Properties

Label 35.5.g.a.22.3
Level $35$
Weight $5$
Character 35.22
Analytic conductor $3.618$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 35.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.61794870793\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.3
Character \(\chi\) \(=\) 35.22
Dual form 35.5.g.a.8.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.63546 - 3.63546i) q^{2} +(2.99367 - 2.99367i) q^{3} +10.4331i q^{4} +(-2.80777 - 24.8418i) q^{5} -21.7667 q^{6} +(-13.0958 - 13.0958i) q^{7} +(-20.2382 + 20.2382i) q^{8} +63.0758i q^{9} +O(q^{10})\) \(q+(-3.63546 - 3.63546i) q^{2} +(2.99367 - 2.99367i) q^{3} +10.4331i q^{4} +(-2.80777 - 24.8418i) q^{5} -21.7667 q^{6} +(-13.0958 - 13.0958i) q^{7} +(-20.2382 + 20.2382i) q^{8} +63.0758i q^{9} +(-80.1039 + 100.519i) q^{10} -220.093 q^{11} +(31.2333 + 31.2333i) q^{12} +(176.455 - 176.455i) q^{13} +95.2184i q^{14} +(-82.7738 - 65.9628i) q^{15} +314.080 q^{16} +(-101.380 - 101.380i) q^{17} +(229.310 - 229.310i) q^{18} -152.947i q^{19} +(259.177 - 29.2937i) q^{20} -78.4091 q^{21} +(800.137 + 800.137i) q^{22} +(596.607 - 596.607i) q^{23} +121.173i q^{24} +(-609.233 + 139.500i) q^{25} -1282.99 q^{26} +(431.316 + 431.316i) q^{27} +(136.630 - 136.630i) q^{28} -801.994i q^{29} +(61.1159 + 540.726i) q^{30} -175.829 q^{31} +(-818.013 - 818.013i) q^{32} +(-658.885 + 658.885i) q^{33} +737.127i q^{34} +(-288.554 + 362.094i) q^{35} -658.077 q^{36} +(423.393 + 423.393i) q^{37} +(-556.032 + 556.032i) q^{38} -1056.50i q^{39} +(559.579 + 445.930i) q^{40} +919.754 q^{41} +(285.053 + 285.053i) q^{42} +(628.316 - 628.316i) q^{43} -2296.25i q^{44} +(1566.92 - 177.102i) q^{45} -4337.88 q^{46} +(-2208.69 - 2208.69i) q^{47} +(940.253 - 940.253i) q^{48} +343.000i q^{49} +(2721.99 + 1707.69i) q^{50} -606.999 q^{51} +(1840.97 + 1840.97i) q^{52} +(554.147 - 554.147i) q^{53} -3136.06i q^{54} +(617.968 + 5467.50i) q^{55} +530.072 q^{56} +(-457.873 - 457.873i) q^{57} +(-2915.61 + 2915.61i) q^{58} +3164.90i q^{59} +(688.196 - 863.588i) q^{60} +5297.88 q^{61} +(639.219 + 639.219i) q^{62} +(826.029 - 826.029i) q^{63} +922.421i q^{64} +(-4878.91 - 3888.02i) q^{65} +4790.70 q^{66} +(-1090.73 - 1090.73i) q^{67} +(1057.71 - 1057.71i) q^{68} -3572.09i q^{69} +(2365.40 - 267.351i) q^{70} -1622.41 q^{71} +(-1276.54 - 1276.54i) q^{72} +(1908.39 - 1908.39i) q^{73} -3078.45i q^{74} +(-1406.23 + 2241.46i) q^{75} +1595.71 q^{76} +(2882.29 + 2882.29i) q^{77} +(-3840.85 + 3840.85i) q^{78} +5038.95i q^{79} +(-881.863 - 7802.32i) q^{80} -2526.71 q^{81} +(-3343.73 - 3343.73i) q^{82} +(-2986.51 + 2986.51i) q^{83} -818.050i q^{84} +(-2233.82 + 2803.12i) q^{85} -4568.43 q^{86} +(-2400.91 - 2400.91i) q^{87} +(4454.28 - 4454.28i) q^{88} +9634.86i q^{89} +(-6340.32 - 5052.62i) q^{90} -4621.64 q^{91} +(6224.45 + 6224.45i) q^{92} +(-526.374 + 526.374i) q^{93} +16059.2i q^{94} +(-3799.48 + 429.439i) q^{95} -4897.73 q^{96} +(-2618.19 - 2618.19i) q^{97} +(1246.96 - 1246.96i) q^{98} -13882.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} + O(q^{10}) \) \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.63546 3.63546i −0.908864 0.908864i 0.0873163 0.996181i \(-0.472171\pi\)
−0.996181 + 0.0873163i \(0.972171\pi\)
\(3\) 2.99367 2.99367i 0.332630 0.332630i −0.520954 0.853585i \(-0.674424\pi\)
0.853585 + 0.520954i \(0.174424\pi\)
\(4\) 10.4331i 0.652069i
\(5\) −2.80777 24.8418i −0.112311 0.993673i
\(6\) −21.7667 −0.604632
\(7\) −13.0958 13.0958i −0.267261 0.267261i
\(8\) −20.2382 + 20.2382i −0.316222 + 0.316222i
\(9\) 63.0758i 0.778714i
\(10\) −80.1039 + 100.519i −0.801039 + 1.00519i
\(11\) −220.093 −1.81895 −0.909473 0.415763i \(-0.863515\pi\)
−0.909473 + 0.415763i \(0.863515\pi\)
\(12\) 31.2333 + 31.2333i 0.216898 + 0.216898i
\(13\) 176.455 176.455i 1.04411 1.04411i 0.0451321 0.998981i \(-0.485629\pi\)
0.998981 0.0451321i \(-0.0143709\pi\)
\(14\) 95.2184i 0.485808i
\(15\) −82.7738 65.9628i −0.367884 0.293168i
\(16\) 314.080 1.22688
\(17\) −101.380 101.380i −0.350797 0.350797i 0.509609 0.860406i \(-0.329790\pi\)
−0.860406 + 0.509609i \(0.829790\pi\)
\(18\) 229.310 229.310i 0.707746 0.707746i
\(19\) 152.947i 0.423676i −0.977305 0.211838i \(-0.932055\pi\)
0.977305 0.211838i \(-0.0679449\pi\)
\(20\) 259.177 29.2937i 0.647943 0.0732343i
\(21\) −78.4091 −0.177798
\(22\) 800.137 + 800.137i 1.65318 + 1.65318i
\(23\) 596.607 596.607i 1.12780 1.12780i 0.137266 0.990534i \(-0.456168\pi\)
0.990534 0.137266i \(-0.0438317\pi\)
\(24\) 121.173i 0.210370i
\(25\) −609.233 + 139.500i −0.974773 + 0.223200i
\(26\) −1282.99 −1.89791
\(27\) 431.316 + 431.316i 0.591654 + 0.591654i
\(28\) 136.630 136.630i 0.174273 0.174273i
\(29\) 801.994i 0.953619i −0.879007 0.476810i \(-0.841793\pi\)
0.879007 0.476810i \(-0.158207\pi\)
\(30\) 61.1159 + 540.726i 0.0679066 + 0.600806i
\(31\) −175.829 −0.182965 −0.0914823 0.995807i \(-0.529160\pi\)
−0.0914823 + 0.995807i \(0.529160\pi\)
\(32\) −818.013 818.013i −0.798841 0.798841i
\(33\) −658.885 + 658.885i −0.605037 + 0.605037i
\(34\) 737.127i 0.637653i
\(35\) −288.554 + 362.094i −0.235554 + 0.295587i
\(36\) −658.077 −0.507775
\(37\) 423.393 + 423.393i 0.309271 + 0.309271i 0.844627 0.535355i \(-0.179822\pi\)
−0.535355 + 0.844627i \(0.679822\pi\)
\(38\) −556.032 + 556.032i −0.385064 + 0.385064i
\(39\) 1056.50i 0.694607i
\(40\) 559.579 + 445.930i 0.349737 + 0.278707i
\(41\) 919.754 0.547147 0.273573 0.961851i \(-0.411794\pi\)
0.273573 + 0.961851i \(0.411794\pi\)
\(42\) 285.053 + 285.053i 0.161595 + 0.161595i
\(43\) 628.316 628.316i 0.339814 0.339814i −0.516483 0.856297i \(-0.672759\pi\)
0.856297 + 0.516483i \(0.172759\pi\)
\(44\) 2296.25i 1.18608i
\(45\) 1566.92 177.102i 0.773787 0.0874579i
\(46\) −4337.88 −2.05004
\(47\) −2208.69 2208.69i −0.999857 0.999857i 0.000142581 1.00000i \(-0.499955\pi\)
−1.00000 0.000142581i \(0.999955\pi\)
\(48\) 940.253 940.253i 0.408096 0.408096i
\(49\) 343.000i 0.142857i
\(50\) 2721.99 + 1707.69i 1.08879 + 0.683077i
\(51\) −606.999 −0.233371
\(52\) 1840.97 + 1840.97i 0.680833 + 0.680833i
\(53\) 554.147 554.147i 0.197275 0.197275i −0.601556 0.798831i \(-0.705452\pi\)
0.798831 + 0.601556i \(0.205452\pi\)
\(54\) 3136.06i 1.07547i
\(55\) 617.968 + 5467.50i 0.204287 + 1.80744i
\(56\) 530.072 0.169028
\(57\) −457.873 457.873i −0.140927 0.140927i
\(58\) −2915.61 + 2915.61i −0.866711 + 0.866711i
\(59\) 3164.90i 0.909192i 0.890698 + 0.454596i \(0.150216\pi\)
−0.890698 + 0.454596i \(0.849784\pi\)
\(60\) 688.196 863.588i 0.191166 0.239885i
\(61\) 5297.88 1.42378 0.711890 0.702291i \(-0.247840\pi\)
0.711890 + 0.702291i \(0.247840\pi\)
\(62\) 639.219 + 639.219i 0.166290 + 0.166290i
\(63\) 826.029 826.029i 0.208120 0.208120i
\(64\) 922.421i 0.225200i
\(65\) −4878.91 3888.02i −1.15477 0.920242i
\(66\) 4790.70 1.09979
\(67\) −1090.73 1090.73i −0.242979 0.242979i 0.575102 0.818081i \(-0.304962\pi\)
−0.818081 + 0.575102i \(0.804962\pi\)
\(68\) 1057.71 1057.71i 0.228744 0.228744i
\(69\) 3572.09i 0.750281i
\(70\) 2365.40 267.351i 0.482735 0.0545615i
\(71\) −1622.41 −0.321842 −0.160921 0.986967i \(-0.551446\pi\)
−0.160921 + 0.986967i \(0.551446\pi\)
\(72\) −1276.54 1276.54i −0.246247 0.246247i
\(73\) 1908.39 1908.39i 0.358114 0.358114i −0.505003 0.863117i \(-0.668509\pi\)
0.863117 + 0.505003i \(0.168509\pi\)
\(74\) 3078.45i 0.562171i
\(75\) −1406.23 + 2241.46i −0.249996 + 0.398482i
\(76\) 1595.71 0.276266
\(77\) 2882.29 + 2882.29i 0.486134 + 0.486134i
\(78\) −3840.85 + 3840.85i −0.631304 + 0.631304i
\(79\) 5038.95i 0.807395i 0.914893 + 0.403697i \(0.132275\pi\)
−0.914893 + 0.403697i \(0.867725\pi\)
\(80\) −881.863 7802.32i −0.137791 1.21911i
\(81\) −2526.71 −0.385110
\(82\) −3343.73 3343.73i −0.497282 0.497282i
\(83\) −2986.51 + 2986.51i −0.433519 + 0.433519i −0.889824 0.456305i \(-0.849173\pi\)
0.456305 + 0.889824i \(0.349173\pi\)
\(84\) 818.050i 0.115937i
\(85\) −2233.82 + 2803.12i −0.309179 + 0.387975i
\(86\) −4568.43 −0.617690
\(87\) −2400.91 2400.91i −0.317203 0.317203i
\(88\) 4454.28 4454.28i 0.575192 0.575192i
\(89\) 9634.86i 1.21637i 0.793796 + 0.608185i \(0.208102\pi\)
−0.793796 + 0.608185i \(0.791898\pi\)
\(90\) −6340.32 5052.62i −0.782755 0.623780i
\(91\) −4621.64 −0.558102
\(92\) 6224.45 + 6224.45i 0.735403 + 0.735403i
\(93\) −526.374 + 526.374i −0.0608596 + 0.0608596i
\(94\) 16059.2i 1.81747i
\(95\) −3799.48 + 429.439i −0.420995 + 0.0475833i
\(96\) −4897.73 −0.531437
\(97\) −2618.19 2618.19i −0.278265 0.278265i 0.554151 0.832416i \(-0.313043\pi\)
−0.832416 + 0.554151i \(0.813043\pi\)
\(98\) 1246.96 1246.96i 0.129838 0.129838i
\(99\) 13882.5i 1.41644i
\(100\) −1455.42 6356.19i −0.145542 0.635619i
\(101\) 17410.5 1.70674 0.853372 0.521303i \(-0.174554\pi\)
0.853372 + 0.521303i \(0.174554\pi\)
\(102\) 2206.72 + 2206.72i 0.212103 + 0.212103i
\(103\) −6794.71 + 6794.71i −0.640466 + 0.640466i −0.950670 0.310204i \(-0.899603\pi\)
0.310204 + 0.950670i \(0.399603\pi\)
\(104\) 7142.28i 0.660344i
\(105\) 220.154 + 1947.82i 0.0199686 + 0.176673i
\(106\) −4029.15 −0.358593
\(107\) 6174.02 + 6174.02i 0.539263 + 0.539263i 0.923313 0.384049i \(-0.125471\pi\)
−0.384049 + 0.923313i \(0.625471\pi\)
\(108\) −4499.96 + 4499.96i −0.385799 + 0.385799i
\(109\) 4665.43i 0.392680i 0.980536 + 0.196340i \(0.0629056\pi\)
−0.980536 + 0.196340i \(0.937094\pi\)
\(110\) 17630.3 22123.5i 1.45705 1.82839i
\(111\) 2535.00 0.205746
\(112\) −4113.13 4113.13i −0.327896 0.327896i
\(113\) 10391.0 10391.0i 0.813769 0.813769i −0.171427 0.985197i \(-0.554838\pi\)
0.985197 + 0.171427i \(0.0548379\pi\)
\(114\) 3329.16i 0.256168i
\(115\) −16495.9 13145.7i −1.24733 0.994001i
\(116\) 8367.28 0.621825
\(117\) 11130.1 + 11130.1i 0.813066 + 0.813066i
\(118\) 11505.8 11505.8i 0.826332 0.826332i
\(119\) 2655.31i 0.187509i
\(120\) 3010.17 340.226i 0.209039 0.0236268i
\(121\) 33799.7 2.30857
\(122\) −19260.2 19260.2i −1.29402 1.29402i
\(123\) 2753.44 2753.44i 0.181998 0.181998i
\(124\) 1834.44i 0.119306i
\(125\) 5176.02 + 14742.8i 0.331265 + 0.943538i
\(126\) −6005.98 −0.378306
\(127\) −4261.99 4261.99i −0.264244 0.264244i 0.562532 0.826776i \(-0.309827\pi\)
−0.826776 + 0.562532i \(0.809827\pi\)
\(128\) −9734.78 + 9734.78i −0.594164 + 0.594164i
\(129\) 3761.95i 0.226065i
\(130\) 3602.34 + 31871.8i 0.213156 + 1.88591i
\(131\) −4451.64 −0.259404 −0.129702 0.991553i \(-0.541402\pi\)
−0.129702 + 0.991553i \(0.541402\pi\)
\(132\) −6874.21 6874.21i −0.394525 0.394525i
\(133\) −2002.96 + 2002.96i −0.113232 + 0.113232i
\(134\) 7930.63i 0.441670i
\(135\) 9503.64 11925.7i 0.521462 0.654360i
\(136\) 4103.51 0.221860
\(137\) −180.184 180.184i −0.00960008 0.00960008i 0.702290 0.711891i \(-0.252161\pi\)
−0.711891 + 0.702290i \(0.752161\pi\)
\(138\) −12986.2 + 12986.2i −0.681904 + 0.681904i
\(139\) 23370.3i 1.20958i −0.796384 0.604791i \(-0.793257\pi\)
0.796384 0.604791i \(-0.206743\pi\)
\(140\) −3777.76 3010.51i −0.192743 0.153597i
\(141\) −13224.2 −0.665166
\(142\) 5898.19 + 5898.19i 0.292511 + 0.292511i
\(143\) −38836.5 + 38836.5i −1.89919 + 1.89919i
\(144\) 19810.9i 0.955385i
\(145\) −19923.0 + 2251.81i −0.947586 + 0.107102i
\(146\) −13875.7 −0.650955
\(147\) 1026.83 + 1026.83i 0.0475186 + 0.0475186i
\(148\) −4417.30 + 4417.30i −0.201666 + 0.201666i
\(149\) 26094.3i 1.17537i −0.809091 0.587684i \(-0.800040\pi\)
0.809091 0.587684i \(-0.199960\pi\)
\(150\) 13261.0 3036.46i 0.589378 0.134954i
\(151\) −762.534 −0.0334430 −0.0167215 0.999860i \(-0.505323\pi\)
−0.0167215 + 0.999860i \(0.505323\pi\)
\(152\) 3095.38 + 3095.38i 0.133976 + 0.133976i
\(153\) 6394.65 6394.65i 0.273170 0.273170i
\(154\) 20956.9i 0.883659i
\(155\) 493.687 + 4367.91i 0.0205489 + 0.181807i
\(156\) 11022.5 0.452932
\(157\) −25099.1 25099.1i −1.01826 1.01826i −0.999830 0.0184285i \(-0.994134\pi\)
−0.0184285 0.999830i \(-0.505866\pi\)
\(158\) 18318.9 18318.9i 0.733812 0.733812i
\(159\) 3317.87i 0.131240i
\(160\) −18024.1 + 22617.7i −0.704068 + 0.883505i
\(161\) −15626.1 −0.602835
\(162\) 9185.73 + 9185.73i 0.350013 + 0.350013i
\(163\) −1589.95 + 1589.95i −0.0598424 + 0.0598424i −0.736395 0.676552i \(-0.763473\pi\)
0.676552 + 0.736395i \(0.263473\pi\)
\(164\) 9595.88i 0.356777i
\(165\) 18217.9 + 14517.9i 0.669161 + 0.533257i
\(166\) 21714.7 0.788020
\(167\) −11320.6 11320.6i −0.405917 0.405917i 0.474395 0.880312i \(-0.342667\pi\)
−0.880312 + 0.474395i \(0.842667\pi\)
\(168\) 1586.86 1586.86i 0.0562238 0.0562238i
\(169\) 33711.8i 1.18034i
\(170\) 18311.6 2069.68i 0.633619 0.0716152i
\(171\) 9647.26 0.329922
\(172\) 6555.28 + 6555.28i 0.221582 + 0.221582i
\(173\) 10012.9 10012.9i 0.334555 0.334555i −0.519758 0.854313i \(-0.673978\pi\)
0.854313 + 0.519758i \(0.173978\pi\)
\(174\) 17456.8i 0.576588i
\(175\) 9805.26 + 6151.53i 0.320172 + 0.200866i
\(176\) −69126.7 −2.23162
\(177\) 9474.66 + 9474.66i 0.302425 + 0.302425i
\(178\) 35027.1 35027.1i 1.10551 1.10551i
\(179\) 20172.5i 0.629584i −0.949161 0.314792i \(-0.898065\pi\)
0.949161 0.314792i \(-0.101935\pi\)
\(180\) 1847.73 + 16347.8i 0.0570286 + 0.504563i
\(181\) 17601.7 0.537276 0.268638 0.963241i \(-0.413427\pi\)
0.268638 + 0.963241i \(0.413427\pi\)
\(182\) 16801.8 + 16801.8i 0.507239 + 0.507239i
\(183\) 15860.1 15860.1i 0.473592 0.473592i
\(184\) 24148.5i 0.713272i
\(185\) 9329.06 11706.6i 0.272580 0.342049i
\(186\) 3827.22 0.110626
\(187\) 22313.0 + 22313.0i 0.638080 + 0.638080i
\(188\) 23043.4 23043.4i 0.651976 0.651976i
\(189\) 11296.9i 0.316252i
\(190\) 15374.1 + 12251.6i 0.425874 + 0.339381i
\(191\) −65848.1 −1.80500 −0.902499 0.430692i \(-0.858270\pi\)
−0.902499 + 0.430692i \(0.858270\pi\)
\(192\) 2761.43 + 2761.43i 0.0749085 + 0.0749085i
\(193\) −7771.80 + 7771.80i −0.208645 + 0.208645i −0.803691 0.595047i \(-0.797134\pi\)
0.595047 + 0.803691i \(0.297134\pi\)
\(194\) 19036.7i 0.505810i
\(195\) −26245.3 + 2966.40i −0.690213 + 0.0780118i
\(196\) −3578.55 −0.0931527
\(197\) 37777.3 + 37777.3i 0.973416 + 0.973416i 0.999656 0.0262392i \(-0.00835317\pi\)
−0.0262392 + 0.999656i \(0.508353\pi\)
\(198\) −50469.3 + 50469.3i −1.28735 + 1.28735i
\(199\) 20867.2i 0.526937i 0.964668 + 0.263469i \(0.0848666\pi\)
−0.964668 + 0.263469i \(0.915133\pi\)
\(200\) 9506.56 15153.0i 0.237664 0.378826i
\(201\) −6530.60 −0.161644
\(202\) −63295.1 63295.1i −1.55120 1.55120i
\(203\) −10502.8 + 10502.8i −0.254866 + 0.254866i
\(204\) 6332.88i 0.152174i
\(205\) −2582.45 22848.4i −0.0614504 0.543685i
\(206\) 49403.7 1.16419
\(207\) 37631.5 + 37631.5i 0.878234 + 0.878234i
\(208\) 55421.0 55421.0i 1.28100 1.28100i
\(209\) 33662.5i 0.770643i
\(210\) 6280.87 7881.60i 0.142423 0.178721i
\(211\) 6527.71 0.146621 0.0733104 0.997309i \(-0.476644\pi\)
0.0733104 + 0.997309i \(0.476644\pi\)
\(212\) 5781.47 + 5781.47i 0.128637 + 0.128637i
\(213\) −4856.95 + 4856.95i −0.107054 + 0.107054i
\(214\) 44890.8i 0.980234i
\(215\) −17372.7 13844.4i −0.375829 0.299499i
\(216\) −17458.1 −0.374189
\(217\) 2302.62 + 2302.62i 0.0488994 + 0.0488994i
\(218\) 16961.0 16961.0i 0.356893 0.356893i
\(219\) 11426.2i 0.238239i
\(220\) −57043.0 + 6447.32i −1.17857 + 0.133209i
\(221\) −35778.1 −0.732543
\(222\) −9215.87 9215.87i −0.186995 0.186995i
\(223\) 49365.9 49365.9i 0.992698 0.992698i −0.00727547 0.999974i \(-0.502316\pi\)
0.999974 + 0.00727547i \(0.00231588\pi\)
\(224\) 21425.1i 0.426998i
\(225\) −8799.09 38427.9i −0.173809 0.759069i
\(226\) −75552.2 −1.47921
\(227\) 60511.8 + 60511.8i 1.17433 + 1.17433i 0.981168 + 0.193158i \(0.0618729\pi\)
0.193158 + 0.981168i \(0.438127\pi\)
\(228\) 4777.03 4777.03i 0.0918943 0.0918943i
\(229\) 83.0802i 0.00158426i 1.00000 0.000792130i \(0.000252143\pi\)
−1.00000 0.000792130i \(0.999748\pi\)
\(230\) 12179.7 + 107761.i 0.230241 + 2.03707i
\(231\) 17257.3 0.323406
\(232\) 16230.9 + 16230.9i 0.301556 + 0.301556i
\(233\) 26936.3 26936.3i 0.496166 0.496166i −0.414076 0.910242i \(-0.635895\pi\)
0.910242 + 0.414076i \(0.135895\pi\)
\(234\) 80925.7i 1.47793i
\(235\) −48666.3 + 61069.2i −0.881237 + 1.10583i
\(236\) −33019.7 −0.592855
\(237\) 15085.0 + 15085.0i 0.268564 + 0.268564i
\(238\) 9653.27 9653.27i 0.170420 0.170420i
\(239\) 2964.31i 0.0518953i 0.999663 + 0.0259476i \(0.00826032\pi\)
−0.999663 + 0.0259476i \(0.991740\pi\)
\(240\) −25997.6 20717.6i −0.451347 0.359680i
\(241\) −4980.66 −0.0857537 −0.0428769 0.999080i \(-0.513652\pi\)
−0.0428769 + 0.999080i \(0.513652\pi\)
\(242\) −122877. 122877.i −2.09817 2.09817i
\(243\) −42500.7 + 42500.7i −0.719753 + 0.719753i
\(244\) 55273.3i 0.928402i
\(245\) 8520.75 963.064i 0.141953 0.0160444i
\(246\) −20020.0 −0.330822
\(247\) −26988.3 26988.3i −0.442365 0.442365i
\(248\) 3558.47 3558.47i 0.0578575 0.0578575i
\(249\) 17881.3i 0.288403i
\(250\) 34779.5 72413.9i 0.556472 1.15862i
\(251\) 51772.6 0.821775 0.410887 0.911686i \(-0.365219\pi\)
0.410887 + 0.911686i \(0.365219\pi\)
\(252\) 8618.04 + 8618.04i 0.135709 + 0.135709i
\(253\) −131309. + 131309.i −2.05141 + 2.05141i
\(254\) 30988.5i 0.480323i
\(255\) 1704.31 + 15079.0i 0.0262101 + 0.231895i
\(256\) 85539.5 1.30523
\(257\) 7872.26 + 7872.26i 0.119188 + 0.119188i 0.764185 0.644997i \(-0.223141\pi\)
−0.644997 + 0.764185i \(0.723141\pi\)
\(258\) −13676.4 + 13676.4i −0.205462 + 0.205462i
\(259\) 11089.3i 0.165313i
\(260\) 40564.1 50902.2i 0.600061 0.752991i
\(261\) 50586.4 0.742597
\(262\) 16183.7 + 16183.7i 0.235763 + 0.235763i
\(263\) 47259.4 47259.4i 0.683246 0.683246i −0.277484 0.960730i \(-0.589501\pi\)
0.960730 + 0.277484i \(0.0895007\pi\)
\(264\) 26669.3i 0.382652i
\(265\) −15321.9 12210.1i −0.218183 0.173871i
\(266\) 14563.4 0.205825
\(267\) 28843.6 + 28843.6i 0.404601 + 0.404601i
\(268\) 11379.7 11379.7i 0.158439 0.158439i
\(269\) 129888.i 1.79500i 0.441010 + 0.897502i \(0.354620\pi\)
−0.441010 + 0.897502i \(0.645380\pi\)
\(270\) −77905.5 + 8805.33i −1.06866 + 0.120786i
\(271\) −55592.0 −0.756962 −0.378481 0.925609i \(-0.623553\pi\)
−0.378481 + 0.925609i \(0.623553\pi\)
\(272\) −31841.5 31841.5i −0.430384 0.430384i
\(273\) −13835.7 + 13835.7i −0.185642 + 0.185642i
\(274\) 1310.10i 0.0174503i
\(275\) 134088. 30702.9i 1.77306 0.405989i
\(276\) 37268.0 0.489235
\(277\) −73039.6 73039.6i −0.951916 0.951916i 0.0469796 0.998896i \(-0.485040\pi\)
−0.998896 + 0.0469796i \(0.985040\pi\)
\(278\) −84961.9 + 84961.9i −1.09935 + 1.09935i
\(279\) 11090.6i 0.142477i
\(280\) −1488.32 13167.9i −0.0189836 0.167959i
\(281\) 86967.1 1.10139 0.550696 0.834706i \(-0.314362\pi\)
0.550696 + 0.834706i \(0.314362\pi\)
\(282\) 48075.9 + 48075.9i 0.604545 + 0.604545i
\(283\) 16152.8 16152.8i 0.201685 0.201685i −0.599037 0.800722i \(-0.704450\pi\)
0.800722 + 0.599037i \(0.204450\pi\)
\(284\) 16926.7i 0.209863i
\(285\) −10088.8 + 12660.0i −0.124208 + 0.155863i
\(286\) 282377. 3.45220
\(287\) −12044.9 12044.9i −0.146231 0.146231i
\(288\) 51596.9 51596.9i 0.622069 0.622069i
\(289\) 62965.1i 0.753883i
\(290\) 80615.6 + 64242.8i 0.958568 + 0.763886i
\(291\) −15676.0 −0.185119
\(292\) 19910.4 + 19910.4i 0.233515 + 0.233515i
\(293\) −5309.17 + 5309.17i −0.0618431 + 0.0618431i −0.737352 0.675509i \(-0.763924\pi\)
0.675509 + 0.737352i \(0.263924\pi\)
\(294\) 7465.99i 0.0863759i
\(295\) 78621.8 8886.29i 0.903439 0.102112i
\(296\) −17137.4 −0.195597
\(297\) −94929.4 94929.4i −1.07619 1.07619i
\(298\) −94864.9 + 94864.9i −1.06825 + 1.06825i
\(299\) 210549.i 2.35510i
\(300\) −23385.4 14671.3i −0.259838 0.163014i
\(301\) −16456.6 −0.181638
\(302\) 2772.16 + 2772.16i 0.0303952 + 0.0303952i
\(303\) 52121.3 52121.3i 0.567715 0.567715i
\(304\) 48037.6i 0.519797i
\(305\) −14875.2 131609.i −0.159906 1.41477i
\(306\) −46494.9 −0.496550
\(307\) −41603.9 41603.9i −0.441425 0.441425i 0.451065 0.892491i \(-0.351044\pi\)
−0.892491 + 0.451065i \(0.851044\pi\)
\(308\) −30071.2 + 30071.2i −0.316993 + 0.316993i
\(309\) 40682.3i 0.426077i
\(310\) 14084.6 17674.1i 0.146562 0.183914i
\(311\) −112022. −1.15819 −0.579096 0.815259i \(-0.696594\pi\)
−0.579096 + 0.815259i \(0.696594\pi\)
\(312\) 21381.6 + 21381.6i 0.219650 + 0.219650i
\(313\) −59284.2 + 59284.2i −0.605133 + 0.605133i −0.941670 0.336537i \(-0.890744\pi\)
0.336537 + 0.941670i \(0.390744\pi\)
\(314\) 182493.i 1.85092i
\(315\) −22839.4 18200.8i −0.230177 0.183429i
\(316\) −52571.9 −0.526477
\(317\) 12194.9 + 12194.9i 0.121355 + 0.121355i 0.765176 0.643821i \(-0.222652\pi\)
−0.643821 + 0.765176i \(0.722652\pi\)
\(318\) −12062.0 + 12062.0i −0.119279 + 0.119279i
\(319\) 176513.i 1.73458i
\(320\) 22914.6 2589.94i 0.223776 0.0252924i
\(321\) 36966.0 0.358751
\(322\) 56807.9 + 56807.9i 0.547895 + 0.547895i
\(323\) −15505.8 + 15505.8i −0.148624 + 0.148624i
\(324\) 26361.4i 0.251118i
\(325\) −82886.8 + 132118.i −0.784727 + 1.25082i
\(326\) 11560.4 0.108777
\(327\) 13966.8 + 13966.8i 0.130617 + 0.130617i
\(328\) −18614.2 + 18614.2i −0.173020 + 0.173020i
\(329\) 57849.0i 0.534446i
\(330\) −13451.2 119010.i −0.123518 1.09283i
\(331\) −31443.4 −0.286995 −0.143497 0.989651i \(-0.545835\pi\)
−0.143497 + 0.989651i \(0.545835\pi\)
\(332\) −31158.6 31158.6i −0.282684 0.282684i
\(333\) −26705.8 + 26705.8i −0.240834 + 0.240834i
\(334\) 82311.2i 0.737846i
\(335\) −24033.3 + 30158.3i −0.214153 + 0.268731i
\(336\) −24626.7 −0.218136
\(337\) −39492.6 39492.6i −0.347741 0.347741i 0.511527 0.859267i \(-0.329080\pi\)
−0.859267 + 0.511527i \(0.829080\pi\)
\(338\) −122558. + 122558.i −1.07277 + 1.07277i
\(339\) 62214.6i 0.541369i
\(340\) −29245.3 23305.7i −0.252987 0.201606i
\(341\) 38698.6 0.332803
\(342\) −35072.2 35072.2i −0.299855 0.299855i
\(343\) 4491.86 4491.86i 0.0381802 0.0381802i
\(344\) 25432.0i 0.214914i
\(345\) −88737.2 + 10029.6i −0.745534 + 0.0842646i
\(346\) −72802.9 −0.608130
\(347\) −93020.1 93020.1i −0.772534 0.772534i 0.206015 0.978549i \(-0.433951\pi\)
−0.978549 + 0.206015i \(0.933951\pi\)
\(348\) 25048.9 25048.9i 0.206838 0.206838i
\(349\) 158624.i 1.30232i −0.758939 0.651162i \(-0.774282\pi\)
0.758939 0.651162i \(-0.225718\pi\)
\(350\) −13283.0 58010.2i −0.108433 0.473553i
\(351\) 152216. 1.23551
\(352\) 180039. + 180039.i 1.45305 + 1.45305i
\(353\) 153311. 153311.i 1.23034 1.23034i 0.266502 0.963834i \(-0.414132\pi\)
0.963834 0.266502i \(-0.0858678\pi\)
\(354\) 68889.5i 0.549726i
\(355\) 4555.34 + 40303.5i 0.0361463 + 0.319806i
\(356\) −100521. −0.793156
\(357\) 7949.13 + 7949.13i 0.0623711 + 0.0623711i
\(358\) −73336.2 + 73336.2i −0.572206 + 0.572206i
\(359\) 17883.8i 0.138762i 0.997590 + 0.0693811i \(0.0221024\pi\)
−0.997590 + 0.0693811i \(0.977898\pi\)
\(360\) −28127.4 + 35295.9i −0.217033 + 0.272345i
\(361\) 106928. 0.820499
\(362\) −63990.2 63990.2i −0.488311 0.488311i
\(363\) 101185. 101185.i 0.767899 0.767899i
\(364\) 48218.0i 0.363921i
\(365\) −52766.2 42049.6i −0.396069 0.315628i
\(366\) −115318. −0.860862
\(367\) 157754. + 157754.i 1.17125 + 1.17125i 0.981912 + 0.189337i \(0.0606337\pi\)
0.189337 + 0.981912i \(0.439366\pi\)
\(368\) 187382. 187382.i 1.38367 1.38367i
\(369\) 58014.2i 0.426071i
\(370\) −76474.3 + 8643.57i −0.558615 + 0.0631378i
\(371\) −14514.0 −0.105448
\(372\) −5491.72 5491.72i −0.0396846 0.0396846i
\(373\) 48628.6 48628.6i 0.349522 0.349522i −0.510410 0.859931i \(-0.670506\pi\)
0.859931 + 0.510410i \(0.170506\pi\)
\(374\) 162236.i 1.15986i
\(375\) 59630.4 + 28639.7i 0.424038 + 0.203660i
\(376\) 89399.8 0.632355
\(377\) −141516. 141516.i −0.995687 0.995687i
\(378\) −41069.2 + 41069.2i −0.287431 + 0.287431i
\(379\) 156941.i 1.09259i 0.837593 + 0.546295i \(0.183962\pi\)
−0.837593 + 0.546295i \(0.816038\pi\)
\(380\) −4480.38 39640.4i −0.0310276 0.274518i
\(381\) −25518.0 −0.175791
\(382\) 239388. + 239388.i 1.64050 + 1.64050i
\(383\) 83467.3 83467.3i 0.569009 0.569009i −0.362842 0.931851i \(-0.618194\pi\)
0.931851 + 0.362842i \(0.118194\pi\)
\(384\) 58285.5i 0.395274i
\(385\) 63508.5 79694.1i 0.428460 0.537656i
\(386\) 56508.1 0.379259
\(387\) 39631.6 + 39631.6i 0.264618 + 0.264618i
\(388\) 27315.9 27315.9i 0.181448 0.181448i
\(389\) 233893.i 1.54567i 0.634605 + 0.772837i \(0.281163\pi\)
−0.634605 + 0.772837i \(0.718837\pi\)
\(390\) 106198. + 84629.6i 0.698212 + 0.556407i
\(391\) −120968. −0.791258
\(392\) −6941.71 6941.71i −0.0451746 0.0451746i
\(393\) −13326.7 + 13326.7i −0.0862857 + 0.0862857i
\(394\) 274676.i 1.76941i
\(395\) 125177. 14148.2i 0.802286 0.0906790i
\(396\) 144838. 0.923616
\(397\) 66916.0 + 66916.0i 0.424570 + 0.424570i 0.886774 0.462204i \(-0.152941\pi\)
−0.462204 + 0.886774i \(0.652941\pi\)
\(398\) 75862.0 75862.0i 0.478915 0.478915i
\(399\) 11992.4i 0.0753289i
\(400\) −191348. + 43814.2i −1.19592 + 0.273839i
\(401\) −236024. −1.46780 −0.733900 0.679257i \(-0.762302\pi\)
−0.733900 + 0.679257i \(0.762302\pi\)
\(402\) 23741.7 + 23741.7i 0.146913 + 0.146913i
\(403\) −31025.9 + 31025.9i −0.191036 + 0.191036i
\(404\) 181645.i 1.11291i
\(405\) 7094.40 + 62768.0i 0.0432519 + 0.382673i
\(406\) 76364.6 0.463276
\(407\) −93185.5 93185.5i −0.562548 0.562548i
\(408\) 12284.6 12284.6i 0.0737972 0.0737972i
\(409\) 9374.36i 0.0560396i 0.999607 + 0.0280198i \(0.00892015\pi\)
−0.999607 + 0.0280198i \(0.991080\pi\)
\(410\) −73675.9 + 92452.6i −0.438286 + 0.549986i
\(411\) −1078.82 −0.00638656
\(412\) −70889.9 70889.9i −0.417628 0.417628i
\(413\) 41446.9 41446.9i 0.242992 0.242992i
\(414\) 273615.i 1.59639i
\(415\) 82575.8 + 65805.0i 0.479465 + 0.382087i
\(416\) −288685. −1.66816
\(417\) −69963.2 69963.2i −0.402344 0.402344i
\(418\) 122378. 122378.i 0.700410 0.700410i
\(419\) 265821.i 1.51412i 0.653343 + 0.757062i \(0.273366\pi\)
−0.653343 + 0.757062i \(0.726634\pi\)
\(420\) −20321.9 + 2296.89i −0.115203 + 0.0130209i
\(421\) −222521. −1.25547 −0.627737 0.778425i \(-0.716019\pi\)
−0.627737 + 0.778425i \(0.716019\pi\)
\(422\) −23731.2 23731.2i −0.133258 0.133258i
\(423\) 139315. 139315.i 0.778603 0.778603i
\(424\) 22429.9i 0.124766i
\(425\) 75906.7 + 47621.6i 0.420245 + 0.263649i
\(426\) 35314.5 0.194596
\(427\) −69380.0 69380.0i −0.380521 0.380521i
\(428\) −64414.2 + 64414.2i −0.351637 + 0.351637i
\(429\) 232527.i 1.26345i
\(430\) 12827.1 + 113488.i 0.0693731 + 0.613782i
\(431\) 259316. 1.39597 0.697983 0.716115i \(-0.254081\pi\)
0.697983 + 0.716115i \(0.254081\pi\)
\(432\) 135468. + 135468.i 0.725886 + 0.725886i
\(433\) −187941. + 187941.i −1.00241 + 1.00241i −0.00241596 + 0.999997i \(0.500769\pi\)
−0.999997 + 0.00241596i \(0.999231\pi\)
\(434\) 16742.2i 0.0888858i
\(435\) −52901.7 + 66384.1i −0.279571 + 0.350821i
\(436\) −48674.9 −0.256054
\(437\) −91249.1 91249.1i −0.477822 0.477822i
\(438\) −41539.4 + 41539.4i −0.216527 + 0.216527i
\(439\) 295109.i 1.53128i −0.643272 0.765638i \(-0.722424\pi\)
0.643272 0.765638i \(-0.277576\pi\)
\(440\) −123159. 98146.0i −0.636153 0.506952i
\(441\) −21635.0 −0.111245
\(442\) 130070. + 130070.i 0.665782 + 0.665782i
\(443\) −7579.35 + 7579.35i −0.0386211 + 0.0386211i −0.726154 0.687533i \(-0.758694\pi\)
0.687533 + 0.726154i \(0.258694\pi\)
\(444\) 26447.9i 0.134161i
\(445\) 239348. 27052.4i 1.20867 0.136611i
\(446\) −358935. −1.80446
\(447\) −78117.9 78117.9i −0.390963 0.390963i
\(448\) 12079.8 12079.8i 0.0601873 0.0601873i
\(449\) 308572.i 1.53061i −0.643669 0.765304i \(-0.722589\pi\)
0.643669 0.765304i \(-0.277411\pi\)
\(450\) −107714. + 171692.i −0.531922 + 0.847860i
\(451\) −202431. −0.995231
\(452\) 108411. + 108411.i 0.530634 + 0.530634i
\(453\) −2282.78 + 2282.78i −0.0111242 + 0.0111242i
\(454\) 439976.i 2.13460i
\(455\) 12976.5 + 114810.i 0.0626808 + 0.554571i
\(456\) 18533.1 0.0891288
\(457\) −47861.1 47861.1i −0.229166 0.229166i 0.583178 0.812344i \(-0.301809\pi\)
−0.812344 + 0.583178i \(0.801809\pi\)
\(458\) 302.034 302.034i 0.00143988 0.00143988i
\(459\) 87453.8i 0.415101i
\(460\) 137150. 172104.i 0.648157 0.813344i
\(461\) 251532. 1.18356 0.591782 0.806098i \(-0.298425\pi\)
0.591782 + 0.806098i \(0.298425\pi\)
\(462\) −62738.0 62738.0i −0.293932 0.293932i
\(463\) −67580.4 + 67580.4i −0.315252 + 0.315252i −0.846940 0.531688i \(-0.821558\pi\)
0.531688 + 0.846940i \(0.321558\pi\)
\(464\) 251890.i 1.16997i
\(465\) 14554.0 + 11598.2i 0.0673097 + 0.0536393i
\(466\) −195852. −0.901895
\(467\) 172621. + 172621.i 0.791517 + 0.791517i 0.981741 0.190223i \(-0.0609213\pi\)
−0.190223 + 0.981741i \(0.560921\pi\)
\(468\) −116121. + 116121.i −0.530175 + 0.530175i
\(469\) 28568.1i 0.129878i
\(470\) 398939. 45090.4i 1.80597 0.204121i
\(471\) −150277. −0.677407
\(472\) −64051.9 64051.9i −0.287507 0.287507i
\(473\) −138288. + 138288.i −0.618103 + 0.618103i
\(474\) 109681.i 0.488176i
\(475\) 21336.1 + 93180.3i 0.0945645 + 0.412988i
\(476\) −27703.1 −0.122269
\(477\) 34953.3 + 34953.3i 0.153621 + 0.153621i
\(478\) 10776.6 10776.6i 0.0471658 0.0471658i
\(479\) 58984.8i 0.257080i −0.991704 0.128540i \(-0.958971\pi\)
0.991704 0.128540i \(-0.0410291\pi\)
\(480\) 13751.7 + 121668.i 0.0596861 + 0.528075i
\(481\) 149420. 0.645829
\(482\) 18107.0 + 18107.0i 0.0779385 + 0.0779385i
\(483\) −46779.4 + 46779.4i −0.200521 + 0.200521i
\(484\) 352636.i 1.50534i
\(485\) −57689.5 + 72392.0i −0.245252 + 0.307756i
\(486\) 309019. 1.30832
\(487\) −145300. 145300.i −0.612645 0.612645i 0.330989 0.943635i \(-0.392618\pi\)
−0.943635 + 0.330989i \(0.892618\pi\)
\(488\) −107220. + 107220.i −0.450231 + 0.450231i
\(489\) 9519.60i 0.0398108i
\(490\) −34478.0 27475.6i −0.143598 0.114434i
\(491\) 141204. 0.585712 0.292856 0.956157i \(-0.405394\pi\)
0.292856 + 0.956157i \(0.405394\pi\)
\(492\) 28726.9 + 28726.9i 0.118675 + 0.118675i
\(493\) −81306.3 + 81306.3i −0.334527 + 0.334527i
\(494\) 196229.i 0.804100i
\(495\) −344867. + 38978.9i −1.40748 + 0.159081i
\(496\) −55224.4 −0.224475
\(497\) 21246.7 + 21246.7i 0.0860159 + 0.0860159i
\(498\) 65006.6 65006.6i 0.262119 0.262119i
\(499\) 105864.i 0.425155i 0.977144 + 0.212578i \(0.0681859\pi\)
−0.977144 + 0.212578i \(0.931814\pi\)
\(500\) −153813. + 54001.9i −0.615251 + 0.216008i
\(501\) −67780.4 −0.270040
\(502\) −188217. 188217.i −0.746882 0.746882i
\(503\) −27040.0 + 27040.0i −0.106874 + 0.106874i −0.758522 0.651648i \(-0.774078\pi\)
0.651648 + 0.758522i \(0.274078\pi\)
\(504\) 33434.7i 0.131624i
\(505\) −48884.6 432508.i −0.191685 1.69595i
\(506\) 954734. 3.72890
\(507\) −100922. 100922.i −0.392618 0.392618i
\(508\) 44465.7 44465.7i 0.172305 0.172305i
\(509\) 382765.i 1.47740i 0.674037 + 0.738698i \(0.264559\pi\)
−0.674037 + 0.738698i \(0.735441\pi\)
\(510\) 48622.9 61014.8i 0.186939 0.234582i
\(511\) −49983.8 −0.191420
\(512\) −155219. 155219.i −0.592112 0.592112i
\(513\) 65968.4 65968.4i 0.250670 0.250670i
\(514\) 57238.5i 0.216652i
\(515\) 187871. + 149715.i 0.708345 + 0.564483i
\(516\) 39248.7 0.147410
\(517\) 486115. + 486115.i 1.81869 + 1.81869i
\(518\) −40314.8 + 40314.8i −0.150247 + 0.150247i
\(519\) 59950.7i 0.222566i
\(520\) 177427. 20053.8i 0.656166 0.0741636i
\(521\) −126422. −0.465743 −0.232871 0.972508i \(-0.574812\pi\)
−0.232871 + 0.972508i \(0.574812\pi\)
\(522\) −183905. 183905.i −0.674920 0.674920i
\(523\) 1542.91 1542.91i 0.00564075 0.00564075i −0.704281 0.709922i \(-0.748730\pi\)
0.709922 + 0.704281i \(0.248730\pi\)
\(524\) 46444.4i 0.169149i
\(525\) 47769.4 10938.1i 0.173313 0.0396846i
\(526\) −343619. −1.24196
\(527\) 17825.6 + 17825.6i 0.0641834 + 0.0641834i
\(528\) −206943. + 206943.i −0.742304 + 0.742304i
\(529\) 432038.i 1.54387i
\(530\) 11312.9 + 100092.i 0.0402738 + 0.356324i
\(531\) −199629. −0.708000
\(532\) −20897.1 20897.1i −0.0738351 0.0738351i
\(533\) 162295. 162295.i 0.571283 0.571283i
\(534\) 209719.i 0.735455i
\(535\) 136039. 170709.i 0.475286 0.596416i
\(536\) 44149.0 0.153671
\(537\) −60389.8 60389.8i −0.209419 0.209419i
\(538\) 472203. 472203.i 1.63142 1.63142i
\(539\) 75491.7i 0.259849i
\(540\) 124422. + 99152.4i 0.426688 + 0.340029i
\(541\) 270804. 0.925252 0.462626 0.886554i \(-0.346907\pi\)
0.462626 + 0.886554i \(0.346907\pi\)
\(542\) 202102. + 202102.i 0.687976 + 0.687976i
\(543\) 52693.7 52693.7i 0.178714 0.178714i
\(544\) 165861.i 0.560461i
\(545\) 115898. 13099.4i 0.390196 0.0441021i
\(546\) 100598. 0.337446
\(547\) 239848. + 239848.i 0.801607 + 0.801607i 0.983347 0.181740i \(-0.0581729\pi\)
−0.181740 + 0.983347i \(0.558173\pi\)
\(548\) 1879.88 1879.88i 0.00625991 0.00625991i
\(549\) 334168.i 1.10872i
\(550\) −599089. 375851.i −1.98046 1.24248i
\(551\) −122663. −0.404025
\(552\) 72292.8 + 72292.8i 0.237256 + 0.237256i
\(553\) 65989.1 65989.1i 0.215785 0.215785i
\(554\) 531065.i 1.73033i
\(555\) −7117.68 62974.0i −0.0231075 0.204444i
\(556\) 243825. 0.788731
\(557\) 28293.7 + 28293.7i 0.0911967 + 0.0911967i 0.751233 0.660037i \(-0.229459\pi\)
−0.660037 + 0.751233i \(0.729459\pi\)
\(558\) −40319.3 + 40319.3i −0.129492 + 0.129492i
\(559\) 221739.i 0.709608i
\(560\) −90629.0 + 113726.i −0.288995 + 0.362648i
\(561\) 133596. 0.424490
\(562\) −316165. 316165.i −1.00102 1.00102i
\(563\) 174942. 174942.i 0.551920 0.551920i −0.375074 0.926995i \(-0.622383\pi\)
0.926995 + 0.375074i \(0.122383\pi\)
\(564\) 137969.i 0.433734i
\(565\) −287308. 228956.i −0.900016 0.717226i
\(566\) −117445. −0.366609
\(567\) 33089.2 + 33089.2i 0.102925 + 0.102925i
\(568\) 32834.6 32834.6i 0.101774 0.101774i
\(569\) 522164.i 1.61281i 0.591367 + 0.806403i \(0.298589\pi\)
−0.591367 + 0.806403i \(0.701411\pi\)
\(570\) 82702.3 9347.49i 0.254547 0.0287704i
\(571\) −447593. −1.37281 −0.686406 0.727219i \(-0.740813\pi\)
−0.686406 + 0.727219i \(0.740813\pi\)
\(572\) −405185. 405185.i −1.23840 1.23840i
\(573\) −197128. + 197128.i −0.600397 + 0.600397i
\(574\) 87577.5i 0.265808i
\(575\) −280246. + 446699.i −0.847624 + 1.35107i
\(576\) −58182.5 −0.175367
\(577\) −203594. 203594.i −0.611524 0.611524i 0.331819 0.943343i \(-0.392338\pi\)
−0.943343 + 0.331819i \(0.892338\pi\)
\(578\) −228907. + 228907.i −0.685178 + 0.685178i
\(579\) 46532.5i 0.138803i
\(580\) −23493.4 207859.i −0.0698376 0.617891i
\(581\) 78221.5 0.231726
\(582\) 56989.6 + 56989.6i 0.168248 + 0.168248i
\(583\) −121964. + 121964.i −0.358833 + 0.358833i
\(584\) 77244.9i 0.226487i
\(585\) 245240. 307742.i 0.716606 0.899237i
\(586\) 38602.5 0.112414
\(587\) −148674. 148674.i −0.431477 0.431477i 0.457654 0.889131i \(-0.348690\pi\)
−0.889131 + 0.457654i \(0.848690\pi\)
\(588\) −10713.0 + 10713.0i −0.0309854 + 0.0309854i
\(589\) 26892.5i 0.0775177i
\(590\) −318132. 253521.i −0.913910 0.728298i
\(591\) 226186. 0.647576
\(592\) 132979. + 132979.i 0.379437 + 0.379437i
\(593\) 184484. 184484.i 0.524626 0.524626i −0.394339 0.918965i \(-0.629026\pi\)
0.918965 + 0.394339i \(0.129026\pi\)
\(594\) 690224.i 1.95622i
\(595\) 65962.8 7455.49i 0.186322 0.0210592i
\(596\) 272245. 0.766421
\(597\) 62469.7 + 62469.7i 0.175275 + 0.175275i
\(598\) −765440. + 765440.i −2.14047 + 2.14047i
\(599\) 63809.1i 0.177840i −0.996039 0.0889199i \(-0.971658\pi\)
0.996039 0.0889199i \(-0.0283415\pi\)
\(600\) −16903.7 73822.7i −0.0469547 0.205063i
\(601\) 364460. 1.00902 0.504511 0.863405i \(-0.331673\pi\)
0.504511 + 0.863405i \(0.331673\pi\)
\(602\) 59827.3 + 59827.3i 0.165084 + 0.165084i
\(603\) 68798.9 68798.9i 0.189211 0.189211i
\(604\) 7955.59i 0.0218071i
\(605\) −94901.7 839647.i −0.259277 2.29396i
\(606\) −378970. −1.03195
\(607\) −55070.6 55070.6i −0.149466 0.149466i 0.628413 0.777880i \(-0.283705\pi\)
−0.777880 + 0.628413i \(0.783705\pi\)
\(608\) −125113. + 125113.i −0.338449 + 0.338449i
\(609\) 62883.6i 0.169552i
\(610\) −424381. + 532537.i −1.14050 + 1.43117i
\(611\) −779468. −2.08793
\(612\) 66716.0 + 66716.0i 0.178126 + 0.178126i
\(613\) −14387.2 + 14387.2i −0.0382873 + 0.0382873i −0.725991 0.687704i \(-0.758619\pi\)
0.687704 + 0.725991i \(0.258619\pi\)
\(614\) 302498.i 0.802392i
\(615\) −76131.5 60669.5i −0.201286 0.160406i
\(616\) −116665. −0.307453
\(617\) −267377. 267377.i −0.702350 0.702350i 0.262564 0.964915i \(-0.415432\pi\)
−0.964915 + 0.262564i \(0.915432\pi\)
\(618\) 147899. 147899.i 0.387246 0.387246i
\(619\) 256622.i 0.669749i 0.942263 + 0.334874i \(0.108694\pi\)
−0.942263 + 0.334874i \(0.891306\pi\)
\(620\) −45570.9 + 5150.68i −0.118551 + 0.0133993i
\(621\) 514652. 1.33454
\(622\) 407249. + 407249.i 1.05264 + 1.05264i
\(623\) 126176. 126176.i 0.325088 0.325088i
\(624\) 331825.i 0.852196i
\(625\) 351704. 169976.i 0.900363 0.435139i
\(626\) 431051. 1.09997
\(627\) 100774. + 100774.i 0.256339 + 0.256339i
\(628\) 261861. 261861.i 0.663975 0.663975i
\(629\) 85847.3i 0.216983i
\(630\) 16863.4 + 149200.i 0.0424878 + 0.375912i
\(631\) 115571. 0.290263 0.145132 0.989412i \(-0.453639\pi\)
0.145132 + 0.989412i \(0.453639\pi\)
\(632\) −101979. 101979.i −0.255316 0.255316i
\(633\) 19541.8 19541.8i 0.0487705 0.0487705i
\(634\) 88668.0i 0.220591i
\(635\) −93908.9 + 117842.i −0.232894 + 0.292249i
\(636\) 34615.6 0.0855772
\(637\) 60524.1 + 60524.1i 0.149159 + 0.149159i
\(638\) 641705. 641705.i 1.57650 1.57650i
\(639\) 102335.i 0.250623i
\(640\) 269163. + 214497.i 0.657136 + 0.523674i
\(641\) −393645. −0.958050 −0.479025 0.877801i \(-0.659010\pi\)
−0.479025 + 0.877801i \(0.659010\pi\)
\(642\) −134388. 134388.i −0.326056 0.326056i
\(643\) −145387. + 145387.i −0.351645 + 0.351645i −0.860721 0.509076i \(-0.829987\pi\)
0.509076 + 0.860721i \(0.329987\pi\)
\(644\) 163028.i 0.393090i
\(645\) −93453.6 + 10562.7i −0.224635 + 0.0253895i
\(646\) 112741. 0.270158
\(647\) 520127. + 520127.i 1.24251 + 1.24251i 0.958955 + 0.283557i \(0.0915145\pi\)
0.283557 + 0.958955i \(0.408485\pi\)
\(648\) 51136.1 51136.1i 0.121780 0.121780i
\(649\) 696570.i 1.65377i
\(650\) 781640. 178977.i 1.85003 0.423615i
\(651\) 13786.6 0.0325308
\(652\) −16588.1 16588.1i −0.0390214 0.0390214i
\(653\) −515377. + 515377.i −1.20864 + 1.20864i −0.237179 + 0.971466i \(0.576223\pi\)
−0.971466 + 0.237179i \(0.923777\pi\)
\(654\) 101551.i 0.237427i
\(655\) 12499.2 + 110587.i 0.0291339 + 0.257763i
\(656\) 288876. 0.671281
\(657\) 120373. + 120373.i 0.278869 + 0.278869i
\(658\) 210308. 210308.i 0.485739 0.485739i
\(659\) 682913.i 1.57251i −0.617899 0.786257i \(-0.712016\pi\)
0.617899 0.786257i \(-0.287984\pi\)
\(660\) −151467. + 190069.i −0.347720 + 0.436339i
\(661\) 833390. 1.90742 0.953708 0.300734i \(-0.0972315\pi\)
0.953708 + 0.300734i \(0.0972315\pi\)
\(662\) 114311. + 114311.i 0.260839 + 0.260839i
\(663\) −107108. + 107108.i −0.243666 + 0.243666i
\(664\) 120883.i 0.274177i
\(665\) 55381.1 + 44133.4i 0.125233 + 0.0997985i
\(666\) 194176. 0.437771
\(667\) −478475. 478475.i −1.07549 1.07549i
\(668\) 118109. 118109.i 0.264686 0.264686i
\(669\) 295571.i 0.660403i
\(670\) 197011. 22267.3i 0.438876 0.0496043i
\(671\) −1.16602e6 −2.58978
\(672\) 64139.6 + 64139.6i 0.142033 + 0.142033i
\(673\) −334777. + 334777.i −0.739137 + 0.739137i −0.972411 0.233274i \(-0.925056\pi\)
0.233274 + 0.972411i \(0.425056\pi\)
\(674\) 287147.i 0.632098i
\(675\) −322940. 202603.i −0.708786 0.444671i
\(676\) 351719. 0.769666
\(677\) 456455. + 456455.i 0.995911 + 0.995911i 0.999992 0.00408059i \(-0.00129890\pi\)
−0.00408059 + 0.999992i \(0.501299\pi\)
\(678\) −226179. + 226179.i −0.492031 + 0.492031i
\(679\) 68574.7i 0.148739i
\(680\) −11521.7 101939.i −0.0249172 0.220456i
\(681\) 362305. 0.781232
\(682\) −140687. 140687.i −0.302473 0.302473i
\(683\) 365344. 365344.i 0.783179 0.783179i −0.197187 0.980366i \(-0.563181\pi\)
0.980366 + 0.197187i \(0.0631807\pi\)
\(684\) 100651.i 0.215132i
\(685\) −3970.18 + 4982.01i −0.00846115 + 0.0106175i
\(686\) −32659.9 −0.0694012
\(687\) 248.715 + 248.715i 0.000526973 + 0.000526973i
\(688\) 197342. 197342.i 0.416909 0.416909i
\(689\) 195564.i 0.411956i
\(690\) 359063. + 286138.i 0.754175 + 0.601005i
\(691\) 183959. 0.385269 0.192634 0.981271i \(-0.438297\pi\)
0.192634 + 0.981271i \(0.438297\pi\)
\(692\) 104466. + 104466.i 0.218153 + 0.218153i
\(693\) −181803. + 181803.i −0.378559 + 0.378559i
\(694\) 676341.i 1.40426i
\(695\) −580562. + 65618.5i −1.20193 + 0.135849i
\(696\) 97180.2 0.200613
\(697\) −93244.9 93244.9i −0.191937 0.191937i
\(698\) −576672. + 576672.i −1.18364 + 1.18364i
\(699\) 161277.i 0.330079i
\(700\) −64179.5 + 102299.i −0.130979 + 0.208774i
\(701\) −176822. −0.359833 −0.179916 0.983682i \(-0.557583\pi\)
−0.179916 + 0.983682i \(0.557583\pi\)
\(702\) −553374. 553374.i −1.12291 1.12291i
\(703\) 64756.6 64756.6i 0.131031 0.131031i
\(704\) 203018.i 0.409627i
\(705\) 37130.3 + 328512.i 0.0747052 + 0.660957i
\(706\) −1.11471e6 −2.23642
\(707\) −228004. 228004.i −0.456146 0.456146i
\(708\) −98850.1 + 98850.1i −0.197202 + 0.197202i
\(709\) 715270.i 1.42291i 0.702731 + 0.711455i \(0.251964\pi\)
−0.702731 + 0.711455i \(0.748036\pi\)
\(710\) 129961. 163082.i 0.257808 0.323512i
\(711\) −317836. −0.628730
\(712\) −194993. 194993.i −0.384643 0.384643i
\(713\) −104901. + 104901.i −0.206348 + 0.206348i
\(714\) 57797.5i 0.113374i
\(715\) 1.07381e6 + 855725.i 2.10047 + 1.67387i
\(716\) 210462. 0.410532
\(717\) 8874.18 + 8874.18i 0.0172619 + 0.0172619i
\(718\) 65015.8 65015.8i 0.126116 0.126116i
\(719\) 764914.i 1.47964i −0.672807 0.739818i \(-0.734911\pi\)
0.672807 0.739818i \(-0.265089\pi\)
\(720\) 492138. 55624.3i 0.949340 0.107300i
\(721\) 177964. 0.342344
\(722\) −388733. 388733.i −0.745722 0.745722i
\(723\) −14910.5 + 14910.5i −0.0285243 + 0.0285243i
\(724\) 183640.i 0.350341i
\(725\) 111878. + 488601.i 0.212848 + 0.929562i
\(726\) −735710. −1.39583
\(727\) 535539. + 535539.i 1.01326 + 1.01326i 0.999911 + 0.0133519i \(0.00425016\pi\)
0.0133519 + 0.999911i \(0.495750\pi\)
\(728\) 93533.9 93533.9i 0.176484 0.176484i
\(729\) 49803.3i 0.0937136i
\(730\) 38959.9 + 344699.i 0.0731091 + 0.646836i
\(731\) −127398. −0.238411
\(732\) 165470. + 165470.i 0.308815 + 0.308815i
\(733\) −137194. + 137194.i −0.255345 + 0.255345i −0.823158 0.567813i \(-0.807790\pi\)
0.567813 + 0.823158i \(0.307790\pi\)
\(734\) 1.14702e6i 2.12901i
\(735\) 22625.2 28391.4i 0.0418811 0.0525548i
\(736\) −976064. −1.80187
\(737\) 240062. + 240062.i 0.441966 + 0.441966i
\(738\) 210908. 210908.i 0.387241 0.387241i
\(739\) 98757.6i 0.180835i −0.995904 0.0904173i \(-0.971180\pi\)
0.995904 0.0904173i \(-0.0288201\pi\)
\(740\) 122136. + 97331.0i 0.223040 + 0.177741i
\(741\) −161588. −0.294288
\(742\) 52765.0 + 52765.0i 0.0958381 + 0.0958381i
\(743\) −154662. + 154662.i −0.280160 + 0.280160i −0.833173 0.553013i \(-0.813478\pi\)
0.553013 + 0.833173i \(0.313478\pi\)
\(744\) 21305.8i 0.0384903i
\(745\) −648231. + 73266.8i −1.16793 + 0.132006i
\(746\) −353574. −0.635335
\(747\) −188377. 188377.i −0.337587 0.337587i
\(748\) −232794. + 232794.i −0.416072 + 0.416072i
\(749\) 161708.i 0.288248i
\(750\) −112665. 320902.i −0.200293 0.570493i
\(751\) 649137. 1.15095 0.575475 0.817819i \(-0.304817\pi\)
0.575475 + 0.817819i \(0.304817\pi\)
\(752\) −693704. 693704.i −1.22670 1.22670i
\(753\) 154990. 154990.i 0.273347 0.273347i
\(754\) 1.02895e6i 1.80989i
\(755\) 2141.02 + 18942.7i 0.00375601 + 0.0332314i
\(756\) 117861. 0.206218
\(757\) −524986. 524986.i −0.916128 0.916128i 0.0806176 0.996745i \(-0.474311\pi\)
−0.996745 + 0.0806176i \(0.974311\pi\)
\(758\) 570551. 570551.i 0.993015 0.993015i
\(759\) 786190.i 1.36472i
\(760\) 68203.7 85585.9i 0.118081 0.148175i
\(761\) 804359. 1.38893 0.694465 0.719526i \(-0.255641\pi\)
0.694465 + 0.719526i \(0.255641\pi\)
\(762\) 92769.5 + 92769.5i 0.159770 + 0.159770i
\(763\) 61097.5 61097.5i 0.104948 0.104948i
\(764\) 687000.i 1.17698i
\(765\) −176809. 140900.i −0.302122 0.240762i
\(766\) −606884. −1.03430
\(767\) 558462. + 558462.i 0.949299 + 0.949299i
\(768\) 256077. 256077.i 0.434159 0.434159i
\(769\) 334985.i 0.566465i −0.959051 0.283233i \(-0.908593\pi\)
0.959051 0.283233i \(-0.0914068\pi\)
\(770\) −520607. + 58842.0i −0.878069 + 0.0992444i
\(771\) 47133.9 0.0792912
\(772\) −81084.0 81084.0i −0.136051 0.136051i
\(773\) −160551. + 160551.i −0.268691 + 0.268691i −0.828573 0.559881i \(-0.810847\pi\)
0.559881 + 0.828573i \(0.310847\pi\)
\(774\) 288158.i 0.481004i
\(775\) 107121. 24528.2i 0.178349 0.0408377i
\(776\