LMFDB - Embedded newform 444.2.w.c.125.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [444,2,Mod(29,444)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("444.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(444, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 444 = 2^{2} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	444.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.54535784974$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.7
Character	$\chi$	$=$	444.125
Dual form			444.2.w.c.341.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10038 - 1.33759i) q^{3} +(-0.662862 + 2.47384i) q^{5} +(1.02662 + 1.77815i) q^{7} +(-0.578306 - 2.94373i) q^{9} +2.87686 q^{11} +(3.09226 + 0.828569i) q^{13} +(2.57958 + 3.60881i) q^{15} +(-1.46072 + 0.391399i) q^{17} +(-0.779971 - 0.208993i) q^{19} +(3.50811 + 0.583457i) q^{21} +(5.03244 + 5.03244i) q^{23} +(-1.35035 - 0.779626i) q^{25} +(-4.57387 - 2.46570i) q^{27} +(2.13411 - 2.13411i) q^{29} +(0.584817 + 0.584817i) q^{31} +(3.16566 - 3.84807i) q^{33} +(-5.07936 + 1.36101i) q^{35} +(-2.93536 - 5.32763i) q^{37} +(4.51097 - 3.22444i) q^{39} +(-4.03149 - 6.98275i) q^{41} +(-4.93052 + 4.93052i) q^{43} +(7.66565 + 0.520655i) q^{45} -10.0236i q^{47} +(1.39212 - 2.41122i) q^{49} +(-1.08382 + 2.38454i) q^{51} +(0.0121765 + 0.00703009i) q^{53} +(-1.90696 + 7.11689i) q^{55} +(-1.13782 + 0.813311i) q^{57} +(3.81761 - 1.02293i) q^{59} +(-0.418368 + 1.56137i) q^{61} +(4.64070 - 4.05040i) q^{63} +(-4.09949 + 7.10052i) q^{65} +(-12.3056 + 7.10465i) q^{67} +(12.2690 - 1.19373i) q^{69} +(-13.4744 + 7.77944i) q^{71} +9.50559i q^{73} +(-2.52873 + 0.948331i) q^{75} +(2.95343 + 5.11550i) q^{77} +(-5.78976 - 1.55136i) q^{79} +(-8.33112 + 3.40476i) q^{81} +(-5.18141 - 2.99149i) q^{83} -3.87303i q^{85} +(-0.506226 - 5.20291i) q^{87} +(0.0713475 + 0.266272i) q^{89} +(1.70124 + 6.34913i) q^{91} +(1.42577 - 0.138723i) q^{93} +(1.03403 - 1.79099i) q^{95} +(1.33676 - 1.33676i) q^{97} +(-1.66371 - 8.46872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 10 q^{9} - 24 q^{19} - 18 q^{21} + 32 q^{31} - 44 q^{37} + 62 q^{39} - 4 q^{43} - 54 q^{45} + 24 q^{49} + 14 q^{51} + 20 q^{55} + 34 q^{57} + 36 q^{61} - 36 q^{63} + 12 q^{67} - 50 q^{69} - 20 q^{75}+ \cdots - 12 q^{99}+O(q^{100}) $ 40 * q - 10 * q^9 - 24 * q^19 - 18 * q^21 + 32 * q^31 - 44 * q^37 + 62 * q^39 - 4 * q^43 - 54 * q^45 + 24 * q^49 + 14 * q^51 + 20 * q^55 + 34 * q^57 + 36 * q^61 - 36 * q^63 + 12 * q^67 - 50 * q^69 - 20 * q^75 + 8 * q^79 + 10 * q^81 - 32 * q^87 + 20 * q^91 - 30 * q^93 + 52 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/444\mathbb{Z}\right)^\times$.

$n$	$149$	$223$	$409$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.10038	−	1.33759i	0.635308	−	0.772259i
$3$	1.10038	−	1.33759i	0.635308	−	0.772259i
$4$		0			0
$5$	−0.662862	+	2.47384i	−0.296441	+	1.10633i	0.643625	+	0.765341i	$0.277430\pi$
$5$	−0.662862	+	2.47384i	−0.296441	+	1.10633i	−0.940066	+	0.340992i	$0.889237\pi$
$6$		0			0
$7$	1.02662	+	1.77815i	0.388024	+	0.672078i	0.992184	−	0.124786i	$-0.0398244\pi$
$7$	1.02662	+	1.77815i	0.388024	+	0.672078i	−0.604159	+	0.796863i	$0.706491\pi$
$8$		0			0
$9$	−0.578306	−	2.94373i	−0.192769	−	0.981244i
$10$		0			0
$11$	2.87686			0.867407			0.433703	−	0.901056i	$-0.357207\pi$
$11$	2.87686			0.867407			0.433703	+	0.901056i	$0.357207\pi$
$12$		0			0
$13$	3.09226	+	0.828569i	0.857639	+	0.229804i	0.660735	−	0.750619i	$-0.270245\pi$
$13$	3.09226	+	0.828569i	0.857639	+	0.229804i	0.196904	+	0.980423i	$0.436911\pi$
$14$		0			0
$15$	2.57958	+	3.60881i	0.666045	+	0.931791i
$16$		0			0
$17$	−1.46072	+	0.391399i	−0.354277	+	0.0949283i	−0.431568	−	0.902080i	$-0.642040\pi$
$17$	−1.46072	+	0.391399i	−0.354277	+	0.0949283i	0.0772910	+	0.997009i	$0.475373\pi$
$18$		0			0
$19$	−0.779971	−	0.208993i	−0.178938	−	0.0479462i	0.168238	−	0.985746i	$-0.446192\pi$
$19$	−0.779971	−	0.208993i	−0.178938	−	0.0479462i	−0.347175	+	0.937800i	$0.612859\pi$
$20$		0			0
$21$	3.50811	+	0.583457i	0.765533	+	0.127321i
$22$		0			0
$23$	5.03244	+	5.03244i	1.04934	+	1.04934i	0.998718	+	0.0506173i	$0.0161189\pi$
$23$	5.03244	+	5.03244i	1.04934	+	1.04934i	0.0506173	+	0.998718i	$0.483881\pi$
$24$		0			0
$25$	−1.35035	−	0.779626i	−0.270070	−	0.155925i
$26$		0			0
$27$	−4.57387	−	2.46570i	−0.880242	−	0.474524i
$28$		0			0
$29$	2.13411	−	2.13411i	0.396294	−	0.396294i	−0.480630	−	0.876924i	$-0.659592\pi$
$29$	2.13411	−	2.13411i	0.396294	−	0.396294i	0.876924	+	0.480630i	$0.159592\pi$
$30$		0			0
$31$	0.584817	+	0.584817i	0.105036	+	0.105036i	0.757672	−	0.652636i	$-0.226337\pi$
$31$	0.584817	+	0.584817i	0.105036	+	0.105036i	−0.652636	+	0.757672i	$0.726337\pi$
$32$		0			0
$33$	3.16566	−	3.84807i	0.551070	−	0.669863i
$34$		0			0
$35$	−5.07936	+	1.36101i	−0.858568	+	0.230053i
$36$		0			0
$37$	−2.93536	−	5.32763i	−0.482571	−	0.875857i
$37$	−2.93536	−	5.32763i	−0.482571	−	0.875857i
$38$		0			0
$39$	4.51097	−	3.22444i	0.722333	−	0.516324i
$40$		0			0
$41$	−4.03149	−	6.98275i	−0.629613	−	1.09052i	−0.987629	−	0.156806i	$-0.949880\pi$
$41$	−4.03149	−	6.98275i	−0.629613	−	1.09052i	0.358016	−	0.933715i	$-0.383453\pi$
$42$		0			0
$43$	−4.93052	+	4.93052i	−0.751897	+	0.751897i	−0.974833	−	0.222936i	$-0.928436\pi$
$43$	−4.93052	+	4.93052i	−0.751897	+	0.751897i	0.222936	+	0.974833i	$0.428436\pi$
$44$		0			0
$45$	7.66565	+	0.520655i	1.14273	+	0.0776147i
$46$		0			0
$47$		−	10.0236i		−	1.46209i	−0.682330	−	0.731045i	$-0.739033\pi$
$47$		−	10.0236i		−	1.46209i	0.682330	−	0.731045i	$-0.260967\pi$
$48$		0			0
$49$	1.39212	−	2.41122i	0.198874	−	0.344461i
$50$		0			0
$51$	−1.08382	+	2.38454i	−0.151766	+	0.333903i
$52$		0			0
$53$	0.0121765	+	0.00703009i	0.00167257	+	0.000965658i	0.500836	−	0.865542i	$-0.333026\pi$
$53$	0.0121765	+	0.00703009i	0.00167257	+	0.000965658i	−0.499163	+	0.866508i	$0.666359\pi$
$54$		0			0
$55$	−1.90696	+	7.11689i	−0.257135	+	0.959641i
$56$		0			0
$57$	−1.13782	+	0.813311i	−0.150707	+	0.107726i
$58$		0			0
$59$	3.81761	−	1.02293i	0.497011	−	0.133174i	−0.00160139	−	0.999999i	$-0.500510\pi$
$59$	3.81761	−	1.02293i	0.497011	−	0.133174i	0.498613	+	0.866825i	$0.333843\pi$
$60$		0			0
$61$	−0.418368	+	1.56137i	−0.0535665	+	0.199913i	−0.987523	−	0.157473i	$-0.949665\pi$
$61$	−0.418368	+	1.56137i	−0.0535665	+	0.199913i	0.933957	+	0.357386i	$0.116332\pi$
$62$		0			0
$63$	4.64070	−	4.05040i	0.584673	−	0.510302i
$64$		0			0
$65$	−4.09949	+	7.10052i	−0.508479	+	0.880711i
$66$		0			0
$67$	−12.3056	+	7.10465i	−1.50337	+	0.867971i	−0.503377	+	0.864067i	$0.667909\pi$
$67$	−12.3056	+	7.10465i	−1.50337	+	0.867971i	−0.999992	+	0.00390432i	$0.998757\pi$
$68$		0			0
$69$	12.2690	−	1.19373i	1.47701	−	0.143708i
$70$		0			0
$71$	−13.4744	+	7.77944i	−1.59912	+	0.923250i	−0.607457	+	0.794352i	$0.707810\pi$
$71$	−13.4744	+	7.77944i	−1.59912	+	0.923250i	−0.991658	+	0.128897i	$0.958856\pi$
$72$		0			0
$73$			9.50559i			1.11255i	0.831000	+	0.556273i	$0.187769\pi$
$73$			9.50559i			1.11255i	−0.831000	+	0.556273i	$0.812231\pi$
$74$		0			0
$75$	−2.52873	+	0.948331i	−0.291992	+	0.109504i
$76$		0			0
$77$	2.95343	+	5.11550i	0.336575	+	0.582965i
$78$		0			0
$79$	−5.78976	−	1.55136i	−0.651399	−	0.174542i	−0.0820376	−	0.996629i	$-0.526143\pi$
$79$	−5.78976	−	1.55136i	−0.651399	−	0.174542i	−0.569361	+	0.822087i	$0.692809\pi$
$80$		0			0
$81$	−8.33112	+	3.40476i	−0.925680	+	0.378306i
$82$		0			0
$83$	−5.18141	−	2.99149i	−0.568734	−	0.328359i	0.187910	−	0.982186i	$-0.439829\pi$
$83$	−5.18141	−	2.99149i	−0.568734	−	0.328359i	−0.756643	+	0.653828i	$0.773162\pi$
$84$		0			0
$85$		−	3.87303i		−	0.420089i
$86$		0			0
$87$	−0.506226	−	5.20291i	−0.0542731	−	0.557810i
$88$		0			0
$89$	0.0713475	+	0.266272i	0.00756282	+	0.0282248i	0.969604	−	0.244679i	$-0.0786826\pi$
$89$	0.0713475	+	0.266272i	0.00756282	+	0.0282248i	−0.962041	+	0.272904i	$0.912016\pi$
$90$		0			0
$91$	1.70124	+	6.34913i	0.178339	+	0.665569i
$92$		0			0
$93$	1.42577	−	0.138723i	0.147845	−	0.0143849i
$94$		0			0
$95$	1.03403	−	1.79099i	0.106089	−	0.183751i
$96$		0			0
$97$	1.33676	−	1.33676i	0.135728	−	0.135728i	−0.635979	−	0.771707i	$-0.719403\pi$
$97$	1.33676	−	1.33676i	0.135728	−	0.135728i	0.771707	+	0.635979i	$0.219403\pi$
$98$		0			0
$99$	−1.66371	−	8.46872i	−0.167209	−	0.851138i
$100$		0			0
$101$	16.7021			1.66192			0.830961	−	0.556331i	$-0.187791\pi$
$101$	16.7021			1.66192			0.830961	+	0.556331i	$0.187791\pi$
$102$		0			0
$103$	−4.70047	−	4.70047i	−0.463151	−	0.463151i	0.436536	−	0.899687i	$-0.356205\pi$
$103$	−4.70047	−	4.70047i	−0.463151	−	0.463151i	−0.899687	+	0.436536i	$0.856205\pi$
$104$		0			0
$105$	−3.76877	+	8.29174i	−0.367794	+	0.809191i
$106$		0			0
$107$	12.7883	−	7.38335i	1.23630	−	0.713776i	0.267961	−	0.963430i	$-0.413650\pi$
$107$	12.7883	−	7.38335i	1.23630	−	0.713776i	0.968335	+	0.249654i	$0.0803169\pi$
$108$		0			0
$109$	−1.88602	−	7.03873i	−0.180648	−	0.674188i	−0.995520	−	0.0945475i	$-0.969860\pi$
$109$	−1.88602	−	7.03873i	−0.180648	−	0.674188i	0.814872	−	0.579641i	$-0.196807\pi$
$110$		0			0
$111$	−10.3562	−	1.93613i	−0.982969	−	0.183769i
$112$		0			0
$113$	−0.760983	−	2.84003i	−0.0715872	−	0.267167i	0.920851	−	0.389916i	$-0.127496\pi$
$113$	−0.760983	−	2.84003i	−0.0715872	−	0.267167i	−0.992438	+	0.122748i	$0.960829\pi$
$114$		0			0
$115$	−15.7852	+	9.11361i	−1.47198	+	0.849848i
$116$		0			0
$117$	0.650812	−	9.58196i	0.0601676	−	0.885852i
$118$		0			0
$119$	−2.19557	−	2.19557i	−0.201267	−	0.201267i
$120$		0			0
$121$	−2.72366			−0.247605
$122$		0			0
$123$	−13.7763	−	2.29122i	−1.24216	−	0.206592i
$124$		0			0
$125$	−6.23110	+	6.23110i	−0.557327	+	0.557327i
$126$		0			0
$127$	−6.27676	+	10.8717i	−0.556972	+	0.964705i	0.440775	+	0.897618i	$0.354704\pi$
$127$	−6.27676	+	10.8717i	−0.556972	+	0.964705i	−0.997747	+	0.0670868i	$0.978630\pi$
$128$		0			0
$129$	1.16956	+	12.0205i	0.102974	+	1.05835i
$130$		0			0
$131$	−5.31985	−	19.8539i	−0.464797	−	1.73465i	−0.657561	−	0.753402i	$-0.728412\pi$
$131$	−5.31985	−	19.8539i	−0.464797	−	1.73465i	0.192764	−	0.981245i	$-0.438255\pi$
$132$		0			0
$133$	−0.429110	−	1.60146i	−0.0372086	−	0.138864i
$134$		0			0
$135$	9.13159	−	9.68059i	0.785922	−	0.833173i
$136$		0			0
$137$		−	11.2283i		−	0.959301i	−0.877460	−	0.479650i	$-0.840764\pi$
$137$		−	11.2283i		−	0.959301i	0.877460	−	0.479650i	$-0.159236\pi$
$138$		0			0
$139$	−1.30956	−	0.756076i	−0.111076	−	0.0641295i	0.443433	−	0.896308i	$-0.353760\pi$
$139$	−1.30956	−	0.756076i	−0.111076	−	0.0641295i	−0.554509	+	0.832178i	$0.687094\pi$
$140$		0			0
$141$	−13.4075	−	11.0298i	−1.12911	−	0.928876i
$142$		0			0
$143$	8.89601	+	2.38368i	0.743922	+	0.199333i
$144$		0			0
$145$	3.86481	+	6.69405i	0.320955	+	0.555911i
$146$		0			0
$147$	−1.69337	−	4.51536i	−0.139666	−	0.372421i
$148$		0			0
$149$		−	0.732971i		−	0.0600473i	−0.999549	−	0.0300237i	$-0.990442\pi$
$149$		−	0.732971i		−	0.0600473i	0.999549	−	0.0300237i	$-0.00955826\pi$
$150$		0			0
$151$	−1.32289	+	0.763770i	−0.107655	+	0.0621547i	−0.552861	−	0.833274i	$-0.686464\pi$
$151$	−1.32289	+	0.763770i	−0.107655	+	0.0621547i	0.445206	+	0.895428i	$0.353131\pi$
$152$		0			0
$153$	1.99692	+	4.07363i	0.161441	+	0.329333i
$154$		0			0
$155$	−1.83439	+	1.05909i	−0.147342	+	0.0850680i
$156$		0			0
$157$	9.79030	−	16.9573i	0.781351	−	1.35334i	−0.149804	−	0.988716i	$-0.547864\pi$
$157$	9.79030	−	16.9573i	0.781351	−	1.35334i	0.931155	−	0.364624i	$-0.118802\pi$
$158$		0			0
$159$	0.0228022	−	0.00855136i	0.00180833	−	0.000678167i
$160$		0			0
$161$	−3.78205	+	14.1148i	−0.298067	+	1.11240i
$162$		0			0
$163$	9.58339	−	2.56786i	0.750629	−	0.201130i	0.136832	−	0.990594i	$-0.456308\pi$
$163$	9.58339	−	2.56786i	0.750629	−	0.201130i	0.613797	+	0.789464i	$0.289641\pi$
$164$		0			0
$165$	7.42110	+	10.3821i	0.577732	+	0.808242i
$166$		0			0
$167$	−5.09381	+	19.0103i	−0.394171	+	1.47106i	0.429017	+	0.903296i	$0.358860\pi$
$167$	−5.09381	+	19.0103i	−0.394171	+	1.47106i	−0.823188	+	0.567769i	$0.807807\pi$
$168$		0			0
$169$	−2.38277	−	1.37570i	−0.183290	−	0.105823i
$170$		0			0
$171$	−0.164156	+	2.41689i	−0.0125533	+	0.184824i
$172$		0			0
$173$	−0.593573	+	1.02810i	−0.0451285	+	0.0781649i	−0.887707	−	0.460408i	$-0.847703\pi$
$173$	−0.593573	+	1.02810i	−0.0451285	+	0.0781649i	0.842579	+	0.538573i	$0.181036\pi$
$174$		0			0
$175$		−	3.20150i		−	0.242011i
$176$		0			0
$177$	2.83259	−	6.23203i	0.212910	−	0.468428i
$178$		0			0
$179$	−6.02413	+	6.02413i	−0.450264	+	0.450264i	−0.895442	−	0.445178i	$-0.853140\pi$
$179$	−6.02413	+	6.02413i	−0.450264	+	0.450264i	0.445178	+	0.895442i	$0.353140\pi$
$180$		0			0
$181$	−6.63278	−	11.4883i	−0.493010	−	0.853919i	0.506957	−	0.861971i	$-0.330770\pi$
$181$	−6.63278	−	11.4883i	−0.493010	−	0.853919i	−0.999968	+	0.00805227i	$0.997437\pi$
$182$		0			0
$183$	1.62811	+	2.27771i	0.120353	+	0.168373i
$184$		0			0
$185$	15.1254	−	3.73012i	1.11204	−	0.274244i
$186$		0			0
$187$	−4.20230	+	1.12600i	−0.307303	+	0.0823415i
$188$		0			0
$189$	−0.311223	−	10.6644i	−0.0226381	−	0.775718i
$190$		0			0
$191$	14.7464	+	14.7464i	1.06701	+	1.06701i	0.997587	+	0.0694219i	$0.0221155\pi$
$191$	14.7464	+	14.7464i	1.06701	+	1.06701i	0.0694219	+	0.997587i	$0.477885\pi$
$192$		0			0
$193$	16.1890	−	16.1890i	1.16531	−	1.16531i	0.182013	−	0.983296i	$-0.441739\pi$
$193$	16.1890	−	16.1890i	1.16531	−	1.16531i	0.983296	−	0.182013i	$-0.0582614\pi$
$194$		0			0
$195$	4.98659	+	13.2968i	0.357097	+	0.952200i
$196$		0			0
$197$	2.89250	+	1.66999i	0.206082	+	0.118982i	0.599489	−	0.800383i	$-0.295370\pi$
$197$	2.89250	+	1.66999i	0.206082	+	0.118982i	−0.393407	+	0.919364i	$0.628704\pi$
$198$		0			0
$199$	12.0201	+	12.0201i	0.852083	+	0.852083i	0.990389	−	0.138307i	$-0.0441660\pi$
$199$	12.0201	+	12.0201i	0.852083	+	0.852083i	−0.138307	+	0.990389i	$0.544166\pi$
$200$		0			0
$201$	−4.03779	+	24.2777i	−0.284804	+	1.71242i
$202$		0			0
$203$	5.98567	+	1.60386i	0.420112	+	0.112569i
$204$		0			0
$205$	19.9465	−	5.34465i	1.39312	−	0.373286i
$206$		0			0
$207$	11.9039	−	17.7244i	0.827375	−	1.23193i
$208$		0			0
$209$	−2.24387	−	0.601243i	−0.155212	−	0.0415889i
$210$		0			0
$211$	8.11642			0.558757			0.279379	−	0.960181i	$-0.409872\pi$
$211$	8.11642			0.558757			0.279379	+	0.960181i	$0.409872\pi$
$212$		0			0
$213$	−4.42129	+	26.5836i	−0.302942	+	1.82148i
$214$		0			0
$215$	−8.92904	−	15.4656i	−0.608956	−	1.05474i
$216$		0			0
$217$	−0.439510	+	1.64027i	−0.0298359	+	0.111349i
$218$		0			0
$219$	12.7146	+	10.4598i	0.859173	+	0.706808i
$220$		0			0
$221$	−4.84124			−0.325657
$222$		0			0
$223$	22.8725			1.53166			0.765828	−	0.643045i	$-0.222329\pi$
$223$	22.8725			1.53166			0.765828	+	0.643045i	$0.222329\pi$
$224$		0			0
$225$	−1.51409	+	4.42594i	−0.100940	+	0.295062i
$226$		0			0
$227$	−1.77918	+	6.63998i	−0.118088	+	0.440711i	−0.999499	−	0.0316388i	$-0.989927\pi$
$227$	−1.77918	+	6.63998i	−0.118088	+	0.440711i	0.881411	+	0.472350i	$0.156594\pi$
$228$		0			0
$229$	−13.1005	−	22.6907i	−0.865703	−	1.49944i	−0.866347	−	0.499443i	$-0.833538\pi$
$229$	−13.1005	−	22.6907i	−0.865703	−	1.49944i	0.000643475	−	1.00000i	$-0.499795\pi$
$230$		0			0
$231$	10.0924	+	1.67853i	0.664029	+	0.110439i
$232$		0			0
$233$	−24.5611			−1.60905			−0.804526	−	0.593918i	$-0.797580\pi$
$233$	−24.5611			−1.60905			−0.804526	+	0.593918i	$0.797580\pi$
$234$		0			0
$235$	24.7967	+	6.64425i	1.61756	+	0.433423i
$236$		0			0
$237$	−8.44605	+	6.03724i	−0.548630	+	0.392161i
$238$		0			0
$239$	−23.7109	+	6.35331i	−1.53373	+	0.410961i	−0.924233	−	0.381828i	$-0.875295\pi$
$239$	−23.7109	+	6.35331i	−1.53373	+	0.410961i	−0.609495	+	0.792790i	$0.708628\pi$
$240$		0			0
$241$	15.9973	+	4.28646i	1.03048	+	0.276115i	0.734162	−	0.678975i	$-0.237575\pi$
$241$	15.9973	+	4.28646i	1.03048	+	0.276115i	0.296315	+	0.955090i	$0.404242\pi$
$242$		0			0
$243$	−4.61327	+	14.8902i	−0.295941	+	0.955206i
$244$		0			0
$245$	5.04219	+	5.04219i	0.322134	+	0.322134i
$246$		0			0
$247$	−2.23871	−	1.29252i	−0.142446	−	0.0822410i
$248$		0			0
$249$	−9.70294	+	3.63883i	−0.614899	+	0.230601i
$250$		0			0
$251$	5.09873	−	5.09873i	0.321829	−	0.321829i	−0.527639	−	0.849469i	$-0.676923\pi$
$251$	5.09873	−	5.09873i	0.321829	−	0.321829i	0.849469	+	0.527639i	$0.176923\pi$
$252$		0			0
$253$	14.4776	+	14.4776i	0.910201	+	0.910201i
$254$		0			0
$255$	−5.18054	−	4.26183i	−0.324418	−	0.266886i
$256$		0			0
$257$	16.5361	−	4.43082i	1.03149	−	0.276387i	0.296908	−	0.954906i	$-0.404045\pi$
$257$	16.5361	−	4.43082i	1.03149	−	0.276387i	0.734583	+	0.678519i	$0.237378\pi$
$258$		0			0
$259$	6.45984	−	10.6889i	0.401395	−	0.664179i
$260$		0			0
$261$	−7.51641	−	5.04808i	−0.465254	−	0.312468i
$262$		0			0
$263$	−0.208125	−	0.360484i	−0.0128336	−	0.0222284i	0.859537	−	0.511073i	$-0.170752\pi$
$263$	−0.208125	−	0.360484i	−0.0128336	−	0.0222284i	−0.872371	+	0.488845i	$0.837418\pi$
$264$		0			0
$265$	−0.0254626	+	0.0254626i	−0.00156416	+	0.00156416i
$266$		0			0
$267$	0.434674	+	0.197568i	0.0266016	+	0.0120910i
$268$		0			0
$269$		−	15.6753i		−	0.955742i	−0.878430	−	0.477871i	$-0.841409\pi$
$269$		−	15.6753i		−	0.955742i	0.878430	−	0.477871i	$-0.158591\pi$
$270$		0			0
$271$	−3.83078	+	6.63510i	−0.232703	+	0.403054i	−0.958603	−	0.284747i	$-0.908090\pi$
$271$	−3.83078	+	6.63510i	−0.232703	+	0.403054i	0.725899	+	0.687801i	$0.241424\pi$
$272$		0			0
$273$	10.3646	+	4.71091i	0.627292	+	0.285117i
$274$		0			0
$275$	−3.88478	−	2.24288i	−0.234261	−	0.135251i
$276$		0			0
$277$	5.39948	−	20.1511i	0.324423	−	1.21076i	−0.590467	−	0.807062i	$-0.701057\pi$
$277$	5.39948	−	20.1511i	0.324423	−	1.21076i	0.914890	−	0.403702i	$-0.132277\pi$
$278$		0			0
$279$	1.38334	−	2.05975i	0.0828185	−	0.123314i
$280$		0			0
$281$	−13.1554	+	3.52498i	−0.784786	+	0.210283i	−0.628893	−	0.777491i	$-0.716492\pi$
$281$	−13.1554	+	3.52498i	−0.784786	+	0.210283i	−0.155892	+	0.987774i	$0.549825\pi$
$282$		0			0
$283$	5.53641	−	20.6622i	0.329105	−	1.22824i	−0.581015	−	0.813893i	$-0.697344\pi$
$283$	5.53641	−	20.6622i	0.329105	−	1.22824i	0.910120	−	0.414345i	$-0.135989\pi$
$284$		0			0
$285$	−1.25778	−	3.35388i	−0.0745046	−	0.198667i
$286$		0			0
$287$	8.27758	−	14.3372i	0.488610	−	0.846298i
$288$		0			0
$289$	−12.7419	+	7.35655i	−0.749524	+	0.432738i
$290$		0			0
$291$	−0.317090	−	3.25900i	−0.0185881	−	0.191046i
$292$		0			0
$293$	9.08241	−	5.24373i	0.530600	−	0.306342i	−0.210661	−	0.977559i	$-0.567562\pi$
$293$	9.08241	−	5.24373i	0.530600	−	0.306342i	0.741261	+	0.671217i	$0.234228\pi$
$294$		0			0
$295$			10.1222i			0.589338i
$296$		0			0
$297$	−13.1584	−	7.09348i	−0.763528	−	0.411606i
$298$		0			0
$299$	11.3919	+	19.7313i	0.658810	+	1.14109i
$300$		0			0
$301$	−13.8290	−	3.70546i	−0.797088	−	0.213579i
$302$		0			0
$303$	18.3787	−	22.3406i	1.05583	−	1.28343i
$304$		0			0
$305$	−3.58525	−	2.06995i	−0.205291	−	0.118525i
$306$		0			0
$307$		−	11.6594i		−	0.665436i	−0.943026	−	0.332718i	$-0.892034\pi$
$307$		−	11.6594i		−	0.665436i	0.943026	−	0.332718i	$-0.107966\pi$
$308$		0			0
$309$	−11.4596	+	1.11499i	−0.651916	+	0.0634294i
$310$		0			0
$311$	−0.0284178	−	0.106057i	−0.00161143	−	0.00601392i	0.965115	−	0.261825i	$-0.0843242\pi$
$311$	−0.0284178	−	0.106057i	−0.00161143	−	0.00601392i	−0.966727	+	0.255811i	$0.917658\pi$
$312$		0			0
$313$	6.74334	+	25.1665i	0.381156	+	1.42249i	0.844138	+	0.536126i	$0.180113\pi$
$313$	6.74334	+	25.1665i	0.381156	+	1.42249i	−0.462982	+	0.886368i	$0.653221\pi$
$314$		0			0
$315$	6.94387	+	14.1652i	0.391243	+	0.798118i
$316$		0			0
$317$	−1.59586	+	2.76411i	−0.0896325	+	0.155248i	−0.907356	−	0.420363i	$-0.861903\pi$
$317$	−1.59586	+	2.76411i	−0.0896325	+	0.155248i	0.817723	+	0.575611i	$0.195236\pi$
$318$		0			0
$319$	6.13954	−	6.13954i	0.343748	−	0.343748i
$320$		0			0
$321$	4.19618	−	25.2301i	0.234208	−	1.40821i
$322$		0			0
$323$	1.22112			0.0679450
$324$		0			0
$325$	−3.52967	−	3.52967i	−0.195791	−	0.195791i
$326$		0			0
$327$	−11.4903	−	5.22258i	−0.635415	−	0.288810i
$328$		0			0
$329$	17.8234	−	10.2904i	0.982638	−	0.567326i
$330$		0			0
$331$	−2.30806	−	8.61380i	−0.126863	−	0.473457i	0.873037	−	0.487655i	$-0.162147\pi$
$331$	−2.30806	−	8.61380i	−0.126863	−	0.473457i	−0.999899	+	0.0141971i	$0.995481\pi$
$332$		0			0
$333$	−13.9856	+	11.7219i	−0.766405	+	0.642357i
$334$		0			0
$335$	−9.41881	−	35.1515i	−0.514604	−	1.92053i
$336$		0			0
$337$	−26.4629	+	15.2784i	−1.44153	+	0.832266i	−0.997952	−	0.0639716i	$-0.979623\pi$
$337$	−26.4629	+	15.2784i	−1.44153	+	0.832266i	−0.443575	+	0.896237i	$0.646290\pi$
$338$		0			0
$339$	−4.63617	−	2.10724i	−0.251802	−	0.114449i
$340$		0			0
$341$	1.68244	+	1.68244i	0.0911091	+	0.0911091i
$342$		0			0
$343$	20.0893			1.08472
$344$		0			0
$345$	−5.17954	+	31.1427i	−0.278857	+	1.67667i
$346$		0			0
$347$	−6.01005	+	6.01005i	−0.322636	+	0.322636i	−0.849778	−	0.527141i	$-0.823264\pi$
$347$	−6.01005	+	6.01005i	−0.322636	+	0.322636i	0.527141	+	0.849778i	$0.323264\pi$
$348$		0			0
$349$	−7.04813	+	12.2077i	−0.377278	+	0.653464i	−0.990665	−	0.136318i	$-0.956473\pi$
$349$	−7.04813	+	12.2077i	−0.377278	+	0.653464i	0.613388	+	0.789782i	$0.289806\pi$
$350$		0			0
$351$	−12.1006	−	11.4144i	−0.645883	−	0.609254i
$352$		0			0
$353$	9.27651	+	34.6204i	0.493739	+	1.84266i	0.536983	+	0.843593i	$0.319564\pi$
$353$	9.27651	+	34.6204i	0.493739	+	1.84266i	−0.0432438	+	0.999065i	$0.513769\pi$
$354$		0			0
$355$	−10.3134	−	38.4901i	−0.547378	−	2.04284i
$356$		0			0
$357$	−5.35274	+	0.520805i	−0.283297	+	0.0275639i
$358$		0			0
$359$			32.8714i			1.73489i	0.497537	+	0.867443i	$0.334238\pi$
$359$			32.8714i			1.73489i	−0.497537	+	0.867443i	$0.665762\pi$
$360$		0			0
$361$	−15.8898	−	9.17398i	−0.836306	−	0.482841i
$362$		0			0
$363$	−2.99707	+	3.64314i	−0.157305	+	0.191215i
$364$		0			0
$365$	−23.5153	−	6.30090i	−1.23085	−	0.329804i
$366$		0			0
$367$	0.980581	+	1.69842i	0.0511859	+	0.0886566i	0.890483	−	0.455016i	$-0.150367\pi$
$367$	0.980581	+	1.69842i	0.0511859	+	0.0886566i	−0.839297	+	0.543673i	$0.817033\pi$
$368$		0			0
$369$	−18.2239	+	15.9058i	−0.948698	+	0.828023i
$370$		0			0
$371$			0.0288688i			0.00149879i
$372$		0			0
$373$	25.0523	−	14.4639i	1.29716	−	0.748914i	0.317244	−	0.948344i	$-0.397242\pi$
$373$	25.0523	−	14.4639i	1.29716	−	0.748914i	0.979912	+	0.199430i	$0.0639091\pi$
$374$		0			0
$375$	1.47806	+	15.1913i	0.0763269	+	0.784475i
$376$		0			0
$377$	8.36748	−	4.83096i	0.430947	−	0.248807i
$378$		0			0
$379$	−12.1950	+	21.1223i	−0.626414	+	1.08498i	0.361852	+	0.932236i	$0.382145\pi$
$379$	−12.1950	+	21.1223i	−0.626414	+	1.08498i	−0.988266	+	0.152745i	$0.951189\pi$
$380$		0			0
$381$	7.63501	+	20.3588i	0.391153	+	1.04301i
$382$		0			0
$383$	−3.14534	+	11.7386i	−0.160719	+	0.599813i	0.837828	+	0.545934i	$0.183825\pi$
$383$	−3.14534	+	11.7386i	−0.160719	+	0.599813i	−0.998547	+	0.0538788i	$0.982842\pi$
$384$		0			0
$385$	−14.6126	+	3.91544i	−0.744728	+	0.199549i
$386$		0			0
$387$	17.3655	+	11.6628i	0.882737	+	0.592852i
$388$		0			0
$389$	2.98050	−	11.1234i	0.151117	−	0.563977i	−0.848289	−	0.529533i	$-0.822367\pi$
$389$	2.98050	−	11.1234i	0.151117	−	0.563977i	0.999407	−	0.0344442i	$-0.0109661\pi$
$390$		0			0
$391$	−9.32069	−	5.38130i	−0.471367	−	0.272144i
$392$		0			0
$393$	−32.4104	−	14.7312i	−1.63489	−	0.743090i
$394$		0			0
$395$	7.67563	−	13.2946i	0.386203	−	0.668923i
$396$		0			0
$397$			3.07799i			0.154480i	0.997013	+	0.0772400i	$0.0246108\pi$
$397$			3.07799i			0.154480i	−0.997013	+	0.0772400i	$0.975389\pi$
$398$		0			0
$399$	−2.61429	−	1.18825i	−0.130878	−	0.0594868i
$400$		0			0
$401$	3.58968	−	3.58968i	0.179260	−	0.179260i	−0.611773	−	0.791033i	$-0.709543\pi$
$401$	3.58968	−	3.58968i	0.179260	−	0.179260i	0.791033	+	0.611773i	$0.209543\pi$
$402$		0			0
$403$	1.32385	+	2.29297i	0.0659454	+	0.114221i
$404$		0			0
$405$	−2.90042	−	22.8667i	−0.144123	−	1.13626i
$406$		0			0
$407$	−8.44463	−	15.3269i	−0.418585	−	0.759725i
$408$		0			0
$409$	−23.1675	+	6.20770i	−1.14556	+	0.306951i	−0.781183	−	0.624302i	$-0.785384\pi$
$409$	−23.1675	+	6.20770i	−1.14556	+	0.306951i	−0.364374	+	0.931253i	$0.618717\pi$
$410$		0			0
$411$	−15.0189	−	12.3555i	−0.740829	−	0.609451i
$412$		0			0
$413$	5.73814	+	5.73814i	0.282355	+	0.282355i
$414$		0			0
$415$	10.8350	−	10.8350i	0.531870	−	0.531870i
$416$		0			0
$417$	−2.45234	+	0.919685i	−0.120092	+	0.0450372i
$418$		0			0
$419$	2.13096	+	1.23031i	0.104104	+	0.0601046i	0.551148	−	0.834407i	$-0.314190\pi$
$419$	2.13096	+	1.23031i	0.104104	+	0.0601046i	−0.447044	+	0.894512i	$0.647523\pi$
$420$		0			0
$421$	10.7557	+	10.7557i	0.524203	+	0.524203i	0.918838	−	0.394635i	$-0.129129\pi$
$421$	10.7557	+	10.7557i	0.524203	+	0.524203i	−0.394635	+	0.918838i	$0.629129\pi$
$422$		0			0
$423$	−29.5067	+	5.79670i	−1.43467	+	0.281845i
$424$		0			0
$425$	2.27763	+	0.610290i	0.110482	+	0.0296034i
$426$		0			0
$427$	−3.20585	+	0.859005i	−0.155142	+	0.0415702i
$428$		0			0
$429$	12.9774	−	9.27628i	0.626556	−	0.447863i
$430$		0			0
$431$	31.4266	+	8.42073i	1.51377	+	0.405612i	0.917684	−	0.397311i	$-0.130057\pi$
$431$	31.4266	+	8.42073i	1.51377	+	0.405612i	0.596082	+	0.802924i	$0.296723\pi$
$432$		0			0
$433$	15.7898			0.758810			0.379405	−	0.925231i	$-0.376129\pi$
$433$	15.7898			0.758810			0.379405	+	0.925231i	$0.376129\pi$
$434$		0			0
$435$	13.2067	+	2.19649i	0.633213	+	0.105314i
$436$		0			0
$437$	−2.87341	−	4.97690i	−0.137454	−	0.238077i
$438$		0			0
$439$	−3.12653	+	11.6684i	−0.149221	+	0.556901i	0.850310	+	0.526282i	$0.176414\pi$
$439$	−3.12653	+	11.6684i	−0.149221	+	0.556901i	−0.999531	+	0.0306186i	$0.990252\pi$
$440$		0			0
$441$	−7.90307	−	2.70361i	−0.376337	−	0.128743i
$442$		0			0
$443$	1.00366			0.0476853			0.0238427	−	0.999716i	$-0.492410\pi$
$443$	1.00366			0.0476853			0.0238427	+	0.999716i	$0.492410\pi$
$444$		0			0
$445$	−0.706008			−0.0334680
$446$		0			0
$447$	−0.980416	−	0.806550i	−0.0463721	−	0.0381485i
$448$		0			0
$449$	10.2672	−	38.3178i	0.484540	−	1.80833i	−0.0975848	−	0.995227i	$-0.531112\pi$
$449$	10.2672	−	38.3178i	0.484540	−	1.80833i	0.582125	−	0.813100i	$-0.302222\pi$
$450$		0			0
$451$	−11.5980	−	20.0884i	−0.546131	−	0.945926i
$452$		0			0
$453$	−0.434074	+	2.60993i	−0.0203946	+	0.122625i
$454$		0			0
$455$	−16.8344			−0.789209
$456$		0			0
$457$	19.2760	+	5.16499i	0.901694	+	0.241608i	0.679744	−	0.733450i	$-0.262091\pi$
$457$	19.2760	+	5.16499i	0.901694	+	0.241608i	0.221950	+	0.975058i	$0.428758\pi$
$458$		0			0
$459$	7.64623	+	1.81149i	0.356896	+	0.0845533i
$460$		0			0
$461$	−31.1013	+	8.33358i	−1.44853	+	0.388134i	−0.895514	−	0.445034i	$-0.853192\pi$
$461$	−31.1013	+	8.33358i	−1.44853	+	0.388134i	−0.553020	+	0.833168i	$0.686525\pi$
$462$		0			0
$463$	6.31133	+	1.69112i	0.293312	+	0.0785928i	0.402475	−	0.915431i	$-0.368150\pi$
$463$	6.31133	+	1.69112i	0.293312	+	0.0785928i	−0.109162	+	0.994024i	$0.534817\pi$
$464$		0			0
$465$	−0.601912	+	3.61908i	−0.0279130	+	0.167831i
$466$		0			0
$467$	13.6292	+	13.6292i	0.630683	+	0.630683i	0.948239	−	0.317556i	$-0.102862\pi$
$467$	13.6292	+	13.6292i	0.630683	+	0.630683i	−0.317556	+	0.948239i	$0.602862\pi$
$468$		0			0
$469$	−25.2663	−	14.5875i	−1.16669	−	0.673588i
$470$		0			0
$471$	−11.9089	−	31.7550i	−0.548731	−	1.46319i
$472$		0			0
$473$	−14.1844	+	14.1844i	−0.652201	+	0.652201i
$474$		0			0
$475$	0.890299	+	0.890299i	0.0408497	+	0.0408497i
$476$		0			0
$477$	0.0136530	−	0.0399098i	0.000625127	−	0.00182735i
$478$		0			0
$479$	−8.16021	+	2.18652i	−0.372849	+	0.0999047i	−0.440378	−	0.897813i	$-0.645155\pi$
$479$	−8.16021	+	2.18652i	−0.372849	+	0.0999047i	0.0675282	+	0.997717i	$0.478489\pi$
$480$		0			0
$481$	−4.66260	−	18.9066i	−0.212596	−	0.862066i
$482$		0			0
$483$	14.7181	+	20.5906i	0.669699	+	0.936903i
$484$		0			0
$485$	2.42084	+	4.19302i	0.109925	+	0.190395i
$486$		0			0
$487$	−28.7786	+	28.7786i	−1.30408	+	1.30408i	−0.378468	+	0.925614i	$0.623549\pi$
$487$	−28.7786	+	28.7786i	−1.30408	+	1.30408i	−0.925614	+	0.378468i	$0.876451\pi$
$488$		0			0
$489$	7.11066	−	15.6443i	0.321555	−	0.707460i
$490$		0			0
$491$			27.6804i			1.24920i	0.780945	+	0.624600i	$0.214738\pi$
$491$			27.6804i			1.24920i	−0.780945	+	0.624600i	$0.785262\pi$
$492$		0			0
$493$	−2.28205	+	3.95263i	−0.102778	+	0.178017i
$494$		0			0
$495$	22.0530	+	1.49785i	0.991210	+	0.0673235i
$496$		0			0
$497$	−27.6660	−	15.9730i	−1.24099	−	0.716486i
$498$		0			0
$499$	6.83888	−	25.5231i	0.306150	−	1.14257i	−0.625800	−	0.779983i	$-0.715227\pi$
$499$	6.83888	−	25.5231i	0.306150	−	1.14257i	0.931951	−	0.362585i	$-0.118106\pi$
$500$		0			0
$501$	19.8229	+	27.7321i	0.885624	+	1.23898i
$502$		0			0
$503$	27.3029	−	7.31579i	1.21738	−	0.326195i	0.407724	−	0.913105i	$-0.366323\pi$
$503$	27.3029	−	7.31579i	1.21738	−	0.326195i	0.809652	+	0.586911i	$0.199656\pi$
$504$		0			0
$505$	−11.0712	+	41.3183i	−0.492662	+	1.83864i
$506$		0			0
$507$	−4.46209	+	1.67339i	−0.198168	+	0.0743177i
$508$		0			0
$509$	1.07119	−	1.85536i	0.0474798	−	0.0822374i	−0.841309	−	0.540555i	$-0.818214\pi$
$509$	1.07119	−	1.85536i	0.0474798	−	0.0822374i	0.888789	+	0.458317i	$0.151548\pi$
$510$		0			0
$511$	−16.9024	+	9.75859i	−0.747717	+	0.431694i
$512$		0			0
$513$	3.05218	+	2.87908i	0.134757	+	0.127115i
$514$		0			0
$515$	14.7440	−	8.51243i	0.649697	−	0.375103i
$516$		0			0
$517$		−	28.8365i		−	1.26823i
$518$		0			0
$519$	0.722018	+	1.92526i	0.0316931	+	0.0845096i
$520$		0			0
$521$	−15.1367	−	26.2176i	−0.663152	−	1.14861i	−0.979783	−	0.200065i	$-0.935885\pi$
$521$	−15.1367	−	26.2176i	−0.663152	−	1.14861i	0.316630	−	0.948549i	$-0.397449\pi$
$522$		0			0
$523$	31.3860	+	8.40985i	1.37241	+	0.367737i	0.868359	−	0.495936i	$-0.165175\pi$
$523$	31.3860	+	8.40985i	1.37241	+	0.367737i	0.504053	+	0.863672i	$0.331841\pi$
$524$		0			0
$525$	−4.28231	−	3.52289i	−0.186895	−	0.153751i
$526$		0			0
$527$	−1.08315	−	0.625358i	−0.0471828	−	0.0272410i
$528$		0			0
$529$			27.6508i			1.20221i
$530$		0			0
$531$	−5.21897	−	10.6465i	−0.226484	−	0.462018i
$532$		0			0
$533$	−6.68074	−	24.9328i	−0.289375	−	1.07996i
$534$		0			0
$535$	9.78829	+	36.5304i	0.423185	+	1.57935i
$536$		0			0
$537$	1.42897	+	14.6867i	0.0616645	+	0.633777i
$538$		0			0
$539$	4.00494	−	6.93676i	0.172505	−	0.298788i
$540$		0			0
$541$	−12.0582	+	12.0582i	−0.518422	+	0.518422i	−0.917094	−	0.398671i	$-0.869471\pi$
$541$	−12.0582	+	12.0582i	−0.518422	+	0.518422i	0.398671	+	0.917094i	$0.369471\pi$
$542$		0			0
$543$	−22.6653	−	3.76961i	−0.972660	−	0.161769i
$544$		0			0
$545$	18.6628			0.799428
$546$		0			0
$547$	−14.9813	−	14.9813i	−0.640553	−	0.640553i	0.310138	−	0.950691i	$-0.399625\pi$
$547$	−14.9813	−	14.9813i	−0.640553	−	0.640553i	−0.950691	+	0.310138i	$0.899625\pi$
$548$		0			0
$549$	4.83820	+	0.328613i	0.206489	+	0.0140249i
$550$		0			0
$551$	−2.11055	+	1.21853i	−0.0899127	+	0.0519111i
$552$		0			0
$553$	−3.18530	−	11.8877i	−0.135453	−	0.505517i
$554$		0			0
$555$	11.6544	−	24.3362i	0.494702	−	1.03302i
$556$		0			0
$557$	11.2809	+	42.1010i	0.477988	+	1.78388i	0.609750	+	0.792594i	$0.291270\pi$
$557$	11.2809	+	42.1010i	0.477988	+	1.78388i	−0.131762	+	0.991281i	$0.542063\pi$
$558$		0			0
$559$	−19.3317	+	11.1612i	−0.817645	+	0.472068i
$560$		0			0
$561$	−3.11801	+	6.86000i	−0.131643	+	0.289629i
$562$		0			0
$563$	9.09523	+	9.09523i	0.383318	+	0.383318i	0.872296	−	0.488978i	$-0.162630\pi$
$563$	9.09523	+	9.09523i	0.383318	+	0.383318i	−0.488978	+	0.872296i	$0.662630\pi$
$564$		0			0
$565$	7.53019			0.316797
$566$		0			0
$567$	−14.6070	−	11.3186i	−0.613438	−	0.475337i
$568$		0			0
$569$	−20.3741	+	20.3741i	−0.854127	+	0.854127i	−0.990638	−	0.136512i	$-0.956411\pi$
$569$	−20.3741	+	20.3741i	−0.854127	+	0.854127i	0.136512	+	0.990638i	$0.456411\pi$
$570$		0			0
$571$	−6.88764	+	11.9297i	−0.288239	+	0.499244i	−0.973389	−	0.229157i	$-0.926403\pi$
$571$	−6.88764	+	11.9297i	−0.288239	+	0.499244i	0.685151	+	0.728401i	$0.259736\pi$
$572$		0			0
$573$	35.9513	−	3.49795i	1.50189	−	0.146129i
$574$		0			0
$575$	−2.87214	−	10.7190i	−0.119777	−	0.447012i
$576$		0			0
$577$	−1.68875	−	6.30249i	−0.0703035	−	0.262376i	0.921824	−	0.387609i	$-0.126699\pi$
$577$	−1.68875	−	6.30249i	−0.0703035	−	0.262376i	−0.992127	+	0.125233i	$0.960032\pi$
$578$		0			0
$579$	−3.84015	−	39.4684i	−0.159591	−	1.64025i
$580$		0			0
$581$		−	12.2844i		−	0.509644i
$582$		0			0
$583$	0.0350301	+	0.0202246i	0.00145080	+	0.000837618i
$584$		0			0
$585$	23.2728	+	7.96152i	0.962212	+	0.329168i
$586$		0			0
$587$	−20.6523	−	5.53376i	−0.852411	−	0.228403i	−0.193944	−	0.981013i	$-0.562128\pi$
$587$	−20.6523	−	5.53376i	−0.852411	−	0.228403i	−0.658467	+	0.752610i	$0.728795\pi$
$588$		0			0
$589$	−0.333918	−	0.578362i	−0.0137588	−	0.0238310i
$590$		0			0
$591$	5.41662	−	2.03136i	0.222810	−	0.0835589i
$592$		0			0
$593$			28.2289i			1.15922i	0.814894	+	0.579610i	$0.196795\pi$
$593$			28.2289i			1.15922i	−0.814894	+	0.579610i	$0.803205\pi$
$594$		0			0
$595$	6.88683	−	3.97612i	0.282333	−	0.163005i
$596$		0			0
$597$	29.3047	−	2.85126i	1.19936	−	0.116694i
$598$		0			0
$599$	17.1386	−	9.89496i	0.700263	−	0.404297i	−0.107182	−	0.994239i	$-0.534183\pi$
$599$	17.1386	−	9.89496i	0.700263	−	0.404297i	0.807446	+	0.589942i	$0.200849\pi$
$600$		0			0
$601$	4.31244	−	7.46936i	0.175908	−	0.304682i	−0.764567	−	0.644544i	$-0.777047\pi$
$601$	4.31244	−	7.46936i	0.175908	−	0.304682i	0.940475	+	0.339863i	$0.110381\pi$
$602$		0			0
$603$	28.0306	+	32.1158i	1.14149	+	1.30786i
$604$		0			0
$605$	1.80541	−	6.73788i	0.0734004	−	0.273934i
$606$		0			0
$607$	−18.0031	+	4.82393i	−0.730725	+	0.195797i	−0.604952	−	0.796262i	$-0.706808\pi$
$607$	−18.0031	+	4.82393i	−0.730725	+	0.195797i	−0.125773	+	0.992059i	$0.540141\pi$
$608$		0			0
$609$	8.73185	−	6.24153i	0.353832	−	0.252920i
$610$		0			0
$611$	8.30523	−	30.9955i	0.335994	−	1.25395i
$612$		0			0
$613$	29.0476	+	16.7706i	1.17322	+	0.677360i	0.954437	−	0.298413i	$-0.0964574\pi$
$613$	29.0476	+	16.7706i	1.17322	+	0.677360i	0.218785	+	0.975773i	$0.429791\pi$
$614$		0			0
$615$	14.7999	−	32.5614i	0.596788	−	1.31300i
$616$		0			0
$617$	−13.9410	+	24.1464i	−0.561242	+	0.972099i	0.436147	+	0.899876i	$0.356343\pi$
$617$	−13.9410	+	24.1464i	−0.561242	+	0.972099i	−0.997388	+	0.0722235i	$0.976991\pi$
$618$		0			0
$619$		−	2.03682i		−	0.0818667i	−0.999162	−	0.0409333i	$-0.986967\pi$
$619$		−	2.03682i		−	0.0818667i	0.999162	−	0.0409333i	$-0.0130331\pi$
$620$		0			0
$621$	−10.6092	−	35.4262i	−0.425734	−	1.42160i
$622$		0			0
$623$	−0.400226	+	0.400226i	−0.0160347	+	0.0160347i
$624$		0			0
$625$	−15.1825	−	26.2969i	−0.607300	−	1.05187i
$626$		0			0
$627$	−3.27334	+	2.33978i	−0.130725	+	0.0934420i
$628$		0			0
$629$	6.37298	+	6.63329i	0.254107	+	0.264487i
$630$		0			0
$631$	−14.3283	+	3.83926i	−0.570401	+	0.152838i	−0.532480	−	0.846442i	$-0.678740\pi$
$631$	−14.3283	+	3.83926i	−0.570401	+	0.152838i	−0.0379205	+	0.999281i	$0.512073\pi$
$632$		0			0
$633$	8.93118	−	10.8565i	0.354983	−	0.431505i
$634$		0			0
$635$	−22.7341	−	22.7341i	−0.902175	−	0.902175i
$636$		0			0
$637$	6.30267	−	6.30267i	0.249721	−	0.249721i
$638$		0			0
$639$	30.6929	+	35.1661i	1.21419	+	1.39115i
$640$		0			0
$641$	−9.79637	−	5.65593i	−0.386933	−	0.223396i	0.293897	−	0.955837i	$-0.405048\pi$
$641$	−9.79637	−	5.65593i	−0.386933	−	0.223396i	−0.680830	+	0.732441i	$0.738381\pi$
$642$		0			0
$643$	−1.62868	−	1.62868i	−0.0642291	−	0.0642291i	0.674263	−	0.738492i	$-0.264462\pi$
$643$	−1.62868	−	1.62868i	−0.0642291	−	0.0642291i	−0.738492	+	0.674263i	$0.764462\pi$
$644$		0			0
$645$	−30.5120	−	5.07464i	−1.20141	−	0.199814i
$646$		0			0
$647$	−34.3218	−	9.19650i	−1.34933	−	0.361552i	−0.489443	−	0.872036i	$-0.662800\pi$
$647$	−34.3218	−	9.19650i	−1.34933	−	0.361552i	−0.859887	+	0.510484i	$0.829466\pi$
$648$		0			0
$649$	10.9828	−	2.94282i	0.431111	−	0.115516i
$650$		0			0
$651$	1.71039	+	2.39282i	0.0670354	+	0.0937819i
$652$		0			0
$653$	−12.2798	−	3.29036i	−0.480546	−	0.128762i	0.0104109	−	0.999946i	$-0.496686\pi$
$653$	−12.2798	−	3.29036i	−0.480546	−	0.128762i	−0.490957	+	0.871184i	$0.663353\pi$
$654$		0			0
$655$	52.6417			2.05688
$656$		0			0
$657$	27.9819	−	5.49714i	1.09168	−	0.214464i
$658$		0			0
$659$	14.1723	+	24.5472i	0.552076	+	0.956223i	0.998125	+	0.0612145i	$0.0194974\pi$
$659$	14.1723	+	24.5472i	0.552076	+	0.956223i	−0.446049	+	0.895009i	$0.647169\pi$
$660$		0			0
$661$	6.23683	−	23.2762i	0.242584	−	0.905338i	−0.731998	−	0.681307i	$-0.761412\pi$
$661$	6.23683	−	23.2762i	0.242584	−	0.905338i	0.974582	−	0.224030i	$-0.0719215\pi$
$662$		0			0
$663$	−5.32723	+	6.47560i	−0.206892	+	0.251492i
$664$		0			0
$665$	4.24619			0.164660
$666$		0			0
$667$	21.4795			0.831690
$668$		0			0
$669$	25.1686	−	30.5941i	0.973073	−	1.18284i
$670$		0			0
$671$	−1.20359	+	4.49185i	−0.0464639	+	0.173406i
$672$		0			0
$673$	11.4091	+	19.7612i	0.439789	+	0.761737i	0.997673	−	0.0681823i	$-0.0217200\pi$
$673$	11.4091	+	19.7612i	0.439789	+	0.761737i	−0.557884	+	0.829919i	$0.688387\pi$
$674$		0			0
$675$	4.25401	+	6.89547i	0.163737	+	0.265407i
$676$		0			0
$677$	28.4018			1.09157			0.545785	−	0.837925i	$-0.316231\pi$
$677$	28.4018			1.09157			0.545785	+	0.837925i	$0.316231\pi$
$678$		0			0
$679$	3.74931	+	1.00462i	0.143885	+	0.0385539i
$680$		0			0
$681$	6.92381	+	9.68635i	0.265321	+	0.371182i
$682$		0			0
$683$	−30.9316	+	8.28809i	−1.18356	+	0.317135i	−0.796339	−	0.604850i	$-0.793233\pi$
$683$	−30.9316	+	8.28809i	−1.18356	+	0.317135i	−0.387225	+	0.921985i	$0.626566\pi$
$684$		0			0
$685$	27.7770	+	7.44283i	1.06131	+	0.284376i
$686$		0			0
$687$	−44.7664	−	7.44539i	−1.70795	−	0.284059i
$688$		0			0
$689$	0.0318279	+	0.0318279i	0.00121255	+	0.00121255i
$690$		0			0
$691$	−31.1411	−	17.9793i	−1.18466	−	0.683965i	−0.227574	−	0.973761i	$-0.573079\pi$
$691$	−31.1411	−	17.9793i	−1.18466	−	0.683965i	−0.957088	+	0.289796i	$0.906413\pi$
$692$		0			0
$693$	13.3507	−	11.6524i	0.507150	−	0.442640i
$694$		0			0
$695$	2.73847	−	2.73847i	0.103876	−	0.103876i
$696$		0			0
$697$	8.62193	+	8.62193i	0.326579	+	0.326579i
$698$		0			0
$699$	−27.0267	+	32.8527i	−1.02224	+	1.24260i
$700$		0			0
$701$	45.8279	−	12.2796i	1.73090	−	0.463793i	0.750508	−	0.660861i	$-0.229809\pi$
$701$	45.8279	−	12.2796i	1.73090	−	0.463793i	0.980390	+	0.197069i	$0.0631422\pi$
$702$		0			0
$703$	1.17606	+	4.76887i	0.0443560	+	0.179861i
$704$		0			0
$705$	36.1732	−	25.8566i	1.36236	−	0.973817i
$706$		0			0
$707$	17.1466	+	29.6989i	0.644866	+	1.11694i
$708$		0			0
$709$	−21.7903	+	21.7903i	−0.818353	+	0.818353i	−0.985869	−	0.167516i	$-0.946425\pi$
$709$	−21.7903	+	21.7903i	−0.818353	+	0.818353i	0.167516	+	0.985869i	$0.446425\pi$
$710$		0			0
$711$	−1.21854	+	17.9407i	−0.0456988	+	0.672828i
$712$		0			0
$713$			5.88611i			0.220436i
$714$		0			0
$715$	−11.7937	+	20.4272i	−0.441058	+	0.763935i
$716$		0			0
$717$	−17.5929	+	38.7066i	−0.657021	+	1.44552i
$718$		0			0
$719$	10.3547	+	5.97829i	0.386165	+	0.222953i	0.680497	−	0.732751i	$-0.261764\pi$
$719$	10.3547	+	5.97829i	0.386165	+	0.222953i	−0.294332	+	0.955703i	$0.595097\pi$
$720$		0			0
$721$	3.53257	−	13.1837i	0.131560	−	0.490988i
$722$		0			0
$723$	23.3367	−	16.6811i	0.867902	−	0.620377i
$724$		0			0
$725$	−4.54560	+	1.21799i	−0.168819	+	0.0452350i
$726$		0			0
$727$	−8.30741	+	31.0037i	−0.308105	+	1.14986i	0.622135	+	0.782910i	$0.286266\pi$
$727$	−8.30741	+	31.0037i	−0.308105	+	1.14986i	−0.930240	+	0.366953i	$0.880401\pi$
$728$		0			0
$729$	14.8406	+	22.5556i	0.549653	+	0.835393i
$730$		0			0
$731$	5.27232	−	9.13192i	0.195004	−	0.337756i
$732$		0			0
$733$	10.5003	−	6.06232i	0.387836	−	0.223917i	−0.293386	−	0.955994i	$-0.594782\pi$
$733$	10.5003	−	6.06232i	0.387836	−	0.223917i	0.681222	+	0.732077i	$0.261449\pi$
$734$		0			0
$735$	12.2927	−	1.19604i	0.453425	−	0.0441168i
$736$		0			0
$737$	−35.4016	+	20.4391i	−1.30403	+	0.752884i
$738$		0			0
$739$		−	10.7299i		−	0.394706i	−0.980333	−	0.197353i	$-0.936766\pi$
$739$		−	10.7299i		−	0.394706i	0.980333	−	0.197353i	$-0.0632345\pi$
$740$		0			0
$741$	−4.19231	+	1.57221i	−0.154008	+	0.0577566i
$742$		0			0
$743$	−3.47635	−	6.02121i	−0.127535	−	0.220897i	0.795186	−	0.606365i	$-0.207373\pi$
$743$	−3.47635	−	6.02121i	−0.127535	−	0.220897i	−0.922721	+	0.385469i	$0.874040\pi$
$744$		0			0
$745$	1.81325	+	0.485859i	0.0664323	+	0.0178005i
$746$		0			0
$747$	−5.80970	+	16.9827i	−0.212566	+	0.621364i
$748$		0			0
$749$	26.2574	+	15.1597i	0.959425	+	0.553924i
$750$		0			0
$751$		−	25.7348i		−	0.939075i	−0.882913	−	0.469537i	$-0.844421\pi$
$751$		−	25.7348i		−	0.939075i	0.882913	−	0.469537i	$-0.155579\pi$
$752$		0			0
$753$	−1.20946	−	12.4306i	−0.0440751	−	0.452996i
$754$		0			0
$755$	−1.01255	−	3.77888i	−0.0368504	−	0.137528i
$756$		0			0
$757$	13.9345	+	52.0042i	0.506458	+	1.89013i	0.452901	+	0.891561i	$0.350389\pi$
$757$	13.9345	+	52.0042i	0.506458	+	1.89013i	0.0535561	+	0.998565i	$0.482944\pi$
$758$		0			0
$759$	35.2961	−	3.43420i	1.28117	−	0.124654i
$760$		0			0
$761$	13.0209	−	22.5528i	0.472006	−	0.817538i	−0.527481	−	0.849567i	$-0.676863\pi$
$761$	13.0209	−	22.5528i	0.472006	−	0.817538i	0.999487	+	0.0320287i	$0.0101968\pi$
$762$		0			0
$763$	10.5797	−	10.5797i	0.383011	−	0.383011i
$764$		0			0
$765$	−11.4012	+	2.23980i	−0.412210	+	0.0809801i
$766$		0			0
$767$	12.6526			0.456860
$768$		0			0
$769$	−26.6867	−	26.6867i	−0.962346	−	0.962346i	0.0369706	−	0.999316i	$-0.488229\pi$
$769$	−26.6867	−	26.6867i	−0.962346	−	0.962346i	−0.999316	+	0.0369706i	$0.988229\pi$
$770$		0			0
$771$	12.2694	−	26.9941i	0.441871	−	0.972169i
$772$		0			0
$773$	−26.2263	+	15.1418i	−0.943296	+	0.544612i	−0.890992	−	0.454019i	$-0.849990\pi$
$773$	−26.2263	+	15.1418i	−0.943296	+	0.544612i	−0.0523040	+	0.998631i	$0.516656\pi$
$774$		0			0
$775$	−0.333770	−	1.24565i	−0.0119894	−	0.0447449i
$776$		0			0
$777$	−7.18914	−	20.4026i	−0.257909	−	0.731939i
$778$		0			0
$779$	1.68510	+	6.28889i	0.0603751	+	0.225323i
$780$		0			0
$781$	−38.7640	+	22.3804i	−1.38708	+	0.800833i
$782$		0			0
$783$	−15.0232	+	4.49907i	−0.536886	+	0.160784i
$784$		0			0
$785$	35.4600	+	35.4600i	1.26562	+	1.26562i
$786$		0			0
$787$	31.5199			1.12356			0.561782	−	0.827285i	$-0.310116\pi$
$787$	31.5199			1.12356			0.561782	+	0.827285i	$0.310116\pi$
$788$		0			0
$789$	−0.711198	−	0.118284i	−0.0253193	−	0.00421102i
$790$		0			0
$791$	4.26876	−	4.26876i	0.151780	−	0.151780i
$792$		0			0
$793$	−2.58740	+	4.48152i	−0.0918814	+	0.159143i
$794$		0			0
$795$	0.00603992	+	0.0620773i	0.000214214	+	0.00220166i
$796$		0			0
$797$	1.72799	+	6.44896i	0.0612087	+	0.228434i	0.989754	−	0.142786i	$-0.0456062\pi$
$797$	1.72799	+	6.44896i	0.0612087	+	0.228434i	−0.928545	+	0.371220i	$0.878940\pi$
$798$		0			0
$799$	3.92322	+	14.6417i	0.138794	+	0.517985i
$800$		0			0
$801$	0.742574	−	0.364015i	0.0262376	−	0.0128618i
$802$		0			0
$803$			27.3463i			0.965029i
$804$		0			0
$805$	−32.4107	−	18.7123i	−1.14233	−	0.659524i
$806$		0			0
$807$	−20.9672	−	17.2489i	−0.738081	−	0.607190i
$808$		0			0
$809$	7.72620	+	2.07023i	0.271639	+	0.0727854i	0.392067	−	0.919937i	$-0.371760\pi$
$809$	7.72620	+	2.07023i	0.271639	+	0.0727854i	−0.120428	+	0.992722i	$0.538427\pi$
$810$		0			0
$811$	9.92137	+	17.1843i	0.348386	+	0.603423i	0.985963	−	0.166964i	$-0.0533964\pi$
$811$	9.92137	+	17.1843i	0.348386	+	0.603423i	−0.637577	+	0.770387i	$0.720063\pi$
$812$		0			0
$813$	4.65973	+	12.4252i	0.163424	+	0.435770i
$814$		0			0
$815$			25.4099i			0.890069i
$816$		0			0
$817$	4.87610	−	2.81522i	0.170593	−	0.0984921i
$818$		0			0
$819$	17.7063	−	8.67975i	0.618708	−	0.303295i
$820$		0			0
$821$	12.2606	−	7.07868i	0.427899	−	0.247048i	−0.270552	−	0.962705i	$-0.587206\pi$
$821$	12.2606	−	7.07868i	0.427899	−	0.247048i	0.698451	+	0.715658i	$0.253873\pi$
$822$		0			0
$823$	−7.03250	+	12.1807i	−0.245138	+	0.424591i	−0.962170	−	0.272449i	$-0.912166\pi$
$823$	−7.03250	+	12.1807i	−0.245138	+	0.424591i	0.717033	+	0.697040i	$0.245500\pi$
$824$		0			0
$825$	−7.27481	+	2.72822i	−0.253276	+	0.0949844i
$826$		0			0
$827$	2.42928	−	9.06620i	0.0844744	−	0.315263i	−0.910740	−	0.412981i	$-0.864488\pi$
$827$	2.42928	−	9.06620i	0.0844744	−	0.315263i	0.995214	+	0.0977180i	$0.0311543\pi$
$828$		0			0
$829$	−43.1854	+	11.5715i	−1.49989	+	0.401894i	−0.913063	−	0.407818i	$-0.866290\pi$
$829$	−43.1854	+	11.5715i	−1.49989	+	0.401894i	−0.586827	+	0.809713i	$0.699623\pi$
$830$		0			0
$831$	−21.0125	−	29.3963i	−0.728915	−	1.01975i
$832$		0			0
$833$	−1.08975	+	4.06701i	−0.0377576	+	0.140913i
$834$		0			0
$835$	−43.6520	−	25.2025i	−1.51064	−	0.872168i
$836$		0			0
$837$	−1.23289	−	4.11686i	−0.0426151	−	0.142300i
$838$		0			0
$839$	−1.90898	+	3.30645i	−0.0659054	+	0.114151i	−0.897095	−	0.441837i	$-0.854327\pi$
$839$	−1.90898	+	3.30645i	−0.0659054	+	0.114151i	0.831190	+	0.555989i	$0.187660\pi$
$840$		0			0
$841$			19.8912i			0.685902i
$842$		0			0
$843$	−9.76102	+	21.4754i	−0.336187	+	0.739652i
$844$		0			0
$845$	4.98270	−	4.98270i	0.171410	−	0.171410i
$846$		0			0
$847$	−2.79615	−	4.84307i	−0.0960768	−	0.166410i
$848$		0			0
$849$	−21.5454	−	30.1418i	−0.739435	−	1.03446i
$850$		0			0
$851$	12.0389	−	41.5830i	0.412690	−	1.42545i
$852$		0			0
$853$	37.4976	−	10.0475i	1.28389	−	0.344018i	0.448556	−	0.893755i	$-0.351939\pi$
$853$	37.4976	−	10.0475i	1.28389	−	0.344018i	0.835338	+	0.549737i	$0.185272\pi$
$854$		0			0
$855$	−5.87017	−	2.00816i	−0.200756	−	0.0686776i
$856$		0			0
$857$	−36.8816	−	36.8816i	−1.25985	−	1.25985i	−0.951163	−	0.308688i	$-0.900110\pi$
$857$	−36.8816	−	36.8816i	−1.25985	−	1.25985i	−0.308688	−	0.951163i	$-0.599890\pi$
$858$		0			0
$859$	33.8361	−	33.8361i	1.15447	−	1.15447i	0.168828	−	0.985646i	$-0.446002\pi$
$859$	33.8361	−	33.8361i	1.15447	−	1.15447i	0.985646	−	0.168828i	$-0.0539982\pi$
$860$		0			0
$861$	−10.0688	−	26.8485i	−0.343144	−	0.914993i
$862$		0			0
$863$	−13.6328	−	7.87091i	−0.464067	−	0.267929i	0.249686	−	0.968327i	$-0.419673\pi$
$863$	−13.6328	−	7.87091i	−0.464067	−	0.267929i	−0.713753	+	0.700398i	$0.753006\pi$
$864$		0			0
$865$	−2.14989	−	2.14989i	−0.0730984	−	0.0730984i
$866$		0			0
$867$	−4.18095	+	25.1385i	−0.141992	+	0.853749i
$868$		0			0
$869$	−16.6563	−	4.46306i	−0.565028	−	0.151399i
$870$		0			0
$871$	−43.9389	+	11.7734i	−1.48881	+	0.398926i
$872$		0			0
$873$	−4.70813	−	3.16201i	−0.159346	−	0.107018i
$874$		0			0
$875$	−17.4768	−	4.68289i	−0.590823	−	0.158311i
$876$		0			0
$877$	13.0731			0.441448			0.220724	−	0.975336i	$-0.429158\pi$
$877$	13.0731			0.441448			0.220724	+	0.975336i	$0.429158\pi$
$878$		0			0
$879$	2.98017	−	17.9187i	0.100519	−	0.604382i
$880$		0			0
$881$	10.5047	+	18.1947i	0.353912	+	0.612994i	0.986931	−	0.161143i	$-0.0515179\pi$
$881$	10.5047	+	18.1947i	0.353912	+	0.612994i	−0.633019	+	0.774136i	$0.718185\pi$
$882$		0			0
$883$	−11.0370	+	41.1908i	−0.371426	+	1.38618i	0.487071	+	0.873362i	$0.338065\pi$
$883$	−11.0370	+	41.1908i	−0.371426	+	1.38618i	−0.858497	+	0.512818i	$0.828601\pi$
$884$		0			0
$885$	13.5394	+	11.1383i	0.455122	+	0.374411i
$886$		0			0
$887$	26.8301			0.900867			0.450434	−	0.892810i	$-0.351269\pi$
$887$	26.8301			0.900867			0.450434	+	0.892810i	$0.351269\pi$
$888$		0			0
$889$	−25.7753			−0.864475
$890$		0			0
$891$	−23.9675	+	9.79502i	−0.802942	+	0.328146i
$892$		0			0
$893$	−2.09485	+	7.81810i	−0.0701016	+	0.261623i
$894$		0			0
$895$	−10.9095	−	18.8959i	−0.364665	−	0.631619i
$896$		0			0
$897$	38.9279	+	6.47435i	1.29977	+	0.216172i
$898$		0			0
$899$	2.49612			0.0832504
$900$		0			0
$901$	−0.0205380	−	0.00550315i	−0.000684221	−	0.000183337i
$902$		0			0
$903$	−20.1736	+	14.4201i	−0.671334	+	0.479870i
$904$		0			0
$905$	32.8168	−	8.79324i	1.09087	−	0.292297i
$906$		0			0
$907$	−38.8092	−	10.3989i	−1.28864	−	0.345290i	−0.451495	−	0.892273i	$-0.649109\pi$
$907$	−38.8092	−	10.3989i	−1.28864	−	0.345290i	−0.837143	+	0.546984i	$0.815776\pi$
$908$		0			0
$909$	−9.65893	−	49.1665i	−0.320367	−	1.63075i
$910$		0			0
$911$	−14.4690	−	14.4690i	−0.479379	−	0.479379i	0.425554	−	0.904933i	$-0.360079\pi$
$911$	−14.4690	−	14.4690i	−0.479379	−	0.479379i	−0.904933	+	0.425554i	$0.860079\pi$
$912$		0			0
$913$	−14.9062	−	8.60610i	−0.493323	−	0.284820i
$914$		0			0
$915$	−6.71390	+	2.51787i	−0.221955	+	0.0832381i
$916$		0			0
$917$	29.8419	−	29.8419i	0.985465	−	0.985465i
$918$		0			0
$919$	27.5170	+	27.5170i	0.907703	+	0.907703i	0.996086	−	0.0883840i	$-0.0281702\pi$
$919$	27.5170	+	27.5170i	0.907703	+	0.907703i	−0.0883840	+	0.996086i	$0.528170\pi$
$920$		0			0
$921$	−15.5955	−	12.8298i	−0.513889	−	0.422756i
$922$		0			0
$923$	−48.1121	+	12.8916i	−1.58363	+	0.424332i
$924$		0			0
$925$	−0.189788	+	9.48266i	−0.00624020	+	0.311788i
$926$		0			0
$927$	−11.1186	+	16.5552i	−0.365183	+	0.543746i
$928$		0			0
$929$	−28.3785	−	49.1530i	−0.931068	−	1.61266i	−0.781500	−	0.623905i	$-0.785545\pi$
$929$	−28.3785	−	49.1530i	−0.931068	−	1.61266i	−0.149568	−	0.988751i	$-0.547788\pi$
$930$		0			0
$931$	−1.58974	+	1.58974i	−0.0521017	+	0.0521017i
$932$		0			0
$933$	−0.173131	−	0.0786917i	−0.00566806	−	0.00257625i
$934$		0			0
$935$		−	11.1422i		−	0.364388i
$936$		0			0
$937$	4.87283	−	8.43999i	0.159188	−	0.275723i	−0.775388	−	0.631485i	$-0.782446\pi$
$937$	4.87283	−	8.43999i	0.159188	−	0.275723i	0.934576	+	0.355763i	$0.115779\pi$
$938$		0			0
$939$	41.0827	+	18.6730i	1.34068	+	0.609369i
$940$		0			0
$941$	−12.6302	−	7.29208i	−0.411734	−	0.237715i	0.279800	−	0.960058i	$-0.409732\pi$
$941$	−12.6302	−	7.29208i	−0.411734	−	0.237715i	−0.691535	+	0.722343i	$0.743065\pi$
$942$		0			0
$943$	14.8520	−	55.4284i	0.483648	−	1.80500i
$944$		0			0
$945$	26.5882	+	6.29909i	0.864914	+	0.204909i
$946$		0			0
$947$	−28.3632	+	7.59989i	−0.921679	+	0.246963i	−0.688303	−	0.725423i	$-0.741644\pi$
$947$	−28.3632	+	7.59989i	−0.921679	+	0.246963i	−0.233376	+	0.972387i	$0.574977\pi$
$948$		0			0
$949$	−7.87604	+	29.3938i	−0.255667	+	0.954162i
$950$		0			0
$951$	1.94119	+	5.17620i	0.0629475	+	0.167850i
$952$		0			0
$953$	15.9221	−	27.5778i	0.515766	−	0.893333i	−0.484067	−	0.875031i	$-0.660841\pi$
$953$	15.9221	−	27.5778i	0.515766	−	0.893333i	0.999833	−	0.0183017i	$-0.00582593\pi$
$954$		0			0
$955$	−46.2549	+	26.7053i	−1.49677	+	0.864162i
$956$		0			0
$957$	−1.45634	−	14.9681i	−0.0470769	−	0.483848i
$958$		0			0
$959$	19.9656	−	11.5272i	0.644724	−	0.372232i
$960$		0			0
$961$		−	30.3160i		−	0.977935i
$962$		0			0
$963$	−29.1302	−	33.3756i	−0.938707	−	1.07551i
$964$		0			0
$965$	29.3178	+	50.7800i	0.943775	+	1.63467i
$966$		0			0
$967$	27.4652	+	7.35927i	0.883221	+	0.236658i	0.671796	−	0.740736i	$-0.265523\pi$
$967$	27.4652	+	7.35927i	0.883221	+	0.236658i	0.211425	+	0.977394i	$0.432190\pi$
$968$		0			0
$969$	1.34370	−	1.63336i	0.0431660	−	0.0524711i
$970$		0			0
$971$	−24.9854	−	14.4253i	−0.801820	−	0.462931i	0.0422873	−	0.999105i	$-0.486536\pi$
$971$	−24.9854	−	14.4253i	−0.801820	−	0.462931i	−0.844107	+	0.536175i	$0.819869\pi$
$972$		0			0
$973$		−	3.10480i		−	0.0995352i
$974$		0			0
$975$	−8.60525	+	0.837263i	−0.275589	+	0.0268139i
$976$		0			0
$977$	−8.80958	−	32.8778i	−0.281844	−	1.05185i	−0.951115	−	0.308837i	$-0.900060\pi$
$977$	−8.80958	−	32.8778i	−0.281844	−	1.05185i	0.669272	−	0.743018i	$-0.266606\pi$
$978$		0			0
$979$	0.205257	+	0.766029i	0.00656004	+	0.0244824i
$980$		0			0
$981$	−19.6294	+	9.62249i	−0.626720	+	0.307222i
$982$		0			0
$983$	15.7517	−	27.2827i	0.502401	−	0.870184i	−0.497595	−	0.867409i	$-0.665783\pi$
$983$	15.7517	−	27.2827i	0.502401	−	0.870184i	0.999996	−	0.00277464i	$-0.000883198\pi$
$984$		0			0
$985$	−6.04860	+	6.04860i	−0.192724	+	0.192724i
$986$		0			0
$987$	5.84833	−	35.1638i	0.186154	−	1.11928i
$988$		0			0
$989$	−49.6250			−1.57798
$990$		0			0
$991$	−2.59065	−	2.59065i	−0.0822946	−	0.0822946i	0.664761	−	0.747056i	$-0.268533\pi$
$991$	−2.59065	−	2.59065i	−0.0822946	−	0.0822946i	−0.747056	+	0.664761i	$0.768533\pi$
$992$		0			0
$993$	−14.0615	−	6.39125i	−0.446229	−	0.202820i
$994$		0			0
$995$	−37.7034	+	21.7681i	−1.19528	+	0.690095i
$996$		0			0
$997$	−4.00115	−	14.9325i	−0.126718	−	0.472917i	0.873177	−	0.487403i	$-0.162056\pi$
$997$	−4.00115	−	14.9325i	−0.126718	−	0.472917i	−0.999895	+	0.0144855i	$0.995389\pi$
$998$		0			0
$999$	0.289629	+	31.6056i	0.00916345	+	0.999958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	444.2.w.c.125.7	✓	40
3.2	odd	2	inner	444.2.w.c.125.10	yes	40
37.8	odd	12	inner	444.2.w.c.341.10	yes	40
111.8	even	12	inner	444.2.w.c.341.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
444.2.w.c.125.7	✓	40	1.1	even	1	trivial
444.2.w.c.125.10	yes	40	3.2	odd	2	inner
444.2.w.c.341.7	yes	40	111.8	even	12	inner
444.2.w.c.341.10	yes	40	37.8	odd	12	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10038 - 1.33759i) q^{3} +(-0.662862 + 2.47384i) q^{5} +(1.02662 + 1.77815i) q^{7} +(-0.578306 - 2.94373i) q^{9} +2.87686 q^{11} +(3.09226 + 0.828569i) q^{13} +(2.57958 + 3.60881i) q^{15} +(-1.46072 + 0.391399i) q^{17} +(-0.779971 - 0.208993i) q^{19} +(3.50811 + 0.583457i) q^{21} +(5.03244 + 5.03244i) q^{23} +(-1.35035 - 0.779626i) q^{25} +(-4.57387 - 2.46570i) q^{27} +(2.13411 - 2.13411i) q^{29} +(0.584817 + 0.584817i) q^{31} +(3.16566 - 3.84807i) q^{33} +(-5.07936 + 1.36101i) q^{35} +(-2.93536 - 5.32763i) q^{37} +(4.51097 - 3.22444i) q^{39} +(-4.03149 - 6.98275i) q^{41} +(-4.93052 + 4.93052i) q^{43} +(7.66565 + 0.520655i) q^{45} -10.0236i q^{47} +(1.39212 - 2.41122i) q^{49} +(-1.08382 + 2.38454i) q^{51} +(0.0121765 + 0.00703009i) q^{53} +(-1.90696 + 7.11689i) q^{55} +(-1.13782 + 0.813311i) q^{57} +(3.81761 - 1.02293i) q^{59} +(-0.418368 + 1.56137i) q^{61} +(4.64070 - 4.05040i) q^{63} +(-4.09949 + 7.10052i) q^{65} +(-12.3056 + 7.10465i) q^{67} +(12.2690 - 1.19373i) q^{69} +(-13.4744 + 7.77944i) q^{71} +9.50559i q^{73} +(-2.52873 + 0.948331i) q^{75} +(2.95343 + 5.11550i) q^{77} +(-5.78976 - 1.55136i) q^{79} +(-8.33112 + 3.40476i) q^{81} +(-5.18141 - 2.99149i) q^{83} -3.87303i q^{85} +(-0.506226 - 5.20291i) q^{87} +(0.0713475 + 0.266272i) q^{89} +(1.70124 + 6.34913i) q^{91} +(1.42577 - 0.138723i) q^{93} +(1.03403 - 1.79099i) q^{95} +(1.33676 - 1.33676i) q^{97} +(-1.66371 - 8.46872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 10 q^{9} - 24 q^{19} - 18 q^{21} + 32 q^{31} - 44 q^{37} + 62 q^{39} - 4 q^{43} - 54 q^{45} + 24 q^{49} + 14 q^{51} + 20 q^{55} + 34 q^{57} + 36 q^{61} - 36 q^{63} + 12 q^{67} - 50 q^{69} - 20 q^{75}+ \cdots - 12 q^{99}+O(q^{100}) \) 40 * q - 10 * q^9 - 24 * q^19 - 18 * q^21 + 32 * q^31 - 44 * q^37 + 62 * q^39 - 4 * q^43 - 54 * q^45 + 24 * q^49 + 14 * q^51 + 20 * q^55 + 34 * q^57 + 36 * q^61 - 36 * q^63 + 12 * q^67 - 50 * q^69 - 20 * q^75 + 8 * q^79 + 10 * q^81 - 32 * q^87 + 20 * q^91 - 30 * q^93 + 52 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more