LMFDB - Embedded newform 2394.2.o.v.505.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(505,2394)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("2394.505");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.o (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 11x^{6} - 6x^{5} + 104x^{4} - 72x^{3} + 104x^{2} + 32x + 16 $ x^8 - x^7 + 11x^6 - 6x^5 + 104x^4 - 72x^3 + 104x^2 + 32x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 266)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.4
Root			$-0.176135 - 0.305076i$ of defining polynomial
Character	$\chi$	$=$	2394.505
Dual form			2394.2.o.v.1261.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.16259 - 3.74571i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.16259 - 3.74571i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +(2.16259 + 3.74571i) q^{10} -2.35227 q^{11} +(0.400772 + 0.694158i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.11409 - 5.39376i) q^{17} +(3.69100 - 2.31874i) q^{19} -4.32518 q^{20} +(1.17614 - 2.03713i) q^{22} +(-0.887226 - 1.53672i) q^{23} +(-6.85358 - 11.8708i) q^{25} -0.801544 q^{26} +(-0.500000 - 0.866025i) q^{28} +(2.91563 + 5.05002i) q^{29} -5.12672 q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.11409 + 5.39376i) q^{34} +(2.16259 - 3.74571i) q^{35} +10.6504 q^{37} +(0.162589 + 4.35587i) q^{38} +(2.16259 - 3.74571i) q^{40} +(-1.82386 + 3.15903i) q^{41} +(-0.436639 + 0.756280i) q^{43} +(1.17614 + 2.03713i) q^{44} +1.77445 q^{46} +(-2.91563 - 5.05002i) q^{47} +1.00000 q^{49} +13.7072 q^{50} +(0.400772 - 0.694158i) q^{52} +(0.563361 + 0.975771i) q^{53} +(-5.08700 + 8.81094i) q^{55} +1.00000 q^{56} -5.83126 q^{58} +(-7.10054 + 12.2985i) q^{59} +(1.36105 + 2.35740i) q^{61} +(2.56336 - 4.43987i) q^{62} +1.00000 q^{64} +3.46682 q^{65} +(-2.29022 - 3.96678i) q^{67} -6.22818 q^{68} +(2.16259 + 3.74571i) q^{70} +(7.00131 - 12.1266i) q^{71} +(4.61540 - 7.99411i) q^{73} +(-5.32518 + 9.22348i) q^{74} +(-3.85358 - 2.03713i) q^{76} -2.35227 q^{77} +(3.52363 - 6.10311i) q^{79} +(2.16259 + 3.74571i) q^{80} +(-1.82386 - 3.15903i) q^{82} -15.5560 q^{83} +(-13.4690 - 23.3290i) q^{85} +(-0.436639 - 0.756280i) q^{86} -2.35227 q^{88} +(3.64773 + 6.31805i) q^{89} +(0.400772 + 0.694158i) q^{91} +(-0.887226 + 1.53672i) q^{92} +5.83126 q^{94} +(-0.703228 - 18.8399i) q^{95} +(-1.52841 + 2.64728i) q^{97} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + q^{5} + 8 q^{7} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + q^5 + 8 * q^7 + 8 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} + q^{5} + 8 q^{7} + 8 q^{8} + q^{10} - 14 q^{11} + 5 q^{13} - 4 q^{14} - 4 q^{16} + 2 q^{17} + 6 q^{19} - 2 q^{20} + 7 q^{22} + 5 q^{23} - 15 q^{25} - 10 q^{26} - 4 q^{28} + 4 q^{29} - 12 q^{31} - 4 q^{32} + 2 q^{34} + q^{35} + 20 q^{37} - 15 q^{38} + q^{40} - 17 q^{41} - 18 q^{43} + 7 q^{44} - 10 q^{46} - 4 q^{47} + 8 q^{49} + 30 q^{50} + 5 q^{52} - 10 q^{53} + 10 q^{55} + 8 q^{56} - 8 q^{58} - 20 q^{59} - 9 q^{61} + 6 q^{62} + 8 q^{64} + 6 q^{65} + 7 q^{67} - 4 q^{68} + q^{70} + 21 q^{71} - 21 q^{73} - 10 q^{74} + 9 q^{76} - 14 q^{77} - 8 q^{79} + q^{80} - 17 q^{82} + 24 q^{83} - 10 q^{85} - 18 q^{86} - 14 q^{88} + 34 q^{89} + 5 q^{91} + 5 q^{92} + 8 q^{94} - 31 q^{95} - 5 q^{97} - 4 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + q^5 + 8 * q^7 + 8 * q^8 + q^10 - 14 * q^11 + 5 * q^13 - 4 * q^14 - 4 * q^16 + 2 * q^17 + 6 * q^19 - 2 * q^20 + 7 * q^22 + 5 * q^23 - 15 * q^25 - 10 * q^26 - 4 * q^28 + 4 * q^29 - 12 * q^31 - 4 * q^32 + 2 * q^34 + q^35 + 20 * q^37 - 15 * q^38 + q^40 - 17 * q^41 - 18 * q^43 + 7 * q^44 - 10 * q^46 - 4 * q^47 + 8 * q^49 + 30 * q^50 + 5 * q^52 - 10 * q^53 + 10 * q^55 + 8 * q^56 - 8 * q^58 - 20 * q^59 - 9 * q^61 + 6 * q^62 + 8 * q^64 + 6 * q^65 + 7 * q^67 - 4 * q^68 + q^70 + 21 * q^71 - 21 * q^73 - 10 * q^74 + 9 * q^76 - 14 * q^77 - 8 * q^79 + q^80 - 17 * q^82 + 24 * q^83 - 10 * q^85 - 18 * q^86 - 14 * q^88 + 34 * q^89 + 5 * q^91 + 5 * q^92 + 8 * q^94 - 31 * q^95 - 5 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.16259	−	3.74571i	0.967139	−	1.67513i	0.263385	−	0.964691i	$-0.415161\pi$
$5$	2.16259	−	3.74571i	0.967139	−	1.67513i	0.703754	−	0.710444i	$-0.251506\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	1.00000			0.353553
$9$		0			0
$10$	2.16259	+	3.74571i	0.683871	+	1.18450i
$11$	−2.35227			−0.709236			−0.354618	−	0.935011i	$-0.615389\pi$
$11$	−2.35227			−0.709236			−0.354618	+	0.935011i	$0.615389\pi$
$12$		0			0
$13$	0.400772	+	0.694158i	0.111154	+	0.192525i	0.916236	−	0.400639i	$-0.131212\pi$
$13$	0.400772	+	0.694158i	0.111154	+	0.192525i	−0.805082	+	0.593164i	$0.797879\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.11409	−	5.39376i	0.755277	−	1.30818i	−0.189959	−	0.981792i	$-0.560836\pi$
$17$	3.11409	−	5.39376i	0.755277	−	1.30818i	0.945236	−	0.326387i	$-0.105831\pi$
$18$		0			0
$19$	3.69100	−	2.31874i	0.846772	−	0.531955i
$19$	3.69100	−	2.31874i	0.846772	−	0.531955i
$20$	−4.32518			−0.967139
$21$		0			0
$22$	1.17614	−	2.03713i	0.250753	−	0.434317i
$23$	−0.887226	−	1.53672i	−0.184999	−	0.320428i	0.758577	−	0.651583i	$-0.225895\pi$
$23$	−0.887226	−	1.53672i	−0.184999	−	0.320428i	−0.943576	+	0.331155i	$0.892562\pi$
$24$		0			0
$25$	−6.85358	−	11.8708i	−1.37072	−	2.37415i
$26$	−0.801544			−0.157196
$27$		0			0
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	2.91563	+	5.05002i	0.541419	+	0.937766i	0.998823	+	0.0485065i	$0.0154462\pi$
$29$	2.91563	+	5.05002i	0.541419	+	0.937766i	−0.457404	+	0.889259i	$0.651220\pi$
$30$		0			0
$31$	−5.12672			−0.920787			−0.460393	−	0.887715i	$-0.652292\pi$
$31$	−5.12672			−0.920787			−0.460393	+	0.887715i	$0.652292\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	3.11409	+	5.39376i	0.534062	+	0.925022i
$35$	2.16259	−	3.74571i	0.365544	−	0.633141i
$36$		0			0
$37$	10.6504			1.75091			0.875454	−	0.483302i	$-0.160563\pi$
$37$	10.6504			1.75091			0.875454	+	0.483302i	$0.160563\pi$
$38$	0.162589	+	4.35587i	0.0263755	+	0.706615i
$39$		0			0
$40$	2.16259	−	3.74571i	0.341935	−	0.592249i
$41$	−1.82386	+	3.15903i	−0.284840	+	0.493357i	−0.972570	−	0.232609i	$-0.925274\pi$
$41$	−1.82386	+	3.15903i	−0.284840	+	0.493357i	0.687731	+	0.725966i	$0.258607\pi$
$42$		0			0
$43$	−0.436639	+	0.756280i	−0.0665868	+	0.115332i	−0.897397	−	0.441224i	$-0.854544\pi$
$43$	−0.436639	+	0.756280i	−0.0665868	+	0.115332i	0.830810	+	0.556556i	$0.187878\pi$
$44$	1.17614	+	2.03713i	0.177309	+	0.307108i
$45$		0			0
$46$	1.77445			0.261629
$47$	−2.91563	−	5.05002i	−0.425289	−	0.736622i	0.571159	−	0.820840i	$-0.306494\pi$
$47$	−2.91563	−	5.05002i	−0.425289	−	0.736622i	−0.996447	+	0.0842181i	$0.973161\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	13.7072			1.93849
$51$		0			0
$52$	0.400772	−	0.694158i	0.0555771	−	0.0962623i
$53$	0.563361	+	0.975771i	0.0773836	+	0.134032i	0.902120	−	0.431484i	$-0.142010\pi$
$53$	0.563361	+	0.975771i	0.0773836	+	0.134032i	−0.824737	+	0.565517i	$0.808677\pi$
$54$		0			0
$55$	−5.08700	+	8.81094i	−0.685930	+	1.18807i
$56$	1.00000			0.133631
$57$		0			0
$58$	−5.83126			−0.765683
$59$	−7.10054	+	12.2985i	−0.924412	+	1.60113i	−0.131907	+	0.991262i	$0.542110\pi$
$59$	−7.10054	+	12.2985i	−0.924412	+	1.60113i	−0.792504	+	0.609866i	$0.791223\pi$
$60$		0			0
$61$	1.36105	+	2.35740i	0.174264	+	0.301834i	0.939906	−	0.341432i	$-0.110912\pi$
$61$	1.36105	+	2.35740i	0.174264	+	0.301834i	−0.765642	+	0.643267i	$0.777579\pi$
$62$	2.56336	−	4.43987i	0.325547	−	0.563864i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.46682			0.430006
$66$		0			0
$67$	−2.29022	−	3.96678i	−0.279795	−	0.484620i	0.691538	−	0.722340i	$-0.256933\pi$
$67$	−2.29022	−	3.96678i	−0.279795	−	0.484620i	−0.971334	+	0.237720i	$0.923600\pi$
$68$	−6.22818			−0.755277
$69$		0			0
$70$	2.16259	+	3.74571i	0.258479	+	0.447699i
$71$	7.00131	−	12.1266i	0.830903	−	1.43917i	−0.0664198	−	0.997792i	$-0.521158\pi$
$71$	7.00131	−	12.1266i	0.830903	−	1.43917i	0.897323	−	0.441375i	$-0.145509\pi$
$72$		0			0
$73$	4.61540	−	7.99411i	0.540192	−	0.935640i	−0.458701	−	0.888591i	$-0.651685\pi$
$73$	4.61540	−	7.99411i	0.540192	−	0.935640i	0.998893	−	0.0470490i	$-0.0149817\pi$
$74$	−5.32518	+	9.22348i	−0.619039	+	1.07221i
$75$		0			0
$76$	−3.85358	−	2.03713i	−0.442037	−	0.233674i
$77$	−2.35227			−0.268066
$78$		0			0
$79$	3.52363	−	6.10311i	0.396440	−	0.686654i	−0.596844	−	0.802357i	$-0.703579\pi$
$79$	3.52363	−	6.10311i	0.396440	−	0.686654i	0.993284	+	0.115703i	$0.0369122\pi$
$80$	2.16259	+	3.74571i	0.241785	+	0.418784i
$81$		0			0
$82$	−1.82386	−	3.15903i	−0.201412	−	0.348856i
$83$	−15.5560			−1.70749			−0.853745	−	0.520691i	$-0.825675\pi$
$83$	−15.5560			−1.70749			−0.853745	+	0.520691i	$0.825675\pi$
$84$		0			0
$85$	−13.4690	−	23.3290i	−1.46092	−	2.53038i
$86$	−0.436639	−	0.756280i	−0.0470840	−	0.0815518i
$87$		0			0
$88$	−2.35227			−0.250753
$89$	3.64773	+	6.31805i	0.386659	+	0.669712i	0.991998	−	0.126255i	$-0.0402959\pi$
$89$	3.64773	+	6.31805i	0.386659	+	0.669712i	−0.605339	+	0.795968i	$0.706963\pi$
$90$		0			0
$91$	0.400772	+	0.694158i	0.0420123	+	0.0727675i
$92$	−0.887226	+	1.53672i	−0.0924997	+	0.160214i
$93$		0			0
$94$	5.83126			0.601449
$95$	−0.703228	−	18.8399i	−0.0721496	−	1.93293i
$96$		0			0
$97$	−1.52841	+	2.64728i	−0.155186	+	0.268790i	−0.933127	−	0.359547i	$-0.882931\pi$
$97$	−1.52841	+	2.64728i	−0.155186	+	0.268790i	0.777941	+	0.628338i	$0.216264\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$		0			0
$100$	−6.85358	+	11.8708i	−0.685358	+	1.18708i
$101$	0.761817	+	1.31951i	0.0758036	+	0.131296i	0.901435	−	0.432914i	$-0.142514\pi$
$101$	0.761817	+	1.31951i	0.0758036	+	0.131296i	−0.825632	+	0.564209i	$0.809181\pi$
$102$		0			0
$103$	−11.5236			−1.13546			−0.567729	−	0.823216i	$-0.692178\pi$
$103$	−11.5236			−1.13546			−0.567729	+	0.823216i	$0.692178\pi$
$104$	0.400772	+	0.694158i	0.0392989	+	0.0680678i
$105$		0			0
$106$	−1.12672			−0.109437
$107$	−16.0053			−1.54729			−0.773643	−	0.633621i	$-0.781568\pi$
$107$	−16.0053			−1.54729			−0.773643	+	0.633621i	$0.781568\pi$
$108$		0			0
$109$	3.62017	−	6.27033i	0.346750	−	0.600588i	−0.638920	−	0.769273i	$-0.720619\pi$
$109$	3.62017	−	6.27033i	0.346750	−	0.600588i	0.985670	+	0.168685i	$0.0539520\pi$
$110$	−5.08700	−	8.81094i	−0.485026	−	0.840090i
$111$		0			0
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	−1.47637			−0.138885			−0.0694424	−	0.997586i	$-0.522122\pi$
$113$	−1.47637			−0.138885			−0.0694424	+	0.997586i	$0.522122\pi$
$114$		0			0
$115$	−7.67482			−0.715681
$116$	2.91563	−	5.05002i	0.270710	−	0.468883i
$117$		0			0
$118$	−7.10054	−	12.2985i	−0.653658	−	1.13217i
$119$	3.11409	−	5.39376i	0.285468	−	0.494445i
$120$		0			0
$121$	−5.46682			−0.496984
$122$	−2.72209			−0.246446
$123$		0			0
$124$	2.56336	+	4.43987i	0.230197	+	0.398712i
$125$	−37.6601			−3.36842
$126$		0			0
$127$	3.11540	+	5.39603i	0.276447	+	0.478821i	0.970499	−	0.241104i	$-0.0775096\pi$
$127$	3.11540	+	5.39603i	0.276447	+	0.478821i	−0.694052	+	0.719925i	$0.744176\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.73341	+	3.00236i	−0.152030	+	0.263324i
$131$	−1.83264	+	3.17422i	−0.160118	+	0.277333i	−0.934911	−	0.354882i	$-0.884521\pi$
$131$	−1.83264	+	3.17422i	−0.160118	+	0.277333i	0.774793	+	0.632216i	$0.217854\pi$
$132$		0			0
$133$	3.69100	−	2.31874i	0.320050	−	0.201060i
$134$	4.58045			0.395690
$135$		0			0
$136$	3.11409	−	5.39376i	0.267031	−	0.462511i
$137$	1.69846	+	2.94181i	0.145109	+	0.251336i	0.929414	−	0.369040i	$-0.120313\pi$
$137$	1.69846	+	2.94181i	0.145109	+	0.251336i	−0.784305	+	0.620376i	$0.786980\pi$
$138$		0			0
$139$	2.59832	+	4.50042i	0.220386	+	0.381720i	0.954925	−	0.296846i	$-0.0959349\pi$
$139$	2.59832	+	4.50042i	0.220386	+	0.381720i	−0.734539	+	0.678566i	$0.762602\pi$
$140$	−4.32518			−0.365544
$141$		0			0
$142$	7.00131	+	12.1266i	0.587537	+	1.01764i
$143$	−0.942725	−	1.63285i	−0.0788346	−	0.136546i
$144$		0			0
$145$	25.2213			2.09451
$146$	4.61540	+	7.99411i	0.381973	+	0.661597i
$147$		0			0
$148$	−5.32518	−	9.22348i	−0.437727	−	0.758165i
$149$	7.32518	−	12.6876i	0.600102	−	1.03941i	−0.392703	−	0.919665i	$-0.628460\pi$
$149$	7.32518	−	12.6876i	0.600102	−	1.03941i	0.992805	−	0.119742i	$-0.0382067\pi$
$150$		0			0
$151$	5.46682			0.444884			0.222442	−	0.974946i	$-0.428597\pi$
$151$	5.46682			0.444884			0.222442	+	0.974946i	$0.428597\pi$
$152$	3.69100	−	2.31874i	0.299379	−	0.188075i
$153$		0			0
$154$	1.17614	−	2.03713i	0.0947757	−	0.164156i
$155$	−11.0870	+	19.2032i	−0.890529	+	1.54244i
$156$		0			0
$157$	1.72595	−	2.98943i	0.137746	−	0.238583i	−0.788897	−	0.614525i	$-0.789348\pi$
$157$	1.72595	−	2.98943i	0.137746	−	0.238583i	0.926643	+	0.375942i	$0.122681\pi$
$158$	3.52363	+	6.10311i	0.280325	+	0.485538i
$159$		0			0
$160$	−4.32518			−0.341935
$161$	−0.887226	−	1.53672i	−0.0699232	−	0.121111i
$162$		0			0
$163$	8.65990			0.678296			0.339148	−	0.940733i	$-0.389861\pi$
$163$	8.65990			0.678296			0.339148	+	0.940733i	$0.389861\pi$
$164$	3.64773			0.284840
$165$		0			0
$166$	7.77799	−	13.4719i	0.603689	−	1.04562i
$167$	−3.02972	−	5.24763i	−0.234447	−	0.406074i	0.724665	−	0.689101i	$-0.241995\pi$
$167$	−3.02972	−	5.24763i	−0.234447	−	0.406074i	−0.959112	+	0.283028i	$0.908661\pi$
$168$		0			0
$169$	6.17876	−	10.7019i	0.475289	−	0.823226i
$170$	26.9380			2.06605
$171$		0			0
$172$	0.873277			0.0665868
$173$	7.81295	−	13.5324i	0.594007	−	1.02885i	−0.399679	−	0.916655i	$-0.630878\pi$
$173$	7.81295	−	13.5324i	0.594007	−	1.02885i	0.993686	−	0.112196i	$-0.0357883\pi$
$174$		0			0
$175$	−6.85358	−	11.8708i	−0.518082	−	0.897345i
$176$	1.17614	−	2.03713i	0.0886545	−	0.153554i
$177$		0			0
$178$	−7.29546			−0.546818
$179$	−11.3995			−0.852042			−0.426021	−	0.904713i	$-0.640085\pi$
$179$	−11.3995			−0.852042			−0.426021	+	0.904713i	$0.640085\pi$
$180$		0			0
$181$	−1.63895	−	2.83875i	−0.121823	−	0.211003i	0.798664	−	0.601777i	$-0.205541\pi$
$181$	−1.63895	−	2.83875i	−0.121823	−	0.211003i	−0.920486	+	0.390775i	$0.872207\pi$
$182$	−0.801544			−0.0594144
$183$		0			0
$184$	−0.887226	−	1.53672i	−0.0654072	−	0.113289i
$185$	23.0323	−	39.8932i	1.69337	−	2.93301i
$186$		0			0
$187$	−7.32518	+	12.6876i	−0.535670	+	0.927808i
$188$	−2.91563	+	5.05002i	−0.212644	+	0.368311i
$189$		0			0
$190$	16.6674	+	8.81094i	1.20918	+	0.639212i
$191$	3.23865			0.234340			0.117170	−	0.993112i	$-0.462618\pi$
$191$	3.23865			0.234340			0.117170	+	0.993112i	$0.462618\pi$
$192$		0			0
$193$	−6.02841	+	10.4415i	−0.433934	+	0.751596i	−0.997208	−	0.0746743i	$-0.976208\pi$
$193$	−6.02841	+	10.4415i	−0.433934	+	0.751596i	0.563274	+	0.826270i	$0.309542\pi$
$194$	−1.52841	−	2.64728i	−0.109733	−	0.190063i
$195$		0			0
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	20.9380			1.49177			0.745884	−	0.666075i	$-0.232027\pi$
$197$	20.9380			1.49177			0.745884	+	0.666075i	$0.232027\pi$
$198$		0			0
$199$	−4.56336	−	7.90397i	−0.323488	−	0.560298i	0.657717	−	0.753265i	$-0.271522\pi$
$199$	−4.56336	−	7.90397i	−0.323488	−	0.560298i	−0.981205	+	0.192967i	$0.938189\pi$
$200$	−6.85358	−	11.8708i	−0.484622	−	0.839389i
$201$		0			0
$202$	−1.52363			−0.107203
$203$	2.91563	+	5.05002i	0.204637	+	0.354442i
$204$		0			0
$205$	7.88854	+	13.6634i	0.550960	+	0.954290i
$206$	5.76182	−	9.97976i	0.401445	−	0.695323i
$207$		0			0
$208$	−0.801544			−0.0555771
$209$	−8.68222	+	5.45430i	−0.600562	+	0.377282i
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	0.563361	−	0.975771i	0.0386918	−	0.0670162i
$213$		0			0
$214$	8.00263	−	13.8610i	0.547048	−	0.947516i
$215$	1.88854	+	3.27105i	0.128797	+	0.223084i
$216$		0			0
$217$	−5.12672			−0.348025
$218$	3.62017	+	6.27033i	0.245189	+	0.424680i
$219$		0			0
$220$	10.1740			0.685930
$221$	4.99216			0.335809
$222$		0			0
$223$	6.12672	−	10.6118i	0.410276	−	0.710618i	−0.584644	−	0.811290i	$-0.698766\pi$
$223$	6.12672	−	10.6118i	0.410276	−	0.710618i	0.994920	+	0.100672i	$0.0320991\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$	0.738183	−	1.27857i	0.0491032	−	0.0850492i
$227$	23.3531			1.55000			0.774999	−	0.631962i	$-0.217750\pi$
$227$	23.3531			1.55000			0.774999	+	0.631962i	$0.217750\pi$
$228$		0			0
$229$	−25.8830			−1.71040			−0.855198	−	0.518302i	$-0.826564\pi$
$229$	−25.8830			−1.71040			−0.855198	+	0.518302i	$0.826564\pi$
$230$	3.83741	−	6.64659i	0.253031	−	0.438263i
$231$		0			0
$232$	2.91563	+	5.05002i	0.191421	+	0.331550i
$233$	−1.30154	+	2.25434i	−0.0852670	+	0.147687i	−0.905505	−	0.424336i	$-0.860508\pi$
$233$	−1.30154	+	2.25434i	−0.0852670	+	0.147687i	0.820238	+	0.572022i	$0.193841\pi$
$234$		0			0
$235$	−25.2213			−1.64525
$236$	14.2011			0.924412
$237$		0			0
$238$	3.11409	+	5.39376i	0.201856	+	0.349625i
$239$	23.2781			1.50573			0.752867	−	0.658173i	$-0.228670\pi$
$239$	23.2781			1.50573			0.752867	+	0.658173i	$0.228670\pi$
$240$		0			0
$241$	4.47159	+	7.74503i	0.288041	+	0.498901i	0.973342	−	0.229359i	$-0.0736628\pi$
$241$	4.47159	+	7.74503i	0.288041	+	0.498901i	−0.685301	+	0.728260i	$0.740329\pi$
$242$	2.73341	−	4.73441i	0.175710	−	0.304339i
$243$		0			0
$244$	1.36105	−	2.35740i	0.0871320	−	0.150917i
$245$	2.16259	−	3.74571i	0.138163	−	0.239305i
$246$		0			0
$247$	3.08882	+	1.63285i	0.196537	+	0.103896i
$248$	−5.12672			−0.325547
$249$		0			0
$250$	18.8300	−	32.6146i	1.19092	−	2.06273i
$251$	13.6936	+	23.7181i	0.864334	+	1.49707i	0.867707	+	0.497076i	$0.165593\pi$
$251$	13.6936	+	23.7181i	0.864334	+	1.49707i	−0.00337324	+	0.999994i	$0.501074\pi$
$252$		0			0
$253$	2.08700	+	3.61478i	0.131208	+	0.227259i
$254$	−6.23080			−0.390955
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.24605	+	7.35437i	0.264861	+	0.458753i	0.967527	−	0.252767i	$-0.0813406\pi$
$257$	4.24605	+	7.35437i	0.264861	+	0.458753i	−0.702666	+	0.711520i	$0.748007\pi$
$258$		0			0
$259$	10.6504			0.661781
$260$	−1.73341	−	3.00236i	−0.107502	−	0.186198i
$261$		0			0
$262$	−1.83264	−	3.17422i	−0.113221	−	0.196104i
$263$	−2.87459	+	4.97894i	−0.177255	+	0.307014i	−0.940939	−	0.338575i	$-0.890055\pi$
$263$	−2.87459	+	4.97894i	−0.177255	+	0.307014i	0.763684	+	0.645590i	$0.223388\pi$
$264$		0			0
$265$	4.87328			0.299363
$266$	0.162589	+	4.35587i	0.00996899	+	0.267075i
$267$		0			0
$268$	−2.29022	+	3.96678i	−0.139898	+	0.242310i
$269$	−4.21109	+	7.29382i	−0.256755	+	0.444712i	−0.965371	−	0.260882i	$-0.915987\pi$
$269$	−4.21109	+	7.29382i	−0.256755	+	0.444712i	0.708616	+	0.705594i	$0.249320\pi$
$270$		0			0
$271$	−10.3649	+	17.9525i	−0.629623	+	1.09054i	0.358004	+	0.933720i	$0.383457\pi$
$271$	−10.3649	+	17.9525i	−0.629623	+	1.09054i	−0.987627	+	0.156819i	$0.949876\pi$
$272$	3.11409	+	5.39376i	0.188819	+	0.327045i
$273$		0			0
$274$	−3.39691			−0.205215
$275$	16.1215	+	27.9232i	0.972162	+	1.68383i
$276$		0			0
$277$	17.4442			1.04812			0.524060	−	0.851682i	$-0.324417\pi$
$277$	17.4442			1.04812			0.524060	+	0.851682i	$0.324417\pi$
$278$	−5.19663			−0.311673
$279$		0			0
$280$	2.16259	−	3.74571i	0.129239	−	0.223849i
$281$	1.06205	+	1.83952i	0.0633564	+	0.109737i	0.895964	−	0.444127i	$-0.146486\pi$
$281$	1.06205	+	1.83952i	0.0633564	+	0.109737i	−0.832607	+	0.553864i	$0.813153\pi$
$282$		0			0
$283$	13.8348	−	23.9626i	0.822394	−	1.42443i	−0.0815012	−	0.996673i	$-0.525971\pi$
$283$	13.8348	−	23.9626i	0.822394	−	1.42443i	0.903895	−	0.427754i	$-0.140695\pi$
$284$	−14.0026			−0.830903
$285$		0			0
$286$	1.88545			0.111489
$287$	−1.82386	+	3.15903i	−0.107659	+	0.186471i
$288$		0			0
$289$	−10.8951	−	18.8708i	−0.640888	−	1.11005i
$290$	−12.6106	+	21.8423i	−0.740522	+	1.28262i
$291$		0			0
$292$	−9.23080			−0.540192
$293$	13.2326			0.773058			0.386529	−	0.922277i	$-0.373674\pi$
$293$	13.2326			0.773058			0.386529	+	0.922277i	$0.373674\pi$
$294$		0			0
$295$	30.7111	+	53.1932i	1.78807	+	3.09703i
$296$	10.6504			0.619039
$297$		0			0
$298$	7.32518	+	12.6876i	0.424336	+	0.734972i
$299$	0.711151	−	1.23175i	0.0411269	−	0.0712339i
$300$		0			0
$301$	−0.436639	+	0.756280i	−0.0251674	+	0.0435913i
$302$	−2.73341	+	4.73441i	−0.157290	+	0.272434i
$303$		0			0
$304$	0.162589	+	4.35587i	0.00932514	+	0.249826i
$305$	11.7735			0.674150
$306$		0			0
$307$	−12.4699	+	21.5985i	−0.711695	+	1.23269i	0.252526	+	0.967590i	$0.418739\pi$
$307$	−12.4699	+	21.5985i	−0.711695	+	1.23269i	−0.964221	+	0.265101i	$0.914595\pi$
$308$	1.17614	+	2.03713i	0.0670165	+	0.116076i
$309$		0			0
$310$	−11.0870	−	19.2032i	−0.629699	−	1.09067i
$311$	−15.9458			−0.904204			−0.452102	−	0.891966i	$-0.649326\pi$
$311$	−15.9458			−0.904204			−0.452102	+	0.891966i	$0.649326\pi$
$312$		0			0
$313$	6.36013	+	11.0161i	0.359496	+	0.622665i	0.987877	−	0.155241i	$-0.0496153\pi$
$313$	6.36013	+	11.0161i	0.359496	+	0.622665i	−0.628381	+	0.777906i	$0.716282\pi$
$314$	1.72595	+	2.98943i	0.0974010	+	0.168704i
$315$		0			0
$316$	−7.04727			−0.396440
$317$	−16.4545	−	28.5001i	−0.924178	−	1.60072i	−0.792877	−	0.609382i	$-0.791418\pi$
$317$	−16.4545	−	28.5001i	−0.924178	−	1.60072i	−0.131301	−	0.991343i	$-0.541916\pi$
$318$		0			0
$319$	−6.85836	−	11.8790i	−0.383994	−	0.665098i
$320$	2.16259	−	3.74571i	0.120892	−	0.209392i
$321$		0			0
$322$	1.77445			0.0988863
$323$	−1.01263	−	27.1291i	−0.0563445	−	1.50950i
$324$		0			0
$325$	5.49345	−	9.51494i	0.304722	−	0.527794i
$326$	−4.32995	+	7.49969i	−0.239814	+	0.415370i
$327$		0			0
$328$	−1.82386	+	3.15903i	−0.100706	+	0.174428i
$329$	−2.91563	−	5.05002i	−0.160744	−	0.278417i
$330$		0			0
$331$	−19.0079			−1.04477			−0.522384	−	0.852710i	$-0.674957\pi$
$331$	−19.0079			−1.04477			−0.522384	+	0.852710i	$0.674957\pi$
$332$	7.77799	+	13.4719i	0.426873	+	0.739365i
$333$		0			0
$334$	6.05944			0.331558
$335$	−19.8113			−1.08240
$336$		0			0
$337$	−14.0957	+	24.4145i	−0.767842	+	1.32994i	0.170889	+	0.985290i	$0.445336\pi$
$337$	−14.0957	+	24.4145i	−0.767842	+	1.32994i	−0.938731	+	0.344651i	$0.887997\pi$
$338$	6.17876	+	10.7019i	0.336080	+	0.582108i
$339$		0			0
$340$	−13.4690	+	23.3290i	−0.730458	+	1.26519i
$341$	12.0594			0.653055
$342$		0			0
$343$	1.00000			0.0539949
$344$	−0.436639	+	0.756280i	−0.0235420	+	0.0407759i
$345$		0			0
$346$	7.81295	+	13.5324i	0.420027	+	0.727507i
$347$	11.3646	−	19.6840i	0.610083	−	1.05669i	−0.381143	−	0.924516i	$-0.624469\pi$
$347$	11.3646	−	19.6840i	0.610083	−	1.05669i	0.991226	−	0.132178i	$-0.0421972\pi$
$348$		0			0
$349$	−4.72981			−0.253181			−0.126590	−	0.991955i	$-0.540403\pi$
$349$	−4.72981			−0.253181			−0.126590	+	0.991955i	$0.540403\pi$
$350$	13.7072			0.732679
$351$		0			0
$352$	1.17614	+	2.03713i	0.0626882	+	0.108579i
$353$	5.76135			0.306646			0.153323	−	0.988176i	$-0.451003\pi$
$353$	5.76135			0.306646			0.153323	+	0.988176i	$0.451003\pi$
$354$		0			0
$355$	−30.2819	−	52.4498i	−1.60720	−	2.78375i
$356$	3.64773	−	6.31805i	0.193329	−	0.334856i
$357$		0			0
$358$	5.69977	−	9.87229i	0.301242	−	0.521767i
$359$	−9.97554	+	17.2781i	−0.526489	+	0.911905i	0.473035	+	0.881044i	$0.343158\pi$
$359$	−9.97554	+	17.2781i	−0.526489	+	0.911905i	−0.999524	+	0.0308615i	$0.990175\pi$
$360$		0			0
$361$	8.24690	−	17.1169i	0.434047	−	0.900890i
$362$	3.27791			0.172283
$363$		0			0
$364$	0.400772	−	0.694158i	0.0210062	−	0.0363837i
$365$	−19.9624	−	34.5760i	−1.04488	−	1.80979i
$366$		0			0
$367$	0.620174	+	1.07417i	0.0323728	+	0.0560714i	0.881758	−	0.471702i	$-0.156360\pi$
$367$	0.620174	+	1.07417i	0.0323728	+	0.0560714i	−0.849385	+	0.527774i	$0.823027\pi$
$368$	1.77445			0.0924997
$369$		0			0
$370$	23.0323	+	39.8932i	1.19739	+	2.07395i
$371$	0.563361	+	0.975771i	0.0292483	+	0.0506595i
$372$		0			0
$373$	24.8733			1.28789			0.643945	−	0.765072i	$-0.277297\pi$
$373$	24.8733			1.28789			0.643945	+	0.765072i	$0.277297\pi$
$374$	−7.32518	−	12.6876i	−0.378776	−	0.656059i
$375$		0			0
$376$	−2.91563	−	5.05002i	−0.150362	−	0.260435i
$377$	−2.33701	+	4.04782i	−0.120362	+	0.208473i
$378$		0			0
$379$	32.4274			1.66569			0.832843	−	0.553510i	$-0.186712\pi$
$379$	32.4274			1.66569			0.832843	+	0.553510i	$0.186712\pi$
$380$	−15.9642	+	10.0290i	−0.818947	+	0.514475i
$381$		0			0
$382$	−1.61932	+	2.80475i	−0.0828518	+	0.143503i
$383$	−7.25527	+	12.5665i	−0.370727	+	0.642118i	−0.989678	−	0.143312i	$-0.954225\pi$
$383$	−7.25527	+	12.5665i	−0.370727	+	0.642118i	0.618951	+	0.785430i	$0.287558\pi$
$384$		0			0
$385$	−5.08700	+	8.81094i	−0.259257	+	0.449047i
$386$	−6.02841	−	10.4415i	−0.306838	−	0.531459i
$387$		0			0
$388$	3.05681			0.155186
$389$	12.7618	+	22.1041i	0.647050	+	1.12072i	0.983824	+	0.179138i	$0.0573308\pi$
$389$	12.7618	+	22.1041i	0.647050	+	1.12072i	−0.336774	+	0.941585i	$0.609336\pi$
$390$		0			0
$391$	−11.0516			−0.558903
$392$	1.00000			0.0505076
$393$		0			0
$394$	−10.4690	+	18.1328i	−0.527420	+	0.913518i
$395$	−15.2403	−	26.3971i	−0.766825	−	1.32818i
$396$		0			0
$397$	−5.81863	+	10.0782i	−0.292029	+	0.505808i	−0.974289	−	0.225301i	$-0.927664\pi$
$397$	−5.81863	+	10.0782i	−0.292029	+	0.505808i	0.682261	+	0.731109i	$0.260997\pi$
$398$	9.12672			0.457481
$399$		0			0
$400$	13.7072			0.685358
$401$	−12.5870	+	21.8013i	−0.628565	+	1.08871i	0.359275	+	0.933232i	$0.383024\pi$
$401$	−12.5870	+	21.8013i	−0.628565	+	1.08871i	−0.987840	+	0.155474i	$0.950309\pi$
$402$		0			0
$403$	−2.05465	−	3.55875i	−0.102349	−	0.177274i
$404$	0.761817	−	1.31951i	0.0379018	−	0.0656479i
$405$		0			0
$406$	−5.83126			−0.289401
$407$	−25.0525			−1.24181
$408$		0			0
$409$	−15.8139	−	27.3904i	−0.781945	−	1.35437i	−0.930807	−	0.365510i	$-0.880894\pi$
$409$	−15.8139	−	27.3904i	−0.781945	−	1.35437i	0.148862	−	0.988858i	$-0.452439\pi$
$410$	−15.7771			−0.779174
$411$		0			0
$412$	5.76182	+	9.97976i	0.283864	+	0.491667i
$413$	−7.10054	+	12.2985i	−0.349395	+	0.605170i
$414$		0			0
$415$	−33.6412	+	58.2683i	−1.65138	+	2.86028i
$416$	0.400772	−	0.694158i	0.0196495	−	0.0340339i
$417$		0			0
$418$	−0.382454	−	10.2462i	−0.0187064	−	0.501157i
$419$	19.9205			0.973182			0.486591	−	0.873630i	$-0.338240\pi$
$419$	19.9205			0.973182			0.486591	+	0.873630i	$0.338240\pi$
$420$		0			0
$421$	−7.21372	+	12.4945i	−0.351575	+	0.608946i	−0.986526	−	0.163607i	$-0.947687\pi$
$421$	−7.21372	+	12.4945i	−0.351575	+	0.608946i	0.634950	+	0.772553i	$0.281020\pi$
$422$	2.00000	+	3.46410i	0.0973585	+	0.168630i
$423$		0			0
$424$	0.563361	+	0.975771i	0.0273592	+	0.0473876i
$425$	−85.3707			−4.14109
$426$		0			0
$427$	1.36105	+	2.35740i	0.0658656	+	0.114083i
$428$	8.00263	+	13.8610i	0.386822	+	0.669995i
$429$		0			0
$430$	−3.77708			−0.182147
$431$	−7.32518	−	12.6876i	−0.352841	−	0.611139i	0.633905	−	0.773411i	$-0.281451\pi$
$431$	−7.32518	−	12.6876i	−0.352841	−	0.611139i	−0.986746	+	0.162272i	$0.948118\pi$
$432$		0			0
$433$	9.00217	+	15.5922i	0.432616	+	0.749314i	0.997098	−	0.0761322i	$-0.0242571\pi$
$433$	9.00217	+	15.5922i	0.432616	+	0.749314i	−0.564481	+	0.825446i	$0.690924\pi$
$434$	2.56336	−	4.43987i	0.123045	−	0.213121i
$435$		0			0
$436$	−7.24035			−0.346750
$437$	−6.83800	−	3.61478i	−0.327106	−	0.172919i
$438$		0			0
$439$	10.8168	−	18.7353i	0.516258	−	0.894185i	−0.483564	−	0.875309i	$-0.660658\pi$
$439$	10.8168	−	18.7353i	0.516258	−	0.894185i	0.999822	−	0.0188760i	$-0.00600878\pi$
$440$	−5.08700	+	8.81094i	−0.242513	+	0.420045i
$441$		0			0
$442$	−2.49608	+	4.32334i	−0.118726	+	0.205640i
$443$	−1.72732	−	2.99181i	−0.0820677	−	0.142145i	0.822070	−	0.569386i	$-0.192819\pi$
$443$	−1.72732	−	2.99181i	−0.0820677	−	0.142145i	−0.904138	+	0.427241i	$0.859486\pi$
$444$		0			0
$445$	31.5542			1.49581
$446$	6.12672	+	10.6118i	0.290109	+	0.502483i
$447$		0			0
$448$	1.00000			0.0472456
$449$	19.5069			0.920587			0.460294	−	0.887767i	$-0.347744\pi$
$449$	19.5069			0.920587			0.460294	+	0.887767i	$0.347744\pi$
$450$		0			0
$451$	4.29022	−	7.43089i	0.202019	−	0.349907i
$452$	0.738183	+	1.27857i	0.0347212	+	0.0601389i
$453$		0			0
$454$	−11.6765	+	20.2244i	−0.548007	+	0.949176i
$455$	3.46682			0.162527
$456$		0			0
$457$	−13.2876			−0.621568			−0.310784	−	0.950480i	$-0.600592\pi$
$457$	−13.2876			−0.621568			−0.310784	+	0.950480i	$0.600592\pi$
$458$	12.9415	−	22.4153i	0.604716	−	1.04740i
$459$		0			0
$460$	3.83741	+	6.64659i	0.178920	+	0.309899i
$461$	8.09577	−	14.0223i	0.377058	−	0.653083i	−0.613575	−	0.789636i	$-0.710269\pi$
$461$	8.09577	−	14.0223i	0.377058	−	0.653083i	0.990633	+	0.136553i	$0.0436025\pi$
$462$		0			0
$463$	21.5010			0.999236			0.499618	−	0.866246i	$-0.333474\pi$
$463$	21.5010			0.999236			0.499618	+	0.866246i	$0.333474\pi$
$464$	−5.83126			−0.270710
$465$		0			0
$466$	−1.30154	−	2.25434i	−0.0602929	−	0.104430i
$467$	7.95536			0.368130			0.184065	−	0.982914i	$-0.441074\pi$
$467$	7.95536			0.368130			0.184065	+	0.982914i	$0.441074\pi$
$468$		0			0
$469$	−2.29022	−	3.96678i	−0.105753	−	0.183169i
$470$	12.6106	−	21.8423i	0.581685	−	1.00751i
$471$		0			0
$472$	−7.10054	+	12.2985i	−0.326829	+	0.566084i
$473$	1.02709	−	1.77898i	0.0472258	−	0.0817974i
$474$		0			0
$475$	−52.8217	−	27.9232i	−2.42363	−	1.28121i
$476$	−6.22818			−0.285468
$477$		0			0
$478$	−11.6390	+	20.1594i	−0.532357	+	0.922070i
$479$	−13.3178	−	23.0671i	−0.608506	−	1.05396i	−0.991487	−	0.130207i	$-0.958436\pi$
$479$	−13.3178	−	23.0671i	−0.608506	−	1.05396i	0.382981	−	0.923756i	$-0.374897\pi$
$480$		0			0
$481$	4.26837	+	7.39303i	0.194621	+	0.337093i
$482$	−8.94319			−0.407351
$483$		0			0
$484$	2.73341	+	4.73441i	0.124246	+	0.215200i
$485$	6.61063	+	11.4499i	0.300173	+	0.519915i
$486$		0			0
$487$	5.34964			0.242415			0.121208	−	0.992627i	$-0.461323\pi$
$487$	5.34964			0.242415			0.121208	+	0.992627i	$0.461323\pi$
$488$	1.36105	+	2.35740i	0.0616116	+	0.106714i
$489$		0			0
$490$	2.16259	+	3.74571i	0.0976958	+	0.169214i
$491$	0.228176	−	0.395213i	0.0102974	−	0.0178357i	−0.860831	−	0.508891i	$-0.830055\pi$
$491$	0.228176	−	0.395213i	0.0102974	−	0.0178357i	0.871128	+	0.491056i	$0.163389\pi$
$492$		0			0
$493$	36.3181			1.63569
$494$	−2.95850	+	1.85857i	−0.133109	+	0.0836211i
$495$		0			0
$496$	2.56336	−	4.43987i	0.115098	−	0.199356i
$497$	7.00131	−	12.1266i	0.314052	−	0.543954i
$498$		0			0
$499$	2.99523	−	5.18789i	0.134085	−	0.232242i	−0.791163	−	0.611606i	$-0.790524\pi$
$499$	2.99523	−	5.18789i	0.134085	−	0.232242i	0.925247	+	0.379364i	$0.123857\pi$
$500$	18.8300	+	32.6146i	0.842105	+	1.45857i
$501$		0			0
$502$	−27.3872			−1.22235
$503$	14.1464	+	24.5023i	0.630758	+	1.09251i	0.987397	+	0.158263i	$0.0505894\pi$
$503$	14.1464	+	24.5023i	0.630758	+	1.09251i	−0.356639	+	0.934242i	$0.616077\pi$
$504$		0			0
$505$	6.58999			0.293251
$506$	−4.17399			−0.185557
$507$		0			0
$508$	3.11540	−	5.39603i	0.138224	−	0.239410i
$509$	9.54949	+	16.5402i	0.423274	+	0.733132i	0.996257	−	0.0864349i	$-0.0275475\pi$
$509$	9.54949	+	16.5402i	0.423274	+	0.733132i	−0.572984	+	0.819567i	$0.694214\pi$
$510$		0			0
$511$	4.61540	−	7.99411i	0.204173	−	0.353639i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−8.49209			−0.374570
$515$	−24.9209	+	43.1642i	−1.09815	+	1.90204i
$516$		0			0
$517$	6.85836	+	11.8790i	0.301630	+	0.522439i
$518$	−5.32518	+	9.22348i	−0.233975	+	0.405256i
$519$		0			0
$520$	3.46682			0.152030
$521$	−24.1294			−1.05713			−0.528563	−	0.848894i	$-0.677269\pi$
$521$	−24.1294			−1.05713			−0.528563	+	0.848894i	$0.677269\pi$
$522$		0			0
$523$	5.96027	+	10.3235i	0.260625	+	0.451415i	0.966408	−	0.257013i	$-0.0827382\pi$
$523$	5.96027	+	10.3235i	0.260625	+	0.451415i	−0.705783	+	0.708428i	$0.749405\pi$
$524$	3.66528			0.160118
$525$		0			0
$526$	−2.87459	−	4.97894i	−0.125338	−	0.217092i
$527$	−15.9651	+	27.6523i	−0.695449	+	1.20455i
$528$		0			0
$529$	9.92566	−	17.1917i	0.431550	−	0.747467i
$530$	−2.43664	+	4.22038i	−0.105841	+	0.183322i
$531$		0			0
$532$	−3.85358	−	2.03713i	−0.167074	−	0.0883206i
$533$	−2.92382			−0.126645
$534$		0			0
$535$	−34.6128	+	59.9511i	−1.49644	+	2.59191i
$536$	−2.29022	−	3.96678i	−0.0989226	−	0.171339i
$537$		0			0
$538$	−4.21109	−	7.29382i	−0.181553	−	0.314459i
$539$	−2.35227			−0.101319
$540$		0			0
$541$	−5.92055	−	10.2547i	−0.254544	−	0.440883i	0.710227	−	0.703972i	$-0.248592\pi$
$541$	−5.92055	−	10.2547i	−0.254544	−	0.440883i	−0.964772	+	0.263089i	$0.915259\pi$
$542$	−10.3649	−	17.9525i	−0.445211	−	0.771128i
$543$		0			0
$544$	−6.22818			−0.267031
$545$	−15.6579	−	27.1203i	−0.670711	−	1.16171i
$546$		0			0
$547$	−17.7374	−	30.7220i	−0.758394	−	1.31358i	−0.943669	−	0.330891i	$-0.892651\pi$
$547$	−17.7374	−	30.7220i	−0.758394	−	1.31358i	0.185275	−	0.982687i	$-0.440683\pi$
$548$	1.69846	−	2.94181i	0.0725544	−	0.125668i
$549$		0			0
$550$	−32.2430			−1.37485
$551$	22.4713	+	11.8790i	0.957308	+	0.506063i
$552$		0			0
$553$	3.52363	−	6.10311i	0.149840	−	0.259531i
$554$	−8.72209	+	15.1071i	−0.370566	+	0.641839i
$555$		0			0
$556$	2.59832	−	4.50042i	0.110193	−	0.190860i
$557$	5.84881	+	10.1304i	0.247822	+	0.429241i	0.962921	−	0.269782i	$-0.0869518\pi$
$557$	5.84881	+	10.1304i	0.247822	+	0.429241i	−0.715099	+	0.699023i	$0.753618\pi$
$558$		0			0
$559$	−0.699970			−0.0296056
$560$	2.16259	+	3.74571i	0.0913861	+	0.158285i
$561$		0			0
$562$	−2.12409			−0.0895995
$563$	12.2562			0.516537			0.258268	−	0.966073i	$-0.416848\pi$
$563$	12.2562			0.516537			0.258268	+	0.966073i	$0.416848\pi$
$564$		0			0
$565$	−3.19277	+	5.53004i	−0.134321	+	0.232651i
$566$	13.8348	+	23.9626i	0.581520	+	1.00722i
$567$		0			0
$568$	7.00131	−	12.1266i	0.293769	−	0.508822i
$569$	−5.80862			−0.243510			−0.121755	−	0.992560i	$-0.538852\pi$
$569$	−5.80862			−0.243510			−0.121755	+	0.992560i	$0.538852\pi$
$570$		0			0
$571$	37.2308			1.55806			0.779030	−	0.626986i	$-0.215712\pi$
$571$	37.2308			1.55806			0.779030	+	0.626986i	$0.215712\pi$
$572$	−0.942725	+	1.63285i	−0.0394173	+	0.0682728i
$573$		0			0
$574$	−1.82386	−	3.15903i	−0.0761266	−	0.131855i
$575$	−12.1614	+	21.0641i	−0.507164	+	0.878433i
$576$		0			0
$577$	−17.3444			−0.722058			−0.361029	−	0.932555i	$-0.617574\pi$
$577$	−17.3444			−0.722058			−0.361029	+	0.932555i	$0.617574\pi$
$578$	21.7902			0.906352
$579$		0			0
$580$	−12.6106	−	21.8423i	−0.523628	−	0.906950i
$581$	−15.5560			−0.645371
$582$		0			0
$583$	−1.32518	−	2.29528i	−0.0548833	−	0.0950606i
$584$	4.61540	−	7.99411i	0.190987	−	0.330799i
$585$		0			0
$586$	−6.61631	+	11.4598i	−0.273317	+	0.473400i
$587$	−16.8781	+	29.2337i	−0.696633	+	1.20660i	0.272995	+	0.962016i	$0.411986\pi$
$587$	−16.8781	+	29.2337i	−0.696633	+	1.20660i	−0.969627	+	0.244587i	$0.921347\pi$
$588$		0			0
$589$	−18.9227	+	11.8875i	−0.779697	+	0.489817i
$590$	−61.4222			−2.52871
$591$		0			0
$592$	−5.32518	+	9.22348i	−0.218863	+	0.379083i
$593$	−7.75395	−	13.4302i	−0.318417	−	0.551514i	0.661741	−	0.749732i	$-0.269818\pi$
$593$	−7.75395	−	13.4302i	−0.318417	−	0.551514i	−0.980158	+	0.198218i	$0.936484\pi$
$594$		0			0
$595$	−13.4690	−	23.3290i	−0.552175	−	0.956395i
$596$	−14.6504			−0.600102
$597$		0			0
$598$	0.711151	+	1.23175i	0.0290811	+	0.0503700i
$599$	19.0608	+	33.0142i	0.778801	+	1.34892i	0.932633	+	0.360826i	$0.117505\pi$
$599$	19.0608	+	33.0142i	0.778801	+	1.34892i	−0.153832	+	0.988097i	$0.549161\pi$
$600$		0			0
$601$	13.4799			0.549857			0.274929	−	0.961465i	$-0.411346\pi$
$601$	13.4799			0.549857			0.274929	+	0.961465i	$0.411346\pi$
$602$	−0.436639	−	0.756280i	−0.0177961	−	0.0308237i
$603$		0			0
$604$	−2.73341	−	4.73441i	−0.111221	−	0.192640i
$605$	−11.8225	+	20.4772i	−0.480653	+	0.832515i
$606$		0			0
$607$	−6.25345			−0.253820			−0.126910	−	0.991914i	$-0.540506\pi$
$607$	−6.25345			−0.253820			−0.126910	+	0.991914i	$0.540506\pi$
$608$	−3.85358	−	2.03713i	−0.156284	−	0.0826164i
$609$		0			0
$610$	−5.88676	+	10.1962i	−0.238348	+	0.412831i
$611$	2.33701	−	4.04782i	0.0945452	−	0.163757i
$612$		0			0
$613$	−2.75999	+	4.78045i	−0.111475	+	0.193081i	−0.916365	−	0.400343i	$-0.868891\pi$
$613$	−2.75999	+	4.78045i	−0.111475	+	0.193081i	0.804890	+	0.593424i	$0.202224\pi$
$614$	−12.4699	−	21.5985i	−0.503244	−	0.871644i
$615$		0			0
$616$	−2.35227			−0.0947757
$617$	11.3912	+	19.7301i	0.458591	+	0.794303i	0.998887	−	0.0471721i	$-0.0150209\pi$
$617$	11.3912	+	19.7301i	0.458591	+	0.794303i	−0.540296	+	0.841475i	$0.681688\pi$
$618$		0			0
$619$	−10.6879			−0.429584			−0.214792	−	0.976660i	$-0.568907\pi$
$619$	−10.6879			−0.429584			−0.214792	+	0.976660i	$0.568907\pi$
$620$	22.1740			0.890529
$621$		0			0
$622$	7.97291	−	13.8095i	0.319684	−	0.553710i
$623$	3.64773	+	6.31805i	0.146143	+	0.253127i
$624$		0			0
$625$	−47.1753	+	81.7101i	−1.88701	+	3.26840i
$626$	−12.7203			−0.508404
$627$		0			0
$628$	−3.45190			−0.137746
$629$	33.1661	−	57.4455i	1.32242	−	2.29050i
$630$		0			0
$631$	10.2534	+	17.7595i	0.408183	+	0.706994i	0.994686	−	0.102953i	$-0.0328291\pi$
$631$	10.2534	+	17.7595i	0.408183	+	0.706994i	−0.586503	+	0.809947i	$0.699496\pi$
$632$	3.52363	−	6.10311i	0.140163	−	0.242769i
$633$		0			0
$634$	32.9091			1.30699
$635$	26.9493			1.06945
$636$		0			0
$637$	0.400772	+	0.694158i	0.0158792	+	0.0275035i
$638$	13.7167			0.543050
$639$		0			0
$640$	2.16259	+	3.74571i	0.0854838	+	0.148062i
$641$	11.1508	−	19.3138i	0.440431	−	0.762849i	−0.557290	−	0.830318i	$-0.688159\pi$
$641$	11.1508	−	19.3138i	0.440431	−	0.762849i	0.997721	+	0.0674689i	$0.0214923\pi$
$642$		0			0
$643$	1.39600	−	2.41794i	0.0550529	−	0.0953544i	−0.837186	−	0.546919i	$-0.815801\pi$
$643$	1.39600	−	2.41794i	0.0550529	−	0.0953544i	0.892238	+	0.451565i	$0.149134\pi$
$644$	−0.887226	+	1.53672i	−0.0349616	+	0.0605553i
$645$		0			0
$646$	24.0008	+	12.6876i	0.944299	+	0.499186i
$647$	5.69144			0.223754			0.111877	−	0.993722i	$-0.464314\pi$
$647$	5.69144			0.223754			0.111877	+	0.993722i	$0.464314\pi$
$648$		0			0
$649$	16.7024	−	28.9294i	0.655626	−	1.13558i
$650$	5.49345	+	9.51494i	0.215471	+	0.373207i
$651$		0			0
$652$	−4.32995	−	7.49969i	−0.169574	−	0.293711i
$653$	−0.485267			−0.0189900			−0.00949499	−	0.999955i	$-0.503022\pi$
$653$	−0.485267			−0.0189900			−0.00949499	+	0.999955i	$0.503022\pi$
$654$		0			0
$655$	7.92649	+	13.7291i	0.309714	+	0.536440i
$656$	−1.82386	−	3.15903i	−0.0712099	−	0.123339i
$657$		0			0
$658$	5.83126			0.227326
$659$	−8.90117	−	15.4173i	−0.346741	−	0.600572i	0.638928	−	0.769267i	$-0.279378\pi$
$659$	−8.90117	−	15.4173i	−0.346741	−	0.600572i	−0.985668	+	0.168694i	$0.946045\pi$
$660$		0			0
$661$	−9.93967	−	17.2160i	−0.386608	−	0.669625i	0.605383	−	0.795935i	$-0.293020\pi$
$661$	−9.93967	−	17.2160i	−0.386608	−	0.669625i	−0.991991	+	0.126309i	$0.959687\pi$
$662$	9.50394	−	16.4613i	0.369381	−	0.639787i
$663$		0			0
$664$	−15.5560			−0.603689
$665$	−0.703228	−	18.8399i	−0.0272700	−	0.730580i
$666$		0			0
$667$	5.17365	−	8.96102i	0.200324	−	0.346972i
$668$	−3.02972	+	5.24763i	−0.117223	+	0.203037i
$669$		0			0
$670$	9.90563	−	17.1570i	0.382688	−	0.662835i
$671$	−3.20155	−	5.54524i	−0.123594	−	0.214072i
$672$		0			0
$673$	−23.8339			−0.918729			−0.459365	−	0.888248i	$-0.651923\pi$
$673$	−23.8339			−0.918729			−0.459365	+	0.888248i	$0.651923\pi$
$674$	−14.0957	−	24.4145i	−0.542946	−	0.940411i
$675$		0			0
$676$	−12.3575			−0.475289
$677$	24.7893			0.952728			0.476364	−	0.879248i	$-0.341954\pi$
$677$	24.7893			0.952728			0.476364	+	0.879248i	$0.341954\pi$
$678$		0			0
$679$	−1.52841	+	2.64728i	−0.0586549	+	0.101593i
$680$	−13.4690	−	23.3290i	−0.516512	−	0.894625i
$681$		0			0
$682$	−6.02972	+	10.4438i	−0.230890	+	0.399913i
$683$	39.3592			1.50604			0.753020	−	0.657998i	$-0.228597\pi$
$683$	39.3592			1.50604			0.753020	+	0.657998i	$0.228597\pi$
$684$		0			0
$685$	14.6922			0.561362
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	−0.436639	−	0.756280i	−0.0166467	−	0.0288329i
$689$	−0.451559	+	0.782123i	−0.0172030	+	0.0297965i
$690$		0			0
$691$	27.8226			1.05842			0.529211	−	0.848490i	$-0.322488\pi$
$691$	27.8226			1.05842			0.529211	+	0.848490i	$0.322488\pi$
$692$	−15.6259			−0.594007
$693$		0			0
$694$	11.3646	+	19.6840i	0.431394	+	0.747196i
$695$	22.4764			0.852577
$696$		0			0
$697$	11.3593	+	19.6750i	0.430266	+	0.745243i
$698$	2.36491	−	4.09614i	0.0895130	−	0.155041i
$699$		0			0
$700$	−6.85358	+	11.8708i	−0.259041	+	0.448672i
$701$	−18.7666	+	32.5047i	−0.708805	+	1.22769i	0.256496	+	0.966545i	$0.417432\pi$
$701$	−18.7666	+	32.5047i	−0.708805	+	1.22769i	−0.965301	+	0.261141i	$0.915901\pi$
$702$		0			0
$703$	39.3104	−	24.6954i	1.48262	−	0.931405i
$704$	−2.35227			−0.0886545
$705$		0			0
$706$	−2.88068	+	4.98948i	−0.108416	+	0.187782i
$707$	0.761817	+	1.31951i	0.0286511	+	0.0496251i
$708$		0			0
$709$	−5.69008	−	9.85551i	−0.213696	−	0.370132i	0.739173	−	0.673516i	$-0.235217\pi$
$709$	−5.69008	−	9.85551i	−0.213696	−	0.370132i	−0.952868	+	0.303384i	$0.901883\pi$
$710$	60.5639			2.27292
$711$		0			0
$712$	3.64773	+	6.31805i	0.136704	+	0.236779i
$713$	4.54856	+	7.87834i	0.170345	+	0.295046i
$714$		0			0
$715$	−8.15490			−0.304976
$716$	5.69977	+	9.87229i	0.213010	+	0.368945i
$717$		0			0
$718$	−9.97554	−	17.2781i	−0.372284	−	0.644814i
$719$	−20.1609	+	34.9197i	−0.751874	+	1.30228i	0.195039	+	0.980796i	$0.437517\pi$
$719$	−20.1609	+	34.9197i	−0.751874	+	1.30228i	−0.946913	+	0.321489i	$0.895817\pi$
$720$		0			0
$721$	−11.5236			−0.429163
$722$	10.7002	+	15.7005i	0.398221	+	0.584311i
$723$		0			0
$724$	−1.63895	+	2.83875i	−0.0609113	+	0.105501i
$725$	39.9651	−	69.2215i	1.48427	−	2.57082i
$726$		0			0
$727$	−0.778903	+	1.34910i	−0.0288879	+	0.0500353i	−0.880108	−	0.474774i	$-0.842530\pi$
$727$	−0.778903	+	1.34910i	−0.0288879	+	0.0500353i	0.851220	+	0.524809i	$0.175863\pi$
$728$	0.400772	+	0.694158i	0.0148536	+	0.0257272i
$729$		0			0
$730$	39.9249			1.47769
$731$	2.71946	+	4.71025i	0.100583	+	0.174215i
$732$		0			0
$733$	−22.7825			−0.841489			−0.420745	−	0.907179i	$-0.638231\pi$
$733$	−22.7825			−0.841489			−0.420745	+	0.907179i	$0.638231\pi$
$734$	−1.24035			−0.0457821
$735$		0			0
$736$	−0.887226	+	1.53672i	−0.0327036	+	0.0566443i
$737$	5.38723	+	9.33095i	0.198441	+	0.343710i
$738$		0			0
$739$	1.32041	−	2.28701i	0.0485719	−	0.0841291i	−0.840717	−	0.541474i	$-0.817866\pi$
$739$	1.32041	−	2.28701i	0.0485719	−	0.0841291i	0.889289	+	0.457345i	$0.151200\pi$
$740$	−46.0647			−1.69337
$741$		0			0
$742$	−1.12672			−0.0413633
$743$	−9.39776	+	16.2774i	−0.344770	+	0.597160i	−0.985312	−	0.170764i	$-0.945377\pi$
$743$	−9.39776	+	16.2774i	−0.344770	+	0.597160i	0.640542	+	0.767924i	$0.278710\pi$
$744$		0			0
$745$	−31.6827	−	54.8761i	−1.16076	−	2.01050i
$746$	−12.4366	+	21.5409i	−0.455338	+	0.788668i
$747$		0			0
$748$	14.6504			0.535670
$749$	−16.0053			−0.584819
$750$		0			0
$751$	21.3444	+	36.9696i	0.778869	+	1.34904i	0.932594	+	0.360927i	$0.117540\pi$
$751$	21.3444	+	36.9696i	0.778869	+	1.34904i	−0.153725	+	0.988114i	$0.549127\pi$
$752$	5.83126			0.212644
$753$		0			0
$754$	−2.33701	−	4.04782i	−0.0851088	−	0.147413i
$755$	11.8225	−	20.4772i	0.430264	−	0.745240i
$756$		0			0
$757$	−21.9187	+	37.9643i	−0.796650	+	1.37984i	0.125137	+	0.992139i	$0.460063\pi$
$757$	−21.9187	+	37.9643i	−0.796650	+	1.37984i	−0.921786	+	0.387698i	$0.873270\pi$
$758$	−16.2137	+	28.0830i	−0.588909	+	1.02002i
$759$		0			0
$760$	−0.703228	−	18.8399i	−0.0255088	−	0.683395i
$761$	−5.22462			−0.189392			−0.0946962	−	0.995506i	$-0.530188\pi$
$761$	−5.22462			−0.189392			−0.0946962	+	0.995506i	$0.530188\pi$
$762$		0			0
$763$	3.62017	−	6.27033i	0.131059	−	0.227001i
$764$	−1.61932	−	2.80475i	−0.0585850	−	0.101472i
$765$		0			0
$766$	−7.25527	−	12.5665i	−0.262144	−	0.454046i
$767$	−11.3828			−0.411009
$768$		0			0
$769$	16.4839	+	28.5510i	0.594425	+	1.02957i	0.993628	+	0.112712i	$0.0359536\pi$
$769$	16.4839	+	28.5510i	0.594425	+	1.02957i	−0.399203	+	0.916863i	$0.630713\pi$
$770$	−5.08700	−	8.81094i	−0.183323	−	0.317524i
$771$		0			0
$772$	12.0568			0.433934
$773$	21.8453	+	37.8372i	0.785721	+	1.36091i	0.928568	+	0.371163i	$0.121041\pi$
$773$	21.8453	+	37.8372i	0.785721	+	1.36091i	−0.142847	+	0.989745i	$0.545626\pi$
$774$		0			0
$775$	35.1364	+	60.8581i	1.26214	+	2.18609i
$776$	−1.52841	+	2.64728i	−0.0548666	+	0.0950317i
$777$		0			0
$778$	−25.5236			−0.915067
$779$	0.593082	+	15.8890i	0.0212494	+	0.569283i
$780$		0			0
$781$	−16.4690	+	28.5251i	−0.589307	+	1.02071i
$782$	5.52580	−	9.57097i	0.197602	−	0.342257i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	−7.46504	−	12.9298i	−0.266439	−	0.461486i
$786$		0			0
$787$	26.7431			0.953288			0.476644	−	0.879097i	$-0.341853\pi$
$787$	26.7431			0.953288			0.476644	+	0.879097i	$0.341853\pi$
$788$	−10.4690	−	18.1328i	−0.372942	−	0.645955i
$789$		0			0
$790$	30.4807			1.08445
$791$	−1.47637			−0.0524935
$792$		0			0
$793$	−1.09094	+	1.88956i	−0.0387403	+	0.0671002i
$794$	−5.81863	−	10.0782i	−0.206495	−	0.357661i
$795$		0			0
$796$	−4.56336	+	7.90397i	−0.161744	+	0.280149i
$797$	−7.16861			−0.253925			−0.126963	−	0.991907i	$-0.540523\pi$
$797$	−7.16861			−0.253925			−0.126963	+	0.991907i	$0.540523\pi$
$798$		0			0
$799$	−36.3181			−1.28484
$800$	−6.85358	+	11.8708i	−0.242311	+	0.419695i
$801$		0			0
$802$	−12.5870	−	21.8013i	−0.444462	−	0.769831i
$803$	−10.8567	+	18.8043i	−0.383124	+	0.663590i
$804$		0			0
$805$	−7.67482			−0.270502
$806$	4.10929			0.144744
$807$		0			0
$808$	0.761817	+	1.31951i	0.0268006	+	0.0464201i
$809$	−1.58109			−0.0555881			−0.0277941	−	0.999614i	$-0.508848\pi$
$809$	−1.58109			−0.0555881			−0.0277941	+	0.999614i	$0.508848\pi$
$810$		0			0
$811$	−0.705005	−	1.22110i	−0.0247561	−	0.0428788i	0.853382	−	0.521286i	$-0.174548\pi$
$811$	−0.705005	−	1.22110i	−0.0247561	−	0.0428788i	−0.878138	+	0.478407i	$0.841214\pi$
$812$	2.91563	−	5.05002i	0.102319	−	0.177221i
$813$		0			0
$814$	12.5263	−	21.6961i	0.439045	−	0.760449i
$815$	18.7278	−	32.4375i	0.656007	−	1.13624i
$816$		0			0
$817$	0.141986	+	3.80388i	0.00496744	+	0.133081i
$818$	31.6277			1.10584
$819$		0			0
$820$	7.88854	−	13.6634i	0.275480	−	0.477145i
$821$	−16.6057	−	28.7619i	−0.579543	−	1.00380i	−0.995532	−	0.0944287i	$-0.969898\pi$
$821$	−16.6057	−	28.7619i	−0.579543	−	1.00380i	0.415988	−	0.909370i	$-0.363436\pi$
$822$		0			0
$823$	23.5599	+	40.8070i	0.821247	+	1.42244i	0.904754	+	0.425935i	$0.140055\pi$
$823$	23.5599	+	40.8070i	0.821247	+	1.42244i	−0.0835065	+	0.996507i	$0.526612\pi$
$824$	−11.5236			−0.401445
$825$		0			0
$826$	−7.10054	−	12.2985i	−0.247059	−	0.427920i
$827$	8.06421	+	13.9676i	0.280420	+	0.485702i	0.971488	−	0.237088i	$-0.0761929\pi$
$827$	8.06421	+	13.9676i	0.280420	+	0.485702i	−0.691068	+	0.722790i	$0.742860\pi$
$828$		0			0
$829$	46.9266			1.62983			0.814914	−	0.579582i	$-0.196784\pi$
$829$	46.9266			1.62983			0.814914	+	0.579582i	$0.196784\pi$
$830$	−33.6412	−	58.2683i	−1.16770	−	2.02252i
$831$		0			0
$832$	0.400772	+	0.694158i	0.0138943	+	0.0240656i
$833$	3.11409	−	5.39376i	0.107897	−	0.186883i
$834$		0			0
$835$	−26.2082			−0.906971
$836$	9.06468	+	4.79187i	0.313508	+	0.165730i
$837$		0			0
$838$	−9.96027	+	17.2517i	−0.344072	+	0.595950i
$839$	−4.09700	+	7.09622i	−0.141444	+	0.244989i	−0.928041	−	0.372479i	$-0.878508\pi$
$839$	−4.09700	+	7.09622i	−0.141444	+	0.244989i	0.786596	+	0.617467i	$0.211841\pi$
$840$		0			0
$841$	−2.50182	+	4.33328i	−0.0862698	+	0.149424i
$842$	−7.21372	−	12.4945i	−0.248601	−	0.430590i
$843$		0			0
$844$	−4.00000			−0.137686
$845$	−26.7243	−	46.2878i	−0.919342	−	1.59235i
$846$		0			0
$847$	−5.46682			−0.187842
$848$	−1.12672			−0.0386918
$849$		0			0
$850$	42.6853	−	73.9332i	1.46409	−	2.53589i
$851$	−9.44927	−	16.3666i	−0.323917	−	0.561041i
$852$		0			0
$853$	8.38953	−	14.5311i	0.287252	−	0.497535i	−0.685901	−	0.727695i	$-0.740592\pi$
$853$	8.38953	−	14.5311i	0.287252	−	0.497535i	0.973153	+	0.230160i	$0.0739249\pi$
$854$	−2.72209			−0.0931480
$855$		0			0
$856$	−16.0053			−0.547048
$857$	−4.73950	+	8.20905i	−0.161898	+	0.280416i	−0.935549	−	0.353196i	$-0.885095\pi$
$857$	−4.73950	+	8.20905i	−0.161898	+	0.280416i	0.773651	+	0.633612i	$0.218428\pi$
$858$		0			0
$859$	2.79677	+	4.84415i	0.0954246	+	0.165280i	0.909786	−	0.415078i	$-0.136246\pi$
$859$	2.79677	+	4.84415i	0.0954246	+	0.165280i	−0.814361	+	0.580358i	$0.802912\pi$
$860$	1.88854	−	3.27105i	0.0643987	−	0.111542i
$861$		0			0
$862$	14.6504			0.498993
$863$	46.1241			1.57008			0.785042	−	0.619443i	$-0.212641\pi$
$863$	46.1241			1.57008			0.785042	+	0.619443i	$0.212641\pi$
$864$		0			0
$865$	−33.7924	−	58.5301i	−1.14898	−	1.99008i
$866$	−18.0043			−0.611812
$867$		0			0
$868$	2.56336	+	4.43987i	0.0870062	+	0.150699i
$869$	−8.28854	+	14.3562i	−0.281170	+	0.487000i
$870$		0			0
$871$	1.83572	−	3.17955i	0.0622008	−	0.107735i
$872$	3.62017	−	6.27033i	0.122595	−	0.212340i
$873$		0			0
$874$	6.54949	−	4.11449i	0.221540	−	0.139175i
$875$	−37.6601			−1.27314
$876$		0			0
$877$	−8.39908	+	14.5476i	−0.283617	+	0.491238i	−0.972273	−	0.233850i	$-0.924868\pi$
$877$	−8.39908	+	14.5476i	−0.283617	+	0.491238i	0.688656	+	0.725088i	$0.258201\pi$
$878$	10.8168	+	18.7353i	0.365050	+	0.632284i
$879$		0			0
$880$	−5.08700	−	8.81094i	−0.171483	−	0.297017i
$881$	29.9153			1.00787			0.503937	−	0.863741i	$-0.331885\pi$
$881$	29.9153			1.00787			0.503937	+	0.863741i	$0.331885\pi$
$882$		0			0
$883$	13.4642	+	23.3207i	0.453107	+	0.784804i	0.998577	−	0.0533260i	$-0.0169822\pi$
$883$	13.4642	+	23.3207i	0.453107	+	0.784804i	−0.545470	+	0.838130i	$0.683649\pi$
$884$	−2.49608	−	4.32334i	−0.0839522	−	0.145410i
$885$		0			0
$886$	3.45465			0.116061
$887$	12.3454	+	21.3828i	0.414516	+	0.717964i	0.995378	−	0.0960391i	$-0.0306174\pi$
$887$	12.3454	+	21.3828i	0.414516	+	0.717964i	−0.580861	+	0.814003i	$0.697284\pi$
$888$		0			0
$889$	3.11540	+	5.39603i	0.104487	+	0.180977i
$890$	−15.7771	+	27.3267i	−0.528849	+	0.915993i
$891$		0			0
$892$	−12.2534			−0.410276
$893$	−22.4713	−	11.8790i	−0.751972	−	0.397516i
$894$		0			0
$895$	−24.6525	+	42.6994i	−0.824043	+	1.42728i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$		0			0
$898$	−9.75345	+	16.8935i	−0.325477	+	0.563742i
$899$	−14.9476	−	25.8901i	−0.498532	−	0.863482i
$900$		0			0
$901$	7.01743			0.233784
$902$	4.29022	+	7.43089i	0.142849	+	0.247421i
$903$		0			0
$904$	−1.47637			−0.0491032
$905$	−14.1775			−0.471278
$906$		0			0
$907$	18.0691	−	31.2966i	0.599975	−	1.03919i	−0.392848	−	0.919603i	$-0.628510\pi$
$907$	18.0691	−	31.2966i	0.599975	−	1.03919i	0.992824	−	0.119585i	$-0.0381563\pi$
$908$	−11.6765	−	20.2244i	−0.387500	−	0.671169i
$909$		0			0
$910$	−1.73341	+	3.00236i	−0.0574620	+	0.0995271i
$911$	41.0210			1.35909			0.679543	−	0.733636i	$-0.262178\pi$
$911$	41.0210			1.35909			0.679543	+	0.733636i	$0.262178\pi$
$912$		0			0
$913$	36.5919			1.21101
$914$	6.64381	−	11.5074i	0.219758	−	0.380631i
$915$		0			0
$916$	12.9415	+	22.4153i	0.427599	+	0.740623i
$917$	−1.83264	+	3.17422i	−0.0605191	+	0.104822i
$918$		0			0
$919$	−19.4521			−0.641664			−0.320832	−	0.947136i	$-0.603963\pi$
$919$	−19.4521			−0.641664			−0.320832	+	0.947136i	$0.603963\pi$
$920$	−7.67482			−0.253031
$921$		0			0
$922$	8.09577	+	14.0223i	0.266620	+	0.461799i
$923$	11.2237			0.369433
$924$		0			0
$925$	−72.9931	−	126.428i	−2.40000	−	4.15692i
$926$	−10.7505	+	18.6204i	−0.353283	+	0.611905i
$927$		0			0
$928$	2.91563	−	5.05002i	0.0957103	−	0.165775i
$929$	4.43004	−	7.67306i	0.145345	−	0.251745i	−0.784157	−	0.620563i	$-0.786904\pi$
$929$	4.43004	−	7.67306i	0.145345	−	0.251745i	0.929502	+	0.368818i	$0.120237\pi$
$930$		0			0
$931$	3.69100	−	2.31874i	0.120967	−	0.0759936i
$932$	2.60309			0.0852670
$933$		0			0
$934$	−3.97768	+	6.88954i	−0.130154	+	0.225433i
$935$	31.6827	+	54.8761i	1.03614	+	1.79464i
$936$		0			0
$937$	17.8707	+	30.9529i	0.583809	+	1.01119i	0.995023	+	0.0996483i	$0.0317718\pi$
$937$	17.8707	+	30.9529i	0.583809	+	1.01119i	−0.411213	+	0.911539i	$0.634895\pi$
$938$	4.58045			0.149557
$939$		0			0
$940$	12.6106	+	21.8423i	0.411313	+	0.712416i
$941$	20.3064	+	35.1717i	0.661970	+	1.14657i	0.980097	+	0.198517i	$0.0636126\pi$
$941$	20.3064	+	35.1717i	0.661970	+	1.14657i	−0.318128	+	0.948048i	$0.603054\pi$
$942$		0			0
$943$	6.47272			0.210781
$944$	−7.10054	−	12.2985i	−0.231103	−	0.400282i
$945$		0			0
$946$	1.02709	+	1.77898i	0.0333937	+	0.0578395i
$947$	−20.6922	+	35.8400i	−0.672408	+	1.16464i	0.304812	+	0.952413i	$0.401406\pi$
$947$	−20.6922	+	35.8400i	−0.672408	+	1.16464i	−0.977219	+	0.212232i	$0.931927\pi$
$948$		0			0
$949$	7.39890			0.240178
$950$	50.5931	−	31.7834i	1.64146	−	1.03119i
$951$		0			0
$952$	3.11409	−	5.39376i	0.100928	−	0.174813i
$953$	−2.72550	+	4.72071i	−0.0882877	+	0.152919i	−0.906787	−	0.421588i	$-0.861473\pi$
$953$	−2.72550	+	4.72071i	−0.0882877	+	0.152919i	0.818500	+	0.574507i	$0.194806\pi$
$954$		0			0
$955$	7.00386	−	12.1310i	0.226640	−	0.392551i
$956$	−11.6390	−	20.1594i	−0.376433	−	0.652002i
$957$		0			0
$958$	26.6356			0.860557
$959$	1.69846	+	2.94181i	0.0548460	+	0.0949961i
$960$		0			0
$961$	−4.71671			−0.152152
$962$	−8.53673			−0.275235
$963$		0			0
$964$	4.47159	−	7.74503i	0.144020	−	0.249451i
$965$	26.0739	+	45.1614i	0.839350	+	1.45380i
$966$		0			0
$967$	−0.812865	+	1.40792i	−0.0261400	+	0.0452758i	−0.878799	−	0.477191i	$-0.841655\pi$
$967$	−0.812865	+	1.40792i	−0.0261400	+	0.0452758i	0.852659	+	0.522467i	$0.174988\pi$
$968$	−5.46682			−0.175710
$969$		0			0
$970$	−13.2213			−0.424509
$971$	17.5817	−	30.4524i	0.564224	−	0.977264i	−0.432898	−	0.901443i	$-0.642509\pi$
$971$	17.5817	−	30.4524i	0.564224	−	0.977264i	0.997121	−	0.0758210i	$-0.0241578\pi$
$972$		0			0
$973$	2.59832	+	4.50042i	0.0832982	+	0.144277i
$974$	−2.67482	+	4.63293i	−0.0857068	+	0.148449i
$975$		0			0
$976$	−2.72209			−0.0871320
$977$	37.2289			1.19106			0.595528	−	0.803334i	$-0.296943\pi$
$977$	37.2289			1.19106			0.595528	+	0.803334i	$0.296943\pi$
$978$		0			0
$979$	−8.58045	−	14.8618i	−0.274232	−	0.474984i
$980$	−4.32518			−0.138163
$981$		0			0
$982$	0.228176	+	0.395213i	0.00728139	+	0.0126117i
$983$	−0.647729	+	1.12190i	−0.0206594	+	0.0357830i	−0.876170	−	0.482002i	$-0.839910\pi$
$983$	−0.647729	+	1.12190i	−0.0206594	+	0.0357830i	0.855511	+	0.517785i	$0.173243\pi$
$984$		0			0
$985$	45.2802	−	78.4277i	1.44275	−	2.49891i
$986$	−18.1591	+	31.4524i	−0.578303	+	1.00165i
$987$		0			0
$988$	−0.130323	−	3.49142i	−0.00414611	−	0.111077i
$989$	1.54959			0.0492740
$990$		0			0
$991$	−6.89214	+	11.9375i	−0.218936	+	0.379208i	−0.954483	−	0.298265i	$-0.903592\pi$
$991$	−6.89214	+	11.9375i	−0.218936	+	0.379208i	0.735547	+	0.677474i	$0.236925\pi$
$992$	2.56336	+	4.43987i	0.0813868	+	0.140966i
$993$		0			0
$994$	7.00131	+	12.1266i	0.222068	+	0.384633i
$995$	−39.4747			−1.25143
$996$		0			0
$997$	0.428790	+	0.742686i	0.0135799	+	0.0235211i	0.872736	−	0.488193i	$-0.162344\pi$
$997$	0.428790	+	0.742686i	0.0135799	+	0.0235211i	−0.859156	+	0.511714i	$0.829011\pi$
$998$	2.99523	+	5.18789i	0.0948123	+	0.164220i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.o.v.505.4		8
3.2	odd	2		266.2.f.d.239.2	yes	8
19.7	even	3	inner	2394.2.o.v.1261.4		8
57.8	even	6		5054.2.a.x.1.2		4
57.11	odd	6		5054.2.a.w.1.3		4
57.26	odd	6		266.2.f.d.197.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.f.d.197.2	✓	8	57.26	odd	6
266.2.f.d.239.2	yes	8	3.2	odd	2
2394.2.o.v.505.4		8	1.1	even	1	trivial
2394.2.o.v.1261.4		8	19.7	even	3	inner
5054.2.a.w.1.3		4	57.11	odd	6
5054.2.a.x.1.2		4	57.8	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:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.16259 - 3.74571i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.16259 - 3.74571i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +(2.16259 + 3.74571i) q^{10} -2.35227 q^{11} +(0.400772 + 0.694158i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.11409 - 5.39376i) q^{17} +(3.69100 - 2.31874i) q^{19} -4.32518 q^{20} +(1.17614 - 2.03713i) q^{22} +(-0.887226 - 1.53672i) q^{23} +(-6.85358 - 11.8708i) q^{25} -0.801544 q^{26} +(-0.500000 - 0.866025i) q^{28} +(2.91563 + 5.05002i) q^{29} -5.12672 q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.11409 + 5.39376i) q^{34} +(2.16259 - 3.74571i) q^{35} +10.6504 q^{37} +(0.162589 + 4.35587i) q^{38} +(2.16259 - 3.74571i) q^{40} +(-1.82386 + 3.15903i) q^{41} +(-0.436639 + 0.756280i) q^{43} +(1.17614 + 2.03713i) q^{44} +1.77445 q^{46} +(-2.91563 - 5.05002i) q^{47} +1.00000 q^{49} +13.7072 q^{50} +(0.400772 - 0.694158i) q^{52} +(0.563361 + 0.975771i) q^{53} +(-5.08700 + 8.81094i) q^{55} +1.00000 q^{56} -5.83126 q^{58} +(-7.10054 + 12.2985i) q^{59} +(1.36105 + 2.35740i) q^{61} +(2.56336 - 4.43987i) q^{62} +1.00000 q^{64} +3.46682 q^{65} +(-2.29022 - 3.96678i) q^{67} -6.22818 q^{68} +(2.16259 + 3.74571i) q^{70} +(7.00131 - 12.1266i) q^{71} +(4.61540 - 7.99411i) q^{73} +(-5.32518 + 9.22348i) q^{74} +(-3.85358 - 2.03713i) q^{76} -2.35227 q^{77} +(3.52363 - 6.10311i) q^{79} +(2.16259 + 3.74571i) q^{80} +(-1.82386 - 3.15903i) q^{82} -15.5560 q^{83} +(-13.4690 - 23.3290i) q^{85} +(-0.436639 - 0.756280i) q^{86} -2.35227 q^{88} +(3.64773 + 6.31805i) q^{89} +(0.400772 + 0.694158i) q^{91} +(-0.887226 + 1.53672i) q^{92} +5.83126 q^{94} +(-0.703228 - 18.8399i) q^{95} +(-1.52841 + 2.64728i) q^{97} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + q^{5} + 8 q^{7} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + q^5 + 8 * q^7 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + q^{5} + 8 q^{7} + 8 q^{8} + q^{10} - 14 q^{11} + 5 q^{13} - 4 q^{14} - 4 q^{16} + 2 q^{17} + 6 q^{19} - 2 q^{20} + 7 q^{22} + 5 q^{23} - 15 q^{25} - 10 q^{26} - 4 q^{28} + 4 q^{29} - 12 q^{31} - 4 q^{32} + 2 q^{34} + q^{35} + 20 q^{37} - 15 q^{38} + q^{40} - 17 q^{41} - 18 q^{43} + 7 q^{44} - 10 q^{46} - 4 q^{47} + 8 q^{49} + 30 q^{50} + 5 q^{52} - 10 q^{53} + 10 q^{55} + 8 q^{56} - 8 q^{58} - 20 q^{59} - 9 q^{61} + 6 q^{62} + 8 q^{64} + 6 q^{65} + 7 q^{67} - 4 q^{68} + q^{70} + 21 q^{71} - 21 q^{73} - 10 q^{74} + 9 q^{76} - 14 q^{77} - 8 q^{79} + q^{80} - 17 q^{82} + 24 q^{83} - 10 q^{85} - 18 q^{86} - 14 q^{88} + 34 q^{89} + 5 q^{91} + 5 q^{92} + 8 q^{94} - 31 q^{95} - 5 q^{97} - 4 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + q^5 + 8 * q^7 + 8 * q^8 + q^10 - 14 * q^11 + 5 * q^13 - 4 * q^14 - 4 * q^16 + 2 * q^17 + 6 * q^19 - 2 * q^20 + 7 * q^22 + 5 * q^23 - 15 * q^25 - 10 * q^26 - 4 * q^28 + 4 * q^29 - 12 * q^31 - 4 * q^32 + 2 * q^34 + q^35 + 20 * q^37 - 15 * q^38 + q^40 - 17 * q^41 - 18 * q^43 + 7 * q^44 - 10 * q^46 - 4 * q^47 + 8 * q^49 + 30 * q^50 + 5 * q^52 - 10 * q^53 + 10 * q^55 + 8 * q^56 - 8 * q^58 - 20 * q^59 - 9 * q^61 + 6 * q^62 + 8 * q^64 + 6 * q^65 + 7 * q^67 - 4 * q^68 + q^70 + 21 * q^71 - 21 * q^73 - 10 * q^74 + 9 * q^76 - 14 * q^77 - 8 * q^79 + q^80 - 17 * q^82 + 24 * q^83 - 10 * q^85 - 18 * q^86 - 14 * q^88 + 34 * q^89 + 5 * q^91 + 5 * q^92 + 8 * q^94 - 31 * q^95 - 5 * q^97 - 4 * q^98

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