LMFDB - Embedded newform 637.2.q.g.491.4

Newspace parameters

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.4
Root			$0.655911 + 1.25291i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.g.589.4

$q$-expansion

$f(q)$	$=$	$q+(0.156598 - 0.0904119i) q^{2} +(0.913006 + 1.58137i) q^{3} +(-0.983651 + 1.70373i) q^{4} +2.68664i q^{5} +(0.285950 + 0.165093i) q^{6} +0.717383i q^{8} +(-0.167162 + 0.289532i) q^{9} +O(q^{10})$	\(q+(0.156598 - 0.0904119i) q^{2} +(0.913006 + 1.58137i) q^{3} +(-0.983651 + 1.70373i) q^{4} +2.68664i q^{5} +(0.285950 + 0.165093i) q^{6} +0.717383i q^{8} +(-0.167162 + 0.289532i) q^{9} +(0.242904 + 0.420723i) q^{10} +(-2.33328 + 1.34712i) q^{11} -3.59232 q^{12} +(1.92153 + 3.05086i) q^{13} +(-4.24858 + 2.45292i) q^{15} +(-1.90244 - 3.29513i) q^{16} +(2.38247 - 4.12655i) q^{17} +0.0604535i q^{18} +(-0.163180 - 0.0942122i) q^{19} +(-4.57732 - 2.64272i) q^{20} +(-0.243592 + 0.421913i) q^{22} +(2.19964 + 3.80989i) q^{23} +(-1.13445 + 0.654975i) q^{24} -2.21804 q^{25} +(0.576741 + 0.304029i) q^{26} +4.86756 q^{27} +(-3.54280 - 6.13631i) q^{29} +(-0.443546 + 0.768245i) q^{30} -3.69931i q^{31} +(-1.83838 - 1.06139i) q^{32} +(-4.26060 - 2.45986i) q^{33} -0.861613i q^{34} +(-0.328857 - 0.569598i) q^{36} +(-6.88848 + 3.97707i) q^{37} -0.0340716 q^{38} +(-3.07017 + 5.82411i) q^{39} -1.92735 q^{40} +(4.70215 - 2.71479i) q^{41} +(-4.00533 + 6.93743i) q^{43} -5.30039i q^{44} +(-0.777869 - 0.449103i) q^{45} +(0.688919 + 0.397748i) q^{46} +1.84889i q^{47} +(3.47389 - 6.01695i) q^{48} +(-0.347341 + 0.200538i) q^{50} +8.70083 q^{51} +(-7.08796 + 0.272800i) q^{52} -7.07244 q^{53} +(0.762250 - 0.440085i) q^{54} +(-3.61923 - 6.26869i) q^{55} -0.344066i q^{57} +(-1.10959 - 0.640623i) q^{58} +(6.57216 + 3.79444i) q^{59} -9.65128i q^{60} +(0.205782 - 0.356425i) q^{61} +(-0.334461 - 0.579304i) q^{62} +7.22592 q^{64} +(-8.19656 + 5.16247i) q^{65} -0.889602 q^{66} +(9.87358 - 5.70051i) q^{67} +(4.68703 + 8.11818i) q^{68} +(-4.01658 + 6.95692i) q^{69} +(2.89675 + 1.67244i) q^{71} +(-0.207705 - 0.119919i) q^{72} +14.2158i q^{73} +(-0.719148 + 1.24560i) q^{74} +(-2.02509 - 3.50756i) q^{75} +(0.321025 - 0.185344i) q^{76} +(0.0457859 + 1.18962i) q^{78} +9.11059 q^{79} +(8.85283 - 5.11118i) q^{80} +(4.94560 + 8.56603i) q^{81} +(0.490899 - 0.850261i) q^{82} +16.5866i q^{83} +(11.0866 + 6.40083i) q^{85} +1.44852i q^{86} +(6.46920 - 11.2050i) q^{87} +(-0.966401 - 1.67386i) q^{88} +(5.10232 - 2.94582i) q^{89} -0.162417 q^{90} -8.65473 q^{92} +(5.84998 - 3.37749i) q^{93} +(0.167162 + 0.289532i) q^{94} +(0.253115 - 0.438407i) q^{95} -3.87622i q^{96} +(0.390659 + 0.225547i) q^{97} -0.900747i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 4 q^{4} - 9 q^{6} - q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 4 * q^4 - 9 * q^6 - q^9	$ 12 q - 3 q^{3} + 4 q^{4} - 9 q^{6} - q^{9} + 12 q^{10} - 12 q^{11} + 2 q^{12} - 2 q^{13} - 12 q^{15} - 8 q^{16} + 17 q^{17} - 9 q^{19} - 3 q^{20} - 15 q^{22} + 3 q^{23} - 15 q^{24} + 10 q^{25} + 15 q^{26} + 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{32} + 6 q^{33} - 13 q^{36} - 15 q^{37} - 38 q^{38} + 5 q^{39} + 2 q^{40} - 6 q^{41} + 11 q^{43} + 9 q^{45} + 30 q^{46} + 19 q^{48} + 18 q^{50} - 8 q^{51} - 40 q^{52} + 16 q^{53} - 6 q^{54} - 15 q^{55} + 24 q^{58} - 27 q^{59} + 5 q^{61} + 41 q^{62} + 2 q^{64} - 18 q^{65} + 68 q^{66} - 15 q^{67} - 11 q^{68} + 7 q^{69} + 30 q^{71} - 57 q^{72} - 33 q^{74} + q^{75} - 45 q^{76} + 44 q^{78} + 70 q^{79} + 63 q^{80} + 14 q^{81} + 5 q^{82} - 21 q^{85} + 10 q^{87} - 14 q^{88} - 48 q^{89} - 66 q^{92} + 81 q^{93} + q^{94} + 2 q^{95} - 3 q^{97}+O(q^{100}) $ 12 * q - 3 * q^3 + 4 * q^4 - 9 * q^6 - q^9 + 12 * q^10 - 12 * q^11 + 2 * q^12 - 2 * q^13 - 12 * q^15 - 8 * q^16 + 17 * q^17 - 9 * q^19 - 3 * q^20 - 15 * q^22 + 3 * q^23 - 15 * q^24 + 10 * q^25 + 15 * q^26 + 12 * q^27 - q^29 + 11 * q^30 - 18 * q^32 + 6 * q^33 - 13 * q^36 - 15 * q^37 - 38 * q^38 + 5 * q^39 + 2 * q^40 - 6 * q^41 + 11 * q^43 + 9 * q^45 + 30 * q^46 + 19 * q^48 + 18 * q^50 - 8 * q^51 - 40 * q^52 + 16 * q^53 - 6 * q^54 - 15 * q^55 + 24 * q^58 - 27 * q^59 + 5 * q^61 + 41 * q^62 + 2 * q^64 - 18 * q^65 + 68 * q^66 - 15 * q^67 - 11 * q^68 + 7 * q^69 + 30 * q^71 - 57 * q^72 - 33 * q^74 + q^75 - 45 * q^76 + 44 * q^78 + 70 * q^79 + 63 * q^80 + 14 * q^81 + 5 * q^82 - 21 * q^85 + 10 * q^87 - 14 * q^88 - 48 * q^89 - 66 * q^92 + 81 * q^93 + q^94 + 2 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.156598	−	0.0904119i	0.110731	−	0.0639308i	−0.443611	−	0.896219i	$-0.646303\pi$
$2$	0.156598	−	0.0904119i	0.110731	−	0.0639308i	0.554343	+	0.832288i	$0.312970\pi$
$3$	0.913006	+	1.58137i	0.527125	+	0.913006i	0.999500	+	0.0316092i	$0.0100632\pi$
$3$	0.913006	+	1.58137i	0.527125	+	0.913006i	−0.472376	+	0.881397i	$0.656603\pi$
$4$	−0.983651	+	1.70373i	−0.491826	+	0.851867i
$5$			2.68664i			1.20150i	0.799436	+	0.600751i	$0.205132\pi$
$5$			2.68664i			1.20150i	−0.799436	+	0.600751i	$0.794868\pi$
$6$	0.285950	+	0.165093i	0.116739	+	0.0673990i
$7$		0			0
$7$		0			0
$8$			0.717383i			0.253633i
$9$	−0.167162	+	0.289532i	−0.0557205	+	0.0965108i
$10$	0.242904	+	0.420723i	0.0768131	+	0.133044i
$11$	−2.33328	+	1.34712i	−0.703511	+	0.406172i	−0.808654	−	0.588285i	$-0.799803\pi$
$11$	−2.33328	+	1.34712i	−0.703511	+	0.406172i	0.105143	+	0.994457i	$0.466470\pi$
$12$	−3.59232			−1.03701
$13$	1.92153	+	3.05086i	0.532937	+	0.846155i
$13$	1.92153	+	3.05086i	0.532937	+	0.846155i
$14$		0			0
$15$	−4.24858	+	2.45292i	−1.09698	+	0.633342i
$16$	−1.90244	−	3.29513i	−0.475611	−	0.823782i
$17$	2.38247	−	4.12655i	0.577833	−	1.00084i	−0.417894	−	0.908496i	$-0.637232\pi$
$17$	2.38247	−	4.12655i	0.577833	−	1.00084i	0.995727	−	0.0923405i	$-0.0294348\pi$
$18$			0.0604535i			0.0142490i
$19$	−0.163180	−	0.0942122i	−0.0374361	−	0.0216138i	0.481165	−	0.876630i	$-0.340214\pi$
$19$	−0.163180	−	0.0942122i	−0.0374361	−	0.0216138i	−0.518601	+	0.855016i	$0.673547\pi$
$20$	−4.57732	−	2.64272i	−1.02352	−	0.590930i
$21$		0			0
$22$	−0.243592	+	0.421913i	−0.0519339	+	0.0899521i
$23$	2.19964	+	3.80989i	0.458657	+	0.794418i	0.998890	−	0.0470977i	$-0.0149972\pi$
$23$	2.19964	+	3.80989i	0.458657	+	0.794418i	−0.540233	+	0.841516i	$0.681664\pi$
$24$	−1.13445	+	0.654975i	−0.231569	+	0.133696i
$25$	−2.21804			−0.443609
$26$	0.576741	+	0.304029i	0.113108	+	0.0596249i
$27$	4.86756			0.936762
$28$		0			0
$29$	−3.54280	−	6.13631i	−0.657882	−	1.13948i	−0.981163	−	0.193182i	$-0.938119\pi$
$29$	−3.54280	−	6.13631i	−0.657882	−	1.13948i	0.323281	−	0.946303i	$-0.395214\pi$
$30$	−0.443546	+	0.768245i	−0.0809801	+	0.140262i
$31$		−	3.69931i		−	0.664415i	−0.943206	−	0.332207i	$-0.892207\pi$
$31$		−	3.69931i		−	0.664415i	0.943206	−	0.332207i	$-0.107793\pi$
$32$	−1.83838	−	1.06139i	−0.324983	−	0.187629i
$33$	−4.26060	−	2.45986i	−0.741676	−	0.428207i
$34$		−	0.861613i		−	0.147765i
$35$		0			0
$36$	−0.328857	−	0.569598i	−0.0548096	−	0.0949329i
$37$	−6.88848	+	3.97707i	−1.13246	+	0.653826i	−0.944552	−	0.328361i	$-0.893504\pi$
$37$	−6.88848	+	3.97707i	−1.13246	+	0.653826i	−0.187907	+	0.982187i	$0.560170\pi$
$38$	−0.0340716			−0.00552715
$39$	−3.07017	+	5.82411i	−0.491621	+	0.932604i
$40$	−1.92735			−0.304741
$41$	4.70215	−	2.71479i	0.734353	−	0.423979i	−0.0856594	−	0.996324i	$-0.527300\pi$
$41$	4.70215	−	2.71479i	0.734353	−	0.423979i	0.820013	+	0.572345i	$0.193966\pi$
$42$		0			0
$43$	−4.00533	+	6.93743i	−0.610807	+	1.05795i	0.380298	+	0.924864i	$0.375821\pi$
$43$	−4.00533	+	6.93743i	−0.610807	+	1.05795i	−0.991105	+	0.133084i	$0.957512\pi$
$44$		−	5.30039i		−	0.799064i
$45$	−0.777869	−	0.449103i	−0.115958	−	0.0669483i
$46$	0.688919	+	0.397748i	0.101576	+	0.0586447i
$47$			1.84889i			0.269688i	0.990867	+	0.134844i	$0.0430534\pi$
$47$			1.84889i			0.269688i	−0.990867	+	0.134844i	$0.956947\pi$
$48$	3.47389	−	6.01695i	0.501412	−	0.868471i
$49$		0			0
$50$	−0.347341	+	0.200538i	−0.0491215	+	0.0283603i
$51$	8.70083			1.21836
$52$	−7.08796	+	0.272800i	−0.982924	+	0.0378305i
$53$	−7.07244			−0.971474			−0.485737	−	0.874105i	$-0.661449\pi$
$53$	−7.07244			−0.971474			−0.485737	+	0.874105i	$0.661449\pi$
$54$	0.762250	−	0.440085i	0.103729	−	0.0598880i
$55$	−3.61923	−	6.26869i	−0.488017	−	0.845271i
$56$		0			0
$57$		−	0.344066i		−	0.0455726i
$58$	−1.10959	−	0.640623i	−0.145696	−	0.0841179i
$59$	6.57216	+	3.79444i	0.855623	+	0.493994i	0.862544	−	0.505982i	$-0.168870\pi$
$59$	6.57216	+	3.79444i	0.855623	+	0.493994i	−0.00692130	+	0.999976i	$0.502203\pi$
$60$		−	9.65128i		−	1.24597i
$61$	0.205782	−	0.356425i	0.0263477	−	0.0456355i	−0.852551	−	0.522644i	$-0.824946\pi$
$61$	0.205782	−	0.356425i	0.0263477	−	0.0456355i	0.878899	+	0.477009i	$0.158279\pi$
$62$	−0.334461	−	0.579304i	−0.0424766	−	0.0735716i
$63$		0			0
$64$	7.22592			0.903240
$65$	−8.19656	+	5.16247i	−1.01666	+	0.640325i
$66$	−0.889602			−0.109502
$67$	9.87358	−	5.70051i	1.20625	−	0.696429i	0.244312	−	0.969697i	$-0.421438\pi$
$67$	9.87358	−	5.70051i	1.20625	−	0.696429i	0.961938	+	0.273268i	$0.0881046\pi$
$68$	4.68703	+	8.11818i	0.568386	+	0.984474i
$69$	−4.01658	+	6.95692i	−0.483539	+	0.837514i
$70$		0			0
$71$	2.89675	+	1.67244i	0.343781	+	0.198482i	0.661943	−	0.749554i	$-0.269732\pi$
$71$	2.89675	+	1.67244i	0.343781	+	0.198482i	−0.318162	+	0.948037i	$0.603065\pi$
$72$	−0.207705	−	0.119919i	−0.0244783	−	0.0141326i
$73$			14.2158i			1.66383i	0.554900	+	0.831917i	$0.312756\pi$
$73$			14.2158i			1.66383i	−0.554900	+	0.831917i	$0.687244\pi$
$74$	−0.719148	+	1.24560i	−0.0835993	+	0.144798i
$75$	−2.02509	−	3.50756i	−0.233837	−	0.405018i
$76$	0.321025	−	0.185344i	0.0368241	−	0.0212604i
$77$		0			0
$78$	0.0457859	+	1.18962i	0.00518423	+	0.134698i
$79$	9.11059			1.02502			0.512511	−	0.858681i	$-0.328715\pi$
$79$	9.11059			1.02502			0.512511	+	0.858681i	$0.328715\pi$
$80$	8.85283	−	5.11118i	0.989776	−	0.571448i
$81$	4.94560	+	8.56603i	0.549511	+	0.951781i
$82$	0.490899	−	0.850261i	0.0542107	−	0.0938956i
$83$			16.5866i			1.82061i	0.413934	+	0.910307i	$0.364155\pi$
$83$			16.5866i			1.82061i	−0.413934	+	0.910307i	$0.635845\pi$
$84$		0			0
$85$	11.0866	+	6.40083i	1.20251	+	0.694268i
$86$			1.44852i			0.156198i
$87$	6.46920	−	11.2050i	0.693571	−	1.20130i
$88$	−0.966401	−	1.67386i	−0.103019	−	0.178434i
$89$	5.10232	−	2.94582i	0.540844	−	0.312257i	−0.204577	−	0.978851i	$-0.565582\pi$
$89$	5.10232	−	2.94582i	0.540844	−	0.312257i	0.745421	+	0.666594i	$0.232248\pi$
$90$	−0.162417			−0.0171203
$91$		0			0
$92$	−8.65473			−0.902318
$93$	5.84998	−	3.37749i	0.606615	−	0.350229i
$94$	0.167162	+	0.289532i	0.0172414	+	0.0298630i
$95$	0.253115	−	0.438407i	0.0259690	−	0.0449796i
$96$		−	3.87622i		−	0.395615i
$97$	0.390659	+	0.225547i	0.0396654	+	0.0229008i	0.519702	−	0.854348i	$-0.326043\pi$
$97$	0.390659	+	0.225547i	0.0396654	+	0.0229008i	−0.480036	+	0.877249i	$0.659376\pi$
$98$		0			0
$99$		−	0.900747i		−	0.0905285i
$100$	2.18178	−	3.77896i	0.218178	−	0.377896i
$101$	−3.82840	−	6.63098i	−0.380940	−	0.659807i	0.610257	−	0.792204i	$-0.291066\pi$
$101$	−3.82840	−	6.63098i	−0.380940	−	0.659807i	−0.991197	+	0.132396i	$0.957733\pi$
$102$	1.36253	−	0.786658i	0.134911	−	0.0778908i
$103$	−5.15740			−0.508173			−0.254087	−	0.967181i	$-0.581775\pi$
$103$	−5.15740			−0.508173			−0.254087	+	0.967181i	$0.581775\pi$
$104$	−2.18863	+	1.37847i	−0.214613	+	0.135170i
$105$		0			0
$106$	−1.10753	+	0.639433i	−0.107573	+	0.0621072i
$107$	−4.01644	−	6.95669i	−0.388284	−	0.672528i	0.603935	−	0.797034i	$-0.293599\pi$
$107$	−4.01644	−	6.95669i	−0.388284	−	0.672528i	−0.992219	+	0.124506i	$0.960265\pi$
$108$	−4.78798	+	8.29303i	−0.460724	+	0.797997i
$109$			1.33356i			0.127732i	0.997958	+	0.0638660i	$0.0203430\pi$
$109$			1.33356i			0.127732i	−0.997958	+	0.0638660i	$0.979657\pi$
$110$	−1.13353	−	0.654443i	−0.108078	−	0.0623987i
$111$	−12.5785	−	7.26217i	−1.19389	−	0.689295i
$112$		0			0
$113$	9.96917	−	17.2671i	0.937821	−	1.62435i	0.168296	−	0.985736i	$-0.446173\pi$
$113$	9.96917	−	17.2671i	0.937821	−	1.62435i	0.769525	−	0.638617i	$-0.220493\pi$
$114$	−0.0311076	−	0.0538800i	−0.00291349	−	0.00504632i
$115$	−10.2358	+	5.90965i	−0.954495	+	0.551078i
$116$	13.9395			1.29425
$117$	−1.20453	+	0.0463595i	−0.111359	+	0.00428594i
$118$	1.37225			0.126326
$119$		0			0
$120$	−1.75968	−	3.04786i	−0.160636	−	0.278230i
$121$	−1.87053	+	3.23985i	−0.170048	+	0.294532i
$122$		−	0.0744205i		−	0.00673772i
$123$	8.58619	+	4.95724i	0.774191	+	0.446979i
$124$	6.30263	+	3.63883i	0.565993	+	0.326776i
$125$			7.47412i			0.668505i
$126$		0			0
$127$	−3.98361	−	6.89981i	−0.353488	−	0.612259i	0.633370	−	0.773849i	$-0.281671\pi$
$127$	−3.98361	−	6.89981i	−0.353488	−	0.612259i	−0.986858	+	0.161590i	$0.948338\pi$
$128$	4.80833	−	2.77609i	0.425000	−	0.245374i
$129$	−14.6276			−1.28788
$130$	−0.816816	+	1.54950i	−0.0716395	+	0.135900i
$131$	10.0179			0.875271			0.437636	−	0.899152i	$-0.355816\pi$
$131$	10.0179			0.875271			0.437636	+	0.899152i	$0.355816\pi$
$132$	8.38190	−	4.83929i	0.729551	−	0.421206i
$133$		0			0
$134$	1.03079	−	1.78538i	0.0890465	−	0.154233i
$135$			13.0774i			1.12552i
$136$	2.96032	+	1.70914i	0.253845	+	0.146558i
$137$	−4.38811	−	2.53348i	−0.374902	−	0.216450i	0.300696	−	0.953720i	$-0.402781\pi$
$137$	−4.38811	−	2.53348i	−0.374902	−	0.216450i	−0.675598	+	0.737270i	$0.736114\pi$
$138$			1.45259i			0.123652i
$139$	−3.86289	+	6.69073i	−0.327646	+	0.567500i	−0.982044	−	0.188650i	$-0.939589\pi$
$139$	−3.86289	+	6.69073i	−0.327646	+	0.567500i	0.654398	+	0.756150i	$0.272922\pi$
$140$		0			0
$141$	−2.92378	+	1.68805i	−0.246227	+	0.142159i
$142$	0.604834			0.0507566
$143$	−8.59335	−	4.52997i	−0.718612	−	0.378815i
$144$	1.27206			0.106005
$145$	16.4861	−	9.51824i	1.36909	−	0.790447i
$146$	1.28528	+	2.22617i	0.106370	+	0.184239i
$147$		0			0
$148$		−	15.6482i		−	1.28627i
$149$	−12.4002	−	7.15924i	−1.01586	−	0.586507i	−0.102958	−	0.994686i	$-0.532831\pi$
$149$	−12.4002	−	7.15924i	−1.01586	−	0.586507i	−0.912902	+	0.408178i	$0.866164\pi$
$150$	−0.634250	−	0.366184i	−0.0517863	−	0.0298988i
$151$			6.47249i			0.526724i	0.964697	+	0.263362i	$0.0848313\pi$
$151$			6.47249i			0.526724i	−0.964697	+	0.263362i	$0.915169\pi$
$152$	0.0675862	−	0.117063i	0.00548197	−	0.00949504i
$153$	0.796513	+	1.37960i	0.0643943	+	0.111534i
$154$		0			0
$155$	9.93871			0.798296
$156$	−6.90275	−	10.9596i	−0.552663	−	0.877474i
$157$	15.9187			1.27045			0.635227	−	0.772326i	$-0.280907\pi$
$157$	15.9187			1.27045			0.635227	+	0.772326i	$0.280907\pi$
$158$	1.42670	−	0.823705i	0.113502	−	0.0655305i
$159$	−6.45718	−	11.1842i	−0.512088	−	0.886962i
$160$	2.85157	−	4.93907i	0.225437	−	0.390468i
$161$		0			0
$162$	1.54894	+	0.894282i	0.121696	+	0.0702614i
$163$	4.14100	+	2.39081i	0.324348	+	0.187263i	0.653329	−	0.757074i	$-0.273372\pi$
$163$	4.14100	+	2.39081i	0.324348	+	0.187263i	−0.328981	+	0.944337i	$0.606705\pi$
$164$			10.6816i			0.834095i
$165$	6.60876	−	11.4467i	0.514492	−	0.891126i
$166$	1.49962	+	2.59743i	0.116393	+	0.201599i
$167$	−2.34729	+	1.35521i	−0.181639	+	0.104869i	−0.588062	−	0.808816i	$-0.700109\pi$
$167$	−2.34729	+	1.35521i	−0.181639	+	0.104869i	0.406424	+	0.913685i	$0.366776\pi$
$168$		0			0
$169$	−5.61544	+	11.7246i	−0.431957	+	0.901894i
$170$	2.31485			0.177541
$171$	0.0545550	−	0.0314973i	0.00417192	−	0.00240866i
$172$	−7.87969	−	13.6480i	−0.600821	−	1.04065i
$173$	−0.449908	+	0.779264i	−0.0342059	+	0.0592463i	−0.882622	−	0.470084i	$-0.844224\pi$
$173$	−0.449908	+	0.779264i	−0.0342059	+	0.0592463i	0.848416	+	0.529331i	$0.177557\pi$
$174$		−	2.33957i		−	0.177362i
$175$		0			0
$176$	8.87787	+	5.12564i	0.669195	+	0.386360i
$177$			13.8574i			1.04159i
$178$	0.532675	−	0.922620i	0.0399257	−	0.0691533i
$179$	−5.52791	−	9.57462i	−0.413175	−	0.715641i	0.582060	−	0.813146i	$-0.302247\pi$
$179$	−5.52791	−	9.57462i	−0.413175	−	0.715641i	−0.995235	+	0.0975054i	$0.968914\pi$
$180$	1.53030	−	0.883522i	0.114062	−	0.0658538i
$181$	−3.52898			−0.262307			−0.131153	−	0.991362i	$-0.541868\pi$
$181$	−3.52898			−0.262307			−0.131153	+	0.991362i	$0.541868\pi$
$182$		0			0
$183$	0.751521			0.0555540
$184$	−2.73315	+	1.57799i	−0.201491	+	0.116331i
$185$	−10.6850	−	18.5069i	−0.785573	−	1.36065i
$186$	0.610730	−	1.05782i	0.0447809	−	0.0775628i
$187$			12.8379i			0.938799i
$188$	−3.15002	−	1.81866i	−0.229738	−	0.132640i
$189$		0			0
$190$		−	0.0915382i		−	0.00664088i
$191$	10.2002	−	17.6672i	0.738059	−	1.27836i	−0.215309	−	0.976546i	$-0.569076\pi$
$191$	10.2002	−	17.6672i	0.738059	−	1.27836i	0.953368	−	0.301810i	$-0.0975909\pi$
$192$	6.59731	+	11.4269i	0.476120	+	0.824664i
$193$	14.9515	−	8.63228i	1.07624	−	0.621365i	0.146357	−	0.989232i	$-0.453245\pi$
$193$	14.9515	−	8.63228i	1.07624	−	0.621365i	0.929878	+	0.367867i	$0.119912\pi$
$194$	0.0815684			0.00585627
$195$	−15.6473	−	8.24845i	−1.12053	−	0.590684i
$196$		0			0
$197$	−4.29264	+	2.47836i	−0.305838	+	0.176576i	−0.645063	−	0.764130i	$-0.723169\pi$
$197$	−4.29264	+	2.47836i	−0.305838	+	0.176576i	0.339224	+	0.940705i	$0.389835\pi$
$198$	−0.0814383	−	0.141055i	−0.00578757	−	0.0100244i
$199$	3.59097	−	6.21975i	0.254557	−	0.440906i	−0.710218	−	0.703982i	$-0.751404\pi$
$199$	3.59097	−	6.21975i	0.254557	−	0.440906i	0.964775	+	0.263076i	$0.0847369\pi$
$200$		−	1.59119i		−	0.112514i
$201$	18.0293	+	10.4092i	1.27169	+	0.734209i
$202$	−1.19904	−	0.692265i	−0.0843641	−	0.0487076i
$203$		0			0
$204$	−8.55858	+	14.8239i	−0.599221	+	1.03788i
$205$	7.29367	+	12.6330i	0.509412	+	0.882327i
$206$	−0.807638	+	0.466290i	−0.0562708	+	0.0324880i
$207$	−1.47078			−0.102226
$208$	6.39736	−	12.1358i	0.443577	−	0.841464i
$209$	0.507661			0.0351157
$210$		0			0
$211$	8.79636	+	15.2357i	0.605566	+	1.04887i	0.991962	+	0.126539i	$0.0403868\pi$
$211$	8.79636	+	15.2357i	0.605566	+	1.04887i	−0.386395	+	0.922333i	$0.626280\pi$
$212$	6.95682	−	12.0496i	0.477796	−	0.827567i
$213$			6.10780i			0.418499i
$214$	−1.25793	−	0.726269i	−0.0859906	−	0.0496467i
$215$	−18.6384	−	10.7609i	−1.27113	−	0.733886i
$216$			3.49190i			0.237594i
$217$		0			0
$218$	0.120570	+	0.208833i	0.00816602	+	0.0141440i
$219$	−22.4805	+	12.9791i	−1.51909	+	0.877048i
$220$	14.2403			0.960078
$221$	17.1675	−	0.660738i	1.15481	−	0.0444461i
$222$	−2.62635			−0.176269
$223$	12.2157	−	7.05271i	0.818020	−	0.472284i	−0.0317129	−	0.999497i	$-0.510096\pi$
$223$	12.2157	−	7.05271i	0.818020	−	0.472284i	0.849733	+	0.527213i	$0.176763\pi$
$224$		0			0
$225$	0.370772	−	0.642195i	0.0247181	−	0.0428130i
$226$		−	3.60533i		−	0.239823i
$227$	−2.48443	−	1.43439i	−0.164897	−	0.0952035i	0.415280	−	0.909694i	$-0.363684\pi$
$227$	−2.48443	−	1.43439i	−0.164897	−	0.0952035i	−0.580178	+	0.814490i	$0.697017\pi$
$228$	0.586196	+	0.338441i	0.0388218	+	0.0224138i
$229$		−	8.77411i		−	0.579810i	−0.957055	−	0.289905i	$-0.906376\pi$
$229$		−	8.77411i		−	0.579810i	0.957055	−	0.289905i	$-0.0936237\pi$
$230$	−1.06861	+	1.85088i	−0.0704618	+	0.122043i
$231$		0			0
$232$	4.40208	−	2.54154i	0.289011	−	0.166861i
$233$	−5.10743			−0.334599			−0.167299	−	0.985906i	$-0.553505\pi$
$233$	−5.10743			−0.334599			−0.167299	+	0.985906i	$0.553505\pi$
$234$	−0.184435	+	0.116163i	−0.0120569	+	0.00759384i
$235$	−4.96730			−0.324031
$236$	−12.9294	+	7.46481i	−0.841634	+	0.485918i
$237$	8.31803	+	14.4072i	0.540314	+	0.935851i
$238$		0			0
$239$			2.49797i			0.161580i	0.996731	+	0.0807901i	$0.0257443\pi$
$239$			2.49797i			0.161580i	−0.996731	+	0.0807901i	$0.974256\pi$
$240$	16.1654	+	9.33309i	1.04347	+	0.602448i
$241$	−6.91532	−	3.99256i	−0.445455	−	0.257183i	0.260454	−	0.965486i	$-0.416128\pi$
$241$	−6.91532	−	3.99256i	−0.445455	−	0.257183i	−0.705909	+	0.708303i	$0.749461\pi$
$242$			0.676472i			0.0434853i
$243$	−1.72939	+	2.99538i	−0.110940	+	0.192154i
$244$	0.404835	+	0.701195i	0.0259169	+	0.0448894i
$245$		0			0
$246$	1.79277			0.114303
$247$	−0.0261282	−	0.678871i	−0.00166250	−	0.0431956i
$248$	2.65382			0.168518
$249$	−26.2296	+	15.1437i	−1.66223	+	0.959690i
$250$	0.675749	+	1.17043i	0.0427381	+	0.0740246i
$251$	12.6285	−	21.8732i	0.797105	−	1.38063i	−0.124389	−	0.992234i	$-0.539697\pi$
$251$	12.6285	−	21.8732i	0.797105	−	1.38063i	0.921494	−	0.388393i	$-0.126970\pi$
$252$		0			0
$253$	−10.2648	−	5.92637i	−0.645341	−	0.372588i
$254$	−1.24765	−	0.720331i	−0.0782845	−	0.0451976i
$255$			23.3760i			1.46386i
$256$	−6.72394	+	11.6462i	−0.420246	+	0.727888i
$257$	−1.68682	−	2.92165i	−0.105221	−	0.182248i	0.808608	−	0.588348i	$-0.200222\pi$
$257$	−1.68682	−	2.92165i	−0.105221	−	0.182248i	−0.913828	+	0.406101i	$0.866888\pi$
$258$	−2.29065	+	1.32250i	−0.142609	+	0.0823355i
$259$		0			0
$260$	−0.732915	−	19.0428i	−0.0454535	−	1.18099i
$261$	2.36888			0.146630
$262$	1.56879	−	0.905740i	0.0969201	−	0.0559568i
$263$	0.0794677	+	0.137642i	0.00490019	+	0.00848737i	0.868465	−	0.495750i	$-0.165107\pi$
$263$	0.0794677	+	0.137642i	0.00490019	+	0.00848737i	−0.863565	+	0.504238i	$0.831774\pi$
$264$	1.76466	−	3.05648i	0.108607	−	0.188114i
$265$		−	19.0011i		−	1.16723i
$266$		0			0
$267$	9.31689	+	5.37911i	0.570185	+	0.329196i
$268$			22.4293i			1.37009i
$269$	11.6633	−	20.2014i	0.711124	−	1.23170i	−0.253311	−	0.967385i	$-0.581520\pi$
$269$	11.6633	−	20.2014i	0.711124	−	1.23170i	0.964435	−	0.264318i	$-0.0851470\pi$
$270$	1.18235	+	2.04789i	0.0719556	+	0.124631i
$271$	−10.2373	+	5.91049i	−0.621870	+	0.359037i	−0.777597	−	0.628763i	$-0.783561\pi$
$271$	−10.2373	+	5.91049i	−0.621870	+	0.359037i	0.155727	+	0.987800i	$0.450228\pi$
$272$	−18.1300			−1.09929
$273$		0			0
$274$	−0.916226			−0.0553513
$275$	5.17532	−	2.98797i	0.312084	−	0.180182i
$276$	−7.90182	−	13.6864i	−0.475634	−	0.823822i
$277$	−13.6827	+	23.6991i	−0.822111	+	1.42394i	0.0819961	+	0.996633i	$0.473870\pi$
$277$	−13.6827	+	23.6991i	−0.822111	+	1.42394i	−0.904107	+	0.427306i	$0.859463\pi$
$278$			1.39701i			0.0837868i
$279$	1.07107	+	0.618382i	0.0641232	+	0.0370215i
$280$		0			0
$281$		−	28.5383i		−	1.70245i	−0.524801	−	0.851225i	$-0.675860\pi$
$281$		−	28.5383i		−	1.70245i	0.524801	−	0.851225i	$-0.324140\pi$
$282$	−0.305239	+	0.528690i	−0.0181767	+	0.0314830i
$283$	8.98604	+	15.5643i	0.534165	+	0.925201i	0.999203	+	0.0399101i	$0.0127072\pi$
$283$	8.98604	+	15.5643i	0.534165	+	0.925201i	−0.465038	+	0.885290i	$0.653960\pi$
$284$	−5.69879	+	3.29020i	−0.338161	+	0.195237i
$285$	0.924381			0.0547556
$286$	−1.75526	+	0.0675561i	−0.103791	+	0.00399468i
$287$		0			0
$288$	0.614613	−	0.354847i	0.0362164	−	0.0209096i
$289$	−2.85229	−	4.94032i	−0.167782	−	0.290607i
$290$	1.72112	−	2.98107i	0.101068	−	0.175055i
$291$			0.823703i			0.0482863i
$292$	−24.2199	−	13.9834i	−1.41737	−	0.818316i
$293$	12.8943	+	7.44453i	0.753293	+	0.434914i	0.826882	−	0.562375i	$-0.190112\pi$
$293$	12.8943	+	7.44453i	0.753293	+	0.434914i	−0.0735896	+	0.997289i	$0.523446\pi$
$294$		0			0
$295$	−10.1943	+	17.6570i	−0.593535	+	1.02803i
$296$	−2.85308	−	4.94168i	−0.165832	−	0.287229i
$297$	−11.3574	+	6.55719i	−0.659023	+	0.380487i
$298$	−2.58912			−0.149984
$299$	−7.39675	+	14.0316i	−0.427765	+	0.811470i
$300$	7.96793			0.460028
$301$		0			0
$302$	0.585190	+	1.01358i	0.0336739	+	0.0583249i
$303$	6.99071	−	12.1083i	0.401606	−	0.695601i
$304$			0.716934i			0.0411190i
$305$	0.957586	+	0.552862i	0.0548312	+	0.0316568i
$306$	0.249465	+	0.144029i	0.0142610	+	0.00823356i
$307$			23.5161i			1.34214i	0.741396	+	0.671068i	$0.234164\pi$
$307$			23.5161i			1.34214i	−0.741396	+	0.671068i	$0.765836\pi$
$308$		0			0
$309$	−4.70874	−	8.15577i	−0.267871	−	0.463966i
$310$	1.55638	−	0.898577i	0.0883965	−	0.0510358i
$311$	−1.63090			−0.0924799			−0.0462399	−	0.998930i	$-0.514724\pi$
$311$	−1.63090			−0.0924799			−0.0462399	+	0.998930i	$0.514724\pi$
$312$	−4.17811	−	2.20249i	−0.236539	−	0.124691i
$313$	−0.696734			−0.0393817			−0.0196909	−	0.999806i	$-0.506268\pi$
$313$	−0.696734			−0.0393817			−0.0196909	+	0.999806i	$0.506268\pi$
$314$	2.49284	−	1.43924i	0.140679	−	0.0812212i
$315$		0			0
$316$	−8.96164	+	15.5220i	−0.504132	+	0.873182i
$317$		−	21.4288i		−	1.20356i	−0.798662	−	0.601780i	$-0.794458\pi$
$317$		−	21.4288i		−	1.20356i	0.798662	−	0.601780i	$-0.205542\pi$
$318$	−2.02236	−	1.16761i	−0.113409	−	0.0654764i
$319$	16.5327	+	9.54517i	0.925654	+	0.534427i
$320$			19.4135i			1.08525i
$321$	7.33408	−	12.7030i	0.409348	−	0.709012i
$322$		0			0
$323$	−0.777544	+	0.448915i	−0.0432637	+	0.0249783i
$324$	−19.4590			−1.08105
$325$	−4.26204	−	6.76693i	−0.236415	−	0.375362i
$326$	0.864630			0.0478874
$327$	−2.10886	+	1.21755i	−0.116620	+	0.0673307i
$328$	1.94754	+	3.37324i	0.107535	+	0.186256i
$329$		0			0
$330$		−	2.39004i		−	0.131568i
$331$	1.31676	+	0.760232i	0.0723757	+	0.0417861i	0.535751	−	0.844376i	$-0.320029\pi$
$331$	1.31676	+	0.760232i	0.0723757	+	0.0417861i	−0.463375	+	0.886162i	$0.653362\pi$
$332$	−28.2591	−	16.3154i	−1.55092	−	0.895425i
$333$		−	2.65925i		−	0.145726i
$334$	−0.245054	+	0.424446i	−0.0134088	+	0.0232247i
$335$	15.3152	+	26.5268i	0.836761	+	1.44931i
$336$		0			0
$337$	−32.2304			−1.75570			−0.877850	−	0.478936i	$-0.841023\pi$
$337$	−32.2304			−1.75570			−0.877850	+	0.478936i	$0.841023\pi$
$338$	0.180679	+	2.34375i	0.00982766	+	0.127483i
$339$	36.4077			1.97739
$340$	−21.8106	+	12.5924i	−1.18285	+	0.682918i
$341$	4.98341	+	8.63153i	0.269867	+	0.467423i
$342$	0.00569546	−	0.00986483i	0.000307975	−	0.000533429i
$343$		0			0
$344$	−4.97679	−	2.87335i	−0.268331	−	0.154921i
$345$	−18.6907	−	10.7911i	−1.00628	−	0.580974i
$346$			0.162708i			0.00874724i
$347$	−4.09215	+	7.08782i	−0.219678	+	0.380494i	−0.954710	−	0.297539i	$-0.903834\pi$
$347$	−4.09215	+	7.08782i	−0.219678	+	0.380494i	0.735031	+	0.678033i	$0.237167\pi$
$348$	12.7269	+	22.0436i	0.682232	+	1.18166i
$349$	−18.9220	+	10.9246i	−1.01287	+	0.584782i	−0.912031	−	0.410120i	$-0.865487\pi$
$349$	−18.9220	+	10.9246i	−1.01287	+	0.584782i	−0.100841	+	0.994903i	$0.532153\pi$
$350$		0			0
$351$	9.35317	+	14.8502i	0.499235	+	0.792646i
$352$	5.71928			0.304839
$353$	0.491192	−	0.283590i	0.0261435	−	0.0150940i	−0.486871	−	0.873474i	$-0.661862\pi$
$353$	0.491192	−	0.283590i	0.0261435	−	0.0150940i	0.513015	+	0.858380i	$0.328529\pi$
$354$	1.25287	+	2.17004i	0.0665894	+	0.115336i
$355$	−4.49325	+	7.78254i	−0.238477	+	0.413054i
$356$			11.5907i			0.614303i
$357$		0			0
$358$	−1.73132	−	0.999577i	−0.0915030	−	0.0528293i
$359$			32.4043i			1.71024i	0.518434	+	0.855118i	$0.326515\pi$
$359$			32.4043i			1.71024i	−0.518434	+	0.855118i	$0.673485\pi$
$360$	0.322179	−	0.558030i	0.0169803	−	0.0294108i
$361$	−9.48225	−	16.4237i	−0.499066	−	0.864407i
$362$	−0.552631	+	0.319061i	−0.0290456	+	0.0167695i
$363$	−6.83122			−0.358546
$364$		0			0
$365$	−38.1928			−1.99910
$366$	0.117687	−	0.0679464i	0.00615158	−	0.00355162i
$367$	3.93444	+	6.81465i	0.205376	+	0.355722i	0.950252	−	0.311481i	$-0.100825\pi$
$367$	3.93444	+	6.81465i	0.205376	+	0.355722i	−0.744876	+	0.667202i	$0.767492\pi$
$368$	8.36939	−	14.4962i	0.436285	−	0.755667i
$369$			1.81523i			0.0944973i
$370$	−3.34648	−	1.93209i	−0.173975	−	0.100445i
$371$		0			0
$372$			13.2891i			0.689007i
$373$	1.04581	−	1.81140i	0.0541502	−	0.0937909i	−0.837680	−	0.546162i	$-0.816088\pi$
$373$	1.04581	−	1.81140i	0.0541502	−	0.0937909i	0.891830	+	0.452371i	$0.149422\pi$
$374$	1.16070	+	2.01039i	0.0600182	+	0.103955i
$375$	−11.8194	+	6.82392i	−0.610350	+	0.352386i
$376$	−1.32636			−0.0684018
$377$	11.9134	−	22.5997i	0.613571	−	1.16394i
$378$		0			0
$379$	12.3983	−	7.15817i	0.636859	−	0.367691i	−0.146545	−	0.989204i	$-0.546815\pi$
$379$	12.3983	−	7.15817i	0.636859	−	0.367691i	0.783404	+	0.621513i	$0.213482\pi$
$380$	0.497953	+	0.862480i	0.0255444	+	0.0442443i
$381$	7.27412	−	12.5991i	0.372665	−	0.645474i
$382$		−	3.68887i		−	0.188739i
$383$	−21.8129	−	12.5937i	−1.11459	−	0.643507i	−0.174573	−	0.984644i	$-0.555854\pi$
$383$	−21.8129	−	12.5937i	−1.11459	−	0.643507i	−0.940013	+	0.341138i	$0.889188\pi$
$384$	8.78006	+	5.06917i	0.448056	+	0.258685i
$385$		0			0
$386$	1.56092	−	2.70359i	0.0794488	−	0.137609i
$387$	−1.33907	−	2.31934i	−0.0680689	−	0.117899i
$388$	−0.768544	+	0.443719i	−0.0390169	+	0.0225264i
$389$	−28.1023			−1.42484			−0.712422	−	0.701752i	$-0.752402\pi$
$389$	−28.1023			−1.42484			−0.712422	+	0.701752i	$0.752402\pi$
$390$	−3.19609	+	0.123010i	−0.161840	+	0.00622887i
$391$	20.9623			1.06011
$392$		0			0
$393$	9.14644	+	15.8421i	0.461377	+	0.799128i
$394$	−0.448146	+	0.776212i	−0.0225773	+	0.0391050i
$395$			24.4769i			1.23157i
$396$	1.53463	+	0.886021i	0.0771183	+	0.0445243i
$397$	18.8590	+	10.8882i	0.946504	+	0.546465i	0.891993	−	0.452049i	$-0.149307\pi$
$397$	18.8590	+	10.8882i	0.946504	+	0.546465i	0.0545111	+	0.998513i	$0.482640\pi$
$398$		−	1.29867i		−	0.0650963i
$399$		0			0
$400$	4.21970	+	7.30874i	0.210985	+	0.365437i
$401$	17.7786	−	10.2645i	0.887821	−	0.512584i	0.0145918	−	0.999894i	$-0.495355\pi$
$401$	17.7786	−	10.2645i	0.887821	−	0.512584i	0.873229	+	0.487310i	$0.162022\pi$
$402$	3.76447			0.187754
$403$	11.2860	−	7.10833i	0.562198	−	0.354091i
$404$	15.0632			0.749424
$405$	−23.0138	+	13.2871i	−1.14357	+	0.660239i
$406$		0			0
$407$	10.7152	−	18.5592i	0.531132	−	0.919947i
$408$			6.24182i			0.309016i
$409$	−5.42879	−	3.13431i	−0.268436	−	0.154982i	0.359741	−	0.933052i	$-0.382865\pi$
$409$	−5.42879	−	3.13431i	−0.268436	−	0.154982i	−0.628177	+	0.778071i	$0.716199\pi$
$410$	2.28435	+	1.31887i	0.112816	+	0.0651343i
$411$		−	9.25233i		−	0.456384i
$412$	5.07308	−	8.78683i	0.249933	−	0.432896i
$413$		0			0
$414$	−0.230322	+	0.132976i	−0.0113197	+	0.00653543i
$415$	−44.5622			−2.18747
$416$	−0.294359	−	7.64813i	−0.0144321	−	0.374980i
$417$	−14.1074			−0.690841
$418$	0.0794987	−	0.0458986i	0.00388841	−	0.00224497i
$419$	−17.0817	−	29.5864i	−0.834497	−	1.44539i	−0.894439	−	0.447189i	$-0.852425\pi$
$419$	−17.0817	−	29.5864i	−0.834497	−	1.44539i	0.0599424	−	0.998202i	$-0.480908\pi$
$420$		0			0
$421$			11.5233i			0.561613i	0.959764	+	0.280806i	$0.0906019\pi$
$421$			11.5233i			0.561613i	−0.959764	+	0.280806i	$0.909398\pi$
$422$	2.75498	+	1.59059i	0.134111	+	0.0774288i
$423$	−0.535313	−	0.309063i	−0.0260278	−	0.0150272i
$424$		−	5.07364i		−	0.246398i
$425$	−5.28442	+	9.15288i	−0.256332	+	0.443980i
$426$	0.552218	+	0.956469i	0.0267550	+	0.0463411i
$427$		0			0
$428$	15.8031			0.763873
$429$	−0.682202	−	17.7252i	−0.0329370	−	0.855780i
$430$	−3.89164			−0.187672
$431$	7.59505	−	4.38500i	0.365841	−	0.211218i	−0.305799	−	0.952096i	$-0.598924\pi$
$431$	7.59505	−	4.38500i	0.365841	−	0.211218i	0.671640	+	0.740878i	$0.265590\pi$
$432$	−9.26026	−	16.0392i	−0.445534	−	0.771688i
$433$	11.0535	−	19.1452i	0.531196	−	0.920058i	−0.468141	−	0.883654i	$-0.655076\pi$
$433$	11.0535	−	19.1452i	0.531196	−	0.920058i	0.999337	−	0.0364046i	$-0.0115905\pi$
$434$		0			0
$435$	30.1038	+	17.3804i	1.44337	+	0.833328i
$436$	−2.27203	−	1.31176i	−0.108811	−	0.0628219i
$437$		−	0.828933i		−	0.0396533i
$438$	−2.34693	+	4.06501i	−0.112141	+	0.194234i
$439$	−5.18547	−	8.98150i	−0.247489	−	0.428664i	0.715339	−	0.698777i	$-0.246272\pi$
$439$	−5.18547	−	8.98150i	−0.247489	−	0.428664i	−0.962828	+	0.270114i	$0.912939\pi$
$440$	4.49705	−	2.59637i	0.214389	−	0.123777i
$441$		0			0
$442$	2.62866	−	1.65562i	0.125032	−	0.0787496i
$443$	35.8137			1.70156			0.850780	−	0.525522i	$-0.176130\pi$
$443$	35.8137			1.70156			0.850780	+	0.525522i	$0.176130\pi$
$444$	24.7456	−	14.2869i	1.17438	−	0.678026i
$445$	7.91437	+	13.7081i	0.375177	+	0.649826i
$446$	1.27530	−	2.20888i	0.0603871	−	0.104593i
$447$		−	26.1457i		−	1.23665i
$448$		0			0
$449$	−19.7023	−	11.3751i	−0.929809	−	0.536825i	−0.0430575	−	0.999073i	$-0.513710\pi$
$449$	−19.7023	−	11.3751i	−0.929809	−	0.536825i	−0.886751	+	0.462247i	$0.847043\pi$
$450$		−	0.134089i		−	0.00632100i
$451$	−7.31430	+	12.6687i	−0.344417	+	0.596548i
$452$	19.6124	+	33.9696i	0.922489	+	1.59780i
$453$	−10.2354	+	5.90942i	−0.480902	+	0.277649i
$454$	−0.518742			−0.0243458
$455$		0			0
$456$	0.246827			0.0115587
$457$	27.1215	−	15.6586i	1.26869	−	0.732478i	0.293949	−	0.955821i	$-0.405031\pi$
$457$	27.1215	−	15.6586i	1.26869	−	0.732478i	0.974740	+	0.223344i	$0.0716972\pi$
$458$	−0.793284	−	1.37401i	−0.0370677	−	0.0642032i
$459$	11.5968	−	20.0862i	0.541292	−	0.937546i
$460$		−	23.2522i		−	1.08414i
$461$	−7.28113	−	4.20376i	−0.339116	−	0.195789i	0.320765	−	0.947159i	$-0.396060\pi$
$461$	−7.28113	−	4.20376i	−0.339116	−	0.195789i	−0.659881	+	0.751370i	$0.729393\pi$
$462$		0			0
$463$		−	10.0392i		−	0.466563i	−0.972409	−	0.233281i	$-0.925054\pi$
$463$		−	10.0392i		−	0.466563i	0.972409	−	0.233281i	$-0.0749463\pi$
$464$	−13.4800	+	23.3480i	−0.625791	+	1.08390i
$465$	9.07411	+	15.7168i	0.420802	+	0.728850i
$466$	−0.799813	+	0.461772i	−0.0370506	+	0.0213912i
$467$	26.3513			1.21939			0.609696	−	0.792635i	$-0.291291\pi$
$467$	26.3513			1.21939			0.609696	+	0.792635i	$0.291291\pi$
$468$	1.10585	−	2.09780i	0.0511180	−	0.0969706i
$469$		0			0
$470$	−0.777869	+	0.449103i	−0.0358804	+	0.0207156i
$471$	14.5339	+	25.1735i	0.669687	+	1.15993i
$472$	−2.72206	+	4.71475i	−0.125293	+	0.217014i
$473$		−	21.5826i		−	0.992371i
$474$	2.60517	+	1.50410i	0.119660	+	0.0690855i
$475$	0.361941	+	0.208967i	0.0166070	+	0.00958806i
$476$		0			0
$477$	1.18224	−	2.04770i	0.0541310	−	0.0937577i
$478$	0.225846	+	0.391177i	0.0103300	+	0.0178920i
$479$	7.43409	−	4.29207i	0.339672	−	0.196110i	−0.320455	−	0.947264i	$-0.603836\pi$
$479$	7.43409	−	4.29207i	0.339672	−	0.196110i	0.660127	+	0.751154i	$0.270502\pi$
$480$	10.4140			0.475333
$481$	−25.3699	−	13.3737i	−1.15677	−	0.609788i
$482$	−1.44390			−0.0657678
$483$		0			0
$484$	−3.67990	−	6.37377i	−0.167268	−	0.289717i
$485$	−0.605963	+	1.04956i	−0.0275154	+	0.0476580i
$486$			0.625428i			0.0283700i
$487$	−18.4084	−	10.6281i	−0.834166	−	0.481606i	0.0211110	−	0.999777i	$-0.493280\pi$
$487$	−18.4084	−	10.6281i	−0.834166	−	0.481606i	−0.855277	+	0.518171i	$0.826613\pi$
$488$	0.255693	+	0.147624i	0.0115747	+	0.00668264i
$489$			8.73130i			0.394843i
$490$		0			0
$491$	−11.2268	−	19.4453i	−0.506657	−	0.877556i	−0.999970	−	0.00770409i	$-0.997548\pi$
$491$	−11.2268	−	19.4453i	−0.506657	−	0.877556i	0.493313	−	0.869852i	$-0.335786\pi$
$492$	−16.8916	+	9.75240i	−0.761534	+	0.439672i
$493$	−33.7624			−1.52058
$494$	−0.0654697	−	0.103948i	−0.00294562	−	0.00467682i
$495$	2.41999			0.108770
$496$	−12.1897	+	7.03772i	−0.547333	+	0.316003i
$497$		0			0
$498$	−2.73833	+	4.74293i	−0.122708	+	0.212536i
$499$			38.8780i			1.74042i	0.492681	+	0.870210i	$0.336017\pi$
$499$			38.8780i			1.74042i	−0.492681	+	0.870210i	$0.663983\pi$
$500$	−12.7339	−	7.35193i	−0.569478	−	0.328788i
$501$	−4.28619	−	2.47463i	−0.191493	−	0.110558i
$502$		−	4.56707i		−	0.203838i
$503$	−2.72850	+	4.72591i	−0.121658	+	0.210718i	−0.920422	−	0.390927i	$-0.872154\pi$
$503$	−2.72850	+	4.72591i	−0.121658	+	0.210718i	0.798764	+	0.601645i	$0.205488\pi$
$504$		0			0
$505$	17.8151	−	10.2855i	0.792760	−	0.457700i
$506$	−2.14326			−0.0952794
$507$	−23.6679	+	1.82455i	−1.05113	+	0.0810313i
$508$	15.6739			0.695418
$509$	−9.43315	+	5.44623i	−0.418117	+	0.241400i	−0.694271	−	0.719713i	$-0.744273\pi$
$509$	−9.43315	+	5.44623i	−0.418117	+	0.241400i	0.276154	+	0.961113i	$0.410940\pi$
$510$	2.11347	+	3.66064i	0.0935860	+	0.162096i
$511$		0			0
$512$			13.5360i			0.598214i
$513$	−0.794290	−	0.458584i	−0.0350688	−	0.0202470i
$514$	−0.528304	−	0.305017i	−0.0233025	−	0.0134537i
$515$		−	13.8561i		−	0.610572i
$516$	14.3884	−	24.9215i	0.633415	−	1.09711i
$517$	−2.49068	−	4.31398i	−0.109540	−	0.189729i
$518$		0			0
$519$	−1.64308			−0.0721230
$520$	−3.70346	−	5.88007i	−0.162408	−	0.257858i
$521$	27.8961			1.22215			0.611074	−	0.791573i	$-0.290738\pi$
$521$	27.8961			1.22215			0.611074	+	0.791573i	$0.290738\pi$
$522$	0.370962	−	0.214175i	0.0162366	−	0.00937418i
$523$	−8.36180	−	14.4831i	−0.365636	−	0.633300i	0.623242	−	0.782029i	$-0.285815\pi$
$523$	−8.36180	−	14.4831i	−0.365636	−	0.633300i	−0.988878	+	0.148729i	$0.952482\pi$
$524$	−9.85416	+	17.0679i	−0.430481	+	0.745615i
$525$		0			0
$526$	0.0248890	+	0.0143696i	0.00108521	+	0.000626546i
$527$	−15.2654	−	8.81347i	−0.664970	−	0.383921i
$528$			18.7190i			0.814639i
$529$	1.82314	−	3.15777i	0.0792668	−	0.137294i
$530$	−1.71793	−	2.97554i	−0.0746219	−	0.129249i
$531$	−2.19723	+	1.26857i	−0.0953515	+	0.0550512i
$532$		0			0
$533$	17.3178	+	9.12904i	0.750116	+	0.395423i
$534$	1.94534			0.0841832
$535$	18.6901	−	10.7907i	0.808045	−	0.466525i
$536$	4.08945	+	7.08313i	0.176637	+	0.305945i
$537$	10.0940	−	17.4834i	0.435590	−	0.754464i
$538$		−	4.21800i		−	0.181851i
$539$		0			0
$540$	−22.2804	−	12.8636i	−0.958796	−	0.553561i
$541$		−	11.1605i		−	0.479828i	−0.970794	−	0.239914i	$-0.922881\pi$
$541$		−	11.1605i		−	0.479828i	0.970794	−	0.239914i	$-0.0771192\pi$
$542$	−1.06876	+	1.85114i	−0.0459070	+	0.0795133i
$543$	−3.22198	−	5.58063i	−0.138268	−	0.239488i
$544$	−8.75976	+	5.05745i	−0.375572	+	0.216836i
$545$	−3.58280			−0.153470
$546$		0			0
$547$	36.6556			1.56728			0.783640	−	0.621215i	$-0.213361\pi$
$547$	36.6556			1.56728			0.783640	+	0.621215i	$0.213361\pi$
$548$	8.63275	−	4.98412i	0.368773	−	0.212911i
$549$	0.0687976	+	0.119161i	0.00293621	+	0.00508567i
$550$	0.540297	−	0.935821i	0.0230383	−	0.0399036i
$551$			1.33510i			0.0568772i
$552$	−4.99077	−	2.88142i	−0.212421	−	0.122641i
$553$		0			0
$554$			4.94830i			0.210233i
$555$	19.5109	−	33.7938i	0.828190	−	1.43447i
$556$	−7.59948	−	13.1627i	−0.322290	−	0.558222i
$557$	28.6461	−	16.5388i	1.21377	−	0.700772i	0.250193	−	0.968196i	$-0.419506\pi$
$557$	28.6461	−	16.5388i	1.21377	−	0.700772i	0.963579	+	0.267424i	$0.0861725\pi$
$558$	0.223636			0.00946727
$559$	−28.8615	+	1.11081i	−1.22071	+	0.0469823i
$560$		0			0
$561$	−20.3015	+	11.7211i	−0.857130	+	0.494864i
$562$	−2.58020	−	4.46903i	−0.108839	−	0.188515i
$563$	8.89836	−	15.4124i	0.375021	−	0.649556i	−0.615309	−	0.788286i	$-0.710969\pi$
$563$	8.89836	−	15.4124i	0.375021	−	0.649556i	0.990330	+	0.138730i	$0.0443021\pi$
$564$		−	6.64180i		−	0.279670i
$565$	46.3906	+	26.7836i	1.95167	+	1.12679i
$566$	2.81439	+	1.62489i	0.118298	+	0.0682992i
$567$		0			0
$568$	−1.19978	+	2.07808i	−0.0503417	+	0.0871943i
$569$	−4.11047	−	7.11954i	−0.172320	−	0.298467i	0.766911	−	0.641754i	$-0.221793\pi$
$569$	−4.11047	−	7.11954i	−0.172320	−	0.298467i	−0.939231	+	0.343287i	$0.888460\pi$
$570$	0.144756	−	0.0835750i	0.00606317	−	0.00350057i
$571$	25.7553			1.07782			0.538912	−	0.842362i	$-0.318835\pi$
$571$	25.7553			1.07782			0.538912	+	0.842362i	$0.318835\pi$
$572$	16.1707	−	10.1849i	0.676132	−	0.425851i
$573$	37.2513			1.55620
$574$		0			0
$575$	−4.87891	−	8.45051i	−0.203464	−	0.352411i
$576$	−1.20790	+	2.09214i	−0.0503290	+	0.0871724i
$577$		−	0.769393i		−	0.0320302i	−0.999872	−	0.0160151i	$-0.994902\pi$
$577$		−	0.769393i		−	0.0320302i	0.999872	−	0.0160151i	$-0.00509799\pi$
$578$	−0.893326	−	0.515762i	−0.0371575	−	0.0214529i
$579$	27.3017	+	15.7626i	1.13462	+	0.655073i
$580$			37.4505i			1.55505i
$581$		0			0
$582$	0.0744725	+	0.128990i	0.00308698	+	0.00534681i
$583$	16.5020	−	9.52743i	0.683443	−	0.394586i
$584$	−10.1982			−0.422003
$585$	−0.124551	−	3.23613i	−0.00514957	−	0.133798i
$586$	2.69229			0.111218
$587$	−10.4727	+	6.04644i	−0.432256	+	0.249563i	−0.700307	−	0.713841i	$-0.746954\pi$
$587$	−10.4727	+	6.04644i	−0.432256	+	0.249563i	0.268051	+	0.963405i	$0.413620\pi$
$588$		0			0
$589$	−0.348520	+	0.603654i	−0.0143605	+	0.0248731i
$590$			3.68674i			0.151781i
$591$	−7.83842	−	4.52552i	−0.322430	−	0.186155i
$592$	26.2099	+	15.1323i	1.07722	+	0.621933i
$593$			15.9481i			0.654911i	0.944867	+	0.327456i	$0.106191\pi$
$593$			15.9481i			0.654911i	−0.944867	+	0.327456i	$0.893809\pi$
$594$	−1.18570	+	2.05369i	−0.0486497	+	0.0842638i
$595$		0			0
$596$	24.3949	−	14.0844i	0.999253	−	0.576919i
$597$	13.1143			0.536734
$598$	0.110309	+	2.86608i	0.00451086	+	0.117203i
$599$	−7.11022			−0.290516			−0.145258	−	0.989394i	$-0.546401\pi$
$599$	−7.11022			−0.290516			−0.145258	+	0.989394i	$0.546401\pi$
$600$	2.51626	−	1.45276i	0.102726	−	0.0593088i
$601$	−10.3953	−	18.0051i	−0.424032	−	0.734445i	0.572297	−	0.820046i	$-0.306052\pi$
$601$	−10.3953	−	18.0051i	−0.424032	−	0.734445i	−0.996329	+	0.0856011i	$0.972719\pi$
$602$		0			0
$603$			3.81163i			0.155221i
$604$	−11.0274	−	6.36667i	−0.448698	−	0.259056i
$605$	−8.70432	−	5.02544i	−0.353881	−	0.204313i
$606$		−	2.52817i		−	0.102700i
$607$	3.85702	−	6.68056i	0.156552	−	0.271156i	−0.777071	−	0.629413i	$-0.783296\pi$
$607$	3.85702	−	6.68056i	0.156552	−	0.271156i	0.933623	+	0.358257i	$0.116629\pi$
$608$	0.199992	+	0.346396i	0.00811074	+	0.0140482i
$609$		0			0
$610$	0.199941			0.00809539
$611$	−5.64069	+	3.55270i	−0.228198	+	0.143727i
$612$	−3.13397			−0.126683
$613$	17.6997	−	10.2189i	0.714883	−	0.412738i	−0.0979832	−	0.995188i	$-0.531239\pi$
$613$	17.6997	−	10.2189i	0.714883	−	0.412738i	0.812867	+	0.582450i	$0.197906\pi$
$614$	2.12614	+	3.68257i	0.0858038	+	0.148617i
$615$	−13.3183	+	23.0680i	−0.537047	+	0.930193i
$616$		0			0
$617$	−3.98209	−	2.29906i	−0.160313	−	0.0925567i	0.417697	−	0.908586i	$-0.362837\pi$
$617$	−3.98209	−	2.29906i	−0.160313	−	0.0925567i	−0.578010	+	0.816030i	$0.696171\pi$
$618$	−1.47476	−	0.851451i	−0.0593234	−	0.0342504i
$619$		−	10.0528i		−	0.404057i	−0.979380	−	0.202028i	$-0.935247\pi$
$619$		−	10.0528i		−	0.404057i	0.979380	−	0.202028i	$-0.0647533\pi$
$620$	−9.77623	+	16.9329i	−0.392623	+	0.680042i
$621$	10.7069	+	18.5449i	0.429653	+	0.744181i
$622$	−0.255396	+	0.147453i	−0.0102404	+	0.00591232i
$623$		0			0
$624$	25.0320	−	0.963425i	1.00208	−	0.0385679i
$625$	−31.1705			−1.24682
$626$	−0.109107	+	0.0629930i	−0.00436080	+	0.00251771i
$627$	0.463498	+	0.802802i	0.0185103	+	0.0320608i
$628$	−15.6585	+	27.1213i	−0.624842	+	1.08226i
$629$			37.9009i			1.51121i
$630$		0			0
$631$	−6.29923	−	3.63686i	−0.250768	−	0.144781i	0.369348	−	0.929291i	$-0.379581\pi$
$631$	−6.29923	−	3.63686i	−0.250768	−	0.144781i	−0.620116	+	0.784510i	$0.712914\pi$
$632$			6.53578i			0.259979i
$633$	−16.0623	+	27.8207i	−0.638418	+	1.10577i
$634$	−1.93742	−	3.35570i	−0.0769447	−	0.133272i
$635$	18.5373	−	10.7025i	0.735631	−	0.424717i
$636$	25.4065			1.00743
$637$		0			0
$638$	3.45199			0.136665
$639$	−0.968451	+	0.559136i	−0.0383113	+	0.0221191i
$640$	7.45835	+	12.9182i	0.294817	+	0.510639i
$641$	1.92516	−	3.33448i	0.0760394	−	0.131704i	−0.825498	−	0.564404i	$-0.809106\pi$
$641$	1.92516	−	3.33448i	0.0760394	−	0.131704i	0.901538	+	0.432700i	$0.142439\pi$
$642$		−	2.65235i		−	0.104680i
$643$	2.49163	+	1.43855i	0.0982605	+	0.0567307i	0.548325	−	0.836265i	$-0.315266\pi$
$643$	2.49163	+	1.43855i	0.0982605	+	0.0567307i	−0.450065	+	0.892996i	$0.648599\pi$
$644$		0			0
$645$		−	39.2990i		−	1.54740i
$646$	−0.0811745	+	0.140598i	−0.00319377	+	0.00553177i
$647$	18.5501	+	32.1296i	0.729278	+	1.26315i	0.957189	+	0.289464i	$0.0934771\pi$
$647$	18.5501	+	32.1296i	0.729278	+	1.26315i	−0.227911	+	0.973682i	$0.573190\pi$
$648$	−6.14512	+	3.54789i	−0.241403	+	0.139374i
$649$	−20.4463			−0.802587
$650$	−1.27924	−	0.674349i	−0.0501758	−	0.0264501i
$651$		0			0
$652$	−8.14661	+	4.70345i	−0.319046	+	0.184201i
$653$	−10.0475	−	17.4028i	−0.393189	−	0.681023i	0.599679	−	0.800240i	$-0.295295\pi$
$653$	−10.0475	−	17.4028i	−0.393189	−	0.681023i	−0.992868	+	0.119218i	$0.961961\pi$
$654$	−0.220162	+	0.381332i	−0.00860902	+	0.0149113i
$655$			26.9146i			1.05164i
$656$	−17.8912	−	10.3295i	−0.698532	−	0.403298i
$657$	−4.11593	−	2.37634i	−0.160578	−	0.0927097i
$658$		0			0
$659$	−4.95529	+	8.58281i	−0.193031	+	0.334339i	−0.946253	−	0.323427i	$-0.895165\pi$
$659$	−4.95529	+	8.58281i	−0.193031	+	0.334339i	0.753223	+	0.657766i	$0.228498\pi$
$660$	13.0014	+	22.5192i	0.506080	+	0.876557i
$661$	−40.8994	+	23.6133i	−1.59080	+	0.918450i	−0.597633	+	0.801770i	$0.703892\pi$
$661$	−40.8994	+	23.6133i	−1.59080	+	0.918450i	−0.993170	+	0.116680i	$0.962775\pi$
$662$	0.274936			0.0106857
$663$	16.7189	+	26.5450i	0.649309	+	1.03092i
$664$	−11.8989			−0.461768
$665$		0			0
$666$	−0.240428	−	0.416433i	−0.00931639	−	0.0161365i
$667$	15.5858	−	26.9954i	0.603485	−	1.04527i
$668$		−	5.33222i		−	0.206310i
$669$	22.3059	+	12.8783i	0.862397	+	0.497905i
$670$	4.79667	+	2.76936i	0.185312	+	0.106990i
$671$			1.10885i			0.0428068i
$672$		0			0
$673$	3.45845	+	5.99020i	0.133313	+	0.230905i	0.924952	−	0.380084i	$-0.124105\pi$
$673$	3.45845	+	5.99020i	0.133313	+	0.230905i	−0.791639	+	0.610990i	$0.790772\pi$
$674$	−5.04721	+	2.91401i	−0.194411	+	0.112243i
$675$	−10.7965			−0.415556
$676$	−14.4520	−	21.1002i	−0.555847	−	0.811545i
$677$	−12.3291			−0.473844			−0.236922	−	0.971529i	$-0.576139\pi$
$677$	−12.3291			−0.473844			−0.236922	+	0.971529i	$0.576139\pi$
$678$	5.70137	−	3.29169i	0.218960	−	0.126416i
$679$		0			0
$680$	−4.59185	+	7.95331i	−0.176089	+	0.304996i
$681$		−	5.23841i		−	0.200736i
$682$	1.56078	+	0.901120i	0.0597655	+	0.0345057i
$683$	−21.2491	−	12.2682i	−0.813076	−	0.469430i	0.0349470	−	0.999389i	$-0.488874\pi$
$683$	−21.2491	−	12.2682i	−0.813076	−	0.469430i	−0.848023	+	0.529960i	$0.822207\pi$
$684$			0.123930i			0.00473856i
$685$	6.80655	−	11.7893i	0.260065	−	0.450446i
$686$		0			0
$687$	13.8751	−	8.01082i	0.529370	−	0.305632i
$688$	30.4796			1.16202
$689$	−13.5899	−	21.5770i	−0.517734	−	0.822018i
$690$	−3.90258			−0.148569
$691$	7.88703	−	4.55358i	0.300037	−	0.173226i	−0.342423	−	0.939546i	$-0.611247\pi$
$691$	7.88703	−	4.55358i	0.300037	−	0.173226i	0.642459	+	0.766320i	$0.277914\pi$
$692$	−0.885106	−	1.53305i	−0.0336467	−	0.0582777i
$693$		0			0
$694$			1.47992i			0.0561769i
$695$	−17.9756	−	10.3782i	−0.681853	−	0.393668i
$696$	8.03826	+	4.64089i	0.304690	+	0.175913i
$697$		−	25.8716i		−	0.979956i
$698$	−1.97543	+	3.42155i	−0.0747712	+	0.129508i
$699$	−4.66312	−	8.07675i	−0.176375	−	0.305491i
$700$		0			0
$701$	0.286950			0.0108380			0.00541898	−	0.999985i	$-0.498275\pi$
$701$	0.286950			0.0108380			0.00541898	+	0.999985i	$0.498275\pi$
$702$	2.80732	+	1.47988i	0.105956	+	0.0558544i
$703$	1.49875			0.0565265
$704$	−16.8601	+	9.73419i	−0.635440	+	0.366871i
$705$	−4.53518	−	7.85516i	−0.170805	−	0.295842i
$706$	0.0512797	−	0.0888191i	0.00192994	−	0.00334275i
$707$		0			0
$708$	−23.6093	−	13.6308i	−0.887292	−	0.512278i
$709$	−16.0949	−	9.29241i	−0.604457	−	0.348984i	0.166336	−	0.986069i	$-0.446806\pi$
$709$	−16.0949	−	9.29241i	−0.604457	−	0.348984i	−0.770793	+	0.637086i	$0.780140\pi$
$710$			1.62497i			0.0609841i
$711$	−1.52294	+	2.63781i	−0.0571147	+	0.0989256i
$712$	2.11328	+	3.66031i	0.0791986	+	0.137176i
$713$	14.0940	−	8.13715i	0.527823	−	0.304739i
$714$		0			0
$715$	12.1704	−	23.0872i	0.455148	−	0.863414i
$716$	21.7501			0.812841
$717$	−3.95022	+	2.28066i	−0.147524	+	0.0851729i
$718$	2.92974	+	5.07445i	0.109337	+	0.189377i
$719$	20.8475	−	36.1088i	0.777479	−	1.34663i	−0.155912	−	0.987771i	$-0.549832\pi$
$719$	20.8475	−	36.1088i	0.777479	−	1.34663i	0.933391	−	0.358862i	$-0.116835\pi$
$720$			3.41757i			0.127365i
$721$		0			0
$722$	−2.96980	−	1.71462i	−0.110525	−	0.0638114i
$723$		−	14.5809i		−	0.542271i
$724$	3.47128	−	6.01244i	0.129009	−	0.223451i
$725$	7.85809	+	13.6106i	0.291842	+	0.505486i
$726$	−1.06975	+	0.617623i	−0.0397023	+	0.0229221i
$727$	32.7039			1.21292			0.606461	−	0.795113i	$-0.292589\pi$
$727$	32.7039			1.21292			0.606461	+	0.795113i	$0.292589\pi$
$728$		0			0
$729$	23.3578			0.865105
$730$	−5.98091	+	3.45308i	−0.221363	+	0.127804i
$731$	19.0851	+	33.0564i	0.705888	+	1.22263i
$732$	−0.739235	+	1.28039i	−0.0273229	+	0.0473246i
$733$		−	9.93531i		−	0.366969i	−0.983023	−	0.183484i	$-0.941262\pi$
$733$		−	9.93531i		−	0.366969i	0.983023	−	0.183484i	$-0.0587377\pi$
$734$	1.23225	+	0.711440i	0.0454832	+	0.0262597i
$735$		0			0
$736$		−	9.33871i		−	0.344230i
$737$	−15.3586	+	26.6018i	−0.565740	+	0.979891i
$738$	0.164119	+	0.284262i	0.00604129	+	0.0104638i
$739$	9.00853	−	5.20108i	0.331384	−	0.191325i	−0.325071	−	0.945690i	$-0.605388\pi$
$739$	9.00853	−	5.20108i	0.331384	−	0.191325i	0.656455	+	0.754365i	$0.272055\pi$
$740$	42.0411			1.54546
$741$	1.04969	−	0.661133i	0.0385615	−	0.0242873i
$742$		0			0
$743$	−1.47972	+	0.854317i	−0.0542857	+	0.0313419i	−0.526897	−	0.849929i	$-0.676645\pi$
$743$	−1.47972	+	0.854317i	−0.0542857	+	0.0313419i	0.472612	+	0.881271i	$0.343311\pi$
$744$	2.42295	+	4.19668i	0.0888297	+	0.153858i
$745$	19.2343	−	33.3148i	0.704690	−	1.22056i
$746$		−	0.378216i		−	0.0138475i
$747$	−4.80235	−	2.77264i	−0.175709	−	0.101446i
$748$	−21.8723	−	12.6280i	−0.799732	−	0.461726i
$749$		0			0
$750$	−1.23393	+	2.13722i	−0.0450566	+	0.0780404i
$751$	14.9906	+	25.9645i	0.547015	+	0.947458i	0.998477	+	0.0551673i	$0.0175692\pi$
$751$	14.9906	+	25.9645i	0.547015	+	0.947458i	−0.451462	+	0.892290i	$0.649097\pi$
$752$	6.09233	−	3.51741i	0.222164	−	0.128267i
$753$	46.1197			1.68069
$754$	−0.177666	−	4.61618i	−0.00647022	−	0.168111i
$755$	−17.3893			−0.632860
$756$		0			0
$757$	−4.20229	−	7.27858i	−0.152735	−	0.264545i	0.779497	−	0.626406i	$-0.215475\pi$
$757$	−4.20229	−	7.27858i	−0.152735	−	0.264545i	−0.932232	+	0.361861i	$0.882141\pi$
$758$	1.29437	−	2.24191i	0.0470136	−	0.0814299i
$759$		−	21.6433i		−	0.785601i
$760$	0.314506	+	0.181580i	0.0114083	+	0.00658660i
$761$	−44.2184	−	25.5295i	−1.60292	−	0.925444i	−0.990900	−	0.134598i	$-0.957026\pi$
$761$	−44.2184	−	25.5295i	−1.60292	−	0.925444i	−0.612015	−	0.790846i	$-0.709641\pi$
$762$		−	2.63067i		−	0.0952990i
$763$		0			0
$764$	20.0668	+	34.7568i	0.725993	+	1.25746i
$765$	−3.70650	+	2.13995i	−0.134009	+	0.0773699i
$766$	−4.55447			−0.164560
$767$	1.05233	+	27.3419i	0.0379973	+	0.987257i
$768$	−24.5560			−0.886088
$769$	−0.610062	+	0.352220i	−0.0219994	+	0.0127014i	−0.510959	−	0.859605i	$-0.670710\pi$
$769$	−0.610062	+	0.352220i	−0.0219994	+	0.0127014i	0.488960	+	0.872306i	$0.337376\pi$
$770$		0			0
$771$	3.08015	−	5.33498i	0.110929	−	0.192134i
$772$			33.9646i			1.22241i
$773$	1.09571	+	0.632607i	0.0394099	+	0.0227533i	0.519575	−	0.854425i	$-0.326090\pi$
$773$	1.09571	+	0.632607i	0.0394099	+	0.0227533i	−0.480166	+	0.877178i	$0.659423\pi$
$774$	−0.419392	−	0.242136i	−0.0150747	−	0.00870341i
$775$			8.20522i			0.294740i
$776$	−0.161803	+	0.280252i	−0.00580840	+	0.0100604i
$777$		0			0
$778$	−4.40076	+	2.54078i	−0.157775	+	0.0910914i
$779$	−1.02307

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156598 - 0.0904119i) q^{2} +(0.913006 + 1.58137i) q^{3} +(-0.983651 + 1.70373i) q^{4} +2.68664i q^{5} +(0.285950 + 0.165093i) q^{6} +0.717383i q^{8} +(-0.167162 + 0.289532i) q^{9} +O(q^{10})\)	\(q+(0.156598 - 0.0904119i) q^{2} +(0.913006 + 1.58137i) q^{3} +(-0.983651 + 1.70373i) q^{4} +2.68664i q^{5} +(0.285950 + 0.165093i) q^{6} +0.717383i q^{8} +(-0.167162 + 0.289532i) q^{9} +(0.242904 + 0.420723i) q^{10} +(-2.33328 + 1.34712i) q^{11} -3.59232 q^{12} +(1.92153 + 3.05086i) q^{13} +(-4.24858 + 2.45292i) q^{15} +(-1.90244 - 3.29513i) q^{16} +(2.38247 - 4.12655i) q^{17} +0.0604535i q^{18} +(-0.163180 - 0.0942122i) q^{19} +(-4.57732 - 2.64272i) q^{20} +(-0.243592 + 0.421913i) q^{22} +(2.19964 + 3.80989i) q^{23} +(-1.13445 + 0.654975i) q^{24} -2.21804 q^{25} +(0.576741 + 0.304029i) q^{26} +4.86756 q^{27} +(-3.54280 - 6.13631i) q^{29} +(-0.443546 + 0.768245i) q^{30} -3.69931i q^{31} +(-1.83838 - 1.06139i) q^{32} +(-4.26060 - 2.45986i) q^{33} -0.861613i q^{34} +(-0.328857 - 0.569598i) q^{36} +(-6.88848 + 3.97707i) q^{37} -0.0340716 q^{38} +(-3.07017 + 5.82411i) q^{39} -1.92735 q^{40} +(4.70215 - 2.71479i) q^{41} +(-4.00533 + 6.93743i) q^{43} -5.30039i q^{44} +(-0.777869 - 0.449103i) q^{45} +(0.688919 + 0.397748i) q^{46} +1.84889i q^{47} +(3.47389 - 6.01695i) q^{48} +(-0.347341 + 0.200538i) q^{50} +8.70083 q^{51} +(-7.08796 + 0.272800i) q^{52} -7.07244 q^{53} +(0.762250 - 0.440085i) q^{54} +(-3.61923 - 6.26869i) q^{55} -0.344066i q^{57} +(-1.10959 - 0.640623i) q^{58} +(6.57216 + 3.79444i) q^{59} -9.65128i q^{60} +(0.205782 - 0.356425i) q^{61} +(-0.334461 - 0.579304i) q^{62} +7.22592 q^{64} +(-8.19656 + 5.16247i) q^{65} -0.889602 q^{66} +(9.87358 - 5.70051i) q^{67} +(4.68703 + 8.11818i) q^{68} +(-4.01658 + 6.95692i) q^{69} +(2.89675 + 1.67244i) q^{71} +(-0.207705 - 0.119919i) q^{72} +14.2158i q^{73} +(-0.719148 + 1.24560i) q^{74} +(-2.02509 - 3.50756i) q^{75} +(0.321025 - 0.185344i) q^{76} +(0.0457859 + 1.18962i) q^{78} +9.11059 q^{79} +(8.85283 - 5.11118i) q^{80} +(4.94560 + 8.56603i) q^{81} +(0.490899 - 0.850261i) q^{82} +16.5866i q^{83} +(11.0866 + 6.40083i) q^{85} +1.44852i q^{86} +(6.46920 - 11.2050i) q^{87} +(-0.966401 - 1.67386i) q^{88} +(5.10232 - 2.94582i) q^{89} -0.162417 q^{90} -8.65473 q^{92} +(5.84998 - 3.37749i) q^{93} +(0.167162 + 0.289532i) q^{94} +(0.253115 - 0.438407i) q^{95} -3.87622i q^{96} +(0.390659 + 0.225547i) q^{97} -0.900747i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 4 q^{4} - 9 q^{6} - q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 4 * q^4 - 9 * q^6 - q^9	\( 12 q - 3 q^{3} + 4 q^{4} - 9 q^{6} - q^{9} + 12 q^{10} - 12 q^{11} + 2 q^{12} - 2 q^{13} - 12 q^{15} - 8 q^{16} + 17 q^{17} - 9 q^{19} - 3 q^{20} - 15 q^{22} + 3 q^{23} - 15 q^{24} + 10 q^{25} + 15 q^{26} + 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{32} + 6 q^{33} - 13 q^{36} - 15 q^{37} - 38 q^{38} + 5 q^{39} + 2 q^{40} - 6 q^{41} + 11 q^{43} + 9 q^{45} + 30 q^{46} + 19 q^{48} + 18 q^{50} - 8 q^{51} - 40 q^{52} + 16 q^{53} - 6 q^{54} - 15 q^{55} + 24 q^{58} - 27 q^{59} + 5 q^{61} + 41 q^{62} + 2 q^{64} - 18 q^{65} + 68 q^{66} - 15 q^{67} - 11 q^{68} + 7 q^{69} + 30 q^{71} - 57 q^{72} - 33 q^{74} + q^{75} - 45 q^{76} + 44 q^{78} + 70 q^{79} + 63 q^{80} + 14 q^{81} + 5 q^{82} - 21 q^{85} + 10 q^{87} - 14 q^{88} - 48 q^{89} - 66 q^{92} + 81 q^{93} + q^{94} + 2 q^{95} - 3 q^{97}+O(q^{100}) \) 12 * q - 3 * q^3 + 4 * q^4 - 9 * q^6 - q^9 + 12 * q^10 - 12 * q^11 + 2 * q^12 - 2 * q^13 - 12 * q^15 - 8 * q^16 + 17 * q^17 - 9 * q^19 - 3 * q^20 - 15 * q^22 + 3 * q^23 - 15 * q^24 + 10 * q^25 + 15 * q^26 + 12 * q^27 - q^29 + 11 * q^30 - 18 * q^32 + 6 * q^33 - 13 * q^36 - 15 * q^37 - 38 * q^38 + 5 * q^39 + 2 * q^40 - 6 * q^41 + 11 * q^43 + 9 * q^45 + 30 * q^46 + 19 * q^48 + 18 * q^50 - 8 * q^51 - 40 * q^52 + 16 * q^53 - 6 * q^54 - 15 * q^55 + 24 * q^58 - 27 * q^59 + 5 * q^61 + 41 * q^62 + 2 * q^64 - 18 * q^65 + 68 * q^66 - 15 * q^67 - 11 * q^68 + 7 * q^69 + 30 * q^71 - 57 * q^72 - 33 * q^74 + q^75 - 45 * q^76 + 44 * q^78 + 70 * q^79 + 63 * q^80 + 14 * q^81 + 5 * q^82 - 21 * q^85 + 10 * q^87 - 14 * q^88 - 48 * q^89 - 66 * q^92 + 81 * q^93 + q^94 + 2 * q^95 - 3 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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