LMFDB - Embedded newform 950.2.u.g.199.1

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			199.1
Character	$\chi$	$=$	950.199
Dual form			950.2.u.g.549.1

$q$-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	$-0.988658\pi$
$3$	−1.49114	−	1.77707i	−0.860909	−	1.02599i	0.138456	−	0.990369i	$-0.455786\pi$
$4$	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	$-0.953851\pi$
$7$	−4.25802	−	2.45837i	−1.60938	−	0.929177i	−0.619873	−	0.784702i	$-0.712816\pi$
$8$	−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	$-0.413893\pi$
$13$	4.21784	−	5.02662i	1.16982	−	1.39413i	0.902590	−	0.430500i	$-0.141663\pi$
$14$	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	−0.429094	−	0.903260i	$-0.641167\pi$
$17$	−2.15794	+	0.380503i	−0.523377	+	0.0922855i	−0.0942832	+	0.995545i	$0.530056\pi$
$18$		−	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	0.997667	−	0.0682711i	$-0.0217483\pi$
$23$	0.908934	+	2.49728i	0.189526	+	0.520718i	−0.808141	+	0.588989i	$0.799526\pi$
$24$	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	$0.0542276\pi$
$37$			2.06252i			0.339076i	−0.985524	+	0.169538i	$0.945772\pi$
$38$	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	−0.886219	−	0.463266i	$-0.846677\pi$
$43$	0.593093	−	1.62951i	0.0904459	−	0.248498i	0.976665	+	0.214768i	$0.0688996\pi$
$44$	−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	0.385259	−	0.922809i	$-0.374112\pi$
$47$	2.95934	+	0.521812i	0.431664	+	0.0761140i	0.0464056	+	0.998923i	$0.485223\pi$
$48$	−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	0.998495	−	0.0548340i	$-0.0174630\pi$
$53$	1.44406	+	3.96752i	0.198357	+	0.544981i	−0.800139	+	0.599815i	$0.795241\pi$
$54$	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	0.0569765	−	0.998376i	$-0.481854\pi$
$67$	−1.89039	−	0.333326i	−0.230948	−	0.0407223i	−0.287924	+	0.957653i	$0.592965\pi$
$68$	−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	0.595407	−	0.803424i	$-0.296991\pi$
$73$	−2.55639	−	3.04659i	−0.299203	−	0.356576i	−0.894610	+	0.446848i	$0.852546\pi$
$74$	−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	0.561064	−	0.827773i	$-0.310392\pi$
$83$	1.13628	+	0.656032i	0.124723	+	0.0720089i	−0.436340	+	0.899782i	$0.643726\pi$
$84$	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	−0.0699948	−	0.997547i	$-0.522298\pi$
$97$	2.02308	−	0.356724i	0.205413	−	0.0362198i	0.275408	+	0.961328i	$0.411187\pi$
$98$	−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	−0.833219	−	0.552943i	$-0.813505\pi$
$103$	−7.82444	+	4.51744i	−0.770965	+	0.445117i	0.0622537	+	0.998060i	$0.480171\pi$
$104$	−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	0.728564	−	0.684978i	$-0.240188\pi$
$107$	5.16829	+	2.98391i	0.499637	+	0.288466i	−0.228926	+	0.973444i	$0.573522\pi$
$108$	−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	$0.327240\pi$
$113$			18.2051i			1.71259i	−0.516485	+	0.856296i	$0.672760\pi$
$114$	−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	−0.502418	−	0.864625i	$-0.667556\pi$
$127$	4.91703	−	5.85989i	0.436316	−	0.519981i	0.938733	+	0.344644i	$0.112000\pi$
$128$	−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	0.788222	−	0.615391i	$-0.211002\pi$
$137$	−2.47153	−	6.79047i	−0.211157	−	0.580149i	−0.999379	+	0.0352423i	$0.988780\pi$
$138$	−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	−0.845800	−	0.533500i	$-0.820877\pi$
$157$	1.81744	−	4.99337i	0.145047	−	0.398514i	0.990848	+	0.134985i	$0.0430988\pi$
$158$	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	−0.643993	−	0.765031i	$-0.722724\pi$
$163$	−3.87424	+	2.23679i	−0.303454	+	0.175199i	0.340540	+	0.940230i	$0.389390\pi$
$164$	−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	0.978566	−	0.205934i	$-0.0660231\pi$
$167$	1.24795	+	3.42872i	0.0965694	+	0.265322i	−0.881997	+	0.471256i	$0.843801\pi$
$168$	−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	−0.129437	−	0.991588i	$-0.541317\pi$
$173$	1.15844	−	0.204264i	0.0880746	−	0.0155299i	0.217512	+	0.976058i	$0.430206\pi$
$174$	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	0.631657	−	0.775248i	$-0.282375\pi$
$193$	−3.35501	−	3.99835i	−0.241499	−	0.287807i	−0.873156	+	0.487441i	$0.837931\pi$
$194$	−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	0.585498	−	0.810674i	$-0.300899\pi$
$197$	2.47286	+	1.42771i	0.176184	+	0.101720i	−0.409315	+	0.912393i	$0.634232\pi$
$198$	−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	$-0.497952\pi$
$223$	9.62115	−	26.4339i	0.644280	−	1.77014i	0.637846	−	0.770164i	$-0.279826\pi$
$224$	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	$-0.862138\pi$
$227$		−	12.6466i		−	0.839382i	0.907667	−	0.419691i	$-0.137862\pi$
$228$	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	$-0.590305\pi$
$233$	8.41990	−	23.1335i	0.551606	−	1.51552i	0.831517	−	0.555499i	$-0.187473\pi$
$234$	−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	−0.242893	−	0.970053i	$-0.578096\pi$
$257$	−12.8717	−	2.26963i	−0.802915	−	0.141576i	−0.560022	+	0.828478i	$0.689207\pi$
$258$	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	0.976890	−	0.213743i	$-0.0685655\pi$
$263$	9.67780	+	11.5336i	0.596759	+	0.711190i	−0.380131	+	0.924933i	$0.624121\pi$
$264$	−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	−0.283103	−	0.959090i	$-0.591364\pi$
$277$	6.75622	−	3.90071i	0.405942	−	0.234371i	0.689045	+	0.724719i	$0.258030\pi$
$278$	−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	−0.381161	−	0.924509i	$-0.624476\pi$
$283$	−7.11822	+	1.25513i	−0.423134	+	0.0746100i	−0.0419735	+	0.999119i	$0.513365\pi$
$284$	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	−0.183488	−	0.983022i	$-0.558739\pi$
$293$	9.86109	−	5.69330i	0.576091	−	0.332606i	0.759578	+	0.650416i	$0.225405\pi$
$294$	−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	0.667718	−	0.744414i	$-0.267271\pi$
$307$	−3.17725	−	3.78649i	−0.181335	−	0.216107i	−0.849053	+	0.528308i	$0.822827\pi$
$308$	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	−0.778188	−	0.628031i	$-0.783861\pi$
$313$	−30.5050	−	5.37886i	−1.72424	−	0.304031i	−0.946057	+	0.324001i	$0.894972\pi$
$314$	−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	−0.876225	−	0.481903i	$-0.839946\pi$
$317$	−4.44201	+	5.29378i	−0.249488	+	0.297328i	0.626737	+	0.779231i	$0.284390\pi$
$318$	−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	$0.266318\pi$
$337$	−5.88315	+	16.1638i	−0.320476	+	0.880500i	−0.990420	+	0.138088i	$0.955904\pi$
$338$	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	$0.276151\pi$
$347$	−6.31466	+	17.3494i	−0.338989	+	0.931364i	−0.985682	+	0.168614i	$0.946071\pi$
$348$	−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	−0.640401	−	0.768041i	$-0.721232\pi$
$353$	−5.55115	+	3.20496i	−0.295458	+	0.170583i	0.344943	+	0.938624i	$0.387898\pi$
$354$	−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	−0.462714	−	0.886508i	$-0.653124\pi$
$367$	9.39999	−	11.2025i	0.490676	−	0.584764i	0.953389	+	0.301743i	$0.0975686\pi$
$368$	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	0.772155	−	0.635434i	$-0.219179\pi$
$373$	11.7411	+	6.77871i	0.607930	+	0.350989i	−0.164225	+	0.986423i	$0.552512\pi$
$374$	−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	$-0.960667\pi$
$383$	−18.4242	−	21.9571i	−0.941433	−	1.12196i	0.0509425	−	0.998702i	$-0.483777\pi$
$384$	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	0.513932	−	0.857831i	$-0.328188\pi$
$397$	25.7084	−	4.53308i	1.29027	−	0.227509i	0.776334	+	0.630322i	$0.217077\pi$
$398$			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	0.948417	−	0.317025i	$-0.102684\pi$
$433$	0.376798	+	1.03524i	0.0181078	+	0.0497507i	−0.930309	+	0.366776i	$0.880462\pi$
$434$	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	−0.869305	−	0.494275i	$-0.835433\pi$
$443$	−4.87432	+	5.80899i	−0.231586	+	0.275993i	0.637719	+	0.770269i	$0.279878\pi$
$444$	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	$-0.931532\pi$
$457$		−	9.12576i		−	0.426885i	0.976956	−	0.213442i	$-0.0684676\pi$
$458$	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	0.781823	−	0.623500i	$-0.214290\pi$
$463$	13.6156	+	7.86094i	0.632768	+	0.365329i	−0.149055	+	0.988829i	$0.547623\pi$
$464$	−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	−0.355344	−	0.934736i	$-0.615636\pi$
$467$	5.97499	−	3.44966i	0.276490	−	0.159631i	0.631833	+	0.775104i	$0.282303\pi$
$468$	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	−0.0117346	−	0.999931i	$-0.503735\pi$
$487$	−19.4986	−	11.2575i	−0.883568	−	0.510128i	−0.871833	+	0.489803i	$0.837069\pi$
$488$	−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	−0.418528	−	0.908204i	$-0.637454\pi$
$503$	−25.1737	−	4.43880i	−1.12244	−	0.197917i	−0.703912	+	0.710287i	$0.748565\pi$
$504$	−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	0.681849	−	0.731493i	$-0.261176\pi$
$523$	24.5247	+	4.32437i	1.07239	+	0.189092i	0.390543	+	0.920585i	$0.372287\pi$
$524$	−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	0.959466	−	0.281823i	$-0.0909391\pi$
$547$	1.01317	+	2.78367i	0.0433202	+	0.119021i	−0.916146	+	0.400844i	$0.868717\pi$
$548$	−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	$0.448241\pi$
$557$	−19.7784	+	23.5710i	−0.838038	+	0.998734i	−0.999929	+	0.0119259i	$0.996204\pi$
$558$	−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	0.979717	−	0.200387i	$-0.0642201\pi$
$563$	30.7518	+	17.7546i	1.29603	+	0.748266i	0.316318	+	0.948653i	$0.397553\pi$
$564$	−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	0.189453	−	0.981890i	$-0.439329\pi$
$577$	−13.5997	−	7.85178i	−0.566162	−	0.326874i	−0.755615	+	0.655016i	$0.772662\pi$
$578$	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	−0.684155	−	0.729337i	$-0.739829\pi$
$587$	−26.1082	+	4.60359i	−1.07760	+	0.190010i	−0.393448	+	0.919347i	$0.628718\pi$
$588$		−	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	0.958562	−	0.284884i	$-0.0919552\pi$
$593$	1.00184	+	2.75254i	0.0411408	+	0.113033i	−0.917421	+	0.397918i	$0.869733\pi$
$594$	−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	$0.280635\pi$
$607$			38.0294i			1.54357i	−0.635886	+	0.771783i	$0.719365\pi$
$608$	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	$0.263764\pi$
$613$	−7.81429	+	21.4696i	−0.315616	+	0.867149i	−0.991496	+	0.130137i	$0.958458\pi$
$614$	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	0.653588	−	0.756851i	$-0.273263\pi$
$617$	25.0606	+	4.41886i	1.00890	+	0.177896i	0.355313	+	0.934747i	$0.384374\pi$
$618$	−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	0.674492	−	0.738282i	$-0.264363\pi$
$643$	−4.30313	−	5.12827i	−0.169699	−	0.202239i	−0.844191	+	0.536043i	$0.819918\pi$
$644$	−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	$-0.812765\pi$
$647$		−	28.2280i		−	1.10976i	0.831932	−	0.554878i	$-0.187235\pi$
$648$	−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	0.183814	−	0.982961i	$-0.441156\pi$
$653$	−14.7075	−	8.49136i	−0.575548	−	0.332293i	−0.759362	+	0.650668i	$0.774489\pi$
$654$	−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	−0.907842	−	0.419313i	$-0.862271\pi$
$673$	−25.9066	+	14.9572i	−0.998626	+	0.576557i	−0.0907847	+	0.995871i	$0.528938\pi$
$674$	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	−0.125189	−	0.992133i	$-0.539954\pi$
$677$	−27.2420	−	15.7282i	−1.04700	−	0.604483i	−0.921807	+	0.387650i	$0.873287\pi$
$678$	−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	$-0.596356\pi$
$683$		−	49.8920i		−	1.90906i	0.298109	−	0.954532i	$-0.403644\pi$
$684$	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	$-0.594676\pi$
$727$	14.7217	−	40.4476i	0.545999	−	1.50012i	0.839067	−	0.544028i	$-0.183102\pi$
$728$	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	−0.899931	−	0.436032i	$-0.856383\pi$
$733$	−26.3235	+	15.1979i	−0.972282	+	0.561347i	−0.0723507	+	0.997379i	$0.523050\pi$
$734$	−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	−0.598873	−	0.800844i	$-0.704385\pi$
$743$	−24.1976	+	4.26670i	−0.887725	+	0.156530i	−0.288852	+	0.957374i	$0.593274\pi$
$744$	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	0.842332	−	0.538958i	$-0.181182\pi$
$757$	4.54780	+	5.41985i	0.165292	+	0.196988i	−0.677040	+	0.735946i	$0.736738\pi$
$758$	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	−0.757052	−	0.653354i	$-0.773361\pi$
$773$	0.495905	−	0.590996i	0.0178364	−	0.0212567i	0.774889	+	0.632097i	$0.217806\pi$
$774$	−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

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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