LMFDB - Embedded newform 361.2.c.h.68.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(68,361)] 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("361.68"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			68.3
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	361.68
Dual form			361.2.c.h.292.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.439693 - 0.761570i) q^{2} +(0.266044 - 0.460802i) q^{3} +(0.613341 + 1.06234i) q^{4} +(1.26604 - 2.19285i) q^{5} +(-0.233956 - 0.405223i) q^{6} -1.87939 q^{7} +2.83750 q^{8} +(1.35844 + 2.35289i) q^{9} +(-1.11334 - 1.92836i) q^{10} +3.41147 q^{11} +0.652704 q^{12} +(-2.64543 - 4.58202i) q^{13} +(-0.826352 + 1.43128i) q^{14} +(-0.673648 - 1.16679i) q^{15} +(0.0209445 - 0.0362770i) q^{16} +(-0.826352 + 1.43128i) q^{17} +2.38919 q^{18} +3.10607 q^{20} +(-0.500000 + 0.866025i) q^{21} +(1.50000 - 2.59808i) q^{22} +(-0.879385 - 1.52314i) q^{23} +(0.754900 - 1.30753i) q^{24} +(-0.705737 - 1.22237i) q^{25} -4.65270 q^{26} +3.04189 q^{27} +(-1.15270 - 1.99654i) q^{28} +(-1.73396 - 3.00330i) q^{29} -1.18479 q^{30} -1.94356 q^{31} +(2.81908 + 4.88279i) q^{32} +(0.907604 - 1.57202i) q^{33} +(0.726682 + 1.25865i) q^{34} +(-2.37939 + 4.12122i) q^{35} +(-1.66637 + 2.88624i) q^{36} +0.837496 q^{37} -2.81521 q^{39} +(3.59240 - 6.22221i) q^{40} +(-2.24510 + 3.88863i) q^{41} +(0.439693 + 0.761570i) q^{42} +(-2.40033 + 4.15749i) q^{43} +(2.09240 + 3.62414i) q^{44} +6.87939 q^{45} -1.54664 q^{46} +(-0.358441 - 0.620838i) q^{47} +(-0.0111444 - 0.0193026i) q^{48} -3.46791 q^{49} -1.24123 q^{50} +(0.439693 + 0.761570i) q^{51} +(3.24510 - 5.62068i) q^{52} +(-3.05303 - 5.28801i) q^{53} +(1.33750 - 2.31661i) q^{54} +(4.31908 - 7.48086i) q^{55} -5.33275 q^{56} -3.04963 q^{58} +(-5.37939 + 9.31737i) q^{59} +(0.826352 - 1.43128i) q^{60} +(-2.19459 - 3.80115i) q^{61} +(-0.854570 + 1.48016i) q^{62} +(-2.55303 - 4.42198i) q^{63} +5.04189 q^{64} -13.3969 q^{65} +(-0.798133 - 1.38241i) q^{66} +(7.10607 + 12.3081i) q^{67} -2.02734 q^{68} -0.935822 q^{69} +(2.09240 + 3.62414i) q^{70} +(-6.87939 + 11.9154i) q^{71} +(3.85457 + 6.67631i) q^{72} +(3.75877 - 6.51038i) q^{73} +(0.368241 - 0.637812i) q^{74} -0.751030 q^{75} -6.41147 q^{77} +(-1.23783 + 2.14398i) q^{78} +(-3.48158 + 6.03028i) q^{79} +(-0.0530334 - 0.0918566i) q^{80} +(-3.26604 + 5.65695i) q^{81} +(1.97431 + 3.41960i) q^{82} +2.51249 q^{83} -1.22668 q^{84} +(2.09240 + 3.62414i) q^{85} +(2.11081 + 3.65604i) q^{86} -1.84524 q^{87} +9.68004 q^{88} +(-1.14156 - 1.97724i) q^{89} +(3.02481 - 5.23913i) q^{90} +(4.97178 + 8.61138i) q^{91} +(1.07873 - 1.86841i) q^{92} +(-0.517074 + 0.895599i) q^{93} -0.630415 q^{94} +3.00000 q^{96} +(-0.911474 + 1.57872i) q^{97} +(-1.52481 + 2.64106i) q^{98} +(4.63429 + 8.02682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 12 q^{8} + 6 q^{12} - 6 q^{14} - 3 q^{15} - 3 q^{16} - 6 q^{17} + 6 q^{18} - 6 q^{20} - 3 q^{21} + 9 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{25} - 30 q^{26}+ \cdots + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 12 * q^8 + 6 * q^12 - 6 * q^14 - 3 * q^15 - 3 * q^16 - 6 * q^17 + 6 * q^18 - 6 * q^20 - 3 * q^21 + 9 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^25 - 30 * q^26 + 12 * q^27 - 9 * q^28 - 15 * q^29 + 18 * q^31 + 9 * q^33 - 9 * q^34 - 3 * q^35 + 9 * q^36 - 24 * q^39 + 18 * q^40 - 12 * q^41 - 3 * q^42 + 9 * q^44 + 30 * q^45 - 36 * q^46 + 6 * q^47 + 6 * q^48 - 30 * q^49 - 30 * q^50 - 3 * q^51 + 18 * q^52 - 6 * q^53 + 3 * q^54 + 9 * q^55 + 6 * q^56 + 36 * q^58 - 21 * q^59 + 6 * q^60 - 9 * q^61 - 21 * q^62 - 3 * q^63 + 24 * q^64 - 24 * q^65 + 9 * q^66 + 18 * q^67 + 30 * q^68 - 24 * q^69 + 9 * q^70 - 30 * q^71 + 39 * q^72 - 3 * q^74 - 30 * q^75 - 18 * q^77 + 12 * q^78 - 9 * q^79 + 12 * q^80 - 15 * q^81 - 18 * q^82 + 6 * q^84 + 9 * q^85 + 21 * q^86 + 42 * q^87 + 18 * q^88 - 15 * q^89 - 9 * q^90 + 15 * q^91 + 24 * q^92 - 24 * q^93 - 18 * q^94 + 18 * q^96 + 15 * q^97 + 18 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.439693	−	0.761570i	0.310910	−	0.538511i	−0.667650	−	0.744475i	$-0.732700\pi$
$2$	0.439693	−	0.761570i	0.310910	−	0.538511i	0.978560	+	0.205964i	$0.0660330\pi$
$3$	0.266044	−	0.460802i	0.153601	−	0.266044i	−0.778948	−	0.627089i	$-0.784246\pi$
$3$	0.266044	−	0.460802i	0.153601	−	0.266044i	0.932549	+	0.361044i	$0.117580\pi$
$4$	0.613341	+	1.06234i	0.306670	+	0.531169i
$5$	1.26604	−	2.19285i	0.566192	−	0.980674i	−0.430745	−	0.902473i	$-0.641749\pi$
$5$	1.26604	−	2.19285i	0.566192	−	0.980674i	0.996938	−	0.0782003i	$-0.0249174\pi$
$6$	−0.233956	−	0.405223i	−0.0955120	−	0.165432i
$7$	−1.87939			−0.710341			−0.355170	−	0.934802i	$-0.615577\pi$
$7$	−1.87939			−0.710341			−0.355170	+	0.934802i	$0.615577\pi$
$8$	2.83750			1.00321
$9$	1.35844	+	2.35289i	0.452814	+	0.784296i
$10$	−1.11334	−	1.92836i	−0.352069	−	0.609802i
$11$	3.41147			1.02860			0.514299	−	0.857611i	$-0.328052\pi$
$11$	3.41147			1.02860			0.514299	+	0.857611i	$0.328052\pi$
$12$	0.652704			0.188419
$13$	−2.64543	−	4.58202i	−0.733710	−	1.27082i	−0.955287	−	0.295680i	$-0.904454\pi$
$13$	−2.64543	−	4.58202i	−0.733710	−	1.27082i	0.221577	−	0.975143i	$-0.428880\pi$
$14$	−0.826352	+	1.43128i	−0.220852	+	0.382527i
$15$	−0.673648	−	1.16679i	−0.173935	−	0.301265i
$16$	0.0209445	−	0.0362770i	0.00523613	−	0.00906925i
$17$	−0.826352	+	1.43128i	−0.200420	+	0.347137i	−0.948664	−	0.316286i	$-0.897564\pi$
$17$	−0.826352	+	1.43128i	−0.200420	+	0.347137i	0.748244	+	0.663424i	$0.230897\pi$
$18$	2.38919			0.563136
$19$		0			0
$19$		0			0
$20$	3.10607			0.694538
$21$	−0.500000	+	0.866025i	−0.109109	+	0.188982i
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	−0.879385	−	1.52314i	−0.183364	−	0.317597i	0.759660	−	0.650321i	$-0.225366\pi$
$23$	−0.879385	−	1.52314i	−0.183364	−	0.317597i	−0.943024	+	0.332724i	$0.892032\pi$
$24$	0.754900	−	1.30753i	0.154093	−	0.266897i
$25$	−0.705737	−	1.22237i	−0.141147	−	0.244474i
$26$	−4.65270			−0.912470
$27$	3.04189			0.585412
$28$	−1.15270	−	1.99654i	−0.217841	−	0.377311i
$29$	−1.73396	−	3.00330i	−0.321987	−	0.557699i	0.658911	−	0.752221i	$-0.271018\pi$
$29$	−1.73396	−	3.00330i	−0.321987	−	0.557699i	−0.980898	+	0.194523i	$0.937684\pi$
$30$	−1.18479			−0.216313
$31$	−1.94356			−0.349074			−0.174537	−	0.984651i	$-0.555843\pi$
$31$	−1.94356			−0.349074			−0.174537	+	0.984651i	$0.555843\pi$
$32$	2.81908	+	4.88279i	0.498347	+	0.863163i
$33$	0.907604	−	1.57202i	0.157994	−	0.273653i
$34$	0.726682	+	1.25865i	0.124625	+	0.215857i
$35$	−2.37939	+	4.12122i	−0.402190	+	0.696613i
$36$	−1.66637	+	2.88624i	−0.277729	+	0.481041i
$37$	0.837496			0.137684			0.0688418	−	0.997628i	$-0.478070\pi$
$37$	0.837496			0.137684			0.0688418	+	0.997628i	$0.478070\pi$
$38$		0			0
$39$	−2.81521			−0.450794
$40$	3.59240	−	6.22221i	0.568008	−	0.983818i
$41$	−2.24510	+	3.88863i	−0.350626	+	0.607302i	−0.986359	−	0.164607i	$-0.947364\pi$
$41$	−2.24510	+	3.88863i	−0.350626	+	0.607302i	0.635734	+	0.771909i	$0.280698\pi$
$42$	0.439693	+	0.761570i	0.0678460	+	0.117513i
$43$	−2.40033	+	4.15749i	−0.366047	+	0.634012i	−0.988944	−	0.148292i	$-0.952622\pi$
$43$	−2.40033	+	4.15749i	−0.366047	+	0.634012i	0.622897	+	0.782304i	$0.285956\pi$
$44$	2.09240	+	3.62414i	0.315441	+	0.546359i
$45$	6.87939			1.02552
$46$	−1.54664			−0.228039
$47$	−0.358441	−	0.620838i	−0.0522840	−	0.0905585i	0.838699	−	0.544595i	$-0.183317\pi$
$47$	−0.358441	−	0.620838i	−0.0522840	−	0.0905585i	−0.890983	+	0.454037i	$0.849983\pi$
$48$	−0.0111444	−	0.0193026i	−0.00160855	−	0.00278609i
$49$	−3.46791			−0.495416
$50$	−1.24123			−0.175536
$51$	0.439693	+	0.761570i	0.0615693	+	0.106641i
$52$	3.24510	−	5.62068i	0.450014	−	0.779448i
$53$	−3.05303	−	5.28801i	−0.419366	−	0.726364i	0.576509	−	0.817090i	$-0.304414\pi$
$53$	−3.05303	−	5.28801i	−0.419366	−	0.726364i	−0.995876	+	0.0907266i	$0.971081\pi$
$54$	1.33750	−	2.31661i	0.182010	−	0.315251i
$55$	4.31908	−	7.48086i	0.582384	−	1.00872i
$56$	−5.33275			−0.712618
$57$		0			0
$58$	−3.04963			−0.400436
$59$	−5.37939	+	9.31737i	−0.700336	+	1.21302i	0.268012	+	0.963416i	$0.413633\pi$
$59$	−5.37939	+	9.31737i	−0.700336	+	1.21302i	−0.968348	+	0.249603i	$0.919700\pi$
$60$	0.826352	−	1.43128i	0.106682	−	0.184778i
$61$	−2.19459	−	3.80115i	−0.280989	−	0.486687i	0.690640	−	0.723199i	$-0.257329\pi$
$61$	−2.19459	−	3.80115i	−0.280989	−	0.486687i	−0.971629	+	0.236512i	$0.923996\pi$
$62$	−0.854570	+	1.48016i	−0.108531	+	0.187980i
$63$	−2.55303	−	4.42198i	−0.321652	−	0.557118i
$64$	5.04189			0.630236
$65$	−13.3969			−1.66168
$66$	−0.798133	−	1.38241i	−0.0982434	−	0.170163i
$67$	7.10607	+	12.3081i	0.868144	+	1.50367i	0.863891	+	0.503679i	$0.168021\pi$
$67$	7.10607	+	12.3081i	0.868144	+	1.50367i	0.00425333	+	0.999991i	$0.498646\pi$
$68$	−2.02734			−0.245851
$69$	−0.935822			−0.112660
$70$	2.09240	+	3.62414i	0.250089	+	0.433167i
$71$	−6.87939	+	11.9154i	−0.816433	+	1.41410i	0.0918617	+	0.995772i	$0.470718\pi$
$71$	−6.87939	+	11.9154i	−0.816433	+	1.41410i	−0.908294	+	0.418331i	$0.862615\pi$
$72$	3.85457	+	6.67631i	0.454265	+	0.786811i
$73$	3.75877	−	6.51038i	0.439931	−	0.761983i	−0.557753	−	0.830007i	$-0.688336\pi$
$73$	3.75877	−	6.51038i	0.439931	−	0.761983i	0.997684	+	0.0680246i	$0.0216696\pi$
$74$	0.368241	−	0.637812i	0.0428071	−	0.0741441i
$75$	−0.751030			−0.0867214
$76$		0			0
$77$	−6.41147			−0.730655
$78$	−1.23783	+	2.14398i	−0.140156	+	0.242758i
$79$	−3.48158	+	6.03028i	−0.391709	+	0.678459i	−0.992675	−	0.120815i	$-0.961449\pi$
$79$	−3.48158	+	6.03028i	−0.391709	+	0.678459i	0.600966	+	0.799274i	$0.294783\pi$
$80$	−0.0530334	−	0.0918566i	−0.00592932	−	0.0102699i
$81$	−3.26604	+	5.65695i	−0.362894	+	0.628551i
$82$	1.97431	+	3.41960i	0.218026	+	0.377632i
$83$	2.51249			0.275781			0.137891	−	0.990447i	$-0.455968\pi$
$83$	2.51249			0.275781			0.137891	+	0.990447i	$0.455968\pi$
$84$	−1.22668			−0.133842
$85$	2.09240	+	3.62414i	0.226952	+	0.393093i
$86$	2.11081	+	3.65604i	0.227615	+	0.394241i
$87$	−1.84524			−0.197830
$88$	9.68004			1.03190
$89$	−1.14156	−	1.97724i	−0.121005	−	0.209587i	0.799159	−	0.601119i	$-0.205278\pi$
$89$	−1.14156	−	1.97724i	−0.121005	−	0.209587i	−0.920164	+	0.391533i	$0.871945\pi$
$90$	3.02481	−	5.23913i	0.318843	−	0.552253i
$91$	4.97178	+	8.61138i	0.521184	+	0.902718i
$92$	1.07873	−	1.86841i	0.112465	−	0.194795i
$93$	−0.517074	+	0.895599i	−0.0536181	+	0.0928693i
$94$	−0.630415			−0.0650223
$95$		0			0
$96$	3.00000			0.306186
$97$	−0.911474	+	1.57872i	−0.0925462	+	0.160295i	−0.908582	−	0.417707i	$-0.862834\pi$
$97$	−0.911474	+	1.57872i	−0.0925462	+	0.160295i	0.816036	+	0.578002i	$0.196167\pi$
$98$	−1.52481	+	2.64106i	−0.154030	+	0.266787i
$99$	4.63429	+	8.02682i	0.465763	+	0.806726i
$100$	0.865715	−	1.49946i	0.0865715	−	0.149946i
$101$	3.96064	+	6.86002i	0.394098	+	0.682598i	0.992986	−	0.118235i	$-0.0377237\pi$
$101$	3.96064	+	6.86002i	0.394098	+	0.682598i	−0.598887	+	0.800833i	$0.704390\pi$
$102$	0.773318			0.0765699
$103$	0.0145479			0.00143345			0.000716725	−	1.00000i	$-0.499772\pi$
$103$	0.0145479			0.00143345			0.000716725		1.00000i	$0.499772\pi$
$104$	−7.50640	−	13.0015i	−0.736063	−	1.27490i
$105$	1.26604	+	2.19285i	0.123553	+	0.214001i
$106$	−5.36959			−0.521540
$107$	3.55438			0.343615			0.171807	−	0.985131i	$-0.445039\pi$
$107$	3.55438			0.343615			0.171807	+	0.985131i	$0.445039\pi$
$108$	1.86571	+	3.23151i	0.179528	+	0.310952i
$109$	3.68479	−	6.38225i	0.352939	−	0.611308i	−0.633824	−	0.773477i	$-0.718516\pi$
$109$	3.68479	−	6.38225i	0.352939	−	0.611308i	0.986763	+	0.162169i	$0.0518489\pi$
$110$	−3.79813	−	6.57856i	−0.362138	−	0.627241i
$111$	0.222811	−	0.385920i	0.0211483	−	0.0366299i
$112$	−0.0393628	+	0.0681784i	−0.00371944	+	0.00644226i
$113$	−7.37733			−0.694000			−0.347000	−	0.937865i	$-0.612800\pi$
$113$	−7.37733			−0.694000			−0.347000	+	0.937865i	$0.612800\pi$
$114$		0			0
$115$	−4.45336			−0.415278
$116$	2.12701	−	3.68409i	0.197488	−	0.342059i
$117$	7.18732	−	12.4488i	0.664468	−	1.15089i
$118$	4.73055	+	8.19356i	0.435483	+	0.754278i
$119$	1.55303	−	2.68993i	0.142366	−	0.246586i
$120$	−1.91147	−	3.31077i	−0.174493	−	0.302231i
$121$	0.638156			0.0580142
$122$	−3.85978			−0.349449
$123$	1.19459	+	2.06910i	0.107713	+	0.186564i
$124$	−1.19207	−	2.06472i	−0.107051	−	0.185417i
$125$	9.08647			0.812718
$126$	−4.49020			−0.400019
$127$	−0.0505072	−	0.0874810i	−0.00448179	−	0.00776269i	0.863776	−	0.503876i	$-0.168093\pi$
$127$	−0.0505072	−	0.0874810i	−0.00448179	−	0.00776269i	−0.868258	+	0.496114i	$0.834760\pi$
$128$	−3.42127	+	5.92582i	−0.302401	+	0.523774i
$129$	1.27719	+	2.21216i	0.112450	+	0.194769i
$130$	−5.89053	+	10.2027i	−0.516634	+	0.894836i
$131$	1.51842	−	2.62998i	0.132665	−	0.229782i	−0.792038	−	0.610472i	$-0.790980\pi$
$131$	1.51842	−	2.62998i	0.132665	−	0.229782i	0.924703	+	0.380689i	$0.124313\pi$
$132$	2.22668			0.193808
$133$		0			0
$134$	12.4979			1.07966
$135$	3.85117	−	6.67042i	0.331456	−	0.574098i
$136$	−2.34477	+	4.06126i	−0.201062	+	0.348250i
$137$	−9.76991	−	16.9220i	−0.834700	−	1.44574i	−0.894274	−	0.447519i	$-0.852308\pi$
$137$	−9.76991	−	16.9220i	−0.834700	−	1.44574i	0.0595742	−	0.998224i	$-0.481026\pi$
$138$	−0.411474	+	0.712694i	−0.0350270	+	0.0606686i
$139$	−7.69846	−	13.3341i	−0.652975	−	1.13099i	−0.982397	−	0.186803i	$-0.940187\pi$
$139$	−7.69846	−	13.3341i	−0.652975	−	1.13099i	0.329422	−	0.944183i	$-0.393146\pi$
$140$	−5.83750			−0.493358
$141$	−0.381445			−0.0321234
$142$	6.04963	+	10.4783i	0.507674	+	0.879317i
$143$	−9.02481	−	15.6314i	−0.754693	−	1.30717i
$144$	0.113808			0.00948397
$145$	−8.78106			−0.729227
$146$	−3.30541	−	5.72513i	−0.273557	−	0.473815i
$147$	−0.922618	+	1.59802i	−0.0760963	+	0.131803i
$148$	0.513671	+	0.889704i	0.0422235	+	0.0731332i
$149$	1.88326	−	3.26189i	0.154282	−	0.267225i	−0.778515	−	0.627626i	$-0.784027\pi$
$149$	1.88326	−	3.26189i	0.154282	−	0.267225i	0.932797	+	0.360401i	$0.117360\pi$
$150$	−0.330222	+	0.571962i	−0.0269625	+	0.0467005i
$151$	14.5963			1.18783			0.593914	−	0.804529i	$-0.297582\pi$
$151$	14.5963			1.18783			0.593914	+	0.804529i	$0.297582\pi$
$152$		0			0
$153$	−4.49020			−0.363011
$154$	−2.81908	+	4.88279i	−0.227168	+	0.393466i
$155$	−2.46064	+	4.26195i	−0.197643	+	0.342328i
$156$	−1.72668	−	2.99070i	−0.138245	−	0.239448i
$157$	5.18732	−	8.98470i	0.413993	−	0.717057i	−0.581329	−	0.813669i	$-0.697467\pi$
$157$	5.18732	−	8.98470i	0.413993	−	0.717057i	0.995322	+	0.0966115i	$0.0308004\pi$
$158$	3.06165	+	5.30294i	0.243572	+	0.421879i
$159$	−3.24897			−0.257660
$160$	14.2763			1.12864
$161$	1.65270	+	2.86257i	0.130251	+	0.225602i
$162$	2.87211	+	4.97464i	0.225654	+	0.390845i
$163$	−2.02229			−0.158398			−0.0791989	−	0.996859i	$-0.525236\pi$
$163$	−2.02229			−0.158398			−0.0791989	+	0.996859i	$0.525236\pi$
$164$	−5.50805			−0.430106
$165$	−2.29813	−	3.98048i	−0.178909	−	0.309880i
$166$	1.10472	−	1.91344i	0.0857431	−	0.148511i
$167$	−11.6284	−	20.1409i	−0.899829	−	1.55855i	−0.827712	−	0.561154i	$-0.810358\pi$
$167$	−11.6284	−	20.1409i	−0.899829	−	1.55855i	−0.0721175	−	0.997396i	$-0.522976\pi$
$168$	−1.41875	+	2.45734i	−0.109459	+	0.189588i
$169$	−7.49660	+	12.9845i	−0.576661	+	0.998807i
$170$	3.68004			0.282247
$171$		0			0
$172$	−5.88888			−0.449023
$173$	0.448311	−	0.776497i	0.0340844	−	0.0590360i	−0.848480	−	0.529227i	$-0.822482\pi$
$173$	0.448311	−	0.776497i	0.0340844	−	0.0590360i	0.882564	+	0.470191i	$0.155815\pi$
$174$	−0.811337	+	1.40528i	−0.0615073	+	0.106534i
$175$	1.32635	+	2.29731i	0.100263	+	0.173660i
$176$	0.0714517	−	0.123758i	0.00538588	−	0.00932861i
$177$	2.86231	+	4.95767i	0.215144	+	0.372641i
$178$	−2.00774			−0.150487
$179$	21.3182			1.59340			0.796699	−	0.604377i	$-0.206578\pi$
$179$	21.3182			1.59340			0.796699	+	0.604377i	$0.206578\pi$
$180$	4.21941	+	7.30823i	0.314496	+	0.544723i
$181$	−8.04963	−	13.9424i	−0.598324	−	1.03633i	−0.993069	−	0.117537i	$-0.962500\pi$
$181$	−8.04963	−	13.9424i	−0.598324	−	1.03633i	0.394744	−	0.918791i	$-0.370833\pi$
$182$	8.74422			0.648165
$183$	−2.33544			−0.172640
$184$	−2.49525	−	4.32190i	−0.183952	−	0.318615i
$185$	1.06031	−	1.83651i	0.0779553	−	0.135023i
$186$	0.454707	+	0.787576i	0.0333408	+	0.0577479i
$187$	−2.81908	+	4.88279i	−0.206151	+	0.357065i
$188$	0.439693	−	0.761570i	0.0320679	−	0.0555432i
$189$	−5.71688			−0.415842
$190$		0			0
$191$	18.9486			1.37107			0.685537	−	0.728038i	$-0.259568\pi$
$191$	18.9486			1.37107			0.685537	+	0.728038i	$0.259568\pi$
$192$	1.34137	−	2.32332i	0.0968048	−	0.167671i
$193$	6.45084	−	11.1732i	0.464341	−	0.804263i	−0.534830	−	0.844960i	$-0.679624\pi$
$193$	6.45084	−	11.1732i	0.464341	−	0.804263i	0.999172	+	0.0406967i	$0.0129577\pi$
$194$	0.801537	+	1.38830i	0.0575470	+	0.0996743i
$195$	−3.56418	+	6.17334i	−0.255236	+	0.442082i
$196$	−2.12701	−	3.68409i	−0.151929	−	0.263149i
$197$	−23.2003			−1.65295			−0.826476	−	0.562973i	$-0.809658\pi$
$197$	−23.2003			−1.65295			−0.826476	+	0.562973i	$0.809658\pi$
$198$	8.15064			0.579241
$199$	−4.61081	−	7.98617i	−0.326852	−	0.566124i	0.655033	−	0.755600i	$-0.272655\pi$
$199$	−4.61081	−	7.98617i	−0.326852	−	0.566124i	−0.981885	+	0.189476i	$0.939321\pi$
$200$	−2.00253	−	3.46848i	−0.141600	−	0.245258i
$201$	7.56212			0.533391
$202$	6.96585			0.490116
$203$	3.25877	+	5.64436i	0.228721	+	0.396156i
$204$	−0.539363	+	0.934204i	−0.0377630	+	0.0654074i
$205$	5.68479	+	9.84635i	0.397043	+	0.687699i
$206$	0.00639661	−	0.0110793i	0.000445673	−	0.000771929i
$207$	2.38919	−	4.13819i	0.166060	−	0.287624i
$208$	−0.221629			−0.0153672
$209$		0			0
$210$	2.22668			0.153656
$211$	7.31180	−	12.6644i	0.503365	−	0.871854i	−0.496627	−	0.867964i	$-0.665428\pi$
$211$	7.31180	−	12.6644i	0.503365	−	0.871854i	0.999992	−	0.00389033i	$-0.00123833\pi$
$212$	3.74510	−	6.48670i	0.257215	−	0.445509i
$213$	3.66044	+	6.34008i	0.250810	+	0.434415i
$214$	1.56283	−	2.70691i	0.106833	−	0.185040i
$215$	6.07785	+	10.5271i	0.414506	+	0.717945i
$216$	8.63135			0.587289
$217$	3.65270			0.247962
$218$	−3.24035	−	5.61245i	−0.219464	−	0.380123i
$219$	−2.00000	−	3.46410i	−0.135147	−	0.234082i
$220$	10.5963			0.714400
$221$	8.74422			0.588200
$222$	−0.195937	−	0.339373i	−0.0131504	−	0.0227772i
$223$	−1.50727	+	2.61068i	−0.100935	+	0.174824i	−0.912070	−	0.410035i	$-0.865517\pi$
$223$	−1.50727	+	2.61068i	−0.100935	+	0.174824i	0.811135	+	0.584858i	$0.198850\pi$
$224$	−5.29813	−	9.17664i	−0.353996	−	0.613140i
$225$	1.91740	−	3.32104i	0.127827	−	0.221403i
$226$	−3.24376	+	5.61835i	−0.215771	+	0.373727i
$227$	13.7219			0.910757			0.455378	−	0.890298i	$-0.349504\pi$
$227$	13.7219			0.910757			0.455378	+	0.890298i	$0.349504\pi$
$228$		0			0
$229$	9.41416			0.622105			0.311053	−	0.950393i	$-0.399318\pi$
$229$	9.41416			0.622105			0.311053	+	0.950393i	$0.399318\pi$
$230$	−1.95811	+	3.39155i	−0.129114	+	0.223632i
$231$	−1.70574	+	2.95442i	−0.112229	+	0.194387i
$232$	−4.92009	−	8.52185i	−0.323020	−	0.559487i
$233$	12.0929	−	20.9455i	0.792230	−	1.37218i	−0.132354	−	0.991203i	$-0.542253\pi$
$233$	12.0929	−	20.9455i	0.792230	−	1.37218i	0.924583	−	0.380980i	$-0.124413\pi$
$234$	−6.32042	−	10.9473i	−0.413179	−	0.715647i
$235$	−1.81521			−0.118411
$236$	−13.1976			−0.859090
$237$	1.85251	+	3.20864i	0.120334	+	0.208424i
$238$	−1.36571	−	2.36549i	−0.0885261	−	0.153332i
$239$	−23.3259			−1.50883			−0.754415	−	0.656398i	$-0.772079\pi$
$239$	−23.3259			−1.50883			−0.754415	+	0.656398i	$0.772079\pi$
$240$	−0.0564370			−0.00364299
$241$	0.148833	+	0.257787i	0.00958719	+	0.0166055i	0.870779	−	0.491674i	$-0.163615\pi$
$241$	0.148833	+	0.257787i	0.00958719	+	0.0166055i	−0.861192	+	0.508280i	$0.830282\pi$
$242$	0.280592	−	0.486000i	0.0180372	−	0.0312413i
$243$	6.30066	+	10.9131i	0.404187	+	0.700073i
$244$	2.69207	−	4.66280i	0.172342	−	0.298505i
$245$	−4.39053	+	7.60462i	−0.280501	+	0.485841i
$246$	2.10101			0.133956
$247$		0			0
$248$	−5.51485			−0.350193
$249$	0.668434	−	1.15776i	0.0423603	−	0.0733701i
$250$	3.99525	−	6.91998i	0.252682	−	0.437658i
$251$	8.09879	+	14.0275i	0.511191	+	0.885409i	0.999916	+	0.0129711i	$0.00412896\pi$
$251$	8.09879	+	14.0275i	0.511191	+	0.885409i	−0.488725	+	0.872438i	$0.662538\pi$
$252$	3.13176	−	5.42437i	0.197282	−	0.341703i
$253$	−3.00000	−	5.19615i	−0.188608	−	0.326679i
$254$	−0.0888306			−0.00557373
$255$	2.22668			0.139440
$256$	8.05051	+	13.9439i	0.503157	+	0.871493i
$257$	7.67752	+	13.2979i	0.478910	+	0.829497i	0.999708	−	0.0241833i	$-0.00769852\pi$
$257$	7.67752	+	13.2979i	0.478910	+	0.829497i	−0.520797	+	0.853680i	$0.674365\pi$
$258$	2.24628			0.139847
$259$	−1.57398			−0.0978022
$260$	−8.21688	−	14.2321i	−0.509589	−	0.882635i
$261$	4.71095	−	8.15961i	0.291601	−	0.505067i
$262$	−1.33527	−	2.31276i	−0.0824935	−	0.142883i
$263$	−4.82160	+	8.35126i	−0.297313	+	0.514961i	−0.975520	−	0.219910i	$-0.929424\pi$
$263$	−4.82160	+	8.35126i	−0.297313	+	0.514961i	0.678207	+	0.734871i	$0.262757\pi$
$264$	2.57532	−	4.46059i	0.158500	−	0.274530i
$265$	−15.4611			−0.949768
$266$		0			0
$267$	−1.21482			−0.0743459
$268$	−8.71688	+	15.0981i	−0.532468	+	0.922262i
$269$	−9.13950	+	15.8301i	−0.557245	+	0.965177i	0.440480	+	0.897762i	$0.354808\pi$
$269$	−9.13950	+	15.8301i	−0.557245	+	0.965177i	−0.997725	+	0.0674144i	$0.978525\pi$
$270$	−3.38666	−	5.86587i	−0.206106	−	0.356985i
$271$	−9.48205	+	16.4234i	−0.575993	+	0.997650i	0.419939	+	0.907552i	$0.362051\pi$
$271$	−9.48205	+	16.4234i	−0.575993	+	0.997650i	−0.995933	+	0.0900978i	$0.971282\pi$
$272$	0.0346151	+	0.0599551i	0.00209885	+	0.00363531i
$273$	5.29086			0.320217
$274$	−17.1830			−1.03807
$275$	−2.40760	−	4.17009i	−0.145184	−	0.251466i
$276$	−0.573978	−	0.994159i	−0.0345494	−	0.0598413i
$277$	13.7638			0.826988			0.413494	−	0.910507i	$-0.364308\pi$
$277$	13.7638			0.826988			0.413494	+	0.910507i	$0.364308\pi$
$278$	−13.5398			−0.812065
$279$	−2.64022	−	4.57299i	−0.158066	−	0.273778i
$280$	−6.75150	+	11.6939i	−0.403479	+	0.698846i
$281$	6.55556	+	11.3546i	0.391072	+	0.677356i	0.992591	−	0.121502i	$-0.0387710\pi$
$281$	6.55556	+	11.3546i	0.391072	+	0.677356i	−0.601519	+	0.798858i	$0.705438\pi$
$282$	−0.167718	+	0.290497i	−0.00998748	+	0.0172988i
$283$	8.68866	−	15.0492i	0.516487	−	0.894582i	−0.483329	−	0.875439i	$-0.660573\pi$
$283$	8.68866	−	15.0492i	0.516487	−	0.894582i	0.999817	−	0.0191438i	$-0.00609404\pi$
$284$	−16.8776			−1.00150
$285$		0			0
$286$	−15.8726			−0.938565
$287$	4.21941	−	7.30823i	0.249064	−	0.431391i
$288$	−7.65910	+	13.2660i	−0.451317	+	0.781704i
$289$	7.13429	+	12.3569i	0.419664	+	0.726879i
$290$	−3.86097	+	6.68739i	−0.226724	+	0.392697i
$291$	0.484985	+	0.840019i	0.0284303	+	0.0492428i
$292$	9.22163			0.539655
$293$	−15.6040			−0.911596			−0.455798	−	0.890083i	$-0.650646\pi$
$293$	−15.6040			−0.911596			−0.455798	+	0.890083i	$0.650646\pi$
$294$	0.811337	+	1.40528i	0.0473181	+	0.0819574i
$295$	13.6211	+	23.5924i	0.793050	+	1.37360i
$296$	2.37639			0.138125
$297$	10.3773			0.602154
$298$	−1.65611	−	2.86846i	−0.0959357	−	0.166166i
$299$	−4.65270	+	8.05872i	−0.269073	+	0.466048i
$300$	−0.460637	−	0.797847i	−0.0265949	−	0.0460637i
$301$	4.51114	−	7.81353i	0.260018	−	0.450364i
$302$	6.41787	−	11.1161i	0.369307	−	0.639658i
$303$	4.21482			0.242135
$304$		0			0
$305$	−11.1138			−0.636375
$306$	−1.97431	+	3.41960i	−0.112864	+	0.195486i
$307$	10.7601	−	18.6371i	0.614112	−	1.06367i	−0.376427	−	0.926446i	$-0.622848\pi$
$307$	10.7601	−	18.6371i	0.614112	−	1.06367i	0.990540	−	0.137227i	$-0.0438191\pi$
$308$	−3.93242	−	6.81115i	−0.224070	−	0.388101i
$309$	0.00387039	−	0.00670372i	0.000220179	−	0.000381361i
$310$	2.16385	+	3.74789i	0.122898	+	0.212866i
$311$	14.4953			0.821950			0.410975	−	0.911647i	$-0.365188\pi$
$311$	14.4953			0.821950			0.410975	+	0.911647i	$0.365188\pi$
$312$	−7.98814			−0.452239
$313$	−9.75924	−	16.9035i	−0.551625	−	0.955442i	−0.998158	−	0.0606748i	$-0.980675\pi$
$313$	−9.75924	−	16.9035i	−0.551625	−	0.955442i	0.446533	−	0.894767i	$-0.352659\pi$
$314$	−4.56165	−	7.90101i	−0.257429	−	0.445880i
$315$	−12.9290			−0.728467
$316$	−8.54158			−0.480502
$317$	14.1736	+	24.5495i	0.796071	+	1.37884i	0.922157	+	0.386817i	$0.126425\pi$
$317$	14.1736	+	24.5495i	0.796071	+	1.37884i	−0.126085	+	0.992019i	$0.540241\pi$
$318$	−1.42855	+	2.47432i	−0.0801090	+	0.138753i
$319$	−5.91534	−	10.2457i	−0.331196	−	0.573648i
$320$	6.38326	−	11.0561i	0.356835	−	0.618056i
$321$	0.945622	−	1.63787i	0.0527795	−	0.0914168i
$322$	2.90673			0.161986
$323$		0			0
$324$	−8.01279			−0.445155
$325$	−3.73396	+	6.46740i	−0.207123	+	0.358747i
$326$	−0.889185	+	1.54011i	−0.0492474	+	0.0852990i
$327$	−1.96064	−	3.39592i	−0.108423	−	0.187795i
$328$	−6.37046	+	11.0340i	−0.351750	+	0.609249i
$329$	0.673648	+	1.16679i	0.0371394	+	0.0643274i
$330$	−4.04189			−0.222499
$331$	1.71007			0.0939942			0.0469971	−	0.998895i	$-0.485035\pi$
$331$	1.71007			0.0939942			0.0469971	+	0.998895i	$0.485035\pi$
$332$	1.54101	+	2.66911i	0.0845740	+	0.146486i
$333$	1.13769	+	1.97053i	0.0623450	+	0.107985i
$334$	−20.4516			−1.11906
$335$	35.9864			1.96615
$336$	0.0209445	+	0.0362770i	0.00114262	+	0.00197907i
$337$	12.7194	−	22.0307i	0.692870	−	1.20009i	−0.278023	−	0.960574i	$-0.589679\pi$
$337$	12.7194	−	22.0307i	0.692870	−	1.20009i	0.970893	−	0.239512i	$-0.0769875\pi$
$338$	6.59240	+	11.4184i	0.358579	+	0.621077i
$339$	−1.96270	+	3.39949i	−0.106599	+	0.184635i
$340$	−2.56670	+	4.44566i	−0.139199	+	0.241100i
$341$	−6.63041			−0.359057
$342$		0			0
$343$	19.6732			1.06225
$344$	−6.81093	+	11.7969i	−0.367221	+	0.636045i
$345$	−1.18479	+	2.05212i	−0.0637871	+	0.110482i
$346$	−0.394238	−	0.682840i	−0.0211944	−	0.0367097i
$347$	−3.85117	+	6.67042i	−0.206741	+	0.358087i	−0.950686	−	0.310154i	$-0.899619\pi$
$347$	−3.85117	+	6.67042i	−0.206741	+	0.358087i	0.743945	+	0.668241i	$0.232953\pi$
$348$	−1.13176	−	1.96026i	−0.0606687	−	0.105081i
$349$	22.7570			1.21816			0.609078	−	0.793111i	$-0.291540\pi$
$349$	22.7570			1.21816			0.609078	+	0.793111i	$0.291540\pi$
$350$	2.33275			0.124691
$351$	−8.04710	−	13.9380i	−0.429523	−	0.743955i
$352$	9.61721	+	16.6575i	0.512599	+	0.887848i
$353$	−11.4456			−0.609189			−0.304595	−	0.952482i	$-0.598521\pi$
$353$	−11.4456			−0.609189			−0.304595	+	0.952482i	$0.598521\pi$
$354$	5.03415			0.267562
$355$	17.4192	+	30.1710i	0.924516	+	1.60131i
$356$	1.40033	−	2.42544i	0.0742173	−	0.128548i
$357$	−0.826352	−	1.43128i	−0.0437352	−	0.0757515i
$358$	9.37346	−	16.2353i	0.495403	−	0.858062i
$359$	−5.19207	+	8.99292i	−0.274027	+	0.474628i	−0.969889	−	0.243547i	$-0.921689\pi$
$359$	−5.19207	+	8.99292i	−0.274027	+	0.474628i	0.695862	+	0.718175i	$0.255022\pi$
$360$	19.5202			1.02881
$361$		0			0
$362$	−14.1575			−0.744099
$363$	0.169778	−	0.294064i	0.00891102	−	0.0154343i
$364$	−6.09879	+	10.5634i	−0.319664	+	0.553674i
$365$	−9.51754	−	16.4849i	−0.498171	−	0.862857i
$366$	−1.02687	+	1.77860i	−0.0536756	+	0.0929688i
$367$	16.2665	+	28.1744i	0.849105	+	1.47069i	0.882008	+	0.471234i	$0.156191\pi$
$367$	16.2665	+	28.1744i	0.849105	+	1.47069i	−0.0329030	+	0.999459i	$0.510475\pi$
$368$	−0.0736733			−0.00384048
$369$	−12.1993			−0.635072
$370$	−0.932419	−	1.61500i	−0.0484741	−	0.0839597i
$371$	5.73783	+	9.93821i	0.297893	+	0.515966i
$372$	−1.26857			−0.0657723
$373$	−30.4858			−1.57849			−0.789246	−	0.614077i	$-0.789529\pi$
$373$	−30.4858			−1.57849			−0.789246	+	0.614077i	$0.789529\pi$
$374$	2.47906	+	4.29385i	0.128189	+	0.222030i
$375$	2.41740	−	4.18707i	0.124834	−	0.216219i
$376$	−1.01707	−	1.76162i	−0.0524516	−	0.0908488i
$377$	−9.17412	+	15.8900i	−0.472491	+	0.818378i
$378$	−2.51367	+	4.35381i	−0.129289	+	0.223936i
$379$	−17.8598			−0.917396			−0.458698	−	0.888592i	$-0.651684\pi$
$379$	−17.8598			−0.917396			−0.458698	+	0.888592i	$0.651684\pi$
$380$		0			0
$381$	−0.0537486			−0.00275363
$382$	8.33157	−	14.4307i	0.426280	−	0.738339i
$383$	−11.7280	+	20.3135i	−0.599274	+	1.03797i	0.393654	+	0.919259i	$0.371211\pi$
$383$	−11.7280	+	20.3135i	−0.599274	+	1.03797i	−0.992928	+	0.118715i	$0.962123\pi$
$384$	1.82042	+	3.15306i	0.0928980	+	0.160904i
$385$	−8.11721	+	14.0594i	−0.413691	+	0.716535i
$386$	−5.67277	−	9.82553i	−0.288736	−	0.500106i
$387$	−13.0428			−0.663004
$388$	−2.23618			−0.113525
$389$	−1.95471	−	3.38565i	−0.0991076	−	0.171659i	0.812208	−	0.583368i	$-0.198265\pi$
$389$	−1.95471	−	3.38565i	−0.0991076	−	0.171659i	−0.911316	+	0.411709i	$0.864932\pi$
$390$	3.13429	+	5.42874i	0.158711	+	0.274895i
$391$	2.90673			0.146999
$392$	−9.84018			−0.497004
$393$	−0.807934	−	1.39938i	−0.0407549	−	0.0705895i
$394$	−10.2010	+	17.6686i	−0.513918	+	0.890133i
$395$	8.81567	+	15.2692i	0.443565	+	0.768277i
$396$	−5.68479	+	9.84635i	−0.285672	+	0.494798i
$397$	−4.47952	+	7.75876i	−0.224821	+	0.389401i	−0.956266	−	0.292500i	$-0.905513\pi$
$397$	−4.47952	+	7.75876i	−0.224821	+	0.389401i	0.731445	+	0.681901i	$0.238846\pi$
$398$	−8.10936			−0.406486
$399$		0			0
$400$	−0.0591253			−0.00295627
$401$	−1.01367	+	1.75573i	−0.0506203	+	0.0876769i	−0.890225	−	0.455521i	$-0.849453\pi$
$401$	−1.01367	+	1.75573i	−0.0506203	+	0.0876769i	0.839605	+	0.543197i	$0.182786\pi$
$402$	3.32501	−	5.75908i	0.165836	−	0.287237i
$403$	5.14156	+	8.90544i	0.256119	+	0.443612i
$404$	−4.85844	+	8.41507i	−0.241716	+	0.418665i
$405$	8.26991	+	14.3239i	0.410935	+	0.711761i
$406$	5.73143			0.284446
$407$	2.85710			0.141621
$408$	1.24763	+	2.16095i	0.0617667	+	0.106983i
$409$	−16.1040	−	27.8930i	−0.796292	−	1.37922i	−0.922016	−	0.387153i	$-0.873459\pi$
$409$	−16.1040	−	27.8930i	−0.796292	−	1.37922i	0.125724	−	0.992065i	$-0.459875\pi$
$410$	9.99825			0.493778
$411$	−10.3969			−0.512843
$412$	0.00892283	+	0.0154548i	0.000439596	+	0.000761403i
$413$	10.1099	−	17.5109i	0.497477	−	0.861656i
$414$	−2.10101	−	3.63906i	−0.103259	−	0.178850i
$415$	3.18092	−	5.50952i	0.156145	−	0.270452i
$416$	14.9153	−	25.8341i	0.731285	−	1.26662i
$417$	−8.19253			−0.401190
$418$		0			0
$419$	−23.2499			−1.13583			−0.567916	−	0.823086i	$-0.692250\pi$
$419$	−23.2499			−1.13583			−0.567916	+	0.823086i	$0.692250\pi$
$420$	−1.55303	+	2.68993i	−0.0757803	+	0.131255i
$421$	3.22668	−	5.58878i	0.157259	−	0.272380i	−0.776620	−	0.629969i	$-0.783068\pi$
$421$	3.22668	−	5.58878i	0.157259	−	0.272380i	0.933879	+	0.357589i	$0.116401\pi$
$422$	−6.42989	−	11.1369i	−0.313002	−	0.542136i
$423$	0.973841	−	1.68674i	0.0473498	−	0.0820122i
$424$	−8.66297	−	15.0047i	−0.420711	−	0.728693i
$425$	2.33275			0.113155
$426$	6.43788			0.311916
$427$	4.12449	+	7.14382i	0.199598	+	0.345714i
$428$	2.18004	+	3.77595i	0.105376	+	0.182517i
$429$	−9.60401			−0.463686
$430$	10.6895			0.515495
$431$	−6.99866	−	12.1220i	−0.337113	−	0.583898i	0.646775	−	0.762681i	$-0.276117\pi$
$431$	−6.99866	−	12.1220i	−0.337113	−	0.583898i	−0.983888	+	0.178783i	$0.942784\pi$
$432$	0.0637109	−	0.110351i	0.00306529	−	0.00530925i
$433$	−14.3464	−	24.8487i	−0.689445	−	1.19415i	−0.972018	−	0.234908i	$-0.924521\pi$
$433$	−14.3464	−	24.8487i	−0.689445	−	1.19415i	0.282573	−	0.959246i	$-0.408812\pi$
$434$	1.60607	−	2.78179i	0.0770937	−	0.133530i
$435$	−2.33615	+	4.04633i	−0.112010	+	0.194007i
$436$	9.04013			0.432944
$437$		0			0
$438$	−3.51754			−0.168075
$439$	−6.67112	+	11.5547i	−0.318395	+	0.551477i	−0.980153	−	0.198241i	$-0.936477\pi$
$439$	−6.67112	+	11.5547i	−0.318395	+	0.551477i	0.661758	+	0.749717i	$0.269811\pi$
$440$	12.2554	−	21.2269i	0.584252	−	1.01195i
$441$	−4.71095	−	8.15961i	−0.224331	−	0.388553i
$442$	3.84477	−	6.65934i	0.182877	−	0.316752i
$443$	−16.9415	−	29.3435i	−0.804915	−	1.39415i	−0.916348	−	0.400382i	$-0.868877\pi$
$443$	−16.9415	−	29.3435i	−0.804915	−	1.39415i	0.111433	−	0.993772i	$-0.464456\pi$
$444$	0.546637			0.0259422
$445$	−5.78106			−0.274048
$446$	1.32547	+	2.29579i	0.0627630	+	0.108709i
$447$	−1.00206	−	1.73562i	−0.0473958	−	0.0820919i
$448$	−9.47565			−0.447682
$449$	−18.8402			−0.889123			−0.444562	−	0.895748i	$-0.646641\pi$
$449$	−18.8402			−0.889123			−0.444562	+	0.895748i	$0.646641\pi$
$450$	−1.68614	−	2.92047i	−0.0794852	−	0.137672i
$451$	−7.65910	+	13.2660i	−0.360653	+	0.624669i
$452$	−4.52481	−	7.83721i	−0.212829	−	0.368631i
$453$	3.88326	−	6.72600i	0.182451	−	0.316015i
$454$	6.03343	−	10.4502i	0.283163	−	0.490453i
$455$	25.1780			1.18036
$456$		0			0
$457$	14.2790			0.667943			0.333972	−	0.942583i	$-0.391611\pi$
$457$	14.2790			0.667943			0.333972	+	0.942583i	$0.391611\pi$
$458$	4.13934	−	7.16954i	0.193419	−	0.335011i
$459$	−2.51367	+	4.35381i	−0.117328	+	0.203218i
$460$	−2.73143	−	4.73097i	−0.127354	−	0.220583i
$461$	6.96404	−	12.0621i	0.324348	−	0.561787i	−0.657032	−	0.753862i	$-0.728189\pi$
$461$	6.96404	−	12.0621i	0.324348	−	0.561787i	0.981380	+	0.192076i	$0.0615219\pi$
$462$	1.50000	+	2.59808i	0.0697863	+	0.120873i
$463$	−1.76289			−0.0819284			−0.0409642	−	0.999161i	$-0.513043\pi$
$463$	−1.76289			−0.0819284			−0.0409642	+	0.999161i	$0.513043\pi$
$464$	−0.145268			−0.00674388
$465$	1.30928	+	2.26774i	0.0607163	+	0.105164i
$466$	−10.6343	−	18.4191i	−0.492624	−	0.853249i
$467$	22.0419			1.01998			0.509988	−	0.860181i	$-0.329650\pi$
$467$	22.0419			1.01998			0.509988	+	0.860181i	$0.329650\pi$
$468$	17.6331			0.815090
$469$	−13.3550	−	23.1316i	−0.616678	−	1.06812i
$470$	−0.798133	+	1.38241i	−0.0368151	+	0.0637657i
$471$	−2.76011	−	4.78066i	−0.127179	−	0.220281i
$472$	−15.2640	+	26.4380i	−0.702582	+	1.21691i
$473$	−8.18866	+	14.1832i	−0.376515	+	0.652143i
$474$	3.25814			0.149651
$475$		0			0
$476$	3.81016			0.174638
$477$	8.29473	−	14.3669i	0.379790	−	0.657815i
$478$	−10.2562	+	17.7643i	−0.469110	+	0.812522i
$479$	12.7285	+	22.0464i	0.581580	+	1.00733i	0.995292	+	0.0969180i	$0.0308985\pi$
$479$	12.7285	+	22.0464i	0.581580	+	1.00733i	−0.413713	+	0.910407i	$0.635768\pi$
$480$	3.79813	−	6.57856i	0.173360	−	0.300269i
$481$	−2.21554	−	3.83742i	−0.101020	−	0.174971i
$482$	0.261764			0.0119230
$483$	1.75877			0.0800268
$484$	0.391407	+	0.677937i	0.0177912	+	0.0308153i
$485$	2.30793	+	3.99746i	0.104798	+	0.181515i
$486$	11.0814			0.502663
$487$	22.5107			1.02006			0.510029	−	0.860157i	$-0.329635\pi$
$487$	22.5107			1.02006			0.510029	+	0.860157i	$0.329635\pi$
$488$	−6.22715	−	10.7857i	−0.281890	−	0.488247i
$489$	−0.538019	+	0.931876i	−0.0243300	+	0.0421409i
$490$	3.86097	+	6.68739i	0.174421	+	0.302106i
$491$	−7.81702	+	13.5395i	−0.352777	+	0.611028i	−0.986735	−	0.162340i	$-0.948096\pi$
$491$	−7.81702	+	13.5395i	−0.352777	+	0.611028i	0.633958	+	0.773368i	$0.281429\pi$
$492$	−1.46538	+	2.53812i	−0.0660647	+	0.114427i
$493$	5.73143			0.258131
$494$		0			0
$495$	23.4688			1.05485
$496$	−0.0407070	+	0.0705066i	−0.00182780	+	0.00316584i
$497$	12.9290	−	22.3937i	0.579946	−	1.00450i
$498$	−0.587811	−	1.01812i	−0.0263404	−	0.0456230i
$499$	14.3084	−	24.7829i	0.640532	−	1.10943i	−0.344782	−	0.938683i	$-0.612047\pi$
$499$	14.3084	−	24.7829i	0.640532	−	1.10943i	0.985314	−	0.170751i	$-0.0546194\pi$
$500$	5.57310	+	9.65289i	0.249237	+	0.431691i
$501$	−12.3746			−0.552858
$502$	14.2439			0.635737
$503$	12.5228	+	21.6900i	0.558362	+	0.967111i	0.997633	+	0.0687571i	$0.0219033\pi$
$503$	12.5228	+	21.6900i	0.558362	+	0.967111i	−0.439271	+	0.898354i	$0.644763\pi$
$504$	−7.24422	−	12.5474i	−0.322683	−	0.558904i
$505$	20.0574			0.892541
$506$	−5.27631			−0.234561
$507$	3.98886	+	6.90890i	0.177151	+	0.306835i
$508$	0.0619563	−	0.107311i	0.00274886	−	0.00476117i
$509$	16.7606	+	29.0302i	0.742900	+	1.28674i	0.951170	+	0.308669i	$0.0998834\pi$
$509$	16.7606	+	29.0302i	0.742900	+	1.28674i	−0.208270	+	0.978071i	$0.566783\pi$
$510$	0.979055	−	1.69577i	0.0433533	−	0.0750901i
$511$	−7.06418	+	12.2355i	−0.312501	+	0.541267i
$512$	0.473897			0.0209435
$513$		0			0
$514$	13.5030			0.595591
$515$	0.0184183	−	0.0319015i	0.000811608	−	0.00140575i
$516$	−1.56670	+	2.71361i	−0.0689703	+	0.119460i
$517$	−1.22281	−	2.11797i	−0.0537792	−	0.0931483i
$518$	−0.692066	+	1.19869i	−0.0304077	+	0.0526676i
$519$	−0.238541	−	0.413165i	−0.0104708	−	0.0181359i
$520$	−38.0137			−1.66701
$521$	27.4783			1.20385			0.601924	−	0.798553i	$-0.294401\pi$
$521$	27.4783			1.20385			0.601924	+	0.798553i	$0.294401\pi$
$522$	−4.14274	−	7.17544i	−0.181323	−	0.314060i
$523$	−5.17870	−	8.96977i	−0.226449	−	0.392221i	0.730304	−	0.683122i	$-0.239378\pi$
$523$	−5.17870	−	8.96977i	−0.226449	−	0.392221i	−0.956753	+	0.290901i	$0.906045\pi$
$524$	3.72523			0.162737
$525$	1.41147			0.0616018
$526$	4.24005	+	7.34398i	0.184875	+	0.320213i
$527$	1.60607	−	2.78179i	0.0699614	−	0.121177i
$528$	−0.0380187	−	0.0658503i	−0.00165455	−	0.00286577i
$529$	9.95336	−	17.2397i	0.432755	−	0.749554i
$530$	−6.79813	+	11.7747i	−0.295292	+	0.511461i
$531$	−29.2303			−1.26849
$532$		0			0
$533$	23.7570			1.02903
$534$	−0.534148	+	0.925172i	−0.0231149	+	0.0400361i
$535$	4.50000	−	7.79423i	0.194552	−	0.336974i
$536$	20.1634	+	34.9241i	0.870928	+	1.50849i
$537$	5.67159	−	9.82348i	0.244747	−	0.423914i
$538$	8.03714	+	13.9207i	0.346506	+	0.600166i
$539$	−11.8307			−0.509584
$540$	9.44831			0.406591
$541$	−1.26217	−	2.18615i	−0.0542651	−	0.0939899i	0.837617	−	0.546258i	$-0.183948\pi$
$541$	−1.26217	−	2.18615i	−0.0542651	−	0.0939899i	−0.891882	+	0.452268i	$0.850615\pi$
$542$	8.33837	+	14.4425i	0.358164	+	0.620358i
$543$	−8.56624			−0.367612
$544$	−9.31820			−0.399515
$545$	−9.33022	−	16.1604i	−0.399663	−	0.692236i
$546$	2.32635	−	4.02936i	0.0995587	−	0.172441i
$547$	3.83750	+	6.64674i	0.164079	+	0.284194i	0.936328	−	0.351127i	$-0.114201\pi$
$547$	3.83750	+	6.64674i	0.164079	+	0.284194i	−0.772249	+	0.635321i	$0.780868\pi$
$548$	11.9846	−	20.7579i	0.511956	−	0.886733i
$549$	5.96245	−	10.3273i	0.254471	−	0.440757i
$550$	−4.23442			−0.180556
$551$		0			0
$552$	−2.65539			−0.113021
$553$	6.54323	−	11.3332i	0.278247	−	0.481937i
$554$	6.05185	−	10.4821i	0.257119	−	0.445342i
$555$	−0.564178	−	0.977185i	−0.0239480	−	0.0414792i
$556$	9.44356	−	16.3567i	0.400496	−	0.693680i
$557$	−1.62789	−	2.81959i	−0.0689759	−	0.119470i	0.829475	−	0.558544i	$-0.188640\pi$
$557$	−1.62789	−	2.81959i	−0.0689759	−	0.119470i	−0.898451	+	0.439074i	$0.855306\pi$
$558$	−4.64353			−0.196576
$559$	25.3996			1.07429
$560$	0.0996702	+	0.172634i	0.00421184	+	0.00729511i
$561$	1.50000	+	2.59808i	0.0633300	+	0.109691i
$562$	11.5297			0.486352
$563$	−5.25908			−0.221644			−0.110822	−	0.993840i	$-0.535348\pi$
$563$	−5.25908			−0.221644			−0.110822	+	0.993840i	$0.535348\pi$
$564$	−0.233956	−	0.405223i	−0.00985131	−	0.0170630i
$565$	−9.34002	+	16.1774i	−0.392938	+	0.680588i
$566$	−7.64068	−	13.2340i	−0.321162	−	0.556269i
$567$	6.13816	−	10.6316i	0.257778	−	0.446485i
$568$	−19.5202	+	33.8100i	−0.819051	+	1.41864i
$569$	29.9564			1.25584			0.627918	−	0.778280i	$-0.283907\pi$
$569$	29.9564			1.25584			0.627918	+	0.778280i	$0.283907\pi$
$570$		0			0
$571$	−16.7101			−0.699295			−0.349647	−	0.936881i	$-0.613699\pi$
$571$	−16.7101			−0.699295			−0.349647	+	0.936881i	$0.613699\pi$
$572$	11.0706	−	19.1748i	0.462884	−	0.801739i
$573$	5.04117	−	8.73157i	0.210598	−	0.364767i
$574$	−3.71048	−	6.42675i	−0.154873	−	0.268247i
$575$	−1.24123	+	2.14987i	−0.0517628	+	0.0896559i
$576$	6.84911	+	11.8630i	0.285379	+	0.494292i
$577$	−13.6800			−0.569508			−0.284754	−	0.958601i	$-0.591912\pi$
$577$	−13.6800			−0.569508			−0.284754	+	0.958601i	$0.591912\pi$
$578$	12.5476			0.521910
$579$	−3.43242	−	5.94512i	−0.142646	−	0.247071i
$580$	−5.38578	−	9.32845i	−0.223632	−	0.387343i
$581$	−4.72193			−0.195899
$582$	0.852978			0.0353571
$583$	−10.4153	−	18.0399i	−0.431359	−	0.747137i
$584$	10.6655	−	18.4732i	0.441341	−	0.764426i
$585$	−18.1989	−	31.5215i	−0.752433	−	1.30325i
$586$	−6.86097	+	11.8835i	−0.283424	+	0.490905i
$587$	12.0184	−	20.8165i	0.496053	−	0.859189i	−0.503936	−	0.863741i	$-0.668115\pi$
$587$	12.0184	−	20.8165i	0.496053	−	0.859189i	0.999990	+	0.00455138i	$0.00144875\pi$
$588$	−2.26352			−0.0933459
$589$		0			0
$590$	23.9564			0.986268
$591$	−6.17230	+	10.6907i	−0.253895	+	0.439758i
$592$	0.0175410	−	0.0303818i	0.000720929	−	0.00124869i
$593$	2.12061	+	3.67301i	0.0870832	+	0.150833i	0.906277	−	0.422684i	$-0.138912\pi$
$593$	2.12061	+	3.67301i	0.0870832	+	0.150833i	−0.819194	+	0.573517i	$0.805579\pi$
$594$	4.56283	−	7.90306i	0.187215	−	0.324266i
$595$	−3.93242	−	6.81115i	−0.161213	−	0.279230i
$596$	4.62031			0.189255
$597$	−4.90673			−0.200819
$598$	4.09152	+	7.08672i	0.167315	+	0.289797i
$599$	−13.1370	−	22.7539i	−0.536762	−	0.929699i	−0.999076	−	0.0429829i	$-0.986314\pi$
$599$	−13.1370	−	22.7539i	−0.536762	−	0.929699i	0.462314	−	0.886716i	$-0.347019\pi$
$600$	−2.13104			−0.0869995
$601$	42.2395			1.72298			0.861492	−	0.507771i	$-0.169530\pi$
$601$	42.2395			1.72298			0.861492	+	0.507771i	$0.169530\pi$
$602$	−3.96703	−	6.87110i	−0.161684	−	0.280045i
$603$	−19.3063	+	33.4396i	−0.786215	+	1.36176i
$604$	8.95249	+	15.5062i	0.364271	+	0.630937i
$605$	0.807934	−	1.39938i	0.0328472	−	0.0568930i
$606$	1.85323	−	3.20988i	0.0752822	−	0.130393i
$607$	22.0969			0.896885			0.448443	−	0.893812i	$-0.351979\pi$
$607$	22.0969			0.896885			0.448443	+	0.893812i	$0.351979\pi$
$608$		0			0
$609$	3.46791			0.140527
$610$	−4.88666	+	8.46394i	−0.197855	+	0.342695i
$611$	−1.89646	+	3.28476i	−0.0767225	+	0.132887i
$612$	−2.75402	−	4.77011i	−0.111325	−	0.192820i
$613$	−3.58853	+	6.21551i	−0.144939	+	0.251042i	−0.929350	−	0.369199i	$-0.879632\pi$
$613$	−3.58853	+	6.21551i	−0.144939	+	0.251042i	0.784411	+	0.620241i	$0.212965\pi$
$614$	−9.46229	−	16.3892i	−0.381867	−	0.661413i
$615$	6.04963			0.243945
$616$	−18.1925			−0.732998
$617$	24.6864	+	42.7582i	0.993839	+	1.72138i	0.592906	+	0.805272i	$0.297981\pi$
$617$	24.6864	+	42.7582i	0.993839	+	1.72138i	0.400933	+	0.916108i	$0.368686\pi$
$618$	−0.00340357	−	0.00589515i	−0.000136912	−	0.000237138i
$619$	26.4979			1.06504			0.532521	−	0.846417i	$-0.321245\pi$
$619$	26.4979			1.06504			0.532521	+	0.846417i	$0.321245\pi$
$620$	−6.03684			−0.242445
$621$	−2.67499	−	4.63322i	−0.107344	−	0.185925i
$622$	6.37346	−	11.0391i	0.255552	−	0.442630i
$623$	2.14543	+	3.71599i	0.0859548	+	0.148878i
$624$	−0.0589632	+	0.102127i	−0.00236042	+	0.00408836i
$625$	15.0326	−	26.0372i	0.601302	−	1.04149i
$626$	−17.1643			−0.686022
$627$		0			0
$628$	12.7264			0.507838
$629$	−0.692066	+	1.19869i	−0.0275945	+	0.0477951i
$630$	−5.68479	+	9.84635i	−0.226488	+	0.392288i
$631$	−16.6604	−	28.8567i	−0.663242	−	1.14877i	−0.979759	−	0.200182i	$-0.935847\pi$
$631$	−16.6604	−	28.8567i	−0.663242	−	1.14877i	0.316517	−	0.948587i	$-0.397487\pi$
$632$	−9.87897	+	17.1109i	−0.392965	+	0.680635i
$633$	−3.89053	−	6.73859i	−0.154635	−	0.267835i
$634$	24.9282			0.990025
$635$	−0.255777			−0.0101502
$636$	−1.99273	−	3.45150i	−0.0790167	−	0.136861i
$637$	9.17412	+	15.8900i	0.363492	+	0.629586i
$638$	−10.4037			−0.411888
$639$	−37.3809			−1.47877
$640$	8.66297	+	15.0047i	0.342434	+	0.593113i
$641$	−0.0680482	+	0.117863i	−0.00268774	+	0.00465530i	−0.867366	−	0.497671i	$-0.834189\pi$
$641$	−0.0680482	+	0.117863i	−0.00268774	+	0.00465530i	0.864678	+	0.502326i	$0.167522\pi$
$642$	−0.831566	−	1.44032i	−0.0328193	−	0.0568447i
$643$	−24.0890	+	41.7234i	−0.949977	+	1.64541i	−0.204512	+	0.978864i	$0.565561\pi$
$643$	−24.0890	+	41.7234i	−0.949977	+	1.64541i	−0.745465	+	0.666545i	$0.767773\pi$
$644$	−2.02734	+	3.51146i	−0.0798884	+	0.138371i
$645$	6.46791			0.254674
$646$		0			0
$647$	−36.9718			−1.45351			−0.726756	−	0.686895i	$-0.758973\pi$
$647$	−36.9718			−1.45351			−0.726756	+	0.686895i	$0.758973\pi$
$648$	−9.26739	+	16.0516i	−0.364057	+	0.630566i
$649$	−18.3516	+	31.7860i	−0.720365	+	1.24771i
$650$	3.28359	+	5.68734i	0.128793	+	0.223076i
$651$	0.971782	−	1.68317i	0.0380871	−	0.0659688i
$652$	−1.24035	−	2.14835i	−0.0485759	−	0.0841360i
$653$	27.0000			1.05659			0.528296	−	0.849060i	$-0.322831\pi$
$653$	27.0000			1.05659			0.528296	+	0.849060i	$0.322831\pi$
$654$	−3.44831			−0.134840
$655$	−3.84477	−	6.65934i	−0.150228	−	0.260202i
$656$	0.0940451	+	0.162891i	0.00367185	+	0.00635982i
$657$	20.4243			0.796827
$658$	1.18479			0.0461880
$659$	9.43747	+	16.3462i	0.367632	+	0.636757i	0.989195	−	0.146607i	$-0.0468354\pi$
$659$	9.43747	+	16.3462i	0.367632	+	0.636757i	−0.621563	+	0.783364i	$0.713502\pi$
$660$	2.81908	−	4.88279i	0.109732	−	0.190062i
$661$	−15.3059	−	26.5106i	−0.595330	−	1.03114i	−0.993500	−	0.113830i	$-0.963688\pi$
$661$	−15.3059	−	26.5106i	−0.595330	−	1.03114i	0.398171	−	0.917311i	$-0.369645\pi$
$662$	0.751907	−	1.30234i	0.0292237	−	0.0506169i
$663$	2.32635	−	4.02936i	0.0903480	−	0.156487i
$664$	7.12918			0.276666
$665$		0			0
$666$	2.00093			0.0775346
$667$	−3.04963	+	5.28211i	−0.118082	+	0.204524i
$668$	14.2643	−	24.7065i	0.551902	−	0.955922i
$669$	0.802004	+	1.38911i	0.0310073	+	0.0537061i
$670$	15.8229	−	27.4062i	0.611294	−	1.05879i
$671$	−7.48680	−	12.9675i	−0.289025	−	0.500605i
$672$	−5.63816			−0.217497
$673$	−11.9094			−0.459074			−0.229537	−	0.973300i	$-0.573721\pi$
$673$	−11.9094			−0.459074			−0.229537	+	0.973300i	$0.573721\pi$
$674$	−11.1853	−	19.3734i	−0.430840	−	0.746237i
$675$	−2.14677	−	3.71832i	−0.0826294	−	0.143118i
$676$	−18.3919			−0.707380
$677$	−5.78106			−0.222184			−0.111092	−	0.993810i	$-0.535435\pi$
$677$	−5.78106			−0.222184			−0.111092	+	0.993810i	$0.535435\pi$
$678$	1.72597	+	2.98946i	0.0662853	+	0.114810i
$679$	1.71301	−	2.96702i	0.0657393	−	0.113864i
$680$	5.93717	+	10.2835i	0.227680	+	0.394353i
$681$	3.65064	−	6.32310i	0.139893	−	0.242302i
$682$	−2.91534	+	5.04952i	−0.111634	+	0.193356i
$683$	−21.0496			−0.805442			−0.402721	−	0.915323i	$-0.631935\pi$
$683$	−21.0496			−0.805442			−0.402721	+	0.915323i	$0.631935\pi$
$684$		0			0
$685$	−49.4766			−1.89040
$686$	8.65018	−	14.9825i	0.330265	−	0.572036i
$687$	2.50459	−	4.33807i	0.0955559	−	0.165508i
$688$	0.100548	+	0.174154i	0.00383334	+	0.00663954i
$689$	−16.1532	+	27.9781i	−0.615387	+	1.06588i
$690$	1.04189	+	1.80460i	0.0396640	+	0.0687001i
$691$	−32.9377			−1.25301			−0.626504	−	0.779418i	$-0.715515\pi$
$691$	−32.9377			−1.25301			−0.626504	+	0.779418i	$0.715515\pi$
$692$	1.09987			0.0418107
$693$	−8.70961	−	15.0855i	−0.330851	−	0.573050i
$694$	3.38666	+	5.86587i	0.128556	+	0.222665i
$695$	−38.9864			−1.47884
$696$	−5.23585			−0.198464
$697$	−3.71048	−	6.42675i	−0.140545	−	0.243430i
$698$	10.0061	−	17.3311i	0.378736	−	0.655990i
$699$	−6.43448	−	11.1448i	−0.243374	−	0.421537i
$700$	−1.62701	+	2.81807i	−0.0614952	+	0.106513i
$701$	−10.6787	+	18.4961i	−0.403329	+	0.698586i	−0.994125	−	0.108234i	$-0.965480\pi$
$701$	−10.6787	+	18.4961i	−0.403329	+	0.698586i	0.590796	+	0.806821i	$0.298814\pi$
$702$	−14.1530			−0.534171
$703$		0			0
$704$	17.2003			0.648260
$705$	−0.482926	+	0.836452i	−0.0181880	+	0.0315026i
$706$	−5.03256	+	8.71664i	−0.189403	+	0.328055i
$707$	−7.44356	−	12.8926i	−0.279944	−	0.484877i
$708$	−3.51114	+	6.08148i	−0.131957	+	0.228556i
$709$	7.88532	+	13.6578i	0.296139	+	0.512928i	0.975249	−	0.221108i	$-0.0709674\pi$
$709$	7.88532	+	13.6578i	0.296139	+	0.512928i	−0.679110	+	0.734036i	$0.737634\pi$
$710$	30.6364			1.14976
$711$	−18.9181			−0.709484
$712$	−3.23917	−	5.61041i	−0.121393	−	0.210259i
$713$	1.70914	+	2.96032i	0.0640078	+	0.110865i
$714$	−1.45336			−0.0543908
$715$	−45.7033			−1.70921
$716$	13.0753	+	22.6471i	0.488648	+	0.846363i
$717$	−6.20574	+	10.7487i	−0.231757	+	0.401416i
$718$	4.56583	+	7.90824i	0.170395	+	0.295133i
$719$	17.6642	−	30.5952i	0.658762	−	1.14101i	−0.322175	−	0.946680i	$-0.604414\pi$
$719$	17.6642	−	30.5952i	0.658762	−	1.14101i	0.980936	−	0.194329i	$-0.0622528\pi$
$720$	0.144086	−	0.249563i	0.00536975	−	0.00930068i
$721$	−0.0273411			−0.00101824
$722$		0			0
$723$	0.158385			0.00589040
$724$	9.87433	−	17.1028i	0.366977	−	0.635622i
$725$	−2.44743	+	4.23908i	−0.0908954	+	0.157435i
$726$	−0.149300	−	0.258595i	−0.00554105	−	0.00959737i
$727$	−20.2108	+	35.0061i	−0.749577	+	1.29830i	0.198449	+	0.980111i	$0.436410\pi$
$727$	−20.2108	+	35.0061i	−0.749577	+	1.29830i	−0.948026	+	0.318194i	$0.896924\pi$
$728$	14.1074	+	24.4348i	0.522855	+	0.905612i
$729$	−12.8912			−0.477454
$730$	−16.7392			−0.619544
$731$	−3.96703	−	6.87110i	−0.146726	−	0.254137i
$732$	−1.43242	−	2.48102i	−0.0529437	−	0.0917012i
$733$	−36.2763			−1.33990			−0.669948	−	0.742408i	$-0.733684\pi$
$733$	−36.2763			−1.33990			−0.669948	+	0.742408i	$0.733684\pi$
$734$	28.6091			1.05598
$735$	2.33615	+	4.04633i	0.0861703	+	0.149251i
$736$	4.95811	−	8.58770i	0.182758	−	0.316547i
$737$	24.2422	+	41.9887i	0.892972	+	1.54667i
$738$	−5.36396	+	9.29065i	−0.197450	+	0.341994i
$739$	10.3380	−	17.9059i	0.380288	−	0.658678i	−0.610815	−	0.791773i	$-0.709158\pi$
$739$	10.3380	−	17.9059i	0.380288	−	0.658678i	0.991103	+	0.133095i	$0.0424915\pi$
$740$	2.60132			0.0956264
$741$		0			0
$742$	10.0915			0.370471
$743$	3.35204	−	5.80591i	0.122975	−	0.212998i	−0.797965	−	0.602704i	$-0.794090\pi$
$743$	3.35204	−	5.80591i	0.122975	−	0.212998i	0.920939	+	0.389706i	$0.127423\pi$
$744$	−1.46720	+	2.54126i	−0.0537900	+	0.0931670i
$745$	−4.76857	−	8.25941i	−0.174707	−	0.302601i
$746$	−13.4044	+	23.2170i	−0.490769	+	0.850036i
$747$	3.41307	+	5.91160i	0.124878	+	0.216294i
$748$	−6.91622			−0.252882
$749$	−6.68004			−0.244084
$750$	−2.12583	−	3.68204i	−0.0776243	−	0.134449i
$751$	5.35369	+	9.27287i	0.195359	+	0.338372i	0.947018	−	0.321180i	$-0.104079\pi$
$751$	5.35369	+	9.27287i	0.195359	+	0.338372i	−0.751659	+	0.659552i	$0.770746\pi$
$752$	−0.0300295			−0.00109506
$753$	8.61856			0.314078
$754$	8.06758	+	13.9735i	0.293804	+	0.508883i
$755$	18.4795	−	32.0075i	0.672539	−	1.16487i
$756$	−3.50640	−	6.07326i	−0.127526	−	0.220882i
$757$	2.03121	−	3.51816i	0.0738256	−	0.127870i	−0.826749	−	0.562570i	$-0.809813\pi$
$757$	2.03121	−	3.51816i	0.0738256	−	0.127870i	0.900575	+	0.434701i	$0.143146\pi$
$758$	−7.85282	+	13.6015i	−0.285227	+	0.494028i
$759$	−3.19253			−0.115882
$760$		0			0
$761$	−11.0077			−0.399030			−0.199515	−	0.979895i	$-0.563937\pi$
$761$	−11.0077			−0.399030			−0.199515	+	0.979895i	$0.563937\pi$
$762$	−0.0236329	+	0.0409333i	−0.000856129	+	0.00148286i
$763$	−6.92514	+	11.9947i	−0.250707	+	0.434237i
$764$	11.6220	+	20.1298i	0.420468	+	0.728271i
$765$	−5.68479	+	9.84635i	−0.205534	+	0.355996i
$766$	10.3135	+	17.8634i	0.372640	+	0.645432i
$767$	56.9231			2.05538
$768$	8.56717			0.309141
$769$	−10.6736	−	18.4873i	−0.384902	−	0.666669i	0.606854	−	0.794813i	$-0.292431\pi$
$769$	−10.6736	−	18.4873i	−0.384902	−	0.666669i	−0.991756	+	0.128144i	$0.959098\pi$
$770$	7.13816	+	12.3636i	0.257241	+	0.445555i
$771$	8.17024			0.294244
$772$	15.8262			0.569599
$773$	8.95858	+	15.5167i	0.322218	+	0.558097i	0.980945	−	0.194284i	$-0.0622384\pi$
$773$	8.95858	+	15.5167i	0.322218	+	0.558097i	−0.658728	+	0.752381i	$0.728905\pi$
$774$	−5.73483	+	9.93302i	−0.206134	+	0.357035i
$775$	1.37164	+	2.37576i	0.0492709	+	0.0853397i
$776$	−2.58630	+	4.47961i	−0.0928429	+	0.160809i
$777$	−0.418748	+	0.725293i	−0.0150225	+	0.0260197i
$778$	−3.43788			−0.123254
$779$		0			0
$780$	−8.74422			−0.313093
$781$	−23.4688	+	40.6492i	−0.839781	+	1.45454i
$782$	1.27807	−	2.21368i	0.0457036	−	0.0791609i
$783$	−5.27450	−	9.13570i	−0.188495	−	0.326483i
$784$	−0.0726338	+	0.125805i	−0.00259406	+	0.00449305i
$785$	−13.1348	−	22.7501i	−0.468799	−	0.811984i
$786$	−1.42097			−0.0506843
$787$	−48.8316			−1.74066			−0.870330	−	0.492470i	$-0.836094\pi$
$787$	−48.8316			−1.74066			−0.870330	+	0.492470i	$0.836094\pi$
$788$	−14.2297	−	24.6465i	−0.506911	−	0.877996i
$789$	2.56552	+	4.44361i	0.0913350	+	0.158197i
$790$	15.5047			0.551634
$791$	13.8648			0.492977
$792$	13.1498	+	22.7761i	0.467257	+	0.809312i
$793$	−11.6113	+	20.1113i	−0.412329	+	0.714174i
$794$	3.93923	+	6.82294i	0.139798	+	0.242137i
$795$	−4.11334	+	7.12452i	−0.145885	+	0.252681i
$796$	5.65600	−	9.79648i	0.200472	−	0.347227i
$797$	28.5262			1.01045			0.505225	−	0.862988i	$-0.331409\pi$
$797$	28.5262			1.01045			0.505225	+	0.862988i	$0.331409\pi$
$798$		0			0
$799$	1.18479			0.0419149
$800$	3.97906	−	6.89193i	0.140681	−	0.243666i
$801$	3.10148	−	5.37192i	0.109585	−	0.189808i
$802$	0.891407	+	1.54396i	0.0314767	+	0.0545192i
$803$	12.8229	−	22.2100i	0.452512	−	0.783774i
$804$	4.63816	+	8.03352i	0.163575	+	0.283320i
$805$	8.36959			0.294989
$806$	9.04282			0.318520
$807$	4.86303	+	8.42301i	0.171187	+	0.296504i
$808$	11.2383	+	19.4653i	0.395362	+	0.684787i
$809$	−14.8367			−0.521630			−0.260815	−	0.965389i	$-0.583991\pi$
$809$	−14.8367			−0.521630			−0.260815	+	0.965389i	$0.583991\pi$
$810$	14.5449			0.511055
$811$	−4.18866	−	7.25498i	−0.147084	−	0.254757i	0.783065	−	0.621940i	$-0.213655\pi$
$811$	−4.18866	−	7.25498i	−0.147084	−	0.254757i	−0.930148	+	0.367184i	$0.880322\pi$
$812$	−3.99747	+	6.92383i	−0.140284	+	0.242979i
$813$	5.04529	+	8.73870i	0.176946	+	0.306480i
$814$	1.25624	−	2.17588i	0.0440313	−	0.0762645i
$815$	−2.56031	+	4.43458i	−0.0896837	+	0.155337i
$816$	0.0368366			0.00128954
$817$		0			0
$818$	−28.3233			−0.990299
$819$	−13.5077	+	23.3961i	−0.471999	+	0.817526i
$820$	−6.97343	+	12.0783i	−0.243523	+	0.421794i
$821$	−3.13950	−	5.43777i	−0.109569	−	0.189780i	0.806027	−	0.591879i	$-0.201614\pi$
$821$	−3.13950	−	5.43777i	−0.109569	−	0.189780i	−0.915596	+	0.402100i	$0.868280\pi$
$822$	−4.57145	+	7.91799i	−0.159448	+	0.276171i
$823$	−5.51320	−	9.54915i	−0.192178	−	0.332862i	0.753794	−	0.657111i	$-0.228222\pi$
$823$	−5.51320	−	9.54915i	−0.192178	−	0.332862i	−0.945972	+	0.324249i	$0.894888\pi$
$824$	0.0412797			0.00143805
$825$	−2.56212			−0.0892015
$826$	−8.89053	−	15.3988i	−0.309341	−	0.535794i
$827$	16.9679	+	29.3893i	0.590032	+	1.02197i	0.994227	+	0.107293i	$0.0342182\pi$
$827$	16.9679	+	29.3893i	0.590032	+	1.02197i	−0.404195	+	0.914673i	$0.632448\pi$
$828$	5.86154			0.203703
$829$	20.3669			0.707372			0.353686	−	0.935364i	$-0.384928\pi$
$829$	20.3669			0.707372			0.353686	+	0.935364i	$0.384928\pi$
$830$	−2.79726	−	4.84499i	−0.0970942	−	0.168172i
$831$	3.66179	−	6.34240i	0.127026	−	0.220016i
$832$	−13.3380	−	23.1020i	−0.462411	−	0.800919i
$833$	2.86571	−	4.96356i	0.0992911	−	0.171977i
$834$	−3.60220	+	6.23919i	−0.124734	+	0.216045i
$835$	−58.8881			−2.03791
$836$		0			0
$837$	−5.91210			−0.204352
$838$	−10.2228	+	17.7064i	−0.353141	+	0.611658i
$839$	7.90467	−	13.6913i	0.272899	−	0.472676i	−0.696704	−	0.717359i	$-0.745351\pi$
$839$	7.90467	−	13.6913i	0.272899	−	0.472676i	0.969603	+	0.244683i	$0.0786840\pi$
$840$	3.59240	+	6.22221i	0.123949	+	0.214687i
$841$	8.48680	−	14.6996i	0.292648	−	0.506881i
$842$	−2.83750	−	4.91469i	−0.0977866	−	0.169371i
$843$	6.97628			0.240276
$844$	17.9385			0.617469
$845$	18.9820	+	32.8779i	0.653002	+	1.13103i
$846$	−0.856381	−	1.48330i	−0.0294430	−	0.0509968i
$847$	−1.19934			−0.0412098
$848$	−0.255777			−0.00878343
$849$	−4.62314	−	8.00752i	−0.158666	−	0.274817i
$850$	1.02569	−	1.77655i	0.0351810	−	0.0609352i
$851$	−0.736482	−	1.27562i	−0.0252463	−	0.0437278i
$852$	−4.49020	+	7.77725i	−0.153832	+	0.266444i
$853$	26.3246	−	45.5955i	0.901337	−	1.56116i	0.0755770	−	0.997140i	$-0.475920\pi$
$853$	26.3246	−	45.5955i	0.901337	−	1.56116i	0.825760	−	0.564022i	$-0.190747\pi$
$854$	7.25402			0.248228
$855$		0			0
$856$	10.0855			0.344716
$857$	−11.5137	+	19.9423i	−0.393299	+	0.681215i	−0.992883	−	0.119098i	$-0.962000\pi$
$857$	−11.5137	+	19.9423i	−0.393299	+	0.681215i	0.599583	+	0.800313i	$0.295333\pi$
$858$	−4.22281	+	7.31412i	−0.144164	+	0.249700i
$859$	−4.45471	−	7.71578i	−0.151993	−	0.263259i	0.779967	−	0.625820i	$-0.215236\pi$
$859$	−4.45471	−	7.71578i	−0.151993	−	0.263259i	−0.931960	+	0.362561i	$0.881902\pi$
$860$	−7.45558	+	12.9135i	−0.254233	+	0.440345i
$861$	−2.24510	−	3.88863i	−0.0765128	−	0.132524i
$862$	−12.3090			−0.419247
$863$	−29.7698			−1.01338			−0.506688	−	0.862129i	$-0.669130\pi$
$863$	−29.7698			−1.01338			−0.506688	+	0.862129i	$0.669130\pi$
$864$	8.57532	+	14.8529i	0.291738	+	0.505306i
$865$	−1.13516	−	1.96616i	−0.0385967	−	0.0668514i
$866$	−25.2321			−0.857420
$867$	7.59215			0.257843
$868$	2.24035	+	3.88040i	0.0760425	+	0.131709i
$869$	−11.8773	+	20.5721i	−0.402911	+	0.697862i
$870$	2.05438	+	3.55829i	0.0696499	+	0.120637i
$871$	37.5972	−	65.1203i	1.27393	−	2.20652i
$872$	10.4556	−	18.1096i	0.354071	−	0.613269i
$873$	−4.95273			−0.167625
$874$		0			0
$875$	−17.0770			−0.577307
$876$	2.45336	−	4.24935i	0.0828915	−	0.143572i
$877$	−12.5150	+	21.6766i	−0.422602	+	0.731968i	−0.996193	−	0.0871736i	$-0.972217\pi$
$877$	−12.5150	+	21.6766i	−0.422602	+	0.731968i	0.573591	+	0.819142i	$0.305550\pi$
$878$	5.86649	+	10.1611i	0.197984	+	0.342919i
$879$	−4.15136	+	7.19037i	−0.140022	+	0.242525i
$880$	−0.180922	−	0.313366i	−0.00609888	−	0.0105636i
$881$	20.3960			0.687158			0.343579	−	0.939124i	$-0.388361\pi$
$881$	20.3960			0.687158			0.343579	+	0.939124i	$0.388361\pi$
$882$	−8.28548			−0.278987
$883$	5.31403	+	9.20416i	0.178831	+	0.309745i	0.941480	−	0.337068i	$-0.109435\pi$
$883$	5.31403	+	9.20416i	0.178831	+	0.309745i	−0.762649	+	0.646812i	$0.776102\pi$
$884$	5.36319	+	9.28931i	0.180384	+	0.312433i
$885$	14.4953			0.487253
$886$	−29.7962			−1.00102
$887$	−28.1694	−	48.7908i	−0.945835	−	1.63823i	−0.754071	−	0.656793i	$-0.771913\pi$
$887$	−28.1694	−	48.7908i	−0.945835	−	1.63823i	−0.191764	−	0.981441i	$-0.561421\pi$
$888$	0.632226	−	1.09505i	0.0212161	−	0.0367474i
$889$	0.0949225	+	0.164411i	0.00318360	+	0.00551415i
$890$	−2.54189	+	4.40268i	−0.0852043	+	0.147578i
$891$	−11.1420	+	19.2986i	−0.373272	+	0.646526i
$892$	−3.69789			−0.123815
$893$		0			0
$894$	−1.76239			−0.0589432
$895$	26.9898	−	46.7477i	0.902169	−	1.56260i
$896$	6.42989	−	11.1369i	0.214808	−	0.372058i
$897$	2.47565	+	4.28795i	0.0826596	+	0.143171i
$898$	−8.28389	+	14.3481i	−0.276437	+	0.478803i
$899$	3.37005	+	5.83710i	0.112398	+	0.194678i
$900$	4.70409			0.156803
$901$	10.0915			0.336197
$902$	6.73530	+	11.6659i	0.224261	+	0.388431i
$903$	−2.40033	−	4.15749i	−0.0798780	−	0.138353i
$904$	−20.9331			−0.696226
$905$	−40.7648			−1.35507
$906$	−3.41488	−	5.91474i	−0.113452	−	0.196504i
$907$	−2.96182	+	5.13002i	−0.0983456	+	0.170340i	−0.911000	−	0.412406i	$-0.864688\pi$
$907$	−2.96182	+	5.13002i	−0.0983456	+	0.170340i	0.812654	+	0.582746i	$0.198022\pi$
$908$	8.41622	+	14.5773i	0.279302	+	0.483765i
$909$	−10.7606	+	18.6379i	−0.356906	+	0.618179i
$910$	11.0706	−	19.1748i	0.366986	−	0.635638i
$911$	34.0591			1.12843			0.564215	−	0.825628i	$-0.309179\pi$
$911$	34.0591			1.12843			0.564215	+	0.825628i	$0.309179\pi$
$912$		0			0
$913$	8.57129			0.283668
$914$	6.27837	−	10.8745i	0.207670	−	0.359695i
$915$	−2.95677	+	5.12127i	−0.0977477	+	0.169304i
$916$	5.77409	+	10.0010i	0.190781	+	0.330443i
$917$	−2.85369	+	4.94274i	−0.0942372	+	0.163224i
$918$	2.21048	+	3.82867i	0.0729569	+	0.126365i
$919$	−6.27395			−0.206958			−0.103479	−	0.994632i	$-0.532998\pi$
$919$	−6.27395			−0.206958			−0.103479	+	0.994632i	$0.532998\pi$
$920$	−12.6364			−0.416610
$921$	−5.72534	−	9.91658i	−0.188656	−	0.326762i
$922$	−6.12407	−	10.6072i	−0.201686	−	0.349330i
$923$	72.7957			2.39610
$924$	−4.18479			−0.137670
$925$	−0.591052	−	1.02373i	−0.0194337	−	0.0336601i
$926$	−0.775129	+	1.34256i	−0.0254723	+	0.0441194i
$927$	0.0197625	+	0.0342296i	0.000649085	+	0.00112425i
$928$	9.77631	−	16.9331i	0.320923	−	0.555855i
$929$	−14.1616	+	24.5287i	−0.464628	+	0.804759i	−0.999185	−	0.0403735i	$-0.987145\pi$
$929$	−14.1616	+	24.5287i	−0.464628	+	0.804759i	0.534557	+	0.845133i	$0.320479\pi$
$930$	2.30272			0.0755091
$931$		0			0
$932$	29.6682			0.971814
$933$	3.85638	−	6.67945i	0.126252	−	0.218675i
$934$	9.69166	−	16.7864i	0.317121	−	0.549269i
$935$	7.13816	+	12.3636i	0.233443	+	0.404335i
$936$	20.3940	−	35.3234i	0.666598	−	1.15458i
$937$	10.0360	+	17.3828i	0.327860	+	0.567871i	0.982087	−	0.188428i	$-0.0603391\pi$
$937$	10.0360	+	17.3828i	0.327860	+	0.567871i	−0.654227	+	0.756299i	$0.727006\pi$
$938$	−23.4884			−0.766925
$939$	−10.3856			−0.338920
$940$	−1.11334	−	1.92836i	−0.0363132	−	0.0628963i
$941$	2.69759	+	4.67236i	0.0879388	+	0.152314i	0.906640	−	0.421906i	$-0.138639\pi$
$941$	2.69759	+	4.67236i	0.0879388	+	0.152314i	−0.818701	+	0.574220i	$0.805305\pi$
$942$	−4.85441			−0.158165
$943$	7.89723			0.257169
$944$	0.225337	+	0.390296i	0.00733411	+	0.0127030i
$945$	−7.23783	+	12.5363i	−0.235446	+	0.407805i
$946$	7.20099	+	12.4725i	0.234124	+	0.405515i
$947$	−3.32160	+	5.75319i	−0.107938	+	0.186953i	−0.914935	−	0.403602i	$-0.867758\pi$
$947$	−3.32160	+	5.75319i	−0.107938	+	0.186953i	0.806997	+	0.590556i	$0.201091\pi$
$948$	−2.27244	+	3.93598i	−0.0738055	+	0.127835i
$949$	−39.7743			−1.29113
$950$		0			0
$951$	15.0833			0.489109
$952$	4.40673	−	7.63267i	0.142823	−	0.247376i
$953$	−7.41194	+	12.8379i	−0.240096	+	0.415859i	−0.960742	−	0.277445i	$-0.910512\pi$
$953$	−7.41194	+	12.8379i	−0.240096	+	0.415859i	0.720645	+	0.693304i	$0.243846\pi$
$954$	−7.29426	−	12.6340i	−0.236160	−	0.409042i
$955$	23.9898	−	41.5515i	0.776291	−	1.34458i
$956$	−14.3068	−	24.7800i	−0.462713	−	0.801443i
$957$	−6.29498			−0.203488
$958$	22.3865			0.723275
$959$	18.3614	+	31.8029i	0.592922	+	1.02697i
$960$	−3.39646	−	5.88284i	−0.109620	−	0.189868i
$961$	−27.2226			−0.878147
$962$	−3.89662			−0.125632
$963$	4.82841	+	8.36305i	0.155593	+	0.269496i
$964$	−0.182571	+	0.316222i	−0.00588022	+	0.0101848i
$965$	−16.3341	−	28.2915i	−0.525813	−	0.910735i
$966$	0.773318	−	1.33943i	0.0248811	−	0.0430953i
$967$	−10.6108	+	18.3785i	−0.341221	+	0.591012i	−0.984660	−	0.174486i	$-0.944174\pi$
$967$	−10.6108	+	18.3785i	−0.341221	+	0.591012i	0.643439	+	0.765497i	$0.277507\pi$
$968$	1.81076			0.0582002
$969$		0			0
$970$	4.05913			0.130331
$971$	−18.8033	+	32.5684i	−0.603428	+	1.04517i	0.388870	+	0.921293i	$0.372866\pi$
$971$	−18.8033	+	32.5684i	−0.603428	+	1.04517i	−0.992298	+	0.123875i	$0.960468\pi$
$972$	−7.72890	+	13.3869i	−0.247905	+	0.429384i
$973$	14.4684	+	25.0600i	0.463835	+	0.803386i
$974$	9.89780	−	17.1435i	0.317146	−	0.549313i
$975$	1.98680	+	3.44123i	0.0636284	+	0.110208i
$976$	−0.183859			−0.00588518
$977$	46.0215			1.47236			0.736179	−	0.676787i	$-0.236628\pi$
$977$	46.0215			1.47236			0.736179	+	0.676787i	$0.236628\pi$
$978$	0.473126	+	0.819478i	0.0151289	+	0.0262040i
$979$	−3.89440	−	6.74530i	−0.124466	−	0.215581i
$980$	−10.7716			−0.344085
$981$	20.0223			0.639262
$982$	6.87417	+	11.9064i	0.219364	+	0.379949i
$983$	30.2982	−	52.4780i	0.966362	−	1.67379i	0.260452	−	0.965487i	$-0.416128\pi$
$983$	30.2982	−	52.4780i	0.966362	−	1.67379i	0.705910	−	0.708302i	$-0.250538\pi$
$984$	3.38965	+	5.87105i	0.108058	+	0.187162i
$985$	−29.3726	+	50.8748i	−0.935888	+	1.62101i
$986$	2.52007	−	4.36488i	0.0802553	−	0.139006i
$987$	0.716881			0.0228186
$988$		0			0
$989$	8.44326			0.268480
$990$	10.3191	−	17.8732i	0.327962	−	0.568047i
$991$	20.9491	−	36.2849i	0.665470	−	1.15263i	−0.313688	−	0.949526i	$-0.601565\pi$
$991$	20.9491	−	36.2849i	0.665470	−	1.15263i	0.979158	−	0.203101i	$-0.0651020\pi$
$992$	−5.47906	−	9.49000i	−0.173960	−	0.301308i
$993$	0.454956	−	0.788006i	0.0144376	−	0.0250066i
$994$	−11.3696	−	19.6927i	−0.360621	−	0.624614i
$995$	−23.3500			−0.740244
$996$	1.63991			0.0519626
$997$	−16.8576	−	29.1982i	−0.533884	−	0.924715i	−0.999216	−	0.0395787i	$-0.987398\pi$
$997$	−16.8576	−	29.1982i	−0.533884	−	0.924715i	0.465332	−	0.885136i	$-0.345935\pi$
$998$	−12.5826	−	21.7937i	−0.398295	−	0.689867i
$999$	2.54757			0.0806016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.c.h.68.3		6
19.2	odd	18		361.2.e.f.234.1		6
19.3	odd	18		19.2.e.a.4.1	✓	6
19.4	even	9		361.2.e.h.62.1		6
19.5	even	9		361.2.e.a.28.1		6
19.6	even	9		361.2.e.b.54.1		6
19.7	even	3	inner	361.2.c.h.292.3		6
19.8	odd	6		361.2.a.g.1.3		3
19.9	even	9		361.2.e.a.245.1		6
19.10	odd	18		361.2.e.g.245.1		6
19.11	even	3		361.2.a.h.1.1		3
19.12	odd	6		361.2.c.i.292.1		6
19.13	odd	18		361.2.e.f.54.1		6
19.14	odd	18		361.2.e.g.28.1		6
19.15	odd	18		19.2.e.a.5.1	yes	6
19.16	even	9		361.2.e.h.99.1		6
19.17	even	9		361.2.e.b.234.1		6
19.18	odd	2		361.2.c.i.68.1		6
57.8	even	6		3249.2.a.z.1.1		3
57.11	odd	6		3249.2.a.s.1.3		3
57.41	even	18		171.2.u.c.118.1		6
57.53	even	18		171.2.u.c.100.1		6
76.3	even	18		304.2.u.b.289.1		6
76.11	odd	6		5776.2.a.bi.1.3		3
76.15	even	18		304.2.u.b.81.1		6
76.27	even	6		5776.2.a.br.1.1		3
95.3	even	36		475.2.u.a.99.1		12
95.22	even	36		475.2.u.a.99.2		12
95.34	odd	18		475.2.l.a.176.1		6
95.49	even	6		9025.2.a.x.1.3		3
95.53	even	36		475.2.u.a.24.2		12
95.72	even	36		475.2.u.a.24.1		12
95.79	odd	18		475.2.l.a.251.1		6
95.84	odd	6		9025.2.a.bd.1.1		3
133.3	even	18		931.2.v.a.422.1		6
133.34	even	18		931.2.w.a.442.1		6
133.41	even	18		931.2.w.a.99.1		6
133.53	odd	18		931.2.x.a.765.1		6
133.60	odd	18		931.2.v.b.422.1		6
133.72	odd	18		931.2.v.b.214.1		6
133.79	odd	18		931.2.x.a.802.1		6
133.110	even	18		931.2.v.a.214.1		6
133.117	even	18		931.2.x.b.802.1		6
133.129	even	18		931.2.x.b.765.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	19.3	odd	18
19.2.e.a.5.1	yes	6	19.15	odd	18
171.2.u.c.100.1		6	57.53	even	18
171.2.u.c.118.1		6	57.41	even	18
304.2.u.b.81.1		6	76.15	even	18
304.2.u.b.289.1		6	76.3	even	18
361.2.a.g.1.3		3	19.8	odd	6
361.2.a.h.1.1		3	19.11	even	3
361.2.c.h.68.3		6	1.1	even	1	trivial
361.2.c.h.292.3		6	19.7	even	3	inner
361.2.c.i.68.1		6	19.18	odd	2
361.2.c.i.292.1		6	19.12	odd	6
361.2.e.a.28.1		6	19.5	even	9
361.2.e.a.245.1		6	19.9	even	9
361.2.e.b.54.1		6	19.6	even	9
361.2.e.b.234.1		6	19.17	even	9
361.2.e.f.54.1		6	19.13	odd	18
361.2.e.f.234.1		6	19.2	odd	18
361.2.e.g.28.1		6	19.14	odd	18
361.2.e.g.245.1		6	19.10	odd	18
361.2.e.h.62.1		6	19.4	even	9
361.2.e.h.99.1		6	19.16	even	9
475.2.l.a.176.1		6	95.34	odd	18
475.2.l.a.251.1		6	95.79	odd	18
475.2.u.a.24.1		12	95.72	even	36
475.2.u.a.24.2		12	95.53	even	36
475.2.u.a.99.1		12	95.3	even	36
475.2.u.a.99.2		12	95.22	even	36
931.2.v.a.214.1		6	133.110	even	18
931.2.v.a.422.1		6	133.3	even	18
931.2.v.b.214.1		6	133.72	odd	18
931.2.v.b.422.1		6	133.60	odd	18
931.2.w.a.99.1		6	133.41	even	18
931.2.w.a.442.1		6	133.34	even	18
931.2.x.a.765.1		6	133.53	odd	18
931.2.x.a.802.1		6	133.79	odd	18
931.2.x.b.765.1		6	133.129	even	18
931.2.x.b.802.1		6	133.117	even	18
3249.2.a.s.1.3		3	57.11	odd	6
3249.2.a.z.1.1		3	57.8	even	6
5776.2.a.bi.1.3		3	76.11	odd	6
5776.2.a.br.1.1		3	76.27	even	6
9025.2.a.x.1.3		3	95.49	even	6
9025.2.a.bd.1.1		3	95.84	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.439693 - 0.761570i) q^{2} +(0.266044 - 0.460802i) q^{3} +(0.613341 + 1.06234i) q^{4} +(1.26604 - 2.19285i) q^{5} +(-0.233956 - 0.405223i) q^{6} -1.87939 q^{7} +2.83750 q^{8} +(1.35844 + 2.35289i) q^{9} +(-1.11334 - 1.92836i) q^{10} +3.41147 q^{11} +0.652704 q^{12} +(-2.64543 - 4.58202i) q^{13} +(-0.826352 + 1.43128i) q^{14} +(-0.673648 - 1.16679i) q^{15} +(0.0209445 - 0.0362770i) q^{16} +(-0.826352 + 1.43128i) q^{17} +2.38919 q^{18} +3.10607 q^{20} +(-0.500000 + 0.866025i) q^{21} +(1.50000 - 2.59808i) q^{22} +(-0.879385 - 1.52314i) q^{23} +(0.754900 - 1.30753i) q^{24} +(-0.705737 - 1.22237i) q^{25} -4.65270 q^{26} +3.04189 q^{27} +(-1.15270 - 1.99654i) q^{28} +(-1.73396 - 3.00330i) q^{29} -1.18479 q^{30} -1.94356 q^{31} +(2.81908 + 4.88279i) q^{32} +(0.907604 - 1.57202i) q^{33} +(0.726682 + 1.25865i) q^{34} +(-2.37939 + 4.12122i) q^{35} +(-1.66637 + 2.88624i) q^{36} +0.837496 q^{37} -2.81521 q^{39} +(3.59240 - 6.22221i) q^{40} +(-2.24510 + 3.88863i) q^{41} +(0.439693 + 0.761570i) q^{42} +(-2.40033 + 4.15749i) q^{43} +(2.09240 + 3.62414i) q^{44} +6.87939 q^{45} -1.54664 q^{46} +(-0.358441 - 0.620838i) q^{47} +(-0.0111444 - 0.0193026i) q^{48} -3.46791 q^{49} -1.24123 q^{50} +(0.439693 + 0.761570i) q^{51} +(3.24510 - 5.62068i) q^{52} +(-3.05303 - 5.28801i) q^{53} +(1.33750 - 2.31661i) q^{54} +(4.31908 - 7.48086i) q^{55} -5.33275 q^{56} -3.04963 q^{58} +(-5.37939 + 9.31737i) q^{59} +(0.826352 - 1.43128i) q^{60} +(-2.19459 - 3.80115i) q^{61} +(-0.854570 + 1.48016i) q^{62} +(-2.55303 - 4.42198i) q^{63} +5.04189 q^{64} -13.3969 q^{65} +(-0.798133 - 1.38241i) q^{66} +(7.10607 + 12.3081i) q^{67} -2.02734 q^{68} -0.935822 q^{69} +(2.09240 + 3.62414i) q^{70} +(-6.87939 + 11.9154i) q^{71} +(3.85457 + 6.67631i) q^{72} +(3.75877 - 6.51038i) q^{73} +(0.368241 - 0.637812i) q^{74} -0.751030 q^{75} -6.41147 q^{77} +(-1.23783 + 2.14398i) q^{78} +(-3.48158 + 6.03028i) q^{79} +(-0.0530334 - 0.0918566i) q^{80} +(-3.26604 + 5.65695i) q^{81} +(1.97431 + 3.41960i) q^{82} +2.51249 q^{83} -1.22668 q^{84} +(2.09240 + 3.62414i) q^{85} +(2.11081 + 3.65604i) q^{86} -1.84524 q^{87} +9.68004 q^{88} +(-1.14156 - 1.97724i) q^{89} +(3.02481 - 5.23913i) q^{90} +(4.97178 + 8.61138i) q^{91} +(1.07873 - 1.86841i) q^{92} +(-0.517074 + 0.895599i) q^{93} -0.630415 q^{94} +3.00000 q^{96} +(-0.911474 + 1.57872i) q^{97} +(-1.52481 + 2.64106i) q^{98} +(4.63429 + 8.02682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 12 q^{8} + 6 q^{12} - 6 q^{14} - 3 q^{15} - 3 q^{16} - 6 q^{17} + 6 q^{18} - 6 q^{20} - 3 q^{21} + 9 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{25} - 30 q^{26}+ \cdots + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 12 * q^8 + 6 * q^12 - 6 * q^14 - 3 * q^15 - 3 * q^16 - 6 * q^17 + 6 * q^18 - 6 * q^20 - 3 * q^21 + 9 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^25 - 30 * q^26 + 12 * q^27 - 9 * q^28 - 15 * q^29 + 18 * q^31 + 9 * q^33 - 9 * q^34 - 3 * q^35 + 9 * q^36 - 24 * q^39 + 18 * q^40 - 12 * q^41 - 3 * q^42 + 9 * q^44 + 30 * q^45 - 36 * q^46 + 6 * q^47 + 6 * q^48 - 30 * q^49 - 30 * q^50 - 3 * q^51 + 18 * q^52 - 6 * q^53 + 3 * q^54 + 9 * q^55 + 6 * q^56 + 36 * q^58 - 21 * q^59 + 6 * q^60 - 9 * q^61 - 21 * q^62 - 3 * q^63 + 24 * q^64 - 24 * q^65 + 9 * q^66 + 18 * q^67 + 30 * q^68 - 24 * q^69 + 9 * q^70 - 30 * q^71 + 39 * q^72 - 3 * q^74 - 30 * q^75 - 18 * q^77 + 12 * q^78 - 9 * q^79 + 12 * q^80 - 15 * q^81 - 18 * q^82 + 6 * q^84 + 9 * q^85 + 21 * q^86 + 42 * q^87 + 18 * q^88 - 15 * q^89 - 9 * q^90 + 15 * q^91 + 24 * q^92 - 24 * q^93 - 18 * q^94 + 18 * q^96 + 15 * q^97 + 18 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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