LMFDB - Embedded newform 896.2.i.h.641.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(513,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("896.513");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.3010058496.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 6x^{6} + 2x^{5} - 17x^{4} + 6x^{3} + 54x^{2} - 108x + 81 $ x^8 - 4x^7 + 6x^6 + 2x^5 - 17x^4 + 6x^3 + 54x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			641.3
Root			$1.65412 + 0.513691i$ of defining polynomial
Character	$\chi$	$=$	896.641
Dual form			896.2.i.h.513.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.382191 - 0.661975i) q^{3} +(-0.771931 - 1.33702i) q^{5} +(-1.03631 + 2.43435i) q^{7} +(1.20786 + 2.09207i) q^{9} +O(q^{10})$	\(q+(0.382191 - 0.661975i) q^{3} +(-0.771931 - 1.33702i) q^{5} +(-1.03631 + 2.43435i) q^{7} +(1.20786 + 2.09207i) q^{9} +(1.65412 - 2.86502i) q^{11} +1.94448 q^{13} -1.18010 q^{15} +(1.47224 - 2.55000i) q^{17} +(1.88974 + 3.27313i) q^{19} +(1.21541 + 1.61640i) q^{21} +(-1.31812 - 2.28305i) q^{23} +(1.30824 - 2.26595i) q^{25} +4.13968 q^{27} +8.56097 q^{29} +(-3.13391 + 5.42810i) q^{31} +(-1.26438 - 2.18998i) q^{33} +(4.05474 - 0.493573i) q^{35} +(-3.50856 - 6.07700i) q^{37} +(0.743165 - 1.28720i) q^{39} +12.0897 q^{41} -1.08772 q^{43} +(1.86477 - 3.22987i) q^{45} +(0.718194 + 1.24395i) q^{47} +(-4.85211 - 5.04550i) q^{49} +(-1.12536 - 1.94918i) q^{51} +(3.20031 - 5.54310i) q^{53} -5.10747 q^{55} +2.88897 q^{57} +(0.926054 - 1.60397i) q^{59} +(2.43593 + 4.21915i) q^{61} +(-6.34456 + 0.772306i) q^{63} +(-1.50101 - 2.59982i) q^{65} +(5.87054 - 10.1681i) q^{67} -2.01510 q^{69} -8.17545 q^{71} +(-0.735617 + 1.27413i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(5.26028 + 6.99578i) q^{77} +(-1.44626 - 2.50500i) q^{79} +(-2.04143 + 3.53586i) q^{81} -13.8890 q^{83} -4.54588 q^{85} +(3.27193 - 5.66715i) q^{87} +(4.51711 + 7.82387i) q^{89} +(-2.01510 + 4.73355i) q^{91} +(2.39551 + 4.14914i) q^{93} +(2.91750 - 5.05325i) q^{95} +1.43903 q^{97} +7.99179 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9	$ 8 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 20 q^{15} - 4 q^{17} + 8 q^{19} - 10 q^{21} - 4 q^{23} - 8 q^{25} - 40 q^{27} + 6 q^{31} - 8 q^{33} + 8 q^{35} - 2 q^{37} + 2 q^{39} + 24 q^{41} + 24 q^{43} + 8 q^{45} + 2 q^{47} - 4 q^{49} - 4 q^{51} + 18 q^{53} - 32 q^{55} - 40 q^{57} - 10 q^{59} + 14 q^{61} - 22 q^{63} + 8 q^{65} - 2 q^{67} - 4 q^{69} - 8 q^{73} - 8 q^{75} - 14 q^{77} - 16 q^{79} - 40 q^{81} - 48 q^{83} + 20 q^{85} + 18 q^{87} - 16 q^{89} - 4 q^{91} - 30 q^{93} + 32 q^{95} + 80 q^{97} - 44 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 20 * q^15 - 4 * q^17 + 8 * q^19 - 10 * q^21 - 4 * q^23 - 8 * q^25 - 40 * q^27 + 6 * q^31 - 8 * q^33 + 8 * q^35 - 2 * q^37 + 2 * q^39 + 24 * q^41 + 24 * q^43 + 8 * q^45 + 2 * q^47 - 4 * q^49 - 4 * q^51 + 18 * q^53 - 32 * q^55 - 40 * q^57 - 10 * q^59 + 14 * q^61 - 22 * q^63 + 8 * q^65 - 2 * q^67 - 4 * q^69 - 8 * q^73 - 8 * q^75 - 14 * q^77 - 16 * q^79 - 40 * q^81 - 48 * q^83 + 20 * q^85 + 18 * q^87 - 16 * q^89 - 4 * q^91 - 30 * q^93 + 32 * q^95 + 80 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.382191	−	0.661975i	0.220658	−	0.382191i	−0.734350	−	0.678771i	$-0.762513\pi$
$3$	0.382191	−	0.661975i	0.220658	−	0.382191i	0.955008	+	0.296580i	$0.0958461\pi$
$4$		0			0
$5$	−0.771931	−	1.33702i	−0.345218	−	0.597935i	0.640175	−	0.768229i	$-0.278862\pi$
$5$	−0.771931	−	1.33702i	−0.345218	−	0.597935i	−0.985393	+	0.170294i	$0.945528\pi$
$6$		0			0
$7$	−1.03631	+	2.43435i	−0.391690	+	0.920097i
$7$	−1.03631	+	2.43435i	−0.391690	+	0.920097i
$8$		0			0
$9$	1.20786	+	2.09207i	0.402620	+	0.697358i
$10$		0			0
$11$	1.65412	−	2.86502i	0.498737	−	0.863837i	−0.501262	−	0.865295i	$-0.667131\pi$
$11$	1.65412	−	2.86502i	0.498737	−	0.863837i	0.999999	+	0.00145813i	$0.000464138\pi$
$12$		0			0
$13$	1.94448			0.539303			0.269651	−	0.962958i	$-0.413092\pi$
$13$	1.94448			0.539303			0.269651	+	0.962958i	$0.413092\pi$
$14$		0			0
$15$	−1.18010			−0.304701
$16$		0			0
$17$	1.47224	−	2.55000i	0.357071	−	0.618465i	−0.630399	−	0.776271i	$-0.717109\pi$
$17$	1.47224	−	2.55000i	0.357071	−	0.618465i	0.987470	+	0.157806i	$0.0504420\pi$
$18$		0			0
$19$	1.88974	+	3.27313i	0.433536	+	0.750906i	0.997175	−	0.0751149i	$-0.0239324\pi$
$19$	1.88974	+	3.27313i	0.433536	+	0.750906i	−0.563639	+	0.826021i	$0.690599\pi$
$20$		0			0
$21$	1.21541	+	1.61640i	0.265224	+	0.352728i
$22$		0			0
$23$	−1.31812	−	2.28305i	−0.274847	−	0.476049i	0.695250	−	0.718768i	$-0.255294\pi$
$23$	−1.31812	−	2.28305i	−0.274847	−	0.476049i	−0.970097	+	0.242720i	$0.921961\pi$
$24$		0			0
$25$	1.30824	−	2.26595i	0.261649	−	0.453189i
$26$		0			0
$27$	4.13968			0.796682
$28$		0			0
$29$	8.56097			1.58973			0.794867	−	0.606784i	$-0.207541\pi$
$29$	8.56097			1.58973			0.794867	+	0.606784i	$0.207541\pi$
$30$		0			0
$31$	−3.13391	+	5.42810i	−0.562867	+	0.974915i	0.434377	+	0.900731i	$0.356968\pi$
$31$	−3.13391	+	5.42810i	−0.562867	+	0.974915i	−0.997245	+	0.0741838i	$0.976365\pi$
$32$		0			0
$33$	−1.26438	−	2.18998i	−0.220101	−	0.381226i
$34$		0			0
$35$	4.05474	−	0.493573i	0.685377	−	0.0834291i
$36$		0			0
$37$	−3.50856	−	6.07700i	−0.576803	−	0.999052i	−0.995843	−	0.0910845i	$-0.970967\pi$
$37$	−3.50856	−	6.07700i	−0.576803	−	0.999052i	0.419040	−	0.907968i	$-0.362367\pi$
$38$		0			0
$39$	0.743165	−	1.28720i	0.119002	−	0.206117i
$40$		0			0
$41$	12.0897			1.88810			0.944050	−	0.329802i	$-0.106982\pi$
$41$	12.0897			1.88810			0.944050	+	0.329802i	$0.106982\pi$
$42$		0			0
$43$	−1.08772			−0.165876			−0.0829382	−	0.996555i	$-0.526430\pi$
$43$	−1.08772			−0.165876			−0.0829382	+	0.996555i	$0.526430\pi$
$44$		0			0
$45$	1.86477	−	3.22987i	0.277983	−	0.481481i
$46$		0			0
$47$	0.718194	+	1.24395i	0.104759	+	0.181449i	0.913640	−	0.406525i	$-0.133259\pi$
$47$	0.718194	+	1.24395i	0.104759	+	0.181449i	−0.808880	+	0.587973i	$0.799926\pi$
$48$		0			0
$49$	−4.85211	−	5.04550i	−0.693158	−	0.720786i
$50$		0			0
$51$	−1.12536	−	1.94918i	−0.157581	−	0.272939i
$52$		0			0
$53$	3.20031	−	5.54310i	0.439597	−	0.761404i	−0.558062	−	0.829799i	$-0.688455\pi$
$53$	3.20031	−	5.54310i	0.439597	−	0.761404i	0.997658	+	0.0683959i	$0.0217881\pi$
$54$		0			0
$55$	−5.10747			−0.688692
$56$		0			0
$57$	2.88897			0.382653
$58$		0			0
$59$	0.926054	−	1.60397i	0.120562	−	0.208819i	−0.799428	−	0.600763i	$-0.794864\pi$
$59$	0.926054	−	1.60397i	0.120562	−	0.208819i	0.919989	+	0.391943i	$0.128197\pi$
$60$		0			0
$61$	2.43593	+	4.21915i	0.311889	+	0.540207i	0.978771	−	0.204956i	$-0.0657051\pi$
$61$	2.43593	+	4.21915i	0.311889	+	0.540207i	−0.666883	+	0.745163i	$0.732372\pi$
$62$		0			0
$63$	−6.34456	+	0.772306i	−0.799339	+	0.0973014i
$64$		0			0
$65$	−1.50101	−	2.59982i	−0.186177	−	0.322468i
$66$		0			0
$67$	5.87054	−	10.1681i	0.717200	−	1.24223i	−0.244904	−	0.969547i	$-0.578757\pi$
$67$	5.87054	−	10.1681i	0.717200	−	1.24223i	0.962105	−	0.272680i	$-0.0879101\pi$
$68$		0			0
$69$	−2.01510			−0.242589
$70$		0			0
$71$	−8.17545			−0.970247			−0.485124	−	0.874446i	$-0.661225\pi$
$71$	−8.17545			−0.970247			−0.485124	+	0.874446i	$0.661225\pi$
$72$		0			0
$73$	−0.735617	+	1.27413i	−0.0860975	+	0.149125i	−0.905858	−	0.423581i	$-0.860773\pi$
$73$	−0.735617	+	1.27413i	−0.0860975	+	0.149125i	0.819761	+	0.572706i	$0.194106\pi$
$74$		0			0
$75$	−1.00000	−	1.73205i	−0.115470	−	0.200000i
$76$		0			0
$77$	5.26028	+	6.99578i	0.599464	+	0.797243i
$78$		0			0
$79$	−1.44626	−	2.50500i	−0.162717	−	0.281835i	0.773125	−	0.634254i	$-0.218693\pi$
$79$	−1.44626	−	2.50500i	−0.162717	−	0.281835i	−0.935842	+	0.352419i	$0.885359\pi$
$80$		0			0
$81$	−2.04143	+	3.53586i	−0.226825	+	0.392873i
$82$		0			0
$83$	−13.8890			−1.52451			−0.762256	−	0.647275i	$-0.775908\pi$
$83$	−13.8890			−1.52451			−0.762256	+	0.647275i	$0.775908\pi$
$84$		0			0
$85$	−4.54588			−0.493070
$86$		0			0
$87$	3.27193	−	5.66715i	0.350788	−	0.607582i
$88$		0			0
$89$	4.51711	+	7.82387i	0.478813	+	0.829328i	0.999705	−	0.0242943i	$-0.00773387\pi$
$89$	4.51711	+	7.82387i	0.478813	+	0.829328i	−0.520892	+	0.853623i	$0.674401\pi$
$90$		0			0
$91$	−2.01510	+	4.73355i	−0.211239	+	0.496211i
$92$		0			0
$93$	2.39551	+	4.14914i	0.248403	+	0.430246i
$94$		0			0
$95$	2.91750	−	5.05325i	0.299329	−	0.518453i
$96$		0			0
$97$	1.43903			0.146111			0.0730555	−	0.997328i	$-0.476725\pi$
$97$	1.43903			0.146111			0.0730555	+	0.997328i	$0.476725\pi$
$98$		0			0
$99$	7.99179			0.803205
$100$		0			0
$101$	1.64379	−	2.84712i	0.163563	−	0.283299i	−0.772581	−	0.634916i	$-0.781035\pi$
$101$	1.64379	−	2.84712i	0.163563	−	0.283299i	0.936144	+	0.351617i	$0.114368\pi$
$102$		0			0
$103$	9.62636	+	16.6734i	0.948514	+	1.64287i	0.748558	+	0.663069i	$0.230747\pi$
$103$	9.62636	+	16.6734i	0.948514	+	1.64287i	0.199956	+	0.979805i	$0.435920\pi$
$104$		0			0
$105$	1.22296	−	2.87278i	0.119348	−	0.280355i
$106$		0			0
$107$	3.96237	+	6.86302i	0.383057	+	0.663473i	0.991497	−	0.130126i	$-0.0415381\pi$
$107$	3.96237	+	6.86302i	0.383057	+	0.663473i	−0.608441	+	0.793599i	$0.708205\pi$
$108$		0			0
$109$	−1.06508	+	1.84477i	−0.102016	+	0.176697i	−0.912515	−	0.409043i	$-0.865863\pi$
$109$	−1.06508	+	1.84477i	−0.102016	+	0.176697i	0.810499	+	0.585740i	$0.199196\pi$
$110$		0			0
$111$	−5.36376			−0.509106
$112$		0			0
$113$	−12.5912			−1.18448			−0.592239	−	0.805763i	$-0.701756\pi$
$113$	−12.5912			−1.18448			−0.592239	+	0.805763i	$0.701756\pi$
$114$		0			0
$115$	−2.03500	+	3.52472i	−0.189764	+	0.328681i
$116$		0			0
$117$	2.34866	+	4.06801i	0.217134	+	0.376087i
$118$		0			0
$119$	4.68188	+	6.22655i	0.429187	+	0.570787i
$120$		0			0
$121$	0.0277577	+	0.0480778i	0.00252343	+	0.00437071i
$122$		0			0
$123$	4.62060	−	8.00311i	0.416625	−	0.721616i
$124$		0			0
$125$	−11.7588			−1.05174
$126$		0			0
$127$	20.0644			1.78043			0.890215	−	0.455541i	$-0.150554\pi$
$127$	20.0644			1.78043			0.890215	+	0.455541i	$0.150554\pi$
$128$		0			0
$129$	−0.415719	+	0.720046i	−0.0366020	+	0.0633965i
$130$		0			0
$131$	7.03353	+	12.1824i	0.614522	+	1.06438i	0.990468	+	0.137742i	$0.0439845\pi$
$131$	7.03353	+	12.1824i	0.614522	+	1.06438i	−0.375946	+	0.926642i	$0.622682\pi$
$132$		0			0
$133$	−9.92629	+	1.20830i	−0.860719	+	0.104773i
$134$		0			0
$135$	−3.19555	−	5.53485i	−0.275029	−	0.476364i
$136$		0			0
$137$	−5.48734	+	9.50435i	−0.468815	+	0.812011i	−0.999365	−	0.0356425i	$-0.988652\pi$
$137$	−5.48734	+	9.50435i	−0.468815	+	0.812011i	0.530550	+	0.847654i	$0.321986\pi$
$138$		0			0
$139$	−17.7779			−1.50791			−0.753953	−	0.656929i	$-0.771855\pi$
$139$	−17.7779			−1.50791			−0.753953	+	0.656929i	$0.771855\pi$
$140$		0			0
$141$	1.09795			0.0924641
$142$		0			0
$143$	3.21642	−	5.57100i	0.268970	−	0.465870i
$144$		0			0
$145$	−6.60848	−	11.4462i	−0.548805	−	0.950557i
$146$		0			0
$147$	−5.19443	+	1.28363i	−0.428429	+	0.105872i
$148$		0			0
$149$	−4.77193	−	8.26523i	−0.390932	−	0.677114i	0.601641	−	0.798767i	$-0.294514\pi$
$149$	−4.77193	−	8.26523i	−0.390932	−	0.677114i	−0.992573	+	0.121653i	$0.961181\pi$
$150$		0			0
$151$	2.88320	−	4.99385i	0.234631	−	0.406394i	−0.724534	−	0.689239i	$-0.757945\pi$
$151$	2.88320	−	4.99385i	0.234631	−	0.406394i	0.959166	+	0.282845i	$0.0912783\pi$
$152$		0			0
$153$	7.11305			0.575056
$154$		0			0
$155$	9.67666			0.777248
$156$		0			0
$157$	4.85165	−	8.40330i	0.387204	−	0.670656i	−0.604869	−	0.796325i	$-0.706774\pi$
$157$	4.85165	−	8.40330i	0.387204	−	0.670656i	0.992072	+	0.125669i	$0.0401077\pi$
$158$		0			0
$159$	−2.44626	−	4.23705i	−0.194001	−	0.336020i
$160$		0			0
$161$	6.92373	−	0.842806i	0.545666	−	0.0664224i
$162$		0			0
$163$	−4.92605	−	8.53217i	−0.385838	−	0.668292i	0.606047	−	0.795429i	$-0.292754\pi$
$163$	−4.92605	−	8.53217i	−0.385838	−	0.668292i	−0.991885	+	0.127137i	$0.959421\pi$
$164$		0			0
$165$	−1.95203	+	3.38102i	−0.151966	+	0.263212i
$166$		0			0
$167$	−2.86984			−0.222075			−0.111037	−	0.993816i	$-0.535417\pi$
$167$	−2.86984			−0.222075			−0.111037	+	0.993816i	$0.535417\pi$
$168$		0			0
$169$	−9.21898			−0.709152
$170$		0			0
$171$	−4.56508	+	7.90695i	−0.349100	+	0.604660i
$172$		0			0
$173$	4.28804	+	7.42710i	0.326013	+	0.564672i	0.981717	−	0.190347i	$-0.0609612\pi$
$173$	4.28804	+	7.42710i	0.326013	+	0.564672i	−0.655704	+	0.755018i	$0.727628\pi$
$174$		0			0
$175$	4.16035	+	5.53296i	0.314493	+	0.418252i
$176$		0			0
$177$	−0.707859	−	1.22605i	−0.0532060	−	0.0921554i
$178$		0			0
$179$	−7.39520	+	12.8089i	−0.552743	+	0.957379i	0.445332	+	0.895365i	$0.353086\pi$
$179$	−7.39520	+	12.8089i	−0.552743	+	0.957379i	−0.998075	+	0.0620137i	$0.980248\pi$
$180$		0			0
$181$	−25.4479			−1.89153			−0.945765	−	0.324852i	$-0.894685\pi$
$181$	−25.4479			−1.89153			−0.945765	+	0.324852i	$0.894685\pi$
$182$		0			0
$183$	3.72396			0.275283
$184$		0			0
$185$	−5.41673	+	9.38205i	−0.398246	+	0.689782i
$186$		0			0
$187$	−4.87054	−	8.43602i	−0.356169	−	0.616903i
$188$		0			0
$189$	−4.29001	+	10.0774i	−0.312052	+	0.733025i
$190$		0			0
$191$	−3.42706	−	5.93584i	−0.247973	−	0.429503i	0.714990	−	0.699135i	$-0.246431\pi$
$191$	−3.42706	−	5.93584i	−0.247973	−	0.429503i	−0.962963	+	0.269632i	$0.913098\pi$
$192$		0			0
$193$	−12.9408	+	22.4142i	−0.931502	+	1.61341i	−0.150746	+	0.988573i	$0.548168\pi$
$193$	−12.9408	+	22.4142i	−0.931502	+	1.61341i	−0.780756	+	0.624836i	$0.785166\pi$
$194$		0			0
$195$	−2.29469			−0.164326
$196$		0			0
$197$	1.35819			0.0967668			0.0483834	−	0.998829i	$-0.484593\pi$
$197$	1.35819			0.0967668			0.0483834	+	0.998829i	$0.484593\pi$
$198$		0			0
$199$	10.9709	−	19.0022i	0.777708	−	1.34703i	−0.155552	−	0.987828i	$-0.549715\pi$
$199$	10.9709	−	19.0022i	0.777708	−	1.34703i	0.933260	−	0.359202i	$-0.116951\pi$
$200$		0			0
$201$	−4.48734	−	7.77230i	−0.316512	−	0.548216i
$202$		0			0
$203$	−8.87186	+	20.8404i	−0.622682	+	1.46271i
$204$		0			0
$205$	−9.33245	−	16.1643i	−0.651806	−	1.12896i
$206$		0			0
$207$	3.18421	−	5.51521i	0.221318	−	0.383333i
$208$		0			0
$209$	12.5034			0.864881
$210$		0			0
$211$	−25.6669			−1.76698			−0.883491	−	0.468447i	$-0.844814\pi$
$211$	−25.6669			−1.76698			−0.883491	+	0.468447i	$0.844814\pi$
$212$		0			0
$213$	−3.12459	+	5.41194i	−0.214093	+	0.370820i
$214$		0			0
$215$	0.839648	+	1.45431i	0.0572635	+	0.0991833i
$216$		0			0
$217$	−9.96616	−	13.2542i	−0.676547	−	0.899757i
$218$		0			0
$219$	0.562293	+	0.973920i	0.0379962	+	0.0658114i
$220$		0			0
$221$	2.86275	−	4.95843i	0.192570	−	0.333540i
$222$		0			0
$223$	−3.88494			−0.260155			−0.130077	−	0.991504i	$-0.541523\pi$
$223$	−3.88494			−0.260155			−0.130077	+	0.991504i	$0.541523\pi$
$224$		0			0
$225$	6.32070			0.421380
$226$		0			0
$227$	11.2151	−	19.4251i	0.744372	−	1.28929i	−0.206115	−	0.978528i	$-0.566082\pi$
$227$	11.2151	−	19.4251i	0.744372	−	1.28929i	0.950488	−	0.310763i	$-0.100584\pi$
$228$		0			0
$229$	6.60894	+	11.4470i	0.436731	+	0.756441i	0.997435	−	0.0715758i	$-0.0228028\pi$
$229$	6.60894	+	11.4470i	0.436731	+	0.756441i	−0.560704	+	0.828016i	$0.689469\pi$
$230$		0			0
$231$	6.64146	−	0.808447i	0.436976	−	0.0531919i
$232$		0			0
$233$	6.30925	+	10.9279i	0.413333	+	0.715914i	0.995252	−	0.0973332i	$-0.0310312\pi$
$233$	6.30925	+	10.9279i	0.413333	+	0.715914i	−0.581919	+	0.813247i	$0.697698\pi$
$234$		0			0
$235$	1.10879	−	1.92049i	0.0723297	−	0.125279i
$236$		0			0
$237$	−2.21100			−0.143620
$238$		0			0
$239$	14.7588			0.954668			0.477334	−	0.878722i	$-0.341603\pi$
$239$	14.7588			0.954668			0.477334	+	0.878722i	$0.341603\pi$
$240$		0			0
$241$	−8.11649	+	14.0582i	−0.522829	+	0.905567i	0.476818	+	0.879002i	$0.341790\pi$
$241$	−8.11649	+	14.0582i	−0.522829	+	0.905567i	−0.999647	+	0.0265645i	$0.991543\pi$
$242$		0			0
$243$	7.76996	+	13.4580i	0.498443	+	0.863328i
$244$		0			0
$245$	−3.00046	+	10.3822i	−0.191692	+	0.663292i
$246$		0			0
$247$	3.67457	+	6.36454i	0.233807	+	0.404966i
$248$		0			0
$249$	−5.30824	+	9.19415i	−0.336396	+	0.582656i
$250$		0			0
$251$	−11.4863			−0.725011			−0.362505	−	0.931982i	$-0.618079\pi$
$251$	−11.4863			−0.725011			−0.362505	+	0.931982i	$0.618079\pi$
$252$		0			0
$253$	−8.72133			−0.548305
$254$		0			0
$255$	−1.73740	+	3.00926i	−0.108800	+	0.188447i
$256$		0			0
$257$	−8.23197	−	14.2582i	−0.513496	−	0.889402i	−0.999877	−	0.0156549i	$-0.995017\pi$
$257$	−8.23197	−	14.2582i	−0.513496	−	0.889402i	0.486381	−	0.873747i	$-0.338317\pi$
$258$		0			0
$259$	18.4295	−	2.24337i	1.14515	−	0.139396i
$260$		0			0
$261$	10.3405	+	17.9102i	0.640058	+	1.10861i
$262$		0			0
$263$	2.31812	−	4.01510i	0.142941	−	0.247582i	−0.785662	−	0.618656i	$-0.787677\pi$
$263$	2.31812	−	4.01510i	0.142941	−	0.247582i	0.928603	+	0.371075i	$0.121011\pi$
$264$		0			0
$265$	−9.88168			−0.607027
$266$		0			0
$267$	6.90561			0.422616
$268$		0			0
$269$	−15.5003	+	26.8474i	−0.945073	+	1.63691i	−0.189467	+	0.981887i	$0.560676\pi$
$269$	−15.5003	+	26.8474i	−0.945073	+	1.63691i	−0.755605	+	0.655027i	$0.772657\pi$
$270$		0			0
$271$	3.49822	+	6.05910i	0.212502	+	0.368064i	0.952497	−	0.304548i	$-0.0985055\pi$
$271$	3.49822	+	6.05910i	0.212502	+	0.368064i	−0.739995	+	0.672612i	$0.765172\pi$
$272$		0			0
$273$	2.36334	+	3.14307i	0.143036	+	0.190227i
$274$		0			0
$275$	−4.32799	−	7.49631i	−0.260988	−	0.452044i
$276$		0			0
$277$	13.8168	−	23.9314i	0.830171	−	1.43790i	−0.0677311	−	0.997704i	$-0.521576\pi$
$277$	13.8168	−	23.9314i	0.830171	−	1.43790i	0.897902	−	0.440195i	$-0.145091\pi$
$278$		0			0
$279$	−15.1413			−0.906486
$280$		0			0
$281$	−14.5610			−0.868635			−0.434317	−	0.900760i	$-0.643010\pi$
$281$	−14.5610			−0.868635			−0.434317	+	0.900760i	$0.643010\pi$
$282$		0			0
$283$	−0.345878	+	0.599077i	−0.0205603	+	0.0356115i	−0.876122	−	0.482089i	$-0.839878\pi$
$283$	−0.345878	+	0.599077i	−0.0205603	+	0.0356115i	0.855562	+	0.517700i	$0.173212\pi$
$284$		0			0
$285$	−2.23008	−	3.86262i	−0.132099	−	0.228802i
$286$		0			0
$287$	−12.5288	+	29.4306i	−0.739550	+	1.73724i
$288$		0			0
$289$	4.16501	+	7.21400i	0.245000	+	0.424353i
$290$		0			0
$291$	0.549983	−	0.952599i	0.0322406	−	0.0558423i
$292$		0			0
$293$	11.2330			0.656238			0.328119	−	0.944636i	$-0.393585\pi$
$293$	11.2330			0.656238			0.328119	+	0.944636i	$0.393585\pi$
$294$		0			0
$295$	−2.85940			−0.166481
$296$		0			0
$297$	6.84754	−	11.8603i	0.397335	−	0.688204i
$298$		0			0
$299$	−2.56306	−	4.43936i	−0.148226	−	0.256735i
$300$		0			0
$301$	1.12722	−	2.64790i	0.0649721	−	0.152622i
$302$		0			0
$303$	−1.25648	−	2.17629i	−0.0721831	−	0.125025i
$304$		0			0
$305$	3.76074	−	6.51379i	0.215339	−	0.372978i
$306$		0			0
$307$	−30.2097			−1.72416			−0.862079	−	0.506775i	$-0.830838\pi$
$307$	−30.2097			−1.72416			−0.862079	+	0.506775i	$0.830838\pi$
$308$		0			0
$309$	14.7165			0.837190
$310$		0			0
$311$	−3.68390	+	6.38070i	−0.208895	+	0.361816i	−0.951367	−	0.308061i	$-0.900320\pi$
$311$	−3.68390	+	6.38070i	−0.208895	+	0.361816i	0.742472	+	0.669877i	$0.233653\pi$
$312$		0			0
$313$	−13.1684	−	22.8084i	−0.744325	−	1.28921i	−0.950510	−	0.310695i	$-0.899438\pi$
$313$	−13.1684	−	22.8084i	−0.744325	−	1.28921i	0.206185	−	0.978513i	$-0.433895\pi$
$314$		0			0
$315$	5.93015	+	7.88666i	0.334126	+	0.444363i
$316$		0			0
$317$	−3.34355	−	5.79120i	−0.187793	−	0.325266i	0.756721	−	0.653737i	$-0.226800\pi$
$317$	−3.34355	−	5.79120i	−0.187793	−	0.325266i	−0.944514	+	0.328471i	$0.893467\pi$
$318$		0			0
$319$	14.1609	−	24.5274i	0.792858	−	1.37327i
$320$		0			0
$321$	6.05753			0.338098
$322$		0			0
$323$	11.1286			0.619213
$324$		0			0
$325$	2.54386	−	4.40610i	0.141108	−	0.244406i
$326$		0			0
$327$	0.814129	+	1.41011i	0.0450214	+	0.0779794i
$328$		0			0
$329$	−3.77248	+	0.459214i	−0.207984	+	0.0253173i
$330$		0			0
$331$	−13.3740	−	23.1644i	−0.735100	−	1.27323i	−0.954679	−	0.297637i	$-0.903802\pi$
$331$	−13.3740	−	23.1644i	−0.735100	−	1.27323i	0.219579	−	0.975595i	$-0.429532\pi$
$332$		0			0
$333$	8.47569	−	14.6803i	0.464465	−	0.804476i
$334$		0			0
$335$	−18.1266			−0.990362
$336$		0			0
$337$	7.94448			0.432764			0.216382	−	0.976309i	$-0.430574\pi$
$337$	7.94448			0.432764			0.216382	+	0.976309i	$0.430574\pi$
$338$		0			0
$339$	−4.81224	+	8.33504i	−0.261365	+	0.452697i
$340$		0			0
$341$	10.3678	+	17.9575i	0.561445	+	0.972452i
$342$		0			0
$343$	17.3108	−	6.58300i	0.934696	−	0.355449i
$344$		0			0
$345$	1.55552	+	2.69423i	0.0837461	+	0.145053i
$346$		0			0
$347$	13.7020	−	23.7325i	0.735561	−	1.27403i	−0.218916	−	0.975744i	$-0.570252\pi$
$347$	13.7020	−	23.7325i	0.735561	−	1.27403i	0.954477	−	0.298285i	$-0.0964145\pi$
$348$		0			0
$349$	−27.5075			−1.47244			−0.736221	−	0.676742i	$-0.763391\pi$
$349$	−27.5075			−1.47244			−0.736221	+	0.676742i	$0.763391\pi$
$350$		0			0
$351$	8.04955			0.429653
$352$		0			0
$353$	4.28393	−	7.41998i	0.228011	−	0.394926i	−0.729208	−	0.684292i	$-0.760111\pi$
$353$	4.28393	−	7.41998i	0.228011	−	0.394926i	0.957218	+	0.289366i	$0.0934446\pi$
$354$		0			0
$355$	6.31088	+	10.9308i	0.334947	+	0.580145i
$356$		0			0
$357$	5.91119	−	0.719554i	0.312854	−	0.0380828i
$358$		0			0
$359$	−12.2989	−	21.3024i	−0.649112	−	1.12430i	−0.983335	−	0.181801i	$-0.941807\pi$
$359$	−12.2989	−	21.3024i	−0.649112	−	1.12430i	0.334223	−	0.942494i	$-0.391526\pi$
$360$		0			0
$361$	2.35777	−	4.08377i	0.124093	−	0.214936i
$362$		0			0
$363$	0.0424350			0.00222726
$364$		0			0
$365$	2.27138			0.118890
$366$		0			0
$367$	−11.3872	+	19.7232i	−0.594407	+	1.02954i	0.399224	+	0.916854i	$0.369280\pi$
$367$	−11.3872	+	19.7232i	−0.594407	+	1.02954i	−0.993630	+	0.112689i	$0.964054\pi$
$368$		0			0
$369$	14.6027	+	25.2926i	0.760187	+	1.31668i
$370$		0			0
$371$	10.1773	+	13.5351i	0.528380	+	0.702706i
$372$		0			0
$373$	0.929848	+	1.61054i	0.0481457	+	0.0833908i	0.889094	−	0.457725i	$-0.151335\pi$
$373$	0.929848	+	1.61054i	0.0481457	+	0.0833908i	−0.840948	+	0.541116i	$0.818002\pi$
$374$		0			0
$375$	−4.49412	+	7.78404i	−0.232075	+	0.401966i
$376$		0			0
$377$	16.6467			0.857348
$378$		0			0
$379$	25.4397			1.30675			0.653375	−	0.757034i	$-0.273352\pi$
$379$	25.4397			1.30675			0.653375	+	0.757034i	$0.273352\pi$
$380$		0			0
$381$	7.66845	−	13.2821i	0.392867	−	0.680465i
$382$		0			0
$383$	−15.9305	−	27.5924i	−0.814011	−	1.40991i	−0.910036	−	0.414529i	$-0.863946\pi$
$383$	−15.9305	−	27.5924i	−0.814011	−	1.40991i	0.0960253	−	0.995379i	$-0.469387\pi$
$384$		0			0
$385$	5.29295	−	12.4334i	0.269754	−	0.633663i
$386$		0			0
$387$	−1.31382	−	2.27560i	−0.0667851	−	0.115675i
$388$		0			0
$389$	7.39044	−	12.8006i	0.374710	−	0.649017i	−0.615574	−	0.788079i	$-0.711076\pi$
$389$	7.39044	−	12.8006i	0.374710	−	0.649017i	0.990284	+	0.139063i	$0.0444089\pi$
$390$		0			0
$391$	−7.76237			−0.392560
$392$		0			0
$393$	10.7526			0.542398
$394$		0			0
$395$	−2.23283	+	3.86738i	−0.112346	+	0.194589i
$396$		0			0
$397$	−11.0014	−	19.0549i	−0.552142	−	0.956338i	−0.998120	−	0.0612941i	$-0.980477\pi$
$397$	−11.0014	−	19.0549i	−0.552142	−	0.956338i	0.445978	−	0.895044i	$-0.352856\pi$
$398$		0			0
$399$	−2.99388	+	7.03276i	−0.149881	+	0.352078i
$400$		0			0
$401$	10.8475	+	18.7885i	0.541700	+	0.938253i	0.998807	+	0.0488405i	$0.0155526\pi$
$401$	10.8475	+	18.7885i	0.541700	+	0.938253i	−0.457106	+	0.889412i	$0.651114\pi$
$402$		0			0
$403$	−6.09385	+	10.5548i	−0.303556	+	0.525775i
$404$		0			0
$405$	6.30336			0.313217
$406$		0			0
$407$	−23.2143			−1.15069
$408$		0			0
$409$	3.81533	−	6.60835i	0.188656	−	0.326762i	−0.756146	−	0.654403i	$-0.772920\pi$
$409$	3.81533	−	6.60835i	0.188656	−	0.326762i	0.944802	+	0.327641i	$0.106254\pi$
$410$		0			0
$411$	4.19443	+	7.26496i	0.206896	+	0.358354i
$412$		0			0
$413$	2.94494	+	3.91656i	0.144911	+	0.192721i
$414$		0			0
$415$	10.7213	+	18.5699i	0.526289	+	0.911560i
$416$		0			0
$417$	−6.79458	+	11.7686i	−0.332732	+	0.576308i
$418$		0			0
$419$	32.2741			1.57669			0.788346	−	0.615232i	$-0.210938\pi$
$419$	32.2741			1.57669			0.788346	+	0.615232i	$0.210938\pi$
$420$		0			0
$421$	−6.05552			−0.295128			−0.147564	−	0.989053i	$-0.547143\pi$
$421$	−6.05552			−0.295128			−0.147564	+	0.989053i	$0.547143\pi$
$422$		0			0
$423$	−1.73495	+	3.00503i	−0.0843564	+	0.146110i
$424$		0			0
$425$	−3.85211	−	6.67205i	−0.186855	−	0.323642i
$426$		0			0
$427$	−12.7953	+	1.55753i	−0.619207	+	0.0753743i
$428$		0			0
$429$	−2.45857	−	4.25837i	−0.118701	−	0.205596i
$430$		0			0
$431$	7.81057	−	13.5283i	0.376222	−	0.651636i	−0.614287	−	0.789083i	$-0.710556\pi$
$431$	7.81057	−	13.5283i	0.376222	−	0.651636i	0.990509	+	0.137447i	$0.0438897\pi$
$432$		0			0
$433$	20.8475			1.00186			0.500932	−	0.865486i	$-0.332991\pi$
$433$	20.8475			1.00186			0.500932	+	0.865486i	$0.332991\pi$
$434$		0			0
$435$	−10.1028			−0.484393
$436$		0			0
$437$	4.98181	−	8.62874i	0.238312	−	0.412769i
$438$		0			0
$439$	19.7655	+	34.2348i	0.943356	+	1.63394i	0.759010	+	0.651079i	$0.225683\pi$
$439$	19.7655	+	34.2348i	0.943356	+	1.63394i	0.184346	+	0.982861i	$0.440983\pi$
$440$		0			0
$441$	4.69489	−	16.2452i	0.223566	−	0.773582i
$442$		0			0
$443$	5.83221	+	10.1017i	0.277097	+	0.479945i	0.970662	−	0.240448i	$-0.0772945\pi$
$443$	5.83221	+	10.1017i	0.277097	+	0.479945i	−0.693565	+	0.720394i	$0.743961\pi$
$444$		0			0
$445$	6.97380	−	12.0790i	0.330590	−	0.572598i
$446$		0			0
$447$	−7.29516			−0.345049
$448$		0			0
$449$	17.8979			0.844653			0.422326	−	0.906444i	$-0.361214\pi$
$449$	17.8979			0.844653			0.422326	+	0.906444i	$0.361214\pi$
$450$		0			0
$451$	19.9979	−	34.6374i	0.941665	−	1.63101i
$452$		0			0
$453$	−2.20387	−	3.81721i	−0.103547	−	0.179348i
$454$		0			0
$455$	7.88439	−	0.959745i	0.369626	−	0.0449935i
$456$		0			0
$457$	−10.3288	−	17.8900i	−0.483161	−	0.836859i	0.516652	−	0.856195i	$-0.327178\pi$
$457$	−10.3288	−	17.8900i	−0.483161	−	0.836859i	−0.999813	+	0.0193362i	$0.993845\pi$
$458$		0			0
$459$	6.09462	−	10.5562i	0.284472	−	0.492720i
$460$		0			0
$461$	−5.75973			−0.268257			−0.134129	−	0.990964i	$-0.542824\pi$
$461$	−5.75973			−0.268257			−0.134129	+	0.990964i	$0.542824\pi$
$462$		0			0
$463$	−4.40154			−0.204557			−0.102279	−	0.994756i	$-0.532613\pi$
$463$	−4.40154			−0.204557			−0.102279	+	0.994756i	$0.532613\pi$
$464$		0			0
$465$	3.69834	−	6.40571i	0.171506	−	0.297057i
$466$		0			0
$467$	1.54518	+	2.67633i	0.0715024	+	0.123846i	0.899560	−	0.436797i	$-0.143887\pi$
$467$	1.54518	+	2.67633i	0.0715024	+	0.123846i	−0.828058	+	0.560643i	$0.810554\pi$
$468$		0			0
$469$	18.6689	+	24.8282i	0.862050	+	1.14646i
$470$		0			0
$471$	−3.70852	−	6.42334i	−0.170879	−	0.295972i
$472$		0			0
$473$	−1.79923	+	3.11636i	−0.0827286	+	0.143290i
$474$		0			0
$475$	9.88897			0.453737
$476$		0			0
$477$	15.4621			0.707961
$478$		0			0
$479$	−4.46803	+	7.73885i	−0.204149	+	0.353597i	−0.949861	−	0.312671i	$-0.898776\pi$
$479$	−4.46803	+	7.73885i	−0.204149	+	0.353597i	0.745712	+	0.666268i	$0.232110\pi$
$480$		0			0
$481$	−6.82233	−	11.8166i	−0.311072	−	0.538792i
$482$		0			0
$483$	2.08827	−	4.90545i	0.0950197	−	0.223206i
$484$		0			0
$485$	−1.11083	−	1.92401i	−0.0504401	−	0.0873649i
$486$		0			0
$487$	−18.6031	+	32.2214i	−0.842985	+	1.46009i	0.0443746	+	0.999015i	$0.485870\pi$
$487$	−18.6031	+	32.2214i	−0.842985	+	1.46009i	−0.887360	+	0.461078i	$0.847463\pi$
$488$		0			0
$489$	−7.53078			−0.340554
$490$		0			0
$491$	24.6589			1.11284			0.556421	−	0.830901i	$-0.312174\pi$
$491$	24.6589			1.11284			0.556421	+	0.830901i	$0.312174\pi$
$492$		0			0
$493$	12.6038	−	21.8305i	0.567648	−	0.983195i
$494$		0			0
$495$	−6.16911	−	10.6852i	−0.277281	−	0.480265i
$496$		0			0
$497$	8.47233	−	19.9019i	0.380036	−	0.892722i
$498$		0			0
$499$	−6.69509	−	11.5962i	−0.299713	−	0.519119i	0.676357	−	0.736574i	$-0.263558\pi$
$499$	−6.69509	−	11.5962i	−0.299713	−	0.519119i	−0.976070	+	0.217455i	$0.930224\pi$
$500$		0			0
$501$	−1.09683	+	1.89976i	−0.0490027	+	0.0848751i
$502$		0			0
$503$	−20.8355			−0.929008			−0.464504	−	0.885571i	$-0.653767\pi$
$503$	−20.8355			−0.929008			−0.464504	+	0.885571i	$0.653767\pi$
$504$		0			0
$505$	−5.07556			−0.225860
$506$		0			0
$507$	−3.52342	+	6.10273i	−0.156480	+	0.271032i
$508$		0			0
$509$	13.3904	+	23.1929i	0.593521	+	1.02801i	0.993754	+	0.111595i	$0.0355958\pi$
$509$	13.3904	+	23.1929i	0.593521	+	1.02801i	−0.400233	+	0.916413i	$0.631071\pi$
$510$		0			0
$511$	−2.33934	−	3.11114i	−0.103486	−	0.137629i
$512$		0			0
$513$	7.82292	+	13.5497i	0.345390	+	0.598234i
$514$		0			0
$515$	14.8618	−	25.7414i	0.654888	−	1.13430i
$516$		0			0
$517$	4.75192			0.208989
$518$		0			0
$519$	6.55540			0.287750
$520$		0			0
$521$	−7.26083	+	12.5761i	−0.318103	+	0.550970i	−0.980092	−	0.198543i	$-0.936379\pi$
$521$	−7.26083	+	12.5761i	−0.318103	+	0.550970i	0.661990	+	0.749513i	$0.269712\pi$
$522$		0			0
$523$	−0.838878	−	1.45298i	−0.0366816	−	0.0635343i	0.847102	−	0.531431i	$-0.178345\pi$
$523$	−0.838878	−	1.45298i	−0.0366816	−	0.0635343i	−0.883783	+	0.467896i	$0.845012\pi$
$524$		0			0
$525$	5.25273	−	0.639400i	0.229248	−	0.0279057i
$526$		0			0
$527$	9.22776	+	15.9829i	0.401967	+	0.696228i
$528$		0			0
$529$	8.02512	−	13.8999i	0.348918	−	0.604344i
$530$		0			0
$531$	4.47417			0.194162
$532$		0			0
$533$	23.5083			1.01826
$534$		0			0
$535$	6.11735	−	10.5956i	0.264476	−	0.458086i
$536$		0			0
$537$	5.65276	+	9.79087i	0.243935	+	0.422507i
$538$		0			0
$539$	−22.4815	+	5.55553i	−0.968345	+	0.239294i
$540$		0			0
$541$	−3.15746	−	5.46888i	−0.135750	−	0.235125i	0.790134	−	0.612934i	$-0.210011\pi$
$541$	−3.15746	−	5.46888i	−0.135750	−	0.235125i	−0.925884	+	0.377809i	$0.876678\pi$
$542$		0			0
$543$	−9.72598	+	16.8459i	−0.417382	+	0.722926i
$544$		0			0
$545$	3.28867			0.140871
$546$		0			0
$547$	−11.0564			−0.472739			−0.236370	−	0.971663i	$-0.575958\pi$
$547$	−11.0564			−0.472739			−0.236370	+	0.971663i	$0.575958\pi$
$548$		0			0
$549$	−5.88452	+	10.1923i	−0.251145	+	0.434996i
$550$		0			0
$551$	16.1780	+	28.0211i	0.689207	+	1.19374i
$552$		0			0
$553$	7.59683	−	0.924741i	0.323050	−	0.0393240i
$554$		0			0
$555$	4.14045	+	7.17148i	0.175752	+	0.304412i
$556$		0			0
$557$	−2.03774	+	3.52947i	−0.0863419	+	0.149548i	−0.905962	−	0.423359i	$-0.860851\pi$
$557$	−2.03774	+	3.52947i	−0.0863419	+	0.149548i	0.819620	+	0.572907i	$0.194184\pi$
$558$		0			0
$559$	−2.11506			−0.0894576
$560$		0			0
$561$	−7.44591			−0.314367
$562$		0			0
$563$	2.42748	−	4.20452i	0.102306	−	0.177199i	−0.810328	−	0.585976i	$-0.800711\pi$
$563$	2.42748	−	4.20452i	0.102306	−	0.177199i	0.912634	+	0.408777i	$0.134045\pi$
$564$		0			0
$565$	9.71951	+	16.8347i	0.408903	+	0.708241i
$566$		0			0
$567$	−6.49195	−	8.63380i	−0.272636	−	0.362586i
$568$		0			0
$569$	5.76984	+	9.99366i	0.241884	+	0.418956i	0.961251	−	0.275675i	$-0.0889012\pi$
$569$	5.76984	+	9.99366i	0.241884	+	0.418956i	−0.719367	+	0.694631i	$0.755568\pi$
$570$		0			0
$571$	−0.290362	+	0.502922i	−0.0121513	+	0.0210466i	−0.872037	−	0.489440i	$-0.837201\pi$
$571$	−0.290362	+	0.502922i	−0.0121513	+	0.0210466i	0.859886	+	0.510486i	$0.170535\pi$
$572$		0			0
$573$	−5.23917			−0.218870
$574$		0			0
$575$	−6.89769			−0.287654
$576$		0			0
$577$	0.530193	−	0.918321i	0.0220722	−	0.0382302i	−0.854778	−	0.518993i	$-0.826307\pi$
$577$	0.530193	−	0.918321i	0.0220722	−	0.0382302i	0.876851	+	0.480763i	$0.159640\pi$
$578$		0			0
$579$	9.89176	+	17.1330i	0.411087	+	0.712024i
$580$		0			0
$581$	14.3933	−	33.8106i	0.597136	−	1.40270i
$582$		0			0
$583$	−10.5874	−	18.3379i	−0.438486	−	0.759480i
$584$		0			0
$585$	3.62601	−	6.28044i	0.149917	−	0.259664i
$586$		0			0
$587$	7.52165			0.310452			0.155226	−	0.987879i	$-0.450389\pi$
$587$	7.52165			0.310452			0.155226	+	0.987879i	$0.450389\pi$
$588$		0			0
$589$	−23.6891			−0.976093
$590$		0			0
$591$	0.519088	−	0.899086i	0.0213524	−	0.0369835i
$592$		0			0
$593$	5.63615	+	9.76210i	0.231449	+	0.400881i	0.958235	−	0.285983i	$-0.0923200\pi$
$593$	5.63615	+	9.76210i	0.231449	+	0.400881i	−0.726786	+	0.686864i	$0.758987\pi$
$594$		0			0
$595$	4.71096	−	11.0663i	0.193130	−	0.453672i
$596$		0			0
$597$	−8.38599	−	14.5250i	−0.343216	−	0.594467i
$598$		0			0
$599$	20.3846	−	35.3071i	0.832890	−	1.44261i	−0.0628464	−	0.998023i	$-0.520018\pi$
$599$	20.3846	−	35.3071i	0.832890	−	1.44261i	0.895737	−	0.444585i	$-0.146649\pi$
$600$		0			0
$601$	0.189625			0.00773497			0.00386749	−	0.999993i	$-0.498769\pi$
$601$	0.189625			0.00773497			0.00386749	+	0.999993i	$0.498769\pi$
$602$		0			0
$603$	28.3631			1.15504
$604$		0			0
$605$	0.0428541	−	0.0742255i	0.00174227	−	0.00301769i
$606$		0			0
$607$	8.86547	+	15.3554i	0.359838	+	0.623258i	0.987934	−	0.154878i	$-0.0494986\pi$
$607$	8.86547	+	15.3554i	0.359838	+	0.623258i	−0.628095	+	0.778136i	$0.716165\pi$
$608$		0			0
$609$	10.4051	+	13.8380i	0.421635	+	0.560743i
$610$		0			0
$611$	1.39652	+	2.41884i	0.0564970	+	0.0978557i
$612$		0			0
$613$	−19.1124	+	33.1036i	−0.771942	+	1.33704i	0.164555	+	0.986368i	$0.447381\pi$
$613$	−19.1124	+	33.1036i	−0.771942	+	1.33704i	−0.936497	+	0.350675i	$0.885952\pi$
$614$		0			0
$615$	−14.2671			−0.575306
$616$		0			0
$617$	−19.8938			−0.800896			−0.400448	−	0.916320i	$-0.631145\pi$
$617$	−19.8938			−0.800896			−0.400448	+	0.916320i	$0.631145\pi$
$618$		0			0
$619$	−13.8508	+	23.9903i	−0.556710	+	0.964250i	0.441058	+	0.897479i	$0.354603\pi$
$619$	−13.8508	+	23.9903i	−0.556710	+	0.964250i	−0.997768	+	0.0667718i	$0.978730\pi$
$620$		0			0
$621$	−5.45660	−	9.45110i	−0.218966	−	0.379260i
$622$		0			0
$623$	−23.7272	+	2.88824i	−0.950609	+	0.115715i
$624$		0			0
$625$	2.53577	+	4.39208i	0.101431	+	0.175683i
$626$		0			0
$627$	4.77871	−	8.27697i	0.190843	−	0.330550i
$628$		0			0
$629$	−20.6618			−0.823839
$630$		0			0
$631$	−16.7670			−0.667485			−0.333742	−	0.942664i	$-0.608312\pi$
$631$	−16.7670			−0.667485			−0.333742	+	0.942664i	$0.608312\pi$
$632$		0			0
$633$	−9.80967	+	16.9909i	−0.389899	+	0.675326i
$634$		0			0
$635$	−15.4883	−	26.8266i	−0.614636	−	1.06458i
$636$		0			0
$637$	−9.43485	−	9.81089i	−0.373822	−	0.388722i
$638$		0			0
$639$	−9.87479	−	17.1036i	−0.390641	−	0.676610i
$640$		0			0
$641$	5.84511	−	10.1240i	0.230868	−	0.399875i	−0.727196	−	0.686430i	$-0.759177\pi$
$641$	5.84511	−	10.1240i	0.230868	−	0.399875i	0.958064	+	0.286555i	$0.0925102\pi$
$642$		0			0
$643$	−35.1521			−1.38627			−0.693133	−	0.720810i	$-0.743770\pi$
$643$	−35.1521			−1.38627			−0.693133	+	0.720810i	$0.743770\pi$
$644$		0			0
$645$	1.28363			0.0505427
$646$		0			0
$647$	3.67832	−	6.37104i	0.144610	−	0.250472i	−0.784617	−	0.619980i	$-0.787141\pi$
$647$	3.67832	−	6.37104i	0.144610	−	0.250472i	0.929227	+	0.369509i	$0.120474\pi$
$648$		0			0
$649$	−3.06361	−	5.30633i	−0.120257	−	0.208292i
$650$		0			0
$651$	−12.5830	+	1.53169i	−0.493165	+	0.0600316i
$652$		0			0
$653$	22.7935	+	39.4795i	0.891978	+	1.54495i	0.837500	+	0.546437i	$0.184016\pi$
$653$	22.7935	+	39.4795i	0.891978	+	1.54495i	0.0544781	+	0.998515i	$0.482651\pi$
$654$		0			0
$655$	10.8588	−	18.8080i	0.424288	−	0.734889i
$656$		0			0
$657$	−3.55409			−0.138658
$658$		0			0
$659$	−37.2974			−1.45290			−0.726450	−	0.687219i	$-0.758831\pi$
$659$	−37.2974			−1.45290			−0.726450	+	0.687219i	$0.758831\pi$
$660$		0			0
$661$	4.83453	−	8.37366i	0.188042	−	0.325698i	−0.756556	−	0.653929i	$-0.773119\pi$
$661$	4.83453	−	8.37366i	0.188042	−	0.325698i	0.944597	+	0.328232i	$0.106453\pi$
$662$		0			0
$663$	−2.18824	−	3.79014i	−0.0849842	−	0.147197i
$664$		0			0
$665$	9.27794	+	12.3390i	0.359783	+	0.478484i
$666$		0			0
$667$	−11.2844	−	19.5451i	−0.436933	−	0.756791i
$668$		0			0
$669$	−1.48479	+	2.57173i	−0.0574053	+	0.0994289i
$670$		0			0
$671$	16.1173			0.622201
$672$		0			0
$673$	−31.7566			−1.22413			−0.612064	−	0.790808i	$-0.709661\pi$
$673$	−31.7566			−1.22413			−0.612064	+	0.790808i	$0.709661\pi$
$674$		0			0
$675$	5.41572	−	9.38030i	0.208451	−	0.361048i
$676$		0			0
$677$	−25.3869	−	43.9714i	−0.975697	−	1.68996i	−0.677615	−	0.735417i	$-0.736987\pi$
$677$	−25.3869	−	43.9714i	−0.975697	−	1.68996i	−0.298082	−	0.954540i	$-0.596347\pi$
$678$		0			0
$679$	−1.49128	+	3.50309i	−0.0572302	+	0.134436i
$680$		0			0
$681$	−8.57263	−	14.8482i	−0.328504	−	0.568985i
$682$		0			0
$683$	−8.63547	+	14.9571i	−0.330427	+	0.572316i	−0.982596	−	0.185758i	$-0.940526\pi$
$683$	−8.63547	+	14.9571i	−0.330427	+	0.572316i	0.652169	+	0.758074i	$0.273859\pi$
$684$		0			0
$685$	16.9434			0.647374
$686$		0			0
$687$	10.1035			0.385473
$688$		0			0
$689$	6.22296	−	10.7785i	0.237076	−	0.410627i
$690$		0			0
$691$	18.0657	+	31.2908i	0.687253	+	1.19036i	0.972723	+	0.231969i	$0.0745169\pi$
$691$	18.0657	+	31.2908i	0.687253	+	1.19036i	−0.285470	+	0.958388i	$0.592150\pi$
$692$		0			0
$693$	−8.28200	+	19.4548i	−0.314607	+	0.739027i
$694$		0			0
$695$	13.7233	+	23.7695i	0.520556	+	0.901630i
$696$		0			0
$697$	17.7990	−	30.8288i	0.674186	−	1.16772i
$698$		0			0
$699$	9.64537			0.364821
$700$		0			0
$701$	15.8908			0.600188			0.300094	−	0.953910i	$-0.402982\pi$
$701$	15.8908			0.600188			0.300094	+	0.953910i	$0.402982\pi$
$702$		0			0
$703$	13.2605	−	22.9679i	0.500130	−	0.866250i
$704$		0			0
$705$	−0.847542	−	1.46799i	−0.0319203	−	0.0552875i
$706$		0			0
$707$	5.22741	+	6.95207i	0.196597	+	0.261459i
$708$		0			0
$709$	8.55586	+	14.8192i	0.321322	+	0.556546i	0.980761	−	0.195212i	$-0.0625394\pi$
$709$	8.55586	+	14.8192i	0.321322	+	0.556546i	−0.659439	+	0.751758i	$0.729206\pi$
$710$		0			0
$711$	3.49376	−	6.05138i	0.131026	−	0.226944i
$712$		0			0
$713$	16.5235			0.618810
$714$		0			0
$715$	−9.93140			−0.371413
$716$		0			0
$717$	5.64069	−	9.76996i	0.210655	−	0.364866i
$718$		0			0
$719$	−21.3674	−	37.0095i	−0.796871	−	1.38022i	−0.921644	−	0.388036i	$-0.873154\pi$
$719$	−21.3674	−	37.0095i	−0.796871	−	1.38022i	0.124773	−	0.992185i	$-0.460180\pi$
$720$		0			0
$721$	−50.5647	+	6.15510i	−1.88313	+	0.229228i
$722$		0			0
$723$	6.20411	+	10.7458i	0.230733	+	0.399642i
$724$		0			0
$725$	11.1999	−	19.3987i	0.415952	−	0.720450i
$726$		0			0
$727$	10.3509			0.383894			0.191947	−	0.981405i	$-0.438520\pi$
$727$	10.3509			0.383894			0.191947	+	0.981405i	$0.438520\pi$
$728$		0			0
$729$	−0.370120			−0.0137082
$730$		0			0
$731$	−1.60139	+	2.77369i	−0.0592297	+	0.102589i
$732$		0			0
$733$	5.64135	+	9.77111i	0.208368	+	0.360904i	0.951201	−	0.308573i	$-0.0998515\pi$
$733$	5.64135	+	9.77111i	0.208368	+	0.360904i	−0.742832	+	0.669477i	$0.766518\pi$
$734$		0			0
$735$	5.72598	+	5.95420i	0.211206	+	0.219624i
$736$		0			0
$737$	−19.4212	−	33.6385i	−0.715388	−	1.23909i
$738$		0			0
$739$	−15.0199	+	26.0152i	−0.552516	+	0.956986i	0.445576	+	0.895244i	$0.352999\pi$
$739$	−15.0199	+	26.0152i	−0.552516	+	0.956986i	−0.998092	+	0.0617416i	$0.980335\pi$
$740$		0			0
$741$	5.61756			0.206366
$742$		0			0
$743$	−5.88897			−0.216045			−0.108023	−	0.994148i	$-0.534452\pi$
$743$	−5.88897			−0.216045			−0.108023	+	0.994148i	$0.534452\pi$
$744$		0			0
$745$	−7.36720	+	12.7604i	−0.269913	+	0.467504i
$746$		0			0
$747$	−16.7759	−	29.0567i	−0.613799	−	1.06313i
$748$		0			0
$749$	−20.8132	+	2.53354i	−0.760499	+	0.0925735i
$750$		0			0
$751$	12.6374	+	21.8885i	0.461144	+	0.798724i	0.999018	−	0.0443006i	$-0.0141059\pi$
$751$	12.6374	+	21.8885i	0.461144	+	0.798724i	−0.537875	+	0.843025i	$0.680773\pi$
$752$		0			0
$753$	−4.38998	+	7.60366i	−0.159980	+	0.277093i
$754$		0			0
$755$	−8.90252			−0.323996
$756$		0			0
$757$	−17.9050			−0.650768			−0.325384	−	0.945582i	$-0.605494\pi$
$757$	−17.9050			−0.650768			−0.325384	+	0.945582i	$0.605494\pi$
$758$		0			0
$759$	−3.33322	+	5.77330i	−0.120988	+	0.209558i
$760$		0			0
$761$	10.2895	+	17.8219i	0.372994	+	0.646045i	0.990025	−	0.140894i	$-0.0449978\pi$
$761$	10.2895	+	17.8219i	0.372994	+	0.646045i	−0.617030	+	0.786939i	$0.711664\pi$
$762$		0			0
$763$	−3.38706	−	4.50454i	−0.122620	−	0.163075i
$764$		0			0
$765$	−5.49078	−	9.51031i	−0.198520	−	0.343846i
$766$		0			0
$767$	1.80070	−	3.11890i	0.0650194	−	0.112617i
$768$		0			0
$769$	−20.7759			−0.749199			−0.374599	−	0.927187i	$-0.622220\pi$
$769$	−20.7759			−0.749199			−0.374599	+	0.927187i	$0.622220\pi$
$770$		0			0
$771$	−12.5848			−0.453229
$772$		0			0
$773$	−11.4357	+	19.8073i	−0.411314	+	0.712418i	−0.995034	−	0.0995380i	$-0.968264\pi$
$773$	−11.4357	+	19.8073i	−0.411314	+	0.712418i	0.583719	+	0.811956i	$0.301597\pi$
$774$		0			0
$775$	8.19985	+	14.2026i	0.294547	+	0.510171i
$776$		0			0
$777$	5.55854	−	13.0573i	0.199411	−	0.468427i
$778$		0			0
$779$	22.8465	+	39.5712i	0.818559	+	1.41779i
$780$		0			0
$781$	−13.5232	+	23.4229i	−0.483898	+	0.838136i
$782$		0			0
$783$	35.4397			1.26651
$784$		0			0
$785$	−14.9805			−0.534679
$786$		0			0
$787$	13.1834	−	22.8344i	0.469939	−	0.813958i	−0.529470	−	0.848328i	$-0.677609\pi$
$787$	13.1834	−	22.8344i	0.469939	−	0.813958i	0.999409	+	0.0343706i	$0.0109427\pi$
$788$		0			0
$789$	−1.77193	−	3.06907i	−0.0630824	−	0.109262i
$790$		0			0
$791$	13.0484	−	30.6513i	0.463948	−	1.08983i
$792$		0			0
$793$	4.73663	+	8.20408i	0.168202	+	0.291335i
$794$		0			0
$795$	−3.77669	+	6.54142i	−0.133945	+	0.232000i
$796$		0			0
$797$	1.44306			0.0511157			0.0255579	−	0.999673i	$-0.491864\pi$
$797$	1.44306			0.0511157			0.0255579	+	0.999673i	$0.491864\pi$
$798$		0			0
$799$	4.22942			0.149626
$800$		0			0
$801$	−10.9121	+	18.9003i	−0.385559	+	0.667808i
$802$		0			0
$803$	2.43360	+	4.21512i	0.0858799	+	0.148748i
$804$		0			0
$805$	−6.47149	−	8.60660i	−0.228090	−	0.303343i
$806$		0			0
$807$	11.8482	+	20.5217i	0.417076	+	0.722397i
$808$		0			0
$809$	−25.5629	+	44.2762i	−0.898743	+	1.55667i	−0.0696400	+	0.997572i	$0.522185\pi$
$809$	−25.5629	+	44.2762i	−0.898743	+	1.55667i	−0.829103	+	0.559096i	$0.811148\pi$
$810$		0			0
$811$	6.09058			0.213869			0.106935	−	0.994266i	$-0.465896\pi$
$811$	6.09058			0.213869			0.106935	+	0.994266i	$0.465896\pi$
$812$		0			0
$813$	5.34796			0.187561
$814$		0			0
$815$	−7.60515	+	13.1725i	−0.266397	+	0.461413i
$816$		0			0
$817$	−2.05552	−	3.56026i	−0.0719134	−	0.124558i
$818$		0			0
$819$	−12.3369	+	1.50174i	−0.431086	+	0.0524749i
$820$		0			0
$821$	−13.7855	−	23.8772i	−0.481117	−	0.833319i	0.518648	−	0.854988i	$-0.326435\pi$
$821$	−13.7855	−	23.8772i	−0.481117	−	0.833319i	−0.999765	+	0.0216689i	$0.993102\pi$
$822$		0			0
$823$	−4.04007	+	6.99760i	−0.140828	+	0.243921i	−0.927809	−	0.373057i	$-0.878310\pi$
$823$	−4.04007	+	6.99760i	−0.140828	+	0.243921i	0.786981	+	0.616978i	$0.211643\pi$
$824$		0			0
$825$	−6.61649			−0.230357
$826$		0			0
$827$	−21.5577			−0.749635			−0.374818	−	0.927099i	$-0.622295\pi$
$827$	−21.5577			−0.749635			−0.374818	+	0.927099i	$0.622295\pi$
$828$		0			0
$829$	−17.8581	+	30.9312i	−0.620238	+	1.07428i	0.369203	+	0.929349i	$0.379631\pi$
$829$	−17.8581	+	30.9312i	−0.620238	+	1.07428i	−0.989441	+	0.144935i	$0.953703\pi$
$830$		0			0
$831$	−10.5613	−	18.2928i	−0.366368	−	0.634569i
$832$		0			0
$833$	−20.0095	+	4.94467i	−0.693288	+	0.171323i
$834$		0			0
$835$	2.21532	+	3.83705i	0.0766643	+	0.132786i
$836$		0			0
$837$	−12.9734	+	22.4706i	−0.448426	+	0.776697i
$838$		0			0
$839$	32.6600			1.12755			0.563775	−	0.825929i	$-0.309349\pi$
$839$	32.6600			1.12755			0.563775	+	0.825929i	$0.309349\pi$
$840$		0			0
$841$	44.2903			1.52725
$842$		0			0
$843$	−5.56508	+	9.63900i	−0.191672	+	0.331985i
$844$		0			0
$845$	7.11642	+	12.3260i	0.244812	+	0.424027i
$846$		0			0
$847$	−0.145804	+	0.0177483i	−0.00500988	+	0.000609839i
$848$		0			0
$849$	0.264383	+	0.457925i	0.00907360	+	0.0157159i
$850$		0			0
$851$	−9.24939	+	16.0204i	−0.317065	+	0.549173i
$852$		0			0
$853$	−47.6416			−1.63122			−0.815608	−	0.578604i	$-0.803598\pi$
$853$	−47.6416			−1.63122			−0.815608	+	0.578604i	$0.803598\pi$
$854$		0			0
$855$	14.0957			0.482063
$856$		0			0
$857$	18.2411	−	31.5945i	0.623103	−	1.07925i	−0.365801	−	0.930693i	$-0.619205\pi$
$857$	18.2411	−	31.5945i	0.623103	−	1.07925i	0.988904	−	0.148554i	$-0.0474617\pi$
$858$		0			0
$859$	2.17823	+	3.77281i	0.0743204	+	0.128727i	0.900791	−	0.434254i	$-0.142988\pi$
$859$	2.17823	+	3.77281i	0.0743204	+	0.128727i	−0.826470	+	0.562981i	$0.809655\pi$
$860$		0			0
$861$	14.6940	+	19.5419i	0.500769	+	0.665985i
$862$		0			0
$863$	12.6093	+	21.8399i	0.429224	+	0.743438i	0.996804	−	0.0798802i	$-0.0254538\pi$
$863$	12.6093	+	21.8399i	0.429224	+	0.743438i	−0.567581	+	0.823318i	$0.692120\pi$
$864$		0			0
$865$	6.62014	−	11.4664i	0.225091	−	0.389870i
$866$		0			0
$867$	6.36732			0.216245
$868$		0			0
$869$	−9.56918			−0.324612
$870$		0			0
$871$	11.4152	−	19.7717i	0.386788	−	0.669937i
$872$		0			0
$873$	1.73814	+	3.01055i	0.0588271	+	0.101892i
$874$		0			0
$875$	12.1858	−	28.6250i	0.411956	−	0.967703i
$876$		0			0
$877$	1.31487	+	2.27743i	0.0444001	+	0.0769033i	0.887371	−	0.461055i	$-0.152529\pi$
$877$	1.31487	+	2.27743i	0.0444001	+	0.0769033i	−0.842971	+	0.537959i	$0.819196\pi$
$878$		0			0
$879$	4.29315	−	7.43595i	0.144804	−	0.250808i
$880$		0			0
$881$	−26.0573			−0.877893			−0.438946	−	0.898513i	$-0.644648\pi$
$881$	−26.0573			−0.877893			−0.438946	+	0.898513i	$0.644648\pi$
$882$		0			0
$883$	3.46311			0.116543			0.0582714	−	0.998301i	$-0.481441\pi$
$883$	3.46311			0.116543			0.0582714	+	0.998301i	$0.481441\pi$
$884$		0			0
$885$	−1.09284	+	1.89285i	−0.0367353	+	0.0636274i
$886$		0			0
$887$	6.62428	+	11.4736i	0.222421	+	0.385245i	0.955543	−	0.294853i	$-0.0952706\pi$
$887$	6.62428	+	11.4736i	0.222421	+	0.385245i	−0.733121	+	0.680098i	$0.761937\pi$
$888$		0			0
$889$	−20.7930	+	48.8438i	−0.697376	+	1.63817i
$890$		0			0
$891$	6.75354	+	11.6975i	0.226252	+	0.391880i
$892$		0			0
$893$	−2.71440	+	4.70148i	−0.0908339	+	0.157329i
$894$		0			0
$895$	22.8343			0.763268
$896$		0			0
$897$	−3.91832			−0.130829
$898$		0			0
$899$	−26.8293	+	46.4698i	−0.894809	+	1.54985i
$900$		0			0
$901$	−9.42327	−	16.3216i	−0.313935	−	0.543751i
$902$		0			0
$903$	−1.32203	−	1.75820i	−0.0439943	−	0.0585092i
$904$		0			0
$905$	19.6440	+	34.0245i	0.652990	+	1.13101i
$906$		0			0
$907$	4.19853	−	7.27207i	0.139410	−	0.241465i	−0.787863	−	0.615850i	$-0.788813\pi$
$907$	4.19853	−	7.27207i	0.139410	−	0.241465i	0.927273	+	0.374385i	$0.122146\pi$
$908$		0			0
$909$	7.94186			0.263415
$910$		0			0
$911$	41.6345			1.37941			0.689707	−	0.724089i	$-0.257739\pi$
$911$	41.6345			1.37941			0.689707	+	0.724089i	$0.257739\pi$
$912$		0			0
$913$	−22.9741	+	39.7922i	−0.760330	+	1.31693i
$914$		0			0
$915$	−2.87464	−	4.97903i	−0.0950328	−	0.164602i
$916$		0			0
$917$	−36.9452	+	4.49724i	−1.22004	+	0.148512i
$918$		0			0
$919$	−26.5388	−	45.9665i	−0.875434	−	1.51630i	−0.856300	−	0.516479i	$-0.827243\pi$
$919$	−26.5388	−	45.9665i	−0.875434	−	1.51630i	−0.0191337	−	0.999817i	$-0.506091\pi$
$920$		0			0
$921$	−11.5459	+	19.9980i	−0.380450	+	0.658958i
$922$		0			0
$923$	−15.8970			−0.523257
$924$		0			0
$925$	−18.3602			−0.603680
$926$		0			0
$927$	−23.2546	+	40.2781i	−0.763781	+	1.32291i
$928$		0			0
$929$	4.23217	+	7.33034i	0.138853	+	0.240501i	0.927063	−	0.374906i	$-0.122325\pi$
$929$	4.23217	+	7.33034i	0.138853	+	0.240501i	−0.788210	+	0.615407i	$0.788992\pi$
$930$		0			0
$931$	7.34533	−	25.4162i	0.240733	−	0.832983i
$932$		0			0
$933$	2.81591	+	4.87729i	0.0921887	+	0.159675i
$934$		0			0
$935$	−7.51944	+	13.0241i	−0.245912	+	0.425932i
$936$		0			0
$937$	−0.972661			−0.0317755			−0.0158877	−	0.999874i	$-0.505057\pi$
$937$	−0.972661			−0.0317755			−0.0158877	+	0.999874i	$0.505057\pi$
$938$		0			0
$939$	−20.1315			−0.656966
$940$		0			0
$941$	−15.8743	+	27.4952i	−0.517488	+	0.896316i	0.482305	+	0.876003i	$0.339800\pi$
$941$	−15.8743	+	27.4952i	−0.517488	+	0.896316i	−0.999794	+	0.0203130i	$0.993534\pi$
$942$		0			0
$943$	−15.9357	−	27.6015i	−0.518939	−	0.898828i
$944$		0			0
$945$	16.7854	−	2.04324i	0.546028	−	0.0664665i
$946$		0			0
$947$	−15.5919	−	27.0059i	−0.506668	−	0.877574i	−0.999970	−	0.00771617i	$-0.997544\pi$
$947$	−15.5919	−	27.0059i	−0.506668	−	0.877574i	0.493303	−	0.869858i	$-0.335789\pi$
$948$		0			0
$949$	−1.43040	+	2.47752i	−0.0464326	+	0.0804237i
$950$		0			0
$951$	−5.11151			−0.165752
$952$		0			0
$953$	10.6556			0.345168			0.172584	−	0.984995i	$-0.444788\pi$
$953$	10.6556			0.345168			0.172584	+	0.984995i	$0.444788\pi$
$954$		0			0
$955$	−5.29091	+	9.16413i	−0.171210	+	0.296544i
$956$		0			0
$957$	−10.8243	−	18.7483i	−0.349902	−	0.606047i
$958$		0			0
$959$	−17.4503	−	23.2076i	−0.563499	−	0.749412i
$960$		0			0
$961$	−4.14282	−	7.17558i	−0.133639	−	0.231470i
$962$		0			0
$963$	−9.57197	+	16.5791i	−0.308452	+	0.534255i
$964$		0			0
$965$	39.9577			1.28629
$966$		0			0
$967$	−6.11103			−0.196518			−0.0982588	−	0.995161i	$-0.531327\pi$
$967$	−6.11103			−0.196518			−0.0982588	+	0.995161i	$0.531327\pi$
$968$		0			0
$969$	4.25326	−	7.36687i	0.136634	−	0.236658i
$970$		0			0
$971$	−3.56585	−	6.17623i	−0.114434	−	0.198205i	0.803120	−	0.595818i	$-0.203172\pi$
$971$	−3.56585	−	6.17623i	−0.114434	−	0.198205i	−0.917553	+	0.397613i	$0.869839\pi$
$972$		0			0
$973$	18.4235	−	43.2777i	0.590631	−	1.38742i
$974$		0			0
$975$	−1.94448	−	3.36795i	−0.0622733	−	0.107861i
$976$		0			0
$977$	13.8138	−	23.9262i	0.441942	−	0.765467i	−0.555891	−	0.831255i	$-0.687623\pi$
$977$	13.8138	−	23.9262i	0.441942	−	0.765467i	0.997834	+	0.0657884i	$0.0209562\pi$
$978$		0			0
$979$	29.8874			0.955206
$980$		0			0
$981$	−5.14587			−0.164295
$982$		0			0
$983$	13.2594	−	22.9660i	0.422910	−	0.732501i	−0.573313	−	0.819337i	$-0.694342\pi$
$983$	13.2594	−	22.9660i	0.422910	−	0.732501i	0.996223	+	0.0868353i	$0.0276754\pi$
$984$		0			0
$985$	−1.04843	−	1.81593i	−0.0334057	−	0.0578603i
$986$		0			0
$987$	−1.13782	+	2.67279i	−0.0362173	+	0.0850760i
$988$		0			0
$989$	1.43375	+	2.48333i	0.0455906	+	0.0789653i
$990$		0			0
$991$	−22.1469	+	38.3596i	−0.703520	+	1.21853i	0.263703	+	0.964604i	$0.415056\pi$
$991$	−22.1469	+	38.3596i	−0.703520	+	1.21853i	−0.967223	+	0.253929i	$0.918277\pi$
$992$		0			0
$993$	−20.4457			−0.648824
$994$		0			0
$995$	−33.8752			−1.07392
$996$		0			0
$997$	6.29361	−	10.9008i	0.199321	−	0.345233i	−0.748988	−	0.662584i	$-0.769460\pi$
$997$	6.29361	−	10.9008i	0.199321	−	0.345233i	0.948308	+	0.317350i	$0.102793\pi$
$998$		0			0
$999$	−14.5243	−	25.1568i	−0.459529	−	0.795927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.i.h.641.3	yes	8
4.3	odd	2		896.2.i.c.641.2	yes	8
7.2	even	3	inner	896.2.i.h.513.3	yes	8
7.3	odd	6		6272.2.a.bs.1.3		4
7.4	even	3		6272.2.a.y.1.2		4
8.3	odd	2		896.2.i.f.641.3	yes	8
8.5	even	2		896.2.i.a.641.2	yes	8
28.3	even	6		6272.2.a.bf.1.2		4
28.11	odd	6		6272.2.a.br.1.3		4
28.23	odd	6		896.2.i.c.513.2	yes	8
56.3	even	6		6272.2.a.bo.1.3		4
56.11	odd	6		6272.2.a.bc.1.2		4
56.37	even	6		896.2.i.a.513.2	✓	8
56.45	odd	6		6272.2.a.bb.1.2		4
56.51	odd	6		896.2.i.f.513.3	yes	8
56.53	even	6		6272.2.a.bv.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.i.a.513.2	✓	8	56.37	even	6
896.2.i.a.641.2	yes	8	8.5	even	2
896.2.i.c.513.2	yes	8	28.23	odd	6
896.2.i.c.641.2	yes	8	4.3	odd	2
896.2.i.f.513.3	yes	8	56.51	odd	6
896.2.i.f.641.3	yes	8	8.3	odd	2
896.2.i.h.513.3	yes	8	7.2	even	3	inner
896.2.i.h.641.3	yes	8	1.1	even	1	trivial
6272.2.a.y.1.2		4	7.4	even	3
6272.2.a.bb.1.2		4	56.45	odd	6
6272.2.a.bc.1.2		4	56.11	odd	6
6272.2.a.bf.1.2		4	28.3	even	6
6272.2.a.bo.1.3		4	56.3	even	6
6272.2.a.br.1.3		4	28.11	odd	6
6272.2.a.bs.1.3		4	7.3	odd	6
6272.2.a.bv.1.3		4	56.53	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.382191 - 0.661975i) q^{3} +(-0.771931 - 1.33702i) q^{5} +(-1.03631 + 2.43435i) q^{7} +(1.20786 + 2.09207i) q^{9} +O(q^{10})\)	\(q+(0.382191 - 0.661975i) q^{3} +(-0.771931 - 1.33702i) q^{5} +(-1.03631 + 2.43435i) q^{7} +(1.20786 + 2.09207i) q^{9} +(1.65412 - 2.86502i) q^{11} +1.94448 q^{13} -1.18010 q^{15} +(1.47224 - 2.55000i) q^{17} +(1.88974 + 3.27313i) q^{19} +(1.21541 + 1.61640i) q^{21} +(-1.31812 - 2.28305i) q^{23} +(1.30824 - 2.26595i) q^{25} +4.13968 q^{27} +8.56097 q^{29} +(-3.13391 + 5.42810i) q^{31} +(-1.26438 - 2.18998i) q^{33} +(4.05474 - 0.493573i) q^{35} +(-3.50856 - 6.07700i) q^{37} +(0.743165 - 1.28720i) q^{39} +12.0897 q^{41} -1.08772 q^{43} +(1.86477 - 3.22987i) q^{45} +(0.718194 + 1.24395i) q^{47} +(-4.85211 - 5.04550i) q^{49} +(-1.12536 - 1.94918i) q^{51} +(3.20031 - 5.54310i) q^{53} -5.10747 q^{55} +2.88897 q^{57} +(0.926054 - 1.60397i) q^{59} +(2.43593 + 4.21915i) q^{61} +(-6.34456 + 0.772306i) q^{63} +(-1.50101 - 2.59982i) q^{65} +(5.87054 - 10.1681i) q^{67} -2.01510 q^{69} -8.17545 q^{71} +(-0.735617 + 1.27413i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(5.26028 + 6.99578i) q^{77} +(-1.44626 - 2.50500i) q^{79} +(-2.04143 + 3.53586i) q^{81} -13.8890 q^{83} -4.54588 q^{85} +(3.27193 - 5.66715i) q^{87} +(4.51711 + 7.82387i) q^{89} +(-2.01510 + 4.73355i) q^{91} +(2.39551 + 4.14914i) q^{93} +(2.91750 - 5.05325i) q^{95} +1.43903 q^{97} +7.99179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9	\( 8 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 20 q^{15} - 4 q^{17} + 8 q^{19} - 10 q^{21} - 4 q^{23} - 8 q^{25} - 40 q^{27} + 6 q^{31} - 8 q^{33} + 8 q^{35} - 2 q^{37} + 2 q^{39} + 24 q^{41} + 24 q^{43} + 8 q^{45} + 2 q^{47} - 4 q^{49} - 4 q^{51} + 18 q^{53} - 32 q^{55} - 40 q^{57} - 10 q^{59} + 14 q^{61} - 22 q^{63} + 8 q^{65} - 2 q^{67} - 4 q^{69} - 8 q^{73} - 8 q^{75} - 14 q^{77} - 16 q^{79} - 40 q^{81} - 48 q^{83} + 20 q^{85} + 18 q^{87} - 16 q^{89} - 4 q^{91} - 30 q^{93} + 32 q^{95} + 80 q^{97} - 44 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 20 * q^15 - 4 * q^17 + 8 * q^19 - 10 * q^21 - 4 * q^23 - 8 * q^25 - 40 * q^27 + 6 * q^31 - 8 * q^33 + 8 * q^35 - 2 * q^37 + 2 * q^39 + 24 * q^41 + 24 * q^43 + 8 * q^45 + 2 * q^47 - 4 * q^49 - 4 * q^51 + 18 * q^53 - 32 * q^55 - 40 * q^57 - 10 * q^59 + 14 * q^61 - 22 * q^63 + 8 * q^65 - 2 * q^67 - 4 * q^69 - 8 * q^73 - 8 * q^75 - 14 * q^77 - 16 * q^79 - 40 * q^81 - 48 * q^83 + 20 * q^85 + 18 * q^87 - 16 * q^89 - 4 * q^91 - 30 * q^93 + 32 * q^95 + 80 * q^97 - 44 * q^99

Introduction

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