LMFDB - Embedded newform 735.2.q.e.214.6

Newspace parameters

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

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
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			214.6
Root			$-1.16746 - 0.312819i$ of defining polynomial
Character	$\chi$	$=$	735.214
Dual form			735.2.q.e.79.6

$q$-expansion

$f(q)$	$=$	$q+(2.34630 - 1.35464i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.67009 - 4.62473i) q^{4} +(-0.618092 - 2.14894i) q^{5} -2.70928 q^{6} -9.04945i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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	0.685948	−	0.727651i	$-0.259388\pi$
$2$	2.34630	−	1.35464i	1.65909	−	0.957873i	0.973138	−	0.230222i	$-0.0739454\pi$
$3$	−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	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	−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	$-0.291588\pi$
$17$	0.933903	+	0.539189i	0.226505	+	0.130773i	−0.382454	+	0.923975i	$0.624921\pi$
$18$	2.34630	+	1.35464i	0.553029	+	0.319291i
$19$	1.53919	+	2.66595i	0.353114	+	0.611612i	0.986793	−	0.161984i	$-0.0517894\pi$
$19$	1.53919	+	2.66595i	0.353114	+	0.611612i	−0.633679	+	0.773596i	$0.718456\pi$
$20$	−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	$-0.588214\pi$
$23$	2.02665	−	1.17009i	0.422586	−	0.243980i	0.696183	+	0.717864i	$0.254880\pi$
$24$	−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	−0.272832	−	0.962062i	$-0.587960\pi$
$31$	3.87936	−	6.71925i	0.696754	−	1.20681i	0.969586	−	0.244752i	$-0.0787064\pi$
$32$	−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	−0.544265	+	0.838913i	$0.683192\pi$
$37$	−9.38521	+	5.41855i	−1.54292	+	0.890804i	−0.998653	+	0.0518912i	$0.983475\pi$
$38$	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	$-0.330634\pi$
$41$	6.49693			1.01465			0.507325	+	0.861755i	$0.330634\pi$
$42$		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
$45$	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	$-0.777551\pi$
$47$	−4.05330	+	2.34017i	−0.591234	+	0.341349i	0.174351	+	0.984684i	$0.444217\pi$
$48$			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	$-0.416446\pi$
$53$	−3.25515	−	1.87936i	−0.447129	−	0.258150i	−0.706617	+	0.707596i	$0.749780\pi$
$54$	−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	−0.288401	−	0.957510i	$-0.593124\pi$
$59$	5.26180	−	9.11370i	0.685027	−	1.18650i	0.973428	−	0.228992i	$-0.0735431\pi$
$60$	8.59637	+	8.28792i	1.10979	+	1.06997i
$61$	2.07838	+	3.59986i	0.266109	+	0.460914i	0.967854	−	0.251514i	$-0.0809286\pi$
$61$	2.07838	+	3.59986i	0.266109	+	0.460914i	−0.701745	+	0.712429i	$0.747595\pi$
$62$		−	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	0.726725	−	0.686929i	$-0.241042\pi$
$67$	4.05330	+	2.34017i	0.495189	+	0.285898i	−0.231535	+	0.972826i	$0.574375\pi$
$68$	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	$-0.469283\pi$
$73$	−6.13005	−	3.53919i	−0.717469	−	0.414231i	−0.813820	+	0.581117i	$0.802616\pi$
$74$	−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	0.985597	−	0.169111i	$-0.0540895\pi$
$79$	3.07838	+	5.33191i	0.346345	+	0.599886i	−0.639253	+	0.768997i	$0.720756\pi$
$80$	−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	$-0.0209257\pi$
$89$	4.17009	+	7.22280i	0.442028	+	0.765615i	−0.555812	+	0.831308i	$0.687592\pi$
$90$	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	$-0.739882\pi$
$101$	2.90829	−	5.03731i	0.289386	−	0.501231i	0.973663	+	0.227991i	$0.0732156\pi$
$102$	−2.53020	−	1.46081i	−0.250527	−	0.144642i
$103$	−1.86781	+	1.07838i	−0.184040	+	0.106256i	−0.589190	−	0.807995i	$-0.700553\pi$
$103$	−1.86781	+	1.07838i	−0.184040	+	0.106256i	0.405149	+	0.914251i	$0.367220\pi$
$104$	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	$-0.372870\pi$
$107$	14.2868	−	8.24846i	1.38115	−	0.797409i	0.992296	+	0.123889i	$0.0395367\pi$
$108$	−4.62473	−	2.67009i	−0.445014	−	0.256929i
$109$	−6.41855	+	11.1173i	−0.614786	+	1.06484i	0.375636	+	0.926767i	$0.377424\pi$
$109$	−6.41855	+	11.1173i	−0.614786	+	1.06484i	−0.990422	+	0.138073i	$0.955909\pi$
$110$	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	$-0.920805\pi$
$113$		−	5.23513i		−	0.492480i	0.969209	−	0.246240i	$-0.0791951\pi$
$114$	−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	$-0.973939\pi$
$127$		−	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
$130$	3.87522	−	4.01944i	0.339879	−	0.352529i
$131$	−0.738205	−	1.27861i	−0.0644973	−	0.111713i	0.831974	−	0.554815i	$-0.187211\pi$
$131$	−0.738205	−	1.27861i	−0.0644973	−	0.111713i	−0.896471	+	0.443103i	$0.853878\pi$
$132$		−	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	0.655150	−	0.755498i	$-0.272605\pi$
$137$	3.84435	+	2.21953i	0.328445	+	0.189628i	−0.326706	+	0.945126i	$0.605939\pi$
$138$	−5.49075	+	3.17009i	−0.467404	+	0.269856i
$139$	−13.6020			−1.15370			−0.576852	−	0.816849i	$-0.695719\pi$
$139$	−13.6020			−1.15370			−0.576852	+	0.816849i	$0.695719\pi$
$140$		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	0.984977	+	0.172688i	$0.0552452\pi$
$149$	7.83710	+	13.5743i	0.642040	+	1.11205i	−0.342936	+	0.939359i	$0.611421\pi$
$150$	11.4763	−	7.19716i	0.937035	−	0.587646i
$151$	−2.92162	+	5.06040i	−0.237758	+	0.411809i	−0.960071	−	0.279757i	$-0.909746\pi$
$151$	−2.92162	+	5.06040i	−0.237758	+	0.411809i	0.722312	+	0.691567i	$0.243079\pi$
$152$	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	$-0.270410\pi$
$157$	4.26225	+	2.46081i	0.340165	+	0.196394i	−0.320180	+	0.947357i	$0.603743\pi$
$158$	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	$-0.792635\pi$
$163$	−8.52450	+	4.92162i	−0.667690	+	0.385491i	0.127511	+	0.991837i	$0.459301\pi$
$164$	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	$-0.991889\pi$
$173$	−19.4328	+	11.2195i	−1.47745	+	0.853005i	−0.477773	+	0.878483i	$0.658556\pi$
$174$	−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	−0.616417	−	0.787420i	$-0.711416\pi$
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	0.990134	+	0.140122i	$0.0447496\pi$
$180$	−3.30072	−	11.4757i	−0.246021	−	0.855351i
$181$	−8.52359			−0.633553			−0.316777	−	0.948500i	$-0.602601\pi$
$181$	−8.52359			−0.633553			−0.316777	+	0.948500i	$0.602601\pi$
$182$		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	−0.997846	−	0.0655953i	$-0.979105\pi$
$191$	−7.68035	−	13.3027i	−0.555730	−	0.962553i	0.442116	−	0.896958i	$-0.354228\pi$
$192$	21.5273	+	12.4288i	1.55360	+	0.896972i
$193$	−7.24589	−	4.18342i	−0.521571	−	0.301129i	0.216006	−	0.976392i	$-0.430697\pi$
$193$	−7.24589	−	4.18342i	−0.521571	−	0.301129i	−0.737577	+	0.675263i	$0.764030\pi$
$194$	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	0.118145	+	0.992996i	$0.462305\pi$
$199$	−11.2979	+	19.5686i	−0.800888	+	1.38718i	−0.919032	+	0.394182i	$0.871028\pi$
$200$	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	$-0.458174\pi$
$227$	−9.97440	−	5.75872i	−0.662024	−	0.382220i	−0.793048	+	0.609159i	$0.791507\pi$
$228$	−14.2367	−	8.21953i	−0.942845	−	0.544352i
$229$	6.41855	+	11.1173i	0.424150	+	0.734649i	0.996341	−	0.0854716i	$-0.0272397\pi$
$229$	6.41855	+	11.1173i	0.424150	+	0.734649i	−0.572191	+	0.820121i	$0.693906\pi$
$230$	−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	$-0.737792\pi$
$233$	−5.85855	+	3.38243i	−0.383806	+	0.221591i	0.295667	+	0.955291i	$0.404458\pi$
$234$	−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	$-0.676569\pi$
$241$	7.34017	−	12.7136i	0.472822	−	0.818952i	0.999516	+	0.0311030i	$0.00990199\pi$
$242$	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	$-0.406618\pi$
$251$	9.16290			0.578357			0.289179	+	0.957275i	$0.406618\pi$
$252$		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	$-0.616036\pi$
$257$	4.39800	−	2.53919i	0.274340	−	0.158390i	0.630858	+	0.775898i	$0.282703\pi$
$258$			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	$-0.389164\pi$
$263$	−4.90155	−	2.82991i	−0.302243	−	0.174500i	−0.643450	+	0.765488i	$0.722498\pi$
$264$	−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	0.0326200	+	0.999468i	$0.489615\pi$
$269$	−13.9288	+	24.1254i	−0.849255	+	1.47095i	−0.881875	+	0.471484i	$0.843718\pi$
$270$	−4.20478	+	4.36127i	−0.255895	+	0.265419i
$271$	−12.5597	−	21.7541i	−0.762948	−	1.32146i	−0.941325	−	0.337502i	$-0.890418\pi$
$271$	−12.5597	−	21.7541i	−0.762948	−	1.32146i	0.178377	−	0.983962i	$-0.442915\pi$
$272$		−	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	−0.467928	−	0.883767i	$-0.654999\pi$
$277$	−24.4200	−	14.0989i	−1.46726	−	0.847121i	−0.999328	+	0.0366462i	$0.988333\pi$
$278$	−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	$-0.579697\pi$
$283$	−20.3667	−	11.7587i	−1.21068	−	0.698984i	−0.962906	+	0.269836i	$0.913031\pi$
$284$	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	0.300609	+	0.953747i	$0.402810\pi$
$311$	−11.9155	+	20.6382i	−0.675665	+	1.17029i	−0.976274	+	0.216538i	$0.930523\pi$
$312$	−7.22280	−	4.17009i	−0.408911	−	0.236085i
$313$	28.3646	−	16.3763i	1.60326	−	0.925643i	0.612431	−	0.790524i	$-0.290192\pi$
$313$	28.3646	−	16.3763i	1.60326	−	0.925643i	0.990829	−	0.135118i	$-0.0431415\pi$
$314$	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	$-0.498853\pi$
$317$	15.5153	−	8.95774i	0.871424	−	0.503117i	0.867821	+	0.496877i	$0.165520\pi$
$318$	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	0.884117	−	0.467265i	$-0.154761\pi$
$331$	0.680346	+	1.17839i	0.0373952	+	0.0647704i	−0.846722	+	0.532035i	$0.821427\pi$
$332$	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
$340$	−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	0.837849	−	0.545902i	$-0.183813\pi$
$347$	14.6044	+	8.43188i	0.784008	+	0.452647i	−0.0538410	+	0.998550i	$0.517146\pi$
$348$	−30.8948	+	17.8371i	−1.65613	+	0.956169i
$349$	−9.51745			−0.509457			−0.254729	−	0.967013i	$-0.581986\pi$
$349$	−9.51745			−0.509457			−0.254729	+	0.967013i	$0.581986\pi$
$350$		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	0.977008	+	0.213201i	$0.0683889\pi$
$353$	31.0035	+	17.8999i	1.65015	+	0.952715i	0.673142	+	0.739514i	$0.264944\pi$
$354$	−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	−0.994386	−	0.105815i	$-0.966255\pi$
$359$	−11.1568	−	19.3241i	−0.588831	−	1.01989i	0.405555	−	0.914071i	$-0.367078\pi$
$360$	−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	$-0.155458\pi$
$367$	17.5920	+	10.1568i	0.918296	+	0.530178i	0.0352048	+	0.999380i	$0.488792\pi$
$368$	−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	$-0.802614\pi$
$373$	−13.8564	+	8.00000i	−0.717458	+	0.414224i	0.0963587	+	0.995347i	$0.469280\pi$
$374$	−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	$-0.426182\pi$
$383$	23.2416	−	13.4186i	1.18759	−	0.685656i	0.957758	+	0.287574i	$0.0928488\pi$
$384$	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	−0.928552	−	0.371201i	$-0.878946\pi$
$389$	−2.81658	+	4.87846i	−0.142806	+	0.247348i	0.785746	+	0.618549i	$0.212279\pi$
$390$	−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	−0.663173	+	0.748466i	$0.730791\pi$
$397$	−32.7356	+	18.8999i	−1.64295	+	0.948558i	−0.979777	+	0.200092i	$0.935876\pi$
$398$			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	0.984508	−	0.175341i	$-0.0561029\pi$
$401$	6.81658	+	11.8067i	0.340404	+	0.589597i	−0.644104	+	0.764938i	$0.722770\pi$
$402$	−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	$-0.734528\pi$
$409$	6.17727	−	10.6994i	0.305447	−	0.529049i	0.977361	+	0.211580i	$0.0678609\pi$
$410$	−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	$-0.750502\pi$
$419$	−28.9939			−1.41644			−0.708221	+	0.705991i	$0.750502\pi$
$420$		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	−0.714688	−	0.699444i	$-0.753431\pi$
$431$	5.15676	−	8.93176i	0.248392	−	0.430228i	0.963080	+	0.269216i	$0.0867645\pi$
$432$	−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	$-0.298982\pi$
$439$	−8.46081	−	14.6546i	−0.403812	−	0.699424i	−0.994182	+	0.107709i	$0.965649\pi$
$440$	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	$-0.765096\pi$
$443$	−11.0942	+	6.40522i	−0.527100	+	0.304321i	0.212735	+	0.977110i	$0.431763\pi$
$444$	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	−0.758548	−	0.651618i	$-0.774091\pi$
$457$	−12.2601	+	7.07838i	−0.573504	+	0.331113i	0.185044	+	0.982730i	$0.440757\pi$
$458$	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	$-0.497478\pi$
$461$	0.340173			0.0158434			0.00792172	+	0.999969i	$0.497478\pi$
$462$		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
$465$	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	$-0.580805\pi$
$467$	9.97440	−	5.75872i	0.461560	−	0.266482i	0.712700	+	0.701469i	$0.247472\pi$
$468$			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	$-0.980445\pi$
$479$	−9.75872	+	16.9026i	−0.445887	+	0.772300i	0.552226	+	0.833694i	$0.313779\pi$
$480$	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	0.879951	−	0.475065i	$-0.157575\pi$
$487$	20.0490	+	11.5753i	0.908508	+	0.524527i	0.0285570	+	0.999592i	$0.490909\pi$
$488$	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	0.991421	+	0.130709i	$0.0417254\pi$
$499$	13.6020	+	23.5593i	0.608908	+	1.05466i	−0.382513	+	0.923950i	$0.624941\pi$
$500$	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	$-0.118439\pi$
$509$	3.40522	+	5.89801i	0.150934	+	0.261425i	−0.780637	+	0.624984i	$0.785105\pi$
$510$	−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	−0.431478	−	0.902123i	$-0.642008\pi$
$521$	12.9083	−	22.3578i	0.565523	−	0.979514i	0.997001	−	0.0773904i	$-0.0246588\pi$
$522$	15.6741	+	9.04945i	0.686037	+	0.396084i
$523$	3.46410	−	2.00000i	0.151475	−	0.0874539i	−0.422347	−	0.906434i	$-0.638794\pi$
$523$	3.46410	−	2.00000i	0.151475	−	0.0874539i	0.573822	+	0.818980i	$0.305460\pi$
$524$	−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	−0.997791	−	0.0664306i	$-0.978839\pi$
$541$	−12.9421	−	22.4164i	−0.556426	−	0.963758i	0.441365	−	0.897328i	$-0.354494\pi$
$542$	−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
$550$	−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	−0.0762519	−	0.997089i	$-0.524295\pi$
$557$	−23.0788	−	13.3246i	−0.977882	−	0.564580i	−0.901630	+	0.432508i	$0.857629\pi$
$558$	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	−0.953002	−	0.302963i	$-0.902024\pi$
$563$	−40.1442	−	23.1773i	−1.69188	−	0.976806i	−0.738875	−	0.673843i	$-0.764642\pi$
$564$	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	0.675251	−	0.737588i	$-0.264035\pi$
$569$	−7.18342	−	12.4420i	−0.301145	−	0.521598i	−0.976395	+	0.215990i	$0.930702\pi$
$570$	−12.9439	+	13.4256i	−0.542160	+	0.562338i
$571$	−19.3607	+	33.5337i	−0.810220	+	1.40334i	0.102490	+	0.994734i	$0.467319\pi$
$571$	−19.3607	+	33.5337i	−0.810220	+	1.40334i	−0.912710	+	0.408608i	$0.866014\pi$
$572$	−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	0.996474	+	0.0839011i	$0.0267380\pi$
$577$	37.6496	+	21.7370i	1.56737	+	0.904922i	0.570898	+	0.821021i	$0.306595\pi$
$578$	−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	$-0.442902\pi$
$593$	27.2679	−	15.7431i	1.11976	−	0.646493i	0.941339	+	0.337462i	$0.109568\pi$
$594$	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	−0.400636	−	0.916237i	$-0.631211\pi$
$599$	14.5174	−	25.1450i	0.593167	−	1.02740i	0.993803	−	0.111158i	$-0.0354559\pi$
$600$	−1.65267	−	45.2170i	−0.0674698	−	1.84598i
$601$	15.3607			0.626576			0.313288	−	0.949658i	$-0.398570\pi$
$601$	15.3607			0.626576			0.313288	+	0.949658i	$0.398570\pi$
$602$		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	$-0.581366\pi$
$607$	11.2992	−	6.52359i	0.458620	−	0.264784i	0.711464	+	0.702723i	$0.248033\pi$
$608$		−	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	$-0.231875\pi$
$613$	13.4385	+	7.75872i	0.542776	+	0.313372i	−0.203427	+	0.979090i	$0.565208\pi$
$614$	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	$-0.782403\pi$
$619$	3.96388	−	6.86565i	0.159322	−	0.275954i	0.934624	+	0.355637i	$0.115736\pi$
$620$	−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	−0.801313	−	0.598246i	$-0.795865\pi$
$641$	2.97334	−	5.14997i	0.117440	−	0.203412i	0.918752	+	0.394834i	$0.129198\pi$
$642$	−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	$-0.456547\pi$
$647$	−16.6311	−	9.60197i	−0.653836	−	0.377492i	−0.789924	+	0.613204i	$0.789880\pi$
$648$	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	$-0.855373\pi$
$653$	−24.7292	+	14.2774i	−0.967727	+	0.558718i	−0.0691846	+	0.997604i	$0.522040\pi$
$654$	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	$-0.691614\pi$
$661$	11.0722	−	19.1777i	0.430660	−	0.745925i	0.996930	+	0.0782946i	$0.0249475\pi$
$662$	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	$0.0135629\pi$
$673$			2.21008i			0.0851923i	−0.999092	+	0.0425962i	$0.986437\pi$
$674$	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	$-0.789250\pi$
$677$	−16.9296	+	9.77432i	−0.650658	+	0.375658i	0.138050	+	0.990425i	$0.455916\pi$
$678$			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	$-0.405923\pi$
$683$	−10.2335	−	5.90829i	−0.391572	−	0.226074i	−0.682841	+	0.730567i	$0.739256\pi$
$684$	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	$-0.238468\pi$
$691$	−5.87936	−	10.1834i	−0.223661	−	0.387393i	−0.955917	+	0.293637i	$0.905134\pi$
$692$			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	0.743465	−	0.668774i	$-0.233181\pi$
$709$	−5.52359	−	9.56714i	−0.207443	−	0.359301i	−0.950908	+	0.309473i	$0.899847\pi$
$710$	−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	$-0.203291\pi$
$719$	−3.07838	−	5.33191i	−0.114804	−	0.198847i	−0.917701	+	0.397271i	$0.869957\pi$
$720$	−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	$-0.824750\pi$
$733$	−22.3432	+	12.8999i	−0.825267	+	0.476468i	0.0269626	+	0.999636i	$0.491417\pi$
$734$	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	−0.875495	−	0.483227i	$-0.839465\pi$
$739$	−0.523590	+	0.906885i	−0.0192606	+	0.0333603i	0.856234	+	0.516587i	$0.172798\pi$
$740$	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	$-0.941438\pi$
$743$		−	9.97334i		−	0.365886i	0.983123	−	0.182943i	$-0.0585624\pi$
$744$	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	0.834689	−	0.550722i	$-0.185648\pi$
$751$	−1.63317	−	2.82872i	−0.0595950	−	0.103222i	−0.894284	+	0.447501i	$0.852314\pi$
$752$	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
$760$	−44.8440	−	43.2349i	−1.62666	−	1.56829i
$761$	−1.30632	−	2.26262i	−0.0473542	−	0.0820198i	0.841377	−	0.540449i	$-0.181746\pi$
$761$	−1.30632	−	2.26262i	−0.0473542	−	0.0820198i	−0.888731	+	0.458429i	$0.848412\pi$
$762$			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	$-0.408799\pi$
$769$	15.6742			0.565226			0.282613	+	0.959234i	$0.408799\pi$
$770$		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	$-0.366665\pi$
$773$	−5.03338	−	2.90602i	−0.181038	−	0.104522i	−0.587780	+	0.809021i	$0.699998\pi$
$774$	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

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

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