LMFDB - Embedded newform 735.2.q.f.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(79,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("735.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.1
Root			$0.312819 + 1.16746i$ of defining polynomial
Character	$\chi$	$=$	735.79
Dual form			735.2.q.f.214.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.34630 - 1.35464i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.67009 + 4.62473i) q^{4} +(1.55199 - 1.60976i) q^{5} +2.70928 q^{6} -9.04945i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.34630 - 1.35464i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.67009 + 4.62473i) q^{4} +(1.55199 - 1.60976i) q^{5} +2.70928 q^{6} -9.04945i q^{8} +(0.500000 - 0.866025i) q^{9} +(-5.82208 + 1.67458i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-4.62473 - 2.67009i) q^{12} -0.921622i q^{13} +(-0.539189 + 2.17009i) q^{15} +(-6.91855 + 11.9833i) q^{16} +(0.933903 - 0.539189i) q^{17} +(-2.34630 + 1.35464i) q^{18} +(-1.53919 + 2.66595i) q^{19} +(11.5886 + 2.87936i) q^{20} +5.41855i q^{22} +(-2.02665 - 1.17009i) q^{23} +(4.52472 + 7.83705i) q^{24} +(-0.182626 - 4.99666i) q^{25} +(-1.24846 + 2.16240i) q^{26} +1.00000i q^{27} +6.68035 q^{29} +(4.20478 - 4.36127i) q^{30} +(-3.87936 - 6.71925i) q^{31} +(16.7919 - 9.69481i) q^{32} +(1.73205 + 1.00000i) q^{33} -2.92162 q^{34} +5.34017 q^{36} +(9.38521 + 5.41855i) q^{37} +(7.22280 - 4.17009i) q^{38} +(0.460811 + 0.798148i) q^{39} +(-14.5674 - 14.0447i) q^{40} -6.49693 q^{41} -6.52359i q^{43} +(5.34017 - 9.24945i) q^{44} +(-0.618092 - 2.14894i) q^{45} +(3.17009 + 5.49075i) q^{46} +(-4.05330 - 2.34017i) q^{47} -13.8371i q^{48} +(-6.34017 + 11.9711i) q^{50} +(-0.539189 + 0.933903i) q^{51} +(4.26225 - 2.46081i) q^{52} +(3.25515 - 1.87936i) q^{53} +(1.35464 - 2.34630i) q^{54} +(-4.34017 - 1.07838i) q^{55} -3.07838i q^{57} +(-15.6741 - 9.04945i) q^{58} +(-5.26180 - 9.11370i) q^{59} +(-11.4757 + 3.30072i) q^{60} +(-2.07838 + 3.59986i) q^{61} +21.0205i q^{62} -24.8576 q^{64} +(-1.48359 - 1.43035i) q^{65} +(-2.70928 - 4.69260i) q^{66} +(-4.05330 + 2.34017i) q^{67} +(4.98720 + 2.87936i) q^{68} +2.34017 q^{69} +2.00000 q^{71} +(-7.83705 - 4.52472i) q^{72} +(-6.13005 + 3.53919i) q^{73} +(-14.6803 - 25.4271i) q^{74} +(2.65649 + 4.23592i) q^{75} -16.4391 q^{76} -2.49693i q^{78} +(3.07838 - 5.33191i) q^{79} +(8.55260 + 29.7352i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(15.2438 + 8.80098i) q^{82} -6.83710i q^{83} +(0.581449 - 2.34017i) q^{85} +(-8.83710 + 15.3063i) q^{86} +(-5.78535 + 3.34017i) q^{87} +(-15.6741 + 9.04945i) q^{88} +(-4.17009 + 7.22280i) q^{89} +(-1.46081 + 5.87936i) q^{90} -12.4969i q^{92} +(6.71925 + 3.87936i) q^{93} +(6.34017 + 10.9815i) q^{94} +(1.90272 + 6.61526i) q^{95} +(-9.69481 + 16.7919i) q^{96} -8.43907i q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{4} + 2 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 10 * q^4 + 2 * q^5 + 4 * q^6 + 6 * q^9	$ 12 q + 10 q^{4} + 2 q^{5} + 4 q^{6} + 6 q^{9} - 12 q^{10} - 12 q^{11} - 26 q^{16} - 12 q^{19} + 60 q^{20} + 18 q^{24} + 2 q^{25} + 20 q^{26} - 8 q^{29} + 10 q^{30} + 4 q^{31} - 48 q^{34} + 20 q^{36} + 12 q^{39} + 4 q^{40} - 8 q^{41} + 20 q^{44} - 2 q^{45} + 16 q^{46} - 32 q^{50} + 2 q^{54} - 8 q^{55} - 32 q^{59} + 8 q^{60} - 12 q^{61} - 52 q^{64} - 32 q^{65} - 4 q^{66} - 16 q^{69} + 24 q^{71} - 88 q^{74} + 8 q^{75} - 8 q^{76} + 24 q^{79} + 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} - 28 q^{89} - 24 q^{90} + 32 q^{94} - 4 q^{95} - 58 q^{96} - 24 q^{99}+O(q^{100}) $ 12 * q + 10 * q^4 + 2 * q^5 + 4 * q^6 + 6 * q^9 - 12 * q^10 - 12 * q^11 - 26 * q^16 - 12 * q^19 + 60 * q^20 + 18 * q^24 + 2 * q^25 + 20 * q^26 - 8 * q^29 + 10 * q^30 + 4 * q^31 - 48 * q^34 + 20 * q^36 + 12 * q^39 + 4 * q^40 - 8 * q^41 + 20 * q^44 - 2 * q^45 + 16 * q^46 - 32 * q^50 + 2 * q^54 - 8 * q^55 - 32 * q^59 + 8 * q^60 - 12 * q^61 - 52 * q^64 - 32 * q^65 - 4 * q^66 - 16 * q^69 + 24 * q^71 - 88 * q^74 + 8 * q^75 - 8 * q^76 + 24 * q^79 + 46 * q^80 - 6 * q^81 + 64 * q^85 + 8 * q^86 - 28 * q^89 - 24 * q^90 + 32 * q^94 - 4 * q^95 - 58 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.34630	−	1.35464i	−1.65909	−	0.957873i	−0.973138	−	0.230222i	$-0.926055\pi$
$2$	−2.34630	−	1.35464i	−1.65909	−	0.957873i	−0.685948	−	0.727651i	$-0.740612\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	2.67009	+	4.62473i	1.33504	+	2.31236i
$5$	1.55199	−	1.60976i	0.694073	−	0.719905i
$5$	1.55199	−	1.60976i	0.694073	−	0.719905i
$6$	2.70928			1.10606
$7$		0			0
$7$		0			0
$8$		−	9.04945i		−	3.19946i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−5.82208	+	1.67458i	−1.84110	+	0.529549i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	−4.62473	−	2.67009i	−1.33504	−	0.770788i
$13$		−	0.921622i		−	0.255612i	−0.991799	−	0.127806i	$-0.959207\pi$
$13$		−	0.921622i		−	0.255612i	0.991799	−	0.127806i	$-0.0407935\pi$
$14$		0			0
$15$	−0.539189	+	2.17009i	−0.139218	+	0.560314i
$16$	−6.91855	+	11.9833i	−1.72964	+	2.99582i
$17$	0.933903	−	0.539189i	0.226505	−	0.130773i	−0.382454	−	0.923975i	$-0.624921\pi$
$17$	0.933903	−	0.539189i	0.226505	−	0.130773i	0.608959	+	0.793202i	$0.291588\pi$
$18$	−2.34630	+	1.35464i	−0.553029	+	0.319291i
$19$	−1.53919	+	2.66595i	−0.353114	+	0.611612i	−0.986793	−	0.161984i	$-0.948211\pi$
$19$	−1.53919	+	2.66595i	−0.353114	+	0.611612i	0.633679	+	0.773596i	$0.281544\pi$
$20$	11.5886	+	2.87936i	2.59130	+	0.643845i
$21$		0			0
$22$			5.41855i			1.15524i
$23$	−2.02665	−	1.17009i	−0.422586	−	0.243980i	0.273597	−	0.961844i	$-0.411786\pi$
$23$	−2.02665	−	1.17009i	−0.422586	−	0.243980i	−0.696183	+	0.717864i	$0.745120\pi$
$24$	4.52472	+	7.83705i	0.923605	+	1.59973i
$25$	−0.182626	−	4.99666i	−0.0365252	−	0.999333i
$26$	−1.24846	+	2.16240i	−0.244844	+	0.424082i
$27$			1.00000i			0.192450i
$28$		0			0
$29$	6.68035			1.24051			0.620255	−	0.784401i	$-0.287029\pi$
$29$	6.68035			1.24051			0.620255	+	0.784401i	$0.287029\pi$
$30$	4.20478	−	4.36127i	0.767684	−	0.796256i
$31$	−3.87936	−	6.71925i	−0.696754	−	1.20681i	−0.969586	−	0.244752i	$-0.921294\pi$
$31$	−3.87936	−	6.71925i	−0.696754	−	1.20681i	0.272832	−	0.962062i	$-0.412040\pi$
$32$	16.7919	−	9.69481i	2.96842	−	1.71382i
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$	−2.92162			−0.501054
$35$		0			0
$36$	5.34017			0.890029
$37$	9.38521	+	5.41855i	1.54292	+	0.890804i	0.998653	+	0.0518912i	$0.0165249\pi$
$37$	9.38521	+	5.41855i	1.54292	+	0.890804i	0.544265	+	0.838913i	$0.316808\pi$
$38$	7.22280	−	4.17009i	1.17169	−	0.676477i
$39$	0.460811	+	0.798148i	0.0737888	+	0.127806i
$40$	−14.5674	−	14.0447i	−2.30331	−	2.22066i
$41$	−6.49693			−1.01465			−0.507325	−	0.861755i	$-0.669366\pi$
$41$	−6.49693			−1.01465			−0.507325	+	0.861755i	$0.669366\pi$
$42$		0			0
$43$		−	6.52359i		−	0.994838i	−0.867510	−	0.497419i	$-0.834281\pi$
$43$		−	6.52359i		−	0.994838i	0.867510	−	0.497419i	$-0.165719\pi$
$44$	5.34017	−	9.24945i	0.805061	−	1.39441i
$45$	−0.618092	−	2.14894i	−0.0921397	−	0.320346i
$46$	3.17009	+	5.49075i	0.467404	+	0.809567i
$47$	−4.05330	−	2.34017i	−0.591234	−	0.341349i	0.174351	−	0.984684i	$-0.444217\pi$
$47$	−4.05330	−	2.34017i	−0.591234	−	0.341349i	−0.765585	+	0.643334i	$0.777551\pi$
$48$		−	13.8371i		−	1.99721i
$49$		0			0
$50$	−6.34017	+	11.9711i	−0.896636	+	1.69297i
$51$	−0.539189	+	0.933903i	−0.0755015	+	0.130773i
$52$	4.26225	−	2.46081i	0.591068	−	0.341253i
$53$	3.25515	−	1.87936i	0.447129	−	0.258150i	−0.259488	−	0.965746i	$-0.583554\pi$
$53$	3.25515	−	1.87936i	0.447129	−	0.258150i	0.706617	+	0.707596i	$0.250220\pi$
$54$	1.35464	−	2.34630i	0.184343	−	0.319291i
$55$	−4.34017	−	1.07838i	−0.585229	−	0.145408i
$56$		0			0
$57$		−	3.07838i		−	0.407741i
$58$	−15.6741	−	9.04945i	−2.05811	−	1.18825i
$59$	−5.26180	−	9.11370i	−0.685027	−	1.18650i	−0.973428	−	0.228992i	$-0.926457\pi$
$59$	−5.26180	−	9.11370i	−0.685027	−	1.18650i	0.288401	−	0.957510i	$-0.406876\pi$
$60$	−11.4757	+	3.30072i	−1.48151	+	0.426121i
$61$	−2.07838	+	3.59986i	−0.266109	+	0.460914i	−0.967854	−	0.251514i	$-0.919071\pi$
$61$	−2.07838	+	3.59986i	−0.266109	+	0.460914i	0.701745	+	0.712429i	$0.252405\pi$
$62$			21.0205i			2.66961i
$63$		0			0
$64$	−24.8576			−3.10720
$65$	−1.48359	−	1.43035i	−0.184016	−	0.177413i
$66$	−2.70928	−	4.69260i	−0.333489	−	0.577619i
$67$	−4.05330	+	2.34017i	−0.495189	+	0.285898i	−0.726725	−	0.686929i	$-0.758958\pi$
$67$	−4.05330	+	2.34017i	−0.495189	+	0.285898i	0.231535	+	0.972826i	$0.425625\pi$
$68$	4.98720	+	2.87936i	0.604787	+	0.349174i
$69$	2.34017			0.281724
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−7.83705	−	4.52472i	−0.923605	−	0.533244i
$73$	−6.13005	+	3.53919i	−0.717469	+	0.414231i	−0.813820	−	0.581117i	$-0.802616\pi$
$73$	−6.13005	+	3.53919i	−0.717469	+	0.414231i	0.0963516	+	0.995347i	$0.469283\pi$
$74$	−14.6803	−	25.4271i	−1.70656	−	2.95584i
$75$	2.65649	+	4.23592i	0.306745	+	0.489122i
$76$	−16.4391			−1.88569
$77$		0			0
$78$		−	2.49693i		−	0.282721i
$79$	3.07838	−	5.33191i	0.346345	−	0.599886i	−0.639253	−	0.768997i	$-0.720756\pi$
$79$	3.07838	−	5.33191i	0.346345	−	0.599886i	0.985597	+	0.169111i	$0.0540895\pi$
$80$	8.55260	+	29.7352i	0.956210	+	3.32449i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	15.2438	+	8.80098i	1.68339	+	0.971906i
$83$		−	6.83710i		−	0.750469i	−0.926930	−	0.375235i	$-0.877562\pi$
$83$		−	6.83710i		−	0.750469i	0.926930	−	0.375235i	$-0.122438\pi$
$84$		0			0
$85$	0.581449	−	2.34017i	0.0630670	−	0.253827i
$86$	−8.83710	+	15.3063i	−0.952929	+	1.65052i
$87$	−5.78535	+	3.34017i	−0.620255	+	0.358104i
$88$	−15.6741	+	9.04945i	−1.67087	+	0.964674i
$89$	−4.17009	+	7.22280i	−0.442028	+	0.765615i	−0.997840	−	0.0656928i	$-0.979074\pi$
$89$	−4.17009	+	7.22280i	−0.442028	+	0.765615i	0.555812	+	0.831308i	$0.312408\pi$
$90$	−1.46081	+	5.87936i	−0.153983	+	0.619739i
$91$		0			0
$92$		−	12.4969i		−	1.30289i
$93$	6.71925	+	3.87936i	0.696754	+	0.402271i
$94$	6.34017	+	10.9815i	0.653939	+	1.13266i
$95$	1.90272	+	6.61526i	0.195215	+	0.678712i
$96$	−9.69481	+	16.7919i	−0.989472	+	1.71382i
$97$		−	8.43907i		−	0.856858i	−0.903576	−	0.428429i	$-0.859067\pi$
$97$		−	8.43907i		−	0.856858i	0.903576	−	0.428429i	$-0.140933\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	22.6206	−	14.1861i	2.26206	−	1.41861i
$101$	−2.90829	−	5.03731i	−0.289386	−	0.501231i	0.684277	−	0.729222i	$-0.260118\pi$
$101$	−2.90829	−	5.03731i	−0.289386	−	0.501231i	−0.973663	+	0.227991i	$0.926784\pi$
$102$	2.53020	−	1.46081i	0.250527	−	0.144642i
$103$	−1.86781	−	1.07838i	−0.184040	−	0.106256i	0.405149	−	0.914251i	$-0.367220\pi$
$103$	−1.86781	−	1.07838i	−0.184040	−	0.106256i	−0.589190	+	0.807995i	$0.700553\pi$
$104$	−8.34017			−0.817821
$105$		0			0
$106$	−10.1834			−0.989101
$107$	−14.2868	−	8.24846i	−1.38115	−	0.797409i	−0.388857	−	0.921298i	$-0.627130\pi$
$107$	−14.2868	−	8.24846i	−1.38115	−	0.797409i	−0.992296	+	0.123889i	$0.960463\pi$
$108$	−4.62473	+	2.67009i	−0.445014	+	0.256929i
$109$	−6.41855	−	11.1173i	−0.614786	−	1.06484i	−0.990422	−	0.138073i	$-0.955909\pi$
$109$	−6.41855	−	11.1173i	−0.614786	−	1.06484i	0.375636	−	0.926767i	$-0.377424\pi$
$110$	8.72254	+	8.40956i	0.831662	+	0.801820i
$111$	−10.8371			−1.02861
$112$		0			0
$113$		−	5.23513i		−	0.492480i	−0.969209	−	0.246240i	$-0.920805\pi$
$113$		−	5.23513i		−	0.492480i	0.969209	−	0.246240i	$-0.0791951\pi$
$114$	−4.17009	+	7.22280i	−0.390564	+	0.676477i
$115$	−5.02890	+	1.44644i	−0.468948	+	0.134881i
$116$	17.8371	+	30.8948i	1.65613	+	2.86851i
$117$	−0.798148	−	0.460811i	−0.0737888	−	0.0426020i
$118$			28.5113i			2.62468i
$119$		0			0
$120$	19.6381	+	4.87936i	1.79270	+	0.445423i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	9.75300	−	5.63090i	0.882995	−	0.509798i
$123$	5.62651	−	3.24846i	0.507325	−	0.292904i
$124$	20.7165	−	35.8820i	1.86039	−	3.22230i
$125$	−8.32684	−	7.46081i	−0.744775	−	0.667315i
$126$		0			0
$127$		−	1.84324i		−	0.163562i	−0.996650	−	0.0817808i	$-0.973939\pi$
$127$		−	1.84324i		−	0.163562i	0.996650	−	0.0817808i	$-0.0260607\pi$
$128$	24.7397	+	14.2834i	2.18670	+	1.26249i
$129$	3.26180	+	5.64960i	0.287185	+	0.497419i
$130$	1.54333	+	5.36576i	0.135359	+	0.470608i
$131$	0.738205	−	1.27861i	0.0644973	−	0.111713i	−0.831974	−	0.554815i	$-0.812789\pi$
$131$	0.738205	−	1.27861i	0.0644973	−	0.111713i	0.896471	+	0.443103i	$0.146122\pi$
$132$			10.6803i			0.929605i
$133$		0			0
$134$	12.6803			1.09542
$135$	1.60976	+	1.55199i	0.138546	+	0.133574i
$136$	−4.87936	−	8.45130i	−0.418402	−	0.724693i
$137$	−3.84435	+	2.21953i	−0.328445	+	0.189628i	−0.655150	−	0.755498i	$-0.727395\pi$
$137$	−3.84435	+	2.21953i	−0.328445	+	0.189628i	0.326706	+	0.945126i	$0.394061\pi$
$138$	−5.49075	−	3.17009i	−0.467404	−	0.269856i
$139$	13.6020			1.15370			0.576852	−	0.816849i	$-0.304281\pi$
$139$	13.6020			1.15370			0.576852	+	0.816849i	$0.304281\pi$
$140$		0			0
$141$	4.68035			0.394156
$142$	−4.69260	−	2.70928i	−0.393794	−	0.227357i
$143$	−1.59630	+	0.921622i	−0.133489	+	0.0770699i
$144$	6.91855	+	11.9833i	0.576546	+	0.998607i
$145$	10.3679	−	10.7537i	0.861004	−	0.893048i
$146$	19.1773			1.58712
$147$		0			0
$148$			57.8720i			4.75705i
$149$	7.83710	−	13.5743i	0.642040	−	1.11205i	−0.342936	−	0.939359i	$-0.611421\pi$
$149$	7.83710	−	13.5743i	0.642040	−	1.11205i	0.984977	−	0.172688i	$-0.0552452\pi$
$150$	−0.494784	−	13.5373i	−0.0403990	−	1.10532i
$151$	−2.92162	−	5.06040i	−0.237758	−	0.411809i	0.722312	−	0.691567i	$-0.243079\pi$
$151$	−2.92162	−	5.06040i	−0.237758	−	0.411809i	−0.960071	+	0.279757i	$0.909746\pi$
$152$	24.1254	+	13.9288i	1.95683	+	1.12978i
$153$		−	1.07838i		−	0.0871817i
$154$		0			0
$155$	−16.8371	−	4.18342i	−1.35239	−	0.336020i
$156$	−2.46081	+	4.26225i	−0.197023	+	0.341253i
$157$	4.26225	−	2.46081i	0.340165	−	0.196394i	−0.320180	−	0.947357i	$-0.603743\pi$
$157$	4.26225	−	2.46081i	0.340165	−	0.196394i	0.660345	+	0.750963i	$0.270410\pi$
$158$	−14.4456	+	8.34017i	−1.14923	+	0.663509i
$159$	−1.87936	+	3.25515i	−0.149043	+	0.258150i
$160$	10.4547	−	42.0772i	0.826514	−	3.32649i
$161$		0			0
$162$			2.70928i			0.212861i
$163$	8.52450	+	4.92162i	0.667690	+	0.385491i	0.795201	−	0.606346i	$-0.207365\pi$
$163$	8.52450	+	4.92162i	0.667690	+	0.385491i	−0.127511	+	0.991837i	$0.540699\pi$
$164$	−17.3474	−	30.0465i	−1.35460	−	2.34624i
$165$	4.29789	−	1.23618i	0.334590	−	0.0962368i
$166$	−9.26180	+	16.0419i	−0.718855	+	1.24509i
$167$		−	19.2039i		−	1.48605i	−0.669266	−	0.743023i	$-0.733391\pi$
$167$		−	19.2039i		−	1.48605i	0.669266	−	0.743023i	$-0.266609\pi$
$168$		0			0
$169$	12.1506			0.934662
$170$	−4.53434	+	4.70310i	−0.347768	+	0.360711i
$171$	1.53919	+	2.66595i	0.117705	+	0.203871i
$172$	30.1698	−	17.4186i	2.30043	−	1.32815i
$173$	−19.4328	−	11.2195i	−1.47745	−	0.853005i	−0.477773	−	0.878483i	$-0.658556\pi$
$173$	−19.4328	−	11.2195i	−1.47745	−	0.853005i	−0.999675	+	0.0254777i	$0.991889\pi$
$174$	18.0989			1.37207
$175$		0			0
$176$	27.6742			2.08602
$177$	9.11370	+	5.26180i	0.685027	+	0.395501i
$178$	19.5686	−	11.2979i	1.46673	−	0.846814i
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	0.990134	−	0.140122i	$-0.0447496\pi$
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	−0.616417	+	0.787420i	$0.711416\pi$
$180$	8.28792	−	8.59637i	0.617745	−	0.640736i
$181$	8.52359			0.633553			0.316777	−	0.948500i	$-0.397399\pi$
$181$	8.52359			0.633553			0.316777	+	0.948500i	$0.397399\pi$
$182$		0			0
$183$		−	4.15676i		−	0.307276i
$184$	−10.5886	+	18.3401i	−0.780605	+	1.35205i
$185$	23.2883	−	6.69833i	1.71219	−	0.492471i
$186$	−10.5103	−	18.2043i	−0.770650	−	1.33480i
$187$	−1.86781	−	1.07838i	−0.136587	−	0.0788588i
$188$		−	24.9939i		−	1.82286i
$189$		0			0
$190$	4.49693	−	18.0989i	0.326241	−	1.31303i
$191$	−7.68035	+	13.3027i	−0.555730	+	0.962553i	0.442116	+	0.896958i	$0.354228\pi$
$191$	−7.68035	+	13.3027i	−0.555730	+	0.962553i	−0.997846	+	0.0655953i	$0.979105\pi$
$192$	21.5273	−	12.4288i	1.55360	−	0.896972i
$193$	7.24589	−	4.18342i	0.521571	−	0.301129i	−0.216006	−	0.976392i	$-0.569303\pi$
$193$	7.24589	−	4.18342i	0.521571	−	0.301129i	0.737577	+	0.675263i	$0.235970\pi$
$194$	−11.4319	+	19.8006i	−0.820761	+	1.42160i
$195$	2.00000	+	0.496928i	0.143223	+	0.0355858i
$196$		0			0
$197$			11.7587i			0.837774i	0.908038	+	0.418887i	$0.137580\pi$
$197$			11.7587i			0.837774i	−0.908038	+	0.418887i	$0.862420\pi$
$198$	4.69260	+	2.70928i	0.333489	+	0.192540i
$199$	11.2979	+	19.5686i	0.800888	+	1.38718i	0.919032	+	0.394182i	$0.128972\pi$
$199$	11.2979	+	19.5686i	0.800888	+	1.38718i	−0.118145	+	0.992996i	$0.537695\pi$
$200$	−45.2170	+	1.65267i	−3.19733	+	0.116861i
$201$	2.34017	−	4.05330i	0.165063	−	0.285898i
$202$			15.7587i			1.10878i
$203$		0			0
$204$	−5.75872			−0.403191
$205$	−10.0832	+	10.4585i	−0.704241	+	0.730451i
$206$	2.92162	+	5.06040i	0.203559	+	0.352575i
$207$	−2.02665	+	1.17009i	−0.140862	+	0.0813266i
$208$	11.0441	+	6.37629i	0.765768	+	0.442116i
$209$	6.15676			0.425872
$210$		0			0
$211$	−13.6742			−0.941371			−0.470685	−	0.882301i	$-0.655993\pi$
$211$	−13.6742			−0.941371			−0.470685	+	0.882301i	$0.655993\pi$
$212$	17.3831	+	10.0361i	1.19387	+	0.689283i
$213$	−1.73205	+	1.00000i	−0.118678	+	0.0685189i
$214$	22.3474	+	38.7068i	1.52763	+	2.64594i
$215$	−10.5014	−	10.1246i	−0.716189	−	0.690490i
$216$	9.04945			0.615737
$217$		0			0
$218$			34.7792i			2.35555i
$219$	3.53919	−	6.13005i	0.239156	−	0.414231i
$220$	−6.60144	−	22.9515i	−0.445069	−	1.54739i
$221$	−0.496928	−	0.860705i	−0.0334270	−	0.0578973i
$222$	25.4271	+	14.6803i	1.70656	+	0.985280i
$223$			21.6742i			1.45141i	0.688005	+	0.725706i	$0.258487\pi$
$223$			21.6742i			1.45141i	−0.688005	+	0.725706i	$0.741513\pi$
$224$		0			0
$225$	−4.41855	−	2.34017i	−0.294570	−	0.156012i
$226$	−7.09171	+	12.2832i	−0.471733	+	0.817066i
$227$	−9.97440	+	5.75872i	−0.662024	+	0.382220i	−0.793048	−	0.609159i	$-0.791507\pi$
$227$	−9.97440	+	5.75872i	−0.662024	+	0.382220i	0.131024	+	0.991379i	$0.458174\pi$
$228$	14.2367	−	8.21953i	0.942845	−	0.544352i
$229$	−6.41855	+	11.1173i	−0.424150	+	0.734649i	−0.996341	−	0.0854716i	$-0.972760\pi$
$229$	−6.41855	+	11.1173i	−0.424150	+	0.734649i	0.572191	+	0.820121i	$0.306094\pi$
$230$	13.7587	+	3.41855i	0.907223	+	0.225413i
$231$		0			0
$232$		−	60.4534i		−	3.96896i
$233$	5.85855	+	3.38243i	0.383806	+	0.221591i	0.679473	−	0.733701i	$-0.262208\pi$
$233$	5.85855	+	3.38243i	0.383806	+	0.221591i	−0.295667	+	0.955291i	$0.595542\pi$
$234$	1.24846	+	2.16240i	0.0816147	+	0.141361i
$235$	−10.0578	+	2.89288i	−0.656099	+	0.188711i
$236$	28.0989	−	48.6687i	1.82908	−	3.16806i
$237$			6.15676i			0.399924i
$238$		0			0
$239$	23.3607			1.51108			0.755539	−	0.655104i	$-0.227375\pi$
$239$	23.3607			1.51108			0.755539	+	0.655104i	$0.227375\pi$
$240$	−22.2744	−	21.4751i	−1.43780	−	1.38621i
$241$	−7.34017	−	12.7136i	−0.472822	−	0.818952i	0.526694	−	0.850055i	$-0.323431\pi$
$241$	−7.34017	−	12.7136i	−0.472822	−	0.818952i	−0.999516	+	0.0311030i	$0.990098\pi$
$242$	−16.4241	+	9.48246i	−1.05578	+	0.609556i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−22.1978			−1.42107
$245$		0			0
$246$	−17.6020			−1.12226
$247$	2.45700	+	1.41855i	0.156335	+	0.0902602i
$248$	−60.8055	+	35.1061i	−3.86115	+	2.22924i
$249$	3.41855	+	5.92110i	0.216642	+	0.375235i
$250$	9.43058	+	28.7852i	0.596443	+	1.82053i
$251$	−9.16290			−0.578357			−0.289179	−	0.957275i	$-0.593382\pi$
$251$	−9.16290			−0.578357			−0.289179	+	0.957275i	$0.593382\pi$
$252$		0			0
$253$			4.68035i			0.294251i
$254$	−2.49693	+	4.32481i	−0.156671	+	0.271363i
$255$	0.666537	+	2.31737i	0.0417401	+	0.145120i
$256$	−13.8402	−	23.9719i	−0.865011	−	1.49824i
$257$	4.39800	+	2.53919i	0.274340	+	0.158390i	0.630858	−	0.775898i	$-0.282703\pi$
$257$	4.39800	+	2.53919i	0.274340	+	0.158390i	−0.356518	+	0.934288i	$0.616036\pi$
$258$		−	17.6742i		−	1.10035i
$259$		0			0
$260$	2.65368	−	10.6803i	0.164574	−	0.662367i
$261$	3.34017	−	5.78535i	0.206752	−	0.358104i
$262$	−3.46410	+	2.00000i	−0.214013	+	0.123560i
$263$	4.90155	−	2.82991i	0.302243	−	0.174500i	−0.341207	−	0.939988i	$-0.610836\pi$
$263$	4.90155	−	2.82991i	0.302243	−	0.174500i	0.643450	+	0.765488i	$0.277502\pi$
$264$	9.04945	−	15.6741i	0.556955	−	0.964674i
$265$	2.02666	−	8.15676i	0.124497	−	0.501066i
$266$		0			0
$267$		−	8.34017i		−	0.510410i
$268$	−21.6453	−	12.4969i	−1.32220	−	0.763371i
$269$	13.9288	+	24.1254i	0.849255	+	1.47095i	0.881875	+	0.471484i	$0.156282\pi$
$269$	13.9288	+	24.1254i	0.849255	+	1.47095i	−0.0326200	+	0.999468i	$0.510385\pi$
$270$	−1.67458	−	5.82208i	−0.101912	−	0.354321i
$271$	12.5597	−	21.7541i	0.762948	−	1.32146i	−0.178377	−	0.983962i	$-0.557085\pi$
$271$	12.5597	−	21.7541i	0.762948	−	1.32146i	0.941325	−	0.337502i	$-0.109582\pi$
$272$			14.9216i			0.904756i
$273$		0			0
$274$	12.0267			0.726557
$275$	−8.47185	+	5.31298i	−0.510872	+	0.320385i
$276$	6.24846	+	10.8227i	0.376113	+	0.651447i
$277$	24.4200	−	14.0989i	1.46726	−	0.847121i	0.467928	−	0.883767i	$-0.345001\pi$
$277$	24.4200	−	14.0989i	1.46726	−	0.847121i	0.999328	+	0.0366462i	$0.0116675\pi$
$278$	−31.9143	−	18.4257i	−1.91409	−	1.10510i
$279$	−7.75872			−0.464503
$280$		0			0
$281$	−20.3545			−1.21425			−0.607125	−	0.794606i	$-0.707677\pi$
$281$	−20.3545			−1.21425			−0.607125	+	0.794606i	$0.707677\pi$
$282$	−10.9815	−	6.34017i	−0.653939	−	0.377552i
$283$	−20.3667	+	11.7587i	−1.21068	+	0.698984i	−0.962906	−	0.269836i	$-0.913031\pi$
$283$	−20.3667	+	11.7587i	−1.21068	+	0.698984i	−0.247769	+	0.968819i	$0.579697\pi$
$284$	5.34017	+	9.24945i	0.316881	+	0.548854i
$285$	−4.95544	−	4.77763i	−0.293535	−	0.283002i
$286$	4.99386			0.295293
$287$		0			0
$288$		−	19.3896i		−	1.14254i
$289$	−7.91855	+	13.7153i	−0.465797	+	0.806784i
$290$	−38.8935	+	11.1868i	−2.28391	+	0.656911i
$291$	4.21953	+	7.30845i	0.247354	+	0.428429i
$292$	−32.7356	−	18.8999i	−1.91570	−	1.10603i
$293$			2.92162i			0.170683i	0.996352	+	0.0853415i	$0.0271981\pi$
$293$			2.92162i			0.170683i	−0.996352	+	0.0853415i	$0.972802\pi$
$294$		0			0
$295$	−22.8371	−	5.67420i	−1.32963	−	0.330365i
$296$	49.0349	−	84.9309i	2.85010	−	4.93651i
$297$	1.73205	−	1.00000i	0.100504	−	0.0580259i
$298$	−36.7764	+	21.2329i	−2.13040	+	1.22999i
$299$	−1.07838	+	1.86781i	−0.0623642	+	0.108018i
$300$	−12.4969	+	23.5958i	−0.721511	+	1.36231i
$301$		0			0
$302$			15.8310i			0.910969i
$303$	5.03731	+	2.90829i	0.289386	+	0.167077i
$304$	−21.2979	−	36.8891i	−1.22152	−	2.11573i
$305$	2.56926	+	8.93264i	0.147115	+	0.511481i
$306$	−1.46081	+	2.53020i	−0.0835090	+	0.144642i
$307$		−	10.4703i		−	0.597570i	−0.954321	−	0.298785i	$-0.903419\pi$
$307$		−	10.4703i		−	0.597570i	0.954321	−	0.298785i	$-0.0965813\pi$
$308$		0			0
$309$	2.15676			0.122694
$310$	33.8379	+	32.6237i	1.92186	+	1.85290i
$311$	11.9155	+	20.6382i	0.675665	+	1.17029i	0.976274	+	0.216538i	$0.0694767\pi$
$311$	11.9155	+	20.6382i	0.675665	+	1.17029i	−0.300609	+	0.953747i	$0.597190\pi$
$312$	7.22280	−	4.17009i	0.408911	−	0.236085i
$313$	28.3646	+	16.3763i	1.60326	+	0.925643i	0.990829	+	0.135118i	$0.0431415\pi$
$313$	28.3646	+	16.3763i	1.60326	+	0.925643i	0.612431	+	0.790524i	$0.290192\pi$
$314$	−13.3340			−0.752483
$315$		0			0
$316$	32.8781			1.84954
$317$	−15.5153	−	8.95774i	−0.871424	−	0.503117i	−0.00360269	−	0.999994i	$-0.501147\pi$
$317$	−15.5153	−	8.95774i	−0.871424	−	0.503117i	−0.867821	+	0.496877i	$0.834480\pi$
$318$	8.81910	−	5.09171i	0.494550	−	0.285529i
$319$	−6.68035	−	11.5707i	−0.374028	−	0.647835i
$320$	−38.5789	+	40.0147i	−2.15663	+	2.23689i
$321$	16.4969			0.920769
$322$		0			0
$323$			3.31965i			0.184710i
$324$	2.67009	−	4.62473i	0.148338	−	0.256929i
$325$	−4.60504	+	0.168312i	−0.255441	+	0.00933629i
$326$	−13.3340	−	23.0952i	−0.738504	−	1.27913i
$327$	11.1173	+	6.41855i	0.614786	+	0.354947i
$328$			58.7936i			3.24633i
$329$		0			0
$330$	−11.7587	−	2.92162i	−0.647296	−	0.160830i
$331$	0.680346	−	1.17839i	0.0373952	−	0.0647704i	−0.846722	−	0.532035i	$-0.821427\pi$
$331$	0.680346	−	1.17839i	0.0373952	−	0.0647704i	0.884117	+	0.467265i	$0.154761\pi$
$332$	31.6197	−	18.2557i	1.73536	−	1.00191i
$333$	9.38521	−	5.41855i	0.514306	−	0.296935i
$334$	−26.0144	+	45.0582i	−1.42344	+	2.46548i
$335$	−2.52359	+	10.1568i	−0.137878	+	0.554923i
$336$		0			0
$337$			25.3607i			1.38148i	0.723101	+	0.690742i	$0.242716\pi$
$337$			25.3607i			1.38148i	−0.723101	+	0.690742i	$0.757284\pi$
$338$	−28.5090	−	16.4597i	−1.55069	−	0.895288i
$339$	2.61757	+	4.53376i	0.142167	+	0.246240i
$340$	12.3752	−	3.55942i	0.671138	−	0.193037i
$341$	−7.75872	+	13.4385i	−0.420158	+	0.727736i
$342$		−	8.34017i		−	0.450985i
$343$		0			0
$344$	−59.0349			−3.18295
$345$	3.63194	−	3.76711i	0.195537	−	0.202814i
$346$	30.3968	+	52.6488i	1.63414	+	2.83042i
$347$	−14.6044	+	8.43188i	−0.784008	+	0.452647i	−0.837849	−	0.545902i	$-0.816187\pi$
$347$	−14.6044	+	8.43188i	−0.784008	+	0.452647i	0.0538410	+	0.998550i	$0.482854\pi$
$348$	−30.8948	−	17.8371i	−1.65613	−	0.956169i
$349$	9.51745			0.509457			0.254729	−	0.967013i	$-0.418014\pi$
$349$	9.51745			0.509457			0.254729	+	0.967013i	$0.418014\pi$
$350$		0			0
$351$	0.921622			0.0491926
$352$	−33.5838	−	19.3896i	−1.79002	−	1.03347i
$353$	31.0035	−	17.8999i	1.65015	−	0.952715i	0.673142	−	0.739514i	$-0.264944\pi$
$353$	31.0035	−	17.8999i	1.65015	−	0.952715i	0.977008	−	0.213201i	$-0.0683889\pi$
$354$	−14.2557	−	24.6915i	−0.757679	−	1.31234i
$355$	3.10399	−	3.21951i	0.164743	−	0.170874i
$356$	−44.5380			−2.36051
$357$		0			0
$358$		−	27.0928i		−	1.43190i
$359$	−11.1568	+	19.3241i	−0.588831	+	1.01989i	0.405555	+	0.914071i	$0.367078\pi$
$359$	−11.1568	+	19.3241i	−0.588831	+	1.01989i	−0.994386	+	0.105815i	$0.966255\pi$
$360$	−19.4468	+	5.59339i	−1.02493	+	0.294798i
$361$	4.76180	+	8.24767i	0.250621	+	0.434088i
$362$	−19.9989	−	11.5464i	−1.05112	−	0.606864i
$363$			7.00000i			0.367405i
$364$		0			0
$365$	−3.81658	+	15.3607i	−0.199769	+	0.804015i
$366$	−5.63090	+	9.75300i	−0.294332	+	0.509798i
$367$	17.5920	−	10.1568i	0.918296	−	0.530178i	0.0352048	−	0.999380i	$-0.488792\pi$
$367$	17.5920	−	10.1568i	0.918296	−	0.530178i	0.883091	+	0.469202i	$0.155458\pi$
$368$	28.0430	−	16.1906i	1.46184	−	0.843994i
$369$	−3.24846	+	5.62651i	−0.169108	+	0.292904i
$370$	−63.7152	−	15.8310i	−3.31240	−	0.823012i
$371$		0			0
$372$			41.4329i			2.14820i
$373$	13.8564	+	8.00000i	0.717458	+	0.414224i	0.813816	−	0.581122i	$-0.197386\pi$
$373$	13.8564	+	8.00000i	0.717458	+	0.414224i	−0.0963587	+	0.995347i	$0.530720\pi$
$374$	2.92162	+	5.06040i	0.151073	+	0.261667i
$375$	10.9417	+	2.29783i	0.565025	+	0.118659i
$376$	−21.1773	+	36.6801i	−1.09213	+	1.89163i
$377$		−	6.15676i		−	0.317089i
$378$		0			0
$379$	−6.15676			−0.316251			−0.158126	−	0.987419i	$-0.550545\pi$
$379$	−6.15676			−0.316251			−0.158126	+	0.987419i	$0.550545\pi$
$380$	−25.5133	+	26.4629i	−1.30881	+	1.35752i
$381$	0.921622	+	1.59630i	0.0472161	+	0.0817808i
$382$	36.0408	−	20.8082i	1.84401	−	1.06464i
$383$	23.2416	+	13.4186i	1.18759	+	0.685656i	0.957758	−	0.287574i	$-0.0928488\pi$
$383$	23.2416	+	13.4186i	1.18759	+	0.685656i	0.229833	+	0.973230i	$0.426182\pi$
$384$	−28.5669			−1.45780
$385$		0			0
$386$	−22.6681			−1.15377
$387$	−5.64960	−	3.26180i	−0.287185	−	0.165806i
$388$	39.0284	−	22.5330i	1.98137	−	1.14394i
$389$	−2.81658	−	4.87846i	−0.142806	−	0.247348i	0.785746	−	0.618549i	$-0.212279\pi$
$389$	−2.81658	−	4.87846i	−0.142806	−	0.247348i	−0.928552	+	0.371201i	$0.878946\pi$
$390$	−4.01944	−	3.87522i	−0.203532	−	0.196229i
$391$	−2.52359			−0.127623
$392$		0			0
$393$			1.47641i			0.0744750i
$394$	15.9288	−	27.5895i	0.802482	−	1.38994i
$395$	−3.80544	−	13.2305i	−0.191473	−	0.665700i
$396$	−5.34017	−	9.24945i	−0.268354	−	0.464802i
$397$	−32.7356	−	18.8999i	−1.64295	−	0.948558i	−0.979777	−	0.200092i	$-0.935876\pi$
$397$	−32.7356	−	18.8999i	−1.64295	−	0.948558i	−0.663173	−	0.748466i	$-0.730791\pi$
$398$		−	61.2183i		−	3.06860i
$399$		0			0
$400$	61.1399	+	32.3812i	3.05700	+	1.61906i
$401$	6.81658	−	11.8067i	0.340404	−	0.589597i	−0.644104	−	0.764938i	$-0.722770\pi$
$401$	6.81658	−	11.8067i	0.340404	−	0.589597i	0.984508	+	0.175341i	$0.0561029\pi$
$402$	−10.9815	+	6.34017i	−0.547708	+	0.316219i
$403$	−6.19261	+	3.57531i	−0.308476	+	0.178099i
$404$	15.5308	−	26.9001i	0.772685	−	1.33833i
$405$	−2.17009	−	0.539189i	−0.107832	−	0.0267925i
$406$		0			0
$407$		−	21.6742i		−	1.07435i
$408$	8.45130	+	4.87936i	0.418402	+	0.241564i
$409$	−6.17727	−	10.6994i	−0.305447	−	0.529049i	0.671914	−	0.740629i	$-0.265472\pi$
$409$	−6.17727	−	10.6994i	−0.305447	−	0.529049i	−0.977361	+	0.211580i	$0.932139\pi$
$410$	37.8257	−	10.8796i	1.86808	−	0.537307i
$411$	2.21953	−	3.84435i	0.109482	−	0.189628i
$412$		−	11.5174i		−	0.567424i
$413$		0			0
$414$	6.34017			0.311603
$415$	−11.0061	−	10.6111i	−0.540266	−	0.520881i
$416$	−8.93495	−	15.4758i	−0.438072	−	0.758763i
$417$	−11.7797	+	6.80098i	−0.576852	+	0.333046i
$418$	−14.4456	−	8.34017i	−0.706558	−	0.407931i
$419$	28.9939			1.41644			0.708221	−	0.705991i	$-0.249498\pi$
$419$	28.9939			1.41644			0.708221	+	0.705991i	$0.249498\pi$
$420$		0			0
$421$	−15.1629			−0.738994			−0.369497	−	0.929232i	$-0.620470\pi$
$421$	−15.1629			−0.738994			−0.369497	+	0.929232i	$0.620470\pi$
$422$	32.0838	+	18.5236i	1.56181	+	0.901714i
$423$	−4.05330	+	2.34017i	−0.197078	+	0.113783i
$424$	−17.0072	−	29.4573i	−0.825942	−	1.43057i
$425$	−2.86470	−	4.56793i	−0.138958	−	0.221577i
$426$	5.41855			0.262530
$427$		0			0
$428$		−	88.0965i		−	4.25830i
$429$	0.921622	−	1.59630i	0.0444963	−	0.0770699i
$430$	10.9243	+	37.9809i	0.526816	+	1.83160i
$431$	5.15676	+	8.93176i	0.248392	+	0.430228i	0.963080	−	0.269216i	$-0.0867645\pi$
$431$	5.15676	+	8.93176i	0.248392	+	0.430228i	−0.714688	+	0.699444i	$0.753431\pi$
$432$	−11.9833	−	6.91855i	−0.576546	−	0.332869i
$433$		−	20.4391i		−	0.982239i	−0.871092	−	0.491120i	$-0.836588\pi$
$433$		−	20.4391i		−	0.982239i	0.871092	−	0.491120i	$-0.163412\pi$
$434$		0			0
$435$	−3.60197	+	14.4969i	−0.172701	+	0.695075i
$436$	34.2762	−	59.3681i	1.64153	−	2.84321i
$437$	6.23879	−	3.60197i	0.298442	−	0.172306i
$438$	−16.6080	+	9.58864i	−0.793561	+	0.458163i
$439$	8.46081	−	14.6546i	0.403812	−	0.699424i	−0.590370	−	0.807133i	$-0.701018\pi$
$439$	8.46081	−	14.6546i	0.403812	−	0.699424i	0.994182	+	0.107709i	$0.0343515\pi$
$440$	−9.75872	+	39.2762i	−0.465229	+	1.87242i
$441$		0			0
$442$			2.69263i			0.128075i
$443$	11.0942	+	6.40522i	0.527100	+	0.304321i	0.739835	−	0.672789i	$-0.234904\pi$
$443$	11.0942	+	6.40522i	0.527100	+	0.304321i	−0.212735	+	0.977110i	$0.568237\pi$
$444$	−28.9360	−	50.1186i	−1.37324	−	2.37852i
$445$	5.15499	+	17.9226i	0.244370	+	0.849611i
$446$	29.3607	−	50.8542i	1.39027	−	2.40802i
$447$			15.6742i			0.741364i
$448$		0			0
$449$	14.6270			0.690292			0.345146	−	0.938549i	$-0.387829\pi$
$449$	14.6270			0.690292			0.345146	+	0.938549i	$0.387829\pi$
$450$	7.19716	+	11.4763i	0.339278	+	0.540997i
$451$	6.49693	+	11.2530i	0.305928	+	0.529884i
$452$	24.2111	−	13.9783i	1.13879	−	0.657482i
$453$	5.06040	+	2.92162i	0.237758	+	0.137270i
$454$	31.2039			1.46447
$455$		0			0
$456$	−27.8576			−1.30455
$457$	12.2601	+	7.07838i	0.573504	+	0.331113i	0.758548	−	0.651618i	$-0.225909\pi$
$457$	12.2601	+	7.07838i	0.573504	+	0.331113i	−0.185044	+	0.982730i	$0.559243\pi$
$458$	30.1197	−	17.3896i	1.40740	−	0.812564i
$459$	0.539189	+	0.933903i	0.0251672	+	0.0435908i
$460$	−20.1170	−	19.3952i	−0.937960	−	0.904304i
$461$	−0.340173			−0.0158434			−0.00792172	−	0.999969i	$-0.502522\pi$
$461$	−0.340173			−0.0158434			−0.00792172	+	0.999969i	$0.502522\pi$
$462$		0			0
$463$		−	9.84324i		−	0.457454i	−0.973491	−	0.228727i	$-0.926544\pi$
$463$		−	9.84324i		−	0.457454i	0.973491	−	0.228727i	$-0.0734564\pi$
$464$	−46.2183	+	80.0525i	−2.14563	+	3.71634i
$465$	16.6731	−	4.79560i	0.773195	−	0.222391i
$466$	−9.16394	−	15.8724i	−0.424511	−	0.735275i
$467$	9.97440	+	5.75872i	0.461560	+	0.266482i	0.712700	−	0.701469i	$-0.247472\pi$
$467$	9.97440	+	5.75872i	0.461560	+	0.266482i	−0.251140	+	0.967951i	$0.580805\pi$
$468$		−	4.92162i		−	0.227502i
$469$		0			0
$470$	27.5174	+	6.83710i	1.26929	+	0.315372i
$471$	−2.46081	+	4.26225i	−0.113388	+	0.196394i
$472$	−82.4739	+	47.6163i	−3.79617	+	2.19172i
$473$	−11.2992	+	6.52359i	−0.519537	+	0.299955i
$474$	8.34017	−	14.4456i	0.383077	−	0.663509i
$475$	13.6020	+	7.20394i	0.624101	+	0.330539i
$476$		0			0
$477$		−	3.75872i		−	0.172100i
$478$	−54.8112	−	31.6453i	−2.50701	−	1.44742i
$479$	9.75872	+	16.9026i	0.445887	+	0.772300i	0.998114	−	0.0613946i	$-0.0195548\pi$
$479$	9.75872	+	16.9026i	0.445887	+	0.772300i	−0.552226	+	0.833694i	$0.686221\pi$
$480$	11.9846	+	41.6672i	0.547018	+	1.90184i
$481$	4.99386	−	8.64961i	0.227700	−	0.394388i
$482$			39.7731i			1.81162i
$483$		0			0
$484$	37.3812			1.69915
$485$	−13.5848	−	13.0974i	−0.616856	−	0.594722i
$486$	−1.35464	−	2.34630i	−0.0614476	−	0.106430i
$487$	−20.0490	+	11.5753i	−0.908508	+	0.524527i	−0.879951	−	0.475065i	$-0.842425\pi$
$487$	−20.0490	+	11.5753i	−0.908508	+	0.524527i	−0.0285570	+	0.999592i	$0.509091\pi$
$488$	32.5767	+	18.8082i	1.47468	+	0.851406i
$489$	−9.84324			−0.445127
$490$		0			0
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$	30.0465	+	17.3474i	1.35460	+	0.782079i
$493$	6.23879	−	3.60197i	0.280981	−	0.162224i
$494$	−3.84324	−	6.65669i	−0.172916	−	0.299499i
$495$	−3.10399	+	3.21951i	−0.139514	+	0.144706i
$496$	107.358			4.82053
$497$		0			0
$498$		−	18.5236i		−	0.830062i
$499$	13.6020	−	23.5593i	0.608908	−	1.05466i	−0.382513	−	0.923950i	$-0.624941\pi$
$499$	13.6020	−	23.5593i	0.608908	−	1.05466i	0.991421	−	0.130709i	$-0.0417254\pi$
$500$	12.2708	−	58.4304i	0.548768	−	2.61309i
$501$	9.60197	+	16.6311i	0.428984	+	0.743023i
$502$	21.4989	+	12.4124i	0.959544	+	0.553993i
$503$			18.8371i			0.839905i	0.907546	+	0.419952i	$0.137953\pi$
$503$			18.8371i			0.839905i	−0.907546	+	0.419952i	$0.862047\pi$
$504$		0			0
$505$	−12.6225	−	3.13624i	−0.561693	−	0.139561i
$506$	6.34017	−	10.9815i	0.281855	−	0.488187i
$507$	−10.5227	+	6.07531i	−0.467331	+	0.269814i
$508$	8.52450	−	4.92162i	0.378214	−	0.218362i
$509$	−3.40522	+	5.89801i	−0.150934	+	0.261425i	−0.931571	−	0.363560i	$-0.881561\pi$
$509$	−3.40522	+	5.89801i	−0.150934	+	0.261425i	0.780637	+	0.624984i	$0.214895\pi$
$510$	1.57531	−	6.34017i	0.0697557	−	0.280748i
$511$		0			0
$512$			17.8599i			0.789303i
$513$	−2.66595	−	1.53919i	−0.117705	−	0.0679568i
$514$	−6.87936	−	11.9154i	−0.303436	−	0.525566i
$515$	−4.63475	+	1.33307i	−0.204231	+	0.0587422i
$516$	−17.4186	+	30.1698i	−0.766809	+	1.32815i
$517$			9.36069i			0.411683i
$518$		0			0
$519$	22.4391			0.984966
$520$	−12.9439	+	13.4256i	−0.567628	+	0.588753i
$521$	−12.9083	−	22.3578i	−0.565523	−	0.979514i	−0.997001	−	0.0773904i	$-0.975341\pi$
$521$	−12.9083	−	22.3578i	−0.565523	−	0.979514i	0.431478	−	0.902123i	$-0.357992\pi$
$522$	−15.6741	+	9.04945i	−0.686037	+	0.396084i
$523$	3.46410	+	2.00000i	0.151475	+	0.0874539i	0.573822	−	0.818980i	$-0.305460\pi$
$523$	3.46410	+	2.00000i	0.151475	+	0.0874539i	−0.422347	+	0.906434i	$0.638794\pi$
$524$	7.88428			0.344426
$525$		0			0
$526$	−15.3340			−0.668595
$527$	−7.24589	−	4.18342i	−0.315636	−	0.182233i
$528$	−23.9666	+	13.8371i	−1.04301	+	0.602183i
$529$	−8.76180	−	15.1759i	−0.380948	−	0.659821i
$530$	−15.8046	+	16.3928i	−0.686508	+	0.712058i
$531$	−10.5236			−0.456685
$532$		0			0
$533$			5.98771i			0.259357i
$534$	−11.2979	+	19.5686i	−0.488908	+	0.846814i
$535$	−35.4510	+	10.1966i	−1.53268	+	0.440838i
$536$	21.1773	+	36.6801i	0.914719	+	1.58434i
$537$	−8.66025	−	5.00000i	−0.373718	−	0.215766i
$538$		−	75.4740i		−	3.25391i
$539$		0			0
$540$	−2.87936	+	11.5886i	−0.123908	+	0.498696i
$541$	−12.9421	+	22.4164i	−0.556426	+	0.963758i	0.441365	+	0.897328i	$0.354494\pi$
$541$	−12.9421	+	22.4164i	−0.556426	+	0.963758i	−0.997791	+	0.0664306i	$0.978839\pi$
$542$	−58.9377	+	34.0277i	−2.53159	+	1.46162i
$543$	−7.38165	+	4.26180i	−0.316777	+	0.182891i
$544$	10.4547	−	18.1080i	0.448240	−	0.776375i
$545$	−27.8576	−	6.92162i	−1.19329	−	0.296490i
$546$		0			0
$547$		−	11.3197i		−	0.483993i	−0.970277	−	0.241997i	$-0.922198\pi$
$547$		−	11.3197i		−	0.483993i	0.970277	−	0.241997i	$-0.0778023\pi$
$548$	−20.5295	−	11.8527i	−0.876976	−	0.506322i
$549$	2.07838	+	3.59986i	0.0887030	+	0.153638i
$550$	27.0747	−	0.989569i	1.15447	−	0.0421954i
$551$	−10.2823	+	17.8095i	−0.438041	+	0.758710i
$552$		−	21.1773i		−	0.901365i
$553$		0			0
$554$	−76.3956			−3.24574
$555$	−16.8191	+	17.4451i	−0.713932	+	0.740503i
$556$	36.3184	+	62.9054i	1.54024	+	2.66778i
$557$	23.0788	−	13.3246i	0.977882	−	0.564580i	0.0762519	−	0.997089i	$-0.475705\pi$
$557$	23.0788	−	13.3246i	0.977882	−	0.564580i	0.901630	+	0.432508i	$0.142371\pi$
$558$	18.2043	+	10.5103i	0.770650	+	0.444935i
$559$	−6.01229			−0.254293
$560$		0			0
$561$	2.15676			0.0910583
$562$	47.7579	+	27.5730i	2.01455	+	1.16310i
$563$	−40.1442	+	23.1773i	−1.69188	+	0.976806i	−0.738875	+	0.673843i	$0.764642\pi$
$563$	−40.1442	+	23.1773i	−1.69188	+	0.976806i	−0.953002	+	0.302963i	$0.902024\pi$
$564$	12.4969	+	21.6453i	0.526216	+	0.911432i
$565$	−8.42728	−	8.12490i	−0.354539	−	0.341817i
$566$	63.7152			2.67815
$567$		0			0
$568$		−	18.0989i		−	0.759413i
$569$	−7.18342	+	12.4420i	−0.301145	+	0.521598i	−0.976395	−	0.215990i	$-0.930702\pi$
$569$	−7.18342	+	12.4420i	−0.301145	+	0.521598i	0.675251	+	0.737588i	$0.264035\pi$
$570$	5.15499	+	17.9226i	0.215919	+	0.750694i
$571$	−19.3607	−	33.5337i	−0.810220	−	1.40334i	−0.912710	−	0.408608i	$-0.866014\pi$
$571$	−19.3607	−	33.5337i	−0.810220	−	1.40334i	0.102490	−	0.994734i	$-0.467319\pi$
$572$	−8.52450	−	4.92162i	−0.356427	−	0.205783i
$573$		−	15.3607i		−	0.641702i
$574$		0			0
$575$	−5.47641	+	10.3402i	−0.228382	+	0.431215i
$576$	−12.4288	+	21.5273i	−0.517867	+	0.896972i
$577$	37.6496	−	21.7370i	1.56737	−	0.904922i	0.570898	−	0.821021i	$-0.306595\pi$
$577$	37.6496	−	21.7370i	1.56737	−	0.904922i	0.996474	−	0.0839011i	$-0.0267380\pi$
$578$	37.1586	−	21.4535i	1.54559	−	0.892349i
$579$	−4.18342	+	7.24589i	−0.173857	+	0.301129i
$580$	77.4161	+	19.2351i	3.21453	+	0.798695i
$581$		0			0
$582$		−	22.8638i		−	0.947733i
$583$	−6.51030	−	3.75872i	−0.269629	−	0.155670i
$584$	32.0277	+	55.4736i	1.32532	+	2.29551i
$585$	−1.98052	+	0.569647i	−0.0818842	+	0.0235520i
$586$	3.95774	−	6.85501i	0.163493	−	0.283178i
$587$			36.0288i			1.48707i	0.668699	+	0.743533i	$0.266851\pi$
$587$			36.0288i			1.48707i	−0.668699	+	0.743533i	$0.733149\pi$
$588$		0			0
$589$	23.8843			0.984135
$590$	45.8962	+	44.2494i	1.88952	+	1.82172i
$591$	−5.87936	−	10.1834i	−0.241845	−	0.418887i
$592$	−129.864	+	74.9770i	−5.33738	+	3.08154i
$593$	27.2679	+	15.7431i	1.11976	+	0.646493i	0.941339	−	0.337462i	$-0.109568\pi$
$593$	27.2679	+	15.7431i	1.11976	+	0.646493i	0.178419	+	0.983955i	$0.442902\pi$
$594$	−5.41855			−0.222326
$595$		0			0
$596$	83.7030			3.42861
$597$	−19.5686	−	11.2979i	−0.800888	−	0.462393i
$598$	5.06040	−	2.92162i	0.206935	−	0.119474i
$599$	14.5174	+	25.1450i	0.593167	+	1.02740i	0.993803	+	0.111158i	$0.0354559\pi$
$599$	14.5174	+	25.1450i	0.593167	+	1.02740i	−0.400636	+	0.916237i	$0.631211\pi$
$600$	38.3328	−	24.0398i	1.56493	−	0.981420i
$601$	−15.3607			−0.626576			−0.313288	−	0.949658i	$-0.601430\pi$
$601$	−15.3607			−0.626576			−0.313288	+	0.949658i	$0.601430\pi$
$602$		0			0
$603$			4.68035i			0.190598i
$604$	15.6020	−	27.0234i	0.634835	−	1.09957i
$605$	−4.32664	−	15.0426i	−0.175903	−	0.611569i
$606$	−7.87936	−	13.6475i	−0.320077	−	0.554390i
$607$	11.2992	+	6.52359i	0.458620	+	0.264784i	0.711464	−	0.702723i	$-0.248033\pi$
$607$	11.2992	+	6.52359i	0.458620	+	0.264784i	−0.252844	+	0.967507i	$0.581366\pi$
$608$			59.6886i			2.42069i
$609$		0			0
$610$	6.07223	−	24.4391i	0.245858	−	0.989509i
$611$	−2.15676	+	3.73561i	−0.0872530	+	0.151127i
$612$	4.98720	−	2.87936i	0.201596	−	0.116391i
$613$	−13.4385	+	7.75872i	−0.542776	+	0.313372i	−0.746203	−	0.665718i	$-0.768125\pi$
$613$	−13.4385	+	7.75872i	−0.542776	+	0.313372i	0.203427	+	0.979090i	$0.434792\pi$
$614$	−14.1834	+	24.5664i	−0.572396	+	0.991419i
$615$	3.50307	−	14.0989i	0.141257	−	0.568522i
$616$		0			0
$617$			22.7649i			0.916479i	0.888829	+	0.458240i	$0.151520\pi$
$617$			22.7649i			0.916479i	−0.888829	+	0.458240i	$0.848480\pi$
$618$	−5.06040	−	2.92162i	−0.203559	−	0.117525i
$619$	−3.96388	−	6.86565i	−0.159322	−	0.275954i	0.775302	−	0.631590i	$-0.217597\pi$
$619$	−3.96388	−	6.86565i	−0.159322	−	0.275954i	−0.934624	+	0.355637i	$0.884264\pi$
$620$	−25.6094	−	89.0371i	−1.02850	−	3.57581i
$621$	1.17009	−	2.02665i	0.0469540	−	0.0813266i
$622$		−	64.5646i		−	2.58881i
$623$		0			0
$624$	−12.7526			−0.510512
$625$	−24.9333	+	1.82504i	−0.997332	+	0.0730017i
$626$	−44.3679	−	76.8474i	−1.77330	−	3.07144i
$627$	−5.33191	+	3.07838i	−0.212936	+	0.122939i
$628$	22.7612	+	13.1412i	0.908269	+	0.524389i
$629$	11.6865			0.465971
$630$		0			0
$631$	19.2039			0.764497			0.382248	−	0.924060i	$-0.375150\pi$
$631$	19.2039			0.764497			0.382248	+	0.924060i	$0.375150\pi$
$632$	−48.2508	−	27.8576i	−1.91931	−	1.10812i
$633$	11.8422	−	6.83710i	0.470685	−	0.271750i
$634$	24.2690	+	42.0351i	0.963844	+	1.66943i
$635$	−2.96717	−	2.86071i	−0.117749	−	0.113524i
$636$	−20.0722			−0.795916
$637$		0			0
$638$			36.1978i			1.43308i
$639$	1.00000	−	1.73205i	0.0395594	−	0.0685189i
$640$	61.3887	−	17.6570i	2.42660	−	0.697953i
$641$	2.97334	+	5.14997i	0.117440	+	0.203412i	0.918752	−	0.394834i	$-0.129198\pi$
$641$	2.97334	+	5.14997i	0.117440	+	0.203412i	−0.801313	+	0.598246i	$0.795865\pi$
$642$	−38.7068	−	22.3474i	−1.52763	−	0.881980i
$643$			30.8904i			1.21820i	0.793094	+	0.609100i	$0.208469\pi$
$643$			30.8904i			1.21820i	−0.793094	+	0.609100i	$0.791531\pi$
$644$		0			0
$645$	14.1568	+	3.51745i	0.557422	+	0.138499i
$646$	4.49693	−	7.78891i	0.176929	−	0.306451i
$647$	−16.6311	+	9.60197i	−0.653836	+	0.377492i	−0.789924	−	0.613204i	$-0.789880\pi$
$647$	−16.6311	+	9.60197i	−0.653836	+	0.377492i	0.136088	+	0.990697i	$0.456547\pi$
$648$	−7.83705	+	4.52472i	−0.307868	+	0.177748i
$649$	−10.5236	+	18.2274i	−0.413087	+	0.715488i
$650$	11.0328	+	5.84324i	0.432742	+	0.229191i
$651$		0			0
$652$			52.5646i			2.05859i
$653$	24.7292	+	14.2774i	0.967727	+	0.558718i	0.898543	−	0.438886i	$-0.144627\pi$
$653$	24.7292	+	14.2774i	0.967727	+	0.558718i	0.0691846	+	0.997604i	$0.477960\pi$
$654$	−17.3896	−	30.1197i	−0.679988	−	1.17777i
$655$	−0.912557	−	3.17272i	−0.0356565	−	0.123969i
$656$	44.9493	−	77.8545i	1.75498	−	3.03971i
$657$			7.07838i			0.276154i
$658$		0			0
$659$	27.9877			1.09025			0.545123	−	0.838356i	$-0.316483\pi$
$659$	27.9877			1.09025			0.545123	+	0.838356i	$0.316483\pi$
$660$	17.1927	+	16.5758i	0.669227	+	0.645214i
$661$	−11.0722	−	19.1777i	−0.430660	−	0.745925i	0.566270	−	0.824220i	$-0.308386\pi$
$661$	−11.0722	−	19.1777i	−0.430660	−	0.745925i	−0.996930	+	0.0782946i	$0.975053\pi$
$662$	−3.19259	+	1.84324i	−0.124084	+	0.0716397i
$663$	0.860705	+	0.496928i	0.0334270	+	0.0192991i
$664$	−61.8720			−2.40110
$665$		0			0
$666$	−29.3607			−1.13770
$667$	−13.5387	−	7.81658i	−0.524221	−	0.302659i
$668$	88.8129	−	51.2762i	3.43628	−	1.98393i
$669$	−10.8371	−	18.7704i	−0.418987	−	0.725706i
$670$	19.6798	−	20.4123i	0.760298	−	0.788594i
$671$	8.31351			0.320940
$672$		0			0
$673$			2.21008i			0.0851923i	0.999092	+	0.0425962i	$0.0135629\pi$
$673$			2.21008i			0.0851923i	−0.999092	+	0.0425962i	$0.986437\pi$
$674$	34.3545	−	59.5038i	1.32329	−	2.29200i
$675$	4.99666	−	0.182626i	0.192322	−	0.00702928i
$676$	32.4432	+	56.1932i	1.24781	+	2.16128i
$677$	−16.9296	−	9.77432i	−0.650658	−	0.375658i	0.138050	−	0.990425i	$-0.455916\pi$
$677$	−16.9296	−	9.77432i	−0.650658	−	0.375658i	−0.788708	+	0.614768i	$0.789250\pi$
$678$		−	14.1834i		−	0.544711i
$679$		0			0
$680$	−21.1773	−	5.26180i	−0.812111	−	0.201781i
$681$	5.75872	−	9.97440i	0.220675	−	0.382220i
$682$	36.4086	−	21.0205i	1.39416	−	0.804917i
$683$	10.2335	−	5.90829i	0.391572	−	0.226074i	−0.291269	−	0.956641i	$-0.594077\pi$
$683$	10.2335	−	5.90829i	0.391572	−	0.226074i	0.682841	+	0.730567i	$0.260744\pi$
$684$	−8.21953	+	14.2367i	−0.314282	+	0.544352i
$685$	−2.39350	+	9.63317i	−0.0914508	+	0.368064i
$686$		0			0
$687$		−	12.8371i		−	0.489766i
$688$	78.1740	+	45.1338i	2.98036	+	1.72071i
$689$	−1.73206	−	3.00002i	−0.0659863	−	0.114292i
$690$	−13.6247	+	3.91881i	−0.518683	+	0.149187i
$691$	5.87936	−	10.1834i	0.223661	−	0.387393i	−0.732256	−	0.681030i	$-0.761532\pi$
$691$	5.87936	−	10.1834i	0.223661	−	0.387393i	0.955917	+	0.293637i	$0.0948657\pi$
$692$		−	119.829i		−	4.55520i
$693$		0			0
$694$	45.6886			1.73431
$695$	21.1102	−	21.8958i	0.800755	−	0.830557i
$696$	30.2267	+	52.3542i	1.14574	+	1.98448i
$697$	−6.06750	+	3.50307i	−0.229823	+	0.132688i
$698$	−22.3308	−	12.8927i	−0.845233	−	0.487996i
$699$	−6.76487			−0.255871
$700$		0			0
$701$	9.94668			0.375681			0.187840	−	0.982200i	$-0.439851\pi$
$701$	9.94668			0.375681			0.187840	+	0.982200i	$0.439851\pi$
$702$	−2.16240	−	1.24846i	−0.0816147	−	0.0471202i
$703$	−28.8912	+	16.6803i	−1.08965	+	0.629111i
$704$	24.8576	+	43.0547i	0.936857	+	1.62268i
$705$	7.26387	−	7.53421i	0.273573	−	0.283755i
$706$	−96.9914			−3.65032
$707$		0			0
$708$			56.1978i			2.11204i
$709$	−5.52359	+	9.56714i	−0.207443	+	0.359301i	−0.950908	−	0.309473i	$-0.899847\pi$
$709$	−5.52359	+	9.56714i	−0.207443	+	0.359301i	0.743465	+	0.668774i	$0.233181\pi$
$710$	−11.6442	+	3.34916i	−0.436998	+	0.125692i
$711$	−3.07838	−	5.33191i	−0.115448	−	0.199962i
$712$	65.3624	+	37.7370i	2.44956	+	1.41425i
$713$			18.1568i			0.679976i
$714$		0			0
$715$	−0.993857	+	4.00000i	−0.0371681	+	0.149592i
$716$	−26.7009	+	46.2473i	−0.997858	+	1.72834i
$717$	−20.2310	+	11.6803i	−0.755539	+	0.436211i
$718$	52.3542	−	30.2267i	1.95384	−	1.12805i
$719$	3.07838	−	5.33191i	0.114804	−	0.198847i	−0.802897	−	0.596117i	$-0.796709\pi$
$719$	3.07838	−	5.33191i	0.114804	−	0.198847i	0.917701	+	0.397271i	$0.130043\pi$
$720$	30.0277	+	7.46081i	1.11907	+	0.278048i
$721$		0			0
$722$		−	25.8020i		−	0.960252i
$723$	12.7136	+	7.34017i	0.472822	+	0.272984i
$724$	22.7587	+	39.4193i	0.845821	+	1.46501i
$725$	−1.22001	−	33.3794i	−0.0453099	−	1.23968i
$726$	9.48246	−	16.4241i	0.351927	−	0.609556i
$727$			2.89043i			0.107200i	0.998562	+	0.0536000i	$0.0170696\pi$
$727$			2.89043i			0.107200i	−0.998562	+	0.0536000i	$0.982930\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	29.7630	−	30.8707i	1.10158	−	1.14258i
$731$	−3.51745	−	6.09240i	−0.130097	−	0.225335i
$732$	19.2239	−	11.0989i	0.710534	−	0.410227i
$733$	−22.3432	−	12.8999i	−0.825267	−	0.476468i	0.0269626	−	0.999636i	$-0.491417\pi$
$733$	−22.3432	−	12.8999i	−0.825267	−	0.476468i	−0.852229	+	0.523168i	$0.824750\pi$
$734$	−55.0349			−2.03138
$735$		0			0
$736$	−45.3751			−1.67255
$737$	8.10660	+	4.68035i	0.298610	+	0.172403i
$738$	15.2438	−	8.80098i	0.561130	−	0.323969i
$739$	−0.523590	−	0.906885i	−0.0192606	−	0.0333603i	0.856234	−	0.516587i	$-0.172798\pi$
$739$	−0.523590	−	0.906885i	−0.0192606	−	0.0333603i	−0.875495	+	0.483227i	$0.839465\pi$
$740$	93.1598	+	89.8170i	3.42462	+	3.30174i
$741$	−2.83710			−0.104224
$742$		0			0
$743$		−	9.97334i		−	0.365886i	−0.983123	−	0.182943i	$-0.941438\pi$
$743$		−	9.97334i		−	0.365886i	0.983123	−	0.182943i	$-0.0585624\pi$
$744$	35.1061	−	60.8055i	1.28705	−	2.22924i
$745$	−9.68810	−	33.6830i	−0.354944	−	1.23405i
$746$	−21.6742	−	37.5408i	−0.793549	−	1.37447i
$747$	−5.92110	−	3.41855i	−0.216642	−	0.125078i
$748$		−	11.5174i		−	0.421120i
$749$		0			0
$750$	−22.5597	−	20.2134i	−0.823764	−	0.738089i
$751$	−1.63317	+	2.82872i	−0.0595950	+	0.103222i	−0.894284	−	0.447501i	$-0.852314\pi$
$751$	−1.63317	+	2.82872i	−0.0595950	+	0.103222i	0.834689	+	0.550722i	$0.185648\pi$
$752$	56.0859	−	32.3812i	2.04524	−	1.18082i
$753$	7.93530	−	4.58145i	0.289179	−	0.166957i
$754$	−8.34017	+	14.4456i	−0.303731	+	0.526078i
$755$	−12.6803	−	3.15061i	−0.461485	−	0.114663i
$756$		0			0
$757$			49.9877i			1.81683i	0.418065	+	0.908417i	$0.362708\pi$
$757$			49.9877i			1.81683i	−0.418065	+	0.908417i	$0.637292\pi$
$758$	14.4456	+	8.34017i	0.524688	+	0.302929i
$759$	−2.34017	−	4.05330i	−0.0849429	−	0.147125i
$760$	59.8645	−	17.2186i	2.17151	−	0.624583i
$761$	1.30632	−	2.26262i	0.0473542	−	0.0820198i	−0.841377	−	0.540449i	$-0.818254\pi$
$761$	1.30632	−	2.26262i	0.0473542	−	0.0820198i	0.888731	+	0.458429i	$0.151588\pi$
$762$		−	4.99386i		−	0.180908i
$763$		0			0
$764$	−82.0288			−2.96770
$765$	−1.73592	−	1.67364i	−0.0627625	−	0.0605104i
$766$	−36.3545	−	62.9679i	−1.31354	−	2.27512i
$767$	−8.39939	+	4.84939i	−0.303284	+	0.175101i
$768$	23.9719	+	13.8402i	0.865011	+	0.499414i
$769$	−15.6742			−0.565226			−0.282613	−	0.959234i	$-0.591201\pi$
$769$	−15.6742			−0.565226			−0.282613	+	0.959234i	$0.591201\pi$
$770$		0			0
$771$	−5.07838			−0.182893
$772$	38.6943	+	22.3402i	1.39264	+	0.804040i
$773$	−5.03338	+	2.90602i	−0.181038	+	0.104522i	−0.587780	−	0.809021i	$-0.699998\pi$
$773$	−5.03338	+	2.90602i	−0.181038	+	0.104522i	0.406742	+	0.913543i	$0.366665\pi$
$774$	8.83710	+	15.3063i	0.317643	+	0.550174i
$775$	−32.8654	+	20.6110i	−1.18056	+	0.740368i
$776$	−76.3689			−2.74148
$777$		0			0
$778$			15.2618i			0.547162i
$779$	10.0000	−	17.3205i	0.358287	−	0.620572i
$780$	3.04202	+	10.5763i	0.108922	+	0.378692i
$781$	−2.00000	−	3.46410i	−0.0715656	−	0.123955i
$782$	5.92110	+	3.41855i	0.211738	+	0.122247i
$783$			6.68035i			0.238736i
$784$		0			0
$785$	2.65368	−	10.6803i	0.0947140	−	0.381198i
$786$	2.00000	−	3.46410i	0.0713376	−	0.123560i
$787$	34.0767	−	19.6742i	1.21470	−	0.701310i	0.250924	−	0.968007i	$-0.419266\pi$
$787$	34.0767	−	19.6742i	1.21470	−	0.701310i	0.963780	+	0.266697i	$0.0859324\pi$
$788$	−54.3809	+	31.3968i	−1.93724	+	1.11847i
$789$	−2.82991	+	4.90155i	−0.100748	+	0.174500i
$790$	−8.99386	+	36.1978i	−0.319987	+	1.28786i
$791$		0			0
$792$			18.0989i			0.643116i
$793$	3.31771	+	1.91548i	0.117815	+	0.0680207i
$794$	51.2050	+	88.6896i	1.81720	+	3.14748i
$795$	2.32324	+	8.07729i	0.0823967	+	0.286472i
$796$	−60.3328	+	104.499i	−2.13844	+	3.70389i
$797$			28.2823i			1.00181i	0.865502	+	0.500905i	$0.167000\pi$
$797$			28.2823i			1.00181i	−0.865502	+	0.500905i	$0.833000\pi$
$798$		0			0
$799$	−5.04718			−0.178556
$800$	−51.5083	−	82.1330i	−1.82110	−	2.90384i
$801$	4.17009	+	7.22280i	0.147343	+	0.255205i
$802$	−31.9875	+	18.4680i	−1.12952	+	0.652128i
$803$	12.2601	+	7.07838i	0.432650	+	0.249791i
$804$	24.9939			0.881465
$805$		0			0
$806$	19.3730			0.682384
$807$	−24.1254	−	13.9288i	−0.849255	−	0.490317i
$808$	−45.5849	+	26.3184i	−1.60367	+	0.925879i
$809$	−7.83710	−	13.5743i	−0.275538	−	0.477245i	0.694733	−	0.719268i	$-0.255523\pi$
$809$	−7.83710	−	13.5743i	−0.275538	−	0.477245i	−0.970271	+	0.242022i	$0.922189\pi$
$810$	4.36127	+	4.20478i	0.153239	+	0.147741i
$811$	42.1666			1.48067			0.740335	−	0.672238i	$-0.234667\pi$
$811$	42.1666			1.48067			0.740335	+	0.672238i	$0.234667\pi$
$812$		0			0
$813$			25.1194i			0.880976i
$814$	−29.3607	+	50.8542i	−1.02909	+	1.78244i
$815$	21.1526	−	6.08403i	0.740943	−	0.213114i
$816$	−7.46081	−	12.9225i	−0.261181	−	0.452378i
$817$	17.3916	+	10.0410i	0.608455	+	0.351291i
$818$			33.4719i			1.17032i
$819$		0			0
$820$	−75.2905	−	18.7070i	−2.62926	−	0.653277i
$821$	19.5236	−	33.8159i	0.681378	−	1.18018i	−0.293182	−	0.956057i	$-0.594714\pi$
$821$	19.5236	−	33.8159i	0.681378	−	1.18018i	0.974560	−	0.224125i	$-0.0719523\pi$
$822$	−10.4154	+	6.01333i	−0.363279	+	0.209739i
$823$	−31.6659	+	18.2823i	−1.10380	+	0.637281i	−0.937217	−	0.348745i	$-0.886608\pi$
$823$	−31.6659	+	18.2823i	−1.10380	+	0.637281i	−0.166586	+	0.986027i	$0.553274\pi$
$824$	−9.75872	+	16.9026i	−0.339961	+	0.588830i
$825$	4.68035	−	8.83710i	0.162949	−	0.307668i
$826$		0			0
$827$		−	50.2245i		−	1.74648i	−0.487294	−	0.873238i	$-0.662016\pi$
$827$		−	50.2245i		−	1.74648i	0.487294	−	0.873238i	$-0.337984\pi$
$828$	−10.8227	−	6.24846i	−0.376113	−	0.217149i
$829$	−16.4186	−	28.4378i	−0.570240	−	0.987684i	−0.996541	−	0.0831031i	$-0.973517\pi$
$829$	−16.4186	−	28.4378i	−0.570240	−	0.987684i	0.426301	−	0.904581i	$-0.359816\pi$
$830$	11.4493	+	39.8062i	0.397410	+	1.38169i
$831$	−14.0989	+	24.4200i	−0.489085	+	0.847121i
$832$			22.9093i			0.794238i
$833$		0			0
$834$	36.8515			1.27606
$835$	−30.9136	−	29.8044i	−1.06981	−	1.03142i
$836$	16.4391	+	28.4733i	0.568557	+	0.984770i
$837$	6.71925	−	3.87936i	0.232251	−	0.134090i
$838$	−68.0283	−	39.2762i	−2.35000	−	1.35677i
$839$	−13.3607			−0.461262			−0.230631	−	0.973041i	$-0.574079\pi$
$839$	−13.3607			−0.461262			−0.230631	+	0.973041i	$0.574079\pi$
$840$		0			0
$841$	15.6270			0.538863
$842$	35.5767	+	20.5402i	1.22606	+	0.707863i
$843$	17.6276	−	10.1773i	0.607125	−	0.350524i
$844$	−36.5113	−	63.2394i	−1.25677	−	2.17679i
$845$	18.8577	−	19.5595i	0.648724	−	0.672868i
$846$	12.6803			0.435959
$847$		0			0
$848$			52.0098i			1.78603i
$849$	11.7587	−	20.3667i	0.403558	−	0.698984i
$850$	0.533565	+	14.5984i	0.0183011	+	0.500720i
$851$	−12.6803	−	21.9630i	−0.434677	−	0.752882i
$852$	−9.24945	−	5.34017i	−0.316881	−	0.182951i
$853$			39.6430i			1.35735i	0.734438	+	0.678675i	$0.237446\pi$
$853$			39.6430i			1.35735i	−0.734438	+	0.678675i	$0.762554\pi$
$854$		0			0
$855$	6.68035	+	1.65983i	0.228463	+	0.0567649i
$856$	−74.6441	+	129.287i	−2.55128	+	4.41895i
$857$	−25.7256	+	14.8527i	−0.878771	+	0.507359i	−0.870253	−	0.492605i	$-0.836045\pi$
$857$	−25.7256	+	14.8527i	−0.878771	+	0.507359i	−0.00851788	+	0.999964i	$0.502711\pi$
$858$	−4.32481	+	2.49693i	−0.147646	+	0.0852437i
$859$	1.53919	−	2.66595i	0.0525164	−	0.0909612i	−0.838572	−	0.544791i	$-0.816609\pi$
$859$	1.53919	−	2.66595i	0.0525164	−	0.0909612i	0.891089	+	0.453829i	$0.149942\pi$
$860$	18.7838	−	75.5995i	0.640521	−	2.57792i
$861$		0			0
$862$		−	27.9421i		−	0.951713i
$863$	5.53693	+	3.19675i	0.188479	+	0.108819i	0.591270	−	0.806473i	$-0.298627\pi$
$863$	5.53693	+	3.19675i	0.188479	+	0.108819i	−0.402791	+	0.915292i	$0.631960\pi$
$864$	9.69481	+	16.7919i	0.329824	+	0.571272i
$865$	−48.2203	+	13.8694i	−1.63954	+	0.471574i
$866$	−27.6875	+	47.9562i	−0.940861	+	1.62962i
$867$		−	15.8371i		−	0.537856i
$868$		0			0
$869$	−12.3135			−0.417707
$870$	28.0894	−	29.1348i	0.952319	−	0.987762i
$871$	2.15676	+	3.73561i	0.0730789	+	0.126576i
$872$	−100.605	+	58.0843i	−3.40692	+	1.96698i
$873$	−7.30845	−	4.21953i	−0.247354	−	0.142810i
$874$	−19.5174			−0.660188
$875$		0			0
$876$	37.7998			1.27714
$877$	−1.05328	−	0.608111i	−0.0355667	−	0.0205345i	0.482111	−	0.876110i	$-0.339870\pi$
$877$	−1.05328	−	0.608111i	−0.0355667	−	0.0205345i	−0.517678	+	0.855576i	$0.673203\pi$
$878$	−39.7032	+	22.9227i	−1.33992	+	0.773603i
$879$	−1.46081	−	2.53020i	−0.0492719	−	0.0853415i
$880$	42.9502	−	44.5487i	1.44785	−	1.50174i
$881$	−15.9733			−0.538155			−0.269078	−	0.963118i	$-0.586719\pi$
$881$	−15.9733			−0.538155			−0.269078	+	0.963118i	$0.586719\pi$
$882$		0			0
$883$			11.6865i			0.393282i	0.980476	+	0.196641i	$0.0630033\pi$
$883$			11.6865i			0.393282i	−0.980476	+	0.196641i	$0.936997\pi$
$884$	2.65368	−	4.59632i	0.0892531	−	0.154591i
$885$	22.6146	−	6.50455i	0.760182	−	0.218648i
$886$	−17.3535	−	30.0572i	−0.583002	−	1.00979i
$887$	22.1883	+	12.8104i	0.745011	+	0.430132i	0.823889	−	0.566752i	$-0.191800\pi$
$887$	22.1883	+	12.8104i	0.745011	+	0.430132i	−0.0788773	+	0.996884i	$0.525134\pi$
$888$			98.0698i			3.29101i
$889$		0			0
$890$	12.1834	−	49.0349i	0.408389	−	1.64365i
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	−100.237	+	57.8720i	−3.35619	+	1.93770i
$893$	12.4776	−	7.20394i	0.417546	−	0.241071i
$894$	21.2329	−	36.7764i	0.710133	−	1.22999i
$895$	21.7009	+	5.39189i	0.725380	+	0.180231i
$896$		0			0
$897$		−	2.15676i		−	0.0720120i
$898$	−34.3194	−	19.8143i	−1.14525	−	0.661212i
$899$	−25.9155	−	44.8869i	−0.864330	−	1.49706i
$900$	−0.975255	−	26.6830i	−0.0325085	−	0.889435i
$901$	2.02666	−	3.51028i	0.0675179	−	0.116944i
$902$		−	35.2039i		−	1.17216i
$903$		0			0
$904$	−47.3751			−1.57567
$905$	13.2286	−	13.7209i	0.439732	−	0.456098i
$906$	−7.91548	−	13.7100i	−0.262974	−	0.455485i
$907$	50.0184	−	28.8781i	1.66083	−	0.958883i	0.688516	−	0.725221i	$-0.258263\pi$
$907$	50.0184	−	28.8781i	1.66083	−	0.958883i	0.972318	−	0.233662i	$-0.0750708\pi$
$908$	−53.2650	−	30.7526i	−1.76766	−	1.02056i
$909$	−5.81658			−0.192924
$910$		0			0
$911$	−35.9877			−1.19233			−0.596163	−	0.802863i	$-0.703309\pi$
$911$	−35.9877			−1.19233			−0.596163	+	0.802863i	$0.703309\pi$
$912$	36.8891	+	21.2979i	1.22152	+	0.705244i
$913$	−11.8422	+	6.83710i	−0.391920	+	0.226275i
$914$	−19.1773	−	33.2160i	−0.634328	−	1.09869i
$915$	−6.69136	−	6.45126i	−0.221210	−	0.213272i
$916$	−68.5523			−2.26503
$917$		0			0
$918$		−	2.92162i		−	0.0964279i
$919$	23.3607	−	40.4619i	0.770598	−	1.33472i	−0.166637	−	0.986018i	$-0.553291\pi$
$919$	23.3607	−	40.4619i	0.770598	−	1.33472i	0.937236	−	0.348697i	$-0.113376\pi$
$920$	13.0895	+	45.5088i	0.431548	+	1.50038i
$921$	5.23513	+	9.06752i	0.172504	+	0.298785i
$922$	0.798148	+	0.460811i	0.0262856	+	0.0151760i
$923$		−	1.84324i		−	0.0606711i
$924$		0			0
$925$	25.3607	−	47.8843i	0.833854	−	1.57443i
$926$	−13.3340	+	23.0952i	−0.438183	+	0.758956i
$927$	−1.86781	+	1.07838i	−0.0613468	+	0.0354186i
$928$	112.176	−	64.7647i	3.68235	−	2.12601i
$929$	26.5246	−	45.9420i	0.870245	−	1.50731i	0.00850190	−	0.999964i	$-0.497294\pi$
$929$	26.5246	−	45.9420i	0.870245	−	1.50731i	0.861743	−	0.507345i	$-0.169373\pi$
$930$	−45.6163	−	11.3340i	−1.49582	−	0.371657i
$931$		0			0
$932$			36.1256i			1.18333i
$933$	−20.6382	−	11.9155i	−0.675665	−	0.390095i
$934$	−15.6020	−	27.0234i	−0.510512	−	0.884233i
$935$	−4.63475	+	1.33307i	−0.151572	+	0.0435962i
$936$	−4.17009	+	7.22280i	−0.136304	+	0.236085i
$937$		−	16.1256i		−	0.526799i	−0.964687	−	0.263400i	$-0.915156\pi$
$937$		−	16.1256i		−	0.526799i	0.964687	−	0.263400i	$-0.0848437\pi$
$938$		0			0
$939$	−32.7526			−1.06884
$940$	−40.2340	−	38.7903i	−1.31229	−	1.26520i
$941$	12.3535	+	21.3969i	0.402713	+	0.697519i	0.994052	−	0.108904i	$-0.0347340\pi$
$941$	12.3535	+	21.3969i	0.402713	+	0.697519i	−0.591340	+	0.806423i	$0.701401\pi$
$942$	11.5476	−	6.66701i	0.376241	−	0.217223i
$943$	13.1670	+	7.60197i	0.428776	+	0.247554i
$944$	145.616			4.73940
$945$		0			0
$946$	35.3484			1.14928
$947$	−5.66204	−	3.26898i	−0.183992	−	0.106228i	0.405175	−	0.914239i	$-0.367211\pi$
$947$	−5.66204	−	3.26898i	−0.183992	−	0.106228i	−0.589167	+	0.808011i	$0.700544\pi$
$948$	−28.4733	+	16.4391i	−0.924770	+	0.533916i
$949$	3.26180	+	5.64960i	0.105882	+	0.183394i
$950$	−22.1556	−	35.3283i	−0.718822	−	1.14620i
$951$	17.9155			0.580949
$952$		0			0
$953$			6.11327i			0.198028i	0.995086	+	0.0990142i	$0.0315689\pi$
$953$			6.11327i			0.198028i	−0.995086	+	0.0990142i	$0.968431\pi$
$954$	−5.09171	+	8.81910i	−0.164850	+	0.285529i
$955$	9.49432	+	33.0093i	0.307229	+	1.06816i
$956$	62.3751	+	108.037i	2.01735	+	3.49416i
$957$	11.5707	+	6.68035i	0.374028	+	0.215945i
$958$		−	52.8781i		−	1.70842i
$959$		0			0
$960$	13.4030	−	53.9432i	0.432578	−	1.74101i
$961$	−14.5989	+	25.2860i	−0.470932	+	0.815678i
$962$	−23.4342	+	13.5297i	−0.755548	+	0.436216i
$963$	−14.2868	+	8.24846i	−0.460384	+	0.265803i
$964$	39.1978	−	67.8926i	1.26248	−	2.18667i
$965$	4.51130	−	18.1568i	0.145224	−	0.584487i
$966$		0			0
$967$			25.6209i			0.823912i	0.911204	+	0.411956i	$0.135154\pi$
$967$			25.6209i			0.823912i	−0.911204	+	0.411956i	$0.864846\pi$
$968$	−54.8594	−	31.6731i	−1.76325	−	1.01801i
$969$	−1.65983	−	2.87490i	−0.0533213	−	0.0923552i
$970$	14.1319	+	49.1330i	0.453748	+	1.57756i
$971$	2.02666	−	3.51028i	0.0650387	−	0.112650i	−0.831672	−	0.555267i	$-0.812616\pi$
$971$	2.02666	−	3.51028i	0.0650387	−	0.112650i	0.896711	+	0.442616i	$0.145950\pi$
$972$			5.34017i			0.171286i
$973$		0			0
$974$	62.7214			2.00972
$975$	3.90392	−	2.44828i	0.125026	−	0.0784077i
$976$	−28.7587	−	49.8116i	−0.920544	−	1.59443i
$977$	3.30133	−	1.90602i	0.105619	−	0.0609791i	−0.446260	−	0.894903i	$-0.647244\pi$
$977$	3.30133	−	1.90602i	0.105619	−	0.0609791i	0.551879	+	0.833924i	$0.313911\pi$
$978$	23.0952	+	13.3340i	0.738504	+	0.426375i
$979$	16.6803			0.533106
$980$		0			0
$981$	−12.8371			−0.409857
$982$	−4.69260	−	2.70928i	−0.149747	−	0.0864565i
$983$	−20.7846	+	12.0000i	−0.662926	+	0.382741i	−0.793391	−	0.608712i	$-0.791686\pi$
$983$	−20.7846	+	12.0000i	−0.662926	+	0.382741i	0.130465	+	0.991453i	$0.458353\pi$
$984$	−29.3968	−	50.9168i	−0.937136	−	1.62317i
$985$	18.9287	+	18.2495i	0.603118	+	0.581477i
$986$	−19.5174			−0.621562
$987$		0			0
$988$			15.1506i			0.482005i
$989$	−7.63317	+	13.2210i	−0.242721	+	0.420404i
$990$	11.6442	−	3.34916i	0.370076	−	0.106443i
$991$	21.2039	+	36.7263i	0.673565	+	1.16665i	0.976886	+	0.213761i	$0.0685713\pi$
$991$	21.2039	+	36.7263i	0.673565	+	1.16665i	−0.303321	+	0.952888i	$0.598095\pi$
$992$	−130.284	−	75.2194i	−4.13651	−	2.38822i
$993$			1.36069i			0.0431803i
$994$		0			0
$995$	49.0349	+	12.1834i	1.55451	+	0.386240i
$996$	−18.2557	+	31.6197i	−0.578452	+	1.00191i
$997$	37.6496	−	21.7370i	1.19237	−	0.688417i	0.233529	−	0.972350i	$-0.424973\pi$
$997$	37.6496	−	21.7370i	1.19237	−	0.688417i	0.958844	+	0.283933i	$0.0916392\pi$
$998$	−63.8286	+	36.8515i	−2.02046	+	1.16651i
$999$	−5.41855	+	9.38521i	−0.171435	+	0.296935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.q.f.79.1		12
5.4	even	2	inner	735.2.q.f.79.6		12
7.2	even	3		735.2.d.b.589.6		6
7.3	odd	6		735.2.q.e.214.6		12
7.4	even	3	inner	735.2.q.f.214.6		12
7.5	odd	6		105.2.d.b.64.6	yes	6
7.6	odd	2		735.2.q.e.79.1		12
21.2	odd	6		2205.2.d.l.1324.1		6
21.5	even	6		315.2.d.e.64.1		6
28.19	even	6		1680.2.t.k.1009.3		6
35.2	odd	12		3675.2.a.bi.1.1		3
35.4	even	6	inner	735.2.q.f.214.1		12
35.9	even	6		735.2.d.b.589.1		6
35.12	even	12		525.2.a.j.1.1		3
35.19	odd	6		105.2.d.b.64.1	✓	6
35.23	odd	12		3675.2.a.bj.1.3		3
35.24	odd	6		735.2.q.e.214.1		12
35.33	even	12		525.2.a.k.1.3		3
35.34	odd	2		735.2.q.e.79.6		12
84.47	odd	6		5040.2.t.v.1009.1		6
105.44	odd	6		2205.2.d.l.1324.6		6
105.47	odd	12		1575.2.a.x.1.3		3
105.68	odd	12		1575.2.a.w.1.1		3
105.89	even	6		315.2.d.e.64.6		6
140.19	even	6		1680.2.t.k.1009.6		6
140.47	odd	12		8400.2.a.dg.1.2		3
140.103	odd	12		8400.2.a.dj.1.2		3
420.299	odd	6		5040.2.t.v.1009.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.b.64.1	✓	6	35.19	odd	6
105.2.d.b.64.6	yes	6	7.5	odd	6
315.2.d.e.64.1		6	21.5	even	6
315.2.d.e.64.6		6	105.89	even	6
525.2.a.j.1.1		3	35.12	even	12
525.2.a.k.1.3		3	35.33	even	12
735.2.d.b.589.1		6	35.9	even	6
735.2.d.b.589.6		6	7.2	even	3
735.2.q.e.79.1		12	7.6	odd	2
735.2.q.e.79.6		12	35.34	odd	2
735.2.q.e.214.1		12	35.24	odd	6
735.2.q.e.214.6		12	7.3	odd	6
735.2.q.f.79.1		12	1.1	even	1	trivial
735.2.q.f.79.6		12	5.4	even	2	inner
735.2.q.f.214.1		12	35.4	even	6	inner
735.2.q.f.214.6		12	7.4	even	3	inner
1575.2.a.w.1.1		3	105.68	odd	12
1575.2.a.x.1.3		3	105.47	odd	12
1680.2.t.k.1009.3		6	28.19	even	6
1680.2.t.k.1009.6		6	140.19	even	6
2205.2.d.l.1324.1		6	21.2	odd	6
2205.2.d.l.1324.6		6	105.44	odd	6
3675.2.a.bi.1.1		3	35.2	odd	12
3675.2.a.bj.1.3		3	35.23	odd	12
5040.2.t.v.1009.1		6	84.47	odd	6
5040.2.t.v.1009.2		6	420.299	odd	6
8400.2.a.dg.1.2		3	140.47	odd	12
8400.2.a.dj.1.2		3	140.103	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.34630 - 1.35464i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.67009 + 4.62473i) q^{4} +(1.55199 - 1.60976i) q^{5} +2.70928 q^{6} -9.04945i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.34630 - 1.35464i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.67009 + 4.62473i) q^{4} +(1.55199 - 1.60976i) q^{5} +2.70928 q^{6} -9.04945i q^{8} +(0.500000 - 0.866025i) q^{9} +(-5.82208 + 1.67458i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-4.62473 - 2.67009i) q^{12} -0.921622i q^{13} +(-0.539189 + 2.17009i) q^{15} +(-6.91855 + 11.9833i) q^{16} +(0.933903 - 0.539189i) q^{17} +(-2.34630 + 1.35464i) q^{18} +(-1.53919 + 2.66595i) q^{19} +(11.5886 + 2.87936i) q^{20} +5.41855i q^{22} +(-2.02665 - 1.17009i) q^{23} +(4.52472 + 7.83705i) q^{24} +(-0.182626 - 4.99666i) q^{25} +(-1.24846 + 2.16240i) q^{26} +1.00000i q^{27} +6.68035 q^{29} +(4.20478 - 4.36127i) q^{30} +(-3.87936 - 6.71925i) q^{31} +(16.7919 - 9.69481i) q^{32} +(1.73205 + 1.00000i) q^{33} -2.92162 q^{34} +5.34017 q^{36} +(9.38521 + 5.41855i) q^{37} +(7.22280 - 4.17009i) q^{38} +(0.460811 + 0.798148i) q^{39} +(-14.5674 - 14.0447i) q^{40} -6.49693 q^{41} -6.52359i q^{43} +(5.34017 - 9.24945i) q^{44} +(-0.618092 - 2.14894i) q^{45} +(3.17009 + 5.49075i) q^{46} +(-4.05330 - 2.34017i) q^{47} -13.8371i q^{48} +(-6.34017 + 11.9711i) q^{50} +(-0.539189 + 0.933903i) q^{51} +(4.26225 - 2.46081i) q^{52} +(3.25515 - 1.87936i) q^{53} +(1.35464 - 2.34630i) q^{54} +(-4.34017 - 1.07838i) q^{55} -3.07838i q^{57} +(-15.6741 - 9.04945i) q^{58} +(-5.26180 - 9.11370i) q^{59} +(-11.4757 + 3.30072i) q^{60} +(-2.07838 + 3.59986i) q^{61} +21.0205i q^{62} -24.8576 q^{64} +(-1.48359 - 1.43035i) q^{65} +(-2.70928 - 4.69260i) q^{66} +(-4.05330 + 2.34017i) q^{67} +(4.98720 + 2.87936i) q^{68} +2.34017 q^{69} +2.00000 q^{71} +(-7.83705 - 4.52472i) q^{72} +(-6.13005 + 3.53919i) q^{73} +(-14.6803 - 25.4271i) q^{74} +(2.65649 + 4.23592i) q^{75} -16.4391 q^{76} -2.49693i q^{78} +(3.07838 - 5.33191i) q^{79} +(8.55260 + 29.7352i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(15.2438 + 8.80098i) q^{82} -6.83710i q^{83} +(0.581449 - 2.34017i) q^{85} +(-8.83710 + 15.3063i) q^{86} +(-5.78535 + 3.34017i) q^{87} +(-15.6741 + 9.04945i) q^{88} +(-4.17009 + 7.22280i) q^{89} +(-1.46081 + 5.87936i) q^{90} -12.4969i q^{92} +(6.71925 + 3.87936i) q^{93} +(6.34017 + 10.9815i) q^{94} +(1.90272 + 6.61526i) q^{95} +(-9.69481 + 16.7919i) q^{96} -8.43907i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{4} + 2 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 10 * q^4 + 2 * q^5 + 4 * q^6 + 6 * q^9	\( 12 q + 10 q^{4} + 2 q^{5} + 4 q^{6} + 6 q^{9} - 12 q^{10} - 12 q^{11} - 26 q^{16} - 12 q^{19} + 60 q^{20} + 18 q^{24} + 2 q^{25} + 20 q^{26} - 8 q^{29} + 10 q^{30} + 4 q^{31} - 48 q^{34} + 20 q^{36} + 12 q^{39} + 4 q^{40} - 8 q^{41} + 20 q^{44} - 2 q^{45} + 16 q^{46} - 32 q^{50} + 2 q^{54} - 8 q^{55} - 32 q^{59} + 8 q^{60} - 12 q^{61} - 52 q^{64} - 32 q^{65} - 4 q^{66} - 16 q^{69} + 24 q^{71} - 88 q^{74} + 8 q^{75} - 8 q^{76} + 24 q^{79} + 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} - 28 q^{89} - 24 q^{90} + 32 q^{94} - 4 q^{95} - 58 q^{96} - 24 q^{99}+O(q^{100}) \) 12 * q + 10 * q^4 + 2 * q^5 + 4 * q^6 + 6 * q^9 - 12 * q^10 - 12 * q^11 - 26 * q^16 - 12 * q^19 + 60 * q^20 + 18 * q^24 + 2 * q^25 + 20 * q^26 - 8 * q^29 + 10 * q^30 + 4 * q^31 - 48 * q^34 + 20 * q^36 + 12 * q^39 + 4 * q^40 - 8 * q^41 + 20 * q^44 - 2 * q^45 + 16 * q^46 - 32 * q^50 + 2 * q^54 - 8 * q^55 - 32 * q^59 + 8 * q^60 - 12 * q^61 - 52 * q^64 - 32 * q^65 - 4 * q^66 - 16 * q^69 + 24 * q^71 - 88 * q^74 + 8 * q^75 - 8 * q^76 + 24 * q^79 + 46 * q^80 - 6 * q^81 + 64 * q^85 + 8 * q^86 - 28 * q^89 - 24 * q^90 + 32 * q^94 - 4 * q^95 - 58 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more