LMFDB - Embedded newform 361.2.c.i.292.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(68,361)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			292.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	361.292
Dual form			361.2.c.i.68.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.439693 - 0.761570i) q^{2} +(-0.266044 - 0.460802i) q^{3} +(0.613341 - 1.06234i) q^{4} +(1.26604 + 2.19285i) q^{5} +(-0.233956 + 0.405223i) q^{6} -1.87939 q^{7} -2.83750 q^{8} +(1.35844 - 2.35289i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - 12 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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	$-0.267300\pi$
$2$	−0.439693	−	0.761570i	−0.310910	−	0.538511i	−0.978560	+	0.205964i	$0.933967\pi$
$3$	−0.266044	−	0.460802i	−0.153601	−	0.266044i	0.778948	−	0.627089i	$-0.215754\pi$
$3$	−0.266044	−	0.460802i	−0.153601	−	0.266044i	−0.932549	+	0.361044i	$0.882420\pi$
$4$	0.613341	−	1.06234i	0.306670	−	0.531169i
$5$	1.26604	+	2.19285i	0.566192	+	0.980674i	0.996938	+	0.0782003i	$0.0249174\pi$
$5$	1.26604	+	2.19285i	0.566192	+	0.980674i	−0.430745	+	0.902473i	$0.641749\pi$
$6$	−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	−0.221577	−	0.975143i	$-0.571120\pi$
$13$	2.64543	−	4.58202i	0.733710	−	1.27082i	0.955287	−	0.295680i	$-0.0955463\pi$
$14$	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	0.748244	−	0.663424i	$-0.230897\pi$
$17$	−0.826352	−	1.43128i	−0.200420	−	0.347137i	−0.948664	+	0.316286i	$0.897564\pi$
$18$	−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	−0.943024	−	0.332724i	$-0.892032\pi$
$23$	−0.879385	+	1.52314i	−0.183364	+	0.317597i	0.759660	+	0.650321i	$0.225366\pi$
$24$	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	$-0.728982\pi$
$29$	1.73396	−	3.00330i	0.321987	−	0.557699i	0.980898	+	0.194523i	$0.0623158\pi$
$30$	−1.18479			−0.216313
$31$	1.94356			0.349074			0.174537	−	0.984651i	$-0.444157\pi$
$31$	1.94356			0.349074			0.174537	+	0.984651i	$0.444157\pi$
$32$	−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	$-0.521930\pi$
$37$	−0.837496			−0.137684			−0.0688418	+	0.997628i	$0.521930\pi$
$38$		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	$-0.0526356\pi$
$41$	2.24510	+	3.88863i	0.350626	+	0.607302i	−0.635734	+	0.771909i	$0.719302\pi$
$42$	0.439693	−	0.761570i	0.0678460	−	0.117513i
$43$	−2.40033	−	4.15749i	−0.366047	−	0.634012i	0.622897	−	0.782304i	$-0.285956\pi$
$43$	−2.40033	−	4.15749i	−0.366047	−	0.634012i	−0.988944	+	0.148292i	$0.952622\pi$
$44$	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	−0.890983	−	0.454037i	$-0.849983\pi$
$47$	−0.358441	+	0.620838i	−0.0522840	+	0.0905585i	0.838699	+	0.544595i	$0.183317\pi$
$48$	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	$-0.695586\pi$
$53$	3.05303	−	5.28801i	0.419366	−	0.726364i	0.995876	+	0.0907266i	$0.0289189\pi$
$54$	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	0.968348	+	0.249603i	$0.0803000\pi$
$59$	5.37939	+	9.31737i	0.700336	+	1.21302i	−0.268012	+	0.963416i	$0.586367\pi$
$60$	−0.826352	−	1.43128i	−0.106682	−	0.184778i
$61$	−2.19459	+	3.80115i	−0.280989	+	0.486687i	−0.971629	−	0.236512i	$-0.923996\pi$
$61$	−2.19459	+	3.80115i	−0.280989	+	0.486687i	0.690640	+	0.723199i	$0.257329\pi$
$62$	−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	−0.00425333	+	0.999991i	$0.501354\pi$
$67$	−7.10607	+	12.3081i	−0.868144	+	1.50367i	−0.863891	+	0.503679i	$0.831979\pi$
$68$	−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	0.908294	+	0.418331i	$0.137385\pi$
$71$	6.87939	+	11.9154i	0.816433	+	1.41410i	−0.0918617	+	0.995772i	$0.529282\pi$
$72$	−3.85457	+	6.67631i	−0.454265	+	0.786811i
$73$	3.75877	+	6.51038i	0.439931	+	0.761983i	0.997684	−	0.0680246i	$-0.0216696\pi$
$73$	3.75877	+	6.51038i	0.439931	+	0.761983i	−0.557753	+	0.830007i	$0.688336\pi$
$74$	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	$-0.0385508\pi$
$79$	3.48158	+	6.03028i	0.391709	+	0.678459i	−0.600966	+	0.799274i	$0.705217\pi$
$80$	−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	$-0.794722\pi$
$89$	1.14156	−	1.97724i	0.121005	−	0.209587i	0.920164	+	0.391533i	$0.128055\pi$
$90$	−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	$-0.137166\pi$
$97$	0.911474	+	1.57872i	0.0925462	+	0.160295i	−0.816036	+	0.578002i	$0.803833\pi$
$98$	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	−0.598887	−	0.800833i	$-0.704390\pi$
$101$	3.96064	−	6.86002i	0.394098	−	0.682598i	0.992986	+	0.118235i	$0.0377237\pi$
$102$	0.773318			0.0765699
$103$	−0.0145479			−0.00143345			−0.000716725	−	1.00000i	$-0.500228\pi$
$103$	−0.0145479			−0.00143345			−0.000716725		1.00000i	$0.500228\pi$
$104$	−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	$-0.554961\pi$
$107$	−3.55438			−0.343615			−0.171807	+	0.985131i	$0.554961\pi$
$108$	−1.86571	+	3.23151i	−0.179528	+	0.310952i
$109$	−3.68479	−	6.38225i	−0.352939	−	0.611308i	0.633824	−	0.773477i	$-0.281484\pi$
$109$	−3.68479	−	6.38225i	−0.352939	−	0.611308i	−0.986763	+	0.162169i	$0.948151\pi$
$110$	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	$-0.387200\pi$
$113$	7.37733			0.694000			0.347000	+	0.937865i	$0.387200\pi$
$114$		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	$-0.831907\pi$
$127$	0.0505072	−	0.0874810i	0.00448179	−	0.00776269i	0.868258	+	0.496114i	$0.165240\pi$
$128$	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	0.924703	−	0.380689i	$-0.124313\pi$
$131$	1.51842	+	2.62998i	0.132665	+	0.229782i	−0.792038	+	0.610472i	$0.790980\pi$
$132$	−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	0.0595742	+	0.998224i	$0.481026\pi$
$137$	−9.76991	+	16.9220i	−0.834700	+	1.44574i	−0.894274	+	0.447519i	$0.852308\pi$
$138$	−0.411474	−	0.712694i	−0.0350270	−	0.0606686i
$139$	−7.69846	+	13.3341i	−0.652975	+	1.13099i	0.329422	+	0.944183i	$0.393146\pi$
$139$	−7.69846	+	13.3341i	−0.652975	+	1.13099i	−0.982397	+	0.186803i	$0.940187\pi$
$140$	−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	0.932797	−	0.360401i	$-0.117360\pi$
$149$	1.88326	+	3.26189i	0.154282	+	0.267225i	−0.778515	+	0.627626i	$0.784027\pi$
$150$	−0.330222	−	0.571962i	−0.0269625	−	0.0467005i
$151$	−14.5963			−1.18783			−0.593914	−	0.804529i	$-0.702418\pi$
$151$	−14.5963			−1.18783			−0.593914	+	0.804529i	$0.702418\pi$
$152$		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	0.995322	−	0.0966115i	$-0.0308004\pi$
$157$	5.18732	+	8.98470i	0.413993	+	0.717057i	−0.581329	+	0.813669i	$0.697467\pi$
$158$	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	0.0721175	−	0.997396i	$-0.477024\pi$
$167$	11.6284	−	20.1409i	0.899829	−	1.55855i	0.827712	−	0.561154i	$-0.189642\pi$
$168$	−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	$-0.177518\pi$
$173$	−0.448311	−	0.776497i	−0.0340844	−	0.0590360i	−0.882564	+	0.470191i	$0.844185\pi$
$174$	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	$-0.793422\pi$
$179$	−21.3182			−1.59340			−0.796699	+	0.604377i	$0.793422\pi$
$180$	4.21941	−	7.30823i	0.314496	−	0.544723i
$181$	8.04963	−	13.9424i	0.598324	−	1.03633i	−0.394744	−	0.918791i	$-0.629167\pi$
$181$	8.04963	−	13.9424i	0.598324	−	1.03633i	0.993069	−	0.117537i	$-0.0374999\pi$
$182$	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	$-0.320376\pi$
$193$	−6.45084	−	11.1732i	−0.464341	−	0.804263i	−0.999172	+	0.0406967i	$0.987042\pi$
$194$	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	−0.981885	−	0.189476i	$-0.939321\pi$
$199$	−4.61081	+	7.98617i	−0.326852	+	0.566124i	0.655033	+	0.755600i	$0.272655\pi$
$200$	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	−0.999992	−	0.00389033i	$-0.998762\pi$
$211$	−7.31180	−	12.6644i	−0.503365	−	0.871854i	0.496627	−	0.867964i	$-0.334572\pi$
$212$	−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	$-0.134483\pi$
$223$	1.50727	+	2.61068i	0.100935	+	0.174824i	−0.811135	+	0.584858i	$0.801150\pi$
$224$	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	$-0.650496\pi$
$227$	−13.7219			−0.910757			−0.455378	+	0.890298i	$0.650496\pi$
$228$		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	0.924583	+	0.380980i	$0.124413\pi$
$233$	12.0929	+	20.9455i	0.792230	+	1.37218i	−0.132354	+	0.991203i	$0.542253\pi$
$234$	−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	$-0.836385\pi$
$241$	−0.148833	+	0.257787i	−0.00958719	+	0.0166055i	0.861192	+	0.508280i	$0.169718\pi$
$242$	−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	−0.488725	−	0.872438i	$-0.662538\pi$
$251$	8.09879	−	14.0275i	0.511191	−	0.885409i	0.999916	−	0.0129711i	$-0.00412896\pi$
$252$	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	$-0.992301\pi$
$257$	−7.67752	+	13.2979i	−0.478910	+	0.829497i	0.520797	+	0.853680i	$0.325635\pi$
$258$	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	0.678207	−	0.734871i	$-0.262757\pi$
$263$	−4.82160	−	8.35126i	−0.297313	−	0.514961i	−0.975520	+	0.219910i	$0.929424\pi$
$264$	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	0.997725	+	0.0674144i	$0.0214750\pi$
$269$	9.13950	+	15.8301i	0.557245	+	0.965177i	−0.440480	+	0.897762i	$0.645192\pi$
$270$	−3.38666	+	5.86587i	−0.206106	+	0.356985i
$271$	−9.48205	−	16.4234i	−0.575993	−	0.997650i	−0.995933	−	0.0900978i	$-0.971282\pi$
$271$	−9.48205	−	16.4234i	−0.575993	−	0.997650i	0.419939	−	0.907552i	$-0.362051\pi$
$272$	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	$-0.961229\pi$
$281$	−6.55556	+	11.3546i	−0.391072	+	0.677356i	0.601519	+	0.798858i	$0.294562\pi$
$282$	−0.167718	−	0.290497i	−0.00998748	−	0.0172988i
$283$	8.68866	+	15.0492i	0.516487	+	0.894582i	0.999817	+	0.0191438i	$0.00609404\pi$
$283$	8.68866	+	15.0492i	0.516487	+	0.894582i	−0.483329	+	0.875439i	$0.660573\pi$
$284$	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	$-0.349354\pi$
$293$	15.6040			0.911596			0.455798	+	0.890083i	$0.349354\pi$
$294$	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	−0.990540	−	0.137227i	$-0.956181\pi$
$307$	−10.7601	−	18.6371i	−0.614112	−	1.06367i	0.376427	−	0.926446i	$-0.377152\pi$
$308$	−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	0.446533	+	0.894767i	$0.352659\pi$
$313$	−9.75924	+	16.9035i	−0.551625	+	0.955442i	−0.998158	+	0.0606748i	$0.980675\pi$
$314$	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	0.126085	+	0.992019i	$0.459759\pi$
$317$	−14.1736	+	24.5495i	−0.796071	+	1.37884i	−0.922157	+	0.386817i	$0.873575\pi$
$318$	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	$-0.514965\pi$
$331$	−1.71007			−0.0939942			−0.0469971	+	0.998895i	$0.514965\pi$
$332$	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	−0.970893	−	0.239512i	$-0.923013\pi$
$337$	−12.7194	−	22.0307i	−0.692870	−	1.20009i	0.278023	−	0.960574i	$-0.410321\pi$
$338$	−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	0.743945	−	0.668241i	$-0.232953\pi$
$347$	−3.85117	−	6.67042i	−0.206741	−	0.358087i	−0.950686	+	0.310154i	$0.899619\pi$
$348$	−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	0.695862	−	0.718175i	$-0.255022\pi$
$359$	−5.19207	−	8.99292i	−0.274027	−	0.474628i	−0.969889	+	0.243547i	$0.921689\pi$
$360$	−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	−0.0329030	−	0.999459i	$-0.510475\pi$
$367$	16.2665	−	28.1744i	0.849105	−	1.47069i	0.882008	−	0.471234i	$-0.156191\pi$
$368$	−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	$-0.210471\pi$
$373$	30.4858			1.57849			0.789246	+	0.614077i	$0.210471\pi$
$374$	−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	$-0.348316\pi$
$379$	17.8598			0.917396			0.458698	+	0.888592i	$0.348316\pi$
$380$		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	0.992928	+	0.118715i	$0.0378774\pi$
$383$	11.7280	+	20.3135i	0.599274	+	1.03797i	−0.393654	+	0.919259i	$0.628789\pi$
$384$	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	−0.911316	−	0.411709i	$-0.864932\pi$
$389$	−1.95471	+	3.38565i	−0.0991076	+	0.171659i	0.812208	+	0.583368i	$0.198265\pi$
$390$	−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	0.731445	−	0.681901i	$-0.238846\pi$
$397$	−4.47952	−	7.75876i	−0.224821	−	0.389401i	−0.956266	+	0.292500i	$0.905513\pi$
$398$	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	$-0.150547\pi$
$401$	1.01367	+	1.75573i	0.0506203	+	0.0876769i	−0.839605	+	0.543197i	$0.817214\pi$
$402$	−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	−0.125724	−	0.992065i	$-0.540125\pi$
$409$	16.1040	−	27.8930i	0.796292	−	1.37922i	0.922016	−	0.387153i	$-0.126541\pi$
$410$	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	$-0.216932\pi$
$421$	−3.22668	−	5.58878i	−0.157259	−	0.272380i	−0.933879	+	0.357589i	$0.883599\pi$
$422$	−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	$-0.723883\pi$
$431$	6.99866	−	12.1220i	0.337113	−	0.583898i	0.983888	+	0.178783i	$0.0572161\pi$
$432$	−0.0637109	−	0.110351i	−0.00306529	−	0.00530925i
$433$	14.3464	−	24.8487i	0.689445	−	1.19415i	−0.282573	−	0.959246i	$-0.591188\pi$
$433$	14.3464	−	24.8487i	0.689445	−	1.19415i	0.972018	−	0.234908i	$-0.0754788\pi$
$434$	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	$-0.0635227\pi$
$439$	6.67112	+	11.5547i	0.318395	+	0.551477i	−0.661758	+	0.749717i	$0.730189\pi$
$440$	−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	0.111433	+	0.993772i	$0.464456\pi$
$443$	−16.9415	+	29.3435i	−0.804915	+	1.39415i	−0.916348	+	0.400382i	$0.868877\pi$
$444$	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	$-0.353359\pi$
$449$	18.8402			0.889123			0.444562	+	0.895748i	$0.353359\pi$
$450$	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	0.981380	−	0.192076i	$-0.0615219\pi$
$461$	6.96404	+	12.0621i	0.324348	+	0.561787i	−0.657032	+	0.753862i	$0.728189\pi$
$462$	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	−0.413713	−	0.910407i	$-0.635768\pi$
$479$	12.7285	−	22.0464i	0.581580	−	1.00733i	0.995292	−	0.0969180i	$-0.0308985\pi$
$480$	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	$-0.670365\pi$
$487$	−22.5107			−1.02006			−0.510029	+	0.860157i	$0.670365\pi$
$488$	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	0.633958	−	0.773368i	$-0.281429\pi$
$491$	−7.81702	−	13.5395i	−0.352777	−	0.611028i	−0.986735	+	0.162340i	$0.948096\pi$
$492$	−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	0.985314	+	0.170751i	$0.0546194\pi$
$499$	14.3084	+	24.7829i	0.640532	+	1.10943i	−0.344782	+	0.938683i	$0.612047\pi$
$500$	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	−0.439271	−	0.898354i	$-0.644763\pi$
$503$	12.5228	−	21.6900i	0.558362	−	0.967111i	0.997633	−	0.0687571i	$-0.0219033\pi$
$504$	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	0.208270	+	0.978071i	$0.433217\pi$
$509$	−16.7606	+	29.0302i	−0.742900	+	1.28674i	−0.951170	+	0.308669i	$0.900117\pi$
$510$	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	$-0.705599\pi$
$521$	−27.4783			−1.20385			−0.601924	+	0.798553i	$0.705599\pi$
$522$	−4.14274	+	7.17544i	−0.181323	+	0.314060i
$523$	5.17870	−	8.96977i	0.226449	−	0.392221i	−0.730304	−	0.683122i	$-0.760622\pi$
$523$	5.17870	−	8.96977i	0.226449	−	0.392221i	0.956753	+	0.290901i	$0.0939551\pi$
$524$	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	−0.891882	−	0.452268i	$-0.850615\pi$
$541$	−1.26217	+	2.18615i	−0.0542651	+	0.0939899i	0.837617	+	0.546258i	$0.183948\pi$
$542$	−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	$-0.885799\pi$
$547$	−3.83750	+	6.64674i	−0.164079	+	0.284194i	0.772249	+	0.635321i	$0.219132\pi$
$548$	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	−0.898451	−	0.439074i	$-0.855306\pi$
$557$	−1.62789	+	2.81959i	−0.0689759	+	0.119470i	0.829475	+	0.558544i	$0.188640\pi$
$558$	−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	$-0.464652\pi$
$563$	5.25908			0.221644			0.110822	+	0.993840i	$0.464652\pi$
$564$	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	$-0.716093\pi$
$569$	−29.9564			−1.25584			−0.627918	+	0.778280i	$0.716093\pi$
$570$		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	0.999990	−	0.00455138i	$-0.00144875\pi$
$587$	12.0184	+	20.8165i	0.496053	+	0.859189i	−0.503936	+	0.863741i	$0.668115\pi$
$588$	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	−0.819194	−	0.573517i	$-0.805579\pi$
$593$	2.12061	−	3.67301i	0.0870832	−	0.150833i	0.906277	+	0.422684i	$0.138912\pi$
$594$	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	−0.462314	−	0.886716i	$-0.652981\pi$
$599$	13.1370	−	22.7539i	0.536762	−	0.929699i	0.999076	−	0.0429829i	$-0.0136861\pi$
$600$	−2.13104			−0.0869995
$601$	−42.2395			−1.72298			−0.861492	−	0.507771i	$-0.830470\pi$
$601$	−42.2395			−1.72298			−0.861492	+	0.507771i	$0.830470\pi$
$602$	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	$-0.648021\pi$
$607$	−22.0969			−0.896885			−0.448443	+	0.893812i	$0.648021\pi$
$608$		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	0.784411	−	0.620241i	$-0.212965\pi$
$613$	−3.58853	−	6.21551i	−0.144939	−	0.251042i	−0.929350	+	0.369199i	$0.879632\pi$
$614$	−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	0.400933	−	0.916108i	$-0.368686\pi$
$617$	24.6864	−	42.7582i	0.993839	−	1.72138i	0.592906	−	0.805272i	$-0.297981\pi$
$618$	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	0.316517	+	0.948587i	$0.397487\pi$
$631$	−16.6604	+	28.8567i	−0.663242	+	1.14877i	−0.979759	+	0.200182i	$0.935847\pi$
$632$	−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	$-0.165811\pi$
$641$	0.0680482	+	0.117863i	0.00268774	+	0.00465530i	−0.864678	+	0.502326i	$0.832478\pi$
$642$	0.831566	−	1.44032i	0.0328193	−	0.0568447i
$643$	−24.0890	−	41.7234i	−0.949977	−	1.64541i	−0.745465	−	0.666545i	$-0.767773\pi$
$643$	−24.0890	−	41.7234i	−0.949977	−	1.64541i	−0.204512	−	0.978864i	$-0.565561\pi$
$644$	−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	$-0.953165\pi$
$659$	−9.43747	+	16.3462i	−0.367632	+	0.636757i	0.621563	+	0.783364i	$0.286498\pi$
$660$	−2.81908	−	4.88279i	−0.109732	−	0.190062i
$661$	15.3059	−	26.5106i	0.595330	−	1.03114i	−0.398171	−	0.917311i	$-0.630355\pi$
$661$	15.3059	−	26.5106i	0.595330	−	1.03114i	0.993500	−	0.113830i	$-0.0363118\pi$
$662$	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	$-0.426279\pi$
$673$	11.9094			0.459074			0.229537	+	0.973300i	$0.426279\pi$
$674$	−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	$-0.464565\pi$
$677$	5.78106			0.222184			0.111092	+	0.993810i	$0.464565\pi$
$678$	−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	$-0.368065\pi$
$683$	21.0496			0.805442			0.402721	+	0.915323i	$0.368065\pi$
$684$		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	0.590796	−	0.806821i	$-0.298814\pi$
$701$	−10.6787	−	18.4961i	−0.403329	−	0.698586i	−0.994125	+	0.108234i	$0.965480\pi$
$702$	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	−0.679110	−	0.734036i	$-0.737634\pi$
$709$	7.88532	−	13.6578i	0.296139	−	0.512928i	0.975249	+	0.221108i	$0.0709674\pi$
$710$	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	0.980936	+	0.194329i	$0.0622528\pi$
$719$	17.6642	+	30.5952i	0.658762	+	1.14101i	−0.322175	+	0.946680i	$0.604414\pi$
$720$	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	−0.948026	−	0.318194i	$-0.896924\pi$
$727$	−20.2108	−	35.0061i	−0.749577	−	1.29830i	0.198449	−	0.980111i	$-0.436410\pi$
$728$	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	0.991103	−	0.133095i	$-0.0424915\pi$
$739$	10.3380	+	17.9059i	0.380288	+	0.658678i	−0.610815	+	0.791773i	$0.709158\pi$
$740$	−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	$-0.205910\pi$
$743$	−3.35204	−	5.80591i	−0.122975	−	0.212998i	−0.920939	+	0.389706i	$0.872577\pi$
$744$	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	$-0.895921\pi$
$751$	−5.35369	+	9.27287i	−0.195359	+	0.338372i	0.751659	+	0.659552i	$0.229254\pi$
$752$	−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	0.900575	−	0.434701i	$-0.143146\pi$
$757$	2.03121	+	3.51816i	0.0738256	+	0.127870i	−0.826749	+	0.562570i	$0.809813\pi$
$758$	−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	−0.991756	−	0.128144i	$-0.959098\pi$
$769$	−10.6736	+	18.4873i	−0.384902	+	0.666669i	0.606854	+	0.794813i	$0.292431\pi$
$770$	−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	$-0.937762\pi$
$773$	−8.95858	+	15.5167i	−0.322218	+	0.558097i	0.658728	+	0.752381i	$0.271095\pi$
$774$	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	$-0.163906\pi$
$787$	48.8316			1.74066			0.870330	+	0.492470i	$0.163906\pi$
$788$	−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	$-0.668591\pi$
$797$	−28.5262			−1.01045			−0.505225	+	0.862988i	$0.668591\pi$
$798$		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	$-0.786345\pi$
$811$	4.18866	−	7.25498i	0.147084	−	0.254757i	0.930148	+	0.367184i	$0.119678\pi$
$812$	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	−0.915596	−	0.402100i	$-0.868280\pi$
$821$	−3.13950	+	5.43777i	−0.109569	+	0.189780i	0.806027	+	0.591879i	$0.201614\pi$
$822$	−4.57145	−	7.91799i	−0.159448	−	0.276171i
$823$	−5.51320	+	9.54915i	−0.192178	+	0.332862i	−0.945972	−	0.324249i	$-0.894888\pi$
$823$	−5.51320	+	9.54915i	−0.192178	+	0.332862i	0.753794	+	0.657111i	$0.228222\pi$
$824$	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	0.404195	+	0.914673i	$0.367552\pi$
$827$	−16.9679	+	29.3893i	−0.590032	+	1.02197i	−0.994227	+	0.107293i	$0.965782\pi$
$828$	5.86154			0.203703
$829$	−20.3669			−0.707372			−0.353686	−	0.935364i	$-0.615072\pi$
$829$	−20.3669			−0.707372			−0.353686	+	0.935364i	$0.615072\pi$
$830$	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	$-0.254649\pi$
$839$	−7.90467	−	13.6913i	−0.272899	−	0.472676i	−0.969603	+	0.244683i	$0.921316\pi$
$840$	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	0.825760	+	0.564022i	$0.190747\pi$
$853$	26.3246	+	45.5955i	0.901337	+	1.56116i	0.0755770	+	0.997140i	$0.475920\pi$
$854$	−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	$-0.0380002\pi$
$857$	11.5137	+	19.9423i	0.393299	+	0.681215i	−0.599583	+	0.800313i	$0.704667\pi$
$858$	4.22281	+	7.31412i	0.144164	+	0.249700i
$859$	−4.45471	+	7.71578i	−0.151993	+	0.263259i	−0.931960	−	0.362561i	$-0.881902\pi$
$859$	−4.45471	+	7.71578i	−0.151993	+	0.263259i	0.779967	+	0.625820i	$0.215236\pi$
$860$	−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	$-0.330870\pi$
$863$	29.7698			1.01338			0.506688	+	0.862129i	$0.330870\pi$
$864$	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	$-0.0277835\pi$
$877$	12.5150	+	21.6766i	0.422602	+	0.731968i	−0.573591	+	0.819142i	$0.694450\pi$
$878$	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	−0.762649	−	0.646812i	$-0.776102\pi$
$883$	5.31403	−	9.20416i	0.178831	−	0.309745i	0.941480	+	0.337068i	$0.109435\pi$
$884$	−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	0.191764	−	0.981441i	$-0.438579\pi$
$887$	28.1694	−	48.7908i	0.945835	−	1.63823i	0.754071	−	0.656793i	$-0.228087\pi$
$888$	−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	$-0.135312\pi$
$907$	2.96182	+	5.13002i	0.0983456	+	0.170340i	−0.812654	+	0.582746i	$0.801978\pi$
$908$	−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	$-0.690821\pi$
$911$	−34.0591			−1.12843			−0.564215	+	0.825628i	$0.690821\pi$
$912$		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	0.534557	−	0.845133i	$-0.320479\pi$
$929$	−14.1616	−	24.5287i	−0.464628	−	0.804759i	−0.999185	+	0.0403735i	$0.987145\pi$
$930$	−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	−0.654227	−	0.756299i	$-0.727006\pi$
$937$	10.0360	−	17.3828i	0.327860	−	0.567871i	0.982087	+	0.188428i	$0.0603391\pi$
$938$	−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	$-0.861361\pi$
$941$	−2.69759	+	4.67236i	−0.0879388	+	0.152314i	0.818701	+	0.574220i	$0.194695\pi$
$942$	−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	0.806997	−	0.590556i	$-0.201091\pi$
$947$	−3.32160	−	5.75319i	−0.107938	−	0.186953i	−0.914935	+	0.403602i	$0.867758\pi$
$948$	−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	$-0.0894876\pi$
$953$	7.41194	+	12.8379i	0.240096	+	0.415859i	−0.720645	+	0.693304i	$0.756154\pi$
$954$	−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	0.643439	−	0.765497i	$-0.277507\pi$
$967$	−10.6108	−	18.3785i	−0.341221	−	0.591012i	−0.984660	+	0.174486i	$0.944174\pi$
$968$	−1.81076			−0.0582002
$969$		0			0
$970$	4.05913			0.130331
$971$	18.8033	+	32.5684i	0.603428	+	1.04517i	0.992298	+	0.123875i	$0.0395323\pi$
$971$	18.8033	+	32.5684i	0.603428	+	1.04517i	−0.388870	+	0.921293i	$0.627134\pi$
$972$	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	$-0.763372\pi$
$977$	−46.0215			−1.47236			−0.736179	+	0.676787i	$0.763372\pi$
$978$	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	−0.705910	−	0.708302i	$-0.749462\pi$
$983$	−30.2982	−	52.4780i	−0.966362	−	1.67379i	−0.260452	−	0.965487i	$-0.583872\pi$
$984$	−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	−0.979158	−	0.203101i	$-0.934898\pi$
$991$	−20.9491	−	36.2849i	−0.665470	−	1.15263i	0.313688	−	0.949526i	$-0.398435\pi$
$992$	−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	0.465332	+	0.885136i	$0.345935\pi$
$997$	−16.8576	+	29.1982i	−0.533884	+	0.924715i	−0.999216	+	0.0395787i	$0.987398\pi$
$998$	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.i.292.1		6
19.2	odd	18		361.2.e.a.28.1		6
19.3	odd	18		361.2.e.b.234.1		6
19.4	even	9		361.2.e.g.245.1		6
19.5	even	9		19.2.e.a.4.1	✓	6
19.6	even	9		19.2.e.a.5.1	yes	6
19.7	even	3		361.2.a.g.1.3		3
19.8	odd	6		361.2.c.h.68.3		6
19.9	even	9		361.2.e.f.54.1		6
19.10	odd	18		361.2.e.b.54.1		6
19.11	even	3	inner	361.2.c.i.68.1		6
19.12	odd	6		361.2.a.h.1.1		3
19.13	odd	18		361.2.e.h.62.1		6
19.14	odd	18		361.2.e.h.99.1		6
19.15	odd	18		361.2.e.a.245.1		6
19.16	even	9		361.2.e.f.234.1		6
19.17	even	9		361.2.e.g.28.1		6
19.18	odd	2		361.2.c.h.292.3		6
57.5	odd	18		171.2.u.c.118.1		6
57.26	odd	6		3249.2.a.z.1.1		3
57.44	odd	18		171.2.u.c.100.1		6
57.50	even	6		3249.2.a.s.1.3		3
76.7	odd	6		5776.2.a.br.1.1		3
76.31	even	6		5776.2.a.bi.1.3		3
76.43	odd	18		304.2.u.b.289.1		6
76.63	odd	18		304.2.u.b.81.1		6
95.24	even	18		475.2.l.a.251.1		6
95.43	odd	36		475.2.u.a.99.1		12
95.44	even	18		475.2.l.a.176.1		6
95.62	odd	36		475.2.u.a.99.2		12
95.63	odd	36		475.2.u.a.24.2		12
95.64	even	6		9025.2.a.bd.1.1		3
95.69	odd	6		9025.2.a.x.1.3		3
95.82	odd	36		475.2.u.a.24.1		12
133.5	odd	18		931.2.x.b.802.1		6
133.6	odd	18		931.2.w.a.442.1		6
133.24	odd	18		931.2.v.a.422.1		6
133.25	even	9		931.2.x.a.765.1		6
133.44	even	9		931.2.v.b.214.1		6
133.62	odd	18		931.2.w.a.99.1		6
133.81	even	9		931.2.v.b.422.1		6
133.82	odd	18		931.2.v.a.214.1		6
133.100	even	9		931.2.x.a.802.1		6
133.101	odd	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	19.5	even	9
19.2.e.a.5.1	yes	6	19.6	even	9
171.2.u.c.100.1		6	57.44	odd	18
171.2.u.c.118.1		6	57.5	odd	18
304.2.u.b.81.1		6	76.63	odd	18
304.2.u.b.289.1		6	76.43	odd	18
361.2.a.g.1.3		3	19.7	even	3
361.2.a.h.1.1		3	19.12	odd	6
361.2.c.h.68.3		6	19.8	odd	6
361.2.c.h.292.3		6	19.18	odd	2
361.2.c.i.68.1		6	19.11	even	3	inner
361.2.c.i.292.1		6	1.1	even	1	trivial
361.2.e.a.28.1		6	19.2	odd	18
361.2.e.a.245.1		6	19.15	odd	18
361.2.e.b.54.1		6	19.10	odd	18
361.2.e.b.234.1		6	19.3	odd	18
361.2.e.f.54.1		6	19.9	even	9
361.2.e.f.234.1		6	19.16	even	9
361.2.e.g.28.1		6	19.17	even	9
361.2.e.g.245.1		6	19.4	even	9
361.2.e.h.62.1		6	19.13	odd	18
361.2.e.h.99.1		6	19.14	odd	18
475.2.l.a.176.1		6	95.44	even	18
475.2.l.a.251.1		6	95.24	even	18
475.2.u.a.24.1		12	95.82	odd	36
475.2.u.a.24.2		12	95.63	odd	36
475.2.u.a.99.1		12	95.43	odd	36
475.2.u.a.99.2		12	95.62	odd	36
931.2.v.a.214.1		6	133.82	odd	18
931.2.v.a.422.1		6	133.24	odd	18
931.2.v.b.214.1		6	133.44	even	9
931.2.v.b.422.1		6	133.81	even	9
931.2.w.a.99.1		6	133.62	odd	18
931.2.w.a.442.1		6	133.6	odd	18
931.2.x.a.765.1		6	133.25	even	9
931.2.x.a.802.1		6	133.100	even	9
931.2.x.b.765.1		6	133.101	odd	18
931.2.x.b.802.1		6	133.5	odd	18
3249.2.a.s.1.3		3	57.50	even	6
3249.2.a.z.1.1		3	57.26	odd	6
5776.2.a.bi.1.3		3	76.31	even	6
5776.2.a.br.1.1		3	76.7	odd	6
9025.2.a.x.1.3		3	95.69	odd	6
9025.2.a.bd.1.1		3	95.64	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.439693 - 0.761570i) q^{2} +(-0.266044 - 0.460802i) q^{3} +(0.613341 - 1.06234i) q^{4} +(1.26604 + 2.19285i) q^{5} +(-0.233956 + 0.405223i) q^{6} -1.87939 q^{7} -2.83750 q^{8} +(1.35844 - 2.35289i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - 12 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - 12 * q^8	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - 12 q^{8} - 6 q^{12} + 6 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} - 6 q^{18} - 6 q^{20} + 3 q^{21} - 9 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{25} - 30 q^{26} - 12 q^{27} - 9 q^{28} + 15 q^{29} - 18 q^{31} - 9 q^{33} + 9 q^{34} - 3 q^{35} + 9 q^{36} - 24 q^{39} - 18 q^{40} + 12 q^{41} - 3 q^{42} + 9 q^{44} + 30 q^{45} + 36 q^{46} + 6 q^{47} - 6 q^{48} - 30 q^{49} + 30 q^{50} + 3 q^{51} - 18 q^{52} + 6 q^{53} + 3 q^{54} + 9 q^{55} - 6 q^{56} + 36 q^{58} + 21 q^{59} - 6 q^{60} - 9 q^{61} - 21 q^{62} - 3 q^{63} + 24 q^{64} + 24 q^{65} + 9 q^{66} - 18 q^{67} + 30 q^{68} + 24 q^{69} - 9 q^{70} + 30 q^{71} - 39 q^{72} - 3 q^{74} + 30 q^{75} - 18 q^{77} - 12 q^{78} + 9 q^{79} + 12 q^{80} - 15 q^{81} - 18 q^{82} - 6 q^{84} + 9 q^{85} - 21 q^{86} + 42 q^{87} - 18 q^{88} + 15 q^{89} + 9 q^{90} - 15 q^{91} + 24 q^{92} - 24 q^{93} + 18 q^{94} + 18 q^{96} - 15 q^{97} - 18 q^{98} + 18 q^{99}+O(q^{100}) \) 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

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