LMFDB - Embedded newform 750.2.l.c.107.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.5
Character	$\chi$	$=$	750.107
Dual form			750.2.l.c.743.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(1.31434 + 1.12805i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(-1.51403 - 1.51403i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.454984 + 2.96530i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(1.31434 + 1.12805i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(-1.51403 - 1.51403i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.454984 + 2.96530i) q^{9} +(-5.62798 + 1.82864i) q^{11} +(-0.140065 + 1.72638i) q^{12} +(-0.479621 - 0.941310i) q^{13} +(0.661655 + 2.03636i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-5.68203 + 0.899945i) q^{17} +(0.940823 - 2.84866i) q^{18} +(-3.16950 + 4.36244i) q^{19} +(-0.282042 - 3.69786i) q^{21} +(5.84476 + 0.925718i) q^{22} +(0.702799 - 1.37932i) q^{23} +(0.908558 - 1.47463i) q^{24} +1.05646i q^{26} +(-2.74701 + 4.41066i) q^{27} +(0.334951 - 2.11480i) q^{28} +(-3.67723 + 2.67167i) q^{29} +(8.62475 + 6.26624i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-9.45990 - 3.94521i) q^{33} +(5.47129 + 1.77773i) q^{34} +(-2.13154 + 2.11105i) q^{36} +(-0.197006 + 0.100380i) q^{37} +(4.80455 - 2.44804i) q^{38} +(0.431463 - 1.77824i) q^{39} +(1.54235 + 0.501139i) q^{41} +(-1.42749 + 3.42286i) q^{42} +(1.33532 - 1.33532i) q^{43} +(-4.78745 - 3.47829i) q^{44} +(-1.25240 + 0.909919i) q^{46} +(0.752458 - 4.75083i) q^{47} +(-1.47900 + 0.901424i) q^{48} -2.41543i q^{49} +(-8.48331 - 5.22681i) q^{51} +(0.479621 - 0.941310i) q^{52} +(-5.99683 - 0.949805i) q^{53} +(4.45000 - 2.68281i) q^{54} +(-1.25854 + 1.73224i) q^{56} +(-9.08688 + 2.15837i) q^{57} +(4.48935 - 0.711043i) q^{58} +(-2.24119 + 6.89769i) q^{59} +(-1.30934 - 4.02973i) q^{61} +(-4.83989 - 9.49882i) q^{62} +(3.80069 - 5.17841i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(6.63774 + 7.80992i) q^{66} +(-0.202800 - 1.28043i) q^{67} +(-4.06788 - 4.06788i) q^{68} +(2.47967 - 1.02010i) q^{69} +(2.39892 + 3.30183i) q^{71} +(2.85761 - 0.913257i) q^{72} +(-0.278530 - 0.141918i) q^{73} +0.221105 q^{74} -5.39228 q^{76} +(11.2895 + 5.75231i) q^{77} +(-1.19174 + 1.38854i) q^{78} +(-0.555462 - 0.764528i) q^{79} +(-8.58598 + 2.69833i) q^{81} +(-1.14673 - 1.14673i) q^{82} +(1.18337 + 7.47149i) q^{83} +(2.82585 - 2.40172i) q^{84} +(-1.79600 + 0.583556i) q^{86} +(-7.84692 - 0.636640i) q^{87} +(2.68654 + 5.27263i) q^{88} +(-2.67429 - 8.23061i) q^{89} +(-0.699010 + 2.15133i) q^{91} +(1.52899 - 0.242168i) q^{92} +(4.26719 + 17.9652i) q^{93} +(-2.82728 + 3.89142i) q^{94} +(1.72703 - 0.131724i) q^{96} +(11.9156 + 1.88725i) q^{97} +(-1.09658 + 2.15217i) q^{98} +(-7.98311 - 15.8566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$3$	1.31434	+	1.12805i	0.758835	+	0.651283i
$3$	1.31434	+	1.12805i	0.758835	+	0.651283i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	−0.658960	−	1.60180i	−0.269019	−	0.653933i
$7$	−1.51403	−	1.51403i	−0.572249	−	0.572249i	0.360507	−	0.932756i	$-0.382604\pi$
$7$	−1.51403	−	1.51403i	−0.572249	−	0.572249i	−0.932756	+	0.360507i	$0.882604\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	0.454984	+	2.96530i	0.151661	+	0.988433i
$10$		0			0
$11$	−5.62798	+	1.82864i	−1.69690	+	0.551357i	−0.988068	−	0.154020i	$-0.950778\pi$
$11$	−5.62798	+	1.82864i	−1.69690	+	0.551357i	−0.708833	+	0.705376i	$0.750778\pi$
$12$	−0.140065	+	1.72638i	−0.0404334	+	0.498362i
$13$	−0.479621	−	0.941310i	−0.133023	−	0.261072i	0.814881	−	0.579628i	$-0.196802\pi$
$13$	−0.479621	−	0.941310i	−0.133023	−	0.261072i	−0.947904	+	0.318556i	$0.896802\pi$
$14$	0.661655	+	2.03636i	0.176835	+	0.544241i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−5.68203	+	0.899945i	−1.37809	+	0.218269i	−0.801125	−	0.598497i	$-0.795765\pi$
$17$	−5.68203	+	0.899945i	−1.37809	+	0.218269i	−0.576969	+	0.816766i	$0.695765\pi$
$18$	0.940823	−	2.84866i	0.221754	−	0.671435i
$19$	−3.16950	+	4.36244i	−0.727133	+	1.00081i	0.272123	+	0.962262i	$0.412274\pi$
$19$	−3.16950	+	4.36244i	−0.727133	+	1.00081i	−0.999257	+	0.0385508i	$0.987726\pi$
$20$		0			0
$21$	−0.282042	−	3.69786i	−0.0615467	−	0.806939i
$22$	5.84476	+	0.925718i	1.24611	+	0.197364i
$23$	0.702799	−	1.37932i	0.146544	−	0.287608i	−0.806054	−	0.591843i	$-0.798401\pi$
$23$	0.702799	−	1.37932i	0.146544	−	0.287608i	0.952597	+	0.304235i	$0.0984007\pi$
$24$	0.908558	−	1.47463i	0.185459	−	0.301007i
$25$		0			0
$26$			1.05646i			0.207188i
$27$	−2.74701	+	4.41066i	−0.528663	+	0.848832i
$28$	0.334951	−	2.11480i	0.0632998	−	0.399659i
$29$	−3.67723	+	2.67167i	−0.682845	+	0.496116i	−0.874300	−	0.485386i	$-0.838679\pi$
$29$	−3.67723	+	2.67167i	−0.682845	+	0.496116i	0.191455	+	0.981501i	$0.438679\pi$
$30$		0			0
$31$	8.62475	+	6.26624i	1.54905	+	1.12545i	0.944324	+	0.329017i	$0.106718\pi$
$31$	8.62475	+	6.26624i	1.54905	+	1.12545i	0.604726	+	0.796433i	$0.293282\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−9.45990	−	3.94521i	−1.64676	−	0.686774i
$34$	5.47129	+	1.77773i	0.938319	+	0.304878i
$35$		0			0
$36$	−2.13154	+	2.11105i	−0.355257	+	0.351841i
$37$	−0.197006	+	0.100380i	−0.0323876	+	0.0165023i	−0.470109	−	0.882608i	$-0.655786\pi$
$37$	−0.197006	+	0.100380i	−0.0323876	+	0.0165023i	0.437722	+	0.899111i	$0.355786\pi$
$38$	4.80455	−	2.44804i	0.779402	−	0.397125i
$39$	0.431463	−	1.77824i	0.0690894	−	0.284747i
$40$		0			0
$41$	1.54235	+	0.501139i	0.240874	+	0.0782648i	0.426966	−	0.904268i	$-0.359582\pi$
$41$	1.54235	+	0.501139i	0.240874	+	0.0782648i	−0.186092	+	0.982532i	$0.559582\pi$
$42$	−1.42749	+	3.42286i	−0.220267	+	0.528159i
$43$	1.33532	−	1.33532i	0.203634	−	0.203634i	−0.597921	−	0.801555i	$-0.704006\pi$
$43$	1.33532	−	1.33532i	0.203634	−	0.203634i	0.801555	+	0.597921i	$0.204006\pi$
$44$	−4.78745	−	3.47829i	−0.721735	−	0.524371i
$45$		0			0
$46$	−1.25240	+	0.909919i	−0.184656	+	0.134160i
$47$	0.752458	−	4.75083i	0.109757	−	0.692980i	−0.870039	−	0.492983i	$-0.835907\pi$
$47$	0.752458	−	4.75083i	0.109757	−	0.692980i	0.979796	−	0.199998i	$-0.0640935\pi$
$48$	−1.47900	+	0.901424i	−0.213475	+	0.130109i
$49$		−	2.41543i		−	0.345062i
$50$		0			0
$51$	−8.48331	−	5.22681i	−1.18790	−	0.731899i
$52$	0.479621	−	0.941310i	0.0665115	−	0.130536i
$53$	−5.99683	−	0.949805i	−0.823728	−	0.130466i	−0.269680	−	0.962950i	$-0.586918\pi$
$53$	−5.99683	−	0.949805i	−0.823728	−	0.130466i	−0.554049	+	0.832484i	$0.686918\pi$
$54$	4.45000	−	2.68281i	0.605569	−	0.365084i
$55$		0			0
$56$	−1.25854	+	1.73224i	−0.168180	+	0.231480i
$57$	−9.08688	+	2.15837i	−1.20359	+	0.285883i
$58$	4.48935	−	0.711043i	0.589480	−	0.0933645i
$59$	−2.24119	+	6.89769i	−0.291779	+	0.898002i	0.692506	+	0.721412i	$0.256507\pi$
$59$	−2.24119	+	6.89769i	−0.291779	+	0.898002i	−0.984285	+	0.176590i	$0.943493\pi$
$60$		0			0
$61$	−1.30934	−	4.02973i	−0.167644	−	0.515954i	0.831578	−	0.555408i	$-0.187438\pi$
$61$	−1.30934	−	4.02973i	−0.167644	−	0.515954i	−0.999221	+	0.0394543i	$0.987438\pi$
$62$	−4.83989	−	9.49882i	−0.614667	−	1.20635i
$63$	3.80069	−	5.17841i	0.478842	−	0.652418i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	6.63774	+	7.80992i	0.817050	+	0.961334i
$67$	−0.202800	−	1.28043i	−0.0247759	−	0.156429i	0.972199	−	0.234158i	$-0.0752332\pi$
$67$	−0.202800	−	1.28043i	−0.0247759	−	0.156429i	−0.996975	+	0.0777287i	$0.975233\pi$
$68$	−4.06788	−	4.06788i	−0.493303	−	0.493303i
$69$	2.47967	−	1.02010i	0.298517	−	0.122806i
$70$		0			0
$71$	2.39892	+	3.30183i	0.284700	+	0.391856i	0.927283	−	0.374360i	$-0.122138\pi$
$71$	2.39892	+	3.30183i	0.284700	+	0.391856i	−0.642584	+	0.766215i	$0.722138\pi$
$72$	2.85761	−	0.913257i	0.336773	−	0.107628i
$73$	−0.278530	−	0.141918i	−0.0325994	−	0.0166102i	0.437615	−	0.899163i	$-0.355823\pi$
$73$	−0.278530	−	0.141918i	−0.0325994	−	0.0166102i	−0.470214	+	0.882552i	$0.655823\pi$
$74$	0.221105			0.0257030
$75$		0			0
$76$	−5.39228			−0.618537
$77$	11.2895	+	5.75231i	1.28656	+	0.655537i
$78$	−1.19174	+	1.38854i	−0.134938	+	0.157222i
$79$	−0.555462	−	0.764528i	−0.0624944	−	0.0860162i	0.776626	−	0.629962i	$-0.216930\pi$
$79$	−0.555462	−	0.764528i	−0.0624944	−	0.0860162i	−0.839120	+	0.543946i	$0.816930\pi$
$80$		0			0
$81$	−8.58598	+	2.69833i	−0.953998	+	0.299814i
$82$	−1.14673	−	1.14673i	−0.126635	−	0.126635i
$83$	1.18337	+	7.47149i	0.129891	+	0.820102i	0.963493	+	0.267735i	$0.0862752\pi$
$83$	1.18337	+	7.47149i	0.129891	+	0.820102i	−0.833601	+	0.552367i	$0.813725\pi$
$84$	2.82585	−	2.40172i	0.308325	−	0.262050i
$85$		0			0
$86$	−1.79600	+	0.583556i	−0.193668	+	0.0629264i
$87$	−7.84692	−	0.636640i	−0.841278	−	0.0682550i
$88$	2.68654	+	5.27263i	0.286386	+	0.562064i
$89$	−2.67429	−	8.23061i	−0.283474	−	0.872443i	−0.986852	−	0.161627i	$-0.948326\pi$
$89$	−2.67429	−	8.23061i	−0.283474	−	0.872443i	0.703378	−	0.710816i	$-0.251674\pi$
$90$		0			0
$91$	−0.699010	+	2.15133i	−0.0732762	+	0.225521i
$92$	1.52899	−	0.242168i	0.159408	−	0.0252477i
$93$	4.26719	+	17.9652i	0.442487	+	1.86290i
$94$	−2.82728	+	3.89142i	−0.291612	+	0.401369i
$95$		0			0
$96$	1.72703	−	0.131724i	0.176265	−	0.0134440i
$97$	11.9156	+	1.88725i	1.20985	+	0.191621i	0.728584	−	0.684956i	$-0.240179\pi$
$97$	11.9156	+	1.88725i	1.20985	+	0.191621i	0.481262	+	0.876577i	$0.340179\pi$
$98$	−1.09658	+	2.15217i	−0.110772	+	0.217402i
$99$	−7.98311	−	15.8566i	−0.802333	−	1.59365i
$100$		0			0
$101$			0.310282i			0.0308742i	0.999881	+	0.0154371i	$0.00491398\pi$
$101$			0.310282i			0.0308742i	−0.999881	+	0.0154371i	$0.995086\pi$
$102$	5.18576	+	8.50846i	0.513467	+	0.842463i
$103$	−1.38199	+	8.72553i	−0.136171	+	0.859752i	0.821147	+	0.570717i	$0.193335\pi$
$103$	−1.38199	+	8.72553i	−0.136171	+	0.859752i	−0.957318	+	0.289035i	$0.906665\pi$
$104$	−0.854692	+	0.620970i	−0.0838094	+	0.0608911i
$105$		0			0
$106$	4.91201	+	3.56879i	0.477097	+	0.346631i
$107$	−4.19190	+	4.19190i	−0.405246	+	0.405246i	−0.880077	−	0.474831i	$-0.842509\pi$
$107$	−4.19190	+	4.19190i	−0.405246	+	0.405246i	0.474831	+	0.880077i	$0.342509\pi$
$108$	−5.18295	+	0.370140i	−0.498730	+	0.0356167i
$109$	−1.79521	−	0.583300i	−0.171950	−	0.0558700i	0.221777	−	0.975098i	$-0.428814\pi$
$109$	−1.79521	−	0.583300i	−0.171950	−	0.0558700i	−0.393727	+	0.919227i	$0.628814\pi$
$110$		0			0
$111$	−0.372167	−	0.0903007i	−0.0353245	−	0.00857096i
$112$	1.90779	−	0.972066i	0.180269	−	0.0918516i
$113$	−7.55774	+	3.85086i	−0.710972	+	0.362258i	−0.771779	−	0.635891i	$-0.780633\pi$
$113$	−7.55774	+	3.85086i	−0.710972	+	0.362258i	0.0608066	+	0.998150i	$0.480633\pi$
$114$	9.07635	+	2.20224i	0.850078	+	0.206258i
$115$		0			0
$116$	−4.32285	−	1.40458i	−0.401366	−	0.130412i
$117$	2.57304	−	1.85050i	0.237878	−	0.171079i
$118$	5.12840	−	5.12840i	0.472108	−	0.472108i
$119$	9.96530	+	7.24021i	0.913517	+	0.663709i
$120$		0			0
$121$	19.4311	−	14.1175i	1.76646	−	1.28341i
$122$	−0.662830	+	4.18494i	−0.0600098	+	0.378887i
$123$	1.46186	+	2.39852i	0.131811	+	0.216267i
$124$			10.6608i			0.957366i
$125$		0			0
$126$	−5.73738	+	2.88852i	−0.511127	+	0.257330i
$127$	−4.74807	+	9.31862i	−0.421323	+	0.826894i	0.578613	+	0.815602i	$0.303594\pi$
$127$	−4.74807	+	9.31862i	−0.421323	+	0.826894i	−0.999936	+	0.0112913i	$0.996406\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$	3.26138	−	0.248751i	0.287148	−	0.0219013i
$130$		0			0
$131$	11.4805	−	15.8015i	1.00306	−	1.38059i	0.0796236	−	0.996825i	$-0.474628\pi$
$131$	11.4805	−	15.8015i	1.00306	−	1.38059i	0.923432	−	0.383762i	$-0.125372\pi$
$132$	−2.36864	−	9.97216i	−0.206164	−	0.867965i
$133$	11.4036	−	1.80615i	0.988816	−	0.156613i
$134$	−0.400605	+	1.23294i	−0.0346070	+	0.106510i
$135$		0			0
$136$	1.77773	+	5.47129i	0.152439	+	0.469159i
$137$	5.44330	+	10.6831i	0.465053	+	0.912717i	0.997791	+	0.0664369i	$0.0211631\pi$
$137$	5.44330	+	10.6831i	0.465053	+	0.912717i	−0.532738	+	0.846280i	$0.678837\pi$
$138$	−2.67251	−	0.216828i	−0.227500	−	0.0184576i
$139$	−22.1318	+	7.19107i	−1.87720	+	0.609939i	−0.888747	+	0.458399i	$0.848423\pi$
$139$	−22.1318	+	7.19107i	−1.87720	+	0.609939i	−0.988451	+	0.151540i	$0.951577\pi$
$140$		0			0
$141$	6.34819	−	5.39540i	0.534614	−	0.454375i
$142$	−0.638455	−	4.03104i	−0.0535779	−	0.338278i
$143$	4.42062	+	4.42062i	0.369671	+	0.369671i
$144$	−2.96076	−	0.483612i	−0.246730	−	0.0403010i
$145$		0			0
$146$	0.183742	+	0.252900i	0.0152066	+	0.0209301i
$147$	2.72474	−	3.17470i	0.224733	−	0.261845i
$148$	−0.197006	−	0.100380i	−0.0161938	−	0.00825116i
$149$	14.7140			1.20542			0.602711	−	0.797960i	$-0.294087\pi$
$149$	14.7140			1.20542			0.602711	+	0.797960i	$0.294087\pi$
$150$		0			0
$151$	−8.54879			−0.695691			−0.347845	−	0.937552i	$-0.613087\pi$
$151$	−8.54879			−0.695691			−0.347845	+	0.937552i	$0.613087\pi$
$152$	4.80455	+	2.44804i	0.389701	+	0.198562i
$153$	−5.25384	−	16.4394i	−0.424748	−	1.32905i
$154$	−7.44757	−	10.2507i	−0.600142	−	0.826025i
$155$		0			0
$156$	1.69224	−	0.696163i	0.135487	−	0.0557377i
$157$	−17.5864	−	17.5864i	−1.40355	−	1.40355i	−0.788446	−	0.615104i	$-0.789114\pi$
$157$	−17.5864	−	17.5864i	−1.40355	−	1.40355i	−0.615104	−	0.788446i	$-0.710886\pi$
$158$	0.147832	+	0.933375i	0.0117609	+	0.0742553i
$159$	−6.81045	−	8.01312i	−0.540104	−	0.635482i
$160$		0			0
$161$	−3.15239	+	1.02427i	−0.248443	+	0.0807240i
$162$	8.87518	+	1.49373i	0.697300	+	0.117358i
$163$	−0.912200	−	1.79029i	−0.0714490	−	0.140227i	0.852519	−	0.522696i	$-0.175074\pi$
$163$	−0.912200	−	1.79029i	−0.0714490	−	0.140227i	−0.923968	+	0.382469i	$0.875074\pi$
$164$	0.501139	+	1.54235i	0.0391324	+	0.120437i
$165$		0			0
$166$	2.33760	−	7.19438i	0.181433	−	0.558392i
$167$	14.6571	−	2.32146i	1.13420	−	0.179640i	0.439021	−	0.898477i	$-0.355325\pi$
$167$	14.6571	−	2.32146i	1.13420	−	0.179640i	0.695179	+	0.718837i	$0.255325\pi$
$168$	−3.60821	+	0.857043i	−0.278379	+	0.0661223i
$169$	6.98518	−	9.61428i	0.537322	−	0.739560i
$170$		0			0
$171$	−14.3780	−	7.41367i	−1.09951	−	0.566937i
$172$	1.86518	+	0.295415i	0.142218	+	0.0225252i
$173$	−2.27656	+	4.46800i	−0.173084	+	0.339696i	−0.961210	−	0.275818i	$-0.911051\pi$
$173$	−2.27656	+	4.46800i	−0.173084	+	0.339696i	0.788126	+	0.615514i	$0.211051\pi$
$174$	6.70263	+	4.12968i	0.508125	+	0.313070i
$175$		0			0
$176$		−	5.91761i		−	0.446057i
$177$	−10.7267	+	6.53772i	−0.806265	+	0.491405i
$178$	−1.35381	+	8.54762i	−0.101472	+	0.640672i
$179$	2.56353	−	1.86252i	0.191607	−	0.139211i	−0.487846	−	0.872930i	$-0.662217\pi$
$179$	2.56353	−	1.86252i	0.191607	−	0.139211i	0.679453	+	0.733719i	$0.262217\pi$
$180$		0			0
$181$	−5.04884	−	3.66820i	−0.375278	−	0.272655i	0.384118	−	0.923284i	$-0.374505\pi$
$181$	−5.04884	−	3.66820i	−0.375278	−	0.272655i	−0.759396	+	0.650629i	$0.774505\pi$
$182$	1.59951	−	1.59951i	0.118563	−	0.118563i
$183$	2.82484	−	6.77345i	0.208818	−	0.500707i
$184$	−1.47228	−	0.478373i	−0.108538	−	0.0352661i
$185$		0			0
$186$	4.35392	−	17.9443i	0.319245	−	1.31574i
$187$	30.3327	−	15.4553i	2.21815	−	1.13020i
$188$	4.28579	−	2.18372i	0.312573	−	0.159264i
$189$	10.8369	−	2.51881i	0.788270	−	0.183216i
$190$		0			0
$191$	19.9806	+	6.49209i	1.44574	+	0.469751i	0.923683	−	0.383157i	$-0.125163\pi$
$191$	19.9806	+	6.49209i	1.44574	+	0.469751i	0.522062	+	0.852908i	$0.325163\pi$
$192$	−1.59860	−	0.666690i	−0.115369	−	0.0481142i
$193$	7.00922	−	7.00922i	0.504535	−	0.504535i	−0.408309	−	0.912844i	$-0.633881\pi$
$193$	7.00922	−	7.00922i	0.504535	−	0.504535i	0.912844	+	0.408309i	$0.133881\pi$
$194$	−9.76009	−	7.09112i	−0.700734	−	0.509113i
$195$		0			0
$196$	1.95413	−	1.41976i	0.139580	−	0.101411i
$197$	1.59685	−	10.0821i	0.113771	−	0.718320i	−0.863186	−	0.504885i	$-0.831535\pi$
$197$	1.59685	−	10.0821i	0.113771	−	0.718320i	0.976957	−	0.213435i	$-0.0684652\pi$
$198$	−0.0857583	+	17.7526i	−0.00609458	+	1.26162i
$199$			15.1147i			1.07146i	0.844391	+	0.535728i	$0.179963\pi$
$199$			15.1147i			1.07146i	−0.844391	+	0.535728i	$0.820037\pi$
$200$		0			0
$201$	1.17784	−	1.91169i	0.0830786	−	0.134840i
$202$	0.140865	−	0.276463i	0.00991123	−	0.0194519i
$203$	9.61241	+	1.52246i	0.674659	+	0.106856i
$204$	−0.757790	−	9.93538i	−0.0530559	−	0.695616i
$205$		0			0
$206$	5.19267	−	7.14709i	0.361790	−	0.497962i
$207$	4.40986	+	1.45644i	0.306506	+	0.101229i
$208$	1.04345	−	0.165266i	0.0723503	−	0.0114592i
$209$	9.86055	−	30.3476i	0.682068	−	2.09919i
$210$		0			0
$211$	−1.22728	−	3.77719i	−0.0844897	−	0.260033i	0.899883	−	0.436132i	$-0.143652\pi$
$211$	−1.22728	−	3.77719i	−0.0844897	−	0.260033i	−0.984372	+	0.176099i	$0.943652\pi$
$212$	−2.75644	−	5.40982i	−0.189313	−	0.371548i
$213$	−0.571647	+	7.04585i	−0.0391686	+	0.482774i
$214$	5.63809	−	1.83193i	0.385412	−	0.125228i
$215$		0			0
$216$	4.78608	+	2.02321i	0.325652	+	0.137662i
$217$	−3.57084	−	22.5454i	−0.242404	−	1.53048i
$218$	1.33473	+	1.33473i	0.0903996	+	0.0903996i
$219$	−0.205992	−	0.500725i	−0.0139196	−	0.0338359i
$220$		0			0
$221$	3.57235	+	4.91692i	0.240302	+	0.330748i
$222$	0.290608	+	0.249419i	0.0195043	+	0.0167399i
$223$	11.9279	+	6.07755i	0.798748	+	0.406983i	0.805205	−	0.592996i	$-0.202055\pi$
$223$	11.9279	+	6.07755i	0.798748	+	0.406983i	−0.00645660	+	0.999979i	$0.502055\pi$
$224$	−2.14116			−0.143062
$225$		0			0
$226$	8.48225			0.564231
$227$	−0.762629	−	0.388579i	−0.0506175	−	0.0257909i	0.428499	−	0.903542i	$-0.359043\pi$
$227$	−0.762629	−	0.388579i	−0.0506175	−	0.0257909i	−0.479116	+	0.877752i	$0.659043\pi$
$228$	−7.08729	−	6.08278i	−0.469367	−	0.402842i
$229$	9.72545	+	13.3859i	0.642676	+	0.884567i	0.998755	−	0.0498887i	$-0.0158867\pi$
$229$	9.72545	+	13.3859i	0.642676	+	0.884567i	−0.356079	+	0.934456i	$0.615887\pi$
$230$		0			0
$231$	8.34939	+	20.2957i	0.549350	+	1.33536i
$232$	3.21402	+	3.21402i	0.211011	+	0.211011i
$233$	−0.852656	−	5.38346i	−0.0558593	−	0.352682i	−0.999749	−	0.0224200i	$-0.992863\pi$
$233$	−0.852656	−	5.38346i	−0.0558593	−	0.352682i	0.943889	−	0.330262i	$-0.107137\pi$
$234$	−3.13271	+	0.480671i	−0.204792	+	0.0314225i
$235$		0			0
$236$	−6.89769	+	2.24119i	−0.449001	+	0.145889i
$237$	0.132363	−	1.63144i	0.00859790	−	0.105974i
$238$	−5.59216	−	10.9752i	−0.362486	−	0.711418i
$239$	−2.69306	−	8.28837i	−0.174199	−	0.536130i	0.825397	−	0.564553i	$-0.190951\pi$
$239$	−2.69306	−	8.28837i	−0.174199	−	0.536130i	−0.999596	+	0.0284230i	$0.990951\pi$
$240$		0			0
$241$	−7.85699	+	24.1813i	−0.506113	+	1.55766i	0.292779	+	0.956180i	$0.405420\pi$
$241$	−7.85699	+	24.1813i	−0.506113	+	1.55766i	−0.798892	+	0.601475i	$0.794580\pi$
$242$	−23.7224	+	3.75726i	−1.52494	+	0.241526i
$243$	−14.3288	−	6.13893i	−0.919191	−	0.393813i
$244$	2.49051	−	3.42789i	0.159439	−	0.219448i
$245$		0			0
$246$	−0.213620	−	2.80077i	−0.0136199	−	0.178570i
$247$	5.62657	+	0.891162i	0.358010	+	0.0567033i
$248$	4.83989	−	9.49882i	0.307333	−	0.603176i
$249$	−6.87290	+	11.1550i	−0.435552	+	0.706918i
$250$		0			0
$251$			21.0935i			1.33141i	0.746215	+	0.665706i	$0.231869\pi$
$251$			21.0935i			1.33141i	−0.746215	+	0.665706i	$0.768131\pi$
$252$	6.42341	+	0.0310298i	0.404637	+	0.00195469i
$253$	−1.43306	+	9.04796i	−0.0900954	+	0.568840i
$254$	8.46113	−	6.14737i	0.530898	−	0.385720i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−11.8588	+	11.8588i	−0.739734	+	0.739734i	−0.972526	−	0.232792i	$-0.925214\pi$
$257$	−11.8588	+	11.8588i	−0.739734	+	0.739734i	0.232792	+	0.972526i	$0.425214\pi$
$258$	−3.01884	−	1.25900i	−0.187945	−	0.0783816i
$259$	0.450251	+	0.146295i	0.0279772	+	0.00909035i
$260$		0			0
$261$	−9.59537	−	9.68852i	−0.593938	−	0.599704i
$262$	−17.4029	+	8.86724i	−1.07516	+	0.547820i
$263$	−20.2720	+	10.3291i	−1.25002	+	0.636919i	−0.948572	−	0.316562i	$-0.897471\pi$
$263$	−20.2720	+	10.3291i	−1.25002	+	0.636919i	−0.301453	+	0.953481i	$0.597471\pi$
$264$	−2.41679	+	9.96060i	−0.148743	+	0.613033i
$265$		0			0
$266$	−10.9806	−	3.56783i	−0.673266	−	0.218757i
$267$	5.76965	−	13.8346i	0.353097	−	0.846662i
$268$	0.916684	−	0.916684i	0.0559954	−	0.0559954i
$269$	8.37684	+	6.08613i	0.510745	+	0.371078i	0.813106	−	0.582115i	$-0.197775\pi$
$269$	8.37684	+	6.08613i	0.510745	+	0.371078i	−0.302361	+	0.953193i	$0.597775\pi$
$270$		0			0
$271$	−0.517312	+	0.375849i	−0.0314245	+	0.0228312i	−0.603387	−	0.797449i	$-0.706182\pi$
$271$	−0.517312	+	0.375849i	−0.0314245	+	0.0228312i	0.571962	+	0.820280i	$0.306182\pi$
$272$	0.899945	−	5.68203i	0.0545672	−	0.344524i
$273$	−3.34556	+	2.03906i	−0.202482	+	0.123410i
$274$		−	11.9899i		−	0.724336i
$275$		0			0
$276$	2.28279	+	1.40649i	0.137408	+	0.0846608i
$277$	−13.7839	+	27.0524i	−0.828193	+	1.62542i	−0.0488650	+	0.998805i	$0.515560\pi$
$277$	−13.7839	+	27.0524i	−0.828193	+	1.62542i	−0.779328	+	0.626616i	$0.784440\pi$
$278$	22.9843	+	3.64035i	1.37851	+	0.218334i
$279$	−14.6572	+	28.4260i	−0.877501	+	1.70182i
$280$		0			0
$281$	12.7646	−	17.5690i	0.761473	−	1.04808i	−0.235617	−	0.971846i	$-0.575711\pi$
$281$	12.7646	−	17.5690i	0.761473	−	1.04808i	0.997090	−	0.0762322i	$-0.0242890\pi$
$282$	−8.10574	+	1.92532i	−0.482690	+	0.114651i
$283$	3.41737	−	0.541258i	0.203142	−	0.0321745i	−0.0540343	−	0.998539i	$-0.517208\pi$
$283$	3.41737	−	0.541258i	0.203142	−	0.0321745i	0.257176	+	0.966365i	$0.417208\pi$
$284$	−1.26119	+	3.88154i	−0.0748378	+	0.230327i
$285$		0			0
$286$	−1.93188	−	5.94572i	−0.114235	−	0.351578i
$287$	−1.57642	−	3.09390i	−0.0930531	−	0.182627i
$288$	2.41850	+	1.77506i	0.142512	+	0.104596i
$289$	15.3076	−	4.97374i	0.900446	−	0.292573i
$290$		0			0
$291$	13.5323	+	15.9219i	0.793275	+	0.933361i
$292$	−0.0489016	−	0.308752i	−0.00286175	−	0.0180684i
$293$	−12.2527	−	12.2527i	−0.715808	−	0.715808i	0.251936	−	0.967744i	$-0.418933\pi$
$293$	−12.2527	−	12.2527i	−0.715808	−	0.715808i	−0.967744	+	0.251936i	$0.918933\pi$
$294$	−3.86905	+	1.59167i	−0.225647	+	0.0928283i
$295$		0			0
$296$	0.129962	+	0.178878i	0.00755391	+	0.0103971i
$297$	7.39463	−	29.8464i	0.429080	−	1.73187i
$298$	−13.1103	−	6.68004i	−0.759460	−	0.386964i
$299$	−1.63544			−0.0945802
$300$		0			0
$301$	−4.04342			−0.233059
$302$	7.61703	+	3.88107i	0.438311	+	0.223330i
$303$	−0.350015	+	0.407816i	−0.0201078	+	0.0234284i
$304$	−3.16950	−	4.36244i	−0.181783	−	0.250203i
$305$		0			0
$306$	−2.78215	+	17.0328i	−0.159045	+	0.973703i
$307$	16.8133	+	16.8133i	0.959588	+	0.959588i	0.999215	−	0.0396263i	$-0.0126167\pi$
$307$	16.8133	+	16.8133i	0.959588	+	0.959588i	−0.0396263	+	0.999215i	$0.512617\pi$
$308$	1.98211	+	12.5146i	0.112941	+	0.713083i
$309$	−11.6593	+	9.90936i	−0.663273	+	0.563724i
$310$		0			0
$311$	7.39905	−	2.40410i	0.419562	−	0.136324i	−0.0916250	−	0.995794i	$-0.529206\pi$
$311$	7.39905	−	2.40410i	0.419562	−	0.136324i	0.511187	+	0.859470i	$0.329206\pi$
$312$	−1.82384	−	0.147973i	−0.103255	−	0.00837732i
$313$	−9.44284	−	18.5326i	−0.533741	−	1.04753i	−0.987679	−	0.156492i	$-0.949981\pi$
$313$	−9.44284	−	18.5326i	−0.533741	−	1.04753i	0.453939	−	0.891033i	$-0.350019\pi$
$314$	7.68555	+	23.6537i	0.433721	+	1.33486i
$315$		0			0
$316$	0.292024	−	0.898757i	0.0164276	−	0.0505590i
$317$	−0.214085	+	0.0339077i	−0.0120242	+	0.00190445i	−0.162444	−	0.986718i	$-0.551938\pi$
$317$	−0.214085	+	0.0339077i	−0.0120242	+	0.00190445i	0.150419	+	0.988622i	$0.451938\pi$
$318$	2.43027	+	10.2316i	0.136283	+	0.573761i
$319$	15.8099	−	21.7604i	0.885183	−	1.21835i
$320$		0			0
$321$	−10.2383	+	0.780892i	−0.571445	+	0.0435852i
$322$	3.27381	+	0.518520i	0.182442	+	0.0288960i
$323$	14.0832	−	27.6399i	0.783612	−	1.53793i
$324$	−7.22970	−	5.36017i	−0.401650	−	0.297787i
$325$		0			0
$326$			2.00929i			0.111284i
$327$	−1.70153	−	2.79176i	−0.0940947	−	0.154384i
$328$	0.253693	−	1.60175i	0.0140078	−	0.0884421i
$329$	−8.33214	+	6.05366i	−0.459366	+	0.333749i
$330$		0			0
$331$	5.81535	+	4.22510i	0.319640	+	0.232232i	0.736022	−	0.676958i	$-0.236702\pi$
$331$	5.81535	+	4.22510i	0.319640	+	0.232232i	−0.416382	+	0.909190i	$0.636702\pi$
$332$	−5.34899	+	5.34899i	−0.293564	+	0.293564i
$333$	−0.387290	−	0.538511i	−0.0212234	−	0.0295102i
$334$	−14.1135	−	4.58575i	−0.772255	−	0.250921i
$335$		0			0
$336$	3.60403	+	0.874463i	0.196616	+	0.0477058i
$337$	−6.01777	+	3.06621i	−0.327809	+	0.167027i	−0.610147	−	0.792288i	$-0.708890\pi$
$337$	−6.01777	+	3.06621i	−0.327809	+	0.167027i	0.282339	+	0.959315i	$0.408890\pi$
$338$	−10.5886	+	5.39518i	−0.575946	+	0.293459i
$339$	−14.2774	−	3.46420i	−0.775443	−	0.188150i
$340$		0			0
$341$	−59.9987	−	19.4947i	−3.24911	−	1.05570i
$342$	9.44517	+	13.1331i	0.510736	+	0.710157i
$343$	−14.2552	+	14.2552i	−0.769710	+	0.769710i
$344$	−1.52777	−	1.10999i	−0.0823718	−	0.0598466i
$345$		0			0
$346$	4.05686	−	2.94748i	0.218098	−	0.158458i
$347$	−0.716076	+	4.52113i	−0.0384410	+	0.242707i	−0.999425	−	0.0338958i	$-0.989209\pi$
$347$	−0.716076	+	4.52113i	−0.0384410	+	0.242707i	0.960984	+	0.276603i	$0.0892086\pi$
$348$	−4.09725	−	6.72250i	−0.219636	−	0.360364i
$349$			9.78119i			0.523575i	0.965126	+	0.261787i	$0.0843120\pi$
$349$			9.78119i			0.523575i	−0.965126	+	0.261787i	$0.915688\pi$
$350$		0			0
$351$	5.46932	+	0.470345i	0.291931	+	0.0251052i
$352$	−2.68654	+	5.27263i	−0.143193	+	0.281032i
$353$	10.7063	+	1.69571i	0.569840	+	0.0902538i	0.434704	−	0.900573i	$-0.356853\pi$
$353$	10.7063	+	1.69571i	0.569840	+	0.0902538i	0.135136	+	0.990827i	$0.456853\pi$
$354$	12.5256	−	0.955350i	0.665727	−	0.0507763i
$355$		0			0
$356$	5.08679	−	7.00137i	0.269600	−	0.371072i
$357$	4.93044	+	20.7575i	0.260947	+	1.09860i
$358$	−3.12969	+	0.495694i	−0.165409	+	0.0261982i
$359$	−6.51044	+	20.0371i	−0.343608	+	1.05752i	0.618717	+	0.785614i	$0.287653\pi$
$359$	−6.51044	+	20.0371i	−0.343608	+	1.05752i	−0.962325	+	0.271902i	$0.912347\pi$
$360$		0			0
$361$	−3.11386	−	9.58347i	−0.163887	−	0.504393i
$362$	2.83323	+	5.56052i	0.148911	+	0.292254i
$363$	41.4644	+	3.36411i	2.17632	+	0.176570i
$364$	−2.15133	+	0.699010i	−0.112760	+	0.0366381i
$365$		0			0
$366$	−5.59203	+	4.75273i	−0.292300	+	0.248429i
$367$	4.22522	+	26.6770i	0.220555	+	1.39253i	0.810809	+	0.585311i	$0.199028\pi$
$367$	4.22522	+	26.6770i	0.220555	+	1.39253i	−0.590254	+	0.807218i	$0.700972\pi$
$368$	1.09463	+	1.09463i	0.0570618	+	0.0570618i
$369$	−0.784283	+	4.80153i	−0.0408281	+	0.249958i
$370$		0			0
$371$	7.64135	+	10.5174i	0.396719	+	0.546037i
$372$	−12.0259	+	14.0119i	−0.623516	+	0.726483i
$373$	−23.8387	−	12.1464i	−1.23432	−	0.628917i	−0.289711	−	0.957114i	$-0.593559\pi$
$373$	−23.8387	−	12.1464i	−1.23432	−	0.628917i	−0.944609	+	0.328197i	$0.893559\pi$
$374$	−34.0432			−1.76033
$375$		0			0
$376$	−4.81005			−0.248060
$377$	4.27854	+	2.18003i	0.220356	+	0.112277i
$378$	−10.7993	−	2.67559i	−0.555455	−	0.137617i
$379$	−9.28018	−	12.7731i	−0.476691	−	0.656109i	0.501174	−	0.865347i	$-0.332902\pi$
$379$	−9.28018	−	12.7731i	−0.476691	−	0.656109i	−0.977865	+	0.209238i	$0.932902\pi$
$380$		0			0
$381$	−16.7525	+	6.89175i	−0.858257	+	0.353075i
$382$	−14.8555	−	14.8555i	−0.760073	−	0.760073i
$383$	2.49780	+	15.7705i	0.127632	+	0.805836i	0.965584	+	0.260092i	$0.0837529\pi$
$383$	2.49780	+	15.7705i	0.127632	+	0.805836i	−0.837952	+	0.545744i	$0.816247\pi$
$384$	1.12169	+	1.31977i	0.0572411	+	0.0673495i
$385$		0			0
$386$	−9.42739	+	3.06314i	−0.479841	+	0.155910i
$387$	4.56717	+	3.35207i	0.232162	+	0.170395i
$388$	5.47700	+	10.7492i	0.278053	+	0.545709i
$389$	−3.56490	−	10.9716i	−0.180748	−	0.556284i	0.819102	−	0.573648i	$-0.194472\pi$
$389$	−3.56490	−	10.9716i	−0.180748	−	0.556284i	−0.999849	+	0.0173647i	$0.994472\pi$
$390$		0			0
$391$	−2.75201	+	8.46982i	−0.139175	+	0.428337i
$392$	−2.38569	+	0.377857i	−0.120496	+	0.0190847i
$393$	32.9143	−	7.81799i	1.66031	−	0.394365i
$394$	−5.99998	+	8.25827i	−0.302275	+	0.416046i
$395$		0			0
$396$	8.13594	−	15.7788i	0.408846	−	0.792913i
$397$	−20.6866	−	3.27643i	−1.03823	−	0.164439i	−0.386030	−	0.922486i	$-0.626154\pi$
$397$	−20.6866	−	3.27643i	−1.03823	−	0.164439i	−0.652200	+	0.758047i	$0.726154\pi$
$398$	6.86195	−	13.4673i	0.343958	−	0.675057i
$399$	17.0256	+	10.4900i	0.852348	+	0.525155i
$400$		0			0
$401$			24.4394i			1.22045i	0.792229	+	0.610223i	$0.208920\pi$
$401$			24.4394i			1.22045i	−0.792229	+	0.610223i	$0.791080\pi$
$402$	−1.91735	+	1.16859i	−0.0956289	+	0.0582842i
$403$	1.76187	−	11.1240i	0.0877648	−	0.554125i
$404$	−0.251023	+	0.182379i	−0.0124889	+	0.00907370i
$405$		0			0
$406$	−7.87354	−	5.72046i	−0.390757	−	0.283902i
$407$	0.925189	−	0.925189i	0.0458599	−	0.0458599i
$408$	−3.83537	+	9.19652i	−0.189879	+	0.455296i
$409$	9.31361	+	3.02618i	0.460528	+	0.149635i	0.530087	−	0.847943i	$-0.322159\pi$
$409$	9.31361	+	3.02618i	0.460528	+	0.149635i	−0.0695588	+	0.997578i	$0.522159\pi$
$410$		0			0
$411$	−4.89675	+	20.1816i	−0.241539	+	0.995483i
$412$	−7.87141	+	4.01069i	−0.387797	+	0.197592i
$413$	13.8365	−	7.05006i	0.680851	−	0.346911i
$414$	−3.26800	−	3.29973i	−0.160614	−	0.162173i
$415$		0			0
$416$	−1.00475	−	0.326463i	−0.0492619	−	0.0160062i
$417$	−37.2007	−	15.5144i	−1.82173	−	0.759744i
$418$	−22.5634	+	22.5634i	−1.10361	+	1.10361i
$419$	20.8723	+	15.1646i	1.01968	+	0.740840i	0.966217	−	0.257730i	$-0.0829745\pi$
$419$	20.8723	+	15.1646i	1.01968	+	0.740840i	0.0534618	+	0.998570i	$0.482974\pi$
$420$		0			0
$421$	−31.8859	+	23.1664i	−1.55402	+	1.12906i	−0.613316	+	0.789837i	$0.710165\pi$
$421$	−31.8859	+	23.1664i	−1.55402	+	1.12906i	−0.940705	+	0.339225i	$0.889835\pi$
$422$	−0.621291	+	3.92268i	−0.0302440	+	0.190953i
$423$	14.4300	+	0.0697075i	0.701610	+	0.00338930i
$424$			6.07158i			0.294862i
$425$		0			0
$426$	3.70809	−	6.01838i	0.179658	−	0.291591i
$427$	−4.11875	+	8.08350i	−0.199320	+	0.391188i
$428$	−5.85525	−	0.927381i	−0.283024	−	0.0448267i
$429$	0.823500	+	10.7969i	0.0397590	+	0.521280i
$430$		0			0
$431$	−3.61295	+	4.97279i	−0.174030	+	0.239531i	−0.887118	−	0.461543i	$-0.847296\pi$
$431$	−3.61295	+	4.97279i	−0.174030	+	0.239531i	0.713088	+	0.701074i	$0.247296\pi$
$432$	−3.34591	−	3.97553i	−0.160980	−	0.191273i
$433$	−16.5283	+	2.61783i	−0.794299	+	0.125805i	−0.540380	−	0.841421i	$-0.681720\pi$
$433$	−16.5283	+	2.61783i	−0.794299	+	0.125805i	−0.253919	+	0.967225i	$0.581720\pi$
$434$	−7.05375	+	21.7092i	−0.338591	+	1.04208i
$435$		0			0
$436$	−0.583300	−	1.79521i	−0.0279350	−	0.0859752i
$437$	3.78968	+	7.43768i	0.181285	+	0.355792i
$438$	−0.0437846	+	0.539668i	−0.00209211	+	0.0257863i
$439$	19.1311	−	6.21606i	0.913076	−	0.296676i	0.185453	−	0.982653i	$-0.440625\pi$
$439$	19.1311	−	6.21606i	0.913076	−	0.296676i	0.727623	+	0.685977i	$0.240625\pi$
$440$		0			0
$441$	7.16248	−	1.09898i	0.341070	−	0.0523326i
$442$	−0.950753	−	6.00282i	−0.0452227	−	0.285525i
$443$	−17.1571	−	17.1571i	−0.815159	−	0.815159i	0.170243	−	0.985402i	$-0.445545\pi$
$443$	−17.1571	−	17.1571i	−0.815159	−	0.815159i	−0.985402	+	0.170243i	$0.945545\pi$
$444$	−0.145699	−	0.354167i	−0.00691459	−	0.0168080i
$445$		0			0
$446$	−7.86865	−	10.8303i	−0.372591	−	0.512828i
$447$	19.3393	+	16.5983i	0.914716	+	0.785071i
$448$	1.90779	+	0.972066i	0.0901345	+	0.0459258i
$449$	−15.9242			−0.751511			−0.375755	−	0.926719i	$-0.622617\pi$
$449$	−15.9242			−0.751511			−0.375755	+	0.926719i	$0.622617\pi$
$450$		0			0
$451$	−9.59671			−0.451891
$452$	−7.55774	−	3.85086i	−0.355486	−	0.181129i
$453$	−11.2360	−	9.64350i	−0.527914	−	0.453091i
$454$	0.503096	+	0.692453i	0.0236115	+	0.0324984i
$455$		0			0
$456$	3.55330	+	8.63736i	0.166398	+	0.404482i
$457$	2.30257	+	2.30257i	0.107710	+	0.107710i	0.758908	−	0.651198i	$-0.225733\pi$
$457$	2.30257	+	2.30257i	0.107710	+	0.107710i	−0.651198	+	0.758908i	$0.725733\pi$
$458$	−2.58835	−	16.3422i	−0.120946	−	0.763621i
$459$	11.6393	−	27.5337i	0.543274	−	1.28516i
$460$		0			0
$461$	9.43135	−	3.06443i	0.439262	−	0.142725i	−0.0810333	−	0.996711i	$-0.525822\pi$
$461$	9.43135	−	3.06443i	0.439262	−	0.142725i	0.520295	+	0.853987i	$0.325822\pi$
$462$	1.77471	−	21.8742i	0.0825668	−	1.01768i
$463$	10.4958	+	20.5992i	0.487783	+	0.957328i	0.995406	+	0.0957485i	$0.0305245\pi$
$463$	10.4958	+	20.5992i	0.487783	+	0.957328i	−0.507623	+	0.861580i	$0.669476\pi$
$464$	−1.40458	−	4.32285i	−0.0652059	−	0.200683i
$465$		0			0
$466$	−1.68432	+	5.18379i	−0.0780245	+	0.240135i
$467$	4.58995	−	0.726976i	0.212397	−	0.0336405i	−0.0493288	−	0.998783i	$-0.515708\pi$
$467$	4.58995	−	0.726976i	0.212397	−	0.0336405i	0.261726	+	0.965142i	$0.415708\pi$
$468$	3.00948	+	0.993939i	0.139113	+	0.0459448i
$469$	−1.63156	+	2.24565i	−0.0753383	+	0.103694i
$470$		0			0
$471$	−3.27611	−	42.9530i	−0.150955	−	1.97917i
$472$	7.16336	+	1.13457i	0.329721	+	0.0522226i
$473$	−5.07333	+	9.95697i	−0.233272	+	0.457822i
$474$	−0.858596	+	1.39353i	−0.0394366	+	0.0640072i
$475$		0			0
$476$			12.3178i			0.564585i
$477$	0.0879897	−	18.2145i	0.00402877	−	0.833986i
$478$	−1.36331	+	8.60761i	−0.0623564	+	0.393703i
$479$	−12.7801	+	9.28530i	−0.583939	+	0.424256i	−0.840142	−	0.542367i	$-0.817528\pi$
$479$	−12.7801	+	9.28530i	−0.583939	+	0.424256i	0.256203	+	0.966623i	$0.417528\pi$
$480$		0			0
$481$	0.188977	+	0.137300i	0.00861660	+	0.00626032i
$482$	17.9787	−	17.9787i	0.818908	−	0.818908i
$483$	−5.29875	−	2.20982i	−0.241101	−	0.100550i
$484$	22.8426	+	7.42201i	1.03830	+	0.337364i
$485$		0			0
$486$	9.98001	+	11.9750i	0.452702	+	0.543195i
$487$	−0.120793	+	0.0615473i	−0.00547367	+	0.00278898i	−0.456725	−	0.889608i	$-0.650978\pi$
$487$	−0.120793	+	0.0615473i	−0.00547367	+	0.00278898i	0.451252	+	0.892397i	$0.350978\pi$
$488$	−3.77529	+	1.92361i	−0.170899	+	0.0870776i
$489$	0.820608	−	3.38207i	0.0371092	−	0.152942i
$490$		0			0
$491$	8.65368	+	2.81175i	0.390535	+	0.126893i	0.497701	−	0.867349i	$-0.334178\pi$
$491$	8.65368	+	2.81175i	0.390535	+	0.126893i	−0.107166	+	0.994241i	$0.534178\pi$
$492$	−1.08119	+	2.59248i	−0.0487436	+	0.116878i
$493$	18.4898	−	18.4898i	0.832738	−	0.832738i
$494$	−4.60873	−	3.34844i	−0.207357	−	0.150654i
$495$		0			0
$496$	−8.62475	+	6.26624i	−0.387263	+	0.281363i
$497$	1.36703	−	8.63111i	0.0613198	−	0.387158i
$498$	11.1881	−	6.81893i	0.501349	−	0.305564i
$499$		−	27.5900i		−	1.23510i	−0.786532	−	0.617549i	$-0.788126\pi$
$499$		−	27.5900i		−	1.23510i	0.786532	−	0.617549i	$-0.211874\pi$
$500$		0			0
$501$	21.8831	+	13.4828i	0.977667	+	0.602368i
$502$	9.57626	−	18.7945i	0.427409	−	0.838838i
$503$	10.8159	+	1.71307i	0.482257	+	0.0763820i	0.392829	−	0.919611i	$-0.371496\pi$
$503$	10.8159	+	1.71307i	0.482257	+	0.0763820i	0.0894274	+	0.995993i	$0.471496\pi$
$504$	−5.70921	−	2.94381i	−0.254308	−	0.131128i
$505$		0			0
$506$	5.38455	−	7.41120i	0.239372	−	0.329468i
$507$	20.0263	−	4.75677i	0.889401	−	0.211256i
$508$	−10.3298	+	1.63607i	−0.458309	+	0.0725891i
$509$	2.83257	−	8.71775i	0.125551	−	0.386407i	−0.868450	−	0.495777i	$-0.834883\pi$
$509$	2.83257	−	8.71775i	0.125551	−	0.386407i	0.994001	+	0.109370i	$0.0348833\pi$
$510$		0			0
$511$	0.206834	+	0.636570i	0.00914980	+	0.0281602i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	−10.5346	−	25.9633i	−0.465114	−	1.14631i
$514$	15.9501	−	5.18250i	0.703529	−	0.228590i
$515$		0			0
$516$	2.11823	+	2.49230i	0.0932500	+	0.109717i
$517$	4.45276	+	28.1136i	0.195832	+	1.23643i
$518$	−0.334760	−	0.334760i	−0.0147085	−	0.0147085i
$519$	−8.03233	+	3.30439i	−0.352580	+	0.145047i
$520$		0			0
$521$	13.3932	+	18.4342i	0.586767	+	0.807615i	0.994417	−	0.105523i	$-0.0336517\pi$
$521$	13.3932	+	18.4342i	0.586767	+	0.807615i	−0.407650	+	0.913138i	$0.633652\pi$
$522$	4.15104	+	12.9887i	0.181686	+	0.568502i
$523$	−32.1380	−	16.3751i	−1.40530	−	0.716035i	−0.423488	−	0.905902i	$-0.639194\pi$
$523$	−32.1380	−	16.3751i	−1.40530	−	0.716035i	−0.981810	+	0.189867i	$0.939194\pi$
$524$	19.5318			0.853250
$525$		0			0
$526$	22.7518			0.992025
$527$	−54.6453	−	27.8432i	−2.38039	−	1.21287i
$528$	6.67539	−	7.77776i	0.290509	−	0.338484i
$529$	12.1105	+	16.6686i	0.526542	+	0.724723i
$530$		0			0
$531$	−21.4734	−	3.50747i	−0.931866	−	0.152211i
$532$	8.16406	+	8.16406i	0.353957	+	0.353957i
$533$	−0.268016	−	1.69218i	−0.0116090	−	0.0732966i
$534$	−11.4216	+	9.70732i	−0.494259	+	0.420077i
$535$		0			0
$536$	−1.23294	+	0.400605i	−0.0532548	+	0.0173035i
$537$	5.47038	+	0.443825i	0.236064	+	0.0191525i
$538$	−4.70077	−	9.22579i	−0.202665	−	0.397752i
$539$	4.41696	+	13.5940i	0.190252	+	0.585536i
$540$		0			0
$541$	10.6711	−	32.8422i	0.458786	−	1.41200i	−0.407847	−	0.913050i	$-0.633720\pi$
$541$	10.6711	−	32.8422i	0.458786	−	1.41200i	0.866633	−	0.498947i	$-0.166280\pi$
$542$	0.631560	−	0.100029i	0.0271278	−	0.00429663i
$543$	−2.49797	−	10.5166i	−0.107198	−	0.451312i
$544$	−3.38144	+	4.65416i	−0.144978	+	0.199545i
$545$		0			0
$546$	3.90663	−	0.297966i	0.167188	−	0.0127518i
$547$	−22.3156	−	3.53445i	−0.954148	−	0.151122i	−0.340098	−	0.940390i	$-0.610460\pi$
$547$	−22.3156	−	3.53445i	−0.954148	−	0.151122i	−0.614049	+	0.789268i	$0.710460\pi$
$548$	−5.44330	+	10.6831i	−0.232526	+	0.456359i
$549$	11.3536	−	5.71604i	0.484561	−	0.243955i
$550$		0			0
$551$		−	24.5096i		−	1.04414i
$552$	−1.39545	−	2.28956i	−0.0593942	−	0.0974500i
$553$	−0.316532	+	1.99850i	−0.0134603	+	0.0849851i
$554$	24.5631	−	17.8461i	1.04358	−	0.758209i
$555$		0			0
$556$	−18.8265	−	13.6782i	−0.798420	−	0.580086i
$557$	3.76017	−	3.76017i	0.159323	−	0.159323i	−0.622943	−	0.782267i	$-0.714063\pi$
$557$	3.76017	−	3.76017i	0.159323	−	0.159323i	0.782267	+	0.622943i	$0.214063\pi$
$558$	25.9647	−	18.6735i	1.09918	−	0.790513i
$559$	−1.89740	−	0.616502i	−0.0802513	−	0.0260752i
$560$		0			0
$561$	57.3019	+	13.9034i	2.41929	+	0.587003i
$562$	−19.3495	+	9.85907i	−0.816210	+	0.415880i
$563$	−21.6061	+	11.0089i	−0.910590	+	0.463969i	−0.845539	−	0.533913i	$-0.820721\pi$
$563$	−21.6061	+	11.0089i	−0.910590	+	0.463969i	−0.0650508	+	0.997882i	$0.520721\pi$
$564$	8.09634	+	1.96445i	0.340918	+	0.0827185i
$565$		0			0
$566$	−3.29063	−	1.06919i	−0.138315	−	0.0449414i
$567$	17.0848	+	8.91407i	0.717493	+	0.374356i
$568$	2.88591	−	2.88591i	0.121090	−	0.121090i
$569$	−24.5934	−	17.8681i	−1.03101	−	0.749071i	−0.0624977	−	0.998045i	$-0.519907\pi$
$569$	−24.5934	−	17.8681i	−1.03101	−	0.749071i	−0.968510	+	0.248974i	$0.919907\pi$
$570$		0			0
$571$	4.57335	−	3.32274i	0.191389	−	0.139052i	−0.487964	−	0.872864i	$-0.662260\pi$
$571$	4.57335	−	3.32274i	0.191389	−	0.139052i	0.679353	+	0.733811i	$0.262260\pi$
$572$	−0.977982	+	6.17473i	−0.0408915	+	0.258179i
$573$	18.9379	+	31.0720i	0.791141	+	1.29805i
$574$			3.47236i			0.144934i
$575$		0			0
$576$	−1.34904	−	2.67957i	−0.0562101	−	0.111649i
$577$	11.6678	−	22.8994i	0.485739	−	0.953316i	−0.509919	−	0.860223i	$-0.670324\pi$
$577$	11.6678	−	22.8994i	0.485739	−	0.953316i	0.995657	−	0.0930933i	$-0.0296755\pi$
$578$	−15.8972	−	2.51787i	−0.661236	−	0.104729i
$579$	17.1193	−	1.30572i	0.711454	−	0.0542639i
$580$		0			0
$581$	9.52039	−	13.1037i	0.394972	−	0.543633i
$582$	−4.82891	−	20.3301i	−0.200165	−	0.842708i
$583$	35.4869	−	5.62058i	1.46972	−	0.232781i
$584$	−0.0965991	+	0.297301i	−0.00399730	+	0.0123024i
$585$		0			0
$586$	5.35461	+	16.4798i	0.221197	+	0.680773i
$587$	−6.56280	−	12.8802i	−0.270876	−	0.531623i	0.714995	−	0.699129i	$-0.246429\pi$
$587$	−6.56280	−	12.8802i	−0.270876	−	0.531623i	−0.985871	+	0.167506i	$0.946429\pi$
$588$	4.16995	+	0.338318i	0.171966	+	0.0139520i
$589$	−54.6723	+	17.7641i	−2.25273	+	0.731957i
$590$		0			0
$591$	13.4720	−	11.4500i	0.554163	−	0.470990i
$592$	−0.0345885	−	0.218383i	−0.00142158	−	0.00897549i
$593$	−27.1124	−	27.1124i	−1.11337	−	1.11337i	−0.992691	−	0.120680i	$-0.961492\pi$
$593$	−27.1124	−	27.1124i	−1.11337	−	1.11337i	−0.120680	−	0.992691i	$-0.538508\pi$
$594$	−20.1387	+	23.2363i	−0.826299	+	0.953396i
$595$		0			0
$596$	8.64870	+	11.9039i	0.354265	+	0.487603i
$597$	−17.0503	+	19.8659i	−0.697821	+	0.813058i
$598$	1.45719	+	0.742476i	0.0595890	+	0.0303621i
$599$	22.2597			0.909506			0.454753	−	0.890618i	$-0.349728\pi$
$599$	22.2597			0.909506			0.454753	+	0.890618i	$0.349728\pi$
$600$		0			0
$601$	−0.661317			−0.0269757			−0.0134878	−	0.999909i	$-0.504293\pi$
$601$	−0.661317			−0.0269757			−0.0134878	+	0.999909i	$0.504293\pi$
$602$	3.60272	+	1.83568i	0.146836	+	0.0748165i
$603$	3.70457	−	1.18393i	0.150862	−	0.0482135i
$604$	−5.02485	−	6.91612i	−0.204458	−	0.281413i
$605$		0			0
$606$	0.497011	−	0.204463i	0.0201897	−	0.00830576i
$607$	−25.2285	−	25.2285i	−1.02399	−	1.02399i	−0.999705	−	0.0242876i	$-0.992268\pi$
$607$	−25.2285	−	25.2285i	−1.02399	−	1.02399i	−0.0242876	−	0.999705i	$-0.507732\pi$
$608$	0.843538	+	5.32589i	0.0342100	+	0.215993i
$609$	10.9166	+	12.8444i	0.442362	+	0.520480i
$610$		0			0
$611$	−4.83290	+	1.57031i	−0.195518	+	0.0635278i
$612$	10.2117	−	13.9133i	0.412782	−	0.562412i
$613$	11.3412	+	22.2583i	0.458065	+	0.899003i	0.998345	+	0.0575173i	$0.0183184\pi$
$613$	11.3412	+	22.2583i	0.458065	+	0.899003i	−0.540280	+	0.841485i	$0.681682\pi$
$614$	−7.34770	−	22.6139i	−0.296529	−	0.912623i
$615$		0			0
$616$	3.91542	−	12.0504i	0.157757	−	0.485525i
$617$	30.7946	−	4.87738i	1.23974	−	0.196356i	0.498081	−	0.867131i	$-0.334038\pi$
$617$	30.7946	−	4.87738i	1.23974	−	0.196356i	0.741661	+	0.670775i	$0.234038\pi$
$618$	14.8873	−	3.53610i	0.598853	−	0.142243i
$619$	−2.12975	+	2.93135i	−0.0856019	+	0.117821i	−0.849670	−	0.527314i	$-0.823199\pi$
$619$	−2.12975	+	2.93135i	−0.0856019	+	0.117821i	0.764068	+	0.645135i	$0.223199\pi$
$620$		0			0
$621$	4.15311	+	6.88882i	0.166659	+	0.276439i
$622$	−7.68404	−	1.21703i	−0.308102	−	0.0487985i
$623$	−8.41243	+	16.5103i	−0.337037	+	0.661472i
$624$	1.55788	+	0.959853i	0.0623651	+	0.0384249i
$625$		0			0
$626$			20.7996i			0.831321i
$627$	47.1939	−	28.7639i	1.88474	−	1.14872i
$628$	3.89068	−	24.5648i	0.155255	−	0.980241i
$629$	1.02906	−	0.747655i	0.0410312	−	0.0298109i
$630$		0			0
$631$	4.12680	+	2.99829i	0.164285	+	0.119360i	0.666890	−	0.745156i	$-0.267625\pi$
$631$	4.12680	+	2.99829i	0.164285	+	0.119360i	−0.502605	+	0.864516i	$0.667625\pi$
$632$	−0.668222	+	0.668222i	−0.0265805	+	0.0265805i
$633$	2.64781	−	6.34896i	0.105241	−	0.252349i
$634$	0.206145	+	0.0669805i	0.00818706	+	0.00266014i
$635$		0			0
$636$	2.47967	−	10.2198i	0.0983253	−	0.405240i
$637$	−2.27367	+	1.15849i	−0.0900861	+	0.0459012i
$638$	−23.9657	+	12.2112i	−0.948813	+	0.483444i
$639$	−8.69945	+	8.61580i	−0.344145	+	0.340836i
$640$		0			0
$641$	−45.1681	−	14.6760i	−1.78403	−	0.579668i	−0.784836	−	0.619703i	$-0.787253\pi$
$641$	−45.1681	−	14.6760i	−1.78403	−	0.579668i	−0.999198	+	0.0400355i	$0.987253\pi$
$642$	9.47689	+	3.95230i	0.374023	+	0.155985i
$643$	−17.9186	+	17.9186i	−0.706639	+	0.706639i	−0.965827	−	0.259188i	$-0.916545\pi$
$643$	−17.9186	+	17.9186i	−0.706639	+	0.706639i	0.259188	+	0.965827i	$0.416545\pi$
$644$	−2.68158	−	1.94828i	−0.105669	−	0.0767731i
$645$		0			0
$646$	−25.0965	+	18.2337i	−0.987409	+	0.717395i
$647$	−1.11876	+	7.06356i	−0.0439829	+	0.277697i	−0.999871	−	0.0160323i	$-0.994897\pi$
$647$	−1.11876	+	7.06356i	−0.0439829	+	0.277697i	0.955889	+	0.293730i	$0.0948965\pi$
$648$	4.00825	+	8.05816i	0.157459	+	0.316554i
$649$		−	42.9184i		−	1.68469i
$650$		0			0
$651$	20.7391	−	33.6604i	0.812831	−	1.31926i
$652$	0.912200	−	1.79029i	0.0357245	−	0.0701133i
$653$	22.9855	+	3.64054i	0.899490	+	0.142465i	0.589021	−	0.808118i	$-0.299514\pi$
$653$	22.9855	+	3.64054i	0.899490	+	0.142465i	0.310470	+	0.950583i	$0.399514\pi$
$654$	0.248642	+	3.25995i	0.00972269	+	0.127474i
$655$		0			0
$656$	−0.953223	+	1.31200i	−0.0372171	+	0.0512250i
$657$	0.294102	−	0.890494i	0.0114740	−	0.0347415i
$658$	10.1723	−	1.61113i	0.396557	−	0.0628085i
$659$	1.14382	−	3.52031i	0.0445568	−	0.137132i	−0.926303	−	0.376779i	$-0.877032\pi$
$659$	1.14382	−	3.52031i	0.0445568	−	0.137132i	0.970860	+	0.239647i	$0.0770317\pi$
$660$		0			0
$661$	−11.4157	−	35.1339i	−0.444019	−	1.36655i	−0.883556	−	0.468326i	$-0.844857\pi$
$661$	−11.4157	−	35.1339i	−0.444019	−	1.36655i	0.439537	−	0.898224i	$-0.355143\pi$
$662$	−3.26336	−	6.40470i	−0.126834	−	0.248926i
$663$	−0.851267	+	10.4923i	−0.0330605	+	0.407488i
$664$	7.19438	−	2.33760i	0.279196	−	0.0907163i
$665$		0			0
$666$	0.100599	+	0.655643i	0.00389815	+	0.0254056i
$667$	1.10073	+	6.94972i	0.0426203	+	0.269094i
$668$	10.4933	+	10.4933i	0.405999	+	0.405999i
$669$	8.82147	+	21.4432i	0.341058	+	0.829044i
$670$		0			0
$671$	14.7379	+	20.2849i	0.568949	+	0.783092i
$672$	−2.81421	−	2.41535i	−0.108561	−	0.0931740i
$673$	1.06415	+	0.542210i	0.0410198	+	0.0209006i	0.474380	−	0.880320i	$-0.342672\pi$
$673$	1.06415	+	0.542210i	0.0410198	+	0.0209006i	−0.433360	+	0.901221i	$0.642672\pi$
$674$	6.75390			0.260151
$675$		0			0
$676$	11.8839			0.457073
$677$	30.6338	+	15.6087i	1.17735	+	0.599892i	0.929470	−	0.368898i	$-0.120265\pi$
$677$	30.6338	+	15.6087i	1.17735	+	0.599892i	0.247884	+	0.968790i	$0.420265\pi$
$678$	11.1486	+	9.56844i	0.428158	+	0.367474i
$679$	−15.1832	−	20.8979i	−0.582679	−	0.801988i
$680$		0			0
$681$	−0.564016	−	1.37101i	−0.0216132	−	0.0525373i
$682$	44.6088	+	44.6088i	1.70816	+	1.70816i
$683$	7.05008	+	44.5125i	0.269764	+	1.70322i	0.635169	+	0.772373i	$0.280930\pi$
$683$	7.05008	+	44.5125i	0.269764	+	1.70322i	−0.365405	+	0.930849i	$0.619070\pi$
$684$	−2.45340	−	15.9897i	−0.0938081	−	0.611382i
$685$		0			0
$686$	19.1733	−	6.22977i	0.732038	−	0.237854i
$687$	−2.31751	+	28.5645i	−0.0884185	+	1.08980i
$688$	0.857327	+	1.68260i	0.0326853	+	0.0641485i
$689$	1.98215	+	6.10043i	0.0755138	+	0.232408i
$690$		0			0
$691$	1.10289	−	3.39434i	0.0419558	−	0.129127i	−0.927885	−	0.372867i	$-0.878375\pi$
$691$	1.10289	−	3.39434i	0.0419558	−	0.129127i	0.969840	+	0.243741i	$0.0783746\pi$
$692$	−4.95282	+	0.784450i	−0.188278	+	0.0298203i
$693$	−11.9207	+	36.0941i	−0.452832	+	1.37110i
$694$	2.69058	−	3.70326i	0.102133	−	0.140574i
$695$		0			0
$696$	0.598727	+	7.84991i	0.0226947	+	0.297550i
$697$	−9.21466	−	1.45946i	−0.349030	−	0.0552809i
$698$	4.44057	−	8.71510i	0.168078	−	0.329871i
$699$	4.95215	−	8.03754i	0.187308	−	0.304008i
$700$		0			0
$701$		−	19.6139i		−	0.740807i	−0.928871	−	0.370403i	$-0.879219\pi$
$701$		−	19.6139i		−	0.740807i	0.928871	−	0.370403i	$-0.120781\pi$
$702$	−4.65967	−	2.90210i	−0.175868	−	0.109533i
$703$	0.186511	−	1.17758i	0.00703438	−	0.0444133i
$704$	4.78745	−	3.47829i	0.180434	−	0.131093i
$705$		0			0
$706$	−8.76956	−	6.37146i	−0.330047	−	0.239793i
$707$	0.469776	−	0.469776i	0.0176677	−	0.0176677i
$708$	−11.5941	−	4.83527i	−0.435733	−	0.181721i
$709$	22.4237	+	7.28590i	0.842140	+	0.273628i	0.698150	−	0.715951i	$-0.254007\pi$
$709$	22.4237	+	7.28590i	0.842140	+	0.273628i	0.143990	+	0.989579i	$0.454007\pi$
$710$		0			0
$711$	2.01433	−	1.99496i	0.0755432	−	0.0748168i
$712$	−7.71092	+	3.92891i	−0.288979	+	0.147242i
$713$	14.7046	−	7.49238i	0.550692	−	0.280592i
$714$	5.03066	−	20.7335i	0.188268	−	0.775930i
$715$		0			0
$716$	3.01361	+	0.979183i	0.112624	+	0.0365938i
$717$	5.81015	−	13.9317i	0.216984	−	0.520287i
$718$	14.8975	−	14.8975i	0.555969	−	0.555969i
$719$	−30.2210	−	21.9569i	−1.12705	−	0.818853i	−0.141791	−	0.989897i	$-0.545286\pi$
$719$	−30.2210	−	21.9569i	−1.12705	−	0.818853i	−0.985263	+	0.171044i	$0.945286\pi$
$720$		0			0
$721$	15.3031	−	11.1183i	0.569916	−	0.414068i
$722$	−1.57634	+	9.95259i	−0.0586651	+	0.370397i
$723$	−37.6046	+	22.9194i	−1.39853	+	0.852381i
$724$		−	6.24071i		−	0.231934i
$725$		0			0
$726$	−35.4178	−	21.8219i	−1.31448	−	0.809886i
$727$	19.2896	−	37.8579i	0.715411	−	1.40407i	−0.190964	−	0.981597i	$-0.561161\pi$
$727$	19.2896	−	37.8579i	0.715411	−	1.40407i	0.906374	−	0.422476i	$-0.138839\pi$
$728$	2.23419	+	0.353862i	0.0828047	+	0.0131150i
$729$	−11.9078	−	24.2323i	−0.441031	−	0.897492i
$730$		0			0
$731$	−6.38561	+	8.78903i	−0.236180	+	0.325074i
$732$	7.14023	−	1.69599i	0.263911	−	0.0626855i
$733$	−44.0735	+	6.98056i	−1.62789	+	0.257833i	−0.902559	−	0.430565i	$-0.858314\pi$
$733$	−44.0735	+	6.98056i	−1.62789	+	0.257833i	−0.725333	+	0.688398i	$0.758314\pi$
$734$	8.34641	−	25.6876i	0.308072	−	0.948147i
$735$		0			0
$736$	−0.478373	−	1.47228i	−0.0176331	−	0.0542690i
$737$	3.48279	+	6.83537i	0.128290	+	0.251784i
$738$	2.87865	−	3.92214i	0.105965	−	0.144376i
$739$	8.01855	−	2.60538i	0.294967	−	0.0958406i	−0.157795	−	0.987472i	$-0.550439\pi$
$739$	8.01855	−	2.60538i	0.294967	−	0.0958406i	0.452762	+	0.891631i	$0.350439\pi$
$740$		0			0
$741$	6.38996	+	7.51837i	0.234741	+	0.276194i
$742$	−2.03368	−	12.8402i	−0.0746589	−	0.471378i
$743$	24.9192	+	24.9192i	0.914196	+	0.914196i	0.996599	−	0.0824029i	$-0.0262594\pi$
$743$	24.9192	+	24.9192i	0.914196	+	0.914196i	−0.0824029	+	0.996599i	$0.526259\pi$
$744$	17.0765	−	7.02502i	0.626053	−	0.257550i
$745$		0			0
$746$	15.7261	+	21.6451i	0.575772	+	0.792482i
$747$	−21.6168	+	6.90844i	−0.790916	+	0.252767i
$748$	30.3327	+	15.4553i	1.10907	+	0.565101i
$749$	12.6933			0.463804
$750$		0			0
$751$	−8.40064			−0.306544			−0.153272	−	0.988184i	$-0.548981\pi$
$751$	−8.40064			−0.306544			−0.153272	+	0.988184i	$0.548981\pi$
$752$	4.28579	+	2.18372i	0.156287	+	0.0796320i
$753$	−23.7946	+	27.7241i	−0.867125	+	1.01032i
$754$	−2.82250	−	3.88484i	−0.102789	−	0.141477i
$755$		0			0
$756$	8.40754	+	7.28674i	0.305779	+	0.265016i
$757$	5.57829	+	5.57829i	0.202746	+	0.202746i	0.801176	−	0.598429i	$-0.204208\pi$
$757$	5.57829	+	5.57829i	0.202746	+	0.202746i	−0.598429	+	0.801176i	$0.704208\pi$
$758$	2.46985	+	15.5940i	0.0897089	+	0.566400i
$759$	−12.0901	+	10.2755i	−0.438843	+	0.372978i
$760$		0			0
$761$	−5.92036	+	1.92364i	−0.214613	+	0.0697320i	−0.414350	−	0.910118i	$-0.635991\pi$
$761$	−5.92036	+	1.92364i	−0.214613	+	0.0697320i	0.199737	+	0.979849i	$0.435991\pi$
$762$	18.0554	+	1.46488i	0.654077	+	0.0530669i
$763$	1.83487	+	3.60114i	0.0664268	+	0.130370i
$764$	6.49209	+	19.9806i	0.234875	+	0.722872i
$765$		0			0
$766$	4.93411	−	15.1856i	0.178276	−	0.548679i
$767$	7.56779	−	1.19862i	0.273257	−	0.0432796i
$768$	−0.400270	−	1.68517i	−0.0144435	−	0.0608082i
$769$	2.22958	−	3.06876i	0.0804008	−	0.110662i	−0.766922	−	0.641740i	$-0.778213\pi$
$769$	2.22958	−	3.06876i	0.0804008	−	0.110662i	0.847323	+	0.531078i	$0.178213\pi$
$770$		0			0
$771$	−28.9640	+	2.20914i	−1.04311	+	0.0795601i
$772$	9.79050	+	1.55066i	0.352368	+	0.0558096i
$773$	15.4685	−	30.3587i	0.556364	−	1.09193i	−0.425960	−	0.904742i	$-0.640064\pi$
$773$	15.4685	−	30.3587i	0.556364	−	1.09193i	0.982325	−	0.187185i	$-0.0599363\pi$
$774$	−2.54757	−	5.06017i	−0.0915704	−	0.181884i
$775$		0			0
$776$		−	12.0641i		−	0.433077i
$777$	0.426754	+	0.700189i	0.0153097	+	0.0251192i
$778$	−1.80467	+	11.3942i	−0.0647005	+	0.408503i
$779$	−7.07466	+	5.14004i	−0.253476	+	0.184161i
$780$		0			0
$781$	−19.5390	−	14.1959i	−0.699159	−	0.507969i
$782$	6.29727	−	6.29727i	0.225190	−	0.225190i
$783$	−1.68240	−	23.5581i	−0.0601240	−	0.841898i
$784$	2.29721	+	0.746410i	0.0820433	+	0.0266575i
$785$		0			0
$786$	−32.8761	−	7.97690i	−1.17265	−	0.284527i
$787$	−27.9758	+	14.2544i	−0.997230	+	0.508114i	−0.874863	−	0.484371i	$-0.839049\pi$
$787$	−27.9758	+	14.2544i	−0.997230	+	0.508114i	−0.122367	+	0.992485i	$0.539049\pi$
$788$	9.09520	−	4.63424i	0.324003	−	0.165088i
$789$	−38.2961	−	9.29197i	−1.36338	−	0.330803i
$790$		0			0
$791$	17.2729	+	5.61232i	0.614155	+	0.199551i
$792$	−14.4126	+	10.3654i	−0.512129	+	0.368317i
$793$	−3.16524	+	3.16524i	−0.112401	+	0.112401i
$794$	16.9444	+	12.3108i	0.601334	+	0.436895i
$795$		0			0
$796$	−12.2281	+	8.88422i	−0.433413	+	0.314893i
$797$	−1.65300	+	10.4366i	−0.0585523	+	0.369685i	0.940962	+	0.338513i	$0.109924\pi$
$797$	−1.65300	+	10.4366i	−0.0585523	+	0.369685i	−0.999514	+	0.0311718i	$0.990076\pi$
$798$	−10.4076	−	17.0761i	−0.368425	−	0.604488i
$799$			27.6716i			0.978949i
$800$		0			0
$801$	23.1894	−	11.6749i	0.819358	−	0.412511i
$802$	11.0953	−	21.7757i	0.391787	−	0.768926i
$803$	1.82708	+	0.289381i	0.0644762	+	0.0102120i
$804$	2.23890	−	0.170765i	0.0789601	−	0.00602243i
$805$		0			0
$806$	−6.62002	+	9.11167i	−0.233180	+	0.320945i
$807$	4.14454	+	17.4488i	0.145895	+	0.614227i
$808$	0.306462	−	0.0485388i	0.0107813	−	0.00170759i
$809$	−4.15772	+	12.7961i	−0.146178	+	0.449889i	−0.997161	−	0.0753048i	$-0.976007\pi$
$809$	−4.15772	+	12.7961i	−0.146178	+	0.449889i	0.850983	+	0.525193i	$0.176007\pi$
$810$		0			0
$811$	6.32531	+	19.4673i	0.222112	+	0.683590i	0.998572	+	0.0534235i	$0.0170133\pi$
$811$	6.32531	+	19.4673i	0.222112	+	0.683590i	−0.776460	+	0.630166i	$0.782987\pi$
$812$	4.41834	+	8.67148i	0.155053	+	0.304309i
$813$	−1.10390	−	0.0895624i	−0.0387156	−	0.00314109i
$814$	−1.24438	+	0.404322i	−0.0436154	+	0.0141715i
$815$		0			0
$816$	7.59247	−	6.45294i	0.265790	−	0.225898i
$817$	1.59296	+	10.0575i	0.0557306	+	0.351869i
$818$	−6.92463	−	6.92463i	−0.242114	−	0.242114i
$819$	−6.69738	−	1.09395i	−0.234025	−	0.0382257i
$820$		0			0
$821$	11.1279	+	15.3163i	0.388368	+	0.534543i	0.957777	−	0.287512i	$-0.0928280\pi$
$821$	11.1279	+	15.3163i	0.388368	+	0.534543i	−0.569409	+	0.822054i	$0.692828\pi$
$822$	13.5253	−	15.7588i	0.471748	−	0.549652i
$823$	14.0722	+	7.17013i	0.490525	+	0.249935i	0.681715	−	0.731618i	$-0.261235\pi$
$823$	14.0722	+	7.17013i	0.490525	+	0.249935i	−0.191190	+	0.981553i	$0.561235\pi$
$824$	8.83429			0.307757
$825$		0			0
$826$	−15.5291			−0.540326
$827$	−6.05244	−	3.08387i	−0.210464	−	0.107237i	0.345581	−	0.938389i	$-0.387682\pi$
$827$	−6.05244	−	3.08387i	−0.210464	−	0.107237i	−0.556045	+	0.831152i	$0.687682\pi$
$828$	1.41377	+	4.42372i	0.0491317	+	0.153735i
$829$	−11.0240	−	15.1733i	−0.382880	−	0.526989i	0.573465	−	0.819230i	$-0.305599\pi$
$829$	−11.0240	−	15.1733i	−0.382880	−	0.526989i	−0.956345	+	0.292241i	$0.905599\pi$
$830$		0			0
$831$	−48.6333	+	20.0071i	−1.68707	+	0.694038i
$832$	0.747028	+	0.747028i	0.0258985	+	0.0258985i
$833$	2.17376	+	13.7246i	0.0753162	+	0.475528i
$834$	26.1027	+	30.7122i	0.903862	+	1.06348i
$835$		0			0
$836$	30.3476	−	9.86055i	1.04960	−	0.341034i
$837$	−51.3306	+	20.8274i	−1.77424	+	0.719899i
$838$	−11.7128	−	22.9876i	−0.404611	−	0.794093i
$839$	5.00273	+	15.3968i	0.172713	+	0.531557i	0.999522	−	0.0309268i	$-0.00984587\pi$
$839$	5.00273	+	15.3968i	0.172713	+	0.531557i	−0.826808	+	0.562484i	$0.809846\pi$
$840$		0			0
$841$	−2.57725	+	7.93197i	−0.0888709	+	0.273516i
$842$	38.9278	−	6.16556i	1.34154	−	0.212479i
$843$	36.5959	−	8.69245i	1.26043	−	0.299384i
$844$	2.33443	−	3.21307i	0.0803545	−	0.110598i
$845$		0			0
$846$	−12.8256	−	6.61319i	−0.440952	−	0.227366i
$847$	−50.7935	−	8.04490i	−1.74529	−	0.276426i
$848$	2.75644	−	5.40982i	0.0946566	−	0.185774i
$849$	5.10216	+	3.14358i	0.175106	+	0.107887i
$850$		0			0
$851$			0.342281i			0.0117332i
$852$	−6.03622	+	3.67898i	−0.206797	+	0.126040i
$853$	−5.14470	+	32.4823i	−0.176151	+	1.11217i	0.728194	+	0.685371i	$0.240360\pi$
$853$	−5.14470	+	32.4823i	−0.176151	+	1.11217i	−0.904345	+	0.426803i	$0.859640\pi$
$854$	7.33967	−	5.33258i	0.251158	−	0.182477i
$855$		0			0
$856$	4.79605	+	3.48453i	0.163926	+	0.119099i
$857$	14.2417	−	14.2417i	0.486489	−	0.486489i	−0.420708	−	0.907196i	$-0.638218\pi$
$857$	14.2417	−	14.2417i	0.486489	−	0.486489i	0.907196	+	0.420708i	$0.138218\pi$
$858$	4.16795	−	9.99398i	0.142291	−	0.341189i
$859$	−29.9968	−	9.74655i	−1.02348	−	0.332548i	−0.251269	−	0.967917i	$-0.580848\pi$
$859$	−29.9968	−	9.74655i	−1.02348	−	0.332548i	−0.772208	+	0.635369i	$0.780848\pi$
$860$		0			0
$861$	1.41813	−	5.84472i	0.0483299	−	0.199188i
$862$	5.47676	−	2.79055i	0.186539	−	0.0950465i
$863$	−19.3357	+	9.85205i	−0.658196	+	0.335368i	−0.750986	−	0.660318i	$-0.770421\pi$
$863$	−19.3357	+	9.85205i	−0.658196	+	0.335368i	0.0927901	+	0.995686i	$0.470421\pi$
$864$	1.17637	+	5.06124i	0.0400211	+	0.172187i
$865$		0			0
$866$	15.9153	+	5.17119i	0.540824	+	0.175724i
$867$	25.7300	+	10.7306i	0.873838	+	0.364431i
$868$	16.1407	−	16.1407i	0.547852	−	0.547852i
$869$	4.52418	+	3.28701i	0.153472	+	0.111504i
$870$		0			0
$871$	−1.10801	+	0.805017i	−0.0375435	+	0.0272770i
$872$	−0.295286	+	1.86436i	−0.00999963	+	0.0631352i
$873$	−0.174834	+	36.1920i	−0.00591723	+	1.22491i
$874$		−	8.34750i		−	0.282358i
$875$		0			0
$876$	0.284016	−	0.460970i	0.00959602	−	0.0155747i
$877$	3.43493	−	6.74142i	0.115989	−	0.227642i	−0.825712	−	0.564092i	$-0.809226\pi$
$877$	3.43493	−	6.74142i	0.115989	−	0.227642i	0.941701	+	0.336450i	$0.109226\pi$
$878$	−19.8679	−	3.14677i	−0.670510	−	0.106198i
$879$	−2.28250	−	29.9258i	−0.0769868	−	1.00937i
$880$		0			0
$881$	18.8656	−	25.9662i	0.635597	−	0.874825i	−0.362774	−	0.931877i	$-0.618170\pi$
$881$	18.8656	−	25.9662i	0.635597	−	0.874825i	0.998371	+	0.0570525i	$0.0181702\pi$
$882$	−6.88074	−	2.27249i	−0.231687	−	0.0765189i
$883$	−28.3550	+	4.49099i	−0.954222	+	0.151134i	−0.614083	−	0.789241i	$-0.710474\pi$
$883$	−28.3550	+	4.49099i	−0.954222	+	0.151134i	−0.340139	+	0.940375i	$0.610474\pi$
$884$	−1.87810	+	5.78018i	−0.0631672	+	0.194409i
$885$		0			0
$886$	7.49794	+	23.0763i	0.251898	+	0.775263i
$887$	5.50981	+	10.8136i	0.185001	+	0.363086i	0.964816	−	0.262924i	$-0.0846870\pi$
$887$	5.50981	+	10.8136i	0.185001	+	0.363086i	−0.779815	+	0.626010i	$0.784687\pi$
$888$	−0.0309692	+	0.381711i	−0.00103926	+	0.0128094i
$889$	21.2974	−	6.91994i	0.714291	−	0.232087i
$890$		0			0
$891$	43.3875	−	30.8868i	1.45353	−	1.03475i
$892$	2.09418	+	13.2221i	0.0701183	+	0.442710i
$893$	18.3403	+	18.3403i	0.613736	+	0.613736i
$894$	−9.69597	−	23.5690i	−0.324282	−	0.788265i
$895$		0			0
$896$	−1.25854	−	1.73224i	−0.0420450	−	0.0578699i
$897$	−2.14953	−	1.84487i	−0.0717708	−	0.0615985i
$898$	14.1886	+	7.22945i	0.473479	+	0.241250i
$899$	−48.4565			−1.61611
$900$		0			0
$901$	34.9289			1.16365
$902$	8.55073	+	4.35682i	0.284708	+	0.145066i
$903$	−5.31444	−	4.56120i	−0.176853	−	0.151787i
$904$	4.98574	+	6.86228i	0.165823	+	0.228236i
$905$		0			0
$906$	5.63331	+	13.6935i	0.187154	+	0.454935i
$907$	18.7112	+	18.7112i	0.621295	+	0.621295i	0.945863	−	0.324567i	$-0.105219\pi$
$907$	18.7112	+	18.7112i	0.621295	+	0.621295i	−0.324567	+	0.945863i	$0.605219\pi$
$908$	−0.133895	−	0.845381i	−0.00444347	−	0.0280549i
$909$	−0.920078	+	0.141173i	−0.0305171	+	0.00468243i
$910$		0			0
$911$	−37.0222	+	12.0293i	−1.22660	+	0.398547i	−0.849482	−	0.527618i	$-0.823085\pi$
$911$	−37.0222	+	12.0293i	−1.22660	+	0.398547i	−0.377119	+	0.926165i	$0.623085\pi$
$912$	0.755271	−	9.30911i	0.0250095	−	0.308255i
$913$	−20.3226	−	39.8854i	−0.672581	−	1.32002i
$914$	−1.00626	−	3.09695i	−0.0332842	−	0.102438i
$915$		0			0
$916$	−5.11297	+	15.7361i	−0.168937	+	0.519935i
$917$	−41.3058	+	6.54220i	−1.36404	+	0.216042i
$918$	−22.8707	+	19.2486i	−0.754845	+	0.635297i
$919$	−13.4831	+	18.5579i	−0.444766	+	0.612168i	−0.971263	−	0.238009i	$-0.923505\pi$
$919$	−13.4831	+	18.5579i	−0.444766	+	0.612168i	0.526497	+	0.850177i	$0.323505\pi$
$920$		0			0
$921$	3.13209	+	41.0648i	0.103206	+	1.35313i
$922$	−9.79461	−	1.55131i	−0.322568	−	0.0510898i
$923$	1.95747	−	3.84176i	0.0644311	−	0.126453i
$924$	−11.5119	+	18.6843i	−0.378715	+	0.614669i
$925$		0			0
$926$		−	23.1191i		−	0.759740i
$927$	−26.5026	−	0.128027i	−0.870459	−	0.00420496i
$928$	−0.711043	+	4.48935i	−0.0233411	+	0.147370i
$929$	−0.473139	+	0.343755i	−0.0155232	+	0.0112782i	−0.595520	−	0.803341i	$-0.703054\pi$
$929$	−0.473139	+	0.343755i	−0.0155232	+	0.0112782i	0.579997	+	0.814619i	$0.303054\pi$
$930$		0			0
$931$	10.5372	+	7.65572i	0.345342	+	0.250906i
$932$	3.85413	−	3.85413i	0.126246	−	0.126246i
$933$	12.4368	+	5.18673i	0.407163	+	0.169806i
$934$	−4.41971	−	1.43605i	−0.144617	−	0.0469891i
$935$		0			0
$936$	−2.23023	−	2.25188i	−0.0728974	−	0.0736051i
$937$	49.7213	−	25.3343i	1.62432	−	0.827634i	0.625445	−	0.780268i	$-0.284917\pi$
$937$	49.7213	−	25.3343i	1.62432	−	0.827634i	0.998878	−	0.0473659i	$-0.0150827\pi$
$938$	2.47323	−	1.26017i	0.0807538	−	0.0411461i
$939$	8.49469	−	35.0102i	0.277214	−	1.14251i
$940$		0			0
$941$	−12.5712	−	4.08462i	−0.409808	−	0.133155i	0.0968556	−	0.995298i	$-0.469121\pi$
$941$	−12.5712	−	4.08462i	−0.409808	−	0.133155i	−0.506664	+	0.862144i	$0.669121\pi$
$942$	−16.5812	+	39.7588i	−0.540246	+	1.29541i
$943$	1.77519	−	1.77519i	0.0578082	−	0.0578082i
$944$	−5.86752	−	4.26300i	−0.190972	−	0.138749i
$945$		0			0
$946$	9.04074	−	6.56848i	0.293940	−	0.213560i
$947$	−2.82795	+	17.8550i	−0.0918962	+	0.580210i	0.898174	+	0.439639i	$0.144894\pi$
$947$	−2.82795	+	17.8550i	−0.0918962	+	0.580210i	−0.990071	+	0.140571i	$0.955106\pi$
$948$	1.39767	−	0.851854i	0.0453941	−	0.0276669i
$949$			0.330250i			0.0107204i
$950$		0			0
$951$	−0.319630	−	0.196933i	−0.0103647	−	0.00638600i
$952$	5.59216	−	10.9752i	0.181243	−	0.355709i
$953$	−51.6458	−	8.17990i	−1.67297	−	0.264973i	−0.753305	−	0.657671i	$-0.771542\pi$
$953$	−51.6458	−	8.17990i	−1.67297	−	0.264973i	−0.919667	+	0.392698i	$0.871542\pi$
$954$	−8.34763	+	16.1893i	−0.270264	+	0.524149i
$955$		0			0
$956$	5.12250	−	7.05051i	0.165673	−	0.228030i
$957$	45.3265	−	10.7662i	1.46520	−	0.348022i
$958$	15.6026	−	2.47121i	0.504097	−	0.0798412i
$959$	7.93318	−	24.4158i	0.256176	−	0.788428i
$960$		0			0
$961$	25.5409	+	78.6068i	0.823900	+	2.53570i
$962$	−0.106047	−	0.208129i	−0.00341909	−	0.00671033i
$963$	−14.3375	−	10.5230i	−0.462019	−	0.339098i
$964$	−24.1813	+	7.85699i	−0.778828	+	0.253056i
$965$		0			0
$966$	3.71798	+	4.37455i	0.119624	+	0.140749i
$967$	−4.86314	−	30.7047i	−0.156388	−	0.987395i	−0.933642	−	0.358208i	$-0.883388\pi$
$967$	−4.86314	−	30.7047i	−0.156388	−	0.987395i	0.777254	−	0.629187i	$-0.216612\pi$
$968$	−16.9834	−	16.9834i	−0.545867	−	0.545867i
$969$	49.6895	−	20.4416i	1.59626	−	0.656679i
$970$		0			0
$971$	−25.2468	−	34.7493i	−0.810210	−	1.11516i	−0.991291	−	0.131690i	$-0.957960\pi$
$971$	−25.2468	−	34.7493i	−0.810210	−	1.11516i	0.181081	−	0.983468i	$-0.442040\pi$
$972$	−3.45574	−	15.2006i	−0.110843	−	0.487559i
$973$	44.3957	+	22.6208i	1.42326	+	0.725188i
$974$	0.135570			0.00434393
$975$		0			0
$976$	4.23711			0.135627
$977$	−52.8715	−	26.9394i	−1.69151	−	0.861867i	−0.988596	−	0.150590i	$-0.951883\pi$
$977$	−52.8715	−	26.9394i	−1.69151	−	0.861867i	−0.702912	−	0.711276i	$-0.748117\pi$
$978$	−2.26659	+	2.64090i	−0.0724777	+	0.0844466i
$979$	30.1017	+	41.4314i	0.962054	+	1.32415i
$980$		0			0
$981$	0.912865	−	5.58874i	0.0291455	−	0.178435i
$982$	−6.43398	−	6.43398i	−0.205317	−	0.205317i
$983$	−5.94792	−	37.5537i	−0.189709	−	1.19778i	−0.880260	−	0.474492i	$-0.842632\pi$
$983$	−5.94792	−	37.5537i	−0.189709	−	1.19778i	0.690550	−	0.723284i	$-0.257368\pi$
$984$	2.14031	−	1.81907i	0.0682305	−	0.0579899i
$985$		0			0
$986$	−24.8687	+	8.08033i	−0.791981	+	0.257330i
$987$	−17.7801	−	1.44255i	−0.565948	−	0.0459168i
$988$	2.58625	+	5.07580i	0.0822796	+	0.161483i
$989$	−0.903372	−	2.78029i	−0.0287255	−	0.0884081i
$990$		0			0
$991$	9.31171	−	28.6585i	0.295796	−	0.910367i	−0.687157	−	0.726509i	$-0.741141\pi$
$991$	9.31171	−	28.6585i	0.295796	−	0.910367i	0.982953	−	0.183858i	$-0.0588585\pi$
$992$	10.5295	−	1.66771i	0.334313	−	0.0529499i
$993$	2.87721	+	12.1132i	0.0913054	+	0.384402i
$994$	−5.13648	+	7.06976i	−0.162919	+	0.224239i
$995$		0			0
$996$	−13.0644	+	0.996443i	−0.413960	+	0.0315735i
$997$	33.4599	+	5.29952i	1.05968	+	0.167838i	0.661863	−	0.749625i	$-0.269766\pi$
$997$	33.4599	+	5.29952i	1.05968	+	0.167838i	0.397822	+	0.917463i	$0.369766\pi$
$998$	−12.5256	+	24.5829i	−0.396491	+	0.778157i
$999$	0.0984382	−	1.14467i	0.00311445	−	0.0362158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.c.107.5		80
3.2	odd	2	inner	750.2.l.c.107.6		80
5.2	odd	4		750.2.l.b.143.10		80
5.3	odd	4		150.2.l.a.83.1	yes	80
5.4	even	2		750.2.l.a.107.6		80
15.2	even	4		750.2.l.b.143.4		80
15.8	even	4		150.2.l.a.83.7	yes	80
15.14	odd	2		750.2.l.a.107.5		80
25.3	odd	20	inner	750.2.l.c.743.6		80
25.4	even	10		750.2.l.b.257.4		80
25.21	even	5		150.2.l.a.47.7	yes	80
25.22	odd	20		750.2.l.a.743.5		80
75.29	odd	10		750.2.l.b.257.10		80
75.47	even	20		750.2.l.a.743.6		80
75.53	even	20	inner	750.2.l.c.743.5		80
75.71	odd	10		150.2.l.a.47.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.1	✓	80	75.71	odd	10
150.2.l.a.47.7	yes	80	25.21	even	5
150.2.l.a.83.1	yes	80	5.3	odd	4
150.2.l.a.83.7	yes	80	15.8	even	4
750.2.l.a.107.5		80	15.14	odd	2
750.2.l.a.107.6		80	5.4	even	2
750.2.l.a.743.5		80	25.22	odd	20
750.2.l.a.743.6		80	75.47	even	20
750.2.l.b.143.4		80	15.2	even	4
750.2.l.b.143.10		80	5.2	odd	4
750.2.l.b.257.4		80	25.4	even	10
750.2.l.b.257.10		80	75.29	odd	10
750.2.l.c.107.5		80	1.1	even	1	trivial
750.2.l.c.107.6		80	3.2	odd	2	inner
750.2.l.c.743.5		80	75.53	even	20	inner
750.2.l.c.743.6		80	25.3	odd	20	inner

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(1.31434 + 1.12805i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(-1.51403 - 1.51403i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.454984 + 2.96530i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(1.31434 + 1.12805i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(-1.51403 - 1.51403i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.454984 + 2.96530i) q^{9} +(-5.62798 + 1.82864i) q^{11} +(-0.140065 + 1.72638i) q^{12} +(-0.479621 - 0.941310i) q^{13} +(0.661655 + 2.03636i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-5.68203 + 0.899945i) q^{17} +(0.940823 - 2.84866i) q^{18} +(-3.16950 + 4.36244i) q^{19} +(-0.282042 - 3.69786i) q^{21} +(5.84476 + 0.925718i) q^{22} +(0.702799 - 1.37932i) q^{23} +(0.908558 - 1.47463i) q^{24} +1.05646i q^{26} +(-2.74701 + 4.41066i) q^{27} +(0.334951 - 2.11480i) q^{28} +(-3.67723 + 2.67167i) q^{29} +(8.62475 + 6.26624i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-9.45990 - 3.94521i) q^{33} +(5.47129 + 1.77773i) q^{34} +(-2.13154 + 2.11105i) q^{36} +(-0.197006 + 0.100380i) q^{37} +(4.80455 - 2.44804i) q^{38} +(0.431463 - 1.77824i) q^{39} +(1.54235 + 0.501139i) q^{41} +(-1.42749 + 3.42286i) q^{42} +(1.33532 - 1.33532i) q^{43} +(-4.78745 - 3.47829i) q^{44} +(-1.25240 + 0.909919i) q^{46} +(0.752458 - 4.75083i) q^{47} +(-1.47900 + 0.901424i) q^{48} -2.41543i q^{49} +(-8.48331 - 5.22681i) q^{51} +(0.479621 - 0.941310i) q^{52} +(-5.99683 - 0.949805i) q^{53} +(4.45000 - 2.68281i) q^{54} +(-1.25854 + 1.73224i) q^{56} +(-9.08688 + 2.15837i) q^{57} +(4.48935 - 0.711043i) q^{58} +(-2.24119 + 6.89769i) q^{59} +(-1.30934 - 4.02973i) q^{61} +(-4.83989 - 9.49882i) q^{62} +(3.80069 - 5.17841i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(6.63774 + 7.80992i) q^{66} +(-0.202800 - 1.28043i) q^{67} +(-4.06788 - 4.06788i) q^{68} +(2.47967 - 1.02010i) q^{69} +(2.39892 + 3.30183i) q^{71} +(2.85761 - 0.913257i) q^{72} +(-0.278530 - 0.141918i) q^{73} +0.221105 q^{74} -5.39228 q^{76} +(11.2895 + 5.75231i) q^{77} +(-1.19174 + 1.38854i) q^{78} +(-0.555462 - 0.764528i) q^{79} +(-8.58598 + 2.69833i) q^{81} +(-1.14673 - 1.14673i) q^{82} +(1.18337 + 7.47149i) q^{83} +(2.82585 - 2.40172i) q^{84} +(-1.79600 + 0.583556i) q^{86} +(-7.84692 - 0.636640i) q^{87} +(2.68654 + 5.27263i) q^{88} +(-2.67429 - 8.23061i) q^{89} +(-0.699010 + 2.15133i) q^{91} +(1.52899 - 0.242168i) q^{92} +(4.26719 + 17.9652i) q^{93} +(-2.82728 + 3.89142i) q^{94} +(1.72703 - 0.131724i) q^{96} +(11.9156 + 1.88725i) q^{97} +(-1.09658 + 2.15217i) q^{98} +(-7.98311 - 15.8566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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