LMFDB - Embedded newform 352.2.m.f.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(97,352)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.81073415115$
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			289.1
Root			$1.66582 + 1.21029i$ of defining polynomial
Character	$\chi$	$=$	352.289
Dual form			352.2.m.f.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.945302 - 2.90934i) q^{3} +(-2.43185 - 1.76684i) q^{5} +(0.483582 - 1.48831i) q^{7} +(-5.14361 + 3.73705i) q^{9} +(3.21473 - 0.815786i) q^{11} +(-2.95884 + 2.14973i) q^{13} +(-2.84151 + 8.74528i) q^{15} +(3.62100 + 2.63081i) q^{17} +(-0.848695 - 2.61201i) q^{19} -4.78714 q^{21} -4.77580 q^{23} +(1.24708 + 3.83811i) q^{25} +(8.31014 + 6.03767i) q^{27} +(1.53580 - 4.72671i) q^{29} +(0.394554 - 0.286660i) q^{31} +(-5.41229 - 8.58158i) q^{33} +(-3.80561 + 2.76494i) q^{35} +(-3.28946 + 10.1239i) q^{37} +(9.05128 + 6.57614i) q^{39} +(-3.87558 - 11.9278i) q^{41} -7.45745 q^{43} +19.1113 q^{45} +(-3.10162 - 9.54579i) q^{47} +(3.68190 + 2.67505i) q^{49} +(4.23099 - 13.0216i) q^{51} +(4.26078 - 3.09564i) q^{53} +(-9.25911 - 3.69605i) q^{55} +(-6.79696 + 4.93828i) q^{57} +(2.76079 - 8.49684i) q^{59} +(-1.75109 - 1.27224i) q^{61} +(3.07455 + 9.46248i) q^{63} +10.9937 q^{65} -0.709392 q^{67} +(4.51457 + 13.8944i) q^{69} +(0.654053 + 0.475198i) q^{71} +(-0.163185 + 0.502230i) q^{73} +(9.98751 - 7.25635i) q^{75} +(0.340441 - 5.17903i) q^{77} +(4.70380 - 3.41751i) q^{79} +(3.81598 - 11.7444i) q^{81} +(-5.73701 - 4.16818i) q^{83} +(-4.15750 - 12.7955i) q^{85} -15.2034 q^{87} +7.76282 q^{89} +(1.76862 + 5.44325i) q^{91} +(-1.20696 - 0.876911i) q^{93} +(-2.55112 + 7.85154i) q^{95} +(-2.93665 + 2.13360i) q^{97} +(-13.4867 + 16.2097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.945302	−	2.90934i	−0.545770	−	1.67971i	−0.719151	−	0.694854i	$-0.755469\pi$
$3$	−0.945302	−	2.90934i	−0.545770	−	1.67971i	0.173381	−	0.984855i	$-0.444531\pi$
$4$		0			0
$5$	−2.43185	−	1.76684i	−1.08756	−	0.790156i	−0.108572	−	0.994089i	$-0.534628\pi$
$5$	−2.43185	−	1.76684i	−1.08756	−	0.790156i	−0.978985	+	0.203933i	$0.934628\pi$
$6$		0			0
$7$	0.483582	−	1.48831i	0.182777	−	0.562529i	−0.817126	−	0.576459i	$-0.804434\pi$
$7$	0.483582	−	1.48831i	0.182777	−	0.562529i	0.999903	+	0.0139295i	$0.00443405\pi$
$8$		0			0
$9$	−5.14361	+	3.73705i	−1.71454	+	1.24568i
$10$		0			0
$11$	3.21473	−	0.815786i	0.969278	−	0.245969i
$11$	3.21473	−	0.815786i	0.969278	−	0.245969i
$12$		0			0
$13$	−2.95884	+	2.14973i	−0.820635	+	0.596226i	−0.916894	−	0.399130i	$-0.869312\pi$
$13$	−2.95884	+	2.14973i	−0.820635	+	0.596226i	0.0962591	+	0.995356i	$0.469312\pi$
$14$		0			0
$15$	−2.84151	+	8.74528i	−0.733676	+	2.25802i
$16$		0			0
$17$	3.62100	+	2.63081i	0.878222	+	0.638065i	0.932780	−	0.360445i	$-0.117375\pi$
$17$	3.62100	+	2.63081i	0.878222	+	0.638065i	−0.0545588	+	0.998511i	$0.517375\pi$
$18$		0			0
$19$	−0.848695	−	2.61201i	−0.194704	−	0.599237i	−0.999980	−	0.00633684i	$-0.997983\pi$
$19$	−0.848695	−	2.61201i	−0.194704	−	0.599237i	0.805276	−	0.592900i	$-0.202017\pi$
$20$		0			0
$21$	−4.78714			−1.04464
$22$		0			0
$23$	−4.77580			−0.995823			−0.497911	−	0.867228i	$-0.665899\pi$
$23$	−4.77580			−0.995823			−0.497911	+	0.867228i	$0.665899\pi$
$24$		0			0
$25$	1.24708	+	3.83811i	0.249416	+	0.767622i
$26$		0			0
$27$	8.31014	+	6.03767i	1.59929	+	1.16195i
$28$		0			0
$29$	1.53580	−	4.72671i	0.285191	−	0.877728i	−0.701150	−	0.713014i	$-0.747330\pi$
$29$	1.53580	−	4.72671i	0.285191	−	0.877728i	0.986341	−	0.164715i	$-0.0526703\pi$
$30$		0			0
$31$	0.394554	−	0.286660i	0.0708640	−	0.0514857i	−0.551789	−	0.833984i	$-0.686055\pi$
$31$	0.394554	−	0.286660i	0.0708640	−	0.0514857i	0.622653	+	0.782498i	$0.286055\pi$
$32$		0			0
$33$	−5.41229	−	8.58158i	−0.942159	−	1.49386i
$34$		0			0
$35$	−3.80561	+	2.76494i	−0.643266	+	0.467360i
$36$		0			0
$37$	−3.28946	+	10.1239i	−0.540784	+	1.66436i	0.190026	+	0.981779i	$0.439143\pi$
$37$	−3.28946	+	10.1239i	−0.540784	+	1.66436i	−0.730809	+	0.682581i	$0.760857\pi$
$38$		0			0
$39$	9.05128	+	6.57614i	1.44937	+	1.05303i
$40$		0			0
$41$	−3.87558	−	11.9278i	−0.605264	−	1.86281i	−0.494962	−	0.868914i	$-0.664818\pi$
$41$	−3.87558	−	11.9278i	−0.605264	−	1.86281i	−0.110302	−	0.993898i	$-0.535182\pi$
$42$		0			0
$43$	−7.45745			−1.13725			−0.568625	−	0.822597i	$-0.692524\pi$
$43$	−7.45745			−1.13725			−0.568625	+	0.822597i	$0.692524\pi$
$44$		0			0
$45$	19.1113			2.84894
$46$		0			0
$47$	−3.10162	−	9.54579i	−0.452417	−	1.39240i	−0.874141	−	0.485673i	$-0.838575\pi$
$47$	−3.10162	−	9.54579i	−0.452417	−	1.39240i	0.421724	−	0.906724i	$-0.361425\pi$
$48$		0			0
$49$	3.68190	+	2.67505i	0.525985	+	0.382150i
$50$		0			0
$51$	4.23099	−	13.0216i	0.592456	−	1.82339i
$52$		0			0
$53$	4.26078	−	3.09564i	0.585263	−	0.425218i	−0.255355	−	0.966847i	$-0.582192\pi$
$53$	4.26078	−	3.09564i	0.585263	−	0.425218i	0.840618	+	0.541629i	$0.182192\pi$
$54$		0			0
$55$	−9.25911	−	3.69605i	−1.24850	−	0.498376i
$56$		0			0
$57$	−6.79696	+	4.93828i	−0.900280	+	0.654091i
$58$		0			0
$59$	2.76079	−	8.49684i	0.359424	−	1.10619i	−0.593975	−	0.804483i	$-0.702442\pi$
$59$	2.76079	−	8.49684i	0.359424	−	1.10619i	0.953399	−	0.301711i	$-0.0975577\pi$
$60$		0			0
$61$	−1.75109	−	1.27224i	−0.224204	−	0.162894i	0.470013	−	0.882659i	$-0.344249\pi$
$61$	−1.75109	−	1.27224i	−0.224204	−	0.162894i	−0.694217	+	0.719766i	$0.744249\pi$
$62$		0			0
$63$	3.07455	+	9.46248i	0.387356	+	1.19216i
$64$		0			0
$65$	10.9937			1.36360
$66$		0			0
$67$	−0.709392			−0.0866661			−0.0433330	−	0.999061i	$-0.513798\pi$
$67$	−0.709392			−0.0866661			−0.0433330	+	0.999061i	$0.513798\pi$
$68$		0			0
$69$	4.51457	+	13.8944i	0.543490	+	1.67269i
$70$		0			0
$71$	0.654053	+	0.475198i	0.0776218	+	0.0563956i	0.625919	−	0.779888i	$-0.284724\pi$
$71$	0.654053	+	0.475198i	0.0776218	+	0.0563956i	−0.548298	+	0.836283i	$0.684724\pi$
$72$		0			0
$73$	−0.163185	+	0.502230i	−0.0190993	+	0.0587816i	−0.960152	−	0.279479i	$-0.909838\pi$
$73$	−0.163185	+	0.502230i	−0.0190993	+	0.0587816i	0.941053	+	0.338260i	$0.109838\pi$
$74$		0			0
$75$	9.98751	−	7.25635i	1.15326	−	0.837891i
$76$		0			0
$77$	0.340441	−	5.17903i	0.0387969	−	0.590205i
$78$		0			0
$79$	4.70380	−	3.41751i	0.529219	−	0.384500i	−0.290846	−	0.956770i	$-0.593937\pi$
$79$	4.70380	−	3.41751i	0.529219	−	0.384500i	0.820066	+	0.572269i	$0.193937\pi$
$80$		0			0
$81$	3.81598	−	11.7444i	0.423998	−	1.30493i
$82$		0			0
$83$	−5.73701	−	4.16818i	−0.629718	−	0.457517i	0.226584	−	0.973992i	$-0.427244\pi$
$83$	−5.73701	−	4.16818i	−0.629718	−	0.457517i	−0.856303	+	0.516474i	$0.827244\pi$
$84$		0			0
$85$	−4.15750	−	12.7955i	−0.450944	−	1.38786i
$86$		0			0
$87$	−15.2034			−1.62998
$88$		0			0
$89$	7.76282			0.822857			0.411429	−	0.911442i	$-0.365030\pi$
$89$	7.76282			0.822857			0.411429	+	0.911442i	$0.365030\pi$
$90$		0			0
$91$	1.76862	+	5.44325i	0.185402	+	0.570608i
$92$		0			0
$93$	−1.20696	−	0.876911i	−0.125156	−	0.0909315i
$94$		0			0
$95$	−2.55112	+	7.85154i	−0.261739	+	0.805551i
$96$		0			0
$97$	−2.93665	+	2.13360i	−0.298172	+	0.216634i	−0.726805	−	0.686844i	$-0.758995\pi$
$97$	−2.93665	+	2.13360i	−0.298172	+	0.216634i	0.428633	+	0.903479i	$0.358995\pi$
$98$		0			0
$99$	−13.4867	+	16.2097i	−1.35546	+	1.62914i
$100$		0			0
$101$	0.995345	−	0.723160i	0.0990405	−	0.0719571i	−0.537163	−	0.843479i	$-0.680504\pi$
$101$	0.995345	−	0.723160i	0.0990405	−	0.0719571i	0.636203	+	0.771521i	$0.280504\pi$
$102$		0			0
$103$	0.792654	−	2.43954i	0.0781025	−	0.240375i	−0.904380	−	0.426727i	$-0.859667\pi$
$103$	0.792654	−	2.43954i	0.0781025	−	0.240375i	0.982483	+	0.186352i	$0.0596665\pi$
$104$		0			0
$105$	11.6416	+	8.45812i	1.13610	+	0.825428i
$106$		0			0
$107$	4.22154	+	12.9926i	0.408112	+	1.25604i	0.918269	+	0.395957i	$0.129587\pi$
$107$	4.22154	+	12.9926i	0.408112	+	1.25604i	−0.510157	+	0.860081i	$0.670413\pi$
$108$		0			0
$109$	0.935861			0.0896393			0.0448196	−	0.998995i	$-0.485729\pi$
$109$	0.935861			0.0896393			0.0448196	+	0.998995i	$0.485729\pi$
$110$		0			0
$111$	32.5634			3.09078
$112$		0			0
$113$	−0.992485	−	3.05455i	−0.0933651	−	0.287348i	0.893459	−	0.449145i	$-0.148271\pi$
$113$	−0.992485	−	3.05455i	−0.0933651	−	0.287348i	−0.986824	+	0.161796i	$0.948271\pi$
$114$		0			0
$115$	11.6140	+	8.43808i	1.08301	+	0.786855i
$116$		0			0
$117$	7.18551	−	22.1147i	0.664300	−	2.04451i
$118$		0			0
$119$	5.66652	−	4.11697i	0.519449	−	0.377402i
$120$		0			0
$121$	9.66899	−	5.24507i	0.878999	−	0.476824i
$122$		0			0
$123$	−31.0385	+	22.5508i	−2.79865	+	2.03334i
$124$		0			0
$125$	−0.895788	+	2.75695i	−0.0801217	+	0.246589i
$126$		0			0
$127$	8.21981	+	5.97204i	0.729391	+	0.529933i	0.889371	−	0.457187i	$-0.151143\pi$
$127$	8.21981	+	5.97204i	0.729391	+	0.529933i	−0.159980	+	0.987120i	$0.551143\pi$
$128$		0			0
$129$	7.04954	+	21.6963i	0.620677	+	1.91025i
$130$		0			0
$131$	3.01348			0.263289			0.131644	−	0.991297i	$-0.457974\pi$
$131$	3.01348			0.263289			0.131644	+	0.991297i	$0.457974\pi$
$132$		0			0
$133$	−4.29791			−0.372676
$134$		0			0
$135$	−9.54140	−	29.3654i	−0.821193	−	2.52737i
$136$		0			0
$137$	−0.839676	−	0.610060i	−0.0717383	−	0.0521209i	0.551338	−	0.834282i	$-0.314117\pi$
$137$	−0.839676	−	0.610060i	−0.0717383	−	0.0521209i	−0.623076	+	0.782161i	$0.714117\pi$
$138$		0			0
$139$	0.906933	−	2.79125i	0.0769250	−	0.236751i	−0.905198	−	0.424989i	$-0.860278\pi$
$139$	0.906933	−	2.79125i	0.0769250	−	0.236751i	0.982123	+	0.188239i	$0.0602778\pi$
$140$		0			0
$141$	−24.8400	+	18.0473i	−2.09191	+	1.51986i
$142$		0			0
$143$	−7.75817	+	9.32457i	−0.648770	+	0.779760i
$144$		0			0
$145$	−12.0862	+	8.78114i	−1.00370	+	0.729234i
$146$		0			0
$147$	4.30214	−	13.2406i	0.354834	−	1.09207i
$148$		0			0
$149$	−9.95118	−	7.22996i	−0.815233	−	0.592301i	0.100110	−	0.994976i	$-0.468080\pi$
$149$	−9.95118	−	7.22996i	−0.815233	−	0.592301i	−0.915343	+	0.402675i	$0.868080\pi$
$150$		0			0
$151$	−6.23702	−	19.1956i	−0.507561	−	1.56211i	−0.796422	−	0.604741i	$-0.793276\pi$
$151$	−6.23702	−	19.1956i	−0.507561	−	1.56211i	0.288861	−	0.957371i	$-0.406724\pi$
$152$		0			0
$153$	−28.4565			−2.30057
$154$		0			0
$155$	−1.46598			−0.117750
$156$		0			0
$157$	−4.08041	−	12.5582i	−0.325652	−	1.00226i	−0.971145	−	0.238489i	$-0.923348\pi$
$157$	−4.08041	−	12.5582i	−0.325652	−	1.00226i	0.645493	−	0.763766i	$-0.276652\pi$
$158$		0			0
$159$	−13.0340	−	9.46974i	−1.03366	−	0.750999i
$160$		0			0
$161$	−2.30949	+	7.10788i	−0.182013	+	0.560179i
$162$		0			0
$163$	−2.84035	+	2.06364i	−0.222474	+	0.161637i	−0.693439	−	0.720515i	$-0.743906\pi$
$163$	−2.84035	+	2.06364i	−0.222474	+	0.161637i	0.470966	+	0.882151i	$0.343906\pi$
$164$		0			0
$165$	−2.00042	+	30.4318i	−0.155733	+	2.36911i
$166$		0			0
$167$	8.09764	−	5.88328i	0.626614	−	0.455262i	−0.228612	−	0.973518i	$-0.573419\pi$
$167$	8.09764	−	5.88328i	0.626614	−	0.455262i	0.855225	+	0.518256i	$0.173419\pi$
$168$		0			0
$169$	0.116211	−	0.357661i	0.00893933	−	0.0275124i
$170$		0			0
$171$	14.1266	+	10.2636i	1.08029	+	0.784875i
$172$		0			0
$173$	−0.775536	−	2.38686i	−0.0589629	−	0.181469i	0.917237	−	0.398342i	$-0.130414\pi$
$173$	−0.775536	−	2.38686i	−0.0589629	−	0.181469i	−0.976200	+	0.216873i	$0.930414\pi$
$174$		0			0
$175$	6.31538			0.477398
$176$		0			0
$177$	−27.3300			−2.05425
$178$		0			0
$179$	−5.19007	−	15.9734i	−0.387924	−	1.19391i	−0.934337	−	0.356392i	$-0.884007\pi$
$179$	−5.19007	−	15.9734i	−0.387924	−	1.19391i	0.546412	−	0.837516i	$-0.315993\pi$
$180$		0			0
$181$	4.80422	+	3.49047i	0.357095	+	0.259444i	0.751839	−	0.659346i	$-0.229167\pi$
$181$	4.80422	+	3.49047i	0.357095	+	0.259444i	−0.394745	+	0.918791i	$0.629167\pi$
$182$		0			0
$183$	−2.04607	+	6.29716i	−0.151250	+	0.465500i
$184$		0			0
$185$	25.8868	−	18.8079i	1.90324	−	1.38278i
$186$		0			0
$187$	13.7867	+	5.50339i	1.00818	+	0.402447i
$188$		0			0
$189$	13.0046	−	9.44838i	0.945943	−	0.687268i
$190$		0			0
$191$	−2.14500	+	6.60162i	−0.155207	+	0.477677i	−0.998182	−	0.0602757i	$-0.980802\pi$
$191$	−2.14500	+	6.60162i	−0.155207	+	0.477677i	0.842975	+	0.537952i	$0.180802\pi$
$192$		0			0
$193$	−2.96054	−	2.15096i	−0.213104	−	0.154829i	0.476113	−	0.879384i	$-0.342045\pi$
$193$	−2.96054	−	2.15096i	−0.213104	−	0.154829i	−0.689217	+	0.724555i	$0.742045\pi$
$194$		0			0
$195$	−10.3924	−	31.9844i	−0.744212	−	2.29045i
$196$		0			0
$197$	17.5687			1.25172			0.625859	−	0.779936i	$-0.284749\pi$
$197$	17.5687			1.25172			0.625859	+	0.779936i	$0.284749\pi$
$198$		0			0
$199$	−7.12699			−0.505219			−0.252609	−	0.967568i	$-0.581289\pi$
$199$	−7.12699			−0.505219			−0.252609	+	0.967568i	$0.581289\pi$
$200$		0			0
$201$	0.670590	+	2.06386i	0.0472998	+	0.145574i
$202$		0			0
$203$	−6.29214	−	4.57151i	−0.441622	−	0.320857i
$204$		0			0
$205$	−11.6497	+	35.8542i	−0.813653	+	2.50417i
$206$		0			0
$207$	24.5649	−	17.8474i	1.70738	−	1.24048i
$208$		0			0
$209$	−4.85917	−	7.70457i	−0.336116	−	0.532936i
$210$		0			0
$211$	−16.5962	+	12.0578i	−1.14253	+	0.830096i	−0.987470	−	0.157810i	$-0.949557\pi$
$211$	−16.5962	+	12.0578i	−1.14253	+	0.830096i	−0.155059	+	0.987905i	$0.549557\pi$
$212$		0			0
$213$	0.764234	−	2.35207i	0.0523644	−	0.161161i
$214$		0			0
$215$	18.1354	+	13.1761i	1.23682	+	0.898605i
$216$		0			0
$217$	−0.235841	−	0.725844i	−0.0160099	−	0.0492735i
$218$		0			0
$219$	1.61542			0.109160
$220$		0			0
$221$	−16.3695			−1.10113
$222$		0			0
$223$	−1.92982	−	5.93937i	−0.129230	−	0.397730i	0.865418	−	0.501051i	$-0.167053\pi$
$223$	−1.92982	−	5.93937i	−0.129230	−	0.397730i	−0.994648	+	0.103321i	$0.967053\pi$
$224$		0			0
$225$	−20.7577	−	15.0814i	−1.38385	−	1.00542i
$226$		0			0
$227$	−4.86911	+	14.9856i	−0.323174	+	0.994628i	0.649084	+	0.760717i	$0.275152\pi$
$227$	−4.86911	+	14.9856i	−0.323174	+	0.994628i	−0.972258	+	0.233911i	$0.924848\pi$
$228$		0			0
$229$	13.5330	−	9.83230i	0.894286	−	0.649737i	−0.0427060	−	0.999088i	$-0.513598\pi$
$229$	13.5330	−	9.83230i	0.894286	−	0.649737i	0.936992	+	0.349351i	$0.113598\pi$
$230$		0			0
$231$	−15.3894	+	3.90528i	−1.01255	+	0.256949i
$232$		0			0
$233$	9.48338	−	6.89008i	0.621277	−	0.451384i	−0.232090	−	0.972694i	$-0.574557\pi$
$233$	9.48338	−	6.89008i	0.621277	−	0.451384i	0.853367	+	0.521310i	$0.174557\pi$
$234$		0			0
$235$	−9.32325	+	28.6940i	−0.608182	+	1.87179i
$236$		0			0
$237$	−14.3892	−	10.4544i	−0.934681	−	0.679085i
$238$		0			0
$239$	7.83369	+	24.1096i	0.506719	+	1.55952i	0.797861	+	0.602841i	$0.205965\pi$
$239$	7.83369	+	24.1096i	0.506719	+	1.55952i	−0.291142	+	0.956680i	$0.594035\pi$
$240$		0			0
$241$	1.25667			0.0809490			0.0404745	−	0.999181i	$-0.487113\pi$
$241$	1.25667			0.0809490			0.0404745	+	0.999181i	$0.487113\pi$
$242$		0			0
$243$	−6.96000			−0.446484
$244$		0			0
$245$	−4.22742	−	13.0107i	−0.270080	−	0.831221i
$246$		0			0
$247$	8.12626	+	5.90408i	0.517062	+	0.375667i
$248$		0			0
$249$	−6.70345	+	20.6311i	−0.424814	+	1.30744i
$250$		0			0
$251$	18.6517	−	13.5513i	1.17729	−	0.855349i	0.185424	−	0.982659i	$-0.440634\pi$
$251$	18.6517	−	13.5513i	1.17729	−	0.855349i	0.991863	+	0.127309i	$0.0406340\pi$
$252$		0			0
$253$	−15.3529	+	3.89603i	−0.965229	+	0.244941i
$254$		0			0
$255$	−33.2963	+	24.1912i	−2.08510	+	1.51491i
$256$		0			0
$257$	−1.66741	+	5.13176i	−0.104010	+	0.320111i	−0.989497	−	0.144554i	$-0.953825\pi$
$257$	−1.66741	+	5.13176i	−0.104010	+	0.320111i	0.885487	+	0.464665i	$0.153825\pi$
$258$		0			0
$259$	13.4768	+	9.79149i	0.837409	+	0.608413i
$260$		0			0
$261$	9.76441	+	30.0518i	0.604402	+	1.86016i
$262$		0			0
$263$	16.3375			1.00742			0.503708	−	0.863874i	$-0.331969\pi$
$263$	16.3375			1.00742			0.503708	+	0.863874i	$0.331969\pi$
$264$		0			0
$265$	−15.8311			−0.972495
$266$		0			0
$267$	−7.33821	−	22.5847i	−0.449091	−	1.38216i
$268$		0			0
$269$	22.3600	+	16.2455i	1.36331	+	0.990503i	0.998227	+	0.0595289i	$0.0189599\pi$
$269$	22.3600	+	16.2455i	1.36331	+	0.990503i	0.365084	+	0.930974i	$0.381040\pi$
$270$		0			0
$271$	9.23475	−	28.4216i	0.560971	−	1.72649i	−0.118658	−	0.992935i	$-0.537859\pi$
$271$	9.23475	−	28.4216i	0.560971	−	1.72649i	0.679629	−	0.733556i	$-0.262141\pi$
$272$		0			0
$273$	14.1644	−	10.2910i	0.857268	−	0.622842i
$274$		0			0
$275$	7.14010	+	11.3211i	0.430564	+	0.682691i
$276$		0			0
$277$	19.3993	−	14.0944i	1.16559	−	0.846852i	0.175117	−	0.984548i	$-0.443970\pi$
$277$	19.3993	−	14.0944i	1.16559	−	0.846852i	0.990475	+	0.137696i	$0.0439696\pi$
$278$		0			0
$279$	−0.958169	+	2.94894i	−0.0573641	+	0.176548i
$280$		0			0
$281$	−9.29029	−	6.74979i	−0.554212	−	0.402659i	0.275124	−	0.961409i	$-0.411281\pi$
$281$	−9.29029	−	6.74979i	−0.554212	−	0.402659i	−0.829336	+	0.558750i	$0.811281\pi$
$282$		0			0
$283$	5.07083	+	15.6064i	0.301430	+	0.927706i	0.980985	+	0.194082i	$0.0621726\pi$
$283$	5.07083	+	15.6064i	0.301430	+	0.927706i	−0.679556	+	0.733624i	$0.737827\pi$
$284$		0			0
$285$	25.2544			1.49594
$286$		0			0
$287$	−19.6265			−1.15852
$288$		0			0
$289$	0.937189	+	2.88437i	0.0551288	+	0.169669i
$290$		0			0
$291$	8.98339	+	6.52682i	0.526616	+	0.382609i
$292$		0			0
$293$	5.19334	−	15.9835i	0.303398	−	0.933764i	−0.676872	−	0.736101i	$-0.736665\pi$
$293$	5.19334	−	15.9835i	0.303398	−	0.933764i	0.980270	−	0.197663i	$-0.0633352\pi$
$294$		0			0
$295$	−21.7264	+	15.7852i	−1.26496	+	0.919048i
$296$		0			0
$297$	31.6403	+	12.6302i	1.83596	+	0.732877i
$298$		0			0
$299$	14.1308	−	10.2667i	0.817207	−	0.593736i
$300$		0			0
$301$	−3.60629	+	11.0990i	−0.207863	+	0.639737i
$302$		0			0
$303$	−3.04482	−	2.21219i	−0.174920	−	0.127087i
$304$		0			0
$305$	2.01054	+	6.18780i	0.115123	+	0.354312i
$306$		0			0
$307$	−12.3071			−0.702403			−0.351201	−	0.936300i	$-0.614227\pi$
$307$	−12.3071			−0.702403			−0.351201	+	0.936300i	$0.614227\pi$
$308$		0			0
$309$	−7.84675			−0.446386
$310$		0			0
$311$	5.12870	+	15.7845i	0.290822	+	0.895057i	0.984593	+	0.174862i	$0.0559479\pi$
$311$	5.12870	+	15.7845i	0.290822	+	0.895057i	−0.693771	+	0.720195i	$0.744052\pi$
$312$		0			0
$313$	18.4719	+	13.4206i	1.04410	+	0.758580i	0.971081	−	0.238751i	$-0.0767380\pi$
$313$	18.4719	+	13.4206i	1.04410	+	0.758580i	0.0730148	+	0.997331i	$0.476738\pi$
$314$		0			0
$315$	9.24188	−	28.4436i	0.520721	−	1.60261i
$316$		0			0
$317$	3.85676	−	2.80210i	0.216617	−	0.157382i	−0.474185	−	0.880425i	$-0.657257\pi$
$317$	3.85676	−	2.80210i	0.216617	−	0.157382i	0.690803	+	0.723043i	$0.257257\pi$
$318$		0			0
$319$	1.08120	−	16.4480i	0.0605357	−	0.920911i
$320$		0			0
$321$	33.8091	−	24.5638i	1.88704	−	1.37102i
$322$		0			0
$323$	3.79859	−	11.6909i	0.211359	−	0.650497i
$324$		0			0
$325$	−11.9408	−	8.67550i	−0.662356	−	0.481230i
$326$		0			0
$327$	−0.884672	−	2.72274i	−0.0489224	−	0.150568i
$328$		0			0
$329$	−15.7070			−0.865956
$330$		0			0
$331$	32.4925			1.78595			0.892976	−	0.450105i	$-0.148613\pi$
$331$	32.4925			1.78595			0.892976	+	0.450105i	$0.148613\pi$
$332$		0			0
$333$	−20.9139	−	64.3664i	−1.14607	−	3.52726i
$334$		0			0
$335$	1.72514	+	1.25338i	0.0942542	+	0.0684797i
$336$		0			0
$337$	−2.93504	+	9.03312i	−0.159882	+	0.492066i	−0.998623	−	0.0524650i	$-0.983292\pi$
$337$	−2.93504	+	9.03312i	−0.159882	+	0.492066i	0.838741	+	0.544531i	$0.183292\pi$
$338$		0			0
$339$	−7.94854	+	5.77495i	−0.431705	+	0.313652i
$340$		0			0
$341$	1.03453	−	1.24341i	0.0560230	−	0.0673343i
$342$		0			0
$343$	14.6241	−	10.6250i	0.789625	−	0.573696i
$344$		0			0
$345$	13.5705	−	41.7657i	0.730611	−	2.24859i
$346$		0			0
$347$	−28.9950	−	21.0661i	−1.55653	−	1.13089i	−0.938783	−	0.344510i	$-0.888045\pi$
$347$	−28.9950	−	21.0661i	−1.55653	−	1.13089i	−0.617749	−	0.786376i	$-0.711955\pi$
$348$		0			0
$349$	8.03407	+	24.7263i	0.430054	+	1.32357i	0.898071	+	0.439851i	$0.144969\pi$
$349$	8.03407	+	24.7263i	0.430054	+	1.32357i	−0.468017	+	0.883720i	$0.655031\pi$
$350$		0			0
$351$	−37.5677			−2.00522
$352$		0			0
$353$	−16.3264			−0.868969			−0.434484	−	0.900679i	$-0.643069\pi$
$353$	−16.3264			−0.868969			−0.434484	+	0.900679i	$0.643069\pi$
$354$		0			0
$355$	−0.750960	−	2.31122i	−0.0398568	−	0.122667i
$356$		0			0
$357$	−17.3342	−	12.5941i	−0.917425	−	0.666548i
$358$		0			0
$359$	2.38640	−	7.34459i	0.125949	−	0.387633i	−0.868123	−	0.496348i	$-0.834674\pi$
$359$	2.38640	−	7.34459i	0.125949	−	0.387633i	0.994073	+	0.108716i	$0.0346739\pi$
$360$		0			0
$361$	9.26899	−	6.73432i	0.487842	−	0.354438i
$362$		0			0
$363$	−24.3998	−	23.1722i	−1.28066	−	1.21623i
$364$		0			0
$365$	1.28420	−	0.933028i	0.0672182	−	0.0488369i
$366$		0			0
$367$	1.92708	−	5.93094i	0.100593	−	0.309592i	−0.888078	−	0.459692i	$-0.847960\pi$
$367$	1.92708	−	5.93094i	0.100593	−	0.309592i	0.988671	+	0.150100i	$0.0479596\pi$
$368$		0			0
$369$	64.5094	+	46.8688i	3.35823	+	2.43989i
$370$		0			0
$371$	−2.54684	−	7.83836i	−0.132225	−	0.406948i
$372$		0			0
$373$	4.84081			0.250648			0.125324	−	0.992116i	$-0.460003\pi$
$373$	4.84081			0.250648			0.125324	+	0.992116i	$0.460003\pi$
$374$		0			0
$375$	8.86770			0.457926
$376$		0			0
$377$	5.61694	+	17.2871i	0.289287	+	0.890333i
$378$		0			0
$379$	11.0664	+	8.04021i	0.568443	+	0.412998i	0.834539	−	0.550949i	$-0.185734\pi$
$379$	11.0664	+	8.04021i	0.568443	+	0.412998i	−0.266096	+	0.963946i	$0.585734\pi$
$380$		0			0
$381$	9.60450	−	29.5596i	0.492054	−	1.51439i
$382$		0			0
$383$	9.30686	−	6.76183i	0.475558	−	0.345513i	−0.324045	−	0.946042i	$-0.605043\pi$
$383$	9.30686	−	6.76183i	0.475558	−	0.345513i	0.799604	+	0.600528i	$0.205043\pi$
$384$		0			0
$385$	−9.97843	+	11.9931i	−0.508548	+	0.611225i
$386$		0			0
$387$	38.3582	−	27.8689i	1.94986	−	1.41666i
$388$		0			0
$389$	2.87359	−	8.84400i	0.145697	−	0.448408i	−0.851403	−	0.524512i	$-0.824248\pi$
$389$	2.87359	−	8.84400i	0.145697	−	0.448408i	0.997100	+	0.0761033i	$0.0242479\pi$
$390$		0			0
$391$	−17.2932	−	12.5642i	−0.874553	−	0.635400i
$392$		0			0
$393$	−2.84865	−	8.76723i	−0.143695	−	0.442248i
$394$		0			0
$395$	−17.4772			−0.879371
$396$		0			0
$397$	38.3379			1.92413			0.962063	−	0.272828i	$-0.0879589\pi$
$397$	38.3379			1.92413			0.962063	+	0.272828i	$0.0879589\pi$
$398$		0			0
$399$	4.06282	+	12.5041i	0.203395	+	0.625987i
$400$		0			0
$401$	−14.0065	−	10.1763i	−0.699453	−	0.508182i	0.180301	−	0.983611i	$-0.442293\pi$
$401$	−14.0065	−	10.1763i	−0.699453	−	0.508182i	−0.879754	+	0.475429i	$0.842293\pi$
$402$		0			0
$403$	−0.551182	+	1.69637i	−0.0274564	+	0.0845020i
$404$		0			0
$405$	−30.0304	+	21.8184i	−1.49222	+	1.08416i
$406$		0			0
$407$	−2.31577	+	35.2291i	−0.114789	+	1.74624i
$408$		0			0
$409$	−2.17834	+	1.58266i	−0.107712	+	0.0782573i	−0.640337	−	0.768094i	$-0.721205\pi$
$409$	−2.17834	+	1.58266i	−0.107712	+	0.0782573i	0.532625	+	0.846351i	$0.321205\pi$
$410$		0			0
$411$	−0.981125	+	3.01959i	−0.0483953	+	0.148946i
$412$		0			0
$413$	−11.3109	−	8.21784i	−0.556572	−	0.404374i
$414$		0			0
$415$	6.58702	+	20.2728i	0.323344	+	0.995152i
$416$		0			0
$417$	−8.97803			−0.439656
$418$		0			0
$419$	−13.3425			−0.651824			−0.325912	−	0.945400i	$-0.605671\pi$
$419$	−13.3425			−0.651824			−0.325912	+	0.945400i	$0.605671\pi$
$420$		0			0
$421$	6.54615	+	20.1470i	0.319040	+	0.981903i	0.974060	+	0.226291i	$0.0726602\pi$
$421$	6.54615	+	20.1470i	0.319040	+	0.981903i	−0.655020	+	0.755612i	$0.727340\pi$
$422$		0			0
$423$	51.6267	+	37.5090i	2.51017	+	1.82375i
$424$		0			0
$425$	−5.58168	+	17.1786i	−0.270751	+	0.833286i
$426$		0			0
$427$	−2.74029	+	1.99094i	−0.132612	+	0.0963481i
$428$		0			0
$429$	34.4622	+	13.7566i	1.66385	+	0.664175i
$430$		0			0
$431$	−14.0809	+	10.2304i	−0.678253	+	0.492780i	−0.872778	−	0.488118i	$-0.837684\pi$
$431$	−14.0809	+	10.2304i	−0.678253	+	0.492780i	0.194524	+	0.980898i	$0.437684\pi$
$432$		0			0
$433$	1.27401	−	3.92101i	0.0612252	−	0.188432i	−0.915766	−	0.401713i	$-0.868415\pi$
$433$	1.27401	−	3.92101i	0.0612252	−	0.188432i	0.976991	+	0.213281i	$0.0684150\pi$
$434$		0			0
$435$	36.9724	+	26.8620i	1.77269	+	1.28794i
$436$		0			0
$437$	4.05319	+	12.4744i	0.193891	+	0.596734i
$438$		0			0
$439$	−30.8478			−1.47229			−0.736143	−	0.676826i	$-0.763355\pi$
$439$	−30.8478			−1.47229			−0.736143	+	0.676826i	$0.763355\pi$
$440$		0			0
$441$	−28.9351			−1.37786
$442$		0			0
$443$	−2.89223	−	8.90137i	−0.137414	−	0.422917i	0.858544	−	0.512740i	$-0.171370\pi$
$443$	−2.89223	−	8.90137i	−0.137414	−	0.422917i	−0.995958	+	0.0898236i	$0.971370\pi$
$444$		0			0
$445$	−18.8780	−	13.7157i	−0.894904	−	0.650186i
$446$		0			0
$447$	−11.6275	+	35.7859i	−0.549964	+	1.69261i
$448$		0			0
$449$	2.98291	−	2.16721i	0.140772	−	0.102277i	−0.515170	−	0.857088i	$-0.672271\pi$
$449$	2.98291	−	2.16721i	0.140772	−	0.102277i	0.655943	+	0.754811i	$0.272271\pi$
$450$		0			0
$451$	−22.1895	−	35.1831i	−1.04486	−	1.65671i
$452$		0			0
$453$	−49.9506	+	36.2912i	−2.34688	+	1.70511i
$454$		0			0
$455$	5.31635	−	16.3621i	0.249234	−	0.767065i
$456$		0			0
$457$	−26.0090	−	18.8966i	−1.21665	−	0.883946i	−0.220830	−	0.975312i	$-0.570877\pi$
$457$	−26.0090	−	18.8966i	−1.21665	−	0.883946i	−0.995817	+	0.0913659i	$0.970877\pi$
$458$		0			0
$459$	14.2070	+	43.7248i	0.663128	+	2.04090i
$460$		0			0
$461$	−3.41140			−0.158885			−0.0794423	−	0.996839i	$-0.525314\pi$
$461$	−3.41140			−0.158885			−0.0794423	+	0.996839i	$0.525314\pi$
$462$		0			0
$463$	−3.72640			−0.173181			−0.0865903	−	0.996244i	$-0.527597\pi$
$463$	−3.72640			−0.173181			−0.0865903	+	0.996244i	$0.527597\pi$
$464$		0			0
$465$	1.38579	+	4.26503i	0.0642646	+	0.197786i
$466$		0			0
$467$	−1.56111	−	1.13421i	−0.0722394	−	0.0524850i	0.551079	−	0.834453i	$-0.314216\pi$
$467$	−1.56111	−	1.13421i	−0.0722394	−	0.0524850i	−0.623319	+	0.781968i	$0.714216\pi$
$468$		0			0
$469$	−0.343049	+	1.05580i	−0.0158406	+	0.0487522i
$470$		0			0
$471$	−32.6789	+	23.7426i	−1.50576	+	1.09400i
$472$		0			0
$473$	−23.9737	+	6.08368i	−1.10231	+	0.279728i
$474$		0			0
$475$	8.96681	−	6.51477i	0.411426	−	0.298918i
$476$		0			0
$477$	−10.3472	+	31.8455i	−0.473767	+	1.45811i
$478$		0			0
$479$	−22.8844	−	16.6265i	−1.04562	−	0.759685i	−0.0742424	−	0.997240i	$-0.523654\pi$
$479$	−22.8844	−	16.6265i	−1.04562	−	0.759685i	−0.971374	+	0.237555i	$0.923654\pi$
$480$		0			0
$481$	−12.0306	−	37.0265i	−0.548550	−	1.68826i
$482$		0			0
$483$	22.8624			1.04028
$484$		0			0
$485$	10.9112			0.495453
$486$		0			0
$487$	3.60225	+	11.0866i	0.163234	+	0.502382i	0.998902	−	0.0468530i	$-0.0149192\pi$
$487$	3.60225	+	11.0866i	0.163234	+	0.502382i	−0.835668	+	0.549235i	$0.814919\pi$
$488$		0			0
$489$	8.68882	+	6.31279i	0.392922	+	0.285474i
$490$		0			0
$491$	−5.74067	+	17.6680i	−0.259073	+	0.797344i	0.733927	+	0.679228i	$0.237685\pi$
$491$	−5.74067	+	17.6680i	−0.259073	+	0.797344i	−0.993000	+	0.118116i	$0.962315\pi$
$492$		0			0
$493$	17.9962	−	13.0750i	0.810509	−	0.588869i
$494$		0			0
$495$	61.4377	−	15.5907i	2.76142	−	0.700751i
$496$		0			0
$497$	1.02353	−	0.743639i	0.0459117	−	0.0333568i
$498$		0			0
$499$	−1.14606	+	3.52720i	−0.0513045	+	0.157899i	−0.973426	−	0.229001i	$-0.926454\pi$
$499$	−1.14606	+	3.52720i	−0.0513045	+	0.157899i	0.922122	+	0.386900i	$0.126454\pi$
$500$		0			0
$501$	−24.7712	−	17.9973i	−1.10669	−	0.804060i
$502$		0			0
$503$	−9.60505	−	29.5613i	−0.428268	−	1.31807i	−0.899830	−	0.436240i	$-0.856310\pi$
$503$	−9.60505	−	29.5613i	−0.428268	−	1.31807i	0.471562	−	0.881833i	$-0.343690\pi$
$504$		0			0
$505$	−3.69824			−0.164570
$506$		0			0
$507$	−1.15041			−0.0510917
$508$		0			0
$509$	12.0394	+	37.0535i	0.533637	+	1.64237i	0.746575	+	0.665301i	$0.231697\pi$
$509$	12.0394	+	37.0535i	0.533637	+	1.64237i	−0.212938	+	0.977066i	$0.568303\pi$
$510$		0			0
$511$	0.668563	+	0.485739i	0.0295755	+	0.0214878i
$512$		0			0
$513$	8.71770	−	26.8303i	0.384896	−	1.18459i
$514$		0			0
$515$	−6.23790	+	4.53210i	−0.274875	+	0.199708i
$516$		0			0
$517$	−17.7582	−	28.1569i	−0.781004	−	1.23834i
$518$		0			0
$519$	−6.21106	+	4.51260i	−0.272635	+	0.198081i
$520$		0			0
$521$	−3.59202	+	11.0551i	−0.157369	+	0.484333i	−0.998393	−	0.0566650i	$-0.981953\pi$
$521$	−3.59202	+	11.0551i	−0.157369	+	0.484333i	0.841024	+	0.540998i	$0.181953\pi$
$522$		0			0
$523$	−14.3623	−	10.4348i	−0.628019	−	0.456283i	0.227694	−	0.973733i	$-0.426881\pi$
$523$	−14.3623	−	10.4348i	−0.628019	−	0.456283i	−0.855713	+	0.517450i	$0.826881\pi$
$524$		0			0
$525$	−5.96994	−	18.3736i	−0.260550	−	0.801889i
$526$		0			0
$527$	2.18283			0.0950855
$528$		0			0
$529$	−0.191763			−0.00833752
$530$		0			0
$531$	17.5527	+	54.0217i	0.761723	+	2.34434i
$532$		0			0
$533$	37.1088	+	26.9611i	1.60736	+	1.16781i
$534$		0			0
$535$	12.6897	−	39.0548i	0.548622	−	1.68848i
$536$		0			0
$537$	−41.5659	+	30.1994i	−1.79370	+	1.30320i
$538$		0			0
$539$	14.0186	+	5.59594i	0.603823	+	0.241034i
$540$		0			0
$541$	19.6289	−	14.2613i	0.843914	−	0.613139i	−0.0795476	−	0.996831i	$-0.525348\pi$
$541$	19.6289	−	14.2613i	0.843914	−	0.613139i	0.923461	+	0.383692i	$0.125348\pi$
$542$		0			0
$543$	5.61352	−	17.2767i	0.240899	−	0.741412i
$544$		0			0
$545$	−2.27587	−	1.65352i	−0.0974878	−	0.0708290i
$546$		0			0
$547$	2.56209	+	7.88530i	0.109547	+	0.337151i	0.990771	−	0.135548i	$-0.0432796\pi$
$547$	2.56209	+	7.88530i	0.109547	+	0.337151i	−0.881224	+	0.472700i	$0.843280\pi$
$548$		0			0
$549$	13.7614			0.587320
$550$		0			0
$551$	−13.6497			−0.581495
$552$		0			0
$553$	−2.81165	−	8.65338i	−0.119564	−	0.367979i
$554$		0			0
$555$	−79.1894	−	57.5345i	−3.36140	−	2.44220i
$556$		0			0
$557$	−12.9681	+	39.9116i	−0.549474	+	1.69111i	0.160633	+	0.987014i	$0.448646\pi$
$557$	−12.9681	+	39.9116i	−0.549474	+	1.69111i	−0.710107	+	0.704094i	$0.751354\pi$
$558$		0			0
$559$	22.0654	−	16.0315i	0.933268	−	0.678059i
$560$		0			0
$561$	2.97861	−	45.3126i	0.125757	−	1.91310i
$562$		0			0
$563$	27.4232	−	19.9241i	1.15575	−	0.839701i	0.166515	−	0.986039i	$-0.446749\pi$
$563$	27.4232	−	19.9241i	1.15575	−	0.839701i	0.989235	+	0.146338i	$0.0467486\pi$
$564$		0			0
$565$	−2.98334	+	9.18178i	−0.125510	+	0.386280i
$566$		0			0
$567$	−15.6340	−	11.3588i	−0.656566	−	0.477023i
$568$		0			0
$569$	−5.34770	−	16.4585i	−0.224187	−	0.689977i	−0.998373	−	0.0570187i	$-0.981841\pi$
$569$	−5.34770	−	16.4585i	−0.224187	−	0.689977i	0.774186	−	0.632958i	$-0.218159\pi$
$570$		0			0
$571$	−15.8559			−0.663551			−0.331775	−	0.943358i	$-0.607648\pi$
$571$	−15.8559			−0.663551			−0.331775	+	0.943358i	$0.607648\pi$
$572$		0			0
$573$	21.2340			0.887065
$574$		0			0
$575$	−5.95579	−	18.3300i	−0.248374	−	0.764416i
$576$		0			0
$577$	23.3438	+	16.9603i	0.971816	+	0.706066i	0.955865	−	0.293807i	$-0.0949224\pi$
$577$	23.3438	+	16.9603i	0.971816	+	0.706066i	0.0159512	+	0.999873i	$0.494922\pi$
$578$		0			0
$579$	−3.45927	+	10.6465i	−0.143762	+	0.442455i
$580$		0			0
$581$	−8.97787	+	6.52280i	−0.372465	+	0.270612i
$582$		0			0
$583$	11.1719	−	13.4275i	0.462692	−	0.556111i
$584$		0			0
$585$	−56.5473	+	41.0840i	−2.33794	+	1.69862i
$586$		0			0
$587$	−8.44600	+	25.9941i	−0.348604	+	1.07289i	0.611022	+	0.791613i	$0.290759\pi$
$587$	−8.44600	+	25.9941i	−0.348604	+	1.07289i	−0.959626	+	0.281279i	$0.909241\pi$
$588$		0			0
$589$	−1.08362	−	0.787293i	−0.0446496	−	0.0324398i
$590$		0			0
$591$	−16.6077	−	51.1133i	−0.683150	−	2.10252i
$592$		0			0
$593$	−33.4666			−1.37431			−0.687154	−	0.726512i	$-0.741140\pi$
$593$	−33.4666			−1.37431			−0.687154	+	0.726512i	$0.741140\pi$
$594$		0			0
$595$	−21.0542			−0.863137
$596$		0			0
$597$	6.73716	+	20.7348i	0.275733	+	0.848620i
$598$		0			0
$599$	−13.7397	−	9.98248i	−0.561389	−	0.407873i	0.270578	−	0.962698i	$-0.412785\pi$
$599$	−13.7397	−	9.98248i	−0.561389	−	0.407873i	−0.831967	+	0.554825i	$0.812785\pi$
$600$		0			0
$601$	0.00907725	−	0.0279369i	0.000370269	−	0.00113957i	−0.950871	−	0.309587i	$-0.899809\pi$
$601$	0.00907725	−	0.0279369i	0.000370269	−	0.00113957i	0.951241	+	0.308447i	$0.0998093\pi$
$602$		0			0
$603$	3.64884	−	2.65104i	0.148592	−	0.107959i
$604$		0			0
$605$	−32.7807	−	4.32836i	−1.33273	−	0.175973i
$606$		0			0
$607$	−21.0371	+	15.2844i	−0.853870	+	0.620373i	−0.926210	−	0.377007i	$-0.876953\pi$
$607$	−21.0371	+	15.2844i	−0.853870	+	0.620373i	0.0723401	+	0.997380i	$0.476953\pi$
$608$		0			0
$609$	−7.35210	+	22.6274i	−0.297922	+	0.916910i
$610$		0			0
$611$	29.6980	+	21.5769i	1.20145	+	0.872907i
$612$		0			0
$613$	−9.39248	−	28.9071i	−0.379359	−	1.16755i	−0.940491	−	0.339820i	$-0.889634\pi$
$613$	−9.39248	−	28.9071i	−0.379359	−	1.16755i	0.561132	−	0.827726i	$-0.310366\pi$
$614$		0			0
$615$	115.325			4.65034
$616$		0			0
$617$	22.3795			0.900966			0.450483	−	0.892785i	$-0.351252\pi$
$617$	22.3795			0.900966			0.450483	+	0.892785i	$0.351252\pi$
$618$		0			0
$619$	−7.13465	−	21.9582i	−0.286766	−	0.882575i	−0.985864	−	0.167549i	$-0.946415\pi$
$619$	−7.13465	−	21.9582i	−0.286766	−	0.882575i	0.699098	−	0.715026i	$-0.253585\pi$
$620$		0			0
$621$	−39.6875	−	28.8347i	−1.59261	−	1.15710i
$622$		0			0
$623$	3.75396	−	11.5535i	0.150399	−	0.462881i
$624$		0			0
$625$	23.3740	−	16.9822i	0.934960	−	0.679288i
$626$		0			0
$627$	−17.8218	+	21.4201i	−0.711735	+	0.855437i
$628$		0			0
$629$	−38.5452	+	28.0047i	−1.53690	+	1.11662i
$630$		0			0
$631$	−9.28529	+	28.5772i	−0.369641	+	1.13764i	0.577382	+	0.816474i	$0.304074\pi$
$631$	−9.28529	+	28.5772i	−0.369641	+	1.13764i	−0.947023	+	0.321165i	$0.895926\pi$
$632$		0			0
$633$	50.7688	+	36.8857i	2.01788	+	1.46607i
$634$		0			0
$635$	−9.43769	−	29.0462i	−0.374523	−	1.15266i
$636$		0			0
$637$	−16.6448			−0.659490
$638$		0			0
$639$	−5.14004			−0.203337
$640$		0			0
$641$	11.1148	+	34.2078i	0.439007	+	1.35113i	0.888924	+	0.458055i	$0.151454\pi$
$641$	11.1148	+	34.2078i	0.439007	+	1.35113i	−0.449917	+	0.893070i	$0.648546\pi$
$642$		0			0
$643$	14.7433	+	10.7117i	0.581420	+	0.422426i	0.839236	−	0.543768i	$-0.183003\pi$
$643$	14.7433	+	10.7117i	0.581420	+	0.422426i	−0.257816	+	0.966194i	$0.583003\pi$
$644$		0			0
$645$	21.1904	−	65.2175i	0.834373	−	2.56794i
$646$		0			0
$647$	9.00098	−	6.53959i	0.353865	−	0.257098i	−0.396624	−	0.917981i	$-0.629818\pi$
$647$	9.00098	−	6.53959i	0.353865	−	0.257098i	0.750489	+	0.660883i	$0.229818\pi$
$648$		0			0
$649$	1.94359	−	29.5673i	0.0762927	−	1.16062i
$650$		0			0
$651$	−1.88879	+	1.37228i	−0.0740273	+	0.0537840i
$652$		0			0
$653$	−5.11131	+	15.7310i	−0.200021	+	0.615601i	0.799860	+	0.600186i	$0.204907\pi$
$653$	−5.11131	+	15.7310i	−0.200021	+	0.615601i	−0.999881	+	0.0154150i	$0.995093\pi$
$654$		0			0
$655$	−7.32833	−	5.32434i	−0.286341	−	0.208039i
$656$		0			0
$657$	−1.03750	−	3.19311i	−0.0404769	−	0.124575i
$658$		0			0
$659$	26.0957			1.01655			0.508273	−	0.861196i	$-0.330284\pi$
$659$	26.0957			1.01655			0.508273	+	0.861196i	$0.330284\pi$
$660$		0			0
$661$	15.3262			0.596121			0.298061	−	0.954547i	$-0.403660\pi$
$661$	15.3262			0.596121			0.298061	+	0.954547i	$0.403660\pi$
$662$		0			0
$663$	15.4741	+	47.6244i	0.600965	+	1.84958i
$664$		0			0
$665$	10.4519	+	7.59373i	0.405306	+	0.294472i
$666$		0			0
$667$	−7.33468	+	22.5738i	−0.284000	+	0.874062i
$668$		0			0
$669$	−15.4554	+	11.2290i	−0.597540	+	0.434138i
$670$		0			0
$671$	−6.66715	−	2.66140i	−0.257383	−	0.102742i
$672$		0			0
$673$	−25.8605	+	18.7888i	−0.996851	+	0.724254i	−0.961411	−	0.275117i	$-0.911283\pi$
$673$	−25.8605	+	18.7888i	−0.996851	+	0.724254i	−0.0354400	+	0.999372i	$0.511283\pi$
$674$		0			0
$675$	−12.8099	+	39.4247i	−0.493052	+	1.51746i
$676$		0			0
$677$	−10.1028	−	7.34015i	−0.388284	−	0.282105i	0.376468	−	0.926430i	$-0.377138\pi$
$677$	−10.1028	−	7.34015i	−0.388284	−	0.282105i	−0.764752	+	0.644325i	$0.777138\pi$
$678$		0			0
$679$	1.75535	+	5.40243i	0.0673643	+	0.207326i
$680$		0			0
$681$	48.2009			1.84706
$682$		0			0
$683$	26.0471			0.996665			0.498332	−	0.866986i	$-0.333946\pi$
$683$	26.0471			0.996665			0.498332	+	0.866986i	$0.333946\pi$
$684$		0			0
$685$	0.964085	+	2.96715i	0.0368358	+	0.113369i
$686$		0			0
$687$	−41.3983	−	30.0776i	−1.57944	−	1.14753i
$688$		0			0
$689$	−5.95220	+	18.3190i	−0.226761	+	0.697898i
$690$		0			0
$691$	−37.5824	+	27.3052i	−1.42970	+	1.03874i	−0.439632	+	0.898178i	$0.644891\pi$
$691$	−37.5824	+	27.3052i	−1.42970	+	1.03874i	−0.990072	+	0.140562i	$0.955109\pi$
$692$		0			0
$693$	17.6032	+	27.9112i	0.668690	+	1.06026i
$694$		0			0
$695$	−7.13723	+	5.18550i	−0.270730	+	0.196697i
$696$		0			0
$697$	17.3463	−	53.3866i	0.657040	−	2.02216i
$698$		0			0
$699$	−29.0102	−	21.0772i	−1.09727	−	0.797212i
$700$		0			0
$701$	−7.80323	−	24.0159i	−0.294724	−	0.907067i	−0.983314	−	0.181916i	$-0.941770\pi$
$701$	−7.80323	−	24.0159i	−0.294724	−	0.907067i	0.688590	−	0.725151i	$-0.258230\pi$
$702$		0			0
$703$	29.2355			1.10264
$704$		0			0
$705$	92.2939			3.47599
$706$		0			0
$707$	−0.594958	−	1.83109i	−0.0223757	−	0.0688653i
$708$		0			0
$709$	4.69638	+	3.41212i	0.176376	+	0.128145i	0.672471	−	0.740124i	$-0.265233\pi$
$709$	4.69638	+	3.41212i	0.176376	+	0.128145i	−0.496094	+	0.868269i	$0.665233\pi$
$710$		0			0
$711$	−11.4231	+	35.1567i	−0.428400	+	1.31848i
$712$		0			0
$713$	−1.88431	+	1.36903i	−0.0705680	+	0.0512706i
$714$		0			0
$715$	35.3417	−	8.96850i	1.32171	−	0.335403i
$716$		0			0
$717$	62.7379	−	45.5817i	2.34299	−	1.70228i
$718$		0			0
$719$	9.80299	−	30.1705i	0.365590	−	1.12517i	−0.584021	−	0.811738i	$-0.698522\pi$
$719$	9.80299	−	30.1705i	0.365590	−	1.12517i	0.949611	−	0.313431i	$-0.101478\pi$
$720$		0			0
$721$	−3.24748	−	2.35944i	−0.120943	−	0.0878700i
$722$		0			0
$723$	−1.18793	−	3.65607i	−0.0441796	−	0.135971i
$724$		0			0
$725$	20.0569			0.744895
$726$		0			0
$727$	−51.2435			−1.90052			−0.950258	−	0.311464i	$-0.899181\pi$
$727$	−51.2435			−1.90052			−0.950258	+	0.311464i	$0.899181\pi$
$728$		0			0
$729$	−4.86865	−	14.9842i	−0.180320	−	0.554969i
$730$		0			0
$731$	−27.0034	−	19.6191i	−0.998758	−	0.725640i
$732$		0			0
$733$	13.5510	−	41.7056i	0.500517	−	1.54043i	−0.307663	−	0.951495i	$-0.599547\pi$
$733$	13.5510	−	41.7056i	0.500517	−	1.54043i	0.808179	−	0.588936i	$-0.200453\pi$
$734$		0			0
$735$	−33.8562	+	24.5980i	−1.24881	+	0.907311i
$736$		0			0
$737$	−2.28050	+	0.578712i	−0.0840035	+	0.0213171i
$738$		0			0
$739$	25.1036	−	18.2388i	0.923450	−	0.670926i	−0.0209304	−	0.999781i	$-0.506663\pi$
$739$	25.1036	−	18.2388i	0.923450	−	0.670926i	0.944380	+	0.328855i	$0.106663\pi$
$740$		0			0
$741$	9.49519	−	29.2232i	0.348815	−	1.07354i
$742$		0			0
$743$	19.2293	+	13.9709i	0.705455	+	0.512543i	0.881704	−	0.471802i	$-0.156396\pi$
$743$	19.2293	+	13.9709i	0.705455	+	0.512543i	−0.176249	+	0.984346i	$0.556396\pi$
$744$		0			0
$745$	11.4256	+	35.1644i	0.418601	+	1.28832i
$746$		0			0
$747$	45.0857			1.64960
$748$		0			0
$749$	21.3785			0.781152
$750$		0			0
$751$	13.1914	+	40.5989i	0.481360	+	1.48147i	0.837185	+	0.546921i	$0.184200\pi$
$751$	13.1914	+	40.5989i	0.481360	+	1.48147i	−0.355825	+	0.934553i	$0.615800\pi$
$752$		0			0
$753$	−57.0568	−	41.4542i	−2.07927	−	1.51068i
$754$		0			0
$755$	−18.7480	+	57.7006i	−0.682311	+	2.09994i
$756$		0			0
$757$	−19.5386	+	14.1956i	−0.710143	+	0.515949i	−0.883220	−	0.468959i	$-0.844629\pi$
$757$	−19.5386	+	14.1956i	−0.710143	+	0.515949i	0.173077	+	0.984908i	$0.444629\pi$
$758$		0			0
$759$	25.8480	+	40.9839i	0.938223	+	1.48762i
$760$		0			0
$761$	−11.0292	+	8.01318i	−0.399808	+	0.290477i	−0.769463	−	0.638692i	$-0.779476\pi$
$761$	−11.0292	+	8.01318i	−0.399808	+	0.290477i	0.369655	+	0.929169i	$0.379476\pi$
$762$		0			0
$763$	0.452566	−	1.39285i	0.0163840	−	0.0504247i
$764$		0			0
$765$	69.2020	+	50.2782i	2.50200	+	1.81781i
$766$		0			0
$767$	10.0971	+	31.0758i	0.364586	+	1.12208i
$768$		0			0
$769$	17.6960			0.638135			0.319068	−	0.947732i	$-0.396630\pi$
$769$	17.6960			0.638135			0.319068	+	0.947732i	$0.396630\pi$
$770$		0			0
$771$	16.5063			0.594458
$772$		0			0
$773$	−8.52978	−	26.2520i	−0.306795	−	0.944217i	−0.979001	−	0.203854i	$-0.934653\pi$
$773$	−8.52978	−	26.2520i	−0.306795	−	0.944217i	0.672207	−	0.740364i	$-0.265347\pi$
$774$		0			0
$775$	1.59227	+	1.15685i	0.0571962	+	0.0415554i
$776$		0			0
$777$	15.7471	−	48.4646i	0.564924	−	1.73866i
$778$		0			0
$779$	−27.8664	+	20.2462i	−0.998419	+	0.725394i
$780$		0			0
$781$	2.49026	+	0.994064i	0.0891087	+	0.0355704i
$782$		0			0
$783$	41.3010	−	30.0070i	1.47598	−	1.07236i
$784$		0			0
$785$	−12.2654	+	37.7492i	−0.437773	+	1.34733i
$786$		0			0
$787$	−16.2622	−	11.8152i	−0.579684	−	0.421165i	0.258926	−	0.965897i	$-0.416631\pi$
$787$	−16.2622	−	11.8152i	−0.579684	−	0.421165i	−0.838610	+	0.544732i	$0.816631\pi$
$788$		0			0
$789$	−15.4439	−	47.5314i	−0.549817	−	1.69216i
$790$		0			0
$791$	−5.02608			−0.178707
$792$		0			0
$793$	7.91616			0.281111
$794$		0			0
$795$	14.9651	+	46.0580i	0.530759	+	1.63351i
$796$		0			0
$797$	−10.8947	−	7.91546i	−0.385910	−	0.280380i	0.377867	−	0.925860i	$-0.376658\pi$
$797$	−10.8947	−	7.91546i	−0.385910	−	0.280380i	−0.763778	+	0.645480i	$0.776658\pi$
$798$		0			0
$799$	13.8822	−	42.7251i	0.491118	−	1.51150i
$800$		0			0
$801$	−39.9290	+	29.0101i	−1.41082	+	1.02502i
$802$		0			0
$803$	−0.114882	+	1.74766i	−0.00405409	+	0.0616735i
$804$		0			0
$805$	18.1748	−	13.2048i	0.640579	−	0.465408i
$806$		0			0
$807$	26.1267	−	80.4096i	0.919702	−	2.83055i
$808$		0			0
$809$	−7.03614	−	5.11205i	−0.247377	−	0.179730i	0.457186	−	0.889371i	$-0.348857\pi$
$809$	−7.03614	−	5.11205i	−0.247377	−	0.179730i	−0.704564	+	0.709641i	$0.748857\pi$
$810$		0			0
$811$	−3.88841	−	11.9673i	−0.136541	−	0.420229i	0.859286	−	0.511496i	$-0.170908\pi$
$811$	−3.88841	−	11.9673i	−0.136541	−	0.420229i	−0.995826	+	0.0912667i	$0.970908\pi$
$812$		0			0
$813$	−91.4178			−3.20616
$814$		0			0
$815$	10.5534			0.369671
$816$		0			0
$817$	6.32910	+	19.4790i	0.221427	+	0.681482i
$818$		0			0
$819$	−29.4388	−	21.3886i	−1.02868	−	0.747377i
$820$		0			0
$821$	−10.6940	+	32.9126i	−0.373222	+	1.14866i	0.571448	+	0.820638i	$0.306382\pi$
$821$	−10.6940	+	32.9126i	−0.373222	+	1.14866i	−0.944670	+	0.328021i	$0.893618\pi$
$822$		0			0
$823$	37.3875	−	27.1636i	1.30325	−	0.946864i	0.303265	−	0.952906i	$-0.401923\pi$
$823$	37.3875	−	27.1636i	1.30325	−	0.946864i	0.999982	+	0.00604174i	$0.00192316\pi$
$824$		0			0
$825$	26.1875	−	31.4749i	0.911732	−	1.09581i
$826$		0			0
$827$	−10.1882	+	7.40218i	−0.354279	+	0.257399i	−0.750662	−	0.660686i	$-0.770265\pi$
$827$	−10.1882	+	7.40218i	−0.354279	+	0.257399i	0.396383	+	0.918085i	$0.370265\pi$
$828$		0			0
$829$	−9.99844	+	30.7720i	−0.347260	+	1.06876i	0.613102	+	0.790003i	$0.289921\pi$
$829$	−9.99844	+	30.7720i	−0.347260	+	1.06876i	−0.960363	+	0.278754i	$0.910079\pi$
$830$		0			0
$831$	−59.3437	−	43.1157i	−2.05861	−	1.49567i
$832$		0			0
$833$	6.29458	+	19.3727i	0.218094	+	0.671226i
$834$		0			0
$835$	−30.0871			−1.04121
$836$		0			0
$837$	5.00956			0.173156
$838$		0			0
$839$	7.12705	+	21.9348i	0.246053	+	0.757274i	0.995461	+	0.0951658i	$0.0303381\pi$
$839$	7.12705	+	21.9348i	0.246053	+	0.757274i	−0.749408	+	0.662108i	$0.769662\pi$
$840$		0			0
$841$	3.47837	+	2.52719i	0.119944	+	0.0871444i
$842$		0			0
$843$	−10.8553	+	33.4092i	−0.373877	+	1.15067i
$844$		0			0
$845$	−0.914540	+	0.664452i	−0.0314611	+	0.0228578i
$846$		0			0
$847$	−3.13055	−	16.9269i	−0.107567	−	0.581615i
$848$		0			0
$849$	40.6109	−	29.5056i	1.39376	−	1.01263i
$850$		0			0
$851$	15.7098	−	48.3497i	0.538524	−	1.65741i
$852$		0			0
$853$	36.9288	+	26.8303i	1.26442	+	0.918652i	0.998966	−	0.0454720i	$-0.0144792\pi$
$853$	36.9288	+	26.8303i	1.26442	+	0.918652i	0.265451	+	0.964124i	$0.414479\pi$
$854$		0			0
$855$	−16.2196	−	49.9189i	−0.554700	−	1.70719i
$856$		0			0
$857$	25.6018			0.874541			0.437271	−	0.899330i	$-0.355945\pi$
$857$	25.6018			0.874541			0.437271	+	0.899330i	$0.355945\pi$
$858$		0			0
$859$	3.93870			0.134387			0.0671934	−	0.997740i	$-0.478596\pi$
$859$	3.93870			0.134387			0.0671934	+	0.997740i	$0.478596\pi$
$860$		0			0
$861$	18.5530	+	57.1001i	0.632283	+	1.94597i
$862$		0			0
$863$	−21.1595	−	15.3733i	−0.720278	−	0.523313i	0.166195	−	0.986093i	$-0.446852\pi$
$863$	−21.1595	−	15.3733i	−0.720278	−	0.523313i	−0.886473	+	0.462780i	$0.846852\pi$
$864$		0			0
$865$	−2.33121	+	7.17473i	−0.0792635	+	0.243948i
$866$		0			0
$867$	7.50569	−	5.45320i	0.254907	−	0.185201i
$868$		0			0
$869$	12.3335	−	14.8237i	0.418385	−	0.502859i
$870$		0			0
$871$	2.09898	−	1.52500i	0.0711212	−	0.0516726i
$872$		0			0
$873$	7.13161	−	21.9488i	0.241368	−	0.742856i
$874$		0			0
$875$	3.67002	+	2.66643i	0.124069	+	0.0901416i
$876$		0			0
$877$	−5.55847	−	17.1072i	−0.187696	−	0.577669i	0.812288	−	0.583256i	$-0.198222\pi$
$877$	−5.55847	−	17.1072i	−0.187696	−	0.577669i	−0.999984	+	0.00558706i	$0.998222\pi$
$878$		0			0
$879$	−51.4106			−1.73404
$880$		0			0
$881$	−13.1327			−0.442453			−0.221227	−	0.975222i	$-0.571006\pi$
$881$	−13.1327			−0.442453			−0.221227	+	0.975222i	$0.571006\pi$
$882$		0			0
$883$	−7.62752	−	23.4751i	−0.256687	−	0.790000i	−0.993493	−	0.113896i	$-0.963667\pi$
$883$	−7.62752	−	23.4751i	−0.256687	−	0.790000i	0.736806	−	0.676104i	$-0.236333\pi$
$884$		0			0
$885$	66.4624	+	48.2878i	2.23411	+	1.62318i
$886$		0			0
$887$	−7.29062	+	22.4382i	−0.244795	+	0.753401i	0.750875	+	0.660444i	$0.229632\pi$
$887$	−7.29062	+	22.4382i	−0.244795	+	0.753401i	−0.995670	+	0.0929571i	$0.970368\pi$
$888$		0			0
$889$	12.8632	−	9.34568i	0.431419	−	0.313444i
$890$		0			0
$891$	2.68645	−	40.8681i	0.0899993	−	1.36913i
$892$		0			0
$893$	−22.3014	+	16.2029i	−0.746288	+	0.542210i
$894$		0			0
$895$	−15.6010	+	48.0150i	−0.521484	+	1.60496i
$896$		0			0
$897$	−43.2271	−	31.4063i	−1.44331	−	1.04863i
$898$		0			0
$899$	−0.749004	−	2.30520i	−0.0249807	−	0.0768826i
$900$		0			0
$901$	23.5723			0.785307
$902$		0			0
$903$	35.6999			1.18802
$904$		0			0
$905$	−5.51603	−	16.9766i	−0.183359	−	0.564321i
$906$		0			0
$907$	38.5903	+	28.0375i	1.28137	+	0.930970i	0.999593	−	0.0285104i	$-0.00907639\pi$
$907$	38.5903	+	28.0375i	1.28137	+	0.930970i	0.281776	+	0.959480i	$0.409076\pi$
$908$		0			0
$909$	−2.41718	+	7.43932i	−0.0801728	+	0.246747i
$910$		0			0
$911$	−0.798318	+	0.580012i	−0.0264494	+	0.0192166i	−0.600931	−	0.799301i	$-0.705204\pi$
$911$	−0.798318	+	0.580012i	−0.0264494	+	0.0192166i	0.574482	+	0.818517i	$0.305204\pi$
$912$		0			0
$913$	−21.8433	−	8.71940i	−0.722907	−	0.288570i
$914$		0			0
$915$	16.1018	−	11.6987i	0.532310	−	0.386746i
$916$		0			0
$917$	1.45726	−	4.48500i	0.0481231	−	0.148108i
$918$		0			0
$919$	16.1448	+	11.7299i	0.532569	+	0.386934i	0.821318	−	0.570471i	$-0.193239\pi$
$919$	16.1448	+	11.7299i	0.532569	+	0.386934i	−0.288749	+	0.957405i	$0.593239\pi$
$920$		0			0
$921$	11.6339	+	35.8055i	0.383350	+	1.17983i
$922$		0			0
$923$	−2.95678			−0.0973238
$924$		0			0
$925$	−42.9589			−1.41248
$926$		0			0
$927$	5.03958	+	15.5102i	0.165522	+	0.509423i
$928$		0			0
$929$	−21.8609	−	15.8829i	−0.717234	−	0.521101i	0.168265	−	0.985742i	$-0.446183\pi$
$929$	−21.8609	−	15.8829i	−0.717234	−	0.521101i	−0.885499	+	0.464641i	$0.846183\pi$
$930$		0			0
$931$	3.86247	−	11.8875i	0.126587	−	0.389596i
$932$		0			0
$933$	41.0743	−	29.8423i	1.34471	−	0.976992i
$934$		0			0
$935$	−23.8036	−	37.7424i	−0.778462	−	1.23431i
$936$		0			0
$937$	−31.9858	+	23.2391i	−1.04493	+	0.759187i	−0.971242	−	0.238094i	$-0.923477\pi$
$937$	−31.9858	+	23.2391i	−1.04493	+	0.759187i	−0.0736894	+	0.997281i	$0.523477\pi$
$938$		0			0
$939$	21.5837	−	66.4277i	0.704357	−	2.16779i
$940$		0			0
$941$	−19.4808	−	14.1536i	−0.635055	−	0.461395i	0.223092	−	0.974797i	$-0.428385\pi$
$941$	−19.4808	−	14.1536i	−0.635055	−	0.461395i	−0.858148	+	0.513402i	$0.828385\pi$
$942$		0			0
$943$	18.5090	+	56.9648i	0.602736	+	1.85503i
$944$		0			0
$945$	−48.3190			−1.57182
$946$		0			0
$947$	34.6471			1.12588			0.562940	−	0.826498i	$-0.309670\pi$
$947$	34.6471			1.12588			0.562940	+	0.826498i	$0.309670\pi$
$948$		0			0
$949$	−0.596820	−	1.83682i	−0.0193736	−	0.0596258i
$950$		0			0
$951$	−11.7981	−	8.57180i	−0.382579	−	0.277960i
$952$		0			0
$953$	0.283275	−	0.871831i	0.00917618	−	0.0282414i	−0.946364	−	0.323104i	$-0.895274\pi$
$953$	0.283275	−	0.871831i	0.00917618	−	0.0282414i	0.955540	+	0.294862i	$0.0952738\pi$
$954$		0			0
$955$	16.8803	−	12.2643i	0.546235	−	0.396863i
$956$		0			0
$957$	−48.8749	+	12.4027i	−1.57990	+	0.400923i
$958$		0			0
$959$	−1.31401	+	0.954686i	−0.0424317	+	0.0308284i
$960$		0			0
$961$	−9.50603	+	29.2565i	−0.306646	+	0.943760i
$962$		0			0
$963$	−70.2679	−	51.0526i	−2.26435	−	1.64515i
$964$		0			0
$965$	3.39919	+	10.4616i	0.109424	+	0.336772i
$966$		0			0
$967$	−40.8240			−1.31281			−0.656406	−	0.754408i	$-0.727924\pi$
$967$	−40.8240			−1.31281			−0.656406	+	0.754408i	$0.727924\pi$
$968$		0			0
$969$	−37.6035			−1.20800
$970$		0			0
$971$	15.2726	+	47.0041i	0.490120	+	1.50843i	0.824426	+	0.565970i	$0.191498\pi$
$971$	15.2726	+	47.0041i	0.490120	+	1.50843i	−0.334306	+	0.942465i	$0.608502\pi$
$972$		0			0
$973$	−3.71568	−	2.69960i	−0.119119	−	0.0865452i
$974$		0			0
$975$	−13.9523	+	42.9408i	−0.446832	+	1.37521i
$976$		0			0
$977$	19.0475	−	13.8388i	0.609383	−	0.442743i	−0.239814	−	0.970819i	$-0.577086\pi$
$977$	19.0475	−	13.8388i	0.609383	−	0.442743i	0.849197	+	0.528076i	$0.177086\pi$
$978$		0			0
$979$	24.9554	−	6.33280i	0.797577	−	0.202397i
$980$		0			0
$981$	−4.81371	+	3.49736i	−0.153690	+	0.111662i
$982$		0			0
$983$	−1.79966	+	5.53878i	−0.0574002	+	0.176660i	−0.975646	−	0.219352i	$-0.929606\pi$
$983$	−1.79966	+	5.53878i	−0.0574002	+	0.176660i	0.918246	+	0.396011i	$0.129606\pi$
$984$		0			0
$985$	−42.7244	−	31.0411i	−1.36131	−	0.989052i
$986$		0			0
$987$	14.8479	+	45.6971i	0.472613	+	1.45455i
$988$		0			0
$989$	35.6153			1.13250
$990$		0			0
$991$	14.3008			0.454280			0.227140	−	0.973862i	$-0.427062\pi$
$991$	14.3008			0.454280			0.227140	+	0.973862i	$0.427062\pi$
$992$		0			0
$993$	−30.7153	−	94.5318i	−0.974719	−	2.99988i
$994$		0			0
$995$	17.3318	+	12.5923i	0.549454	+	0.399202i
$996$		0			0
$997$	−8.73706	+	26.8899i	−0.276705	+	0.851612i	0.712058	+	0.702121i	$0.247763\pi$
$997$	−8.73706	+	26.8899i	−0.276705	+	0.851612i	−0.988763	+	0.149491i	$0.952237\pi$
$998$		0			0
$999$	−88.4606	+	64.2704i	−2.79877	+	2.03343i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.945302 - 2.90934i) q^{3} +(-2.43185 - 1.76684i) q^{5} +(0.483582 - 1.48831i) q^{7} +(-5.14361 + 3.73705i) q^{9} +(3.21473 - 0.815786i) q^{11} +(-2.95884 + 2.14973i) q^{13} +(-2.84151 + 8.74528i) q^{15} +(3.62100 + 2.63081i) q^{17} +(-0.848695 - 2.61201i) q^{19} -4.78714 q^{21} -4.77580 q^{23} +(1.24708 + 3.83811i) q^{25} +(8.31014 + 6.03767i) q^{27} +(1.53580 - 4.72671i) q^{29} +(0.394554 - 0.286660i) q^{31} +(-5.41229 - 8.58158i) q^{33} +(-3.80561 + 2.76494i) q^{35} +(-3.28946 + 10.1239i) q^{37} +(9.05128 + 6.57614i) q^{39} +(-3.87558 - 11.9278i) q^{41} -7.45745 q^{43} +19.1113 q^{45} +(-3.10162 - 9.54579i) q^{47} +(3.68190 + 2.67505i) q^{49} +(4.23099 - 13.0216i) q^{51} +(4.26078 - 3.09564i) q^{53} +(-9.25911 - 3.69605i) q^{55} +(-6.79696 + 4.93828i) q^{57} +(2.76079 - 8.49684i) q^{59} +(-1.75109 - 1.27224i) q^{61} +(3.07455 + 9.46248i) q^{63} +10.9937 q^{65} -0.709392 q^{67} +(4.51457 + 13.8944i) q^{69} +(0.654053 + 0.475198i) q^{71} +(-0.163185 + 0.502230i) q^{73} +(9.98751 - 7.25635i) q^{75} +(0.340441 - 5.17903i) q^{77} +(4.70380 - 3.41751i) q^{79} +(3.81598 - 11.7444i) q^{81} +(-5.73701 - 4.16818i) q^{83} +(-4.15750 - 12.7955i) q^{85} -15.2034 q^{87} +7.76282 q^{89} +(1.76862 + 5.44325i) q^{91} +(-1.20696 - 0.876911i) q^{93} +(-2.55112 + 7.85154i) q^{95} +(-2.93665 + 2.13360i) q^{97} +(-13.4867 + 16.2097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{7} - q^{9} - 11 q^{11} - 2 q^{13} + 4 q^{15} + 12 q^{17} + 5 q^{19} + 24 q^{21} - 12 q^{23} + 13 q^{25} + 3 q^{27} + 16 q^{31} - 7 q^{33} - 28 q^{35} - 4 q^{37} + 46 q^{39} - 4 q^{41} - 22 q^{43}+ \cdots - 65 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

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