LMFDB - Embedded newform 912.2.ci.h.127.1

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			127.1
Character	$\chi$	$=$	912.127
Dual form			912.2.ci.h.79.1

$q$-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 $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$1$	$-1$

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	−0.891235	−	0.453541i	$-0.850161\pi$
$5$	−0.467043	−	2.64873i	−0.208868	−	1.18455i	0.682367	−	0.731009i	$-0.260950\pi$
$6$		0			0
$7$	0.480437	+	0.277380i	0.181588	+	0.104840i	0.588039	−	0.808833i	$-0.299900\pi$
$7$	0.480437	+	0.277380i	0.181588	+	0.104840i	−0.406450	+	0.913673i	$0.633234\pi$
$8$		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	$-0.572003\pi$
$11$	1.68333	−	0.971873i	0.507544	−	0.293031i	0.731824	+	0.681494i	$0.238669\pi$
$12$		0			0
$13$	−2.00616	−	5.51189i	−0.556410	−	1.52872i	−0.824807	−	0.565415i	$-0.808716\pi$
$13$	−2.00616	−	5.51189i	−0.556410	−	1.52872i	0.268397	−	0.963308i	$-0.413506\pi$
$14$		0			0
$15$	0.467043	−	2.64873i	0.120590	−	0.683900i
$16$		0			0
$17$	−2.18767	+	1.83567i	−0.530587	+	0.445215i	−0.868304	−	0.496032i	$-0.834790\pi$
$17$	−2.18767	+	1.83567i	−0.530587	+	0.445215i	0.337717	+	0.941248i	$0.390345\pi$
$18$		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	$-0.335312\pi$
$23$	3.17546	+	0.559919i	0.662129	+	0.116751i	0.167522	+	0.985868i	$0.446423\pi$
$24$		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	−0.847223	−	0.531238i	$-0.821727\pi$
$29$	−0.952837	+	1.13555i	−0.176937	+	0.210866i	0.670286	+	0.742103i	$0.266172\pi$
$30$		0			0
$31$	3.09386	−	5.35873i	0.555674	−	0.962456i	−0.442176	−	0.896928i	$-0.645793\pi$
$31$	3.09386	−	5.35873i	0.555674	−	0.962456i	0.997851	−	0.0655282i	$-0.0208732\pi$
$32$		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	$-0.830173\pi$
$37$		−	6.18706i		−	1.01715i	0.861019	−	0.508573i	$-0.169827\pi$
$38$		0			0
$39$		−	5.86563i		−	0.939252i
$40$		0			0
$41$	−3.29187	+	9.04434i	−0.514104	+	1.41249i	0.362820	+	0.931859i	$0.381814\pi$
$41$	−3.29187	+	9.04434i	−0.514104	+	1.41249i	−0.876924	+	0.480629i	$0.840408\pi$
$42$		0			0
$43$	2.72931	−	0.481251i	0.416216	−	0.0733900i	0.0383811	−	0.999263i	$-0.487780\pi$
$43$	2.72931	−	0.481251i	0.416216	−	0.0733900i	0.377835	+	0.925873i	$0.376669\pi$
$44$		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	$-0.694689\pi$
$47$	2.27455	−	2.71070i	0.331777	−	0.395397i	0.905983	+	0.423314i	$0.139133\pi$
$48$		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	−0.0602885	−	0.998181i	$-0.519202\pi$
$53$	−3.33676	−	0.588361i	−0.458339	−	0.0808176i	−0.398051	+	0.917363i	$0.630313\pi$
$54$		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	$-0.543655\pi$
$59$	6.26092	−	5.25354i	0.815102	−	0.683952i	0.951820	+	0.306658i	$0.0992108\pi$
$60$		0			0
$61$	−0.549242	+	3.11491i	−0.0703233	+	0.398823i	0.929246	+	0.369463i	$0.120458\pi$
$61$	−0.549242	+	3.11491i	−0.0703233	+	0.398823i	−0.999569	+	0.0293606i	$0.990653\pi$
$62$		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	$-0.347286\pi$
$67$	−2.71675	−	2.27962i	−0.331904	−	0.278500i	−0.793475	+	0.608603i	$0.791730\pi$
$68$		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	$-0.0837135\pi$
$71$	−0.258532	−	1.46621i	−0.0306821	−	0.174007i	−0.996298	+	0.0859659i	$0.972602\pi$
$72$		0			0
$73$	5.13962	+	1.87067i	0.601547	+	0.218945i	0.624801	−	0.780784i	$-0.285180\pi$
$73$	5.13962	+	1.87067i	0.601547	+	0.218945i	−0.0232533	+	0.999730i	$0.507402\pi$
$74$		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	$-0.165312\pi$
$79$	10.7917	+	3.92786i	1.21416	+	0.441919i	0.346017	+	0.938228i	$0.387534\pi$
$80$		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	$-0.0269491\pi$
$83$	12.9495	+	7.47641i	1.42139	+	0.820643i	0.424976	+	0.905204i	$0.360282\pi$
$84$		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	−0.933132	−	0.359535i	$-0.882935\pi$
$89$	−4.23978	−	11.6487i	−0.449416	−	1.23476i	0.483716	−	0.875225i	$-0.339287\pi$
$90$		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	0.945178	−	0.326555i	$-0.105888\pi$
$97$	4.52511	+	5.39282i	0.459456	+	0.547558i	−0.485722	+	0.874113i	$0.661443\pi$
$98$		0			0
$99$	1.91422	+	0.337528i	0.192386	+	0.0339228i
$100$		0			0
$101$	−4.87543	+	1.77451i	−0.485124	+	0.176571i	−0.572991	−	0.819562i	$-0.694217\pi$
$101$	−4.87543	+	1.77451i	−0.485124	+	0.176571i	0.0878673	+	0.996132i	$0.471995\pi$
$102$		0			0
$103$	4.93315	+	8.54447i	0.486078	+	0.841912i	0.999872	−	0.0160018i	$-0.00509375\pi$
$103$	4.93315	+	8.54447i	0.486078	+	0.841912i	−0.513794	+	0.857914i	$0.671760\pi$
$104$		0			0
$105$	0.959092	−	1.14300i	0.0935978	−	0.111546i
$106$		0			0
$107$	−7.87064	+	13.6323i	−0.760883	+	1.31789i	0.181513	+	0.983389i	$0.441901\pi$
$107$	−7.87064	+	13.6323i	−0.760883	+	1.31789i	−0.942396	+	0.334500i	$0.891433\pi$
$108$		0			0
$109$	17.1173	−	3.01823i	1.63954	−	0.289094i	0.723540	−	0.690282i	$-0.242514\pi$
$109$	17.1173	−	3.01823i	1.63954	−	0.289094i	0.915996	+	0.401188i	$0.131403\pi$
$110$		0			0
$111$	2.11610	−	5.81393i	0.200851	−	0.551834i
$112$		0			0
$113$		−	9.29347i		−	0.874256i	−0.899399	−	0.437128i	$-0.855996\pi$
$113$		−	9.29347i		−	0.874256i	0.899399	−	0.437128i	$-0.144004\pi$
$114$		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	$-0.588531\pi$
$127$	1.50116	−	0.546378i	0.133207	−	0.0484832i	0.407763	+	0.913088i	$0.366309\pi$
$128$		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	$-0.0539996\pi$
$131$	7.41924	+	8.84191i	0.648222	+	0.772521i	−0.337423	+	0.941353i	$0.609555\pi$
$132$		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	0.231097	+	0.972931i	$0.425768\pi$
$137$	−3.73175	+	21.1638i	−0.318825	+	1.80815i	−0.549922	+	0.835216i	$0.685343\pi$
$138$		0			0
$139$	−1.46781	−	4.03277i	−0.124498	−	0.342055i	0.861749	−	0.507335i	$-0.169369\pi$
$139$	−1.46781	−	4.03277i	−0.124498	−	0.342055i	−0.986247	+	0.165280i	$0.947147\pi$
$140$		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	0.253288	−	0.967391i	$-0.418488\pi$
$149$	−2.13015	−	0.775311i	−0.174509	−	0.0635159i	−0.427797	+	0.903875i	$0.640710\pi$
$150$		0			0
$151$	−21.6629			−1.76290			−0.881449	−	0.472279i	$-0.843431\pi$
$151$	−21.6629			−1.76290			−0.881449	+	0.472279i	$0.843431\pi$
$152$		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	0.994607	−	0.103713i	$-0.0330723\pi$
$157$	0.307113	+	1.74172i	0.0245103	+	0.139005i	−0.970097	+	0.242717i	$0.921961\pi$
$158$		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	$-0.883528\pi$
$163$	−13.9269	+	8.04069i	−1.09084	+	0.629796i	−0.157039	+	0.987592i	$0.550195\pi$
$164$		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	$-0.912008\pi$
$167$	0.456550	−	2.58922i	0.0353289	−	0.200360i	0.997364	+	0.0725673i	$0.0231192\pi$
$168$		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	0.945876	+	0.324529i	$0.105206\pi$
$173$	14.4843	+	17.2618i	1.10122	+	1.31239i	0.155349	+	0.987860i	$0.450350\pi$
$174$		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	$-0.0393101\pi$
$179$	5.21133	+	9.02628i	0.389513	+	0.674656i	−0.602871	+	0.797839i	$0.705977\pi$
$180$		0			0
$181$	9.90734	−	11.8071i	0.736407	−	0.877616i	−0.259707	−	0.965687i	$-0.583626\pi$
$181$	9.90734	−	11.8071i	0.736407	−	0.877616i	0.996114	+	0.0880716i	$0.0280704\pi$
$182$		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	−0.572514	−	0.819895i	$-0.694032\pi$
$193$	5.46078	−	15.0034i	0.393075	−	1.07997i	0.965590	−	0.260071i	$-0.0837460\pi$
$194$		0			0
$195$	−15.5365	+	2.73950i	−1.11259	+	0.196180i
$196$		0			0
$197$	3.51055	−	6.08045i	0.250116	−	0.433214i	−0.713441	−	0.700715i	$-0.752865\pi$
$197$	3.51055	−	6.08045i	0.250116	−	0.433214i	0.963558	+	0.267501i	$0.0861979\pi$
$198$		0			0
$199$	4.41722	−	5.26423i	0.313128	−	0.373172i	−0.586410	−	0.810015i	$-0.699459\pi$
$199$	4.41722	−	5.26423i	0.313128	−	0.373172i	0.899538	+	0.436843i	$0.143904\pi$
$200$		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	$-0.771757\pi$
$211$	−3.44927	+	2.89428i	−0.237458	+	0.199251i	0.516291	+	0.856413i	$0.327312\pi$
$212$		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	0.943090	+	0.332536i	$0.107904\pi$
$223$	2.54774	+	14.4490i	0.170609	+	0.967574i	−0.772481	+	0.635038i	$0.780984\pi$
$224$		0			0
$225$	−2.09920	−	0.764048i	−0.139947	−	0.0509365i
$226$		0			0
$227$	27.3415			1.81472			0.907361	−	0.420353i	$-0.138094\pi$
$227$	27.3415			1.81472			0.907361	+	0.420353i	$0.138094\pi$
$228$		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	0.841918	+	0.539605i	$0.181427\pi$
$233$	3.59215	+	20.3721i	0.235330	+	1.33462i	−0.606588	+	0.795016i	$0.707462\pi$
$234$		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	$-0.895542\pi$
$239$	−17.6367	+	10.1826i	−1.14083	+	0.658656i	−0.194191	+	0.980964i	$0.562208\pi$
$240$		0			0
$241$	−5.07011	−	13.9300i	−0.326594	−	0.897311i	−0.988967	−	0.148136i	$-0.952673\pi$
$241$	−5.07011	−	13.9300i	−0.326594	−	0.897311i	0.662373	−	0.749175i	$-0.269550\pi$
$242$		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	$-0.454476\pi$
$251$	−0.983287	−	0.173380i	−0.0620645	−	0.0109437i	−0.204594	+	0.978847i	$0.565587\pi$
$252$		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	−0.725730	−	0.687979i	$-0.758498\pi$
$257$	1.24753	−	1.48675i	0.0778188	−	0.0927409i	0.803549	+	0.595238i	$0.202942\pi$
$258$		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	$-0.985350\pi$
$263$	−3.31052	+	9.09558i	−0.204135	+	0.560857i	0.794806	+	0.606864i	$0.207573\pi$
$264$		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	−0.751171	−	0.660108i	$-0.770511\pi$
$269$	4.07683	−	11.2010i	0.248569	−	0.682937i	0.999739	−	0.0228288i	$-0.00726727\pi$
$270$		0			0
$271$	29.6606	−	5.22997i	1.80175	−	0.317698i	0.830730	−	0.556676i	$-0.187924\pi$
$271$	29.6606	−	5.22997i	1.80175	−	0.317698i	0.971025	+	0.238978i	$0.0768124\pi$
$272$		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	−0.999442	−	0.0334093i	$-0.989364\pi$
$277$	−8.79856	−	15.2396i	−0.528654	−	0.915656i	0.470788	−	0.882247i	$-0.343970\pi$
$278$		0			0
$279$	5.81456	−	2.11633i	0.348109	−	0.126701i
$280$		0			0
$281$	10.4530	+	1.84314i	0.623571	+	0.109952i	0.476501	−	0.879174i	$-0.341905\pi$
$281$	10.4530	+	1.84314i	0.623571	+	0.109952i	0.147070	+	0.989126i	$0.453016\pi$
$282$		0			0
$283$	0.500092	+	0.595987i	0.0297274	+	0.0354277i	0.780703	−	0.624902i	$-0.214861\pi$
$283$	0.500092	+	0.595987i	0.0297274	+	0.0354277i	−0.750976	+	0.660330i	$0.770417\pi$
$284$		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	−0.542733	−	0.839905i	$-0.682611\pi$
$293$	−1.48442	+	0.857030i	−0.0867207	+	0.0500682i	0.456013	+	0.889973i	$0.349277\pi$
$294$		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	$-0.388698\pi$
$307$	0.0197993	+	0.00720634i	0.00113000	+	0.000411288i	−0.341455	+	0.939898i	$0.610920\pi$
$308$		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	$-0.278807\pi$
$311$	5.20678	+	3.00613i	0.295249	+	0.170462i	−0.345058	+	0.938582i	$0.612141\pi$
$312$		0			0
$313$	−8.46067	−	7.09935i	−0.478226	−	0.401279i	0.371559	−	0.928409i	$-0.378823\pi$
$313$	−8.46067	−	7.09935i	−0.478226	−	0.401279i	−0.849784	+	0.527131i	$0.823268\pi$
$314$		0			0
$315$	1.29218	−	0.746041i	0.0728062	−	0.0420347i
$316$		0			0
$317$	−2.33312	−	6.41021i	−0.131041	−	0.360033i	0.856768	−	0.515702i	$-0.172469\pi$
$317$	−2.33312	−	6.41021i	−0.131041	−	0.360033i	−0.987809	+	0.155669i	$0.950247\pi$
$318$		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	0.971085	+	0.238734i	$0.0767324\pi$
$331$	12.5952	+	21.8154i	0.692292	+	1.19909i	−0.278793	+	0.960351i	$0.589934\pi$
$332$		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	−0.522518	−	0.852628i	$-0.675007\pi$
$337$	−13.2525	+	2.33677i	−0.721908	+	0.127292i	−0.199390	+	0.979920i	$0.563896\pi$
$338$		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	$-0.261452\pi$
$347$	29.2781	−	5.16253i	1.57173	−	0.277139i	0.890519	+	0.454946i	$0.150341\pi$
$348$		0			0
$349$	−1.67020	+	2.89287i	−0.0894038	+	0.154852i	−0.907259	−	0.420572i	$-0.861830\pi$
$349$	−1.67020	+	2.89287i	−0.0894038	+	0.154852i	0.817855	+	0.575424i	$0.195163\pi$
$350$		0			0
$351$	3.77035	−	4.49333i	0.201247	−	0.239836i
$352$		0			0
$353$	−4.19629	−	7.26819i	−0.223346	−	0.386847i	0.732476	−	0.680793i	$-0.238365\pi$
$353$	−4.19629	−	7.26819i	−0.223346	−	0.386847i	−0.955822	+	0.293946i	$0.905031\pi$
$354$		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	$-0.251481\pi$
$359$	−2.23586	−	2.66459i	−0.118004	−	0.140632i	−0.821812	+	0.569758i	$0.807037\pi$
$360$		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	$-0.136069\pi$
$367$	−1.02641	−	2.82003i	−0.0535781	−	0.147204i	−0.963595	+	0.267367i	$0.913846\pi$
$368$		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	−0.284191	−	0.958768i	$-0.591725\pi$
$373$	−24.2690	−	14.0117i	−1.25660	−	0.725500i	−0.972413	+	0.233267i	$0.925058\pi$
$374$		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	$-0.478921\pi$
$379$	2.57656			0.132349			0.0661746	+	0.997808i	$0.478921\pi$
$380$		0			0
$381$	1.59750			0.0818426
$382$		0			0
$383$	−31.4924	−	11.4623i	−1.60919	−	0.585696i	−0.627907	−	0.778288i	$-0.716088\pi$
$383$	−31.4924	−	11.4623i	−1.60919	−	0.585696i	−0.981279	+	0.192592i	$0.938311\pi$
$384$		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	0.273103	−	0.961985i	$-0.411950\pi$
$389$	−12.3633	−	10.3740i	−0.626843	−	0.525984i	−0.899946	+	0.436001i	$0.856394\pi$
$390$		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	−0.986120	−	0.166036i	$-0.946903\pi$
$397$	−19.8022	+	16.6160i	−0.993844	+	0.833934i	−0.00772389	+	0.999970i	$0.502459\pi$
$398$		0			0
$399$	0.0960780	−	2.41624i	0.00480991	−	0.120963i
$400$		0			0
$401$	6.20348	+	7.39302i	0.309787	+	0.369190i	0.898364	−	0.439251i	$-0.144756\pi$
$401$	6.20348	+	7.39302i	0.309787	+	0.369190i	−0.588577	+	0.808441i	$0.700312\pi$
$402$		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	−0.424693	−	0.905338i	$-0.639618\pi$
$409$	10.9337	−	13.0303i	0.540638	−	0.644307i	0.965331	+	0.261030i	$0.0840623\pi$
$410$		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	−0.358948	−	0.933358i	$-0.616864\pi$
$421$	10.5869	−	29.0872i	0.515973	−	1.41762i	0.874921	−	0.484266i	$-0.160913\pi$
$422$		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	$-0.511473\pi$
$431$	12.0147	−	4.37299i	0.578728	−	0.210640i	0.614764	+	0.788711i	$0.289251\pi$
$432$		0			0
$433$	4.16351	+	0.734140i	0.200086	+	0.0352805i	0.272793	−	0.962073i	$-0.412053\pi$
$433$	4.16351	+	0.734140i	0.200086	+	0.0352805i	−0.0727070	+	0.997353i	$0.523164\pi$
$434$		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	0.344573	−	0.938760i	$-0.388024\pi$
$439$	27.8437	−	23.3636i	1.32891	−	1.11508i	0.984332	−	0.176324i	$-0.0564207\pi$
$440$		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	$-0.196502\pi$
$443$	−3.81612	−	10.4847i	−0.181309	−	0.498143i	−0.996737	+	0.0807154i	$0.974280\pi$
$444$		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	0.389525	−	0.921016i	$-0.372639\pi$
$449$	−4.52051	−	2.60992i	−0.213336	−	0.123170i	−0.602861	+	0.797846i	$0.705973\pi$
$450$		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	0.986233	+	0.165363i	$0.0528794\pi$
$461$	2.49137	+	14.1292i	0.116034	+	0.658064i	−0.870198	+	0.492702i	$0.836009\pi$
$462$		0			0
$463$	0.609195	+	0.351719i	0.0283117	+	0.0163458i	0.514089	−	0.857737i	$-0.328130\pi$
$463$	0.609195	+	0.351719i	0.0283117	+	0.0163458i	−0.485777	+	0.874083i	$0.661463\pi$
$464$		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	$-0.676025\pi$
$467$	−1.10029	+	0.635253i	−0.0509154	+	0.0293960i	0.474326	+	0.880349i	$0.342692\pi$
$468$		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	$-0.234594\pi$
$479$	26.4047	+	4.65586i	1.20646	+	0.212732i	0.465971	+	0.884800i	$0.345705\pi$
$480$		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	−0.108270	−	0.994122i	$-0.534531\pi$
$487$	17.8045	−	30.8383i	0.806799	−	1.39742i	0.915070	−	0.403296i	$-0.132136\pi$
$488$		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	$-0.779918\pi$
$491$	5.08824	−	13.9798i	0.229629	−	0.630900i	0.999977	+	0.00672283i	$0.00213996\pi$
$492$		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	$-0.370251\pi$
$499$	24.1910	−	4.26553i	1.08294	−	0.190952i	0.686515	+	0.727116i	$0.259140\pi$
$500$		0			0
$501$	1.31458	−	2.27693i	0.0587313	−	0.101726i
$502$		0			0
$503$	−19.4729	+	23.2068i	−0.868252	+	1.03474i	0.130809	+	0.991408i	$0.458243\pi$
$503$	−19.4729	+	23.2068i	−0.868252	+	1.03474i	−0.999061	+	0.0433346i	$0.986202\pi$
$504$		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	−0.117922	−	0.993023i	$-0.537623\pi$
$509$	−12.8229	−	2.26103i	−0.568366	−	0.100218i	−0.450444	+	0.892805i	$0.648734\pi$
$510$		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	0.142992	−	0.989724i	$-0.454328\pi$
$521$	24.4601	−	14.1220i	1.07161	−	0.618697i	0.928622	+	0.371027i	$0.120994\pi$
$522$		0			0
$523$	14.2949	+	11.9948i	0.625071	+	0.524496i	0.899393	−	0.437141i	$-0.144009\pi$
$523$	14.2949	+	11.9948i	0.625071	+	0.524496i	−0.274322	+	0.961638i	$0.588453\pi$
$524$		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	0.950535	−	0.310618i	$-0.100536\pi$
$541$	18.8330	+	15.8028i	0.809694	+	0.679414i	−0.140840	+	0.990032i	$0.544980\pi$
$542$		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	0.754406	+	0.656408i	$0.227925\pi$
$547$	−4.18665	+	23.7437i	−0.179008	+	1.01521i	−0.933415	+	0.358799i	$0.883186\pi$
$548$		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	−0.907662	−	0.419701i	$-0.862135\pi$
$557$	−31.4645	+	11.4521i	−1.33319	+	0.485243i	−0.425531	+	0.904944i	$0.639913\pi$
$558$		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	$-0.925126\pi$
$563$	−6.74800	+	11.6879i	−0.284394	+	0.492585i	0.688068	+	0.725646i	$0.258459\pi$
$564$		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	$-0.659223\pi$
$569$		−	41.8624i		−	1.75496i	0.479612	−	0.877481i	$-0.340777\pi$
$570$		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	−0.430940	−	0.902381i	$-0.641818\pi$
$577$	13.5961	−	23.5492i	0.566015	−	0.980367i	0.996954	−	0.0779858i	$-0.0248489\pi$
$578$		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	$-0.104197\pi$
$587$	11.2861	+	13.4502i	0.465827	+	0.555151i	−0.481072	+	0.876681i	$0.659753\pi$
$588$		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	−0.273763	−	0.961797i	$-0.588269\pi$
$593$	7.60851	−	43.1500i	0.312444	−	1.77196i	0.586207	−	0.810161i	$-0.300620\pi$
$594$		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	$-0.552397\pi$
$599$	−28.4838	−	23.9008i	−1.16382	−	0.976560i	−0.999951	+	0.00992274i	$0.996841\pi$
$600$		0			0
$601$	5.57500	+	3.21873i	0.227409	+	0.131295i	0.609376	−	0.792881i	$-0.291420\pi$
$601$	5.57500	+	3.21873i	0.227409	+	0.131295i	−0.381967	+	0.924176i	$0.624753\pi$
$602$		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	$-0.604211\pi$
$607$	−15.8453			−0.643141			−0.321570	+	0.946886i	$0.604211\pi$
$608$		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	0.875074	+	0.483990i	$0.160813\pi$
$613$	5.40504	+	30.6535i	0.218308	+	1.23808i	−0.656766	+	0.754094i	$0.728076\pi$
$614$		0			0
$615$	22.4186	+	12.9434i	0.904006	+	0.521928i
$616$		0			0
$617$	33.1278	+	27.7975i	1.33367	+	1.11909i	0.983204	+	0.182511i	$0.0584226\pi$
$617$	33.1278	+	27.7975i	1.33367	+	1.11909i	0.350470	+	0.936574i	$0.386022\pi$
$618$		0			0
$619$	25.4980	−	14.7213i	1.02485	−	0.591698i	0.109345	−	0.994004i	$-0.465125\pi$
$619$	25.4980	−	14.7213i	1.02485	−	0.591698i	0.915505	+	0.402306i	$0.131791\pi$
$620$		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	$-0.484390\pi$
$631$	−6.19254	−	1.09191i	−0.246521	−	0.0434683i	−0.295543	+	0.955329i	$0.595501\pi$
$632$		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	−0.252356	−	0.967634i	$-0.581206\pi$
$641$	−4.01400	+	0.707776i	−0.158543	+	0.0279555i	0.0938131	+	0.995590i	$0.470094\pi$
$642$		0			0
$643$	−10.5820	+	29.0737i	−0.417312	+	1.14655i	0.535908	+	0.844276i	$0.319969\pi$
$643$	−10.5820	+	29.0737i	−0.417312	+	1.14655i	−0.953220	+	0.302278i	$0.902253\pi$
$644$		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	−0.786728	−	0.617300i	$-0.788227\pi$
$653$	3.60905	−	6.25106i	0.141233	−	0.244623i	0.927961	+	0.372677i	$0.121560\pi$
$654$		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	$-0.632222\pi$
$659$	−3.19735	+	1.16374i	−0.124551	+	0.0453329i	0.278993	+	0.960293i	$0.409999\pi$
$660$		0			0
$661$	−7.87734	−	1.38899i	−0.306393	−	0.0540254i	0.0183377	−	0.999832i	$-0.494163\pi$
$661$	−7.87734	−	1.38899i	−0.306393	−	0.0540254i	−0.324731	+	0.945806i	$0.605274\pi$
$662$		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	−0.405217	−	0.914220i	$-0.632804\pi$
$673$	4.77109	−	2.75459i	0.183912	−	0.106182i	0.589129	+	0.808039i	$0.299471\pi$
$674$		0			0
$675$	−1.71129	−	1.43594i	−0.0658675	−	0.0552694i
$676$		0			0
$677$	−12.4309	−	7.17697i	−0.477758	−	0.275833i	0.241724	−	0.970345i	$-0.422287\pi$
$677$	−12.4309	−	7.17697i	−0.477758	−	0.275833i	−0.719482	+	0.694512i	$0.755620\pi$
$678$		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	$-0.527162\pi$
$683$	−4.45475			−0.170456			−0.0852281	+	0.996361i	$0.527162\pi$
$684$		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	$-0.249715\pi$
$691$	11.8234	+	6.82625i	0.449784	+	0.259683i	−0.257955	+	0.966157i	$0.583049\pi$
$692$		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	−0.968267	−	0.249917i	$-0.919597\pi$
$701$	−23.5715	+	19.7789i	−0.890285	+	0.747038i	0.0779824	+	0.996955i	$0.475152\pi$
$702$		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	−0.996077	−	0.0884857i	$-0.971797\pi$
$709$	−45.3256	+	16.4972i	−1.70224	+	0.619565i	−0.706162	+	0.708050i	$0.749575\pi$
$710$		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	−0.590145	−	0.807298i	$-0.700929\pi$
$719$	10.2123	−	28.0580i	0.380853	−	1.04639i	0.970998	−	0.239088i	$-0.0768485\pi$
$720$		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	$-0.790550\pi$
$727$	−35.7407	+	6.30205i	−1.32555	+	0.233730i	−0.534337	+	0.845271i	$0.679439\pi$
$728$		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	0.921277	−	0.388908i	$-0.127147\pi$
$733$	3.35269	+	5.80704i	0.123835	+	0.214488i	−0.797442	+	0.603395i	$0.793814\pi$
$734$		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	−0.999633	−	0.0270798i	$-0.991379\pi$
$739$	−23.1807	−	27.6257i	−0.852717	−	1.01623i	0.146916	−	0.989149i	$-0.453065\pi$
$740$		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	$-0.845373\pi$
$743$	−15.7571	+	13.2218i	−0.578073	+	0.485061i	0.306240	+	0.951954i	$0.400929\pi$
$744$		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	$-0.198700\pi$
$751$	10.3236	+	8.66257i	0.376715	+	0.316102i	−0.434696	+	0.900577i	$0.643144\pi$
$752$		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	0.901398	−	0.432991i	$-0.142542\pi$
$757$	36.1416	+	13.1545i	1.31359	+	0.478107i	0.412190	+	0.911098i	$0.364764\pi$
$758$		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	−0.995756	−	0.0920280i	$-0.970665\pi$
$769$	−34.9214	−	29.3025i	−1.25930	−	1.05668i	−0.263541	−	0.964648i	$-0.584890\pi$
$770$		0			0
$771$	1.68079	−	0.970407i	0.0605323	−	0.0349483i
$772$		0			0
$773$	−6.67464	−	18.3384i	−0.240070	−	0.659587i	−0.999955	−	0.00952906i	$-0.996967\pi$
$773$	−6.67464	−	18.3384i	−0.240070	−	0.659587i	0.759884	−	0.650058i	$-0.225255\pi$
$774$		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	−0.997304	−	0.0733873i	$-0.976619\pi$
$787$	−15.7719	−	27.3177i	−0.562207	−	0.973771i	0.435096	−	0.900384i	$-0.356714\pi$
$788$		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	$0.309731\pi$
$797$			46.6721i			1.65321i	−0.562782	+	0.826605i	$0.690269\pi$
$798$		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	0.995674	+	0.0929125i	$0.0296177\pi$
$809$	16.4486	+	28.4898i	0.578302	+	1.00165i	−0.417373	+	0.908735i	$0.637049\pi$
$810$		0			0
$811$	−51.0589	+	18.5839i	−1.79292	+	0.652570i	−0.793913	+	0.608031i	$0.791959\pi$
$811$	−51.0589	+	18.5839i	−1.79292	+	0.652570i	−0.999008	+	0.0445382i	$0.985818\pi$
$812$		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	−0.552434	−	0.833556i	$-0.686301\pi$
$821$	7.21420	−	40.9137i	0.251777	−	1.42790i	0.804212	−	0.594343i	$-0.202588\pi$
$822$		0			0
$823$	13.8675	+	38.1007i	0.483391	+	1.32811i	0.906568	+	0.422060i	$0.138693\pi$
$823$	13.8675	+	38.1007i	0.483391	+	1.32811i	−0.423177	+	0.906047i	$0.639085\pi$
$824$		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	$-0.229872\pi$
$827$	6.60593	+	5.54303i	0.229711	+	0.192750i	−0.520666	+	0.853760i	$0.674316\pi$
$828$		0			0
$829$	−41.5107	−	23.9662i	−1.44173	−	0.832382i	−0.443762	−	0.896145i	$-0.646357\pi$
$829$	−41.5107	−	23.9662i	−1.44173	−	0.832382i	−0.997965	+	0.0637629i	$0.979690\pi$
$830$		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	−0.999902	−	0.0139639i	$-0.995555\pi$
$839$	−51.4094	−	18.7115i	−1.77485	−	0.645992i	−0.774946	−	0.632028i	$-0.782223\pi$
$840$		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	−0.699466	−	0.714666i	$-0.746579\pi$
$853$	−3.42059	+	2.87022i	−0.117119	+	0.0982744i	0.582347	+	0.812940i	$0.302134\pi$
$854$		0			0
$855$	−11.1673	+	3.56885i	−0.381913	+	0.122052i
$856$		0			0
$857$	13.1480	+	15.6692i	0.449129	+	0.535251i	0.942339	−	0.334659i	$-0.108621\pi$
$857$	13.1480	+	15.6692i	0.449129	+	0.535251i	−0.493211	+	0.869910i	$0.664177\pi$
$858$		0			0
$859$	−53.1235	−	9.36711i	−1.81255	−	0.319602i	−0.838324	−	0.545173i	$-0.816464\pi$
$859$	−53.1235	−	9.36711i	−1.81255	−	0.319602i	−0.974227	+	0.225571i	$0.927575\pi$
$860$		0			0
$861$	−5.01745	+	1.82620i	−0.170994	+	0.0622368i
$862$		0			0
$863$	23.7597	+	41.1530i	0.808790	+	1.40087i	0.913703	+	0.406384i	$0.133210\pi$
$863$	23.7597	+	41.1530i	0.808790	+	1.40087i	−0.104913	+	0.994481i	$0.533456\pi$
$864$		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	−0.854088	−	0.520128i	$-0.825884\pi$
$877$	3.98350	−	10.9446i	0.134513	−	0.369572i	0.988601	+	0.150556i	$0.0481065\pi$
$878$		0			0
$879$	−1.68802	+	0.297643i	−0.0569355	+	0.0100393i
$880$		0			0
$881$	−19.3525	+	33.5195i	−0.652002	+	1.12930i	0.330634	+	0.943759i	$0.392737\pi$
$881$	−19.3525	+	33.5195i	−0.652002	+	1.12930i	−0.982636	+	0.185542i	$0.940596\pi$
$882$		0			0
$883$	11.3588	−	13.5369i	0.382254	−	0.455553i	−0.540270	−	0.841492i	$-0.681678\pi$
$883$	11.3588	−	13.5369i	0.382254	−	0.455553i	0.922524	+	0.385939i	$0.126122\pi$
$884$		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	$-0.512868\pi$
$887$	17.0025	−	6.18841i	0.570889	−	0.207787i	0.611303	+	0.791396i	$0.290646\pi$
$888$		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	0.906454	+	0.422305i	$0.138779\pi$
$907$	5.99627	+	34.0065i	0.199103	+	1.12917i	−0.707351	+	0.706863i	$0.750110\pi$
$908$		0			0
$909$	−4.87543	−	1.77451i	−0.161708	−	0.0588569i
$910$		0			0
$911$	−50.0415			−1.65795			−0.828975	−	0.559286i	$-0.811075\pi$
$911$	−50.0415			−1.65795			−0.828975	+	0.559286i	$0.811075\pi$
$912$		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	$-0.255256\pi$
$919$	12.7505	+	7.36150i	0.420600	+	0.242834i	−0.274734	+	0.961520i	$0.588590\pi$
$920$		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	0.596136	−	0.802883i	$-0.296702\pi$
$929$	45.4248	−	38.1159i	1.49034	−	1.25054i	0.894204	−	0.447661i	$-0.147743\pi$
$930$		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	0.303952	−	0.952687i	$-0.401694\pi$
$937$	35.1766	−	12.8032i	1.14917	−	0.418263i	0.845216	+	0.534424i	$0.179472\pi$
$938$		0			0
$939$	−5.52231	−	9.56493i	−0.180214	−	0.312140i
$940$		0			0
$941$	12.6500	−	15.0757i	0.412379	−	0.491454i	−0.519374	−	0.854547i	$-0.673835\pi$
$941$	12.6500	−	15.0757i	0.412379	−	0.491454i	0.931753	+	0.363093i	$0.118279\pi$
$942$		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	−0.307829	+	0.951442i	$0.599603\pi$
$947$	−21.0365	+	57.7972i	−0.683593	+	1.87816i	−0.375764	+	0.926715i	$0.622620\pi$
$948$		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	−0.969978	−	0.243193i	$-0.921805\pi$
$953$	−2.17978	+	5.98890i	−0.0706100	+	0.193999i	0.899368	+	0.437193i	$0.144027\pi$
$954$		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	$-0.0134004\pi$
$967$	24.3851	+	29.0611i	0.784173	+	0.934541i	−0.214941	+	0.976627i	$0.568956\pi$
$968$		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	$-0.843034\pi$
$971$	−17.6879	+	14.8419i	−0.567631	+	0.476299i	0.313228	+	0.949678i	$0.398590\pi$
$972$		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	−0.486840	−	0.873491i	$-0.661851\pi$
$977$	0.819102	−	0.472909i	0.0262054	−	0.0151297i	0.513045	+	0.858361i	$0.328517\pi$
$978$		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	0.995928	+	0.0901490i	$0.0287343\pi$
$983$	2.84980	+	16.1620i	0.0908946	+	0.515489i	−0.905034	+	0.425340i	$0.860155\pi$
$984$		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	$-0.594681\pi$
$991$	−35.6404	−	12.9721i	−1.13216	−	0.412071i	−0.839075	+	0.544016i	$0.816903\pi$
$992$		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	0.636836	−	0.771000i	$-0.280243\pi$
$997$	−0.374657	−	0.314375i	−0.0118655	−	0.00995635i	−0.648701	+	0.761043i	$0.724687\pi$
$998$		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.h.127.1	yes	24
4.3	odd	2		912.2.ci.g.127.1	yes	24
19.3	odd	18		912.2.ci.g.79.1	✓	24
76.3	even	18	inner	912.2.ci.h.79.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.g.79.1	✓	24	19.3	odd	18
912.2.ci.g.127.1	yes	24	4.3	odd	2
912.2.ci.h.79.1	yes	24	76.3	even	18	inner
912.2.ci.h.127.1	yes	24	1.1	even	1	trivial

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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