LMFDB - Embedded newform 675.2.k.c.424.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("675.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 $ x^16 - 12x^14 + 102x^12 - 406x^10 + 1167x^8 - 1842x^6 + 2023x^4 - 441*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			424.4
Root			$-0.409850 - 0.236627i$ of defining polynomial
Character	$\chi$	$=$	675.424
Dual form			675.2.k.c.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.409850 - 0.236627i) q^{2} +(-0.888015 - 1.53809i) q^{4} +(2.21967 + 1.28153i) q^{7} +1.78702i q^{8} +O(q^{10})$	\(q+(-0.409850 - 0.236627i) q^{2} +(-0.888015 - 1.53809i) q^{4} +(2.21967 + 1.28153i) q^{7} +1.78702i q^{8} +(-3.08430 + 5.34217i) q^{11} +(1.84662 - 1.06615i) q^{13} +(-0.606488 - 1.05047i) q^{14} +(-1.35317 + 2.34376i) q^{16} +3.16860i q^{17} -0.356267 q^{19} +(2.52821 - 1.45966i) q^{22} +(3.64854 - 2.10649i) q^{23} -1.00912 q^{26} -4.55206i q^{28} +(-0.843116 + 1.46032i) q^{29} +(4.12920 + 7.15199i) q^{31} +(4.20441 - 2.42742i) q^{32} +(0.749778 - 1.29865i) q^{34} -3.63274i q^{37} +(0.146016 + 0.0843024i) q^{38} +(-1.36677 - 2.36731i) q^{41} +(6.64949 + 3.83908i) q^{43} +10.9556 q^{44} -1.99381 q^{46} +(9.89770 + 5.71444i) q^{47} +(-0.215378 - 0.373046i) q^{49} +(-3.27966 - 1.89351i) q^{52} +9.43507i q^{53} +(-2.29012 + 3.96660i) q^{56} +(0.691103 - 0.399008i) q^{58} +(-5.10795 - 8.84723i) q^{59} +(0.00549659 - 0.00952038i) q^{61} -3.90833i q^{62} +3.11511 q^{64} +(-0.851145 + 0.491409i) q^{67} +(4.87359 - 2.81377i) q^{68} +6.43507 q^{71} +6.61467i q^{73} +(-0.859605 + 1.48888i) q^{74} +(0.316370 + 0.547969i) q^{76} +(-13.6923 + 7.90523i) q^{77} +(-4.73569 + 8.20246i) q^{79} +1.29366i q^{82} +(-9.02378 - 5.20988i) q^{83} +(-1.81686 - 3.14690i) q^{86} +(-9.54658 - 5.51172i) q^{88} -6.26940 q^{89} +5.46519 q^{91} +(-6.47993 - 3.74119i) q^{92} +(-2.70439 - 4.68413i) q^{94} +(6.24126 + 3.60339i) q^{97} +0.203858i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 2 q^{11} - 6 q^{14} - 8 q^{16} - 8 q^{19} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 18 q^{34} - 10 q^{41} + 88 q^{44} - 6 q^{49} - 60 q^{56} - 34 q^{59} + 26 q^{61} - 76 q^{64} + 32 q^{71} - 80 q^{74} - 22 q^{76} - 14 q^{79} - 68 q^{86} - 36 q^{89} - 68 q^{91} + 6 q^{94}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^11 - 6 * q^14 - 8 * q^16 - 8 * q^19 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 18 * q^34 - 10 * q^41 + 88 * q^44 - 6 * q^49 - 60 * q^56 - 34 * q^59 + 26 * q^61 - 76 * q^64 + 32 * q^71 - 80 * q^74 - 22 * q^76 - 14 * q^79 - 68 * q^86 - 36 * q^89 - 68 * q^91 + 6 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.409850	−	0.236627i	−0.289808	−	0.167321i	0.348047	−	0.937477i	$-0.386845\pi$
$2$	−0.409850	−	0.236627i	−0.289808	−	0.167321i	−0.637855	+	0.770156i	$0.720178\pi$
$3$		0			0
$3$		0			0
$4$	−0.888015	−	1.53809i	−0.444008	−	0.769044i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.21967	+	1.28153i	0.838956	+	0.484372i	0.856909	−	0.515467i	$-0.172382\pi$
$7$	2.21967	+	1.28153i	0.838956	+	0.484372i	−0.0179531	+	0.999839i	$0.505715\pi$
$8$			1.78702i			0.631808i
$9$		0			0
$10$		0			0
$11$	−3.08430	+	5.34217i	−0.929952	+	1.61072i	−0.146555	+	0.989202i	$0.546819\pi$
$11$	−3.08430	+	5.34217i	−0.929952	+	1.61072i	−0.783397	+	0.621522i	$0.786515\pi$
$12$		0			0
$13$	1.84662	−	1.06615i	0.512161	−	0.295696i	−0.221560	−	0.975147i	$-0.571115\pi$
$13$	1.84662	−	1.06615i	0.512161	−	0.295696i	0.733722	+	0.679450i	$0.237782\pi$
$14$	−0.606488	−	1.05047i	−0.162091	−	0.280750i
$15$		0			0
$16$	−1.35317	+	2.34376i	−0.338293	+	0.585941i
$17$			3.16860i			0.768500i	0.923229	+	0.384250i	$0.125540\pi$
$17$			3.16860i			0.768500i	−0.923229	+	0.384250i	$0.874460\pi$
$18$		0			0
$19$	−0.356267			−0.0817332			−0.0408666	−	0.999165i	$-0.513012\pi$
$19$	−0.356267			−0.0817332			−0.0408666	+	0.999165i	$0.513012\pi$
$20$		0			0
$21$		0			0
$22$	2.52821	−	1.45966i	0.539015	−	0.311201i
$23$	3.64854	−	2.10649i	0.760774	−	0.439233i	−0.0687995	−	0.997631i	$-0.521917\pi$
$23$	3.64854	−	2.10649i	0.760774	−	0.439233i	0.829574	+	0.558397i	$0.188584\pi$
$24$		0			0
$25$		0			0
$26$	−1.00912			−0.197905
$27$		0			0
$28$		−	4.55206i		−	0.860259i
$29$	−0.843116	+	1.46032i	−0.156563	+	0.271174i	−0.933627	−	0.358247i	$-0.883375\pi$
$29$	−0.843116	+	1.46032i	−0.156563	+	0.271174i	0.777064	+	0.629421i	$0.216708\pi$
$30$		0			0
$31$	4.12920	+	7.15199i	0.741627	+	1.28453i	0.951754	+	0.306861i	$0.0992787\pi$
$31$	4.12920	+	7.15199i	0.741627	+	1.28453i	−0.210128	+	0.977674i	$0.567388\pi$
$32$	4.20441	−	2.42742i	0.743242	−	0.429111i
$33$		0			0
$34$	0.749778	−	1.29865i	0.128586	−	0.222717i
$35$		0			0
$36$		0			0
$37$		−	3.63274i		−	0.597219i	−0.954375	−	0.298609i	$-0.903477\pi$
$37$		−	3.63274i		−	0.597219i	0.954375	−	0.298609i	$-0.0965228\pi$
$38$	0.146016	+	0.0843024i	0.0236869	+	0.0136757i
$39$		0			0
$40$		0			0
$41$	−1.36677	−	2.36731i	−0.213453	−	0.369711i	0.739340	−	0.673332i	$-0.235138\pi$
$41$	−1.36677	−	2.36731i	−0.213453	−	0.369711i	−0.952793	+	0.303621i	$0.901804\pi$
$42$		0			0
$43$	6.64949	+	3.83908i	1.01404	+	0.585455i	0.912371	−	0.409364i	$-0.134249\pi$
$43$	6.64949	+	3.83908i	1.01404	+	0.585455i	0.101666	+	0.994819i	$0.467583\pi$
$44$	10.9556			1.65162
$45$		0			0
$46$	−1.99381			−0.293971
$47$	9.89770	+	5.71444i	1.44373	+	0.833537i	0.998096	−	0.0616792i	$-0.0196456\pi$
$47$	9.89770	+	5.71444i	1.44373	+	0.833537i	0.445632	+	0.895216i	$0.352979\pi$
$48$		0			0
$49$	−0.215378	−	0.373046i	−0.0307683	−	0.0532923i
$50$		0			0
$51$		0			0
$52$	−3.27966	−	1.89351i	−0.454807	−	0.262583i
$53$			9.43507i			1.29601i	0.761637	+	0.648003i	$0.224396\pi$
$53$			9.43507i			1.29601i	−0.761637	+	0.648003i	$0.775604\pi$
$54$		0			0
$55$		0			0
$56$	−2.29012	+	3.96660i	−0.306030	+	0.530059i
$57$		0			0
$58$	0.691103	−	0.399008i	0.0907462	−	0.0523924i
$59$	−5.10795	−	8.84723i	−0.664999	−	1.15181i	−0.979286	−	0.202484i	$-0.935099\pi$
$59$	−5.10795	−	8.84723i	−0.664999	−	1.15181i	0.314287	−	0.949328i	$-0.398235\pi$
$60$		0			0
$61$	0.00549659	−	0.00952038i	0.000703767	−	0.00121896i	−0.865673	−	0.500609i	$-0.833109\pi$
$61$	0.00549659	−	0.00952038i	0.000703767	−	0.00121896i	0.866377	+	0.499390i	$0.166443\pi$
$62$		−	3.90833i		−	0.496358i
$63$		0			0
$64$	3.11511			0.389389
$65$		0			0
$66$		0			0
$67$	−0.851145	+	0.491409i	−0.103984	+	0.0600351i	−0.551090	−	0.834446i	$-0.685788\pi$
$67$	−0.851145	+	0.491409i	−0.103984	+	0.0600351i	0.447106	+	0.894481i	$0.352455\pi$
$68$	4.87359	−	2.81377i	0.591010	−	0.341220i
$69$		0			0
$70$		0			0
$71$	6.43507			0.763703			0.381851	−	0.924224i	$-0.375287\pi$
$71$	6.43507			0.763703			0.381851	+	0.924224i	$0.375287\pi$
$72$		0			0
$73$			6.61467i			0.774189i	0.922040	+	0.387094i	$0.126521\pi$
$73$			6.61467i			0.774189i	−0.922040	+	0.387094i	$0.873479\pi$
$74$	−0.859605	+	1.48888i	−0.0999271	+	0.173079i
$75$		0			0
$76$	0.316370	+	0.547969i	0.0362901	+	0.0628564i
$77$	−13.6923	+	7.90523i	−1.56038	+	0.900885i
$78$		0			0
$79$	−4.73569	+	8.20246i	−0.532807	+	0.922848i	0.466459	+	0.884543i	$0.345529\pi$
$79$	−4.73569	+	8.20246i	−0.532807	+	0.922848i	−0.999266	+	0.0383057i	$0.987804\pi$
$80$		0			0
$81$		0			0
$82$			1.29366i			0.142860i
$83$	−9.02378	−	5.20988i	−0.990489	−	0.571859i	−0.0850682	−	0.996375i	$-0.527111\pi$
$83$	−9.02378	−	5.20988i	−0.990489	−	0.571859i	−0.905420	+	0.424516i	$0.860444\pi$
$84$		0			0
$85$		0			0
$86$	−1.81686	−	3.14690i	−0.195917	−	0.339339i
$87$		0			0
$88$	−9.54658	−	5.51172i	−1.01767	−	0.587551i
$89$	−6.26940			−0.664555			−0.332277	−	0.943182i	$-0.607817\pi$
$89$	−6.26940			−0.664555			−0.332277	+	0.943182i	$0.607817\pi$
$90$		0			0
$91$	5.46519			0.572908
$92$	−6.47993	−	3.74119i	−0.675579	−	0.390046i
$93$		0			0
$94$	−2.70439	−	4.68413i	−0.278936	−	0.483131i
$95$		0			0
$96$		0			0
$97$	6.24126	+	3.60339i	0.633704	+	0.365869i	0.782185	−	0.623046i	$-0.214105\pi$
$97$	6.24126	+	3.60339i	0.633704	+	0.365869i	−0.148481	+	0.988915i	$0.547438\pi$
$98$			0.203858i			0.0205927i
$99$		0			0
$100$		0			0
$101$	3.48547	−	6.03701i	0.346817	−	0.600705i	−0.638865	−	0.769319i	$-0.720596\pi$
$101$	3.48547	−	6.03701i	0.346817	−	0.600705i	0.985682	+	0.168614i	$0.0539291\pi$
$102$		0			0
$103$	−5.29584	+	3.05756i	−0.521815	+	0.301270i	−0.737677	−	0.675154i	$-0.764077\pi$
$103$	−5.29584	+	3.05756i	−0.521815	+	0.301270i	0.215862	+	0.976424i	$0.430744\pi$
$104$	1.90523	+	3.29996i	0.186823	+	0.323588i
$105$		0			0
$106$	2.23260	−	3.86697i	0.216849	−	0.375593i
$107$		−	14.5349i		−	1.40514i	−0.711615	−	0.702570i	$-0.752036\pi$
$107$		−	14.5349i		−	1.40514i	0.711615	−	0.702570i	$-0.247964\pi$
$108$		0			0
$109$	−1.90214			−0.182192			−0.0910958	−	0.995842i	$-0.529037\pi$
$109$	−1.90214			−0.182192			−0.0910958	+	0.995842i	$0.529037\pi$
$110$		0			0
$111$		0			0
$112$	−6.00719	+	3.46825i	−0.567626	+	0.327719i
$113$	5.69780	−	3.28962i	0.536004	−	0.309462i	−0.207454	−	0.978245i	$-0.566518\pi$
$113$	5.69780	−	3.28962i	0.536004	−	0.309462i	0.743458	+	0.668783i	$0.233184\pi$
$114$		0			0
$115$		0			0
$116$	2.99480			0.278060
$117$		0			0
$118$			4.83472i			0.445072i
$119$	−4.06065	+	7.03326i	−0.372239	+	0.644737i
$120$		0			0
$121$	−13.5258	−	23.4274i	−1.22962	−	2.12977i
$122$	−0.00450556	+	0.00260129i	−0.000407914	+	0.000235509i
$123$		0			0
$124$	7.33359	−	12.7021i	0.658576	−	1.14069i
$125$		0			0
$126$		0			0
$127$			9.25840i			0.821550i	0.911737	+	0.410775i	$0.134742\pi$
$127$			9.25840i			0.821550i	−0.911737	+	0.410775i	$0.865258\pi$
$128$	−9.68555	−	5.59196i	−0.856090	−	0.494264i
$129$		0			0
$130$		0			0
$131$	0.134698	+	0.233305i	0.0117687	+	0.0203839i	0.871850	−	0.489773i	$-0.162920\pi$
$131$	0.134698	+	0.233305i	0.0117687	+	0.0203839i	−0.860081	+	0.510157i	$0.829587\pi$
$132$		0			0
$133$	−0.790794	−	0.456565i	−0.0685705	−	0.0395892i
$134$	0.465123			0.0401805
$135$		0			0
$136$	−5.66237			−0.485544
$137$	−3.01046	−	1.73809i	−0.257201	−	0.148495i	0.365856	−	0.930671i	$-0.380776\pi$
$137$	−3.01046	−	1.73809i	−0.257201	−	0.148495i	−0.623057	+	0.782176i	$0.714110\pi$
$138$		0			0
$139$	7.37393	+	12.7720i	0.625448	+	1.08331i	0.988454	+	0.151521i	$0.0484172\pi$
$139$	7.37393	+	12.7720i	0.625448	+	1.08331i	−0.363006	+	0.931787i	$0.618249\pi$
$140$		0			0
$141$		0			0
$142$	−2.63742	−	1.52271i	−0.221327	−	0.127783i
$143$			13.1533i			1.09993i
$144$		0			0
$145$		0			0
$146$	1.56521	−	2.71103i	0.129538	−	0.224366i
$147$		0			0
$148$	−5.58747	+	3.22593i	−0.459287	+	0.265170i
$149$	5.07665	+	8.79301i	0.415895	+	0.720352i	0.995522	−	0.0945305i	$-0.0301350\pi$
$149$	5.07665	+	8.79301i	0.415895	+	0.720352i	−0.579627	+	0.814882i	$0.696802\pi$
$150$		0			0
$151$	5.15811	−	8.93410i	0.419761	−	0.727047i	−0.576155	−	0.817341i	$-0.695447\pi$
$151$	5.15811	−	8.93410i	0.419761	−	0.727047i	0.995915	+	0.0902940i	$0.0287807\pi$
$152$		−	0.636657i		−	0.0516397i
$153$		0			0
$154$	7.48237			0.602947
$155$		0			0
$156$		0			0
$157$	−0.920247	+	0.531305i	−0.0734437	+	0.0424028i	−0.536272	−	0.844045i	$-0.680168\pi$
$157$	−0.920247	+	0.531305i	−0.0734437	+	0.0424028i	0.462828	+	0.886448i	$0.346835\pi$
$158$	3.88185	−	2.24119i	0.308823	−	0.178299i
$159$		0			0
$160$		0			0
$161$	10.7981			0.851008
$162$		0			0
$163$		−	17.1386i		−	1.34240i	−0.741278	−	0.671198i	$-0.765780\pi$
$163$		−	17.1386i		−	1.34240i	0.741278	−	0.671198i	$-0.234220\pi$
$164$	−2.42742	+	4.20441i	−0.189549	+	0.328309i
$165$		0			0
$166$	2.46560	+	4.27054i	0.191368	+	0.331459i
$167$	−3.78752	+	2.18672i	−0.293087	+	0.169214i	−0.639333	−	0.768930i	$-0.720790\pi$
$167$	−3.78752	+	2.18672i	−0.293087	+	0.169214i	0.346246	+	0.938144i	$0.387456\pi$
$168$		0			0
$169$	−4.22666	+	7.32078i	−0.325127	+	0.563137i
$170$		0			0
$171$		0			0
$172$		−	13.6367i		−	1.03979i
$173$	−12.6960	−	7.33005i	−0.965260	−	0.557293i	−0.0674723	−	0.997721i	$-0.521493\pi$
$173$	−12.6960	−	7.33005i	−0.965260	−	0.557293i	−0.897788	+	0.440428i	$0.854827\pi$
$174$		0			0
$175$		0			0
$176$	−8.34718	−	14.4577i	−0.629192	−	1.08979i
$177$		0			0
$178$	2.56952	+	1.48351i	0.192593	+	0.111194i
$179$	−6.87014			−0.513499			−0.256749	−	0.966478i	$-0.582651\pi$
$179$	−6.87014			−0.513499			−0.256749	+	0.966478i	$0.582651\pi$
$180$		0			0
$181$	−10.9709			−0.815463			−0.407732	−	0.913102i	$-0.633680\pi$
$181$	−10.9709			−0.815463			−0.407732	+	0.913102i	$0.633680\pi$
$182$	−2.23991	−	1.29321i	−0.166033	−	0.0958593i
$183$		0			0
$184$	3.76434	+	6.52003i	0.277511	+	0.480663i
$185$		0			0
$186$		0			0
$187$	−16.9272	−	9.77294i	−1.23784	−	0.714668i
$188$		−	20.2980i		−	1.48039i
$189$		0			0
$190$		0			0
$191$	6.86627	−	11.8927i	0.496826	−	0.860528i	−0.503167	−	0.864189i	$-0.667832\pi$
$191$	6.86627	−	11.8927i	0.496826	−	0.860528i	0.999993	+	0.00366109i	$0.00116536\pi$
$192$		0			0
$193$	−0.417748	+	0.241187i	−0.0300701	+	0.0173610i	−0.514960	−	0.857214i	$-0.672193\pi$
$193$	−0.417748	+	0.241187i	−0.0300701	+	0.0173610i	0.484890	+	0.874575i	$0.338860\pi$
$194$	−1.70532	−	2.95370i	−0.122435	−	0.212064i
$195$		0			0
$196$	−0.382518	+	0.662541i	−0.0273227	+	0.0473244i
$197$			5.53488i			0.394344i	0.980369	+	0.197172i	$0.0631757\pi$
$197$			5.53488i			0.394344i	−0.980369	+	0.197172i	$0.936824\pi$
$198$		0			0
$199$	−17.4590			−1.23764			−0.618818	−	0.785534i	$-0.712388\pi$
$199$	−17.4590			−1.23764			−0.618818	+	0.785534i	$0.712388\pi$
$200$		0			0
$201$		0			0
$202$	−2.85704	+	1.64951i	−0.201021	+	0.116059i
$203$	−3.74288	+	2.16095i	−0.262698	+	0.151669i
$204$		0			0
$205$		0			0
$206$	2.89401			0.201635
$207$		0			0
$208$			5.77073i			0.400128i
$209$	1.09883	−	1.90324i	0.0760079	−	0.131650i
$210$		0			0
$211$	0.818328	+	1.41739i	0.0563360	+	0.0975769i	0.892818	−	0.450417i	$-0.148725\pi$
$211$	0.818328	+	1.41739i	0.0563360	+	0.0975769i	−0.836482	+	0.547994i	$0.815392\pi$
$212$	14.5120	−	8.37849i	0.996686	−	0.575437i
$213$		0			0
$214$	−3.43935	+	5.95713i	−0.235109	+	0.407221i
$215$		0			0
$216$		0			0
$217$			21.1667i			1.43689i
$218$	0.779592	+	0.450098i	0.0528006	+	0.0304844i
$219$		0			0
$220$		0			0
$221$	3.37820	+	5.85122i	0.227243	+	0.393596i
$222$		0			0
$223$	−6.70984	−	3.87393i	−0.449324	−	0.259417i	0.258221	−	0.966086i	$-0.416864\pi$
$223$	−6.70984	−	3.87393i	−0.449324	−	0.259417i	−0.707545	+	0.706669i	$0.750197\pi$
$224$	12.4432			0.831397
$225$		0			0
$226$	−3.11366			−0.207118
$227$	9.75169	+	5.63014i	0.647242	+	0.373685i	0.787399	−	0.616444i	$-0.211427\pi$
$227$	9.75169	+	5.63014i	0.647242	+	0.373685i	−0.140157	+	0.990129i	$0.544761\pi$
$228$		0			0
$229$	−5.23879	−	9.07384i	−0.346189	−	0.599616i	0.639380	−	0.768891i	$-0.279191\pi$
$229$	−5.23879	−	9.07384i	−0.346189	−	0.599616i	−0.985569	+	0.169274i	$0.945858\pi$
$230$		0			0
$231$		0			0
$232$	−2.60962	−	1.50667i	−0.171330	−	0.0989176i
$233$			2.90214i			0.190125i	0.995471	+	0.0950627i	$0.0303051\pi$
$233$			2.90214i			0.190125i	−0.995471	+	0.0950627i	$0.969695\pi$
$234$		0			0
$235$		0			0
$236$	−9.07188	+	15.7130i	−0.590529	+	1.02283i
$237$		0			0
$238$	3.32852	−	1.92172i	0.215756	−	0.124567i
$239$	−8.17723	−	14.1634i	−0.528941	−	0.916153i	−0.999430	−	0.0337471i	$-0.989256\pi$
$239$	−8.17723	−	14.1634i	−0.528941	−	0.916153i	0.470489	−	0.882406i	$-0.344077\pi$
$240$		0			0
$241$	−8.76194	+	15.1761i	−0.564406	+	0.977580i	0.432698	+	0.901539i	$0.357562\pi$
$241$	−8.76194	+	15.1761i	−0.564406	+	0.977580i	−0.997105	+	0.0760416i	$0.975772\pi$
$242$			12.8023i			0.822965i
$243$		0			0
$244$	−0.0195242			−0.00124991
$245$		0			0
$246$		0			0
$247$	−0.657890	+	0.379833i	−0.0418605	+	0.0241682i
$248$	−12.7808	+	7.37898i	−0.811580	+	0.468566i
$249$		0			0
$250$		0			0
$251$	−8.46999			−0.534621			−0.267311	−	0.963610i	$-0.586135\pi$
$251$	−8.46999			−0.534621			−0.267311	+	0.963610i	$0.586135\pi$
$252$		0			0
$253$			25.9882i			1.63386i
$254$	2.19079	−	3.79456i	0.137462	−	0.238092i
$255$		0			0
$256$	−0.468695	−	0.811804i	−0.0292934	−	0.0507377i
$257$	−2.48766	+	1.43625i	−0.155176	+	0.0895910i	−0.575577	−	0.817747i	$-0.695223\pi$
$257$	−2.48766	+	1.43625i	−0.155176	+	0.0895910i	0.420401	+	0.907338i	$0.361889\pi$
$258$		0			0
$259$	4.65545	−	8.06348i	0.289276	−	0.501040i
$260$		0			0
$261$		0			0
$262$		−	0.127493i		−	0.00787656i
$263$	22.1909	+	12.8119i	1.36835	+	0.790017i	0.990717	−	0.135938i	$-0.0434048\pi$
$263$	22.1909	+	12.8119i	1.36835	+	0.790017i	0.377633	+	0.925955i	$0.376738\pi$
$264$		0			0
$265$		0			0
$266$	0.216072	+	0.374247i	0.0132482	+	0.0229465i
$267$		0			0
$268$	1.51166	+	0.872756i	0.0923392	+	0.0533121i
$269$	0.337210			0.0205600			0.0102800	−	0.999947i	$-0.496728\pi$
$269$	0.337210			0.0205600			0.0102800	+	0.999947i	$0.496728\pi$
$270$		0			0
$271$	21.5927			1.31166			0.655831	−	0.754908i	$-0.272318\pi$
$271$	21.5927			1.31166			0.655831	+	0.754908i	$0.272318\pi$
$272$	−7.42646	−	4.28767i	−0.450295	−	0.259978i
$273$		0			0
$274$	0.822560	+	1.42472i	0.0496927	+	0.0860702i
$275$		0			0
$276$		0			0
$277$	20.9004	+	12.0669i	1.25579	+	0.725028i	0.972252	−	0.233934i	$-0.0751600\pi$
$277$	20.9004	+	12.0669i	1.25579	+	0.725028i	0.283533	+	0.958962i	$0.408493\pi$
$278$		−	6.97949i		−	0.418602i
$279$		0			0
$280$		0			0
$281$	1.68363	−	2.91613i	0.100437	−	0.173962i	−0.811428	−	0.584453i	$-0.801309\pi$
$281$	1.68363	−	2.91613i	0.100437	−	0.173962i	0.911865	+	0.410491i	$0.134643\pi$
$282$		0			0
$283$	18.9224	−	10.9249i	1.12482	−	0.649415i	0.182193	−	0.983263i	$-0.441681\pi$
$283$	18.9224	−	10.9249i	1.12482	−	0.649415i	0.942627	+	0.333848i	$0.108347\pi$
$284$	−5.71444	−	9.89770i	−0.339090	−	0.587321i
$285$		0			0
$286$	3.11243	−	5.39088i	0.184042	−	0.318770i
$287$		−	7.00619i		−	0.413562i
$288$		0			0
$289$	6.95994			0.409408
$290$		0			0
$291$		0			0
$292$	10.1739	−	5.87393i	0.595385	−	0.343746i
$293$	−11.9114	+	6.87702i	−0.695869	+	0.401760i	−0.805807	−	0.592179i	$-0.798268\pi$
$293$	−11.9114	+	6.87702i	−0.695869	+	0.401760i	0.109938	+	0.993938i	$0.464935\pi$
$294$		0			0
$295$		0			0
$296$	6.49179			0.377328
$297$		0			0
$298$		−	4.80509i		−	0.278352i
$299$	4.49166	−	7.77978i	0.259759	−	0.449916i
$300$		0			0
$301$	9.83978	+	17.0430i	0.567155	+	0.982342i
$302$	−4.22810	+	2.44110i	−0.243300	+	0.140469i
$303$		0			0
$304$	0.482090	−	0.835004i	0.0276498	−	0.0478908i
$305$		0			0
$306$		0			0
$307$		−	34.2183i		−	1.95294i	−0.215644	−	0.976472i	$-0.569185\pi$
$307$		−	34.2183i		−	1.95294i	0.215644	−	0.976472i	$-0.430815\pi$
$308$	24.3179	+	14.0399i	1.38564	+	0.799999i
$309$		0			0
$310$		0			0
$311$	11.5199	+	19.9530i	0.653232	+	1.13143i	0.982334	+	0.187136i	$0.0599206\pi$
$311$	11.5199	+	19.9530i	0.653232	+	1.13143i	−0.329102	+	0.944294i	$0.606746\pi$
$312$		0			0
$313$	3.11016	+	1.79565i	0.175796	+	0.101496i	0.585316	−	0.810805i	$-0.300970\pi$
$313$	3.11016	+	1.79565i	0.175796	+	0.101496i	−0.409520	+	0.912301i	$0.634304\pi$
$314$	0.502885			0.0283794
$315$		0			0
$316$	16.8215			0.946281
$317$	−11.4148	−	6.59033i	−0.641118	−	0.370150i	0.143927	−	0.989588i	$-0.454027\pi$
$317$	−11.4148	−	6.59033i	−0.641118	−	0.370150i	−0.785045	+	0.619439i	$0.787360\pi$
$318$		0			0
$319$	−5.20085	−	9.00813i	−0.291192	−	0.504359i
$320$		0			0
$321$		0			0
$322$	−4.42560	−	2.55512i	−0.246629	−	0.142391i
$323$		−	1.12887i		−	0.0628119i
$324$		0			0
$325$		0			0
$326$	−4.05545	+	7.02424i	−0.224611	+	0.389037i
$327$		0			0
$328$	4.23044	−	2.44244i	0.233587	−	0.134861i
$329$	14.6464	+	25.3683i	0.807483	+	1.39860i
$330$		0			0
$331$	−0.591264	+	1.02410i	−0.0324988	+	0.0562896i	−0.881817	−	0.471591i	$-0.843680\pi$
$331$	−0.591264	+	1.02410i	−0.0324988	+	0.0562896i	0.849319	+	0.527881i	$0.177013\pi$
$332$			18.5058i			1.01564i
$333$		0			0
$334$	2.06975			0.113252
$335$		0			0
$336$		0			0
$337$	21.4770	−	12.3997i	1.16993	−	0.675457i	0.216263	−	0.976335i	$-0.430613\pi$
$337$	21.4770	−	12.3997i	1.16993	−	0.675457i	0.953662	+	0.300879i	$0.0972799\pi$
$338$	3.46459	−	2.00028i	0.188449	−	0.108801i
$339$		0			0
$340$		0			0
$341$	−50.9428			−2.75871
$342$		0			0
$343$		−	19.0454i		−	1.02836i
$344$	−6.86053	+	11.8828i	−0.369895	+	0.640677i
$345$		0			0
$346$	3.46898	+	6.00845i	0.186493	+	0.323016i
$347$	19.1991	−	11.0846i	1.03066	−	0.595052i	0.113486	−	0.993540i	$-0.463798\pi$
$347$	19.1991	−	11.0846i	1.03066	−	0.595052i	0.917174	+	0.398488i	$0.130465\pi$
$348$		0			0
$349$	7.45925	−	12.9198i	0.399285	−	0.691581i	−0.594353	−	0.804204i	$-0.702592\pi$
$349$	7.45925	−	12.9198i	0.399285	−	0.691581i	0.993638	+	0.112623i	$0.0359252\pi$
$350$		0			0
$351$		0			0
$352$			29.9476i			1.59621i
$353$	14.6484	+	8.45726i	0.779656	+	0.450134i	0.836308	−	0.548260i	$-0.184709\pi$
$353$	14.6484	+	8.45726i	0.779656	+	0.450134i	−0.0566525	+	0.998394i	$0.518043\pi$
$354$		0			0
$355$		0			0
$356$	5.56732	+	9.64288i	0.295067	+	0.511072i
$357$		0			0
$358$	2.81573	+	1.62566i	0.148816	+	0.0859190i
$359$	0.636657			0.0336015			0.0168007	−	0.999859i	$-0.494652\pi$
$359$	0.636657			0.0336015			0.0168007	+	0.999859i	$0.494652\pi$
$360$		0			0
$361$	−18.8731			−0.993320
$362$	4.49644	+	2.59602i	0.236328	+	0.136444i
$363$		0			0
$364$	−4.85317	−	8.40594i	−0.254375	−	0.440591i
$365$		0			0
$366$		0			0
$367$	17.4053	+	10.0490i	0.908550	+	0.524552i	0.879964	−	0.475040i	$-0.157566\pi$
$367$	17.4053	+	10.0490i	0.908550	+	0.524552i	0.0285858	+	0.999591i	$0.490900\pi$
$368$			11.4018i			0.594358i
$369$		0			0
$370$		0			0
$371$	−12.0913	+	20.9427i	−0.627749	+	1.08729i
$372$		0			0
$373$	−17.0113	+	9.82146i	−0.880810	+	0.508536i	−0.870925	−	0.491415i	$-0.836480\pi$
$373$	−17.0113	+	9.82146i	−0.880810	+	0.508536i	−0.00988448	+	0.999951i	$0.503146\pi$
$374$	4.62509	+	8.01088i	0.239157	+	0.414233i
$375$		0			0
$376$	−10.2118	+	17.6874i	−0.526635	+	0.912159i
$377$			3.59555i			0.185180i
$378$		0			0
$379$	7.94219			0.407963			0.203982	−	0.978975i	$-0.434612\pi$
$379$	7.94219			0.407963			0.203982	+	0.978975i	$0.434612\pi$
$380$		0			0
$381$		0			0
$382$	−5.62829	+	3.24949i	−0.287968	+	0.166259i
$383$	27.0103	−	15.5944i	1.38016	−	0.796836i	0.387983	−	0.921667i	$-0.373172\pi$
$383$	27.0103	−	15.5944i	1.38016	−	0.796836i	0.992178	+	0.124830i	$0.0398387\pi$
$384$		0			0
$385$		0			0
$386$	0.228285			0.0116194
$387$		0			0
$388$		−	12.7995i		−	0.649795i
$389$	15.7247	−	27.2360i	0.797274	−	1.38092i	−0.124111	−	0.992268i	$-0.539608\pi$
$389$	15.7247	−	27.2360i	0.797274	−	1.38092i	0.921385	−	0.388650i	$-0.127059\pi$
$390$		0			0
$391$	6.67463	+	11.5608i	0.337550	+	0.584655i
$392$	0.666642	−	0.384886i	0.0336705	−	0.0194397i
$393$		0			0
$394$	1.30970	−	2.26847i	0.0659819	−	0.114284i
$395$		0			0
$396$		0			0
$397$		−	17.7174i		−	0.889211i	−0.895726	−	0.444606i	$-0.853344\pi$
$397$		−	17.7174i		−	0.889211i	0.895726	−	0.444606i	$-0.146656\pi$
$398$	7.15558	+	4.13128i	0.358677	+	0.207082i
$399$		0			0
$400$		0			0
$401$	−3.57124	−	6.18556i	−0.178339	−	0.308892i	0.762973	−	0.646431i	$-0.223739\pi$
$401$	−3.57124	−	6.18556i	−0.178339	−	0.308892i	−0.941312	+	0.337538i	$0.890406\pi$
$402$		0			0
$403$	15.2502	+	8.80468i	0.759665	+	0.438593i
$404$	−12.3806			−0.615958
$405$		0			0
$406$	2.04536			0.101509
$407$	19.4067	+	11.2045i	0.961955	+	0.555385i
$408$		0			0
$409$	12.3759	+	21.4357i	0.611948	+	1.05993i	0.990912	+	0.134514i	$0.0429472\pi$
$409$	12.3759	+	21.4357i	0.611948	+	1.05993i	−0.378964	+	0.925412i	$0.623719\pi$
$410$		0			0
$411$		0			0
$412$	9.40558	+	5.43031i	0.463380	+	0.267532i
$413$		−	26.1839i		−	1.28843i
$414$		0			0
$415$		0			0
$416$	5.17598	−	8.96505i	0.253773	−	0.439548i
$417$		0			0
$418$	−0.900715	+	0.520028i	−0.0440554	+	0.0254354i
$419$	5.32956	+	9.23106i	0.260366	+	0.450967i	0.966339	−	0.257272i	$-0.0828235\pi$
$419$	5.32956	+	9.23106i	0.260366	+	0.450967i	−0.705973	+	0.708238i	$0.749490\pi$
$420$		0			0
$421$	4.08931	−	7.08288i	0.199301	−	0.345199i	−0.749001	−	0.662569i	$-0.769466\pi$
$421$	4.08931	−	7.08288i	0.199301	−	0.345199i	0.948302	+	0.317370i	$0.102800\pi$
$422$		−	0.774555i		−	0.0377048i
$423$		0			0
$424$	−16.8607			−0.818828
$425$		0			0
$426$		0			0
$427$	0.0244012	−	0.0140881i	0.00118086	−	0.000681769i
$428$	−22.3559	+	12.9072i	−1.08061	+	0.623893i
$429$		0			0
$430$		0			0
$431$	−1.67248			−0.0805604			−0.0402802	−	0.999188i	$-0.512825\pi$
$431$	−1.67248			−0.0805604			−0.0402802	+	0.999188i	$0.512825\pi$
$432$		0			0
$433$		−	9.95994i		−	0.478644i	−0.970940	−	0.239322i	$-0.923075\pi$
$433$		−	9.95994i		−	0.478644i	0.970940	−	0.239322i	$-0.0769252\pi$
$434$	5.00863	−	8.67519i	0.240422	−	0.416423i
$435$		0			0
$436$	1.68913	+	2.92565i	0.0808945	+	0.140113i
$437$	−1.29985	+	0.750471i	−0.0621805	+	0.0358999i
$438$		0			0
$439$	6.40788	−	11.0988i	0.305832	−	0.529716i	−0.671615	−	0.740901i	$-0.734399\pi$
$439$	6.40788	−	11.0988i	0.305832	−	0.529716i	0.977446	+	0.211185i	$0.0677322\pi$
$440$		0			0
$441$		0			0
$442$		−	3.19750i		−	0.152090i
$443$	−6.71520	−	3.87702i	−0.319049	−	0.184203i	0.331920	−	0.943308i	$-0.392304\pi$
$443$	−6.71520	−	3.87702i	−0.319049	−	0.184203i	−0.650968	+	0.759105i	$0.725637\pi$
$444$		0			0
$445$		0			0
$446$	1.83335	+	3.17546i	0.0868118	+	0.150362i
$447$		0			0
$448$	6.91452	+	3.99210i	0.326681	+	0.188609i
$449$	−33.3401			−1.57342			−0.786709	−	0.617324i	$-0.788217\pi$
$449$	−33.3401			−1.57342			−0.786709	+	0.617324i	$0.788217\pi$
$450$		0			0
$451$	16.8621			0.794004
$452$	−10.1195	−	5.84247i	−0.475979	−	0.274807i
$453$		0			0
$454$	−2.66449	−	4.61503i	−0.125051	−	0.216594i
$455$		0			0
$456$		0			0
$457$	−33.0988	−	19.1096i	−1.54830	−	0.893910i	−0.998272	−	0.0587626i	$-0.981285\pi$
$457$	−33.0988	−	19.1096i	−1.54830	−	0.893910i	−0.550026	−	0.835148i	$-0.685382\pi$
$458$			4.95856i			0.231698i
$459$		0			0
$460$		0			0
$461$	15.6517	−	27.1095i	0.728971	−	1.26261i	−0.228348	−	0.973580i	$-0.573332\pi$
$461$	15.6517	−	27.1095i	0.728971	−	1.26261i	0.957319	−	0.289035i	$-0.0933343\pi$
$462$		0			0
$463$	10.4661	−	6.04258i	0.486399	−	0.280823i	−0.236680	−	0.971588i	$-0.576059\pi$
$463$	10.4661	−	6.04258i	0.486399	−	0.280823i	0.723079	+	0.690765i	$0.242726\pi$
$464$	−2.28176	−	3.95212i	−0.105928	−	0.183473i
$465$		0			0
$466$	0.686725	−	1.18944i	0.0318119	−	0.0550998i
$467$		−	7.60466i		−	0.351902i	−0.984399	−	0.175951i	$-0.943700\pi$
$467$		−	7.60466i		−	0.351902i	0.984399	−	0.175951i	$-0.0563000\pi$
$468$		0			0
$469$	−2.51901			−0.116317
$470$		0			0
$471$		0			0
$472$	15.8102	−	9.12803i	0.727724	−	0.420152i
$473$	−41.0181	+	23.6818i	−1.88601	+	1.08889i
$474$		0			0
$475$		0			0
$476$	14.4237			0.661108
$477$		0			0
$478$			7.73982i			0.354011i
$479$	16.2417	−	28.1314i	0.742101	−	1.28536i	−0.209437	−	0.977822i	$-0.567163\pi$
$479$	16.2417	−	28.1314i	0.742101	−	1.28536i	0.951537	−	0.307534i	$-0.0995037\pi$
$480$		0			0
$481$	−3.87304	−	6.70830i	−0.176595	−	0.305872i
$482$	7.18217	−	4.14663i	0.327139	−	0.188874i
$483$		0			0
$484$	−24.0223	+	41.6079i	−1.09192	+	1.89127i
$485$		0			0
$486$		0			0
$487$			4.46121i			0.202157i	0.994878	+	0.101078i	$0.0322293\pi$
$487$			4.46121i			0.202157i	−0.994878	+	0.101078i	$0.967771\pi$
$488$	0.0170131	+	0.00982254i	0.000770148	+	0.000444645i
$489$		0			0
$490$		0			0
$491$	16.4210	+	28.4420i	0.741070	+	1.28357i	0.952008	+	0.306072i	$0.0990148\pi$
$491$	16.4210	+	28.4420i	0.741070	+	1.28357i	−0.210938	+	0.977499i	$0.567652\pi$
$492$		0			0
$493$	−4.62717	−	2.67150i	−0.208397	−	0.120318i
$494$	0.359515			0.0161754
$495$		0			0
$496$	−22.3501			−1.00355
$497$	14.2837	+	8.24672i	0.640713	+	0.369916i
$498$		0			0
$499$	−17.1010	−	29.6198i	−0.765547	−	1.32597i	−0.939957	−	0.341293i	$-0.889135\pi$
$499$	−17.1010	−	29.6198i	−0.765547	−	1.32597i	0.174410	−	0.984673i	$-0.444198\pi$
$500$		0			0
$501$		0			0
$502$	3.47143	+	2.00423i	0.154938	+	0.0894532i
$503$		−	22.1773i		−	0.988837i	−0.869224	−	0.494419i	$-0.835381\pi$
$503$		−	22.1773i		−	0.988837i	0.869224	−	0.494419i	$-0.164619\pi$
$504$		0			0
$505$		0			0
$506$	6.14951	−	10.6513i	0.273379	−	0.473507i
$507$		0			0
$508$	14.2402	−	8.22160i	0.631808	−	0.364775i
$509$	10.7816	+	18.6743i	0.477887	+	0.827724i	0.999679	−	0.0253489i	$-0.00806968\pi$
$509$	10.7816	+	18.6743i	0.477887	+	0.827724i	−0.521792	+	0.853073i	$0.674736\pi$
$510$		0			0
$511$	−8.47688	+	14.6824i	−0.374995	+	0.649510i
$512$			22.8115i			1.00813i
$513$		0			0
$514$	1.35943			0.0599617
$515$		0			0
$516$		0			0
$517$	−61.0550	+	35.2501i	−2.68520	+	1.55030i
$518$	−3.81608	+	2.20321i	−0.167669	+	0.0968037i
$519$		0			0
$520$		0			0
$521$	−20.2626			−0.887718			−0.443859	−	0.896097i	$-0.646391\pi$
$521$	−20.2626			−0.887718			−0.443859	+	0.896097i	$0.646391\pi$
$522$		0			0
$523$			31.8114i			1.39101i	0.718520	+	0.695507i	$0.244820\pi$
$523$			31.8114i			1.39101i	−0.718520	+	0.695507i	$0.755180\pi$
$524$	0.239229	−	0.414356i	0.0104507	−	0.0181012i
$525$		0			0
$526$	−6.06330	−	10.5019i	−0.264373	−	0.457907i
$527$	−22.6618	+	13.0838i	−0.987164	+	0.569940i
$528$		0			0
$529$	−2.62541	+	4.54735i	−0.114148	+	0.197711i
$530$		0			0
$531$		0			0
$532$			1.62175i			0.0703117i
$533$	−5.04780	−	2.91435i	−0.218645	−	0.126235i
$534$		0			0
$535$		0			0
$536$	−0.878159	−	1.52102i	−0.0379307	−	0.0656978i
$537$		0			0
$538$	−0.138205	−	0.0797930i	−0.00595846	−	0.00344012i
$539$	2.65717			0.114452
$540$		0			0
$541$	−15.1315			−0.650553			−0.325277	−	0.945619i	$-0.605457\pi$
$541$	−15.1315			−0.650553			−0.325277	+	0.945619i	$0.605457\pi$
$542$	−8.84977	−	5.10942i	−0.380130	−	0.219468i
$543$		0			0
$544$	7.69153	+	13.3221i	0.329772	+	0.571181i
$545$		0			0
$546$		0			0
$547$	−3.53982	−	2.04372i	−0.151352	−	0.0873831i	0.422411	−	0.906404i	$-0.361184\pi$
$547$	−3.53982	−	2.04372i	−0.151352	−	0.0873831i	−0.573763	+	0.819021i	$0.694517\pi$
$548$			6.17381i			0.263732i
$549$		0			0
$550$		0			0
$551$	0.300374	−	0.520263i	0.0127964	−	0.0221639i
$552$		0			0
$553$	−21.0233	+	12.1378i	−0.894003	+	0.516153i
$554$	−5.71070	−	9.89123i	−0.242625	−	0.420238i
$555$		0			0
$556$	13.0963	−	22.6835i	0.555408	−	0.961994i
$557$		−	13.1425i		−	0.556864i	−0.960456	−	0.278432i	$-0.910185\pi$
$557$		−	13.1425i		−	0.556864i	0.960456	−	0.278432i	$-0.0898147\pi$
$558$		0			0
$559$	16.3721			0.692467
$560$		0			0
$561$		0			0
$562$	−1.38007	+	0.796785i	−0.0582149	+	0.0336104i
$563$	21.2368	−	12.2611i	0.895023	−	0.516742i	0.0194410	−	0.999811i	$-0.493811\pi$
$563$	21.2368	−	12.2611i	0.895023	−	0.516742i	0.875582	+	0.483069i	$0.160478\pi$
$564$		0			0
$565$		0			0
$566$	−10.3405			−0.434642
$567$		0			0
$568$			11.4996i			0.482514i
$569$	−11.3649	+	19.6846i	−0.476442	+	0.825223i	−0.999636	−	0.0269915i	$-0.991407\pi$
$569$	−11.3649	+	19.6846i	−0.476442	+	0.825223i	0.523193	+	0.852214i	$0.324741\pi$
$570$		0			0
$571$	0.247093	+	0.427977i	0.0103405	+	0.0179103i	0.871149	−	0.491018i	$-0.163375\pi$
$571$	0.247093	+	0.427977i	0.0103405	+	0.0179103i	−0.860809	+	0.508928i	$0.830042\pi$
$572$	20.2309	−	11.6803i	0.845897	−	0.488379i
$573$		0			0
$574$	−1.65786	+	2.87149i	−0.0691976	+	0.119854i
$575$		0			0
$576$		0			0
$577$			9.41187i			0.391821i	0.980622	+	0.195911i	$0.0627662\pi$
$577$			9.41187i			0.391821i	−0.980622	+	0.195911i	$0.937234\pi$
$578$	−2.85254	−	1.64691i	−0.118650	−	0.0685025i
$579$		0			0
$580$		0			0
$581$	−13.3532	−	23.1284i	−0.553984	−	0.959529i
$582$		0			0
$583$	−50.4037	−	29.1006i	−2.08751	−	1.20522i
$584$	−11.8206			−0.489139
$585$		0			0
$586$	6.50916			0.268891
$587$	−8.63705	−	4.98661i	−0.356489	−	0.205819i	0.311050	−	0.950393i	$-0.399319\pi$
$587$	−8.63705	−	4.98661i	−0.356489	−	0.205819i	−0.667540	+	0.744574i	$0.732653\pi$
$588$		0			0
$589$	−1.47110	−	2.54801i	−0.0606155	−	0.104989i
$590$		0			0
$591$		0			0
$592$	8.51428	+	4.91572i	0.349935	+	0.202035i
$593$		−	38.3421i		−	1.57452i	−0.616621	−	0.787260i	$-0.711499\pi$
$593$		−	38.3421i		−	1.57452i	0.616621	−	0.787260i	$-0.288501\pi$
$594$		0			0
$595$		0			0
$596$	9.01628	−	15.6167i	0.369321	−	0.639683i
$597$		0			0
$598$	−3.68182	+	2.12570i	−0.150561	+	0.0869262i
$599$	5.07665	+	8.79301i	0.207426	+	0.359273i	0.950903	−	0.309489i	$-0.100158\pi$
$599$	5.07665	+	8.79301i	0.207426	+	0.359273i	−0.743477	+	0.668762i	$0.766825\pi$
$600$		0			0
$601$	10.6371	−	18.4241i	0.433898	−	0.751533i	−0.563307	−	0.826248i	$-0.690471\pi$
$601$	10.6371	−	18.4241i	0.433898	−	0.751533i	0.997205	+	0.0747146i	$0.0238046\pi$
$602$		−	9.31344i		−	0.379587i
$603$		0			0
$604$	−18.3219			−0.745508
$605$		0			0
$606$		0			0
$607$	32.6799	−	18.8678i	1.32644	−	0.765819i	0.341691	−	0.939812i	$-0.389000\pi$
$607$	32.6799	−	18.8678i	1.32644	−	0.765819i	0.984747	+	0.173993i	$0.0556671\pi$
$608$	−1.49789	+	0.864808i	−0.0607475	+	0.0350726i
$609$		0			0
$610$		0			0
$611$	24.3698			0.985895
$612$		0			0
$613$		−	32.2633i		−	1.30310i	−0.758605	−	0.651551i	$-0.774119\pi$
$613$		−	32.2633i		−	1.30310i	0.758605	−	0.651551i	$-0.225881\pi$
$614$	−8.09699	+	14.0244i	−0.326768	+	0.565979i
$615$		0			0
$616$	−14.1268	−	24.4684i	−0.569186	−	0.985860i
$617$	−22.5321	+	13.0089i	−0.907108	+	0.523719i	−0.879499	−	0.475900i	$-0.842122\pi$
$617$	−22.5321	+	13.0089i	−0.907108	+	0.523719i	−0.0276084	+	0.999619i	$0.508789\pi$
$618$		0			0
$619$	−5.94077	+	10.2897i	−0.238780	+	0.413578i	−0.960364	−	0.278748i	$-0.910081\pi$
$619$	−5.94077	+	10.2897i	−0.238780	+	0.413578i	0.721585	+	0.692326i	$0.243414\pi$
$620$		0			0
$621$		0			0
$622$		−	10.9037i		−	0.437197i
$623$	−13.9160	−	8.03440i	−0.557532	−	0.321891i
$624$		0			0
$625$		0			0
$626$	−0.849799	−	1.47189i	−0.0339648	−	0.0588288i
$627$		0			0
$628$	1.63439	+	0.943614i	0.0652191	+	0.0376543i
$629$	11.5107			0.458962
$630$		0			0
$631$	−13.2726			−0.528372			−0.264186	−	0.964472i	$-0.585103\pi$
$631$	−13.2726			−0.528372			−0.264186	+	0.964472i	$0.585103\pi$
$632$	−14.6580	−	8.46279i	−0.583063	−	0.336632i
$633$		0			0
$634$	3.11890	+	5.40210i	0.123867	+	0.214545i
$635$		0			0
$636$		0			0
$637$	−0.795445	−	0.459251i	−0.0315167	−	0.0181962i
$638$			4.92265i			0.194890i
$639$		0			0
$640$		0			0
$641$	22.4075	−	38.8109i	0.885042	−	1.53294i	0.0393765	−	0.999224i	$-0.487463\pi$
$641$	22.4075	−	38.8109i	0.885042	−	1.53294i	0.845665	−	0.533713i	$-0.179204\pi$
$642$		0			0
$643$	−12.9259	+	7.46275i	−0.509747	+	0.294302i	−0.732729	−	0.680520i	$-0.761754\pi$
$643$	−12.9259	+	7.46275i	−0.509747	+	0.294302i	0.222983	+	0.974822i	$0.428421\pi$
$644$	−9.58886	−	16.6084i	−0.377854	−	0.654462i
$645$		0			0
$646$	−0.267121	+	0.462667i	−0.0105097	+	0.0182034i
$647$		−	41.2684i		−	1.62243i	−0.584749	−	0.811214i	$-0.698807\pi$
$647$		−	41.2684i		−	1.62243i	0.584749	−	0.811214i	$-0.301193\pi$
$648$		0			0
$649$	63.0179			2.47367
$650$		0			0
$651$		0			0
$652$	−26.3606	+	15.2193i	−1.03236	+	0.596034i
$653$	−23.9241	+	13.8126i	−0.936223	+	0.540528i	−0.888774	−	0.458345i	$-0.848442\pi$
$653$	−23.9241	+	13.8126i	−0.936223	+	0.540528i	−0.0474484	+	0.998874i	$0.515109\pi$
$654$		0			0
$655$		0			0
$656$	7.39788			0.288839
$657$		0			0
$658$		−	13.8630i		−	0.540435i
$659$	−20.0112	+	34.6605i	−0.779527	+	1.35018i	0.152688	+	0.988274i	$0.451207\pi$
$659$	−20.0112	+	34.6605i	−0.779527	+	1.35018i	−0.932215	+	0.361905i	$0.882126\pi$
$660$		0			0
$661$	−12.4965	−	21.6445i	−0.486056	−	0.841874i	0.513816	−	0.857901i	$-0.328232\pi$
$661$	−12.4965	−	21.6445i	−0.486056	−	0.841874i	−0.999872	+	0.0160270i	$0.994898\pi$
$662$	0.484659	−	0.279818i	0.0188368	−	0.0108754i
$663$		0			0
$664$	9.31018	−	16.1257i	0.361305	−	0.625799i
$665$		0			0
$666$		0			0
$667$			7.10405i			0.275070i
$668$	6.72675	+	3.88369i	0.260266	+	0.150264i
$669$		0			0
$670$		0			0
$671$	0.0339063	+	0.0587274i	0.00130894	+	0.00226715i
$672$		0			0
$673$	35.3380	+	20.4024i	1.36218	+	0.786454i	0.989914	−	0.141672i	$-0.0452479\pi$
$673$	35.3380	+	20.4024i	1.36218	+	0.786454i	0.372265	+	0.928126i	$0.378581\pi$
$674$	−11.7365			−0.452072
$675$		0			0
$676$	15.0133			0.577436
$677$	−35.6710	−	20.5947i	−1.37095	−	0.791518i	−0.379901	−	0.925027i	$-0.624042\pi$
$677$	−35.6710	−	20.5947i	−1.37095	−	0.791518i	−0.991048	+	0.133509i	$0.957375\pi$
$678$		0			0
$679$	9.23569	+	15.9967i	0.354433	+	0.613896i
$680$		0			0
$681$		0			0
$682$	20.8789	+	12.0545i	0.799496	+	0.461589i
$683$		−	1.33820i		−	0.0512047i	−0.999672	−	0.0256023i	$-0.991850\pi$
$683$		−	1.33820i		−	0.0512047i	0.999672	−	0.0256023i	$-0.00815037\pi$
$684$		0			0
$685$		0			0
$686$	−4.50667	+	7.80578i	−0.172065	+	0.298026i
$687$		0			0
$688$	−17.9958	+	10.3899i	−0.686083	+	0.396110i
$689$	10.0592	+	17.4230i	0.383225	+	0.663764i
$690$		0			0
$691$	12.6407	−	21.8943i	0.480874	−	0.832898i	−0.518885	−	0.854844i	$-0.673653\pi$
$691$	12.6407	−	21.8943i	0.480874	−	0.832898i	0.999759	+	0.0219459i	$0.00698617\pi$
$692$			26.0368i			0.989770i
$693$		0			0
$694$	−10.4917			−0.398258
$695$		0			0
$696$		0			0
$697$	7.50106	−	4.33074i	0.284123	−	0.164039i
$698$	−6.11435	+	3.53012i	−0.231432	+	0.133617i
$699$		0			0
$700$		0			0
$701$	18.2064			0.687645			0.343822	−	0.939035i	$-0.388278\pi$
$701$	18.2064			0.687645			0.343822	+	0.939035i	$0.388278\pi$
$702$		0			0
$703$			1.29422i			0.0488126i
$704$	−9.60795	+	16.6415i	−0.362113	+	0.627199i
$705$		0			0
$706$	−4.00244	−	6.93242i	−0.150634	−	0.260905i
$707$	15.4732	−	8.93344i	0.581929	−	0.335977i
$708$		0			0
$709$	20.9103	−	36.2177i	0.785304	−	1.36019i	−0.143514	−	0.989648i	$-0.545840\pi$
$709$	20.9103	−	36.2177i	0.785304	−	1.36019i	0.928818	−	0.370537i	$-0.120826\pi$
$710$		0			0
$711$		0			0
$712$		−	11.2036i		−	0.419871i
$713$	30.1312	+	17.3962i	1.12842	+	0.651494i
$714$		0			0
$715$		0			0
$716$	6.10079	+	10.5669i	0.227997	+	0.394903i
$717$		0			0
$718$	−0.260934	−	0.150650i	−0.00973797	−	0.00562222i
$719$	48.9786			1.82660			0.913298	−	0.407293i	$-0.133527\pi$
$719$	48.9786			1.82660			0.913298	+	0.407293i	$0.133527\pi$
$720$		0			0
$721$	−15.6734			−0.583707
$722$	7.73514	+	4.46588i	0.287872	+	0.166203i
$723$		0			0
$724$	9.74236	+	16.8743i	0.362072	+	0.627127i
$725$		0			0
$726$		0			0
$727$	−37.9327	−	21.9005i	−1.40685	−	0.812243i	−0.411764	−	0.911291i	$-0.635087\pi$
$727$	−37.9327	−	21.9005i	−1.40685	−	0.812243i	−0.995083	+	0.0990474i	$0.968420\pi$
$728$			9.76642i			0.361968i
$729$		0			0
$730$		0			0
$731$	−12.1645	+	21.0696i	−0.449922	+	0.779287i
$732$		0			0
$733$	−5.87740	+	3.39332i	−0.217087	+	0.125335i	−0.604601	−	0.796529i	$-0.706667\pi$
$733$	−5.87740	+	3.39332i	−0.217087	+	0.125335i	0.387514	+	0.921864i	$0.373334\pi$
$734$	−4.75572	−	8.23715i	−0.175537	−	0.304039i
$735$		0			0
$736$	10.2267	−	17.7131i	0.376960	−	0.652913i
$737$		−	6.06261i		−	0.223319i
$738$		0			0
$739$	−28.7245			−1.05665			−0.528324	−	0.849043i	$-0.677179\pi$
$739$	−28.7245			−1.05665			−0.528324	+	0.849043i	$0.677179\pi$
$740$		0			0
$741$		0			0
$742$	9.91125	−	5.72226i	0.363853	−	0.210071i
$743$	27.2385	−	15.7262i	0.999284	−	0.576937i	0.0912477	−	0.995828i	$-0.470915\pi$
$743$	27.2385	−	15.7262i	0.999284	−	0.576937i	0.908036	+	0.418891i	$0.137581\pi$
$744$		0			0
$745$		0			0
$746$	9.29610			0.340354
$747$		0			0
$748$			34.7141i			1.26927i
$749$	18.6268	−	32.2626i	0.680610	−	1.17885i
$750$		0			0
$751$	−5.47659	−	9.48574i	−0.199844	−	0.346139i	0.748634	−	0.662984i	$-0.230710\pi$
$751$	−5.47659	−	9.48574i	−0.199844	−	0.346139i	−0.948478	+	0.316844i	$0.897377\pi$
$752$	−26.7866	+	15.4652i	−0.976806	+	0.563959i
$753$		0			0
$754$	0.850804	−	1.47364i	0.0309845	−	0.0536667i
$755$		0			0
$756$		0			0
$757$			45.7942i			1.66442i	0.554461	+	0.832210i	$0.312925\pi$
$757$			45.7942i			1.66442i	−0.554461	+	0.832210i	$0.687075\pi$
$758$	−3.25511	−	1.87934i	−0.118231	−	0.0682607i
$759$		0			0
$760$		0			0
$761$	−16.9569	−	29.3702i	−0.614687	−	1.06467i	−0.990439	−	0.137948i	$-0.955949\pi$
$761$	−16.9569	−	29.3702i	−0.614687	−	1.06467i	0.375753	−	0.926720i	$-0.377384\pi$
$762$		0			0
$763$	−4.22212	−	2.43764i	−0.152851	−	0.0882485i
$764$	−24.3894			−0.882378
$765$		0			0
$766$	−14.7602			−0.533309
$767$	−18.8649	−	10.8917i	−0.681173	−	0.393275i
$768$		0			0
$769$	3.57986	+	6.20050i	0.129093	+	0.223596i	0.923325	−	0.384018i	$-0.125460\pi$
$769$	3.57986	+	6.20050i	0.129093	+	0.223596i	−0.794232	+	0.607614i	$0.792127\pi$
$770$		0			0
$771$		0			0
$772$	0.741933	+	0.428355i	0.0267027	+	0.0154168i
$773$			14.5998i			0.525117i	0.964916	+	0.262558i	$0.0845663\pi$
$773$			14.5998i			0.525117i	−0.964916	+	0.262558i	$0.915434\pi$
$774$		0			0
$775$		0			0
$776$	−6.43935	+	11.1533i	−0.231159	+	0.400379i
$777$		0			0
$778$	−12.8895	+	7.44178i	−0.462113	+	0.266801i
$779$	0.486933	+	0.843393i	0.0174462	+	0.0302177i
$780$		0			0
$781$	−19.8477	+	34.3772i	−0.710207	+	1.23011i
$782$		−	6.31760i		−	0.225917i
$783$		0			0
$784$	1.16578			0.0416348
$785$		0			0
$786$		0			0
$787$	−15.9979	+	9.23638i	−0.570263	+	0.329242i	−0.757254	−	0.653120i	$-0.773460\pi$
$787$	−15.9979	+	9.23638i	−0.570263	+	0.329242i	0.186991	+	0.982362i	$0.440126\pi$
$788$	8.51312	−	4.91505i	0.303267	−	0.175092i
$789$		0			0
$790$		0			0
$791$	16.8630			0.599578
$792$		0			0
$793$		−	0.0234407i		−	0.000832405i
$794$	−4.19242	+	7.26149i	−0.148783	+	0.257700i
$795$		0			0
$796$	15.5039	+	26.8535i	0.549520	+	0.951796i
$797$	35.5395	−	20.5187i	1.25887	−	0.726810i	0.286017	−	0.958225i	$-0.407669\pi$
$797$	35.5395	−	20.5187i	1.25887	−	0.726810i	0.972855	+	0.231414i	$0.0743353\pi$
$798$		0			0
$799$	−18.1068	+	31.3619i	−0.640573	+	1.10950i
$800$		0			0
$801$		0			0
$802$			3.38021i			0.119359i
$803$	−35.3367	−	20.4016i	−1.24700	−	0.719958i
$804$		0			0
$805$		0			0
$806$	−4.16686	−	7.21721i	−0.146771	−	0.254215i
$807$		0			0
$808$	10.7883	+	6.22861i	0.379530	+	0.219122i
$809$	7.19375			0.252919			0.126459	−	0.991972i	$-0.459639\pi$
$809$	7.19375			0.252919			0.126459	+	0.991972i	$0.459639\pi$
$810$		0			0
$811$	38.2183			1.34203			0.671014	−	0.741445i	$-0.265859\pi$
$811$	38.2183			1.34203			0.671014	+	0.741445i	$0.265859\pi$
$812$	6.64746	+	3.83791i	0.233280	+	0.134684i
$813$		0			0
$814$	−5.30257	−	9.18431i	−0.185855	−	0.321910i
$815$		0			0
$816$		0			0
$817$	−2.36899	−	1.36774i	−0.0828805	−	0.0478511i
$818$		−	11.7139i		−	0.409566i
$819$		0			0
$820$		0			0
$821$	−0.334280	+	0.578990i	−0.0116665	+	0.0202069i	−0.871800	−	0.489863i	$-0.837047\pi$
$821$	−0.334280	+	0.578990i	−0.0116665	+	0.0202069i	0.860133	+	0.510069i	$0.170380\pi$
$822$		0			0
$823$	−1.23004	+	0.710165i	−0.0428766	+	0.0247548i	−0.521285	−	0.853383i	$-0.674547\pi$
$823$	−1.23004	+	0.710165i	−0.0428766	+	0.0247548i	0.478408	+	0.878137i	$0.341214\pi$
$824$	−5.46393	−	9.46380i	−0.190345	−	0.329687i
$825$		0			0
$826$	−6.19583	+	10.7315i	−0.215580	+	0.373396i
$827$			49.8169i			1.73230i	0.499782	+	0.866152i	$0.333414\pi$
$827$			49.8169i			1.73230i	−0.499782	+	0.866152i	$0.666586\pi$
$828$		0			0
$829$	−36.4150			−1.26475			−0.632373	−	0.774664i	$-0.717919\pi$
$829$	−36.4150			−1.26475			−0.632373	+	0.774664i	$0.717919\pi$
$830$		0			0
$831$		0			0
$832$	5.75244	−	3.32117i	0.199430	−	0.115141i
$833$	1.18204	−	0.682449i	0.0409551	−	0.0236455i
$834$		0			0
$835$		0			0
$836$	−3.90312			−0.134992
$837$		0			0
$838$		−	5.04447i		−	0.174258i
$839$	10.0445	−	17.3976i	0.346774	−	0.600631i	−0.638900	−	0.769290i	$-0.720610\pi$
$839$	10.0445	−	17.3976i	0.346774	−	0.600631i	0.985674	+	0.168659i	$0.0539436\pi$
$840$		0			0
$841$	13.0783	+	22.6523i	0.450976	+	0.781114i
$842$	−3.35201	+	1.93528i	−0.115518	+	0.0666942i
$843$		0			0
$844$	1.45338	−	2.51732i	0.0500273	−	0.0866498i
$845$		0			0
$846$		0			0
$847$		−	69.3349i		−	2.38238i
$848$	−22.1136	−	12.7673i	−0.759383	−	0.438430i
$849$		0			0
$850$		0			0
$851$	−7.65232	−	13.2542i	−0.262318	−	0.454349i
$852$		0			0
$853$	−23.3034	−	13.4542i	−0.797892	−	0.460663i	0.0448418	−	0.998994i	$-0.485722\pi$
$853$	−23.3034	−	13.4542i	−0.797892	−	0.460663i	−0.842733	+	0.538331i	$0.819055\pi$
$854$	−0.0133345			−0.000456296
$855$		0			0
$856$	25.9742			0.887779
$857$	42.2973	+	24.4204i	1.44485	+	0.834184i	0.998168	−	0.0605088i	$-0.0192723\pi$
$857$	42.2973	+	24.4204i	1.44485	+	0.834184i	0.446682	+	0.894693i	$0.352606\pi$
$858$		0			0
$859$	−20.7047	−	35.8616i	−0.706435	−	1.22358i	−0.966171	−	0.257902i	$-0.916969\pi$
$859$	−20.7047	−	35.8616i	−0.706435	−	1.22358i	0.259736	−	0.965680i	$-0.416365\pi$
$860$		0			0
$861$		0			0
$862$	0.685465	+	0.395754i	0.0233470	+	0.0134794i
$863$			50.8101i			1.72960i	0.502119	+	0.864799i	$0.332554\pi$
$863$			50.8101i			1.72960i	−0.502119	+	0.864799i	$0.667446\pi$
$864$		0			0
$865$		0			0
$866$	−2.35679	+	4.08209i	−0.0800871	+	0.138715i
$867$		0			0
$868$	32.5563	−	18.7964i	1.10503	−	0.637991i
$869$	−29.2126	−	50.5977i	−0.990970	−	1.71641i
$870$		0			0
$871$	−1.04783	+	1.81489i	−0.0355043	+	0.0614953i
$872$		−	3.39916i		−	0.115110i
$873$		0			0
$874$	0.710328			0.0240272
$875$		0			0
$876$		0			0
$877$	0.354715	−	0.204795i	0.0119779	−	0.00691542i	−0.493999	−	0.869462i	$-0.664465\pi$
$877$	0.354715	−	0.204795i	0.0119779	−	0.00691542i	0.505977	+	0.862547i	$0.331132\pi$
$878$	−5.25255	+	3.03256i	−0.177265	+	0.102344i
$879$		0			0
$880$		0			0
$881$	5.32851			0.179522			0.0897610	−	0.995963i	$-0.471390\pi$
$881$	5.32851			0.179522			0.0897610	+	0.995963i	$0.471390\pi$
$882$		0			0
$883$		−	14.2064i		−	0.478083i	−0.971009	−	0.239042i	$-0.923167\pi$
$883$		−	14.2064i		−	0.478083i	0.971009	−	0.239042i	$-0.0768333\pi$
$884$	5.99979	−	10.3919i	0.201795	−	0.349519i
$885$		0			0
$886$	1.83482	+	3.17800i	0.0616419	+	0.106767i
$887$	−6.26304	+	3.61597i	−0.210292	+	0.121412i	−0.601447	−	0.798913i	$-0.705409\pi$
$887$	−6.26304	+	3.61597i	−0.210292	+	0.121412i	0.391155	+	0.920325i	$0.372076\pi$
$888$		0			0
$889$	−11.8649	+	20.5506i	−0.397936	+	0.689245i
$890$		0			0
$891$		0			0
$892$			13.7604i			0.460733i
$893$	−3.52622	−	2.03586i	−0.118000	−	0.0681276i
$894$		0			0
$895$		0			0
$896$	−14.3325	−	24.8246i	−0.478815	−	0.829331i
$897$		0			0
$898$	13.6645	+	7.88919i	0.455989	+	0.263266i
$899$	−13.9256			−0.464444
$900$		0			0
$901$	−29.8960			−0.995981
$902$	−6.91093	−	3.99003i	−0.230109	−	0.132853i
$903$		0			0
$904$	5.87864	+	10.1821i	0.195521	+	0.338651i
$905$		0			0
$906$		0			0
$907$	33.6106	+	19.4051i	1.11602	+	0.644335i	0.940382	−	0.340120i	$-0.110468\pi$
$907$	33.6106	+	19.4051i	1.11602	+	0.644335i	0.175639	+	0.984455i	$0.443801\pi$
$908$		−	19.9986i		−	0.663677i
$909$		0			0
$910$		0			0
$911$	−20.1390	+	34.8819i	−0.667236	+	1.15569i	0.311437	+	0.950267i	$0.399190\pi$
$911$	−20.1390	+	34.8819i	−0.667236	+	1.15569i	−0.978674	+	0.205421i	$0.934144\pi$
$912$		0			0
$913$	55.6641	−	32.1377i	1.84221	−	1.06360i
$914$	9.04371	+	15.6642i	0.299139	+	0.518125i
$915$		0			0
$916$	−9.30424	+	16.1154i	−0.307421	+	0.532468i
$917$			0.690479i			0.0228016i
$918$		0			0
$919$	13.0468			0.430375			0.215187	−	0.976573i	$-0.430964\pi$
$919$	13.0468			0.430375			0.215187	+	0.976573i	$0.430964\pi$
$920$		0			0
$921$		0			0
$922$	−12.8297	+	7.40722i	−0.422523	+	0.243944i
$923$	11.8832	−	6.86074i	0.391139	−	0.225824i
$924$		0			0
$925$		0			0
$926$	−5.71936			−0.187950
$927$		0			0
$928$			8.18638i			0.268731i
$929$	−0.146912	+	0.254460i	−0.00482004	+	0.00834855i	−0.868425	−	0.495820i	$-0.834868\pi$
$929$	−0.146912	+	0.254460i	−0.00482004	+	0.00834855i	0.863605	+	0.504168i	$0.168201\pi$
$930$		0			0
$931$	0.0767321	+	0.132904i	0.00251479	+	0.00435575i
$932$	4.46374	−	2.57714i	0.146215	−	0.0844171i
$933$		0			0
$934$	−1.79947	+	3.11678i	−0.0588805	+	0.101984i
$935$		0			0
$936$		0			0
$937$			16.9141i			0.552559i	0.961077	+	0.276280i	$0.0891016\pi$
$937$			16.9141i			0.552559i	−0.961077	+	0.276280i	$0.910898\pi$
$938$	1.03242	+	0.596067i	0.0337097	+	0.0194623i
$939$		0			0
$940$		0			0
$941$	28.6046	+	49.5447i	0.932485	+	1.61511i	0.779059	+	0.626951i	$0.215697\pi$
$941$	28.6046	+	49.5447i	0.932485	+	1.61511i	0.153426	+	0.988160i	$0.450969\pi$
$942$		0			0
$943$	−9.97342	−	5.75815i	−0.324779	−	0.187511i
$944$	27.6478			0.899858
$945$		0			0
$946$	22.4150			0.728775
$947$	33.6664	+	19.4373i	1.09401	+	0.631627i	0.934641	−	0.355592i	$-0.115721\pi$
$947$	33.6664	+	19.4373i	1.09401	+	0.631627i	0.159369	+	0.987219i	$0.449054\pi$
$948$		0			0
$949$	7.05222	+	12.2148i	0.228925	+	0.396509i
$950$		0			0
$951$		0			0
$952$	−12.5686	−	7.25648i	−0.407350	−	0.235184i
$953$			54.4516i			1.76386i	0.471381	+	0.881930i	$0.343756\pi$
$953$			54.4516i			1.76386i	−0.471381	+	0.881930i	$0.656244\pi$
$954$		0			0
$955$		0			0
$956$	−14.5230	+	25.1546i	−0.469708	+	0.813557i
$957$		0			0
$958$	−13.3133	+	7.68644i	−0.430133	+	0.248338i
$959$	−4.45482	−	7.71598i	−0.143854	−	0.249162i
$960$		0			0
$961$	−18.6006	+	32.2172i	−0.600020	+	1.03926i
$962$			3.66587i			0.118192i
$963$		0			0
$964$	31.1229			1.00240
$965$		0			0
$966$		0			0
$967$	16.9482	−	9.78507i	0.545018	−	0.314666i	−0.202092	−	0.979367i	$-0.564774\pi$
$967$	16.9482	−	9.78507i	0.545018	−	0.314666i	0.747110	+	0.664700i	$0.231441\pi$
$968$	41.8654	−	24.1710i	1.34560	−	0.776885i
$969$		0			0
$970$		0			0
$971$	−6.31009			−0.202500			−0.101250	−	0.994861i	$-0.532284\pi$
$971$	−6.31009			−0.202500			−0.101250	+	0.994861i	$0.532284\pi$
$972$		0			0
$973$			37.7995i			1.21180i
$974$	1.05564	−	1.82843i	0.0338250	−	0.0585866i
$975$		0			0
$976$	0.0148757	+	0.0257654i	0.000476158	+	0.000824731i
$977$	6.42514	−	3.70955i	0.205558	−	0.118679i	−0.393687	−	0.919244i	$-0.628801\pi$
$977$	6.42514	−	3.70955i	0.205558	−	0.118679i	0.599245	+	0.800565i	$0.295467\pi$
$978$		0			0
$979$	19.3367	−	33.4922i	0.618004	−	1.07041i
$980$		0			0
$981$		0			0
$982$		−	15.5426i		−	0.495986i
$983$	−9.51134	−	5.49137i	−0.303365	−	0.175148i	0.340589	−	0.940212i	$-0.389374\pi$
$983$	−9.51134	−	5.49137i	−0.303365	−	0.175148i	−0.643953	+	0.765065i	$0.722707\pi$
$984$		0			0
$985$		0			0
$986$	1.26430	+	2.18983i	0.0402635	+	0.0697384i
$987$		0			0
$988$	1.16843	+	0.674595i	0.0371728	+	0.0214617i
$989$	32.3479			1.02860
$990$		0			0
$991$	−21.3721			−0.678908			−0.339454	−	0.940623i	$-0.610242\pi$
$991$	−21.3721			−0.678908			−0.339454	+	0.940623i	$0.610242\pi$
$992$	34.7217	+	20.0466i	1.10242	+	0.636480i
$993$		0			0
$994$	−3.90280	−	6.75984i	−0.123789	−	0.214409i
$995$		0			0
$996$		0			0
$997$	−26.4439	−	15.2674i	−0.837487	−	0.483524i	0.0189220	−	0.999821i	$-0.493977\pi$
$997$	−26.4439	−	15.2674i	−0.837487	−	0.483524i	−0.856409	+	0.516297i	$0.827310\pi$
$998$			16.1863i			0.512368i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.k.c.424.4		16
3.2	odd	2		225.2.k.c.124.5		16
5.2	odd	4		675.2.e.c.451.3		8
5.3	odd	4		675.2.e.e.451.2		8
5.4	even	2	inner	675.2.k.c.424.5		16
9.2	odd	6		2025.2.b.n.649.4		8
9.4	even	3	inner	675.2.k.c.199.5		16
9.5	odd	6		225.2.k.c.49.4		16
9.7	even	3		2025.2.b.o.649.5		8
15.2	even	4		225.2.e.e.151.2	yes	8
15.8	even	4		225.2.e.c.151.3	yes	8
15.14	odd	2		225.2.k.c.124.4		16
45.2	even	12		2025.2.a.q.1.3		4
45.4	even	6	inner	675.2.k.c.199.4		16
45.7	odd	12		2025.2.a.z.1.2		4
45.13	odd	12		675.2.e.e.226.2		8
45.14	odd	6		225.2.k.c.49.5		16
45.22	odd	12		675.2.e.c.226.3		8
45.23	even	12		225.2.e.c.76.3	✓	8
45.29	odd	6		2025.2.b.n.649.5		8
45.32	even	12		225.2.e.e.76.2	yes	8
45.34	even	6		2025.2.b.o.649.4		8
45.38	even	12		2025.2.a.y.1.2		4
45.43	odd	12		2025.2.a.p.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.e.c.76.3	✓	8	45.23	even	12
225.2.e.c.151.3	yes	8	15.8	even	4
225.2.e.e.76.2	yes	8	45.32	even	12
225.2.e.e.151.2	yes	8	15.2	even	4
225.2.k.c.49.4		16	9.5	odd	6
225.2.k.c.49.5		16	45.14	odd	6
225.2.k.c.124.4		16	15.14	odd	2
225.2.k.c.124.5		16	3.2	odd	2
675.2.e.c.226.3		8	45.22	odd	12
675.2.e.c.451.3		8	5.2	odd	4
675.2.e.e.226.2		8	45.13	odd	12
675.2.e.e.451.2		8	5.3	odd	4
675.2.k.c.199.4		16	45.4	even	6	inner
675.2.k.c.199.5		16	9.4	even	3	inner
675.2.k.c.424.4		16	1.1	even	1	trivial
675.2.k.c.424.5		16	5.4	even	2	inner
2025.2.a.p.1.3		4	45.43	odd	12
2025.2.a.q.1.3		4	45.2	even	12
2025.2.a.y.1.2		4	45.38	even	12
2025.2.a.z.1.2		4	45.7	odd	12
2025.2.b.n.649.4		8	9.2	odd	6
2025.2.b.n.649.5		8	45.29	odd	6
2025.2.b.o.649.4		8	45.34	even	6
2025.2.b.o.649.5		8	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.409850 - 0.236627i) q^{2} +(-0.888015 - 1.53809i) q^{4} +(2.21967 + 1.28153i) q^{7} +1.78702i q^{8} +O(q^{10})\)	\(q+(-0.409850 - 0.236627i) q^{2} +(-0.888015 - 1.53809i) q^{4} +(2.21967 + 1.28153i) q^{7} +1.78702i q^{8} +(-3.08430 + 5.34217i) q^{11} +(1.84662 - 1.06615i) q^{13} +(-0.606488 - 1.05047i) q^{14} +(-1.35317 + 2.34376i) q^{16} +3.16860i q^{17} -0.356267 q^{19} +(2.52821 - 1.45966i) q^{22} +(3.64854 - 2.10649i) q^{23} -1.00912 q^{26} -4.55206i q^{28} +(-0.843116 + 1.46032i) q^{29} +(4.12920 + 7.15199i) q^{31} +(4.20441 - 2.42742i) q^{32} +(0.749778 - 1.29865i) q^{34} -3.63274i q^{37} +(0.146016 + 0.0843024i) q^{38} +(-1.36677 - 2.36731i) q^{41} +(6.64949 + 3.83908i) q^{43} +10.9556 q^{44} -1.99381 q^{46} +(9.89770 + 5.71444i) q^{47} +(-0.215378 - 0.373046i) q^{49} +(-3.27966 - 1.89351i) q^{52} +9.43507i q^{53} +(-2.29012 + 3.96660i) q^{56} +(0.691103 - 0.399008i) q^{58} +(-5.10795 - 8.84723i) q^{59} +(0.00549659 - 0.00952038i) q^{61} -3.90833i q^{62} +3.11511 q^{64} +(-0.851145 + 0.491409i) q^{67} +(4.87359 - 2.81377i) q^{68} +6.43507 q^{71} +6.61467i q^{73} +(-0.859605 + 1.48888i) q^{74} +(0.316370 + 0.547969i) q^{76} +(-13.6923 + 7.90523i) q^{77} +(-4.73569 + 8.20246i) q^{79} +1.29366i q^{82} +(-9.02378 - 5.20988i) q^{83} +(-1.81686 - 3.14690i) q^{86} +(-9.54658 - 5.51172i) q^{88} -6.26940 q^{89} +5.46519 q^{91} +(-6.47993 - 3.74119i) q^{92} +(-2.70439 - 4.68413i) q^{94} +(6.24126 + 3.60339i) q^{97} +0.203858i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 2 q^{11} - 6 q^{14} - 8 q^{16} - 8 q^{19} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 18 q^{34} - 10 q^{41} + 88 q^{44} - 6 q^{49} - 60 q^{56} - 34 q^{59} + 26 q^{61} - 76 q^{64} + 32 q^{71} - 80 q^{74} - 22 q^{76} - 14 q^{79} - 68 q^{86} - 36 q^{89} - 68 q^{91} + 6 q^{94}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^11 - 6 * q^14 - 8 * q^16 - 8 * q^19 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 18 * q^34 - 10 * q^41 + 88 * q^44 - 6 * q^49 - 60 * q^56 - 34 * q^59 + 26 * q^61 - 76 * q^64 + 32 * q^71 - 80 * q^74 - 22 * q^76 - 14 * q^79 - 68 * q^86 - 36 * q^89 - 68 * q^91 + 6 * q^94

Introduction

L-functions

Modular forms

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Database

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