LMFDB - Embedded newform 720.2.z.f.667.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(163,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("720.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.z (of order $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			667.4
Root			$0.237728 + 1.39409i$ of defining polynomial
Character	$\chi$	$=$	720.667
Dual form			720.2.z.f.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.429059 - 1.34756i) q^{2} +(-1.63182 + 1.15636i) q^{4} +(-2.23531 + 0.0583995i) q^{5} +(0.747384 + 0.747384i) q^{7} +(2.25841 + 1.70282i) q^{8} +(1.03777 + 2.98714i) q^{10} +(0.920311 - 0.920311i) q^{11} -0.996441i q^{13} +(0.686471 - 1.32781i) q^{14} +(1.32566 - 3.77394i) q^{16} +(0.982332 + 0.982332i) q^{17} +(-1.03458 + 1.03458i) q^{19} +(3.58008 - 2.68012i) q^{20} +(-1.63504 - 0.845304i) q^{22} +(4.77394 - 4.77394i) q^{23} +(4.99318 - 0.261081i) q^{25} +(-1.34276 + 0.427532i) q^{26} +(-2.08384 - 0.355348i) q^{28} +(2.95516 + 2.95516i) q^{29} -10.4545i q^{31} +(-5.65438 - 0.167155i) q^{32} +(0.902270 - 1.74523i) q^{34} +(-1.71428 - 1.62698i) q^{35} -8.22694i q^{37} +(1.83805 + 0.950259i) q^{38} +(-5.14767 - 3.67443i) q^{40} -5.70040i q^{41} +5.22869i q^{43} +(-0.437567 + 2.56599i) q^{44} +(-8.48146 - 4.38486i) q^{46} +(-0.0548243 + 0.0548243i) q^{47} -5.88283i q^{49} +(-2.49419 - 6.61657i) q^{50} +(1.15225 + 1.62601i) q^{52} -5.13957 q^{53} +(-2.00343 + 2.11092i) q^{55} +(0.415238 + 2.96056i) q^{56} +(2.71431 - 5.25018i) q^{58} +(2.30403 + 2.30403i) q^{59} +(10.8244 - 10.8244i) q^{61} +(-14.0880 + 4.48559i) q^{62} +(2.20081 + 7.69132i) q^{64} +(0.0581916 + 2.22735i) q^{65} +8.99029i q^{67} +(-2.73892 - 0.467056i) q^{68} +(-1.45693 + 3.00816i) q^{70} +14.1421 q^{71} +(6.35840 + 6.35840i) q^{73} +(-11.0863 + 3.52984i) q^{74} +(0.491897 - 2.88459i) q^{76} +1.37565 q^{77} -8.76588 q^{79} +(-2.74285 + 8.51333i) q^{80} +(-7.68161 + 2.44581i) q^{82} -12.3589 q^{83} +(-2.25318 - 2.13845i) q^{85} +(7.04595 - 2.24341i) q^{86} +(3.64556 - 0.511314i) q^{88} +18.0456 q^{89} +(0.744724 - 0.744724i) q^{91} +(-2.26980 + 13.3106i) q^{92} +(0.0974017 + 0.0503560i) q^{94} +(2.25218 - 2.37302i) q^{95} +(1.29787 + 1.29787i) q^{97} +(-7.92745 + 2.52408i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 14 q^{10} + 4 q^{14} - 8 q^{16} + 8 q^{17} + 8 q^{19} + 12 q^{20} - 8 q^{22} + 32 q^{25} - 20 q^{26} + 12 q^{28} - 12 q^{29} + 28 q^{32} + 20 q^{35}+ \cdots - 30 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 14 * q^10 + 4 * q^14 - 8 * q^16 + 8 * q^17 + 8 * q^19 + 12 * q^20 - 8 * q^22 + 32 * q^25 - 20 * q^26 + 12 * q^28 - 12 * q^29 + 28 * q^32 + 20 * q^35 + 16 * q^38 - 44 * q^40 - 52 * q^44 - 16 * q^46 + 32 * q^47 - 22 * q^50 + 8 * q^52 - 16 * q^53 - 4 * q^55 - 20 * q^56 - 44 * q^58 + 24 * q^59 + 40 * q^61 - 40 * q^62 - 8 * q^64 + 4 * q^65 - 24 * q^68 + 56 * q^70 + 8 * q^73 - 64 * q^74 + 16 * q^76 + 72 * q^77 - 48 * q^79 - 16 * q^80 + 8 * q^82 + 8 * q^83 - 8 * q^85 + 8 * q^86 - 16 * q^88 - 40 * q^91 - 20 * q^94 - 8 * q^95 + 48 * q^97 - 30 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.429059	−	1.34756i	−0.303390	−	0.952866i
$2$	−0.429059	−	1.34756i	−0.303390	−	0.952866i
$3$		0			0
$3$		0			0
$4$	−1.63182	+	1.15636i	−0.815909	+	0.578181i
$5$	−2.23531	+	0.0583995i	−0.999659	+	0.0261170i
$5$	−2.23531	+	0.0583995i	−0.999659	+	0.0261170i
$6$		0			0
$7$	0.747384	+	0.747384i	0.282485	+	0.282485i	0.834099	−	0.551615i	$-0.185988\pi$
$7$	0.747384	+	0.747384i	0.282485	+	0.282485i	−0.551615	+	0.834099i	$0.685988\pi$
$8$	2.25841	+	1.70282i	0.798468	+	0.602038i
$9$		0			0
$10$	1.03777	+	2.98714i	0.328173	+	0.944618i
$11$	0.920311	−	0.920311i	0.277484	−	0.277484i	−0.554620	−	0.832104i	$-0.687136\pi$
$11$	0.920311	−	0.920311i	0.277484	−	0.277484i	0.832104	+	0.554620i	$0.187136\pi$
$12$		0			0
$13$		−	0.996441i		−	0.276363i	−0.990407	−	0.138182i	$-0.955874\pi$
$13$		−	0.996441i		−	0.276363i	0.990407	−	0.138182i	$-0.0441257\pi$
$14$	0.686471	−	1.32781i	0.183467	−	0.354873i
$15$		0			0
$16$	1.32566	−	3.77394i	0.331414	−	0.943485i
$17$	0.982332	+	0.982332i	0.238251	+	0.238251i	0.816125	−	0.577875i	$-0.196118\pi$
$17$	0.982332	+	0.982332i	0.238251	+	0.238251i	−0.577875	+	0.816125i	$0.696118\pi$
$18$		0			0
$19$	−1.03458	+	1.03458i	−0.237349	+	0.237349i	−0.815751	−	0.578403i	$-0.803676\pi$
$19$	−1.03458	+	1.03458i	−0.237349	+	0.237349i	0.578403	+	0.815751i	$0.303676\pi$
$20$	3.58008	−	2.68012i	0.800530	−	0.599293i
$21$		0			0
$22$	−1.63504	−	0.845304i	−0.348591	−	0.180219i
$23$	4.77394	−	4.77394i	0.995436	−	0.995436i	−0.00455400	−	0.999990i	$-0.501450\pi$
$23$	4.77394	−	4.77394i	0.995436	−	0.995436i	0.999990	+	0.00455400i	$0.00144959\pi$
$24$		0			0
$25$	4.99318	−	0.261081i	0.998636	−	0.0522163i
$26$	−1.34276	+	0.427532i	−0.263337	+	0.0838458i
$27$		0			0
$28$	−2.08384	−	0.355348i	−0.393809	−	0.0671545i
$29$	2.95516	+	2.95516i	0.548760	+	0.548760i	0.926082	−	0.377322i	$-0.123155\pi$
$29$	2.95516	+	2.95516i	0.548760	+	0.548760i	−0.377322	+	0.926082i	$0.623155\pi$
$30$		0			0
$31$		−	10.4545i		−	1.87768i	−0.344351	−	0.938841i	$-0.611901\pi$
$31$		−	10.4545i		−	1.87768i	0.344351	−	0.938841i	$-0.388099\pi$
$32$	−5.65438	−	0.167155i	−0.999563	−	0.0295491i
$33$		0			0
$34$	0.902270	−	1.74523i	0.154738	−	0.299304i
$35$	−1.71428	−	1.62698i	−0.289766	−	0.275011i
$36$		0			0
$37$		−	8.22694i		−	1.35250i	−0.736672	−	0.676251i	$-0.763604\pi$
$37$		−	8.22694i		−	1.35250i	0.736672	−	0.676251i	$-0.236396\pi$
$38$	1.83805	+	0.950259i	0.298171	+	0.154152i
$39$		0			0
$40$	−5.14767	−	3.67443i	−0.813919	−	0.580979i
$41$		−	5.70040i		−	0.890253i	−0.895468	−	0.445127i	$-0.853159\pi$
$41$		−	5.70040i		−	0.890253i	0.895468	−	0.445127i	$-0.146841\pi$
$42$		0			0
$43$			5.22869i			0.797368i	0.917088	+	0.398684i	$0.130533\pi$
$43$			5.22869i			0.797368i	−0.917088	+	0.398684i	$0.869467\pi$
$44$	−0.437567	+	2.56599i	−0.0659658	+	0.386838i
$45$		0			0
$46$	−8.48146	−	4.38486i	−1.25052	−	0.646512i
$47$	−0.0548243	+	0.0548243i	−0.00799695	+	0.00799695i	−0.711094	−	0.703097i	$-0.751800\pi$
$47$	−0.0548243	+	0.0548243i	−0.00799695	+	0.00799695i	0.703097	+	0.711094i	$0.251800\pi$
$48$		0			0
$49$		−	5.88283i		−	0.840405i
$50$	−2.49419	−	6.61657i	−0.352731	−	0.935725i
$51$		0			0
$52$	1.15225	+	1.62601i	0.159788	+	0.225487i
$53$	−5.13957			−0.705974			−0.352987	−	0.935628i	$-0.614834\pi$
$53$	−5.13957			−0.705974			−0.352987	+	0.935628i	$0.614834\pi$
$54$		0			0
$55$	−2.00343	+	2.11092i	−0.270142	+	0.284637i
$56$	0.415238	+	2.96056i	0.0554885	+	0.395621i
$57$		0			0
$58$	2.71431	−	5.25018i	0.356406	−	0.689383i
$59$	2.30403	+	2.30403i	0.299959	+	0.299959i	0.840998	−	0.541039i	$-0.181969\pi$
$59$	2.30403	+	2.30403i	0.299959	+	0.299959i	−0.541039	+	0.840998i	$0.681969\pi$
$60$		0			0
$61$	10.8244	−	10.8244i	1.38592	−	1.38592i	0.552234	−	0.833689i	$-0.313776\pi$
$61$	10.8244	−	10.8244i	1.38592	−	1.38592i	0.833689	−	0.552234i	$-0.186224\pi$
$62$	−14.0880	+	4.48559i	−1.78918	+	0.569670i
$63$		0			0
$64$	2.20081	+	7.69132i	0.275101	+	0.961415i
$65$	0.0581916	+	2.22735i	0.00721778	+	0.276269i
$66$		0			0
$67$			8.99029i			1.09834i	0.835711	+	0.549169i	$0.185056\pi$
$67$			8.99029i			1.09834i	−0.835711	+	0.549169i	$0.814944\pi$
$68$	−2.73892	−	0.467056i	−0.332143	−	0.0566388i
$69$		0			0
$70$	−1.45693	+	3.00816i	−0.174136	+	0.359544i
$71$	14.1421			1.67836			0.839180	−	0.543853i	$-0.183035\pi$
$71$	14.1421			1.67836			0.839180	+	0.543853i	$0.183035\pi$
$72$		0			0
$73$	6.35840	+	6.35840i	0.744195	+	0.744195i	0.973382	−	0.229188i	$-0.0736070\pi$
$73$	6.35840	+	6.35840i	0.744195	+	0.744195i	−0.229188	+	0.973382i	$0.573607\pi$
$74$	−11.0863	+	3.52984i	−1.28875	+	0.410336i
$75$		0			0
$76$	0.491897	−	2.88459i	0.0564245	−	0.330886i
$77$	1.37565			0.156770
$78$		0			0
$79$	−8.76588			−0.986238			−0.493119	−	0.869962i	$-0.664143\pi$
$79$	−8.76588			−0.986238			−0.493119	+	0.869962i	$0.664143\pi$
$80$	−2.74285	+	8.51333i	−0.306660	+	0.951819i
$81$		0			0
$82$	−7.68161	+	2.44581i	−0.848292	+	0.270094i
$83$	−12.3589			−1.35657			−0.678284	−	0.734800i	$-0.737276\pi$
$83$	−12.3589			−1.35657			−0.678284	+	0.734800i	$0.737276\pi$
$84$		0			0
$85$	−2.25318	−	2.13845i	−0.244392	−	0.231947i
$86$	7.04595	−	2.24341i	0.759785	−	0.241914i
$87$		0			0
$88$	3.64556	−	0.511314i	0.388618	−	0.0545062i
$89$	18.0456			1.91283			0.956414	−	0.292014i	$-0.0943254\pi$
$89$	18.0456			1.91283			0.956414	+	0.292014i	$0.0943254\pi$
$90$		0			0
$91$	0.744724	−	0.744724i	0.0780683	−	0.0780683i
$92$	−2.26980	+	13.3106i	−0.236643	+	1.38773i
$93$		0			0
$94$	0.0974017	+	0.0503560i	0.0100462	+	0.00519383i
$95$	2.25218	−	2.37302i	0.231069	−	0.243467i
$96$		0			0
$97$	1.29787	+	1.29787i	0.131779	+	0.131779i	0.769920	−	0.638141i	$-0.220296\pi$
$97$	1.29787	+	1.29787i	0.131779	+	0.131779i	−0.638141	+	0.769920i	$0.720296\pi$
$98$	−7.92745	+	2.52408i	−0.800794	+	0.254971i
$99$		0			0
$100$	−7.84605	+	6.19996i	−0.784605	+	0.619996i
$101$	−4.25125	−	4.25125i	−0.423015	−	0.423015i	0.463225	−	0.886241i	$-0.346692\pi$
$101$	−4.25125	−	4.25125i	−0.423015	−	0.423015i	−0.886241	+	0.463225i	$0.846692\pi$
$102$		0			0
$103$	−5.92346	+	5.92346i	−0.583656	+	0.583656i	−0.935906	−	0.352250i	$-0.885417\pi$
$103$	−5.92346	+	5.92346i	−0.583656	+	0.583656i	0.352250	+	0.935906i	$0.385417\pi$
$104$	1.69676	−	2.25037i	0.166381	−	0.220667i
$105$		0			0
$106$	2.20518	+	6.92586i	0.214186	+	0.672699i
$107$	0.0554707			0.00536256			0.00268128	−	0.999996i	$-0.499147\pi$
$107$	0.0554707			0.00536256			0.00268128	+	0.999996i	$0.499147\pi$
$108$		0			0
$109$	−0.947769	−	0.947769i	−0.0907798	−	0.0907798i	0.660259	−	0.751038i	$-0.270447\pi$
$109$	−0.947769	−	0.947769i	−0.0907798	−	0.0907798i	−0.751038	+	0.660259i	$0.770447\pi$
$110$	3.70418	+	1.79403i	0.353179	+	0.171054i
$111$		0			0
$112$	3.81136	−	1.82981i	0.360139	−	0.172901i
$113$	10.8801	−	10.8801i	1.02351	−	1.02351i	0.0237977	−	0.999717i	$-0.492424\pi$
$113$	10.8801	−	10.8801i	1.02351	−	1.02351i	0.999717	−	0.0237977i	$-0.00757577\pi$
$114$		0			0
$115$	−10.3924	+	10.9500i	−0.969098	+	1.02109i
$116$	−8.23952	−	1.40505i	−0.765020	−	0.130456i
$117$		0			0
$118$	2.11624	−	4.09337i	0.194816	−	0.376825i
$119$			1.46836i			0.134604i
$120$		0			0
$121$			9.30606i			0.846005i
$122$	−19.2308	−	9.94219i	−1.74107	−	0.900124i
$123$		0			0
$124$	12.0892	+	17.0598i	1.08564	+	1.53202i
$125$	−11.1460	+	0.875196i	−0.996931	+	0.0782799i
$126$		0			0
$127$	−9.61338	+	9.61338i	−0.853050	+	0.853050i	−0.990508	−	0.137458i	$-0.956107\pi$
$127$	−9.61338	+	9.61338i	−0.853050	+	0.853050i	0.137458	+	0.990508i	$0.456107\pi$
$128$	9.42021	−	6.26575i	0.832637	−	0.553819i
$129$		0			0
$130$	2.97651	−	1.03408i	0.261057	−	0.0906948i
$131$	−5.60184	−	5.60184i	−0.489435	−	0.489435i	0.418693	−	0.908128i	$-0.362488\pi$
$131$	−5.60184	−	5.60184i	−0.489435	−	0.489435i	−0.908128	+	0.418693i	$0.862488\pi$
$132$		0			0
$133$	−1.54646			−0.134095
$134$	12.1149	−	3.85736i	1.04657	−	0.333225i
$135$		0			0
$136$	0.545772	+	3.89124i	0.0467996	+	0.333671i
$137$	4.68373	−	4.68373i	0.400158	−	0.400158i	−0.478130	−	0.878289i	$-0.658685\pi$
$137$	4.68373	−	4.68373i	0.400158	−	0.400158i	0.878289	+	0.478130i	$0.158685\pi$
$138$		0			0
$139$	−1.64971	−	1.64971i	−0.139926	−	0.139926i	0.633674	−	0.773600i	$-0.281546\pi$
$139$	−1.64971	−	1.64971i	−0.139926	−	0.139926i	−0.773600	+	0.633674i	$0.781546\pi$
$140$	4.67877	+	0.672616i	0.395428	+	0.0568465i
$141$		0			0
$142$	−6.06780	−	19.0573i	−0.509198	−	1.59925i
$143$	−0.917036	−	0.917036i	−0.0766864	−	0.0766864i
$144$		0			0
$145$	−6.77827	−	6.43311i	−0.562905	−	0.534241i
$146$	5.84018	−	11.2964i	0.483337	−	0.934899i
$147$		0			0
$148$	9.51332	+	13.4249i	0.781990	+	1.10352i
$149$	12.0813	−	12.0813i	0.989742	−	0.989742i	−0.0102058	−	0.999948i	$-0.503249\pi$
$149$	12.0813	−	12.0813i	0.989742	−	0.989742i	0.999948	+	0.0102058i	$0.00324866\pi$
$150$		0			0
$151$	12.6503			1.02947			0.514735	−	0.857350i	$-0.327890\pi$
$151$	12.6503			1.02947			0.514735	+	0.857350i	$0.327890\pi$
$152$	−4.09821	+	0.574800i	−0.332408	+	0.0466225i
$153$		0			0
$154$	−0.590235	−	1.85377i	−0.0475625	−	0.149381i
$155$	0.610537	+	23.3690i	0.0490395	+	1.87704i
$156$		0			0
$157$	−6.31279			−0.503816			−0.251908	−	0.967751i	$-0.581058\pi$
$157$	−6.31279			−0.503816			−0.251908	+	0.967751i	$0.581058\pi$
$158$	3.76107	+	11.8125i	0.299215	+	0.939753i
$159$		0			0
$160$	12.6490	+	0.0434293i	0.999994	+	0.00343339i
$161$	7.13593			0.562390
$162$		0			0
$163$	14.6329			1.14613			0.573067	−	0.819508i	$-0.305753\pi$
$163$	14.6329			1.14613			0.573067	+	0.819508i	$0.305753\pi$
$164$	6.59172	+	9.30201i	0.514727	+	0.726365i
$165$		0			0
$166$	5.30270	+	16.6543i	0.411569	+	1.29263i
$167$	−5.31380	−	5.31380i	−0.411194	−	0.411194i	0.470960	−	0.882155i	$-0.343908\pi$
$167$	−5.31380	−	5.31380i	−0.411194	−	0.411194i	−0.882155	+	0.470960i	$0.843908\pi$
$168$		0			0
$169$	12.0071			0.923623
$170$	−1.91493	+	3.95381i	−0.146868	+	0.303243i
$171$		0			0
$172$	−6.04625	−	8.53227i	−0.461023	−	0.650579i
$173$		−	13.1537i		−	1.00006i	−0.866008	−	0.500029i	$-0.833322\pi$
$173$		−	13.1537i		−	1.00006i	0.866008	−	0.500029i	$-0.166678\pi$
$174$		0			0
$175$	3.92695	+	3.53669i	0.296849	+	0.267349i
$176$	−2.25318	−	4.69322i	−0.169840	−	0.353764i
$177$		0			0
$178$	−7.74261	−	24.3174i	−0.580333	−	1.82267i
$179$	−12.2215	+	12.2215i	−0.913479	+	0.913479i	−0.996544	−	0.0830647i	$-0.973529\pi$
$179$	−12.2215	+	12.2215i	−0.913479	+	0.913479i	0.0830647	+	0.996544i	$0.473529\pi$
$180$		0			0
$181$	7.77734	+	7.77734i	0.578085	+	0.578085i	0.934375	−	0.356290i	$-0.115959\pi$
$181$	7.77734	+	7.77734i	0.578085	+	0.578085i	−0.356290	+	0.934375i	$0.615959\pi$
$182$	−1.32309	−	0.684027i	−0.0980738	−	0.0507035i
$183$		0			0
$184$	18.9107	−	2.65235i	1.39411	−	0.195534i
$185$	0.480449	+	18.3897i	0.0353233	+	1.35204i
$186$		0			0
$187$	1.80810			0.132222
$188$	0.0260665	−	0.152860i	0.00190110	−	0.0111485i
$189$		0			0
$190$	−4.16410	−	2.01678i	−0.302095	−	0.146313i
$191$			18.2743i			1.32228i	0.750262	+	0.661141i	$0.229927\pi$
$191$			18.2743i			1.32228i	−0.750262	+	0.661141i	$0.770073\pi$
$192$		0			0
$193$	−11.3061	+	11.3061i	−0.813832	+	0.813832i	−0.985206	−	0.171374i	$-0.945179\pi$
$193$	−11.3061	+	11.3061i	−0.813832	+	0.813832i	0.171374	+	0.985206i	$0.445179\pi$
$194$	1.19209	−	2.30582i	0.0855873	−	0.165548i
$195$		0			0
$196$	6.80268	+	9.59971i	0.485906	+	0.685694i
$197$			11.1767i			0.796305i	0.917319	+	0.398153i	$0.130349\pi$
$197$			11.1767i			0.796305i	−0.917319	+	0.398153i	$0.869651\pi$
$198$		0			0
$199$		−	18.8869i		−	1.33886i	−0.742877	−	0.669428i	$-0.766539\pi$
$199$		−	18.8869i		−	1.33886i	0.742877	−	0.669428i	$-0.233461\pi$
$200$	11.7212	+	7.91285i	0.828815	+	0.559523i
$201$		0			0
$202$	−3.90477	+	7.55284i	−0.274738	+	0.531416i
$203$			4.41728i			0.310032i
$204$		0			0
$205$	0.332900	+	12.7421i	0.0232508	+	0.889949i
$206$	10.5237	+	5.44069i	0.733222	+	0.379071i
$207$		0			0
$208$	−3.76051	−	1.32094i	−0.260744	−	0.0915906i
$209$			1.90427i			0.131721i
$210$		0			0
$211$	−7.95311	−	7.95311i	−0.547514	−	0.547514i	0.378207	−	0.925721i	$-0.376541\pi$
$211$	−7.95311	−	7.95311i	−0.547514	−	0.547514i	−0.925721	+	0.378207i	$0.876541\pi$
$212$	8.38684	−	5.94320i	0.576011	−	0.408181i
$213$		0			0
$214$	−0.0238002	−	0.0747499i	−0.00162695	−	0.00510980i
$215$	−0.305353	−	11.6877i	−0.0208249	−	0.797096i
$216$		0			0
$217$	7.81352	−	7.81352i	0.530416	−	0.530416i
$218$	−0.870524	+	1.68382i	−0.0589593	+	0.114043i
$219$		0			0
$220$	0.828244	−	5.76133i	0.0558402	−	0.388429i
$221$	0.978836	−	0.978836i	0.0658437	−	0.0658437i
$222$		0			0
$223$	4.22843	+	4.22843i	0.283157	+	0.283157i	0.834367	−	0.551210i	$-0.185834\pi$
$223$	4.22843	+	4.22843i	0.283157	+	0.283157i	−0.551210	+	0.834367i	$0.685834\pi$
$224$	−4.10107	−	4.35092i	−0.274014	−	0.290708i
$225$		0			0
$226$	−19.3298	−	9.99336i	−1.28580	−	0.664748i
$227$			15.7654i			1.04639i	0.852214	+	0.523193i	$0.175259\pi$
$227$			15.7654i			1.04639i	−0.852214	+	0.523193i	$0.824741\pi$
$228$		0			0
$229$	−0.746140	+	0.746140i	−0.0493063	+	0.0493063i	−0.731330	−	0.682024i	$-0.761100\pi$
$229$	−0.746140	+	0.746140i	−0.0493063	+	0.0493063i	0.682024	+	0.731330i	$0.261100\pi$
$230$	19.2147	+	9.30618i	1.26698	+	0.613631i
$231$		0			0
$232$	1.64185	+	11.7061i	0.107793	+	0.768541i
$233$	5.74517	+	5.74517i	0.376379	+	0.376379i	0.869794	−	0.493415i	$-0.164252\pi$
$233$	5.74517	+	5.74517i	0.376379	+	0.376379i	−0.493415	+	0.869794i	$0.664252\pi$
$234$		0			0
$235$	0.119347	−	0.125751i	0.00778536	−	0.00820308i
$236$	−6.42404	−	1.09546i	−0.418169	−	0.0713086i
$237$		0			0
$238$	1.97870	−	0.630012i	0.128260	−	0.0408376i
$239$	−27.9736			−1.80946			−0.904729	−	0.425987i	$-0.859927\pi$
$239$	−27.9736			−1.80946			−0.904729	+	0.425987i	$0.859927\pi$
$240$		0			0
$241$	−7.01072			−0.451600			−0.225800	−	0.974174i	$-0.572500\pi$
$241$	−7.01072			−0.451600			−0.225800	+	0.974174i	$0.572500\pi$
$242$	12.5404	−	3.99284i	0.806130	−	0.256670i
$243$		0			0
$244$	−5.14653	+	30.1804i	−0.329473	+	1.93210i
$245$	0.343555	+	13.1499i	0.0219489	+	0.840118i
$246$		0			0
$247$	1.03090	+	1.03090i	0.0655945	+	0.0655945i
$248$	17.8021	−	23.6105i	1.13044	−	1.49927i
$249$		0			0
$250$	5.96168	+	14.6444i	0.377050	+	0.926193i
$251$	5.41619	−	5.41619i	0.341867	−	0.341867i	−0.515202	−	0.857069i	$-0.672283\pi$
$251$	5.41619	−	5.41619i	0.341867	−	0.341867i	0.857069	+	0.515202i	$0.172283\pi$
$252$		0			0
$253$		−	8.78702i		−	0.552435i
$254$	17.0793	+	8.82987i	1.07165	+	0.554036i
$255$		0			0
$256$	−12.4853	−	10.0059i	−0.780329	−	0.625369i
$257$	−17.0268	−	17.0268i	−1.06210	−	1.06210i	−0.997940	−	0.0641616i	$-0.979563\pi$
$257$	−17.0268	−	17.0268i	−1.06210	−	1.06210i	−0.0641616	−	0.997940i	$-0.520437\pi$
$258$		0			0
$259$	6.14869	−	6.14869i	0.382061	−	0.382061i
$260$	−2.67058	−	3.56734i	−0.165622	−	0.221237i
$261$		0			0
$262$	−5.14528	+	9.95232i	−0.317877	+	0.614856i
$263$	−7.04662	+	7.04662i	−0.434513	+	0.434513i	−0.890160	−	0.455647i	$-0.849408\pi$
$263$	−7.04662	+	7.04662i	−0.434513	+	0.434513i	0.455647	+	0.890160i	$0.349408\pi$
$264$		0			0
$265$	11.4885	−	0.300148i	0.705734	−	0.0184380i
$266$	0.663520	+	2.08394i	0.0406830	+	0.127774i
$267$		0			0
$268$	−10.3960	−	14.6705i	−0.635038	−	0.896144i
$269$	−13.1762	−	13.1762i	−0.803366	−	0.803366i	0.180254	−	0.983620i	$-0.442308\pi$
$269$	−13.1762	−	13.1762i	−0.803366	−	0.803366i	−0.983620	+	0.180254i	$0.942308\pi$
$270$		0			0
$271$		−	2.01115i		−	0.122169i	−0.998133	−	0.0610845i	$-0.980544\pi$
$271$		−	2.01115i		−	0.122169i	0.998133	−	0.0610845i	$-0.0194559\pi$
$272$	5.00950	−	2.40503i	0.303746	−	0.145826i
$273$		0			0
$274$	−8.32119	−	4.30200i	−0.502702	−	0.259893i
$275$	4.35500	−	4.83555i	0.262616	−	0.291595i
$276$		0			0
$277$		−	5.15280i		−	0.309602i	−0.987946	−	0.154801i	$-0.950526\pi$
$277$		−	5.15280i		−	0.309602i	0.987946	−	0.154801i	$-0.0494736\pi$
$278$	−1.51525	+	2.93089i	−0.0908787	+	0.175783i
$279$		0			0
$280$	−1.10108	−	6.59350i	−0.0658020	−	0.394037i
$281$			14.7480i			0.879791i	0.898049	+	0.439895i	$0.144984\pi$
$281$			14.7480i			0.879791i	−0.898049	+	0.439895i	$0.855016\pi$
$282$		0			0
$283$			7.82068i			0.464891i	0.972609	+	0.232446i	$0.0746728\pi$
$283$			7.82068i			0.464891i	−0.972609	+	0.232446i	$0.925327\pi$
$284$	−23.0774	+	16.3534i	−1.36939	+	0.970396i
$285$		0			0
$286$	−0.842295	+	1.62922i	−0.0498060	+	0.0963378i
$287$	4.26039	−	4.26039i	0.251483	−	0.251483i
$288$		0			0
$289$		−	15.0700i		−	0.886473i
$290$	−5.76070	+	11.8943i	−0.338280	+	0.698456i
$291$		0			0
$292$	−17.7284	−	3.02314i	−1.03747	−	0.176916i
$293$	−19.1115			−1.11651			−0.558254	−	0.829670i	$-0.688529\pi$
$293$	−19.1115			−1.11651			−0.558254	+	0.829670i	$0.688529\pi$
$294$		0			0
$295$	−5.28476	−	5.01565i	−0.307690	−	0.292022i
$296$	14.0090	−	18.5798i	0.814257	−	1.07993i
$297$		0			0
$298$	−21.4639	−	11.0967i	−1.24337	−	0.642814i
$299$	−4.75695	−	4.75695i	−0.275102	−	0.275102i
$300$		0			0
$301$	−3.90784	+	3.90784i	−0.225244	+	0.225244i
$302$	−5.42773	−	17.0470i	−0.312331	−	0.980947i
$303$		0			0
$304$	2.53295	+	5.27594i	0.145274	+	0.302596i
$305$	−23.5637	+	24.8280i	−1.34925	+	1.42165i
$306$		0			0
$307$			3.29048i			0.187798i	0.995582	+	0.0938988i	$0.0299330\pi$
$307$			3.29048i			0.187798i	−0.995582	+	0.0938988i	$0.970067\pi$
$308$	−2.24481	+	1.59075i	−0.127910	+	0.0906414i
$309$		0			0
$310$	31.2291	−	10.8494i	1.77369	−	0.616204i
$311$	10.6744			0.605292			0.302646	−	0.953103i	$-0.402130\pi$
$311$	10.6744			0.605292			0.302646	+	0.953103i	$0.402130\pi$
$312$		0			0
$313$	−21.5451	−	21.5451i	−1.21780	−	1.21780i	−0.968400	−	0.249401i	$-0.919766\pi$
$313$	−21.5451	−	21.5451i	−1.21780	−	1.21780i	−0.249401	−	0.968400i	$-0.580234\pi$
$314$	2.70856	+	8.50684i	0.152853	+	0.480069i
$315$		0			0
$316$	14.3043	−	10.1365i	0.804680	−	0.570224i
$317$	16.1238			0.905603			0.452801	−	0.891611i	$-0.350425\pi$
$317$	16.1238			0.905603			0.452801	+	0.891611i	$0.350425\pi$
$318$		0			0
$319$	5.43934			0.304544
$320$	−5.36865	−	17.0639i	−0.300117	−	0.953902i
$321$		0			0
$322$	−3.06173	−	9.61607i	−0.170624	−	0.535883i
$323$	−2.03260			−0.113097
$324$		0			0
$325$	−0.260152	−	4.97541i	−0.0144306	−	0.275986i
$326$	−6.27835	−	19.7186i	−0.347726	−	1.09211i
$327$		0			0
$328$	9.70675	−	12.8738i	0.535966	−	0.710838i
$329$	−0.0819496			−0.00451803
$330$		0			0
$331$	1.97876	−	1.97876i	0.108762	−	0.108762i	−0.650631	−	0.759394i	$-0.725496\pi$
$331$	1.97876	−	1.97876i	0.108762	−	0.108762i	0.759394	+	0.650631i	$0.225496\pi$
$332$	20.1675	−	14.2914i	1.10684	−	0.784341i
$333$		0			0
$334$	−4.88072	+	9.44058i	−0.267061	+	0.516566i
$335$	−0.525028	−	20.0960i	−0.0286854	−	1.09796i
$336$		0			0
$337$	25.2423	+	25.2423i	1.37503	+	1.37503i	0.852806	+	0.522229i	$0.174899\pi$
$337$	25.2423	+	25.2423i	1.37503	+	1.37503i	0.522229	+	0.852806i	$0.325101\pi$
$338$	−5.15175	−	16.1803i	−0.280218	−	0.880090i
$339$		0			0
$340$	6.14960	+	0.884061i	0.333509	+	0.0479449i
$341$	−9.62138	−	9.62138i	−0.521027	−	0.521027i
$342$		0			0
$343$	9.62842	−	9.62842i	0.519886	−	0.519886i
$344$	−8.90351	+	11.8085i	−0.480045	+	0.636672i
$345$		0			0
$346$	−17.7254	+	5.64372i	−0.952923	+	0.303408i
$347$	−24.1967			−1.29895			−0.649475	−	0.760383i	$-0.725011\pi$
$347$	−24.1967			−1.29895			−0.649475	+	0.760383i	$0.725011\pi$
$348$		0			0
$349$	2.28867	+	2.28867i	0.122510	+	0.122510i	0.765704	−	0.643194i	$-0.222391\pi$
$349$	2.28867	+	2.28867i	0.122510	+	0.122510i	−0.643194	+	0.765704i	$0.722391\pi$
$350$	3.08100	−	6.80924i	0.164687	−	0.363969i
$351$		0			0
$352$	−5.35763	+	5.04996i	−0.285562	+	0.269164i
$353$	9.70578	−	9.70578i	0.516587	−	0.516587i	−0.399950	−	0.916537i	$-0.630973\pi$
$353$	9.70578	−	9.70578i	0.516587	−	0.516587i	0.916537	+	0.399950i	$0.130973\pi$
$354$		0			0
$355$	−31.6120	+	0.825893i	−1.67779	+	0.0438338i
$356$	−29.4471	+	20.8672i	−1.56069	+	1.10596i
$357$		0			0
$358$	21.7129	+	11.2254i	1.14756	+	0.593283i
$359$		−	27.1463i		−	1.43273i	−0.697726	−	0.716365i	$-0.745805\pi$
$359$		−	27.1463i		−	1.43273i	0.697726	−	0.716365i	$-0.254195\pi$
$360$		0			0
$361$			16.8593i			0.887331i
$362$	7.14347	−	13.8173i	0.375452	−	0.726223i
$363$		0			0
$364$	−0.354083	+	2.07642i	−0.0185590	+	0.108834i
$365$	−14.5843	−	13.8416i	−0.763377	−	0.724505i
$366$		0			0
$367$	−16.3750	+	16.3750i	−0.854769	+	0.854769i	−0.990716	−	0.135947i	$-0.956592\pi$
$367$	−16.3750	+	16.3750i	−0.854769	+	0.854769i	0.135947	+	0.990716i	$0.456592\pi$
$368$	−11.6880	−	24.3452i	−0.609278	−	1.26908i
$369$		0			0
$370$	24.5751	−	8.53771i	1.27760	−	0.443854i
$371$	−3.84123	−	3.84123i	−0.199427	−	0.199427i
$372$		0			0
$373$	−29.7473			−1.54026			−0.770129	−	0.637888i	$-0.779808\pi$
$373$	−29.7473			−1.54026			−0.770129	+	0.637888i	$0.779808\pi$
$374$	−0.775782	−	2.43652i	−0.0401147	−	0.125989i
$375$		0			0
$376$	−0.217172	+	0.0304597i	−0.0111998	+	0.00157084i
$377$	2.94464	−	2.94464i	0.151657	−	0.151657i
$378$		0			0
$379$	−11.0584	−	11.0584i	−0.568031	−	0.568031i	0.363546	−	0.931576i	$-0.381566\pi$
$379$	−11.0584	−	11.0584i	−0.568031	−	0.568031i	−0.931576	+	0.363546i	$0.881566\pi$
$380$	−0.931082	+	6.47667i	−0.0477635	+	0.332246i
$381$		0			0
$382$	24.6256	−	7.84074i	1.25996	−	0.401167i
$383$	16.2297	+	16.2297i	0.829298	+	0.829298i	0.987420	−	0.158122i	$-0.0505439\pi$
$383$	16.2297	+	16.2297i	0.829298	+	0.829298i	−0.158122	+	0.987420i	$0.550544\pi$
$384$		0			0
$385$	−3.07500	+	0.0803373i	−0.156717	+	0.00409437i
$386$	20.0866	+	10.3846i	1.02238	+	0.528565i
$387$		0			0
$388$	−3.61870	−	0.617081i	−0.183712	−	0.0313276i
$389$	−12.6341	+	12.6341i	−0.640575	+	0.640575i	−0.950697	−	0.310122i	$-0.899630\pi$
$389$	−12.6341	+	12.6341i	−0.640575	+	0.640575i	0.310122	+	0.950697i	$0.399630\pi$
$390$		0			0
$391$	9.37920			0.474326
$392$	10.0174	−	13.2858i	0.505955	−	0.671036i
$393$		0			0
$394$	15.0612	−	4.79545i	0.758773	−	0.241591i
$395$	19.5944	−	0.511923i	0.985902	−	0.0257576i
$396$		0			0
$397$	−5.42044			−0.272044			−0.136022	−	0.990706i	$-0.543432\pi$
$397$	−5.42044			−0.272044			−0.136022	+	0.990706i	$0.543432\pi$
$398$	−25.4512	+	8.10358i	−1.27575	+	0.406196i
$399$		0			0
$400$	5.63393	−	19.1901i	0.281697	−	0.959504i
$401$	−15.7550			−0.786765			−0.393382	−	0.919375i	$-0.628695\pi$
$401$	−15.7550			−0.786765			−0.393382	+	0.919375i	$0.628695\pi$
$402$		0			0
$403$	−10.4173			−0.518922
$404$	11.8533	+	2.02128i	0.589721	+	0.100563i
$405$		0			0
$406$	5.95254	−	1.89527i	0.295419	−	0.0940608i
$407$	−7.57135	−	7.57135i	−0.375298	−	0.375298i
$408$		0			0
$409$	−30.9442			−1.53009			−0.765046	−	0.643976i	$-0.777284\pi$
$409$	−30.9442			−1.53009			−0.765046	+	0.643976i	$0.777284\pi$
$410$	17.0279	−	5.91573i	0.840949	−	0.292157i
$411$		0			0
$412$	2.81635	−	16.5157i	0.138751	−	0.813669i
$413$			3.44398i			0.169467i
$414$		0			0
$415$	27.6260	−	0.721754i	1.35610	−	0.0354295i
$416$	−0.166560	+	5.63426i	−0.00816628	+	0.276242i
$417$		0			0
$418$	2.56611	−	0.817043i	0.125513	−	0.0399629i
$419$	15.2385	−	15.2385i	0.744451	−	0.744451i	−0.228980	−	0.973431i	$-0.573539\pi$
$419$	15.2385	−	15.2385i	0.744451	−	0.744451i	0.973431	+	0.228980i	$0.0735391\pi$
$420$		0			0
$421$	14.4008	+	14.4008i	0.701852	+	0.701852i	0.964808	−	0.262956i	$-0.0846974\pi$
$421$	14.4008	+	14.4008i	0.701852	+	0.701852i	−0.262956	+	0.964808i	$0.584697\pi$
$422$	−7.30491	+	14.1296i	−0.355598	+	0.687819i
$423$		0			0
$424$	−11.6072	−	8.75176i	−0.563698	−	0.425023i
$425$	5.16143	+	4.64849i	0.250366	+	0.225485i
$426$		0			0
$427$	16.1800			0.783004
$428$	−0.0905181	+	0.0641442i	−0.00437536	+	0.00310053i
$429$		0			0
$430$	−15.6188	+	5.42619i	−0.753208	+	0.261674i
$431$		−	4.47310i		−	0.215461i	−0.994180	−	0.107731i	$-0.965642\pi$
$431$		−	4.47310i		−	0.215461i	0.994180	−	0.107731i	$-0.0343584\pi$
$432$		0			0
$433$	20.8589	−	20.8589i	1.00242	−	1.00242i	0.00241793	−	0.999997i	$-0.499230\pi$
$433$	20.8589	−	20.8589i	1.00242	−	1.00242i	0.999997	−	0.00241793i	$-0.000769652\pi$
$434$	−13.8816	−	7.17670i	−0.666339	−	0.344493i
$435$		0			0
$436$	2.64255	+	0.450622i	0.126555	+	0.0215809i
$437$			9.87805i			0.472531i
$438$		0			0
$439$			0.257771i			0.0123027i	0.999981	+	0.00615136i	$0.00195805\pi$
$439$			0.257771i			0.0123027i	−0.999981	+	0.00615136i	$0.998042\pi$
$440$	−8.11908	+	1.35584i	−0.387062	+	0.0646372i
$441$		0			0
$442$	−1.73902	−	0.899059i	−0.0827165	−	0.0427639i
$443$			27.8275i			1.32212i	0.750331	+	0.661062i	$0.229894\pi$
$443$			27.8275i			1.32212i	−0.750331	+	0.661062i	$0.770106\pi$
$444$		0			0
$445$	−40.3374	+	1.05385i	−1.91218	+	0.0499574i
$446$	3.88380	−	7.51229i	0.183903	−	0.355717i
$447$		0			0
$448$	−4.10352	+	7.39322i	−0.193873	+	0.349297i
$449$		−	7.32170i		−	0.345533i	−0.984963	−	0.172766i	$-0.944729\pi$
$449$		−	7.32170i		−	0.345533i	0.984963	−	0.172766i	$-0.0552705\pi$
$450$		0			0
$451$	−5.24614	−	5.24614i	−0.247031	−	0.247031i
$452$	−5.17301	+	30.3357i	−0.243318	+	1.42687i
$453$		0			0
$454$	21.2448	−	6.76428i	0.997066	−	0.317463i
$455$	−1.62119	+	1.70818i	−0.0760027	+	0.0800806i
$456$		0			0
$457$	13.1962	−	13.1962i	0.617293	−	0.617293i	−0.327543	−	0.944836i	$-0.606221\pi$
$457$	13.1962	−	13.1962i	0.617293	−	0.617293i	0.944836	+	0.327543i	$0.106221\pi$
$458$	1.32560	+	0.685328i	0.0619414	+	0.0320233i
$459$		0			0
$460$	4.29636	−	29.8858i	0.200319	−	1.39343i
$461$	19.6030	−	19.6030i	0.913002	−	0.913002i	−0.0835057	−	0.996507i	$-0.526612\pi$
$461$	19.6030	−	19.6030i	0.913002	−	0.913002i	0.996507	+	0.0835057i	$0.0266117\pi$
$462$		0			0
$463$	−17.2918	−	17.2918i	−0.803619	−	0.803619i	0.180040	−	0.983659i	$-0.442377\pi$
$463$	−17.2918	−	17.2918i	−0.803619	−	0.803619i	−0.983659	+	0.180040i	$0.942377\pi$
$464$	15.0701	−	7.23508i	0.699614	−	0.335880i
$465$		0			0
$466$	5.27693	−	10.2070i	0.244449	−	0.472828i
$467$			31.3895i			1.45253i	0.687413	+	0.726267i	$0.258746\pi$
$467$			31.3895i			1.45253i	−0.687413	+	0.726267i	$0.741254\pi$
$468$		0			0
$469$	−6.71920	+	6.71920i	−0.310264	+	0.310264i
$470$	−0.220663	−	0.106873i	−0.0101784	−	0.00492968i
$471$		0			0
$472$	1.28009	+	9.12677i	0.0589209	+	0.420094i
$473$	4.81202	+	4.81202i	0.221257	+	0.221257i
$474$		0			0
$475$	−4.89573	+	5.43595i	−0.224632	+	0.249419i
$476$	−1.69795	−	2.39609i	−0.0778256	−	0.109825i
$477$		0			0
$478$	12.0023	+	37.6959i	0.548972	+	1.72417i
$479$	−10.4863			−0.479133			−0.239566	−	0.970880i	$-0.577005\pi$
$479$	−10.4863			−0.479133			−0.239566	+	0.970880i	$0.577005\pi$
$480$		0			0
$481$	−8.19767			−0.373781
$482$	3.00801	+	9.44735i	0.137011	+	0.430315i
$483$		0			0
$484$	−10.7612	−	15.1858i	−0.489144	−	0.690263i
$485$	−2.97694	−	2.82535i	−0.135176	−	0.128292i
$486$		0			0
$487$	4.72750	+	4.72750i	0.214224	+	0.214224i	0.806059	−	0.591835i	$-0.201596\pi$
$487$	4.72750	+	4.72750i	0.214224	+	0.214224i	−0.591835	+	0.806059i	$0.701596\pi$
$488$	42.8779	−	6.01391i	1.94099	−	0.272237i
$489$		0			0
$490$	17.5729	−	6.10505i	0.793861	−	0.275798i
$491$	3.00877	−	3.00877i	0.135784	−	0.135784i	−0.635948	−	0.771732i	$-0.719391\pi$
$491$	3.00877	−	3.00877i	0.135784	−	0.135784i	0.771732	+	0.635948i	$0.219391\pi$
$492$		0			0
$493$			5.80590i			0.261485i
$494$	0.946877	−	1.83151i	0.0426020	−	0.0824035i
$495$		0			0
$496$	−39.4546	−	13.8591i	−1.77157	−	0.622290i
$497$	10.5696	+	10.5696i	0.474111	+	0.474111i
$498$		0			0
$499$	−8.75769	+	8.75769i	−0.392048	+	0.392048i	−0.875417	−	0.483369i	$-0.839413\pi$
$499$	−8.75769	+	8.75769i	−0.392048	+	0.392048i	0.483369	+	0.875417i	$0.339413\pi$
$500$	17.1762	−	14.3170i	0.768145	−	0.640276i
$501$		0			0
$502$	−9.62249	−	4.97476i	−0.429473	−	0.222034i
$503$	3.79393	−	3.79393i	0.169163	−	0.169163i	−0.617448	−	0.786611i	$-0.711834\pi$
$503$	3.79393	−	3.79393i	0.169163	−	0.169163i	0.786611	+	0.617448i	$0.211834\pi$
$504$		0			0
$505$	9.75112	+	9.25457i	0.433919	+	0.411823i
$506$	−11.8410	+	3.77015i	−0.526397	+	0.167603i
$507$		0			0
$508$	4.57074	−	26.8038i	0.202794	−	1.18923i
$509$	9.92183	+	9.92183i	0.439777	+	0.439777i	0.891937	−	0.452160i	$-0.149346\pi$
$509$	9.92183	+	9.92183i	0.439777	+	0.439777i	−0.452160	+	0.891937i	$0.649346\pi$
$510$		0			0
$511$			9.50433i			0.420447i
$512$	−8.12660	+	21.1177i	−0.359149	+	0.933280i
$513$		0			0
$514$	−15.6391	+	30.2500i	−0.689809	+	1.33427i
$515$	12.8948	−	13.5867i	0.568214	−	0.598701i
$516$		0			0
$517$			0.100911i			0.00443805i
$518$	−10.9238	−	5.64756i	−0.479966	−	0.248139i
$519$		0			0
$520$	−3.66135	+	5.12935i	−0.160561	+	0.224937i
$521$			31.9555i			1.39999i	0.714146	+	0.699997i	$0.246815\pi$
$521$			31.9555i			1.39999i	−0.714146	+	0.699997i	$0.753185\pi$
$522$		0			0
$523$			24.3222i			1.06354i	0.846890	+	0.531768i	$0.178472\pi$
$523$			24.3222i			1.06354i	−0.846890	+	0.531768i	$0.821528\pi$
$524$	15.6189	+	2.66343i	0.682317	+	0.116352i
$525$		0			0
$526$	12.5191	+	6.47231i	0.545860	+	0.282206i
$527$	10.2698	−	10.2698i	0.447359	−	0.447359i
$528$		0			0
$529$		−	22.5810i		−	0.981784i
$530$	−5.33371	−	15.3526i	−0.231682	−	0.666876i
$531$		0			0
$532$	2.52353	−	1.78826i	0.109409	−	0.0775310i
$533$	−5.68011			−0.246033
$534$		0			0
$535$	−0.123994	+	0.00323946i	−0.00536073	+	0.000140054i
$536$	−15.3088	+	20.3037i	−0.661241	+	0.876988i
$537$		0			0
$538$	−12.1023	+	23.4090i	−0.521767	+	1.00923i
$539$	−5.41404	−	5.41404i	−0.233199	−	0.233199i
$540$		0			0
$541$	24.3708	−	24.3708i	1.04778	−	1.04778i	0.0489835	−	0.998800i	$-0.484402\pi$
$541$	24.3708	−	24.3708i	1.04778	−	1.04778i	0.998800	−	0.0489835i	$-0.0155982\pi$
$542$	−2.71015	+	0.862903i	−0.116411	+	0.0370649i
$543$		0			0
$544$	−5.39028	−	5.71869i	−0.231106	−	0.245187i
$545$	2.17390	+	2.06320i	0.0931197	+	0.0883779i
$546$		0			0
$547$		−	46.2500i		−	1.97751i	−0.149550	−	0.988754i	$-0.547782\pi$
$547$		−	46.2500i		−	1.97751i	0.149550	−	0.988754i	$-0.452218\pi$
$548$	−2.22691	+	13.0591i	−0.0951289	+	0.557857i
$549$		0			0
$550$	−8.38473	−	3.79387i	−0.357526	−	0.161771i
$551$	−6.11470			−0.260495
$552$		0			0
$553$	−6.55147	−	6.55147i	−0.278597	−	0.278597i
$554$	−6.94369	+	2.21085i	−0.295009	+	0.0939301i
$555$		0			0
$556$	4.59967	+	0.784362i	0.195070	+	0.0332644i
$557$	3.18081			0.134775			0.0673876	−	0.997727i	$-0.478534\pi$
$557$	3.18081			0.134775			0.0673876	+	0.997727i	$0.478534\pi$
$558$		0			0
$559$	5.21008			0.220363
$560$	−8.41269	+	4.31276i	−0.355501	+	0.182247i
$561$		0			0
$562$	19.8737	−	6.32775i	0.838323	−	0.266920i
$563$	26.5795			1.12019			0.560096	−	0.828427i	$-0.310764\pi$
$563$	26.5795			1.12019			0.560096	+	0.828427i	$0.310764\pi$
$564$		0			0
$565$	−23.6850	+	24.9558i	−0.996434	+	1.04990i
$566$	10.5388	−	3.35553i	0.442979	−	0.141044i
$567$		0			0
$568$	31.9387	+	24.0815i	1.34012	+	1.01044i
$569$	6.17442			0.258845			0.129423	−	0.991590i	$-0.458688\pi$
$569$	6.17442			0.258845			0.129423	+	0.991590i	$0.458688\pi$
$570$		0			0
$571$	−22.1640	+	22.1640i	−0.927533	+	0.927533i	−0.997546	−	0.0700130i	$-0.977696\pi$
$571$	−22.1640	+	22.1640i	−0.927533	+	0.927533i	0.0700130	+	0.997546i	$0.477696\pi$
$572$	2.55686	+	0.436010i	0.106908	+	0.0182305i
$573$		0			0
$574$	−7.56907	−	3.91316i	−0.315927	−	0.163332i
$575$	22.5908	−	25.0835i	0.942100	−	1.04606i
$576$		0			0
$577$	16.5888	+	16.5888i	0.690601	+	0.690601i	0.962364	−	0.271764i	$-0.0876068\pi$
$577$	16.5888	+	16.5888i	0.690601	+	0.690601i	−0.271764	+	0.962364i	$0.587607\pi$
$578$	−20.3077	+	6.46593i	−0.844691	+	0.268947i
$579$		0			0
$580$	18.4999	+	2.65953i	0.768166	+	0.110431i
$581$	−9.23686	−	9.23686i	−0.383209	−	0.383209i
$582$		0			0
$583$	−4.73000	+	4.73000i	−0.195897	+	0.195897i
$584$	3.53265	+	25.1871i	0.146182	+	1.04225i
$585$		0			0
$586$	8.19997	+	25.7539i	0.338738	+	1.06388i
$587$	−4.69495			−0.193781			−0.0968907	−	0.995295i	$-0.530890\pi$
$587$	−4.69495			−0.193781			−0.0968907	+	0.995295i	$0.530890\pi$
$588$		0			0
$589$	10.8160	+	10.8160i	0.445666	+	0.445666i
$590$	−4.49140	+	9.27351i	−0.184908	+	0.381785i
$591$		0			0
$592$	−31.0480	−	10.9061i	−1.27607	−	0.448238i
$593$	−16.7482	+	16.7482i	−0.687765	+	0.687765i	−0.961738	−	0.273972i	$-0.911662\pi$
$593$	−16.7482	+	16.7482i	−0.687765	+	0.687765i	0.273972	+	0.961738i	$0.411662\pi$
$594$		0			0
$595$	−0.0857514	−	3.28223i	−0.00351546	−	0.134558i
$596$	−5.74415	+	33.6849i	−0.235289	+	1.37979i
$597$		0			0
$598$	−4.36925	+	8.45127i	−0.178672	+	0.345598i
$599$		−	3.09289i		−	0.126372i	−0.998002	−	0.0631860i	$-0.979874\pi$
$599$		−	3.09289i		−	0.126372i	0.998002	−	0.0631860i	$-0.0201261\pi$
$600$		0			0
$601$			23.3900i			0.954099i	0.878876	+	0.477050i	$0.158294\pi$
$601$			23.3900i			0.954099i	−0.878876	+	0.477050i	$0.841706\pi$
$602$	6.94272	+	3.58934i	0.282964	+	0.146291i
$603$		0			0
$604$	−20.6430	+	14.6284i	−0.839953	+	0.595219i
$605$	−0.543469	−	20.8019i	−0.0220952	−	0.845716i
$606$		0			0
$607$	25.7183	−	25.7183i	1.04387	−	1.04387i	0.0448798	−	0.998992i	$-0.485710\pi$
$607$	25.7183	−	25.7183i	1.04387	−	1.04387i	0.998992	−	0.0448798i	$-0.0142905\pi$
$608$	6.02285	−	5.67698i	0.244259	−	0.230232i
$609$		0			0
$610$	43.5673	+	21.1008i	1.76399	+	0.854345i
$611$	0.0546292	+	0.0546292i	0.00221006	+	0.00221006i
$612$		0			0
$613$	35.2830			1.42507			0.712533	−	0.701639i	$-0.247548\pi$
$613$	35.2830			1.42507			0.712533	+	0.701639i	$0.247548\pi$
$614$	4.43411	−	1.41181i	0.178946	−	0.0569760i
$615$		0			0
$616$	3.10678	+	2.34249i	0.125176	+	0.0943814i
$617$	−4.50814	+	4.50814i	−0.181491	+	0.181491i	−0.792005	−	0.610514i	$-0.790963\pi$
$617$	−4.50814	+	4.50814i	−0.181491	+	0.181491i	0.610514	+	0.792005i	$0.290963\pi$
$618$		0			0
$619$	1.70323	+	1.70323i	0.0684586	+	0.0684586i	0.740507	−	0.672048i	$-0.234585\pi$
$619$	1.70323	+	1.70323i	0.0684586	+	0.0684586i	−0.672048	+	0.740507i	$0.734585\pi$
$620$	−28.0193	−	37.4279i	−1.12528	−	1.50314i
$621$		0			0
$622$	−4.57996	−	14.3844i	−0.183640	−	0.576763i
$623$	13.4870	+	13.4870i	0.540344	+	0.540344i
$624$		0			0
$625$	24.8637	−	2.60725i	0.994547	−	0.104290i
$626$	−19.7891	+	38.2774i	−0.790933	+	1.52987i
$627$		0			0
$628$	10.3013	−	7.29987i	0.411068	−	0.291296i
$629$	8.08159	−	8.08159i	0.322234	−	0.322234i
$630$		0			0
$631$	16.8799			0.671980			0.335990	−	0.941866i	$-0.390929\pi$
$631$	16.8799			0.671980			0.335990	+	0.941866i	$0.390929\pi$
$632$	−19.7969	−	14.9267i	−0.787479	−	0.593752i
$633$		0			0
$634$	−6.91805	−	21.7277i	−0.274751	−	0.862918i
$635$	20.9274	−	22.0503i	0.830480	−	0.875038i
$636$		0			0
$637$	−5.86190			−0.232257
$638$	−2.33379	−	7.32981i	−0.0923958	−	0.290190i
$639$		0			0
$640$	−20.6911	+	14.5560i	−0.817889	+	0.575376i
$641$	36.2647			1.43237			0.716185	−	0.697911i	$-0.245887\pi$
$641$	36.2647			1.43237			0.716185	+	0.697911i	$0.245887\pi$
$642$		0			0
$643$	43.9474			1.73312			0.866559	−	0.499074i	$-0.166327\pi$
$643$	43.9474			1.73312			0.866559	+	0.499074i	$0.166327\pi$
$644$	−11.6445	+	8.25172i	−0.458859	+	0.325163i
$645$		0			0
$646$	0.872106	+	2.73905i	0.0343125	+	0.107766i
$647$	2.77825	+	2.77825i	0.109224	+	0.109224i	0.759607	−	0.650382i	$-0.225391\pi$
$647$	2.77825	+	2.77825i	0.109224	+	0.109224i	−0.650382	+	0.759607i	$0.725391\pi$
$648$		0			0
$649$	4.24084			0.166468
$650$	−6.59302	+	2.48531i	−0.258600	+	0.0974819i
$651$		0			0
$652$	−23.8782	+	16.9209i	−0.935141	+	0.662673i
$653$			15.8532i			0.620384i	0.950674	+	0.310192i	$0.100393\pi$
$653$			15.8532i			0.620384i	−0.950674	+	0.310192i	$0.899607\pi$
$654$		0			0
$655$	12.8490	+	12.1947i	0.502051	+	0.476486i
$656$	−21.5130	−	7.55677i	−0.839941	−	0.295042i
$657$		0			0
$658$	0.0351612	+	0.110432i	0.00137073	+	0.00430508i
$659$	−3.02357	+	3.02357i	−0.117781	+	0.117781i	−0.763541	−	0.645759i	$-0.776541\pi$
$659$	−3.02357	+	3.02357i	−0.117781	+	0.117781i	0.645759	+	0.763541i	$0.276541\pi$
$660$		0			0
$661$	−14.5980	−	14.5980i	−0.567797	−	0.567797i	0.363714	−	0.931511i	$-0.381509\pi$
$661$	−14.5980	−	14.5980i	−0.567797	−	0.567797i	−0.931511	+	0.363714i	$0.881509\pi$
$662$	−3.51549	−	1.81749i	−0.136634	−	0.0706386i
$663$		0			0
$664$	−27.9115	−	21.0450i	−1.08318	−	0.816705i
$665$	3.45680	−	0.0903123i	0.134049	−	0.00350216i
$666$		0			0
$667$	28.2155			1.09251
$668$	14.8158	+	2.52648i	0.573242	+	0.0977524i
$669$		0			0
$670$	−26.8553	+	9.32989i	−1.03751	+	0.360445i
$671$		−	19.9236i		−	0.769143i
$672$		0			0
$673$	−11.2973	+	11.2973i	−0.435481	+	0.435481i	−0.890488	−	0.455007i	$-0.849637\pi$
$673$	−11.2973	+	11.2973i	−0.435481	+	0.435481i	0.455007	+	0.890488i	$0.349637\pi$
$674$	23.1850	−	44.8458i	0.893052	−	1.72740i
$675$		0			0
$676$	−19.5934	+	13.8846i	−0.753592	+	0.534021i
$677$		−	9.23434i		−	0.354905i	−0.984129	−	0.177452i	$-0.943214\pi$
$677$		−	9.23434i		−	0.354905i	0.984129	−	0.177452i	$-0.0567855\pi$
$678$		0			0
$679$			1.94002i			0.0744510i
$680$	−1.44721	−	8.66624i	−0.0554981	−	0.332335i
$681$		0			0
$682$	−8.83722	+	17.0935i	−0.338395	+	0.654544i
$683$			10.8971i			0.416967i	0.978026	+	0.208483i	$0.0668527\pi$
$683$			10.8971i			0.416967i	−0.978026	+	0.208483i	$0.933147\pi$
$684$		0			0
$685$	−10.1960	+	10.7431i	−0.389571	+	0.410473i
$686$	−17.1060	−	8.84369i	−0.653110	−	0.337654i
$687$		0			0
$688$	19.7328	+	6.93144i	0.752305	+	0.264259i
$689$			5.12128i			0.195105i
$690$		0			0
$691$	−12.7458	−	12.7458i	−0.484873	−	0.484873i	0.421811	−	0.906684i	$-0.361395\pi$
$691$	−12.7458	−	12.7458i	−0.484873	−	0.484873i	−0.906684	+	0.421811i	$0.861395\pi$
$692$	15.2105	+	21.4645i	0.578215	+	0.815957i
$693$		0			0
$694$	10.3818	+	32.6065i	0.394089	+	1.23773i
$695$	3.78394	+	3.59125i	0.143533	+	0.136224i
$696$		0			0
$697$	5.59969	−	5.59969i	0.212103	−	0.212103i
$698$	2.10214	−	4.06609i	0.0795673	−	0.153904i
$699$		0			0
$700$	−10.4978	−	1.23027i	−0.396778	−	0.0464997i
$701$	−28.0269	+	28.0269i	−1.05856	+	1.05856i	−0.0603853	+	0.998175i	$0.519233\pi$
$701$	−28.0269	+	28.0269i	−1.05856	+	1.05856i	−0.998175	+	0.0603853i	$0.980767\pi$
$702$		0			0
$703$	8.51143	+	8.51143i	0.321015	+	0.321015i
$704$	9.10384	+	5.05298i	0.343114	+	0.190441i
$705$		0			0
$706$	−17.2434	−	8.91474i	−0.648965	−	0.335511i
$707$		−	6.35463i		−	0.238991i
$708$		0			0
$709$	6.39995	−	6.39995i	0.240355	−	0.240355i	−0.576642	−	0.816997i	$-0.695637\pi$
$709$	6.39995	−	6.39995i	0.240355	−	0.240355i	0.816997	+	0.576642i	$0.195637\pi$
$710$	14.6763	+	42.2445i	0.550792	+	1.58541i
$711$		0			0
$712$	40.7543	+	30.7284i	1.52733	+	1.15159i
$713$	−49.9091	−	49.9091i	−1.86911	−	1.86911i
$714$		0			0
$715$	2.10341	+	1.99630i	0.0786630	+	0.0746574i
$716$	5.81080	−	34.0758i	0.217160	−	1.27347i
$717$		0			0
$718$	−36.5812	+	11.6474i	−1.36520	+	0.434676i
$719$	−11.7136			−0.436843			−0.218422	−	0.975854i	$-0.570091\pi$
$719$	−11.7136			−0.436843			−0.218422	+	0.975854i	$0.570091\pi$
$720$		0			0
$721$	−8.85420			−0.329748
$722$	22.7188	−	7.23362i	0.845508	−	0.269208i
$723$		0			0
$724$	−21.6846	−	3.69778i	−0.805902	−	0.137427i
$725$	15.5272	+	13.9841i	0.576665	+	0.519357i
$726$		0			0
$727$	−7.19783	−	7.19783i	−0.266953	−	0.266953i	0.560918	−	0.827871i	$-0.310448\pi$
$727$	−7.19783	−	7.19783i	−0.266953	−	0.266953i	−0.827871	+	0.560918i	$0.810448\pi$
$728$	2.95002	−	0.413760i	0.109335	−	0.0153350i
$729$		0			0
$730$	−12.3949	+	25.5920i	−0.458755	+	0.947204i
$731$	−5.13631	+	5.13631i	−0.189973	+	0.189973i
$732$		0			0
$733$			10.6158i			0.392103i	0.980594	+	0.196052i	$0.0628120\pi$
$733$			10.6158i			0.392103i	−0.980594	+	0.196052i	$0.937188\pi$
$734$	29.0921	+	15.0404i	1.07381	+	0.555152i
$735$		0			0
$736$	−27.7917	+	26.1957i	−1.02442	+	0.965587i
$737$	8.27386	+	8.27386i	0.304772	+	0.304772i
$738$		0			0
$739$	30.4725	−	30.4725i	1.12095	−	1.12095i	0.129349	−	0.991599i	$-0.458711\pi$
$739$	30.4725	−	30.4725i	1.12095	−	1.12095i	0.991599	−	0.129349i	$-0.0412888\pi$
$740$	−22.0492	−	29.4531i	−0.810544	−	1.08272i
$741$		0			0
$742$	−3.52816	+	6.82439i	−0.129523	+	0.250531i
$743$	−6.20995	+	6.20995i	−0.227821	+	0.227821i	−0.811782	−	0.583961i	$-0.801502\pi$
$743$	−6.20995	+	6.20995i	−0.227821	+	0.227821i	0.583961	+	0.811782i	$0.301502\pi$
$744$		0			0
$745$	−26.2999	+	27.7110i	−0.963555	+	1.01525i
$746$	12.7634	+	40.0862i	0.467299	+	1.46766i
$747$		0			0
$748$	−2.95049	+	2.09082i	−0.107881	+	0.0764480i
$749$	0.0414579	+	0.0414579i	0.00151484	+	0.00151484i
$750$		0			0
$751$		−	11.3219i		−	0.413143i	−0.978432	−	0.206571i	$-0.933769\pi$
$751$		−	11.3219i		−	0.413143i	0.978432	−	0.206571i	$-0.0662305\pi$
$752$	0.134226	+	0.279582i	0.00489470	+	0.0101953i
$753$		0			0
$754$	−5.23150	−	2.70465i	−0.190520	−	0.0984975i
$755$	−28.2774	+	0.738773i	−1.02912	+	0.0268867i
$756$		0			0
$757$			11.1139i			0.403942i	0.979391	+	0.201971i	$0.0647348\pi$
$757$			11.1139i			0.403942i	−0.979391	+	0.201971i	$0.935265\pi$
$758$	−10.1571	+	19.6465i	−0.368922	+	0.713592i
$759$		0			0
$760$	9.12717	−	1.52419i	0.331077	−	0.0552881i
$761$		−	4.08171i		−	0.147962i	−0.997260	−	0.0739810i	$-0.976430\pi$
$761$		−	4.08171i		−	0.147962i	0.997260	−	0.0739810i	$-0.0235704\pi$
$762$		0			0
$763$		−	1.41669i		−	0.0512878i
$764$	−21.1317	−	29.8203i	−0.764518	−	1.07886i
$765$		0			0
$766$	14.9069	−	28.8339i	0.538609	−	1.04181i
$767$	2.29583	−	2.29583i	0.0828975	−	0.0828975i
$768$		0			0
$769$			31.6143i			1.14004i	0.821631	+	0.570020i	$0.193065\pi$
$769$			31.6143i			1.14004i	−0.821631	+	0.570020i	$0.806935\pi$
$770$	1.42761	+	4.10927i	0.0514477	+	0.148088i
$771$		0			0
$772$	5.37556	−	31.5235i	0.193471	−	1.13455i
$773$	−22.3964			−0.805542			−0.402771	−	0.915301i	$-0.631953\pi$
$773$	−22.3964			−0.805542			−0.402771	+	0.915301i	$0.631953\pi$
$774$		0			0
$775$	−2.72947	−	52.2011i	−0.0980455	−	1.87512i
$776$	0.721083	+	5.14117i	0.0258854	+	0.184557i
$777$		0			0
$778$	22.4460	+	11.6044i	0.804727	+	0.416038i
$779$	5.89752	+	5.89752i	0.211301	+	0.211301i
$780$		0			0
$781$	13.0151	−	13.0151i	0.465719	−	0.465719i
$782$	−4.02422	−	12.6390i	−0.143906	−	0.451970i
$783$		0			0
$784$	−22.2015	−	7.79862i	−0.792910	−	0.278522i
$785$	14.1110	−	0.368664i	0.503644	−	0.0131582i
$786$		0			0
$787$			45.2339i			1.61242i	0.591633	+	0.806208i	$0.298484\pi$
$787$			45.2339i			1.61242i	−0.591633	+	0.806208i	$0.701516\pi$
$788$	−12.9243	−	18.2383i	−0.460408	−	0.649713i
$789$		0			0
$790$	−9.09699	−	26.1849i	−0.323656	−	0.931618i
$791$	16.2632			0.578254
$792$		0			0
$793$	−10.7859	−	10.7859i	−0.383018	−	0.383018i
$794$	2.32569	+	7.30435i	0.0825356	+	0.259222i
$795$		0			0
$796$	21.8401	+	30.8200i	0.774101	+	1.09238i
$797$	33.6337			1.19137			0.595684	−	0.803219i	$-0.296881\pi$
$797$	33.6337			1.19137			0.595684	+	0.803219i	$0.296881\pi$
$798$		0			0
$799$	−0.107711			−0.00381056
$800$	−28.2770	+	0.641619i	−0.999743	+	0.0226847i
$801$		0			0
$802$	6.75980	+	21.2307i	0.238697	+	0.749682i
$803$	11.7034			0.413004
$804$		0			0
$805$	−15.9510	+	0.416735i	−0.562199	+	0.0146880i
$806$	4.46962	+	14.0379i	0.157436	+	0.494463i
$807$		0			0
$808$	−2.36195	−	16.8402i	−0.0830929	−	0.592435i
$809$	−7.75023			−0.272483			−0.136242	−	0.990676i	$-0.543502\pi$
$809$	−7.75023			−0.272483			−0.136242	+	0.990676i	$0.543502\pi$
$810$		0			0
$811$	15.5679	−	15.5679i	0.546661	−	0.546661i	−0.378812	−	0.925474i	$-0.623667\pi$
$811$	15.5679	−	15.5679i	0.546661	−	0.546661i	0.925474	+	0.378812i	$0.123667\pi$
$812$	−5.10797	−	7.20820i	−0.179255	−	0.252958i
$813$		0			0
$814$	−6.95427	+	13.4514i	−0.243747	+	0.471470i
$815$	−32.7089	+	0.854552i	−1.14574	+	0.0299336i
$816$		0			0
$817$	−5.40950	−	5.40950i	−0.189254	−	0.189254i
$818$	13.2769	+	41.6990i	0.464215	+	1.45797i
$819$		0			0
$820$	−15.2777	−	20.4079i	−0.533522	−	0.712674i
$821$	25.2360	+	25.2360i	0.880741	+	0.880741i	0.993610	−	0.112869i	$-0.0360041\pi$
$821$	25.2360	+	25.2360i	0.880741	+	0.880741i	−0.112869	+	0.993610i	$0.536004\pi$
$822$		0			0
$823$	−24.2751	+	24.2751i	−0.846178	+	0.846178i	−0.989654	−	0.143476i	$-0.954172\pi$
$823$	−24.2751	+	24.2751i	−0.846178	+	0.846178i	0.143476	+	0.989654i	$0.454172\pi$
$824$	−23.4642	+	3.29101i	−0.817414	+	0.114648i
$825$		0			0
$826$	4.64096	−	1.47767i	0.161480	−	0.0514147i
$827$	8.03445			0.279385			0.139693	−	0.990195i	$-0.455389\pi$
$827$	8.03445			0.279385			0.139693	+	0.990195i	$0.455389\pi$
$828$		0			0
$829$	17.2385	+	17.2385i	0.598718	+	0.598718i	0.939971	−	0.341254i	$-0.110852\pi$
$829$	17.2385	+	17.2385i	0.598718	+	0.598718i	−0.341254	+	0.939971i	$0.610852\pi$
$830$	−12.8258	−	36.9179i	−0.445189	−	1.28144i
$831$		0			0
$832$	7.66395	−	2.19298i	0.265700	−	0.0760279i
$833$	5.77890	−	5.77890i	0.200227	−	0.200227i
$834$		0			0
$835$	12.1883	+	11.5676i	0.421793	+	0.400315i
$836$	−2.20202	−	3.10742i	−0.0761586	−	0.107472i
$837$		0			0
$838$	−27.0730	−	13.9966i	−0.935221	−	0.483503i
$839$			23.0026i			0.794136i	0.917789	+	0.397068i	$0.129972\pi$
$839$			23.0026i			0.794136i	−0.917789	+	0.397068i	$0.870028\pi$
$840$		0			0
$841$		−	11.5340i		−	0.397726i
$842$	13.2271	−	25.5847i	0.455836	−	0.881706i
$843$		0			0
$844$	22.1747	+	3.78135i	0.763284	+	0.130160i
$845$	−26.8395	+	0.701209i	−0.923308	+	0.0241223i
$846$		0			0
$847$	−6.95520	+	6.95520i	−0.238983	+	0.238983i
$848$	−6.81331	+	19.3964i	−0.233970	+	0.666077i
$849$		0			0
$850$	4.04955	−	8.94980i	0.138898	−	0.306975i
$851$	−39.2750	−	39.2750i	−1.34633	−	1.34633i
$852$		0			0
$853$	−17.9417			−0.614312			−0.307156	−	0.951659i	$-0.599377\pi$
$853$	−17.9417			−0.614312			−0.307156	+	0.951659i	$0.599377\pi$
$854$	−6.94216	−	21.8034i	−0.237556	−	0.746098i
$855$		0			0
$856$	0.125276	+	0.0944566i	0.00428183	+	0.00322846i
$857$	27.5741	−	27.5741i	0.941914	−	0.941914i	−0.0564890	−	0.998403i	$-0.517991\pi$
$857$	27.5741	−	27.5741i	0.941914	−	0.941914i	0.998403	+	0.0564890i	$0.0179906\pi$
$858$		0			0
$859$	−22.0003	−	22.0003i	−0.750640	−	0.750640i	0.223959	−	0.974599i	$-0.428102\pi$
$859$	−22.0003	−	22.0003i	−0.750640	−	0.750640i	−0.974599	+	0.223959i	$0.928102\pi$
$860$	14.0135	+	18.7191i	0.477856	+	0.638317i
$861$		0			0
$862$	−6.02775	+	1.91922i	−0.205306	+	0.0653689i
$863$	16.4456	+	16.4456i	0.559814	+	0.559814i	0.929254	−	0.369440i	$-0.120451\pi$
$863$	16.4456	+	16.4456i	0.559814	+	0.559814i	−0.369440	+	0.929254i	$0.620451\pi$
$864$		0			0
$865$	0.768171	+	29.4026i	0.0261186	+	0.999718i
$866$	−37.0582	−	19.1589i	−1.25929	−	0.651045i
$867$		0			0
$868$	−3.71498	+	21.7855i	−0.126095	+	0.739447i
$869$	−8.06733	+	8.06733i	−0.273665	+	0.273665i
$870$		0			0
$871$	8.95830			0.303540
$872$	−0.526569	−	3.75433i	−0.0178319	−	0.127138i
$873$		0			0
$874$	13.3112	−	4.23826i	0.450259	−	0.143361i
$875$	−8.98447	−	7.67626i	−0.303731	−	0.259505i
$876$		0			0
$877$	6.59281			0.222623			0.111312	−	0.993786i	$-0.464495\pi$
$877$	6.59281			0.222623			0.111312	+	0.993786i	$0.464495\pi$
$878$	0.347360	−	0.110599i	0.0117228	−	0.00373252i
$879$		0			0
$880$	5.31063	+	10.3592i	0.179021	+	0.349208i
$881$	−22.1698			−0.746920			−0.373460	−	0.927646i	$-0.621829\pi$
$881$	−22.1698			−0.746920			−0.373460	+	0.927646i	$0.621829\pi$
$882$		0			0
$883$	38.7205			1.30305			0.651524	−	0.758628i	$-0.274130\pi$
$883$	38.7205			1.30305			0.651524	+	0.758628i	$0.274130\pi$
$884$	−0.465394	+	2.72917i	−0.0156529	+	0.0917920i
$885$		0			0
$886$	37.4991	−	11.9396i	1.25981	−	0.401120i
$887$	25.2413	+	25.2413i	0.847518	+	0.847518i	0.989823	−	0.142305i	$-0.0454512\pi$
$887$	25.2413	+	25.2413i	0.847518	+	0.847518i	−0.142305	+	0.989823i	$0.545451\pi$
$888$		0			0
$889$	−14.3698			−0.481947
$890$	18.7272	+	53.9047i	0.627738	+	1.80689i
$891$		0			0
$892$	−11.7896	−	2.01043i	−0.394746	−	0.0673142i
$893$		−	0.113440i		−	0.00379613i
$894$		0			0
$895$	26.6051	−	28.0326i	0.889310	−	0.937025i
$896$	11.7234	+	2.35760i	0.391652	+	0.0787619i
$897$		0			0
$898$	−9.86641	+	3.14144i	−0.329246	+	0.104831i
$899$	30.8947	−	30.8947i	1.03040	−	1.03040i
$900$		0			0
$901$	−5.04877	−	5.04877i	−0.168199	−	0.168199i
$902$	−4.81857	+	9.32037i	−0.160441	+	0.310335i
$903$		0			0
$904$	43.0986	−	6.04486i	1.43344	−	0.201049i
$905$	−17.8389	−	16.9305i	−0.592986	−	0.562790i
$906$		0			0
$907$	9.44895			0.313747			0.156874	−	0.987619i	$-0.449858\pi$
$907$	9.44895			0.313747			0.156874	+	0.987619i	$0.449858\pi$
$908$	−18.2305	−	25.7262i	−0.605000	−	0.853755i
$909$		0			0
$910$	2.99745	+	1.45174i	0.0993646	+	0.0481248i
$911$			36.1798i			1.19869i	0.800490	+	0.599346i	$0.204573\pi$
$911$			36.1798i			1.19869i	−0.800490	+	0.599346i	$0.795427\pi$
$912$		0			0
$913$	−11.3740	+	11.3740i	−0.376426	+	0.376426i
$914$	−23.4446	−	12.1207i	−0.775478	−	0.400917i
$915$		0			0
$916$	0.354757	−	2.08037i	0.0117215	−	0.0687374i
$917$		−	8.37345i		−	0.276516i
$918$		0			0
$919$			45.3587i			1.49624i	0.663561	+	0.748122i	$0.269044\pi$
$919$			45.3587i			1.49624i	−0.663561	+	0.748122i	$0.730956\pi$
$920$	−42.1162	+	7.03318i	−1.38853	+	0.231877i
$921$		0			0
$922$	−34.8269	−	18.0053i	−1.14696	−	0.592973i
$923$		−	14.0918i		−	0.463837i
$924$		0			0
$925$	−2.14790	−	41.0786i	−0.0706226	−	1.35066i
$926$	−15.8825	+	30.7209i	−0.521932	+	1.00955i
$927$		0			0
$928$	−16.2156	−	17.2036i	−0.532305	−	0.564735i
$929$			0.551101i			0.0180810i	0.999959	+	0.00904052i	$0.00287773\pi$
$929$			0.551101i			0.0180810i	−0.999959	+	0.00904052i	$0.997122\pi$
$930$		0			0
$931$	6.08626	+	6.08626i	0.199469	+	0.199469i
$932$	−16.0186	−	2.73158i	−0.524706	−	0.0894758i
$933$		0			0
$934$	42.2992	−	13.4679i	1.38407	−	0.440685i
$935$	−4.04166	+	0.105592i	−0.132176	+	0.00345324i
$936$		0			0
$937$	−10.4271	+	10.4271i	−0.340639	+	0.340639i	−0.856607	−	0.515969i	$-0.827432\pi$
$937$	−10.4271	+	10.4271i	−0.340639	+	0.340639i	0.515969	+	0.856607i	$0.327432\pi$
$938$	11.9374	+	6.17157i	0.389771	+	0.201509i
$939$		0			0
$940$	−0.0493397	+	0.343211i	−0.00160928	+	0.0111943i
$941$	−7.44442	+	7.44442i	−0.242681	+	0.242681i	−0.817958	−	0.575277i	$-0.804894\pi$
$941$	−7.44442	+	7.44442i	−0.242681	+	0.242681i	0.575277	+	0.817958i	$0.304894\pi$
$942$		0			0
$943$	−27.2134	−	27.2134i	−0.886190	−	0.886190i
$944$	11.7496	−	5.64091i	0.382417	−	0.183596i
$945$		0			0
$946$	4.41983	−	8.54911i	0.143701	−	0.277955i
$947$		−	15.8341i		−	0.514539i	−0.966340	−	0.257270i	$-0.917177\pi$
$947$		−	15.8341i		−	0.514539i	0.966340	−	0.257270i	$-0.0828229\pi$
$948$		0			0
$949$	6.33577	−	6.33577i	0.205668	−	0.205668i
$950$	9.42581	+	4.26493i	0.305814	+	0.138373i
$951$		0			0
$952$	−2.50035	+	3.31615i	−0.0810368	+	0.107477i
$953$	−14.8928	−	14.8928i	−0.482424	−	0.482424i	0.423481	−	0.905905i	$-0.360808\pi$
$953$	−14.8928	−	14.8928i	−0.482424	−	0.482424i	−0.905905	+	0.423481i	$0.860808\pi$
$954$		0			0
$955$	−1.06721	−	40.8486i	−0.0345341	−	1.32183i
$956$	45.6477	−	32.3475i	1.47635	−	1.04619i
$957$		0			0
$958$	4.49925	+	14.1309i	0.145364	+	0.456549i
$959$	7.00109			0.226077
$960$		0			0
$961$	−78.2963			−2.52569
$962$	3.51728	+	11.0468i	0.113402	+	0.356164i
$963$		0			0
$964$	11.4402	−	8.10693i	0.368465	−	0.261107i
$965$	24.6123	−	25.9329i	0.792300	−	0.834809i
$966$		0			0
$967$	−27.8728	−	27.8728i	−0.896330	−	0.896330i	0.0987795	−	0.995109i	$-0.468506\pi$
$967$	−27.8728	−	27.8728i	−0.896330	−	0.896330i	−0.995109	+	0.0987795i	$0.968506\pi$
$968$	−15.8465	+	21.0169i	−0.509327	+	0.675508i
$969$		0			0
$970$	−2.53003	+	5.22383i	−0.0812345	+	0.167727i
$971$	30.0958	−	30.0958i	0.965819	−	0.965819i	−0.0336155	−	0.999435i	$-0.510702\pi$
$971$	30.0958	−	30.0958i	0.965819	−	0.965819i	0.999435	+	0.0336155i	$0.0107022\pi$
$972$		0			0
$973$		−	2.46593i		−	0.0790540i
$974$	4.34220	−	8.39895i	0.139133	−	0.269120i
$975$		0			0
$976$	−26.5012	−	55.2001i	−0.848284	−	1.76691i
$977$	9.03427	+	9.03427i	0.289032	+	0.289032i	0.836697	−	0.547666i	$-0.184483\pi$
$977$	9.03427	+	9.03427i	0.289032	+	0.289032i	−0.547666	+	0.836697i	$0.684483\pi$
$978$		0			0
$979$	16.6075	−	16.6075i	0.530780	−	0.530780i
$980$	−15.7667	−	21.0610i	−0.503648	−	0.672769i
$981$		0			0
$982$	−5.34543	−	2.76355i	−0.170579	−	0.0881884i
$983$	−24.5191	+	24.5191i	−0.782039	+	0.782039i	−0.980175	−	0.198135i	$-0.936511\pi$
$983$	−24.5191	+	24.5191i	−0.782039	+	0.782039i	0.198135	+	0.980175i	$0.436511\pi$
$984$		0			0
$985$	−0.652712	−	24.9833i	−0.0207971	−	0.796034i
$986$	7.82378	−	2.49107i	0.249160	−	0.0793319i
$987$		0			0
$988$	−2.87433	−	0.490147i	−0.0914445	−	0.0155936i
$989$	24.9615	+	24.9615i	0.793728	+	0.793728i
$990$		0			0
$991$			25.8872i			0.822334i	0.911560	+	0.411167i	$0.134879\pi$
$991$			25.8872i			0.822334i	−0.911560	+	0.411167i	$0.865121\pi$
$992$	−1.74752	+	59.1137i	−0.0554838	+	1.87686i
$993$		0			0
$994$	9.70815	−	18.7781i	0.307924	−	0.595605i
$995$	1.10298	+	42.2180i	0.0349670	+	1.33840i
$996$		0			0
$997$			16.7546i			0.530624i	0.964163	+	0.265312i	$0.0854750\pi$
$997$			16.7546i			0.530624i	−0.964163	+	0.265312i	$0.914525\pi$
$998$	15.5591	+	8.04392i	0.492513	+	0.254626i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.z.f.667.4		16
3.2	odd	2		240.2.y.e.187.5	yes	16
5.3	odd	4		720.2.bd.f.523.1		16
12.11	even	2		960.2.y.e.847.8		16
15.8	even	4		240.2.bc.e.43.8	yes	16
16.3	odd	4		720.2.bd.f.307.1		16
24.5	odd	2		1920.2.y.i.1567.1		16
24.11	even	2		1920.2.y.j.1567.1		16
48.5	odd	4		1920.2.bc.j.607.3		16
48.11	even	4		1920.2.bc.i.607.3		16
48.29	odd	4		960.2.bc.e.367.6		16
48.35	even	4		240.2.bc.e.67.8	yes	16
60.23	odd	4		960.2.bc.e.463.6		16
80.3	even	4	inner	720.2.z.f.163.4		16
120.53	even	4		1920.2.bc.i.1183.3		16
120.83	odd	4		1920.2.bc.j.1183.3		16
240.53	even	4		1920.2.y.j.223.1		16
240.83	odd	4		240.2.y.e.163.5	✓	16
240.173	even	4		960.2.y.e.943.8		16
240.203	odd	4		1920.2.y.i.223.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.5	✓	16	240.83	odd	4
240.2.y.e.187.5	yes	16	3.2	odd	2
240.2.bc.e.43.8	yes	16	15.8	even	4
240.2.bc.e.67.8	yes	16	48.35	even	4
720.2.z.f.163.4		16	80.3	even	4	inner
720.2.z.f.667.4		16	1.1	even	1	trivial
720.2.bd.f.307.1		16	16.3	odd	4
720.2.bd.f.523.1		16	5.3	odd	4
960.2.y.e.847.8		16	12.11	even	2
960.2.y.e.943.8		16	240.173	even	4
960.2.bc.e.367.6		16	48.29	odd	4
960.2.bc.e.463.6		16	60.23	odd	4
1920.2.y.i.223.1		16	240.203	odd	4
1920.2.y.i.1567.1		16	24.5	odd	2
1920.2.y.j.223.1		16	240.53	even	4
1920.2.y.j.1567.1		16	24.11	even	2
1920.2.bc.i.607.3		16	48.11	even	4
1920.2.bc.i.1183.3		16	120.53	even	4
1920.2.bc.j.607.3		16	48.5	odd	4
1920.2.bc.j.1183.3		16	120.83	odd	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.429059 - 1.34756i) q^{2} +(-1.63182 + 1.15636i) q^{4} +(-2.23531 + 0.0583995i) q^{5} +(0.747384 + 0.747384i) q^{7} +(2.25841 + 1.70282i) q^{8} +(1.03777 + 2.98714i) q^{10} +(0.920311 - 0.920311i) q^{11} -0.996441i q^{13} +(0.686471 - 1.32781i) q^{14} +(1.32566 - 3.77394i) q^{16} +(0.982332 + 0.982332i) q^{17} +(-1.03458 + 1.03458i) q^{19} +(3.58008 - 2.68012i) q^{20} +(-1.63504 - 0.845304i) q^{22} +(4.77394 - 4.77394i) q^{23} +(4.99318 - 0.261081i) q^{25} +(-1.34276 + 0.427532i) q^{26} +(-2.08384 - 0.355348i) q^{28} +(2.95516 + 2.95516i) q^{29} -10.4545i q^{31} +(-5.65438 - 0.167155i) q^{32} +(0.902270 - 1.74523i) q^{34} +(-1.71428 - 1.62698i) q^{35} -8.22694i q^{37} +(1.83805 + 0.950259i) q^{38} +(-5.14767 - 3.67443i) q^{40} -5.70040i q^{41} +5.22869i q^{43} +(-0.437567 + 2.56599i) q^{44} +(-8.48146 - 4.38486i) q^{46} +(-0.0548243 + 0.0548243i) q^{47} -5.88283i q^{49} +(-2.49419 - 6.61657i) q^{50} +(1.15225 + 1.62601i) q^{52} -5.13957 q^{53} +(-2.00343 + 2.11092i) q^{55} +(0.415238 + 2.96056i) q^{56} +(2.71431 - 5.25018i) q^{58} +(2.30403 + 2.30403i) q^{59} +(10.8244 - 10.8244i) q^{61} +(-14.0880 + 4.48559i) q^{62} +(2.20081 + 7.69132i) q^{64} +(0.0581916 + 2.22735i) q^{65} +8.99029i q^{67} +(-2.73892 - 0.467056i) q^{68} +(-1.45693 + 3.00816i) q^{70} +14.1421 q^{71} +(6.35840 + 6.35840i) q^{73} +(-11.0863 + 3.52984i) q^{74} +(0.491897 - 2.88459i) q^{76} +1.37565 q^{77} -8.76588 q^{79} +(-2.74285 + 8.51333i) q^{80} +(-7.68161 + 2.44581i) q^{82} -12.3589 q^{83} +(-2.25318 - 2.13845i) q^{85} +(7.04595 - 2.24341i) q^{86} +(3.64556 - 0.511314i) q^{88} +18.0456 q^{89} +(0.744724 - 0.744724i) q^{91} +(-2.26980 + 13.3106i) q^{92} +(0.0974017 + 0.0503560i) q^{94} +(2.25218 - 2.37302i) q^{95} +(1.29787 + 1.29787i) q^{97} +(-7.92745 + 2.52408i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 14 q^{10} + 4 q^{14} - 8 q^{16} + 8 q^{17} + 8 q^{19} + 12 q^{20} - 8 q^{22} + 32 q^{25} - 20 q^{26} + 12 q^{28} - 12 q^{29} + 28 q^{32} + 20 q^{35}+ \cdots - 30 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 14 * q^10 + 4 * q^14 - 8 * q^16 + 8 * q^17 + 8 * q^19 + 12 * q^20 - 8 * q^22 + 32 * q^25 - 20 * q^26 + 12 * q^28 - 12 * q^29 + 28 * q^32 + 20 * q^35 + 16 * q^38 - 44 * q^40 - 52 * q^44 - 16 * q^46 + 32 * q^47 - 22 * q^50 + 8 * q^52 - 16 * q^53 - 4 * q^55 - 20 * q^56 - 44 * q^58 + 24 * q^59 + 40 * q^61 - 40 * q^62 - 8 * q^64 + 4 * q^65 - 24 * q^68 + 56 * q^70 + 8 * q^73 - 64 * q^74 + 16 * q^76 + 72 * q^77 - 48 * q^79 - 16 * q^80 + 8 * q^82 + 8 * q^83 - 8 * q^85 + 8 * q^86 - 16 * q^88 - 40 * q^91 - 20 * q^94 - 8 * q^95 + 48 * q^97 - 30 * q^98

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