LMFDB - Embedded newform 675.2.k.b.424.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(199,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("675.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 $ x^12 - 16x^8 - 24x^7 + 96x^5 + 304x^4 + 384x^3 + 288x^2 + 144*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			424.6
Root			$-0.673288 + 0.180407i$ of defining polynomial
Character	$\chi$	$=$	675.424
Dual form			675.2.k.b.199.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17731 + 1.25707i) q^{2} +(2.16044 + 3.74200i) q^{4} +(0.445256 + 0.257068i) q^{7} +5.83502i q^{8} +O(q^{10})$	\(q+(2.17731 + 1.25707i) q^{2} +(2.16044 + 3.74200i) q^{4} +(0.445256 + 0.257068i) q^{7} +5.83502i q^{8} +(-1.66044 + 2.87597i) q^{11} +(1.14392 - 0.660442i) q^{13} +(0.646305 + 1.11943i) q^{14} +(-3.01414 + 5.22064i) q^{16} +3.32088i q^{17} +1.32088 q^{19} +(-7.23058 + 4.17458i) q^{22} +(3.57463 - 2.06382i) q^{23} +3.32088 q^{26} +2.22153i q^{28} +(0.693252 - 1.20075i) q^{29} +(-4.36783 - 7.56531i) q^{31} +(-3.01885 + 1.74293i) q^{32} +(-4.17458 + 7.23058i) q^{34} +0.292611i q^{37} +(2.87597 + 1.66044i) q^{38} +(-5.67458 - 9.82866i) q^{41} +(8.96263 + 5.17458i) q^{43} -14.3492 q^{44} +10.3774 q^{46} +(-4.21174 - 2.43165i) q^{47} +(-3.36783 - 5.83326i) q^{49} +(4.94274 + 2.85369i) q^{52} -5.02827i q^{53} +(-1.50000 + 2.59808i) q^{56} +(3.01885 - 1.74293i) q^{58} +(2.51414 + 4.35461i) q^{59} +(-3.67458 + 6.36456i) q^{61} -21.9627i q^{62} +3.29261 q^{64} +(8.18266 - 4.72426i) q^{67} +(-12.4267 + 7.17458i) q^{68} -8.99093 q^{71} -6.05655i q^{73} +(-0.367832 + 0.637103i) q^{74} +(2.85369 + 4.94274i) q^{76} +(-1.47864 + 0.853695i) q^{77} +(-4.02827 + 6.97717i) q^{79} -28.5333i q^{82} +(-1.33577 - 0.771205i) q^{83} +(13.0096 + 22.5333i) q^{86} +(-16.7813 - 9.68872i) q^{88} -3.00000 q^{89} +0.679116 q^{91} +(15.4456 + 8.91751i) q^{92} +(-6.11350 - 10.5889i) q^{94} +(10.6134 + 6.12763i) q^{97} -16.9344i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{4}+O(q^{10}) $ 12 * q + 10 * q^4	$ 12 q + 10 q^{4} - 4 q^{11} + 18 q^{14} - 10 q^{16} - 16 q^{19} + 8 q^{26} + 14 q^{29} - 16 q^{31} - 8 q^{34} - 26 q^{41} - 88 q^{44} - 12 q^{46} - 4 q^{49} - 18 q^{56} + 4 q^{59} - 2 q^{61} + 60 q^{64} + 40 q^{71} + 32 q^{74} + 24 q^{76} + 4 q^{79} + 56 q^{86} - 36 q^{89} + 40 q^{91} - 62 q^{94}+O(q^{100}) $ 12 * q + 10 * q^4 - 4 * q^11 + 18 * q^14 - 10 * q^16 - 16 * q^19 + 8 * q^26 + 14 * q^29 - 16 * q^31 - 8 * q^34 - 26 * q^41 - 88 * q^44 - 12 * q^46 - 4 * q^49 - 18 * q^56 + 4 * q^59 - 2 * q^61 + 60 * q^64 + 40 * q^71 + 32 * q^74 + 24 * q^76 + 4 * q^79 + 56 * q^86 - 36 * q^89 + 40 * q^91 - 62 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.17731	+	1.25707i	1.53959	+	0.888882i	0.998863	+	0.0476826i	$0.0151836\pi$
$2$	2.17731	+	1.25707i	1.53959	+	0.888882i	0.540726	+	0.841199i	$0.318150\pi$
$3$		0			0
$3$		0			0
$4$	2.16044	+	3.74200i	1.08022	+	1.87100i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.445256	+	0.257068i	0.168291	+	0.0971627i	0.581780	−	0.813346i	$-0.302357\pi$
$7$	0.445256	+	0.257068i	0.168291	+	0.0971627i	−0.413489	+	0.910509i	$0.635690\pi$
$8$			5.83502i			2.06299i
$9$		0			0
$10$		0			0
$11$	−1.66044	+	2.87597i	−0.500642	+	0.867138i	0.499358	+	0.866396i	$0.333569\pi$
$11$	−1.66044	+	2.87597i	−0.500642	+	0.867138i	−1.00000		0.000741679i	$0.999764\pi$
$12$		0			0
$13$	1.14392	−	0.660442i	0.317266	−	0.183174i	−0.332907	−	0.942960i	$-0.608030\pi$
$13$	1.14392	−	0.660442i	0.317266	−	0.183174i	0.650173	+	0.759786i	$0.274696\pi$
$14$	0.646305	+	1.11943i	0.172732	+	0.299181i
$15$		0			0
$16$	−3.01414	+	5.22064i	−0.753534	+	1.30516i
$17$			3.32088i			0.805433i	0.915325	+	0.402716i	$0.131934\pi$
$17$			3.32088i			0.805433i	−0.915325	+	0.402716i	$0.868066\pi$
$18$		0			0
$19$	1.32088			0.303032			0.151516	−	0.988455i	$-0.451585\pi$
$19$	1.32088			0.303032			0.151516	+	0.988455i	$0.451585\pi$
$20$		0			0
$21$		0			0
$22$	−7.23058	+	4.17458i	−1.54157	+	0.890023i
$23$	3.57463	−	2.06382i	0.745363	−	0.430335i	−0.0786532	−	0.996902i	$-0.525062\pi$
$23$	3.57463	−	2.06382i	0.745363	−	0.430335i	0.824016	+	0.566567i	$0.191729\pi$
$24$		0			0
$25$		0			0
$26$	3.32088			0.651279
$27$		0			0
$28$			2.22153i			0.419829i
$29$	0.693252	−	1.20075i	0.128734	−	0.222973i	−0.794453	−	0.607326i	$-0.792242\pi$
$29$	0.693252	−	1.20075i	0.128734	−	0.222973i	0.923186	+	0.384353i	$0.125575\pi$
$30$		0			0
$31$	−4.36783	−	7.56531i	−0.784486	−	1.35877i	−0.929306	−	0.369311i	$-0.879594\pi$
$31$	−4.36783	−	7.56531i	−0.784486	−	1.35877i	0.144820	−	0.989458i	$-0.453740\pi$
$32$	−3.01885	+	1.74293i	−0.533662	+	0.308110i
$33$		0			0
$34$	−4.17458	+	7.23058i	−0.715934	+	1.24003i
$35$		0			0
$36$		0			0
$37$			0.292611i			0.0481049i	0.999711	+	0.0240524i	$0.00765687\pi$
$37$			0.292611i			0.0481049i	−0.999711	+	0.0240524i	$0.992343\pi$
$38$	2.87597	+	1.66044i	0.466544	+	0.269359i
$39$		0			0
$40$		0			0
$41$	−5.67458	−	9.82866i	−0.886220	−	1.53498i	−0.844308	−	0.535857i	$-0.819988\pi$
$41$	−5.67458	−	9.82866i	−0.886220	−	1.53498i	−0.0419119	−	0.999121i	$-0.513345\pi$
$42$		0			0
$43$	8.96263	+	5.17458i	1.36679	+	0.789116i	0.990517	−	0.137393i	$-0.0438724\pi$
$43$	8.96263	+	5.17458i	1.36679	+	0.789116i	0.376272	+	0.926509i	$0.377206\pi$
$44$	−14.3492			−2.16322
$45$		0			0
$46$	10.3774			1.53007
$47$	−4.21174	−	2.43165i	−0.614345	−	0.354692i	0.160319	−	0.987065i	$-0.448748\pi$
$47$	−4.21174	−	2.43165i	−0.614345	−	0.354692i	−0.774664	+	0.632373i	$0.782081\pi$
$48$		0			0
$49$	−3.36783	−	5.83326i	−0.481119	−	0.833322i
$50$		0			0
$51$		0			0
$52$	4.94274	+	2.85369i	0.685435	+	0.395736i
$53$		−	5.02827i		−	0.690687i	−0.938476	−	0.345343i	$-0.887762\pi$
$53$		−	5.02827i		−	0.690687i	0.938476	−	0.345343i	$-0.112238\pi$
$54$		0			0
$55$		0			0
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$		0			0
$58$	3.01885	−	1.74293i	0.396394	−	0.228858i
$59$	2.51414	+	4.35461i	0.327313	+	0.566922i	0.981978	−	0.188997i	$-0.0605236\pi$
$59$	2.51414	+	4.35461i	0.327313	+	0.566922i	−0.654665	+	0.755919i	$0.727190\pi$
$60$		0			0
$61$	−3.67458	+	6.36456i	−0.470482	+	0.814898i	−0.999430	−	0.0337558i	$-0.989253\pi$
$61$	−3.67458	+	6.36456i	−0.470482	+	0.814898i	0.528948	+	0.848654i	$0.322586\pi$
$62$		−	21.9627i		−	2.78926i
$63$		0			0
$64$	3.29261			0.411576
$65$		0			0
$66$		0			0
$67$	8.18266	−	4.72426i	0.999670	−	0.577160i	0.0915197	−	0.995803i	$-0.470828\pi$
$67$	8.18266	−	4.72426i	0.999670	−	0.577160i	0.908151	+	0.418643i	$0.137494\pi$
$68$	−12.4267	+	7.17458i	−1.50696	+	0.870046i
$69$		0			0
$70$		0			0
$71$	−8.99093			−1.06703			−0.533513	−	0.845792i	$-0.679129\pi$
$71$	−8.99093			−1.06703			−0.533513	+	0.845792i	$0.679129\pi$
$72$		0			0
$73$		−	6.05655i		−	0.708865i	−0.935082	−	0.354433i	$-0.884674\pi$
$73$		−	6.05655i		−	0.708865i	0.935082	−	0.354433i	$-0.115326\pi$
$74$	−0.367832	+	0.637103i	−0.0427596	+	0.0740617i
$75$		0			0
$76$	2.85369	+	4.94274i	0.327341	+	0.566972i
$77$	−1.47864	+	0.853695i	−0.168507	+	0.0972875i
$78$		0			0
$79$	−4.02827	+	6.97717i	−0.453216	+	0.784994i	−0.998584	−	0.0532036i	$-0.983057\pi$
$79$	−4.02827	+	6.97717i	−0.453216	+	0.784994i	0.545367	+	0.838197i	$0.316390\pi$
$80$		0			0
$81$		0			0
$82$		−	28.5333i		−	3.15098i
$83$	−1.33577	−	0.771205i	−0.146619	−	0.0846508i	0.424896	−	0.905242i	$-0.360311\pi$
$83$	−1.33577	−	0.771205i	−0.146619	−	0.0846508i	−0.571515	+	0.820592i	$0.693644\pi$
$84$		0			0
$85$		0			0
$86$	13.0096	+	22.5333i	1.40286	+	2.42983i
$87$		0			0
$88$	−16.7813	−	9.68872i	−1.78890	−	1.03282i
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	0.679116			0.0711906
$92$	15.4456	+	8.91751i	1.61031	+	0.929715i
$93$		0			0
$94$	−6.11350	−	10.5889i	−0.630559	−	1.09216i
$95$		0			0
$96$		0			0
$97$	10.6134	+	6.12763i	1.07762	+	0.622167i	0.930255	−	0.366915i	$-0.119586\pi$
$97$	10.6134	+	6.12763i	1.07762	+	0.622167i	0.147370	+	0.989081i	$0.452919\pi$
$98$		−	16.9344i		−	1.71063i
$99$		0			0
$100$		0			0
$101$	5.83502	−	10.1066i	0.580606	−	1.00564i	−0.414801	−	0.909912i	$-0.636149\pi$
$101$	5.83502	−	10.1066i	0.580606	−	1.00564i	0.995408	−	0.0957276i	$-0.0305178\pi$
$102$		0			0
$103$	−0.253408	+	0.146305i	−0.0249691	+	0.0144159i	−0.512433	−	0.858727i	$-0.671256\pi$
$103$	−0.253408	+	0.146305i	−0.0249691	+	0.0144159i	0.487464	+	0.873143i	$0.337922\pi$
$104$	3.85369	+	6.67479i	0.377886	+	0.654517i
$105$		0			0
$106$	6.32088	−	10.9481i	0.613939	−	1.06337i
$107$		−	1.87237i		−	0.181009i	−0.995896	−	0.0905043i	$-0.971152\pi$
$107$		−	1.87237i		−	0.181009i	0.995896	−	0.0905043i	$-0.0288479\pi$
$108$		0			0
$109$	−5.54787			−0.531390			−0.265695	−	0.964057i	$-0.585601\pi$
$109$	−5.54787			−0.531390			−0.265695	+	0.964057i	$0.585601\pi$
$110$		0			0
$111$		0			0
$112$	−2.68412	+	1.54968i	−0.253626	+	0.146431i
$113$	6.75611	−	3.90064i	0.635561	−	0.366942i	−0.147341	−	0.989086i	$-0.547072\pi$
$113$	6.75611	−	3.90064i	0.635561	−	0.366942i	0.782903	+	0.622144i	$0.213738\pi$
$114$		0			0
$115$		0			0
$116$	5.99093			0.556244
$117$		0			0
$118$			12.6418i			1.16377i
$119$	−0.853695	+	1.47864i	−0.0782581	+	0.135547i
$120$		0			0
$121$	−0.0141369	−	0.0244859i	−0.00128518	−	0.00222599i
$122$	−16.0014	+	9.23840i	−1.44870	+	0.836405i
$123$		0			0
$124$	18.8729	−	32.6888i	1.69484	−	2.93554i
$125$		0			0
$126$		0			0
$127$			17.8916i			1.58762i	0.608166	+	0.793810i	$0.291906\pi$
$127$			17.8916i			1.58762i	−0.608166	+	0.793810i	$0.708094\pi$
$128$	13.2067	+	7.62490i	1.16732	+	0.673952i
$129$		0			0
$130$		0			0
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	0.588131	+	0.339558i	0.0509974	+	0.0294434i
$134$	23.7549			2.05211
$135$		0			0
$136$	−19.3774			−1.66160
$137$	4.91040	+	2.83502i	0.419524	+	0.242212i	0.694874	−	0.719132i	$-0.255460\pi$
$137$	4.91040	+	2.83502i	0.419524	+	0.242212i	−0.275350	+	0.961344i	$0.588794\pi$
$138$		0			0
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		0			0
$141$		0			0
$142$	−19.5760	−	11.3022i	−1.64278	−	0.948460i
$143$			4.38650i			0.366818i
$144$		0			0
$145$		0			0
$146$	7.61350	−	13.1870i	0.630097	−	1.09136i
$147$		0			0
$148$	−1.09495	+	0.632168i	−0.0900042	+	0.0519639i
$149$	−8.83049	−	15.2948i	−0.723422	−	1.25300i	−0.959620	−	0.281298i	$-0.909235\pi$
$149$	−8.83049	−	15.2948i	−0.723422	−	1.25300i	0.236199	−	0.971705i	$-0.424098\pi$
$150$		0			0
$151$	−0.632168	+	1.09495i	−0.0514451	+	0.0891056i	−0.890601	−	0.454785i	$-0.849716\pi$
$151$	−0.632168	+	1.09495i	−0.0514451	+	0.0891056i	0.839156	+	0.543891i	$0.183049\pi$
$152$			7.70739i			0.625152i
$153$		0			0
$154$	−4.29261			−0.345908
$155$		0			0
$156$		0			0
$157$	−13.5707	+	7.83502i	−1.08306	+	0.625303i	−0.931719	−	0.363179i	$-0.881691\pi$
$157$	−13.5707	+	7.83502i	−1.08306	+	0.625303i	−0.151337	+	0.988482i	$0.548358\pi$
$158$	−17.5416	+	10.1276i	−1.39553	+	0.805711i
$159$		0			0
$160$		0			0
$161$	2.12217			0.167250
$162$		0			0
$163$		−	15.7074i		−	1.23030i	−0.788411	−	0.615149i	$-0.789096\pi$
$163$		−	15.7074i		−	1.23030i	0.788411	−	0.615149i	$-0.210904\pi$
$164$	24.5192	−	42.4685i	1.91463	−	3.31623i
$165$		0			0
$166$	−1.93892	−	3.35830i	−0.150489	−	0.260655i
$167$	−5.33903	+	3.08249i	−0.413146	+	0.238530i	−0.692141	−	0.721763i	$-0.743332\pi$
$167$	−5.33903	+	3.08249i	−0.413146	+	0.238530i	0.278994	+	0.960293i	$0.409999\pi$
$168$		0			0
$169$	−5.62763	+	9.74734i	−0.432895	+	0.749796i
$170$		0			0
$171$		0			0
$172$			44.7175i			3.40968i
$173$	−7.43502	−	4.29261i	−0.565274	−	0.326361i	0.189986	−	0.981787i	$-0.439156\pi$
$173$	−7.43502	−	4.29261i	−0.565274	−	0.326361i	−0.755260	+	0.655426i	$0.772489\pi$
$174$		0			0
$175$		0			0
$176$	−10.0096	−	17.3371i	−0.754502	−	1.30684i
$177$		0			0
$178$	−6.53192	−	3.77121i	−0.489588	−	0.282664i
$179$	−1.06562			−0.0796482			−0.0398241	−	0.999207i	$-0.512680\pi$
$179$	−1.06562			−0.0796482			−0.0398241	+	0.999207i	$0.512680\pi$
$180$		0			0
$181$	−12.6700			−0.941757			−0.470878	−	0.882198i	$-0.656063\pi$
$181$	−12.6700			−0.941757			−0.470878	+	0.882198i	$0.656063\pi$
$182$	1.47864	+	0.853695i	0.109604	+	0.0632801i
$183$		0			0
$184$	12.0424	+	20.8581i	0.887778	+	1.53768i
$185$		0			0
$186$		0			0
$187$	−9.55077	−	5.51414i	−0.698421	−	0.403234i
$188$		−	21.0137i		−	1.53258i
$189$		0			0
$190$		0			0
$191$	−8.46719	+	14.6656i	−0.612664	+	1.06117i	0.378125	+	0.925754i	$0.376569\pi$
$191$	−8.46719	+	14.6656i	−0.612664	+	1.06117i	−0.990789	+	0.135411i	$0.956764\pi$
$192$		0			0
$193$	−23.1380	+	13.3588i	−1.66551	+	0.961585i	−0.695502	+	0.718524i	$0.744818\pi$
$193$	−23.1380	+	13.3588i	−1.66551	+	0.961585i	−0.970011	+	0.243060i	$0.921849\pi$
$194$	15.4057	+	26.6835i	1.10607	+	1.91576i
$195$		0			0
$196$	14.5520	−	25.2048i	1.03943	−	1.80034i
$197$			14.2553i			1.01565i	0.861462	+	0.507823i	$0.169550\pi$
$197$			14.2553i			1.01565i	−0.861462	+	0.507823i	$0.830450\pi$
$198$		0			0
$199$	24.6610			1.74817			0.874085	−	0.485773i	$-0.161462\pi$
$199$	24.6610			1.74817			0.874085	+	0.485773i	$0.161462\pi$
$200$		0			0
$201$		0			0
$202$	25.4093	−	14.6700i	1.78779	−	1.03218i
$203$	0.617349	−	0.356427i	0.0433294	−	0.0250162i
$204$		0			0
$205$		0			0
$206$	−0.735663			−0.0512561
$207$		0			0
$208$			7.96265i			0.552111i
$209$	−2.19325	+	3.79882i	−0.151710	+	0.262770i
$210$		0			0
$211$	2.68872	+	4.65699i	0.185099	+	0.320601i	0.943610	−	0.331060i	$-0.107406\pi$
$211$	2.68872	+	4.65699i	0.185099	+	0.320601i	−0.758511	+	0.651660i	$0.774073\pi$
$212$	18.8158	−	10.8633i	1.29227	−	0.746094i
$213$		0			0
$214$	2.35369	−	4.07672i	0.160895	−	0.278679i
$215$		0			0
$216$		0			0
$217$		−	4.49133i		−	0.304891i
$218$	−12.0794	−	6.97406i	−0.818122	−	0.472343i
$219$		0			0
$220$		0			0
$221$	2.19325	+	3.79882i	0.147534	+	0.255537i
$222$		0			0
$223$	7.50375	+	4.33229i	0.502488	+	0.290112i	0.729740	−	0.683724i	$-0.239641\pi$
$223$	7.50375	+	4.33229i	0.502488	+	0.290112i	−0.227252	+	0.973836i	$0.572974\pi$
$224$	−1.79221			−0.119747
$225$		0			0
$226$	19.6135			1.30467
$227$	2.87597	+	1.66044i	0.190885	+	0.110207i	0.592397	−	0.805646i	$-0.298182\pi$
$227$	2.87597	+	1.66044i	0.190885	+	0.110207i	−0.401512	+	0.915854i	$0.631515\pi$
$228$		0			0
$229$	−12.6559	−	21.9207i	−0.836326	−	1.44856i	−0.892946	−	0.450163i	$-0.851366\pi$
$229$	−12.6559	−	21.9207i	−0.836326	−	1.44856i	0.0566206	−	0.998396i	$-0.481967\pi$
$230$		0			0
$231$		0			0
$232$	7.00639	+	4.04514i	0.459992	+	0.265577i
$233$			27.6327i			1.81028i	0.425116	+	0.905139i	$0.360233\pi$
$233$			27.6327i			1.81028i	−0.425116	+	0.905139i	$0.639767\pi$
$234$		0			0
$235$		0			0
$236$	−10.8633	+	18.8158i	−0.707140	+	1.22480i
$237$		0			0
$238$	−3.71751	+	2.14631i	−0.240970	+	0.139124i
$239$	2.09936	+	3.63620i	0.135796	+	0.235206i	0.925901	−	0.377765i	$-0.123307\pi$
$239$	2.09936	+	3.63620i	0.135796	+	0.235206i	−0.790105	+	0.612971i	$0.789974\pi$
$240$		0			0
$241$	−1.80221	+	3.12152i	−0.116091	+	0.201075i	−0.918215	−	0.396082i	$-0.870370\pi$
$241$	−1.80221	+	3.12152i	−0.116091	+	0.201075i	0.802125	+	0.597157i	$0.203703\pi$
$242$		−	0.0710844i		−	0.00456948i
$243$		0			0
$244$	−31.7549			−2.03290
$245$		0			0
$246$		0			0
$247$	1.51099	−	0.872368i	0.0961417	−	0.0555074i
$248$	44.1437	−	25.4864i	2.80313	−	1.61839i
$249$		0			0
$250$		0			0
$251$	6.87783			0.434125			0.217062	−	0.976158i	$-0.430352\pi$
$251$	6.87783			0.434125			0.217062	+	0.976158i	$0.430352\pi$
$252$		0			0
$253$			13.7074i			0.861776i
$254$	−22.4909	+	38.9554i	−1.41121	+	2.44428i
$255$		0			0
$256$	15.8774	+	27.5005i	0.992340	+	1.71878i
$257$	15.5885	−	9.00000i	0.972381	−	0.561405i	0.0724199	−	0.997374i	$-0.476928\pi$
$257$	15.5885	−	9.00000i	0.972381	−	0.561405i	0.899961	+	0.435970i	$0.143595\pi$
$258$		0			0
$259$	−0.0752210	+	0.130287i	−0.00467400	+	0.00809561i
$260$		0			0
$261$		0			0
$262$		−	15.0848i		−	0.931943i
$263$	−5.40059	−	3.11803i	−0.333015	−	0.192266i	0.324164	−	0.946001i	$-0.394917\pi$
$263$	−5.40059	−	3.11803i	−0.333015	−	0.192266i	−0.657179	+	0.753735i	$0.728250\pi$
$264$		0			0
$265$		0			0
$266$	0.853695	+	1.47864i	0.0523434	+	0.0906614i
$267$		0			0
$268$	35.3563	+	20.4130i	2.15973	+	1.24692i
$269$	9.92345			0.605044			0.302522	−	0.953142i	$-0.402172\pi$
$269$	9.92345			0.605044			0.302522	+	0.953142i	$0.402172\pi$
$270$		0			0
$271$	6.60442			0.401190			0.200595	−	0.979674i	$-0.435712\pi$
$271$	6.60442			0.401190			0.200595	+	0.979674i	$0.435712\pi$
$272$	−17.3371	−	10.0096i	−1.05122	−	0.606921i
$273$		0			0
$274$	7.12763	+	12.3454i	0.430596	+	0.745814i
$275$		0			0
$276$		0			0
$277$	−19.6250	−	11.3305i	−1.17915	−	0.680783i	−0.223333	−	0.974742i	$-0.571694\pi$
$277$	−19.6250	−	11.3305i	−1.17915	−	0.680783i	−0.955818	+	0.293959i	$0.905027\pi$
$278$			20.1131i			1.20630i
$279$		0			0
$280$		0			0
$281$	−7.77394	+	13.4649i	−0.463754	+	0.803246i	−0.999144	−	0.0413590i	$-0.986831\pi$
$281$	−7.77394	+	13.4649i	−0.463754	+	0.803246i	0.535390	+	0.844605i	$0.320165\pi$
$282$		0			0
$283$	−0.558913	+	0.322689i	−0.0332240	+	0.0191819i	−0.516520	−	0.856275i	$-0.672773\pi$
$283$	−0.558913	+	0.322689i	−0.0332240	+	0.0191819i	0.483296	+	0.875457i	$0.339439\pi$
$284$	−19.4244	−	33.6440i	−1.15262	−	1.99640i
$285$		0			0
$286$	−5.51414	+	9.55077i	−0.326058	+	0.564749i
$287$		−	5.83502i		−	0.344430i
$288$		0			0
$289$	5.97173			0.351278
$290$		0			0
$291$		0			0
$292$	22.6636	−	13.0848i	1.32629	−	0.765731i
$293$	−1.19289	+	0.688716i	−0.0696895	+	0.0402352i	−0.534440	−	0.845207i	$-0.679477\pi$
$293$	−1.19289	+	0.688716i	−0.0696895	+	0.0402352i	0.464750	+	0.885442i	$0.346144\pi$
$294$		0			0
$295$		0			0
$296$	−1.70739			−0.0992400
$297$		0			0
$298$		−	44.4021i		−	2.57214i
$299$	2.72606	−	4.72168i	0.157652	−	0.273062i
$300$		0			0
$301$	2.66044	+	4.60802i	0.153345	+	0.265602i
$302$	−2.75285	+	1.58936i	−0.158409	+	0.0914573i
$303$		0			0
$304$	−3.98133	+	6.89586i	−0.228345	+	0.395505i
$305$		0			0
$306$		0			0
$307$		−	7.98546i		−	0.455754i	−0.973690	−	0.227877i	$-0.926822\pi$
$307$		−	7.98546i		−	0.455754i	0.973690	−	0.227877i	$-0.0731785\pi$
$308$	−6.38904	−	3.68872i	−0.364050	−	0.210184i
$309$		0			0
$310$		0			0
$311$	4.81635	+	8.34216i	0.273110	+	0.473040i	0.969657	−	0.244471i	$-0.0786143\pi$
$311$	4.81635	+	8.34216i	0.273110	+	0.473040i	−0.696547	+	0.717512i	$0.745281\pi$
$312$		0			0
$313$	−21.2496	−	12.2685i	−1.20110	−	0.693455i	−0.240300	−	0.970699i	$-0.577246\pi$
$313$	−21.2496	−	12.2685i	−1.20110	−	0.693455i	−0.960800	+	0.277244i	$0.910579\pi$
$314$	−39.3966			−2.22328
$315$		0			0
$316$	−34.8114			−1.95829
$317$	−17.6229	−	10.1746i	−0.989800	−	0.571461i	−0.0845855	−	0.996416i	$-0.526957\pi$
$317$	−17.6229	−	10.1746i	−0.989800	−	0.571461i	−0.905215	+	0.424955i	$0.860290\pi$
$318$		0			0
$319$	2.30221	+	3.98755i	0.128899	+	0.223260i
$320$		0			0
$321$		0			0
$322$	4.62061	+	2.66771i	0.257497	+	0.148666i
$323$			4.38650i			0.244072i
$324$		0			0
$325$		0			0
$326$	19.7453	−	34.1998i	1.09359	−	1.89415i
$327$		0			0
$328$	57.3504	−	33.1113i	3.16665	−	1.82827i
$329$	−1.25020	−	2.16541i	−0.0689257	−	0.119383i
$330$		0			0
$331$	−8.22153	+	14.2401i	−0.451896	+	0.782707i	−0.998504	−	0.0546819i	$-0.982586\pi$
$331$	−8.22153	+	14.2401i	−0.451896	+	0.782707i	0.546608	+	0.837389i	$0.315919\pi$
$332$		−	6.66458i		−	0.365766i
$333$		0			0
$334$	−15.4996			−0.848100
$335$		0			0
$336$		0			0
$337$	4.24096	−	2.44852i	0.231020	−	0.133379i	−0.380023	−	0.924977i	$-0.624084\pi$
$337$	4.24096	−	2.44852i	0.231020	−	0.133379i	0.611042	+	0.791598i	$0.290751\pi$
$338$	−24.5062	+	14.1486i	−1.33296	+	0.769584i
$339$		0			0
$340$		0			0
$341$	29.0101			1.57099
$342$		0			0
$343$		−	7.06201i		−	0.381313i
$344$	−30.1938	+	52.2972i	−1.62794	+	2.81967i
$345$		0			0
$346$	−10.7922	−	18.6927i	−0.580193	−	1.00492i
$347$	−19.2903	+	11.1372i	−1.03556	+	0.597878i	−0.918571	−	0.395256i	$-0.870656\pi$
$347$	−19.2903	+	11.1372i	−1.03556	+	0.597878i	−0.116984	+	0.993134i	$0.537323\pi$
$348$		0			0
$349$	−1.47173	+	2.54910i	−0.0787797	+	0.136450i	−0.902724	−	0.430221i	$-0.858436\pi$
$349$	−1.47173	+	2.54910i	−0.0787797	+	0.136450i	0.823944	+	0.566671i	$0.191769\pi$
$350$		0			0
$351$		0			0
$352$		−	11.5761i		−	0.617011i
$353$	−16.3069	−	9.41478i	−0.867927	−	0.501098i	−0.00126845	−	0.999999i	$-0.500404\pi$
$353$	−16.3069	−	9.41478i	−0.867927	−	0.501098i	−0.866659	+	0.498901i	$0.833737\pi$
$354$		0			0
$355$		0			0
$356$	−6.48133	−	11.2260i	−0.343510	−	0.594976i
$357$		0			0
$358$	−2.32018	−	1.33956i	−0.122625	−	0.0707978i
$359$	−31.8770			−1.68241			−0.841203	−	0.540720i	$-0.818152\pi$
$359$	−31.8770			−1.68241			−0.841203	+	0.540720i	$0.818152\pi$
$360$		0			0
$361$	−17.2553			−0.908172
$362$	−27.5866	−	15.9271i	−1.44992	−	0.837110i
$363$		0			0
$364$	1.46719	+	2.54125i	0.0769016	+	0.133198i
$365$		0			0
$366$		0			0
$367$	15.8908	+	9.17458i	0.829495	+	0.478909i	0.853680	−	0.520798i	$-0.174366\pi$
$367$	15.8908	+	9.17458i	0.829495	+	0.478909i	−0.0241848	+	0.999708i	$0.507699\pi$
$368$			24.8825i			1.29709i
$369$		0			0
$370$		0			0
$371$	1.29261	−	2.23887i	0.0671090	−	0.116236i
$372$		0			0
$373$	1.90414	−	1.09936i	0.0985929	−	0.0569226i	−0.449893	−	0.893083i	$-0.648538\pi$
$373$	1.90414	−	1.09936i	0.0985929	−	0.0569226i	0.548486	+	0.836160i	$0.315205\pi$
$374$	−13.8633	−	24.0119i	−0.716854	−	1.24163i
$375$		0			0
$376$	14.1887	−	24.5756i	0.731727	−	1.26739i
$377$		−	1.83141i		−	0.0943226i
$378$		0			0
$379$	−15.4713			−0.794709			−0.397354	−	0.917665i	$-0.630072\pi$
$379$	−15.4713			−0.794709			−0.397354	+	0.917665i	$0.630072\pi$
$380$		0			0
$381$		0			0
$382$	−36.8713	+	21.2877i	−1.88650	+	1.08917i
$383$	6.67479	−	3.85369i	0.341066	−	0.196915i	−0.319677	−	0.947526i	$-0.603574\pi$
$383$	6.67479	−	3.85369i	0.341066	−	0.196915i	0.660743	+	0.750612i	$0.270241\pi$
$384$		0			0
$385$		0			0
$386$	−67.1715			−3.41894
$387$		0			0
$388$			52.9536i			2.68831i
$389$	12.3163	−	21.3325i	0.624464	−	1.08160i	−0.364181	−	0.931328i	$-0.618651\pi$
$389$	12.3163	−	21.3325i	0.624464	−	1.08160i	0.988644	−	0.150274i	$-0.0480157\pi$
$390$		0			0
$391$	6.85369	+	11.8709i	0.346606	+	0.600340i
$392$	34.0372	−	19.6514i	1.71914	−	0.992544i
$393$		0			0
$394$	−17.9198	+	31.0381i	−0.902789	+	1.56368i
$395$		0			0
$396$		0			0
$397$		−	6.77301i		−	0.339928i	−0.985450	−	0.169964i	$-0.945635\pi$
$397$		−	6.77301i		−	0.339928i	0.985450	−	0.169964i	$-0.0543651\pi$
$398$	53.6945	+	31.0005i	2.69146	+	1.55392i
$399$		0			0
$400$		0			0
$401$	−9.24980	−	16.0211i	−0.461913	−	0.800057i	0.537143	−	0.843491i	$-0.319503\pi$
$401$	−9.24980	−	16.0211i	−0.461913	−	0.800057i	−0.999056	+	0.0434343i	$0.986170\pi$
$402$		0			0
$403$	−9.99290	−	5.76940i	−0.497782	−	0.287394i
$404$	50.4249			2.50873
$405$		0			0
$406$	1.79221			0.0889459
$407$	−0.841540	−	0.485863i	−0.0417136	−	0.0240833i
$408$		0			0
$409$	−6.70739	−	11.6175i	−0.331659	−	0.574450i	0.651178	−	0.758925i	$-0.274275\pi$
$409$	−6.70739	−	11.6175i	−0.331659	−	0.574450i	−0.982837	+	0.184474i	$0.940942\pi$
$410$		0			0
$411$		0			0
$412$	−1.09495	−	0.632168i	−0.0539442	−	0.0311447i
$413$			2.58522i			0.127210i
$414$		0			0
$415$		0			0
$416$	−2.30221	+	3.98755i	−0.112875	+	0.195506i
$417$		0			0
$418$	−9.55077	+	5.51414i	−0.467143	+	0.269705i
$419$	16.5575	+	28.6784i	0.808886	+	1.40103i	0.913636	+	0.406532i	$0.133262\pi$
$419$	16.5575	+	28.6784i	0.808886	+	1.40103i	−0.104751	+	0.994499i	$0.533404\pi$
$420$		0			0
$421$	7.34916	−	12.7291i	0.358176	−	0.620379i	−0.629480	−	0.777017i	$-0.716732\pi$
$421$	7.34916	−	12.7291i	0.358176	−	0.620379i	0.987656	+	0.156637i	$0.0500654\pi$
$422$			13.5196i			0.658124i
$423$		0			0
$424$	29.3401			1.42488
$425$		0			0
$426$		0			0
$427$	−3.27225	+	1.88924i	−0.158355	+	0.0914266i
$428$	7.00639	−	4.04514i	0.338667	−	0.195529i
$429$		0			0
$430$		0			0
$431$	32.7549			1.57775			0.788873	−	0.614556i	$-0.210665\pi$
$431$	32.7549			1.57775			0.788873	+	0.614556i	$0.210665\pi$
$432$		0			0
$433$			11.8314i			0.568581i	0.958738	+	0.284291i	$0.0917581\pi$
$433$			11.8314i			0.568581i	−0.958738	+	0.284291i	$0.908242\pi$
$434$	5.64591	−	9.77900i	0.271012	−	0.469407i
$435$		0			0
$436$	−11.9859	−	20.7601i	−0.574019	−	0.994230i
$437$	4.72168	−	2.72606i	0.225869	−	0.130405i
$438$		0			0
$439$	4.15591	−	7.19824i	0.198351	−	0.343553i	−0.749643	−	0.661842i	$-0.769775\pi$
$439$	4.15591	−	7.19824i	0.198351	−	0.343553i	0.947994	+	0.318289i	$0.103108\pi$
$440$		0			0
$441$		0			0
$442$			11.0283i			0.524561i
$443$	25.2664	+	14.5876i	1.20044	+	0.693076i	0.960654	−	0.277750i	$-0.0895885\pi$
$443$	25.2664	+	14.5876i	1.20044	+	0.693076i	0.239789	+	0.970825i	$0.422922\pi$
$444$		0			0
$445$		0			0
$446$	10.8920	+	18.8654i	0.515750	+	0.893305i
$447$		0			0
$448$	1.46605	+	0.846426i	0.0692645	+	0.0399899i
$449$	18.9717			0.895331			0.447666	−	0.894201i	$-0.352256\pi$
$449$	18.9717			0.895331			0.447666	+	0.894201i	$0.352256\pi$
$450$		0			0
$451$	37.6892			1.77472
$452$	29.1924	+	16.8542i	1.37309	+	0.792756i
$453$		0			0
$454$	4.17458	+	7.23058i	0.195923	+	0.339348i
$455$		0			0
$456$		0			0
$457$	20.1223	+	11.6176i	0.941283	+	0.543450i	0.890362	−	0.455253i	$-0.150451\pi$
$457$	20.1223	+	11.6176i	0.941283	+	0.543450i	0.0509206	+	0.998703i	$0.483784\pi$
$458$		−	63.6374i		−	2.97358i
$459$		0			0
$460$		0			0
$461$	2.21285	−	3.83277i	0.103063	−	0.178510i	−0.809882	−	0.586592i	$-0.800469\pi$
$461$	2.21285	−	3.83277i	0.103063	−	0.178510i	0.912945	+	0.408082i	$0.133802\pi$
$462$		0			0
$463$	16.8950	−	9.75434i	0.785178	−	0.453322i	−0.0530845	−	0.998590i	$-0.516905\pi$
$463$	16.8950	−	9.75434i	0.785178	−	0.453322i	0.838262	+	0.545268i	$0.183572\pi$
$464$	4.17912	+	7.23844i	0.194011	+	0.336036i
$465$		0			0
$466$	−34.7362	+	60.1648i	−1.60912	+	2.78708i
$467$			24.5935i			1.13805i	0.822320	+	0.569026i	$0.192679\pi$
$467$			24.5935i			1.13805i	−0.822320	+	0.569026i	$0.807321\pi$
$468$		0			0
$469$	4.85783			0.224314
$470$		0			0
$471$		0			0
$472$	−25.4093	+	14.6700i	−1.16956	+	0.675243i
$473$	−29.7639	+	17.1842i	−1.36854	+	0.790129i
$474$		0			0
$475$		0			0
$476$	−7.37743			−0.338144
$477$		0			0
$478$			10.5561i			0.482827i
$479$	−16.3774	+	28.3665i	−0.748304	+	1.29610i	0.200331	+	0.979728i	$0.435798\pi$
$479$	−16.3774	+	28.3665i	−0.748304	+	1.29610i	−0.948635	+	0.316372i	$0.897535\pi$
$480$		0			0
$481$	0.193252	+	0.334723i	0.00881155	+	0.0152621i
$482$	−7.84793	+	4.53101i	−0.357464	+	0.206382i
$483$		0			0
$484$	0.0610840	−	0.105801i	0.00277655	−	0.00480912i
$485$		0			0
$486$		0			0
$487$		−	6.03735i		−	0.273578i	−0.990600	−	0.136789i	$-0.956322\pi$
$487$		−	6.03735i		−	0.273578i	0.990600	−	0.136789i	$-0.0436783\pi$
$488$	−37.1373	−	21.4412i	−1.68113	−	0.970600i
$489$		0			0
$490$		0			0
$491$	7.22153	+	12.5081i	0.325903	+	0.564480i	0.981695	−	0.190461i	$-0.0609984\pi$
$491$	7.22153	+	12.5081i	0.325903	+	0.564480i	−0.655792	+	0.754942i	$0.727665\pi$
$492$		0			0
$493$	3.98755	+	2.30221i	0.179590	+	0.103686i
$494$	4.38650			0.197358
$495$		0			0
$496$	52.6610			2.36455
$497$	−4.00326	−	2.31128i	−0.179571	−	0.103675i
$498$		0			0
$499$	10.4859	+	18.1620i	0.469412	+	0.813045i	0.999388	−	0.0349673i	$-0.0111327\pi$
$499$	10.4859	+	18.1620i	0.469412	+	0.813045i	−0.529977	+	0.848012i	$0.677799\pi$
$500$		0			0
$501$		0			0
$502$	14.9751	+	8.64591i	0.668374	+	0.385886i
$503$		−	5.31728i		−	0.237086i	−0.992949	−	0.118543i	$-0.962178\pi$
$503$		−	5.31728i		−	0.237086i	0.992949	−	0.118543i	$-0.0378223\pi$
$504$		0			0
$505$		0			0
$506$	−17.2311	+	29.8452i	−0.766017	+	1.32678i
$507$		0			0
$508$	−66.9502	+	38.6537i	−2.97043	+	1.71498i
$509$	−9.11350	−	15.7850i	−0.403949	−	0.699659i	0.590250	−	0.807221i	$-0.299029\pi$
$509$	−9.11350	−	15.7850i	−0.403949	−	0.699659i	−0.994198	+	0.107561i	$0.965696\pi$
$510$		0			0
$511$	1.55695	−	2.69671i	0.0688753	−	0.119296i
$512$			49.3365i			2.18038i
$513$		0			0
$514$	45.2545			1.99609
$515$		0			0
$516$		0			0
$517$	13.9867	−	8.07522i	0.615134	−	0.355148i
$518$	−0.327558	+	0.189116i	−0.0143921	+	0.00830927i
$519$		0			0
$520$		0			0
$521$	−40.1232			−1.75783			−0.878915	−	0.476978i	$-0.841732\pi$
$521$	−40.1232			−1.75783			−0.878915	+	0.476978i	$0.841732\pi$
$522$		0			0
$523$		−	18.9873i		−	0.830257i	−0.909763	−	0.415129i	$-0.863737\pi$
$523$		−	18.9873i		−	0.830257i	0.909763	−	0.415129i	$-0.136263\pi$
$524$	12.9627	−	22.4520i	0.566276	−	0.980819i
$525$		0			0
$526$	−7.83916	−	13.5778i	−0.341804	−	0.592021i
$527$	25.1235	−	14.5051i	1.09440	−	0.631851i
$528$		0			0
$529$	−2.98133	+	5.16381i	−0.129623	+	0.224513i
$530$		0			0
$531$		0			0
$532$			2.93438i			0.127221i
$533$	−12.9825	−	7.49546i	−0.562336	−	0.324665i
$534$		0			0
$535$		0			0
$536$	27.5661	+	47.7460i	1.19068	+	2.06231i
$537$		0			0
$538$	21.6064	+	12.4745i	0.931518	+	0.537812i
$539$	22.3684			0.963473
$540$		0			0
$541$	16.5279			0.710589			0.355294	−	0.934754i	$-0.384381\pi$
$541$	16.5279			0.710589			0.355294	+	0.934754i	$0.384381\pi$
$542$	14.3799	+	8.30221i	0.617668	+	0.356611i
$543$		0			0
$544$	−5.78807	−	10.0252i	−0.248162	−	0.429829i
$545$		0			0
$546$		0			0
$547$	−15.3058	−	8.83683i	−0.654430	−	0.377835i	0.135721	−	0.990747i	$-0.456665\pi$
$547$	−15.3058	−	8.83683i	−0.654430	−	0.377835i	−0.790151	+	0.612912i	$0.789998\pi$
$548$			24.4996i			1.04657i
$549$		0			0
$550$		0			0
$551$	0.915706	−	1.58605i	0.0390104	−	0.0675680i
$552$		0			0
$553$	−3.58722	+	2.07108i	−0.152544	+	0.0880715i
$554$	−28.4864	−	49.3399i	−1.21027	−	2.09625i
$555$		0			0
$556$	−17.2835	+	29.9360i	−0.732985	+	1.26957i
$557$		−	17.3401i		−	0.734723i	−0.930078	−	0.367362i	$-0.880261\pi$
$557$		−	17.3401i		−	0.734723i	0.930078	−	0.367362i	$-0.119739\pi$
$558$		0			0
$559$	13.6700			0.578181
$560$		0			0
$561$		0			0
$562$	−33.8525	+	19.5447i	−1.42798	+	0.824445i
$563$	11.2536	−	6.49727i	0.474283	−	0.273827i	−0.243748	−	0.969839i	$-0.578377\pi$
$563$	11.2536	−	6.49727i	0.474283	−	0.273827i	0.718031	+	0.696011i	$0.245044\pi$
$564$		0			0
$565$		0			0
$566$	−1.62257			−0.0682016
$567$		0			0
$568$		−	52.4623i		−	2.20127i
$569$	8.34009	−	14.4455i	0.349635	−	0.605585i	−0.636550	−	0.771236i	$-0.719639\pi$
$569$	8.34009	−	14.4455i	0.349635	−	0.605585i	0.986184	+	0.165651i	$0.0529724\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−16.4143	+	9.47679i	−0.686316	+	0.396245i
$573$		0			0
$574$	7.33502	−	12.7046i	0.306158	−	0.530281i
$575$		0			0
$576$		0			0
$577$		−	23.5953i		−	0.982287i	−0.871079	−	0.491144i	$-0.836579\pi$
$577$		−	23.5953i		−	0.982287i	0.871079	−	0.491144i	$-0.163421\pi$
$578$	13.0023	+	7.50687i	0.540823	+	0.312245i
$579$		0			0
$580$		0			0
$581$	−0.396505	−	0.686767i	−0.0164498	−	0.0284919i
$582$		0			0
$583$	14.4612	+	8.34916i	0.598920	+	0.345787i
$584$	35.3401			1.46238
$585$		0			0
$586$	−3.46305			−0.143057
$587$	24.3592	+	14.0638i	1.00541	+	0.580476i	0.909846	−	0.414947i	$-0.136200\pi$
$587$	24.3592	+	14.0638i	1.00541	+	0.580476i	0.0955681	+	0.995423i	$0.469533\pi$
$588$		0			0
$589$	−5.76940	−	9.99290i	−0.237724	−	0.411750i
$590$		0			0
$591$		0			0
$592$	−1.52761	−	0.881969i	−0.0627846	−	0.0362487i
$593$		−	9.17872i		−	0.376925i	−0.982080	−	0.188462i	$-0.939650\pi$
$593$		−	9.17872i		−	0.376925i	0.982080	−	0.188462i	$-0.0603503\pi$
$594$		0			0
$595$		0			0
$596$	38.1555	−	66.0873i	1.56291	−	2.70704i
$597$		0			0
$598$	11.8709	−	6.85369i	0.485439	−	0.280268i
$599$	15.7357	+	27.2550i	0.642942	+	1.11361i	0.984773	+	0.173846i	$0.0556196\pi$
$599$	15.7357	+	27.2550i	0.642942	+	1.11361i	−0.341831	+	0.939761i	$0.611047\pi$
$600$		0			0
$601$	14.6327	−	25.3446i	0.596880	−	1.03383i	−0.396398	−	0.918079i	$-0.629740\pi$
$601$	14.6327	−	25.3446i	0.596880	−	1.03383i	0.993279	−	0.115748i	$-0.0369265\pi$
$602$			13.3774i			0.545223i
$603$		0			0
$604$	−5.46305			−0.222288
$605$		0			0
$606$		0			0
$607$	−38.2813	+	22.1017i	−1.55379	+	0.897080i	−0.555960	+	0.831209i	$0.687649\pi$
$607$	−38.2813	+	22.1017i	−1.55379	+	0.897080i	−0.997828	+	0.0658708i	$0.979017\pi$
$608$	−3.98755	+	2.30221i	−0.161716	+	0.0933670i
$609$		0			0
$610$		0			0
$611$	−6.42385			−0.259881
$612$		0			0
$613$			35.1715i			1.42056i	0.703918	+	0.710282i	$0.251432\pi$
$613$			35.1715i			1.42056i	−0.703918	+	0.710282i	$0.748568\pi$
$614$	10.0383	−	17.3868i	0.405112	−	0.701674i
$615$		0			0
$616$	−4.98133	−	8.62791i	−0.200703	−	0.347628i
$617$	6.43085	−	3.71285i	0.258896	−	0.149474i	−0.364935	−	0.931033i	$-0.618909\pi$
$617$	6.43085	−	3.71285i	0.258896	−	0.149474i	0.623831	+	0.781559i	$0.285575\pi$
$618$		0			0
$619$	4.27394	−	7.40268i	0.171784	−	0.297539i	−0.767260	−	0.641337i	$-0.778380\pi$
$619$	4.27394	−	7.40268i	0.171784	−	0.297539i	0.939044	+	0.343798i	$0.111714\pi$
$620$		0			0
$621$		0			0
$622$			24.2179i			0.971050i
$623$	−1.33577	−	0.771205i	−0.0535164	−	0.0308977i
$624$		0			0
$625$		0			0
$626$	−30.8446	−	53.4245i	−1.23280	−	2.13527i
$627$		0			0
$628$	−58.6372	−	33.8542i	−2.33988	−	1.35093i
$629$	−0.971726			−0.0387453
$630$		0			0
$631$	−2.36836			−0.0942829			−0.0471415	−	0.998888i	$-0.515011\pi$
$631$	−2.36836			−0.0942829			−0.0471415	+	0.998888i	$0.515011\pi$
$632$	−40.7120	−	23.5051i	−1.61944	−	0.934981i
$633$		0			0
$634$	−25.5803	−	44.3064i	−1.01592	−	1.75963i
$635$		0			0
$636$		0			0
$637$	−7.70506	−	4.44852i	−0.305285	−	0.176257i
$638$			11.5761i			0.458304i
$639$		0			0
$640$		0			0
$641$	−0.0665480	+	0.115265i	−0.00262849	+	0.00455268i	−0.867337	−	0.497722i	$-0.834170\pi$
$641$	−0.0665480	+	0.115265i	−0.00262849	+	0.00455268i	0.864708	+	0.502275i	$0.167503\pi$
$642$		0			0
$643$	19.6124	−	11.3232i	0.773437	−	0.446544i	−0.0606623	−	0.998158i	$-0.519321\pi$
$643$	19.6124	−	11.3232i	0.773437	−	0.446544i	0.834099	+	0.551614i	$0.185988\pi$
$644$	4.58482	+	7.94114i	0.180667	+	0.312925i
$645$		0			0
$646$	−5.51414	+	9.55077i	−0.216951	+	0.375770i
$647$		−	46.3912i		−	1.82383i	−0.410385	−	0.911913i	$-0.634606\pi$
$647$		−	46.3912i		−	1.82383i	0.410385	−	0.911913i	$-0.365394\pi$
$648$		0			0
$649$	−16.6983			−0.655466
$650$		0			0
$651$		0			0
$652$	58.7770	−	33.9349i	2.30188	−	1.32899i
$653$	31.5283	−	18.2029i	1.23380	−	0.712333i	0.265977	−	0.963979i	$-0.414305\pi$
$653$	31.5283	−	18.2029i	1.23380	−	0.712333i	0.967819	+	0.251647i	$0.0809721\pi$
$654$		0			0
$655$		0			0
$656$	68.4158			2.67119
$657$		0			0
$658$		−	6.28635i		−	0.245067i
$659$	−9.57068	+	16.5769i	−0.372821	+	0.645745i	−0.989998	−	0.141079i	$-0.954943\pi$
$659$	−9.57068	+	16.5769i	−0.372821	+	0.645745i	0.617177	+	0.786824i	$0.288276\pi$
$660$		0			0
$661$	−19.9536	−	34.5606i	−0.776104	−	1.34425i	−0.934172	−	0.356824i	$-0.883860\pi$
$661$	−19.9536	−	34.5606i	−0.776104	−	1.34425i	0.158067	−	0.987428i	$-0.449474\pi$
$662$	−35.8016	+	20.6700i	−1.39147	+	0.803364i
$663$		0			0
$664$	4.50000	−	7.79423i	0.174634	−	0.302475i
$665$		0			0
$666$		0			0
$667$		−	5.72298i		−	0.221595i
$668$	−23.0693	−	13.3191i	−0.892579	−	0.515331i
$669$		0			0
$670$		0			0
$671$	−12.2029	−	21.1360i	−0.471086	−	0.815945i
$672$		0			0
$673$	20.4822	+	11.8254i	0.789532	+	0.455836i	0.839798	−	0.542899i	$-0.182674\pi$
$673$	20.4822	+	11.8254i	0.789532	+	0.455836i	−0.0502658	+	0.998736i	$0.516007\pi$
$674$	12.3118			0.474233
$675$		0			0
$676$	−48.6327			−1.87049
$677$	−12.8199	−	7.40157i	−0.492709	−	0.284465i	0.232989	−	0.972479i	$-0.425149\pi$
$677$	−12.8199	−	7.40157i	−0.492709	−	0.284465i	−0.725697	+	0.688014i	$0.758483\pi$
$678$		0			0
$679$	3.15044	+	5.45673i	0.120903	+	0.209410i
$680$		0			0
$681$		0			0
$682$	63.1639	+	36.4677i	2.41867	+	1.39642i
$683$		−	4.95252i		−	0.189503i	−0.995501	−	0.0947515i	$-0.969794\pi$
$683$		−	4.95252i		−	0.189503i	0.995501	−	0.0947515i	$-0.0302057\pi$
$684$		0			0
$685$		0			0
$686$	8.87743	−	15.3762i	0.338942	−	0.587065i
$687$		0			0
$688$	−54.0292	+	31.1938i	−2.05984	+	1.18925i
$689$	−3.32088	−	5.75194i	−0.126516	−	0.219131i
$690$		0			0
$691$	9.60442	−	16.6353i	0.365369	−	0.632838i	−0.623466	−	0.781851i	$-0.714276\pi$
$691$	9.60442	−	16.6353i	0.365369	−	0.632838i	0.988835	+	0.149012i	$0.0476093\pi$
$692$		−	37.0957i		−	1.41017i
$693$		0			0
$694$	−56.0011			−2.12577
$695$		0			0
$696$		0			0
$697$	32.6398	−	18.8446i	1.23632	−	0.713791i
$698$	−6.40880	+	3.70012i	−0.242577	+	0.140052i
$699$		0			0
$700$		0			0
$701$	29.3492			1.10850			0.554251	−	0.832349i	$-0.313005\pi$
$701$	29.3492			1.10850			0.554251	+	0.832349i	$0.313005\pi$
$702$		0			0
$703$			0.386505i			0.0145773i
$704$	−5.46719	+	9.46945i	−0.206052	+	0.356893i
$705$		0			0
$706$	−23.6700	−	40.9977i	−0.890834	−	1.54297i
$707$	5.19615	−	3.00000i	0.195421	−	0.112827i
$708$		0			0
$709$	19.3633	−	33.5382i	0.727204	−	1.25955i	−0.230857	−	0.972988i	$-0.574153\pi$
$709$	19.3633	−	33.5382i	0.727204	−	1.25955i	0.958060	−	0.286566i	$-0.0925138\pi$
$710$		0			0
$711$		0			0
$712$		−	17.5051i		−	0.656030i
$713$	−31.2268	−	18.0288i	−1.16945	−	0.675184i
$714$		0			0
$715$		0			0
$716$	−2.30221	−	3.98755i	−0.0860377	−	0.149022i
$717$		0			0
$718$	−69.4061	−	40.0716i	−2.59021	−	1.49546i
$719$	−15.0848			−0.562569			−0.281284	−	0.959624i	$-0.590760\pi$
$719$	−15.0848			−0.562569			−0.281284	+	0.959624i	$0.590760\pi$
$720$		0			0
$721$	−0.150442			−0.00560275
$722$	−37.5700	−	21.6910i	−1.39821	−	0.807257i
$723$		0			0
$724$	−27.3729	−	47.4112i	−1.01731	−	1.76203i
$725$		0			0
$726$		0			0
$727$	−10.6916	−	6.17277i	−0.396528	−	0.228936i	0.288457	−	0.957493i	$-0.406858\pi$
$727$	−10.6916	−	6.17277i	−0.396528	−	0.228936i	−0.684985	+	0.728557i	$0.740191\pi$
$728$			3.96265i			0.146866i
$729$		0			0
$730$		0			0
$731$	−17.1842	+	29.7639i	−0.635580	+	1.10086i
$732$		0			0
$733$	19.0526	−	11.0000i	0.703722	−	0.406294i	−0.105010	−	0.994471i	$-0.533487\pi$
$733$	19.0526	−	11.0000i	0.703722	−	0.406294i	0.808732	+	0.588177i	$0.200154\pi$
$734$	23.0661	+	39.9517i	0.851387	+	1.47465i
$735$		0			0
$736$	−7.19418	+	12.4607i	−0.265181	+	0.459307i
$737$			31.3774i			1.15580i
$738$		0			0
$739$	−29.7266			−1.09351			−0.546755	−	0.837293i	$-0.684137\pi$
$739$	−29.7266			−1.09351			−0.546755	+	0.837293i	$0.684137\pi$
$740$		0			0
$741$		0			0
$742$	5.62882	−	3.24980i	0.206640	−	0.119304i
$743$	41.8851	−	24.1824i	1.53662	−	0.887165i	0.537582	−	0.843212i	$-0.319338\pi$
$743$	41.8851	−	24.1824i	1.53662	−	0.887165i	0.999034	−	0.0439537i	$-0.0139954\pi$
$744$		0			0
$745$		0			0
$746$	5.52787			0.202390
$747$		0			0
$748$		−	47.6519i		−	1.74233i
$749$	0.481327	−	0.833682i	0.0175873	−	0.0304621i
$750$		0			0
$751$	15.9102	+	27.5573i	0.580573	+	1.00558i	0.995411	+	0.0956869i	$0.0305047\pi$
$751$	15.9102	+	27.5573i	0.580573	+	1.00558i	−0.414838	+	0.909895i	$0.636162\pi$
$752$	25.3895	−	14.6586i	0.925860	−	0.534546i
$753$		0			0
$754$	2.30221	−	3.98755i	0.0838416	−	0.145218i
$755$		0			0
$756$		0			0
$757$			4.94531i			0.179740i	0.995953	+	0.0898701i	$0.0286452\pi$
$757$			4.94531i			0.179740i	−0.995953	+	0.0898701i	$0.971355\pi$
$758$	−33.6858	−	19.4485i	−1.22352	−	0.706402i
$759$		0			0
$760$		0			0
$761$	17.7125	+	30.6789i	0.642076	+	1.11211i	0.984969	+	0.172734i	$0.0552600\pi$
$761$	17.7125	+	30.6789i	0.642076	+	1.11211i	−0.342893	+	0.939375i	$0.611407\pi$
$762$		0			0
$763$	−2.47022	−	1.42618i	−0.0894281	−	0.0516313i
$764$	−73.1715			−2.64725
$765$		0			0
$766$	19.3774			0.700135
$767$	5.75194	+	3.32088i	0.207691	+	0.119910i
$768$		0			0
$769$	24.7125	+	42.8032i	0.891154	+	1.54352i	0.838494	+	0.544911i	$0.183437\pi$
$769$	24.7125	+	42.8032i	0.891154	+	1.54352i	0.0526602	+	0.998612i	$0.483230\pi$
$770$		0			0
$771$		0			0
$772$	−99.9768	−	57.7217i	−3.59825	−	2.07745i
$773$			12.6599i			0.455345i	0.973738	+	0.227673i	$0.0731116\pi$
$773$			12.6599i			0.455345i	−0.973738	+	0.227673i	$0.926888\pi$
$774$		0			0
$775$		0			0
$776$	−35.7549	+	61.9292i	−1.28352	+	2.22313i
$777$		0			0
$778$	53.6329	−	30.9650i	1.92283	−	1.11015i
$779$	−7.49546	−	12.9825i	−0.268553	−	0.465147i
$780$		0			0
$781$	14.9289	−	25.8576i	0.534199	−	0.925259i
$782$			34.4623i			1.23237i
$783$		0			0
$784$	40.6044			1.45016
$785$		0			0
$786$		0			0
$787$	26.7900	−	15.4672i	0.954959	−	0.551346i	0.0603410	−	0.998178i	$-0.480781\pi$
$787$	26.7900	−	15.4672i	0.954959	−	0.551346i	0.894618	+	0.446832i	$0.147448\pi$
$788$	−53.3431	+	30.7977i	−1.90027	+	1.09712i
$789$		0			0
$790$		0			0
$791$	4.01093			0.142612
$792$		0			0
$793$			9.70739i			0.344720i
$794$	8.51414	−	14.7469i	0.302155	−	0.523349i
$795$		0			0
$796$	53.2786	+	92.2812i	1.88841	+	3.27082i
$797$	26.4947	−	15.2967i	0.938492	−	0.541839i	0.0490047	−	0.998799i	$-0.484395\pi$
$797$	26.4947	−	15.2967i	0.938492	−	0.541839i	0.889487	+	0.456960i	$0.151062\pi$
$798$		0			0
$799$	8.07522	−	13.9867i	0.285681	−	0.494814i
$800$		0			0
$801$		0			0
$802$		−	46.5105i		−	1.64234i
$803$	17.4185	+	10.0565i	0.614684	+	0.354888i
$804$		0			0
$805$		0			0
$806$	−14.5051	−	25.1235i	−0.510919	−	0.884938i
$807$		0			0
$808$	58.9720	+	34.0475i	2.07463	+	1.19779i
$809$	−2.89703			−0.101854			−0.0509271	−	0.998702i	$-0.516218\pi$
$809$	−2.89703			−0.101854			−0.0509271	+	0.998702i	$0.516218\pi$
$810$		0			0
$811$	−14.8861			−0.522722			−0.261361	−	0.965241i	$-0.584171\pi$
$811$	−14.8861			−0.522722			−0.261361	+	0.965241i	$0.584171\pi$
$812$	2.66749	+	1.54008i	0.0936107	+	0.0540462i
$813$		0			0
$814$	−1.22153	−	2.11575i	−0.0428145	−	0.0741568i
$815$		0			0
$816$		0			0
$817$	11.8386	+	6.83502i	0.414180	+	0.239127i
$818$		−	33.7266i		−	1.17922i
$819$		0			0
$820$		0			0
$821$	−4.47586	+	7.75242i	−0.156209	+	0.270561i	−0.933498	−	0.358581i	$-0.883261\pi$
$821$	−4.47586	+	7.75242i	−0.156209	+	0.270561i	0.777290	+	0.629143i	$0.216594\pi$
$822$		0			0
$823$	−2.59334	+	1.49727i	−0.0903983	+	0.0521915i	−0.544518	−	0.838749i	$-0.683287\pi$
$823$	−2.59334	+	1.49727i	−0.0903983	+	0.0521915i	0.454119	+	0.890941i	$0.349954\pi$
$824$	−0.853695	−	1.47864i	−0.0297399	−	0.0515110i
$825$		0			0
$826$	−3.24980	+	5.62882i	−0.113075	+	0.195852i
$827$		−	31.9663i		−	1.11158i	−0.831324	−	0.555788i	$-0.812417\pi$
$827$		−	31.9663i		−	1.11158i	0.831324	−	0.555788i	$-0.187583\pi$
$828$		0			0
$829$	−22.7458			−0.789994			−0.394997	−	0.918682i	$-0.629254\pi$
$829$	−22.7458			−0.789994			−0.394997	+	0.918682i	$0.629254\pi$
$830$		0			0
$831$		0			0
$832$	3.76648	−	2.17458i	0.130579	−	0.0753900i
$833$	19.3716	−	11.1842i	0.671185	−	0.387509i
$834$		0			0
$835$		0			0
$836$	−18.9536			−0.655523
$837$		0			0
$838$			83.2555i			2.87601i
$839$	11.6322	−	20.1475i	0.401587	−	0.695569i	−0.592331	−	0.805695i	$-0.701792\pi$
$839$	11.6322	−	20.1475i	0.401587	−	0.695569i	0.993918	+	0.110126i	$0.0351254\pi$
$840$		0			0
$841$	13.5388	+	23.4499i	0.466855	+	0.808617i
$842$	32.0027	−	18.4768i	1.10289	−	0.636752i
$843$		0			0
$844$	−11.6176	+	20.1223i	−0.399895	+	0.692639i
$845$		0			0
$846$		0			0
$847$		−	0.0145366i		−	0.000499485i
$848$	26.2508	+	15.1559i	0.901456	+	0.520456i
$849$		0			0
$850$		0			0
$851$	0.603895	+	1.04598i	0.0207012	+	0.0358556i
$852$		0			0
$853$	9.51842	+	5.49546i	0.325905	+	0.188161i	0.654021	−	0.756476i	$-0.273081\pi$
$853$	9.51842	+	5.49546i	0.325905	+	0.188161i	−0.328117	+	0.944637i	$0.606414\pi$
$854$	−9.49960			−0.325070
$855$		0			0
$856$	10.9253			0.373419
$857$	−13.9867	−	8.07522i	−0.477776	−	0.275844i	0.241713	−	0.970348i	$-0.422291\pi$
$857$	−13.9867	−	8.07522i	−0.477776	−	0.275844i	−0.719489	+	0.694503i	$0.755624\pi$
$858$		0			0
$859$	14.2594	+	24.6980i	0.486524	+	0.842685i	0.999880	−	0.0154909i	$-0.00493111\pi$
$859$	14.2594	+	24.6980i	0.486524	+	0.842685i	−0.513356	+	0.858176i	$0.671598\pi$
$860$		0			0
$861$		0			0
$862$	71.3174	+	41.1751i	2.42908	+	1.40243i
$863$			12.2890i			0.418322i	0.977881	+	0.209161i	$0.0670734\pi$
$863$			12.2890i			0.418322i	−0.977881	+	0.209161i	$0.932927\pi$
$864$		0			0
$865$		0			0
$866$	−14.8729	+	25.7606i	−0.505402	+	0.875381i
$867$		0			0
$868$	16.8065	−	9.70325i	0.570451	−	0.329350i
$869$	−13.3774	−	23.1704i	−0.453798	−	0.786002i
$870$		0			0
$871$	6.24020	−	10.8083i	0.211441	−	0.366227i
$872$		−	32.3720i		−	1.09625i
$873$		0			0
$874$	13.7074			0.463659
$875$		0			0
$876$		0			0
$877$	−34.3814	+	19.8501i	−1.16098	+	0.670290i	−0.951538	−	0.307532i	$-0.900497\pi$
$877$	−34.3814	+	19.8501i	−1.16098	+	0.670290i	−0.209438	+	0.977822i	$0.567164\pi$
$878$	18.0974	−	10.4485i	0.610756	−	0.352620i
$879$		0			0
$880$		0			0
$881$	−32.1040			−1.08161			−0.540806	−	0.841147i	$-0.681881\pi$
$881$	−32.1040			−1.08161			−0.540806	+	0.841147i	$0.681881\pi$
$882$		0			0
$883$		−	13.5051i		−	0.454482i	−0.973839	−	0.227241i	$-0.927030\pi$
$883$		−	13.5051i		−	0.454482i	0.973839	−	0.227241i	$-0.0729704\pi$
$884$	−9.47679	+	16.4143i	−0.318739	+	0.552072i
$885$		0			0
$886$	36.6751	+	63.5231i	1.23212	+	2.13410i
$887$	−30.4167	+	17.5611i	−1.02129	+	0.589643i	−0.914478	−	0.404635i	$-0.867398\pi$
$887$	−30.4167	+	17.5611i	−1.02129	+	0.589643i	−0.106814	+	0.994279i	$0.534065\pi$
$888$		0			0
$889$	−4.59936	+	7.96632i	−0.154258	+	0.267182i
$890$		0			0
$891$		0			0
$892$			37.4386i			1.25354i
$893$	−5.56322	−	3.21193i	−0.186166	−	0.107483i
$894$		0			0
$895$		0			0
$896$	3.92024	+	6.79006i	0.130966	+	0.226840i
$897$		0			0
$898$	41.3073	+	23.8488i	1.37844	+	0.795843i
$899$	−12.1120			−0.403959
$900$		0			0
$901$	16.6983			0.556302
$902$	82.0610	+	47.3780i	2.73233	+	1.57751i
$903$		0			0
$904$	22.7603	+	39.4220i	0.756997	+	1.31116i
$905$		0			0
$906$		0			0
$907$	−13.0931	−	7.55928i	−0.434748	−	0.251002i	0.266619	−	0.963802i	$-0.414093\pi$
$907$	−13.0931	−	7.55928i	−0.434748	−	0.251002i	−0.701367	+	0.712800i	$0.747427\pi$
$908$			14.3492i			0.476194i
$909$		0			0
$910$		0			0
$911$	26.2781	−	45.5150i	0.870631	−	1.50798i	0.00928675	−	0.999957i	$-0.497044\pi$
$911$	26.2781	−	45.5150i	0.870631	−	1.50798i	0.861345	−	0.508021i	$-0.169623\pi$
$912$		0			0
$913$	4.43593	−	2.56108i	0.146808	−	0.0847595i
$914$	29.2083	+	50.5903i	0.966125	+	1.67338i
$915$		0			0
$916$	54.6847	−	94.7167i	1.80683	−	3.12953i
$917$		−	3.08482i		−	0.101870i
$918$		0			0
$919$	54.5489			1.79940			0.899702	−	0.436505i	$-0.143784\pi$
$919$	54.5489			1.79940			0.899702	+	0.436505i	$0.143784\pi$
$920$		0			0
$921$		0			0
$922$	9.63612	−	5.56342i	0.317349	−	0.183221i
$923$	−10.2849	+	5.93799i	−0.338532	+	0.195451i
$924$		0			0
$925$		0			0
$926$	49.0475			1.61180
$927$		0			0
$928$			4.83317i			0.158656i
$929$	−10.1896	+	17.6490i	−0.334311	+	0.579044i	−0.983352	−	0.181709i	$-0.941837\pi$
$929$	−10.1896	+	17.6490i	−0.334311	+	0.579044i	0.649041	+	0.760753i	$0.275170\pi$
$930$		0			0
$931$	−4.44852	−	7.70506i	−0.145794	−	0.252523i
$932$	−103.401	+	59.6988i	−3.38703	+	1.95550i
$933$		0			0
$934$	−30.9157	+	53.5476i	−1.01159	+	1.75213i
$935$		0			0
$936$		0			0
$937$			49.1979i			1.60723i	0.595152	+	0.803613i	$0.297092\pi$
$937$			49.1979i			1.60723i	−0.595152	+	0.803613i	$0.702908\pi$
$938$	10.5770	+	6.10663i	0.345351	+	0.199388i
$939$		0			0
$940$		0			0
$941$	−11.6186	−	20.1239i	−0.378754	−	0.656022i	0.612127	−	0.790759i	$-0.290314\pi$
$941$	−11.6186	−	20.1239i	−0.378754	−	0.656022i	−0.990881	+	0.134738i	$0.956981\pi$
$942$		0			0
$943$	−40.5691	−	23.4226i	−1.32111	−	0.762744i
$944$	−30.3118			−0.986565
$945$		0			0
$946$	−86.4068			−2.80933
$947$	32.1851	+	18.5821i	1.04588	+	0.603837i	0.921492	−	0.388397i	$-0.126971\pi$
$947$	32.1851	+	18.5821i	1.04588	+	0.603837i	0.124384	+	0.992234i	$0.460305\pi$
$948$		0			0
$949$	−4.00000	−	6.92820i	−0.129845	−	0.224899i
$950$		0			0
$951$		0			0
$952$	−8.62791	−	4.98133i	−0.279632	−	0.161446i
$953$		−	23.5761i		−	0.763706i	−0.924223	−	0.381853i	$-0.875286\pi$
$953$		−	23.5761i		−	0.763706i	0.924223	−	0.381853i	$-0.124714\pi$
$954$		0			0
$955$		0			0
$956$	−9.07108	+	15.7116i	−0.293380	+	0.508149i
$957$		0			0
$958$	−71.3174	+	41.1751i	−2.30416	+	1.33031i
$959$	1.45759	+	2.52462i	0.0470680	+	0.0815242i
$960$		0			0
$961$	−22.6559	+	39.2412i	−0.730836	+	1.26584i
$962$			0.971726i			0.0313297i
$963$		0			0
$964$	−15.5743			−0.501614
$965$		0			0
$966$		0			0
$967$	7.25980	−	4.19145i	0.233459	−	0.134788i	−0.378708	−	0.925516i	$-0.623631\pi$
$967$	7.25980	−	4.19145i	0.233459	−	0.134788i	0.612167	+	0.790729i	$0.290298\pi$
$968$	0.142876	−	0.0824893i	0.00459220	−	0.00265131i
$969$		0			0
$970$		0			0
$971$	−13.2078			−0.423858			−0.211929	−	0.977285i	$-0.567975\pi$
$971$	−13.2078			−0.423858			−0.211929	+	0.977285i	$0.567975\pi$
$972$		0			0
$973$			4.11310i			0.131860i
$974$	7.58936	−	13.1452i	0.243179	−	0.421198i
$975$		0			0
$976$	−22.1514	−	38.3673i	−0.709048	−	1.22811i
$977$	12.4110	−	7.16551i	0.397064	−	0.229245i	−0.288153	−	0.957585i	$-0.593041\pi$
$977$	12.4110	−	7.16551i	0.397064	−	0.229245i	0.685216	+	0.728340i	$0.259708\pi$
$978$		0			0
$979$	4.98133	−	8.62791i	0.159204	−	0.275749i
$980$		0			0
$981$		0			0
$982$			36.3118i			1.15876i
$983$	27.9797	+	16.1541i	0.892415	+	0.515236i	0.874732	−	0.484608i	$-0.161038\pi$
$983$	27.9797	+	16.1541i	0.892415	+	0.515236i	0.0176831	+	0.999844i	$0.494371\pi$
$984$		0			0
$985$		0			0
$986$	5.78807	+	10.0252i	0.184330	+	0.319269i
$987$		0			0
$988$	6.52879	+	3.76940i	0.207709	+	0.119921i
$989$	42.7175			1.35834
$990$		0			0
$991$	−39.6700			−1.26016			−0.630080	−	0.776530i	$-0.716978\pi$
$991$	−39.6700			−1.26016			−0.630080	+	0.776530i	$0.716978\pi$
$992$	26.3716	+	15.2257i	0.837300	+	0.483415i
$993$		0			0
$994$	−5.81088	−	10.0647i	−0.184310	−	0.319234i
$995$		0			0
$996$		0			0
$997$	−33.5043	−	19.3437i	−1.06109	−	0.612621i	−0.135357	−	0.990797i	$-0.543218\pi$
$997$	−33.5043	−	19.3437i	−1.06109	−	0.612621i	−0.925734	+	0.378176i	$0.876551\pi$
$998$			52.7258i			1.66901i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.k.b.424.6		12
3.2	odd	2		225.2.k.b.124.1		12
5.2	odd	4		675.2.e.b.451.1		6
5.3	odd	4		135.2.e.b.46.3		6
5.4	even	2	inner	675.2.k.b.424.1		12
9.2	odd	6		2025.2.b.l.649.6		6
9.4	even	3	inner	675.2.k.b.199.1		12
9.5	odd	6		225.2.k.b.49.6		12
9.7	even	3		2025.2.b.m.649.1		6
15.2	even	4		225.2.e.b.151.3		6
15.8	even	4		45.2.e.b.16.1	✓	6
15.14	odd	2		225.2.k.b.124.6		12
20.3	even	4		2160.2.q.k.721.1		6
45.2	even	12		2025.2.a.n.1.1		3
45.4	even	6	inner	675.2.k.b.199.6		12
45.7	odd	12		2025.2.a.o.1.3		3
45.13	odd	12		135.2.e.b.91.3		6
45.14	odd	6		225.2.k.b.49.1		12
45.22	odd	12		675.2.e.b.226.1		6
45.23	even	12		45.2.e.b.31.1	yes	6
45.29	odd	6		2025.2.b.l.649.1		6
45.32	even	12		225.2.e.b.76.3		6
45.34	even	6		2025.2.b.m.649.6		6
45.38	even	12		405.2.a.j.1.3		3
45.43	odd	12		405.2.a.i.1.1		3
60.23	odd	4		720.2.q.i.241.1		6
180.23	odd	12		720.2.q.i.481.1		6
180.43	even	12		6480.2.a.bs.1.3		3
180.83	odd	12		6480.2.a.bv.1.3		3
180.103	even	12		2160.2.q.k.1441.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.1	✓	6	15.8	even	4
45.2.e.b.31.1	yes	6	45.23	even	12
135.2.e.b.46.3		6	5.3	odd	4
135.2.e.b.91.3		6	45.13	odd	12
225.2.e.b.76.3		6	45.32	even	12
225.2.e.b.151.3		6	15.2	even	4
225.2.k.b.49.1		12	45.14	odd	6
225.2.k.b.49.6		12	9.5	odd	6
225.2.k.b.124.1		12	3.2	odd	2
225.2.k.b.124.6		12	15.14	odd	2
405.2.a.i.1.1		3	45.43	odd	12
405.2.a.j.1.3		3	45.38	even	12
675.2.e.b.226.1		6	45.22	odd	12
675.2.e.b.451.1		6	5.2	odd	4
675.2.k.b.199.1		12	9.4	even	3	inner
675.2.k.b.199.6		12	45.4	even	6	inner
675.2.k.b.424.1		12	5.4	even	2	inner
675.2.k.b.424.6		12	1.1	even	1	trivial
720.2.q.i.241.1		6	60.23	odd	4
720.2.q.i.481.1		6	180.23	odd	12
2025.2.a.n.1.1		3	45.2	even	12
2025.2.a.o.1.3		3	45.7	odd	12
2025.2.b.l.649.1		6	45.29	odd	6
2025.2.b.l.649.6		6	9.2	odd	6
2025.2.b.m.649.1		6	9.7	even	3
2025.2.b.m.649.6		6	45.34	even	6
2160.2.q.k.721.1		6	20.3	even	4
2160.2.q.k.1441.1		6	180.103	even	12
6480.2.a.bs.1.3		3	180.43	even	12
6480.2.a.bv.1.3		3	180.83	odd	12

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.17731 + 1.25707i) q^{2} +(2.16044 + 3.74200i) q^{4} +(0.445256 + 0.257068i) q^{7} +5.83502i q^{8} +O(q^{10})\)	\(q+(2.17731 + 1.25707i) q^{2} +(2.16044 + 3.74200i) q^{4} +(0.445256 + 0.257068i) q^{7} +5.83502i q^{8} +(-1.66044 + 2.87597i) q^{11} +(1.14392 - 0.660442i) q^{13} +(0.646305 + 1.11943i) q^{14} +(-3.01414 + 5.22064i) q^{16} +3.32088i q^{17} +1.32088 q^{19} +(-7.23058 + 4.17458i) q^{22} +(3.57463 - 2.06382i) q^{23} +3.32088 q^{26} +2.22153i q^{28} +(0.693252 - 1.20075i) q^{29} +(-4.36783 - 7.56531i) q^{31} +(-3.01885 + 1.74293i) q^{32} +(-4.17458 + 7.23058i) q^{34} +0.292611i q^{37} +(2.87597 + 1.66044i) q^{38} +(-5.67458 - 9.82866i) q^{41} +(8.96263 + 5.17458i) q^{43} -14.3492 q^{44} +10.3774 q^{46} +(-4.21174 - 2.43165i) q^{47} +(-3.36783 - 5.83326i) q^{49} +(4.94274 + 2.85369i) q^{52} -5.02827i q^{53} +(-1.50000 + 2.59808i) q^{56} +(3.01885 - 1.74293i) q^{58} +(2.51414 + 4.35461i) q^{59} +(-3.67458 + 6.36456i) q^{61} -21.9627i q^{62} +3.29261 q^{64} +(8.18266 - 4.72426i) q^{67} +(-12.4267 + 7.17458i) q^{68} -8.99093 q^{71} -6.05655i q^{73} +(-0.367832 + 0.637103i) q^{74} +(2.85369 + 4.94274i) q^{76} +(-1.47864 + 0.853695i) q^{77} +(-4.02827 + 6.97717i) q^{79} -28.5333i q^{82} +(-1.33577 - 0.771205i) q^{83} +(13.0096 + 22.5333i) q^{86} +(-16.7813 - 9.68872i) q^{88} -3.00000 q^{89} +0.679116 q^{91} +(15.4456 + 8.91751i) q^{92} +(-6.11350 - 10.5889i) q^{94} +(10.6134 + 6.12763i) q^{97} -16.9344i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{4}+O(q^{10}) \) 12 * q + 10 * q^4	\( 12 q + 10 q^{4} - 4 q^{11} + 18 q^{14} - 10 q^{16} - 16 q^{19} + 8 q^{26} + 14 q^{29} - 16 q^{31} - 8 q^{34} - 26 q^{41} - 88 q^{44} - 12 q^{46} - 4 q^{49} - 18 q^{56} + 4 q^{59} - 2 q^{61} + 60 q^{64} + 40 q^{71} + 32 q^{74} + 24 q^{76} + 4 q^{79} + 56 q^{86} - 36 q^{89} + 40 q^{91} - 62 q^{94}+O(q^{100}) \) 12 * q + 10 * q^4 - 4 * q^11 + 18 * q^14 - 10 * q^16 - 16 * q^19 + 8 * q^26 + 14 * q^29 - 16 * q^31 - 8 * q^34 - 26 * q^41 - 88 * q^44 - 12 * q^46 - 4 * q^49 - 18 * q^56 + 4 * q^59 - 2 * q^61 + 60 * q^64 + 40 * q^71 + 32 * q^74 + 24 * q^76 + 4 * q^79 + 56 * q^86 - 36 * q^89 + 40 * q^91 - 62 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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