LMFDB - Embedded newform 1216.2.t.d.353.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(353,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1216.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.3
Character	$\chi$	$=$	1216.353
Dual form			1216.2.t.d.1185.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80664 - 1.04307i) q^{3} +(-0.410474 - 0.236987i) q^{5} -3.88259 q^{7} +(0.675970 + 1.17081i) q^{9} +O(q^{10})$	\(q+(-1.80664 - 1.04307i) q^{3} +(-0.410474 - 0.236987i) q^{5} -3.88259 q^{7} +(0.675970 + 1.17081i) q^{9} -6.19156i q^{11} +(4.97986 - 2.87512i) q^{13} +(0.494386 + 0.856302i) q^{15} +(0.442610 - 0.766623i) q^{17} +(4.19123 + 1.19731i) q^{19} +(7.01445 + 4.04979i) q^{21} +(-0.917273 - 1.58876i) q^{23} +(-2.38767 - 4.13557i) q^{25} +3.43807i q^{27} +(-6.58038 + 3.79918i) q^{29} -6.70591 q^{31} +(-6.45820 + 11.1859i) q^{33} +(1.59370 + 0.920123i) q^{35} +1.54096i q^{37} -11.9958 q^{39} +(-3.44115 + 5.96025i) q^{41} +(-6.45827 - 3.72868i) q^{43} -0.640784i q^{45} +(6.71860 + 11.6370i) q^{47} +8.07449 q^{49} +(-1.59927 + 0.923342i) q^{51} +(2.06834 - 1.19416i) q^{53} +(-1.46732 + 2.54147i) q^{55} +(-6.32318 - 6.53484i) q^{57} +(-10.1996 - 5.88874i) q^{59} +(2.12308 - 1.22576i) q^{61} +(-2.62451 - 4.54579i) q^{63} -2.72547 q^{65} +(8.74568 - 5.04932i) q^{67} +3.82710i q^{69} +(-3.98294 + 6.89866i) q^{71} +(-3.01795 + 5.22724i) q^{73} +9.96200i q^{75} +24.0393i q^{77} +(-2.52019 + 4.36511i) q^{79} +(5.61404 - 9.72380i) q^{81} -10.3080i q^{83} +(-0.363359 + 0.209786i) q^{85} +15.8512 q^{87} +(-1.84416 - 3.19418i) q^{89} +(-19.3347 + 11.1629i) q^{91} +(12.1152 + 6.99470i) q^{93} +(-1.43664 - 1.48473i) q^{95} +(-0.213162 + 0.369207i) q^{97} +(7.24916 - 4.18531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{5} + 8 q^{9}+O(q^{10}) $ 24 * q - 6 * q^5 + 8 * q^9	$ 24 q - 6 q^{5} + 8 q^{9} + 30 q^{13} + 6 q^{17} + 24 q^{21} + 6 q^{25} + 42 q^{29} - 14 q^{33} - 24 q^{41} + 24 q^{49} - 18 q^{53} - 42 q^{57} + 18 q^{61} - 20 q^{65} - 16 q^{73} + 52 q^{81} - 78 q^{85} + 14 q^{89} + 60 q^{93} - 4 q^{97}+O(q^{100}) $ 24 * q - 6 * q^5 + 8 * q^9 + 30 * q^13 + 6 * q^17 + 24 * q^21 + 6 * q^25 + 42 * q^29 - 14 * q^33 - 24 * q^41 + 24 * q^49 - 18 * q^53 - 42 * q^57 + 18 * q^61 - 20 * q^65 - 16 * q^73 + 52 * q^81 - 78 * q^85 + 14 * q^89 + 60 * q^93 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.80664	−	1.04307i	−1.04307	−	0.602214i	−0.122365	−	0.992485i	$-0.539048\pi$
$3$	−1.80664	−	1.04307i	−1.04307	−	0.602214i	−0.920700	+	0.390271i	$0.872381\pi$
$4$		0			0
$5$	−0.410474	−	0.236987i	−0.183569	−	0.105984i	0.405399	−	0.914140i	$-0.367133\pi$
$5$	−0.410474	−	0.236987i	−0.183569	−	0.105984i	−0.588969	+	0.808156i	$0.700466\pi$
$6$		0			0
$7$	−3.88259			−1.46748			−0.733740	−	0.679430i	$-0.762227\pi$
$7$	−3.88259			−1.46748			−0.733740	+	0.679430i	$0.762227\pi$
$8$		0			0
$9$	0.675970	+	1.17081i	0.225323	+	0.390271i
$10$		0			0
$11$		−	6.19156i		−	1.86683i	−0.358804	−	0.933413i	$-0.616816\pi$
$11$		−	6.19156i		−	1.86683i	0.358804	−	0.933413i	$-0.383184\pi$
$12$		0			0
$13$	4.97986	−	2.87512i	1.38116	−	0.797415i	0.388866	−	0.921294i	$-0.372867\pi$
$13$	4.97986	−	2.87512i	1.38116	−	0.797415i	0.992297	+	0.123879i	$0.0395336\pi$
$14$		0			0
$15$	0.494386	+	0.856302i	0.127650	+	0.221096i
$16$		0			0
$17$	0.442610	−	0.766623i	0.107349	−	0.185933i	−0.807347	−	0.590077i	$-0.799097\pi$
$17$	0.442610	−	0.766623i	0.107349	−	0.185933i	0.914695	+	0.404144i	$0.132431\pi$
$18$		0			0
$19$	4.19123	+	1.19731i	0.961535	+	0.274682i
$19$	4.19123	+	1.19731i	0.961535	+	0.274682i
$20$		0			0
$21$	7.01445	+	4.04979i	1.53068	+	0.883737i
$22$		0			0
$23$	−0.917273	−	1.58876i	−0.191265	−	0.331280i	0.754405	−	0.656409i	$-0.227926\pi$
$23$	−0.917273	−	1.58876i	−0.191265	−	0.331280i	−0.945670	+	0.325129i	$0.894592\pi$
$24$		0			0
$25$	−2.38767	−	4.13557i	−0.477535	−	0.827115i
$26$		0			0
$27$			3.43807i			0.661657i
$28$		0			0
$29$	−6.58038	+	3.79918i	−1.22195	+	0.705491i	−0.965332	−	0.261024i	$-0.915940\pi$
$29$	−6.58038	+	3.79918i	−1.22195	+	0.705491i	−0.256613	+	0.966514i	$0.582607\pi$
$30$		0			0
$31$	−6.70591			−1.20442			−0.602208	−	0.798339i	$-0.705712\pi$
$31$	−6.70591			−1.20442			−0.602208	+	0.798339i	$0.705712\pi$
$32$		0			0
$33$	−6.45820	+	11.1859i	−1.12423	+	1.94722i
$34$		0			0
$35$	1.59370	+	0.920123i	0.269385	+	0.155529i
$36$		0			0
$37$			1.54096i			0.253332i	0.991945	+	0.126666i	$0.0404277\pi$
$37$			1.54096i			0.253332i	−0.991945	+	0.126666i	$0.959572\pi$
$38$		0			0
$39$	−11.9958			−1.92086
$40$		0			0
$41$	−3.44115	+	5.96025i	−0.537418	+	0.930835i	0.461624	+	0.887075i	$0.347267\pi$
$41$	−3.44115	+	5.96025i	−0.537418	+	0.930835i	−0.999042	+	0.0437593i	$0.986067\pi$
$42$		0			0
$43$	−6.45827	−	3.72868i	−0.984877	−	0.568619i	−0.0811380	−	0.996703i	$-0.525855\pi$
$43$	−6.45827	−	3.72868i	−0.984877	−	0.568619i	−0.903739	+	0.428084i	$0.859189\pi$
$44$		0			0
$45$		−	0.640784i		−	0.0955225i
$46$		0			0
$47$	6.71860	+	11.6370i	0.980009	+	1.69742i	0.662304	+	0.749235i	$0.269579\pi$
$47$	6.71860	+	11.6370i	0.980009	+	1.69742i	0.317705	+	0.948190i	$0.397088\pi$
$48$		0			0
$49$	8.07449			1.15350
$50$		0			0
$51$	−1.59927	+	0.923342i	−0.223943	+	0.129294i
$52$		0			0
$53$	2.06834	−	1.19416i	0.284109	−	0.164030i	−0.351173	−	0.936310i	$-0.614217\pi$
$53$	2.06834	−	1.19416i	0.284109	−	0.164030i	0.635282	+	0.772280i	$0.280884\pi$
$54$		0			0
$55$	−1.46732	+	2.54147i	−0.197853	+	0.342692i
$56$		0			0
$57$	−6.32318	−	6.53484i	−0.837526	−	0.865561i
$58$		0			0
$59$	−10.1996	−	5.88874i	−1.32787	−	0.766648i	−0.342903	−	0.939371i	$-0.611410\pi$
$59$	−10.1996	−	5.88874i	−1.32787	−	0.766648i	−0.984971	+	0.172723i	$0.944744\pi$
$60$		0			0
$61$	2.12308	−	1.22576i	0.271832	−	0.156942i	−0.357888	−	0.933765i	$-0.616503\pi$
$61$	2.12308	−	1.22576i	0.271832	−	0.156942i	0.629720	+	0.776822i	$0.283170\pi$
$62$		0			0
$63$	−2.62451	−	4.54579i	−0.330657	−	0.572715i
$64$		0			0
$65$	−2.72547			−0.338052
$66$		0			0
$67$	8.74568	−	5.04932i	1.06845	−	0.616872i	0.140696	−	0.990053i	$-0.455066\pi$
$67$	8.74568	−	5.04932i	1.06845	−	0.616872i	0.927759	+	0.373180i	$0.121733\pi$
$68$		0			0
$69$			3.82710i			0.460729i
$70$		0			0
$71$	−3.98294	+	6.89866i	−0.472688	+	0.818720i	−0.999511	−	0.0312550i	$-0.990050\pi$
$71$	−3.98294	+	6.89866i	−0.472688	+	0.818720i	0.526823	+	0.849975i	$0.323383\pi$
$72$		0			0
$73$	−3.01795	+	5.22724i	−0.353224	+	0.611802i	−0.986812	−	0.161869i	$-0.948248\pi$
$73$	−3.01795	+	5.22724i	−0.353224	+	0.611802i	0.633588	+	0.773670i	$0.281581\pi$
$74$		0			0
$75$			9.96200i			1.15031i
$76$		0			0
$77$			24.0393i			2.73953i
$78$		0			0
$79$	−2.52019	+	4.36511i	−0.283544	+	0.491113i	−0.972255	−	0.233923i	$-0.924844\pi$
$79$	−2.52019	+	4.36511i	−0.283544	+	0.491113i	0.688711	+	0.725036i	$0.258177\pi$
$80$		0			0
$81$	5.61404	−	9.72380i	0.623782	−	1.08042i
$82$		0			0
$83$		−	10.3080i		−	1.13145i	−0.824594	−	0.565725i	$-0.808596\pi$
$83$		−	10.3080i		−	1.13145i	0.824594	−	0.565725i	$-0.191404\pi$
$84$		0			0
$85$	−0.363359	+	0.209786i	−0.0394119	+	0.0227544i
$86$		0			0
$87$	15.8512			1.69942
$88$		0			0
$89$	−1.84416	−	3.19418i	−0.195481	−	0.338582i	0.751577	−	0.659645i	$-0.229293\pi$
$89$	−1.84416	−	3.19418i	−0.195481	−	0.338582i	−0.947058	+	0.321063i	$0.895960\pi$
$90$		0			0
$91$	−19.3347	+	11.1629i	−2.02683	+	1.17019i
$92$		0			0
$93$	12.1152	+	6.99470i	1.25628	+	0.725316i
$94$		0			0
$95$	−1.43664	−	1.48473i	−0.147397	−	0.152330i
$96$		0			0
$97$	−0.213162	+	0.369207i	−0.0216433	+	0.0374873i	−0.876644	−	0.481139i	$-0.840223\pi$
$97$	−0.213162	+	0.369207i	−0.0216433	+	0.0374873i	0.855001	+	0.518627i	$0.173556\pi$
$98$		0			0
$99$	7.24916	−	4.18531i	0.728568	−	0.420639i
$100$		0			0
$101$	−8.75943	+	5.05726i	−0.871596	+	0.503216i	−0.867878	−	0.496777i	$-0.834517\pi$
$101$	−8.75943	+	5.05726i	−0.871596	+	0.503216i	−0.00371767	+	0.999993i	$0.501183\pi$
$102$		0			0
$103$	16.2109			1.59731			0.798654	−	0.601791i	$-0.205546\pi$
$103$	16.2109			1.59731			0.798654	+	0.601791i	$0.205546\pi$
$104$		0			0
$105$	−1.91950	−	3.32467i	−0.187324	−	0.324454i
$106$		0			0
$107$			1.64189i			0.158728i	0.996846	+	0.0793640i	$0.0252889\pi$
$107$			1.64189i			0.158728i	−0.996846	+	0.0793640i	$0.974711\pi$
$108$		0			0
$109$	3.45759	+	1.99624i	0.331177	+	0.191205i	0.656363	−	0.754445i	$-0.272094\pi$
$109$	3.45759	+	1.99624i	0.331177	+	0.191205i	−0.325187	+	0.945650i	$0.605427\pi$
$110$		0			0
$111$	1.60732	−	2.78396i	0.152560	−	0.264242i
$112$		0			0
$113$	6.25583			0.588499			0.294250	−	0.955729i	$-0.404930\pi$
$113$	6.25583			0.588499			0.294250	+	0.955729i	$0.404930\pi$
$114$		0			0
$115$			0.869527i			0.0810838i
$116$		0			0
$117$	6.73246	+	3.88699i	0.622416	+	0.359352i
$118$		0			0
$119$	−1.71847	+	2.97648i	−0.157532	+	0.272853i
$120$		0			0
$121$	−27.3354			−2.48504
$122$		0			0
$123$	12.4339	−	7.17869i	1.12112	−	0.647281i
$124$		0			0
$125$			4.63326i			0.414412i
$126$		0			0
$127$	6.26718	+	10.8551i	0.556122	+	0.963232i	0.997815	+	0.0660659i	$0.0210447\pi$
$127$	6.26718	+	10.8551i	0.556122	+	0.963232i	−0.441693	+	0.897166i	$0.645622\pi$
$128$		0			0
$129$	7.77852	+	13.4728i	0.684861	+	1.18621i
$130$		0			0
$131$	7.49950	+	4.32984i	0.655234	+	0.378299i	0.790459	−	0.612515i	$-0.209842\pi$
$131$	7.49950	+	4.32984i	0.655234	+	0.378299i	−0.135225	+	0.990815i	$0.543176\pi$
$132$		0			0
$133$	−16.2728	−	4.64867i	−1.41103	−	0.403091i
$134$		0			0
$135$	0.814778	−	1.41124i	0.0701249	−	0.121460i
$136$		0			0
$137$	−1.47834	−	2.56057i	−0.126304	−	0.218764i	0.795938	−	0.605378i	$-0.206978\pi$
$137$	−1.47834	−	2.56057i	−0.126304	−	0.218764i	−0.922242	+	0.386614i	$0.873645\pi$
$138$		0			0
$139$	−1.90857	+	1.10191i	−0.161883	+	0.0934630i	−0.578753	−	0.815503i	$-0.696460\pi$
$139$	−1.90857	+	1.10191i	−0.161883	+	0.0934630i	0.416870	+	0.908966i	$0.363127\pi$
$140$		0			0
$141$		−	28.0318i		−	2.36070i
$142$		0			0
$143$	−17.8015	−	30.8331i	−1.48863	−	2.57839i
$144$		0			0
$145$	3.60143			0.299082
$146$		0			0
$147$	−14.5877	−	8.42222i	−1.20317	−	0.694653i
$148$		0			0
$149$	−0.788437	−	0.455204i	−0.0645913	−	0.0372918i	0.467357	−	0.884069i	$-0.345206\pi$
$149$	−0.788437	−	0.455204i	−0.0645913	−	0.0372918i	−0.531948	+	0.846777i	$0.678540\pi$
$150$		0			0
$151$	−13.8149			−1.12424			−0.562119	−	0.827056i	$-0.690014\pi$
$151$	−13.8149			−1.12424			−0.562119	+	0.827056i	$0.690014\pi$
$152$		0			0
$153$	1.19676			0.0967525
$154$		0			0
$155$	2.75260	+	1.58921i	0.221094	+	0.127649i
$156$		0			0
$157$	−16.5058	−	9.52962i	−1.31731	−	0.760546i	−0.334011	−	0.942569i	$-0.608402\pi$
$157$	−16.5058	−	9.52962i	−1.31731	−	0.760546i	−0.983294	+	0.182023i	$0.941736\pi$
$158$		0			0
$159$	−4.98234			−0.395125
$160$		0			0
$161$	3.56139	+	6.16851i	0.280677	+	0.486147i
$162$		0			0
$163$			13.5700i			1.06288i	0.847095	+	0.531442i	$0.178350\pi$
$163$			13.5700i			1.06288i	−0.847095	+	0.531442i	$0.821650\pi$
$164$		0			0
$165$	5.30184	−	3.06102i	0.412748	−	0.238300i
$166$		0			0
$167$	2.50475	+	4.33835i	0.193823	+	0.335712i	0.946514	−	0.322662i	$-0.104578\pi$
$167$	2.50475	+	4.33835i	0.193823	+	0.335712i	−0.752691	+	0.658374i	$0.771245\pi$
$168$		0			0
$169$	10.0326	−	17.3770i	0.771741	−	1.33670i
$170$		0			0
$171$	1.43132	+	5.71650i	0.109456	+	0.437152i
$172$		0			0
$173$	−8.26939	−	4.77433i	−0.628710	−	0.362986i	0.151542	−	0.988451i	$-0.451576\pi$
$173$	−8.26939	−	4.77433i	−0.628710	−	0.362986i	−0.780252	+	0.625465i	$0.784909\pi$
$174$		0			0
$175$	9.27036	+	16.0567i	0.700773	+	1.21377i
$176$		0			0
$177$	12.2847	+	21.2777i	0.923372	+	1.59933i
$178$		0			0
$179$			8.86935i			0.662926i	0.943468	+	0.331463i	$0.107542\pi$
$179$			8.86935i			0.662926i	−0.943468	+	0.331463i	$0.892458\pi$
$180$		0			0
$181$	9.23350	−	5.33096i	0.686321	−	0.396247i	−0.115911	−	0.993260i	$-0.536979\pi$
$181$	9.23350	−	5.33096i	0.686321	−	0.396247i	0.802232	+	0.597012i	$0.203646\pi$
$182$		0			0
$183$	−5.11419			−0.378052
$184$		0			0
$185$	0.365188	−	0.632524i	0.0268491	−	0.0465041i
$186$		0			0
$187$	−4.74659	−	2.74044i	−0.347105	−	0.200401i
$188$		0			0
$189$		−	13.3486i		−	0.970968i
$190$		0			0
$191$	−6.91060			−0.500034			−0.250017	−	0.968241i	$-0.580436\pi$
$191$	−6.91060			−0.500034			−0.250017	+	0.968241i	$0.580436\pi$
$192$		0			0
$193$	0.0839459	−	0.145398i	0.00604256	−	0.0104660i	−0.862988	−	0.505224i	$-0.831410\pi$
$193$	0.0839459	−	0.145398i	0.00604256	−	0.0104660i	0.869031	+	0.494758i	$0.164743\pi$
$194$		0			0
$195$	4.92394	+	2.84284i	0.352611	+	0.203580i
$196$		0			0
$197$		−	10.3533i		−	0.737644i	−0.929500	−	0.368822i	$-0.879761\pi$
$197$		−	10.3533i		−	0.737644i	0.929500	−	0.368822i	$-0.120239\pi$
$198$		0			0
$199$	1.98995	+	3.44669i	0.141064	+	0.244330i	0.927897	−	0.372835i	$-0.121614\pi$
$199$	1.98995	+	3.44669i	0.141064	+	0.244330i	−0.786834	+	0.617165i	$0.788281\pi$
$200$		0			0
$201$	−21.0671			−1.48596
$202$		0			0
$203$	25.5489	−	14.7507i	1.79318	−	1.03529i
$204$		0			0
$205$	2.82501	−	1.63102i	0.197307	−	0.113915i
$206$		0			0
$207$	1.24010	−	2.14791i	0.0861927	−	0.149290i
$208$		0			0
$209$	7.41323	−	25.9503i	0.512784	−	1.79502i
$210$		0			0
$211$	6.27438	+	3.62251i	0.431946	+	0.249384i	0.700175	−	0.713971i	$-0.253105\pi$
$211$	6.27438	+	3.62251i	0.431946	+	0.249384i	−0.268229	+	0.963355i	$0.586439\pi$
$212$		0			0
$213$	14.3915	−	8.30893i	0.986089	−	0.569319i
$214$		0			0
$215$	1.76730	+	3.06105i	0.120529	+	0.208762i
$216$		0			0
$217$	26.0363			1.76746
$218$		0			0
$219$	10.9047	−	6.29583i	0.736871	−	0.425433i
$220$		0			0
$221$		−	5.09023i		−	0.342406i
$222$		0			0
$223$	10.1214	−	17.5307i	0.677776	−	1.17394i	−0.297873	−	0.954605i	$-0.596277\pi$
$223$	10.1214	−	17.5307i	0.677776	−	1.17394i	0.975649	−	0.219337i	$-0.0703893\pi$
$224$		0			0
$225$	3.22799	−	5.59104i	0.215199	−	0.372736i
$226$		0			0
$227$		−	0.208373i		−	0.0138302i	−0.999976	−	0.00691510i	$-0.997799\pi$
$227$		−	0.208373i		−	0.0138302i	0.999976	−	0.00691510i	$-0.00220116\pi$
$228$		0			0
$229$			16.9898i			1.12272i	0.827572	+	0.561359i	$0.189721\pi$
$229$			16.9898i			1.12272i	−0.827572	+	0.561359i	$0.810279\pi$
$230$		0			0
$231$	25.0745	−	43.4304i	1.64978	−	2.85751i
$232$		0			0
$233$	1.84818	−	3.20114i	0.121078	−	0.209713i	−0.799115	−	0.601178i	$-0.794698\pi$
$233$	1.84818	−	3.20114i	0.121078	−	0.209713i	0.920193	+	0.391465i	$0.128032\pi$
$234$		0			0
$235$		−	6.36889i		−	0.415460i
$236$		0			0
$237$	9.10618	−	5.25745i	0.591510	−	0.341508i
$238$		0			0
$239$	−17.4095			−1.12613			−0.563064	−	0.826413i	$-0.690378\pi$
$239$	−17.4095			−1.12613			−0.563064	+	0.826413i	$0.690378\pi$
$240$		0			0
$241$	0.446418	+	0.773218i	0.0287563	+	0.0498074i	0.880045	−	0.474890i	$-0.157512\pi$
$241$	0.446418	+	0.773218i	0.0287563	+	0.0498074i	−0.851289	+	0.524697i	$0.824179\pi$
$242$		0			0
$243$	−11.3527	+	6.55451i	−0.728279	+	0.420472i
$244$		0			0
$245$	−3.31437	−	1.91355i	−0.211747	−	0.122252i
$246$		0			0
$247$	24.3142	−	6.08787i	1.54707	−	0.387362i
$248$		0			0
$249$	−10.7519	+	18.6229i	−0.681375	+	1.18018i
$250$		0			0
$251$	−0.812038	+	0.468830i	−0.0512554	+	0.0295923i	−0.525409	−	0.850850i	$-0.676088\pi$
$251$	−0.812038	+	0.468830i	−0.0512554	+	0.0295923i	0.474153	+	0.880442i	$0.342754\pi$
$252$		0			0
$253$	−9.83692	+	5.67935i	−0.618442	+	0.357058i
$254$		0			0
$255$	0.875280			0.0548122
$256$		0			0
$257$	2.53719	+	4.39455i	0.158266	+	0.274124i	0.934243	−	0.356636i	$-0.116076\pi$
$257$	2.53719	+	4.39455i	0.158266	+	0.274124i	−0.775978	+	0.630760i	$0.782743\pi$
$258$		0			0
$259$		−	5.98292i		−	0.371760i
$260$		0			0
$261$	−8.89627	−	5.13626i	−0.550665	−	0.317927i
$262$		0			0
$263$	−10.0626	+	17.4289i	−0.620485	+	1.07471i	0.368910	+	0.929465i	$0.379731\pi$
$263$	−10.0626	+	17.4289i	−0.620485	+	1.07471i	−0.989395	+	0.145247i	$0.953602\pi$
$264$		0			0
$265$	−1.13200			−0.0695382
$266$		0			0
$267$			7.69432i			0.470885i
$268$		0			0
$269$	−15.0445	−	8.68595i	−0.917280	−	0.529592i	−0.0345134	−	0.999404i	$-0.510988\pi$
$269$	−15.0445	−	8.68595i	−0.917280	−	0.529592i	−0.882766	+	0.469813i	$0.844321\pi$
$270$		0			0
$271$	8.74902	−	15.1537i	0.531465	−	0.920524i	−0.467861	−	0.883802i	$-0.654975\pi$
$271$	8.74902	−	15.1537i	0.531465	−	0.920524i	0.999326	−	0.0367219i	$-0.0116916\pi$
$272$		0			0
$273$	46.5746			2.81882
$274$		0			0
$275$	−25.6056	+	14.7834i	−1.54408	+	0.891474i
$276$		0			0
$277$		−	12.9305i		−	0.776917i	−0.921466	−	0.388458i	$-0.873008\pi$
$277$		−	12.9305i		−	0.776917i	0.921466	−	0.388458i	$-0.126992\pi$
$278$		0			0
$279$	−4.53299	−	7.85137i	−0.271383	−	0.470049i
$280$		0			0
$281$	−6.28839	−	10.8918i	−0.375134	−	0.649751i	0.615213	−	0.788361i	$-0.289070\pi$
$281$	−6.28839	−	10.8918i	−0.375134	−	0.649751i	−0.990347	+	0.138610i	$0.955737\pi$
$282$		0			0
$283$	5.06797	+	2.92600i	0.301260	+	0.173932i	0.643009	−	0.765859i	$-0.277686\pi$
$283$	5.06797	+	2.92600i	0.301260	+	0.173932i	−0.341749	+	0.939791i	$0.611019\pi$
$284$		0			0
$285$	1.04683	+	4.18089i	0.0620087	+	0.247655i
$286$		0			0
$287$	13.3606	−	23.1412i	0.788650	−	1.36598i
$288$		0			0
$289$	8.10819	+	14.0438i	0.476953	+	0.826106i
$290$		0			0
$291$	0.770215	−	0.444684i	0.0451508	−	0.0260678i
$292$		0			0
$293$		−	11.6114i		−	0.678344i	−0.940724	−	0.339172i	$-0.889853\pi$
$293$		−	11.6114i		−	0.678344i	0.940724	−	0.339172i	$-0.110147\pi$
$294$		0			0
$295$	2.79111	+	4.83434i	0.162505	+	0.281466i
$296$		0			0
$297$	21.2870			1.23520
$298$		0			0
$299$	−9.13577	−	5.27454i	−0.528335	−	0.305034i
$300$		0			0
$301$	25.0748	+	14.4769i	1.44529	+	0.834437i
$302$		0			0
$303$	21.1002			1.21218
$304$		0			0
$305$	−1.16196			−0.0665334
$306$		0			0
$307$	6.53168	+	3.77107i	0.372783	+	0.215226i	0.674674	−	0.738116i	$-0.264284\pi$
$307$	6.53168	+	3.77107i	0.372783	+	0.215226i	−0.301891	+	0.953343i	$0.597618\pi$
$308$		0			0
$309$	−29.2873	−	16.9090i	−1.66610	−	0.961921i
$310$		0			0
$311$	−24.5174			−1.39025			−0.695127	−	0.718887i	$-0.744652\pi$
$311$	−24.5174			−1.39025			−0.695127	+	0.718887i	$0.744652\pi$
$312$		0			0
$313$	−13.4505	−	23.2969i	−0.760266	−	1.31682i	−0.942714	−	0.333603i	$-0.891735\pi$
$313$	−13.4505	−	23.2969i	−0.760266	−	1.31682i	0.182448	−	0.983216i	$-0.441598\pi$
$314$		0			0
$315$			2.48790i			0.140177i
$316$		0			0
$317$	−12.7605	+	7.36729i	−0.716702	+	0.413788i	−0.813538	−	0.581512i	$-0.802461\pi$
$317$	−12.7605	+	7.36729i	−0.716702	+	0.413788i	0.0968357	+	0.995300i	$0.469128\pi$
$318$		0			0
$319$	23.5229	+	40.7428i	1.31703	+	2.28116i
$320$		0			0
$321$	1.71260	−	2.96632i	0.0955882	−	0.165564i
$322$		0			0
$323$	2.77297	−	2.68315i	0.154292	−	0.149295i
$324$		0			0
$325$	−23.7805	−	13.7297i	−1.31911	−	0.761587i
$326$		0			0
$327$	−4.16442	−	7.21298i	−0.230293	−	0.398879i
$328$		0			0
$329$	−26.0856	−	45.1815i	−1.43814	−	2.49094i
$330$		0			0
$331$		−	5.18499i		−	0.284993i	−0.989795	−	0.142496i	$-0.954487\pi$
$331$		−	5.18499i		−	0.284993i	0.989795	−	0.142496i	$-0.0455129\pi$
$332$		0			0
$333$	−1.80418	+	1.04164i	−0.0988683	+	0.0570817i
$334$		0			0
$335$	−4.78649			−0.261514
$336$		0			0
$337$	−7.80883	+	13.5253i	−0.425374	+	0.736770i	−0.996455	−	0.0841240i	$-0.973191\pi$
$337$	−7.80883	+	13.5253i	−0.425374	+	0.736770i	0.571081	+	0.820894i	$0.306524\pi$
$338$		0			0
$339$	−11.3020	−	6.52524i	−0.613843	−	0.354402i
$340$		0			0
$341$			41.5200i			2.24843i
$342$		0			0
$343$	−4.17180			−0.225256
$344$		0			0
$345$	0.906973	−	1.57092i	0.0488298	−	0.0845757i
$346$		0			0
$347$	21.6328	+	12.4897i	1.16131	+	0.670483i	0.951618	−	0.307284i	$-0.0994202\pi$
$347$	21.6328	+	12.4897i	1.16131	+	0.670483i	0.209693	+	0.977767i	$0.432754\pi$
$348$		0			0
$349$		−	14.2928i		−	0.765078i	−0.923939	−	0.382539i	$-0.875050\pi$
$349$		−	14.2928i		−	0.765078i	0.923939	−	0.382539i	$-0.124950\pi$
$350$		0			0
$351$	9.88486	+	17.1211i	0.527615	+	0.913856i
$352$		0			0
$353$	−32.0467			−1.70567			−0.852837	−	0.522177i	$-0.825120\pi$
$353$	−32.0467			−1.70567			−0.852837	+	0.522177i	$0.825120\pi$
$354$		0			0
$355$	3.26979	−	1.88781i	0.173542	−	0.100195i
$356$		0			0
$357$	6.20932	−	3.58495i	0.328632	−	0.189736i
$358$		0			0
$359$	−2.87827	+	4.98531i	−0.151909	+	0.263114i	−0.931929	−	0.362640i	$-0.881875\pi$
$359$	−2.87827	+	4.98531i	−0.151909	+	0.263114i	0.780020	+	0.625754i	$0.215209\pi$
$360$		0			0
$361$	16.1329	+	10.0364i	0.849099	+	0.528233i
$362$		0			0
$363$	49.3853	+	28.5126i	2.59206	+	1.49652i
$364$		0			0
$365$	2.47758	−	1.43043i	0.129682	−	0.0748721i
$366$		0			0
$367$	3.72071	+	6.44446i	0.194219	+	0.336398i	0.946644	−	0.322280i	$-0.104449\pi$
$367$	3.72071	+	6.44446i	0.194219	+	0.336398i	−0.752425	+	0.658678i	$0.771116\pi$
$368$		0			0
$369$	−9.30446			−0.484371
$370$		0			0
$371$	−8.03052	+	4.63642i	−0.416924	+	0.240711i
$372$		0			0
$373$		−	18.0165i		−	0.932858i	−0.884559	−	0.466429i	$-0.845540\pi$
$373$		−	18.0165i		−	0.932858i	0.884559	−	0.466429i	$-0.154460\pi$
$374$		0			0
$375$	4.83280	−	8.37065i	0.249564	−	0.432258i
$376$		0			0
$377$	−21.8462	+	37.8388i	−1.12514	+	1.94880i
$378$		0			0
$379$			7.03714i			0.361474i	0.983531	+	0.180737i	$0.0578483\pi$
$379$			7.03714i			0.361474i	−0.983531	+	0.180737i	$0.942152\pi$
$380$		0			0
$381$		−	26.1483i		−	1.33962i
$382$		0			0
$383$	5.19372	−	8.99579i	0.265387	−	0.459663i	−0.702278	−	0.711903i	$-0.747834\pi$
$383$	5.19372	−	8.99579i	0.265387	−	0.459663i	0.967665	+	0.252239i	$0.0811670\pi$
$384$		0			0
$385$	5.69700	−	9.86749i	0.290346	−	0.502894i
$386$		0			0
$387$		−	10.0819i		−	0.512492i
$388$		0			0
$389$	−10.7920	+	6.23075i	−0.547175	+	0.315911i	−0.747982	−	0.663719i	$-0.768977\pi$
$389$	−10.7920	+	6.23075i	−0.547175	+	0.315911i	0.200807	+	0.979631i	$0.435644\pi$
$390$		0			0
$391$	−1.62398			−0.0821280
$392$		0			0
$393$	−9.03260	−	15.6449i	−0.455634	−	0.789182i
$394$		0			0
$395$	2.06895	−	1.19451i	0.104100	−	0.0601022i
$396$		0			0
$397$	−19.0425	−	10.9942i	−0.955716	−	0.551783i	−0.0608638	−	0.998146i	$-0.519386\pi$
$397$	−19.0425	−	10.9942i	−0.955716	−	0.551783i	−0.894852	+	0.446363i	$0.852719\pi$
$398$		0			0
$399$	24.5503	+	25.3721i	1.22905	+	1.27019i
$400$		0			0
$401$	8.15592	−	14.1265i	0.407287	−	0.705442i	−0.587297	−	0.809371i	$-0.699808\pi$
$401$	8.15592	−	14.1265i	0.407287	−	0.705442i	0.994585	+	0.103929i	$0.0331414\pi$
$402$		0			0
$403$	−33.3944	+	19.2803i	−1.66350	+	0.960420i
$404$		0			0
$405$	−4.60883	+	2.66091i	−0.229015	+	0.132222i
$406$		0			0
$407$	9.54095			0.472927
$408$		0			0
$409$	3.59918	+	6.23396i	0.177968	+	0.308249i	0.941184	−	0.337894i	$-0.109714\pi$
$409$	3.59918	+	6.23396i	0.177968	+	0.308249i	−0.763217	+	0.646143i	$0.776381\pi$
$410$		0			0
$411$			6.16804i			0.304247i
$412$		0			0
$413$	39.6008	+	22.8635i	1.94863	+	1.12504i
$414$		0			0
$415$	−2.44286	+	4.23116i	−0.119915	+	0.207700i
$416$		0			0
$417$	4.59747			0.225139
$418$		0			0
$419$		−	8.54152i		−	0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$419$		−	8.54152i		−	0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$420$		0			0
$421$	28.8602	+	16.6624i	1.40656	+	0.812077i	0.995054	−	0.0993317i	$-0.0316705\pi$
$421$	28.8602	+	16.6624i	1.40656	+	0.812077i	0.411503	+	0.911408i	$0.365004\pi$
$422$		0			0
$423$	−9.08314	+	15.7325i	−0.441637	+	0.764938i
$424$		0			0
$425$	−4.22723			−0.205051
$426$		0			0
$427$	−8.24303	+	4.75912i	−0.398908	+	0.230310i
$428$		0			0
$429$			74.2724i			3.58591i
$430$		0			0
$431$	−13.7299	−	23.7810i	−0.661348	−	1.14549i	−0.980262	−	0.197705i	$-0.936651\pi$
$431$	−13.7299	−	23.7810i	−0.661348	−	1.14549i	0.318913	−	0.947784i	$-0.396682\pi$
$432$		0			0
$433$	14.2399	+	24.6642i	0.684324	+	1.18528i	0.973649	+	0.228053i	$0.0732358\pi$
$433$	14.2399	+	24.6642i	0.684324	+	1.18528i	−0.289325	+	0.957231i	$0.593431\pi$
$434$		0			0
$435$	−6.50649	−	3.75653i	−0.311962	−	0.180112i
$436$		0			0
$437$	−1.94226	−	7.75714i	−0.0929109	−	0.371074i
$438$		0			0
$439$	15.3792	−	26.6376i	0.734010	−	1.27134i	−0.221147	−	0.975240i	$-0.570980\pi$
$439$	15.3792	−	26.6376i	0.734010	−	1.27134i	0.955157	−	0.296101i	$-0.0956866\pi$
$440$		0			0
$441$	5.45811	+	9.45372i	0.259910	+	0.450177i
$442$		0			0
$443$	−26.3711	+	15.2253i	−1.25293	+	0.723378i	−0.971690	−	0.236260i	$-0.924078\pi$
$443$	−26.3711	+	15.2253i	−1.25293	+	0.723378i	−0.281237	+	0.959638i	$0.590745\pi$
$444$		0			0
$445$			1.74817i			0.0828712i
$446$		0			0
$447$	0.949615	+	1.64478i	0.0449153	+	0.0777955i
$448$		0			0
$449$	−27.9756			−1.32025			−0.660126	−	0.751155i	$-0.729497\pi$
$449$	−27.9756			−1.32025			−0.660126	+	0.751155i	$0.729497\pi$
$450$		0			0
$451$	36.9032	+	21.3061i	1.73771	+	1.00327i
$452$		0			0
$453$	24.9585	+	14.4098i	1.17265	+	0.677032i
$454$		0			0
$455$	10.5819			0.496085
$456$		0			0
$457$	−7.56863			−0.354046			−0.177023	−	0.984207i	$-0.556647\pi$
$457$	−7.56863			−0.354046			−0.177023	+	0.984207i	$0.556647\pi$
$458$		0			0
$459$	2.63570	+	1.52172i	0.123024	+	0.0710279i
$460$		0			0
$461$	−33.8209	−	19.5265i	−1.57520	−	0.909441i	−0.995516	−	0.0945974i	$-0.969844\pi$
$461$	−33.8209	−	19.5265i	−1.57520	−	0.909441i	−0.579682	−	0.814843i	$-0.696823\pi$
$462$		0			0
$463$	−18.9364			−0.880049			−0.440025	−	0.897986i	$-0.645030\pi$
$463$	−18.9364			−0.880049			−0.440025	+	0.897986i	$0.645030\pi$
$464$		0			0
$465$	−3.31531	−	5.74228i	−0.153744	−	0.266292i
$466$		0			0
$467$		−	21.8665i		−	1.01186i	−0.862574	−	0.505930i	$-0.831149\pi$
$467$		−	21.8665i		−	1.01186i	0.862574	−	0.505930i	$-0.168851\pi$
$468$		0			0
$469$	−33.9559	+	19.6044i	−1.56794	+	0.905248i
$470$		0			0
$471$	19.8800	+	34.4332i	0.916023	+	1.58660i
$472$		0			0
$473$	−23.0864	+	39.9868i	−1.06151	+	1.83859i
$474$		0			0
$475$	−5.05573	−	20.1919i	−0.231973	−	0.926470i
$476$		0			0
$477$	2.79627	+	1.61443i	0.128032	+	0.0739196i
$478$		0			0
$479$	−3.59930	−	6.23417i	−0.164456	−	0.284846i	0.772006	−	0.635615i	$-0.219254\pi$
$479$	−3.59930	−	6.23417i	−0.164456	−	0.284846i	−0.936462	+	0.350769i	$0.885920\pi$
$480$		0			0
$481$	4.43045	+	7.67376i	0.202011	+	0.349893i
$482$		0			0
$483$		−	14.8591i		−	0.676110i
$484$		0			0
$485$	0.174995	−	0.101033i	0.00794610	−	0.00458769i
$486$		0			0
$487$	−25.4865			−1.15490			−0.577452	−	0.816425i	$-0.695953\pi$
$487$	−25.4865			−1.15490			−0.577452	+	0.816425i	$0.695953\pi$
$488$		0			0
$489$	14.1544	−	24.5161i	0.640084	−	1.10866i
$490$		0			0
$491$	−7.48161	−	4.31951i	−0.337641	−	0.194937i	0.321588	−	0.946880i	$-0.395784\pi$
$491$	−7.48161	−	4.31951i	−0.337641	−	0.194937i	−0.659228	+	0.751943i	$0.729117\pi$
$492$		0			0
$493$			6.72622i			0.302934i
$494$		0			0
$495$	−3.96745			−0.178324
$496$		0			0
$497$	15.4641	−	26.7846i	0.693661	−	1.20146i
$498$		0			0
$499$	−19.4655	−	11.2384i	−0.871397	−	0.503101i	−0.00358493	−	0.999994i	$-0.501141\pi$
$499$	−19.4655	−	11.2384i	−0.871397	−	0.503101i	−0.867812	+	0.496892i	$0.834474\pi$
$500$		0			0
$501$		−	10.4505i		−	0.466892i
$502$		0			0
$503$	−13.6820	−	23.6979i	−0.610051	−	1.05664i	−0.991231	−	0.132138i	$-0.957816\pi$
$503$	−13.6820	−	23.6979i	−0.610051	−	1.05664i	0.381180	−	0.924501i	$-0.375518\pi$
$504$		0			0
$505$	4.79402			0.213331
$506$		0			0
$507$	−36.2508	+	20.9294i	−1.60995	+	0.929507i
$508$		0			0
$509$	−27.8941	+	16.1046i	−1.23638	+	0.713826i	−0.968353	−	0.249585i	$-0.919706\pi$
$509$	−27.8941	+	16.1046i	−1.23638	+	0.713826i	−0.268029	+	0.963411i	$0.586372\pi$
$510$		0			0
$511$	11.7174	−	20.2952i	0.518349	−	0.897807i
$512$		0			0
$513$	−4.11644	+	14.4098i	−0.181745	+	0.636206i
$514$		0			0
$515$	−6.65415	−	3.84177i	−0.293217	−	0.169289i
$516$		0			0
$517$	72.0509	−	41.5986i	3.16880	−	1.82951i
$518$		0			0
$519$	9.95988	+	17.2510i	0.437190	+	0.757236i
$520$		0			0
$521$	13.5385			0.593133			0.296566	−	0.955012i	$-0.404158\pi$
$521$	13.5385			0.593133			0.296566	+	0.955012i	$0.404158\pi$
$522$		0			0
$523$	21.8590	−	12.6203i	0.955825	−	0.551846i	0.0609396	−	0.998141i	$-0.480590\pi$
$523$	21.8590	−	12.6203i	0.955825	−	0.551846i	0.894886	+	0.446295i	$0.147257\pi$
$524$		0			0
$525$		−	38.6783i		−	1.68806i
$526$		0			0
$527$	−2.96810	+	5.14090i	−0.129292	+	0.223941i
$528$		0			0
$529$	9.81722	−	17.0039i	0.426836	−	0.739301i
$530$		0			0
$531$		−	15.9224i		−	0.690974i
$532$		0			0
$533$			39.5749i			1.71418i
$534$		0			0
$535$	0.389108	−	0.673955i	0.0168226	−	0.0291376i
$536$		0			0
$537$	9.25131	−	16.0237i	0.399223	−	0.691475i
$538$		0			0
$539$		−	49.9937i		−	2.15338i
$540$		0			0
$541$	12.8414	−	7.41397i	0.552094	−	0.318752i	−0.197872	−	0.980228i	$-0.563403\pi$
$541$	12.8414	−	7.41397i	0.552094	−	0.318752i	0.749966	+	0.661476i	$0.230070\pi$
$542$		0			0
$543$	−22.2422			−0.954503
$544$		0			0
$545$	−0.946166	−	1.63881i	−0.0405293	−	0.0701988i
$546$		0			0
$547$	−0.743989	+	0.429542i	−0.0318107	+	0.0183659i	−0.515821	−	0.856696i	$-0.672513\pi$
$547$	−0.743989	+	0.429542i	−0.0318107	+	0.0183659i	0.484010	+	0.875062i	$0.339180\pi$
$548$		0			0
$549$	2.87027	+	1.65715i	0.122500	+	0.0707255i
$550$		0			0
$551$	−32.1287	+	8.04450i	−1.36873	+	0.342707i
$552$		0			0
$553$	9.78488	−	16.9479i	0.416095	−	0.720698i
$554$		0			0
$555$	−1.31953	+	0.761829i	−0.0560108	+	0.0323379i
$556$		0			0
$557$	21.6333	−	12.4900i	0.916631	−	0.529217i	0.0340721	−	0.999419i	$-0.489152\pi$
$557$	21.6333	−	12.4900i	0.916631	−	0.529217i	0.882559	+	0.470202i	$0.155819\pi$
$558$		0			0
$559$	−42.8817			−1.81370
$560$		0			0
$561$	5.71692	+	9.90200i	0.241369	+	0.418063i
$562$		0			0
$563$		−	34.9158i		−	1.47153i	−0.677238	−	0.735764i	$-0.736823\pi$
$563$		−	34.9158i		−	1.47153i	0.677238	−	0.735764i	$-0.263177\pi$
$564$		0			0
$565$	−2.56785	−	1.48255i	−0.108030	−	0.0623714i
$566$		0			0
$567$	−21.7970	+	37.7535i	−0.915388	+	1.58550i
$568$		0			0
$569$	−17.2641			−0.723747			−0.361874	−	0.932227i	$-0.617863\pi$
$569$	−17.2641			−0.723747			−0.361874	+	0.932227i	$0.617863\pi$
$570$		0			0
$571$		−	38.1980i		−	1.59854i	−0.600975	−	0.799268i	$-0.705221\pi$
$571$		−	38.1980i		−	1.59854i	0.600975	−	0.799268i	$-0.294779\pi$
$572$		0			0
$573$	12.4850	+	7.20821i	0.521568	+	0.301127i
$574$		0			0
$575$	−4.38030	+	7.58690i	−0.182671	+	0.316395i
$576$		0			0
$577$	39.0174			1.62431			0.812157	−	0.583439i	$-0.198293\pi$
$577$	39.0174			1.62431			0.812157	+	0.583439i	$0.198293\pi$
$578$		0			0
$579$	−0.303320	+	0.175122i	−0.0126056	+	0.00727782i
$580$		0			0
$581$			40.0217i			1.66038i
$582$		0			0
$583$	−7.39370	−	12.8063i	−0.306216	−	0.530381i
$584$		0			0
$585$	−1.84233	−	3.19101i	−0.0761711	−	0.131932i
$586$		0			0
$587$	16.1727	+	9.33728i	0.667517	+	0.385391i	0.795135	−	0.606432i	$-0.207400\pi$
$587$	16.1727	+	9.33728i	0.667517	+	0.385391i	−0.127618	+	0.991823i	$0.540733\pi$
$588$		0			0
$589$	−28.1060	−	8.02906i	−1.15809	−	0.330832i
$590$		0			0
$591$	−10.7992	+	18.7048i	−0.444220	+	0.769411i
$592$		0			0
$593$	4.16454	+	7.21319i	0.171017	+	0.296210i	0.938776	−	0.344529i	$-0.111961\pi$
$593$	4.16454	+	7.21319i	0.171017	+	0.296210i	−0.767759	+	0.640739i	$0.778628\pi$
$594$		0			0
$595$	1.41077	−	0.814511i	0.0578361	−	0.0333917i
$596$		0			0
$597$		−	8.30259i		−	0.339802i
$598$		0			0
$599$	−17.8471	−	30.9121i	−0.729214	−	1.26303i	−0.957216	−	0.289374i	$-0.906553\pi$
$599$	−17.8471	−	30.9121i	−0.729214	−	1.26303i	0.228002	−	0.973661i	$-0.426781\pi$
$600$		0			0
$601$	9.71808			0.396409			0.198204	−	0.980161i	$-0.436489\pi$
$601$	9.71808			0.396409			0.198204	+	0.980161i	$0.436489\pi$
$602$		0			0
$603$	11.8236	+	6.82637i	0.481495	+	0.277991i
$604$		0			0
$605$	11.2205	+	6.47814i	0.456177	+	0.263374i
$606$		0			0
$607$	−31.3506			−1.27248			−0.636240	−	0.771491i	$-0.719511\pi$
$607$	−31.3506			−1.27248			−0.636240	+	0.771491i	$0.719511\pi$
$608$		0			0
$609$	−61.5436			−2.49387
$610$		0			0
$611$	66.9153	+	38.6336i	2.70710	+	1.56295i
$612$		0			0
$613$	18.7390	+	10.8189i	0.756859	+	0.436973i	0.828167	−	0.560481i	$-0.189384\pi$
$613$	18.7390	+	10.8189i	0.756859	+	0.436973i	−0.0713076	+	0.997454i	$0.522717\pi$
$614$		0			0
$615$	−6.80503			−0.274405
$616$		0			0
$617$	19.5116	+	33.7952i	0.785509	+	1.36054i	0.928694	+	0.370846i	$0.120932\pi$
$617$	19.5116	+	33.7952i	0.785509	+	1.36054i	−0.143185	+	0.989696i	$0.545734\pi$
$618$		0			0
$619$			19.7275i			0.792917i	0.918053	+	0.396458i	$0.129761\pi$
$619$			19.7275i			0.792917i	−0.918053	+	0.396458i	$0.870239\pi$
$620$		0			0
$621$	5.46228	−	3.15365i	0.219194	−	0.126551i
$622$		0			0
$623$	7.16012	+	12.4017i	0.286864	+	0.496863i
$624$		0			0
$625$	−10.8403	+	18.7760i	−0.433614	+	0.751041i
$626$		0			0
$627$	−40.4609	+	39.1504i	−1.61585	+	1.56352i
$628$		0			0
$629$	1.18134	+	0.682044i	0.0471029	+	0.0271949i
$630$		0			0
$631$	12.7059	+	22.0072i	0.505812	+	0.876092i	0.999977	+	0.00672429i	$0.00214042\pi$
$631$	12.7059	+	22.0072i	0.505812	+	0.876092i	−0.494165	+	0.869368i	$0.664526\pi$
$632$		0			0
$633$	−7.55703	−	13.0892i	−0.300365	−	0.520248i
$634$		0			0
$635$		−	5.94096i		−	0.235760i
$636$		0			0
$637$	40.2098	−	23.2151i	1.59317	−	0.919817i
$638$		0			0
$639$	−10.7694			−0.426030
$640$		0			0
$641$	−8.56131	+	14.8286i	−0.338151	+	0.585695i	−0.984085	−	0.177698i	$-0.943135\pi$
$641$	−8.56131	+	14.8286i	−0.338151	+	0.585695i	0.645934	+	0.763394i	$0.276468\pi$
$642$		0			0
$643$	−11.4168	−	6.59148i	−0.450234	−	0.259943i	0.257695	−	0.966226i	$-0.417037\pi$
$643$	−11.4168	−	6.59148i	−0.450234	−	0.259943i	−0.707929	+	0.706284i	$0.750370\pi$
$644$		0			0
$645$		−	7.37364i		−	0.290337i
$646$		0			0
$647$	26.0712			1.02496			0.512482	−	0.858698i	$-0.328726\pi$
$647$	26.0712			1.02496			0.512482	+	0.858698i	$0.328726\pi$
$648$		0			0
$649$	−36.4605	+	63.1514i	−1.43120	+	2.47891i
$650$		0			0
$651$	−47.0382	−	27.1575i	−1.84357	−	1.06439i
$652$		0			0
$653$			4.00791i			0.156842i	0.996920	+	0.0784208i	$0.0249878\pi$
$653$			4.00791i			0.156842i	−0.996920	+	0.0784208i	$0.975012\pi$
$654$		0			0
$655$	−2.05223	−	3.55457i	−0.0801873	−	0.138888i
$656$		0			0
$657$	−8.16016			−0.318358
$658$		0			0
$659$	−16.4520	+	9.49856i	−0.640879	+	0.370012i	−0.784953	−	0.619555i	$-0.787313\pi$
$659$	−16.4520	+	9.49856i	−0.640879	+	0.370012i	0.144074	+	0.989567i	$0.453980\pi$
$660$		0			0
$661$	25.2938	−	14.6034i	0.983816	−	0.568006i	0.0803956	−	0.996763i	$-0.474382\pi$
$661$	25.2938	−	14.6034i	0.983816	−	0.568006i	0.903420	+	0.428757i	$0.141048\pi$
$662$		0			0
$663$	−5.30944	+	9.19621i	−0.206201	+	0.357151i
$664$		0			0
$665$	5.57790	+	5.76461i	0.216302	+	0.223542i
$666$		0			0
$667$	12.0720	+	6.96977i	0.467430	+	0.269871i
$668$		0			0
$669$	−36.5713	+	21.1145i	−1.41393	+	0.816332i
$670$		0			0
$671$	−7.58936	−	13.1452i	−0.292984	−	0.507463i
$672$		0			0
$673$	−0.756650			−0.0291667			−0.0145834	−	0.999894i	$-0.504642\pi$
$673$	−0.756650			−0.0291667			−0.0145834	+	0.999894i	$0.504642\pi$
$674$		0			0
$675$	14.2184	−	8.20899i	0.547266	−	0.315964i
$676$		0			0
$677$		−	2.95195i		−	0.113453i	−0.998390	−	0.0567263i	$-0.981934\pi$
$677$		−	2.95195i		−	0.113453i	0.998390	−	0.0567263i	$-0.0180662\pi$
$678$		0			0
$679$	0.827620	−	1.43348i	0.0317611	−	0.0550119i
$680$		0			0
$681$	−0.217346	+	0.376455i	−0.00832874	+	0.0144258i
$682$		0			0
$683$		−	49.3496i		−	1.88831i	−0.329504	−	0.944154i	$-0.606882\pi$
$683$		−	49.3496i		−	1.88831i	0.329504	−	0.944154i	$-0.393118\pi$
$684$		0			0
$685$			1.40139i			0.0535445i
$686$		0			0
$687$	17.7215	−	30.6945i	0.676117	−	1.17107i
$688$		0			0
$689$	6.86669	−	11.8935i	0.261600	−	0.453105i
$690$		0			0
$691$			25.0013i			0.951094i	0.879690	+	0.475547i	$0.157750\pi$
$691$			25.0013i			0.951094i	−0.879690	+	0.475547i	$0.842250\pi$
$692$		0			0
$693$	−28.1455	+	16.2498i	−1.06916	+	0.617280i
$694$		0			0
$695$	1.04456			0.0396223
$696$		0			0
$697$	3.04618	+	5.27613i	0.115382	+	0.199848i
$698$		0			0
$699$	−6.67799	+	3.85554i	−0.252585	+	0.145830i
$700$		0			0
$701$	28.9678	+	16.7246i	1.09410	+	0.631678i	0.934664	−	0.355531i	$-0.115700\pi$
$701$	28.9678	+	16.7246i	1.09410	+	0.631678i	0.159433	+	0.987209i	$0.449033\pi$
$702$		0			0
$703$	−1.84501	+	6.45853i	−0.0695859	+	0.243588i
$704$		0			0
$705$	−6.64316	+	11.5063i	−0.250196	+	0.433352i
$706$		0			0
$707$	34.0093	−	19.6353i	1.27905	−	0.738460i
$708$		0			0
$709$	−19.6572	+	11.3491i	−0.738241	+	0.426224i	−0.821429	−	0.570310i	$-0.806823\pi$
$709$	−19.6572	+	11.3491i	−0.738241	+	0.426224i	0.0831885	+	0.996534i	$0.473490\pi$
$710$		0			0
$711$	−6.81430			−0.255556
$712$		0			0
$713$	6.15114	+	10.6541i	0.230362	+	0.398999i
$714$		0			0
$715$			16.8749i			0.631085i
$716$		0			0
$717$	31.4528	+	18.1593i	1.17463	+	0.678170i
$718$		0			0
$719$	−19.1099	+	33.0994i	−0.712680	+	1.23440i	0.251167	+	0.967944i	$0.419186\pi$
$719$	−19.1099	+	33.0994i	−0.712680	+	1.23440i	−0.963847	+	0.266455i	$0.914148\pi$
$720$		0			0
$721$	−62.9402			−2.34402
$722$		0			0
$723$		−	1.86257i		−	0.0692698i
$724$		0			0
$725$	31.4236	+	18.1424i	1.16704	+	0.673793i
$726$		0			0
$727$	−7.00968	+	12.1411i	−0.259974	+	0.450289i	−0.966235	−	0.257663i	$-0.917047\pi$
$727$	−7.00968	+	12.1411i	−0.259974	+	0.450289i	0.706260	+	0.707952i	$0.250381\pi$
$728$		0			0
$729$	−6.33710			−0.234707
$730$		0			0
$731$	−5.71699	+	3.30070i	−0.211450	+	0.122081i
$732$		0			0
$733$		−	4.01023i		−	0.148121i	−0.997254	−	0.0740605i	$-0.976404\pi$
$733$		−	4.01023i		−	0.148121i	0.997254	−	0.0740605i	$-0.0235958\pi$
$734$		0			0
$735$	3.99191	+	6.91420i	0.147244	+	0.255034i
$736$		0			0
$737$	−31.2632	−	54.1494i	−1.15159	−	1.99462i
$738$		0			0
$739$	−21.0648	−	12.1618i	−0.774882	−	0.447379i	0.0597311	−	0.998215i	$-0.480976\pi$
$739$	−21.0648	−	12.1618i	−0.774882	−	0.447379i	−0.834614	+	0.550836i	$0.814309\pi$
$740$		0			0
$741$	−50.2770	−	14.3627i	−1.84697	−	0.527625i
$742$		0			0
$743$	7.90861	−	13.6981i	0.290139	−	0.502535i	−0.683704	−	0.729760i	$-0.739632\pi$
$743$	7.90861	−	13.6981i	0.290139	−	0.502535i	0.973842	+	0.227225i	$0.0729652\pi$
$744$		0			0
$745$	0.215755	+	0.373699i	0.00790465	+	0.0136913i
$746$		0			0
$747$	12.0688	−	6.96790i	0.441572	−	0.254942i
$748$		0			0
$749$		−	6.37480i		−	0.232930i
$750$		0			0
$751$	−7.73354	−	13.3949i	−0.282201	−	0.488786i	0.689726	−	0.724071i	$-0.257731\pi$
$751$	−7.73354	−	13.3949i	−0.282201	−	0.488786i	−0.971927	+	0.235284i	$0.924398\pi$
$752$		0			0
$753$	1.95608			0.0712836
$754$		0			0
$755$	5.67064	+	3.27395i	0.206376	+	0.119151i
$756$		0			0
$757$	−11.9925	−	6.92387i	−0.435875	−	0.251652i	0.265972	−	0.963981i	$-0.414307\pi$
$757$	−11.9925	−	6.92387i	−0.435875	−	0.251652i	−0.701846	+	0.712329i	$0.747641\pi$
$758$		0			0
$759$	23.6957			0.860100
$760$		0			0
$761$	41.4414			1.50225			0.751125	−	0.660160i	$-0.229511\pi$
$761$	41.4414			1.50225			0.751125	+	0.660160i	$0.229511\pi$
$762$		0			0
$763$	−13.4244	−	7.75058i	−0.485996	−	0.280590i
$764$		0			0
$765$	−0.491240	−	0.283617i	−0.0177608	−	0.0102542i
$766$		0			0
$767$	−67.7233			−2.44535
$768$		0			0
$769$	8.33105	+	14.4298i	0.300425	+	0.520352i	0.976232	−	0.216727i	$-0.0695380\pi$
$769$	8.33105	+	14.4298i	0.300425	+	0.520352i	−0.675807	+	0.737079i	$0.736205\pi$
$770$		0			0
$771$		−	10.5858i		−	0.381239i
$772$		0			0
$773$	−2.16244	+	1.24849i	−0.0777776	+	0.0449049i	−0.538384	−	0.842699i	$-0.680965\pi$
$773$	−2.16244	+	1.24849i	−0.0777776	+	0.0449049i	0.460607	+	0.887604i	$0.347632\pi$
$774$		0			0
$775$	16.0115	+	27.7328i	0.575151	+	0.996190i
$776$		0			0
$777$	−6.24057	+	10.8090i	−0.223879	+	0.387770i
$778$		0			0
$779$	−21.5590	+	20.8607i	−0.772430	+	0.747411i
$780$		0			0
$781$	42.7134	+	24.6606i	1.52841	+	0.882426i
$782$		0			0
$783$	−13.0619	−	22.6238i	−0.466793	−	0.808509i
$784$		0			0
$785$	4.51679	+	7.82332i	0.161211	+	0.279226i
$786$		0			0
$787$			5.56533i			0.198383i	0.995068	+	0.0991913i	$0.0316256\pi$
$787$			5.56533i			0.198383i	−0.995068	+	0.0991913i	$0.968374\pi$
$788$		0			0
$789$	36.3590	−	20.9919i	1.29441	−	0.747330i
$790$		0			0
$791$	−24.2888			−0.863611
$792$		0			0
$793$	7.04841	−	12.2082i	0.250296	−	0.433526i
$794$		0			0
$795$	2.04512	+	1.18075i	0.0725329	+	0.0418769i
$796$		0			0
$797$		−	29.6954i		−	1.05187i	−0.850526	−	0.525933i	$-0.823716\pi$
$797$		−	29.6954i		−	1.05187i	0.850526	−	0.525933i	$-0.176284\pi$
$798$		0			0
$799$	11.8949			0.420810
$800$		0			0
$801$	2.49319	−	4.31834i	0.0880927	−	0.152581i
$802$		0			0
$803$	32.3647	+	18.6858i	1.14213	+	0.659407i
$804$		0			0
$805$		−	3.37602i		−	0.118989i
$806$		0			0
$807$	18.1200	+	31.3848i	0.637855	+	1.10480i
$808$		0			0
$809$	5.89638			0.207306			0.103653	−	0.994614i	$-0.466947\pi$
$809$	5.89638			0.207306			0.103653	+	0.994614i	$0.466947\pi$
$810$		0			0
$811$	15.0969	−	8.71622i	0.530125	−	0.306068i	−0.210942	−	0.977498i	$-0.567653\pi$
$811$	15.0969	−	8.71622i	0.530125	−	0.306068i	0.741067	+	0.671431i	$0.234320\pi$
$812$		0			0
$813$	−31.6127	+	18.2516i	−1.10870	+	0.640111i
$814$		0			0
$815$	3.21591	−	5.57013i	0.112649	−	0.195113i
$816$		0			0
$817$	−22.6037	−	23.3604i	−0.790804	−	0.817275i
$818$		0			0
$819$	−26.1394	−	15.0916i	−0.913384	−	0.527342i
$820$		0			0
$821$	−36.2832	+	20.9481i	−1.26629	+	0.731095i	−0.974285	−	0.225321i	$-0.927657\pi$
$821$	−36.2832	+	20.9481i	−1.26629	+	0.731095i	−0.292008	+	0.956416i	$0.594324\pi$
$822$		0			0
$823$	15.0436	+	26.0563i	0.524388	+	0.908266i	0.999597	+	0.0283934i	$0.00903912\pi$
$823$	15.0436	+	26.0563i	0.524388	+	0.908266i	−0.475209	+	0.879873i	$0.657628\pi$
$824$		0			0
$825$	61.6803			2.14743
$826$		0			0
$827$	−8.57793	+	4.95247i	−0.298284	+	0.172214i	−0.641672	−	0.766979i	$-0.721759\pi$
$827$	−8.57793	+	4.95247i	−0.298284	+	0.172214i	0.343388	+	0.939194i	$0.388425\pi$
$828$		0			0
$829$			31.5253i			1.09492i	0.836833	+	0.547459i	$0.184405\pi$
$829$			31.5253i			1.09492i	−0.836833	+	0.547459i	$0.815595\pi$
$830$		0			0
$831$	−13.4873	+	23.3607i	−0.467870	+	0.810375i
$832$		0			0
$833$	3.57385	−	6.19009i	0.123826	−	0.214474i
$834$		0			0
$835$		−	2.37437i		−	0.0821685i
$836$		0			0
$837$		−	23.0554i		−	0.796910i
$838$		0			0
$839$	0.272805	−	0.472512i	0.00941828	−	0.0163129i	−0.861278	−	0.508134i	$-0.830335\pi$
$839$	0.272805	−	0.472512i	0.00941828	−	0.0163129i	0.870696	+	0.491821i	$0.163669\pi$
$840$		0			0
$841$	14.3676	−	24.8854i	0.495434	−	0.858117i
$842$		0			0
$843$			26.2368i			0.903644i
$844$		0			0
$845$	−8.23627	+	4.75521i	−0.283336	+	0.163584i
$846$		0			0
$847$	106.132			3.64674
$848$		0			0
$849$	−6.10401	−	10.5725i	−0.209489	−	0.362846i
$850$		0			0
$851$	2.44822	−	1.41348i	0.0839239	−	0.0484535i
$852$		0			0
$853$	−27.5009	−	15.8776i	−0.941611	−	0.543640i	−0.0511462	−	0.998691i	$-0.516287\pi$
$853$	−27.5009	−	15.8776i	−0.941611	−	0.543640i	−0.890465	+	0.455052i	$0.849621\pi$
$854$		0			0
$855$	0.767219	−	2.68568i	0.0262383	−	0.0918482i
$856$		0			0
$857$	13.9795	−	24.2133i	0.477532	−	0.827110i	−0.522136	−	0.852862i	$-0.674865\pi$
$857$	13.9795	−	24.2133i	0.477532	−	0.827110i	0.999668	+	0.0257523i	$0.00819812\pi$
$858$		0			0
$859$	−24.8994	+	14.3757i	−0.849557	+	0.490492i	−0.860501	−	0.509448i	$-0.829849\pi$
$859$	−24.8994	+	14.3757i	−0.849557	+	0.490492i	0.0109446	+	0.999940i	$0.496516\pi$
$860$		0			0
$861$	−48.2756	+	27.8719i	−1.64523	+	0.949872i
$862$		0			0
$863$	5.76082			0.196101			0.0980503	−	0.995181i	$-0.468739\pi$
$863$	5.76082			0.196101			0.0980503	+	0.995181i	$0.468739\pi$
$864$		0			0
$865$	2.26291	+	3.91948i	0.0769413	+	0.133266i
$866$		0			0
$867$		−	33.8295i		−	1.14891i
$868$		0			0
$869$	27.0268	+	15.6039i	0.916822	+	0.529327i
$870$		0			0
$871$	29.0348	−	50.2897i	0.983807	−	1.70400i
$872$		0			0
$873$	−0.576364			−0.0195070
$874$		0			0
$875$		−	17.9891i		−	0.608141i
$876$		0			0
$877$	4.55469	+	2.62965i	0.153801	+	0.0887971i	0.574925	−	0.818206i	$-0.305031\pi$
$877$	4.55469	+	2.62965i	0.153801	+	0.0887971i	−0.421124	+	0.907003i	$0.638364\pi$
$878$		0			0
$879$	−12.1114	+	20.9776i	−0.408508	+	0.707557i
$880$		0			0
$881$	12.3106			0.414754			0.207377	−	0.978261i	$-0.433507\pi$
$881$	12.3106			0.414754			0.207377	+	0.978261i	$0.433507\pi$
$882$		0			0
$883$	5.68998	−	3.28511i	0.191483	−	0.110553i	−0.401194	−	0.915993i	$-0.631405\pi$
$883$	5.68998	−	3.28511i	0.191483	−	0.110553i	0.592677	+	0.805441i	$0.298071\pi$
$884$		0			0
$885$		−	11.6452i		−	0.391450i
$886$		0			0
$887$	9.00049	+	15.5893i	0.302207	+	0.523437i	0.976636	−	0.214902i	$-0.0689434\pi$
$887$	9.00049	+	15.5893i	0.302207	+	0.523437i	−0.674429	+	0.738340i	$0.735610\pi$
$888$		0			0
$889$	−24.3329	−	42.1458i	−0.816099	−	1.41352i
$890$		0			0
$891$	−60.2055	−	34.7597i	−2.01696	−	1.16449i
$892$		0			0
$893$	14.2262	+	56.8175i	0.476060	+	1.90132i
$894$		0			0
$895$	2.10192	−	3.64063i	0.0702595	−	0.121693i
$896$		0			0
$897$	11.0034	+	19.0584i	0.367392	+	0.636342i
$898$		0			0
$899$	44.1274	−	25.4770i	1.47173	−	0.849704i
$900$		0			0
$901$		−	2.11418i		−	0.0704336i
$902$		0			0
$903$	−30.2008	−	52.3093i	−1.00502	−	1.74074i
$904$		0			0
$905$	−5.05348			−0.167983
$906$		0			0
$907$	−5.70050	−	3.29118i	−0.189282	−	0.109282i	0.402364	−	0.915480i	$-0.368188\pi$
$907$	−5.70050	−	3.29118i	−0.189282	−	0.109282i	−0.591646	+	0.806198i	$0.701522\pi$
$908$		0			0
$909$	−11.8422	−	6.83711i	−0.392782	−	0.226773i
$910$		0			0
$911$	50.4912			1.67285			0.836425	−	0.548082i	$-0.184642\pi$
$911$	50.4912			1.67285			0.836425	+	0.548082i	$0.184642\pi$
$912$		0			0
$913$	−63.8226			−2.11222
$914$		0			0
$915$	2.09924	+	1.21200i	0.0693987	+	0.0400674i
$916$		0			0
$917$	−29.1175	−	16.8110i	−0.961543	−	0.555147i
$918$		0			0
$919$	−55.4103			−1.82782			−0.913908	−	0.405920i	$-0.866951\pi$
$919$	−55.4103			−1.82782			−0.913908	+	0.405920i	$0.866951\pi$
$920$		0			0
$921$	−7.86694	−	13.6259i	−0.259225	−	0.448990i
$922$		0			0
$923$			45.8057i			1.50771i
$924$		0			0
$925$	6.37276	−	3.67931i	0.209535	−	0.120975i
$926$		0			0
$927$	10.9581	+	18.9799i	0.359910	+	0.623383i
$928$		0			0
$929$	18.5500	−	32.1295i	0.608605	−	1.05414i	−0.382865	−	0.923804i	$-0.625063\pi$
$929$	18.5500	−	32.1295i	0.608605	−	1.05414i	0.991471	−	0.130331i	$-0.0416041\pi$
$930$		0			0
$931$	33.8421	+	9.66768i	1.10913	+	0.316845i
$932$		0			0
$933$	44.2942	+	25.5732i	1.45013	+	0.837230i
$934$		0			0
$935$	1.29890	+	2.24976i	0.0424786	+	0.0735750i
$936$		0			0
$937$	8.34179	+	14.4484i	0.272514	+	0.472009i	0.969505	−	0.245072i	$-0.0788114\pi$
$937$	8.34179	+	14.4484i	0.272514	+	0.472009i	−0.696991	+	0.717080i	$0.745478\pi$
$938$		0			0
$939$			56.1189i			1.83137i
$940$		0			0
$941$	−21.4646	+	12.3926i	−0.699725	+	0.403986i	−0.807245	−	0.590217i	$-0.799042\pi$
$941$	−21.4646	+	12.3926i	−0.699725	+	0.403986i	0.107520	+	0.994203i	$0.465709\pi$
$942$		0			0
$943$	12.6259			0.411156
$944$		0			0
$945$	−3.16345	+	5.47925i	−0.102907	+	0.178240i
$946$		0			0
$947$	14.7255	+	8.50179i	0.478515	+	0.276271i	0.719798	−	0.694184i	$-0.244235\pi$
$947$	14.7255	+	8.50179i	0.478515	+	0.276271i	−0.241282	+	0.970455i	$0.577568\pi$
$948$		0			0
$949$			34.7078i			1.12666i
$950$		0			0
$951$	30.7382			0.996755
$952$		0			0
$953$	−10.0852	+	17.4680i	−0.326691	+	0.565846i	−0.981853	−	0.189643i	$-0.939267\pi$
$953$	−10.0852	+	17.4680i	−0.326691	+	0.565846i	0.655162	+	0.755488i	$0.272600\pi$
$954$		0			0
$955$	2.83662	+	1.63772i	0.0917909	+	0.0529955i
$956$		0			0
$957$		−	98.1435i		−	3.17253i
$958$		0			0
$959$	5.73980	+	9.94163i	0.185348	+	0.321032i
$960$		0			0
$961$	13.9692			0.450618
$962$		0			0
$963$	−1.92235	+	1.10987i	−0.0619470	+	0.0357651i
$964$		0			0
$965$	−0.0689151	+	0.0397882i	−0.00221846	+	0.00128083i
$966$		0			0
$967$	19.2952	−	33.4203i	0.620492	−	1.07472i	−0.368903	−	0.929468i	$-0.620266\pi$
$967$	19.2952	−	33.4203i	0.620492	−	1.07472i	0.989394	−	0.145255i	$-0.0464002\pi$
$968$		0			0
$969$	−7.80846	+	1.95511i	−0.250844	+	0.0628072i
$970$		0			0
$971$	−41.9596	−	24.2254i	−1.34655	−	0.777430i	−0.358790	−	0.933418i	$-0.616810\pi$
$971$	−41.9596	−	24.2254i	−1.34655	−	0.777430i	−0.987759	+	0.155988i	$0.950144\pi$
$972$		0			0
$973$	7.41019	−	4.27827i	0.237560	−	0.137155i
$974$		0			0
$975$	28.6419	+	49.6093i	0.917276	+	1.58877i
$976$		0			0
$977$	−50.7651			−1.62412			−0.812059	−	0.583575i	$-0.801653\pi$
$977$	−50.7651			−1.62412			−0.812059	+	0.583575i	$0.801653\pi$
$978$		0			0
$979$	−19.7770	+	11.4182i	−0.632074	+	0.364928i
$980$		0			0
$981$			5.39759i			0.172332i
$982$		0			0
$983$	14.8881	−	25.7870i	0.474858	−	0.822478i	−0.524727	−	0.851270i	$-0.675833\pi$
$983$	14.8881	−	25.7870i	0.474858	−	0.822478i	0.999585	+	0.0287921i	$0.00916607\pi$
$984$		0			0
$985$	−2.45361	+	4.24977i	−0.0781784	+	0.135409i
$986$		0			0
$987$			108.836i			3.46428i
$988$		0			0
$989$			13.6809i			0.435027i
$990$		0			0
$991$	17.9822	−	31.1461i	0.571223	−	0.989388i	−0.425217	−	0.905091i	$-0.639802\pi$
$991$	17.9822	−	31.1461i	0.571223	−	0.989388i	0.996441	−	0.0842966i	$-0.0268643\pi$
$992$		0			0
$993$	−5.40828	+	9.36742i	−0.171627	+	0.297266i
$994$		0			0
$995$		−	1.88637i		−	0.0598019i
$996$		0			0
$997$	−14.9391	+	8.62508i	−0.473126	+	0.273159i	−0.717547	−	0.696510i	$-0.754735\pi$
$997$	−14.9391	+	8.62508i	−0.473126	+	0.273159i	0.244422	+	0.969669i	$0.421402\pi$
$998$		0			0
$999$	−5.29793			−0.167619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.t.d.353.3	✓	24
4.3	odd	2	inner	1216.2.t.d.353.9	yes	24
8.3	odd	2		1216.2.t.e.353.3	yes	24
8.5	even	2		1216.2.t.e.353.9	yes	24
19.7	even	3		1216.2.t.e.1185.9	yes	24
76.7	odd	6		1216.2.t.e.1185.3	yes	24
152.45	even	6	inner	1216.2.t.d.1185.3	yes	24
152.83	odd	6	inner	1216.2.t.d.1185.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1216.2.t.d.353.3	✓	24	1.1	even	1	trivial
1216.2.t.d.353.9	yes	24	4.3	odd	2	inner
1216.2.t.d.1185.3	yes	24	152.45	even	6	inner
1216.2.t.d.1185.9	yes	24	152.83	odd	6	inner
1216.2.t.e.353.3	yes	24	8.3	odd	2
1216.2.t.e.353.9	yes	24	8.5	even	2
1216.2.t.e.1185.3	yes	24	76.7	odd	6
1216.2.t.e.1185.9	yes	24	19.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80664 - 1.04307i) q^{3} +(-0.410474 - 0.236987i) q^{5} -3.88259 q^{7} +(0.675970 + 1.17081i) q^{9} +O(q^{10})\)	\(q+(-1.80664 - 1.04307i) q^{3} +(-0.410474 - 0.236987i) q^{5} -3.88259 q^{7} +(0.675970 + 1.17081i) q^{9} -6.19156i q^{11} +(4.97986 - 2.87512i) q^{13} +(0.494386 + 0.856302i) q^{15} +(0.442610 - 0.766623i) q^{17} +(4.19123 + 1.19731i) q^{19} +(7.01445 + 4.04979i) q^{21} +(-0.917273 - 1.58876i) q^{23} +(-2.38767 - 4.13557i) q^{25} +3.43807i q^{27} +(-6.58038 + 3.79918i) q^{29} -6.70591 q^{31} +(-6.45820 + 11.1859i) q^{33} +(1.59370 + 0.920123i) q^{35} +1.54096i q^{37} -11.9958 q^{39} +(-3.44115 + 5.96025i) q^{41} +(-6.45827 - 3.72868i) q^{43} -0.640784i q^{45} +(6.71860 + 11.6370i) q^{47} +8.07449 q^{49} +(-1.59927 + 0.923342i) q^{51} +(2.06834 - 1.19416i) q^{53} +(-1.46732 + 2.54147i) q^{55} +(-6.32318 - 6.53484i) q^{57} +(-10.1996 - 5.88874i) q^{59} +(2.12308 - 1.22576i) q^{61} +(-2.62451 - 4.54579i) q^{63} -2.72547 q^{65} +(8.74568 - 5.04932i) q^{67} +3.82710i q^{69} +(-3.98294 + 6.89866i) q^{71} +(-3.01795 + 5.22724i) q^{73} +9.96200i q^{75} +24.0393i q^{77} +(-2.52019 + 4.36511i) q^{79} +(5.61404 - 9.72380i) q^{81} -10.3080i q^{83} +(-0.363359 + 0.209786i) q^{85} +15.8512 q^{87} +(-1.84416 - 3.19418i) q^{89} +(-19.3347 + 11.1629i) q^{91} +(12.1152 + 6.99470i) q^{93} +(-1.43664 - 1.48473i) q^{95} +(-0.213162 + 0.369207i) q^{97} +(7.24916 - 4.18531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{5} + 8 q^{9}+O(q^{10}) \) 24 * q - 6 * q^5 + 8 * q^9	\( 24 q - 6 q^{5} + 8 q^{9} + 30 q^{13} + 6 q^{17} + 24 q^{21} + 6 q^{25} + 42 q^{29} - 14 q^{33} - 24 q^{41} + 24 q^{49} - 18 q^{53} - 42 q^{57} + 18 q^{61} - 20 q^{65} - 16 q^{73} + 52 q^{81} - 78 q^{85} + 14 q^{89} + 60 q^{93} - 4 q^{97}+O(q^{100}) \) 24 * q - 6 * q^5 + 8 * q^9 + 30 * q^13 + 6 * q^17 + 24 * q^21 + 6 * q^25 + 42 * q^29 - 14 * q^33 - 24 * q^41 + 24 * q^49 - 18 * q^53 - 42 * q^57 + 18 * q^61 - 20 * q^65 - 16 * q^73 + 52 * q^81 - 78 * q^85 + 14 * q^89 + 60 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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