LMFDB - Embedded newform 950.2.l.m.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	950.101
Dual form			950.2.l.m.301.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.476729 + 0.173515i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.476729 - 0.173515i) q^{6} +(-0.753583 + 1.30524i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.10097 - 1.76292i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(0.476729 + 0.173515i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.476729 - 0.173515i) q^{6} +(-0.753583 + 1.30524i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.10097 - 1.76292i) q^{9} +(1.03564 + 1.79379i) q^{11} +(0.253662 - 0.439356i) q^{12} +(5.26367 - 1.91582i) q^{13} +(0.261717 + 1.48427i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(2.67504 - 2.24462i) q^{17} -2.74262 q^{18} +(3.36316 - 2.77293i) q^{19} +(-0.585735 + 0.491490i) q^{21} +(1.94637 + 0.708422i) q^{22} +(1.20473 - 6.83236i) q^{23} +(-0.0880960 - 0.499618i) q^{24} +(2.80074 - 4.85102i) q^{26} +(-1.45669 - 2.52306i) q^{27} +(1.15456 + 0.968788i) q^{28} +(6.38459 + 5.35731i) q^{29} +(0.844480 - 1.46268i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.182472 + 1.03485i) q^{33} +(0.606382 - 3.43896i) q^{34} +(-2.10097 + 1.76292i) q^{36} -0.297593 q^{37} +(0.793930 - 4.28599i) q^{38} +2.84177 q^{39} +(-2.94472 - 1.07179i) q^{41} +(-0.132775 + 0.753007i) q^{42} +(-1.40309 - 7.95732i) q^{43} +(1.94637 - 0.708422i) q^{44} +(-3.46888 - 6.00828i) q^{46} +(-3.39149 - 2.84580i) q^{47} +(-0.388633 - 0.326102i) q^{48} +(2.36423 + 4.09496i) q^{49} +(1.66475 - 0.605918i) q^{51} +(-0.972686 - 5.51638i) q^{52} +(-1.25223 + 7.10177i) q^{53} +(-2.73768 - 0.996433i) q^{54} +1.50717 q^{56} +(2.08447 - 0.738375i) q^{57} +8.33449 q^{58} +(-8.89828 + 7.46654i) q^{59} +(-2.23366 + 12.6677i) q^{61} +(-0.293285 - 1.66330i) q^{62} +(3.88430 - 1.41377i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.804971 + 0.675451i) q^{66} +(7.34453 + 6.16279i) q^{67} +(-1.74601 - 3.02417i) q^{68} +(1.75985 - 3.04815i) q^{69} +(0.508252 + 2.88244i) q^{71} +(-0.476251 + 2.70095i) q^{72} +(-5.58812 - 2.03391i) q^{73} +(-0.227970 + 0.191289i) q^{74} +(-2.14679 - 3.79358i) q^{76} -3.12177 q^{77} +(2.17692 - 1.82665i) q^{78} +(-11.2210 - 4.08411i) q^{79} +(1.17210 + 6.64729i) q^{81} +(-2.94472 + 1.07179i) q^{82} +(1.94881 - 3.37544i) q^{83} +(0.382311 + 0.662183i) q^{84} +(-6.18970 - 5.19377i) q^{86} +(2.11415 + 3.66181i) q^{87} +(1.03564 - 1.79379i) q^{88} +(-5.44096 + 1.98035i) q^{89} +(-1.46600 + 8.31409i) q^{91} +(-6.51936 - 2.37285i) q^{92} +(0.656386 - 0.550773i) q^{93} -4.42728 q^{94} -0.507325 q^{96} +(12.3746 - 10.3835i) q^{97} +(4.44329 + 1.61723i) q^{98} +(0.986452 - 5.59445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 12 q^{7} - 15 q^{8}+O(q^{10}) $ 30 * q + 12 * q^7 - 15 * q^8	$ 30 q + 12 q^{7} - 15 q^{8} + 6 q^{11} + 6 q^{14} + 30 q^{18} + 24 q^{19} + 24 q^{21} - 3 q^{22} - 3 q^{23} + 3 q^{26} + 18 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{33} - 24 q^{37} + 12 q^{38} - 24 q^{39} - 3 q^{41} - 12 q^{42} - 6 q^{43} - 3 q^{44} - 48 q^{47} + 15 q^{49} - 90 q^{51} + 18 q^{53} + 18 q^{54} - 24 q^{56} + 42 q^{57} - 36 q^{58} - 18 q^{59} - 60 q^{61} + 24 q^{62} + 21 q^{63} - 15 q^{64} - 78 q^{66} + 30 q^{67} + 12 q^{68} + 24 q^{69} - 30 q^{73} - 9 q^{74} - 3 q^{76} - 78 q^{77} - 6 q^{79} + 60 q^{81} - 3 q^{82} + 42 q^{83} - 6 q^{84} + 12 q^{86} + 54 q^{87} + 6 q^{88} - 30 q^{89} - 6 q^{91} + 6 q^{92} - 72 q^{93} - 78 q^{94} + 42 q^{97} - 6 q^{98} - 99 q^{99}+O(q^{100}) $ 30 * q + 12 * q^7 - 15 * q^8 + 6 * q^11 + 6 * q^14 + 30 * q^18 + 24 * q^19 + 24 * q^21 - 3 * q^22 - 3 * q^23 + 3 * q^26 + 18 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^33 - 24 * q^37 + 12 * q^38 - 24 * q^39 - 3 * q^41 - 12 * q^42 - 6 * q^43 - 3 * q^44 - 48 * q^47 + 15 * q^49 - 90 * q^51 + 18 * q^53 + 18 * q^54 - 24 * q^56 + 42 * q^57 - 36 * q^58 - 18 * q^59 - 60 * q^61 + 24 * q^62 + 21 * q^63 - 15 * q^64 - 78 * q^66 + 30 * q^67 + 12 * q^68 + 24 * q^69 - 30 * q^73 - 9 * q^74 - 3 * q^76 - 78 * q^77 - 6 * q^79 + 60 * q^81 - 3 * q^82 + 42 * q^83 - 6 * q^84 + 12 * q^86 + 54 * q^87 + 6 * q^88 - 30 * q^89 - 6 * q^91 + 6 * q^92 - 72 * q^93 - 78 * q^94 + 42 * q^97 - 6 * q^98 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	0.476729	+	0.173515i	0.275240	+	0.100179i	0.475952	−	0.879471i	$-0.342103\pi$
$3$	0.476729	+	0.173515i	0.275240	+	0.100179i	−0.200712	+	0.979650i	$0.564326\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	0.476729	−	0.173515i	0.194624	−	0.0708373i
$7$	−0.753583	+	1.30524i	−0.284828	+	0.493336i	−0.972567	−	0.232621i	$-0.925270\pi$
$7$	−0.753583	+	1.30524i	−0.284828	+	0.493336i	0.687740	+	0.725957i	$0.258603\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.10097	−	1.76292i	−0.700323	−	0.587641i
$10$		0			0
$11$	1.03564	+	1.79379i	0.312258	+	0.540847i	0.978851	−	0.204575i	$-0.0655813\pi$
$11$	1.03564	+	1.79379i	0.312258	+	0.540847i	−0.666593	+	0.745422i	$0.732248\pi$
$12$	0.253662	−	0.439356i	0.0732260	−	0.126831i
$13$	5.26367	−	1.91582i	1.45988	−	0.531352i	0.514546	−	0.857463i	$-0.327960\pi$
$13$	5.26367	−	1.91582i	1.45988	−	0.531352i	0.945332	+	0.326110i	$0.105738\pi$
$14$	0.261717	+	1.48427i	0.0699467	+	0.396688i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	2.67504	−	2.24462i	0.648792	−	0.544402i	−0.257912	−	0.966168i	$-0.583034\pi$
$17$	2.67504	−	2.24462i	0.648792	−	0.544402i	0.906704	+	0.421767i	$0.138590\pi$
$18$	−2.74262			−0.646442
$19$	3.36316	−	2.77293i	0.771563	−	0.636153i
$19$	3.36316	−	2.77293i	0.771563	−	0.636153i
$20$		0			0
$21$	−0.585735	+	0.491490i	−0.127818	+	0.107252i
$22$	1.94637	+	0.708422i	0.414968	+	0.151036i
$23$	1.20473	−	6.83236i	0.251204	−	1.42465i	−0.554429	−	0.832231i	$-0.687063\pi$
$23$	1.20473	−	6.83236i	0.251204	−	1.42465i	0.805633	−	0.592415i	$-0.201825\pi$
$24$	−0.0880960	−	0.499618i	−0.0179825	−	0.101984i
$25$		0			0
$26$	2.80074	−	4.85102i	0.549270	−	0.951363i
$27$	−1.45669	−	2.52306i	−0.280340	−	0.485562i
$28$	1.15456	+	0.968788i	0.218191	+	0.183084i
$29$	6.38459	+	5.35731i	1.18559	+	0.994827i	0.999925	+	0.0122134i	$0.00388773\pi$
$29$	6.38459	+	5.35731i	1.18559	+	0.994827i	0.185663	+	0.982613i	$0.440557\pi$
$30$		0			0
$31$	0.844480	−	1.46268i	0.151673	−	0.262705i	−0.780170	−	0.625568i	$-0.784867\pi$
$31$	0.844480	−	1.46268i	0.151673	−	0.262705i	0.931843	+	0.362863i	$0.118201\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.182472	+	1.03485i	0.0317643	+	0.180144i
$34$	0.606382	−	3.43896i	0.103994	−	0.589778i
$35$		0			0
$36$	−2.10097	+	1.76292i	−0.350162	+	0.293821i
$37$	−0.297593			−0.0489240			−0.0244620	−	0.999701i	$-0.507787\pi$
$37$	−0.297593			−0.0489240			−0.0244620	+	0.999701i	$0.507787\pi$
$38$	0.793930	−	4.28599i	0.128793	−	0.695279i
$39$	2.84177			0.455047
$40$		0			0
$41$	−2.94472	−	1.07179i	−0.459888	−	0.167386i	0.101678	−	0.994817i	$-0.467579\pi$
$41$	−2.94472	−	1.07179i	−0.459888	−	0.167386i	−0.561566	+	0.827432i	$0.689801\pi$
$42$	−0.132775	+	0.753007i	−0.0204877	+	0.116191i
$43$	−1.40309	−	7.95732i	−0.213969	−	1.21348i	−0.882686	−	0.469963i	$-0.844267\pi$
$43$	−1.40309	−	7.95732i	−0.213969	−	1.21348i	0.668717	−	0.743517i	$-0.266844\pi$
$44$	1.94637	−	0.708422i	0.293427	−	0.106799i
$45$		0			0
$46$	−3.46888	−	6.00828i	−0.511459	−	0.885872i
$47$	−3.39149	−	2.84580i	−0.494700	−	0.415103i	0.361007	−	0.932563i	$-0.382433\pi$
$47$	−3.39149	−	2.84580i	−0.494700	−	0.415103i	−0.855707	+	0.517460i	$0.826877\pi$
$48$	−0.388633	−	0.326102i	−0.0560944	−	0.0470688i
$49$	2.36423	+	4.09496i	0.337746	+	0.584994i
$50$		0			0
$51$	1.66475	−	0.605918i	0.233111	−	0.0848456i
$52$	−0.972686	−	5.51638i	−0.134887	−	0.764984i
$53$	−1.25223	+	7.10177i	−0.172008	+	0.975504i	0.769534	+	0.638606i	$0.220489\pi$
$53$	−1.25223	+	7.10177i	−0.172008	+	0.975504i	−0.941541	+	0.336898i	$0.890622\pi$
$54$	−2.73768	−	0.996433i	−0.372551	−	0.135597i
$55$		0			0
$56$	1.50717			0.201404
$57$	2.08447	−	0.738375i	0.276094	−	0.0978002i
$58$	8.33449			1.09437
$59$	−8.89828	+	7.46654i	−1.15846	+	0.972061i	−0.999883	−	0.0152860i	$-0.995134\pi$
$59$	−8.89828	+	7.46654i	−1.15846	+	0.972061i	−0.158574	+	0.987347i	$0.550690\pi$
$60$		0			0
$61$	−2.23366	+	12.6677i	−0.285991	+	1.62193i	0.415734	+	0.909486i	$0.363525\pi$
$61$	−2.23366	+	12.6677i	−0.285991	+	1.62193i	−0.701725	+	0.712448i	$0.747586\pi$
$62$	−0.293285	−	1.66330i	−0.0372472	−	0.211239i
$63$	3.88430	−	1.41377i	0.489376	−	0.178118i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	0.804971	+	0.675451i	0.0990851	+	0.0831423i
$67$	7.34453	+	6.16279i	0.897277	+	0.752904i	0.969656	−	0.244473i	$-0.0786148\pi$
$67$	7.34453	+	6.16279i	0.897277	+	0.752904i	−0.0723796	+	0.997377i	$0.523059\pi$
$68$	−1.74601	−	3.02417i	−0.211735	−	0.366735i
$69$	1.75985	−	3.04815i	0.211861	−	0.366954i
$70$		0			0
$71$	0.508252	+	2.88244i	0.0603184	+	0.342082i	1.00000		3.21012e-5i	$1.02181e-5\pi$
$71$	0.508252	+	2.88244i	0.0603184	+	0.342082i	−0.939682	+	0.342050i	$0.888879\pi$
$72$	−0.476251	+	2.70095i	−0.0561267	+	0.318311i
$73$	−5.58812	−	2.03391i	−0.654040	−	0.238051i	−0.00637874	−	0.999980i	$-0.502030\pi$
$73$	−5.58812	−	2.03391i	−0.654040	−	0.238051i	−0.647661	+	0.761929i	$0.724253\pi$
$74$	−0.227970	+	0.191289i	−0.0265009	+	0.0222369i
$75$		0			0
$76$	−2.14679	−	3.79358i	−0.246254	−	0.435154i
$77$	−3.12177			−0.355759
$78$	2.17692	−	1.82665i	0.246488	−	0.206828i
$79$	−11.2210	−	4.08411i	−1.26246	−	0.459498i	−0.377867	−	0.925860i	$-0.623342\pi$
$79$	−11.2210	−	4.08411i	−1.26246	−	0.459498i	−0.884594	+	0.466361i	$0.845565\pi$
$80$		0			0
$81$	1.17210	+	6.64729i	0.130233	+	0.738588i
$82$	−2.94472	+	1.07179i	−0.325190	+	0.118360i
$83$	1.94881	−	3.37544i	0.213910	−	0.370503i	−0.739025	−	0.673678i	$-0.764713\pi$
$83$	1.94881	−	3.37544i	0.213910	−	0.370503i	0.952935	+	0.303175i	$0.0980467\pi$
$84$	0.382311	+	0.662183i	0.0417136	+	0.0722501i
$85$		0			0
$86$	−6.18970	−	5.19377i	−0.667452	−	0.560059i
$87$	2.11415	+	3.66181i	0.226660	+	0.392587i
$88$	1.03564	−	1.79379i	0.110400	−	0.191218i
$89$	−5.44096	+	1.98035i	−0.576741	+	0.209916i	−0.613888	−	0.789393i	$-0.710395\pi$
$89$	−5.44096	+	1.98035i	−0.576741	+	0.209916i	0.0371471	+	0.999310i	$0.488173\pi$
$90$		0			0
$91$	−1.46600	+	8.31409i	−0.153678	+	0.871554i
$92$	−6.51936	−	2.37285i	−0.679691	−	0.247387i
$93$	0.656386	−	0.550773i	0.0680641	−	0.0571125i
$94$	−4.42728			−0.456639
$95$		0			0
$96$	−0.507325			−0.0517786
$97$	12.3746	−	10.3835i	1.25645	−	1.05429i	0.260401	−	0.965501i	$-0.416145\pi$
$97$	12.3746	−	10.3835i	1.25645	−	1.05429i	0.996051	−	0.0887875i	$-0.0282992\pi$
$98$	4.44329	+	1.61723i	0.448840	+	0.163364i
$99$	0.986452	−	5.59445i	0.0991422	−	0.562263i
$100$		0			0
$101$	13.4064	−	4.87952i	1.33398	−	0.485530i	0.426071	−	0.904690i	$-0.359897\pi$
$101$	13.4064	−	4.87952i	1.33398	−	0.485530i	0.907913	+	0.419160i	$0.137675\pi$
$102$	0.885793	−	1.53424i	0.0877066	−	0.151912i
$103$	−1.08491	−	1.87912i	−0.106900	−	0.185156i	0.807613	−	0.589713i	$-0.200759\pi$
$103$	−1.08491	−	1.87912i	−0.106900	−	0.185156i	−0.914513	+	0.404557i	$0.867426\pi$
$104$	−4.29098	−	3.60056i	−0.420765	−	0.353064i
$105$		0			0
$106$	3.60567	+	6.24520i	0.350213	+	0.606587i
$107$	−1.73942	+	3.01276i	−0.168156	+	0.291254i	−0.937771	−	0.347253i	$-0.887115\pi$
$107$	−1.73942	+	3.01276i	−0.168156	+	0.291254i	0.769616	+	0.638507i	$0.220448\pi$
$108$	−2.73768	+	0.996433i	−0.263433	+	0.0958818i
$109$	0.117999	+	0.669206i	0.0113023	+	0.0640983i	0.989937	−	0.141507i	$-0.0451948\pi$
$109$	0.117999	+	0.669206i	0.0113023	+	0.0640983i	−0.978635	+	0.205605i	$0.934084\pi$
$110$		0			0
$111$	−0.141871	−	0.0516370i	−0.0134658	−	0.00490116i
$112$	1.15456	−	0.968788i	0.109095	−	0.0915418i
$113$	−6.68249			−0.628636			−0.314318	−	0.949318i	$-0.601776\pi$
$113$	−6.68249			−0.628636			−0.314318	+	0.949318i	$0.601776\pi$
$114$	1.12217	−	1.90550i	0.105101	−	0.178466i
$115$		0			0
$116$	6.38459	−	5.35731i	0.592794	−	0.497413i
$117$	−14.4362	−	5.25436i	−1.33463	−	0.485766i
$118$	−2.01708	+	11.4394i	−0.185687	+	1.05308i
$119$	0.913919	+	5.18309i	0.0837788	+	0.475133i
$120$		0			0
$121$	3.35489	−	5.81084i	0.304990	−	0.528258i
$122$	6.43156	+	11.1398i	0.582286	+	1.00855i
$123$	−1.21786	−	1.02191i	−0.109811	−	0.0921424i
$124$	−1.29382	−	1.08564i	−0.116188	−	0.0974935i
$125$		0			0
$126$	2.06679	−	3.57979i	0.184125	−	0.318913i
$127$	4.32433	−	1.57393i	0.383723	−	0.139664i	−0.142954	−	0.989729i	$-0.545660\pi$
$127$	4.32433	−	1.57393i	0.383723	−	0.139664i	0.526677	+	0.850066i	$0.323438\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	0.711823	−	4.03695i	0.0626725	−	0.355433i
$130$		0			0
$131$	−6.72241	+	5.64077i	−0.587339	+	0.492836i	−0.887348	−	0.461100i	$-0.847455\pi$
$131$	−6.72241	+	5.64077i	−0.587339	+	0.492836i	0.300009	+	0.953936i	$0.403010\pi$
$132$	1.05081			0.0914617
$133$	1.08492	+	6.47938i	0.0940747	+	0.561834i
$134$	9.58760			0.828242
$135$		0			0
$136$	−3.28142	−	1.19434i	−0.281380	−	0.102414i
$137$	−0.822109	+	4.66241i	−0.0702375	+	0.398337i	0.929339	+	0.369228i	$0.120378\pi$
$137$	−0.822109	+	4.66241i	−0.0702375	+	0.398337i	−0.999576	+	0.0291085i	$0.990733\pi$
$138$	−0.611190	−	3.46623i	−0.0520279	−	0.295065i
$139$	−15.2785	+	5.56090i	−1.29590	+	0.471670i	−0.895660	−	0.444740i	$-0.853296\pi$
$139$	−15.2785	+	5.56090i	−1.29590	+	0.471670i	−0.400242	+	0.916410i	$0.631074\pi$
$140$		0			0
$141$	−1.12303	−	1.94515i	−0.0945766	−	0.163811i
$142$	2.24214	+	1.88138i	0.188156	+	0.157882i
$143$	8.88784	+	7.45779i	0.743239	+	0.623651i
$144$	1.37131	+	2.37518i	0.114276	+	0.197932i
$145$		0			0
$146$	−5.58812	+	2.03391i	−0.462476	+	0.168327i
$147$	0.416558	+	2.36242i	0.0343571	+	0.194849i
$148$	−0.0516765	+	0.293072i	−0.00424778	+	0.0240904i
$149$	7.49692	+	2.72866i	0.614172	+	0.223540i	0.630328	−	0.776329i	$-0.282921\pi$
$149$	7.49692	+	2.72866i	0.614172	+	0.223540i	−0.0161558	+	0.999869i	$0.505143\pi$
$150$		0			0
$151$	−14.3540			−1.16811			−0.584057	−	0.811712i	$-0.698536\pi$
$151$	−14.3540			−1.16811			−0.584057	+	0.811712i	$0.698536\pi$
$152$	−4.08301	−	1.52612i	−0.331176	−	0.123785i
$153$	−9.57728			−0.774277
$154$	−2.39142	+	2.00664i	−0.192706	+	0.161699i
$155$		0			0
$156$	0.493468	−	2.79860i	0.0395090	−	0.224067i
$157$	0.0159536	+	0.0904771i	0.00127323	+	0.00722086i	0.985438	−	0.170037i	$-0.0543886\pi$
$157$	0.0159536	+	0.0904771i	0.00127323	+	0.00722086i	−0.984165	+	0.177257i	$0.943277\pi$
$158$	−11.2210	+	4.08411i	−0.892695	+	0.324914i
$159$	−1.82924	+	3.16834i	−0.145068	+	0.251266i
$160$		0			0
$161$	8.01004	+	6.72122i	0.631279	+	0.529706i
$162$	5.17067	+	4.33871i	0.406247	+	0.340881i
$163$	9.31917	+	16.1413i	0.729934	+	1.26428i	0.956911	+	0.290382i	$0.0937825\pi$
$163$	9.31917	+	16.1413i	0.729934	+	1.26428i	−0.226977	+	0.973900i	$0.572884\pi$
$164$	−1.56685	+	2.71387i	−0.122351	+	0.211918i
$165$		0			0
$166$	−0.676816	−	3.83841i	−0.0525311	−	0.297919i
$167$	0.465767	−	2.64150i	0.0360421	−	0.204405i	−0.961469	−	0.274913i	$-0.911351\pi$
$167$	0.465767	−	2.64150i	0.0360421	−	0.204405i	0.997511	+	0.0705080i	$0.0224620\pi$
$168$	0.718510	+	0.261516i	0.0554343	+	0.0201764i
$169$	14.0772	−	11.8122i	1.08286	−	0.908631i
$170$		0			0
$171$	−11.9544	−	0.103164i	−0.914173	−	0.00788917i
$172$	−8.08007			−0.616100
$173$	−1.96206	+	1.64637i	−0.149173	+	0.125171i	−0.714320	−	0.699819i	$-0.753264\pi$
$173$	−1.96206	+	1.64637i	−0.149173	+	0.125171i	0.565147	+	0.824990i	$0.308819\pi$
$174$	3.97330	+	1.44616i	0.301215	+	0.109633i
$175$		0			0
$176$	−0.359675	−	2.03982i	−0.0271115	−	0.153757i
$177$	−5.53763	+	2.01553i	−0.416234	+	0.151497i
$178$	−2.89507	+	5.01441i	−0.216995	+	0.375846i
$179$	10.6448	+	18.4373i	0.795629	+	1.37807i	0.922439	+	0.386143i	$0.126193\pi$
$179$	10.6448	+	18.4373i	0.795629	+	1.37807i	−0.126810	+	0.991927i	$0.540474\pi$
$180$		0			0
$181$	−7.68024	−	6.44449i	−0.570868	−	0.479015i	0.311066	−	0.950388i	$-0.399314\pi$
$181$	−7.68024	−	6.44449i	−0.570868	−	0.479015i	−0.881934	+	0.471373i	$0.843758\pi$
$182$	4.22118	+	7.31129i	0.312894	+	0.541949i
$183$	−3.26289	+	5.65150i	−0.241200	+	0.417771i
$184$	−6.51936	+	2.37285i	−0.480614	+	0.174929i
$185$		0			0
$186$	0.148791	−	0.843834i	0.0109099	−	0.0618729i
$187$	6.79676	+	2.47382i	0.497029	+	0.180904i
$188$	−3.39149	+	2.84580i	−0.247350	+	0.207551i
$189$	4.39094			0.319394
$190$		0			0
$191$	3.95696			0.286316			0.143158	−	0.989700i	$-0.454274\pi$
$191$	3.95696			0.286316			0.143158	+	0.989700i	$0.454274\pi$
$192$	−0.388633	+	0.326102i	−0.0280472	+	0.0235344i
$193$	−0.698208	−	0.254127i	−0.0502581	−	0.0182925i	0.316769	−	0.948503i	$-0.397402\pi$
$193$	−0.698208	−	0.254127i	−0.0502581	−	0.0182925i	−0.367027	+	0.930210i	$0.619624\pi$
$194$	2.80510	−	15.9085i	0.201394	−	1.14216i
$195$		0			0
$196$	4.44329	−	1.61723i	0.317378	−	0.115516i
$197$	−7.06203	+	12.2318i	−0.503149	+	0.871479i	0.496845	+	0.867839i	$0.334492\pi$
$197$	−7.06203	+	12.2318i	−0.503149	+	0.871479i	−0.999993	+	0.00363946i	$0.998842\pi$
$198$	−2.84038	−	4.91968i	−0.201857	−	0.349626i
$199$	−3.77459	−	3.16726i	−0.267574	−	0.224521i	0.499122	−	0.866532i	$-0.333656\pi$
$199$	−3.77459	−	3.16726i	−0.267574	−	0.224521i	−0.766696	+	0.642011i	$0.778100\pi$
$200$		0			0
$201$	2.43201	+	4.21237i	0.171541	+	0.297118i
$202$	7.13338	−	12.3554i	0.501903	−	0.869321i
$203$	−11.8039	+	4.29627i	−0.828472	+	0.301539i
$204$	−0.307633	−	1.74467i	−0.0215386	−	0.122152i
$205$		0			0
$206$	−2.03897	−	0.742124i	−0.142062	−	0.0517062i
$207$	−14.5760	+	12.2307i	−1.01310	+	0.850095i
$208$	−5.60148			−0.388392
$209$	8.45708	+	3.16104i	0.584988	+	0.218653i
$210$		0			0
$211$	16.7992	−	14.0962i	1.15651	−	0.970424i	0.156655	−	0.987653i	$-0.449929\pi$
$211$	16.7992	−	14.0962i	1.15651	−	0.970424i	0.999852	+	0.0172289i	$0.00548441\pi$
$212$	6.77643	+	2.46642i	0.465407	+	0.169394i
$213$	−0.257849	+	1.46233i	−0.0176675	+	0.100197i
$214$	0.604093	+	3.42598i	0.0412950	+	0.234195i
$215$		0			0
$216$	−1.45669	+	2.52306i	−0.0991150	+	0.171672i
$217$	1.27277	+	2.20450i	0.0864013	+	0.149651i
$218$	0.520550	+	0.436793i	0.0352561	+	0.0295834i
$219$	−2.31111	−	1.93925i	−0.156170	−	0.131042i
$220$		0			0
$221$	9.78022	−	16.9398i	0.657889	−	1.13950i
$222$	−0.141871	+	0.0516370i	−0.00952179	+	0.00346565i
$223$	−0.540647	−	3.06616i	−0.0362044	−	0.205325i	0.961340	−	0.275365i	$-0.0887986\pi$
$223$	−0.540647	−	3.06616i	−0.0362044	−	0.205325i	−0.997544	+	0.0700394i	$0.977688\pi$
$224$	0.261717	−	1.48427i	0.0174867	−	0.0991719i
$225$		0			0
$226$	−5.11908	+	4.29542i	−0.340516	+	0.285727i
$227$	−28.7124			−1.90571			−0.952855	−	0.303425i	$-0.901870\pi$
$227$	−28.7124			−1.90571			−0.952855	+	0.303425i	$0.901870\pi$
$228$	−0.365194	−	2.18101i	−0.0241856	−	0.144441i
$229$	11.7887			0.779020			0.389510	−	0.921022i	$-0.372644\pi$
$229$	11.7887			0.779020			0.389510	+	0.921022i	$0.372644\pi$
$230$		0			0
$231$	−1.48824	−	0.541675i	−0.0979190	−	0.0356396i
$232$	1.44727	−	8.20787i	0.0950179	−	0.538873i
$233$	−0.454661	−	2.57851i	−0.0297858	−	0.168924i	0.966286	−	0.257470i	$-0.0828889\pi$
$233$	−0.454661	−	2.57851i	−0.0297858	−	0.168924i	−0.996072	+	0.0885465i	$0.971778\pi$
$234$	−14.4362	+	5.25436i	−0.943727	+	0.343488i
$235$		0			0
$236$	5.80794	+	10.0596i	0.378065	+	0.654827i
$237$	−4.64073	−	3.89403i	−0.301448	−	0.252945i
$238$	4.03173	+	3.38302i	0.261338	+	0.219289i
$239$	−11.4218	−	19.7832i	−0.738818	−	1.27967i	−0.953028	−	0.302883i	$-0.902051\pi$
$239$	−11.4218	−	19.7832i	−0.738818	−	1.27967i	0.214210	−	0.976788i	$-0.431282\pi$
$240$		0			0
$241$	−4.17385	+	1.51916i	−0.268861	+	0.0978575i	−0.472933	−	0.881098i	$-0.656805\pi$
$241$	−4.17385	+	1.51916i	−0.268861	+	0.0978575i	0.204072	+	0.978956i	$0.434582\pi$
$242$	−1.16514	−	6.60784i	−0.0748980	−	0.424768i
$243$	−2.11234	+	11.9797i	−0.135507	+	0.768497i
$244$	12.0874	+	4.39945i	0.773816	+	0.281646i
$245$		0			0
$246$	−1.58981			−0.101362
$247$	12.3902	−	21.0390i	0.788366	−	1.33868i
$248$	−1.68896			−0.107249
$249$	1.51475	−	1.27102i	0.0959933	−	0.0805479i
$250$		0			0
$251$	−2.13238	+	12.0933i	−0.134595	+	0.763323i	0.840547	+	0.541739i	$0.182234\pi$
$251$	−2.13238	+	12.0933i	−0.134595	+	0.763323i	−0.975141	+	0.221584i	$0.928877\pi$
$252$	−0.717790	−	4.07079i	−0.0452165	−	0.256435i
$253$	13.5035	−	4.91486i	0.848956	−	0.308995i
$254$	2.30093	−	3.98533i	0.144373	−	0.250062i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	8.01779	+	6.72772i	0.500136	+	0.419664i	0.857642	−	0.514247i	$-0.171928\pi$
$257$	8.01779	+	6.72772i	0.500136	+	0.419664i	−0.357506	+	0.933911i	$0.616373\pi$
$258$	−2.04961	−	3.55003i	−0.127603	−	0.221015i
$259$	0.224261	−	0.388432i	0.0139349	−	0.0241360i
$260$		0			0
$261$	−3.96931	−	22.5111i	−0.245694	−	1.39340i
$262$	−1.52385	+	8.64216i	−0.0941435	+	0.533914i
$263$	−6.93921	−	2.52566i	−0.427890	−	0.155739i	0.119093	−	0.992883i	$-0.462001\pi$
$263$	−6.93921	−	2.52566i	−0.427890	−	0.155739i	−0.546983	+	0.837144i	$0.684224\pi$
$264$	0.804971	−	0.675451i	0.0495425	−	0.0415711i
$265$		0			0
$266$	4.99596	+	4.26612i	0.306322	+	0.261573i
$267$	−2.93749			−0.179771
$268$	7.34453	−	6.16279i	0.448638	−	0.376452i
$269$	3.70287	+	1.34773i	0.225768	+	0.0821727i	0.452427	−	0.891801i	$-0.350558\pi$
$269$	3.70287	+	1.34773i	0.225768	+	0.0821727i	−0.226659	+	0.973974i	$0.572780\pi$
$270$		0			0
$271$	3.27127	+	18.5523i	0.198716	+	1.12697i	0.907027	+	0.421073i	$0.138346\pi$
$271$	3.27127	+	18.5523i	0.198716	+	1.12697i	−0.708311	+	0.705900i	$0.750543\pi$
$272$	−3.28142	+	1.19434i	−0.198965	+	0.0724175i
$273$	−2.14151	+	3.70920i	−0.129610	+	0.224491i
$274$	2.36717	+	4.10006i	0.143006	+	0.247693i
$275$		0			0
$276$	−2.69625	−	2.26242i	−0.162295	−	0.136182i
$277$	3.24061	+	5.61290i	0.194709	+	0.337246i	0.946805	−	0.321807i	$-0.104290\pi$
$277$	3.24061	+	5.61290i	0.194709	+	0.337246i	−0.752096	+	0.659054i	$0.770957\pi$
$278$	−8.12950	+	14.0807i	−0.487575	+	0.844504i
$279$	−4.35282	+	1.58430i	−0.260597	+	0.0948494i
$280$		0			0
$281$	−5.21918	+	29.5995i	−0.311350	+	1.76576i	0.280642	+	0.959813i	$0.409453\pi$
$281$	−5.21918	+	29.5995i	−0.311350	+	1.76576i	−0.591992	+	0.805944i	$0.701658\pi$
$282$	−2.11061	−	0.768201i	−0.125685	−	0.0457457i
$283$	−21.6462	+	18.1633i	−1.28673	+	1.07970i	−0.294452	+	0.955666i	$0.595137\pi$
$283$	−21.6462	+	18.1633i	−1.28673	+	1.07970i	−0.992279	+	0.124029i	$0.960418\pi$
$284$	2.92690			0.173680
$285$		0			0
$286$	11.6023			0.686056
$287$	3.61804	−	3.03590i	0.213566	−	0.179203i
$288$	2.57722	+	0.938032i	0.151864	+	0.0552741i
$289$	−0.834522	+	4.73281i	−0.0490895	+	0.278401i
$290$		0			0
$291$	7.70105	−	2.80295i	0.451443	−	0.164312i
$292$	−2.97338	+	5.15004i	−0.174004	+	0.301383i
$293$	12.9686	+	22.4623i	0.757634	+	1.31226i	0.944054	+	0.329790i	$0.106978\pi$
$293$	12.9686	+	22.4623i	0.757634	+	1.31226i	−0.186420	+	0.982470i	$0.559689\pi$
$294$	1.83763	+	1.54196i	0.107173	+	0.0899288i
$295$		0			0
$296$	0.148797	+	0.257723i	0.00864863	+	0.0149799i
$297$	3.01722	−	5.22597i	0.175077	−	0.303242i
$298$	7.49692	−	2.72866i	0.434285	−	0.158067i
$299$	−6.74826	−	38.2713i	−0.390262	−	2.21329i
$300$		0			0
$301$	11.4436	+	4.16513i	0.659597	+	0.240074i
$302$	−10.9958	+	9.22660i	−0.632739	+	0.530931i
$303$	7.23788			0.415805
$304$	−4.10874	+	1.45543i	−0.235652	+	0.0834746i
$305$		0			0
$306$	−7.33662	+	6.15616i	−0.419407	+	0.351924i
$307$	26.7839	+	9.74855i	1.52864	+	0.556379i	0.963288	−	0.268472i	$-0.0865186\pi$
$307$	26.7839	+	9.74855i	1.52864	+	0.556379i	0.565351	+	0.824851i	$0.308741\pi$
$308$	−0.542090	+	3.07434i	−0.0308884	+	0.175177i
$309$	−0.191153	−	1.08408i	−0.0108743	−	0.0616713i
$310$		0			0
$311$	7.31521	−	12.6703i	0.414807	−	0.718467i	−0.580601	−	0.814188i	$-0.697182\pi$
$311$	7.31521	−	12.6703i	0.414807	−	0.718467i	0.995408	+	0.0957209i	$0.0305156\pi$
$312$	−1.42088	−	2.46104i	−0.0804417	−	0.139329i
$313$	−9.75171	−	8.18266i	−0.551199	−	0.462511i	0.324148	−	0.946006i	$-0.394923\pi$
$313$	−9.75171	−	8.18266i	−0.551199	−	0.462511i	−0.875347	+	0.483495i	$0.839367\pi$
$314$	0.0703787	+	0.0590548i	0.00397170	+	0.00333265i
$315$		0			0
$316$	−5.97057	+	10.3413i	−0.335871	+	0.581745i
$317$	−16.2902	+	5.92914i	−0.914947	+	0.333014i	−0.756227	−	0.654310i	$-0.772959\pi$
$317$	−16.2902	+	5.92914i	−0.914947	+	0.333014i	−0.158721	+	0.987324i	$0.550737\pi$
$318$	0.635290	+	3.60291i	0.0356253	+	0.202041i
$319$	−2.99771	+	17.0008i	−0.167839	+	0.951865i
$320$		0			0
$321$	−1.35199	+	1.13446i	−0.0754608	+	0.0633191i
$322$	10.4564			0.582710
$323$	2.77242	−	14.9667i	0.154261	−	0.832771i
$324$	6.74984			0.374991
$325$		0			0
$326$	17.5143	+	6.37469i	0.970028	+	0.353061i
$327$	−0.0598639	+	0.339505i	−0.00331048	+	0.0187747i
$328$	0.544163	+	3.08610i	0.0300464	+	0.170401i
$329$	6.27023	−	2.28218i	0.345689	−	0.125821i
$330$		0			0
$331$	−8.63998	−	14.9649i	−0.474896	−	0.822544i	0.524690	−	0.851293i	$-0.324181\pi$
$331$	−8.63998	−	14.9649i	−0.474896	−	0.822544i	−0.999587	+	0.0287487i	$0.990848\pi$
$332$	−2.98576	−	2.50535i	−0.163865	−	0.137499i
$333$	0.625234	+	0.524634i	0.0342626	+	0.0287498i
$334$	−1.34112	−	2.32289i	−0.0733830	−	0.127103i
$335$		0			0
$336$	0.718510	−	0.261516i	0.0391980	−	0.0142669i
$337$	3.32720	+	18.8695i	0.181244	+	1.02789i	0.930687	+	0.365817i	$0.119211\pi$
$337$	3.32720	+	18.8695i	0.181244	+	1.02789i	−0.749442	+	0.662070i	$0.769678\pi$
$338$	3.19105	−	18.0973i	0.173570	−	0.984366i
$339$	−3.18574	−	1.15951i	−0.173026	−	0.0629762i
$340$		0			0
$341$	3.49832			0.189445
$342$	−9.22389	+	7.60509i	−0.498771	+	0.411236i
$343$	−17.6767			−0.954453
$344$	−6.18970	+	5.19377i	−0.333726	+	0.280029i
$345$		0			0
$346$	−0.444764	+	2.52238i	−0.0239106	+	0.135604i
$347$	−6.17489	−	35.0195i	−0.331485	−	1.87995i	−0.459506	−	0.888175i	$-0.651974\pi$
$347$	−6.17489	−	35.0195i	−0.331485	−	1.87995i	0.128021	−	0.991771i	$-0.459138\pi$
$348$	3.97330	−	1.44616i	0.212991	−	0.0775224i
$349$	6.85656	−	11.8759i	0.367023	−	0.635703i	−0.622076	−	0.782957i	$-0.713710\pi$
$349$	6.85656	−	11.8759i	0.367023	−	0.635703i	0.989099	+	0.147255i	$0.0470437\pi$
$350$		0			0
$351$	−12.5012	−	10.4898i	−0.667266	−	0.559903i
$352$	−1.58670	−	1.33140i	−0.0845712	−	0.0709637i
$353$	−2.50768	−	4.34343i	−0.133470	−	0.231177i	0.791542	−	0.611115i	$-0.209279\pi$
$353$	−2.50768	−	4.34343i	−0.133470	−	0.231177i	−0.925012	+	0.379938i	$0.875945\pi$
$354$	−2.94651	+	5.10351i	−0.156605	+	0.271248i
$355$		0			0
$356$	1.00545	+	5.70218i	0.0532887	+	0.302215i
$357$	−0.463654	+	2.62951i	−0.0245392	+	0.139168i
$358$	20.0057	+	7.28147i	1.05733	+	0.384837i
$359$	−24.1341	+	20.2509i	−1.27375	+	1.06880i	−0.279674	+	0.960095i	$0.590226\pi$
$359$	−24.1341	+	20.2509i	−1.27375	+	1.06880i	−0.994074	+	0.108706i	$0.965329\pi$
$360$		0			0
$361$	3.62175	−	18.6516i	0.190619	−	0.981664i
$362$	−10.0258			−0.526947
$363$	2.60764	−	2.18807i	0.136866	−	0.114844i
$364$	7.93322	+	2.88745i	0.415814	+	0.151344i
$365$		0			0
$366$	1.13319	+	6.42664i	0.0592328	+	0.335926i
$367$	20.6915	−	7.53110i	1.08009	−	0.393120i	0.260148	−	0.965569i	$-0.416228\pi$
$367$	20.6915	−	7.53110i	1.08009	−	0.393120i	0.819941	+	0.572448i	$0.194006\pi$
$368$	−3.46888	+	6.00828i	−0.180828	+	0.313203i
$369$	4.29729	+	7.44312i	0.223708	+	0.387473i
$370$		0			0
$371$	−8.32589	−	6.98625i	−0.432258	−	0.362708i
$372$	−0.428426	−	0.742055i	−0.0222128	−	0.0384738i
$373$	15.5190	−	26.8796i	0.803541	−	1.39177i	−0.113731	−	0.993512i	$-0.536280\pi$
$373$	15.5190	−	26.8796i	0.803541	−	1.39177i	0.917272	−	0.398262i	$-0.130386\pi$
$374$	6.79676	−	2.47382i	0.351452	−	0.127918i
$375$		0			0
$376$	−0.768789	+	4.36002i	−0.0396473	+	0.224851i
$377$	43.8700	+	15.9674i	2.25942	+	0.822361i
$378$	3.36365	−	2.82244i	0.173008	−	0.145171i
$379$	1.10212			0.0566121			0.0283061	−	0.999599i	$-0.490989\pi$
$379$	1.10212			0.0566121			0.0283061	+	0.999599i	$0.490989\pi$
$380$		0			0
$381$	2.33464			0.119607
$382$	3.03121	−	2.54349i	0.155090	−	0.130136i
$383$	13.0711	+	4.75750i	0.667903	+	0.243097i	0.653645	−	0.756802i	$-0.273239\pi$
$383$	13.0711	+	4.75750i	0.667903	+	0.243097i	0.0142581	+	0.999898i	$0.495461\pi$
$384$	−0.0880960	+	0.499618i	−0.00449563	+	0.0254960i
$385$		0			0
$386$	−0.698208	+	0.254127i	−0.0355379	+	0.0129347i
$387$	−11.0803	+	19.1916i	−0.563243	+	0.975565i
$388$	−8.07695	−	13.9897i	−0.410045	−	0.710219i
$389$	−4.82525	−	4.04887i	−0.244650	−	0.205286i	0.512214	−	0.858858i	$-0.328825\pi$
$389$	−4.82525	−	4.04887i	−0.244650	−	0.205286i	−0.756864	+	0.653572i	$0.773270\pi$
$390$		0			0
$391$	−12.1134	−	20.9810i	−0.612601	−	1.06106i
$392$	2.36423	−	4.09496i	0.119411	−	0.206827i
$393$	−4.18353	+	1.52268i	−0.211031	+	0.0768091i
$394$	2.45262	+	13.9095i	0.123561	+	0.700749i
$395$		0			0
$396$	−5.33816	−	1.94293i	−0.268253	−	0.0976360i
$397$	10.6640	−	8.94815i	0.535210	−	0.449095i	−0.334686	−	0.942330i	$-0.608630\pi$
$397$	10.6640	−	8.94815i	0.535210	−	0.449095i	0.869896	+	0.493235i	$0.164186\pi$
$398$	−4.92738			−0.246987
$399$	−0.607057	+	3.27716i	−0.0303909	+	0.164063i
$400$		0			0
$401$	−7.14215	+	5.99297i	−0.356662	+	0.299275i	−0.803459	−	0.595361i	$-0.797009\pi$
$401$	−7.14215	+	5.99297i	−0.356662	+	0.299275i	0.446797	+	0.894636i	$0.352565\pi$
$402$	4.57069	+	1.66360i	0.227965	+	0.0829726i
$403$	1.64283	−	9.31693i	0.0818350	−	0.464110i
$404$	−2.47740	−	14.0500i	−0.123255	−	0.699014i
$405$		0			0
$406$	−6.28073	+	10.8785i	−0.311707	+	0.539893i
$407$	−0.308200	−	0.533818i	−0.0152769	−	0.0264604i
$408$	−1.35711	−	1.13875i	−0.0671872	−	0.0563767i
$409$	7.89867	+	6.62777i	0.390564	+	0.327722i	0.816833	−	0.576874i	$-0.195728\pi$
$409$	7.89867	+	6.62777i	0.390564	+	0.327722i	−0.426269	+	0.904597i	$0.640172\pi$
$410$		0			0
$411$	−1.20092	+	2.08006i	−0.0592372	+	0.102602i
$412$	−2.03897	+	0.742124i	−0.100453	+	0.0365618i
$413$	−3.04007	−	17.2411i	−0.149592	−	0.848378i
$414$	−3.30412	+	18.7386i	−0.162389	+	0.920951i
$415$		0			0
$416$	−4.29098	+	3.60056i	−0.210383	+	0.176532i
$417$	−8.24859			−0.403935
$418$	8.51037	−	3.01461i	0.416256	−	0.147449i
$419$	−19.7467			−0.964691			−0.482346	−	0.875981i	$-0.660215\pi$
$419$	−19.7467			−0.964691			−0.482346	+	0.875981i	$0.660215\pi$
$420$		0			0
$421$	−1.84846	−	0.672783i	−0.0900882	−	0.0327894i	0.296583	−	0.955007i	$-0.404153\pi$
$421$	−1.84846	−	0.672783i	−0.0900882	−	0.0327894i	−0.386671	+	0.922218i	$0.626375\pi$
$422$	3.80808	−	21.5967i	0.185374	−	1.05131i
$423$	2.10850	+	11.9579i	0.102519	+	0.581412i
$424$	6.77643	−	2.46642i	0.329093	−	0.119780i
$425$		0			0
$426$	0.742446	+	1.28595i	0.0359716	+	0.0623047i
$427$	−14.8512	−	12.4616i	−0.718700	−	0.603061i
$428$	2.66494	+	2.23615i	0.128815	+	0.108088i
$429$	2.94306	+	5.09752i	0.142092	+	0.246111i
$430$		0			0
$431$	−18.3883	+	6.69279i	−0.885733	+	0.322380i	−0.744521	−	0.667599i	$-0.767322\pi$
$431$	−18.3883	+	6.69279i	−0.885733	+	0.322380i	−0.141212	+	0.989979i	$0.545100\pi$
$432$	0.505902	+	2.86911i	0.0243402	+	0.138040i
$433$	3.65698	−	20.7398i	0.175743	−	0.996690i	−0.761539	−	0.648119i	$-0.775556\pi$
$433$	3.65698	−	20.7398i	0.175743	−	0.996690i	0.937282	−	0.348571i	$-0.113333\pi$
$434$	2.39203	+	0.870627i	0.114821	+	0.0417914i
$435$		0			0
$436$	0.679530			0.0325436
$437$	−14.8939	−	26.3190i	−0.712474	−	1.25901i
$438$	−3.01693			−0.144155
$439$	28.4242	−	23.8507i	1.35661	−	1.13833i	0.379599	−	0.925151i	$-0.376062\pi$
$439$	28.4242	−	23.8507i	1.35661	−	1.13833i	0.977013	−	0.213181i	$-0.0683825\pi$
$440$		0			0
$441$	2.25193	−	12.7713i	0.107235	−	0.608159i
$442$	−3.39664	−	19.2633i	−0.161561	−	0.916261i
$443$	−7.61560	+	2.77185i	−0.361828	+	0.131695i	−0.516536	−	0.856266i	$-0.672779\pi$
$443$	−7.61560	+	2.77185i	−0.361828	+	0.131695i	0.154708	+	0.987960i	$0.450556\pi$
$444$	−0.0754882	+	0.130749i	−0.00358251	+	0.00620509i
$445$		0			0
$446$	−2.38505	−	2.00129i	−0.112935	−	0.0947640i
$447$	3.10054	+	2.60166i	0.146651	+	0.123054i
$448$	−0.753583	−	1.30524i	−0.0356034	−	0.0616670i
$449$	1.19036	−	2.06177i	0.0561767	−	0.0973008i	−0.836569	−	0.547861i	$-0.815442\pi$
$449$	1.19036	−	2.06177i	0.0561767	−	0.0973008i	0.892746	+	0.450560i	$0.148776\pi$
$450$		0			0
$451$	−1.12712	−	6.39219i	−0.0530738	−	0.300997i
$452$	−1.16040	+	6.58097i	−0.0545807	+	0.309543i
$453$	−6.84299	−	2.49065i	−0.321512	−	0.117021i
$454$	−21.9950	+	18.4560i	−1.03228	+	0.866183i
$455$		0			0
$456$	−1.68168	−	1.43601i	−0.0787521	−	0.0672474i
$457$	−29.9107			−1.39916			−0.699582	−	0.714553i	$-0.746630\pi$
$457$	−29.9107			−1.39916			−0.699582	+	0.714553i	$0.746630\pi$
$458$	9.03068	−	7.57764i	0.421976	−	0.354080i
$459$	−9.56001	−	3.47956i	−0.446223	−	0.162412i
$460$		0			0
$461$	−1.41445	−	8.02177i	−0.0658777	−	0.373611i	−0.999867	−	0.0163101i	$-0.994808\pi$
$461$	−1.41445	−	8.02177i	−0.0658777	−	0.373611i	0.933989	−	0.357301i	$-0.116303\pi$
$462$	−1.48824	+	0.541675i	−0.0692392	+	0.0252010i
$463$	13.0159	−	22.5442i	0.604901	−	1.04772i	−0.387166	−	0.922010i	$-0.626546\pi$
$463$	13.0159	−	22.5442i	0.604901	−	1.04772i	0.992067	−	0.125710i	$-0.0401208\pi$
$464$	−4.16724	−	7.21788i	−0.193459	−	0.335082i
$465$		0			0
$466$	−2.00572	−	1.68300i	−0.0929133	−	0.0779636i
$467$	11.7605	+	20.3698i	0.544212	+	0.942602i	0.998656	+	0.0518273i	$0.0165045\pi$
$467$	11.7605	+	20.3698i	0.544212	+	0.942602i	−0.454444	+	0.890775i	$0.650162\pi$
$468$	−7.68136	+	13.3045i	−0.355071	+	0.615001i
$469$	−13.5787	+	4.94223i	−0.627004	+	0.228211i
$470$		0			0
$471$	−0.00809364	+	0.0459013i	−0.000372935	+	0.00211502i
$472$	10.9154	+	3.97286i	0.502420	+	0.182866i
$473$	12.8206	−	10.7578i	0.589493	−	0.494643i
$474$	−6.05804			−0.278255
$475$		0			0
$476$	5.26305			0.241231
$477$	15.1508	−	12.7130i	0.693707	−	0.582089i
$478$	−21.4661	−	7.81300i	−0.981834	−	0.357358i
$479$	−4.48051	+	25.4102i	−0.204720	+	1.16102i	0.693161	+	0.720783i	$0.256217\pi$
$479$	−4.48051	+	25.4102i	−0.204720	+	1.16102i	−0.897880	+	0.440239i	$0.854894\pi$
$480$		0			0
$481$	−1.56643	+	0.570134i	−0.0714231	+	0.0259959i
$482$	−2.22086	+	3.84664i	−0.101157	+	0.175210i
$483$	2.65239	+	4.59407i	0.120688	+	0.209037i
$484$	−5.13999	−	4.31296i	−0.233636	−	0.196044i
$485$		0			0
$486$	6.08224	+	10.5348i	0.275896	+	0.477866i
$487$	4.35999	−	7.55172i	0.197570	−	0.342201i	−0.750170	−	0.661245i	$-0.770028\pi$
$487$	4.35999	−	7.55172i	0.197570	−	0.342201i	0.947740	+	0.319044i	$0.103362\pi$
$488$	12.0874	−	4.39945i	0.547170	−	0.199154i
$489$	1.64196	+	9.31204i	0.0742522	+	0.421105i
$490$		0			0
$491$	−26.1326	−	9.51149i	−1.17935	−	0.429248i	−0.323377	−	0.946270i	$-0.604818\pi$
$491$	−26.1326	−	9.51149i	−1.17935	−	0.429248i	−0.855972	+	0.517023i	$0.827040\pi$
$492$	−1.21786	+	1.02191i	−0.0549055	+	0.0460712i
$493$	29.1042			1.31079
$494$	−4.03218	−	24.0810i	−0.181416	−	1.08346i
$495$		0			0
$496$	−1.29382	+	1.08564i	−0.0580941	+	0.0487468i
$497$	−4.14529	−	1.50876i	−0.185942	−	0.0676773i
$498$	0.343366	−	1.94732i	0.0153866	−	0.0872616i
$499$	1.23589	+	7.00908i	0.0553261	+	0.313770i	0.999894	−	0.0145457i	$-0.00463021\pi$
$499$	1.23589	+	7.00908i	0.0553261	+	0.313770i	−0.944568	+	0.328315i	$0.893519\pi$
$500$		0			0
$501$	0.680385	−	1.17846i	0.0303974	−	0.0526498i
$502$	6.13994	+	10.6347i	0.274039	+	0.474649i
$503$	4.91520	+	4.12434i	0.219158	+	0.183895i	0.745756	−	0.666219i	$-0.232088\pi$
$503$	4.91520	+	4.12434i	0.219158	+	0.183895i	−0.526598	+	0.850114i	$0.676533\pi$
$504$	−3.16651	−	2.65702i	−0.141048	−	0.118353i
$505$		0			0
$506$	7.18505	−	12.4449i	0.319414	−	0.553242i
$507$	8.76063	−	3.18861i	0.389073	−	0.141611i
$508$	−0.799105	−	4.53195i	−0.0354545	−	0.201073i
$509$	0.808400	−	4.58467i	0.0358317	−	0.203212i	−0.961636	−	0.274327i	$-0.911545\pi$
$509$	0.808400	−	4.58467i	0.0358317	−	0.203212i	0.997468	+	0.0711156i	$0.0226559\pi$
$510$		0			0
$511$	6.86586	−	5.76114i	0.303728	−	0.254858i
$512$	1.00000			0.0441942
$513$	−11.8953	−	4.44617i	−0.525192	−	0.196303i
$514$	10.4665			0.461657
$515$		0			0
$516$	−3.85201	−	1.40202i	−0.169575	−	0.0617203i
$517$	1.59238	−	9.03085i	0.0700329	−	0.397176i
$518$	−0.0778851	−	0.441708i	−0.00342207	−	0.0194075i
$519$	−1.22104	+	0.444423i	−0.0535978	+	0.0195080i
$520$		0			0
$521$	16.0289	+	27.7629i	0.702239	+	1.21631i	0.967679	+	0.252186i	$0.0811496\pi$
$521$	16.0289	+	27.7629i	0.702239	+	1.21631i	−0.265440	+	0.964127i	$0.585517\pi$
$522$	−17.5105	−	14.6931i	−0.766414	−	0.643098i
$523$	19.8697	+	16.6727i	0.868841	+	0.729044i	0.963854	−	0.266432i	$-0.0858447\pi$
$523$	19.8697	+	16.6727i	0.868841	+	0.729044i	−0.0950126	+	0.995476i	$0.530289\pi$
$524$	4.38774	+	7.59979i	0.191679	+	0.331998i
$525$		0			0
$526$	−6.93921	+	2.52566i	−0.302564	+	0.110124i
$527$	−1.02415	−	5.80827i	−0.0446129	−	0.253012i
$528$	0.182472	−	1.03485i	0.00794108	−	0.0450361i
$529$	−23.6169	−	8.59584i	−1.02682	−	0.373732i
$530$		0			0
$531$	31.8580			1.38252
$532$	6.56934	+	0.0566924i	0.284817	+	0.00245793i
$533$	−17.5534			−0.760321
$534$	−2.25024	+	1.88818i	−0.0973776	+	0.0817095i
$535$		0			0
$536$	1.66487	−	9.44194i	0.0719114	−	0.407830i
$537$	1.87553	+	10.6366i	0.0809350	+	0.459005i
$538$	3.70287	−	1.34773i	0.159642	−	0.0581049i
$539$	−4.89699	+	8.48183i	−0.210928	+	0.365338i
$540$		0			0
$541$	−19.5394	−	16.3955i	−0.840065	−	0.704899i	0.117513	−	0.993071i	$-0.462508\pi$
$541$	−19.5394	−	16.3955i	−0.840065	−	0.704899i	−0.957578	+	0.288173i	$0.906952\pi$
$542$	14.4311	+	12.1092i	0.619871	+	0.520133i
$543$	−2.54318	−	4.40492i	−0.109138	−	0.189033i
$544$	−1.74601	+	3.02417i	−0.0748595	+	0.129660i
$545$		0			0
$546$	0.743738	+	4.21795i	0.0318290	+	0.180511i
$547$	2.47247	−	14.0221i	0.105715	−	0.599541i	−0.885217	−	0.465178i	$-0.845990\pi$
$547$	2.47247	−	14.0221i	0.105715	−	0.599541i	0.990932	−	0.134363i	$-0.0428987\pi$
$548$	4.44882	+	1.61924i	0.190044	+	0.0691705i
$549$	27.0250	−	22.6767i	1.15340	−	0.967818i
$550$		0			0
$551$	36.3278	+	0.313504i	1.54762	+	0.0133557i
$552$	−3.51970			−0.149808
$553$	13.7867	−	11.5684i	0.586271	−	0.491940i
$554$	6.09035	+	2.21671i	0.258754	+	0.0941788i
$555$		0			0
$556$	2.82334	+	16.0120i	0.119736	+	0.679059i
$557$	−24.2493	+	8.82601i	−1.02747	+	0.373970i	−0.800119	−	0.599842i	$-0.795230\pi$
$557$	−24.2493	+	8.82601i	−1.02747	+	0.373970i	−0.227355	+	0.973812i	$0.573008\pi$
$558$	−2.31609	+	4.01158i	−0.0980478	+	0.169824i
$559$	−22.6302	−	39.1966i	−0.957154	−	1.65784i
$560$		0			0
$561$	2.81097	+	2.35869i	0.118679	+	0.0995838i
$562$	15.0280	+	26.0293i	0.633920	+	1.09798i
$563$	18.9375	−	32.8007i	0.798121	−	1.38239i	−0.122718	−	0.992442i	$-0.539161\pi$
$563$	18.9375	−	32.8007i	0.798121	−	1.38239i	0.920839	−	0.389944i	$-0.127506\pi$
$564$	−2.11061	+	0.768201i	−0.0888729	+	0.0323471i
$565$		0			0
$566$	−4.90679	+	27.8278i	−0.206248	+	1.16969i
$567$	−9.55961	−	3.47941i	−0.401466	−	0.146122i
$568$	2.24214	−	1.88138i	0.0940780	−	0.0789408i
$569$	22.7856			0.955220			0.477610	−	0.878572i	$-0.341503\pi$
$569$	22.7856			0.955220			0.477610	+	0.878572i	$0.341503\pi$
$570$		0			0
$571$	31.8020			1.33087			0.665437	−	0.746454i	$-0.268245\pi$
$571$	31.8020			1.33087			0.665437	+	0.746454i	$0.268245\pi$
$572$	8.88784	−	7.45779i	0.371619	−	0.311826i
$573$	1.88640	+	0.686594i	0.0788055	+	0.0286829i
$574$	0.820143	−	4.65126i	0.0342321	−	0.194140i
$575$		0			0
$576$	2.57722	−	0.938032i	0.107384	−	0.0390847i
$577$	7.13176	−	12.3526i	0.296899	−	0.514245i	−0.678526	−	0.734577i	$-0.737381\pi$
$577$	7.13176	−	12.3526i	0.296899	−	0.514245i	0.975425	+	0.220332i	$0.0707141\pi$
$578$	2.40291	+	4.16196i	0.0999479	+	0.173115i
$579$	−0.288761	−	0.242300i	−0.0120005	−	0.0100696i
$580$		0			0
$581$	2.93719	+	5.08735i	0.121855	+	0.211059i
$582$	4.09764	−	7.09732i	0.169853	−	0.294193i
$583$	−14.0359	+	5.10866i	−0.581309	+	0.211579i
$584$	1.03264	+	5.85641i	0.0427310	+	0.242340i
$585$		0			0
$586$	24.3730	+	8.87105i	1.00684	+	0.366460i
$587$	−19.2386	+	16.1431i	−0.794064	+	0.666299i	−0.946748	−	0.321977i	$-0.895653\pi$
$587$	−19.2386	+	16.1431i	−0.794064	+	0.666299i	0.152684	+	0.988275i	$0.451208\pi$
$588$	2.39886			0.0989274
$589$	−1.21579	−	7.26092i	−0.0500956	−	0.299181i
$590$		0			0
$591$	−5.48908	+	4.60588i	−0.225791	+	0.189461i
$592$	0.279646	+	0.101783i	0.0114934	+	0.00418325i
$593$	−4.70911	+	26.7067i	−0.193380	+	1.09671i	0.721327	+	0.692595i	$0.243532\pi$
$593$	−4.70911	+	26.7067i	−0.193380	+	1.09671i	−0.914707	+	0.404118i	$0.867579\pi$
$594$	−1.04787	−	5.94276i	−0.0429946	−	0.243834i
$595$		0			0
$596$	3.98903	−	6.90920i	0.163397	−	0.283012i
$597$	−1.24989	−	2.16488i	−0.0511547	−	0.0886025i
$598$	−29.7698	−	24.9798i	−1.21738	−	1.02150i
$599$	−0.134971	−	0.113254i	−0.00551476	−	0.00462744i	0.640026	−	0.768353i	$-0.278924\pi$
$599$	−0.134971	−	0.113254i	−0.00551476	−	0.00462744i	−0.645541	+	0.763726i	$0.723368\pi$
$600$		0			0
$601$	−5.93311	+	10.2764i	−0.242016	+	0.419185i	−0.961289	−	0.275544i	$-0.911142\pi$
$601$	−5.93311	+	10.2764i	−0.242016	+	0.419185i	0.719272	+	0.694728i	$0.244475\pi$
$602$	11.4436	−	4.16513i	0.466406	−	0.169758i
$603$	−4.56610	−	25.8957i	−0.185946	−	1.05455i
$604$	−2.49255	+	14.1360i	−0.101421	+	0.575184i
$605$		0			0
$606$	5.54454	−	4.65242i	0.225231	−	0.188992i
$607$	−40.3158			−1.63637			−0.818184	−	0.574957i	$-0.805019\pi$
$607$	−40.3158			−1.63637			−0.818184	+	0.574957i	$0.805019\pi$
$608$	−2.21194	+	3.75597i	−0.0897062	+	0.152325i
$609$	−6.37274			−0.258236
$610$		0			0
$611$	−23.3037	−	8.48186i	−0.942767	−	0.343139i
$612$	−1.66308	+	9.43178i	−0.0672259	+	0.381257i
$613$	−4.55538	−	25.8348i	−0.183990	−	1.04346i	−0.927246	−	0.374452i	$-0.877831\pi$
$613$	−4.55538	−	25.8348i	−0.183990	−	1.04346i	0.743256	−	0.669007i	$-0.233280\pi$
$614$	26.7839	−	9.74855i	1.08091	−	0.393419i
$615$		0			0
$616$	1.56089	+	2.70353i	0.0628899	+	0.108928i
$617$	−7.68584	−	6.44919i	−0.309420	−	0.259634i	0.474832	−	0.880076i	$-0.342509\pi$
$617$	−7.68584	−	6.44919i	−0.309420	−	0.259634i	−0.784252	+	0.620442i	$0.786953\pi$
$618$	−0.843267	−	0.707585i	−0.0339212	−	0.0284632i
$619$	2.17023	+	3.75895i	0.0872290	+	0.151085i	0.906339	−	0.422552i	$-0.138865\pi$
$619$	2.17023	+	3.75895i	0.0872290	+	0.151085i	−0.819110	+	0.573637i	$0.805532\pi$
$620$		0			0
$621$	−18.9934	+	6.91302i	−0.762177	+	0.277410i
$622$	−2.54054	−	14.4081i	−0.101867	−	0.577714i
$623$	1.51538	−	8.59414i	0.0607123	−	0.344317i
$624$	−2.67039	−	0.971942i	−0.106901	−	0.0389088i
$625$		0			0
$626$	−12.7300			−0.508791
$627$	3.48325	+	2.97439i	0.139108	+	0.118786i
$628$	0.0918729			0.00366613
$629$	−0.796074	+	0.667985i	−0.0317415	+	0.0266343i
$630$		0			0
$631$	−0.986670	+	5.59568i	−0.0392787	+	0.222761i	−0.998128	−	0.0611537i	$-0.980522\pi$
$631$	−0.986670	+	5.59568i	−0.0392787	+	0.222761i	0.958850	+	0.283914i	$0.0916331\pi$
$632$	2.07356	+	11.7597i	0.0824817	+	0.467777i
$633$	10.4546	−	3.80516i	0.415533	−	0.151242i
$634$	−8.66782	+	15.0131i	−0.344243	+	0.596247i
$635$		0			0
$636$	2.80256	+	2.35163i	0.111129	+	0.0932482i
$637$	20.2897	+	17.0251i	0.803907	+	0.674558i
$638$	8.63156	+	14.9503i	0.341727	+	0.591888i
$639$	4.01369	−	6.95192i	0.158779	−	0.275014i
$640$		0			0
$641$	2.11713	+	12.0069i	0.0836217	+	0.474242i	0.997645	+	0.0685818i	$0.0218474\pi$
$641$	2.11713	+	12.0069i	0.0836217	+	0.474242i	−0.914024	+	0.405661i	$0.867041\pi$
$642$	−0.306472	+	1.73809i	−0.0120955	+	0.0685968i
$643$	27.3412	+	9.95140i	1.07823	+	0.392445i	0.819250	−	0.573437i	$-0.194390\pi$
$643$	27.3412	+	9.95140i	1.07823	+	0.392445i	0.258984	+	0.965882i	$0.416612\pi$
$644$	8.01004	−	6.72122i	0.315640	−	0.264853i
$645$		0			0
$646$	−7.49663	−	13.2473i	−0.294951	−	0.521206i
$647$	−8.56834			−0.336856			−0.168428	−	0.985714i	$-0.553869\pi$
$647$	−8.56834			−0.336856			−0.168428	+	0.985714i	$0.553869\pi$
$648$	5.17067	−	4.33871i	0.203123	−	0.170441i
$649$	−22.6088	−	8.22894i	−0.887474	−	0.323014i
$650$		0			0
$651$	0.224252	+	1.27180i	0.00878914	+	0.0498457i
$652$	17.5143	−	6.37469i	0.685913	−	0.249652i
$653$	−24.3230	+	42.1287i	−0.951834	+	1.64862i	−0.210381	+	0.977619i	$0.567471\pi$
$653$	−24.3230	+	42.1287i	−0.951834	+	1.64862i	−0.741453	+	0.671005i	$0.765863\pi$
$654$	0.172371	+	0.298556i	0.00674025	+	0.0116745i
$655$		0			0
$656$	2.40056	+	2.01431i	0.0937261	+	0.0786455i
$657$	8.15484	+	14.1246i	0.318151	+	0.551053i
$658$	3.33632	−	5.77868i	0.130063	−	0.225276i
$659$	−15.3337	+	5.58102i	−0.597318	+	0.217406i	−0.622945	−	0.782266i	$-0.714064\pi$
$659$	−15.3337	+	5.58102i	−0.597318	+	0.217406i	0.0256272	+	0.999672i	$0.491842\pi$
$660$		0			0
$661$	7.05327	−	40.0011i	0.274341	−	1.55586i	−0.466708	−	0.884411i	$-0.654560\pi$
$661$	7.05327	−	40.0011i	0.274341	−	1.55586i	0.741049	−	0.671451i	$-0.234329\pi$
$662$	−16.2379	−	5.91009i	−0.631102	−	0.229702i
$663$	7.60184	−	6.37870i	0.295231	−	0.247728i
$664$	−3.89763			−0.151257
$665$		0			0
$666$	0.816185			0.0316265
$667$	44.2948	−	37.1677i	1.71510	−	1.43914i
$668$	−2.52049	−	0.917382i	−0.0975206	−	0.0354946i
$669$	0.274284	−	1.55554i	0.0106044	−	0.0601406i
$670$		0			0
$671$	−25.0364	+	9.11252i	−0.966521	+	0.351785i
$672$	0.382311	−	0.662183i	0.0147480	−	0.0255443i
$673$	4.90823	+	8.50130i	0.189198	+	0.327701i	0.944983	−	0.327119i	$-0.106078\pi$
$673$	4.90823	+	8.50130i	0.189198	+	0.327701i	−0.755785	+	0.654820i	$0.772744\pi$
$674$	14.6779	+	12.3162i	0.565370	+	0.474402i
$675$		0			0
$676$	−9.18826	−	15.9145i	−0.353395	−	0.612098i
$677$	17.2555	−	29.8874i	0.663184	−	1.14867i	−0.316591	−	0.948562i	$-0.602538\pi$
$677$	17.2555	−	29.8874i	0.663184	−	1.14867i	0.979774	−	0.200105i	$-0.0641285\pi$
$678$	−3.18574	+	1.15951i	−0.122348	+	0.0445309i
$679$	4.22775	+	23.9767i	0.162246	+	0.920143i
$680$		0			0
$681$	−13.6881	−	4.98205i	−0.524528	−	0.190912i
$682$	2.67987	−	2.24868i	0.102617	−	0.0861062i
$683$	−29.4264			−1.12597			−0.562985	−	0.826467i	$-0.690347\pi$
$683$	−29.4264			−1.12597			−0.562985	+	0.826467i	$0.690347\pi$
$684$	−2.17745	+	11.7548i	−0.0832569	+	0.449457i
$685$		0			0
$686$	−13.5412	+	11.3624i	−0.517004	+	0.433818i
$687$	5.62003	+	2.04552i	0.214417	+	0.0780416i
$688$	−1.40309	+	7.95732i	−0.0534923	+	0.303370i
$689$	7.01436	+	39.7804i	0.267226	+	1.51551i
$690$		0			0
$691$	−22.9288	+	39.7138i	−0.872251	+	1.51078i	−0.0125893	+	0.999921i	$0.504007\pi$
$691$	−22.9288	+	39.7138i	−0.872251	+	1.51078i	−0.859662	+	0.510863i	$0.829326\pi$
$692$	1.28065	+	2.21814i	0.0486828	+	0.0843212i
$693$	6.55875	+	5.50344i	0.249146	+	0.209059i
$694$	−27.2403	−	22.8574i	−1.03403	−	0.867654i
$695$		0			0
$696$	2.11415	−	3.66181i	0.0801365	−	0.138801i
$697$	−10.2830	+	3.74271i	−0.389497	+	0.141765i
$698$	−2.38126	−	13.5048i	−0.0901319	−	0.511164i
$699$	0.230661	−	1.30814i	0.00872439	−	0.0494785i
$700$		0			0
$701$	32.6414	−	27.3894i	1.23285	−	1.03448i	0.234800	−	0.972044i	$-0.424557\pi$
$701$	32.6414	−	27.3894i	1.23285	−	1.03448i	0.998049	−	0.0624390i	$-0.0198879\pi$
$702$	−16.3192			−0.615928
$703$	−1.00085	+	0.825204i	−0.0377480	+	0.0311232i
$704$	−2.07129			−0.0780645
$705$		0			0
$706$	−4.71289	−	1.71535i	−0.177372	−	0.0645582i
$707$	−3.73385	+	21.1757i	−0.140426	+	0.796394i
$708$	1.02331	+	5.80350i	0.0384585	+	0.218109i
$709$	46.7420	−	17.0127i	1.75543	−	0.638925i	0.755563	−	0.655076i	$-0.227363\pi$
$709$	46.7420	−	17.0127i	1.75543	−	0.638925i	0.999870	+	0.0161506i	$0.00514113\pi$
$710$		0			0
$711$	16.3750	+	28.3624i	0.614111	+	1.06367i
$712$	4.43551	+	3.72184i	0.166228	+	0.139482i
$713$	−8.97620	−	7.53193i	−0.336161	−	0.282073i
$714$	1.33504	+	2.31235i	0.0499625	+	0.0865376i
$715$		0			0
$716$	20.0057	−	7.28147i	0.747647	−	0.272121i
$717$	−2.01244	−	11.4131i	−0.0751559	−	0.426230i
$718$	−5.47075	+	31.0262i	−0.204167	+	1.15789i
$719$	16.3768	+	5.96067i	0.610752	+	0.222295i	0.628832	−	0.777541i	$-0.283533\pi$
$719$	16.3768	+	5.96067i	0.610752	+	0.222295i	−0.0180804	+	0.999837i	$0.505755\pi$
$720$		0			0
$721$	3.27029			0.121792
$722$	−9.21461	−	16.6160i	−0.342932	−	0.618383i
$723$	−2.25339			−0.0838046
$724$	−7.68024	+	6.44449i	−0.285434	+	0.239507i
$725$		0			0
$726$	0.591105	−	3.35232i	0.0219380	−	0.124416i
$727$	−4.43925	−	25.1762i	−0.164643	−	0.933735i	−0.949432	−	0.313972i	$-0.898340\pi$
$727$	−4.43925	−	25.1762i	−0.164643	−	0.933735i	0.784789	−	0.619763i	$-0.212771\pi$
$728$	7.93322	−	2.88745i	0.294025	−	0.107016i
$729$	7.03908	−	12.1920i	0.260707	−	0.451557i
$730$		0			0
$731$	−21.6145	−	18.1367i	−0.799442	−	0.670811i
$732$	4.99904	+	4.19469i	0.184770	+	0.155040i
$733$	8.20133	+	14.2051i	0.302923	+	0.524678i	0.976797	−	0.214168i	$-0.0687041\pi$
$733$	8.20133	+	14.2051i	0.302923	+	0.524678i	−0.673874	+	0.738847i	$0.735371\pi$
$734$	11.0097	−	19.0694i	0.406377	−	0.703865i
$735$		0			0
$736$	1.20473	+	6.83236i	0.0444069	+	0.251844i
$737$	−3.44842	+	19.5570i	−0.127024	+	0.720390i
$738$	8.07626	+	2.93952i	0.297291	+	0.108205i
$739$	14.3127	−	12.0098i	0.526501	−	0.441786i	−0.340390	−	0.940284i	$-0.610559\pi$
$739$	14.3127	−	12.0098i	0.526501	−	0.441786i	0.866891	+	0.498498i	$0.166115\pi$
$740$		0			0
$741$	9.55733	−	7.88002i	0.351097	−	0.289480i
$742$	−10.8687			−0.399002
$743$	−14.9903	+	12.5783i	−0.549940	+	0.461454i	−0.874921	−	0.484266i	$-0.839087\pi$
$743$	−14.9903	+	12.5783i	−0.549940	+	0.461454i	0.324981	+	0.945721i	$0.394642\pi$
$744$	−0.805177	−	0.293060i	−0.0295192	−	0.0107441i
$745$		0			0
$746$	−5.38967	−	30.5664i	−0.197330	−	1.11911i
$747$	−10.0450	+	3.65610i	−0.367529	+	0.133770i
$748$	3.61648	−	6.26393i	0.132232	−	0.229032i
$749$	−2.62159	−	4.54073i	−0.0957908	−	0.165915i
$750$		0			0
$751$	−4.91074	−	4.12060i	−0.179195	−	0.150363i	0.548778	−	0.835968i	$-0.315093\pi$
$751$	−4.91074	−	4.12060i	−0.179195	−	0.150363i	−0.727973	+	0.685605i	$0.759538\pi$
$752$	2.21364	+	3.83414i	0.0807231	+	0.139817i
$753$	−3.11494	+	5.39524i	−0.113515	+	0.196614i
$754$	43.8700	−	15.9674i	1.59765	−	0.581497i
$755$		0			0
$756$	0.762479	−	4.32423i	0.0277311	−	0.157271i
$757$	38.5080	+	14.0157i	1.39960	+	0.509411i	0.928058	−	0.372435i	$-0.121477\pi$
$757$	38.5080	+	14.0157i	1.39960	+	0.509411i	0.471537	+	0.881846i	$0.343699\pi$
$758$	0.844273	−	0.708430i	0.0306654	−	0.0257313i
$759$	7.29031			0.264621
$760$		0			0
$761$	0.336640			0.0122032			0.00610159	−	0.999981i	$-0.498058\pi$
$761$	0.336640			0.0122032			0.00610159	+	0.999981i	$0.498058\pi$
$762$	1.78844	−	1.50068i	0.0647882	−	0.0543638i
$763$	−0.962400	−	0.350285i	−0.0348412	−	0.0126812i
$764$	0.687119	−	3.89685i	0.0248591	−	0.140983i
$765$		0			0
$766$	13.0711	−	4.75750i	0.472279	−	0.171895i
$767$	−32.5330	+	56.3489i	−1.17470	+	2.03464i
$768$	0.253662	+	0.439356i	0.00915326	+	0.0158539i
$769$	34.9638	+	29.3381i	1.26083	+	1.05796i	0.995593	+	0.0937766i	$0.0298940\pi$
$769$	34.9638	+	29.3381i	1.26083	+	1.05796i	0.265235	+	0.964184i	$0.414550\pi$
$770$		0			0
$771$	2.65495	+	4.59851i	0.0956158	+	0.165611i
$772$	−0.371509	+	0.643472i	−0.0133709	+	0.0231591i
$773$	4.97442	−	1.81054i	0.178917	−	0.0651206i	−0.251008	−	0.967985i	$-0.580762\pi$
$773$	4.97442	−	1.81054i	0.178917	−	0.0651206i	0.429925	+	0.902864i	$0.358540\pi$
$774$	3.84814	+	21.8239i	0.138319	+	0.784444i
$775$		0			0
$776$	−15.1797	−	5.52496i	−0.544920	−	0.198335i
$777$	0.174311	−	0.146264i	0.00625336	−	0.00524719i
$778$	−6.29892			−0.225827
$779$	−12.8756	+	4.56089i	−0.461316	+	0.163411i
$780$		0			0
$781$	−4.64411	+	3.89687i	−0.166179	+	0.139441i
$782$	−22.7657	−	8.28605i	−0.814101	−	0.296308i
$783$	4.21644	−	23.9126i	0.150683	−	0.854567i
$784$	−0.821087	−	4.65661i	−0.0293245	−	0.166308i
$785$		0			0
$786$	−2.22601	+	3.85556i	−0.0793991	+	0.137523i
$787$	22.4447	+	38.8753i	0.800067	+	1.38576i	0.919572	+	0.392922i	$0.128536\pi$
$787$	22.4447	+	38.8753i	0.800067	+	1.38576i	−0.119505	+	0.992834i	$0.538131\pi$
$788$	10.8197	+	9.07877i	0.385434	+	0.323418i
$789$	−2.86988	−	2.40812i	−0.102171	−	0.0857312i
$790$		0			0
$791$	5.03581	−	8.72228i	0.179053	−	0.310128i
$792$	−5.33816	+	1.94293i	−0.189683	+	0.0690391i
$793$	12.5118	+	70.9579i	0.444307	+	2.51979i
$794$	2.41733	−	13.7094i	0.0857879	−	0.486527i
$795$		0			0
$796$	−3.77459	+	3.16726i	−0.133787	+	0.112261i
$797$	19.0863			0.676071			0.338035	−	0.941133i	$-0.390238\pi$
$797$	19.0863			0.676071			0.338035	+	0.941133i	$0.390238\pi$
$798$	1.64149	+	2.90066i	0.0581080	+	0.102682i
$799$	−15.4601			−0.546940
$800$		0			0
$801$	14.9225	+	5.43134i	0.527260	+	0.191907i
$802$	−1.61899	+	9.18177i	−0.0571686	+	0.324220i
$803$	−2.13890	−	12.1303i	−0.0754801	−	0.428069i
$804$	4.57069	−	1.66360i	0.161196	−	0.0586705i
$805$		0			0
$806$	−4.73033	−	8.19318i	−0.166619	−	0.288592i
$807$	1.53141	+	1.28501i	0.0539083	+	0.0452344i
$808$	−10.9290	−	9.17049i	−0.384480	−	0.322617i
$809$	13.3369	+	23.1002i	0.468900	+	0.812159i	0.999368	−	0.0355463i	$-0.0113171\pi$
$809$	13.3369	+	23.1002i	0.468900	+	0.812159i	−0.530468	+	0.847705i	$0.677984\pi$
$810$		0			0
$811$	−7.04130	+	2.56282i	−0.247253	+	0.0899929i	−0.462674	−	0.886528i	$-0.653110\pi$
$811$	−7.04130	+	2.56282i	−0.247253	+	0.0899929i	0.215421	+	0.976521i	$0.430888\pi$
$812$	2.18127	+	12.3706i	0.0765477	+	0.434124i
$813$	−1.65960	+	9.41205i	−0.0582047	+	0.330095i
$814$	−0.579227	−	0.210821i	−0.0203019	−	0.00738929i
$815$		0			0
$816$	−1.77159			−0.0620179
$817$	−26.7839	−	22.8711i	−0.937050	−	0.800159i
$818$	10.3110			0.360515
$819$	17.7371	−	14.8832i	0.619785	−	0.520062i
$820$		0			0
$821$	5.44547	−	30.8828i	0.190048	−	1.07782i	−0.729248	−	0.684250i	$-0.760130\pi$
$821$	5.44547	−	30.8828i	0.190048	−	1.07782i	0.919296	−	0.393567i	$-0.128759\pi$
$822$	0.417076	+	2.36536i	0.0145472	+	0.0825013i
$823$	−51.1929	+	18.6327i	−1.78447	+	0.649495i	−0.784920	+	0.619597i	$0.787296\pi$
$823$	−51.1929	+	18.6327i	−1.78447	+	0.649495i	−0.999553	+	0.0298978i	$0.990482\pi$
$824$	−1.08491	+	1.87912i	−0.0377947	+	0.0654624i
$825$		0			0
$826$	−13.4112	−	11.2533i	−0.466635	−	0.391553i
$827$	17.2538	+	14.4777i	0.599974	+	0.503438i	0.891437	−	0.453144i	$-0.149698\pi$
$827$	17.2538	+	14.4777i	0.599974	+	0.503438i	−0.291464	+	0.956582i	$0.594142\pi$
$828$	9.51383	+	16.4784i	0.330628	+	0.572665i
$829$	7.31630	−	12.6722i	0.254106	−	0.440124i	−0.710547	−	0.703650i	$-0.751552\pi$
$829$	7.31630	−	12.6722i	0.254106	−	0.440124i	0.964652	+	0.263526i	$0.0848856\pi$
$830$		0			0
$831$	0.570969	+	3.23813i	0.0198067	+	0.112329i
$832$	−0.972686	+	5.51638i	−0.0337218	+	0.191246i
$833$	15.5160	+	5.64738i	0.537599	+	0.195670i
$834$	−6.31879	+	5.30209i	−0.218802	+	0.183596i
$835$		0			0
$836$	4.58157	−	7.77969i	0.158457	−	0.269066i
$837$	−4.92057			−0.170080
$838$	−15.1269	+	12.6930i	−0.522549	+	0.438471i
$839$	−1.46240	−	0.532270i	−0.0504876	−	0.0183760i	0.316653	−	0.948541i	$-0.397441\pi$
$839$	−1.46240	−	0.532270i	−0.0504876	−	0.0183760i	−0.367141	+	0.930165i	$0.619663\pi$
$840$		0			0
$841$	7.02645	+	39.8490i	0.242291	+	1.37410i
$842$	−1.84846	+	0.672783i	−0.0637020	+	0.0231856i
$843$	−7.62410	+	13.2053i	−0.262588	+	0.454816i
$844$	−10.9649	−	18.9918i	−0.377428	−	0.653725i
$845$		0			0
$846$	9.30158	+	7.80495i	0.319795	+	0.268340i
$847$	5.05637	+	8.75789i	0.173739	+	0.300925i
$848$	3.60567	−	6.24520i	0.123819	−	0.214461i
$849$	−13.4710	+	4.90303i	−0.462323	+	0.168272i
$850$		0			0
$851$	−0.358519	+	2.03326i	−0.0122899	+	0.0696994i
$852$	1.39534	+	0.507863i	0.0478036	+	0.0173991i
$853$	−7.65393	+	6.42241i	−0.262065	+	0.219899i	−0.764347	−	0.644805i	$-0.776939\pi$
$853$	−7.65393	+	6.42241i	−0.262065	+	0.219899i	0.502282	+	0.864704i	$0.332494\pi$
$854$	−19.3869			−0.663405
$855$		0			0
$856$	3.47883			0.118904
$857$	26.3297	−	22.0933i	0.899406	−	0.754691i	−0.0706680	−	0.997500i	$-0.522513\pi$
$857$	26.3297	−	22.0933i	0.899406	−	0.754691i	0.970074	+	0.242808i	$0.0780686\pi$
$858$	5.53114	+	2.01317i	0.188830	+	0.0687285i
$859$	−8.00494	+	45.3983i	−0.273125	+	1.54897i	0.471730	+	0.881743i	$0.343630\pi$
$859$	−8.00494	+	45.3983i	−0.273125	+	1.54897i	−0.744855	+	0.667226i	$0.767481\pi$
$860$		0			0
$861$	2.25160	−	0.819516i	0.0767344	−	0.0279290i
$862$	−9.78421	+	16.9467i	−0.333251	+	0.577208i
$863$	−19.1322	−	33.1380i	−0.651268	−	1.12803i	−0.982815	−	0.184591i	$-0.940904\pi$
$863$	−19.1322	−	33.1380i	−0.651268	−	1.12803i	0.331547	−	0.943439i	$-0.392429\pi$
$864$	2.23177	+	1.87268i	0.0759265	+	0.0637099i
$865$		0			0
$866$	−10.5299	−	18.2382i	−0.357819	−	0.619761i
$867$	−1.21906	+	2.11147i	−0.0414013	+	0.0717092i
$868$	2.39203	−	0.870627i	0.0811907	−	0.0295510i
$869$	−4.29493	−	24.3578i	−0.145696	−	0.826281i
$870$		0			0
$871$	50.4659	+	18.3681i	1.70997	+	0.622379i
$872$	0.520550	−	0.436793i	0.0176280	−	0.0147917i
$873$	−44.3041			−1.49947
$874$	−28.3269	−	10.5879i	−0.958173	−	0.358140i
$875$		0			0
$876$	−2.31111	+	1.93925i	−0.0780850	+	0.0655211i
$877$	−15.2800	−	5.56146i	−0.515969	−	0.187797i	0.0708937	−	0.997484i	$-0.477415\pi$
$877$	−15.2800	−	5.56146i	−0.515969	−	0.187797i	−0.586863	+	0.809687i	$0.699637\pi$
$878$	6.44324	−	36.5414i	0.217449	−	1.23321i
$879$	2.28497	+	12.9587i	0.0770700	+	0.437086i
$880$		0			0
$881$	−17.3862	+	30.1137i	−0.585755	+	1.01456i	0.409025	+	0.912523i	$0.365869\pi$
$881$	−17.3862	+	30.1137i	−0.585755	+	1.01456i	−0.994781	+	0.102035i	$0.967465\pi$
$882$	−6.48418	−	11.2309i	−0.218334	−	0.378165i
$883$	−3.06827	−	2.57458i	−0.103255	−	0.0866416i	0.589698	−	0.807624i	$-0.299247\pi$
$883$	−3.06827	−	2.57458i	−0.103255	−	0.0866416i	−0.692954	+	0.720982i	$0.743691\pi$
$884$	−14.9842	−	12.5732i	−0.503972	−	0.422883i
$885$		0			0
$886$	−4.05218	+	7.01858i	−0.136136	+	0.235794i
$887$	−4.37166	+	1.59115i	−0.146786	+	0.0534257i	−0.414368	−	0.910109i	$-0.635997\pi$
$887$	−4.37166	+	1.59115i	−0.146786	+	0.0534257i	0.267582	+	0.963535i	$0.413775\pi$
$888$	0.0262168	+	0.148683i	0.000879778	+	0.00498947i
$889$	−1.20438	+	6.83040i	−0.0403937	+	0.229084i
$890$		0			0
$891$	−10.7099	+	8.98671i	−0.358797	+	0.301066i
$892$	−3.11346			−0.104246
$893$	−19.2973	−	0.166533i	−0.645761	−	0.00557282i
$894$	4.04747			0.135368
$895$		0			0
$896$	−1.41627	−	0.515481i	−0.0473144	−	0.0172210i
$897$	3.42356	−	19.4160i	0.114309	−	0.648281i
$898$	−0.413408	−	2.34456i	−0.0137956	−	0.0782388i
$899$	13.2277	−	4.81449i	0.441168	−	0.160572i
$900$		0			0
$901$	12.5910	+	21.8083i	0.419468	+	0.726541i
$902$	−4.97224	−	4.17221i	−0.165558	−	0.138919i
$903$	4.73278	+	3.97128i	0.157497	+	0.132156i
$904$	3.34124	+	5.78720i	0.111128	+	0.192480i
$905$		0			0
$906$	−6.84299	+	2.49065i	−0.227343	+	0.0827461i
$907$	−1.09023	−	6.18302i	−0.0362006	−	0.205304i	0.961343	−	0.275354i	$-0.0887951\pi$
$907$	−1.09023	−	6.18302i	−0.0362006	−	0.205304i	−0.997543	+	0.0700504i	$0.977684\pi$
$908$	−4.98586	+	28.2762i	−0.165462	+	0.938379i
$909$	−36.7686	−	13.3827i	−1.21954	−	0.443875i
$910$		0			0
$911$	−43.9247			−1.45529			−0.727645	−	0.685954i	$-0.759385\pi$
$911$	−43.9247			−1.45529			−0.727645	+	0.685954i	$0.759385\pi$
$912$	−2.21130	−	0.0190831i	−0.0732233	−	0.000631906i
$913$	8.07310			0.267181
$914$	−22.9129	+	19.2262i	−0.757892	+	0.635947i
$915$		0			0
$916$	2.04709	−	11.6096i	0.0676377	−	0.383593i
$917$	−2.29669	−	13.0252i	−0.0758433	−	0.430129i
$918$	−9.56001	+	3.47956i	−0.315527	+	0.114843i
$919$	22.4374	−	38.8627i	0.740141	−	1.28196i	−0.212289	−	0.977207i	$-0.568092\pi$
$919$	22.4374	−	38.8627i	0.740141	−	1.28196i	0.952431	−	0.304756i	$-0.0985748\pi$
$920$		0			0
$921$	11.0772	+	9.29484i	0.365005	+	0.306275i
$922$	−6.23983	−	5.23584i	−0.205498	−	0.172433i
$923$	8.19749	+	14.1985i	0.269824	+	0.467348i
$924$	−0.791876	+	1.37157i	−0.0260508	+	0.0451213i
$925$		0			0
$926$	−4.52038	−	25.6364i	−0.148549	−	0.842463i
$927$	−1.03338	+	5.86060i	−0.0339407	+	0.192487i
$928$	−7.83186	−	2.85056i	−0.257093	−	0.0935743i
$929$	−31.1430	+	26.1321i	−1.02177	+	0.857366i	−0.989849	−	0.142125i	$-0.954607\pi$
$929$	−31.1430	+	26.1321i	−1.02177	+	0.857366i	−0.0319199	+	0.999490i	$0.510162\pi$
$930$		0			0
$931$	19.3063	+	7.21620i	0.632738	+	0.236501i
$932$	−2.61829			−0.0857648
$933$	5.68587	−	4.77101i	0.186147	−	0.156196i
$934$	22.1025	+	8.04467i	0.723217	+	0.263230i
$935$		0			0
$936$	2.66771	+	15.1293i	0.0871968	+	0.494518i
$937$	−44.7350	+	16.2822i	−1.46143	+	0.531916i	−0.945758	−	0.324871i	$-0.894679\pi$
$937$	−44.7350	+	16.2822i	−1.46143	+	0.531916i	−0.515670	+	0.856787i	$0.672457\pi$
$938$	−7.22505	+	12.5142i	−0.235906	+	0.408602i
$939$	−3.22911	−	5.59298i	−0.105378	−	0.182520i
$940$		0			0
$941$	24.2193	+	20.3224i	0.789528	+	0.662492i	0.945629	−	0.325249i	$-0.105448\pi$
$941$	24.2193	+	20.3224i	0.789528	+	0.662492i	−0.156101	+	0.987741i	$0.549892\pi$
$942$	0.0233047	+	0.0403649i	0.000759308	+	0.00131516i
$943$	−10.8705	+	18.8282i	−0.353991	+	0.613130i
$944$	10.9154	−	3.97286i	0.355265	−	0.129306i
$945$		0			0
$946$	2.90620	−	16.4819i	0.0944887	−	0.535872i
$947$	−16.7426	−	6.09383i	−0.544063	−	0.198023i	0.0553437	−	0.998467i	$-0.482375\pi$
$947$	−16.7426	−	6.09383i	−0.544063	−	0.198023i	−0.599407	+	0.800445i	$0.704597\pi$
$948$	−4.64073	+	3.89403i	−0.150724	+	0.126472i
$949$	−33.3106			−1.08131
$950$		0			0
$951$	−8.79480			−0.285191
$952$	4.03173	−	3.38302i	0.130669	−	0.109644i
$953$	11.5629	+	4.20856i	0.374560	+	0.136329i	0.522439	−	0.852677i	$-0.325022\pi$
$953$	11.5629	+	4.20856i	0.374560	+	0.136329i	−0.147879	+	0.989005i	$0.547245\pi$
$954$	3.43441	−	19.4775i	0.111193	−	0.630607i
$955$		0			0
$956$	−21.4661	+	7.81300i	−0.694262	+	0.252691i
$957$	−4.37900	+	7.58466i	−0.141553	+	0.245177i
$958$	12.9011	+	22.3454i	0.416816	+	0.721946i
$959$	−5.46606	−	4.58657i	−0.176508	−	0.148108i
$960$		0			0
$961$	14.0737	+	24.3764i	0.453991	+	0.786335i
$962$	−0.833480	+	1.44363i	−0.0268725	+	0.0465445i
$963$	8.96573	−	3.26326i	0.288917	−	0.105157i
$964$	0.771296	+	4.37424i	0.0248418	+	0.140885i
$965$		0			0
$966$	4.98486	+	1.81434i	0.160385	+	0.0583754i
$967$	20.9868	−	17.6100i	0.674890	−	0.566300i	−0.239618	−	0.970867i	$-0.577022\pi$
$967$	20.9868	−	17.6100i	0.674890	−	0.566300i	0.914508	+	0.404567i	$0.132578\pi$
$968$	−6.70977			−0.215660
$969$	3.91865	−	6.65403i	0.125885	−	0.213758i
$970$		0			0
$971$	15.6706	−	13.1492i	0.502893	−	0.421978i	−0.355727	−	0.934590i	$-0.615767\pi$
$971$	15.6706	−	13.1492i	0.502893	−	0.421978i	0.858620	+	0.512612i	$0.171322\pi$
$972$	11.4309	+	4.16050i	0.366646	+	0.133448i
$973$	4.25525	−	24.1327i	0.136417	−	0.773659i
$974$	−1.51421	−	8.58750i	−0.0485183	−	0.275161i
$975$		0			0
$976$	6.43156	−	11.1398i	0.205869	−	0.356576i
$977$	−19.8916	−	34.4532i	−0.636387	−	1.10225i	−0.986219	−	0.165442i	$-0.947095\pi$
$977$	−19.8916	−	34.4532i	−0.636387	−	1.10225i	0.349832	−	0.936812i	$-0.386239\pi$
$978$	7.24348	+	6.07800i	0.231621	+	0.194353i
$979$	−9.18721	−	7.70898i	−0.293625	−	0.246380i
$980$		0			0
$981$	0.931847	−	1.61401i	0.0297516	−	0.0515312i
$982$	−26.1326	+	9.51149i	−0.833925	+	0.303524i
$983$	6.85424	+	38.8723i	0.218616	+	1.23983i	0.874520	+	0.484989i	$0.161177\pi$
$983$	6.85424	+	38.8723i	0.218616	+	1.23983i	−0.655904	+	0.754844i	$0.727712\pi$
$984$	−0.276067	+	1.56566i	−0.00880070	+	0.0499113i
$985$		0			0
$986$	22.2951	−	18.7078i	0.710020	−	0.595778i
$987$	3.38520			0.107752
$988$	−18.5678	−	15.8553i	−0.590721	−	0.504424i
$989$	−56.0576			−1.78253
$990$		0			0
$991$	12.9715	+	4.72123i	0.412052	+	0.149975i	0.539725	−	0.841842i	$-0.318528\pi$
$991$	12.9715	+	4.72123i	0.412052	+	0.149975i	−0.127672	+	0.991816i	$0.540751\pi$
$992$	−0.293285	+	1.66330i	−0.00931180	+	0.0528098i
$993$	−1.52230	−	8.63337i	−0.0483086	−	0.273972i
$994$	−4.14529	+	1.50876i	−0.131481	+	0.0478551i
$995$		0			0
$996$	−0.988682	−	1.71245i	−0.0313276	−	0.0542610i
$997$	−6.63858	−	5.57043i	−0.210246	−	0.176417i	0.531583	−	0.847006i	$-0.321597\pi$
$997$	−6.63858	−	5.57043i	−0.210246	−	0.176417i	−0.741829	+	0.670589i	$0.766042\pi$
$998$	5.45210	+	4.57486i	0.172583	+	0.144815i
$999$	0.433500	+	0.750844i	0.0137153	+	0.0237557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.m.101.4		30
5.2	odd	4		190.2.p.a.139.9	yes	60
5.3	odd	4		190.2.p.a.139.2	✓	60
5.4	even	2		950.2.l.l.101.2		30
19.16	even	9	inner	950.2.l.m.301.4		30
95.54	even	18		950.2.l.l.301.2		30
95.73	odd	36		190.2.p.a.149.9	yes	60
95.92	odd	36		190.2.p.a.149.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.p.a.139.2	✓	60	5.3	odd	4
190.2.p.a.139.9	yes	60	5.2	odd	4
190.2.p.a.149.2	yes	60	95.92	odd	36
190.2.p.a.149.9	yes	60	95.73	odd	36
950.2.l.l.101.2		30	5.4	even	2
950.2.l.l.301.2		30	95.54	even	18
950.2.l.m.101.4		30	1.1	even	1	trivial
950.2.l.m.301.4		30	19.16	even	9	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.476729 + 0.173515i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.476729 - 0.173515i) q^{6} +(-0.753583 + 1.30524i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.10097 - 1.76292i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.476729 + 0.173515i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.476729 - 0.173515i) q^{6} +(-0.753583 + 1.30524i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.10097 - 1.76292i) q^{9} +(1.03564 + 1.79379i) q^{11} +(0.253662 - 0.439356i) q^{12} +(5.26367 - 1.91582i) q^{13} +(0.261717 + 1.48427i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(2.67504 - 2.24462i) q^{17} -2.74262 q^{18} +(3.36316 - 2.77293i) q^{19} +(-0.585735 + 0.491490i) q^{21} +(1.94637 + 0.708422i) q^{22} +(1.20473 - 6.83236i) q^{23} +(-0.0880960 - 0.499618i) q^{24} +(2.80074 - 4.85102i) q^{26} +(-1.45669 - 2.52306i) q^{27} +(1.15456 + 0.968788i) q^{28} +(6.38459 + 5.35731i) q^{29} +(0.844480 - 1.46268i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.182472 + 1.03485i) q^{33} +(0.606382 - 3.43896i) q^{34} +(-2.10097 + 1.76292i) q^{36} -0.297593 q^{37} +(0.793930 - 4.28599i) q^{38} +2.84177 q^{39} +(-2.94472 - 1.07179i) q^{41} +(-0.132775 + 0.753007i) q^{42} +(-1.40309 - 7.95732i) q^{43} +(1.94637 - 0.708422i) q^{44} +(-3.46888 - 6.00828i) q^{46} +(-3.39149 - 2.84580i) q^{47} +(-0.388633 - 0.326102i) q^{48} +(2.36423 + 4.09496i) q^{49} +(1.66475 - 0.605918i) q^{51} +(-0.972686 - 5.51638i) q^{52} +(-1.25223 + 7.10177i) q^{53} +(-2.73768 - 0.996433i) q^{54} +1.50717 q^{56} +(2.08447 - 0.738375i) q^{57} +8.33449 q^{58} +(-8.89828 + 7.46654i) q^{59} +(-2.23366 + 12.6677i) q^{61} +(-0.293285 - 1.66330i) q^{62} +(3.88430 - 1.41377i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.804971 + 0.675451i) q^{66} +(7.34453 + 6.16279i) q^{67} +(-1.74601 - 3.02417i) q^{68} +(1.75985 - 3.04815i) q^{69} +(0.508252 + 2.88244i) q^{71} +(-0.476251 + 2.70095i) q^{72} +(-5.58812 - 2.03391i) q^{73} +(-0.227970 + 0.191289i) q^{74} +(-2.14679 - 3.79358i) q^{76} -3.12177 q^{77} +(2.17692 - 1.82665i) q^{78} +(-11.2210 - 4.08411i) q^{79} +(1.17210 + 6.64729i) q^{81} +(-2.94472 + 1.07179i) q^{82} +(1.94881 - 3.37544i) q^{83} +(0.382311 + 0.662183i) q^{84} +(-6.18970 - 5.19377i) q^{86} +(2.11415 + 3.66181i) q^{87} +(1.03564 - 1.79379i) q^{88} +(-5.44096 + 1.98035i) q^{89} +(-1.46600 + 8.31409i) q^{91} +(-6.51936 - 2.37285i) q^{92} +(0.656386 - 0.550773i) q^{93} -4.42728 q^{94} -0.507325 q^{96} +(12.3746 - 10.3835i) q^{97} +(4.44329 + 1.61723i) q^{98} +(0.986452 - 5.59445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{7} - 15 q^{8}+O(q^{10}) \) 30 * q + 12 * q^7 - 15 * q^8	\( 30 q + 12 q^{7} - 15 q^{8} + 6 q^{11} + 6 q^{14} + 30 q^{18} + 24 q^{19} + 24 q^{21} - 3 q^{22} - 3 q^{23} + 3 q^{26} + 18 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{33} - 24 q^{37} + 12 q^{38} - 24 q^{39} - 3 q^{41} - 12 q^{42} - 6 q^{43} - 3 q^{44} - 48 q^{47} + 15 q^{49} - 90 q^{51} + 18 q^{53} + 18 q^{54} - 24 q^{56} + 42 q^{57} - 36 q^{58} - 18 q^{59} - 60 q^{61} + 24 q^{62} + 21 q^{63} - 15 q^{64} - 78 q^{66} + 30 q^{67} + 12 q^{68} + 24 q^{69} - 30 q^{73} - 9 q^{74} - 3 q^{76} - 78 q^{77} - 6 q^{79} + 60 q^{81} - 3 q^{82} + 42 q^{83} - 6 q^{84} + 12 q^{86} + 54 q^{87} + 6 q^{88} - 30 q^{89} - 6 q^{91} + 6 q^{92} - 72 q^{93} - 78 q^{94} + 42 q^{97} - 6 q^{98} - 99 q^{99}+O(q^{100}) \) 30 * q + 12 * q^7 - 15 * q^8 + 6 * q^11 + 6 * q^14 + 30 * q^18 + 24 * q^19 + 24 * q^21 - 3 * q^22 - 3 * q^23 + 3 * q^26 + 18 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^33 - 24 * q^37 + 12 * q^38 - 24 * q^39 - 3 * q^41 - 12 * q^42 - 6 * q^43 - 3 * q^44 - 48 * q^47 + 15 * q^49 - 90 * q^51 + 18 * q^53 + 18 * q^54 - 24 * q^56 + 42 * q^57 - 36 * q^58 - 18 * q^59 - 60 * q^61 + 24 * q^62 + 21 * q^63 - 15 * q^64 - 78 * q^66 + 30 * q^67 + 12 * q^68 + 24 * q^69 - 30 * q^73 - 9 * q^74 - 3 * q^76 - 78 * q^77 - 6 * q^79 + 60 * q^81 - 3 * q^82 + 42 * q^83 - 6 * q^84 + 12 * q^86 + 54 * q^87 + 6 * q^88 - 30 * q^89 - 6 * q^91 + 6 * q^92 - 72 * q^93 - 78 * q^94 + 42 * q^97 - 6 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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