	0.185703i
$718$		0			0
$719$	−10.1388	+	17.5609i	−0.378113	+	0.654910i	−0.990788	−	0.135425i	$-0.956760\pi$
$719$	−10.1388	+	17.5609i	−0.378113	+	0.654910i	0.612675	+	0.790335i	$0.290093\pi$
$720$		0			0
$721$	17.0012	+	10.9377i	0.633159	+	0.407342i
$722$		0			0
$723$	−9.83902	+	17.0417i	−0.365917	+	0.633787i
$724$		0			0
$725$	−5.34693	−	9.26116i	−0.198580	−	0.343951i
$726$		0			0
$727$	−21.6753			−0.803891			−0.401945	−	0.915664i	$-0.631666\pi$
$727$	−21.6753			−0.803891			−0.401945	+	0.915664i	$0.631666\pi$
$728$		0			0
$729$	4.69353			0.173835
$730$		0			0
$731$	−10.7186	−	18.5651i	−0.396441	−	0.686656i
$732$		0			0
$733$	−3.08010	+	5.33489i	−0.113766	+	0.197049i	−0.917286	−	0.398229i	$-0.869625\pi$
$733$	−3.08010	+	5.33489i	−0.113766	+	0.197049i	0.803520	+	0.595278i	$0.202958\pi$
$734$		0			0
$735$	−7.44912	−	0.718628i	−0.274765	−	0.0265070i
$736$		0			0
$737$	−36.4253	+	63.0904i	−1.34174	+	2.32396i
$738$		0			0
$739$	−10.2142	−	17.6915i	−0.375734	−	0.650791i	0.614702	−	0.788759i	$-0.289276\pi$
$739$	−10.2142	−	17.6915i	−0.375734	−	0.650791i	−0.990437	+	0.137968i	$0.955943\pi$
$740$		0			0
$741$	−6.81590			−0.250388
$742$		0			0
$743$	−25.8822			−0.949527			−0.474763	−	0.880114i	$-0.657466\pi$
$743$	−25.8822			−0.949527			−0.474763	+	0.880114i	$0.657466\pi$
$744$		0			0
$745$	5.31656	+	9.20854i	0.194784	+	0.337375i
$746$		0			0
$747$	12.9026	−	22.3480i	0.472083	−	0.817672i
$748$		0			0
$749$	12.0050	+	7.72343i	0.438655	+	0.282208i
$750$		0			0
$751$	−15.4222	+	26.7121i	−0.562765	+	0.974737i	0.434489	+	0.900677i	$0.356929\pi$
$751$	−15.4222	+	26.7121i	−0.562765	+	0.974737i	−0.997254	+	0.0740600i	$0.976404\pi$
$752$		0			0
$753$	11.7638	+	20.3754i	0.428695	+	0.742522i
$754$		0			0
$755$	13.1687			0.479256
$756$		0			0
$757$	35.3275			1.28400			0.641999	−	0.766705i	$-0.278105\pi$
$757$	35.3275			1.28400			0.641999	+	0.766705i	$0.278105\pi$
$758$		0			0
$759$	2.42609	+	4.20211i	0.0880614	+	0.152527i
$760$		0			0
$761$	−7.23633	+	12.5337i	−0.262317	+	0.454346i	−0.966857	−	0.255318i	$-0.917820\pi$
$761$	−7.23633	+	12.5337i	−0.262317	+	0.454346i	0.704540	+	0.709664i	$0.251153\pi$
$762$		0			0
$763$	10.5189	−	5.41637i	0.380809	−	0.196086i
$764$		0			0
$765$	−5.22990	+	9.05845i	−0.189087	+	0.327509i
$766$		0			0
$767$	10.0896	+	17.4757i	0.364314	+	0.631010i
$768$		0			0
$769$	−51.7723			−1.86696			−0.933478	−	0.358634i	$-0.883243\pi$
$769$	−51.7723			−1.86696			−0.933478	+	0.358634i	$0.883243\pi$
$770$		0			0
$771$	8.68276			0.312702
$772$		0			0
$773$	−4.60500	−	7.97609i	−0.165630	−	0.286880i	0.771249	−	0.636534i	$-0.219633\pi$
$773$	−4.60500	−	7.97609i	−0.165630	−	0.286880i	−0.936879	+	0.349654i	$0.886299\pi$
$774$		0			0
$775$	2.42242	−	4.19576i	0.0870159	−	0.150716i
$776$		0			0
$777$	0.141665	−	2.94374i	0.00508220	−	0.105606i
$778$		0			0
$779$	5.73353	−	9.93077i	0.205425	−	0.355807i
$780$		0			0
$781$	−35.9527	−	62.2720i	−1.28649	−	2.22827i
$782$		0			0
$783$	14.0274			0.501298
$784$		0			0
$785$	12.6987			0.453238
$786$		0			0
$787$	−5.37752	−	9.31413i	−0.191688	−	0.332013i	0.754122	−	0.656734i	$-0.228063\pi$
$787$	−5.37752	−	9.31413i	−0.191688	−	0.332013i	−0.945810	+	0.324721i	$0.894729\pi$
$788$		0			0
$789$	−5.83537	+	10.1072i	−0.207745	+	0.359824i
$790$		0			0
$791$	−0.264635	+	5.49902i	−0.00940935	+	0.195523i
$792$		0			0
$793$	3.94853	−	6.83906i	0.140217	−	0.242862i
$794$		0			0
$795$	−4.59440	−	7.95774i	−0.162947	−	0.282232i
$796$		0			0
$797$	26.1940			0.927841			0.463920	−	0.885877i	$-0.346442\pi$
$797$	26.1940			0.927841			0.463920	+	0.885877i	$0.346442\pi$
$798$		0			0
$799$	−16.9223			−0.598666
$800$		0			0
$801$	2.01074	+	3.48270i	0.0710460	+	0.123055i
$802$		0			0
$803$	−26.9525	+	46.6830i	−0.951132	+	1.64741i
$804$		0			0
$805$	2.95063	−	1.51933i	0.103996	−	0.0535495i
$806$		0			0
$807$	−9.50006	+	16.4546i	−0.334418	+	0.579229i
$808$		0			0
$809$	8.16336	+	14.1394i	0.287009	+	0.497114i	0.973094	−	0.230407i	$-0.0740058\pi$
$809$	8.16336	+	14.1394i	0.287009	+	0.497114i	−0.686086	+	0.727521i	$0.740672\pi$
$810$		0			0
$811$	−2.83871			−0.0996805			−0.0498403	−	0.998757i	$-0.515871\pi$
$811$	−2.83871			−0.0996805			−0.0498403	+	0.998757i	$0.515871\pi$
$812$		0			0
$813$	−4.77632			−0.167513
$814$		0			0
$815$	−2.97027	−	5.14467i	−0.104044	−	0.180210i
$816$		0			0
$817$	14.9414	−	25.8793i	0.522734	−	0.905403i
$818$		0			0
$819$	7.91353	+	5.09117i	0.276521	+	0.177900i
$820$		0			0
$821$	9.07542	−	15.7191i	0.316734	−	0.548600i	−0.663070	−	0.748557i	$-0.730747\pi$
$821$	9.07542	−	15.7191i	0.316734	−	0.548600i	0.979805	+	0.199957i	$0.0640803\pi$
$822$		0			0
$823$	−27.6925	−	47.9648i	−0.965299	−	1.67195i	−0.708811	−	0.705399i	$-0.750768\pi$
$823$	−27.6925	−	47.9648i	−0.965299	−	1.67195i	−0.256488	−	0.966548i	$-0.582565\pi$
$824$		0			0
$825$	−16.6259			−0.578840
$826$		0			0
$827$	35.4033			1.23109			0.615546	−	0.788101i	$-0.288935\pi$
$827$	35.4033			1.23109			0.615546	+	0.788101i	$0.288935\pi$
$828$		0			0
$829$	−14.9642	−	25.9188i	−0.519730	−	0.900198i	−0.999737	−	0.0229335i	$-0.992699\pi$
$829$	−14.9642	−	25.9188i	−0.519730	−	0.900198i	0.480007	−	0.877264i	$-0.340634\pi$
$830$		0			0
$831$	8.80298	−	15.2472i	0.305372	−	0.528920i
$832$		0			0
$833$	−10.6420	−	23.3630i	−0.368724	−	0.809479i
$834$		0			0
$835$	−12.6297	+	21.8752i	−0.437068	+	0.757024i
$836$		0			0
$837$	3.17755	+	5.50367i	0.109832	+	0.190235i
$838$		0			0
$839$	50.4631			1.74218			0.871090	−	0.491123i	$-0.163413\pi$
$839$	50.4631			1.74218			0.871090	+	0.491123i	$0.163413\pi$
$840$		0			0
$841$	−19.2597			−0.664129
$842$		0			0
$843$	−12.1663	−	21.0726i	−0.419029	−	0.725779i
$844$		0			0
$845$	6.61885	−	11.4642i	0.227695	−	0.394380i
$846$		0			0
$847$	47.6428	+	30.6509i	1.63702	+	1.05318i
$848$		0			0
$849$	3.79227	−	6.56840i	0.130150	−	0.225427i
$850$		0			0
$851$	0.653491	+	1.13188i	0.0224014	+	0.0388003i
$852$		0			0
$853$	−15.5762			−0.533319			−0.266659	−	0.963791i	$-0.585920\pi$
$853$	−15.5762			−0.533319			−0.266659	+	0.963791i	$0.585920\pi$
$854$		0			0
$855$	−14.5807			−0.498649
$856$		0			0
$857$	26.6647	+	46.1845i	0.910847	+	1.57763i	0.812870	+	0.582445i	$0.197904\pi$
$857$	26.6647	+	46.1845i	0.910847	+	1.57763i	0.0979770	+	0.995189i	$0.468763\pi$
$858$		0			0
$859$	−14.4857	+	25.0899i	−0.494244	+	0.856057i	−0.999978	−	0.00663319i	$-0.997889\pi$
$859$	−14.4857	+	25.0899i	−0.494244	+	0.856057i	0.505734	+	0.862690i	$0.331222\pi$
$860$		0			0
$861$	4.49665	−	2.31541i	0.153245	−	0.0789091i
$862$		0			0
$863$	15.1539	−	26.2473i	0.515844	−	0.893468i	−0.483987	−	0.875075i	$-0.660812\pi$
$863$	15.1539	−	26.2473i	0.515844	−	0.893468i	0.999831	−	0.0183928i	$-0.00585494\pi$
$864$		0			0
$865$	2.07249	+	3.58965i	0.0704667	+	0.122052i
$866$		0			0
$867$	−3.02506			−0.102737
$868$		0			0
$869$	35.9780			1.22047
$870$		0			0
$871$	10.0084	+	17.3350i	0.339121	+	0.587374i
$872$		0			0
$873$	−7.87667	+	13.6428i	−0.266585	+	0.461739i
$874$		0			0
$875$	−1.34428	+	27.9337i	−0.0454451	+	0.944331i
$876$		0			0
$877$	28.0796	−	48.6354i	0.948182	−	1.64230i	0.198931	−	0.980013i	$-0.436253\pi$
$877$	28.0796	−	48.6354i	0.948182	−	1.64230i	0.749251	−	0.662286i	$-0.230414\pi$
$878$		0			0
$879$	−3.34610	−	5.79562i	−0.112861	−	0.195481i
$880$		0			0
$881$	−13.9372			−0.469555			−0.234777	−	0.972049i	$-0.575436\pi$
$881$	−13.9372			−0.469555			−0.234777	+	0.972049i	$0.575436\pi$
$882$		0			0
$883$	−18.4755			−0.621751			−0.310875	−	0.950451i	$-0.600622\pi$
$883$	−18.4755			−0.621751			−0.310875	+	0.950451i	$0.600622\pi$
$884$		0			0
$885$	−6.89570	−	11.9437i	−0.231796	−	0.401483i
$886$		0			0
$887$	19.1000	−	33.0822i	0.641315	−	1.11079i	−0.343824	−	0.939034i	$-0.611722\pi$
$887$	19.1000	−	33.0822i	0.641315	−	1.11079i	0.985139	−	0.171757i	$-0.0549443\pi$
$888$		0			0
$889$	−1.11266	+	23.1206i	−0.0373174	+	0.775441i
$890$		0			0
$891$	−8.51175	+	14.7428i	−0.285154	+	0.493902i
$892$		0			0
$893$	−11.7946	−	20.4288i	−0.394691	−	0.683625i
$894$		0			0
$895$	20.6971			0.691829
$896$		0			0
$897$	1.33321			0.0445144
$898$		0			0
$899$	2.20641	+	3.82161i	0.0735877	+	0.127458i
$900$		0			0
$901$	15.7609	−	27.2987i	0.525073	−	0.909453i
$902$		0			0
$903$	11.7182	−	6.03390i	0.389956	−	0.200796i
$904$		0			0
$905$	−7.41556	+	12.8441i	−0.246501	+	0.426953i
$906$		0			0
$907$	29.3392	+	50.8170i	0.974192	+	1.68735i	0.682577	+	0.730813i	$0.260859\pi$
$907$	29.3392	+	50.8170i	0.974192	+	1.68735i	0.291614	+	0.956536i	$0.405808\pi$
$908$		0			0
$909$	28.8466			0.956780
$910$		0			0
$911$	−40.3639			−1.33731			−0.668657	−	0.743571i	$-0.733131\pi$
$911$	−40.3639			−1.33731			−0.668657	+	0.743571i	$0.733131\pi$
$912$		0			0
$913$	−32.3083	−	55.9597i	−1.06925	−	1.85199i
$914$		0			0
$915$	−2.69861	+	4.67413i	−0.0892134	+	0.154522i
$916$		0			0
$917$	−41.7603	−	26.8665i	−1.37905	−	0.887209i
$918$		0			0
$919$	4.28646	−	7.42437i	0.141397	−	0.244907i	−0.786626	−	0.617430i	$-0.788174\pi$
$919$	4.28646	−	7.42437i	0.141397	−	0.244907i	0.928023	+	0.372523i	$0.121507\pi$
$920$		0			0
$921$	−4.98961	−	8.64226i	−0.164413	−	0.284772i
$922$		0			0
$923$	−19.7571			−0.650312
$924$		0			0
$925$	−4.47836			−0.147248
$926$		0			0
$927$	8.68615	+	15.0449i	0.285291	+	0.494138i
$928$		0			0
$929$	−17.1893	+	29.7727i	−0.563961	+	0.976810i	0.433184	+	0.901305i	$0.357390\pi$
$929$	−17.1893	+	29.7727i	−0.563961	+	0.976810i	−0.997145	+	0.0755044i	$0.975943\pi$
$930$		0			0
$931$	20.7868	−	29.1309i	0.681260	−	0.954727i
$932$		0			0
$933$	−13.4444	+	23.2864i	−0.440151	+	0.762364i
$934$		0			0
$935$	13.0957	+	22.6824i	0.428275	+	0.741795i
$936$		0			0
$937$	−44.6318			−1.45806			−0.729028	−	0.684483i	$-0.760028\pi$
$937$	−44.6318			−1.45806			−0.729028	+	0.684483i	$0.760028\pi$
$938$		0			0
$939$	−12.3453			−0.402873
$940$		0			0
$941$	−5.40074	−	9.35436i	−0.176059	−	0.304943i	0.764468	−	0.644662i	$-0.223002\pi$
$941$	−5.40074	−	9.35436i	−0.176059	−	0.304943i	−0.940527	+	0.339718i	$0.889668\pi$
$942$		0			0
$943$	−1.12149	+	1.94248i	−0.0365208	+	0.0632559i
$944$		0			0
$945$	−12.5449	−	8.07074i	−0.408085	−	0.262541i
$946$		0			0
$947$	5.65981	−	9.80307i	0.183919	−	0.318557i	−0.759293	−	0.650749i	$-0.774455\pi$
$947$	5.65981	−	9.80307i	0.183919	−	0.318557i	0.943212	+	0.332192i	$0.107788\pi$
$948$		0			0
$949$	7.40559	+	12.8268i	0.240395	+	0.416377i
$950$		0			0
$951$	−17.2648			−0.559850
$952$		0			0
$953$	14.6644			0.475025			0.237513	−	0.971384i	$-0.423668\pi$
$953$	14.6644			0.475025			0.237513	+	0.971384i	$0.423668\pi$
$954$		0			0
$955$	7.53381	+	13.0489i	0.243788	+	0.422254i
$956$		0			0
$957$	7.57167	−	13.1145i	0.244757	−	0.423932i
$958$		0			0
$959$	17.4587	−	8.98984i	0.563772	−	0.290297i
$960$		0			0
$961$	14.5004	−	25.1154i	0.467755	−	0.810175i
$962$		0			0
$963$	6.13353	+	10.6236i	0.197650	+	0.342340i
$964$		0			0
$965$	7.29452			0.234819
$966$		0			0
$967$	−12.0906			−0.388806			−0.194403	−	0.980922i	$-0.562277\pi$
$967$	−12.0906			−0.388806			−0.194403	+	0.980922i	$0.562277\pi$
$968$		0			0
$969$	7.99007	+	13.8392i	0.256678	+	0.444579i
$970$		0			0
$971$	5.92045	−	10.2545i	0.189996	−	0.329083i	−0.755252	−	0.655434i	$-0.772486\pi$
$971$	5.92045	−	10.2545i	0.189996	−	0.329083i	0.945249	+	0.326351i	$0.105819\pi$
$972$		0			0
$973$	0.941958	−	19.5735i	0.0301978	−	0.627499i
$974$		0			0
$975$	−2.28411	+	3.95619i	−0.0731500	+	0.126699i
$976$		0			0
$977$	12.2865	+	21.2809i	0.393082	+	0.680837i	0.992854	−	0.119333i	$-0.0380757\pi$
$977$	12.2865	+	21.2809i	0.393082	+	0.680837i	−0.599773	+	0.800170i	$0.704742\pi$
$978$		0			0
$979$	10.0698			0.321833
$980$		0			0
$981$	10.1673			0.324618
$982$		0			0
$983$	−3.17793	−	5.50434i	−0.101360	−	0.175561i	0.810885	−	0.585205i	$-0.198986\pi$
$983$	−3.17793	−	5.50434i	−0.101360	−	0.175561i	−0.912245	+	0.409644i	$0.865653\pi$
$984$		0			0
$985$	−6.61443	+	11.4565i	−0.210753	+	0.365036i
$986$		0			0
$987$	0.500126	−	10.3924i	0.0159192	−	0.330795i
$988$		0			0
$989$	−2.92258	+	5.06206i	−0.0929326	+	0.160964i
$990$		0			0
$991$	11.3599	+	19.6760i	0.360861	+	0.625029i	0.988103	−	0.153795i	$-0.0491497\pi$
$991$	11.3599	+	19.6760i	0.360861	+	0.625029i	−0.627242	+	0.778824i	$0.715816\pi$
$992$		0			0
$993$	−4.25629			−0.135069
$994$		0			0
$995$	−10.1918			−0.323100
$996$		0			0
$997$	21.4500	+	37.1524i	0.679327	+	1.17663i	0.975184	+	0.221396i	$0.0710615\pi$
$997$	21.4500	+	37.1524i	0.679327	+	1.17663i	−0.295857	+	0.955232i	$0.595605\pi$
$998$		0			0
$999$	2.93719	−	5.08736i	0.0929284	−	0.160957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1288.2.q.b.737.5	✓	22
7.2	even	3		9016.2.a.bn.1.7		11
7.4	even	3	inner	1288.2.q.b.921.5	yes	22
7.5	odd	6		9016.2.a.bo.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.b.737.5	✓	22	1.1	even	1	trivial
1288.2.q.b.921.5	yes	22	7.4	even	3	inner
9016.2.a.bn.1.7		11	7.2	even	3
9016.2.a.bo.1.5		11	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:	\( N \)	\(=\)	\( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1288.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.426141 - 0.738098i) q^{3} +(-0.627198 + 1.08634i) q^{5} +(0.127177 - 2.64269i) q^{7} +(1.13681 - 1.96901i) q^{9} +O(q^{10})\)	\(q+(-0.426141 - 0.738098i) q^{3} +(-0.627198 + 1.08634i) q^{5} +(0.127177 - 2.64269i) q^{7} +(1.13681 - 1.96901i) q^{9} +(-2.84658 - 4.93041i) q^{11} -1.56428 q^{13} +1.06910 q^{15} +(1.83376 + 3.17616i) q^{17} +(-2.55621 + 4.42748i) q^{19} +(-2.00476 + 1.03229i) q^{21} +(0.500000 - 0.866025i) q^{23} +(1.71324 + 2.96743i) q^{25} -4.49461 q^{27} -3.12094 q^{29} +(-0.706969 - 1.22451i) q^{31} +(-2.42609 + 4.20211i) q^{33} +(2.79110 + 1.79565i) q^{35} +(-0.653491 + 1.13188i) q^{37} +(0.666603 + 1.15459i) q^{39} -2.24298 q^{41} -5.84516 q^{43} +(1.42601 + 2.46992i) q^{45} +(-2.30705 + 3.99593i) q^{47} +(-6.96765 - 0.672180i) q^{49} +(1.56288 - 2.70698i) q^{51} +(-4.29745 - 7.44340i) q^{53} +7.14147 q^{55} +4.35722 q^{57} +(-6.45000 - 11.1717i) q^{59} +(-2.52419 + 4.37203i) q^{61} +(-5.05891 - 3.25465i) q^{63} +(0.981112 - 1.69934i) q^{65} +(-6.39808 - 11.0818i) q^{67} -0.852282 q^{69} +12.6302 q^{71} +(-4.73419 - 8.19986i) q^{73} +(1.46017 - 2.52909i) q^{75} +(-13.3916 + 6.89559i) q^{77} +(-3.15976 + 5.47287i) q^{79} +(-1.49508 - 2.58956i) q^{81} +11.3499 q^{83} -4.60051 q^{85} +(1.32996 + 2.30356i) q^{87} +(-0.884380 + 1.53179i) q^{89} +(-0.198940 + 4.13390i) q^{91} +(-0.602537 + 1.04362i) q^{93} +(-3.20650 - 5.55381i) q^{95} -6.92877 q^{97} -12.9440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} - 9 q^{5} - q^{7} - 11 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 - 9 * q^5 - q^7 - 11 * q^9	\( 22 q + 2 q^{3} - 9 q^{5} - q^{7} - 11 q^{9} + 30 q^{13} - 4 q^{15} - 5 q^{17} + 3 q^{21} + 11 q^{23} - 22 q^{25} - 10 q^{27} + 10 q^{29} - 6 q^{31} - 14 q^{33} + 25 q^{35} + q^{37} - 11 q^{39} + 40 q^{41} - 14 q^{43} - 41 q^{45} + 3 q^{47} + 9 q^{49} + 13 q^{51} - 19 q^{53} - 6 q^{55} - 10 q^{57} - 7 q^{59} - 39 q^{61} + 81 q^{63} - 5 q^{65} - 7 q^{67} + 4 q^{69} - 38 q^{71} + 5 q^{73} - 16 q^{75} - 17 q^{77} - 11 q^{79} - 43 q^{81} + 66 q^{83} - 26 q^{85} + 30 q^{87} - 34 q^{89} + 8 q^{91} + 12 q^{93} - 37 q^{95} + 34 q^{97} - 98 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 - 9 * q^5 - q^7 - 11 * q^9 + 30 * q^13 - 4 * q^15 - 5 * q^17 + 3 * q^21 + 11 * q^23 - 22 * q^25 - 10 * q^27 + 10 * q^29 - 6 * q^31 - 14 * q^33 + 25 * q^35 + q^37 - 11 * q^39 + 40 * q^41 - 14 * q^43 - 41 * q^45 + 3 * q^47 + 9 * q^49 + 13 * q^51 - 19 * q^53 - 6 * q^55 - 10 * q^57 - 7 * q^59 - 39 * q^61 + 81 * q^63 - 5 * q^65 - 7 * q^67 + 4 * q^69 - 38 * q^71 + 5 * q^73 - 16 * q^75 - 17 * q^77 - 11 * q^79 - 43 * q^81 + 66 * q^83 - 26 * q^85 + 30 * q^87 - 34 * q^89 + 8 * q^91 + 12 * q^93 - 37 * q^95 + 34 * q^97 - 98 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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