LMFDB - Embedded newform 693.2.i.k.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(100,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("693.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 11 x^{10} - 4 x^{9} + 88 x^{8} - 32 x^{7} + 325 x^{6} - 154 x^{5} + 878 x^{4} - 246 x^{3} + \cdots + 441 $ x^12 + 11x^10 - 4x^9 + 88x^8 - 32x^7 + 325x^6 - 154x^5 + 878x^4 - 246x^3 + 793x^2 + 210x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.2
Root			$0.823543 + 1.42642i$ of defining polynomial
Character	$\chi$	$=$	693.100
Dual form			693.2.i.k.298.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.823543 + 1.42642i) q^{2} +(-0.356445 - 0.617380i) q^{4} +(0.143555 - 0.248645i) q^{5} +(-0.883533 - 2.49387i) q^{7} -2.11998 q^{8} +O(q^{10})$	\(q+(-0.823543 + 1.42642i) q^{2} +(-0.356445 - 0.617380i) q^{4} +(0.143555 - 0.248645i) q^{5} +(-0.883533 - 2.49387i) q^{7} -2.11998 q^{8} +(0.236448 + 0.409540i) q^{10} +(-0.500000 - 0.866025i) q^{11} +5.70645 q^{13} +(4.28492 + 0.793518i) q^{14} +(2.45878 - 4.25874i) q^{16} +(2.91322 + 5.04584i) q^{17} +(-1.03540 + 1.79337i) q^{19} -0.204678 q^{20} +1.64709 q^{22} +(-2.56509 + 4.44286i) q^{23} +(2.45878 + 4.25874i) q^{25} +(-4.69951 + 8.13978i) q^{26} +(-1.22473 + 1.43440i) q^{28} +7.56614 q^{29} +(0.168143 + 0.291233i) q^{31} +(1.92985 + 3.34259i) q^{32} -9.59663 q^{34} +(-0.746924 - 0.138322i) q^{35} +(5.48662 - 9.50310i) q^{37} +(-1.70540 - 2.95383i) q^{38} +(-0.304335 + 0.527123i) q^{40} +9.13223 q^{41} +6.28460 q^{43} +(-0.356445 + 0.617380i) q^{44} +(-4.22492 - 7.31777i) q^{46} +(-2.65723 + 4.60246i) q^{47} +(-5.43874 + 4.40683i) q^{49} -8.09965 q^{50} +(-2.03403 - 3.52305i) q^{52} +(-0.881033 - 1.52599i) q^{53} -0.287111 q^{55} +(1.87307 + 5.28695i) q^{56} +(-6.23104 + 10.7925i) q^{58} +(-5.56509 - 9.63901i) q^{59} +(-4.50031 + 7.79477i) q^{61} -0.553893 q^{62} +3.47790 q^{64} +(0.819192 - 1.41888i) q^{65} +(6.22661 + 10.7848i) q^{67} +(2.07680 - 3.59712i) q^{68} +(0.812428 - 0.951511i) q^{70} -13.4418 q^{71} +(-4.24351 - 7.34997i) q^{73} +(9.03693 + 15.6524i) q^{74} +1.47625 q^{76} +(-1.71799 + 2.01210i) q^{77} +(-6.04920 + 10.4775i) q^{79} +(-0.705943 - 1.22273i) q^{80} +(-7.52078 + 13.0264i) q^{82} +16.7071 q^{83} +1.67283 q^{85} +(-5.17564 + 8.96447i) q^{86} +(1.05999 + 1.83596i) q^{88} +(6.16182 - 10.6726i) q^{89} +(-5.04184 - 14.2311i) q^{91} +3.65725 q^{92} +(-4.37669 - 7.58065i) q^{94} +(0.297275 + 0.514896i) q^{95} -6.63046 q^{97} +(-1.80694 - 11.3871i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} - 4 q^{5} + 6 q^{7} - 12 q^{8}+O(q^{10}) $ 12 * q - 10 * q^4 - 4 * q^5 + 6 * q^7 - 12 * q^8	$ 12 q - 10 q^{4} - 4 q^{5} + 6 q^{7} - 12 q^{8} + 6 q^{10} - 6 q^{11} - 4 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{17} - 6 q^{19} + 72 q^{20} + 2 q^{23} - 2 q^{25} - 8 q^{26} - 28 q^{28} - 4 q^{29} - 4 q^{31} + 12 q^{32} + 28 q^{34} + 26 q^{35} + 6 q^{37} - 10 q^{38} + 18 q^{40} + 60 q^{41} - 24 q^{43} - 10 q^{44} + 4 q^{46} - 14 q^{47} - 12 q^{49} - 48 q^{50} + 22 q^{52} - 16 q^{53} + 8 q^{55} + 60 q^{56} - 2 q^{58} - 34 q^{59} + 2 q^{61} + 52 q^{62} + 4 q^{64} + 20 q^{65} + 20 q^{67} - 18 q^{68} - 24 q^{70} - 12 q^{71} - 26 q^{73} - 14 q^{74} - 8 q^{76} - 6 q^{77} - 2 q^{79} - 44 q^{80} + 4 q^{82} + 16 q^{83} + 20 q^{85} - 78 q^{86} + 6 q^{88} - 20 q^{89} + 20 q^{91} - 60 q^{92} + 10 q^{94} + 10 q^{95} - 28 q^{97} + 90 q^{98}+O(q^{100}) $ 12 * q - 10 * q^4 - 4 * q^5 + 6 * q^7 - 12 * q^8 + 6 * q^10 - 6 * q^11 - 4 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^17 - 6 * q^19 + 72 * q^20 + 2 * q^23 - 2 * q^25 - 8 * q^26 - 28 * q^28 - 4 * q^29 - 4 * q^31 + 12 * q^32 + 28 * q^34 + 26 * q^35 + 6 * q^37 - 10 * q^38 + 18 * q^40 + 60 * q^41 - 24 * q^43 - 10 * q^44 + 4 * q^46 - 14 * q^47 - 12 * q^49 - 48 * q^50 + 22 * q^52 - 16 * q^53 + 8 * q^55 + 60 * q^56 - 2 * q^58 - 34 * q^59 + 2 * q^61 + 52 * q^62 + 4 * q^64 + 20 * q^65 + 20 * q^67 - 18 * q^68 - 24 * q^70 - 12 * q^71 - 26 * q^73 - 14 * q^74 - 8 * q^76 - 6 * q^77 - 2 * q^79 - 44 * q^80 + 4 * q^82 + 16 * q^83 + 20 * q^85 - 78 * q^86 + 6 * q^88 - 20 * q^89 + 20 * q^91 - 60 * q^92 + 10 * q^94 + 10 * q^95 - 28 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.823543	+	1.42642i	−0.582333	+	1.00863i	0.412870	+	0.910790i	$0.364526\pi$
$2$	−0.823543	+	1.42642i	−0.582333	+	1.00863i	−0.995202	+	0.0978394i	$0.968807\pi$
$3$		0			0
$3$		0			0
$4$	−0.356445	−	0.617380i	−0.178222	−	0.308690i
$5$	0.143555	−	0.248645i	0.0641999	−	0.111198i	−0.832139	−	0.554567i	$-0.812884\pi$
$5$	0.143555	−	0.248645i	0.0641999	−	0.111198i	0.896339	+	0.443370i	$0.146217\pi$
$6$		0			0
$7$	−0.883533	−	2.49387i	−0.333944	−	0.942593i
$7$	−0.883533	−	2.49387i	−0.333944	−	0.942593i
$8$	−2.11998			−0.749526
$9$		0			0
$10$	0.236448	+	0.409540i	0.0747714	+	0.129508i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	5.70645			1.58269			0.791343	−	0.611373i	$-0.209382\pi$
$13$	5.70645			1.58269			0.791343	+	0.611373i	$0.209382\pi$
$14$	4.28492	+	0.793518i	1.14519	+	0.212077i
$15$		0			0
$16$	2.45878	−	4.25874i	0.614696	−	1.06468i
$17$	2.91322	+	5.04584i	0.706559	+	1.22380i	0.966126	+	0.258071i	$0.0830868\pi$
$17$	2.91322	+	5.04584i	0.706559	+	1.22380i	−0.259567	+	0.965725i	$0.583580\pi$
$18$		0			0
$19$	−1.03540	+	1.79337i	−0.237538	+	0.411427i	−0.960007	−	0.279976i	$-0.909674\pi$
$19$	−1.03540	+	1.79337i	−0.237538	+	0.411427i	0.722470	+	0.691403i	$0.243007\pi$
$20$	−0.204678			−0.0457674
$21$		0			0
$22$	1.64709			0.351160
$23$	−2.56509	+	4.44286i	−0.534857	+	0.926400i	0.464313	+	0.885671i	$0.346301\pi$
$23$	−2.56509	+	4.44286i	−0.534857	+	0.926400i	−0.999170	+	0.0407290i	$0.987032\pi$
$24$		0			0
$25$	2.45878	+	4.25874i	0.491757	+	0.851748i
$26$	−4.69951	+	8.13978i	−0.921649	+	1.59634i
$27$		0			0
$28$	−1.22473	+	1.43440i	−0.231453	+	0.271076i
$29$	7.56614			1.40500			0.702499	−	0.711685i	$-0.252068\pi$
$29$	7.56614			1.40500			0.702499	+	0.711685i	$0.252068\pi$
$30$		0			0
$31$	0.168143	+	0.291233i	0.0301994	+	0.0523069i	0.880730	−	0.473618i	$-0.157052\pi$
$31$	0.168143	+	0.291233i	0.0301994	+	0.0523069i	−0.850531	+	0.525925i	$0.823719\pi$
$32$	1.92985	+	3.34259i	0.341152	+	0.590892i
$33$		0			0
$34$	−9.59663			−1.64581
$35$	−0.746924	−	0.138322i	−0.126253	−	0.0233806i
$36$		0			0
$37$	5.48662	−	9.50310i	0.901994	−	1.56230i	0.0770925	−	0.997024i	$-0.475436\pi$
$37$	5.48662	−	9.50310i	0.901994	−	1.56230i	0.824902	−	0.565276i	$-0.191230\pi$
$38$	−1.70540	−	2.95383i	−0.276652	−	0.479175i
$39$		0			0
$40$	−0.304335	+	0.527123i	−0.0481195	+	0.0833455i
$41$	9.13223			1.42621			0.713107	−	0.701055i	$-0.247287\pi$
$41$	9.13223			1.42621			0.713107	+	0.701055i	$0.247287\pi$
$42$		0			0
$43$	6.28460			0.958393			0.479196	−	0.877708i	$-0.340928\pi$
$43$	6.28460			0.958393			0.479196	+	0.877708i	$0.340928\pi$
$44$	−0.356445	+	0.617380i	−0.0537361	+	0.0930736i
$45$		0			0
$46$	−4.22492	−	7.31777i	−0.622930	−	1.07895i
$47$	−2.65723	+	4.60246i	−0.387597	+	0.671338i	−0.992126	−	0.125245i	$-0.960028\pi$
$47$	−2.65723	+	4.60246i	−0.387597	+	0.671338i	0.604528	+	0.796584i	$0.293362\pi$
$48$		0			0
$49$	−5.43874	+	4.40683i	−0.776963	+	0.629547i
$50$	−8.09965			−1.14546
$51$		0			0
$52$	−2.03403	−	3.52305i	−0.282070	−	0.488559i
$53$	−0.881033	−	1.52599i	−0.121019	−	0.209611i	0.799151	−	0.601131i	$-0.205283\pi$
$53$	−0.881033	−	1.52599i	−0.121019	−	0.209611i	−0.920170	+	0.391519i	$0.871950\pi$
$54$		0			0
$55$	−0.287111			−0.0387140
$56$	1.87307	+	5.28695i	0.250300	+	0.706498i
$57$		0			0
$58$	−6.23104	+	10.7925i	−0.818176	+	1.41712i
$59$	−5.56509	−	9.63901i	−0.724513	−	1.25489i	−0.959174	−	0.282815i	$-0.908732\pi$
$59$	−5.56509	−	9.63901i	−0.724513	−	1.25489i	0.234662	−	0.972077i	$-0.424602\pi$
$60$		0			0
$61$	−4.50031	+	7.79477i	−0.576206	+	0.998018i	0.419704	+	0.907661i	$0.362134\pi$
$61$	−4.50031	+	7.79477i	−0.576206	+	0.998018i	−0.995909	+	0.0903566i	$0.971199\pi$
$62$	−0.553893			−0.0703444
$63$		0			0
$64$	3.47790			0.434737
$65$	0.819192	−	1.41888i	0.101608	−	0.175991i
$66$		0			0
$67$	6.22661	+	10.7848i	0.760702	+	1.31757i	0.942489	+	0.334236i	$0.108478\pi$
$67$	6.22661	+	10.7848i	0.760702	+	1.31757i	−0.181788	+	0.983338i	$0.558188\pi$
$68$	2.07680	−	3.59712i	0.251849	−	0.436215i
$69$		0			0
$70$	0.812428	−	0.951511i	0.0971037	−	0.113727i
$71$	−13.4418			−1.59525			−0.797623	−	0.603156i	$-0.793910\pi$
$71$	−13.4418			−1.59525			−0.797623	+	0.603156i	$0.793910\pi$
$72$		0			0
$73$	−4.24351	−	7.34997i	−0.496665	−	0.860249i	0.503328	−	0.864096i	$-0.332109\pi$
$73$	−4.24351	−	7.34997i	−0.496665	−	0.860249i	−0.999993	+	0.00384669i	$0.998776\pi$
$74$	9.03693	+	15.6524i	1.05052	+	1.81956i
$75$		0			0
$76$	1.47625			0.169338
$77$	−1.71799	+	2.01210i	−0.195783	+	0.229300i
$78$		0			0
$79$	−6.04920	+	10.4775i	−0.680589	+	1.17881i	0.294213	+	0.955740i	$0.404942\pi$
$79$	−6.04920	+	10.4775i	−0.680589	+	1.17881i	−0.974802	+	0.223074i	$0.928391\pi$
$80$	−0.705943	−	1.22273i	−0.0789268	−	0.136705i
$81$		0			0
$82$	−7.52078	+	13.0264i	−0.830531	+	1.43852i
$83$	16.7071			1.83384			0.916920	−	0.399071i	$-0.130667\pi$
$83$	16.7071			1.83384			0.916920	+	0.399071i	$0.130667\pi$
$84$		0			0
$85$	1.67283			0.181444
$86$	−5.17564	+	8.96447i	−0.558103	+	0.966663i
$87$		0			0
$88$	1.05999	+	1.83596i	0.112995	+	0.195714i
$89$	6.16182	−	10.6726i	0.653152	−	1.13129i	−0.329202	−	0.944259i	$-0.606780\pi$
$89$	6.16182	−	10.6726i	0.653152	−	1.13129i	0.982354	−	0.187032i	$-0.0598869\pi$
$90$		0			0
$91$	−5.04184	−	14.2311i	−0.528528	−	1.49183i
$92$	3.65725			0.381294
$93$		0			0
$94$	−4.37669	−	7.58065i	−0.451421	−	0.781884i
$95$	0.297275	+	0.514896i	0.0304998	+	0.0528272i
$96$		0			0
$97$	−6.63046			−0.673221			−0.336610	−	0.941644i	$-0.609281\pi$
$97$	−6.63046			−0.673221			−0.336610	+	0.941644i	$0.609281\pi$
$98$	−1.80694	−	11.3871i	−0.182529	−	1.15027i
$99$		0			0
$100$	1.75284	−	3.03601i	0.175284	−	0.303601i
$101$	−7.31679	−	12.6731i	−0.728048	−	1.26102i	−0.957707	−	0.287745i	$-0.907094\pi$
$101$	−7.31679	−	12.6731i	−0.728048	−	1.26102i	0.229659	−	0.973271i	$-0.426239\pi$
$102$		0			0
$103$	−1.52281	+	2.63759i	−0.150047	+	0.259889i	−0.931245	−	0.364395i	$-0.881276\pi$
$103$	−1.52281	+	2.63759i	−0.150047	+	0.259889i	0.781197	+	0.624284i	$0.214609\pi$
$104$	−12.0976			−1.18626
$105$		0			0
$106$	2.90227			0.281893
$107$	3.94996	−	6.84153i	0.381857	−	0.661396i	−0.609471	−	0.792809i	$-0.708618\pi$
$107$	3.94996	−	6.84153i	0.381857	−	0.661396i	0.991328	+	0.131413i	$0.0419513\pi$
$108$		0			0
$109$	3.83141	+	6.63619i	0.366982	+	0.635632i	0.989092	−	0.147298i	$-0.0470576\pi$
$109$	3.83141	+	6.63619i	0.366982	+	0.635632i	−0.622110	+	0.782930i	$0.713724\pi$
$110$	0.236448	−	0.409540i	0.0225444	−	0.0390481i
$111$		0			0
$112$	−12.7931	−	2.36914i	−1.20884	−	0.223863i
$113$	12.8407			1.20795			0.603976	−	0.797002i	$-0.293582\pi$
$113$	12.8407			1.20795			0.603976	+	0.797002i	$0.293582\pi$
$114$		0			0
$115$	0.736464	+	1.27559i	0.0686756	+	0.118950i
$116$	−2.69691	−	4.67119i	−0.250402	−	0.433709i
$117$		0			0
$118$	18.3323			1.68763
$119$	10.0097	−	11.7233i	0.917590	−	1.07468i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−7.41240	−	12.8386i	−0.671087	−	1.16236i
$123$		0			0
$124$	0.119868	−	0.207617i	0.0107644	−	0.0186445i
$125$	2.84744			0.254683
$126$		0			0
$127$	3.89146			0.345311			0.172655	−	0.984982i	$-0.444765\pi$
$127$	3.89146			0.345311			0.172655	+	0.984982i	$0.444765\pi$
$128$	−6.72389	+	11.6461i	−0.594313	+	1.02938i
$129$		0			0
$130$	1.34928	+	2.33702i	0.118340	+	0.204970i
$131$	−4.31244	+	7.46937i	−0.376780	+	0.652602i	−0.990592	−	0.136850i	$-0.956302\pi$
$131$	−4.31244	+	7.46937i	−0.376780	+	0.652602i	0.613812	+	0.789452i	$0.289635\pi$
$132$		0			0
$133$	5.38724	+	0.997654i	0.467133	+	0.0865076i
$134$	−20.5115			−1.77193
$135$		0			0
$136$	−6.17596	−	10.6971i	−0.529585	−	0.917267i
$137$	−4.25109	−	7.36310i	−0.363195	−	0.629072i	0.625290	−	0.780392i	$-0.284981\pi$
$137$	−4.25109	−	7.36310i	−0.363195	−	0.629072i	−0.988485	+	0.151321i	$0.951647\pi$
$138$		0			0
$139$	12.4772			1.05830			0.529151	−	0.848528i	$-0.322511\pi$
$139$	12.4772			1.05830			0.529151	+	0.848528i	$0.322511\pi$
$140$	0.180840	+	0.510440i	0.0152838	+	0.0431401i
$141$		0			0
$142$	11.0699	−	19.1736i	0.928964	−	1.60901i
$143$	−2.85323	−	4.94193i	−0.238599	−	0.413265i
$144$		0			0
$145$	1.08616	−	1.88128i	0.0902007	−	0.156232i
$146$	13.9788			1.15690
$147$		0			0
$148$	−7.82270			−0.643022
$149$	−1.01097	+	1.75105i	−0.0828219	+	0.143452i	−0.904461	−	0.426556i	$-0.859727\pi$
$149$	−1.01097	+	1.75105i	−0.0828219	+	0.143452i	0.821639	+	0.570008i	$0.193060\pi$
$150$		0			0
$151$	−1.45785	−	2.52507i	−0.118638	−	0.205487i	0.800590	−	0.599212i	$-0.204520\pi$
$151$	−1.45785	−	2.52507i	−0.118638	−	0.205487i	−0.919228	+	0.393725i	$0.871186\pi$
$152$	2.19503	−	3.80191i	0.178041	−	0.308376i
$153$		0			0
$154$	−1.45525	−	4.10761i	−0.117268	−	0.331001i
$155$	0.0965515			0.00775520
$156$		0			0
$157$	2.15022	+	3.72429i	0.171606	+	0.297230i	0.938981	−	0.343968i	$-0.111771\pi$
$157$	2.15022	+	3.72429i	0.171606	+	0.297230i	−0.767375	+	0.641198i	$0.778438\pi$
$158$	−9.96355	−	17.2574i	−0.792658	−	1.37292i
$159$		0			0
$160$	1.10816			0.0876076
$161$	13.3462	+	2.47157i	1.05183	+	0.194787i
$162$		0			0
$163$	3.15581	−	5.46602i	0.247182	−	0.428131i	−0.715561	−	0.698550i	$-0.753829\pi$
$163$	3.15581	−	5.46602i	0.247182	−	0.428131i	0.962743	+	0.270419i	$0.0871622\pi$
$164$	−3.25513	−	5.63806i	−0.254183	−	0.440258i
$165$		0			0
$166$	−13.7590	+	23.8313i	−1.06790	+	1.84966i
$167$	−0.928817			−0.0718740			−0.0359370	−	0.999354i	$-0.511442\pi$
$167$	−0.928817			−0.0718740			−0.0359370	+	0.999354i	$0.511442\pi$
$168$		0			0
$169$	19.5636			1.50489
$170$	−1.37765	+	2.38616i	−0.105661	+	0.183010i
$171$		0			0
$172$	−2.24011	−	3.87999i	−0.170807	−	0.295846i
$173$	0.775802	−	1.34373i	0.0589832	−	0.102162i	−0.835026	−	0.550210i	$-0.814548\pi$
$173$	0.775802	−	1.34373i	0.0589832	−	0.102162i	0.894009	+	0.448049i	$0.147881\pi$
$174$		0			0
$175$	8.44831	−	9.89461i	0.638632	−	0.747962i
$176$	−4.91757			−0.370676
$177$		0			0
$178$	10.1490	+	17.5787i	0.760703	+	1.31758i
$179$	−1.11689	−	1.93451i	−0.0834804	−	0.144592i	0.821262	−	0.570551i	$-0.193270\pi$
$179$	−1.11689	−	1.93451i	−0.0834804	−	0.144592i	−0.904743	+	0.425959i	$0.859937\pi$
$180$		0			0
$181$	−25.8823			−1.92381			−0.961907	−	0.273377i	$-0.911859\pi$
$181$	−25.8823			−1.92381			−0.961907	+	0.273377i	$0.911859\pi$
$182$	24.4517	+	4.52817i	1.81248	+	0.335651i
$183$		0			0
$184$	5.43793	−	9.41878i	0.400890	−	0.694362i
$185$	−1.57527	−	2.72844i	−0.115816	−	0.200599i
$186$		0			0
$187$	2.91322	−	5.04584i	0.213036	−	0.368988i
$188$	3.78863			0.276314
$189$		0			0
$190$	−0.979275			−0.0710441
$191$	−2.52710	+	4.37707i	−0.182855	+	0.316714i	−0.942852	−	0.333213i	$-0.891867\pi$
$191$	−2.52710	+	4.37707i	−0.182855	+	0.316714i	0.759997	+	0.649927i	$0.225201\pi$
$192$		0			0
$193$	0.167130	+	0.289477i	0.0120303	+	0.0208370i	0.871978	−	0.489545i	$-0.162837\pi$
$193$	0.167130	+	0.289477i	0.0120303	+	0.0208370i	−0.859948	+	0.510382i	$0.829504\pi$
$194$	5.46046	−	9.45780i	0.392038	−	0.679030i
$195$		0			0
$196$	4.65930	+	1.78698i	0.332807	+	0.127641i
$197$	−2.20719			−0.157256			−0.0786278	−	0.996904i	$-0.525054\pi$
$197$	−2.20719			−0.157256			−0.0786278	+	0.996904i	$0.525054\pi$
$198$		0			0
$199$	−10.3750	−	17.9700i	−0.735464	−	1.27386i	−0.954520	−	0.298148i	$-0.903631\pi$
$199$	−10.3750	−	17.9700i	−0.735464	−	1.27386i	0.219056	−	0.975712i	$-0.429702\pi$
$200$	−5.21257	−	9.02844i	−0.368585	−	0.638407i
$201$		0			0
$202$	24.1028			1.69586
$203$	−6.68494	−	18.8689i	−0.469191	−	1.32434i
$204$		0			0
$205$	1.31098	−	2.27069i	0.0915629	−	0.158592i
$206$	−2.50820	−	4.34434i	−0.174755	−	0.302684i
$207$		0			0
$208$	14.0309	−	24.3023i	0.972870	−	1.68506i
$209$	2.07081			0.143241
$210$		0			0
$211$	7.24058			0.498462			0.249231	−	0.968444i	$-0.419822\pi$
$211$	7.24058			0.498462			0.249231	+	0.968444i	$0.419822\pi$
$212$	−0.628079	+	1.08786i	−0.0431366	+	0.0747148i
$213$		0			0
$214$	6.50592	+	11.2686i	0.444736	+	0.770305i
$215$	0.902188	−	1.56264i	0.0615287	−	0.106571i
$216$		0			0
$217$	0.577735	−	0.676641i	0.0392192	−	0.0459334i
$218$	−12.6213			−0.854823
$219$		0			0
$220$	0.102339	+	0.177256i	0.00689970	+	0.0119506i
$221$	16.6241	+	28.7938i	1.11826	+	1.93688i
$222$		0			0
$223$	−6.88099			−0.460785			−0.230393	−	0.973098i	$-0.574001\pi$
$223$	−6.88099			−0.460785			−0.230393	+	0.973098i	$0.574001\pi$
$224$	6.63089	−	7.76606i	0.443045	−	0.518892i
$225$		0			0
$226$	−10.5749	+	18.3162i	−0.703430	+	1.21838i
$227$	−0.501176	−	0.868062i	−0.0332642	−	0.0576153i	0.848914	−	0.528531i	$-0.177257\pi$
$227$	−0.501176	−	0.868062i	−0.0332642	−	0.0576153i	−0.882178	+	0.470916i	$0.843924\pi$
$228$		0			0
$229$	2.14254	−	3.71099i	0.141583	−	0.245229i	−0.786510	−	0.617578i	$-0.788114\pi$
$229$	2.14254	−	3.71099i	0.141583	−	0.245229i	0.928093	+	0.372349i	$0.121447\pi$
$230$	−2.42604			−0.159968
$231$		0			0
$232$	−16.0401			−1.05308
$233$	−3.45859	+	5.99046i	−0.226580	+	0.392448i	−0.956792	−	0.290772i	$-0.906088\pi$
$233$	−3.45859	+	5.99046i	−0.226580	+	0.392448i	0.730212	+	0.683220i	$0.239421\pi$
$234$		0			0
$235$	0.762920	+	1.32142i	0.0497674	+	0.0861997i
$236$	−3.96729	+	6.87155i	−0.258249	+	0.447300i
$237$		0			0
$238$	8.47894	+	23.9327i	0.549608	+	1.55133i
$239$	18.3080			1.18425			0.592124	−	0.805847i	$-0.298290\pi$
$239$	18.3080			1.18425			0.592124	+	0.805847i	$0.298290\pi$
$240$		0			0
$241$	−3.88169	−	6.72329i	−0.250042	−	0.433085i	0.713495	−	0.700660i	$-0.247111\pi$
$241$	−3.88169	−	6.72329i	−0.250042	−	0.433085i	−0.963537	+	0.267575i	$0.913778\pi$
$242$	−0.823543	−	1.42642i	−0.0529393	−	0.0916936i
$243$		0			0
$244$	6.41645			0.410771
$245$	0.314976	+	1.98494i	0.0201231	+	0.126813i
$246$		0			0
$247$	−5.90848	+	10.2338i	−0.375947	+	0.651160i
$248$	−0.356461	−	0.617408i	−0.0226353	−	0.0392054i
$249$		0			0
$250$	−2.34499	+	4.06164i	−0.148310	+	0.256881i
$251$	−22.6066			−1.42692			−0.713458	−	0.700698i	$-0.752872\pi$
$251$	−22.6066			−1.42692			−0.713458	+	0.700698i	$0.752872\pi$
$252$		0			0
$253$	5.13017			0.322531
$254$	−3.20478	+	5.55084i	−0.201086	+	0.348291i
$255$		0			0
$256$	−7.59692	−	13.1582i	−0.474807	−	0.822390i
$257$	−2.57905	+	4.46704i	−0.160877	+	0.278647i	−0.935183	−	0.354164i	$-0.884765\pi$
$257$	−2.57905	+	4.46704i	−0.160877	+	0.278647i	0.774307	+	0.632811i	$0.218099\pi$
$258$		0			0
$259$	−28.5471	−	5.28659i	−1.77383	−	0.328493i
$260$	−1.16799			−0.0724354
$261$		0			0
$262$	−7.10296	−	12.3027i	−0.438822	−	0.760063i
$263$	8.88413	+	15.3878i	0.547819	+	0.948850i	0.998424	+	0.0561265i	$0.0178750\pi$
$263$	8.88413	+	15.3878i	0.547819	+	0.948850i	−0.450605	+	0.892724i	$0.648792\pi$
$264$		0			0
$265$	−0.505908			−0.0310777
$266$	−5.85969	+	6.86284i	−0.359281	+	0.420788i
$267$		0			0
$268$	4.43888	−	7.68837i	0.271148	−	0.469642i
$269$	−13.6614	−	23.6623i	−0.832952	−	1.44271i	−0.895687	−	0.444684i	$-0.853316\pi$
$269$	−13.6614	−	23.6623i	−0.832952	−	1.44271i	0.0627357	−	0.998030i	$-0.480017\pi$
$270$		0			0
$271$	−1.80924	+	3.13370i	−0.109904	+	0.190359i	−0.915731	−	0.401792i	$-0.868388\pi$
$271$	−1.80924	+	3.13370i	−0.109904	+	0.190359i	0.805827	+	0.592150i	$0.201721\pi$
$272$	28.6519			1.73728
$273$		0			0
$274$	14.0038			0.846000
$275$	2.45878	−	4.25874i	0.148270	−	0.256812i
$276$		0			0
$277$	−4.76001	−	8.24457i	−0.286001	−	0.495368i	0.686850	−	0.726799i	$-0.258993\pi$
$277$	−4.76001	−	8.24457i	−0.286001	−	0.495368i	−0.972851	+	0.231430i	$0.925659\pi$
$278$	−10.2755	+	17.7977i	−0.616283	+	1.06743i
$279$		0			0
$280$	1.58346	+	0.293239i	0.0946301	+	0.0175244i
$281$	4.45138			0.265547			0.132774	−	0.991146i	$-0.457612\pi$
$281$	4.45138			0.265547			0.132774	+	0.991146i	$0.457612\pi$
$282$		0			0
$283$	7.52767	+	13.0383i	0.447473	+	0.775047i	0.998221	−	0.0596253i	$-0.0189906\pi$
$283$	7.52767	+	13.0383i	0.447473	+	0.775047i	−0.550747	+	0.834672i	$0.685657\pi$
$284$	4.79125	+	8.29869i	0.284308	+	0.492437i
$285$		0			0
$286$	9.39901			0.555775
$287$	−8.06863	−	22.7746i	−0.476276	−	1.34434i
$288$		0			0
$289$	−8.47366	+	14.6768i	−0.498451	+	0.863342i
$290$	1.78900	+	3.09864i	0.105054	+	0.181958i
$291$		0			0
$292$	−3.02515	+	5.23972i	−0.177034	+	0.306631i
$293$	5.53879			0.323579			0.161790	−	0.986825i	$-0.448273\pi$
$293$	5.53879			0.323579			0.161790	+	0.986825i	$0.448273\pi$
$294$		0			0
$295$	−3.19559			−0.186055
$296$	−11.6315	+	20.1464i	−0.676069	+	1.17099i
$297$		0			0
$298$	−1.66515	−	2.88413i	−0.0964597	−	0.167073i
$299$	−14.6375	+	25.3530i	−0.846511	+	1.46620i
$300$		0			0
$301$	−5.55265	−	15.6730i	−0.320050	−	0.903374i
$302$	4.80240			0.276347
$303$		0			0
$304$	5.09166	+	8.81902i	0.292027	+	0.505805i
$305$	1.29209	+	2.23796i	0.0739847	+	0.128145i
$306$		0			0
$307$	−12.1723			−0.694711			−0.347356	−	0.937734i	$-0.612920\pi$
$307$	−12.1723			−0.694711			−0.347356	+	0.937734i	$0.612920\pi$
$308$	1.85459	+	0.343450i	0.105675	+	0.0195699i
$309$		0			0
$310$	−0.0795142	+	0.137723i	−0.00451611	+	0.00782212i
$311$	−5.18222	−	8.97587i	−0.293857	−	0.508975i	0.680862	−	0.732412i	$-0.261606\pi$
$311$	−5.18222	−	8.97587i	−0.293857	−	0.508975i	−0.974718	+	0.223437i	$0.928272\pi$
$312$		0			0
$313$	−0.454260	+	0.786801i	−0.0256763	+	0.0444726i	−0.878578	−	0.477599i	$-0.841507\pi$
$313$	−0.454260	+	0.786801i	−0.0256763	+	0.0444726i	0.852902	+	0.522071i	$0.174841\pi$
$314$	−7.08318			−0.399727
$315$		0			0
$316$	8.62482			0.485184
$317$	0.117099	−	0.202821i	0.00657693	−	0.0113916i	−0.862718	−	0.505685i	$-0.831240\pi$
$317$	0.117099	−	0.202821i	0.00657693	−	0.0113916i	0.869295	+	0.494293i	$0.164573\pi$
$318$		0			0
$319$	−3.78307	−	6.55247i	−0.211811	−	0.366868i
$320$	0.499271	−	0.864762i	0.0279101	−	0.0483417i
$321$		0			0
$322$	−14.5167	+	17.0019i	−0.808983	+	0.947477i
$323$	−12.0654			−0.671337
$324$		0			0
$325$	14.0309	+	24.3023i	0.778296	+	1.34805i
$326$	5.19788	+	9.00299i	0.287884	+	0.498630i
$327$		0			0
$328$	−19.3602			−1.06899
$329$	13.8257	+	2.56036i	0.762235	+	0.141157i
$330$		0			0
$331$	−5.99249	+	10.3793i	−0.329377	+	0.570498i	−0.982388	−	0.186850i	$-0.940172\pi$
$331$	−5.99249	+	10.3793i	−0.329377	+	0.570498i	0.653011	+	0.757348i	$0.273505\pi$
$332$	−5.95515	−	10.3146i	−0.326831	−	0.566088i
$333$		0			0
$334$	0.764920	−	1.32488i	0.0418546	−	0.0724942i
$335$	3.57545			0.195348
$336$		0			0
$337$	−34.6332			−1.88659			−0.943294	−	0.331958i	$-0.892291\pi$
$337$	−34.6332			−1.88659			−0.943294	+	0.331958i	$0.892291\pi$
$338$	−16.1115	+	27.9059i	−0.876348	+	1.51788i
$339$		0			0
$340$	−0.596272	−	1.03277i	−0.0323374	−	0.0560100i
$341$	0.168143	−	0.291233i	0.00910547	−	0.0157711i
$342$		0			0
$343$	15.7953	+	9.66991i	0.852868	+	0.522126i
$344$	−13.3232			−0.718341
$345$		0			0
$346$	1.27781	+	2.21324i	0.0686956	+	0.118984i
$347$	5.69424	+	9.86271i	0.305683	+	0.529458i	0.977413	−	0.211338i	$-0.0677820\pi$
$347$	5.69424	+	9.86271i	0.305683	+	0.529458i	−0.671730	+	0.740796i	$0.734449\pi$
$348$		0			0
$349$	−19.6396			−1.05128			−0.525641	−	0.850706i	$-0.676175\pi$
$349$	−19.6396			−1.05128			−0.525641	+	0.850706i	$0.676175\pi$
$350$	7.15631	+	20.1994i	0.382521	+	1.07971i
$351$		0			0
$352$	1.92985	−	3.34259i	0.102861	−	0.178161i
$353$	11.4613	+	19.8515i	0.610023	+	1.05659i	0.991236	+	0.132104i	$0.0421732\pi$
$353$	11.4613	+	19.8515i	0.610023	+	1.05659i	−0.381213	+	0.924487i	$0.624493\pi$
$354$		0			0
$355$	−1.92964	+	3.34223i	−0.102415	+	0.177387i
$356$	−8.78539			−0.465625
$357$		0			0
$358$	3.67923			0.194453
$359$	3.33837	−	5.78223i	0.176193	−	0.305174i	−0.764381	−	0.644765i	$-0.776955\pi$
$359$	3.33837	−	5.78223i	0.176193	−	0.305174i	0.940573	+	0.339591i	$0.110289\pi$
$360$		0			0
$361$	7.35588	+	12.7408i	0.387152	+	0.670566i
$362$	21.3152	−	36.9189i	1.12030	−	1.94042i
$363$		0			0
$364$	−6.98888	+	8.18534i	−0.366317	+	0.429028i
$365$	−2.43671			−0.127543
$366$		0			0
$367$	7.76780	+	13.4542i	0.405476	+	0.702305i	0.994377	−	0.105900i	$-0.0337725\pi$
$367$	7.76780	+	13.4542i	0.405476	+	0.702305i	−0.588901	+	0.808205i	$0.700439\pi$
$368$	12.6140	+	21.8481i	0.657549	+	1.13891i
$369$		0			0
$370$	5.18920			0.269773
$371$	−3.02720	+	3.54544i	−0.157164	+	0.184070i
$372$		0			0
$373$	8.78802	−	15.2213i	0.455026	−	0.788129i	−0.543663	−	0.839303i	$-0.682963\pi$
$373$	8.78802	−	15.2213i	0.455026	−	0.788129i	0.998690	+	0.0511745i	$0.0162965\pi$
$374$	4.79832	+	8.31093i	0.248115	+	0.429748i
$375$		0			0
$376$	5.63328	−	9.75713i	0.290514	−	0.503186i
$377$	43.1758			2.22367
$378$		0			0
$379$	−20.2906			−1.04226			−0.521129	−	0.853478i	$-0.674489\pi$
$379$	−20.2906			−1.04226			−0.521129	+	0.853478i	$0.674489\pi$
$380$	0.211924	−	0.367064i	0.0108715	−	0.0188300i
$381$		0			0
$382$	−4.16236	−	7.20941i	−0.212965	−	0.368866i
$383$	8.58601	−	14.8714i	0.438724	−	0.759893i	−0.558867	−	0.829257i	$-0.688764\pi$
$383$	8.58601	−	14.8714i	0.438724	−	0.759893i	0.997591	+	0.0693643i	$0.0220971\pi$
$384$		0			0
$385$	0.253672	+	0.716016i	0.0129283	+	0.0364915i
$386$	−0.550554			−0.0280225
$387$		0			0
$388$	2.36339	+	4.09351i	0.119983	+	0.207817i
$389$	15.4713	+	26.7971i	0.784428	+	1.35867i	0.929340	+	0.369225i	$0.120377\pi$
$389$	15.4713	+	26.7971i	0.784428	+	1.35867i	−0.144912	+	0.989445i	$0.546290\pi$
$390$		0			0
$391$	−29.8906			−1.51163
$392$	11.5300	−	9.34239i	0.582354	−	0.471862i
$393$		0			0
$394$	1.81771	−	3.14837i	0.0915751	−	0.158613i
$395$	1.73679	+	3.00821i	0.0873874	+	0.151359i
$396$		0			0
$397$	−0.597338	+	1.03462i	−0.0299795	+	0.0519261i	−0.880626	−	0.473812i	$-0.842878\pi$
$397$	−0.597338	+	1.03462i	−0.0299795	+	0.0519261i	0.850646	+	0.525738i	$0.176211\pi$
$398$	34.1770			1.71314
$399$		0			0
$400$	24.1825			1.20912
$401$	−15.2026	+	26.3317i	−0.759182	+	1.31494i	0.184086	+	0.982910i	$0.441068\pi$
$401$	−15.2026	+	26.3317i	−0.759182	+	1.31494i	−0.943268	+	0.332032i	$0.892266\pi$
$402$		0			0
$403$	0.959502	+	1.66191i	0.0477962	+	0.0827854i
$404$	−5.21606	+	9.03449i	−0.259509	+	0.449483i
$405$		0			0
$406$	32.4203	+	6.00387i	1.60899	+	0.297967i
$407$	−10.9732			−0.543923
$408$		0			0
$409$	−8.64935	−	14.9811i	−0.427683	−	0.740769i	0.568984	−	0.822349i	$-0.307337\pi$
$409$	−8.64935	−	14.9811i	−0.427683	−	0.740769i	−0.996667	+	0.0815801i	$0.974003\pi$
$410$	2.15930	+	3.74001i	0.106640	+	0.184706i
$411$		0			0
$412$	2.17119			0.106967
$413$	−19.1215	+	22.3950i	−0.940906	+	1.10198i
$414$		0			0
$415$	2.39839	−	4.15413i	0.117732	−	0.203918i
$416$	11.0126	+	19.0743i	0.539936	+	0.935196i
$417$		0			0
$418$	−1.70540	+	2.95383i	−0.0834136	+	0.144477i
$419$	−27.8445			−1.36029			−0.680146	−	0.733076i	$-0.738084\pi$
$419$	−27.8445			−1.36029			−0.680146	+	0.733076i	$0.738084\pi$
$420$		0			0
$421$	−22.1149			−1.07782			−0.538908	−	0.842364i	$-0.681163\pi$
$421$	−22.1149			−1.07782			−0.538908	+	0.842364i	$0.681163\pi$
$422$	−5.96293	+	10.3281i	−0.290271	+	0.502764i
$423$		0			0
$424$	1.86777	+	3.23508i	0.0907070	+	0.157109i
$425$	−14.3259	+	24.8133i	−0.694910	+	1.20362i
$426$		0			0
$427$	23.4153	+	4.33624i	1.13314	+	0.209845i
$428$	−5.63177			−0.272222
$429$		0			0
$430$	1.48598	+	2.57379i	0.0716604	+	0.124119i
$431$	−17.5620	−	30.4182i	−0.845930	−	1.46519i	−0.884811	−	0.465949i	$-0.845713\pi$
$431$	−17.5620	−	30.4182i	−0.845930	−	1.46519i	0.0388817	−	0.999244i	$-0.487620\pi$
$432$		0			0
$433$	23.7336			1.14056			0.570282	−	0.821449i	$-0.306834\pi$
$433$	23.7336			1.14056			0.570282	+	0.821449i	$0.306834\pi$
$434$	0.489382	+	1.38133i	0.0234911	+	0.0663062i
$435$		0			0
$436$	2.73137	−	4.73087i	0.130809	−	0.226568i
$437$	−5.31179	−	9.20030i	−0.254098	−	0.440110i
$438$		0			0
$439$	16.1392	−	27.9540i	0.770283	−	1.33417i	−0.167125	−	0.985936i	$-0.553448\pi$
$439$	16.1392	−	27.9540i	0.770283	−	1.33417i	0.937408	−	0.348234i	$-0.113218\pi$
$440$	0.608669			0.0290172
$441$		0			0
$442$	−54.7627			−2.60480
$443$	6.19992	−	10.7386i	0.294567	−	0.510205i	−0.680317	−	0.732918i	$-0.738158\pi$
$443$	6.19992	−	10.7386i	0.294567	−	0.510205i	0.974884	+	0.222713i	$0.0714912\pi$
$444$		0			0
$445$	−1.76912	−	3.06421i	−0.0838645	−	0.145258i
$446$	5.66679	−	9.81516i	0.268330	−	0.464761i
$447$		0			0
$448$	−3.07284	−	8.67341i	−0.145178	−	0.409780i
$449$	10.8346			0.511315			0.255657	−	0.966767i	$-0.417708\pi$
$449$	10.8346			0.511315			0.255657	+	0.966767i	$0.417708\pi$
$450$		0			0
$451$	−4.56612	−	7.90874i	−0.215010	−	0.372408i
$452$	−4.57700	−	7.92760i	−0.215284	−	0.372883i
$453$		0			0
$454$	1.65096			0.0774833
$455$	−4.26228	−	0.789326i	−0.199819	−	0.0370042i
$456$		0			0
$457$	5.10836	−	8.84794i	0.238959	−	0.413889i	−0.721457	−	0.692459i	$-0.756527\pi$
$457$	5.10836	−	8.84794i	0.238959	−	0.413889i	0.960416	+	0.278570i	$0.0898605\pi$
$458$	3.52895	+	6.11232i	0.164897	+	0.285610i
$459$		0			0
$460$	0.525017	−	0.909356i	0.0244790	−	0.0423990i
$461$	−15.8924			−0.740183			−0.370091	−	0.928995i	$-0.620674\pi$
$461$	−15.8924			−0.740183			−0.370091	+	0.928995i	$0.620674\pi$
$462$		0			0
$463$	5.16509			0.240042			0.120021	−	0.992771i	$-0.461704\pi$
$463$	5.16509			0.240042			0.120021	+	0.992771i	$0.461704\pi$
$464$	18.6035	−	32.2222i	0.863646	−	1.49588i
$465$		0			0
$466$	−5.69660	−	9.86680i	−0.263890	−	0.457071i
$467$	0.400757	−	0.694131i	0.0185448	−	0.0321206i	−0.856604	−	0.515974i	$-0.827430\pi$
$467$	0.400757	−	0.694131i	0.0185448	−	0.0321206i	0.875149	+	0.483854i	$0.160763\pi$
$468$		0			0
$469$	21.3944	−	25.0571i	0.987904	−	1.15703i
$470$	−2.51319			−0.115925
$471$		0			0
$472$	11.7979	+	20.4345i	0.543041	+	0.940575i
$473$	−3.14230	−	5.44262i	−0.144483	−	0.250252i
$474$		0			0
$475$	−10.1833			−0.467243
$476$	−10.8057	−	2.00109i	−0.495277	−	0.0917196i
$477$		0			0
$478$	−15.0774	+	26.1149i	−0.689626	+	1.19447i
$479$	−9.58983	−	16.6101i	−0.438171	−	0.758934i	0.559378	−	0.828913i	$-0.311040\pi$
$479$	−9.58983	−	16.6101i	−0.438171	−	0.758934i	−0.997548	+	0.0699791i	$0.977707\pi$
$480$		0			0
$481$	31.3091	−	54.2290i	1.42757	−	2.47263i
$482$	12.7870			0.582430
$483$		0			0
$484$	0.712889			0.0324041
$485$	−0.951838	+	1.64863i	−0.0432207	+	0.0748605i
$486$		0			0
$487$	6.46676	+	11.2008i	0.293037	+	0.507555i	0.974526	−	0.224273i	$-0.0720008\pi$
$487$	6.46676	+	11.2008i	0.293037	+	0.507555i	−0.681489	+	0.731828i	$0.738667\pi$
$488$	9.54057	−	16.5248i	0.431881	−	0.748041i
$489$		0			0
$490$	−3.09075	−	1.18540i	−0.139626	−	0.0535507i
$491$	−23.7463			−1.07165			−0.535827	−	0.844328i	$-0.680000\pi$
$491$	−23.7463			−1.07165			−0.535827	+	0.844328i	$0.680000\pi$
$492$		0			0
$493$	22.0418	+	38.1775i	0.992713	+	1.71943i
$494$	−9.73176	−	16.8559i	−0.437853	−	0.758383i
$495$		0			0
$496$	1.65371			0.0742538
$497$	11.8763	+	33.5220i	0.532723	+	1.50367i
$498$		0			0
$499$	4.15394	−	7.19483i	0.185956	−	0.322085i	−0.757942	−	0.652321i	$-0.773795\pi$
$499$	4.15394	−	7.19483i	0.185956	−	0.322085i	0.943898	+	0.330237i	$0.107129\pi$
$500$	−1.01495	−	1.75795i	−0.0453902	−	0.0786181i
$501$		0			0
$502$	18.6175	−	32.2464i	0.830940	−	1.43923i
$503$	−40.0084			−1.78389			−0.891943	−	0.452148i	$-0.850658\pi$
$503$	−40.0084			−1.78389			−0.891943	+	0.452148i	$0.850658\pi$
$504$		0			0
$505$	−4.20146			−0.186963
$506$	−4.22492	+	7.31777i	−0.187820	+	0.325314i
$507$		0			0
$508$	−1.38709	−	2.40251i	−0.0615421	−	0.106594i
$509$	−14.2461	+	24.6750i	−0.631448	+	1.09370i	0.355808	+	0.934559i	$0.384206\pi$
$509$	−14.2461	+	24.6750i	−0.631448	+	1.09370i	−0.987256	+	0.159141i	$0.949127\pi$
$510$		0			0
$511$	−14.5806	+	17.0767i	−0.645006	+	0.755428i
$512$	−1.87001			−0.0826436
$513$		0			0
$514$	−4.24791	−	7.35760i	−0.187367	−	0.324530i
$515$	0.437216	+	0.757280i	0.0192660	+	0.0333698i
$516$		0			0
$517$	5.31447			0.233730
$518$	31.0506	−	36.3663i	1.36429	−	1.59784i
$519$		0			0
$520$	−1.73667	+	3.00800i	−0.0761581	+	0.131910i
$521$	−5.76188	−	9.97986i	−0.252432	−	0.437226i	0.711763	−	0.702420i	$-0.247897\pi$
$521$	−5.76188	−	9.97986i	−0.252432	−	0.437226i	−0.964195	+	0.265194i	$0.914564\pi$
$522$		0			0
$523$	−5.10091	+	8.83504i	−0.223047	+	0.386329i	−0.955732	−	0.294239i	$-0.904934\pi$
$523$	−5.10091	+	8.83504i	−0.223047	+	0.386329i	0.732684	+	0.680568i	$0.238267\pi$
$524$	6.14859			0.268602
$525$		0			0
$526$	−29.2658			−1.27605
$527$	−0.979676	+	1.69685i	−0.0426753	+	0.0739159i
$528$		0			0
$529$	−1.65934	−	2.87405i	−0.0721450	−	0.124959i
$530$	0.416637	−	0.721636i	0.0180975	−	0.0313459i
$531$		0			0
$532$	−1.30432	−	3.68158i	−0.0565494	−	0.159617i
$533$	52.1126			2.25725
$534$		0			0
$535$	−1.13408	−	1.96428i	−0.0490304	−	0.0849231i
$536$	−13.2003	−	22.8636i	−0.570166	−	0.987556i
$537$		0			0
$538$	45.0031			1.94022
$539$	6.53579	+	2.50667i	0.281517	+	0.107970i
$540$		0			0
$541$	−12.0735	+	20.9118i	−0.519078	+	0.899070i	0.480676	+	0.876898i	$0.340391\pi$
$541$	−12.0735	+	20.9118i	−0.519078	+	0.899070i	−0.999754	+	0.0221716i	$0.992942\pi$
$542$	−2.97997	−	5.16147i	−0.128001	−	0.221704i
$543$		0			0
$544$	−11.2441	+	19.4754i	−0.482087	+	0.835000i
$545$	2.20008			0.0942409
$546$		0			0
$547$	28.8966			1.23553			0.617765	−	0.786363i	$-0.288038\pi$
$547$	28.8966			1.23553			0.617765	+	0.786363i	$0.288038\pi$
$548$	−3.03055	+	5.24907i	−0.129459	+	0.224229i
$549$		0			0
$550$	4.04983	+	7.01450i	0.172685	+	0.299099i
$551$	−7.83400	+	13.5689i	−0.333740	+	0.578054i
$552$		0			0
$553$	31.4742	+	5.82866i	1.33842	+	0.247860i
$554$	15.6803			0.666191
$555$		0			0
$556$	−4.44743	−	7.70317i	−0.188613	−	0.326687i
$557$	−6.50762	−	11.2715i	−0.275737	−	0.477590i	0.694584	−	0.719411i	$-0.255588\pi$
$557$	−6.50762	−	11.2715i	−0.275737	−	0.477590i	−0.970321	+	0.241822i	$0.922255\pi$
$558$		0			0
$559$	35.8628			1.51683
$560$	−2.42560	+	2.84085i	−0.102500	+	0.120048i
$561$		0			0
$562$	−3.66590	+	6.34953i	−0.154637	+	0.267839i
$563$	8.79467	+	15.2328i	0.370651	+	0.641987i	0.989666	−	0.143393i	$-0.0458012\pi$
$563$	8.79467	+	15.2328i	0.370651	+	0.641987i	−0.619015	+	0.785379i	$0.712468\pi$
$564$		0			0
$565$	1.84335	−	3.19278i	0.0775504	−	0.134321i
$566$	−24.7974			−1.04231
$567$		0			0
$568$	28.4963			1.19568
$569$	19.7245	−	34.1638i	0.826893	−	1.43222i	−0.0735704	−	0.997290i	$-0.523439\pi$
$569$	19.7245	−	34.1638i	0.826893	−	1.43222i	0.900464	−	0.434931i	$-0.143227\pi$
$570$		0			0
$571$	−11.4412	−	19.8168i	−0.478801	−	0.829308i	0.520903	−	0.853616i	$-0.325595\pi$
$571$	−11.4412	−	19.8168i	−0.478801	−	0.829308i	−0.999705	+	0.0243075i	$0.992262\pi$
$572$	−2.03403	+	3.52305i	−0.0850473	+	0.147306i
$573$		0			0
$574$	39.1309	+	7.24659i	1.63329	+	0.302467i
$575$	−25.2280			−1.05208
$576$		0			0
$577$	−6.41635	−	11.1134i	−0.267116	−	0.462659i	0.701000	−	0.713162i	$-0.252737\pi$
$577$	−6.41635	−	11.1134i	−0.267116	−	0.462659i	−0.968116	+	0.250503i	$0.919404\pi$
$578$	−13.9568	−	24.1740i	−0.580528	−	1.00550i
$579$		0			0
$580$	−1.54862			−0.0643031
$581$	−14.7613	−	41.6652i	−0.612400	−	1.72856i
$582$		0			0
$583$	−0.881033	+	1.52599i	−0.0364886	+	0.0632002i
$584$	8.99615	+	15.5818i	0.372264	+	0.644779i
$585$		0			0
$586$	−4.56143	+	7.90062i	−0.188431	+	0.326372i
$587$	−1.17610			−0.0485428			−0.0242714	−	0.999705i	$-0.507727\pi$
$587$	−1.17610			−0.0485428			−0.0242714	+	0.999705i	$0.507727\pi$
$588$		0			0
$589$	−0.696384			−0.0286940
$590$	2.63171	−	4.55825i	0.108346	−	0.187660i
$591$		0			0
$592$	−26.9808	−	46.7321i	−1.10890	−	1.92068i
$593$	−12.7901	+	22.1531i	−0.525226	+	0.909718i	0.474342	+	0.880340i	$0.342686\pi$
$593$	−12.7901	+	22.1531i	−0.525226	+	0.909718i	−0.999568	+	0.0293775i	$0.990647\pi$
$594$		0			0
$595$	−1.47800	−	4.17182i	−0.0605922	−	0.171028i
$596$	1.44142			0.0590428
$597$		0			0
$598$	−24.1093	−	41.7585i	−0.985902	−	1.70763i
$599$	11.9588	+	20.7132i	0.488623	+	0.846319i	0.999914	−	0.0130880i	$-0.00416615\pi$
$599$	11.9588	+	20.7132i	0.488623	+	0.846319i	−0.511292	+	0.859407i	$0.670833\pi$
$600$		0			0
$601$	−42.6473			−1.73962			−0.869810	−	0.493386i	$-0.835759\pi$
$601$	−42.6473			−1.73962			−0.869810	+	0.493386i	$0.835759\pi$
$602$	26.9290	+	4.98695i	1.09755	+	0.203253i
$603$		0			0
$604$	−1.03929	+	1.80009i	−0.0422879	+	0.0732448i
$605$	0.143555	+	0.248645i	0.00583636	+	0.0101089i
$606$		0			0
$607$	14.9905	−	25.9642i	0.608444	−	1.05386i	−0.383053	−	0.923726i	$-0.625127\pi$
$607$	14.9905	−	25.9642i	0.608444	−	1.05386i	0.991497	−	0.130129i	$-0.0415393\pi$
$608$	−7.99267			−0.324145
$609$		0			0
$610$	−4.25636			−0.172335
$611$	−15.1634	+	26.2637i	−0.613445	+	1.06252i
$612$		0			0
$613$	2.45129	+	4.24576i	0.0990067	+	0.171485i	0.911274	−	0.411801i	$-0.135100\pi$
$613$	2.45129	+	4.24576i	0.0990067	+	0.171485i	−0.812267	+	0.583286i	$0.801767\pi$
$614$	10.0244	−	17.3628i	0.404553	−	0.700706i
$615$		0			0
$616$	3.64210	−	4.26560i	0.146744	−	0.171866i
$617$	16.6101			0.668697			0.334348	−	0.942450i	$-0.391484\pi$
$617$	16.6101			0.668697			0.334348	+	0.942450i	$0.391484\pi$
$618$		0			0
$619$	4.73619	+	8.20332i	0.190363	+	0.329719i	0.945371	−	0.325997i	$-0.105700\pi$
$619$	4.73619	+	8.20332i	0.190363	+	0.329719i	−0.755007	+	0.655716i	$0.772367\pi$
$620$	−0.0344153	−	0.0596090i	−0.00138215	−	0.00239395i
$621$		0			0
$622$	17.0711			0.684489
$623$	−32.0602	−	5.93717i	−1.28446	−	0.237868i
$624$		0			0
$625$	−11.8852	+	20.5857i	−0.475406	+	0.823428i
$626$	−0.748205	−	1.29593i	−0.0299043	−	0.0517957i
$627$		0			0
$628$	1.53287	−	2.65500i	0.0611680	−	0.105946i
$629$	63.9348			2.54925
$630$		0			0
$631$	−1.91811			−0.0763588			−0.0381794	−	0.999271i	$-0.512156\pi$
$631$	−1.91811			−0.0763588			−0.0381794	+	0.999271i	$0.512156\pi$
$632$	12.8242	−	22.2122i	0.510119	−	0.883552i
$633$		0			0
$634$	0.192872	+	0.334064i	0.00765992	+	0.0132674i
$635$	0.558639	−	0.967592i	0.0221689	−	0.0383977i
$636$		0			0
$637$	−31.0359	+	25.1473i	−1.22969	+	0.996374i
$638$	12.4621			0.493379
$639$		0			0
$640$	1.93050	+	3.34372i	0.0763097	+	0.132172i
$641$	−19.8186	−	34.3269i	−0.782788	−	1.35583i	−0.930311	−	0.366771i	$-0.880463\pi$
$641$	−19.8186	−	34.3269i	−0.782788	−	1.35583i	0.147523	−	0.989059i	$-0.452870\pi$
$642$		0			0
$643$	−8.11061			−0.319851			−0.159926	−	0.987129i	$-0.551125\pi$
$643$	−8.11061			−0.319851			−0.159926	+	0.987129i	$0.551125\pi$
$644$	−3.23130	−	9.12068i	−0.127331	−	0.359405i
$645$		0			0
$646$	9.93638	−	17.2103i	0.390942	−	0.677131i
$647$	−17.4017	−	30.1406i	−0.684131	−	1.18495i	−0.973709	−	0.227796i	$-0.926848\pi$
$647$	−17.4017	−	30.1406i	−0.684131	−	1.18495i	0.289578	−	0.957154i	$-0.406485\pi$
$648$		0			0
$649$	−5.56509	+	9.63901i	−0.218449	+	0.378364i
$650$	−46.2203			−1.81291
$651$		0			0
$652$	−4.49948			−0.176213
$653$	10.0143	−	17.3452i	0.391889	−	0.678772i	−0.600810	−	0.799392i	$-0.705155\pi$
$653$	10.0143	−	17.3452i	0.391889	−	0.678772i	0.992699	+	0.120620i	$0.0384884\pi$
$654$		0			0
$655$	1.23815	+	2.14454i	0.0483785	+	0.0837940i
$656$	22.4542	−	38.8918i	0.876688	−	1.51847i
$657$		0			0
$658$	−15.0382	+	17.6126i	−0.586249	+	0.686612i
$659$	29.2285			1.13858			0.569291	−	0.822136i	$-0.307218\pi$
$659$	29.2285			1.13858			0.569291	+	0.822136i	$0.307218\pi$
$660$		0			0
$661$	1.48029	+	2.56394i	0.0575768	+	0.0997259i	0.893377	−	0.449308i	$-0.148329\pi$
$661$	1.48029	+	2.56394i	0.0575768	+	0.0997259i	−0.835800	+	0.549033i	$0.814996\pi$
$662$	−9.87014	−	17.0956i	−0.383614	−	0.664439i
$663$		0			0
$664$	−35.4187			−1.37451
$665$	1.02143	−	1.19629i	0.0396093	−	0.0463902i
$666$		0			0
$667$	−19.4078	+	33.6153i	−0.751473	+	1.30159i
$668$	0.331072	+	0.573433i	0.0128096	+	0.0221868i
$669$		0			0
$670$	−2.94454	+	5.10009i	−0.113757	+	0.197034i
$671$	9.00062			0.347465
$672$		0			0
$673$	7.87554			0.303580			0.151790	−	0.988413i	$-0.451496\pi$
$673$	7.87554			0.303580			0.151790	+	0.988413i	$0.451496\pi$
$674$	28.5219	−	49.4013i	1.09862	−	1.90287i
$675$		0			0
$676$	−6.97334	−	12.0782i	−0.268205	−	0.464545i
$677$	−5.33526	+	9.24095i	−0.205051	+	0.355159i	−0.950149	−	0.311796i	$-0.899069\pi$
$677$	−5.33526	+	9.24095i	−0.205051	+	0.355159i	0.745098	+	0.666955i	$0.232403\pi$
$678$		0			0
$679$	5.85823	+	16.5355i	0.224818	+	0.634573i
$680$	−3.54637			−0.135997
$681$		0			0
$682$	0.276946	+	0.479685i	0.0106048	+	0.0183681i
$683$	6.32982	+	10.9636i	0.242204	+	0.419509i	0.961342	−	0.275358i	$-0.0887964\pi$
$683$	6.32982	+	10.9636i	0.242204	+	0.419509i	−0.719138	+	0.694867i	$0.755463\pi$
$684$		0			0
$685$	−2.44106			−0.0932683
$686$	−26.8015	+	14.5672i	−1.02328	+	0.556177i
$687$		0			0
$688$	15.4525	−	26.7645i	0.589120	−	1.02039i
$689$	−5.02757	−	8.70801i	−0.191535	−	0.331749i
$690$		0			0
$691$	19.0243	−	32.9510i	0.723718	−	1.25352i	−0.235782	−	0.971806i	$-0.575765\pi$
$691$	19.0243	−	32.9510i	0.723718	−	1.25352i	0.959500	−	0.281710i	$-0.0909015\pi$
$692$	−1.10612			−0.0420485
$693$		0			0
$694$	−18.7578			−0.712036
$695$	1.79117	−	3.10239i	0.0679428	−	0.117680i
$696$		0			0
$697$	26.6042	+	46.0798i	1.00770	+	1.74540i
$698$	16.1740	−	28.0142i	0.612196	−	1.06035i
$699$		0			0
$700$	−9.12009	−	1.68894i	−0.344707	−	0.0638358i
$701$	−20.5417			−0.775851			−0.387925	−	0.921691i	$-0.626808\pi$
$701$	−20.5417			−0.775851			−0.387925	+	0.921691i	$0.626808\pi$
$702$		0			0
$703$	11.3617	+	19.6791i	0.428515	+	0.742210i
$704$	−1.73895	−	3.01195i	−0.0655391	−	0.113517i
$705$		0			0
$706$	−37.7555			−1.42095
$707$	−25.1403	+	29.4442i	−0.945498	+	1.10736i
$708$		0			0
$709$	7.33575	−	12.7059i	0.275500	−	0.477180i	−0.694761	−	0.719241i	$-0.744490\pi$
$709$	7.33575	−	12.7059i	0.275500	−	0.477180i	0.970261	+	0.242061i	$0.0778233\pi$
$710$	−3.17828	−	5.50495i	−0.119279	−	0.206597i
$711$		0			0
$712$	−13.0629	+	22.6257i	−0.489554	+	0.847933i
$713$	−1.72521			−0.0646095
$714$		0			0
$715$	−1.63838			−0.0612721
$716$	−0.796220	+	1.37909i	−0.0297561	+	0.0515392i
$717$		0			0
$718$	5.49858	+	9.52383i	0.205205	+	0.355426i
$719$	4.96085	−	8.59245i	0.185009	−	0.320444i	−0.758571	−	0.651591i	$-0.774102\pi$
$719$	4.96085	−	8.59245i	0.185009	−	0.320444i	0.943579	+	0.331146i	$0.107435\pi$
$720$		0			0
$721$	7.92325	+	1.46730i	0.295077	+	0.0546449i
$722$	−24.2315			−0.901804
$723$		0			0
$724$	9.22560	+	15.9792i	0.342867	+	0.593862i
$725$	18.6035	+	32.2222i	0.690917	+	1.19670i
$726$		0			0
$727$	−1.91971			−0.0711983			−0.0355991	−	0.999366i	$-0.511334\pi$
$727$	−1.91971			−0.0711983			−0.0355991	+	0.999366i	$0.511334\pi$
$728$	10.6886	+	30.1697i	0.396146	+	1.11816i
$729$		0			0
$730$	2.00674	−	3.47577i	0.0742727	−	0.128644i
$731$	18.3084	+	31.7111i	0.677161	+	1.17288i
$732$		0			0
$733$	16.6842	−	28.8980i	0.616247	−	1.06737i	−0.373918	−	0.927462i	$-0.621986\pi$
$733$	16.6842	−	28.8980i	0.616247	−	1.06737i	0.990164	−	0.139909i	$-0.0446809\pi$
$734$	−25.5885			−0.944487
$735$		0			0
$736$	−19.8009			−0.729870
$737$	6.22661	−	10.7848i	0.229360	−	0.397263i
$738$		0			0
$739$	8.50797	+	14.7362i	0.312971	+	0.542081i	0.979004	−	0.203841i	$-0.0653425\pi$
$739$	8.50797	+	14.7362i	0.312971	+	0.542081i	−0.666033	+	0.745922i	$0.732009\pi$
$740$	−1.12299	+	1.94508i	−0.0412820	+	0.0715024i
$741$		0			0
$742$	−2.56425	−	7.23788i	−0.0941367	−	0.265711i
$743$	−22.8034			−0.836575			−0.418288	−	0.908315i	$-0.637370\pi$
$743$	−22.8034			−0.836575			−0.418288	+	0.908315i	$0.637370\pi$
$744$		0			0
$745$	0.290260	+	0.502745i	0.0106343	+	0.0184192i
$746$	14.4746	+	25.0708i	0.529953	+	0.917906i
$747$		0			0
$748$	−4.15360			−0.151871
$749$	−20.5518	−	3.80595i	−0.750946	−	0.139067i
$750$		0			0
$751$	6.31158	−	10.9320i	0.230313	−	0.398913i	−0.727587	−	0.686015i	$-0.759358\pi$
$751$	6.31158	−	10.9320i	0.230313	−	0.398913i	0.957900	+	0.287102i	$0.0926917\pi$
$752$	13.0671	+	22.6329i	0.476509	+	0.825338i
$753$		0			0
$754$	−35.5571	+	61.5868i	−1.29491	+	2.24286i
$755$	−0.837128			−0.0304662
$756$		0			0
$757$	−16.4464			−0.597755			−0.298877	−	0.954292i	$-0.596612\pi$
$757$	−16.4464			−0.597755			−0.298877	+	0.954292i	$0.596612\pi$
$758$	16.7102	−	28.9429i	0.606941	−	1.05125i
$759$		0			0
$760$	−0.630218	−	1.09157i	−0.0228604	−	0.0395954i
$761$	−22.7326	+	39.3740i	−0.824055	+	1.42731i	0.0785842	+	0.996907i	$0.474960\pi$
$761$	−22.7326	+	39.3740i	−0.824055	+	1.42731i	−0.902639	+	0.430398i	$0.858373\pi$
$762$		0			0
$763$	13.1646	−	15.4183i	0.476591	−	0.558180i
$764$	3.60309			0.130355
$765$		0			0
$766$	14.1419	+	24.4945i	0.510967	+	0.885021i
$767$	−31.7569	−	55.0046i	−1.14668	−	1.98610i
$768$		0			0
$769$	20.4966			0.739127			0.369563	−	0.929205i	$-0.379507\pi$
$769$	20.4966			0.739127			0.369563	+	0.929205i	$0.379507\pi$
$770$	−1.23025	−	0.227828i	−0.0443350	−	0.00821034i
$771$		0			0
$772$	0.119145	−	0.206365i	0.00428813	−	0.00742725i
$773$	−8.26744	−	14.3196i	−0.297359	−	0.515041i	0.678172	−	0.734903i	$-0.262772\pi$
$773$	−8.26744	−	14.3196i	−0.297359	−	0.515041i	−0.975531	+	0.219862i	$0.929439\pi$
$774$		0			0
$775$	−0.826856	+	1.43216i	−0.0297015	+	0.0514446i
$776$	14.0564			0.504597
$777$		0			0
$778$	−50.9652			−1.82719
$779$	−9.45554	+	16.3775i	−0.338780	+	0.586784i
$780$		0			0
$781$	6.72089	+	11.6409i	0.240492	+	0.416545i
$782$	24.6162	−	42.6365i	0.880273	−	1.52468i
$783$		0			0
$784$	5.39484	+	33.9976i	0.192673	+	1.21420i
$785$	1.23470			0.0440684
$786$		0			0
$787$	−12.2279	−	21.1794i	−0.435878	−	0.754963i	0.561489	−	0.827484i	$-0.310229\pi$
$787$	−12.2279	−	21.1794i	−0.435878	−	0.754963i	−0.997367	+	0.0725212i	$0.976896\pi$
$788$	0.786740	+	1.36267i	0.0280265	+	0.0485433i
$789$		0			0
$790$	−5.72129			−0.203554
$791$	−11.3452	−	32.0230i	−0.403389	−	1.13861i
$792$		0			0
$793$	−25.6808	+	44.4805i	−0.911952	+	1.57955i
$794$	−0.983867	−	1.70411i	−0.0349161	−	0.0604765i
$795$		0			0
$796$	−7.39622	+	12.8106i	−0.262152	+	0.454061i
$797$	10.0452			0.355819			0.177910	−	0.984047i	$-0.443067\pi$
$797$	10.0452			0.355819			0.177910	+	0.984047i	$0.443067\pi$
$798$		0			0
$799$	−30.9644			−1.09544
$800$	−9.49014	+	16.4374i	−0.335527	+	0.581150i
$801$		0			0
$802$	−25.0400	−	43.3705i	−0.884193	−	1.53147i
$803$	−4.24351	+	7.34997i	−0.149750	+	0.259375i
$804$		0			0
$805$	2.53047	−	2.96367i	0.0891873	−	0.104456i
$806$	−3.16076			−0.111333
$807$		0			0
$808$	15.5115	+	26.8666i	0.545691	+	0.945165i
$809$	−18.9460	−	32.8155i	−0.666107	−	1.15373i	−0.978984	−	0.203937i	$-0.934626\pi$
$809$	−18.9460	−	32.8155i	−0.666107	−	1.15373i	0.312877	−	0.949794i	$-0.398707\pi$
$810$		0			0
$811$	−7.34358			−0.257868			−0.128934	−	0.991653i	$-0.541156\pi$
$811$	−7.34358			−0.257868			−0.128934	+	0.991653i	$0.541156\pi$
$812$	−9.26651	+	10.8529i	−0.325191	+	0.380862i
$813$		0			0
$814$	9.03693	−	15.6524i	0.316744	−	0.548617i
$815$	−0.906066	−	1.56935i	−0.0317381	−	0.0549720i
$816$		0			0
$817$	−6.50709	+	11.2706i	−0.227654	+	0.394309i
$818$	28.4924			0.996215
$819$		0			0
$820$	−1.86917			−0.0652742
$821$	−2.01120	+	3.48351i	−0.0701915	+	0.121575i	−0.898985	−	0.437979i	$-0.855694\pi$
$821$	−2.01120	+	3.48351i	−0.0701915	+	0.121575i	0.828794	+	0.559554i	$0.189028\pi$
$822$		0			0
$823$	−3.49164	−	6.04770i	−0.121711	−	0.210810i	0.798731	−	0.601688i	$-0.205505\pi$
$823$	−3.49164	−	6.04770i	−0.121711	−	0.210810i	−0.920443	+	0.390878i	$0.872171\pi$
$824$	3.22834	−	5.59164i	0.112464	−	0.194794i
$825$		0			0
$826$	−16.1972	−	45.7184i	−0.563574	−	1.59075i
$827$	25.5420			0.888183			0.444092	−	0.895981i	$-0.353526\pi$
$827$	25.5420			0.888183			0.444092	+	0.895981i	$0.353526\pi$
$828$		0			0
$829$	−12.3043	−	21.3117i	−0.427346	−	0.740186i	0.569290	−	0.822137i	$-0.307218\pi$
$829$	−12.3043	−	21.3117i	−0.427346	−	0.740186i	−0.996636	+	0.0819512i	$0.973885\pi$
$830$	3.95035	+	6.84221i	0.137119	+	0.237497i
$831$		0			0
$832$	19.8465			0.688052
$833$	−38.0804	−	14.6050i	−1.31941	−	0.506032i
$834$		0			0
$835$	−0.133337	+	0.230946i	−0.00461430	+	0.00799221i
$836$	−0.738127	−	1.27847i	−0.0255287	−	0.0442170i
$837$		0			0
$838$	22.9311	−	39.7179i	0.792143	−	1.37203i
$839$	7.92504			0.273603			0.136801	−	0.990598i	$-0.456318\pi$
$839$	7.92504			0.273603			0.136801	+	0.990598i	$0.456318\pi$
$840$		0			0
$841$	28.2465			0.974018
$842$	18.2126	−	31.5451i	0.627648	−	1.08712i
$843$		0			0
$844$	−2.58087	−	4.47019i	−0.0888371	−	0.153870i
$845$	2.80846	−	4.86440i	0.0966140	−	0.167340i
$846$		0			0
$847$	2.60152	+	0.481771i	0.0893892	+	0.0165539i
$848$	−8.66507			−0.297560
$849$		0			0
$850$	−23.5960	−	40.8695i	−0.809338	−	1.40181i
$851$	28.1473	+	48.7525i	0.964877	+	1.67122i
$852$		0			0
$853$	−3.57567			−0.122429			−0.0612143	−	0.998125i	$-0.519497\pi$
$853$	−3.57567			−0.122429			−0.0612143	+	0.998125i	$0.519497\pi$
$854$	−25.4688	+	29.8289i	−0.871523	+	1.02072i
$855$		0			0
$856$	−8.37384	+	14.5039i	−0.286212	+	0.495734i
$857$	14.1578	+	24.5220i	0.483621	+	0.837656i	0.999823	−	0.0188105i	$-0.00598792\pi$
$857$	14.1578	+	24.5220i	0.483621	+	0.837656i	−0.516202	+	0.856467i	$0.672655\pi$
$858$		0			0
$859$	−7.48067	+	12.9569i	−0.255237	+	0.442083i	−0.964960	−	0.262398i	$-0.915487\pi$
$859$	−7.48067	+	12.9569i	−0.255237	+	0.442083i	0.709723	+	0.704481i	$0.248820\pi$
$860$	−1.28632			−0.0438632
$861$		0			0
$862$	57.8521			1.97045
$863$	12.4402	−	21.5471i	0.423470	−	0.733472i	−0.572806	−	0.819691i	$-0.694145\pi$
$863$	12.4402	−	21.5471i	0.423470	−	0.733472i	0.996276	+	0.0862189i	$0.0274785\pi$
$864$		0			0
$865$	−0.222741	−	0.385799i	−0.00757343	−	0.0131176i
$866$	−19.5456	+	33.8540i	−0.664188	+	1.15041i
$867$		0			0
$868$	−0.623675	−	0.115497i	−0.0211689	−	0.00392024i
$869$	12.0984			0.410410
$870$		0			0
$871$	35.5319	+	61.5430i	1.20395	+	2.08530i
$872$	−8.12251	−	14.0686i	−0.275063	−	0.476423i
$873$		0			0
$874$	17.4980			0.591877
$875$	−2.51581	−	7.10113i	−0.0850498	−	0.240062i
$876$		0			0
$877$	−12.3632	+	21.4136i	−0.417474	+	0.723086i	−0.995685	−	0.0928012i	$-0.970418\pi$
$877$	−12.3632	+	21.4136i	−0.417474	+	0.723086i	0.578210	+	0.815888i	$0.303751\pi$
$878$	26.5827	+	46.0425i	0.897122	+	1.55386i
$879$		0			0
$880$	−0.705943	+	1.22273i	−0.0237973	+	0.0412182i
$881$	−28.3944			−0.956632			−0.478316	−	0.878188i	$-0.658753\pi$
$881$	−28.3944			−0.956632			−0.478316	+	0.878188i	$0.658753\pi$
$882$		0			0
$883$	−11.6366			−0.391603			−0.195801	−	0.980644i	$-0.562731\pi$
$883$	−11.6366			−0.391603			−0.195801	+	0.980644i	$0.562731\pi$
$884$	11.8512	−	20.5268i	0.398598	−	0.690392i
$885$		0			0
$886$	10.2118	+	17.6874i	0.343072	+	0.594218i
$887$	13.4411	−	23.2808i	0.451310	−	0.781691i	−0.547158	−	0.837029i	$-0.684290\pi$
$887$	13.4411	−	23.2808i	0.451310	−	0.781691i	0.998468	+	0.0553381i	$0.0176237\pi$
$888$		0			0
$889$	−3.43823	−	9.70477i	−0.115315	−	0.325488i
$890$	5.82780			0.195348
$891$		0			0
$892$	2.45269	+	4.24819i	0.0821222	+	0.142240i
$893$	−5.50261	−	9.53081i	−0.184138	−	0.318936i
$894$		0			0
$895$	−0.641343			−0.0214377
$896$	34.9846	+	6.47875i	1.16875	+	0.216440i
$897$		0			0
$898$	−8.92273	+	15.4546i	−0.297755	+	0.515727i
$899$	1.27220	+	2.20351i	0.0424301	+	0.0734911i
$900$		0			0
$901$	5.13328	−	8.89110i	0.171014	−	0.296205i
$902$	15.0416			0.500829
$903$		0			0
$904$	−27.2221			−0.905392
$905$	−3.71554	+	6.43550i	−0.123509	+	0.213923i
$906$		0			0
$907$	−11.9719	−	20.7359i	−0.397519	−	0.688523i	0.595900	−	0.803059i	$-0.296795\pi$
$907$	−11.9719	−	20.7359i	−0.397519	−	0.688523i	−0.993419	+	0.114535i	$0.963462\pi$
$908$	−0.357283	+	0.618832i	−0.0118568	+	0.0205367i
$909$		0			0
$910$	4.63608	−	5.42975i	0.153685	−	0.179995i
$911$	8.31272			0.275413			0.137706	−	0.990473i	$-0.456027\pi$
$911$	8.31272			0.275413			0.137706	+	0.990473i	$0.456027\pi$
$912$		0			0
$913$	−8.35354	−	14.4688i	−0.276462	−	0.478846i
$914$	8.41390	+	14.5733i	0.278307	+	0.482042i
$915$		0			0
$916$	−3.05479			−0.100933
$917$	22.4378	+	4.15522i	0.740961	+	0.137218i
$918$		0			0
$919$	21.4865	−	37.2157i	0.708774	−	1.22763i	−0.256538	−	0.966534i	$-0.582582\pi$
$919$	21.4865	−	37.2157i	0.708774	−	1.22763i	0.965312	−	0.261098i	$-0.0840846\pi$
$920$	−1.56129	−	2.70423i	−0.0514742	−	0.0891559i
$921$		0			0
$922$	13.0881	−	22.6692i	0.431032	−	0.746570i
$923$	−76.7049			−2.52477
$924$		0			0
$925$	53.9616			1.77425
$926$	−4.25367	+	7.36757i	−0.139784	+	0.242113i
$927$		0			0
$928$	14.6015	+	25.2905i	0.479317	+	0.830202i
$929$	11.7686	−	20.3838i	0.386116	−	0.668772i	−0.605808	−	0.795611i	$-0.707150\pi$
$929$	11.7686	−	20.3838i	0.386116	−	0.668772i	0.991923	+	0.126839i	$0.0404832\pi$
$930$		0			0
$931$	−2.27179	−	14.3165i	−0.0744548	−	0.469205i
$932$	4.93119			0.161527
$933$		0			0
$934$	0.660081	+	1.14329i	0.0215985	+	0.0374097i
$935$	−0.836416	−	1.44871i	−0.0273537	−	0.0473780i
$936$		0			0
$937$	−7.10555			−0.232128			−0.116064	−	0.993242i	$-0.537028\pi$
$937$	−7.10555			−0.232128			−0.116064	+	0.993242i	$0.537028\pi$
$938$	18.1226	+	51.1530i	0.591724	+	1.67020i
$939$		0			0
$940$	0.543878	−	0.942024i	0.0177393	−	0.0307254i
$941$	21.9631	+	38.0413i	0.715978	+	1.24011i	0.962581	+	0.270993i	$0.0873521\pi$
$941$	21.9631	+	38.0413i	0.715978	+	1.24011i	−0.246604	+	0.969116i	$0.579315\pi$
$942$		0			0
$943$	−23.4250	+	40.5732i	−0.762822	+	1.32125i
$944$	−54.7334			−1.78142
$945$		0			0
$946$	10.3513			0.336549
$947$	−24.6367	+	42.6721i	−0.800586	+	1.38666i	0.118645	+	0.992937i	$0.462145\pi$
$947$	−24.6367	+	42.6721i	−0.800586	+	1.38666i	−0.919231	+	0.393719i	$0.871188\pi$
$948$		0			0
$949$	−24.2154	−	41.9423i	−0.786064	−	1.36150i
$950$	8.38640	−	14.5257i	0.272091	−	0.471275i
$951$		0			0
$952$	−21.2204	+	24.8533i	−0.687758	+	0.805499i
$953$	47.5295			1.53963			0.769816	−	0.638266i	$-0.220348\pi$
$953$	47.5295			1.53963			0.769816	+	0.638266i	$0.220348\pi$
$954$		0			0
$955$	0.725559	+	1.25670i	0.0234785	+	0.0406660i
$956$	−6.52580	−	11.3030i	−0.211059	−	0.365566i
$957$		0			0
$958$	31.5905			1.02064
$959$	−14.6066	+	17.1072i	−0.471672	+	0.552420i
$960$		0			0
$961$	15.4435	−	26.7488i	0.498176	−	0.862866i
$962$	51.5688	+	89.3198i	1.66264	+	2.87978i
$963$		0			0
$964$	−2.76722	+	4.79296i	−0.0891260	+	0.154371i
$965$	0.0959695			0.00308937
$966$		0			0
$967$	5.97320			0.192085			0.0960425	−	0.995377i	$-0.469382\pi$
$967$	5.97320			0.192085			0.0960425	+	0.995377i	$0.469382\pi$
$968$	1.05999	−	1.83596i	0.0340694	−	0.0590099i
$969$		0			0
$970$	−1.56776	−	2.71544i	−0.0503377	−	0.0871874i
$971$	0.255622	−	0.442750i	0.00820329	−	0.0142085i	−0.861895	−	0.507087i	$-0.830722\pi$
$971$	0.255622	−	0.442750i	0.00820329	−	0.0142085i	0.870098	+	0.492879i	$0.164055\pi$
$972$		0			0
$973$	−11.0240	−	31.1164i	−0.353413	−	0.997547i
$974$	−21.3026			−0.682580
$975$		0			0
$976$	22.1306	+	38.3313i	0.708383	+	1.22695i
$977$	13.9384	+	24.1420i	0.445929	+	0.772372i	0.998116	−	0.0613480i	$-0.0195400\pi$
$977$	13.9384	+	24.1420i	0.445929	+	0.772372i	−0.552187	+	0.833720i	$0.686207\pi$
$978$		0			0
$979$	−12.3236			−0.393865
$980$	1.11319	−	0.901981i	0.0355596	−	0.0288127i
$981$		0			0
$982$	19.5561	−	33.8721i	0.624059	−	1.08090i
$983$	−11.9707	−	20.7338i	−0.381805	−	0.661305i	0.609516	−	0.792774i	$-0.291364\pi$
$983$	−11.9707	−	20.7338i	−0.381805	−	0.661305i	−0.991320	+	0.131469i	$0.958031\pi$
$984$		0			0
$985$	−0.316854	+	0.548807i	−0.0100958	+	0.0174864i
$986$	−72.6095			−2.31236
$987$		0			0
$988$	8.42418			0.268009
$989$	−16.1205	+	27.9216i	−0.512603	+	0.887855i
$990$		0			0
$991$	23.4178	+	40.5608i	0.743890	+	1.28846i	0.950712	+	0.310077i	$0.100355\pi$
$991$	23.4178	+	40.5608i	0.743890	+	1.28846i	−0.206822	+	0.978379i	$0.566312\pi$
$992$	−0.648981	+	1.12407i	−0.0206052	+	0.0356892i
$993$		0			0
$994$	−57.5970	−	10.6663i	−1.82687	−	0.338314i
$995$	−5.95754			−0.188867
$996$		0			0
$997$	−1.29253	−	2.23872i	−0.0409348	−	0.0709011i	0.844832	−	0.535031i	$-0.179700\pi$
$997$	−1.29253	−	2.23872i	−0.0409348	−	0.0709011i	−0.885767	+	0.464130i	$0.846367\pi$
$998$	6.84189	+	11.8505i	0.216576	+	0.375121i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.i.k.100.2	✓	12
3.2	odd	2		693.2.i.l.100.5	yes	12
7.2	even	3		4851.2.a.cd.1.5		6
7.4	even	3	inner	693.2.i.k.298.2	yes	12
7.5	odd	6		4851.2.a.cb.1.5		6
21.2	odd	6		4851.2.a.cc.1.2		6
21.5	even	6		4851.2.a.ce.1.2		6
21.11	odd	6		693.2.i.l.298.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.i.k.100.2	✓	12	1.1	even	1	trivial
693.2.i.k.298.2	yes	12	7.4	even	3	inner
693.2.i.l.100.5	yes	12	3.2	odd	2
693.2.i.l.298.5	yes	12	21.11	odd	6
4851.2.a.cb.1.5		6	7.5	odd	6
4851.2.a.cc.1.2		6	21.2	odd	6
4851.2.a.cd.1.5		6	7.2	even	3
4851.2.a.ce.1.2		6	21.5	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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.823543 + 1.42642i) q^{2} +(-0.356445 - 0.617380i) q^{4} +(0.143555 - 0.248645i) q^{5} +(-0.883533 - 2.49387i) q^{7} -2.11998 q^{8} +O(q^{10})\)	\(q+(-0.823543 + 1.42642i) q^{2} +(-0.356445 - 0.617380i) q^{4} +(0.143555 - 0.248645i) q^{5} +(-0.883533 - 2.49387i) q^{7} -2.11998 q^{8} +(0.236448 + 0.409540i) q^{10} +(-0.500000 - 0.866025i) q^{11} +5.70645 q^{13} +(4.28492 + 0.793518i) q^{14} +(2.45878 - 4.25874i) q^{16} +(2.91322 + 5.04584i) q^{17} +(-1.03540 + 1.79337i) q^{19} -0.204678 q^{20} +1.64709 q^{22} +(-2.56509 + 4.44286i) q^{23} +(2.45878 + 4.25874i) q^{25} +(-4.69951 + 8.13978i) q^{26} +(-1.22473 + 1.43440i) q^{28} +7.56614 q^{29} +(0.168143 + 0.291233i) q^{31} +(1.92985 + 3.34259i) q^{32} -9.59663 q^{34} +(-0.746924 - 0.138322i) q^{35} +(5.48662 - 9.50310i) q^{37} +(-1.70540 - 2.95383i) q^{38} +(-0.304335 + 0.527123i) q^{40} +9.13223 q^{41} +6.28460 q^{43} +(-0.356445 + 0.617380i) q^{44} +(-4.22492 - 7.31777i) q^{46} +(-2.65723 + 4.60246i) q^{47} +(-5.43874 + 4.40683i) q^{49} -8.09965 q^{50} +(-2.03403 - 3.52305i) q^{52} +(-0.881033 - 1.52599i) q^{53} -0.287111 q^{55} +(1.87307 + 5.28695i) q^{56} +(-6.23104 + 10.7925i) q^{58} +(-5.56509 - 9.63901i) q^{59} +(-4.50031 + 7.79477i) q^{61} -0.553893 q^{62} +3.47790 q^{64} +(0.819192 - 1.41888i) q^{65} +(6.22661 + 10.7848i) q^{67} +(2.07680 - 3.59712i) q^{68} +(0.812428 - 0.951511i) q^{70} -13.4418 q^{71} +(-4.24351 - 7.34997i) q^{73} +(9.03693 + 15.6524i) q^{74} +1.47625 q^{76} +(-1.71799 + 2.01210i) q^{77} +(-6.04920 + 10.4775i) q^{79} +(-0.705943 - 1.22273i) q^{80} +(-7.52078 + 13.0264i) q^{82} +16.7071 q^{83} +1.67283 q^{85} +(-5.17564 + 8.96447i) q^{86} +(1.05999 + 1.83596i) q^{88} +(6.16182 - 10.6726i) q^{89} +(-5.04184 - 14.2311i) q^{91} +3.65725 q^{92} +(-4.37669 - 7.58065i) q^{94} +(0.297275 + 0.514896i) q^{95} -6.63046 q^{97} +(-1.80694 - 11.3871i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} - 4 q^{5} + 6 q^{7} - 12 q^{8}+O(q^{10}) \) 12 * q - 10 * q^4 - 4 * q^5 + 6 * q^7 - 12 * q^8	\( 12 q - 10 q^{4} - 4 q^{5} + 6 q^{7} - 12 q^{8} + 6 q^{10} - 6 q^{11} - 4 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{17} - 6 q^{19} + 72 q^{20} + 2 q^{23} - 2 q^{25} - 8 q^{26} - 28 q^{28} - 4 q^{29} - 4 q^{31} + 12 q^{32} + 28 q^{34} + 26 q^{35} + 6 q^{37} - 10 q^{38} + 18 q^{40} + 60 q^{41} - 24 q^{43} - 10 q^{44} + 4 q^{46} - 14 q^{47} - 12 q^{49} - 48 q^{50} + 22 q^{52} - 16 q^{53} + 8 q^{55} + 60 q^{56} - 2 q^{58} - 34 q^{59} + 2 q^{61} + 52 q^{62} + 4 q^{64} + 20 q^{65} + 20 q^{67} - 18 q^{68} - 24 q^{70} - 12 q^{71} - 26 q^{73} - 14 q^{74} - 8 q^{76} - 6 q^{77} - 2 q^{79} - 44 q^{80} + 4 q^{82} + 16 q^{83} + 20 q^{85} - 78 q^{86} + 6 q^{88} - 20 q^{89} + 20 q^{91} - 60 q^{92} + 10 q^{94} + 10 q^{95} - 28 q^{97} + 90 q^{98}+O(q^{100}) \) 12 * q - 10 * q^4 - 4 * q^5 + 6 * q^7 - 12 * q^8 + 6 * q^10 - 6 * q^11 - 4 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^17 - 6 * q^19 + 72 * q^20 + 2 * q^23 - 2 * q^25 - 8 * q^26 - 28 * q^28 - 4 * q^29 - 4 * q^31 + 12 * q^32 + 28 * q^34 + 26 * q^35 + 6 * q^37 - 10 * q^38 + 18 * q^40 + 60 * q^41 - 24 * q^43 - 10 * q^44 + 4 * q^46 - 14 * q^47 - 12 * q^49 - 48 * q^50 + 22 * q^52 - 16 * q^53 + 8 * q^55 + 60 * q^56 - 2 * q^58 - 34 * q^59 + 2 * q^61 + 52 * q^62 + 4 * q^64 + 20 * q^65 + 20 * q^67 - 18 * q^68 - 24 * q^70 - 12 * q^71 - 26 * q^73 - 14 * q^74 - 8 * q^76 - 6 * q^77 - 2 * q^79 - 44 * q^80 + 4 * q^82 + 16 * q^83 + 20 * q^85 - 78 * q^86 + 6 * q^88 - 20 * q^89 + 20 * q^91 - 60 * q^92 + 10 * q^94 + 10 * q^95 - 28 * q^97 + 90 * q^98

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