LMFDB - Embedded newform 598.2.h.c.277.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [598,2,Mod(231,598)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("598.231"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(598, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 598 = 2 \cdot 13 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	598.h (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.77505404087$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			277.4
Character	$\chi$	$=$	598.277
Dual form			598.2.h.c.231.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.0928940 - 0.160897i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.931614i q^{5} +(-0.160897 + 0.0928940i) q^{6} +(3.98172 - 2.29885i) q^{7} -1.00000i q^{8} +(1.48274 + 2.56818i) q^{9} +(0.465807 - 0.806802i) q^{10} +(-2.91576 - 1.68341i) q^{11} +0.185788 q^{12} +(3.47321 + 0.967896i) q^{13} -4.59769 q^{14} +(0.149894 + 0.0865414i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.465659 + 0.806545i) q^{17} -2.96548i q^{18} +(-5.89207 + 3.40179i) q^{19} +(-0.806802 + 0.465807i) q^{20} -0.854196i q^{21} +(1.68341 + 2.91576i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.160897 - 0.0928940i) q^{24} +4.13209 q^{25} +(-2.52394 - 2.57483i) q^{26} +1.10832 q^{27} +(3.98172 + 2.29885i) q^{28} +(4.67356 - 8.09485i) q^{29} +(-0.0865414 - 0.149894i) q^{30} +5.60799i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.541713 + 0.312758i) q^{33} -0.931318i q^{34} +(2.14164 + 3.70943i) q^{35} +(-1.48274 + 2.56818i) q^{36} +(7.57172 + 4.37154i) q^{37} +6.80357 q^{38} +(0.478372 - 0.468918i) q^{39} +0.931614 q^{40} +(-1.32898 - 0.767286i) q^{41} +(-0.427098 + 0.739756i) q^{42} +(0.537107 + 0.930297i) q^{43} -3.36683i q^{44} +(-2.39256 + 1.38134i) q^{45} +(-0.866025 + 0.500000i) q^{46} -9.75604i q^{47} +(0.0928940 + 0.160897i) q^{48} +(7.06940 - 12.2446i) q^{49} +(-3.57850 - 2.06605i) q^{50} +0.173028 q^{51} +(0.898382 + 3.49183i) q^{52} +6.13312 q^{53} +(-0.959829 - 0.554158i) q^{54} +(1.56829 - 2.71636i) q^{55} +(-2.29885 - 3.98172i) q^{56} +1.26402i q^{57} +(-8.09485 + 4.67356i) q^{58} +(-8.23076 + 4.75203i) q^{59} +0.173083i q^{60} +(4.49780 + 7.79041i) q^{61} +(2.80399 - 4.85666i) q^{62} +(11.8077 + 6.81719i) q^{63} -1.00000 q^{64} +(-0.901706 + 3.23569i) q^{65} +0.625516 q^{66} +(-4.20377 - 2.42705i) q^{67} +(-0.465659 + 0.806545i) q^{68} +(-0.0928940 - 0.160897i) q^{69} -4.28328i q^{70} +(8.63841 - 4.98739i) q^{71} +(2.56818 - 1.48274i) q^{72} -13.0992i q^{73} +(-4.37154 - 7.57172i) q^{74} +(0.383847 - 0.664842i) q^{75} +(-5.89207 - 3.40179i) q^{76} -15.4796 q^{77} +(-0.648741 + 0.166909i) q^{78} -2.71106 q^{79} +(-0.806802 - 0.465807i) q^{80} +(-4.34527 + 7.52623i) q^{81} +(0.767286 + 1.32898i) q^{82} +6.49704i q^{83} +(0.739756 - 0.427098i) q^{84} +(-0.751389 + 0.433815i) q^{85} -1.07421i q^{86} +(-0.868292 - 1.50393i) q^{87} +(-1.68341 + 2.91576i) q^{88} +(-5.82171 - 3.36116i) q^{89} +2.76269 q^{90} +(16.0544 - 4.13049i) q^{91} +1.00000 q^{92} +(0.902309 + 0.520948i) q^{93} +(-4.87802 + 8.44898i) q^{94} +(-3.16915 - 5.48913i) q^{95} -0.185788i q^{96} +(-4.90466 + 2.83171i) q^{97} +(-12.2446 + 7.06940i) q^{98} -9.98427i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{3} + 14 q^{4} - 6 q^{9} + 8 q^{10} - 8 q^{12} + 2 q^{13} + 4 q^{14} + 12 q^{15} - 14 q^{16} - 2 q^{17} - 12 q^{19} - 12 q^{22} + 14 q^{23} - 28 q^{25} - 10 q^{26} + 20 q^{27} - 14 q^{29} + 8 q^{30}+ \cdots + 12 q^{98}+O(q^{100}) $ 28 * q - 4 * q^3 + 14 * q^4 - 6 * q^9 + 8 * q^10 - 8 * q^12 + 2 * q^13 + 4 * q^14 + 12 * q^15 - 14 * q^16 - 2 * q^17 - 12 * q^19 - 12 * q^22 + 14 * q^23 - 28 * q^25 - 10 * q^26 + 20 * q^27 - 14 * q^29 + 8 * q^30 + 18 * q^33 + 18 * q^35 + 6 * q^36 - 12 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^40 + 24 * q^41 - 6 * q^42 + 12 * q^43 - 36 * q^45 - 4 * q^48 + 36 * q^49 - 36 * q^50 - 12 * q^51 - 2 * q^52 + 8 * q^53 - 18 * q^54 - 12 * q^55 + 2 * q^56 + 18 * q^58 - 30 * q^59 + 6 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^64 - 66 * q^65 + 44 * q^66 + 42 * q^67 + 2 * q^68 + 4 * q^69 - 60 * q^71 + 44 * q^75 - 12 * q^76 + 16 * q^77 - 48 * q^78 + 68 * q^79 + 2 * q^81 + 40 * q^82 + 42 * q^84 - 72 * q^85 + 10 * q^87 + 12 * q^88 - 6 * q^89 - 36 * q^90 + 4 * q^91 + 28 * q^92 + 60 * q^93 - 26 * q^94 + 16 * q^95 - 12 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/598\mathbb{Z}\right)^\times$.

$n$	$93$	$235$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.0928940	−	0.160897i	0.0536324	−	0.0928940i	−0.837963	−	0.545727i	$-0.816253\pi$
$3$	0.0928940	−	0.160897i	0.0536324	−	0.0928940i	0.891595	+	0.452833i	$0.149587\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			0.931614i			0.416631i	0.978062	+	0.208315i	$0.0667980\pi$
$5$			0.931614i			0.416631i	−0.978062	+	0.208315i	$0.933202\pi$
$6$	−0.160897	+	0.0928940i	−0.0656860	+	0.0379238i
$7$	3.98172	−	2.29885i	1.50495	−	0.868883i	0.504965	−	0.863140i	$-0.331505\pi$
$7$	3.98172	−	2.29885i	1.50495	−	0.868883i	0.999984	−	0.00574307i	$-0.00182809\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.48274	+	2.56818i	0.494247	+	0.856061i
$10$	0.465807	−	0.806802i	0.147301	−	0.255133i
$11$	−2.91576	−	1.68341i	−0.879134	−	0.507568i	−0.00876135	−	0.999962i	$-0.502789\pi$
$11$	−2.91576	−	1.68341i	−0.879134	−	0.507568i	−0.870373	+	0.492393i	$0.836122\pi$
$12$	0.185788			0.0536324
$13$	3.47321	+	0.967896i	0.963295	+	0.268446i
$13$	3.47321	+	0.967896i	0.963295	+	0.268446i
$14$	−4.59769			−1.22879
$15$	0.149894	+	0.0865414i	0.0387025	+	0.0223449i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.465659	+	0.806545i	0.112939	+	0.195616i	0.916954	−	0.398993i	$-0.130640\pi$
$17$	0.465659	+	0.806545i	0.112939	+	0.195616i	−0.804015	+	0.594609i	$0.797307\pi$
$18$		−	2.96548i		−	0.698971i
$19$	−5.89207	+	3.40179i	−1.35173	+	0.780423i	−0.988492	−	0.151272i	$-0.951663\pi$
$19$	−5.89207	+	3.40179i	−1.35173	+	0.780423i	−0.363241	+	0.931695i	$0.618330\pi$
$20$	−0.806802	+	0.465807i	−0.180406	+	0.104158i
$21$		−	0.854196i		−	0.186401i
$22$	1.68341	+	2.91576i	0.358905	+	0.621642i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	−0.160897	−	0.0928940i	−0.0328430	−	0.0189619i
$25$	4.13209			0.826419
$26$	−2.52394	−	2.57483i	−0.494985	−	0.504965i
$27$	1.10832			0.213295
$28$	3.98172	+	2.29885i	0.752474	+	0.434441i
$29$	4.67356	−	8.09485i	0.867859	−	1.50318i	0.00367880	−	0.999993i	$-0.498829\pi$
$29$	4.67356	−	8.09485i	0.867859	−	1.50318i	0.864180	−	0.503183i	$-0.167838\pi$
$30$	−0.0865414	−	0.149894i	−0.0158002	−	0.0273668i
$31$			5.60799i			1.00722i	0.863930	+	0.503612i	$0.167996\pi$
$31$			5.60799i			1.00722i	−0.863930	+	0.503612i	$0.832004\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.541713	+	0.312758i	−0.0943001	+	0.0544442i
$34$		−	0.931318i		−	0.159720i
$35$	2.14164	+	3.70943i	0.362003	+	0.627008i
$36$	−1.48274	+	2.56818i	−0.247124	+	0.428031i
$37$	7.57172	+	4.37154i	1.24478	+	0.718676i	0.970064	−	0.242848i	$-0.0780818\pi$
$37$	7.57172	+	4.37154i	1.24478	+	0.718676i	0.274719	+	0.961525i	$0.411415\pi$
$38$	6.80357			1.10369
$39$	0.478372	−	0.468918i	0.0766008	−	0.0750869i
$40$	0.931614			0.147301
$41$	−1.32898	−	0.767286i	−0.207552	−	0.119830i	0.392621	−	0.919700i	$-0.371568\pi$
$41$	−1.32898	−	0.767286i	−0.207552	−	0.119830i	−0.600173	+	0.799870i	$0.704902\pi$
$42$	−0.427098	+	0.739756i	−0.0659027	+	0.114147i
$43$	0.537107	+	0.930297i	0.0819081	+	0.141869i	0.904070	−	0.427385i	$-0.140565\pi$
$43$	0.537107	+	0.930297i	0.0819081	+	0.141869i	−0.822161	+	0.569254i	$0.807232\pi$
$44$		−	3.36683i		−	0.507568i
$45$	−2.39256	+	1.38134i	−0.356661	+	0.205918i
$46$	−0.866025	+	0.500000i	−0.127688	+	0.0737210i
$47$		−	9.75604i		−	1.42306i	−0.702653	−	0.711532i	$-0.748002\pi$
$47$		−	9.75604i		−	1.42306i	0.702653	−	0.711532i	$-0.251998\pi$
$48$	0.0928940	+	0.160897i	0.0134081	+	0.0232235i
$49$	7.06940	−	12.2446i	1.00991	−	1.74922i
$50$	−3.57850	−	2.06605i	−0.506076	−	0.292183i
$51$	0.173028			0.0242287
$52$	0.898382	+	3.49183i	0.124583	+	0.484230i
$53$	6.13312			0.842449			0.421224	−	0.906956i	$-0.361600\pi$
$53$	6.13312			0.842449			0.421224	+	0.906956i	$0.361600\pi$
$54$	−0.959829	−	0.554158i	−0.130616	−	0.0754113i
$55$	1.56829	−	2.71636i	0.211469	−	0.366274i
$56$	−2.29885	−	3.98172i	−0.307196	−	0.532080i
$57$			1.26402i			0.167424i
$58$	−8.09485	+	4.67356i	−1.06291	+	0.613669i
$59$	−8.23076	+	4.75203i	−1.07155	+	0.618662i	−0.928605	−	0.371069i	$-0.878991\pi$
$59$	−8.23076	+	4.75203i	−1.07155	+	0.618662i	−0.142948	+	0.989730i	$0.545658\pi$
$60$			0.173083i			0.0223449i
$61$	4.49780	+	7.79041i	0.575884	+	0.997460i	0.995945	+	0.0899645i	$0.0286753\pi$
$61$	4.49780	+	7.79041i	0.575884	+	0.997460i	−0.420061	+	0.907496i	$0.637991\pi$
$62$	2.80399	−	4.85666i	0.356108	−	0.616797i
$63$	11.8077	+	6.81719i	1.48763	+	0.858886i
$64$	−1.00000			−0.125000
$65$	−0.901706	+	3.23569i	−0.111843	+	0.401338i
$66$	0.625516			0.0769957
$67$	−4.20377	−	2.42705i	−0.513572	−	0.296511i	0.220729	−	0.975335i	$-0.429156\pi$
$67$	−4.20377	−	2.42705i	−0.513572	−	0.296511i	−0.734301	+	0.678824i	$0.762490\pi$
$68$	−0.465659	+	0.806545i	−0.0564695	+	0.0978080i
$69$	−0.0928940	−	0.160897i	−0.0111831	−	0.0193697i
$70$		−	4.28328i		−	0.511950i
$71$	8.63841	−	4.98739i	1.02519	−	0.591894i	0.109587	−	0.993977i	$-0.465047\pi$
$71$	8.63841	−	4.98739i	1.02519	−	0.591894i	0.915603	+	0.402083i	$0.131714\pi$
$72$	2.56818	−	1.48274i	0.302663	−	0.174743i
$73$		−	13.0992i		−	1.53314i	−0.642161	−	0.766570i	$-0.721962\pi$
$73$		−	13.0992i		−	1.53314i	0.642161	−	0.766570i	$-0.278038\pi$
$74$	−4.37154	−	7.57172i	−0.508181	−	0.880195i
$75$	0.383847	−	0.664842i	0.0443228	−	0.0767694i
$76$	−5.89207	−	3.40179i	−0.675866	−	0.390212i
$77$	−15.4796			−1.76407
$78$	−0.648741	+	0.166909i	−0.0734554	+	0.0188987i
$79$	−2.71106			−0.305018			−0.152509	−	0.988302i	$-0.548735\pi$
$79$	−2.71106			−0.305018			−0.152509	+	0.988302i	$0.548735\pi$
$80$	−0.806802	−	0.465807i	−0.0902032	−	0.0520788i
$81$	−4.34527	+	7.52623i	−0.482808	+	0.836247i
$82$	0.767286	+	1.32898i	0.0847326	+	0.146761i
$83$			6.49704i			0.713143i	0.934268	+	0.356571i	$0.116054\pi$
$83$			6.49704i			0.713143i	−0.934268	+	0.356571i	$0.883946\pi$
$84$	0.739756	−	0.427098i	0.0807140	−	0.0466002i
$85$	−0.751389	+	0.433815i	−0.0814996	+	0.0470538i
$86$		−	1.07421i		−	0.115836i
$87$	−0.868292	−	1.50393i	−0.0930907	−	0.161238i
$88$	−1.68341	+	2.91576i	−0.179453	+	0.310821i
$89$	−5.82171	−	3.36116i	−0.617100	−	0.356283i	0.158639	−	0.987337i	$-0.449289\pi$
$89$	−5.82171	−	3.36116i	−0.617100	−	0.356283i	−0.775739	+	0.631054i	$0.782623\pi$
$90$	2.76269			0.291213
$91$	16.0544	−	4.13049i	1.68296	−	0.432992i
$92$	1.00000			0.104257
$93$	0.902309	+	0.520948i	0.0935651	+	0.0540198i
$94$	−4.87802	+	8.44898i	−0.503129	+	0.871446i
$95$	−3.16915	−	5.48913i	−0.325148	−	0.563173i
$96$		−	0.185788i		−	0.0189619i
$97$	−4.90466	+	2.83171i	−0.497993	+	0.287516i	−0.727884	−	0.685700i	$-0.759496\pi$
$97$	−4.90466	+	2.83171i	−0.497993	+	0.287516i	0.229892	+	0.973216i	$0.426163\pi$
$98$	−12.2446	+	7.06940i	−1.23689	+	0.714117i
$99$		−	9.98427i		−	1.00346i
$100$	2.06605	+	3.57850i	0.206605	+	0.357850i
$101$	−3.01747	+	5.22642i	−0.300250	+	0.520048i	−0.976192	−	0.216906i	$-0.930403\pi$
$101$	−3.01747	+	5.22642i	−0.300250	+	0.520048i	0.675943	+	0.736954i	$0.263737\pi$
$102$	−0.149846	−	0.0865139i	−0.0148370	−	0.00856615i
$103$	−2.91580			−0.287303			−0.143651	−	0.989628i	$-0.545884\pi$
$103$	−2.91580			−0.287303			−0.143651	+	0.989628i	$0.545884\pi$
$104$	0.967896	−	3.47321i	0.0949100	−	0.340576i
$105$	0.795782			0.0776603
$106$	−5.31144	−	3.06656i	−0.515892	−	0.297851i
$107$	−5.63193	+	9.75478i	−0.544459	+	0.943030i	0.454182	+	0.890909i	$0.349932\pi$
$107$	−5.63193	+	9.75478i	−0.544459	+	0.943030i	−0.998641	+	0.0521214i	$0.983402\pi$
$108$	0.554158	+	0.959829i	0.0533238	+	0.0923596i
$109$		−	9.96692i		−	0.954658i	−0.878725	−	0.477329i	$-0.841605\pi$
$109$		−	9.96692i		−	0.954658i	0.878725	−	0.477329i	$-0.158395\pi$
$110$	−2.71636	+	1.56829i	−0.258995	+	0.149531i
$111$	1.40673	−	0.812179i	0.133521	−	0.0770886i
$112$			4.59769i			0.434441i
$113$	8.39006	+	14.5320i	0.789270	+	1.36706i	0.926415	+	0.376505i	$0.122874\pi$
$113$	8.39006	+	14.5320i	0.789270	+	1.36706i	−0.137145	+	0.990551i	$0.543793\pi$
$114$	0.632011	−	1.09468i	0.0591933	−	0.102526i
$115$	0.806802	+	0.465807i	0.0752346	+	0.0434367i
$116$	9.34713			0.867859
$117$	2.66414	+	10.3550i	0.246299	+	0.957318i
$118$	9.50406			0.874920
$119$	3.70825	+	2.14096i	0.339935	+	0.196261i
$120$	0.0865414	−	0.149894i	0.00790011	−	0.0136834i
$121$	0.167764	+	0.290576i	0.0152513	+	0.0264160i
$122$		−	8.99560i		−	0.814423i
$123$	−0.246908	+	0.142553i	−0.0222630	+	0.0128535i
$124$	−4.85666	+	2.80399i	−0.436141	+	0.251806i
$125$			8.50759i			0.760942i
$126$	−6.81719	−	11.8077i	−0.607324	−	1.05192i
$127$	6.46405	−	11.1961i	0.573592	−	0.993490i	−0.422601	−	0.906316i	$-0.638883\pi$
$127$	6.46405	−	11.1961i	0.573592	−	0.993490i	0.996193	−	0.0871744i	$-0.0277837\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	0.199576			0.0175717
$130$	2.39875	−	2.35134i	0.210384	−	0.206226i
$131$	−5.98121			−0.522580			−0.261290	−	0.965260i	$-0.584148\pi$
$131$	−5.98121			−0.522580			−0.261290	+	0.965260i	$0.584148\pi$
$132$	−0.541713	−	0.312758i	−0.0471501	−	0.0272221i
$133$	−15.6404	+	27.0899i	−1.35619	+	2.34899i
$134$	2.42705	+	4.20377i	0.209665	+	0.363150i
$135$			1.03252i			0.0888654i
$136$	0.806545	−	0.465659i	0.0691607	−	0.0399299i
$137$	−9.62382	+	5.55632i	−0.822219	+	0.474708i	−0.851181	−	0.524872i	$-0.824113\pi$
$137$	−9.62382	+	5.55632i	−0.822219	+	0.474708i	0.0289622	+	0.999581i	$0.490780\pi$
$138$			0.185788i			0.0158153i
$139$	−5.32253	−	9.21889i	−0.451451	−	0.781936i	0.547026	−	0.837116i	$-0.315760\pi$
$139$	−5.32253	−	9.21889i	−0.451451	−	0.781936i	−0.998476	+	0.0551802i	$0.982427\pi$
$140$	−2.14164	+	3.70943i	−0.181002	+	0.313504i
$141$	−1.56972	−	0.906277i	−0.132194	−	0.0763223i
$142$	−9.97477			−0.837065
$143$	−8.49767	−	8.66900i	−0.710611	−	0.724938i
$144$	−2.96548			−0.247124
$145$	7.54128	+	4.35396i	0.626269	+	0.361577i
$146$	−6.54958	+	11.3442i	−0.542047	+	0.938853i
$147$	−1.31341	−	2.27489i	−0.108328	−	0.187630i
$148$			8.74307i			0.718676i
$149$	−1.91405	+	1.10508i	−0.156805	+	0.0905315i	−0.576349	−	0.817203i	$-0.695523\pi$
$149$	−1.91405	+	1.10508i	−0.156805	+	0.0905315i	0.419544	+	0.907735i	$0.362190\pi$
$150$	−0.664842	+	0.383847i	−0.0542841	+	0.0313410i
$151$		−	0.0765627i		−	0.00623058i	−0.999995	−	0.00311529i	$-0.999008\pi$
$151$		−	0.0765627i		−	0.00623058i	0.999995	−	0.00311529i	$-0.000991630\pi$
$152$	3.40179	+	5.89207i	0.275921	+	0.477910i
$153$	−1.38090	+	2.39180i	−0.111639	+	0.193365i
$154$	13.4058	+	7.73982i	1.08027	+	0.623693i
$155$	−5.22448			−0.419641
$156$	0.645280	+	0.179823i	0.0516638	+	0.0143974i
$157$	−10.7112			−0.854843			−0.427422	−	0.904052i	$-0.640578\pi$
$157$	−10.7112			−0.854843			−0.427422	+	0.904052i	$0.640578\pi$
$158$	2.34784	+	1.35553i	0.186784	+	0.107840i
$159$	0.569730	−	0.986801i	0.0451825	−	0.0782584i
$160$	0.465807	+	0.806802i	0.0368253	+	0.0637833i
$161$		−	4.59769i		−	0.362349i
$162$	7.52623	−	4.34527i	0.591316	−	0.341397i
$163$	−17.2095	+	9.93590i	−1.34795	+	0.778240i	−0.987959	−	0.154716i	$-0.950554\pi$
$163$	−17.2095	+	9.93590i	−1.34795	+	0.778240i	−0.359992	+	0.932955i	$0.617220\pi$
$164$		−	1.53457i		−	0.119830i
$165$	−0.291370	−	0.504667i	−0.0226831	−	0.0392883i
$166$	3.24852	−	5.62660i	0.252134	−	0.436709i
$167$	−13.2333	−	7.64025i	−1.02402	−	0.591221i	−0.108757	−	0.994068i	$-0.534687\pi$
$167$	−13.2333	−	7.64025i	−1.02402	−	0.591221i	−0.915267	+	0.402848i	$0.868020\pi$
$168$	−0.854196			−0.0659027
$169$	11.1264	+	6.72341i	0.855873	+	0.517185i
$170$	0.867629			0.0665441
$171$	−17.4728	−	10.0879i	−1.33618	−	0.771444i
$172$	−0.537107	+	0.930297i	−0.0409541	+	0.0709345i
$173$	−4.35427	−	7.54182i	−0.331049	−	0.573394i	0.651669	−	0.758504i	$-0.274069\pi$
$173$	−4.35427	−	7.54182i	−0.331049	−	0.573394i	−0.982718	+	0.185110i	$0.940736\pi$
$174$			1.73658i			0.131650i
$175$	16.4528	−	9.49906i	1.24372	−	0.718061i
$176$	2.91576	−	1.68341i	0.219784	−	0.126892i
$177$			1.76574i			0.132721i
$178$	3.36116	+	5.82171i	0.251930	+	0.436355i
$179$	−12.7616	+	22.1038i	−0.953849	+	1.65211i	−0.216868	+	0.976201i	$0.569584\pi$
$179$	−12.7616	+	22.1038i	−0.953849	+	1.65211i	−0.736981	+	0.675914i	$0.763749\pi$
$180$	−2.39256	−	1.38134i	−0.178331	−	0.102959i
$181$	−13.0118			−0.967159			−0.483579	−	0.875300i	$-0.660664\pi$
$181$	−13.0118			−0.967159			−0.483579	+	0.875300i	$0.660664\pi$
$182$	−15.9688	−	4.45009i	−1.18368	−	0.329863i
$183$	1.67127			0.123544
$184$	−0.866025	−	0.500000i	−0.0638442	−	0.0368605i
$185$	−4.07259	+	7.05393i	−0.299422	+	0.518615i
$186$	−0.520948	−	0.902309i	−0.0381978	−	0.0661605i
$187$		−	3.13559i		−	0.229297i
$188$	8.44898	−	4.87802i	0.616205	−	0.355766i
$189$	4.41300	−	2.54785i	0.320999	−	0.185329i
$190$			6.33831i			0.459829i
$191$	−0.362379	−	0.627659i	−0.0262208	−	0.0454158i	0.852617	−	0.522536i	$-0.175014\pi$
$191$	−0.362379	−	0.627659i	−0.0262208	−	0.0454158i	−0.878838	+	0.477120i	$0.841681\pi$
$192$	−0.0928940	+	0.160897i	−0.00670405	+	0.0116117i
$193$	−18.1176	−	10.4602i	−1.30414	−	0.752943i	−0.323025	−	0.946390i	$-0.604700\pi$
$193$	−18.1176	−	10.4602i	−1.30414	−	0.752943i	−0.981111	+	0.193447i	$0.938033\pi$
$194$	5.66341			0.406609
$195$	0.436850	+	0.445658i	0.0312835	+	0.0319142i
$196$	14.1388			1.00991
$197$	−15.8145	−	9.13052i	−1.12674	−	0.650523i	−0.183626	−	0.982996i	$-0.558783\pi$
$197$	−15.8145	−	9.13052i	−1.12674	−	0.650523i	−0.943113	+	0.332473i	$0.892117\pi$
$198$	−4.99213	+	8.64663i	−0.354776	+	0.614489i
$199$	−5.32495	−	9.22308i	−0.377476	−	0.653807i	0.613219	−	0.789913i	$-0.289874\pi$
$199$	−5.32495	−	9.22308i	−0.377476	−	0.653807i	−0.990694	+	0.136106i	$0.956541\pi$
$200$		−	4.13209i		−	0.292183i
$201$	−0.781010	+	0.450916i	−0.0550882	+	0.0318052i
$202$	5.22642	−	3.01747i	0.367730	−	0.212309i
$203$		−	42.9752i		−	3.01627i
$204$	0.0865139	+	0.149846i	0.00605718	+	0.0104913i
$205$	0.714815	−	1.23810i	0.0499248	−	0.0864724i
$206$	2.52516	+	1.45790i	0.175936	+	0.101577i
$207$	2.96548			0.206115
$208$	−2.57483	+	2.52394i	−0.178532	+	0.175004i
$209$	22.9065			1.58447
$210$	−0.689167	−	0.397891i	−0.0475571	−	0.0274571i
$211$	0.569311	−	0.986076i	0.0391930	−	0.0678842i	−0.845764	−	0.533558i	$-0.820855\pi$
$211$	0.569311	−	0.986076i	0.0391930	−	0.0678842i	0.884956	+	0.465674i	$0.154188\pi$
$212$	3.06656	+	5.31144i	0.210612	+	0.364791i
$213$		−	1.85319i		−	0.126979i
$214$	9.75478	−	5.63193i	0.666823	−	0.384991i
$215$	−0.866678	+	0.500377i	−0.0591070	+	0.0341254i
$216$		−	1.10832i		−	0.0754113i
$217$	12.8919	+	22.3294i	0.875160	+	1.51582i
$218$	−4.98346	+	8.63161i	−0.337523	+	0.584606i
$219$	−2.10762	−	1.21683i	−0.142419	−	0.0822259i
$220$	3.13658			0.211469
$221$	0.836679	+	3.25201i	0.0562811	+	0.218754i
$222$	−1.62436			−0.109020
$223$	5.80774	+	3.35310i	0.388915	+	0.224540i	0.681690	−	0.731641i	$-0.261245\pi$
$223$	5.80774	+	3.35310i	0.388915	+	0.224540i	−0.292775	+	0.956181i	$0.594579\pi$
$224$	2.29885	−	3.98172i	0.153598	−	0.266040i
$225$	6.12683	+	10.6120i	0.408455	+	0.707465i
$226$		−	16.7801i		−	1.11620i
$227$	20.2485	−	11.6905i	1.34394	−	0.775923i	0.356555	−	0.934274i	$-0.383951\pi$
$227$	20.2485	−	11.6905i	1.34394	−	0.775923i	0.987383	+	0.158351i	$0.0506178\pi$
$228$	−1.09468	+	0.632011i	−0.0724966	+	0.0418560i
$229$			17.1494i			1.13326i	0.823971	+	0.566632i	$0.191754\pi$
$229$			17.1494i			1.13326i	−0.823971	+	0.566632i	$0.808246\pi$
$230$	−0.465807	−	0.806802i	−0.0307144	−	0.0531989i
$231$	−1.43797	+	2.49063i	−0.0946112	+	0.163871i
$232$	−8.09485	−	4.67356i	−0.531453	−	0.306834i
$233$	−3.47011			−0.227334			−0.113667	−	0.993519i	$-0.536260\pi$
$233$	−3.47011			−0.227334			−0.113667	+	0.993519i	$0.536260\pi$
$234$	2.87028	−	10.2997i	0.187636	−	0.673315i
$235$	9.08887			0.592892
$236$	−8.23076	−	4.75203i	−0.535777	−	0.309331i
$237$	−0.251841	+	0.436201i	−0.0163588	+	0.0283343i
$238$	−2.14096	−	3.70825i	−0.138778	−	0.240370i
$239$		−	2.81350i		−	0.181990i	−0.995851	−	0.0909950i	$-0.970995\pi$
$239$		−	2.81350i		−	0.181990i	0.995851	−	0.0909950i	$-0.0290047\pi$
$240$	−0.149894	+	0.0865414i	−0.00967562	+	0.00558622i
$241$	20.7970	−	12.0071i	1.33965	−	0.773448i	0.352896	−	0.935663i	$-0.385197\pi$
$241$	20.7970	−	12.0071i	1.33965	−	0.773448i	0.986755	+	0.162215i	$0.0518638\pi$
$242$		−	0.335528i		−	0.0215686i
$243$	2.46977	+	4.27777i	0.158436	+	0.274419i
$244$	−4.49780	+	7.79041i	−0.287942	+	0.498730i
$245$	11.4072	+	6.58595i	0.728780	+	0.420761i
$246$	0.285105			0.0181776
$247$	−23.7570	+	6.11221i	−1.51162	+	0.388910i
$248$	5.60799			0.356108
$249$	1.04536	+	0.603536i	0.0662467	+	0.0382475i
$250$	4.25380	−	7.36779i	0.269034	−	0.465980i
$251$	0.392182	+	0.679279i	0.0247543	+	0.0428757i	0.878137	−	0.478409i	$-0.158786\pi$
$251$	0.392182	+	0.679279i	0.0247543	+	0.0428757i	−0.853383	+	0.521285i	$0.825453\pi$
$252$			13.6344i			0.858886i
$253$	−2.91576	+	1.68341i	−0.183312	+	0.105835i
$254$	−11.1961	+	6.46405i	−0.702504	+	0.405591i
$255$			0.161195i			0.0100944i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.763027	+	1.32160i	−0.0475963	+	0.0824392i	−0.888842	−	0.458214i	$-0.848489\pi$
$257$	−0.763027	+	1.32160i	−0.0475963	+	0.0824392i	0.841246	+	0.540653i	$0.181823\pi$
$258$	−0.172838	−	0.0997881i	−0.0107604	−	0.00621254i
$259$	40.1980			2.49778
$260$	−3.25304	+	0.836945i	−0.201745	+	0.0519051i
$261$	27.7187			1.71575
$262$	5.17988	+	2.99060i	0.320014	+	0.184760i
$263$	−2.91324	+	5.04589i	−0.179638	+	0.311143i	−0.941757	−	0.336295i	$-0.890826\pi$
$263$	−2.91324	+	5.04589i	−0.179638	+	0.311143i	0.762118	+	0.647438i	$0.224159\pi$
$264$	0.312758	+	0.541713i	0.0192489	+	0.0333401i
$265$			5.71370i			0.350990i
$266$	27.0899	−	15.6404i	1.66099	−	0.958973i
$267$	−1.08160	+	0.624464i	−0.0661930	+	0.0382166i
$268$		−	4.85409i		−	0.296511i
$269$	−7.39939	−	12.8161i	−0.451149	−	0.781413i	0.547309	−	0.836931i	$-0.315652\pi$
$269$	−7.39939	−	12.8161i	−0.451149	−	0.781413i	−0.998458	+	0.0555181i	$0.982319\pi$
$270$	0.516261	−	0.894190i	0.0314187	−	0.0544187i
$271$	18.2337	+	10.5272i	1.10762	+	0.639482i	0.938211	−	0.346064i	$-0.112482\pi$
$271$	18.2337	+	10.5272i	1.10762	+	0.639482i	0.169405	+	0.985547i	$0.445815\pi$
$272$	−0.931318			−0.0564695
$273$	0.826773	−	2.96680i	0.0500386	−	0.179559i
$274$	11.1126			0.671339
$275$	−12.0482	−	6.95603i	−0.726533	−	0.419464i
$276$	0.0928940	−	0.160897i	0.00559156	−	0.00968487i
$277$	11.0097	+	19.0694i	0.661510	+	1.14577i	0.980219	+	0.197916i	$0.0634175\pi$
$277$	11.0097	+	19.0694i	0.661510	+	1.14577i	−0.318709	+	0.947853i	$0.603249\pi$
$278$			10.6451i			0.638448i
$279$	−14.4023	+	8.31520i	−0.862246	+	0.497818i
$280$	3.70943	−	2.14164i	0.221681	−	0.127987i
$281$		−	8.53270i		−	0.509018i	−0.967070	−	0.254509i	$-0.918086\pi$
$281$		−	8.53270i		−	0.509018i	0.967070	−	0.254509i	$-0.0819139\pi$
$282$	0.906277	+	1.56972i	0.0539680	+	0.0934754i
$283$	5.12331	−	8.87384i	0.304549	−	0.527495i	−0.672612	−	0.739996i	$-0.734827\pi$
$283$	5.12331	−	8.87384i	0.304549	−	0.527495i	0.977161	+	0.212501i	$0.0681608\pi$
$284$	8.63841	+	4.98739i	0.512595	+	0.295947i
$285$	−1.17758			−0.0697539
$286$	3.02470	+	11.7564i	0.178854	+	0.695171i
$287$	−7.05550			−0.416473
$288$	2.56818	+	1.48274i	0.151332	+	0.0873714i
$289$	8.06632	−	13.9713i	0.474490	−	0.821840i
$290$	−4.35396	−	7.54128i	−0.255673	−	0.442839i
$291$			1.05219i			0.0616807i
$292$	11.3442	−	6.54958i	0.663869	−	0.383285i
$293$	−15.5608	+	8.98405i	−0.909073	+	0.524854i	−0.880133	−	0.474728i	$-0.842547\pi$
$293$	−15.5608	+	8.98405i	−0.909073	+	0.524854i	−0.0289403	+	0.999581i	$0.509213\pi$
$294$			2.62682i			0.153199i
$295$	−4.42706	−	7.66789i	−0.257753	−	0.446442i
$296$	4.37154	−	7.57172i	0.254090	−	0.440097i
$297$	−3.23158	−	1.86575i	−0.187515	−	0.108262i
$298$	2.21015			0.128031
$299$	2.57483	−	2.52394i	0.148906	−	0.145963i
$300$	0.767694			0.0443228
$301$	4.27722	+	2.46946i	0.246535	+	0.142337i
$302$	−0.0382813	+	0.0663052i	−0.00220284	+	0.00381544i
$303$	0.560610	+	0.971006i	0.0322062	+	0.0557828i
$304$		−	6.80357i		−	0.390212i
$305$	−7.25766	+	4.19021i	−0.415573	+	0.239931i
$306$	2.39180	−	1.38090i	0.136730	−	0.0789410i
$307$		−	22.4041i		−	1.27867i	−0.768930	−	0.639333i	$-0.779210\pi$
$307$		−	22.4041i		−	1.27867i	0.768930	−	0.639333i	$-0.220790\pi$
$308$	−7.73982	−	13.4058i	−0.441017	−	0.763864i
$309$	−0.270861	+	0.469144i	−0.0154087	+	0.0266887i
$310$	4.52454	+	2.61224i	0.256976	+	0.148365i
$311$	7.11927			0.403696			0.201848	−	0.979417i	$-0.435305\pi$
$311$	7.11927			0.403696			0.201848	+	0.979417i	$0.435305\pi$
$312$	−0.468918	−	0.478372i	−0.0265472	−	0.0270825i
$313$	−1.06576			−0.0602404			−0.0301202	−	0.999546i	$-0.509589\pi$
$313$	−1.06576			−0.0602404			−0.0301202	+	0.999546i	$0.509589\pi$
$314$	9.27613	+	5.35558i	0.523482	+	0.302233i
$315$	−6.35099	+	11.0002i	−0.357838	+	0.619794i
$316$	−1.35553	−	2.34784i	−0.0762544	−	0.132077i
$317$		−	26.1585i		−	1.46921i	−0.678497	−	0.734603i	$-0.737368\pi$
$317$		−	26.1585i		−	1.46921i	0.678497	−	0.734603i	$-0.262632\pi$
$318$	−0.986801	+	0.569730i	−0.0553371	+	0.0319489i
$319$	−27.2540	+	15.7351i	−1.52593	+	0.880995i
$320$		−	0.931614i		−	0.0520788i
$321$	1.04634	+	1.81232i	0.0584012	+	0.101154i
$322$	−2.29885	+	3.98172i	−0.128110	+	0.221893i
$323$	−5.48739	−	3.16815i	−0.305327	−	0.176280i
$324$	−8.69054			−0.482808
$325$	14.3516	+	3.99944i	0.796085	+	0.221849i
$326$	19.8718			1.10060
$327$	−1.60365	−	0.925867i	−0.0886820	−	0.0512006i
$328$	−0.767286	+	1.32898i	−0.0423663	+	0.0733806i
$329$	−22.4276	−	38.8458i	−1.23648	−	2.14164i
$330$			0.582740i			0.0320788i
$331$	1.97362	−	1.13947i	0.108480	−	0.0626310i	−0.444778	−	0.895641i	$-0.646718\pi$
$331$	1.97362	−	1.13947i	0.108480	−	0.0626310i	0.553258	+	0.833010i	$0.313384\pi$
$332$	−5.62660	+	3.24852i	−0.308800	+	0.178286i
$333$			25.9274i			1.42081i
$334$	7.64025	+	13.2333i	0.418056	+	0.724094i
$335$	2.26107	−	3.91629i	0.123536	−	0.213970i
$336$	0.739756	+	0.427098i	0.0403570	+	0.0233001i
$337$	−7.83952			−0.427046			−0.213523	−	0.976938i	$-0.568494\pi$
$337$	−7.83952			−0.427046			−0.213523	+	0.976938i	$0.568494\pi$
$338$	−6.27400	−	11.3858i	−0.341261	−	0.619307i
$339$	3.11754			0.169322
$340$	−0.751389	−	0.433815i	−0.0407498	−	0.0235269i
$341$	9.44057	−	16.3515i	0.511235	−	0.885486i
$342$	10.0879	+	17.4728i	0.545493	+	0.944822i
$343$		−	32.8220i		−	1.77222i
$344$	0.930297	−	0.537107i	0.0501583	−	0.0289589i
$345$	0.149894	−	0.0865414i	0.00807003	−	0.00465923i
$346$			8.70854i			0.468174i
$347$	2.19018	+	3.79350i	0.117575	+	0.203646i	0.918806	−	0.394709i	$-0.129155\pi$
$347$	2.19018	+	3.79350i	0.117575	+	0.203646i	−0.801231	+	0.598355i	$0.795821\pi$
$348$	0.868292	−	1.50393i	0.0465453	−	0.0806189i
$349$	−21.9366	−	12.6651i	−1.17424	−	0.677948i	−0.219565	−	0.975598i	$-0.570464\pi$
$349$	−21.9366	−	12.6651i	−1.17424	−	0.677948i	−0.954675	+	0.297650i	$0.903797\pi$
$350$	−18.9981			−1.01549
$351$	3.84941	+	1.07273i	0.205466	+	0.0572583i
$352$	−3.36683			−0.179453
$353$	19.4262	+	11.2157i	1.03395	+	0.596954i	0.918115	−	0.396314i	$-0.129711\pi$
$353$	19.4262	+	11.2157i	1.03395	+	0.596954i	0.115840	+	0.993268i	$0.463044\pi$
$354$	0.882870	−	1.52918i	0.0469240	−	0.0812748i
$355$	4.64632	+	8.04767i	0.246601	+	0.427126i
$356$		−	6.72233i		−	0.356283i
$357$	0.688948	−	0.397764i	0.0364630	−	0.0210519i
$358$	22.1038	−	12.7616i	1.16822	−	0.674473i
$359$			18.4969i			0.976232i	0.872779	+	0.488116i	$0.162316\pi$
$359$			18.4969i			0.976232i	−0.872779	+	0.488116i	$0.837684\pi$
$360$	1.38134	+	2.39256i	0.0728032	+	0.126099i
$361$	13.6443	−	23.6326i	0.718121	−	1.24382i
$362$	11.2685	+	6.50590i	0.592261	+	0.341942i
$363$	0.0623371			0.00327185
$364$	11.6043	+	11.8383i	0.608231	+	0.620494i
$365$	12.2034			0.638753
$366$	−1.44737	−	0.835637i	−0.0756550	−	0.0436794i
$367$	−14.9564	+	25.9052i	−0.780715	+	1.35224i	0.150810	+	0.988563i	$0.451812\pi$
$367$	−14.9564	+	25.9052i	−0.780715	+	1.35224i	−0.931526	+	0.363676i	$0.881522\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$		−	4.55075i		−	0.236903i
$370$	7.05393	−	4.07259i	0.366716	−	0.211724i
$371$	24.4204	−	14.0991i	1.26784	−	0.731989i
$372$			1.04190i			0.0540198i
$373$	−1.35010	−	2.33845i	−0.0699057	−	0.121080i	0.828954	−	0.559317i	$-0.188937\pi$
$373$	−1.35010	−	2.33845i	−0.0699057	−	0.121080i	−0.898860	+	0.438237i	$0.855603\pi$
$374$	−1.56779	+	2.71550i	−0.0810687	+	0.140415i
$375$	1.36885	+	0.790304i	0.0706869	+	0.0408111i
$376$	−9.75604			−0.503129
$377$	24.0672	−	23.5916i	1.23953	−	1.21503i
$378$	−5.09569			−0.262094
$379$	−14.3272	−	8.27181i	−0.735938	−	0.424894i	0.0846524	−	0.996411i	$-0.473022\pi$
$379$	−14.3272	−	8.27181i	−0.735938	−	0.424894i	−0.820591	+	0.571516i	$0.806355\pi$
$380$	3.16915	−	5.48913i	0.162574	−	0.281587i
$381$	−1.20094	−	2.08009i	−0.0615262	−	0.106566i
$382$			0.724759i			0.0370819i
$383$	−13.0948	+	7.56030i	−0.669114	+	0.386313i	−0.795741	−	0.605637i	$-0.792918\pi$
$383$	−13.0948	+	7.56030i	−0.669114	+	0.386313i	0.126627	+	0.991950i	$0.459585\pi$
$384$	0.160897	−	0.0928940i	0.00821075	−	0.00474048i
$385$		−	14.4211i		−	0.734965i
$386$	10.4602	+	18.1176i	0.532411	+	0.922163i
$387$	−1.59278	+	2.75878i	−0.0809657	+	0.140237i
$388$	−4.90466	−	2.83171i	−0.248996	−	0.143758i
$389$	5.24377			0.265870			0.132935	−	0.991125i	$-0.457560\pi$
$389$	5.24377			0.265870			0.132935	+	0.991125i	$0.457560\pi$
$390$	−0.155494	−	0.604376i	−0.00787376	−	0.0306038i
$391$	0.931318			0.0470988
$392$	−12.2446	−	7.06940i	−0.618444	−	0.357059i
$393$	−0.555618	+	0.962359i	−0.0280272	+	0.0485446i
$394$	9.13052	+	15.8145i	0.459989	+	0.796724i
$395$		−	2.52566i		−	0.127080i
$396$	8.64663	−	4.99213i	0.434510	−	0.250864i
$397$	−20.4554	+	11.8099i	−1.02663	+	0.592724i	−0.916017	−	0.401140i	$-0.868614\pi$
$397$	−20.4554	+	11.8099i	−1.02663	+	0.592724i	−0.110611	+	0.993864i	$0.535281\pi$
$398$			10.6499i			0.533831i
$399$	2.90579	+	5.03298i	0.145472	+	0.251964i
$400$	−2.06605	+	3.57850i	−0.103302	+	0.178925i
$401$	30.6608	+	17.7020i	1.53113	+	0.883996i	0.999310	+	0.0371363i	$0.0118236\pi$
$401$	30.6608	+	17.7020i	1.53113	+	0.883996i	0.531816	+	0.846860i	$0.321510\pi$
$402$	0.901832			0.0449793
$403$	−5.42795	+	19.4777i	−0.270385	+	0.970254i
$404$	−6.03495			−0.300250
$405$	−7.01154	−	4.04811i	−0.348406	−	0.201152i
$406$	−21.4876	+	37.2176i	−1.06641	+	1.84708i
$407$	−14.7182	−	25.4927i	−0.729554	−	1.26363i
$408$		−	0.173028i		−	0.00856615i
$409$	−30.9710	+	17.8811i	−1.53142	+	0.884163i	−0.532119	+	0.846670i	$0.678604\pi$
$409$	−30.9710	+	17.8811i	−1.53142	+	0.884163i	−0.999297	+	0.0374933i	$0.988063\pi$
$410$	−1.23810	+	0.714815i	−0.0611452	+	0.0353022i
$411$			2.06459i			0.101839i
$412$	−1.45790	−	2.52516i	−0.0718257	−	0.124406i
$413$	−21.8484	+	37.8425i	−1.07509	+	1.86211i
$414$	−2.56818	−	1.48274i	−0.126219	−	0.0728728i
$415$	−6.05274			−0.297117
$416$	3.49183	−	0.898382i	0.171201	−	0.0440468i
$417$	−1.97772			−0.0968495
$418$	−19.8376	−	11.4532i	−0.970288	−	0.560196i
$419$	−4.43283	+	7.67789i	−0.216558	+	0.375089i	−0.953753	−	0.300590i	$-0.902816\pi$
$419$	−4.43283	+	7.67789i	−0.216558	+	0.375089i	0.737195	+	0.675680i	$0.236150\pi$
$420$	0.397891	+	0.689167i	0.0194151	+	0.0336279i
$421$		−	11.7495i		−	0.572636i	−0.958135	−	0.286318i	$-0.907569\pi$
$421$		−	11.7495i		−	0.572636i	0.958135	−	0.286318i	$-0.0924313\pi$
$422$	−0.986076	+	0.569311i	−0.0480014	+	0.0277136i
$423$	25.0553	−	14.4657i	1.21823	−	0.703346i
$424$		−	6.13312i		−	0.297851i
$425$	1.92415	+	3.33272i	0.0933349	+	0.161661i
$426$	−0.926597	+	1.60491i	−0.0448938	+	0.0777583i
$427$	35.8179	+	20.6795i	1.73335	+	1.00075i
$428$	−11.2639			−0.544459
$429$	−2.18420	+	0.561952i	−0.105454	+	0.0271313i
$430$	1.00075			0.0482606
$431$	16.9054	+	9.76035i	0.814306	+	0.470140i	0.848449	−	0.529277i	$-0.177537\pi$
$431$	16.9054	+	9.76035i	0.814306	+	0.470140i	−0.0341432	+	0.999417i	$0.510870\pi$
$432$	−0.554158	+	0.959829i	−0.0266619	+	0.0461798i
$433$	−4.59001	−	7.95013i	−0.220582	−	0.382059i	0.734403	−	0.678714i	$-0.237462\pi$
$433$	−4.59001	−	7.95013i	−0.220582	−	0.382059i	−0.954985	+	0.296655i	$0.904129\pi$
$434$		−	25.7838i		−	1.23766i
$435$	1.40108	−	0.808913i	0.0671766	−	0.0387844i
$436$	8.63161	−	4.98346i	0.413379	−	0.238664i
$437$			6.80357i			0.325459i
$438$	1.21683	+	2.10762i	0.0581425	+	0.100706i
$439$	3.54694	−	6.14348i	0.169286	−	0.293212i	−0.768883	−	0.639390i	$-0.779187\pi$
$439$	3.54694	−	6.14348i	0.169286	−	0.293212i	0.938169	+	0.346177i	$0.112520\pi$
$440$	−2.71636	−	1.56829i	−0.129497	−	0.0747654i
$441$	41.9284			1.99659
$442$	0.901419	−	3.23466i	0.0428761	−	0.153857i
$443$	−9.68048			−0.459934			−0.229967	−	0.973198i	$-0.573862\pi$
$443$	−9.68048			−0.459934			−0.229967	+	0.973198i	$0.573862\pi$
$444$	1.40673	+	0.812179i	0.0667607	+	0.0385443i
$445$	3.13131	−	5.42359i	0.148438	−	0.257103i
$446$	−3.35310	−	5.80774i	−0.158774	−	0.275005i
$447$			0.410620i			0.0194217i
$448$	−3.98172	+	2.29885i	−0.188119	+	0.108610i
$449$	−28.2676	+	16.3203i	−1.33403	+	0.770203i	−0.985915	−	0.167249i	$-0.946512\pi$
$449$	−28.2676	+	16.3203i	−1.33403	+	0.770203i	−0.348115	+	0.937452i	$0.613178\pi$
$450$		−	12.2537i		−	0.577643i
$451$	2.58332	+	4.47444i	0.121644	+	0.210693i
$452$	−8.39006	+	14.5320i	−0.394635	+	0.683528i
$453$	−0.0123187	−	0.00711221i	−0.000578784	−	0.000334161i
$454$	−23.3809			−1.09732
$455$	3.84802	+	14.9565i	0.180398	+	0.701172i
$456$	1.26402			0.0591933
$457$	−33.4141	−	19.2916i	−1.56305	−	0.902425i	−0.996947	−	0.0780875i	$-0.975119\pi$
$457$	−33.4141	−	19.2916i	−1.56305	−	0.902425i	−0.566099	−	0.824337i	$-0.691548\pi$
$458$	8.57470	−	14.8518i	0.400669	−	0.693980i
$459$	0.516097	+	0.893906i	0.0240893	+	0.0417240i
$460$			0.931614i			0.0434367i
$461$	−6.02606	+	3.47915i	−0.280661	+	0.162040i	−0.633723	−	0.773560i	$-0.718474\pi$
$461$	−6.02606	+	3.47915i	−0.280661	+	0.162040i	0.353061	+	0.935600i	$0.385141\pi$
$462$	2.49063	−	1.43797i	0.115875	−	0.0669002i
$463$		−	36.8005i		−	1.71026i	−0.518411	−	0.855132i	$-0.673476\pi$
$463$		−	36.8005i		−	1.71026i	0.518411	−	0.855132i	$-0.326524\pi$
$464$	4.67356	+	8.09485i	0.216965	+	0.375794i
$465$	−0.485323	+	0.840604i	−0.0225063	+	0.0389821i
$466$	3.00520	+	1.73506i	0.139213	+	0.0803749i
$467$	6.06650			0.280724			0.140362	−	0.990100i	$-0.455173\pi$
$467$	6.06650			0.280724			0.140362	+	0.990100i	$0.455173\pi$
$468$	−7.63560	+	7.48470i	−0.352956	+	0.345980i
$469$	−22.3176			−1.03053
$470$	−7.87119	−	4.54443i	−0.363071	−	0.209619i
$471$	−0.995002	+	1.72339i	−0.0458473	+	0.0794098i
$472$	4.75203	+	8.23076i	0.218730	+	0.378851i
$473$		−	3.61670i		−	0.166296i
$474$	0.436201	−	0.251841i	0.0200354	−	0.0115674i
$475$	−24.3466	+	14.0565i	−1.11710	+	0.644957i
$476$			4.28192i			0.196261i
$477$	9.09383	+	15.7510i	0.416378	+	0.721188i
$478$	−1.40675	+	2.43656i	−0.0643432	+	0.111446i
$479$	24.5871	+	14.1954i	1.12342	+	0.648604i	0.942271	−	0.334852i	$-0.108686\pi$
$479$	24.5871	+	14.1954i	1.12342	+	0.648604i	0.181145	+	0.983456i	$0.442020\pi$
$480$	0.173083			0.00790011
$481$	22.0670	+	22.5119i	1.00617	+	1.02645i
$482$	−24.0143			−1.09382
$483$	−0.739756	−	0.427098i	−0.0336601	−	0.0194336i
$484$	−0.167764	+	0.290576i	−0.00762564	+	0.0132080i
$485$	−2.63806	−	4.56925i	−0.119788	−	0.207479i
$486$		−	4.93954i		−	0.224062i
$487$	−6.26791	+	3.61878i	−0.284026	+	0.163983i	−0.635245	−	0.772311i	$-0.719101\pi$
$487$	−6.26791	+	3.61878i	−0.284026	+	0.163983i	0.351219	+	0.936294i	$0.385767\pi$
$488$	7.79041	−	4.49780i	0.352655	−	0.203606i
$489$			3.69194i			0.166955i
$490$	−6.58595	−	11.4072i	−0.297523	−	0.515325i
$491$	15.4442	−	26.7501i	0.696985	−	1.20721i	−0.272522	−	0.962150i	$-0.587858\pi$
$491$	15.4442	−	26.7501i	0.696985	−	1.20721i	0.969507	−	0.245064i	$-0.0788090\pi$
$492$	−0.246908	−	0.142553i	−0.0111315	−	0.00642677i
$493$	8.70515			0.392060
$494$	23.6302	+	6.58515i	1.06317	+	0.296280i
$495$	9.30149			0.418071
$496$	−4.85666	−	2.80399i	−0.218071	−	0.125903i
$497$	22.9305	−	39.7168i	1.02857	−	1.78154i
$498$	−0.603536	−	1.04536i	−0.0270451	−	0.0468435i
$499$			6.00635i			0.268881i	0.990922	+	0.134441i	$0.0429238\pi$
$499$			6.00635i			0.268881i	−0.990922	+	0.134441i	$0.957076\pi$
$500$	−7.36779	+	4.25380i	−0.329498	+	0.190236i
$501$	−2.45859	+	1.41947i	−0.109842	+	0.0634171i
$502$		−	0.784363i		−	0.0350078i
$503$	15.3353	+	26.5615i	0.683766	+	1.18432i	0.973823	+	0.227308i	$0.0729924\pi$
$503$	15.3353	+	26.5615i	0.683766	+	1.18432i	−0.290057	+	0.957009i	$0.593674\pi$
$504$	6.81719	−	11.8077i	0.303662	−	0.525958i
$505$	−4.86901	−	2.81112i	−0.216668	−	0.125093i
$506$	3.36683			0.149674
$507$	2.11535	−	1.16563i	0.0939459	−	0.0517676i
$508$	12.9281			0.573592
$509$	−20.6506	−	11.9227i	−0.915324	−	0.528462i	−0.0331836	−	0.999449i	$-0.510565\pi$
$509$	−20.6506	−	11.9227i	−0.915324	−	0.528462i	−0.882140	+	0.470987i	$0.843898\pi$
$510$	0.0805976	−	0.139599i	0.00356892	−	0.00618155i
$511$	−30.1130	−	52.1572i	−1.33212	−	2.30730i
$512$			1.00000i			0.0441942i
$513$	−6.53027	+	3.77025i	−0.288318	+	0.166461i
$514$	1.32160	−	0.763027i	0.0582933	−	0.0336557i
$515$		−	2.71640i		−	0.119699i
$516$	0.0997881	+	0.172838i	0.00439293	+	0.00760877i
$517$	−16.4235	+	28.4463i	−0.722303	+	1.25106i
$518$	−34.8125	−	20.0990i	−1.52957	−	0.883099i
$519$	−1.61794			−0.0710198
$520$	3.23569	+	0.901706i	0.141894	+	0.0395424i
$521$	−0.0678549			−0.00297278			−0.00148639	−	0.999999i	$-0.500473\pi$
$521$	−0.0678549			−0.00297278			−0.00148639	+	0.999999i	$0.500473\pi$
$522$	−24.0051	−	13.8594i	−1.05068	−	0.606608i
$523$	−22.3100	+	38.6421i	−0.975550	+	1.68970i	−0.297442	+	0.954740i	$0.596133\pi$
$523$	−22.3100	+	38.6421i	−0.975550	+	1.68970i	−0.678108	+	0.734962i	$0.737200\pi$
$524$	−2.99060	−	5.17988i	−0.130645	−	0.226284i
$525$		−	3.52962i		−	0.154045i
$526$	5.04589	−	2.91324i	0.220011	−	0.127023i
$527$	−4.52310	+	2.61141i	−0.197029	+	0.113755i
$528$		−	0.625516i		−	0.0272221i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	2.85685	−	4.94821i	0.124094	−	0.214937i
$531$	−24.4082	−	14.0921i	−1.05922	−	0.611543i
$532$	−31.2808			−1.35619
$533$	−3.87317	−	3.95126i	−0.167766	−	0.171148i
$534$	1.24893			0.0540464
$535$	−9.08769	−	5.24678i	−0.392895	−	0.226838i
$536$	−2.42705	+	4.20377i	−0.104832	+	0.181575i
$537$	2.37096	+	4.10662i	0.102314	+	0.177214i
$538$			14.7988i			0.638021i
$539$	−41.2253	+	23.8014i	−1.77570	+	1.02520i
$540$	−0.894190	+	0.516261i	−0.0384798	+	0.0222163i
$541$		−	15.8698i		−	0.682295i	−0.940010	−	0.341148i	$-0.889184\pi$
$541$		−	15.8698i		−	0.682295i	0.940010	−	0.341148i	$-0.110816\pi$
$542$	−10.5272	−	18.2337i	−0.452182	−	0.783203i
$543$	−1.20872	+	2.09356i	−0.0518710	+	0.0898433i
$544$	0.806545	+	0.465659i	0.0345803	+	0.0199650i
$545$	9.28533			0.397740
$546$	−2.19941	+	2.15594i	−0.0941260	+	0.0922657i
$547$	32.0177			1.36898			0.684490	−	0.729022i	$-0.260025\pi$
$547$	32.0177			1.36898			0.684490	+	0.729022i	$0.260025\pi$
$548$	−9.62382	−	5.55632i	−0.411109	−	0.237354i
$549$	−13.3381	+	23.1023i	−0.569258	+	0.985984i
$550$	6.95603	+	12.0482i	0.296606	+	0.513737i
$551$			63.5939i			2.70919i
$552$	−0.160897	+	0.0928940i	−0.00684824	+	0.00395383i
$553$	−10.7947	+	6.23231i	−0.459036	+	0.265025i
$554$		−	22.0194i		−	0.935517i
$555$	0.756637	+	1.31053i	0.0321175	+	0.0556291i
$556$	5.32253	−	9.21889i	0.225725	−	0.390968i
$557$	11.8284	+	6.82913i	0.501185	+	0.289359i	0.729203	−	0.684298i	$-0.239891\pi$
$557$	11.8284	+	6.82913i	0.501185	+	0.289359i	−0.228018	+	0.973657i	$0.573224\pi$
$558$	16.6304			0.704021
$559$	0.965055	+	3.75098i	0.0408175	+	0.158650i
$560$	−4.28328			−0.181002
$561$	−0.504507	−	0.291277i	−0.0213003	−	0.0122977i
$562$	−4.26635	+	7.38953i	−0.179965	+	0.311709i
$563$	−20.0183	−	34.6727i	−0.843671	−	1.46128i	−0.886770	−	0.462210i	$-0.847057\pi$
$563$	−20.0183	−	34.6727i	−0.843671	−	1.46128i	0.0430995	−	0.999071i	$-0.486277\pi$
$564$		−	1.81255i		−	0.0763223i
$565$	−13.5382	+	7.81630i	−0.569557	+	0.328834i
$566$	−8.87384	+	5.12331i	−0.372995	+	0.215349i
$567$			39.9564i			1.67801i
$568$	−4.98739	−	8.63841i	−0.209266	−	0.362460i
$569$	−9.53431	+	16.5139i	−0.399699	+	0.692299i	−0.993689	−	0.112174i	$-0.964219\pi$
$569$	−9.53431	+	16.5139i	−0.399699	+	0.692299i	0.593989	+	0.804473i	$0.297552\pi$
$570$	1.01982	+	0.588791i	0.0427154	+	0.0246617i
$571$	20.7997			0.870442			0.435221	−	0.900324i	$-0.356670\pi$
$571$	20.7997			0.870442			0.435221	+	0.900324i	$0.356670\pi$
$572$	3.25874	−	11.6937i	0.136255	−	0.488938i
$573$	−0.134651			−0.00562514
$574$	6.11024	+	3.52775i	0.255036	+	0.147245i
$575$	2.06605	−	3.57850i	0.0861601	−	0.149234i
$576$	−1.48274	−	2.56818i	−0.0617809	−	0.107008i
$577$			34.9614i			1.45546i	0.685863	+	0.727731i	$0.259425\pi$
$577$			34.9614i			1.45546i	−0.685863	+	0.727731i	$0.740575\pi$
$578$	−13.9713	+	8.06632i	−0.581129	+	0.335515i
$579$	−3.36604	+	1.94338i	−0.139888	+	0.0807642i
$580$			8.70792i			0.361577i
$581$	14.9357	+	25.8694i	0.619637	+	1.07324i
$582$	0.526097	−	0.911227i	0.0218074	−	0.0377716i
$583$	−17.8827	−	10.3246i	−0.740626	−	0.427600i
$584$	−13.0992			−0.542047
$585$	−9.64684	+	2.48195i	−0.398848	+	0.102616i
$586$	17.9681			0.742255
$587$	12.9709	+	7.48873i	0.535365	+	0.309093i	0.743198	−	0.669071i	$-0.233308\pi$
$587$	12.9709	+	7.48873i	0.535365	+	0.309093i	−0.207834	+	0.978164i	$0.566641\pi$
$588$	1.31341	−	2.27489i	0.0541641	−	0.0938150i
$589$	−19.0772	−	33.0426i	−0.786062	−	1.36150i
$590$			8.85412i			0.364518i
$591$	−2.93815	+	1.69634i	−0.120859	+	0.0697782i
$592$	−7.57172	+	4.37154i	−0.311196	+	0.179669i
$593$			10.9637i			0.450227i	0.974333	+	0.225113i	$0.0722753\pi$
$593$			10.9637i			0.450227i	−0.974333	+	0.225113i	$0.927725\pi$
$594$	1.86575	+	3.23158i	0.0765528	+	0.132593i
$595$	−1.99455	+	3.45466i	−0.0817685	+	0.141627i
$596$	−1.91405	−	1.10508i	−0.0784025	−	0.0452657i
$597$	−1.97862			−0.0809797
$598$	−3.49183	+	0.898382i	−0.142792	+	0.0367376i
$599$	−18.6340			−0.761366			−0.380683	−	0.924706i	$-0.624311\pi$
$599$	−18.6340			−0.761366			−0.380683	+	0.924706i	$0.624311\pi$
$600$	−0.664842	−	0.383847i	−0.0271421	−	0.0156705i
$601$	12.0526	−	20.8758i	0.491638	−	0.851541i	−0.508316	−	0.861171i	$-0.669732\pi$
$601$	12.0526	−	20.8758i	0.491638	−	0.851541i	0.999954	+	0.00962921i	$0.00306512\pi$
$602$	−2.46946	−	4.27722i	−0.100648	−	0.174327i
$603$		−	14.3947i		−	0.586199i
$604$	0.0663052	−	0.0382813i	0.00269792	−	0.00155765i
$605$	−0.270705	+	0.156291i	−0.0110057	+	0.00635415i
$606$		−	1.12122i		−	0.0455465i
$607$	2.47781	+	4.29170i	0.100571	+	0.174195i	0.911920	−	0.410368i	$-0.134600\pi$
$607$	2.47781	+	4.29170i	0.100571	+	0.174195i	−0.811349	+	0.584562i	$0.801266\pi$
$608$	−3.40179	+	5.89207i	−0.137961	+	0.238955i
$609$	−6.91459	−	3.99214i	−0.280193	−	0.161770i
$610$	8.38043			0.339314
$611$	9.44283	−	33.8848i	0.382016	−	1.37083i
$612$	−2.76181			−0.111639
$613$	41.1190	+	23.7400i	1.66078	+	0.958851i	0.972344	+	0.233553i	$0.0750353\pi$
$613$	41.1190	+	23.7400i	1.66078	+	0.958851i	0.688435	+	0.725298i	$0.258298\pi$
$614$	−11.2020	+	19.4025i	−0.452077	+	0.783020i
$615$	−0.132804	−	0.230023i	−0.00535518	−	0.00927544i
$616$			15.4796i			0.623693i
$617$	32.1053	−	18.5360i	1.29251	−	0.746231i	0.313412	−	0.949617i	$-0.398528\pi$
$617$	32.1053	−	18.5360i	1.29251	−	0.746231i	0.979099	+	0.203386i	$0.0651946\pi$
$618$	0.469144	−	0.270861i	0.0188718	−	0.0108956i
$619$		−	32.5360i		−	1.30773i	−0.756611	−	0.653866i	$-0.773146\pi$
$619$		−	32.5360i		−	1.30773i	0.756611	−	0.653866i	$-0.226854\pi$
$620$	−2.61224	−	4.52454i	−0.104910	−	0.181710i
$621$	0.554158	−	0.959829i	0.0222376	−	0.0385166i
$622$	−6.16546	−	3.55963i	−0.247213	−	0.142728i
$623$	−30.9072			−1.23827
$624$	0.166909	+	0.648741i	0.00668169	+	0.0259704i
$625$	12.7347			0.509387
$626$	0.922977	+	0.532881i	0.0368896	+	0.0212982i
$627$	2.12787	−	3.68558i	0.0849790	−	0.147188i
$628$	−5.35558	−	9.27613i	−0.213711	−	0.370158i
$629$			8.14258i			0.324666i
$630$	11.0002	−	6.35099i	0.438260	−	0.253030i
$631$	8.65720	−	4.99824i	0.344638	−	0.198977i	−0.317683	−	0.948197i	$-0.602905\pi$
$631$	8.65720	−	4.99824i	0.344638	−	0.198977i	0.662321	+	0.749220i	$0.269572\pi$
$632$			2.71106i			0.107840i
$633$	−0.105771	−	0.183201i	−0.00420403	−	0.00728159i
$634$	−13.0792	+	22.6539i	−0.519443	+	0.899701i
$635$	10.4304	+	6.02200i	0.413918	+	0.238976i
$636$	1.13946			0.0451825
$637$	36.4050	−	35.6855i	1.44242	−	1.41391i
$638$	31.4702			1.24592
$639$	25.6171	+	14.7900i	1.01339	+	0.585084i
$640$	−0.465807	+	0.806802i	−0.0184126	+	0.0318916i
$641$	14.0752	+	24.3790i	0.555938	+	0.962913i	0.997830	+	0.0658450i	$0.0209743\pi$
$641$	14.0752	+	24.3790i	0.555938	+	0.962913i	−0.441892	+	0.897068i	$0.645692\pi$
$642$		−	2.09269i		−	0.0825918i
$643$	19.4660	−	11.2387i	0.767664	−	0.443211i	−0.0643764	−	0.997926i	$-0.520506\pi$
$643$	19.4660	−	11.2387i	0.767664	−	0.443211i	0.832041	+	0.554714i	$0.187172\pi$
$644$	3.98172	−	2.29885i	0.156902	−	0.0905873i
$645$			0.185928i			0.00732091i
$646$	3.16815	+	5.48739i	0.124649	+	0.215898i
$647$	17.5083	−	30.3252i	0.688321	−	1.19221i	−0.284059	−	0.958807i	$-0.591681\pi$
$647$	17.5083	−	30.3252i	0.688321	−	1.19221i	0.972381	−	0.233401i	$-0.0749854\pi$
$648$	7.52623	+	4.34527i	0.295658	+	0.170698i
$649$	31.9985			1.25605
$650$	−10.4292	−	10.6394i	−0.409065	−	0.417313i
$651$	4.79032			0.187748
$652$	−17.2095	−	9.93590i	−0.673975	−	0.389120i
$653$	−22.8877	+	39.6427i	−0.895666	+	1.55134i	−0.0626879	+	0.998033i	$0.519967\pi$
$653$	−22.8877	+	39.6427i	−0.895666	+	1.55134i	−0.832978	+	0.553306i	$0.813366\pi$
$654$	0.925867	+	1.60365i	0.0362043	+	0.0627076i
$655$		−	5.57218i		−	0.217723i
$656$	1.32898	−	0.767286i	0.0518879	−	0.0299575i
$657$	33.6410	−	19.4227i	1.31246	−	0.757750i
$658$			44.8553i			1.74864i
$659$	−8.03364	−	13.9147i	−0.312946	−	0.542039i	0.666053	−	0.745905i	$-0.267983\pi$
$659$	−8.03364	−	13.9147i	−0.312946	−	0.542039i	−0.978999	+	0.203866i	$0.934649\pi$
$660$	0.291370	−	0.504667i	0.0113416	−	0.0196442i
$661$	−25.8895	−	14.9473i	−1.00698	−	0.581382i	−0.0966767	−	0.995316i	$-0.530821\pi$
$661$	−25.8895	−	14.9473i	−1.00698	−	0.581382i	−0.910307	+	0.413933i	$0.864155\pi$
$662$	−2.27894			−0.0885737
$663$	0.600961	+	0.167473i	0.0233394	+	0.00650411i
$664$	6.49704			0.252134
$665$	−25.2374	−	14.5708i	−0.978663	−	0.565031i
$666$	12.9637	−	22.4538i	0.502334	−	0.870068i
$667$	−4.67356	−	8.09485i	−0.180961	−	0.313434i
$668$		−	15.2805i		−	0.591221i
$669$	1.07901	−	0.622966i	0.0417169	−	0.0240853i
$670$	−3.91629	+	2.26107i	−0.151300	+	0.0873528i
$671$		−	30.2866i		−	1.16920i
$672$	−0.427098	−	0.739756i	−0.0164757	−	0.0285367i
$673$	7.61605	−	13.1914i	0.293577	−	0.508491i	−0.681076	−	0.732213i	$-0.738488\pi$
$673$	7.61605	−	13.1914i	0.293577	−	0.508491i	0.974653	+	0.223722i	$0.0718209\pi$
$674$	6.78922	+	3.91976i	0.261511	+	0.150984i
$675$	4.57966			0.176271
$676$	−0.259466	+	12.9974i	−0.00997945	+	0.499900i
$677$	−17.0655			−0.655881			−0.327941	−	0.944698i	$-0.606355\pi$
$677$	−17.0655			−0.655881			−0.327941	+	0.944698i	$0.606355\pi$
$678$	−2.69987	−	1.55877i	−0.103688	−	0.0598643i
$679$	−13.0193	+	22.5501i	−0.499636	+	0.865394i
$680$	0.433815	+	0.751389i	0.0166360	+	0.0288145i
$681$		−	4.34389i		−	0.166458i
$682$	−16.3515	+	9.44057i	−0.626133	+	0.361498i
$683$	38.0096	−	21.9448i	1.45440	−	0.839695i	0.455669	−	0.890149i	$-0.349400\pi$
$683$	38.0096	−	21.9448i	1.45440	−	0.839695i	0.998726	+	0.0504539i	$0.0160668\pi$
$684$		−	20.1759i		−	0.771444i
$685$	−5.17635	−	8.96569i	−0.197778	−	0.342562i
$686$	−16.4110	+	28.4247i	−0.626575	+	1.08526i
$687$	2.75929	+	1.59308i	0.105273	+	0.0607796i
$688$	−1.07421			−0.0409541
$689$	21.3016	+	5.93622i	0.811526	+	0.226152i
$690$	−0.173083			−0.00658915
$691$	27.9512	+	16.1376i	1.06331	+	0.613905i	0.926347	−	0.376671i	$-0.122931\pi$
$691$	27.9512	+	16.1376i	1.06331	+	0.613905i	0.136967	+	0.990576i	$0.456264\pi$
$692$	4.35427	−	7.54182i	0.165525	−	0.286697i
$693$	−22.9523	−	39.7546i	−0.871886	−	1.51015i
$694$		−	4.38036i		−	0.166276i
$695$	8.58845	−	4.95854i	0.325778	−	0.188088i
$696$	−1.50393	+	0.868292i	−0.0570062	+	0.0329125i
$697$		−	1.42918i		−	0.0541339i
$698$	12.6651	+	21.9366i	0.479382	+	0.830313i
$699$	−0.322352	+	0.558331i	−0.0121925	+	0.0211180i
$700$	16.4528	+	9.49906i	0.621859	+	0.359031i
$701$	0.905975			0.0342182			0.0171091	−	0.999854i	$-0.494554\pi$
$701$	0.905975			0.0342182			0.0171091	+	0.999854i	$0.494554\pi$
$702$	−2.79732	−	2.85372i	−0.105578	−	0.107707i
$703$	−59.4841			−2.24349
$704$	2.91576	+	1.68341i	0.109892	+	0.0634460i
$705$	0.844301	−	1.46237i	0.0317982	−	0.0550761i
$706$	−11.2157	−	19.4262i	−0.422110	−	0.731117i
$707$			27.7468i			1.04353i
$708$	−1.52918	+	0.882870i	−0.0574700	+	0.0331803i
$709$	1.65110	−	0.953261i	0.0620082	−	0.0358005i	−0.468675	−	0.883370i	$-0.655269\pi$
$709$	1.65110	−	0.953261i	0.0620082	−	0.0358005i	0.530684	+	0.847570i	$0.321935\pi$
$710$		−	9.29264i		−	0.348747i
$711$	−4.01980	−	6.96249i	−0.150754	−	0.261114i
$712$	−3.36116	+	5.82171i	−0.125965	+	0.218178i
$713$	4.85666	+	2.80399i	0.181883	+	0.105010i
$714$	−0.795529			−0.0297719
$715$	8.07616	−	7.91655i	0.302031	−	0.296062i
$716$	−25.5233			−0.953849
$717$	−0.452683	−	0.261357i	−0.0169058	−	0.00976055i
$718$	9.24847	−	16.0188i	0.345150	−	0.597817i
$719$	3.88449	+	6.72813i	0.144867	+	0.250917i	0.929323	−	0.369267i	$-0.120391\pi$
$719$	3.88449	+	6.72813i	0.144867	+	0.250917i	−0.784456	+	0.620184i	$0.787058\pi$
$720$		−	2.76269i		−	0.102959i
$721$	−11.6099	+	6.70299i	−0.432376	+	0.249632i
$722$	−23.6326	+	13.6443i	−0.879515	+	0.507788i
$723$		−	4.46156i		−	0.165927i
$724$	−6.50590	−	11.2685i	−0.241790	−	0.418792i
$725$	19.3116	−	33.4487i	0.717215	−	1.24225i
$726$	−0.0539855	−	0.0311685i	−0.00200359	−	0.00115677i
$727$	2.07837			0.0770824			0.0385412	−	0.999257i	$-0.487729\pi$
$727$	2.07837			0.0770824			0.0385412	+	0.999257i	$0.487729\pi$
$728$	−4.13049	−	16.0544i	−0.153086	−	0.595015i
$729$	−25.1539			−0.931626
$730$	−10.5684	−	6.10168i	−0.391155	−	0.225833i
$731$	−0.500218	+	0.866403i	−0.0185012	+	0.0320451i
$732$	0.835637	+	1.44737i	0.0308860	+	0.0534962i
$733$			16.2092i			0.598701i	0.954143	+	0.299351i	$0.0967700\pi$
$733$			16.2092i			0.598701i	−0.954143	+	0.299351i	$0.903230\pi$
$734$	25.9052	−	14.9564i	0.956177	−	0.552049i
$735$	2.11932	−	1.22359i	0.0781724	−	0.0451328i
$736$		−	1.00000i		−	0.0368605i
$737$	8.17145	+	14.1534i	0.300999	+	0.521346i
$738$	−2.27537	+	3.94106i	−0.0837577	+	0.145073i
$739$	33.7886	+	19.5078i	1.24293	+	0.717608i	0.969690	−	0.244338i	$-0.0785705\pi$
$739$	33.7886	+	19.5078i	1.24293	+	0.717608i	0.273243	+	0.961945i	$0.411904\pi$
$740$	−8.14517			−0.299422
$741$	−1.22344	+	4.39021i	−0.0449443	+	0.161278i
$742$	−28.1982			−1.03519
$743$	−0.284535	−	0.164276i	−0.0104386	−	0.00602672i	0.494772	−	0.869023i	$-0.335252\pi$
$743$	−0.284535	−	0.164276i	−0.0104386	−	0.00602672i	−0.505210	+	0.862996i	$0.668585\pi$
$744$	0.520948	−	0.902309i	0.0190989	−	0.0330803i
$745$	−1.02951	−	1.78316i	−0.0377182	−	0.0653298i
$746$			2.70021i			0.0988616i
$747$	−16.6856	+	9.63343i	−0.610494	+	0.352469i
$748$	2.71550	−	1.56779i	0.0992885	−	0.0573242i
$749$			51.7878i			1.89228i
$750$	−0.790304	−	1.36885i	−0.0288578	−	0.0499832i
$751$	23.3685	−	40.4754i	0.852729	−	1.47697i	−0.0260071	−	0.999662i	$-0.508279\pi$
$751$	23.3685	−	40.4754i	0.852729	−	1.47697i	0.878736	−	0.477308i	$-0.158387\pi$
$752$	8.44898	+	4.87802i	0.308103	+	0.177883i
$753$	0.145725			0.00531052
$754$	−32.6386	+	8.39729i	−1.18863	+	0.305811i
$755$	0.0713269			0.00259585
$756$	4.41300	+	2.54785i	0.160499	+	0.0926643i
$757$	6.54429	−	11.3350i	0.237856	−	0.411979i	−0.722243	−	0.691640i	$-0.756889\pi$
$757$	6.54429	−	11.3350i	0.237856	−	0.411979i	0.960099	+	0.279661i	$0.0902219\pi$
$758$	8.27181	+	14.3272i	0.300446	+	0.520387i
$759$			0.625516i			0.0227048i
$760$	−5.48913	+	3.16915i	−0.199112	+	0.114957i
$761$	−35.6831	+	20.6017i	−1.29351	+	0.746810i	−0.979275	−	0.202535i	$-0.935082\pi$
$761$	−35.6831	+	20.6017i	−1.29351	+	0.746810i	−0.314237	+	0.949345i	$0.601749\pi$
$762$			2.40189i			0.0870112i
$763$	−22.9124	−	39.6855i	−0.829486	−	1.43671i
$764$	0.362379	−	0.627659i	0.0131104	−	0.0227079i
$765$	−2.22823	−	1.28647i	−0.0805619	−	0.0465124i
$766$	15.1206			0.546330
$767$	−33.1866	+	8.53827i	−1.19830	+	0.308299i
$768$	−0.185788			−0.00670405
$769$	−12.2346	−	7.06367i	−0.441192	−	0.254722i	0.262911	−	0.964820i	$-0.415317\pi$
$769$	−12.2346	−	7.06367i	−0.441192	−	0.254722i	−0.704103	+	0.710098i	$0.748651\pi$
$770$	−7.21053	+	12.4890i	−0.259849	+	0.450072i
$771$	0.141761	+	0.245538i	0.00510540	+	0.00884282i
$772$		−	20.9204i		−	0.752943i
$773$	−2.27414	+	1.31297i	−0.0817951	+	0.0472244i	−0.540340	−	0.841447i	$-0.681704\pi$
$773$	−2.27414	+	1.31297i	−0.0817951	+	0.0472244i	0.458545	+	0.888671i	$0.348371\pi$
$774$	2.75878	−	1.59278i	0.0991623	−	0.0572514i
$775$			23.1727i			0.832389i
$776$	2.83171	+	4.90466i	0.101652	+	0.176067i
$777$	3.73415	−	6.46774i	0.133962	−	0.232029i
$778$	−4.54124	−	2.62189i	−0.162811	−	0.0939992i
$779$	10.4406			0.374073
$780$	−0.167526	+	0.601153i	−0.00599840	+	0.0215247i
$781$	−33.5833			−1.20171
$782$	−0.806545	−	0.465659i	−0.0288420	−	0.0166519i
$783$	5.17978	−	8.97164i	0.185110	−	0.320620i
$784$	7.06940	+	12.2446i	0.252479	+	0.437306i
$785$		−	9.97866i		−	0.356154i
$786$	0.962359	−	0.555618i	0.0343262	−	0.0198182i
$787$	−34.1808	+	19.7343i	−1.21841	+	0.703451i	−0.964578	−	0.263797i	$-0.915025\pi$
$787$	−34.1808	+	19.7343i	−1.21841	+	0.703451i	−0.253834	+	0.967248i	$0.581692\pi$
$788$		−	18.2610i		−	0.650523i
$789$	0.541246	+	0.937465i	0.0192689	+	0.0333746i
$790$	−1.26283	+	2.18729i	−0.0449295	+	0.0778201i
$791$	66.8137	+	38.5749i	2.37562	+	1.37157i
$792$	−9.98427			−0.354776
$793$	8.08148	+	31.4111i	0.286982	+	1.11544i
$794$	23.6199			0.838238
$795$	0.919318	+	0.530769i	0.0326049	+	0.0188244i
$796$	5.32495	−	9.22308i	0.188738	−	0.326904i
$797$	9.75133	+	16.8898i	0.345410	+	0.598267i	0.985428	−	0.170092i	$-0.0544066\pi$
$797$	9.75133	+	16.8898i	0.345410	+	0.598267i	−0.640018	+	0.768360i	$0.721073\pi$
$798$		−	5.81159i		−	0.205728i
$799$	7.86869	−	4.54299i	0.278374	−	0.160719i
$800$	3.57850	−	2.06605i	0.126519	−	0.0730458i
$801$		−	19.9349i		−	0.704367i
$802$	−17.7020	−	30.6608i	−0.625080	−	1.08267i
$803$	−22.0513	+	38.1940i	−0.778173	+	1.34784i
$804$	−0.781010	−	0.450916i	−0.0275441	−	0.0159026i
$805$	4.28328			0.150966
$806$	14.4396	−	14.1542i	0.508613	−	0.498561i
$807$	−2.74944			−0.0967847
$808$	5.22642	+	3.01747i	0.183865	+	0.106154i
$809$	2.54265	−	4.40400i	0.0893949	−	0.154837i	−0.817861	−	0.575416i	$-0.804840\pi$
$809$	2.54265	−	4.40400i	0.0893949	−	0.154837i	0.907256	+	0.420580i	$0.138173\pi$
$810$	4.04811	+	7.01154i	0.142236	+	0.246360i
$811$			18.0206i			0.632790i	0.948627	+	0.316395i	$0.102473\pi$
$811$			18.0206i			0.632790i	−0.948627	+	0.316395i	$0.897527\pi$
$812$	37.2176	−	21.4876i	1.30608	−	0.754068i
$813$	3.38759	−	1.95583i	0.118808	−	0.0685939i
$814$			29.4364i			1.03175i
$815$	−9.25643	−	16.0326i	−0.324239	−	0.561598i
$816$	−0.0865139	+	0.149846i	−0.00302859	+	0.00524567i
$817$	−6.32935	−	3.65425i	−0.221436	−	0.127846i
$818$	35.7622			1.25040
$819$	34.4124	+	35.1062i	1.20246	+	1.22671i
$820$	1.42963			0.0499248
$821$	−3.18243	−	1.83738i	−0.111068	−	0.0641250i	0.443437	−	0.896306i	$-0.353759\pi$
$821$	−3.18243	−	1.83738i	−0.111068	−	0.0641250i	−0.554505	+	0.832181i	$0.687092\pi$
$822$	1.03230	−	1.78799i	0.0360055	−	0.0623633i
$823$	17.5423	+	30.3841i	0.611485	+	1.05912i	0.990990	+	0.133934i	$0.0427609\pi$
$823$	17.5423	+	30.3841i	0.611485	+	1.05912i	−0.379505	+	0.925190i	$0.623906\pi$
$824$			2.91580i			0.101577i
$825$	−2.23841	+	1.29235i	−0.0779314	+	0.0449937i
$826$	37.8425	−	21.8484i	1.31671	−	0.760203i
$827$			1.82423i			0.0634346i	0.999497	+	0.0317173i	$0.0100976\pi$
$827$			1.82423i			0.0634346i	−0.999497	+	0.0317173i	$0.989902\pi$
$828$	1.48274	+	2.56818i	0.0515288	+	0.0892505i
$829$	22.8679	−	39.6083i	0.794233	−	1.37565i	−0.129092	−	0.991633i	$-0.541206\pi$
$829$	22.8679	−	39.6083i	0.794233	−	1.37565i	0.923325	−	0.384020i	$-0.125461\pi$
$830$	5.24182	+	3.02637i	0.181946	+	0.105047i
$831$	4.09095			0.141913
$832$	−3.47321	−	0.967896i	−0.120412	−	0.0335558i
$833$	13.1677			0.456234
$834$	1.71276	+	0.988861i	0.0593080	+	0.0342415i
$835$	7.11777	−	12.3283i	0.246321	−	0.426640i
$836$	11.4532	+	19.8376i	0.396118	+	0.686097i
$837$			6.21542i			0.214836i
$838$	7.67789	−	4.43283i	0.265228	−	0.153130i
$839$	10.2455	−	5.91523i	0.353713	−	0.204216i	−0.312606	−	0.949883i	$-0.601202\pi$
$839$	10.2455	−	5.91523i	0.353713	−	0.204216i	0.666319	+	0.745666i	$0.267869\pi$
$840$		−	0.795782i		−	0.0274571i
$841$	−29.1844	−	50.5488i	−1.00636	−	1.74306i
$842$	−5.87475	+	10.1754i	−0.202457	+	0.350666i
$843$	−1.37289	−	0.792636i	−0.0472847	−	0.0272998i
$844$	1.13862			0.0391930
$845$	−6.26362	+	10.3655i	−0.215475	+	0.356583i
$846$	−28.9314			−0.994681
$847$	1.33598	+	0.771328i	0.0459048	+	0.0265031i
$848$	−3.06656	+	5.31144i	−0.105306	+	0.182396i
$849$	−0.951850	−	1.64865i	−0.0326674	−	0.0565816i
$850$		−	3.84829i		−	0.131995i
$851$	7.57172	−	4.37154i	0.259555	−	0.149854i
$852$	1.60491	−	0.926597i	0.0549834	−	0.0317447i
$853$		−	20.9822i		−	0.718416i	−0.933258	−	0.359208i	$-0.883047\pi$
$853$		−	20.9822i		−	0.718416i	0.933258	−	0.359208i	$-0.116953\pi$
$854$	−20.6795	−	35.8179i	−0.707638	−	1.22566i
$855$	9.39807	−	16.2779i	0.321407	−	0.556694i
$856$	9.75478	+	5.63193i	0.333412	+	0.192495i
$857$	21.8764			0.747283			0.373641	−	0.927573i	$-0.378109\pi$
$857$	21.8764			0.747283			0.373641	+	0.927573i	$0.378109\pi$
$858$	2.17255	+	0.605435i	0.0741696	+	0.0206692i
$859$	−7.73002			−0.263745			−0.131872	−	0.991267i	$-0.542099\pi$
$859$	−7.73002			−0.263745			−0.131872	+	0.991267i	$0.542099\pi$
$860$	−0.866678	−	0.500377i	−0.0295535	−	0.0170627i
$861$	−0.655413	+	1.13521i	−0.0223364	+	0.0386878i
$862$	−9.76035	−	16.9054i	−0.332439	−	0.575801i
$863$			25.6702i			0.873823i	0.899505	+	0.436911i	$0.143928\pi$
$863$			25.6702i			0.873823i	−0.899505	+	0.436911i	$0.856072\pi$
$864$	0.959829	−	0.554158i	0.0326540	−	0.0188528i
$865$	7.02607	−	4.05650i	0.238893	−	0.137925i
$866$			9.18001i			0.311950i
$867$	−1.49863	−	2.59570i	−0.0508960	−	0.0881545i
$868$	−12.8919	+	22.3294i	−0.437580	+	0.757911i
$869$	7.90479	+	4.56383i	0.268151	+	0.154817i
$870$	−1.61783			−0.0548495
$871$	−12.2514	−	12.4984i	−0.415124	−	0.423494i
$872$	−9.96692			−0.337523
$873$	−14.5447	−	8.39737i	−0.492263	−	0.284208i
$874$	3.40179	−	5.89207i	0.115067	−	0.199302i
$875$	19.5577	+	33.8748i	0.661169	+	1.14518i
$876$		−	2.43367i		−	0.0822259i
$877$	43.6437	−	25.1977i	1.47374	−	0.850866i	0.474181	−	0.880427i	$-0.342744\pi$
$877$	43.6437	−	25.1977i	1.47374	−	0.850866i	0.999563	+	0.0295610i	$0.00941092\pi$
$878$	−6.14348	+	3.54694i	−0.207333	+	0.119703i
$879$			3.33826i			0.112597i
$880$	1.56829	+	2.71636i	0.0528671	+	0.0915686i
$881$	−7.84484	+	13.5877i	−0.264299	+	0.457780i	−0.967380	−	0.253330i	$-0.918474\pi$
$881$	−7.84484	+	13.5877i	−0.264299	+	0.457780i	0.703080	+	0.711110i	$0.251807\pi$
$882$	−36.3110	−	20.9642i	−1.22266	−	0.705901i
$883$	−29.3676			−0.988299			−0.494150	−	0.869377i	$-0.664521\pi$
$883$	−29.3676			−0.988299			−0.494150	+	0.869377i	$0.664521\pi$
$884$	−2.39798	+	2.35059i	−0.0806529	+	0.0790589i
$885$	−1.64499			−0.0552957
$886$	8.38355	+	4.84024i	0.281651	+	0.162611i
$887$	19.4662	−	33.7165i	0.653611	−	1.13209i	−0.328629	−	0.944459i	$-0.606587\pi$
$887$	19.4662	−	33.7165i	0.653611	−	1.13209i	0.982240	−	0.187629i	$-0.0600801\pi$
$888$	−0.812179	−	1.40673i	−0.0272549	−	0.0472069i
$889$		−	59.4395i		−	1.99354i
$890$	−5.42359	+	3.13131i	−0.181799	+	0.104962i
$891$	25.3395	−	14.6298i	0.848905	−	0.490116i
$892$			6.70621i			0.224540i
$893$	33.1880	+	57.4832i	1.11059	+	1.92360i
$894$	0.205310	−	0.355607i	0.00686660	−	0.0118933i
$895$	−20.5922	−	11.8889i	−0.688322	−	0.397403i
$896$	4.59769			0.153598
$897$	−0.166909	−	0.648741i	−0.00557291	−	0.0216608i
$898$	32.6406			1.08923
$899$	45.3958	+	26.2093i	1.51404	+	0.874129i
$900$	−6.12683	+	10.6120i	−0.204228	+	0.353733i
$901$	2.85594	+	4.94664i	0.0951453	+	0.164796i
$902$		−	5.16664i		−	0.172030i
$903$	0.794657	−	0.458795i	0.0264445	−	0.0152677i
$904$	14.5320	−	8.39006i	0.483327	−	0.279049i
$905$		−	12.1220i		−	0.402948i
$906$	0.00711221	+	0.0123187i	0.000236287	+	0.000409262i
$907$	−16.8542	+	29.1923i	−0.559634	+	0.969315i	0.437892	+	0.899027i	$0.355725\pi$
$907$	−16.8542	+	29.1923i	−0.559634	+	0.969315i	−0.997527	+	0.0702879i	$0.977608\pi$
$908$	20.2485	+	11.6905i	0.671969	+	0.387962i
$909$	−17.8965			−0.593591
$910$	4.14577	−	14.8767i	0.137431	−	0.493158i
$911$	−46.7305			−1.54825			−0.774126	−	0.633032i	$-0.781810\pi$
$911$	−46.7305			−1.54825			−0.774126	+	0.633032i	$0.781810\pi$
$912$	−1.09468	−	0.632011i	−0.0362483	−	0.0209280i
$913$	10.9372	−	18.9438i	0.361969	−	0.626948i
$914$	19.2916	+	33.4141i	0.638111	+	1.10524i
$915$			1.55698i			0.0514723i
$916$	−14.8518	+	8.57470i	−0.490718	+	0.283316i
$917$	−23.8155	+	13.7499i	−0.786457	+	0.454061i
$918$		−	1.03219i		−	0.0340675i
$919$	−1.60639	−	2.78236i	−0.0529901	−	0.0917815i	0.838314	−	0.545188i	$-0.183542\pi$
$919$	−1.60639	−	2.78236i	−0.0529901	−	0.0917815i	−0.891304	+	0.453407i	$0.850208\pi$
$920$	0.465807	−	0.806802i	0.0153572	−	0.0265995i
$921$	−3.60475	−	2.08120i	−0.118780	−	0.0685779i
$922$	6.95829			0.229159
$923$	34.8303	−	8.96116i	1.14645	−	0.294960i
$924$	−2.87593			−0.0946112
$925$	31.2871	+	18.0636i	1.02871	+	0.593927i
$926$	−18.4002	+	31.8702i	−0.604670	+	1.04732i
$927$	−4.32338	−	7.48832i	−0.141999	−	0.245949i
$928$		−	9.34713i		−	0.306834i
$929$	3.13481	−	1.80988i	0.102850	−	0.0593803i	−0.447693	−	0.894187i	$-0.647754\pi$
$929$	3.13481	−	1.80988i	0.102850	−	0.0593803i	0.550543	+	0.834807i	$0.314421\pi$
$930$	0.840604	−	0.485323i	0.0275645	−	0.0159144i
$931$			96.1943i			3.15264i
$932$	−1.73506	−	3.00520i	−0.0568336	−	0.0984387i
$933$	0.661337	−	1.14547i	0.0216512	−	0.0375010i
$934$	−5.25374	−	3.03325i	−0.171908	−	0.0992510i
$935$	2.92116			0.0955321
$936$	10.3550	−	2.66414i	0.338463	−	0.0870800i
$937$	39.2422			1.28199			0.640993	−	0.767546i	$-0.278523\pi$
$937$	39.2422			1.28199			0.640993	+	0.767546i	$0.278523\pi$
$938$	19.3276	+	11.1588i	0.631070	+	0.364348i
$939$	−0.0990029	+	0.171478i	−0.00323084	+	0.00559597i
$940$	4.54443	+	7.87119i	0.148223	+	0.256730i
$941$			24.3513i			0.793830i	0.917855	+	0.396915i	$0.129919\pi$
$941$			24.3513i			0.793830i	−0.917855	+	0.396915i	$0.870081\pi$
$942$	1.72339	−	0.995002i	0.0561512	−	0.0324189i
$943$	−1.32898	+	0.767286i	−0.0432775	+	0.0249863i
$944$		−	9.50406i		−	0.309331i
$945$	2.37361	+	4.11121i	0.0772136	+	0.133738i
$946$	−1.80835	+	3.13215i	−0.0587945	+	0.101835i
$947$	28.2109	+	16.2876i	0.916732	+	0.529276i	0.882591	−	0.470141i	$-0.155797\pi$
$947$	28.2109	+	16.2876i	0.916732	+	0.529276i	0.0341411	+	0.999417i	$0.489130\pi$
$948$	−0.503682			−0.0163588
$949$	12.6786	−	45.4961i	0.411565	−	1.47687i
$950$	28.1130			0.912106
$951$	−4.20882	−	2.42997i	−0.136480	−	0.0787970i
$952$	2.14096	−	3.70825i	0.0693889	−	0.120185i
$953$	−14.0971	−	24.4169i	−0.456649	−	0.790939i	0.542132	−	0.840293i	$-0.317617\pi$
$953$	−14.0971	−	24.4169i	−0.456649	−	0.790939i	−0.998781	+	0.0493537i	$0.984284\pi$
$954$		−	18.1877i		−	0.588847i
$955$	0.584736	−	0.337598i	0.0189216	−	0.0109244i
$956$	2.43656	−	1.40675i	0.0788040	−	0.0454975i
$957$			5.84678i			0.189000i
$958$	−14.1954	−	24.5871i	−0.458632	−	0.794375i
$959$	−25.5463	+	44.2474i	−0.824932	+	1.42882i
$960$	−0.149894	−	0.0865414i	−0.00483781	−	0.00279311i
$961$	−0.449541			−0.0145013
$962$	−7.85462	−	30.5294i	−0.253243	−	0.984306i
$963$	−33.4028			−1.07639
$964$	20.7970	+	12.0071i	0.669825	+	0.386724i
$965$	9.74489	−	16.8786i	0.313699	−	0.543343i
$966$	0.427098	+	0.739756i	0.0137417	+	0.0238013i
$967$			29.0095i			0.932881i	0.884552	+	0.466441i	$0.154464\pi$
$967$			29.0095i			0.932881i	−0.884552	+	0.466441i	$0.845536\pi$
$968$	0.290576	−	0.167764i	0.00933946	−	0.00539214i
$969$	−1.01949	+	0.588603i	−0.0327508	+	0.0189087i
$970$			5.27612i			0.169406i
$971$	−3.57926	−	6.19946i	−0.114864	−	0.198950i	0.802861	−	0.596166i	$-0.203310\pi$
$971$	−3.57926	−	6.19946i	−0.114864	−	0.198950i	−0.917725	+	0.397216i	$0.869977\pi$
$972$	−2.46977	+	4.27777i	−0.0792179	+	0.137210i
$973$	−42.3856	−	24.4713i	−1.35882	−	0.784515i
$974$	7.23756			0.231906
$975$	1.97668	−	1.93761i	0.0633044	−	0.0620532i
$976$	−8.99560			−0.287942
$977$	−40.8978	−	23.6124i	−1.30844	−	0.755427i	−0.326603	−	0.945162i	$-0.605904\pi$
$977$	−40.8978	−	23.6124i	−1.30844	−	0.755427i	−0.981835	+	0.189735i	$0.939237\pi$
$978$	1.84597	−	3.19732i	0.0590276	−	0.102239i
$979$	11.3165	+	19.6007i	0.361676	+	0.626441i
$980$			13.1719i			0.420761i
$981$	25.5969	−	14.7784i	0.817245	−	0.471837i
$982$	−26.7501	+	15.4442i	−0.853629	+	0.492843i
$983$		−	27.0467i		−	0.862654i	−0.902196	−	0.431327i	$-0.858045\pi$
$983$		−	27.0467i		−	0.862654i	0.902196	−	0.431327i	$-0.141955\pi$
$984$	0.142553	+	0.246908i	0.00454441	+	0.00787115i
$985$	8.50613	−	14.7330i	0.271028	−	0.469434i
$986$	−7.53888	−	4.35257i	−0.240087	−	0.138614i
$987$	−8.33357			−0.265261
$988$	−17.1718	−	17.5180i	−0.546308	−	0.557323i
$989$	1.07421			0.0341580
$990$	−8.05533	−	4.65074i	−0.256015	−	0.147810i
$991$	12.4604	−	21.5820i	0.395817	−	0.685576i	−0.597388	−	0.801953i	$-0.703795\pi$
$991$	12.4604	−	21.5820i	0.395817	−	0.685576i	0.993205	+	0.116377i	$0.0371280\pi$
$992$	2.80399	+	4.85666i	0.0890269	+	0.154199i
$993$		−	0.423400i		−	0.0134362i
$994$	−39.7168	+	22.9305i	−1.25974	+	0.727311i
$995$	8.59236	−	4.96080i	0.272396	−	0.157268i
$996$			1.20707i			0.0382475i
$997$	−2.55695	−	4.42877i	−0.0809794	−	0.140260i	0.822691	−	0.568488i	$-0.192471\pi$
$997$	−2.55695	−	4.42877i	−0.0809794	−	0.140260i	−0.903671	+	0.428228i	$0.859138\pi$
$998$	3.00318	−	5.20166i	0.0950639	−	0.164656i
$999$	8.39185	+	4.84504i	0.265506	+	0.153290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	598.2.h.c.277.4	yes	28
13.6	odd	12		7774.2.a.bm.1.7		14
13.7	odd	12		7774.2.a.bl.1.7		14
13.10	even	6	inner	598.2.h.c.231.4	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
598.2.h.c.231.4	✓	28	13.10	even	6	inner
598.2.h.c.277.4	yes	28	1.1	even	1	trivial
7774.2.a.bl.1.7		14	13.7	odd	12
7774.2.a.bm.1.7		14	13.6	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 598 = 2 \cdot 13 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	598.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.0928940 - 0.160897i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.931614i q^{5} +(-0.160897 + 0.0928940i) q^{6} +(3.98172 - 2.29885i) q^{7} -1.00000i q^{8} +(1.48274 + 2.56818i) q^{9} +(0.465807 - 0.806802i) q^{10} +(-2.91576 - 1.68341i) q^{11} +0.185788 q^{12} +(3.47321 + 0.967896i) q^{13} -4.59769 q^{14} +(0.149894 + 0.0865414i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.465659 + 0.806545i) q^{17} -2.96548i q^{18} +(-5.89207 + 3.40179i) q^{19} +(-0.806802 + 0.465807i) q^{20} -0.854196i q^{21} +(1.68341 + 2.91576i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.160897 - 0.0928940i) q^{24} +4.13209 q^{25} +(-2.52394 - 2.57483i) q^{26} +1.10832 q^{27} +(3.98172 + 2.29885i) q^{28} +(4.67356 - 8.09485i) q^{29} +(-0.0865414 - 0.149894i) q^{30} +5.60799i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.541713 + 0.312758i) q^{33} -0.931318i q^{34} +(2.14164 + 3.70943i) q^{35} +(-1.48274 + 2.56818i) q^{36} +(7.57172 + 4.37154i) q^{37} +6.80357 q^{38} +(0.478372 - 0.468918i) q^{39} +0.931614 q^{40} +(-1.32898 - 0.767286i) q^{41} +(-0.427098 + 0.739756i) q^{42} +(0.537107 + 0.930297i) q^{43} -3.36683i q^{44} +(-2.39256 + 1.38134i) q^{45} +(-0.866025 + 0.500000i) q^{46} -9.75604i q^{47} +(0.0928940 + 0.160897i) q^{48} +(7.06940 - 12.2446i) q^{49} +(-3.57850 - 2.06605i) q^{50} +0.173028 q^{51} +(0.898382 + 3.49183i) q^{52} +6.13312 q^{53} +(-0.959829 - 0.554158i) q^{54} +(1.56829 - 2.71636i) q^{55} +(-2.29885 - 3.98172i) q^{56} +1.26402i q^{57} +(-8.09485 + 4.67356i) q^{58} +(-8.23076 + 4.75203i) q^{59} +0.173083i q^{60} +(4.49780 + 7.79041i) q^{61} +(2.80399 - 4.85666i) q^{62} +(11.8077 + 6.81719i) q^{63} -1.00000 q^{64} +(-0.901706 + 3.23569i) q^{65} +0.625516 q^{66} +(-4.20377 - 2.42705i) q^{67} +(-0.465659 + 0.806545i) q^{68} +(-0.0928940 - 0.160897i) q^{69} -4.28328i q^{70} +(8.63841 - 4.98739i) q^{71} +(2.56818 - 1.48274i) q^{72} -13.0992i q^{73} +(-4.37154 - 7.57172i) q^{74} +(0.383847 - 0.664842i) q^{75} +(-5.89207 - 3.40179i) q^{76} -15.4796 q^{77} +(-0.648741 + 0.166909i) q^{78} -2.71106 q^{79} +(-0.806802 - 0.465807i) q^{80} +(-4.34527 + 7.52623i) q^{81} +(0.767286 + 1.32898i) q^{82} +6.49704i q^{83} +(0.739756 - 0.427098i) q^{84} +(-0.751389 + 0.433815i) q^{85} -1.07421i q^{86} +(-0.868292 - 1.50393i) q^{87} +(-1.68341 + 2.91576i) q^{88} +(-5.82171 - 3.36116i) q^{89} +2.76269 q^{90} +(16.0544 - 4.13049i) q^{91} +1.00000 q^{92} +(0.902309 + 0.520948i) q^{93} +(-4.87802 + 8.44898i) q^{94} +(-3.16915 - 5.48913i) q^{95} -0.185788i q^{96} +(-4.90466 + 2.83171i) q^{97} +(-12.2446 + 7.06940i) q^{98} -9.98427i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{3} + 14 q^{4} - 6 q^{9} + 8 q^{10} - 8 q^{12} + 2 q^{13} + 4 q^{14} + 12 q^{15} - 14 q^{16} - 2 q^{17} - 12 q^{19} - 12 q^{22} + 14 q^{23} - 28 q^{25} - 10 q^{26} + 20 q^{27} - 14 q^{29} + 8 q^{30}+ \cdots + 12 q^{98}+O(q^{100}) \) 28 * q - 4 * q^3 + 14 * q^4 - 6 * q^9 + 8 * q^10 - 8 * q^12 + 2 * q^13 + 4 * q^14 + 12 * q^15 - 14 * q^16 - 2 * q^17 - 12 * q^19 - 12 * q^22 + 14 * q^23 - 28 * q^25 - 10 * q^26 + 20 * q^27 - 14 * q^29 + 8 * q^30 + 18 * q^33 + 18 * q^35 + 6 * q^36 - 12 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^40 + 24 * q^41 - 6 * q^42 + 12 * q^43 - 36 * q^45 - 4 * q^48 + 36 * q^49 - 36 * q^50 - 12 * q^51 - 2 * q^52 + 8 * q^53 - 18 * q^54 - 12 * q^55 + 2 * q^56 + 18 * q^58 - 30 * q^59 + 6 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^64 - 66 * q^65 + 44 * q^66 + 42 * q^67 + 2 * q^68 + 4 * q^69 - 60 * q^71 + 44 * q^75 - 12 * q^76 + 16 * q^77 - 48 * q^78 + 68 * q^79 + 2 * q^81 + 40 * q^82 + 42 * q^84 - 72 * q^85 + 10 * q^87 + 12 * q^88 - 6 * q^89 - 36 * q^90 + 4 * q^91 + 28 * q^92 + 60 * q^93 - 26 * q^94 + 16 * q^95 - 12 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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