LMFDB - Embedded newform 675.2.k.b.199.1

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			199.1
Root			$-0.180407 + 0.673288i$ of defining polynomial
Character	$\chi$	$=$	675.199
Dual form			675.2.k.b.424.1

$q$-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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−2.17731	+	1.25707i	−1.53959	+	0.888882i	−0.540726	+	0.841199i	$0.681850\pi$
$2$	−2.17731	+	1.25707i	−1.53959	+	0.888882i	−0.998863	+	0.0476826i	$0.984816\pi$
$3$		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	$-0.697643\pi$
$7$	−0.445256	+	0.257068i	−0.168291	+	0.0971627i	0.413489	+	0.910509i	$0.364310\pi$
$8$			5.83502i			2.06299i
$9$		0			0
$10$		0			0
$11$	−1.66044	−	2.87597i	−0.500642	−	0.867138i	−1.00000		0.000741679i	$-0.999764\pi$
$11$	−1.66044	−	2.87597i	−0.500642	−	0.867138i	0.499358	−	0.866396i	$-0.333569\pi$
$12$		0			0
$13$	−1.14392	−	0.660442i	−0.317266	−	0.183174i	0.332907	−	0.942960i	$-0.391970\pi$
$13$	−1.14392	−	0.660442i	−0.317266	−	0.183174i	−0.650173	+	0.759786i	$0.725304\pi$
$14$	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	$-0.474938\pi$
$23$	−3.57463	−	2.06382i	−0.745363	−	0.430335i	−0.824016	+	0.566567i	$0.808271\pi$
$24$		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	0.923186	−	0.384353i	$-0.125575\pi$
$29$	0.693252	+	1.20075i	0.128734	+	0.222973i	−0.794453	+	0.607326i	$0.792242\pi$
$30$		0			0
$31$	−4.36783	+	7.56531i	−0.784486	+	1.35877i	0.144820	+	0.989458i	$0.453740\pi$
$31$	−4.36783	+	7.56531i	−0.784486	+	1.35877i	−0.929306	+	0.369311i	$0.879594\pi$
$32$	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	−0.0419119	+	0.999121i	$0.513345\pi$
$41$	−5.67458	+	9.82866i	−0.886220	+	1.53498i	−0.844308	+	0.535857i	$0.819988\pi$
$42$		0			0
$43$	−8.96263	+	5.17458i	−1.36679	+	0.789116i	−0.990517	−	0.137393i	$-0.956128\pi$
$43$	−8.96263	+	5.17458i	−1.36679	+	0.789116i	−0.376272	+	0.926509i	$0.622794\pi$
$44$	−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	$-0.551252\pi$
$47$	4.21174	−	2.43165i	0.614345	−	0.354692i	0.774664	+	0.632373i	$0.217919\pi$
$48$		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	−0.654665	−	0.755919i	$-0.727190\pi$
$59$	2.51414	−	4.35461i	0.327313	−	0.566922i	0.981978	+	0.188997i	$0.0605236\pi$
$60$		0			0
$61$	−3.67458	−	6.36456i	−0.470482	−	0.814898i	0.528948	−	0.848654i	$-0.322586\pi$
$61$	−3.67458	−	6.36456i	−0.470482	−	0.814898i	−0.999430	+	0.0337558i	$0.989253\pi$
$62$		−	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	$-0.529172\pi$
$67$	−8.18266	−	4.72426i	−0.999670	−	0.577160i	−0.908151	+	0.418643i	$0.862506\pi$
$68$	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	0.545367	−	0.838197i	$-0.316390\pi$
$79$	−4.02827	−	6.97717i	−0.453216	−	0.784994i	−0.998584	+	0.0532036i	$0.983057\pi$
$80$		0			0
$81$		0			0
$82$		−	28.5333i		−	3.15098i
$83$	1.33577	−	0.771205i	0.146619	−	0.0846508i	−0.424896	−	0.905242i	$-0.639689\pi$
$83$	1.33577	−	0.771205i	0.146619	−	0.0846508i	0.571515	+	0.820592i	$0.306356\pi$
$84$		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	$-0.880414\pi$
$97$	−10.6134	+	6.12763i	−1.07762	+	0.622167i	−0.147370	+	0.989081i	$0.547081\pi$
$98$		−	16.9344i		−	1.71063i
$99$		0			0
$100$		0			0
$101$	5.83502	+	10.1066i	0.580606	+	1.00564i	0.995408	+	0.0957276i	$0.0305178\pi$
$101$	5.83502	+	10.1066i	0.580606	+	1.00564i	−0.414801	+	0.909912i	$0.636149\pi$
$102$		0			0
$103$	0.253408	+	0.146305i	0.0249691	+	0.0144159i	0.512433	−	0.858727i	$-0.328744\pi$
$103$	0.253408	+	0.146305i	0.0249691	+	0.0144159i	−0.487464	+	0.873143i	$0.662078\pi$
$104$	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	$-0.452928\pi$
$113$	−6.75611	−	3.90064i	−0.635561	−	0.366942i	−0.782903	+	0.622144i	$0.786262\pi$
$114$		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	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		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	$-0.744540\pi$
$137$	−4.91040	+	2.83502i	−0.419524	+	0.242212i	0.275350	+	0.961344i	$0.411206\pi$
$138$		0			0
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	−0.645021	−	0.764165i	$-0.723151\pi$
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	0.984297	+	0.176522i	$0.0564848\pi$
$140$		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	0.236199	+	0.971705i	$0.424098\pi$
$149$	−8.83049	+	15.2948i	−0.723422	+	1.25300i	−0.959620	+	0.281298i	$0.909235\pi$
$150$		0			0
$151$	−0.632168	−	1.09495i	−0.0514451	−	0.0891056i	0.839156	−	0.543891i	$-0.183049\pi$
$151$	−0.632168	−	1.09495i	−0.0514451	−	0.0891056i	−0.890601	+	0.454785i	$0.849716\pi$
$152$			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	$-0.118309\pi$
$157$	13.5707	+	7.83502i	1.08306	+	0.625303i	0.151337	+	0.988482i	$0.451642\pi$
$158$	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	$-0.256668\pi$
$167$	5.33903	+	3.08249i	0.413146	+	0.238530i	−0.278994	+	0.960293i	$0.590001\pi$
$168$		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	$-0.560844\pi$
$173$	7.43502	−	4.29261i	0.565274	−	0.326361i	0.755260	+	0.655426i	$0.227511\pi$
$174$		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	−0.990789	−	0.135411i	$-0.956764\pi$
$191$	−8.46719	−	14.6656i	−0.612664	−	1.06117i	0.378125	−	0.925754i	$-0.376569\pi$
$192$		0			0
$193$	23.1380	+	13.3588i	1.66551	+	0.961585i	0.970011	+	0.243060i	$0.0781513\pi$
$193$	23.1380	+	13.3588i	1.66551	+	0.961585i	0.695502	+	0.718524i	$0.255182\pi$
$194$	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	−0.758511	−	0.651660i	$-0.774073\pi$
$211$	2.68872	−	4.65699i	0.185099	−	0.320601i	0.943610	+	0.331060i	$0.107406\pi$
$212$	−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	$-0.760359\pi$
$223$	−7.50375	+	4.33229i	−0.502488	+	0.290112i	0.227252	+	0.973836i	$0.427026\pi$
$224$	−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	$-0.701818\pi$
$227$	−2.87597	+	1.66044i	−0.190885	+	0.110207i	0.401512	+	0.915854i	$0.368485\pi$
$228$		0			0
$229$	−12.6559	+	21.9207i	−0.836326	+	1.44856i	0.0566206	+	0.998396i	$0.481967\pi$
$229$	−12.6559	+	21.9207i	−0.836326	+	1.44856i	−0.892946	+	0.450163i	$0.851366\pi$
$230$		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	−0.790105	−	0.612971i	$-0.789974\pi$
$239$	2.09936	−	3.63620i	0.135796	−	0.235206i	0.925901	+	0.377765i	$0.123307\pi$
$240$		0			0
$241$	−1.80221	−	3.12152i	−0.116091	−	0.201075i	0.802125	−	0.597157i	$-0.203703\pi$
$241$	−1.80221	−	3.12152i	−0.116091	−	0.201075i	−0.918215	+	0.396082i	$0.870370\pi$
$242$		−	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	$-0.523072\pi$
$257$	−15.5885	−	9.00000i	−0.972381	−	0.561405i	−0.899961	+	0.435970i	$0.856405\pi$
$258$		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	$-0.605083\pi$
$263$	5.40059	−	3.11803i	0.333015	−	0.192266i	0.657179	+	0.753735i	$0.271750\pi$
$264$		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	$-0.428306\pi$
$277$	19.6250	−	11.3305i	1.17915	−	0.680783i	0.955818	+	0.293959i	$0.0949731\pi$
$278$			20.1131i			1.20630i
$279$		0			0
$280$		0			0
$281$	−7.77394	−	13.4649i	−0.463754	−	0.803246i	0.535390	−	0.844605i	$-0.320165\pi$
$281$	−7.77394	−	13.4649i	−0.463754	−	0.803246i	−0.999144	+	0.0413590i	$0.986831\pi$
$282$		0			0
$283$	0.558913	+	0.322689i	0.0332240	+	0.0191819i	0.516520	−	0.856275i	$-0.327227\pi$
$283$	0.558913	+	0.322689i	0.0332240	+	0.0191819i	−0.483296	+	0.875457i	$0.660561\pi$
$284$	−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	$-0.320523\pi$
$293$	1.19289	+	0.688716i	0.0696895	+	0.0402352i	−0.464750	+	0.885442i	$0.653856\pi$
$294$		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	−0.696547	−	0.717512i	$-0.745281\pi$
$311$	4.81635	−	8.34216i	0.273110	−	0.473040i	0.969657	+	0.244471i	$0.0786143\pi$
$312$		0			0
$313$	21.2496	−	12.2685i	1.20110	−	0.693455i	0.240300	−	0.970699i	$-0.422754\pi$
$313$	21.2496	−	12.2685i	1.20110	−	0.693455i	0.960800	+	0.277244i	$0.0894209\pi$
$314$	−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	$-0.473043\pi$
$317$	17.6229	−	10.1746i	0.989800	−	0.571461i	0.905215	+	0.424955i	$0.139710\pi$
$318$		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	0.546608	−	0.837389i	$-0.315919\pi$
$331$	−8.22153	−	14.2401i	−0.451896	−	0.782707i	−0.998504	+	0.0546819i	$0.982586\pi$
$332$		−	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	$-0.375916\pi$
$337$	−4.24096	−	2.44852i	−0.231020	−	0.133379i	−0.611042	+	0.791598i	$0.709249\pi$
$338$	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	$-0.129344\pi$
$347$	19.2903	+	11.1372i	1.03556	+	0.597878i	0.116984	+	0.993134i	$0.462677\pi$
$348$		0			0
$349$	−1.47173	−	2.54910i	−0.0787797	−	0.136450i	0.823944	−	0.566671i	$-0.191769\pi$
$349$	−1.47173	−	2.54910i	−0.0787797	−	0.136450i	−0.902724	+	0.430221i	$0.858436\pi$
$350$		0			0
$351$		0			0
$352$		−	11.5761i		−	0.617011i
$353$	16.3069	−	9.41478i	0.867927	−	0.501098i	0.00126845	−	0.999999i	$-0.499596\pi$
$353$	16.3069	−	9.41478i	0.867927	−	0.501098i	0.866659	+	0.498901i	$0.166263\pi$
$354$		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	$-0.825634\pi$
$367$	−15.8908	+	9.17458i	−0.829495	+	0.478909i	0.0241848	+	0.999708i	$0.492301\pi$
$368$			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	$-0.351462\pi$
$373$	−1.90414	−	1.09936i	−0.0985929	−	0.0569226i	−0.548486	+	0.836160i	$0.684795\pi$
$374$	−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	$-0.396426\pi$
$383$	−6.67479	−	3.85369i	−0.341066	−	0.196915i	−0.660743	+	0.750612i	$0.729759\pi$
$384$		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	0.988644	+	0.150274i	$0.0480157\pi$
$389$	12.3163	+	21.3325i	0.624464	+	1.08160i	−0.364181	+	0.931328i	$0.618651\pi$
$390$		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	−0.999056	−	0.0434343i	$-0.986170\pi$
$401$	−9.24980	+	16.0211i	−0.461913	+	0.800057i	0.537143	+	0.843491i	$0.319503\pi$
$402$		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	−0.982837	−	0.184474i	$-0.940942\pi$
$409$	−6.70739	+	11.6175i	−0.331659	+	0.574450i	0.651178	+	0.758925i	$0.274275\pi$
$410$		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	−0.104751	−	0.994499i	$-0.533404\pi$
$419$	16.5575	−	28.6784i	0.808886	−	1.40103i	0.913636	−	0.406532i	$-0.133262\pi$
$420$		0			0
$421$	7.34916	+	12.7291i	0.358176	+	0.620379i	0.987656	−	0.156637i	$-0.0500654\pi$
$421$	7.34916	+	12.7291i	0.358176	+	0.620379i	−0.629480	+	0.777017i	$0.716732\pi$
$422$			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	0.947994	−	0.318289i	$-0.103108\pi$
$439$	4.15591	+	7.19824i	0.198351	+	0.343553i	−0.749643	+	0.661842i	$0.769775\pi$
$440$		0			0
$441$		0			0
$442$			11.0283i			0.524561i
$443$	−25.2664	+	14.5876i	−1.20044	+	0.693076i	−0.960654	−	0.277750i	$-0.910411\pi$
$443$	−25.2664	+	14.5876i	−1.20044	+	0.693076i	−0.239789	+	0.970825i	$0.577078\pi$
$444$		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	$-0.849549\pi$
$457$	−20.1223	+	11.6176i	−0.941283	+	0.543450i	−0.0509206	+	0.998703i	$0.516216\pi$
$458$		−	63.6374i		−	2.97358i
$459$		0			0
$460$		0			0
$461$	2.21285	+	3.83277i	0.103063	+	0.178510i	0.912945	−	0.408082i	$-0.133802\pi$
$461$	2.21285	+	3.83277i	0.103063	+	0.178510i	−0.809882	+	0.586592i	$0.800469\pi$
$462$		0			0
$463$	−16.8950	−	9.75434i	−0.785178	−	0.453322i	0.0530845	−	0.998590i	$-0.483095\pi$
$463$	−16.8950	−	9.75434i	−0.785178	−	0.453322i	−0.838262	+	0.545268i	$0.816428\pi$
$464$	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	−0.948635	−	0.316372i	$-0.897535\pi$
$479$	−16.3774	−	28.3665i	−0.748304	−	1.29610i	0.200331	−	0.979728i	$-0.435798\pi$
$480$		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	−0.655792	−	0.754942i	$-0.727665\pi$
$491$	7.22153	−	12.5081i	0.325903	−	0.564480i	0.981695	+	0.190461i	$0.0609984\pi$
$492$		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	−0.529977	−	0.848012i	$-0.677799\pi$
$499$	10.4859	−	18.1620i	0.469412	−	0.813045i	0.999388	+	0.0349673i	$0.0111327\pi$
$500$		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	−0.994198	−	0.107561i	$-0.965696\pi$
$509$	−9.11350	+	15.7850i	−0.403949	+	0.699659i	0.590250	+	0.807221i	$0.299029\pi$
$510$		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	$-0.543335\pi$
$547$	15.3058	−	8.83683i	0.654430	−	0.377835i	0.790151	+	0.612912i	$0.210002\pi$
$548$			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	$-0.421623\pi$
$563$	−11.2536	−	6.49727i	−0.474283	−	0.273827i	−0.718031	+	0.696011i	$0.754956\pi$
$564$		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	0.986184	−	0.165651i	$-0.0529724\pi$
$569$	8.34009	+	14.4455i	0.349635	+	0.605585i	−0.636550	+	0.771236i	$0.719639\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	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	$-0.863800\pi$
$587$	−24.3592	+	14.0638i	−1.00541	+	0.580476i	−0.0955681	+	0.995423i	$0.530467\pi$
$588$		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	−0.341831	−	0.939761i	$-0.611047\pi$
$599$	15.7357	−	27.2550i	0.642942	−	1.11361i	0.984773	−	0.173846i	$-0.0556196\pi$
$600$		0			0
$601$	14.6327	+	25.3446i	0.596880	+	1.03383i	0.993279	+	0.115748i	$0.0369265\pi$
$601$	14.6327	+	25.3446i	0.596880	+	1.03383i	−0.396398	+	0.918079i	$0.629740\pi$
$602$			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	0.997828	+	0.0658708i	$0.0209825\pi$
$607$	38.2813	+	22.1017i	1.55379	+	0.897080i	0.555960	+	0.831209i	$0.312351\pi$
$608$	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	$-0.381091\pi$
$617$	−6.43085	−	3.71285i	−0.258896	−	0.149474i	−0.623831	+	0.781559i	$0.714425\pi$
$618$		0			0
$619$	4.27394	+	7.40268i	0.171784	+	0.297539i	0.939044	−	0.343798i	$-0.111714\pi$
$619$	4.27394	+	7.40268i	0.171784	+	0.297539i	−0.767260	+	0.641337i	$0.778380\pi$
$620$		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	0.864708	−	0.502275i	$-0.167503\pi$
$641$	−0.0665480	−	0.115265i	−0.00262849	−	0.00455268i	−0.867337	+	0.497722i	$0.834170\pi$
$642$		0			0
$643$	−19.6124	−	11.3232i	−0.773437	−	0.446544i	0.0606623	−	0.998158i	$-0.480679\pi$
$643$	−19.6124	−	11.3232i	−0.773437	−	0.446544i	−0.834099	+	0.551614i	$0.814012\pi$
$644$	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	$-0.585695\pi$
$653$	−31.5283	−	18.2029i	−1.23380	−	0.712333i	−0.967819	+	0.251647i	$0.919028\pi$
$654$		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	0.617177	−	0.786824i	$-0.288276\pi$
$659$	−9.57068	−	16.5769i	−0.372821	−	0.645745i	−0.989998	+	0.141079i	$0.954943\pi$
$660$		0			0
$661$	−19.9536	+	34.5606i	−0.776104	+	1.34425i	0.158067	+	0.987428i	$0.449474\pi$
$661$	−19.9536	+	34.5606i	−0.776104	+	1.34425i	−0.934172	+	0.356824i	$0.883860\pi$
$662$	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	$-0.817326\pi$
$673$	−20.4822	+	11.8254i	−0.789532	+	0.455836i	0.0502658	+	0.998736i	$0.483993\pi$
$674$	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	$-0.574851\pi$
$677$	12.8199	−	7.40157i	0.492709	−	0.284465i	0.725697	+	0.688014i	$0.241517\pi$
$678$		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	0.988835	−	0.149012i	$-0.0476093\pi$
$691$	9.60442	+	16.6353i	0.365369	+	0.632838i	−0.623466	+	0.781851i	$0.714276\pi$
$692$		−	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	0.958060	+	0.286566i	$0.0925138\pi$
$709$	19.3633	+	33.5382i	0.727204	+	1.25955i	−0.230857	+	0.972988i	$0.574153\pi$
$710$		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	$-0.593142\pi$
$727$	10.6916	−	6.17277i	0.396528	−	0.228936i	0.684985	+	0.728557i	$0.259809\pi$
$728$			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	$-0.466513\pi$
$733$	−19.0526	−	11.0000i	−0.703722	−	0.406294i	−0.808732	+	0.588177i	$0.799846\pi$
$734$	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	−0.999034	−	0.0439537i	$-0.986005\pi$
$743$	−41.8851	−	24.1824i	−1.53662	−	0.887165i	−0.537582	−	0.843212i	$-0.680662\pi$
$744$		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	−0.414838	−	0.909895i	$-0.636162\pi$
$751$	15.9102	−	27.5573i	0.580573	−	1.00558i	0.995411	−	0.0956869i	$-0.0305047\pi$
$752$	−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	−0.342893	−	0.939375i	$-0.611407\pi$
$761$	17.7125	−	30.6789i	0.642076	−	1.11211i	0.984969	−	0.172734i	$-0.0552600\pi$
$762$		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	0.0526602	−	0.998612i	$-0.483230\pi$
$769$	24.7125	−	42.8032i	0.891154	−	1.54352i	0.838494	−	0.544911i	$-0.183437\pi$
$770$		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	$-0.519219\pi$
$787$	−26.7900	−	15.4672i	−0.954959	−	0.551346i	−0.894618	+	0.446832i	$0.852552\pi$
$788$	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	$-0.515605\pi$
$797$	−26.4947	−	15.2967i	−0.938492	−	0.541839i	−0.889487	+	0.456960i	$0.848938\pi$
$798$		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	0.777290	−	0.629143i	$-0.216594\pi$
$821$	−4.47586	−	7.75242i	−0.156209	−	0.270561i	−0.933498	+	0.358581i	$0.883261\pi$
$822$		0			0
$823$	2.59334	+	1.49727i	0.0903983	+	0.0521915i	0.544518	−	0.838749i	$-0.316713\pi$
$823$	2.59334	+	1.49727i	0.0903983	+	0.0521915i	−0.454119	+	0.890941i	$0.650046\pi$
$824$	−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	0.993918	−	0.110126i	$-0.0351254\pi$
$839$	11.6322	+	20.1475i	0.401587	+	0.695569i	−0.592331	+	0.805695i	$0.701792\pi$
$840$		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	$-0.726919\pi$
$853$	−9.51842	+	5.49546i	−0.325905	+	0.188161i	0.328117	+	0.944637i	$0.393586\pi$
$854$	−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	$-0.577709\pi$
$857$	13.9867	−	8.07522i	0.477776	−	0.275844i	0.719489	+	0.694503i	$0.244376\pi$
$858$		0			0
$859$	14.2594	−	24.6980i	0.486524	−	0.842685i	−0.513356	−	0.858176i	$-0.671598\pi$
$859$	14.2594	−	24.6980i	0.486524	−	0.842685i	0.999880	+	0.0154909i	$0.00493111\pi$
$860$		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	$-0.0995031\pi$
$877$	34.3814	+	19.8501i	1.16098	+	0.670290i	0.209438	+	0.977822i	$0.432836\pi$
$878$	−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	$-0.132602\pi$
$887$	30.4167	+	17.5611i	1.02129	+	0.589643i	0.106814	+	0.994279i	$0.465935\pi$
$888$		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	$-0.585907\pi$
$907$	13.0931	−	7.55928i	0.434748	−	0.251002i	0.701367	+	0.712800i	$0.252573\pi$
$908$			14.3492i			0.476194i
$909$		0			0
$910$		0			0
$911$	26.2781	+	45.5150i	0.870631	+	1.50798i	0.861345	+	0.508021i	$0.169623\pi$
$911$	26.2781	+	45.5150i	0.870631	+	1.50798i	0.00928675	+	0.999957i	$0.497044\pi$
$912$		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	0.649041	−	0.760753i	$-0.275170\pi$
$929$	−10.1896	−	17.6490i	−0.334311	−	0.579044i	−0.983352	+	0.181709i	$0.941837\pi$
$930$		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	−0.990881	−	0.134738i	$-0.956981\pi$
$941$	−11.6186	+	20.1239i	−0.378754	+	0.656022i	0.612127	+	0.790759i	$0.290314\pi$
$942$		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	$-0.873029\pi$
$947$	−32.1851	+	18.5821i	−1.04588	+	0.603837i	−0.124384	+	0.992234i	$0.539695\pi$
$948$		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	$-0.376369\pi$
$967$	−7.25980	−	4.19145i	−0.233459	−	0.134788i	−0.612167	+	0.790729i	$0.709702\pi$
$968$	−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	$-0.406959\pi$
$977$	−12.4110	−	7.16551i	−0.397064	−	0.229245i	−0.685216	+	0.728340i	$0.740292\pi$
$978$		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	$-0.838962\pi$
$983$	−27.9797	+	16.1541i	−0.892415	+	0.515236i	−0.0176831	+	0.999844i	$0.505629\pi$
$984$		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	$-0.456782\pi$
$997$	33.5043	−	19.3437i	1.06109	−	0.612621i	0.925734	+	0.378176i	$0.123449\pi$
$998$			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.199.1		12
3.2	odd	2		225.2.k.b.49.6		12
5.2	odd	4		675.2.e.b.226.1		6
5.3	odd	4		135.2.e.b.91.3		6
5.4	even	2	inner	675.2.k.b.199.6		12
9.2	odd	6		225.2.k.b.124.1		12
9.4	even	3		2025.2.b.m.649.1		6
9.5	odd	6		2025.2.b.l.649.6		6
9.7	even	3	inner	675.2.k.b.424.6		12
15.2	even	4		225.2.e.b.76.3		6
15.8	even	4		45.2.e.b.31.1	yes	6
15.14	odd	2		225.2.k.b.49.1		12
20.3	even	4		2160.2.q.k.1441.1		6
45.2	even	12		225.2.e.b.151.3		6
45.4	even	6		2025.2.b.m.649.6		6
45.7	odd	12		675.2.e.b.451.1		6
45.13	odd	12		405.2.a.i.1.1		3
45.14	odd	6		2025.2.b.l.649.1		6
45.22	odd	12		2025.2.a.o.1.3		3
45.23	even	12		405.2.a.j.1.3		3
45.29	odd	6		225.2.k.b.124.6		12
45.32	even	12		2025.2.a.n.1.1		3
45.34	even	6	inner	675.2.k.b.424.1		12
45.38	even	12		45.2.e.b.16.1	✓	6
45.43	odd	12		135.2.e.b.46.3		6
60.23	odd	4		720.2.q.i.481.1		6
180.23	odd	12		6480.2.a.bv.1.3		3
180.43	even	12		2160.2.q.k.721.1		6
180.83	odd	12		720.2.q.i.241.1		6
180.103	even	12		6480.2.a.bs.1.3		3

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

Fields

Representations

Groups

Database

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