LMFDB - Embedded newform 230.3.d.a.91.13

Newspace parameters

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.d (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
Defining polynomial:	$ x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 $ x^16 + 78x^14 + 2165x^12 + 28310x^10 + 184804x^8 + 569634x^6 + 696037x^4 + 285578*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.13
Root			$-2.26343i$ of defining polynomial
Character	$\chi$	$=$	230.91
Dual form			230.3.d.a.91.14

$q$-expansion

$f(q)$	$=$	$q+1.41421 q^{2} +1.43837 q^{3} +2.00000 q^{4} -2.23607i q^{5} +2.03417 q^{6} -10.1866i q^{7} +2.82843 q^{8} -6.93108 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +1.43837 q^{3} +2.00000 q^{4} -2.23607i q^{5} +2.03417 q^{6} -10.1866i q^{7} +2.82843 q^{8} -6.93108 q^{9} -3.16228i q^{10} -13.0237i q^{11} +2.87675 q^{12} +23.2154 q^{13} -14.4060i q^{14} -3.21630i q^{15} +4.00000 q^{16} +28.2228i q^{17} -9.80202 q^{18} +11.6665i q^{19} -4.47214i q^{20} -14.6521i q^{21} -18.4183i q^{22} +(-17.3999 + 15.0414i) q^{23} +4.06834 q^{24} -5.00000 q^{25} +32.8315 q^{26} -22.9149 q^{27} -20.3731i q^{28} +42.4794 q^{29} -4.54854i q^{30} +18.7683 q^{31} +5.65685 q^{32} -18.7330i q^{33} +39.9131i q^{34} -22.7778 q^{35} -13.8622 q^{36} +1.14094i q^{37} +16.4989i q^{38} +33.3924 q^{39} -6.32456i q^{40} -72.8198 q^{41} -20.7212i q^{42} +4.96573i q^{43} -26.0474i q^{44} +15.4984i q^{45} +(-24.6071 + 21.2718i) q^{46} -0.813360 q^{47} +5.75350 q^{48} -54.7661 q^{49} -7.07107 q^{50} +40.5950i q^{51} +46.4308 q^{52} -26.7286i q^{53} -32.4065 q^{54} -29.1219 q^{55} -28.8120i q^{56} +16.7808i q^{57} +60.0750 q^{58} +94.0845 q^{59} -6.43261i q^{60} +74.5293i q^{61} +26.5423 q^{62} +70.6039i q^{63} +8.00000 q^{64} -51.9112i q^{65} -26.4925i q^{66} -80.0906i q^{67} +56.4456i q^{68} +(-25.0275 + 21.6352i) q^{69} -32.2127 q^{70} -83.5303 q^{71} -19.6040 q^{72} -8.98897 q^{73} +1.61354i q^{74} -7.19187 q^{75} +23.3330i q^{76} -132.667 q^{77} +47.2241 q^{78} +80.2841i q^{79} -8.94427i q^{80} +29.4195 q^{81} -102.983 q^{82} +94.6451i q^{83} -29.3042i q^{84} +63.1081 q^{85} +7.02261i q^{86} +61.1014 q^{87} -36.8367i q^{88} +136.812i q^{89} +21.9180i q^{90} -236.485i q^{91} +(-34.7997 + 30.0829i) q^{92} +26.9958 q^{93} -1.15026 q^{94} +26.0871 q^{95} +8.13668 q^{96} +2.32666i q^{97} -77.4509 q^{98} +90.2684i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 + 24 * q^13 + 64 * q^16 - 32 * q^18 + 4 * q^23 - 16 * q^24 - 80 * q^25 + 96 * q^26 - 96 * q^27 - 108 * q^29 - 116 * q^31 + 60 * q^35 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 - 128 * q^47 - 28 * q^49 + 48 * q^52 + 224 * q^54 + 160 * q^58 + 204 * q^59 + 64 * q^62 + 128 * q^64 - 268 * q^69 - 120 * q^70 + 236 * q^71 - 64 * q^72 - 112 * q^73 - 936 * q^77 - 432 * q^78 - 136 * q^81 - 64 * q^82 + 60 * q^85 - 152 * q^87 + 8 * q^92 + 856 * q^93 - 216 * q^94 - 160 * q^95 - 32 * q^96 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	1.43837			0.479458			0.239729	−	0.970840i	$-0.422941\pi$
$3$	1.43837			0.479458			0.239729	+	0.970840i	$0.422941\pi$
$4$	2.00000			0.500000
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	2.03417			0.339028
$7$		−	10.1866i		−	1.45522i	−0.685989	−	0.727612i	$-0.740630\pi$
$7$		−	10.1866i		−	1.45522i	0.685989	−	0.727612i	$-0.259370\pi$
$8$	2.82843			0.353553
$9$	−6.93108			−0.770120
$10$		−	3.16228i		−	0.316228i
$11$		−	13.0237i		−	1.18397i	−0.805947	−	0.591987i	$-0.798343\pi$
$11$		−	13.0237i		−	1.18397i	0.805947	−	0.591987i	$-0.201657\pi$
$12$	2.87675			0.239729
$13$	23.2154			1.78580			0.892900	−	0.450255i	$-0.148667\pi$
$13$	23.2154			1.78580			0.892900	+	0.450255i	$0.148667\pi$
$14$		−	14.4060i		−	1.02900i
$15$		−	3.21630i		−	0.214420i
$16$	4.00000			0.250000
$17$			28.2228i			1.66016i	0.557641	+	0.830082i	$0.311707\pi$
$17$			28.2228i			1.66016i	−0.557641	+	0.830082i	$0.688293\pi$
$18$	−9.80202			−0.544557
$19$			11.6665i			0.614027i	0.951705	+	0.307013i	$0.0993297\pi$
$19$			11.6665i			0.614027i	−0.951705	+	0.307013i	$0.900670\pi$
$20$		−	4.47214i		−	0.223607i
$21$		−	14.6521i		−	0.697719i
$22$		−	18.4183i		−	0.837197i
$23$	−17.3999	+	15.0414i	−0.756516	+	0.653976i
$23$	−17.3999	+	15.0414i	−0.756516	+	0.653976i
$24$	4.06834			0.169514
$25$	−5.00000			−0.200000
$26$	32.8315			1.26275
$27$	−22.9149			−0.848699
$28$		−	20.3731i		−	0.727612i
$29$	42.4794			1.46481			0.732404	−	0.680870i	$-0.238398\pi$
$29$	42.4794			1.46481			0.732404	+	0.680870i	$0.238398\pi$
$30$		−	4.54854i		−	0.151618i
$31$	18.7683			0.605428			0.302714	−	0.953082i	$-0.402107\pi$
$31$	18.7683			0.605428			0.302714	+	0.953082i	$0.402107\pi$
$32$	5.65685			0.176777
$33$		−	18.7330i		−	0.567667i
$34$			39.9131i			1.17391i
$35$	−22.7778			−0.650796
$36$	−13.8622			−0.385060
$37$			1.14094i			0.0308363i	0.999881	+	0.0154182i	$0.00490795\pi$
$37$			1.14094i			0.0308363i	−0.999881	+	0.0154182i	$0.995092\pi$
$38$			16.4989i			0.434183i
$39$	33.3924			0.856217
$40$		−	6.32456i		−	0.158114i
$41$	−72.8198			−1.77609			−0.888046	−	0.459755i	$-0.847937\pi$
$41$	−72.8198			−1.77609			−0.888046	+	0.459755i	$0.847937\pi$
$42$		−	20.7212i		−	0.493362i
$43$			4.96573i			0.115482i	0.998332	+	0.0577411i	$0.0183898\pi$
$43$			4.96573i			0.115482i	−0.998332	+	0.0577411i	$0.981610\pi$
$44$		−	26.0474i		−	0.591987i
$45$			15.4984i			0.344408i
$46$	−24.6071	+	21.2718i	−0.534937	+	0.462431i
$47$	−0.813360			−0.0173055			−0.00865277	−	0.999963i	$-0.502754\pi$
$47$	−0.813360			−0.0173055			−0.00865277	+	0.999963i	$0.502754\pi$
$48$	5.75350			0.119865
$49$	−54.7661			−1.11768
$50$	−7.07107			−0.141421
$51$			40.5950i			0.795980i
$52$	46.4308			0.892900
$53$		−	26.7286i		−	0.504313i	−0.967686	−	0.252157i	$-0.918860\pi$
$53$		−	26.7286i		−	0.504313i	0.967686	−	0.252157i	$-0.0811398\pi$
$54$	−32.4065			−0.600121
$55$	−29.1219			−0.529490
$56$		−	28.8120i		−	0.514499i
$57$			16.7808i			0.294400i
$58$	60.0750			1.03578
$59$	94.0845			1.59465			0.797326	−	0.603549i	$-0.206247\pi$
$59$	94.0845			1.59465			0.797326	+	0.603549i	$0.206247\pi$
$60$		−	6.43261i		−	0.107210i
$61$			74.5293i			1.22179i	0.791711	+	0.610896i	$0.209191\pi$
$61$			74.5293i			1.22179i	−0.791711	+	0.610896i	$0.790809\pi$
$62$	26.5423			0.428102
$63$			70.6039i			1.12070i
$64$	8.00000			0.125000
$65$		−	51.9112i		−	0.798634i
$66$		−	26.4925i		−	0.401401i
$67$		−	80.0906i		−	1.19538i	−0.801727	−	0.597691i	$-0.796085\pi$
$67$		−	80.0906i		−	1.19538i	0.801727	−	0.597691i	$-0.203915\pi$
$68$			56.4456i			0.830082i
$69$	−25.0275	+	21.6352i	−0.362718	+	0.313554i
$70$	−32.2127			−0.460182
$71$	−83.5303			−1.17648			−0.588241	−	0.808686i	$-0.700179\pi$
$71$	−83.5303			−1.17648			−0.588241	+	0.808686i	$0.700179\pi$
$72$	−19.6040			−0.272278
$73$	−8.98897			−0.123137			−0.0615683	−	0.998103i	$-0.519610\pi$
$73$	−8.98897			−0.123137			−0.0615683	+	0.998103i	$0.519610\pi$
$74$			1.61354i			0.0218046i
$75$	−7.19187			−0.0958917
$76$			23.3330i			0.307013i
$77$	−132.667			−1.72295
$78$	47.2241			0.605437
$79$			80.2841i			1.01626i	0.861282	+	0.508128i	$0.169662\pi$
$79$			80.2841i			1.01626i	−0.861282	+	0.508128i	$0.830338\pi$
$80$		−	8.94427i		−	0.111803i
$81$	29.4195			0.363204
$82$	−102.983			−1.25589
$83$			94.6451i			1.14030i	0.821540	+	0.570151i	$0.193115\pi$
$83$			94.6451i			1.14030i	−0.821540	+	0.570151i	$0.806885\pi$
$84$		−	29.3042i		−	0.348859i
$85$	63.1081			0.742448
$86$			7.02261i			0.0816582i
$87$	61.1014			0.702315
$88$		−	36.8367i		−	0.418598i
$89$			136.812i			1.53722i	0.639720	+	0.768608i	$0.279050\pi$
$89$			136.812i			1.53722i	−0.639720	+	0.768608i	$0.720950\pi$
$90$			21.9180i			0.243533i
$91$		−	236.485i		−	2.59874i
$92$	−34.7997	+	30.0829i	−0.378258	+	0.326988i
$93$	26.9958			0.290277
$94$	−1.15026			−0.0122369
$95$	26.0871			0.274601
$96$	8.13668			0.0847571
$97$			2.32666i			0.0239862i	0.999928	+	0.0119931i	$0.00381761\pi$
$97$			2.32666i			0.0239862i	−0.999928	+	0.0119931i	$0.996182\pi$
$98$	−77.4509			−0.790316
$99$			90.2684i			0.911802i
$100$	−10.0000			−0.100000
$101$	12.9918			0.128632			0.0643161	−	0.997930i	$-0.479513\pi$
$101$	12.9918			0.128632			0.0643161	+	0.997930i	$0.479513\pi$
$102$			57.4100i			0.562843i
$103$		−	90.3165i		−	0.876859i	−0.898766	−	0.438430i	$-0.855535\pi$
$103$		−	90.3165i		−	0.876859i	0.898766	−	0.438430i	$-0.144465\pi$
$104$	65.6631			0.631376
$105$	−32.7631			−0.312029
$106$		−	37.7999i		−	0.356603i
$107$		−	185.173i		−	1.73059i	−0.501264	−	0.865294i	$-0.667131\pi$
$107$		−	185.173i		−	1.73059i	0.501264	−	0.865294i	$-0.332869\pi$
$108$	−45.8297			−0.424349
$109$		−	13.8248i		−	0.126833i	−0.997987	−	0.0634167i	$-0.979800\pi$
$109$		−	13.8248i		−	0.126833i	0.997987	−	0.0634167i	$-0.0201997\pi$
$110$	−41.1846			−0.374406
$111$			1.64110i			0.0147847i
$112$		−	40.7463i		−	0.363806i
$113$			178.530i			1.57991i	0.613164	+	0.789956i	$0.289897\pi$
$113$			178.530i			1.57991i	−0.613164	+	0.789956i	$0.710103\pi$
$114$			23.7317i			0.208172i
$115$	33.6337	+	38.9073i	0.292467	+	0.338324i
$116$	84.9589			0.732404
$117$	−160.908			−1.37528
$118$	133.056			1.12759
$119$	287.493			2.41591
$120$		−	9.09708i		−	0.0758090i
$121$	−48.6174			−0.401797
$122$			105.400i			0.863938i
$123$	−104.742			−0.851562
$124$	37.5365			0.302714
$125$			11.1803i			0.0894427i
$126$			99.8489i			0.792452i
$127$	−112.959			−0.889442			−0.444721	−	0.895669i	$-0.646697\pi$
$127$	−112.959			−0.889442			−0.444721	+	0.895669i	$0.646697\pi$
$128$	11.3137			0.0883883
$129$			7.14258i			0.0553689i
$130$		−	73.4135i		−	0.564720i
$131$	−12.1419			−0.0926860			−0.0463430	−	0.998926i	$-0.514757\pi$
$131$	−12.1419			−0.0926860			−0.0463430	+	0.998926i	$0.514757\pi$
$132$		−	37.4660i		−	0.283833i
$133$	118.842			0.893546
$134$		−	113.265i		−	0.845263i
$135$			51.2392i			0.379550i
$136$			79.8261i			0.586957i
$137$		−	170.543i		−	1.24484i	−0.782685	−	0.622418i	$-0.786150\pi$
$137$		−	170.543i		−	1.24484i	0.782685	−	0.622418i	$-0.213850\pi$
$138$	−35.3943	+	30.5968i	−0.256480	+	0.221716i
$139$	38.5478			0.277322			0.138661	−	0.990340i	$-0.455720\pi$
$139$	38.5478			0.277322			0.138661	+	0.990340i	$0.455720\pi$
$140$	−45.5557			−0.325398
$141$	−1.16992			−0.00829728
$142$	−118.130			−0.831899
$143$		−	302.351i		−	2.11434i
$144$	−27.7243			−0.192530
$145$		−	94.9869i		−	0.655082i
$146$	−12.7123			−0.0870707
$147$	−78.7742			−0.535879
$148$			2.28189i			0.0154182i
$149$			81.4125i			0.546393i	0.961958	+	0.273196i	$0.0880808\pi$
$149$			81.4125i			0.546393i	−0.961958	+	0.273196i	$0.911919\pi$
$150$	−10.1708			−0.0678056
$151$	159.680			1.05748			0.528742	−	0.848782i	$-0.322664\pi$
$151$	159.680			1.05748			0.528742	+	0.848782i	$0.322664\pi$
$152$			32.9979i			0.217091i
$153$		−	195.614i		−	1.27853i
$154$	−187.619			−1.21831
$155$		−	41.9671i		−	0.270755i
$156$	66.7849			0.428108
$157$		−	38.5953i		−	0.245830i	−0.992417	−	0.122915i	$-0.960776\pi$
$157$		−	38.5953i		−	0.245830i	0.992417	−	0.122915i	$-0.0392242\pi$
$158$			113.539i			0.718601i
$159$		−	38.4457i		−	0.241797i
$160$		−	12.6491i		−	0.0790569i
$161$	153.221	+	177.245i	0.951681	+	1.10090i
$162$	41.6055			0.256824
$163$	150.291			0.922028			0.461014	−	0.887393i	$-0.347486\pi$
$163$	150.291			0.922028			0.461014	+	0.887393i	$0.347486\pi$
$164$	−145.640			−0.888046
$165$	−41.8883			−0.253868
$166$			133.848i			0.806316i
$167$	27.7604			0.166230			0.0831149	−	0.996540i	$-0.473513\pi$
$167$	27.7604			0.166230			0.0831149	+	0.996540i	$0.473513\pi$
$168$		−	41.4424i		−	0.246681i
$169$	369.955			2.18908
$170$	89.2483			0.524990
$171$		−	80.8615i		−	0.472874i
$172$			9.93146i			0.0577411i
$173$	−24.0064			−0.138765			−0.0693826	−	0.997590i	$-0.522103\pi$
$173$	−24.0064			−0.138765			−0.0693826	+	0.997590i	$0.522103\pi$
$174$	86.4104			0.496611
$175$			50.9328i			0.291045i
$176$		−	52.0949i		−	0.295994i
$177$	135.329			0.764569
$178$			193.482i			1.08698i
$179$	−201.178			−1.12390			−0.561949	−	0.827172i	$-0.689948\pi$
$179$	−201.178			−1.12390			−0.561949	+	0.827172i	$0.689948\pi$
$180$			30.9967i			0.172204i
$181$		−	202.358i		−	1.11800i	−0.829168	−	0.558999i	$-0.811186\pi$
$181$		−	202.358i		−	1.11800i	0.829168	−	0.558999i	$-0.188814\pi$
$182$		−	334.441i		−	1.83759i
$183$			107.201i			0.585798i
$184$	−49.2142	+	42.5436i	−0.267469	+	0.231215i
$185$	2.55123			0.0137904
$186$	38.1778			0.205257
$187$	367.566			1.96559
$188$	−1.62672			−0.00865277
$189$			233.424i			1.23505i
$190$	36.8927			0.194172
$191$			111.302i			0.582735i	0.956611	+	0.291368i	$0.0941103\pi$
$191$			111.302i			0.582735i	−0.956611	+	0.291368i	$0.905890\pi$
$192$	11.5070			0.0599323
$193$	−164.081			−0.850163			−0.425081	−	0.905155i	$-0.639754\pi$
$193$	−164.081			−0.850163			−0.425081	+	0.905155i	$0.639754\pi$
$194$			3.29040i			0.0169608i
$195$		−	74.6678i		−	0.382912i
$196$	−109.532			−0.558838
$197$	−329.562			−1.67290			−0.836451	−	0.548042i	$-0.815373\pi$
$197$	−329.562			−1.67290			−0.836451	+	0.548042i	$0.815373\pi$
$198$			127.659i			0.644742i
$199$		−	337.886i		−	1.69792i	−0.528455	−	0.848961i	$-0.677229\pi$
$199$		−	337.886i		−	1.69792i	0.528455	−	0.848961i	$-0.322771\pi$
$200$	−14.1421			−0.0707107
$201$		−	115.200i		−	0.573136i
$202$	18.3732			0.0909566
$203$		−	432.720i		−	2.13162i
$204$			81.1899i			0.397990i
$205$			162.830i			0.794292i
$206$		−	127.727i		−	0.620033i
$207$	120.600	−	104.253i	0.582608	−	0.503640i
$208$	92.8616			0.446450
$209$	151.941			0.726992
$210$	−46.3340			−0.220638
$211$	111.656			0.529173			0.264587	−	0.964362i	$-0.414765\pi$
$211$	111.656			0.529173			0.264587	+	0.964362i	$0.414765\pi$
$212$		−	53.4572i		−	0.252157i
$213$	−120.148			−0.564074
$214$		−	261.874i		−	1.22371i
$215$	11.1037			0.0516452
$216$	−64.8130			−0.300060
$217$		−	191.184i		−	0.881032i
$218$		−	19.5513i		−	0.0896847i
$219$	−12.9295			−0.0590389
$220$	−58.2439			−0.264745
$221$			655.204i			2.96472i
$222$			2.32087i			0.0104544i
$223$	−363.545			−1.63025			−0.815123	−	0.579288i	$-0.803331\pi$
$223$	−363.545			−1.63025			−0.815123	+	0.579288i	$0.803331\pi$
$224$		−	57.6239i		−	0.257250i
$225$	34.6554			0.154024
$226$			252.480i			1.11717i
$227$			11.3368i			0.0499418i	0.999688	+	0.0249709i	$0.00794931\pi$
$227$			11.3368i			0.0499418i	−0.999688	+	0.0249709i	$0.992051\pi$
$228$			33.5616i			0.147200i
$229$		−	112.509i		−	0.491306i	−0.969358	−	0.245653i	$-0.920998\pi$
$229$		−	112.509i		−	0.491306i	0.969358	−	0.245653i	$-0.0790024\pi$
$230$	47.5652	+	55.0232i	0.206805	+	0.239231i
$231$	−190.825			−0.826082
$232$	120.150			0.517888
$233$	−381.634			−1.63791			−0.818957	−	0.573855i	$-0.805447\pi$
$233$	−381.634			−1.63791			−0.818957	+	0.573855i	$0.805447\pi$
$234$	−227.558			−0.972470
$235$			1.81873i			0.00773927i
$236$	188.169			0.797326
$237$			115.479i			0.487252i
$238$	406.577			1.70831
$239$	139.296			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$239$	139.296			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$240$		−	12.8652i		−	0.0536051i
$241$		−	82.3347i		−	0.341638i	−0.985302	−	0.170819i	$-0.945359\pi$
$241$		−	82.3347i		−	0.341638i	0.985302	−	0.170819i	$-0.0546413\pi$
$242$	−68.7554			−0.284113
$243$	248.550			1.02284
$244$			149.059i			0.610896i
$245$			122.461i			0.499840i
$246$	−148.128			−0.602145
$247$			270.843i			1.09653i
$248$	53.0846			0.214051
$249$			136.135i			0.546728i
$250$			15.8114i			0.0632456i
$251$		−	323.924i		−	1.29054i	−0.763957	−	0.645268i	$-0.776746\pi$
$251$		−	323.924i		−	1.29054i	0.763957	−	0.645268i	$-0.223254\pi$
$252$			141.208i			0.560348i
$253$	195.896	+	226.611i	0.774291	+	0.895695i
$254$	−159.748			−0.628931
$255$	90.7731			0.355973
$256$	16.0000			0.0625000
$257$	−250.796			−0.975858			−0.487929	−	0.872883i	$-0.662248\pi$
$257$	−250.796			−0.975858			−0.487929	+	0.872883i	$0.662248\pi$
$258$			10.1011i			0.0391517i
$259$	11.6223			0.0448737
$260$		−	103.822i		−	0.399317i
$261$	−294.428			−1.12808
$262$	−17.1712			−0.0655389
$263$			276.878i			1.05277i	0.850247	+	0.526384i	$0.176452\pi$
$263$			276.878i			1.05277i	−0.850247	+	0.526384i	$0.823548\pi$
$264$		−	52.9849i		−	0.200700i
$265$	−59.7670			−0.225536
$266$	168.067			0.631833
$267$			196.787i			0.737031i
$268$		−	160.181i		−	0.597691i
$269$	−78.1002			−0.290335			−0.145168	−	0.989407i	$-0.546372\pi$
$269$	−78.1002			−0.290335			−0.145168	+	0.989407i	$0.546372\pi$
$270$			72.4632i			0.268382i
$271$	331.551			1.22343			0.611717	−	0.791076i	$-0.290479\pi$
$271$	331.551			1.22343			0.611717	+	0.791076i	$0.290479\pi$
$272$			112.891i			0.415041i
$273$		−	340.154i		−	1.24599i
$274$		−	241.184i		−	0.880232i
$275$			65.1186i			0.236795i
$276$	−50.0550	+	43.2705i	−0.181359	+	0.156777i
$277$	−355.974			−1.28511			−0.642553	−	0.766241i	$-0.722125\pi$
$277$	−355.974			−1.28511			−0.642553	+	0.766241i	$0.722125\pi$
$278$	54.5148			0.196097
$279$	−130.084			−0.466252
$280$	−64.4255			−0.230091
$281$			391.437i			1.39301i	0.717550	+	0.696507i	$0.245264\pi$
$281$			391.437i			1.39301i	−0.717550	+	0.696507i	$0.754736\pi$
$282$	−1.65451			−0.00586706
$283$			133.616i			0.472143i	0.971736	+	0.236071i	$0.0758599\pi$
$283$			133.616i			0.472143i	−0.971736	+	0.236071i	$0.924140\pi$
$284$	−167.061			−0.588241
$285$	37.5230			0.131660
$286$		−	427.589i		−	1.49507i
$287$			741.783i			2.58461i
$288$	−39.2081			−0.136139
$289$	−507.527			−1.75615
$290$		−	134.332i		−	0.463213i
$291$			3.34661i			0.0115004i
$292$	−17.9779			−0.0615683
$293$			533.454i			1.82066i	0.413880	+	0.910331i	$0.364173\pi$
$293$			533.454i			1.82066i	−0.413880	+	0.910331i	$0.635827\pi$
$294$	−111.403			−0.378923
$295$		−	210.379i		−	0.713150i
$296$			3.22708i			0.0109023i
$297$			298.437i			1.00484i
$298$			115.135i			0.386358i
$299$	−403.945	+	349.193i	−1.35099	+	1.16787i
$300$	−14.3837			−0.0479458
$301$	50.5837			0.168052
$302$	225.822			0.747755
$303$	18.6871			0.0616737
$304$			46.6660i			0.153507i
$305$	166.653			0.546402
$306$		−	276.641i		−	0.904054i
$307$	282.656			0.920705			0.460352	−	0.887736i	$-0.347723\pi$
$307$	282.656			0.920705			0.460352	+	0.887736i	$0.347723\pi$
$308$	−265.334			−0.861474
$309$		−	129.909i		−	0.420417i
$310$		−	59.3504i		−	0.191453i
$311$	−193.206			−0.621241			−0.310620	−	0.950534i	$-0.600537\pi$
$311$	−193.206			−0.621241			−0.310620	+	0.950534i	$0.600537\pi$
$312$	94.4481			0.302718
$313$		−	399.279i		−	1.27565i	−0.770181	−	0.637826i	$-0.779834\pi$
$313$		−	399.279i		−	1.27565i	0.770181	−	0.637826i	$-0.220166\pi$
$314$		−	54.5820i		−	0.173828i
$315$	157.875			0.501191
$316$			160.568i			0.508128i
$317$	−36.5297			−0.115236			−0.0576178	−	0.998339i	$-0.518350\pi$
$317$	−36.5297			−0.115236			−0.0576178	+	0.998339i	$0.518350\pi$
$318$		−	54.3705i		−	0.170976i
$319$		−	553.241i		−	1.73430i
$320$		−	17.8885i		−	0.0559017i
$321$		−	266.348i		−	0.829745i
$322$	216.687	+	250.662i	0.672940	+	0.778453i
$323$	−329.262			−1.01939
$324$	58.8391			0.181602
$325$	−116.077			−0.357160
$326$	212.543			0.651973
$327$		−	19.8853i		−	0.0608113i
$328$	−205.965			−0.627943
$329$			8.28534i			0.0251834i
$330$	−59.2389			−0.179512
$331$	85.9406			0.259639			0.129820	−	0.991538i	$-0.458560\pi$
$331$	85.9406			0.259639			0.129820	+	0.991538i	$0.458560\pi$
$332$			189.290i			0.570151i
$333$		−	7.90797i		−	0.0237476i
$334$	39.2591			0.117542
$335$	−179.088			−0.534591
$336$		−	58.6084i		−	0.174430i
$337$		−	548.713i		−	1.62823i	−0.580706	−	0.814114i	$-0.697223\pi$
$337$		−	548.713i		−	1.62823i	0.580706	−	0.814114i	$-0.302777\pi$
$338$	523.195			1.54791
$339$			256.793i			0.757502i
$340$	126.216			0.371224
$341$		−	244.433i		−	0.716811i
$342$		−	114.355i		−	0.334373i
$343$			58.7366i			0.171244i
$344$			14.0452i			0.0408291i
$345$	48.3778	+	55.9632i	0.140226	+	0.162212i
$346$	−33.9502			−0.0981219
$347$	62.0036			0.178685			0.0893424	−	0.996001i	$-0.471523\pi$
$347$	62.0036			0.178685			0.0893424	+	0.996001i	$0.471523\pi$
$348$	122.203			0.351157
$349$	−131.393			−0.376485			−0.188242	−	0.982123i	$-0.560279\pi$
$349$	−131.393			−0.376485			−0.188242	+	0.982123i	$0.560279\pi$
$350$			72.0299i			0.205800i
$351$	−531.978			−1.51561
$352$		−	73.6733i		−	0.209299i
$353$	−176.990			−0.501389			−0.250694	−	0.968066i	$-0.580659\pi$
$353$	−176.990			−0.501389			−0.250694	+	0.968066i	$0.580659\pi$
$354$	191.384			0.540632
$355$			186.779i			0.526139i
$356$			273.624i			0.768608i
$357$	413.523			1.15833
$358$	−284.508			−0.794716
$359$			187.851i			0.523260i	0.965168	+	0.261630i	$0.0842601\pi$
$359$			187.851i			0.523260i	−0.965168	+	0.261630i	$0.915740\pi$
$360$			43.8360i			0.121767i
$361$	224.893			0.622971
$362$		−	286.177i		−	0.790544i
$363$	−69.9300			−0.192645
$364$		−	472.970i		−	1.29937i
$365$			20.0999i			0.0550684i
$366$			151.605i			0.414222i
$367$			128.510i			0.350162i	0.984554	+	0.175081i	$0.0560188\pi$
$367$			128.510i			0.350162i	−0.984554	+	0.175081i	$0.943981\pi$
$368$	−69.5994	+	60.1658i	−0.189129	+	0.163494i
$369$	504.719			1.36780
$370$	3.60798			0.00975130
$371$	−272.273			−0.733888
$372$	53.9916			0.145139
$373$			79.2928i			0.212581i	0.994335	+	0.106291i	$0.0338974\pi$
$373$			79.2928i			0.212581i	−0.994335	+	0.106291i	$0.966103\pi$
$374$	519.817			1.38988
$375$			16.0815i			0.0428841i
$376$	−2.30053			−0.00611843
$377$	986.177			2.61585
$378$			330.111i			0.873309i
$379$			402.569i			1.06219i	0.847313	+	0.531094i	$0.178219\pi$
$379$			402.569i			1.06219i	−0.847313	+	0.531094i	$0.821781\pi$
$380$	52.1742			0.137301
$381$	−162.478			−0.426450
$382$			157.405i			0.412056i
$383$		−	370.198i		−	0.966575i	−0.875462	−	0.483288i	$-0.839443\pi$
$383$		−	370.198i		−	0.966575i	0.875462	−	0.483288i	$-0.160557\pi$
$384$	16.2734			0.0423785
$385$			296.652i			0.770526i
$386$	−232.046			−0.601156
$387$		−	34.4179i		−	0.0889351i
$388$			4.65332i			0.0119931i
$389$			12.0598i			0.0310021i	0.999880	+	0.0155011i	$0.00493434\pi$
$389$			12.0598i			0.0310021i	−0.999880	+	0.0155011i	$0.995066\pi$
$390$		−	105.596i		−	0.270759i
$391$	−424.512	−	491.073i	−1.08571	−	1.25594i
$392$	−154.902			−0.395158
$393$	−17.4645			−0.0444391
$394$	−466.071			−1.18292
$395$	179.521			0.454483
$396$			180.537i			0.455901i
$397$	233.543			0.588270			0.294135	−	0.955764i	$-0.404968\pi$
$397$	233.543			0.588270			0.294135	+	0.955764i	$0.404968\pi$
$398$		−	477.844i		−	1.20061i
$399$	170.939			0.428418
$400$	−20.0000			−0.0500000
$401$			114.072i			0.284469i	0.989833	+	0.142235i	$0.0454287\pi$
$401$			114.072i			0.284469i	−0.989833	+	0.142235i	$0.954571\pi$
$402$		−	162.918i		−	0.405268i
$403$	435.713			1.08117
$404$	25.9837			0.0643161
$405$		−	65.7841i		−	0.162430i
$406$		−	611.958i		−	1.50729i
$407$	14.8593			0.0365094
$408$			114.820i			0.281421i
$409$	125.952			0.307950			0.153975	−	0.988075i	$-0.450792\pi$
$409$	125.952			0.307950			0.153975	+	0.988075i	$0.450792\pi$
$410$			230.276i			0.561650i
$411$		−	245.304i		−	0.596847i
$412$		−	180.633i		−	0.438430i
$413$		−	958.397i		−	2.32057i
$414$	170.554	−	147.437i	0.411966	−	0.356127i
$415$	211.633			0.509959
$416$	131.326			0.315688
$417$	55.4462			0.132965
$418$	214.878			0.514061
$419$		−	135.868i		−	0.324268i	−0.986769	−	0.162134i	$-0.948162\pi$
$419$		−	135.868i		−	0.324268i	0.986769	−	0.162134i	$-0.0518377\pi$
$420$	−65.5262			−0.156015
$421$		−	194.111i		−	0.461070i	−0.973064	−	0.230535i	$-0.925952\pi$
$421$		−	194.111i		−	0.461070i	0.973064	−	0.230535i	$-0.0740477\pi$
$422$	157.905			0.374182
$423$	5.63746			0.0133273
$424$		−	75.5999i		−	0.178302i
$425$		−	141.114i		−	0.332033i
$426$	−169.915			−0.398861
$427$	759.198			1.77798
$428$		−	370.346i		−	0.865294i
$429$		−	434.894i		−	1.01374i
$430$	15.7030			0.0365187
$431$		−	421.699i		−	0.978420i	−0.872166	−	0.489210i	$-0.837285\pi$
$431$		−	421.699i		−	0.978420i	0.872166	−	0.489210i	$-0.162715\pi$
$432$	−91.6595			−0.212175
$433$		−	3.78505i		−	0.00874144i	−0.999990	−	0.00437072i	$-0.998609\pi$
$433$		−	3.78505i		−	0.00874144i	0.999990	−	0.00437072i	$-0.00139125\pi$
$434$		−	270.375i		−	0.622984i
$435$		−	136.627i		−	0.314085i
$436$		−	27.6497i		−	0.0634167i
$437$	−175.481	−	202.996i	−0.401559	−	0.464521i
$438$	−18.2851			−0.0417468
$439$	−6.17744			−0.0140716			−0.00703581	−	0.999975i	$-0.502240\pi$
$439$	−6.17744			−0.0140716			−0.00703581	+	0.999975i	$0.502240\pi$
$440$	−82.3693			−0.187203
$441$	379.588			0.860744
$442$			926.598i			2.09638i
$443$	−406.821			−0.918331			−0.459166	−	0.888351i	$-0.651852\pi$
$443$	−406.821			−0.918331			−0.459166	+	0.888351i	$0.651852\pi$
$444$			3.28221i			0.00739236i
$445$	305.921			0.687464
$446$	−514.130			−1.15276
$447$			117.102i			0.261972i
$448$		−	81.4925i		−	0.181903i
$449$	−289.981			−0.645837			−0.322918	−	0.946427i	$-0.604664\pi$
$449$	−289.981			−0.645837			−0.322918	+	0.946427i	$0.604664\pi$
$450$	49.0101			0.108911
$451$			948.385i			2.10285i
$452$			357.060i			0.789956i
$453$	229.680			0.507020
$454$			16.0326i			0.0353142i
$455$	−528.797			−1.16219
$456$			47.4633i			0.104086i
$457$		−	224.430i		−	0.491094i	−0.969385	−	0.245547i	$-0.921032\pi$
$457$		−	224.430i		−	0.491094i	0.969385	−	0.245547i	$-0.0789676\pi$
$458$		−	159.112i		−	0.347406i
$459$		−	646.722i		−	1.40898i
$460$	67.2674	+	77.8145i	0.146233	+	0.169162i
$461$	534.660			1.15978			0.579891	−	0.814694i	$-0.303095\pi$
$461$	534.660			1.15978			0.579891	+	0.814694i	$0.303095\pi$
$462$	−269.867			−0.584128
$463$	166.226			0.359019			0.179509	−	0.983756i	$-0.442549\pi$
$463$	166.226			0.359019			0.179509	+	0.983756i	$0.442549\pi$
$464$	169.918			0.366202
$465$		−	60.3644i		−	0.129816i
$466$	−539.712			−1.15818
$467$			113.755i			0.243587i	0.992555	+	0.121794i	$0.0388646\pi$
$467$			113.755i			0.243587i	−0.992555	+	0.121794i	$0.961135\pi$
$468$	−321.815			−0.687640
$469$	−815.848			−1.73955
$470$			2.57207i			0.00547249i
$471$		−	55.5145i		−	0.117865i
$472$	266.111			0.563795
$473$	64.6723			0.136728
$474$			163.312i			0.344539i
$475$		−	58.3326i		−	0.122805i
$476$	574.987			1.20796
$477$			185.258i			0.388382i
$478$	196.994			0.412121
$479$		−	156.314i		−	0.326334i	−0.986598	−	0.163167i	$-0.947829\pi$
$479$		−	156.314i		−	0.326334i	0.986598	−	0.163167i	$-0.0521710\pi$
$480$		−	18.1942i		−	0.0379045i
$481$			26.4875i			0.0550675i
$482$		−	116.439i		−	0.241574i
$483$	220.389	+	254.944i	0.456291	+	0.527835i
$484$	−97.2348			−0.200898
$485$	5.20257			0.0107270
$486$	351.503			0.723257
$487$	−207.919			−0.426938			−0.213469	−	0.976950i	$-0.568476\pi$
$487$	−207.919			−0.426938			−0.213469	+	0.976950i	$0.568476\pi$
$488$			210.801i			0.431969i
$489$	216.174			0.442074
$490$			173.186i			0.353440i
$491$	−463.345			−0.943676			−0.471838	−	0.881685i	$-0.656409\pi$
$491$	−463.345			−0.943676			−0.471838	+	0.881685i	$0.656409\pi$
$492$	−209.484			−0.425781
$493$			1198.89i			2.43182i
$494$			383.029i			0.775363i
$495$	201.846			0.407770
$496$	75.0730			0.151357
$497$			850.886i			1.71204i
$498$			192.524i			0.386595i
$499$	−50.7777			−0.101759			−0.0508794	−	0.998705i	$-0.516202\pi$
$499$	−50.7777			−0.101759			−0.0508794	+	0.998705i	$0.516202\pi$
$500$			22.3607i			0.0447214i
$501$	39.9298			0.0797003
$502$		−	458.098i		−	0.912546i
$503$		−	91.1857i		−	0.181284i	−0.995884	−	0.0906419i	$-0.971108\pi$
$503$		−	91.1857i		−	0.181284i	0.995884	−	0.0906419i	$-0.0288919\pi$
$504$			199.698i			0.396226i
$505$		−	29.0506i		−	0.0575260i
$506$	277.038	+	320.476i	0.547506	+	0.633352i
$507$	532.134			1.04957
$508$	−225.918			−0.444721
$509$	317.681			0.624128			0.312064	−	0.950061i	$-0.398980\pi$
$509$	317.681			0.624128			0.312064	+	0.950061i	$0.398980\pi$
$510$	128.373			0.251711
$511$			91.5667i			0.179191i
$512$	22.6274			0.0441942
$513$		−	267.337i		−	0.521124i
$514$	−354.678			−0.690036
$515$	−201.954			−0.392143
$516$			14.2852i			0.0276844i
$517$			10.5930i			0.0204893i
$518$	16.4364			0.0317305
$519$	−34.5302			−0.0665322
$520$		−	146.827i		−	0.282360i
$521$		−	522.346i		−	1.00258i	−0.865279	−	0.501291i	$-0.832858\pi$
$521$		−	522.346i		−	1.00258i	0.865279	−	0.501291i	$-0.167142\pi$
$522$	−416.385			−0.797671
$523$			245.926i			0.470221i	0.971969	+	0.235111i	$0.0755452\pi$
$523$			245.926i			0.470221i	−0.971969	+	0.235111i	$0.924455\pi$
$524$	−24.2837			−0.0463430
$525$			73.2605i			0.139544i
$526$			391.564i			0.744419i
$527$			529.693i			1.00511i
$528$		−	74.9320i		−	0.141917i
$529$	76.5101	−	523.438i	0.144632	−	0.989486i
$530$	−84.5232			−0.159478
$531$	−652.107			−1.22807
$532$	237.683			0.446773
$533$	−1690.54			−3.17174
$534$			278.299i			0.521160i
$535$	−414.059			−0.773943
$536$		−	226.530i		−	0.422631i
$537$	−289.369			−0.538862
$538$	−110.450			−0.205298
$539$			713.258i			1.32330i
$540$			102.478i			0.189775i
$541$	−307.138			−0.567723			−0.283861	−	0.958865i	$-0.591616\pi$
$541$	−307.138			−0.567723			−0.283861	+	0.958865i	$0.591616\pi$
$542$	468.884			0.865099
$543$		−	291.066i		−	0.536033i
$544$			159.652i			0.293478i
$545$	−30.9133			−0.0567216
$546$		−	481.051i		−	0.881046i
$547$	−712.547			−1.30265			−0.651323	−	0.758801i	$-0.725786\pi$
$547$	−712.547			−1.30265			−0.651323	+	0.758801i	$0.725786\pi$
$548$		−	341.085i		−	0.622418i
$549$		−	516.569i		−	0.940926i
$550$			92.0916i			0.167439i
$551$			495.587i			0.899432i
$552$	−70.7885	+	61.1937i	−0.128240	+	0.110858i
$553$	817.820			1.47888
$554$	−503.424			−0.908707
$555$	3.66962			0.00661193
$556$	77.0956			0.138661
$557$		−	1.17109i		−	0.00210250i	−0.999999	−	0.00105125i	$-0.999665\pi$
$557$		−	1.17109i		−	0.00210250i	0.999999	−	0.00105125i	$-0.000334623\pi$
$558$	−183.967			−0.329690
$559$			115.281i			0.206228i
$560$	−91.1114			−0.162699
$561$	528.698			0.942420
$562$			553.575i			0.985010i
$563$		−	900.058i		−	1.59868i	−0.600878	−	0.799341i	$-0.705182\pi$
$563$		−	900.058i		−	1.59868i	0.600878	−	0.799341i	$-0.294818\pi$
$564$	−2.33983			−0.00414864
$565$	399.205			0.706558
$566$			188.962i			0.333855i
$567$		−	299.684i		−	0.528543i
$568$	−236.259			−0.415949
$569$			589.836i			1.03662i	0.855193	+	0.518309i	$0.173438\pi$
$569$			589.836i			1.03662i	−0.855193	+	0.518309i	$0.826562\pi$
$570$	53.0656			0.0930976
$571$		−	117.755i		−	0.206225i	−0.994670	−	0.103113i	$-0.967120\pi$
$571$		−	117.755i		−	0.206225i	0.994670	−	0.103113i	$-0.0328802\pi$
$572$		−	604.702i		−	1.05717i
$573$			160.095i			0.279397i
$574$			1049.04i			1.82760i
$575$	86.9993	−	75.2072i	0.151303	−	0.130795i
$576$	−55.4486			−0.0962650
$577$	−403.533			−0.699365			−0.349682	−	0.936868i	$-0.613710\pi$
$577$	−403.533			−0.699365			−0.349682	+	0.936868i	$0.613710\pi$
$578$	−717.751			−1.24178
$579$	−236.011			−0.407618
$580$		−	189.974i		−	0.327541i
$581$	964.109			1.65940
$582$			4.73282i			0.00813200i
$583$	−348.106			−0.597094
$584$	−25.4246			−0.0435354
$585$			359.801i			0.615044i
$586$			754.418i			1.28740i
$587$	607.731			1.03532			0.517659	−	0.855587i	$-0.326804\pi$
$587$	607.731			1.03532			0.517659	+	0.855587i	$0.326804\pi$
$588$	−157.548			−0.267939
$589$			218.960i			0.371749i
$590$		−	297.521i		−	0.504273i
$591$	−474.033			−0.802087
$592$			4.56377i			0.00770908i
$593$	428.555			0.722690			0.361345	−	0.932432i	$-0.382318\pi$
$593$	428.555			0.722690			0.361345	+	0.932432i	$0.382318\pi$
$594$			422.053i			0.710528i
$595$		−	642.855i		−	1.08043i
$596$			162.825i			0.273196i
$597$		−	486.007i		−	0.814083i
$598$	−571.264	+	493.834i	−0.955291	+	0.825809i
$599$	−162.171			−0.270736			−0.135368	−	0.990795i	$-0.543222\pi$
$599$	−162.171			−0.270736			−0.135368	+	0.990795i	$0.543222\pi$
$600$	−20.3417			−0.0339028
$601$	957.407			1.59302			0.796512	−	0.604623i	$-0.206676\pi$
$601$	957.407			1.59302			0.796512	+	0.604623i	$0.206676\pi$
$602$	71.5362			0.118831
$603$			555.114i			0.920587i
$604$	319.360			0.528742
$605$			108.712i			0.179689i
$606$	26.4276			0.0436099
$607$	−989.893			−1.63080			−0.815398	−	0.578901i	$-0.803482\pi$
$607$	−989.893			−1.63080			−0.815398	+	0.578901i	$0.803482\pi$
$608$			65.9958i			0.108546i
$609$		−	622.413i		−	1.02202i
$610$	235.682			0.386365
$611$	−18.8825			−0.0309042
$612$		−	391.229i		−	0.639263i
$613$			134.181i			0.218892i	0.993993	+	0.109446i	$0.0349076\pi$
$613$			134.181i			0.218892i	−0.993993	+	0.109446i	$0.965092\pi$
$614$	399.736			0.651037
$615$			234.211i			0.380830i
$616$	−375.239			−0.609154
$617$		−	151.269i		−	0.245168i	−0.992458	−	0.122584i	$-0.960882\pi$
$617$		−	151.269i		−	0.245168i	0.992458	−	0.122584i	$-0.0391181\pi$
$618$		−	183.719i		−	0.297280i
$619$			115.852i			0.187159i	0.995612	+	0.0935797i	$0.0298310\pi$
$619$			115.852i			0.187159i	−0.995612	+	0.0935797i	$0.970169\pi$
$620$		−	83.9342i		−	0.135378i
$621$	398.715	−	344.673i	0.642054	−	0.555028i
$622$	−273.234			−0.439284
$623$	1393.65			2.23699
$624$	133.570			0.214054
$625$	25.0000			0.0400000
$626$		−	564.665i		−	0.902022i
$627$	218.549			0.348563
$628$		−	77.1906i		−	0.122915i
$629$	−32.2006			−0.0511934
$630$	223.269			0.354395
$631$			730.187i			1.15719i	0.815615	+	0.578595i	$0.196399\pi$
$631$			730.187i			1.15719i	−0.815615	+	0.578595i	$0.803601\pi$
$632$			227.078i			0.359300i
$633$	160.602			0.253716
$634$	−51.6608			−0.0814839
$635$			252.584i			0.397771i
$636$		−	76.8915i		−	0.120899i
$637$	−1271.42			−1.99594
$638$		−	782.400i		−	1.22633i
$639$	578.955			0.906032
$640$		−	25.2982i		−	0.0395285i
$641$		−	725.551i		−	1.13190i	−0.824438	−	0.565952i	$-0.808509\pi$
$641$		−	725.551i		−	1.13190i	0.824438	−	0.565952i	$-0.191491\pi$
$642$		−	376.673i		−	0.586718i
$643$			505.908i			0.786792i	0.919369	+	0.393396i	$0.128700\pi$
$643$			505.908i			0.786792i	−0.919369	+	0.393396i	$0.871300\pi$
$644$	306.441	+	354.490i	0.475840	+	0.550450i
$645$	15.9713			0.0247617
$646$	−465.646			−0.720815
$647$	−324.943			−0.502230			−0.251115	−	0.967957i	$-0.580797\pi$
$647$	−324.943			−0.502230			−0.251115	+	0.967957i	$0.580797\pi$
$648$	83.2110			0.128412
$649$		−	1225.33i		−	1.88803i
$650$	−164.158			−0.252550
$651$		−	274.994i		−	0.422418i
$652$	300.581			0.461014
$653$	−146.801			−0.224810			−0.112405	−	0.993662i	$-0.535855\pi$
$653$	−146.801			−0.224810			−0.112405	+	0.993662i	$0.535855\pi$
$654$		−	28.1220i		−	0.0430001i
$655$			27.1500i			0.0414504i
$656$	−291.279			−0.444023
$657$	62.3033			0.0948299
$658$			11.7172i			0.0178074i
$659$			366.667i			0.556399i	0.960523	+	0.278200i	$0.0897377\pi$
$659$			366.667i			0.556399i	−0.960523	+	0.278200i	$0.910262\pi$
$660$	−83.7765			−0.126934
$661$			1241.87i			1.87878i	0.342852	+	0.939389i	$0.388607\pi$
$661$			1241.87i			1.87878i	−0.342852	+	0.939389i	$0.611393\pi$
$662$	121.538			0.183593
$663$			942.428i			1.42146i
$664$			267.697i			0.403158i
$665$		−	265.738i		−	0.399606i
$666$		−	11.1836i		−	0.0167921i
$667$	−739.136	+	638.952i	−1.10815	+	0.957949i
$668$	55.5208			0.0831149
$669$	−522.914			−0.781635
$670$	−253.269			−0.378013
$671$	970.649			1.44657
$672$		−	82.8848i		−	0.123340i
$673$	812.966			1.20797			0.603987	−	0.796994i	$-0.293578\pi$
$673$	812.966			1.20797			0.603987	+	0.796994i	$0.293578\pi$
$674$		−	775.997i		−	1.15133i
$675$	114.574			0.169740
$676$	739.910			1.09454
$677$		−	1053.03i		−	1.55544i	−0.628610	−	0.777721i	$-0.716376\pi$
$677$		−	1053.03i		−	1.55544i	0.628610	−	0.777721i	$-0.283624\pi$
$678$			363.160i			0.535635i
$679$	23.7007			0.0349053
$680$	178.497			0.262495
$681$			16.3066i			0.0239450i
$682$		−	345.680i		−	0.506862i
$683$	947.718			1.38758			0.693791	−	0.720177i	$-0.255939\pi$
$683$	947.718			1.38758			0.693791	+	0.720177i	$0.255939\pi$
$684$		−	161.723i		−	0.236437i
$685$	−381.345			−0.556708
$686$			83.0661i			0.121088i
$687$		−	161.830i		−	0.235561i
$688$			19.8629i			0.0288705i
$689$		−	620.515i		−	0.900602i
$690$	68.4166	+	79.1440i	0.0991545	+	0.114701i
$691$	−600.541			−0.869090			−0.434545	−	0.900650i	$-0.643091\pi$
$691$	−600.541			−0.869090			−0.434545	+	0.900650i	$0.643091\pi$
$692$	−48.0128			−0.0693826
$693$	919.525			1.32688
$694$	87.6863			0.126349
$695$		−	86.1955i		−	0.124022i
$696$	172.821			0.248306
$697$		−	2055.18i		−	2.94861i
$698$	−185.818			−0.266215
$699$	−548.932			−0.785311
$700$			101.866i			0.145522i
$701$			907.376i			1.29440i	0.762319	+	0.647201i	$0.224061\pi$
$701$			907.376i			1.29440i	−0.762319	+	0.647201i	$0.775939\pi$
$702$	−752.330			−1.07170
$703$	−13.3108			−0.0189343
$704$		−	104.190i		−	0.147997i
$705$			2.61601i			0.00371066i
$706$	−250.302			−0.354536
$707$		−	132.342i		−	0.187188i
$708$	270.657			0.382285
$709$			657.300i			0.927081i	0.886076	+	0.463540i	$0.153421\pi$
$709$			657.300i			0.927081i	−0.886076	+	0.463540i	$0.846579\pi$
$710$			264.146i			0.372036i
$711$		−	556.456i		−	0.782638i
$712$			386.963i			0.543488i
$713$	−326.565	+	282.302i	−0.458015	+	0.395935i
$714$	584.810			0.819062
$715$	−676.077			−0.945563
$716$	−402.356			−0.561949
$717$	200.360			0.279442
$718$			265.661i			0.370001i
$719$	1095.72			1.52395			0.761975	−	0.647606i	$-0.224230\pi$
$719$	1095.72			1.52395			0.761975	+	0.647606i	$0.224230\pi$
$720$			61.9934i			0.0861020i
$721$	−920.015			−1.27603
$722$	318.046			0.440507
$723$		−	118.428i		−	0.163801i
$724$		−	404.715i		−	0.558999i
$725$	−212.397			−0.292962
$726$	−98.8960			−0.136220
$727$			814.942i			1.12097i	0.828166	+	0.560483i	$0.189384\pi$
$727$			814.942i			1.12097i	−0.828166	+	0.560483i	$0.810616\pi$
$728$		−	668.881i		−	0.918793i
$729$	92.7324			0.127205
$730$			28.4256i			0.0389392i
$731$	−140.147			−0.191719
$732$			214.402i			0.292899i
$733$		−	742.293i		−	1.01268i	−0.862335	−	0.506339i	$-0.830999\pi$
$733$		−	742.293i		−	1.01268i	0.862335	−	0.506339i	$-0.169001\pi$
$734$			181.740i			0.247602i
$735$			176.144i			0.239652i
$736$	−98.4285	+	85.0872i	−0.133734	+	0.115608i
$737$	−1043.08			−1.41530
$738$	713.781			0.967183
$739$	−288.013			−0.389733			−0.194866	−	0.980830i	$-0.562427\pi$
$739$	−288.013			−0.389733			−0.194866	+	0.980830i	$0.562427\pi$
$740$	5.10245			0.00689521
$741$			389.573i			0.525740i
$742$	−385.052			−0.518937
$743$			199.651i			0.268709i	0.990933	+	0.134354i	$0.0428961\pi$
$743$			199.651i			0.268709i	−0.990933	+	0.134354i	$0.957104\pi$
$744$	76.3556			0.102629
$745$	182.044			0.244354
$746$			112.137i			0.150318i
$747$		−	655.993i		−	0.878170i
$748$	735.132			0.982797
$749$	−1886.28			−2.51839
$750$			22.7427i			0.0303236i
$751$			610.667i			0.813138i	0.913620	+	0.406569i	$0.133275\pi$
$751$			610.667i			0.813138i	−0.913620	+	0.406569i	$0.866725\pi$
$752$	−3.25344			−0.00432638
$753$		−	465.925i		−	0.618758i
$754$	1394.67			1.84969
$755$		−	357.056i		−	0.472922i
$756$			466.847i			0.617523i
$757$			241.235i			0.318672i	0.987224	+	0.159336i	$0.0509354\pi$
$757$			241.235i			0.318672i	−0.987224	+	0.159336i	$0.949065\pi$
$758$			569.319i			0.751080i
$759$	281.771	+	325.952i	0.371240	+	0.429449i
$760$	73.7855			0.0970862
$761$	568.126			0.746552			0.373276	−	0.927720i	$-0.378235\pi$
$761$	568.126			0.746552			0.373276	+	0.927720i	$0.378235\pi$
$762$	−229.778			−0.301546
$763$	−140.828			−0.184571
$764$			222.605i			0.291368i
$765$	−437.407			−0.571774
$766$		−	523.539i		−	0.683472i
$767$	2184.21			2.84773
$768$	23.0140			0.0299661
$769$		−	425.966i		−	0.553922i	−0.960881	−	0.276961i	$-0.910673\pi$
$769$		−	425.966i		−	0.553922i	0.960881	−	0.276961i	$-0.0893273\pi$
$770$			419.530i			0.544844i
$771$	−360.738			−0.467883
$772$	−328.163			−0.425081
$773$			849.417i			1.09886i	0.835540	+	0.549429i	$0.185155\pi$
$773$			849.417i			1.09886i	−0.835540	+	0.549429i	$0.814845\pi$
$774$		−	48.6742i		−	0.0628866i
$775$	−93.8413			−0.121086
$776$			6.58079i			0.00848040i
$777$	16.7172			0.0215151
$778$			17.0552i			0.0219218i
$779$		−	849.553i		−	1.09057i
$780$		−	149.336i		−	0.191456i
$781$			1087.87i			1.39293i
$782$	−600.350	−	694.482i	−0.767711	−	0.888084i
$783$	−973.411			−1.24318
$784$	−219.064			−0.279419
$785$	−86.3017			−0.109938
$786$	−24.6986			−0.0314232
$787$		−	1448.81i		−	1.84093i	−0.390828	−	0.920464i	$-0.627811\pi$
$787$		−	1448.81i		−	1.84093i	0.390828	−	0.920464i	$-0.372189\pi$

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +1.43837 q^{3} +2.00000 q^{4} -2.23607i q^{5} +2.03417 q^{6} -10.1866i q^{7} +2.82843 q^{8} -6.93108 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +1.43837 q^{3} +2.00000 q^{4} -2.23607i q^{5} +2.03417 q^{6} -10.1866i q^{7} +2.82843 q^{8} -6.93108 q^{9} -3.16228i q^{10} -13.0237i q^{11} +2.87675 q^{12} +23.2154 q^{13} -14.4060i q^{14} -3.21630i q^{15} +4.00000 q^{16} +28.2228i q^{17} -9.80202 q^{18} +11.6665i q^{19} -4.47214i q^{20} -14.6521i q^{21} -18.4183i q^{22} +(-17.3999 + 15.0414i) q^{23} +4.06834 q^{24} -5.00000 q^{25} +32.8315 q^{26} -22.9149 q^{27} -20.3731i q^{28} +42.4794 q^{29} -4.54854i q^{30} +18.7683 q^{31} +5.65685 q^{32} -18.7330i q^{33} +39.9131i q^{34} -22.7778 q^{35} -13.8622 q^{36} +1.14094i q^{37} +16.4989i q^{38} +33.3924 q^{39} -6.32456i q^{40} -72.8198 q^{41} -20.7212i q^{42} +4.96573i q^{43} -26.0474i q^{44} +15.4984i q^{45} +(-24.6071 + 21.2718i) q^{46} -0.813360 q^{47} +5.75350 q^{48} -54.7661 q^{49} -7.07107 q^{50} +40.5950i q^{51} +46.4308 q^{52} -26.7286i q^{53} -32.4065 q^{54} -29.1219 q^{55} -28.8120i q^{56} +16.7808i q^{57} +60.0750 q^{58} +94.0845 q^{59} -6.43261i q^{60} +74.5293i q^{61} +26.5423 q^{62} +70.6039i q^{63} +8.00000 q^{64} -51.9112i q^{65} -26.4925i q^{66} -80.0906i q^{67} +56.4456i q^{68} +(-25.0275 + 21.6352i) q^{69} -32.2127 q^{70} -83.5303 q^{71} -19.6040 q^{72} -8.98897 q^{73} +1.61354i q^{74} -7.19187 q^{75} +23.3330i q^{76} -132.667 q^{77} +47.2241 q^{78} +80.2841i q^{79} -8.94427i q^{80} +29.4195 q^{81} -102.983 q^{82} +94.6451i q^{83} -29.3042i q^{84} +63.1081 q^{85} +7.02261i q^{86} +61.1014 q^{87} -36.8367i q^{88} +136.812i q^{89} +21.9180i q^{90} -236.485i q^{91} +(-34.7997 + 30.0829i) q^{92} +26.9958 q^{93} -1.15026 q^{94} +26.0871 q^{95} +8.13668 q^{96} +2.32666i q^{97} -77.4509 q^{98} +90.2684i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 + 24 * q^13 + 64 * q^16 - 32 * q^18 + 4 * q^23 - 16 * q^24 - 80 * q^25 + 96 * q^26 - 96 * q^27 - 108 * q^29 - 116 * q^31 + 60 * q^35 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 - 128 * q^47 - 28 * q^49 + 48 * q^52 + 224 * q^54 + 160 * q^58 + 204 * q^59 + 64 * q^62 + 128 * q^64 - 268 * q^69 - 120 * q^70 + 236 * q^71 - 64 * q^72 - 112 * q^73 - 936 * q^77 - 432 * q^78 - 136 * q^81 - 64 * q^82 + 60 * q^85 - 152 * q^87 + 8 * q^92 + 856 * q^93 - 216 * q^94 - 160 * q^95 - 32 * q^96 + 256 * q^98

Introduction

L-functions

Modular forms

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