LMFDB - Embedded newform 735.2.q.f.79.6

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			79.6
Root			$-1.16746 + 0.312819i$ of defining polynomial
Character	$\chi$	$=$	735.79
Dual form			735.2.q.f.214.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.34630 + 1.35464i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.67009 + 4.62473i) q^{4} +(0.618092 - 2.14894i) q^{5} +2.70928 q^{6} +9.04945i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(2.34630 + 1.35464i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.67009 + 4.62473i) q^{4} +(0.618092 - 2.14894i) q^{5} +2.70928 q^{6} +9.04945i q^{8} +(0.500000 - 0.866025i) q^{9} +(4.36127 - 4.20478i) 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} +(-4.23592 - 2.65649i) q^{25} +(-1.24846 + 2.16240i) q^{26} -1.00000i q^{27} +6.68035 q^{29} +(1.67458 - 5.82208i) 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} +(19.4468 + 5.59339i) q^{40} -6.49693 q^{41} +6.52359i q^{43} +(5.34017 - 9.24945i) q^{44} +(-1.55199 - 1.60976i) 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} +(8.59637 - 8.28792i) q^{60} +(-2.07838 + 3.59986i) q^{61} -21.0205i q^{62} -24.8576 q^{64} +(1.98052 + 0.569647i) 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} +(-4.99666 - 0.182626i) q^{75} -16.4391 q^{76} +2.49693i q^{78} +(3.07838 - 5.33191i) q^{79} +(21.4751 + 22.2744i) 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} +(4.77763 + 4.95544i) 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	$0.0739454\pi$
$2$	2.34630	+	1.35464i	1.65909	+	0.957873i	0.685948	+	0.727651i	$0.259388\pi$
$3$	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
$5$	0.618092	−	2.14894i	0.276419	−	0.961037i
$5$	0.618092	−	2.14894i	0.276419	−	0.961037i
$6$	2.70928			1.10606
$7$		0			0
$7$		0			0
$8$			9.04945i			3.19946i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	4.36127	−	4.20478i	1.37916	−	1.32967i
$11$	−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	$0.0407935\pi$
$13$			0.921622i			0.255612i	−0.991799	+	0.127806i	$0.959207\pi$
$14$		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	−0.608959	−	0.793202i	$-0.708412\pi$
$17$	−0.933903	+	0.539189i	−0.226505	+	0.130773i	0.382454	+	0.923975i	$0.375079\pi$
$18$	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	0.696183	−	0.717864i	$-0.254880\pi$
$23$	2.02665	+	1.17009i	0.422586	+	0.243980i	−0.273597	+	0.961844i	$0.588214\pi$
$24$	4.52472	+	7.83705i	0.923605	+	1.59973i
$25$	−4.23592	−	2.65649i	−0.847185	−	0.531298i
$26$	−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	$0.287029\pi$
$30$	1.67458	−	5.82208i	0.305735	−	1.06296i
$31$	−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	$-0.983475\pi$
$37$	−9.38521	−	5.41855i	−1.54292	−	0.890804i	−0.544265	−	0.838913i	$-0.683192\pi$
$38$	−7.22280	+	4.17009i	−1.17169	+	0.676477i
$39$	0.460811	+	0.798148i	0.0737888	+	0.127806i
$40$	19.4468	+	5.59339i	3.07480	+	0.884393i
$41$	−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	$0.165719\pi$
$43$			6.52359i			0.994838i	−0.867510	+	0.497419i	$0.834281\pi$
$44$	5.34017	−	9.24945i	0.805061	−	1.39441i
$45$	−1.55199	−	1.60976i	−0.231358	−	0.239968i
$46$	3.17009	+	5.49075i	0.467404	+	0.809567i
$47$	4.05330	+	2.34017i	0.591234	+	0.341349i	0.765585	−	0.643334i	$-0.222449\pi$
$47$	4.05330	+	2.34017i	0.591234	+	0.341349i	−0.174351	+	0.984684i	$0.555783\pi$
$48$			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	−0.706617	−	0.707596i	$-0.749780\pi$
$53$	−3.25515	+	1.87936i	−0.447129	+	0.258150i	0.259488	+	0.965746i	$0.416446\pi$
$54$	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	$-0.406876\pi$
$60$	8.59637	−	8.28792i	1.10979	−	1.06997i
$61$	−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
$65$	1.98052	+	0.569647i	0.245653	+	0.0706561i
$66$	−2.70928	−	4.69260i	−0.333489	−	0.577619i
$67$	4.05330	−	2.34017i	0.495189	−	0.285898i	−0.231535	−	0.972826i	$-0.574375\pi$
$67$	4.05330	−	2.34017i	0.495189	−	0.285898i	0.726725	+	0.686929i	$0.241042\pi$
$68$	−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	−0.0963516	−	0.995347i	$-0.530717\pi$
$73$	6.13005	−	3.53919i	0.717469	−	0.414231i	0.813820	+	0.581117i	$0.197384\pi$
$74$	−14.6803	−	25.4271i	−1.70656	−	2.95584i
$75$	−4.99666	−	0.182626i	−0.576965	−	0.0210878i
$76$	−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	$0.0540895\pi$
$80$	21.4751	+	22.2744i	2.40099	+	2.49035i
$81$	−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	$0.122438\pi$
$83$			6.83710i			0.750469i	−0.926930	+	0.375235i	$0.877562\pi$
$84$		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
$95$	4.77763	+	4.95544i	0.490174	+	0.508417i
$96$	−9.69481	+	16.7919i	−0.989472	+	1.71382i
$97$			8.43907i			0.856858i	0.903576	+	0.428429i	$0.140933\pi$
$97$			8.43907i			0.856858i	−0.903576	+	0.428429i	$0.859067\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	0.975255	−	26.6830i	0.0975255	−	2.66830i
$101$	−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	0.589190	−	0.807995i	$-0.299447\pi$
$103$	1.86781	+	1.07838i	0.184040	+	0.106256i	−0.405149	+	0.914251i	$0.632780\pi$
$104$	−8.34017			−0.817821
$105$		0			0
$106$	−10.1834			−0.989101
$107$	14.2868	+	8.24846i	1.38115	+	0.797409i	0.992296	−	0.123889i	$-0.0395367\pi$
$107$	14.2868	+	8.24846i	1.38115	+	0.797409i	0.388857	+	0.921298i	$0.372870\pi$
$108$	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	$-0.377424\pi$
$110$	−11.6442	−	3.34916i	−1.11023	−	0.319330i
$111$	−10.8371			−1.02861
$112$		0			0
$113$			5.23513i			0.492480i	0.969209	+	0.246240i	$0.0791951\pi$
$113$			5.23513i			0.492480i	−0.969209	+	0.246240i	$0.920805\pi$
$114$	−4.17009	+	7.22280i	−0.390564	+	0.676477i
$115$	3.76711	−	3.63194i	0.351284	−	0.338680i
$116$	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	$0.0260607\pi$
$127$			1.84324i			0.163562i	−0.996650	+	0.0817808i	$0.973939\pi$
$128$	−24.7397	−	14.2834i	−2.18670	−	1.26249i
$129$	3.26180	+	5.64960i	0.287185	+	0.497419i
$130$	3.87522	+	4.01944i	0.339879	+	0.352529i
$131$	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
$135$	−2.14894	−	0.618092i	−0.184952	−	0.0531969i
$136$	−4.87936	−	8.45130i	−0.418402	−	0.724693i
$137$	3.84435	−	2.21953i	0.328445	−	0.189628i	−0.326706	−	0.945126i	$-0.605939\pi$
$137$	3.84435	−	2.21953i	0.328445	−	0.189628i	0.655150	+	0.755498i	$0.272605\pi$
$138$	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
$145$	4.12907	−	14.3557i	0.342900	−	1.19218i
$146$	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	$-0.0552452\pi$
$150$	−11.4763	−	7.19716i	−0.937035	−	0.587646i
$151$	−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	−0.660345	−	0.750963i	$-0.729590\pi$
$157$	−4.26225	+	2.46081i	−0.340165	+	0.196394i	0.320180	+	0.947357i	$0.396257\pi$
$158$	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	0.127511	−	0.991837i	$-0.459301\pi$
$163$	−8.52450	−	4.92162i	−0.667690	−	0.385491i	−0.795201	+	0.606346i	$0.792635\pi$
$164$	−17.3474	−	30.0465i	−1.35460	−	2.34624i
$165$	−3.21951	+	3.10399i	−0.250639	+	0.241645i
$166$	−9.26180	+	16.0419i	−0.718855	+	1.24509i
$167$			19.2039i			1.48605i	0.669266	+	0.743023i	$0.266609\pi$
$167$			19.2039i			1.48605i	−0.669266	+	0.743023i	$0.733391\pi$
$168$		0			0
$169$	12.1506			0.934662
$170$	−1.80583	+	6.27840i	−0.138501	+	0.481532i
$171$	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	0.999675	−	0.0254777i	$-0.00811068\pi$
$173$	19.4328	+	11.2195i	1.47745	+	0.853005i	0.477773	+	0.878483i	$0.341444\pi$
$174$	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	$0.711416\pi$
$180$	3.30072	−	11.4757i	0.246021	−	0.855351i
$181$	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
$185$	−17.4451	+	16.8191i	−1.28259	+	1.23657i
$186$	−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	−0.737577	−	0.675263i	$-0.764030\pi$
$193$	−7.24589	+	4.18342i	−0.521571	+	0.301129i	0.216006	+	0.976392i	$0.430697\pi$
$194$	−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	$-0.862420\pi$
$197$		−	11.7587i		−	0.837774i	0.908038	−	0.418887i	$-0.137580\pi$
$198$	−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	$0.537695\pi$
$200$	24.0398	−	38.3328i	1.69987	−	2.71054i
$201$	2.34017	−	4.05330i	0.165063	−	0.285898i
$202$		−	15.7587i		−	1.10878i
$203$		0			0
$204$	−5.75872			−0.403191
$205$	−4.01570	+	13.9615i	−0.280469	+	0.975116i
$206$	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
$215$	14.0188	+	4.03218i	0.956077	+	0.274992i
$216$	9.04945			0.615737
$217$		0			0
$218$		−	34.7792i		−	2.35555i
$219$	3.53919	−	6.13005i	0.239156	−	0.414231i
$220$	−16.5758	−	17.1927i	−1.11754	−	1.15913i
$221$	−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	$-0.741513\pi$
$223$		−	21.6742i		−	1.45141i	0.688005	−	0.725706i	$-0.258487\pi$
$224$		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	−0.131024	−	0.991379i	$-0.541826\pi$
$227$	9.97440	−	5.75872i	0.662024	−	0.382220i	0.793048	+	0.609159i	$0.208493\pi$
$228$	−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	0.295667	−	0.955291i	$-0.404458\pi$
$233$	−5.85855	−	3.38243i	−0.383806	−	0.221591i	−0.679473	+	0.733701i	$0.737792\pi$
$234$	1.24846	+	2.16240i	0.0816147	+	0.141361i
$235$	7.53421	−	7.26387i	0.491478	−	0.473843i
$236$	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	$0.227375\pi$
$240$	29.7352	+	8.55260i	1.91940	+	0.552068i
$241$	−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
$250$	−29.6440	+	6.22546i	−1.87485	+	0.393732i
$251$	−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
$255$	1.67364	+	1.73592i	0.104807	+	0.108708i
$256$	−13.8402	−	23.9719i	−0.865011	−	1.49824i
$257$	−4.39800	−	2.53919i	−0.274340	−	0.158390i	0.356518	−	0.934288i	$-0.383964\pi$
$257$	−4.39800	−	2.53919i	−0.274340	−	0.158390i	−0.630858	+	0.775898i	$0.717297\pi$
$258$			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	−0.643450	−	0.765488i	$-0.722498\pi$
$263$	−4.90155	+	2.82991i	−0.302243	+	0.174500i	0.341207	+	0.939988i	$0.389164\pi$
$264$	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	$0.510385\pi$
$270$	−4.20478	−	4.36127i	−0.255895	−	0.265419i
$271$	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
$275$	−0.365252	+	9.99333i	−0.0220255	+	0.602620i
$276$	6.24846	+	10.8227i	0.376113	+	0.651447i
$277$	−24.4200	+	14.0989i	−1.46726	+	0.847121i	−0.999328	−	0.0366462i	$-0.988333\pi$
$277$	−24.4200	+	14.0989i	−1.46726	+	0.847121i	−0.467928	+	0.883767i	$0.654999\pi$
$278$	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	0.247769	−	0.968819i	$-0.420303\pi$
$283$	20.3667	−	11.7587i	1.21068	−	0.698984i	0.962906	+	0.269836i	$0.0869694\pi$
$284$	5.34017	+	9.24945i	0.316881	+	0.548854i
$285$	6.61526	+	1.90272i	0.391854	+	0.112707i
$286$	4.99386			0.295293
$287$		0			0
$288$			19.3896i			1.14254i
$289$	−7.91855	+	13.7153i	−0.465797	+	0.806784i
$290$	29.1348	−	28.0894i	1.71085	−	1.64947i
$291$	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	$-0.972802\pi$
$293$		−	2.92162i		−	0.170683i	0.996352	−	0.0853415i	$-0.0271981\pi$
$294$		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
$305$	6.45126	+	6.69136i	0.369398	+	0.383146i
$306$	−1.46081	+	2.53020i	−0.0835090	+	0.144642i
$307$			10.4703i			0.597570i	0.954321	+	0.298785i	$0.0965813\pi$
$307$			10.4703i			0.597570i	−0.954321	+	0.298785i	$0.903419\pi$
$308$		0			0
$309$	2.15676			0.122694
$310$	−45.1719	−	12.9926i	−2.56559	−	0.737931i
$311$	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	$-0.956859\pi$
$313$	−28.3646	−	16.3763i	−1.60326	−	0.925643i	−0.612431	−	0.790524i	$-0.709808\pi$
$314$	−13.3340			−0.752483
$315$		0			0
$316$	32.8781			1.84954
$317$	15.5153	+	8.95774i	0.871424	+	0.503117i	0.867821	−	0.496877i	$-0.165520\pi$
$317$	15.5153	+	8.95774i	0.871424	+	0.503117i	0.00360269	+	0.999994i	$0.498853\pi$
$318$	−8.81910	+	5.09171i	−0.494550	+	0.285529i
$319$	−6.68035	−	11.5707i	−0.374028	−	0.647835i
$320$	−15.3643	+	53.4176i	−0.858890	+	2.98614i
$321$	16.4969			0.920769
$322$		0			0
$323$		−	3.31965i		−	0.184710i
$324$	2.67009	−	4.62473i	0.148338	−	0.256929i
$325$	2.44828	−	3.90392i	0.135806	−	0.216551i
$326$	−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	$-0.757284\pi$
$337$		−	25.3607i		−	1.38148i	0.723101	−	0.690742i	$-0.242716\pi$
$338$	28.5090	+	16.4597i	1.55069	+	0.895288i
$339$	2.61757	+	4.53376i	0.142167	+	0.246240i
$340$	−9.27014	+	8.93751i	−0.502744	+	0.484704i
$341$	−7.75872	+	13.4385i	−0.420158	+	0.727736i
$342$			8.34017i			0.450985i
$343$		0			0
$344$	−59.0349			−3.18295
$345$	1.44644	−	5.02890i	0.0778738	−	0.270747i
$346$	30.3968	+	52.6488i	1.63414	+	2.83042i
$347$	14.6044	−	8.43188i	0.784008	−	0.452647i	−0.0538410	−	0.998550i	$-0.517146\pi$
$347$	14.6044	−	8.43188i	0.784008	−	0.452647i	0.837849	+	0.545902i	$0.183813\pi$
$348$	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	$0.735056\pi$
$353$	−31.0035	+	17.8999i	−1.65015	+	0.952715i	−0.977008	+	0.213201i	$0.931611\pi$
$354$	−14.2557	−	24.6915i	−0.757679	−	1.31234i
$355$	1.23618	−	4.29789i	0.0656098	−	0.228108i
$356$	−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	$0.966255\pi$
$360$	14.5674	−	14.0447i	0.767769	−	0.740220i
$361$	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	−0.883091	−	0.469202i	$-0.844542\pi$
$367$	−17.5920	+	10.1568i	−0.918296	+	0.530178i	−0.0352048	+	0.999380i	$0.511208\pi$
$368$	−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	0.0963587	−	0.995347i	$-0.469280\pi$
$373$	−13.8564	−	8.00000i	−0.717458	−	0.414224i	−0.813816	+	0.581122i	$0.802614\pi$
$374$	2.92162	+	5.06040i	0.151073	+	0.261667i
$375$	−3.48085	+	10.6247i	−0.179750	+	0.548656i
$376$	−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	$0.550545\pi$
$380$	−10.1609	+	35.3266i	−0.521241	+	1.81222i
$381$	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	−0.229833	−	0.973230i	$-0.573818\pi$
$383$	−23.2416	−	13.4186i	−1.18759	−	0.685656i	−0.957758	+	0.287574i	$0.907151\pi$
$384$	−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	$0.878946\pi$
$390$	5.36576	+	1.54333i	0.271706	+	0.0781496i
$391$	−2.52359			−0.127623
$392$		0			0
$393$		−	1.47641i		−	0.0744750i
$394$	15.9288	−	27.5895i	0.802482	−	1.38994i
$395$	−9.55525	−	9.91087i	−0.480777	−	0.498670i
$396$	−5.34017	−	9.24945i	−0.268354	−	0.464802i
$397$	32.7356	+	18.8999i	1.64295	+	0.948558i	0.979777	+	0.200092i	$0.0641241\pi$
$397$	32.7356	+	18.8999i	1.64295	+	0.948558i	0.663173	+	0.748466i	$0.269209\pi$
$398$			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	$0.932139\pi$
$410$	−28.3349	+	27.3182i	−1.39936	+	1.34915i
$411$	2.21953	−	3.84435i	0.109482	−	0.189628i
$412$			11.5174i			0.567424i
$413$		0			0
$414$	6.34017			0.311603
$415$	14.6926	+	4.22596i	0.721229	+	0.207444i
$416$	−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
$425$	5.38829	+	0.196940i	0.261370	+	0.00955299i
$426$	5.41855			0.262530
$427$		0			0
$428$			88.0965i			4.25830i
$429$	0.921622	−	1.59630i	0.0444963	−	0.0770699i
$430$	27.4303	+	28.4511i	1.32280	+	1.37204i
$431$	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	$0.163412\pi$
$433$			20.4391i			0.982239i	−0.871092	+	0.491120i	$0.836588\pi$
$434$		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	0.212735	−	0.977110i	$-0.431763\pi$
$443$	−11.0942	−	6.40522i	−0.527100	−	0.304321i	−0.739835	+	0.672789i	$0.765096\pi$
$444$	−28.9360	−	50.1186i	−1.37324	−	2.37852i
$445$	12.9439	+	13.4256i	0.613600	+	0.636436i
$446$	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	$0.387829\pi$
$450$	−13.5373	−	0.494784i	−0.638156	−	0.0233244i
$451$	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	0.185044	−	0.982730i	$-0.440757\pi$
$457$	−12.2601	−	7.07838i	−0.573504	−	0.331113i	−0.758548	+	0.651618i	$0.774091\pi$
$458$	−30.1197	+	17.3896i	−1.40740	+	0.812564i
$459$	0.539189	+	0.933903i	0.0251672	+	0.0435908i
$460$	26.8552	+	7.72425i	1.25213	+	0.360145i
$461$	−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	$0.0734564\pi$
$463$			9.84324i			0.457454i	−0.973491	+	0.228727i	$0.926544\pi$
$464$	−46.2183	+	80.0525i	−2.14563	+	3.71634i
$465$	−12.4896	+	12.0415i	−0.579194	+	0.558411i
$466$	−9.16394	−	15.8724i	−0.424511	−	0.735275i
$467$	−9.97440	−	5.75872i	−0.461560	−	0.266482i	0.251140	−	0.967951i	$-0.419195\pi$
$467$	−9.97440	−	5.75872i	−0.461560	−	0.266482i	−0.712700	+	0.701469i	$0.752528\pi$
$468$			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	$0.686221\pi$
$480$	30.0926	+	31.2126i	1.37353	+	1.42465i
$481$	4.99386	−	8.64961i	0.227700	−	0.394388i
$482$		−	39.7731i		−	1.81162i
$483$		0			0
$484$	37.3812			1.69915
$485$	18.1351	+	5.21612i	0.823472	+	0.236852i
$486$	−1.35464	−	2.34630i	−0.0614476	−	0.106430i
$487$	20.0490	−	11.5753i	0.908508	−	0.524527i	0.0285570	−	0.999592i	$-0.490909\pi$
$487$	20.0490	−	11.5753i	0.908508	−	0.524527i	0.879951	+	0.475065i	$0.157575\pi$
$488$	−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
$495$	−1.23618	+	4.29789i	−0.0555623	+	0.193176i
$496$	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	$-0.0417254\pi$
$500$	−56.7376	−	18.5883i	−2.53738	−	0.831296i
$501$	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	$-0.862047\pi$
$503$		−	18.8371i		−	0.839905i	0.907546	−	0.419952i	$-0.137953\pi$
$504$		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
$515$	3.47185	−	3.34727i	0.152988	−	0.147498i
$516$	−17.4186	+	30.1698i	−0.766809	+	1.32815i
$517$		−	9.36069i		−	0.411683i
$518$		0			0
$519$	22.4391			0.984966
$520$	−5.15499	+	17.9226i	−0.226061	+	0.785957i
$521$	−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	0.422347	−	0.906434i	$-0.361206\pi$
$523$	−3.46410	−	2.00000i	−0.151475	−	0.0874539i	−0.573822	+	0.818980i	$0.694540\pi$
$524$	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
$530$	−6.29429	+	21.8836i	−0.273406	+	0.950563i
$531$	−10.5236			−0.456685
$532$		0			0
$533$		−	5.98771i		−	0.259357i
$534$	−11.2979	+	19.5686i	−0.488908	+	0.846814i
$535$	26.5560	−	25.6031i	1.14812	−	1.10692i
$536$	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	$0.0778023\pi$
$547$			11.3197i			0.483993i	−0.970277	+	0.241997i	$0.922198\pi$
$548$	20.5295	+	11.8527i	0.876976	+	0.506322i
$549$	2.07838	+	3.59986i	0.0887030	+	0.153638i
$550$	−14.3943	+	22.9526i	−0.613776	+	0.978701i
$551$	−10.2823	+	17.8095i	−0.438041	+	0.758710i
$552$			21.1773i			0.901365i
$553$		0			0
$554$	−76.3956			−3.24574
$555$	−6.69833	+	23.2883i	−0.284328	+	0.988535i
$556$	36.3184	+	62.9054i	1.54024	+	2.66778i
$557$	−23.0788	+	13.3246i	−0.977882	+	0.564580i	−0.901630	−	0.432508i	$-0.857629\pi$
$557$	−23.0788	+	13.3246i	−0.977882	+	0.564580i	−0.0762519	+	0.997089i	$0.524295\pi$
$558$	−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	$-0.235358\pi$
$563$	40.1442	−	23.1773i	1.69188	−	0.976806i	0.953002	−	0.302963i	$-0.0979758\pi$
$564$	12.4969	+	21.6453i	0.526216	+	0.911432i
$565$	11.2500	+	3.23579i	0.473292	+	0.136131i
$566$	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	$0.264035\pi$
$570$	12.9439	+	13.4256i	0.542160	+	0.562338i
$571$	−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	$0.693405\pi$
$577$	−37.6496	+	21.7370i	−1.56737	+	0.904922i	−0.996474	+	0.0839011i	$0.973262\pi$
$578$	−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
$585$	1.48359	−	1.43035i	0.0613388	−	0.0591378i
$586$	3.95774	−	6.85501i	0.163493	−	0.283178i
$587$		−	36.0288i		−	1.48707i	−0.668699	−	0.743533i	$-0.733149\pi$
$587$		−	36.0288i		−	1.48707i	0.668699	−	0.743533i	$-0.266851\pi$
$588$		0			0
$589$	23.8843			0.984135
$590$	−61.2692	−	17.6226i	−2.52241	−	0.725511i
$591$	−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	−0.178419	−	0.983955i	$-0.557098\pi$
$593$	−27.2679	−	15.7431i	−1.11976	−	0.646493i	−0.941339	+	0.337462i	$0.890432\pi$
$594$	−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	$0.631211\pi$
$600$	1.65267	−	45.2170i	0.0674698	−	1.84598i
$601$	−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
$605$	−10.8640	−	11.2683i	−0.441683	−	0.458121i
$606$	−7.87936	−	13.6475i	−0.320077	−	0.554390i
$607$	−11.2992	−	6.52359i	−0.458620	−	0.264784i	0.252844	−	0.967507i	$-0.418634\pi$
$607$	−11.2992	−	6.52359i	−0.458620	−	0.264784i	−0.711464	+	0.702723i	$0.751967\pi$
$608$		−	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	−0.203427	−	0.979090i	$-0.565208\pi$
$613$	13.4385	−	7.75872i	0.542776	−	0.313372i	0.746203	+	0.665718i	$0.231875\pi$
$614$	−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	$-0.848480\pi$
$617$		−	22.7649i		−	0.916479i	0.888829	−	0.458240i	$-0.151520\pi$
$618$	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	$0.884264\pi$
$620$	−64.3037	−	66.6969i	−2.58250	−	2.67861i
$621$	1.17009	−	2.02665i	0.0469540	−	0.0813266i
$622$			64.5646i			2.58881i
$623$		0			0
$624$	−12.7526			−0.510512
$625$	10.8861	+	22.5054i	0.435445	+	0.900216i
$626$	−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
$635$	3.96103	+	1.13929i	0.157189	+	0.0452115i
$636$	−20.0722			−0.795916
$637$		0			0
$638$		−	36.1978i		−	1.43308i
$639$	1.00000	−	1.73205i	0.0395594	−	0.0685189i
$640$	−45.9857	+	44.3357i	−1.81775	+	1.75252i
$641$	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	$-0.791531\pi$
$643$		−	30.8904i		−	1.21820i	0.793094	−	0.609100i	$-0.208469\pi$
$644$		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	−0.136088	−	0.990697i	$-0.543453\pi$
$647$	16.6311	−	9.60197i	0.653836	−	0.377492i	0.789924	+	0.613204i	$0.210120\pi$
$648$	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	−0.0691846	−	0.997604i	$-0.522040\pi$
$653$	−24.7292	−	14.2774i	−0.967727	−	0.558718i	−0.898543	+	0.438886i	$0.855373\pi$
$654$	−17.3896	−	30.1197i	−0.679988	−	1.17777i
$655$	−2.29138	−	2.37666i	−0.0895316	−	0.0928637i
$656$	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	$0.316483\pi$
$660$	−22.9515	−	6.60144i	−0.893385	−	0.256961i
$661$	−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
$670$	7.83762	−	27.2494i	0.302794	−	1.05273i
$671$	8.31351			0.320940
$672$		0			0
$673$		−	2.21008i		−	0.0851923i	−0.999092	−	0.0425962i	$-0.986437\pi$
$673$		−	2.21008i		−	0.0851923i	0.999092	−	0.0425962i	$-0.0135629\pi$
$674$	34.3545	−	59.5038i	1.32329	−	2.29200i
$675$	−2.65649	+	4.23592i	−0.102248	+	0.163041i
$676$	32.4432	+	56.1932i	1.24781	+	2.16128i
$677$	16.9296	+	9.77432i	0.650658	+	0.375658i	0.788708	−	0.614768i	$-0.210750\pi$
$677$	16.9296	+	9.77432i	0.650658	+	0.375658i	−0.138050	+	0.990425i	$0.544084\pi$
$678$			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	−0.682841	−	0.730567i	$-0.739256\pi$
$683$	−10.2335	+	5.90829i	−0.391572	+	0.226074i	0.291269	+	0.956641i	$0.405923\pi$
$684$	−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
$690$	10.2061	−	9.83991i	0.388541	−	0.374599i
$691$	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
$695$	8.40727	−	29.2299i	0.318906	−	1.10875i
$696$	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
$705$	2.89288	−	10.0578i	0.108952	−	0.378799i
$706$	−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	$0.233181\pi$
$710$	8.72254	−	8.40956i	0.327351	−	0.315605i
$711$	−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
$725$	−28.2974	−	17.7463i	−1.05094	−	0.659080i
$726$	9.48246	−	16.4241i	0.351927	−	0.609556i
$727$		−	2.89043i		−	0.107200i	−0.998562	−	0.0536000i	$-0.982930\pi$
$727$		−	2.89043i		−	0.107200i	0.998562	−	0.0536000i	$-0.0170696\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	11.8533	−	41.2109i	0.438711	−	1.52528i
$731$	−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	0.852229	−	0.523168i	$-0.175250\pi$
$733$	22.3432	+	12.8999i	0.825267	+	0.476468i	−0.0269626	+	0.999636i	$0.508583\pi$
$734$	−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	$0.839465\pi$
$740$	−124.364	−	35.7702i	−4.57170	−	1.31494i
$741$	−2.83710			−0.104224
$742$		0			0
$743$			9.97334i			0.365886i	0.983123	+	0.182943i	$0.0585624\pi$
$743$			9.97334i			0.365886i	−0.983123	+	0.182943i	$0.941438\pi$
$744$	35.1061	−	60.8055i	1.28705	−	2.22924i
$745$	−24.3263	−	25.2316i	−0.891246	−	0.924416i
$746$	−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	$-0.637292\pi$
$757$		−	49.9877i		−	1.81683i	0.418065	−	0.908417i	$-0.362708\pi$
$758$	−14.4456	−	8.34017i	−0.524688	−	0.302929i
$759$	−2.34017	−	4.05330i	−0.0849429	−	0.147125i
$760$	−44.8440	+	43.2349i	−1.62666	+	1.56829i
$761$	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
$765$	2.31737	+	0.666537i	0.0837848	+	0.0240987i
$766$	−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	−0.406742	−	0.913543i	$-0.633335\pi$
$773$	5.03338	−	2.90602i	0.181038	−	0.104522i	0.587780	+	0.809021i	$0.300002\pi$
$774$	8.83710	+	15.3063i	0.317643	+	0.550174i
$775$	−1.41695	+	38.7677i	−0.0508982	+	1.39258i
$776$	−76.3689			−2.74148
$777$		0			0
$778$		−	15.2618i		−	0.547162i
$779$	10.0000	−	17.3205i	0.358287	−	0.620572i
$780$	7.63833	+	7.92261i	0.273496	+	0.283675i
$781$	−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	−0.963780	−	0.266697i	$-0.914068\pi$
$787$	−34.0767	+	19.6742i	−1.21470	+	0.701310i	−0.250924	+	0.968007i	$0.580734\pi$
$788$	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
$795$	5.83352	+	6.05063i	0.206894	+	0.214594i
$796$	−60.3328	+	104.499i	−2.13844	+	3.70389i
$797$		−	28.2823i		−	1.00181i	−0.865502	−	0.500905i	$-0.833000\pi$
$797$		−	28.2823i		−	1.00181i	0.865502	−	0.500905i	$-0.167000\pi$
$798$		0			0
$799$	−5.04718			−0.178556
$800$	96.8834	+	3.54105i	3.42535	+	0.125195i
$801$	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	$0.922189\pi$
$810$	−5.82208	−	1.67458i	−0.204567	−	0.0588388i
$811$	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
$815$	−15.8452	+	15.2767i	−0.555034	+	0.535118i
$816$	−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	0.166586	−	0.986027i	$-0.446726\pi$
$823$	31.6659	−	18.2823i	1.10380	−	0.637281i	0.937217	+	0.348745i	$0.113392\pi$
$824$	−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	$0.337984\pi$
$827$			50.2245i			1.74648i	−0.487294	+	0.873238i	$0.662016\pi$
$828$	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	$-0.359816\pi$
$830$	28.7485	+	29.8185i	0.997875	+	1.03501i
$831$	−14.0989	+	24.4200i	−0.489085	+	0.847121i
$832$		−	22.9093i		−	0.794238i
$833$		0			0
$834$	36.8515			1.27606
$835$	41.2682	+	11.8698i	1.42814	+	0.410771i
$836$	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
$845$	7.51020	−	26.1110i	0.258359	−	0.898245i
$846$	12.6803			0.435959
$847$		0			0
$848$		−	52.0098i		−	1.78603i
$849$	11.7587	−	20.3667i	0.403558	−	0.698984i
$850$	12.3758	+	7.76126i	0.424485	+	0.266209i
$851$	−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	$-0.762554\pi$
$853$		−	39.6430i		−	1.35735i	0.734438	−	0.678675i	$-0.237446\pi$
$854$		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	0.00851788	−	0.999964i	$-0.497289\pi$
$857$	25.7256	−	14.8527i	0.878771	−	0.507359i	0.870253	+	0.492605i	$0.163955\pi$
$858$	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	0.402791	−	0.915292i	$-0.368040\pi$
$863$	−5.53693	−	3.19675i	−0.188479	−	0.108819i	−0.591270	+	0.806473i	$0.701373\pi$
$864$	9.69481	+	16.7919i	0.329824	+	0.571272i
$865$	36.1214	−	34.8253i	1.22817	−	1.18410i
$866$	−27.6875	+	47.9562i	−0.940861	+	1.62962i
$867$			15.8371i			0.537856i
$868$		0			0
$869$	−12.3135			−0.417707
$870$	11.1868	−	38.8935i	0.379267	−	1.31861i
$871$	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	0.517678	−	0.855576i	$-0.326797\pi$
$877$	1.05328	+	0.608111i	0.0355667	+	0.0205345i	−0.482111	+	0.876110i	$0.660130\pi$
$878$	39.7032	−	22.9227i	1.33992	−	0.773603i
$879$	−1.46081	−	2.53020i	−0.0492719	−	0.0853415i
$880$	17.1052	−	59.4703i	0.576616	−	2.00474i
$881$	−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	$-0.936997\pi$
$883$		−	11.6865i		−	0.393282i	0.980476	−	0.196641i	$-0.0630033\pi$
$884$	2.65368	−	4.59632i	0.0892531	−	0.154591i
$885$	−16.9404	+	16.3326i	−0.569446	+	0.549013i
$886$	−17.3535	−	30.0572i	−0.583002	−	1.00979i
$887$	−22.1883	−	12.8104i	−0.745011	−	0.430132i	0.0788773	−	0.996884i	$-0.474866\pi$
$887$	−22.1883	−	12.8104i	−0.745011	−	0.430132i	−0.823889	+	0.566752i	$0.808200\pi$
$888$		−	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
$900$	−22.6206	−	14.1861i	−0.754019	−	0.472871i
$901$	2.02666	−	3.51028i	0.0675179	−	0.116944i
$902$			35.2039i			1.17216i
$903$		0			0
$904$	−47.3751			−1.57567
$905$	5.26836	−	18.3167i	0.175126	−	0.608868i
$906$	−7.91548	−	13.7100i	−0.262974	−	0.455485i
$907$	−50.0184	+	28.8781i	−1.66083	+	0.958883i	−0.688516	+	0.725221i	$0.741737\pi$
$907$	−50.0184	+	28.8781i	−1.66083	+	0.958883i	−0.972318	+	0.233662i	$0.924929\pi$
$908$	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
$915$	8.93264	+	2.56926i	0.295304	+	0.0849370i
$916$	−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	$-0.113376\pi$
$920$	32.8670	+	34.0902i	1.08359	+	1.12392i
$921$	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
$935$	3.47185	−	3.34727i	0.113542	−	0.109468i
$936$	−4.17009	+	7.22280i	−0.136304	+	0.236085i
$937$			16.1256i			0.526799i	0.964687	+	0.263400i	$0.0848437\pi$
$937$			16.1256i			0.526799i	−0.964687	+	0.263400i	$0.915156\pi$
$938$		0			0
$939$	−32.7526			−1.06884
$940$	53.7104	+	15.4485i	1.75184	+	0.503875i
$941$	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	0.589167	−	0.808011i	$-0.299456\pi$
$947$	5.66204	+	3.26898i	0.183992	+	0.106228i	−0.405175	+	0.914239i	$0.632789\pi$
$948$	28.4733	−	16.4391i	0.924770	−	0.533916i
$949$	3.26180	+	5.64960i	0.105882	+	0.183394i
$950$	41.6730	+	1.52313i	1.35205	+	0.0494170i
$951$	17.9155			0.580949
$952$		0			0
$953$		−	6.11327i		−	0.198028i	−0.995086	−	0.0990142i	$-0.968431\pi$
$953$		−	6.11327i		−	0.198028i	0.995086	−	0.0990142i	$-0.0315689\pi$
$954$	−5.09171	+	8.81910i	−0.164850	+	0.285529i
$955$	23.8397	+	24.7270i	0.771435	+	0.800146i
$956$	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	$-0.864846\pi$
$967$		−	25.6209i		−	0.823912i	0.911204	−	0.411956i	$-0.135154\pi$
$968$	54.8594	+	31.6731i	1.76325	+	1.01801i
$969$	−1.65983	−	2.87490i	−0.0533213	−	0.0923552i
$970$	35.4844	+	36.8051i	1.13934	+	1.18174i
$971$	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
$975$	0.168312	−	4.60504i	0.00539031	−	0.147479i
$976$	−28.7587	−	49.8116i	−0.920544	−	1.59443i
$977$	−3.30133	+	1.90602i	−0.105619	+	0.0609791i	−0.551879	−	0.833924i	$-0.686089\pi$
$977$	−3.30133	+	1.90602i	−0.105619	+	0.0609791i	0.446260	+	0.894903i	$0.352756\pi$
$978$	−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	−0.130465	−	0.991453i	$-0.541647\pi$
$983$	20.7846	−	12.0000i	0.662926	−	0.382741i	0.793391	+	0.608712i	$0.208314\pi$
$984$	−29.3968	−	50.9168i	−0.937136	−	1.62317i
$985$	−25.2688	−	7.26797i	−0.805132	−	0.231577i
$986$	−19.5174			−0.621562
$987$		0			0
$988$		−	15.1506i		−	0.482005i
$989$	−7.63317	+	13.2210i	−0.242721	+	0.420404i
$990$	−8.72254	+	8.40956i	−0.277221	+	0.267273i
$991$	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	−0.958844	−	0.283933i	$-0.908361\pi$
$997$	−37.6496	+	21.7370i	−1.19237	+	0.688417i	−0.233529	+	0.972350i	$0.575027\pi$
$998$	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.79.6		12
5.4	even	2	inner	735.2.q.f.79.1		12
7.2	even	3		735.2.d.b.589.1		6
7.3	odd	6		735.2.q.e.214.1		12
7.4	even	3	inner	735.2.q.f.214.1		12
7.5	odd	6		105.2.d.b.64.1	✓	6
7.6	odd	2		735.2.q.e.79.6		12
21.2	odd	6		2205.2.d.l.1324.6		6
21.5	even	6		315.2.d.e.64.6		6
28.19	even	6		1680.2.t.k.1009.6		6
35.2	odd	12		3675.2.a.bj.1.3		3
35.4	even	6	inner	735.2.q.f.214.6		12
35.9	even	6		735.2.d.b.589.6		6
35.12	even	12		525.2.a.k.1.3		3
35.19	odd	6		105.2.d.b.64.6	yes	6
35.23	odd	12		3675.2.a.bi.1.1		3
35.24	odd	6		735.2.q.e.214.6		12
35.33	even	12		525.2.a.j.1.1		3
35.34	odd	2		735.2.q.e.79.1		12
84.47	odd	6		5040.2.t.v.1009.2		6
105.44	odd	6		2205.2.d.l.1324.1		6
105.47	odd	12		1575.2.a.w.1.1		3
105.68	odd	12		1575.2.a.x.1.3		3
105.89	even	6		315.2.d.e.64.1		6
140.19	even	6		1680.2.t.k.1009.3		6
140.47	odd	12		8400.2.a.dj.1.2		3
140.103	odd	12		8400.2.a.dg.1.2		3
420.299	odd	6		5040.2.t.v.1009.1		6

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

\(f(q)\)	\(=\)	\(q+(2.34630 + 1.35464i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.67009 + 4.62473i) q^{4} +(0.618092 - 2.14894i) q^{5} +2.70928 q^{6} +9.04945i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(2.34630 + 1.35464i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.67009 + 4.62473i) q^{4} +(0.618092 - 2.14894i) q^{5} +2.70928 q^{6} +9.04945i q^{8} +(0.500000 - 0.866025i) q^{9} +(4.36127 - 4.20478i) 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} +(-4.23592 - 2.65649i) q^{25} +(-1.24846 + 2.16240i) q^{26} -1.00000i q^{27} +6.68035 q^{29} +(1.67458 - 5.82208i) 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} +(19.4468 + 5.59339i) q^{40} -6.49693 q^{41} +6.52359i q^{43} +(5.34017 - 9.24945i) q^{44} +(-1.55199 - 1.60976i) 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} +(8.59637 - 8.28792i) q^{60} +(-2.07838 + 3.59986i) q^{61} -21.0205i q^{62} -24.8576 q^{64} +(1.98052 + 0.569647i) 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} +(-4.99666 - 0.182626i) q^{75} -16.4391 q^{76} +2.49693i q^{78} +(3.07838 - 5.33191i) q^{79} +(21.4751 + 22.2744i) 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} +(4.77763 + 4.95544i) 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