LMFDB - Embedded newform 675.2.k.b.424.1

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			424.1
Root			$-0.180407 - 0.673288i$ of defining polynomial
Character	$\chi$	$=$	675.424
Dual form			675.2.k.b.199.1

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

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

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	$-0.984816\pi$
$2$	−2.17731	−	1.25707i	−1.53959	−	0.888882i	−0.540726	−	0.841199i	$-0.681850\pi$
$3$		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	0.413489	−	0.910509i	$-0.364310\pi$
$7$	−0.445256	−	0.257068i	−0.168291	−	0.0971627i	−0.581780	+	0.813346i	$0.697643\pi$
$8$		−	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	−0.650173	−	0.759786i	$-0.725304\pi$
$13$	−1.14392	+	0.660442i	−0.317266	+	0.183174i	0.332907	+	0.942960i	$0.391970\pi$
$14$	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	$-0.868066\pi$
$17$		−	3.32088i		−	0.805433i	0.915325	−	0.402716i	$-0.131934\pi$
$18$		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	−0.824016	−	0.566567i	$-0.808271\pi$
$23$	−3.57463	+	2.06382i	−0.745363	+	0.430335i	0.0786532	+	0.996902i	$0.474938\pi$
$24$		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	$-0.992343\pi$
$37$		−	0.292611i		−	0.0481049i	0.999711	−	0.0240524i	$-0.00765687\pi$
$38$	−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	−0.376272	−	0.926509i	$-0.622794\pi$
$43$	−8.96263	−	5.17458i	−1.36679	−	0.789116i	−0.990517	+	0.137393i	$0.956128\pi$
$44$	−14.3492			−2.16322
$45$		0			0
$46$	10.3774			1.53007
$47$	4.21174	+	2.43165i	0.614345	+	0.354692i	0.774664	−	0.632373i	$-0.217919\pi$
$47$	4.21174	+	2.43165i	0.614345	+	0.354692i	−0.160319	+	0.987065i	$0.551252\pi$
$48$		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	$0.112238\pi$
$53$			5.02827i			0.690687i	−0.938476	+	0.345343i	$0.887762\pi$
$54$		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	−0.908151	−	0.418643i	$-0.862506\pi$
$67$	−8.18266	+	4.72426i	−0.999670	+	0.577160i	−0.0915197	+	0.995803i	$0.529172\pi$
$68$	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	$0.115326\pi$
$73$			6.05655i			0.708865i	−0.935082	+	0.354433i	$0.884674\pi$
$74$	−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	0.571515	−	0.820592i	$-0.306356\pi$
$83$	1.33577	+	0.771205i	0.146619	+	0.0846508i	−0.424896	+	0.905242i	$0.639689\pi$
$84$		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	−0.147370	−	0.989081i	$-0.547081\pi$
$97$	−10.6134	−	6.12763i	−1.07762	−	0.622167i	−0.930255	+	0.366915i	$0.880414\pi$
$98$			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	−0.487464	−	0.873143i	$-0.662078\pi$
$103$	0.253408	−	0.146305i	0.0249691	−	0.0144159i	0.512433	+	0.858727i	$0.328744\pi$
$104$	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	$0.0288479\pi$
$107$			1.87237i			0.181009i	−0.995896	+	0.0905043i	$0.971152\pi$
$108$		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	−0.782903	−	0.622144i	$-0.786262\pi$
$113$	−6.75611	+	3.90064i	−0.635561	+	0.366942i	0.147341	+	0.989086i	$0.452928\pi$
$114$		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	$-0.708094\pi$
$127$		−	17.8916i		−	1.58762i	0.608166	−	0.793810i	$-0.291906\pi$
$128$	−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	0.275350	−	0.961344i	$-0.411206\pi$
$137$	−4.91040	−	2.83502i	−0.419524	−	0.242212i	−0.694874	+	0.719132i	$0.744540\pi$
$138$		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	0.151337	−	0.988482i	$-0.451642\pi$
$157$	13.5707	−	7.83502i	1.08306	−	0.625303i	0.931719	+	0.363179i	$0.118309\pi$
$158$	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	$0.210904\pi$
$163$			15.7074i			1.23030i	−0.788411	+	0.615149i	$0.789096\pi$
$164$	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	−0.278994	−	0.960293i	$-0.590001\pi$
$167$	5.33903	−	3.08249i	0.413146	−	0.238530i	0.692141	+	0.721763i	$0.256668\pi$
$168$		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	0.755260	−	0.655426i	$-0.227511\pi$
$173$	7.43502	+	4.29261i	0.565274	+	0.326361i	−0.189986	+	0.981787i	$0.560844\pi$
$174$		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	$-0.255182\pi$
$193$	23.1380	−	13.3588i	1.66551	−	0.961585i	0.970011	−	0.243060i	$-0.0781513\pi$
$194$	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	$-0.830450\pi$
$197$		−	14.2553i		−	1.01565i	0.861462	−	0.507823i	$-0.169550\pi$
$198$		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	0.227252	−	0.973836i	$-0.427026\pi$
$223$	−7.50375	−	4.33229i	−0.502488	−	0.290112i	−0.729740	+	0.683724i	$0.760359\pi$
$224$	−1.79221			−0.119747
$225$		0			0
$226$	19.6135			1.30467
$227$	−2.87597	−	1.66044i	−0.190885	−	0.110207i	0.401512	−	0.915854i	$-0.368485\pi$
$227$	−2.87597	−	1.66044i	−0.190885	−	0.110207i	−0.592397	+	0.805646i	$0.701818\pi$
$228$		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	$-0.639767\pi$
$233$		−	27.6327i		−	1.81028i	0.425116	−	0.905139i	$-0.360233\pi$
$234$		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	−0.899961	−	0.435970i	$-0.856405\pi$
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.0724199	+	0.997374i	$0.523072\pi$
$258$		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	0.657179	−	0.753735i	$-0.271750\pi$
$263$	5.40059	+	3.11803i	0.333015	+	0.192266i	−0.324164	+	0.946001i	$0.605083\pi$
$264$		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	0.955818	−	0.293959i	$-0.0949731\pi$
$277$	19.6250	+	11.3305i	1.17915	+	0.680783i	0.223333	+	0.974742i	$0.428306\pi$
$278$		−	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	−0.483296	−	0.875457i	$-0.660561\pi$
$283$	0.558913	−	0.322689i	0.0332240	−	0.0191819i	0.516520	+	0.856275i	$0.327227\pi$
$284$	−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	−0.464750	−	0.885442i	$-0.653856\pi$
$293$	1.19289	−	0.688716i	0.0696895	−	0.0402352i	0.534440	+	0.845207i	$0.320523\pi$
$294$		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	$0.0731785\pi$
$307$			7.98546i			0.455754i	−0.973690	+	0.227877i	$0.926822\pi$
$308$	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	0.960800	−	0.277244i	$-0.0894209\pi$
$313$	21.2496	+	12.2685i	1.20110	+	0.693455i	0.240300	+	0.970699i	$0.422754\pi$
$314$	−39.3966			−2.22328
$315$		0			0
$316$	−34.8114			−1.95829
$317$	17.6229	+	10.1746i	0.989800	+	0.571461i	0.905215	−	0.424955i	$-0.139710\pi$
$317$	17.6229	+	10.1746i	0.989800	+	0.571461i	0.0845855	+	0.996416i	$0.473043\pi$
$318$		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	−0.611042	−	0.791598i	$-0.709249\pi$
$337$	−4.24096	+	2.44852i	−0.231020	+	0.133379i	0.380023	+	0.924977i	$0.375916\pi$
$338$	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	0.116984	−	0.993134i	$-0.462677\pi$
$347$	19.2903	−	11.1372i	1.03556	−	0.597878i	0.918571	+	0.395256i	$0.129344\pi$
$348$		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	0.866659	−	0.498901i	$-0.166263\pi$
$353$	16.3069	+	9.41478i	0.867927	+	0.501098i	0.00126845	+	0.999999i	$0.499596\pi$
$354$		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	0.0241848	−	0.999708i	$-0.492301\pi$
$367$	−15.8908	−	9.17458i	−0.829495	−	0.478909i	−0.853680	+	0.520798i	$0.825634\pi$
$368$		−	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	−0.548486	−	0.836160i	$-0.684795\pi$
$373$	−1.90414	+	1.09936i	−0.0985929	+	0.0569226i	0.449893	+	0.893083i	$0.351462\pi$
$374$	−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	−0.660743	−	0.750612i	$-0.729759\pi$
$383$	−6.67479	+	3.85369i	−0.341066	+	0.196915i	0.319677	+	0.947526i	$0.396426\pi$
$384$		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	$0.0543651\pi$
$397$			6.77301i			0.339928i	−0.985450	+	0.169964i	$0.945635\pi$
$398$	−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	$-0.908242\pi$
$433$		−	11.8314i		−	0.568581i	0.958738	−	0.284291i	$-0.0917581\pi$
$434$	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	−0.239789	−	0.970825i	$-0.577078\pi$
$443$	−25.2664	−	14.5876i	−1.20044	−	0.693076i	−0.960654	+	0.277750i	$0.910411\pi$
$444$		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	−0.0509206	−	0.998703i	$-0.516216\pi$
$457$	−20.1223	−	11.6176i	−0.941283	−	0.543450i	−0.890362	+	0.455253i	$0.849549\pi$
$458$			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	−0.838262	−	0.545268i	$-0.816428\pi$
$463$	−16.8950	+	9.75434i	−0.785178	+	0.453322i	0.0530845	+	0.998590i	$0.483095\pi$
$464$	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	$-0.807321\pi$
$467$		−	24.5935i		−	1.13805i	0.822320	−	0.569026i	$-0.192679\pi$
$468$		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	$0.0436783\pi$
$487$			6.03735i			0.273578i	−0.990600	+	0.136789i	$0.956322\pi$
$488$	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	$0.0378223\pi$
$503$			5.31728i			0.237086i	−0.992949	+	0.118543i	$0.962178\pi$
$504$		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	$0.136263\pi$
$523$			18.9873i			0.830257i	−0.909763	+	0.415129i	$0.863737\pi$
$524$	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	0.790151	−	0.612912i	$-0.210002\pi$
$547$	15.3058	+	8.83683i	0.654430	+	0.377835i	−0.135721	+	0.990747i	$0.543335\pi$
$548$		−	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	$0.119739\pi$
$557$			17.3401i			0.734723i	−0.930078	+	0.367362i	$0.880261\pi$
$558$		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	−0.718031	−	0.696011i	$-0.754956\pi$
$563$	−11.2536	+	6.49727i	−0.474283	+	0.273827i	0.243748	+	0.969839i	$0.421623\pi$
$564$		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	$0.163421\pi$
$577$			23.5953i			0.982287i	−0.871079	+	0.491144i	$0.836579\pi$
$578$	−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	−0.0955681	−	0.995423i	$-0.530467\pi$
$587$	−24.3592	−	14.0638i	−1.00541	−	0.580476i	−0.909846	+	0.414947i	$0.863800\pi$
$588$		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	$0.0603503\pi$
$593$			9.17872i			0.376925i	−0.982080	+	0.188462i	$0.939650\pi$
$594$		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	$-0.312351\pi$
$607$	38.2813	−	22.1017i	1.55379	−	0.897080i	0.997828	−	0.0658708i	$-0.0209825\pi$
$608$	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	$-0.748568\pi$
$613$		−	35.1715i		−	1.42056i	0.703918	−	0.710282i	$-0.251432\pi$
$614$	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	−0.623831	−	0.781559i	$-0.714425\pi$
$617$	−6.43085	+	3.71285i	−0.258896	+	0.149474i	0.364935	+	0.931033i	$0.381091\pi$
$618$		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	−0.834099	−	0.551614i	$-0.814012\pi$
$643$	−19.6124	+	11.3232i	−0.773437	+	0.446544i	0.0606623	+	0.998158i	$0.480679\pi$
$644$	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	$0.365394\pi$
$647$			46.3912i			1.82383i	−0.410385	+	0.911913i	$0.634606\pi$
$648$		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	−0.967819	−	0.251647i	$-0.919028\pi$
$653$	−31.5283	+	18.2029i	−1.23380	+	0.712333i	−0.265977	+	0.963979i	$0.585695\pi$
$654$		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	0.0502658	−	0.998736i	$-0.483993\pi$
$673$	−20.4822	−	11.8254i	−0.789532	−	0.455836i	−0.839798	+	0.542899i	$0.817326\pi$
$674$	12.3118			0.474233
$675$		0			0
$676$	−48.6327			−1.87049
$677$	12.8199	+	7.40157i	0.492709	+	0.284465i	0.725697	−	0.688014i	$-0.241517\pi$
$677$	12.8199	+	7.40157i	0.492709	+	0.284465i	−0.232989	+	0.972479i	$0.574851\pi$
$678$		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	$0.0302057\pi$
$683$			4.95252i			0.189503i	−0.995501	+	0.0947515i	$0.969794\pi$
$684$		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	0.684985	−	0.728557i	$-0.259809\pi$
$727$	10.6916	+	6.17277i	0.396528	+	0.228936i	−0.288457	+	0.957493i	$0.593142\pi$
$728$		−	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	−0.808732	−	0.588177i	$-0.799846\pi$
$733$	−19.0526	+	11.0000i	−0.703722	+	0.406294i	0.105010	+	0.994471i	$0.466513\pi$
$734$	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	$0.680662\pi$
$743$	−41.8851	+	24.1824i	−1.53662	+	0.887165i	−0.999034	+	0.0439537i	$0.986005\pi$
$744$		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	$-0.971355\pi$
$757$		−	4.94531i		−	0.179740i	0.995953	−	0.0898701i	$-0.0286452\pi$
$758$	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	$-0.926888\pi$
$773$		−	12.6599i		−	0.455345i	0.973738	−	0.227673i	$-0.0731116\pi$
$774$		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	−0.894618	−	0.446832i	$-0.852552\pi$
$787$	−26.7900	+	15.4672i	−0.954959	+	0.551346i	−0.0603410	+	0.998178i	$0.519219\pi$
$788$	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	−0.889487	−	0.456960i	$-0.848938\pi$
$797$	−26.4947	+	15.2967i	−0.938492	+	0.541839i	−0.0490047	+	0.998799i	$0.515605\pi$
$798$		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	−0.454119	−	0.890941i	$-0.650046\pi$
$823$	2.59334	−	1.49727i	0.0903983	−	0.0521915i	0.544518	+	0.838749i	$0.316713\pi$
$824$	−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	$0.187583\pi$
$827$			31.9663i			1.11158i	−0.831324	+	0.555788i	$0.812417\pi$
$828$		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	0.328117	−	0.944637i	$-0.393586\pi$
$853$	−9.51842	−	5.49546i	−0.325905	−	0.188161i	−0.654021	+	0.756476i	$0.726919\pi$
$854$	−9.49960			−0.325070
$855$		0			0
$856$	10.9253			0.373419
$857$	13.9867	+	8.07522i	0.477776	+	0.275844i	0.719489	−	0.694503i	$-0.244376\pi$
$857$	13.9867	+	8.07522i	0.477776	+	0.275844i	−0.241713	+	0.970348i	$0.577709\pi$
$858$		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	$-0.932927\pi$
$863$		−	12.2890i		−	0.418322i	0.977881	−	0.209161i	$-0.0670734\pi$
$864$		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	0.209438	−	0.977822i	$-0.432836\pi$
$877$	34.3814	−	19.8501i	1.16098	−	0.670290i	0.951538	+	0.307532i	$0.0995031\pi$
$878$	−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	$0.0729704\pi$
$883$			13.5051i			0.454482i	−0.973839	+	0.227241i	$0.927030\pi$
$884$	−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	0.106814	−	0.994279i	$-0.465935\pi$
$887$	30.4167	−	17.5611i	1.02129	−	0.589643i	0.914478	+	0.404635i	$0.132602\pi$
$888$		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	0.701367	−	0.712800i	$-0.252573\pi$
$907$	13.0931	+	7.55928i	0.434748	+	0.251002i	−0.266619	+	0.963802i	$0.585907\pi$
$908$		−	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	$-0.702908\pi$
$937$		−	49.1979i		−	1.60723i	0.595152	−	0.803613i	$-0.297092\pi$
$938$	−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	−0.124384	−	0.992234i	$-0.539695\pi$
$947$	−32.1851	−	18.5821i	−1.04588	−	0.603837i	−0.921492	+	0.388397i	$0.873029\pi$
$948$		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	$0.124714\pi$
$953$			23.5761i			0.763706i	−0.924223	+	0.381853i	$0.875286\pi$
$954$		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	−0.612167	−	0.790729i	$-0.709702\pi$
$967$	−7.25980	+	4.19145i	−0.233459	+	0.134788i	0.378708	+	0.925516i	$0.376369\pi$
$968$	−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	−0.685216	−	0.728340i	$-0.740292\pi$
$977$	−12.4110	+	7.16551i	−0.397064	+	0.229245i	0.288153	+	0.957585i	$0.406959\pi$
$978$		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	−0.0176831	−	0.999844i	$-0.505629\pi$
$983$	−27.9797	−	16.1541i	−0.892415	−	0.515236i	−0.874732	+	0.484608i	$0.838962\pi$
$984$		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	0.925734	−	0.378176i	$-0.123449\pi$
$997$	33.5043	+	19.3437i	1.06109	+	0.612621i	0.135357	+	0.990797i	$0.456782\pi$
$998$		−	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.424.1		12
3.2	odd	2		225.2.k.b.124.6		12
5.2	odd	4		135.2.e.b.46.3		6
5.3	odd	4		675.2.e.b.451.1		6
5.4	even	2	inner	675.2.k.b.424.6		12
9.2	odd	6		2025.2.b.l.649.1		6
9.4	even	3	inner	675.2.k.b.199.6		12
9.5	odd	6		225.2.k.b.49.1		12
9.7	even	3		2025.2.b.m.649.6		6
15.2	even	4		45.2.e.b.16.1	✓	6
15.8	even	4		225.2.e.b.151.3		6
15.14	odd	2		225.2.k.b.124.1		12
20.7	even	4		2160.2.q.k.721.1		6
45.2	even	12		405.2.a.j.1.3		3
45.4	even	6	inner	675.2.k.b.199.1		12
45.7	odd	12		405.2.a.i.1.1		3
45.13	odd	12		675.2.e.b.226.1		6
45.14	odd	6		225.2.k.b.49.6		12
45.22	odd	12		135.2.e.b.91.3		6
45.23	even	12		225.2.e.b.76.3		6
45.29	odd	6		2025.2.b.l.649.6		6
45.32	even	12		45.2.e.b.31.1	yes	6
45.34	even	6		2025.2.b.m.649.1		6
45.38	even	12		2025.2.a.n.1.1		3
45.43	odd	12		2025.2.a.o.1.3		3
60.47	odd	4		720.2.q.i.241.1		6
180.7	even	12		6480.2.a.bs.1.3		3
180.47	odd	12		6480.2.a.bv.1.3		3
180.67	even	12		2160.2.q.k.1441.1		6
180.167	odd	12		720.2.q.i.481.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.1	✓	6	15.2	even	4
45.2.e.b.31.1	yes	6	45.32	even	12
135.2.e.b.46.3		6	5.2	odd	4
135.2.e.b.91.3		6	45.22	odd	12
225.2.e.b.76.3		6	45.23	even	12
225.2.e.b.151.3		6	15.8	even	4
225.2.k.b.49.1		12	9.5	odd	6
225.2.k.b.49.6		12	45.14	odd	6
225.2.k.b.124.1		12	15.14	odd	2
225.2.k.b.124.6		12	3.2	odd	2
405.2.a.i.1.1		3	45.7	odd	12
405.2.a.j.1.3		3	45.2	even	12
675.2.e.b.226.1		6	45.13	odd	12
675.2.e.b.451.1		6	5.3	odd	4
675.2.k.b.199.1		12	45.4	even	6	inner
675.2.k.b.199.6		12	9.4	even	3	inner
675.2.k.b.424.1		12	1.1	even	1	trivial
675.2.k.b.424.6		12	5.4	even	2	inner
720.2.q.i.241.1		6	60.47	odd	4
720.2.q.i.481.1		6	180.167	odd	12
2025.2.a.n.1.1		3	45.38	even	12
2025.2.a.o.1.3		3	45.43	odd	12
2025.2.b.l.649.1		6	9.2	odd	6
2025.2.b.l.649.6		6	45.29	odd	6
2025.2.b.m.649.1		6	45.34	even	6
2025.2.b.m.649.6		6	9.7	even	3
2160.2.q.k.721.1		6	20.7	even	4
2160.2.q.k.1441.1		6	180.67	even	12
6480.2.a.bs.1.3		3	180.7	even	12
6480.2.a.bv.1.3		3	180.47	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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