LMFDB - Embedded newform 950.2.q.g.107.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (of order $12$, degree $4$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	950.107
Dual form			950.2.q.g.293.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.680416 - 2.53935i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.31446 + 2.27672i) q^{6} +(2.47691 + 2.47691i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-3.38724 - 1.95563i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.680416 - 2.53935i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.31446 + 2.27672i) q^{6} +(2.47691 + 2.47691i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-3.38724 - 1.95563i) q^{9} +0.295831 q^{11} +(1.85893 - 1.85893i) q^{12} +(-1.29839 + 0.347904i) q^{13} +(-1.75144 - 3.03358i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.182999 + 0.682961i) q^{17} +(2.76567 + 2.76567i) q^{18} +(1.91986 - 3.91333i) q^{19} +(7.97505 - 4.60440i) q^{21} +(-0.285751 - 0.0765667i) q^{22} +(-2.00849 - 7.49578i) q^{23} +(-2.27672 + 1.31446i) q^{24} +1.34420 q^{26} +(-1.69396 + 1.69396i) q^{27} +(0.906611 + 3.38352i) q^{28} +(2.37798 - 4.11878i) q^{29} -6.65346i q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.201288 - 0.751218i) q^{33} +(0.353527 - 0.612326i) q^{34} +(-1.95563 - 3.38724i) q^{36} +(-2.70335 + 2.70335i) q^{37} +(-2.86728 + 3.28309i) q^{38} +3.53379i q^{39} +(7.26797 - 4.19616i) q^{41} +(-8.89502 + 2.38341i) q^{42} +(9.73843 + 2.60940i) q^{43} +(0.256197 + 0.147915i) q^{44} +7.76020i q^{46} +(7.72671 - 2.07037i) q^{47} +(2.53935 - 0.680416i) q^{48} +5.27013i q^{49} +(1.60976 + 0.929395i) q^{51} +(-1.29839 - 0.347904i) q^{52} +(-2.20478 + 0.590770i) q^{53} +(2.07467 - 1.19781i) q^{54} -3.50287i q^{56} +(-8.63101 - 7.53787i) q^{57} +(-3.36297 + 3.36297i) q^{58} +(-6.62955 - 11.4827i) q^{59} +(-6.50406 + 11.2654i) q^{61} +(-1.72204 + 6.42675i) q^{62} +(-3.54598 - 13.2338i) q^{63} +1.00000i q^{64} +(-0.388859 + 0.673523i) q^{66} +(-2.19747 - 8.20107i) q^{67} +(-0.499962 + 0.499962i) q^{68} -20.4010 q^{69} +(-3.84390 + 2.21928i) q^{71} +(1.01231 + 3.77798i) q^{72} +(6.80840 + 1.82431i) q^{73} +(3.31091 - 1.91156i) q^{74} +(3.61931 - 2.42912i) q^{76} +(0.732746 + 0.732746i) q^{77} +(0.914613 - 3.41338i) q^{78} +(8.58478 + 14.8693i) q^{79} +(-2.71793 - 4.70759i) q^{81} +(-8.10636 + 2.17209i) q^{82} +(-12.4285 + 12.4285i) q^{83} +9.20880 q^{84} +(-8.73124 - 5.04098i) q^{86} +(-8.84099 - 8.84099i) q^{87} +(-0.209184 - 0.209184i) q^{88} +(0.137304 - 0.237817i) q^{89} +(-4.07773 - 2.35428i) q^{91} +(2.00849 - 7.49578i) q^{92} +(-16.8955 - 4.52712i) q^{93} -7.99928 q^{94} -2.62893 q^{96} +(5.63547 + 1.51002i) q^{97} +(1.36401 - 5.09055i) q^{98} +(-1.00205 - 0.578535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) $ 32 * q + 12 * q^3 - 24 * q^7	$ 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) $ 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.680416	−	2.53935i	0.392838	−	1.46609i	−0.432592	−	0.901590i	$-0.642401\pi$
$3$	0.680416	−	2.53935i	0.392838	−	1.46609i	0.825431	−	0.564503i	$-0.190932\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.31446	+	2.27672i	−0.536627	+	0.929466i
$7$	2.47691	+	2.47691i	0.936182	+	0.936182i	0.998082	−	0.0618999i	$-0.0197160\pi$
$7$	2.47691	+	2.47691i	0.936182	+	0.936182i	−0.0618999	+	0.998082i	$0.519716\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−3.38724	−	1.95563i	−1.12908	−	0.651876i
$10$		0			0
$11$	0.295831			0.0891964			0.0445982	−	0.999005i	$-0.485799\pi$
$11$	0.295831			0.0891964			0.0445982	+	0.999005i	$0.485799\pi$
$12$	1.85893	−	1.85893i	0.536627	−	0.536627i
$13$	−1.29839	+	0.347904i	−0.360110	+	0.0964912i	−0.434338	−	0.900750i	$-0.643018\pi$
$13$	−1.29839	+	0.347904i	−0.360110	+	0.0964912i	0.0742277	+	0.997241i	$0.476351\pi$
$14$	−1.75144	−	3.03358i	−0.468091	−	0.810758i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.182999	+	0.682961i	−0.0443837	+	0.165642i	−0.984560	−	0.175045i	$-0.943993\pi$
$17$	−0.182999	+	0.682961i	−0.0443837	+	0.165642i	0.940177	+	0.340687i	$0.110660\pi$
$18$	2.76567	+	2.76567i	0.651876	+	0.651876i
$19$	1.91986	−	3.91333i	0.440445	−	0.897780i
$19$	1.91986	−	3.91333i	0.440445	−	0.897780i
$20$		0			0
$21$	7.97505	−	4.60440i	1.74030	−	1.00476i
$22$	−0.285751	−	0.0765667i	−0.0609223	−	0.0163241i
$23$	−2.00849	−	7.49578i	−0.418799	−	1.56298i	−0.777103	−	0.629373i	$-0.783312\pi$
$23$	−2.00849	−	7.49578i	−0.418799	−	1.56298i	0.358305	−	0.933605i	$-0.383355\pi$
$24$	−2.27672	+	1.31446i	−0.464733	+	0.268314i
$25$		0			0
$26$	1.34420			0.263619
$27$	−1.69396	+	1.69396i	−0.326002	+	0.326002i
$28$	0.906611	+	3.38352i	0.171333	+	0.639425i
$29$	2.37798	−	4.11878i	0.441579	−	0.764838i	−0.556228	−	0.831030i	$-0.687752\pi$
$29$	2.37798	−	4.11878i	0.441579	−	0.764838i	0.997807	+	0.0661924i	$0.0210851\pi$
$30$		0			0
$31$		−	6.65346i		−	1.19500i	−0.801870	−	0.597499i	$-0.796161\pi$
$31$		−	6.65346i		−	1.19500i	0.801870	−	0.597499i	$-0.203839\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.201288	−	0.751218i	0.0350398	−	0.130770i
$34$	0.353527	−	0.612326i	0.0606293	−	0.105013i
$35$		0			0
$36$	−1.95563	−	3.38724i	−0.325938	−	0.564541i
$37$	−2.70335	+	2.70335i	−0.444428	+	0.444428i	−0.893497	−	0.449069i	$-0.851756\pi$
$37$	−2.70335	+	2.70335i	−0.444428	+	0.444428i	0.449069	+	0.893497i	$0.351756\pi$
$38$	−2.86728	+	3.28309i	−0.465135	+	0.532588i
$39$			3.53379i			0.565860i
$40$		0			0
$41$	7.26797	−	4.19616i	1.13507	−	0.655330i	0.189862	−	0.981811i	$-0.439196\pi$
$41$	7.26797	−	4.19616i	1.13507	−	0.655330i	0.945204	+	0.326480i	$0.105863\pi$
$42$	−8.89502	+	2.38341i	−1.37253	+	0.367768i
$43$	9.73843	+	2.60940i	1.48510	+	0.397930i	0.908078	−	0.418801i	$-0.137549\pi$
$43$	9.73843	+	2.60940i	1.48510	+	0.397930i	0.577018	+	0.816731i	$0.304216\pi$
$44$	0.256197	+	0.147915i	0.0386232	+	0.0222991i
$45$		0			0
$46$			7.76020i			1.14418i
$47$	7.72671	−	2.07037i	1.12706	−	0.301994i	0.353320	−	0.935502i	$-0.385053\pi$
$47$	7.72671	−	2.07037i	1.12706	−	0.301994i	0.773736	+	0.633509i	$0.218386\pi$
$48$	2.53935	−	0.680416i	0.366523	−	0.0982096i
$49$			5.27013i			0.752875i
$50$		0			0
$51$	1.60976	+	0.929395i	0.225411	+	0.130141i
$52$	−1.29839	−	0.347904i	−0.180055	−	0.0482456i
$53$	−2.20478	+	0.590770i	−0.302850	+	0.0811485i	−0.407044	−	0.913409i	$-0.633440\pi$
$53$	−2.20478	+	0.590770i	−0.302850	+	0.0811485i	0.104194	+	0.994557i	$0.466774\pi$
$54$	2.07467	−	1.19781i	0.282326	−	0.163001i
$55$		0			0
$56$		−	3.50287i		−	0.468091i
$57$	−8.63101	−	7.53787i	−1.14320	−	0.998416i
$58$	−3.36297	+	3.36297i	−0.441579	+	0.441579i
$59$	−6.62955	−	11.4827i	−0.863094	−	1.49492i	−0.868928	−	0.494939i	$-0.835190\pi$
$59$	−6.62955	−	11.4827i	−0.863094	−	1.49492i	0.00583396	−	0.999983i	$-0.498143\pi$
$60$		0			0
$61$	−6.50406	+	11.2654i	−0.832759	+	1.44238i	0.0630825	+	0.998008i	$0.479907\pi$
$61$	−6.50406	+	11.2654i	−0.832759	+	1.44238i	−0.895842	+	0.444373i	$0.853426\pi$
$62$	−1.72204	+	6.42675i	−0.218700	+	0.816198i
$63$	−3.54598	−	13.2338i	−0.446752	−	1.66730i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−0.388859	+	0.673523i	−0.0478652	+	0.0829050i
$67$	−2.19747	−	8.20107i	−0.268464	−	1.00192i	−0.960096	−	0.279670i	$-0.909775\pi$
$67$	−2.19747	−	8.20107i	−0.268464	−	1.00192i	0.691632	−	0.722250i	$-0.256892\pi$
$68$	−0.499962	+	0.499962i	−0.0606293	+	0.0606293i
$69$	−20.4010			−2.45599
$70$		0			0
$71$	−3.84390	+	2.21928i	−0.456187	+	0.263380i	−0.710440	−	0.703758i	$-0.751504\pi$
$71$	−3.84390	+	2.21928i	−0.456187	+	0.263380i	0.254253	+	0.967138i	$0.418171\pi$
$72$	1.01231	+	3.77798i	0.119302	+	0.445239i
$73$	6.80840	+	1.82431i	0.796863	+	0.213519i	0.634206	−	0.773164i	$-0.281327\pi$
$73$	6.80840	+	1.82431i	0.796863	+	0.213519i	0.162657	+	0.986683i	$0.447994\pi$
$74$	3.31091	−	1.91156i	0.384886	−	0.222214i
$75$		0			0
$76$	3.61931	−	2.42912i	0.415163	−	0.278639i
$77$	0.732746	+	0.732746i	0.0835041	+	0.0835041i
$78$	0.914613	−	3.41338i	0.103560	−	0.386490i
$79$	8.58478	+	14.8693i	0.965863	+	1.67292i	0.707279	+	0.706935i	$0.249923\pi$
$79$	8.58478	+	14.8693i	0.965863	+	1.67292i	0.258584	+	0.965989i	$0.416744\pi$
$80$		0			0
$81$	−2.71793	−	4.70759i	−0.301992	−	0.523066i
$82$	−8.10636	+	2.17209i	−0.895198	+	0.239868i
$83$	−12.4285	+	12.4285i	−1.36420	+	1.36420i	−0.495715	+	0.868486i	$0.665094\pi$
$83$	−12.4285	+	12.4285i	−1.36420	+	1.36420i	−0.868486	+	0.495715i	$0.834906\pi$
$84$	9.20880			1.00476
$85$		0			0
$86$	−8.73124	−	5.04098i	−0.941514	−	0.543583i
$87$	−8.84099	−	8.84099i	−0.947854	−	0.947854i
$88$	−0.209184	−	0.209184i	−0.0222991	−	0.0222991i
$89$	0.137304	−	0.237817i	0.0145541	−	0.0252085i	−0.858657	−	0.512551i	$-0.828700\pi$
$89$	0.137304	−	0.237817i	0.0145541	−	0.0252085i	0.873211	+	0.487343i	$0.162034\pi$
$90$		0			0
$91$	−4.07773	−	2.35428i	−0.427462	−	0.246795i
$92$	2.00849	−	7.49578i	0.209399	−	0.781489i
$93$	−16.8955	−	4.52712i	−1.75198	−	0.469441i
$94$	−7.99928			−0.825062
$95$		0			0
$96$	−2.62893			−0.268314
$97$	5.63547	+	1.51002i	0.572195	+	0.153319i	0.533303	−	0.845924i	$-0.320950\pi$
$97$	5.63547	+	1.51002i	0.572195	+	0.153319i	0.0388920	+	0.999243i	$0.487617\pi$
$98$	1.36401	−	5.09055i	0.137786	−	0.514223i
$99$	−1.00205	−	0.578535i	−0.100710	−	0.0581450i
$100$		0			0
$101$	−1.36751	+	2.36859i	−0.136072	+	0.235684i	−0.926006	−	0.377508i	$-0.876781\pi$
$101$	−1.36751	+	2.36859i	−0.136072	+	0.235684i	0.789934	+	0.613191i	$0.210115\pi$
$102$	−1.31436	−	1.31436i	−0.130141	−	0.130141i
$103$	5.49484	+	5.49484i	0.541423	+	0.541423i	0.923946	−	0.382523i	$-0.124945\pi$
$103$	5.49484	+	5.49484i	0.541423	+	0.541423i	−0.382523	+	0.923946i	$0.624945\pi$
$104$	1.16411	+	0.672099i	0.114150	+	0.0659047i
$105$		0			0
$106$	2.28256			0.221702
$107$	2.89624	−	2.89624i	0.279991	−	0.279991i	−0.553115	−	0.833105i	$-0.686561\pi$
$107$	2.89624	−	2.89624i	0.279991	−	0.279991i	0.833105	+	0.553115i	$0.186561\pi$
$108$	−2.31399	+	0.620032i	−0.222664	+	0.0596626i
$109$	−4.05608	−	7.02534i	−0.388502	−	0.672905i	0.603746	−	0.797177i	$-0.293674\pi$
$109$	−4.05608	−	7.02534i	−0.388502	−	0.672905i	−0.992248	+	0.124271i	$0.960341\pi$
$110$		0			0
$111$	5.02534	+	8.70414i	0.476984	+	0.826160i
$112$	−0.906611	+	3.38352i	−0.0856666	+	0.319712i
$113$	3.00672	+	3.00672i	0.282849	+	0.282849i	0.834244	−	0.551395i	$-0.185904\pi$
$113$	3.00672	+	3.00672i	0.282849	+	0.282849i	−0.551395	+	0.834244i	$0.685904\pi$
$114$	6.38597	+	9.51490i	0.598101	+	0.891152i
$115$		0			0
$116$	4.11878	−	2.37798i	0.382419	−	0.220790i
$117$	5.07835	+	1.36074i	0.469494	+	0.125800i
$118$	3.43171	+	12.8073i	0.315914	+	1.17901i
$119$	−2.14490	+	1.23836i	−0.196623	+	0.113520i
$120$		0			0
$121$	−10.9125			−0.992044
$122$	9.19813	−	9.19813i	0.832759	−	0.832759i
$123$	−5.71027	−	21.3110i	−0.514878	−	1.92155i
$124$	3.32673	−	5.76207i	0.298749	−	0.517449i
$125$		0			0
$126$			13.7006i			1.22055i
$127$	0.416469	+	1.55428i	0.0369557	+	0.137920i	0.981939	−	0.189198i	$-0.0605889\pi$
$127$	0.416469	+	1.55428i	0.0369557	+	0.137920i	−0.944983	+	0.327119i	$0.893922\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	13.2524	−	22.9538i	1.16681	−	2.02097i
$130$		0			0
$131$	3.42017	+	5.92391i	0.298822	+	0.517574i	0.975867	−	0.218367i	$-0.0700731\pi$
$131$	3.42017	+	5.92391i	0.298822	+	0.517574i	−0.677045	+	0.735942i	$0.736740\pi$
$132$	0.549930	−	0.549930i	0.0478652	−	0.0478652i
$133$	14.4483	−	4.93765i	1.25282	−	0.428149i
$134$			8.49037i			0.733456i
$135$		0			0
$136$	0.612326	−	0.353527i	0.0525065	−	0.0303147i
$137$	5.92426	−	1.58740i	0.506144	−	0.135621i	0.00329385	−	0.999995i	$-0.498952\pi$
$137$	5.92426	−	1.58740i	0.506144	−	0.135621i	0.502850	+	0.864374i	$0.332285\pi$
$138$	19.7058	+	5.28017i	1.67747	+	0.449478i
$139$	−2.68024	−	1.54744i	−0.227335	−	0.131252i	0.382007	−	0.924159i	$-0.375233\pi$
$139$	−2.68024	−	1.54744i	−0.227335	−	0.131252i	−0.609342	+	0.792908i	$0.708566\pi$
$140$		0			0
$141$		−	21.0295i		−	1.77100i
$142$	4.28731	−	1.14878i	0.359783	−	0.0964036i
$143$	−0.384105	+	0.102921i	−0.0321205	+	0.00860666i
$144$		−	3.91125i		−	0.325938i
$145$		0			0
$146$	−6.10425	−	3.52429i	−0.505191	−	0.291672i
$147$	13.3827	+	3.58588i	1.10379	+	0.295758i
$148$	−3.69284	+	0.989494i	−0.303550	+	0.0813359i
$149$	1.07405	−	0.620104i	0.0879897	−	0.0508009i	−0.455360	−	0.890308i	$-0.650489\pi$
$149$	1.07405	−	0.620104i	0.0879897	−	0.0508009i	0.543349	+	0.839507i	$0.317156\pi$
$150$		0			0
$151$			21.6748i			1.76387i	0.471368	+	0.881936i	$0.343760\pi$
$151$			21.6748i			1.76387i	−0.471368	+	0.881936i	$0.656240\pi$
$152$	−4.12469	+	1.40960i	−0.334556	+	0.114334i
$153$	1.95548	−	1.95548i	0.158091	−	0.158091i
$154$	−0.518129	−	0.897426i	−0.0417521	−	0.0723167i
$155$		0			0
$156$	−1.76690	+	3.06036i	−0.141465	+	0.245025i
$157$	1.48707	−	5.54982i	0.118681	−	0.442924i	−0.880855	−	0.473387i	$-0.843031\pi$
$157$	1.48707	−	5.54982i	0.118681	−	0.442924i	0.999536	+	0.0304627i	$0.00969806\pi$
$158$	−4.44381	−	16.5845i	−0.353530	−	1.31939i
$159$			6.00068i			0.475885i
$160$		0			0
$161$	13.5915	−	23.5412i	1.07116	−	1.85530i
$162$	1.40690	+	5.25063i	0.110537	+	0.412529i
$163$	−10.1619	+	10.1619i	−0.795940	+	0.795940i	−0.982453	−	0.186513i	$-0.940281\pi$
$163$	−10.1619	+	10.1619i	−0.795940	+	0.795940i	0.186513	+	0.982453i	$0.440281\pi$
$164$	8.39232			0.655330
$165$		0			0
$166$	15.2217	−	8.78824i	1.18143	−	0.682100i
$167$	4.34794	+	16.2267i	0.336454	+	1.25566i	0.902284	+	0.431141i	$0.141889\pi$
$167$	4.34794	+	16.2267i	0.336454	+	1.25566i	−0.565830	+	0.824522i	$0.691444\pi$
$168$	−8.89502	−	2.38341i	−0.686265	−	0.183884i
$169$	−9.69354	+	5.59657i	−0.745657	+	0.430505i
$170$		0			0
$171$	−14.1560	+	9.50089i	−1.08254	+	0.726551i
$172$	7.12903	+	7.12903i	0.543583	+	0.543583i
$173$	3.09816	−	11.5625i	0.235549	−	0.879080i	−0.742352	−	0.670010i	$-0.766290\pi$
$173$	3.09816	−	11.5625i	0.235549	−	0.879080i	0.977901	−	0.209070i	$-0.0670435\pi$
$174$	6.25153	+	10.8280i	0.473927	+	0.820865i
$175$		0			0
$176$	0.147915	+	0.256197i	0.0111495	+	0.0193116i
$177$	−33.6695	+	9.02170i	−2.53075	+	0.678113i
$178$	−0.194176	+	0.194176i	−0.0145541	+	0.0145541i
$179$	15.2297			1.13832			0.569162	−	0.822225i	$-0.307268\pi$
$179$	15.2297			1.13832			0.569162	+	0.822225i	$0.307268\pi$
$180$		0			0
$181$	−1.82454	−	1.05340i	−0.135617	−	0.0782987i	0.430656	−	0.902516i	$-0.358282\pi$
$181$	−1.82454	−	1.05340i	−0.135617	−	0.0782987i	−0.566274	+	0.824217i	$0.691615\pi$
$182$	3.32945	+	3.32945i	0.246795	+	0.246795i
$183$	24.1812	+	24.1812i	1.78753	+	1.78753i
$184$	−3.88010	+	6.72053i	−0.286045	+	0.495444i
$185$		0			0
$186$	15.1481	+	8.74573i	1.11071	+	0.641268i
$187$	−0.0541367	+	0.202041i	−0.00395887	+	0.0147747i
$188$	7.72671	+	2.07037i	0.563528	+	0.150997i
$189$	−8.39155			−0.610395
$190$		0			0
$191$	1.60707			0.116284			0.0581419	−	0.998308i	$-0.481482\pi$
$191$	1.60707			0.116284			0.0581419	+	0.998308i	$0.481482\pi$
$192$	2.53935	+	0.680416i	0.183262	+	0.0491048i
$193$	−0.624215	+	2.32960i	−0.0449320	+	0.167688i	−0.984746	−	0.173998i	$-0.944331\pi$
$193$	−0.624215	+	2.32960i	−0.0449320	+	0.167688i	0.939814	+	0.341686i	$0.110998\pi$
$194$	−5.05262	−	2.91713i	−0.362757	−	0.209438i
$195$		0			0
$196$	−2.63506	+	4.56406i	−0.188219	+	0.326005i
$197$	5.12179	+	5.12179i	0.364913	+	0.364913i	0.865618	−	0.500705i	$-0.166926\pi$
$197$	5.12179	+	5.12179i	0.364913	+	0.364913i	−0.500705	+	0.865618i	$0.666926\pi$
$198$	0.818172	+	0.818172i	0.0581450	+	0.0581450i
$199$	8.90231	+	5.13975i	0.631068	+	0.364347i	0.781166	−	0.624324i	$-0.214625\pi$
$199$	8.90231	+	5.13975i	0.631068	+	0.364347i	−0.150098	+	0.988671i	$0.547959\pi$
$200$		0			0
$201$	−22.3206			−1.57437
$202$	1.93395	−	1.93395i	0.136072	−	0.136072i
$203$	16.0918	−	4.31180i	1.12943	−	0.302629i
$204$	0.929395	+	1.60976i	0.0650707	+	0.112706i
$205$		0			0
$206$	−3.88544	−	6.72978i	−0.270711	−	0.468886i
$207$	−7.85570	+	29.3179i	−0.546009	+	2.03773i
$208$	−0.950491	−	0.950491i	−0.0659047	−	0.0659047i
$209$	0.567953	−	1.15768i	0.0392861	−	0.0800787i
$210$		0			0
$211$	8.23977	−	4.75723i	0.567249	−	0.327501i	−0.188801	−	0.982015i	$-0.560460\pi$
$211$	8.23977	−	4.75723i	0.567249	−	0.327501i	0.756050	+	0.654514i	$0.227127\pi$
$212$	−2.20478	−	0.590770i	−0.151425	−	0.0405742i
$213$	3.02006	+	11.2710i	0.206931	+	0.772278i
$214$	−3.54716	+	2.04795i	−0.242479	+	0.139995i
$215$		0			0
$216$	2.39562			0.163001
$217$	16.4800	−	16.4800i	1.11874	−	1.11874i
$218$	2.09958	+	7.83574i	0.142202	+	0.530704i
$219$	9.26509	−	16.0476i	0.626077	−	1.08440i
$220$		0			0
$221$		−	0.950419i		−	0.0639321i
$222$	−2.60131	−	9.70821i	−0.174588	−	0.651572i
$223$	−1.49381	+	5.57498i	−0.100033	+	0.373328i	−0.997734	−	0.0672762i	$-0.978569\pi$
$223$	−1.49381	+	5.57498i	−0.100033	+	0.373328i	0.897701	+	0.440604i	$0.145236\pi$
$224$	1.75144	−	3.03358i	0.117023	−	0.202689i
$225$		0			0
$226$	−2.12607	−	3.68247i	−0.141424	−	0.244954i
$227$	−9.81048	+	9.81048i	−0.651144	+	0.651144i	−0.953269	−	0.302124i	$-0.902304\pi$
$227$	−9.81048	+	9.81048i	−0.651144	+	0.651144i	0.302124	+	0.953269i	$0.402304\pi$
$228$	−3.70573	−	10.8435i	−0.245418	−	0.718128i
$229$			10.8632i			0.717857i	0.933365	+	0.358929i	$0.116858\pi$
$229$			10.8632i			0.717857i	−0.933365	+	0.358929i	$0.883142\pi$
$230$		0			0
$231$	2.35927	−	1.36212i	0.155228	−	0.0896212i
$232$	−4.59390	+	1.23093i	−0.301604	+	0.0808146i
$233$	−22.1658	−	5.93930i	−1.45213	−	0.389097i	−0.555365	−	0.831607i	$-0.687421\pi$
$233$	−22.1658	−	5.93930i	−1.45213	−	0.389097i	−0.896763	+	0.442510i	$0.854088\pi$
$234$	−4.55312	−	2.62875i	−0.297647	−	0.171847i
$235$		0			0
$236$		−	13.2591i		−	0.863094i
$237$	43.5995	−	11.6824i	2.83209	−	0.758856i
$238$	2.39233	−	0.641022i	0.155071	−	0.0415513i
$239$			8.37568i			0.541778i	0.962611	+	0.270889i	$0.0873176\pi$
$239$			8.37568i			0.541778i	−0.962611	+	0.270889i	$0.912682\pi$
$240$		0			0
$241$	−5.99626	−	3.46194i	−0.386253	−	0.223003i	0.294282	−	0.955719i	$-0.404919\pi$
$241$	−5.99626	−	3.46194i	−0.386253	−	0.223003i	−0.680535	+	0.732715i	$0.738253\pi$
$242$	10.5407	+	2.82436i	0.677579	+	0.181557i
$243$	−20.7455	+	5.55874i	−1.33082	+	0.356593i
$244$	−11.2654	+	6.50406i	−0.721191	+	0.416380i
$245$		0			0
$246$			22.0628i			1.40667i
$247$	−1.13127	+	5.74897i	−0.0719808	+	0.365798i
$248$	−4.70471	+	4.70471i	−0.298749	+	0.298749i
$249$	23.1036	+	40.0167i	1.46413	+	2.53595i
$250$		0			0
$251$	−6.43930	+	11.1532i	−0.406445	+	0.703983i	−0.994488	−	0.104846i	$-0.966565\pi$
$251$	−6.43930	+	11.1532i	−0.406445	+	0.703983i	0.588044	+	0.808829i	$0.299898\pi$
$252$	3.54598	−	13.2338i	0.223376	−	0.833650i
$253$	−0.594173	−	2.21748i	−0.0373553	−	0.139412i
$254$		−	1.60911i		−	0.100965i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.81690	−	21.7090i	−0.362848	−	1.35417i	−0.870315	−	0.492496i	$-0.836085\pi$
$257$	−5.81690	−	21.7090i	−0.362848	−	1.35417i	0.507467	−	0.861671i	$-0.330582\pi$
$258$	−18.7417	+	18.7417i	−1.16681	+	1.16681i
$259$	−13.3919			−0.832131
$260$		0			0
$261$	−16.1096	+	9.30087i	−0.997158	+	0.575709i
$262$	−1.77041	−	6.60726i	−0.109376	−	0.408198i
$263$	−14.2683	−	3.82318i	−0.879821	−	0.235747i	−0.209491	−	0.977811i	$-0.567181\pi$
$263$	−14.2683	−	3.82318i	−0.879821	−	0.235747i	−0.670330	+	0.742063i	$0.733847\pi$
$264$	−0.673523	+	0.388859i	−0.0414525	+	0.0239326i
$265$		0			0
$266$	−15.2339	+	1.02992i	−0.934050	+	0.0631486i
$267$	−0.510476	−	0.510476i	−0.0312406	−	0.0312406i
$268$	2.19747	−	8.20107i	0.134232	−	0.500960i
$269$	1.82085	+	3.15380i	0.111019	+	0.192291i	0.916181	−	0.400764i	$-0.131255\pi$
$269$	1.82085	+	3.15380i	0.111019	+	0.192291i	−0.805162	+	0.593054i	$0.797922\pi$
$270$		0			0
$271$	10.8504	+	18.7935i	0.659116	+	1.14162i	0.980845	+	0.194791i	$0.0624027\pi$
$271$	10.8504	+	18.7935i	0.659116	+	1.14162i	−0.321729	+	0.946832i	$0.604264\pi$
$272$	−0.682961	+	0.182999i	−0.0414106	+	0.0110959i
$273$	−8.75288	+	8.75288i	−0.529748	+	0.529748i
$274$	−6.13325			−0.370523
$275$		0			0
$276$	−17.6678	−	10.2005i	−1.06348	−	0.613998i
$277$	10.1634	+	10.1634i	0.610661	+	0.610661i	0.943118	−	0.332458i	$-0.107878\pi$
$277$	10.1634	+	10.1634i	0.610661	+	0.610661i	−0.332458	+	0.943118i	$0.607878\pi$
$278$	2.18840	+	2.18840i	0.131252	+	0.131252i
$279$	−13.0117	+	22.5369i	−0.778989	+	1.34925i
$280$		0			0
$281$	5.84445	+	3.37429i	0.348650	+	0.201293i	0.664091	−	0.747652i	$-0.268819\pi$
$281$	5.84445	+	3.37429i	0.348650	+	0.201293i	−0.315440	+	0.948945i	$0.602152\pi$
$282$	−5.44284	+	20.3129i	−0.324116	+	1.20962i
$283$	−12.3992	−	3.32235i	−0.737054	−	0.197493i	−0.129285	−	0.991607i	$-0.541268\pi$
$283$	−12.3992	−	3.32235i	−0.737054	−	0.197493i	−0.607768	+	0.794114i	$0.707935\pi$
$284$	−4.43855			−0.263380
$285$		0			0
$286$	0.397655			0.0235138
$287$	28.3956	+	7.60857i	1.67614	+	0.449120i
$288$	−1.01231	+	3.77798i	−0.0596508	+	0.222620i
$289$	14.2895	+	8.25004i	0.840558	+	0.485296i
$290$		0			0
$291$	7.66893	−	13.2830i	0.449561	−	0.778662i
$292$	4.98410	+	4.98410i	0.291672	+	0.291672i
$293$	8.89790	+	8.89790i	0.519821	+	0.519821i	0.917517	−	0.397696i	$-0.130190\pi$
$293$	8.89790	+	8.89790i	0.519821	+	0.519821i	−0.397696	+	0.917517i	$0.630190\pi$
$294$	−11.9986	−	6.92739i	−0.699772	−	0.404013i
$295$		0			0
$296$	3.82311			0.222214
$297$	−0.501125	+	0.501125i	−0.0290782	+	0.0290782i
$298$	−1.19795	+	0.320989i	−0.0693953	+	0.0185944i
$299$	5.21562	+	9.03372i	0.301627	+	0.522433i
$300$		0			0
$301$	17.6579	+	30.5844i	1.01779	+	1.76286i
$302$	5.60986	−	20.9363i	0.322811	−	1.20475i
$303$	5.08420	+	5.08420i	0.292080	+	0.292080i
$304$	4.34897	−	0.294022i	0.249431	−	0.0168633i
$305$		0			0
$306$	−2.39496	+	1.38273i	−0.136911	+	0.0790455i
$307$	−3.10768	−	0.832701i	−0.177365	−	0.0475248i	0.169043	−	0.985609i	$-0.445932\pi$
$307$	−3.10768	−	0.832701i	−0.177365	−	0.0475248i	−0.346408	+	0.938084i	$0.612599\pi$
$308$	0.268203	+	1.00095i	0.0152823	+	0.0570344i
$309$	17.6921	−	10.2145i	1.00647	−	0.581085i
$310$		0			0
$311$	27.0453			1.53360			0.766800	−	0.641886i	$-0.221848\pi$
$311$	27.0453			1.53360			0.766800	+	0.641886i	$0.221848\pi$
$312$	2.49877	−	2.49877i	0.141465	−	0.141465i
$313$	0.582137	+	2.17256i	0.0329043	+	0.122801i	0.980425	−	0.196895i	$-0.0630859\pi$
$313$	0.582137	+	2.17256i	0.0329043	+	0.122801i	−0.947520	+	0.319696i	$0.896419\pi$
$314$	−2.87280	+	4.97583i	−0.162121	+	0.280802i
$315$		0			0
$316$			17.1696i			0.965863i
$317$	−4.61308	−	17.2162i	−0.259096	−	0.966960i	−0.965766	−	0.259416i	$-0.916470\pi$
$317$	−4.61308	−	17.2162i	−0.259096	−	0.966960i	0.706669	−	0.707544i	$-0.250197\pi$
$318$	1.55309	−	5.79621i	0.0870930	−	0.325035i
$319$	0.703479	−	1.21846i	0.0393873	−	0.0682208i
$320$		0			0
$321$	−5.38392	−	9.32522i	−0.300501	−	0.520483i
$322$	−19.2213	+	19.2213i	−1.07116	+	1.07116i
$323$	2.32132	+	2.02732i	0.129162	+	0.112803i
$324$		−	5.43586i		−	0.301992i
$325$		0			0
$326$	12.4457	−	7.18554i	0.689304	−	0.397970i
$327$	−20.5996	+	5.51964i	−1.13916	+	0.305237i
$328$	−8.10636	−	2.17209i	−0.447599	−	0.119934i
$329$	24.2664	+	14.0102i	1.33785	+	0.772409i
$330$		0			0
$331$		−	14.0486i		−	0.772179i	−0.922461	−	0.386090i	$-0.873826\pi$
$331$		−	14.0486i		−	0.772179i	0.922461	−	0.386090i	$-0.126174\pi$
$332$	−16.9776	+	4.54913i	−0.931766	+	0.249666i
$333$	14.4436	−	3.87016i	0.791506	−	0.212084i
$334$		−	16.7992i		−	0.919209i
$335$		0			0
$336$	7.97505	+	4.60440i	0.435075	+	0.251191i
$337$	−28.9851	−	7.76653i	−1.57892	−	0.423070i	−0.640327	−	0.768103i	$-0.721201\pi$
$337$	−28.9851	−	7.76653i	−1.57892	−	0.423070i	−0.938591	+	0.345033i	$0.887868\pi$
$338$	10.8117	−	2.89700i	0.588081	−	0.157576i
$339$	9.68094	−	5.58929i	0.525796	−	0.303569i
$340$		0			0
$341$		−	1.96830i		−	0.106589i
$342$	16.1327	−	5.51330i	0.872356	−	0.298125i
$343$	4.28473	−	4.28473i	0.231354	−	0.231354i
$344$	−5.04098	−	8.73124i	−0.271792	−	0.470757i
$345$		0			0
$346$	−5.98518	+	10.3666i	−0.321765	+	0.557314i
$347$	3.85050	−	14.3703i	0.206706	−	0.771437i	−0.782217	−	0.623006i	$-0.785911\pi$
$347$	3.85050	−	14.3703i	0.206706	−	0.771437i	0.988923	−	0.148431i	$-0.0474222\pi$
$348$	−3.23603	−	12.0770i	−0.173469	−	0.647396i
$349$		−	17.2112i		−	0.921296i	−0.887583	−	0.460648i	$-0.847617\pi$
$349$		−	17.2112i		−	0.921296i	0.887583	−	0.460648i	$-0.152383\pi$
$350$		0			0
$351$	1.61009	−	2.78876i	0.0859403	−	0.148853i
$352$	−0.0765667	−	0.285751i	−0.00408102	−	0.0152306i
$353$	−5.89921	+	5.89921i	−0.313983	+	0.313983i	−0.846450	−	0.532467i	$-0.821265\pi$
$353$	−5.89921	+	5.89921i	−0.313983	+	0.313983i	0.532467	+	0.846450i	$0.321265\pi$
$354$	34.8572			1.85264
$355$		0			0
$356$	0.237817	−	0.137304i	0.0126043	−	0.00727707i
$357$	1.68520	+	6.28925i	0.0891902	+	0.332862i
$358$	−14.7108	−	3.94175i	−0.777490	−	0.208328i
$359$	−31.8260	+	18.3748i	−1.67971	+	0.969783i	−0.717872	+	0.696176i	$0.754883\pi$
$359$	−31.8260	+	18.3748i	−1.67971	+	0.969783i	−0.961842	+	0.273607i	$0.911783\pi$
$360$		0			0
$361$	−11.6283	−	15.0261i	−0.612016	−	0.790845i
$362$	1.48973	+	1.48973i	0.0782987	+	0.0782987i
$363$	−7.42503	+	27.7106i	−0.389713	+	1.45443i
$364$	−2.35428	−	4.07773i	−0.123398	−	0.213731i
$365$		0			0
$366$	−17.0987	−	29.6158i	−0.893763	−	1.54804i
$367$	17.3334	−	4.64447i	0.904796	−	0.242439i	0.223721	−	0.974653i	$-0.428179\pi$
$367$	17.3334	−	4.64447i	0.904796	−	0.242439i	0.681075	+	0.732214i	$0.261513\pi$
$368$	5.48729	−	5.48729i	0.286045	−	0.286045i
$369$	−32.8245			−1.70878
$370$		0			0
$371$	−6.92432	−	3.99776i	−0.359493	−	0.207553i
$372$	−12.3683	−	12.3683i	−0.641268	−	0.641268i
$373$	11.0953	+	11.0953i	0.574491	+	0.574491i	0.933380	−	0.358889i	$-0.116844\pi$
$373$	11.0953	+	11.0953i	0.574491	+	0.574491i	−0.358889	+	0.933380i	$0.616844\pi$
$374$	0.104584	−	0.181145i	0.00540792	−	0.00936678i
$375$		0			0
$376$	−6.92758	−	3.99964i	−0.357262	−	0.206266i
$377$	−1.65461	+	6.17510i	−0.0852170	+	0.318034i
$378$	8.10561	+	2.17189i	0.416908	+	0.111710i
$379$	−10.6177			−0.545392			−0.272696	−	0.962100i	$-0.587915\pi$
$379$	−10.6177			−0.545392			−0.272696	+	0.962100i	$0.587915\pi$
$380$		0			0
$381$	4.23024			0.216722
$382$	−1.55231	−	0.415941i	−0.0794233	−	0.0212814i
$383$	0.315965	−	1.17920i	0.0161451	−	0.0602542i	−0.957383	−	0.288820i	$-0.906737\pi$
$383$	0.315965	−	1.17920i	0.0161451	−	0.0602542i	0.973528	+	0.228566i	$0.0734037\pi$
$384$	−2.27672	−	1.31446i	−0.116183	−	0.0670784i
$385$		0			0
$386$	1.20589	−	2.08866i	0.0613782	−	0.106310i
$387$	−27.8834	−	27.8834i	−1.41739	−	1.41739i
$388$	4.12545	+	4.12545i	0.209438	+	0.209438i
$389$	−15.7626	−	9.10054i	−0.799195	−	0.461416i	0.0439944	−	0.999032i	$-0.485992\pi$
$389$	−15.7626	−	9.10054i	−0.799195	−	0.461416i	−0.843190	+	0.537616i	$0.819325\pi$
$390$		0			0
$391$	5.48687			0.277483
$392$	3.72654	−	3.72654i	0.188219	−	0.188219i
$393$	17.3700	−	4.65428i	0.876201	−	0.234777i
$394$	−3.62165	−	6.27289i	−0.182456	−	0.316024i
$395$		0			0
$396$	−0.578535	−	1.00205i	−0.0290725	−	0.0503550i
$397$	0.608640	−	2.27148i	0.0305468	−	0.114002i	−0.948969	−	0.315369i	$-0.897872\pi$
$397$	0.608640	−	2.27148i	0.0305468	−	0.114002i	0.979516	+	0.201367i	$0.0645384\pi$
$398$	−7.26871	−	7.26871i	−0.364347	−	0.364347i
$399$	−2.70759	−	40.0488i	−0.135549	−	2.00495i
$400$		0			0
$401$	−16.4762	+	9.51251i	−0.822780	+	0.475032i	−0.851374	−	0.524559i	$-0.824230\pi$
$401$	−16.4762	+	9.51251i	−0.822780	+	0.475032i	0.0285944	+	0.999591i	$0.490897\pi$
$402$	21.5600	+	5.77699i	1.07532	+	0.288130i
$403$	2.31476	+	8.63882i	0.115307	+	0.430330i
$404$	−2.36859	+	1.36751i	−0.117842	+	0.0680360i
$405$		0			0
$406$	−16.6595			−0.826797
$407$	−0.799734	+	0.799734i	−0.0396413	+	0.0396413i
$408$	−0.481090	−	1.79545i	−0.0238175	−	0.0888882i
$409$	11.8472	−	20.5199i	0.585806	−	1.01465i	−0.408969	−	0.912548i	$-0.634111\pi$
$409$	11.8472	−	20.5199i	0.585806	−	1.01465i	0.994774	−	0.102097i	$-0.0325552\pi$
$410$		0			0
$411$		−	16.1239i		−	0.795331i
$412$	2.01125	+	7.50609i	0.0990873	+	0.369799i
$413$	12.0208	−	44.8624i	0.591507	−	2.20753i
$414$	15.1761	−	26.2857i	0.745862	−	1.29187i
$415$		0			0
$416$	0.672099	+	1.16411i	0.0329523	+	0.0570751i
$417$	−5.75316	+	5.75316i	−0.281733	+	0.281733i
$418$	−0.848231	+	0.971240i	−0.0414883	+	0.0475049i
$419$		−	2.76000i		−	0.134835i	−0.997725	−	0.0674174i	$-0.978524\pi$
$419$		−	2.76000i		−	0.134835i	0.997725	−	0.0674174i	$-0.0214759\pi$
$420$		0			0
$421$	−15.9526	+	9.21023i	−0.777482	+	0.448879i	−0.835537	−	0.549434i	$-0.814843\pi$
$421$	−15.9526	+	9.21023i	−0.777482	+	0.448879i	0.0580554	+	0.998313i	$0.481510\pi$
$422$	−9.19026	+	2.46252i	−0.447375	+	0.119874i
$423$	−30.2211	−	8.09772i	−1.46940	−	0.393725i
$424$	1.97675	+	1.14128i	0.0959997	+	0.0554254i
$425$		0			0
$426$		−	11.6686i		−	0.565347i
$427$	−44.0132	+	11.7933i	−2.12995	+	0.570718i
$428$	3.95634	−	1.06010i	0.191237	−	0.0512418i
$429$			1.04541i			0.0504727i
$430$		0			0
$431$	22.5688	+	13.0301i	1.08710	+	0.627637i	0.932803	−	0.360387i	$-0.117355\pi$
$431$	22.5688	+	13.0301i	1.08710	+	0.627637i	0.154297	+	0.988025i	$0.450689\pi$
$432$	−2.31399	−	0.620032i	−0.111332	−	0.0298313i
$433$	24.9480	−	6.68479i	1.19892	−	0.321251i	0.396516	−	0.918028i	$-0.370219\pi$
$433$	24.9480	−	6.68479i	1.19892	−	0.321251i	0.802407	+	0.596777i	$0.203552\pi$
$434$	−20.1838	+	11.6531i	−0.968853	+	0.559368i
$435$		0			0
$436$		−	8.11216i		−	0.388502i
$437$	−33.1895	−	6.53093i	−1.58767	−	0.312417i
$438$	−13.1028	+	13.1028i	−0.626077	+	0.626077i
$439$	−9.53059	−	16.5075i	−0.454870	−	0.787859i	0.543810	−	0.839208i	$-0.316981\pi$
$439$	−9.53059	−	16.5075i	−0.454870	−	0.787859i	−0.998681	+	0.0513495i	$0.983648\pi$
$440$		0			0
$441$	10.3064	−	17.8512i	0.490781	−	0.850058i
$442$	−0.245986	+	0.918034i	−0.0117004	+	0.0436664i
$443$	−3.27987	−	12.2406i	−0.155831	−	0.581570i	−0.999033	−	0.0439725i	$-0.985999\pi$
$443$	−3.27987	−	12.2406i	−0.155831	−	0.581570i	0.843201	−	0.537598i	$-0.180668\pi$
$444$			10.0507i			0.476984i
$445$		0			0
$446$	2.88582	−	4.99839i	0.136648	−	0.236681i
$447$	−0.843857	−	3.14932i	−0.0399131	−	0.148958i
$448$	−2.47691	+	2.47691i	−0.117023	+	0.117023i
$449$	14.6874			0.693143			0.346571	−	0.938024i	$-0.387346\pi$
$449$	14.6874			0.693143			0.346571	+	0.938024i	$0.387346\pi$
$450$		0			0
$451$	2.15009	−	1.24135i	0.101244	−	0.0584531i
$452$	1.10054	+	4.10726i	0.0517649	+	0.193189i
$453$	55.0399	+	14.7479i	2.58600	+	0.692917i
$454$	12.0153	−	6.93706i	0.563908	−	0.325572i
$455$		0			0
$456$	0.772962	+	11.4331i	0.0361973	+	0.535405i
$457$	6.83282	+	6.83282i	0.319626	+	0.319626i	0.848623	−	0.528997i	$-0.177432\pi$
$457$	6.83282	+	6.83282i	0.319626	+	0.319626i	−0.528997	+	0.848623i	$0.677432\pi$
$458$	2.81159	−	10.4930i	0.131377	−	0.490306i
$459$	−0.846915	−	1.46690i	−0.0395306	−	0.0684690i
$460$		0			0
$461$	−12.0742	−	20.9131i	−0.562350	−	0.974018i	−0.997291	−	0.0735593i	$-0.976564\pi$
$461$	−12.0742	−	20.9131i	−0.562350	−	0.974018i	0.434941	−	0.900459i	$-0.356769\pi$
$462$	−2.63142	+	0.705087i	−0.122425	+	0.0328036i
$463$	13.7653	−	13.7653i	0.639726	−	0.639726i	−0.310762	−	0.950488i	$-0.600584\pi$
$463$	13.7653	−	13.7653i	0.639726	−	0.639726i	0.950488	+	0.310762i	$0.100584\pi$
$464$	4.75595			0.220790
$465$		0			0
$466$	19.8733	+	11.4739i	0.920612	+	0.531516i
$467$	13.7514	+	13.7514i	0.636338	+	0.636338i	0.949650	−	0.313312i	$-0.101439\pi$
$467$	13.7514	+	13.7514i	0.636338	+	0.636338i	−0.313312	+	0.949650i	$0.601439\pi$
$468$	3.71761	+	3.71761i	0.171847	+	0.171847i
$469$	14.8704	−	25.7562i	0.686649	−	1.18931i
$470$		0			0
$471$	−13.0811	−	7.55238i	−0.602745	−	0.347995i
$472$	−3.43171	+	12.8073i	−0.157957	+	0.589504i
$473$	2.88093	+	0.771943i	0.132465	+	0.0354940i
$474$	−45.1375			−2.07323
$475$		0			0
$476$	−2.47672			−0.113520
$477$	8.62346	+	2.31065i	0.394841	+	0.105797i
$478$	2.16779	−	8.09029i	0.0991523	−	0.370041i
$479$	−9.40280	−	5.42871i	−0.429625	−	0.248044i	0.269562	−	0.962983i	$-0.413121\pi$
$479$	−9.40280	−	5.42871i	−0.429625	−	0.248044i	−0.699187	+	0.714939i	$0.746454\pi$
$480$		0			0
$481$	2.56951	−	4.45052i	0.117159	−	0.202926i
$482$	4.89593	+	4.89593i	0.223003	+	0.223003i
$483$	−50.5313	−	50.5313i	−2.29926	−	2.29926i
$484$	−9.45049	−	5.45624i	−0.429568	−	0.248011i
$485$		0			0
$486$	21.4773			0.974231
$487$	−23.4934	+	23.4934i	−1.06459	+	1.06459i	−0.0668248	+	0.997765i	$0.521287\pi$
$487$	−23.4934	+	23.4934i	−1.06459	+	1.06459i	−0.997765	+	0.0668248i	$0.978713\pi$
$488$	12.5649	−	3.36675i	0.568785	−	0.152406i
$489$	18.8902	+	32.7189i	0.854246	+	1.47960i
$490$		0			0
$491$	−14.2831	−	24.7390i	−0.644586	−	1.11646i	−0.984397	−	0.175962i	$-0.943696\pi$
$491$	−14.2831	−	24.7390i	−0.644586	−	1.11646i	0.339811	−	0.940494i	$-0.389637\pi$
$492$	5.71027	−	21.3110i	0.257439	−	0.960775i
$493$	2.37780	+	2.37780i	0.107091	+	0.107091i
$494$	2.58066	−	5.26029i	0.116110	−	0.236672i
$495$		0			0
$496$	5.76207	−	3.32673i	0.258724	−	0.149375i
$497$	−15.0179	−	4.02404i	−0.673646	−	0.180503i
$498$	−11.9593	−	44.6328i	−0.535910	−	2.00004i
$499$	14.6185	−	8.43998i	0.654413	−	0.377825i	−0.135732	−	0.990746i	$-0.543339\pi$
$499$	14.6185	−	8.43998i	0.654413	−	0.377825i	0.790145	+	0.612920i	$0.210005\pi$
$500$		0			0
$501$	44.1638			1.97309
$502$	9.10654	−	9.10654i	0.406445	−	0.406445i
$503$	0.338249	+	1.26236i	0.0150818	+	0.0562860i	0.973057	−	0.230566i	$-0.0740578\pi$
$503$	0.338249	+	1.26236i	0.0150818	+	0.0562860i	−0.957975	+	0.286852i	$0.907391\pi$
$504$	−6.85031	+	11.8651i	−0.305137	+	0.528513i
$505$		0			0
$506$			2.29571i			0.102057i
$507$	7.61599	+	28.4233i	0.338238	+	1.26232i
$508$	−0.416469	+	1.55428i	−0.0184778	+	0.0689602i
$509$	−1.74993	+	3.03097i	−0.0775644	+	0.134345i	−0.902199	−	0.431321i	$-0.858048\pi$
$509$	−1.74993	+	3.03097i	−0.0775644	+	0.134345i	0.824634	+	0.565666i	$0.191381\pi$
$510$		0			0
$511$	12.3451	+	21.3824i	0.546117	+	0.945902i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	3.37686	+	9.88117i	0.149092	+	0.436264i
$514$			22.4748i			0.991319i
$515$		0			0
$516$	22.9538	−	13.2524i	1.01048	−	0.583403i
$517$	2.28580	−	0.612478i	0.100529	−	0.0269368i
$518$	12.9356	+	3.46607i	0.568356	+	0.152290i
$519$	−27.2531	−	15.7346i	−1.19628	−	0.690673i
$520$		0			0
$521$			33.2993i			1.45887i	0.684050	+	0.729435i	$0.260217\pi$
$521$			33.2993i			1.45887i	−0.684050	+	0.729435i	$0.739783\pi$
$522$	17.9679	−	4.81448i	0.786434	−	0.210724i
$523$	28.1739	−	7.54917i	1.23196	−	0.330102i	0.416616	−	0.909083i	$-0.363216\pi$
$523$	28.1739	−	7.54917i	1.23196	−	0.330102i	0.815341	+	0.578981i	$0.196549\pi$
$524$			6.84034i			0.298822i
$525$		0			0
$526$	12.7926	+	7.38581i	0.557784	+	0.322037i
$527$	4.54405	+	1.21758i	0.197942	+	0.0530384i
$528$	0.751218	−	0.201288i	0.0326926	−	0.00875994i
$529$	−32.2341	+	18.6104i	−1.40148	+	0.809146i
$530$		0			0
$531$			51.8597i			2.25052i
$532$	14.9814	+	2.94799i	0.649525	+	0.127812i
$533$	−7.97683	+	7.97683i	−0.345515	+	0.345515i
$534$	0.360961	+	0.625202i	0.0156203	+	0.0270552i
$535$		0			0
$536$	−4.24519	+	7.35288i	−0.183364	+	0.317596i
$537$	10.3626	−	38.6736i	0.447178	−	1.66889i
$538$	−0.942540	−	3.51761i	−0.0406358	−	0.151655i
$539$			1.55907i			0.0671538i
$540$		0			0
$541$	−1.49252	+	2.58512i	−0.0641685	+	0.111143i	−0.896325	−	0.443398i	$-0.853773\pi$
$541$	−1.49252	+	2.58512i	−0.0641685	+	0.111143i	0.832156	+	0.554541i	$0.187106\pi$
$542$	−5.61659	−	20.9614i	−0.241253	−	0.900369i
$543$	−3.91640	+	3.91640i	−0.168069	+	0.168069i
$544$	0.707053			0.0303147
$545$		0			0
$546$	10.7200	−	6.18922i	0.458775	−	0.264874i
$547$	−2.40916	−	8.99110i	−0.103008	−	0.384432i	0.895103	−	0.445859i	$-0.147102\pi$
$547$	−2.40916	−	8.99110i	−0.103008	−	0.384432i	−0.998112	+	0.0614269i	$0.980435\pi$
$548$	5.92426	+	1.58740i	0.253072	+	0.0678104i
$549$	44.0617	−	25.4390i	1.88051	−	1.08571i
$550$		0			0
$551$	−11.5528	−	17.2133i	−0.492164	−	0.733310i
$552$	14.4257	+	14.4257i	0.613998	+	0.613998i
$553$	−15.5661	+	58.0935i	−0.661938	+	2.47039i
$554$	−7.18662	−	12.4476i	−0.305330	−	0.528848i
$555$		0			0
$556$	−1.54744	−	2.68024i	−0.0656259	−	0.113667i
$557$	18.8029	−	5.03823i	0.796705	−	0.213477i	0.162568	−	0.986697i	$-0.448022\pi$
$557$	18.8029	−	5.03823i	0.796705	−	0.213477i	0.634137	+	0.773221i	$0.281356\pi$
$558$	18.4013	−	18.4013i	0.778989	−	0.778989i
$559$	−13.5521			−0.573195
$560$		0			0
$561$	0.476217	+	0.274944i	0.0201059	+	0.0116081i
$562$	−4.77197	−	4.77197i	−0.201293	−	0.201293i
$563$	−4.18223	−	4.18223i	−0.176260	−	0.176260i	0.613463	−	0.789723i	$-0.289776\pi$
$563$	−4.18223	−	4.18223i	−0.176260	−	0.176260i	−0.789723	+	0.613463i	$0.789776\pi$
$564$	10.5148	−	18.2121i	0.442751	−	0.766867i
$565$		0			0
$566$	11.1168	+	6.41828i	0.467273	+	0.269780i
$567$	4.92820	−	18.3923i	0.206965	−	0.772404i
$568$	4.28731	+	1.14878i	0.179892	+	0.0482018i
$569$	14.4981			0.607793			0.303896	−	0.952705i	$-0.401712\pi$
$569$	14.4981			0.607793			0.303896	+	0.952705i	$0.401712\pi$
$570$		0			0
$571$	28.5932			1.19659			0.598294	−	0.801277i	$-0.295846\pi$
$571$	28.5932			1.19659			0.598294	+	0.801277i	$0.295846\pi$
$572$	−0.384105	−	0.102921i	−0.0160603	−	0.00430333i
$573$	1.09348	−	4.08092i	0.0456807	−	0.170483i
$574$	−25.4588	−	14.6986i	−1.06263	−	0.613509i
$575$		0			0
$576$	1.95563	−	3.38724i	0.0814844	−	0.141135i
$577$	20.4684	+	20.4684i	0.852109	+	0.852109i	0.990393	−	0.138283i	$-0.0441584\pi$
$577$	20.4684	+	20.4684i	0.852109	+	0.852109i	−0.138283	+	0.990393i	$0.544158\pi$
$578$	−11.6673	−	11.6673i	−0.485296	−	0.485296i
$579$	5.49094	+	3.17020i	0.228196	+	0.131749i
$580$		0			0
$581$	−61.5682			−2.55428
$582$	−10.8455	+	10.8455i	−0.449561	+	0.449561i
$583$	−0.652243	+	0.174768i	−0.0270131	+	0.00723815i
$584$	−3.52429	−	6.10425i	−0.145836	−	0.252595i
$585$		0			0
$586$	−6.29177	−	10.8977i	−0.259910	−	0.450178i
$587$	−7.61118	+	28.4053i	−0.314147	+	1.17241i	0.610634	+	0.791913i	$0.290915\pi$
$587$	−7.61118	+	28.4053i	−0.314147	+	1.17241i	−0.924781	+	0.380500i	$0.875752\pi$
$588$	9.79681	+	9.79681i	0.404013	+	0.404013i
$589$	−26.0372	−	12.7737i	−1.07284	−	0.526331i
$590$		0			0
$591$	16.4910	−	9.52106i	0.678347	−	0.391644i
$592$	−3.69284	−	0.989494i	−0.151775	−	0.0406679i
$593$	4.44729	+	16.5975i	0.182629	+	0.681579i	0.995126	+	0.0986139i	$0.0314409\pi$
$593$	4.44729	+	16.5975i	0.182629	+	0.681579i	−0.812497	+	0.582965i	$0.801892\pi$
$594$	0.613751	−	0.354349i	0.0251825	−	0.0145391i
$595$		0			0
$596$	1.24021			0.0508009
$597$	19.1089	−	19.1089i	0.782075	−	0.782075i
$598$	−2.69980	−	10.0758i	−0.110403	−	0.412030i
$599$	−1.71975	+	2.97870i	−0.0702672	+	0.121706i	−0.899018	−	0.437911i	$-0.855719\pi$
$599$	−1.71975	+	2.97870i	−0.0702672	+	0.121706i	0.828751	+	0.559617i	$0.189052\pi$
$600$		0			0
$601$			12.5288i			0.511062i	0.966801	+	0.255531i	$0.0822502\pi$
$601$			12.5288i			0.511062i	−0.966801	+	0.255531i	$0.917750\pi$
$602$	−9.14042	−	34.1125i	−0.372536	−	1.39032i
$603$	−8.59486	+	32.0765i	−0.350010	+	1.30625i
$604$	−10.8374	+	18.7710i	−0.440968	+	0.763779i
$605$		0			0
$606$	−3.59507	−	6.22685i	−0.146040	−	0.252948i
$607$	−9.72517	+	9.72517i	−0.394732	+	0.394732i	−0.876370	−	0.481638i	$-0.840042\pi$
$607$	−9.72517	+	9.72517i	−0.394732	+	0.394732i	0.481638	+	0.876370i	$0.340042\pi$
$608$	−4.27688	−	0.841593i	−0.173450	−	0.0341311i
$609$		−	43.7966i		−	1.77473i
$610$		0			0
$611$	−9.31203	+	5.37630i	−0.376724	+	0.217502i
$612$	2.67123	−	0.715755i	0.107978	−	0.0289327i
$613$	−5.26915	−	1.41186i	−0.212819	−	0.0570247i	0.150834	−	0.988559i	$-0.451804\pi$
$613$	−5.26915	−	1.41186i	−0.212819	−	0.0570247i	−0.363653	+	0.931534i	$0.618471\pi$
$614$	2.78627	+	1.60866i	0.112445	+	0.0649201i
$615$		0			0
$616$		−	1.03626i		−	0.0417521i
$617$	−20.3292	+	5.44721i	−0.818425	+	0.219296i	−0.643658	−	0.765314i	$-0.722584\pi$
$617$	−20.3292	+	5.44721i	−0.818425	+	0.219296i	−0.174767	+	0.984610i	$0.555917\pi$
$618$	−19.7330	+	5.28743i	−0.793776	+	0.212692i
$619$		−	0.117023i		−	0.00470357i	−0.999997	−	0.00235178i	$-0.999251\pi$
$619$		−	0.117023i		−	0.00470357i	0.999997	−	0.00235178i	$-0.000748597\pi$
$620$		0			0
$621$	16.0998	+	9.29524i	0.646064	+	0.373005i
$622$	−26.1238	−	6.99985i	−1.04747	−	0.280668i
$623$	0.929137	−	0.248962i	0.0372251	−	0.00997444i
$624$	−3.06036	+	1.76690i	−0.122512	+	0.0707325i
$625$		0			0
$626$		−	2.24920i		−	0.0898963i
$627$	−2.55332	−	2.22994i	−0.101970	−	0.0890551i
$628$	4.06275	−	4.06275i	0.162121	−	0.162121i
$629$	−1.35157	−	2.34099i	−0.0538907	−	0.0933414i
$630$		0			0
$631$	−12.7422	+	22.0701i	−0.507257	+	0.878595i	0.492707	+	0.870195i	$0.336007\pi$
$631$	−12.7422	+	22.0701i	−0.507257	+	0.878595i	−0.999965	+	0.00840037i	$0.997326\pi$
$632$	4.44381	−	16.5845i	0.176765	−	0.659697i
$633$	−6.47379	−	24.1605i	−0.257310	−	0.960295i
$634$			17.8236i			0.707864i
$635$		0			0
$636$	−3.00034	+	5.19674i	−0.118971	+	0.206064i
$637$	−1.83350	−	6.84270i	−0.0726458	−	0.271118i
$638$	−0.994870	+	0.994870i	−0.0393873	+	0.0393873i
$639$	17.3603			0.686763
$640$		0			0
$641$	24.8283	−	14.3346i	0.980659	−	0.566184i	0.0781900	−	0.996938i	$-0.475086\pi$
$641$	24.8283	−	14.3346i	0.980659	−	0.566184i	0.902469	+	0.430755i	$0.141753\pi$
$642$	2.78692	+	10.4009i	0.109991	+	0.410492i
$643$	0.328816	+	0.0881060i	0.0129672	+	0.00347456i	0.265297	−	0.964167i	$-0.414530\pi$
$643$	0.328816	+	0.0881060i	0.0129672	+	0.00347456i	−0.252330	+	0.967641i	$0.581197\pi$
$644$	23.5412	−	13.5915i	0.927652	−	0.535580i
$645$		0			0
$646$	−1.71751	−	2.55904i	−0.0675747	−	0.100684i
$647$	−19.8561	−	19.8561i	−0.780624	−	0.780624i	0.199312	−	0.979936i	$-0.436129\pi$
$647$	−19.8561	−	19.8561i	−0.780624	−	0.780624i	−0.979936	+	0.199312i	$0.936129\pi$
$648$	−1.40690	+	5.25063i	−0.0552684	+	0.206264i
$649$	−1.96123	−	3.39694i	−0.0769848	−	0.133342i
$650$		0			0
$651$	−30.6352	−	53.0617i	−1.20069	−	2.07965i
$652$	−13.8814	+	3.71951i	−0.543637	+	0.145667i
$653$	−4.32219	+	4.32219i	−0.169140	+	0.169140i	−0.786601	−	0.617461i	$-0.788161\pi$
$653$	−4.32219	+	4.32219i	−0.169140	+	0.169140i	0.617461	+	0.786601i	$0.288161\pi$
$654$	21.3263			0.833923
$655$		0			0
$656$	7.26797	+	4.19616i	0.283766	+	0.163833i
$657$	−19.4941	−	19.4941i	−0.760536	−	0.760536i
$658$	−19.8135	−	19.8135i	−0.772409	−	0.772409i
$659$	−4.29920	+	7.44643i	−0.167473	+	0.290072i	−0.937531	−	0.347902i	$-0.886894\pi$
$659$	−4.29920	+	7.44643i	−0.167473	+	0.290072i	0.770058	+	0.637974i	$0.220227\pi$
$660$		0			0
$661$	−9.70074	−	5.60073i	−0.377315	−	0.217843i	0.299334	−	0.954148i	$-0.403235\pi$
$661$	−9.70074	−	5.60073i	−0.377315	−	0.217843i	−0.676649	+	0.736305i	$0.736569\pi$
$662$	−3.63604	+	13.5699i	−0.141319	+	0.527408i
$663$	−2.41344	−	0.646680i	−0.0937304	−	0.0251150i
$664$	17.5765			0.682100
$665$		0			0
$666$	−14.9532			−0.579423
$667$	−35.6496	−	9.55227i	−1.38036	−	0.369865i
$668$	−4.34794	+	16.2267i	−0.168227	+	0.627832i
$669$	13.1404	+	7.58661i	0.508037	+	0.293315i
$670$		0			0
$671$	−1.92410	+	3.33264i	−0.0742791	+	0.128655i
$672$	−6.51160	−	6.51160i	−0.251191	−	0.251191i
$673$	−11.2945	−	11.2945i	−0.435370	−	0.435370i	0.455081	−	0.890450i	$-0.349610\pi$
$673$	−11.2945	−	11.2945i	−0.435370	−	0.435370i	−0.890450	+	0.455081i	$0.849610\pi$
$674$	25.9873	+	15.0038i	1.00099	+	0.577924i
$675$		0			0
$676$	−11.1931			−0.430505
$677$	−10.1384	+	10.1384i	−0.389652	+	0.389652i	−0.874563	−	0.484911i	$-0.838852\pi$
$677$	−10.1384	+	10.1384i	−0.389652	+	0.389652i	0.484911	+	0.874563i	$0.338852\pi$
$678$	−10.7977	+	2.89323i	−0.414683	+	0.111114i
$679$	10.2184	+	17.6987i	0.392144	+	0.679214i
$680$		0			0
$681$	18.2370	+	31.5874i	0.698844	+	1.21043i
$682$	−0.509434	+	1.90123i	−0.0195072	+	0.0728019i
$683$	10.3024	+	10.3024i	0.394211	+	0.394211i	0.876185	−	0.481974i	$-0.160080\pi$
$683$	10.3024	+	10.3024i	0.394211	+	0.394211i	−0.481974	+	0.876185i	$0.660080\pi$
$684$	−17.0099	+	1.14999i	−0.650391	+	0.0439711i
$685$		0			0
$686$	−5.24771	+	3.02976i	−0.200358	+	0.115677i
$687$	27.5853	+	7.39146i	1.05245	+	0.282002i
$688$	2.60940	+	9.73843i	0.0994826	+	0.371274i
$689$	2.65715	−	1.53410i	0.101229	−	0.0584447i
$690$		0			0
$691$	−31.9056			−1.21375			−0.606873	−	0.794799i	$-0.707576\pi$
$691$	−31.9056			−1.21375			−0.606873	+	0.794799i	$0.707576\pi$
$692$	8.46433	−	8.46433i	0.321765	−	0.321765i
$693$	−1.04901	−	3.91497i	−0.0398487	−	0.148717i
$694$	−7.43860	+	12.8840i	−0.282366	+	0.489071i
$695$		0			0
$696$			12.5031i			0.473927i
$697$	1.53579	+	5.73163i	0.0581720	+	0.217101i
$698$	−4.45459	+	16.6248i	−0.168609	+	0.629257i
$699$	−30.1639	+	52.2454i	−1.14090	+	1.97610i
$700$		0			0
$701$	1.88871	+	3.27133i	0.0713354	+	0.123557i	0.899487	−	0.436948i	$-0.143941\pi$
$701$	1.88871	+	3.27133i	0.0713354	+	0.123557i	−0.828151	+	0.560504i	$0.810607\pi$
$702$	−2.27701	+	2.27701i	−0.0859403	+	0.0859403i
$703$	5.38906	+	15.7691i	0.203252	+	0.594744i
$704$			0.295831i			0.0111495i
$705$		0			0
$706$	7.22502	−	4.17137i	0.271917	−	0.156992i
$707$	−9.25396	+	2.47959i	−0.348031	+	0.0932546i
$708$	−33.6695	−	9.02170i	−1.26538	−	0.339056i
$709$	14.2479	+	8.22602i	0.535090	+	0.308935i	0.743087	−	0.669195i	$-0.233361\pi$
$709$	14.2479	+	8.22602i	0.535090	+	0.308935i	−0.207996	+	0.978130i	$0.566694\pi$
$710$		0			0
$711$		−	67.1545i		−	2.51849i
$712$	−0.265250	+	0.0710735i	−0.00994066	+	0.00266359i
$713$	−49.8729	+	13.3634i	−1.86775	+	0.500463i
$714$		−	6.51111i		−	0.243672i
$715$		0			0
$716$	13.1893	+	7.61487i	0.492909	+	0.284581i
$717$	21.2688	+	5.69895i	0.794297	+	0.212831i
$718$	35.4973	−	9.51148i	1.32475	−	0.354965i
$719$	−5.34008	+	3.08309i	−0.199151	+	0.114980i	−0.596260	−	0.802792i	$-0.703347\pi$
$719$	−5.34008	+	3.08309i	−0.199151	+	0.114980i	0.397108	+	0.917772i	$0.370014\pi$
$720$		0			0
$721$			27.2204i			1.01374i
$722$	7.34306	+	17.5237i	0.273280	+	0.652164i
$723$	−12.8710	+	12.8710i	−0.478679	+	0.478679i
$724$	−1.05340	−	1.82454i	−0.0391493	−	0.0678086i
$725$		0			0
$726$	14.3441	−	24.8446i	0.532358	−	0.922071i
$727$	−12.4117	+	46.3210i	−0.460324	+	1.71795i	0.211623	+	0.977351i	$0.432125\pi$
$727$	−12.4117	+	46.3210i	−0.460324	+	1.71795i	−0.671947	+	0.740600i	$0.734542\pi$
$728$	1.21866	+	4.54811i	0.0451667	+	0.168564i
$729$			40.1547i			1.48721i
$730$		0			0
$731$	−3.56424	+	6.17345i	−0.131828	+	0.228333i
$732$	8.85093	+	33.0321i	0.327140	+	1.22090i
$733$	−25.2803	+	25.2803i	−0.933748	+	0.933748i	−0.997938	−	0.0641901i	$-0.979554\pi$
$733$	−25.2803	+	25.2803i	−0.933748	+	0.933748i	0.0641901	+	0.997938i	$0.479554\pi$
$734$	−17.9449			−0.662357
$735$		0			0
$736$	−6.72053	+	3.88010i	−0.247722	+	0.143022i
$737$	−0.650080	−	2.42613i	−0.0239460	−	0.0893677i
$738$	31.7060	+	8.49561i	1.16712	+	0.312728i
$739$	−6.82072	+	3.93794i	−0.250904	+	0.144860i	−0.620178	−	0.784461i	$-0.712940\pi$
$739$	−6.82072	+	3.93794i	−0.250904	+	0.144860i	0.369274	+	0.929321i	$0.379606\pi$
$740$		0			0
$741$	13.8289	+	6.78437i	0.508018	+	0.249230i
$742$	5.65368	+	5.65368i	0.207553	+	0.207553i
$743$	6.14780	−	22.9439i	0.225541	−	0.841730i	−0.756646	−	0.653825i	$-0.773163\pi$
$743$	6.14780	−	22.9439i	0.225541	−	0.841730i	0.982187	−	0.187906i	$-0.0601699\pi$
$744$	8.74573	+	15.1481i	0.320634	+	0.555355i
$745$		0			0
$746$	−7.84554	−	13.5889i	−0.287246	−	0.497524i
$747$	66.4036	−	17.7928i	2.42958	−	0.651005i
$748$	−0.147904	+	0.147904i	−0.00540792	+	0.00540792i
$749$	14.3475			0.524244
$750$		0			0
$751$	−10.3780	−	5.99175i	−0.378699	−	0.218642i	0.298553	−	0.954393i	$-0.403496\pi$
$751$	−10.3780	−	5.99175i	−0.378699	−	0.218642i	−0.677252	+	0.735751i	$0.736829\pi$
$752$	5.65634	+	5.65634i	0.206266	+	0.206266i
$753$	23.9404	+	23.9404i	0.872438	+	0.872438i
$754$	3.19647	−	5.53645i	0.116409	−	0.201626i
$755$		0			0
$756$	−7.26729	−	4.19577i	−0.264309	−	0.152599i
$757$	13.3377	−	49.7768i	0.484765	−	1.80917i	−0.0963491	−	0.995348i	$-0.530717\pi$
$757$	13.3377	−	49.7768i	0.484765	−	1.80917i	0.581115	−	0.813822i	$-0.302617\pi$
$758$	10.2559	+	2.74805i	0.372510	+	0.0998137i
$759$	−6.03525			−0.219066
$760$		0			0
$761$	15.3801			0.557527			0.278764	−	0.960360i	$-0.410075\pi$
$761$	15.3801			0.557527			0.278764	+	0.960360i	$0.410075\pi$
$762$	−4.08610	−	1.09487i	−0.148024	−	0.0396628i
$763$	7.35457	−	27.4476i	0.266253	−	0.993671i
$764$	1.39177	+	0.803537i	0.0503524	+	0.0290709i
$765$		0			0
$766$	−0.610397	+	1.05724i	−0.0220546	+	0.0381996i
$767$	12.6027	+	12.6027i	0.455055	+	0.455055i
$768$	1.85893	+	1.85893i	0.0670784	+	0.0670784i
$769$	−13.8525	−	7.99775i	−0.499534	−	0.288406i	0.228987	−	0.973430i	$-0.426459\pi$
$769$	−13.8525	−	7.99775i	−0.499534	−	0.288406i	−0.728521	+	0.685023i	$0.759792\pi$
$770$		0			0
$771$	−59.0845			−2.12788
$772$	−1.70539	+	1.70539i	−0.0613782	+	0.0613782i
$773$	−49.7087	+	13.3194i	−1.78790	+	0.479066i	−0.991986	−	0.126347i	$-0.959675\pi$
$773$	−49.7087	+	13.3194i	−1.78790	+	0.479066i	−0.795912	+	0.605413i	$0.793008\pi$
$774$	19.7166	+	34.1501i	0.708697	+	1.22750i
$775$		0			0
$776$	−2.91713	−	5.05262i	−0.104719	−	0.181379i
$777$	−9.11205	+	34.0066i	−0.326893	+	1.21998i
$778$	12.8701	+	12.8701i	0.461416	+	0.461416i
$779$	−2.46753	−	36.4980i	−0.0884084	−	1.30768i
$780$		0			0
$781$	−1.13714	+	0.656531i	−0.0406902	+	0.0234925i
$782$	−5.29991	−	1.42011i	−0.189524	−	0.0507829i
$783$	2.94884	+	11.0052i	0.105383	+	0.393295i
$784$	−4.56406	+	2.63506i	−0.163002	+	0.0941094i
$785$		0			0
$786$	−17.9828			−0.641424
$787$	−13.3471	+	13.3471i	−0.475775	+	0.475775i	−0.903777	−	0.428003i	$-0.859217\pi$
$787$	−13.3471	+	13.3471i	−0.475775	+	0.475775i	0.428003	+	0.903777i	$0.359217\pi$
$788$	1.87471	+	6.99650i	0.0667836	+	0.249240i
$789$	−19.4168	+	33.6308i	−0.691255	+	1.19729i
$790$		0			0
$791$			14.8947i			0.529596i
$792$	0.299472	+	1.11764i	0.0106413	+	0.0397137i
$793$	4.52557	−	16.8897i	0.160708	−	0.599770i
$794$	−1.17580	+	2.03655i	−0.0417277	+	0.0722745i
$795$		0			0
$796$	5.13975	+	8.90231i	0.182174	+	0.315534i
$797$	−23.0014	+	23.0014i	−0.814753	+	0.814753i	−0.985342	−	0.170589i	$-0.945433\pi$
$797$	−23.0014	+	23.0014i	−0.814753	+	0.814753i	0.170589	+	0.985342i	$0.445433\pi$
$798$	−7.75006	+	39.3849i	−0.274349	+	1.39421i
$799$			5.65591i			0.200092i
$800$		0			0
$801$	−0.930161	+	0.537029i	−0.0328656	+	0.0189750i
$802$	18.3768	−	4.92404i	0.648906	−	0.173874i
$803$	2.01414	+	0.539686i	0.0710773	+	0.0190451i
$804$	−19.3302	−	11.1603i	−0.681723	−	0.393593i
$805$		0			0
$806$		−	8.94356i		−	0.315024i
$807$	9.24753	−	2.47787i	0.325529	−	0.0872251i
$808$	2.64182	−	0.707873i	0.0929389	−	0.0249029i
$809$		−	40.6369i		−	1.42872i	−0.699780	−	0.714358i	$-0.746719\pi$
$809$		−	40.6369i		−	1.42872i	0.699780	−	0.714358i	$-0.253281\pi$
$810$		0			0
$811$	9.26987	+	5.35196i	0.325509	+	0.187933i	0.653845	−	0.756628i	$-0.273155\pi$
$811$	9.26987	+	5.35196i	0.325509	+	0.187933i	−0.328336	+	0.944561i	$0.606488\pi$
$812$	16.0918	+	4.31180i	0.564713	+	0.151314i
$813$	55.1060	−	14.7656i	1.93265	−	0.517852i
$814$	0.979470	−	0.565497i	0.0343304	−	0.0198207i
$815$		0			0
$816$			1.85879i			0.0650707i
$817$	28.9078	−	33.1000i	1.01136	−	1.15802i
$818$	−16.7545	+	16.7545i	−0.585806	+	0.585806i
$819$	9.20817	+	15.9490i	0.321760	+	0.557304i
$820$		0			0
$821$	10.9056	−	18.8891i	0.380609	−	0.659235i	−0.610540	−	0.791985i	$-0.709048\pi$
$821$	10.9056	−	18.8891i	0.380609	−	0.659235i	0.991149	+	0.132751i	$0.0423810\pi$
$822$	−4.17316	+	15.5744i	−0.145556	+	0.543221i
$823$	6.62397	+	24.7210i	0.230897	+	0.861719i	0.979956	+	0.199216i	$0.0638394\pi$
$823$	6.62397	+	24.7210i	0.230897	+	0.861719i	−0.749059	+	0.662504i	$0.769494\pi$
$824$		−	7.77088i		−	0.270711i
$825$		0			0
$826$	−23.2225	+	40.2225i	−0.808013	+	1.39952i
$827$	2.94982	+	11.0089i	0.102575	+	0.382816i	0.998059	−	0.0622788i	$-0.0198368\pi$
$827$	2.94982	+	11.0089i	0.102575	+	0.382816i	−0.895484	+	0.445094i	$0.853170\pi$
$828$	−21.4622	+	21.4622i	−0.745862	+	0.745862i
$829$	−17.5995			−0.611255			−0.305627	−	0.952151i	$-0.598866\pi$
$829$	−17.5995			−0.611255			−0.305627	+	0.952151i	$0.598866\pi$
$830$		0			0
$831$	32.7238	−	18.8931i	1.13518	−	0.655394i
$832$	−0.347904	−	1.29839i	−0.0120614	−	0.0450137i
$833$	−3.59929	−	0.964427i	−0.124708	−	0.0334154i
$834$	7.04615	−	4.06810i	0.243988	−	0.140867i
$835$		0			0
$836$	1.07070	−	0.718608i	0.0370311	−	0.0248536i
$837$	11.2707	+	11.2707i	0.389572	+	0.389572i
$838$	−0.714340	+	2.66595i	−0.0246765	+	0.0920939i
$839$	25.2082	+	43.6618i	0.870283	+	1.50737i	0.861704	+	0.507411i	$0.169397\pi$
$839$	25.2082	+	43.6618i	0.870283	+	1.50737i	0.00857864	+	0.999963i	$0.497269\pi$
$840$		0			0
$841$	3.19045	+	5.52603i	0.110016	+	0.190553i
$842$	17.7928	−	4.76757i	0.613180	−	0.164301i
$843$	12.5452	−	12.5452i	0.432078	−	0.432078i
$844$	9.51446			0.327501
$845$		0			0
$846$	27.0955	+	15.6436i	0.931563	+	0.537838i
$847$	−27.0292	−	27.0292i	−0.928734	−	0.928734i
$848$	−1.61401	−	1.61401i	−0.0554254	−	0.0554254i
$849$	−16.8732	+	29.2252i	−0.579086	+	1.00301i
$850$		0			0
$851$	25.6933	+	14.8341i	0.880756	+	0.508505i
$852$	−3.02006	+	11.2710i	−0.103466	+	0.386139i
$853$	−15.4684	−	4.14475i	−0.529628	−	0.141914i	−0.0159118	−	0.999873i	$-0.505065\pi$
$853$	−15.4684	−	4.14475i	−0.529628	−	0.141914i	−0.513717	+	0.857960i	$0.671732\pi$
$854$	45.5658			1.55923
$855$		0			0
$856$	−4.09591			−0.139995
$857$	26.1005	+	6.99362i	0.891578	+	0.238898i	0.675396	−	0.737456i	$-0.263973\pi$
$857$	26.1005	+	6.99362i	0.891578	+	0.238898i	0.216182	+	0.976353i	$0.430640\pi$
$858$	0.270571	−	1.00978i	0.00923714	−	0.0344735i
$859$	8.22004	+	4.74584i	0.280464	+	0.161926i	0.633634	−	0.773633i	$-0.281563\pi$
$859$	8.22004	+	4.74584i	0.280464	+	0.161926i	−0.353169	+	0.935559i	$0.614896\pi$
$860$		0			0
$861$	38.6416	−	66.9292i	1.31690	−	2.28094i
$862$	−18.4273	−	18.4273i	−0.627637	−	0.627637i
$863$	−8.35613	−	8.35613i	−0.284446	−	0.284446i	0.550433	−	0.834879i	$-0.314463\pi$
$863$	−8.35613	−	8.35613i	−0.284446	−	0.284446i	−0.834879	+	0.550433i	$0.814463\pi$
$864$	2.07467	+	1.19781i	0.0705816	+	0.0407503i
$865$		0			0
$866$	−25.8281			−0.877673
$867$	30.6725	−	30.6725i	1.04169	−	1.04169i
$868$	22.5121	−	6.03210i	0.764111	−	0.204743i
$869$	2.53964	+	4.39879i	0.0861515	+	0.149219i
$870$		0			0
$871$	5.70637	+	9.88372i	0.193353	+	0.334897i
$872$	−2.09958	+	7.83574i	−0.0711008	+	0.265352i
$873$	−16.1357	−	16.1357i	−0.546110	−	0.546110i
$874$	30.3682	+	14.8985i	1.02722	+	0.503948i
$875$		0			0
$876$	16.0476	−	9.26509i	0.542199	−	0.313038i
$877$	−29.8492	−	7.99807i	−1.00794	−	0.270076i	−0.283169	−	0.959070i	$-0.591386\pi$
$877$	−29.8492	−	7.99807i	−1.00794	−	0.270076i	−0.724767	+	0.688994i	$0.758053\pi$
$878$	4.93340	+	18.4117i	0.166494	+	0.621365i
$879$	28.6491	−	16.5406i	0.966312	−	0.557900i
$880$		0			0
$881$	−2.07958			−0.0700629			−0.0350315	−	0.999386i	$-0.511153\pi$
$881$	−2.07958			−0.0700629			−0.0350315	+	0.999386i	$0.511153\pi$
$882$	−14.5755	+	14.5755i	−0.490781	+	0.490781i
$883$	2.69137	+	10.0443i	0.0905720	+	0.338019i	0.996311	−	0.0858168i	$-0.0273500\pi$
$883$	2.69137	+	10.0443i	0.0905720	+	0.338019i	−0.905739	+	0.423836i	$0.860683\pi$
$884$	0.475209	−	0.823087i	0.0159830	−	0.0276834i
$885$		0			0
$886$			12.6724i			0.425739i
$887$	6.90633	+	25.7748i	0.231892	+	0.865432i	0.979525	+	0.201321i	$0.0645234\pi$
$887$	6.90633	+	25.7748i	0.231892	+	0.865432i	−0.747633	+	0.664112i	$0.768810\pi$
$888$	2.60131	−	9.70821i	0.0872941	−	0.325786i
$889$	−2.81826	+	4.88137i	−0.0945214	+	0.163716i
$890$		0			0
$891$	−0.804047	−	1.39265i	−0.0269366	−	0.0466556i
$892$	−4.08117	+	4.08117i	−0.136648	+	0.136648i
$893$	6.73214	−	34.2120i	0.225282	−	1.14486i
$894$			3.26041i			0.109045i
$895$		0			0
$896$	3.03358	−	1.75144i	0.101345	−	0.0585114i
$897$	26.4885	−	7.09758i	0.884427	−	0.236981i
$898$	−14.1870	−	3.80139i	−0.473425	−	0.126854i
$899$	−27.4041	−	15.8218i	−0.913979	−	0.527686i
$900$		0			0
$901$		−	1.61389i		−	0.0537665i
$902$	−2.39811	+	0.642572i	−0.0798484	+	0.0213953i
$903$	89.6792	−	24.0295i	2.98434	−	0.799651i
$904$		−	4.25215i		−	0.141424i
$905$		0			0
$906$	−49.3475	−	28.4908i	−1.63946	−	0.946542i
$907$	53.3876	+	14.3052i	1.77271	+	0.474995i	0.989223	−	0.146418i	$-0.0467745\pi$
$907$	53.3876	+	14.3052i	1.77271	+	0.474995i	0.783483	+	0.621413i	$0.213441\pi$
$908$	−13.4014	+	3.59089i	−0.444740	+	0.119168i
$909$	9.26416	−	5.34866i	0.307273	−	0.177404i
$910$		0			0
$911$			44.5434i			1.47579i	0.674916	+	0.737895i	$0.264180\pi$
$911$			44.5434i			1.47579i	−0.674916	+	0.737895i	$0.735820\pi$
$912$	2.21249	−	11.2436i	0.0732627	−	0.372313i
$913$	−3.67672	+	3.67672i	−0.121682	+	0.121682i
$914$	−4.83154	−	8.36847i	−0.159813	−	0.276804i
$915$		0			0
$916$	−5.43158	+	9.40776i	−0.179464	+	0.310841i
$917$	−6.20153	+	23.1444i	−0.204792	+	0.764296i
$918$	0.438395	+	1.63611i	0.0144692	+	0.0539998i
$919$			0.319695i			0.0105458i	0.999986	+	0.00527288i	$0.00167842\pi$
$919$			0.319695i			0.0105458i	−0.999986	+	0.00527288i	$0.998322\pi$
$920$		0			0
$921$	−4.22904	+	7.32491i	−0.139351	+	0.241364i
$922$	6.25004	+	23.3255i	0.205834	+	0.768184i
$923$	4.21880	−	4.21880i	0.138864	−	0.138864i
$924$	2.72425			0.0896212
$925$		0			0
$926$	−16.8589	+	9.73351i	−0.554019	+	0.319863i
$927$	−7.86652	−	29.3582i	−0.258370	−	0.964251i
$928$	−4.59390	−	1.23093i	−0.150802	−	0.0404073i
$929$	−16.7515	+	9.67149i	−0.549599	+	0.317311i	−0.748960	−	0.662615i	$-0.769447\pi$
$929$	−16.7515	+	9.67149i	−0.549599	+	0.317311i	0.199361	+	0.979926i	$0.436113\pi$
$930$		0			0
$931$	20.6237	+	10.1179i	0.675916	+	0.331600i
$932$	−16.2265	−	16.2265i	−0.531516	−	0.531516i
$933$	18.4021	−	68.6775i	0.602457	−	2.24840i
$934$	−9.72369	−	16.8419i	−0.318169	−	0.551085i
$935$		0			0
$936$	−2.62875	−	4.55312i	−0.0859233	−	0.148824i
$937$	53.2284	−	14.2625i	1.73889	−	0.465935i	0.756694	−	0.653769i	$-0.226813\pi$
$937$	53.2284	−	14.2625i	1.73889	−	0.465935i	0.982201	+	0.187834i	$0.0601466\pi$
$938$	−21.0299	+	21.0299i	−0.686649	+	0.686649i
$939$	5.91299			0.192963
$940$		0			0
$941$	17.3858	+	10.0377i	0.566761	+	0.327220i	0.755855	−	0.654739i	$-0.227222\pi$
$941$	17.3858	+	10.0377i	0.566761	+	0.327220i	−0.189094	+	0.981959i	$0.560555\pi$
$942$	10.6807	+	10.6807i	0.347995	+	0.347995i
$943$	−46.0511	−	46.0511i	−1.49963	−	1.49963i
$944$	6.62955	−	11.4827i	0.215773	−	0.373731i
$945$		0			0
$946$	−2.58297	−	1.49128i	−0.0839796	−	0.0484857i
$947$	−10.1890	+	38.0259i	−0.331099	+	1.23568i	0.576939	+	0.816787i	$0.304247\pi$
$947$	−10.1890	+	38.0259i	−0.331099	+	1.23568i	−0.908037	+	0.418889i	$0.862420\pi$
$948$	43.5995	+	11.6824i	1.41604	+	0.379428i
$949$	−9.47467			−0.307561
$950$		0			0
$951$	−46.8568			−1.51944
$952$	2.39233	+	0.641022i	0.0775357	+	0.0207756i
$953$	−7.62471	+	28.4558i	−0.246988	+	0.921773i	0.725385	+	0.688343i	$0.241662\pi$
$953$	−7.62471	+	28.4558i	−0.246988	+	0.921773i	−0.972374	+	0.233430i	$0.925005\pi$
$954$	−7.73159	−	4.46383i	−0.250319	−	0.144522i
$955$		0			0
$956$	−4.18784	+	7.25356i	−0.135444	+	0.234597i
$957$	−2.61544	−	2.61544i	−0.0845451	−	0.0845451i
$958$	7.67736	+	7.67736i	0.248044	+	0.248044i
$959$	18.6057	+	10.7420i	0.600809	+	0.346877i
$960$		0			0
$961$	−13.2686			−0.428018
$962$	−3.63383	+	3.63383i	−0.117159	+	0.117159i
$963$	−15.4743	+	4.14632i	−0.498651	+	0.133613i
$964$	−3.46194	−	5.99626i	−0.111502	−	0.193127i
$965$		0			0
$966$	35.7311	+	61.8880i	1.14963	+	1.99121i
$967$	13.9012	−	51.8801i	0.447033	−	1.66835i	−0.263478	−	0.964666i	$-0.584869\pi$
$967$	13.9012	−	51.8801i	0.447033	−	1.66835i	0.710511	−	0.703686i	$-0.248464\pi$
$968$	7.71629	+	7.71629i	0.248011	+	0.248011i
$969$	6.72754	−	4.51522i	0.216120	−	0.145050i
$970$		0			0
$971$	−37.6138	+	21.7164i	−1.20709	+	0.696911i	−0.962121	−	0.272621i	$-0.912109\pi$
$971$	−37.6138	+	21.7164i	−1.20709	+	0.696911i	−0.244964	+	0.969532i	$0.578776\pi$
$972$	−20.7455	−	5.55874i	−0.665412	−	0.178297i
$973$	−2.80584	−	10.4716i	−0.0899512	−	0.335702i
$974$	28.7735	−	16.6124i	0.921962	−	0.532295i
$975$		0			0
$976$	−13.0081			−0.416380
$977$	−13.7205	+	13.7205i	−0.438959	+	0.438959i	−0.891661	−	0.452703i	$-0.850460\pi$
$977$	−13.7205	+	13.7205i	−0.438959	+	0.438959i	0.452703	+	0.891661i	$0.350460\pi$
$978$	−9.77831	−	36.4931i	−0.312676	−	1.16692i
$979$	0.0406186	−	0.0703535i	0.00129818	−	0.00224851i
$980$		0			0
$981$			31.7287i			1.01302i
$982$	7.39347	+	27.5928i	0.235935	+	0.880521i
$983$	10.5930	−	39.5335i	0.337864	−	1.26092i	−0.562868	−	0.826547i	$-0.690302\pi$
$983$	10.5930	−	39.5335i	0.337864	−	1.26092i	0.900731	−	0.434377i	$-0.143031\pi$
$984$	−11.0314	+	19.1069i	−0.351668	+	0.609107i
$985$		0			0
$986$	−1.68136	−	2.91219i	−0.0535453	−	0.0927431i
$987$	52.0881	−	52.0881i	1.65798	−	1.65798i
$988$	−3.85419	+	4.41312i	−0.122618	+	0.140400i
$989$		−	78.2381i		−	2.48783i
$990$		0			0
$991$	37.3443	−	21.5607i	1.18628	−	0.684899i	0.228821	−	0.973469i	$-0.426513\pi$
$991$	37.3443	−	21.5607i	1.18628	−	0.684899i	0.957459	+	0.288570i	$0.0931797\pi$
$992$	−6.42675	+	1.72204i	−0.204050	+	0.0546749i
$993$	−35.6742	−	9.55887i	−1.13209	−	0.303342i
$994$	13.4647	+	7.77384i	0.427074	+	0.246571i
$995$		0			0
$996$			46.2073i			1.46413i
$997$	50.8247	−	13.6184i	1.60963	−	0.431300i	0.661700	−	0.749768i	$-0.269835\pi$
$997$	50.8247	−	13.6184i	1.60963	−	0.431300i	0.947934	+	0.318468i	$0.103168\pi$
$998$	−16.3048	+	4.36885i	−0.516119	+	0.138294i
$999$		−	9.15871i		−	0.289769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.g.107.4		32
5.2	odd	4		190.2.m.b.183.5	yes	32
5.3	odd	4	inner	950.2.q.g.943.4		32
5.4	even	2		190.2.m.b.107.5	yes	32
19.8	odd	6	inner	950.2.q.g.407.4		32
95.8	even	12	inner	950.2.q.g.293.4		32
95.27	even	12		190.2.m.b.103.5	yes	32
95.84	odd	6		190.2.m.b.27.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.m.b.27.5	✓	32	95.84	odd	6
190.2.m.b.103.5	yes	32	95.27	even	12
190.2.m.b.107.5	yes	32	5.4	even	2
190.2.m.b.183.5	yes	32	5.2	odd	4
950.2.q.g.107.4		32	1.1	even	1	trivial
950.2.q.g.293.4		32	95.8	even	12	inner
950.2.q.g.407.4		32	19.8	odd	6	inner
950.2.q.g.943.4		32	5.3	odd	4	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.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.680416 - 2.53935i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.31446 + 2.27672i) q^{6} +(2.47691 + 2.47691i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-3.38724 - 1.95563i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.680416 - 2.53935i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.31446 + 2.27672i) q^{6} +(2.47691 + 2.47691i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-3.38724 - 1.95563i) q^{9} +0.295831 q^{11} +(1.85893 - 1.85893i) q^{12} +(-1.29839 + 0.347904i) q^{13} +(-1.75144 - 3.03358i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.182999 + 0.682961i) q^{17} +(2.76567 + 2.76567i) q^{18} +(1.91986 - 3.91333i) q^{19} +(7.97505 - 4.60440i) q^{21} +(-0.285751 - 0.0765667i) q^{22} +(-2.00849 - 7.49578i) q^{23} +(-2.27672 + 1.31446i) q^{24} +1.34420 q^{26} +(-1.69396 + 1.69396i) q^{27} +(0.906611 + 3.38352i) q^{28} +(2.37798 - 4.11878i) q^{29} -6.65346i q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.201288 - 0.751218i) q^{33} +(0.353527 - 0.612326i) q^{34} +(-1.95563 - 3.38724i) q^{36} +(-2.70335 + 2.70335i) q^{37} +(-2.86728 + 3.28309i) q^{38} +3.53379i q^{39} +(7.26797 - 4.19616i) q^{41} +(-8.89502 + 2.38341i) q^{42} +(9.73843 + 2.60940i) q^{43} +(0.256197 + 0.147915i) q^{44} +7.76020i q^{46} +(7.72671 - 2.07037i) q^{47} +(2.53935 - 0.680416i) q^{48} +5.27013i q^{49} +(1.60976 + 0.929395i) q^{51} +(-1.29839 - 0.347904i) q^{52} +(-2.20478 + 0.590770i) q^{53} +(2.07467 - 1.19781i) q^{54} -3.50287i q^{56} +(-8.63101 - 7.53787i) q^{57} +(-3.36297 + 3.36297i) q^{58} +(-6.62955 - 11.4827i) q^{59} +(-6.50406 + 11.2654i) q^{61} +(-1.72204 + 6.42675i) q^{62} +(-3.54598 - 13.2338i) q^{63} +1.00000i q^{64} +(-0.388859 + 0.673523i) q^{66} +(-2.19747 - 8.20107i) q^{67} +(-0.499962 + 0.499962i) q^{68} -20.4010 q^{69} +(-3.84390 + 2.21928i) q^{71} +(1.01231 + 3.77798i) q^{72} +(6.80840 + 1.82431i) q^{73} +(3.31091 - 1.91156i) q^{74} +(3.61931 - 2.42912i) q^{76} +(0.732746 + 0.732746i) q^{77} +(0.914613 - 3.41338i) q^{78} +(8.58478 + 14.8693i) q^{79} +(-2.71793 - 4.70759i) q^{81} +(-8.10636 + 2.17209i) q^{82} +(-12.4285 + 12.4285i) q^{83} +9.20880 q^{84} +(-8.73124 - 5.04098i) q^{86} +(-8.84099 - 8.84099i) q^{87} +(-0.209184 - 0.209184i) q^{88} +(0.137304 - 0.237817i) q^{89} +(-4.07773 - 2.35428i) q^{91} +(2.00849 - 7.49578i) q^{92} +(-16.8955 - 4.52712i) q^{93} -7.99928 q^{94} -2.62893 q^{96} +(5.63547 + 1.51002i) q^{97} +(1.36401 - 5.09055i) q^{98} +(-1.00205 - 0.578535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) \) 32 * q + 12 * q^3 - 24 * q^7	\( 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) \) 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

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