LMFDB - Embedded newform 189.2.p.d.80.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(26,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("189.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
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} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 $ x^12 - 9x^10 + 59x^8 - 180x^6 + 403x^4 - 198*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			80.4
Root			$-1.65604 + 0.956115i$ of defining polynomial
Character	$\chi$	$=$	189.80
Dual form			189.2.p.d.26.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.568650 - 0.328310i) q^{2} +(-0.784425 + 1.35866i) q^{4} +(1.65604 + 2.86834i) q^{5} +(-2.58392 - 0.568650i) q^{7} +2.34338i q^{8} +O(q^{10})$	\(q+(0.568650 - 0.328310i) q^{2} +(-0.784425 + 1.35866i) q^{4} +(1.65604 + 2.86834i) q^{5} +(-2.58392 - 0.568650i) q^{7} +2.34338i q^{8} +(1.88341 + 1.08739i) q^{10} +(2.02943 + 1.17169i) q^{11} -1.58003i q^{13} +(-1.65604 + 0.524964i) q^{14} +(-0.799494 - 1.38476i) q^{16} +(0.568650 - 0.984931i) q^{17} +(3.85327 - 2.22469i) q^{19} -5.19615 q^{20} +1.53871 q^{22} +(8.13484 - 4.69665i) q^{23} +(-2.98493 + 5.17005i) q^{25} +(-0.518739 - 0.898482i) q^{26} +(2.79949 - 3.06461i) q^{28} +3.65662i q^{29} +(-6.33821 - 3.65936i) q^{31} +(-4.96812 - 2.86834i) q^{32} -0.746774i q^{34} +(-2.64799 - 8.35327i) q^{35} +(2.58392 + 4.47548i) q^{37} +(1.46078 - 2.53014i) q^{38} +(-6.72162 + 3.88073i) q^{40} -9.64553 q^{41} -2.16784 q^{43} +(-3.18386 + 1.83821i) q^{44} +(3.08392 - 5.34150i) q^{46} +(-2.79334 - 4.83821i) q^{47} +(6.35327 + 2.93869i) q^{49} +3.91993i q^{50} +(2.14673 + 1.23941i) q^{52} +(8.70349 + 5.02496i) q^{53} +7.76146i q^{55} +(1.33256 - 6.05510i) q^{56} +(1.20051 + 2.07934i) q^{58} +(1.08739 - 1.88341i) q^{59} +(3.46986 - 2.00333i) q^{61} -4.80563 q^{62} -0.568850 q^{64} +(4.53206 - 2.61659i) q^{65} +(5.38341 - 9.32435i) q^{67} +(0.892126 + 1.54521i) q^{68} +(-4.24824 - 3.88073i) q^{70} +6.39331i q^{71} +(-9.25176 - 5.34150i) q^{73} +(2.93869 + 1.69665i) q^{74} +6.98041i q^{76} +(-4.57759 - 4.18158i) q^{77} +(-0.616587 - 1.06796i) q^{79} +(2.64799 - 4.58645i) q^{80} +(-5.48493 + 3.16673i) q^{82} +1.03748 q^{83} +3.76683 q^{85} +(-1.23274 + 0.711723i) q^{86} +(-2.74571 + 4.75572i) q^{88} +(3.73538 + 6.46986i) q^{89} +(-0.898482 + 4.08266i) q^{91} +14.7367i q^{92} +(-3.17686 - 1.83416i) q^{94} +(12.7623 + 7.36834i) q^{95} -13.5524i q^{97} +(4.57759 - 0.414758i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} - 8 q^{7}+O(q^{10}) $ 12 * q + 8 * q^4 - 8 * q^7	$ 12 q + 8 q^{4} - 8 q^{7} - 6 q^{10} - 4 q^{16} - 6 q^{19} - 40 q^{22} - 24 q^{25} + 28 q^{28} - 12 q^{31} + 8 q^{37} + 12 q^{40} + 20 q^{43} + 14 q^{46} + 24 q^{49} + 78 q^{52} + 20 q^{58} + 18 q^{61} + 28 q^{64} + 36 q^{67} - 120 q^{70} - 42 q^{73} - 36 q^{79} - 54 q^{82} - 12 q^{85} - 74 q^{88} + 6 q^{91} - 114 q^{94}+O(q^{100}) $ 12 * q + 8 * q^4 - 8 * q^7 - 6 * q^10 - 4 * q^16 - 6 * q^19 - 40 * q^22 - 24 * q^25 + 28 * q^28 - 12 * q^31 + 8 * q^37 + 12 * q^40 + 20 * q^43 + 14 * q^46 + 24 * q^49 + 78 * q^52 + 20 * q^58 + 18 * q^61 + 28 * q^64 + 36 * q^67 - 120 * q^70 - 42 * q^73 - 36 * q^79 - 54 * q^82 - 12 * q^85 - 74 * q^88 + 6 * q^91 - 114 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.568650	−	0.328310i	0.402096	−	0.232150i	−0.285292	−	0.958441i	$-0.592091\pi$
$2$	0.568650	−	0.328310i	0.402096	−	0.232150i	0.687388	+	0.726290i	$0.258757\pi$
$3$		0			0
$3$		0			0
$4$	−0.784425	+	1.35866i	−0.392212	+	0.679332i
$5$	1.65604	+	2.86834i	0.740603	+	1.28276i	0.952221	+	0.305410i	$0.0987935\pi$
$5$	1.65604	+	2.86834i	0.740603	+	1.28276i	−0.211618	+	0.977352i	$0.567873\pi$
$6$		0			0
$7$	−2.58392	−	0.568650i	−0.976630	−	0.214929i
$7$	−2.58392	−	0.568650i	−0.976630	−	0.214929i
$8$			2.34338i			0.828510i
$9$		0			0
$10$	1.88341	+	1.08739i	0.595588	+	0.343863i
$11$	2.02943	+	1.17169i	0.611895	+	0.353278i	0.773707	−	0.633544i	$-0.218400\pi$
$11$	2.02943	+	1.17169i	0.611895	+	0.353278i	−0.161812	+	0.986822i	$0.551734\pi$
$12$		0			0
$13$		−	1.58003i		−	0.438221i	−0.975700	−	0.219110i	$-0.929685\pi$
$13$		−	1.58003i		−	0.438221i	0.975700	−	0.219110i	$-0.0703155\pi$
$14$	−1.65604	+	0.524964i	−0.442595	+	0.140303i
$15$		0			0
$16$	−0.799494	−	1.38476i	−0.199874	−	0.346191i
$17$	0.568650	−	0.984931i	0.137918	−	0.238881i	−0.788790	−	0.614662i	$-0.789292\pi$
$17$	0.568650	−	0.984931i	0.137918	−	0.238881i	0.926708	+	0.375781i	$0.122626\pi$
$18$		0			0
$19$	3.85327	−	2.22469i	0.884002	−	0.510379i	0.0120260	−	0.999928i	$-0.496172\pi$
$19$	3.85327	−	2.22469i	0.884002	−	0.510379i	0.871976	+	0.489549i	$0.162839\pi$
$20$	−5.19615			−1.16190
$21$		0			0
$22$	1.53871			0.328054
$23$	8.13484	−	4.69665i	1.69623	−	0.979320i	0.746957	−	0.664872i	$-0.231514\pi$
$23$	8.13484	−	4.69665i	1.69623	−	0.979320i	0.949275	−	0.314448i	$-0.101819\pi$
$24$		0			0
$25$	−2.98493	+	5.17005i	−0.596986	+	1.03401i
$26$	−0.518739	−	0.898482i	−0.101733	−	0.176207i
$27$		0			0
$28$	2.79949	−	3.06461i	0.529055	−	0.579158i
$29$			3.65662i			0.679017i	0.940603	+	0.339509i	$0.110261\pi$
$29$			3.65662i			0.679017i	−0.940603	+	0.339509i	$0.889739\pi$
$30$		0			0
$31$	−6.33821	−	3.65936i	−1.13838	−	0.657241i	−0.192347	−	0.981327i	$-0.561610\pi$
$31$	−6.33821	−	3.65936i	−1.13838	−	0.657241i	−0.946028	+	0.324086i	$0.894943\pi$
$32$	−4.96812	−	2.86834i	−0.878247	−	0.507056i
$33$		0			0
$34$		−	0.746774i		−	0.128071i
$35$	−2.64799	−	8.35327i	−0.447592	−	1.41196i
$36$		0			0
$37$	2.58392	+	4.47548i	0.424794	+	0.735764i	0.996401	−	0.0847630i	$-0.0270133\pi$
$37$	2.58392	+	4.47548i	0.424794	+	0.735764i	−0.571607	+	0.820527i	$0.693680\pi$
$38$	1.46078	−	2.53014i	0.236969	−	0.410443i
$39$		0			0
$40$	−6.72162	+	3.88073i	−1.06278	+	0.613597i
$41$	−9.64553			−1.50638			−0.753189	−	0.657804i	$-0.771486\pi$
$41$	−9.64553			−1.50638			−0.753189	+	0.657804i	$0.771486\pi$
$42$		0			0
$43$	−2.16784			−0.330592			−0.165296	−	0.986244i	$-0.552858\pi$
$43$	−2.16784			−0.330592			−0.165296	+	0.986244i	$0.552858\pi$
$44$	−3.18386	+	1.83821i	−0.479986	+	0.277120i
$45$		0			0
$46$	3.08392	−	5.34150i	0.454699	−	0.787562i
$47$	−2.79334	−	4.83821i	−0.407450	−	0.705725i	0.587153	−	0.809476i	$-0.300249\pi$
$47$	−2.79334	−	4.83821i	−0.407450	−	0.705725i	−0.994603	+	0.103751i	$0.966915\pi$
$48$		0			0
$49$	6.35327	+	2.93869i	0.907611	+	0.419813i
$50$			3.91993i			0.554362i
$51$		0			0
$52$	2.14673	+	1.23941i	0.297697	+	0.171876i
$53$	8.70349	+	5.02496i	1.19552	+	0.690232i	0.959552	−	0.281530i	$-0.0908418\pi$
$53$	8.70349	+	5.02496i	1.19552	+	0.690232i	0.235964	+	0.971762i	$0.424175\pi$
$54$		0			0
$55$			7.76146i			1.04655i
$56$	1.33256	−	6.05510i	0.178071	−	0.809147i
$57$		0			0
$58$	1.20051	+	2.07934i	0.157634	+	0.273030i
$59$	1.08739	−	1.88341i	0.141566	−	0.245200i	−0.786521	−	0.617564i	$-0.788120\pi$
$59$	1.08739	−	1.88341i	0.141566	−	0.245200i	0.928087	+	0.372365i	$0.121453\pi$
$60$		0			0
$61$	3.46986	−	2.00333i	0.444270	−	0.256500i	−0.261137	−	0.965302i	$-0.584097\pi$
$61$	3.46986	−	2.00333i	0.444270	−	0.256500i	0.705407	+	0.708802i	$0.250764\pi$
$62$	−4.80563			−0.610315
$63$		0			0
$64$	−0.568850			−0.0711062
$65$	4.53206	−	2.61659i	0.562133	−	0.324548i
$66$		0			0
$67$	5.38341	−	9.32435i	0.657689	−	1.13915i	−0.323524	−	0.946220i	$-0.604868\pi$
$67$	5.38341	−	9.32435i	0.657689	−	1.13915i	0.981213	−	0.192930i	$-0.0617990\pi$
$68$	0.892126	+	1.54521i	0.108186	+	0.187384i
$69$		0			0
$70$	−4.24824	−	3.88073i	−0.507762	−	0.463836i
$71$			6.39331i			0.758746i	0.925244	+	0.379373i	$0.123860\pi$
$71$			6.39331i			0.758746i	−0.925244	+	0.379373i	$0.876140\pi$
$72$		0			0
$73$	−9.25176	−	5.34150i	−1.08284	−	0.625176i	−0.151176	−	0.988507i	$-0.548306\pi$
$73$	−9.25176	−	5.34150i	−1.08284	−	0.625176i	−0.931660	+	0.363331i	$0.881639\pi$
$74$	2.93869	+	1.69665i	0.341616	+	0.197232i
$75$		0			0
$76$			6.98041i			0.800707i
$77$	−4.57759	−	4.18158i	−0.521665	−	0.476536i
$78$		0			0
$79$	−0.616587	−	1.06796i	−0.0693714	−	0.120155i	0.829253	−	0.558873i	$-0.188766\pi$
$79$	−0.616587	−	1.06796i	−0.0693714	−	0.120155i	−0.898625	+	0.438718i	$0.855433\pi$
$80$	2.64799	−	4.58645i	0.296054	−	0.512780i
$81$		0			0
$82$	−5.48493	+	3.16673i	−0.605709	+	0.349706i
$83$	1.03748			0.113878			0.0569390	−	0.998378i	$-0.481866\pi$
$83$	1.03748			0.113878			0.0569390	+	0.998378i	$0.481866\pi$
$84$		0			0
$85$	3.76683			0.408570
$86$	−1.23274	+	0.711723i	−0.132930	+	0.0767471i
$87$		0			0
$88$	−2.74571	+	4.75572i	−0.292694	+	0.506961i
$89$	3.73538	+	6.46986i	0.395949	+	0.685804i	0.993222	−	0.116234i	$-0.0370823\pi$
$89$	3.73538	+	6.46986i	0.395949	+	0.685804i	−0.597273	+	0.802038i	$0.703749\pi$
$90$		0			0
$91$	−0.898482	+	4.08266i	−0.0941866	+	0.427979i
$92$			14.7367i			1.53641i
$93$		0			0
$94$	−3.17686	−	1.83416i	−0.327669	−	0.189180i
$95$	12.7623	+	7.36834i	1.30939	+	0.755976i
$96$		0			0
$97$		−	13.5524i		−	1.37603i	−0.725695	−	0.688017i	$-0.758482\pi$
$97$		−	13.5524i		−	1.37603i	0.725695	−	0.688017i	$-0.241518\pi$
$98$	4.57759	−	0.414758i	0.462407	−	0.0418969i
$99$		0			0
$100$	−4.68291	−	8.11103i	−0.468291	−	0.811103i
$101$	−6.85219	+	11.8683i	−0.681819	+	1.18094i	0.292607	+	0.956233i	$0.405477\pi$
$101$	−6.85219	+	11.8683i	−0.681819	+	1.18094i	−0.974425	+	0.224711i	$0.927856\pi$
$102$		0			0
$103$	4.23669	−	2.44605i	0.417453	−	0.241017i	−0.276534	−	0.961004i	$-0.589186\pi$
$103$	4.23669	−	2.44605i	0.417453	−	0.241017i	0.693987	+	0.719987i	$0.255852\pi$
$104$	3.70260			0.363070
$105$		0			0
$106$	6.59899			0.640950
$107$	2.12487	−	1.22679i	0.205419	−	0.118599i	−0.393762	−	0.919213i	$-0.628827\pi$
$107$	2.12487	−	1.22679i	0.205419	−	0.118599i	0.599180	+	0.800614i	$0.295493\pi$
$108$		0			0
$109$	−2.16784	+	3.75481i	−0.207641	+	0.359645i	−0.950971	−	0.309280i	$-0.899912\pi$
$109$	−2.16784	+	3.75481i	−0.207641	+	0.359645i	0.743330	+	0.668925i	$0.233245\pi$
$110$	2.54817	+	4.41355i	0.242958	+	0.420816i
$111$		0			0
$112$	1.27838	+	4.03275i	0.120796	+	0.381059i
$113$			7.16013i			0.673569i	0.941582	+	0.336784i	$0.109339\pi$
$113$			7.16013i			0.673569i	−0.941582	+	0.336784i	$0.890661\pi$
$114$		0			0
$115$	26.9432	+	15.5557i	2.51247	+	1.45058i
$116$	−4.96812	−	2.86834i	−0.461278	−	0.266319i
$117$		0			0
$118$		−	1.42800i		−	0.131458i
$119$	−2.02943	+	2.22162i	−0.186037	+	0.203655i
$120$		0			0
$121$	−2.75429	−	4.77056i	−0.250390	−	0.433688i
$122$	1.31542	−	2.27838i	0.119093	−	0.206275i
$123$		0			0
$124$	9.94369	−	5.74099i	0.892970	−	0.515556i
$125$	−3.21226			−0.287313
$126$		0			0
$127$	−17.7065			−1.57120			−0.785601	−	0.618733i	$-0.787646\pi$
$127$	−17.7065			−1.57120			−0.785601	+	0.618733i	$0.787646\pi$
$128$	9.61276	−	5.54993i	0.849656	−	0.490549i
$129$		0			0
$130$	1.71810	−	2.97584i	0.150688	−	0.260999i
$131$	−6.80228	−	11.7819i	−0.594318	−	1.02939i	−0.993643	−	0.112579i	$-0.964089\pi$
$131$	−6.80228	−	11.7819i	−0.594318	−	1.02939i	0.399325	−	0.916810i	$-0.369245\pi$
$132$		0			0
$133$	−11.2216	+	3.55725i	−0.973038	+	0.308453i
$134$		−	7.06972i		−	0.610731i
$135$		0			0
$136$	2.30807	+	1.33256i	0.197915	+	0.114266i
$137$	−8.79893	−	5.08007i	−0.751744	−	0.434019i	0.0745799	−	0.997215i	$-0.476238\pi$
$137$	−8.79893	−	5.08007i	−0.751744	−	0.434019i	−0.826324	+	0.563196i	$0.809572\pi$
$138$		0			0
$139$			3.85463i			0.326945i	0.986548	+	0.163473i	$0.0522695\pi$
$139$			3.85463i			0.326945i	−0.986548	+	0.163473i	$0.947730\pi$
$140$	13.4264	+	2.95479i	1.13474	+	0.249725i
$141$		0			0
$142$	2.09899	+	3.63555i	0.176143	+	0.305089i
$143$	1.85130	−	3.20655i	0.154814	−	0.268145i
$144$		0			0
$145$	−10.4884	+	6.05551i	−0.871018	+	0.502882i
$146$	−7.01468			−0.580539
$147$		0			0
$148$	−8.10756			−0.666437
$149$	−4.39947	+	2.54003i	−0.360418	+	0.208088i	−0.669264	−	0.743024i	$-0.733391\pi$
$149$	−4.39947	+	2.54003i	−0.360418	+	0.208088i	0.308846	+	0.951112i	$0.400057\pi$
$150$		0			0
$151$	−9.15277	+	15.8531i	−0.744842	+	1.29010i	0.205427	+	0.978672i	$0.434142\pi$
$151$	−9.15277	+	15.8531i	−0.744842	+	1.29010i	−0.950269	+	0.311431i	$0.899192\pi$
$152$	5.21329	+	9.02968i	0.422854	+	0.732404i
$153$		0			0
$154$	−3.97590	−	0.874988i	−0.320387	−	0.0705085i
$155$		−	24.2402i		−	1.94702i
$156$		0			0
$157$	2.86834	+	1.65604i	0.228919	+	0.132166i	0.610073	−	0.792345i	$-0.291140\pi$
$157$	2.86834	+	1.65604i	0.228919	+	0.132166i	−0.381154	+	0.924511i	$0.624473\pi$
$158$	−0.701244	−	0.404864i	−0.0557880	−	0.0322092i
$159$		0			0
$160$		−	19.0004i		−	1.50211i
$161$	−23.6905	+	7.50989i	−1.86708	+	0.591863i
$162$		0			0
$163$	1.14673	+	1.98619i	0.0898185	+	0.155570i	0.907434	−	0.420194i	$-0.138038\pi$
$163$	1.14673	+	1.98619i	0.0898185	+	0.155570i	−0.817616	+	0.575764i	$0.804705\pi$
$164$	7.56619	−	13.1050i	0.590820	−	1.02333i
$165$		0			0
$166$	0.589962	−	0.340615i	0.0457899	−	0.0264368i
$167$	−2.66513			−0.206234			−0.103117	−	0.994669i	$-0.532882\pi$
$167$	−2.66513			−0.206234			−0.103117	+	0.994669i	$0.532882\pi$
$168$		0			0
$169$	10.5035			0.807963
$170$	2.14201	−	1.23669i	0.164284	−	0.0948496i
$171$		0			0
$172$	1.70051	−	2.94536i	0.129662	−	0.224582i
$173$	1.28265	+	2.22162i	0.0975182	+	0.168907i	0.910657	−	0.413164i	$-0.135576\pi$
$173$	1.28265	+	2.22162i	0.0975182	+	0.168907i	−0.813139	+	0.582070i	$0.802243\pi$
$174$		0			0
$175$	10.6528	−	11.6616i	0.805274	−	0.881535i
$176$		−	3.74704i		−	0.282444i
$177$		0			0
$178$	4.24824	+	2.45272i	0.318419	+	0.183839i
$179$	−11.9828	−	6.91827i	−0.895636	−	0.517096i	−0.0198545	−	0.999803i	$-0.506320\pi$
$179$	−11.9828	−	6.91827i	−0.895636	−	0.517096i	−0.875782	+	0.482707i	$0.839654\pi$
$180$		0			0
$181$		−	4.74008i		−	0.352328i	−0.984361	−	0.176164i	$-0.943631\pi$
$181$		−	4.74008i		−	0.352328i	0.984361	−	0.176164i	$-0.0563688\pi$
$182$	0.829458	+	2.61659i	0.0614835	+	0.193954i
$183$		0			0
$184$	11.0060	+	19.0630i	0.811376	+	1.40534i
$185$	−8.55814	+	14.8231i	−0.629207	+	1.08982i
$186$		0			0
$187$	2.30807	−	1.33256i	0.168783	−	0.0974466i
$188$	8.76466			0.639228
$189$		0			0
$190$	9.67641			0.702001
$191$	−7.22558	+	4.17169i	−0.522825	+	0.301853i	−0.738090	−	0.674703i	$-0.764272\pi$
$191$	−7.22558	+	4.17169i	−0.522825	+	0.301853i	0.215265	+	0.976556i	$0.430938\pi$
$192$		0			0
$193$	8.92212	−	15.4536i	0.642229	−	1.11237i	−0.342706	−	0.939443i	$-0.611343\pi$
$193$	8.92212	−	15.4536i	0.642229	−	1.11237i	0.984934	−	0.172930i	$-0.0553233\pi$
$194$	−4.44938	−	7.70655i	−0.319447	−	0.553298i
$195$		0			0
$196$	−8.97636	+	6.32678i	−0.641168	+	0.451913i
$197$		−	15.1102i		−	1.07656i	−0.842767	−	0.538279i	$-0.819075\pi$
$197$		−	15.1102i		−	1.07656i	0.842767	−	0.538279i	$-0.180925\pi$
$198$		0			0
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	0.210032	−	0.977695i	$-0.432643\pi$
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	−0.741693	+	0.670740i	$0.765977\pi$
$200$	−12.1154	−	6.99483i	−0.856688	−	0.494609i
$201$		0			0
$202$			8.99858i			0.633138i
$203$	2.07934	−	9.44841i	0.145941	−	0.663148i
$204$		0			0
$205$	−15.9734	−	27.6667i	−1.11563	−	1.93233i
$206$	1.60613	−	2.78190i	0.111904	−	0.193824i
$207$		0			0
$208$	−2.18797	+	1.26322i	−0.151708	+	0.0875887i
$209$	10.4266			0.721222
$210$		0			0
$211$	−14.5809			−1.00379			−0.501897	−	0.864928i	$-0.667364\pi$
$211$	−14.5809			−1.00379			−0.501897	+	0.864928i	$0.667364\pi$
$212$	−13.6545	+	7.88341i	−0.937793	+	0.541435i
$213$		0			0
$214$	0.805537	−	1.39523i	0.0550654	−	0.0953760i
$215$	−3.59002	−	6.21810i	−0.244838	−	0.424071i
$216$		0			0
$217$	14.2965	+	13.0597i	0.970510	+	0.886552i
$218$			2.84689i			0.192816i
$219$		0			0
$220$	−10.5452	−	6.08828i	−0.710958	−	0.410472i
$221$	−1.55622	−	0.898482i	−0.104683	−	0.0604385i
$222$		0			0
$223$			10.5832i			0.708703i	0.935112	+	0.354351i	$0.115298\pi$
$223$			10.5832i			0.708703i	−0.935112	+	0.354351i	$0.884702\pi$
$224$	11.2061	+	10.2367i	0.748741	+	0.683967i
$225$		0			0
$226$	2.35075	+	4.07161i	0.156369	+	0.270839i
$227$	−3.36199	+	5.82314i	−0.223143	+	0.386495i	−0.955761	−	0.294145i	$-0.904965\pi$
$227$	−3.36199	+	5.82314i	−0.223143	+	0.386495i	0.732618	+	0.680640i	$0.238298\pi$
$228$		0			0
$229$	−10.6201	+	6.13152i	−0.701796	+	0.405182i	−0.808016	−	0.589161i	$-0.799459\pi$
$229$	−10.6201	+	6.13152i	−0.701796	+	0.405182i	0.106220	+	0.994343i	$0.466125\pi$
$230$	20.4284			1.34701
$231$		0			0
$232$	−8.56885			−0.562573
$233$	4.87268	−	2.81324i	0.319220	−	0.184302i	−0.331825	−	0.943341i	$-0.607664\pi$
$233$	4.87268	−	2.81324i	0.319220	−	0.184302i	0.651045	+	0.759039i	$0.274331\pi$
$234$		0			0
$235$	9.25176	−	16.0245i	0.603518	−	1.04532i
$236$	1.70595	+	2.95479i	0.111048	+	0.192341i
$237$		0			0
$238$	−0.424653	+	1.92960i	−0.0275262	+	0.125078i
$239$		−	15.9595i		−	1.03234i	−0.856488	−	0.516168i	$-0.827358\pi$
$239$		−	15.9595i		−	1.03234i	0.856488	−	0.516168i	$-0.172642\pi$
$240$		0			0
$241$	−3.97338	−	2.29403i	−0.255948	−	0.147771i	0.366537	−	0.930403i	$-0.380543\pi$
$241$	−3.97338	−	2.29403i	−0.255948	−	0.147771i	−0.622485	+	0.782632i	$0.713877\pi$
$242$	−3.13245	−	1.80852i	−0.201361	−	0.116256i
$243$		0			0
$244$			6.28583i			0.402409i
$245$	2.09209	+	23.0900i	0.133659	+	1.47516i
$246$		0			0
$247$	−3.51507	−	6.08828i	−0.223659	−	0.387388i
$248$	8.57528	−	14.8528i	0.544531	−	0.943155i
$249$		0			0
$250$	−1.82665	+	1.05462i	−0.115527	+	0.0666998i
$251$	13.8042			0.871314			0.435657	−	0.900113i	$-0.356516\pi$
$251$	13.8042			0.871314			0.435657	+	0.900113i	$0.356516\pi$
$252$		0			0
$253$	22.0121			1.38389
$254$	−10.0688	+	5.81324i	−0.631774	+	0.364755i
$255$		0			0
$256$	4.21305	−	7.29721i	0.263315	−	0.456076i
$257$	4.48215	+	7.76331i	0.279589	+	0.484262i	0.971283	−	0.237929i	$-0.0764685\pi$
$257$	4.48215	+	7.76331i	0.279589	+	0.484262i	−0.691694	+	0.722191i	$0.743135\pi$
$258$		0			0
$259$	−4.13166	−	13.0336i	−0.256729	−	0.809870i
$260$			8.21006i			0.509166i
$261$		0			0
$262$	−7.73623	−	4.46652i	−0.477946	−	0.275942i
$263$	24.7280	+	14.2767i	1.52479	+	0.880340i	0.999568	+	0.0293774i	$0.00935247\pi$
$263$	24.7280	+	14.2767i	1.52479	+	0.880340i	0.525226	+	0.850963i	$0.323981\pi$
$264$		0			0
$265$			33.2861i			2.04475i
$266$	−5.21329	+	5.70700i	−0.319647	+	0.349919i
$267$		0			0
$268$	8.44577	+	14.6285i	0.515907	+	0.893578i
$269$	−11.9657	+	20.7251i	−0.729559	+	1.26363i	0.227510	+	0.973776i	$0.426941\pi$
$269$	−11.9657	+	20.7251i	−0.729559	+	1.26363i	−0.957070	+	0.289858i	$0.906392\pi$
$270$		0			0
$271$	12.6467	−	7.30159i	0.768234	−	0.443540i	−0.0640103	−	0.997949i	$-0.520389\pi$
$271$	12.6467	−	7.30159i	0.768234	−	0.443540i	0.832244	+	0.554409i	$0.187056\pi$
$272$	−1.81853			−0.110265
$273$		0			0
$274$	−6.67135			−0.403031
$275$	−12.1154	+	6.99483i	−0.730586	+	0.421804i
$276$		0			0
$277$	−11.1915	+	19.3842i	−0.672431	+	1.16468i	0.304782	+	0.952422i	$0.401416\pi$
$277$	−11.1915	+	19.3842i	−0.672431	+	1.16468i	−0.977213	+	0.212262i	$0.931917\pi$
$278$	1.26551	+	2.19193i	0.0759005	+	0.131463i
$279$		0			0
$280$	19.5749	−	6.20524i	1.16982	−	0.370834i
$281$		−	11.6067i		−	0.692397i	−0.938161	−	0.346199i	$-0.887472\pi$
$281$		−	11.6067i		−	0.692397i	0.938161	−	0.346199i	$-0.112528\pi$
$282$		0			0
$283$	−12.9849	−	7.49685i	−0.771874	−	0.445642i	0.0616687	−	0.998097i	$-0.480358\pi$
$283$	−12.9849	−	7.49685i	−0.771874	−	0.445642i	−0.833543	+	0.552455i	$0.813691\pi$
$284$	−8.68635	−	5.01507i	−0.515440	−	0.297590i
$285$		0			0
$286$		−	2.43121i		−	0.143760i
$287$	24.9233	+	5.48493i	1.47117	+	0.323765i
$288$		0			0
$289$	7.85327	+	13.6023i	0.461957	+	0.800134i
$290$	−3.97617	+	6.88693i	−0.233489	+	0.404414i
$291$		0			0
$292$	14.5146	−	8.38002i	0.849404	−	0.490403i
$293$	16.3352			0.954314			0.477157	−	0.878818i	$-0.341667\pi$
$293$	16.3352			0.954314			0.477157	+	0.878818i	$0.341667\pi$
$294$		0			0
$295$	7.20304			0.419377
$296$	−10.4877	+	6.05510i	−0.609588	+	0.351946i
$297$		0			0
$298$	−1.66784	+	2.88878i	−0.0966153	+	0.167343i
$299$	−7.42084	−	12.8533i	−0.429158	−	0.743324i
$300$		0			0
$301$	5.60152	+	1.23274i	0.322866	+	0.0710540i
$302$			12.0198i			0.691661i
$303$		0			0
$304$	−6.16134	−	3.55725i	−0.353377	−	0.204022i
$305$	11.4925	+	6.63517i	0.658056	+	0.379929i
$306$		0			0
$307$		−	3.17340i		−	0.181115i	−0.995891	−	0.0905577i	$-0.971135\pi$
$307$		−	3.17340i		−	0.181115i	0.995891	−	0.0905577i	$-0.0288650\pi$
$308$	9.27214	−	2.93927i	0.528329	−	0.167480i
$309$		0			0
$310$	−7.95831	−	13.7842i	−0.452001	−	0.782889i
$311$	−12.5671	+	21.7668i	−0.712614	+	1.23428i	0.251259	+	0.967920i	$0.419155\pi$
$311$	−12.5671	+	21.7668i	−0.712614	+	1.23428i	−0.963873	+	0.266364i	$0.914178\pi$
$312$		0			0
$313$	−16.1463	+	9.32205i	−0.912641	+	0.526914i	−0.881280	−	0.472594i	$-0.843318\pi$
$313$	−16.1463	+	9.32205i	−0.912641	+	0.526914i	−0.0313612	+	0.999508i	$0.509984\pi$
$314$	2.17478			0.122730
$315$		0			0
$316$	1.93466			0.108833
$317$	−6.91924	+	3.99483i	−0.388623	+	0.224372i	−0.681563	−	0.731759i	$-0.738700\pi$
$317$	−6.91924	+	3.99483i	−0.388623	+	0.224372i	0.292940	+	0.956131i	$0.405366\pi$
$318$		0			0
$319$	−4.28442	+	7.42084i	−0.239882	+	0.415487i
$320$	−0.942037	−	1.63166i	−0.0526615	−	0.0912124i
$321$		0			0
$322$	−11.0060	+	12.0483i	−0.613343	+	0.671428i
$323$		−	5.06028i		−	0.281561i
$324$		0			0
$325$	8.16882	+	4.71627i	0.453125	+	0.261612i
$326$	1.30417	+	0.752963i	0.0722313	+	0.0417028i
$327$		0			0
$328$		−	22.6031i		−	1.24805i
$329$	4.46652	+	14.0900i	0.246247	+	0.776805i
$330$		0			0
$331$	4.46733	+	7.73765i	0.245547	+	0.425299i	0.962285	−	0.272043i	$-0.0876992\pi$
$331$	4.46733	+	7.73765i	0.245547	+	0.425299i	−0.716738	+	0.697342i	$0.754366\pi$
$332$	−0.813824	+	1.40958i	−0.0446644	+	0.0773610i
$333$		0			0
$334$	−1.51552	+	0.874988i	−0.0829258	+	0.0478772i
$335$	35.6606			1.94835
$336$		0			0
$337$	4.24526			0.231254			0.115627	−	0.993293i	$-0.463112\pi$
$337$	4.24526			0.231254			0.115627	+	0.993293i	$0.463112\pi$
$338$	5.97282	−	3.44841i	0.324879	−	0.187569i
$339$		0			0
$340$	−2.95479	+	5.11785i	−0.160246	+	0.277554i
$341$	−8.57528	−	14.8528i	−0.464377	−	0.804325i
$342$		0			0
$343$	−14.7453	−	11.2061i	−0.796169	−	0.605074i
$344$		−	5.08007i		−	0.273899i
$345$		0			0
$346$	1.45876	+	0.842215i	0.0784234	+	0.0452778i
$347$	−2.27460	−	1.31324i	−0.122107	−	0.0704985i	0.437702	−	0.899120i	$-0.355792\pi$
$347$	−2.27460	−	1.31324i	−0.122107	−	0.0704985i	−0.559809	+	0.828621i	$0.689126\pi$
$348$		0			0
$349$		−	32.4918i		−	1.73924i	−0.493718	−	0.869622i	$-0.664363\pi$
$349$		−	32.4918i		−	1.73924i	0.493718	−	0.869622i	$-0.335637\pi$
$350$	2.22907	−	10.1288i	0.119149	−	0.541407i
$351$		0			0
$352$	−6.72162	−	11.6422i	−0.358263	−	0.620531i
$353$	11.6921	−	20.2513i	0.622307	−	1.07787i	−0.366748	−	0.930321i	$-0.619529\pi$
$353$	11.6921	−	20.2513i	0.622307	−	1.07787i	0.989055	−	0.147548i	$-0.0471380\pi$
$354$		0			0
$355$	−18.3382	+	10.5876i	−0.973291	+	0.561930i
$356$	−11.7205			−0.621185
$357$		0			0
$358$	−9.08536			−0.480176
$359$	−18.4900	+	10.6752i	−0.975865	+	0.563416i	−0.901019	−	0.433779i	$-0.857180\pi$
$359$	−18.4900	+	10.6752i	−0.975865	+	0.563416i	−0.0748455	+	0.997195i	$0.523846\pi$
$360$		0			0
$361$	0.398482	−	0.690192i	0.0209728	−	0.0363259i
$362$	−1.55622	−	2.69545i	−0.0817930	−	0.141670i
$363$		0			0
$364$	−4.84217	−	4.42328i	−0.253799	−	0.231843i
$365$		−	35.3830i		−	1.85203i
$366$		0			0
$367$	13.4432	+	7.76146i	0.701731	+	0.405145i	0.807992	−	0.589194i	$-0.200554\pi$
$367$	13.4432	+	7.76146i	0.701731	+	0.405145i	−0.106261	+	0.994338i	$0.533888\pi$
$368$	−13.0075	−	7.50989i	−0.678064	−	0.391480i
$369$		0			0
$370$			11.2389i			0.584283i
$371$	−19.6317	−	17.9333i	−1.01923	−	0.931053i
$372$		0			0
$373$	11.6764	+	20.2241i	0.604582	+	1.04717i	0.992117	+	0.125311i	$0.0399930\pi$
$373$	11.6764	+	20.2241i	0.604582	+	1.04717i	−0.387536	+	0.921855i	$0.626674\pi$
$374$	0.874988	−	1.51552i	0.0452445	−	0.0783659i
$375$		0			0
$376$	11.3378	−	6.54585i	0.584700	−	0.337577i
$377$	5.77756			0.297559
$378$		0			0
$379$	2.53871			0.130405			0.0652024	−	0.997872i	$-0.479231\pi$
$379$	2.53871			0.130405			0.0652024	+	0.997872i	$0.479231\pi$
$380$	−20.0222	+	11.5598i	−1.02712	+	0.593006i
$381$		0			0
$382$	−2.73922	+	4.74446i	−0.140151	+	0.242748i
$383$	8.10207	+	14.0332i	0.413996	+	0.717063i	0.995323	−	0.0966078i	$-0.0307992\pi$
$383$	8.10207	+	14.0332i	0.413996	+	0.717063i	−0.581326	+	0.813671i	$0.697466\pi$
$384$		0			0
$385$	4.41355	−	20.0550i	0.224935	−	1.02210i
$386$		−	11.7169i		−	0.596374i
$387$		0			0
$388$	18.4131	+	10.6308i	0.934783	+	0.539697i
$389$	−19.3410	−	11.1665i	−0.980626	−	0.566165i	−0.0781671	−	0.996940i	$-0.524907\pi$
$389$	−19.3410	−	11.1665i	−0.980626	−	0.566165i	−0.902459	+	0.430775i	$0.858240\pi$
$390$		0			0
$391$		−	10.6830i		−	0.540263i
$392$	−6.88647	+	14.8881i	−0.347819	+	0.751964i
$393$		0			0
$394$	−4.96083	−	8.59242i	−0.249923	−	0.432880i
$395$	2.04218	−	3.53717i	0.102753	−	0.177974i
$396$		0			0
$397$	28.3116	−	16.3457i	1.42092	−	0.820367i	0.424540	−	0.905409i	$-0.360436\pi$
$397$	28.3116	−	16.3457i	1.42092	−	0.820367i	0.996377	+	0.0850420i	$0.0271025\pi$
$398$	−5.68650			−0.285038
$399$		0			0
$400$	9.54574			0.477287
$401$	25.0515	−	14.4635i	1.25101	−	0.722272i	0.279701	−	0.960087i	$-0.409765\pi$
$401$	25.0515	−	14.4635i	1.25101	−	0.722272i	0.971310	+	0.237815i	$0.0764313\pi$
$402$		0			0
$403$	−5.78190	+	10.0145i	−0.288017	+	0.498860i
$404$	−10.7501	−	18.6196i	−0.534835	−	0.926362i
$405$		0			0
$406$	−1.91959	−	6.05551i	−0.0952679	−	0.300530i
$407$			12.1102i			0.600281i
$408$		0			0
$409$	0.910038	+	0.525411i	0.0449985	+	0.0259799i	0.522330	−	0.852743i	$-0.325063\pi$
$409$	0.910038	+	0.525411i	0.0449985	+	0.0259799i	−0.477332	+	0.878723i	$0.658396\pi$
$410$	−18.1665	−	10.4884i	−0.897180	−	0.517987i
$411$		0			0
$412$			7.67498i			0.378119i
$413$	−3.88073	+	4.24824i	−0.190958	+	0.209042i
$414$		0			0
$415$	1.71810	+	2.97584i	0.0843384	+	0.146078i
$416$	−4.53206	+	7.84976i	−0.222203	+	0.384866i
$417$		0			0
$418$	5.92908	−	3.42315i	0.290001	−	0.167432i
$419$	−3.12120			−0.152480			−0.0762402	−	0.997089i	$-0.524292\pi$
$419$	−3.12120			−0.152480			−0.0762402	+	0.997089i	$0.524292\pi$
$420$		0			0
$421$	−8.70655			−0.424331			−0.212166	−	0.977234i	$-0.568052\pi$
$421$	−8.70655			−0.424331			−0.212166	+	0.977234i	$0.568052\pi$
$422$	−8.29145	+	4.78707i	−0.403621	+	0.233031i
$423$		0			0
$424$	−11.7754	+	20.3956i	−0.571864	+	0.990497i
$425$	3.39476	+	5.87990i	0.164670	+	0.285217i
$426$		0			0
$427$	−10.1050	+	3.20329i	−0.489017	+	0.155018i
$428$			3.84931i			0.186063i
$429$		0			0
$430$	−4.08293	−	2.35728i	−0.196897	−	0.113678i
$431$	23.6279	+	13.6416i	1.13811	+	0.657090i	0.945963	−	0.324275i	$-0.105120\pi$
$431$	23.6279	+	13.6416i	1.13811	+	0.657090i	0.192151	+	0.981365i	$0.438454\pi$
$432$		0			0
$433$		−	12.8711i		−	0.618547i	−0.950973	−	0.309274i	$-0.899914\pi$
$433$		−	12.8711i		−	0.618547i	0.950973	−	0.309274i	$-0.100086\pi$
$434$	12.4174	+	2.73272i	0.596052	+	0.131175i
$435$		0			0
$436$	−3.40101	−	5.89073i	−0.162879	−	0.282115i
$437$	20.8972	−	36.1950i	0.999648	−	1.73144i
$438$		0			0
$439$	15.9734	−	9.22223i	0.762368	−	0.440153i	−0.0677776	−	0.997700i	$-0.521591\pi$
$439$	15.9734	−	9.22223i	0.762368	−	0.440153i	0.830145	+	0.557547i	$0.188257\pi$
$440$	−18.1880			−0.867081
$441$		0			0
$442$	−1.17992			−0.0561233
$443$	−2.48550	+	1.43500i	−0.118090	+	0.0681790i	−0.557881	−	0.829921i	$-0.688386\pi$
$443$	−2.48550	+	1.43500i	−0.118090	+	0.0681790i	0.439792	+	0.898100i	$0.355052\pi$
$444$		0			0
$445$	−12.3719	+	21.4287i	−0.586482	+	1.01582i
$446$	3.47457	+	6.01813i	0.164526	+	0.284967i
$447$		0			0
$448$	1.46986	+	0.323476i	0.0694444	+	0.0152828i
$449$		−	1.81675i		−	0.0857380i	−0.999081	−	0.0428690i	$-0.986350\pi$
$449$		−	1.81675i		−	0.0857380i	0.999081	−	0.0428690i	$-0.0136498\pi$
$450$		0			0
$451$	−19.5749	−	11.3016i	−0.921746	−	0.532170i
$452$	−9.72821	−	5.61659i	−0.457577	−	0.264182i
$453$		0			0
$454$			4.41510i			0.207211i
$455$	−13.1984	+	4.18389i	−0.618751	+	0.196144i
$456$		0			0
$457$	−3.07788	−	5.33104i	−0.143977	−	0.249375i	0.785014	−	0.619478i	$-0.212656\pi$
$457$	−3.07788	−	5.33104i	−0.143977	−	0.249375i	−0.928991	+	0.370103i	$0.879322\pi$
$458$	−4.02608	+	6.97338i	−0.188126	+	0.325844i
$459$		0			0
$460$	−42.2699	+	24.4045i	−1.97084	+	1.13787i
$461$	−17.0507			−0.794132			−0.397066	−	0.917790i	$-0.629972\pi$
$461$	−17.0507			−0.794132			−0.397066	+	0.917790i	$0.629972\pi$
$462$		0			0
$463$	29.4131			1.36694			0.683471	−	0.729977i	$-0.260469\pi$
$463$	29.4131			1.36694			0.683471	+	0.729977i	$0.260469\pi$
$464$	5.06356	−	2.92345i	0.235070	−	0.135718i
$465$		0			0
$466$	1.84723	−	3.19950i	0.0855713	−	0.148214i
$467$	−13.5590	−	23.4849i	−0.627437	−	1.08675i	−0.988064	−	0.154043i	$-0.950771\pi$
$467$	−13.5590	−	23.4849i	−0.627437	−	1.08675i	0.360627	−	0.932710i	$-0.382563\pi$
$468$		0			0
$469$	−19.2126	+	21.0321i	−0.887155	+	0.971171i
$470$		−	12.1498i		−	0.560428i
$471$		0			0
$472$	4.41355	+	2.54817i	0.203150	+	0.117289i
$473$	−4.39947	−	2.54003i	−0.202288	−	0.116791i
$474$		0			0
$475$			26.5622i			1.21876i
$476$	−1.42650	−	4.50000i	−0.0653835	−	0.206257i
$477$		0			0
$478$	−5.23967	−	9.07538i	−0.239657	−	0.415098i
$479$	−10.7784	+	18.6688i	−0.492480	+	0.853000i	−0.999962	−	0.00866176i	$-0.997243\pi$
$479$	−10.7784	+	18.6688i	−0.492480	+	0.853000i	0.507483	+	0.861662i	$0.330576\pi$
$480$		0			0
$481$	7.07138	−	4.08266i	0.322427	−	0.186153i
$482$	−3.01261			−0.137221
$483$		0			0
$484$	8.64212			0.392824
$485$	38.8728	−	22.4432i	1.76512	−	1.01909i
$486$		0			0
$487$	7.29047	−	12.6275i	0.330363	−	0.572205i	−0.652220	−	0.758029i	$-0.726162\pi$
$487$	7.29047	−	12.6275i	0.330363	−	0.572205i	0.982583	+	0.185825i	$0.0594956\pi$
$488$	4.69455	+	8.13120i	0.212512	+	0.368082i
$489$		0			0
$490$	8.77034	+	12.4433i	0.396204	+	0.562129i
$491$		−	0.283102i		−	0.0127762i	−0.999980	−	0.00638811i	$-0.997967\pi$
$491$		−	0.283102i		−	0.0127762i	0.999980	−	0.00638811i	$-0.00203341\pi$
$492$		0			0
$493$	3.60152	+	2.07934i	0.162204	+	0.0936486i
$494$	−3.99769	−	2.30807i	−0.179864	−	0.103845i
$495$		0			0
$496$			11.7026i			0.525461i
$497$	3.63555	−	16.5198i	0.163077	−	0.741014i
$498$		0			0
$499$	−6.15277	−	10.6569i	−0.275436	−	0.477069i	0.694809	−	0.719194i	$-0.255489\pi$
$499$	−6.15277	−	10.6569i	−0.275436	−	0.477069i	−0.970245	+	0.242125i	$0.922155\pi$
$500$	2.51977	−	4.36438i	0.112688	−	0.195181i
$501$		0			0
$502$	7.84976	−	4.53206i	0.350352	−	0.202276i
$503$	−1.78425			−0.0795559			−0.0397779	−	0.999209i	$-0.512665\pi$
$503$	−1.78425			−0.0795559			−0.0397779	+	0.999209i	$0.512665\pi$
$504$		0			0
$505$	−45.3900			−2.01983
$506$	12.5172	−	7.22679i	0.556456	−	0.321270i
$507$		0			0
$508$	13.8895	−	24.0572i	0.616245	−	1.06737i
$509$	19.5362	+	33.8378i	0.865928	+	1.49983i	0.866122	+	0.499832i	$0.166605\pi$
$509$	19.5362	+	33.8378i	0.865928	+	1.49983i	−0.000194027		1.00000i	$0.500062\pi$
$510$		0			0
$511$	20.8683	+	19.0630i	0.923161	+	0.843299i
$512$			16.6670i			0.736583i
$513$		0			0
$514$	5.09755	+	2.94307i	0.224843	+	0.129813i
$515$	14.0322	+	8.10152i	0.618334	+	0.356996i
$516$		0			0
$517$		−	13.0917i		−	0.575773i
$518$	−6.62854	−	6.05510i	−0.291241	−	0.266046i
$519$		0			0
$520$	6.13166	+	10.6203i	0.268891	+	0.465733i
$521$	−10.1814	+	17.6347i	−0.446056	+	0.772591i	−0.998125	−	0.0612072i	$-0.980505\pi$
$521$	−10.1814	+	17.6347i	−0.446056	+	0.772591i	0.552070	+	0.833798i	$0.313838\pi$
$522$		0			0
$523$	1.24066	−	0.716293i	0.0542501	−	0.0313213i	−0.472630	−	0.881261i	$-0.656695\pi$
$523$	1.24066	−	0.716293i	0.0542501	−	0.0313213i	0.526880	+	0.849940i	$0.323362\pi$
$524$	21.3435			0.932396
$525$		0			0
$526$	18.7488			0.817485
$527$	−7.20844	+	4.16179i	−0.314005	+	0.181291i
$528$		0			0
$529$	32.6171	−	56.4945i	1.41814	−	2.45628i
$530$	10.9282	+	18.9282i	0.474690	+	0.822187i
$531$		0			0
$532$	3.96941	−	18.0368i	0.172096	−	0.781994i
$533$			15.2402i			0.660126i
$534$		0			0
$535$	7.03773	+	4.06323i	0.304267	+	0.175669i
$536$	21.8505	+	12.6154i	0.943797	+	0.544901i
$537$		0			0
$538$			15.7138i			0.677470i
$539$	9.45027	+	13.4079i	0.407052	+	0.577520i
$540$		0			0
$541$	5.04521	+	8.73856i	0.216910	+	0.375700i	0.953862	−	0.300246i	$-0.0970687\pi$
$541$	5.04521	+	8.73856i	0.216910	+	0.375700i	−0.736951	+	0.675946i	$0.763735\pi$
$542$	4.79437	−	8.30410i	0.205936	−	0.356692i
$543$		0			0
$544$	−5.65024	+	3.26217i	−0.242252	+	0.139864i
$545$	−14.3601			−0.615119
$546$		0			0
$547$	7.30048			0.312146			0.156073	−	0.987746i	$-0.450117\pi$
$547$	7.30048			0.312146			0.156073	+	0.987746i	$0.450117\pi$
$548$	13.8042	−	7.96986i	0.589686	−	0.340456i
$549$		0			0
$550$	−4.59295	+	7.95521i	−0.195844	+	0.339211i
$551$	8.13484	+	14.0900i	0.346556	+	0.600253i
$552$		0			0
$553$	0.985915	+	3.11014i	0.0419254	+	0.132257i
$554$			14.6971i			0.624420i
$555$		0			0
$556$	−5.23714	−	3.02367i	−0.222104	−	0.128232i
$557$	−19.7970	−	11.4298i	−0.838828	−	0.484297i	0.0180379	−	0.999837i	$-0.494258\pi$
$557$	−19.7970	−	11.4298i	−0.838828	−	0.484297i	−0.856866	+	0.515540i	$0.827591\pi$
$558$		0			0
$559$			3.42524i			0.144872i
$560$	−9.45027	+	10.3452i	−0.399347	+	0.437166i
$561$		0			0
$562$	−3.81060	−	6.60015i	−0.160740	−	0.278410i
$563$	−10.5548	+	18.2814i	−0.444832	+	0.770471i	−0.998040	−	0.0625717i	$-0.980070\pi$
$563$	−10.5548	+	18.2814i	−0.444832	+	0.770471i	0.553209	+	0.833043i	$0.313403\pi$
$564$		0			0
$565$	−20.5377	+	11.8575i	−0.864029	+	0.498847i
$566$	−9.84517			−0.413824
$567$		0			0
$568$	−14.9819			−0.628629
$569$	22.9095	−	13.2268i	0.960415	−	0.554496i	0.0641144	−	0.997943i	$-0.479578\pi$
$569$	22.9095	−	13.2268i	0.960415	−	0.554496i	0.896301	+	0.443447i	$0.146244\pi$
$570$		0			0
$571$	−6.01507	+	10.4184i	−0.251723	+	0.435997i	−0.964000	−	0.265901i	$-0.914330\pi$
$571$	−6.01507	+	10.4184i	−0.251723	+	0.435997i	0.712277	+	0.701898i	$0.247664\pi$
$572$	2.90441	+	5.03059i	0.121440	+	0.210340i
$573$		0			0
$574$	15.9734	−	5.06356i	0.666716	−	0.211349i
$575$			56.0767i			2.33856i
$576$		0			0
$577$	−31.9055	−	18.4207i	−1.32824	−	0.766862i	−0.343216	−	0.939257i	$-0.611516\pi$
$577$	−31.9055	−	18.4207i	−1.32824	−	0.766862i	−0.985028	+	0.172395i	$0.944850\pi$
$578$	8.93153	+	5.15662i	0.371503	+	0.214487i
$579$		0			0
$580$		−	19.0004i		−	0.788947i
$581$	−2.68076	−	0.589962i	−0.111217	−	0.0244757i
$582$		0			0
$583$	11.7754	+	20.3956i	0.487687	+	0.844699i
$584$	12.5172	−	21.6804i	0.517964	−	0.897140i
$585$		0			0
$586$	9.28903	−	5.36302i	0.383726	−	0.221544i
$587$	−28.7712			−1.18752			−0.593758	−	0.804644i	$-0.702356\pi$
$587$	−28.7712			−1.18752			−0.593758	+	0.804644i	$0.702356\pi$
$588$		0			0
$589$	−32.5638			−1.34177
$590$	4.09601	−	2.36483i	0.168630	−	0.0973585i
$591$		0			0
$592$	4.13166	−	7.15624i	0.169810	−	0.294120i
$593$	5.29159	+	9.16531i	0.217300	+	0.376374i	0.953982	−	0.299865i	$-0.0969418\pi$
$593$	5.29159	+	9.16531i	0.217300	+	0.376374i	−0.736682	+	0.676240i	$0.763608\pi$
$594$		0			0
$595$	−9.73317	−	2.14201i	−0.399021	−	0.0878137i
$596$		−	7.96986i		−	0.326458i
$597$		0			0
$598$	−8.43972	−	4.87268i	−0.345126	−	0.199259i
$599$	15.7553	+	9.09634i	0.643745	+	0.371666i	0.786056	−	0.618156i	$-0.212120\pi$
$599$	15.7553	+	9.09634i	0.643745	+	0.371666i	−0.142311	+	0.989822i	$0.545453\pi$
$600$		0			0
$601$			26.4101i			1.07729i	0.842532	+	0.538646i	$0.181064\pi$
$601$			26.4101i			1.07729i	−0.842532	+	0.538646i	$0.818936\pi$
$602$	3.59002	−	1.13804i	0.146318	−	0.0463829i
$603$		0			0
$604$	−14.3593	−	24.8711i	−0.584272	−	1.01199i
$605$	9.12241	−	15.8005i	0.370879	−	0.642381i
$606$		0			0
$607$	−21.6312	+	12.4888i	−0.877983	+	0.506904i	−0.869993	−	0.493064i	$-0.835877\pi$
$607$	−21.6312	+	12.4888i	−0.877983	+	0.506904i	−0.00799043	+	0.999968i	$0.502543\pi$
$608$	−25.5247			−1.03516
$609$		0			0
$610$	8.71358			0.352802
$611$	−7.64450	+	4.41355i	−0.309263	+	0.178553i
$612$		0			0
$613$	7.05631	−	12.2219i	0.285002	−	0.493637i	−0.687608	−	0.726082i	$-0.741339\pi$
$613$	7.05631	−	12.2219i	0.285002	−	0.493637i	0.972610	+	0.232445i	$0.0746725\pi$
$614$	−1.04186	−	1.80455i	−0.0420460	−	0.0728258i
$615$		0			0
$616$	9.79904	−	10.7270i	0.394815	−	0.432205i
$617$			14.6265i			0.588840i	0.955676	+	0.294420i	$0.0951264\pi$
$617$			14.6265i			0.588840i	−0.955676	+	0.294420i	$0.904874\pi$
$618$		0			0
$619$	−22.9880	−	13.2721i	−0.923965	−	0.533452i	−0.0390674	−	0.999237i	$-0.512439\pi$
$619$	−22.9880	−	13.2721i	−0.923965	−	0.533452i	−0.884898	+	0.465785i	$0.845772\pi$
$620$	32.9343	+	19.0146i	1.32267	+	0.763645i
$621$		0			0
$622$			16.5036i			0.661734i
$623$	−5.97282	−	18.8417i	−0.239296	−	0.754878i
$624$		0			0
$625$	9.60503	+	16.6364i	0.384201	+	0.665456i
$626$	−6.12105	+	10.6020i	−0.244646	+	0.423740i
$627$		0			0
$628$	−4.50000	+	2.59808i	−0.179570	+	0.103675i
$629$	5.87738			0.234347
$630$		0			0
$631$	−8.20304			−0.326558			−0.163279	−	0.986580i	$-0.552207\pi$
$631$	−8.20304			−0.326558			−0.163279	+	0.986580i	$0.552207\pi$
$632$	2.50264	−	1.44490i	0.0995495	−	0.0574749i
$633$		0			0
$634$	−2.62308	+	4.54331i	−0.104176	+	0.180438i
$635$	−29.3227	−	50.7885i	−1.16364	−	2.01548i
$636$		0			0
$637$	4.64321	−	10.0383i	0.183971	−	0.397734i
$638$			5.62648i			0.222755i
$639$		0			0
$640$	31.8382	+	18.3818i	1.25852	+	0.726604i
$641$	13.8996	+	8.02496i	0.549003	+	0.316967i	0.748720	−	0.662887i	$-0.230669\pi$
$641$	13.8996	+	8.02496i	0.549003	+	0.316967i	−0.199717	+	0.979854i	$0.564002\pi$
$642$		0			0
$643$		−	26.4101i		−	1.04151i	−0.853705	−	0.520757i	$-0.825650\pi$
$643$		−	26.4101i		−	1.04151i	0.853705	−	0.520757i	$-0.174350\pi$
$644$	8.38002	−	38.0784i	0.330219	−	1.50050i
$645$		0			0
$646$	−1.66134	−	2.87753i	−0.0653646	−	0.113215i
$647$	15.8508	−	27.4543i	0.623158	−	1.07934i	−0.365736	−	0.930719i	$-0.619183\pi$
$647$	15.8508	−	27.4543i	0.623158	−	1.07934i	0.988894	−	0.148623i	$-0.0474840\pi$
$648$		0			0
$649$	4.41355	−	2.54817i	0.173247	−	0.100024i
$650$	6.19360			0.242933
$651$		0			0
$652$	−3.59808			−0.140912
$653$	−11.5096	+	6.64506i	−0.450405	+	0.260041i	−0.708001	−	0.706211i	$-0.750403\pi$
$653$	−11.5096	+	6.64506i	−0.450405	+	0.260041i	0.257596	+	0.966253i	$0.417070\pi$
$654$		0			0
$655$	22.5297	−	39.0226i	0.880308	−	1.52474i
$656$	7.71155	+	13.3568i	0.301085	+	0.521495i
$657$		0			0
$658$	7.16576	+	6.54585i	0.279351	+	0.255184i
$659$			36.2125i			1.41064i	0.708890	+	0.705319i	$0.249196\pi$
$659$			36.2125i			1.41064i	−0.708890	+	0.705319i	$0.750804\pi$
$660$		0			0
$661$	43.9880	+	25.3965i	1.71093	+	0.987809i	0.933304	+	0.359087i	$0.116912\pi$
$661$	43.9880	+	25.3965i	1.71093	+	0.987809i	0.777630	+	0.628722i	$0.216422\pi$
$662$	5.08070	+	2.93334i	0.197467	+	0.114008i
$663$		0			0
$664$			2.43121i			0.0943491i
$665$	−28.7869	−	26.2965i	−1.11631	−	1.01973i
$666$		0			0
$667$	17.1739	+	29.7460i	0.664975	+	1.15177i
$668$	2.09059	−	3.62101i	0.0808874	−	0.140101i
$669$		0			0
$670$	20.2784	−	11.7077i	0.783422	−	0.452309i
$671$	9.38910			0.362462
$672$		0			0
$673$	3.32865			0.128310			0.0641550	−	0.997940i	$-0.479565\pi$
$673$	3.32865			0.128310			0.0641550	+	0.997940i	$0.479565\pi$
$674$	2.41407	−	1.39376i	0.0929864	−	0.0536857i
$675$		0			0
$676$	−8.23922	+	14.2707i	−0.316893	+	0.548875i
$677$	9.96901	+	17.2668i	0.383140	+	0.663618i	0.991509	−	0.130036i	$-0.0415093\pi$
$677$	9.96901	+	17.2668i	0.383140	+	0.663618i	−0.608369	+	0.793654i	$0.708176\pi$
$678$		0			0
$679$	−7.70655	+	35.0182i	−0.295750	+	1.34388i
$680$			8.82710i			0.338504i
$681$		0			0
$682$	−9.75267	−	5.63070i	−0.373449	−	0.215611i
$683$	−24.8234	−	14.3318i	−0.949843	−	0.548392i	−0.0568107	−	0.998385i	$-0.518093\pi$
$683$	−24.8234	−	14.3318i	−0.949843	−	0.548392i	−0.893032	+	0.449993i	$0.851426\pi$
$684$		0			0
$685$		−	33.6512i		−	1.28574i
$686$	−12.0640	−	1.53135i	−0.460605	−	0.0584670i
$687$		0			0
$688$	1.73317	+	3.00195i	0.0660766	+	0.114448i
$689$	7.93958	−	13.7518i	0.302474	−	0.523900i
$690$		0			0
$691$	−17.6387	+	10.1837i	−0.671007	+	0.387406i	−0.796458	−	0.604694i	$-0.793296\pi$
$691$	−17.6387	+	10.1837i	−0.671007	+	0.387406i	0.125451	+	0.992100i	$0.459962\pi$
$692$	−4.02458			−0.152991
$693$		0			0
$694$	−1.72460			−0.0654650
$695$	−11.0564	+	6.38341i	−0.419393	+	0.242137i
$696$		0			0
$697$	−5.48493	+	9.50018i	−0.207757	+	0.359845i
$698$	−10.6674	−	18.4764i	−0.403766	−	0.699343i
$699$		0			0
$700$	7.48791	+	23.6212i	0.283017	+	0.892797i
$701$		−	49.1172i		−	1.85513i	−0.373659	−	0.927566i	$-0.621897\pi$
$701$		−	49.1172i		−	1.85513i	0.373659	−	0.927566i	$-0.378103\pi$
$702$		0			0
$703$	19.9131	+	11.4968i	0.751037	+	0.433611i
$704$	−1.15444	−	0.666515i	−0.0435095	−	0.0251202i
$705$		0			0
$706$		−	15.3545i		−	0.577876i
$707$	24.4544	−	26.7703i	0.919704	−	1.00680i
$708$		0			0
$709$	−11.6829	−	20.2354i	−0.438761	−	0.759956i	0.558833	−	0.829280i	$-0.311249\pi$
$709$	−11.6829	−	20.2354i	−0.438761	−	0.759956i	−0.997594	+	0.0693240i	$0.977916\pi$
$710$	−6.95201	+	12.0412i	−0.260904	+	0.451900i
$711$		0			0
$712$	−15.1613	+	8.75340i	−0.568195	+	0.328048i
$713$	−68.7471			−2.57460
$714$		0			0
$715$	12.2633			0.458622
$716$	18.7992	−	10.8537i	0.702559	−	0.405623i
$717$		0			0
$718$	−7.00956	+	12.1409i	−0.261594	+	0.453095i
$719$	6.33345	+	10.9699i	0.236198	+	0.409107i	0.959620	−	0.281299i	$-0.0907653\pi$
$719$	6.33345	+	10.9699i	0.236198	+	0.409107i	−0.723422	+	0.690406i	$0.757432\pi$
$720$		0			0
$721$	−12.3382	+	3.91121i	−0.459499	+	0.145661i
$722$		−	0.523303i		−	0.0194753i
$723$		0			0
$724$	6.44018	+	3.71824i	0.239347	+	0.138187i
$725$	−18.9049	−	10.9148i	−0.702111	−	0.405364i
$726$		0			0
$727$		−	2.70398i		−	0.100285i	−0.998742	−	0.0501426i	$-0.984032\pi$
$727$		−	2.70398i		−	0.100285i	0.998742	−	0.0501426i	$-0.0159676\pi$
$728$	−9.56723	−	2.10549i	−0.354585	−	0.0780345i
$729$		0			0
$730$	−11.6166	−	20.1205i	−0.429949	−	0.744694i
$731$	−1.23274	+	2.13517i	−0.0455946	+	0.0789721i
$732$		0			0
$733$	18.8869	−	10.9044i	0.697605	−	0.402762i	−0.108850	−	0.994058i	$-0.534717\pi$
$733$	18.8869	−	10.9044i	0.697605	−	0.402762i	0.806455	+	0.591296i	$0.201384\pi$
$734$	10.1927			0.376218
$735$		0			0
$736$	−53.8865			−1.98628
$737$	21.8505	−	12.6154i	0.804873	−	0.464694i
$738$		0			0
$739$	−16.0633	+	27.8225i	−0.590899	+	1.02347i	0.403212	+	0.915107i	$0.367894\pi$
$739$	−16.0633	+	27.8225i	−0.590899	+	1.02347i	−0.994112	+	0.108361i	$0.965440\pi$
$740$	−13.4264	−	23.2553i	−0.493566	−	0.854881i
$741$		0			0
$742$	−17.0513	−	3.75251i	−0.625971	−	0.137759i
$743$			41.2728i			1.51415i	0.653328	+	0.757075i	$0.273372\pi$
$743$			41.2728i			1.51415i	−0.653328	+	0.757075i	$0.726628\pi$
$744$		0			0
$745$	−14.5714	−	8.41279i	−0.533854	−	0.308221i
$746$	13.2796	+	7.66697i	0.486200	+	0.280708i
$747$		0			0
$748$			4.18118i			0.152879i
$749$	−6.18810	+	1.96163i	−0.226108	+	0.0716763i
$750$		0			0
$751$	−22.9045	−	39.6718i	−0.835798	−	1.44764i	−0.893379	−	0.449304i	$-0.851672\pi$
$751$	−22.9045	−	39.6718i	−0.835798	−	1.44764i	0.0575810	−	0.998341i	$-0.481661\pi$
$752$	−4.46652	+	7.73623i	−0.162877	+	0.282111i
$753$		0			0
$754$	3.28541	−	1.89683i	0.119648	−	0.0690785i
$755$	−60.6294			−2.20653
$756$		0			0
$757$	50.3427			1.82974			0.914868	−	0.403752i	$-0.132294\pi$
$757$	50.3427			1.82974			0.914868	+	0.403752i	$0.132294\pi$
$758$	1.44364	−	0.833485i	0.0524353	−	0.0302735i
$759$		0			0
$760$	−17.2668	+	29.9070i	−0.626334	+	1.08484i
$761$	−15.1823	−	26.2965i	−0.550358	−	0.953248i	−0.998249	−	0.0591594i	$-0.981158\pi$
$761$	−15.1823	−	26.2965i	−0.550358	−	0.953248i	0.447891	−	0.894088i	$-0.352175\pi$
$762$		0			0
$763$	7.73669	−	8.46937i	0.280087	−	0.306612i
$764$		−	13.0895i		−	0.473562i
$765$		0			0
$766$	9.21448	+	5.31999i	0.332933	+	0.192219i
$767$	−2.97584	−	1.71810i	−0.107452	−	0.0620372i
$768$		0			0
$769$			41.3383i			1.49070i	0.666675	+	0.745349i	$0.267717\pi$
$769$			41.3383i			1.49070i	−0.666675	+	0.745349i	$0.732283\pi$
$770$	−4.07449	−	12.8533i	−0.146834	−	0.463200i
$771$		0			0
$772$	13.9975	+	24.2443i	0.503780	+	0.872573i
$773$	−6.99754	+	12.1201i	−0.251684	+	0.435930i	−0.963990	−	0.265940i	$-0.914318\pi$
$773$	−6.99754	+	12.1201i	−0.251684	+	0.435930i	0.712305	+	0.701870i	$0.247651\pi$
$774$		0			0
$775$	37.8382	−	21.8459i	1.35919	−	0.784728i
$776$	31.7583			1.14006
$777$		0			0
$778$	−14.6643			−0.525741
$779$	−37.1669	+	21.4583i	−1.33164	+	0.768824i
$780$		0			0
$781$	−7.49097	+	12.9747i	−0.268048	+	0.464273i
$782$	−3.50734	−	6.07489i	−0.125422	−	0.217238i
$783$		0			0
$784$	−1.01001	−	11.1473i	−0.0360718	−	0.398116i
$785$			10.9699i			0.391531i
$786$		0			0
$787$	11.6799	+	6.74341i	0.416344	+	0.240377i	0.693512	−	0.720445i	$-0.256062\pi$
$787$	11.6799	+	6.74341i	0.416344	+	0.240377i	−0.277168	+	0.960822i	$0.589396\pi$
$788$	20.5297	+	11.8528i	0.731340	+	0.422239i
$789$		0			0
$790$		−	2.68188i		−	0.0954170i
$791$	4.07161	−	18.5012i	0.144770	−	0.657827i
$792$		0			0
$793$	−3.16531	−	5.48248i	−0.112403	−	0.194688i
$794$	10.7329	−	18.5900i	0.380897	−	0.659733i
$795$		0			0
$796$	11.7664	−	6.79332i	0.417048	−	0.240783i
$797$	−8.31735			−0.294616			−0.147308	−	0.989091i	$-0.547061\pi$
$797$	−8.31735			−0.294616			−0.147308	+	0.989091i	$0.547061\pi$
$798$		0			0
$799$	−6.35373			−0.224779
$800$	29.6590	−	17.1236i	1.04860	−	0.605411i
$801$		0			0
$802$	9.49702	−	16.4493i	0.335351	−	0.580846i
$803$	−12.5172	−	21.6804i	−0.441721	−	0.765084i
$804$		0			0
$805$	−60.7734	−	55.5159i	−2.14198	−	1.95668i
$806$			7.59302i			0.267453i
$807$		0			0
$808$	−27.8120	−	16.0573i	−0.978424	−	0.564893i
$809$	−12.5955	−	7.27200i	−0.442833	−	0.255670i	0.261965	−	0.965077i	$-0.415629\pi$
$809$	−12.5955	−	7.27200i	−0.442833	−	0.255670i	−0.704799	+	0.709407i	$0.748963\pi$
$810$		0			0
$811$		−	41.8287i		−	1.46880i	−0.678715	−	0.734401i	$-0.737463\pi$
$811$		−	41.8287i		−	1.46880i	0.678715	−	0.734401i	$-0.262537\pi$
$812$	11.2061	+	10.2367i	0.393258	+	0.359237i
$813$		0			0
$814$	3.97590	+	6.88647i	0.139355	+	0.241371i
$815$	−3.79804	+	6.57841i	−0.133040	+	0.230432i
$816$		0			0
$817$	−8.35327	+	4.82277i	−0.292244	+	0.168727i
$818$	0.689991			0.0241250
$819$		0			0
$820$	50.1196			1.75025
$821$	40.2553	−	23.2414i	1.40492	−	0.811131i	0.410027	−	0.912073i	$-0.365519\pi$
$821$	40.2553	−	23.2414i	1.40492	−	0.811131i	0.994892	+	0.100942i	$0.0321858\pi$
$822$		0			0
$823$	−3.86834	+	6.70017i	−0.134842	+	0.233553i	−0.925537	−	0.378657i	$-0.876386\pi$
$823$	−3.86834	+	6.70017i	−0.134842	+	0.233553i	0.790695	+	0.612210i	$0.209719\pi$
$824$	5.73203	+	9.92817i	0.199685	+	0.345864i
$825$		0			0
$826$	−0.812034	+	3.68985i	−0.0282543	+	0.128386i
$827$			20.8898i			0.726409i	0.931709	+	0.363205i	$0.118317\pi$
$827$			20.8898i			0.726409i	−0.931709	+	0.363205i	$0.881683\pi$
$828$		0			0
$829$	41.2282	+	23.8031i	1.43191	+	0.826716i	0.997267	−	0.0738846i	$-0.0235396\pi$
$829$	41.2282	+	23.8031i	1.43191	+	0.826716i	0.434647	+	0.900601i	$0.356873\pi$
$830$	1.95400	+	1.12814i	0.0678243	+	0.0391584i
$831$		0			0
$832$			0.898798i			0.0311602i
$833$	6.50720	−	4.58645i	0.225461	−	0.158911i
$834$		0			0
$835$	−4.41355	−	7.64450i	−0.152737	−	0.264549i
$836$	−8.17887	+	14.1662i	−0.282872	+	0.489949i
$837$		0			0
$838$	−1.77487	+	1.02472i	−0.0613118	+	0.0353984i
$839$	−22.4035			−0.773455			−0.386727	−	0.922194i	$-0.626395\pi$
$839$	−22.4035			−0.773455			−0.386727	+	0.922194i	$0.626395\pi$
$840$		0			0
$841$	15.6291			0.538935
$842$	−4.95098	+	2.85845i	−0.170622	+	0.0985087i
$843$		0			0
$844$	11.4376	−	19.8106i	0.393700	−	0.681909i
$845$	17.3942	+	30.1277i	0.598380	+	1.03642i
$846$		0			0
$847$	4.40407	+	13.8930i	0.151326	+	0.477368i
$848$		−	16.0697i		−	0.551836i
$849$		0			0
$850$	3.86086	+	2.22907i	0.132426	+	0.0764565i
$851$	42.0396	+	24.2715i	1.44110	+	0.832018i
$852$		0			0
$853$			48.4273i			1.65812i	0.559160	+	0.829060i	$0.311124\pi$
$853$			48.4273i			1.65812i	−0.559160	+	0.829060i	$0.688876\pi$
$854$	−4.69455	+	5.13914i	−0.160644	+	0.175858i
$855$		0			0
$856$	2.87484	+	4.97937i	0.0982600	+	0.170191i
$857$	24.5327	−	42.4920i	0.838023	−	1.45150i	−0.0535230	−	0.998567i	$-0.517045\pi$
$857$	24.5327	−	42.4920i	0.838023	−	1.45150i	0.891546	−	0.452931i	$-0.149622\pi$
$858$		0			0
$859$	−10.4136	+	6.01227i	−0.355306	+	0.205136i	−0.667020	−	0.745040i	$-0.732430\pi$
$859$	−10.4136	+	6.01227i	−0.355306	+	0.205136i	0.311714	+	0.950176i	$0.399097\pi$
$860$	11.2644			0.384113
$861$		0			0
$862$	17.9146			0.610175
$863$	−39.8804	+	23.0250i	−1.35754	+	0.783779i	−0.989292	−	0.145947i	$-0.953377\pi$
$863$	−39.8804	+	23.0250i	−1.35754	+	0.783779i	−0.368252	+	0.929726i	$0.620044\pi$
$864$		0			0
$865$	−4.24824	+	7.35817i	−0.144445	+	0.250185i
$866$	−4.22572	−	7.31917i	−0.143596	−	0.248715i
$867$		0			0
$868$	−28.9583	+	9.17978i	−0.982909	+	0.311582i
$869$		−	2.88979i		−	0.0980296i
$870$		0			0
$871$	−14.7327	−	8.50594i	−0.499199	−	0.288213i
$872$	−8.79893	−	5.08007i	−0.297970	−	0.172033i
$873$		0			0
$874$		−	27.4430i		−	0.928275i
$875$	8.30021	+	1.82665i	0.280598	+	0.0617520i
$876$		0			0
$877$	−6.73669	−	11.6683i	−0.227482	−	0.394010i	0.729579	−	0.683896i	$-0.239716\pi$
$877$	−6.73669	−	11.6683i	−0.227482	−	0.394010i	−0.957061	+	0.289886i	$0.906383\pi$
$878$	6.05551	−	10.4884i	0.204363	−	0.353968i
$879$		0			0
$880$	10.7478	−	6.20524i	0.362308	−	0.209179i
$881$	25.5247			0.859949			0.429974	−	0.902841i	$-0.358523\pi$
$881$	25.5247			0.859949			0.429974	+	0.902841i	$0.358523\pi$
$882$		0			0
$883$	6.45532			0.217239			0.108619	−	0.994083i	$-0.465357\pi$
$883$	6.45532			0.217239			0.108619	+	0.994083i	$0.465357\pi$
$884$	2.44147	−	1.40958i	0.0821156	−	0.0474094i
$885$		0			0
$886$	−0.942252	+	1.63203i	−0.0316556	+	0.0548291i
$887$	16.5604	+	28.6834i	0.556043	+	0.963096i	0.997822	+	0.0659712i	$0.0210145\pi$
$887$	16.5604	+	28.6834i	0.556043	+	0.963096i	−0.441778	+	0.897124i	$0.645652\pi$
$888$		0			0
$889$	45.7523	+	10.0688i	1.53448	+	0.337698i
$890$			16.2472i			0.544608i
$891$		0			0
$892$	−14.3790	−	8.30171i	−0.481444	−	0.277962i
$893$	−21.5270	−	12.4286i	−0.720374	−	0.415908i
$894$		0			0
$895$		−	45.8277i		−	1.53185i
$896$	−27.9946	+	8.87427i	−0.935232	+	0.296469i
$897$		0			0
$898$	−0.596459	−	1.03310i	−0.0199041	−	0.0344749i
$899$	13.3809	−	23.1764i	0.446278	−	0.772977i
$900$		0			0
$901$	9.89848	−	5.71489i	0.329766	−	0.190391i
$902$	−14.8417			−0.494174
$903$		0			0
$904$	−16.7789			−0.558058
$905$	13.5962	−	7.84976i	0.451952	−	0.260935i
$906$		0			0
$907$	−3.10756	+	5.38245i	−0.103185	+	0.178721i	−0.912995	−	0.407970i	$-0.866237\pi$
$907$	−3.10756	+	5.38245i	−0.103185	+	0.178721i	0.809810	+	0.586692i	$0.199570\pi$
$908$	−5.27446	−	9.13562i	−0.175039	−	0.303176i
$909$		0			0
$910$	−6.13166	+	6.71234i	−0.203262	+	0.222512i
$911$			18.0475i			0.597941i	0.954262	+	0.298970i	$0.0966432\pi$
$911$			18.0475i			0.597941i	−0.954262	+	0.298970i	$0.903357\pi$
$912$		0			0
$913$	2.10549	+	1.21560i	0.0696814	+	0.0402306i
$914$	−3.50047	−	2.02100i	−0.115785	−	0.0668486i
$915$		0			0
$916$		−	19.2389i		−	0.635670i
$917$	10.8768	+	34.3116i	0.359182	+	1.13307i
$918$		0			0
$919$	4.12913	+	7.15186i	0.136207	+	0.235918i	0.926058	−	0.377381i	$-0.123175\pi$
$919$	4.12913	+	7.15186i	0.136207	+	0.235918i	−0.789851	+	0.613299i	$0.789842\pi$
$920$	−36.4529	+	63.1382i	−1.20182	+	2.08161i
$921$		0			0
$922$	−9.69590	+	5.59793i	−0.319318	+	0.184358i
$923$	10.1016			0.332498
$924$		0			0
$925$	−30.8513			−1.01438
$926$	16.7258	−	9.65662i	0.549642	−	0.317336i
$927$		0			0
$928$	10.4884	−	18.1665i	0.344300	−	0.596345i
$929$	17.3855	+	30.1125i	0.570399	+	0.987960i	0.996525	+	0.0832958i	$0.0265446\pi$
$929$	17.3855	+	30.1125i	0.570399	+	0.987960i	−0.426126	+	0.904664i	$0.640122\pi$
$930$		0			0
$931$	31.0186	−	2.81048i	1.01659	−	0.0921097i
$932$			8.82710i			0.289141i
$933$		0			0
$934$	−15.4207	−	8.90314i	−0.504580	−	0.291320i
$935$	7.64450	+	4.41355i	0.250002	+	0.144339i
$936$		0			0
$937$			51.0703i			1.66839i	0.551466	+	0.834197i	$0.314069\pi$
$937$			51.0703i			1.66839i	−0.551466	+	0.834197i	$0.685931\pi$
$938$	−4.02020	+	18.2676i	−0.131264	+	0.596458i
$939$		0			0
$940$	14.5146	+	25.1401i	0.473415	+	0.819978i
$941$	−1.73872	+	3.01156i	−0.0566807	+	0.0981739i	−0.892974	−	0.450109i	$-0.851385\pi$
$941$	−1.73872	+	3.01156i	−0.0566807	+	0.0981739i	0.836293	+	0.548283i	$0.184718\pi$
$942$		0			0
$943$	−78.4649	+	45.3017i	−2.55517	+	1.47523i
$944$	−3.47744			−0.113181
$945$		0			0
$946$	−3.33568			−0.108452
$947$	12.4189	−	7.17003i	0.403559	−	0.232995i	−0.284460	−	0.958688i	$-0.591814\pi$
$947$	12.4189	−	7.17003i	0.403559	−	0.232995i	0.688018	+	0.725693i	$0.258481\pi$
$948$		0			0
$949$	−8.43972	+	14.6180i	−0.273965	+	0.474521i
$950$	8.72063	+	15.1046i	0.282935	+	0.490057i
$951$		0			0
$952$	−5.20609	−	4.75572i	−0.168730	−	0.154134i
$953$			7.53697i			0.244147i	0.992521	+	0.122073i	$0.0389543\pi$
$953$			7.53697i			0.244147i	−0.992521	+	0.122073i	$0.961046\pi$
$954$		0			0
$955$	−23.9317	−	13.8170i	−0.774411	−	0.447106i
$956$	21.6836	+	12.5190i	0.701298	+	0.404895i
$957$		0			0
$958$			14.1547i			0.457318i
$959$	19.8470	+	18.1300i	0.640892	+	0.585448i
$960$		0			0
$961$	11.2819	+	19.5408i	0.363932	+	0.630349i
$962$	2.68076	−	4.64321i	0.0864312	−	0.149703i
$963$		0			0
$964$	6.23363	−	3.59899i	0.200772	−	0.115916i
$965$	59.1015			1.90255
$966$		0			0
$967$	−11.6161			−0.373550			−0.186775	−	0.982403i	$-0.559803\pi$
$967$	−11.6161			−0.373550			−0.186775	+	0.982403i	$0.559803\pi$
$968$	11.1792	−	6.45434i	0.359314	−	0.207450i
$969$		0			0
$970$	14.7367	−	25.5247i	0.473167	−	0.819548i
$971$	17.7476	+	30.7397i	0.569548	+	0.986485i	0.996611	+	0.0822636i	$0.0262149\pi$
$971$	17.7476	+	30.7397i	0.569548	+	0.986485i	−0.427063	+	0.904222i	$0.640452\pi$
$972$		0			0
$973$	2.19193	−	9.96004i	0.0702702	−	0.319304i
$974$		−	9.57414i		−	0.306775i
$975$		0			0
$976$	−5.54827	−	3.20329i	−0.177596	−	0.102535i
$977$	−27.7210	−	16.0047i	−0.886873	−	0.512036i	−0.0139546	−	0.999903i	$-0.504442\pi$
$977$	−27.7210	−	16.0047i	−0.886873	−	0.512036i	−0.872918	+	0.487866i	$0.837775\pi$
$978$		0			0
$979$			17.5068i			0.559520i
$980$	−33.0126	−	15.2699i	−1.05455	−	0.487779i
$981$		0			0
$982$	−0.0929453	−	0.160986i	−0.00296600	−	0.00513727i
$983$	−24.7324	+	42.8378i	−0.788841	+	1.36631i	0.137837	+	0.990455i	$0.455985\pi$
$983$	−24.7324	+	42.8378i	−0.788841	+	1.36631i	−0.926678	+	0.375857i	$0.877348\pi$
$984$		0			0
$985$	43.3413	−	25.0231i	1.38097	−	0.797302i
$986$	2.73067			0.0869623
$987$		0			0
$988$	11.0292			0.350887
$989$	−17.6350	+	10.1816i	−0.560761	+	0.323756i
$990$		0			0
$991$	−8.97590	+	15.5467i	−0.285129	+	0.493858i	−0.972640	−	0.232316i	$-0.925370\pi$
$991$	−8.97590	+	15.5467i	−0.285129	+	0.493858i	0.687511	+	0.726174i	$0.258703\pi$
$992$	20.9926	+	36.3603i	0.666517	+	1.15444i
$993$		0			0
$994$	−3.35626	−	10.5876i	−0.106454	−	0.335817i
$995$		−	28.6834i		−	0.909326i
$996$		0			0
$997$	−29.0151	−	16.7519i	−0.918916	−	0.530537i	−0.0356272	−	0.999365i	$-0.511343\pi$
$997$	−29.0151	−	16.7519i	−0.918916	−	0.530537i	−0.883289	+	0.468828i	$0.844676\pi$
$998$	−6.99754	−	4.04003i	−0.221503	−	0.127885i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.p.d.80.4	yes	12
3.2	odd	2	inner	189.2.p.d.80.3	yes	12
7.3	odd	6		1323.2.c.d.1322.8		12
7.4	even	3		1323.2.c.d.1322.7		12
7.5	odd	6	inner	189.2.p.d.26.3	✓	12
9.2	odd	6		567.2.s.f.458.4		12
9.4	even	3		567.2.i.f.269.4		12
9.5	odd	6		567.2.i.f.269.3		12
9.7	even	3		567.2.s.f.458.3		12
21.5	even	6	inner	189.2.p.d.26.4	yes	12
21.11	odd	6		1323.2.c.d.1322.6		12
21.17	even	6		1323.2.c.d.1322.5		12
63.5	even	6		567.2.s.f.26.3		12
63.40	odd	6		567.2.s.f.26.4		12
63.47	even	6		567.2.i.f.215.3		12
63.61	odd	6		567.2.i.f.215.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.d.26.3	✓	12	7.5	odd	6	inner
189.2.p.d.26.4	yes	12	21.5	even	6	inner
189.2.p.d.80.3	yes	12	3.2	odd	2	inner
189.2.p.d.80.4	yes	12	1.1	even	1	trivial
567.2.i.f.215.3		12	63.47	even	6
567.2.i.f.215.4		12	63.61	odd	6
567.2.i.f.269.3		12	9.5	odd	6
567.2.i.f.269.4		12	9.4	even	3
567.2.s.f.26.3		12	63.5	even	6
567.2.s.f.26.4		12	63.40	odd	6
567.2.s.f.458.3		12	9.7	even	3
567.2.s.f.458.4		12	9.2	odd	6
1323.2.c.d.1322.5		12	21.17	even	6
1323.2.c.d.1322.6		12	21.11	odd	6
1323.2.c.d.1322.7		12	7.4	even	3
1323.2.c.d.1322.8		12	7.3	odd	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.568650 - 0.328310i) q^{2} +(-0.784425 + 1.35866i) q^{4} +(1.65604 + 2.86834i) q^{5} +(-2.58392 - 0.568650i) q^{7} +2.34338i q^{8} +O(q^{10})\)	\(q+(0.568650 - 0.328310i) q^{2} +(-0.784425 + 1.35866i) q^{4} +(1.65604 + 2.86834i) q^{5} +(-2.58392 - 0.568650i) q^{7} +2.34338i q^{8} +(1.88341 + 1.08739i) q^{10} +(2.02943 + 1.17169i) q^{11} -1.58003i q^{13} +(-1.65604 + 0.524964i) q^{14} +(-0.799494 - 1.38476i) q^{16} +(0.568650 - 0.984931i) q^{17} +(3.85327 - 2.22469i) q^{19} -5.19615 q^{20} +1.53871 q^{22} +(8.13484 - 4.69665i) q^{23} +(-2.98493 + 5.17005i) q^{25} +(-0.518739 - 0.898482i) q^{26} +(2.79949 - 3.06461i) q^{28} +3.65662i q^{29} +(-6.33821 - 3.65936i) q^{31} +(-4.96812 - 2.86834i) q^{32} -0.746774i q^{34} +(-2.64799 - 8.35327i) q^{35} +(2.58392 + 4.47548i) q^{37} +(1.46078 - 2.53014i) q^{38} +(-6.72162 + 3.88073i) q^{40} -9.64553 q^{41} -2.16784 q^{43} +(-3.18386 + 1.83821i) q^{44} +(3.08392 - 5.34150i) q^{46} +(-2.79334 - 4.83821i) q^{47} +(6.35327 + 2.93869i) q^{49} +3.91993i q^{50} +(2.14673 + 1.23941i) q^{52} +(8.70349 + 5.02496i) q^{53} +7.76146i q^{55} +(1.33256 - 6.05510i) q^{56} +(1.20051 + 2.07934i) q^{58} +(1.08739 - 1.88341i) q^{59} +(3.46986 - 2.00333i) q^{61} -4.80563 q^{62} -0.568850 q^{64} +(4.53206 - 2.61659i) q^{65} +(5.38341 - 9.32435i) q^{67} +(0.892126 + 1.54521i) q^{68} +(-4.24824 - 3.88073i) q^{70} +6.39331i q^{71} +(-9.25176 - 5.34150i) q^{73} +(2.93869 + 1.69665i) q^{74} +6.98041i q^{76} +(-4.57759 - 4.18158i) q^{77} +(-0.616587 - 1.06796i) q^{79} +(2.64799 - 4.58645i) q^{80} +(-5.48493 + 3.16673i) q^{82} +1.03748 q^{83} +3.76683 q^{85} +(-1.23274 + 0.711723i) q^{86} +(-2.74571 + 4.75572i) q^{88} +(3.73538 + 6.46986i) q^{89} +(-0.898482 + 4.08266i) q^{91} +14.7367i q^{92} +(-3.17686 - 1.83416i) q^{94} +(12.7623 + 7.36834i) q^{95} -13.5524i q^{97} +(4.57759 - 0.414758i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} - 8 q^{7}+O(q^{10}) \) 12 * q + 8 * q^4 - 8 * q^7	\( 12 q + 8 q^{4} - 8 q^{7} - 6 q^{10} - 4 q^{16} - 6 q^{19} - 40 q^{22} - 24 q^{25} + 28 q^{28} - 12 q^{31} + 8 q^{37} + 12 q^{40} + 20 q^{43} + 14 q^{46} + 24 q^{49} + 78 q^{52} + 20 q^{58} + 18 q^{61} + 28 q^{64} + 36 q^{67} - 120 q^{70} - 42 q^{73} - 36 q^{79} - 54 q^{82} - 12 q^{85} - 74 q^{88} + 6 q^{91} - 114 q^{94}+O(q^{100}) \) 12 * q + 8 * q^4 - 8 * q^7 - 6 * q^10 - 4 * q^16 - 6 * q^19 - 40 * q^22 - 24 * q^25 + 28 * q^28 - 12 * q^31 + 8 * q^37 + 12 * q^40 + 20 * q^43 + 14 * q^46 + 24 * q^49 + 78 * q^52 + 20 * q^58 + 18 * q^61 + 28 * q^64 + 36 * q^67 - 120 * q^70 - 42 * q^73 - 36 * q^79 - 54 * q^82 - 12 * q^85 - 74 * q^88 + 6 * q^91 - 114 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more