LMFDB - Embedded newform 352.2.m.f.289.3

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			289.3
Root			$-1.36475 - 0.991547i$ of defining polynomial
Character	$\chi$	$=$	352.289
Dual form			352.2.m.f.257.3

$q$ -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 $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$ .

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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	0.993448	−	0.114289i	$-0.0364590\pi$
$3$	0.212270	+	0.653300i	0.122554	+	0.377183i	−0.870893	+	0.491472i	$0.836459\pi$
$4$		0			0
$5$	−0.607036	−	0.441038i	−0.271475	−	0.197238i	0.443716	−	0.896168i	$-0.353660\pi$
$5$	−0.607036	−	0.441038i	−0.271475	−	0.197238i	−0.715190	+	0.698930i	$0.753660\pi$
$6$		0			0
$7$	0.944137	−	2.90576i	0.356850	−	1.09827i	−0.598079	−	0.801438i	$-0.704069\pi$
$7$	0.944137	−	2.90576i	0.356850	−	1.09827i	0.954929	−	0.296835i	$-0.0959311\pi$
$8$		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	0.397755	−	0.917492i	$-0.369789\pi$
$13$	5.02345	−	3.64975i	1.39325	−	1.01226i	0.995499	−	0.0947671i	$-0.0302106\pi$
$14$		0			0
$15$	0.159274	−	0.490196i	0.0411244	−	0.126568i
$16$		0			0
$17$	2.49320	+	1.81142i	0.604691	+	0.439333i	0.847541	−	0.530730i	$-0.178082\pi$
$17$	2.49320	+	1.81142i	0.604691	+	0.439333i	−0.242850	+	0.970064i	$0.578082\pi$
$18$		0			0
$19$	1.30894	+	4.02849i	0.300290	+	0.924199i	0.981393	+	0.192011i	$0.0615008\pi$
$19$	1.30894	+	4.02849i	0.300290	+	0.924199i	−0.681103	+	0.732188i	$0.738499\pi$
$20$		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	−0.987327	−	0.158700i	$-0.949270\pi$
$29$	−0.513105	+	1.57918i	−0.0952813	+	0.293246i	0.892046	+	0.451945i	$0.149270\pi$
$30$		0			0
$31$	3.39534	−	2.46686i	0.609821	−	0.443061i	−0.239530	−	0.970889i	$-0.576993\pi$
$31$	3.39534	−	2.46686i	0.609821	−	0.443061i	0.849351	+	0.527828i	$0.176993\pi$
$32$		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	−0.992986	−	0.118235i	$-0.962276\pi$
$37$	−0.730823	+	2.24924i	−0.120147	+	0.369773i	0.872839	+	0.488008i	$0.162276\pi$
$38$		0			0
$39$	3.45071	+	2.50709i	0.552556	+	0.401455i
$40$		0			0
$41$	1.75476	+	5.40060i	0.274048	+	0.843432i	0.989470	+	0.144740i	$0.0462345\pi$
$41$	1.75476	+	5.40060i	0.274048	+	0.843432i	−0.715422	+	0.698693i	$0.753765\pi$
$42$		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	−0.774761	−	0.632255i	$-0.782130\pi$
$47$	−3.56217	−	10.9632i	−0.519596	−	1.59915i	0.255165	−	0.966898i	$-0.417870\pi$
$48$		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	−0.805098	−	0.593142i	$-0.797887\pi$
$53$	−3.56561	+	2.59057i	−0.489775	+	0.355842i	0.315323	+	0.948984i	$0.397887\pi$
$54$		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	−0.966467	−	0.256791i	$-0.917335\pi$
$59$	−0.258400	+	0.795272i	−0.0336407	+	0.103536i	0.932826	+	0.360327i	$0.117335\pi$
$60$		0			0
$61$	−5.06629	−	3.68088i	−0.648672	−	0.471288i	0.214147	−	0.976802i	$-0.431303\pi$
$61$	−5.06629	−	3.68088i	−0.648672	−	0.471288i	−0.862819	+	0.505514i	$0.831303\pi$
$62$		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	0.960945	−	0.276739i	$-0.0892538\pi$
$71$	8.38148	+	6.08950i	0.994699	+	0.722691i	0.0337539	+	0.999430i	$0.489254\pi$
$72$		0			0
$73$	−2.61683	+	8.05376i	−0.306276	+	0.942621i	0.672922	+	0.739714i	$0.265039\pi$
$73$	−2.61683	+	8.05376i	−0.306276	+	0.942621i	−0.979198	+	0.202908i	$0.934961\pi$
$74$		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	−0.340491	+	0.940248i	$0.610593\pi$
$79$	−11.9096	+	8.65285i	−1.33994	+	0.973521i	−0.999446	+	0.0332737i	$0.989407\pi$
$80$		0			0
$81$	1.53764	−	4.73238i	0.170849	−	0.525820i
$82$		0			0
$83$	8.89570	+	6.46311i	0.976430	+	0.709418i	0.956908	−	0.290391i	$-0.0937854\pi$
$83$	8.89570	+	6.46311i	0.976430	+	0.709418i	0.0195224	+	0.999809i	$0.493785\pi$
$84$		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	−0.551001	−	0.834505i	$-0.685754\pi$
$97$	0.712979	−	0.518009i	0.0723920	−	0.0525959i	0.623393	+	0.781909i	$0.285754\pi$
$98$		0			0
$99$	−5.94495	+	5.91304i	−0.597489	+	0.594283i
$100$		0			0
$101$	−9.30209	+	6.75837i	−0.925593	+	0.672483i	−0.944910	−	0.327331i	$-0.893851\pi$
$101$	−9.30209	+	6.75837i	−0.925593	+	0.672483i	0.0193169	+	0.999813i	$0.493851\pi$
$102$		0			0
$103$	−3.37708	+	10.3936i	−0.332753	+	1.02411i	0.635065	+	0.772459i	$0.280973\pi$
$103$	−3.37708	+	10.3936i	−0.332753	+	1.02411i	−0.967818	+	0.251651i	$0.919027\pi$
$104$		0			0
$105$	−1.27401	−	0.925624i	−0.124331	−	0.0903317i
$106$		0			0
$107$	−0.645212	−	1.98576i	−0.0623750	−	0.191970i	0.915013	−	0.403424i	$-0.132180\pi$
$107$	−0.645212	−	1.98576i	−0.0623750	−	0.191970i	−0.977388	+	0.211454i	$0.932180\pi$
$108$		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	0.928361	+	0.371679i	$0.121218\pi$
$113$	4.20708	+	12.9481i	0.395769	+	1.21805i	−0.532592	+	0.846372i	$0.678782\pi$
$114$		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	0.841174	−	0.540764i	$-0.181865\pi$
$127$	6.61306	+	4.80467i	0.586814	+	0.426345i	−0.254360	+	0.967110i	$0.581865\pi$
$128$		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	0.836350	−	0.548196i	$-0.184685\pi$
$137$	6.71184	+	4.87644i	0.573431	+	0.416622i	−0.262919	+	0.964818i	$0.584685\pi$
$138$		0			0
$139$	5.62320	−	17.3064i	0.476953	−	1.46791i	−0.366352	−	0.930476i	$-0.619393\pi$
$139$	5.62320	−	17.3064i	0.476953	−	1.46791i	0.843305	−	0.537435i	$-0.180607\pi$
$140$		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	0.160639	−	0.987013i	$-0.448645\pi$
$149$	−8.89158	−	6.46011i	−0.728426	−	0.529233i	−0.889065	+	0.457781i	$0.848645\pi$
$150$		0			0
$151$	5.42468	+	16.6955i	0.441454	+	1.35866i	0.886326	+	0.463062i	$0.153249\pi$
$151$	5.42468	+	16.6955i	0.441454	+	1.35866i	−0.444871	+	0.895594i	$0.646751\pi$
$152$		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	−0.970754	−	0.240077i	$-0.922827\pi$
$157$	−4.09117	−	12.5913i	−0.326511	−	1.00490i	0.644243	−	0.764821i	$-0.277173\pi$
$158$		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	0.441714	−	0.897156i	$-0.354371\pi$
$163$	18.2756	−	13.2780i	1.43146	−	1.04001i	0.989743	−	0.142859i	$-0.0456295\pi$
$164$		0			0
$165$	−0.271961	+	1.68769i	−0.0211721	+	0.131387i
$166$		0			0
$167$	−13.0270	+	9.46466i	−1.00806	+	0.732397i	−0.963801	−	0.266623i	$-0.914092\pi$
$167$	−13.0270	+	9.46466i	−1.00806	+	0.732397i	−0.0442572	+	0.999020i	$0.514092\pi$
$168$		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	0.999797	+	0.0201688i	$0.00642035\pi$
$173$	2.66741	+	8.20943i	0.202799	+	0.624151i	−0.796998	+	0.603983i	$0.793580\pi$
$174$		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	−0.977070	−	0.212920i	$-0.931703\pi$
$179$	−4.17100	−	12.8370i	−0.311755	−	0.959483i	0.665315	−	0.746563i	$-0.268297\pi$
$180$		0			0
$181$	6.62903	+	4.81627i	0.492732	+	0.357991i	0.806234	−	0.591597i	$-0.201502\pi$
$181$	6.62903	+	4.81627i	0.492732	+	0.357991i	−0.313502	+	0.949588i	$0.601502\pi$
$182$		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	−0.447339	−	0.894364i	$-0.647628\pi$
$191$	6.08452	−	18.7262i	0.440260	−	1.35498i	0.887599	−	0.460617i	$-0.152372\pi$
$192$		0			0
$193$	19.3032	+	14.0246i	1.38948	+	1.00951i	0.995922	+	0.0902141i	$0.0287551\pi$
$193$	19.3032	+	14.0246i	1.38948	+	1.00951i	0.393556	+	0.919301i	$0.371245\pi$
$194$		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	−0.888004	−	0.459835i	$-0.847909\pi$
$211$	−10.5325	+	7.65227i	−0.725084	+	0.526804i	0.162921	+	0.986639i	$0.447909\pi$
$212$		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	0.908333	−	0.418248i	$-0.137356\pi$
$223$	−1.08063	−	3.32583i	−0.0723642	−	0.222714i	−0.980697	+	0.195534i	$0.937356\pi$
$224$		0			0
$225$	−9.07502	−	6.59339i	−0.605001	−	0.439559i
$226$		0			0
$227$	−3.37711	+	10.3937i	−0.224147	+	0.689852i	0.774231	+	0.632904i	$0.218137\pi$
$227$	−3.37711	+	10.3937i	−0.224147	+	0.689852i	−0.998377	+	0.0569486i	$0.981863\pi$
$228$		0			0
$229$	−9.45596	+	6.87016i	−0.624868	+	0.453993i	−0.854618	−	0.519257i	$-0.826209\pi$
$229$	−9.45596	+	6.87016i	−0.624868	+	0.453993i	0.229751	+	0.973250i	$0.426209\pi$
$230$		0			0
$231$	−6.87795	+	1.07040i	−0.452536	+	0.0704271i
$232$		0			0
$233$	−3.81746	+	2.77354i	−0.250090	+	0.181701i	−0.705767	−	0.708444i	$-0.749397\pi$
$233$	−3.81746	+	2.77354i	−0.250090	+	0.181701i	0.455677	+	0.890145i	$0.349397\pi$
$234$		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	0.938220	−	0.346038i	$-0.112473\pi$
$239$	−0.374310	−	1.15201i	−0.0242121	−	0.0745172i	−0.962432	+	0.271521i	$0.912473\pi$
$240$		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	−0.567266	−	0.823534i	$-0.691999\pi$
$251$	0.644281	−	0.468097i	0.0406666	−	0.0295460i	0.607933	+	0.793988i	$0.291999\pi$
$252$		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	0.685319	+	0.728243i	$0.259663\pi$
$257$	−4.76394	+	14.6619i	−0.297166	+	0.914584i	−0.982485	+	0.186341i	$0.940337\pi$
$258$		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	−0.196768	−	0.980450i	$-0.563045\pi$
$269$	−19.5180	−	14.1807i	−1.19004	−	0.864612i	−0.993268	+	0.115838i	$0.963045\pi$
$270$		0			0
$271$	−1.56539	+	4.81777i	−0.0950905	+	0.292658i	−0.987277	−	0.159008i	$-0.949170\pi$
$271$	−1.56539	+	4.81777i	−0.0950905	+	0.292658i	0.892187	+	0.451667i	$0.149170\pi$
$272$		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	−0.435985	−	0.899954i	$-0.643600\pi$
$277$	4.74659	−	3.44860i	0.285195	−	0.207206i	0.721180	+	0.692748i	$0.243600\pi$
$278$		0			0
$279$	3.27876	−	10.0910i	0.196294	−	0.604131i
$280$		0			0
$281$	22.6389	+	16.4481i	1.35052	+	0.981212i	0.998985	+	0.0450385i	$0.0143411\pi$
$281$	22.6389	+	16.4481i	1.35052	+	0.981212i	0.351538	+	0.936174i	$0.385659\pi$
$282$		0			0
$283$	−2.34921	−	7.23013i	−0.139646	−	0.429786i	0.856638	−	0.515919i	$-0.172549\pi$
$283$	−2.34921	−	7.23013i	−0.139646	−	0.429786i	−0.996284	+	0.0861321i	$0.972549\pi$
$284$		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	−0.909157	−	0.416454i	$-0.863273\pi$
$293$	1.21793	−	3.74840i	0.0711522	−	0.218984i	0.980309	+	0.197470i	$0.0632726\pi$
$294$		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	−0.868710	−	0.495322i	$-0.835050\pi$
$311$	−8.06019	−	24.8067i	−0.457051	−	1.40666i	0.411658	−	0.911338i	$-0.364950\pi$
$312$		0			0
$313$	2.43382	+	1.76827i	0.137568	+	0.0999487i	0.654441	−	0.756113i	$-0.272904\pi$
$313$	2.43382	+	1.76827i	0.137568	+	0.0999487i	−0.516873	+	0.856062i	$0.672904\pi$
$314$		0			0
$315$	−1.79099	+	5.51210i	−0.100911	+	0.310572i
$316$		0			0
$317$	−26.2108	+	19.0433i	−1.47214	+	1.06958i	−0.492160	+	0.870505i	$0.663792\pi$
$317$	−26.2108	+	19.0433i	−1.47214	+	1.06958i	−0.979985	+	0.199071i	$0.936208\pi$
$318$		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	0.637772	+	0.770225i	$0.279856\pi$
$337$	−6.07494	+	18.6967i	−0.330923	+	1.01848i	−0.968696	+	0.248252i	$0.920144\pi$
$338$		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	0.615535	−	0.788110i	$-0.288940\pi$
$347$	1.04704	+	0.760720i	0.0562081	+	0.0408376i	−0.559326	+	0.828947i	$0.688940\pi$
$348$		0			0
$349$	−3.54495	−	10.9102i	−0.189757	−	0.584011i	0.810241	−	0.586097i	$-0.199336\pi$
$349$	−3.54495	−	10.9102i	−0.189757	−	0.584011i	−0.999998	+	0.00208547i	$0.999336\pi$
$350$		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	−0.770289	−	0.637695i	$-0.779888\pi$
$359$	4.31460	−	13.2790i	0.227716	−	0.700837i	0.998005	−	0.0631419i	$-0.0201121\pi$
$360$		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	0.745640	+	0.666349i	$0.232144\pi$
$367$	−4.77524	+	14.6967i	−0.249266	+	0.767161i	−0.994906	+	0.100812i	$0.967856\pi$
$368$		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	0.953418	−	0.301651i	$-0.0975379\pi$
$379$	18.7117	+	13.5948i	0.961153	+	0.698319i	0.00773497	+	0.999970i	$0.497538\pi$
$380$		0			0
$381$	−1.73514	+	5.34020i	−0.0888937	+	0.273587i
$382$		0			0
$383$	19.3862	−	14.0849i	0.990591	−	0.719706i	0.0305402	−	0.999534i	$-0.490277\pi$
$383$	19.3862	−	14.0849i	0.990591	−	0.719706i	0.960050	+	0.279827i	$0.0902772\pi$
$384$		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	−0.790613	−	0.612316i	$-0.790238\pi$
$389$	4.12049	−	12.6815i	0.208917	−	0.642980i	0.999530	−	0.0306637i	$-0.00976210\pi$
$390$		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	0.280543	−	0.959841i	$-0.409485\pi$
$401$	−10.9262	−	7.93833i	−0.545627	−	0.396421i	−0.826171	+	0.563420i	$0.809485\pi$
$402$		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	−0.538528	+	0.842608i	$0.681019\pi$
$409$	−30.4632	+	22.1328i	−1.50631	+	1.09440i	−0.967782	+	0.251790i	$0.918981\pi$
$410$		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	0.932080	−	0.362251i	$-0.117992\pi$
$421$	−0.716385	−	2.20481i	−0.0349145	−	0.107456i	−0.966995	+	0.254796i	$0.917992\pi$
$422$		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	−0.509038	−	0.860744i	$-0.669999\pi$
$431$	3.16135	−	2.29685i	0.152277	−	0.110636i	0.661315	+	0.750108i	$0.269999\pi$
$432$		0			0
$433$	6.06021	−	18.6514i	0.291235	−	0.896329i	−0.693225	−	0.720721i	$-0.743811\pi$
$433$	6.06021	−	18.6514i	0.291235	−	0.896329i	0.984460	−	0.175608i	$-0.0561891\pi$
$434$		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	0.353292	+	0.935513i	$0.385062\pi$
$443$	12.9938	+	39.9908i	0.617354	+	1.90002i	0.264061	+	0.964506i	$0.414938\pi$
$444$		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	−0.00624385	−	0.999981i	$-0.501987\pi$
$449$	19.9789	−	14.5156i	0.942865	−	0.685031i	0.949109	+	0.314949i	$0.101987\pi$
$450$		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	0.196043	−	0.980595i	$-0.437191\pi$
$457$	−14.4508	−	10.4991i	−0.675978	−	0.491127i	−0.872021	+	0.489468i	$0.837191\pi$
$458$		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	−0.0812167	−	0.996696i	$-0.525881\pi$
$467$	−22.7821	−	16.5521i	−1.05423	−	0.765942i	−0.973012	+	0.230754i	$0.925881\pi$
$468$		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	0.917065	−	0.398739i	$-0.130552\pi$
$479$	17.9735	+	13.0585i	0.821230	+	0.596659i	−0.0958345	+	0.995397i	$0.530552\pi$
$480$		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	0.999919	−	0.0127614i	$-0.00406220\pi$
$487$	4.04875	+	12.4608i	0.183466	+	0.564652i	−0.816452	+	0.577413i	$0.804062\pi$
$488$		0			0
$489$	12.5539	+	9.12094i	0.567707	+	0.412463i
$490$		0			0
$491$	−4.19446	+	12.9092i	−0.189293	+	0.582585i	−0.999996	−	0.00287325i	$-0.999085\pi$
$491$	−4.19446	+	12.9092i	−0.189293	+	0.582585i	0.810703	+	0.585458i	$0.199085\pi$
$492$		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	−0.712747	−	0.701421i	$-0.752549\pi$
$499$	6.16899	−	18.9862i	0.276162	−	0.849940i	0.988910	−	0.148519i	$-0.0474506\pi$
$500$		0			0
$501$	−8.94850	−	6.50147i	−0.399789	−	0.290464i
$502$		0			0
$503$	−2.50003	−	7.69431i	−0.111471	−	0.343072i	0.879724	−	0.475485i	$-0.157728\pi$
$503$	−2.50003	−	7.69431i	−0.111471	−	0.343072i	−0.991195	+	0.132413i	$0.957728\pi$
$504$		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	−0.896199	−	0.443652i	$-0.853683\pi$
$509$	−9.74481	−	29.9914i	−0.431931	−	1.32935i	0.464268	−	0.885695i	$-0.346317\pi$
$510$		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	−0.307179	−	0.951652i	$-0.599385\pi$
$521$	11.4287	−	35.1740i	0.500701	−	1.54100i	0.807880	−	0.589347i	$-0.200615\pi$
$522$		0			0
$523$	−5.99740	−	4.35736i	−0.262248	−	0.190534i	0.448890	−	0.893587i	$-0.351820\pi$
$523$	−5.99740	−	4.35736i	−0.262248	−	0.190534i	−0.711137	+	0.703053i	$0.751820\pi$
$524$		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	−0.367896	−	0.929867i	$-0.619922\pi$
$541$	9.36829	−	6.80646i	0.402774	−	0.292633i	0.770670	+	0.637234i	$0.219922\pi$
$542$		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	0.862606	−	0.505876i	$-0.168831\pi$
$547$	−3.10133	−	9.54491i	−0.132603	−	0.408111i	−0.995210	+	0.0977649i	$0.968831\pi$
$548$		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	−0.511381	−	0.859354i	$-0.670866\pi$
$557$	9.61618	−	29.5955i	0.407450	−	1.25400i	0.918832	−	0.394650i	$-0.129134\pi$
$558$		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	−0.139090	−	0.990280i	$-0.544418\pi$
$563$	18.0268	−	13.0973i	0.759741	−	0.551984i	0.898831	+	0.438296i	$0.144418\pi$
$564$		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	−0.920818	−	0.389992i	$-0.872478\pi$
$569$	−9.66296	−	29.7395i	−0.405092	−	1.24675i	0.515726	−	0.856754i	$-0.327522\pi$
$570$		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	0.469611	−	0.882874i	$-0.344394\pi$
$577$	−5.40311	−	3.92559i	−0.224934	−	0.163424i	−0.694545	+	0.719449i	$0.744394\pi$
$578$		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	−0.242345	−	0.970190i	$-0.577916\pi$
$587$	12.6950	−	39.0713i	0.523980	−	1.61264i	0.766324	−	0.642454i	$-0.222084\pi$
$588$		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	−0.997210	−	0.0746511i	$-0.976216\pi$
$599$	−33.6857	−	24.4741i	−1.37636	−	0.999985i	−0.379152	−	0.925334i	$-0.623784\pi$
$600$		0			0
$601$	1.90750	−	5.87068i	0.0778085	−	0.239470i	−0.904585	−	0.426293i	$-0.859819\pi$
$601$	1.90750	−	5.87068i	0.0778085	−	0.239470i	0.982394	+	0.186823i	$0.0598192\pi$
$602$		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	0.335810	−	0.941930i	$-0.390990\pi$
$607$	32.9010	−	23.9040i	1.33541	−	0.970232i	0.999599	−	0.0283021i	$-0.00901005\pi$
$608$		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	0.999122	+	0.0418838i	$0.0133359\pi$
$613$	5.33390	+	16.4160i	0.215434	+	0.663038i	−0.783688	+	0.621154i	$0.786664\pi$
$614$		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	0.998563	−	0.0535908i	$-0.0170667\pi$
$619$	3.96107	+	12.1909i	0.159209	+	0.489994i	−0.839354	+	0.543585i	$0.817067\pi$
$620$		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	−0.982833	−	0.184500i	$-0.940934\pi$
$631$	−1.99094	+	6.12748i	−0.0792581	+	0.243931i	0.903574	+	0.428431i	$0.140934\pi$
$632$		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	−0.995644	−	0.0932338i	$-0.970280\pi$
$641$	−6.20170	−	19.0869i	−0.244953	−	0.753887i	0.750692	−	0.660653i	$-0.229720\pi$
$642$		0			0
$643$	26.2589	+	19.0782i	1.03555	+	0.752371i	0.969412	−	0.245440i	$-0.0789324\pi$
$643$	26.2589	+	19.0782i	1.03555	+	0.752371i	0.0661375	+	0.997811i	$0.478932\pi$
$644$		0			0
$645$	−1.57773	+	4.85576i	−0.0621231	+	0.191195i
$646$		0			0
$647$	−12.7925	+	9.29429i	−0.502925	+	0.365396i	−0.810133	−	0.586246i	$-0.800605\pi$
$647$	−12.7925	+	9.29429i	−0.502925	+	0.365396i	0.307208	+	0.951642i	$0.400605\pi$
$648$		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	−0.967569	−	0.252606i	$-0.918713\pi$
$653$	−0.927899	+	2.85578i	−0.0363115	+	0.111755i	0.931258	+	0.364361i	$0.118713\pi$
$654$		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	−0.281703	−	0.959502i	$-0.590899\pi$
$673$	14.1071	−	10.2494i	0.543787	−	0.395084i	0.825489	+	0.564417i	$0.190899\pi$
$674$		0			0
$675$	5.20663	−	16.0244i	0.200403	−	0.616778i
$676$		0			0
$677$	−32.2671	−	23.4434i	−1.24012	−	0.901003i	−0.242517	−	0.970147i	$-0.577973\pi$
$677$	−32.2671	−	23.4434i	−1.24012	−	0.901003i	−0.997607	+	0.0691445i	$0.977973\pi$
$678$		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	−0.947247	−	0.320504i	$-0.896148\pi$
$691$	−24.5820	+	17.8599i	−0.935145	+	0.679423i	0.0121022	+	0.999927i	$0.496148\pi$
$692$		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	0.999768	−	0.0215239i	$-0.00685180\pi$
$701$	4.72041	+	14.5279i	0.178287	+	0.548712i	−0.821481	+	0.570236i	$0.806852\pi$
$702$		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	−0.0879861	−	0.996122i	$-0.528043\pi$
$709$	−28.2924	−	20.5556i	−1.06254	−	0.771983i	−0.974557	+	0.224139i	$0.928043\pi$
$710$		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	−0.993210	−	0.116334i	$-0.962886\pi$
$719$	−3.25274	+	10.0109i	−0.121307	+	0.373344i	0.871903	+	0.489678i	$0.162886\pi$
$720$		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	0.341370	+	0.939929i	$0.389109\pi$
$733$	−13.1926	+	40.6027i	−0.487280	+	1.49969i	−0.828651	+	0.559766i	$0.810891\pi$
$734$		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	0.230904	−	0.972976i	$-0.425832\pi$
$739$	33.3721	−	24.2463i	1.22761	−	0.891913i	0.996709	+	0.0810632i	$0.0258316\pi$
$740$		0			0
$741$	−5.58302	+	17.1828i	−0.205097	+	0.631225i
$742$		0			0
$743$	−28.1799	−	20.4739i	−1.03382	−	0.751115i	−0.0647518	−	0.997901i	$-0.520626\pi$
$743$	−28.1799	−	20.4739i	−1.03382	−	0.751115i	−0.969070	+	0.246786i	$0.920626\pi$
$744$		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	0.921427	+	0.388553i	$0.127025\pi$
$751$	11.0813	+	34.1047i	0.404362	+	1.24450i	−0.517064	+	0.855947i	$0.672975\pi$
$752$		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	−0.738031	−	0.674767i	$-0.764244\pi$
$757$	−8.92416	+	6.48378i	−0.324354	+	0.235657i	0.413677	+	0.910424i	$0.364244\pi$
$758$		0			0
$759$	0.272239	+	0.537873i	0.00988167	+	0.0195235i
$760$		0			0
$761$	−7.07652	+	5.14139i	−0.256524	+	0.186375i	−0.708613	−	0.705597i	$-0.750679\pi$
$761$	−7.07652	+	5.14139i	−0.256524	+	0.186375i	0.452089	+	0.891973i	$0.350679\pi$
$762$		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	0.907859	−	0.419275i	$-0.137716\pi$
$773$	−2.03122	−	6.25146i	−0.0730580	−	0.224849i	−0.980917	+	0.194426i	$0.937716\pi$
$774$		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	0.610723	−	0.791844i	$-0.290879\pi$
$787$	1.30052	+	0.944881i	0.0463584	+	0.0336814i	−0.564365	+	0.825526i	$0.690879\pi$
$788$		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	0.268242	−	0.963352i	$-0.413557\pi$
$797$	−15.9525	−	11.5902i	−0.565068	−	0.410546i	−0.833310	+	0.552805i	$0.813557\pi$
$798$		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	0.650939	−	0.759130i	$-0.274375\pi$
$809$	3.70085	+	2.68882i	0.130115	+	0.0945340i	−0.520824	+	0.853664i	$0.674375\pi$
$810$		0			0
$811$	1.08998	+	3.35461i	0.0382743	+	0.117796i	0.968368	−	0.249526i	$-0.0802747\pi$
$811$	1.08998	+	3.35461i	0.0382743	+	0.117796i	−0.930094	+	0.367322i	$0.880275\pi$
$812$		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	−0.963480	−	0.267781i	$-0.913709\pi$
$821$	−0.762466	+	2.34663i	−0.0266102	+	0.0818979i	0.936869	+	0.349679i	$0.113709\pi$
$822$		0			0
$823$	−6.02028	+	4.37399i	−0.209854	+	0.152468i	−0.687748	−	0.725950i	$-0.741400\pi$
$823$	−6.02028	+	4.37399i	−0.209854	+	0.152468i	0.477894	+	0.878418i	$0.341400\pi$
$824$		0			0
$825$	−7.16707	+	7.12861i	−0.249525	+	0.248186i
$826$		0			0
$827$	−8.74279	+	6.35201i	−0.304016	+	0.220881i	−0.729325	−	0.684168i	$-0.760166\pi$
$827$	−8.74279	+	6.35201i	−0.304016	+	0.220881i	0.425308	+	0.905049i	$0.360166\pi$
$828$		0			0
$829$	−6.89204	+	21.2115i	−0.239371	+	0.736707i	0.757141	+	0.653252i	$0.226596\pi$
$829$	−6.89204	+	21.2115i	−0.239371	+	0.736707i	−0.996512	+	0.0834553i	$0.973404\pi$
$830$		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	0.963927	+	0.266165i	$0.0857566\pi$
$839$	9.86396	+	30.3581i	0.340542	+	1.04808i	−0.623386	+	0.781914i	$0.714243\pi$
$840$		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	0.795515	−	0.605934i	$-0.207201\pi$
$853$	13.5827	+	9.86844i	0.465064	+	0.337889i	−0.330450	+	0.943823i	$0.607201\pi$
$854$		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	0.674649	−	0.738139i	$-0.264295\pi$
$863$	5.32058	+	3.86562i	0.181115	+	0.131587i	−0.493534	+	0.869726i	$0.664295\pi$
$864$		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	0.863270	+	0.504742i	$0.168412\pi$
$877$	13.6684	+	42.0671i	0.461550	+	1.42050i	−0.401720	+	0.915762i	$0.631588\pi$
$878$		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	0.985059	+	0.172214i	$0.0550922\pi$
$883$	8.59827	+	26.4627i	0.289355	+	0.890542i	−0.695705	+	0.718328i	$0.744908\pi$
$884$		0			0
$885$	0.348683	+	0.253333i	0.0117208	+	0.00851569i
$886$		0			0
$887$	−3.66741	+	11.2871i	−0.123140	+	0.378985i	−0.993558	−	0.113329i	$-0.963849\pi$
$887$	−3.66741	+	11.2871i	−0.123140	+	0.378985i	0.870418	+	0.492314i	$0.163849\pi$
$888$		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	0.442559	−	0.896739i	$-0.354071\pi$
$907$	−8.23782	−	5.98513i	−0.273532	−	0.198733i	−0.716092	+	0.698006i	$0.754071\pi$
$908$		0			0
$909$	−8.98269	+	27.6459i	−0.297937	+	0.916956i
$910$		0			0
$911$	13.0498	−	9.48123i	0.432359	−	0.314127i	−0.350233	−	0.936663i	$-0.613897\pi$
$911$	13.0498	−	9.48123i	0.432359	−	0.314127i	0.782591	+	0.622536i	$0.213897\pi$
$912$		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	0.307036	−	0.951698i	$-0.400663\pi$
$919$	−15.2546	−	11.0831i	−0.503203	−	0.365598i	−0.810239	+	0.586100i	$0.800663\pi$
$920$		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	0.405910	−	0.913913i	$-0.366955\pi$
$929$	−10.2972	−	7.48135i	−0.337840	−	0.245455i	−0.743750	+	0.668458i	$0.766955\pi$
$930$		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	−0.699405	−	0.714725i	$-0.746552\pi$
$937$	−7.21762	+	5.24391i	−0.235789	+	0.171311i	0.463616	+	0.886036i	$0.346552\pi$
$938$		0			0
$939$	−0.638586	+	1.96537i	−0.0208395	+	0.0641373i
$940$		0			0
$941$	11.1981	+	8.13587i	0.365047	+	0.265222i	0.755154	−	0.655548i	$-0.227562\pi$
$941$	11.1981	+	8.13587i	0.365047	+	0.265222i	−0.390107	+	0.920769i	$0.627562\pi$
$942$		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	−0.728615	−	0.684923i	$-0.759836\pi$
$953$	8.13241	−	25.0290i	0.263435	−	0.810769i	0.992050	−	0.125845i	$-0.0401643\pi$
$954$		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	0.999576	−	0.0291339i	$-0.00927491\pi$
$971$	5.41506	+	16.6658i	0.173777	+	0.534832i	−0.825798	+	0.563966i	$0.809275\pi$
$972$		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	−0.266858	−	0.963736i	$-0.585985\pi$
$977$	17.7304	−	12.8819i	0.567246	−	0.412128i	0.834104	+	0.551608i	$0.185985\pi$
$978$		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	−0.640172	−	0.768232i	$-0.721137\pi$
$983$	10.3243	−	31.7749i	0.329293	−	1.01346i	0.969465	−	0.245229i	$-0.0788632\pi$
$984$		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	−0.310174	−	0.950680i	$-0.600387\pi$
$997$	15.7737	−	48.5464i	0.499558	−	1.53748i	0.809732	−	0.586800i	$-0.199613\pi$
$998$		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.289.3	yes	12
4.3	odd	2		352.2.m.e.289.1	yes	12
8.3	odd	2		704.2.m.m.641.3		12
8.5	even	2		704.2.m.n.641.1		12
11.2	odd	10		3872.2.a.bo.1.5		6
11.4	even	5	inner	352.2.m.f.257.3	yes	12
11.9	even	5		3872.2.a.bn.1.5		6
44.15	odd	10		352.2.m.e.257.1	✓	12
44.31	odd	10		3872.2.a.bq.1.2		6
44.35	even	10		3872.2.a.bp.1.2		6
88.13	odd	10		7744.2.a.dw.1.2		6
88.35	even	10		7744.2.a.dt.1.5		6
88.37	even	10		704.2.m.n.257.1		12
88.53	even	10		7744.2.a.dv.1.2		6
88.59	odd	10		704.2.m.m.257.3		12
88.75	odd	10		7744.2.a.du.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.m.e.257.1	✓	12	44.15	odd	10
352.2.m.e.289.1	yes	12	4.3	odd	2
352.2.m.f.257.3	yes	12	11.4	even	5	inner
352.2.m.f.289.3	yes	12	1.1	even	1	trivial
704.2.m.m.257.3		12	88.59	odd	10
704.2.m.m.641.3		12	8.3	odd	2
704.2.m.n.257.1		12	88.37	even	10
704.2.m.n.641.1		12	8.5	even	2
3872.2.a.bn.1.5		6	11.9	even	5
3872.2.a.bo.1.5		6	11.2	odd	10
3872.2.a.bp.1.2		6	44.35	even	10
3872.2.a.bq.1.2		6	44.31	odd	10
7744.2.a.dt.1.5		6	88.35	even	10
7744.2.a.du.1.5		6	88.75	odd	10
7744.2.a.dv.1.2		6	88.53	even	10
7744.2.a.dw.1.2		6	88.13	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.289.3

Level	$352$
Weight	$2$
Character	352.289
Analytic conductor	$2.811$
Analytic rank	$0$
Dimension	$12$
Inner twists	$2$