LMFDB - Embedded newform 950.2.u.g.199.6

Newspace parameters

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.6
Character	$\chi$	$=$	950.199
Dual form			950.2.u.g.549.6

$q$-expansion

$f(q)$	$=$	$q+(0.984808 - 0.173648i) q^{2} +(1.49114 + 1.77707i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.77707 + 1.49114i) q^{6} +(4.25802 + 2.45837i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.413538 + 2.34529i) q^{9} +O(q^{10})$	\(q+(0.984808 - 0.173648i) q^{2} +(1.49114 + 1.77707i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.77707 + 1.49114i) q^{6} +(4.25802 + 2.45837i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.413538 + 2.34529i) q^{9} +(-1.42329 - 2.46520i) q^{11} +(2.00901 + 1.15990i) q^{12} +(-4.21784 + 5.02662i) q^{13} +(4.62023 + 1.68163i) q^{14} +(0.766044 - 0.642788i) q^{16} +(2.15794 - 0.380503i) q^{17} +2.38147i q^{18} +(-4.17271 - 1.26036i) q^{19} +(1.98061 + 11.2326i) q^{21} +(-1.82974 - 2.18060i) q^{22} +(-0.908934 - 2.49728i) q^{23} +(2.17990 + 0.793418i) q^{24} +(-3.28089 + 5.68268i) q^{26} +(1.24263 - 0.717435i) q^{27} +(4.84205 + 0.853783i) q^{28} +(1.32004 - 7.48630i) q^{29} +(2.70769 - 4.68986i) q^{31} +(0.642788 - 0.766044i) q^{32} +(2.25852 - 6.20524i) q^{33} +(2.05908 - 0.749444i) q^{34} +(0.413538 + 2.34529i) q^{36} -2.06252i q^{37} +(-4.32817 - 0.516628i) q^{38} -15.2220 q^{39} +(-7.16810 + 6.01475i) q^{41} +(3.90103 + 10.7180i) q^{42} +(-0.593093 + 1.62951i) q^{43} +(-2.18060 - 1.82974i) q^{44} +(-1.32877 - 2.30150i) q^{46} +(-2.95934 - 0.521812i) q^{47} +(2.28456 + 0.402829i) q^{48} +(8.58718 + 14.8734i) q^{49} +(3.89396 + 3.26742i) q^{51} +(-2.24426 + 6.16606i) q^{52} +(-1.44406 - 3.96752i) q^{53} +(1.09917 - 0.922316i) q^{54} +4.91674 q^{56} +(-3.98234 - 9.29456i) q^{57} -7.60179i q^{58} +(0.167500 + 0.949937i) q^{59} +(7.04727 - 2.56500i) q^{61} +(1.85217 - 5.08880i) q^{62} +(-7.52644 + 8.96967i) q^{63} +(0.500000 - 0.866025i) q^{64} +(1.14668 - 6.50315i) q^{66} +(1.89039 + 0.333326i) q^{67} +(1.89766 - 1.09561i) q^{68} +(3.08249 - 5.33902i) q^{69} +(5.79354 + 2.10868i) q^{71} +(0.814510 + 2.23785i) q^{72} +(2.55639 + 3.04659i) q^{73} +(-0.358153 - 2.03119i) q^{74} +(-4.35213 + 0.242800i) q^{76} -13.9959i q^{77} +(-14.9908 + 2.64328i) q^{78} +(-11.7380 + 9.84938i) q^{79} +(9.84141 + 3.58198i) q^{81} +(-6.01475 + 7.16810i) q^{82} +(-1.13628 - 0.656032i) q^{83} +(5.70293 + 9.87776i) q^{84} +(-0.301121 + 1.70774i) q^{86} +(15.2720 - 8.81731i) q^{87} +(-2.46520 - 1.42329i) q^{88} +(8.25512 + 6.92687i) q^{89} +(-30.3170 + 11.0345i) q^{91} +(-1.70824 - 2.03580i) q^{92} +(12.3718 - 2.18147i) q^{93} -3.00499 q^{94} +2.31980 q^{96} +(-2.02308 + 0.356724i) q^{97} +(11.0395 + 13.1563i) q^{98} +(6.37020 - 2.31856i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36q + 36q^{9} + O(q^{10}) $	$ 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$3$	1.49114	+	1.77707i	0.860909	+	1.02599i	0.999365	+	0.0356229i	$0.0113415\pi$
$3$	1.49114	+	1.77707i	0.860909	+	1.02599i	−0.138456	+	0.990369i	$0.544214\pi$
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	1.77707	+	1.49114i	0.725486	+	0.608755i
$7$	4.25802	+	2.45837i	1.60938	+	0.929177i	0.989508	+	0.144475i	$0.0461494\pi$
$7$	4.25802	+	2.45837i	1.60938	+	0.929177i	0.619873	+	0.784702i	$0.287184\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−0.413538	+	2.34529i	−0.137846	+	0.781763i
$10$		0			0
$11$	−1.42329	−	2.46520i	−0.429137	−	0.743287i	0.567660	−	0.823263i	$-0.307849\pi$
$11$	−1.42329	−	2.46520i	−0.429137	−	0.743287i	−0.996797	+	0.0799763i	$0.974516\pi$
$12$	2.00901	+	1.15990i	0.579950	+	0.334834i
$13$	−4.21784	+	5.02662i	−1.16982	+	1.39413i	−0.267227	+	0.963634i	$0.586107\pi$
$13$	−4.21784	+	5.02662i	−1.16982	+	1.39413i	−0.902590	+	0.430500i	$0.858337\pi$
$14$	4.62023	+	1.68163i	1.23481	+	0.449433i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	2.15794	−	0.380503i	0.523377	−	0.0922855i	0.0942832	−	0.995545i	$-0.469944\pi$
$17$	2.15794	−	0.380503i	0.523377	−	0.0922855i	0.429094	+	0.903260i	$0.358833\pi$
$18$			2.38147i			0.561317i
$19$	−4.17271	−	1.26036i	−0.957285	−	0.289146i
$19$	−4.17271	−	1.26036i	−0.957285	−	0.289146i
$20$		0			0
$21$	1.98061	+	11.2326i	0.432204	+	2.45115i
$22$	−1.82974	−	2.18060i	−0.390102	−	0.464906i
$23$	−0.908934	−	2.49728i	−0.189526	−	0.520718i	0.808141	−	0.588989i	$-0.200474\pi$
$23$	−0.908934	−	2.49728i	−0.189526	−	0.520718i	−0.997667	+	0.0682711i	$0.978252\pi$
$24$	2.17990	+	0.793418i	0.444970	+	0.161956i
$25$		0			0
$26$	−3.28089	+	5.68268i	−0.643436	+	1.11446i
$27$	1.24263	−	0.717435i	0.239145	−	0.138070i
$28$	4.84205	+	0.853783i	0.915061	+	0.161350i
$29$	1.32004	−	7.48630i	0.245125	−	1.39017i	−0.575079	−	0.818098i	$-0.695029\pi$
$29$	1.32004	−	7.48630i	0.245125	−	1.39017i	0.820203	−	0.572072i	$-0.193860\pi$
$30$		0			0
$31$	2.70769	−	4.68986i	0.486316	−	0.842324i	−0.513560	−	0.858054i	$-0.671674\pi$
$31$	2.70769	−	4.68986i	0.486316	−	0.842324i	0.999876	+	0.0157295i	$0.00500705\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	2.25852	−	6.20524i	0.393158	−	1.08019i
$34$	2.05908	−	0.749444i	0.353130	−	0.128529i
$35$		0			0
$36$	0.413538	+	2.34529i	0.0689229	+	0.390881i
$37$		−	2.06252i		−	0.339076i	−0.985524	−	0.169538i	$-0.945772\pi$
$37$		−	2.06252i		−	0.339076i	0.985524	−	0.169538i	$-0.0542276\pi$
$38$	−4.32817	−	0.516628i	−0.702123	−	0.0838081i
$39$	−15.2220			−2.43748
$40$		0			0
$41$	−7.16810	+	6.01475i	−1.11947	+	0.939346i	−0.998578	−	0.0533193i	$-0.983020\pi$
$41$	−7.16810	+	6.01475i	−1.11947	+	0.939346i	−0.120892	+	0.992666i	$0.538575\pi$
$42$	3.90103	+	10.7180i	0.601942	+	1.65382i
$43$	−0.593093	+	1.62951i	−0.0904459	+	0.248498i	−0.976665	−	0.214768i	$-0.931100\pi$
$43$	−0.593093	+	1.62951i	−0.0904459	+	0.248498i	0.886219	+	0.463266i	$0.153323\pi$
$44$	−2.18060	−	1.82974i	−0.328738	−	0.275844i
$45$		0			0
$46$	−1.32877	−	2.30150i	−0.195917	−	0.339338i
$47$	−2.95934	−	0.521812i	−0.431664	−	0.0761140i	−0.0464056	−	0.998923i	$-0.514777\pi$
$47$	−2.95934	−	0.521812i	−0.431664	−	0.0761140i	−0.385259	+	0.922809i	$0.625888\pi$
$48$	2.28456	+	0.402829i	0.329747	+	0.0581433i
$49$	8.58718	+	14.8734i	1.22674	+	2.12478i
$50$		0			0
$51$	3.89396	+	3.26742i	0.545264	+	0.457531i
$52$	−2.24426	+	6.16606i	−0.311223	+	0.855079i
$53$	−1.44406	−	3.96752i	−0.198357	−	0.544981i	0.800139	−	0.599815i	$-0.204759\pi$
$53$	−1.44406	−	3.96752i	−0.198357	−	0.544981i	−0.998495	+	0.0548340i	$0.982537\pi$
$54$	1.09917	−	0.922316i	0.149579	−	0.125511i
$55$		0			0
$56$	4.91674			0.657027
$57$	−3.98234	−	9.29456i	−0.527474	−	1.23109i
$58$		−	7.60179i		−	0.998163i
$59$	0.167500	+	0.949937i	0.0218066	+	0.123671i	0.993768	−	0.111470i	$-0.0355559\pi$
$59$	0.167500	+	0.949937i	0.0218066	+	0.123671i	−0.971961	+	0.235141i	$0.924445\pi$
$60$		0			0
$61$	7.04727	−	2.56500i	0.902311	−	0.328414i	0.151132	−	0.988514i	$-0.451708\pi$
$61$	7.04727	−	2.56500i	0.902311	−	0.328414i	0.751178	+	0.660099i	$0.229486\pi$
$62$	1.85217	−	5.08880i	0.235226	−	0.646278i
$63$	−7.52644	+	8.96967i	−0.948243	+	1.13007i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	1.14668	−	6.50315i	0.141147	−	0.800483i
$67$	1.89039	+	0.333326i	0.230948	+	0.0407223i	0.287924	−	0.957653i	$-0.407035\pi$
$67$	1.89039	+	0.333326i	0.230948	+	0.0407223i	−0.0569765	+	0.998376i	$0.518146\pi$
$68$	1.89766	−	1.09561i	0.230125	−	0.132863i
$69$	3.08249	−	5.33902i	0.371088	−	0.642743i
$70$		0			0
$71$	5.79354	+	2.10868i	0.687567	+	0.250254i	0.662093	−	0.749422i	$-0.269668\pi$
$71$	5.79354	+	2.10868i	0.687567	+	0.250254i	0.0254738	+	0.999675i	$0.491891\pi$
$72$	0.814510	+	2.23785i	0.0959909	+	0.263733i
$73$	2.55639	+	3.04659i	0.299203	+	0.356576i	0.894610	−	0.446848i	$-0.147454\pi$
$73$	2.55639	+	3.04659i	0.299203	+	0.356576i	−0.595407	+	0.803424i	$0.703009\pi$
$74$	−0.358153	−	2.03119i	−0.0416344	−	0.236121i
$75$		0			0
$76$	−4.35213	+	0.242800i	−0.499224	+	0.0278511i
$77$		−	13.9959i		−	1.59498i
$78$	−14.9908	+	2.64328i	−1.69737	+	0.299292i
$79$	−11.7380	+	9.84938i	−1.32063	+	1.10814i	−0.334461	+	0.942409i	$0.608554\pi$
$79$	−11.7380	+	9.84938i	−1.32063	+	1.10814i	−0.986171	+	0.165732i	$0.947001\pi$
$80$		0			0
$81$	9.84141	+	3.58198i	1.09349	+	0.397998i
$82$	−6.01475	+	7.16810i	−0.664218	+	0.791584i
$83$	−1.13628	−	0.656032i	−0.124723	−	0.0720089i	0.436340	−	0.899782i	$-0.356274\pi$
$83$	−1.13628	−	0.656032i	−0.124723	−	0.0720089i	−0.561064	+	0.827773i	$0.689608\pi$
$84$	5.70293	+	9.87776i	0.622240	+	1.07775i
$85$		0			0
$86$	−0.301121	+	1.70774i	−0.0324708	+	0.184151i
$87$	15.2720	−	8.81731i	1.63733	−	0.945315i
$88$	−2.46520	−	1.42329i	−0.262792	−	0.151723i
$89$	8.25512	+	6.92687i	0.875041	+	0.734247i	0.965153	−	0.261685i	$-0.0842782\pi$
$89$	8.25512	+	6.92687i	0.875041	+	0.734247i	−0.0901123	+	0.995932i	$0.528723\pi$
$90$		0			0
$91$	−30.3170	+	11.0345i	−3.17808	+	1.15673i
$92$	−1.70824	−	2.03580i	−0.178096	−	0.212247i
$93$	12.3718	−	2.18147i	1.28289	−	0.226208i
$94$	−3.00499			−0.309941
$95$		0			0
$96$	2.31980			0.236764
$97$	−2.02308	+	0.356724i	−0.205413	+	0.0362198i	−0.275408	−	0.961328i	$-0.588813\pi$
$97$	−2.02308	+	0.356724i	−0.205413	+	0.0362198i	0.0699948	+	0.997547i	$0.477702\pi$
$98$	11.0395	+	13.1563i	1.11515	+	1.32899i
$99$	6.37020	−	2.31856i	0.640229	−	0.233024i
$100$		0			0
$101$	−3.83762	−	3.22015i	−0.381857	−	0.320416i	0.431574	−	0.902078i	$-0.357959\pi$
$101$	−3.83762	−	3.22015i	−0.381857	−	0.320416i	−0.813431	+	0.581661i	$0.802403\pi$
$102$	4.40219	+	2.54161i	0.435882	+	0.251656i
$103$	7.82444	−	4.51744i	0.770965	−	0.445117i	−0.0622537	−	0.998060i	$-0.519829\pi$
$103$	7.82444	−	4.51744i	0.770965	−	0.445117i	0.833219	+	0.552943i	$0.186495\pi$
$104$	−1.13944	+	6.46210i	−0.111732	+	0.633661i
$105$		0			0
$106$	−2.11108	−	3.65649i	−0.205046	−	0.355150i
$107$	−5.16829	−	2.98391i	−0.499637	−	0.288466i	0.228926	−	0.973444i	$-0.426478\pi$
$107$	−5.16829	−	2.98391i	−0.499637	−	0.288466i	−0.728564	+	0.684978i	$0.759812\pi$
$108$	0.922316	−	1.09917i	0.0887499	−	0.105768i
$109$	−14.8753	−	5.41417i	−1.42480	−	0.518583i	−0.489360	−	0.872082i	$-0.662770\pi$
$109$	−14.8753	−	5.41417i	−1.42480	−	0.518583i	−0.935435	+	0.353499i	$0.884992\pi$
$110$		0			0
$111$	3.66524	−	3.07550i	0.347889	−	0.291914i
$112$	4.84205	−	0.853783i	0.457530	−	0.0806750i
$113$		−	18.2051i		−	1.71259i	−0.516485	−	0.856296i	$-0.672760\pi$
$113$		−	18.2051i		−	1.71259i	0.516485	−	0.856296i	$-0.327240\pi$
$114$	−5.53582	−	8.46183i	−0.518477	−	0.792523i
$115$		0			0
$116$	−1.32004	−	7.48630i	−0.122562	−	0.695085i
$117$	−10.0446	−	11.9707i	−0.928628	−	1.10670i
$118$	0.329910	+	0.906420i	0.0303707	+	0.0834427i
$119$	10.1240	+	3.68482i	0.928063	+	0.337787i
$120$		0			0
$121$	1.44851	−	2.50890i	0.131683	−	0.228082i
$122$	6.49480	−	3.74977i	0.588012	−	0.339489i
$123$	−21.3773	−	3.76939i	−1.92752	−	0.339874i
$124$	0.940372	−	5.33311i	0.0844479	−	0.478928i
$125$		0			0
$126$	−5.85453	+	10.1404i	−0.521563	+	0.903374i
$127$	−4.91703	+	5.85989i	−0.436316	+	0.519981i	−0.938733	−	0.344644i	$-0.888000\pi$
$127$	−4.91703	+	5.85989i	−0.436316	+	0.519981i	0.502418	+	0.864625i	$0.332444\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	−3.78014	+	1.37586i	−0.332823	+	0.121137i
$130$		0			0
$131$	−2.31209	−	13.1125i	−0.202008	−	1.14564i	−0.902079	−	0.431571i	$-0.857960\pi$
$131$	−2.31209	−	13.1125i	−0.202008	−	1.14564i	0.700071	−	0.714073i	$-0.253152\pi$
$132$		−	6.60347i		−	0.574759i
$133$	−14.6691	−	15.6247i	−1.27197	−	1.35483i
$134$	1.91955			0.165824
$135$		0			0
$136$	1.67858	−	1.40849i	0.143937	−	0.120777i
$137$	2.47153	+	6.79047i	0.211157	+	0.580149i	0.999379	−	0.0352423i	$-0.0112203\pi$
$137$	2.47153	+	6.79047i	0.211157	+	0.580149i	−0.788222	+	0.615391i	$0.788998\pi$
$138$	2.10854	−	5.79318i	0.179491	−	0.493148i
$139$	1.84752	+	1.55026i	0.156705	+	0.131491i	0.717769	−	0.696281i	$-0.245163\pi$
$139$	1.84752	+	1.55026i	0.156705	+	0.131491i	−0.561064	+	0.827772i	$0.689608\pi$
$140$		0			0
$141$	−3.48549	−	6.03705i	−0.293531	−	0.508411i
$142$	6.07169	+	1.07060i	0.509525	+	0.0898430i
$143$	18.3948	+	3.24351i	1.53825	+	0.271236i
$144$	1.19073	+	2.06241i	0.0992279	+	0.171868i
$145$		0			0
$146$	3.04659	+	2.55639i	0.252137	+	0.211568i
$147$	−13.6264	+	37.4384i	−1.12389	+	3.08786i
$148$	−0.705424	−	1.93814i	−0.0579855	−	0.159314i
$149$	5.34602	−	4.48584i	0.437963	−	0.367495i	−0.396983	−	0.917826i	$-0.629943\pi$
$149$	5.34602	−	4.48584i	0.437963	−	0.367495i	0.834946	+	0.550331i	$0.185499\pi$
$150$		0			0
$151$	−5.69362			−0.463340			−0.231670	−	0.972794i	$-0.574419\pi$
$151$	−5.69362			−0.463340			−0.231670	+	0.972794i	$0.574419\pi$
$152$	−4.24385	+	0.994851i	−0.344222	+	0.0806931i
$153$			5.21834i			0.421878i
$154$	−2.43036	−	13.7832i	−0.195844	−	1.11068i
$155$		0			0
$156$	−14.3040	+	5.20624i	−1.14524	+	0.416833i
$157$	−1.81744	+	4.99337i	−0.145047	+	0.398514i	−0.990848	−	0.134985i	$-0.956901\pi$
$157$	−1.81744	+	4.99337i	−0.145047	+	0.398514i	0.845800	+	0.533500i	$0.179123\pi$
$158$	−9.84938	+	11.7380i	−0.783575	+	0.933828i
$159$	4.89727	−	8.48232i	0.388379	−	0.672692i
$160$		0			0
$161$	2.26897	−	12.8680i	0.178820	−	1.01414i
$162$	10.3139	+	1.81862i	0.810337	+	0.142884i
$163$	3.87424	−	2.23679i	0.303454	−	0.175199i	−0.340540	−	0.940230i	$-0.610610\pi$
$163$	3.87424	−	2.23679i	0.303454	−	0.175199i	0.643993	+	0.765031i	$0.277276\pi$
$164$	−4.67865	+	8.10365i	−0.365341	+	0.632789i
$165$		0			0
$166$	−1.23294	−	0.448753i	−0.0956945	−	0.0348300i
$167$	−1.24795	−	3.42872i	−0.0965694	−	0.265322i	0.881997	−	0.471256i	$-0.156199\pi$
$167$	−1.24795	−	3.42872i	−0.0965694	−	0.265322i	−0.978566	+	0.205934i	$0.933977\pi$
$168$	7.33154	+	8.73739i	0.565641	+	0.674104i
$169$	−5.21936	−	29.6004i	−0.401489	−	2.27696i
$170$		0			0
$171$	4.68148	−	9.26500i	0.358002	−	0.708512i
$172$			1.73409i			0.132223i
$173$	−1.15844	+	0.204264i	−0.0880746	+	0.0155299i	−0.217512	−	0.976058i	$-0.569794\pi$
$173$	−1.15844	+	0.204264i	−0.0880746	+	0.0155299i	0.129437	+	0.991588i	$0.458683\pi$
$174$	13.5089	−	11.3353i	1.02411	−	0.859328i
$175$		0			0
$176$	−2.67490	−	0.973585i	−0.201628	−	0.0733867i
$177$	−1.43834	+	1.71415i	−0.108112	+	0.128843i
$178$	9.33254	+	5.38815i	0.699504	+	0.403859i
$179$	2.16529	+	3.75038i	0.161841	+	0.280317i	0.935529	−	0.353250i	$-0.114923\pi$
$179$	2.16529	+	3.75038i	0.161841	+	0.280317i	−0.773688	+	0.633567i	$0.781590\pi$
$180$		0			0
$181$	0.237758	−	1.34839i	0.0176724	−	0.100225i	−0.974696	−	0.223536i	$-0.928240\pi$
$181$	0.237758	−	1.34839i	0.0176724	−	0.100225i	0.992368	+	0.123311i	$0.0393511\pi$
$182$	−27.9403	+	16.1313i	−2.07107	+	1.19573i
$183$	15.0666	+	8.69872i	1.11376	+	0.643028i
$184$	−2.03580	−	1.70824i	−0.150081	−	0.125933i
$185$		0			0
$186$	11.8050	−	4.29667i	0.865584	−	0.315047i
$187$	−4.00938	−	4.77819i	−0.293195	−	0.349416i
$188$	−2.95934	+	0.521812i	−0.215832	+	0.0380570i
$189$	7.05488			0.513167
$190$		0			0
$191$	13.6338			0.986505			0.493252	−	0.869886i	$-0.335808\pi$
$191$	13.6338			0.986505			0.493252	+	0.869886i	$0.335808\pi$
$192$	2.28456	−	0.402829i	0.164874	−	0.0290717i
$193$	3.35501	+	3.99835i	0.241499	+	0.287807i	0.873156	−	0.487441i	$-0.162069\pi$
$193$	3.35501	+	3.99835i	0.241499	+	0.287807i	−0.631657	+	0.775248i	$0.717625\pi$
$194$	−1.93040	+	0.702609i	−0.138595	+	0.0504444i
$195$		0			0
$196$	13.1563	+	11.0395i	0.939737	+	0.788533i
$197$	−2.47286	−	1.42771i	−0.176184	−	0.101720i	0.409315	−	0.912393i	$-0.365768\pi$
$197$	−2.47286	−	1.42771i	−0.176184	−	0.101720i	−0.585498	+	0.810674i	$0.699101\pi$
$198$	5.87080	−	3.38951i	0.417220	−	0.240882i
$199$	0.254330	−	1.44238i	0.0180290	−	0.102247i	−0.974465	−	0.224538i	$-0.927913\pi$
$199$	0.254330	−	1.44238i	0.0180290	−	0.102247i	0.992494	+	0.122290i	$0.0390239\pi$
$200$		0			0
$201$	2.22649	+	3.85639i	0.157044	+	0.272009i
$202$	−4.33849	−	2.50483i	−0.305255	−	0.176239i
$203$	24.0248	−	28.6317i	1.68621	−	2.00955i
$204$	4.77666	+	1.73856i	0.334433	+	0.121724i
$205$		0			0
$206$	6.92112	−	5.80751i	0.482218	−	0.404629i
$207$	6.23271	−	1.09900i	0.433203	−	0.0763855i
$208$			6.56179i			0.454978i
$209$	2.83192	+	12.0804i	0.195888	+	0.835621i
$210$		0			0
$211$	0.227567	+	1.29059i	0.0156663	+	0.0888482i	0.991638	−	0.129047i	$-0.0411919\pi$
$211$	0.227567	+	1.29059i	0.0156663	+	0.0888482i	−0.975972	+	0.217896i	$0.930081\pi$
$212$	−2.71395	−	3.23435i	−0.186395	−	0.222136i
$213$	4.89171	+	13.4399i	0.335174	+	0.920883i
$214$	−5.60792	−	2.04112i	−0.383350	−	0.139528i
$215$		0			0
$216$	0.717435	−	1.24263i	0.0488152	−	0.0845505i
$217$	23.0588	−	13.3130i	1.56534	−	0.903747i
$218$	−15.5895	−	2.74884i	−1.05585	−	0.186175i
$219$	−1.60206	+	9.08576i	−0.108257	+	0.613959i
$220$		0			0
$221$	−7.18919	+	12.4520i	−0.483597	+	0.837615i
$222$	3.07550	−	3.66524i	0.206414	−	0.245995i
$223$	−9.62115	+	26.4339i	−0.644280	+	1.77014i	−0.00643379	+	0.999979i	$0.502048\pi$
$223$	−9.62115	+	26.4339i	−0.644280	+	1.77014i	−0.637846	+	0.770164i	$0.720174\pi$
$224$	4.62023	−	1.68163i	0.308702	−	0.112358i
$225$		0			0
$226$	−3.16128	−	17.9285i	−0.210285	−	1.19259i
$227$			12.6466i			0.839382i	0.907667	+	0.419691i	$0.137862\pi$
$227$			12.6466i			0.839382i	−0.907667	+	0.419691i	$0.862138\pi$
$228$	−6.92110	−	7.37199i	−0.458361	−	0.488222i
$229$	−13.7440			−0.908227			−0.454113	−	0.890944i	$-0.650044\pi$
$229$	−13.7440			−0.908227			−0.454113	+	0.890944i	$0.650044\pi$
$230$		0			0
$231$	24.8716	−	20.8698i	1.63643	−	1.37313i
$232$	−2.59996	−	7.14334i	−0.170696	−	0.468983i
$233$	−8.41990	+	23.1335i	−0.551606	+	1.51552i	0.279911	+	0.960026i	$0.409695\pi$
$233$	−8.41990	+	23.1335i	−0.551606	+	1.51552i	−0.831517	+	0.555499i	$0.812527\pi$
$234$	−11.9707	−	10.0446i	−0.782552	−	0.656639i
$235$		0			0
$236$	0.482296	+	0.835361i	0.0313948	+	0.0543774i
$237$	−35.0061	−	6.17251i	−2.27389	−	0.400948i
$238$	10.6100	+	1.87083i	0.687746	+	0.121268i
$239$	−8.14698	−	14.1110i	−0.526984	−	0.912763i	−0.999506	−	0.0314439i	$-0.989989\pi$
$239$	−8.14698	−	14.1110i	−0.526984	−	0.912763i	0.472522	−	0.881319i	$-0.343344\pi$
$240$		0			0
$241$	−14.7500	−	12.3767i	−0.950133	−	0.797256i	0.0291873	−	0.999574i	$-0.490708\pi$
$241$	−14.7500	−	12.3767i	−0.950133	−	0.797256i	−0.979320	+	0.202318i	$0.935153\pi$
$242$	0.990842	−	2.72232i	0.0636938	−	0.174997i
$243$	6.83722	+	18.7851i	0.438608	+	1.20506i
$244$	5.74499	−	4.82062i	0.367785	−	0.308608i
$245$		0			0
$246$	−21.7070			−1.38399
$247$	23.9351	−	15.6586i	1.52296	−	0.996335i
$248$		−	5.41539i		−	0.343877i
$249$	−0.528538	−	2.99749i	−0.0334947	−	0.189958i
$250$		0			0
$251$	26.0953	−	9.49792i	1.64712	−	0.599504i	0.658860	−	0.752266i	$-0.271039\pi$
$251$	26.0953	−	9.49792i	1.64712	−	0.599504i	0.988263	+	0.152762i	$0.0488169\pi$
$252$	−4.00474	+	11.0029i	−0.252275	+	0.693119i
$253$	−4.86262	+	5.79505i	−0.305710	+	0.364331i
$254$	−3.82477	+	6.62470i	−0.239987	+	0.415671i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	12.8717	+	2.26963i	0.802915	+	0.141576i	0.560022	−	0.828478i	$-0.310793\pi$
$257$	12.8717	+	2.26963i	0.802915	+	0.141576i	0.242893	+	0.970053i	$0.421904\pi$
$258$	−3.48379	+	2.01137i	−0.216891	+	0.125222i
$259$	5.07044	−	8.78226i	0.315062	−	0.545703i
$260$		0			0
$261$	17.0116	+	6.19173i	1.05299	+	0.383259i
$262$	−4.55392	−	12.5118i	−0.281342	−	0.772981i
$263$	−9.67780	−	11.5336i	−0.596759	−	0.711190i	0.380131	−	0.924933i	$-0.375879\pi$
$263$	−9.67780	−	11.5336i	−0.596759	−	0.711190i	−0.976890	+	0.213743i	$0.931434\pi$
$264$	−1.14668	−	6.50315i	−0.0705734	−	0.400241i
$265$		0			0
$266$	−17.1594	−	12.8401i	−1.05211	−	0.787276i
$267$			24.9988i			1.52990i
$268$	1.89039	−	0.333326i	0.115474	−	0.0203612i
$269$	−18.7339	+	15.7196i	−1.14222	+	0.958439i	−0.999509	−	0.0313248i	$-0.990027\pi$
$269$	−18.7339	+	15.7196i	−1.14222	+	0.958439i	−0.142714	+	0.989764i	$0.545583\pi$
$270$		0			0
$271$	−8.41094	−	3.06133i	−0.510928	−	0.185963i	0.0736745	−	0.997282i	$-0.476527\pi$
$271$	−8.41094	−	3.06133i	−0.510928	−	0.185963i	−0.584603	+	0.811320i	$0.698750\pi$
$272$	1.40849	−	1.67858i	0.0854025	−	0.101779i
$273$	−64.8158	−	37.4214i	−3.92283	−	2.26485i
$274$	3.61313	+	6.25813i	0.218277	+	0.378067i
$275$		0			0
$276$	1.07054	−	6.07131i	0.0644387	−	0.365450i
$277$	−6.75622	+	3.90071i	−0.405942	+	0.234371i	−0.689045	−	0.724719i	$-0.741970\pi$
$277$	−6.75622	+	3.90071i	−0.405942	+	0.234371i	0.283103	+	0.959090i	$0.408636\pi$
$278$	2.08866	+	1.20589i	0.125269	+	0.0723242i
$279$	9.87935	+	8.28976i	0.591461	+	0.496295i
$280$		0			0
$281$	−17.1947	+	6.25837i	−1.02575	+	0.373343i	−0.799462	−	0.600717i	$-0.794882\pi$
$281$	−17.1947	+	6.25837i	−1.02575	+	0.373343i	−0.226290	+	0.974060i	$0.572660\pi$
$282$	−4.48086	−	5.34008i	−0.266831	−	0.317997i
$283$	7.11822	−	1.25513i	0.423134	−	0.0746100i	0.0419735	−	0.999119i	$-0.486635\pi$
$283$	7.11822	−	1.25513i	0.423134	−	0.0746100i	0.381161	+	0.924509i	$0.375524\pi$
$284$	6.16536			0.365847
$285$		0			0
$286$	18.6786			1.10449
$287$	−45.3084	+	7.98910i	−2.67447	+	0.471582i
$288$	1.53078	+	1.82431i	0.0902020	+	0.107499i
$289$	−11.4629	+	4.17214i	−0.674286	+	0.245420i
$290$		0			0
$291$	−3.65062	−	3.06323i	−0.214003	−	0.179570i
$292$	3.44421	+	1.98852i	0.201557	+	0.116369i
$293$	−9.86109	+	5.69330i	−0.576091	+	0.332606i	−0.759578	−	0.650416i	$-0.774595\pi$
$293$	−9.86109	+	5.69330i	−0.576091	+	0.332606i	0.183488	+	0.983022i	$0.441261\pi$
$294$	−6.91833	+	39.2358i	−0.403485	+	2.28828i
$295$		0			0
$296$	−1.03126	−	1.78620i	−0.0599408	−	0.103821i
$297$	−3.53724	−	2.04223i	−0.205252	−	0.118502i
$298$	4.48584	−	5.34602i	0.259858	−	0.309687i
$299$	16.3866	+	5.96423i	0.947662	+	0.344921i
$300$		0			0
$301$	−6.53135	+	5.48045i	−0.376461	+	0.315888i
$302$	−5.60712	+	0.988686i	−0.322653	+	0.0568925i
$303$		−	11.6214i		−	0.667632i
$304$	−4.00662	+	1.71667i	−0.229796	+	0.0984580i
$305$		0			0
$306$	0.906156	+	5.13906i	0.0518015	+	0.293781i
$307$	3.17725	+	3.78649i	0.181335	+	0.216107i	0.849053	−	0.528308i	$-0.177173\pi$
$307$	3.17725	+	3.78649i	0.181335	+	0.216107i	−0.667718	+	0.744414i	$0.732729\pi$
$308$	−4.78687	−	13.1518i	−0.272757	−	0.749394i
$309$	19.6951	+	7.16844i	1.12042	+	0.407798i
$310$		0			0
$311$	−12.0586	+	20.8861i	−0.683782	+	1.18434i	0.290036	+	0.957016i	$0.406333\pi$
$311$	−12.0586	+	20.8861i	−0.683782	+	1.18434i	−0.973818	+	0.227329i	$0.927001\pi$
$312$	−13.1827	+	7.61102i	−0.746322	+	0.430889i
$313$	30.5050	+	5.37886i	1.72424	+	0.304031i	0.946057	−	0.324001i	$-0.105028\pi$
$313$	30.5050	+	5.37886i	1.72424	+	0.304031i	0.778188	+	0.628031i	$0.216139\pi$
$314$	−0.922737	+	5.23310i	−0.0520731	+	0.295321i
$315$		0			0
$316$	−7.66146	+	13.2700i	−0.430991	+	0.746498i
$317$	4.44201	−	5.29378i	0.249488	−	0.297328i	−0.626737	−	0.779231i	$-0.715610\pi$
$317$	4.44201	−	5.29378i	0.249488	−	0.297328i	0.876225	+	0.481903i	$0.160054\pi$
$318$	3.34993	−	9.20386i	0.187855	−	0.516127i
$319$	−20.3340	+	7.40098i	−1.13849	+	0.414376i
$320$		0			0
$321$	−2.40401	−	13.6338i	−0.134179	−	0.760966i
$322$		−	13.0665i		−	0.728166i
$323$	−9.48402	−	1.13205i	−0.527705	−	0.0629890i
$324$	10.4730			0.581834
$325$		0			0
$326$	3.42697	−	2.87557i	0.189802	−	0.159263i
$327$	−12.5598	−	34.5077i	−0.694557	−	1.90828i
$328$	−3.20038	+	8.79298i	−0.176712	+	0.485511i
$329$	−11.3181	−	9.49705i	−0.623989	−	0.523589i
$330$		0			0
$331$	−2.08943	−	3.61900i	−0.114845	−	0.198918i	0.802873	−	0.596151i	$-0.203304\pi$
$331$	−2.08943	−	3.61900i	−0.114845	−	0.198918i	−0.917718	+	0.397233i	$0.869971\pi$
$332$	−1.29213	−	0.227838i	−0.0709149	−	0.0125042i
$333$	4.83721	+	0.852930i	0.265077	+	0.0467403i
$334$	−1.82438	−	3.15992i	−0.0998258	−	0.172903i
$335$		0			0
$336$	8.73739	+	7.33154i	0.476664	+	0.399968i
$337$	5.88315	−	16.1638i	0.320476	−	0.880500i	−0.669944	−	0.742411i	$-0.733682\pi$
$337$	5.88315	−	16.1638i	0.320476	−	0.880500i	0.990420	−	0.138088i	$-0.0440958\pi$
$338$	−10.2801	−	28.2444i	−0.559165	−	1.53629i
$339$	32.3517	−	27.1463i	1.75710	−	1.47439i
$340$		0			0
$341$	−15.4153			−0.834784
$342$	3.00151	−	9.93717i	0.162303	−	0.537341i
$343$			50.0247i			2.70108i
$344$	0.301121	+	1.70774i	0.0162354	+	0.0920754i
$345$		0			0
$346$	−1.10537	+	0.402322i	−0.0594251	+	0.0216290i
$347$	6.31466	−	17.3494i	0.338989	−	0.931364i	−0.646693	−	0.762750i	$-0.723849\pi$
$347$	6.31466	−	17.3494i	0.338989	−	0.931364i	0.985682	−	0.168614i	$-0.0539291\pi$
$348$	11.3353	−	13.5089i	0.607637	−	0.724153i
$349$	12.3704	−	21.4262i	0.662174	−	1.14692i	−0.317870	−	0.948134i	$-0.602967\pi$
$349$	12.3704	−	21.4262i	0.662174	−	1.14692i	0.980043	−	0.198784i	$-0.0636992\pi$
$350$		0			0
$351$	−1.63495	+	9.27227i	−0.0872672	+	0.494917i
$352$	−2.80333	−	0.494302i	−0.149418	−	0.0263464i
$353$	5.55115	−	3.20496i	0.295458	−	0.170583i	−0.344943	−	0.938624i	$-0.612102\pi$
$353$	5.55115	−	3.20496i	0.295458	−	0.170583i	0.640401	+	0.768041i	$0.278768\pi$
$354$	−1.11883	+	1.93787i	−0.0594651	+	0.102997i
$355$		0			0
$356$	10.1264	+	3.68571i	0.536698	+	0.195342i
$357$	8.54805	+	23.4856i	0.452411	+	1.24299i
$358$	2.78364	+	3.31741i	0.147120	+	0.175331i
$359$	6.39293	+	36.2561i	0.337406	+	1.91353i	0.402051	+	0.915617i	$0.368297\pi$
$359$	6.39293	+	36.2561i	0.337406	+	1.91353i	−0.0646449	+	0.997908i	$0.520591\pi$
$360$		0			0
$361$	15.8230	+	10.5182i	0.832789	+	0.553591i
$362$		−	1.36920i		−	0.0719633i
$363$	6.61843	−	1.16701i	0.347377	−	0.0612520i
$364$	−24.7146	+	20.7380i	−1.29540	+	1.08697i
$365$		0			0
$366$	16.3483	+	5.95028i	0.854537	+	0.311026i
$367$	−9.39999	+	11.2025i	−0.490676	+	0.584764i	−0.953389	−	0.301743i	$-0.902431\pi$
$367$	−9.39999	+	11.2025i	−0.490676	+	0.584764i	0.462714	+	0.886508i	$0.346876\pi$
$368$	−2.30150	−	1.32877i	−0.119974	−	0.0692671i
$369$	−11.1420	−	19.2986i	−0.580032	−	1.00464i
$370$		0			0
$371$	3.60480	−	20.4438i	0.187152	−	1.06139i
$372$	10.8795	−	6.28130i	0.564078	−	0.325670i
$373$	−11.7411	−	6.77871i	−0.607930	−	0.350989i	0.164225	−	0.986423i	$-0.447488\pi$
$373$	−11.7411	−	6.77871i	−0.607930	−	0.350989i	−0.772155	+	0.635434i	$0.780821\pi$
$374$	−4.77819	−	4.00938i	−0.247075	−	0.207320i
$375$		0			0
$376$	−2.82377	+	1.02777i	−0.145625	+	0.0530031i
$377$	32.0631	+	38.2113i	1.65133	+	1.96798i
$378$	6.94770	−	1.22507i	0.357351	−	0.0630107i
$379$	−30.2899			−1.55589			−0.777944	−	0.628333i	$-0.783738\pi$
$379$	−30.2899			−1.55589			−0.777944	+	0.628333i	$0.783738\pi$
$380$		0			0
$381$	−17.7454			−0.909124
$382$	13.4266	−	2.36748i	0.686967	−	0.121131i
$383$	18.4242	+	21.9571i	0.941433	+	1.12196i	0.992375	+	0.123254i	$0.0393330\pi$
$383$	18.4242	+	21.9571i	0.941433	+	1.12196i	−0.0509425	+	0.998702i	$0.516223\pi$
$384$	2.17990	−	0.793418i	0.111242	−	0.0404889i
$385$		0			0
$386$	3.99835	+	3.35501i	0.203511	+	0.170766i
$387$	−3.57641	−	2.06484i	−0.181799	−	0.104962i
$388$	−1.77907	+	1.02715i	−0.0903186	+	0.0521454i
$389$	−2.97395	+	16.8661i	−0.150785	+	0.855145i	0.811754	+	0.584000i	$0.198513\pi$
$389$	−2.97395	+	16.8661i	−0.150785	+	0.855145i	−0.962539	+	0.271145i	$0.912598\pi$
$390$		0			0
$391$	−2.91165	−	5.04312i	−0.147248	−	0.255041i
$392$	14.8734	+	8.58718i	0.751222	+	0.433718i
$393$	19.8542	−	23.6613i	1.00151	−	1.19355i
$394$	−2.68321	−	0.976608i	−0.135178	−	0.0492008i
$395$		0			0
$396$	5.19303	−	4.35747i	0.260960	−	0.218971i
$397$	−25.7084	+	4.53308i	−1.29027	+	0.227509i	−0.776334	−	0.630322i	$-0.782923\pi$
$397$	−25.7084	+	4.53308i	−1.29027	+	0.227509i	−0.513932	+	0.857831i	$0.671812\pi$
$398$		−	1.46463i		−	0.0734151i
$399$	5.89259	−	49.3665i	0.294998	−	2.47142i
$400$		0			0
$401$	−1.61683	−	9.16948i	−0.0807405	−	0.457902i	−0.998195	−	0.0600607i	$-0.980871\pi$
$401$	−1.61683	−	9.16948i	−0.0807405	−	0.457902i	0.917454	−	0.397841i	$-0.130241\pi$
$402$	2.86232	+	3.41117i	0.142759	+	0.170134i
$403$	12.1536	+	33.3916i	0.605412	+	1.66336i
$404$	−4.70754	−	1.71340i	−0.234209	−	0.0852450i
$405$		0			0
$406$	18.6880	−	32.3686i	0.927471	−	1.60643i
$407$	−5.08453	+	2.93556i	−0.252031	+	0.145510i
$408$	5.00598	+	0.882690i	0.247833	+	0.0436997i
$409$	−2.53175	+	14.3583i	−0.125187	+	0.709972i	0.856009	+	0.516960i	$0.172937\pi$
$409$	−2.53175	+	14.3583i	−0.125187	+	0.709972i	−0.981196	+	0.193012i	$0.938175\pi$
$410$		0			0
$411$	−8.38174	+	14.5176i	−0.413441	+	0.716101i
$412$	5.80751	−	6.92112i	0.286116	−	0.340979i
$413$	−1.62208	+	4.45663i	−0.0798174	+	0.219297i
$414$	5.94718	−	2.16460i	0.292288	−	0.106384i
$415$		0			0
$416$	1.13944	+	6.46210i	0.0558658	+	0.316831i
$417$			5.59483i			0.273980i
$418$	4.88664	+	11.4051i	0.239013	+	0.557844i
$419$	−14.5969			−0.713103			−0.356552	−	0.934276i	$-0.616048\pi$
$419$	−14.5969			−0.713103			−0.356552	+	0.934276i	$0.616048\pi$
$420$		0			0
$421$	−30.0605	+	25.2237i	−1.46506	+	1.22933i	−0.544478	+	0.838775i	$0.683272\pi$
$421$	−30.0605	+	25.2237i	−1.46506	+	1.22933i	−0.920580	+	0.390554i	$0.872283\pi$
$422$	0.448219	+	1.23147i	0.0218190	+	0.0599471i
$423$	2.44760	−	6.72472i	0.119006	−	0.326967i
$424$	−3.23435	−	2.71395i	−0.157074	−	0.131801i
$425$		0			0
$426$	7.15120	+	12.3862i	0.346477	+	0.600115i
$427$	36.3132	+	6.40299i	1.75732	+	0.309862i
$428$	−5.87716	−	1.03630i	−0.284083	−	0.0500916i
$429$	21.6653	+	37.5254i	1.04601	+	1.81174i
$430$		0			0
$431$	16.7585	+	14.0620i	0.807228	+	0.677345i	0.949944	−	0.312419i	$-0.101139\pi$
$431$	16.7585	+	14.0620i	0.807228	+	0.677345i	−0.142716	+	0.989764i	$0.545584\pi$
$432$	0.490754	−	1.34834i	0.0236114	−	0.0648718i
$433$	−0.376798	−	1.03524i	−0.0181078	−	0.0497507i	0.930309	−	0.366776i	$-0.119538\pi$
$433$	−0.376798	−	1.03524i	−0.0181078	−	0.0497507i	−0.948417	+	0.317025i	$0.897316\pi$
$434$	20.3967	−	17.1149i	0.979075	−	0.821542i
$435$		0			0
$436$	−15.8300			−0.758118
$437$	0.645253	+	11.5660i	0.0308666	+	0.553276i
$438$			9.22592i			0.440832i
$439$	0.732304	+	4.15310i	0.0349510	+	0.198217i	0.997284	−	0.0736582i	$-0.0234674\pi$
$439$	0.732304	+	4.15310i	0.0349510	+	0.198217i	−0.962333	+	0.271875i	$0.912356\pi$
$440$		0			0
$441$	−38.4336	+	13.9887i	−1.83017	+	0.666128i
$442$	−4.91770	+	13.5113i	−0.233911	+	0.642665i
$443$	4.87432	−	5.80899i	0.231586	−	0.275993i	−0.637719	−	0.770269i	$-0.720122\pi$
$443$	4.87432	−	5.80899i	0.231586	−	0.275993i	0.869305	+	0.494275i	$0.164567\pi$
$444$	2.39232	−	4.14362i	0.113534	−	0.196647i
$445$		0			0
$446$	−4.88478	+	27.7030i	−0.231301	+	1.31177i
$447$	15.9433	+	2.81124i	0.754093	+	0.132967i
$448$	4.25802	−	2.45837i	0.201173	−	0.116147i
$449$	14.8487	−	25.7188i	0.700756	−	1.21374i	−0.267446	−	0.963573i	$-0.586180\pi$
$449$	14.8487	−	25.7188i	0.700756	−	1.21374i	0.968202	−	0.250171i	$-0.0804870\pi$
$450$		0			0
$451$	25.0298	+	9.11012i	1.17861	+	0.428979i
$452$	−6.22651	−	17.1072i	−0.292871	−	0.804655i
$453$	−8.48997	−	10.1180i	−0.398894	−	0.475383i
$454$	2.19605	+	12.4544i	0.103066	+	0.584515i
$455$		0			0
$456$	−8.09609	−	6.05816i	−0.379134	−	0.283699i
$457$			9.12576i			0.426885i	0.976956	+	0.213442i	$0.0684676\pi$
$457$			9.12576i			0.426885i	−0.976956	+	0.213442i	$0.931532\pi$
$458$	−13.5352	+	2.38661i	−0.632456	+	0.111519i
$459$	2.40854	−	2.02101i	0.112421	−	0.0943324i
$460$		0			0
$461$	24.7943	+	9.02439i	1.15479	+	0.420308i	0.847232	−	0.531223i	$-0.178267\pi$
$461$	24.7943	+	9.02439i	1.15479	+	0.420308i	0.307554	+	0.951531i	$0.400490\pi$
$462$	20.8698	−	24.8716i	0.970949	−	1.15713i
$463$	−13.6156	−	7.86094i	−0.632768	−	0.365329i	0.149055	−	0.988829i	$-0.452377\pi$
$463$	−13.6156	−	7.86094i	−0.632768	−	0.365329i	−0.781823	+	0.623500i	$0.785710\pi$
$464$	−3.80089	−	6.58334i	−0.176452	−	0.305624i
$465$		0			0
$466$	−4.27489	+	24.2441i	−0.198031	+	1.12309i
$467$	−5.97499	+	3.44966i	−0.276490	+	0.159631i	−0.631833	−	0.775104i	$-0.717697\pi$
$467$	−5.97499	+	3.44966i	−0.276490	+	0.159631i	0.355344	+	0.934736i	$0.384364\pi$
$468$	−13.5331	−	7.81335i	−0.625568	−	0.361172i
$469$	7.22988	+	6.06659i	0.333845	+	0.280129i
$470$		0			0
$471$	−11.5836	+	4.21609i	−0.533745	+	0.194267i
$472$	0.620028	+	0.738920i	0.0285391	+	0.0340116i
$473$	4.86122	−	0.857164i	0.223519	−	0.0394124i
$474$	−35.5461			−1.63269
$475$		0			0
$476$	10.7737			0.493812
$477$	9.90216	−	1.74602i	0.453389	−	0.0799447i
$478$	−10.4735	−	12.4819i	−0.479049	−	0.570908i
$479$	−3.42858	+	1.24790i	−0.156656	+	0.0570180i	−0.419158	−	0.907913i	$-0.637675\pi$
$479$	−3.42858	+	1.24790i	−0.156656	+	0.0570180i	0.262502	+	0.964931i	$0.415452\pi$
$480$		0			0
$481$	10.3675	+	8.69938i	0.472718	+	0.396657i
$482$	−16.6751	−	9.62739i	−0.759532	−	0.438516i
$483$	26.2506	−	15.1558i	1.19444	−	0.689612i
$484$	0.503064	−	2.85302i	0.0228665	−	0.129683i
$485$		0			0
$486$	9.99534	+	17.3124i	0.453398	+	0.785308i
$487$	19.4986	+	11.2575i	0.883568	+	0.510128i	0.871833	−	0.489803i	$-0.162931\pi$
$487$	19.4986	+	11.2575i	0.883568	+	0.510128i	0.0117346	+	0.999931i	$0.496265\pi$
$488$	4.82062	−	5.74499i	0.218219	−	0.260063i
$489$	9.75196	+	3.54942i	0.440999	+	0.160510i
$490$		0			0
$491$	19.2746	−	16.1733i	0.869849	−	0.729890i	−0.0942175	−	0.995552i	$-0.530035\pi$
$491$	19.2746	−	16.1733i	0.869849	−	0.729890i	0.964066	+	0.265662i	$0.0855905\pi$
$492$	−21.3773	+	3.76939i	−0.963761	+	0.169937i
$493$		−	16.6573i		−	0.750205i
$494$	20.8524	−	19.5770i	0.938195	−	0.880813i
$495$		0			0
$496$	−0.940372	−	5.33311i	−0.0422239	−	0.239464i
$497$	19.4851	+	23.2215i	0.874027	+	1.04163i
$498$	−1.04102	−	2.86017i	−0.0466490	−	0.128167i
$499$	29.8561	+	10.8667i	1.33654	+	0.486461i	0.908721	−	0.417403i	$-0.137060\pi$
$499$	29.8561	+	10.8667i	1.33654	+	0.486461i	0.427819	+	0.903864i	$0.359282\pi$
$500$		0			0
$501$	4.23220	−	7.33039i	0.189081	−	0.327498i
$502$	24.0496	−	13.8850i	1.07339	−	0.619719i
$503$	25.1737	+	4.43880i	1.12244	+	0.197917i	0.703912	−	0.710287i	$-0.251435\pi$
$503$	25.1737	+	4.43880i	1.12244	+	0.197917i	0.418528	+	0.908204i	$0.362546\pi$
$504$	−2.03326	+	11.5312i	−0.0905685	+	0.513640i
$505$		0			0
$506$	−3.78245	+	6.55139i	−0.168150	+	0.291245i
$507$	44.8192	−	53.4135i	1.99049	−	2.37218i
$508$	−2.61630	+	7.18822i	−0.116079	+	0.318926i
$509$	9.28595	−	3.37981i	0.411592	−	0.149807i	−0.127921	−	0.991784i	$-0.540830\pi$
$509$	9.28595	−	3.37981i	0.411592	−	0.149807i	0.539513	+	0.841977i	$0.318608\pi$
$510$		0			0
$511$	3.39553	+	19.2570i	0.150209	+	0.851879i
$512$		−	1.00000i		−	0.0441942i
$513$	−6.08937	+	1.42748i	−0.268852	+	0.0630248i
$514$	13.0703			0.576505
$515$		0			0
$516$	−3.08160	+	2.58577i	−0.135660	+	0.113832i
$517$	2.92562	+	8.03806i	0.128668	+	0.353514i
$518$	3.46839	−	9.52932i	0.152392	−	0.418694i
$519$	−2.09039	−	1.75404i	−0.0917578	−	0.0769940i
$520$		0			0
$521$	2.14888	+	3.72196i	0.0941440	+	0.163062i	0.909251	−	0.416248i	$-0.136655\pi$
$521$	2.14888	+	3.72196i	0.0941440	+	0.163062i	−0.815107	+	0.579310i	$0.803322\pi$
$522$	17.8284	+	3.14362i	0.780327	+	0.137593i
$523$	−24.5247	−	4.32437i	−1.07239	−	0.189092i	−0.390543	−	0.920585i	$-0.627713\pi$
$523$	−24.5247	−	4.32437i	−1.07239	−	0.189092i	−0.681849	+	0.731493i	$0.738824\pi$
$524$	−6.65739	−	11.5309i	−0.290829	−	0.503731i
$525$		0			0
$526$	−11.5336	−	9.67780i	−0.502887	−	0.421972i
$527$	4.05853	−	11.1507i	0.176792	−	0.485733i
$528$	−2.25852	−	6.20524i	−0.0982895	−	0.270048i
$529$	12.2088	−	10.2444i	0.530817	−	0.445408i
$530$		0			0
$531$	−2.29714			−0.0996876
$532$	−19.1284	−	9.66531i	−0.829320	−	0.419044i
$533$		−	61.4006i		−	2.65955i
$534$	4.34100	+	24.6191i	0.187854	+	1.06537i
$535$		0			0
$536$	1.80379	−	0.656525i	0.0779118	−	0.0283576i
$537$	−3.43595	+	9.44020i	−0.148272	+	0.407375i
$538$	−15.7196	+	18.7339i	−0.677719	+	0.807674i
$539$	24.4440	−	42.3383i	1.05288	−	1.82364i
$540$		0			0
$541$	−3.80139	+	21.5587i	−0.163434	+	0.926882i	0.787230	+	0.616660i	$0.211515\pi$
$541$	−3.80139	+	21.5587i	−0.163434	+	0.926882i	−0.950664	+	0.310222i	$0.899596\pi$
$542$	−8.81475	−	1.55428i	−0.378626	−	0.0667620i
$543$	2.75072	−	1.58813i	0.118045	−	0.0681531i
$544$	1.09561	−	1.89766i	0.0469741	−	0.0813615i
$545$		0			0
$546$	−70.3292	−	25.5978i	−3.00981	−	1.09548i
$547$	−1.01317	−	2.78367i	−0.0433202	−	0.119021i	0.916146	−	0.400844i	$-0.131283\pi$
$547$	−1.01317	−	2.78367i	−0.0433202	−	0.119021i	−0.959466	+	0.281823i	$0.909061\pi$
$548$	4.64495	+	5.53564i	0.198423	+	0.236471i
$549$	3.10135	+	17.5886i	0.132362	+	0.750663i
$550$		0			0
$551$	−14.9435	+	29.5744i	−0.636617	+	1.25991i
$552$		−	6.16497i		−	0.262399i
$553$	−74.1943	+	13.0825i	−3.15506	+	0.556322i
$554$	−5.97623	+	5.01465i	−0.253906	+	0.213052i
$555$		0			0
$556$	2.26632	+	0.824874i	0.0961135	+	0.0349825i
$557$	19.7784	−	23.5710i	0.838038	−	0.998734i	−0.161891	−	0.986809i	$-0.551759\pi$
$557$	19.7784	−	23.5710i	0.838038	−	0.998734i	0.999929	−	0.0119259i	$-0.00379621\pi$
$558$	11.1688	+	6.44829i	0.472811	+	0.272978i
$559$	−5.68936	−	9.85426i	−0.240634	−	0.416791i
$560$		0			0
$561$	2.51264	−	14.2499i	0.106084	−	0.601631i
$562$	−15.8467	+	9.14912i	−0.668455	+	0.385933i
$563$	−30.7518	−	17.7546i	−1.29603	−	0.748266i	−0.316318	−	0.948653i	$-0.602447\pi$
$563$	−30.7518	−	17.7546i	−1.29603	−	0.748266i	−0.979717	+	0.200387i	$0.935780\pi$
$564$	−5.34008	−	4.48086i	−0.224858	−	0.188678i
$565$		0			0
$566$	6.79213	−	2.47213i	0.285494	−	0.103911i
$567$	33.0991	+	39.4460i	1.39003	+	1.65658i
$568$	6.07169	−	1.07060i	0.254763	−	0.0449215i
$569$	−33.0813			−1.38684			−0.693421	−	0.720533i	$-0.743897\pi$
$569$	−33.0813			−1.38684			−0.693421	+	0.720533i	$0.743897\pi$
$570$		0			0
$571$	2.29342			0.0959766			0.0479883	−	0.998848i	$-0.484719\pi$
$571$	2.29342			0.0959766			0.0479883	+	0.998848i	$0.484719\pi$
$572$	18.3948	−	3.24351i	0.769127	−	0.135618i
$573$	20.3298	+	24.2282i	0.849291	+	1.01215i
$574$	−43.2328	+	15.7355i	−1.80450	+	0.656785i
$575$		0			0
$576$	1.82431	+	1.53078i	0.0760129	+	0.0637824i
$577$	13.5997	+	7.85178i	0.566162	+	0.326874i	0.755615	−	0.655016i	$-0.227338\pi$
$577$	13.5997	+	7.85178i	0.566162	+	0.326874i	−0.189453	+	0.981890i	$0.560671\pi$
$578$	−10.5642	+	6.09926i	−0.439414	+	0.253696i
$579$	−2.10255	+	11.9242i	−0.0873792	+	0.495552i
$580$		0			0
$581$	−3.22554	−	5.58680i	−0.133818	−	0.231780i
$582$	−4.12708	−	2.38277i	−0.171073	−	0.0987691i
$583$	−7.72544	+	9.20682i	−0.319955	+	0.381308i
$584$	3.73719	+	1.36023i	0.154646	+	0.0562865i
$585$		0			0
$586$	−8.72264	+	7.31917i	−0.360329	+	0.302352i
$587$	26.1082	−	4.60359i	1.07760	−	0.190010i	0.393448	−	0.919347i	$-0.371282\pi$
$587$	26.1082	−	4.60359i	1.07760	−	0.190010i	0.684155	+	0.729337i	$0.260171\pi$
$588$			39.8411i			1.64302i
$589$	−17.2093	+	16.1568i	−0.709098	+	0.665728i
$590$		0			0
$591$	−1.15024	−	6.52335i	−0.0473146	−	0.268335i
$592$	−1.32576	−	1.57998i	−0.0544885	−	0.0649369i
$593$	−1.00184	−	2.75254i	−0.0411408	−	0.113033i	0.917421	−	0.397918i	$-0.130267\pi$
$593$	−1.00184	−	2.75254i	−0.0411408	−	0.113033i	−0.958562	+	0.284884i	$0.908045\pi$
$594$	−3.83813	−	1.39697i	−0.157481	−	0.0573182i
$595$		0			0
$596$	3.48937	−	6.04376i	0.142930	−	0.247562i
$597$	2.94244	−	1.69882i	0.120426	−	0.0695281i
$598$	17.1733	+	3.02812i	0.702270	+	0.123829i
$599$	−6.43428	+	36.4906i	−0.262897	+	1.49097i	0.512059	+	0.858950i	$0.328883\pi$
$599$	−6.43428	+	36.4906i	−0.262897	+	1.49097i	−0.774956	+	0.632015i	$0.782228\pi$
$600$		0			0
$601$	4.84799	−	8.39697i	0.197754	−	0.342520i	−0.750046	−	0.661386i	$-0.769969\pi$
$601$	4.84799	−	8.39697i	0.197754	−	0.342520i	0.947800	+	0.318866i	$0.103302\pi$
$602$	−5.48045	+	6.53135i	−0.223367	+	0.266198i
$603$	−1.56349	+	4.29566i	−0.0636704	+	0.174933i
$604$	−5.35025	+	1.94733i	−0.217699	+	0.0792358i
$605$		0			0
$606$	−2.01803	−	11.4448i	−0.0819771	−	0.464915i
$607$		−	38.0294i		−	1.54357i	−0.635886	−	0.771783i	$-0.719365\pi$
$607$		−	38.0294i		−	1.54357i	0.635886	−	0.771783i	$-0.280635\pi$
$608$	−3.64766	+	2.38634i	−0.147932	+	0.0967787i
$609$	86.7049			3.51346
$610$		0			0
$611$	15.1050	−	12.6746i	0.611081	−	0.512758i
$612$	1.78478	+	4.90364i	0.0721454	+	0.198218i
$613$	7.81429	−	21.4696i	0.315616	−	0.867149i	−0.675880	−	0.737012i	$-0.736236\pi$
$613$	7.81429	−	21.4696i	0.315616	−	0.867149i	0.991496	−	0.130137i	$-0.0415416\pi$
$614$	3.78649	+	3.17725i	0.152810	+	0.128223i
$615$		0			0
$616$	−6.99793	−	12.1208i	−0.281955	−	0.488360i
$617$	−25.0606	−	4.41886i	−1.00890	−	0.177896i	−0.355313	−	0.934747i	$-0.615626\pi$
$617$	−25.0606	−	4.41886i	−1.00890	−	0.177896i	−0.653588	+	0.756851i	$0.726737\pi$
$618$	20.6407	+	3.63951i	0.830291	+	0.146403i
$619$	7.95778	+	13.7833i	0.319850	+	0.553997i	0.980457	−	0.196736i	$-0.0630341\pi$
$619$	7.95778	+	13.7833i	0.319850	+	0.553997i	−0.660606	+	0.750733i	$0.729701\pi$
$620$		0			0
$621$	−2.92110	−	2.45110i	−0.117220	−	0.0983591i
$622$	−8.24858	+	22.6628i	−0.330738	+	0.908695i
$623$	18.1217	+	49.7889i	0.726030	+	1.99475i
$624$	−11.6608	+	9.78453i	−0.466804	+	0.391695i
$625$		0			0
$626$	30.9756			1.23803
$627$	−17.2450	+	23.0461i	−0.688698	+	0.920372i
$628$			5.31383i			0.212045i
$629$	−0.784795	−	4.45079i	−0.0312918	−	0.177465i
$630$		0			0
$631$	18.7345	−	6.81880i	0.745808	−	0.271452i	0.0589675	−	0.998260i	$-0.481219\pi$
$631$	18.7345	−	6.81880i	0.745808	−	0.271452i	0.686841	+	0.726808i	$0.258997\pi$
$632$	−5.24075	+	14.3988i	−0.208466	+	0.572755i
$633$	−1.95414	+	2.32886i	−0.0776702	+	0.0925637i
$634$	3.45527	−	5.98470i	0.137226	−	0.237683i
$635$		0			0
$636$	1.70080	−	9.64574i	0.0674413	−	0.382478i
$637$	−110.982	−	19.5692i	−4.39728	−	0.775360i
$638$	−18.7399	+	10.8195i	−0.741922	+	0.428349i
$639$	−7.34130	+	12.7155i	−0.290417	+	0.503018i
$640$		0			0
$641$	−2.28156	−	0.830421i	−0.0901163	−	0.0327996i	0.296569	−	0.955012i	$-0.404158\pi$
$641$	−2.28156	−	0.830421i	−0.0901163	−	0.0327996i	−0.386685	+	0.922212i	$0.626380\pi$
$642$	−4.73498	−	13.0093i	−0.186875	−	0.513434i
$643$	4.30313	+	5.12827i	0.169699	+	0.202239i	0.844191	−	0.536043i	$-0.180082\pi$
$643$	4.30313	+	5.12827i	0.169699	+	0.202239i	−0.674492	+	0.738282i	$0.735637\pi$
$644$	−2.26897	−	12.8680i	−0.0894099	−	0.507069i
$645$		0			0
$646$	−9.53651	+	0.532031i	−0.375209	+	0.0209325i
$647$			28.2280i			1.10976i	0.831932	+	0.554878i	$0.187235\pi$
$647$			28.2280i			1.10976i	−0.831932	+	0.554878i	$0.812765\pi$
$648$	10.3139	−	1.81862i	0.405168	−	0.0714421i
$649$	2.10339	−	1.76495i	0.0825652	−	0.0692805i
$650$		0			0
$651$	58.0421	+	21.1256i	2.27485	+	0.827977i
$652$	2.87557	−	3.42697i	0.112616	−	0.134210i
$653$	14.7075	+	8.49136i	0.575548	+	0.332293i	0.759362	−	0.650668i	$-0.225511\pi$
$653$	14.7075	+	8.49136i	0.575548	+	0.332293i	−0.183814	+	0.982961i	$0.558844\pi$
$654$	−18.3612	−	31.8025i	−0.717978	−	1.24358i
$655$		0			0
$656$	−1.62488	+	9.21513i	−0.0634408	+	0.359791i
$657$	−8.20228	+	4.73559i	−0.320002	+	0.184753i
$658$	−12.7953	−	7.38739i	−0.498814	−	0.287990i
$659$	14.0188	+	11.7632i	0.546095	+	0.458228i	0.873616	−	0.486616i	$-0.161769\pi$
$659$	14.0188	+	11.7632i	0.546095	+	0.458228i	−0.327521	+	0.944844i	$0.606213\pi$
$660$		0			0
$661$	−5.11150	+	1.86043i	−0.198814	+	0.0723625i	−0.439508	−	0.898239i	$-0.644847\pi$
$661$	−5.11150	+	1.86043i	−0.198814	+	0.0723625i	0.240694	+	0.970601i	$0.422625\pi$
$662$	−2.68612	−	3.20119i	−0.104399	−	0.124418i
$663$	−32.8482	+	5.79203i	−1.27572	+	0.224944i
$664$	−1.31206			−0.0509180
$665$		0			0
$666$	4.91183			0.190329
$667$	−19.8952	+	3.50806i	−0.770344	+	0.135833i
$668$	−2.34538	−	2.79512i	−0.0907456	−	0.108146i
$669$	−61.3213	+	22.3191i	−2.37082	+	0.862907i
$670$		0			0
$671$	−16.3535	−	13.7222i	−0.631321	−	0.529741i
$672$	9.87776	+	5.70293i	0.381043	+	0.219995i
$673$	25.9066	−	14.9572i	0.998626	−	0.576557i	0.0907847	−	0.995871i	$-0.471062\pi$
$673$	25.9066	−	14.9572i	0.998626	−	0.576557i	0.907842	+	0.419313i	$0.137729\pi$
$674$	2.98695	−	16.9399i	0.115053	−	0.652499i
$675$		0			0
$676$	−15.0285	−	26.0302i	−0.578021	−	1.00116i
$677$	27.2420	+	15.7282i	1.04700	+	0.604483i	0.921807	−	0.387650i	$-0.126713\pi$
$677$	27.2420	+	15.7282i	1.04700	+	0.604483i	0.125189	+	0.992133i	$0.460046\pi$
$678$	27.1463	−	32.3517i	1.04255	−	1.24246i
$679$	−9.49130	−	3.45455i	−0.364243	−	0.132573i
$680$		0			0
$681$	−22.4738	+	18.8578i	−0.861199	+	0.722631i
$682$	−15.1811	+	2.67684i	−0.581314	+	0.102501i
$683$			49.8920i			1.90906i	0.298109	+	0.954532i	$0.403644\pi$
$683$			49.8920i			1.90906i	−0.298109	+	0.954532i	$0.596356\pi$
$684$	1.23033	−	10.3074i	0.0470430	−	0.394114i
$685$		0			0
$686$	8.68670	+	49.2647i	0.331660	+	1.88094i
$687$	−20.4941	−	24.4240i	−0.781900	−	0.931833i
$688$	0.593093	+	1.62951i	0.0226115	+	0.0621245i
$689$	26.0341	+	9.47562i	0.991818	+	0.360992i
$690$		0			0
$691$	−9.36370	+	16.2184i	−0.356212	+	0.616977i	−0.987325	−	0.158714i	$-0.949265\pi$
$691$	−9.36370	+	16.2184i	−0.356212	+	0.616977i	0.631113	+	0.775691i	$0.282599\pi$
$692$	−1.01872	+	0.588156i	−0.0387258	+	0.0223583i
$693$	32.8243	+	5.78782i	1.24689	+	0.219861i
$694$	3.20604	−	18.1823i	0.121699	−	0.690192i
$695$		0			0
$696$	8.81731	−	15.2720i	0.334219	−	0.578885i
$697$	−13.1797	+	15.7069i	−0.499217	+	0.594943i
$698$	8.46187	−	23.2488i	0.320286	−	0.879980i
$699$	−53.6650	+	19.5325i	−2.02980	+	0.738786i
$700$		0			0
$701$	−3.10915	−	17.6329i	−0.117431	−	0.665984i	−0.985518	−	0.169572i	$-0.945761\pi$
$701$	−3.10915	−	17.6329i	−0.117431	−	0.665984i	0.868087	−	0.496412i	$-0.165350\pi$
$702$			9.41531i			0.355358i
$703$	−2.59952	+	8.60630i	−0.0980426	+	0.324593i
$704$	−2.84657			−0.107284
$705$		0			0
$706$	4.91028	−	4.12021i	0.184801	−	0.155066i
$707$	−8.42437	−	23.1458i	−0.316831	−	0.870486i
$708$	−0.765324	+	2.10271i	−0.0287627	+	0.0790247i
$709$	−20.6673	−	17.3419i	−0.776177	−	0.651290i	0.166106	−	0.986108i	$-0.446881\pi$
$709$	−20.6673	−	17.3419i	−0.776177	−	0.651290i	−0.942283	+	0.334818i	$0.891325\pi$
$710$		0			0
$711$	−18.2455	−	31.6022i	−0.684260	−	1.18517i
$712$	10.6126	+	1.87128i	0.397723	+	0.0701293i
$713$	−14.1730	−	2.49908i	−0.530783	−	0.0935913i
$714$	12.4964	+	21.6444i	0.467667	+	0.810023i
$715$		0			0
$716$	3.31741	+	2.78364i	0.123977	+	0.104029i
$717$	12.9279	−	35.5192i	0.482802	−	1.32649i
$718$	12.5916	+	34.5952i	0.469915	+	1.29108i
$719$	−32.4936	+	27.2653i	−1.21180	+	1.01683i	−0.212593	+	0.977141i	$0.568191\pi$
$719$	−32.4936	+	27.2653i	−1.21180	+	1.01683i	−0.999212	+	0.0396842i	$0.987365\pi$
$720$		0			0
$721$	44.4222			1.65437
$722$	17.4091	+	7.61079i	0.647899	+	0.283244i
$723$		−	44.6672i		−	1.66119i
$724$	−0.237758	−	1.34839i	−0.00883622	−	0.0501127i
$725$		0			0
$726$	6.31523	−	2.29856i	0.234380	−	0.0853074i
$727$	−14.7217	+	40.4476i	−0.545999	+	1.50012i	0.293068	+	0.956092i	$0.405324\pi$
$727$	−14.7217	+	40.4476i	−0.545999	+	1.50012i	−0.839067	+	0.544028i	$0.816898\pi$
$728$	−20.7380	+	24.7146i	−0.768602	+	0.915984i
$729$	−7.47766	+	12.9517i	−0.276950	+	0.479692i
$730$		0			0
$731$	−0.659826	+	3.74206i	−0.0244045	+	0.138405i
$732$	17.1331	+	3.02104i	0.633259	+	0.111661i
$733$	26.3235	−	15.1979i	0.972282	−	0.561347i	0.0723507	−	0.997379i	$-0.476950\pi$
$733$	26.3235	−	15.1979i	0.972282	−	0.561347i	0.899931	+	0.436032i	$0.143617\pi$
$734$	−7.31190	+	12.6646i	−0.269887	+	0.467458i
$735$		0			0
$736$	−2.49728	−	0.908934i	−0.0920508	−	0.0335038i
$737$	−1.86885	−	5.13461i	−0.0688398	−	0.189136i
$738$	−14.3239	−	17.0706i	−0.527272	−	0.628378i
$739$	6.40630	+	36.3319i	0.235659	+	1.33649i	0.841221	+	0.540692i	$0.181838\pi$
$739$	6.40630	+	36.3319i	0.235659	+	1.33649i	−0.605561	+	0.795799i	$0.707051\pi$
$740$		0			0
$741$	63.5171	+	19.1852i	2.33336	+	0.704787i
$742$		−	20.7592i		−	0.762095i
$743$	24.1976	−	4.26670i	0.887725	−	0.156530i	0.288852	−	0.957374i	$-0.406726\pi$
$743$	24.1976	−	4.26670i	0.887725	−	0.156530i	0.598873	+	0.800844i	$0.295615\pi$
$744$	9.62352	−	8.07509i	0.352815	−	0.296047i
$745$		0			0
$746$	−12.7398	−	4.63691i	−0.466438	−	0.169769i
$747$	2.00848	−	2.39361i	0.0734865	−	0.0875778i
$748$	−5.40182	−	3.11874i	−0.197510	−	0.114033i
$749$	−14.6711	−	25.4112i	−0.536072	−	0.928503i
$750$		0			0
$751$	1.64514	−	9.33008i	0.0600322	−	0.340459i	−0.939967	−	0.341264i	$-0.889145\pi$
$751$	1.64514	−	9.33008i	0.0600322	−	0.340459i	1.00000		0.000804564i	$0.000256101\pi$
$752$	−2.60240	+	1.50250i	−0.0948998	+	0.0547904i
$753$	55.7902	+	32.2105i	2.03311	+	1.17382i
$754$	38.2113	+	32.0631i	1.39157	+	1.16767i
$755$		0			0
$756$	6.62942	−	2.41291i	0.241110	−	0.0877568i
$757$	−4.54780	−	5.41985i	−0.165292	−	0.196988i	0.677040	−	0.735946i	$-0.263262\pi$
$757$	−4.54780	−	5.41985i	−0.165292	−	0.196988i	−0.842332	+	0.538958i	$0.818818\pi$
$758$	−29.8298	+	5.25979i	−1.08347	+	0.191044i
$759$	−17.5490			−0.636990
$760$		0			0
$761$	−45.9880			−1.66706			−0.833531	−	0.552472i	$-0.813684\pi$
$761$	−45.9880			−1.66706			−0.833531	+	0.552472i	$0.813684\pi$
$762$	−17.4758	+	3.08146i	−0.633082	+	0.111629i
$763$	−50.0293	−	59.6227i	−1.81118	−	2.15849i
$764$	12.8116	−	4.66302i	0.463506	−	0.168702i
$765$		0			0
$766$	21.9571	+	18.4242i	0.793342	+	0.665693i
$767$	−5.48146	−	3.16472i	−0.197924	−	0.114272i
$768$	2.00901	−	1.15990i	0.0724937	−	0.0418543i
$769$	7.83899	−	44.4571i	0.282681	−	1.60317i	−0.430771	−	0.902461i	$-0.641758\pi$
$769$	7.83899	−	44.4571i	0.282681	−	1.60317i	0.713452	−	0.700704i	$-0.247131\pi$
$770$		0			0
$771$	15.1602	+	26.2582i	0.545981	+	0.945667i
$772$	4.52019	+	2.60974i	0.162685	+	0.0939264i
$773$	−0.495905	+	0.590996i	−0.0178364	+	0.0212567i	−0.774889	−	0.632097i	$-0.782194\pi$
$773$	−0.495905	+	0.590996i	−0.0178364	+	0.0212567i	0.757052	+	0.653354i	$0.226639\pi$
$774$	−3.88063	−	1.41243i	−0.139486	−	0.0507689i
$775$		0			0
$776$	−1.57368	+	1.32047i	−0.0564918	+	0.0474022i
$777$	23.1674	−	4.08504i	0.831127	−	0.146550i
$778$			17.1263i			0.614007i
$779$	37.4911	−	16.0634i	1.34326	−	0.575532i
$780$		0			0
$781$	−3.04755	−	17.2835i	−0.109050	−	0.618452i
$782$	−3.74314	−	4.46090i	−0.133854	−	0.159521i
$783$	−3.73061	−	10.2498i

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(1.49114 + 1.77707i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.77707 + 1.49114i) q^{6} +(4.25802 + 2.45837i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.413538 + 2.34529i) q^{9} +O(q^{10})\)	\(q+(0.984808 - 0.173648i) q^{2} +(1.49114 + 1.77707i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.77707 + 1.49114i) q^{6} +(4.25802 + 2.45837i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.413538 + 2.34529i) q^{9} +(-1.42329 - 2.46520i) q^{11} +(2.00901 + 1.15990i) q^{12} +(-4.21784 + 5.02662i) q^{13} +(4.62023 + 1.68163i) q^{14} +(0.766044 - 0.642788i) q^{16} +(2.15794 - 0.380503i) q^{17} +2.38147i q^{18} +(-4.17271 - 1.26036i) q^{19} +(1.98061 + 11.2326i) q^{21} +(-1.82974 - 2.18060i) q^{22} +(-0.908934 - 2.49728i) q^{23} +(2.17990 + 0.793418i) q^{24} +(-3.28089 + 5.68268i) q^{26} +(1.24263 - 0.717435i) q^{27} +(4.84205 + 0.853783i) q^{28} +(1.32004 - 7.48630i) q^{29} +(2.70769 - 4.68986i) q^{31} +(0.642788 - 0.766044i) q^{32} +(2.25852 - 6.20524i) q^{33} +(2.05908 - 0.749444i) q^{34} +(0.413538 + 2.34529i) q^{36} -2.06252i q^{37} +(-4.32817 - 0.516628i) q^{38} -15.2220 q^{39} +(-7.16810 + 6.01475i) q^{41} +(3.90103 + 10.7180i) q^{42} +(-0.593093 + 1.62951i) q^{43} +(-2.18060 - 1.82974i) q^{44} +(-1.32877 - 2.30150i) q^{46} +(-2.95934 - 0.521812i) q^{47} +(2.28456 + 0.402829i) q^{48} +(8.58718 + 14.8734i) q^{49} +(3.89396 + 3.26742i) q^{51} +(-2.24426 + 6.16606i) q^{52} +(-1.44406 - 3.96752i) q^{53} +(1.09917 - 0.922316i) q^{54} +4.91674 q^{56} +(-3.98234 - 9.29456i) q^{57} -7.60179i q^{58} +(0.167500 + 0.949937i) q^{59} +(7.04727 - 2.56500i) q^{61} +(1.85217 - 5.08880i) q^{62} +(-7.52644 + 8.96967i) q^{63} +(0.500000 - 0.866025i) q^{64} +(1.14668 - 6.50315i) q^{66} +(1.89039 + 0.333326i) q^{67} +(1.89766 - 1.09561i) q^{68} +(3.08249 - 5.33902i) q^{69} +(5.79354 + 2.10868i) q^{71} +(0.814510 + 2.23785i) q^{72} +(2.55639 + 3.04659i) q^{73} +(-0.358153 - 2.03119i) q^{74} +(-4.35213 + 0.242800i) q^{76} -13.9959i q^{77} +(-14.9908 + 2.64328i) q^{78} +(-11.7380 + 9.84938i) q^{79} +(9.84141 + 3.58198i) q^{81} +(-6.01475 + 7.16810i) q^{82} +(-1.13628 - 0.656032i) q^{83} +(5.70293 + 9.87776i) q^{84} +(-0.301121 + 1.70774i) q^{86} +(15.2720 - 8.81731i) q^{87} +(-2.46520 - 1.42329i) q^{88} +(8.25512 + 6.92687i) q^{89} +(-30.3170 + 11.0345i) q^{91} +(-1.70824 - 2.03580i) q^{92} +(12.3718 - 2.18147i) q^{93} -3.00499 q^{94} +2.31980 q^{96} +(-2.02308 + 0.356724i) q^{97} +(11.0395 + 13.1563i) q^{98} +(6.37020 - 2.31856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36q + 36q^{9} + O(q^{10}) \)	\( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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