LMFDB - Embedded newform 1216.2.t.d.353.9

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			353.9
Character	$\chi$	$=$	1216.353
Dual form			1216.2.t.d.1185.9

$q$-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	0.920700	−	0.390271i	$-0.127619\pi$
$3$	1.80664	+	1.04307i	1.04307	+	0.602214i	0.122365	+	0.992485i	$0.460952\pi$
$4$		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	$-0.237773\pi$
$7$	3.88259			1.46748			0.733740	+	0.679430i	$0.237773\pi$
$8$		0			0
$9$	0.675970	+	1.17081i	0.225323	+	0.390271i
$10$		0			0
$11$			6.19156i			1.86683i	0.358804	+	0.933413i	$0.383184\pi$
$11$			6.19156i			1.86683i	−0.358804	+	0.933413i	$0.616816\pi$
$12$		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	0.945670	−	0.325129i	$-0.105408\pi$
$23$	0.917273	+	1.58876i	0.191265	+	0.331280i	−0.754405	+	0.656409i	$0.772074\pi$
$24$		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	$-0.294288\pi$
$31$	6.70591			1.20442			0.602208	+	0.798339i	$0.294288\pi$
$32$		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	0.903739	−	0.428084i	$-0.140811\pi$
$43$	6.45827	+	3.72868i	0.984877	+	0.568619i	0.0811380	+	0.996703i	$0.474145\pi$
$44$		0			0
$45$		−	0.640784i		−	0.0955225i
$46$		0			0
$47$	−6.71860	−	11.6370i	−0.980009	−	1.69742i	−0.662304	−	0.749235i	$-0.730421\pi$
$47$	−6.71860	−	11.6370i	−0.980009	−	1.69742i	−0.317705	−	0.948190i	$-0.602912\pi$
$48$		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	0.984971	−	0.172723i	$-0.0552564\pi$
$59$	10.1996	+	5.88874i	1.32787	+	0.766648i	0.342903	+	0.939371i	$0.388590\pi$
$60$		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	−0.927759	−	0.373180i	$-0.878267\pi$
$67$	−8.74568	+	5.04932i	−1.06845	+	0.616872i	−0.140696	+	0.990053i	$0.544934\pi$
$68$		0			0
$69$			3.82710i			0.460729i
$70$		0			0
$71$	3.98294	−	6.89866i	0.472688	−	0.818720i	−0.526823	−	0.849975i	$-0.676617\pi$
$71$	3.98294	−	6.89866i	0.472688	−	0.818720i	0.999511	+	0.0312550i	$0.00995038\pi$
$72$		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	−0.688711	−	0.725036i	$-0.741823\pi$
$79$	2.52019	−	4.36511i	0.283544	−	0.491113i	0.972255	+	0.233923i	$0.0751564\pi$
$80$		0			0
$81$	5.61404	−	9.72380i	0.623782	−	1.08042i
$82$		0			0
$83$			10.3080i			1.13145i	0.824594	+	0.565725i	$0.191404\pi$
$83$			10.3080i			1.13145i	−0.824594	+	0.565725i	$0.808596\pi$
$84$		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	$-0.794454\pi$
$103$	−16.2109			−1.59731			−0.798654	+	0.601791i	$0.794454\pi$
$104$		0			0
$105$	−1.91950	−	3.32467i	−0.187324	−	0.324454i
$106$		0			0
$107$		−	1.64189i		−	0.158728i	−0.996846	−	0.0793640i	$-0.974711\pi$
$107$		−	1.64189i		−	0.158728i	0.996846	−	0.0793640i	$-0.0252889\pi$
$108$		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	$-0.978955\pi$
$127$	−6.26718	−	10.8551i	−0.556122	−	0.963232i	0.441693	−	0.897166i	$-0.354378\pi$
$128$		0			0
$129$	7.77852	+	13.4728i	0.684861	+	1.18621i
$130$		0			0
$131$	−7.49950	−	4.32984i	−0.655234	−	0.378299i	0.135225	−	0.990815i	$-0.456824\pi$
$131$	−7.49950	−	4.32984i	−0.655234	−	0.378299i	−0.790459	+	0.612515i	$0.790158\pi$
$132$		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	−0.416870	−	0.908966i	$-0.636873\pi$
$139$	1.90857	−	1.10191i	0.161883	−	0.0934630i	0.578753	+	0.815503i	$0.303540\pi$
$140$		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	$-0.309986\pi$
$151$	13.8149			1.12424			0.562119	+	0.827056i	$0.309986\pi$
$152$		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	$-0.821650\pi$
$163$		−	13.5700i		−	1.06288i	0.847095	−	0.531442i	$-0.178350\pi$
$164$		0			0
$165$	5.30184	−	3.06102i	0.412748	−	0.238300i
$166$		0			0
$167$	−2.50475	−	4.33835i	−0.193823	−	0.335712i	0.752691	−	0.658374i	$-0.228755\pi$
$167$	−2.50475	−	4.33835i	−0.193823	−	0.335712i	−0.946514	+	0.322662i	$0.895422\pi$
$168$		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	$-0.892458\pi$
$179$		−	8.86935i		−	0.662926i	0.943468	−	0.331463i	$-0.107542\pi$
$180$		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	$-0.419564\pi$
$191$	6.91060			0.500034			0.250017	+	0.968241i	$0.419564\pi$
$192$		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	0.786834	−	0.617165i	$-0.211719\pi$
$199$	−1.98995	−	3.44669i	−0.141064	−	0.244330i	−0.927897	+	0.372835i	$0.878386\pi$
$200$		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	0.268229	−	0.963355i	$-0.413561\pi$
$211$	−6.27438	−	3.62251i	−0.431946	−	0.249384i	−0.700175	+	0.713971i	$0.746895\pi$
$212$		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	$0.403723\pi$
$223$	−10.1214	+	17.5307i	−0.677776	+	1.17394i	−0.975649	+	0.219337i	$0.929611\pi$
$224$		0			0
$225$	3.22799	−	5.59104i	0.215199	−	0.372736i
$226$		0			0
$227$			0.208373i			0.0138302i	0.999976	+	0.00691510i	$0.00220116\pi$
$227$			0.208373i			0.0138302i	−0.999976	+	0.00691510i	$0.997799\pi$
$228$		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	$-0.309622\pi$
$239$	17.4095			1.12613			0.563064	+	0.826413i	$0.309622\pi$
$240$		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	−0.474153	−	0.880442i	$-0.657246\pi$
$251$	0.812038	−	0.468830i	0.0512554	−	0.0295923i	0.525409	+	0.850850i	$0.323912\pi$
$252$		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	$-0.620269\pi$
$263$	10.0626	−	17.4289i	0.620485	−	1.07471i	0.989395	−	0.145247i	$-0.0463977\pi$
$264$		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	$0.345025\pi$
$271$	−8.74902	+	15.1537i	−0.531465	+	0.920524i	−0.999326	+	0.0367219i	$0.988308\pi$
$272$		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	0.341749	−	0.939791i	$-0.388981\pi$
$283$	−5.06797	−	2.92600i	−0.301260	−	0.173932i	−0.643009	+	0.765859i	$0.722314\pi$
$284$		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	0.301891	−	0.953343i	$-0.402382\pi$
$307$	−6.53168	−	3.77107i	−0.372783	−	0.215226i	−0.674674	+	0.738116i	$0.735716\pi$
$308$		0			0
$309$	−29.2873	−	16.9090i	−1.66610	−	0.961921i
$310$		0			0
$311$	24.5174			1.39025			0.695127	−	0.718887i	$-0.255348\pi$
$311$	24.5174			1.39025			0.695127	+	0.718887i	$0.255348\pi$
$312$		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	$0.0455129\pi$
$331$			5.18499i			0.284993i	−0.989795	+	0.142496i	$0.954487\pi$
$332$		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	−0.209693	−	0.977767i	$-0.567246\pi$
$347$	−21.6328	−	12.4897i	−1.16131	−	0.670483i	−0.951618	+	0.307284i	$0.900580\pi$
$348$		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	−0.780020	−	0.625754i	$-0.784791\pi$
$359$	2.87827	−	4.98531i	0.151909	−	0.263114i	0.931929	+	0.362640i	$0.118125\pi$
$360$		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	0.752425	−	0.658678i	$-0.228884\pi$
$367$	−3.72071	−	6.44446i	−0.194219	−	0.336398i	−0.946644	+	0.322280i	$0.895551\pi$
$368$		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	$-0.942152\pi$
$379$		−	7.03714i		−	0.361474i	0.983531	−	0.180737i	$-0.0578483\pi$
$380$		0			0
$381$		−	26.1483i		−	1.33962i
$382$		0			0
$383$	−5.19372	+	8.99579i	−0.265387	+	0.459663i	−0.967665	−	0.252239i	$-0.918833\pi$
$383$	−5.19372	+	8.99579i	−0.265387	+	0.459663i	0.702278	+	0.711903i	$0.252166\pi$
$384$		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	$0.0669038\pi$
$419$			8.54152i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$420$		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	$0.0633487\pi$
$431$	13.7299	+	23.7810i	0.661348	+	1.14549i	−0.318913	+	0.947784i	$0.603318\pi$
$432$		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	$0.429020\pi$
$439$	−15.3792	+	26.6376i	−0.734010	+	1.27134i	−0.955157	+	0.296101i	$0.904313\pi$
$440$		0			0
$441$	5.45811	+	9.45372i	0.259910	+	0.450177i
$442$		0			0
$443$	26.3711	−	15.2253i	1.25293	−	0.723378i	0.281237	−	0.959638i	$-0.409255\pi$
$443$	26.3711	−	15.2253i	1.25293	−	0.723378i	0.971690	+	0.236260i	$0.0759219\pi$
$444$		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	$-0.354970\pi$
$463$	18.9364			0.880049			0.440025	+	0.897986i	$0.354970\pi$
$464$		0			0
$465$	−3.31531	−	5.74228i	−0.153744	−	0.266292i
$466$		0			0
$467$			21.8665i			1.01186i	0.862574	+	0.505930i	$0.168851\pi$
$467$			21.8665i			1.01186i	−0.862574	+	0.505930i	$0.831149\pi$
$468$		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	0.936462	−	0.350769i	$-0.114080\pi$
$479$	3.59930	+	6.23417i	0.164456	+	0.284846i	−0.772006	+	0.635615i	$0.780746\pi$
$480$		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	$-0.304047\pi$
$487$	25.4865			1.15490			0.577452	+	0.816425i	$0.304047\pi$
$488$		0			0
$489$	14.1544	−	24.5161i	0.640084	−	1.10866i
$490$		0			0
$491$	7.48161	+	4.31951i	0.337641	+	0.194937i	0.659228	−	0.751943i	$-0.270883\pi$
$491$	7.48161	+	4.31951i	0.337641	+	0.194937i	−0.321588	+	0.946880i	$0.604216\pi$
$492$		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	0.867812	−	0.496892i	$-0.165526\pi$
$499$	19.4655	+	11.2384i	0.871397	+	0.503101i	0.00358493	+	0.999994i	$0.498859\pi$
$500$		0			0
$501$		−	10.4505i		−	0.466892i
$502$		0			0
$503$	13.6820	+	23.6979i	0.610051	+	1.05664i	0.991231	+	0.132138i	$0.0421844\pi$
$503$	13.6820	+	23.6979i	0.610051	+	1.05664i	−0.381180	+	0.924501i	$0.624482\pi$
$504$		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	−0.894886	−	0.446295i	$-0.852743\pi$
$523$	−21.8590	+	12.6203i	−0.955825	+	0.551846i	−0.0609396	+	0.998141i	$0.519410\pi$
$524$		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	−0.484010	−	0.875062i	$-0.660820\pi$
$547$	0.743989	−	0.429542i	0.0318107	−	0.0183659i	0.515821	+	0.856696i	$0.327487\pi$
$548$		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	$0.263177\pi$
$563$			34.9158i			1.47153i	−0.677238	+	0.735764i	$0.736823\pi$
$564$		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	$0.294779\pi$
$571$			38.1980i			1.59854i	−0.600975	+	0.799268i	$0.705221\pi$
$572$		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	0.127618	−	0.991823i	$-0.459267\pi$
$587$	−16.1727	−	9.33728i	−0.667517	−	0.385391i	−0.795135	+	0.606432i	$0.792600\pi$
$588$		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	$0.0934472\pi$
$599$	17.8471	+	30.9121i	0.729214	+	1.26303i	−0.228002	+	0.973661i	$0.573219\pi$
$600$		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	$-0.280489\pi$
$607$	31.3506			1.27248			0.636240	+	0.771491i	$0.280489\pi$
$608$		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	$-0.870239\pi$
$619$		−	19.7275i		−	0.792917i	0.918053	−	0.396458i	$-0.129761\pi$
$620$		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	$-0.997860\pi$
$631$	−12.7059	−	22.0072i	−0.505812	−	0.876092i	0.494165	−	0.869368i	$-0.335474\pi$
$632$		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	0.707929	−	0.706284i	$-0.249630\pi$
$643$	11.4168	+	6.59148i	0.450234	+	0.259943i	−0.257695	+	0.966226i	$0.582963\pi$
$644$		0			0
$645$		−	7.37364i		−	0.290337i
$646$		0			0
$647$	−26.0712			−1.02496			−0.512482	−	0.858698i	$-0.671274\pi$
$647$	−26.0712			−1.02496			−0.512482	+	0.858698i	$0.671274\pi$
$648$		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	−0.144074	−	0.989567i	$-0.546020\pi$
$659$	16.4520	−	9.49856i	0.640879	−	0.370012i	0.784953	+	0.619555i	$0.212687\pi$
$660$		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	$0.393118\pi$
$683$			49.3496i			1.88831i	−0.329504	+	0.944154i	$0.606882\pi$
$684$		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	$-0.842250\pi$
$691$		−	25.0013i		−	0.951094i	0.879690	−	0.475547i	$-0.157750\pi$
$692$		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	$-0.580814\pi$
$719$	19.1099	−	33.0994i	0.712680	−	1.23440i	0.963847	−	0.266455i	$-0.0858523\pi$
$720$		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	−0.706260	−	0.707952i	$-0.749619\pi$
$727$	7.00968	−	12.1411i	0.259974	−	0.450289i	0.966235	+	0.257663i	$0.0829525\pi$
$728$		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	0.834614	−	0.550836i	$-0.185691\pi$
$739$	21.0648	+	12.1618i	0.774882	+	0.447379i	−0.0597311	+	0.998215i	$0.519024\pi$
$740$		0			0
$741$	−50.2770	−	14.3627i	−1.84697	−	0.527625i
$742$		0			0
$743$	−7.90861	+	13.6981i	−0.290139	+	0.502535i	−0.973842	−	0.227225i	$-0.927035\pi$
$743$	−7.90861	+	13.6981i	−0.290139	+	0.502535i	0.683704	+	0.729760i	$0.260368\pi$
$744$		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	0.971927	−	0.235284i	$-0.0756022\pi$
$751$	7.73354	+	13.3949i	0.282201	+	0.488786i	−0.689726	+	0.724071i	$0.742269\pi$
$752$		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	$-0.968374\pi$
$787$		−	5.56533i		−	0.198383i	0.995068	−	0.0991913i	$-0.0316256\pi$
$788$		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	−0.741067	−	0.671431i	$-0.765680\pi$
$811$	−15.0969	+	8.71622i	−0.530125	+	0.306068i	0.210942	+	0.977498i	$0.432347\pi$
$812$		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	$-0.990961\pi$
$823$	−15.0436	−	26.0563i	−0.524388	−	0.908266i	0.475209	−	0.879873i	$-0.342372\pi$
$824$		0			0
$825$	61.6803			2.14743
$826$		0			0
$827$	8.57793	−	4.95247i	0.298284	−	0.172214i	−0.343388	−	0.939194i	$-0.611575\pi$
$827$	8.57793	−	4.95247i	0.298284	−	0.172214i	0.641672	+	0.766979i	$0.278241\pi$
$828$		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	−0.870696	−	0.491821i	$-0.836331\pi$
$839$	−0.272805	+	0.472512i	−0.00941828	+	0.0163129i	0.861278	+	0.508134i	$0.169665\pi$
$840$		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	−0.0109446	−	0.999940i	$-0.503484\pi$
$859$	24.8994	−	14.3757i	0.849557	−	0.490492i	0.860501	+	0.509448i	$0.170151\pi$
$860$		0			0
$861$	−48.2756	+	27.8719i	−1.64523	+	0.949872i
$862$		0			0
$863$	−5.76082			−0.196101			−0.0980503	−	0.995181i	$-0.531261\pi$
$863$	−5.76082			−0.196101			−0.0980503	+	0.995181i	$0.531261\pi$
$864$		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	−0.592677	−	0.805441i	$-0.701929\pi$
$883$	−5.68998	+	3.28511i	−0.191483	+	0.110553i	0.401194	+	0.915993i	$0.368595\pi$
$884$		0			0
$885$		−	11.6452i		−	0.391450i
$886$		0			0
$887$	−9.00049	−	15.5893i	−0.302207	−	0.523437i	0.674429	−	0.738340i	$-0.264390\pi$
$887$	−9.00049	−	15.5893i	−0.302207	−	0.523437i	−0.976636	+	0.214902i	$0.931057\pi$
$888$		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	0.591646	−	0.806198i	$-0.298478\pi$
$907$	5.70050	+	3.29118i	0.189282	+	0.109282i	−0.402364	+	0.915480i	$0.631812\pi$
$908$		0			0
$909$	−11.8422	−	6.83711i	−0.392782	−	0.226773i
$910$		0			0
$911$	−50.4912			−1.67285			−0.836425	−	0.548082i	$-0.815358\pi$
$911$	−50.4912			−1.67285			−0.836425	+	0.548082i	$0.815358\pi$
$912$		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	$-0.133049\pi$
$919$	55.4103			1.82782			0.913908	+	0.405920i	$0.133049\pi$
$920$		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	0.241282	−	0.970455i	$-0.422432\pi$
$947$	−14.7255	−	8.50179i	−0.478515	−	0.276271i	−0.719798	+	0.694184i	$0.755765\pi$
$948$		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	$0.379734\pi$
$967$	−19.2952	+	33.4203i	−0.620492	+	1.07472i	−0.989394	+	0.145255i	$0.953600\pi$
$968$		0			0
$969$	−7.80846	+	1.95511i	−0.250844	+	0.0628072i
$970$		0			0
$971$	41.9596	+	24.2254i	1.34655	+	0.777430i	0.987759	−	0.155988i	$-0.0498563\pi$
$971$	41.9596	+	24.2254i	1.34655	+	0.777430i	0.358790	+	0.933418i	$0.383190\pi$
$972$		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	−0.999585	−	0.0287921i	$-0.990834\pi$
$983$	−14.8881	+	25.7870i	−0.474858	+	0.822478i	0.524727	+	0.851270i	$0.324167\pi$
$984$		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	$0.360198\pi$
$991$	−17.9822	+	31.1461i	−0.571223	+	0.989388i	−0.996441	+	0.0842966i	$0.973136\pi$
$992$		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.353.9	yes	24
4.3	odd	2	inner	1216.2.t.d.353.3	✓	24
8.3	odd	2		1216.2.t.e.353.9	yes	24
8.5	even	2		1216.2.t.e.353.3	yes	24
19.7	even	3		1216.2.t.e.1185.3	yes	24
76.7	odd	6		1216.2.t.e.1185.9	yes	24
152.45	even	6	inner	1216.2.t.d.1185.9	yes	24
152.83	odd	6	inner	1216.2.t.d.1185.3	yes	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
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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