LMFDB - Embedded newform 912.2.ci.g.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			79.1
Character	$\chi$	$=$	912.79
Dual form			912.2.ci.g.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{3} +(-0.467043 + 2.64873i) q^{5} +(-0.480437 + 0.277380i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{3} +(-0.467043 + 2.64873i) q^{5} +(-0.480437 + 0.277380i) q^{7} +(0.766044 - 0.642788i) q^{9} +(-1.68333 - 0.971873i) q^{11} +(-2.00616 + 5.51189i) q^{13} +(-0.467043 - 2.64873i) q^{15} +(-2.18767 - 1.83567i) q^{17} +(3.22515 - 2.93230i) q^{19} +(0.356593 - 0.424972i) q^{21} +(-3.17546 + 0.559919i) q^{23} +(-2.09920 - 0.764048i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-0.952837 - 1.13555i) q^{29} +(-3.09386 - 5.35873i) q^{31} +(1.91422 + 0.337528i) q^{33} +(-0.510322 - 1.40210i) q^{35} +6.18706i q^{37} -5.86563i q^{39} +(-3.29187 - 9.04434i) q^{41} +(-2.72931 - 0.481251i) q^{43} +(1.34480 + 2.32926i) q^{45} +(-2.27455 - 2.71070i) q^{47} +(-3.34612 + 5.79565i) q^{49} +(2.68357 + 0.976739i) q^{51} +(-3.33676 + 0.588361i) q^{53} +(3.36042 - 4.00480i) q^{55} +(-2.02774 + 3.85853i) q^{57} +(-6.26092 - 5.25354i) q^{59} +(-0.549242 - 3.11491i) q^{61} +(-0.189739 + 0.521305i) q^{63} +(-13.6626 - 7.88809i) q^{65} +(2.71675 - 2.27962i) q^{67} +(2.79245 - 1.61222i) q^{69} +(0.258532 - 1.46621i) q^{71} +(5.13962 - 1.87067i) q^{73} +2.23393 q^{75} +1.07831 q^{77} +(-10.7917 + 3.92786i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-12.9495 + 7.47641i) q^{83} +(5.88394 - 4.93721i) q^{85} +(1.28375 + 0.741175i) q^{87} +(-4.23978 + 11.6487i) q^{89} +(-0.565055 - 3.20459i) q^{91} +(4.74008 + 3.97740i) q^{93} +(6.26061 + 9.91208i) q^{95} +(4.52511 - 5.39282i) q^{97} +(-1.91422 + 0.337528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{7}+O(q^{10}) $ 24 * q - 9 * q^7	$ 24 q - 9 q^{7} + 9 q^{11} - 9 q^{13} - 6 q^{17} - 3 q^{19} - 6 q^{21} + 15 q^{23} + 6 q^{25} - 12 q^{27} - 6 q^{29} + 12 q^{31} - 3 q^{33} + 30 q^{41} - 9 q^{43} + 3 q^{45} - 15 q^{47} + 27 q^{49} + 3 q^{51} + 6 q^{53} + 21 q^{55} - 9 q^{57} - 36 q^{59} - 21 q^{61} - 3 q^{63} - 9 q^{65} + 45 q^{67} - 36 q^{71} + 42 q^{75} + 108 q^{77} + 36 q^{79} - 27 q^{83} - 9 q^{85} - 9 q^{87} - 27 q^{89} - 36 q^{91} - 18 q^{93} + 30 q^{95} - 51 q^{97} + 3 q^{99}+O(q^{100}) $ 24 * q - 9 * q^7 + 9 * q^11 - 9 * q^13 - 6 * q^17 - 3 * q^19 - 6 * q^21 + 15 * q^23 + 6 * q^25 - 12 * q^27 - 6 * q^29 + 12 * q^31 - 3 * q^33 + 30 * q^41 - 9 * q^43 + 3 * q^45 - 15 * q^47 + 27 * q^49 + 3 * q^51 + 6 * q^53 + 21 * q^55 - 9 * q^57 - 36 * q^59 - 21 * q^61 - 3 * q^63 - 9 * q^65 + 45 * q^67 - 36 * q^71 + 42 * q^75 + 108 * q^77 + 36 * q^79 - 27 * q^83 - 9 * q^85 - 9 * q^87 - 27 * q^89 - 36 * q^91 - 18 * q^93 + 30 * q^95 - 51 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$		0			0
$5$	−0.467043	+	2.64873i	−0.208868	+	1.18455i	0.682367	+	0.731009i	$0.260950\pi$
$5$	−0.467043	+	2.64873i	−0.208868	+	1.18455i	−0.891235	+	0.453541i	$0.850161\pi$
$6$		0			0
$7$	−0.480437	+	0.277380i	−0.181588	+	0.104840i	−0.588039	−	0.808833i	$-0.700100\pi$
$7$	−0.480437	+	0.277380i	−0.181588	+	0.104840i	0.406450	+	0.913673i	$0.366766\pi$
$8$		0			0
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$		0			0
$11$	−1.68333	−	0.971873i	−0.507544	−	0.293031i	0.224279	−	0.974525i	$-0.427997\pi$
$11$	−1.68333	−	0.971873i	−0.507544	−	0.293031i	−0.731824	+	0.681494i	$0.761331\pi$
$12$		0			0
$13$	−2.00616	+	5.51189i	−0.556410	+	1.52872i	0.268397	+	0.963308i	$0.413506\pi$
$13$	−2.00616	+	5.51189i	−0.556410	+	1.52872i	−0.824807	+	0.565415i	$0.808716\pi$
$14$		0			0
$15$	−0.467043	−	2.64873i	−0.120590	−	0.683900i
$16$		0			0
$17$	−2.18767	−	1.83567i	−0.530587	−	0.445215i	0.337717	−	0.941248i	$-0.390345\pi$
$17$	−2.18767	−	1.83567i	−0.530587	−	0.445215i	−0.868304	+	0.496032i	$0.834790\pi$
$18$		0			0
$19$	3.22515	−	2.93230i	0.739900	−	0.672717i
$19$	3.22515	−	2.93230i	0.739900	−	0.672717i
$20$		0			0
$21$	0.356593	−	0.424972i	0.0778151	−	0.0927364i
$22$		0			0
$23$	−3.17546	+	0.559919i	−0.662129	+	0.116751i	−0.494606	−	0.869117i	$-0.664688\pi$
$23$	−3.17546	+	0.559919i	−0.662129	+	0.116751i	−0.167522	+	0.985868i	$0.553577\pi$
$24$		0			0
$25$	−2.09920	−	0.764048i	−0.419841	−	0.152810i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	−0.952837	−	1.13555i	−0.176937	−	0.210866i	0.670286	−	0.742103i	$-0.266172\pi$
$29$	−0.952837	−	1.13555i	−0.176937	−	0.210866i	−0.847223	+	0.531238i	$0.821727\pi$
$30$		0			0
$31$	−3.09386	−	5.35873i	−0.555674	−	0.962456i	−0.997851	−	0.0655282i	$-0.979127\pi$
$31$	−3.09386	−	5.35873i	−0.555674	−	0.962456i	0.442176	−	0.896928i	$-0.354207\pi$
$32$		0			0
$33$	1.91422	+	0.337528i	0.333222	+	0.0587561i
$34$		0			0
$35$	−0.510322	−	1.40210i	−0.0862602	−	0.236998i
$36$		0			0
$37$			6.18706i			1.01715i	0.861019	+	0.508573i	$0.169827\pi$
$37$			6.18706i			1.01715i	−0.861019	+	0.508573i	$0.830173\pi$
$38$		0			0
$39$		−	5.86563i		−	0.939252i
$40$		0			0
$41$	−3.29187	−	9.04434i	−0.514104	−	1.41249i	−0.876924	−	0.480629i	$-0.840408\pi$
$41$	−3.29187	−	9.04434i	−0.514104	−	1.41249i	0.362820	−	0.931859i	$-0.381814\pi$
$42$		0			0
$43$	−2.72931	−	0.481251i	−0.416216	−	0.0733900i	−0.0383811	−	0.999263i	$-0.512220\pi$
$43$	−2.72931	−	0.481251i	−0.416216	−	0.0733900i	−0.377835	+	0.925873i	$0.623331\pi$
$44$		0			0
$45$	1.34480	+	2.32926i	0.200471	+	0.347225i
$46$		0			0
$47$	−2.27455	−	2.71070i	−0.331777	−	0.395397i	0.574206	−	0.818711i	$-0.305311\pi$
$47$	−2.27455	−	2.71070i	−0.331777	−	0.395397i	−0.905983	+	0.423314i	$0.860867\pi$
$48$		0			0
$49$	−3.34612	+	5.79565i	−0.478017	+	0.827950i
$50$		0			0
$51$	2.68357	+	0.976739i	0.375775	+	0.136771i
$52$		0			0
$53$	−3.33676	+	0.588361i	−0.458339	+	0.0808176i	−0.398051	−	0.917363i	$-0.630313\pi$
$53$	−3.33676	+	0.588361i	−0.458339	+	0.0808176i	−0.0602885	+	0.998181i	$0.519202\pi$
$54$		0			0
$55$	3.36042	−	4.00480i	0.453120	−	0.540007i
$56$		0			0
$57$	−2.02774	+	3.85853i	−0.268581	+	0.511075i
$58$		0			0
$59$	−6.26092	−	5.25354i	−0.815102	−	0.683952i	0.136717	−	0.990610i	$-0.456345\pi$
$59$	−6.26092	−	5.25354i	−0.815102	−	0.683952i	−0.951820	+	0.306658i	$0.900789\pi$
$60$		0			0
$61$	−0.549242	−	3.11491i	−0.0703233	−	0.398823i	−0.999569	−	0.0293606i	$-0.990653\pi$
$61$	−0.549242	−	3.11491i	−0.0703233	−	0.398823i	0.929246	−	0.369463i	$-0.120458\pi$
$62$		0			0
$63$	−0.189739	+	0.521305i	−0.0239049	+	0.0656782i
$64$		0			0
$65$	−13.6626	−	7.88809i	−1.69463	−	0.978397i
$66$		0			0
$67$	2.71675	−	2.27962i	0.331904	−	0.278500i	−0.461571	−	0.887103i	$-0.652714\pi$
$67$	2.71675	−	2.27962i	0.331904	−	0.278500i	0.793475	+	0.608603i	$0.208270\pi$
$68$		0			0
$69$	2.79245	−	1.61222i	0.336172	−	0.194089i
$70$		0			0
$71$	0.258532	−	1.46621i	0.0306821	−	0.174007i	−0.965616	−	0.259972i	$-0.916287\pi$
$71$	0.258532	−	1.46621i	0.0306821	−	0.174007i	0.996298	+	0.0859659i	$0.0273976\pi$
$72$		0			0
$73$	5.13962	−	1.87067i	0.601547	−	0.218945i	−0.0232533	−	0.999730i	$-0.507402\pi$
$73$	5.13962	−	1.87067i	0.601547	−	0.218945i	0.624801	+	0.780784i	$0.285180\pi$
$74$		0			0
$75$	2.23393			0.257952
$76$		0			0
$77$	1.07831			0.122885
$78$		0			0
$79$	−10.7917	+	3.92786i	−1.21416	+	0.441919i	−0.868146	−	0.496309i	$-0.834688\pi$
$79$	−10.7917	+	3.92786i	−1.21416	+	0.441919i	−0.346017	+	0.938228i	$0.612466\pi$
$80$		0			0
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$		0			0
$83$	−12.9495	+	7.47641i	−1.42139	+	0.820643i	−0.996418	−	0.0845618i	$-0.973051\pi$
$83$	−12.9495	+	7.47641i	−1.42139	+	0.820643i	−0.424976	+	0.905204i	$0.639718\pi$
$84$		0			0
$85$	5.88394	−	4.93721i	0.638202	−	0.535515i
$86$		0			0
$87$	1.28375	+	0.741175i	0.137633	+	0.0794623i
$88$		0			0
$89$	−4.23978	+	11.6487i	−0.449416	+	1.23476i	0.483716	+	0.875225i	$0.339287\pi$
$89$	−4.23978	+	11.6487i	−0.449416	+	1.23476i	−0.933132	+	0.359535i	$0.882935\pi$
$90$		0			0
$91$	−0.565055	−	3.20459i	−0.0592339	−	0.335932i
$92$		0			0
$93$	4.74008	+	3.97740i	0.491523	+	0.412437i
$94$		0			0
$95$	6.26061	+	9.91208i	0.642325	+	1.01696i
$96$		0			0
$97$	4.52511	−	5.39282i	0.459456	−	0.547558i	−0.485722	−	0.874113i	$-0.661443\pi$
$97$	4.52511	−	5.39282i	0.459456	−	0.547558i	0.945178	+	0.326555i	$0.105888\pi$
$98$		0			0
$99$	−1.91422	+	0.337528i	−0.192386	+	0.0339228i
$100$		0			0
$101$	−4.87543	−	1.77451i	−0.485124	−	0.176571i	0.0878673	−	0.996132i	$-0.471995\pi$
$101$	−4.87543	−	1.77451i	−0.485124	−	0.176571i	−0.572991	+	0.819562i	$0.694217\pi$
$102$		0			0
$103$	−4.93315	+	8.54447i	−0.486078	+	0.841912i	−0.999872	−	0.0160018i	$-0.994906\pi$
$103$	−4.93315	+	8.54447i	−0.486078	+	0.841912i	0.513794	+	0.857914i	$0.328240\pi$
$104$		0			0
$105$	0.959092	+	1.14300i	0.0935978	+	0.111546i
$106$		0			0
$107$	7.87064	+	13.6323i	0.760883	+	1.31789i	0.942396	+	0.334500i	$0.108567\pi$
$107$	7.87064	+	13.6323i	0.760883	+	1.31789i	−0.181513	+	0.983389i	$0.558099\pi$
$108$		0			0
$109$	17.1173	+	3.01823i	1.63954	+	0.289094i	0.915996	−	0.401188i	$-0.131403\pi$
$109$	17.1173	+	3.01823i	1.63954	+	0.289094i	0.723540	+	0.690282i	$0.242514\pi$
$110$		0			0
$111$	−2.11610	−	5.81393i	−0.200851	−	0.551834i
$112$		0			0
$113$			9.29347i			0.874256i	0.899399	+	0.437128i	$0.144004\pi$
$113$			9.29347i			0.874256i	−0.899399	+	0.437128i	$0.855996\pi$
$114$		0			0
$115$		−	8.67245i		−	0.808710i
$116$		0			0
$117$	2.00616	+	5.51189i	0.185470	+	0.509574i
$118$		0			0
$119$	1.56021	+	0.275108i	0.143025	+	0.0252191i
$120$		0			0
$121$	−3.61092	−	6.25431i	−0.328266	−	0.568573i
$122$		0			0
$123$	6.18669	+	7.37301i	0.557835	+	0.664802i
$124$		0			0
$125$	−3.71981	+	6.44290i	−0.332710	+	0.576270i
$126$		0			0
$127$	−1.50116	−	0.546378i	−0.133207	−	0.0484832i	0.274557	−	0.961571i	$-0.411469\pi$
$127$	−1.50116	−	0.546378i	−0.133207	−	0.0484832i	−0.407763	+	0.913088i	$0.633691\pi$
$128$		0			0
$129$	2.72931	−	0.481251i	0.240302	−	0.0423718i
$130$		0			0
$131$	−7.41924	+	8.84191i	−0.648222	+	0.772521i	−0.985645	−	0.168832i	$-0.946000\pi$
$131$	−7.41924	+	8.84191i	−0.648222	+	0.772521i	0.337423	+	0.941353i	$0.390445\pi$
$132$		0			0
$133$	−0.736118	+	2.30338i	−0.0638295	+	0.199728i
$134$		0			0
$135$	−2.06035	−	1.72884i	−0.177327	−	0.148795i
$136$		0			0
$137$	−3.73175	−	21.1638i	−0.318825	−	1.80815i	−0.549922	−	0.835216i	$-0.685343\pi$
$137$	−3.73175	−	21.1638i	−0.318825	−	1.80815i	0.231097	−	0.972931i	$-0.425768\pi$
$138$		0			0
$139$	1.46781	−	4.03277i	0.124498	−	0.342055i	−0.861749	−	0.507335i	$-0.830631\pi$
$139$	1.46781	−	4.03277i	0.124498	−	0.342055i	0.986247	+	0.165280i	$0.0528528\pi$
$140$		0			0
$141$	3.06449	+	1.76929i	0.258077	+	0.149001i
$142$		0			0
$143$	8.73390	−	7.32861i	0.730365	−	0.612849i
$144$		0			0
$145$	3.45278	−	1.99346i	0.286738	−	0.165548i
$146$		0			0
$147$	1.16210	−	6.59057i	0.0958480	−	0.543581i
$148$		0			0
$149$	−2.13015	+	0.775311i	−0.174509	+	0.0635159i	−0.427797	−	0.903875i	$-0.640710\pi$
$149$	−2.13015	+	0.775311i	−0.174509	+	0.0635159i	0.253288	+	0.967391i	$0.418488\pi$
$150$		0			0
$151$	21.6629			1.76290			0.881449	−	0.472279i	$-0.156569\pi$
$151$	21.6629			1.76290			0.881449	+	0.472279i	$0.156569\pi$
$152$		0			0
$153$	−2.85579			−0.230877
$154$		0			0
$155$	15.6388	−	5.69207i	1.25614	−	0.457198i
$156$		0			0
$157$	0.307113	−	1.74172i	0.0245103	−	0.139005i	−0.970097	−	0.242717i	$-0.921961\pi$
$157$	0.307113	−	1.74172i	0.0245103	−	0.139005i	0.994607	+	0.103713i	$0.0330723\pi$
$158$		0			0
$159$	2.93430	−	1.69412i	0.232705	−	0.134352i
$160$		0			0
$161$	1.37030	−	1.14982i	0.107995	−	0.0906182i
$162$		0			0
$163$	13.9269	+	8.04069i	1.09084	+	0.629796i	0.933799	−	0.357797i	$-0.116472\pi$
$163$	13.9269	+	8.04069i	1.09084	+	0.629796i	0.157039	+	0.987592i	$0.449805\pi$
$164$		0			0
$165$	−1.78804	+	4.91261i	−0.139199	+	0.382446i
$166$		0			0
$167$	−0.456550	−	2.58922i	−0.0353289	−	0.200360i	0.962035	−	0.272927i	$-0.0879919\pi$
$167$	−0.456550	−	2.58922i	−0.0353289	−	0.200360i	−0.997364	+	0.0725673i	$0.976881\pi$
$168$		0			0
$169$	−16.3977	−	13.7593i	−1.26136	−	1.05840i
$170$		0			0
$171$	0.585760	−	4.31936i	0.0447942	−	0.330310i
$172$		0			0
$173$	14.4843	−	17.2618i	1.10122	−	1.31239i	0.155349	−	0.987860i	$-0.450350\pi$
$173$	14.4843	−	17.2618i	1.10122	−	1.31239i	0.945876	−	0.324529i	$-0.105206\pi$
$174$		0			0
$175$	1.22047	−	0.215201i	0.0922587	−	0.0162677i
$176$		0			0
$177$	7.68016	+	2.79535i	0.577276	+	0.210111i
$178$		0			0
$179$	−5.21133	+	9.02628i	−0.389513	+	0.674656i	−0.992384	−	0.123183i	$-0.960690\pi$
$179$	−5.21133	+	9.02628i	−0.389513	+	0.674656i	0.602871	+	0.797839i	$0.294023\pi$
$180$		0			0
$181$	9.90734	+	11.8071i	0.736407	+	0.877616i	0.996114	−	0.0880716i	$-0.0280704\pi$
$181$	9.90734	+	11.8071i	0.736407	+	0.877616i	−0.259707	+	0.965687i	$0.583626\pi$
$182$		0			0
$183$	1.58148	+	2.73920i	0.116906	+	0.202488i
$184$		0			0
$185$	−16.3879	−	2.88962i	−1.20486	−	0.212449i
$186$		0			0
$187$	1.89853	+	5.21618i	0.138835	+	0.381445i
$188$		0			0
$189$		−	0.554761i		−	0.0403529i
$190$		0			0
$191$			24.4853i			1.77169i	0.463978	+	0.885847i	$0.346422\pi$
$191$			24.4853i			1.77169i	−0.463978	+	0.885847i	$0.653578\pi$
$192$		0			0
$193$	5.46078	+	15.0034i	0.393075	+	1.07997i	0.965590	+	0.260071i	$0.0837460\pi$
$193$	5.46078	+	15.0034i	0.393075	+	1.07997i	−0.572514	+	0.819895i	$0.694032\pi$
$194$		0			0
$195$	15.5365	+	2.73950i	1.11259	+	0.196180i
$196$		0			0
$197$	3.51055	+	6.08045i	0.250116	+	0.433214i	0.963558	−	0.267501i	$-0.0861979\pi$
$197$	3.51055	+	6.08045i	0.250116	+	0.433214i	−0.713441	+	0.700715i	$0.752865\pi$
$198$		0			0
$199$	−4.41722	−	5.26423i	−0.313128	−	0.373172i	0.586410	−	0.810015i	$-0.300541\pi$
$199$	−4.41722	−	5.26423i	−0.313128	−	0.373172i	−0.899538	+	0.436843i	$0.856096\pi$
$200$		0			0
$201$	−1.77323	+	3.07133i	−0.125074	+	0.216635i
$202$		0			0
$203$	0.772757	+	0.281260i	0.0542369	+	0.0197406i
$204$		0			0
$205$	25.4935	−	4.49519i	1.78054	−	0.313958i
$206$		0			0
$207$	−2.07263	+	2.47007i	−0.144058	+	0.171682i
$208$		0			0
$209$	−8.27883	+	1.80161i	−0.572659	+	0.124620i
$210$		0			0
$211$	3.44927	+	2.89428i	0.237458	+	0.199251i	0.753749	−	0.657162i	$-0.228243\pi$
$211$	3.44927	+	2.89428i	0.237458	+	0.199251i	−0.516291	+	0.856413i	$0.672688\pi$
$212$		0			0
$213$	0.258532	+	1.46621i	0.0177143	+	0.100463i
$214$		0			0
$215$	2.54941	−	7.00445i	0.173868	−	0.477699i
$216$		0			0
$217$	2.97281	+	1.71636i	0.201808	+	0.116514i
$218$		0			0
$219$	−4.18986	+	3.51571i	−0.283124	+	0.237570i
$220$		0			0
$221$	14.5068	−	8.37552i	0.975834	−	0.563398i
$222$		0			0
$223$	−2.54774	+	14.4490i	−0.170609	+	0.967574i	0.772481	+	0.635038i	$0.219016\pi$
$223$	−2.54774	+	14.4490i	−0.170609	+	0.967574i	−0.943090	+	0.332536i	$0.892096\pi$
$224$		0			0
$225$	−2.09920	+	0.764048i	−0.139947	+	0.0509365i
$226$		0			0
$227$	−27.3415			−1.81472			−0.907361	−	0.420353i	$-0.861906\pi$
$227$	−27.3415			−1.81472			−0.907361	+	0.420353i	$0.861906\pi$
$228$		0			0
$229$	−11.2526			−0.743594			−0.371797	−	0.928314i	$-0.621258\pi$
$229$	−11.2526			−0.743594			−0.371797	+	0.928314i	$0.621258\pi$
$230$		0			0
$231$	−1.01328	+	0.368805i	−0.0666692	+	0.0242656i
$232$		0			0
$233$	3.59215	−	20.3721i	0.235330	−	1.33462i	−0.606588	−	0.795016i	$-0.707462\pi$
$233$	3.59215	−	20.3721i	0.235330	−	1.33462i	0.841918	−	0.539605i	$-0.181427\pi$
$234$		0			0
$235$	8.24225	−	4.75867i	0.537665	−	0.310421i
$236$		0			0
$237$	8.79748	−	7.38196i	0.571458	−	0.479510i
$238$		0			0
$239$	17.6367	+	10.1826i	1.14083	+	0.658656i	0.946635	−	0.322307i	$-0.104458\pi$
$239$	17.6367	+	10.1826i	1.14083	+	0.658656i	0.194191	+	0.980964i	$0.437792\pi$
$240$		0			0
$241$	−5.07011	+	13.9300i	−0.326594	+	0.897311i	0.662373	+	0.749175i	$0.269550\pi$
$241$	−5.07011	+	13.9300i	−0.326594	+	0.897311i	−0.988967	+	0.148136i	$0.952673\pi$
$242$		0			0
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$		0			0
$245$	−13.7884	−	11.5698i	−0.880906	−	0.739168i
$246$		0			0
$247$	9.69235	+	23.6594i	0.616710	+	1.50541i
$248$		0			0
$249$	9.61149	−	11.4545i	0.609103	−	0.725901i
$250$		0			0
$251$	0.983287	−	0.173380i	0.0620645	−	0.0109437i	−0.142530	−	0.989791i	$-0.545524\pi$
$251$	0.983287	−	0.173380i	0.0620645	−	0.0109437i	0.204594	+	0.978847i	$0.434413\pi$
$252$		0			0
$253$	5.88953	+	2.14361i	0.370271	+	0.134768i
$254$		0			0
$255$	−3.84047	+	6.65188i	−0.240499	+	0.416557i
$256$		0			0
$257$	1.24753	+	1.48675i	0.0778188	+	0.0927409i	0.803549	−	0.595238i	$-0.202942\pi$
$257$	1.24753	+	1.48675i	0.0778188	+	0.0927409i	−0.725730	+	0.687979i	$0.758498\pi$
$258$		0			0
$259$	−1.71617	−	2.97249i	−0.106638	−	0.184702i
$260$		0			0
$261$	−1.45983	−	0.257408i	−0.0903612	−	0.0159331i
$262$		0			0
$263$	3.31052	+	9.09558i	0.204135	+	0.560857i	0.998941	−	0.0460066i	$-0.0146495\pi$
$263$	3.31052	+	9.09558i	0.204135	+	0.560857i	−0.794806	+	0.606864i	$0.792427\pi$
$264$		0			0
$265$		−	9.11298i		−	0.559806i
$266$		0			0
$267$		−	12.3963i		−	0.758640i
$268$		0			0
$269$	4.07683	+	11.2010i	0.248569	+	0.682937i	0.999739	+	0.0228288i	$0.00726727\pi$
$269$	4.07683	+	11.2010i	0.248569	+	0.682937i	−0.751171	+	0.660108i	$0.770511\pi$
$270$		0			0
$271$	−29.6606	−	5.22997i	−1.80175	−	0.317698i	−0.830730	−	0.556676i	$-0.812076\pi$
$271$	−29.6606	−	5.22997i	−1.80175	−	0.317698i	−0.971025	+	0.238978i	$0.923188\pi$
$272$		0			0
$273$	1.62701	+	2.81807i	0.0984712	+	0.170557i
$274$		0			0
$275$	2.79110	+	3.32631i	0.168310	+	0.200584i
$276$		0			0
$277$	−8.79856	+	15.2396i	−0.528654	+	0.915656i	0.470788	+	0.882247i	$0.343970\pi$
$277$	−8.79856	+	15.2396i	−0.528654	+	0.915656i	−0.999442	+	0.0334093i	$0.989364\pi$
$278$		0			0
$279$	−5.81456	−	2.11633i	−0.348109	−	0.126701i
$280$		0			0
$281$	10.4530	−	1.84314i	0.623571	−	0.109952i	0.147070	−	0.989126i	$-0.453016\pi$
$281$	10.4530	−	1.84314i	0.623571	−	0.109952i	0.476501	+	0.879174i	$0.341905\pi$
$282$		0			0
$283$	−0.500092	+	0.595987i	−0.0297274	+	0.0354277i	−0.780703	−	0.624902i	$-0.785139\pi$
$283$	−0.500092	+	0.595987i	−0.0297274	+	0.0354277i	0.750976	+	0.660330i	$0.229583\pi$
$284$		0			0
$285$	−9.27318	−	7.17306i	−0.549296	−	0.424895i
$286$		0			0
$287$	4.09026	+	3.43214i	0.241440	+	0.202593i
$288$		0			0
$289$	−1.53582	−	8.71007i	−0.0903424	−	0.512357i
$290$		0			0
$291$	−2.40776	+	6.61527i	−0.141146	+	0.387794i
$292$		0			0
$293$	−1.48442	−	0.857030i	−0.0867207	−	0.0500682i	0.456013	−	0.889973i	$-0.349277\pi$
$293$	−1.48442	−	0.857030i	−0.0867207	−	0.0500682i	−0.542733	+	0.839905i	$0.682611\pi$
$294$		0			0
$295$	16.8393	−	14.1299i	0.980425	−	0.822674i
$296$		0			0
$297$	1.68333	−	0.971873i	0.0976769	−	0.0563938i
$298$		0			0
$299$	3.28428	−	18.6261i	0.189935	−	1.07717i
$300$		0			0
$301$	1.44475	−	0.525846i	0.0832740	−	0.0303093i
$302$		0			0
$303$	5.18833			0.298062
$304$		0			0
$305$	8.50709			0.487114
$306$		0			0
$307$	−0.0197993	+	0.00720634i	−0.00113000	+	0.000411288i	−0.342585	−	0.939487i	$-0.611302\pi$
$307$	−0.0197993	+	0.00720634i	−0.00113000	+	0.000411288i	0.341455	+	0.939898i	$0.389080\pi$
$308$		0			0
$309$	1.71327	−	9.71641i	0.0974643	−	0.552748i
$310$		0			0
$311$	−5.20678	+	3.00613i	−0.295249	+	0.170462i	−0.640307	−	0.768119i	$-0.721193\pi$
$311$	−5.20678	+	3.00613i	−0.295249	+	0.170462i	0.345058	+	0.938582i	$0.387859\pi$
$312$		0			0
$313$	−8.46067	+	7.09935i	−0.478226	+	0.401279i	−0.849784	−	0.527131i	$-0.823268\pi$
$313$	−8.46067	+	7.09935i	−0.478226	+	0.401279i	0.371559	+	0.928409i	$0.378823\pi$
$314$		0			0
$315$	−1.29218	−	0.746041i	−0.0728062	−	0.0420347i
$316$		0			0
$317$	−2.33312	+	6.41021i	−0.131041	+	0.360033i	−0.987809	−	0.155669i	$-0.950247\pi$
$317$	−2.33312	+	6.41021i	−0.131041	+	0.360033i	0.856768	+	0.515702i	$0.172469\pi$
$318$		0			0
$319$	0.500335	+	2.83754i	0.0280134	+	0.158872i
$320$		0			0
$321$	−12.0585	−	10.1183i	−0.673041	−	0.564748i
$322$		0			0
$323$	−12.4383	+	0.494589i	−0.692085	+	0.0275197i
$324$		0			0
$325$	8.42269	−	10.0378i	0.467207	−	0.556796i
$326$		0			0
$327$	−17.1173	+	3.01823i	−0.946586	+	0.166909i
$328$		0			0
$329$	1.84467	+	0.671407i	0.101700	+	0.0370159i
$330$		0			0
$331$	−12.5952	+	21.8154i	−0.692292	+	1.19909i	0.278793	+	0.960351i	$0.410066\pi$
$331$	−12.5952	+	21.8154i	−0.692292	+	1.19909i	−0.971085	+	0.238734i	$0.923268\pi$
$332$		0			0
$333$	3.97696	+	4.73956i	0.217936	+	0.259726i
$334$		0			0
$335$	4.76928	+	8.26063i	0.260573	+	0.451326i
$336$		0			0
$337$	−13.2525	−	2.33677i	−0.721908	−	0.127292i	−0.199390	−	0.979920i	$-0.563896\pi$
$337$	−13.2525	−	2.33677i	−0.721908	−	0.127292i	−0.522518	+	0.852628i	$0.675007\pi$
$338$		0			0
$339$	−3.17856	−	8.73301i	−0.172635	−	0.474312i
$340$		0			0
$341$			12.0274i			0.651319i
$342$		0			0
$343$		−	7.59592i		−	0.410141i
$344$		0			0
$345$	2.96615	+	8.14944i	0.159692	+	0.438751i
$346$		0			0
$347$	−29.2781	−	5.16253i	−1.57173	−	0.277139i	−0.681214	−	0.732085i	$-0.738548\pi$
$347$	−29.2781	−	5.16253i	−1.57173	−	0.277139i	−0.890519	+	0.454946i	$0.849659\pi$
$348$		0			0
$349$	−1.67020	−	2.89287i	−0.0894038	−	0.154852i	0.817855	−	0.575424i	$-0.195163\pi$
$349$	−1.67020	−	2.89287i	−0.0894038	−	0.154852i	−0.907259	+	0.420572i	$0.861830\pi$
$350$		0			0
$351$	−3.77035	−	4.49333i	−0.201247	−	0.239836i
$352$		0			0
$353$	−4.19629	+	7.26819i	−0.223346	+	0.386847i	−0.955822	−	0.293946i	$-0.905031\pi$
$353$	−4.19629	+	7.26819i	−0.223346	+	0.386847i	0.732476	+	0.680793i	$0.238365\pi$
$354$		0			0
$355$	3.76284	+	1.36956i	0.199711	+	0.0726889i
$356$		0			0
$357$	−1.56021	+	0.275108i	−0.0825753	+	0.0145603i
$358$		0			0
$359$	2.23586	−	2.66459i	0.118004	−	0.140632i	−0.703808	−	0.710390i	$-0.748519\pi$
$359$	2.23586	−	2.66459i	0.118004	−	0.140632i	0.821812	+	0.569758i	$0.192963\pi$
$360$		0			0
$361$	1.80319	−	18.9142i	0.0949048	−	0.995486i
$362$		0			0
$363$	5.53226	+	4.64212i	0.290368	+	0.243648i
$364$		0			0
$365$	2.55448	+	14.4872i	0.133708	+	0.758294i
$366$		0			0
$367$	1.02641	−	2.82003i	0.0535781	−	0.147204i	−0.910017	−	0.414572i	$-0.863931\pi$
$367$	1.02641	−	2.82003i	0.0535781	−	0.147204i	0.963595	+	0.267367i	$0.0861536\pi$
$368$		0			0
$369$	−8.33531	−	4.81239i	−0.433919	−	0.250523i
$370$		0			0
$371$	1.43990	−	1.20822i	0.0747560	−	0.0627278i
$372$		0			0
$373$	−24.2690	+	14.0117i	−1.25660	+	0.725500i	−0.972413	−	0.233267i	$-0.925058\pi$
$373$	−24.2690	+	14.0117i	−1.25660	+	0.725500i	−0.284191	+	0.958768i	$0.591725\pi$
$374$		0			0
$375$	1.29188	−	7.32660i	0.0667122	−	0.378344i
$376$		0			0
$377$	8.17055	−	2.97384i	0.420805	−	0.153160i
$378$		0			0
$379$	−2.57656			−0.132349			−0.0661746	−	0.997808i	$-0.521079\pi$
$379$	−2.57656			−0.132349			−0.0661746	+	0.997808i	$0.521079\pi$
$380$		0			0
$381$	1.59750			0.0818426
$382$		0			0
$383$	31.4924	−	11.4623i	1.60919	−	0.585696i	0.627907	−	0.778288i	$-0.283912\pi$
$383$	31.4924	−	11.4623i	1.60919	−	0.585696i	0.981279	+	0.192592i	$0.0616894\pi$
$384$		0			0
$385$	−0.503620	+	2.85617i	−0.0256668	+	0.145564i
$386$		0			0
$387$	−2.40011	+	1.38571i	−0.122005	+	0.0704394i
$388$		0			0
$389$	−12.3633	+	10.3740i	−0.626843	+	0.525984i	−0.899946	−	0.436001i	$-0.856394\pi$
$389$	−12.3633	+	10.3740i	−0.626843	+	0.525984i	0.273103	+	0.961985i	$0.411950\pi$
$390$		0			0
$391$	7.97466	+	4.60417i	0.403296	+	0.232843i
$392$		0			0
$393$	3.94770	−	10.8462i	0.199135	−	0.547119i
$394$		0			0
$395$	−5.36367	−	30.4189i	−0.269875	−	1.53054i
$396$		0			0
$397$	−19.8022	−	16.6160i	−0.993844	−	0.833934i	−0.00772389	−	0.999970i	$-0.502459\pi$
$397$	−19.8022	−	16.6160i	−0.993844	−	0.833934i	−0.986120	+	0.166036i	$0.946903\pi$
$398$		0			0
$399$	−0.0960780	−	2.41624i	−0.00480991	−	0.120963i
$400$		0			0
$401$	6.20348	−	7.39302i	0.309787	−	0.369190i	−0.588577	−	0.808441i	$-0.700312\pi$
$401$	6.20348	−	7.39302i	0.309787	−	0.369190i	0.898364	+	0.439251i	$0.144756\pi$
$402$		0			0
$403$	35.7435	−	6.30255i	1.78051	−	0.313952i
$404$		0			0
$405$	2.52739	+	0.919896i	0.125587	+	0.0457100i
$406$		0			0
$407$	6.01304	−	10.4149i	0.298055	−	0.516247i
$408$		0			0
$409$	10.9337	+	13.0303i	0.540638	+	0.644307i	0.965331	−	0.261030i	$-0.0840623\pi$
$409$	10.9337	+	13.0303i	0.540638	+	0.644307i	−0.424693	+	0.905338i	$0.639618\pi$
$410$		0			0
$411$	10.7451	+	18.6111i	0.530019	+	0.918020i
$412$		0			0
$413$	4.46521	+	0.787336i	0.219718	+	0.0387423i
$414$		0			0
$415$	−13.7550	−	37.7917i	−0.675208	−	1.85512i
$416$		0			0
$417$			4.29158i			0.210160i
$418$		0			0
$419$		−	39.5947i		−	1.93433i	−0.254158	−	0.967163i	$-0.581798\pi$
$419$		−	39.5947i		−	1.93433i	0.254158	−	0.967163i	$-0.418202\pi$
$420$		0			0
$421$	10.5869	+	29.0872i	0.515973	+	1.41762i	0.874921	+	0.484266i	$0.160913\pi$
$421$	10.5869	+	29.0872i	0.515973	+	1.41762i	−0.358948	+	0.933358i	$0.616864\pi$
$422$		0			0
$423$	−3.48481	−	0.614467i	−0.169437	−	0.0298764i
$424$		0			0
$425$	3.18982	+	5.52493i	0.154729	+	0.267998i
$426$		0			0
$427$	1.12789	+	1.34417i	0.0545825	+	0.0650489i
$428$		0			0
$429$	−5.70065	+	9.87381i	−0.275230	+	0.476712i
$430$		0			0
$431$	−12.0147	−	4.37299i	−0.578728	−	0.210640i	0.0360367	−	0.999350i	$-0.488527\pi$
$431$	−12.0147	−	4.37299i	−0.578728	−	0.210640i	−0.614764	+	0.788711i	$0.710749\pi$
$432$		0			0
$433$	4.16351	−	0.734140i	0.200086	−	0.0352805i	−0.0727070	−	0.997353i	$-0.523164\pi$
$433$	4.16351	−	0.734140i	0.200086	−	0.0352805i	0.272793	+	0.962073i	$0.412053\pi$
$434$		0			0
$435$	−2.56275	+	3.05416i	−0.122874	+	0.146436i
$436$		0			0
$437$	−8.59948	+	11.1172i	−0.411369	+	0.531809i
$438$		0			0
$439$	−27.8437	−	23.3636i	−1.32891	−	1.11508i	−0.984332	−	0.176324i	$-0.943579\pi$
$439$	−27.8437	−	23.3636i	−1.32891	−	1.11508i	−0.344573	−	0.938760i	$-0.611976\pi$
$440$		0			0
$441$	1.16210	+	6.59057i	0.0553379	+	0.313837i
$442$		0			0
$443$	3.81612	−	10.4847i	0.181309	−	0.498143i	−0.815428	−	0.578859i	$-0.803498\pi$
$443$	3.81612	−	10.4847i	0.181309	−	0.498143i	0.996737	+	0.0807154i	$0.0257205\pi$
$444$		0			0
$445$	−28.8742	−	16.6705i	−1.36877	−	0.790258i
$446$		0			0
$447$	1.73651	−	1.45711i	0.0821342	−	0.0689188i
$448$		0			0
$449$	−4.52051	+	2.60992i	−0.213336	+	0.123170i	−0.602861	−	0.797846i	$-0.705973\pi$
$449$	−4.52051	+	2.60992i	−0.213336	+	0.123170i	0.389525	+	0.921016i	$0.372639\pi$
$450$		0			0
$451$	−3.24864	+	18.4239i	−0.152972	+	0.867549i
$452$		0			0
$453$	−20.3564	+	7.40913i	−0.956428	+	0.348111i
$454$		0			0
$455$	8.75201			0.410300
$456$		0			0
$457$	35.9862			1.68336			0.841681	−	0.539974i	$-0.181566\pi$
$457$	35.9862			1.68336			0.841681	+	0.539974i	$0.181566\pi$
$458$		0			0
$459$	2.68357	−	0.976739i	0.125258	−	0.0455903i
$460$		0			0
$461$	2.49137	−	14.1292i	0.116034	−	0.658064i	−0.870198	−	0.492702i	$-0.836009\pi$
$461$	2.49137	−	14.1292i	0.116034	−	0.658064i	0.986233	−	0.165363i	$-0.0528794\pi$
$462$		0			0
$463$	−0.609195	+	0.351719i	−0.0283117	+	0.0163458i	−0.514089	−	0.857737i	$-0.671870\pi$
$463$	−0.609195	+	0.351719i	−0.0283117	+	0.0163458i	0.485777	+	0.874083i	$0.338537\pi$
$464$		0			0
$465$	−12.7489	+	10.6976i	−0.591215	+	0.496089i
$466$		0			0
$467$	1.10029	+	0.635253i	0.0509154	+	0.0293960i	0.525242	−	0.850953i	$-0.323975\pi$
$467$	1.10029	+	0.635253i	0.0509154	+	0.0293960i	−0.474326	+	0.880349i	$0.657308\pi$
$468$		0			0
$469$	−0.672904	+	1.84879i	−0.0310718	+	0.0853691i
$470$		0			0
$471$	0.307113	+	1.74172i	0.0141510	+	0.0802543i
$472$		0			0
$473$	4.12662	+	3.46265i	0.189742	+	0.159213i
$474$		0			0
$475$	−9.01067	+	3.69133i	−0.413438	+	0.169370i
$476$		0			0
$477$	−2.17791	+	2.59554i	−0.0997199	+	0.118842i
$478$		0			0
$479$	−26.4047	+	4.65586i	−1.20646	+	0.212732i	−0.740489	−	0.672068i	$-0.765406\pi$
$479$	−26.4047	+	4.65586i	−1.20646	+	0.212732i	−0.465971	+	0.884800i	$0.654295\pi$
$480$		0			0
$481$	−34.1024	−	12.4122i	−1.55493	−	0.565950i
$482$		0			0
$483$	−0.894398	+	1.54914i	−0.0406965	+	0.0704884i
$484$		0			0
$485$	12.1707	+	14.5045i	0.552644	+	0.658616i
$486$		0			0
$487$	−17.8045	−	30.8383i	−0.806799	−	1.39742i	−0.915070	−	0.403296i	$-0.867864\pi$
$487$	−17.8045	−	30.8383i	−0.806799	−	1.39742i	0.108270	−	0.994122i	$-0.465469\pi$
$488$		0			0
$489$	−15.8371	−	2.79250i	−0.716177	−	0.126281i
$490$		0			0
$491$	−5.08824	−	13.9798i	−0.229629	−	0.630900i	0.770348	−	0.637623i	$-0.220082\pi$
$491$	−5.08824	−	13.9798i	−0.229629	−	0.630900i	−0.999977	+	0.00672283i	$0.997860\pi$
$492$		0			0
$493$			4.23329i			0.190658i
$494$		0			0
$495$		−	5.22789i		−	0.234976i
$496$		0			0
$497$	0.282489	+	0.776131i	0.0126713	+	0.0348142i
$498$		0			0
$499$	−24.1910	−	4.26553i	−1.08294	−	0.190952i	−0.396425	−	0.918067i	$-0.629749\pi$
$499$	−24.1910	−	4.26553i	−1.08294	−	0.190952i	−0.686515	+	0.727116i	$0.740860\pi$
$500$		0			0
$501$	1.31458	+	2.27693i	0.0587313	+	0.101726i
$502$		0			0
$503$	19.4729	+	23.2068i	0.868252	+	1.03474i	0.999061	+	0.0433346i	$0.0137981\pi$
$503$	19.4729	+	23.2068i	0.868252	+	1.03474i	−0.130809	+	0.991408i	$0.541757\pi$
$504$		0			0
$505$	6.97725	−	12.0850i	0.310484	−	0.537774i
$506$		0			0
$507$	20.1147	+	7.32115i	0.893325	+	0.325144i
$508$		0			0
$509$	−12.8229	+	2.26103i	−0.568366	+	0.100218i	−0.450444	−	0.892805i	$-0.648734\pi$
$509$	−12.8229	+	2.26103i	−0.568366	+	0.100218i	−0.117922	+	0.993023i	$0.537623\pi$
$510$		0			0
$511$	−1.95038	+	2.32437i	−0.0862797	+	0.102824i
$512$		0			0
$513$	0.926874	+	4.25921i	0.0409225	+	0.188049i
$514$		0			0
$515$	−20.3280	−	17.0573i	−0.895761	−	0.751632i
$516$		0			0
$517$	1.19437	+	6.77360i	0.0525282	+	0.297902i
$518$		0			0
$519$	−7.70696	+	21.1747i	−0.338298	+	0.929466i
$520$		0			0
$521$	24.4601	+	14.1220i	1.07161	+	0.618697i	0.928622	−	0.371027i	$-0.120994\pi$
$521$	24.4601	+	14.1220i	1.07161	+	0.618697i	0.142992	+	0.989724i	$0.454328\pi$
$522$		0			0
$523$	−14.2949	+	11.9948i	−0.625071	+	0.524496i	−0.899393	−	0.437141i	$-0.855991\pi$
$523$	−14.2949	+	11.9948i	−0.625071	+	0.524496i	0.274322	+	0.961638i	$0.411547\pi$
$524$		0			0
$525$	−1.07326	+	0.619648i	−0.0468410	+	0.0270436i
$526$		0			0
$527$	−3.06852	+	17.4024i	−0.133667	+	0.758061i
$528$		0			0
$529$	−11.8429	+	4.31047i	−0.514909	+	0.187412i
$530$		0			0
$531$	−8.17305			−0.354680
$532$		0			0
$533$	56.4554			2.44536
$534$		0			0
$535$	−39.7844	+	14.4803i	−1.72003	+	0.626040i
$536$		0			0
$537$	1.80987	−	10.2643i	0.0781019	−	0.442938i
$538$		0			0
$539$	11.2653	−	6.50401i	0.485230	−	0.280148i
$540$		0			0
$541$	18.8330	−	15.8028i	0.809694	−	0.679414i	−0.140840	−	0.990032i	$-0.544980\pi$
$541$	18.8330	−	15.8028i	0.809694	−	0.679414i	0.950535	+	0.310618i	$0.100536\pi$
$542$		0			0
$543$	−13.3481	−	7.70655i	−0.572823	−	0.330720i
$544$		0			0
$545$	−15.9890	+	43.9294i	−0.684894	+	1.88173i
$546$		0			0
$547$	4.18665	+	23.7437i	0.179008	+	1.01521i	0.933415	+	0.358799i	$0.116814\pi$
$547$	4.18665	+	23.7437i	0.179008	+	1.01521i	−0.754406	+	0.656408i	$0.772075\pi$
$548$		0			0
$549$	−2.42297	−	2.03311i	−0.103410	−	0.0867711i
$550$		0			0
$551$	−6.40281	−	0.868302i	−0.272769	−	0.0369909i
$552$		0			0
$553$	4.09523	−	4.88050i	0.174147	−	0.207540i
$554$		0			0
$555$	16.3879	−	2.88962i	0.695627	−	0.122658i
$556$		0			0
$557$	−31.4645	−	11.4521i	−1.33319	−	0.485243i	−0.425531	−	0.904944i	$-0.639913\pi$
$557$	−31.4645	−	11.4521i	−1.33319	−	0.485243i	−0.907662	+	0.419701i	$0.862135\pi$
$558$		0			0
$559$	8.12804	−	14.0782i	0.343779	−	0.595443i
$560$		0			0
$561$	−3.56808	−	4.25227i	−0.150644	−	0.179531i
$562$		0			0
$563$	6.74800	+	11.6879i	0.284394	+	0.492585i	0.972462	−	0.233061i	$-0.0748742\pi$
$563$	6.74800	+	11.6879i	0.284394	+	0.492585i	−0.688068	+	0.725646i	$0.741541\pi$
$564$		0			0
$565$	−24.6159	−	4.34046i	−1.03560	−	0.182604i
$566$		0			0
$567$	0.189739	+	0.521305i	0.00796831	+	0.0218927i
$568$		0			0
$569$			41.8624i			1.75496i	0.479612	+	0.877481i	$0.340777\pi$
$569$			41.8624i			1.75496i	−0.479612	+	0.877481i	$0.659223\pi$
$570$		0			0
$571$		−	10.4649i		−	0.437944i	−0.975731	−	0.218972i	$-0.929730\pi$
$571$		−	10.4649i		−	0.437944i	0.975731	−	0.218972i	$-0.0702703\pi$
$572$		0			0
$573$	−8.37446	−	23.0086i	−0.349848	−	0.961200i
$574$		0			0
$575$	7.09374	+	1.25082i	0.295829	+	0.0521627i
$576$		0			0
$577$	13.5961	+	23.5492i	0.566015	+	0.980367i	0.996954	+	0.0779858i	$0.0248489\pi$
$577$	13.5961	+	23.5492i	0.566015	+	0.980367i	−0.430940	+	0.902381i	$0.641818\pi$
$578$		0			0
$579$	−10.2629	−	12.2309i	−0.426512	−	0.508297i
$580$		0			0
$581$	4.14762	−	7.18389i	0.172072	−	0.298038i
$582$		0			0
$583$	6.18869	+	2.25250i	0.256309	+	0.0932890i
$584$		0			0
$585$	−15.5365	+	2.73950i	−0.642355	+	0.113265i
$586$		0			0
$587$	−11.2861	+	13.4502i	−0.465827	+	0.555151i	−0.946899	−	0.321530i	$-0.895803\pi$
$587$	−11.2861	+	13.4502i	−0.465827	+	0.555151i	0.481072	+	0.876681i	$0.340247\pi$
$588$		0			0
$589$	−25.6916	−	8.21056i	−1.05860	−	0.338310i
$590$		0			0
$591$	−5.37847	−	4.51307i	−0.221241	−	0.185643i
$592$		0			0
$593$	7.60851	+	43.1500i	0.312444	+	1.77196i	0.586207	+	0.810161i	$0.300620\pi$
$593$	7.60851	+	43.1500i	0.312444	+	1.77196i	−0.273763	+	0.961797i	$0.588269\pi$
$594$		0			0
$595$	−1.45738	+	4.00411i	−0.0597466	+	0.164152i
$596$		0			0
$597$	5.95130	+	3.43598i	0.243570	+	0.140625i
$598$		0			0
$599$	28.4838	−	23.9008i	1.16382	−	0.976560i	0.163868	−	0.986482i	$-0.447603\pi$
$599$	28.4838	−	23.9008i	1.16382	−	0.976560i	0.999951	+	0.00992274i	$0.00315856\pi$
$600$		0			0
$601$	5.57500	−	3.21873i	0.227409	−	0.131295i	−0.381967	−	0.924176i	$-0.624753\pi$
$601$	5.57500	−	3.21873i	0.227409	−	0.131295i	0.609376	+	0.792881i	$0.291420\pi$
$602$		0			0
$603$	0.615837	−	3.49258i	0.0250788	−	0.142229i
$604$		0			0
$605$	18.2525	−	6.64335i	0.742068	−	0.270091i
$606$		0			0
$607$	15.8453			0.643141			0.321570	−	0.946886i	$-0.395789\pi$
$607$	15.8453			0.643141			0.321570	+	0.946886i	$0.395789\pi$
$608$		0			0
$609$	−0.822350			−0.0333233
$610$		0			0
$611$	19.5042	−	7.09896i	0.789056	−	0.287193i
$612$		0			0
$613$	5.40504	−	30.6535i	0.218308	−	1.23808i	−0.656766	−	0.754094i	$-0.728076\pi$
$613$	5.40504	−	30.6535i	0.218308	−	1.23808i	0.875074	−	0.483990i	$-0.160813\pi$
$614$		0			0
$615$	−22.4186	+	12.9434i	−0.904006	+	0.521928i
$616$		0			0
$617$	33.1278	−	27.7975i	1.33367	−	1.11909i	0.350470	−	0.936574i	$-0.386022\pi$
$617$	33.1278	−	27.7975i	1.33367	−	1.11909i	0.983204	−	0.182511i	$-0.0584226\pi$
$618$		0			0
$619$	−25.4980	−	14.7213i	−1.02485	−	0.591698i	−0.109345	−	0.994004i	$-0.534875\pi$
$619$	−25.4980	−	14.7213i	−1.02485	−	0.591698i	−0.915505	+	0.402306i	$0.868209\pi$
$620$		0			0
$621$	1.10282	−	3.02999i	0.0442548	−	0.121589i
$622$		0			0
$623$	−1.19417	−	6.77250i	−0.0478436	−	0.271334i
$624$		0			0
$625$	−23.8847	−	20.0416i	−0.955386	−	0.801664i
$626$		0			0
$627$	7.16337	−	4.52449i	0.286078	−	0.180691i
$628$		0			0
$629$	11.3574	−	13.5352i	0.452849	−	0.539684i
$630$		0			0
$631$	6.19254	−	1.09191i	0.246521	−	0.0434683i	−0.0490221	−	0.998798i	$-0.515610\pi$
$631$	6.19254	−	1.09191i	0.246521	−	0.0434683i	0.295543	+	0.955329i	$0.404499\pi$
$632$		0			0
$633$	−4.23116	−	1.54002i	−0.168173	−	0.0612101i
$634$		0			0
$635$	2.14832	−	3.72100i	0.0852535	−	0.147663i
$636$		0			0
$637$	−25.2321	−	30.0705i	−0.999733	−	1.19144i
$638$		0			0
$639$	−0.744412	−	1.28936i	−0.0294485	−	0.0510063i
$640$		0			0
$641$	−4.01400	−	0.707776i	−0.158543	−	0.0279555i	0.0938131	−	0.995590i	$-0.470094\pi$
$641$	−4.01400	−	0.707776i	−0.158543	−	0.0279555i	−0.252356	+	0.967634i	$0.581206\pi$
$642$		0			0
$643$	10.5820	+	29.0737i	0.417312	+	1.14655i	0.953220	+	0.302278i	$0.0977472\pi$
$643$	10.5820	+	29.0737i	0.417312	+	1.14655i	−0.535908	+	0.844276i	$0.680031\pi$
$644$		0			0
$645$			7.45398i			0.293500i
$646$		0			0
$647$		−	33.2566i		−	1.30745i	−0.756731	−	0.653727i	$-0.773205\pi$
$647$		−	33.2566i		−	1.30745i	0.756731	−	0.653727i	$-0.226795\pi$
$648$		0			0
$649$	5.43345	+	14.9283i	0.213282	+	0.585986i
$650$		0			0
$651$	−3.38056	−	0.596084i	−0.132495	−	0.0233624i
$652$		0			0
$653$	3.60905	+	6.25106i	0.141233	+	0.244623i	0.927961	−	0.372677i	$-0.121560\pi$
$653$	3.60905	+	6.25106i	0.141233	+	0.244623i	−0.786728	+	0.617300i	$0.788227\pi$
$654$		0			0
$655$	−19.9548	−	23.7812i	−0.779697	−	0.929207i
$656$		0			0
$657$	2.73474	−	4.73670i	0.106692	−	0.184796i
$658$		0			0
$659$	3.19735	+	1.16374i	0.124551	+	0.0453329i	0.403544	−	0.914960i	$-0.367778\pi$
$659$	3.19735	+	1.16374i	0.124551	+	0.0453329i	−0.278993	+	0.960293i	$0.590001\pi$
$660$		0			0
$661$	−7.87734	+	1.38899i	−0.306393	+	0.0540254i	−0.324731	−	0.945806i	$-0.605274\pi$
$661$	−7.87734	+	1.38899i	−0.306393	+	0.0540254i	0.0183377	+	0.999832i	$0.494163\pi$
$662$		0			0
$663$	−10.7674	+	12.8320i	−0.418169	+	0.498355i
$664$		0			0
$665$	−5.75725	−	3.02556i	−0.223256	−	0.117326i
$666$		0			0
$667$	3.66151	+	3.07237i	0.141774	+	0.118963i
$668$		0			0
$669$	−2.54774	−	14.4490i	−0.0985014	−	0.558629i
$670$		0			0
$671$	−2.10274	+	5.77722i	−0.0811753	+	0.223027i
$672$		0			0
$673$	4.77109	+	2.75459i	0.183912	+	0.106182i	0.589129	−	0.808039i	$-0.299471\pi$
$673$	4.77109	+	2.75459i	0.183912	+	0.106182i	−0.405217	+	0.914220i	$0.632804\pi$
$674$		0			0
$675$	1.71129	−	1.43594i	0.0658675	−	0.0552694i
$676$		0			0
$677$	−12.4309	+	7.17697i	−0.477758	+	0.275833i	−0.719482	−	0.694512i	$-0.755620\pi$
$677$	−12.4309	+	7.17697i	−0.477758	+	0.275833i	0.241724	+	0.970345i	$0.422287\pi$
$678$		0			0
$679$	−0.678169	+	3.84609i	−0.0260258	+	0.147599i
$680$		0			0
$681$	25.6926	−	9.35136i	0.984544	−	0.358345i
$682$		0			0
$683$	4.45475			0.170456			0.0852281	−	0.996361i	$-0.472838\pi$
$683$	4.45475			0.170456			0.0852281	+	0.996361i	$0.472838\pi$
$684$		0			0
$685$	57.8002			2.20843
$686$		0			0
$687$	10.5740	−	3.84862i	0.403423	−	0.146834i
$688$		0			0
$689$	3.45111	−	19.5722i	0.131477	−	0.745641i
$690$		0			0
$691$	−11.8234	+	6.82625i	−0.449784	+	0.259683i	−0.707739	−	0.706474i	$-0.750285\pi$
$691$	−11.8234	+	6.82625i	−0.449784	+	0.259683i	0.257955	+	0.966157i	$0.416951\pi$
$692$		0			0
$693$	0.826037	−	0.693127i	0.0313785	−	0.0263297i
$694$		0			0
$695$	9.99621	+	5.77131i	0.379178	+	0.218918i
$696$		0			0
$697$	−9.40091	+	25.8288i	−0.356085	+	0.978335i
$698$		0			0
$699$	3.59215	+	20.3721i	0.135868	+	0.770544i
$700$		0			0
$701$	−23.5715	−	19.7789i	−0.890285	−	0.747038i	0.0779824	−	0.996955i	$-0.475152\pi$
$701$	−23.5715	−	19.7789i	−0.890285	−	0.747038i	−0.968267	+	0.249917i	$0.919597\pi$
$702$		0			0
$703$	18.1423	+	19.9542i	0.684251	+	0.752587i
$704$		0			0
$705$	−6.11762	+	7.29070i	−0.230403	+	0.274584i
$706$		0			0
$707$	2.83455	−	0.499808i	0.106604	−	0.0187972i
$708$		0			0
$709$	−45.3256	−	16.4972i	−1.70224	−	0.619565i	−0.706162	−	0.708050i	$-0.749575\pi$
$709$	−45.3256	−	16.4972i	−1.70224	−	0.619565i	−0.996077	+	0.0884857i	$0.971797\pi$
$710$		0			0
$711$	−5.74215	+	9.94569i	−0.215347	+	0.372993i
$712$		0			0
$713$	12.8249	+	15.2841i	0.480296	+	0.572394i
$714$		0			0
$715$	15.3324	+	26.5566i	0.573401	+	0.993159i
$716$		0			0
$717$	−20.0558	−	3.53637i	−0.748997	−	0.132068i
$718$		0			0
$719$	−10.2123	−	28.0580i	−0.380853	−	1.04639i	−0.970998	−	0.239088i	$-0.923151\pi$
$719$	−10.2123	−	28.0580i	−0.380853	−	1.04639i	0.590145	−	0.807298i	$-0.299071\pi$
$720$		0			0
$721$		−	5.47344i		−	0.203842i
$722$		0			0
$723$		−	14.8240i		−	0.551311i
$724$		0			0
$725$	1.13259	+	3.11176i	0.0420632	+	0.115568i
$726$		0			0
$727$	35.7407	+	6.30205i	1.32555	+	0.233730i	0.791213	−	0.611541i	$-0.209450\pi$
$727$	35.7407	+	6.30205i	1.32555	+	0.233730i	0.534337	+	0.845271i	$0.320561\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	5.08740	+	6.06292i	0.188164	+	0.224245i
$732$		0			0
$733$	3.35269	−	5.80704i	0.123835	−	0.214488i	−0.797442	−	0.603395i	$-0.793814\pi$
$733$	3.35269	−	5.80704i	0.123835	−	0.214488i	0.921277	+	0.388908i	$0.127147\pi$
$734$		0			0
$735$	16.9139	+	6.15617i	0.623880	+	0.227074i
$736$		0			0
$737$	−6.78870	+	1.19703i	−0.250065	+	0.0440932i
$738$		0			0
$739$	23.1807	−	27.6257i	0.852717	−	1.01623i	−0.146916	−	0.989149i	$-0.546935\pi$
$739$	23.1807	−	27.6257i	0.852717	−	1.01623i	0.999633	−	0.0270798i	$-0.00862081\pi$
$740$		0			0
$741$	−17.1998	−	18.9175i	−0.631851	−	0.694953i
$742$		0			0
$743$	15.7571	+	13.2218i	0.578073	+	0.485061i	0.884314	−	0.466893i	$-0.154627\pi$
$743$	15.7571	+	13.2218i	0.578073	+	0.485061i	−0.306240	+	0.951954i	$0.599071\pi$
$744$		0			0
$745$	−1.05872	−	6.00430i	−0.0387885	−	0.219981i
$746$		0			0
$747$	−5.11417	+	14.0511i	−0.187118	+	0.514101i
$748$		0			0
$749$	−7.56269	−	4.36632i	−0.276335	−	0.159542i
$750$		0			0
$751$	−10.3236	+	8.66257i	−0.376715	+	0.316102i	−0.811411	−	0.584476i	$-0.801300\pi$
$751$	−10.3236	+	8.66257i	−0.376715	+	0.316102i	0.434696	+	0.900577i	$0.356856\pi$
$752$		0			0
$753$	−0.864688	+	0.499228i	−0.0315110	+	0.0181929i
$754$		0			0
$755$	−10.1175	+	57.3792i	−0.368213	+	2.08824i
$756$		0			0
$757$	36.1416	−	13.1545i	1.31359	−	0.478107i	0.412190	−	0.911098i	$-0.364764\pi$
$757$	36.1416	−	13.1545i	1.31359	−	0.478107i	0.901398	+	0.432991i	$0.142542\pi$
$758$		0			0
$759$	−6.26750			−0.227496
$760$		0			0
$761$	47.7980			1.73268			0.866338	−	0.499458i	$-0.166467\pi$
$761$	47.7980			1.73268			0.866338	+	0.499458i	$0.166467\pi$
$762$		0			0
$763$	−9.06096	+	3.29792i	−0.328029	+	0.119393i
$764$		0			0
$765$	1.33378	−	7.56424i	0.0482229	−	0.273486i
$766$		0			0
$767$	41.5173	−	23.9700i	1.49910	−	0.865508i
$768$		0			0
$769$	−34.9214	+	29.3025i	−1.25930	+	1.05668i	−0.263541	+	0.964648i	$0.584890\pi$
$769$	−34.9214	+	29.3025i	−1.25930	+	1.05668i	−0.995756	+	0.0920280i	$0.970665\pi$
$770$		0			0
$771$	−1.68079	−	0.970407i	−0.0605323	−	0.0349483i
$772$		0			0
$773$	−6.67464	+	18.3384i	−0.240070	+	0.659587i	0.759884	+	0.650058i	$0.225255\pi$
$773$	−6.67464	+	18.3384i	−0.240070	+	0.659587i	−0.999955	+	0.00952906i	$0.996967\pi$
$774$		0			0
$775$	2.40033	+	13.6129i	0.0862223	+	0.488991i
$776$		0			0
$777$	2.62932	+	2.20626i	0.0943265	+	0.0791493i
$778$		0			0
$779$	−37.1375	−	19.5166i	−1.33059	−	0.699255i
$780$		0			0
$781$	−1.86016	+	2.21685i	−0.0665618	+	0.0793253i
$782$		0			0
$783$	1.45983	−	0.257408i	0.0521701	−	0.00919899i
$784$		0			0
$785$	4.46993	+	1.62692i	0.159539	+	0.0580673i
$786$		0			0
$787$	15.7719	−	27.3177i	0.562207	−	0.973771i	−0.435096	−	0.900384i	$-0.643286\pi$
$787$	15.7719	−	27.3177i	0.562207	−	0.973771i	0.997304	−	0.0733873i	$-0.0233809\pi$
$788$		0			0
$789$	−6.22174	−	7.41478i	−0.221500	−	0.263973i
$790$		0			0
$791$	−2.57783	−	4.46493i	−0.0916570	−	0.158755i
$792$		0			0
$793$	18.2709	+	3.22165i	0.648819	+	0.114404i
$794$		0			0
$795$	3.11682	+	8.56340i	0.110542	+	0.303713i
$796$		0			0
$797$		−	46.6721i		−	1.65321i	−0.562782	−	0.826605i	$-0.690269\pi$
$797$		−	46.6721i		−	1.65321i	0.562782	−	0.826605i	$-0.309731\pi$
$798$		0			0
$799$			10.1054i			0.357505i
$800$		0			0
$801$	4.23978	+	11.6487i	0.149805	+	0.411587i
$802$		0			0
$803$	−10.4698	−	1.84610i	−0.369470	−	0.0651475i
$804$		0			0
$805$	2.40557	+	4.16657i	0.0847852	+	0.146852i
$806$		0			0
$807$	−7.66193	−	9.13114i	−0.269713	−	0.321431i
$808$		0			0
$809$	16.4486	−	28.4898i	0.578302	−	1.00165i	−0.417373	−	0.908735i	$-0.637049\pi$
$809$	16.4486	−	28.4898i	0.578302	−	1.00165i	0.995674	−	0.0929125i	$-0.0296177\pi$
$810$		0			0
$811$	51.0589	+	18.5839i	1.79292	+	0.652570i	0.999008	+	0.0445382i	$0.0141817\pi$
$811$	51.0589	+	18.5839i	1.79292	+	0.652570i	0.793913	+	0.608031i	$0.208041\pi$
$812$		0			0
$813$	29.6606	−	5.22997i	1.04024	−	0.183423i
$814$		0			0
$815$	−27.8021	+	33.1333i	−0.973866	+	1.16061i
$816$		0			0
$817$	−10.2136	+	6.45105i	−0.357329	+	0.225694i
$818$		0			0
$819$	−2.49273	−	2.09165i	−0.0871029	−	0.0730880i
$820$		0			0
$821$	7.21420	+	40.9137i	0.251777	+	1.42790i	0.804212	+	0.594343i	$0.202588\pi$
$821$	7.21420	+	40.9137i	0.251777	+	1.42790i	−0.552434	+	0.833556i	$0.686301\pi$
$822$		0			0
$823$	−13.8675	+	38.1007i	−0.483391	+	1.32811i	0.423177	+	0.906047i	$0.360915\pi$
$823$	−13.8675	+	38.1007i	−0.483391	+	1.32811i	−0.906568	+	0.422060i	$0.861307\pi$
$824$		0			0
$825$	−3.76044	−	2.17109i	−0.130922	−	0.0755878i
$826$		0			0
$827$	−6.60593	+	5.54303i	−0.229711	+	0.192750i	−0.750377	−	0.661010i	$-0.770128\pi$
$827$	−6.60593	+	5.54303i	−0.229711	+	0.192750i	0.520666	+	0.853760i	$0.325684\pi$
$828$		0			0
$829$	−41.5107	+	23.9662i	−1.44173	+	0.832382i	−0.997965	−	0.0637629i	$-0.979690\pi$
$829$	−41.5107	+	23.9662i	−1.44173	+	0.832382i	−0.443762	+	0.896145i	$0.646357\pi$
$830$		0			0
$831$	3.05571	−	17.3298i	0.106001	−	0.601163i
$832$		0			0
$833$	17.9591	−	6.53657i	0.622246	−	0.226479i
$834$		0			0
$835$	7.07140			0.244716
$836$		0			0
$837$	6.18773			0.213879
$838$		0			0
$839$	51.4094	−	18.7115i	1.77485	−	0.645992i	0.774946	−	0.632028i	$-0.217777\pi$
$839$	51.4094	−	18.7115i	1.77485	−	0.645992i	0.999902	−	0.0139639i	$-0.00444500\pi$
$840$		0			0
$841$	4.65423	−	26.3954i	0.160491	−	0.910188i
$842$		0			0
$843$	−9.19217	+	5.30710i	−0.316595	+	0.182786i
$844$		0			0
$845$	44.1031	−	37.0069i	1.51719	−	1.27307i
$846$		0			0
$847$	3.46964	+	2.00320i	0.119218	+	0.0688308i
$848$		0			0
$849$	0.266094	−	0.731086i	0.00913231	−	0.0250908i
$850$		0			0
$851$	−3.46425	−	19.6467i	−0.118753	−	0.673482i
$852$		0			0
$853$	−3.42059	−	2.87022i	−0.117119	−	0.0982744i	0.582347	−	0.812940i	$-0.302134\pi$
$853$	−3.42059	−	2.87022i	−0.117119	−	0.0982744i	−0.699466	+	0.714666i	$0.746579\pi$
$854$		0			0
$855$	11.1673	+	3.56885i	0.381913	+	0.122052i
$856$		0			0
$857$	13.1480	−	15.6692i	0.449129	−	0.535251i	−0.493211	−	0.869910i	$-0.664177\pi$
$857$	13.1480	−	15.6692i	0.449129	−	0.535251i	0.942339	+	0.334659i	$0.108621\pi$
$858$		0			0
$859$	53.1235	−	9.36711i	1.81255	−	0.319602i	0.838324	−	0.545173i	$-0.183536\pi$
$859$	53.1235	−	9.36711i	1.81255	−	0.319602i	0.974227	+	0.225571i	$0.0724248\pi$
$860$		0			0
$861$	−5.01745	−	1.82620i	−0.170994	−	0.0622368i
$862$		0			0
$863$	−23.7597	+	41.1530i	−0.808790	+	1.40087i	0.104913	+	0.994481i	$0.466544\pi$
$863$	−23.7597	+	41.1530i	−0.808790	+	1.40087i	−0.913703	+	0.406384i	$0.866790\pi$
$864$		0			0
$865$	38.9570	+	46.4272i	1.32458	+	1.57857i
$866$		0			0
$867$	4.42222	+	7.65951i	0.150186	+	0.260131i
$868$		0			0
$869$	21.9834	+	3.87627i	0.745737	+	0.131494i
$870$		0			0
$871$	7.11478	+	19.5477i	0.241075	+	0.662349i
$872$		0			0
$873$		−	7.03983i		−	0.238262i
$874$		0			0
$875$		−	4.12721i		−	0.139525i
$876$		0			0
$877$	3.98350	+	10.9446i	0.134513	+	0.369572i	0.988601	−	0.150556i	$-0.0481065\pi$
$877$	3.98350	+	10.9446i	0.134513	+	0.369572i	−0.854088	+	0.520128i	$0.825884\pi$
$878$		0			0
$879$	1.68802	+	0.297643i	0.0569355	+	0.0100393i
$880$		0			0
$881$	−19.3525	−	33.5195i	−0.652002	−	1.12930i	−0.982636	−	0.185542i	$-0.940596\pi$
$881$	−19.3525	−	33.5195i	−0.652002	−	1.12930i	0.330634	−	0.943759i	$-0.392737\pi$
$882$		0			0
$883$	−11.3588	−	13.5369i	−0.382254	−	0.455553i	0.540270	−	0.841492i	$-0.318322\pi$
$883$	−11.3588	−	13.5369i	−0.382254	−	0.455553i	−0.922524	+	0.385939i	$0.873878\pi$
$884$		0			0
$885$	−10.9911	+	19.0372i	−0.369462	+	0.639927i
$886$		0			0
$887$	−17.0025	−	6.18841i	−0.570889	−	0.207787i	0.0404143	−	0.999183i	$-0.487132\pi$
$887$	−17.0025	−	6.18841i	−0.570889	−	0.207787i	−0.611303	+	0.791396i	$0.709354\pi$
$888$		0			0
$889$	0.872769	−	0.153893i	0.0292717	−	0.00516140i
$890$		0			0
$891$	−1.24942	+	1.48900i	−0.0418570	+	0.0498833i
$892$		0			0
$893$	−15.2844	−	2.07276i	−0.511472	−	0.0693621i
$894$		0			0
$895$	−21.4743	−	18.0191i	−0.717807	−	0.602312i
$896$		0			0
$897$	3.28428	+	18.6261i	0.109659	+	0.621906i
$898$		0			0
$899$	−3.13714	+	8.61922i	−0.104629	+	0.287467i
$900$		0			0
$901$	8.37975	+	4.83805i	0.279170	+	0.161179i
$902$		0			0
$903$	−1.17777	+	0.988267i	−0.0391938	+	0.0328875i
$904$		0			0
$905$	−35.9011	+	20.7275i	−1.19339	+	0.689005i
$906$		0			0
$907$	−5.99627	+	34.0065i	−0.199103	+	1.12917i	0.707351	+	0.706863i	$0.249890\pi$
$907$	−5.99627	+	34.0065i	−0.199103	+	1.12917i	−0.906454	+	0.422305i	$0.861221\pi$
$908$		0			0
$909$	−4.87543	+	1.77451i	−0.161708	+	0.0588569i
$910$		0			0
$911$	50.0415			1.65795			0.828975	−	0.559286i	$-0.188925\pi$
$911$	50.0415			1.65795			0.828975	+	0.559286i	$0.188925\pi$
$912$		0			0
$913$	29.0645			0.961894
$914$		0			0
$915$	−7.99405	+	2.90960i	−0.264275	+	0.0961882i
$916$		0			0
$917$	1.11191	−	6.30593i	0.0367184	−	0.208240i
$918$		0			0
$919$	−12.7505	+	7.36150i	−0.420600	+	0.242834i	−0.695334	−	0.718687i	$-0.744744\pi$
$919$	−12.7505	+	7.36150i	−0.420600	+	0.242834i	0.274734	+	0.961520i	$0.411410\pi$
$920$		0			0
$921$	0.0161405	−	0.0135435i	0.000531848	−	0.000446273i
$922$		0			0
$923$	7.56291	+	4.36645i	0.248936	+	0.143723i
$924$		0			0
$925$	4.72721	−	12.9879i	0.155430	−	0.427039i
$926$		0			0
$927$	1.71327	+	9.71641i	0.0562710	+	0.319129i
$928$		0			0
$929$	45.4248	+	38.1159i	1.49034	+	1.25054i	0.894204	+	0.447661i	$0.147743\pi$
$929$	45.4248	+	38.1159i	1.49034	+	1.25054i	0.596136	+	0.802883i	$0.296702\pi$
$930$		0			0
$931$	6.20286	+	28.5037i	0.203291	+	0.934171i
$932$		0			0
$933$	3.86461	−	4.60566i	0.126522	−	0.150783i
$934$		0			0
$935$	−14.7030	+	2.59253i	−0.480839	+	0.0847848i
$936$		0			0
$937$	35.1766	+	12.8032i	1.14917	+	0.418263i	0.845216	−	0.534424i	$-0.179472\pi$
$937$	35.1766	+	12.8032i	1.14917	+	0.418263i	0.303952	+	0.952687i	$0.401694\pi$
$938$		0			0
$939$	5.52231	−	9.56493i	0.180214	−	0.312140i
$940$		0			0
$941$	12.6500	+	15.0757i	0.412379	+	0.491454i	0.931753	−	0.363093i	$-0.118279\pi$
$941$	12.6500	+	15.0757i	0.412379	+	0.491454i	−0.519374	+	0.854547i	$0.673835\pi$
$942$		0			0
$943$	15.5173	+	26.8767i	0.505313	+	0.875227i
$944$		0			0
$945$	1.46941	+	0.259097i	0.0478001	+	0.00842844i
$946$		0			0
$947$	21.0365	+	57.7972i	0.683593	+	1.87816i	0.375764	+	0.926715i	$0.377380\pi$
$947$	21.0365	+	57.7972i	0.683593	+	1.87816i	0.307829	+	0.951442i	$0.400397\pi$
$948$		0			0
$949$			32.0819i			1.04142i
$950$		0			0
$951$		−	6.82160i		−	0.221206i
$952$		0			0
$953$	−2.17978	−	5.98890i	−0.0706100	−	0.193999i	0.899368	−	0.437193i	$-0.144027\pi$
$953$	−2.17978	−	5.98890i	−0.0706100	−	0.193999i	−0.969978	+	0.243193i	$0.921805\pi$
$954$		0			0
$955$	−64.8550	−	11.4357i	−2.09866	−	0.370050i
$956$		0			0
$957$	−1.44066	−	2.49529i	−0.0465698	−	0.0806613i
$958$		0			0
$959$	7.66330	+	9.13276i	0.247461	+	0.294912i
$960$		0			0
$961$	−3.64399	+	6.31158i	−0.117548	+	0.203599i
$962$		0			0
$963$	14.7920	+	5.38383i	0.476664	+	0.173492i
$964$		0			0
$965$	−42.2904	+	7.45693i	−1.36137	+	0.240047i
$966$		0			0
$967$	−24.3851	+	29.0611i	−0.784173	+	0.934541i	−0.999114	−	0.0420862i	$-0.986600\pi$
$967$	−24.3851	+	29.0611i	−0.784173	+	0.934541i	0.214941	+	0.976627i	$0.431044\pi$
$968$		0			0
$969$	11.5190	−	4.71891i	0.370044	−	0.151593i
$970$		0			0
$971$	17.6879	+	14.8419i	0.567631	+	0.476299i	0.880859	−	0.473379i	$-0.156966\pi$
$971$	17.6879	+	14.8419i	0.567631	+	0.476299i	−0.313228	+	0.949678i	$0.601410\pi$
$972$		0			0
$973$	0.413422	+	2.34463i	0.0132537	+	0.0751655i
$974$		0			0
$975$	−4.48162	+	12.3132i	−0.143527	+	0.394337i
$976$		0			0
$977$	0.819102	+	0.472909i	0.0262054	+	0.0151297i	0.513045	−	0.858361i	$-0.328517\pi$
$977$	0.819102	+	0.472909i	0.0262054	+	0.0151297i	−0.486840	+	0.873491i	$0.661851\pi$
$978$		0			0
$979$	18.4580	−	15.4881i	0.589921	−	0.495002i
$980$		0			0
$981$	15.0527	−	8.69066i	0.480595	−	0.277471i
$982$		0			0
$983$	−2.84980	+	16.1620i	−0.0908946	+	0.515489i	0.905034	+	0.425340i	$0.139845\pi$
$983$	−2.84980	+	16.1620i	−0.0908946	+	0.515489i	−0.995928	+	0.0901490i	$0.971266\pi$
$984$		0			0
$985$	−17.7451	+	6.45868i	−0.565405	+	0.205791i
$986$		0			0
$987$	−1.96306			−0.0624850
$988$		0			0
$989$	8.93626			0.284157
$990$		0			0
$991$	35.6404	−	12.9721i	1.13216	−	0.412071i	0.293081	−	0.956088i	$-0.405319\pi$
$991$	35.6404	−	12.9721i	1.13216	−	0.412071i	0.839075	+	0.544016i	$0.183097\pi$
$992$		0			0
$993$	4.37425	−	24.8076i	0.138813	−	0.787246i
$994$		0			0
$995$	16.0066	−	9.24141i	0.507443	−	0.292972i
$996$		0			0
$997$	−0.374657	+	0.314375i	−0.0118655	+	0.00995635i	−0.648701	−	0.761043i	$-0.724687\pi$
$997$	−0.374657	+	0.314375i	−0.0118655	+	0.00995635i	0.636836	+	0.771000i	$0.280243\pi$
$998$		0			0
$999$	−5.35815	−	3.09353i	−0.169524	−	0.0978749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.g.79.1	✓	24
4.3	odd	2		912.2.ci.h.79.1	yes	24
19.13	odd	18		912.2.ci.h.127.1	yes	24
76.51	even	18	inner	912.2.ci.g.127.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.g.79.1	✓	24	1.1	even	1	trivial
912.2.ci.g.127.1	yes	24	76.51	even	18	inner
912.2.ci.h.79.1	yes	24	4.3	odd	2
912.2.ci.h.127.1	yes	24	19.13	odd	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{3} +(-0.467043 + 2.64873i) q^{5} +(-0.480437 + 0.277380i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{3} +(-0.467043 + 2.64873i) q^{5} +(-0.480437 + 0.277380i) q^{7} +(0.766044 - 0.642788i) q^{9} +(-1.68333 - 0.971873i) q^{11} +(-2.00616 + 5.51189i) q^{13} +(-0.467043 - 2.64873i) q^{15} +(-2.18767 - 1.83567i) q^{17} +(3.22515 - 2.93230i) q^{19} +(0.356593 - 0.424972i) q^{21} +(-3.17546 + 0.559919i) q^{23} +(-2.09920 - 0.764048i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-0.952837 - 1.13555i) q^{29} +(-3.09386 - 5.35873i) q^{31} +(1.91422 + 0.337528i) q^{33} +(-0.510322 - 1.40210i) q^{35} +6.18706i q^{37} -5.86563i q^{39} +(-3.29187 - 9.04434i) q^{41} +(-2.72931 - 0.481251i) q^{43} +(1.34480 + 2.32926i) q^{45} +(-2.27455 - 2.71070i) q^{47} +(-3.34612 + 5.79565i) q^{49} +(2.68357 + 0.976739i) q^{51} +(-3.33676 + 0.588361i) q^{53} +(3.36042 - 4.00480i) q^{55} +(-2.02774 + 3.85853i) q^{57} +(-6.26092 - 5.25354i) q^{59} +(-0.549242 - 3.11491i) q^{61} +(-0.189739 + 0.521305i) q^{63} +(-13.6626 - 7.88809i) q^{65} +(2.71675 - 2.27962i) q^{67} +(2.79245 - 1.61222i) q^{69} +(0.258532 - 1.46621i) q^{71} +(5.13962 - 1.87067i) q^{73} +2.23393 q^{75} +1.07831 q^{77} +(-10.7917 + 3.92786i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-12.9495 + 7.47641i) q^{83} +(5.88394 - 4.93721i) q^{85} +(1.28375 + 0.741175i) q^{87} +(-4.23978 + 11.6487i) q^{89} +(-0.565055 - 3.20459i) q^{91} +(4.74008 + 3.97740i) q^{93} +(6.26061 + 9.91208i) q^{95} +(4.52511 - 5.39282i) q^{97} +(-1.91422 + 0.337528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{7}+O(q^{10}) \) 24 * q - 9 * q^7	\( 24 q - 9 q^{7} + 9 q^{11} - 9 q^{13} - 6 q^{17} - 3 q^{19} - 6 q^{21} + 15 q^{23} + 6 q^{25} - 12 q^{27} - 6 q^{29} + 12 q^{31} - 3 q^{33} + 30 q^{41} - 9 q^{43} + 3 q^{45} - 15 q^{47} + 27 q^{49} + 3 q^{51} + 6 q^{53} + 21 q^{55} - 9 q^{57} - 36 q^{59} - 21 q^{61} - 3 q^{63} - 9 q^{65} + 45 q^{67} - 36 q^{71} + 42 q^{75} + 108 q^{77} + 36 q^{79} - 27 q^{83} - 9 q^{85} - 9 q^{87} - 27 q^{89} - 36 q^{91} - 18 q^{93} + 30 q^{95} - 51 q^{97} + 3 q^{99}+O(q^{100}) \) 24 * q - 9 * q^7 + 9 * q^11 - 9 * q^13 - 6 * q^17 - 3 * q^19 - 6 * q^21 + 15 * q^23 + 6 * q^25 - 12 * q^27 - 6 * q^29 + 12 * q^31 - 3 * q^33 + 30 * q^41 - 9 * q^43 + 3 * q^45 - 15 * q^47 + 27 * q^49 + 3 * q^51 + 6 * q^53 + 21 * q^55 - 9 * q^57 - 36 * q^59 - 21 * q^61 - 3 * q^63 - 9 * q^65 + 45 * q^67 - 36 * q^71 + 42 * q^75 + 108 * q^77 + 36 * q^79 - 27 * q^83 - 9 * q^85 - 9 * q^87 - 27 * q^89 - 36 * q^91 - 18 * q^93 + 30 * q^95 - 51 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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