LMFDB - Embedded newform 1232.2.bn.b.593.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(241,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))

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

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

chi := DirichletCharacter("1232.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.bn (of order $6$, degree $2$, not 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.3
Root			$-1.29724 - 0.347596i$ of defining polynomial
Character	$\chi$	$=$	1232.593
Dual form			1232.2.bn.b.241.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35034 + 0.779618i) q^{3} +(0.882559 + 0.509546i) q^{5} +(-2.25578 - 1.38256i) q^{7} +(-0.284392 + 0.492581i) q^{9} +O(q^{10})$	\(q+(-1.35034 + 0.779618i) q^{3} +(0.882559 + 0.509546i) q^{5} +(-2.25578 - 1.38256i) q^{7} +(-0.284392 + 0.492581i) q^{9} +(0.510616 + 3.27708i) q^{11} -0.167247 q^{13} -1.58900 q^{15} +(-1.47616 - 2.55678i) q^{17} +(0.155850 - 0.269940i) q^{19} +(4.12393 + 0.108278i) q^{21} +(-0.237719 + 0.411742i) q^{23} +(-1.98073 - 3.43072i) q^{25} -5.56458i q^{27} +1.89701i q^{29} +(2.20834 - 1.27498i) q^{31} +(-3.24438 - 4.02708i) q^{33} +(-1.28638 - 2.36961i) q^{35} +(-3.04667 + 5.27699i) q^{37} +(0.225839 - 0.130388i) q^{39} -10.2084 q^{41} -10.1222i q^{43} +(-0.501985 + 0.289821i) q^{45} +(3.28968 + 1.89930i) q^{47} +(3.17706 + 6.23749i) q^{49} +(3.98663 + 2.30168i) q^{51} +(-4.21079 - 7.29330i) q^{53} +(-1.21917 + 3.15240i) q^{55} +0.486014i q^{57} +(-5.40617 + 3.12126i) q^{59} +(5.93960 - 10.2877i) q^{61} +(1.32255 - 0.717964i) q^{63} +(-0.147605 - 0.0852198i) q^{65} +(-5.19151 - 8.99196i) q^{67} -0.741321i q^{69} -14.5206 q^{71} +(-4.85385 - 8.40712i) q^{73} +(5.34930 + 3.08842i) q^{75} +(3.37892 - 8.09833i) q^{77} +(-6.06709 - 3.50284i) q^{79} +(3.48507 + 6.03631i) q^{81} +14.6915 q^{83} -3.00868i q^{85} +(-1.47894 - 2.56161i) q^{87} +(5.97639 + 3.45047i) q^{89} +(0.377271 + 0.231228i) q^{91} +(-1.98800 + 3.44332i) q^{93} +(0.275094 - 0.158826i) q^{95} -11.0218i q^{97} +(-1.75944 - 0.680455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q - 12 * q^5 + 16 * q^9	$ 16 q - 12 q^{5} + 16 q^{9} - 8 q^{11} + 8 q^{15} - 16 q^{23} + 12 q^{31} - 24 q^{33} - 16 q^{37} - 108 q^{45} - 24 q^{47} + 8 q^{49} - 28 q^{53} - 60 q^{59} - 12 q^{67} - 8 q^{71} - 60 q^{75} + 44 q^{77} - 8 q^{81} + 96 q^{89} + 36 q^{91} - 44 q^{93} - 56 q^{99}+O(q^{100}) $ 16 * q - 12 * q^5 + 16 * q^9 - 8 * q^11 + 8 * q^15 - 16 * q^23 + 12 * q^31 - 24 * q^33 - 16 * q^37 - 108 * q^45 - 24 * q^47 + 8 * q^49 - 28 * q^53 - 60 * q^59 - 12 * q^67 - 8 * q^71 - 60 * q^75 + 44 * q^77 - 8 * q^81 + 96 * q^89 + 36 * q^91 - 44 * q^93 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.35034	+	0.779618i	−0.779618	+	0.450113i	−0.836295	−	0.548280i	$-0.815283\pi$
$3$	−1.35034	+	0.779618i	−0.779618	+	0.450113i	0.0566769	+	0.998393i	$0.481950\pi$
$4$		0			0
$5$	0.882559	+	0.509546i	0.394692	+	0.227876i	0.684191	−	0.729303i	$-0.260155\pi$
$5$	0.882559	+	0.509546i	0.394692	+	0.227876i	−0.289499	+	0.957178i	$0.593489\pi$
$6$		0			0
$7$	−2.25578	−	1.38256i	−0.852604	−	0.522558i
$7$	−2.25578	−	1.38256i	−0.852604	−	0.522558i
$8$		0			0
$9$	−0.284392	+	0.492581i	−0.0947972	+	0.164194i
$10$		0			0
$11$	0.510616	+	3.27708i	0.153957	+	0.988078i
$11$	0.510616	+	3.27708i	0.153957	+	0.988078i
$12$		0			0
$13$	−0.167247			−0.0463859			−0.0231929	−	0.999731i	$-0.507383\pi$
$13$	−0.167247			−0.0463859			−0.0231929	+	0.999731i	$0.507383\pi$
$14$		0			0
$15$	−1.58900			−0.410279
$16$		0			0
$17$	−1.47616	−	2.55678i	−0.358021	−	0.620111i	0.629609	−	0.776912i	$-0.283215\pi$
$17$	−1.47616	−	2.55678i	−0.358021	−	0.620111i	−0.987630	+	0.156801i	$0.949882\pi$
$18$		0			0
$19$	0.155850	−	0.269940i	0.0357545	−	0.0619286i	−0.847594	−	0.530645i	$-0.821950\pi$
$19$	0.155850	−	0.269940i	0.0357545	−	0.0619286i	0.883349	+	0.468716i	$0.155283\pi$
$20$		0			0
$21$	4.12393	+	0.108278i	0.899915	+	0.0236281i
$22$		0			0
$23$	−0.237719	+	0.411742i	−0.0495679	+	0.0858541i	−0.889745	−	0.456458i	$-0.849118\pi$
$23$	−0.237719	+	0.411742i	−0.0495679	+	0.0858541i	0.840177	+	0.542312i	$0.182451\pi$
$24$		0			0
$25$	−1.98073	−	3.43072i	−0.396145	−	0.686144i
$26$		0			0
$27$		−	5.56458i		−	1.07090i
$28$		0			0
$29$			1.89701i			0.352266i	0.984366	+	0.176133i	$0.0563589\pi$
$29$			1.89701i			0.352266i	−0.984366	+	0.176133i	$0.943641\pi$
$30$		0			0
$31$	2.20834	−	1.27498i	0.396629	−	0.228994i	−0.288400	−	0.957510i	$-0.593123\pi$
$31$	2.20834	−	1.27498i	0.396629	−	0.228994i	0.685028	+	0.728516i	$0.259790\pi$
$32$		0			0
$33$	−3.24438	−	4.02708i	−0.564774	−	0.701025i
$34$		0			0
$35$	−1.28638	−	2.36961i	−0.217438	−	0.400537i
$36$		0			0
$37$	−3.04667	+	5.27699i	−0.500870	+	0.867532i	0.499130	+	0.866527i	$0.333653\pi$
$37$	−3.04667	+	5.27699i	−0.500870	+	0.867532i	−0.999999	+	0.00100474i	$0.999680\pi$
$38$		0			0
$39$	0.225839	−	0.130388i	0.0361633	−	0.0208789i
$40$		0			0
$41$	−10.2084			−1.59428			−0.797138	−	0.603797i	$-0.793654\pi$
$41$	−10.2084			−1.59428			−0.797138	+	0.603797i	$0.793654\pi$
$42$		0			0
$43$		−	10.1222i		−	1.54363i	−0.635848	−	0.771814i	$-0.719350\pi$
$43$		−	10.1222i		−	1.54363i	0.635848	−	0.771814i	$-0.280650\pi$
$44$		0			0
$45$	−0.501985	+	0.289821i	−0.0748315	+	0.0432040i
$46$		0			0
$47$	3.28968	+	1.89930i	0.479849	+	0.277041i	0.720354	−	0.693607i	$-0.243980\pi$
$47$	3.28968	+	1.89930i	0.479849	+	0.277041i	−0.240505	+	0.970648i	$0.577313\pi$
$48$		0			0
$49$	3.17706	+	6.23749i	0.453866	+	0.891070i
$50$		0			0
$51$	3.98663	+	2.30168i	0.558239	+	0.322300i
$52$		0			0
$53$	−4.21079	−	7.29330i	−0.578396	−	1.00181i	−0.995664	−	0.0930275i	$-0.970346\pi$
$53$	−4.21079	−	7.29330i	−0.578396	−	1.00181i	0.417268	−	0.908784i	$-0.362988\pi$
$54$		0			0
$55$	−1.21917	+	3.15240i	−0.164393	+	0.425070i
$56$		0			0
$57$			0.486014i			0.0643742i
$58$		0			0
$59$	−5.40617	+	3.12126i	−0.703824	+	0.406353i	−0.808770	−	0.588125i	$-0.799866\pi$
$59$	−5.40617	+	3.12126i	−0.703824	+	0.406353i	0.104946	+	0.994478i	$0.466533\pi$
$60$		0			0
$61$	5.93960	−	10.2877i	0.760488	−	1.31720i	−0.182111	−	0.983278i	$-0.558293\pi$
$61$	5.93960	−	10.2877i	0.760488	−	1.31720i	0.942599	−	0.333926i	$-0.108374\pi$
$62$		0			0
$63$	1.32255	−	0.717964i	0.166625	−	0.0904550i
$64$		0			0
$65$	−0.147605	−	0.0852198i	−0.0183081	−	0.0105702i
$66$		0			0
$67$	−5.19151	−	8.99196i	−0.634244	−	1.09854i	−0.986675	−	0.162705i	$-0.947978\pi$
$67$	−5.19151	−	8.99196i	−0.634244	−	1.09854i	0.352431	−	0.935838i	$-0.385355\pi$
$68$		0			0
$69$		−	0.741321i		−	0.0892445i
$70$		0			0
$71$	−14.5206			−1.72328			−0.861639	−	0.507522i	$-0.830561\pi$
$71$	−14.5206			−1.72328			−0.861639	+	0.507522i	$0.830561\pi$
$72$		0			0
$73$	−4.85385	−	8.40712i	−0.568101	−	0.983979i	−0.996754	−	0.0805099i	$-0.974345\pi$
$73$	−4.85385	−	8.40712i	−0.568101	−	0.983979i	0.428653	−	0.903469i	$-0.358988\pi$
$74$		0			0
$75$	5.34930	+	3.08842i	0.617684	+	0.356620i
$76$		0			0
$77$	3.37892	−	8.09833i	0.385064	−	0.922890i
$78$		0			0
$79$	−6.06709	−	3.50284i	−0.682601	−	0.394100i	0.118233	−	0.992986i	$-0.462277\pi$
$79$	−6.06709	−	3.50284i	−0.682601	−	0.394100i	−0.800834	+	0.598886i	$0.795610\pi$
$80$		0			0
$81$	3.48507	+	6.03631i	0.387230	+	0.670702i
$82$		0			0
$83$	14.6915			1.61261			0.806303	−	0.591502i	$-0.201465\pi$
$83$	14.6915			1.61261			0.806303	+	0.591502i	$0.201465\pi$
$84$		0			0
$85$		−	3.00868i		−	0.326337i
$86$		0			0
$87$	−1.47894	−	2.56161i	−0.158559	−	0.274633i
$88$		0			0
$89$	5.97639	+	3.45047i	0.633496	+	0.365749i	0.782105	−	0.623147i	$-0.214146\pi$
$89$	5.97639	+	3.45047i	0.633496	+	0.365749i	−0.148609	+	0.988896i	$0.547480\pi$
$90$		0			0
$91$	0.377271	+	0.231228i	0.0395488	+	0.0242393i
$92$		0			0
$93$	−1.98800	+	3.44332i	−0.206146	+	0.357055i
$94$		0			0
$95$	0.275094	−	0.158826i	0.0282240	−	0.0162952i
$96$		0			0
$97$		−	11.0218i		−	1.11909i	−0.828799	−	0.559547i	$-0.810975\pi$
$97$		−	11.0218i		−	1.11909i	0.828799	−	0.559547i	$-0.189025\pi$
$98$		0			0
$99$	−1.75944	−	0.680455i	−0.176831	−	0.0683883i
$100$		0			0
$101$	−2.66752	−	4.62028i	−0.265428	−	0.459735i	0.702248	−	0.711933i	$-0.252180\pi$
$101$	−2.66752	−	4.62028i	−0.265428	−	0.459735i	−0.967676	+	0.252198i	$0.918847\pi$
$102$		0			0
$103$	10.7849	+	6.22664i	1.06266	+	0.613529i	0.926168	−	0.377112i	$-0.123083\pi$
$103$	10.7849	+	6.22664i	1.06266	+	0.613529i	0.136496	+	0.990641i	$0.456416\pi$
$104$		0			0
$105$	3.58444	+	2.19689i	0.349805	+	0.214395i
$106$		0			0
$107$	−6.28227	−	3.62707i	−0.607330	−	0.350642i	0.164590	−	0.986362i	$-0.447370\pi$
$107$	−6.28227	−	3.62707i	−0.607330	−	0.350642i	−0.771920	+	0.635720i	$0.780703\pi$
$108$		0			0
$109$	1.01103	−	0.583716i	0.0968387	−	0.0559098i	−0.450799	−	0.892626i	$-0.648861\pi$
$109$	1.01103	−	0.583716i	0.0968387	−	0.0559098i	0.547637	+	0.836716i	$0.315527\pi$
$110$		0			0
$111$		−	9.50096i		−	0.901791i
$112$		0			0
$113$	−8.40135			−0.790333			−0.395166	−	0.918610i	$-0.629313\pi$
$113$	−8.40135			−0.790333			−0.395166	+	0.918610i	$0.629313\pi$
$114$		0			0
$115$	−0.419602	+	0.242258i	−0.0391281	+	0.0225906i
$116$		0			0
$117$	0.0475636	−	0.0823825i	0.00439725	−	0.00761626i
$118$		0			0
$119$	−0.205017	+	7.80841i	−0.0187939	+	0.715796i
$120$		0			0
$121$	−10.4785	+	3.34666i	−0.952595	+	0.304242i
$122$		0			0
$123$	13.7847	−	7.95862i	1.24293	−	0.717604i
$124$		0			0
$125$		−	9.13254i		−	0.816839i
$126$		0			0
$127$			3.53324i			0.313525i	0.987636	+	0.156762i	$0.0501057\pi$
$127$			3.53324i			0.313525i	−0.987636	+	0.156762i	$0.949894\pi$
$128$		0			0
$129$	7.89149	+	13.6685i	0.694807	+	1.20344i
$130$		0			0
$131$	6.98984	−	12.1068i	0.610705	−	1.05777i	−0.380417	−	0.924815i	$-0.624219\pi$
$131$	6.98984	−	12.1068i	0.610705	−	1.05777i	0.991122	−	0.132957i	$-0.0424473\pi$
$132$		0			0
$133$	−0.724772	+	0.393453i	−0.0628457	+	0.0341167i
$134$		0			0
$135$	2.83541	−	4.91107i	0.244033	−	0.422677i
$136$		0			0
$137$	3.50529	+	6.07134i	0.299477	+	0.518709i	0.976016	−	0.217697i	$-0.0698545\pi$
$137$	3.50529	+	6.07134i	0.299477	+	0.518709i	−0.676539	+	0.736406i	$0.736521\pi$
$138$		0			0
$139$	−11.4615			−0.972148			−0.486074	−	0.873918i	$-0.661571\pi$
$139$	−11.4615			−0.972148			−0.486074	+	0.873918i	$0.661571\pi$
$140$		0			0
$141$	−5.92291			−0.498799
$142$		0			0
$143$	−0.0853989	−	0.548081i	−0.00714141	−	0.0458328i
$144$		0			0
$145$	−0.966613	+	1.67422i	−0.0802729	+	0.139037i
$146$		0			0
$147$	−9.15297	−	5.94583i	−0.754924	−	0.490403i
$148$		0			0
$149$	12.2602	+	7.07841i	1.00439	+	0.579886i	0.909545	−	0.415606i	$-0.136430\pi$
$149$	12.2602	+	7.07841i	1.00439	+	0.579886i	0.0948474	+	0.995492i	$0.469764\pi$
$150$		0			0
$151$	−20.1819	+	11.6520i	−1.64238	+	0.948228i	−0.662394	+	0.749156i	$0.730459\pi$
$151$	−20.1819	+	11.6520i	−1.64238	+	0.948228i	−0.979985	+	0.199072i	$0.936207\pi$
$152$		0			0
$153$	1.67923			0.135758
$154$		0			0
$155$	2.59865			0.208728
$156$		0			0
$157$	3.49234	−	2.01630i	0.278719	−	0.160919i	−0.354124	−	0.935198i	$-0.615221\pi$
$157$	3.49234	−	2.01630i	0.278719	−	0.160919i	0.632843	+	0.774280i	$0.281888\pi$
$158$		0			0
$159$	11.3720	+	6.56561i	0.901856	+	0.520687i
$160$		0			0
$161$	1.10550	−	0.600137i	0.0871255	−	0.0472974i
$162$		0			0
$163$	−2.76994	+	4.79768i	−0.216958	+	0.375783i	−0.953877	−	0.300199i	$-0.902947\pi$
$163$	−2.76994	+	4.79768i	−0.216958	+	0.375783i	0.736918	+	0.675982i	$0.236280\pi$
$164$		0			0
$165$	−0.811371	−	5.20730i	−0.0631652	−	0.405388i
$166$		0			0
$167$	−21.2252			−1.64245			−0.821226	−	0.570603i	$-0.806709\pi$
$167$	−21.2252			−1.64245			−0.821226	+	0.570603i	$0.806709\pi$
$168$		0			0
$169$	−12.9720			−0.997848
$170$		0			0
$171$	0.0886450	+	0.153538i	0.00677885	+	0.0117413i
$172$		0			0
$173$	−7.53277	+	13.0471i	−0.572706	+	0.991956i	0.423581	+	0.905858i	$0.360773\pi$
$173$	−7.53277	+	13.0471i	−0.572706	+	0.991956i	−0.996287	+	0.0860973i	$0.972560\pi$
$174$		0			0
$175$	−0.275094	+	10.4774i	−0.0207951	+	0.792018i
$176$		0			0
$177$	4.86677	−	8.42950i	0.365809	−	0.633600i
$178$		0			0
$179$	−1.08088	−	1.87214i	−0.0807887	−	0.139930i	0.822800	−	0.568331i	$-0.192411\pi$
$179$	−1.08088	−	1.87214i	−0.0807887	−	0.139930i	−0.903589	+	0.428401i	$0.859077\pi$
$180$		0			0
$181$		−	5.39285i		−	0.400848i	−0.979709	−	0.200424i	$-0.935768\pi$
$181$		−	5.39285i		−	0.400848i	0.979709	−	0.200424i	$-0.0642319\pi$
$182$		0			0
$183$			18.5225i			1.36922i
$184$		0			0
$185$	−5.37774	+	3.10484i	−0.395379	+	0.228272i
$186$		0			0
$187$	7.62504	−	6.14303i	0.557598	−	0.449223i
$188$		0			0
$189$	−7.69335	+	12.5524i	−0.559609	+	0.913056i
$190$		0			0
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$		0			0
$193$	8.31348	−	4.79979i	0.598417	−	0.345496i	−0.170001	−	0.985444i	$-0.554377\pi$
$193$	8.31348	−	4.79979i	0.598417	−	0.345496i	0.768419	+	0.639947i	$0.221044\pi$
$194$		0			0
$195$	0.265756			0.0190311
$196$		0			0
$197$			14.8180i			1.05574i	0.849325	+	0.527870i	$0.177009\pi$
$197$			14.8180i			1.05574i	−0.849325	+	0.527870i	$0.822991\pi$
$198$		0			0
$199$	−3.55962	+	2.05515i	−0.252335	+	0.145686i	−0.620833	−	0.783943i	$-0.713205\pi$
$199$	−3.55962	+	2.05515i	−0.252335	+	0.145686i	0.368498	+	0.929629i	$0.379872\pi$
$200$		0			0
$201$	14.0206	+	8.09479i	0.988936	+	0.570963i
$202$		0			0
$203$	2.62273	−	4.27923i	0.184079	−	0.300343i
$204$		0			0
$205$	−9.00947	−	5.20162i	−0.629249	−	0.363297i
$206$		0			0
$207$	−0.135211	−	0.234192i	−0.00939780	−	0.0162775i
$208$		0			0
$209$	0.964197	+	0.372898i	0.0666949	+	0.0257939i
$210$		0			0
$211$			7.52456i			0.518012i	0.965876	+	0.259006i	$0.0833950\pi$
$211$			7.52456i			0.518012i	−0.965876	+	0.259006i	$0.916605\pi$
$212$		0			0
$213$	19.6077	−	11.3205i	1.34350	−	0.775669i
$214$		0			0
$215$	5.15775	−	8.93348i	0.351755	−	0.609258i
$216$		0			0
$217$	−6.74425	−	0.177076i	−0.457830	−	0.0120207i
$218$		0			0
$219$	13.1087	+	7.56830i	0.885803	+	0.511418i
$220$		0			0
$221$	0.246883	+	0.427613i	0.0166071	+	0.0287644i
$222$		0			0
$223$			13.5885i			0.909951i	0.890504	+	0.454975i	$0.150352\pi$
$223$			13.5885i			0.909951i	−0.890504	+	0.454975i	$0.849648\pi$
$224$		0			0
$225$	2.25321			0.150214
$226$		0			0
$227$	10.8318	+	18.7611i	0.718929	+	1.24522i	0.961425	+	0.275069i	$0.0887006\pi$
$227$	10.8318	+	18.7611i	0.718929	+	1.24522i	−0.242496	+	0.970152i	$0.577966\pi$
$228$		0			0
$229$	26.0355	+	15.0316i	1.72047	+	0.993317i	0.917948	+	0.396700i	$0.129845\pi$
$229$	26.0355	+	15.0316i	1.72047	+	0.993317i	0.802527	+	0.596616i	$0.203489\pi$
$230$		0			0
$231$	1.75091	+	13.5697i	0.115201	+	0.892824i
$232$		0			0
$233$	14.0223	+	8.09580i	0.918633	+	0.530373i	0.883199	−	0.468999i	$-0.155385\pi$
$233$	14.0223	+	8.09580i	0.918633	+	0.530373i	0.0354345	+	0.999372i	$0.488718\pi$
$234$		0			0
$235$	1.93556	+	3.35248i	0.126262	+	0.218692i
$236$		0			0
$237$	10.9235			0.709558
$238$		0			0
$239$			26.0701i			1.68633i	0.537652	+	0.843167i	$0.319311\pi$
$239$			26.0701i			1.68633i	−0.537652	+	0.843167i	$0.680689\pi$
$240$		0			0
$241$	6.60221	+	11.4354i	0.425286	+	0.736617i	0.996447	−	0.0842210i	$-0.0268402\pi$
$241$	6.60221	+	11.4354i	0.425286	+	0.736617i	−0.571161	+	0.820838i	$0.693507\pi$
$242$		0			0
$243$	5.04515	+	2.91282i	0.323647	+	0.186858i
$244$		0			0
$245$	−0.374342	+	7.12381i	−0.0239159	+	0.455124i
$246$		0			0
$247$	−0.0260654	+	0.0451466i	−0.00165850	+	0.00287261i
$248$		0			0
$249$	−19.8386	+	11.4538i	−1.25722	+	0.725855i
$250$		0			0
$251$		−	28.9829i		−	1.82939i	−0.404149	−	0.914693i	$-0.632432\pi$
$251$		−	28.9829i		−	1.82939i	0.404149	−	0.914693i	$-0.367568\pi$
$252$		0			0
$253$	−1.47070	−	0.568783i	−0.0924618	−	0.0357591i
$254$		0			0
$255$	2.34562	+	4.06274i	0.146889	+	0.254419i
$256$		0			0
$257$	6.05007	+	3.49301i	0.377393	+	0.217888i	0.676683	−	0.736274i	$-0.263417\pi$
$257$	6.05007	+	3.49301i	0.377393	+	0.217888i	−0.299290	+	0.954162i	$0.596750\pi$
$258$		0			0
$259$	14.1684	−	7.69151i	0.880379	−	0.477927i
$260$		0			0
$261$	−0.934431	−	0.539494i	−0.0578398	−	0.0333938i
$262$		0			0
$263$	3.87174	−	2.23535i	0.238741	−	0.137837i	−0.375857	−	0.926678i	$-0.622652\pi$
$263$	3.87174	−	2.23535i	0.238741	−	0.137837i	0.614598	+	0.788840i	$0.289318\pi$
$264$		0			0
$265$		−	8.58235i		−	0.527210i
$266$		0			0
$267$	−10.7602			−0.658513
$268$		0			0
$269$	1.92024	−	1.10865i	0.117079	−	0.0675956i	−0.440317	−	0.897842i	$-0.645134\pi$
$269$	1.92024	−	1.10865i	0.117079	−	0.0675956i	0.557396	+	0.830247i	$0.311801\pi$
$270$		0			0
$271$	−11.2561	+	19.4961i	−0.683759	+	1.18431i	0.290066	+	0.957007i	$0.406323\pi$
$271$	−11.2561	+	19.4961i	−0.683759	+	1.18431i	−0.973825	+	0.227299i	$0.927011\pi$
$272$		0			0
$273$	−0.689713	−	0.0181091i	−0.0417433	−	0.00109601i
$274$		0			0
$275$	10.2314	−	8.24279i	0.616974	−	0.497059i
$276$		0			0
$277$	−21.1880	+	12.2329i	−1.27306	+	0.735004i	−0.975563	−	0.219718i	$-0.929486\pi$
$277$	−21.1880	+	12.2329i	−1.27306	+	0.735004i	−0.297500	+	0.954722i	$0.596153\pi$
$278$		0			0
$279$			1.45038i			0.0868319i
$280$		0			0
$281$		−	11.3532i		−	0.677273i	−0.940917	−	0.338636i	$-0.890034\pi$
$281$		−	11.3532i		−	0.677273i	0.940917	−	0.338636i	$-0.109966\pi$
$282$		0			0
$283$	−10.8268	−	18.7526i	−0.643589	−	1.11473i	−0.984626	−	0.174679i	$-0.944111\pi$
$283$	−10.8268	−	18.7526i	−0.643589	−	1.11473i	0.341037	−	0.940050i	$-0.389222\pi$
$284$		0			0
$285$	−0.247646	+	0.428936i	−0.0146693	+	0.0254080i
$286$		0			0
$287$	23.0278	+	14.1137i	1.35929	+	0.833102i
$288$		0			0
$289$	4.14191	−	7.17400i	0.243642	−	0.422000i
$290$		0			0
$291$	8.59279	+	14.8831i	0.503718	+	0.872465i
$292$		0			0
$293$	12.1233			0.708249			0.354124	−	0.935198i	$-0.384779\pi$
$293$	12.1233			0.708249			0.354124	+	0.935198i	$0.384779\pi$
$294$		0			0
$295$	−6.36169			−0.370392
$296$		0			0
$297$	18.2356	−	2.84136i	1.05814	−	0.164873i
$298$		0			0
$299$	0.0397577	−	0.0688624i	0.00229925	−	0.00398242i
$300$		0			0
$301$	−13.9946	+	22.8335i	−0.806636	+	1.31610i
$302$		0			0
$303$	7.20410	+	4.15929i	0.413865	+	0.238945i
$304$		0			0
$305$	10.4841	−	6.05300i	0.600318	−	0.346594i
$306$		0			0
$307$	−9.65817			−0.551221			−0.275610	−	0.961269i	$-0.588880\pi$
$307$	−9.65817			−0.551221			−0.275610	+	0.961269i	$0.588880\pi$
$308$		0			0
$309$	−19.4176			−1.10463
$310$		0			0
$311$	15.3094	−	8.83890i	0.868118	−	0.501208i	0.00139530	−	0.999999i	$-0.499556\pi$
$311$	15.3094	−	8.83890i	0.868118	−	0.501208i	0.866722	+	0.498791i	$0.166223\pi$
$312$		0			0
$313$	−24.9505	−	14.4052i	−1.41028	−	0.814228i	−0.414869	−	0.909881i	$-0.636173\pi$
$313$	−24.9505	−	14.4052i	−1.41028	−	0.814228i	−0.995415	+	0.0956530i	$0.969506\pi$
$314$		0			0
$315$	1.53306	+	0.0402519i	0.0863782	+	0.00226794i
$316$		0			0
$317$	−5.17280	+	8.95955i	−0.290533	+	0.503218i	−0.973936	−	0.226823i	$-0.927166\pi$
$317$	−5.17280	+	8.95955i	−0.290533	+	0.503218i	0.683403	+	0.730042i	$0.260499\pi$
$318$		0			0
$319$	−6.21666	+	0.968644i	−0.348066	+	0.0542337i
$320$		0			0
$321$	11.3109			0.631314
$322$		0			0
$323$	−0.920239			−0.0512034
$324$		0			0
$325$	0.331270	+	0.573776i	0.0183755	+	0.0318274i
$326$		0			0
$327$	−0.910151	+	1.57643i	−0.0503315	+	0.0871766i
$328$		0			0
$329$	−4.79489	−	8.83257i	−0.264351	−	0.486955i
$330$		0			0
$331$	−13.4224	+	23.2483i	−0.737763	+	1.27784i	0.215737	+	0.976451i	$0.430785\pi$
$331$	−13.4224	+	23.2483i	−0.737763	+	1.27784i	−0.953500	+	0.301392i	$0.902549\pi$
$332$		0			0
$333$	−1.73290	−	3.00147i	−0.0949622	−	0.164479i
$334$		0			0
$335$		−	10.5813i		−	0.578116i
$336$		0			0
$337$			14.5505i			0.792614i	0.918118	+	0.396307i	$0.129708\pi$
$337$			14.5505i			0.792614i	−0.918118	+	0.396307i	$0.870292\pi$
$338$		0			0
$339$	11.3447	−	6.54984i	0.616158	−	0.355739i
$340$		0			0
$341$	5.30584	+	6.58587i	0.287327	+	0.356645i
$342$		0			0
$343$	1.45696	−	18.4629i	0.0786683	−	0.996901i
$344$		0			0
$345$	0.377737	−	0.654259i	0.0203367	−	0.0352241i
$346$		0			0
$347$	24.7179	−	14.2709i	1.32693	−	0.766101i	0.342102	−	0.939663i	$-0.388861\pi$
$347$	24.7179	−	14.2709i	1.32693	−	0.766101i	0.984823	+	0.173562i	$0.0555278\pi$
$348$		0			0
$349$	−34.6026			−1.85224			−0.926118	−	0.377235i	$-0.876875\pi$
$349$	−34.6026			−1.85224			−0.926118	+	0.377235i	$0.876875\pi$
$350$		0			0
$351$			0.930656i			0.0496748i
$352$		0			0
$353$	−14.6534	+	8.46017i	−0.779924	+	0.450289i	−0.836403	−	0.548114i	$-0.815346\pi$
$353$	−14.6534	+	8.46017i	−0.779924	+	0.450289i	0.0564792	+	0.998404i	$0.482013\pi$
$354$		0			0
$355$	−12.8153	−	7.39891i	−0.680164	−	0.392693i
$356$		0			0
$357$	−5.81073	−	10.7038i	−0.307537	−	0.566507i
$358$		0			0
$359$	−26.2848	−	15.1755i	−1.38726	−	0.800934i	−0.394254	−	0.919002i	$-0.628997\pi$
$359$	−26.2848	−	15.1755i	−1.38726	−	0.800934i	−0.993006	+	0.118067i	$0.962330\pi$
$360$		0			0
$361$	9.45142	+	16.3703i	0.497443	+	0.861597i
$362$		0			0
$363$	11.5405	−	12.6884i	0.605717	−	0.665968i
$364$		0			0
$365$		−	9.89304i		−	0.517825i
$366$		0			0
$367$	15.0875	−	8.71075i	0.787559	−	0.454698i	−0.0515432	−	0.998671i	$-0.516414\pi$
$367$	15.0875	−	8.71075i	0.787559	−	0.454698i	0.839103	+	0.543973i	$0.183081\pi$
$368$		0			0
$369$	2.90317	−	5.02844i	0.151133	−	0.261770i
$370$		0			0
$371$	−0.584817	+	22.2737i	−0.0303622	+	1.15639i
$372$		0			0
$373$	7.92596	+	4.57606i	0.410391	+	0.236939i	0.690958	−	0.722895i	$-0.257189\pi$
$373$	7.92596	+	4.57606i	0.410391	+	0.236939i	−0.280567	+	0.959834i	$0.590522\pi$
$374$		0			0
$375$	7.11989	+	12.3320i	0.367670	+	0.636822i
$376$		0			0
$377$		−	0.317269i		−	0.0163402i
$378$		0			0
$379$	6.15382			0.316100			0.158050	−	0.987431i	$-0.449479\pi$
$379$	6.15382			0.316100			0.158050	+	0.987431i	$0.449479\pi$
$380$		0			0
$381$	−2.75458	−	4.77107i	−0.141121	−	0.244429i
$382$		0			0
$383$	−11.2281	−	6.48253i	−0.573728	−	0.331242i	0.184909	−	0.982756i	$-0.440801\pi$
$383$	−11.2281	−	6.48253i	−0.573728	−	0.331242i	−0.758637	+	0.651514i	$0.774134\pi$
$384$		0			0
$385$	7.10857	−	5.42553i	0.362286	−	0.276511i
$386$		0			0
$387$	4.98603	+	2.87868i	0.253454	+	0.146332i
$388$		0			0
$389$	−2.58323	−	4.47429i	−0.130975	−	0.226856i	0.793078	−	0.609121i	$-0.208477\pi$
$389$	−2.58323	−	4.47429i	−0.130975	−	0.226856i	−0.924053	+	0.382265i	$0.875144\pi$
$390$		0			0
$391$	1.40365			0.0709854
$392$		0			0
$393$			21.7976i			1.09954i
$394$		0			0
$395$	−3.56971	−	6.18292i	−0.179612	−	0.311097i
$396$		0			0
$397$	8.01690	+	4.62856i	0.402357	+	0.232301i	0.687500	−	0.726184i	$-0.258708\pi$
$397$	8.01690	+	4.62856i	0.402357	+	0.232301i	−0.285144	+	0.958485i	$0.592041\pi$
$398$		0			0
$399$	0.671943	−	1.09634i	0.0336392	−	0.0548856i
$400$		0			0
$401$	15.4624	−	26.7816i	0.772155	−	1.33741i	−0.164225	−	0.986423i	$-0.552512\pi$
$401$	15.4624	−	26.7816i	0.772155	−	1.33741i	0.936380	−	0.350988i	$-0.114154\pi$
$402$		0			0
$403$	−0.369337	+	0.213237i	−0.0183980	+	0.0106221i
$404$		0			0
$405$			7.10320i			0.352961i
$406$		0			0
$407$	−18.8488	−	7.28968i	−0.934301	−	0.361336i
$408$		0			0
$409$	−11.9198	−	20.6458i	−0.589399	−	1.02087i	−0.994311	−	0.106513i	$-0.966031\pi$
$409$	−11.9198	−	20.6458i	−0.589399	−	1.02087i	0.404913	−	0.914355i	$-0.367302\pi$
$410$		0			0
$411$	−9.46665	−	5.46557i	−0.466955	−	0.269597i
$412$		0			0
$413$	16.5104	+	0.433497i	0.812426	+	0.0213310i
$414$		0			0
$415$	12.9662	+	7.48601i	0.636484	+	0.367474i
$416$		0			0
$417$	15.4768	−	8.93556i	0.757904	−	0.437576i
$418$		0			0
$419$		−	5.03426i		−	0.245940i	−0.992410	−	0.122970i	$-0.960758\pi$
$419$		−	5.03426i		−	0.245940i	0.992410	−	0.122970i	$-0.0392418\pi$
$420$		0			0
$421$	−16.9250			−0.824872			−0.412436	−	0.910987i	$-0.635322\pi$
$421$	−16.9250			−0.824872			−0.412436	+	0.910987i	$0.635322\pi$
$422$		0			0
$423$	−1.87112	+	1.08029i	−0.0909767	+	0.0525254i
$424$		0			0
$425$	−5.84773	+	10.1286i	−0.283657	+	0.491308i
$426$		0			0
$427$	−27.6218	+	14.9949i	−1.33671	+	0.725654i
$428$		0			0
$429$	0.542611	+	0.673516i	0.0261975	+	0.0325177i
$430$		0			0
$431$	5.19535	−	2.99953i	0.250251	−	0.144482i	−0.369628	−	0.929180i	$-0.620515\pi$
$431$	5.19535	−	2.99953i	0.250251	−	0.144482i	0.619879	+	0.784697i	$0.287182\pi$
$432$		0			0
$433$		−	36.1175i		−	1.73570i	−0.496829	−	0.867849i	$-0.665502\pi$
$433$		−	36.1175i		−	1.73570i	0.496829	−	0.867849i	$-0.334498\pi$
$434$		0			0
$435$		−	3.01436i		−	0.144527i
$436$		0			0
$437$	0.0740971	+	0.128340i	0.00354455	+	0.00613934i
$438$		0			0
$439$	−5.67481	+	9.82906i	−0.270844	+	0.469116i	−0.969078	−	0.246754i	$-0.920636\pi$
$439$	−5.67481	+	9.82906i	−0.270844	+	0.469116i	0.698234	+	0.715869i	$0.253969\pi$
$440$		0			0
$441$	−3.97600	−	0.208931i	−0.189333	−	0.00994909i
$442$		0			0
$443$	−2.37538	+	4.11428i	−0.112858	+	0.195475i	−0.916921	−	0.399068i	$-0.869334\pi$
$443$	−2.37538	+	4.11428i	−0.112858	+	0.195475i	0.804064	+	0.594543i	$0.202667\pi$
$444$		0			0
$445$	3.51634	+	6.09048i	0.166691	+	0.288717i
$446$		0			0
$447$	−22.0738			−1.04406
$448$		0			0
$449$	7.33297			0.346064			0.173032	−	0.984916i	$-0.444644\pi$
$449$	7.33297			0.346064			0.173032	+	0.984916i	$0.444644\pi$
$450$		0			0
$451$	−5.21255	−	33.4536i	−0.245449	−	1.57527i
$452$		0			0
$453$	18.1682	−	31.4683i	0.853619	−	1.47851i
$454$		0			0
$455$	0.215143	+	0.396310i	0.0100860	+	0.0185793i
$456$		0			0
$457$	−11.7066	−	6.75879i	−0.547610	−	0.316163i	0.200547	−	0.979684i	$-0.435728\pi$
$457$	−11.7066	−	6.75879i	−0.547610	−	0.316163i	−0.748158	+	0.663521i	$0.769061\pi$
$458$		0			0
$459$	−14.2274	+	8.21420i	−0.664079	+	0.383406i
$460$		0			0
$461$	−18.5730			−0.865033			−0.432516	−	0.901626i	$-0.642374\pi$
$461$	−18.5730			−0.865033			−0.432516	+	0.901626i	$0.642374\pi$
$462$		0			0
$463$	−28.2849			−1.31451			−0.657256	−	0.753667i	$-0.728283\pi$
$463$	−28.2849			−1.31451			−0.657256	+	0.753667i	$0.728283\pi$
$464$		0			0
$465$	−3.50905	+	2.02595i	−0.162728	+	0.0939513i
$466$		0			0
$467$	18.6881	+	10.7896i	0.864782	+	0.499282i	0.865611	−	0.500717i	$-0.166930\pi$
$467$	18.6881	+	10.7896i	0.864782	+	0.499282i	−0.000828665		1.00000i	$0.500264\pi$
$468$		0			0
$469$	−0.721025	+	27.4614i	−0.0332938	+	1.26805i
$470$		0			0
$471$	−3.14389	+	5.44538i	−0.144863	+	0.250910i
$472$		0			0
$473$	33.1714	−	5.16859i	1.52522	−	0.237652i
$474$		0			0
$475$	−1.23479			−0.0566559
$476$		0			0
$477$	4.79005			0.219321
$478$		0			0
$479$	3.46780	+	6.00641i	0.158448	+	0.274440i	0.934309	−	0.356464i	$-0.116018\pi$
$479$	3.46780	+	6.00641i	0.158448	+	0.274440i	−0.775861	+	0.630904i	$0.782684\pi$
$480$		0			0
$481$	0.509546	−	0.882559i	0.0232333	−	0.0402412i
$482$		0			0
$483$	−1.02492	+	1.67225i	−0.0466355	+	0.0760902i
$484$		0			0
$485$	5.61611	−	9.72738i	0.255014	−	0.441698i
$486$		0			0
$487$	−6.08702	−	10.5430i	−0.275829	−	0.477750i	0.694515	−	0.719478i	$-0.255619\pi$
$487$	−6.08702	−	10.5430i	−0.275829	−	0.477750i	−0.970344	+	0.241728i	$0.922286\pi$
$488$		0			0
$489$		−	8.63798i		−	0.390623i
$490$		0			0
$491$			2.37152i			0.107025i	0.998567	+	0.0535125i	$0.0170417\pi$
$491$			2.37152i			0.107025i	−0.998567	+	0.0535125i	$0.982958\pi$
$492$		0			0
$493$	4.85024	−	2.80029i	0.218444	−	0.126119i
$494$		0			0
$495$	−1.20609	−	1.49706i	−0.0542097	−	0.0672878i
$496$		0			0
$497$	32.7552	+	20.0756i	1.46927	+	0.900513i
$498$		0			0
$499$	−1.96446	+	3.40255i	−0.0879413	+	0.152319i	−0.906641	−	0.421903i	$-0.861362\pi$
$499$	−1.96446	+	3.40255i	−0.0879413	+	0.152319i	0.818699	+	0.574222i	$0.194695\pi$
$500$		0			0
$501$	28.6611	−	16.5475i	1.28048	−	0.739288i
$502$		0			0
$503$	19.8703			0.885971			0.442986	−	0.896529i	$-0.353919\pi$
$503$	19.8703			0.885971			0.442986	+	0.896529i	$0.353919\pi$
$504$		0			0
$505$		−	5.43689i		−	0.241938i
$506$		0			0
$507$	17.5166	−	10.1132i	0.777940	−	0.449144i
$508$		0			0
$509$	13.2438	+	7.64634i	0.587023	+	0.338918i	0.763920	−	0.645312i	$-0.223272\pi$
$509$	13.2438	+	7.64634i	0.587023	+	0.338918i	−0.176896	+	0.984229i	$0.556606\pi$
$510$		0			0
$511$	−0.674129	+	25.6753i	−0.0298217	+	1.13581i
$512$		0			0
$513$	−1.50210	−	0.867240i	−0.0663195	−	0.0382896i
$514$		0			0
$515$	6.34552	+	10.9908i	0.279617	+	0.484311i
$516$		0			0
$517$	−4.54439	+	11.7504i	−0.199862	+	0.516780i
$518$		0			0
$519$		−	23.4907i		−	1.03113i
$520$		0			0
$521$	−0.121861	+	0.0703565i	−0.00533883	+	0.00308237i	−0.502667	−	0.864480i	$-0.667648\pi$
$521$	−0.121861	+	0.0703565i	−0.00533883	+	0.00308237i	0.497328	+	0.867562i	$0.334314\pi$
$522$		0			0
$523$	4.56153	−	7.90081i	0.199462	−	0.345478i	−0.748892	−	0.662692i	$-0.769414\pi$
$523$	4.56153	−	7.90081i	0.199462	−	0.345478i	0.948354	+	0.317214i	$0.102747\pi$
$524$		0			0
$525$	−7.79691	−	14.3625i	−0.340285	−	0.626831i
$526$		0			0
$527$	−6.51971	−	3.76416i	−0.284003	−	0.163969i
$528$		0			0
$529$	11.3870	+	19.7228i	0.495086	+	0.857514i
$530$		0			0
$531$		−	3.55064i		−	0.154085i
$532$		0			0
$533$	1.70731			0.0739519
$534$		0			0
$535$	−3.69632	−	6.40221i	−0.159806	−	0.276792i
$536$		0			0
$537$	2.91910	+	1.68534i	0.125969	+	0.0727280i
$538$		0			0
$539$	−18.8185	+	13.5965i	−0.810571	+	0.585641i
$540$		0			0
$541$	−21.6730	−	12.5129i	−0.931797	−	0.537973i	−0.0444172	−	0.999013i	$-0.514143\pi$
$541$	−21.6730	−	12.5129i	−0.931797	−	0.537973i	−0.887379	+	0.461040i	$0.847476\pi$
$542$		0			0
$543$	4.20437	+	7.28217i	0.180427	+	0.312508i
$544$		0			0
$545$	1.18972			0.0509620
$546$		0			0
$547$		−	36.7246i		−	1.57023i	−0.619348	−	0.785116i	$-0.712603\pi$
$547$		−	36.7246i		−	1.57023i	0.619348	−	0.785116i	$-0.287397\pi$
$548$		0			0
$549$	3.37835	+	5.85147i	0.144184	+	0.249735i
$550$		0			0
$551$	0.512080	+	0.295649i	0.0218153	+	0.0125951i
$552$		0			0
$553$	8.84313	+	16.2897i	0.376048	+	0.692710i
$554$		0			0
$555$	4.84117	−	8.38516i	0.205496	−	0.355930i
$556$		0			0
$557$	−33.5815	+	19.3883i	−1.42290	+	0.821509i	−0.996545	−	0.0830490i	$-0.973534\pi$
$557$	−33.5815	+	19.3883i	−1.42290	+	0.821509i	−0.426350	+	0.904558i	$0.640201\pi$
$558$		0			0
$559$			1.69291i			0.0716025i
$560$		0			0
$561$	−5.50716	+	14.2398i	−0.232512	+	0.601204i
$562$		0			0
$563$	21.6247	+	37.4550i	0.911371	+	1.57854i	0.812129	+	0.583477i	$0.198308\pi$
$563$	21.6247	+	37.4550i	0.911371	+	1.57854i	0.0992415	+	0.995063i	$0.468358\pi$
$564$		0			0
$565$	−7.41469	−	4.28087i	−0.311938	−	0.180098i
$566$		0			0
$567$	0.484025	−	18.4349i	0.0203271	−	0.774193i
$568$		0			0
$569$	−18.4783	−	10.6685i	−0.774651	−	0.447245i	0.0598803	−	0.998206i	$-0.480928\pi$
$569$	−18.4783	−	10.6685i	−0.774651	−	0.447245i	−0.834531	+	0.550961i	$0.814261\pi$
$570$		0			0
$571$	−19.5677	+	11.2974i	−0.818883	+	0.472782i	−0.850031	−	0.526733i	$-0.823417\pi$
$571$	−19.5677	+	11.2974i	−0.818883	+	0.472782i	0.0311482	+	0.999515i	$0.490084\pi$
$572$		0			0
$573$			9.35542i			0.390828i
$574$		0			0
$575$	1.88343			0.0785443
$576$		0			0
$577$	−29.3358	+	16.9370i	−1.22126	+	0.705097i	−0.965187	−	0.261559i	$-0.915763\pi$
$577$	−29.3358	+	16.9370i	−1.22126	+	0.705097i	−0.256077	+	0.966656i	$0.582430\pi$
$578$		0			0
$579$	−7.48400	+	12.9627i	−0.311025	+	0.538710i
$580$		0			0
$581$	−33.1409	−	20.3119i	−1.37491	−	0.842681i
$582$		0			0
$583$	21.7506	−	17.5232i	0.900819	−	0.725736i
$584$		0			0
$585$	0.0839553	−	0.0484716i	0.00347112	−	0.00200405i
$586$		0			0
$587$		−	6.07819i		−	0.250874i	−0.992102	−	0.125437i	$-0.959967\pi$
$587$		−	6.07819i		−	0.250874i	0.992102	−	0.125437i	$-0.0400332\pi$
$588$		0			0
$589$		−	0.794825i		−	0.0327502i
$590$		0			0
$591$	−11.5524	−	20.0093i	−0.475202	−	0.823074i
$592$		0			0
$593$	−0.809196	+	1.40157i	−0.0332297	+	0.0575555i	−0.882162	−	0.470946i	$-0.843913\pi$
$593$	−0.809196	+	1.40157i	−0.0332297	+	0.0575555i	0.848932	+	0.528502i	$0.177246\pi$
$594$		0			0
$595$	−4.15968	+	6.78692i	−0.170530	+	0.278236i
$596$		0			0
$597$	3.20446	−	5.55029i	0.131150	−	0.227158i
$598$		0			0
$599$	2.63955	+	4.57184i	0.107849	+	0.186800i	0.914899	−	0.403684i	$-0.132270\pi$
$599$	2.63955	+	4.57184i	0.107849	+	0.186800i	−0.807050	+	0.590484i	$0.798937\pi$
$600$		0			0
$601$	−32.7945			−1.33771			−0.668857	−	0.743391i	$-0.733216\pi$
$601$	−32.7945			−1.33771			−0.668857	+	0.743391i	$0.733216\pi$
$602$		0			0
$603$	5.90569			0.240498
$604$		0			0
$605$	−10.9532	−	2.38567i	−0.445311	−	0.0969912i
$606$		0			0
$607$	−0.332910	+	0.576616i	−0.0135124	+	0.0234041i	−0.872703	−	0.488252i	$-0.837635\pi$
$607$	−0.332910	+	0.576616i	−0.0135124	+	0.0234041i	0.859190	+	0.511656i	$0.170968\pi$
$608$		0			0
$609$	−0.205404	+	7.82314i	−0.00832337	+	0.317009i
$610$		0			0
$611$	−0.550188	−	0.317651i	−0.0222582	−	0.0128508i
$612$		0			0
$613$	3.71908	−	2.14721i	0.150212	−	0.0867251i	−0.423010	−	0.906125i	$-0.639027\pi$
$613$	3.71908	−	2.14721i	0.150212	−	0.0867251i	0.573222	+	0.819400i	$0.305693\pi$
$614$		0			0
$615$	16.2211			0.654098
$616$		0			0
$617$	−30.9913			−1.24766			−0.623831	−	0.781559i	$-0.714425\pi$
$617$	−30.9913			−1.24766			−0.623831	+	0.781559i	$0.714425\pi$
$618$		0			0
$619$	0.685357	−	0.395691i	0.0275468	−	0.0159042i	−0.486163	−	0.873868i	$-0.661604\pi$
$619$	0.685357	−	0.395691i	0.0275468	−	0.0159042i	0.513710	+	0.857964i	$0.328271\pi$
$620$		0			0
$621$	2.29117	+	1.32281i	0.0919414	+	0.0530824i
$622$		0			0
$623$	−8.71092	−	16.0462i	−0.348996	−	0.642877i
$624$		0			0
$625$	−5.25019	+	9.09359i	−0.210007	+	0.363744i
$626$		0			0
$627$	−1.59271	+	0.248167i	−0.0636067	+	0.00991083i
$628$		0			0
$629$	17.9895			0.717288
$630$		0			0
$631$	34.3677			1.36816			0.684078	−	0.729409i	$-0.260205\pi$
$631$	34.3677			1.36816			0.684078	+	0.729409i	$0.260205\pi$
$632$		0			0
$633$	−5.86628	−	10.1607i	−0.233164	−	0.403852i
$634$		0			0
$635$	−1.80035	+	3.11830i	−0.0714447	+	0.123746i
$636$		0			0
$637$	−0.531353	−	1.04320i	−0.0210530	−	0.0413331i
$638$		0			0
$639$	4.12954	−	7.15257i	0.163362	−	0.282951i
$640$		0			0
$641$	−2.47939	−	4.29443i	−0.0979301	−	0.169620i	0.812898	−	0.582407i	$-0.197889\pi$
$641$	−2.47939	−	4.29443i	−0.0979301	−	0.169620i	−0.910828	+	0.412787i	$0.864556\pi$
$642$		0			0
$643$		−	48.1404i		−	1.89847i	−0.314562	−	0.949237i	$-0.601858\pi$
$643$		−	48.1404i		−	1.89847i	0.314562	−	0.949237i	$-0.398142\pi$
$644$		0			0
$645$			16.0843i			0.633318i
$646$		0			0
$647$	2.74160	−	1.58286i	0.107783	−	0.0622287i	−0.445139	−	0.895461i	$-0.646846\pi$
$647$	2.74160	−	1.58286i	0.107783	−	0.0622287i	0.552923	+	0.833233i	$0.313513\pi$
$648$		0			0
$649$	−12.9891	−	16.1227i	−0.509867	−	0.632872i
$650$		0			0
$651$	9.24507	−	5.01883i	0.362343	−	0.196703i
$652$		0			0
$653$	11.0606	−	19.1575i	0.432833	−	0.749689i	−0.564283	−	0.825582i	$-0.690847\pi$
$653$	11.0606	−	19.1575i	0.432833	−	0.749689i	0.997116	+	0.0758922i	$0.0241805\pi$
$654$		0			0
$655$	12.3379	−	7.12329i	0.482081	−	0.278330i
$656$		0			0
$657$	5.52158			0.215417
$658$		0			0
$659$			24.6258i			0.959286i	0.877464	+	0.479643i	$0.159234\pi$
$659$			24.6258i			0.959286i	−0.877464	+	0.479643i	$0.840766\pi$
$660$		0			0
$661$	24.0205	−	13.8682i	0.934289	−	0.539412i	0.0461236	−	0.998936i	$-0.485313\pi$
$661$	24.0205	−	13.8682i	0.934289	−	0.539412i	0.888166	+	0.459524i	$0.151980\pi$
$662$		0			0
$663$	−0.666750	−	0.384948i	−0.0258944	−	0.0149502i
$664$		0			0
$665$	−0.840136	−	0.0220585i	−0.0325791	−	0.000855394i
$666$		0			0
$667$	−0.781078	−	0.450956i	−0.0302435	−	0.0174611i
$668$		0			0
$669$	−10.5938	−	18.3490i	−0.409580	−	0.709414i
$670$		0			0
$671$	36.7465	+	14.2115i	1.41858	+	0.548629i
$672$		0			0
$673$		−	15.9518i		−	0.614897i	−0.951565	−	0.307449i	$-0.900525\pi$
$673$		−	15.9518i		−	0.614897i	0.951565	−	0.307449i	$-0.0994752\pi$
$674$		0			0
$675$	−19.0905	+	11.0219i	−0.734793	+	0.424233i
$676$		0			0
$677$	7.52574	−	13.0350i	0.289238	−	0.500974i	−0.684390	−	0.729116i	$-0.739932\pi$
$677$	7.52574	−	13.0350i	0.289238	−	0.500974i	0.973628	+	0.228141i	$0.0732649\pi$
$678$		0			0
$679$	−15.2383	+	24.8627i	−0.584792	+	0.954143i
$680$		0			0
$681$	−29.2531	−	16.8893i	−1.12098	−	0.647198i
$682$		0			0
$683$	−2.64673	−	4.58427i	−0.101274	−	0.175412i	0.810936	−	0.585135i	$-0.198959\pi$
$683$	−2.64673	−	4.58427i	−0.101274	−	0.175412i	−0.912210	+	0.409723i	$0.865625\pi$
$684$		0			0
$685$			7.14442i			0.272974i
$686$		0			0
$687$	−46.8756			−1.78842
$688$		0			0
$689$	0.704240	+	1.21978i	0.0268294	+	0.0464699i
$690$		0			0
$691$	23.4089	+	13.5151i	0.890517	+	0.514140i	0.874112	−	0.485725i	$-0.161444\pi$
$691$	23.4089	+	13.5151i	0.890517	+	0.514140i	0.0164055	+	0.999865i	$0.494778\pi$
$692$		0			0
$693$	3.02814	+	3.96749i	0.115030	+	0.150712i
$694$		0			0
$695$	−10.1154	−	5.84014i	−0.383699	−	0.221529i
$696$		0			0
$697$	15.0692	+	26.1005i	0.570785	+	0.988629i
$698$		0			0
$699$	−25.2465			−0.954911
$700$		0			0
$701$			19.9250i			0.752555i	0.926507	+	0.376278i	$0.122796\pi$
$701$			19.9250i			0.752555i	−0.926507	+	0.376278i	$0.877204\pi$
$702$		0			0
$703$	0.949649	+	1.64484i	0.0358167	+	0.0620363i
$704$		0			0
$705$	−5.22731	−	3.01799i	−0.196872	−	0.113664i
$706$		0			0
$707$	−0.370479	+	14.1103i	−0.0139333	+	0.530673i
$708$		0			0
$709$	−4.98412	+	8.63276i	−0.187183	+	0.324210i	−0.944310	−	0.329058i	$-0.893269\pi$
$709$	−4.98412	+	8.63276i	−0.187183	+	0.324210i	0.757127	+	0.653268i	$0.226602\pi$
$710$		0			0
$711$	3.45086	−	1.99236i	0.129417	−	0.0747192i
$712$		0			0
$713$			1.21235i			0.0454029i
$714$		0			0
$715$	0.203903	−	0.527228i	0.00762553	−	0.0197172i
$716$		0			0
$717$	−20.3247	−	35.2034i	−0.759040	−	1.31470i
$718$		0			0
$719$	−35.6817	−	20.6008i	−1.33070	−	0.768282i	−0.345295	−	0.938494i	$-0.612221\pi$
$719$	−35.6817	−	20.6008i	−1.33070	−	0.768282i	−0.985407	+	0.170212i	$0.945555\pi$
$720$		0			0
$721$	−15.7195	−	28.9566i	−0.585426	−	1.07840i
$722$		0			0
$723$	−17.8304	−	10.2944i	−0.663121	−	0.382853i
$724$		0			0
$725$	6.50811	−	3.75746i	0.241705	−	0.139549i
$726$		0			0
$727$			0.0415718i			0.00154181i	1.00000		0.000770906i	$0.000245387\pi$
$727$			0.0415718i			0.00154181i	−1.00000		0.000770906i	$0.999755\pi$
$728$		0			0
$729$	−29.9940			−1.11089
$730$		0			0
$731$	−25.8804	+	14.9420i	−0.957221	+	0.552652i
$732$		0			0
$733$	4.40404	−	7.62803i	0.162667	−	0.281748i	−0.773157	−	0.634214i	$-0.781324\pi$
$733$	4.40404	−	7.62803i	0.162667	−	0.281748i	0.935824	+	0.352467i	$0.114657\pi$
$734$		0			0
$735$	−5.04836	−	9.91140i	−0.186212	−	0.365587i
$736$		0			0
$737$	26.8165	−	21.6045i	0.987800	−	0.795810i
$738$		0			0
$739$	28.4003	−	16.3969i	1.04472	−	0.603170i	0.123555	−	0.992338i	$-0.460571\pi$
$739$	28.4003	−	16.3969i	1.04472	−	0.603170i	0.921167	+	0.389167i	$0.127237\pi$
$740$		0			0
$741$		−	0.0812842i		−	0.00298605i
$742$		0			0
$743$		−	25.7575i		−	0.944952i	−0.881344	−	0.472476i	$-0.843360\pi$
$743$		−	25.7575i		−	0.944952i	0.881344	−	0.472476i	$-0.156640\pi$
$744$		0			0
$745$	7.21355	+	12.4942i	0.264284	+	0.457753i
$746$		0			0
$747$	−4.17815	+	7.23678i	−0.152871	+	0.264780i
$748$		0			0
$749$	9.15676	+	16.8675i	0.334581	+	0.616324i
$750$		0			0
$751$	5.73290	−	9.92967i	0.209196	−	0.362339i	−0.742265	−	0.670106i	$-0.766249\pi$
$751$	5.73290	−	9.92967i	0.209196	−	0.362339i	0.951462	+	0.307767i	$0.0995819\pi$
$752$		0			0
$753$	22.5956	+	39.1367i	0.823430	+	1.42622i
$754$		0			0
$755$	−23.7489			−0.864313
$756$		0			0
$757$	21.9741			0.798661			0.399331	−	0.916807i	$-0.369243\pi$
$757$	21.9741			0.798661			0.399331	+	0.916807i	$0.369243\pi$
$758$		0			0
$759$	2.42937	−	0.378530i	0.0881805	−	0.0137398i
$760$		0			0
$761$	13.0047	−	22.5249i	0.471421	−	0.816526i	−0.528044	−	0.849217i	$-0.677074\pi$
$761$	13.0047	−	22.5249i	0.471421	−	0.816526i	0.999466	+	0.0326910i	$0.0104077\pi$
$762$		0			0
$763$	−3.08767	−	0.0810696i	−0.111781	−	0.00293492i
$764$		0			0
$765$	1.48202	+	0.855644i	0.0535825	+	0.0309359i
$766$		0			0
$767$	0.904164	−	0.522020i	0.0326475	−	0.0188490i
$768$		0			0
$769$	−40.8753			−1.47400			−0.737001	−	0.675891i	$-0.763759\pi$
$769$	−40.8753			−1.47400			−0.737001	+	0.675891i	$0.763759\pi$
$770$		0			0
$771$	−10.8929			−0.392296
$772$		0			0
$773$	40.8229	−	23.5691i	1.46830	−	0.847722i	0.468928	−	0.883236i	$-0.344640\pi$
$773$	40.8229	−	23.5691i	1.46830	−	0.847722i	0.999369	+	0.0355144i	$0.0113070\pi$
$774$		0			0
$775$	−8.74822	−	5.05078i	−0.314245	−	0.181430i
$776$		0			0
$777$	−13.1356	+	21.4321i	−0.471239	+	0.768871i
$778$		0			0
$779$	−1.59097	+	2.75565i	−0.0570025	+	0.0987313i
$780$		0			0
$781$	−7.41445	−	47.5852i	−0.265310	−	1.70273i
$782$		0			0
$783$	10.5561			0.377243
$784$		0			0
$785$	4.10960			0.146678
$786$		0			0
$787$	−12.0746	−	20.9137i	−0.430411	−	0.745494i	0.566497	−	0.824064i	$-0.308298\pi$
$787$	−12.0746	−	20.9137i	−0.430411	−	0.745494i	−0.996909	+	0.0785692i	$0.974965\pi$
$788$		0			0
$789$	−3.48543	+	6.03695i	−0.124085	+	0.214921i
$790$		0			0
$791$	18.9516	+	11.6154i	0.673840	+	0.412995i
$792$		0			0
$793$	−0.993379	+	1.72058i	−0.0352759	+	0.0610997i
$794$		0			0
$795$	6.69096	+	11.5891i	0.237304	+	0.411022i
$796$		0			0
$797$			20.3073i			0.719321i	0.933083	+	0.359660i	$0.117107\pi$
$797$			20.3073i			0.719321i	−0.933083	+	0.359660i	$0.882893\pi$
$798$		0			0
$799$		−	11.2147i		−	0.396746i
$800$		0			0
$801$	−3.39927	+	1.96257i	−0.120107	+	0.0693440i
$802$		0			0
$803$	25.0724	−	20.1993i	0.884785	−	0.712818i
$804$		0			0
$805$	1.28147	+	0.0336460i	0.0451657	+	0.00118587i
$806$		0			0
$807$	−1.72865	+	2.99410i	−0.0608513	+	0.105397i
$808$		0			0
$809$	−23.4501	+	13.5389i	−0.824461	+	0.476003i	−0.851953	−	0.523619i	$-0.824582\pi$
$809$	−23.4501	+	13.5389i	−0.824461	+	0.476003i	0.0274911	+	0.999622i	$0.491248\pi$
$810$		0			0
$811$	−23.5808			−0.828033			−0.414016	−	0.910269i	$-0.635874\pi$
$811$	−23.5808			−0.828033			−0.414016	+	0.910269i	$0.635874\pi$
$812$		0			0
$813$		−	35.1018i		−	1.23107i
$814$		0			0
$815$	−4.88927	+	2.82282i	−0.171264	+	0.0988792i
$816$		0			0
$817$	−2.73240	−	1.57755i	−0.0955947	−	0.0551916i
$818$		0			0
$819$	−0.221191	+	0.120077i	−0.00772905	+	0.00419583i
$820$		0			0
$821$	29.4247	+	16.9884i	1.02693	+	0.592898i	0.916104	−	0.400942i	$-0.131317\pi$
$821$	29.4247	+	16.9884i	1.02693	+	0.592898i	0.110826	+	0.993840i	$0.464650\pi$
$822$		0			0
$823$	−5.90033	−	10.2197i	−0.205673	−	0.356235i	0.744674	−	0.667428i	$-0.232605\pi$
$823$	−5.90033	−	10.2197i	−0.205673	−	0.356235i	−0.950347	+	0.311193i	$0.899272\pi$
$824$		0			0
$825$	−7.38957	+	19.1071i	−0.257272	+	0.665224i
$826$		0			0
$827$			17.0595i			0.593217i	0.954999	+	0.296609i	$0.0958557\pi$
$827$			17.0595i			0.593217i	−0.954999	+	0.296609i	$0.904144\pi$
$828$		0			0
$829$	−21.7387	+	12.5508i	−0.755015	+	0.435908i	−0.827503	−	0.561461i	$-0.810239\pi$
$829$	−21.7387	+	12.5508i	−0.755015	+	0.435908i	0.0724880	+	0.997369i	$0.476906\pi$
$830$		0			0
$831$	19.0740	−	33.0371i	0.661669	−	1.14604i
$832$		0			0
$833$	11.2581	−	17.3306i	0.390069	−	0.600469i
$834$		0			0
$835$	−18.7324	−	10.8152i	−0.648263	−	0.374275i
$836$		0			0
$837$	−7.09474	−	12.2884i	−0.245230	−	0.424751i
$838$		0			0
$839$			41.1030i			1.41903i	0.704688	+	0.709517i	$0.251087\pi$
$839$			41.1030i			1.41903i	−0.704688	+	0.709517i	$0.748913\pi$
$840$		0			0
$841$	25.4014			0.875909
$842$		0			0
$843$	8.85113	+	15.3306i	0.304849	+	0.528014i
$844$		0			0
$845$	−11.4486	−	6.60984i	−0.393843	−	0.227385i
$846$		0			0
$847$	28.2642	+	6.93787i	0.971170	+	0.238388i
$848$		0			0
$849$	29.2398	+	16.8816i	1.00351	+	0.579375i
$850$		0			0
$851$	−1.44851	−	2.50888i	−0.0496541	−	0.0860035i
$852$		0			0
$853$	52.7195			1.80508			0.902541	−	0.430605i	$-0.141700\pi$
$853$	52.7195			1.80508			0.902541	+	0.430605i	$0.141700\pi$
$854$		0			0
$855$			0.180675i			0.00617894i
$856$		0			0
$857$	−10.9387	−	18.9464i	−0.373659	−	0.647197i	0.616466	−	0.787382i	$-0.288564\pi$
$857$	−10.9387	−	18.9464i	−0.373659	−	0.647197i	−0.990125	+	0.140184i	$0.955230\pi$
$858$		0			0
$859$	−11.8529	−	6.84326i	−0.404415	−	0.233489i	0.283972	−	0.958832i	$-0.408348\pi$
$859$	−11.8529	−	6.84326i	−0.404415	−	0.233489i	−0.688387	+	0.725344i	$0.741681\pi$
$860$		0			0
$861$	−42.0985	−	1.10534i	−1.43471	−	0.0376697i
$862$		0			0
$863$	15.0240	−	26.0223i	0.511423	−	0.885810i	−0.488490	−	0.872570i	$-0.662452\pi$
$863$	15.0240	−	26.0223i	0.511423	−	0.885810i	0.999912	−	0.0132402i	$-0.00421461\pi$
$864$		0			0
$865$	−13.2962	+	7.67658i	−0.452085	+	0.261012i
$866$		0			0
$867$			12.9164i			0.438665i
$868$		0			0
$869$	8.38113	−	21.6710i	0.284310	−	0.735137i
$870$		0			0
$871$	0.868263	+	1.50388i	0.0294200	+	0.0509569i
$872$		0			0
$873$	5.42913	+	3.13451i	0.183748	+	0.106087i
$874$		0			0
$875$	−12.6263	+	20.6010i	−0.426846	+	0.696440i
$876$		0			0
$877$	−12.2786	−	7.08908i	−0.414620	−	0.239381i	0.278153	−	0.960537i	$-0.410278\pi$
$877$	−12.2786	−	7.08908i	−0.414620	−	0.239381i	−0.692773	+	0.721156i	$0.743611\pi$
$878$		0			0
$879$	−16.3705	+	9.45151i	−0.552163	+	0.318792i
$880$		0			0
$881$		−	22.3264i		−	0.752196i	−0.926580	−	0.376098i	$-0.877266\pi$
$881$		−	22.3264i		−	0.752196i	0.926580	−	0.376098i	$-0.122734\pi$
$882$		0			0
$883$	4.45618			0.149962			0.0749812	−	0.997185i	$-0.476110\pi$
$883$	4.45618			0.149962			0.0749812	+	0.997185i	$0.476110\pi$
$884$		0			0
$885$	8.59043	−	4.95969i	0.288764	−	0.166718i
$886$		0			0
$887$	4.50070	−	7.79545i	0.151119	−	0.261746i	−0.780520	−	0.625131i	$-0.785046\pi$
$887$	4.50070	−	7.79545i	0.151119	−	0.261746i	0.931639	+	0.363385i	$0.118379\pi$
$888$		0			0
$889$	4.88492	−	7.97021i	0.163835	−	0.267312i
$890$		0			0
$891$	−18.0020	+	14.5031i	−0.603089	+	0.485872i
$892$		0			0
$893$	1.02539	−	0.592012i	0.0343135	−	0.0198109i
$894$		0			0
$895$		−	2.20303i		−	0.0736391i
$896$		0			0
$897$			0.123983i			0.00413968i
$898$		0			0
$899$	2.41866	+	4.18924i	0.0806667	+	0.139719i
$900$		0			0
$901$	−12.4316	+	21.5321i	−0.414156	+	0.717339i
$902$		0			0
$903$	1.09601	−	41.7434i	0.0364730	−	1.38913i
$904$		0			0
$905$	2.74791	−	4.75951i	0.0913435	−	0.158212i
$906$		0			0
$907$	10.6872	+	18.5107i	0.354862	+	0.614638i	0.987094	−	0.160140i	$-0.0511947\pi$
$907$	10.6872	+	18.5107i	0.354862	+	0.614638i	−0.632233	+	0.774779i	$0.717861\pi$
$908$		0			0
$909$	3.03448			0.100647
$910$		0			0
$911$	28.4299			0.941924			0.470962	−	0.882153i	$-0.343907\pi$
$911$	28.4299			0.941924			0.470962	+	0.882153i	$0.343907\pi$
$912$		0			0
$913$	7.50174	+	48.1454i	0.248271	+	1.59338i
$914$		0			0
$915$	−9.43805	+	16.3472i	−0.312012	+	0.540421i
$916$		0			0
$917$	−32.5058	+	17.6463i	−1.07344	+	0.582732i
$918$		0			0
$919$	−18.2320	−	10.5263i	−0.601419	−	0.347229i	0.168181	−	0.985756i	$-0.446211\pi$
$919$	−18.2320	−	10.5263i	−0.601419	−	0.347229i	−0.769600	+	0.638527i	$0.779544\pi$
$920$		0			0
$921$	13.0418	−	7.52968i	0.429741	−	0.248111i
$922$		0			0
$923$	2.42852			0.0799357
$924$		0			0
$925$	24.1385			0.793669
$926$		0			0
$927$	−6.13425	+	3.54161i	−0.201475	+	0.116322i
$928$		0			0
$929$	10.8055	+	6.23858i	0.354518	+	0.204681i	0.666674	−	0.745350i	$-0.267718\pi$
$929$	10.8055	+	6.23858i	0.354518	+	0.204681i	−0.312155	+	0.950031i	$0.601051\pi$
$930$		0			0
$931$	2.17890	+	0.114497i	0.0714104	+	0.00375248i
$932$		0			0
$933$	−13.7819	+	23.8710i	−0.451200	+	0.781501i
$934$		0			0
$935$	9.85970	−	1.53628i	0.322447	−	0.0502418i
$936$		0			0
$937$	43.2128			1.41170			0.705850	−	0.708362i	$-0.250565\pi$
$937$	43.2128			1.41170			0.705850	+	0.708362i	$0.250565\pi$
$938$		0			0
$939$	44.9221			1.46598
$940$		0			0
$941$	7.73754	+	13.4018i	0.252236	+	0.436886i	0.964141	−	0.265390i	$-0.0855006\pi$
$941$	7.73754	+	13.4018i	0.252236	+	0.436886i	−0.711905	+	0.702276i	$0.752167\pi$
$942$		0			0
$943$	2.42672	−	4.20321i	0.0790249	−	0.136875i
$944$		0			0
$945$	−13.1859	+	7.15816i	−0.428937	+	0.232855i
$946$		0			0
$947$	16.7488	−	29.0098i	0.544264	−	0.942693i	−0.454389	−	0.890803i	$-0.650142\pi$
$947$	16.7488	−	29.0098i	0.544264	−	0.942693i	0.998653	−	0.0518895i	$-0.0165244\pi$
$948$		0			0
$949$	0.811791	+	1.40606i	0.0263518	+	0.0456427i
$950$		0			0
$951$		−	16.1312i		−	0.523091i
$952$		0			0
$953$		−	25.4820i		−	0.825444i	−0.910857	−	0.412722i	$-0.864578\pi$
$953$		−	25.4820i		−	0.825444i	0.910857	−	0.412722i	$-0.135422\pi$
$954$		0			0
$955$	5.29535	−	3.05727i	0.171354	−	0.0989311i
$956$		0			0
$957$	7.63942	−	6.15462i	0.246947	−	0.198951i
$958$		0			0
$959$	0.486833	−	18.5419i	0.0157207	−	0.598748i
$960$		0			0
$961$	−12.2488	+	21.2156i	−0.395124	+	0.684374i
$962$		0			0
$963$	3.57325	−	2.06302i	0.115146	−	0.0664798i
$964$		0			0
$965$	9.78285			0.314921
$966$		0			0
$967$			39.6417i			1.27479i	0.770537	+	0.637395i	$0.219988\pi$
$967$			39.6417i			1.27479i	−0.770537	+	0.637395i	$0.780012\pi$
$968$		0			0
$969$	1.24263	−	0.717434i	0.0399191	−	0.0230473i
$970$		0			0
$971$	16.5082	+	9.53101i	0.529773	+	0.305865i	0.740924	−	0.671589i	$-0.234388\pi$
$971$	16.5082	+	9.53101i	0.529773	+	0.305865i	−0.211151	+	0.977454i	$0.567721\pi$
$972$		0			0
$973$	25.8545	+	15.8461i	0.828857	+	0.508004i
$974$		0			0
$975$	−0.894652	−	0.516528i	−0.0286518	−	0.0165421i
$976$		0			0
$977$	−23.8348	−	41.2832i	−0.762544	−	1.32077i	−0.941535	−	0.336915i	$-0.890617\pi$
$977$	−23.8348	−	41.2832i	−0.762544	−	1.32077i	0.178991	−	0.983851i	$-0.442717\pi$
$978$		0			0
$979$	−8.25583	+	21.3470i	−0.263857	+	0.682252i
$980$		0			0
$981$			0.664016i			0.0212004i
$982$		0			0
$983$	−40.2377	+	23.2312i	−1.28338	+	0.740961i	−0.977465	−	0.211097i	$-0.932296\pi$
$983$	−40.2377	+	23.2312i	−1.28338	+	0.740961i	−0.305917	+	0.952058i	$0.598963\pi$
$984$		0			0
$985$	−7.55046	+	13.0778i	−0.240578	+	0.416693i
$986$		0			0
$987$	13.3608	+	8.18877i	0.425278	+	0.260651i
$988$		0			0
$989$	4.16775	+	2.40625i	0.132527	+	0.0765144i
$990$		0			0
$991$	−7.28588	−	12.6195i	−0.231444	−	0.400872i	0.726790	−	0.686860i	$-0.241012\pi$
$991$	−7.28588	−	12.6195i	−0.231444	−	0.400872i	−0.958233	+	0.285988i	$0.907678\pi$
$992$		0			0
$993$		−	41.8575i		−	1.32831i
$994$		0			0
$995$	−4.18877			−0.132793
$996$		0			0
$997$	−2.05848	−	3.56539i	−0.0651927	−	0.112917i	0.831587	−	0.555395i	$-0.187433\pi$
$997$	−2.05848	−	3.56539i	−0.0651927	−	0.112917i	−0.896779	+	0.442478i	$0.854100\pi$
$998$		0			0
$999$	29.3642	+	16.9534i	0.929043	+	0.536383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.bn.b.593.3		16
4.3	odd	2		154.2.i.a.131.3	yes	16
7.3	odd	6	inner	1232.2.bn.b.241.4		16
11.10	odd	2	inner	1232.2.bn.b.593.4		16
12.11	even	2		1386.2.bk.c.901.6		16
28.3	even	6		154.2.i.a.87.7	yes	16
28.11	odd	6		1078.2.i.c.1011.6		16
28.19	even	6		1078.2.c.b.1077.11		16
28.23	odd	6		1078.2.c.b.1077.14		16
28.27	even	2		1078.2.i.c.901.2		16
44.43	even	2		154.2.i.a.131.7	yes	16
77.10	even	6	inner	1232.2.bn.b.241.3		16
84.59	odd	6		1386.2.bk.c.703.2		16
132.131	odd	2		1386.2.bk.c.901.2		16
308.87	odd	6		154.2.i.a.87.3	✓	16
308.131	odd	6		1078.2.c.b.1077.3		16
308.219	even	6		1078.2.c.b.1077.6		16
308.263	even	6		1078.2.i.c.1011.2		16
308.307	odd	2		1078.2.i.c.901.6		16
924.395	even	6		1386.2.bk.c.703.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.3	✓	16	308.87	odd	6
154.2.i.a.87.7	yes	16	28.3	even	6
154.2.i.a.131.3	yes	16	4.3	odd	2
154.2.i.a.131.7	yes	16	44.43	even	2
1078.2.c.b.1077.3		16	308.131	odd	6
1078.2.c.b.1077.6		16	308.219	even	6
1078.2.c.b.1077.11		16	28.19	even	6
1078.2.c.b.1077.14		16	28.23	odd	6
1078.2.i.c.901.2		16	28.27	even	2
1078.2.i.c.901.6		16	308.307	odd	2
1078.2.i.c.1011.2		16	308.263	even	6
1078.2.i.c.1011.6		16	28.11	odd	6
1232.2.bn.b.241.3		16	77.10	even	6	inner
1232.2.bn.b.241.4		16	7.3	odd	6	inner
1232.2.bn.b.593.3		16	1.1	even	1	trivial
1232.2.bn.b.593.4		16	11.10	odd	2	inner
1386.2.bk.c.703.2		16	84.59	odd	6
1386.2.bk.c.703.6		16	924.395	even	6
1386.2.bk.c.901.2		16	132.131	odd	2
1386.2.bk.c.901.6		16	12.11	even	2

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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.35034 + 0.779618i) q^{3} +(0.882559 + 0.509546i) q^{5} +(-2.25578 - 1.38256i) q^{7} +(-0.284392 + 0.492581i) q^{9} +O(q^{10})\)	\(q+(-1.35034 + 0.779618i) q^{3} +(0.882559 + 0.509546i) q^{5} +(-2.25578 - 1.38256i) q^{7} +(-0.284392 + 0.492581i) q^{9} +(0.510616 + 3.27708i) q^{11} -0.167247 q^{13} -1.58900 q^{15} +(-1.47616 - 2.55678i) q^{17} +(0.155850 - 0.269940i) q^{19} +(4.12393 + 0.108278i) q^{21} +(-0.237719 + 0.411742i) q^{23} +(-1.98073 - 3.43072i) q^{25} -5.56458i q^{27} +1.89701i q^{29} +(2.20834 - 1.27498i) q^{31} +(-3.24438 - 4.02708i) q^{33} +(-1.28638 - 2.36961i) q^{35} +(-3.04667 + 5.27699i) q^{37} +(0.225839 - 0.130388i) q^{39} -10.2084 q^{41} -10.1222i q^{43} +(-0.501985 + 0.289821i) q^{45} +(3.28968 + 1.89930i) q^{47} +(3.17706 + 6.23749i) q^{49} +(3.98663 + 2.30168i) q^{51} +(-4.21079 - 7.29330i) q^{53} +(-1.21917 + 3.15240i) q^{55} +0.486014i q^{57} +(-5.40617 + 3.12126i) q^{59} +(5.93960 - 10.2877i) q^{61} +(1.32255 - 0.717964i) q^{63} +(-0.147605 - 0.0852198i) q^{65} +(-5.19151 - 8.99196i) q^{67} -0.741321i q^{69} -14.5206 q^{71} +(-4.85385 - 8.40712i) q^{73} +(5.34930 + 3.08842i) q^{75} +(3.37892 - 8.09833i) q^{77} +(-6.06709 - 3.50284i) q^{79} +(3.48507 + 6.03631i) q^{81} +14.6915 q^{83} -3.00868i q^{85} +(-1.47894 - 2.56161i) q^{87} +(5.97639 + 3.45047i) q^{89} +(0.377271 + 0.231228i) q^{91} +(-1.98800 + 3.44332i) q^{93} +(0.275094 - 0.158826i) q^{95} -11.0218i q^{97} +(-1.75944 - 0.680455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q - 12 * q^5 + 16 * q^9	\( 16 q - 12 q^{5} + 16 q^{9} - 8 q^{11} + 8 q^{15} - 16 q^{23} + 12 q^{31} - 24 q^{33} - 16 q^{37} - 108 q^{45} - 24 q^{47} + 8 q^{49} - 28 q^{53} - 60 q^{59} - 12 q^{67} - 8 q^{71} - 60 q^{75} + 44 q^{77} - 8 q^{81} + 96 q^{89} + 36 q^{91} - 44 q^{93} - 56 q^{99}+O(q^{100}) \) 16 * q - 12 * q^5 + 16 * q^9 - 8 * q^11 + 8 * q^15 - 16 * q^23 + 12 * q^31 - 24 * q^33 - 16 * q^37 - 108 * q^45 - 24 * q^47 + 8 * q^49 - 28 * q^53 - 60 * q^59 - 12 * q^67 - 8 * q^71 - 60 * q^75 + 44 * q^77 - 8 * q^81 + 96 * q^89 + 36 * q^91 - 44 * q^93 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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