LMFDB - Embedded newform 245.4.e.k.116.1

Newspace parameters

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{11})$
Defining polynomial:	$ x^{4} + 11x^{2} + 121 $ x^4 + 11*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.1
Root			$-1.65831 - 2.87228i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.4.e.k.226.1

$q$-expansion

$f(q)$	$=$	$q+(-2.15831 - 3.73831i) q^{2} +(2.50000 - 4.33013i) q^{3} +(-5.31662 + 9.20866i) q^{4} +(2.50000 + 4.33013i) q^{5} -21.5831 q^{6} +11.3668 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-2.15831 - 3.73831i) q^{2} +(2.50000 - 4.33013i) q^{3} +(-5.31662 + 9.20866i) q^{4} +(2.50000 + 4.33013i) q^{5} -21.5831 q^{6} +11.3668 q^{8} +(1.00000 + 1.73205i) q^{9} +(10.7916 - 18.6915i) q^{10} +(-9.86675 + 17.0897i) q^{11} +(26.5831 + 46.0433i) q^{12} -71.3325 q^{13} +25.0000 q^{15} +(18.0000 + 31.1769i) q^{16} +(-15.6662 + 27.1347i) q^{17} +(4.31662 - 7.47661i) q^{18} +(68.1662 + 118.067i) q^{19} -53.1662 q^{20} +85.1821 q^{22} +(50.4327 + 87.3521i) q^{23} +(28.4169 - 49.2195i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(153.958 + 266.663i) q^{26} +145.000 q^{27} -288.198 q^{29} +(-53.9578 - 93.4577i) q^{30} +(-104.499 + 180.997i) q^{31} +(123.166 - 213.330i) q^{32} +(49.3338 + 85.4486i) q^{33} +135.251 q^{34} -21.2665 q^{36} +(-154.966 - 268.409i) q^{37} +(294.248 - 509.653i) q^{38} +(-178.331 + 308.879i) q^{39} +(28.4169 + 49.2195i) q^{40} +181.662 q^{41} -18.2005 q^{43} +(-104.916 - 181.719i) q^{44} +(-5.00000 + 8.66025i) q^{45} +(217.699 - 377.066i) q^{46} +(-73.8325 - 127.882i) q^{47} +180.000 q^{48} +107.916 q^{50} +(78.3312 + 135.674i) q^{51} +(379.248 - 656.877i) q^{52} +(63.9975 - 110.847i) q^{53} +(-312.955 - 542.054i) q^{54} -98.6675 q^{55} +681.662 q^{57} +(622.021 + 1077.37i) q^{58} +(161.332 - 279.436i) q^{59} +(-132.916 + 230.217i) q^{60} +(170.501 + 295.317i) q^{61} +902.164 q^{62} -775.325 q^{64} +(-178.331 - 308.879i) q^{65} +(212.955 - 368.849i) q^{66} +(42.1980 - 73.0891i) q^{67} +(-166.583 - 288.530i) q^{68} +504.327 q^{69} -315.736 q^{71} +(11.3668 + 19.6878i) q^{72} +(-546.662 + 946.847i) q^{73} +(-668.929 + 1158.62i) q^{74} +(62.5000 + 108.253i) q^{75} -1449.66 q^{76} +1539.58 q^{78} +(-616.593 - 1067.97i) q^{79} +(-90.0000 + 155.885i) q^{80} +(335.500 - 581.103i) q^{81} +(-392.084 - 679.110i) q^{82} +643.325 q^{83} -156.662 q^{85} +(39.2824 + 68.0391i) q^{86} +(-720.495 + 1247.93i) q^{87} +(-112.153 + 194.255i) q^{88} +(570.159 + 987.544i) q^{89} +43.1662 q^{90} -1072.53 q^{92} +(522.494 + 904.986i) q^{93} +(-318.707 + 552.017i) q^{94} +(-340.831 + 590.337i) q^{95} +(-615.831 - 1066.65i) q^{96} -1411.99 q^{97} -39.4670 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 10 * q^3 - 8 * q^4 + 10 * q^5 - 20 * q^6 + 72 * q^8 + 4 * q^9	\( 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9} + 10 q^{10} - 66 q^{11} + 40 q^{12} - 20 q^{13} + 100 q^{15} + 72 q^{16} + 70 q^{17} + 4 q^{18} + 140 q^{19} - 80 q^{20} - 44 q^{22} + 16 q^{23} + 180 q^{24} - 50 q^{25} + 450 q^{26} + 580 q^{27} - 516 q^{29} - 50 q^{30} - 20 q^{31} + 360 q^{32} + 330 q^{33} + 740 q^{34} - 32 q^{36} - 328 q^{37} + 580 q^{38} - 50 q^{39} + 180 q^{40} - 600 q^{41} - 232 q^{43} - 88 q^{44} - 20 q^{45} + 632 q^{46} - 30 q^{47} + 720 q^{48} + 100 q^{50} - 350 q^{51} + 920 q^{52} - 540 q^{53} - 290 q^{54} - 660 q^{55} + 1400 q^{57} + 1314 q^{58} + 380 q^{59} - 200 q^{60} + 1080 q^{61} + 2680 q^{62} - 448 q^{64} - 50 q^{65} - 110 q^{66} - 468 q^{67} - 600 q^{68} + 160 q^{69} - 2112 q^{71} + 72 q^{72} - 860 q^{73} - 1296 q^{74} + 250 q^{75} - 2880 q^{76} + 4500 q^{78} - 158 q^{79} - 360 q^{80} + 1342 q^{81} - 1900 q^{82} - 80 q^{83} + 700 q^{85} - 148 q^{86} - 1290 q^{87} - 1364 q^{88} - 240 q^{89} + 40 q^{90} - 2592 q^{92} + 100 q^{93} - 910 q^{94} - 700 q^{95} - 1800 q^{96} - 3260 q^{97} - 264 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 10 * q^3 - 8 * q^4 + 10 * q^5 - 20 * q^6 + 72 * q^8 + 4 * q^9 + 10 * q^10 - 66 * q^11 + 40 * q^12 - 20 * q^13 + 100 * q^15 + 72 * q^16 + 70 * q^17 + 4 * q^18 + 140 * q^19 - 80 * q^20 - 44 * q^22 + 16 * q^23 + 180 * q^24 - 50 * q^25 + 450 * q^26 + 580 * q^27 - 516 * q^29 - 50 * q^30 - 20 * q^31 + 360 * q^32 + 330 * q^33 + 740 * q^34 - 32 * q^36 - 328 * q^37 + 580 * q^38 - 50 * q^39 + 180 * q^40 - 600 * q^41 - 232 * q^43 - 88 * q^44 - 20 * q^45 + 632 * q^46 - 30 * q^47 + 720 * q^48 + 100 * q^50 - 350 * q^51 + 920 * q^52 - 540 * q^53 - 290 * q^54 - 660 * q^55 + 1400 * q^57 + 1314 * q^58 + 380 * q^59 - 200 * q^60 + 1080 * q^61 + 2680 * q^62 - 448 * q^64 - 50 * q^65 - 110 * q^66 - 468 * q^67 - 600 * q^68 + 160 * q^69 - 2112 * q^71 + 72 * q^72 - 860 * q^73 - 1296 * q^74 + 250 * q^75 - 2880 * q^76 + 4500 * q^78 - 158 * q^79 - 360 * q^80 + 1342 * q^81 - 1900 * q^82 - 80 * q^83 + 700 * q^85 - 148 * q^86 - 1290 * q^87 - 1364 * q^88 - 240 * q^89 + 40 * q^90 - 2592 * q^92 + 100 * q^93 - 910 * q^94 - 700 * q^95 - 1800 * q^96 - 3260 * q^97 - 264 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.15831	−	3.73831i	−0.763079	−	1.32169i	−0.941256	−	0.337693i	$-0.890354\pi$
$2$	−2.15831	−	3.73831i	−0.763079	−	1.32169i	0.178178	−	0.983998i	$-0.442980\pi$
$3$	2.50000	−	4.33013i	0.481125	−	0.833333i	−0.518640	−	0.854993i	$-0.673562\pi$
$3$	2.50000	−	4.33013i	0.481125	−	0.833333i	0.999765	+	0.0216593i	$0.00689490\pi$
$4$	−5.31662	+	9.20866i	−0.664578	+	1.15108i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	−21.5831			−1.46855
$7$		0			0
$7$		0			0
$8$	11.3668			0.502344
$9$	1.00000	+	1.73205i	0.0370370	+	0.0641500i
$10$	10.7916	−	18.6915i	0.341259	−	0.591078i
$11$	−9.86675	+	17.0897i	−0.270449	+	0.468431i	−0.968977	−	0.247152i	$-0.920505\pi$
$11$	−9.86675	+	17.0897i	−0.270449	+	0.468431i	0.698528	+	0.715583i	$0.253839\pi$
$12$	26.5831	+	46.0433i	0.639491	+	1.10763i
$13$	−71.3325			−1.52185			−0.760926	−	0.648839i	$-0.775255\pi$
$13$	−71.3325			−1.52185			−0.760926	+	0.648839i	$0.775255\pi$
$14$		0			0
$15$	25.0000			0.430331
$16$	18.0000	+	31.1769i	0.281250	+	0.487139i
$17$	−15.6662	+	27.1347i	−0.223507	+	0.387126i	−0.955871	−	0.293788i	$-0.905084\pi$
$17$	−15.6662	+	27.1347i	−0.223507	+	0.387126i	0.732363	+	0.680914i	$0.238417\pi$
$18$	4.31662	−	7.47661i	0.0565243	−	0.0979030i
$19$	68.1662	+	118.067i	0.823074	+	1.42561i	0.903382	+	0.428836i	$0.141076\pi$
$19$	68.1662	+	118.067i	0.823074	+	1.42561i	−0.0803080	+	0.996770i	$0.525590\pi$
$20$	−53.1662			−0.594417
$21$		0			0
$22$	85.1821			0.825495
$23$	50.4327	+	87.3521i	0.457215	+	0.791920i	0.998813	−	0.0487178i	$-0.0155135\pi$
$23$	50.4327	+	87.3521i	0.457215	+	0.791920i	−0.541597	+	0.840638i	$0.682180\pi$
$24$	28.4169	−	49.2195i	0.241690	−	0.418620i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	153.958	+	266.663i	1.16129	+	2.01142i
$27$	145.000			1.03353
$28$		0			0
$29$	−288.198			−1.84541			−0.922707	−	0.385501i	$-0.874029\pi$
$29$	−288.198			−1.84541			−0.922707	+	0.385501i	$0.874029\pi$
$30$	−53.9578	−	93.4577i	−0.328377	−	0.568765i
$31$	−104.499	+	180.997i	−0.605436	+	1.04865i	0.386546	+	0.922270i	$0.373668\pi$
$31$	−104.499	+	180.997i	−0.605436	+	1.04865i	−0.991982	+	0.126376i	$0.959665\pi$
$32$	123.166	−	213.330i	0.680404	−	1.17849i
$33$	49.3338	+	85.4486i	0.260240	+	0.450748i
$34$	135.251			0.682214
$35$		0			0
$36$	−21.2665			−0.0984560
$37$	−154.966	−	268.409i	−0.688546	−	1.19260i	−0.972308	−	0.233702i	$-0.924916\pi$
$37$	−154.966	−	268.409i	−0.688546	−	1.19260i	0.283762	−	0.958895i	$-0.408417\pi$
$38$	294.248	−	509.653i	1.25614	−	2.17570i
$39$	−178.331	+	308.879i	−0.732201	+	1.26821i
$40$	28.4169	+	49.2195i	0.112328	+	0.194557i
$41$	181.662			0.691973			0.345987	−	0.938239i	$-0.387544\pi$
$41$	181.662			0.691973			0.345987	+	0.938239i	$0.387544\pi$
$42$		0			0
$43$	−18.2005			−0.0645477			−0.0322738	−	0.999479i	$-0.510275\pi$
$43$	−18.2005			−0.0645477			−0.0322738	+	0.999479i	$0.510275\pi$
$44$	−104.916	−	181.719i	−0.359469	−	0.622618i
$45$	−5.00000	+	8.66025i	−0.0165635	+	0.0286888i
$46$	217.699	−	377.066i	0.697783	−	1.20860i
$47$	−73.8325	−	127.882i	−0.229140	−	0.396882i	0.728414	−	0.685138i	$-0.240258\pi$
$47$	−73.8325	−	127.882i	−0.229140	−	0.396882i	−0.957553	+	0.288256i	$0.906925\pi$
$48$	180.000			0.541266
$49$		0			0
$50$	107.916			0.305231
$51$	78.3312	+	135.674i	0.215070	+	0.372512i
$52$	379.248	−	656.877i	1.01139	−	1.75178i
$53$	63.9975	−	110.847i	0.165863	−	0.287283i	−0.771099	−	0.636716i	$-0.780292\pi$
$53$	63.9975	−	110.847i	0.165863	−	0.287283i	0.936961	+	0.349433i	$0.113626\pi$
$54$	−312.955	−	542.054i	−0.788663	−	1.36601i
$55$	−98.6675			−0.241897
$56$		0			0
$57$	681.662			1.58401
$58$	622.021	+	1077.37i	1.40820	+	2.43907i
$59$	161.332	−	279.436i	0.355995	−	0.616601i	−0.631293	−	0.775545i	$-0.717475\pi$
$59$	161.332	−	279.436i	0.355995	−	0.616601i	0.987288	+	0.158943i	$0.0508087\pi$
$60$	−132.916	+	230.217i	−0.285989	+	0.495347i
$61$	170.501	+	295.317i	0.357876	+	0.619860i	0.987606	−	0.156955i	$-0.0501676\pi$
$61$	170.501	+	295.317i	0.357876	+	0.619860i	−0.629730	+	0.776814i	$0.716834\pi$
$62$	902.164			1.84798
$63$		0			0
$64$	−775.325			−1.51431
$65$	−178.331	−	308.879i	−0.340296	−	0.589411i
$66$	212.955	−	368.849i	0.397166	−	0.687912i
$67$	42.1980	−	73.0891i	0.0769449	−	0.133272i	−0.824986	−	0.565154i	$-0.808817\pi$
$67$	42.1980	−	73.0891i	0.0769449	−	0.133272i	0.901930	+	0.431881i	$0.142150\pi$
$68$	−166.583	−	288.530i	−0.297076	−	0.514551i
$69$	504.327			0.879911
$70$		0			0
$71$	−315.736			−0.527760			−0.263880	−	0.964555i	$-0.585002\pi$
$71$	−315.736			−0.527760			−0.263880	+	0.964555i	$0.585002\pi$
$72$	11.3668	+	19.6878i	0.0186053	+	0.0322254i
$73$	−546.662	+	946.847i	−0.876466	+	1.51808i	−0.0212727	+	0.999774i	$0.506772\pi$
$73$	−546.662	+	946.847i	−0.876466	+	1.51808i	−0.855193	+	0.518310i	$0.826561\pi$
$74$	−668.929	+	1158.62i	−1.05083	+	1.82009i
$75$	62.5000	+	108.253i	0.0962250	+	0.166667i
$76$	−1449.66			−2.18799
$77$		0			0
$78$	1539.58			2.23491
$79$	−616.593	−	1067.97i	−0.878128	−	1.52096i	−0.853393	−	0.521268i	$-0.825459\pi$
$79$	−616.593	−	1067.97i	−0.878128	−	1.52096i	−0.0247348	−	0.999694i	$-0.507874\pi$
$80$	−90.0000	+	155.885i	−0.125779	+	0.217855i
$81$	335.500	−	581.103i	0.460219	−	0.797124i
$82$	−392.084	−	679.110i	−0.528030	−	0.914575i
$83$	643.325			0.850772			0.425386	−	0.905012i	$-0.360138\pi$
$83$	643.325			0.850772			0.425386	+	0.905012i	$0.360138\pi$
$84$		0			0
$85$	−156.662			−0.199911
$86$	39.2824	+	68.0391i	0.0492550	+	0.0853121i
$87$	−720.495	+	1247.93i	−0.887876	+	1.53785i
$88$	−112.153	+	194.255i	−0.135858	+	0.235314i
$89$	570.159	+	987.544i	0.679064	+	1.17617i	0.975263	+	0.221047i	$0.0709475\pi$
$89$	570.159	+	987.544i	0.679064	+	1.17617i	−0.296199	+	0.955126i	$0.595719\pi$
$90$	43.1662			0.0505569
$91$		0			0
$92$	−1072.53			−1.21542
$93$	522.494	+	904.986i	0.582581	+	1.00906i
$94$	−318.707	+	552.017i	−0.349704	+	0.605704i
$95$	−340.831	+	590.337i	−0.368090	+	0.637551i
$96$	−615.831	−	1066.65i	−0.654719	−	1.13401i
$97$	−1411.99			−1.47800			−0.739001	−	0.673705i	$-0.764702\pi$
$97$	−1411.99			−1.47800			−0.739001	+	0.673705i	$0.764702\pi$
$98$		0			0
$99$	−39.4670			−0.0400665
$100$	−132.916	−	230.217i	−0.132916	−	0.230217i
$101$	−272.836	+	472.566i	−0.268794	+	0.465565i	−0.968551	−	0.248816i	$-0.919959\pi$
$101$	−272.836	+	472.566i	−0.268794	+	0.465565i	0.699756	+	0.714381i	$0.253292\pi$
$102$	338.127	−	585.652i	0.328231	−	0.568512i
$103$	390.495	+	676.357i	0.373559	+	0.647024i	0.990110	−	0.140291i	$-0.0448039\pi$
$103$	390.495	+	676.357i	0.373559	+	0.647024i	−0.616551	+	0.787315i	$0.711471\pi$
$104$	−810.819			−0.764493
$105$		0			0
$106$	−552.506			−0.506266
$107$	310.330	+	537.507i	0.280381	+	0.485634i	0.971478	−	0.237128i	$-0.0762060\pi$
$107$	310.330	+	537.507i	0.280381	+	0.485634i	−0.691098	+	0.722761i	$0.742873\pi$
$108$	−770.911	+	1335.26i	−0.686860	+	1.18968i
$109$	−2.09397	+	3.62686i	−0.00184005	+	0.00318707i	−0.866944	−	0.498406i	$-0.833919\pi$
$109$	−2.09397	+	3.62686i	−0.00184005	+	0.00318707i	0.865104	+	0.501593i	$0.167252\pi$
$110$	212.955	+	368.849i	0.184586	+	0.319713i
$111$	−1549.66			−1.32511
$112$		0			0
$113$	1413.53			1.17676			0.588379	−	0.808585i	$-0.299766\pi$
$113$	1413.53			1.17676			0.588379	+	0.808585i	$0.299766\pi$
$114$	−1471.24	−	2548.26i	−1.20872	−	2.09357i
$115$	−252.164	+	436.760i	−0.204473	+	0.354158i
$116$	1532.24	−	2653.92i	1.22642	−	2.12423i
$117$	−71.3325	−	123.552i	−0.0563649	−	0.0976268i
$118$	−1392.82			−1.08661
$119$		0			0
$120$	284.169			0.216175
$121$	470.794	+	815.440i	0.353715	+	0.612652i
$122$	735.990	−	1274.77i	0.546175	−	0.946004i
$123$	454.156	−	786.622i	0.332926	−	0.576645i
$124$	−1111.16	−	1924.59i	−0.804720	−	1.39382i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−2046.26			−1.42974			−0.714868	−	0.699259i	$-0.753513\pi$
$127$	−2046.26			−1.42974			−0.714868	+	0.699259i	$0.753513\pi$
$128$	688.063	+	1191.76i	0.475131	+	0.822951i
$129$	−45.5013	+	78.8105i	−0.0310555	+	0.0537897i
$130$	−769.789	+	1333.31i	−0.519346	+	0.899533i
$131$	570.159	+	987.544i	0.380267	+	0.658642i	0.991100	−	0.133117i	$-0.0424987\pi$
$131$	570.159	+	987.544i	0.380267	+	0.658642i	−0.610833	+	0.791759i	$0.709165\pi$
$132$	−1049.16			−0.691798
$133$		0			0
$134$	−364.306			−0.234860
$135$	362.500	+	627.868i	0.231104	+	0.400284i
$136$	−178.074	+	308.434i	−0.112278	+	0.194470i
$137$	245.171	−	424.649i	0.152893	−	0.264819i	−0.779397	−	0.626531i	$-0.784474\pi$
$137$	245.171	−	424.649i	0.152893	−	0.264819i	0.932290	+	0.361712i	$0.117808\pi$
$138$	−1088.50	−	1885.33i	−0.671442	−	1.16297i
$139$	−2800.00			−1.70858			−0.854291	−	0.519795i	$-0.826008\pi$
$139$	−2800.00			−1.70858			−0.854291	+	0.519795i	$0.826008\pi$
$140$		0			0
$141$	−738.325			−0.440980
$142$	681.457	+	1180.32i	0.402723	+	0.697536i
$143$	703.820	−	1219.05i	0.411583	−	0.712883i
$144$	−36.0000	+	62.3538i	−0.0208333	+	0.0360844i
$145$	−720.495	−	1247.93i	−0.412647	−	0.714726i
$146$	4719.47			2.67525
$147$		0			0
$148$	3295.58			1.83037
$149$	−583.058	−	1009.89i	−0.320577	−	0.555256i	0.660030	−	0.751239i	$-0.270544\pi$
$149$	−583.058	−	1009.89i	−0.320577	−	0.555256i	−0.980607	+	0.195983i	$0.937210\pi$
$150$	269.789	−	467.288i	0.146855	−	0.254360i
$151$	−479.791	+	831.022i	−0.258575	+	0.447865i	−0.965860	−	0.259063i	$-0.916586\pi$
$151$	−479.791	+	831.022i	−0.258575	+	0.447865i	0.707285	+	0.706928i	$0.249920\pi$
$152$	774.829	+	1342.04i	0.413467	+	0.716145i
$153$	−62.6650			−0.0331122
$154$		0			0
$155$	−1044.99			−0.541519
$156$	−1896.24	−	3284.39i	−0.973210	−	1.68565i
$157$	−510.330	+	883.917i	−0.259419	+	0.449327i	−0.966086	−	0.258219i	$-0.916864\pi$
$157$	−510.330	+	883.917i	−0.259419	+	0.449327i	0.706667	+	0.707546i	$0.250198\pi$
$158$	−2661.60	+	4610.03i	−1.34016	+	2.32123i
$159$	−319.987	−	554.234i	−0.159602	−	0.276438i
$160$	1231.66			0.608572
$161$		0			0
$162$	−2896.46			−1.40473
$163$	783.008	+	1356.21i	0.376257	+	0.651696i	0.990514	−	0.137410i	$-0.0438777\pi$
$163$	783.008	+	1356.21i	0.376257	+	0.651696i	−0.614257	+	0.789106i	$0.710544\pi$
$164$	−965.831	+	1672.87i	−0.459870	+	0.796519i
$165$	−246.669	+	427.243i	−0.116383	+	0.201581i
$166$	−1388.50	−	2404.95i	−0.649206	−	1.12446i
$167$	1130.30			0.523746			0.261873	−	0.965102i	$-0.415660\pi$
$167$	1130.30			0.523746			0.261873	+	0.965102i	$0.415660\pi$
$168$		0			0
$169$	2891.32			1.31603
$170$	338.127	+	585.652i	0.152548	+	0.264221i
$171$	−136.332	+	236.135i	−0.0609685	+	0.105600i
$172$	96.7652	−	167.602i	0.0428970	−	0.0742997i
$173$	1271.67	+	2202.59i	0.558862	+	0.967978i	0.997592	+	0.0693588i	$0.0220953\pi$
$173$	1271.67	+	2202.59i	0.558862	+	0.967978i	−0.438729	+	0.898619i	$0.644571\pi$
$174$	6220.21			2.71008
$175$		0			0
$176$	−710.406			−0.304255
$177$	−806.662	−	1397.18i	−0.342556	−	0.593325i
$178$	2461.16	−	4262.86i	1.03636	−	1.79503i
$179$	605.325	−	1048.45i	0.252760	−	0.437794i	−0.711524	−	0.702661i	$-0.751995\pi$
$179$	605.325	−	1048.45i	0.252760	−	0.437794i	0.964285	+	0.264868i	$0.0853282\pi$
$180$	−53.1662	−	92.0866i	−0.0220154	−	0.0381319i
$181$	3031.32			1.24484			0.622421	−	0.782683i	$-0.286149\pi$
$181$	3031.32			1.24484			0.622421	+	0.782683i	$0.286149\pi$
$182$		0			0
$183$	1705.01			0.688733
$184$	573.256	+	992.909i	0.229679	+	0.397817i
$185$	774.829	−	1342.04i	0.307927	−	0.533346i
$186$	2255.41	−	3906.48i	0.889111	−	1.53999i
$187$	−309.150	−	535.463i	−0.120895	−	0.209396i
$188$	1570.16			0.609125
$189$		0			0
$190$	2942.48			1.12353
$191$	1084.32	+	1878.10i	0.410778	+	0.711488i	0.994975	−	0.100124i	$-0.0319239\pi$
$191$	1084.32	+	1878.10i	0.410778	+	0.711488i	−0.584197	+	0.811612i	$0.698591\pi$
$192$	−1938.31	+	3357.26i	−0.728571	+	1.26192i
$193$	−745.240	+	1290.79i	−0.277946	+	0.481416i	−0.970874	−	0.239590i	$-0.922987\pi$
$193$	−745.240	+	1290.79i	−0.277946	+	0.481416i	0.692928	+	0.721006i	$0.256320\pi$
$194$	3047.52	+	5278.46i	1.12783	+	1.95346i
$195$	−1783.31			−0.654901
$196$		0			0
$197$	3380.57			1.22262			0.611308	−	0.791393i	$-0.290644\pi$
$197$	3380.57			1.22262			0.611308	+	0.791393i	$0.290644\pi$
$198$	85.1821	+	147.540i	0.0305739	+	0.0529555i
$199$	2297.66	−	3979.67i	0.818478	−	1.41765i	−0.0883251	−	0.996092i	$-0.528151\pi$
$199$	2297.66	−	3979.67i	0.818478	−	1.41765i	0.906803	−	0.421554i	$-0.138515\pi$
$200$	−142.084	+	246.097i	−0.0502344	+	0.0870086i
$201$	−210.990	−	365.445i	−0.0740402	−	0.128241i
$202$	2355.46			0.820445
$203$		0			0
$204$	−1665.83			−0.571723
$205$	454.156	+	786.622i	0.154730	+	0.268000i
$206$	1685.62	−	2919.58i	0.570110	−	0.987460i
$207$	−100.865	+	174.704i	−0.0338678	+	0.0586608i
$208$	−1283.98	−	2223.93i	−0.428021	−	0.741354i
$209$	−2690.32			−0.890398
$210$		0			0
$211$	−4988.66			−1.62765			−0.813824	−	0.581112i	$-0.802618\pi$
$211$	−4988.66			−1.62765			−0.813824	+	0.581112i	$0.802618\pi$
$212$	680.501	+	1178.66i	0.220458	+	0.381844i
$213$	−789.340	+	1367.18i	−0.253919	+	0.439800i
$214$	1339.58	−	2320.22i	0.427905	−	0.741153i
$215$	−45.5013	−	78.8105i	−0.0144333	−	0.0249992i
$216$	1648.18			0.519187
$217$		0			0
$218$	18.0778			0.00561643
$219$	2733.31	+	4734.24i	0.843380	+	1.46078i
$220$	524.578	−	908.596i	0.160759	−	0.278443i
$221$	1117.51	−	1935.59i	0.340145	−	0.589148i
$222$	3344.64	+	5793.09i	1.01116	+	1.75138i
$223$	−3792.97			−1.13900			−0.569498	−	0.821993i	$-0.692862\pi$
$223$	−3792.97			−1.13900			−0.569498	+	0.821993i	$0.692862\pi$
$224$		0			0
$225$	−50.0000			−0.0148148
$226$	−3050.84	−	5284.21i	−0.897960	−	1.55531i
$227$	1955.48	−	3386.99i	0.571762	−	0.990320i	−0.424623	−	0.905370i	$-0.639593\pi$
$227$	1955.48	−	3386.99i	0.571762	−	0.990320i	0.996385	−	0.0849504i	$-0.0270732\pi$
$228$	−3624.14	+	6277.20i	−1.05270	+	1.82332i
$229$	177.164	+	306.857i	0.0511236	+	0.0885487i	0.890455	−	0.455072i	$-0.150386\pi$
$229$	177.164	+	306.857i	0.0511236	+	0.0885487i	−0.839331	+	0.543621i	$0.817053\pi$
$230$	2176.99			0.624116
$231$		0			0
$232$	−3275.87			−0.927033
$233$	−3246.24	−	5622.65i	−0.912739	−	1.58091i	−0.810178	−	0.586184i	$-0.800630\pi$
$233$	−3246.24	−	5622.65i	−0.912739	−	1.58091i	−0.102561	−	0.994727i	$-0.532704\pi$
$234$	−307.916	+	533.325i	−0.0860217	+	0.148994i
$235$	369.162	−	639.408i	0.102474	−	0.177491i
$236$	1715.49	+	2971.31i	0.473173	+	0.819559i
$237$	−6165.93			−1.68996
$238$		0			0
$239$	−342.688			−0.0927474			−0.0463737	−	0.998924i	$-0.514766\pi$
$239$	−342.688			−0.0927474			−0.0463737	+	0.998924i	$0.514766\pi$
$240$	450.000	+	779.423i	0.121031	+	0.209631i
$241$	1156.83	−	2003.69i	0.309204	−	0.535557i	−0.668984	−	0.743277i	$-0.733271\pi$
$241$	1156.83	−	2003.69i	0.309204	−	0.535557i	0.978189	+	0.207719i	$0.0666040\pi$
$242$	2032.24	−	3519.95i	0.539825	−	0.935003i
$243$	280.000	+	484.974i	0.0739177	+	0.128029i
$244$	−3625.96			−0.951347
$245$		0			0
$246$	−3920.84			−1.01619
$247$	−4862.47	−	8422.04i	−1.25260	−	2.16956i
$248$	−1187.81	+	2057.35i	−0.304137	+	0.526781i
$249$	1608.31	−	2785.68i	0.409328	−	0.708977i
$250$	269.789	+	467.288i	0.0682518	+	0.118216i
$251$	−3989.29			−1.00319			−0.501597	−	0.865101i	$-0.667254\pi$
$251$	−3989.29			−1.00319			−0.501597	+	0.865101i	$0.667254\pi$
$252$		0			0
$253$	−1990.43			−0.494614
$254$	4416.48	+	7649.56i	1.09100	+	1.88967i
$255$	−391.656	+	678.368i	−0.0961822	+	0.166592i
$256$	−131.188	+	227.224i	−0.0320283	+	0.0554747i
$257$	1145.66	+	1984.34i	0.278071	+	0.481633i	0.970905	−	0.239463i	$-0.0769715\pi$
$257$	1145.66	+	1984.34i	0.278071	+	0.481633i	−0.692834	+	0.721097i	$0.743638\pi$
$258$	392.824			0.0947912
$259$		0			0
$260$	3792.48			0.904614
$261$	−288.198	−	499.174i	−0.0683487	−	0.118383i
$262$	2461.16	−	4262.86i	0.580348	−	1.00519i
$263$	−3180.24	+	5508.33i	−0.745634	+	1.29148i	0.204264	+	0.978916i	$0.434520\pi$
$263$	−3180.24	+	5508.33i	−0.745634	+	1.29148i	−0.949898	+	0.312560i	$0.898813\pi$
$264$	560.764	+	971.273i	0.130730	+	0.226431i
$265$	639.975			0.148352
$266$		0			0
$267$	5701.59			1.30686
$268$	448.702	+	777.174i	0.102272	+	0.177140i
$269$	−495.673	+	858.530i	−0.112348	+	0.194593i	−0.916717	−	0.399538i	$-0.869171\pi$
$269$	−495.673	+	858.530i	−0.112348	+	0.194593i	0.804368	+	0.594131i	$0.202504\pi$
$270$	1564.78	−	2710.27i	0.352701	−	0.610896i
$271$	365.489	+	633.045i	0.0819257	+	0.141899i	0.904077	−	0.427370i	$-0.140560\pi$
$271$	365.489	+	633.045i	0.0819257	+	0.141899i	−0.822151	+	0.569269i	$0.807226\pi$
$272$	−1127.97			−0.251446
$273$		0			0
$274$	−2116.62			−0.466679
$275$	−246.669	−	427.243i	−0.0540898	−	0.0936862i
$276$	−2681.32	+	4644.18i	−0.584770	+	1.01285i
$277$	1769.31	−	3064.54i	0.383783	−	0.664731i	−0.607817	−	0.794077i	$-0.707954\pi$
$277$	1769.31	−	3064.54i	0.383783	−	0.664731i	0.991600	+	0.129346i	$0.0412878\pi$
$278$	6043.27	+	10467.3i	1.30378	+	2.25822i
$279$	−417.995			−0.0896943
$280$		0			0
$281$	−4663.20			−0.989975			−0.494988	−	0.868900i	$-0.664827\pi$
$281$	−4663.20			−0.989975			−0.494988	+	0.868900i	$0.664827\pi$
$282$	1593.54	+	2760.09i	0.336502	+	0.582839i
$283$	−1052.47	+	1822.94i	−0.221071	+	0.382906i	−0.955134	−	0.296176i	$-0.904289\pi$
$283$	−1052.47	+	1822.94i	−0.221071	+	0.382906i	0.734062	+	0.679082i	$0.237622\pi$
$284$	1678.65	−	2907.51i	0.350738	−	0.607496i
$285$	1704.16	+	2951.69i	0.354195	+	0.613483i
$286$	−6076.25			−1.25628
$287$		0			0
$288$	492.665			0.100801
$289$	1965.64	+	3404.58i	0.400089	+	0.692975i
$290$	−3110.11	+	5386.86i	−0.629765	+	1.09078i
$291$	−3529.98	+	6114.11i	−0.711104	+	1.23167i
$292$	−5812.80	−	10068.1i	−1.16496	−	2.01777i
$293$	6594.66			1.31489			0.657447	−	0.753501i	$-0.271636\pi$
$293$	6594.66			1.31489			0.657447	+	0.753501i	$0.271636\pi$
$294$		0			0
$295$	1613.32			0.318412
$296$	−1761.46	−	3050.93i	−0.345887	−	0.599094i
$297$	−1430.68	+	2478.01i	−0.279517	+	0.484137i
$298$	−2516.84	+	4359.30i	−0.489251	+	0.847408i
$299$	−3597.49	−	6231.04i	−0.695814	−	1.20519i
$300$	−1329.16			−0.255796
$301$		0			0
$302$	4142.15			0.789252
$303$	1364.18	+	2362.83i	0.258647	+	0.447990i
$304$	−2453.98	+	4250.43i	−0.462979	+	0.801904i
$305$	−852.506	+	1476.58i	−0.160047	+	0.277210i
$306$	135.251	+	234.261i	0.0252672	+	0.0437641i
$307$	2672.97			0.496920			0.248460	−	0.968642i	$-0.420076\pi$
$307$	2672.97			0.496920			0.248460	+	0.968642i	$0.420076\pi$
$308$		0			0
$309$	3904.95			0.718915
$310$	2255.41	+	3906.48i	0.413221	+	0.715721i
$311$	−427.849	+	741.056i	−0.0780099	+	0.135117i	−0.902391	−	0.430918i	$-0.858190\pi$
$311$	−427.849	+	741.056i	−0.0780099	+	0.135117i	0.824381	+	0.566035i	$0.191523\pi$
$312$	−2027.05	+	3510.95i	−0.367817	+	0.637078i
$313$	−1674.99	−	2901.17i	−0.302480	−	0.523911i	0.674217	−	0.738533i	$-0.264481\pi$
$313$	−1674.99	−	2901.17i	−0.302480	−	0.523911i	−0.976697	+	0.214622i	$0.931148\pi$
$314$	4405.81			0.791828
$315$		0			0
$316$	13112.8			2.33434
$317$	−3816.53	−	6610.42i	−0.676206	−	1.17122i	−0.976115	−	0.217256i	$-0.930289\pi$
$317$	−3816.53	−	6610.42i	−0.676206	−	1.17122i	0.299908	−	0.953968i	$-0.403044\pi$
$318$	−1381.27	+	2392.42i	−0.243577	+	0.421888i
$319$	2843.58	−	4925.22i	0.499090	−	0.864450i
$320$	−1938.31	−	3357.26i	−0.338609	−	0.586488i
$321$	3103.30			0.539593
$322$		0			0
$323$	−4271.64			−0.735852
$324$	3567.46	+	6179.01i	0.611704	+	1.05950i
$325$	891.656	−	1544.39i	0.152185	−	0.263592i
$326$	3379.95	−	5854.24i	0.574227	−	0.994591i
$327$	10.4698	+	18.1343i	0.00177059	+	0.00306676i
$328$	2064.91			0.347609
$329$		0			0
$330$	2129.55			0.355236
$331$	1660.85	+	2876.68i	0.275796	+	0.477693i	0.970336	−	0.241761i	$-0.0777251\pi$
$331$	1660.85	+	2876.68i	0.275796	+	0.477693i	−0.694539	+	0.719455i	$0.744392\pi$
$332$	−3420.32	+	5924.16i	−0.565405	+	0.979309i
$333$	309.931	−	536.817i	0.0510034	−	0.0883405i
$334$	−2439.55	−	4225.43i	−0.399660	−	0.692231i
$335$	421.980			0.0688216
$336$		0			0
$337$	−2233.98			−0.361107			−0.180553	−	0.983565i	$-0.557789\pi$
$337$	−2233.98			−0.361107			−0.180553	+	0.983565i	$0.557789\pi$
$338$	−6240.38	−	10808.7i	−1.00424	−	1.73939i
$339$	3533.83	−	6120.77i	0.566168	−	0.980632i
$340$	832.916	−	1442.65i	0.132856	−	0.230114i
$341$	−2062.13	−	3571.71i	−0.327479	−	0.567211i
$342$	1176.99			0.186095
$343$		0			0
$344$	−206.881			−0.0324252
$345$	1260.82	+	2183.80i	0.196754	+	0.340788i
$346$	5489.32	−	9507.78i	0.852912	−	1.47729i
$347$	−1264.31	+	2189.84i	−0.195595	+	0.338781i	−0.947095	−	0.320952i	$-0.895997\pi$
$347$	−1264.31	+	2189.84i	−0.195595	+	0.338781i	0.751500	+	0.659733i	$0.229330\pi$
$348$	−7661.20	−	13269.6i	−1.18013	−	2.04404i
$349$	−1291.00			−0.198011			−0.0990054	−	0.995087i	$-0.531566\pi$
$349$	−1291.00			−0.198011			−0.0990054	+	0.995087i	$0.531566\pi$
$350$		0			0
$351$	−10343.2			−1.57288
$352$	2430.50	+	4209.75i	0.368029	+	0.637445i
$353$	−3884.32	+	6727.84i	−0.585670	+	1.01441i	0.409121	+	0.912480i	$0.365835\pi$
$353$	−3884.32	+	6727.84i	−0.585670	+	1.01441i	−0.994792	+	0.101930i	$0.967498\pi$
$354$	−3482.06	+	6031.10i	−0.522795	+	0.905507i
$355$	−789.340	−	1367.18i	−0.118011	−	0.204401i
$356$	−12125.3			−1.80516
$357$		0			0
$358$	−5225.92			−0.771504
$359$	1142.07	+	1978.12i	0.167900	+	0.290811i	0.937681	−	0.347496i	$-0.112968\pi$
$359$	1142.07	+	1978.12i	0.167900	+	0.290811i	−0.769781	+	0.638308i	$0.779635\pi$
$360$	−56.8338	+	98.4389i	−0.00832056	+	0.0144116i
$361$	−5863.77	+	10156.4i	−0.854902	+	1.48073i
$362$	−6542.54	−	11332.0i	−0.949912	−	1.64530i
$363$	4707.94			0.680725
$364$		0			0
$365$	−5466.62			−0.783935
$366$	−3679.95	−	6373.86i	−0.525558	−	0.910292i
$367$	5353.50	−	9272.54i	0.761446	−	1.31886i	−0.180660	−	0.983546i	$-0.557823\pi$
$367$	5353.50	−	9272.54i	0.761446	−	1.31886i	0.942105	−	0.335317i	$-0.108843\pi$
$368$	−1815.58	+	3144.67i	−0.257184	+	0.445455i
$369$	181.662	+	314.649i	0.0256286	+	0.0443901i
$370$	−6689.29			−0.939891
$371$		0			0
$372$	−11111.6			−1.54868
$373$	415.215	+	719.173i	0.0576381	+	0.0998321i	0.893405	−	0.449253i	$-0.148310\pi$
$373$	415.215	+	719.173i	0.0576381	+	0.0998321i	−0.835767	+	0.549085i	$0.814976\pi$
$374$	−1334.48	+	2311.39i	−0.184504	+	0.319570i
$375$	−312.500	+	541.266i	−0.0430331	+	0.0745356i
$376$	−839.236	−	1453.60i	−0.115107	−	0.199371i
$377$	20557.9			2.80845
$378$		0			0
$379$	5253.17			0.711972			0.355986	−	0.934491i	$-0.384145\pi$
$379$	5253.17			0.711972			0.355986	+	0.934491i	$0.384145\pi$
$380$	−3624.14	−	6277.20i	−0.489249	−	0.847404i
$381$	−5115.66	+	8860.58i	−0.687882	+	1.19145i
$382$	4680.60	−	8107.03i	0.626911	−	1.08584i
$383$	−5621.95	−	9737.51i	−0.750048	−	1.29912i	−0.947799	−	0.318869i	$-0.896697\pi$
$383$	−5621.95	−	9737.51i	−0.750048	−	1.29912i	0.197750	−	0.980252i	$-0.436636\pi$
$384$	6880.63			0.914390
$385$		0			0
$386$	6433.84			0.848378
$387$	−18.2005	−	31.5242i	−0.00239066	−	0.00414074i
$388$	7507.03	−	13002.6i	0.982247	−	1.70130i
$389$	4253.43	−	7367.15i	0.554389	−	0.960230i	−0.443562	−	0.896244i	$-0.646285\pi$
$389$	4253.43	−	7367.15i	0.554389	−	0.960230i	0.997951	−	0.0639860i	$-0.0203813\pi$
$390$	3848.95	+	6666.57i	0.499741	+	0.865576i
$391$	−3160.37			−0.408764
$392$		0			0
$393$	5701.59			0.731824
$394$	−7296.32	−	12637.6i	−0.932952	−	1.61592i
$395$	3082.96	−	5339.85i	0.392711	−	0.680195i
$396$	209.831	−	363.438i	0.0266273	−	0.0461199i
$397$	1561.62	+	2704.80i	0.197419	+	0.341940i	0.947691	−	0.319190i	$-0.103411\pi$
$397$	1561.62	+	2704.80i	0.197419	+	0.341940i	−0.750272	+	0.661130i	$0.770077\pi$
$398$	−19836.3			−2.49825
$399$		0			0
$400$	−900.000			−0.112500
$401$	5627.67	+	9747.40i	0.700828	+	1.21387i	0.968176	+	0.250270i	$0.0805195\pi$
$401$	5627.67	+	9747.40i	0.700828	+	1.21387i	−0.267348	+	0.963600i	$0.586147\pi$
$402$	−910.764	+	1577.49i	−0.112997	+	0.195717i
$403$	7454.16	−	12911.0i	0.921385	−	1.59588i
$404$	−2901.14	−	5024.92i	−0.357270	−	0.618809i
$405$	3355.00			0.411633
$406$		0			0
$407$	6116.03			0.744866
$408$	890.372	+	1542.17i	0.108039	+	0.187129i
$409$	−3959.96	+	6858.86i	−0.478747	+	0.829214i	−0.999703	−	0.0243694i	$-0.992242\pi$
$409$	−3959.96	+	6858.86i	−0.478747	+	0.829214i	0.520956	+	0.853584i	$0.325576\pi$
$410$	1960.42	−	3395.55i	0.236142	−	0.409010i
$411$	−1225.86	−	2123.25i	−0.147122	−	0.254822i
$412$	−8304.46			−0.993037
$413$		0			0
$414$	870.797			0.103375
$415$	1608.31	+	2785.68i	0.190238	+	0.329503i
$416$	−8785.76	+	15217.4i	−1.03547	+	1.79349i
$417$	−7000.00	+	12124.4i	−0.822042	+	1.42382i
$418$	5806.55	+	10057.2i	0.679444	+	1.17683i
$419$	5257.28			0.612972			0.306486	−	0.951875i	$-0.400847\pi$
$419$	5257.28			0.612972			0.306486	+	0.951875i	$0.400847\pi$
$420$		0			0
$421$	1457.36			0.168711			0.0843556	−	0.996436i	$-0.473117\pi$
$421$	1457.36			0.168711			0.0843556	+	0.996436i	$0.473117\pi$
$422$	10767.1	+	18649.2i	1.24202	+	2.15125i
$423$	147.665	−	255.763i	0.0169733	−	0.0293987i
$424$	727.443	−	1259.97i	0.0833202	−	0.144315i
$425$	−391.656	−	678.368i	−0.0447014	−	0.0774252i
$426$	6814.57			0.775040
$427$		0			0
$428$	−6599.63			−0.745339
$429$	−3519.10	−	6095.26i	−0.396046	−	0.685972i
$430$	−196.412	+	340.195i	−0.0220275	+	0.0381527i
$431$	7645.59	−	13242.6i	0.854467	−	1.47998i	−0.0226716	−	0.999743i	$-0.507217\pi$
$431$	7645.59	−	13242.6i	0.854467	−	1.47998i	0.877139	−	0.480237i	$-0.159449\pi$
$432$	2610.00	+	4520.65i	0.290680	+	0.503472i
$433$	−187.260			−0.0207832			−0.0103916	−	0.999946i	$-0.503308\pi$
$433$	−187.260			−0.0207832			−0.0103916	+	0.999946i	$0.503308\pi$
$434$		0			0
$435$	−7204.95			−0.794140
$436$	−22.2657	−	38.5653i	−0.00244572	−	0.00423611i
$437$	−6875.62	+	11908.9i	−0.752644	+	1.30362i
$438$	11798.7	−	20435.9i	1.28713	−	2.22937i
$439$	1793.96	+	3107.23i	0.195037	+	0.337813i	0.946912	−	0.321491i	$-0.104184\pi$
$439$	1793.96	+	3107.23i	0.195037	+	0.337813i	−0.751876	+	0.659305i	$0.770851\pi$
$440$	−1121.53			−0.121515
$441$		0			0
$442$	−9647.76			−1.03823
$443$	−2457.82	−	4257.08i	−0.263600	−	0.456568i	0.703596	−	0.710600i	$-0.251577\pi$
$443$	−2457.82	−	4257.08i	−0.263600	−	0.456568i	−0.967196	+	0.254032i	$0.918243\pi$
$444$	8238.95	−	14270.3i	0.880638	−	1.52531i
$445$	−2850.79	+	4937.72i	−0.303687	+	0.526001i
$446$	8186.41	+	14179.3i	0.869143	+	1.50540i
$447$	−5830.58			−0.616951
$448$		0			0
$449$	7091.12			0.745324			0.372662	−	0.927967i	$-0.378445\pi$
$449$	7091.12			0.745324			0.372662	+	0.927967i	$0.378445\pi$
$450$	107.916	+	186.915i	0.0113049	+	0.0195806i
$451$	−1792.42	+	3104.56i	−0.187143	+	0.324142i
$452$	−7515.21	+	13016.7i	−0.782048	+	1.35455i
$453$	2398.95	+	4155.11i	0.248814	+	0.430958i
$454$	−16882.2			−1.74520
$455$		0			0
$456$	7748.29			0.795717
$457$	−2525.91	−	4375.00i	−0.258549	−	0.447820i	0.707304	−	0.706909i	$-0.249911\pi$
$457$	−2525.91	−	4375.00i	−0.258549	−	0.447820i	−0.965853	+	0.259089i	$0.916578\pi$
$458$	764.749	−	1324.58i	0.0780227	−	0.135139i
$459$	−2271.61	+	3934.54i	−0.231001	+	0.400106i
$460$	−2681.32	−	4644.18i	−0.271776	−	0.470731i
$461$	16681.3			1.68531			0.842653	−	0.538456i	$-0.180992\pi$
$461$	16681.3			1.68531			0.842653	+	0.538456i	$0.180992\pi$
$462$		0			0
$463$	15569.6			1.56280			0.781402	−	0.624027i	$-0.214505\pi$
$463$	15569.6			1.56280			0.781402	+	0.624027i	$0.214505\pi$
$464$	−5187.56	−	8985.12i	−0.519023	−	0.898974i
$465$	−2612.47	+	4524.93i	−0.260538	+	0.451266i
$466$	−14012.8	+	24270.9i	−1.39298	+	2.41272i
$467$	1664.18	+	2882.44i	0.164901	+	0.285617i	0.936620	−	0.350346i	$-0.113936\pi$
$467$	1664.18	+	2882.44i	0.164901	+	0.285617i	−0.771719	+	0.635964i	$0.780603\pi$
$468$	1516.99			0.149835
$469$		0			0
$470$	−3187.07			−0.312784
$471$	2551.65	+	4419.59i	0.249626	+	0.432365i
$472$	1833.83	−	3176.28i	0.178832	−	0.309746i
$473$	179.580	−	311.041i	0.0174568	−	0.0302361i
$474$	13308.0	+	23050.1i	1.28957	+	2.23360i
$475$	−3408.31			−0.329230
$476$		0			0
$477$	255.990			0.0245723
$478$	739.627	+	1281.07i	0.0707735	+	0.122583i
$479$	−7303.75	+	12650.5i	−0.696695	+	1.20671i	0.272911	+	0.962039i	$0.412014\pi$
$479$	−7303.75	+	12650.5i	−0.696695	+	1.20671i	−0.969606	+	0.244672i	$0.921320\pi$
$480$	3079.16	−	5333.25i	0.292799	−	0.507143i
$481$	11054.1	+	19146.3i	1.04787	+	1.81496i
$482$	−9987.23			−0.943789
$483$		0			0
$484$	−10012.2			−0.940285
$485$	−3529.98	−	6114.11i	−0.330491	−	0.572427i
$486$	1208.65	−	2093.45i	0.112810	−	0.195393i
$487$	939.744	−	1627.68i	0.0874412	−	0.151453i	−0.818988	−	0.573811i	$-0.805464\pi$
$487$	939.744	−	1627.68i	0.0874412	−	0.151453i	0.906429	+	0.422359i	$0.138798\pi$
$488$	1938.05	+	3356.79i	0.179777	+	0.311383i
$489$	7830.08			0.724107
$490$		0			0
$491$	3221.13			0.296064			0.148032	−	0.988983i	$-0.452706\pi$
$491$	3221.13			0.296064			0.148032	+	0.988983i	$0.452706\pi$
$492$	4829.16	+	8364.34i	0.442511	+	0.766451i
$493$	4514.98	−	7820.18i	0.412464	−	0.714408i
$494$	−20989.5	+	36354.8i	−1.91166	+	3.31109i
$495$	−98.6675	−	170.897i	−0.00895914	−	0.0155177i
$496$	−7523.91			−0.681116
$497$		0			0
$498$	−13885.0			−1.24940
$499$	−4856.91	−	8412.41i	−0.435721	−	0.754692i	0.561633	−	0.827387i	$-0.310173\pi$
$499$	−4856.91	−	8412.41i	−0.435721	−	0.754692i	−0.997354	+	0.0726950i	$0.976840\pi$
$500$	664.578	−	1151.08i	0.0594417	−	0.102956i
$501$	2825.76	−	4894.36i	0.251988	−	0.436455i
$502$	8610.13	+	14913.2i	0.765516	+	1.32591i
$503$	−2078.32			−0.184230			−0.0921152	−	0.995748i	$-0.529363\pi$
$503$	−2078.32			−0.184230			−0.0921152	+	0.995748i	$0.529363\pi$
$504$		0			0
$505$	−2728.36			−0.240417
$506$	4295.97	+	7440.84i	0.377429	+	0.653726i
$507$	7228.31	−	12519.8i	0.633177	−	1.09669i
$508$	10879.2	−	18843.4i	0.950172	−	1.64575i
$509$	−9487.23	−	16432.4i	−0.826158	−	1.43095i	−0.901031	−	0.433754i	$-0.857189\pi$
$509$	−9487.23	−	16432.4i	−0.826158	−	1.43095i	0.0748736	−	0.997193i	$-0.476145\pi$
$510$	3381.27			0.293578
$511$		0			0
$512$	12141.6			1.04802
$513$	9884.11	+	17119.8i	0.850670	+	1.47340i
$514$	4945.38	−	8565.66i	0.424380	−	0.735048i
$515$	−1952.47	+	3381.79i	−0.167061	+	0.289358i
$516$	−483.826	−	838.012i	−0.0412776	−	0.0714950i
$517$	2913.95			0.247883
$518$		0			0
$519$	12716.7			1.07553
$520$	−2027.05	−	3510.95i	−0.170946	−	0.296087i
$521$	8761.78	−	15175.9i	0.736777	−	1.27613i	−0.217163	−	0.976135i	$-0.569680\pi$
$521$	8761.78	−	15175.9i	0.736777	−	1.27613i	0.953939	−	0.299999i	$-0.0969865\pi$
$522$	−1244.04	+	2154.74i	−0.104311	+	0.180672i
$523$	7609.29	+	13179.7i	0.636197	+	1.10193i	0.986260	+	0.165199i	$0.0528268\pi$
$523$	7609.29	+	13179.7i	0.636197	+	1.10193i	−0.350063	+	0.936726i	$0.613840\pi$
$524$	−12125.3			−1.01087
$525$		0			0
$526$	27455.8			2.27591
$527$	−3274.21	−	5671.09i	−0.270639	−	0.468760i
$528$	−1776.02	+	3076.15i	−0.146385	+	0.253546i
$529$	996.576	−	1726.12i	0.0819081	−	0.141869i
$530$	−1381.27	−	2392.42i	−0.113204	−	0.196076i
$531$	645.330			0.0527400
$532$		0			0
$533$	−12958.4			−1.05308
$534$	−12305.8	−	21314.3i	−0.997237	−	1.72726i
$535$	−1551.65	+	2687.54i	−0.125390	+	0.217182i
$536$	479.654	−	830.785i	0.0386528	−	0.0669486i
$537$	−3026.62	−	5242.27i	−0.243219	−	0.421267i
$538$	4279.26			0.342922
$539$		0			0
$540$	−7709.11			−0.614346
$541$	7779.63	+	13474.7i	0.618249	+	1.07084i	0.989805	+	0.142428i	$0.0454909\pi$
$541$	7779.63	+	13474.7i	0.618249	+	1.07084i	−0.371557	+	0.928410i	$0.621176\pi$
$542$	1577.68	−	2732.62i	0.125031	−	0.216561i
$543$	7578.30	−	13126.0i	0.598924	−	1.03737i
$544$	3859.11	+	6684.17i	0.304150	+	0.526804i
$545$	−20.9397			−0.00164579
$546$		0			0
$547$	−8690.70			−0.679319			−0.339660	−	0.940548i	$-0.610312\pi$
$547$	−8690.70			−0.679319			−0.339660	+	0.940548i	$0.610312\pi$
$548$	2606.97	+	4515.40i	0.203219	+	0.351986i
$549$	−341.003	+	590.634i	−0.0265093	+	0.0459155i
$550$	−1064.78	+	1844.25i	−0.0825495	+	0.142980i
$551$	−19645.4	−	34026.8i	−1.51891	−	2.63083i
$552$	5732.56			0.442018
$553$		0			0
$554$	−15274.9			−1.17143
$555$	−3874.14	−	6710.21i	−0.296303	−	0.513212i
$556$	14886.5	−	25784.3i	1.13549	−	1.96672i
$557$	3688.13	−	6388.03i	0.280559	−	0.485942i	−0.690964	−	0.722889i	$-0.742814\pi$
$557$	3688.13	−	6388.03i	0.280559	−	0.485942i	0.971522	+	0.236948i	$0.0761469\pi$
$558$	902.164	+	1562.59i	0.0684438	+	0.118548i
$559$	1298.29			0.0982320
$560$		0			0
$561$	−3091.50			−0.232662
$562$	10064.6	+	17432.5i	0.755429	+	1.30844i
$563$	6437.70	−	11150.4i	0.481913	−	0.834697i	−0.517872	−	0.855458i	$-0.673276\pi$
$563$	6437.70	−	11150.4i	0.481913	−	0.834697i	0.999784	+	0.0207610i	$0.00660892\pi$
$564$	3925.40	−	6798.99i	0.293066	−	0.507605i
$565$	3533.83	+	6120.77i	0.263131	+	0.455757i
$566$	9086.28			0.674779
$567$		0			0
$568$	−3588.89			−0.265117
$569$	6032.30	+	10448.2i	0.444441	+	0.769795i	0.998013	−	0.0630067i	$-0.0200689\pi$
$569$	6032.30	+	10448.2i	0.444441	+	0.769795i	−0.553572	+	0.832801i	$0.686736\pi$
$570$	7356.20	−	12741.3i	0.540557	−	0.936272i
$571$	−11872.8	+	20564.3i	−0.870158	+	1.50716i	−0.00832580	+	0.999965i	$0.502650\pi$
$571$	−11872.8	+	20564.3i	−0.870158	+	1.50716i	−0.861832	+	0.507193i	$0.830683\pi$
$572$	7483.89	+	12962.5i	0.547058	+	0.947533i
$573$	10843.2			0.790542
$574$		0			0
$575$	−2521.64			−0.182886
$576$	−775.325	−	1342.90i	−0.0560854	−	0.0971428i
$577$	−4923.04	+	8526.95i	−0.355197	+	0.615220i	−0.987152	−	0.159786i	$-0.948920\pi$
$577$	−4923.04	+	8526.95i	−0.355197	+	0.615220i	0.631954	+	0.775006i	$0.282253\pi$
$578$	8484.92	−	14696.3i	0.610599	−	1.05759i
$579$	3726.20	+	6453.97i	0.267453	+	0.463243i
$580$	15322.4			1.09695
$581$		0			0
$582$	30475.2			2.17051
$583$	1262.89	+	2187.40i	0.0897148	+	0.155391i
$584$	−6213.78	+	10762.6i	−0.440287	+	0.762600i
$585$	356.662	−	617.758i	0.0252071	−	0.0436601i
$586$	−14233.3	−	24652.9i	−1.00337	−	1.73788i
$587$	−10074.7			−0.708392			−0.354196	−	0.935171i	$-0.615245\pi$
$587$	−10074.7			−0.708392			−0.354196	+	0.935171i	$0.615245\pi$
$588$		0			0
$589$	−28493.1			−1.99328
$590$	−3482.06	−	6031.10i	−0.242973	−	0.420842i
$591$	8451.42	−	14638.3i	0.588231	−	1.01885i
$592$	5578.77	−	9662.71i	0.387307	−	0.670836i
$593$	−3693.62	−	6397.54i	−0.255782	−	0.443028i	0.709325	−	0.704881i	$-0.249000\pi$
$593$	−3693.62	−	6397.54i	−0.255782	−	0.443028i	−0.965108	+	0.261853i	$0.915666\pi$
$594$	12351.4			0.853172
$595$		0			0
$596$	12399.6			0.852194
$597$	−11488.3	−	19898.4i	−0.787581	−	1.36413i
$598$	−15529.0	+	26897.1i	−1.06192	+	1.83930i
$599$	−626.365	+	1084.90i	−0.0427255	+	0.0740027i	−0.886597	−	0.462542i	$-0.846937\pi$
$599$	−626.365	+	1084.90i	−0.0427255	+	0.0740027i	0.843872	+	0.536545i	$0.180271\pi$
$600$	710.422	+	1230.49i	0.0483381	+	0.0837240i
$601$	1800.81			0.122224			0.0611120	−	0.998131i	$-0.480535\pi$
$601$	1800.81			0.122224			0.0611120	+	0.998131i	$0.480535\pi$
$602$		0			0
$603$	168.792			0.0113992
$604$	−5101.73	−	8836.46i	−0.343686	−	0.595282i
$605$	−2353.97	+	4077.20i	−0.158186	+	0.273986i
$606$	5888.66	−	10199.5i	0.394737	−	0.683704i
$607$	1248.53	+	2162.51i	0.0834863	+	0.144602i	0.904745	−	0.425953i	$-0.140061\pi$
$607$	1248.53	+	2162.51i	0.0834863	+	0.144602i	−0.821259	+	0.570556i	$0.806728\pi$
$608$	33583.1			2.24009
$609$		0			0
$610$	7359.90			0.488514
$611$	5266.66	+	9122.12i	0.348717	+	0.603996i
$612$	333.166	−	577.061i	0.0220056	−	0.0381149i
$613$	9875.39	−	17104.7i	0.650674	−	1.12700i	−0.332286	−	0.943179i	$-0.607820\pi$
$613$	9875.39	−	17104.7i	0.650674	−	1.12700i	0.982960	−	0.183821i	$-0.0588468\pi$
$614$	−5769.10	−	9992.38i	−0.379189	−	0.656775i
$615$	4541.56			0.297778
$616$		0			0
$617$	16797.4			1.09601			0.548004	−	0.836476i	$-0.315388\pi$
$617$	16797.4			1.09601			0.548004	+	0.836476i	$0.315388\pi$
$618$	−8428.10	−	14597.9i	−0.548589	−	0.950184i
$619$	13273.7	−	22990.7i	0.861897	−	1.49285i	−0.00819917	−	0.999966i	$-0.502610\pi$
$619$	13273.7	−	22990.7i	0.861897	−	1.49285i	0.870096	−	0.492883i	$-0.164057\pi$
$620$	5555.81	−	9622.94i	0.359882	−	0.623333i
$621$	7312.75	+	12666.1i	0.472545	+	0.818472i
$622$	3693.73			0.238111
$623$		0			0
$624$	−12839.8			−0.823727
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−7230.32	+	12523.3i	−0.461632	+	0.799570i
$627$	−6725.79	+	11649.4i	−0.428393	+	0.741998i
$628$	−5426.47	−	9398.91i	−0.344808	−	0.597225i
$629$	9710.93			0.615580
$630$		0			0
$631$	5394.86			0.340358			0.170179	−	0.985413i	$-0.445565\pi$
$631$	5394.86			0.340358			0.170179	+	0.985413i	$0.445565\pi$
$632$	−7008.66	−	12139.3i	−0.441122	−	0.764046i
$633$	−12471.7	+	21601.5i	−0.783102	+	1.35637i
$634$	−16474.5	+	28534.7i	−1.03200	+	1.78747i
$635$	−5115.66	−	8860.58i	−0.319699	−	0.553735i
$636$	6805.01			0.424271
$637$		0			0
$638$	−24549.3			−1.52338
$639$	−315.736	−	546.871i	−0.0195467	−	0.0338558i
$640$	−3440.32	+	5958.80i	−0.212485	+	0.368035i
$641$	−1226.20	+	2123.85i	−0.0755572	+	0.130869i	−0.901328	−	0.433136i	$-0.857407\pi$
$641$	−1226.20	+	2123.85i	−0.0755572	+	0.130869i	0.825771	+	0.564005i	$0.190740\pi$
$642$	−6697.89	−	11601.1i	−0.411752	−	0.713175i
$643$	−7074.97			−0.433919			−0.216959	−	0.976181i	$-0.569614\pi$
$643$	−7074.97			−0.433919			−0.216959	+	0.976181i	$0.569614\pi$
$644$		0			0
$645$	−455.013			−0.0277769
$646$	9219.53	+	15968.7i	0.561513	+	0.972569i
$647$	1670.69	−	2893.71i	0.101517	−	0.175832i	−0.810793	−	0.585333i	$-0.800964\pi$
$647$	1670.69	−	2893.71i	0.101517	−	0.175832i	0.912310	+	0.409501i	$0.134297\pi$
$648$	3813.54	−	6605.25i	0.231189	−	0.400430i
$649$	3183.65	+	5514.25i	0.192557	+	0.333518i
$650$	−7697.89			−0.464517
$651$		0			0
$652$	−16651.8			−1.00021
$653$	11530.8	+	19971.9i	0.691019	+	1.19688i	0.971504	+	0.237022i	$0.0761712\pi$
$653$	11530.8	+	19971.9i	0.691019	+	1.19688i	−0.280486	+	0.959858i	$0.590495\pi$
$654$	45.1944	−	78.2790i	0.00270220	−	0.00468035i
$655$	−2850.79	+	4937.72i	−0.170061	+	0.294554i
$656$	3269.92	+	5663.68i	0.194618	+	0.337087i
$657$	−2186.65			−0.129847
$658$		0			0
$659$	1742.64			0.103010			0.0515049	−	0.998673i	$-0.483598\pi$
$659$	1742.64			0.103010			0.0515049	+	0.998673i	$0.483598\pi$
$660$	−2622.89	−	4542.98i	−0.154691	−	0.267932i
$661$	−6288.26	+	10891.6i	−0.370023	+	0.640898i	−0.989569	−	0.144062i	$-0.953983\pi$
$661$	−6288.26	+	10891.6i	−0.370023	+	0.640898i	0.619546	+	0.784960i	$0.287317\pi$
$662$	7169.27	−	12417.5i	0.420909	−	0.729035i
$663$	−5587.56	−	9677.94i	−0.327305	−	0.566908i
$664$	7312.51			0.427380
$665$		0			0
$666$	−2675.72			−0.155679
$667$	−14534.6	−	25174.7i	−0.843752	−	1.46142i
$668$	−6009.41	+	10408.6i	−0.348070	+	0.602875i
$669$	−9482.42	+	16424.0i	−0.548000	+	0.949163i
$670$	−910.764	−	1577.49i	−0.0525163	−	0.0909608i
$671$	−6729.17			−0.387149
$672$		0			0
$673$	−10680.8			−0.611760			−0.305880	−	0.952070i	$-0.598951\pi$
$673$	−10680.8			−0.611760			−0.305880	+	0.952070i	$0.598951\pi$
$674$	4821.64	+	8351.32i	0.275553	+	0.477271i
$675$	−1812.50	+	3139.34i	−0.103353	+	0.179012i
$676$	−15372.1	+	26625.2i	−0.874607	+	1.51486i
$677$	−14779.6	−	25599.0i	−0.839032	−	1.45325i	−0.890705	−	0.454582i	$-0.849789\pi$
$677$	−14779.6	−	25599.0i	−0.839032	−	1.45325i	0.0516726	−	0.998664i	$-0.483545\pi$
$678$	−30508.4			−1.72812
$679$		0			0
$680$	−1780.74			−0.100424
$681$	−9777.41	−	16935.0i	−0.550178	−	0.952936i
$682$	−8901.42	+	15417.7i	−0.499785	+	0.865652i
$683$	−5125.21	+	8877.13i	−0.287132	+	0.497327i	−0.973124	−	0.230282i	$-0.926035\pi$
$683$	−5125.21	+	8877.13i	−0.287132	+	0.497327i	0.685992	+	0.727609i	$0.259368\pi$
$684$	−1449.66	−	2510.88i	−0.0810366	−	0.140360i
$685$	2451.71			0.136752
$686$		0			0
$687$	1771.64			0.0983875
$688$	−327.609	−	567.436i	−0.0181540	−	0.0314437i
$689$	−4565.10	+	7906.99i	−0.252419	+	0.437202i
$690$	5442.48	−	9426.65i	0.300278	−	0.520096i
$691$	−4437.02	−	7685.14i	−0.244272	−	0.423092i	0.717655	−	0.696399i	$-0.245216\pi$
$691$	−4437.02	−	7685.14i	−0.244272	−	0.423092i	−0.961927	+	0.273307i	$0.911882\pi$
$692$	−27043.9			−1.48563
$693$		0			0
$694$	10915.1			0.597018
$695$	−7000.00	−	12124.4i	−0.382051	−	0.661731i
$696$	−8189.69	+	14185.0i	−0.446019	+	0.772528i
$697$	−2845.97	+	4929.36i	−0.154661	+	0.267881i
$698$	2786.39	+	4826.16i	0.151098	+	0.261709i
$699$	−32462.4			−1.75657
$700$		0			0
$701$	−22086.2			−1.18999			−0.594996	−	0.803729i	$-0.702846\pi$
$701$	−22086.2			−1.18999			−0.594996	+	0.803729i	$0.702846\pi$
$702$	22323.9	+	38666.1i	1.20023	+	2.07886i
$703$	21126.9	−	36592.8i	1.13345	−	1.96319i
$704$	7649.94	−	13250.1i	0.409542	−	0.709348i
$705$	−1845.81	−	3197.04i	−0.0986061	−	0.170791i
$706$	33534.3			1.78765
$707$		0			0
$708$	17154.9			0.910622
$709$	13939.4	+	24143.8i	0.738373	+	1.27890i	0.953228	+	0.302254i	$0.0977390\pi$
$709$	13939.4	+	24143.8i	0.738373	+	1.27890i	−0.214854	+	0.976646i	$0.568928\pi$
$710$	−3407.28	+	5901.59i	−0.180103	+	0.311948i
$711$	1233.19	−	2135.94i	0.0650465	−	0.112664i
$712$	6480.85	+	11225.2i	0.341124	+	0.590844i
$713$	−21080.6			−1.10726
$714$		0			0
$715$	7038.20			0.368131
$716$	6436.57	+	11148.5i	0.335958	+	0.581896i
$717$	−856.719	+	1483.88i	−0.0446231	+	0.0772895i
$718$	4929.88	−	8538.80i	0.256242	−	0.443824i
$719$	12931.6	+	22398.3i	0.670750	+	1.16177i	0.977692	+	0.210044i	$0.0673608\pi$
$719$	12931.6	+	22398.3i	0.670750	+	1.16177i	−0.306942	+	0.951728i	$0.599306\pi$
$720$	−360.000			−0.0186339
$721$		0			0
$722$	50623.4			2.60943
$723$	−5784.17	−	10018.5i	−0.297532	−	0.515340i
$724$	−16116.4	+	27914.4i	−0.827294	+	1.43292i
$725$	3602.47	−	6239.67i	0.184541	−	0.319635i
$726$	−10161.2	−	17599.7i	−0.519446	−	0.899708i
$727$	−29157.0			−1.48744			−0.743722	−	0.668489i	$-0.766941\pi$
$727$	−29157.0			−1.48744			−0.743722	+	0.668489i	$0.766941\pi$
$728$		0			0
$729$	20917.0			1.06269
$730$	11798.7	+	20435.9i	0.598204	+	1.03612i
$731$	285.134	−	493.866i	0.0144269	−	0.0249881i
$732$	−9064.91	+	15700.9i	−0.457717	+	0.792789i
$733$	5503.03	+	9531.52i	0.277297	+	0.480293i	0.970712	−	0.240246i	$-0.0772280\pi$
$733$	5503.03	+	9531.52i	0.277297	+	0.480293i	−0.693415	+	0.720539i	$0.743895\pi$
$734$	−46218.1			−2.32417
$735$		0			0
$736$	24846.4			1.24436
$737$	832.714	+	1442.30i	0.0416193	+	0.0720867i
$738$	784.169	−	1358.22i	0.0391133	−	0.0677463i
$739$	18607.2	−	32228.6i	0.926221	−	1.60426i	0.136634	−	0.990622i	$-0.456371\pi$
$739$	18607.2	−	32228.6i	0.926221	−	1.60426i	0.789586	−	0.613640i	$-0.210295\pi$
$740$	8238.95	+	14270.3i	0.409283	+	0.708900i
$741$	−48624.7			−2.41062
$742$		0			0
$743$	11214.5			0.553730			0.276865	−	0.960909i	$-0.410704\pi$
$743$	11214.5			0.553730			0.276865	+	0.960909i	$0.410704\pi$
$744$	5939.06	+	10286.7i	0.292656	+	0.506896i
$745$	2915.29	−	5049.43i	0.143367	−	0.248318i
$746$	1792.33	−	3104.40i	0.0879648	−	0.152359i
$747$	643.325	+	1114.27i	0.0315101	+	0.0545771i
$748$	6574.54			0.321375
$749$		0			0
$750$	2697.89			0.131351
$751$	−3482.63	−	6032.09i	−0.169218	−	0.293095i	0.768927	−	0.639337i	$-0.220791\pi$
$751$	−3482.63	−	6032.09i	−0.169218	−	0.293095i	−0.938145	+	0.346242i	$0.887458\pi$
$752$	2657.97	−	4603.74i	0.128891	−	0.223246i
$753$	−9973.22	+	17274.1i	−0.482662	+	0.835995i
$754$	−44370.3	−	76851.7i	−2.14307	−	3.71190i
$755$	−4797.91			−0.231276
$756$		0			0
$757$	−19352.8			−0.929180			−0.464590	−	0.885526i	$-0.653798\pi$
$757$	−19352.8			−0.929180			−0.464590	+	0.885526i	$0.653798\pi$
$758$	−11338.0	−	19638.0i	−0.543291	−	0.941007i
$759$	−4976.07	+	8618.81i	−0.237971	+	0.412178i
$760$	−3874.14	+	6710.21i	−0.184908	+	0.320270i
$761$	16191.8	+	28045.0i	0.771291	+	1.33591i	0.936856	+	0.349716i	$0.113722\pi$
$761$	16191.8	+	28045.0i	0.771291	+	1.33591i	−0.165565	+	0.986199i	$0.552945\pi$
$762$	44164.8			2.09963
$763$		0			0
$764$	−23059.7			−1.09198
$765$	−156.662	−	271.347i	−0.00740411	−	0.0128243i
$766$	−24267.9	+	42033.2i	−1.14469	+	1.98266i
$767$	−11508.2	+	19932.9i	−0.541772	+	0.938376i
$768$	655.940	+	1136.12i	0.0308193	+	0.0533805i
$769$	25353.9			1.18893			0.594463	−	0.804123i	$-0.297365\pi$
$769$	25353.9			1.18893			0.594463	+	0.804123i	$0.297365\pi$
$770$		0			0
$771$	11456.6			0.535148
$772$	−7924.32	−	13725.3i	−0.369433	−	0.639877i
$773$	13058.5	−	22618.0i	0.607610	−	1.05241i	−0.384023	−	0.923323i	$-0.625462\pi$
$773$	13058.5	−	22618.0i	0.607610	−	1.05241i	0.991633	−	0.129088i	$-0.0412049\pi$
$774$	−78.5647	+	136.078i	−0.00364852	+	0.00631941i
$775$	−2612.47	−	4524.93i	−0.121087	−	0.209729i
$776$	−16049.8			−0.742465
$777$		0			0
$778$	−36720

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.15831 - 3.73831i) q^{2} +(2.50000 - 4.33013i) q^{3} +(-5.31662 + 9.20866i) q^{4} +(2.50000 + 4.33013i) q^{5} -21.5831 q^{6} +11.3668 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-2.15831 - 3.73831i) q^{2} +(2.50000 - 4.33013i) q^{3} +(-5.31662 + 9.20866i) q^{4} +(2.50000 + 4.33013i) q^{5} -21.5831 q^{6} +11.3668 q^{8} +(1.00000 + 1.73205i) q^{9} +(10.7916 - 18.6915i) q^{10} +(-9.86675 + 17.0897i) q^{11} +(26.5831 + 46.0433i) q^{12} -71.3325 q^{13} +25.0000 q^{15} +(18.0000 + 31.1769i) q^{16} +(-15.6662 + 27.1347i) q^{17} +(4.31662 - 7.47661i) q^{18} +(68.1662 + 118.067i) q^{19} -53.1662 q^{20} +85.1821 q^{22} +(50.4327 + 87.3521i) q^{23} +(28.4169 - 49.2195i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(153.958 + 266.663i) q^{26} +145.000 q^{27} -288.198 q^{29} +(-53.9578 - 93.4577i) q^{30} +(-104.499 + 180.997i) q^{31} +(123.166 - 213.330i) q^{32} +(49.3338 + 85.4486i) q^{33} +135.251 q^{34} -21.2665 q^{36} +(-154.966 - 268.409i) q^{37} +(294.248 - 509.653i) q^{38} +(-178.331 + 308.879i) q^{39} +(28.4169 + 49.2195i) q^{40} +181.662 q^{41} -18.2005 q^{43} +(-104.916 - 181.719i) q^{44} +(-5.00000 + 8.66025i) q^{45} +(217.699 - 377.066i) q^{46} +(-73.8325 - 127.882i) q^{47} +180.000 q^{48} +107.916 q^{50} +(78.3312 + 135.674i) q^{51} +(379.248 - 656.877i) q^{52} +(63.9975 - 110.847i) q^{53} +(-312.955 - 542.054i) q^{54} -98.6675 q^{55} +681.662 q^{57} +(622.021 + 1077.37i) q^{58} +(161.332 - 279.436i) q^{59} +(-132.916 + 230.217i) q^{60} +(170.501 + 295.317i) q^{61} +902.164 q^{62} -775.325 q^{64} +(-178.331 - 308.879i) q^{65} +(212.955 - 368.849i) q^{66} +(42.1980 - 73.0891i) q^{67} +(-166.583 - 288.530i) q^{68} +504.327 q^{69} -315.736 q^{71} +(11.3668 + 19.6878i) q^{72} +(-546.662 + 946.847i) q^{73} +(-668.929 + 1158.62i) q^{74} +(62.5000 + 108.253i) q^{75} -1449.66 q^{76} +1539.58 q^{78} +(-616.593 - 1067.97i) q^{79} +(-90.0000 + 155.885i) q^{80} +(335.500 - 581.103i) q^{81} +(-392.084 - 679.110i) q^{82} +643.325 q^{83} -156.662 q^{85} +(39.2824 + 68.0391i) q^{86} +(-720.495 + 1247.93i) q^{87} +(-112.153 + 194.255i) q^{88} +(570.159 + 987.544i) q^{89} +43.1662 q^{90} -1072.53 q^{92} +(522.494 + 904.986i) q^{93} +(-318.707 + 552.017i) q^{94} +(-340.831 + 590.337i) q^{95} +(-615.831 - 1066.65i) q^{96} -1411.99 q^{97} -39.4670 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 10 * q^3 - 8 * q^4 + 10 * q^5 - 20 * q^6 + 72 * q^8 + 4 * q^9	\( 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9} + 10 q^{10} - 66 q^{11} + 40 q^{12} - 20 q^{13} + 100 q^{15} + 72 q^{16} + 70 q^{17} + 4 q^{18} + 140 q^{19} - 80 q^{20} - 44 q^{22} + 16 q^{23} + 180 q^{24} - 50 q^{25} + 450 q^{26} + 580 q^{27} - 516 q^{29} - 50 q^{30} - 20 q^{31} + 360 q^{32} + 330 q^{33} + 740 q^{34} - 32 q^{36} - 328 q^{37} + 580 q^{38} - 50 q^{39} + 180 q^{40} - 600 q^{41} - 232 q^{43} - 88 q^{44} - 20 q^{45} + 632 q^{46} - 30 q^{47} + 720 q^{48} + 100 q^{50} - 350 q^{51} + 920 q^{52} - 540 q^{53} - 290 q^{54} - 660 q^{55} + 1400 q^{57} + 1314 q^{58} + 380 q^{59} - 200 q^{60} + 1080 q^{61} + 2680 q^{62} - 448 q^{64} - 50 q^{65} - 110 q^{66} - 468 q^{67} - 600 q^{68} + 160 q^{69} - 2112 q^{71} + 72 q^{72} - 860 q^{73} - 1296 q^{74} + 250 q^{75} - 2880 q^{76} + 4500 q^{78} - 158 q^{79} - 360 q^{80} + 1342 q^{81} - 1900 q^{82} - 80 q^{83} + 700 q^{85} - 148 q^{86} - 1290 q^{87} - 1364 q^{88} - 240 q^{89} + 40 q^{90} - 2592 q^{92} + 100 q^{93} - 910 q^{94} - 700 q^{95} - 1800 q^{96} - 3260 q^{97} - 264 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 10 * q^3 - 8 * q^4 + 10 * q^5 - 20 * q^6 + 72 * q^8 + 4 * q^9 + 10 * q^10 - 66 * q^11 + 40 * q^12 - 20 * q^13 + 100 * q^15 + 72 * q^16 + 70 * q^17 + 4 * q^18 + 140 * q^19 - 80 * q^20 - 44 * q^22 + 16 * q^23 + 180 * q^24 - 50 * q^25 + 450 * q^26 + 580 * q^27 - 516 * q^29 - 50 * q^30 - 20 * q^31 + 360 * q^32 + 330 * q^33 + 740 * q^34 - 32 * q^36 - 328 * q^37 + 580 * q^38 - 50 * q^39 + 180 * q^40 - 600 * q^41 - 232 * q^43 - 88 * q^44 - 20 * q^45 + 632 * q^46 - 30 * q^47 + 720 * q^48 + 100 * q^50 - 350 * q^51 + 920 * q^52 - 540 * q^53 - 290 * q^54 - 660 * q^55 + 1400 * q^57 + 1314 * q^58 + 380 * q^59 - 200 * q^60 + 1080 * q^61 + 2680 * q^62 - 448 * q^64 - 50 * q^65 - 110 * q^66 - 468 * q^67 - 600 * q^68 + 160 * q^69 - 2112 * q^71 + 72 * q^72 - 860 * q^73 - 1296 * q^74 + 250 * q^75 - 2880 * q^76 + 4500 * q^78 - 158 * q^79 - 360 * q^80 + 1342 * q^81 - 1900 * q^82 - 80 * q^83 + 700 * q^85 - 148 * q^86 - 1290 * q^87 - 1364 * q^88 - 240 * q^89 + 40 * q^90 - 2592 * q^92 + 100 * q^93 - 910 * q^94 - 700 * q^95 - 1800 * q^96 - 3260 * q^97 - 264 * q^99

Introduction

L-functions

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