Properties

Label 912.2.cc.c.641.2
Level $912$
Weight $2$
Character 912.641
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 641.2
Root \(-0.396613 - 1.68603i\) of defining polynomial
Character \(\chi\) \(=\) 912.641
Dual form 912.2.cc.c.737.2

$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(1\) \(-1\) \(1\)

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 −0.167081 0.985943i \(-0.553434\pi\)
0.999978 0.00666440i \(-0.00212136\pi\)
\(6\) 0 0
\(7\) −0.562083 0.973556i −0.212447 0.367969i 0.740033 0.672571i \(-0.234810\pi\)
−0.952480 + 0.304602i \(0.901477\pi\)
\(8\) 0 0
\(9\) −1.78340 + 2.41236i −0.594467 + 0.804120i
\(10\) 0 0
\(11\) −2.70920 1.56416i −0.816855 0.471611i 0.0324759 0.999473i \(-0.489661\pi\)
−0.849331 + 0.527861i \(0.822994\pi\)
\(12\) 0 0
\(13\) −5.18404 + 0.914087i −1.43780 + 0.253522i −0.837579 0.546316i \(-0.816030\pi\)
−0.600216 + 0.799838i \(0.704919\pi\)
\(14\) 0 0
\(15\) −4.88511 1.14915i −1.26133 0.296709i
\(16\) 0 0
\(17\) −0.880484 2.41911i −0.213549 0.586720i 0.785953 0.618286i \(-0.212173\pi\)
−0.999502 + 0.0315662i \(0.989951\pi\)
\(18\) 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 0.996993 + 0.0774881i \(0.0246900\pi\)
−0.0968152 + 0.995302i \(0.530866\pi\)
\(24\) 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 0.238214 0.971213i \(-0.423438\pi\)
−0.441801 + 0.897113i \(0.645660\pi\)
\(30\) 0 0
\(31\) 3.90801 2.25629i 0.701899 0.405241i −0.106155 0.994350i \(-0.533854\pi\)
0.808054 + 0.589108i \(0.200521\pi\)
\(32\) 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 \(-0.539848\pi\)
0.124859 0.992174i \(-0.460152\pi\)
\(38\) 0 0
\(39\) 5.45687 + 7.30426i 0.873799 + 1.16962i
\(40\) 0 0
\(41\) −1.06170 + 6.02118i −0.165809 + 0.940350i 0.782417 + 0.622755i \(0.213986\pi\)
−0.948226 + 0.317595i \(0.897125\pi\)
\(42\) 0 0
\(43\) −2.21295 1.85688i −0.337471 0.283172i 0.458265 0.888816i \(-0.348471\pi\)
−0.795736 + 0.605644i \(0.792916\pi\)
\(44\) 0 0
\(45\) 2.03290 + 8.45114i 0.303047 + 1.25982i
\(46\) 0 0
\(47\) −0.377793 + 1.03798i −0.0551068 + 0.151405i −0.964192 0.265206i \(-0.914560\pi\)
0.909085 + 0.416611i \(0.136782\pi\)
\(48\) 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 −0.942887 0.333111i \(-0.891901\pi\)
0.164320 + 0.986407i \(0.447457\pi\)
\(54\) 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 −0.724153 0.689639i \(-0.757769\pi\)
−0.111442 + 0.993771i \(0.535547\pi\)
\(60\) 0 0
\(61\) −5.58223 + 4.68405i −0.714732 + 0.599731i −0.925922 0.377714i \(-0.876710\pi\)
0.211191 + 0.977445i \(0.432266\pi\)
\(62\) 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 −0.699508 0.714625i \(-0.746597\pi\)
0.995206 0.0977999i \(-0.0311805\pi\)
\(68\) 0 0
\(69\) 4.58962 10.6892i 0.552525 1.28682i
\(70\) 0 0
\(71\) −3.31294 2.77989i −0.393174 0.329912i 0.424674 0.905346i \(-0.360389\pi\)
−0.817848 + 0.575434i \(0.804833\pi\)
\(72\) 0 0
\(73\) −1.30735 + 7.41438i −0.153014 + 0.867787i 0.807565 + 0.589779i \(0.200785\pi\)
−0.960579 + 0.278008i \(0.910326\pi\)
\(74\) 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 −0.0741064 0.997250i \(-0.523610\pi\)
−0.410717 + 0.911763i \(0.634722\pi\)
\(80\) 0 0
\(81\) −2.63897 8.60441i −0.293219 0.956045i
\(82\) 0 0
\(83\) 12.5112 7.22333i 1.37328 0.792863i 0.381940 0.924187i \(-0.375256\pi\)
0.991340 + 0.131324i \(0.0419227\pi\)
\(84\) 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 −0.802710 0.596369i \(-0.796609\pi\)
0.550331 0.834947i \(-0.314502\pi\)
\(90\) 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 0.842187 0.539186i \(-0.181268\pi\)
−0.991735 + 0.128307i \(0.959046\pi\)
\(98\) 0 0
\(99\) 8.60490 3.74605i 0.864825 0.376492i
\(100\) 0 0
\(101\) 5.82418 1.02696i 0.579528 0.102186i 0.123802 0.992307i \(-0.460491\pi\)
0.455725 + 0.890121i \(0.349380\pi\)
\(102\) 0 0
\(103\) −17.2614 9.96588i −1.70082 0.981967i −0.944934 0.327261i \(-0.893874\pi\)
−0.755884 0.654706i \(-0.772792\pi\)
\(104\) 0 0
\(105\) 1.62707 + 5.40184i 0.158786 + 0.527165i
\(106\) 0 0
\(107\) −2.39183 4.14277i −0.231227 0.400496i 0.726943 0.686698i \(-0.240941\pi\)
−0.958169 + 0.286202i \(0.907607\pi\)
\(108\) 0 0
\(109\) −5.52889 + 6.58908i −0.529572 + 0.631119i −0.962816 0.270157i \(-0.912924\pi\)
0.433244 + 0.901276i \(0.357369\pi\)
\(110\) 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 −0.500095 0.865970i \(-0.666702\pi\)
−0.173756 + 0.984789i \(0.555591\pi\)
\(128\) 0 0
\(129\) −1.14573 + 4.87060i −0.100876 + 0.428832i
\(130\) 0 0
\(131\) 0.757267 + 2.08057i 0.0661627 + 0.181781i 0.968368 0.249526i \(-0.0802749\pi\)
−0.902205 + 0.431307i \(0.858053\pi\)
\(132\) 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 0.771939 0.635697i \(-0.219287\pi\)
−0.760085 + 0.649824i \(0.774843\pi\)
\(138\) 0 0
\(139\) −3.25695 18.4711i −0.276251 1.56670i −0.734961 0.678110i \(-0.762799\pi\)
0.458710 0.888586i \(-0.348312\pi\)
\(140\) 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 0.342457 0.939533i \(-0.388741\pi\)
0.000465272 1.00000i \(0.499852\pi\)
\(150\) 0 0
\(151\) 8.94139i 0.727640i 0.931469 + 0.363820i \(0.118528\pi\)
−0.931469 + 0.363820i \(0.881472\pi\)
\(152\) 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 0.702656 0.711529i \(-0.251997\pi\)
−0.578705 + 0.815537i \(0.696442\pi\)
\(158\) 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 −0.623400 0.781903i \(-0.714249\pi\)
0.988848 + 0.148929i \(0.0475825\pi\)
\(164\) 0 0
\(165\) 11.4373 + 10.7543i 0.890391 + 0.837225i
\(166\) 0 0
\(167\) −9.70512 + 8.14356i −0.751005 + 0.630168i −0.935768 0.352615i \(-0.885292\pi\)
0.184764 + 0.982783i \(0.440848\pi\)
\(168\) 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 −0.656152 0.754629i \(-0.727817\pi\)
−0.0175755 + 0.999846i \(0.505595\pi\)
\(174\) 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 −0.691475 0.722401i \(-0.743039\pi\)
0.971355 + 0.237634i \(0.0763720\pi\)
\(180\) 0 0
\(181\) 5.46326 15.0102i 0.406081 1.11570i −0.553151 0.833081i \(-0.686575\pi\)
0.959232 0.282618i \(-0.0912030\pi\)
\(182\) 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 \(-0.911126\pi\)
0.961275 0.275592i \(-0.0888738\pi\)
\(192\) 0 0
\(193\) 11.8171 + 2.08368i 0.850616 + 0.149987i 0.581928 0.813241i \(-0.302299\pi\)
0.268688 + 0.963227i \(0.413410\pi\)
\(194\) 0 0
\(195\) 26.3750 + 1.49182i 1.88875 + 0.106831i
\(196\) 0 0
\(197\) 15.2618 8.81139i 1.08736 0.627786i 0.154485 0.987995i \(-0.450628\pi\)
0.932871 + 0.360210i \(0.117295\pi\)
\(198\) 0 0
\(199\) 2.12679 + 0.774087i 0.150764 + 0.0548736i 0.416300 0.909227i \(-0.363327\pi\)
−0.265536 + 0.964101i \(0.585549\pi\)
\(200\) 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 0.976738 0.214435i \(-0.0687911\pi\)
−0.886061 + 0.463568i \(0.846569\pi\)
\(212\) 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 −0.632813 0.774305i \(-0.718100\pi\)
0.872428 + 0.488743i \(0.162544\pi\)
\(224\) 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 −0.0911239 0.995840i \(-0.529046\pi\)
0.996534 0.0831862i \(-0.0265096\pi\)
\(234\) 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 0.119846 0.992793i \(-0.461760\pi\)
−0.799861 + 0.600186i \(0.795093\pi\)
\(240\) 0 0
\(241\) −21.4162 + 3.77626i −1.37954 + 0.243250i −0.813709 0.581272i \(-0.802555\pi\)
−0.565830 + 0.824522i \(0.691444\pi\)
\(242\) 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 0.210181 0.977663i \(-0.432595\pi\)
−0.999307 + 0.0372181i \(0.988150\pi\)
\(252\) 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 0.00418306 0.999991i \(-0.498668\pi\)
−0.639578 + 0.768727i \(0.720891\pi\)
\(258\) 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 0.991484 0.130227i \(-0.0415706\pi\)
0.887150 + 0.461481i \(0.152682\pi\)
\(264\) 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 −0.946145 0.323744i \(-0.895058\pi\)
0.999812 + 0.0193811i \(0.00616958\pi\)
\(270\) 0 0
\(271\) −4.01481 3.36882i −0.243882 0.204641i 0.512650 0.858597i \(-0.328664\pi\)
−0.756533 + 0.653956i \(0.773108\pi\)
\(272\) 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 −0.793929 0.608010i \(-0.791968\pi\)
0.923517 + 0.383558i \(0.125301\pi\)
\(278\) 0 0
\(279\) −1.52655 + 13.4514i −0.0913924 + 0.805314i
\(280\) 0 0
\(281\) −8.43804 + 7.08036i −0.503371 + 0.422379i −0.858789 0.512329i \(-0.828783\pi\)
0.355418 + 0.934707i \(0.384339\pi\)
\(282\) 0 0
\(283\) 3.71261 1.35128i 0.220691 0.0803251i −0.229308 0.973354i \(-0.573646\pi\)
0.450000 + 0.893029i \(0.351424\pi\)
\(284\) 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 0.406036 + 0.913857i \(0.366911\pi\)
−0.994441 + 0.105291i \(0.966422\pi\)
\(294\) 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 0.354836 0.934929i \(-0.384537\pi\)
0.0136720 + 0.999907i \(0.495648\pi\)
\(308\) 0 0
\(309\) −1.94956 + 34.4677i −0.110906 + 1.96080i
\(310\) 0 0
\(311\) −1.86672 + 1.07775i −0.105852 + 0.0611137i −0.551991 0.833850i \(-0.686132\pi\)
0.446139 + 0.894963i \(0.352799\pi\)
\(312\) 0 0
\(313\) 15.9106 + 5.79098i 0.899320 + 0.327326i 0.749980 0.661460i \(-0.230063\pi\)
0.149340 + 0.988786i \(0.452285\pi\)
\(314\) 0 0
\(315\) 7.08499 6.72938i 0.399194 0.379157i
\(316\) 0 0
\(317\) 0.961500 + 5.45293i 0.0540032 + 0.306267i 0.999831 0.0184023i \(-0.00585798\pi\)
−0.945827 + 0.324670i \(0.894747\pi\)
\(318\) 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 0.672106 0.740455i \(-0.265390\pi\)
−0.305200 + 0.952288i \(0.598723\pi\)
\(332\) 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 −0.497252 0.867606i \(-0.665657\pi\)
0.940772 + 0.339039i \(0.110102\pi\)
\(338\) 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 −0.681600 0.731725i \(-0.738716\pi\)
0.838967 + 0.544182i \(0.183160\pi\)
\(348\) 0 0
\(349\) 0.809906 + 1.40280i 0.0433533 + 0.0750901i 0.886888 0.461985i \(-0.152863\pi\)
−0.843535 + 0.537075i \(0.819529\pi\)
\(350\) 0 0
\(351\) −27.3523 + 0.137530i −1.45996 + 0.00734079i
\(352\) 0 0
\(353\) 5.92549 + 3.42108i 0.315382 + 0.182086i 0.649332 0.760505i \(-0.275048\pi\)
−0.333950 + 0.942591i \(0.608382\pi\)
\(354\) 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 0.897310 0.441401i \(-0.145518\pi\)
−0.971106 + 0.238647i \(0.923296\pi\)
\(360\) 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 0.996236 + 0.0866798i \(0.0276257\pi\)
−0.906510 + 0.422185i \(0.861263\pi\)
\(368\) 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 −0.310418 0.950600i \(-0.600469\pi\)
0.668035 + 0.744130i \(0.267136\pi\)
\(374\) 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 \(0.0890323\pi\)
−0.961137 + 0.276071i \(0.910968\pi\)
\(380\) 0 0
\(381\) 7.99358 + 10.6997i 0.409523 + 0.548165i
\(382\) 0 0
\(383\) −0.913805 + 5.18245i −0.0466933 + 0.264811i −0.999213 0.0396663i \(-0.987371\pi\)
0.952520 + 0.304477i \(0.0984816\pi\)
\(384\) 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 −0.722457 0.691416i \(-0.756987\pi\)
0.997868 0.0652695i \(-0.0207907\pi\)
\(390\) 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 −0.994542 0.104334i \(-0.966729\pi\)
−0.694799 + 0.719204i \(0.744507\pi\)
\(398\) 0 0
\(399\) 2.17405 8.20409i 0.108839 0.410718i
\(400\) 0 0
\(401\) 5.57564 2.02937i 0.278434 0.101342i −0.199029 0.979994i \(-0.563779\pi\)
0.477463 + 0.878652i \(0.341557\pi\)
\(402\) 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 −0.485536 0.874217i \(-0.661375\pi\)
0.933878 0.357592i \(-0.116402\pi\)
\(410\) 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 \(-0.935686\pi\)
0.979658 0.200675i \(-0.0643135\pi\)
\(420\) 0 0
\(421\) −16.5911 2.92547i −0.808603 0.142578i −0.245961 0.969280i \(-0.579104\pi\)
−0.562641 + 0.826701i \(0.690215\pi\)
\(422\) 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 0.826467 + 0.562985i \(0.190347\pi\)
−0.584073 + 0.811701i \(0.698542\pi\)
\(432\) 0 0
\(433\) −17.6845 21.0756i −0.849863 1.01283i −0.999709 0.0241176i \(-0.992322\pi\)
0.149846 0.988709i \(-0.452122\pi\)
\(434\) 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 0.999758 + 0.0220034i \(0.00700448\pi\)
−0.751715 + 0.659488i \(0.770773\pi\)
\(440\) 0 0
\(441\) 6.86897 + 15.7784i 0.327094 + 0.751353i
\(442\) 0 0
\(443\) −4.75117 + 0.837760i −0.225735 + 0.0398032i −0.285371 0.958417i \(-0.592117\pi\)
0.0596365 + 0.998220i \(0.481006\pi\)
\(444\) 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 0.905100 0.425198i \(-0.139796\pi\)
−0.820783 + 0.571241i \(0.806462\pi\)
\(450\) 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 −0.532019 0.846732i \(-0.678567\pi\)
0.926253 + 0.376903i \(0.123011\pi\)
\(462\) 0 0
\(463\) 10.6868 + 18.5101i 0.496659 + 0.860238i 0.999993 0.00385369i \(-0.00122667\pi\)
−0.503334 + 0.864092i \(0.667893\pi\)
\(464\) 0 0
\(465\) −21.6838 + 6.53133i −1.00556 + 0.302883i
\(466\) 0 0
\(467\) 8.01942 + 4.63001i 0.371094 + 0.214251i 0.673936 0.738789i \(-0.264602\pi\)
−0.302842 + 0.953041i \(0.597935\pi\)
\(468\) 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 0.842329 0.538964i \(-0.181184\pi\)
−0.677045 + 0.735942i \(0.736740\pi\)
\(480\) 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 −0.844885 0.534948i \(-0.820331\pi\)
0.0408365 + 0.999166i \(0.486998\pi\)
\(488\) 0 0
\(489\) −16.1368 0.912725i −0.729730 0.0412748i
\(490\) 0 0
\(491\) 32.2309 + 5.68317i 1.45456 + 0.256478i 0.844363 0.535772i \(-0.179979\pi\)
0.610196 + 0.792250i \(0.291091\pi\)
\(492\) 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 0.219243 0.975670i \(-0.429641\pi\)
−0.922776 + 0.385336i \(0.874086\pi\)
\(500\) 0 0
\(501\) 20.1635 + 8.65763i 0.900838 + 0.386794i
\(502\) 0 0
\(503\) 7.95923 21.8678i 0.354885 0.975037i −0.625893 0.779909i \(-0.715265\pi\)
0.980778 0.195128i \(-0.0625124\pi\)
\(504\) 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 −0.932362 0.361525i \(-0.882256\pi\)
0.194130 + 0.980976i \(0.437812\pi\)
\(510\) 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 −0.982558 0.185957i \(-0.940462\pi\)
0.652322 + 0.757942i \(0.273795\pi\)
\(522\) 0 0
\(523\) −2.38040 + 6.54010i −0.104088 + 0.285979i −0.980794 0.195048i \(-0.937514\pi\)
0.876706 + 0.481027i \(0.159736\pi\)
\(524\) 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 0.240427 0.970667i \(-0.422713\pi\)
−0.439755 + 0.898118i \(0.644935\pi\)
\(542\) 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 0.536021 0.844205i \(-0.319927\pi\)
−0.924458 + 0.381283i \(0.875482\pi\)
\(548\) 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 −0.164657 0.986351i \(-0.552652\pi\)
0.182625 + 0.983183i \(0.441540\pi\)
\(558\) 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 0.913010 0.407937i \(-0.133752\pi\)
−0.809789 + 0.586721i \(0.800418\pi\)
\(564\) 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 0.839074 0.544017i \(-0.183097\pi\)
−0.890670 + 0.454651i \(0.849764\pi\)
\(578\) 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 0.839859 + 0.542804i \(0.182637\pi\)
−0.294462 + 0.955663i \(0.595140\pi\)
\(588\) 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 0.820741 0.571300i \(-0.193561\pi\)
−0.705141 + 0.709067i \(0.749116\pi\)
\(594\) 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 −0.657380 0.753559i \(-0.728335\pi\)
−0.987961 + 0.154704i \(0.950558\pi\)
\(600\) 0 0
\(601\) −24.0390 + 13.8789i −0.980571 + 0.566133i −0.902443 0.430810i \(-0.858228\pi\)
−0.0781288 + 0.996943i \(0.524895\pi\)
\(602\) 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 \(-0.893989\pi\)
0.945051 0.326922i \(-0.106011\pi\)
\(608\) 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 0.920339 0.391121i \(-0.127913\pi\)
−0.225364 + 0.974275i \(0.572357\pi\)
\(614\) 0 0
\(615\) 12.1057 28.1940i 0.488150 1.13689i
\(616\) 0 0
\(617\) −15.8059 + 43.4264i −0.636322 + 1.74828i 0.0266596 + 0.999645i \(0.491513\pi\)
−0.662982 + 0.748636i \(0.730709\pi\)
\(618\) 0 0
\(619\) 20.8534 36.1192i 0.838170 1.45175i −0.0532532 0.998581i \(-0.516959\pi\)
0.891423 0.453172i \(-0.149708\pi\)
\(620\) 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 −0.573734 0.819042i \(-0.694506\pi\)
0.706971 + 0.707243i \(0.250061\pi\)
\(632\) 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 0.684917 0.728621i \(-0.259838\pi\)
−0.598617 + 0.801035i \(0.704283\pi\)
\(642\) 0 0
\(643\) −7.65253 + 43.3997i −0.301786 + 1.71152i 0.336471 + 0.941694i \(0.390766\pi\)
−0.638258 + 0.769823i \(0.720345\pi\)
\(644\) 0 0
\(645\) 8.67664 + 11.6141i 0.341643 + 0.457303i
\(646\) 0 0
\(647\) 20.3269i 0.799131i −0.916705 0.399566i \(-0.869161\pi\)
0.916705 0.399566i \(-0.130839\pi\)
\(648\) 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 0.384603 0.923082i \(-0.374338\pi\)
0.991714 + 0.128465i \(0.0410051\pi\)
\(654\) 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 0.816354 + 0.577552i \(0.195992\pi\)
−0.569588 + 0.821930i \(0.692897\pi\)
\(660\) 0 0
\(661\) −2.71797 3.23916i −0.105717 0.125989i 0.710591 0.703605i \(-0.248427\pi\)
−0.816308 + 0.577616i \(0.803983\pi\)
\(662\) 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 0.865975 0.500088i \(-0.166699\pi\)
−0.000101249 1.00000i \(0.500032\pi\)
\(674\) 0 0
\(675\) −0.0886972 17.6404i −0.00341396 0.678978i
\(676\) 0 0
\(677\) −16.1874 28.0374i −0.622132 1.07756i −0.989088 0.147326i \(-0.952934\pi\)
0.366956 0.930238i \(-0.380400\pi\)
\(678\) 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 0.975980 0.217859i \(-0.0699073\pi\)
−0.676662 + 0.736294i \(0.736574\pi\)
\(692\) 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 0.957094 + 0.289777i \(0.0935812\pi\)
−0.546911 + 0.837191i \(0.684197\pi\)
\(702\) 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 0.853687 + 0.520787i \(0.174361\pi\)
−0.624084 + 0.781358i \(0.714528\pi\)
\(710\) 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 0.440994 0.897510i \(-0.354626\pi\)
0.107432 + 0.994212i \(0.465737\pi\)
\(720\) 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 0.958651 0.284583i \(-0.0918551\pi\)
−0.113791 + 0.993505i \(0.536300\pi\)
\(728\) 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 −0.834339 0.551252i \(-0.814150\pi\)
0.894567 + 0.446933i \(0.147484\pi\)
\(734\) 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 −0.238078 0.971246i \(-0.576517\pi\)
0.441927 + 0.897051i \(0.354295\pi\)
\(740\) 0 0
\(741\) −32.6179 22.7055i −1.19825 0.834106i
\(742\) 0 0
\(743\) 27.7676 10.1066i 1.01870 0.370775i 0.221930 0.975063i \(-0.428764\pi\)
0.796766 + 0.604288i \(0.206542\pi\)
\(744\) 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 −0.773515 0.633778i \(-0.781503\pi\)
0.999932 + 0.0117037i \(0.00372548\pi\)
\(752\) 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 0.840701 + 0.541500i \(0.182143\pi\)
−0.975204 + 0.221307i \(0.928968\pi\)
\(758\) 0 0
\(759\) −29.1537 + 21.7802i −1.05821 + 0.790571i
\(760\) 0 0
\(761\) 29.1728i 1.05751i −0.848774 0.528757i \(-0.822658\pi\)
0.848774 0.528757i \(-0.177342\pi\)
\(762\) 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 −0.171493 0.985185i \(-0.554859\pi\)
−0.764636 + 0.644462i \(0.777081\pi\)
\(770\) 0 0
\(771\) 2.21092 + 18.6446i 0.0796244 + 0.671468i
\(772\) 0 0
\(773\) 7.60654 + 43.1388i 0.273588 + 1.55160i 0.743411 + 0.668835i \(0.233207\pi\)
−0.469823 + 0.882761i \(0.655682\pi\)
\(774\) 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 −0.192412 0.981314i \(-0.561631\pi\)
−0.946049 + 0.324023i \(0.894964\pi\)
\(788\) 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
\(794\)