Properties

Label 403.2.l.c.25.3
Level 403
Weight 2
Character 403.25
Analytic conductor 3.218
Analytic rank 0
Dimension 68
CM No

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.l (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(\zeta_{6})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 25.3
Character \(\chi\) = 403.25
Dual form 403.2.l.c.129.32

$q$-expansion

\(f(q)\) \(=\) \(q-2.46210i q^{2} +(0.199198 + 0.345021i) q^{3} -4.06196 q^{4} +(3.00007 + 1.73209i) q^{5} +(0.849477 - 0.490446i) q^{6} +(-1.28546 + 0.742161i) q^{7} +5.07675i q^{8} +(1.42064 - 2.46062i) q^{9} +O(q^{10})\) \(q-2.46210i q^{2} +(0.199198 + 0.345021i) q^{3} -4.06196 q^{4} +(3.00007 + 1.73209i) q^{5} +(0.849477 - 0.490446i) q^{6} +(-1.28546 + 0.742161i) q^{7} +5.07675i q^{8} +(1.42064 - 2.46062i) q^{9} +(4.26458 - 7.38647i) q^{10} +(4.37174 + 2.52402i) q^{11} +(-0.809133 - 1.40146i) q^{12} +(-0.987523 - 3.46768i) q^{13} +(1.82728 + 3.16494i) q^{14} +1.38011i q^{15} +4.37557 q^{16} +(-1.11215 - 1.92631i) q^{17} +(-6.05831 - 3.49776i) q^{18} +(6.03502 - 3.48432i) q^{19} +(-12.1861 - 7.03567i) q^{20} +(-0.512122 - 0.295674i) q^{21} +(6.21441 - 10.7637i) q^{22} -4.24394 q^{23} +(-1.75158 + 1.01128i) q^{24} +(3.50026 + 6.06263i) q^{25} +(-8.53779 + 2.43138i) q^{26} +2.32714 q^{27} +(5.22148 - 3.01462i) q^{28} +2.92107 q^{29} +3.39798 q^{30} +(-2.38419 + 5.03146i) q^{31} -0.619609i q^{32} +2.01112i q^{33} +(-4.74276 + 2.73824i) q^{34} -5.14195 q^{35} +(-5.77058 + 9.99493i) q^{36} +(1.44635 - 0.835052i) q^{37} +(-8.57876 - 14.8588i) q^{38} +(0.999709 - 1.03147i) q^{39} +(-8.79338 + 15.2306i) q^{40} +(0.651993 + 0.376429i) q^{41} +(-0.727979 + 1.26090i) q^{42} +(-4.05686 - 7.02669i) q^{43} +(-17.7578 - 10.2525i) q^{44} +(8.52403 - 4.92135i) q^{45} +10.4490i q^{46} +8.29508i q^{47} +(0.871604 + 1.50966i) q^{48} +(-2.39840 + 4.15414i) q^{49} +(14.9268 - 8.61801i) q^{50} +(0.443077 - 0.767432i) q^{51} +(4.01127 + 14.0856i) q^{52} +(-1.69421 + 2.93446i) q^{53} -5.72966i q^{54} +(8.74366 + 15.1445i) q^{55} +(-3.76776 - 6.52596i) q^{56} +(2.40433 + 1.38814i) q^{57} -7.19198i q^{58} +(-5.22180 + 3.01481i) q^{59} -5.60596i q^{60} -3.30204 q^{61} +(12.3880 + 5.87013i) q^{62} +4.21737i q^{63} +7.22559 q^{64} +(3.04369 - 12.1137i) q^{65} +4.95159 q^{66} +(-6.91629 - 3.99312i) q^{67} +(4.51752 + 7.82457i) q^{68} +(-0.845383 - 1.46425i) q^{69} +12.6600i q^{70} +(4.65051 + 2.68498i) q^{71} +(12.4920 + 7.21223i) q^{72} +(-10.1346 - 5.85124i) q^{73} +(-2.05598 - 3.56107i) q^{74} +(-1.39449 + 2.41533i) q^{75} +(-24.5140 + 14.1532i) q^{76} -7.49292 q^{77} +(-2.53959 - 2.46139i) q^{78} +(-0.119947 - 0.207754i) q^{79} +(13.1270 + 7.57887i) q^{80} +(-3.79836 - 6.57895i) q^{81} +(0.926806 - 1.60528i) q^{82} +(13.9719 + 8.06666i) q^{83} +(2.08022 + 1.20101i) q^{84} -7.70539i q^{85} +(-17.3004 + 9.98841i) q^{86} +(0.581871 + 1.00783i) q^{87} +(-12.8138 + 22.1942i) q^{88} -11.9872i q^{89} +(-12.1169 - 20.9870i) q^{90} +(3.84300 + 3.72466i) q^{91} +17.2387 q^{92} +(-2.21089 + 0.179661i) q^{93} +20.4233 q^{94} +24.1406 q^{95} +(0.213778 - 0.123425i) q^{96} +14.2496i q^{97} +(10.2279 + 5.90510i) q^{98} +(12.4213 - 7.17146i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68q - 6q^{3} - 76q^{4} - 40q^{9} + O(q^{10}) \) \( 68q - 6q^{3} - 76q^{4} - 40q^{9} + 8q^{10} - 10q^{12} - 3q^{13} + 10q^{14} + 84q^{16} + 6q^{17} + 4q^{22} - 44q^{23} + 30q^{25} - 3q^{26} - 12q^{27} + 48q^{29} - 4q^{30} - 48q^{35} + 40q^{36} + 60q^{38} - 14q^{39} + 20q^{40} - 10q^{42} - 12q^{43} + 32q^{48} + 58q^{49} + 20q^{51} - 27q^{52} + 8q^{53} - 36q^{55} - 50q^{56} - 12q^{61} - 74q^{62} - 15q^{65} + 164q^{66} + 4q^{68} - 34q^{69} - 4q^{74} + 20q^{75} - 200q^{77} - 58q^{78} - 80q^{79} - 82q^{81} - 66q^{82} + 52q^{87} + 16q^{88} - 14q^{90} - 70q^{91} + 108q^{92} - 4q^{94} + 76q^{95} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.46210i 1.74097i −0.492195 0.870485i \(-0.663805\pi\)
0.492195 0.870485i \(-0.336195\pi\)
\(3\) 0.199198 + 0.345021i 0.115007 + 0.199198i 0.917783 0.397083i \(-0.129978\pi\)
−0.802776 + 0.596281i \(0.796644\pi\)
\(4\) −4.06196 −2.03098
\(5\) 3.00007 + 1.73209i 1.34167 + 0.774614i 0.987052 0.160398i \(-0.0512777\pi\)
0.354618 + 0.935011i \(0.384611\pi\)
\(6\) 0.849477 0.490446i 0.346798 0.200224i
\(7\) −1.28546 + 0.742161i −0.485858 + 0.280510i −0.722855 0.691000i \(-0.757170\pi\)
0.236996 + 0.971511i \(0.423837\pi\)
\(8\) 5.07675i 1.79490i
\(9\) 1.42064 2.46062i 0.473547 0.820207i
\(10\) 4.26458 7.38647i 1.34858 2.33581i
\(11\) 4.37174 + 2.52402i 1.31813 + 0.761022i 0.983427 0.181303i \(-0.0580314\pi\)
0.334701 + 0.942324i \(0.391365\pi\)
\(12\) −0.809133 1.40146i −0.233576 0.404566i
\(13\) −0.987523 3.46768i −0.273890 0.961761i
\(14\) 1.82728 + 3.16494i 0.488360 + 0.845865i
\(15\) 1.38011i 0.356344i
\(16\) 4.37557 1.09389
\(17\) −1.11215 1.92631i −0.269737 0.467198i 0.699057 0.715066i \(-0.253603\pi\)
−0.968794 + 0.247868i \(0.920270\pi\)
\(18\) −6.05831 3.49776i −1.42796 0.824431i
\(19\) 6.03502 3.48432i 1.38453 0.799358i 0.391837 0.920035i \(-0.371840\pi\)
0.992692 + 0.120677i \(0.0385065\pi\)
\(20\) −12.1861 7.03567i −2.72490 1.57322i
\(21\) −0.512122 0.295674i −0.111754 0.0645213i
\(22\) 6.21441 10.7637i 1.32492 2.29482i
\(23\) −4.24394 −0.884922 −0.442461 0.896788i \(-0.645894\pi\)
−0.442461 + 0.896788i \(0.645894\pi\)
\(24\) −1.75158 + 1.01128i −0.357540 + 0.206426i
\(25\) 3.50026 + 6.06263i 0.700052 + 1.21253i
\(26\) −8.53779 + 2.43138i −1.67440 + 0.476834i
\(27\) 2.32714 0.447859
\(28\) 5.22148 3.01462i 0.986767 0.569710i
\(29\) 2.92107 0.542430 0.271215 0.962519i \(-0.412575\pi\)
0.271215 + 0.962519i \(0.412575\pi\)
\(30\) 3.39798 0.620384
\(31\) −2.38419 + 5.03146i −0.428214 + 0.903678i
\(32\) 0.619609i 0.109532i
\(33\) 2.01112i 0.350091i
\(34\) −4.74276 + 2.73824i −0.813377 + 0.469604i
\(35\) −5.14195 −0.869149
\(36\) −5.77058 + 9.99493i −0.961763 + 1.66582i
\(37\) 1.44635 0.835052i 0.237779 0.137282i −0.376377 0.926467i \(-0.622830\pi\)
0.614155 + 0.789185i \(0.289497\pi\)
\(38\) −8.57876 14.8588i −1.39166 2.41042i
\(39\) 0.999709 1.03147i 0.160082 0.165167i
\(40\) −8.79338 + 15.2306i −1.39035 + 2.40817i
\(41\) 0.651993 + 0.376429i 0.101824 + 0.0587883i 0.550047 0.835133i \(-0.314610\pi\)
−0.448223 + 0.893922i \(0.647943\pi\)
\(42\) −0.727979 + 1.26090i −0.112330 + 0.194561i
\(43\) −4.05686 7.02669i −0.618666 1.07156i −0.989729 0.142953i \(-0.954340\pi\)
0.371064 0.928607i \(-0.378993\pi\)
\(44\) −17.7578 10.2525i −2.67709 1.54562i
\(45\) 8.52403 4.92135i 1.27069 0.733632i
\(46\) 10.4490i 1.54062i
\(47\) 8.29508i 1.20996i 0.796240 + 0.604981i \(0.206819\pi\)
−0.796240 + 0.604981i \(0.793181\pi\)
\(48\) 0.871604 + 1.50966i 0.125805 + 0.217901i
\(49\) −2.39840 + 4.15414i −0.342628 + 0.593449i
\(50\) 14.9268 8.61801i 2.11097 1.21877i
\(51\) 0.443077 0.767432i 0.0620432 0.107462i
\(52\) 4.01127 + 14.0856i 0.556264 + 1.95332i
\(53\) −1.69421 + 2.93446i −0.232718 + 0.403079i −0.958607 0.284733i \(-0.908095\pi\)
0.725889 + 0.687812i \(0.241428\pi\)
\(54\) 5.72966i 0.779708i
\(55\) 8.74366 + 15.1445i 1.17900 + 2.04208i
\(56\) −3.76776 6.52596i −0.503488 0.872067i
\(57\) 2.40433 + 1.38814i 0.318461 + 0.183863i
\(58\) 7.19198i 0.944354i
\(59\) −5.22180 + 3.01481i −0.679821 + 0.392495i −0.799788 0.600283i \(-0.795055\pi\)
0.119967 + 0.992778i \(0.461721\pi\)
\(60\) 5.60596i 0.723726i
\(61\) −3.30204 −0.422782 −0.211391 0.977402i \(-0.567799\pi\)
−0.211391 + 0.977402i \(0.567799\pi\)
\(62\) 12.3880 + 5.87013i 1.57328 + 0.745507i
\(63\) 4.21737i 0.531339i
\(64\) 7.22559 0.903199
\(65\) 3.04369 12.1137i 0.377524 1.50252i
\(66\) 4.95159 0.609498
\(67\) −6.91629 3.99312i −0.844960 0.487838i 0.0139872 0.999902i \(-0.495548\pi\)
−0.858947 + 0.512064i \(0.828881\pi\)
\(68\) 4.51752 + 7.82457i 0.547829 + 0.948868i
\(69\) −0.845383 1.46425i −0.101772 0.176275i
\(70\) 12.6600i 1.51316i
\(71\) 4.65051 + 2.68498i 0.551915 + 0.318648i 0.749894 0.661558i \(-0.230105\pi\)
−0.197979 + 0.980206i \(0.563438\pi\)
\(72\) 12.4920 + 7.21223i 1.47219 + 0.849970i
\(73\) −10.1346 5.85124i −1.18617 0.684836i −0.228736 0.973488i \(-0.573459\pi\)
−0.957434 + 0.288653i \(0.906793\pi\)
\(74\) −2.05598 3.56107i −0.239003 0.413966i
\(75\) −1.39449 + 2.41533i −0.161022 + 0.278898i
\(76\) −24.5140 + 14.1532i −2.81195 + 1.62348i
\(77\) −7.49292 −0.853898
\(78\) −2.53959 2.46139i −0.287552 0.278697i
\(79\) −0.119947 0.207754i −0.0134951 0.0233742i 0.859199 0.511642i \(-0.170962\pi\)
−0.872694 + 0.488267i \(0.837629\pi\)
\(80\) 13.1270 + 7.57887i 1.46764 + 0.847344i
\(81\) −3.79836 6.57895i −0.422040 0.730995i
\(82\) 0.926806 1.60528i 0.102349 0.177273i
\(83\) 13.9719 + 8.06666i 1.53361 + 0.885431i 0.999191 + 0.0402111i \(0.0128030\pi\)
0.534419 + 0.845219i \(0.320530\pi\)
\(84\) 2.08022 + 1.20101i 0.226970 + 0.131041i
\(85\) 7.70539i 0.835767i
\(86\) −17.3004 + 9.98841i −1.86555 + 1.07708i
\(87\) 0.581871 + 1.00783i 0.0623832 + 0.108051i
\(88\) −12.8138 + 22.1942i −1.36596 + 2.36591i
\(89\) 11.9872i 1.27064i −0.772248 0.635322i \(-0.780868\pi\)
0.772248 0.635322i \(-0.219132\pi\)
\(90\) −12.1169 20.9870i −1.27723 2.21223i
\(91\) 3.84300 + 3.72466i 0.402855 + 0.390451i
\(92\) 17.2387 1.79726
\(93\) −2.21089 + 0.179661i −0.229258 + 0.0186299i
\(94\) 20.4233 2.10651
\(95\) 24.1406 2.47677
\(96\) 0.213778 0.123425i 0.0218186 0.0125970i
\(97\) 14.2496i 1.44683i 0.690415 + 0.723414i \(0.257428\pi\)
−0.690415 + 0.723414i \(0.742572\pi\)
\(98\) 10.2279 + 5.90510i 1.03318 + 0.596505i
\(99\) 12.4213 7.17146i 1.24839 0.720759i
\(100\) −14.2179 24.6261i −1.42179 2.46261i
\(101\) −3.84809 −0.382899 −0.191450 0.981502i \(-0.561319\pi\)
−0.191450 + 0.981502i \(0.561319\pi\)
\(102\) −1.88950 1.09090i −0.187088 0.108015i
\(103\) −7.09556 + 12.2899i −0.699146 + 1.21096i 0.269616 + 0.962968i \(0.413103\pi\)
−0.968763 + 0.247989i \(0.920230\pi\)
\(104\) 17.6045 5.01340i 1.72627 0.491605i
\(105\) −1.02427 1.77408i −0.0999581 0.173133i
\(106\) 7.22494 + 4.17132i 0.701748 + 0.405155i
\(107\) −6.15370 10.6585i −0.594900 1.03040i −0.993561 0.113299i \(-0.963858\pi\)
0.398661 0.917099i \(-0.369475\pi\)
\(108\) −9.45274 −0.909591
\(109\) 8.60809i 0.824505i −0.911070 0.412253i \(-0.864742\pi\)
0.911070 0.412253i \(-0.135258\pi\)
\(110\) 37.2873 21.5278i 3.55520 2.05260i
\(111\) 0.576220 + 0.332681i 0.0546924 + 0.0315767i
\(112\) −5.62462 + 3.24737i −0.531476 + 0.306848i
\(113\) 5.06054 8.76510i 0.476055 0.824552i −0.523569 0.851984i \(-0.675400\pi\)
0.999624 + 0.0274319i \(0.00873294\pi\)
\(114\) 3.41774 5.91970i 0.320101 0.554431i
\(115\) −12.7321 7.35087i −1.18727 0.685472i
\(116\) −11.8653 −1.10166
\(117\) −9.93556 2.49641i −0.918543 0.230793i
\(118\) 7.42278 + 12.8566i 0.683322 + 1.18355i
\(119\) 2.85926 + 1.65079i 0.262108 + 0.151328i
\(120\) −7.00649 −0.639602
\(121\) 7.24139 + 12.5425i 0.658308 + 1.14022i
\(122\) 8.12995i 0.736051i
\(123\) 0.299935i 0.0270442i
\(124\) 9.68448 20.4376i 0.869692 1.83535i
\(125\) 6.93017i 0.619853i
\(126\) 10.3836 0.925046
\(127\) 5.52173 + 9.56392i 0.489974 + 0.848661i 0.999933 0.0115381i \(-0.00367276\pi\)
−0.509959 + 0.860199i \(0.670339\pi\)
\(128\) 19.0294i 1.68198i
\(129\) 1.61624 2.79940i 0.142302 0.246474i
\(130\) −29.8253 7.49389i −2.61585 0.657258i
\(131\) 5.36778 + 9.29727i 0.468985 + 0.812306i 0.999371 0.0354498i \(-0.0112864\pi\)
−0.530386 + 0.847756i \(0.677953\pi\)
\(132\) 8.16908i 0.711027i
\(133\) −5.17185 + 8.95791i −0.448456 + 0.776749i
\(134\) −9.83149 + 17.0286i −0.849311 + 1.47105i
\(135\) 6.98158 + 4.03081i 0.600878 + 0.346917i
\(136\) 9.77937 5.64612i 0.838574 0.484151i
\(137\) −16.6561 9.61638i −1.42302 0.821583i −0.426467 0.904503i \(-0.640242\pi\)
−0.996556 + 0.0829198i \(0.973575\pi\)
\(138\) −3.60513 + 2.08142i −0.306889 + 0.177182i
\(139\) −7.93064 −0.672668 −0.336334 0.941743i \(-0.609187\pi\)
−0.336334 + 0.941743i \(0.609187\pi\)
\(140\) 20.8864 1.76522
\(141\) −2.86197 + 1.65236i −0.241022 + 0.139154i
\(142\) 6.61069 11.4500i 0.554757 0.960867i
\(143\) 4.43531 17.6523i 0.370899 1.47616i
\(144\) 6.21611 10.7666i 0.518009 0.897218i
\(145\) 8.76341 + 5.05956i 0.727761 + 0.420173i
\(146\) −14.4064 + 24.9525i −1.19228 + 2.06509i
\(147\) −1.91102 −0.157618
\(148\) −5.87502 + 3.39194i −0.482923 + 0.278816i
\(149\) −4.98855 + 2.88014i −0.408678 + 0.235950i −0.690222 0.723598i \(-0.742487\pi\)
0.281544 + 0.959548i \(0.409154\pi\)
\(150\) 5.94678 + 3.43338i 0.485553 + 0.280334i
\(151\) 22.9377i 1.86665i 0.359037 + 0.933323i \(0.383105\pi\)
−0.359037 + 0.933323i \(0.616895\pi\)
\(152\) 17.6890 + 30.6383i 1.43477 + 2.48509i
\(153\) −6.31988 −0.510932
\(154\) 18.4484i 1.48661i
\(155\) −15.8677 + 10.9651i −1.27452 + 0.880737i
\(156\) −4.06077 + 4.18979i −0.325122 + 0.335451i
\(157\) −6.13397 −0.489544 −0.244772 0.969581i \(-0.578713\pi\)
−0.244772 + 0.969581i \(0.578713\pi\)
\(158\) −0.511513 + 0.295322i −0.0406938 + 0.0234946i
\(159\) −1.34993 −0.107057
\(160\) 1.07322 1.85887i 0.0848454 0.146956i
\(161\) 5.45541 3.14968i 0.429947 0.248230i
\(162\) −16.1981 + 9.35196i −1.27264 + 0.734759i
\(163\) 18.6598i 1.46155i 0.682621 + 0.730773i \(0.260840\pi\)
−0.682621 + 0.730773i \(0.739160\pi\)
\(164\) −2.64837 1.52904i −0.206803 0.119398i
\(165\) −3.48344 + 6.03349i −0.271185 + 0.469707i
\(166\) 19.8609 34.4002i 1.54151 2.66997i
\(167\) −2.41317 + 1.39324i −0.186737 + 0.107812i −0.590454 0.807071i \(-0.701051\pi\)
0.403717 + 0.914884i \(0.367718\pi\)
\(168\) 1.50106 2.59991i 0.115809 0.200588i
\(169\) −11.0496 + 6.84883i −0.849969 + 0.526833i
\(170\) −18.9715 −1.45505
\(171\) 19.7999i 1.51413i
\(172\) 16.4788 + 28.5421i 1.25650 + 2.17631i
\(173\) −11.5632 + 20.0280i −0.879131 + 1.52270i −0.0268346 + 0.999640i \(0.508543\pi\)
−0.852296 + 0.523059i \(0.824791\pi\)
\(174\) 2.48138 1.43263i 0.188113 0.108607i
\(175\) −8.99889 5.19551i −0.680252 0.392744i
\(176\) 19.1288 + 11.0440i 1.44189 + 0.832476i
\(177\) −2.08034 1.20109i −0.156368 0.0902793i
\(178\) −29.5138 −2.21215
\(179\) −1.17909 2.04225i −0.0881296 0.152645i 0.818591 0.574377i \(-0.194756\pi\)
−0.906721 + 0.421732i \(0.861422\pi\)
\(180\) −34.6242 + 19.9903i −2.58074 + 1.48999i
\(181\) 7.21894 12.5036i 0.536579 0.929383i −0.462506 0.886616i \(-0.653050\pi\)
0.999085 0.0427665i \(-0.0136171\pi\)
\(182\) 9.17050 9.46186i 0.679763 0.701359i
\(183\) −0.657758 1.13927i −0.0486229 0.0842173i
\(184\) 21.5454i 1.58835i
\(185\) 5.78554 0.425361
\(186\) 0.442343 + 5.44343i 0.0324342 + 0.399132i
\(187\) 11.2284i 0.821102i
\(188\) 33.6942i 2.45740i
\(189\) −2.99145 + 1.72711i −0.217596 + 0.125629i
\(190\) 59.4367i 4.31199i
\(191\) −0.572538 + 0.991665i −0.0414274 + 0.0717544i −0.885996 0.463694i \(-0.846524\pi\)
0.844568 + 0.535448i \(0.179857\pi\)
\(192\) 1.43932 + 2.49298i 0.103874 + 0.179915i
\(193\) −8.15663 + 4.70923i −0.587127 + 0.338978i −0.763961 0.645263i \(-0.776748\pi\)
0.176834 + 0.984241i \(0.443415\pi\)
\(194\) 35.0840 2.51888
\(195\) 4.78579 1.36289i 0.342718 0.0975988i
\(196\) 9.74217 16.8739i 0.695870 1.20528i
\(197\) −8.47055 4.89047i −0.603502 0.348432i 0.166916 0.985971i \(-0.446619\pi\)
−0.770418 + 0.637539i \(0.779952\pi\)
\(198\) −17.6569 30.5826i −1.25482 2.17341i
\(199\) 6.11906 10.5985i 0.433769 0.751309i −0.563426 0.826167i \(-0.690517\pi\)
0.997194 + 0.0748575i \(0.0238502\pi\)
\(200\) −30.7784 + 17.7699i −2.17636 + 1.25652i
\(201\) 3.18169i 0.224419i
\(202\) 9.47439i 0.666616i
\(203\) −3.75492 + 2.16790i −0.263544 + 0.152157i
\(204\) −1.79976 + 3.11727i −0.126008 + 0.218253i
\(205\) 1.30402 + 2.25862i 0.0910764 + 0.157749i
\(206\) 30.2589 + 17.4700i 2.10824 + 1.21719i
\(207\) −6.02911 + 10.4427i −0.419052 + 0.725819i
\(208\) −4.32097 15.1731i −0.299606 1.05206i
\(209\) 35.1780 2.43331
\(210\) −4.36797 + 2.52185i −0.301419 + 0.174024i
\(211\) 4.19236 + 7.26138i 0.288614 + 0.499894i 0.973479 0.228776i \(-0.0734723\pi\)
−0.684865 + 0.728670i \(0.740139\pi\)
\(212\) 6.88181 11.9196i 0.472644 0.818644i
\(213\) 2.13937i 0.146587i
\(214\) −26.2424 + 15.1510i −1.79389 + 1.03570i
\(215\) 28.1074i 1.91691i
\(216\) 11.8143i 0.803862i
\(217\) −0.669370 8.23720i −0.0454398 0.559177i
\(218\) −21.1940 −1.43544
\(219\) 4.66222i 0.315043i
\(220\) −35.5164 61.5162i −2.39451 4.14742i
\(221\) −5.58153 + 5.75886i −0.375454 + 0.387383i
\(222\) 0.819095 1.41871i 0.0549741 0.0952179i
\(223\) 2.95461 1.70585i 0.197856 0.114232i −0.397799 0.917472i \(-0.630226\pi\)
0.595655 + 0.803241i \(0.296893\pi\)
\(224\) 0.459850 + 0.796483i 0.0307250 + 0.0532173i
\(225\) 19.8905 1.32603
\(226\) −21.5806 12.4596i −1.43552 0.828798i
\(227\) −6.80984 3.93166i −0.451985 0.260954i 0.256683 0.966496i \(-0.417370\pi\)
−0.708668 + 0.705542i \(0.750704\pi\)
\(228\) −9.76626 5.63855i −0.646787 0.373422i
\(229\) 6.66003 3.84517i 0.440107 0.254096i −0.263536 0.964650i \(-0.584889\pi\)
0.703643 + 0.710553i \(0.251555\pi\)
\(230\) −18.0986 + 31.3477i −1.19339 + 2.06701i
\(231\) −1.49257 2.58521i −0.0982042 0.170095i
\(232\) 14.8295i 0.973607i
\(233\) 24.7033 1.61836 0.809182 0.587558i \(-0.199911\pi\)
0.809182 + 0.587558i \(0.199911\pi\)
\(234\) −6.14641 + 24.4624i −0.401803 + 1.59916i
\(235\) −14.3678 + 24.8858i −0.937253 + 1.62337i
\(236\) 21.2107 12.2460i 1.38070 0.797148i
\(237\) 0.0477864 0.0827685i 0.00310406 0.00537639i
\(238\) 4.06442 7.03978i 0.263457 0.456321i
\(239\) −14.1051 8.14357i −0.912382 0.526764i −0.0311853 0.999514i \(-0.509928\pi\)
−0.881197 + 0.472750i \(0.843262\pi\)
\(240\) 6.03878i 0.389802i
\(241\) −1.71627 + 0.990888i −0.110555 + 0.0638287i −0.554258 0.832345i \(-0.686998\pi\)
0.443703 + 0.896174i \(0.353664\pi\)
\(242\) 30.8808 17.8290i 1.98509 1.14609i
\(243\) 5.00396 8.66712i 0.321004 0.555996i
\(244\) 13.4127 0.858661
\(245\) −14.3907 + 8.30847i −0.919387 + 0.530808i
\(246\) 0.738471 0.0470832
\(247\) −18.0422 17.4867i −1.14800 1.11265i
\(248\) −25.5435 12.1039i −1.62201 0.768601i
\(249\) 6.42744i 0.407323i
\(250\) 17.0628 1.07915
\(251\) −2.02285 3.50367i −0.127681 0.221150i 0.795097 0.606483i \(-0.207420\pi\)
−0.922778 + 0.385333i \(0.874087\pi\)
\(252\) 17.1308i 1.07914i
\(253\) −18.5534 10.7118i −1.16644 0.673445i
\(254\) 23.5474 13.5951i 1.47749 0.853031i
\(255\) 2.65852 1.53490i 0.166483 0.0961190i
\(256\) −32.4011 −2.02507
\(257\) −2.95729 + 5.12217i −0.184470 + 0.319512i −0.943398 0.331663i \(-0.892390\pi\)
0.758927 + 0.651175i \(0.225724\pi\)
\(258\) −6.89242 3.97934i −0.429103 0.247743i
\(259\) −1.23949 + 2.14685i −0.0770179 + 0.133399i
\(260\) −12.3633 + 49.2055i −0.766742 + 3.05159i
\(261\) 4.14979 7.18765i 0.256866 0.444905i
\(262\) 22.8908 13.2160i 1.41420 0.816490i
\(263\) −9.61129 −0.592658 −0.296329 0.955086i \(-0.595762\pi\)
−0.296329 + 0.955086i \(0.595762\pi\)
\(264\) −10.2099 −0.628379
\(265\) −10.1655 + 5.86905i −0.624461 + 0.360533i
\(266\) 22.0553 + 12.7336i 1.35230 + 0.780749i
\(267\) 4.13584 2.38783i 0.253109 0.146133i
\(268\) 28.0937 + 16.2199i 1.71609 + 0.990788i
\(269\) 12.7942 22.1603i 0.780078 1.35113i −0.151818 0.988409i \(-0.548513\pi\)
0.931896 0.362726i \(-0.118154\pi\)
\(270\) 9.92428 17.1894i 0.603973 1.04611i
\(271\) 2.87701i 0.174766i 0.996175 + 0.0873831i \(0.0278504\pi\)
−0.996175 + 0.0873831i \(0.972150\pi\)
\(272\) −4.86630 8.42868i −0.295063 0.511064i
\(273\) −0.519569 + 2.06786i −0.0314458 + 0.125152i
\(274\) −23.6765 + 41.0090i −1.43035 + 2.47744i
\(275\) 35.3390i 2.13102i
\(276\) 3.43391 + 5.94770i 0.206697 + 0.358010i
\(277\) −4.47522 −0.268890 −0.134445 0.990921i \(-0.542925\pi\)
−0.134445 + 0.990921i \(0.542925\pi\)
\(278\) 19.5261i 1.17110i
\(279\) 8.99345 + 13.0145i 0.538424 + 0.779157i
\(280\) 26.1044i 1.56004i
\(281\) 5.66132i 0.337726i 0.985640 + 0.168863i \(0.0540095\pi\)
−0.985640 + 0.168863i \(0.945990\pi\)
\(282\) 4.06829 + 7.04648i 0.242263 + 0.419612i
\(283\) 13.1662 0.782648 0.391324 0.920253i \(-0.372017\pi\)
0.391324 + 0.920253i \(0.372017\pi\)
\(284\) −18.8902 10.9063i −1.12093 0.647167i
\(285\) 4.80876 + 8.32901i 0.284846 + 0.493368i
\(286\) −43.4618 10.9202i −2.56995 0.645725i
\(287\) −1.11748 −0.0659629
\(288\) −1.52462 0.880242i −0.0898393 0.0518688i
\(289\) 6.02623 10.4377i 0.354484 0.613985i
\(290\) 12.4572 21.5764i 0.731509 1.26701i
\(291\) −4.91641 + 2.83849i −0.288205 + 0.166395i
\(292\) 41.1665 + 23.7675i 2.40909 + 1.39089i
\(293\) 28.0869 16.2160i 1.64085 0.947348i 0.660324 0.750981i \(-0.270419\pi\)
0.980531 0.196367i \(-0.0629143\pi\)
\(294\) 4.70513i 0.274409i
\(295\) −20.8877 −1.21613
\(296\) 4.23935 + 7.34276i 0.246407 + 0.426790i
\(297\) 10.1736 + 5.87376i 0.590335 + 0.340830i
\(298\) 7.09121 + 12.2823i 0.410783 + 0.711496i
\(299\) 4.19098 + 14.7166i 0.242371 + 0.851083i
\(300\) 5.66435 9.81095i 0.327032 0.566435i
\(301\) 10.4299 + 6.02169i 0.601168 + 0.347084i
\(302\) 56.4751 3.24978
\(303\) −0.766531 1.32767i −0.0440361 0.0762727i
\(304\) 26.4066 15.2459i 1.51452 0.874411i
\(305\) −9.90632 5.71942i −0.567234 0.327493i
\(306\) 15.5602i 0.889517i
\(307\) 28.3557 16.3712i 1.61835 0.934353i 0.630998 0.775784i \(-0.282645\pi\)
0.987348 0.158568i \(-0.0506878\pi\)
\(308\) 30.4359 1.73425
\(309\) −5.65368 −0.321627
\(310\) 26.9972 + 39.0679i 1.53334 + 2.21891i
\(311\) −12.9861 −0.736376 −0.368188 0.929751i \(-0.620022\pi\)
−0.368188 + 0.929751i \(0.620022\pi\)
\(312\) 5.23651 + 5.07527i 0.296459 + 0.287331i
\(313\) −11.9078 20.6249i −0.673069 1.16579i −0.977029 0.213106i \(-0.931642\pi\)
0.303960 0.952685i \(-0.401691\pi\)
\(314\) 15.1025i 0.852281i
\(315\) −7.30486 + 12.6524i −0.411583 + 0.712882i
\(316\) 0.487220 + 0.843889i 0.0274082 + 0.0474725i
\(317\) 14.9941 8.65687i 0.842154 0.486218i −0.0158416 0.999875i \(-0.505043\pi\)
0.857996 + 0.513657i \(0.171709\pi\)
\(318\) 3.32367i 0.186382i
\(319\) 12.7702 + 7.37285i 0.714992 + 0.412801i
\(320\) 21.6773 + 12.5154i 1.21180 + 0.699630i
\(321\) 2.45161 4.24631i 0.136835 0.237006i
\(322\) −7.75484 13.4318i −0.432161 0.748524i
\(323\) −13.4237 7.75019i −0.746916 0.431232i
\(324\) 15.4288 + 26.7234i 0.857154 + 1.48463i
\(325\) 17.5667 18.1248i 0.974424 1.00538i
\(326\) 45.9423 2.54451
\(327\) 2.96997 1.71471i 0.164240 0.0948238i
\(328\) −1.91103 + 3.31001i −0.105519 + 0.182764i
\(329\) −6.15628 10.6630i −0.339407 0.587870i
\(330\) 14.8551 + 8.57659i 0.817745 + 0.472126i
\(331\) −3.27545 1.89108i −0.180035 0.103943i 0.407274 0.913306i \(-0.366479\pi\)
−0.587309 + 0.809363i \(0.699813\pi\)
\(332\) −56.7531 32.7664i −3.11473 1.79829i
\(333\) 4.74523i 0.260037i
\(334\) 3.43031 + 5.94147i 0.187698 + 0.325103i
\(335\) −13.8329 23.9593i −0.755772 1.30903i
\(336\) −2.24082 1.29374i −0.122247 0.0705793i
\(337\) 25.1289 1.36886 0.684429 0.729079i \(-0.260051\pi\)
0.684429 + 0.729079i \(0.260051\pi\)
\(338\) 16.8625 + 27.2053i 0.917200 + 1.47977i
\(339\) 4.03219 0.218999
\(340\) 31.2989i 1.69742i
\(341\) −23.1226 + 15.9785i −1.25216 + 0.865283i
\(342\) −48.7493 −2.63606
\(343\) 17.5102i 0.945463i
\(344\) 35.6727 20.5957i 1.92334 1.11044i
\(345\) 5.85711i 0.315336i
\(346\) 49.3110 + 28.4697i 2.65097 + 1.53054i
\(347\) −12.8766 22.3030i −0.691253 1.19729i −0.971428 0.237336i \(-0.923726\pi\)
0.280175 0.959949i \(-0.409608\pi\)
\(348\) −2.36354 4.09376i −0.126699 0.219449i
\(349\) 33.9441i 1.81699i 0.417899 + 0.908493i \(0.362767\pi\)
−0.417899 + 0.908493i \(0.637233\pi\)
\(350\) −12.7919 + 22.1562i −0.683755 + 1.18430i
\(351\) −2.29811 8.06978i −0.122664 0.430733i
\(352\) 1.56391 2.70877i 0.0833566 0.144378i
\(353\) −23.3452 + 13.4783i −1.24254 + 0.717380i −0.969610 0.244654i \(-0.921326\pi\)
−0.272928 + 0.962034i \(0.587992\pi\)
\(354\) −2.95720 + 5.12202i −0.157173 + 0.272232i
\(355\) 9.30123 + 16.1102i 0.493658 + 0.855041i
\(356\) 48.6916i 2.58065i
\(357\) 1.31534i 0.0696150i
\(358\) −5.02823 + 2.90305i −0.265750 + 0.153431i
\(359\) −21.2179 12.2502i −1.11984 0.646540i −0.178480 0.983944i \(-0.557118\pi\)
−0.941360 + 0.337404i \(0.890451\pi\)
\(360\) 24.9845 + 43.2743i 1.31680 + 2.28076i
\(361\) 14.7810 25.6014i 0.777946 1.34744i
\(362\) −30.7851 17.7738i −1.61803 0.934169i
\(363\) −2.88494 + 4.99686i −0.151420 + 0.262267i
\(364\) −15.6101 15.1294i −0.818190 0.792997i
\(365\) −20.2697 35.1082i −1.06097 1.83765i
\(366\) −2.80500 + 1.61947i −0.146620 + 0.0846510i
\(367\) 6.46581 11.1991i 0.337513 0.584589i −0.646452 0.762955i \(-0.723748\pi\)
0.983964 + 0.178366i \(0.0570811\pi\)
\(368\) −18.5696 −0.968009
\(369\) 1.85250 1.06954i 0.0964371 0.0556780i
\(370\) 14.2446i 0.740541i
\(371\) 5.02951i 0.261119i
\(372\) 8.98052 0.729774i 0.465618 0.0378370i
\(373\) 11.5002 0.595458 0.297729 0.954650i \(-0.403771\pi\)
0.297729 + 0.954650i \(0.403771\pi\)
\(374\) −27.6455 −1.42951
\(375\) −2.39105 + 1.38047i −0.123473 + 0.0712874i
\(376\) −42.1120 −2.17176
\(377\) −2.88463 10.1293i −0.148566 0.521688i
\(378\) 4.25233 + 7.36525i 0.218716 + 0.378828i
\(379\) −1.36411 + 0.787568i −0.0700695 + 0.0404547i −0.534625 0.845089i \(-0.679547\pi\)
0.464556 + 0.885544i \(0.346214\pi\)
\(380\) −98.0580 −5.03027
\(381\) −2.19983 + 3.81022i −0.112701 + 0.195204i
\(382\) 2.44158 + 1.40965i 0.124922 + 0.0721239i
\(383\) 10.8329 + 6.25438i 0.553536 + 0.319584i 0.750547 0.660817i \(-0.229790\pi\)
−0.197011 + 0.980401i \(0.563124\pi\)
\(384\) 6.56553 3.79061i 0.335046 0.193439i
\(385\) −22.4793 12.9784i −1.14565 0.661441i
\(386\) 11.5946 + 20.0825i 0.590151 + 1.02217i
\(387\) −23.0534 −1.17187
\(388\) 57.8812i 2.93847i
\(389\) −1.39417 2.41477i −0.0706872 0.122434i 0.828515 0.559966i \(-0.189186\pi\)
−0.899203 + 0.437532i \(0.855853\pi\)
\(390\) −3.35559 11.7831i −0.169917 0.596661i
\(391\) 4.71991 + 8.17512i 0.238696 + 0.413433i
\(392\) −21.0895 12.1760i −1.06518 0.614983i
\(393\) −2.13850 + 3.70399i −0.107873 + 0.186842i
\(394\) −12.0409 + 20.8554i −0.606609 + 1.05068i
\(395\) 0.831036i 0.0418140i
\(396\) −50.4549 + 29.1301i −2.53545 + 1.46384i
\(397\) 10.6286 6.13644i 0.533436 0.307979i −0.208979 0.977920i \(-0.567014\pi\)
0.742414 + 0.669941i \(0.233681\pi\)
\(398\) −26.0947 15.0658i −1.30801 0.755178i
\(399\) −4.12089 −0.206302
\(400\) 15.3156 + 26.5275i 0.765782 + 1.32637i
\(401\) 10.7458i 0.536618i 0.963333 + 0.268309i \(0.0864648\pi\)
−0.963333 + 0.268309i \(0.913535\pi\)
\(402\) −7.83364 −0.390707
\(403\) 19.8019 + 3.29893i 0.986405 + 0.164331i
\(404\) 15.6308 0.777659
\(405\) 26.3164i 1.30767i
\(406\) 5.33761 + 9.24501i 0.264901 + 0.458822i
\(407\) 8.43076 0.417897
\(408\) 3.89606 + 2.24939i 0.192884 + 0.111361i
\(409\) −8.12291 + 4.68976i −0.401652 + 0.231894i −0.687197 0.726472i \(-0.741159\pi\)
0.285545 + 0.958365i \(0.407826\pi\)
\(410\) 5.56096 3.21062i 0.274636 0.158561i
\(411\) 7.66225i 0.377951i
\(412\) 28.8218 49.9209i 1.41995 2.45943i
\(413\) 4.47495 7.75084i 0.220198 0.381394i
\(414\) 25.7111 + 14.8443i 1.26363 + 0.729557i
\(415\) 27.9443 + 48.4010i 1.37173 + 2.37591i
\(416\) −2.14861 + 0.611878i −0.105344 + 0.0299998i
\(417\) −1.57977 2.73624i −0.0773615 0.133994i
\(418\) 86.6119i 4.23633i
\(419\) 21.8811 1.06896 0.534482 0.845180i \(-0.320507\pi\)
0.534482 + 0.845180i \(0.320507\pi\)
\(420\) 4.16052 + 7.20623i 0.203013 + 0.351628i
\(421\) 10.0173 + 5.78349i 0.488213 + 0.281870i 0.723833 0.689975i \(-0.242379\pi\)
−0.235620 + 0.971845i \(0.575712\pi\)
\(422\) 17.8783 10.3220i 0.870301 0.502468i
\(423\) 20.4110 + 11.7843i 0.992419 + 0.572973i
\(424\) −14.8975 8.60108i −0.723487 0.417705i
\(425\) 7.78565 13.4851i 0.377660 0.654126i
\(426\) 5.26734 0.255203
\(427\) 4.24463 2.45064i 0.205412 0.118595i
\(428\) 24.9960 + 43.2944i 1.20823 + 2.09271i
\(429\) 6.97392 1.98603i 0.336704 0.0958863i
\(430\) −69.2033 −3.33728
\(431\) −5.95706 + 3.43931i −0.286941 + 0.165666i −0.636562 0.771226i \(-0.719644\pi\)
0.349620 + 0.936891i \(0.386311\pi\)
\(432\) 10.1826 0.489909
\(433\) 4.73695 0.227643 0.113822 0.993501i \(-0.463691\pi\)
0.113822 + 0.993501i \(0.463691\pi\)
\(434\) −20.2808 + 1.64806i −0.973511 + 0.0791094i
\(435\) 4.03141i 0.193291i
\(436\) 34.9657i 1.67455i
\(437\) −25.6122 + 14.7872i −1.22520 + 0.707369i
\(438\) −11.4789 −0.548481
\(439\) 4.00379 6.93476i 0.191090 0.330978i −0.754522 0.656275i \(-0.772131\pi\)
0.945612 + 0.325297i \(0.105464\pi\)
\(440\) −76.8846 + 44.3894i −3.66533 + 2.11618i
\(441\) 6.81451 + 11.8031i 0.324501 + 0.562052i
\(442\) 14.1789 + 13.7423i 0.674422 + 0.653655i
\(443\) 3.94248 6.82858i 0.187313 0.324436i −0.757040 0.653368i \(-0.773355\pi\)
0.944354 + 0.328932i \(0.106689\pi\)
\(444\) −2.34058 1.35134i −0.111079 0.0641315i
\(445\) 20.7629 35.9625i 0.984257 1.70478i
\(446\) −4.19997 7.27456i −0.198874 0.344461i
\(447\) −1.98742 1.14744i −0.0940016 0.0542718i
\(448\) −9.28821 + 5.36255i −0.438827 + 0.253357i
\(449\) 35.0216i 1.65277i 0.563106 + 0.826385i \(0.309606\pi\)
−0.563106 + 0.826385i \(0.690394\pi\)
\(450\) 48.9724i 2.30858i
\(451\) 1.90023 + 3.29129i 0.0894783 + 0.154981i
\(452\) −20.5557 + 35.6035i −0.966857 + 1.67465i
\(453\) −7.91400 + 4.56915i −0.371832 + 0.214677i
\(454\) −9.68016 + 16.7665i −0.454312 + 0.786892i
\(455\) 5.07780 + 17.8306i 0.238051 + 0.835913i
\(456\) −7.04723 + 12.2062i −0.330017 + 0.571605i
\(457\) 17.0800i 0.798968i 0.916740 + 0.399484i \(0.130811\pi\)
−0.916740 + 0.399484i \(0.869189\pi\)
\(458\) −9.46721 16.3977i −0.442374 0.766214i
\(459\) −2.58814 4.48278i −0.120804 0.209238i
\(460\) 51.7172 + 29.8589i 2.41133 + 1.39218i
\(461\) 26.3842i 1.22884i −0.788981 0.614418i \(-0.789391\pi\)
0.788981 0.614418i \(-0.210609\pi\)
\(462\) −6.36507 + 3.67487i −0.296130 + 0.170971i
\(463\) 24.9390i 1.15901i 0.814968 + 0.579507i \(0.196755\pi\)
−0.814968 + 0.579507i \(0.803245\pi\)
\(464\) 12.7814 0.593359
\(465\) −6.94399 3.29046i −0.322020 0.152591i
\(466\) 60.8220i 2.81752i
\(467\) 12.0669 0.558391 0.279195 0.960234i \(-0.409932\pi\)
0.279195 + 0.960234i \(0.409932\pi\)
\(468\) 40.3578 + 10.1403i 1.86554 + 0.468735i
\(469\) 11.8542 0.547374
\(470\) 61.2714 + 35.3750i 2.82624 + 1.63173i
\(471\) −1.22187 2.11635i −0.0563009 0.0975161i
\(472\) −15.3054 26.5098i −0.704489 1.22021i
\(473\) 40.9585i 1.88327i
\(474\) −0.203785 0.117655i −0.00936014 0.00540408i
\(475\) 42.2483 + 24.3921i 1.93848 + 1.11918i
\(476\) −11.6142 6.70544i −0.532335 0.307344i
\(477\) 4.81373 + 8.33762i 0.220405 + 0.381753i
\(478\) −20.0503 + 34.7282i −0.917081 + 1.58843i
\(479\) 22.2703 12.8578i 1.01756 0.587487i 0.104162 0.994560i \(-0.466784\pi\)
0.913395 + 0.407073i \(0.133451\pi\)
\(480\) 0.855131 0.0390312
\(481\) −4.32400 4.19085i −0.197157 0.191086i
\(482\) 2.43967 + 4.22563i 0.111124 + 0.192472i
\(483\) 2.17341 + 1.25482i 0.0988937 + 0.0570963i
\(484\) −29.4142 50.9469i −1.33701 2.31577i
\(485\) −24.6816 + 42.7497i −1.12073 + 1.94116i
\(486\) −21.3393 12.3203i −0.967972 0.558859i
\(487\) 1.12492 + 0.649473i 0.0509750 + 0.0294305i 0.525271 0.850935i \(-0.323964\pi\)
−0.474296 + 0.880365i \(0.657297\pi\)
\(488\) 16.7636i 0.758852i
\(489\) −6.43801 + 3.71699i −0.291137 + 0.168088i
\(490\) 20.4563 + 35.4314i 0.924122 + 1.60063i
\(491\) 10.2354 17.7282i 0.461916 0.800062i −0.537140 0.843493i \(-0.680495\pi\)
0.999056 + 0.0434305i \(0.0138287\pi\)
\(492\) 1.21832i 0.0549262i
\(493\) −3.24868 5.62688i −0.146313 0.253422i
\(494\) −43.0540 + 44.4218i −1.93709 + 1.99863i
\(495\) 49.6864 2.23324
\(496\) −10.4322 + 22.0155i −0.468420 + 0.988526i
\(497\) −7.97073 −0.357536
\(498\) 15.8250 0.709136
\(499\) −21.4683 + 12.3947i −0.961052 + 0.554864i −0.896497 0.443050i \(-0.853896\pi\)
−0.0645556 + 0.997914i \(0.520563\pi\)
\(500\) 28.1500i 1.25891i
\(501\) −0.961396 0.555062i −0.0429520 0.0247984i
\(502\) −8.62641 + 4.98046i −0.385015 + 0.222289i
\(503\) −4.61974 8.00163i −0.205984 0.356775i 0.744462 0.667665i \(-0.232706\pi\)
−0.950446 + 0.310890i \(0.899373\pi\)
\(504\) −21.4105 −0.953701
\(505\) −11.5445 6.66523i −0.513724 0.296599i
\(506\) −26.3735 + 45.6803i −1.17245 + 2.03074i
\(507\) −4.56404 2.44807i −0.202696 0.108723i
\(508\) −22.4290 38.8482i −0.995127 1.72361i
\(509\) 5.24740 + 3.02959i 0.232587 + 0.134284i 0.611765 0.791040i \(-0.290460\pi\)
−0.379178 + 0.925324i \(0.623793\pi\)
\(510\) −3.77908 6.54555i −0.167340 0.289842i
\(511\) 17.3702 0.768414
\(512\) 41.7162i 1.84361i
\(513\) 14.0443 8.10850i 0.620073 0.357999i
\(514\) 12.6113 + 7.28115i 0.556261 + 0.321158i
\(515\) −42.5743 + 24.5803i −1.87605 + 1.08314i
\(516\) −6.56508 + 11.3710i −0.289011 + 0.500583i
\(517\) −20.9370 + 36.2639i −0.920807 + 1.59488i
\(518\) 5.28577 + 3.05174i 0.232243 + 0.134086i
\(519\) −9.21343 −0.404425
\(520\) 61.4984 + 15.4521i 2.69688 + 0.677618i
\(521\) −5.22040 9.04200i −0.228710 0.396137i 0.728716 0.684816i \(-0.240117\pi\)
−0.957426 + 0.288679i \(0.906784\pi\)
\(522\) −17.6967 10.2172i −0.774566 0.447196i
\(523\) −18.7336 −0.819163 −0.409581 0.912274i \(-0.634325\pi\)
−0.409581 + 0.912274i \(0.634325\pi\)
\(524\) −21.8037 37.7651i −0.952499 1.64978i
\(525\) 4.13974i 0.180673i
\(526\) 23.6640i 1.03180i
\(527\) 12.3437 1.00307i 0.537701 0.0436946i
\(528\) 8.79979i 0.382962i
\(529\) −4.98901 −0.216913
\(530\) 14.4502 + 25.0285i 0.627677 + 1.08717i
\(531\) 17.1318i 0.743459i
\(532\) 21.0078 36.3866i 0.910805 1.57756i
\(533\) 0.661475 2.63264i 0.0286517 0.114032i
\(534\) −5.87908 10.1829i −0.254413 0.440656i
\(535\) 42.6350i 1.84327i
\(536\) 20.2721 35.1123i 0.875621 1.51662i
\(537\) 0.469746 0.813624i 0.0202710 0.0351105i
\(538\) −54.5609 31.5007i −2.35229 1.35809i
\(539\) −20.9703 + 12.1072i −0.903255 + 0.521494i
\(540\) −28.3588 16.3730i −1.22037 0.704581i
\(541\) −7.65848 + 4.42162i −0.329264 + 0.190100i −0.655514 0.755183i \(-0.727548\pi\)
0.326250 + 0.945283i \(0.394215\pi\)
\(542\) 7.08351 0.304263
\(543\) 5.75199 0.246841
\(544\) −1.19356 + 0.689100i −0.0511733 + 0.0295449i
\(545\) 14.9100 25.8248i 0.638673 1.10621i
\(546\) 5.09128 + 1.27923i 0.217887 + 0.0547461i
\(547\) 4.54988 7.88063i 0.194539 0.336951i −0.752210 0.658923i \(-0.771012\pi\)
0.946749 + 0.321972i \(0.104346\pi\)
\(548\) 67.6562 + 39.0613i 2.89013 + 1.66862i
\(549\) −4.69100 + 8.12506i −0.200207 + 0.346769i
\(550\) 87.0082 3.71004
\(551\) 17.6287 10.1780i 0.751009 0.433595i
\(552\) 7.43361 4.29180i 0.316395 0.182671i
\(553\) 0.308374 + 0.178040i 0.0131134 + 0.00757103i
\(554\) 11.0185i 0.468130i
\(555\) 1.15247 + 1.99613i 0.0489195 + 0.0847310i
\(556\) 32.2139 1.36617
\(557\) 35.9167i 1.52184i −0.648846 0.760919i \(-0.724748\pi\)
0.648846 0.760919i \(-0.275252\pi\)
\(558\) 32.0430 22.1428i 1.35649 0.937379i
\(559\) −20.3601 + 21.0069i −0.861139 + 0.888498i
\(560\) −22.4990 −0.950755
\(561\) 3.87403 2.23667i 0.163562 0.0944324i
\(562\) 13.9388 0.587971
\(563\) 16.1439 27.9620i 0.680383 1.17846i −0.294481 0.955657i \(-0.595147\pi\)
0.974864 0.222801i \(-0.0715200\pi\)
\(564\) 11.6252 6.71182i 0.489510 0.282619i
\(565\) 30.3639 17.5306i 1.27742 0.737518i
\(566\) 32.4165i 1.36257i
\(567\) 9.76528 + 5.63799i 0.410103 + 0.236773i
\(568\) −13.6309 + 23.6095i −0.571942 + 0.990632i
\(569\) 15.0085 25.9955i 0.629189 1.08979i −0.358526 0.933520i \(-0.616720\pi\)
0.987715 0.156268i \(-0.0499462\pi\)
\(570\) 20.5069 11.8397i 0.858939 0.495909i
\(571\) 3.20425 5.54993i 0.134094 0.232257i −0.791157 0.611613i \(-0.790521\pi\)
0.925251 + 0.379356i \(0.123854\pi\)
\(572\) −18.0160 + 71.7029i −0.753289 + 2.99805i
\(573\) −0.456194 −0.0190578
\(574\) 2.75136i 0.114839i
\(575\) −14.8549 25.7294i −0.619492 1.07299i
\(576\) 10.2650 17.7795i 0.427707 0.740811i
\(577\) 19.9965 11.5450i 0.832467 0.480625i −0.0222295 0.999753i \(-0.507076\pi\)
0.854697 + 0.519128i \(0.173743\pi\)
\(578\) −25.6988 14.8372i −1.06893 0.617147i
\(579\) −3.24957 1.87614i −0.135047 0.0779696i
\(580\) −35.5966 20.5517i −1.47807 0.853362i
\(581\) −23.9470 −0.993490
\(582\) 6.98865 + 12.1047i 0.289689 + 0.501756i
\(583\) −14.8133 + 8.55245i −0.613504 + 0.354206i
\(584\) 29.7053 51.4510i 1.22921 2.12906i
\(585\) −25.4833 24.6987i −1.05361 1.02116i
\(586\) −39.9254 69.1529i −1.64930 2.85668i
\(587\) 8.04079i 0.331879i −0.986136 0.165940i \(-0.946934\pi\)
0.986136 0.165940i \(-0.0530657\pi\)
\(588\) 7.76248 0.320119
\(589\) 3.14258 + 38.6723i 0.129488 + 1.59346i
\(590\) 51.4276i 2.11724i
\(591\) 3.89669i 0.160288i
\(592\) 6.32861 3.65383i 0.260104 0.150171i
\(593\) 2.18862i 0.0898759i 0.998990 + 0.0449379i \(0.0143090\pi\)
−0.998990 + 0.0449379i \(0.985691\pi\)
\(594\) 14.4618 25.0486i 0.593375 1.02776i
\(595\) 5.71864 + 9.90497i 0.234441 + 0.406064i
\(596\) 20.2633 11.6990i 0.830016 0.479210i
\(597\) 4.87561 0.199546
\(598\) 36.2338 10.3186i 1.48171 0.421960i
\(599\) −17.5330 + 30.3680i −0.716377 + 1.24080i 0.246049 + 0.969257i \(0.420868\pi\)
−0.962426 + 0.271544i \(0.912466\pi\)
\(600\) −12.2620 7.07947i −0.500594 0.289018i
\(601\) −10.1110 17.5128i −0.412436 0.714360i 0.582719 0.812673i \(-0.301989\pi\)
−0.995156 + 0.0983131i \(0.968655\pi\)
\(602\) 14.8260 25.6794i 0.604263 1.04661i
\(603\) −19.6511 + 11.3456i −0.800256 + 0.462028i
\(604\) 93.1721i 3.79112i
\(605\) 50.1709i 2.03974i
\(606\) −3.26886 + 1.88728i −0.132788 + 0.0766655i
\(607\) −14.4354 + 25.0029i −0.585917 + 1.01484i 0.408844 + 0.912604i \(0.365932\pi\)
−0.994760 + 0.102233i \(0.967401\pi\)
\(608\) −2.15892 3.73935i −0.0875557 0.151651i
\(609\) −1.49594 0.863684i −0.0606187 0.0349982i
\(610\) −14.0818 + 24.3904i −0.570155 + 0.987538i
\(611\) 28.7647 8.19158i 1.16369 0.331396i
\(612\) 25.6711 1.03769
\(613\) −29.0142 + 16.7513i −1.17187 + 0.676581i −0.954120 0.299424i \(-0.903206\pi\)
−0.217752 + 0.976004i \(0.569872\pi\)
\(614\) −40.3075 69.8147i −1.62668 2.81749i
\(615\) −0.519514 + 0.899825i −0.0209488 + 0.0362844i
\(616\) 38.0397i 1.53266i
\(617\) 0.0633847 0.0365952i 0.00255177 0.00147327i −0.498724 0.866761i \(-0.666198\pi\)
0.501275 + 0.865288i \(0.332864\pi\)
\(618\) 13.9200i 0.559943i
\(619\) 11.9477i 0.480218i −0.970746 0.240109i \(-0.922817\pi\)
0.970746 0.240109i \(-0.0771832\pi\)
\(620\) 64.4538 44.5397i 2.58853 1.78876i
\(621\) −9.87624 −0.396320
\(622\) 31.9732i 1.28201i
\(623\) 8.89644 + 15.4091i 0.356429 + 0.617352i
\(624\) 4.37429 4.51327i 0.175112 0.180675i
\(625\) 5.49764 9.52219i 0.219906 0.380888i
\(626\) −50.7807 + 29.3183i −2.02961 + 1.17179i
\(627\) 7.00739 + 12.1371i 0.279848 + 0.484711i
\(628\) 24.9159 0.994252
\(629\) −3.21713 1.85741i −0.128275 0.0740598i
\(630\) 31.1515 + 17.9853i 1.24111 + 0.716553i
\(631\) −10.4585 6.03822i −0.416346 0.240378i 0.277167 0.960822i \(-0.410605\pi\)
−0.693513 + 0.720444i \(0.743938\pi\)
\(632\) 1.05472 0.608941i 0.0419544 0.0242224i
\(633\) −1.67022 + 2.89290i −0.0663852 + 0.114983i
\(634\) −21.3141 36.9171i −0.846491 1.46617i
\(635\) 38.2565i 1.51816i
\(636\) 5.48336 0.217430
\(637\) 16.7737 + 4.21455i 0.664598 + 0.166987i
\(638\) 18.1527 31.4415i 0.718674 1.24478i
\(639\) 13.2134 7.62877i 0.522715 0.301789i
\(640\) 32.9606 57.0894i 1.30288 2.25666i
\(641\) −13.0191 + 22.5498i −0.514224 + 0.890663i 0.485640 + 0.874159i \(0.338587\pi\)
−0.999864 + 0.0165034i \(0.994747\pi\)
\(642\) −10.4548 6.03611i −0.412620 0.238226i
\(643\) 10.0878i 0.397824i 0.980017 + 0.198912i \(0.0637408\pi\)
−0.980017 + 0.198912i \(0.936259\pi\)
\(644\) −22.1596 + 12.7939i −0.873212 + 0.504149i
\(645\) 9.69763 5.59893i 0.381844 0.220458i
\(646\) −19.0818 + 33.0506i −0.750763 + 1.30036i
\(647\) −45.5255 −1.78979 −0.894896 0.446275i \(-0.852750\pi\)
−0.894896 + 0.446275i \(0.852750\pi\)
\(648\) 33.3997 19.2833i 1.31206 0.757520i
\(649\) −30.4378 −1.19479
\(650\) −44.6251 43.2510i −1.75034 1.69644i
\(651\) 2.70867 1.87178i 0.106161 0.0733608i
\(652\) 75.7951i 2.96837i
\(653\) 2.71514 0.106252 0.0531259 0.998588i \(-0.483082\pi\)
0.0531259 + 0.998588i \(0.483082\pi\)
\(654\) −4.22180 7.31237i −0.165085 0.285936i
\(655\) 37.1899i 1.45313i
\(656\) 2.85284 + 1.64709i 0.111385 + 0.0643080i
\(657\) −28.7954 + 16.6250i −1.12341 + 0.648604i
\(658\) −26.2534 + 15.1574i −1.02346 + 0.590897i
\(659\) 38.9080 1.51564 0.757819 0.652464i \(-0.226265\pi\)
0.757819 + 0.652464i \(0.226265\pi\)
\(660\) 14.1496 24.5078i 0.550771 0.953964i
\(661\) 28.8118 + 16.6345i 1.12065 + 0.647008i 0.941567 0.336826i \(-0.109353\pi\)
0.179084 + 0.983834i \(0.442687\pi\)
\(662\) −4.65604 + 8.06450i −0.180962 + 0.313436i
\(663\) −3.09876 0.778592i −0.120346 0.0302380i
\(664\) −40.9524 + 70.9316i −1.58926 + 2.75268i
\(665\) −31.0318 + 17.9162i −1.20336 + 0.694761i
\(666\) −11.6833 −0.452717
\(667\) −12.3968 −0.480008
\(668\) 9.80218 5.65929i 0.379258 0.218965i
\(669\) 1.17711 + 0.679602i 0.0455095 + 0.0262749i
\(670\) −58.9902 + 34.0580i −2.27899 + 1.31578i
\(671\) −14.4356 8.33441i −0.557281 0.321746i
\(672\) −0.183202 + 0.317315i −0.00706718 + 0.0122407i
\(673\) −10.8109 + 18.7250i −0.416728 + 0.721794i −0.995608 0.0936185i \(-0.970157\pi\)
0.578880 + 0.815413i \(0.303490\pi\)
\(674\) 61.8700i 2.38314i
\(675\) 8.14560 + 14.1086i 0.313524 + 0.543040i
\(676\) 44.8830 27.8196i 1.72627 1.06999i
\(677\) −0.0328535 + 0.0569039i −0.00126266 + 0.00218699i −0.866656 0.498906i \(-0.833735\pi\)
0.865393 + 0.501093i \(0.167069\pi\)
\(678\) 9.92767i 0.381270i
\(679\) −10.5755 18.3173i −0.405850 0.702953i
\(680\) 39.1183 1.50012
\(681\) 3.13271i 0.120046i
\(682\) 39.3407 + 56.9302i 1.50643 + 2.17997i
\(683\) 37.4224i 1.43193i −0.698137 0.715964i \(-0.745987\pi\)
0.698137 0.715964i \(-0.254013\pi\)
\(684\) 80.4262i 3.07517i
\(685\) −33.3129 57.6996i −1.27282 2.20459i
\(686\) −43.1120 −1.64602
\(687\) 2.65333 + 1.53190i 0.101231 + 0.0584456i
\(688\) −17.7511 30.7458i −0.676753 1.17217i
\(689\) 11.8488 + 2.97713i 0.451405 + 0.113420i
\(690\) −14.4208 −0.548991
\(691\) −5.38461 3.10881i −0.204840 0.118265i 0.394071 0.919080i \(-0.371066\pi\)
−0.598911 + 0.800815i \(0.704400\pi\)
\(692\) 46.9690 81.3528i 1.78549 3.09257i
\(693\) −10.6447 + 18.4372i −0.404361 + 0.700373i
\(694\) −54.9122 + 31.7036i −2.08444 + 1.20345i
\(695\) −23.7924 13.7366i −0.902499 0.521058i
\(696\) −5.11650 + 2.95401i −0.193940 + 0.111972i
\(697\) 1.67458i 0.0634294i
\(698\) 83.5739 3.16332
\(699\) 4.92084 + 8.52314i 0.186123 + 0.322375i
\(700\) 36.5531 + 21.1039i 1.38158 + 0.797654i
\(701\) 26.0757 + 45.1645i 0.984866 + 1.70584i 0.642530 + 0.766261i \(0.277885\pi\)
0.342337 + 0.939577i \(0.388782\pi\)
\(702\) −19.8686 + 5.65817i −0.749893 + 0.213554i
\(703\) 5.81918 10.0791i 0.219474 0.380141i
\(704\) 31.5884 + 18.2376i 1.19053 + 0.687354i
\(705\) −11.4481 −0.431162
\(706\) 33.1851 + 57.4783i 1.24894 + 2.16322i
\(707\) 4.94656 2.85590i 0.186035 0.107407i
\(708\) 8.45026 + 4.87876i 0.317580 + 0.183355i
\(709\) 37.5718i 1.41104i −0.708690 0.705520i \(-0.750714\pi\)
0.708690 0.705520i \(-0.249286\pi\)
\(710\) 39.6650 22.9006i 1.48860 0.859444i
\(711\) −0.681607 −0.0255623
\(712\) 60.8561 2.28068
\(713\) 10.1184 21.3532i 0.378936 0.799684i
\(714\) 3.23850 0.121198
\(715\) 43.8816 45.2757i 1.64108 1.69322i
\(716\) 4.78943 + 8.29553i 0.178989 + 0.310019i
\(717\) 6.48873i 0.242326i
\(718\) −30.1612 + 52.2408i −1.12561 + 1.94961i
\(719\) 11.1938 + 19.3882i 0.417459 + 0.723060i 0.995683 0.0928181i \(-0.0295875\pi\)
−0.578224 + 0.815878i \(0.696254\pi\)
\(720\) 37.2975 21.5337i 1.38999 0.802514i
\(721\) 21.0642i 0.784471i
\(722\) −63.0333 36.3923i −2.34586 1.35438i
\(723\) −0.683754 0.394766i −0.0254291 0.0146815i
\(724\) −29.3230 + 50.7889i −1.08978 + 1.88756i
\(725\) 10.2245 + 17.7094i 0.379729 + 0.657710i
\(726\) 12.3028 + 7.10302i 0.456599 + 0.263618i
\(727\) 8.86102 + 15.3477i 0.328637 + 0.569216i 0.982242 0.187620i \(-0.0600774\pi\)
−0.653605 + 0.756836i \(0.726744\pi\)
\(728\) −18.9092 + 19.5099i −0.700820 + 0.723086i
\(729\) −18.8030 −0.696409
\(730\) −86.4400 + 49.9062i −3.19929 + 1.84711i
\(731\) −9.02370 + 15.6295i −0.333754 + 0.578078i
\(732\) 2.67178 + 4.62767i 0.0987520 + 0.171043i
\(733\) 19.8408 + 11.4551i 0.732835 + 0.423103i 0.819459 0.573138i \(-0.194274\pi\)
−0.0866231 + 0.996241i \(0.527608\pi\)
\(734\) −27.5734 15.9195i −1.01775 0.587599i
\(735\) −5.73319 3.31006i −0.211472 0.122093i
\(736\) 2.62958i 0.0969277i
\(737\) −20.1575 34.9138i −0.742510 1.28607i
\(738\) −2.63332 4.56104i −0.0969337 0.167894i
\(739\) 3.52125 + 2.03300i 0.129531 + 0.0747849i 0.563365 0.826208i \(-0.309506\pi\)
−0.433834 + 0.900993i \(0.642840\pi\)
\(740\) −23.5006 −0.863899
\(741\) 2.43929 9.70825i 0.0896096 0.356641i
\(742\) −12.3832 −0.454600
\(743\) 3.34822i 0.122834i 0.998112 + 0.0614172i \(0.0195620\pi\)
−0.998112 + 0.0614172i \(0.980438\pi\)
\(744\) −0.912092 11.2241i −0.0334389 0.411496i
\(745\) −19.9546 −0.731081
\(746\) 28.3147i 1.03667i
\(747\) 39.6980 22.9196i 1.45247 0.838586i
\(748\) 45.6093i 1.66764i
\(749\) 15.8207 + 9.13406i 0.578074 + 0.333751i
\(750\) 3.39887 + 5.88702i 0.124109 + 0.214964i
\(751\) 10.0102 + 17.3381i 0.365276 + 0.632676i 0.988820 0.149112i \(-0.0476414\pi\)
−0.623545 + 0.781788i \(0.714308\pi\)
\(752\) 36.2957i 1.32357i
\(753\) 0.805894 1.39585i 0.0293684 0.0508676i
\(754\) −24.9395 + 7.10225i −0.908243 + 0.258649i
\(755\) −39.7302 + 68.8147i −1.44593 + 2.50442i
\(756\) 12.1511 7.01545i 0.441932 0.255150i
\(757\) 19.9026 34.4722i 0.723371 1.25291i −0.236271 0.971687i \(-0.575925\pi\)
0.959641 0.281227i \(-0.0907415\pi\)
\(758\) 1.93907 + 3.35858i 0.0704304 + 0.121989i
\(759\) 8.53506i 0.309803i
\(760\) 122.556i 4.44556i
\(761\) 17.7746 10.2622i 0.644329 0.372004i −0.141951 0.989874i \(-0.545338\pi\)
0.786280 + 0.617870i \(0.212004\pi\)
\(762\) 9.38117 + 5.41622i 0.339844 + 0.196209i
\(763\) 6.38859 + 11.0654i 0.231282 + 0.400593i
\(764\) 2.32562 4.02810i 0.0841382 0.145732i
\(765\) −18.9600 10.9466i