LMFDB - Embedded newform 1078.2.i.c.1011.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(901,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1078.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.i (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:	$8.60787333789$
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:	$\Z[a_1, \ldots, a_{5}]$
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			1011.2
Root			$-1.29724 + 0.347596i$ of defining polynomial
Character	$\chi$	$=$	1078.1011
Dual form			1078.2.i.c.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.35034 - 0.779618i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.882559 + 0.509546i) q^{5} +1.55924 q^{6} +1.00000i q^{8} +(-0.284392 - 0.492581i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.35034 - 0.779618i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.882559 + 0.509546i) q^{5} +1.55924 q^{6} +1.00000i q^{8} +(-0.284392 - 0.492581i) q^{9} +(0.509546 - 0.882559i) q^{10} +(-0.510616 + 3.27708i) q^{11} +(-1.35034 + 0.779618i) q^{12} +0.167247 q^{13} +1.58900 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.47616 - 2.55678i) q^{17} +(0.492581 + 0.284392i) q^{18} +(0.155850 + 0.269940i) q^{19} +1.01909i q^{20} +(-1.19633 - 3.09335i) q^{22} +(0.237719 + 0.411742i) q^{23} +(0.779618 - 1.35034i) q^{24} +(-1.98073 + 3.43072i) q^{25} +(-0.144840 + 0.0836233i) q^{26} +5.56458i q^{27} -1.89701i q^{29} +(-1.37612 + 0.794502i) q^{30} +(2.20834 + 1.27498i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.24438 - 4.02708i) q^{33} +2.95232i q^{34} -0.568783 q^{36} +(-3.04667 - 5.27699i) q^{37} +(-0.269940 - 0.155850i) q^{38} +(-0.225839 - 0.130388i) q^{39} +(-0.509546 - 0.882559i) q^{40} +10.2084 q^{41} -10.1222i q^{43} +(2.58273 + 2.08075i) q^{44} +(0.501985 + 0.289821i) q^{45} +(-0.411742 - 0.237719i) q^{46} +(3.28968 - 1.89930i) q^{47} +1.55924i q^{48} -3.96145i q^{50} +(-3.98663 + 2.30168i) q^{51} +(0.0836233 - 0.144840i) q^{52} +(-4.21079 + 7.29330i) q^{53} +(-2.78229 - 4.81906i) q^{54} +(-1.21917 - 3.15240i) q^{55} -0.486014i q^{57} +(0.948505 + 1.64286i) q^{58} +(-5.40617 - 3.12126i) q^{59} +(0.794502 - 1.37612i) q^{60} +(-5.93960 - 10.2877i) q^{61} -2.54997 q^{62} -1.00000 q^{64} +(-0.147605 + 0.0852198i) q^{65} +(-0.796171 + 5.10974i) q^{66} +(5.19151 - 8.99196i) q^{67} +(-1.47616 - 2.55678i) q^{68} -0.741321i q^{69} +14.5206 q^{71} +(0.492581 - 0.284392i) q^{72} +(4.85385 - 8.40712i) q^{73} +(5.27699 + 3.04667i) q^{74} +(5.34930 - 3.08842i) q^{75} +0.311700 q^{76} +0.260777 q^{78} +(6.06709 - 3.50284i) q^{79} +(0.882559 + 0.509546i) q^{80} +(3.48507 - 6.03631i) q^{81} +(-8.84069 + 5.10418i) q^{82} +14.6915 q^{83} +3.00868i q^{85} +(5.06112 + 8.76612i) q^{86} +(-1.47894 + 2.56161i) q^{87} +(-3.27708 - 0.510616i) q^{88} +(-5.97639 + 3.45047i) q^{89} -0.579642 q^{90} +0.475438 q^{92} +(-1.98800 - 3.44332i) q^{93} +(-1.89930 + 3.28968i) q^{94} +(-0.275094 - 0.158826i) q^{95} +(-0.779618 - 1.35034i) q^{96} -11.0218i q^{97} +(1.75944 - 0.680455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 36 q^{26} + 12 q^{31} + 24 q^{33} + 32 q^{36} - 16 q^{37} - 12 q^{38} - 8 q^{44} + 108 q^{45} - 24 q^{47} - 28 q^{53} - 12 q^{58} - 60 q^{59} - 4 q^{60} - 16 q^{64} - 48 q^{66} + 12 q^{67} + 8 q^{71} - 60 q^{75} - 16 q^{78} - 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} - 96 q^{89} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9 + 8 * q^11 - 8 * q^15 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 36 * q^26 + 12 * q^31 + 24 * q^33 + 32 * q^36 - 16 * q^37 - 12 * q^38 - 8 * q^44 + 108 * q^45 - 24 * q^47 - 28 * q^53 - 12 * q^58 - 60 * q^59 - 4 * q^60 - 16 * q^64 - 48 * q^66 + 12 * q^67 + 8 * q^71 - 60 * q^75 - 16 * q^78 - 12 * q^80 - 8 * q^81 + 20 * q^86 - 4 * q^88 - 96 * q^89 + 32 * q^92 - 44 * q^93 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.35034	−	0.779618i	−0.779618	−	0.450113i	0.0566769	−	0.998393i	$-0.481950\pi$
$3$	−1.35034	−	0.779618i	−0.779618	−	0.450113i	−0.836295	+	0.548280i	$0.815283\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.882559	+	0.509546i	−0.394692	+	0.227876i	−0.684191	−	0.729303i	$-0.739845\pi$
$5$	−0.882559	+	0.509546i	−0.394692	+	0.227876i	0.289499	+	0.957178i	$0.406511\pi$
$6$	1.55924			0.636555
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−0.284392	−	0.492581i	−0.0947972	−	0.164194i
$10$	0.509546	−	0.882559i	0.161132	−	0.279090i
$11$	−0.510616	+	3.27708i	−0.153957	+	0.988078i
$11$	−0.510616	+	3.27708i	−0.153957	+	0.988078i
$12$	−1.35034	+	0.779618i	−0.389809	+	0.225056i
$13$	0.167247			0.0463859			0.0231929	−	0.999731i	$-0.492617\pi$
$13$	0.167247			0.0463859			0.0231929	+	0.999731i	$0.492617\pi$
$14$		0			0
$15$	1.58900			0.410279
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.47616	−	2.55678i	0.358021	−	0.620111i	−0.629609	−	0.776912i	$-0.716785\pi$
$17$	1.47616	−	2.55678i	0.358021	−	0.620111i	0.987630	+	0.156801i	$0.0501182\pi$
$18$	0.492581	+	0.284392i	0.116102	+	0.0670318i
$19$	0.155850	+	0.269940i	0.0357545	+	0.0619286i	0.883349	−	0.468716i	$-0.155283\pi$
$19$	0.155850	+	0.269940i	0.0357545	+	0.0619286i	−0.847594	+	0.530645i	$0.821950\pi$
$20$			1.01909i			0.227876i
$21$		0			0
$22$	−1.19633	−	3.09335i	−0.255059	−	0.659503i
$23$	0.237719	+	0.411742i	0.0495679	+	0.0858541i	0.889745	−	0.456458i	$-0.150882\pi$
$23$	0.237719	+	0.411742i	0.0495679	+	0.0858541i	−0.840177	+	0.542312i	$0.817549\pi$
$24$	0.779618	−	1.35034i	0.159139	−	0.275637i
$25$	−1.98073	+	3.43072i	−0.396145	+	0.686144i
$26$	−0.144840	+	0.0836233i	−0.0284054	+	0.0163999i
$27$			5.56458i			1.07090i
$28$		0			0
$29$		−	1.89701i		−	0.352266i	−0.984366	−	0.176133i	$-0.943641\pi$
$29$		−	1.89701i		−	0.352266i	0.984366	−	0.176133i	$-0.0563589\pi$
$30$	−1.37612	+	0.794502i	−0.251244	+	0.145056i
$31$	2.20834	+	1.27498i	0.396629	+	0.228994i	0.685028	−	0.728516i	$-0.259790\pi$
$31$	2.20834	+	1.27498i	0.396629	+	0.228994i	−0.288400	+	0.957510i	$0.593123\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	3.24438	−	4.02708i	0.564774	−	0.701025i
$34$			2.95232i			0.506318i
$35$		0			0
$36$	−0.568783			−0.0947972
$37$	−3.04667	−	5.27699i	−0.500870	−	0.867532i	−0.999999	−	0.00100474i	$-0.999680\pi$
$37$	−3.04667	−	5.27699i	−0.500870	−	0.867532i	0.499130	−	0.866527i	$-0.333653\pi$
$38$	−0.269940	−	0.155850i	−0.0437901	−	0.0252822i
$39$	−0.225839	−	0.130388i	−0.0361633	−	0.0208789i
$40$	−0.509546	−	0.882559i	−0.0805662	−	0.139545i
$41$	10.2084			1.59428			0.797138	−	0.603797i	$-0.206346\pi$
$41$	10.2084			1.59428			0.797138	+	0.603797i	$0.206346\pi$
$42$		0			0
$43$		−	10.1222i		−	1.54363i	−0.635848	−	0.771814i	$-0.719350\pi$
$43$		−	10.1222i		−	1.54363i	0.635848	−	0.771814i	$-0.280650\pi$
$44$	2.58273	+	2.08075i	0.389361	+	0.313685i
$45$	0.501985	+	0.289821i	0.0748315	+	0.0432040i
$46$	−0.411742	−	0.237719i	−0.0607080	−	0.0350498i
$47$	3.28968	−	1.89930i	0.479849	−	0.277041i	−0.240505	−	0.970648i	$-0.577313\pi$
$47$	3.28968	−	1.89930i	0.479849	−	0.277041i	0.720354	+	0.693607i	$0.243980\pi$
$48$			1.55924i			0.225056i
$49$		0			0
$50$		−	3.96145i		−	0.560234i
$51$	−3.98663	+	2.30168i	−0.558239	+	0.322300i
$52$	0.0836233	−	0.144840i	0.0115965	−	0.0200857i
$53$	−4.21079	+	7.29330i	−0.578396	+	1.00181i	0.417268	+	0.908784i	$0.362988\pi$
$53$	−4.21079	+	7.29330i	−0.578396	+	1.00181i	−0.995664	+	0.0930275i	$0.970346\pi$
$54$	−2.78229	−	4.81906i	−0.378621	−	0.655791i
$55$	−1.21917	−	3.15240i	−0.164393	−	0.425070i
$56$		0			0
$57$		−	0.486014i		−	0.0643742i
$58$	0.948505	+	1.64286i	0.124545	+	0.215718i
$59$	−5.40617	−	3.12126i	−0.703824	−	0.406353i	0.104946	−	0.994478i	$-0.466533\pi$
$59$	−5.40617	−	3.12126i	−0.703824	−	0.406353i	−0.808770	+	0.588125i	$0.799866\pi$
$60$	0.794502	−	1.37612i	0.102570	−	0.177656i
$61$	−5.93960	−	10.2877i	−0.760488	−	1.31720i	−0.942599	−	0.333926i	$-0.891626\pi$
$61$	−5.93960	−	10.2877i	−0.760488	−	1.31720i	0.182111	−	0.983278i	$-0.441707\pi$
$62$	−2.54997			−0.323846
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.147605	+	0.0852198i	−0.0183081	+	0.0105702i
$66$	−0.796171	+	5.10974i	−0.0980019	+	0.628966i
$67$	5.19151	−	8.99196i	0.634244	−	1.09854i	−0.352431	−	0.935838i	$-0.614645\pi$
$67$	5.19151	−	8.99196i	0.634244	−	1.09854i	0.986675	−	0.162705i	$-0.0520219\pi$
$68$	−1.47616	−	2.55678i	−0.179011	−	0.310055i
$69$		−	0.741321i		−	0.0892445i
$70$		0			0
$71$	14.5206			1.72328			0.861639	−	0.507522i	$-0.169439\pi$
$71$	14.5206			1.72328			0.861639	+	0.507522i	$0.169439\pi$
$72$	0.492581	−	0.284392i	0.0580512	−	0.0335159i
$73$	4.85385	−	8.40712i	0.568101	−	0.983979i	−0.428653	−	0.903469i	$-0.641012\pi$
$73$	4.85385	−	8.40712i	0.568101	−	0.983979i	0.996754	−	0.0805099i	$-0.0256549\pi$
$74$	5.27699	+	3.04667i	0.613438	+	0.354168i
$75$	5.34930	−	3.08842i	0.617684	−	0.356620i
$76$	0.311700			0.0357545
$77$		0			0
$78$	0.260777			0.0295272
$79$	6.06709	−	3.50284i	0.682601	−	0.394100i	−0.118233	−	0.992986i	$-0.537723\pi$
$79$	6.06709	−	3.50284i	0.682601	−	0.394100i	0.800834	+	0.598886i	$0.204390\pi$
$80$	0.882559	+	0.509546i	0.0986731	+	0.0569689i
$81$	3.48507	−	6.03631i	0.387230	−	0.670702i
$82$	−8.84069	+	5.10418i	−0.976291	+	0.563662i
$83$	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
$86$	5.06112	+	8.76612i	0.545755	+	0.945275i
$87$	−1.47894	+	2.56161i	−0.158559	+	0.274633i
$88$	−3.27708	−	0.510616i	−0.349338	−	0.0544319i
$89$	−5.97639	+	3.45047i	−0.633496	+	0.365749i	−0.782105	−	0.623147i	$-0.785854\pi$
$89$	−5.97639	+	3.45047i	−0.633496	+	0.365749i	0.148609	+	0.988896i	$0.452520\pi$
$90$	−0.579642			−0.0610997
$91$		0			0
$92$	0.475438			0.0495679
$93$	−1.98800	−	3.44332i	−0.206146	−	0.357055i
$94$	−1.89930	+	3.28968i	−0.195898	+	0.339305i
$95$	−0.275094	−	0.158826i	−0.0282240	−	0.0162952i
$96$	−0.779618	−	1.35034i	−0.0795694	−	0.137818i
$97$		−	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
$100$	1.98073	+	3.43072i	0.198073	+	0.343072i
$101$	2.66752	−	4.62028i	0.265428	−	0.459735i	−0.702248	−	0.711933i	$-0.747820\pi$
$101$	2.66752	−	4.62028i	0.265428	−	0.459735i	0.967676	+	0.252198i	$0.0811534\pi$
$102$	2.30168	−	3.98663i	0.227900	−	0.394735i
$103$	10.7849	−	6.22664i	1.06266	−	0.613529i	0.136496	−	0.990641i	$-0.456416\pi$
$103$	10.7849	−	6.22664i	1.06266	−	0.613529i	0.926168	+	0.377112i	$0.123083\pi$
$104$			0.167247i			0.0163999i
$105$		0			0
$106$		−	8.42157i		−	0.817975i
$107$	6.28227	−	3.62707i	0.607330	−	0.350642i	−0.164590	−	0.986362i	$-0.552630\pi$
$107$	6.28227	−	3.62707i	0.607330	−	0.350642i	0.771920	+	0.635720i	$0.219297\pi$
$108$	4.81906	+	2.78229i	0.463715	+	0.267726i
$109$	1.01103	+	0.583716i	0.0968387	+	0.0559098i	0.547637	−	0.836716i	$-0.315527\pi$
$109$	1.01103	+	0.583716i	0.0968387	+	0.0559098i	−0.450799	+	0.892626i	$0.648861\pi$
$110$	2.63204	+	2.12047i	0.250955	+	0.202179i
$111$			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	$0.629313\pi$
$114$	0.243007	+	0.420901i	0.0227597	+	0.0394210i
$115$	−0.419602	−	0.242258i	−0.0391281	−	0.0225906i
$116$	−1.64286	−	0.948505i	−0.152536	−	0.0880665i
$117$	−0.0475636	−	0.0823825i	−0.00439725	−	0.00761626i
$118$	6.24251			0.574670
$119$		0			0
$120$			1.58900i			0.145056i
$121$	−10.4785	−	3.34666i	−0.952595	−	0.304242i
$122$	10.2877	+	5.93960i	0.931404	+	0.537746i
$123$	−13.7847	−	7.95862i	−1.24293	−	0.717604i
$124$	2.20834	−	1.27498i	0.198314	−	0.114497i
$125$		−	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	$0.949894\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−7.89149	+	13.6685i	−0.694807	+	1.20344i
$130$	0.0852198	−	0.147605i	0.00747427	−	0.0129458i
$131$	6.98984	+	12.1068i	0.610705	+	1.05777i	0.991122	+	0.132957i	$0.0424473\pi$
$131$	6.98984	+	12.1068i	0.610705	+	1.05777i	−0.380417	+	0.924815i	$0.624219\pi$
$132$	−1.86537	−	4.82325i	−0.162359	−	0.419810i
$133$		0			0
$134$			10.3830i			0.896957i
$135$	−2.83541	−	4.91107i	−0.244033	−	0.422677i
$136$	2.55678	+	1.47616i	0.219242	+	0.126580i
$137$	3.50529	−	6.07134i	0.299477	−	0.518709i	−0.676539	−	0.736406i	$-0.736521\pi$
$137$	3.50529	−	6.07134i	0.299477	−	0.518709i	0.976016	+	0.217697i	$0.0698545\pi$
$138$	0.370660	+	0.642003i	0.0315527	+	0.0546509i
$139$	−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
$142$	−12.5752	+	7.26030i	−1.05529	+	0.609270i
$143$	−0.0853989	+	0.548081i	−0.00714141	+	0.0458328i
$144$	−0.284392	+	0.492581i	−0.0236993	+	0.0410484i
$145$	0.966613	+	1.67422i	0.0802729	+	0.139037i
$146$			9.70771i			0.803416i
$147$		0			0
$148$	−6.09335			−0.500870
$149$	12.2602	−	7.07841i	1.00439	−	0.579886i	0.0948474	−	0.995492i	$-0.469764\pi$
$149$	12.2602	−	7.07841i	1.00439	−	0.579886i	0.909545	+	0.415606i	$0.136430\pi$
$150$	−3.08842	+	5.34930i	−0.252168	+	0.436768i
$151$	20.1819	+	11.6520i	1.64238	+	0.948228i	0.979985	+	0.199072i	$0.0637928\pi$
$151$	20.1819	+	11.6520i	1.64238	+	0.948228i	0.662394	+	0.749156i	$0.269541\pi$
$152$	−0.269940	+	0.155850i	−0.0218951	+	0.0126411i
$153$	−1.67923			−0.135758
$154$		0			0
$155$	−2.59865			−0.208728
$156$	−0.225839	+	0.130388i	−0.0180816	+	0.0104394i
$157$	−3.49234	−	2.01630i	−0.278719	−	0.160919i	0.354124	−	0.935198i	$-0.384779\pi$
$157$	−3.49234	−	2.01630i	−0.278719	−	0.160919i	−0.632843	+	0.774280i	$0.718112\pi$
$158$	−3.50284	+	6.06709i	−0.278671	+	0.482672i
$159$	11.3720	−	6.56561i	0.901856	−	0.520687i
$160$	−1.01909			−0.0805662
$161$		0			0
$162$			6.97014i			0.547626i
$163$	2.76994	+	4.79768i	0.216958	+	0.375783i	0.953877	−	0.300199i	$-0.0970530\pi$
$163$	2.76994	+	4.79768i	0.216958	+	0.375783i	−0.736918	+	0.675982i	$0.763720\pi$
$164$	5.10418	−	8.84069i	0.398569	−	0.690342i
$165$	−0.811371	+	5.20730i	−0.0631652	+	0.405388i
$166$	−12.7233	+	7.34577i	−0.987516	+	0.570143i
$167$	−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
$170$	−1.50434	−	2.60560i	−0.115378	−	0.199840i
$171$	0.0886450	−	0.153538i	0.00677885	−	0.0117413i
$172$	−8.76612	−	5.06112i	−0.668411	−	0.385907i
$173$	7.53277	+	13.0471i	0.572706	+	0.991956i	0.996287	+	0.0860973i	$0.0274396\pi$
$173$	7.53277	+	13.0471i	0.572706	+	0.991956i	−0.423581	+	0.905858i	$0.639227\pi$
$174$		−	2.95789i		−	0.224237i
$175$		0			0
$176$	3.09335	−	1.19633i	0.233170	−	0.0901771i
$177$	4.86677	+	8.42950i	0.365809	+	0.633600i
$178$	3.45047	−	5.97639i	0.258623	−	0.447949i
$179$	1.08088	−	1.87214i	0.0807887	−	0.139930i	−0.822800	−	0.568331i	$-0.807589\pi$
$179$	1.08088	−	1.87214i	0.0807887	−	0.139930i	0.903589	+	0.428401i	$0.140923\pi$
$180$	0.501985	−	0.289821i	0.0374158	−	0.0216020i
$181$		−	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
$184$	−0.411742	+	0.237719i	−0.0303540	+	0.0175249i
$185$	5.37774	+	3.10484i	0.395379	+	0.228272i
$186$	3.44332	+	1.98800i	0.252476	+	0.145767i
$187$	7.62504	+	6.14303i	0.557598	+	0.449223i
$188$		−	3.79859i		−	0.277041i
$189$		0			0
$190$	0.317651			0.0230448
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$	1.35034	+	0.779618i	0.0974522	+	0.0562641i
$193$	8.31348	+	4.79979i	0.598417	+	0.345496i	0.768419	−	0.639947i	$-0.221044\pi$
$193$	8.31348	+	4.79979i	0.598417	+	0.345496i	−0.170001	+	0.985444i	$0.554377\pi$
$194$	5.51090	+	9.54515i	0.395659	+	0.685302i
$195$	0.265756			0.0190311
$196$		0			0
$197$		−	14.8180i		−	1.05574i	−0.849325	−	0.527870i	$-0.822991\pi$
$197$		−	14.8180i		−	1.05574i	0.849325	−	0.527870i	$-0.177009\pi$
$198$	−1.18350	+	1.46901i	−0.0841073	+	0.104398i
$199$	−3.55962	−	2.05515i	−0.252335	−	0.145686i	0.368498	−	0.929629i	$-0.379872\pi$
$199$	−3.55962	−	2.05515i	−0.252335	−	0.145686i	−0.620833	+	0.783943i	$0.713205\pi$
$200$	−3.43072	−	1.98073i	−0.242588	−	0.140059i
$201$	−14.0206	+	8.09479i	−0.988936	+	0.570963i
$202$			5.33504i			0.375372i
$203$		0			0
$204$			4.60336i			0.322300i
$205$	−9.00947	+	5.20162i	−0.629249	+	0.363297i
$206$	−6.22664	+	10.7849i	−0.433831	+	0.751417i
$207$	0.135211	−	0.234192i	0.00939780	−	0.0162775i
$208$	−0.0836233	−	0.144840i	−0.00579823	−	0.0100428i
$209$	−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	$0.916605\pi$
$212$	4.21079	+	7.29330i	0.289198	+	0.500906i
$213$	−19.6077	−	11.3205i	−1.34350	−	0.775669i
$214$	−3.62707	+	6.28227i	−0.247941	+	0.429447i
$215$	5.15775	+	8.93348i	0.351755	+	0.609258i
$216$	−5.56458			−0.378621
$217$		0			0
$218$	−1.16743			−0.0790685
$219$	−13.1087	+	7.56830i	−0.885803	+	0.511418i
$220$	−3.33965	−	0.520365i	−0.225159	−	0.0350830i
$221$	0.246883	−	0.427613i	0.0166071	−	0.0287644i
$222$	−4.75048	−	8.22807i	−0.318831	−	0.552232i
$223$		−	13.5885i		−	0.909951i	−0.890504	−	0.454975i	$-0.849648\pi$
$223$		−	13.5885i		−	0.909951i	0.890504	−	0.454975i	$-0.150352\pi$
$224$		0			0
$225$	2.25321			0.150214
$226$	7.27578	−	4.20068i	0.483978	−	0.279425i
$227$	10.8318	−	18.7611i	0.718929	−	1.24522i	−0.242496	−	0.970152i	$-0.577966\pi$
$227$	10.8318	−	18.7611i	0.718929	−	1.24522i	0.961425	−	0.275069i	$-0.0887006\pi$
$228$	−0.420901	−	0.243007i	−0.0278748	−	0.0160935i
$229$	−26.0355	+	15.0316i	−1.72047	+	0.993317i	−0.802527	+	0.596616i	$0.796511\pi$
$229$	−26.0355	+	15.0316i	−1.72047	+	0.993317i	−0.917948	+	0.396700i	$0.870155\pi$
$230$	0.484515			0.0319480
$231$		0			0
$232$	1.89701			0.124545
$233$	14.0223	−	8.09580i	0.918633	−	0.530373i	0.0354345	−	0.999372i	$-0.488718\pi$
$233$	14.0223	−	8.09580i	0.918633	−	0.530373i	0.883199	+	0.468999i	$0.155385\pi$
$234$	0.0823825	+	0.0475636i	0.00538551	+	0.00310933i
$235$	−1.93556	+	3.35248i	−0.126262	+	0.218692i
$236$	−5.40617	+	3.12126i	−0.351912	+	0.203176i
$237$	−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	$0.680689\pi$
$240$	−0.794502	−	1.37612i	−0.0512849	−	0.0888280i
$241$	−6.60221	+	11.4354i	−0.425286	+	0.736617i	−0.996447	−	0.0842210i	$-0.973160\pi$
$241$	−6.60221	+	11.4354i	−0.425286	+	0.736617i	0.571161	+	0.820838i	$0.306493\pi$
$242$	10.7480	−	2.34098i	0.690909	−	0.150484i
$243$	5.04515	−	2.91282i	0.323647	−	0.186858i
$244$	−11.8792			−0.760488
$245$		0			0
$246$	15.9172			1.01485
$247$	0.0260654	+	0.0451466i	0.00165850	+	0.00287261i
$248$	−1.27498	+	2.20834i	−0.0809615	+	0.140229i
$249$	−19.8386	−	11.4538i	−1.25722	−	0.725855i
$250$	4.56627	+	7.90901i	0.288796	+	0.500210i
$251$			28.9829i			1.82939i	0.404149	+	0.914693i	$0.367568\pi$
$251$			28.9829i			1.82939i	−0.404149	+	0.914693i	$0.632432\pi$
$252$		0			0
$253$	−1.47070	+	0.568783i	−0.0924618	+	0.0357591i
$254$	−1.76662	−	3.05988i	−0.110848	−	0.191994i
$255$	2.34562	−	4.06274i	0.146889	−	0.254419i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.05007	+	3.49301i	−0.377393	+	0.217888i	−0.676683	−	0.736274i	$-0.736583\pi$
$257$	−6.05007	+	3.49301i	−0.377393	+	0.217888i	0.299290	+	0.954162i	$0.403250\pi$
$258$		−	15.7830i		−	0.982605i
$259$		0			0
$260$			0.170440i			0.0105702i
$261$	−0.934431	+	0.539494i	−0.0578398	+	0.0333938i
$262$	−12.1068	−	6.98984i	−0.747958	−	0.431834i
$263$	−3.87174	−	2.23535i	−0.238741	−	0.137837i	0.375857	−	0.926678i	$-0.377348\pi$
$263$	−3.87174	−	2.23535i	−0.238741	−	0.137837i	−0.614598	+	0.788840i	$0.710682\pi$
$264$	4.02708	+	3.24438i	0.247850	+	0.199678i
$265$		−	8.58235i		−	0.527210i
$266$		0			0
$267$	10.7602			0.658513
$268$	−5.19151	−	8.99196i	−0.317122	−	0.549272i
$269$	−1.92024	−	1.10865i	−0.117079	−	0.0675956i	0.440317	−	0.897842i	$-0.354866\pi$
$269$	−1.92024	−	1.10865i	−0.117079	−	0.0675956i	−0.557396	+	0.830247i	$0.688199\pi$
$270$	4.91107	+	2.83541i	0.298878	+	0.172557i
$271$	−11.2561	−	19.4961i	−0.683759	−	1.18431i	−0.973825	−	0.227299i	$-0.927011\pi$
$271$	−11.2561	−	19.4961i	−0.683759	−	1.18431i	0.290066	−	0.957007i	$-0.406323\pi$
$272$	−2.95232			−0.179011
$273$		0			0
$274$			7.01058i			0.423524i
$275$	−10.2314	−	8.24279i	−0.616974	−	0.497059i
$276$	−0.642003	−	0.370660i	−0.0386440	−	0.0223111i
$277$	−21.1880	−	12.2329i	−1.27306	−	0.735004i	−0.297500	−	0.954722i	$-0.596153\pi$
$277$	−21.1880	−	12.2329i	−1.27306	−	0.735004i	−0.975563	+	0.219718i	$0.929486\pi$
$278$	9.92591	−	5.73073i	0.595317	−	0.343706i
$279$		−	1.45038i		−	0.0868319i
$280$		0			0
$281$			11.3532i			0.677273i	0.940917	+	0.338636i	$0.109966\pi$
$281$			11.3532i			0.677273i	−0.940917	+	0.338636i	$0.890034\pi$
$282$	5.12939	−	2.96145i	0.305451	−	0.176352i
$283$	−10.8268	+	18.7526i	−0.643589	+	1.11473i	0.341037	+	0.940050i	$0.389222\pi$
$283$	−10.8268	+	18.7526i	−0.643589	+	1.11473i	−0.984626	+	0.174679i	$0.944111\pi$
$284$	7.26030	−	12.5752i	0.430819	−	0.746201i
$285$	0.247646	+	0.428936i	0.0146693	+	0.0254080i
$286$	−0.200083	−	0.517352i	−0.0118312	−	0.0305916i
$287$		0			0
$288$		−	0.568783i		−	0.0335159i
$289$	4.14191	+	7.17400i	0.243642	+	0.422000i
$290$	−1.67422	−	0.966613i	−0.0983138	−	0.0567615i
$291$	−8.59279	+	14.8831i	−0.503718	+	0.872465i
$292$	−4.85385	−	8.40712i	−0.284050	−	0.491990i
$293$	−12.1233			−0.708249			−0.354124	−	0.935198i	$-0.615221\pi$
$293$	−12.1233			−0.708249			−0.354124	+	0.935198i	$0.615221\pi$
$294$		0			0
$295$	6.36169			0.370392
$296$	5.27699	−	3.04667i	0.306719	−	0.177084i
$297$	−18.2356	−	2.84136i	−1.05814	−	0.164873i
$298$	−7.07841	+	12.2602i	−0.410041	+	0.710213i
$299$	0.0397577	+	0.0688624i	0.00229925	+	0.00398242i
$300$		−	6.17684i		−	0.356620i
$301$		0			0
$302$	−23.3040			−1.34100
$303$	−7.20410	+	4.15929i	−0.413865	+	0.238945i
$304$	0.155850	−	0.269940i	0.00893862	−	0.0154821i
$305$	10.4841	+	6.05300i	0.600318	+	0.346594i
$306$	1.45426	−	0.839615i	0.0831343	−	0.0479976i
$307$	−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
$310$	2.25050	−	1.29932i	0.127820	−	0.0737967i
$311$	15.3094	+	8.83890i	0.868118	+	0.501208i	0.866722	−	0.498791i	$-0.166223\pi$
$311$	15.3094	+	8.83890i	0.868118	+	0.501208i	0.00139530	+	0.999999i	$0.499556\pi$
$312$	0.130388	−	0.225839i	0.00738179	−	0.0127856i
$313$	24.9505	−	14.4052i	1.41028	−	0.814228i	0.414869	−	0.909881i	$-0.363827\pi$
$313$	24.9505	−	14.4052i	1.41028	−	0.814228i	0.995415	+	0.0956530i	$0.0304939\pi$
$314$	4.03261			0.227573
$315$		0			0
$316$		−	7.00567i		−	0.394100i
$317$	−5.17280	−	8.95955i	−0.290533	−	0.503218i	0.683403	−	0.730042i	$-0.260499\pi$
$317$	−5.17280	−	8.95955i	−0.290533	−	0.503218i	−0.973936	+	0.226823i	$0.927166\pi$
$318$	−6.56561	+	11.3720i	−0.368181	+	0.637708i
$319$	6.21666	+	0.968644i	0.348066	+	0.0542337i
$320$	0.882559	−	0.509546i	0.0493366	−	0.0284845i
$321$	−11.3109			−0.631314
$322$		0			0
$323$	0.920239			0.0512034
$324$	−3.48507	−	6.03631i	−0.193615	−	0.335351i
$325$	−0.331270	+	0.573776i	−0.0183755	+	0.0318274i
$326$	−4.79768	−	2.76994i	−0.265719	−	0.153413i
$327$	−0.910151	−	1.57643i	−0.0503315	−	0.0871766i
$328$			10.2084i			0.563662i
$329$		0			0
$330$	−1.90098	−	4.91534i	−0.104646	−	0.270580i
$331$	13.4224	+	23.2483i	0.737763	+	1.27784i	0.953500	+	0.301392i	$0.0974512\pi$
$331$	13.4224	+	23.2483i	0.737763	+	1.27784i	−0.215737	+	0.976451i	$0.569215\pi$
$332$	7.34577	−	12.7233i	0.403152	−	0.698279i
$333$	−1.73290	+	3.00147i	−0.0949622	+	0.164479i
$334$	18.3815	−	10.6126i	1.00579	−	0.580694i
$335$			10.5813i			0.578116i
$336$		0			0
$337$		−	14.5505i		−	0.792614i	−0.918118	−	0.396307i	$-0.870292\pi$
$337$		−	14.5505i		−	0.792614i	0.918118	−	0.396307i	$-0.129708\pi$
$338$	11.2341	−	6.48601i	0.611055	−	0.352793i
$339$	11.3447	+	6.54984i	0.616158	+	0.355739i
$340$	2.60560	+	1.50434i	0.141308	+	0.0815844i
$341$	−5.30584	+	6.58587i	−0.287327	+	0.356645i
$342$			0.177290i			0.00958674i
$343$		0			0
$344$	10.1222			0.545755
$345$	0.377737	+	0.654259i	0.0203367	+	0.0352241i
$346$	−13.0471	−	7.53277i	−0.701418	−	0.404964i
$347$	−24.7179	−	14.2709i	−1.32693	−	0.766101i	−0.342102	−	0.939663i	$-0.611139\pi$
$347$	−24.7179	−	14.2709i	−1.32693	−	0.766101i	−0.984823	+	0.173562i	$0.944472\pi$
$348$	1.47894	+	2.56161i	0.0792797	+	0.137316i
$349$	34.6026			1.85224			0.926118	−	0.377235i	$-0.123125\pi$
$349$	34.6026			1.85224			0.926118	+	0.377235i	$0.123125\pi$
$350$		0			0
$351$			0.930656i			0.0496748i
$352$	−2.08075	+	2.58273i	−0.110904	+	0.137660i
$353$	14.6534	+	8.46017i	0.779924	+	0.450289i	0.836403	−	0.548114i	$-0.184654\pi$
$353$	14.6534	+	8.46017i	0.779924	+	0.450289i	−0.0564792	+	0.998404i	$0.517987\pi$
$354$	−8.42950	−	4.86677i	−0.448023	−	0.258666i
$355$	−12.8153	+	7.39891i	−0.680164	+	0.392693i
$356$			6.90094i			0.365749i
$357$		0			0
$358$			2.16176i			0.114252i
$359$	26.2848	−	15.1755i	1.38726	−	0.800934i	0.394254	−	0.919002i	$-0.371003\pi$
$359$	26.2848	−	15.1755i	1.38726	−	0.800934i	0.993006	+	0.118067i	$0.0376698\pi$
$360$	−0.289821	+	0.501985i	−0.0152749	+	0.0264569i
$361$	9.45142	−	16.3703i	0.497443	−	0.861597i
$362$	2.69643	+	4.67035i	0.141721	+	0.245468i
$363$	11.5405	+	12.6884i	0.605717	+	0.665968i
$364$		0			0
$365$			9.89304i			0.517825i
$366$	−9.26124	−	16.0409i	−0.484093	−	0.838474i
$367$	15.0875	+	8.71075i	0.787559	+	0.454698i	0.839103	−	0.543973i	$-0.183081\pi$
$367$	15.0875	+	8.71075i	0.787559	+	0.454698i	−0.0515432	+	0.998671i	$0.516414\pi$
$368$	0.237719	−	0.411742i	0.0123920	−	0.0214635i
$369$	−2.90317	−	5.02844i	−0.151133	−	0.261770i
$370$	−6.20968			−0.322826
$371$		0			0
$372$	−3.97600			−0.206146
$373$	7.92596	−	4.57606i	0.410391	−	0.236939i	−0.280567	−	0.959834i	$-0.590522\pi$
$373$	7.92596	−	4.57606i	0.410391	−	0.236939i	0.690958	+	0.722895i	$0.257189\pi$
$374$	−9.67499	−	1.50750i	−0.500282	−	0.0779511i
$375$	−7.11989	+	12.3320i	−0.367670	+	0.636822i
$376$	1.89930	+	3.28968i	0.0979488	+	0.169652i
$377$		−	0.317269i		−	0.0163402i
$378$		0			0
$379$	−6.15382			−0.316100			−0.158050	−	0.987431i	$-0.550521\pi$
$379$	−6.15382			−0.316100			−0.158050	+	0.987431i	$0.550521\pi$
$380$	−0.275094	+	0.158826i	−0.0141120	+	0.00814758i
$381$	2.75458	−	4.77107i	0.141121	−	0.244429i
$382$	5.19615	+	3.00000i	0.265858	+	0.153493i
$383$	−11.2281	+	6.48253i	−0.573728	+	0.331242i	−0.758637	−	0.651514i	$-0.774134\pi$
$383$	−11.2281	+	6.48253i	−0.573728	+	0.331242i	0.184909	+	0.982756i	$0.440801\pi$
$384$	−1.55924			−0.0795694
$385$		0			0
$386$	−9.59958			−0.488606
$387$	−4.98603	+	2.87868i	−0.253454	+	0.146332i
$388$	−9.54515	−	5.51090i	−0.484582	−	0.279773i
$389$	−2.58323	+	4.47429i	−0.130975	+	0.226856i	−0.924053	−	0.382265i	$-0.875144\pi$
$389$	−2.58323	+	4.47429i	−0.130975	+	0.226856i	0.793078	+	0.609121i	$0.208477\pi$
$390$	−0.230151	+	0.132878i	−0.0116542	+	0.00672853i
$391$	1.40365			0.0709854
$392$		0			0
$393$		−	21.7976i		−	1.09954i
$394$	7.40901	+	12.8328i	0.373261	+	0.646506i
$395$	−3.56971	+	6.18292i	−0.179612	+	0.311097i
$396$	0.290430	−	1.86395i	0.0145947	−	0.0936670i
$397$	−8.01690	+	4.62856i	−0.402357	+	0.232301i	−0.687500	−	0.726184i	$-0.741292\pi$
$397$	−8.01690	+	4.62856i	−0.402357	+	0.232301i	0.285144	+	0.958485i	$0.407959\pi$
$398$	4.11030			0.206030
$399$		0			0
$400$	3.96145			0.198073
$401$	15.4624	+	26.7816i	0.772155	+	1.33741i	0.936380	+	0.350988i	$0.114154\pi$
$401$	15.4624	+	26.7816i	0.772155	+	1.33741i	−0.164225	+	0.986423i	$0.552512\pi$
$402$	8.09479	−	14.0206i	0.403732	−	0.699284i
$403$	0.369337	+	0.213237i	0.0183980	+	0.0106221i
$404$	−2.66752	−	4.62028i	−0.132714	−	0.229867i
$405$			7.10320i			0.352961i
$406$		0			0
$407$	18.8488	−	7.28968i	0.934301	−	0.361336i
$408$	−2.30168	−	3.98663i	−0.113950	−	0.197367i
$409$	11.9198	−	20.6458i	0.589399	−	1.02087i	−0.404913	−	0.914355i	$-0.632698\pi$
$409$	11.9198	−	20.6458i	0.589399	−	1.02087i	0.994311	−	0.106513i	$-0.0339686\pi$
$410$	5.20162	−	9.00947i	0.256890	−	0.444946i
$411$	−9.46665	+	5.46557i	−0.466955	+	0.269597i
$412$		−	12.4533i		−	0.613529i
$413$		0			0
$414$			0.270422i			0.0132905i
$415$	−12.9662	+	7.48601i	−0.636484	+	0.367474i
$416$	0.144840	+	0.0836233i	0.00710136	+	0.00409997i
$417$	15.4768	+	8.93556i	0.757904	+	0.437576i
$418$	0.648570	−	0.805037i	0.0317226	−	0.0393757i
$419$			5.03426i			0.245940i	0.992410	+	0.122970i	$0.0392418\pi$
$419$			5.03426i			0.245940i	−0.992410	+	0.122970i	$0.960758\pi$
$420$		0			0
$421$	−16.9250			−0.824872			−0.412436	−	0.910987i	$-0.635322\pi$
$421$	−16.9250			−0.824872			−0.412436	+	0.910987i	$0.635322\pi$
$422$	−3.76228	−	6.51646i	−0.183145	−	0.317216i
$423$	−1.87112	−	1.08029i	−0.0909767	−	0.0525254i
$424$	−7.29330	−	4.21079i	−0.354194	−	0.204494i
$425$	5.84773	+	10.1286i	0.283657	+	0.491308i
$426$	22.6410			1.09696
$427$		0			0
$428$		−	7.25414i		−	0.350642i
$429$	0.542611	−	0.673516i	0.0261975	−	0.0325177i
$430$	−8.93348	−	5.15775i	−0.430811	−	0.248729i
$431$	−5.19535	−	2.99953i	−0.250251	−	0.144482i	0.369628	−	0.929180i	$-0.379485\pi$
$431$	−5.19535	−	2.99953i	−0.250251	−	0.144482i	−0.619879	+	0.784697i	$0.712818\pi$
$432$	4.81906	−	2.78229i	0.231857	−	0.133863i
$433$		−	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
$436$	1.01103	−	0.583716i	0.0484193	−	0.0279549i
$437$	−0.0740971	+	0.128340i	−0.00354455	+	0.00613934i
$438$	7.56830	−	13.1087i	0.361627	−	0.626357i
$439$	−5.67481	−	9.82906i	−0.270844	−	0.469116i	0.698234	−	0.715869i	$-0.253969\pi$
$439$	−5.67481	−	9.82906i	−0.270844	−	0.469116i	−0.969078	+	0.246754i	$0.920636\pi$
$440$	3.15240	−	1.21917i	0.150285	−	0.0581219i
$441$		0			0
$442$			0.493765i			0.0234860i
$443$	2.37538	+	4.11428i	0.112858	+	0.195475i	0.916921	−	0.399068i	$-0.130666\pi$
$443$	2.37538	+	4.11428i	0.112858	+	0.195475i	−0.804064	+	0.594543i	$0.797333\pi$
$444$	8.22807	+	4.75048i	0.390487	+	0.225448i
$445$	3.51634	−	6.09048i	0.166691	−	0.288717i
$446$	6.79423	+	11.7680i	0.321716	+	0.557229i
$447$	−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	$0.444644\pi$
$450$	−1.95134	+	1.12660i	−0.0919869	+	0.0531086i
$451$	−5.21255	+	33.4536i	−0.245449	+	1.57527i
$452$	−4.20068	+	7.27578i	−0.197583	+	0.342224i
$453$	−18.1682	−	31.4683i	−0.853619	−	1.47851i
$454$			21.6635i			1.01672i
$455$		0			0
$456$	0.486014			0.0227597
$457$	−11.7066	+	6.75879i	−0.547610	+	0.316163i	−0.748158	−	0.663521i	$-0.769061\pi$
$457$	−11.7066	+	6.75879i	−0.547610	+	0.316163i	0.200547	+	0.979684i	$0.435728\pi$
$458$	15.0316	−	26.0355i	0.702381	−	1.21656i
$459$	14.2274	+	8.21420i	0.664079	+	0.383406i
$460$	−0.419602	+	0.242258i	−0.0195641	+	0.0112953i
$461$	18.5730			0.865033			0.432516	−	0.901626i	$-0.357626\pi$
$461$	18.5730			0.865033			0.432516	+	0.901626i	$0.357626\pi$
$462$		0			0
$463$	28.2849			1.31451			0.657256	−	0.753667i	$-0.271717\pi$
$463$	28.2849			1.31451			0.657256	+	0.753667i	$0.271717\pi$
$464$	−1.64286	+	0.948505i	−0.0762678	+	0.0440332i
$465$	3.50905	+	2.02595i	0.162728	+	0.0939513i
$466$	−8.09580	+	14.0223i	−0.375030	+	0.649572i
$467$	18.6881	−	10.7896i	0.864782	−	0.499282i	−0.000828665	−	1.00000i	$-0.500264\pi$
$467$	18.6881	−	10.7896i	0.864782	−	0.499282i	0.865611	+	0.500717i	$0.166930\pi$
$468$	−0.0951271			−0.00439725
$469$		0			0
$470$		−	3.87112i		−	0.178561i
$471$	3.14389	+	5.44538i	0.144863	+	0.250910i
$472$	3.12126	−	5.40617i	0.143667	−	0.248839i
$473$	33.1714	+	5.16859i	1.52522	+	0.237652i
$474$	9.46003	−	5.46175i	0.434513	−	0.250866i
$475$	−1.23479			−0.0566559
$476$		0			0
$477$	4.79005			0.219321
$478$	−13.0350	−	22.5774i	−0.596209	−	1.03266i
$479$	3.46780	−	6.00641i	0.158448	−	0.274440i	−0.775861	−	0.630904i	$-0.782684\pi$
$479$	3.46780	−	6.00641i	0.158448	−	0.274440i	0.934309	+	0.356464i	$0.116018\pi$
$480$	1.37612	+	0.794502i	0.0628109	+	0.0362639i
$481$	−0.509546	−	0.882559i	−0.0232333	−	0.0402412i
$482$		−	13.2044i		−	0.601445i
$483$		0			0
$484$	−8.13757	+	7.40135i	−0.369889	+	0.336425i
$485$	5.61611	+	9.72738i	0.255014	+	0.441698i
$486$	−2.91282	+	5.04515i	−0.132128	+	0.228853i
$487$	6.08702	−	10.5430i	0.275829	−	0.477750i	−0.694515	−	0.719478i	$-0.744381\pi$
$487$	6.08702	−	10.5430i	0.275829	−	0.477750i	0.970344	+	0.241728i	$0.0777143\pi$
$488$	10.2877	−	5.93960i	0.465702	−	0.268873i
$489$		−	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	$0.982958\pi$
$492$	−13.7847	+	7.95862i	−0.621463	+	0.358802i
$493$	−4.85024	−	2.80029i	−0.218444	−	0.126119i
$494$	−0.0451466	−	0.0260654i	−0.00203124	−	0.00117274i
$495$	−1.20609	+	1.49706i	−0.0542097	+	0.0672878i
$496$		−	2.54997i		−	0.114497i
$497$		0			0
$498$	22.9076			1.02651
$499$	1.96446	+	3.40255i	0.0879413	+	0.152319i	0.906641	−	0.421903i	$-0.138638\pi$
$499$	1.96446	+	3.40255i	0.0879413	+	0.152319i	−0.818699	+	0.574222i	$0.805305\pi$
$500$	−7.90901	−	4.56627i	−0.353702	−	0.204210i
$501$	28.6611	+	16.5475i	1.28048	+	0.739288i
$502$	−14.4915	−	25.1000i	−0.646786	−	1.12027i
$503$	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
$506$	0.989268	−	1.22793i	0.0439783	−	0.0545881i
$507$	17.5166	+	10.1132i	0.777940	+	0.449144i
$508$	3.05988	+	1.76662i	0.135760	+	0.0783812i
$509$	−13.2438	+	7.64634i	−0.587023	+	0.338918i	−0.763920	−	0.645312i	$-0.776728\pi$
$509$	−13.2438	+	7.64634i	−0.587023	+	0.338918i	0.176896	+	0.984229i	$0.443394\pi$
$510$			4.69125i			0.207732i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−1.50210	+	0.867240i	−0.0663195	+	0.0382896i
$514$	3.49301	−	6.05007i	0.154070	−	0.266857i
$515$	−6.34552	+	10.9908i	−0.279617	+	0.484311i
$516$	7.89149	+	13.6685i	0.347403	+	0.601720i
$517$	4.54439	+	11.7504i	0.199862	+	0.516780i
$518$		0			0
$519$		−	23.4907i		−	1.03113i
$520$	−0.0852198	−	0.147605i	−0.00373714	−	0.00647291i
$521$	0.121861	+	0.0703565i	0.00533883	+	0.00308237i	0.502667	−	0.864480i	$-0.332352\pi$
$521$	0.121861	+	0.0703565i	0.00533883	+	0.00308237i	−0.497328	+	0.867562i	$0.665686\pi$
$522$	0.539494	−	0.934431i	0.0236130	−	0.0408989i
$523$	4.56153	+	7.90081i	0.199462	+	0.345478i	0.948354	−	0.317214i	$-0.102747\pi$
$523$	4.56153	+	7.90081i	0.199462	+	0.345478i	−0.748892	+	0.662692i	$0.769414\pi$
$524$	13.9797			0.610705
$525$		0			0
$526$	4.47070			0.194932
$527$	6.51971	−	3.76416i	0.284003	−	0.163969i
$528$	−5.10974	−	0.796171i	−0.222373	−	0.0346489i
$529$	11.3870	−	19.7228i	0.495086	−	0.857514i
$530$	4.29118	+	7.43253i	0.186397	+	0.322849i
$531$			3.55064i			0.154085i
$532$		0			0
$533$	1.70731			0.0739519
$534$	−9.31859	+	5.38009i	−0.403255	+	0.232819i
$535$	−3.69632	+	6.40221i	−0.159806	+	0.276792i
$536$	8.99196	+	5.19151i	0.388394	+	0.224239i
$537$	−2.91910	+	1.68534i	−0.125969	+	0.0727280i
$538$	2.21730			0.0955946
$539$		0			0
$540$	−5.67081			−0.244033
$541$	−21.6730	+	12.5129i	−0.931797	+	0.537973i	−0.887379	−	0.461040i	$-0.847476\pi$
$541$	−21.6730	+	12.5129i	−0.931797	+	0.537973i	−0.0444172	+	0.999013i	$0.514143\pi$
$542$	19.4961	+	11.2561i	0.837430	+	0.483491i
$543$	−4.20437	+	7.28217i	−0.180427	+	0.312508i
$544$	2.55678	−	1.47616i	0.109621	−	0.0632898i
$545$	−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	$-0.287397\pi$
$548$	−3.50529	−	6.07134i	−0.149738	−	0.259355i
$549$	−3.37835	+	5.85147i	−0.144184	+	0.249735i
$550$	12.9820	+	2.02278i	0.553555	+	0.0862517i
$551$	0.512080	−	0.295649i	0.0218153	−	0.0125951i
$552$	0.741321			0.0315527
$553$		0			0
$554$	24.4658			1.03945
$555$	−4.84117	−	8.38516i	−0.205496	−	0.355930i
$556$	−5.73073	+	9.92591i	−0.243037	+	0.420952i
$557$	−33.5815	−	19.3883i	−1.42290	−	0.821509i	−0.426350	−	0.904558i	$-0.640201\pi$
$557$	−33.5815	−	19.3883i	−1.42290	−	0.821509i	−0.996545	+	0.0830490i	$0.973534\pi$
$558$	0.725189	+	1.25606i	0.0306997	+	0.0531735i
$559$		−	1.69291i		−	0.0716025i
$560$		0			0
$561$	−5.50716	−	14.2398i	−0.232512	−	0.601204i
$562$	−5.67658	−	9.83212i	−0.239452	−	0.414743i
$563$	21.6247	−	37.4550i	0.911371	−	1.57854i	0.0992415	−	0.995063i	$-0.468358\pi$
$563$	21.6247	−	37.4550i	0.911371	−	1.57854i	0.812129	−	0.583477i	$-0.198308\pi$
$564$	−2.96145	+	5.12939i	−0.124700	+	0.215986i
$565$	7.41469	−	4.28087i	0.311938	−	0.180098i
$566$		−	21.6537i		−	0.910172i
$567$		0			0
$568$			14.5206i			0.609270i
$569$	−18.4783	+	10.6685i	−0.774651	+	0.447245i	−0.834531	−	0.550961i	$-0.814261\pi$
$569$	−18.4783	+	10.6685i	−0.774651	+	0.447245i	0.0598803	+	0.998206i	$0.480928\pi$
$570$	−0.428936	−	0.247646i	−0.0179662	−	0.0103728i
$571$	19.5677	+	11.2974i	0.818883	+	0.472782i	0.850031	−	0.526733i	$-0.176583\pi$
$571$	19.5677	+	11.2974i	0.818883	+	0.472782i	−0.0311482	+	0.999515i	$0.509916\pi$
$572$	0.431953	+	0.347998i	0.0180608	+	0.0145505i
$573$			9.35542i			0.390828i
$574$		0			0
$575$	−1.88343			−0.0785443
$576$	0.284392	+	0.492581i	0.0118497	+	0.0205242i
$577$	29.3358	+	16.9370i	1.22126	+	0.705097i	0.965187	−	0.261559i	$-0.0842366\pi$
$577$	29.3358	+	16.9370i	1.22126	+	0.705097i	0.256077	+	0.966656i	$0.417570\pi$
$578$	−7.17400	−	4.14191i	−0.298399	−	0.172281i
$579$	−7.48400	−	12.9627i	−0.311025	−	0.538710i
$580$	1.93323			0.0802729
$581$		0			0
$582$		−	17.1856i		−	0.712365i
$583$	−21.7506	−	17.5232i	−0.900819	−	0.725736i
$584$	8.40712	+	4.85385i	0.347889	+	0.200854i
$585$	0.0839553	+	0.0484716i	0.00347112	+	0.00200405i
$586$	10.4991	−	6.06163i	0.433712	−	0.250404i
$587$			6.07819i			0.250874i	0.992102	+	0.125437i	$0.0400332\pi$
$587$			6.07819i			0.250874i	−0.992102	+	0.125437i	$0.959967\pi$
$588$		0			0
$589$			0.794825i			0.0327502i
$590$	−5.50939	+	3.18085i	−0.226818	+	0.130953i
$591$	−11.5524	+	20.0093i	−0.475202	+	0.823074i
$592$	−3.04667	+	5.27699i	−0.125217	+	0.216883i
$593$	0.809196	+	1.40157i	0.0332297	+	0.0575555i	0.882162	−	0.470946i	$-0.156087\pi$
$593$	0.809196	+	1.40157i	0.0332297	+	0.0575555i	−0.848932	+	0.528502i	$0.822754\pi$
$594$	17.2132	−	6.65709i	0.706264	−	0.273144i
$595$		0			0
$596$		−	14.1568i		−	0.579886i
$597$	3.20446	+	5.55029i	0.131150	+	0.227158i
$598$	−0.0688624	−	0.0397577i	−0.00281599	−	0.00162581i
$599$	−2.63955	+	4.57184i	−0.107849	+	0.186800i	−0.914899	−	0.403684i	$-0.867730\pi$
$599$	−2.63955	+	4.57184i	−0.107849	+	0.186800i	0.807050	+	0.590484i	$0.201063\pi$
$600$	3.08842	+	5.34930i	0.126084	+	0.218384i
$601$	32.7945			1.33771			0.668857	−	0.743391i	$-0.266784\pi$
$601$	32.7945			1.33771			0.668857	+	0.743391i	$0.266784\pi$
$602$		0			0
$603$	−5.90569			−0.240498
$604$	20.1819	−	11.6520i	0.821189	−	0.474114i
$605$	10.9532	−	2.38567i	0.445311	−	0.0969912i
$606$	4.15929	−	7.20410i	0.168960	−	0.292647i
$607$	−0.332910	−	0.576616i	−0.0135124	−	0.0234041i	0.859190	−	0.511656i	$-0.170968\pi$
$607$	−0.332910	−	0.576616i	−0.0135124	−	0.0234041i	−0.872703	+	0.488252i	$0.837635\pi$
$608$			0.311700i			0.0126411i
$609$		0			0
$610$	−12.1060			−0.490158
$611$	0.550188	−	0.317651i	0.0222582	−	0.0128508i
$612$	−0.839615	+	1.45426i	−0.0339394	+	0.0587848i
$613$	3.71908	+	2.14721i	0.150212	+	0.0867251i	0.573222	−	0.819400i	$-0.305693\pi$
$613$	3.71908	+	2.14721i	0.150212	+	0.0867251i	−0.423010	+	0.906125i	$0.639027\pi$
$614$	8.36422	−	4.82908i	0.337552	−	0.194886i
$615$	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	$0.714425\pi$
$618$	16.8161	−	9.70880i	0.676444	−	0.390545i
$619$	0.685357	+	0.395691i	0.0275468	+	0.0159042i	0.513710	−	0.857964i	$-0.328271\pi$
$619$	0.685357	+	0.395691i	0.0275468	+	0.0159042i	−0.486163	+	0.873868i	$0.661604\pi$
$620$	−1.29932	+	2.25050i	−0.0521821	+	0.0903821i
$621$	−2.29117	+	1.32281i	−0.0919414	+	0.0530824i
$622$	−17.6778			−0.708815
$623$		0			0
$624$			0.260777i			0.0104394i
$625$	−5.25019	−	9.09359i	−0.210007	−	0.363744i
$626$	−14.4052	+	24.9505i	−0.575746	+	0.997222i
$627$	1.59271	+	0.248167i	0.0636067	+	0.00991083i
$628$	−3.49234	+	2.01630i	−0.139360	+	0.0804593i
$629$	−17.9895			−0.717288
$630$		0			0
$631$	−34.3677			−1.36816			−0.684078	−	0.729409i	$-0.739795\pi$
$631$	−34.3677			−1.36816			−0.684078	+	0.729409i	$0.739795\pi$
$632$	3.50284	+	6.06709i	0.139335	+	0.241336i
$633$	5.86628	−	10.1607i	0.233164	−	0.403852i
$634$	8.95955	+	5.17280i	0.355829	+	0.205438i
$635$	−1.80035	−	3.11830i	−0.0714447	−	0.123746i
$636$		−	13.1312i		−	0.520687i
$637$		0			0
$638$	−5.86811	+	2.26946i	−0.232321	+	0.0898488i
$639$	−4.12954	−	7.15257i	−0.163362	−	0.282951i
$640$	−0.509546	+	0.882559i	−0.0201416	+	0.0348862i
$641$	−2.47939	+	4.29443i	−0.0979301	+	0.169620i	−0.910828	−	0.412787i	$-0.864556\pi$
$641$	−2.47939	+	4.29443i	−0.0979301	+	0.169620i	0.812898	+	0.582407i	$0.197889\pi$
$642$	9.79554	−	5.65546i	0.386599	−	0.223203i
$643$			48.1404i			1.89847i	0.314562	+	0.949237i	$0.398142\pi$
$643$			48.1404i			1.89847i	−0.314562	+	0.949237i	$0.601858\pi$
$644$		0			0
$645$		−	16.0843i		−	0.633318i
$646$	−0.796950	+	0.460119i	−0.0313556	+	0.0181031i
$647$	2.74160	+	1.58286i	0.107783	+	0.0622287i	0.552923	−	0.833233i	$-0.313513\pi$
$647$	2.74160	+	1.58286i	0.107783	+	0.0622287i	−0.445139	+	0.895461i	$0.646846\pi$
$648$	6.03631	+	3.48507i	0.237129	+	0.136906i
$649$	12.9891	−	16.1227i	0.509867	−	0.632872i
$650$		−	0.662540i		−	0.0259869i
$651$		0			0
$652$	5.53988			0.216958
$653$	11.0606	+	19.1575i	0.432833	+	0.749689i	0.997116	−	0.0758922i	$-0.0241805\pi$
$653$	11.0606	+	19.1575i	0.432833	+	0.749689i	−0.564283	+	0.825582i	$0.690847\pi$
$654$	1.57643	+	0.910151i	0.0616432	+	0.0355897i
$655$	−12.3379	−	7.12329i	−0.482081	−	0.278330i
$656$	−5.10418	−	8.84069i	−0.199285	−	0.345171i
$657$	−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	$0.840766\pi$
$660$	4.10397	+	3.30632i	0.159747	+	0.128698i
$661$	−24.0205	−	13.8682i	−0.934289	−	0.539412i	−0.0461236	−	0.998936i	$-0.514687\pi$
$661$	−24.0205	−	13.8682i	−0.934289	−	0.539412i	−0.888166	+	0.459524i	$0.848020\pi$
$662$	−23.2483	−	13.4224i	−0.903572	−	0.521677i
$663$	−0.666750	+	0.384948i	−0.0258944	+	0.0149502i
$664$			14.6915i			0.570143i
$665$		0			0
$666$		−	3.46579i		−	0.134297i
$667$	0.781078	−	0.450956i	0.0302435	−	0.0174611i
$668$	−10.6126	+	18.3815i	−0.410613	+	0.711202i
$669$	−10.5938	+	18.3490i	−0.409580	+	0.709414i
$670$	−5.29063	−	9.16363i	−0.204395	−	0.354022i
$671$	36.7465	−	14.2115i	1.41858	−	0.548629i
$672$		0			0
$673$			15.9518i			0.614897i	0.951565	+	0.307449i	$0.0994752\pi$
$673$			15.9518i			0.614897i	−0.951565	+	0.307449i	$0.900525\pi$
$674$	7.27523	+	12.6011i	0.280231	+	0.485375i
$675$	−19.0905	−	11.0219i	−0.734793	−	0.424233i
$676$	−6.48601	+	11.2341i	−0.249462	+	0.432081i
$677$	−7.52574	−	13.0350i	−0.289238	−	0.500974i	0.684390	−	0.729116i	$-0.260068\pi$
$677$	−7.52574	−	13.0350i	−0.289238	−	0.500974i	−0.973628	+	0.228141i	$0.926735\pi$
$678$	−13.0997			−0.503091
$679$		0			0
$680$	−3.00868			−0.115378
$681$	−29.2531	+	16.8893i	−1.12098	+	0.647198i
$682$	1.30205	−	8.35645i	0.0498582	−	0.319985i
$683$	2.64673	−	4.58427i	0.101274	−	0.175412i	−0.810936	−	0.585135i	$-0.801041\pi$
$683$	2.64673	−	4.58427i	0.101274	−	0.175412i	0.912210	+	0.409723i	$0.134375\pi$
$684$	−0.0886450	−	0.153538i	−0.00338943	−	0.00587066i
$685$			7.14442i			0.272974i
$686$		0			0
$687$	46.8756			1.78842
$688$	−8.76612	+	5.06112i	−0.334205	+	0.192954i
$689$	−0.704240	+	1.21978i	−0.0268294	+	0.0464699i
$690$	−0.654259	−	0.377737i	−0.0249072	−	0.0143802i
$691$	23.4089	−	13.5151i	0.890517	−	0.514140i	0.0164055	−	0.999865i	$-0.494778\pi$
$691$	23.4089	−	13.5151i	0.890517	−	0.514140i	0.874112	+	0.485725i	$0.161444\pi$
$692$	15.0655			0.572706
$693$		0			0
$694$	28.5417			1.08343
$695$	10.1154	−	5.84014i	0.383699	−	0.221529i
$696$	−2.56161	−	1.47894i	−0.0970974	−	0.0560592i
$697$	15.0692	−	26.1005i	0.570785	−	0.988629i
$698$	−29.9667	+	17.3013i	−1.13426	+	0.654864i
$699$	−25.2465			−0.954911
$700$		0			0
$701$		−	19.9250i		−	0.752555i	−0.926507	−	0.376278i	$-0.877204\pi$
$701$		−	19.9250i		−	0.752555i	0.926507	−	0.376278i	$-0.122796\pi$
$702$	−0.465328	−	0.805972i	−0.0175627	−	0.0304195i
$703$	0.949649	−	1.64484i	0.0358167	−	0.0620363i
$704$	0.510616	−	3.27708i	0.0192446	−	0.123510i
$705$	5.22731	−	3.01799i	0.196872	−	0.113664i
$706$	−16.9203			−0.636805
$707$		0			0
$708$	9.73355			0.365809
$709$	−4.98412	−	8.63276i	−0.187183	−	0.324210i	0.757127	−	0.653268i	$-0.226602\pi$
$709$	−4.98412	−	8.63276i	−0.187183	−	0.324210i	−0.944310	+	0.329058i	$0.893269\pi$
$710$	7.39891	−	12.8153i	0.277676	−	0.480949i
$711$	−3.45086	−	1.99236i	−0.129417	−	0.0747192i
$712$	−3.45047	−	5.97639i	−0.129312	−	0.223975i
$713$			1.21235i			0.0454029i
$714$		0			0
$715$	−0.203903	−	0.527228i	−0.00762553	−	0.0197172i
$716$	−1.08088	−	1.87214i	−0.0403943	−	0.0699650i
$717$	20.3247	−	35.2034i	0.759040	−	1.31470i
$718$	−15.1755	+	26.2848i	−0.566346	+	0.980940i
$719$	−35.6817	+	20.6008i	−1.33070	+	0.768282i	−0.985407	−	0.170212i	$-0.945555\pi$
$719$	−35.6817	+	20.6008i	−1.33070	+	0.768282i	−0.345295	+	0.938494i	$0.612221\pi$
$720$		−	0.579642i		−	0.0216020i
$721$		0			0
$722$			18.9028i			0.703491i
$723$	17.8304	−	10.2944i	0.663121	−	0.382853i
$724$	−4.67035	−	2.69643i	−0.173572	−	0.100212i
$725$	6.50811	+	3.75746i	0.241705	+	0.139549i
$726$	−16.3385	−	5.21824i	−0.606379	−	0.193667i
$727$		−	0.0415718i		−	0.00154181i	−1.00000		0.000770906i	$-0.999755\pi$
$727$		−	0.0415718i		−	0.00154181i	1.00000		0.000770906i	$-0.000245387\pi$
$728$		0			0
$729$	−29.9940			−1.11089
$730$	−4.94652	−	8.56762i	−0.183079	−	0.317102i
$731$	−25.8804	−	14.9420i	−0.957221	−	0.552652i
$732$	16.0409	+	9.26124i	0.592890	+	0.342305i
$733$	−4.40404	−	7.62803i	−0.162667	−	0.281748i	0.773157	−	0.634214i	$-0.218676\pi$
$733$	−4.40404	−	7.62803i	−0.162667	−	0.281748i	−0.935824	+	0.352467i	$0.885343\pi$
$734$	−17.4215			−0.643040
$735$		0			0
$736$			0.475438i			0.0175249i
$737$	26.8165	+	21.6045i	0.987800	+	0.795810i
$738$	5.02844	+	2.90317i	0.185099	+	0.106867i
$739$	−28.4003	−	16.3969i	−1.04472	−	0.603170i	−0.123555	−	0.992338i	$-0.539429\pi$
$739$	−28.4003	−	16.3969i	−1.04472	−	0.603170i	−0.921167	+	0.389167i	$0.872763\pi$
$740$	5.37774	−	3.10484i	0.197690	−	0.114136i
$741$		−	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	$-0.156640\pi$
$744$	3.44332	−	1.98800i	0.126238	−	0.0728836i
$745$	−7.21355	+	12.4942i	−0.264284	+	0.457753i
$746$	−4.57606	+	7.92596i	−0.167541	+	0.290190i
$747$	−4.17815	−	7.23678i	−0.152871	−	0.264780i
$748$	9.13254	−	3.53196i	0.333919	−	0.129141i
$749$		0			0
$750$		−	14.2398i		−	0.519963i
$751$	−5.73290	−	9.92967i	−0.209196	−	0.362339i	0.742265	−	0.670106i	$-0.233751\pi$
$751$	−5.73290	−	9.92967i	−0.209196	−	0.362339i	−0.951462	+	0.307767i	$0.900418\pi$
$752$	−3.28968	−	1.89930i	−0.119962	−	0.0692603i
$753$	22.5956	−	39.1367i	0.823430	−	1.42622i
$754$	0.158634	+	0.274763i	0.00577712	+	0.0100063i
$755$	−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	$0.369243\pi$
$758$	5.32936	−	3.07691i	0.193571	−	0.111758i
$759$	2.42937	+	0.378530i	0.0881805	+	0.0137398i
$760$	0.158826	−	0.275094i	0.00576121	−	0.00997871i
$761$	−13.0047	−	22.5249i	−0.471421	−	0.816526i	0.528044	−	0.849217i	$-0.322926\pi$
$761$	−13.0047	−	22.5249i	−0.471421	−	0.816526i	−0.999466	+	0.0326910i	$0.989592\pi$
$762$			5.50916i			0.199576i
$763$		0			0
$764$	−6.00000			−0.217072
$765$	1.48202	−	0.855644i	0.0535825	−	0.0309359i
$766$	6.48253	−	11.2281i	0.234223	−	0.405687i
$767$	−0.904164	−	0.522020i	−0.0326475	−	0.0188490i
$768$	1.35034	−	0.779618i	0.0487261	−	0.0281320i
$769$	40.8753			1.47400			0.737001	−	0.675891i	$-0.236241\pi$
$769$	40.8753			1.47400			0.737001	+	0.675891i	$0.236241\pi$
$770$		0			0
$771$	10.8929			0.392296
$772$	8.31348	−	4.79979i	0.299209	−	0.172748i
$773$	−40.8229	−	23.5691i	−1.46830	−	0.847722i	−0.468928	−	0.883236i	$-0.655360\pi$
$773$	−40.8229	−	23.5691i	−1.46830	−	0.847722i	−0.999369	+	0.0355144i	$0.988693\pi$
$774$	2.87868	−	4.98603i	0.103472	−	0.179219i
$775$	−8.74822	+	5.05078i	−0.314245	+	0.181430i
$776$	11.0218			0.395659
$777$		0			0
$778$		−	5.16647i		−	0.185227i
$779$	1.59097	+	2.75565i	0.0570025	+	0.0987313i
$780$	0.132878	−	0.230151i	0.00475779	−	0.00824073i
$781$	−7.41445	+	47.5852i	−0.265310	+	1.70273i
$782$	−1.21559	+	0.701823i	−0.0434695	+	0.0250971i
$783$	10.5561			0.377243
$784$		0			0
$785$	4.10960			0.146678
$786$	10.8988	+	18.8773i	0.388748	+	0.673331i
$787$	−12.0746	+	20.9137i	−0.430411	+	0.745494i	−0.996909	−	0.0785692i	$-0.974965\pi$
$787$	−12.0746	+	20.9137i	−0.430411	+	0.745494i	0.566497	+	0.824064i	$0.308298\pi$
$788$	−12.8328	−	7.40901i	−0.457149	−	0.263935i
$789$	3.48543	+	6.03695i	0.124085	+	0.214921i
$790$		−	7.13942i		−	0.254009i
$791$		0			0
$792$	0.680455	+	1.75944i	0.0241789	+	0.0625191i
$793$	−0.993379	−	1.72058i	−0.0352759	−	0.0610997i
$794$	4.62856	−	8.01690i	0.164261	−	0.284509i
$795$	−6.69096	+	11.5891i	−0.237304	+	0.411022i
$796$	−3.55962	+	2.05515i	−0.126167	+	0.0728428i
$797$			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
$800$	−3.43072	+	1.98073i	−0.121294	+	0.0700293i
$801$	3.39927	+	1.96257i	0.120107	+	0.0693440i
$802$	−26.7816	−	15.4624i	−0.945692	−	0.545996i
$803$	25.0724	+	20.1993i	0.884785	+	0.712818i
$804$			16.1896i			0.570963i
$805$		0			0
$806$	−0.426473			−0.0150219
$807$	1.72865	+	2.99410i	0.0608513	+	0.105397i
$808$	4.62028	+	2.66752i	0.162541	+	0.0938430i
$809$	−23.4501	−	13.5389i	−0.824461	−	0.476003i	0.0274911	−	0.999622i	$-0.491248\pi$
$809$	−23.4501	−	13.5389i	−0.824461	−	0.476003i	−0.851953	+	0.523619i	$0.824582\pi$
$810$	−3.55160	−	6.15156i	−0.124791	−	0.216144i
$811$	−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
$814$	−12.6787	+	15.7375i	−0.444389	+	0.551598i
$815$	−4.88927	−	2.82282i	−0.171264	−	0.0988792i
$816$	3.98663	+	2.30168i	0.139560	+	0.0805749i
$817$	2.73240	−	1.57755i	0.0955947	−	0.0551916i
$818$			23.8397i			0.833535i
$819$		0			0
$820$			10.4032i			0.363297i
$821$	29.4247	−	16.9884i	1.02693	−	0.592898i	0.110826	−	0.993840i	$-0.464650\pi$
$821$	29.4247	−	16.9884i	1.02693	−	0.592898i	0.916104	+	0.400942i	$0.131317\pi$
$822$	5.46557	−	9.46665i	0.190634	−	0.330187i
$823$	5.90033	−	10.2197i	0.205673	−	0.356235i	−0.744674	−	0.667428i	$-0.767395\pi$
$823$	5.90033	−	10.2197i	0.205673	−	0.356235i	0.950347	+	0.311193i	$0.100728\pi$
$824$	6.22664	+	10.7849i	0.216915	+	0.375708i
$825$	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	$0.904144\pi$
$828$	−0.135211	−	0.234192i	−0.00469890	−	0.00813873i
$829$	21.7387	+	12.5508i	0.755015	+	0.435908i	0.827503	−	0.561461i	$-0.189761\pi$
$829$	21.7387	+	12.5508i	0.755015	+	0.435908i	−0.0724880	+	0.997369i	$0.523094\pi$
$830$	7.48601	−	12.9662i	0.259843	−	0.450062i
$831$	19.0740	+	33.0371i	0.661669	+	1.14604i
$832$	−0.167247			−0.00579823
$833$		0			0
$834$	−17.8711			−0.618826
$835$	18.7324	−	10.8152i	0.648263	−	0.374275i
$836$	−0.159159	+	1.02147i	−0.00550464	+	0.0353282i
$837$	−7.09474	+	12.2884i	−0.245230	+	0.424751i
$838$	−2.51713	−	4.35980i	−0.0869528	−	0.150607i
$839$		−	41.1030i		−	1.41903i	−0.704688	−	0.709517i	$-0.748913\pi$
$839$		−	41.1030i		−	1.41903i	0.704688	−	0.709517i	$-0.251087\pi$
$840$		0			0
$841$	25.4014			0.875909
$842$	14.6574	−	8.46248i	0.505129	−	0.291636i
$843$	8.85113	−	15.3306i	0.304849	−	0.528014i
$844$	6.51646	+	3.76228i	0.224306	+	0.129503i
$845$	11.4486	−	6.60984i	0.393843	−	0.227385i
$846$	2.16058			0.0742822
$847$		0			0
$848$	8.42157			0.289198
$849$	29.2398	−	16.8816i	1.00351	−	0.579375i
$850$	−10.1286	−	5.84773i	−0.347407	−	0.200576i
$851$	1.44851	−	2.50888i	0.0496541	−	0.0860035i
$852$	−19.6077	+	11.3205i	−0.671749	+	0.387834i
$853$	−52.7195			−1.80508			−0.902541	−	0.430605i	$-0.858300\pi$
$853$	−52.7195			−1.80508			−0.902541	+	0.430605i	$0.858300\pi$
$854$		0			0
$855$			0.180675i			0.00617894i
$856$	3.62707	+	6.28227i	0.123971	+	0.214724i
$857$	10.9387	−	18.9464i	0.373659	−	0.647197i	−0.616466	−	0.787382i	$-0.711436\pi$
$857$	10.9387	−	18.9464i	0.373659	−	0.647197i	0.990125	+	0.140184i	$0.0447695\pi$
$858$	−0.133157	+	0.854588i	−0.00454590	+	0.0291751i
$859$	−11.8529	+	6.84326i	−0.404415	+	0.233489i	−0.688387	−	0.725344i	$-0.741681\pi$
$859$	−11.8529	+	6.84326i	−0.404415	+	0.233489i	0.283972	+	0.958832i	$0.408348\pi$
$860$	10.3155			0.351755
$861$		0			0
$862$	5.99907			0.204329
$863$	−15.0240	−	26.0223i	−0.511423	−	0.885810i	−0.999912	−	0.0132402i	$-0.995785\pi$
$863$	−15.0240	−	26.0223i	−0.511423	−	0.885810i	0.488490	−	0.872570i	$-0.337548\pi$
$864$	−2.78229	+	4.81906i	−0.0946553	+	0.163948i
$865$	−13.2962	−	7.67658i	−0.452085	−	0.261012i
$866$	18.0588	+	31.2787i	0.613662	+	1.06289i
$867$		−	12.9164i		−	0.438665i
$868$		0			0
$869$	8.38113	+	21.6710i	0.284310	+	0.735137i
$870$	1.50718	+	2.61051i	0.0510981	+	0.0885046i
$871$	0.868263	−	1.50388i	0.0294200	−	0.0509569i
$872$	−0.583716	+	1.01103i	−0.0197671	+	0.0342377i
$873$	−5.42913	+	3.13451i	−0.183748	+	0.106087i
$874$		−	0.148194i		−	0.00501275i
$875$		0			0
$876$			15.1366i			0.511418i
$877$	−12.2786	+	7.08908i	−0.414620	+	0.239381i	−0.692773	−	0.721156i	$-0.743611\pi$
$877$	−12.2786	+	7.08908i	−0.414620	+	0.239381i	0.278153	+	0.960537i	$0.410278\pi$
$878$	9.82906	+	5.67481i	0.331715	+	0.191516i
$879$	16.3705	+	9.45151i	0.552163	+	0.318792i
$880$	−2.12047	+	2.63204i	−0.0714811	+	0.0887259i
$881$		−	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	$-0.523890\pi$
$883$	−4.45618			−0.149962			−0.0749812	+	0.997185i	$0.523890\pi$
$884$	−0.246883	−	0.427613i	−0.00830356	−	0.0143822i
$885$	−8.59043	−	4.95969i	−0.288764	−	0.166718i
$886$	−4.11428	−	2.37538i	−0.138222	−	0.0798025i
$887$	4.50070	+	7.79545i	0.151119	+	0.261746i	0.931639	−	0.363385i	$-0.118379\pi$
$887$	4.50070	+	7.79545i	0.151119	+	0.261746i	−0.780520	+	0.625131i	$0.785046\pi$
$888$	−9.50096			−0.318831
$889$		0			0
$890$			7.03268i			0.235736i
$891$	18.0020	+	14.5031i	0.603089	+	0.485872i
$892$	−11.7680	−	6.79423i	−0.394020	−	0.227488i
$893$	1.02539	+	0.592012i	0.0343135	+	0.0198109i
$894$	19.1165	−	11.0369i	0.639351	−	0.369130i
$895$			2.20303i			0.0736391i
$896$		0			0
$897$		−	0.123983i		−	0.00413968i
$898$	−6.35054	+	3.66649i	−0.211920	+	0.122352i
$899$	2.41866	−	4.18924i	0.0806667	−	0.139719i
$900$	1.12660	−	1.95134i	0.0375535	−	0.0650445i
$901$	12.4316	+	21.5321i	0.414156	+	0.717339i
$902$	−12.2126	−	31.5780i	−0.406635	−	1.05143i
$903$		0			0
$904$		−	8.40135i		−	0.279425i
$905$	2.74791	+	4.75951i	0.0913435	+	0.158212i
$906$	31.4683	+	18.1682i	1.04547	+	0.603600i
$907$	−10.6872	+	18.5107i	−0.354862	+	0.614638i	−0.987094	−	0.160140i	$-0.948805\pi$
$907$	−10.6872	+	18.5107i	−0.354862	+	0.614638i	0.632233	+	0.774779i	$0.282139\pi$
$908$	−10.8318	−	18.7611i	−0.359464	−	0.622611i
$909$	−3.03448			−0.100647
$910$		0			0
$911$	−28.4299			−0.941924			−0.470962	−	0.882153i	$-0.656093\pi$
$911$	−28.4299			−0.941924			−0.470962	+	0.882153i	$0.656093\pi$
$912$	−0.420901	+	0.243007i	−0.0139374	+	0.00804677i
$913$	−7.50174	+	48.1454i	−0.248271	+	1.59338i
$914$	6.75879	−	11.7066i	0.223561	−	0.387219i
$915$	−9.43805	−	16.3472i	−0.312012	−	0.540421i
$916$			30.0632i			0.993317i
$917$		0			0
$918$	−16.4284			−0.542218
$919$	18.2320	−	10.5263i	0.601419	−	0.347229i	−0.168181	−	0.985756i	$-0.553789\pi$
$919$	18.2320	−	10.5263i	0.601419	−	0.347229i	0.769600	+	0.638527i	$0.220456\pi$
$920$	0.242258	−	0.419602i	0.00798700	−	0.0138339i
$921$	13.0418	+	7.52968i	0.429741	+	0.248111i
$922$	−16.0847	+	9.28652i	−0.529722	+	0.305835i
$923$	2.42852			0.0799357
$924$		0			0
$925$	24.1385			0.793669
$926$	−24.4955	+	14.1425i	−0.804971	+	0.464750i
$927$	−6.13425	−	3.54161i	−0.201475	−	0.116322i
$928$	0.948505	−	1.64286i	0.0311362	−	0.0539295i
$929$	−10.8055	+	6.23858i	−0.354518	+	0.204681i	−0.666674	−	0.745350i	$-0.732282\pi$
$929$	−10.8055	+	6.23858i	−0.354518	+	0.204681i	0.312155	+	0.950031i	$0.398949\pi$
$930$	−4.05191			−0.132867
$931$		0			0
$932$		−	16.1916i		−	0.530373i
$933$	−13.7819	−	23.8710i	−0.451200	−	0.781501i
$934$	−10.7896	+	18.6881i	−0.353046	+	0.611493i
$935$	−9.85970	−	1.53628i	−0.322447	−	0.0502418i
$936$	0.0823825	−	0.0475636i	0.00269276	−	0.00155466i
$937$	−43.2128			−1.41170			−0.705850	−	0.708362i	$-0.749435\pi$
$937$	−43.2128			−1.41170			−0.705850	+	0.708362i	$0.749435\pi$
$938$		0			0
$939$	−44.9221			−1.46598
$940$	1.93556	+	3.35248i	0.0631309	+	0.109346i
$941$	−7.73754	+	13.4018i	−0.252236	+	0.436886i	−0.964141	−	0.265390i	$-0.914499\pi$
$941$	−7.73754	+	13.4018i	−0.252236	+	0.436886i	0.711905	+	0.702276i	$0.247833\pi$
$942$	−5.44538	−	3.14389i	−0.177420	−	0.102434i
$943$	2.42672	+	4.20321i	0.0790249	+	0.136875i
$944$			6.24251i			0.203176i
$945$		0			0
$946$	−31.3116	+	12.1096i	−1.01803	+	0.393717i
$947$	−16.7488	−	29.0098i	−0.544264	−	0.942693i	−0.998653	−	0.0518895i	$-0.983476\pi$
$947$	−16.7488	−	29.0098i	−0.544264	−	0.942693i	0.454389	−	0.890803i	$-0.349858\pi$
$948$	−5.46175	+	9.46003i	−0.177389	+	0.307247i
$949$	0.811791	−	1.40606i	0.0263518	−	0.0456427i
$950$	1.06936	−	0.617393i	0.0346945	−	0.0200309i
$951$			16.1312i			0.523091i
$952$		0			0
$953$			25.4820i			0.825444i	0.910857	+	0.412722i	$0.135422\pi$
$953$			25.4820i			0.825444i	−0.910857	+	0.412722i	$0.864578\pi$
$954$	−4.14831	+	2.39503i	−0.134306	+	0.0775418i
$955$	5.29535	+	3.05727i	0.171354	+	0.0989311i
$956$	22.5774	+	13.0350i	0.730204	+	0.421583i
$957$	−7.63942	−	6.15462i	−0.246947	−	0.198951i
$958$			6.93560i			0.224079i
$959$		0			0
$960$	−1.58900			−0.0512849
$961$	−12.2488	−	21.2156i	−0.395124	−	0.684374i
$962$	0.882559	+	0.509546i	0.0284548	+	0.0164284i
$963$	−3.57325	−	2.06302i	−0.115146	−	0.0664798i
$964$	6.60221	+	11.4354i	0.212643	+	0.368309i
$965$	−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	$0.780012\pi$
$968$	3.34666	−	10.4785i	0.107566	−	0.336793i
$969$	−1.24263	−	0.717434i	−0.0399191	−	0.0230473i
$970$	−9.72738	−	5.61611i	−0.312327	−	0.180322i
$971$	16.5082	−	9.53101i	0.529773	−	0.305865i	−0.211151	−	0.977454i	$-0.567721\pi$
$971$	16.5082	−	9.53101i	0.529773	−	0.305865i	0.740924	+	0.671589i	$0.234388\pi$
$972$		−	5.82564i		−	0.186858i
$973$		0			0
$974$			12.1740i			0.390081i
$975$	0.894652	−	0.516528i	0.0286518	−	0.0165421i
$976$	−5.93960	+	10.2877i	−0.190122	+	0.329301i
$977$	−23.8348	+	41.2832i	−0.762544	+	1.32077i	0.178991	+	0.983851i	$0.442717\pi$
$977$	−23.8348	+	41.2832i	−0.762544	+	1.32077i	−0.941535	+	0.336915i	$0.890617\pi$
$978$	4.31899	+	7.48071i	0.138106	+	0.239207i
$979$	−8.25583	−	21.3470i	−0.263857	−	0.682252i
$980$		0			0
$981$		−	0.664016i		−	0.0212004i
$982$	−1.18576	−	2.05379i	−0.0378391	−	0.0655392i
$983$	−40.2377	−	23.2312i	−1.28338	−	0.740961i	−0.305917	−	0.952058i	$-0.598963\pi$
$983$	−40.2377	−	23.2312i	−1.28338	−	0.740961i	−0.977465	+	0.211097i	$0.932296\pi$
$984$	7.95862	−	13.7847i	0.253711	−	0.439441i
$985$	7.55046	+	13.0778i	0.240578	+	0.416693i
$986$	5.60058			0.178359
$987$		0			0
$988$	0.0521308			0.00165850
$989$	4.16775	−	2.40625i	0.132527	−	0.0765144i
$990$	0.295975	−	1.89954i	0.00940670	−	0.0603712i
$991$	7.28588	−	12.6195i	0.231444	−	0.400872i	−0.726790	−	0.686860i	$-0.758988\pi$
$991$	7.28588	−	12.6195i	0.231444	−	0.400872i	0.958233	+	0.285988i	$0.0923218\pi$
$992$	1.27498	+	2.20834i	0.0404808	+	0.0701147i
$993$		−	41.8575i		−	1.32831i
$994$		0			0
$995$	4.18877			0.132793
$996$	−19.8386	+	11.4538i	−0.628609	+	0.362927i
$997$	2.05848	−	3.56539i	0.0651927	−	0.112917i	−0.831587	−	0.555395i	$-0.812567\pi$
$997$	2.05848	−	3.56539i	0.0651927	−	0.112917i	0.896779	+	0.442478i	$0.145900\pi$
$998$	−3.40255	−	1.96446i	−0.107706	−	0.0621839i
$999$	29.3642	−	16.9534i	0.929043	−	0.536383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.i.c.1011.2		16
7.2	even	3		154.2.i.a.131.7	yes	16
7.3	odd	6		1078.2.c.b.1077.3		16
7.4	even	3		1078.2.c.b.1077.6		16
7.5	odd	6	inner	1078.2.i.c.901.6		16
7.6	odd	2		154.2.i.a.87.3	✓	16
11.10	odd	2	inner	1078.2.i.c.1011.6		16
21.2	odd	6		1386.2.bk.c.901.2		16
21.20	even	2		1386.2.bk.c.703.6		16
28.23	odd	6		1232.2.bn.b.593.4		16
28.27	even	2		1232.2.bn.b.241.3		16
77.10	even	6		1078.2.c.b.1077.11		16
77.32	odd	6		1078.2.c.b.1077.14		16
77.54	even	6	inner	1078.2.i.c.901.2		16
77.65	odd	6		154.2.i.a.131.3	yes	16
77.76	even	2		154.2.i.a.87.7	yes	16
231.65	even	6		1386.2.bk.c.901.6		16
231.230	odd	2		1386.2.bk.c.703.2		16
308.219	even	6		1232.2.bn.b.593.3		16
308.307	odd	2		1232.2.bn.b.241.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.3	✓	16	7.6	odd	2
154.2.i.a.87.7	yes	16	77.76	even	2
154.2.i.a.131.3	yes	16	77.65	odd	6
154.2.i.a.131.7	yes	16	7.2	even	3
1078.2.c.b.1077.3		16	7.3	odd	6
1078.2.c.b.1077.6		16	7.4	even	3
1078.2.c.b.1077.11		16	77.10	even	6
1078.2.c.b.1077.14		16	77.32	odd	6
1078.2.i.c.901.2		16	77.54	even	6	inner
1078.2.i.c.901.6		16	7.5	odd	6	inner
1078.2.i.c.1011.2		16	1.1	even	1	trivial
1078.2.i.c.1011.6		16	11.10	odd	2	inner
1232.2.bn.b.241.3		16	28.27	even	2
1232.2.bn.b.241.4		16	308.307	odd	2
1232.2.bn.b.593.3		16	308.219	even	6
1232.2.bn.b.593.4		16	28.23	odd	6
1386.2.bk.c.703.2		16	231.230	odd	2
1386.2.bk.c.703.6		16	21.20	even	2
1386.2.bk.c.901.2		16	21.2	odd	6
1386.2.bk.c.901.6		16	231.65	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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.35034 - 0.779618i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.882559 + 0.509546i) q^{5} +1.55924 q^{6} +1.00000i q^{8} +(-0.284392 - 0.492581i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.35034 - 0.779618i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.882559 + 0.509546i) q^{5} +1.55924 q^{6} +1.00000i q^{8} +(-0.284392 - 0.492581i) q^{9} +(0.509546 - 0.882559i) q^{10} +(-0.510616 + 3.27708i) q^{11} +(-1.35034 + 0.779618i) q^{12} +0.167247 q^{13} +1.58900 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.47616 - 2.55678i) q^{17} +(0.492581 + 0.284392i) q^{18} +(0.155850 + 0.269940i) q^{19} +1.01909i q^{20} +(-1.19633 - 3.09335i) q^{22} +(0.237719 + 0.411742i) q^{23} +(0.779618 - 1.35034i) q^{24} +(-1.98073 + 3.43072i) q^{25} +(-0.144840 + 0.0836233i) q^{26} +5.56458i q^{27} -1.89701i q^{29} +(-1.37612 + 0.794502i) q^{30} +(2.20834 + 1.27498i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.24438 - 4.02708i) q^{33} +2.95232i q^{34} -0.568783 q^{36} +(-3.04667 - 5.27699i) q^{37} +(-0.269940 - 0.155850i) q^{38} +(-0.225839 - 0.130388i) q^{39} +(-0.509546 - 0.882559i) q^{40} +10.2084 q^{41} -10.1222i q^{43} +(2.58273 + 2.08075i) q^{44} +(0.501985 + 0.289821i) q^{45} +(-0.411742 - 0.237719i) q^{46} +(3.28968 - 1.89930i) q^{47} +1.55924i q^{48} -3.96145i q^{50} +(-3.98663 + 2.30168i) q^{51} +(0.0836233 - 0.144840i) q^{52} +(-4.21079 + 7.29330i) q^{53} +(-2.78229 - 4.81906i) q^{54} +(-1.21917 - 3.15240i) q^{55} -0.486014i q^{57} +(0.948505 + 1.64286i) q^{58} +(-5.40617 - 3.12126i) q^{59} +(0.794502 - 1.37612i) q^{60} +(-5.93960 - 10.2877i) q^{61} -2.54997 q^{62} -1.00000 q^{64} +(-0.147605 + 0.0852198i) q^{65} +(-0.796171 + 5.10974i) q^{66} +(5.19151 - 8.99196i) q^{67} +(-1.47616 - 2.55678i) q^{68} -0.741321i q^{69} +14.5206 q^{71} +(0.492581 - 0.284392i) q^{72} +(4.85385 - 8.40712i) q^{73} +(5.27699 + 3.04667i) q^{74} +(5.34930 - 3.08842i) q^{75} +0.311700 q^{76} +0.260777 q^{78} +(6.06709 - 3.50284i) q^{79} +(0.882559 + 0.509546i) q^{80} +(3.48507 - 6.03631i) q^{81} +(-8.84069 + 5.10418i) q^{82} +14.6915 q^{83} +3.00868i q^{85} +(5.06112 + 8.76612i) q^{86} +(-1.47894 + 2.56161i) q^{87} +(-3.27708 - 0.510616i) q^{88} +(-5.97639 + 3.45047i) q^{89} -0.579642 q^{90} +0.475438 q^{92} +(-1.98800 - 3.44332i) q^{93} +(-1.89930 + 3.28968i) q^{94} +(-0.275094 - 0.158826i) q^{95} +(-0.779618 - 1.35034i) q^{96} -11.0218i q^{97} +(1.75944 - 0.680455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 36 q^{26} + 12 q^{31} + 24 q^{33} + 32 q^{36} - 16 q^{37} - 12 q^{38} - 8 q^{44} + 108 q^{45} - 24 q^{47} - 28 q^{53} - 12 q^{58} - 60 q^{59} - 4 q^{60} - 16 q^{64} - 48 q^{66} + 12 q^{67} + 8 q^{71} - 60 q^{75} - 16 q^{78} - 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} - 96 q^{89} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9 + 8 * q^11 - 8 * q^15 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 36 * q^26 + 12 * q^31 + 24 * q^33 + 32 * q^36 - 16 * q^37 - 12 * q^38 - 8 * q^44 + 108 * q^45 - 24 * q^47 - 28 * q^53 - 12 * q^58 - 60 * q^59 - 4 * q^60 - 16 * q^64 - 48 * q^66 + 12 * q^67 + 8 * q^71 - 60 * q^75 - 16 * q^78 - 12 * q^80 - 8 * q^81 + 20 * q^86 - 4 * q^88 - 96 * q^89 + 32 * q^92 - 44 * q^93 + 56 * q^99

Introduction

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