LMFDB - Embedded newform 735.2.j.h.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(197,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("735.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.j (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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.1
Character	$\chi$	$=$	735.197
Dual form			735.2.j.h.638.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79963 + 1.79963i) q^{2} +(1.66094 + 0.491204i) q^{3} -4.47734i q^{4} +(-1.87996 + 1.21069i) q^{5} +(-3.87306 + 2.10509i) q^{6} +(4.45829 + 4.45829i) q^{8} +(2.51744 + 1.63172i) q^{9} +O(q^{10})$	\(q+(-1.79963 + 1.79963i) q^{2} +(1.66094 + 0.491204i) q^{3} -4.47734i q^{4} +(-1.87996 + 1.21069i) q^{5} +(-3.87306 + 2.10509i) q^{6} +(4.45829 + 4.45829i) q^{8} +(2.51744 + 1.63172i) q^{9} +(1.20443 - 5.56202i) q^{10} -1.56870i q^{11} +(2.19929 - 7.43658i) q^{12} +(-2.21881 + 2.21881i) q^{13} +(-3.71719 + 1.08744i) q^{15} -7.09187 q^{16} +(-3.60725 + 3.60725i) q^{17} +(-7.46695 + 1.59396i) q^{18} +1.68040i q^{19} +(5.42066 + 8.41719i) q^{20} +(2.82308 + 2.82308i) q^{22} +(0.995850 + 0.995850i) q^{23} +(5.21502 + 9.59488i) q^{24} +(2.06847 - 4.55208i) q^{25} -7.98606i q^{26} +(3.37980 + 3.94676i) q^{27} -8.91955 q^{29} +(4.73258 - 8.64655i) q^{30} -2.74834 q^{31} +(3.84616 - 3.84616i) q^{32} +(0.770553 - 2.60552i) q^{33} -12.9834i q^{34} +(7.30576 - 11.2714i) q^{36} +(0.440360 + 0.440360i) q^{37} +(-3.02410 - 3.02410i) q^{38} +(-4.77519 + 2.59542i) q^{39} +(-13.7790 - 2.98379i) q^{40} -6.44292i q^{41} +(-5.47734 + 5.47734i) q^{43} -7.02360 q^{44} +(-6.70817 - 0.0197326i) q^{45} -3.58432 q^{46} +(-3.69358 + 3.69358i) q^{47} +(-11.7792 - 3.48356i) q^{48} +(4.46958 + 11.9145i) q^{50} +(-7.76331 + 4.21952i) q^{51} +(9.93435 + 9.93435i) q^{52} +(2.83358 + 2.83358i) q^{53} +(-13.1851 - 1.02033i) q^{54} +(1.89921 + 2.94909i) q^{55} +(-0.825420 + 2.79104i) q^{57} +(16.0519 - 16.0519i) q^{58} -5.54871 q^{59} +(4.86882 + 16.6431i) q^{60} -7.40665 q^{61} +(4.94599 - 4.94599i) q^{62} -0.340400i q^{64} +(1.48498 - 6.85754i) q^{65} +(3.30226 + 6.07568i) q^{66} +(-3.75240 - 3.75240i) q^{67} +(16.1509 + 16.1509i) q^{68} +(1.16488 + 2.14321i) q^{69} -3.61943i q^{71} +(3.94878 + 18.4981i) q^{72} +(5.89737 - 5.89737i) q^{73} -1.58497 q^{74} +(5.67160 - 6.54469i) q^{75} +7.52372 q^{76} +(3.92279 - 13.2644i) q^{78} +17.0572i q^{79} +(13.3324 - 8.58604i) q^{80} +(3.67497 + 8.21551i) q^{81} +(11.5949 + 11.5949i) q^{82} +(-3.21312 - 3.21312i) q^{83} +(2.41421 - 11.1487i) q^{85} -19.7144i q^{86} +(-14.8148 - 4.38132i) q^{87} +(6.99372 - 6.99372i) q^{88} +9.40273 q^{89} +(12.1077 - 12.0367i) q^{90} +(4.45876 - 4.45876i) q^{92} +(-4.56482 - 1.35000i) q^{93} -13.2941i q^{94} +(-2.03444 - 3.15908i) q^{95} +(8.27749 - 4.49899i) q^{96} +(-4.39640 - 4.39640i) q^{97} +(2.55968 - 3.94911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3}+O(q^{10}) $ 24 * q + 4 * q^3	$ 24 q + 4 q^{3} + 16 q^{10} - 16 q^{12} + 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 8 q^{22} - 16 q^{25} + 16 q^{27} + 20 q^{30} - 28 q^{33} + 16 q^{36} - 16 q^{37} - 64 q^{40} - 40 q^{43} - 20 q^{45} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} - 32 q^{61} + 16 q^{66} + 24 q^{67} - 8 q^{72} - 32 q^{73} + 60 q^{75} - 32 q^{76} + 60 q^{78} + 52 q^{81} + 80 q^{82} + 24 q^{85} - 4 q^{87} + 96 q^{88} + 24 q^{90} - 76 q^{93} + 96 q^{96} - 24 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 + 16 * q^10 - 16 * q^12 + 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 8 * q^22 - 16 * q^25 + 16 * q^27 + 20 * q^30 - 28 * q^33 + 16 * q^36 - 16 * q^37 - 64 * q^40 - 40 * q^43 - 20 * q^45 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 - 32 * q^61 + 16 * q^66 + 24 * q^67 - 8 * q^72 - 32 * q^73 + 60 * q^75 - 32 * q^76 + 60 * q^78 + 52 * q^81 + 80 * q^82 + 24 * q^85 - 4 * q^87 + 96 * q^88 + 24 * q^90 - 76 * q^93 + 96 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.79963	+	1.79963i	−1.27253	+	1.27253i	−0.327775	+	0.944756i	$0.606299\pi$
$2$	−1.79963	+	1.79963i	−1.27253	+	1.27253i	−0.944756	+	0.327775i	$0.893701\pi$
$3$	1.66094	+	0.491204i	0.958944	+	0.283597i
$3$	1.66094	+	0.491204i	0.958944	+	0.283597i
$4$		−	4.47734i		−	2.23867i
$5$	−1.87996	+	1.21069i	−0.840742	+	0.541436i
$5$	−1.87996	+	1.21069i	−0.840742	+	0.541436i
$6$	−3.87306	+	2.10509i	−1.58117	+	0.859399i
$7$		0			0
$7$		0			0
$8$	4.45829	+	4.45829i	1.57624	+	1.57624i
$9$	2.51744	+	1.63172i	0.839146	+	0.543907i
$10$	1.20443	−	5.56202i	0.380876	−	1.75886i
$11$		−	1.56870i		−	0.472981i	−0.971634	−	0.236491i	$-0.924003\pi$
$11$		−	1.56870i		−	0.472981i	0.971634	−	0.236491i	$-0.0759973\pi$
$12$	2.19929	−	7.43658i	0.634880	−	2.14676i
$13$	−2.21881	+	2.21881i	−0.615386	+	0.615386i	−0.944345	−	0.328958i	$-0.893303\pi$
$13$	−2.21881	+	2.21881i	−0.615386	+	0.615386i	0.328958	+	0.944345i	$0.393303\pi$
$14$		0			0
$15$	−3.71719	+	1.08744i	−0.959774	+	0.280775i
$16$	−7.09187			−1.77297
$17$	−3.60725	+	3.60725i	−0.874886	+	0.874886i	−0.993000	−	0.118114i	$-0.962315\pi$
$17$	−3.60725	+	3.60725i	−0.874886	+	0.874886i	0.118114	+	0.993000i	$0.462315\pi$
$18$	−7.46695	+	1.59396i	−1.75998	+	0.375700i
$19$			1.68040i			0.385510i	0.981247	+	0.192755i	$0.0617423\pi$
$19$			1.68040i			0.385510i	−0.981247	+	0.192755i	$0.938258\pi$
$20$	5.42066	+	8.41719i	1.21210	+	1.88214i
$21$		0			0
$22$	2.82308	+	2.82308i	0.601883	+	0.601883i
$23$	0.995850	+	0.995850i	0.207649	+	0.207649i	0.803268	−	0.595618i	$-0.203093\pi$
$23$	0.995850	+	0.995850i	0.207649	+	0.207649i	−0.595618	+	0.803268i	$0.703093\pi$
$24$	5.21502	+	9.59488i	1.06451	+	1.95855i
$25$	2.06847	−	4.55208i	0.413694	−	0.910416i
$26$		−	7.98606i		−	1.56620i
$27$	3.37980	+	3.94676i	0.650443	+	0.759555i
$28$		0			0
$29$	−8.91955			−1.65632			−0.828159	−	0.560493i	$-0.810612\pi$
$29$	−8.91955			−1.65632			−0.828159	+	0.560493i	$0.810612\pi$
$30$	4.73258	−	8.64655i	0.864047	−	1.57864i
$31$	−2.74834			−0.493616			−0.246808	−	0.969064i	$-0.579382\pi$
$31$	−2.74834			−0.493616			−0.246808	+	0.969064i	$0.579382\pi$
$32$	3.84616	−	3.84616i	0.679912	−	0.679912i
$33$	0.770553	−	2.60552i	0.134136	−	0.453562i
$34$		−	12.9834i		−	2.22664i
$35$		0			0
$36$	7.30576	−	11.2714i	1.21763	−	1.87857i
$37$	0.440360	+	0.440360i	0.0723947	+	0.0723947i	0.742377	−	0.669982i	$-0.233698\pi$
$37$	0.440360	+	0.440360i	0.0723947	+	0.0723947i	−0.669982	+	0.742377i	$0.733698\pi$
$38$	−3.02410	−	3.02410i	−0.490574	−	0.490574i
$39$	−4.77519	+	2.59542i	−0.764643	+	0.415599i
$40$	−13.7790	−	2.98379i	−2.17865	−	0.471778i
$41$		−	6.44292i		−	1.00622i	−0.864224	−	0.503108i	$-0.832190\pi$
$41$		−	6.44292i		−	1.00622i	0.864224	−	0.503108i	$-0.167810\pi$
$42$		0			0
$43$	−5.47734	+	5.47734i	−0.835286	+	0.835286i	−0.988234	−	0.152948i	$-0.951123\pi$
$43$	−5.47734	+	5.47734i	−0.835286	+	0.835286i	0.152948	+	0.988234i	$0.451123\pi$
$44$	−7.02360			−1.05885
$45$	−6.70817	−	0.0197326i	−0.999996	−	0.00294156i
$46$	−3.58432			−0.528480
$47$	−3.69358	+	3.69358i	−0.538763	+	0.538763i	−0.923166	−	0.384402i	$-0.874408\pi$
$47$	−3.69358	+	3.69358i	−0.538763	+	0.538763i	0.384402	+	0.923166i	$0.374408\pi$
$48$	−11.7792	−	3.48356i	−1.70018	−	0.502808i
$49$		0			0
$50$	4.46958	+	11.9145i	0.632095	+	1.68497i
$51$	−7.76331	+	4.21952i	−1.08708	+	0.590851i
$52$	9.93435	+	9.93435i	1.37765	+	1.37765i
$53$	2.83358	+	2.83358i	0.389222	+	0.389222i	0.874410	−	0.485188i	$-0.161249\pi$
$53$	2.83358	+	2.83358i	0.389222	+	0.389222i	−0.485188	+	0.874410i	$0.661249\pi$
$54$	−13.1851	−	1.02033i	−1.79427	−	0.138849i
$55$	1.89921	+	2.94909i	0.256089	+	0.397655i
$56$		0			0
$57$	−0.825420	+	2.79104i	−0.109330	+	0.369683i
$58$	16.0519	−	16.0519i	2.10772	−	2.10772i
$59$	−5.54871			−0.722381			−0.361191	−	0.932492i	$-0.617630\pi$
$59$	−5.54871			−0.722381			−0.361191	+	0.932492i	$0.617630\pi$
$60$	4.86882	+	16.6431i	0.628562	+	2.14861i
$61$	−7.40665			−0.948325			−0.474162	−	0.880437i	$-0.657249\pi$
$61$	−7.40665			−0.948325			−0.474162	+	0.880437i	$0.657249\pi$
$62$	4.94599	−	4.94599i	0.628141	−	0.628141i
$63$		0			0
$64$		−	0.340400i		−	0.0425500i
$65$	1.48498	−	6.85754i	0.184189	−	0.850574i
$66$	3.30226	+	6.07568i	0.406480	+	0.747864i
$67$	−3.75240	−	3.75240i	−0.458429	−	0.458429i	0.439711	−	0.898139i	$-0.355081\pi$
$67$	−3.75240	−	3.75240i	−0.458429	−	0.458429i	−0.898139	+	0.439711i	$0.855081\pi$
$68$	16.1509	+	16.1509i	1.95858	+	1.95858i
$69$	1.16488	+	2.14321i	0.140235	+	0.258012i
$70$		0			0
$71$		−	3.61943i		−	0.429548i	−0.976664	−	0.214774i	$-0.931099\pi$
$71$		−	3.61943i		−	0.429548i	0.976664	−	0.214774i	$-0.0689015\pi$
$72$	3.94878	+	18.4981i	0.465368	+	2.18003i
$73$	5.89737	−	5.89737i	0.690235	−	0.690235i	−0.272049	−	0.962284i	$-0.587701\pi$
$73$	5.89737	−	5.89737i	0.690235	−	0.690235i	0.962284	+	0.272049i	$0.0877011\pi$
$74$	−1.58497			−0.184249
$75$	5.67160	−	6.54469i	0.654900	−	0.755715i
$76$	7.52372			0.863030
$77$		0			0
$78$	3.92279	−	13.2644i	0.444168	−	1.50189i
$79$			17.0572i			1.91909i	0.281558	+	0.959544i	$0.409149\pi$
$79$			17.0572i			1.91909i	−0.281558	+	0.959544i	$0.590851\pi$
$80$	13.3324	−	8.58604i	1.49061	−	0.959949i
$81$	3.67497	+	8.21551i	0.408330	+	0.912834i
$82$	11.5949	+	11.5949i	1.28044	+	1.28044i
$83$	−3.21312	−	3.21312i	−0.352686	−	0.352686i	0.508422	−	0.861108i	$-0.330229\pi$
$83$	−3.21312	−	3.21312i	−0.352686	−	0.352686i	−0.861108	+	0.508422i	$0.830229\pi$
$84$		0			0
$85$	2.41421	−	11.1487i	0.261858	−	1.20925i
$86$		−	19.7144i		−	2.12585i
$87$	−14.8148	−	4.38132i	−1.58832	−	0.469727i
$88$	6.99372	−	6.99372i	0.745533	−	0.745533i
$89$	9.40273			0.996688			0.498344	−	0.866979i	$-0.333942\pi$
$89$	9.40273			0.996688			0.498344	+	0.866979i	$0.333942\pi$
$90$	12.1077	−	12.0367i	1.27627	−	1.26878i
$91$		0			0
$92$	4.45876	−	4.45876i	0.464858	−	0.464858i
$93$	−4.56482	−	1.35000i	−0.473350	−	0.139988i
$94$		−	13.2941i		−	1.37119i
$95$	−2.03444	−	3.15908i	−0.208729	−	0.324115i
$96$	8.27749	−	4.49899i	0.844818	−	0.459176i
$97$	−4.39640	−	4.39640i	−0.446386	−	0.446386i	0.447765	−	0.894151i	$-0.352220\pi$
$97$	−4.39640	−	4.39640i	−0.446386	−	0.446386i	−0.894151	+	0.447765i	$0.852220\pi$
$98$		0			0
$99$	2.55968	−	3.94911i	0.257258	−	0.396900i
$100$	−20.3812	−	9.26123i	−2.03812	−	0.926123i
$101$		−	1.01132i		−	0.100630i	−0.998733	−	0.0503152i	$-0.983977\pi$
$101$		−	1.01132i		−	0.100630i	0.998733	−	0.0503152i	$-0.0160226\pi$
$102$	6.37751	−	21.5647i	0.631468	−	2.13522i
$103$	4.03058	−	4.03058i	0.397145	−	0.397145i	−0.480080	−	0.877225i	$-0.659392\pi$
$103$	4.03058	−	4.03058i	0.397145	−	0.397145i	0.877225	+	0.480080i	$0.159392\pi$
$104$	−19.7842			−1.94000
$105$		0			0
$106$	−10.1988			−0.990593
$107$	2.81760	−	2.81760i	0.272388	−	0.272388i	−0.557673	−	0.830061i	$-0.688306\pi$
$107$	2.81760	−	2.81760i	0.272388	−	0.272388i	0.830061	+	0.557673i	$0.188306\pi$
$108$	17.6710	−	15.1325i	1.70039	−	1.45613i
$109$		−	6.42246i		−	0.615160i	−0.951522	−	0.307580i	$-0.900481\pi$
$109$		−	6.42246i		−	0.615160i	0.951522	−	0.307580i	$-0.0995192\pi$
$110$	−8.72514	−	1.88940i	−0.831910	−	0.180147i
$111$	0.515104	+	0.947718i	0.0488915	+	0.0899534i
$112$		0			0
$113$	3.29246	+	3.29246i	0.309729	+	0.309729i	0.844804	−	0.535075i	$-0.179717\pi$
$113$	3.29246	+	3.29246i	0.309729	+	0.309729i	−0.535075	+	0.844804i	$0.679717\pi$
$114$	−3.53739	−	6.50830i	−0.331307	−	0.609558i
$115$	−3.07782	−	0.666490i	−0.287008	−	0.0621505i
$116$			39.9358i			3.70795i
$117$	−9.20618	+	1.96523i	−0.851112	+	0.181686i
$118$	9.98563	−	9.98563i	0.919252	−	0.919252i
$119$		0			0
$120$	−21.4204	−	11.7242i	−1.95541	−	1.07027i
$121$	8.53918			0.776289
$122$	13.3292	−	13.3292i	1.20677	−	1.20677i
$123$	3.16479	−	10.7013i	0.285360	−	0.964904i
$124$			12.3052i			1.10504i
$125$	1.62252	+	11.0620i	0.145123	+	0.989414i
$126$		0			0
$127$	14.2818	+	14.2818i	1.26730	+	1.26730i	0.947476	+	0.319826i	$0.103624\pi$
$127$	14.2818	+	14.2818i	1.26730	+	1.26730i	0.319826	+	0.947476i	$0.396376\pi$
$128$	8.30492	+	8.30492i	0.734058	+	0.734058i
$129$	−11.7880	+	6.40703i	−1.03788	+	0.564108i
$130$	9.66863	+	15.0134i	0.847995	+	1.31677i
$131$			4.89729i			0.427878i	0.976847	+	0.213939i	$0.0686294\pi$
$131$			4.89729i			0.427878i	−0.976847	+	0.213939i	$0.931371\pi$
$132$	−11.6658	−	3.45002i	−1.01538	−	0.300286i
$133$		0			0
$134$	13.5059			1.16673
$135$	−11.1322	−	3.32786i	−0.958105	−	0.286417i
$136$	−32.1643			−2.75807
$137$	−4.55880	+	4.55880i	−0.389485	+	0.389485i	−0.874504	−	0.485019i	$-0.838813\pi$
$137$	−4.55880	+	4.55880i	−0.389485	+	0.389485i	0.485019	+	0.874504i	$0.338813\pi$
$138$	−5.95334	−	1.76064i	−0.506782	−	0.149875i
$139$			10.2045i			0.865536i	0.901505	+	0.432768i	$0.142463\pi$
$139$			10.2045i			0.865536i	−0.901505	+	0.432768i	$0.857537\pi$
$140$		0			0
$141$	−7.94911	+	4.32050i	−0.669435	+	0.363852i
$142$	6.51364	+	6.51364i	0.546613	+	0.546613i
$143$	3.48065	+	3.48065i	0.291066	+	0.291066i
$144$	−17.8533	−	11.5720i	−1.48778	−	0.964329i
$145$	16.7684	−	10.7988i	1.39254	−	0.896791i
$146$			21.2262i			1.75669i
$147$		0			0
$148$	1.97164	−	1.97164i	0.162068	−	0.162068i
$149$	−0.923124			−0.0756253			−0.0378126	−	0.999285i	$-0.512039\pi$
$149$	−0.923124			−0.0756253			−0.0378126	+	0.999285i	$0.512039\pi$
$150$	1.57123	+	21.9848i	0.128291	+	1.79505i
$151$	−13.7310			−1.11741			−0.558705	−	0.829366i	$-0.688702\pi$
$151$	−13.7310			−1.11741			−0.558705	+	0.829366i	$0.688702\pi$
$152$	−7.49171	+	7.49171i	−0.607658	+	0.607658i
$153$	−14.9670	+	3.19499i	−1.21001	+	0.258300i
$154$		0			0
$155$	5.16675	−	3.32738i	0.415004	−	0.267262i
$156$	11.6205	+	21.3801i	0.930389	+	1.71178i
$157$	13.7211	+	13.7211i	1.09506	+	1.09506i	0.994979	+	0.100086i	$0.0319118\pi$
$157$	13.7211	+	13.7211i	1.09506	+	1.09506i	0.100086	+	0.994979i	$0.468088\pi$
$158$	−30.6967	−	30.6967i	−2.44210	−	2.44210i
$159$	3.31453	+	6.09826i	0.262859	+	0.483624i
$160$	−2.57411	+	11.8871i	−0.203501	+	0.939759i
$161$		0			0
$162$	−21.3985	−	8.17128i	−1.68122	−	0.641997i
$163$	6.60566	−	6.60566i	0.517395	−	0.517395i	−0.399387	−	0.916782i	$-0.630777\pi$
$163$	6.60566	−	6.60566i	0.517395	−	0.517395i	0.916782	+	0.399387i	$0.130777\pi$
$164$	−28.8471			−2.25258
$165$	1.70586	+	5.83116i	0.132801	+	0.453955i
$166$	11.5649			0.897607
$167$	3.11442	−	3.11442i	0.241001	−	0.241001i	−0.576263	−	0.817264i	$-0.695490\pi$
$167$	3.11442	−	3.11442i	0.241001	−	0.241001i	0.817264	+	0.576263i	$0.195490\pi$
$168$		0			0
$169$			3.15379i			0.242599i
$170$	15.7189	+	24.4083i	1.20558	+	1.87203i
$171$	−2.74195	+	4.23030i	−0.209682	+	0.323499i
$172$	24.5239	+	24.5239i	1.86993	+	1.86993i
$173$	−8.12870	−	8.12870i	−0.618013	−	0.618013i	0.327008	−	0.945022i	$-0.393960\pi$
$173$	−8.12870	−	8.12870i	−0.618013	−	0.618013i	−0.945022	+	0.327008i	$0.893960\pi$
$174$	34.5460	−	18.7764i	2.61892	−	1.42344i
$175$		0			0
$176$			11.1250i			0.838580i
$177$	−9.21608	−	2.72555i	−0.692723	−	0.204865i
$178$	−16.9214	+	16.9214i	−1.26832	+	1.26832i
$179$	16.5980			1.24059			0.620297	−	0.784367i	$-0.287012\pi$
$179$	16.5980			1.24059			0.620297	+	0.784367i	$0.287012\pi$
$180$	−0.0883493	+	30.0348i	−0.00658517	+	2.23866i
$181$	−11.6532			−0.866174			−0.433087	−	0.901352i	$-0.642576\pi$
$181$	−11.6532			−0.866174			−0.433087	+	0.901352i	$0.642576\pi$
$182$		0			0
$183$	−12.3020	−	3.63818i	−0.909390	−	0.268942i
$184$			8.87958i			0.654611i
$185$	−1.36100	−	0.294719i	−0.100062	−	0.0216681i
$186$	10.6445	−	5.78550i	0.780491	−	0.424213i
$187$	5.65869	+	5.65869i	0.413805	+	0.413805i
$188$	16.5374	+	16.5374i	1.20611	+	1.20611i
$189$		0			0
$190$	9.34642	+	2.02393i	0.678060	+	0.146831i
$191$			12.8543i			0.930108i	0.885282	+	0.465054i	$0.153965\pi$
$191$			12.8543i			0.930108i	−0.885282	+	0.465054i	$0.846035\pi$
$192$	0.167206	−	0.565384i	0.0120671	−	0.0408031i
$193$	−8.06158	+	8.06158i	−0.580285	+	0.580285i	−0.934982	−	0.354696i	$-0.884584\pi$
$193$	−8.06158	+	8.06158i	−0.580285	+	0.580285i	0.354696	+	0.934982i	$0.384584\pi$
$194$	15.8238			1.13608
$195$	5.83491	−	10.6605i	0.417847	−	0.763417i
$196$		0			0
$197$	−18.7512	+	18.7512i	−1.33597	+	1.33597i	−0.436036	+	0.899929i	$0.643618\pi$
$197$	−18.7512	+	18.7512i	−1.33597	+	1.33597i	−0.899929	+	0.436036i	$0.856382\pi$
$198$	2.50045	+	11.7134i	0.177699	+	0.832436i
$199$			4.20728i			0.298246i	0.988819	+	0.149123i	$0.0476451\pi$
$199$			4.20728i			0.298246i	−0.988819	+	0.149123i	$0.952355\pi$
$200$	29.5163	−	11.0727i	2.08712	−	0.782956i
$201$	−4.38931	−	8.07570i	−0.309598	−	0.569616i
$202$	1.82001	+	1.82001i	0.128055	+	0.128055i
$203$		0			0
$204$	18.8922	+	34.7590i	1.32272	+	2.43361i
$205$	7.80037	+	12.1124i	0.544802	+	0.845967i
$206$			14.5071i			1.01076i
$207$	0.882040	+	4.13194i	0.0613060	+	0.287190i
$208$	15.7355	−	15.7355i	1.09106	−	1.09106i
$209$	2.63605			0.182339
$210$		0			0
$211$	−21.5211			−1.48158			−0.740788	−	0.671739i	$-0.765548\pi$
$211$	−21.5211			−1.48158			−0.740788	+	0.671739i	$0.765548\pi$
$212$	12.6869	−	12.6869i	0.871338	−	0.871338i
$213$	1.77788	−	6.01166i	0.121818	−	0.411912i
$214$			10.1413i			0.693244i
$215$	3.66580	−	16.9285i	0.250006	−	1.15451i
$216$	−2.52769	+	32.6639i	−0.171988	+	2.22250i
$217$		0			0
$218$	11.5581	+	11.5581i	0.782810	+	0.782810i
$219$	12.6920	−	6.89836i	0.857645	−	0.466148i
$220$	13.2041	−	8.50339i	0.890218	−	0.573299i
$221$		−	16.0076i		−	1.07679i
$222$	−2.63254	−	0.778544i	−0.176684	−	0.0522525i
$223$	−12.4001	+	12.4001i	−0.830375	+	0.830375i	−0.987568	−	0.157193i	$-0.949756\pi$
$223$	−12.4001	+	12.4001i	−0.830375	+	0.830375i	0.157193	+	0.987568i	$0.449756\pi$
$224$		0			0
$225$	12.6350	−	8.08441i	0.842331	−	0.538961i
$226$	−11.8504			−0.788279
$227$	8.70556	−	8.70556i	0.577809	−	0.577809i	−0.356490	−	0.934299i	$-0.616027\pi$
$227$	8.70556	−	8.70556i	0.577809	−	0.577809i	0.934299	+	0.356490i	$0.116027\pi$
$228$	12.4964	+	3.69568i	0.827597	+	0.244753i
$229$			4.46342i			0.294951i	0.989066	+	0.147476i	$0.0471148\pi$
$229$			4.46342i			0.294951i	−0.989066	+	0.147476i	$0.952885\pi$
$230$	6.73837	−	4.33950i	0.444315	−	0.286138i
$231$		0			0
$232$	−39.7659	−	39.7659i	−2.61076	−	2.61076i
$233$	−5.64161	−	5.64161i	−0.369594	−	0.369594i	0.497735	−	0.867329i	$-0.334165\pi$
$233$	−5.64161	−	5.64161i	−0.369594	−	0.369594i	−0.867329	+	0.497735i	$0.834165\pi$
$234$	13.0310	−	20.1044i	0.851865	−	1.31427i
$235$	2.47199	−	11.4155i	0.161255	−	0.744667i
$236$			24.8435i			1.61717i
$237$	−8.37859	+	28.3310i	−0.544248	+	1.84030i
$238$		0			0
$239$	11.8594			0.767124			0.383562	−	0.923515i	$-0.374697\pi$
$239$	11.8594			0.767124			0.383562	+	0.923515i	$0.374697\pi$
$240$	26.3618	−	7.71196i	1.70165	−	0.497805i
$241$	18.0723			1.16414			0.582071	−	0.813138i	$-0.302243\pi$
$241$	18.0723			1.16414			0.582071	+	0.813138i	$0.302243\pi$
$242$	−15.3674	+	15.3674i	−0.987851	+	0.987851i
$243$	2.06841	+	15.4506i	0.132689	+	0.991158i
$244$			33.1621i			2.12298i
$245$		0			0
$246$	13.5629	+	24.9538i	0.864741	+	1.59100i
$247$	−3.72849	−	3.72849i	−0.237238	−	0.237238i
$248$	−12.2529	−	12.2529i	−0.778059	−	0.778059i
$249$	−3.75850	−	6.91510i	−0.238185	−	0.438226i
$250$	−22.8274	−	16.9875i	−1.44373	−	1.07439i
$251$			3.19253i			0.201511i	0.994911	+	0.100755i	$0.0321259\pi$
$251$			3.19253i			0.201511i	−0.994911	+	0.100755i	$0.967874\pi$
$252$		0			0
$253$	1.56219	−	1.56219i	0.0982141	−	0.0982141i
$254$	−51.4038			−3.22536
$255$	9.48616	−	17.3315i	0.594046	−	1.08534i
$256$	−29.2108			−1.82567
$257$	−11.8118	+	11.8118i	−0.736799	+	0.736799i	−0.971957	−	0.235158i	$-0.924439\pi$
$257$	−11.8118	+	11.8118i	−0.736799	+	0.736799i	0.235158	+	0.971957i	$0.424439\pi$
$258$	9.68378	−	32.7443i	0.602886	−	2.03857i
$259$		0			0
$260$	−30.7035	−	6.64874i	−1.90415	−	0.412337i
$261$	−22.4544	−	14.5542i	−1.38989	−	0.900883i
$262$	−8.81331	−	8.81331i	−0.544488	−	0.544488i
$263$	13.1502	+	13.1502i	0.810874	+	0.810874i	0.984765	−	0.173891i	$-0.0556339\pi$
$263$	13.1502	+	13.1502i	0.810874	+	0.810874i	−0.173891	+	0.984765i	$0.555634\pi$
$264$	15.0515	−	8.18080i	0.926356	−	0.503493i
$265$	−8.75757	−	1.89642i	−0.537974	−	0.116496i
$266$		0			0
$267$	15.6174	+	4.61866i	0.955767	+	0.282658i
$268$	−16.8008	+	16.8008i	−1.02627	+	1.02627i
$269$	29.3405			1.78892			0.894461	−	0.447146i	$-0.147559\pi$
$269$	29.3405			1.78892			0.894461	+	0.447146i	$0.147559\pi$
$270$	26.0227	−	14.0449i	1.58369	−	0.854744i
$271$	−3.18366			−0.193394			−0.0966968	−	0.995314i	$-0.530828\pi$
$271$	−3.18366			−0.193394			−0.0966968	+	0.995314i	$0.530828\pi$
$272$	25.5821	−	25.5821i	1.55114	−	1.55114i
$273$		0			0
$274$		−	16.4083i		−	0.991263i
$275$	−7.14085	−	3.24481i	−0.430610	−	0.195669i
$276$	9.59588	−	5.21556i	0.577604	−	0.313940i
$277$	16.8636	+	16.8636i	1.01324	+	1.01324i	0.999911	+	0.0133247i	$0.00424152\pi$
$277$	16.8636	+	16.8636i	1.01324	+	1.01324i	0.0133247	+	0.999911i	$0.495758\pi$
$278$	−18.3644	−	18.3644i	−1.10142	−	1.10142i
$279$	−6.91877	−	4.48452i	−0.414216	−	0.268481i
$280$		0			0
$281$		−	24.8052i		−	1.47975i	−0.672742	−	0.739877i	$-0.734884\pi$
$281$		−	24.8052i		−	1.47975i	0.672742	−	0.739877i	$-0.265116\pi$
$282$	6.53014	−	22.0808i	0.388864	−	1.31489i
$283$	−5.41918	+	5.41918i	−0.322137	+	0.322137i	−0.849586	−	0.527449i	$-0.823148\pi$
$283$	−5.41918	+	5.41918i	−0.322137	+	0.322137i	0.527449	+	0.849586i	$0.323148\pi$
$284$	−16.2054			−0.961615
$285$	−1.82733	−	6.24636i	−0.108242	−	0.370003i
$286$	−12.5277			−0.740781
$287$		0			0
$288$	15.9583	−	3.40661i	0.940354	−	0.200736i
$289$		−	9.02446i		−	0.530850i
$290$	−10.7430	+	49.6107i	−0.630851	+	2.91324i
$291$	−5.14262	−	9.46168i	−0.301466	−	0.554653i
$292$	−26.4045	−	26.4045i	−1.54521	−	1.54521i
$293$	−8.60739	−	8.60739i	−0.502849	−	0.502849i	0.409473	−	0.912322i	$-0.365712\pi$
$293$	−8.60739	−	8.60739i	−0.502849	−	0.502849i	−0.912322	+	0.409473i	$0.865712\pi$
$294$		0			0
$295$	10.4313	−	6.71776i	0.607336	−	0.391123i
$296$			3.92650i			0.228223i
$297$	6.19129	−	5.30190i	0.359255	−	0.307647i
$298$	1.66128	−	1.66128i	0.0962355	−	0.0962355i
$299$	−4.41920			−0.255569
$300$	−29.3028	−	25.3937i	−1.69180	−	1.46610i
$301$		0			0
$302$	24.7107	−	24.7107i	1.42194	−	1.42194i
$303$	0.496766	−	1.67975i	0.0285385	−	0.0964989i
$304$		−	11.9172i		−	0.683497i
$305$	13.9242	−	8.96715i	0.797296	−	0.513457i
$306$	21.1853	−	32.6849i	1.21108	−	1.86847i
$307$	11.8525	+	11.8525i	0.676457	+	0.676457i	0.959197	−	0.282740i	$-0.0912434\pi$
$307$	11.8525	+	11.8525i	0.676457	+	0.676457i	−0.282740	+	0.959197i	$0.591243\pi$
$308$		0			0
$309$	8.67440	−	4.71471i	0.493469	−	0.268211i
$310$	−3.31019	+	15.2863i	−0.188006	+	0.868203i
$311$		−	29.2800i		−	1.66032i	−0.557528	−	0.830158i	$-0.688250\pi$
$311$		−	29.2800i		−	1.66032i	0.557528	−	0.830158i	$-0.311750\pi$
$312$	−32.8603	−	9.71807i	−1.86035	−	0.550177i
$313$	−1.22577	+	1.22577i	−0.0692848	+	0.0692848i	−0.740900	−	0.671615i	$-0.765601\pi$
$313$	−1.22577	+	1.22577i	−0.0692848	+	0.0692848i	0.671615	+	0.740900i	$0.265601\pi$
$314$	−49.3859			−2.78701
$315$		0			0
$316$	76.3710			4.29620
$317$	−4.30159	+	4.30159i	−0.241601	+	0.241601i	−0.817512	−	0.575911i	$-0.804647\pi$
$317$	−4.30159	+	4.30159i	−0.241601	+	0.241601i	0.575911	+	0.817512i	$0.304647\pi$
$318$	−16.9395	−	5.00968i	−0.949922	−	0.280929i
$319$			13.9921i			0.783408i
$320$	0.412119	+	0.639937i	0.0230381	+	0.0357736i
$321$	6.06388	−	3.29585i	0.338453	−	0.183956i
$322$		0			0
$323$	−6.06162	−	6.06162i	−0.337278	−	0.337278i
$324$	36.7836	−	16.4541i	2.04353	−	0.914116i
$325$	5.51066	+	14.6897i	0.305676	+	0.814839i
$326$			23.7755i			1.31680i
$327$	3.15474	−	10.6673i	0.174458	−	0.589904i
$328$	28.7244	−	28.7244i	1.58604	−	1.58604i
$329$		0			0
$330$	−13.5638	−	7.42400i	−0.746665	−	0.408678i
$331$	33.2602			1.82815			0.914074	−	0.405548i	$-0.132919\pi$
$331$	33.2602			1.82815			0.914074	+	0.405548i	$0.132919\pi$
$332$	−14.3862	+	14.3862i	−0.789547	+	0.789547i
$333$	0.390034	+	1.82712i	0.0213737	+	0.100126i
$334$			11.2096i			0.613363i
$335$	11.5973	+	2.51136i	0.633630	+	0.137210i
$336$		0			0
$337$	10.3056	+	10.3056i	0.561383	+	0.561383i	0.929700	−	0.368317i	$-0.120066\pi$
$337$	10.3056	+	10.3056i	0.561383	+	0.561383i	−0.368317	+	0.929700i	$0.620066\pi$
$338$	−5.67565	−	5.67565i	−0.308715	−	0.308715i
$339$	3.85131	+	7.08585i	0.209174	+	0.384851i
$340$	−49.9166	−	10.8092i	−2.70711	−	0.586214i
$341$			4.31132i			0.233471i
$342$	−2.67849	−	12.5475i	−0.144836	−	0.678489i
$343$		0			0
$344$	−48.8391			−2.63323
$345$	−4.78469	−	2.61884i	−0.257599	−	0.140993i
$346$	29.2573			1.57288
$347$	19.2241	−	19.2241i	1.03200	−	1.03200i	0.0325323	−	0.999471i	$-0.489643\pi$
$347$	19.2241	−	19.2241i	1.03200	−	1.03200i	0.999471	−	0.0325323i	$-0.0103572\pi$
$348$	−19.6166	+	66.3310i	−1.05156	+	3.55571i
$349$		−	30.1301i		−	1.61283i	−0.591353	−	0.806413i	$-0.701406\pi$
$349$		−	30.1301i		−	1.61283i	0.591353	−	0.806413i	$-0.298594\pi$
$350$		0			0
$351$	−16.2562	−	1.25799i	−0.867694	−	0.0671463i
$352$	−6.03348	−	6.03348i	−0.321586	−	0.321586i
$353$	17.0339	+	17.0339i	0.906625	+	0.906625i	0.995998	−	0.0893729i	$-0.0284863\pi$
$353$	17.0339	+	17.0339i	0.906625	+	0.906625i	−0.0893729	+	0.995998i	$0.528486\pi$
$354$	21.4905	−	11.6805i	1.14221	−	0.620814i
$355$	4.38201	+	6.80438i	0.232573	+	0.361139i
$356$		−	42.0992i		−	2.23125i
$357$		0			0
$358$	−29.8703	+	29.8703i	−1.57869	+	1.57869i
$359$	0.737982			0.0389492			0.0194746	−	0.999810i	$-0.493801\pi$
$359$	0.737982			0.0389492			0.0194746	+	0.999810i	$0.493801\pi$
$360$	−29.8190	−	29.9950i	−1.57160	−	1.58087i
$361$	16.1763			0.851382
$362$	20.9714	−	20.9714i	1.10223	−	1.10223i
$363$	14.1831	+	4.19448i	0.744417	+	0.220153i
$364$		0			0
$365$	−3.94692	+	18.2267i	−0.206591	+	0.954028i
$366$	28.6864	−	15.5917i	1.49946	−	0.814990i
$367$	−23.2923	−	23.2923i	−1.21585	−	1.21585i	−0.969073	−	0.246776i	$-0.920629\pi$
$367$	−23.2923	−	23.2923i	−1.21585	−	1.21585i	−0.246776	−	0.969073i	$-0.579371\pi$
$368$	−7.06244	−	7.06244i	−0.368155	−	0.368155i
$369$	10.5131	−	16.2196i	0.547288	−	0.844361i
$370$	2.97967	−	1.91890i	0.154906	−	0.0997591i
$371$		0			0
$372$	−6.04438	+	20.4382i	−0.313387	+	1.05967i
$373$	−5.28110	+	5.28110i	−0.273445	+	0.273445i	−0.830485	−	0.557040i	$-0.811937\pi$
$373$	−5.28110	+	5.28110i	−0.273445	+	0.273445i	0.557040	+	0.830485i	$0.311937\pi$
$374$	−20.3671			−1.05316
$375$	−2.73878	+	19.1703i	−0.141430	+	0.989948i
$376$	−32.9341			−1.69844
$377$	19.7908	−	19.7908i	1.01928	−	1.01928i
$378$		0			0
$379$			3.38353i			0.173800i	0.996217	+	0.0869000i	$0.0276961\pi$
$379$			3.38353i			0.173800i	−0.996217	+	0.0869000i	$0.972304\pi$
$380$	−14.1443	+	9.10888i	−0.725585	+	0.467276i
$381$	16.7059	+	30.7364i	0.855868	+	1.57467i
$382$	−23.1331	−	23.1331i	−1.18359	−	1.18359i
$383$	−2.86741	−	2.86741i	−0.146518	−	0.146518i	0.630043	−	0.776561i	$-0.283037\pi$
$383$	−2.86741	−	2.86741i	−0.146518	−	0.146518i	−0.776561	+	0.630043i	$0.783037\pi$
$384$	9.71455	+	17.8734i	0.495744	+	0.912097i
$385$		0			0
$386$		−	29.0157i		−	1.47686i
$387$	−22.7263	+	4.85136i	−1.15524	+	0.246609i
$388$	−19.6841	+	19.6841i	−0.999311	+	0.999311i
$389$	−10.2102			−0.517675			−0.258838	−	0.965921i	$-0.583339\pi$
$389$	−10.2102			−0.517675			−0.258838	+	0.965921i	$0.583339\pi$
$390$	8.68434	+	29.6857i	0.439749	+	1.50319i
$391$	−7.18455			−0.363339
$392$		0			0
$393$	−2.40557	+	8.13410i	−0.121345	+	0.410311i
$394$		−	67.4903i		−	3.40011i
$395$	−20.6510	−	32.0668i	−1.03906	−	1.61346i
$396$	−17.6815	−	11.4606i	−0.888528	−	0.575915i
$397$	24.0534	+	24.0534i	1.20721	+	1.20721i	0.971928	+	0.235280i	$0.0756009\pi$
$397$	24.0534	+	24.0534i	1.20721	+	1.20721i	0.235280	+	0.971928i	$0.424399\pi$
$398$	−7.57156	−	7.57156i	−0.379528	−	0.379528i
$399$		0			0
$400$	−14.6693	+	32.2828i	−0.733465	+	1.61414i
$401$			20.0912i			1.00331i	0.865068	+	0.501654i	$0.167275\pi$
$401$			20.0912i			1.00331i	−0.865068	+	0.501654i	$0.832725\pi$
$402$	22.4324	+	6.63414i	1.11883	+	0.330881i
$403$	6.09803	−	6.09803i	0.303765	−	0.303765i
$404$	−4.52803			−0.225278
$405$	−16.8552	−	10.9955i	−0.837542	−	0.546373i
$406$		0			0
$407$	0.690793	−	0.690793i	0.0342413	−	0.0342413i
$408$	−53.4229	−	15.7992i	−2.64483	−	0.782179i
$409$			33.5102i			1.65697i	0.560008	+	0.828487i	$0.310798\pi$
$409$			33.5102i			1.65697i	−0.560008	+	0.828487i	$0.689202\pi$
$410$	−35.8356	−	7.76008i	−1.76980	−	0.383243i
$411$	−9.81120	+	5.33259i	−0.483951	+	0.263037i
$412$	−18.0463	−	18.0463i	−0.889077	−	0.889077i
$413$		0			0
$414$	−9.02331	−	5.84862i	−0.443471	−	0.287444i
$415$	9.93061	+	2.15044i	0.487475	+	0.105561i
$416$			17.0678i			0.836817i
$417$	−5.01251	+	16.9491i	−0.245463	+	0.830000i
$418$	−4.74391	+	4.74391i	−0.232032	+	0.232032i
$419$	−25.8773			−1.26419			−0.632093	−	0.774892i	$-0.717804\pi$
$419$	−25.8773			−1.26419			−0.632093	+	0.774892i	$0.717804\pi$
$420$		0			0
$421$	10.4030			0.507013			0.253507	−	0.967334i	$-0.418416\pi$
$421$	10.4030			0.507013			0.253507	+	0.967334i	$0.418416\pi$
$422$	38.7301	−	38.7301i	1.88535	−	1.88535i
$423$	−15.3252	+	3.27146i	−0.745138	+	0.159064i
$424$			25.2658i			1.22702i
$425$	8.95900	+	23.8820i	0.434576	+	1.15844i
$426$	7.61923	+	14.0183i	0.369153	+	0.679188i
$427$		0			0
$428$	−12.6154	−	12.6154i	−0.609786	−	0.609786i
$429$	4.07143	+	7.49085i	0.196571	+	0.361662i
$430$	23.8679	+	37.0621i	1.15101	+	1.78729i
$431$		−	0.449005i		−	0.0216278i	−0.999942	−	0.0108139i	$-0.996558\pi$
$431$		−	0.449005i		−	0.0216278i	0.999942	−	0.0108139i	$-0.00344224\pi$
$432$	−23.9691	−	27.9899i	−1.15321	−	1.34667i
$433$	17.7813	−	17.7813i	0.854517	−	0.854517i	−0.136169	−	0.990686i	$-0.543479\pi$
$433$	17.7813	−	17.7813i	0.854517	−	0.854517i	0.990686	+	0.136169i	$0.0434790\pi$
$434$		0			0
$435$	33.1556	−	9.69944i	1.58969	−	0.465053i
$436$	−28.7555			−1.37714
$437$	−1.67343	+	1.67343i	−0.0800509	+	0.0800509i
$438$	−10.4264	+	35.2554i	−0.498192	+	1.68457i
$439$		−	29.5293i		−	1.40936i	−0.709526	−	0.704679i	$-0.751091\pi$
$439$		−	29.5293i		−	1.40936i	0.709526	−	0.704679i	$-0.248909\pi$
$440$	−4.68067	+	21.6151i	−0.223142	+	1.03046i
$441$		0			0
$442$	28.8077	+	28.8077i	1.37024	+	1.37024i
$443$	−15.5643	−	15.5643i	−0.739483	−	0.739483i	0.232995	−	0.972478i	$-0.425147\pi$
$443$	−15.5643	−	15.5643i	−0.739483	−	0.739483i	−0.972478	+	0.232995i	$0.925147\pi$
$444$	4.24325	−	2.30630i	0.201376	−	0.109452i
$445$	−17.6767	+	11.3838i	−0.837957	+	0.539643i
$446$		−	44.6313i		−	2.11336i
$447$	−1.53325	−	0.453443i	−0.0725204	−	0.0214471i
$448$		0			0
$449$	16.3214			0.770252			0.385126	−	0.922864i	$-0.374158\pi$
$449$	16.3214			0.770252			0.385126	+	0.922864i	$0.374158\pi$
$450$	−8.18931	+	37.2872i	−0.386048	+	1.75774i
$451$	−10.1070			−0.475921
$452$	14.7415	−	14.7415i	0.693380	−	0.693380i
$453$	−22.8063	−	6.74471i	−1.07153	−	0.316894i
$454$			31.3336i			1.47056i
$455$		0			0
$456$	−16.1232	+	8.76332i	−0.755040	+	0.410380i
$457$	−20.6299	−	20.6299i	−0.965028	−	0.965028i	0.0343811	−	0.999409i	$-0.489054\pi$
$457$	−20.6299	−	20.6299i	−0.965028	−	0.965028i	−0.999409	+	0.0343811i	$0.989054\pi$
$458$	−8.03251	−	8.03251i	−0.375335	−	0.375335i
$459$	−26.4287	−	2.04518i	−1.23359	−	0.0954609i
$460$	−2.98410	+	13.7804i	−0.139134	+	0.642516i
$461$		−	15.2893i		−	0.712094i	−0.934468	−	0.356047i	$-0.884124\pi$
$461$		−	15.2893i		−	0.712094i	0.934468	−	0.356047i	$-0.115876\pi$
$462$		0			0
$463$	0.492195	−	0.492195i	0.0228743	−	0.0228743i	−0.695577	−	0.718451i	$-0.744851\pi$
$463$	0.492195	−	0.492195i	0.0228743	−	0.0228743i	0.718451	+	0.695577i	$0.244851\pi$
$464$	63.2563			2.93660
$465$	10.2161	−	2.98864i	0.473760	−	0.138595i
$466$	20.3056			0.940640
$467$	9.00044	−	9.00044i	0.416491	−	0.416491i	−0.467501	−	0.883992i	$-0.654846\pi$
$467$	9.00044	−	9.00044i	0.416491	−	0.416491i	0.883992	+	0.467501i	$0.154846\pi$
$468$	8.79901	+	41.2192i	0.406734	+	1.90536i
$469$		0			0
$470$	16.0951	+	24.9924i	0.742410	+	1.15281i
$471$	16.0501	+	29.5298i	0.739548	+	1.36066i
$472$	−24.7378	−	24.7378i	−1.13865	−	1.13865i
$473$	8.59230	+	8.59230i	0.395075	+	0.395075i
$474$	−35.9070	−	66.0637i	−1.64926	−	3.03441i
$475$	7.64932	+	3.47586i	0.350975	+	0.159483i
$476$		0			0
$477$	2.50974	+	11.7570i	0.114913	+	0.538314i
$478$	−21.3426	+	21.3426i	−0.976188	+	0.976188i
$479$	22.7572			1.03980			0.519901	−	0.854226i	$-0.325969\pi$
$479$	22.7572			1.03980			0.519901	+	0.854226i	$0.325969\pi$
$480$	−10.1144	+	18.4794i	−0.461659	+	0.843464i
$481$	−1.95415			−0.0891015
$482$	−32.5235	+	32.5235i	−1.48141	+	1.48141i
$483$		0			0
$484$		−	38.2328i		−	1.73785i
$485$	13.5877	+	2.94237i	0.616986	+	0.133606i
$486$	−31.5278	−	24.0830i	−1.43013	−	1.09243i
$487$	−11.4919	−	11.4919i	−0.520746	−	0.520746i	0.397051	−	0.917797i	$-0.370034\pi$
$487$	−11.4919	−	11.4919i	−0.520746	−	0.520746i	−0.917797	+	0.397051i	$0.870034\pi$
$488$	−33.0210	−	33.0210i	−1.49479	−	1.49479i
$489$	14.2163	−	7.72687i	0.642884	−	0.349421i
$490$		0			0
$491$			0.301729i			0.0136168i	0.999977	+	0.00680841i	$0.00216720\pi$
$491$			0.301729i			0.0136168i	−0.999977	+	0.00680841i	$0.997833\pi$
$492$	−47.9133	−	14.1698i	−2.16010	−	0.638826i
$493$	32.1750	−	32.1750i	1.44909	−	1.44909i
$494$	13.4198			0.603785
$495$	−0.0309545	+	10.5231i	−0.00139130	+	0.472979i
$496$	19.4909			0.875165
$497$		0			0
$498$	19.2085	+	5.68071i	0.860754	+	0.254559i
$499$			20.2207i			0.905202i	0.891713	+	0.452601i	$0.149504\pi$
$499$			20.2207i			0.905202i	−0.891713	+	0.452601i	$0.850496\pi$
$500$	49.5282	−	7.26458i	2.21497	−	0.324882i
$501$	6.70268	−	3.64305i	0.299454	−	0.162759i
$502$	−5.74537	−	5.74537i	−0.256428	−	0.256428i
$503$	23.8859	+	23.8859i	1.06502	+	1.06502i	0.997734	+	0.0672882i	$0.0214347\pi$
$503$	23.8859	+	23.8859i	1.06502	+	1.06502i	0.0672882	+	0.997734i	$0.478565\pi$
$504$		0			0
$505$	1.22440	+	1.90124i	0.0544850	+	0.0846042i
$506$			5.62273i			0.249961i
$507$	−1.54915	+	5.23825i	−0.0688004	+	0.232639i
$508$	63.9443	−	63.9443i	2.83707	−	2.83707i
$509$	11.7721			0.521788			0.260894	−	0.965368i	$-0.415983\pi$
$509$	11.7721			0.521788			0.260894	+	0.965368i	$0.415983\pi$
$510$	14.1186	+	48.2618i	0.625184	+	2.13707i
$511$		0			0
$512$	35.9587	−	35.9587i	1.58917	−	1.58917i
$513$	−6.63215	+	5.67942i	−0.292816	+	0.250752i
$514$		−	42.5137i		−	1.87520i
$515$	−2.69754	+	12.4571i	−0.118868	+	0.548925i
$516$	28.6864	+	52.7789i	1.26285	+	2.32346i
$517$	5.79412	+	5.79412i	0.254825	+	0.254825i
$518$		0			0
$519$	−9.50842	−	17.4941i	−0.417373	−	0.767907i
$520$	37.1934	−	23.9525i	1.63104	−	1.05038i
$521$			29.7872i			1.30500i	0.757789	+	0.652500i	$0.226280\pi$
$521$			29.7872i			1.30500i	−0.757789	+	0.652500i	$0.773720\pi$
$522$	66.6018	−	14.2174i	2.91508	−	0.622279i
$523$	−17.4673	+	17.4673i	−0.763792	+	0.763792i	−0.977006	−	0.213214i	$-0.931607\pi$
$523$	−17.4673	+	17.4673i	−0.763792	+	0.763792i	0.213214	+	0.977006i	$0.431607\pi$
$524$	21.9268			0.957877
$525$		0			0
$526$	−47.3309			−2.06373
$527$	9.91393	−	9.91393i	0.431858	−	0.431858i
$528$	−5.46466	+	18.4780i	−0.237819	+	0.804151i
$529$		−	21.0166i		−	0.913764i
$530$	19.1732	−	12.3475i	0.832833	−	0.536343i
$531$	−13.9685	−	9.05395i	−0.606183	−	0.392908i
$532$		0			0
$533$	14.2956	+	14.2956i	0.619211	+	0.619211i
$534$	−36.4174	+	19.7936i	−1.57593	+	0.856553i
$535$	−1.88573	+	8.70821i	−0.0815272	+	0.376489i
$536$		−	33.4586i		−	1.44519i
$537$	27.5683	+	8.15302i	1.18966	+	0.351829i
$538$	−52.8021	+	52.8021i	−2.27646	+	2.27646i
$539$		0			0
$540$	−14.8999	+	49.8425i	−0.641192	+	2.14488i
$541$	−23.1117			−0.993650			−0.496825	−	0.867851i	$-0.665501\pi$
$541$	−23.1117			−0.993650			−0.496825	+	0.867851i	$0.665501\pi$
$542$	5.72941	−	5.72941i	0.246099	−	0.246099i
$543$	−19.3552	−	5.72409i	−0.830612	−	0.245644i
$544$			27.7481i			1.18969i
$545$	7.77560	+	12.0739i	0.333070	+	0.517191i
$546$		0			0
$547$	−25.6689	−	25.6689i	−1.09752	−	1.09752i	−0.994700	−	0.102823i	$-0.967213\pi$
$547$	−25.6689	−	25.6689i	−1.09752	−	1.09752i	−0.102823	−	0.994700i	$-0.532787\pi$
$548$	20.4113	+	20.4113i	0.871928	+	0.871928i
$549$	−18.6458	−	12.0856i	−0.795783	−	0.515801i
$550$	18.6904	−	7.01144i	0.796959	−	0.298969i
$551$		−	14.9884i		−	0.638528i
$552$	−4.36169	+	14.7484i	−0.185646	+	0.627735i
$553$		0			0
$554$	−60.6965			−2.57875
$555$	−2.11576	−	1.15804i	−0.0898092	−	0.0491559i
$556$	45.6891			1.93765
$557$	−10.5779	+	10.5779i	−0.448199	+	0.448199i	−0.894756	−	0.446556i	$-0.852650\pi$
$557$	−10.5779	+	10.5779i	−0.448199	+	0.448199i	0.446556	+	0.894756i	$0.352650\pi$
$558$	20.5217	−	4.38074i	0.868753	−	0.185452i
$559$		−	24.3063i		−	1.02805i
$560$		0			0
$561$	6.61917	+	12.1783i	0.279462	+	0.514169i
$562$	44.6402	+	44.6402i	1.88303	+	1.88303i
$563$	10.9216	+	10.9216i	0.460291	+	0.460291i	0.898751	−	0.438460i	$-0.144476\pi$
$563$	10.9216	+	10.9216i	0.460291	+	0.460291i	−0.438460	+	0.898751i	$0.644476\pi$
$564$	19.3444	+	35.5908i	0.814544	+	1.49864i
$565$	−10.1758	−	2.20354i	−0.428100	−	0.0927036i
$566$		−	19.5050i		−	0.819858i
$567$		0			0
$568$	16.1365	−	16.1365i	0.677072	−	0.677072i
$569$	42.0710			1.76371			0.881854	−	0.471523i	$-0.156295\pi$
$569$	42.0710			1.76371			0.881854	+	0.471523i	$0.156295\pi$
$570$	14.5297	+	7.95263i	0.608581	+	0.333099i
$571$	10.8342			0.453399			0.226699	−	0.973965i	$-0.427207\pi$
$571$	10.8342			0.453399			0.226699	+	0.973965i	$0.427207\pi$
$572$	15.5840	−	15.5840i	0.651601	−	0.651601i
$573$	−6.31411	+	21.3503i	−0.263776	+	0.891921i
$574$		0			0
$575$	6.59308	−	2.47331i	0.274950	−	0.103144i
$576$	0.555438	−	0.856936i	0.0231433	−	0.0357057i
$577$	−14.6975	−	14.6975i	−0.611865	−	0.611865i	0.331567	−	0.943432i	$-0.392423\pi$
$577$	−14.6975	−	14.6975i	−0.611865	−	0.611865i	−0.943432	+	0.331567i	$0.892423\pi$
$578$	16.2407	+	16.2407i	0.675523	+	0.675523i
$579$	−17.3497	+	9.42991i	−0.721028	+	0.391894i
$580$	−48.3498	−	75.0776i	−2.00762	−	3.11743i
$581$		0			0
$582$	26.2823	+	7.77271i	1.08944	+	0.322189i
$583$	4.44503	−	4.44503i	0.184094	−	0.184094i
$584$	52.5844			2.17596
$585$	14.9279	−	14.8404i	0.617194	−	0.613574i
$586$	30.9802			1.27978
$587$	−4.89737	+	4.89737i	−0.202136	+	0.202136i	−0.800915	−	0.598779i	$-0.795653\pi$
$587$	−4.89737	+	4.89737i	−0.202136	+	0.202136i	0.598779	+	0.800915i	$0.295653\pi$
$588$		0			0
$589$		−	4.61831i		−	0.190294i
$590$	−6.68306	+	30.8620i	−0.275137	+	1.27057i
$591$	−40.3552	+	21.9339i	−1.65999	+	0.902240i
$592$	−3.12297	−	3.12297i	−0.128353	−	0.128353i
$593$	22.5635	+	22.5635i	0.926573	+	0.926573i	0.997483	−	0.0709102i	$-0.0225904\pi$
$593$	22.5635	+	22.5635i	0.926573	+	0.926573i	−0.0709102	+	0.997483i	$0.522590\pi$
$594$	−1.60059	+	20.6835i	−0.0656729	+	0.848654i
$595$		0			0
$596$			4.13314i			0.169300i
$597$	−2.06664	+	6.98804i	−0.0845818	+	0.286002i
$598$	7.95292	−	7.95292i	0.325219	−	0.325219i
$599$	6.81971			0.278646			0.139323	−	0.990247i	$-0.455507\pi$
$599$	6.81971			0.278646			0.139323	+	0.990247i	$0.455507\pi$
$600$	54.4637	−	3.89247i	2.22347	−	0.158910i
$601$	8.46733			0.345390			0.172695	−	0.984975i	$-0.444753\pi$
$601$	8.46733			0.345390			0.172695	+	0.984975i	$0.444753\pi$
$602$		0			0
$603$	−3.32356	−	15.5693i	−0.135346	−	0.634031i
$604$			61.4782i			2.50151i
$605$	−16.0533	+	10.3383i	−0.652658	+	0.420311i
$606$	2.12893	+	3.91692i	0.0864817	+	0.159114i
$607$	−6.30295	−	6.30295i	−0.255829	−	0.255829i	0.567526	−	0.823355i	$-0.307900\pi$
$607$	−6.30295	−	6.30295i	−0.255829	−	0.255829i	−0.823355	+	0.567526i	$0.807900\pi$
$608$	6.46309	+	6.46309i	0.262113	+	0.262113i
$609$		0			0
$610$	−8.92083	+	41.1959i	−0.361194	+	1.66797i
$611$		−	16.3907i		−	0.663095i
$612$	14.3051	+	67.0125i	0.578248	+	2.70882i
$613$	−5.24728	+	5.24728i	−0.211935	+	0.211935i	−0.805089	−	0.593154i	$-0.797883\pi$
$613$	−5.24728	+	5.24728i	−0.211935	+	0.211935i	0.593154	+	0.805089i	$0.297883\pi$
$614$	−42.6601			−1.72162
$615$	7.00627	+	23.9496i	0.282520	+	0.965739i
$616$		0			0
$617$	−2.10719	+	2.10719i	−0.0848323	+	0.0848323i	−0.748250	−	0.663417i	$-0.769105\pi$
$617$	−2.10719	+	2.10719i	−0.0848323	+	0.0848323i	0.663417	+	0.748250i	$0.269105\pi$
$618$	−7.12596	+	24.0954i	−0.286648	+	0.969261i
$619$		−	21.0734i		−	0.847012i	−0.905893	−	0.423506i	$-0.860799\pi$
$619$		−	21.0734i		−	0.847012i	0.905893	−	0.423506i	$-0.139201\pi$
$620$	−14.8978	−	23.1333i	−0.598310	−	0.929055i
$621$	−0.564612	+	7.29616i	−0.0226571	+	0.292785i
$622$	52.6932	+	52.6932i	2.11280	+	2.11280i
$623$		0			0
$624$	33.8650	−	18.4063i	1.35569	−	0.736844i
$625$	−16.4429	−	18.8317i	−0.657715	−	0.753267i
$626$		−	4.41188i		−	0.176334i
$627$	4.37831	+	1.29484i	0.174853	+	0.0517108i
$628$	61.4341	−	61.4341i	2.45149	−	2.45149i
$629$	−3.17697			−0.126674
$630$		0			0
$631$	−11.6376			−0.463287			−0.231643	−	0.972801i	$-0.574410\pi$
$631$	−11.6376			−0.463287			−0.231643	+	0.972801i	$0.574410\pi$
$632$	−76.0461	+	76.0461i	−3.02495	+	3.02495i
$633$	−35.7453	−	10.5713i	−1.42075	−	0.420170i
$634$		−	15.4825i		−	0.614890i
$635$	−44.1399	−	9.55833i	−1.75164	−	0.379311i
$636$	27.3040	−	14.8403i	1.08267	−	0.588455i
$637$		0			0
$638$	−25.1806	−	25.1806i	−0.996910	−	0.996910i
$639$	5.90591	−	9.11170i	0.233634	−	0.360453i
$640$	−25.6675	−	5.55821i	−1.01460	−	0.219708i
$641$		−	36.1036i		−	1.42601i	−0.701161	−	0.713003i	$-0.747335\pi$
$641$		−	36.1036i		−	1.42601i	0.701161	−	0.713003i	$-0.252665\pi$
$642$	−4.98144	+	16.8441i	−0.196602	+	0.664782i
$643$	21.0115	−	21.0115i	0.828614	−	0.828614i	−0.158711	−	0.987325i	$-0.550734\pi$
$643$	21.0115	−	21.0115i	0.828614	−	0.828614i	0.987325	+	0.158711i	$0.0507337\pi$
$644$		0			0
$645$	14.4040	−	26.3165i	0.567158	−	1.03621i
$646$	21.8173			0.858392
$647$	−18.9025	+	18.9025i	−0.743133	+	0.743133i	−0.973180	−	0.230046i	$-0.926112\pi$
$647$	−18.9025	+	18.9025i	−0.743133	+	0.743133i	0.230046	+	0.973180i	$0.426112\pi$
$648$	−20.2430	+	53.0112i	−0.795221	+	2.08248i
$649$			8.70428i			0.341673i
$650$	−36.3532	−	16.5189i	−1.42589	−	0.647925i
$651$		0			0
$652$	−29.5757	−	29.5757i	−1.15828	−	1.15828i
$653$	12.2864	+	12.2864i	0.480803	+	0.480803i	0.905388	−	0.424585i	$-0.139580\pi$
$653$	12.2864	+	12.2864i	0.480803	+	0.480803i	−0.424585	+	0.905388i	$0.639580\pi$
$654$	13.5199	+	24.8746i	0.528668	+	0.972674i
$655$	−5.92909	−	9.20669i	−0.231669	−	0.359735i
$656$			45.6924i			1.78399i
$657$	24.4691	−	5.22339i	0.954631	−	0.203784i
$658$		0			0
$659$	0.708622			0.0276040			0.0138020	−	0.999905i	$-0.495607\pi$
$659$	0.708622			0.0276040			0.0138020	+	0.999905i	$0.495607\pi$
$660$	26.1080	−	7.63772i	1.01625	−	0.297298i
$661$	−17.4206			−0.677582			−0.338791	−	0.940862i	$-0.610018\pi$
$661$	−17.4206			−0.677582			−0.338791	+	0.940862i	$0.610018\pi$
$662$	−59.8561	+	59.8561i	−2.32637	+	2.32637i
$663$	7.86299	−	26.5876i	0.305373	−	1.03258i
$664$		−	28.6500i		−	1.11184i
$665$		0			0
$666$	−3.99006	−	2.58623i	−0.154612	−	0.100214i
$667$	−8.88253	−	8.88253i	−0.343933	−	0.343933i
$668$	−13.9443	−	13.9443i	−0.539522	−	0.539522i
$669$	−26.6869	+	14.5049i	−1.03177	+	0.560791i
$670$	−25.3904	+	16.3514i	−0.980918	+	0.631709i
$671$			11.6188i			0.448540i
$672$		0			0
$673$	−8.20389	+	8.20389i	−0.316237	+	0.316237i	−0.847320	−	0.531083i	$-0.821785\pi$
$673$	−8.20389	+	8.20389i	−0.316237	+	0.316237i	0.531083	+	0.847320i	$0.321785\pi$
$674$	−37.0926			−1.42875
$675$	24.9570	−	7.22137i	0.960595	−	0.277951i
$676$	14.1206			0.543099
$677$	−32.8605	+	32.8605i	−1.26293	+	1.26293i	−0.313264	+	0.949666i	$0.601422\pi$
$677$	−32.8605	+	32.8605i	−1.26293	+	1.26293i	−0.949666	+	0.313264i	$0.898578\pi$
$678$	−19.6828	−	5.82098i	−0.755915	−	0.223554i
$679$		0			0
$680$	60.4675	−	38.9409i	2.31882	−	1.49332i
$681$	18.7356	−	10.1832i	0.717951	−	0.390221i
$682$	−7.75878	−	7.75878i	−0.297099	−	0.297099i
$683$	−28.4978	−	28.4978i	−1.09044	−	1.09044i	−0.995481	−	0.0949562i	$-0.969729\pi$
$683$	−28.4978	−	28.4978i	−1.09044	−	1.09044i	−0.0949562	−	0.995481i	$-0.530271\pi$
$684$	18.9405	+	12.2766i	0.724208	+	0.469408i
$685$	3.05106	−	14.0896i	0.116575	−	0.538338i
$686$		0			0
$687$	−2.19245	+	7.41347i	−0.0836473	+	0.282842i
$688$	38.8446	−	38.8446i	1.48093	−	1.48093i
$689$	−12.5743			−0.479043
$690$	13.3236	−	3.89773i	0.507221	−	0.148384i
$691$	−5.79939			−0.220619			−0.110310	−	0.993897i	$-0.535184\pi$
$691$	−5.79939			−0.220619			−0.110310	+	0.993897i	$0.535184\pi$
$692$	−36.3949	+	36.3949i	−1.38353	+	1.38353i
$693$		0			0
$694$			69.1925i			2.62651i
$695$	−12.3545	−	19.1840i	−0.468633	−	0.727692i
$696$	−46.5156	−	85.5820i	−1.76317	−	3.24398i
$697$	23.2412	+	23.2412i	0.880324	+	0.880324i
$698$	54.2230	+	54.2230i	2.05237	+	2.05237i
$699$	−6.59919	−	12.1416i	−0.249604	−	0.459236i
$700$		0			0
$701$			4.92775i			0.186118i	0.995661	+	0.0930592i	$0.0296646\pi$
$701$			4.92775i			0.186118i	−0.995661	+	0.0930592i	$0.970335\pi$
$702$	31.5191	−	26.9913i	1.18961	−	1.01872i
$703$	−0.739981	+	0.739981i	−0.0279089	+	0.0279089i
$704$	−0.533986			−0.0201254
$705$	9.71318	−	17.7462i	0.365820	−	0.668362i
$706$	−61.3096			−2.30742
$707$		0			0
$708$	−12.2032	+	41.2635i	−0.458625	+	1.55078i
$709$		−	17.1922i		−	0.645666i	−0.946456	−	0.322833i	$-0.895365\pi$
$709$		−	17.1922i		−	0.645666i	0.946456	−	0.322833i	$-0.104635\pi$
$710$	−20.1313	−	4.35937i	−0.755516	−	0.163604i
$711$	−27.8326	+	42.9405i	−1.04381	+	1.61039i
$712$	41.9201	+	41.9201i	1.57102	+	1.57102i
$713$	−2.73693	−	2.73693i	−0.102499	−	0.102499i
$714$		0			0
$715$	−10.7574	−	2.32948i	−0.402305	−	0.0871177i
$716$		−	74.3149i		−	2.77728i
$717$	19.6978	+	5.82541i	0.735628	+	0.217554i
$718$	−1.32809	+	1.32809i	−0.0495640	+	0.0495640i
$719$	−12.2556			−0.457059			−0.228529	−	0.973537i	$-0.573392\pi$
$719$	−12.2556			−0.457059			−0.228529	+	0.973537i	$0.573392\pi$
$720$	47.5735	+	0.139941i	1.77296	+	0.00521528i
$721$		0			0
$722$	−29.1113	+	29.1113i	−1.08341	+	1.08341i
$723$	30.0170	+	8.87721i	1.11635	+	0.330147i
$724$			52.1752i			1.93908i
$725$	−18.4498	+	40.6025i	−0.685208	+	1.50794i
$726$	−33.0728	+	17.9757i	−1.22745	+	0.667142i
$727$	−5.83842	−	5.83842i	−0.216535	−	0.216535i	0.590501	−	0.807037i	$-0.298930\pi$
$727$	−5.83842	−	5.83842i	−0.216535	−	0.216535i	−0.807037	+	0.590501i	$0.798930\pi$
$728$		0			0
$729$	−4.15390	+	26.6786i	−0.153848	+	0.988094i
$730$	−25.6983	−	39.9043i	−0.951136	−	1.47692i
$731$		−	39.5162i		−	1.46156i
$732$	−16.2894	+	55.0802i	−0.602072	+	2.03582i
$733$	−13.5940	+	13.5940i	−0.502105	+	0.502105i	−0.912091	−	0.409987i	$-0.865533\pi$
$733$	−13.5940	+	13.5940i	−0.502105	+	0.502105i	0.409987	+	0.912091i	$0.365533\pi$
$734$	83.8351			3.09441
$735$		0			0
$736$	7.66040			0.282366
$737$	−5.88639	+	5.88639i	−0.216828	+	0.216828i
$738$	10.2698	+	48.1090i	0.378035	+	1.77092i
$739$		−	15.1801i		−	0.558411i	−0.960231	−	0.279205i	$-0.909929\pi$
$739$		−	15.1801i		−	0.558411i	0.960231	−	0.279205i	$-0.0900710\pi$
$740$	−1.31955	+	6.09364i	−0.0485078	+	0.224007i
$741$	−4.36134	−	8.02424i	−0.160218	−	0.294778i
$742$		0			0
$743$	−34.4215	−	34.4215i	−1.26280	−	1.26280i	−0.949729	−	0.313073i	$-0.898642\pi$
$743$	−34.4215	−	34.4215i	−1.26280	−	1.26280i	−0.313073	−	0.949729i	$-0.601358\pi$
$744$	−14.3326	−	26.3700i	−0.525459	−	0.966770i
$745$	1.73543	−	1.11762i	0.0635813	−	0.0409463i
$746$		−	19.0080i		−	0.695934i
$747$	−2.84591	−	13.3317i	−0.104126	−	0.487783i
$748$	25.3359	−	25.3359i	0.926371	−	0.926371i
$749$		0			0
$750$	−29.5706	−	39.4282i	−1.07977	−	1.43971i
$751$	−22.2515			−0.811970			−0.405985	−	0.913880i	$-0.633071\pi$
$751$	−22.2515			−0.811970			−0.405985	+	0.913880i	$0.633071\pi$
$752$	26.1944	−	26.1944i	0.955210	−	0.955210i
$753$	−1.56818	+	5.30260i	−0.0571478	+	0.193237i
$754$			71.2321i			2.59412i
$755$	25.8136	−	16.6239i	0.939454	−	0.605007i
$756$		0			0
$757$	−1.88407	−	1.88407i	−0.0684777	−	0.0684777i	0.672038	−	0.740516i	$-0.265419\pi$
$757$	−1.88407	−	1.88407i	−0.0684777	−	0.0684777i	−0.740516	+	0.672038i	$0.765419\pi$
$758$	−6.08909	−	6.08909i	−0.221166	−	0.221166i
$759$	3.36206	−	1.82735i	0.122035	−	0.0663286i
$760$	5.01396	−	23.1542i	0.181875	−	0.839892i
$761$		−	35.6674i		−	1.29294i	−0.762938	−	0.646472i	$-0.776244\pi$
$761$		−	35.6674i		−	1.29294i	0.762938	−	0.646472i	$-0.223756\pi$
$762$	−85.3786	−	25.2498i	−3.09294	−	0.914703i
$763$		0			0
$764$	57.5532			2.08220
$765$	24.2692	−	24.1269i	0.877456	−	0.872309i
$766$	10.3206			0.372897
$767$	12.3115	−	12.3115i	0.444543	−	0.444543i
$768$	−48.5173	−	14.3485i	−1.75072	−	0.517755i
$769$			31.7331i			1.14432i	0.820141	+	0.572162i	$0.193895\pi$
$769$			31.7331i			1.14432i	−0.820141	+	0.572162i	$0.806105\pi$
$770$		0			0
$771$	−25.4207	+	13.8167i	−0.915503	+	0.497595i
$772$	36.0944	+	36.0944i	1.29907	+	1.29907i
$773$	−4.97844	−	4.97844i	−0.179062	−	0.179062i	0.611885	−	0.790947i	$-0.290412\pi$
$773$	−4.97844	−	4.97844i	−0.179062	−	0.179062i	−0.790947	+	0.611885i	$0.790412\pi$
$774$	32.1683	−	49.6296i	1.15627	−	1.78390i
$775$	−5.68485	+	12.5107i	−0.204206	+	0.449396i
$776$		−	39.2008i		−	1.40723i
$777$		0			0
$778$	18.3745	−	18.3745i	0.658758	−	0.658758i
$779$	10.8267			0.387907
$780$	−47.7308	−	26.1249i	−1.70904	−	0.935420i
$781$	−5.67781			−0.203168
$782$	12.9295	−	12.9295i	0.462359	−	0.462359i
$783$	−30.1463	−	35.2034i	−1.07734	−	1.25807i
$784$		0			0
$785$	−42.4071	−	9.18310i	−1.51357	−	0.327759i
$786$	−10.3092	−	18.9675i	−0.367718	−	0.676548i
$787$	−18.7554	−	18.7554i	−0.668557	−	0.668557i	0.288825	−	0.957382i	$-0.406735\pi$
$787$	−18.7554	−	18.7554i	−0.668557	−	0.668557i	−0.957382	+	0.288825i	$0.906735\pi$
$788$	83.9553	+	83.9553i	2.99078	+	2.99078i
$789$	15.3822	+	28.3011i	0.547621	+	1.00754i
$790$	94.8726	+	20.5443i	3.37542	+	0.730934i
$791$		0			0
$792$	29.0181	−	6.19445i	1.03111	−	0.220110i
$793$	16.4339	−	16.4339i	0.583586	−	0.583586i
$794$	−86.5746			−3.07242
$795$	−13.6143	−	7.45160i	−0.482848	−	0.264281i
$796$	18.8374			0.667675
$797$	7.92792	−	7.92792i	0.280821	−	0.280821i	−0.552615	−	0.833437i	$-0.686370\pi$
$797$	7.92792	−	7.92792i	0.280821	−	0.280821i	0.833437	+	0.552615i	$0.186370\pi$
$798$		0			0
$799$		−	26.6473i		−	0.942713i
$800$	−9.55238	−	25.4637i	−0.337728	−	0.900278i
$801$	23.6708	+	15.3426i	0.836366	+	0.542105i
$802$	−36.1568	−	36.1568i	−1.27674	−	1.27674i
$803$	−9.25121	−	9.25121i	−0.326468	−	0.326468i
$804$	−36.1576	+	19.6524i	−1.27518	+	0.693088i
$805$		0			0
$806$			21.9484i			0.773099i
$807$	48.7328	+	14.4122i	1.71548	+	0.507333i
$808$	4.50877	−	4.50877i	0.158618	−	0.158618i
$809$	33.2281			1.16824			0.584119	−	0.811668i	$-0.301440\pi$
$809$	33.2281			1.16824			0.584119	+	0.811668i	$0.301440\pi$
$810$	50.1210	−	10.5452i	1.76107	−	0.370521i
$811$	49.8680			1.75110			0.875550	−	0.483127i	$-0.160499\pi$
$811$	49.8680			1.75110			0.875550	+	0.483127i	$0.160499\pi$
$812$		0			0
$813$	−5.28787	−	1.56383i	−0.185454	−	0.0548458i
$814$			2.48634i			0.0871463i
$815$	−4.42095	+	20.4157i	−0.154859	+	0.715132i
$816$	55.0564	−	29.9243i	1.92736	−	1.04756i
$817$	−9.20412	−	9.20412i	−0.322011	−	0.322011i
$818$	−60.3060	−	60.3060i	−2.10855	−	2.10855i
$819$		0			0
$820$	54.2313	−	34.9249i	1.89384	−	1.21963i
$821$			32.4420i			1.13223i	0.824325	+	0.566116i	$0.191555\pi$
$821$			32.4420i			1.13223i	−0.824325	+	0.566116i	$0.808445\pi$
$822$	8.05984	−	27.2532i	0.281119	−	0.950565i
$823$	−32.7235	+	32.7235i	−1.14067	+	1.14067i	−0.152341	+	0.988328i	$0.548681\pi$
$823$	−32.7235	+	32.7235i	−1.14067	+	1.14067i	−0.988328	+	0.152341i	$0.951319\pi$
$824$	35.9390			1.25200
$825$	−10.2667	−	8.89705i	−0.357439	−	0.309755i
$826$		0			0
$827$	−36.7198	+	36.7198i	−1.27687	+	1.27687i	−0.334465	+	0.942408i	$0.608556\pi$
$827$	−36.7198	+	36.7198i	−1.27687	+	1.27687i	−0.942408	+	0.334465i	$0.891444\pi$
$828$	18.5001	−	3.94919i	0.642922	−	0.137244i
$829$		−	14.2972i		−	0.496562i	−0.968688	−	0.248281i	$-0.920134\pi$
$829$		−	14.2972i		−	0.496562i	0.968688	−	0.248281i	$-0.0798657\pi$
$830$	−21.7414	+	14.0014i	−0.754656	+	0.485997i
$831$	19.7259	+	36.2929i	0.684285	+	1.25899i
$832$	0.755282	+	0.755282i	0.0261847	+	0.0261847i
$833$		0			0
$834$	−21.4814	−	39.5227i	−0.743841	−	1.36856i
$835$	−2.08438	+	9.62557i	−0.0721330	+	0.333107i
$836$		−	11.8025i		−	0.408197i
$837$	−9.28883	−	10.8470i	−0.321069	−	0.374929i
$838$	46.5695	−	46.5695i	1.60872	−	1.60872i
$839$	33.6309			1.16107			0.580534	−	0.814236i	$-0.302844\pi$
$839$	33.6309			1.16107			0.580534	+	0.814236i	$0.302844\pi$
$840$		0			0
$841$	50.5583			1.74339
$842$	−18.7216	+	18.7216i	−0.645190	+	0.645190i
$843$	12.1844	−	41.1999i	0.419654	−	1.41900i
$844$			96.3574i			3.31676i
$845$	−3.81826	−	5.92898i	−0.131352	−	0.203963i
$846$	21.6923	−	33.4672i	0.745798	−	1.15062i
$847$		0			0
$848$	−20.0953	−	20.0953i	−0.690077	−	0.690077i
$849$	−11.6629	+	6.33901i	−0.400268	+	0.217554i
$850$	−59.1016	−	26.8558i	−2.02717	−	0.921146i
$851$			0.877065i			0.0300654i
$852$	−26.9162	−	7.96017i	−0.922134	−	0.272711i
$853$	−26.5544	+	26.5544i	−0.909206	+	0.909206i	−0.996208	−	0.0870025i	$-0.972271\pi$
$853$	−26.5544	+	26.5544i	−0.909206	+	0.909206i	0.0870025	+	0.996208i	$0.472271\pi$
$854$		0			0
$855$	0.0331586	−	11.2724i	0.00113400	−	0.385509i
$856$	25.1234			0.858699
$857$	−23.0711	+	23.0711i	−0.788092	+	0.788092i	−0.981181	−	0.193089i	$-0.938149\pi$
$857$	−23.0711	+	23.0711i	−0.788092	+	0.788092i	0.193089	+	0.981181i	$0.438149\pi$
$858$	−20.8078	−	6.15368i	−0.710367	−	0.210083i
$859$		−	17.3242i		−	0.591095i	−0.955328	−	0.295548i	$-0.904498\pi$
$859$		−	17.3242i		−	0.591095i	0.955328	−	0.295548i	$-0.0955021\pi$
$860$	−75.7946	−	16.4130i	−2.58457	−	0.559680i
$861$		0			0
$862$	0.808044	+	0.808044i	0.0275221	+	0.0275221i
$863$	−9.05228	−	9.05228i	−0.308143	−	0.308143i	0.536046	−	0.844189i	$-0.319917\pi$
$863$	−9.05228	−	9.05228i	−0.308143	−	0.308143i	−0.844189	+	0.536046i	$0.819917\pi$
$864$	28.1792	+	2.18064i	0.958674	+	0.0741868i
$865$	25.1229	+	5.44027i	0.854204	+	0.184975i
$866$			63.9997i			2.17480i
$867$	4.43285	−	14.9891i	0.150548	−	0.509056i
$868$		0			0
$869$	26.7577			0.907693
$870$	−42.2125	+	77.1233i	−1.43114	+	2.61472i
$871$	16.6517			0.564221
$872$	28.6332	−	28.6332i	0.969642	−	0.969642i
$873$	−3.89396	−	18.2413i	−0.131790	−	0.617376i
$874$		−	6.02310i		−	0.203734i
$875$		0			0
$876$	−30.8863	−	56.8263i	−1.04355	−	1.91998i
$877$	15.4630	+	15.4630i	0.522148	+	0.522148i	0.918220	−	0.396072i	$-0.129627\pi$
$877$	15.4630	+	15.4630i	0.522148	+	0.522148i	−0.396072	+	0.918220i	$0.629627\pi$
$878$	53.1419	+	53.1419i	1.79345	+	1.79345i
$879$	−10.0684	−	18.5243i	−0.339597	−	0.624810i
$880$	−13.4689	−	20.9146i	−0.454038	−	0.705029i
$881$			3.93409i			0.132543i	0.997802	+	0.0662714i	$0.0211103\pi$
$881$			3.93409i			0.132543i	−0.997802	+	0.0662714i	$0.978890\pi$
$882$		0			0
$883$	13.5688	−	13.5688i	0.456625	−	0.456625i	−0.440921	−	0.897546i	$-0.645348\pi$
$883$	13.5688	−	13.5688i	0.456625	−	0.456625i	0.897546	+	0.440921i	$0.145348\pi$
$884$	−71.6713			−2.41057
$885$	20.6256	−	6.03388i	0.693322	−	0.202827i
$886$	56.0200			1.88203
$887$	−4.92491	+	4.92491i	−0.165362	+	0.165362i	−0.784937	−	0.619575i	$-0.787305\pi$
$887$	−4.92491	+	4.92491i	−0.165362	+	0.165362i	0.619575	+	0.784937i	$0.287305\pi$
$888$	−1.92872	+	6.52168i	−0.0647235	+	0.218853i
$889$		0			0
$890$	11.3250	−	52.2982i	0.379614	−	1.75304i
$891$	12.8877	−	5.76494i	0.431753	−	0.193133i
$892$	55.5196	+	55.5196i	1.85893	+	1.85893i
$893$	−6.20669	−	6.20669i	−0.207699	−	0.207699i
$894$	3.57532	−	1.94326i	0.119577	−	0.0649923i
$895$	−31.2035	+	20.0950i	−1.04302	+	0.671703i
$896$		0			0
$897$	−7.34002	−	2.17073i	−0.245076	−	0.0724786i
$898$	−29.3724	+	29.3724i	−0.980170	+	0.980170i
$899$	24.5139			0.817585
$900$	−36.1966	−	56.5710i	−1.20655	−	1.88570i
$901$	−20.4428			−0.681049
$902$	18.1889	−	18.1889i	0.605624	−	0.605624i
$903$		0			0
$904$			29.3575i			0.976416i
$905$	21.9075	−	14.1084i	0.728229	−	0.468978i
$906$	53.1809	−	28.9049i	1.76682	−	0.960302i
$907$	−19.0317	−	19.0317i	−0.631938	−	0.631938i	0.316616	−	0.948554i	$-0.397453\pi$
$907$	−19.0317	−	19.0317i	−0.631938	−	0.631938i	−0.948554	+	0.316616i	$0.897453\pi$
$908$	−38.9777	−	38.9777i	−1.29352	−	1.29352i
$909$	1.65020	−	2.54594i	0.0547336	−	0.0844436i
$910$		0			0
$911$			17.7669i			0.588644i	0.955706	+	0.294322i	$0.0950938\pi$
$911$			17.7669i			0.588644i	−0.955706	+	0.294322i	$0.904906\pi$
$912$	5.85377	−	19.7937i	0.193838	−	0.655435i
$913$	−5.04043	+	5.04043i	−0.166814	+	0.166814i
$914$	74.2525			2.45605
$915$	27.5319	−	8.05427i	0.910177	−	0.266266i
$916$	19.9842			0.660298
$917$		0			0
$918$	51.2425	−	43.8814i	1.69125	−	1.44830i
$919$			8.50470i			0.280544i	0.990113	+	0.140272i	$0.0447977\pi$
$919$			8.50470i			0.280544i	−0.990113	+	0.140272i	$0.955202\pi$
$920$	−10.7504	−	16.6932i	−0.354430	−	0.550359i
$921$	13.8643	+	25.5082i	0.456843	+	0.840525i
$922$	27.5151	+	27.5151i	0.906162	+	0.906162i
$923$	8.03083	+	8.03083i	0.264338	+	0.264338i
$924$		0			0
$925$	2.91542	−	1.09368i	0.0958586	−	0.0359601i
$926$			1.77154i			0.0582164i
$927$	16.7235	−	3.56995i	0.549273	−	0.117253i
$928$	−34.3060	+	34.3060i	−1.12615	+	1.12615i
$929$	14.1589			0.464538			0.232269	−	0.972652i	$-0.425385\pi$
$929$	14.1589			0.464538			0.232269	+	0.972652i	$0.425385\pi$
$930$	−13.0067	+	23.7636i	−0.426507	+	0.779240i
$931$		0			0
$932$	−25.2594	+	25.2594i	−0.827399	+	0.827399i
$933$	14.3825	−	48.6323i	0.470861	−	1.59215i
$934$			32.3949i			1.05999i
$935$	−17.4890	−	3.78718i	−0.571952	−	0.123854i
$936$	−49.8054	−	32.2822i	−1.62794	−	1.05518i
$937$	−28.7165	−	28.7165i	−0.938127	−	0.938127i	0.0600678	−	0.998194i	$-0.480868\pi$
$937$	−28.7165	−	28.7165i	−0.938127	−	0.938127i	−0.998194	+	0.0600678i	$0.980868\pi$
$938$		0			0
$939$	−2.63804	+	1.43383i	−0.0860891	+	0.0467912i
$940$	−51.1112	−	11.0679i	−1.66706	−	0.360996i
$941$			17.4001i			0.567228i	0.958939	+	0.283614i	$0.0915335\pi$
$941$			17.4001i			0.567228i	−0.958939	+	0.283614i	$0.908467\pi$
$942$	−82.0269	−	24.2586i	−2.67258	−	0.790387i
$943$	6.41619	−	6.41619i	0.208940	−	0.208940i
$944$	39.3508			1.28076
$945$		0			0
$946$	−30.9259			−1.00549
$947$	−8.15693	+	8.15693i	−0.265065	+	0.265065i	−0.827108	−	0.562043i	$-0.810015\pi$
$947$	−8.15693	+	8.15693i	−0.265065	+	0.265065i	0.562043	+	0.827108i	$0.310015\pi$
$948$	126.848	+	37.5138i	4.11982	+	1.21839i
$949$			26.1703i			0.849522i
$950$	−20.0212	+	7.51069i	−0.649574	+	0.243679i
$951$	−9.25764	+	5.03172i	−0.300199	+	0.163165i
$952$		0			0
$953$	38.6159	+	38.6159i	1.25089	+	1.25089i	0.955321	+	0.295569i	$0.0955091\pi$
$953$	38.6159	+	38.6159i	1.25089	+	1.25089i	0.295569	+	0.955321i	$0.404491\pi$
$954$	−25.6748	−	16.6416i	−0.831251	−	0.538790i
$955$	−15.5626	−	24.1656i	−0.503594	−	0.781981i
$956$		−	53.0987i		−	1.71734i
$957$	−6.87298	+	23.2400i	−0.222172	+	0.751244i
$958$	−40.9545	+	40.9545i	−1.32318	+	1.32318i
$959$		0			0
$960$	0.370164	+	1.26533i	0.0119470	+	0.0408384i
$961$	−23.4466			−0.756343
$962$	3.51674	−	3.51674i	0.113384	−	0.113384i
$963$	11.6907	−	2.49559i	0.376727	−	0.0804194i
$964$		−	80.9159i		−	2.60613i
$965$	5.39535	−	24.9155i	0.173683	−	0.802058i
$966$		0			0
$967$	−18.6836	−	18.6836i	−0.600824	−	0.600824i	0.339707	−	0.940531i	$-0.389672\pi$
$967$	−18.6836	−	18.6836i	−0.600824	−	0.600824i	−0.940531	+	0.339707i	$0.889672\pi$
$968$	38.0701	+	38.0701i	1.22362	+	1.22362i
$969$	−7.09049	−	13.0455i	−0.227779	−	0.419081i
$970$	−29.7480	+	19.1577i	−0.955151	+	0.615115i
$971$			57.4980i			1.84520i	0.385761	+	0.922599i	$0.373939\pi$
$971$			57.4980i			1.84520i	−0.385761	+	0.922599i	$0.626061\pi$
$972$	69.1776	−	9.26098i	2.21887	−	0.297046i
$973$		0			0
$974$	41.3622			1.32533
$975$	1.93721	+	27.1056i	0.0620404	+	0.868074i
$976$	52.5270			1.68135
$977$	−2.08515	+	2.08515i	−0.0667100	+	0.0667100i	−0.739675	−	0.672965i	$-0.765021\pi$
$977$	−2.08515	+	2.08515i	−0.0667100	+	0.0667100i	0.672965	+	0.739675i	$0.265021\pi$
$978$	−11.6786	+	39.4896i	−0.373441	+	1.26274i
$979$		−	14.7501i		−	0.471415i
$980$		0			0
$981$	10.4797	−	16.1681i	0.334590	−	0.516209i
$982$	−0.543000	−	0.543000i	−0.0173278	−	0.0173278i
$983$	−11.6041	−	11.6041i	−0.370114	−	0.370114i	0.497405	−	0.867519i	$-0.334286\pi$
$983$	−11.6041	−	11.6041i	−0.370114	−	0.370114i	−0.867519	+	0.497405i	$0.834286\pi$
$984$	61.8191	−	33.5999i	1.97072	−	1.07113i
$985$	12.5496	−	57.9532i	0.399862	−	1.84654i
$986$			115.806i			3.68802i
$987$		0			0
$988$	−16.6937	+	16.6937i	−0.531097	+	0.531097i
$989$	−10.9092			−0.346893
$990$	−18.8820	−	18.9934i	−0.600110	−	0.603651i
$991$	−6.34125			−0.201436			−0.100718	−	0.994915i	$-0.532114\pi$
$991$	−6.34125			−0.201436			−0.100718	+	0.994915i	$0.532114\pi$
$992$	−10.5706	+	10.5706i	−0.335615	+	0.335615i
$993$	55.2432	+	16.3376i	1.75309	+	0.518457i
$994$		0			0
$995$	−5.09371	−	7.90951i	−0.161481	−	0.250748i
$996$	−30.9612	+	16.8281i	−0.981044	+	0.533218i
$997$	−1.89647	−	1.89647i	−0.0600618	−	0.0600618i	0.676438	−	0.736500i	$-0.263523\pi$
$997$	−1.89647	−	1.89647i	−0.0600618	−	0.0600618i	−0.736500	+	0.676438i	$0.763523\pi$
$998$	−36.3897	−	36.3897i	−1.15190	−	1.15190i
$999$	−0.249668	+	3.22633i	−0.00789916	+	0.102076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.j.h.197.1		24
3.2	odd	2	inner	735.2.j.h.197.12		24
5.3	odd	4	inner	735.2.j.h.638.12		24
7.2	even	3		735.2.y.g.557.12		48
7.3	odd	6		735.2.y.j.422.1		48
7.4	even	3		735.2.y.g.422.1		48
7.5	odd	6		735.2.y.j.557.12		48
7.6	odd	2		105.2.j.a.92.1	yes	24
15.8	even	4	inner	735.2.j.h.638.1		24
21.2	odd	6		735.2.y.g.557.1		48
21.5	even	6		735.2.y.j.557.1		48
21.11	odd	6		735.2.y.g.422.12		48
21.17	even	6		735.2.y.j.422.12		48
21.20	even	2		105.2.j.a.92.12	yes	24
35.3	even	12		735.2.y.j.128.1		48
35.13	even	4		105.2.j.a.8.12	yes	24
35.18	odd	12		735.2.y.g.128.1		48
35.23	odd	12		735.2.y.g.263.12		48
35.27	even	4		525.2.j.b.218.1		24
35.33	even	12		735.2.y.j.263.12		48
35.34	odd	2		525.2.j.b.407.12		24
105.23	even	12		735.2.y.g.263.1		48
105.38	odd	12		735.2.y.j.128.12		48
105.53	even	12		735.2.y.g.128.12		48
105.62	odd	4		525.2.j.b.218.12		24
105.68	odd	12		735.2.y.j.263.1		48
105.83	odd	4		105.2.j.a.8.1	✓	24
105.104	even	2		525.2.j.b.407.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.1	✓	24	105.83	odd	4
105.2.j.a.8.12	yes	24	35.13	even	4
105.2.j.a.92.1	yes	24	7.6	odd	2
105.2.j.a.92.12	yes	24	21.20	even	2
525.2.j.b.218.1		24	35.27	even	4
525.2.j.b.218.12		24	105.62	odd	4
525.2.j.b.407.1		24	105.104	even	2
525.2.j.b.407.12		24	35.34	odd	2
735.2.j.h.197.1		24	1.1	even	1	trivial
735.2.j.h.197.12		24	3.2	odd	2	inner
735.2.j.h.638.1		24	15.8	even	4	inner
735.2.j.h.638.12		24	5.3	odd	4	inner
735.2.y.g.128.1		48	35.18	odd	12
735.2.y.g.128.12		48	105.53	even	12
735.2.y.g.263.1		48	105.23	even	12
735.2.y.g.263.12		48	35.23	odd	12
735.2.y.g.422.1		48	7.4	even	3
735.2.y.g.422.12		48	21.11	odd	6
735.2.y.g.557.1		48	21.2	odd	6
735.2.y.g.557.12		48	7.2	even	3
735.2.y.j.128.1		48	35.3	even	12
735.2.y.j.128.12		48	105.38	odd	12
735.2.y.j.263.1		48	105.68	odd	12
735.2.y.j.263.12		48	35.33	even	12
735.2.y.j.422.1		48	7.3	odd	6
735.2.y.j.422.12		48	21.17	even	6
735.2.y.j.557.1		48	21.5	even	6
735.2.y.j.557.12		48	7.5	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79963 + 1.79963i) q^{2} +(1.66094 + 0.491204i) q^{3} -4.47734i q^{4} +(-1.87996 + 1.21069i) q^{5} +(-3.87306 + 2.10509i) q^{6} +(4.45829 + 4.45829i) q^{8} +(2.51744 + 1.63172i) q^{9} +O(q^{10})\)	\(q+(-1.79963 + 1.79963i) q^{2} +(1.66094 + 0.491204i) q^{3} -4.47734i q^{4} +(-1.87996 + 1.21069i) q^{5} +(-3.87306 + 2.10509i) q^{6} +(4.45829 + 4.45829i) q^{8} +(2.51744 + 1.63172i) q^{9} +(1.20443 - 5.56202i) q^{10} -1.56870i q^{11} +(2.19929 - 7.43658i) q^{12} +(-2.21881 + 2.21881i) q^{13} +(-3.71719 + 1.08744i) q^{15} -7.09187 q^{16} +(-3.60725 + 3.60725i) q^{17} +(-7.46695 + 1.59396i) q^{18} +1.68040i q^{19} +(5.42066 + 8.41719i) q^{20} +(2.82308 + 2.82308i) q^{22} +(0.995850 + 0.995850i) q^{23} +(5.21502 + 9.59488i) q^{24} +(2.06847 - 4.55208i) q^{25} -7.98606i q^{26} +(3.37980 + 3.94676i) q^{27} -8.91955 q^{29} +(4.73258 - 8.64655i) q^{30} -2.74834 q^{31} +(3.84616 - 3.84616i) q^{32} +(0.770553 - 2.60552i) q^{33} -12.9834i q^{34} +(7.30576 - 11.2714i) q^{36} +(0.440360 + 0.440360i) q^{37} +(-3.02410 - 3.02410i) q^{38} +(-4.77519 + 2.59542i) q^{39} +(-13.7790 - 2.98379i) q^{40} -6.44292i q^{41} +(-5.47734 + 5.47734i) q^{43} -7.02360 q^{44} +(-6.70817 - 0.0197326i) q^{45} -3.58432 q^{46} +(-3.69358 + 3.69358i) q^{47} +(-11.7792 - 3.48356i) q^{48} +(4.46958 + 11.9145i) q^{50} +(-7.76331 + 4.21952i) q^{51} +(9.93435 + 9.93435i) q^{52} +(2.83358 + 2.83358i) q^{53} +(-13.1851 - 1.02033i) q^{54} +(1.89921 + 2.94909i) q^{55} +(-0.825420 + 2.79104i) q^{57} +(16.0519 - 16.0519i) q^{58} -5.54871 q^{59} +(4.86882 + 16.6431i) q^{60} -7.40665 q^{61} +(4.94599 - 4.94599i) q^{62} -0.340400i q^{64} +(1.48498 - 6.85754i) q^{65} +(3.30226 + 6.07568i) q^{66} +(-3.75240 - 3.75240i) q^{67} +(16.1509 + 16.1509i) q^{68} +(1.16488 + 2.14321i) q^{69} -3.61943i q^{71} +(3.94878 + 18.4981i) q^{72} +(5.89737 - 5.89737i) q^{73} -1.58497 q^{74} +(5.67160 - 6.54469i) q^{75} +7.52372 q^{76} +(3.92279 - 13.2644i) q^{78} +17.0572i q^{79} +(13.3324 - 8.58604i) q^{80} +(3.67497 + 8.21551i) q^{81} +(11.5949 + 11.5949i) q^{82} +(-3.21312 - 3.21312i) q^{83} +(2.41421 - 11.1487i) q^{85} -19.7144i q^{86} +(-14.8148 - 4.38132i) q^{87} +(6.99372 - 6.99372i) q^{88} +9.40273 q^{89} +(12.1077 - 12.0367i) q^{90} +(4.45876 - 4.45876i) q^{92} +(-4.56482 - 1.35000i) q^{93} -13.2941i q^{94} +(-2.03444 - 3.15908i) q^{95} +(8.27749 - 4.49899i) q^{96} +(-4.39640 - 4.39640i) q^{97} +(2.55968 - 3.94911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3}+O(q^{10}) \) 24 * q + 4 * q^3	\( 24 q + 4 q^{3} + 16 q^{10} - 16 q^{12} + 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 8 q^{22} - 16 q^{25} + 16 q^{27} + 20 q^{30} - 28 q^{33} + 16 q^{36} - 16 q^{37} - 64 q^{40} - 40 q^{43} - 20 q^{45} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} - 32 q^{61} + 16 q^{66} + 24 q^{67} - 8 q^{72} - 32 q^{73} + 60 q^{75} - 32 q^{76} + 60 q^{78} + 52 q^{81} + 80 q^{82} + 24 q^{85} - 4 q^{87} + 96 q^{88} + 24 q^{90} - 76 q^{93} + 96 q^{96} - 24 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 + 16 * q^10 - 16 * q^12 + 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 8 * q^22 - 16 * q^25 + 16 * q^27 + 20 * q^30 - 28 * q^33 + 16 * q^36 - 16 * q^37 - 64 * q^40 - 40 * q^43 - 20 * q^45 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 - 32 * q^61 + 16 * q^66 + 24 * q^67 - 8 * q^72 - 32 * q^73 + 60 * q^75 - 32 * q^76 + 60 * q^78 + 52 * q^81 + 80 * q^82 + 24 * q^85 - 4 * q^87 + 96 * q^88 + 24 * q^90 - 76 * q^93 + 96 * q^96 - 24 * q^97

Introduction

L-functions

Modular forms

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