LMFDB - Embedded newform 231.2.j.g.148.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.2
Root			$0.648215 - 1.99500i$ of defining polynomial
Character	$\chi$	$=$	231.148
Dual form			231.2.j.g.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.648215 - 1.99500i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.94181 + 1.41081i) q^{4} +(0.976330 - 3.00483i) q^{5} +(-0.648215 + 1.99500i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.679172 + 0.493447i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.648215 - 1.99500i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.94181 + 1.41081i) q^{4} +(0.976330 - 3.00483i) q^{5} +(-0.648215 + 1.99500i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.679172 + 0.493447i) q^{8} +(0.309017 + 0.951057i) q^{9} -6.62751 q^{10} +(-0.965987 - 3.17283i) q^{11} +2.40021 q^{12} +(0.657781 + 2.02444i) q^{13} +(-1.69705 - 1.23298i) q^{14} +(-2.55606 + 1.85709i) q^{15} +(-0.939232 + 2.89066i) q^{16} +(-1.48152 + 4.55965i) q^{17} +(1.69705 - 1.23298i) q^{18} +(-1.24465 - 0.904290i) q^{19} +(2.34339 + 7.21222i) q^{20} -1.00000 q^{21} +(-5.70363 + 3.98382i) q^{22} +5.11509 q^{23} +(-0.259421 - 0.798414i) q^{24} +(-4.03072 - 2.92849i) q^{25} +(3.61238 - 2.62455i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.741705 + 2.28273i) q^{28} +(0.775237 - 0.563243i) q^{29} +(5.36177 + 3.89556i) q^{30} +(-2.23122 - 6.86698i) q^{31} +8.05469 q^{32} +(-1.08344 + 3.13467i) q^{33} +10.0569 q^{34} +(-0.976330 - 3.00483i) q^{35} +(-1.94181 - 1.41081i) q^{36} +(-1.94084 + 1.41010i) q^{37} +(-0.997259 + 3.06925i) q^{38} +(0.657781 - 2.02444i) q^{39} +(2.14582 - 1.55903i) q^{40} +(-0.215938 - 0.156888i) q^{41} +(0.648215 + 1.99500i) q^{42} +9.28678 q^{43} +(6.35202 + 4.79821i) q^{44} +3.15947 q^{45} +(-3.31568 - 10.2046i) q^{46} +(-8.35271 - 6.06860i) q^{47} +(2.45894 - 1.78653i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.22956 + 9.93958i) q^{50} +(3.87867 - 2.81802i) q^{51} +(-4.13338 - 3.00308i) q^{52} +(-0.292206 - 0.899319i) q^{53} -2.09767 q^{54} +(-10.4770 - 0.195099i) q^{55} +0.839503 q^{56} +(0.475413 + 1.46317i) q^{57} +(-1.62619 - 1.18150i) q^{58} +(7.72673 - 5.61380i) q^{59} +(2.34339 - 7.21222i) q^{60} +(2.64443 - 8.13872i) q^{61} +(-12.2533 + 8.90256i) q^{62} +(0.809017 + 0.587785i) q^{63} +(-3.34271 - 10.2878i) q^{64} +6.72532 q^{65} +(6.95597 + 0.129532i) q^{66} +13.2710 q^{67} +(-3.55596 - 10.9441i) q^{68} +(-4.13820 - 3.00658i) q^{69} +(-5.36177 + 3.89556i) q^{70} +(4.37458 - 13.4636i) q^{71} +(-0.259421 + 0.798414i) q^{72} +(-6.24721 + 4.53887i) q^{73} +(4.07123 + 2.95792i) q^{74} +(1.53960 + 4.73840i) q^{75} +3.69265 q^{76} +(-2.64644 - 1.99908i) q^{77} -4.46514 q^{78} +(2.87765 + 8.85649i) q^{79} +(7.76895 + 5.64447i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.173018 + 0.532493i) q^{82} +(-5.20805 + 16.0287i) q^{83} +(1.94181 - 1.41081i) q^{84} +(12.2545 + 8.90345i) q^{85} +(-6.01983 - 18.5271i) q^{86} -0.958246 q^{87} +(0.909554 - 2.63156i) q^{88} -11.2670 q^{89} +(-2.04801 - 6.30314i) q^{90} +(1.72209 + 1.25117i) q^{91} +(-9.93253 + 7.21641i) q^{92} +(-2.23122 + 6.86698i) q^{93} +(-6.69251 + 20.5974i) q^{94} +(-3.93243 + 2.85708i) q^{95} +(-6.51638 - 4.73443i) q^{96} +(2.19028 + 6.74098i) q^{97} -2.09767 q^{98} +(2.71904 - 1.89917i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.648215	−	1.99500i	−0.458357	−	1.41068i	−0.867148	−	0.498050i	$-0.834050\pi$
$2$	−0.648215	−	1.99500i	−0.458357	−	1.41068i	0.408791	−	0.912628i	$-0.365950\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−1.94181	+	1.41081i	−0.970904	+	0.705403i
$5$	0.976330	−	3.00483i	0.436628	−	1.34380i	−0.454781	−	0.890603i	$-0.650283\pi$
$5$	0.976330	−	3.00483i	0.436628	−	1.34380i	0.891409	−	0.453199i	$-0.149717\pi$
$6$	−0.648215	+	1.99500i	−0.264633	+	0.814455i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	0.679172	+	0.493447i	0.240124	+	0.174460i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−6.62751			−2.09580
$11$	−0.965987	−	3.17283i	−0.291256	−	0.956645i
$11$	−0.965987	−	3.17283i	−0.291256	−	0.956645i
$12$	2.40021			0.692880
$13$	0.657781	+	2.02444i	0.182436	+	0.561479i	0.999895	−	0.0145076i	$-0.00461808\pi$
$13$	0.657781	+	2.02444i	0.182436	+	0.561479i	−0.817459	+	0.575986i	$0.804618\pi$
$14$	−1.69705	−	1.23298i	−0.453555	−	0.329527i
$15$	−2.55606	+	1.85709i	−0.659973	+	0.479498i
$16$	−0.939232	+	2.89066i	−0.234808	+	0.722665i
$17$	−1.48152	+	4.55965i	−0.359322	+	1.10588i	0.594139	+	0.804362i	$0.297493\pi$
$17$	−1.48152	+	4.55965i	−0.359322	+	1.10588i	−0.953461	+	0.301516i	$0.902507\pi$
$18$	1.69705	−	1.23298i	0.399998	−	0.290616i
$19$	−1.24465	−	0.904290i	−0.285542	−	0.207458i	0.435789	−	0.900049i	$-0.356469\pi$
$19$	−1.24465	−	0.904290i	−0.285542	−	0.207458i	−0.721331	+	0.692590i	$0.756469\pi$
$20$	2.34339	+	7.21222i	0.523999	+	1.61270i
$21$	−1.00000			−0.218218
$22$	−5.70363	+	3.98382i	−1.21602	+	0.849354i
$23$	5.11509			1.06657			0.533285	−	0.845935i	$-0.320957\pi$
$23$	5.11509			1.06657			0.533285	+	0.845935i	$0.320957\pi$
$24$	−0.259421	−	0.798414i	−0.0529540	−	0.162976i
$25$	−4.03072	−	2.92849i	−0.806144	−	0.585698i
$26$	3.61238	−	2.62455i	0.708445	−	0.514716i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.741705	+	2.28273i	−0.140169	+	0.431396i
$29$	0.775237	−	0.563243i	0.143958	−	0.104592i	−0.513475	−	0.858104i	$-0.671642\pi$
$29$	0.775237	−	0.563243i	0.143958	−	0.104592i	0.657433	+	0.753513i	$0.271642\pi$
$30$	5.36177	+	3.89556i	0.978921	+	0.711228i
$31$	−2.23122	−	6.86698i	−0.400739	−	1.23335i	−0.924401	−	0.381421i	$-0.875435\pi$
$31$	−2.23122	−	6.86698i	−0.400739	−	1.23335i	0.523663	−	0.851926i	$-0.324565\pi$
$32$	8.05469			1.42388
$33$	−1.08344	+	3.13467i	−0.188603	+	0.545676i
$34$	10.0569			1.72474
$35$	−0.976330	−	3.00483i	−0.165030	−	0.507910i
$36$	−1.94181	−	1.41081i	−0.323635	−	0.235134i
$37$	−1.94084	+	1.41010i	−0.319072	+	0.231819i	−0.735779	−	0.677221i	$-0.763184\pi$
$37$	−1.94084	+	1.41010i	−0.319072	+	0.231819i	0.416707	+	0.909041i	$0.363184\pi$
$38$	−0.997259	+	3.06925i	−0.161777	+	0.497898i
$39$	0.657781	−	2.02444i	0.105329	−	0.324170i
$40$	2.14582	−	1.55903i	0.339284	−	0.246504i
$41$	−0.215938	−	0.156888i	−0.0337238	−	0.0245018i	0.570796	−	0.821092i	$-0.306635\pi$
$41$	−0.215938	−	0.156888i	−0.0337238	−	0.0245018i	−0.604519	+	0.796590i	$0.706635\pi$
$42$	0.648215	+	1.99500i	0.100022	+	0.307835i
$43$	9.28678			1.41622			0.708110	−	0.706102i	$-0.249548\pi$
$43$	9.28678			1.41622			0.708110	+	0.706102i	$0.249548\pi$
$44$	6.35202	+	4.79821i	0.957603	+	0.723358i
$45$	3.15947			0.470986
$46$	−3.31568	−	10.2046i	−0.488870	−	1.50459i
$47$	−8.35271	−	6.06860i	−1.21837	−	0.885196i	−0.222404	−	0.974954i	$-0.571391\pi$
$47$	−8.35271	−	6.06860i	−1.21837	−	0.885196i	−0.995964	+	0.0897583i	$0.971391\pi$
$48$	2.45894	−	1.78653i	0.354918	−	0.257863i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−3.22956	+	9.93958i	−0.456729	+	1.40567i
$51$	3.87867	−	2.81802i	0.543123	−	0.394602i
$52$	−4.13338	−	3.00308i	−0.573197	−	0.416452i
$53$	−0.292206	−	0.899319i	−0.0401376	−	0.123531i	0.928980	−	0.370130i	$-0.120687\pi$
$53$	−0.292206	−	0.899319i	−0.0401376	−	0.123531i	−0.969118	+	0.246599i	$0.920687\pi$
$54$	−2.09767			−0.285456
$55$	−10.4770	−	0.195099i	−1.41271	−	0.0263071i
$56$	0.839503			0.112183
$57$	0.475413	+	1.46317i	0.0629700	+	0.193802i
$58$	−1.62619	−	1.18150i	−0.213529	−	0.155138i
$59$	7.72673	−	5.61380i	1.00593	−	0.730855i	0.0425824	−	0.999093i	$-0.486442\pi$
$59$	7.72673	−	5.61380i	1.00593	−	0.730855i	0.963353	+	0.268238i	$0.0864415\pi$
$60$	2.34339	−	7.21222i	0.302531	−	0.931094i
$61$	2.64443	−	8.13872i	0.338585	−	1.04206i	−0.626345	−	0.779546i	$-0.715450\pi$
$61$	2.64443	−	8.13872i	0.338585	−	1.04206i	0.964929	−	0.262510i	$-0.0845503\pi$
$62$	−12.2533	+	8.90256i	−1.55617	+	1.13063i
$63$	0.809017	+	0.587785i	0.101927	+	0.0740540i
$64$	−3.34271	−	10.2878i	−0.417838	−	1.28597i
$65$	6.72532			0.834173
$66$	6.95597	+	0.129532i	0.856221	+	0.0159443i
$67$	13.2710			1.62131			0.810657	−	0.585521i	$-0.199110\pi$
$67$	13.2710			1.62131			0.810657	+	0.585521i	$0.199110\pi$
$68$	−3.55596	−	10.9441i	−0.431223	−	1.32717i
$69$	−4.13820	−	3.00658i	−0.498180	−	0.361949i
$70$	−5.36177	+	3.89556i	−0.640854	+	0.465608i
$71$	4.37458	−	13.4636i	0.519167	−	1.59783i	−0.256402	−	0.966570i	$-0.582537\pi$
$71$	4.37458	−	13.4636i	0.519167	−	1.59783i	0.775570	−	0.631262i	$-0.217463\pi$
$72$	−0.259421	+	0.798414i	−0.0305730	+	0.0940940i
$73$	−6.24721	+	4.53887i	−0.731181	+	0.531234i	−0.889937	−	0.456084i	$-0.849252\pi$
$73$	−6.24721	+	4.53887i	−0.731181	+	0.531234i	0.158756	+	0.987318i	$0.449252\pi$
$74$	4.07123	+	2.95792i	0.473271	+	0.343852i
$75$	1.53960	+	4.73840i	0.177777	+	0.547143i
$76$	3.69265			0.423576
$77$	−2.64644	−	1.99908i	−0.301590	−	0.227817i
$78$	−4.46514			−0.505578
$79$	2.87765	+	8.85649i	0.323761	+	0.996432i	0.971997	+	0.234993i	$0.0755068\pi$
$79$	2.87765	+	8.85649i	0.323761	+	0.996432i	−0.648236	+	0.761439i	$0.724493\pi$
$80$	7.76895	+	5.64447i	0.868595	+	0.631071i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−0.173018	+	0.532493i	−0.0191066	+	0.0588040i
$83$	−5.20805	+	16.0287i	−0.571658	+	1.75938i	0.0756307	+	0.997136i	$0.475903\pi$
$83$	−5.20805	+	16.0287i	−0.571658	+	1.75938i	−0.647288	+	0.762245i	$0.724097\pi$
$84$	1.94181	−	1.41081i	0.211869	−	0.153932i
$85$	12.2545	+	8.90345i	1.32919	+	0.965715i
$86$	−6.01983	−	18.5271i	−0.649135	−	1.99783i
$87$	−0.958246			−0.102735
$88$	0.909554	−	2.63156i	0.0969588	−	0.280526i
$89$	−11.2670			−1.19430			−0.597150	−	0.802130i	$-0.703700\pi$
$89$	−11.2670			−1.19430			−0.597150	+	0.802130i	$0.703700\pi$
$90$	−2.04801	−	6.30314i	−0.215880	−	0.664409i
$91$	1.72209	+	1.25117i	0.180524	+	0.131159i
$92$	−9.93253	+	7.21641i	−1.03554	+	0.752363i
$93$	−2.23122	+	6.86698i	−0.231367	+	0.712073i
$94$	−6.69251	+	20.5974i	−0.690279	+	2.12446i
$95$	−3.93243	+	2.85708i	−0.403459	+	0.293130i
$96$	−6.51638	−	4.73443i	−0.665076	−	0.483206i
$97$	2.19028	+	6.74098i	0.222389	+	0.684443i	0.998546	+	0.0539036i	$0.0171664\pi$
$97$	2.19028	+	6.74098i	0.222389	+	0.684443i	−0.776157	+	0.630540i	$0.782834\pi$
$98$	−2.09767			−0.211896
$99$	2.71904	−	1.89917i	0.273273	−	0.190874i
$100$	11.9584			1.19584
$101$	2.57908	+	7.93761i	0.256629	+	0.789821i	0.993504	+	0.113793i	$0.0363002\pi$
$101$	2.57908	+	7.93761i	0.256629	+	0.789821i	−0.736876	+	0.676028i	$0.763700\pi$
$102$	−8.13617	−	5.91127i	−0.805601	−	0.585303i
$103$	6.09639	−	4.42929i	0.600695	−	0.436431i	−0.245430	−	0.969414i	$-0.578929\pi$
$103$	6.09639	−	4.42929i	0.600695	−	0.436431i	0.846126	+	0.532984i	$0.178929\pi$
$104$	−0.552209	+	1.69952i	−0.0541485	+	0.166652i
$105$	−0.976330	+	3.00483i	−0.0952800	+	0.293242i
$106$	−1.60473	+	1.16590i	−0.155865	+	0.113243i
$107$	−12.4497	−	9.04525i	−1.20356	−	0.874437i	−0.208930	−	0.977931i	$-0.566998\pi$
$107$	−12.4497	−	9.04525i	−1.20356	−	0.874437i	−0.994630	+	0.103493i	$0.966998\pi$
$108$	0.741705	+	2.28273i	0.0713706	+	0.219656i
$109$	20.2581			1.94038			0.970188	−	0.242353i	$-0.0779192\pi$
$109$	20.2581			1.94038			0.970188	+	0.242353i	$0.0779192\pi$
$110$	6.40210	+	21.0280i	0.610416	+	2.00494i
$111$	2.39901			0.227704
$112$	0.939232	+	2.89066i	0.0887491	+	0.273142i
$113$	14.6447	+	10.6400i	1.37766	+	1.00093i	0.997095	+	0.0761731i	$0.0242702\pi$
$113$	14.6447	+	10.6400i	1.37766	+	1.00093i	0.380564	+	0.924755i	$0.375730\pi$
$114$	2.61086	−	1.89690i	0.244529	−	0.177661i
$115$	4.99402	−	15.3700i	0.465694	−	1.43326i
$116$	−0.710736	+	2.18742i	−0.0659902	+	0.203097i
$117$	−1.72209	+	1.25117i	−0.159207	+	0.115671i
$118$	−16.2081	−	11.7759i	−1.49208	−	1.08406i
$119$	1.48152	+	4.55965i	0.135811	+	0.417983i
$120$	−2.65238			−0.242128
$121$	−9.13374	+	6.12983i	−0.830340	+	0.557258i
$122$	−17.9509			−1.62520
$123$	0.0824809	+	0.253850i	0.00743706	+	0.0228889i
$124$	14.0206	+	10.1866i	1.25909	+	0.914779i
$125$	0.0453845	−	0.0329738i	0.00405932	−	0.00294927i
$126$	0.648215	−	1.99500i	0.0577476	−	0.177729i
$127$	−4.74993	+	14.6188i	−0.421488	+	1.29721i	0.484830	+	0.874608i	$0.338882\pi$
$127$	−4.74993	+	14.6188i	−0.421488	+	1.29721i	−0.906318	+	0.422597i	$0.861118\pi$
$128$	−5.32459	+	3.86854i	−0.470632	+	0.341934i
$129$	−7.51316	−	5.45863i	−0.661497	−	0.480606i
$130$	−4.35945	−	13.4170i	−0.382349	−	1.17675i
$131$	−10.7418			−0.938516			−0.469258	−	0.883061i	$-0.655478\pi$
$131$	−10.7418			−0.938516			−0.469258	+	0.883061i	$0.655478\pi$
$132$	−2.31857	−	7.61546i	−0.201806	−	0.662841i
$133$	−1.53847			−0.133402
$134$	−8.60248	−	26.4757i	−0.743141	−	2.28715i
$135$	−2.55606	−	1.85709i	−0.219991	−	0.159833i
$136$	−3.25616	+	2.36574i	−0.279213	+	0.202860i
$137$	−1.36775	+	4.20949i	−0.116855	+	0.359641i	−0.992329	−	0.123623i	$-0.960549\pi$
$137$	−1.36775	+	4.20949i	−0.116855	+	0.359641i	0.875475	+	0.483264i	$0.160549\pi$
$138$	−3.31568	+	10.2046i	−0.282249	+	0.868674i
$139$	−3.66084	+	2.65976i	−0.310509	+	0.225598i	−0.732115	−	0.681181i	$-0.761467\pi$
$139$	−3.66084	+	2.65976i	−0.310509	+	0.225598i	0.421606	+	0.906779i	$0.361467\pi$
$140$	6.13508	+	4.45740i	0.518509	+	0.376719i
$141$	3.19045	+	9.81920i	0.268684	+	0.826926i
$142$	−29.6955			−2.49199
$143$	5.78780	−	4.04261i	0.484001	−	0.338060i
$144$	−3.03942			−0.253285
$145$	−0.935564	−	2.87937i	−0.0776944	−	0.239119i
$146$	13.1046	+	9.52103i	1.08454	+	0.787966i
$147$	−0.809017	+	0.587785i	−0.0667266	+	0.0484797i
$148$	1.77936	−	5.47629i	0.146262	−	0.450149i
$149$	0.925416	−	2.84814i	0.0758130	−	0.233329i	−0.905967	−	0.423347i	$-0.860855\pi$
$149$	0.925416	−	2.84814i	0.0758130	−	0.233329i	0.981780	+	0.190019i	$0.0608550\pi$
$150$	8.45511	−	6.14300i	0.690357	−	0.501574i
$151$	−7.12954	−	5.17991i	−0.580194	−	0.421535i	0.258600	−	0.965984i	$-0.416739\pi$
$151$	−7.12954	−	5.17991i	−0.580194	−	0.421535i	−0.838794	+	0.544449i	$0.816739\pi$
$152$	−0.399111	−	1.22834i	−0.0323722	−	0.0996313i
$153$	−4.79430			−0.387597
$154$	−2.27271	+	6.57549i	−0.183140	+	0.529868i
$155$	−22.8125			−1.83235
$156$	1.57881	+	4.85908i	0.126406	+	0.389038i
$157$	−1.26737	−	0.920796i	−0.101147	−	0.0734875i	0.536062	−	0.844178i	$-0.319911\pi$
$157$	−1.26737	−	0.920796i	−0.101147	−	0.0734875i	−0.637209	+	0.770691i	$0.719911\pi$
$158$	15.8034	−	11.4818i	1.25725	−	0.913444i
$159$	−0.292206	+	0.899319i	−0.0231735	+	0.0713206i
$160$	7.86404	−	24.2030i	0.621707	−	1.91342i
$161$	4.13820	−	3.00658i	0.326136	−	0.236951i
$162$	1.69705	+	1.23298i	0.133333	+	0.0968719i
$163$	−2.10307	−	6.47258i	−0.164725	−	0.506972i	0.834291	−	0.551325i	$-0.185877\pi$
$163$	−2.10307	−	6.47258i	−0.164725	−	0.506972i	−0.999016	+	0.0443528i	$0.985877\pi$
$164$	0.640649			0.0500263
$165$	8.36136	+	6.31604i	0.650931	+	0.491703i
$166$	35.3532			2.74394
$167$	−3.78538	−	11.6502i	−0.292921	−	0.901519i	−0.983912	−	0.178655i	$-0.942825\pi$
$167$	−3.78538	−	11.6502i	−0.292921	−	0.901519i	0.690990	−	0.722864i	$-0.257175\pi$
$168$	−0.679172	−	0.493447i	−0.0523992	−	0.0380703i
$169$	6.85154	−	4.97793i	0.527041	−	0.382918i
$170$	9.81881	−	30.2192i	0.753068	−	2.31771i
$171$	0.475413	−	1.46317i	0.0363558	−	0.111892i
$172$	−18.0331	+	13.1018i	−1.37501	+	0.999007i
$173$	16.0590	+	11.6675i	1.22094	+	0.887066i	0.996178	−	0.0873476i	$-0.0278391\pi$
$173$	16.0590	+	11.6675i	1.22094	+	0.887066i	0.224763	+	0.974413i	$0.427839\pi$
$174$	0.621149	+	1.91170i	0.0470892	+	0.144926i
$175$	−4.98224			−0.376622
$176$	10.0789	+	0.187686i	0.759723	+	0.0141473i
$177$	−9.55077			−0.717880
$178$	7.30344	+	22.4777i	0.547416	+	1.68477i
$179$	−6.65199	−	4.83295i	−0.497193	−	0.361232i	0.310751	−	0.950491i	$-0.399420\pi$
$179$	−6.65199	−	4.83295i	−0.497193	−	0.361232i	−0.807944	+	0.589260i	$0.799420\pi$
$180$	−6.13508	+	4.45740i	−0.457282	+	0.332235i
$181$	3.22357	−	9.92113i	0.239606	−	0.737432i	−0.756871	−	0.653564i	$-0.773273\pi$
$181$	3.22357	−	9.92113i	0.239606	−	0.737432i	0.996477	−	0.0838672i	$-0.0267271\pi$
$182$	1.37981	−	4.24660i	0.102278	−	0.314779i
$183$	−6.92321	+	5.03000i	−0.511778	+	0.371829i
$184$	3.47403	+	2.52403i	0.256109	+	0.186074i
$185$	2.34222	+	7.20862i	0.172204	+	0.529988i
$186$	15.1459			1.11055
$187$	15.8982	+	0.296051i	1.16259	+	0.0216494i
$188$	24.7810			1.80734
$189$	−0.309017	−	0.951057i	−0.0224777	−	0.0691792i
$190$	8.24893	+	5.99320i	0.598440	+	0.434792i
$191$	−11.5012	+	8.35609i	−0.832195	+	0.604625i	−0.920180	−	0.391497i	$-0.871957\pi$
$191$	−11.5012	+	8.35609i	−0.832195	+	0.604625i	0.0879842	+	0.996122i	$0.471957\pi$
$192$	−3.34271	+	10.2878i	−0.241239	+	0.742458i
$193$	−2.16817	+	6.67293i	−0.156068	+	0.480328i	−0.998268	−	0.0588382i	$-0.981260\pi$
$193$	−2.16817	+	6.67293i	−0.156068	+	0.480328i	0.842200	+	0.539166i	$0.181260\pi$
$194$	12.0285	−	8.73921i	0.863595	−	0.627439i
$195$	−5.44090	−	3.95304i	−0.389631	−	0.283083i
$196$	0.741705	+	2.28273i	0.0529789	+	0.163052i
$197$	−3.60302			−0.256705			−0.128352	−	0.991729i	$-0.540969\pi$
$197$	−3.60302			−0.256705			−0.128352	+	0.991729i	$0.540969\pi$
$198$	−5.55136	−	4.19341i	−0.394518	−	0.298013i
$199$	−3.85136			−0.273015			−0.136508	−	0.990639i	$-0.543588\pi$
$199$	−3.85136			−0.273015			−0.136508	+	0.990639i	$0.543588\pi$
$200$	−1.29250	−	3.97790i	−0.0913933	−	0.281280i
$201$	−10.7365	−	7.80052i	−0.757294	−	0.550206i
$202$	14.1637	−	10.2905i	0.996556	−	0.724041i
$203$	0.296114	−	0.911346i	0.0207831	−	0.0639640i
$204$	−3.55596	+	10.9441i	−0.248967	+	0.766242i
$205$	−0.682249	+	0.495683i	−0.0476503	+	0.0346200i
$206$	−12.7882	−	9.29117i	−0.890996	−	0.647347i
$207$	1.58065	+	4.86474i	0.109863	+	0.338123i
$208$	−6.46978			−0.448598
$209$	−1.66685	+	4.82259i	−0.115298	+	0.333586i
$210$	6.62751			0.457342
$211$	3.44012	+	10.5876i	0.236828	+	0.728881i	0.996874	+	0.0790118i	$0.0251765\pi$
$211$	3.44012	+	10.5876i	0.236828	+	0.728881i	−0.760046	+	0.649870i	$0.774824\pi$
$212$	1.83617	+	1.33406i	0.126109	+	0.0916235i
$213$	−11.4528	+	8.32095i	−0.784733	+	0.570142i
$214$	−9.97518	+	30.7005i	−0.681890	+	2.09864i
$215$	9.06696	−	27.9052i	0.618361	−	1.90312i
$216$	0.679172	−	0.493447i	0.0462118	−	0.0335748i
$217$	−5.84141	−	4.24403i	−0.396540	−	0.288103i
$218$	−13.1316	−	40.4150i	−0.889385	−	2.73725i
$219$	7.72198			0.521803
$220$	20.6195	−	14.4021i	1.39017	−	0.970990i
$221$	−10.2053			−0.686481
$222$	−1.55507	−	4.78602i	−0.104370	−	0.321217i
$223$	4.26448	+	3.09833i	0.285571	+	0.207479i	0.721344	−	0.692577i	$-0.243525\pi$
$223$	4.26448	+	3.09833i	0.285571	+	0.207479i	−0.435773	+	0.900057i	$0.643525\pi$
$224$	6.51638	−	4.73443i	0.435394	−	0.316332i
$225$	1.53960	−	4.73840i	0.102640	−	0.315893i
$226$	11.7339	−	36.1132i	0.780527	−	2.40222i
$227$	11.9899	−	8.71118i	0.795799	−	0.578182i	−0.113880	−	0.993495i	$-0.536328\pi$
$227$	11.9899	−	8.71118i	0.795799	−	0.578182i	0.909679	+	0.415313i	$0.136328\pi$
$228$	−2.98741	−	2.17048i	−0.197846	−	0.143744i
$229$	2.35001	+	7.23258i	0.155293	+	0.477942i	0.998190	−	0.0601317i	$-0.0191521\pi$
$229$	2.35001	+	7.23258i	0.155293	+	0.477942i	−0.842898	+	0.538074i	$0.819152\pi$
$230$	−33.9004			−2.23532
$231$	0.965987	+	3.17283i	0.0635573	+	0.208757i
$232$	0.804450			0.0528147
$233$	−0.465207	−	1.43176i	−0.0304767	−	0.0937978i	0.934661	−	0.355540i	$-0.115703\pi$
$233$	−0.465207	−	1.43176i	−0.0304767	−	0.0937978i	−0.965138	+	0.261742i	$0.915703\pi$
$234$	3.61238	+	2.62455i	0.236148	+	0.171572i
$235$	−26.3901	+	19.1736i	−1.72150	+	1.25074i
$236$	−7.08385	+	21.8019i	−0.461119	+	1.41918i
$237$	2.87765	−	8.85649i	0.186923	−	0.575291i
$238$	8.13617	−	5.91127i	0.527389	−	0.383171i
$239$	4.06399	+	2.95266i	0.262877	+	0.190992i	0.711415	−	0.702773i	$-0.248055\pi$
$239$	4.06399	+	2.95266i	0.262877	+	0.190992i	−0.448537	+	0.893764i	$0.648055\pi$
$240$	−2.96747	−	9.13295i	−0.191550	−	0.589529i
$241$	16.1502			1.04033			0.520164	−	0.854066i	$-0.325871\pi$
$241$	16.1502			1.04033			0.520164	+	0.854066i	$0.325871\pi$
$242$	18.1496	+	14.2484i	1.16670	+	0.915919i
$243$	1.00000			0.0641500
$244$	6.34718	+	19.5346i	0.406337	+	1.25058i
$245$	−2.55606	−	1.85709i	−0.163301	−	0.118645i
$246$	0.452966	−	0.329099i	0.0288800	−	0.0209826i
$247$	1.01198	−	3.11454i	0.0643905	−	0.198174i
$248$	1.87311	−	5.76485i	0.118943	−	0.366068i
$249$	13.6348	−	9.90630i	0.864073	−	0.627786i
$250$	−0.0952016	−	0.0691680i	−0.00602108	−	0.00437457i
$251$	7.96538	+	24.5149i	0.502770	+	1.54737i	0.804487	+	0.593971i	$0.202440\pi$
$251$	7.96538	+	24.5149i	0.502770	+	1.54737i	−0.301716	+	0.953398i	$0.597560\pi$
$252$	−2.40021			−0.151199
$253$	−4.94112	−	16.2293i	−0.310645	−	1.02033i
$254$	32.2434			2.02313
$255$	−4.68082	−	14.4061i	−0.293124	−	0.902144i
$256$	−6.33342	−	4.60150i	−0.395839	−	0.287594i
$257$	−14.2935	+	10.3848i	−0.891605	+	0.647789i	−0.936296	−	0.351212i	$-0.885770\pi$
$257$	−14.2935	+	10.3848i	−0.891605	+	0.647789i	0.0446908	+	0.999001i	$0.485770\pi$
$258$	−6.01983	+	18.5271i	−0.374778	+	1.15345i
$259$	−0.741334	+	2.28159i	−0.0460643	+	0.141771i
$260$	−13.0593	+	9.48812i	−0.809902	+	0.588429i
$261$	0.775237	+	0.563243i	0.0479860	+	0.0348639i
$262$	6.96300	+	21.4299i	0.430175	+	1.32394i
$263$	18.6325			1.14893			0.574465	−	0.818529i	$-0.305210\pi$
$263$	18.6325			1.14893			0.574465	+	0.818529i	$0.305210\pi$
$264$	−2.28264	+	1.59436i	−0.140487	+	0.0981259i
$265$	−2.98759			−0.183526
$266$	0.997259	+	3.06925i	0.0611459	+	0.188188i
$267$	9.11520	+	6.62258i	0.557841	+	0.405295i
$268$	−25.7698	+	18.7229i	−1.57414	+	1.14368i
$269$	−6.40055	+	19.6989i	−0.390248	+	1.20106i	0.542352	+	0.840151i	$0.317534\pi$
$269$	−6.40055	+	19.6989i	−0.390248	+	1.20106i	−0.932601	+	0.360910i	$0.882466\pi$
$270$	−2.04801	+	6.30314i	−0.124638	+	0.383597i
$271$	−12.0088	+	8.72494i	−0.729486	+	0.530002i	−0.889401	−	0.457128i	$-0.848878\pi$
$271$	−12.0088	+	8.72494i	−0.729486	+	0.530002i	0.159915	+	0.987131i	$0.448878\pi$
$272$	−11.7889	−	8.56515i	−0.714808	−	0.519338i
$273$	−0.657781	−	2.02444i	−0.0398107	−	0.122525i
$274$	9.28453			0.560899
$275$	−5.39798	+	15.6177i	−0.325511	+	0.941782i
$276$	12.2773			0.739006
$277$	−0.949638	−	2.92268i	−0.0570582	−	0.175607i	0.918466	−	0.395501i	$-0.129429\pi$
$277$	−0.949638	−	2.92268i	−0.0570582	−	0.175607i	−0.975524	+	0.219894i	$0.929429\pi$
$278$	7.67923	+	5.57929i	0.460570	+	0.334624i
$279$	5.84141	−	4.24403i	0.349716	−	0.254083i
$280$	0.819631	−	2.52257i	0.0489823	−	0.150752i
$281$	1.26604	−	3.89646i	0.0755254	−	0.232443i	−0.906166	−	0.422923i	$-0.861004\pi$
$281$	1.26604	−	3.89646i	0.0755254	−	0.232443i	0.981691	+	0.190479i	$0.0610042\pi$
$282$	17.5212	−	12.7299i	1.04337	−	0.758055i
$283$	5.98511	+	4.34844i	0.355778	+	0.258488i	0.751289	−	0.659973i	$-0.229432\pi$
$283$	5.98511	+	4.34844i	0.355778	+	0.258488i	−0.395511	+	0.918461i	$0.629432\pi$
$284$	10.4999	+	32.3154i	0.623055	+	1.91756i
$285$	4.86075			0.287926
$286$	−11.8168	−	8.92619i	−0.698739	−	0.527817i
$287$	−0.266914			−0.0157554
$288$	2.48904	+	7.66047i	0.146668	+	0.451397i
$289$	−4.84225	−	3.51810i	−0.284839	−	0.206947i
$290$	−5.13790	+	3.73290i	−0.301708	+	0.219203i
$291$	2.19028	−	6.74098i	0.128396	−	0.395163i
$292$	5.72743	−	17.6272i	0.335172	−	1.03155i
$293$	8.53424	−	6.20049i	0.498576	−	0.362236i	−0.309897	−	0.950770i	$-0.600295\pi$
$293$	8.53424	−	6.20049i	0.498576	−	0.362236i	0.808473	+	0.588534i	$0.200295\pi$
$294$	1.69705	+	1.23298i	0.0989739	+	0.0719087i
$295$	−9.32470	−	28.6985i	−0.542905	−	1.67089i
$296$	−2.01397			−0.117060
$297$	−3.31605	−	0.0617506i	−0.192417	−	0.00358313i
$298$	−6.28190			−0.363901
$299$	3.36461	+	10.3552i	0.194580	+	0.598857i
$300$	−9.67457	−	7.02898i	−0.558561	−	0.405819i
$301$	7.51316	−	5.45863i	0.433051	−	0.314630i
$302$	−5.71246	+	17.5811i	−0.328715	+	1.01168i
$303$	2.57908	−	7.93761i	0.148165	−	0.456004i
$304$	3.78301	−	2.74852i	0.216970	−	0.157638i
$305$	−21.8737	−	15.8921i	−1.25248	−	0.909982i
$306$	3.10774	+	9.56464i	0.177658	+	0.546774i
$307$	1.74955			0.0998522			0.0499261	−	0.998753i	$-0.484101\pi$
$307$	1.74955			0.0998522			0.0499261	+	0.998753i	$0.484101\pi$
$308$	7.95921	+	0.148214i	0.453518	+	0.00844529i
$309$	−7.53555			−0.428683
$310$	14.7874	+	45.5110i	0.839870	+	2.58485i
$311$	18.6134	+	13.5235i	1.05547	+	0.766845i	0.973245	−	0.229769i	$-0.0737970\pi$
$311$	18.6134	+	13.5235i	1.05547	+	0.766845i	0.0822263	+	0.996614i	$0.473797\pi$
$312$	1.44570	−	1.05036i	0.0818467	−	0.0594651i
$313$	5.64166	−	17.3632i	0.318885	−	0.981428i	−0.655240	−	0.755421i	$-0.727433\pi$
$313$	5.64166	−	17.3632i	0.318885	−	0.981428i	0.974126	−	0.226007i	$-0.0725674\pi$
$314$	−1.01546	+	3.12527i	−0.0573058	+	0.176369i
$315$	2.55606	−	1.85709i	0.144018	−	0.104635i
$316$	−18.0826	−	13.1378i	−1.01723	−	0.739059i
$317$	10.0803	+	31.0241i	0.566168	+	1.74249i	0.664456	+	0.747327i	$0.268663\pi$
$317$	10.0803	+	31.0241i	0.566168	+	1.74249i	−0.0982886	+	0.995158i	$0.531337\pi$
$318$	1.98355			0.111232
$319$	−2.53594	−	1.91561i	−0.141986	−	0.107254i
$320$	−34.1767			−1.91054
$321$	4.75537	+	14.6355i	0.265419	+	0.816875i
$322$	−8.68056	−	6.30680i	−0.483749	−	0.351464i
$323$	5.96722	−	4.33544i	0.332025	−	0.241230i
$324$	0.741705	−	2.28273i	0.0412058	−	0.126819i
$325$	3.27722	−	10.0863i	0.181788	−	0.559485i
$326$	−11.5496	+	8.39125i	−0.639671	+	0.464748i
$327$	−16.3892	−	11.9074i	−0.906323	−	0.658482i
$328$	−0.0692430	−	0.213108i	−0.00382330	−	0.0117669i
$329$	−10.3245			−0.569209
$330$	7.18054	−	20.7751i	0.395276	−	1.14363i
$331$	6.80537			0.374057			0.187029	−	0.982354i	$-0.440114\pi$
$331$	6.80537			0.374057			0.187029	+	0.982354i	$0.440114\pi$
$332$	−12.5004	−	38.4723i	−0.686048	−	2.11144i
$333$	−1.94084	−	1.41010i	−0.106357	−	0.0772731i
$334$	−20.7884	+	15.1037i	−1.13749	+	0.826435i
$335$	12.9569	−	39.8772i	0.707911	−	2.17873i
$336$	0.939232	−	2.89066i	0.0512393	−	0.157698i
$337$	−0.300988	+	0.218680i	−0.0163958	+	0.0119123i	−0.595953	−	0.803019i	$-0.703226\pi$
$337$	−0.300988	+	0.218680i	−0.0163958	+	0.0119123i	0.579557	+	0.814932i	$0.303226\pi$
$338$	−14.3722	−	10.4420i	−0.781747	−	0.567972i
$339$	−5.59378	−	17.2159i	−0.303813	−	0.935039i
$340$	−36.3570			−1.97174
$341$	−19.6325	+	13.7127i	−1.06316	+	0.742584i
$342$	−3.22720			−0.174507
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	6.30732	+	4.58254i	0.340068	+	0.247074i
$345$	−13.0745	+	9.49918i	−0.703908	+	0.511419i
$346$	12.8671	−	39.6007i	0.691737	−	2.12895i
$347$	1.77708	−	5.46929i	0.0953986	−	0.293607i	−0.891959	−	0.452117i	$-0.850669\pi$
$347$	1.77708	−	5.46929i	0.0953986	−	0.293607i	0.987357	+	0.158510i	$0.0506690\pi$
$348$	1.86073	−	1.35190i	0.0997456	−	0.0724694i
$349$	0.523048	+	0.380017i	0.0279981	+	0.0203418i	0.601696	−	0.798725i	$-0.294492\pi$
$349$	0.523048	+	0.380017i	0.0279981	+	0.0203418i	−0.573698	+	0.819067i	$0.694492\pi$
$350$	3.22956	+	9.93958i	0.172627	+	0.531293i
$351$	2.12862			0.113617
$352$	−7.78073	−	25.5562i	−0.414714	−	1.36215i
$353$	−18.3601			−0.977209			−0.488604	−	0.872505i	$-0.662494\pi$
$353$	−18.3601			−0.977209			−0.488604	+	0.872505i	$0.662494\pi$
$354$	6.19095	+	19.0538i	0.329045	+	1.01270i
$355$	−36.1848	−	26.2898i	−1.92049	−	1.39532i
$356$	21.8784	−	15.8956i	1.15955	−	0.842463i
$357$	1.48152	−	4.55965i	0.0784104	−	0.241323i
$358$	−5.32982	+	16.4035i	−0.281690	+	0.866952i
$359$	−21.8235	+	15.8557i	−1.15180	+	0.836832i	−0.988719	−	0.149781i	$-0.952143\pi$
$359$	−21.8235	+	15.8557i	−1.15180	+	0.836832i	−0.163081	+	0.986613i	$0.552143\pi$
$360$	2.14582	+	1.55903i	0.113095	+	0.0821682i
$361$	−5.13991	−	15.8190i	−0.270522	−	0.832580i
$362$	−21.8822			−1.15010
$363$	10.9924	+	0.409536i	0.576950	+	0.0214951i
$364$	−5.10914			−0.267792
$365$	7.53920	+	23.2033i	0.394620	+	1.21451i
$366$	14.5226	+	10.5513i	0.759108	+	0.551524i
$367$	−22.9126	+	16.6470i	−1.19603	+	0.868966i	−0.993888	−	0.110391i	$-0.964790\pi$
$367$	−22.9126	+	16.6470i	−1.19603	+	0.868966i	−0.202140	+	0.979357i	$0.564790\pi$
$368$	−4.80426	+	14.7860i	−0.250439	+	0.770773i
$369$	0.0824809	−	0.253850i	0.00429379	−	0.0132149i
$370$	12.8629	−	9.34547i	0.668712	−	0.485848i
$371$	−0.765006	−	0.555810i	−0.0397171	−	0.0288562i
$372$	−5.35539	−	16.4822i	−0.277664	−	0.854562i
$373$	−12.9215			−0.669050			−0.334525	−	0.942387i	$-0.608576\pi$
$373$	−12.9215			−0.669050			−0.334525	+	0.942387i	$0.608576\pi$
$374$	−9.71480	−	31.9087i	−0.502340	−	1.64996i
$375$	−0.0560984			−0.00289691
$376$	−2.67839	−	8.24324i	−0.138128	−	0.425113i
$377$	1.65019	+	1.19893i	0.0849890	+	0.0617481i
$378$	−1.69705	+	1.23298i	−0.0872868	+	0.0634175i
$379$	6.47330	−	19.9228i	0.332511	−	1.02336i	−0.635424	−	0.772163i	$-0.719175\pi$
$379$	6.47330	−	19.9228i	0.332511	−	1.02336i	0.967935	−	0.251200i	$-0.0808253\pi$
$380$	3.60524	−	11.0958i	0.184945	−	0.569202i
$381$	12.4355	−	9.03489i	0.637088	−	0.462872i
$382$	24.1256	+	17.5283i	1.23437	+	0.896825i
$383$	7.71813	+	23.7540i	0.394378	+	1.21377i	0.929445	+	0.368961i	$0.120286\pi$
$383$	7.71813	+	23.7540i	0.394378	+	1.21377i	−0.535067	+	0.844810i	$0.679714\pi$
$384$	6.58156			0.335864
$385$	−8.59071	+	6.00036i	−0.437823	+	0.305807i
$386$	14.7179			0.749123
$387$	2.86977	+	8.83225i	0.145879	+	0.448969i
$388$	−13.7633	−	9.99964i	−0.698727	−	0.507655i
$389$	10.9848	−	7.98093i	0.556952	−	0.404649i	−0.273390	−	0.961903i	$-0.588145\pi$
$389$	10.9848	−	7.98093i	0.556952	−	0.404649i	0.830342	+	0.557254i	$0.188145\pi$
$390$	−4.35945	+	13.4170i	−0.220749	+	0.679397i
$391$	−7.57812	+	23.3231i	−0.383242	+	1.17950i
$392$	0.679172	−	0.493447i	0.0343034	−	0.0249229i
$393$	8.69030	+	6.31387i	0.438368	+	0.318493i
$394$	2.33553	+	7.18802i	0.117662	+	0.362127i
$395$	29.4218			1.48037
$396$	−2.60049	+	7.52386i	−0.130680	+	0.378088i
$397$	−4.26450			−0.214029			−0.107014	−	0.994257i	$-0.534129\pi$
$397$	−4.26450			−0.214029			−0.107014	+	0.994257i	$0.534129\pi$
$398$	2.49651	+	7.68346i	0.125139	+	0.385137i
$399$	1.24465	+	0.904290i	0.0623104	+	0.0452711i
$400$	12.2510	−	8.90091i	0.612552	−	0.445045i
$401$	−10.0252	+	30.8544i	−0.500636	+	1.54080i	0.307351	+	0.951596i	$0.400558\pi$
$401$	−10.0252	+	30.8544i	−0.500636	+	1.54080i	−0.807986	+	0.589201i	$0.799442\pi$
$402$	−8.60248	+	26.4757i	−0.429053	+	1.32049i
$403$	12.4341	−	9.03394i	0.619389	−	0.450013i
$404$	−16.2065	−	11.7747i	−0.806304	−	0.585814i
$405$	0.976330	+	3.00483i	0.0485142	+	0.149311i
$406$	−2.01008			−0.0997587
$407$	6.34884	+	4.79581i	0.314700	+	0.237720i
$408$	4.02483			0.199259
$409$	−7.69071	−	23.6696i	−0.380281	−	1.17039i	−0.939846	−	0.341599i	$-0.889032\pi$
$409$	−7.69071	−	23.6696i	−0.380281	−	1.17039i	0.559565	−	0.828787i	$-0.310968\pi$
$410$	1.43113	+	1.03978i	0.0706786	+	0.0513510i
$411$	3.58081	−	2.60161i	0.176628	−	0.128328i
$412$	−5.58916	+	17.2017i	−0.275358	+	0.847465i
$413$	2.95135	−	9.08332i	0.145226	−	0.446961i
$414$	8.68056	−	6.30680i	0.426626	−	0.309962i
$415$	43.0789	+	31.2986i	2.11466	+	1.53639i
$416$	5.29822	+	16.3063i	0.259767	+	0.799480i
$417$	4.52505			0.221593
$418$	10.7016	+	0.199281i	0.523430	+	0.00974717i
$419$	10.5948			0.517588			0.258794	−	0.965933i	$-0.416675\pi$
$419$	10.5948			0.517588			0.258794	+	0.965933i	$0.416675\pi$
$420$	−2.34339	−	7.21222i	−0.114346	−	0.351921i
$421$	30.6320	+	22.2554i	1.49291	+	1.08466i	0.973100	+	0.230382i	$0.0739976\pi$
$421$	30.6320	+	22.2554i	1.49291	+	1.08466i	0.519811	+	0.854281i	$0.326002\pi$
$422$	18.8924	−	13.7261i	0.919665	−	0.668176i
$423$	3.19045	−	9.81920i	0.155125	−	0.477426i
$424$	0.245308	−	0.754980i	0.0119132	−	0.0366651i
$425$	19.3245	−	14.0401i	0.937376	−	0.681044i
$426$	24.0242	+	17.4546i	1.16397	+	0.845677i
$427$	−2.64443	−	8.13872i	−0.127973	−	0.393860i
$428$	36.9361			1.78537
$429$	−7.05862	−	0.131444i	−0.340793	−	0.00634616i
$430$	−61.5483			−2.96812
$431$	1.74437	+	5.36860i	0.0840231	+	0.258597i	0.984238	−	0.176850i	$-0.0565906\pi$
$431$	1.74437	+	5.36860i	0.0840231	+	0.258597i	−0.900215	+	0.435446i	$0.856591\pi$
$432$	2.45894	+	1.78653i	0.118306	+	0.0859542i
$433$	2.18053	−	1.58425i	0.104790	−	0.0761341i	−0.534156	−	0.845386i	$-0.679371\pi$
$433$	2.18053	−	1.58425i	0.104790	−	0.0761341i	0.638946	+	0.769252i	$0.279371\pi$
$434$	−4.68035	+	14.4046i	−0.224664	+	0.691445i
$435$	−0.935564	+	2.87937i	−0.0448569	+	0.138055i
$436$	−39.3374	+	28.5803i	−1.88392	+	1.36875i
$437$	−6.36649	−	4.62553i	−0.304551	−	0.221269i
$438$	−5.00550	−	15.4053i	−0.239172	−	0.736096i
$439$	30.5668			1.45888			0.729438	−	0.684047i	$-0.239782\pi$
$439$	30.5668			1.45888			0.729438	+	0.684047i	$0.239782\pi$
$440$	−7.01938	−	5.30233i	−0.334636	−	0.252779i
$441$	1.00000			0.0476190
$442$	6.61521	+	20.3595i	0.314653	+	0.968403i
$443$	19.9318	+	14.4813i	0.946990	+	0.688028i	0.950093	−	0.311967i	$-0.100988\pi$
$443$	19.9318	+	14.4813i	0.946990	+	0.688028i	−0.00310332	+	0.999995i	$0.500988\pi$
$444$	−4.65841	+	3.38454i	−0.221079	+	0.160623i
$445$	−11.0003	+	33.8555i	−0.521465	+	1.60490i
$446$	3.41686	−	10.5160i	0.161793	−	0.497948i
$447$	−2.42277	+	1.76025i	−0.114593	+	0.0832568i
$448$	−8.75132	−	6.35821i	−0.413461	−	0.300397i
$449$	−4.75131	−	14.6230i	−0.224228	−	0.690103i	−0.998369	−	0.0570896i	$-0.981818\pi$
$449$	−4.75131	−	14.6230i	−0.224228	−	0.690103i	0.774141	−	0.633013i	$-0.218182\pi$
$450$	−10.4511			−0.492669
$451$	−0.289186	+	0.836687i	−0.0136173	+	0.0393980i
$452$	−43.4482			−2.04363
$453$	2.72324	+	8.38128i	0.127949	+	0.393787i
$454$	−25.1509	−	18.2732i	−1.18039	−	0.857602i
$455$	5.44090	−	3.95304i	0.255073	−	0.185322i
$456$	−0.399111	+	1.22834i	−0.0186901	+	0.0575221i
$457$	4.39924	−	13.5395i	0.205788	−	0.633350i	−0.793892	−	0.608058i	$-0.791949\pi$
$457$	4.39924	−	13.5395i	0.205788	−	0.633350i	0.999680	−	0.0252913i	$-0.00805134\pi$
$458$	12.9057	−	9.37653i	0.603043	−	0.438137i
$459$	3.87867	+	2.81802i	0.181041	+	0.131534i
$460$	11.9867	+	36.8912i	0.558882	+	1.72006i
$461$	−36.7148			−1.70998			−0.854990	−	0.518645i	$-0.826437\pi$
$461$	−36.7148			−1.70998			−0.854990	+	0.518645i	$0.826437\pi$
$462$	5.70363	−	3.98382i	0.265357	−	0.185344i
$463$	−34.7682			−1.61582			−0.807908	−	0.589308i	$-0.799400\pi$
$463$	−34.7682			−1.61582			−0.807908	+	0.589308i	$0.799400\pi$
$464$	0.900015	+	2.76996i	0.0417822	+	0.128592i
$465$	18.4557	+	13.4089i	0.855864	+	0.621822i
$466$	−2.55481	+	1.85618i	−0.118349	+	0.0859858i
$467$	4.18828	−	12.8902i	0.193811	−	0.596488i	−0.806178	−	0.591673i	$-0.798468\pi$
$467$	4.18828	−	12.8902i	0.193811	−	0.596488i	0.999988	−	0.00481441i	$-0.00153248\pi$
$468$	1.57881	−	4.85908i	0.0729805	−	0.224611i
$469$	10.7365	−	7.80052i	0.495765	−	0.360194i
$470$	55.3577	+	40.2197i	2.55346	+	1.85520i
$471$	0.484091	+	1.48988i	0.0223057	+	0.0686500i
$472$	8.01789			0.369053
$473$	−8.97091	−	29.4654i	−0.412483	−	1.35482i
$474$	−19.5340			−0.897227
$475$	2.36863	+	7.28988i	0.108680	+	0.334483i
$476$	−9.30962	−	6.76384i	−0.426706	−	0.310020i
$477$	0.765006	−	0.555810i	0.0350272	−	0.0254488i
$478$	3.25622	−	10.0216i	0.148936	−	0.458378i
$479$	8.52803	−	26.2466i	0.389656	−	1.19924i	−0.543390	−	0.839480i	$-0.682860\pi$
$479$	8.52803	−	26.2466i	0.389656	−	1.19924i	0.933046	−	0.359757i	$-0.117140\pi$
$480$	−20.5883	+	14.9583i	−0.939724	+	0.682749i
$481$	−4.13131	−	3.00157i	−0.188372	−	0.136860i
$482$	−10.4688	−	32.2197i	−0.476842	−	1.46757i
$483$	−5.11509			−0.232745
$484$	9.08796	−	24.7889i	0.413089	−	1.12677i
$485$	22.3940			1.01686
$486$	−0.648215	−	1.99500i	−0.0294036	−	0.0904950i
$487$	16.5669	+	12.0365i	0.750716	+	0.545427i	0.896049	−	0.443956i	$-0.146425\pi$
$487$	16.5669	+	12.0365i	0.750716	+	0.545427i	−0.145333	+	0.989383i	$0.546425\pi$
$488$	5.81205	−	4.22270i	0.263099	−	0.191153i
$489$	−2.10307	+	6.47258i	−0.0951041	+	0.292700i
$490$	−2.04801	+	6.30314i	−0.0925199	+	0.284747i
$491$	−23.3534	+	16.9672i	−1.05392	+	0.765721i	−0.972955	−	0.230996i	$-0.925802\pi$
$491$	−23.3534	+	16.9672i	−1.05392	+	0.765721i	−0.0809698	+	0.996717i	$0.525802\pi$
$492$	−0.518296	−	0.376564i	−0.0233666	−	0.0169768i
$493$	1.41966	+	4.36927i	0.0639384	+	0.196782i
$494$	−6.86949			−0.309073
$495$	−3.05201	−	10.0245i	−0.137178	−	0.450566i
$496$	21.9457			0.985393
$497$	−4.37458	−	13.4636i	−0.196227	−	0.603924i
$498$	−28.6014	−	20.7801i	−1.28166	−	0.931179i
$499$	17.3890	−	12.6338i	0.778438	−	0.565568i	−0.126072	−	0.992021i	$-0.540237\pi$
$499$	17.3890	−	12.6338i	0.778438	−	0.565568i	0.904510	+	0.426453i	$0.140237\pi$
$500$	−0.0416084	+	0.128058i	−0.00186079	+	0.00572691i
$501$	−3.78538	+	11.6502i	−0.169118	+	0.520492i
$502$	43.7440	−	31.7819i	1.95239	−	1.41849i
$503$	6.95915	+	5.05612i	0.310293	+	0.225441i	0.732022	−	0.681281i	$-0.238577\pi$
$503$	6.95915	+	5.05612i	0.310293	+	0.225441i	−0.421729	+	0.906722i	$0.638577\pi$
$504$	0.259421	+	0.798414i	0.0115555	+	0.0355642i
$505$	26.3692			1.17342
$506$	−29.1746	+	20.3776i	−1.29697	+	0.905896i
$507$	−8.46896			−0.376120
$508$	−11.4008	−	35.0881i	−0.505829	−	1.55678i
$509$	−8.93456	−	6.49134i	−0.396017	−	0.287724i	0.371899	−	0.928273i	$-0.378707\pi$
$509$	−8.93456	−	6.49134i	−0.396017	−	0.287724i	−0.767917	+	0.640550i	$0.778707\pi$
$510$	−25.7060	+	18.6765i	−1.13828	+	0.827008i
$511$	−2.38622	+	7.34404i	−0.105560	+	0.324881i
$512$	−9.14220	+	28.1368i	−0.404032	+	1.24348i
$513$	−1.24465	+	0.904290i	−0.0549526	+	0.0399254i
$514$	29.9830	+	21.7840i	1.32250	+	0.960849i
$515$	−7.35718	−	22.6431i	−0.324196	−	0.997773i
$516$	22.2902			0.981271
$517$	−11.1860	+	32.3639i	−0.491961	+	1.42336i
$518$	5.03232			0.221107
$519$	−6.13398	−	18.8785i	−0.269252	−	0.828672i
$520$	4.56765	+	3.31859i	0.200305	+	0.145530i
$521$	10.2110	−	7.41876i	0.447354	−	0.325022i	−0.341196	−	0.939992i	$-0.610832\pi$
$521$	10.2110	−	7.41876i	0.447354	−	0.325022i	0.788550	+	0.614970i	$0.210832\pi$
$522$	0.621149	−	1.91170i	0.0271870	−	0.0836729i
$523$	−13.5689	+	41.7609i	−0.593328	+	1.82608i	−0.0304515	+	0.999536i	$0.509695\pi$
$523$	−13.5689	+	41.7609i	−0.593328	+	1.82608i	−0.562877	+	0.826541i	$0.690305\pi$
$524$	20.8585	−	15.1546i	0.911209	−	0.662032i
$525$	4.03072	+	2.92849i	0.175915	+	0.127810i
$526$	−12.0779	−	37.1719i	−0.526620	−	1.62077i
$527$	34.6167			1.50793
$528$	−8.04365	−	6.07605i	−0.350055	−	0.264426i
$529$	3.16418			0.137573
$530$	1.93660	+	5.96025i	0.0841206	+	0.258897i
$531$	7.72673	+	5.61380i	0.335312	+	0.243618i
$532$	2.98741	−	2.17048i	0.129521	−	0.0941024i
$533$	0.175571	−	0.540351i	0.00760482	−	0.0234052i
$534$	7.30344	−	22.4777i	0.316051	−	0.972704i
$535$	−39.3345	+	28.5782i	−1.70058	+	1.23554i
$536$	9.01331	+	6.54855i	0.389316	+	0.282854i
$537$	2.54083	+	7.81988i	0.109645	+	0.337453i
$538$	43.4482			1.87318
$539$	−3.31605	−	0.0617506i	−0.142832	−	0.00265979i
$540$	7.58338			0.326337
$541$	−8.44011	−	25.9760i	−0.362869	−	1.11680i	−0.951305	−	0.308252i	$-0.900256\pi$
$541$	−8.44011	−	25.9760i	−0.362869	−	1.11680i	0.588436	−	0.808544i	$-0.299744\pi$
$542$	25.1906	+	18.3020i	1.08203	+	0.786139i
$543$	−8.43942	+	6.13159i	−0.362170	+	0.263132i
$544$	−11.9332	+	36.7266i	−0.511632	+	1.57464i
$545$	19.7786	−	60.8723i	0.847222	−	2.60748i
$546$	−3.61238	+	2.62455i	−0.154595	+	0.112320i
$547$	−14.8125	−	10.7619i	−0.633335	−	0.460145i	0.224219	−	0.974539i	$-0.428017\pi$
$547$	−14.8125	−	10.7619i	−0.633335	−	0.460145i	−0.857554	+	0.514394i	$0.828017\pi$
$548$	−3.28288	−	10.1037i	−0.140238	−	0.431607i
$549$	8.55756			0.365228
$550$	34.6563	+	0.645361i	1.47775	+	0.0275183i
$551$	−1.47423			−0.0628044
$552$	−1.32696	−	4.08396i	−0.0564792	−	0.173825i
$553$	7.53378	+	5.47361i	0.320369	+	0.232762i
$554$	−5.21519	+	3.78905i	−0.221572	+	0.160981i
$555$	2.34222	−	7.20862i	0.0994218	−	0.305989i
$556$	3.35625	−	10.3295i	0.142337	−	0.438068i
$557$	3.09637	−	2.24965i	0.131198	−	0.0953206i	−0.520251	−	0.854013i	$-0.674162\pi$
$557$	3.09637	−	2.24965i	0.131198	−	0.0953206i	0.651449	+	0.758693i	$0.274162\pi$
$558$	−12.2533	−	8.90256i	−0.518725	−	0.376875i
$559$	6.10866	+	18.8005i	0.258369	+	0.795178i
$560$	9.60295			0.405799
$561$	−12.6879	−	9.58421i	−0.535682	−	0.404646i
$562$	−8.59411			−0.362520
$563$	−11.1700	−	34.3776i	−0.470758	−	1.44884i	−0.851594	−	0.524202i	$-0.824364\pi$
$563$	−11.1700	−	34.3776i	−0.470758	−	1.44884i	0.380836	−	0.924643i	$-0.375636\pi$
$564$	−20.0482	−	14.5659i	−0.844183	−	0.613335i
$565$	46.2695	−	33.6168i	1.94657	−	1.41427i
$566$	4.79550	−	14.7590i	0.201570	−	0.620368i
$567$	−0.309017	+	0.951057i	−0.0129775	+	0.0399406i
$568$	9.61466	−	6.98546i	0.403422	−	0.293103i
$569$	7.73098	+	5.61689i	0.324100	+	0.235472i	0.737923	−	0.674885i	$-0.235807\pi$
$569$	7.73098	+	5.61689i	0.324100	+	0.235472i	−0.413823	+	0.910357i	$0.635807\pi$
$570$	−3.15081	−	9.69719i	−0.131973	−	0.406171i
$571$	−31.8446			−1.33265			−0.666327	−	0.745659i	$-0.732135\pi$
$571$	−31.8446			−1.33265			−0.666327	+	0.745659i	$0.732135\pi$
$572$	−5.53546	+	16.0155i	−0.231449	+	0.669640i
$573$	14.2162			0.593891
$574$	0.173018	+	0.532493i	0.00722161	+	0.0222258i
$575$	−20.6175	−	14.9795i	−0.859810	−	0.624688i
$576$	8.75132	−	6.35821i	0.364638	−	0.264925i
$577$	2.67605	−	8.23603i	0.111405	−	0.342870i	−0.879775	−	0.475390i	$-0.842307\pi$
$577$	2.67605	−	8.23603i	0.111405	−	0.342870i	0.991180	+	0.132520i	$0.0423069\pi$
$578$	−3.87980	+	11.9408i	−0.161378	+	0.496671i
$579$	5.67633	−	4.12410i	0.235900	−	0.171392i
$580$	5.87892	+	4.27129i	0.244109	+	0.177355i
$581$	5.20805	+	16.0287i	0.216066	+	0.664984i
$582$	−14.8680			−0.616300
$583$	−2.57112	+	1.79585i	−0.106485	+	0.0743766i
$584$	−6.48262			−0.268253
$585$	2.07824	+	6.39616i	0.0859246	+	0.264449i
$586$	−17.9020	−	13.0066i	−0.739525	−	0.537296i
$587$	4.31139	−	3.13241i	0.177950	−	0.129288i	−0.495245	−	0.868754i	$-0.664922\pi$
$587$	4.31139	−	3.13241i	0.177950	−	0.129288i	0.673195	+	0.739465i	$0.264922\pi$
$588$	0.741705	−	2.28273i	0.0305874	−	0.0941383i
$589$	−3.43266	+	10.5646i	−0.141440	+	0.435309i
$590$	−51.2090	+	37.2055i	−2.10824	+	1.53173i
$591$	2.91490	+	2.11780i	0.119903	+	0.0871147i
$592$	−2.25322	−	6.93471i	−0.0926070	−	0.285015i
$593$	11.0464			0.453622			0.226811	−	0.973939i	$-0.427170\pi$
$593$	11.0464			0.453622			0.226811	+	0.973939i	$0.427170\pi$
$594$	2.02632	+	6.65555i	0.0831409	+	0.273080i
$595$	15.1475			0.620985
$596$	2.22119	+	6.83612i	0.0909835	+	0.280018i
$597$	3.11581	+	2.26377i	0.127522	+	0.0926500i
$598$	18.4776	−	13.4248i	0.755607	−	0.548981i
$599$	8.12195	−	24.9968i	0.331854	−	1.02134i	−0.636397	−	0.771362i	$-0.719576\pi$
$599$	8.12195	−	24.9968i	0.331854	−	1.02134i	0.968251	−	0.249980i	$-0.0804240\pi$
$600$	−1.29250	+	3.97790i	−0.0527660	+	0.162397i
$601$	−10.4904	+	7.62173i	−0.427913	+	0.310897i	−0.780814	−	0.624764i	$-0.785195\pi$
$601$	−10.4904	+	7.62173i	−0.427913	+	0.310897i	0.352901	+	0.935661i	$0.385195\pi$
$602$	−15.7601	−	11.4504i	−0.642334	−	0.466683i
$603$	4.10097	+	12.6215i	0.167005	+	0.513987i
$604$	21.1521			0.860665
$605$	9.50159	+	33.4301i	0.386295	+	1.35913i
$606$	−17.5073			−0.711187
$607$	−6.98658	−	21.5025i	−0.283576	−	0.872758i	−0.986822	−	0.161811i	$-0.948266\pi$
$607$	−6.98658	−	21.5025i	−0.283576	−	0.872758i	0.703245	−	0.710947i	$-0.251734\pi$
$608$	−10.0253	−	7.28378i	−0.406578	−	0.295396i
$609$	−0.775237	+	0.563243i	−0.0314142	+	0.0228238i
$610$	−17.5260	+	53.9395i	−0.709607	+	2.18395i
$611$	6.79127	−	20.9014i	0.274745	−	0.845579i
$612$	9.30962	−	6.76384i	0.376319	−	0.273412i
$613$	17.9126	+	13.0143i	0.723484	+	0.525642i	0.887495	−	0.460816i	$-0.152443\pi$
$613$	17.9126	+	13.0143i	0.723484	+	0.525642i	−0.164011	+	0.986458i	$0.552443\pi$
$614$	−1.13408	−	3.49035i	−0.0457679	−	0.140859i
$615$	0.843306			0.0340054
$616$	−0.810949	−	2.66360i	−0.0326741	−	0.107320i
$617$	−20.4747			−0.824281			−0.412140	−	0.911120i	$-0.635219\pi$
$617$	−20.4747			−0.824281			−0.412140	+	0.911120i	$0.635219\pi$
$618$	4.88466	+	15.0334i	0.196490	+	0.604733i
$619$	−32.4426	−	23.5709i	−1.30398	−	0.947396i	−0.303993	−	0.952674i	$-0.598320\pi$
$619$	−32.4426	−	23.5709i	−1.30398	−	0.947396i	−0.999986	+	0.00527850i	$0.998320\pi$
$620$	44.2976	−	32.1841i	1.77903	−	1.29254i
$621$	1.58065	−	4.86474i	0.0634293	−	0.195215i
$622$	14.9138	−	45.8999i	0.597989	−	1.84042i
$623$	−9.11520	+	6.62258i	−0.365193	+	0.265328i
$624$	5.23416	+	3.80284i	0.209534	+	0.152235i
$625$	−7.75276	−	23.8605i	−0.310110	−	0.954422i
$626$	−38.2967			−1.53064
$627$	4.18316	−	2.92181i	0.167059	−	0.116686i
$628$	3.76005			0.150042
$629$	−3.55418	−	10.9386i	−0.141715	−	0.436152i
$630$	−5.36177	−	3.89556i	−0.213618	−	0.155203i
$631$	−23.5482	+	17.1088i	−0.937441	+	0.681091i	−0.947803	−	0.318856i	$-0.896702\pi$
$631$	−23.5482	+	17.1088i	−0.937441	+	0.681091i	0.0103623	+	0.999946i	$0.496702\pi$
$632$	−2.41579	+	7.43504i	−0.0960950	+	0.295750i
$633$	3.44012	−	10.5876i	0.136733	−	0.420820i
$634$	55.3588	−	40.2205i	2.19858	−	1.59736i
$635$	39.2895	+	28.5455i	1.55915	+	1.13279i
$636$	−0.701356	−	2.15855i	−0.0278106	−	0.0855922i
$637$	2.12862			0.0843391
$638$	−2.17781	+	6.30094i	−0.0862203	+	0.249457i
$639$	14.1564			0.560020
$640$	6.42577	+	19.7765i	0.254001	+	0.781735i
$641$	−3.03963	−	2.20842i	−0.120058	−	0.0872275i	0.526136	−	0.850401i	$-0.323640\pi$
$641$	−3.03963	−	2.20842i	−0.120058	−	0.0872275i	−0.646194	+	0.763173i	$0.723640\pi$
$642$	26.1154	−	18.9739i	1.03069	−	0.748841i
$643$	−3.07802	+	9.47317i	−0.121385	+	0.373585i	−0.993225	−	0.116205i	$-0.962927\pi$
$643$	−3.07802	+	9.47317i	−0.121385	+	0.373585i	0.871840	+	0.489791i	$0.162927\pi$
$644$	−3.79389	+	11.6764i	−0.149500	+	0.460114i
$645$	−23.7376	+	17.2464i	−0.934667	+	0.679075i
$646$	−12.5173	−	9.09431i	−0.492485	−	0.357811i
$647$	−3.55423	−	10.9388i	−0.139731	−	0.430049i	0.856565	−	0.516040i	$-0.172594\pi$
$647$	−3.55423	−	10.9388i	−0.139731	−	0.430049i	−0.996296	+	0.0859911i	$0.972594\pi$
$648$	−0.839503			−0.0329788
$649$	−25.2756	−	19.0928i	−0.992153	−	0.749457i
$650$	−22.2464			−0.872577
$651$	2.23122	+	6.86698i	0.0874483	+	0.269138i
$652$	13.2153	+	9.60149i	0.517552	+	0.376024i
$653$	4.11019	−	2.98623i	0.160844	−	0.116860i	−0.504452	−	0.863440i	$-0.668305\pi$
$653$	4.11019	−	2.98623i	0.160844	−	0.116860i	0.665296	+	0.746580i	$0.268305\pi$
$654$	−13.1316	+	40.4150i	−0.513487	+	1.58035i
$655$	−10.4875	+	32.2773i	−0.409782	+	1.26118i
$656$	0.656326	−	0.476848i	0.0256252	−	0.0186178i
$657$	−6.24721	−	4.53887i	−0.243727	−	0.177078i
$658$	6.69251	+	20.5974i	0.260901	+	0.802971i
$659$	−42.3777			−1.65080			−0.825401	−	0.564547i	$-0.809051\pi$
$659$	−42.3777			−1.65080			−0.825401	+	0.564547i	$0.809051\pi$
$660$	−25.1469	−	0.468278i	−0.978841	−	0.0182277i
$661$	−12.7151			−0.494559			−0.247280	−	0.968944i	$-0.579537\pi$
$661$	−12.7151			−0.494559			−0.247280	+	0.968944i	$0.579537\pi$
$662$	−4.41134	−	13.5767i	−0.171452	−	0.527674i
$663$	8.25623	+	5.99851i	0.320646	+	0.232963i
$664$	−11.4465	+	8.31636i	−0.444210	+	0.322737i
$665$	−1.50205	+	4.62285i	−0.0582472	+	0.179266i
$666$	−1.55507	+	4.78602i	−0.0602578	+	0.185455i
$667$	3.96541	−	2.88104i	0.153541	−	0.111554i
$668$	23.7866	+	17.2820i	0.920333	+	0.668661i
$669$	−1.62889	−	5.01320i	−0.0629764	−	0.193822i
$670$	−87.9539			−3.39796
$671$	−28.3773	−	0.528434i	−1.09549	−	0.0204000i
$672$	−8.05469			−0.310717
$673$	−8.65977	−	26.6520i	−0.333809	−	1.02736i	−0.967306	−	0.253614i	$-0.918381\pi$
$673$	−8.65977	−	26.6520i	−0.333809	−	1.02736i	0.633496	−	0.773746i	$-0.281619\pi$
$674$	0.631372	+	0.458719i	0.0243195	+	0.0176692i
$675$	−4.03072	+	2.92849i	−0.155142	+	0.112718i
$676$	−6.28147	+	19.3324i	−0.241595	+	0.743553i
$677$	3.81736	−	11.7486i	0.146713	−	0.451536i	−0.850514	−	0.525952i	$-0.823709\pi$
$677$	3.81736	−	11.7486i	0.146713	−	0.451536i	0.997227	+	0.0744157i	$0.0237092\pi$
$678$	−30.7197	+	22.3192i	−1.17978	+	0.857163i
$679$	5.73422	+	4.16616i	0.220059	+	0.159882i
$680$	3.92956	+	12.0939i	0.150692	+	0.463782i
$681$	−14.8204			−0.567917
$682$	40.0829	+	30.2780i	1.53485	+	1.15940i
$683$	4.43874			0.169844			0.0849219	−	0.996388i	$-0.472936\pi$
$683$	4.43874			0.169844			0.0849219	+	0.996388i	$0.472936\pi$
$684$	1.14109	+	3.51192i	0.0436307	+	0.134281i
$685$	11.3135	+	8.21970i	0.432265	+	0.314059i
$686$	−1.69705	+	1.23298i	−0.0647936	+	0.0470753i
$687$	2.35001	−	7.23258i	0.0896584	−	0.275940i
$688$	−8.72244	+	26.8449i	−0.332540	+	1.02345i
$689$	1.62841	−	1.18311i	0.0620375	−	0.0450729i
$690$	27.4260	+	19.9261i	1.04409	+	0.758575i
$691$	10.2415	+	31.5202i	0.389606	+	1.19908i	0.933084	+	0.359660i	$0.117107\pi$
$691$	10.2415	+	31.5202i	0.389606	+	1.19908i	−0.543478	+	0.839424i	$0.682893\pi$
$692$	−47.6441			−1.81116
$693$	1.08344	−	3.13467i	0.0411566	−	0.119076i
$694$	−12.0632			−0.457911
$695$	4.41794	+	13.5970i	0.167582	+	0.515765i
$696$	−0.650814	−	0.472844i	−0.0246690	−	0.0179231i
$697$	1.03527	−	0.752169i	0.0392137	−	0.0284904i
$698$	0.419086	−	1.28981i	0.0158626	−	0.0488201i
$699$	−0.465207	+	1.43176i	−0.0175958	+	0.0541542i
$700$	9.67457	−	7.02898i	0.365664	−	0.265671i
$701$	−3.74246	−	2.71906i	−0.141351	−	0.102697i	0.514863	−	0.857273i	$-0.327843\pi$
$701$	−3.74246	−	2.71906i	−0.141351	−	0.102697i	−0.656213	+	0.754575i	$0.727843\pi$
$702$	−1.37981	−	4.24660i	−0.0520774	−	0.160278i
$703$	3.69080			0.139201
$704$	−29.4124	+	20.5437i	−1.10852	+	0.774271i
$705$	32.6200			1.22854
$706$	11.9013	+	36.6284i	0.447911	+	1.37853i
$707$	6.75213	+	4.90571i	0.253940	+	0.184498i
$708$	18.5458	−	13.4743i	0.696992	−	0.506395i
$709$	4.60926	−	14.1858i	0.173104	−	0.532761i	−0.826437	−	0.563029i	$-0.809636\pi$
$709$	4.60926	−	14.1858i	0.173104	−	0.532761i	0.999542	+	0.0302680i	$0.00963608\pi$
$710$	−28.9926	+	89.2300i	−1.08807	+	3.34874i
$711$	−7.53378	+	5.47361i	−0.282539	+	0.205276i
$712$	−7.65223	−	5.55967i	−0.286779	−	0.208357i
$713$	−11.4129	−	35.1253i	−0.427416	−	1.31545i
$714$	−10.0569			−0.376368
$715$	−6.49657	−	21.3383i	−0.242958	−	0.798008i
$716$	19.7352			0.737541
$717$	−1.55230	−	4.77750i	−0.0579719	−	0.178419i
$718$	45.7784	+	33.2600i	1.70844	+	1.24125i
$719$	−26.7436	+	19.4304i	−0.997369	+	0.724631i	−0.961522	−	0.274726i	$-0.911413\pi$
$719$	−26.7436	+	19.4304i	−0.997369	+	0.724631i	−0.0358465	+	0.999357i	$0.511413\pi$
$720$	−2.96747	+	9.13295i	−0.110591	+	0.340365i
$721$	2.32861	−	7.16674i	0.0867221	−	0.266903i
$722$	−28.2272	+	20.5083i	−1.05051	+	0.763238i
$723$	−13.0658	−	9.49288i	−0.485923	−	0.353044i
$724$	7.73724	+	23.8128i	0.287552	+	0.884995i
$725$	−4.77422			−0.177310
$726$	−6.30840	−	22.1953i	−0.234127	−	0.823743i
$727$	6.06384			0.224895			0.112448	−	0.993658i	$-0.464131\pi$
$727$	6.06384			0.224895			0.112448	+	0.993658i	$0.464131\pi$
$728$	0.552209	+	1.69952i	0.0204662	+	0.0629885i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	41.4035	−	30.0814i	1.53241	−	1.11336i
$731$	−13.7586	+	42.3445i	−0.508879	+	1.56617i
$732$	6.34718	−	19.5346i	0.234599	−	0.722020i
$733$	0.749170	−	0.544304i	0.0276712	−	0.0201043i	−0.573864	−	0.818951i	$-0.694556\pi$
$733$	0.749170	−	0.544304i	0.0276712	−	0.0201043i	0.601535	+	0.798847i	$0.294556\pi$
$734$	48.0630	+	34.9198i	1.77404	+	1.28891i
$735$	0.976330	+	3.00483i	0.0360125	+	0.110835i
$736$	41.2005			1.51867
$737$	−12.8196	−	42.1068i	−0.472218	−	1.55102i
$738$	−0.559897			−0.0206101
$739$	−9.42384	−	29.0036i	−0.346662	−	1.06691i	−0.960688	−	0.277629i	$-0.910451\pi$
$739$	−9.42384	−	29.0036i	−0.346662	−	1.06691i	0.614027	−	0.789285i	$-0.289549\pi$
$740$	−14.7181	−	10.6933i	−0.541049	−	0.393095i
$741$	−2.64939	+	1.92489i	−0.0973277	+	0.0707127i
$742$	−0.612952	+	1.88647i	−0.0225022	+	0.0692545i
$743$	5.51656	−	16.9782i	0.202383	−	0.622871i	−0.797428	−	0.603414i	$-0.793806\pi$
$743$	5.51656	−	16.9782i	0.202383	−	0.622871i	0.999811	−	0.0194563i	$-0.00619354\pi$
$744$	−4.90387	+	3.56287i	−0.179785	+	0.130621i
$745$	−7.65467	−	5.56144i	−0.280445	−	0.203755i
$746$	8.37591	+	25.7784i	0.306664	+	0.943815i
$747$	−16.8536			−0.616641
$748$	−31.2888	+	21.8543i	−1.14403	+	0.799074i
$749$	−15.3887			−0.562291
$750$	0.0363638	+	0.111916i	0.00132782	+	0.00408660i
$751$	−28.9497	−	21.0332i	−1.05639	−	0.767511i	−0.0829711	−	0.996552i	$-0.526441\pi$
$751$	−28.9497	−	21.0332i	−1.05639	−	0.767511i	−0.973417	+	0.229041i	$0.926441\pi$
$752$	25.3874	−	18.4450i	0.925783	−	0.672620i
$753$	7.96538	−	24.5149i	0.290275	−	0.893373i
$754$	1.32219	−	4.06929i	0.0481514	−	0.148195i
$755$	−22.5256	+	16.3658i	−0.819789	+	0.595612i
$756$	1.94181	+	1.41081i	0.0706229	+	0.0513105i
$757$	13.1371	+	40.4318i	0.477475	+	1.46952i	0.842590	+	0.538556i	$0.181030\pi$
$757$	13.1371	+	40.4318i	0.477475	+	1.46952i	−0.365115	+	0.930963i	$0.618970\pi$
$758$	−43.9420			−1.59605
$759$	−5.54192	+	16.0341i	−0.201159	+	0.582002i
$760$	−4.08061			−0.148019
$761$	2.81382	+	8.66004i	0.102001	+	0.313926i	0.989015	−	0.147816i	$-0.0472245\pi$
$761$	2.81382	+	8.66004i	0.102001	+	0.313926i	−0.887014	+	0.461742i	$0.847224\pi$
$762$	−26.0855	−	18.9522i	−0.944977	−	0.686566i
$763$	16.3892	−	11.9074i	0.593328	−	0.431078i
$764$	10.5442	−	32.4519i	0.381477	−	1.17407i
$765$	−4.68082	+	14.4061i	−0.169235	+	0.520853i
$766$	42.3862	−	30.7953i	1.53147	−	1.11268i
$767$	16.4473	+	11.9497i	0.593878	+	0.431477i
$768$	2.41915	+	7.44538i	0.0872936	+	0.268662i
$769$	−6.93312			−0.250015			−0.125007	−	0.992156i	$-0.539895\pi$
$769$	−6.93312			−0.250015			−0.125007	+	0.992156i	$0.539895\pi$
$770$	17.5394	+	13.2489i	0.632074	+	0.477459i
$771$	17.6678			0.636289
$772$	−5.20405	−	16.0164i	−0.187298	−	0.576443i
$773$	14.7750	+	10.7347i	0.531421	+	0.386100i	0.820889	−	0.571088i	$-0.193478\pi$
$773$	14.7750	+	10.7347i	0.531421	+	0.386100i	−0.289468	+	0.957188i	$0.593478\pi$
$774$	15.7601	−	11.4504i	0.566486	−	0.411576i
$775$	−11.1165	+	34.2130i	−0.399316	+	1.22897i
$776$	−1.83874	+	5.65907i	−0.0660071	+	0.203149i
$777$	1.94084	−	1.41010i	0.0696272	−	0.0505871i
$778$	−23.0425	−	16.7413i	−0.826112	−	0.600206i
$779$	0.126894	+	0.390541i	0.00454647	+	0.0139926i
$780$	16.1422			0.577982
$781$	−46.9435	−	0.874168i	−1.67977	−	0.0312802i
$782$	51.4418			1.83955
$783$	−0.296114	−	0.911346i	−0.0105823	−	0.0325689i
$784$	2.45894	+	1.78653i	0.0878193	+	0.0638045i
$785$	−4.00421	+	2.90923i	−0.142916	+	0.103835i
$786$	6.96300	−	21.4299i	0.248362	−	0.764379i
$787$	−3.78765	+	11.6572i	−0.135015	+	0.415534i	−0.995592	−	0.0937860i	$-0.970103\pi$
$787$	−3.78765	+	11.6572i	−0.135015	+	0.415534i	0.860577	+	0.509320i	$0.170103\pi$
$788$	6.99638	−	5.08316i	0.249236	−	0.181080i
$789$	−15.0740	−	10.9519i	−0.536649	−	0.389898i
$790$	−19.0716	−	58.6965i	−0.678539	−	2.08833i
$791$	18.1019			0.643628
$792$	2.78383	+	0.0518398i	0.0989192	+	0.00184205i
$793$	18.2158			0.646862
$794$	2.76431	+	8.50767i	0.0981017	+	0.301926i
$795$	2.41701	+	1.75606i	0.0857226	+	0.0622811i
$796$	7.47860	−	5.43352i	0.265072	−	0.192586i
$797$	−7.06294	+	21.7375i	−0.250182	+	0.769981i	0.744559	+	0.667557i	$0.232660\pi$
$797$	−7.06294	+	21.7375i	−0.250182	+	0.769981i	−0.994741	+	0.102424i	$0.967340\pi$
$798$	0.997259	−	3.06925i	0.0353026	−	0.108650i
$799$	40.0454	−	29.0947i	1.41671	−	1.02930i
$800$	−32.4662	−	23.5881i	−1.14785	−	0.833965i
$801$	−3.48169	−	10.7156i	−0.123020	−	0.378616i
$802$	68.0531			2.40304
$803$	20.4358	+	15.4369i	0.721163	+	0.544755i
$804$	31.8532			1.12338
$805$	−4.99402	−	15.3700i	−0.176016	−	0.541721i
$806$	−26.0827	−	18.9502i	−0.918724	−	0.667492i
$807$	16.7569	−	12.1746i	0.589869	−	0.428565i
$808$	−2.16515	+	6.66364i	−0.0761697	+	0.234426i
$809$	−13.4837	+	41.4986i	−0.474062	+	1.45901i	0.373157	+	0.927768i	$0.378275\pi$
$809$	−13.4837	+	41.4986i	−0.474062	+	1.45901i	−0.847219	+	0.531244i	$0.821725\pi$
$810$	5.36177	−	3.89556i	0.188393	−	0.136876i
$811$	11.1903	+	8.13021i	0.392944	+	0.285490i	0.766661	−	0.642052i	$-0.221917\pi$
$811$	11.1903	+	8.13021i	0.392944	+	0.285490i	−0.373717	+	0.927543i	$0.621917\pi$
$812$	0.710736	+	2.18742i	0.0249419	+	0.0767634i
$813$	14.8438			0.520593
$814$	5.45224	−	15.7747i	0.191101	−	0.552901i
$815$	−21.5023			−0.753194
$816$	4.50296	+	13.8587i	0.157635	+	0.485151i
$817$	−11.5588	−	8.39794i	−0.404390	−	0.293807i
$818$	−42.2356	+	30.6859i	−1.47673	+	1.07291i
$819$	−0.657781	+	2.02444i	−0.0229847	+	0.0707397i
$820$	0.625484	−	1.92504i	0.0218429	−	0.0672254i
$821$	15.8557	−	11.5198i	0.553368	−	0.402045i	−0.275658	−	0.961256i	$-0.588896\pi$
$821$	15.8557	−	11.5198i	0.553368	−	0.402045i	0.829026	+	0.559211i	$0.188896\pi$
$822$	−7.51134	−	5.45731i	−0.261988	−	0.190346i
$823$	11.7569	+	36.1840i	0.409819	+	1.26129i	0.916804	+	0.399338i	$0.130760\pi$
$823$	11.7569	+	36.1840i	0.409819	+	1.26129i	−0.506985	+	0.861955i	$0.669240\pi$
$824$	6.32612			0.220381
$825$	13.5469	−	9.46212i	0.471643	−	0.329429i
$826$	−20.0343			−0.697084
$827$	−0.835400	−	2.57110i	−0.0290497	−	0.0894058i	0.935480	−	0.353378i	$-0.114967\pi$
$827$	−0.835400	−	2.57110i	−0.0290497	−	0.0894058i	−0.964530	+	0.263973i	$0.914967\pi$
$828$	−9.93253	−	7.21641i	−0.345179	−	0.250788i
$829$	14.3125	−	10.3987i	0.497095	−	0.361161i	−0.310811	−	0.950472i	$-0.600601\pi$
$829$	14.3125	−	10.3987i	0.497095	−	0.361161i	0.807906	+	0.589311i	$0.200601\pi$
$830$	34.5164	−	106.231i	1.19808	−	3.68732i
$831$	−0.949638	+	2.92268i	−0.0329426	+	0.101387i
$832$	18.6283	−	13.5342i	0.645819	−	0.469215i
$833$	3.87867	+	2.81802i	0.134388	+	0.0976387i
$834$	−2.93321	−	9.02748i	−0.101569	−	0.312596i
$835$	−38.7027			−1.33936
$836$	−3.56705	−	11.7162i	−0.123369	−	0.405212i
$837$	−7.22037			−0.249573
$838$	−6.86768	−	21.1365i	−0.237240	−	0.730150i
$839$	−0.136448	−	0.0991353i	−0.00471071	−	0.00342253i	0.585427	−	0.810725i	$-0.300927\pi$
$839$	−0.136448	−	0.0991353i	−0.00471071	−	0.00342253i	−0.590138	+	0.807302i	$0.700927\pi$
$840$	−2.14582	+	1.55903i	−0.0740379	+	0.0537917i
$841$	−8.67774	+	26.7073i	−0.299233	+	0.920943i
$842$	24.5435	−	75.5371i	0.845825	−	2.60318i
$843$	−3.31453	+	2.40815i	−0.114158	+	0.0829409i
$844$	−21.6171	−	15.7058i	−0.744093	−	0.540615i
$845$	−8.26850	−	25.4478i	−0.284445	−	0.875432i
$846$	−21.6574			−0.744597
$847$	−3.78632	+	10.3278i	−0.130100	+	0.354868i
$848$	2.87407			0.0986961
$849$	−2.28611	−	7.03592i	−0.0784591	−	0.241472i
$850$	−40.5364	−	29.4514i	−1.39039	−	1.01017i
$851$	−9.92757	+	7.21280i	−0.340313	+	0.247252i
$852$	10.4999	−	32.3154i	0.359721	−	1.10711i
$853$	−13.2806	+	40.8736i	−0.454720	+	1.39948i	0.416743	+	0.909024i	$0.363171\pi$
$853$	−13.2806	+	40.8736i	−0.454720	+	1.39948i	−0.871464	+	0.490460i	$0.836829\pi$
$854$	−14.5226	+	10.5513i	−0.496953	+	0.361057i
$855$	−3.93243	−	2.85708i	−0.134486	−	0.0977100i
$856$	−3.99215	−	12.2866i	−0.136449	−	0.419946i
$857$	−3.31550			−0.113255			−0.0566276	−	0.998395i	$-0.518035\pi$
$857$	−3.31550			−0.113255			−0.0566276	+	0.998395i	$0.518035\pi$
$858$	4.31327	+	14.1672i	0.147253	+	0.483659i
$859$	12.5924			0.429646			0.214823	−	0.976653i	$-0.431083\pi$
$859$	12.5924			0.429646			0.214823	+	0.976653i	$0.431083\pi$
$860$	21.7626	+	66.9783i	0.742098	+	2.28394i
$861$	0.215938	+	0.156888i	0.00735914	+	0.00534673i
$862$	9.57964	−	6.96002i	0.326284	−	0.237059i
$863$	−17.2547	+	53.1045i	−0.587357	+	1.80770i	0.00223669	+	0.999997i	$0.499288\pi$
$863$	−17.2547	+	53.1045i	−0.587357	+	1.80770i	−0.589593	+	0.807700i	$0.700712\pi$
$864$	2.48904	−	7.66047i	0.0846788	−	0.260614i
$865$	50.7378	−	36.8632i	1.72514	−	1.25339i
$866$	−4.57403	−	3.32323i	−0.155432	−	0.112928i
$867$	1.84958	+	5.69241i	0.0628149	+	0.193324i
$868$	17.3304			0.588232
$869$	25.3204	−	17.6855i	0.858935	−	0.599941i
$870$	6.35079			0.215312
$871$	8.72943	+	26.8664i	0.295785	+	0.910334i
$872$	13.7587	+	9.99632i	0.465930	+	0.338518i
$873$	−5.73422	+	4.16616i	−0.194074	+	0.141003i
$874$	−5.10107	+	15.6995i	−0.172546	+	0.531043i
$875$	0.0173353	−	0.0533527i	0.000586042	−	0.00180365i
$876$	−14.9946	+	10.8942i	−0.506621	+	0.368082i
$877$	−6.68843	−	4.85943i	−0.225852	−	0.164091i	0.469105	−	0.883143i	$-0.344577\pi$
$877$	−6.68843	−	4.85943i	−0.225852	−	0.164091i	−0.694957	+	0.719051i	$0.744577\pi$
$878$	−19.8139	−	60.9809i	−0.668686	−	2.05800i
$879$	−10.5489			−0.355806
$880$	10.4043	−	30.1021i	0.350727	−	1.01474i
$881$	26.0843			0.878803			0.439401	−	0.898291i	$-0.355191\pi$
$881$	26.0843			0.878803			0.439401	+	0.898291i	$0.355191\pi$
$882$	−0.648215	−	1.99500i	−0.0218265	−	0.0671751i
$883$	−0.740321	−	0.537874i	−0.0249138	−	0.0181009i	0.575259	−	0.817972i	$-0.304901\pi$
$883$	−0.740321	−	0.537874i	−0.0249138	−	0.0181009i	−0.600172	+	0.799871i	$0.704901\pi$
$884$	19.8167	−	14.3977i	0.666507	−	0.484246i
$885$	−9.32470	+	28.6985i	−0.313446	+	0.964688i
$886$	15.9701	−	49.1510i	0.536527	−	1.65126i
$887$	45.3512	−	32.9496i	1.52274	−	1.10634i	0.562638	−	0.826703i	$-0.309786\pi$
$887$	45.3512	−	32.9496i	1.52274	−	1.10634i	0.960106	−	0.279635i	$-0.0902136\pi$
$888$	1.62934	+	1.18378i	0.0546770	+	0.0397252i
$889$	4.74993	+	14.6188i	0.159307	+	0.490298i
$890$	74.6722			2.50302
$891$	2.64644	+	1.99908i	0.0886592	+	0.0669718i
$892$	−12.6520			−0.423619
$893$	4.90841	+	15.1065i	0.164254	+	0.505521i
$894$	5.08217	+	3.69241i	0.169973	+	0.123493i
$895$	−21.0167	+	15.2696i	−0.702512	+	0.510405i
$896$	−2.03381	+	6.25944i	−0.0679450	+	0.209113i
$897$	3.36461	−	10.3552i	0.112341	−	0.345750i
$898$	−26.0930	+	18.9577i	−0.870736	+	0.632627i
$899$	−5.59750	−	4.06682i	−0.186687	−	0.135636i
$900$	3.69536	+	11.3731i	0.123179	+	0.379104i
$901$	4.53349			0.151033
$902$	1.85665	+	0.0345739i	0.0618195	+	0.00115119i
$903$	−9.28678			−0.309045
$904$	4.69600	+	14.4528i	0.156186	+	0.480693i
$905$	−26.6641	−	19.3726i	−0.886344	−	0.643966i
$906$	14.9554	−	10.8657i	0.496860	−	0.360990i
$907$	2.85729	−	8.79382i	0.0948746	−	0.291994i	−0.892346	−	0.451351i	$-0.850942\pi$
$907$	2.85729	−	8.79382i	0.0948746	−	0.291994i	0.987221	+	0.159357i	$0.0509422\pi$
$908$	−10.9923	+	33.8309i	−0.364793	+	1.12272i
$909$	−6.75213	+	4.90571i	−0.223954	+	0.162712i
$910$	−11.4132	−	8.29217i	−0.378344	−	0.274883i
$911$	−11.5250	−	35.4704i	−0.381841	−	1.17519i	−0.938746	−	0.344609i	$-0.888011\pi$
$911$	−11.5250	−	35.4704i	−0.381841	−	1.17519i	0.556905	−	0.830576i	$-0.311989\pi$
$912$	−4.67605			−0.154840
$913$	55.8874	+	1.04072i	1.84960	+	0.0344428i
$914$	−29.8629			−0.987777
$915$	8.35499	+	25.7140i	0.276208	+	0.850080i
$916$	−14.7670	−	10.7289i	−0.487917	−	0.354492i
$917$	−8.69030	+	6.31387i	−0.286979	+	0.208502i
$918$	3.10774	−	9.56464i	0.102571	−	0.315680i
$919$	−4.52355	+	13.9220i	−0.149218	+	0.459246i	−0.997529	−	0.0702519i	$-0.977620\pi$
$919$	−4.52355	+	13.9220i	−0.149218	+	0.459246i	0.848311	+	0.529498i	$0.177620\pi$
$920$	10.9761	−	7.97459i	0.361871	−	0.262914i
$921$	−1.41542	−	1.02836i	−0.0466396	−	0.0338856i
$922$	23.7991	+	73.2461i	0.783781	+	2.41223i
$923$	30.1337			0.991864
$924$	−6.35202	−	4.79821i	−0.208966	−	0.157850i
$925$	11.9524			0.392994
$926$	22.5373	+	69.3626i	0.740621	+	2.27940i
$927$	6.09639	+	4.42929i	0.200232	+	0.145477i
$928$	6.24430	−	4.53675i	0.204979	−	0.148926i
$929$	−2.41246	+	7.42479i	−0.0791503	+	0.243600i	−0.982800	−	0.184673i	$-0.940878\pi$
$929$	−2.41246	+	7.42479i	−0.0791503	+	0.243600i	0.903650	+	0.428272i	$0.140878\pi$
$930$	14.7874	−	45.5110i	0.484899	−	1.49237i
$931$	−1.24465	+	0.904290i	−0.0407917	+	0.0296369i
$932$	2.92328	+	2.12389i	0.0957553	+	0.0695703i
$933$	−7.10970	−	21.8814i	−0.232761	−	0.716365i
$934$	−28.4309			−0.930287
$935$	16.4114	−	47.4823i	0.536711	−	1.55284i
$936$	−1.78698			−0.0584094
$937$	−16.4092	−	50.5023i	−0.536065	−	1.64984i	−0.741336	−	0.671134i	$-0.765808\pi$
$937$	−16.4092	−	50.5023i	−0.536065	−	1.64984i	0.205271	−	0.978705i	$-0.434192\pi$
$938$	−22.5216	−	16.3629i	−0.735356	−	0.534267i
$939$	−14.7700	+	10.7311i	−0.482002	+	0.350195i
$940$	24.1944	−	74.4627i	0.789135	−	2.42871i
$941$	−4.03537	+	12.4196i	−0.131549	+	0.404867i	−0.995037	−	0.0995022i	$-0.968275\pi$
$941$	−4.03537	+	12.4196i	−0.131549	+	0.404867i	0.863488	+	0.504369i	$0.168275\pi$
$942$	2.65851	−	1.93152i	0.0866191	−	0.0629325i
$943$	−1.10454	−	0.802497i	−0.0359689	−	0.0261329i
$944$	8.97039	+	27.6080i	0.291961	+	0.898564i
$945$	−3.15947			−0.102778
$946$	−52.9684	+	36.9969i	−1.72215	+	1.20287i
$947$	−39.8291			−1.29427			−0.647136	−	0.762375i	$-0.724033\pi$
$947$	−39.8291			−1.29427			−0.647136	+	0.762375i	$0.724033\pi$
$948$	6.90695	+	21.2574i	0.224327	+	0.690408i
$949$	−13.2980	−	9.66153i	−0.431670	−	0.313627i
$950$	13.0079	−	9.45082i	0.422033	−	0.306625i
$951$	10.0803	−	31.0241i	0.326877	−	1.00602i
$952$	−1.24374	+	3.82784i	−0.0403099	+	0.124061i
$953$	−3.06721	+	2.22846i	−0.0993567	+	0.0721869i	−0.636354	−	0.771397i	$-0.719558\pi$
$953$	−3.06721	+	2.22846i	−0.0993567	+	0.0721869i	0.536998	+	0.843584i	$0.319558\pi$
$954$	−1.60473	−	1.16590i	−0.0519550	−	0.0377475i
$955$	13.8797	+	42.7174i	0.449137	+	1.38230i
$956$	−12.0571			−0.389955
$957$	0.925654	+	3.04035i	0.0299221	+	0.0982807i
$958$	−57.8899			−1.87034
$959$	1.36775	+	4.20949i	0.0441669	+	0.135932i
$960$	27.6495	+	20.0886i	0.892385	+	0.648356i
$961$	−17.0976	+	12.4221i	−0.551536	+	0.400714i
$962$	−3.31016	+	10.1876i	−0.106724	+	0.328463i
$963$	4.75537	−	14.6355i	0.153240	−	0.471623i
$964$	−31.3607	+	22.7849i	−1.01006	+	0.733851i
$965$	17.9342	+	13.0300i	0.577322	+	0.419449i
$966$	3.31568	+	10.2046i	0.106680	+	0.328328i
$967$	5.63563			0.181230			0.0906149	−	0.995886i	$-0.471117\pi$
$967$	5.63563			0.181230			0.0906149	+	0.995886i	$0.471117\pi$
$968$	−9.22813	−	0.343806i	−0.296603	−	0.0110504i
$969$	−7.37589			−0.236948
$970$	−14.5161	−	44.6760i	−0.466084	−	1.43446i
$971$	1.95559	+	1.42082i	0.0627578	+	0.0455962i	0.618722	−	0.785610i	$-0.287651\pi$
$971$	1.95559	+	1.42082i	0.0627578	+	0.0455962i	−0.555964	+	0.831206i	$0.687651\pi$
$972$	−1.94181	+	1.41081i	−0.0622835	+	0.0452516i
$973$	−1.39832	+	4.30358i	−0.0448280	+	0.137966i
$974$	13.2740	−	40.8531i	0.425326	−	1.30902i
$975$	−8.57988	+	6.23365i	−0.274776	+	0.199637i
$976$	21.0425	+	15.2883i	0.673555	+	0.489366i
$977$	14.4134	+	44.3597i	0.461124	+	1.41919i	0.863792	+	0.503848i	$0.168083\pi$
$977$	14.4134	+	44.3597i	0.461124	+	1.41919i	−0.402668	+	0.915346i	$0.631917\pi$
$978$	14.2760			0.456498
$979$	10.8838	+	35.7483i	0.347847	+	1.14252i
$980$	7.58338			0.242242
$981$	6.26010	+	19.2666i	0.199870	+	0.615136i
$982$	48.9877	+	35.5916i	1.56326	+	1.13577i
$983$	−17.5480	+	12.7494i	−0.559695	+	0.406642i	−0.831347	−	0.555753i	$-0.812430\pi$
$983$	−17.5480	+	12.7494i	−0.559695	+	0.406642i	0.271652	+	0.962395i	$0.412430\pi$
$984$	−0.0692430	+	0.213108i	−0.00220739	+	0.00679363i
$985$	−3.51773	+	10.8265i	−0.112084	+	0.344960i
$986$	7.79645	−	5.66445i	0.248290	−	0.180393i
$987$	8.35271	+	6.06860i	0.265870	+	0.193166i
$988$	2.42895	+	7.47555i	0.0772753	+	0.237829i
$989$	47.5027			1.51050
$990$	−18.0205	+	12.5868i	−0.572728	+	0.400034i
$991$	33.7715			1.07279			0.536394	−	0.843968i	$-0.319786\pi$
$991$	33.7715			1.07279			0.536394	+	0.843968i	$0.319786\pi$
$992$	−17.9718	−	55.3114i	−0.570605	−	1.75614i
$993$	−5.50566	−	4.00010i	−0.174717	−	0.126939i
$994$	−24.0242	+	17.4546i	−0.762000	+	0.553626i
$995$	−3.76019	+	11.5727i	−0.119206	+	0.366879i
$996$	−12.5004	+	38.4723i	−0.396090	+	1.21904i
$997$	−0.505573	+	0.367320i	−0.0160117	+	0.0116331i	−0.595762	−	0.803161i	$-0.703150\pi$
$997$	−0.505573	+	0.367320i	−0.0160117	+	0.0116331i	0.579751	+	0.814794i	$0.303150\pi$
$998$	−36.4763	−	26.5016i	−1.15464	−	0.838893i
$999$	0.741334	+	2.28159i	0.0234548	+	0.0721864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.g.148.2	yes	20
3.2	odd	2		693.2.m.j.379.4		20
11.3	even	5		2541.2.a.bq.1.3		10
11.8	odd	10		2541.2.a.br.1.8		10
11.9	even	5	inner	231.2.j.g.64.2	✓	20
33.8	even	10		7623.2.a.cy.1.3		10
33.14	odd	10		7623.2.a.cx.1.8		10
33.20	odd	10		693.2.m.j.64.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.64.2	✓	20	11.9	even	5	inner
231.2.j.g.148.2	yes	20	1.1	even	1	trivial
693.2.m.j.64.4		20	33.20	odd	10
693.2.m.j.379.4		20	3.2	odd	2
2541.2.a.bq.1.3		10	11.3	even	5
2541.2.a.br.1.8		10	11.8	odd	10
7623.2.a.cx.1.8		10	33.14	odd	10
7623.2.a.cy.1.3		10	33.8	even	10

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.648215 - 1.99500i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.94181 + 1.41081i) q^{4} +(0.976330 - 3.00483i) q^{5} +(-0.648215 + 1.99500i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.679172 + 0.493447i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.648215 - 1.99500i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.94181 + 1.41081i) q^{4} +(0.976330 - 3.00483i) q^{5} +(-0.648215 + 1.99500i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.679172 + 0.493447i) q^{8} +(0.309017 + 0.951057i) q^{9} -6.62751 q^{10} +(-0.965987 - 3.17283i) q^{11} +2.40021 q^{12} +(0.657781 + 2.02444i) q^{13} +(-1.69705 - 1.23298i) q^{14} +(-2.55606 + 1.85709i) q^{15} +(-0.939232 + 2.89066i) q^{16} +(-1.48152 + 4.55965i) q^{17} +(1.69705 - 1.23298i) q^{18} +(-1.24465 - 0.904290i) q^{19} +(2.34339 + 7.21222i) q^{20} -1.00000 q^{21} +(-5.70363 + 3.98382i) q^{22} +5.11509 q^{23} +(-0.259421 - 0.798414i) q^{24} +(-4.03072 - 2.92849i) q^{25} +(3.61238 - 2.62455i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.741705 + 2.28273i) q^{28} +(0.775237 - 0.563243i) q^{29} +(5.36177 + 3.89556i) q^{30} +(-2.23122 - 6.86698i) q^{31} +8.05469 q^{32} +(-1.08344 + 3.13467i) q^{33} +10.0569 q^{34} +(-0.976330 - 3.00483i) q^{35} +(-1.94181 - 1.41081i) q^{36} +(-1.94084 + 1.41010i) q^{37} +(-0.997259 + 3.06925i) q^{38} +(0.657781 - 2.02444i) q^{39} +(2.14582 - 1.55903i) q^{40} +(-0.215938 - 0.156888i) q^{41} +(0.648215 + 1.99500i) q^{42} +9.28678 q^{43} +(6.35202 + 4.79821i) q^{44} +3.15947 q^{45} +(-3.31568 - 10.2046i) q^{46} +(-8.35271 - 6.06860i) q^{47} +(2.45894 - 1.78653i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.22956 + 9.93958i) q^{50} +(3.87867 - 2.81802i) q^{51} +(-4.13338 - 3.00308i) q^{52} +(-0.292206 - 0.899319i) q^{53} -2.09767 q^{54} +(-10.4770 - 0.195099i) q^{55} +0.839503 q^{56} +(0.475413 + 1.46317i) q^{57} +(-1.62619 - 1.18150i) q^{58} +(7.72673 - 5.61380i) q^{59} +(2.34339 - 7.21222i) q^{60} +(2.64443 - 8.13872i) q^{61} +(-12.2533 + 8.90256i) q^{62} +(0.809017 + 0.587785i) q^{63} +(-3.34271 - 10.2878i) q^{64} +6.72532 q^{65} +(6.95597 + 0.129532i) q^{66} +13.2710 q^{67} +(-3.55596 - 10.9441i) q^{68} +(-4.13820 - 3.00658i) q^{69} +(-5.36177 + 3.89556i) q^{70} +(4.37458 - 13.4636i) q^{71} +(-0.259421 + 0.798414i) q^{72} +(-6.24721 + 4.53887i) q^{73} +(4.07123 + 2.95792i) q^{74} +(1.53960 + 4.73840i) q^{75} +3.69265 q^{76} +(-2.64644 - 1.99908i) q^{77} -4.46514 q^{78} +(2.87765 + 8.85649i) q^{79} +(7.76895 + 5.64447i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.173018 + 0.532493i) q^{82} +(-5.20805 + 16.0287i) q^{83} +(1.94181 - 1.41081i) q^{84} +(12.2545 + 8.90345i) q^{85} +(-6.01983 - 18.5271i) q^{86} -0.958246 q^{87} +(0.909554 - 2.63156i) q^{88} -11.2670 q^{89} +(-2.04801 - 6.30314i) q^{90} +(1.72209 + 1.25117i) q^{91} +(-9.93253 + 7.21641i) q^{92} +(-2.23122 + 6.86698i) q^{93} +(-6.69251 + 20.5974i) q^{94} +(-3.93243 + 2.85708i) q^{95} +(-6.51638 - 4.73443i) q^{96} +(2.19028 + 6.74098i) q^{97} -2.09767 q^{98} +(2.71904 - 1.89917i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

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