Properties

Label 912.2.cc.c.737.2
Level $912$
Weight $2$
Character 912.737
Analytic conductor $7.282$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.cc (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + 162 x^{7} + 270 x^{6} + 2916 x^{5} - 4374 x^{4} - 729 x^{3} + 19683\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 737.2
Root \(-0.396613 + 1.68603i\) of defining polynomial
Character \(\chi\) \(=\) 912.737
Dual form 912.2.cc.c.641.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.779936 + 1.54651i) q^{3} +(1.86241 + 2.21954i) q^{5} +(-0.562083 + 0.973556i) q^{7} +(-1.78340 - 2.41236i) q^{9} +O(q^{10})\) \(q+(-0.779936 + 1.54651i) q^{3} +(1.86241 + 2.21954i) q^{5} +(-0.562083 + 0.973556i) q^{7} +(-1.78340 - 2.41236i) q^{9} +(-2.70920 + 1.56416i) q^{11} +(-5.18404 - 0.914087i) q^{13} +(-4.88511 + 1.14915i) q^{15} +(-0.880484 + 2.41911i) q^{17} +(-4.13617 - 1.37554i) q^{19} +(-1.06723 - 1.62858i) q^{21} +(4.31710 - 5.14492i) q^{23} +(-0.589524 + 3.34336i) q^{25} +(5.12168 - 0.876562i) q^{27} +(-1.09635 + 0.399039i) q^{29} +(3.90801 + 2.25629i) q^{31} +(-0.305986 - 5.40975i) q^{33} +(-3.20767 + 0.565599i) q^{35} +12.0703i q^{37} +(5.45687 - 7.30426i) q^{39} +(-1.06170 - 6.02118i) q^{41} +(-2.21295 + 1.85688i) q^{43} +(2.03290 - 8.45114i) q^{45} +(-0.377793 - 1.03798i) q^{47} +(2.86813 + 4.96774i) q^{49} +(-3.05446 - 3.24843i) q^{51} +(-5.66806 - 4.75606i) q^{53} +(-8.51736 - 3.10007i) q^{55} +(5.35324 - 5.32380i) q^{57} +(-6.41833 - 2.33608i) q^{59} +(-5.58223 - 4.68405i) q^{61} +(3.35099 - 0.380292i) q^{63} +(-7.62598 - 13.2086i) q^{65} +(2.42040 + 6.64999i) q^{67} +(4.58962 + 10.6892i) q^{69} +(-3.31294 + 2.77989i) q^{71} +(-1.30735 - 7.41438i) q^{73} +(-4.71075 - 3.51931i) q^{75} -3.51674i q^{77} +(-4.30920 + 0.759829i) q^{79} +(-2.63897 + 8.60441i) q^{81} +(12.5112 + 7.22333i) q^{83} +(-7.00913 + 2.55111i) q^{85} +(0.237965 - 2.00675i) q^{87} +(-2.38095 + 13.5030i) q^{89} +(3.80378 - 4.53316i) q^{91} +(-6.53737 + 4.28402i) q^{93} +(-4.65018 - 11.7422i) q^{95} +(-1.47287 + 4.04669i) q^{97} +(8.60490 + 3.74605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 3q^{3} - 3q^{9} + O(q^{10}) \) \( 18q - 3q^{3} - 3q^{9} - 12q^{13} - 18q^{15} + 6q^{17} + 6q^{19} - 18q^{25} + 6q^{27} - 6q^{29} - 24q^{33} + 24q^{35} - 6q^{39} + 3q^{41} + 6q^{43} - 54q^{45} - 30q^{47} + 21q^{49} - 42q^{51} - 60q^{53} - 30q^{55} + 12q^{57} - 3q^{59} + 54q^{61} + 18q^{63} + 24q^{65} + 15q^{67} + 30q^{69} - 36q^{71} - 42q^{73} + 6q^{79} - 3q^{81} - 36q^{83} - 60q^{89} + 18q^{91} - 66q^{93} - 6q^{95} + 9q^{97} + 102q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{11}{18}\right)\) \(1\) \(-1\) \(1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.779936 + 1.54651i −0.450296 + 0.892879i
\(4\) 0 0
\(5\) 1.86241 + 2.21954i 0.832897 + 0.992608i 0.999978 + 0.00666440i \(0.00212136\pi\)
−0.167081 + 0.985943i \(0.553434\pi\)
\(6\) 0 0
\(7\) −0.562083 + 0.973556i −0.212447 + 0.367969i −0.952480 0.304602i \(-0.901477\pi\)
0.740033 + 0.672571i \(0.234810\pi\)
\(8\) 0 0
\(9\) −1.78340 2.41236i −0.594467 0.804120i
\(10\) 0 0
\(11\) −2.70920 + 1.56416i −0.816855 + 0.471611i −0.849331 0.527861i \(-0.822994\pi\)
0.0324759 + 0.999473i \(0.489661\pi\)
\(12\) 0 0
\(13\) −5.18404 0.914087i −1.43780 0.253522i −0.600216 0.799838i \(-0.704919\pi\)
−0.837579 + 0.546316i \(0.816030\pi\)
\(14\) 0 0
\(15\) −4.88511 + 1.14915i −1.26133 + 0.296709i
\(16\) 0 0
\(17\) −0.880484 + 2.41911i −0.213549 + 0.586720i −0.999502 0.0315662i \(-0.989951\pi\)
0.785953 + 0.618286i \(0.212173\pi\)
\(18\) 0 0
\(19\) −4.13617 1.37554i −0.948902 0.315571i
\(20\) 0 0
\(21\) −1.06723 1.62858i −0.232888 0.355385i
\(22\) 0 0
\(23\) 4.31710 5.14492i 0.900178 1.07279i −0.0968152 0.995302i \(-0.530866\pi\)
0.996993 0.0774881i \(-0.0246900\pi\)
\(24\) 0 0
\(25\) −0.589524 + 3.34336i −0.117905 + 0.668671i
\(26\) 0 0
\(27\) 5.12168 0.876562i 0.985668 0.168694i
\(28\) 0 0
\(29\) −1.09635 + 0.399039i −0.203587 + 0.0740998i −0.441801 0.897113i \(-0.645660\pi\)
0.238214 + 0.971213i \(0.423438\pi\)
\(30\) 0 0
\(31\) 3.90801 + 2.25629i 0.701899 + 0.405241i 0.808054 0.589108i \(-0.200521\pi\)
−0.106155 + 0.994350i \(0.533854\pi\)
\(32\) 0 0
\(33\) −0.305986 5.40975i −0.0532653 0.941717i
\(34\) 0 0
\(35\) −3.20767 + 0.565599i −0.542196 + 0.0956038i
\(36\) 0 0
\(37\) 12.0703i 1.98435i 0.124859 + 0.992174i \(0.460152\pi\)
−0.124859 + 0.992174i \(0.539848\pi\)
\(38\) 0 0
\(39\) 5.45687 7.30426i 0.873799 1.16962i
\(40\) 0 0
\(41\) −1.06170 6.02118i −0.165809 0.940350i −0.948226 0.317595i \(-0.897125\pi\)
0.782417 0.622755i \(-0.213986\pi\)
\(42\) 0 0
\(43\) −2.21295 + 1.85688i −0.337471 + 0.283172i −0.795736 0.605644i \(-0.792916\pi\)
0.458265 + 0.888816i \(0.348471\pi\)
\(44\) 0 0
\(45\) 2.03290 8.45114i 0.303047 1.25982i
\(46\) 0 0
\(47\) −0.377793 1.03798i −0.0551068 0.151405i 0.909085 0.416611i \(-0.136782\pi\)
−0.964192 + 0.265206i \(0.914560\pi\)
\(48\) 0 0
\(49\) 2.86813 + 4.96774i 0.409732 + 0.709677i
\(50\) 0 0
\(51\) −3.05446 3.24843i −0.427710 0.454871i
\(52\) 0 0
\(53\) −5.66806 4.75606i −0.778568 0.653296i 0.164320 0.986407i \(-0.447457\pi\)
−0.942887 + 0.333111i \(0.891901\pi\)
\(54\) 0 0
\(55\) −8.51736 3.10007i −1.14848 0.418013i
\(56\) 0 0
\(57\) 5.35324 5.32380i 0.709054 0.705154i
\(58\) 0 0
\(59\) −6.41833 2.33608i −0.835596 0.304132i −0.111442 0.993771i \(-0.535547\pi\)
−0.724153 + 0.689639i \(0.757769\pi\)
\(60\) 0 0
\(61\) −5.58223 4.68405i −0.714732 0.599731i 0.211191 0.977445i \(-0.432266\pi\)
−0.925922 + 0.377714i \(0.876710\pi\)
\(62\) 0 0
\(63\) 3.35099 0.380292i 0.422184 0.0479123i
\(64\) 0 0
\(65\) −7.62598 13.2086i −0.945887 1.63832i
\(66\) 0 0
\(67\) 2.42040 + 6.64999i 0.295699 + 0.812425i 0.995206 + 0.0977999i \(0.0311805\pi\)
−0.699508 + 0.714625i \(0.746597\pi\)
\(68\) 0 0
\(69\) 4.58962 + 10.6892i 0.552525 + 1.28682i
\(70\) 0 0
\(71\) −3.31294 + 2.77989i −0.393174 + 0.329912i −0.817848 0.575434i \(-0.804833\pi\)
0.424674 + 0.905346i \(0.360389\pi\)
\(72\) 0 0
\(73\) −1.30735 7.41438i −0.153014 0.867787i −0.960579 0.278008i \(-0.910326\pi\)
0.807565 0.589779i \(-0.200785\pi\)
\(74\) 0 0
\(75\) −4.71075 3.51931i −0.543950 0.406375i
\(76\) 0 0
\(77\) 3.51674i 0.400770i
\(78\) 0 0
\(79\) −4.30920 + 0.759829i −0.484823 + 0.0854874i −0.410717 0.911763i \(-0.634722\pi\)
−0.0741064 + 0.997250i \(0.523610\pi\)
\(80\) 0 0
\(81\) −2.63897 + 8.60441i −0.293219 + 0.956045i
\(82\) 0 0
\(83\) 12.5112 + 7.22333i 1.37328 + 0.792863i 0.991340 0.131324i \(-0.0419227\pi\)
0.381940 + 0.924187i \(0.375256\pi\)
\(84\) 0 0
\(85\) −7.00913 + 2.55111i −0.760247 + 0.276707i
\(86\) 0 0
\(87\) 0.237965 2.00675i 0.0255125 0.215146i
\(88\) 0 0
\(89\) −2.38095 + 13.5030i −0.252380 + 1.43132i 0.550331 + 0.834947i \(0.314502\pi\)
−0.802710 + 0.596369i \(0.796609\pi\)
\(90\) 0 0
\(91\) 3.80378 4.53316i 0.398744 0.475205i
\(92\) 0 0
\(93\) −6.53737 + 4.28402i −0.677894 + 0.444232i
\(94\) 0 0
\(95\) −4.65018 11.7422i −0.477098 1.20473i
\(96\) 0 0
\(97\) −1.47287 + 4.04669i −0.149548 + 0.410879i −0.991735 0.128307i \(-0.959046\pi\)
0.842187 + 0.539186i \(0.181268\pi\)
\(98\) 0 0
\(99\) 8.60490 + 3.74605i 0.864825 + 0.376492i
\(100\) 0 0
\(101\) 5.82418 + 1.02696i 0.579528 + 0.102186i 0.455725 0.890121i \(-0.349380\pi\)
0.123802 + 0.992307i \(0.460491\pi\)
\(102\) 0 0
\(103\) −17.2614 + 9.96588i −1.70082 + 0.981967i −0.755884 + 0.654706i \(0.772792\pi\)
−0.944934 + 0.327261i \(0.893874\pi\)
\(104\) 0 0
\(105\) 1.62707 5.40184i 0.158786 0.527165i
\(106\) 0 0
\(107\) −2.39183 + 4.14277i −0.231227 + 0.400496i −0.958169 0.286202i \(-0.907607\pi\)
0.726943 + 0.686698i \(0.240941\pi\)
\(108\) 0 0
\(109\) −5.52889 6.58908i −0.529572 0.631119i 0.433244 0.901276i \(-0.357369\pi\)
−0.962816 + 0.270157i \(0.912924\pi\)
\(110\) 0 0
\(111\) −18.6669 9.41408i −1.77178 0.893545i
\(112\) 0 0
\(113\) 16.1668 1.52085 0.760424 0.649427i \(-0.224991\pi\)
0.760424 + 0.649427i \(0.224991\pi\)
\(114\) 0 0
\(115\) 19.4596 1.81462
\(116\) 0 0
\(117\) 7.04012 + 14.1360i 0.650859 + 1.30687i
\(118\) 0 0
\(119\) −1.86023 2.21694i −0.170527 0.203226i
\(120\) 0 0
\(121\) −0.606822 + 1.05105i −0.0551656 + 0.0955496i
\(122\) 0 0
\(123\) 10.1399 + 3.05421i 0.914282 + 0.275389i
\(124\) 0 0
\(125\) 4.02747 2.32526i 0.360228 0.207978i
\(126\) 0 0
\(127\) −7.59392 1.33901i −0.673852 0.118818i −0.173756 0.984789i \(-0.555591\pi\)
−0.500095 + 0.865970i \(0.666702\pi\)
\(128\) 0 0
\(129\) −1.14573 4.87060i −0.100876 0.428832i
\(130\) 0 0
\(131\) 0.757267 2.08057i 0.0661627 0.181781i −0.902205 0.431307i \(-0.858053\pi\)
0.968368 + 0.249526i \(0.0802749\pi\)
\(132\) 0 0
\(133\) 3.66404 3.25362i 0.317712 0.282125i
\(134\) 0 0
\(135\) 11.4843 + 9.73525i 0.988407 + 0.837877i
\(136\) 0 0
\(137\) 0.138747 0.165352i 0.0118540 0.0141270i −0.760085 0.649824i \(-0.774843\pi\)
0.771939 + 0.635697i \(0.219287\pi\)
\(138\) 0 0
\(139\) −3.25695 + 18.4711i −0.276251 + 1.56670i 0.458710 + 0.888586i \(0.348312\pi\)
−0.734961 + 0.678110i \(0.762799\pi\)
\(140\) 0 0
\(141\) 1.89990 + 0.225295i 0.160000 + 0.0189732i
\(142\) 0 0
\(143\) 15.4744 5.63222i 1.29403 0.470990i
\(144\) 0 0
\(145\) −2.92754 1.69022i −0.243119 0.140365i
\(146\) 0 0
\(147\) −9.91963 + 0.561072i −0.818157 + 0.0462765i
\(148\) 0 0
\(149\) 4.18590 0.738088i 0.342923 0.0604665i 0.000465272 1.00000i \(-0.499852\pi\)
0.342457 + 0.939533i \(0.388741\pi\)
\(150\) 0 0
\(151\) 8.94139i 0.727640i −0.931469 0.363820i \(-0.881472\pi\)
0.931469 0.363820i \(-0.118528\pi\)
\(152\) 0 0
\(153\) 7.40602 2.19019i 0.598741 0.177067i
\(154\) 0 0
\(155\) 2.27041 + 12.8761i 0.182363 + 1.03423i
\(156\) 0 0
\(157\) 1.55311 1.30322i 0.123952 0.104008i −0.578705 0.815537i \(-0.696442\pi\)
0.702656 + 0.711529i \(0.251997\pi\)
\(158\) 0 0
\(159\) 11.7760 5.05629i 0.933900 0.400990i
\(160\) 0 0
\(161\) 2.58230 + 7.09481i 0.203514 + 0.559149i
\(162\) 0 0
\(163\) 4.66573 + 8.08128i 0.365448 + 0.632975i 0.988848 0.148929i \(-0.0475825\pi\)
−0.623400 + 0.781903i \(0.714249\pi\)
\(164\) 0 0
\(165\) 11.4373 10.7543i 0.890391 0.837225i
\(166\) 0 0
\(167\) −9.70512 8.14356i −0.751005 0.630168i 0.184764 0.982783i \(-0.440848\pi\)
−0.935768 + 0.352615i \(0.885292\pi\)
\(168\) 0 0
\(169\) 13.8228 + 5.03107i 1.06329 + 0.387006i
\(170\) 0 0
\(171\) 4.05813 + 12.4311i 0.310333 + 0.950628i
\(172\) 0 0
\(173\) −8.86150 3.22532i −0.673727 0.245217i −0.0175755 0.999846i \(-0.505595\pi\)
−0.656152 + 0.754629i \(0.727817\pi\)
\(174\) 0 0
\(175\) −2.92358 2.45318i −0.221002 0.185443i
\(176\) 0 0
\(177\) 8.61867 8.10403i 0.647819 0.609137i
\(178\) 0 0
\(179\) 3.74454 + 6.48573i 0.279880 + 0.484766i 0.971355 0.237634i \(-0.0763720\pi\)
−0.691475 + 0.722401i \(0.743039\pi\)
\(180\) 0 0
\(181\) 5.46326 + 15.0102i 0.406081 + 1.11570i 0.959232 + 0.282618i \(0.0912030\pi\)
−0.553151 + 0.833081i \(0.686575\pi\)
\(182\) 0 0
\(183\) 11.5977 4.97973i 0.857329 0.368112i
\(184\) 0 0
\(185\) −26.7905 + 22.4799i −1.96968 + 1.65276i
\(186\) 0 0
\(187\) −1.39846 7.93107i −0.102266 0.579977i
\(188\) 0 0
\(189\) −2.02543 + 5.47894i −0.147328 + 0.398534i
\(190\) 0 0
\(191\) 7.61751i 0.551184i 0.961275 + 0.275592i \(0.0888738\pi\)
−0.961275 + 0.275592i \(0.911126\pi\)
\(192\) 0 0
\(193\) 11.8171 2.08368i 0.850616 0.149987i 0.268688 0.963227i \(-0.413410\pi\)
0.581928 + 0.813241i \(0.302299\pi\)
\(194\) 0 0
\(195\) 26.3750 1.49182i 1.88875 0.106831i
\(196\) 0 0
\(197\) 15.2618 + 8.81139i 1.08736 + 0.627786i 0.932871 0.360210i \(-0.117295\pi\)
0.154485 + 0.987995i \(0.450628\pi\)
\(198\) 0 0
\(199\) 2.12679 0.774087i 0.150764 0.0548736i −0.265536 0.964101i \(-0.585549\pi\)
0.416300 + 0.909227i \(0.363327\pi\)
\(200\) 0 0
\(201\) −12.1720 1.44339i −0.858549 0.101809i
\(202\) 0 0
\(203\) 0.227753 1.29165i 0.0159851 0.0906562i
\(204\) 0 0
\(205\) 11.3869 13.5704i 0.795297 0.947798i
\(206\) 0 0
\(207\) −20.1105 1.23896i −1.39778 0.0861135i
\(208\) 0 0
\(209\) 13.3573 2.74299i 0.923942 0.189737i
\(210\) 0 0
\(211\) 1.31716 3.61886i 0.0906769 0.249133i −0.886061 0.463568i \(-0.846569\pi\)
0.976738 + 0.214435i \(0.0687911\pi\)
\(212\) 0 0
\(213\) −1.71525 7.29164i −0.117527 0.499615i
\(214\) 0 0
\(215\) −8.24284 1.45344i −0.562157 0.0991235i
\(216\) 0 0
\(217\) −4.39325 + 2.53644i −0.298233 + 0.172185i
\(218\) 0 0
\(219\) 12.4861 + 3.76090i 0.843731 + 0.254138i
\(220\) 0 0
\(221\) 6.77574 11.7359i 0.455786 0.789444i
\(222\) 0 0
\(223\) 3.57822 + 4.26435i 0.239615 + 0.285562i 0.872428 0.488743i \(-0.162544\pi\)
−0.632813 + 0.774305i \(0.718100\pi\)
\(224\) 0 0
\(225\) 9.11674 4.54039i 0.607783 0.302693i
\(226\) 0 0
\(227\) 24.7738 1.64430 0.822148 0.569274i \(-0.192776\pi\)
0.822148 + 0.569274i \(0.192776\pi\)
\(228\) 0 0
\(229\) −24.7947 −1.63848 −0.819241 0.573449i \(-0.805605\pi\)
−0.819241 + 0.573449i \(0.805605\pi\)
\(230\) 0 0
\(231\) 5.43869 + 2.74283i 0.357839 + 0.180465i
\(232\) 0 0
\(233\) 13.8205 + 16.4706i 0.905410 + 1.07903i 0.996534 + 0.0831862i \(0.0265096\pi\)
−0.0911239 + 0.995840i \(0.529046\pi\)
\(234\) 0 0
\(235\) 1.60022 2.77167i 0.104387 0.180804i
\(236\) 0 0
\(237\) 2.18582 7.25685i 0.141984 0.471383i
\(238\) 0 0
\(239\) −10.5128 + 6.06955i −0.680015 + 0.392607i −0.799861 0.600186i \(-0.795093\pi\)
0.119846 + 0.992793i \(0.461760\pi\)
\(240\) 0 0
\(241\) −21.4162 3.77626i −1.37954 0.243250i −0.565830 0.824522i \(-0.691444\pi\)
−0.813709 + 0.581272i \(0.802555\pi\)
\(242\) 0 0
\(243\) −11.2486 10.7921i −0.721597 0.692313i
\(244\) 0 0
\(245\) −5.68445 + 15.6179i −0.363166 + 0.997791i
\(246\) 0 0
\(247\) 20.1847 + 10.9117i 1.28432 + 0.694295i
\(248\) 0 0
\(249\) −20.9289 + 13.7149i −1.32631 + 0.869149i
\(250\) 0 0
\(251\) −12.5021 + 14.8994i −0.789127 + 0.940445i −0.999307 0.0372181i \(-0.988150\pi\)
0.210181 + 0.977663i \(0.432595\pi\)
\(252\) 0 0
\(253\) −3.64843 + 20.6913i −0.229375 + 1.30085i
\(254\) 0 0
\(255\) 1.52134 12.8294i 0.0952702 0.803409i
\(256\) 0 0
\(257\) −10.1861 + 3.70746i −0.635395 + 0.231265i −0.639578 0.768727i \(-0.720891\pi\)
0.00418306 + 0.999991i \(0.498668\pi\)
\(258\) 0 0
\(259\) −11.7511 6.78452i −0.730180 0.421569i
\(260\) 0 0
\(261\) 2.91786 + 1.93315i 0.180611 + 0.119659i
\(262\) 0 0
\(263\) 30.4663 5.37204i 1.87863 0.331254i 0.887150 0.461481i \(-0.152682\pi\)
0.991484 + 0.130227i \(0.0415706\pi\)
\(264\) 0 0
\(265\) 21.4382i 1.31694i
\(266\) 0 0
\(267\) −19.0256 14.2136i −1.16435 0.869861i
\(268\) 0 0
\(269\) 0.880210 + 4.99192i 0.0536673 + 0.304363i 0.999812 0.0193811i \(-0.00616958\pi\)
−0.946145 + 0.323744i \(0.895058\pi\)
\(270\) 0 0
\(271\) −4.01481 + 3.36882i −0.243882 + 0.204641i −0.756533 0.653956i \(-0.773108\pi\)
0.512650 + 0.858597i \(0.328664\pi\)
\(272\) 0 0
\(273\) 4.04389 + 9.41816i 0.244747 + 0.570013i
\(274\) 0 0
\(275\) −3.63240 9.97993i −0.219042 0.601812i
\(276\) 0 0
\(277\) 2.15677 + 3.73563i 0.129588 + 0.224453i 0.923517 0.383558i \(-0.125301\pi\)
−0.793929 + 0.608010i \(0.791968\pi\)
\(278\) 0 0
\(279\) −1.52655 13.4514i −0.0913924 0.805314i
\(280\) 0 0
\(281\) −8.43804 7.08036i −0.503371 0.422379i 0.355418 0.934707i \(-0.384339\pi\)
−0.858789 + 0.512329i \(0.828783\pi\)
\(282\) 0 0
\(283\) 3.71261 + 1.35128i 0.220691 + 0.0803251i 0.450000 0.893029i \(-0.351424\pi\)
−0.229308 + 0.973354i \(0.573646\pi\)
\(284\) 0 0
\(285\) 21.7863 + 1.96661i 1.29051 + 0.116492i
\(286\) 0 0
\(287\) 6.45871 + 2.35078i 0.381246 + 0.138762i
\(288\) 0 0
\(289\) 7.94592 + 6.66742i 0.467407 + 0.392201i
\(290\) 0 0
\(291\) −5.10951 5.43398i −0.299525 0.318545i
\(292\) 0 0
\(293\) −10.0719 17.4450i −0.588406 1.01915i −0.994441 0.105291i \(-0.966422\pi\)
0.406036 0.913857i \(-0.366911\pi\)
\(294\) 0 0
\(295\) −6.76857 18.5965i −0.394081 1.08273i
\(296\) 0 0
\(297\) −12.5046 + 10.3859i −0.725590 + 0.602651i
\(298\) 0 0
\(299\) −27.0830 + 22.7253i −1.56625 + 1.31424i
\(300\) 0 0
\(301\) −0.563920 3.19815i −0.0325038 0.184338i
\(302\) 0 0
\(303\) −6.13070 + 8.20620i −0.352199 + 0.471434i
\(304\) 0 0
\(305\) 21.1136i 1.20896i
\(306\) 0 0
\(307\) 6.45677 1.13850i 0.368508 0.0649778i 0.0136720 0.999907i \(-0.495648\pi\)
0.354836 + 0.934929i \(0.384537\pi\)
\(308\) 0 0
\(309\) −1.94956 34.4677i −0.110906 1.96080i
\(310\) 0 0
\(311\) −1.86672 1.07775i −0.105852 0.0611137i 0.446139 0.894963i \(-0.352799\pi\)
−0.551991 + 0.833850i \(0.686132\pi\)
\(312\) 0 0
\(313\) 15.9106 5.79098i 0.899320 0.327326i 0.149340 0.988786i \(-0.452285\pi\)
0.749980 + 0.661460i \(0.230063\pi\)
\(314\) 0 0
\(315\) 7.08499 + 6.72938i 0.399194 + 0.379157i
\(316\) 0 0
\(317\) 0.961500 5.45293i 0.0540032 0.306267i −0.945827 0.324670i \(-0.894747\pi\)
0.999831 + 0.0184023i \(0.00585798\pi\)
\(318\) 0 0
\(319\) 2.34608 2.79595i 0.131355 0.156543i
\(320\) 0 0
\(321\) −4.54137 6.93009i −0.253474 0.386800i
\(322\) 0 0
\(323\) 6.96942 8.79469i 0.387789 0.489350i
\(324\) 0 0
\(325\) 6.11224 16.7932i 0.339046 0.931521i
\(326\) 0 0
\(327\) 14.5023 3.41144i 0.801977 0.188653i
\(328\) 0 0
\(329\) 1.22288 + 0.215627i 0.0674195 + 0.0118879i
\(330\) 0 0
\(331\) 6.67525 3.85396i 0.366905 0.211833i −0.305200 0.952288i \(-0.598723\pi\)
0.672106 + 0.740455i \(0.265390\pi\)
\(332\) 0 0
\(333\) 29.1180 21.5262i 1.59566 1.17963i
\(334\) 0 0
\(335\) −10.2521 + 17.7572i −0.560133 + 0.970179i
\(336\) 0 0
\(337\) 8.14195 + 9.70320i 0.443520 + 0.528567i 0.940772 0.339039i \(-0.110102\pi\)
−0.497252 + 0.867606i \(0.665657\pi\)
\(338\) 0 0
\(339\) −12.6091 + 25.0022i −0.684832 + 1.35793i
\(340\) 0 0
\(341\) −14.1168 −0.764466
\(342\) 0 0
\(343\) −14.3177 −0.773081
\(344\) 0 0
\(345\) −15.1772 + 30.0945i −0.817115 + 1.62023i
\(346\) 0 0
\(347\) 2.93143 + 3.49354i 0.157367 + 0.187543i 0.838967 0.544182i \(-0.183160\pi\)
−0.681600 + 0.731725i \(0.738716\pi\)
\(348\) 0 0
\(349\) 0.809906 1.40280i 0.0433533 0.0750901i −0.843535 0.537075i \(-0.819529\pi\)
0.886888 + 0.461985i \(0.152863\pi\)
\(350\) 0 0
\(351\) −27.3523 0.137530i −1.45996 0.00734079i
\(352\) 0 0
\(353\) 5.92549 3.42108i 0.315382 0.182086i −0.333950 0.942591i \(-0.608382\pi\)
0.649332 + 0.760505i \(0.275048\pi\)
\(354\) 0 0
\(355\) −12.3401 2.17590i −0.654947 0.115485i
\(356\) 0 0
\(357\) 4.87938 1.14780i 0.258244 0.0607481i
\(358\) 0 0
\(359\) −1.39824 + 3.84165i −0.0737965 + 0.202754i −0.971106 0.238647i \(-0.923296\pi\)
0.897310 + 0.441401i \(0.145518\pi\)
\(360\) 0 0
\(361\) 15.2158 + 11.3790i 0.800829 + 0.598893i
\(362\) 0 0
\(363\) −1.15217 1.75821i −0.0604734 0.0922819i
\(364\) 0 0
\(365\) 14.0217 16.7104i 0.733927 0.874660i
\(366\) 0 0
\(367\) 1.71891 9.74845i 0.0897266 0.508865i −0.906510 0.422185i \(-0.861263\pi\)
0.996236 0.0866798i \(-0.0276257\pi\)
\(368\) 0 0
\(369\) −12.6318 + 13.2994i −0.657587 + 0.692337i
\(370\) 0 0
\(371\) 7.81621 2.84487i 0.405797 0.147698i
\(372\) 0 0
\(373\) 6.90673 + 3.98760i 0.357617 + 0.206470i 0.668035 0.744130i \(-0.267136\pi\)
−0.310418 + 0.950600i \(0.600469\pi\)
\(374\) 0 0
\(375\) 0.454875 + 8.04209i 0.0234897 + 0.415292i
\(376\) 0 0
\(377\) 6.04829 1.06648i 0.311503 0.0549264i
\(378\) 0 0
\(379\) 10.7490i 0.552141i −0.961137 0.276071i \(-0.910968\pi\)
0.961137 0.276071i \(-0.0890323\pi\)
\(380\) 0 0
\(381\) 7.99358 10.6997i 0.409523 0.548165i
\(382\) 0 0
\(383\) −0.913805 5.18245i −0.0466933 0.264811i 0.952520 0.304477i \(-0.0984816\pi\)
−0.999213 + 0.0396663i \(0.987371\pi\)
\(384\) 0 0
\(385\) 7.80554 6.54963i 0.397807 0.333800i
\(386\) 0 0
\(387\) 8.42604 + 2.02686i 0.428320 + 0.103031i
\(388\) 0 0
\(389\) 5.43196 + 14.9242i 0.275411 + 0.756686i 0.997868 + 0.0652695i \(0.0207907\pi\)
−0.722457 + 0.691416i \(0.756987\pi\)
\(390\) 0 0
\(391\) 8.64499 + 14.9736i 0.437196 + 0.757245i
\(392\) 0 0
\(393\) 2.62701 + 2.79384i 0.132515 + 0.140930i
\(394\) 0 0
\(395\) −9.71199 8.14933i −0.488663 0.410037i
\(396\) 0 0
\(397\) −33.6599 12.2512i −1.68934 0.614870i −0.694799 0.719204i \(-0.744507\pi\)
−0.994542 + 0.104334i \(0.966729\pi\)
\(398\) 0 0
\(399\) 2.17405 + 8.20409i 0.108839 + 0.410718i
\(400\) 0 0
\(401\) 5.57564 + 2.02937i 0.278434 + 0.101342i 0.477463 0.878652i \(-0.341557\pi\)
−0.199029 + 0.979994i \(0.563779\pi\)
\(402\) 0 0
\(403\) −18.1968 15.2690i −0.906449 0.760601i
\(404\) 0 0
\(405\) −24.0127 + 10.1677i −1.19320 + 0.505235i
\(406\) 0 0
\(407\) −18.8799 32.7009i −0.935841 1.62092i
\(408\) 0 0
\(409\) 9.06715 + 24.9118i 0.448342 + 1.23181i 0.933878 + 0.357592i \(0.116402\pi\)
−0.485536 + 0.874217i \(0.661375\pi\)
\(410\) 0 0
\(411\) 0.147506 + 0.343539i 0.00727592 + 0.0169455i
\(412\) 0 0
\(413\) 5.88194 4.93553i 0.289431 0.242862i
\(414\) 0 0
\(415\) 7.26852 + 41.2218i 0.356798 + 2.02350i
\(416\) 0 0
\(417\) −26.0255 19.4432i −1.27448 0.952136i
\(418\) 0 0
\(419\) 8.21543i 0.401350i 0.979658 + 0.200675i \(0.0643135\pi\)
−0.979658 + 0.200675i \(0.935686\pi\)
\(420\) 0 0
\(421\) −16.5911 + 2.92547i −0.808603 + 0.142578i −0.562641 0.826701i \(-0.690215\pi\)
−0.245961 + 0.969280i \(0.579104\pi\)
\(422\) 0 0
\(423\) −1.83022 + 2.76250i −0.0889884 + 0.134317i
\(424\) 0 0
\(425\) −7.56888 4.36989i −0.367144 0.211971i
\(426\) 0 0
\(427\) 7.69786 2.80179i 0.372526 0.135588i
\(428\) 0 0
\(429\) −3.35874 + 28.3241i −0.162162 + 1.36750i
\(430\) 0 0
\(431\) 5.03223 28.5392i 0.242394 1.37469i −0.584073 0.811701i \(-0.698542\pi\)
0.826467 0.562985i \(-0.190347\pi\)
\(432\) 0 0
\(433\) −17.6845 + 21.0756i −0.849863 + 1.01283i 0.149846 + 0.988709i \(0.452122\pi\)
−0.999709 + 0.0241176i \(0.992322\pi\)
\(434\) 0 0
\(435\) 4.89724 3.20922i 0.234805 0.153870i
\(436\) 0 0
\(437\) −24.9333 + 15.3419i −1.19272 + 0.733902i
\(438\) 0 0
\(439\) 5.19707 14.2788i 0.248042 0.681491i −0.751715 0.659488i \(-0.770773\pi\)
0.999758 0.0220034i \(-0.00700448\pi\)
\(440\) 0 0
\(441\) 6.86897 15.7784i 0.327094 0.751353i
\(442\) 0 0
\(443\) −4.75117 0.837760i −0.225735 0.0398032i 0.0596365 0.998220i \(-0.481006\pi\)
−0.285371 + 0.958417i \(0.592117\pi\)
\(444\) 0 0
\(445\) −34.4047 + 19.8636i −1.63094 + 0.941624i
\(446\) 0 0
\(447\) −2.12328 + 7.04921i −0.100427 + 0.333416i
\(448\) 0 0
\(449\) 1.78666 3.09458i 0.0843176 0.146042i −0.820783 0.571241i \(-0.806462\pi\)
0.905100 + 0.425198i \(0.139796\pi\)
\(450\) 0 0
\(451\) 12.2944 + 14.6519i 0.578921 + 0.689932i
\(452\) 0 0
\(453\) 13.8280 + 6.97372i 0.649695 + 0.327654i
\(454\) 0 0
\(455\) 17.1457 0.803804
\(456\) 0 0
\(457\) 26.0709 1.21955 0.609774 0.792576i \(-0.291260\pi\)
0.609774 + 0.792576i \(0.291260\pi\)
\(458\) 0 0
\(459\) −2.38906 + 13.1617i −0.111512 + 0.614336i
\(460\) 0 0
\(461\) 8.46456 + 10.0877i 0.394234 + 0.469830i 0.926253 0.376903i \(-0.123011\pi\)
−0.532019 + 0.846732i \(0.678567\pi\)
\(462\) 0 0
\(463\) 10.6868 18.5101i 0.496659 0.860238i −0.503334 0.864092i \(-0.667893\pi\)
0.999993 + 0.00385369i \(0.00122667\pi\)
\(464\) 0 0
\(465\) −21.6838 6.53133i −1.00556 0.302883i
\(466\) 0 0
\(467\) 8.01942 4.63001i 0.371094 0.214251i −0.302842 0.953041i \(-0.597935\pi\)
0.673936 + 0.738789i \(0.264602\pi\)
\(468\) 0 0
\(469\) −7.83459 1.38145i −0.361768 0.0637894i
\(470\) 0 0
\(471\) 0.804111 + 3.41833i 0.0370515 + 0.157508i
\(472\) 0 0
\(473\) 3.09086 8.49206i 0.142118 0.390465i
\(474\) 0 0
\(475\) 7.03730 13.0178i 0.322894 0.597296i
\(476\) 0 0
\(477\) −1.36494 + 22.1554i −0.0624961 + 1.01442i
\(478\) 0 0
\(479\) 3.61743 4.31108i 0.165284 0.196978i −0.677045 0.735942i \(-0.736740\pi\)
0.842329 + 0.538964i \(0.181184\pi\)
\(480\) 0 0
\(481\) 11.0333 62.5731i 0.503076 2.85309i
\(482\) 0 0
\(483\) −12.9862 1.53994i −0.590894 0.0700697i
\(484\) 0 0
\(485\) −11.7249 + 4.26751i −0.532400 + 0.193778i
\(486\) 0 0
\(487\) −17.7438 10.2444i −0.804048 0.464217i 0.0408365 0.999166i \(-0.486998\pi\)
−0.844885 + 0.534948i \(0.820331\pi\)
\(488\) 0 0
\(489\) −16.1368 + 0.912725i −0.729730 + 0.0412748i
\(490\) 0 0
\(491\) 32.2309 5.68317i 1.45456 0.256478i 0.610196 0.792250i \(-0.291091\pi\)
0.844363 + 0.535772i \(0.179979\pi\)
\(492\) 0 0
\(493\) 3.00354i 0.135273i
\(494\) 0 0
\(495\) 7.71138 + 26.0756i 0.346601 + 1.17201i
\(496\) 0 0
\(497\) −0.844229 4.78786i −0.0378689 0.214765i
\(498\) 0 0
\(499\) −15.7157 + 13.1871i −0.703533 + 0.590334i −0.922776 0.385336i \(-0.874086\pi\)
0.219243 + 0.975670i \(0.429641\pi\)
\(500\) 0 0
\(501\) 20.1635 8.65763i 0.900838 0.386794i
\(502\) 0 0
\(503\) 7.95923 + 21.8678i 0.354885 + 0.975037i 0.980778 + 0.195128i \(0.0625124\pi\)
−0.625893 + 0.779909i \(0.715265\pi\)
\(504\) 0 0
\(505\) 8.56766 + 14.8396i 0.381256 + 0.660354i
\(506\) 0 0
\(507\) −18.5615 + 17.4532i −0.824345 + 0.775122i
\(508\) 0 0
\(509\) −16.6553 13.9754i −0.738232 0.619450i 0.194130 0.980976i \(-0.437812\pi\)
−0.932362 + 0.361525i \(0.882256\pi\)
\(510\) 0 0
\(511\) 7.95315 + 2.89471i 0.351827 + 0.128054i
\(512\) 0 0
\(513\) −22.3899 3.41950i −0.988538 0.150974i
\(514\) 0 0
\(515\) −54.2675 19.7518i −2.39131 0.870367i
\(516\) 0 0
\(517\) 2.64708 + 2.22116i 0.116418 + 0.0976866i
\(518\) 0 0
\(519\) 11.8994 11.1889i 0.522326 0.491137i
\(520\) 0 0
\(521\) −7.53777 13.0558i −0.330236 0.571985i 0.652322 0.757942i \(-0.273795\pi\)
−0.982558 + 0.185957i \(0.940462\pi\)
\(522\) 0 0
\(523\) −2.38040 6.54010i −0.104088 0.285979i 0.876706 0.481027i \(-0.159736\pi\)
−0.980794 + 0.195048i \(0.937514\pi\)
\(524\) 0 0
\(525\) 6.07407 2.60803i 0.265094 0.113824i
\(526\) 0 0
\(527\) −8.89914 + 7.46727i −0.387653 + 0.325279i
\(528\) 0 0
\(529\) −3.83894 21.7717i −0.166911 0.946597i
\(530\) 0 0
\(531\) 5.81098 + 19.6495i 0.252175 + 0.852716i
\(532\) 0 0
\(533\) 32.1845i 1.39407i
\(534\) 0 0
\(535\) −13.6496 + 2.40679i −0.590124 + 0.104055i
\(536\) 0 0
\(537\) −12.9508 + 0.732519i −0.558867 + 0.0316105i
\(538\) 0 0
\(539\) −15.5407 8.97240i −0.669384 0.386469i
\(540\) 0 0
\(541\) −4.63626 + 1.68746i −0.199328 + 0.0725495i −0.439755 0.898118i \(-0.644935\pi\)
0.240427 + 0.970667i \(0.422713\pi\)
\(542\) 0 0
\(543\) −27.4744 3.25799i −1.17904 0.139814i
\(544\) 0 0
\(545\) 4.32762 24.5432i 0.185375 1.05131i
\(546\) 0 0
\(547\) −9.08478 + 10.8268i −0.388437 + 0.462922i −0.924458 0.381283i \(-0.875482\pi\)
0.536021 + 0.844205i \(0.319927\pi\)
\(548\) 0 0
\(549\) −1.34427 + 21.8199i −0.0573720 + 0.931250i
\(550\) 0 0
\(551\) 5.08359 0.142413i 0.216568 0.00606701i
\(552\) 0 0
\(553\) 1.68239 4.62234i 0.0715426 0.196562i
\(554\) 0 0
\(555\) −13.8706 58.9648i −0.588773 2.50292i
\(556\) 0 0
\(557\) 0.424076 + 0.0747760i 0.0179687 + 0.00316836i 0.182625 0.983183i \(-0.441540\pi\)
−0.164657 + 0.986351i \(0.552652\pi\)
\(558\) 0 0
\(559\) 13.1694 7.60334i 0.557005 0.321587i
\(560\) 0 0
\(561\) 13.3562 + 4.02299i 0.563899 + 0.169851i
\(562\) 0 0
\(563\) 2.44919 4.24212i 0.103221 0.178784i −0.809789 0.586721i \(-0.800418\pi\)
0.913010 + 0.407937i \(0.133752\pi\)
\(564\) 0 0
\(565\) 30.1093 + 35.8829i 1.26671 + 1.50961i
\(566\) 0 0
\(567\) −6.89355 7.40557i −0.289502 0.311005i
\(568\) 0 0
\(569\) 9.33523 0.391353 0.195677 0.980668i \(-0.437310\pi\)
0.195677 + 0.980668i \(0.437310\pi\)
\(570\) 0 0
\(571\) −23.4478 −0.981260 −0.490630 0.871368i \(-0.663233\pi\)
−0.490630 + 0.871368i \(0.663233\pi\)
\(572\) 0 0
\(573\) −11.7806 5.94117i −0.492141 0.248196i
\(574\) 0 0
\(575\) 14.6563 + 17.4667i 0.611209 + 0.728410i
\(576\) 0 0
\(577\) −1.23938 + 2.14667i −0.0515960 + 0.0893669i −0.890670 0.454651i \(-0.849764\pi\)
0.839074 + 0.544017i \(0.183097\pi\)
\(578\) 0 0
\(579\) −5.99417 + 19.9005i −0.249109 + 0.827036i
\(580\) 0 0
\(581\) −14.0646 + 8.12021i −0.583499 + 0.336883i
\(582\) 0 0
\(583\) 22.7951 + 4.01940i 0.944078 + 0.166466i
\(584\) 0 0
\(585\) −18.2637 + 41.9528i −0.755112 + 1.73454i
\(586\) 0 0
\(587\) 13.2139 36.3050i 0.545398 1.49847i −0.294462 0.955663i \(-0.595140\pi\)
0.839859 0.542804i \(-0.182637\pi\)
\(588\) 0 0
\(589\) −13.0605 14.7080i −0.538150 0.606034i
\(590\) 0 0
\(591\) −25.5301 + 16.7302i −1.05017 + 0.688188i
\(592\) 0 0
\(593\) 2.81505 3.35484i 0.115600 0.137767i −0.705141 0.709067i \(-0.749116\pi\)
0.820741 + 0.571300i \(0.193561\pi\)
\(594\) 0 0
\(595\) 1.45606 8.25771i 0.0596925 0.338533i
\(596\) 0 0
\(597\) −0.461622 + 3.89284i −0.0188929 + 0.159323i
\(598\) 0 0
\(599\) −40.2689 + 14.6567i −1.64534 + 0.598855i −0.987961 0.154704i \(-0.950558\pi\)
−0.657380 + 0.753559i \(0.728335\pi\)
\(600\) 0 0
\(601\) −24.0390 13.8789i −0.980571 0.566133i −0.0781288 0.996943i \(-0.524895\pi\)
−0.902443 + 0.430810i \(0.858228\pi\)
\(602\) 0 0
\(603\) 11.7256 17.6985i 0.477505 0.720737i
\(604\) 0 0
\(605\) −3.46299 + 0.610618i −0.140791 + 0.0248252i
\(606\) 0 0
\(607\) 16.1090i 0.653844i 0.945051 + 0.326922i \(0.106011\pi\)
−0.945051 + 0.326922i \(0.893989\pi\)
\(608\) 0 0
\(609\) 1.81992 + 1.35963i 0.0737470 + 0.0550950i
\(610\) 0 0
\(611\) 1.00969 + 5.72626i 0.0408478 + 0.231660i
\(612\) 0 0
\(613\) 17.2068 14.4382i 0.694975 0.583154i −0.225364 0.974275i \(-0.572357\pi\)
0.920339 + 0.391121i \(0.127913\pi\)
\(614\) 0 0
\(615\) 12.1057 + 28.1940i 0.488150 + 1.13689i
\(616\) 0 0
\(617\) −15.8059 43.4264i −0.636322 1.74828i −0.662982 0.748636i \(-0.730709\pi\)
0.0266596 0.999645i \(-0.491513\pi\)
\(618\) 0 0
\(619\) 20.8534 + 36.1192i 0.838170 + 1.45175i 0.891423 + 0.453172i \(0.149708\pi\)
−0.0532532 + 0.998581i \(0.516959\pi\)
\(620\) 0 0
\(621\) 17.6010 30.1349i 0.706303 1.20927i
\(622\) 0 0
\(623\) −11.8076 9.90779i −0.473063 0.396947i
\(624\) 0 0
\(625\) 28.6128 + 10.4142i 1.14451 + 0.416568i
\(626\) 0 0
\(627\) −6.17575 + 22.7965i −0.246636 + 0.910406i
\(628\) 0 0
\(629\) −29.1994 10.6277i −1.16426 0.423755i
\(630\) 0 0
\(631\) 3.34686 + 2.80835i 0.133236 + 0.111799i 0.706971 0.707243i \(-0.250061\pi\)
−0.573734 + 0.819042i \(0.694506\pi\)
\(632\) 0 0
\(633\) 4.56932 + 4.85948i 0.181614 + 0.193147i
\(634\) 0 0
\(635\) −11.1710 19.3488i −0.443309 0.767834i
\(636\) 0 0
\(637\) −10.3275 28.3747i −0.409192 1.12425i
\(638\) 0 0
\(639\) 12.6144 + 3.03436i 0.499018 + 0.120038i
\(640\) 0 0
\(641\) 2.18494 1.83339i 0.0863001 0.0724144i −0.598617 0.801035i \(-0.704283\pi\)
0.684917 + 0.728621i \(0.259838\pi\)
\(642\) 0 0
\(643\) −7.65253 43.3997i −0.301786 1.71152i −0.638258 0.769823i \(-0.720345\pi\)
0.336471 0.941694i \(-0.390766\pi\)
\(644\) 0 0
\(645\) 8.67664 11.6141i 0.341643 0.457303i
\(646\) 0 0
\(647\) 20.3269i 0.799131i 0.916705 + 0.399566i \(0.130839\pi\)
−0.916705 + 0.399566i \(0.869161\pi\)
\(648\) 0 0
\(649\) 21.0426 3.71037i 0.825992 0.145645i
\(650\) 0 0
\(651\) −0.496187 8.77247i −0.0194471 0.343820i
\(652\) 0 0
\(653\) 35.1702 + 20.3055i 1.37632 + 0.794617i 0.991714 0.128465i \(-0.0410051\pi\)
0.384603 + 0.923082i \(0.374338\pi\)
\(654\) 0 0
\(655\) 6.02826 2.19411i 0.235543 0.0857308i
\(656\) 0 0
\(657\) −15.5546 + 16.3766i −0.606843 + 0.638912i
\(658\) 0 0
\(659\) 6.33474 35.9261i 0.246766 1.39948i −0.569588 0.821930i \(-0.692897\pi\)
0.816354 0.577552i \(-0.195992\pi\)
\(660\) 0 0
\(661\) −2.71797 + 3.23916i −0.105717 + 0.125989i −0.816308 0.577616i \(-0.803983\pi\)
0.710591 + 0.703605i \(0.248427\pi\)
\(662\) 0 0
\(663\) 12.8651 + 19.6320i 0.499640 + 0.762445i
\(664\) 0 0
\(665\) 14.0455 + 2.07288i 0.544660 + 0.0803830i
\(666\) 0 0
\(667\) −2.68004 + 7.36334i −0.103771 + 0.285110i
\(668\) 0 0
\(669\) −9.38565 + 2.20783i −0.362870 + 0.0853598i
\(670\) 0 0
\(671\) 22.4500 + 3.95854i 0.866672 + 0.152818i
\(672\) 0 0
\(673\) 22.4627 12.9688i 0.865874 0.499912i −0.000101249 1.00000i \(-0.500032\pi\)
0.865975 + 0.500088i \(0.166699\pi\)
\(674\) 0 0
\(675\) −0.0886972 + 17.6404i −0.00341396 + 0.678978i
\(676\) 0 0
\(677\) −16.1874 + 28.0374i −0.622132 + 1.07756i 0.366956 + 0.930238i \(0.380400\pi\)
−0.989088 + 0.147326i \(0.952934\pi\)
\(678\) 0 0
\(679\) −3.11180 3.70850i −0.119420 0.142319i
\(680\) 0 0
\(681\) −19.3220 + 38.3130i −0.740420 + 1.46816i
\(682\) 0 0
\(683\) 12.5635 0.480728 0.240364 0.970683i \(-0.422733\pi\)
0.240364 + 0.970683i \(0.422733\pi\)
\(684\) 0 0
\(685\) 0.625411 0.0238957
\(686\) 0 0
\(687\) 19.3383 38.3454i 0.737802 1.46297i
\(688\) 0 0
\(689\) 25.0360 + 29.8367i 0.953796 + 1.13669i
\(690\) 0 0
\(691\) 7.86815 13.6280i 0.299319 0.518435i −0.676662 0.736294i \(-0.736574\pi\)
0.975980 + 0.217859i \(0.0699073\pi\)
\(692\) 0 0
\(693\) −8.48365 + 6.27176i −0.322267 + 0.238244i
\(694\) 0 0
\(695\) −47.0630 + 27.1719i −1.78520 + 1.03069i
\(696\) 0 0
\(697\) 15.5007 + 2.73319i 0.587130 + 0.103527i
\(698\) 0 0
\(699\) −36.2511 + 8.52752i −1.37114 + 0.322541i
\(700\) 0 0
\(701\) 10.8602 29.8381i 0.410183 1.12697i −0.546911 0.837191i \(-0.684197\pi\)
0.957094 0.289777i \(-0.0935812\pi\)
\(702\) 0 0
\(703\) 16.6033 49.9249i 0.626204 1.88295i
\(704\) 0 0
\(705\) 3.03835 + 4.63649i 0.114431 + 0.174620i
\(706\) 0 0
\(707\) −4.27347 + 5.09293i −0.160721 + 0.191539i
\(708\) 0 0
\(709\) 6.11366 34.6723i 0.229603 1.30214i −0.624084 0.781358i \(-0.714528\pi\)
0.853687 0.520787i \(-0.174361\pi\)
\(710\) 0 0
\(711\) 9.51801 + 9.04028i 0.356953 + 0.339037i
\(712\) 0 0
\(713\) 28.4797 10.3658i 1.06657 0.388201i
\(714\) 0 0
\(715\) 41.3206 + 23.8565i 1.54530 + 0.892182i
\(716\) 0 0
\(717\) −1.18735 20.9920i −0.0443422 0.783961i
\(718\) 0 0
\(719\) 14.7056 2.59299i 0.548426 0.0967023i 0.107432 0.994212i \(-0.465737\pi\)
0.440994 + 0.897510i \(0.354626\pi\)
\(720\) 0 0
\(721\) 22.4066i 0.834465i
\(722\) 0 0
\(723\) 22.5433 30.1752i 0.838394 1.12223i
\(724\) 0 0
\(725\) −0.687805 3.90074i −0.0255444 0.144870i
\(726\) 0 0
\(727\) 22.7799 19.1146i 0.844860 0.708922i −0.113791 0.993505i \(-0.536300\pi\)
0.958651 + 0.284583i \(0.0918551\pi\)
\(728\) 0 0
\(729\) 25.4633 8.97894i 0.943084 0.332553i
\(730\) 0 0
\(731\) −2.54354 6.98831i −0.0940761 0.258472i
\(732\) 0 0
\(733\) 1.63062 + 2.82432i 0.0602284 + 0.104319i 0.894567 0.446933i \(-0.147484\pi\)
−0.834339 + 0.551252i \(0.814150\pi\)
\(734\) 0 0
\(735\) −19.7198 20.9720i −0.727375 0.773565i
\(736\) 0 0
\(737\) −16.9590 14.2303i −0.624692 0.524178i
\(738\) 0 0
\(739\) 5.54154 + 2.01696i 0.203849 + 0.0741950i 0.441927 0.897051i \(-0.354295\pi\)
−0.238078 + 0.971246i \(0.576517\pi\)
\(740\) 0 0
\(741\) −32.6179 + 22.7055i −1.19825 + 0.834106i
\(742\) 0 0
\(743\) 27.7676 + 10.1066i 1.01870 + 0.370775i 0.796766 0.604288i \(-0.206542\pi\)
0.221930 + 0.975063i \(0.428764\pi\)
\(744\) 0 0
\(745\) 9.43410 + 7.91615i 0.345639 + 0.290025i
\(746\) 0 0
\(747\) −4.88714 43.0635i −0.178811 1.57561i
\(748\) 0 0
\(749\) −2.68881 4.65716i −0.0982470 0.170169i
\(750\) 0 0
\(751\) 6.20481 + 17.0476i 0.226417 + 0.622074i 0.999932 0.0117037i \(-0.00372548\pi\)
−0.773515 + 0.633778i \(0.781503\pi\)
\(752\) 0 0
\(753\) −13.2913 30.9553i −0.484363 1.12807i
\(754\) 0 0
\(755\) 19.8458 16.6526i 0.722261 0.606049i
\(756\) 0 0
\(757\) −3.70068 20.9876i −0.134504 0.762807i −0.975204 0.221307i \(-0.928968\pi\)
0.840701 0.541500i \(-0.182143\pi\)
\(758\) 0 0
\(759\) −29.1537 21.7802i −1.05821 0.790571i
\(760\) 0 0
\(761\) 29.1728i 1.05751i 0.848774 + 0.528757i \(0.177342\pi\)
−0.848774 + 0.528757i \(0.822658\pi\)
\(762\) 0 0
\(763\) 9.52252 1.67908i 0.344739 0.0607867i
\(764\) 0 0
\(765\) 18.6543 + 12.3589i 0.674447 + 0.446837i
\(766\) 0 0
\(767\) 31.1375 + 17.9773i 1.12431 + 0.649122i
\(768\) 0 0
\(769\) −25.9596 + 9.44854i −0.936129 + 0.340723i −0.764636 0.644462i \(-0.777081\pi\)
−0.171493 + 0.985185i \(0.554859\pi\)
\(770\) 0 0
\(771\) 2.21092 18.6446i 0.0796244 0.671468i
\(772\) 0 0
\(773\) 7.60654 43.1388i 0.273588 1.55160i −0.469823 0.882761i \(-0.655682\pi\)
0.743411 0.668835i \(-0.233207\pi\)
\(774\) 0 0
\(775\) −9.84744 + 11.7357i −0.353731 + 0.421560i
\(776\) 0 0
\(777\) 19.6575 12.8818i 0.705208 0.462131i
\(778\) 0 0
\(779\) −3.89104 + 26.3650i −0.139411 + 0.944624i
\(780\) 0 0
\(781\) 4.62724 12.7132i 0.165576 0.454916i
\(782\) 0 0
\(783\) −5.26538 + 3.00477i −0.188169 + 0.107382i
\(784\) 0 0
\(785\) 5.78507 + 1.02006i 0.206478 + 0.0364077i
\(786\) 0 0
\(787\) −31.9379 + 18.4393i −1.13846 + 0.657291i −0.946049 0.324023i \(-0.894964\pi\)
−0.192412 + 0.981314i \(0.561631\pi\)
\(788\) 0 0
\(789\) −15.4539 + 51.3064i −0.550172 + 1.82656i
\(790\) 0 0
\(791\) −9.08710 + 15.7393i −0.323100 + 0.559626i
\(792\) 0 0
\(793\) 24.6569 + 29.3850i 0.875593 + 1.04349i