LMFDB - Embedded newform 352.2.m.f.257.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [352,2,Mod(97,352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("352.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(352, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$352 = 2^{5} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	352.m (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} + \cdots + 25$ x^12 - 2x^11 + 11x^10 - 11x^9 + 39x^8 - 43x^7 + 99x^6 + 36x^5 + 431x^4 - 350x^3 + 510x^2 - 175*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			257.3
Root			$-1.36475 + 0.991547i$ of defining polynomial
Character	$\chi$	$=$	352.257
Dual form			352.2.m.f.289.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.212270 - 0.653300i) q^{3} +(-0.607036 + 0.441038i) q^{5} +(0.944137 + 2.90576i) q^{7} +(2.04531 + 1.48600i) q^{9} +(-3.27718 - 0.510019i) q^{11} +(5.02345 + 3.64975i) q^{13} +(0.159274 + 0.490196i) q^{15} +(2.49320 - 1.81142i) q^{17} +(1.30894 - 4.02849i) q^{19} +2.09874 q^{21} -0.264608 q^{23} +(-1.37111 + 4.21983i) q^{25} +(3.07215 - 2.23205i) q^{27} +(-0.513105 - 1.57918i) q^{29} +(3.39534 + 2.46686i) q^{31} +(-1.02884 + 2.03272i) q^{33} +(-1.85467 - 1.34750i) q^{35} +(-0.730823 - 2.24924i) q^{37} +(3.45071 - 2.50709i) q^{39} +(1.75476 - 5.40060i) q^{41} -9.90575 q^{43} -1.89696 q^{45} +(-3.56217 + 10.9632i) q^{47} +(-1.88890 + 1.37237i) q^{49} +(-0.654167 - 2.01332i) q^{51} +(-3.56561 - 2.59057i) q^{53} +(2.21430 - 1.13576i) q^{55} +(-2.35396 - 1.71025i) q^{57} +(-0.258400 - 0.795272i) q^{59} +(-5.06629 + 3.68088i) q^{61} +(-2.38691 + 7.34616i) q^{63} -4.65909 q^{65} +7.76323 q^{67} +(-0.0561683 + 0.172868i) q^{69} +(8.38148 - 6.08950i) q^{71} +(-2.61683 - 8.05376i) q^{73} +(2.46577 + 1.79149i) q^{75} +(-1.61211 - 10.0042i) q^{77} +(-11.9096 - 8.65285i) q^{79} +(1.53764 + 4.73238i) q^{81} +(8.89570 - 6.46311i) q^{83} +(-0.714561 + 2.19919i) q^{85} -1.14059 q^{87} -15.9492 q^{89} +(-5.86246 + 18.0428i) q^{91} +(2.33233 - 1.69454i) q^{93} +(0.982144 + 3.02273i) q^{95} +(0.712979 + 0.518009i) q^{97} +(-5.94495 - 5.91304i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q + 6 q^{7} - q^{9} - 11 q^{11} - 2 q^{13} + 4 q^{15} + 12 q^{17} + 5 q^{19} + 24 q^{21} - 12 q^{23} + 13 q^{25} + 3 q^{27} + 16 q^{31} - 7 q^{33} - 28 q^{35} - 4 q^{37} + 46 q^{39} - 4 q^{41} - 22 q^{43}+ \cdots - 65 q^{99}+O(q^{100})$ 12 * q + 6 * q^7 - q^9 - 11 * q^11 - 2 * q^13 + 4 * q^15 + 12 * q^17 + 5 * q^19 + 24 * q^21 - 12 * q^23 + 13 * q^25 + 3 * q^27 + 16 * q^31 - 7 * q^33 - 28 * q^35 - 4 * q^37 + 46 * q^39 - 4 * q^41 - 22 * q^43 + 28 * q^45 - 24 * q^47 - 5 * q^49 + 17 * q^51 - 14 * q^53 - 46 * q^55 - 37 * q^57 + 31 * q^59 - 14 * q^61 + 58 * q^63 - 52 * q^65 - 62 * q^67 - 18 * q^69 + 6 * q^71 - 8 * q^73 + 53 * q^75 - 46 * q^77 - 4 * q^79 - 22 * q^81 + 41 * q^83 - 36 * q^85 - 76 * q^87 - 2 * q^89 - 22 * q^91 + 8 * q^93 + 16 * q^95 + 3 * q^97 - 65 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$ .

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	0.212270	−	0.653300i	0.122554	−	0.377183i	−0.870893	−	0.491472i	$-0.836459\pi$
$3$	0.212270	−	0.653300i	0.122554	−	0.377183i	0.993448	+	0.114289i	$0.0364590\pi$
$4$		0			0
$5$	−0.607036	+	0.441038i	−0.271475	+	0.197238i	−0.715190	−	0.698930i	$-0.753660\pi$
$5$	−0.607036	+	0.441038i	−0.271475	+	0.197238i	0.443716	+	0.896168i	$0.353660\pi$
$6$		0			0
$7$	0.944137	+	2.90576i	0.356850	+	1.09827i	0.954929	+	0.296835i	$0.0959311\pi$
$7$	0.944137	+	2.90576i	0.356850	+	1.09827i	−0.598079	+	0.801438i	$0.704069\pi$
$8$		0			0
$9$	2.04531	+	1.48600i	0.681770	+	0.495335i
$10$		0			0
$11$	−3.27718	−	0.510019i	−0.988106	−	0.153777i
$11$	−3.27718	−	0.510019i	−0.988106	−	0.153777i
$12$		0			0
$13$	5.02345	+	3.64975i	1.39325	+	1.01226i	0.995499	+	0.0947671i	$0.0302106\pi$
$13$	5.02345	+	3.64975i	1.39325	+	1.01226i	0.397755	+	0.917492i	$0.369789\pi$
$14$		0			0
$15$	0.159274	+	0.490196i	0.0411244	+	0.126568i
$16$		0			0
$17$	2.49320	−	1.81142i	0.604691	−	0.439333i	−0.242850	−	0.970064i	$-0.578082\pi$
$17$	2.49320	−	1.81142i	0.604691	−	0.439333i	0.847541	+	0.530730i	$0.178082\pi$
$18$		0			0
$19$	1.30894	−	4.02849i	0.300290	−	0.924199i	−0.681103	−	0.732188i	$-0.738499\pi$
$19$	1.30894	−	4.02849i	0.300290	−	0.924199i	0.981393	−	0.192011i	$-0.0615008\pi$
$20$		0			0
$21$	2.09874			0.457983
$22$		0			0
$23$	−0.264608			−0.0551745			−0.0275873	−	0.999619i	$-0.508782\pi$
$23$	−0.264608			−0.0551745			−0.0275873	+	0.999619i	$0.508782\pi$
$24$		0			0
$25$	−1.37111	+	4.21983i	−0.274221	+	0.843966i
$26$		0			0
$27$	3.07215	−	2.23205i	0.591236	−	0.429558i
$28$		0			0
$29$	−0.513105	−	1.57918i	−0.0952813	−	0.293246i	0.892046	−	0.451945i	$-0.149270\pi$
$29$	−0.513105	−	1.57918i	−0.0952813	−	0.293246i	−0.987327	+	0.158700i	$0.949270\pi$
$30$		0			0
$31$	3.39534	+	2.46686i	0.609821	+	0.443061i	0.849351	−	0.527828i	$-0.176993\pi$
$31$	3.39534	+	2.46686i	0.609821	+	0.443061i	−0.239530	+	0.970889i	$0.576993\pi$
$32$		0			0
$33$	−1.02884	+	2.03272i	−0.179098	+	0.353851i
$34$		0			0
$35$	−1.85467	−	1.34750i	−0.313497	−	0.227769i
$36$		0			0
$37$	−0.730823	−	2.24924i	−0.120147	−	0.369773i	0.872839	−	0.488008i	$-0.162276\pi$
$37$	−0.730823	−	2.24924i	−0.120147	−	0.369773i	−0.992986	+	0.118235i	$0.962276\pi$
$38$		0			0
$39$	3.45071	−	2.50709i	0.552556	−	0.401455i
$40$		0			0
$41$	1.75476	−	5.40060i	0.274048	−	0.843432i	−0.715422	−	0.698693i	$-0.753765\pi$
$41$	1.75476	−	5.40060i	0.274048	−	0.843432i	0.989470	−	0.144740i	$-0.0462345\pi$
$42$		0			0
$43$	−9.90575			−1.51061			−0.755306	−	0.655372i	$-0.772512\pi$
$43$	−9.90575			−1.51061			−0.755306	+	0.655372i	$0.772512\pi$
$44$		0			0
$45$	−1.89696			−0.282782
$46$		0			0
$47$	−3.56217	+	10.9632i	−0.519596	+	1.59915i	0.255165	+	0.966898i	$0.417870\pi$
$47$	−3.56217	+	10.9632i	−0.519596	+	1.59915i	−0.774761	+	0.632255i	$0.782130\pi$
$48$		0			0
$49$	−1.88890	+	1.37237i	−0.269843	+	0.196052i
$50$		0			0
$51$	−0.654167	−	2.01332i	−0.0916017	−	0.281921i
$52$		0			0
$53$	−3.56561	−	2.59057i	−0.489775	−	0.355842i	0.315323	−	0.948984i	$-0.397887\pi$
$53$	−3.56561	−	2.59057i	−0.489775	−	0.355842i	−0.805098	+	0.593142i	$0.797887\pi$
$54$		0			0
$55$	2.21430	−	1.13576i	0.298576	−	0.153146i
$56$		0			0
$57$	−2.35396	−	1.71025i	−0.311790	−	0.226529i
$58$		0			0
$59$	−0.258400	−	0.795272i	−0.0336407	−	0.103536i	0.932826	−	0.360327i	$-0.117335\pi$
$59$	−0.258400	−	0.795272i	−0.0336407	−	0.103536i	−0.966467	+	0.256791i	$0.917335\pi$
$60$		0			0
$61$	−5.06629	+	3.68088i	−0.648672	+	0.471288i	−0.862819	−	0.505514i	$-0.831303\pi$
$61$	−5.06629	+	3.68088i	−0.648672	+	0.471288i	0.214147	+	0.976802i	$0.431303\pi$
$62$		0			0
$63$	−2.38691	+	7.34616i	−0.300723	+	0.925529i
$64$		0			0
$65$	−4.65909			−0.577889
$66$		0			0
$67$	7.76323			0.948430			0.474215	−	0.880409i	$-0.342732\pi$
$67$	7.76323			0.948430			0.474215	+	0.880409i	$0.342732\pi$
$68$		0			0
$69$	−0.0561683	+	0.172868i	−0.00676187	+	0.0208109i
$70$		0			0
$71$	8.38148	−	6.08950i	0.994699	−	0.722691i	0.0337539	−	0.999430i	$-0.489254\pi$
$71$	8.38148	−	6.08950i	0.994699	−	0.722691i	0.960945	+	0.276739i	$0.0892538\pi$
$72$		0			0
$73$	−2.61683	−	8.05376i	−0.306276	−	0.942621i	−0.979198	−	0.202908i	$-0.934961\pi$
$73$	−2.61683	−	8.05376i	−0.306276	−	0.942621i	0.672922	−	0.739714i	$-0.265039\pi$
$74$		0			0
$75$	2.46577	+	1.79149i	0.284723	+	0.206863i
$76$		0			0
$77$	−1.61211	−	10.0042i	−0.183717	−	1.14008i
$78$		0			0
$79$	−11.9096	−	8.65285i	−1.33994	−	0.973521i	−0.999446	−	0.0332737i	$-0.989407\pi$
$79$	−11.9096	−	8.65285i	−1.33994	−	0.973521i	−0.340491	−	0.940248i	$-0.610593\pi$
$80$		0			0
$81$	1.53764	+	4.73238i	0.170849	+	0.525820i
$82$		0			0
$83$	8.89570	−	6.46311i	0.976430	−	0.709418i	0.0195224	−	0.999809i	$-0.493785\pi$
$83$	8.89570	−	6.46311i	0.976430	−	0.709418i	0.956908	+	0.290391i	$0.0937854\pi$
$84$		0			0
$85$	−0.714561	+	2.19919i	−0.0775050	+	0.238536i
$86$		0			0
$87$	−1.14059			−0.122284
$88$		0			0
$89$	−15.9492			−1.69061			−0.845306	−	0.534282i	$-0.820582\pi$
$89$	−15.9492			−1.69061			−0.845306	+	0.534282i	$0.820582\pi$
$90$		0			0
$91$	−5.86246	+	18.0428i	−0.614552	+	1.89140i
$92$		0			0
$93$	2.33233	−	1.69454i	0.241851	−	0.175715i
$94$		0			0
$95$	0.982144	+	3.02273i	0.100766	+	0.310125i
$96$		0			0
$97$	0.712979	+	0.518009i	0.0723920	+	0.0525959i	0.623393	−	0.781909i	$-0.285754\pi$
$97$	0.712979	+	0.518009i	0.0723920	+	0.0525959i	−0.551001	+	0.834505i	$0.685754\pi$
$98$		0			0
$99$	−5.94495	−	5.91304i	−0.597489	−	0.594283i
$100$		0			0
$101$	−9.30209	−	6.75837i	−0.925593	−	0.672483i	0.0193169	−	0.999813i	$-0.493851\pi$
$101$	−9.30209	−	6.75837i	−0.925593	−	0.672483i	−0.944910	+	0.327331i	$0.893851\pi$
$102$		0			0
$103$	−3.37708	−	10.3936i	−0.332753	−	1.02411i	−0.967818	−	0.251651i	$-0.919027\pi$
$103$	−3.37708	−	10.3936i	−0.332753	−	1.02411i	0.635065	−	0.772459i	$-0.280973\pi$
$104$		0			0
$105$	−1.27401	+	0.925624i	−0.124331	+	0.0903317i
$106$		0			0
$107$	−0.645212	+	1.98576i	−0.0623750	+	0.191970i	−0.977388	−	0.211454i	$-0.932180\pi$
$107$	−0.645212	+	1.98576i	−0.0623750	+	0.191970i	0.915013	+	0.403424i	$0.132180\pi$
$108$		0			0
$109$	−3.88713			−0.372320			−0.186160	−	0.982519i	$-0.559604\pi$
$109$	−3.88713			−0.372320			−0.186160	+	0.982519i	$0.559604\pi$
$110$		0			0
$111$	−1.62456			−0.154197
$112$		0			0
$113$	4.20708	−	12.9481i	0.395769	−	1.21805i	−0.532592	−	0.846372i	$-0.678782\pi$
$113$	4.20708	−	12.9481i	0.395769	−	1.21805i	0.928361	−	0.371679i	$-0.121218\pi$
$114$		0			0
$115$	0.160626	−	0.116702i	0.0149785	−	0.0108825i
$116$		0			0
$117$	4.85096	+	14.9297i	0.448472	+	1.38025i
$118$		0			0
$119$	7.61746	+	5.53441i	0.698292	+	0.507339i
$120$		0			0
$121$	10.4798	+	3.34284i	0.952706	+	0.303895i
$122$		0			0
$123$	−3.15573	−	2.29277i	−0.284543	−	0.206732i
$124$		0			0
$125$	−2.18813	−	6.73437i	−0.195712	−	0.602340i
$126$		0			0
$127$	6.61306	−	4.80467i	0.586814	−	0.426345i	−0.254360	−	0.967110i	$-0.581865\pi$
$127$	6.61306	−	4.80467i	0.586814	−	0.426345i	0.841174	+	0.540764i	$0.181865\pi$
$128$		0			0
$129$	−2.10269	+	6.47143i	−0.185132	+	0.569777i
$130$		0			0
$131$	5.90996			0.516356			0.258178	−	0.966097i	$-0.416878\pi$
$131$	5.90996			0.516356			0.258178	+	0.966097i	$0.416878\pi$
$132$		0			0
$133$	12.9416			1.12218
$134$		0			0
$135$	−0.880490	+	2.70987i	−0.0757806	+	0.233229i
$136$		0			0
$137$	6.71184	−	4.87644i	0.573431	−	0.416622i	−0.262919	−	0.964818i	$-0.584685\pi$
$137$	6.71184	−	4.87644i	0.573431	−	0.416622i	0.836350	+	0.548196i	$0.184685\pi$
$138$		0			0
$139$	5.62320	+	17.3064i	0.476953	+	1.46791i	0.843305	+	0.537435i	$0.180607\pi$
$139$	5.62320	+	17.3064i	0.476953	+	1.46791i	−0.366352	+	0.930476i	$0.619393\pi$
$140$		0			0
$141$	6.40614	+	4.65433i	0.539494	+	0.391966i
$142$		0			0
$143$	−14.6013	−	14.5229i	−1.22102	−	1.21447i
$144$		0			0
$145$	1.00795	+	0.732318i	0.0837057	+	0.0608157i
$146$		0			0
$147$	0.495610	+	1.52533i	0.0408773	+	0.125807i
$148$		0			0
$149$	−8.89158	+	6.46011i	−0.728426	+	0.529233i	−0.889065	−	0.457781i	$-0.848645\pi$
$149$	−8.89158	+	6.46011i	−0.728426	+	0.529233i	0.160639	+	0.987013i	$0.448645\pi$
$150$		0			0
$151$	5.42468	−	16.6955i	0.441454	−	1.35866i	−0.444871	−	0.895594i	$-0.646751\pi$
$151$	5.42468	−	16.6955i	0.441454	−	1.35866i	0.886326	−	0.463062i	$-0.153249\pi$
$152$		0			0
$153$	7.79114			0.629877
$154$		0			0
$155$	−3.14907			−0.252940
$156$		0			0
$157$	−4.09117	+	12.5913i	−0.326511	+	1.00490i	0.644243	+	0.764821i	$0.277173\pi$
$157$	−4.09117	+	12.5913i	−0.326511	+	1.00490i	−0.970754	+	0.240077i	$0.922827\pi$
$158$		0			0
$159$	−2.44929	+	1.77952i	−0.194242	+	0.141125i
$160$		0			0
$161$	−0.249826	−	0.768885i	−0.0196890	−	0.0605967i
$162$		0			0
$163$	18.2756	+	13.2780i	1.43146	+	1.04001i	0.989743	+	0.142859i	$0.0456295\pi$
$163$	18.2756	+	13.2780i	1.43146	+	1.04001i	0.441714	+	0.897156i	$0.354371\pi$
$164$		0			0
$165$	−0.271961	−	1.68769i	−0.0211721	−	0.131387i
$166$		0			0
$167$	−13.0270	−	9.46466i	−1.00806	−	0.732397i	−0.0442572	−	0.999020i	$-0.514092\pi$
$167$	−13.0270	−	9.46466i	−1.00806	−	0.732397i	−0.963801	+	0.266623i	$0.914092\pi$
$168$		0			0
$169$	7.89716	+	24.3050i	0.607474	+	1.86961i
$170$		0			0
$171$	8.66352	−	6.29442i	0.662516	−	0.481346i
$172$		0			0
$173$	2.66741	−	8.20943i	0.202799	−	0.624151i	−0.796998	−	0.603983i	$-0.793580\pi$
$173$	2.66741	−	8.20943i	0.202799	−	0.624151i	0.999797	−	0.0201688i	$-0.00642035\pi$
$174$		0			0
$175$	−13.5563			−1.02476
$176$		0			0
$177$	−0.574402			−0.0431747
$178$		0			0
$179$	−4.17100	+	12.8370i	−0.311755	+	0.959483i	0.665315	+	0.746563i	$0.268297\pi$
$179$	−4.17100	+	12.8370i	−0.311755	+	0.959483i	−0.977070	+	0.212920i	$0.931703\pi$
$180$		0			0
$181$	6.62903	−	4.81627i	0.492732	−	0.357991i	−0.313502	−	0.949588i	$-0.601502\pi$
$181$	6.62903	−	4.81627i	0.492732	−	0.357991i	0.806234	+	0.591597i	$0.201502\pi$
$182$		0			0
$183$	1.32929	+	4.09115i	0.0982643	+	0.302426i
$184$		0			0
$185$	1.43564	+	1.04305i	0.105550	+	0.0766866i
$186$		0			0
$187$	−9.09452	+	4.66475i	−0.665057	+	0.341121i
$188$		0			0
$189$	9.38633	+	6.81957i	0.682755	+	0.496051i
$190$		0			0
$191$	6.08452	+	18.7262i	0.440260	+	1.35498i	0.887599	+	0.460617i	$0.152372\pi$
$191$	6.08452	+	18.7262i	0.440260	+	1.35498i	−0.447339	+	0.894364i	$0.647628\pi$
$192$		0			0
$193$	19.3032	−	14.0246i	1.38948	−	1.00951i	0.393556	−	0.919301i	$-0.371245\pi$
$193$	19.3032	−	14.0246i	1.38948	−	1.00951i	0.995922	−	0.0902141i	$-0.0287551\pi$
$194$		0			0
$195$	−0.988986	+	3.04379i	−0.0708228	+	0.217970i
$196$		0			0
$197$	18.9000			1.34657			0.673283	−	0.739385i	$-0.264884\pi$
$197$	18.9000			1.34657			0.673283	+	0.739385i	$0.264884\pi$
$198$		0			0
$199$	9.81826			0.695998			0.347999	−	0.937495i	$-0.386861\pi$
$199$	9.81826			0.695998			0.347999	+	0.937495i	$0.386861\pi$
$200$		0			0
$201$	1.64790	−	5.07172i	0.116234	−	0.357732i
$202$		0			0
$203$	4.10426	−	2.98192i	0.288062	−	0.209290i
$204$		0			0
$205$	1.31666	+	4.05228i	0.0919598	+	0.283023i
$206$		0			0
$207$	−0.541204	−	0.393208i	−0.0376163	−	0.0273298i
$208$		0			0
$209$	−6.34422	+	12.5345i	−0.438839	+	0.867028i
$210$		0			0
$211$	−10.5325	−	7.65227i	−0.725084	−	0.526804i	0.162921	−	0.986639i	$-0.447909\pi$
$211$	−10.5325	−	7.65227i	−0.725084	−	0.526804i	−0.888004	+	0.459835i	$0.847909\pi$
$212$		0			0
$213$	−2.19914	−	6.76824i	−0.150682	−	0.463752i
$214$		0			0
$215$	6.01315	−	4.36881i	0.410093	−	0.297950i
$216$		0			0
$217$	−3.96242	+	12.1951i	−0.268987	+	0.827857i
$218$		0			0
$219$	−5.81700			−0.393076
$220$		0			0
$221$	19.1357			1.28721
$222$		0			0
$223$	−1.08063	+	3.32583i	−0.0723642	+	0.222714i	−0.980697	−	0.195534i	$-0.937356\pi$
$223$	−1.08063	+	3.32583i	−0.0723642	+	0.222714i	0.908333	+	0.418248i	$0.137356\pi$
$224$		0			0
$225$	−9.07502	+	6.59339i	−0.605001	+	0.439559i
$226$		0			0
$227$	−3.37711	−	10.3937i	−0.224147	−	0.689852i	−0.998377	−	0.0569486i	$-0.981863\pi$
$227$	−3.37711	−	10.3937i	−0.224147	−	0.689852i	0.774231	−	0.632904i	$-0.218137\pi$
$228$		0			0
$229$	−9.45596	−	6.87016i	−0.624868	−	0.453993i	0.229751	−	0.973250i	$-0.426209\pi$
$229$	−9.45596	−	6.87016i	−0.624868	−	0.453993i	−0.854618	+	0.519257i	$0.826209\pi$
$230$		0			0
$231$	−6.87795	−	1.07040i	−0.452536	−	0.0704271i
$232$		0			0
$233$	−3.81746	−	2.77354i	−0.250090	−	0.181701i	0.455677	−	0.890145i	$-0.349397\pi$
$233$	−3.81746	−	2.77354i	−0.250090	−	0.181701i	−0.705767	+	0.708444i	$0.749397\pi$
$234$		0			0
$235$	−2.67283	−	8.22613i	−0.174356	−	0.536614i
$236$		0			0
$237$	−8.18096	+	5.94382i	−0.531411	+	0.386092i
$238$		0			0
$239$	−0.374310	+	1.15201i	−0.0242121	+	0.0745172i	−0.962432	−	0.271521i	$-0.912473\pi$
$239$	−0.374310	+	1.15201i	−0.0242121	+	0.0745172i	0.938220	+	0.346038i	$0.112473\pi$
$240$		0			0
$241$	−17.6151			−1.13469			−0.567344	−	0.823481i	$-0.692029\pi$
$241$	−17.6151			−1.13469			−0.567344	+	0.823481i	$0.692029\pi$
$242$		0			0
$243$	14.8102			0.950077
$244$		0			0
$245$	0.541366	−	1.66615i	0.0345866	−	0.106447i
$246$		0			0
$247$	21.2783	−	15.4596i	1.35391	−	0.983672i
$248$		0			0
$249$	−2.33406	−	7.18349i	−0.147915	−	0.455235i
$250$		0			0
$251$	0.644281	+	0.468097i	0.0406666	+	0.0295460i	0.607933	−	0.793988i	$-0.291999\pi$
$251$	0.644281	+	0.468097i	0.0406666	+	0.0295460i	−0.567266	+	0.823534i	$0.691999\pi$
$252$		0			0
$253$	0.867166	+	0.134955i	0.0545183	+	0.00848455i
$254$		0			0
$255$	1.28505	+	0.933645i	0.0804731	+	0.0584671i
$256$		0			0
$257$	−4.76394	−	14.6619i	−0.297166	−	0.914584i	−0.982485	−	0.186341i	$-0.940337\pi$
$257$	−4.76394	−	14.6619i	−0.297166	−	0.914584i	0.685319	−	0.728243i	$-0.259663\pi$
$258$		0			0
$259$	5.84575	−	4.24718i	0.363237	−	0.263907i
$260$		0			0
$261$	1.29720	−	3.99238i	0.0802948	−	0.247122i
$262$		0			0
$263$	−23.1291			−1.42620			−0.713101	−	0.701062i	$-0.752710\pi$
$263$	−23.1291			−1.42620			−0.713101	+	0.701062i	$0.752710\pi$
$264$		0			0
$265$	3.30700			0.203147
$266$		0			0
$267$	−3.38554	+	10.4196i	−0.207192	+	0.637670i
$268$		0			0
$269$	−19.5180	+	14.1807i	−1.19004	+	0.864612i	−0.993268	−	0.115838i	$-0.963045\pi$
$269$	−19.5180	+	14.1807i	−1.19004	+	0.864612i	−0.196768	+	0.980450i	$0.563045\pi$
$270$		0			0
$271$	−1.56539	−	4.81777i	−0.0950905	−	0.292658i	0.892187	−	0.451667i	$-0.149170\pi$
$271$	−1.56539	−	4.81777i	−0.0950905	−	0.292658i	−0.987277	+	0.159008i	$0.949170\pi$
$272$		0			0
$273$	10.5429	+	7.65989i	0.638087	+	0.463597i
$274$		0			0
$275$	6.64555	−	13.1298i	0.400742	−	0.791759i
$276$		0			0
$277$	4.74659	+	3.44860i	0.285195	+	0.207206i	0.721180	−	0.692748i	$-0.243600\pi$
$277$	4.74659	+	3.44860i	0.285195	+	0.207206i	−0.435985	+	0.899954i	$0.643600\pi$
$278$		0			0
$279$	3.27876	+	10.0910i	0.196294	+	0.604131i
$280$		0			0
$281$	22.6389	−	16.4481i	1.35052	−	0.981212i	0.351538	−	0.936174i	$-0.385659\pi$
$281$	22.6389	−	16.4481i	1.35052	−	0.981212i	0.998985	−	0.0450385i	$-0.0143411\pi$
$282$		0			0
$283$	−2.34921	+	7.23013i	−0.139646	+	0.429786i	−0.996284	−	0.0861321i	$-0.972549\pi$
$283$	−2.34921	+	7.23013i	−0.139646	+	0.429786i	0.856638	+	0.515919i	$0.172549\pi$
$284$		0			0
$285$	2.18323			0.129323
$286$		0			0
$287$	17.3496			1.02411
$288$		0			0
$289$	−2.31846	+	7.13550i	−0.136380	+	0.419735i
$290$		0			0
$291$	0.489760	−	0.355831i	0.0287102	−	0.0208592i
$292$		0			0
$293$	1.21793	+	3.74840i	0.0711522	+	0.218984i	0.980309	−	0.197470i	$-0.0632726\pi$
$293$	1.21793	+	3.74840i	0.0711522	+	0.218984i	−0.909157	+	0.416454i	$0.863273\pi$
$294$		0			0
$295$	0.507603	+	0.368795i	0.0295538	+	0.0214721i
$296$		0			0
$297$	−11.2064	+	5.74797i	−0.650260	+	0.333531i
$298$		0			0
$299$	−1.32924	−	0.965752i	−0.0768722	−	0.0558509i
$300$		0			0
$301$	−9.35239	−	28.7837i	−0.539063	−	1.65906i
$302$		0			0
$303$	−6.38980	+	4.64246i	−0.367084	+	0.266702i
$304$		0			0
$305$	1.45202	−	4.46885i	0.0831422	−	0.255885i
$306$		0			0
$307$	−10.7552			−0.613829			−0.306915	−	0.951737i	$-0.599297\pi$
$307$	−10.7552			−0.613829			−0.306915	+	0.951737i	$0.599297\pi$
$308$		0			0
$309$	−7.50698			−0.427057
$310$		0			0
$311$	−8.06019	+	24.8067i	−0.457051	+	1.40666i	0.411658	+	0.911338i	$0.364950\pi$
$311$	−8.06019	+	24.8067i	−0.457051	+	1.40666i	−0.868710	+	0.495322i	$0.835050\pi$
$312$		0			0
$313$	2.43382	−	1.76827i	0.137568	−	0.0999487i	−0.516873	−	0.856062i	$-0.672904\pi$
$313$	2.43382	−	1.76827i	0.137568	−	0.0999487i	0.654441	+	0.756113i	$0.272904\pi$
$314$		0			0
$315$	−1.79099	−	5.51210i	−0.100911	−	0.310572i
$316$		0			0
$317$	−26.2108	−	19.0433i	−1.47214	−	1.06958i	−0.979985	−	0.199071i	$-0.936208\pi$
$317$	−26.2108	−	19.0433i	−1.47214	−	1.06958i	−0.492160	−	0.870505i	$-0.663792\pi$
$318$		0			0
$319$	0.876127	+	5.43693i	0.0490537	+	0.304410i
$320$		0			0
$321$	1.16034	+	0.843034i	0.0647637	+	0.0470536i
$322$		0			0
$323$	−4.03383	−	12.4149i	−0.224449	−	0.690782i
$324$		0			0
$325$	−22.2890	+	16.1939i	−1.23637	+	0.898277i
$326$		0			0
$327$	−0.825122	+	2.53946i	−0.0456294	+	0.140433i
$328$		0			0
$329$	−35.2197			−1.94172
$330$		0			0
$331$	−19.2715			−1.05926			−0.529629	−	0.848229i	$-0.677669\pi$
$331$	−19.2715			−1.05926			−0.529629	+	0.848229i	$0.677669\pi$
$332$		0			0
$333$	1.84762	−	5.68640i	0.101249	−	0.311613i
$334$		0			0
$335$	−4.71256	+	3.42388i	−0.257475	+	0.187066i
$336$		0			0
$337$	−6.07494	−	18.6967i	−0.330923	−	1.01848i	−0.968696	−	0.248252i	$-0.920144\pi$
$337$	−6.07494	−	18.6967i	−0.330923	−	1.01848i	0.637772	−	0.770225i	$-0.279856\pi$
$338$		0			0
$339$	−7.56593	−	5.49697i	−0.410925	−	0.298555i
$340$		0			0
$341$	−9.86899	−	9.81602i	−0.534436	−	0.531568i
$342$		0			0
$343$	11.5313	+	8.37801i	0.622634	+	0.452370i
$344$		0			0
$345$	−0.0421452	−	0.129710i	−0.00226902	−	0.00698333i
$346$		0			0
$347$	1.04704	−	0.760720i	0.0562081	−	0.0408376i	−0.559326	−	0.828947i	$-0.688940\pi$
$347$	1.04704	−	0.760720i	0.0562081	−	0.0408376i	0.615535	+	0.788110i	$0.288940\pi$
$348$		0			0
$349$	−3.54495	+	10.9102i	−0.189757	+	0.584011i	−0.999998	−	0.00208547i	$-0.999336\pi$
$349$	−3.54495	+	10.9102i	−0.189757	+	0.584011i	0.810241	+	0.586097i	$0.199336\pi$
$350$		0			0
$351$	23.5792			1.25857
$352$		0			0
$353$	−15.5104			−0.825534			−0.412767	−	0.910837i	$-0.635438\pi$
$353$	−15.5104			−0.825534			−0.412767	+	0.910837i	$0.635438\pi$
$354$		0			0
$355$	−2.40216	+	7.39310i	−0.127494	+	0.392385i
$356$		0			0
$357$	5.23259	−	3.80170i	0.276938	−	0.201207i
$358$		0			0
$359$	4.31460	+	13.2790i	0.227716	+	0.700837i	0.998005	+	0.0631419i	$0.0201121\pi$
$359$	4.31460	+	13.2790i	0.227716	+	0.700837i	−0.770289	+	0.637695i	$0.779888\pi$
$360$		0			0
$361$	0.855919	+	0.621861i	0.0450484	+	0.0327295i
$362$		0			0
$363$	4.40842	−	6.13684i	0.231382	−	0.322101i
$364$		0			0
$365$	5.14052	+	3.73481i	0.269067	+	0.195489i
$366$		0			0
$367$	−4.77524	−	14.6967i	−0.249266	−	0.767161i	−0.994906	−	0.100812i	$-0.967856\pi$
$367$	−4.77524	−	14.6967i	−0.249266	−	0.767161i	0.745640	−	0.666349i	$-0.232144\pi$
$368$		0			0
$369$	11.6143	−	8.43832i	0.604619	−	0.439281i
$370$		0			0
$371$	4.16114	−	12.8067i	0.216035	−	0.664889i
$372$		0			0
$373$	6.75664			0.349846			0.174923	−	0.984582i	$-0.444032\pi$
$373$	6.75664			0.349846			0.174923	+	0.984582i	$0.444032\pi$
$374$		0			0
$375$	−4.86404			−0.251178
$376$		0			0
$377$	3.18604	−	9.80562i	0.164089	−	0.505015i
$378$		0			0
$379$	18.7117	−	13.5948i	0.961153	−	0.698319i	0.00773497	−	0.999970i	$-0.497538\pi$
$379$	18.7117	−	13.5948i	0.961153	−	0.698319i	0.953418	+	0.301651i	$0.0975379\pi$
$380$		0			0
$381$	−1.73514	−	5.34020i	−0.0888937	−	0.273587i
$382$		0			0
$383$	19.3862	+	14.0849i	0.990591	+	0.719706i	0.960050	−	0.279827i	$-0.0902772\pi$
$383$	19.3862	+	14.0849i	0.990591	+	0.719706i	0.0305402	+	0.999534i	$0.490277\pi$
$384$		0			0
$385$	5.39084	+	5.36191i	0.274743	+	0.273268i
$386$		0			0
$387$	−20.2603	−	14.7200i	−1.02989	−	0.748259i
$388$		0			0
$389$	4.12049	+	12.6815i	0.208917	+	0.642980i	0.999530	+	0.0306637i	$0.00976210\pi$
$389$	4.12049	+	12.6815i	0.208917	+	0.642980i	−0.790613	+	0.612316i	$0.790238\pi$
$390$		0			0
$391$	−0.659721	+	0.479315i	−0.0333635	+	0.0242400i
$392$		0			0
$393$	1.25451	−	3.86098i	0.0632816	−	0.194761i
$394$		0			0
$395$	11.0458			0.555775
$396$		0			0
$397$	23.8585			1.19742			0.598712	−	0.800964i	$-0.295679\pi$
$397$	23.8585			1.19742			0.598712	+	0.800964i	$0.295679\pi$
$398$		0			0
$399$	2.74712	−	8.45476i	0.137528	−	0.423267i
$400$		0			0
$401$	−10.9262	+	7.93833i	−0.545627	+	0.396421i	−0.826171	−	0.563420i	$-0.809485\pi$
$401$	−10.9262	+	7.93833i	−0.545627	+	0.396421i	0.280543	+	0.959841i	$0.409485\pi$
$402$		0			0
$403$	8.05291	+	24.7843i	0.401144	+	1.23459i
$404$		0			0
$405$	−3.02056	−	2.19457i	−0.150093	−	0.109049i
$406$		0			0
$407$	1.24788	+	7.74389i	0.0618551	+	0.383850i
$408$		0			0
$409$	−30.4632	−	22.1328i	−1.50631	−	1.09440i	−0.967782	−	0.251790i	$-0.918981\pi$
$409$	−30.4632	−	22.1328i	−1.50631	−	1.09440i	−0.538528	−	0.842608i	$-0.681019\pi$
$410$		0			0
$411$	−1.76105	−	5.41997i	−0.0868664	−	0.267347i
$412$		0			0
$413$	2.06690	−	1.50169i	0.101706	−	0.0738934i
$414$		0			0
$415$	−2.54954	+	7.84668i	−0.125152	+	0.385178i
$416$		0			0
$417$	12.4999			0.612124
$418$		0			0
$419$	−13.2409			−0.646862			−0.323431	−	0.946252i	$-0.604836\pi$
$419$	−13.2409			−0.646862			−0.323431	+	0.946252i	$0.604836\pi$
$420$		0			0
$421$	−0.716385	+	2.20481i	−0.0349145	+	0.107456i	−0.966995	−	0.254796i	$-0.917992\pi$
$421$	−0.716385	+	2.20481i	−0.0349145	+	0.107456i	0.932080	+	0.362251i	$0.117992\pi$
$422$		0			0
$423$	−23.5771	+	17.1298i	−1.14636	+	0.832879i
$424$		0			0
$425$	4.22543	+	13.0045i	0.204964	+	0.630813i
$426$		0			0
$427$	−15.4790	−	11.2461i	−0.749081	−	0.544239i
$428$		0			0
$429$	−12.5872	+	6.45624i	−0.607718	+	0.311710i
$430$		0			0
$431$	3.16135	+	2.29685i	0.152277	+	0.110636i	0.661315	−	0.750108i	$-0.269999\pi$
$431$	3.16135	+	2.29685i	0.152277	+	0.110636i	−0.509038	+	0.860744i	$0.669999\pi$
$432$		0			0
$433$	6.06021	+	18.6514i	0.291235	+	0.896329i	0.984460	+	0.175608i	$0.0561891\pi$
$433$	6.06021	+	18.6514i	0.291235	+	0.896329i	−0.693225	+	0.720721i	$0.743811\pi$
$434$		0			0
$435$	0.692381	−	0.503044i	0.0331971	−	0.0241191i
$436$		0			0
$437$	−0.346354	+	1.06597i	−0.0165684	+	0.0509922i
$438$		0			0
$439$	4.69615			0.224135			0.112068	−	0.993701i	$-0.464253\pi$
$439$	4.69615			0.224135			0.112068	+	0.993701i	$0.464253\pi$
$440$		0			0
$441$	−5.90273			−0.281082
$442$		0			0
$443$	12.9938	−	39.9908i	0.617354	−	1.90002i	0.264061	−	0.964506i	$-0.414938\pi$
$443$	12.9938	−	39.9908i	0.617354	−	1.90002i	0.353292	−	0.935513i	$-0.385062\pi$
$444$		0			0
$445$	9.68175	−	7.03420i	0.458959	−	0.333453i
$446$		0			0
$447$	2.33297	+	7.18015i	0.110346	+	0.339610i
$448$		0			0
$449$	19.9789	+	14.5156i	0.942865	+	0.685031i	0.949109	−	0.314949i	$-0.101987\pi$
$449$	19.9789	+	14.5156i	0.942865	+	0.685031i	−0.00624385	+	0.999981i	$0.501987\pi$
$450$		0			0
$451$	−8.50507	+	16.8038i	−0.400488	+	0.791258i
$452$		0			0
$453$	−9.75564	−	7.08789i	−0.458360	−	0.333018i
$454$		0			0
$455$	−4.39882	−	13.5382i	−0.206220	−	0.634680i
$456$		0			0
$457$	−14.4508	+	10.4991i	−0.675978	+	0.491127i	−0.872021	−	0.489468i	$-0.837191\pi$
$457$	−14.4508	+	10.4991i	−0.675978	+	0.491127i	0.196043	+	0.980595i	$0.437191\pi$
$458$		0			0
$459$	3.61633	−	11.1299i	0.168796	−	0.519500i
$460$		0			0
$461$	29.9746			1.39606			0.698028	−	0.716071i	$-0.254061\pi$
$461$	29.9746			1.39606			0.698028	+	0.716071i	$0.254061\pi$
$462$		0			0
$463$	−29.0359			−1.34941			−0.674705	−	0.738087i	$-0.735729\pi$
$463$	−29.0359			−1.34941			−0.674705	+	0.738087i	$0.735729\pi$
$464$		0			0
$465$	−0.668454	+	2.05729i	−0.0309988	+	0.0954045i
$466$		0			0
$467$	−22.7821	+	16.5521i	−1.05423	+	0.765942i	−0.973012	−	0.230754i	$-0.925881\pi$
$467$	−22.7821	+	16.5521i	−1.05423	+	0.765942i	−0.0812167	+	0.996696i	$0.525881\pi$
$468$		0			0
$469$	7.32956	+	22.5581i	0.338447	+	1.04163i
$470$		0			0
$471$	7.35748	+	5.34552i	0.339015	+	0.246309i
$472$		0			0
$473$	32.4629	+	5.05212i	1.49264	+	0.232297i
$474$		0			0
$475$	15.2049	+	11.0470i	0.697646	+	0.506870i
$476$		0			0
$477$	−3.44318	−	10.5970i	−0.157653	−	0.485205i
$478$		0			0
$479$	17.9735	−	13.0585i	0.821230	−	0.596659i	−0.0958345	−	0.995397i	$-0.530552\pi$
$479$	17.9735	−	13.0585i	0.821230	−	0.596659i	0.917065	+	0.398739i	$0.130552\pi$
$480$		0			0
$481$	4.53792	−	13.9663i	0.206911	−	0.636807i
$482$		0			0
$483$	−0.555343			−0.0252690
$484$		0			0
$485$	−0.661265			−0.0300265
$486$		0			0
$487$	4.04875	−	12.4608i	0.183466	−	0.564652i	−0.816452	−	0.577413i	$-0.804062\pi$
$487$	4.04875	−	12.4608i	0.183466	−	0.564652i	0.999919	+	0.0127614i	$0.00406220\pi$
$488$		0			0
$489$	12.5539	−	9.12094i	0.567707	−	0.412463i
$490$		0			0
$491$	−4.19446	−	12.9092i	−0.189293	−	0.582585i	0.810703	−	0.585458i	$-0.199085\pi$
$491$	−4.19446	−	12.9092i	−0.189293	−	0.582585i	−0.999996	+	0.00287325i	$0.999085\pi$
$492$		0			0
$493$	−4.13982	−	3.00776i	−0.186448	−	0.135463i
$494$		0			0
$495$	6.21667	+	0.967485i	0.279419	+	0.0434852i
$496$		0			0
$497$	25.6079	+	18.6052i	1.14867	+	0.834558i
$498$		0			0
$499$	6.16899	+	18.9862i	0.276162	+	0.849940i	0.988910	+	0.148519i	$0.0474506\pi$
$499$	6.16899	+	18.9862i	0.276162	+	0.849940i	−0.712747	+	0.701421i	$0.752549\pi$
$500$		0			0
$501$	−8.94850	+	6.50147i	−0.399789	+	0.290464i
$502$		0			0
$503$	−2.50003	+	7.69431i	−0.111471	+	0.343072i	−0.991195	−	0.132413i	$-0.957728\pi$
$503$	−2.50003	+	7.69431i	−0.111471	+	0.343072i	0.879724	+	0.475485i	$0.157728\pi$
$504$		0			0
$505$	8.62740			0.383914
$506$		0			0
$507$	17.5548			0.779634
$508$		0			0
$509$	−9.74481	+	29.9914i	−0.431931	+	1.32935i	0.464268	+	0.885695i	$0.346317\pi$
$509$	−9.74481	+	29.9914i	−0.431931	+	1.32935i	−0.896199	+	0.443652i	$0.853683\pi$
$510$		0			0
$511$	20.9316	−	15.2077i	0.925960	−	0.672750i
$512$		0			0
$513$	−4.97054	−	15.2977i	−0.219455	−	0.675412i
$514$		0			0
$515$	6.63397	+	4.81986i	0.292328	+	0.212388i
$516$		0			0
$517$	17.2653	−	34.1117i	0.759328	−	1.50023i
$518$		0			0
$519$	−4.79701	−	3.48523i	−0.210565	−	0.152985i
$520$		0			0
$521$	11.4287	+	35.1740i	0.500701	+	1.54100i	0.807880	+	0.589347i	$0.200615\pi$
$521$	11.4287	+	35.1740i	0.500701	+	1.54100i	−0.307179	+	0.951652i	$0.599385\pi$
$522$		0			0
$523$	−5.99740	+	4.35736i	−0.262248	+	0.190534i	−0.711137	−	0.703053i	$-0.751820\pi$
$523$	−5.99740	+	4.35736i	−0.262248	+	0.190534i	0.448890	+	0.893587i	$0.351820\pi$
$524$		0			0
$525$	−2.87760	+	8.85634i	−0.125589	+	0.386522i
$526$		0			0
$527$	12.9338			0.563405
$528$		0			0
$529$	−22.9300			−0.996956
$530$		0			0
$531$	0.653270	−	2.01056i	0.0283495	−	0.0872508i
$532$		0			0
$533$	28.5258	−	20.7252i	1.23559	−	0.897709i
$534$		0			0
$535$	−0.484127	−	1.48999i	−0.0209306	−	0.0644179i
$536$		0			0
$537$	7.50104	+	5.44983i	0.323694	+	0.235177i
$538$		0			0
$539$	6.89019	−	3.53411i	0.296782	−	0.152225i
$540$		0			0
$541$	9.36829	+	6.80646i	0.402774	+	0.292633i	0.770670	−	0.637234i	$-0.219922\pi$
$541$	9.36829	+	6.80646i	0.402774	+	0.292633i	−0.367896	+	0.929867i	$0.619922\pi$
$542$		0			0
$543$	−1.73933	−	5.35310i	−0.0746417	−	0.229723i
$544$		0			0
$545$	2.35963	−	1.71437i	0.101075	−	0.0734356i
$546$		0			0
$547$	−3.10133	+	9.54491i	−0.132603	+	0.408111i	−0.995210	−	0.0977649i	$-0.968831\pi$
$547$	−3.10133	+	9.54491i	−0.132603	+	0.408111i	0.862606	+	0.505876i	$0.168831\pi$
$548$		0			0
$549$	−15.8319			−0.675690
$550$		0			0
$551$	−7.03331			−0.299629
$552$		0			0
$553$	13.8987	−	42.7759i	0.591035	−	1.81902i
$554$		0			0
$555$	0.986167	−	0.716492i	0.0418605	−	0.0304134i
$556$		0			0
$557$	9.61618	+	29.5955i	0.407450	+	1.25400i	0.918832	+	0.394650i	$0.129134\pi$
$557$	9.61618	+	29.5955i	0.407450	+	1.25400i	−0.511381	+	0.859354i	$0.670866\pi$
$558$		0			0
$559$	−49.7610	−	36.1535i	−2.10467	−	1.52913i
$560$		0			0
$561$	1.11699	+	6.93164i	0.0471593	+	0.292654i
$562$		0			0
$563$	18.0268	+	13.0973i	0.759741	+	0.551984i	0.898831	−	0.438296i	$-0.144418\pi$
$563$	18.0268	+	13.0973i	0.759741	+	0.551984i	−0.139090	+	0.990280i	$0.544418\pi$
$564$		0			0
$565$	3.15673	+	9.71542i	0.132805	+	0.408731i
$566$		0			0
$567$	−12.2994	+	8.93603i	−0.516526	+	0.375278i
$568$		0			0
$569$	−9.66296	+	29.7395i	−0.405092	+	1.24675i	0.515726	+	0.856754i	$0.327522\pi$
$569$	−9.66296	+	29.7395i	−0.405092	+	1.24675i	−0.920818	+	0.389992i	$0.872478\pi$
$570$		0			0
$571$	−5.93719			−0.248464			−0.124232	−	0.992253i	$-0.539647\pi$
$571$	−5.93719			−0.248464			−0.124232	+	0.992253i	$0.539647\pi$
$572$		0			0
$573$	13.5254			0.565032
$574$		0			0
$575$	0.362805	−	1.11660i	0.0151300	−	0.0465654i
$576$		0			0
$577$	−5.40311	+	3.92559i	−0.224934	+	0.163424i	−0.694545	−	0.719449i	$-0.744394\pi$
$577$	−5.40311	+	3.92559i	−0.224934	+	0.163424i	0.469611	+	0.882874i	$0.344394\pi$
$578$		0			0
$579$	−5.06479	−	15.5878i	−0.210485	−	0.647808i
$580$		0			0
$581$	27.1790	+	19.7467i	1.12757	+	0.819230i
$582$		0			0
$583$	10.3639	+	10.3083i	0.429229	+	0.426926i
$584$		0			0
$585$	−9.52928	−	6.92343i	−0.393987	−	0.286249i
$586$		0			0
$587$	12.6950	+	39.0713i	0.523980	+	1.61264i	0.766324	+	0.642454i	$0.222084\pi$
$587$	12.6950	+	39.0713i	0.523980	+	1.61264i	−0.242345	+	0.970190i	$0.577916\pi$
$588$		0			0
$589$	14.3820	−	10.4491i	0.592600	−	0.430549i
$590$		0			0
$591$	4.01189	−	12.3473i	0.165027	−	0.507902i
$592$		0			0
$593$	−0.283994			−0.0116622			−0.00583111	−	0.999983i	$-0.501856\pi$
$593$	−0.283994			−0.0116622			−0.00583111	+	0.999983i	$0.501856\pi$
$594$		0			0
$595$	−7.06496			−0.289635
$596$		0			0
$597$	2.08412	−	6.41427i	0.0852974	−	0.262519i
$598$		0			0
$599$	−33.6857	+	24.4741i	−1.37636	+	0.999985i	−0.379152	+	0.925334i	$0.623784\pi$
$599$	−33.6857	+	24.4741i	−1.37636	+	0.999985i	−0.997210	+	0.0746511i	$0.976216\pi$
$600$		0			0
$601$	1.90750	+	5.87068i	0.0778085	+	0.239470i	0.982394	−	0.186823i	$-0.0598192\pi$
$601$	1.90750	+	5.87068i	0.0778085	+	0.239470i	−0.904585	+	0.426293i	$0.859819\pi$
$602$		0			0
$603$	15.8782	+	11.5362i	0.646610	+	0.469790i
$604$		0			0
$605$	−7.83591	+	2.59274i	−0.318575	+	0.105410i
$606$		0			0
$607$	32.9010	+	23.9040i	1.33541	+	0.970232i	0.999599	+	0.0283021i	$0.00901005\pi$
$607$	32.9010	+	23.9040i	1.33541	+	0.970232i	0.335810	+	0.941930i	$0.390990\pi$
$608$		0			0
$609$	−1.07688	−	3.31428i	−0.0436372	−	0.134302i
$610$		0			0
$611$	−57.9075	+	42.0722i	−2.34269	+	1.70206i
$612$		0			0
$613$	5.33390	−	16.4160i	0.215434	−	0.663038i	−0.783688	−	0.621154i	$-0.786664\pi$
$613$	5.33390	−	16.4160i	0.215434	−	0.663038i	0.999122	−	0.0418838i	$-0.0133359\pi$
$614$		0			0
$615$	2.92684			0.118022
$616$		0			0
$617$	13.2729			0.534346			0.267173	−	0.963649i	$-0.413911\pi$
$617$	13.2729			0.534346			0.267173	+	0.963649i	$0.413911\pi$
$618$		0			0
$619$	3.96107	−	12.1909i	0.159209	−	0.489994i	−0.839354	−	0.543585i	$-0.817067\pi$
$619$	3.96107	−	12.1909i	0.159209	−	0.489994i	0.998563	+	0.0535908i	$0.0170667\pi$
$620$		0			0
$621$	−0.812916	+	0.590618i	−0.0326212	+	0.0237007i
$622$		0			0
$623$	−15.0582	−	46.3445i	−0.603296	−	1.85675i
$624$		0			0
$625$	−13.6496	−	9.91704i	−0.545985	−	0.396682i
$626$		0			0
$627$	6.84209	+	6.80537i	0.273247	+	0.271780i
$628$		0			0
$629$	−5.89640	−	4.28399i	−0.235105	−	0.170814i
$630$		0			0
$631$	−1.99094	−	6.12748i	−0.0792581	−	0.243931i	0.903574	−	0.428431i	$-0.140934\pi$
$631$	−1.99094	−	6.12748i	−0.0792581	−	0.243931i	−0.982833	+	0.184500i	$0.940934\pi$
$632$		0			0
$633$	−7.23496	+	5.25650i	−0.287564	+	0.208927i
$634$		0			0
$635$	−1.89533	+	5.83321i	−0.0752137	+	0.231484i
$636$		0			0
$637$	−14.4976			−0.574416
$638$		0			0
$639$	26.1917			1.03613
$640$		0			0
$641$	−6.20170	+	19.0869i	−0.244953	+	0.753887i	0.750692	+	0.660653i	$0.229720\pi$
$641$	−6.20170	+	19.0869i	−0.244953	+	0.753887i	−0.995644	+	0.0932338i	$0.970280\pi$
$642$		0			0
$643$	26.2589	−	19.0782i	1.03555	−	0.752371i	0.0661375	−	0.997811i	$-0.478932\pi$
$643$	26.2589	−	19.0782i	1.03555	−	0.752371i	0.969412	+	0.245440i	$0.0789324\pi$
$644$		0			0
$645$	−1.57773	−	4.85576i	−0.0621231	−	0.191195i
$646$		0			0
$647$	−12.7925	−	9.29429i	−0.502925	−	0.365396i	0.307208	−	0.951642i	$-0.400605\pi$
$647$	−12.7925	−	9.29429i	−0.502925	−	0.365396i	−0.810133	+	0.586246i	$0.800605\pi$
$648$		0			0
$649$	0.441217	+	2.73803i	0.0173193	+	0.107477i
$650$		0			0
$651$	7.12595	+	5.17730i	0.279288	+	0.202915i
$652$		0			0
$653$	−0.927899	−	2.85578i	−0.0363115	−	0.111755i	0.931258	−	0.364361i	$-0.118713\pi$
$653$	−0.927899	−	2.85578i	−0.0363115	−	0.111755i	−0.967569	+	0.252606i	$0.918713\pi$
$654$		0			0
$655$	−3.58756	+	2.60652i	−0.140178	+	0.101845i
$656$		0			0
$657$	6.61570	−	20.3610i	0.258103	−	0.794360i
$658$		0			0
$659$	−3.17515			−0.123686			−0.0618431	−	0.998086i	$-0.519698\pi$
$659$	−3.17515			−0.123686			−0.0618431	+	0.998086i	$0.519698\pi$
$660$		0			0
$661$	−30.6169			−1.19086			−0.595430	−	0.803408i	$-0.703018\pi$
$661$	−30.6169			−1.19086			−0.595430	+	0.803408i	$0.703018\pi$
$662$		0			0
$663$	4.06194	−	12.5014i	0.157753	−	0.485513i
$664$		0			0
$665$	−7.85603	+	5.70774i	−0.304644	+	0.221337i
$666$		0			0
$667$	0.135772	+	0.417862i	0.00525710	+	0.0161797i
$668$		0			0
$669$	1.94338	+	1.41195i	0.0751354	+	0.0545891i
$670$		0			0
$671$	18.4804	−	9.47897i	0.713429	−	0.365932i
$672$		0			0
$673$	14.1071	+	10.2494i	0.543787	+	0.395084i	0.825489	−	0.564417i	$-0.190899\pi$
$673$	14.1071	+	10.2494i	0.543787	+	0.395084i	−0.281703	+	0.959502i	$0.590899\pi$
$674$		0			0
$675$	5.20663	+	16.0244i	0.200403	+	0.616778i
$676$		0			0
$677$	−32.2671	+	23.4434i	−1.24012	+	0.901003i	−0.997607	−	0.0691445i	$-0.977973\pi$
$677$	−32.2671	+	23.4434i	−1.24012	+	0.901003i	−0.242517	+	0.970147i	$0.577973\pi$
$678$		0			0
$679$	−0.832059	+	2.56081i	−0.0319315	+	0.0982750i
$680$		0			0
$681$	−7.50705			−0.287671
$682$		0			0
$683$	37.9702			1.45289			0.726445	−	0.687225i	$-0.241171\pi$
$683$	37.9702			1.45289			0.726445	+	0.687225i	$0.241171\pi$
$684$		0			0
$685$	−1.92364	+	5.92034i	−0.0734984	+	0.226205i
$686$		0			0
$687$	−6.49549	+	4.71925i	−0.247819	+	0.180051i
$688$		0			0
$689$	−8.45675	−	26.0272i	−0.322177	−	0.991558i
$690$		0			0
$691$	−24.5820	−	17.8599i	−0.935145	−	0.679423i	0.0121022	−	0.999927i	$-0.496148\pi$
$691$	−24.5820	−	17.8599i	−0.935145	−	0.679423i	−0.947247	+	0.320504i	$0.896148\pi$
$692$		0			0
$693$	11.5690	−	22.8573i	0.439470	−	0.868276i
$694$		0			0
$695$	−11.0463	−	8.02558i	−0.419009	−	0.304428i
$696$		0			0
$697$	−5.40777	−	16.6434i	−0.204834	−	0.630414i
$698$		0			0
$699$	−2.62229	+	1.90520i	−0.0991840	+	0.0720614i
$700$		0			0
$701$	4.72041	−	14.5279i	0.178287	−	0.548712i	−0.821481	−	0.570236i	$-0.806852\pi$
$701$	4.72041	−	14.5279i	0.178287	−	0.548712i	0.999768	+	0.0215239i	$0.00685180\pi$
$702$		0			0
$703$	−10.0176			−0.377822
$704$		0			0
$705$	−5.94149			−0.223770
$706$		0			0
$707$	10.8557	−	33.4104i	0.408271	−	1.25653i
$708$		0			0
$709$	−28.2924	+	20.5556i	−1.06254	+	0.771983i	−0.974557	−	0.224139i	$-0.928043\pi$
$709$	−28.2924	+	20.5556i	−1.06254	+	0.771983i	−0.0879861	+	0.996122i	$0.528043\pi$
$710$		0			0
$711$	−11.5007	−	35.3955i	−0.431310	−	1.32743i
$712$		0			0
$713$	−0.898434	−	0.652750i	−0.0336466	−	0.0244457i
$714$		0			0
$715$	15.2687	+	2.37623i	0.571016	+	0.0888658i
$716$		0			0
$717$	0.673152	+	0.489074i	0.0251393	+	0.0182648i
$718$		0			0
$719$	−3.25274	−	10.0109i	−0.121307	−	0.373344i	0.871903	−	0.489678i	$-0.162886\pi$
$719$	−3.25274	−	10.0109i	−0.121307	−	0.373344i	−0.993210	+	0.116334i	$0.962886\pi$
$720$		0			0
$721$	27.0128	−	19.6259i	1.00601	−	0.730908i
$722$		0			0
$723$	−3.73916	+	11.5079i	−0.139061	+	0.427985i
$724$		0			0
$725$	7.36738			0.273618
$726$		0			0
$727$	−8.67301			−0.321664			−0.160832	−	0.986982i	$-0.551418\pi$
$727$	−8.67301			−0.321664			−0.160832	+	0.986982i	$0.551418\pi$
$728$		0			0
$729$	−1.46916	+	4.52160i	−0.0544132	+	0.167467i
$730$		0			0
$731$	−24.6970	+	17.9435i	−0.913453	+	0.663663i
$732$		0			0
$733$	−13.1926	−	40.6027i	−0.487280	−	1.49969i	−0.828651	−	0.559766i	$-0.810891\pi$
$733$	−13.1926	−	40.6027i	−0.487280	−	1.49969i	0.341370	−	0.939929i	$-0.389109\pi$
$734$		0			0
$735$	−0.973582	−	0.707349i	−0.0359111	−	0.0260909i
$736$		0			0
$737$	−25.4415	−	3.95940i	−0.937149	−	0.145846i
$738$		0			0
$739$	33.3721	+	24.2463i	1.22761	+	0.891913i	0.996709	−	0.0810632i	$-0.0258316\pi$
$739$	33.3721	+	24.2463i	1.22761	+	0.891913i	0.230904	+	0.972976i	$0.425832\pi$
$740$		0			0
$741$	−5.58302	−	17.1828i	−0.205097	−	0.631225i
$742$		0			0
$743$	−28.1799	+	20.4739i	−1.03382	+	0.751115i	−0.969070	−	0.246786i	$-0.920626\pi$
$743$	−28.1799	+	20.4739i	−1.03382	+	0.751115i	−0.0647518	+	0.997901i	$0.520626\pi$
$744$		0			0
$745$	2.54836	−	7.84304i	0.0933646	−	0.287347i
$746$		0			0
$747$	27.7987			1.01710
$748$		0			0
$749$	−6.37930			−0.233094
$750$		0			0
$751$	11.0813	−	34.1047i	0.404362	−	1.24450i	−0.517064	−	0.855947i	$-0.672975\pi$
$751$	11.0813	−	34.1047i	0.404362	−	1.24450i	0.921427	−	0.388553i	$-0.127025\pi$
$752$		0			0
$753$	0.442570	−	0.321546i	0.0161281	−	0.0117178i
$754$		0			0
$755$	4.07034	+	12.5272i	0.148135	+	0.455913i
$756$		0			0
$757$	−8.92416	−	6.48378i	−0.324354	−	0.235657i	0.413677	−	0.910424i	$-0.364244\pi$
$757$	−8.92416	−	6.48378i	−0.324354	−	0.235657i	−0.738031	+	0.674767i	$0.764244\pi$
$758$		0			0
$759$	0.272239	−	0.537873i	0.00988167	−	0.0195235i
$760$		0			0
$761$	−7.07652	−	5.14139i	−0.256524	−	0.186375i	0.452089	−	0.891973i	$-0.350679\pi$
$761$	−7.07652	−	5.14139i	−0.256524	−	0.186375i	−0.708613	+	0.705597i	$0.750679\pi$
$762$		0			0
$763$	−3.66999	−	11.2951i	−0.132862	−	0.408909i
$764$		0			0
$765$	−4.72950	+	3.43619i	−0.170996	+	0.124236i
$766$		0			0
$767$	1.60449	−	4.93810i	0.0579347	−	0.178305i
$768$		0			0
$769$	9.61551			0.346744			0.173372	−	0.984856i	$-0.444534\pi$
$769$	9.61551			0.346744			0.173372	+	0.984856i	$0.444534\pi$
$770$		0			0
$771$	−10.5899			−0.381384
$772$		0			0
$773$	−2.03122	+	6.25146i	−0.0730580	+	0.224849i	−0.980917	−	0.194426i	$-0.937716\pi$
$773$	−2.03122	+	6.25146i	−0.0730580	+	0.224849i	0.907859	+	0.419275i	$0.137716\pi$
$774$		0			0
$775$	−15.0651	+	10.9454i	−0.541155	+	0.393172i
$776$		0			0
$777$	−1.53381	−	4.72058i	−0.0550251	−	0.169350i
$778$		0			0
$779$	−19.4594	−	14.1381i	−0.697205	−	0.506549i
$780$		0			0
$781$	−30.5734	+	15.6817i	−1.09400	+	0.561134i
$782$		0			0
$783$	−5.10114	−	3.70620i	−0.182300	−	0.132449i
$784$		0			0
$785$	−3.06976	−	9.44775i	−0.109564	−	0.337205i
$786$		0			0
$787$	1.30052	−	0.944881i	0.0463584	−	0.0336814i	−0.564365	−	0.825526i	$-0.690879\pi$
$787$	1.30052	−	0.944881i	0.0463584	−	0.0336814i	0.610723	+	0.791844i	$0.290879\pi$
$788$		0			0
$789$	−4.90962	+	15.1102i	−0.174787	+	0.537939i
$790$		0			0
$791$	41.5960			1.47898
$792$		0			0
$793$	−38.8845			−1.38083
$794$		0			0
$795$	0.701976	−	2.16046i	0.0248965	−	0.0766236i
$796$		0			0
$797$	−15.9525	+	11.5902i	−0.565068	+	0.410546i	−0.833310	−	0.552805i	$-0.813557\pi$
$797$	−15.9525	+	11.5902i	−0.565068	+	0.410546i	0.268242	+	0.963352i	$0.413557\pi$
$798$		0			0
$799$	10.9778	+	33.7862i	0.388366	+	1.19527i
$800$		0			0
$801$	−32.6211	−	23.7006i	−1.15261	−	0.837419i
$802$		0			0
$803$	4.46823	+	27.7282i	0.157680	+	0.978508i
$804$		0			0
$805$	0.490761	+	0.356558i	0.0172970	+	0.0125670i
$806$		0			0
$807$	5.12115	+	15.7613i	0.180273	+	0.554823i
$808$		0			0
$809$	3.70085	−	2.68882i	0.130115	−	0.0945340i	−0.520824	−	0.853664i	$-0.674375\pi$
$809$	3.70085	−	2.68882i	0.130115	−	0.0945340i	0.650939	+	0.759130i	$0.274375\pi$
$810$		0			0
$811$	1.08998	−	3.35461i	0.0382743	−	0.117796i	−0.930094	−	0.367322i	$-0.880275\pi$
$811$	1.08998	−	3.35461i	0.0382743	−	0.117796i	0.968368	+	0.249526i	$0.0802747\pi$
$812$		0			0
$813$	−3.47973			−0.122040
$814$		0			0
$815$	−16.9501			−0.593735
$816$		0			0
$817$	−12.9660	+	39.9052i	−0.453622	+	1.39611i
$818$		0			0
$819$	−38.8022	+	28.1914i	−1.35586	+	0.985088i
$820$		0			0
$821$	−0.762466	−	2.34663i	−0.0266102	−	0.0818979i	0.936869	−	0.349679i	$-0.113709\pi$
$821$	−0.762466	−	2.34663i	−0.0266102	−	0.0818979i	−0.963480	+	0.267781i	$0.913709\pi$
$822$		0			0
$823$	−6.02028	−	4.37399i	−0.209854	−	0.152468i	0.477894	−	0.878418i	$-0.341400\pi$
$823$	−6.02028	−	4.37399i	−0.209854	−	0.152468i	−0.687748	+	0.725950i	$0.741400\pi$
$824$		0			0
$825$	−7.16707	−	7.12861i	−0.249525	−	0.248186i
$826$		0			0
$827$	−8.74279	−	6.35201i	−0.304016	−	0.220881i	0.425308	−	0.905049i	$-0.360166\pi$
$827$	−8.74279	−	6.35201i	−0.304016	−	0.220881i	−0.729325	+	0.684168i	$0.760166\pi$
$828$		0			0
$829$	−6.89204	−	21.2115i	−0.239371	−	0.736707i	−0.996512	−	0.0834553i	$-0.973404\pi$
$829$	−6.89204	−	21.2115i	−0.239371	−	0.736707i	0.757141	−	0.653252i	$-0.226596\pi$
$830$		0			0
$831$	3.26053	−	2.36891i	0.113106	−	0.0821767i
$832$		0			0
$833$	−2.22348	+	6.84318i	−0.0770391	+	0.237102i
$834$		0			0
$835$	12.0821			0.418119
$836$		0			0
$837$	15.9372			0.550869
$838$		0			0
$839$	9.86396	−	30.3581i	0.340542	−	1.04808i	−0.623386	−	0.781914i	$-0.714243\pi$
$839$	9.86396	−	30.3581i	0.340542	−	1.04808i	0.963927	−	0.266165i	$-0.0857566\pi$
$840$		0			0
$841$	21.2310	−	15.4252i	0.732102	−	0.531904i
$842$		0			0
$843$	−5.94000	−	18.2814i	−0.204584	−	0.629646i
$844$		0			0
$845$	−15.5133	−	11.2710i	−0.533672	−	0.387736i
$846$		0			0
$847$	0.180846	+	33.6077i	0.00621394	+	1.15478i
$848$		0			0
$849$	4.22478	+	3.06948i	0.144994	+	0.105344i
$850$		0			0
$851$	0.193381	+	0.595166i	0.00662903	+	0.0204020i
$852$		0			0
$853$	13.5827	−	9.86844i	0.465064	−	0.337889i	−0.330450	−	0.943823i	$-0.607201\pi$
$853$	13.5827	−	9.86844i	0.465064	−	0.337889i	0.795515	+	0.605934i	$0.207201\pi$
$854$		0			0
$855$	−2.48300	+	7.64188i	−0.0849167	+	0.261347i
$856$		0			0
$857$	−11.2278			−0.383534			−0.191767	−	0.981440i	$-0.561422\pi$
$857$	−11.2278			−0.383534			−0.191767	+	0.981440i	$0.561422\pi$
$858$		0			0
$859$	−50.2349			−1.71399			−0.856996	−	0.515324i	$-0.827672\pi$
$859$	−50.2349			−1.71399			−0.856996	+	0.515324i	$0.827672\pi$
$860$		0			0
$861$	3.68279	−	11.3345i	0.125509	−	0.386278i
$862$		0			0
$863$	5.32058	−	3.86562i	0.181115	−	0.131587i	−0.493534	−	0.869726i	$-0.664295\pi$
$863$	5.32058	−	3.86562i	0.181115	−	0.131587i	0.674649	+	0.738139i	$0.264295\pi$
$864$		0			0
$865$	2.00146	+	6.15985i	0.0680515	+	0.209441i
$866$		0			0
$867$	4.16948	+	3.02930i	0.141603	+	0.102881i
$868$		0			0
$869$	34.6168	+	34.4310i	1.17429	+	1.16799i
$870$		0			0
$871$	38.9982	+	28.3339i	1.32140	+	0.960056i
$872$		0			0
$873$	0.688498	+	2.11898i	0.0233021	+	0.0717166i
$874$		0			0
$875$	17.5025	−	12.7163i	0.591694	−	0.429891i
$876$		0			0
$877$	13.6684	−	42.0671i	0.461550	−	1.42050i	−0.401720	−	0.915762i	$-0.631588\pi$
$877$	13.6684	−	42.0671i	0.461550	−	1.42050i	0.863270	−	0.504742i	$-0.168412\pi$
$878$		0			0
$879$	2.70736			0.0913170
$880$		0			0
$881$	37.0273			1.24748			0.623741	−	0.781631i	$-0.285612\pi$
$881$	37.0273			1.24748			0.623741	+	0.781631i	$0.285612\pi$
$882$		0			0
$883$	8.59827	−	26.4627i	0.289355	−	0.890542i	−0.695705	−	0.718328i	$-0.744908\pi$
$883$	8.59827	−	26.4627i	0.289355	−	0.890542i	0.985059	−	0.172214i	$-0.0550922\pi$
$884$		0			0
$885$	0.348683	−	0.253333i	0.0117208	−	0.00851569i
$886$		0			0
$887$	−3.66741	−	11.2871i	−0.123140	−	0.378985i	0.870418	−	0.492314i	$-0.163849\pi$
$887$	−3.66741	−	11.2871i	−0.123140	−	0.378985i	−0.993558	+	0.113329i	$0.963849\pi$
$888$		0			0
$889$	20.2048	+	14.6797i	0.677648	+	0.492340i
$890$		0			0
$891$	−2.62552	−	16.2931i	−0.0879583	−	0.545838i
$892$		0			0
$893$	39.5026	+	28.7003i	1.32190	+	0.960420i
$894$		0			0
$895$	−3.12966	−	9.63210i	−0.104613	−	0.321965i
$896$		0			0
$897$	−0.913085	+	0.663395i	−0.0304870	+	0.0221501i
$898$		0			0
$899$	2.15344	−	6.62760i	0.0718212	−	0.221043i
$900$		0			0
$901$	−13.5824			−0.452496
$902$		0			0
$903$	−20.7896			−0.691835
$904$		0			0
$905$	−1.89990	+	5.84730i	−0.0631549	+	0.194371i
$906$		0			0
$907$	−8.23782	+	5.98513i	−0.273532	+	0.198733i	−0.716092	−	0.698006i	$-0.754071\pi$
$907$	−8.23782	+	5.98513i	−0.273532	+	0.198733i	0.442559	+	0.896739i	$0.354071\pi$
$908$		0			0
$909$	−8.98269	−	27.6459i	−0.297937	−	0.916956i
$910$		0			0
$911$	13.0498	+	9.48123i	0.432359	+	0.314127i	0.782591	−	0.622536i	$-0.213897\pi$
$911$	13.0498	+	9.48123i	0.432359	+	0.314127i	−0.350233	+	0.936663i	$0.613897\pi$
$912$		0			0
$913$	−32.4491	+	16.6438i	−1.07391	+	0.550828i
$914$		0			0
$915$	−2.61128	−	1.89721i	−0.0863262	−	0.0627197i
$916$		0			0
$917$	5.57982	+	17.1729i	0.184262	+	0.567099i
$918$		0			0
$919$	−15.2546	+	11.0831i	−0.503203	+	0.365598i	−0.810239	−	0.586100i	$-0.800663\pi$
$919$	−15.2546	+	11.0831i	−0.503203	+	0.365598i	0.307036	+	0.951698i	$0.400663\pi$
$920$		0			0
$921$	−2.28300	+	7.02635i	−0.0752273	+	0.231526i
$922$		0			0
$923$	64.3291			2.11742
$924$		0			0
$925$	10.4935			0.345023
$926$		0			0
$927$	8.53773	−	26.2764i	0.280416	−	0.863031i
$928$		0			0
$929$	−10.2972	+	7.48135i	−0.337840	+	0.245455i	−0.743750	−	0.668458i	$-0.766955\pi$
$929$	−10.2972	+	7.48135i	−0.337840	+	0.245455i	0.405910	+	0.913913i	$0.366955\pi$
$930$		0			0
$931$	3.05612	+	9.40576i	0.100160	+	0.308261i
$932$		0			0
$933$	14.4953	+	10.5314i	0.474555	+	0.344784i
$934$		0			0
$935$	3.46337	−	6.84270i	0.113264	−	0.223780i
$936$		0			0
$937$	−7.21762	−	5.24391i	−0.235789	−	0.171311i	0.463616	−	0.886036i	$-0.346552\pi$
$937$	−7.21762	−	5.24391i	−0.235789	−	0.171311i	−0.699405	+	0.714725i	$0.746552\pi$
$938$		0			0
$939$	−0.638586	−	1.96537i	−0.0208395	−	0.0641373i
$940$		0			0
$941$	11.1981	−	8.13587i	0.365047	−	0.265222i	−0.390107	−	0.920769i	$-0.627562\pi$
$941$	11.1981	−	8.13587i	0.365047	−	0.265222i	0.755154	+	0.655548i	$0.227562\pi$
$942$		0			0
$943$	−0.464324	+	1.42904i	−0.0151205	+	0.0465360i
$944$		0			0
$945$	−8.70553			−0.283191
$946$		0			0
$947$	−34.5104			−1.12144			−0.560719	−	0.828006i	$-0.689475\pi$
$947$	−34.5104			−1.12144			−0.560719	+	0.828006i	$0.689475\pi$
$948$		0			0
$949$	16.2487	−	50.0084i	0.527456	−	1.62334i
$950$		0			0
$951$	−18.0047	+	13.0812i	−0.583843	+	0.424187i
$952$		0			0
$953$	8.13241	+	25.0290i	0.263435	+	0.810769i	0.992050	+	0.125845i	$0.0401643\pi$
$953$	8.13241	+	25.0290i	0.263435	+	0.810769i	−0.728615	+	0.684923i	$0.759836\pi$
$954$		0			0
$955$	−11.9525	−	8.68399i	−0.386773	−	0.281007i
$956$		0			0
$957$	3.73792	+	0.581724i	0.120830	+	0.0188045i
$958$		0			0
$959$	20.5066	+	14.8989i	0.662193	+	0.481112i
$960$		0			0
$961$	−4.13658	−	12.7311i	−0.133438	−	0.410680i
$962$		0			0
$963$	−4.27050	+	3.10270i	−0.137615	+	0.0999831i
$964$		0			0
$965$	−5.53238	+	17.0269i	−0.178094	+	0.548116i
$966$		0			0
$967$	−4.18054			−0.134437			−0.0672185	−	0.997738i	$-0.521412\pi$
$967$	−4.18054			−0.134437			−0.0672185	+	0.997738i	$0.521412\pi$
$968$		0			0
$969$	−8.96690			−0.288058
$970$		0			0
$971$	5.41506	−	16.6658i	0.173777	−	0.534832i	−0.825798	−	0.563966i	$-0.809275\pi$
$971$	5.41506	−	16.6658i	0.173777	−	0.534832i	0.999576	+	0.0291339i	$0.00927491\pi$
$972$		0			0
$973$	−44.9792	+	32.6793i	−1.44197	+	1.04765i
$974$		0			0
$975$	5.84820	+	17.9989i	0.187292	+	0.576426i
$976$		0			0
$977$	17.7304	+	12.8819i	0.567246	+	0.412128i	0.834104	−	0.551608i	$-0.185985\pi$
$977$	17.7304	+	12.8819i	0.567246	+	0.412128i	−0.266858	+	0.963736i	$0.585985\pi$
$978$		0			0
$979$	52.2684	+	8.13440i	1.67050	+	0.259977i
$980$		0			0
$981$	−7.95039	−	5.77629i	−0.253836	−	0.184423i
$982$		0			0
$983$	10.3243	+	31.7749i	0.329293	+	1.01346i	0.969465	+	0.245229i	$0.0788632\pi$
$983$	10.3243	+	31.7749i	0.329293	+	1.01346i	−0.640172	+	0.768232i	$0.721137\pi$
$984$		0			0
$985$	−11.4730	+	8.33559i	−0.365559	+	0.265594i
$986$		0			0
$987$	−7.47608	+	23.0090i	−0.237966	+	0.732385i
$988$		0			0
$989$	2.62114			0.0833473
$990$		0			0
$991$	−17.4811			−0.555307			−0.277653	−	0.960681i	$-0.589557\pi$
$991$	−17.4811			−0.555307			−0.277653	+	0.960681i	$0.589557\pi$
$992$		0			0
$993$	−4.09077	+	12.5901i	−0.129817	+	0.399534i
$994$		0			0
$995$	−5.96004	+	4.33022i	−0.188946	+	0.137277i
$996$		0			0
$997$	15.7737	+	48.5464i	0.499558	+	1.53748i	0.809732	+	0.586800i	$0.199613\pi$
$997$	15.7737	+	48.5464i	0.499558	+	1.53748i	−0.310174	+	0.950680i	$0.600387\pi$
$998$		0			0
$999$	−7.26562	−	5.27878i	−0.229874	−	0.167013i

Display

a_p

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.m.f.257.3	yes	12
4.3	odd	2		352.2.m.e.257.1	✓	12
8.3	odd	2		704.2.m.m.257.3		12
8.5	even	2		704.2.m.n.257.1		12
11.3	even	5	inner	352.2.m.f.289.3	yes	12
11.5	even	5		3872.2.a.bn.1.5		6
11.6	odd	10		3872.2.a.bo.1.5		6
44.3	odd	10		352.2.m.e.289.1	yes	12
44.27	odd	10		3872.2.a.bq.1.2		6
44.39	even	10		3872.2.a.bp.1.2		6
88.3	odd	10		704.2.m.m.641.3		12
88.5	even	10		7744.2.a.dv.1.2		6
88.27	odd	10		7744.2.a.du.1.5		6
88.61	odd	10		7744.2.a.dw.1.2		6
88.69	even	10		704.2.m.n.641.1		12
88.83	even	10		7744.2.a.dt.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.m.e.257.1	✓	12	4.3	odd	2
352.2.m.e.289.1	yes	12	44.3	odd	10
352.2.m.f.257.3	yes	12	1.1	even	1	trivial
352.2.m.f.289.3	yes	12	11.3	even	5	inner
704.2.m.m.257.3		12	8.3	odd	2
704.2.m.m.641.3		12	88.3	odd	10
704.2.m.n.257.1		12	8.5	even	2
704.2.m.n.641.1		12	88.69	even	10
3872.2.a.bn.1.5		6	11.5	even	5
3872.2.a.bo.1.5		6	11.6	odd	10
3872.2.a.bp.1.2		6	44.39	even	10
3872.2.a.bq.1.2		6	44.27	odd	10
7744.2.a.dt.1.5		6	88.83	even	10
7744.2.a.du.1.5		6	88.27	odd	10
7744.2.a.dv.1.2		6	88.5	even	10
7744.2.a.dw.1.2		6	88.61	odd	10

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	352.2.m.f.257.3

Level	$352$
Weight	$2$
Character	352.257
Analytic conductor	$2.811$
Analytic rank	$0$
Dimension	$12$
Inner twists	$2$