LMFDB - Embedded newform 280.2.x.a.97.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(97,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("280.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.x (of order $4$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.11
Character	$\chi$	$=$	280.97
Dual form			280.2.x.a.153.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.16341 + 2.16341i) q^{3} +(-1.91827 + 1.14901i) q^{5} +(-2.61380 - 0.409966i) q^{7} +6.36066i q^{9} +O(q^{10})$	\(q+(2.16341 + 2.16341i) q^{3} +(-1.91827 + 1.14901i) q^{5} +(-2.61380 - 0.409966i) q^{7} +6.36066i q^{9} +0.796216 q^{11} +(3.25130 + 3.25130i) q^{13} +(-6.63578 - 1.66422i) q^{15} +(2.52106 - 2.52106i) q^{17} +2.29803 q^{19} +(-4.76778 - 6.54163i) q^{21} +(-2.08441 + 2.08441i) q^{23} +(2.35954 - 4.40824i) q^{25} +(-7.27046 + 7.27046i) q^{27} -10.0797i q^{29} -3.63347i q^{31} +(1.72254 + 1.72254i) q^{33} +(5.48503 - 2.21686i) q^{35} +(7.30001 + 7.30001i) q^{37} +14.0678i q^{39} +2.81026i q^{41} +(2.33689 - 2.33689i) q^{43} +(-7.30847 - 12.2015i) q^{45} +(-4.09923 + 4.09923i) q^{47} +(6.66386 + 2.14314i) q^{49} +10.9082 q^{51} +(6.50379 - 6.50379i) q^{53} +(-1.52736 + 0.914862i) q^{55} +(4.97156 + 4.97156i) q^{57} -11.4005 q^{59} -3.35941i q^{61} +(2.60765 - 16.6255i) q^{63} +(-9.97268 - 2.50110i) q^{65} +(-2.49153 - 2.49153i) q^{67} -9.01885 q^{69} -2.93777 q^{71} +(4.93694 + 4.93694i) q^{73} +(14.6415 - 4.43217i) q^{75} +(-2.08115 - 0.326422i) q^{77} -6.53223i q^{79} -12.3760 q^{81} +(1.14828 + 1.14828i) q^{83} +(-1.93935 + 7.73282i) q^{85} +(21.8066 - 21.8066i) q^{87} -14.0949 q^{89} +(-7.16532 - 9.83117i) q^{91} +(7.86067 - 7.86067i) q^{93} +(-4.40824 + 2.64046i) q^{95} +(4.30685 - 4.30685i) q^{97} +5.06446i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{7}+O(q^{10}) $ 24 * q + 4 * q^7	$ 24 q + 4 q^{7} + 8 q^{11} - 8 q^{15} + 16 q^{21} - 32 q^{23} + 8 q^{25} + 12 q^{35} - 8 q^{37} + 16 q^{43} - 24 q^{51} - 16 q^{53} + 20 q^{63} - 48 q^{65} - 32 q^{67} - 32 q^{71} - 40 q^{77} - 72 q^{81} + 16 q^{85} - 64 q^{91} + 72 q^{93} - 24 q^{95}+O(q^{100}) $ 24 * q + 4 * q^7 + 8 * q^11 - 8 * q^15 + 16 * q^21 - 32 * q^23 + 8 * q^25 + 12 * q^35 - 8 * q^37 + 16 * q^43 - 24 * q^51 - 16 * q^53 + 20 * q^63 - 48 * q^65 - 32 * q^67 - 32 * q^71 - 40 * q^77 - 72 * q^81 + 16 * q^85 - 64 * q^91 + 72 * q^93 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.16341	+	2.16341i	1.24904	+	1.24904i	0.956143	+	0.292900i	$0.0946204\pi$
$3$	2.16341	+	2.16341i	1.24904	+	1.24904i	0.292900	+	0.956143i	$0.405380\pi$
$4$		0			0
$5$	−1.91827	+	1.14901i	−0.857878	+	0.513854i
$5$	−1.91827	+	1.14901i	−0.857878	+	0.513854i
$6$		0			0
$7$	−2.61380	−	0.409966i	−0.987922	−	0.154953i
$7$	−2.61380	−	0.409966i	−0.987922	−	0.154953i
$8$		0			0
$9$			6.36066i			2.12022i
$10$		0			0
$11$	0.796216			0.240068			0.120034	−	0.992770i	$-0.461700\pi$
$11$	0.796216			0.240068			0.120034	+	0.992770i	$0.461700\pi$
$12$		0			0
$13$	3.25130	+	3.25130i	0.901750	+	0.901750i	0.995587	−	0.0938379i	$-0.0299135\pi$
$13$	3.25130	+	3.25130i	0.901750	+	0.901750i	−0.0938379	+	0.995587i	$0.529914\pi$
$14$		0			0
$15$	−6.63578	−	1.66422i	−1.71335	−	0.429700i
$16$		0			0
$17$	2.52106	−	2.52106i	0.611447	−	0.611447i	−0.331876	−	0.943323i	$-0.607682\pi$
$17$	2.52106	−	2.52106i	0.611447	−	0.611447i	0.943323	+	0.331876i	$0.107682\pi$
$18$		0			0
$19$	2.29803			0.527203			0.263602	−	0.964632i	$-0.415090\pi$
$19$	2.29803			0.527203			0.263602	+	0.964632i	$0.415090\pi$
$20$		0			0
$21$	−4.76778	−	6.54163i	−1.04041	−	1.42750i
$22$		0			0
$23$	−2.08441	+	2.08441i	−0.434630	+	0.434630i	−0.890200	−	0.455570i	$-0.849435\pi$
$23$	−2.08441	+	2.08441i	−0.434630	+	0.434630i	0.455570	+	0.890200i	$0.349435\pi$
$24$		0			0
$25$	2.35954	−	4.40824i	0.471908	−	0.881648i
$26$		0			0
$27$	−7.27046	+	7.27046i	−1.39920	+	1.39920i
$28$		0			0
$29$		−	10.0797i		−	1.87176i	−0.352319	−	0.935880i	$-0.614607\pi$
$29$		−	10.0797i		−	1.87176i	0.352319	−	0.935880i	$-0.385393\pi$
$30$		0			0
$31$		−	3.63347i		−	0.652590i	−0.945268	−	0.326295i	$-0.894200\pi$
$31$		−	3.63347i		−	0.652590i	0.945268	−	0.326295i	$-0.105800\pi$
$32$		0			0
$33$	1.72254	+	1.72254i	0.299856	+	0.299856i
$34$		0			0
$35$	5.48503	−	2.21686i	0.927139	−	0.374717i
$36$		0			0
$37$	7.30001	+	7.30001i	1.20011	+	1.20011i	0.974131	+	0.225982i	$0.0725592\pi$
$37$	7.30001	+	7.30001i	1.20011	+	1.20011i	0.225982	+	0.974131i	$0.427441\pi$
$38$		0			0
$39$			14.0678i			2.25265i
$40$		0			0
$41$			2.81026i			0.438889i	0.975625	+	0.219444i	$0.0704245\pi$
$41$			2.81026i			0.438889i	−0.975625	+	0.219444i	$0.929576\pi$
$42$		0			0
$43$	2.33689	−	2.33689i	0.356373	−	0.356373i	−0.506101	−	0.862474i	$-0.668914\pi$
$43$	2.33689	−	2.33689i	0.356373	−	0.356373i	0.862474	+	0.506101i	$0.168914\pi$
$44$		0			0
$45$	−7.30847	−	12.2015i	−1.08948	−	1.81889i
$46$		0			0
$47$	−4.09923	+	4.09923i	−0.597934	+	0.597934i	−0.939762	−	0.341829i	$-0.888954\pi$
$47$	−4.09923	+	4.09923i	−0.597934	+	0.597934i	0.341829	+	0.939762i	$0.388954\pi$
$48$		0			0
$49$	6.66386	+	2.14314i	0.951979	+	0.306162i
$50$		0			0
$51$	10.9082			1.52745
$52$		0			0
$53$	6.50379	−	6.50379i	0.893364	−	0.893364i	−0.101474	−	0.994838i	$-0.532356\pi$
$53$	6.50379	−	6.50379i	0.893364	−	0.893364i	0.994838	+	0.101474i	$0.0323558\pi$
$54$		0			0
$55$	−1.52736	+	0.914862i	−0.205949	+	0.123360i
$56$		0			0
$57$	4.97156	+	4.97156i	0.658500	+	0.658500i
$58$		0			0
$59$	−11.4005			−1.48422			−0.742112	−	0.670276i	$-0.766176\pi$
$59$	−11.4005			−1.48422			−0.742112	+	0.670276i	$0.766176\pi$
$60$		0			0
$61$		−	3.35941i		−	0.430128i	−0.976600	−	0.215064i	$-0.931004\pi$
$61$		−	3.35941i		−	0.430128i	0.976600	−	0.215064i	$-0.0689960\pi$
$62$		0			0
$63$	2.60765	−	16.6255i	0.328533	−	2.09461i
$64$		0			0
$65$	−9.97268	−	2.50110i	−1.23696	−	0.310223i
$66$		0			0
$67$	−2.49153	−	2.49153i	−0.304389	−	0.304389i	0.538339	−	0.842728i	$-0.319052\pi$
$67$	−2.49153	−	2.49153i	−0.304389	−	0.304389i	−0.842728	+	0.538339i	$0.819052\pi$
$68$		0			0
$69$	−9.01885			−1.08574
$70$		0			0
$71$	−2.93777			−0.348650			−0.174325	−	0.984688i	$-0.555774\pi$
$71$	−2.93777			−0.348650			−0.174325	+	0.984688i	$0.555774\pi$
$72$		0			0
$73$	4.93694	+	4.93694i	0.577826	+	0.577826i	0.934304	−	0.356478i	$-0.116023\pi$
$73$	4.93694	+	4.93694i	0.577826	+	0.577826i	−0.356478	+	0.934304i	$0.616023\pi$
$74$		0			0
$75$	14.6415	−	4.43217i	1.69065	−	0.511783i
$76$		0			0
$77$	−2.08115	−	0.326422i	−0.237169	−	0.0371992i
$78$		0			0
$79$		−	6.53223i		−	0.734933i	−0.930037	−	0.367467i	$-0.880225\pi$
$79$		−	6.53223i		−	0.734933i	0.930037	−	0.367467i	$-0.119775\pi$
$80$		0			0
$81$	−12.3760			−1.37511
$82$		0			0
$83$	1.14828	+	1.14828i	0.126040	+	0.126040i	0.767313	−	0.641273i	$-0.221593\pi$
$83$	1.14828	+	1.14828i	0.126040	+	0.126040i	−0.641273	+	0.767313i	$0.721593\pi$
$84$		0			0
$85$	−1.93935	+	7.73282i	−0.210352	+	0.838742i
$86$		0			0
$87$	21.8066	−	21.8066i	2.33791	−	2.33791i
$88$		0			0
$89$	−14.0949			−1.49405			−0.747026	−	0.664795i	$-0.768519\pi$
$89$	−14.0949			−1.49405			−0.747026	+	0.664795i	$0.768519\pi$
$90$		0			0
$91$	−7.16532	−	9.83117i	−0.751130	−	1.03059i
$92$		0			0
$93$	7.86067	−	7.86067i	0.815114	−	0.815114i
$94$		0			0
$95$	−4.40824	+	2.64046i	−0.452276	+	0.270905i
$96$		0			0
$97$	4.30685	−	4.30685i	0.437295	−	0.437295i	−0.453806	−	0.891101i	$-0.649934\pi$
$97$	4.30685	−	4.30685i	0.437295	−	0.437295i	0.891101	+	0.453806i	$0.149934\pi$
$98$		0			0
$99$			5.06446i			0.508997i
$100$		0			0
$101$			11.6450i			1.15872i	0.815072	+	0.579360i	$0.196697\pi$
$101$			11.6450i			1.15872i	−0.815072	+	0.579360i	$0.803303\pi$
$102$		0			0
$103$	−3.54280	−	3.54280i	−0.349082	−	0.349082i	0.510685	−	0.859768i	$-0.329392\pi$
$103$	−3.54280	−	3.54280i	−0.349082	−	0.349082i	−0.859768	+	0.510685i	$0.829392\pi$
$104$		0			0
$105$	16.6623	+	7.07038i	1.62608	+	0.689999i
$106$		0			0
$107$	−9.21284	−	9.21284i	−0.890639	−	0.890639i	0.103944	−	0.994583i	$-0.466854\pi$
$107$	−9.21284	−	9.21284i	−0.890639	−	0.890639i	−0.994583	+	0.103944i	$0.966854\pi$
$108$		0			0
$109$		−	6.01531i		−	0.576162i	−0.957606	−	0.288081i	$-0.906983\pi$
$109$		−	6.01531i		−	0.576162i	0.957606	−	0.288081i	$-0.0930173\pi$
$110$		0			0
$111$			31.5858i			2.99799i
$112$		0			0
$113$	3.56399	−	3.56399i	0.335272	−	0.335272i	−0.519312	−	0.854585i	$-0.673812\pi$
$113$	3.56399	−	3.56399i	0.335272	−	0.335272i	0.854585	+	0.519312i	$0.173812\pi$
$114$		0			0
$115$	1.60345	−	6.39348i	0.149523	−	0.596195i
$116$		0			0
$117$	−20.6804	+	20.6804i	−1.91191	+	1.91191i
$118$		0			0
$119$	−7.62309	+	5.55599i	−0.698807	+	0.509317i
$120$		0			0
$121$	−10.3660			−0.942367
$122$		0			0
$123$	−6.07973	+	6.07973i	−0.548191	+	0.548191i
$124$		0			0
$125$	0.538882	+	11.1673i	0.0481991	+	0.998838i
$126$		0			0
$127$	14.2615	+	14.2615i	1.26551	+	1.26551i	0.948384	+	0.317123i	$0.102717\pi$
$127$	14.2615	+	14.2615i	1.26551	+	1.26551i	0.317123	+	0.948384i	$0.397283\pi$
$128$		0			0
$129$	10.1113			0.890250
$130$		0			0
$131$		−	8.24139i		−	0.720054i	−0.932942	−	0.360027i	$-0.882768\pi$
$131$		−	8.24139i		−	0.720054i	0.932942	−	0.360027i	$-0.117232\pi$
$132$		0			0
$133$	−6.00657	−	0.942113i	−0.520836	−	0.0816915i
$134$		0			0
$135$	5.59288	−	22.3006i	0.481358	−	1.91933i
$136$		0			0
$137$	5.79622	+	5.79622i	0.495204	+	0.495204i	0.909941	−	0.414737i	$-0.136126\pi$
$137$	5.79622	+	5.79622i	0.495204	+	0.495204i	−0.414737	+	0.909941i	$0.636126\pi$
$138$		0			0
$139$	−7.89813			−0.669911			−0.334955	−	0.942234i	$-0.608721\pi$
$139$	−7.89813			−0.669911			−0.334955	+	0.942234i	$0.608721\pi$
$140$		0			0
$141$	−17.7366			−1.49369
$142$		0			0
$143$	2.58874	+	2.58874i	0.216481	+	0.216481i
$144$		0			0
$145$	11.5817	+	19.3357i	0.961811	+	1.60574i
$146$		0			0
$147$	9.78015	+	19.0531i	0.806654	+	1.57147i
$148$		0			0
$149$			5.09736i			0.417592i	0.977959	+	0.208796i	$0.0669545\pi$
$149$			5.09736i			0.417592i	−0.977959	+	0.208796i	$0.933045\pi$
$150$		0			0
$151$	13.4201			1.09211			0.546057	−	0.837748i	$-0.316128\pi$
$151$	13.4201			1.09211			0.546057	+	0.837748i	$0.316128\pi$
$152$		0			0
$153$	16.0356	+	16.0356i	1.29640	+	1.29640i
$154$		0			0
$155$	4.17490	+	6.96999i	0.335336	+	0.559843i
$156$		0			0
$157$	2.73434	−	2.73434i	0.218224	−	0.218224i	−0.589525	−	0.807750i	$-0.700685\pi$
$157$	2.73434	−	2.73434i	0.218224	−	0.218224i	0.807750	+	0.589525i	$0.200685\pi$
$158$		0			0
$159$	28.1407			2.23170
$160$		0			0
$161$	6.30276	−	4.59368i	0.496727	−	0.362033i
$162$		0			0
$163$	−15.4971	+	15.4971i	−1.21383	+	1.21383i	−0.244068	+	0.969758i	$0.578482\pi$
$163$	−15.4971	+	15.4971i	−1.21383	+	1.21383i	−0.969758	+	0.244068i	$0.921518\pi$
$164$		0			0
$165$	−5.28352	−	1.32508i	−0.411321	−	0.103157i
$166$		0			0
$167$	−4.74279	+	4.74279i	−0.367008	+	0.367008i	−0.866385	−	0.499377i	$-0.833562\pi$
$167$	−4.74279	+	4.74279i	−0.367008	+	0.367008i	0.499377	+	0.866385i	$0.333562\pi$
$168$		0			0
$169$			8.14196i			0.626305i
$170$		0			0
$171$			14.6169i			1.11779i
$172$		0			0
$173$	−10.5915	−	10.5915i	−0.805253	−	0.805253i	0.178658	−	0.983911i	$-0.442824\pi$
$173$	−10.5915	−	10.5915i	−0.805253	−	0.805253i	−0.983911	+	0.178658i	$0.942824\pi$
$174$		0			0
$175$	−7.97458	+	10.5549i	−0.602822	+	0.797876i
$176$		0			0
$177$	−24.6640	−	24.6640i	−1.85386	−	1.85386i
$178$		0			0
$179$		−	18.0880i		−	1.35196i	−0.736918	−	0.675982i	$-0.763720\pi$
$179$		−	18.0880i		−	1.35196i	0.736918	−	0.675982i	$-0.236280\pi$
$180$		0			0
$181$		−	14.0287i		−	1.04274i	−0.853329	−	0.521372i	$-0.825420\pi$
$181$		−	14.0287i		−	1.04274i	0.853329	−	0.521372i	$-0.174580\pi$
$182$		0			0
$183$	7.26776	−	7.26776i	0.537248	−	0.537248i
$184$		0			0
$185$	−22.3912	−	5.61560i	−1.64623	−	0.412867i
$186$		0			0
$187$	2.00731	−	2.00731i	0.146789	−	0.146789i
$188$		0			0
$189$	21.9841	−	16.0229i	1.59911	−	1.16549i
$190$		0			0
$191$	5.39084			0.390068			0.195034	−	0.980796i	$-0.437518\pi$
$191$	5.39084			0.390068			0.195034	+	0.980796i	$0.437518\pi$
$192$		0			0
$193$	−3.66005	+	3.66005i	−0.263456	+	0.263456i	−0.826457	−	0.563000i	$-0.809647\pi$
$193$	−3.66005	+	3.66005i	−0.263456	+	0.263456i	0.563000	+	0.826457i	$0.309647\pi$
$194$		0			0
$195$	−16.1641	−	26.9858i	−1.15753	−	1.93250i
$196$		0			0
$197$	−9.16340	−	9.16340i	−0.652865	−	0.652865i	0.300817	−	0.953682i	$-0.402741\pi$
$197$	−9.16340	−	9.16340i	−0.652865	−	0.652865i	−0.953682	+	0.300817i	$0.902741\pi$
$198$		0			0
$199$	−15.9276			−1.12908			−0.564539	−	0.825406i	$-0.690946\pi$
$199$	−15.9276			−1.12908			−0.564539	+	0.825406i	$0.690946\pi$
$200$		0			0
$201$		−	10.7804i		−	0.760391i
$202$		0			0
$203$	−4.13235	+	26.3464i	−0.290034	+	1.84915i
$204$		0			0
$205$	−3.22902	−	5.39084i	−0.225525	−	0.376513i
$206$		0			0
$207$	−13.2582	−	13.2582i	−0.921510	−	0.921510i
$208$		0			0
$209$	1.82972			0.126565
$210$		0			0
$211$	4.20382			0.289403			0.144701	−	0.989475i	$-0.453778\pi$
$211$	4.20382			0.289403			0.144701	+	0.989475i	$0.453778\pi$
$212$		0			0
$213$	−6.35560	−	6.35560i	−0.435479	−	0.435479i
$214$		0			0
$215$	−1.79768	+	7.16792i	−0.122601	+	0.488848i
$216$		0			0
$217$	−1.48960	+	9.49715i	−0.101121	+	0.644708i
$218$		0			0
$219$			21.3612i			1.44346i
$220$		0			0
$221$	16.3935			1.10274
$222$		0			0
$223$	−8.79408	−	8.79408i	−0.588895	−	0.588895i	0.348437	−	0.937332i	$-0.386712\pi$
$223$	−8.79408	−	8.79408i	−0.588895	−	0.588895i	−0.937332	+	0.348437i	$0.886712\pi$
$224$		0			0
$225$	28.0393	+	15.0082i	1.86929	+	1.00055i
$226$		0			0
$227$	12.9267	−	12.9267i	0.857973	−	0.857973i	−0.133126	−	0.991099i	$-0.542502\pi$
$227$	12.9267	−	12.9267i	0.857973	−	0.857973i	0.991099	+	0.133126i	$0.0425015\pi$
$228$		0			0
$229$	15.2917			1.01050			0.505252	−	0.862972i	$-0.331400\pi$
$229$	15.2917			1.01050			0.505252	+	0.862972i	$0.331400\pi$
$230$		0			0
$231$	−3.79618	−	5.20855i	−0.249770	−	0.342697i
$232$		0			0
$233$	−6.89086	+	6.89086i	−0.451435	+	0.451435i	−0.895831	−	0.444395i	$-0.853419\pi$
$233$	−6.89086	+	6.89086i	−0.451435	+	0.451435i	0.444395	+	0.895831i	$0.353419\pi$
$234$		0			0
$235$	3.15337	−	12.5735i	0.205703	−	0.820205i
$236$		0			0
$237$	14.1319	−	14.1319i	0.917963	−	0.917963i
$238$		0			0
$239$			4.40870i			0.285175i	0.989782	+	0.142588i	$0.0455423\pi$
$239$			4.40870i			0.285175i	−0.989782	+	0.142588i	$0.954458\pi$
$240$		0			0
$241$		−	9.82692i		−	0.633008i	−0.948591	−	0.316504i	$-0.897491\pi$
$241$		−	9.82692i		−	0.633008i	0.948591	−	0.316504i	$-0.102509\pi$
$242$		0			0
$243$	−4.96286	−	4.96286i	−0.318368	−	0.318368i
$244$		0			0
$245$	−15.2456	+	3.54574i	−0.974004	+	0.226529i
$246$		0			0
$247$	7.47158	+	7.47158i	0.475405	+	0.475405i
$248$		0			0
$249$			4.96840i			0.314860i
$250$		0			0
$251$			0.723170i			0.0456461i	0.999740	+	0.0228230i	$0.00726543\pi$
$251$			0.723170i			0.0456461i	−0.999740	+	0.0228230i	$0.992735\pi$
$252$		0			0
$253$	−1.65964	+	1.65964i	−0.104341	+	0.104341i
$254$		0			0
$255$	−20.9248	+	12.5336i	−1.31036	+	0.784885i
$256$		0			0
$257$	−6.32060	+	6.32060i	−0.394268	+	0.394268i	−0.876206	−	0.481938i	$-0.839933\pi$
$257$	−6.32060	+	6.32060i	−0.394268	+	0.394268i	0.481938	+	0.876206i	$0.339933\pi$
$258$		0			0
$259$	−16.0880	−	22.0735i	−0.999658	−	1.37158i
$260$		0			0
$261$	64.1137			3.96854
$262$		0			0
$263$	6.22755	−	6.22755i	0.384007	−	0.384007i	−0.488537	−	0.872543i	$-0.662469\pi$
$263$	6.22755	−	6.22755i	0.384007	−	0.384007i	0.872543	+	0.488537i	$0.162469\pi$
$264$		0			0
$265$	−5.00311	+	19.9490i	−0.307338	+	1.22546i
$266$		0			0
$267$	−30.4929	−	30.4929i	−1.86613	−	1.86613i
$268$		0			0
$269$	−3.12088			−0.190283			−0.0951417	−	0.995464i	$-0.530330\pi$
$269$	−3.12088			−0.190283			−0.0951417	+	0.995464i	$0.530330\pi$
$270$		0			0
$271$		−	5.17480i		−	0.314347i	−0.987571	−	0.157173i	$-0.949762\pi$
$271$		−	5.17480i		−	0.314347i	0.987571	−	0.157173i	$-0.0502382\pi$
$272$		0			0
$273$	5.76732	−	36.7703i	0.349054	−	2.22544i
$274$		0			0
$275$	1.87870	−	3.50991i	0.113290	−	0.211656i
$276$		0			0
$277$	18.9267	+	18.9267i	1.13719	+	1.13719i	0.988951	+	0.148242i	$0.0473616\pi$
$277$	18.9267	+	18.9267i	1.13719	+	1.13719i	0.148242	+	0.988951i	$0.452638\pi$
$278$		0			0
$279$	23.1112			1.38363
$280$		0			0
$281$	−10.2646			−0.612333			−0.306166	−	0.951978i	$-0.599046\pi$
$281$	−10.2646			−0.612333			−0.306166	+	0.951978i	$0.599046\pi$
$282$		0			0
$283$	23.3112	+	23.3112i	1.38571	+	1.38571i	0.834110	+	0.551598i	$0.185982\pi$
$283$	23.3112	+	23.3112i	1.38571	+	1.38571i	0.551598	+	0.834110i	$0.314018\pi$
$284$		0			0
$285$	−15.2492	−	3.82442i	−0.903285	−	0.226539i
$286$		0			0
$287$	1.15211	−	7.34545i	0.0680070	−	0.433588i
$288$		0			0
$289$			4.28850i			0.252265i
$290$		0			0
$291$	18.6349			1.09240
$292$		0			0
$293$	−7.53673	−	7.53673i	−0.440301	−	0.440301i	0.451812	−	0.892113i	$-0.350778\pi$
$293$	−7.53673	−	7.53673i	−0.440301	−	0.440301i	−0.892113	+	0.451812i	$0.850778\pi$
$294$		0			0
$295$	21.8693	−	13.0994i	1.27328	−	0.762674i
$296$		0			0
$297$	−5.78886	+	5.78886i	−0.335904	+	0.335904i
$298$		0			0
$299$	−13.5541			−0.783854
$300$		0			0
$301$	−7.06621	+	5.15011i	−0.407289	+	0.296848i
$302$		0			0
$303$	−25.1929	+	25.1929i	−1.44729	+	1.44729i
$304$		0			0
$305$	3.86000	+	6.44426i	0.221023	+	0.368997i
$306$		0			0
$307$	−5.09625	+	5.09625i	−0.290858	+	0.290858i	−0.837419	−	0.546561i	$-0.815937\pi$
$307$	−5.09625	+	5.09625i	−0.290858	+	0.290858i	0.546561	+	0.837419i	$0.315937\pi$
$308$		0			0
$309$		−	15.3290i		−	0.872038i
$310$		0			0
$311$		−	8.88013i		−	0.503546i	−0.967786	−	0.251773i	$-0.918986\pi$
$311$		−	8.88013i		−	0.503546i	0.967786	−	0.251773i	$-0.0810136\pi$
$312$		0			0
$313$	−6.50060	−	6.50060i	−0.367436	−	0.367436i	0.499105	−	0.866541i	$-0.333662\pi$
$313$	−6.50060	−	6.50060i	−0.367436	−	0.367436i	−0.866541	+	0.499105i	$0.833662\pi$
$314$		0			0
$315$	14.1007	+	34.8884i	0.794482	+	1.96574i
$316$		0			0
$317$	3.87753	+	3.87753i	0.217784	+	0.217784i	0.807564	−	0.589780i	$-0.200786\pi$
$317$	3.87753	+	3.87753i	0.217784	+	0.217784i	−0.589780	+	0.807564i	$0.700786\pi$
$318$		0			0
$319$		−	8.02565i		−	0.449350i
$320$		0			0
$321$		−	39.8623i		−	2.22489i
$322$		0			0
$323$	5.79346	−	5.79346i	0.322357	−	0.322357i
$324$		0			0
$325$	22.0041	−	6.66094i	1.22057	−	0.369483i
$326$		0			0
$327$	13.0136	−	13.0136i	0.719652	−	0.719652i
$328$		0			0
$329$	12.3951	−	9.03400i	0.683363	−	0.498060i
$330$		0			0
$331$	6.56299			0.360735			0.180367	−	0.983599i	$-0.442271\pi$
$331$	6.56299			0.360735			0.180367	+	0.983599i	$0.442271\pi$
$332$		0			0
$333$	−46.4328	+	46.4328i	−2.54450	+	2.54450i
$334$		0			0
$335$	7.64225	+	1.91664i	0.417540	+	0.104717i
$336$		0			0
$337$	3.62582	+	3.62582i	0.197511	+	0.197511i	0.798932	−	0.601421i	$-0.205399\pi$
$337$	3.62582	+	3.62582i	0.197511	+	0.197511i	−0.601421	+	0.798932i	$0.705399\pi$
$338$		0			0
$339$	15.4207			0.837540
$340$		0			0
$341$		−	2.89303i		−	0.156666i
$342$		0			0
$343$	−16.5393	−	8.33367i	−0.893041	−	0.449976i
$344$		0			0
$345$	17.3006	−	10.3628i	0.931434	−	0.557913i
$346$		0			0
$347$	−0.698071	−	0.698071i	−0.0374744	−	0.0374744i	0.688121	−	0.725596i	$-0.258436\pi$
$347$	−0.698071	−	0.698071i	−0.0374744	−	0.0374744i	−0.725596	+	0.688121i	$0.758436\pi$
$348$		0			0
$349$	1.36446			0.0730378			0.0365189	−	0.999333i	$-0.488373\pi$
$349$	1.36446			0.0730378			0.0365189	+	0.999333i	$0.488373\pi$
$350$		0			0
$351$	−47.2770			−2.52346
$352$		0			0
$353$	8.57760	+	8.57760i	0.456539	+	0.456539i	0.897518	−	0.440978i	$-0.145368\pi$
$353$	8.57760	+	8.57760i	0.456539	+	0.456539i	−0.440978	+	0.897518i	$0.645368\pi$
$354$		0			0
$355$	5.63545	−	3.37554i	0.299099	−	0.179155i
$356$		0			0
$357$	−28.5117	−	4.47198i	−1.50900	−	0.236682i
$358$		0			0
$359$			20.0825i			1.05992i	0.848024	+	0.529958i	$0.177792\pi$
$359$			20.0825i			1.05992i	−0.848024	+	0.529958i	$0.822208\pi$
$360$		0			0
$361$	−13.7191			−0.722057
$362$		0			0
$363$	−22.4260	−	22.4260i	−1.17706	−	1.17706i
$364$		0			0
$365$	−15.1430	−	3.79779i	−0.792622	−	0.198786i
$366$		0			0
$367$	−18.7210	+	18.7210i	−0.977228	+	0.977228i	−0.999746	−	0.0225182i	$-0.992832\pi$
$367$	−18.7210	+	18.7210i	−0.977228	+	0.977228i	0.0225182	+	0.999746i	$0.492832\pi$
$368$		0			0
$369$	−17.8751			−0.930540
$370$		0			0
$371$	−19.6659	+	14.3332i	−1.02100	+	0.744145i
$372$		0			0
$373$	−14.2070	+	14.2070i	−0.735612	+	0.735612i	−0.971726	−	0.236113i	$-0.924126\pi$
$373$	−14.2070	+	14.2070i	−0.735612	+	0.735612i	0.236113	+	0.971726i	$0.424126\pi$
$374$		0			0
$375$	−22.9937	+	25.3253i	−1.18739	+	1.30779i
$376$		0			0
$377$	32.7723	−	32.7723i	1.68786	−	1.68786i
$378$		0			0
$379$		−	32.8094i		−	1.68530i	−0.538459	−	0.842652i	$-0.680993\pi$
$379$		−	32.8094i		−	1.68530i	0.538459	−	0.842652i	$-0.319007\pi$
$380$		0			0
$381$			61.7070i			3.16135i
$382$		0			0
$383$	4.07047	+	4.07047i	0.207991	+	0.207991i	0.803413	−	0.595422i	$-0.203015\pi$
$383$	4.07047	+	4.07047i	0.207991	+	0.207991i	−0.595422	+	0.803413i	$0.703015\pi$
$384$		0			0
$385$	4.36727	−	1.76510i	0.222577	−	0.0899577i
$386$		0			0
$387$	14.8642	+	14.8642i	0.755588	+	0.755588i
$388$		0			0
$389$		−	7.60774i		−	0.385728i	−0.981226	−	0.192864i	$-0.938222\pi$
$389$		−	7.60774i		−	0.385728i	0.981226	−	0.192864i	$-0.0617776\pi$
$390$		0			0
$391$			10.5099i			0.531506i
$392$		0			0
$393$	17.8295	−	17.8295i	0.899378	−	0.899378i
$394$		0			0
$395$	7.50561	+	12.5306i	0.377648	+	0.630483i
$396$		0			0
$397$	18.7106	−	18.7106i	0.939059	−	0.939059i	−0.0591880	−	0.998247i	$-0.518851\pi$
$397$	18.7106	−	18.7106i	0.939059	−	0.939059i	0.998247	+	0.0591880i	$0.0188511\pi$
$398$		0			0
$399$	−10.9565	−	15.0328i	−0.548510	−	0.752582i
$400$		0			0
$401$	4.07435			0.203463			0.101732	−	0.994812i	$-0.467562\pi$
$401$	4.07435			0.203463			0.101732	+	0.994812i	$0.467562\pi$
$402$		0			0
$403$	11.8135	−	11.8135i	0.588473	−	0.588473i
$404$		0			0
$405$	23.7405	−	14.2201i	1.17967	−	0.706605i
$406$		0			0
$407$	5.81238	+	5.81238i	0.288109	+	0.288109i
$408$		0			0
$409$	−7.30032			−0.360978			−0.180489	−	0.983577i	$-0.557768\pi$
$409$	−7.30032			−0.360978			−0.180489	+	0.983577i	$0.557768\pi$
$410$		0			0
$411$			25.0791i			1.23706i
$412$		0			0
$413$	29.7987	+	4.67383i	1.46630	+	0.229984i
$414$		0			0
$415$	−3.52211	−	0.883327i	−0.172893	−	0.0433608i
$416$		0			0
$417$	−17.0869	−	17.0869i	−0.836748	−	0.836748i
$418$		0			0
$419$	38.4444			1.87813			0.939066	−	0.343737i	$-0.111693\pi$
$419$	38.4444			1.87813			0.939066	+	0.343737i	$0.111693\pi$
$420$		0			0
$421$	−18.4603			−0.899698			−0.449849	−	0.893105i	$-0.648522\pi$
$421$	−18.4603			−0.899698			−0.449849	+	0.893105i	$0.648522\pi$
$422$		0			0
$423$	−26.0738	−	26.0738i	−1.26775	−	1.26775i
$424$		0			0
$425$	−5.16490	−	17.0620i	−0.250534	−	0.827628i
$426$		0			0
$427$	−1.37724	+	8.78080i	−0.0666495	+	0.424933i
$428$		0			0
$429$			11.2010i			0.540789i
$430$		0			0
$431$	18.3985			0.886227			0.443113	−	0.896466i	$-0.353874\pi$
$431$	18.3985			0.886227			0.443113	+	0.896466i	$0.353874\pi$
$432$		0			0
$433$	−13.6373	−	13.6373i	−0.655368	−	0.655368i	0.298913	−	0.954280i	$-0.403376\pi$
$433$	−13.6373	−	13.6373i	−0.655368	−	0.655368i	−0.954280	+	0.298913i	$0.903376\pi$
$434$		0			0
$435$	−16.7749	+	66.8870i	−0.804296	+	3.20698i
$436$		0			0
$437$	−4.79003	+	4.79003i	−0.229138	+	0.229138i
$438$		0			0
$439$	13.8974			0.663285			0.331642	−	0.943405i	$-0.392397\pi$
$439$	13.8974			0.663285			0.331642	+	0.943405i	$0.392397\pi$
$440$		0			0
$441$	−13.6317	+	42.3865i	−0.649131	+	2.01840i
$442$		0			0
$443$	18.8725	−	18.8725i	0.896659	−	0.896659i	−0.0984802	−	0.995139i	$-0.531398\pi$
$443$	18.8725	−	18.8725i	0.896659	−	0.896659i	0.995139	+	0.0984802i	$0.0313981\pi$
$444$		0			0
$445$	27.0378	−	16.1952i	1.28171	−	0.767724i
$446$		0			0
$447$	−11.0277	+	11.0277i	−0.521591	+	0.521591i
$448$		0			0
$449$		−	5.54414i		−	0.261644i	−0.991406	−	0.130822i	$-0.958238\pi$
$449$		−	5.54414i		−	0.261644i	0.991406	−	0.130822i	$-0.0417617\pi$
$450$		0			0
$451$			2.23757i			0.105363i
$452$		0			0
$453$	29.0332	+	29.0332i	1.36410	+	1.36410i
$454$		0			0
$455$	25.0412	+	10.6258i	1.17395	+	0.498146i
$456$		0			0
$457$	−20.7321	−	20.7321i	−0.969806	−	0.969806i	0.0297514	−	0.999557i	$-0.490528\pi$
$457$	−20.7321	−	20.7321i	−0.969806	−	0.969806i	−0.999557	+	0.0297514i	$0.990528\pi$
$458$		0			0
$459$			36.6586i			1.71108i
$460$		0			0
$461$			19.0221i			0.885950i	0.896534	+	0.442975i	$0.146077\pi$
$461$			19.0221i			0.885950i	−0.896534	+	0.442975i	$0.853923\pi$
$462$		0			0
$463$	−14.5483	+	14.5483i	−0.676115	+	0.676115i	−0.959119	−	0.283004i	$-0.908669\pi$
$463$	−14.5483	+	14.5483i	−0.676115	+	0.676115i	0.283004	+	0.959119i	$0.408669\pi$
$464$		0			0
$465$	−6.04690	+	24.1109i	−0.280418	+	1.11812i
$466$		0			0
$467$	6.09112	−	6.09112i	0.281863	−	0.281863i	−0.551989	−	0.833852i	$-0.686131\pi$
$467$	6.09112	−	6.09112i	0.281863	−	0.281863i	0.833852	+	0.551989i	$0.186131\pi$
$468$		0			0
$469$	5.49092	+	7.53381i	0.253547	+	0.347879i
$470$		0			0
$471$	11.8310			0.545143
$472$		0			0
$473$	1.86067	−	1.86067i	0.0855538	−	0.0855538i
$474$		0			0
$475$	5.42228	−	10.1302i	0.248791	−	0.464808i
$476$		0			0
$477$	41.3684	+	41.3684i	1.89413	+	1.89413i
$478$		0			0
$479$	−17.2499			−0.788169			−0.394085	−	0.919074i	$-0.628938\pi$
$479$	−17.2499			−0.788169			−0.394085	+	0.919074i	$0.628938\pi$
$480$		0			0
$481$			47.4691i			2.16440i
$482$		0			0
$483$	23.5734	+	3.69742i	1.07263	+	0.168239i
$484$		0			0
$485$	−3.31309	+	13.2103i	−0.150440	+	0.599851i
$486$		0			0
$487$	−19.7915	−	19.7915i	−0.896839	−	0.896839i	0.0983164	−	0.995155i	$-0.468654\pi$
$487$	−19.7915	−	19.7915i	−0.896839	−	0.896839i	−0.995155	+	0.0983164i	$0.968654\pi$
$488$		0			0
$489$	−67.0530			−3.03224
$490$		0			0
$491$	38.8114			1.75153			0.875767	−	0.482735i	$-0.160357\pi$
$491$	38.8114			1.75153			0.875767	+	0.482735i	$0.160357\pi$
$492$		0			0
$493$	−25.4116	−	25.4116i	−1.14448	−	1.14448i
$494$		0			0
$495$	−5.81912	−	9.71501i	−0.261550	−	0.436657i
$496$		0			0
$497$	7.67874	+	1.20439i	0.344439	+	0.0540242i
$498$		0			0
$499$		−	8.21748i		−	0.367865i	−0.982939	−	0.183932i	$-0.941117\pi$
$499$		−	8.21748i		−	0.367865i	0.982939	−	0.183932i	$-0.0588828\pi$
$500$		0			0
$501$	−20.5212			−0.916818
$502$		0			0
$503$	13.7880	+	13.7880i	0.614775	+	0.614775i	0.944187	−	0.329411i	$-0.106850\pi$
$503$	13.7880	+	13.7880i	0.614775	+	0.614775i	−0.329411	+	0.944187i	$0.606850\pi$
$504$		0			0
$505$	−13.3802	−	22.3383i	−0.595413	−	0.994040i
$506$		0			0
$507$	−17.6144	+	17.6144i	−0.782282	+	0.782282i
$508$		0			0
$509$	−3.30389			−0.146442			−0.0732212	−	0.997316i	$-0.523328\pi$
$509$	−3.30389			−0.146442			−0.0732212	+	0.997316i	$0.523328\pi$
$510$		0			0
$511$	−10.8802	−	14.9281i	−0.481311	−	0.660382i
$512$		0			0
$513$	−16.7077	+	16.7077i	−0.737663	+	0.737663i
$514$		0			0
$515$	10.8668	+	2.72533i	0.478847	+	0.120092i
$516$		0			0
$517$	−3.26387	+	3.26387i	−0.143545	+	0.143545i
$518$		0			0
$519$		−	45.8272i		−	2.01159i
$520$		0			0
$521$		−	17.8887i		−	0.783717i	−0.920025	−	0.391859i	$-0.871832\pi$
$521$		−	17.8887i		−	0.783717i	0.920025	−	0.391859i	$-0.128168\pi$
$522$		0			0
$523$	−8.57838	−	8.57838i	−0.375106	−	0.375106i	0.494227	−	0.869333i	$-0.335451\pi$
$523$	−8.57838	−	8.57838i	−0.375106	−	0.375106i	−0.869333	+	0.494227i	$0.835451\pi$
$524$		0			0
$525$	−40.0868	+	5.58228i	−1.74953	+	0.243631i
$526$		0			0
$527$	−9.16020	−	9.16020i	−0.399025	−	0.399025i
$528$		0			0
$529$			14.3105i			0.622194i
$530$		0			0
$531$		−	72.5149i		−	3.14688i
$532$		0			0
$533$	−9.13701	+	9.13701i	−0.395768	+	0.395768i
$534$		0			0
$535$	28.2584	+	7.08707i	1.22172	+	0.306401i
$536$		0			0
$537$	39.1318	−	39.1318i	1.68866	−	1.68866i
$538$		0			0
$539$	5.30587	+	1.70640i	0.228540	+	0.0734998i
$540$		0			0
$541$	9.47422			0.407328			0.203664	−	0.979041i	$-0.434715\pi$
$541$	9.47422			0.407328			0.203664	+	0.979041i	$0.434715\pi$
$542$		0			0
$543$	30.3498	−	30.3498i	1.30243	−	1.30243i
$544$		0			0
$545$	6.91167	+	11.5390i	0.296063	+	0.494277i
$546$		0			0
$547$	7.34561	+	7.34561i	0.314076	+	0.314076i	0.846486	−	0.532411i	$-0.178714\pi$
$547$	7.34561	+	7.34561i	0.314076	+	0.314076i	−0.532411	+	0.846486i	$0.678714\pi$
$548$		0			0
$549$	21.3680			0.911965
$550$		0			0
$551$		−	23.1635i		−	0.986798i
$552$		0			0
$553$	−2.67799	+	17.0739i	−0.113880	+	0.726056i
$554$		0			0
$555$	−36.2924	−	60.5901i	−1.54053	−	2.57191i
$556$		0			0
$557$	8.79776	+	8.79776i	0.372773	+	0.372773i	0.868486	−	0.495713i	$-0.165093\pi$
$557$	8.79776	+	8.79776i	0.372773	+	0.372773i	−0.495713	+	0.868486i	$0.665093\pi$
$558$		0			0
$559$	15.1959			0.642718
$560$		0			0
$561$	8.68525			0.366692
$562$		0			0
$563$	−2.78671	−	2.78671i	−0.117446	−	0.117446i	0.645941	−	0.763387i	$-0.276465\pi$
$563$	−2.78671	−	2.78671i	−0.117446	−	0.117446i	−0.763387	+	0.645941i	$0.776465\pi$
$564$		0			0
$565$	−2.74164	+	10.9318i	−0.115342	+	0.459904i
$566$		0			0
$567$	32.3483	+	5.07373i	1.35850	+	0.213077i
$568$		0			0
$569$		−	0.247978i		−	0.0103958i	−0.999986	−	0.00519788i	$-0.998345\pi$
$569$		−	0.247978i		−	0.0103958i	0.999986	−	0.00519788i	$-0.00165455\pi$
$570$		0			0
$571$	−39.7125			−1.66192			−0.830959	−	0.556334i	$-0.812208\pi$
$571$	−39.7125			−1.66192			−0.830959	+	0.556334i	$0.812208\pi$
$572$		0			0
$573$	11.6626	+	11.6626i	0.487212	+	0.487212i
$574$		0			0
$575$	4.27033	+	14.1068i	0.178085	+	0.588295i
$576$		0			0
$577$	−28.2036	+	28.2036i	−1.17413	+	1.17413i	−0.192916	+	0.981215i	$0.561795\pi$
$577$	−28.2036	+	28.2036i	−1.17413	+	1.17413i	−0.981215	+	0.192916i	$0.938205\pi$
$578$		0			0
$579$	−15.8364			−0.658136
$580$		0			0
$581$	−2.53062	−	3.47213i	−0.104988	−	0.144048i
$582$		0			0
$583$	5.17842	−	5.17842i	0.214468	−	0.214468i
$584$		0			0
$585$	15.9086	−	63.4328i	0.657741	−	2.62262i
$586$		0			0
$587$	24.6383	−	24.6383i	1.01693	−	1.01693i	0.0170778	−	0.999854i	$-0.494564\pi$
$587$	24.6383	−	24.6383i	1.01693	−	1.01693i	0.999854	−	0.0170778i	$-0.00543629\pi$
$588$		0			0
$589$		−	8.34981i		−	0.344048i
$590$		0			0
$591$		−	39.6483i		−	1.63091i
$592$		0			0
$593$	−29.6964	−	29.6964i	−1.21948	−	1.21948i	−0.967813	−	0.251670i	$-0.919020\pi$
$593$	−29.6964	−	29.6964i	−1.21948	−	1.21948i	−0.251670	−	0.967813i	$-0.580980\pi$
$594$		0			0
$595$	8.23926	−	19.4169i	0.337777	−	0.796017i
$596$		0			0
$597$	−34.4579	−	34.4579i	−1.41027	−	1.41027i
$598$		0			0
$599$			28.4830i			1.16378i	0.813267	+	0.581891i	$0.197687\pi$
$599$			28.4830i			1.16378i	−0.813267	+	0.581891i	$0.802313\pi$
$600$		0			0
$601$		−	11.7809i		−	0.480555i	−0.970704	−	0.240277i	$-0.922762\pi$
$601$		−	11.7809i		−	0.480555i	0.970704	−	0.240277i	$-0.0772384\pi$
$602$		0			0
$603$	15.8478	−	15.8478i	0.645372	−	0.645372i
$604$		0			0
$605$	19.8849	−	11.9107i	0.808436	−	0.484239i
$606$		0			0
$607$	−28.0405	+	28.0405i	−1.13813	+	1.13813i	−0.149344	+	0.988785i	$0.547716\pi$
$607$	−28.0405	+	28.0405i	−1.13813	+	1.13813i	−0.988785	+	0.149344i	$0.952284\pi$
$608$		0			0
$609$	−65.9379	+	48.0579i	−2.67194	+	1.94741i
$610$		0			0
$611$	−26.6557			−1.07837
$612$		0			0
$613$	28.8251	−	28.8251i	1.16423	−	1.16423i	0.180695	−	0.983539i	$-0.442165\pi$
$613$	28.8251	−	28.8251i	1.16423	−	1.16423i	0.983539	−	0.180695i	$-0.0578346\pi$
$614$		0			0
$615$	4.67690	−	18.6483i	0.188591	−	0.751971i
$616$		0			0
$617$	6.96881	+	6.96881i	0.280554	+	0.280554i	0.833330	−	0.552776i	$-0.186432\pi$
$617$	6.96881	+	6.96881i	0.280554	+	0.280554i	−0.552776	+	0.833330i	$0.686432\pi$
$618$		0			0
$619$	20.2636			0.814464			0.407232	−	0.913325i	$-0.366494\pi$
$619$	20.2636			0.814464			0.407232	+	0.913325i	$0.366494\pi$
$620$		0			0
$621$		−	30.3093i		−	1.21627i
$622$		0			0
$623$	36.8411	+	5.77841i	1.47601	+	0.231507i
$624$		0			0
$625$	−13.8651	−	20.8028i	−0.554606	−	0.832113i
$626$		0			0
$627$	3.95844	+	3.95844i	0.158085	+	0.158085i
$628$		0			0
$629$	36.8075			1.46761
$630$		0			0
$631$	2.95896			0.117794			0.0588972	−	0.998264i	$-0.481242\pi$
$631$	2.95896			0.117794			0.0588972	+	0.998264i	$0.481242\pi$
$632$		0			0
$633$	9.09457	+	9.09457i	0.361477	+	0.361477i
$634$		0			0
$635$	−43.7442	−	10.9708i	−1.73594	−	0.435364i
$636$		0			0
$637$	14.6982	+	28.6342i	0.582365	+	1.13453i
$638$		0			0
$639$		−	18.6862i		−	0.739213i
$640$		0			0
$641$	23.8186			0.940776			0.470388	−	0.882460i	$-0.344114\pi$
$641$	23.8186			0.940776			0.470388	+	0.882460i	$0.344114\pi$
$642$		0			0
$643$	−25.3400	−	25.3400i	−0.999312	−	0.999312i	0.000687568	−	1.00000i	$-0.499781\pi$
$643$	−25.3400	−	25.3400i	−0.999312	−	0.999312i	−1.00000		0.000687568i	$0.999781\pi$
$644$		0			0
$645$	−19.3962	+	11.6180i	−0.763726	+	0.457459i
$646$		0			0
$647$	−16.4265	+	16.4265i	−0.645792	+	0.645792i	−0.951973	−	0.306181i	$-0.900949\pi$
$647$	−16.4265	+	16.4265i	−0.645792	+	0.645792i	0.306181	+	0.951973i	$0.400949\pi$
$648$		0			0
$649$	−9.07729			−0.356315
$650$		0			0
$651$	−23.7688	+	17.3236i	−0.931573	+	0.678965i
$652$		0			0
$653$	−22.4103	+	22.4103i	−0.876984	+	0.876984i	−0.993221	−	0.116237i	$-0.962917\pi$
$653$	−22.4103	+	22.4103i	−0.876984	+	0.876984i	0.116237	+	0.993221i	$0.462917\pi$
$654$		0			0
$655$	9.46946	+	15.8092i	0.370003	+	0.617718i
$656$		0			0
$657$	−31.4022	+	31.4022i	−1.22512	+	1.22512i
$658$		0			0
$659$			45.0537i			1.75504i	0.479537	+	0.877521i	$0.340805\pi$
$659$			45.0537i			1.75504i	−0.479537	+	0.877521i	$0.659195\pi$
$660$		0			0
$661$		−	28.5466i		−	1.11033i	−0.831739	−	0.555167i	$-0.812655\pi$
$661$		−	28.5466i		−	1.11033i	0.831739	−	0.555167i	$-0.187345\pi$
$662$		0			0
$663$	35.4658	+	35.4658i	1.37738	+	1.37738i
$664$		0			0
$665$	12.6047	−	5.09439i	0.488791	−	0.197552i
$666$		0			0
$667$	21.0103	+	21.0103i	0.813522	+	0.813522i
$668$		0			0
$669$		−	38.0503i		−	1.47111i
$670$		0			0
$671$		−	2.67481i		−	0.103260i
$672$		0			0
$673$	1.86064	−	1.86064i	0.0717223	−	0.0717223i	−0.670336	−	0.742058i	$-0.733850\pi$
$673$	1.86064	−	1.86064i	0.0717223	−	0.0717223i	0.742058	+	0.670336i	$0.233850\pi$
$674$		0			0
$675$	14.8950	+	49.2049i	0.573309	+	1.89390i
$676$		0			0
$677$	−2.24734	+	2.24734i	−0.0863723	+	0.0863723i	−0.748973	−	0.662601i	$-0.769453\pi$
$677$	−2.24734	+	2.24734i	−0.0863723	+	0.0863723i	0.662601	+	0.748973i	$0.269453\pi$
$678$		0			0
$679$	−13.0229	+	9.49157i	−0.499773	+	0.364253i
$680$		0			0
$681$	55.9313			2.14329
$682$		0			0
$683$	−23.1882	+	23.1882i	−0.887271	+	0.887271i	−0.994260	−	0.106989i	$-0.965879\pi$
$683$	−23.1882	+	23.1882i	−0.887271	+	0.887271i	0.106989	+	0.994260i	$0.465879\pi$
$684$		0			0
$685$	−17.7786	−	4.45880i	−0.679287	−	0.170362i
$686$		0			0
$687$	33.0821	+	33.0821i	1.26216	+	1.26216i
$688$		0			0
$689$	42.2916			1.61118
$690$		0			0
$691$		−	26.5659i		−	1.01061i	−0.862940	−	0.505307i	$-0.831379\pi$
$691$		−	26.5659i		−	1.01061i	0.862940	−	0.505307i	$-0.168621\pi$
$692$		0			0
$693$	2.07626	−	13.2375i	0.0788704	−	0.502849i
$694$		0			0
$695$	15.1508	−	9.07505i	0.574702	−	0.344236i
$696$		0			0
$697$	7.08484	+	7.08484i	0.268357	+	0.268357i
$698$		0			0
$699$	−29.8155			−1.12772
$700$		0			0
$701$	24.7343			0.934201			0.467100	−	0.884204i	$-0.345299\pi$
$701$	24.7343			0.934201			0.467100	+	0.884204i	$0.345299\pi$
$702$		0			0
$703$	16.7756	+	16.7756i	0.632704	+	0.632704i
$704$		0			0
$705$	34.0236	−	20.3796i	1.28140	−	0.767539i
$706$		0			0
$707$	4.77405	−	30.4376i	0.179547	−	1.14473i
$708$		0			0
$709$		−	2.16805i		−	0.0814230i	−0.999171	−	0.0407115i	$-0.987038\pi$
$709$		−	2.16805i		−	0.0814230i	0.999171	−	0.0407115i	$-0.0129625\pi$
$710$		0			0
$711$	41.5492			1.55822
$712$		0			0
$713$	7.57364	+	7.57364i	0.283635	+	0.283635i
$714$		0			0
$715$	−7.94041	−	1.99141i	−0.296954	−	0.0744747i
$716$		0			0
$717$	−9.53781	+	9.53781i	−0.356196	+	0.356196i
$718$		0			0
$719$	−39.9675			−1.49054			−0.745269	−	0.666764i	$-0.767679\pi$
$719$	−39.9675			−1.49054			−0.745269	+	0.666764i	$0.767679\pi$
$720$		0			0
$721$	7.80772	+	10.7126i	0.290775	+	0.398957i
$722$		0			0
$723$	21.2596	−	21.2596i	0.790654	−	0.790654i
$724$		0			0
$725$	−44.4339	−	23.7835i	−1.65023	−	0.883298i
$726$		0			0
$727$	−10.2654	+	10.2654i	−0.380722	+	0.380722i	−0.871362	−	0.490641i	$-0.836763\pi$
$727$	−10.2654	+	10.2654i	−0.380722	+	0.380722i	0.490641	+	0.871362i	$0.336763\pi$
$728$		0			0
$729$			15.6545i			0.579798i
$730$		0			0
$731$		−	11.7829i		−	0.435806i
$732$		0			0
$733$	34.1656	+	34.1656i	1.26194	+	1.26194i	0.950154	+	0.311781i	$0.100926\pi$
$733$	34.1656	+	34.1656i	1.26194	+	1.26194i	0.311781	+	0.950154i	$0.399074\pi$
$734$		0			0
$735$	−40.6533	−	25.3115i	−1.49952	−	0.933630i
$736$		0			0
$737$	−1.98380	−	1.98380i	−0.0730742	−	0.0730742i
$738$		0			0
$739$			27.7193i			1.01967i	0.860272	+	0.509835i	$0.170293\pi$
$739$			27.7193i			1.01967i	−0.860272	+	0.509835i	$0.829707\pi$
$740$		0			0
$741$			32.3281i			1.18760i
$742$		0			0
$743$	18.8434	−	18.8434i	0.691299	−	0.691299i	−0.271219	−	0.962518i	$-0.587427\pi$
$743$	18.8434	−	18.8434i	0.691299	−	0.691299i	0.962518	+	0.271219i	$0.0874268\pi$
$744$		0			0
$745$	−5.85694	−	9.77814i	−0.214582	−	0.358243i
$746$		0			0
$747$	−7.30382	+	7.30382i	−0.267233	+	0.267233i
$748$		0			0
$749$	20.3035	+	27.8574i	0.741875	+	1.01789i
$750$		0			0
$751$	−3.96211			−0.144580			−0.0722898	−	0.997384i	$-0.523031\pi$
$751$	−3.96211			−0.144580			−0.0722898	+	0.997384i	$0.523031\pi$
$752$		0			0
$753$	−1.56451	+	1.56451i	−0.0570139	+	0.0570139i
$754$		0			0
$755$	−25.7435	+	15.4199i	−0.936901	+	0.561187i
$756$		0			0
$757$	−12.4177	−	12.4177i	−0.451328	−	0.451328i	0.444467	−	0.895795i	$-0.353393\pi$
$757$	−12.4177	−	12.4177i	−0.451328	−	0.451328i	−0.895795	+	0.444467i	$0.853393\pi$
$758$		0			0
$759$	−7.18096			−0.260652
$760$		0			0
$761$			18.1007i			0.656148i	0.944652	+	0.328074i	$0.106400\pi$
$761$			18.1007i			0.656148i	−0.944652	+	0.328074i	$0.893600\pi$
$762$		0			0
$763$	−2.46607	+	15.7228i	−0.0892779	+	0.569204i
$764$		0			0
$765$	−49.1858	−	12.3355i	−1.77832	−	0.445993i
$766$		0			0
$767$	−37.0666	−	37.0666i	−1.33840	−	1.33840i
$768$		0			0
$769$	21.5274			0.776299			0.388149	−	0.921596i	$-0.373114\pi$
$769$	21.5274			0.776299			0.388149	+	0.921596i	$0.373114\pi$
$770$		0			0
$771$	−27.3480			−0.984915
$772$		0			0
$773$	−12.4318	−	12.4318i	−0.447143	−	0.447143i	0.447261	−	0.894403i	$-0.352400\pi$
$773$	−12.4318	−	12.4318i	−0.447143	−	0.447143i	−0.894403	+	0.447261i	$0.852400\pi$
$774$		0			0
$775$	−16.0172	−	8.57332i	−0.575355	−	0.307963i
$776$		0			0
$777$	12.9491	−	82.5587i	0.464546	−	2.96178i
$778$		0			0
$779$			6.45805i			0.231384i
$780$		0			0
$781$	−2.33910			−0.0836997
$782$		0			0
$783$	73.2843	+	73.2843i	2.61897	+	2.61897i
$784$		0			0
$785$	−2.10342	+	8.38701i	−0.0750743	+	0.299345i
$786$		0			0
$787$	−23.9985	+	23.9985i	−0.855455	+	0.855455i	−0.990799	−	0.135343i	$-0.956786\pi$
$787$	−23.9985	+	23.9985i	−0.855455	+	0.855455i	0.135343	+	0.990799i	$0.456786\pi$
$788$		0			0
$789$	26.9454			0.959283
$790$		0			0
$791$	−10.7767	+	7.85444i	−0.383174	+	0.279272i
$792$		0			0
$793$	10.9225	−	10.9225i	0.387868	−	0.387868i
$794$		0			0
$795$	−53.9815	+	32.3340i	−1.91453	+	1.14677i
$796$		0			0
$797$	−14.6111	+	14.6111i	−0.517552	+	0.517552i	−0.916830	−	0.399278i	$-0.869261\pi$
$797$	−14.6111	+	14.6111i	−0.517552	+	0.517552i	0.399278	+	0.916830i	$0.369261\pi$
$798$		0			0
$799$			20.6688i			0.731210i
$800$		0			0
$801$		−	89.6525i		−	3.16772i
$802$		0			0
$803$	3.93087	+	3.93087i	0.138718	+	0.138718i
$804$		0			0
$805$	−6.81221	+	16.0539i	−0.240099	+	0.565825i
$806$		0			0
$807$	−6.75173	−	6.75173i	−0.237672	−	0.237672i
$808$		0			0
$809$			10.5234i			0.369983i	0.982740	+	0.184991i	$0.0592258\pi$
$809$			10.5234i			0.369983i	−0.982740	+	0.184991i	$0.940774\pi$
$810$		0			0
$811$			30.8109i			1.08192i	0.841050	+	0.540958i	$0.181938\pi$
$811$			30.8109i			1.08192i	−0.841050	+	0.540958i	$0.818062\pi$
$812$		0			0
$813$	11.1952	−	11.1952i	0.392633	−	0.392633i
$814$		0			0
$815$	11.9213	−	47.5340i	0.417585	−	1.66504i
$816$		0			0
$817$	5.37024	−	5.37024i	0.187881	−	0.187881i
$818$		0			0
$819$	62.5327	−	45.5761i	2.18507	−	1.59256i
$820$		0			0
$821$	5.63075			0.196515			0.0982573	−	0.995161i	$-0.468673\pi$
$821$	5.63075			0.196515			0.0982573	+	0.995161i	$0.468673\pi$
$822$		0			0
$823$	−32.8777	+	32.8777i	−1.14604	+	1.14604i	−0.158720	+	0.987324i	$0.550737\pi$
$823$	−32.8777	+	32.8777i	−1.14604	+	1.14604i	−0.987324	+	0.158720i	$0.949263\pi$
$824$		0			0
$825$	11.6578	−	3.52896i	0.405871	−	0.122863i
$826$		0			0
$827$	−4.06998	−	4.06998i	−0.141527	−	0.141527i	0.632794	−	0.774321i	$-0.281908\pi$
$827$	−4.06998	−	4.06998i	−0.141527	−	0.141527i	−0.774321	+	0.632794i	$0.781908\pi$
$828$		0			0
$829$	−25.8830			−0.898955			−0.449478	−	0.893292i	$-0.648390\pi$
$829$	−25.8830			−0.898955			−0.449478	+	0.893292i	$0.648390\pi$
$830$		0			0
$831$			81.8922i			2.84081i
$832$		0			0
$833$	22.2030	−	11.3970i	0.769287	−	0.394883i
$834$		0			0
$835$	3.64844	−	14.5475i	0.126259	−	0.503437i
$836$		0			0
$837$	26.4170	+	26.4170i	0.913105	+	0.913105i
$838$		0			0
$839$	17.6763			0.610253			0.305126	−	0.952312i	$-0.401301\pi$
$839$	17.6763			0.610253			0.305126	+	0.952312i	$0.401301\pi$
$840$		0			0
$841$	−72.6011			−2.50348
$842$		0			0
$843$	−22.2064	−	22.2064i	−0.764830	−	0.764830i
$844$		0			0
$845$	−9.35522	−	15.6185i	−0.321829	−	0.537293i
$846$		0			0
$847$	27.0947	+	4.24973i	0.930985	+	0.146022i
$848$		0			0
$849$			100.863i			3.46162i
$850$		0			0
$851$	−30.4324			−1.04321
$852$		0			0
$853$	−40.0308	−	40.0308i	−1.37063	−	1.37063i	−0.859511	−	0.511117i	$-0.829232\pi$
$853$	−40.0308	−	40.0308i	−1.37063	−	1.37063i	−0.511117	−	0.859511i	$-0.670768\pi$
$854$		0			0
$855$	−16.7951	−	28.0393i	−0.574379	−	0.958923i
$856$		0			0
$857$	−30.8266	+	30.8266i	−1.05302	+	1.05302i	−0.0545034	+	0.998514i	$0.517358\pi$
$857$	−30.8266	+	30.8266i	−1.05302	+	1.05302i	−0.998514	+	0.0545034i	$0.982642\pi$
$858$		0			0
$859$	46.9929			1.60338			0.801689	−	0.597741i	$-0.203935\pi$
$859$	46.9929			1.60338			0.801689	+	0.597741i	$0.203935\pi$
$860$		0			0
$861$	18.3837	−	13.3987i	0.626514	−	0.456626i
$862$		0			0
$863$	−22.4965	+	22.4965i	−0.765789	+	0.765789i	−0.977362	−	0.211573i	$-0.932141\pi$
$863$	−22.4965	+	22.4965i	−0.765789	+	0.765789i	0.211573	+	0.977362i	$0.432141\pi$
$864$		0			0
$865$	32.4870	+	8.14758i	1.10459	+	0.277026i
$866$		0			0
$867$	−9.27776	+	9.27776i	−0.315089	+	0.315089i
$868$		0			0
$869$		−	5.20106i		−	0.176434i
$870$		0			0
$871$		−	16.2015i		−	0.548966i
$872$		0			0
$873$	27.3944	+	27.3944i	0.927160	+	0.927160i
$874$		0			0
$875$	3.16971	−	29.4101i	0.107156	−	0.994242i
$876$		0			0
$877$	19.0005	+	19.0005i	0.641602	+	0.641602i	0.950949	−	0.309347i	$-0.100110\pi$
$877$	19.0005	+	19.0005i	0.641602	+	0.641602i	−0.309347	+	0.950949i	$0.600110\pi$
$878$		0			0
$879$		−	32.6100i		−	1.09991i
$880$		0			0
$881$			18.8855i			0.636268i	0.948046	+	0.318134i	$0.103056\pi$
$881$			18.8855i			0.636268i	−0.948046	+	0.318134i	$0.896944\pi$
$882$		0			0
$883$	2.94189	−	2.94189i	0.0990023	−	0.0990023i	−0.655871	−	0.754873i	$-0.727698\pi$
$883$	2.94189	−	2.94189i	0.0990023	−	0.0990023i	0.754873	+	0.655871i	$0.227698\pi$
$884$		0			0
$885$	75.6515	+	18.9730i	2.54300	+	0.637771i
$886$		0			0
$887$	−0.662275	+	0.662275i	−0.0222370	+	0.0222370i	−0.718138	−	0.695901i	$-0.755005\pi$
$887$	−0.662275	+	0.662275i	−0.0222370	+	0.0222370i	0.695901	+	0.718138i	$0.255005\pi$
$888$		0			0
$889$	−31.4300	−	43.1235i	−1.05413	−	1.44632i
$890$		0			0
$891$	−9.85394			−0.330120
$892$		0			0
$893$	−9.42013	+	9.42013i	−0.315233	+	0.315233i
$894$		0			0
$895$	20.7834	+	34.6978i	0.694712	+	1.15982i
$896$		0			0
$897$	−29.3230	−	29.3230i	−0.979068	−	0.979068i
$898$		0			0
$899$	−36.6244			−1.22149
$900$		0			0
$901$		−	32.7929i		−	1.09249i
$902$		0			0
$903$	−26.4289	−	4.14529i	−0.879498	−	0.137947i
$904$		0			0
$905$	16.1191	+	26.9109i	0.535818	+	0.894547i
$906$		0			0
$907$	32.0100	+	32.0100i	1.06288	+	1.06288i	0.997886	+	0.0649902i	$0.0207016\pi$
$907$	32.0100	+	32.0100i	1.06288	+	1.06288i	0.0649902	+	0.997886i	$0.479298\pi$
$908$		0			0
$909$	−74.0698			−2.45674
$910$		0			0
$911$	−42.6612			−1.41343			−0.706714	−	0.707499i	$-0.749823\pi$
$911$	−42.6612			−1.41343			−0.706714	+	0.707499i	$0.749823\pi$
$912$		0			0
$913$	0.914280	+	0.914280i	0.0302583	+	0.0302583i
$914$		0			0
$915$	−5.59080	+	22.2923i	−0.184826	+	0.736961i
$916$		0			0
$917$	−3.37869	+	21.5413i	−0.111574	+	0.711357i
$918$		0			0
$919$		−	30.3500i		−	1.00115i	−0.865692	−	0.500577i	$-0.833121\pi$
$919$		−	30.3500i		−	1.00115i	0.865692	−	0.500577i	$-0.166879\pi$
$920$		0			0
$921$	−22.0505			−0.726589
$922$		0			0
$923$	−9.55160	−	9.55160i	−0.314395	−	0.314395i
$924$		0			0
$925$	49.4048	−	14.9555i	1.62442	−	0.491734i
$926$		0			0
$927$	22.5345	−	22.5345i	0.740130	−	0.740130i
$928$		0			0
$929$	−16.7434			−0.549334			−0.274667	−	0.961539i	$-0.588568\pi$
$929$	−16.7434			−0.549334			−0.274667	+	0.961539i	$0.588568\pi$
$930$		0			0
$931$	15.3137	+	4.92498i	0.501887	+	0.161410i
$932$		0			0
$933$	19.2113	−	19.2113i	0.628951	−	0.628951i
$934$		0			0
$935$	−1.54414	+	6.15699i	−0.0504989	+	0.201355i
$936$		0			0
$937$	−31.0760	+	31.0760i	−1.01521	+	1.01521i	−0.0153259	+	0.999883i	$0.504879\pi$
$937$	−31.0760	+	31.0760i	−1.01521	+	1.01521i	−0.999883	+	0.0153259i	$0.995121\pi$
$938$		0			0
$939$		−	28.1269i		−	0.917886i
$940$		0			0
$941$			45.0141i			1.46742i	0.679464	+	0.733709i	$0.262212\pi$
$941$			45.0141i			1.46742i	−0.679464	+	0.733709i	$0.737788\pi$
$942$		0			0
$943$	−5.85773	−	5.85773i	−0.190754	−	0.190754i
$944$		0			0
$945$	−23.7611	+	55.9963i	−0.772949	+	1.82156i
$946$		0			0
$947$	18.7267	+	18.7267i	0.608535	+	0.608535i	0.942563	−	0.334028i	$-0.108408\pi$
$947$	18.7267	+	18.7267i	0.608535	+	0.608535i	−0.334028	+	0.942563i	$0.608408\pi$
$948$		0			0
$949$			32.1030i			1.04211i
$950$		0			0
$951$			16.7773i			0.544042i
$952$		0			0
$953$	−3.06721	+	3.06721i	−0.0993566	+	0.0993566i	−0.755038	−	0.655681i	$-0.772382\pi$
$953$	−3.06721	+	3.06721i	−0.0993566	+	0.0993566i	0.655681	+	0.755038i	$0.272382\pi$
$954$		0			0
$955$	−10.3411	+	6.19415i	−0.334630	+	0.200438i
$956$		0			0
$957$	17.3627	−	17.3627i	0.561258	−	0.561258i
$958$		0			0
$959$	−12.7739	−	17.5264i	−0.412490	−	0.565956i
$960$		0			0
$961$	17.7979			0.574126
$962$		0			0
$963$	58.5997	−	58.5997i	1.88835	−	1.88835i
$964$		0			0
$965$	2.81553	−	11.2264i	0.0906351	−	0.361391i
$966$		0			0
$967$	−20.0904	−	20.0904i	−0.646063	−	0.646063i	0.305976	−	0.952039i	$-0.401017\pi$
$967$	−20.0904	−	20.0904i	−0.646063	−	0.646063i	−0.952039	+	0.305976i	$0.901017\pi$
$968$		0			0
$969$	25.0672			0.805276
$970$		0			0
$971$			43.8425i			1.40697i	0.710708	+	0.703487i	$0.248375\pi$
$971$			43.8425i			1.40697i	−0.710708	+	0.703487i	$0.751625\pi$
$972$		0			0
$973$	20.6441	+	3.23797i	0.661820	+	0.103804i
$974$		0			0
$975$	62.0142	+	33.1935i	1.98604	+	1.06304i
$976$		0			0
$977$	25.5360	+	25.5360i	0.816968	+	0.816968i	0.985667	−	0.168700i	$-0.0539568\pi$
$977$	25.5360	+	25.5360i	0.816968	+	0.816968i	−0.168700	+	0.985667i	$0.553957\pi$
$978$		0			0
$979$	−11.2225			−0.358674
$980$		0			0
$981$	38.2613			1.22159
$982$		0			0
$983$	−13.5331	−	13.5331i	−0.431639	−	0.431639i	0.457547	−	0.889186i	$-0.348728\pi$
$983$	−13.5331	−	13.5331i	−0.431639	−	0.431639i	−0.889186	+	0.457547i	$0.848728\pi$
$984$		0			0
$985$	28.1068	+	7.04904i	0.895556	+	0.224601i
$986$		0			0
$987$	46.3598	+	7.27140i	1.47565	+	0.231451i
$988$		0			0
$989$			9.74209i			0.309780i
$990$		0			0
$991$	−16.6536			−0.529019			−0.264510	−	0.964383i	$-0.585210\pi$
$991$	−16.6536			−0.529019			−0.264510	+	0.964383i	$0.585210\pi$
$992$		0			0
$993$	14.1984	+	14.1984i	0.450573	+	0.450573i
$994$		0			0
$995$	30.5535	−	18.3010i	0.968611	−	0.580182i
$996$		0			0
$997$	31.7663	−	31.7663i	1.00605	−	1.00605i	0.00606773	−	0.999982i	$-0.498069\pi$
$997$	31.7663	−	31.7663i	1.00605	−	1.00605i	0.999982	−	0.00606773i	$-0.00193143\pi$
$998$		0			0
$999$	−106.149			−3.35840

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.x.a.97.11	yes	24
4.3	odd	2		560.2.bj.d.97.2		24
5.2	odd	4		1400.2.x.b.993.11		24
5.3	odd	4	inner	280.2.x.a.153.2	yes	24
5.4	even	2		1400.2.x.b.657.2		24
7.6	odd	2	inner	280.2.x.a.97.2	✓	24
20.3	even	4		560.2.bj.d.433.11		24
28.27	even	2		560.2.bj.d.97.11		24
35.13	even	4	inner	280.2.x.a.153.11	yes	24
35.27	even	4		1400.2.x.b.993.2		24
35.34	odd	2		1400.2.x.b.657.11		24
140.83	odd	4		560.2.bj.d.433.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.x.a.97.2	✓	24	7.6	odd	2	inner
280.2.x.a.97.11	yes	24	1.1	even	1	trivial
280.2.x.a.153.2	yes	24	5.3	odd	4	inner
280.2.x.a.153.11	yes	24	35.13	even	4	inner
560.2.bj.d.97.2		24	4.3	odd	2
560.2.bj.d.97.11		24	28.27	even	2
560.2.bj.d.433.2		24	140.83	odd	4
560.2.bj.d.433.11		24	20.3	even	4
1400.2.x.b.657.2		24	5.4	even	2
1400.2.x.b.657.11		24	35.34	odd	2
1400.2.x.b.993.2		24	35.27	even	4
1400.2.x.b.993.11		24	5.2	odd	4

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.16341 + 2.16341i) q^{3} +(-1.91827 + 1.14901i) q^{5} +(-2.61380 - 0.409966i) q^{7} +6.36066i q^{9} +O(q^{10})\)	\(q+(2.16341 + 2.16341i) q^{3} +(-1.91827 + 1.14901i) q^{5} +(-2.61380 - 0.409966i) q^{7} +6.36066i q^{9} +0.796216 q^{11} +(3.25130 + 3.25130i) q^{13} +(-6.63578 - 1.66422i) q^{15} +(2.52106 - 2.52106i) q^{17} +2.29803 q^{19} +(-4.76778 - 6.54163i) q^{21} +(-2.08441 + 2.08441i) q^{23} +(2.35954 - 4.40824i) q^{25} +(-7.27046 + 7.27046i) q^{27} -10.0797i q^{29} -3.63347i q^{31} +(1.72254 + 1.72254i) q^{33} +(5.48503 - 2.21686i) q^{35} +(7.30001 + 7.30001i) q^{37} +14.0678i q^{39} +2.81026i q^{41} +(2.33689 - 2.33689i) q^{43} +(-7.30847 - 12.2015i) q^{45} +(-4.09923 + 4.09923i) q^{47} +(6.66386 + 2.14314i) q^{49} +10.9082 q^{51} +(6.50379 - 6.50379i) q^{53} +(-1.52736 + 0.914862i) q^{55} +(4.97156 + 4.97156i) q^{57} -11.4005 q^{59} -3.35941i q^{61} +(2.60765 - 16.6255i) q^{63} +(-9.97268 - 2.50110i) q^{65} +(-2.49153 - 2.49153i) q^{67} -9.01885 q^{69} -2.93777 q^{71} +(4.93694 + 4.93694i) q^{73} +(14.6415 - 4.43217i) q^{75} +(-2.08115 - 0.326422i) q^{77} -6.53223i q^{79} -12.3760 q^{81} +(1.14828 + 1.14828i) q^{83} +(-1.93935 + 7.73282i) q^{85} +(21.8066 - 21.8066i) q^{87} -14.0949 q^{89} +(-7.16532 - 9.83117i) q^{91} +(7.86067 - 7.86067i) q^{93} +(-4.40824 + 2.64046i) q^{95} +(4.30685 - 4.30685i) q^{97} +5.06446i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{7}+O(q^{10}) \) 24 * q + 4 * q^7	\( 24 q + 4 q^{7} + 8 q^{11} - 8 q^{15} + 16 q^{21} - 32 q^{23} + 8 q^{25} + 12 q^{35} - 8 q^{37} + 16 q^{43} - 24 q^{51} - 16 q^{53} + 20 q^{63} - 48 q^{65} - 32 q^{67} - 32 q^{71} - 40 q^{77} - 72 q^{81} + 16 q^{85} - 64 q^{91} + 72 q^{93} - 24 q^{95}+O(q^{100}) \) 24 * q + 4 * q^7 + 8 * q^11 - 8 * q^15 + 16 * q^21 - 32 * q^23 + 8 * q^25 + 12 * q^35 - 8 * q^37 + 16 * q^43 - 24 * q^51 - 16 * q^53 + 20 * q^63 - 48 * q^65 - 32 * q^67 - 32 * q^71 - 40 * q^77 - 72 * q^81 + 16 * q^85 - 64 * q^91 + 72 * q^93 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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