LMFDB - Embedded newform 315.2.bh.b.274.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(169,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3, 0]))

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

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

chi := DirichletCharacter("315.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bh (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			274.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.274
Dual form			315.2.bh.b.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 + 1.00000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.133975 - 2.23205i) q^{5} +(3.00000 + 1.73205i) q^{6} +(0.866025 - 0.500000i) q^{7} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.73205 + 1.00000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.133975 - 2.23205i) q^{5} +(3.00000 + 1.73205i) q^{6} +(0.866025 - 0.500000i) q^{7} +(-1.50000 + 2.59808i) q^{9} +(2.00000 + 4.00000i) q^{10} +(-1.50000 - 2.59808i) q^{11} -3.46410 q^{12} +(1.73205 + 1.00000i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-3.46410 + 1.73205i) q^{15} +(2.00000 + 3.46410i) q^{16} +2.00000i q^{17} -6.00000i q^{18} -6.00000 q^{19} +(-3.73205 - 2.46410i) q^{20} +(-1.50000 - 0.866025i) q^{21} +(5.19615 + 3.00000i) q^{22} +(-5.19615 - 3.00000i) q^{23} +(-4.96410 - 0.598076i) q^{25} -4.00000 q^{26} +5.19615 q^{27} -2.00000i q^{28} +(-2.50000 - 4.33013i) q^{29} +(4.26795 - 6.46410i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-6.92820 - 4.00000i) q^{32} +(-2.59808 + 4.50000i) q^{33} +(-2.00000 - 3.46410i) q^{34} +(-1.00000 - 2.00000i) q^{35} +(3.00000 + 5.19615i) q^{36} -2.00000i q^{37} +(10.3923 - 6.00000i) q^{38} -3.46410i q^{39} +(-4.00000 + 6.92820i) q^{41} +3.46410 q^{42} +(1.73205 - 1.00000i) q^{43} -6.00000 q^{44} +(5.59808 + 3.69615i) q^{45} +12.0000 q^{46} +(-2.59808 + 1.50000i) q^{47} +(3.46410 - 6.00000i) q^{48} +(0.500000 - 0.866025i) q^{49} +(9.19615 - 3.92820i) q^{50} +(3.00000 - 1.73205i) q^{51} +(3.46410 - 2.00000i) q^{52} +(-9.00000 + 5.19615i) q^{54} +(-6.00000 + 3.00000i) q^{55} +(5.19615 + 9.00000i) q^{57} +(8.66025 + 5.00000i) q^{58} +(-7.00000 + 12.1244i) q^{59} +(-0.464102 + 7.73205i) q^{60} +(-5.00000 - 8.66025i) q^{61} +8.00000i q^{62} +3.00000i q^{63} +8.00000 q^{64} +(2.46410 - 3.73205i) q^{65} -10.3923i q^{66} +(-8.66025 - 5.00000i) q^{67} +(3.46410 + 2.00000i) q^{68} +10.3923i q^{69} +(3.73205 + 2.46410i) q^{70} +7.00000 q^{71} +9.00000i q^{73} +(2.00000 + 3.46410i) q^{74} +(3.40192 + 7.96410i) q^{75} +(-6.00000 + 10.3923i) q^{76} +(-2.59808 - 1.50000i) q^{77} +(3.46410 + 6.00000i) q^{78} +(0.500000 + 0.866025i) q^{79} +(8.00000 - 4.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} -16.0000i q^{82} +(14.7224 - 8.50000i) q^{83} +(-3.00000 + 1.73205i) q^{84} +(4.46410 + 0.267949i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(-4.33013 + 7.50000i) q^{87} +12.0000 q^{89} +(-13.3923 - 0.803848i) q^{90} +2.00000 q^{91} +(-10.3923 + 6.00000i) q^{92} -6.92820 q^{93} +(3.00000 - 5.19615i) q^{94} +(-0.803848 + 13.3923i) q^{95} +13.8564i q^{96} +(-6.06218 + 3.50000i) q^{97} +2.00000i q^{98} +9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} + 4 q^{5} + 12 q^{6} - 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^4 + 4 * q^5 + 12 * q^6 - 6 * q^9	$ 4 q + 4 q^{4} + 4 q^{5} + 12 q^{6} - 6 q^{9} + 8 q^{10} - 6 q^{11} - 4 q^{14} + 8 q^{16} - 24 q^{19} - 8 q^{20} - 6 q^{21} - 6 q^{25} - 16 q^{26} - 10 q^{29} + 24 q^{30} + 8 q^{31} - 8 q^{34} - 4 q^{35} + 12 q^{36} - 16 q^{41} - 24 q^{44} + 12 q^{45} + 48 q^{46} + 2 q^{49} + 16 q^{50} + 12 q^{51} - 36 q^{54} - 24 q^{55} - 28 q^{59} + 12 q^{60} - 20 q^{61} + 32 q^{64} - 4 q^{65} + 8 q^{70} + 28 q^{71} + 8 q^{74} + 24 q^{75} - 24 q^{76} + 2 q^{79} + 32 q^{80} - 18 q^{81} - 12 q^{84} + 4 q^{85} - 8 q^{86} + 48 q^{89} - 12 q^{90} + 8 q^{91} + 12 q^{94} - 24 q^{95} + 36 q^{99}+O(q^{100}) $ 4 * q + 4 * q^4 + 4 * q^5 + 12 * q^6 - 6 * q^9 + 8 * q^10 - 6 * q^11 - 4 * q^14 + 8 * q^16 - 24 * q^19 - 8 * q^20 - 6 * q^21 - 6 * q^25 - 16 * q^26 - 10 * q^29 + 24 * q^30 + 8 * q^31 - 8 * q^34 - 4 * q^35 + 12 * q^36 - 16 * q^41 - 24 * q^44 + 12 * q^45 + 48 * q^46 + 2 * q^49 + 16 * q^50 + 12 * q^51 - 36 * q^54 - 24 * q^55 - 28 * q^59 + 12 * q^60 - 20 * q^61 + 32 * q^64 - 4 * q^65 + 8 * q^70 + 28 * q^71 + 8 * q^74 + 24 * q^75 - 24 * q^76 + 2 * q^79 + 32 * q^80 - 18 * q^81 - 12 * q^84 + 4 * q^85 - 8 * q^86 + 48 * q^89 - 12 * q^90 + 8 * q^91 + 12 * q^94 - 24 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.73205	+	1.00000i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.73205	+	1.00000i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	0.133975	−	2.23205i	0.0599153	−	0.998203i
$5$	0.133975	−	2.23205i	0.0599153	−	0.998203i
$6$	3.00000	+	1.73205i	1.22474	+	0.707107i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		0			0
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	2.00000	+	4.00000i	0.632456	+	1.26491i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	−3.46410			−1.00000
$13$	1.73205	+	1.00000i	0.480384	+	0.277350i	0.720577	−	0.693375i	$-0.243877\pi$
$13$	1.73205	+	1.00000i	0.480384	+	0.277350i	−0.240192	+	0.970725i	$0.577210\pi$
$14$	−1.00000	+	1.73205i	−0.267261	+	0.462910i
$15$	−3.46410	+	1.73205i	−0.894427	+	0.447214i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		−	6.00000i		−	1.41421i
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$	−3.73205	−	2.46410i	−0.834512	−	0.550990i
$21$	−1.50000	−	0.866025i	−0.327327	−	0.188982i
$22$	5.19615	+	3.00000i	1.10782	+	0.639602i
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.151642	−	0.988436i	$-0.548456\pi$
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.931831	+	0.362892i	$0.881789\pi$
$24$		0			0
$25$	−4.96410	−	0.598076i	−0.992820	−	0.119615i
$26$	−4.00000			−0.784465
$27$	5.19615			1.00000
$28$		−	2.00000i		−	0.377964i
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	0.534928	−	0.844897i	$-0.320339\pi$
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	−0.999167	+	0.0408130i	$0.987005\pi$
$30$	4.26795	−	6.46410i	0.779217	−	1.18018i
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−6.92820	−	4.00000i	−1.22474	−	0.707107i
$33$	−2.59808	+	4.50000i	−0.452267	+	0.783349i
$34$	−2.00000	−	3.46410i	−0.342997	−	0.594089i
$35$	−1.00000	−	2.00000i	−0.169031	−	0.338062i
$36$	3.00000	+	5.19615i	0.500000	+	0.866025i
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	10.3923	−	6.00000i	1.68585	−	0.973329i
$39$		−	3.46410i		−	0.554700i
$40$		0			0
$41$	−4.00000	+	6.92820i	−0.624695	+	1.08200i	0.363905	+	0.931436i	$0.381443\pi$
$41$	−4.00000	+	6.92820i	−0.624695	+	1.08200i	−0.988600	+	0.150567i	$0.951890\pi$
$42$	3.46410			0.534522
$43$	1.73205	−	1.00000i	0.264135	−	0.152499i	−0.362084	−	0.932145i	$-0.617935\pi$
$43$	1.73205	−	1.00000i	0.264135	−	0.152499i	0.626219	+	0.779647i	$0.284601\pi$
$44$	−6.00000			−0.904534
$45$	5.59808	+	3.69615i	0.834512	+	0.550990i
$46$	12.0000			1.76930
$47$	−2.59808	+	1.50000i	−0.378968	+	0.218797i	−0.677369	−	0.735643i	$-0.736880\pi$
$47$	−2.59808	+	1.50000i	−0.378968	+	0.218797i	0.298401	+	0.954441i	$0.403547\pi$
$48$	3.46410	−	6.00000i	0.500000	−	0.866025i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	9.19615	−	3.92820i	1.30053	−	0.555532i
$51$	3.00000	−	1.73205i	0.420084	−	0.242536i
$52$	3.46410	−	2.00000i	0.480384	−	0.277350i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−9.00000	+	5.19615i	−1.22474	+	0.707107i
$55$	−6.00000	+	3.00000i	−0.809040	+	0.404520i
$56$		0			0
$57$	5.19615	+	9.00000i	0.688247	+	1.19208i
$58$	8.66025	+	5.00000i	1.13715	+	0.656532i
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.0991242	+	0.995075i	$0.531604\pi$
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.812198	+	0.583382i	$0.801729\pi$
$60$	−0.464102	+	7.73205i	−0.0599153	+	0.998203i
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$			8.00000i			1.01600i
$63$			3.00000i			0.377964i
$64$	8.00000			1.00000
$65$	2.46410	−	3.73205i	0.305634	−	0.462904i
$66$		−	10.3923i		−	1.27920i
$67$	−8.66025	−	5.00000i	−1.05802	−	0.610847i	−0.133135	−	0.991098i	$-0.542504\pi$
$67$	−8.66025	−	5.00000i	−1.05802	−	0.610847i	−0.924883	+	0.380251i	$0.875838\pi$
$68$	3.46410	+	2.00000i	0.420084	+	0.242536i
$69$			10.3923i			1.25109i
$70$	3.73205	+	2.46410i	0.446065	+	0.294516i
$71$	7.00000			0.830747			0.415374	−	0.909651i	$-0.363651\pi$
$71$	7.00000			0.830747			0.415374	+	0.909651i	$0.363651\pi$
$72$		0			0
$73$			9.00000i			1.05337i	0.850060	+	0.526685i	$0.176565\pi$
$73$			9.00000i			1.05337i	−0.850060	+	0.526685i	$0.823435\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	3.40192	+	7.96410i	0.392820	+	0.919615i
$76$	−6.00000	+	10.3923i	−0.688247	+	1.19208i
$77$	−2.59808	−	1.50000i	−0.296078	−	0.170941i
$78$	3.46410	+	6.00000i	0.392232	+	0.679366i
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	8.00000	−	4.00000i	0.894427	−	0.447214i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		−	16.0000i		−	1.76690i
$83$	14.7224	−	8.50000i	1.61600	−	0.932996i	0.628055	−	0.778169i	$-0.283851\pi$
$83$	14.7224	−	8.50000i	1.61600	−	0.932996i	0.987942	−	0.154828i	$-0.0494822\pi$
$84$	−3.00000	+	1.73205i	−0.327327	+	0.188982i
$85$	4.46410	+	0.267949i	0.484200	+	0.0290632i
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	−4.33013	+	7.50000i	−0.464238	+	0.804084i
$88$		0			0
$89$	12.0000			1.27200			0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000			1.27200			0.635999	+	0.771690i	$0.280588\pi$
$90$	−13.3923	−	0.803848i	−1.41167	−	0.0847330i
$91$	2.00000			0.209657
$92$	−10.3923	+	6.00000i	−1.08347	+	0.625543i
$93$	−6.92820			−0.718421
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$	−0.803848	+	13.3923i	−0.0824730	+	1.37402i
$96$			13.8564i			1.41421i
$97$	−6.06218	+	3.50000i	−0.615521	+	0.355371i	−0.775123	−	0.631810i	$-0.782312\pi$
$97$	−6.06218	+	3.50000i	−0.615521	+	0.355371i	0.159602	+	0.987181i	$0.448979\pi$
$98$			2.00000i			0.202031i
$99$	9.00000			0.904534
$100$	−6.00000	+	8.00000i	−0.600000	+	0.800000i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	−3.46410	+	6.00000i	−0.342997	+	0.594089i
$103$	−4.33013	−	2.50000i	−0.426660	−	0.246332i	0.271263	−	0.962505i	$-0.412559\pi$
$103$	−4.33013	−	2.50000i	−0.426660	−	0.246332i	−0.697923	+	0.716173i	$0.745892\pi$
$104$		0			0
$105$	−2.13397	+	3.23205i	−0.208255	+	0.315416i
$106$		0			0
$107$		−	16.0000i		−	1.54678i	−0.633932	−	0.773389i	$-0.718560\pi$
$107$		−	16.0000i		−	1.54678i	0.633932	−	0.773389i	$-0.281440\pi$
$108$	5.19615	−	9.00000i	0.500000	−	0.866025i
$109$	19.0000			1.81987			0.909935	−	0.414751i	$-0.136131\pi$
$109$	19.0000			1.81987			0.909935	+	0.414751i	$0.136131\pi$
$110$	7.39230	−	11.1962i	0.704829	−	1.06751i
$111$	−3.00000	+	1.73205i	−0.284747	+	0.164399i
$112$	3.46410	+	2.00000i	0.327327	+	0.188982i
$113$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$113$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$114$	−18.0000	−	10.3923i	−1.68585	−	0.973329i
$115$	−7.39230	+	11.1962i	−0.689336	+	1.04405i
$116$	−10.0000			−0.928477
$117$	−5.19615	+	3.00000i	−0.480384	+	0.277350i
$118$		−	28.0000i		−	2.57761i
$119$	1.00000	+	1.73205i	0.0916698	+	0.158777i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	17.3205	+	10.0000i	1.56813	+	0.905357i
$123$	13.8564			1.24939
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$	−3.00000	−	5.19615i	−0.267261	−	0.462910i
$127$		−	20.0000i		−	1.77471i	−0.461084	−	0.887357i	$-0.652539\pi$
$127$		−	20.0000i		−	1.77471i	0.461084	−	0.887357i	$-0.347461\pi$
$128$		0			0
$129$	−3.00000	−	1.73205i	−0.264135	−	0.152499i
$130$	−0.535898	+	8.92820i	−0.0470014	+	0.783055i
$131$	7.00000	−	12.1244i	0.611593	−	1.05931i	−0.379379	−	0.925241i	$-0.623862\pi$
$131$	7.00000	−	12.1244i	0.611593	−	1.05931i	0.990972	−	0.134069i	$-0.0428042\pi$
$132$	5.19615	+	9.00000i	0.452267	+	0.783349i
$133$	−5.19615	+	3.00000i	−0.450564	+	0.260133i
$134$	20.0000			1.72774
$135$	0.696152	−	11.5981i	0.0599153	−	0.998203i
$136$		0			0
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.985577	−	0.169226i	$-0.945873\pi$
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.346235	+	0.938148i	$0.612540\pi$
$138$	−10.3923	−	18.0000i	−0.884652	−	1.53226i
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	−0.0346338	−	0.999400i	$-0.511026\pi$
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	0.882823	−	0.469706i	$-0.155640\pi$
$140$	−4.46410	−	0.267949i	−0.377285	−	0.0226458i
$141$	4.50000	+	2.59808i	0.378968	+	0.218797i
$142$	−12.1244	+	7.00000i	−1.01745	+	0.587427i
$143$		−	6.00000i		−	0.501745i
$144$	−12.0000			−1.00000
$145$	−10.0000	+	5.00000i	−0.830455	+	0.415227i
$146$	−9.00000	−	15.5885i	−0.744845	−	1.29011i
$147$	−1.73205			−0.142857
$148$	−3.46410	−	2.00000i	−0.284747	−	0.164399i
$149$	−2.50000	+	4.33013i	−0.204808	+	0.354738i	−0.950072	−	0.312032i	$-0.898990\pi$
$149$	−2.50000	+	4.33013i	−0.204808	+	0.354738i	0.745264	+	0.666770i	$0.232324\pi$
$150$	−13.8564	−	10.3923i	−1.13137	−	0.848528i
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	−0.910195	−	0.414181i	$-0.864068\pi$
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	0.0964061	−	0.995342i	$-0.469265\pi$
$152$		0			0
$153$	−5.19615	−	3.00000i	−0.420084	−	0.242536i
$154$	6.00000			0.483494
$155$	−7.46410	−	4.92820i	−0.599531	−	0.395843i
$156$	−6.00000	−	3.46410i	−0.480384	−	0.277350i
$157$	7.79423	+	4.50000i	0.622047	+	0.359139i	0.777666	−	0.628678i	$-0.216404\pi$
$157$	7.79423	+	4.50000i	0.622047	+	0.359139i	−0.155618	+	0.987817i	$0.549737\pi$
$158$	−1.73205	−	1.00000i	−0.137795	−	0.0795557i
$159$		0			0
$160$	−9.85641	+	14.9282i	−0.779217	+	1.18018i
$161$	−6.00000			−0.472866
$162$	15.5885	+	9.00000i	1.22474	+	0.707107i
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	8.00000	+	13.8564i	0.624695	+	1.08200i
$165$	9.69615	+	6.40192i	0.754844	+	0.498389i
$166$	−17.0000	+	29.4449i	−1.31946	+	2.28536i
$167$	−10.3923	−	6.00000i	−0.804181	−	0.464294i	0.0407502	−	0.999169i	$-0.487025\pi$
$167$	−10.3923	−	6.00000i	−0.804181	−	0.464294i	−0.844931	+	0.534875i	$0.820359\pi$
$168$		0			0
$169$	−4.50000	−	7.79423i	−0.346154	−	0.599556i
$170$	−8.00000	+	4.00000i	−0.613572	+	0.306786i
$171$	9.00000	−	15.5885i	0.688247	−	1.19208i
$172$		−	4.00000i		−	0.304997i
$173$	12.9904	−	7.50000i	0.987640	−	0.570214i	0.0830722	−	0.996544i	$-0.473527\pi$
$173$	12.9904	−	7.50000i	0.987640	−	0.570214i	0.904568	+	0.426329i	$0.140193\pi$
$174$		−	17.3205i		−	1.31306i
$175$	−4.59808	+	1.96410i	−0.347582	+	0.148472i
$176$	6.00000	−	10.3923i	0.452267	−	0.783349i
$177$	24.2487			1.82264
$178$	−20.7846	+	12.0000i	−1.55787	+	0.899438i
$179$	11.0000			0.822179			0.411089	−	0.911595i	$-0.365148\pi$
$179$	11.0000			0.822179			0.411089	+	0.911595i	$0.365148\pi$
$180$	12.0000	−	6.00000i	0.894427	−	0.447214i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	−3.46410	+	2.00000i	−0.256776	+	0.148250i
$183$	−8.66025	+	15.0000i	−0.640184	+	1.10883i
$184$		0			0
$185$	−4.46410	−	0.267949i	−0.328207	−	0.0197000i
$186$	12.0000	−	6.92820i	0.879883	−	0.508001i
$187$	5.19615	−	3.00000i	0.379980	−	0.219382i
$188$			6.00000i			0.437595i
$189$	4.50000	−	2.59808i	0.327327	−	0.188982i
$190$	−12.0000	−	24.0000i	−0.870572	−	1.74114i
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$	−6.92820	−	12.0000i	−0.500000	−	0.866025i
$193$	12.1244	+	7.00000i	0.872730	+	0.503871i	0.868255	−	0.496119i	$-0.165242\pi$
$193$	12.1244	+	7.00000i	0.872730	+	0.503871i	0.00447566	+	0.999990i	$0.498575\pi$
$194$	7.00000	−	12.1244i	0.502571	−	0.870478i
$195$	−7.73205	−	0.464102i	−0.553704	−	0.0332350i
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$	−15.5885	+	9.00000i	−1.10782	+	0.639602i
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$		0			0
$201$			17.3205i			1.22169i
$202$		0			0
$203$	−4.33013	−	2.50000i	−0.303915	−	0.175466i
$204$		−	6.92820i		−	0.485071i
$205$	14.9282	+	9.85641i	1.04263	+	0.688401i
$206$	10.0000			0.696733
$207$	15.5885	−	9.00000i	1.08347	−	0.625543i
$208$			8.00000i			0.554700i
$209$	9.00000	+	15.5885i	0.622543	+	1.07828i
$210$	0.464102	−	7.73205i	0.0320261	−	0.533562i
$211$	−8.50000	+	14.7224i	−0.585164	+	1.01353i	0.409691	+	0.912224i	$0.365637\pi$
$211$	−8.50000	+	14.7224i	−0.585164	+	1.01353i	−0.994855	+	0.101310i	$0.967697\pi$
$212$		0			0
$213$	−6.06218	−	10.5000i	−0.415374	−	0.719448i
$214$	16.0000	+	27.7128i	1.09374	+	1.89441i
$215$	−2.00000	−	4.00000i	−0.136399	−	0.272798i
$216$		0			0
$217$		−	4.00000i		−	0.271538i
$218$	−32.9090	+	19.0000i	−2.22888	+	1.28684i
$219$	13.5000	−	7.79423i	0.912245	−	0.526685i
$220$	−0.803848	+	13.3923i	−0.0541954	+	0.902909i
$221$	−2.00000	+	3.46410i	−0.134535	+	0.233021i
$222$	3.46410	−	6.00000i	0.232495	−	0.402694i
$223$	20.7846	−	12.0000i	1.39184	−	0.803579i	0.398321	−	0.917246i	$-0.369593\pi$
$223$	20.7846	−	12.0000i	1.39184	−	0.803579i	0.993519	+	0.113666i	$0.0362595\pi$
$224$	−8.00000			−0.534522
$225$	9.00000	−	12.0000i	0.600000	−	0.800000i
$226$		0			0
$227$	−17.3205	+	10.0000i	−1.14960	+	0.663723i	−0.948790	−	0.315906i	$-0.897691\pi$
$227$	−17.3205	+	10.0000i	−1.14960	+	0.663723i	−0.200812	+	0.979630i	$0.564358\pi$
$228$	20.7846			1.37649
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$	1.60770	−	26.7846i	0.106008	−	1.76612i
$231$			5.19615i			0.341882i
$232$		0			0
$233$			16.0000i			1.04819i	0.851658	+	0.524097i	$0.175597\pi$
$233$			16.0000i			1.04819i	−0.851658	+	0.524097i	$0.824403\pi$
$234$	6.00000	−	10.3923i	0.392232	−	0.679366i
$235$	3.00000	+	6.00000i	0.195698	+	0.391397i
$236$	14.0000	+	24.2487i	0.911322	+	1.57846i
$237$	0.866025	−	1.50000i	0.0562544	−	0.0974355i
$238$	−3.46410	−	2.00000i	−0.224544	−	0.129641i
$239$	−4.50000	+	7.79423i	−0.291081	+	0.504167i	−0.974066	−	0.226266i	$-0.927348\pi$
$239$	−4.50000	+	7.79423i	−0.291081	+	0.504167i	0.682985	+	0.730433i	$0.260682\pi$
$240$	−12.9282	−	8.53590i	−0.834512	−	0.550990i
$241$	−2.00000	−	3.46410i	−0.128831	−	0.223142i	0.794393	−	0.607404i	$-0.207789\pi$
$241$	−2.00000	−	3.46410i	−0.128831	−	0.223142i	−0.923224	+	0.384262i	$0.874456\pi$
$242$			4.00000i			0.257130i
$243$	−7.79423	+	13.5000i	−0.500000	+	0.866025i
$244$	−20.0000			−1.28037
$245$	−1.86603	−	1.23205i	−0.119216	−	0.0787128i
$246$	−24.0000	+	13.8564i	−1.53018	+	0.883452i
$247$	−10.3923	−	6.00000i	−0.661247	−	0.381771i
$248$		0			0
$249$	−25.5000	−	14.7224i	−1.61600	−	0.932996i
$250$	−7.53590	−	21.0526i	−0.476612	−	1.33148i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$	5.19615	+	3.00000i	0.327327	+	0.188982i
$253$			18.0000i			1.13165i
$254$	20.0000	+	34.6410i	1.25491	+	2.17357i
$255$	−3.46410	−	6.92820i	−0.216930	−	0.433861i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	6.06218	+	3.50000i	0.378148	+	0.218324i	0.677012	−	0.735972i	$-0.263274\pi$
$257$	6.06218	+	3.50000i	0.378148	+	0.218324i	−0.298864	+	0.954296i	$0.596608\pi$
$258$	6.92820			0.431331
$259$	−1.00000	−	1.73205i	−0.0621370	−	0.107624i
$260$	−4.00000	−	8.00000i	−0.248069	−	0.496139i
$261$	15.0000			0.928477
$262$			28.0000i			1.72985i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$		0			0
$265$		0			0
$266$	6.00000	−	10.3923i	0.367884	−	0.637193i
$267$	−10.3923	−	18.0000i	−0.635999	−	1.10158i
$268$	−17.3205	+	10.0000i	−1.05802	+	0.610847i
$269$	−16.0000			−0.975537			−0.487769	−	0.872973i	$-0.662189\pi$
$269$	−16.0000			−0.975537			−0.487769	+	0.872973i	$0.662189\pi$
$270$	10.3923	+	20.7846i	0.632456	+	1.26491i
$271$	−14.0000			−0.850439			−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000			−0.850439			−0.425220	+	0.905090i	$0.639803\pi$
$272$	−6.92820	+	4.00000i	−0.420084	+	0.242536i
$273$	−1.73205	−	3.00000i	−0.104828	−	0.181568i
$274$	18.0000	−	31.1769i	1.08742	−	1.88347i
$275$	5.89230	+	13.7942i	0.355319	+	0.831823i
$276$	18.0000	+	10.3923i	1.08347	+	0.625543i
$277$	24.2487	−	14.0000i	1.45696	−	0.841178i	0.458103	−	0.888899i	$-0.348529\pi$
$277$	24.2487	−	14.0000i	1.45696	−	0.841178i	0.998861	+	0.0477206i	$0.0151957\pi$
$278$			40.0000i			2.39904i
$279$	6.00000	+	10.3923i	0.359211	+	0.622171i
$280$		0			0
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	0.742542	−	0.669800i	$-0.233620\pi$
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	−0.951334	+	0.308160i	$0.900287\pi$
$282$	−10.3923			−0.618853
$283$	6.06218	+	3.50000i	0.360359	+	0.208053i	0.669238	−	0.743048i	$-0.266621\pi$
$283$	6.06218	+	3.50000i	0.360359	+	0.208053i	−0.308879	+	0.951101i	$0.599954\pi$
$284$	7.00000	−	12.1244i	0.415374	−	0.719448i
$285$	20.7846	−	10.3923i	1.23117	−	0.615587i
$286$	6.00000	+	10.3923i	0.354787	+	0.614510i
$287$			8.00000i			0.472225i
$288$	20.7846	−	12.0000i	1.22474	−	0.707107i
$289$	13.0000			0.764706
$290$	12.3205	−	18.6603i	0.723485	−	1.09577i
$291$	10.5000	+	6.06218i	0.615521	+	0.355371i
$292$	15.5885	+	9.00000i	0.912245	+	0.526685i
$293$	−23.3827	−	13.5000i	−1.36603	−	0.788678i	−0.375613	−	0.926777i	$-0.622568\pi$
$293$	−23.3827	−	13.5000i	−1.36603	−	0.788678i	−0.990419	+	0.138098i	$0.955901\pi$
$294$	3.00000	−	1.73205i	0.174964	−	0.101015i
$295$	26.1244	+	17.2487i	1.52102	+	1.00426i
$296$		0			0
$297$	−7.79423	−	13.5000i	−0.452267	−	0.783349i
$298$		−	10.0000i		−	0.579284i
$299$	−6.00000	−	10.3923i	−0.346989	−	0.601003i
$300$	17.1962	+	2.07180i	0.992820	+	0.119615i
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$	34.6410	+	20.0000i	1.99337	+	1.15087i
$303$		0			0
$304$	−12.0000	−	20.7846i	−0.688247	−	1.19208i
$305$	−20.0000	+	10.0000i	−1.14520	+	0.572598i
$306$	12.0000			0.685994
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$	−5.19615	+	3.00000i	−0.296078	+	0.170941i
$309$			8.66025i			0.492665i
$310$	17.8564	+	1.07180i	1.01418	+	0.0608740i
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	7.79423	−	4.50000i	0.440556	−	0.254355i	−0.263278	−	0.964720i	$-0.584803\pi$
$313$	7.79423	−	4.50000i	0.440556	−	0.254355i	0.703833	+	0.710365i	$0.251470\pi$
$314$	−18.0000			−1.01580
$315$	6.69615	+	0.401924i	0.377285	+	0.0226458i
$316$	2.00000			0.112509
$317$	25.9808	−	15.0000i	1.45922	−	0.842484i	0.460252	−	0.887788i	$-0.347759\pi$
$317$	25.9808	−	15.0000i	1.45922	−	0.842484i	0.998973	+	0.0453045i	$0.0144258\pi$
$318$		0			0
$319$	−7.50000	+	12.9904i	−0.419919	+	0.727322i
$320$	1.07180	−	17.8564i	0.0599153	−	0.998203i
$321$	−24.0000	+	13.8564i	−1.33955	+	0.773389i
$322$	10.3923	−	6.00000i	0.579141	−	0.334367i
$323$		−	12.0000i		−	0.667698i
$324$	−18.0000			−1.00000
$325$	−8.00000	−	6.00000i	−0.443760	−	0.332820i
$326$	−4.00000	−	6.92820i	−0.221540	−	0.383718i
$327$	−16.4545	−	28.5000i	−0.909935	−	1.57605i
$328$		0			0
$329$	−1.50000	+	2.59808i	−0.0826977	+	0.143237i
$330$	−23.1962	−	1.39230i	−1.27691	−	0.0766439i
$331$	−13.5000	−	23.3827i	−0.742027	−	1.28523i	−0.951571	−	0.307429i	$-0.900531\pi$
$331$	−13.5000	−	23.3827i	−0.742027	−	1.28523i	0.209544	−	0.977799i	$-0.432802\pi$
$332$		−	34.0000i		−	1.86599i
$333$	5.19615	+	3.00000i	0.284747	+	0.164399i
$334$	24.0000			1.31322
$335$	−12.3205	+	18.6603i	−0.673141	+	1.01952i
$336$		−	6.92820i		−	0.377964i
$337$	−15.5885	−	9.00000i	−0.849157	−	0.490261i	0.0112091	−	0.999937i	$-0.496432\pi$
$337$	−15.5885	−	9.00000i	−0.849157	−	0.490261i	−0.860366	+	0.509676i	$0.829765\pi$
$338$	15.5885	+	9.00000i	0.847900	+	0.489535i
$339$		0			0
$340$	4.92820	−	7.46410i	0.267269	−	0.404798i
$341$	−12.0000			−0.649836
$342$			36.0000i			1.94666i
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	23.1962	+	1.39230i	1.24884	+	0.0749592i
$346$	−15.0000	+	25.9808i	−0.806405	+	1.39673i
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$	8.66025	+	15.0000i	0.464238	+	0.804084i
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$	6.00000	−	8.00000i	0.320713	−	0.427618i
$351$	9.00000	+	5.19615i	0.480384	+	0.277350i
$352$			24.0000i			1.27920i
$353$	9.52628	−	5.50000i	0.507033	−	0.292735i	−0.224580	−	0.974456i	$-0.572101\pi$
$353$	9.52628	−	5.50000i	0.507033	−	0.292735i	0.731613	+	0.681720i	$0.238768\pi$
$354$	−42.0000	+	24.2487i	−2.23227	+	1.28880i
$355$	0.937822	−	15.6244i	0.0497744	−	0.829255i
$356$	12.0000	−	20.7846i	0.635999	−	1.10158i
$357$	1.73205	−	3.00000i	0.0916698	−	0.158777i
$358$	−19.0526	+	11.0000i	−1.00696	+	0.581368i
$359$	−4.00000			−0.211112			−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000			−0.211112			−0.105556	+	0.994413i	$0.533662\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$		0			0
$363$	−3.46410			−0.181818
$364$	2.00000	−	3.46410i	0.104828	−	0.181568i
$365$	20.0885	+	1.20577i	1.05148	+	0.0631130i
$366$		−	34.6410i		−	1.81071i
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$		−	24.0000i		−	1.25109i
$369$	−12.0000	−	20.7846i	−0.624695	−	1.08200i
$370$	8.00000	−	4.00000i	0.415900	−	0.207950i
$371$		0			0
$372$	−6.92820	+	12.0000i	−0.359211	+	0.622171i
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$	−6.00000	+	10.3923i	−0.310253	+	0.537373i
$375$	18.2321	−	6.52628i	0.941499	−	0.337016i
$376$		0			0
$377$		−	10.0000i		−	0.515026i
$378$	−5.19615	+	9.00000i	−0.267261	+	0.462910i
$379$	−23.0000			−1.18143			−0.590715	−	0.806880i	$-0.701154\pi$
$379$	−23.0000			−1.18143			−0.590715	+	0.806880i	$0.701154\pi$
$380$	22.3923	+	14.7846i	1.14870	+	0.758434i
$381$	−30.0000	+	17.3205i	−1.53695	+	0.887357i
$382$	−5.19615	−	3.00000i	−0.265858	−	0.153493i
$383$	4.33013	+	2.50000i	0.221259	+	0.127744i	0.606533	−	0.795058i	$-0.292560\pi$
$383$	4.33013	+	2.50000i	0.221259	+	0.127744i	−0.385274	+	0.922802i	$0.625893\pi$
$384$		0			0
$385$	−3.69615	+	5.59808i	−0.188373	+	0.285304i
$386$	−28.0000			−1.42516
$387$			6.00000i			0.304997i
$388$			14.0000i			0.710742i
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	0.518110	−	0.855314i	$-0.326636\pi$
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	−0.999779	+	0.0210389i	$0.993303\pi$
$390$	13.8564	−	6.92820i	0.701646	−	0.350823i
$391$	6.00000	−	10.3923i	0.303433	−	0.525561i
$392$		0			0
$393$	−24.2487			−1.22319
$394$	8.00000	+	13.8564i	0.403034	+	0.698076i
$395$	2.00000	−	1.00000i	0.100631	−	0.0503155i
$396$	9.00000	−	15.5885i	0.452267	−	0.783349i
$397$			17.0000i			0.853206i	0.904439	+	0.426603i	$0.140290\pi$
$397$			17.0000i			0.853206i	−0.904439	+	0.426603i	$0.859710\pi$
$398$	13.8564	−	8.00000i	0.694559	−	0.401004i
$399$	9.00000	+	5.19615i	0.450564	+	0.260133i
$400$	−7.85641	−	18.3923i	−0.392820	−	0.919615i
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$	−17.3205	−	30.0000i	−0.863868	−	1.49626i
$403$	6.92820	−	4.00000i	0.345118	−	0.199254i
$404$		0			0
$405$	−18.0000	+	9.00000i	−0.894427	+	0.447214i
$406$	10.0000			0.496292
$407$	−5.19615	+	3.00000i	−0.257564	+	0.148704i
$408$		0			0
$409$	4.00000	−	6.92820i	0.197787	−	0.342578i	−0.750023	−	0.661411i	$-0.769958\pi$
$409$	4.00000	−	6.92820i	0.197787	−	0.342578i	0.947811	+	0.318834i	$0.103291\pi$
$410$	−35.7128	−	2.14359i	−1.76373	−	0.105865i
$411$	27.0000	+	15.5885i	1.33181	+	0.768922i
$412$	−8.66025	+	5.00000i	−0.426660	+	0.246332i
$413$			14.0000i			0.688895i
$414$	−18.0000	+	31.1769i	−0.884652	+	1.53226i
$415$	−17.0000	−	34.0000i	−0.834497	−	1.66899i
$416$	−8.00000	−	13.8564i	−0.392232	−	0.679366i
$417$	−34.6410			−1.69638
$418$	−31.1769	−	18.0000i	−1.52491	−	0.880409i
$419$	−15.0000	+	25.9808i	−0.732798	+	1.26924i	0.222885	+	0.974845i	$0.428453\pi$
$419$	−15.0000	+	25.9808i	−0.732798	+	1.26924i	−0.955683	+	0.294398i	$0.904881\pi$
$420$	3.46410	+	6.92820i	0.169031	+	0.338062i
$421$	7.50000	+	12.9904i	0.365528	+	0.633112i	0.988861	−	0.148844i	$-0.0475552\pi$
$421$	7.50000	+	12.9904i	0.365528	+	0.633112i	−0.623333	+	0.781956i	$0.714222\pi$
$422$		−	34.0000i		−	1.65509i
$423$		−	9.00000i		−	0.437595i
$424$		0			0
$425$	1.19615	−	9.92820i	0.0580219	−	0.481589i
$426$	21.0000	+	12.1244i	1.01745	+	0.587427i
$427$	−8.66025	−	5.00000i	−0.419099	−	0.241967i
$428$	−27.7128	−	16.0000i	−1.33955	−	0.773389i
$429$	−9.00000	+	5.19615i	−0.434524	+	0.250873i
$430$	7.46410	+	4.92820i	0.359951	+	0.237659i
$431$	16.0000			0.770693			0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000			0.770693			0.385346	+	0.922772i	$0.374082\pi$
$432$	10.3923	+	18.0000i	0.500000	+	0.866025i
$433$			2.00000i			0.0961139i	0.998845	+	0.0480569i	$0.0153029\pi$
$433$			2.00000i			0.0961139i	−0.998845	+	0.0480569i	$0.984697\pi$
$434$	4.00000	+	6.92820i	0.192006	+	0.332564i
$435$	16.1603	+	10.6699i	0.774825	+	0.511581i
$436$	19.0000	−	32.9090i	0.909935	−	1.57605i
$437$	31.1769	+	18.0000i	1.49139	+	0.861057i
$438$	−15.5885	+	27.0000i	−0.744845	+	1.29011i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$		−	8.00000i		−	0.380521i
$443$	−3.46410	+	2.00000i	−0.164584	+	0.0950229i	−0.580030	−	0.814595i	$-0.696959\pi$
$443$	−3.46410	+	2.00000i	−0.164584	+	0.0950229i	0.415445	+	0.909618i	$0.363626\pi$
$444$			6.92820i			0.328798i
$445$	1.60770	−	26.7846i	0.0762121	−	1.26971i
$446$	−24.0000	+	41.5692i	−1.13643	+	1.96836i
$447$	8.66025			0.409616
$448$	6.92820	−	4.00000i	0.327327	−	0.188982i
$449$	−31.0000			−1.46298			−0.731490	−	0.681852i	$-0.761175\pi$
$449$	−31.0000			−1.46298			−0.731490	+	0.681852i	$0.761175\pi$
$450$	−3.58846	+	29.7846i	−0.169161	+	1.40406i
$451$	24.0000			1.13012
$452$		0			0
$453$	−17.3205	+	30.0000i	−0.813788	+	1.40952i
$454$	20.0000	−	34.6410i	0.938647	−	1.62578i
$455$	0.267949	−	4.46410i	0.0125617	−	0.209280i
$456$		0			0
$457$	−24.2487	+	14.0000i	−1.13431	+	0.654892i	−0.945015	−	0.327028i	$-0.893953\pi$
$457$	−24.2487	+	14.0000i	−1.13431	+	0.654892i	−0.189292	+	0.981921i	$0.560619\pi$
$458$		−	20.0000i		−	0.934539i
$459$			10.3923i			0.485071i
$460$	12.0000	+	24.0000i	0.559503	+	1.11901i
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	0.971248	−	0.238071i	$-0.0765153\pi$
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	−0.691800	+	0.722089i	$0.743182\pi$
$462$	−5.19615	−	9.00000i	−0.241747	−	0.418718i
$463$	5.19615	+	3.00000i	0.241486	+	0.139422i	0.615859	−	0.787856i	$-0.288809\pi$
$463$	5.19615	+	3.00000i	0.241486	+	0.139422i	−0.374374	+	0.927278i	$0.622142\pi$
$464$	10.0000	−	17.3205i	0.464238	−	0.804084i
$465$	−0.928203	+	15.4641i	−0.0430444	+	0.717131i
$466$	−16.0000	−	27.7128i	−0.741186	−	1.28377i
$467$			3.00000i			0.138823i	0.997588	+	0.0694117i	$0.0221122\pi$
$467$			3.00000i			0.138823i	−0.997588	+	0.0694117i	$0.977888\pi$
$468$			12.0000i			0.554700i
$469$	−10.0000			−0.461757
$470$	−11.1962	−	7.39230i	−0.516440	−	0.340982i
$471$		−	15.5885i		−	0.718278i
$472$		0			0
$473$	−5.19615	−	3.00000i	−0.238919	−	0.137940i
$474$			3.46410i			0.159111i
$475$	29.7846	+	3.58846i	1.36661	+	0.164650i
$476$	4.00000			0.183340
$477$		0			0
$478$		−	18.0000i		−	0.823301i
$479$	18.0000	+	31.1769i	0.822441	+	1.42451i	0.903859	+	0.427830i	$0.140722\pi$
$479$	18.0000	+	31.1769i	0.822441	+	1.42451i	−0.0814184	+	0.996680i	$0.525945\pi$
$480$	30.9282	+	1.85641i	1.41167	+	0.0847330i
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$	6.92820	+	4.00000i	0.315571	+	0.182195i
$483$	5.19615	+	9.00000i	0.236433	+	0.409514i
$484$	−2.00000	−	3.46410i	−0.0909091	−	0.157459i
$485$	7.00000	+	14.0000i	0.317854	+	0.635707i
$486$		−	31.1769i		−	1.41421i
$487$			12.0000i			0.543772i	0.962329	+	0.271886i	$0.0876473\pi$
$487$			12.0000i			0.543772i	−0.962329	+	0.271886i	$0.912353\pi$
$488$		0			0
$489$	6.00000	−	3.46410i	0.271329	−	0.156652i
$490$	4.46410	+	0.267949i	0.201668	+	0.0121047i
$491$	−14.0000	+	24.2487i	−0.631811	+	1.09433i	0.355370	+	0.934726i	$0.384355\pi$
$491$	−14.0000	+	24.2487i	−0.631811	+	1.09433i	−0.987181	+	0.159603i	$0.948978\pi$
$492$	13.8564	−	24.0000i	0.624695	−	1.08200i
$493$	8.66025	−	5.00000i	0.390038	−	0.225189i
$494$	24.0000			1.07981
$495$	1.20577	−	20.0885i	0.0541954	−	0.902909i
$496$	16.0000			0.718421
$497$	6.06218	−	3.50000i	0.271926	−	0.156996i
$498$	58.8897			2.63891
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	17.0526	+	14.4641i	0.762614	+	0.646854i
$501$			20.7846i			0.928588i
$502$	−31.1769	+	18.0000i	−1.39149	+	0.803379i
$503$			27.0000i			1.20387i	0.798545	+	0.601935i	$0.205603\pi$
$503$			27.0000i			1.20387i	−0.798545	+	0.601935i	$0.794397\pi$
$504$		0			0
$505$		0			0
$506$	−18.0000	−	31.1769i	−0.800198	−	1.38598i
$507$	−7.79423	+	13.5000i	−0.346154	+	0.599556i
$508$	−34.6410	−	20.0000i	−1.53695	−	0.887357i
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$	12.9282	+	8.53590i	0.572470	+	0.377976i
$511$	4.50000	+	7.79423i	0.199068	+	0.344796i
$512$		−	32.0000i		−	1.41421i
$513$	−31.1769			−1.37649
$514$	−14.0000			−0.617514
$515$	−6.16025	+	9.33013i	−0.271453	+	0.411135i
$516$	−6.00000	+	3.46410i	−0.264135	+	0.152499i
$517$	7.79423	+	4.50000i	0.342790	+	0.197910i
$518$	3.46410	+	2.00000i	0.152204	+	0.0878750i
$519$	−22.5000	−	12.9904i	−0.987640	−	0.570214i
$520$		0			0
$521$	2.00000			0.0876216			0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000			0.0876216			0.0438108	+	0.999040i	$0.486050\pi$
$522$	−25.9808	+	15.0000i	−1.13715	+	0.656532i
$523$			23.0000i			1.00572i	0.864368	+	0.502860i	$0.167719\pi$
$523$			23.0000i			1.00572i	−0.864368	+	0.502860i	$0.832281\pi$
$524$	−14.0000	−	24.2487i	−0.611593	−	1.05931i
$525$	6.92820	+	5.19615i	0.302372	+	0.226779i
$526$		0			0
$527$	6.92820	+	4.00000i	0.301797	+	0.174243i
$528$	−20.7846			−0.904534
$529$	6.50000	+	11.2583i	0.282609	+	0.489493i
$530$		0			0
$531$	−21.0000	−	36.3731i	−0.911322	−	1.57846i
$532$			12.0000i			0.520266i
$533$	−13.8564	+	8.00000i	−0.600188	+	0.346518i
$534$	36.0000	+	20.7846i	1.55787	+	0.899438i
$535$	−35.7128	−	2.14359i	−1.54400	−	0.0926756i
$536$		0			0
$537$	−9.52628	−	16.5000i	−0.411089	−	0.712028i
$538$	27.7128	−	16.0000i	1.19478	−	0.689809i
$539$	−3.00000			−0.129219
$540$	−19.3923	−	12.8038i	−0.834512	−	0.550990i
$541$	−30.0000			−1.28980			−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000			−1.28980			−0.644900	+	0.764267i	$0.723101\pi$
$542$	24.2487	−	14.0000i	1.04157	−	0.601351i
$543$		0			0
$544$	8.00000	−	13.8564i	0.342997	−	0.594089i
$545$	2.54552	−	42.4090i	0.109038	−	1.81660i
$546$	6.00000	+	3.46410i	0.256776	+	0.148250i
$547$	19.0526	−	11.0000i	0.814629	−	0.470326i	−0.0339321	−	0.999424i	$-0.510803\pi$
$547$	19.0526	−	11.0000i	0.814629	−	0.470326i	0.848561	+	0.529098i	$0.177470\pi$
$548$			36.0000i			1.53784i
$549$	30.0000			1.28037
$550$	−24.0000	−	18.0000i	−1.02336	−	0.767523i
$551$	15.0000	+	25.9808i	0.639021	+	1.10682i
$552$		0			0
$553$	0.866025	+	0.500000i	0.0368271	+	0.0212622i
$554$	−28.0000	+	48.4974i	−1.18961	+	2.06046i
$555$	3.46410	+	6.92820i	0.147043	+	0.294086i
$556$	−20.0000	−	34.6410i	−0.848189	−	1.46911i
$557$		−	2.00000i		−	0.0847427i	−0.999102	−	0.0423714i	$-0.986509\pi$
$557$		−	2.00000i		−	0.0847427i	0.999102	−	0.0423714i	$-0.0134913\pi$
$558$	−20.7846	−	12.0000i	−0.879883	−	0.508001i
$559$	4.00000			0.169182
$560$	4.92820	−	7.46410i	0.208255	−	0.315416i
$561$	−9.00000	−	5.19615i	−0.379980	−	0.219382i
$562$	12.1244	+	7.00000i	0.511435	+	0.295277i
$563$	−7.79423	−	4.50000i	−0.328488	−	0.189652i	0.326682	−	0.945134i	$-0.394069\pi$
$563$	−7.79423	−	4.50000i	−0.328488	−	0.189652i	−0.655169	+	0.755482i	$0.727403\pi$
$564$	9.00000	−	5.19615i	0.378968	−	0.218797i
$565$		0			0
$566$	−14.0000			−0.588464
$567$	−7.79423	−	4.50000i	−0.327327	−	0.188982i
$568$		0			0
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	−0.907532	−	0.419984i	$-0.862036\pi$
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	0.0900490	−	0.995937i	$-0.471298\pi$
$570$	−25.6077	+	38.7846i	−1.07259	+	1.62451i
$571$	22.5000	−	38.9711i	0.941596	−	1.63089i	0.179168	−	0.983819i	$-0.442660\pi$
$571$	22.5000	−	38.9711i	0.941596	−	1.63089i	0.762428	−	0.647073i	$-0.224007\pi$
$572$	−10.3923	−	6.00000i	−0.434524	−	0.250873i
$573$	2.59808	−	4.50000i	0.108536	−	0.187990i
$574$	−8.00000	−	13.8564i	−0.333914	−	0.578355i
$575$	24.0000	+	18.0000i	1.00087	+	0.750652i
$576$	−12.0000	+	20.7846i	−0.500000	+	0.866025i
$577$			7.00000i			0.291414i	0.989328	+	0.145707i	$0.0465456\pi$
$577$			7.00000i			0.291414i	−0.989328	+	0.145707i	$0.953454\pi$
$578$	−22.5167	+	13.0000i	−0.936570	+	0.540729i
$579$		−	24.2487i		−	1.00774i
$580$	−1.33975	+	22.3205i	−0.0556299	+	0.926809i
$581$	8.50000	−	14.7224i	0.352639	−	0.610789i
$582$	−24.2487			−1.00514
$583$		0			0
$584$		0			0
$585$	6.00000	+	12.0000i	0.248069	+	0.496139i
$586$	54.0000			2.23072
$587$	20.7846	−	12.0000i	0.857873	−	0.495293i	−0.00542667	−	0.999985i	$-0.501727\pi$
$587$	20.7846	−	12.0000i	0.857873	−	0.495293i	0.863299	+	0.504692i	$0.168394\pi$
$588$	−1.73205	+	3.00000i	−0.0714286	+	0.123718i
$589$	−12.0000	+	20.7846i	−0.494451	+	0.856415i
$590$	−62.4974	−	3.75129i	−2.57298	−	0.154438i
$591$	−12.0000	+	6.92820i	−0.493614	+	0.284988i
$592$	6.92820	−	4.00000i	0.284747	−	0.164399i
$593$		−	43.0000i		−	1.76580i	−0.469563	−	0.882899i	$-0.655588\pi$
$593$		−	43.0000i		−	1.76580i	0.469563	−	0.882899i	$-0.344412\pi$
$594$	27.0000	+	15.5885i	1.10782	+	0.639602i
$595$	4.00000	−	2.00000i	0.163984	−	0.0819920i
$596$	5.00000	+	8.66025i	0.204808	+	0.354738i
$597$	6.92820	+	12.0000i	0.283552	+	0.491127i
$598$	20.7846	+	12.0000i	0.849946	+	0.490716i
$599$	20.0000	−	34.6410i	0.817178	−	1.41539i	−0.0905757	−	0.995890i	$-0.528871\pi$
$599$	20.0000	−	34.6410i	0.817178	−	1.41539i	0.907754	−	0.419504i	$-0.137796\pi$
$600$		0			0
$601$	4.00000	+	6.92820i	0.163163	+	0.282607i	0.936002	−	0.351996i	$-0.114497\pi$
$601$	4.00000	+	6.92820i	0.163163	+	0.282607i	−0.772838	+	0.634603i	$0.781164\pi$
$602$			4.00000i			0.163028i
$603$	25.9808	−	15.0000i	1.05802	−	0.610847i
$604$	−40.0000			−1.62758
$605$	−3.73205	−	2.46410i	−0.151729	−	0.100180i
$606$		0			0
$607$	33.7750	+	19.5000i	1.37088	+	0.791481i	0.991039	−	0.133570i	$-0.0426439\pi$
$607$	33.7750	+	19.5000i	1.37088	+	0.791481i	0.379845	+	0.925050i	$0.375977\pi$
$608$	41.5692	+	24.0000i	1.68585	+	0.973329i
$609$			8.66025i			0.350931i
$610$	24.6410	−	37.3205i	0.997686	−	1.51106i
$611$	−6.00000			−0.242734
$612$	−10.3923	+	6.00000i	−0.420084	+	0.242536i
$613$		−	8.00000i		−	0.323117i	−0.986863	−	0.161558i	$-0.948348\pi$
$613$		−	8.00000i		−	0.323117i	0.986863	−	0.161558i	$-0.0516520\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$	1.85641	−	30.9282i	0.0748575	−	1.24715i
$616$		0			0
$617$	−6.92820	−	4.00000i	−0.278919	−	0.161034i	0.354015	−	0.935240i	$-0.384816\pi$
$617$	−6.92820	−	4.00000i	−0.278919	−	0.161034i	−0.632934	+	0.774206i	$0.718150\pi$
$618$	−8.66025	−	15.0000i	−0.348367	−	0.603388i
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$	−16.0000	+	8.00000i	−0.642575	+	0.321288i
$621$	−27.0000	−	15.5885i	−1.08347	−	0.625543i
$622$			12.0000i			0.481156i
$623$	10.3923	−	6.00000i	0.416359	−	0.240385i
$624$	12.0000	−	6.92820i	0.480384	−	0.277350i
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	−9.00000	+	15.5885i	−0.359712	+	0.623040i
$627$	15.5885	−	27.0000i	0.622543	−	1.07828i
$628$	15.5885	−	9.00000i	0.622047	−	0.359139i
$629$	4.00000			0.159490
$630$	−12.0000	+	6.00000i	−0.478091	+	0.239046i
$631$	−5.00000			−0.199047			−0.0995234	−	0.995035i	$-0.531732\pi$
$631$	−5.00000			−0.199047			−0.0995234	+	0.995035i	$0.531732\pi$
$632$		0			0
$633$	29.4449			1.17033
$634$	−30.0000	+	51.9615i	−1.19145	+	2.06366i
$635$	−44.6410	−	2.67949i	−1.77152	−	0.106332i
$636$		0			0
$637$	1.73205	−	1.00000i	0.0686264	−	0.0396214i
$638$		−	30.0000i		−	1.18771i
$639$	−10.5000	+	18.1865i	−0.415374	+	0.719448i
$640$		0			0
$641$	−17.0000	−	29.4449i	−0.671460	−	1.16300i	−0.977490	−	0.210981i	$-0.932334\pi$
$641$	−17.0000	−	29.4449i	−0.671460	−	1.16300i	0.306031	−	0.952022i	$-0.400999\pi$
$642$	27.7128	−	48.0000i	1.09374	−	1.89441i
$643$	4.33013	+	2.50000i	0.170764	+	0.0985904i	0.582946	−	0.812511i	$-0.301900\pi$
$643$	4.33013	+	2.50000i	0.170764	+	0.0985904i	−0.412182	+	0.911101i	$0.635233\pi$
$644$	−6.00000	+	10.3923i	−0.236433	+	0.409514i
$645$	−4.26795	+	6.46410i	−0.168050	+	0.254524i
$646$	12.0000	+	20.7846i	0.472134	+	0.817760i
$647$			32.0000i			1.25805i	0.777385	+	0.629025i	$0.216546\pi$
$647$			32.0000i			1.25805i	−0.777385	+	0.629025i	$0.783454\pi$
$648$		0			0
$649$	42.0000			1.64864
$650$	19.8564	+	2.39230i	0.778832	+	0.0938339i
$651$	−6.00000	+	3.46410i	−0.235159	+	0.135769i
$652$	6.92820	+	4.00000i	0.271329	+	0.156652i
$653$	8.66025	+	5.00000i	0.338902	+	0.195665i	0.659786	−	0.751453i	$-0.270647\pi$
$653$	8.66025	+	5.00000i	0.338902	+	0.195665i	−0.320884	+	0.947118i	$0.603980\pi$
$654$	57.0000	+	32.9090i	2.22888	+	1.28684i
$655$	−26.1244	−	17.2487i	−1.02076	−	0.673963i
$656$	−32.0000			−1.24939
$657$	−23.3827	−	13.5000i	−0.912245	−	0.526685i
$658$		−	6.00000i		−	0.233904i
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$	20.7846	−	10.3923i	0.809040	−	0.404520i
$661$	−12.0000	+	20.7846i	−0.466746	+	0.808428i	−0.999278	−	0.0379819i	$-0.987907\pi$
$661$	−12.0000	+	20.7846i	−0.466746	+	0.808428i	0.532533	+	0.846410i	$0.321240\pi$
$662$	46.7654	+	27.0000i	1.81759	+	1.04938i
$663$	6.92820			0.269069
$664$		0			0
$665$	6.00000	+	12.0000i	0.232670	+	0.465340i
$666$	−12.0000			−0.464991
$667$			30.0000i			1.16160i
$668$	−20.7846	+	12.0000i	−0.804181	+	0.464294i
$669$	−36.0000	−	20.7846i	−1.39184	−	0.803579i
$670$	2.67949	−	44.6410i	0.103518	−	1.72463i
$671$	−15.0000	+	25.9808i	−0.579069	+	1.00298i
$672$	6.92820	+	12.0000i	0.267261	+	0.462910i
$673$	−10.3923	+	6.00000i	−0.400594	+	0.231283i	−0.686740	−	0.726903i	$-0.740959\pi$
$673$	−10.3923	+	6.00000i	−0.400594	+	0.231283i	0.286146	+	0.958186i	$0.407626\pi$
$674$	36.0000			1.38667
$675$	−25.7942	−	3.10770i	−0.992820	−	0.119615i
$676$	−18.0000			−0.692308
$677$	19.0526	−	11.0000i	0.732249	−	0.422764i	−0.0869952	−	0.996209i	$-0.527726\pi$
$677$	19.0526	−	11.0000i	0.732249	−	0.422764i	0.819244	+	0.573444i	$0.194393\pi$
$678$		0			0
$679$	−3.50000	+	6.06218i	−0.134318	+	0.232645i
$680$		0			0
$681$	30.0000	+	17.3205i	1.14960	+	0.663723i
$682$	20.7846	−	12.0000i	0.795884	−	0.459504i
$683$			4.00000i			0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$			4.00000i			0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$	−18.0000	−	31.1769i	−0.688247	−	1.19208i
$685$	18.0000	+	36.0000i	0.687745	+	1.37549i
$686$	1.00000	+	1.73205i	0.0381802	+	0.0661300i
$687$	17.3205			0.660819
$688$	6.92820	+	4.00000i	0.264135	+	0.152499i
$689$		0			0
$690$	−41.5692	+	20.7846i	−1.58251	+	0.791257i
$691$	25.0000	+	43.3013i	0.951045	+	1.64726i	0.743170	+	0.669102i	$0.233321\pi$
$691$	25.0000	+	43.3013i	0.951045	+	1.64726i	0.207875	+	0.978155i	$0.433345\pi$
$692$		−	30.0000i		−	1.14043i
$693$	7.79423	−	4.50000i	0.296078	−	0.170941i
$694$		0			0
$695$	−37.3205	−	24.6410i	−1.41565	−	0.934687i
$696$		0			0
$697$	−13.8564	−	8.00000i	−0.524849	−	0.303022i
$698$	−17.3205	−	10.0000i	−0.655591	−	0.378506i
$699$	24.0000	−	13.8564i	0.907763	−	0.524097i
$700$	−1.19615	+	9.92820i	−0.0452103	+	0.375251i
$701$	26.0000			0.982006			0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000			0.982006			0.491003	+	0.871158i	$0.336630\pi$
$702$	−20.7846			−0.784465
$703$			12.0000i			0.452589i
$704$	−12.0000	−	20.7846i	−0.452267	−	0.783349i
$705$	6.40192	−	9.69615i	0.241110	−	0.365178i
$706$	−11.0000	+	19.0526i	−0.413990	+	0.717053i
$707$		0			0
$708$	24.2487	−	42.0000i	0.911322	−	1.57846i
$709$	17.5000	+	30.3109i	0.657226	+	1.13835i	0.981331	+	0.192328i	$0.0616038\pi$
$709$	17.5000	+	30.3109i	0.657226	+	1.13835i	−0.324104	+	0.946021i	$0.605063\pi$
$710$	14.0000	+	28.0000i	0.525411	+	1.05082i
$711$	−3.00000			−0.112509
$712$		0			0
$713$	−20.7846	+	12.0000i	−0.778390	+	0.449404i
$714$			6.92820i			0.259281i
$715$	−13.3923	−	0.803848i	−0.500844	−	0.0300622i
$716$	11.0000	−	19.0526i	0.411089	−	0.712028i
$717$	15.5885			0.582162
$718$	6.92820	−	4.00000i	0.258558	−	0.149279i
$719$	18.0000			0.671287			0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000			0.671287			0.335643	+	0.941989i	$0.391046\pi$
$720$	−1.60770	+	26.7846i	−0.0599153	+	0.998203i
$721$	−5.00000			−0.186210
$722$	−29.4449	+	17.0000i	−1.09582	+	0.632674i
$723$	−3.46410	+	6.00000i	−0.128831	+	0.223142i
$724$		0			0
$725$	9.82051	+	22.9904i	0.364725	+	0.853841i
$726$	6.00000	−	3.46410i	0.222681	−	0.128565i
$727$	−40.7032	+	23.5000i	−1.50960	+	0.871567i	−0.509661	+	0.860376i	$0.670229\pi$
$727$	−40.7032	+	23.5000i	−1.50960	+	0.871567i	−0.999937	+	0.0111912i	$0.996438\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	−36.0000	+	18.0000i	−1.33242	+	0.666210i
$731$	2.00000	+	3.46410i	0.0739727	+	0.128124i
$732$	17.3205	+	30.0000i	0.640184	+	1.10883i
$733$	9.52628	+	5.50000i	0.351861	+	0.203147i	0.665505	−	0.746394i	$-0.268216\pi$
$733$	9.52628	+	5.50000i	0.351861	+	0.203147i	−0.313644	+	0.949541i	$0.601550\pi$
$734$		0			0
$735$	−0.232051	+	3.86603i	−0.00855932	+	0.142600i
$736$	24.0000	+	41.5692i	0.884652	+	1.53226i
$737$			30.0000i			1.10506i
$738$	41.5692	+	24.0000i	1.53018	+	0.883452i
$739$	−1.00000			−0.0367856			−0.0183928	−	0.999831i	$-0.505855\pi$
$739$	−1.00000			−0.0367856			−0.0183928	+	0.999831i	$0.505855\pi$
$740$	−4.92820	+	7.46410i	−0.181164	+	0.274386i
$741$			20.7846i			0.763542i
$742$		0			0
$743$	−8.66025	−	5.00000i	−0.317714	−	0.183432i	0.332659	−	0.943047i	$-0.392054\pi$
$743$	−8.66025	−	5.00000i	−0.317714	−	0.183432i	−0.650373	+	0.759615i	$0.725387\pi$
$744$		0			0
$745$	9.33013	+	6.16025i	0.341829	+	0.225694i
$746$		0			0
$747$			51.0000i			1.86599i
$748$		−	12.0000i		−	0.438763i
$749$	−8.00000	−	13.8564i	−0.292314	−	0.506302i
$750$	−25.0526	+	29.5359i	−0.914790	+	1.07850i
$751$	−7.50000	+	12.9904i	−0.273679	+	0.474026i	−0.969801	−	0.243898i	$-0.921574\pi$
$751$	−7.50000	+	12.9904i	−0.273679	+	0.474026i	0.696122	+	0.717923i	$0.254907\pi$
$752$	−10.3923	−	6.00000i	−0.378968	−	0.218797i
$753$	−15.5885	−	27.0000i	−0.568075	−	0.983935i
$754$	10.0000	+	17.3205i	0.364179	+	0.630776i
$755$	−40.0000	+	20.0000i	−1.45575	+	0.727875i
$756$		−	10.3923i		−	0.377964i
$757$			10.0000i			0.363456i	0.983349	+	0.181728i	$0.0581691\pi$
$757$			10.0000i			0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$	39.8372	−	23.0000i	1.44695	−	0.835398i
$759$	27.0000	−	15.5885i	0.980038	−	0.565825i
$760$		0			0
$761$	−7.00000	+	12.1244i	−0.253750	+	0.439508i	−0.964555	−	0.263881i	$-0.914997\pi$
$761$	−7.00000	+	12.1244i	−0.253750	+	0.439508i	0.710805	+	0.703389i	$0.248331\pi$
$762$	34.6410	−	60.0000i	1.25491	−	2.17357i
$763$	16.4545	−	9.50000i	0.595692	−	0.343923i
$764$	6.00000			0.217072
$765$	−7.39230	+	11.1962i	−0.267269	+	0.404798i
$766$	−10.0000			−0.361315
$767$	−24.2487	+	14.0000i	−0.875570	+	0.505511i
$768$	27.7128			1.00000
$769$	9.00000	−	15.5885i	0.324548	−	0.562134i	−0.656873	−	0.754002i	$-0.728121\pi$
$769$	9.00000	−	15.5885i	0.324548	−	0.562134i	0.981421	+	0.191867i	$0.0614544\pi$
$770$	0.803848	−	13.3923i	0.0289687	−	0.482625i
$771$		−	12.1244i		−	0.436648i
$772$	24.2487	−	14.0000i	0.872730	−	0.503871i
$773$		−	27.0000i		−	0.971123i	−0.874203	−	0.485561i	$-0.838615\pi$
$773$		−	27.0000i		−	0.971123i	0.874203	−	0.485561i	$-0.161385\pi$
$774$	−6.00000	−	10.3923i	−0.215666	−	0.373544i
$775$	−12.0000	+	16.0000i	−0.431053	+	0.574737i
$776$		0			0
$777$	−1.73205	+	3.00000i	−0.0621370	+	0.107624i
$778$	32.9090	+	19.0000i	1.17984	+	0.681183i
$779$	24.0000	−	41.5692i	0.859889	−	1.48937i
$780$	−8.53590	+	12.9282i	−0.305634	+	0.462904i
$781$	−10.5000	−	18.1865i	−0.375720	−	0.650765i
$782$			24.0000i			0.858238i
$783$	−12.9904	−	22.5000i	−0.464238	−	0.804084i
$784$	4.00000			0.142857
$785$	11.0885	−	16.7942i	0.395764	−	0.599412i
$786$	42.0000	−	24.2487i	1.49809	−	0.864923i
$787$	−34.6410	−	20.0000i	−1.23482	−	0.712923i	−0.266788	−	0.963755i	$-0.585962\pi$
$787$	−34.6410	−	20.0000i	−1.23482	−	0.712923i	−0.968031	+	0.250832i	$0.919296\pi$
$788$	−13.8564	−	8.00000i	−0.493614	−	0.284988i
$789$		0			0
$790$	−2.46410	+	3.73205i	−0.0876688	+	0.132780i
$791$		0			0
$792$		0			0
$793$		−	20.0000i		−	0.710221i
$794$	−17.0000	−	29.4449i	−0.603307	−	1.04496i
$795$		0			0
$796$	−8.00000	+	13.8564i	−0.283552	+	0.491127i
$797$	−19.0526	−	11.0000i	−0.674876	−	0.389640i	0.123045	−	0.992401i	$-0.460734\pi$
$797$	−19.0526	−	11.0000i	−0.674876	−	0.389640i	−0.797922	+	0.602761i	$0.794067\pi$
$798$	−20.7846			−0.735767
$799$	−3.00000	−	5.19615i	−0.106132	−	0.183827i
$800$	32.0000	+	24.0000i	1.13137	+	0.848528i
$801$	−18.0000	+	31.1769i	−0.635999	+	1.10158i
$802$			30.0000i			1.05934i
$803$	23.3827	−	13.5000i	0.825157	−	0.476405i
$804$	30.0000	+	17.3205i	1.05802	+	0.610847i
$805$	−0.803848	+	13.3923i	−0.0283319	+	0.472017i
$806$	−8.00000	+	13.8564i	−0.281788	+	0.488071i
$807$	13.8564	+	24.0000i	0.487769	+	0.844840i
$808$		0			0
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$	22.1769	−	33.5885i	0.779217	−	1.18018i
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$	−8.66025	+	5.00000i	−0.303915	+	0.175466i
$813$	12.1244	+	21.0000i	0.425220	+	0.736502i
$814$	6.00000	−	10.3923i	0.210300	−	0.364250i
$815$	8.92820	+	0.535898i	0.312741	+	0.0187717i
$816$	12.0000	+	6.92820i	0.420084	+	0.242536i
$817$	−10.3923	+	6.00000i	−0.363581	+	0.209913i
$818$			16.0000i			0.559427i
$819$	−3.00000	+	5.19615i	−0.104828	+	0.181568i
$820$	32.0000	−	16.0000i	1.11749	−	0.558744i
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.859396	+	0.511311i	$0.170840\pi$
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.0131101	+	0.999914i	$0.495827\pi$
$822$	−62.3538			−2.17484
$823$	3.46410	+	2.00000i	0.120751	+	0.0697156i	0.559159	−	0.829060i	$-0.311124\pi$
$823$	3.46410	+	2.00000i	0.120751	+	0.0697156i	−0.438408	+	0.898776i	$0.644457\pi$
$824$		0			0
$825$	15.5885	−	20.7846i	0.542720	−	0.723627i
$826$	−14.0000	−	24.2487i	−0.487122	−	0.843721i
$827$		−	30.0000i		−	1.04320i	−0.853189	−	0.521601i	$-0.825335\pi$
$827$		−	30.0000i		−	1.04320i	0.853189	−	0.521601i	$-0.174665\pi$
$828$		−	36.0000i		−	1.25109i
$829$	24.0000			0.833554			0.416777	−	0.909009i	$-0.363160\pi$
$829$	24.0000			0.833554			0.416777	+	0.909009i	$0.363160\pi$
$830$	63.4449	+	41.8897i	2.20220	+	1.45401i
$831$	−42.0000	−	24.2487i	−1.45696	−	0.841178i
$832$	13.8564	+	8.00000i	0.480384	+	0.277350i
$833$	1.73205	+	1.00000i	0.0600120	+	0.0346479i
$834$	60.0000	−	34.6410i	2.07763	−	1.19952i
$835$	−14.7846	+	22.3923i	−0.511643	+	0.774918i
$836$	36.0000			1.24509
$837$	10.3923	−	18.0000i	0.359211	−	0.622171i
$838$		−	60.0000i		−	2.07267i
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	0.899158	+	0.437623i	$0.144180\pi$
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	−0.0705865	+	0.997506i	$0.522487\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$	−25.9808	−	15.0000i	−0.895356	−	0.516934i
$843$	−6.06218	+	10.5000i	−0.208792	+	0.361639i
$844$	17.0000	+	29.4449i	0.585164	+	1.01353i
$845$	−18.0000	+	9.00000i	−0.619219	+	0.309609i
$846$	9.00000	+	15.5885i	0.309426	+	0.535942i
$847$		−	2.00000i		−	0.0687208i
$848$		0			0
$849$		−	12.1244i		−	0.416107i
$850$	7.85641	+	18.3923i	0.269473	+	0.630851i
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$	−24.2487			−0.830747
$853$	−36.3731	+	21.0000i	−1.24539	+	0.719026i	−0.970186	−	0.242360i	$-0.922079\pi$
$853$	−36.3731	+	21.0000i	−1.24539	+	0.719026i	−0.275204	+	0.961386i	$0.588745\pi$
$854$	20.0000			0.684386
$855$	−33.5885	−	22.1769i	−1.14870	−	0.758434i
$856$		0			0
$857$	−18.1865	+	10.5000i	−0.621240	+	0.358673i	−0.777352	−	0.629066i	$-0.783437\pi$
$857$	−18.1865	+	10.5000i	−0.621240	+	0.358673i	0.156112	+	0.987739i	$0.450104\pi$
$858$	10.3923	−	18.0000i	0.354787	−	0.614510i
$859$	−19.0000	+	32.9090i	−0.648272	+	1.12284i	0.335264	+	0.942124i	$0.391175\pi$
$859$	−19.0000	+	32.9090i	−0.648272	+	1.12284i	−0.983535	+	0.180715i	$0.942159\pi$
$860$	−8.92820	−	0.535898i	−0.304449	−	0.0182740i
$861$	12.0000	−	6.92820i	0.408959	−	0.236113i
$862$	−27.7128	+	16.0000i	−0.943902	+	0.544962i
$863$		−	6.00000i		−	0.204242i	−0.994772	−	0.102121i	$-0.967437\pi$
$863$		−	6.00000i		−	0.204242i	0.994772	−	0.102121i	$-0.0325630\pi$
$864$	−36.0000	−	20.7846i	−1.22474	−	0.707107i
$865$	−15.0000	−	30.0000i	−0.510015	−	1.02003i
$866$	−2.00000	−	3.46410i	−0.0679628	−	0.117715i
$867$	−11.2583	−	19.5000i	−0.382353	−	0.662255i
$868$	−6.92820	−	4.00000i	−0.235159	−	0.135769i
$869$	1.50000	−	2.59808i	0.0508840	−	0.0881337i
$870$	−38.6603	−	2.32051i	−1.31071	−	0.0786726i
$871$	−10.0000	−	17.3205i	−0.338837	−	0.586883i
$872$		0			0
$873$		−	21.0000i		−	0.710742i
$874$	−72.0000			−2.43544
$875$	3.76795	+	10.5263i	0.127380	+	0.355853i
$876$		−	31.1769i		−	1.05337i
$877$	−29.4449	−	17.0000i	−0.994282	−	0.574049i	−0.0877308	−	0.996144i	$-0.527962\pi$
$877$	−29.4449	−	17.0000i	−0.994282	−	0.574049i	−0.906552	+	0.422095i	$0.861295\pi$
$878$		0			0
$879$			46.7654i			1.57736i
$880$	−22.3923	−	14.7846i	−0.754844	−	0.498389i
$881$	50.0000			1.68454			0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000			1.68454			0.842271	+	0.539054i	$0.181218\pi$
$882$	−5.19615	−	3.00000i	−0.174964	−	0.101015i
$883$			42.0000i			1.41341i	0.707507	+	0.706706i	$0.249820\pi$
$883$			42.0000i			1.41341i	−0.707507	+	0.706706i	$0.750180\pi$
$884$	4.00000	+	6.92820i	0.134535	+	0.233021i
$885$	3.24871	−	54.1244i	0.109204	−	1.81937i
$886$	4.00000	−	6.92820i	0.134383	−	0.232758i
$887$	−13.8564	−	8.00000i	−0.465253	−	0.268614i	0.248998	−	0.968504i	$-0.419899\pi$
$887$	−13.8564	−	8.00000i	−0.465253	−	0.268614i	−0.714250	+	0.699890i	$0.753232\pi$
$888$		0			0
$889$	−10.0000	−	17.3205i	−0.335389	−	0.580911i
$890$	24.0000	+	48.0000i	0.804482	+	1.60896i
$891$	−13.5000	+	23.3827i	−0.452267	+	0.783349i
$892$		−	48.0000i		−	1.60716i
$893$	15.5885	−	9.00000i	0.521648	−	0.301174i
$894$	−15.0000	+	8.66025i	−0.501675	+	0.289642i
$895$	1.47372	−	24.5526i	0.0492610	−	0.820702i
$896$		0			0
$897$	−10.3923	+	18.0000i	−0.346989	+	0.601003i
$898$	53.6936	−	31.0000i	1.79178	−	1.03448i
$899$	−20.0000			−0.667037
$900$	−11.7846	−	27.5885i	−0.392820	−	0.919615i
$901$		0			0
$902$	−41.5692	+	24.0000i	−1.38410	+	0.799113i
$903$	−3.46410			−0.115278
$904$		0			0
$905$		0			0
$906$		−	69.2820i		−	2.30174i
$907$	12.1244	−	7.00000i	0.402583	−	0.232431i	−0.285015	−	0.958523i	$-0.591999\pi$
$907$	12.1244	−	7.00000i	0.402583	−	0.232431i	0.687598	+	0.726092i	$0.258665\pi$
$908$			40.0000i			1.32745i
$909$		0			0
$910$	4.00000	+	8.00000i	0.132599	+	0.265197i
$911$	13.5000	+	23.3827i	0.447275	+	0.774703i	0.998208	−	0.0598468i	$-0.0190612\pi$
$911$	13.5000	+	23.3827i	0.447275	+	0.774703i	−0.550933	+	0.834550i	$0.685728\pi$
$912$	−20.7846	+	36.0000i	−0.688247	+	1.19208i
$913$	−44.1673	−	25.5000i	−1.46172	−	0.843927i
$914$	28.0000	−	48.4974i	0.926158	−	1.60415i
$915$	32.3205	+	21.3397i	1.06848	+	0.705470i
$916$	10.0000	+	17.3205i	0.330409	+	0.572286i
$917$		−	14.0000i		−	0.462321i
$918$	−10.3923	−	18.0000i	−0.342997	−	0.594089i
$919$	−55.0000			−1.81428			−0.907141	−	0.420826i	$-0.861740\pi$
$919$	−55.0000			−1.81428			−0.907141	+	0.420826i	$0.861740\pi$
$920$		0			0
$921$	−6.00000	+	3.46410i	−0.197707	+	0.114146i
$922$	−20.7846	−	12.0000i	−0.684505	−	0.395199i
$923$	12.1244	+	7.00000i	0.399078	+	0.230408i
$924$	9.00000	+	5.19615i	0.296078	+	0.170941i
$925$	−1.19615	+	9.92820i	−0.0393292	+	0.326437i
$926$	−12.0000			−0.394344
$927$	12.9904	−	7.50000i	0.426660	−	0.246332i
$928$			40.0000i			1.31306i
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$	−13.8564	−	27.7128i	−0.454369	−	0.908739i
$931$	−3.00000	+	5.19615i	−0.0983210	+	0.170297i
$932$	27.7128	+	16.0000i	0.907763	+	0.524097i
$933$	−10.3923			−0.340229
$934$	−3.00000	−	5.19615i	−0.0981630	−	0.170023i
$935$	−6.00000	−	12.0000i	−0.196221	−	0.392442i
$936$		0			0
$937$		−	26.0000i		−	0.849383i	−0.905338	−	0.424691i	$-0.860383\pi$
$937$		−	26.0000i		−	0.849383i	0.905338	−	0.424691i	$-0.139617\pi$
$938$	17.3205	−	10.0000i	0.565535	−	0.326512i
$939$	−13.5000	−	7.79423i	−0.440556	−	0.254355i
$940$	13.3923	+	0.803848i	0.436809	+	0.0262186i
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	−0.510934	−	0.859620i	$-0.670700\pi$
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	0.999920	+	0.0126715i	$0.00403357\pi$
$942$	15.5885	+	27.0000i	0.507899	+	0.879708i
$943$	41.5692	−	24.0000i	1.35368	−	0.781548i
$944$	−56.0000			−1.82264
$945$	−5.19615	−	10.3923i	−0.169031	−	0.338062i
$946$	12.0000			0.390154
$947$	−31.1769	+	18.0000i	−1.01311	+	0.584921i	−0.912102	−	0.409964i	$-0.865541\pi$
$947$	−31.1769	+	18.0000i	−1.01311	+	0.584921i	−0.101012	+	0.994885i	$0.532208\pi$
$948$	−1.73205	−	3.00000i	−0.0562544	−	0.0974355i
$949$	−9.00000	+	15.5885i	−0.292152	+	0.506023i
$950$	−55.1769	+	23.5692i	−1.79018	+	0.764686i
$951$	−45.0000	−	25.9808i	−1.45922	−	0.842484i
$952$		0			0
$953$		−	24.0000i		−	0.777436i	−0.921357	−	0.388718i	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$		0			0
$955$	6.00000	−	3.00000i	0.194155	−	0.0970777i
$956$	9.00000	+	15.5885i	0.291081	+	0.504167i
$957$	25.9808			0.839839
$958$	−62.3538	−	36.0000i	−2.01456	−	1.16311i
$959$	−9.00000	+	15.5885i	−0.290625	+	0.503378i
$960$	−27.7128	+	13.8564i	−0.894427	+	0.447214i
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$			8.00000i			0.257930i
$963$	41.5692	+	24.0000i	1.33955	+	0.773389i
$964$	−8.00000			−0.257663
$965$	17.2487	−	26.1244i	0.555256	−	0.840973i
$966$	−18.0000	−	10.3923i	−0.579141	−	0.334367i
$967$	−1.73205	−	1.00000i	−0.0556990	−	0.0321578i	0.471892	−	0.881656i	$-0.343571\pi$
$967$	−1.73205	−	1.00000i	−0.0556990	−	0.0321578i	−0.527591	+	0.849499i	$0.676905\pi$
$968$		0			0
$969$	−18.0000	+	10.3923i	−0.578243	+	0.333849i
$970$	−26.1244	−	17.2487i	−0.838803	−	0.553823i
$971$	10.0000			0.320915			0.160458	−	0.987043i	$-0.448703\pi$
$971$	10.0000			0.320915			0.160458	+	0.987043i	$0.448703\pi$
$972$	15.5885	+	27.0000i	0.500000	+	0.866025i
$973$		−	20.0000i		−	0.641171i
$974$	−12.0000	−	20.7846i	−0.384505	−	0.665982i
$975$	−2.07180	+	17.1962i	−0.0663506	+	0.550718i
$976$	20.0000	−	34.6410i	0.640184	−	1.10883i
$977$	36.3731	+	21.0000i	1.16368	+	0.671850i	0.952183	−	0.305530i	$-0.0988335\pi$
$977$	36.3731	+	21.0000i	1.16368	+	0.671850i	0.211495	+	0.977379i	$0.432167\pi$
$978$	−6.92820	+	12.0000i	−0.221540	+	0.383718i
$979$	−18.0000	−	31.1769i	−0.575282	−	0.996419i
$980$	−4.00000	+	2.00000i	−0.127775	+	0.0638877i
$981$	−28.5000	+	49.3634i	−0.909935	+	1.57605i
$982$		−	56.0000i		−	1.78703i
$983$	−2.59808	+	1.50000i	−0.0828658	+	0.0478426i	−0.540860	−	0.841112i	$-0.681901\pi$
$983$	−2.59808	+	1.50000i	−0.0828658	+	0.0478426i	0.457995	+	0.888955i	$0.348568\pi$
$984$		0			0
$985$	−17.8564	−	1.07180i	−0.568952	−	0.0341503i
$986$	−10.0000	+	17.3205i	−0.318465	+	0.551597i
$987$	5.19615			0.165395
$988$	−20.7846	+	12.0000i	−0.661247	+	0.381771i
$989$	−12.0000			−0.381578
$990$	18.0000	+	36.0000i	0.572078	+	1.14416i
$991$	−35.0000			−1.11181			−0.555906	−	0.831245i	$-0.687628\pi$
$991$	−35.0000			−1.11181			−0.555906	+	0.831245i	$0.687628\pi$
$992$	−27.7128	+	16.0000i	−0.879883	+	0.508001i
$993$	−23.3827	+	40.5000i	−0.742027	+	1.28523i
$994$	−7.00000	+	12.1244i	−0.222027	+	0.384561i
$995$	−1.07180	+	17.8564i	−0.0339782	+	0.566086i
$996$	−51.0000	+	29.4449i	−1.61600	+	0.932996i
$997$	21.6506	−	12.5000i	0.685682	−	0.395879i	−0.116310	−	0.993213i	$-0.537107\pi$
$997$	21.6506	−	12.5000i	0.685682	−	0.395879i	0.801993	+	0.597334i	$0.203773\pi$
$998$			8.00000i			0.253236i
$999$		−	10.3923i		−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bh.b.274.1	yes	4
3.2	odd	2		945.2.bh.b.64.2		4
5.4	even	2	inner	315.2.bh.b.274.2	yes	4
9.2	odd	6		945.2.bh.b.694.1		4
9.7	even	3	inner	315.2.bh.b.169.2	yes	4
15.14	odd	2		945.2.bh.b.64.1		4
45.29	odd	6		945.2.bh.b.694.2		4
45.34	even	6	inner	315.2.bh.b.169.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bh.b.169.1	✓	4	45.34	even	6	inner
315.2.bh.b.169.2	yes	4	9.7	even	3	inner
315.2.bh.b.274.1	yes	4	1.1	even	1	trivial
315.2.bh.b.274.2	yes	4	5.4	even	2	inner
945.2.bh.b.64.1		4	15.14	odd	2
945.2.bh.b.64.2		4	3.2	odd	2
945.2.bh.b.694.1		4	9.2	odd	6
945.2.bh.b.694.2		4	45.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.133975 - 2.23205i) q^{5} +(3.00000 + 1.73205i) q^{6} +(0.866025 - 0.500000i) q^{7} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.73205 + 1.00000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.133975 - 2.23205i) q^{5} +(3.00000 + 1.73205i) q^{6} +(0.866025 - 0.500000i) q^{7} +(-1.50000 + 2.59808i) q^{9} +(2.00000 + 4.00000i) q^{10} +(-1.50000 - 2.59808i) q^{11} -3.46410 q^{12} +(1.73205 + 1.00000i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-3.46410 + 1.73205i) q^{15} +(2.00000 + 3.46410i) q^{16} +2.00000i q^{17} -6.00000i q^{18} -6.00000 q^{19} +(-3.73205 - 2.46410i) q^{20} +(-1.50000 - 0.866025i) q^{21} +(5.19615 + 3.00000i) q^{22} +(-5.19615 - 3.00000i) q^{23} +(-4.96410 - 0.598076i) q^{25} -4.00000 q^{26} +5.19615 q^{27} -2.00000i q^{28} +(-2.50000 - 4.33013i) q^{29} +(4.26795 - 6.46410i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-6.92820 - 4.00000i) q^{32} +(-2.59808 + 4.50000i) q^{33} +(-2.00000 - 3.46410i) q^{34} +(-1.00000 - 2.00000i) q^{35} +(3.00000 + 5.19615i) q^{36} -2.00000i q^{37} +(10.3923 - 6.00000i) q^{38} -3.46410i q^{39} +(-4.00000 + 6.92820i) q^{41} +3.46410 q^{42} +(1.73205 - 1.00000i) q^{43} -6.00000 q^{44} +(5.59808 + 3.69615i) q^{45} +12.0000 q^{46} +(-2.59808 + 1.50000i) q^{47} +(3.46410 - 6.00000i) q^{48} +(0.500000 - 0.866025i) q^{49} +(9.19615 - 3.92820i) q^{50} +(3.00000 - 1.73205i) q^{51} +(3.46410 - 2.00000i) q^{52} +(-9.00000 + 5.19615i) q^{54} +(-6.00000 + 3.00000i) q^{55} +(5.19615 + 9.00000i) q^{57} +(8.66025 + 5.00000i) q^{58} +(-7.00000 + 12.1244i) q^{59} +(-0.464102 + 7.73205i) q^{60} +(-5.00000 - 8.66025i) q^{61} +8.00000i q^{62} +3.00000i q^{63} +8.00000 q^{64} +(2.46410 - 3.73205i) q^{65} -10.3923i q^{66} +(-8.66025 - 5.00000i) q^{67} +(3.46410 + 2.00000i) q^{68} +10.3923i q^{69} +(3.73205 + 2.46410i) q^{70} +7.00000 q^{71} +9.00000i q^{73} +(2.00000 + 3.46410i) q^{74} +(3.40192 + 7.96410i) q^{75} +(-6.00000 + 10.3923i) q^{76} +(-2.59808 - 1.50000i) q^{77} +(3.46410 + 6.00000i) q^{78} +(0.500000 + 0.866025i) q^{79} +(8.00000 - 4.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} -16.0000i q^{82} +(14.7224 - 8.50000i) q^{83} +(-3.00000 + 1.73205i) q^{84} +(4.46410 + 0.267949i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(-4.33013 + 7.50000i) q^{87} +12.0000 q^{89} +(-13.3923 - 0.803848i) q^{90} +2.00000 q^{91} +(-10.3923 + 6.00000i) q^{92} -6.92820 q^{93} +(3.00000 - 5.19615i) q^{94} +(-0.803848 + 13.3923i) q^{95} +13.8564i q^{96} +(-6.06218 + 3.50000i) q^{97} +2.00000i q^{98} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} + 4 q^{5} + 12 q^{6} - 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^4 + 4 * q^5 + 12 * q^6 - 6 * q^9	\( 4 q + 4 q^{4} + 4 q^{5} + 12 q^{6} - 6 q^{9} + 8 q^{10} - 6 q^{11} - 4 q^{14} + 8 q^{16} - 24 q^{19} - 8 q^{20} - 6 q^{21} - 6 q^{25} - 16 q^{26} - 10 q^{29} + 24 q^{30} + 8 q^{31} - 8 q^{34} - 4 q^{35} + 12 q^{36} - 16 q^{41} - 24 q^{44} + 12 q^{45} + 48 q^{46} + 2 q^{49} + 16 q^{50} + 12 q^{51} - 36 q^{54} - 24 q^{55} - 28 q^{59} + 12 q^{60} - 20 q^{61} + 32 q^{64} - 4 q^{65} + 8 q^{70} + 28 q^{71} + 8 q^{74} + 24 q^{75} - 24 q^{76} + 2 q^{79} + 32 q^{80} - 18 q^{81} - 12 q^{84} + 4 q^{85} - 8 q^{86} + 48 q^{89} - 12 q^{90} + 8 q^{91} + 12 q^{94} - 24 q^{95} + 36 q^{99}+O(q^{100}) \) 4 * q + 4 * q^4 + 4 * q^5 + 12 * q^6 - 6 * q^9 + 8 * q^10 - 6 * q^11 - 4 * q^14 + 8 * q^16 - 24 * q^19 - 8 * q^20 - 6 * q^21 - 6 * q^25 - 16 * q^26 - 10 * q^29 + 24 * q^30 + 8 * q^31 - 8 * q^34 - 4 * q^35 + 12 * q^36 - 16 * q^41 - 24 * q^44 + 12 * q^45 + 48 * q^46 + 2 * q^49 + 16 * q^50 + 12 * q^51 - 36 * q^54 - 24 * q^55 - 28 * q^59 + 12 * q^60 - 20 * q^61 + 32 * q^64 - 4 * q^65 + 8 * q^70 + 28 * q^71 + 8 * q^74 + 24 * q^75 - 24 * q^76 + 2 * q^79 + 32 * q^80 - 18 * q^81 - 12 * q^84 + 4 * q^85 - 8 * q^86 + 48 * q^89 - 12 * q^90 + 8 * q^91 + 12 * q^94 - 24 * q^95 + 36 * q^99

Introduction

L-functions

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Database

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