LMFDB - Embedded Newform 20.4.e.b.7.3

Newspace parameters

Level:	$ N $	=	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	=	$ 4 $
Character orbit:	$[\chi]$	=	20.e (of order $4$ and degree $2$)

Newform invariants

Self dual:	No
Analytic conductor:	$1.18003820011$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.3
Root			$-1.76129 - 0.947553i$
Character	$\chi$	=	20.7
Dual form			20.4.e.b.3.3

$q$-expansion

$f(q)$	$=$	$q+(-0.813737 + 2.70884i) q^{2} +(2.61822 + 2.61822i) q^{3} +(-6.67566 - 4.40857i) q^{4} +(-0.435501 + 11.1719i) q^{5} +(-9.22289 + 4.96181i) q^{6} +(17.7783 - 17.7783i) q^{7} +(17.3744 - 14.4959i) q^{8} -13.2899i q^{9} +O(q^{10})$	\(q+(-0.813737 + 2.70884i) q^{2} +(2.61822 + 2.61822i) q^{3} +(-6.67566 - 4.40857i) q^{4} +(-0.435501 + 11.1719i) q^{5} +(-9.22289 + 4.96181i) q^{6} +(17.7783 - 17.7783i) q^{7} +(17.3744 - 14.4959i) q^{8} -13.2899i q^{9} +(-29.9084 - 10.2707i) q^{10} +7.37590i q^{11} +(-5.93575 - 29.0210i) q^{12} +(-2.68249 + 2.68249i) q^{13} +(33.6917 + 62.6254i) q^{14} +(-30.3906 + 28.1101i) q^{15} +(25.1290 + 58.8603i) q^{16} +(-20.2367 - 20.2367i) q^{17} +(36.0001 + 10.8144i) q^{18} -135.808 q^{19} +(52.1592 - 72.6596i) q^{20} +93.0948 q^{21} +(-19.9802 - 6.00204i) q^{22} +(71.0426 + 71.0426i) q^{23} +(83.4434 + 7.53642i) q^{24} +(-124.621 - 9.73070i) q^{25} +(-5.08361 - 9.44930i) q^{26} +(105.488 - 105.488i) q^{27} +(-197.059 + 40.3050i) q^{28} -34.2890i q^{29} +(-51.4160 - 105.198i) q^{30} -187.974i q^{31} +(-179.892 + 20.1737i) q^{32} +(-19.3117 + 19.3117i) q^{33} +(71.2855 - 38.3507i) q^{34} +(190.874 + 206.359i) q^{35} +(-58.5893 + 88.7186i) q^{36} +(250.679 + 250.679i) q^{37} +(110.512 - 367.882i) q^{38} -14.0467 q^{39} +(154.380 + 200.417i) q^{40} -211.105 q^{41} +(-75.7547 + 252.179i) q^{42} +(-46.7326 - 46.7326i) q^{43} +(32.5172 - 49.2390i) q^{44} +(148.472 + 5.78774i) q^{45} +(-250.253 + 134.633i) q^{46} +(-189.707 + 189.707i) q^{47} +(-88.3159 + 219.902i) q^{48} -289.134i q^{49} +(127.767 - 329.660i) q^{50} -105.968i q^{51} +(29.7334 - 6.08147i) q^{52} +(-74.5742 + 74.5742i) q^{53} +(199.910 + 371.589i) q^{54} +(-82.4025 - 3.21221i) q^{55} +(51.1739 - 566.598i) q^{56} +(-355.575 - 355.575i) q^{57} +(92.8835 + 27.9022i) q^{58} -101.072 q^{59} +(326.803 - 53.6747i) q^{60} +232.112 q^{61} +(509.191 + 152.961i) q^{62} +(-236.271 - 236.271i) q^{63} +(91.7370 - 503.715i) q^{64} +(-28.8002 - 31.1367i) q^{65} +(-36.5978 - 68.0271i) q^{66} +(34.7419 - 34.7419i) q^{67} +(45.8785 + 224.309i) q^{68} +372.010i q^{69} +(-714.314 + 349.126i) q^{70} +614.600i q^{71} +(-192.649 - 230.903i) q^{72} +(-37.4378 + 37.4378i) q^{73} +(-883.036 + 475.063i) q^{74} +(-300.807 - 351.761i) q^{75} +(906.607 + 598.718i) q^{76} +(131.131 + 131.131i) q^{77} +(11.4303 - 38.0504i) q^{78} +1002.91 q^{79} +(-668.522 + 255.104i) q^{80} +193.554 q^{81} +(171.784 - 571.850i) q^{82} +(423.190 + 423.190i) q^{83} +(-621.470 - 410.415i) q^{84} +(234.895 - 217.269i) q^{85} +(164.619 - 88.5632i) q^{86} +(89.7761 - 89.7761i) q^{87} +(106.920 + 128.152i) q^{88} +1049.38i q^{89} +(-136.495 + 397.478i) q^{90} +95.3802i q^{91} +(-161.060 - 787.453i) q^{92} +(492.156 - 492.156i) q^{93} +(-359.514 - 668.257i) q^{94} +(59.1444 - 1517.22i) q^{95} +(-523.815 - 418.177i) q^{96} +(-536.526 - 536.526i) q^{97} +(783.218 + 235.279i) q^{98} +98.0246 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12q - 6q^{2} + 8q^{6} - 12q^{8} + O(q^{10}) $	$ 12q - 6q^{2} + 8q^{6} - 12q^{8} - 110q^{10} - 80q^{12} + 116q^{13} + 312q^{16} - 332q^{17} + 198q^{18} + 140q^{20} - 144q^{21} + 360q^{22} + 340q^{25} - 164q^{26} - 880q^{28} - 1240q^{30} - 376q^{32} + 80q^{33} + 460q^{36} + 508q^{37} + 1600q^{38} + 1420q^{40} - 656q^{41} + 1160q^{42} + 1180q^{45} - 1432q^{46} - 2720q^{48} - 1570q^{50} - 932q^{52} - 644q^{53} + 2048q^{56} - 960q^{57} + 1576q^{58} + 3280q^{60} - 896q^{61} + 2440q^{62} - 2740q^{65} - 1680q^{66} - 844q^{68} - 3040q^{70} - 3036q^{72} + 1436q^{73} + 800q^{76} + 3120q^{77} + 3720q^{78} + 1840q^{80} + 5988q^{81} - 1352q^{82} + 500q^{85} - 2552q^{86} - 2400q^{88} - 750q^{90} - 1840q^{92} - 3280q^{93} + 1088q^{96} - 4772q^{97} + 1698q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character Values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.813737	+	2.70884i	−0.287699	+	0.957721i
$2$	−0.813737	+	2.70884i	−0.287699	+	0.957721i
$3$	2.61822	+	2.61822i	0.503877	+	0.503877i	0.912640	−	0.408764i	$-0.134040\pi$
$3$	2.61822	+	2.61822i	0.503877	+	0.503877i	−0.408764	+	0.912640i	$0.634040\pi$
$4$	−6.67566	−	4.40857i	−0.834458	−	0.551071i
$5$	−0.435501	+	11.1719i	−0.0389524	+	0.999241i
$5$	−0.435501	+	11.1719i	−0.0389524	+	0.999241i
$6$	−9.22289	+	4.96181i	−0.627538	+	0.337608i
$7$	17.7783	−	17.7783i	0.959936	−	0.959936i	−0.0392914	−	0.999228i	$-0.512510\pi$
$7$	17.7783	−	17.7783i	0.959936	−	0.959936i	0.999228	+	0.0392914i	$0.0125101\pi$
$8$	17.3744	−	14.4959i	0.767846	−	0.640635i
$9$		−	13.2899i		−	0.492217i
$10$	−29.9084	−	10.2707i	−0.945787	−	0.324787i
$11$			7.37590i			0.202174i	0.994878	+	0.101087i	$0.0322321\pi$
$11$			7.37590i			0.202174i	−0.994878	+	0.101087i	$0.967768\pi$
$12$	−5.93575	−	29.0210i	−0.142792	−	0.698136i
$13$	−2.68249	+	2.68249i	−0.0572300	+	0.0572300i	−0.735143	−	0.677913i	$-0.762885\pi$
$13$	−2.68249	+	2.68249i	−0.0572300	+	0.0572300i	0.677913	+	0.735143i	$0.262885\pi$
$14$	33.6917	+	62.6254i	0.643178	+	1.19552i
$15$	−30.3906	+	28.1101i	−0.523121	+	0.483867i
$16$	25.1290	+	58.8603i	0.392641	+	0.919692i
$17$	−20.2367	−	20.2367i	−0.288713	−	0.288713i	0.547858	−	0.836571i	$-0.315443\pi$
$17$	−20.2367	−	20.2367i	−0.288713	−	0.288713i	−0.836571	+	0.547858i	$0.815443\pi$
$18$	36.0001	+	10.8144i	0.471406	+	0.141610i
$19$	−135.808			−1.63981			−0.819906	−	0.572498i	$-0.805975\pi$
$19$	−135.808			−1.63981			−0.819906	+	0.572498i	$0.805975\pi$
$20$	52.1592	−	72.6596i	0.583157	−	0.812359i
$21$	93.0948			0.967379
$22$	−19.9802	−	6.00204i	−0.193627	−	0.0581654i
$23$	71.0426	+	71.0426i	0.644061	+	0.644061i	0.951551	−	0.307490i	$-0.0994892\pi$
$23$	71.0426	+	71.0426i	0.644061	+	0.644061i	−0.307490	+	0.951551i	$0.599489\pi$
$24$	83.4434	+	7.53642i	0.709700	+	0.0640985i
$25$	−124.621	−	9.73070i	−0.996965	−	0.0778456i
$26$	−5.08361	−	9.44930i	−0.0383453	−	0.0712754i
$27$	105.488	−	105.488i	0.751893	−	0.751893i
$28$	−197.059	+	40.3050i	−1.33002	+	0.272033i
$29$		−	34.2890i		−	0.219562i	−0.993956	−	0.109781i	$-0.964985\pi$
$29$		−	34.2890i		−	0.219562i	0.993956	−	0.109781i	$-0.0350150\pi$
$30$	−51.4160	−	105.198i	−0.312908	−	0.640213i
$31$		−	187.974i		−	1.08907i	−0.838739	−	0.544533i	$-0.816707\pi$
$31$		−	187.974i		−	1.08907i	0.838739	−	0.544533i	$-0.183293\pi$
$32$	−179.892	+	20.1737i	−0.993771	+	0.111445i
$33$	−19.3117	+	19.3117i	−0.101871	+	0.101871i
$34$	71.2855	−	38.3507i	0.359569	−	0.193444i
$35$	190.874	+	206.359i	0.921816	+	0.996600i
$36$	−58.5893	+	88.7186i	−0.271247	+	0.410734i
$37$	250.679	+	250.679i	1.11382	+	1.11382i	0.992629	+	0.121190i	$0.0386712\pi$
$37$	250.679	+	250.679i	1.11382	+	1.11382i	0.121190	+	0.992629i	$0.461329\pi$
$38$	110.512	−	367.882i	0.471773	−	1.57048i
$39$	−14.0467			−0.0576737
$40$	154.380	+	200.417i	0.610239	+	0.792217i
$41$	−211.105			−0.804122			−0.402061	−	0.915613i	$-0.631706\pi$
$41$	−211.105			−0.804122			−0.402061	+	0.915613i	$0.631706\pi$
$42$	−75.7547	+	252.179i	−0.278314	+	0.926479i
$43$	−46.7326	−	46.7326i	−0.165736	−	0.165736i	0.619366	−	0.785102i	$-0.287390\pi$
$43$	−46.7326	−	46.7326i	−0.165736	−	0.165736i	−0.785102	+	0.619366i	$0.787390\pi$
$44$	32.5172	−	49.2390i	0.111412	−	0.168706i
$45$	148.472	+	5.78774i	0.491843	+	0.0191730i
$46$	−250.253	+	134.633i	−0.802126	+	0.431535i
$47$	−189.707	+	189.707i	−0.588757	+	0.588757i	−0.937295	−	0.348538i	$-0.886678\pi$
$47$	−189.707	+	189.707i	−0.588757	+	0.588757i	0.348538	+	0.937295i	$0.386678\pi$
$48$	−88.3159	+	219.902i	−0.265569	+	0.661254i
$49$		−	289.134i		−	0.842956i
$50$	127.767	−	329.660i	0.361381	−	0.932418i
$51$		−	105.968i		−	0.290952i
$52$	29.7334	−	6.08147i	0.0792939	−	0.0162182i
$53$	−74.5742	+	74.5742i	−0.193275	+	0.193275i	−0.797109	−	0.603835i	$-0.793639\pi$
$53$	−74.5742	+	74.5742i	−0.193275	+	0.193275i	0.603835	+	0.797109i	$0.293639\pi$
$54$	199.910	+	371.589i	0.503784	+	0.936423i
$55$	−82.4025	−	3.21221i	−0.202021	−	0.00787517i
$56$	51.1739	−	566.598i	0.122114	−	1.35205i
$57$	−355.575	−	355.575i	−0.826263	−	0.826263i
$58$	92.8835	+	27.9022i	0.210279	+	0.0631679i
$59$	−101.072			−0.223024			−0.111512	−	0.993763i	$-0.535569\pi$
$59$	−101.072			−0.223024			−0.111512	+	0.993763i	$0.535569\pi$
$60$	326.803	−	53.6747i	0.703168	−	0.115489i
$61$	232.112			0.487196			0.243598	−	0.969876i	$-0.421672\pi$
$61$	232.112			0.487196			0.243598	+	0.969876i	$0.421672\pi$
$62$	509.191	+	152.961i	1.04302	+	0.313324i
$63$	−236.271	−	236.271i	−0.472497	−	0.472497i
$64$	91.7370	−	503.715i	0.179174	−	0.983817i
$65$	−28.8002	−	31.1367i	−0.0549573	−	0.0594158i
$66$	−36.5978	−	68.0271i	−0.0682557	−	0.126872i
$67$	34.7419	−	34.7419i	0.0633493	−	0.0633493i	−0.674722	−	0.738072i	$-0.735737\pi$
$67$	34.7419	−	34.7419i	0.0633493	−	0.0633493i	0.738072	+	0.674722i	$0.235737\pi$
$68$	45.8785	+	224.309i	0.0818175	+	0.400021i
$69$			372.010i			0.649054i
$70$	−714.314	+	349.126i	−1.21967	+	0.596121i
$71$			614.600i			1.02732i	0.857994	+	0.513660i	$0.171711\pi$
$71$			614.600i			1.02732i	−0.857994	+	0.513660i	$0.828289\pi$
$72$	−192.649	−	230.903i	−0.315331	−	0.377946i
$73$	−37.4378	+	37.4378i	−0.0600242	+	0.0600242i	−0.736482	−	0.676457i	$-0.763514\pi$
$73$	−37.4378	+	37.4378i	−0.0600242	+	0.0600242i	0.676457	+	0.736482i	$0.263514\pi$
$74$	−883.036	+	475.063i	−1.38717	+	0.746283i
$75$	−300.807	−	351.761i	−0.463123	−	0.541572i
$76$	906.607	+	598.718i	1.36836	+	0.903654i
$77$	131.131	+	131.131i	0.194074	+	0.194074i
$78$	11.4303	−	38.0504i	0.0165927	−	0.0552353i
$79$	1002.91			1.42831			0.714153	−	0.699990i	$-0.246812\pi$
$79$	1002.91			1.42831			0.714153	+	0.699990i	$0.246812\pi$
$80$	−668.522	+	255.104i	−0.934288	+	0.356518i
$81$	193.554			0.265506
$82$	171.784	−	571.850i	0.231346	−	0.770125i
$83$	423.190	+	423.190i	0.559652	+	0.559652i	0.929208	−	0.369556i	$-0.120490\pi$
$83$	423.190	+	423.190i	0.559652	+	0.559652i	−0.369556	+	0.929208i	$0.620490\pi$
$84$	−621.470	−	410.415i	−0.807237	−	0.533095i
$85$	234.895	−	217.269i	0.299740	−	0.277248i
$86$	164.619	−	88.5632i	0.206411	−	0.111047i
$87$	89.7761	−	89.7761i	0.110632	−	0.110632i
$88$	106.920	+	128.152i	0.129520	+	0.155239i
$89$			1049.38i			1.24982i	0.780695	+	0.624912i	$0.214865\pi$
$89$			1049.38i			1.24982i	−0.780695	+	0.624912i	$0.785135\pi$
$90$	−136.495	+	397.478i	−0.159865	+	0.465532i
$91$			95.3802i			0.109874i
$92$	−161.060	−	787.453i	−0.182518	−	0.892365i
$93$	492.156	−	492.156i	0.548755	−	0.548755i
$94$	−359.514	−	668.257i	−0.394479	−	0.733249i
$95$	59.1444	−	1517.22i	0.0638746	−	1.63857i
$96$	−523.815	−	418.177i	−0.556892	−	0.444583i
$97$	−536.526	−	536.526i	−0.561608	−	0.561608i	0.368156	−	0.929764i	$-0.379989\pi$
$97$	−536.526	−	536.526i	−0.561608	−	0.561608i	−0.929764	+	0.368156i	$0.879989\pi$
$98$	783.218	+	235.279i	0.807316	+	0.242518i
$99$	98.0246			0.0995136
$100$	789.027	+	614.358i	0.789027	+	0.614358i
$101$	−1415.80			−1.39483			−0.697414	−	0.716668i	$-0.745666\pi$
$101$	−1415.80			−1.39483			−0.697414	+	0.716668i	$0.745666\pi$
$102$	287.052	+	86.2303i	0.278650	+	0.0837066i
$103$	−284.920	−	284.920i	−0.272563	−	0.272563i	0.557568	−	0.830131i	$-0.311735\pi$
$103$	−284.920	−	284.920i	−0.272563	−	0.272563i	−0.830131	+	0.557568i	$0.811735\pi$
$104$	−7.72143	+	85.4919i	−0.00728027	+	0.0806074i
$105$	−40.5429	+	1040.04i	−0.0376817	+	0.966645i
$106$	−141.326	−	262.694i	−0.129498	−	0.240708i
$107$	−464.315	+	464.315i	−0.419505	+	0.419505i	−0.885033	−	0.465528i	$-0.845864\pi$
$107$	−464.315	+	464.315i	−0.419505	+	0.419505i	0.465528	+	0.885033i	$0.345864\pi$
$108$	−1169.25	+	239.150i	−1.04177	+	0.213076i
$109$		−	638.365i		−	0.560957i	−0.959860	−	0.280478i	$-0.909507\pi$
$109$		−	638.365i		−	0.560957i	0.959860	−	0.280478i	$-0.0904931\pi$
$110$	75.7553	−	220.601i	0.0656635	−	0.191214i
$111$			1312.66i			1.12246i
$112$	1493.18	+	599.684i	1.25976	+	0.505936i
$113$	1001.84	−	1001.84i	0.834027	−	0.834027i	−0.154038	−	0.988065i	$-0.549228\pi$
$113$	1001.84	−	1001.84i	0.834027	−	0.834027i	0.988065	+	0.154038i	$0.0492277\pi$
$114$	1252.54	−	673.852i	1.02905	−	0.553614i
$115$	−824.616	+	762.738i	−0.668660	+	0.618484i
$116$	−151.165	+	228.902i	−0.120994	+	0.183216i
$117$	35.6500	+	35.6500i	0.0281696	+	0.0281696i
$118$	82.2456	−	273.787i	0.0641638	−	0.213594i
$119$	−719.548			−0.554293
$120$	−120.535	+	928.935i	−0.0916944	+	0.706665i
$121$	1276.60			0.959126
$122$	−188.878	+	628.756i	−0.140166	+	0.466598i
$123$	−552.718	−	552.718i	−0.405178	−	0.405178i
$124$	−828.695	+	1254.85i	−0.600153	+	0.908780i
$125$	162.982	−	1388.01i	0.116621	−	0.993177i
$126$	832.282	−	447.758i	0.588457	−	0.316583i
$127$	−619.456	+	619.456i	−0.432818	+	0.432818i	−0.889586	−	0.456768i	$-0.849007\pi$
$127$	−619.456	+	619.456i	−0.432818	+	0.432818i	0.456768	+	0.889586i	$0.349007\pi$
$128$	1289.83	+	658.392i	0.890674	+	0.454642i
$129$		−	244.712i		−	0.167021i
$130$	107.780	−	52.6782i	0.0727150	−	0.0355399i
$131$		−	1620.12i		−	1.08054i	−0.841491	−	0.540270i	$-0.818322\pi$
$131$		−	1620.12i		−	1.08054i	0.841491	−	0.540270i	$-0.181678\pi$
$132$	214.056	−	43.7815i	0.141145	−	0.0288689i
$133$	−2414.43	+	2414.43i	−1.57412	+	1.57412i
$134$	65.8397	+	122.381i	0.0424454	+	0.0788965i
$135$	1132.55	+	1224.43i	0.722034	+	0.780611i
$136$	−644.950	−	58.2504i	−0.406647	−	0.0367274i
$137$	825.076	+	825.076i	0.514533	+	0.514533i	0.915912	−	0.401379i	$-0.131469\pi$
$137$	825.076	+	825.076i	0.514533	+	0.514533i	−0.401379	+	0.915912i	$0.631469\pi$
$138$	−1007.72	−	302.718i	−0.621613	−	0.186733i
$139$	1264.21			0.771430			0.385715	−	0.922618i	$-0.373955\pi$
$139$	1264.21			0.771430			0.385715	+	0.922618i	$0.373955\pi$
$140$	−364.462	−	2219.06i	−0.220019	−	1.33961i
$141$	−993.387			−0.593321
$142$	−1664.86	−	500.123i	−0.983885	−	0.295559i
$143$	−19.7858	−	19.7858i	−0.0115704	−	0.0115704i
$144$	782.244	−	333.961i	0.452688	−	0.193264i
$145$	383.072	+	14.9329i	0.219396	+	0.00855247i
$146$	−70.9487	−	131.878i	−0.0402175	−	0.0747553i
$147$	757.016	−	757.016i	0.424746	−	0.424746i
$148$	−568.312	−	2778.58i	−0.315642	−	1.54323i
$149$		−	1351.49i		−	0.743079i	−0.928417	−	0.371539i	$-0.878830\pi$
$149$		−	1351.49i		−	0.743079i	0.928417	−	0.371539i	$-0.121170\pi$
$150$	1197.64	−	528.598i	0.651915	−	0.287732i
$151$		−	2325.64i		−	1.25336i	−0.779275	−	0.626682i	$-0.784412\pi$
$151$		−	2325.64i		−	1.25336i	0.779275	−	0.626682i	$-0.215588\pi$
$152$	−2359.57	+	1968.66i	−1.25912	+	1.05052i
$153$	−268.943	+	268.943i	−0.142109	+	0.142109i
$154$	−461.918	+	248.507i	−0.241704	+	0.130034i
$155$	2100.01	+	81.8626i	1.08824	+	0.0424217i
$156$	93.7712	+	61.9260i	0.0481263	+	0.0317823i
$157$	162.486	+	162.486i	0.0825976	+	0.0825976i	0.747199	−	0.664601i	$-0.231398\pi$
$157$	162.486	+	162.486i	0.0825976	+	0.0825976i	−0.664601	+	0.747199i	$0.731398\pi$
$158$	−816.105	+	2716.73i	−0.410923	+	1.36792i
$159$	−390.503			−0.194773
$160$	−147.035	−	2018.51i	−0.0726509	−	0.997357i
$161$	2526.03			1.23651
$162$	−157.502	+	524.307i	−0.0763859	+	0.254281i
$163$	932.441	+	932.441i	0.448064	+	0.448064i	0.894710	−	0.446647i	$-0.147382\pi$
$163$	932.441	+	932.441i	0.448064	+	0.448064i	−0.446647	+	0.894710i	$0.647382\pi$
$164$	1409.26	+	930.670i	0.671006	+	0.443129i
$165$	−207.337	−	224.158i	−0.0978255	−	0.105762i
$166$	−1490.72	+	801.990i	−0.697002	+	0.374979i
$167$	976.461	−	976.461i	0.452460	−	0.452460i	−0.443710	−	0.896170i	$-0.646338\pi$
$167$	976.461	−	976.461i	0.452460	−	0.452460i	0.896170	+	0.443710i	$0.146338\pi$
$168$	1617.46	−	1349.49i	0.742798	−	0.619737i
$169$			2182.61i			0.993449i
$170$	397.404	+	813.093i	0.179291	+	0.366831i
$171$			1804.87i			0.807143i
$172$	105.947	+	517.995i	0.0469674	+	0.229632i
$173$	761.698	−	761.698i	0.334745	−	0.334745i	−0.519640	−	0.854385i	$-0.673934\pi$
$173$	761.698	−	761.698i	0.334745	−	0.334745i	0.854385	+	0.519640i	$0.173934\pi$
$174$	170.135	+	316.244i	0.0741260	+	0.137784i
$175$	−2388.54	+	2042.54i	−1.03175	+	0.882296i
$176$	−434.148	+	185.349i	−0.185938	+	0.0793818i
$177$	−264.628	−	264.628i	−0.112376	−	0.112376i
$178$	−2842.61	−	853.921i	−1.19698	−	0.359574i
$179$	−4003.32			−1.67163			−0.835816	−	0.549009i	$-0.815005\pi$
$179$	−4003.32			−1.67163			−0.835816	+	0.549009i	$0.815005\pi$
$180$	−965.635	−	693.188i	−0.399857	−	0.287040i
$181$	−1950.00			−0.800785			−0.400392	−	0.916344i	$-0.631126\pi$
$181$	−1950.00			−0.800785			−0.400392	+	0.916344i	$0.631126\pi$
$182$	−258.370	−	77.6144i	−0.105229	−	0.0316108i
$183$	607.721	+	607.721i	0.245487	+	0.245487i
$184$	2264.15	+	204.493i	0.907147	+	0.0819315i
$185$	−2909.72	+	2691.38i	−1.15636	+	1.06959i
$186$	932.688	+	1733.66i	0.367677	+	0.683430i
$187$	149.264	−	149.264i	0.0583704	−	0.0583704i
$188$	2102.75	−	430.083i	0.815740	−	0.166846i
$189$		−	3750.78i		−	1.44354i
$190$	4061.80	+	1394.83i	1.55091	+	0.532589i
$191$		−	1458.80i		−	0.552644i	−0.961065	−	0.276322i	$-0.910884\pi$
$191$		−	1458.80i		−	0.552644i	0.961065	−	0.276322i	$-0.0891156\pi$
$192$	1559.02	−	1078.65i	0.586004	−	0.405441i
$193$	2264.70	−	2264.70i	0.844647	−	0.844647i	−0.144812	−	0.989459i	$-0.546258\pi$
$193$	2264.70	−	2264.70i	0.844647	−	0.844647i	0.989459	+	0.144812i	$0.0462577\pi$
$194$	1889.96	−	1016.77i	0.699438	−	0.376289i
$195$	6.11736	−	156.928i	0.00224653	−	0.0576300i
$196$	−1274.67	+	1930.16i	−0.464529	+	0.703411i
$197$	2092.70	+	2092.70i	0.756845	+	0.756845i	0.975747	−	0.218902i	$-0.0702474\pi$
$197$	2092.70	+	2092.70i	0.756845	+	0.756845i	−0.218902	+	0.975747i	$0.570247\pi$
$198$	−79.7662	+	265.533i	−0.0286300	+	0.0953062i
$199$	−2087.70			−0.743683			−0.371842	−	0.928296i	$-0.621274\pi$
$199$	−2087.70			−0.743683			−0.371842	+	0.928296i	$0.621274\pi$
$200$	−2306.26	+	1637.43i	−0.815386	+	0.578917i
$201$	181.924			0.0638405
$202$	1152.09	−	3835.19i	0.401291	−	1.33586i
$203$	−609.599	−	609.599i	−0.210766	−	0.210766i
$204$	−467.169	+	707.409i	−0.160335	+	0.242787i
$205$	91.9363	−	2358.43i	0.0313225	−	0.803512i
$206$	1003.65	−	539.954i	0.339456	−	0.182623i
$207$	944.145	−	944.145i	0.317018	−	0.317018i
$208$	−225.301	−	90.4840i	−0.0751048	−	0.0301632i
$209$		−	1001.70i		−	0.331528i
$210$	−2784.32	−	956.145i	−0.914935	−	0.314192i
$211$			199.597i			0.0651223i	0.999470	+	0.0325611i	$0.0103664\pi$
$211$			199.597i			0.0651223i	−0.999470	+	0.0325611i	$0.989634\pi$
$212$	826.598	−	169.067i	0.267788	−	0.0547714i
$213$	−1609.16	+	1609.16i	−0.517642	+	0.517642i
$214$	−879.926	−	1635.59i	−0.281077	−	0.522460i
$215$	542.442	−	501.738i	0.172066	−	0.159155i
$216$	303.641	−	3361.92i	0.0956489	−	1.05903i
$217$	−3341.84	−	3341.84i	−1.04543	−	1.04543i
$218$	1729.23	+	519.461i	0.537240	+	0.161387i
$219$	−196.041			−0.0604896
$220$	535.930	+	384.721i	0.164238	+	0.117899i
$221$	108.570			0.0330461
$222$	−3555.80	−	1068.16i	−1.07500	−	0.322930i
$223$	3340.24	+	3340.24i	1.00304	+	1.00304i	0.999995	+	0.00304854i	$0.000970381\pi$
$223$	3340.24	+	3340.24i	1.00304	+	1.00304i	0.00304854	+	0.999995i	$0.499030\pi$
$224$	−2839.51	+	3556.82i	−0.846976	+	1.06094i
$225$	−129.320	+	1656.19i	−0.0383169	+	0.490723i
$226$	1898.59	+	3529.06i	0.558816	+	1.03871i
$227$	824.316	−	824.316i	0.241021	−	0.241021i	−0.576251	−	0.817272i	$-0.695485\pi$
$227$	824.316	−	824.316i	0.241021	−	0.241021i	0.817272	+	0.576251i	$0.195485\pi$
$228$	806.121	+	3941.27i	0.234152	+	1.14481i
$229$			4512.23i			1.30208i	0.759043	+	0.651041i	$0.225667\pi$
$229$			4512.23i			1.30208i	−0.759043	+	0.651041i	$0.774333\pi$
$230$	−1395.12	−	2854.42i	−0.399962	−	0.818327i
$231$			686.658i			0.195579i
$232$	−497.050	−	595.749i	−0.140659	−	0.168590i
$233$	−292.574	+	292.574i	−0.0822625	+	0.0822625i	−0.747041	−	0.664778i	$-0.768526\pi$
$233$	−292.574	+	292.574i	−0.0822625	+	0.0822625i	0.664778	+	0.747041i	$0.268526\pi$
$234$	−125.580	+	67.5605i	−0.0350829	+	0.0188742i
$235$	−2036.76	−	2201.99i	−0.565376	−	0.611243i
$236$	674.720	+	445.581i	0.186104	+	0.122902i
$237$	2625.84	+	2625.84i	0.719690	+	0.719690i
$238$	585.522	−	1949.14i	0.159470	−	0.530858i
$239$	2925.20			0.791696			0.395848	−	0.918316i	$-0.370451\pi$
$239$	2925.20			0.791696			0.395848	+	0.918316i	$0.370451\pi$
$240$	−2418.26	−	1082.42i	−0.650407	−	0.291125i
$241$	4259.40			1.13847			0.569236	−	0.822174i	$-0.307239\pi$
$241$	4259.40			1.13847			0.569236	+	0.822174i	$0.307239\pi$
$242$	−1038.81	+	3458.10i	−0.275940	+	0.918574i
$243$	−2341.40	−	2341.40i	−0.618111	−	0.618111i
$244$	−1549.50	−	1023.28i	−0.406544	−	0.268480i
$245$	3230.16	+	125.918i	0.842316	+	0.0328351i
$246$	1947.00	−	1047.46i	0.504617	−	0.271478i
$247$	364.304	−	364.304i	0.0938465	−	0.0938465i
$248$	−2724.85	−	3265.92i	−0.697694	−	0.836235i
$249$			2216.01i			0.563991i
$250$	3627.27	+	1570.97i	0.917634	+	0.397426i
$251$			5268.72i			1.32493i	0.749091	+	0.662467i	$0.230491\pi$
$251$			5268.72i			1.32493i	−0.749091	+	0.662467i	$0.769509\pi$
$252$	535.647	+	2618.88i	0.133899	+	0.654658i
$253$	−524.003	+	524.003i	−0.130213	+	0.130213i
$254$	−1173.94	−	2182.08i	−0.289997	−	0.539040i
$255$	1183.86	+	46.1493i	0.290731	+	0.0113333i
$256$	−2833.07	+	2958.20i	−0.691667	+	0.722217i
$257$	−5635.08	−	5635.08i	−1.36773	−	1.36773i	−0.863668	−	0.504061i	$-0.831839\pi$
$257$	−5635.08	−	5635.08i	−1.36773	−	1.36773i	−0.504061	−	0.863668i	$-0.668161\pi$
$258$	662.888	+	199.132i	0.159960	+	0.0480519i
$259$	8913.27			2.13839
$260$	54.9923	+	334.826i	0.0131172	+	0.0798654i
$261$	−455.696			−0.108072
$262$	4388.66	+	1318.35i	1.03486	+	0.310871i
$263$	−2721.99	−	2721.99i	−0.638195	−	0.638195i	0.311915	−	0.950110i	$-0.399030\pi$
$263$	−2721.99	−	2721.99i	−0.638195	−	0.638195i	−0.950110	+	0.311915i	$0.899030\pi$
$264$	−55.5878	+	615.470i	−0.0129591	+	0.143483i
$265$	−800.655	−	865.609i	−0.185599	−	0.200656i
$266$	−4575.60	−	8505.01i	−1.05469	−	1.96044i
$267$	−2747.51	+	2747.51i	−0.629757	+	0.629757i
$268$	−385.088	+	78.7632i	−0.0877723	+	0.0179523i
$269$		−	603.964i		−	0.136893i	−0.997655	−	0.0684467i	$-0.978196\pi$
$269$		−	603.964i		−	0.136893i	0.997655	−	0.0684467i	$-0.0218043\pi$
$270$	−4238.40	+	2071.54i	−0.955336	+	0.466926i
$271$		−	4232.24i		−	0.948672i	−0.880344	−	0.474336i	$-0.842688\pi$
$271$		−	4232.24i		−	0.948672i	0.880344	−	0.474336i	$-0.157312\pi$
$272$	682.611	−	1699.67i	0.152167	−	0.378888i
$273$	−249.726	+	249.726i	−0.0553631	+	0.0553631i
$274$	−2906.40	+	1563.61i	−0.640810	+	0.344748i
$275$	71.7727	−	919.189i	0.0157384	−	0.201561i
$276$	1640.03	−	2483.41i	0.357675	−	0.541609i
$277$	3214.07	+	3214.07i	0.697165	+	0.697165i	0.963798	−	0.266633i	$-0.0859113\pi$
$277$	3214.07	+	3214.07i	0.697165	+	0.697165i	−0.266633	+	0.963798i	$0.585911\pi$
$278$	−1028.73	+	3424.54i	−0.221940	+	0.738815i
$279$	−2498.14			−0.536056
$280$	6307.67	+	818.461i	1.34627	+	0.174687i
$281$	−7574.78			−1.60809			−0.804046	−	0.594567i	$-0.797323\pi$
$281$	−7574.78			−1.60809			−0.804046	+	0.594567i	$0.797323\pi$
$282$	808.356	−	2690.93i	0.170698	−	0.568236i
$283$	−504.094	−	504.094i	−0.105884	−	0.105884i	0.652180	−	0.758064i	$-0.273855\pi$
$283$	−504.094	−	504.094i	−0.105884	−	0.105884i	−0.758064	+	0.652180i	$0.773855\pi$
$284$	2709.51	−	4102.87i	0.566126	−	0.857255i
$285$	4127.28	−	3817.58i	0.857821	−	0.793451i
$286$	69.6971	−	37.4962i	0.0144101	−	0.00775244i
$287$	−3753.08	+	3753.08i	−0.771906	+	0.771906i
$288$	268.106	+	2390.73i	0.0548552	+	0.489150i
$289$		−	4093.95i		−	0.833289i
$290$	−352.170	+	1025.53i	−0.0713109	+	0.207659i
$291$		−	2809.49i		−	0.565962i
$292$	414.970	−	84.8750i	0.0831653	−	0.0170101i
$293$	−244.144	+	244.144i	−0.0486793	+	0.0486793i	−0.731027	−	0.682348i	$-0.760959\pi$
$293$	−244.144	+	244.144i	−0.0486793	+	0.0486793i	0.682348	+	0.731027i	$0.260959\pi$
$294$	1434.63	+	2666.65i	0.284589	+	0.528987i
$295$	44.0167	−	1129.16i	0.00868730	−	0.222854i
$296$	7989.20	+	721.566i	1.56879	+	0.141690i
$297$	778.066	+	778.066i	0.152013	+	0.152013i
$298$	3660.99	+	1099.76i	0.711662	+	0.213783i
$299$	−381.143			−0.0737192
$300$	457.323	+	3674.37i	0.0880118	+	0.707133i
$301$	−1661.65			−0.318192
$302$	6299.80	+	1892.46i	1.20037	+	0.360592i
$303$	−3706.88	−	3706.88i	−0.702822	−	0.702822i
$304$	−3412.71	−	7993.69i	−0.643857	−	1.50812i
$305$	−101.085	+	2593.13i	−0.0189774	+	0.486826i
$306$	−509.676	−	947.373i	−0.0952164	−	0.176986i
$307$	−6853.22	+	6853.22i	−1.27405	+	1.27405i	−0.330110	+	0.943942i	$0.607086\pi$
$307$	−6853.22	+	6853.22i	−1.27405	+	1.27405i	−0.943942	+	0.330110i	$0.892914\pi$
$308$	−297.286	−	1453.48i	−0.0549981	−	0.268896i
$309$		−	1491.97i		−	0.274676i
$310$	−1930.61	+	5621.99i	−0.353714	+	1.03002i
$311$			10802.7i			1.96966i	0.173510	+	0.984832i	$0.444489\pi$
$311$			10802.7i			1.96966i	−0.173510	+	0.984832i	$0.555511\pi$
$312$	−244.053	+	203.620i	−0.0442845	+	0.0369478i
$313$	2618.43	−	2618.43i	0.472851	−	0.472851i	−0.429985	−	0.902836i	$-0.641481\pi$
$313$	2618.43	−	2618.43i	0.472851	−	0.472851i	0.902836	+	0.429985i	$0.141481\pi$
$314$	−572.372	+	307.929i	−0.102869	+	0.0553422i
$315$	2742.48	−	2536.68i	0.490543	−	0.453733i
$316$	−6695.09	−	4421.40i	−1.19186	−	0.787098i
$317$	3652.64	+	3652.64i	0.647170	+	0.647170i	0.952308	−	0.305138i	$-0.0987027\pi$
$317$	3652.64	+	3652.64i	0.647170	+	0.647170i	−0.305138	+	0.952308i	$0.598703\pi$
$318$	317.767	−	1057.81i	0.0560361	−	0.186538i
$319$	252.912			0.0443898
$320$	5587.47	+	1244.24i	0.976092	+	0.217360i
$321$	−2431.36			−0.422757
$322$	−2055.52	+	6842.61i	−0.355745	+	1.18424i
$323$	2748.30	+	2748.30i	0.473436	+	0.473436i
$324$	−1292.10	−	853.296i	−0.221554	−	0.146313i
$325$	360.397	−	308.192i	0.0615115	−	0.0526012i
$326$	−3284.60	+	1767.07i	−0.558028	+	0.300212i
$327$	1671.38	−	1671.38i	0.282653	−	0.282653i
$328$	−3667.81	+	3060.16i	−0.617442	+	0.515149i
$329$			6745.31i			1.13034i
$330$	775.927	−	379.239i	0.129434	−	0.0632619i
$331$		−	7839.91i		−	1.30187i	−0.759131	−	0.650937i	$-0.774376\pi$
$331$		−	7839.91i		−	1.30187i	0.759131	−	0.650937i	$-0.225624\pi$
$332$	−959.411	−	4690.74i	−0.158598	−	0.775415i
$333$	3331.48	−	3331.48i	0.548241	−	0.548241i
$334$	1850.50	+	3439.66i	0.303158	+	0.563503i
$335$	373.002	+	403.262i	0.0608336	+	0.0657688i
$336$	2339.38	+	5479.59i	0.379832	+	0.889691i
$337$	−4503.23	−	4503.23i	−0.727912	−	0.727912i	0.242291	−	0.970204i	$-0.422101\pi$
$337$	−4503.23	−	4503.23i	−0.727912	−	0.727912i	−0.970204	+	0.242291i	$0.922101\pi$
$338$	−5912.34	−	1776.07i	−0.951447	−	0.285815i
$339$	5246.07			0.840494
$340$	−2525.92	+	414.862i	−0.402904	+	0.0661736i
$341$	1386.47			0.220181
$342$	−4889.10	−	1468.69i	−0.773018	−	0.232215i
$343$	957.648	+	957.648i	0.150753	+	0.150753i
$344$	−1489.38	−	134.517i	−0.233436	−	0.0210834i
$345$	−4156.04	−	162.011i	−0.648562	−	0.0252822i
$346$	1443.50	+	2683.14i	0.224286	+	0.416898i
$347$	8458.77	−	8458.77i	1.30862	−	1.30862i	0.386205	−	0.922413i	$-0.373786\pi$
$347$	8458.77	−	8458.77i	1.30862	−	1.30862i	0.922413	−	0.386205i	$-0.126214\pi$
$348$	−995.100	+	203.531i	−0.153284	+	0.0313517i
$349$			5515.41i			0.845941i	0.906144	+	0.422970i	$0.139013\pi$
$349$			5515.41i			0.845941i	−0.906144	+	0.422970i	$0.860987\pi$
$350$	−3589.30	−	8132.26i	−0.548160	−	1.24196i
$351$			565.940i			0.0860617i
$352$	−148.799	−	1326.86i	−0.0225314	−	0.200915i
$353$	−761.447	+	761.447i	−0.114810	+	0.114810i	−0.762178	−	0.647368i	$-0.775870\pi$
$353$	−761.447	+	761.447i	−0.114810	+	0.114810i	0.647368	+	0.762178i	$0.275870\pi$
$354$	932.172	−	501.497i	0.139956	−	0.0752946i
$355$	−6866.23	−	267.659i	−1.02654	−	0.0400165i
$356$	4626.28	−	7005.33i	0.688742	−	1.04293i
$357$	−1883.93	−	1883.93i	−0.279295	−	0.279295i
$358$	3257.65	−	10844.4i	0.480928	−	1.60096i
$359$	3564.71			0.524062			0.262031	−	0.965059i	$-0.415608\pi$
$359$	3564.71			0.524062			0.262031	+	0.965059i	$0.415608\pi$
$360$	2663.51	−	2051.68i	0.389942	−	0.300370i
$361$	11584.8			1.68899
$362$	1586.78	−	5282.23i	0.230385	−	0.766928i
$363$	3342.41	+	3342.41i	0.483281	+	0.483281i
$364$	420.491	−	636.726i	0.0605486	−	0.0916855i
$365$	−401.946	−	434.554i	−0.0576405	−	0.0623167i
$366$	−2140.75	+	1151.70i	−0.305734	+	0.164481i
$367$	4407.82	−	4407.82i	0.626939	−	0.626939i	−0.320358	−	0.947297i	$-0.603803\pi$
$367$	4407.82	−	4407.82i	0.626939	−	0.626939i	0.947297	+	0.320358i	$0.103803\pi$
$368$	−2396.36	+	5966.81i	−0.339453	+	0.845222i
$369$			2805.55i			0.395802i
$370$	−4922.77	−	10072.0i	−0.691683	−	1.41519i
$371$			2651.60i			0.371063i
$372$	−5455.17	+	1115.76i	−0.760316	+	0.155510i
$373$	−8371.19	+	8371.19i	−1.16205	+	1.16205i	−0.178021	+	0.984027i	$0.556970\pi$
$373$	−8371.19	+	8371.19i	−1.16205	+	1.16205i	−0.984027	+	0.178021i	$0.943030\pi$
$374$	282.871	+	525.794i	0.0391094	+	0.0726957i
$375$	4060.83	−	3207.38i	0.559201	−	0.441676i
$376$	−546.061	+	6046.00i	−0.0748962	+	0.829252i
$377$	91.9800	+	91.9800i	0.0125656	+	0.0125656i
$378$	10160.3	+	3052.15i	1.38251	+	0.415305i
$379$	−11130.1			−1.50848			−0.754240	−	0.656599i	$-0.771994\pi$
$379$	−11130.1			−1.50848			−0.754240	+	0.656599i	$0.771994\pi$
$380$	−7083.62	+	9867.74i	−0.956269	+	1.33212i
$381$	−3243.75			−0.436174
$382$	3951.66	+	1187.08i	0.529279	+	0.158995i
$383$	1006.62	+	1006.62i	0.134297	+	0.134297i	0.771060	−	0.636763i	$-0.219727\pi$
$383$	1006.62	+	1006.62i	0.134297	+	0.134297i	−0.636763	+	0.771060i	$0.719727\pi$
$384$	1653.25	+	5100.88i	0.219706	+	0.677873i
$385$	−1522.08	+	1407.87i	−0.201487	+	0.186367i
$386$	4291.85	+	7977.60i	0.565932	+	1.05194i
$387$	−621.069	+	621.069i	−0.0815781	+	0.0815781i
$388$	1216.35	+	5946.98i	0.159152	+	0.778124i
$389$		−	13548.4i		−	1.76589i	−0.469478	−	0.882944i	$-0.655558\pi$
$389$		−	13548.4i		−	1.76589i	0.469478	−	0.882944i	$-0.344442\pi$
$390$	420.115	+	144.269i	0.0545471	+	0.0187317i
$391$		−	2875.34i		−	0.371898i
$392$	−4191.26	−	5023.52i	−0.540027	−	0.647260i
$393$	4241.84	−	4241.84i	0.544459	−	0.544459i
$394$	−7371.69	+	3965.88i	−0.942590	+	0.507102i
$395$	−436.768	+	11204.4i	−0.0556359	+	1.42722i
$396$	−654.379	−	432.148i	−0.0830399	−	0.0548391i
$397$	1822.81	+	1822.81i	0.230439	+	0.230439i	0.812876	−	0.582437i	$-0.197901\pi$
$397$	1822.81	+	1822.81i	0.230439	+	0.230439i	−0.582437	+	0.812876i	$0.697901\pi$
$398$	1698.84	−	5655.25i	0.213957	−	0.712241i
$399$	−12643.0			−1.58632
$400$	−2558.84	−	7579.73i	−0.319855	−	0.947466i
$401$	5922.04			0.737488			0.368744	−	0.929531i	$-0.379788\pi$
$401$	5922.04			0.737488			0.368744	+	0.929531i	$0.379788\pi$
$402$	−148.038	+	492.804i	−0.0183669	+	0.0611413i
$403$	504.238	+	504.238i	0.0623273	+	0.0623273i
$404$	9451.43	+	6241.67i	1.16393	+	0.768650i
$405$	−84.2929	+	2162.36i	−0.0103421	+	0.265305i
$406$	2147.36	−	1155.25i	0.262492	−	0.141218i
$407$	−1848.98	+	1848.98i	−0.225186	+	0.225186i
$408$	−1536.11	−	1841.13i	−0.186394	−	0.223406i
$409$		−	8533.05i		−	1.03162i	−0.856703	−	0.515809i	$-0.827491\pi$
$409$		−	8533.05i		−	1.03162i	0.856703	−	0.515809i	$-0.172509\pi$
$410$	6313.81	+	2168.18i	0.760529	+	0.261168i
$411$			4320.46i			0.518522i
$412$	645.940	+	3158.12i	0.0772408	+	0.377644i
$413$	−1796.88	+	1796.88i	−0.214088	+	0.214088i
$414$	1789.26	+	3325.83i	0.212408	+	0.394820i
$415$	−4912.12	+	4543.52i	−0.581027	+	0.537428i
$416$	428.443	−	536.674i	0.0504955	−	0.0632515i
$417$	3309.98	+	3309.98i	0.388706	+	0.388706i
$418$	2713.46	+	815.124i	0.317511	+	0.0953804i
$419$	−7128.02			−0.831089			−0.415545	−	0.909573i	$-0.636409\pi$
$419$	−7128.02			−0.831089			−0.415545	+	0.909573i	$0.636409\pi$
$420$	4855.75	−	6764.24i	0.564134	−	0.785859i
$421$	−611.239			−0.0707601			−0.0353800	−	0.999374i	$-0.511264\pi$
$421$	−611.239			−0.0707601			−0.0353800	+	0.999374i	$0.511264\pi$
$422$	−540.676	−	162.419i	−0.0623690	−	0.0187356i
$423$	2521.17	+	2521.17i	0.289796	+	0.289796i
$424$	−214.658	+	2376.70i	−0.0245866	+	0.272223i
$425$	2325.00	+	2718.83i	0.265362	+	0.310312i
$426$	−3049.53	−	5668.39i	−0.346831	−	0.644682i
$427$	4126.56	−	4126.56i	0.467677	−	0.467677i
$428$	5146.58	−	1052.65i	0.581236	−	0.118882i
$429$		−	103.607i		−	0.0116601i
$430$	917.724	+	1877.67i	0.102922	+	0.210580i
$431$		−	9361.72i		−	1.04626i	−0.852253	−	0.523130i	$-0.824764\pi$
$431$		−	9361.72i		−	1.04626i	0.852253	−	0.523130i	$-0.175236\pi$
$432$	8859.84	+	3558.24i	0.986734	+	0.396286i
$433$	−1769.48	+	1769.48i	−0.196388	+	0.196388i	−0.798450	−	0.602062i	$-0.794346\pi$
$433$	−1769.48	+	1769.48i	−0.196388	+	0.196388i	0.602062	+	0.798450i	$0.294346\pi$
$434$	11771.9	−	6333.15i	1.30200	−	0.700463i
$435$	963.868	+	1042.06i	0.106239	+	0.114858i
$436$	−2814.28	+	4261.51i	−0.309127	+	0.468095i
$437$	−9648.13	−	9648.13i	−1.05614	−	1.05614i
$438$	159.526	−	531.044i	0.0174028	−	0.0579321i
$439$	7823.34			0.850541			0.425271	−	0.905066i	$-0.360179\pi$
$439$	7823.34			0.850541			0.425271	+	0.905066i	$0.360179\pi$
$440$	−1478.25	+	1138.69i	−0.160166	+	0.123375i
$441$	−3842.54			−0.414917
$442$	−88.3472	+	294.099i	−0.00950735	+	0.0316490i
$443$	−9066.48	−	9066.48i	−0.972374	−	0.972374i	0.0272545	−	0.999629i	$-0.491324\pi$
$443$	−9066.48	−	9066.48i	−0.972374	−	0.972374i	−0.999629	+	0.0272545i	$0.991324\pi$
$444$	5786.97	−	8762.91i	0.618553	−	0.936642i
$445$	−11723.5	−	457.007i	−1.24888	−	0.0486836i
$446$	−11766.3	+	6330.10i	−1.24921	+	0.672061i
$447$	3538.51	−	3538.51i	0.374420	−	0.374420i
$448$	−7324.25	−	10586.1i	−0.772407	−	1.11640i
$449$			3381.93i			0.355464i	0.984079	+	0.177732i	$0.0568759\pi$
$449$			3381.93i			0.355464i	−0.984079	+	0.177732i	$0.943124\pi$
$450$	−4381.13	−	1698.01i	−0.458952	−	0.177878i
$451$		−	1557.09i		−	0.162573i
$452$	−11104.6	+	2271.26i	−1.15557	+	0.236352i
$453$	6089.04	−	6089.04i	0.631541	−	0.631541i
$454$	1562.17	+	2903.72i	0.161489	+	0.300173i
$455$	−1065.57	−	41.5382i	−0.109791	−	0.00427987i
$456$	−11332.3	−	1023.50i	−1.16378	−	0.105110i
$457$	10289.7	+	10289.7i	1.05324	+	1.05324i	0.998501	+	0.0547399i	$0.0174330\pi$
$457$	10289.7	+	10289.7i	1.05324	+	1.05324i	0.0547399	+	0.998501i	$0.482567\pi$
$458$	−12222.9	−	3671.77i	−1.24703	−	0.374608i
$459$	−4269.45			−0.434163
$460$	8867.45	−	1456.40i	0.898798	−	0.147620i
$461$	−5310.20			−0.536488			−0.268244	−	0.963351i	$-0.586443\pi$
$461$	−5310.20			−0.536488			−0.268244	+	0.963351i	$0.586443\pi$
$462$	−1860.05	−	558.759i	−0.187310	−	0.0562680i
$463$	7686.78	+	7686.78i	0.771566	+	0.771566i	0.978380	−	0.206814i	$-0.0663096\pi$
$463$	7686.78	+	7686.78i	0.771566	+	0.771566i	−0.206814	+	0.978380i	$0.566310\pi$
$464$	2018.26	−	861.648i	0.201930	−	0.0862091i
$465$	5283.96	+	5712.63i	0.526963	+	0.569714i
$466$	−554.459	−	1030.62i	−0.0551176	−	0.102451i
$467$	4535.99	−	4535.99i	0.449466	−	0.449466i	−0.445711	−	0.895177i	$-0.647049\pi$
$467$	4535.99	−	4535.99i	0.449466	−	0.449466i	0.895177	+	0.445711i	$0.147049\pi$
$468$	−80.8218	−	395.153i	−0.00798288	−	0.0390298i
$469$		−	1235.30i		−	0.121623i
$470$	7622.24	−	3725.42i	0.748059	−	0.365618i
$471$			850.850i			0.0832380i
$472$	−1756.05	+	1465.12i	−0.171248	+	0.142877i
$473$	344.695	−	344.695i	0.0335076	−	0.0335076i
$474$	−9249.72	+	4976.24i	−0.896316	+	0.482208i
$475$	16924.5	+	1321.51i	1.63484	+	0.127652i
$476$	4803.46	+	3172.18i	0.462534	+	0.305455i
$477$	991.080	+	991.080i	0.0951330	+	0.0951330i
$478$	−2380.34	+	7923.91i	−0.227771	+	0.758224i
$479$	10969.6			1.04638			0.523189	−	0.852217i	$-0.324742\pi$
$479$	10969.6			1.04638			0.523189	+	0.852217i	$0.324742\pi$
$480$	4899.93	−	5669.87i	0.465938	−	0.539152i
$481$	−1344.89			−0.127488
$482$	−3466.03	+	11538.0i	−0.327538	+	1.09034i
$483$	6613.70	+	6613.70i	0.623051	+	0.623051i
$484$	−8522.13	−	5627.97i	−0.800350	−	0.528547i
$485$	6227.65	−	5760.33i	0.583058	−	0.539306i
$486$	8247.77	−	4437.20i	0.769808	−	0.414147i
$487$	−12736.0	+	12736.0i	−1.18506	+	1.18506i	−0.206646	+	0.978416i	$0.566255\pi$
$487$	−12736.0	+	12736.0i	−1.18506	+	1.18506i	−0.978416	+	0.206646i	$0.933745\pi$
$488$	4032.80	−	3364.68i	0.374091	−	0.312115i
$489$			4882.67i			0.451538i
$490$	−2969.59	+	8647.53i	−0.273781	+	0.797257i
$491$		−	10518.6i		−	0.966796i	−0.875401	−	0.483398i	$-0.839402\pi$
$491$		−	10518.6i		−	0.966796i	0.875401	−	0.483398i	$-0.160598\pi$
$492$	1253.06	+	6126.46i	0.114822	+	0.561387i
$493$	−693.897	+	693.897i	−0.0633905	+	0.0633905i
$494$	690.394	+	1283.29i	0.0628792	+	0.116878i
$495$	−42.6898	+	1095.12i	−0.00387629	+	0.0994380i
$496$	11064.2	−	4723.59i	1.00161	−	0.427612i
$497$	10926.5	+	10926.5i	0.986161	+	0.986161i
$498$	−6002.82	−	1803.25i	−0.540146	−	0.162260i
$499$	−2445.26			−0.219368			−0.109684	−	0.993966i	$-0.534984\pi$
$499$	−2445.26			−0.219368			−0.109684	+	0.993966i	$0.534984\pi$
$500$	−7207.14	+	8547.35i	−0.644626	+	0.764498i
$501$	5113.18			0.455968
$502$	−14272.1	−	4287.35i	−1.26892	−	0.381183i
$503$	−12216.7	−	12216.7i	−1.08293	−	1.08293i	−0.996235	−	0.0866986i	$-0.972368\pi$
$503$	−12216.7	−	12216.7i	−1.08293	−	1.08293i	−0.0866986	−	0.996235i	$1.47237\pi$
$504$	−7530.01	−	680.093i	−0.665502	−	0.0601066i
$505$	616.584	−	15817.1i	0.0543319	−	1.39377i
$506$	−993.041	−	1845.84i	−0.0872452	−	0.162169i
$507$	−5714.55	+	5714.55i	−0.500576	+	0.500576i
$508$	6866.20	−	1404.37i	0.599682	−	0.122655i
$509$			5615.75i			0.489025i	0.969646	+	0.244512i	$0.0786279\pi$
$509$			5615.75i			0.489025i	−0.969646	+	0.244512i	$0.921372\pi$
$510$	−1088.36	+	3169.35i	−0.0944972	+	0.275178i
$511$			1331.16i			0.115239i
$512$	−5707.93	−	10081.5i	−0.492690	−	0.870205i
$513$	−14326.0	+	14326.0i	−1.23296	+	1.23296i
$514$	19850.0	−	10679.1i	1.70340	−	0.916408i
$515$	3307.17	−	3059.00i	0.282973	−	0.261739i
$516$	−1078.83	+	1633.62i	−0.0920406	+	0.139372i
$517$	−1399.26	−	1399.26i	−0.119031	−	0.119031i
$518$	−7253.05	+	24144.6i	−0.615214	+	2.04798i
$519$	3988.58			0.337340
$520$	−951.740	−	123.494i	−0.0802626	−	0.0104146i
$521$	5287.10			0.444591			0.222296	−	0.974979i	$-0.428645\pi$
$521$	5287.10			0.444591			0.222296	+	0.974979i	$0.428645\pi$
$522$	370.816	−	1234.41i	0.0310923	−	0.103503i
$523$	4328.34	+	4328.34i	0.361883	+	0.361883i	0.864506	−	0.502623i	$-0.167631\pi$
$523$	4328.34	+	4328.34i	0.361883	+	0.361883i	−0.502623	+	0.864506i	$0.667631\pi$
$524$	−7142.43	+	10815.4i	−0.595455	+	0.901666i
$525$	−11601.5	−	905.878i	−0.964443	−	0.0753062i
$526$	9588.45	−	5158.47i	0.794821	−	0.427605i
$527$	−3803.97	+	3803.97i	−0.314428	+	0.314428i
$528$	−1621.98	−	651.409i	−0.133688	−	0.0536912i
$529$		−	2072.91i		−	0.170371i
$530$	2996.32	−	1464.47i	0.245570	−	0.120024i
$531$			1343.23i			0.109776i
$532$	26762.1	−	5473.73i	2.18098	−	0.446083i
$533$	566.287	−	566.287i	0.0460199	−	0.0460199i
$534$	−5206.83	−	9678.34i	−0.421951	−	0.784312i
$535$	−4985.05	−	5389.47i	−0.402846	−	0.435527i
$536$	100.003	−	1107.23i	0.00805871	−	0.0892262i
$537$	−10481.6	−	10481.6i	−0.842297	−	0.842297i
$538$	1636.04	+	491.468i	0.131106	+	0.0393841i
$539$	2132.62			0.170424
$540$	−2162.54	−	13166.8i	−0.172335	−	1.04928i
$541$	−13608.6			−1.08148			−0.540739	−	0.841190i	$-0.681855\pi$
$541$	−13608.6			−1.08148			−0.540739	+	0.841190i	$0.681855\pi$
$542$	11464.5	+	3443.93i	0.908563	+	0.272932i
$543$	−5105.52	−	5105.52i	−0.403497	−	0.403497i
$544$	4048.67	+	3232.17i	0.319090	+	0.254739i
$545$	7131.72	+	278.009i	0.560531	+	0.0218506i
$546$	−473.258	−	879.681i	−0.0370945	−	0.0689503i
$547$	2884.33	−	2884.33i	0.225457	−	0.225457i	−0.585335	−	0.810792i	$-0.699037\pi$
$547$	2884.33	−	2884.33i	0.225457	−	0.225457i	0.810792	+	0.585335i	$0.199037\pi$
$548$	−1870.52	−	9145.34i	−0.145812	−	0.712901i
$549$		−	3084.74i		−	0.239806i
$550$	2431.54	+	942.399i	0.188511	+	0.0730619i
$551$			4656.71i			0.360041i
$552$	5392.63	+	6463.44i	0.415807	+	0.498374i
$553$	17830.0	−	17830.0i	1.37108	−	1.37108i
$554$	−11321.8	+	6091.00i	−0.868263	+	0.467115i
$555$	−14664.9	−	571.666i	−1.12160	−	0.0437223i
$556$	−8439.43	−	5573.35i	−0.643726	−	0.425113i
$557$	−6538.87	−	6538.87i	−0.497416	−	0.497416i	0.413216	−	0.910633i	$-0.364405\pi$
$557$	−6538.87	−	6538.87i	−0.497416	−	0.497416i	−0.910633	+	0.413216i	$0.864405\pi$
$558$	2032.83	−	6767.07i	0.154223	−	0.513392i
$559$	250.720			0.0189702
$560$	−7349.87	+	16420.5i	−0.554622	+	1.23909i
$561$	781.612			0.0588229
$562$	6163.88	−	20518.9i	0.462647	−	1.54010i
$563$	−6499.93	−	6499.93i	−0.486571	−	0.486571i	0.420651	−	0.907222i	$-0.361802\pi$
$563$	−6499.93	−	6499.93i	−0.486571	−	0.486571i	−0.907222	+	0.420651i	$0.861802\pi$
$564$	6631.52	+	4379.42i	0.495102	+	0.326962i
$565$	10756.1	+	11628.7i	0.800907	+	0.865882i
$566$	1775.71	−	955.311i	0.131870	−	0.0709447i
$567$	3441.05	−	3441.05i	0.254869	−	0.254869i
$568$	8909.19	+	10678.3i	0.658136	+	0.788822i
$569$		−	5264.67i		−	0.387885i	−0.981013	−	0.193942i	$-0.937872\pi$
$569$		−	5264.67i		−	0.387885i	0.981013	−	0.193942i	$-0.0621275\pi$
$570$	6982.69	+	14286.7i	0.513110	+	1.04983i
$571$			22034.0i			1.61488i	0.589952	+	0.807438i	$0.299147\pi$
$571$			22034.0i			1.61488i	−0.589952	+	0.807438i	$0.700853\pi$
$572$	44.8563	+	219.311i	0.00327891	+	0.0160312i
$573$	3819.46	−	3819.46i	0.278464	−	0.278464i
$574$	−7112.48	−	13220.5i	−0.517194	−	0.961348i
$575$	−8162.08	−	9544.67i	−0.591969	−	0.692244i
$576$	−6694.29	−	1219.17i	−0.484251	−	0.0881924i
$577$	−9208.58	−	9208.58i	−0.664399	−	0.664399i	0.292015	−	0.956414i	$-0.405674\pi$
$577$	−9208.58	−	9208.58i	−0.664399	−	0.664399i	−0.956414	+	0.292015i	$0.905674\pi$
$578$	11089.9	+	3331.40i	0.798059	+	0.239737i
$579$	11859.0			0.851196
$580$	−2491.43	−	1788.49i	−0.178363	−	0.128039i
$581$	15047.2			1.07446
$582$	7610.46	+	2286.18i	0.542034	+	0.162827i
$583$	−550.052	−	550.052i	−0.0390751	−	0.0390751i
$584$	−107.763	+	1193.15i	−0.00763572	+	0.0845429i
$585$	−413.802	+	382.751i	−0.0292455	+	0.0270509i
$586$	−462.679	−	860.016i	−0.0326162	−	0.0606262i
$587$	−6536.20	+	6536.20i	−0.459587	+	0.459587i	−0.898520	−	0.438933i	$-0.855357\pi$
$587$	−6536.20	+	6536.20i	−0.459587	+	0.459587i	0.438933	+	0.898520i	$0.355357\pi$
$588$	−8390.94	+	1716.23i	−0.588498	+	0.120367i
$589$			25528.3i			1.78586i
$590$	3022.89	+	1038.07i	0.210933	+	0.0724351i
$591$			10958.3i			0.762713i
$592$	−8455.72	+	21054.3i	−0.587040	+	1.46170i
$593$	−11033.7	+	11033.7i	−0.764079	+	0.764079i	−0.977057	−	0.212978i	$-0.931684\pi$
$593$	−11033.7	+	11033.7i	−0.764079	+	0.764079i	0.212978	+	0.977057i	$0.431684\pi$
$594$	−2740.80	+	1474.52i	−0.189321	+	0.101852i
$595$	313.364	−	8038.68i	0.0215910	−	0.553872i
$596$	−5958.16	+	9022.12i	−0.409489	+	0.620068i
$597$	−5466.05	−	5466.05i	−0.374725	−	0.374725i
$598$	310.150	−	1032.46i	0.0212090	−	0.0706024i
$599$	−1861.62			−0.126985			−0.0634923	−	0.997982i	$-0.520224\pi$
$599$	−1861.62			−0.126985			−0.0634923	+	0.997982i	$0.520224\pi$
$600$	−10325.4	−	1751.16i	−0.702557	−	0.119151i
$601$	−21693.2			−1.47235			−0.736177	−	0.676789i	$-0.763371\pi$
$601$	−21693.2			−1.47235			−0.736177	+	0.676789i	$0.763371\pi$
$602$	1352.15	−	4501.15i	0.0915437	−	0.304739i
$603$	−461.715	−	461.715i	−0.0311816	−	0.0311816i
$604$	−10252.8	+	15525.2i	−0.690693	+	1.04588i
$605$	−555.959	+	14261.9i	−0.0373602	+	0.958398i
$606$	13057.8	−	7024.94i	0.875308	−	0.470905i
$607$	−617.817	+	617.817i	−0.0413121	+	0.0413121i	−0.727461	−	0.686149i	$-0.759300\pi$
$607$	−617.817	+	617.817i	−0.0413121	+	0.0413121i	0.686149	+	0.727461i	$0.259300\pi$
$608$	24430.7	−	2739.75i	1.62960	−	0.182749i
$609$		−	3192.13i		−	0.212400i
$610$	−6942.11	−	2383.95i	−0.460784	−	0.158235i
$611$		−	1017.77i		−	0.0673891i
$612$	2981.03	−	609.719i	0.196897	−	0.0402719i
$613$	5656.87	−	5656.87i	0.372722	−	0.372722i	−0.495745	−	0.868468i	$-0.665105\pi$
$613$	5656.87	−	5656.87i	0.372722	−	0.372722i	0.868468	+	0.495745i	$0.165105\pi$
$614$	−12987.6	−	24141.0i	−0.853642	−	1.58673i
$615$	6415.60	−	5934.18i	0.420654	−	0.389088i
$616$	4179.17	+	377.453i	0.273350	+	0.0246884i
$617$	12811.8	+	12811.8i	0.835953	+	0.835953i	0.988323	−	0.152370i	$-0.0486907\pi$
$617$	12811.8	+	12811.8i	0.835953	+	0.835953i	−0.152370	+	0.988323i	$0.548691\pi$
$618$	4041.50	+	1214.07i	0.263063	+	0.0790243i
$619$	12163.2			0.789788			0.394894	−	0.918727i	$-0.370781\pi$
$619$	12163.2			0.789788			0.394894	+	0.918727i	$0.370781\pi$
$620$	−13658.1	−	9804.55i	−0.884713	−	0.635097i
$621$	14988.2			0.968530
$622$	−29262.9	−	8790.56i	−1.88639	−	0.566671i
$623$	18656.2	+	18656.2i	1.19975	+	1.19975i
$624$	−352.980	−	826.794i	−0.0226450	−	0.0530421i
$625$	15435.6	+	2425.29i	0.987880	+	0.155219i
$626$	4962.20	+	9223.62i	0.316820	+	0.588898i
$627$	2622.68	−	2622.68i	0.167049	−	0.167049i
$628$	−368.372	−	1801.04i	−0.0234071	−	0.114441i
$629$		−	10145.8i		−	0.643149i
$630$	4639.83	+	9493.13i	0.293421	+	0.600342i
$631$			3347.17i			0.211171i	0.994410	+	0.105585i	$0.0336716\pi$
$631$			3347.17i			0.211171i	−0.994410	+	0.105585i	$0.966328\pi$
$632$	17424.9	−	14538.1i	1.09672	−	0.915023i
$633$	−522.588	+	522.588i	−0.0328136	+	0.0328136i
$634$	−12866.7	+	6922.14i	−0.805998	+	0.433617i
$635$	−6650.70	−	7190.25i	−0.415630	−	0.449349i
$636$	2606.87	+	1721.56i	0.162530	+	0.107334i
$637$	775.600	+	775.600i	0.0482424	+	0.0482424i
$638$	−205.804	+	685.099i	−0.0127709	+	0.0425131i
$639$	8167.95			0.505664
$640$	−7917.19	+	14123.1i	−0.488991	+	0.872289i
$641$	−24791.3			−1.52761			−0.763803	−	0.645449i	$-0.776670\pi$
$641$	−24791.3			−1.52761			−0.763803	+	0.645449i	$0.776670\pi$
$642$	1978.48	−	6586.17i	0.121627	−	0.404884i
$643$	−12922.9	−	12922.9i	−0.792583	−	0.792583i	0.189330	−	0.981913i	$-0.439368\pi$
$643$	−12922.9	−	12922.9i	−0.792583	−	0.792583i	−0.981913	+	0.189330i	$0.939368\pi$
$644$	−16862.9	−	11136.2i	−1.03182	−	0.681408i
$645$	2733.89	+	106.572i	0.166894	+	0.00650587i
$646$	−9681.12	+	5208.33i	−0.589626	+	0.317212i
$647$	16924.5	−	16924.5i	1.02840	−	1.02840i	0.0288113	−	0.999585i	$-0.490828\pi$
$647$	16924.5	−	16924.5i	1.02840	−	1.02840i	0.999585	−	0.0288113i	$-0.00917218\pi$
$648$	3362.88	−	2805.74i	0.203868	−	0.170092i
$649$		−	745.493i		−	0.0450896i
$650$	541.575	+	1227.05i	0.0326805	+	0.0740441i
$651$		−	17499.4i		−	1.05354i
$652$	−2113.93	−	10335.4i	−0.126975	−	0.620806i
$653$	10391.0	−	10391.0i	0.622715	−	0.622715i	−0.323510	−	0.946225i	$-0.604863\pi$
$653$	10391.0	−	10391.0i	0.622715	−	0.622715i	0.946225	+	0.323510i	$0.104863\pi$
$654$	3167.44	+	5887.57i	0.189384	+	0.352022i
$655$	18099.8	+	705.565i	1.07972	+	0.0420896i
$656$	−5304.85	−	12425.7i	−0.315731	−	0.739545i
$657$	497.543	+	497.543i	0.0295449	+	0.0295449i
$658$	−18272.0	−	5488.91i	−1.08255	−	0.325197i
$659$	−773.045			−0.0456958			−0.0228479	−	0.999739i	$-0.507273\pi$
$659$	−773.045			−0.0456958			−0.0228479	+	0.999739i	$0.507273\pi$
$660$	395.899	+	2410.47i	0.0233490	+	0.142163i
$661$	17856.3			1.05073			0.525364	−	0.850878i	$-0.323929\pi$
$661$	17856.3			1.05073			0.525364	+	0.850878i	$0.323929\pi$
$662$	21237.1	+	6379.62i	1.24683	+	0.374549i
$663$	284.260	+	284.260i	0.0166512	+	0.0166512i
$664$	13487.2	+	1218.13i	0.788259	+	0.0711938i
$665$	−25922.1	−	28025.1i	−1.51161	−	1.63424i
$666$	6313.51	+	11735.4i	0.367333	+	0.682790i
$667$	2435.98	−	2435.98i	0.141411	−	0.141411i
$668$	−10823.3	+	2213.73i	−0.626896	+	0.128221i
$669$			17490.9i			1.01082i
$670$	−1395.90	+	682.254i	−0.0804900	+	0.0393400i
$671$			1712.04i			0.0984985i
$672$	−16747.0	+	1878.07i	−0.961353	+	0.107810i
$673$	−19931.6	+	19931.6i	−1.14161	+	1.14161i	−0.153459	+	0.988155i	$0.549041\pi$
$673$	−19931.6	+	19931.6i	−1.14161	+	1.14161i	−0.988155	+	0.153459i	$0.950959\pi$
$674$	15863.0	−	8534.10i	0.906557	−	0.487717i
$675$	−14172.4	+	12119.5i	−0.808143	+	0.691080i
$676$	9622.18	−	14570.4i	0.547462	−	0.828992i
$677$	−5515.73	−	5515.73i	−0.313126	−	0.313126i	0.532993	−	0.846120i	$-0.321067\pi$
$677$	−5515.73	−	5515.73i	−0.313126	−	0.313126i	−0.846120	+	0.532993i	$0.821067\pi$
$678$	−4268.92	+	14210.8i	−0.241810	+	0.804958i
$679$	−19077.0			−1.07822
$680$	931.641	−	7179.92i	0.0525394	−	0.404908i
$681$	4316.48			0.242890
$682$	−1128.22	+	3755.74i	−0.0633460	+	0.210872i
$683$	19946.1	+	19946.1i	1.11745	+	1.11745i	0.992115	+	0.125331i	$0.0399992\pi$
$683$	19946.1	+	19946.1i	1.11745	+	1.11745i	0.125331	+	0.992115i	$0.460001\pi$
$684$	7956.88	−	12048.7i	0.444794	−	0.673527i
$685$	−9576.95	+	8858.31i	−0.534185	+	0.494100i
$686$	−3373.39	+	1814.85i	−0.187750	+	0.101007i
$687$	−11814.0	+	11814.0i	−0.656089	+	0.656089i
$688$	1576.35	−	3925.04i	0.0873515	−	0.217501i
$689$		−	400.090i		−	0.0221222i
$690$	3820.79	−	11126.2i	0.210804	−	0.613867i
$691$		−	356.654i		−	0.0196350i	−0.999952	−	0.00981748i	$-0.996875\pi$
$691$		−	356.654i		−	0.0196350i	0.999952	−	0.00981748i	$-0.00312505\pi$
$692$	−8442.84	+	1726.84i	−0.463798	+	0.0948621i
$693$	1742.71	−	1742.71i	0.0955267	−	0.0955267i
$694$	16030.3	+	29796.7i	0.876802	+	1.62978i
$695$	−550.564	+	14123.6i	−0.0300490	+	0.770845i
$696$	258.416	−	2861.19i	0.0140736	−	0.155823i
$697$	4272.07	+	4272.07i	0.232161	+	0.232161i
$698$	−14940.4	−	4488.09i	−0.810175	−	0.243377i
$699$	−1532.05			−0.0829003
$700$	24949.8	−	3105.32i	1.34716	−	0.167671i
$701$	17230.0			0.928343			0.464172	−	0.885745i	$-0.346352\pi$
$701$	17230.0			0.928343			0.464172	+	0.885745i	$0.346352\pi$
$702$	−1533.04	−	460.526i	−0.0824231	−	0.0247599i
$703$	−34044.1	−	34044.1i	−1.82646	−	1.82646i
$704$	3715.35	+	676.643i	0.198903	+	0.0362243i
$705$	432.621	−	11098.0i	0.0231113	−	0.592871i
$706$	−1443.02	−	2682.26i	−0.0769248	−	0.142986i
$707$	−25170.5	+	25170.5i	−1.33895	+	1.33895i
$708$	599.935	+	2933.19i	0.0318460	+	0.155701i
$709$		−	8153.11i		−	0.431871i	−0.976408	−	0.215935i	$-0.930720\pi$
$709$		−	8153.11i		−	0.431871i	0.976408	−	0.215935i	$-0.0692801\pi$
$710$	6312.35	−	18381.7i	0.333659	−	0.971625i
$711$		−	13328.5i		−	0.703036i
$712$	15211.8	+	18232.4i	0.800681	+	0.959672i
$713$	13354.1	−	13354.1i	0.701425	−	0.701425i
$714$	6636.31	−	3570.26i	0.347840	−	0.187134i
$715$	229.661	−	212.427i	0.0120124	−	0.0111110i
$716$	26724.8	+	17648.9i	1.39491	+	0.921189i
$717$	7658.81	+	7658.81i	0.398917	+	0.398917i
$718$	−2900.74	+	9656.25i	−0.150772	+	0.501905i
$719$	−17219.3			−0.893147			−0.446573	−	0.894747i	$-0.647356\pi$
$719$	−17219.3			−0.893147			−0.446573	+	0.894747i	$0.647356\pi$
$720$	3390.29	+	8884.56i	0.175484	+	0.459872i
$721$	−10130.8			−0.523287
$722$	−9426.94	+	31381.3i	−0.485920	+	1.61758i
$723$	11152.0	+	11152.0i	0.573649	+	0.573649i
$724$	13017.5	+	8596.70i	0.668221	+	0.441290i
$725$	−333.656	+	4273.12i	−0.0170920	+	0.218896i
$726$	−11773.9	+	6334.22i	−0.601888	+	0.323809i
$727$	8881.73	−	8881.73i	0.453102	−	0.453102i	−0.443281	−	0.896383i	$-0.646186\pi$
$727$	8881.73	−	8881.73i	0.453102	−	0.453102i	0.896383	+	0.443281i	$0.146186\pi$
$728$	1382.62	+	1657.17i	0.0703893	+	0.0843665i
$729$		−	17486.6i		−	0.888409i
$730$	1504.22	−	735.195i	0.0762652	−	0.0372751i
$731$			1891.43i			0.0957004i
$732$	−1377.76	−	6736.12i	−0.0695676	−	0.340129i
$733$	4401.20	−	4401.20i	0.221776	−	0.221776i	−0.587470	−	0.809246i	$-0.699876\pi$
$733$	4401.20	−	4401.20i	0.221776	−	0.221776i	0.809246	+	0.587470i	$0.199876\pi$
$734$	8353.30	+	15526.9i	0.420062	+	0.780802i
$735$	8127.59	+	8786.95i	0.407878	+	0.440968i
$736$	−14213.2	−	11346.8i	−0.711826	−	0.568271i
$737$	256.253	+	256.253i	0.0128076	+	0.0128076i
$738$	−7599.79	−	2282.98i	−0.379068	−	0.113872i
$739$	−23097.8			−1.14975			−0.574875	−	0.818241i	$-0.694949\pi$
$739$	−23097.8			−1.14975			−0.574875	+	0.818241i	$0.694949\pi$
$740$	31289.4	−	5139.03i	1.55435	−	0.255290i
$741$	1907.65			0.0945741
$742$	−7182.77	−	2157.70i	−0.355374	−	0.106754i
$743$	17404.1	+	17404.1i	0.859348	+	0.859348i	0.991261	−	0.131913i	$-0.0421119\pi$
$743$	17404.1	+	17404.1i	0.859348	+	0.859348i	−0.131913	+	0.991261i	$0.542112\pi$
$744$	1416.65	−	15685.1i	0.0698075	−	0.772911i
$745$	15098.7	+	588.577i	0.742515	+	0.0289447i
$746$	−15864.3	−	29488.2i	−0.778597	−	1.44724i
$747$	5624.13	−	5624.13i	0.275470	−	0.275470i
$748$	−1654.48	+	338.395i	−0.0808739	+	0.0165414i
$749$			16509.4i			0.805396i
$750$	5383.85	+	13610.1i	0.262120	+	0.662628i
$751$			2347.75i			0.114075i	0.998372	+	0.0570377i	$0.0181655\pi$
$751$			2347.75i			0.114075i	−0.998372	+	0.0570377i	$0.981834\pi$
$752$	−15933.3	−	6399.05i	−0.772644	−	0.310305i
$753$	−13794.7	+	13794.7i	−0.667604	+	0.667604i
$754$	−324.007	+	174.312i	−0.0156494	+	0.00841919i
$755$	25981.7	+	1012.82i	1.25241	+	0.0488215i
$756$	−16535.6	+	25038.9i	−0.795493	+	1.20457i
$757$	−7078.12	−	7078.12i	−0.339840	−	0.339840i	0.516467	−	0.856307i	$-0.327247\pi$
$757$	−7078.12	−	7078.12i	−0.339840	−	0.339840i	−0.856307	+	0.516467i	$0.827247\pi$
$758$	9056.95	−	30149.6i	0.433989	−	1.44470i
$759$	−2743.91			−0.131222
$760$	−20966.0	−	27218.2i	−1.00068	−	1.29909i
$761$	−27017.6			−1.28697			−0.643486	−	0.765458i	$-0.722513\pi$
$761$	−27017.6			−1.28697			−0.643486	+	0.765458i	$0.722513\pi$
$762$	2639.56	−	8786.80i	0.125487	−	0.417732i
$763$	−11349.0	−	11349.0i	−0.538483	−	0.538483i
$764$	−6431.22	+	9738.45i	−0.304546	+	0.461158i
$765$	−2887.47	−	3121.72i	−0.136466	−	0.147537i
$766$	−3545.90	+	1907.65i	−0.167257	+	0.0899821i
$767$	271.124	−	271.124i	0.0127636	−	0.0127636i
$768$	−15162.8	+	327.626i	−0.712423	+	0.0153935i
$769$		−	41584.0i		−	1.95001i	−0.222183	−	0.975005i	$-0.571318\pi$
$769$		−	41584.0i		−	1.95001i	0.222183	−	0.975005i	$-0.428682\pi$
$770$	−2575.11	−	5268.71i	−0.120520	−	0.246586i
$771$		−	29507.7i		−

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Character orbit:	\([\chi]\)	=	20.e (of order \(4\) and degree \(2\))

\(f(q)\)	\(=\)	\(q+(-0.813737 + 2.70884i) q^{2} +(2.61822 + 2.61822i) q^{3} +(-6.67566 - 4.40857i) q^{4} +(-0.435501 + 11.1719i) q^{5} +(-9.22289 + 4.96181i) q^{6} +(17.7783 - 17.7783i) q^{7} +(17.3744 - 14.4959i) q^{8} -13.2899i q^{9} +O(q^{10})\)	\(q+(-0.813737 + 2.70884i) q^{2} +(2.61822 + 2.61822i) q^{3} +(-6.67566 - 4.40857i) q^{4} +(-0.435501 + 11.1719i) q^{5} +(-9.22289 + 4.96181i) q^{6} +(17.7783 - 17.7783i) q^{7} +(17.3744 - 14.4959i) q^{8} -13.2899i q^{9} +(-29.9084 - 10.2707i) q^{10} +7.37590i q^{11} +(-5.93575 - 29.0210i) q^{12} +(-2.68249 + 2.68249i) q^{13} +(33.6917 + 62.6254i) q^{14} +(-30.3906 + 28.1101i) q^{15} +(25.1290 + 58.8603i) q^{16} +(-20.2367 - 20.2367i) q^{17} +(36.0001 + 10.8144i) q^{18} -135.808 q^{19} +(52.1592 - 72.6596i) q^{20} +93.0948 q^{21} +(-19.9802 - 6.00204i) q^{22} +(71.0426 + 71.0426i) q^{23} +(83.4434 + 7.53642i) q^{24} +(-124.621 - 9.73070i) q^{25} +(-5.08361 - 9.44930i) q^{26} +(105.488 - 105.488i) q^{27} +(-197.059 + 40.3050i) q^{28} -34.2890i q^{29} +(-51.4160 - 105.198i) q^{30} -187.974i q^{31} +(-179.892 + 20.1737i) q^{32} +(-19.3117 + 19.3117i) q^{33} +(71.2855 - 38.3507i) q^{34} +(190.874 + 206.359i) q^{35} +(-58.5893 + 88.7186i) q^{36} +(250.679 + 250.679i) q^{37} +(110.512 - 367.882i) q^{38} -14.0467 q^{39} +(154.380 + 200.417i) q^{40} -211.105 q^{41} +(-75.7547 + 252.179i) q^{42} +(-46.7326 - 46.7326i) q^{43} +(32.5172 - 49.2390i) q^{44} +(148.472 + 5.78774i) q^{45} +(-250.253 + 134.633i) q^{46} +(-189.707 + 189.707i) q^{47} +(-88.3159 + 219.902i) q^{48} -289.134i q^{49} +(127.767 - 329.660i) q^{50} -105.968i q^{51} +(29.7334 - 6.08147i) q^{52} +(-74.5742 + 74.5742i) q^{53} +(199.910 + 371.589i) q^{54} +(-82.4025 - 3.21221i) q^{55} +(51.1739 - 566.598i) q^{56} +(-355.575 - 355.575i) q^{57} +(92.8835 + 27.9022i) q^{58} -101.072 q^{59} +(326.803 - 53.6747i) q^{60} +232.112 q^{61} +(509.191 + 152.961i) q^{62} +(-236.271 - 236.271i) q^{63} +(91.7370 - 503.715i) q^{64} +(-28.8002 - 31.1367i) q^{65} +(-36.5978 - 68.0271i) q^{66} +(34.7419 - 34.7419i) q^{67} +(45.8785 + 224.309i) q^{68} +372.010i q^{69} +(-714.314 + 349.126i) q^{70} +614.600i q^{71} +(-192.649 - 230.903i) q^{72} +(-37.4378 + 37.4378i) q^{73} +(-883.036 + 475.063i) q^{74} +(-300.807 - 351.761i) q^{75} +(906.607 + 598.718i) q^{76} +(131.131 + 131.131i) q^{77} +(11.4303 - 38.0504i) q^{78} +1002.91 q^{79} +(-668.522 + 255.104i) q^{80} +193.554 q^{81} +(171.784 - 571.850i) q^{82} +(423.190 + 423.190i) q^{83} +(-621.470 - 410.415i) q^{84} +(234.895 - 217.269i) q^{85} +(164.619 - 88.5632i) q^{86} +(89.7761 - 89.7761i) q^{87} +(106.920 + 128.152i) q^{88} +1049.38i q^{89} +(-136.495 + 397.478i) q^{90} +95.3802i q^{91} +(-161.060 - 787.453i) q^{92} +(492.156 - 492.156i) q^{93} +(-359.514 - 668.257i) q^{94} +(59.1444 - 1517.22i) q^{95} +(-523.815 - 418.177i) q^{96} +(-536.526 - 536.526i) q^{97} +(783.218 + 235.279i) q^{98} +98.0246 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12q - 6q^{2} + 8q^{6} - 12q^{8} + O(q^{10}) \)	\( 12q - 6q^{2} + 8q^{6} - 12q^{8} - 110q^{10} - 80q^{12} + 116q^{13} + 312q^{16} - 332q^{17} + 198q^{18} + 140q^{20} - 144q^{21} + 360q^{22} + 340q^{25} - 164q^{26} - 880q^{28} - 1240q^{30} - 376q^{32} + 80q^{33} + 460q^{36} + 508q^{37} + 1600q^{38} + 1420q^{40} - 656q^{41} + 1160q^{42} + 1180q^{45} - 1432q^{46} - 2720q^{48} - 1570q^{50} - 932q^{52} - 644q^{53} + 2048q^{56} - 960q^{57} + 1576q^{58} + 3280q^{60} - 896q^{61} + 2440q^{62} - 2740q^{65} - 1680q^{66} - 844q^{68} - 3040q^{70} - 3036q^{72} + 1436q^{73} + 800q^{76} + 3120q^{77} + 3720q^{78} + 1840q^{80} + 5988q^{81} - 1352q^{82} + 500q^{85} - 2552q^{86} - 2400q^{88} - 750q^{90} - 1840q^{92} - 3280q^{93} + 1088q^{96} - 4772q^{97} + 1698q^{98} + O(q^{100}) \)

\(n\)	\(11\)	\(17\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{1}{4}\right)\)

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L-functions

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