Properties

Label 300.5.c.c.151.8
Level $300$
Weight $5$
Character 300.151
Analytic conductor $31.011$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(31.0109889252\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + 234752 x^{8} - 632832 x^{7} + 1884160 x^{6} - 8847360 x^{5} + 32243712 x^{4} - 113246208 x^{3} + 335544320 x^{2} - 1610612736 x + 4294967296\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.8
Root \(-3.04390 - 2.59512i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.5.c.c.151.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.725488 + 3.93366i) q^{2} +5.19615i q^{3} +(-14.9473 + 5.70765i) q^{4} +(-20.4399 + 3.76975i) q^{6} +36.7329i q^{7} +(-33.2960 - 54.6569i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(0.725488 + 3.93366i) q^{2} +5.19615i q^{3} +(-14.9473 + 5.70765i) q^{4} +(-20.4399 + 3.76975i) q^{6} +36.7329i q^{7} +(-33.2960 - 54.6569i) q^{8} -27.0000 q^{9} +156.989i q^{11} +(-29.6578 - 77.6686i) q^{12} -62.1869 q^{13} +(-144.495 + 26.6493i) q^{14} +(190.846 - 170.628i) q^{16} -306.493 q^{17} +(-19.5882 - 106.209i) q^{18} +242.784i q^{19} -190.870 q^{21} +(-617.541 + 113.894i) q^{22} -571.211i q^{23} +(284.005 - 173.011i) q^{24} +(-45.1158 - 244.622i) q^{26} -140.296i q^{27} +(-209.658 - 549.059i) q^{28} -266.538 q^{29} -759.271i q^{31} +(809.649 + 626.932i) q^{32} -815.738 q^{33} +(-222.357 - 1205.64i) q^{34} +(403.578 - 154.106i) q^{36} -1214.97 q^{37} +(-955.029 + 176.137i) q^{38} -323.132i q^{39} +2677.60 q^{41} +(-138.474 - 750.816i) q^{42} -2635.37i q^{43} +(-896.037 - 2346.57i) q^{44} +(2246.95 - 414.407i) q^{46} +2374.46i q^{47} +(886.610 + 991.663i) q^{48} +1051.70 q^{49} -1592.58i q^{51} +(929.528 - 354.941i) q^{52} -1396.48 q^{53} +(551.877 - 101.783i) q^{54} +(2007.70 - 1223.06i) q^{56} -1261.54 q^{57} +(-193.370 - 1048.47i) q^{58} -2901.75i q^{59} -4786.97 q^{61} +(2986.71 - 550.842i) q^{62} -991.788i q^{63} +(-1878.75 + 3639.72i) q^{64} +(-591.809 - 3208.84i) q^{66} +4656.43i q^{67} +(4581.25 - 1749.35i) q^{68} +2968.10 q^{69} -6767.57i q^{71} +(898.993 + 1475.74i) q^{72} +6581.94 q^{73} +(-881.450 - 4779.29i) q^{74} +(-1385.72 - 3628.97i) q^{76} -5766.65 q^{77} +(1271.09 - 234.429i) q^{78} +8545.74i q^{79} +729.000 q^{81} +(1942.57 + 10532.8i) q^{82} -2173.65i q^{83} +(2852.99 - 1089.42i) q^{84} +(10366.6 - 1911.93i) q^{86} -1384.97i q^{87} +(8580.52 - 5227.11i) q^{88} +6633.68 q^{89} -2284.30i q^{91} +(3260.27 + 8538.08i) q^{92} +3945.29 q^{93} +(-9340.31 + 1722.64i) q^{94} +(-3257.64 + 4207.06i) q^{96} -15704.1 q^{97} +(762.993 + 4137.01i) q^{98} -4238.70i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + O(q^{10}) \) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + 176q^{13} + 78q^{14} - 376q^{16} - 162q^{18} - 144q^{21} - 788q^{22} + 108q^{24} + 678q^{26} + 3368q^{28} + 1728q^{29} + 2016q^{32} - 2932q^{34} - 216q^{36} - 1568q^{37} - 6990q^{38} + 1248q^{41} + 162q^{42} + 8088q^{44} + 5956q^{46} + 2088q^{48} - 10720q^{49} + 3128q^{52} - 288q^{53} - 486q^{54} - 10236q^{56} + 5616q^{57} - 16164q^{58} - 3760q^{61} - 12714q^{62} + 10544q^{64} + 8100q^{66} + 26136q^{68} + 9792q^{69} + 4860q^{72} + 11040q^{73} - 17004q^{74} - 28344q^{76} + 768q^{77} - 16830q^{78} + 11664q^{81} - 21280q^{82} + 15120q^{84} + 24414q^{86} + 52840q^{88} - 768q^{89} + 23736q^{92} - 9936q^{93} - 45156q^{94} - 11088q^{96} + 7248q^{97} - 58140q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.725488 + 3.93366i 0.181372 + 0.983415i
\(3\) 5.19615i 0.577350i
\(4\) −14.9473 + 5.70765i −0.934208 + 0.356728i
\(5\) 0 0
\(6\) −20.4399 + 3.76975i −0.567775 + 0.104715i
\(7\) 36.7329i 0.749650i 0.927095 + 0.374825i \(0.122297\pi\)
−0.927095 + 0.374825i \(0.877703\pi\)
\(8\) −33.2960 54.6569i −0.520251 0.854014i
\(9\) −27.0000 −0.333333
\(10\) 0 0
\(11\) 156.989i 1.29743i 0.761032 + 0.648715i \(0.224693\pi\)
−0.761032 + 0.648715i \(0.775307\pi\)
\(12\) −29.6578 77.6686i −0.205957 0.539365i
\(13\) −62.1869 −0.367970 −0.183985 0.982929i \(-0.558900\pi\)
−0.183985 + 0.982929i \(0.558900\pi\)
\(14\) −144.495 + 26.6493i −0.737217 + 0.135966i
\(15\) 0 0
\(16\) 190.846 170.628i 0.745490 0.666516i
\(17\) −306.493 −1.06053 −0.530264 0.847832i \(-0.677907\pi\)
−0.530264 + 0.847832i \(0.677907\pi\)
\(18\) −19.5882 106.209i −0.0604574 0.327805i
\(19\) 242.784i 0.672532i 0.941767 + 0.336266i \(0.109164\pi\)
−0.941767 + 0.336266i \(0.890836\pi\)
\(20\) 0 0
\(21\) −190.870 −0.432811
\(22\) −617.541 + 113.894i −1.27591 + 0.235317i
\(23\) 571.211i 1.07979i −0.841731 0.539897i \(-0.818463\pi\)
0.841731 0.539897i \(-0.181537\pi\)
\(24\) 284.005 173.011i 0.493065 0.300367i
\(25\) 0 0
\(26\) −45.1158 244.622i −0.0667394 0.361867i
\(27\) 140.296i 0.192450i
\(28\) −209.658 549.059i −0.267421 0.700330i
\(29\) −266.538 −0.316930 −0.158465 0.987365i \(-0.550654\pi\)
−0.158465 + 0.987365i \(0.550654\pi\)
\(30\) 0 0
\(31\) 759.271i 0.790084i −0.918663 0.395042i \(-0.870730\pi\)
0.918663 0.395042i \(-0.129270\pi\)
\(32\) 809.649 + 626.932i 0.790673 + 0.612239i
\(33\) −815.738 −0.749071
\(34\) −222.357 1205.64i −0.192350 1.04294i
\(35\) 0 0
\(36\) 403.578 154.106i 0.311403 0.118909i
\(37\) −1214.97 −0.887490 −0.443745 0.896153i \(-0.646350\pi\)
−0.443745 + 0.896153i \(0.646350\pi\)
\(38\) −955.029 + 176.137i −0.661377 + 0.121978i
\(39\) 323.132i 0.212447i
\(40\) 0 0
\(41\) 2677.60 1.59286 0.796431 0.604730i \(-0.206719\pi\)
0.796431 + 0.604730i \(0.206719\pi\)
\(42\) −138.474 750.816i −0.0784998 0.425633i
\(43\) 2635.37i 1.42530i −0.701522 0.712648i \(-0.747496\pi\)
0.701522 0.712648i \(-0.252504\pi\)
\(44\) −896.037 2346.57i −0.462829 1.21207i
\(45\) 0 0
\(46\) 2246.95 414.407i 1.06188 0.195844i
\(47\) 2374.46i 1.07490i 0.843295 + 0.537451i \(0.180613\pi\)
−0.843295 + 0.537451i \(0.819387\pi\)
\(48\) 886.610 + 991.663i 0.384813 + 0.430409i
\(49\) 1051.70 0.438024
\(50\) 0 0
\(51\) 1592.58i 0.612297i
\(52\) 929.528 354.941i 0.343760 0.131265i
\(53\) −1396.48 −0.497143 −0.248572 0.968613i \(-0.579961\pi\)
−0.248572 + 0.968613i \(0.579961\pi\)
\(54\) 551.877 101.783i 0.189258 0.0349051i
\(55\) 0 0
\(56\) 2007.70 1223.06i 0.640212 0.390006i
\(57\) −1261.54 −0.388286
\(58\) −193.370 1048.47i −0.0574822 0.311673i
\(59\) 2901.75i 0.833597i −0.908999 0.416798i \(-0.863152\pi\)
0.908999 0.416798i \(-0.136848\pi\)
\(60\) 0 0
\(61\) −4786.97 −1.28647 −0.643237 0.765667i \(-0.722409\pi\)
−0.643237 + 0.765667i \(0.722409\pi\)
\(62\) 2986.71 550.842i 0.776980 0.143299i
\(63\) 991.788i 0.249883i
\(64\) −1878.75 + 3639.72i −0.458678 + 0.888602i
\(65\) 0 0
\(66\) −591.809 3208.84i −0.135861 0.736647i
\(67\) 4656.43i 1.03730i 0.854987 + 0.518649i \(0.173565\pi\)
−0.854987 + 0.518649i \(0.826435\pi\)
\(68\) 4581.25 1749.35i 0.990755 0.378320i
\(69\) 2968.10 0.623419
\(70\) 0 0
\(71\) 6767.57i 1.34251i −0.741228 0.671253i \(-0.765756\pi\)
0.741228 0.671253i \(-0.234244\pi\)
\(72\) 898.993 + 1475.74i 0.173417 + 0.284671i
\(73\) 6581.94 1.23512 0.617559 0.786525i \(-0.288122\pi\)
0.617559 + 0.786525i \(0.288122\pi\)
\(74\) −881.450 4779.29i −0.160966 0.872771i
\(75\) 0 0
\(76\) −1385.72 3628.97i −0.239911 0.628285i
\(77\) −5766.65 −0.972618
\(78\) 1271.09 234.429i 0.208924 0.0385320i
\(79\) 8545.74i 1.36929i 0.728876 + 0.684645i \(0.240043\pi\)
−0.728876 + 0.684645i \(0.759957\pi\)
\(80\) 0 0
\(81\) 729.000 0.111111
\(82\) 1942.57 + 10532.8i 0.288901 + 1.56644i
\(83\) 2173.65i 0.315525i −0.987477 0.157763i \(-0.949572\pi\)
0.987477 0.157763i \(-0.0504281\pi\)
\(84\) 2852.99 1089.42i 0.404336 0.154396i
\(85\) 0 0
\(86\) 10366.6 1911.93i 1.40166 0.258509i
\(87\) 1384.97i 0.182980i
\(88\) 8580.52 5227.11i 1.10802 0.674988i
\(89\) 6633.68 0.837480 0.418740 0.908106i \(-0.362472\pi\)
0.418740 + 0.908106i \(0.362472\pi\)
\(90\) 0 0
\(91\) 2284.30i 0.275849i
\(92\) 3260.27 + 8538.08i 0.385192 + 1.00875i
\(93\) 3945.29 0.456155
\(94\) −9340.31 + 1722.64i −1.05707 + 0.194957i
\(95\) 0 0
\(96\) −3257.64 + 4207.06i −0.353476 + 0.456495i
\(97\) −15704.1 −1.66905 −0.834525 0.550970i \(-0.814258\pi\)
−0.834525 + 0.550970i \(0.814258\pi\)
\(98\) 762.993 + 4137.01i 0.0794454 + 0.430759i
\(99\) 4238.70i 0.432476i
\(100\) 0 0
\(101\) −13188.7 −1.29288 −0.646440 0.762965i \(-0.723743\pi\)
−0.646440 + 0.762965i \(0.723743\pi\)
\(102\) 6264.68 1155.40i 0.602141 0.111054i
\(103\) 2187.77i 0.206218i 0.994670 + 0.103109i \(0.0328791\pi\)
−0.994670 + 0.103109i \(0.967121\pi\)
\(104\) 2070.58 + 3398.94i 0.191436 + 0.314251i
\(105\) 0 0
\(106\) −1013.13 5493.26i −0.0901680 0.488898i
\(107\) 12415.4i 1.08441i −0.840246 0.542205i \(-0.817590\pi\)
0.840246 0.542205i \(-0.182410\pi\)
\(108\) 800.761 + 2097.05i 0.0686523 + 0.179788i
\(109\) 13504.8 1.13667 0.568336 0.822797i \(-0.307588\pi\)
0.568336 + 0.822797i \(0.307588\pi\)
\(110\) 0 0
\(111\) 6313.19i 0.512393i
\(112\) 6267.66 + 7010.31i 0.499654 + 0.558857i
\(113\) −24496.4 −1.91843 −0.959213 0.282683i \(-0.908775\pi\)
−0.959213 + 0.282683i \(0.908775\pi\)
\(114\) −915.234 4962.48i −0.0704243 0.381846i
\(115\) 0 0
\(116\) 3984.03 1521.30i 0.296079 0.113058i
\(117\) 1679.05 0.122657
\(118\) 11414.5 2105.19i 0.819771 0.151191i
\(119\) 11258.4i 0.795026i
\(120\) 0 0
\(121\) −10004.5 −0.683322
\(122\) −3472.89 18830.3i −0.233330 1.26514i
\(123\) 13913.2i 0.919639i
\(124\) 4333.65 + 11349.1i 0.281845 + 0.738103i
\(125\) 0 0
\(126\) 3901.35 719.530i 0.245739 0.0453219i
\(127\) 6927.31i 0.429494i −0.976670 0.214747i \(-0.931107\pi\)
0.976670 0.214747i \(-0.0688927\pi\)
\(128\) −15680.4 4749.78i −0.957056 0.289903i
\(129\) 13693.8 0.822895
\(130\) 0 0
\(131\) 1893.13i 0.110316i −0.998478 0.0551579i \(-0.982434\pi\)
0.998478 0.0551579i \(-0.0175662\pi\)
\(132\) 12193.1 4655.95i 0.699788 0.267215i
\(133\) −8918.15 −0.504164
\(134\) −18316.8 + 3378.19i −1.02009 + 0.188137i
\(135\) 0 0
\(136\) 10205.0 + 16751.9i 0.551741 + 0.905706i
\(137\) −35998.2 −1.91796 −0.958981 0.283470i \(-0.908514\pi\)
−0.958981 + 0.283470i \(0.908514\pi\)
\(138\) 2153.32 + 11675.5i 0.113071 + 0.613079i
\(139\) 1899.55i 0.0983155i 0.998791 + 0.0491577i \(0.0156537\pi\)
−0.998791 + 0.0491577i \(0.984346\pi\)
\(140\) 0 0
\(141\) −12338.0 −0.620595
\(142\) 26621.3 4909.80i 1.32024 0.243493i
\(143\) 9762.65i 0.477414i
\(144\) −5152.83 + 4606.96i −0.248497 + 0.222172i
\(145\) 0 0
\(146\) 4775.12 + 25891.1i 0.224016 + 1.21463i
\(147\) 5464.77i 0.252893i
\(148\) 18160.6 6934.64i 0.829101 0.316593i
\(149\) 6118.77 0.275608 0.137804 0.990460i \(-0.455996\pi\)
0.137804 + 0.990460i \(0.455996\pi\)
\(150\) 0 0
\(151\) 30282.1i 1.32810i 0.747687 + 0.664052i \(0.231165\pi\)
−0.747687 + 0.664052i \(0.768835\pi\)
\(152\) 13269.8 8083.74i 0.574351 0.349885i
\(153\) 8275.31 0.353510
\(154\) −4183.64 22684.0i −0.176406 0.956487i
\(155\) 0 0
\(156\) 1844.33 + 4829.97i 0.0757859 + 0.198470i
\(157\) −11389.8 −0.462078 −0.231039 0.972945i \(-0.574212\pi\)
−0.231039 + 0.972945i \(0.574212\pi\)
\(158\) −33616.0 + 6199.84i −1.34658 + 0.248351i
\(159\) 7256.30i 0.287026i
\(160\) 0 0
\(161\) 20982.2 0.809468
\(162\) 528.881 + 2867.64i 0.0201525 + 0.109268i
\(163\) 10601.7i 0.399027i 0.979895 + 0.199513i \(0.0639361\pi\)
−0.979895 + 0.199513i \(0.936064\pi\)
\(164\) −40023.0 + 15282.8i −1.48806 + 0.568218i
\(165\) 0 0
\(166\) 8550.41 1576.96i 0.310292 0.0572275i
\(167\) 15333.5i 0.549803i −0.961472 0.274902i \(-0.911355\pi\)
0.961472 0.274902i \(-0.0886453\pi\)
\(168\) 6355.20 + 10432.3i 0.225170 + 0.369626i
\(169\) −24693.8 −0.864598
\(170\) 0 0
\(171\) 6555.17i 0.224177i
\(172\) 15041.8 + 39391.8i 0.508443 + 1.33152i
\(173\) −37712.5 −1.26007 −0.630033 0.776568i \(-0.716959\pi\)
−0.630033 + 0.776568i \(0.716959\pi\)
\(174\) 5448.01 1004.78i 0.179945 0.0331874i
\(175\) 0 0
\(176\) 26786.7 + 29960.6i 0.864758 + 0.967221i
\(177\) 15077.9 0.481277
\(178\) 4812.65 + 26094.6i 0.151895 + 0.823590i
\(179\) 26116.7i 0.815101i 0.913183 + 0.407551i \(0.133617\pi\)
−0.913183 + 0.407551i \(0.866383\pi\)
\(180\) 0 0
\(181\) −44004.0 −1.34318 −0.671591 0.740922i \(-0.734389\pi\)
−0.671591 + 0.740922i \(0.734389\pi\)
\(182\) 8985.66 1657.23i 0.271273 0.0500312i
\(183\) 24873.8i 0.742746i
\(184\) −31220.6 + 19019.1i −0.922158 + 0.561763i
\(185\) 0 0
\(186\) 2862.26 + 15519.4i 0.0827338 + 0.448590i
\(187\) 48116.0i 1.37596i
\(188\) −13552.6 35491.8i −0.383448 1.00418i
\(189\) 5153.48 0.144270
\(190\) 0 0
\(191\) 34103.8i 0.934839i 0.884036 + 0.467419i \(0.154816\pi\)
−0.884036 + 0.467419i \(0.845184\pi\)
\(192\) −18912.5 9762.25i −0.513035 0.264818i
\(193\) −27574.1 −0.740263 −0.370132 0.928979i \(-0.620687\pi\)
−0.370132 + 0.928979i \(0.620687\pi\)
\(194\) −11393.1 61774.5i −0.302719 1.64137i
\(195\) 0 0
\(196\) −15720.1 + 6002.71i −0.409206 + 0.156255i
\(197\) −45162.5 −1.16371 −0.581856 0.813292i \(-0.697673\pi\)
−0.581856 + 0.813292i \(0.697673\pi\)
\(198\) 16673.6 3075.13i 0.425304 0.0784391i
\(199\) 56574.1i 1.42860i 0.699838 + 0.714302i \(0.253255\pi\)
−0.699838 + 0.714302i \(0.746745\pi\)
\(200\) 0 0
\(201\) −24195.5 −0.598885
\(202\) −9568.23 51879.7i −0.234492 1.27144i
\(203\) 9790.71i 0.237587i
\(204\) 9089.90 + 23804.9i 0.218423 + 0.572013i
\(205\) 0 0
\(206\) −8605.94 + 1587.20i −0.202798 + 0.0374023i
\(207\) 15422.7i 0.359931i
\(208\) −11868.1 + 10610.8i −0.274318 + 0.245258i
\(209\) −38114.4 −0.872562
\(210\) 0 0
\(211\) 75965.3i 1.70628i 0.521681 + 0.853140i \(0.325305\pi\)
−0.521681 + 0.853140i \(0.674695\pi\)
\(212\) 20873.6 7970.59i 0.464436 0.177345i
\(213\) 35165.3 0.775096
\(214\) 48838.0 9007.23i 1.06642 0.196682i
\(215\) 0 0
\(216\) −7668.15 + 4671.31i −0.164355 + 0.100122i
\(217\) 27890.2 0.592287
\(218\) 9797.57 + 53123.2i 0.206160 + 1.11782i
\(219\) 34200.8i 0.713096i
\(220\) 0 0
\(221\) 19059.8 0.390242
\(222\) 24833.9 4580.15i 0.503895 0.0929338i
\(223\) 92718.2i 1.86447i 0.361854 + 0.932235i \(0.382144\pi\)
−0.361854 + 0.932235i \(0.617856\pi\)
\(224\) −23029.0 + 29740.7i −0.458965 + 0.592728i
\(225\) 0 0
\(226\) −17771.8 96360.4i −0.347949 1.88661i
\(227\) 35666.1i 0.692155i 0.938206 + 0.346078i \(0.112487\pi\)
−0.938206 + 0.346078i \(0.887513\pi\)
\(228\) 18856.7 7200.44i 0.362740 0.138513i
\(229\) 103760. 1.97861 0.989307 0.145850i \(-0.0465916\pi\)
0.989307 + 0.145850i \(0.0465916\pi\)
\(230\) 0 0
\(231\) 29964.4i 0.561541i
\(232\) 8874.66 + 14568.1i 0.164883 + 0.270662i
\(233\) −17612.7 −0.324425 −0.162213 0.986756i \(-0.551863\pi\)
−0.162213 + 0.986756i \(0.551863\pi\)
\(234\) 1218.13 + 6604.79i 0.0222465 + 0.120622i
\(235\) 0 0
\(236\) 16562.2 + 43373.4i 0.297367 + 0.778753i
\(237\) −44405.0 −0.790560
\(238\) 44286.6 8167.81i 0.781840 0.144196i
\(239\) 57194.0i 1.00128i −0.865656 0.500639i \(-0.833098\pi\)
0.865656 0.500639i \(-0.166902\pi\)
\(240\) 0 0
\(241\) −32787.4 −0.564512 −0.282256 0.959339i \(-0.591083\pi\)
−0.282256 + 0.959339i \(0.591083\pi\)
\(242\) −7258.16 39354.4i −0.123936 0.671989i
\(243\) 3788.00i 0.0641500i
\(244\) 71552.4 27322.3i 1.20183 0.458921i
\(245\) 0 0
\(246\) −54729.8 + 10093.9i −0.904386 + 0.166797i
\(247\) 15098.0i 0.247471i
\(248\) −41499.4 + 25280.7i −0.674743 + 0.411042i
\(249\) 11294.6 0.182169
\(250\) 0 0
\(251\) 28803.4i 0.457190i −0.973522 0.228595i \(-0.926587\pi\)
0.973522 0.228595i \(-0.0734131\pi\)
\(252\) 5660.77 + 14824.6i 0.0891404 + 0.233443i
\(253\) 89673.7 1.40096
\(254\) 27249.7 5025.69i 0.422371 0.0778983i
\(255\) 0 0
\(256\) 7308.04 65127.3i 0.111512 0.993763i
\(257\) 97466.3 1.47567 0.737833 0.674983i \(-0.235849\pi\)
0.737833 + 0.674983i \(0.235849\pi\)
\(258\) 9934.69 + 53866.7i 0.149250 + 0.809247i
\(259\) 44629.5i 0.665308i
\(260\) 0 0
\(261\) 7196.53 0.105643
\(262\) 7446.93 1373.44i 0.108486 0.0200082i
\(263\) 82950.9i 1.19925i −0.800281 0.599625i \(-0.795316\pi\)
0.800281 0.599625i \(-0.204684\pi\)
\(264\) 27160.9 + 44585.7i 0.389705 + 0.639717i
\(265\) 0 0
\(266\) −6470.01 35081.0i −0.0914412 0.495802i
\(267\) 34469.6i 0.483519i
\(268\) −26577.3 69601.3i −0.370033 0.969053i
\(269\) −76939.2 −1.06327 −0.531634 0.846974i \(-0.678422\pi\)
−0.531634 + 0.846974i \(0.678422\pi\)
\(270\) 0 0
\(271\) 73991.7i 1.00750i −0.863850 0.503749i \(-0.831954\pi\)
0.863850 0.503749i \(-0.168046\pi\)
\(272\) −58492.8 + 52296.3i −0.790614 + 0.706860i
\(273\) 11869.6 0.159261
\(274\) −26116.3 141605.i −0.347865 1.88615i
\(275\) 0 0
\(276\) −44365.1 + 16940.9i −0.582403 + 0.222391i
\(277\) 40327.2 0.525580 0.262790 0.964853i \(-0.415357\pi\)
0.262790 + 0.964853i \(0.415357\pi\)
\(278\) −7472.19 + 1378.10i −0.0966849 + 0.0178317i
\(279\) 20500.3i 0.263361i
\(280\) 0 0
\(281\) 39798.8 0.504031 0.252016 0.967723i \(-0.418907\pi\)
0.252016 + 0.967723i \(0.418907\pi\)
\(282\) −8951.11 48533.7i −0.112559 0.610302i
\(283\) 29271.4i 0.365486i 0.983161 + 0.182743i \(0.0584976\pi\)
−0.983161 + 0.182743i \(0.941502\pi\)
\(284\) 38626.9 + 101157.i 0.478909 + 1.25418i
\(285\) 0 0
\(286\) 38402.9 7082.69i 0.469496 0.0865896i
\(287\) 98356.0i 1.19409i
\(288\) −21860.5 16927.2i −0.263558 0.204080i
\(289\) 10416.9 0.124722
\(290\) 0 0
\(291\) 81600.8i 0.963626i
\(292\) −98382.5 + 37567.4i −1.15386 + 0.440601i
\(293\) −14569.2 −0.169707 −0.0848535 0.996393i \(-0.527042\pi\)
−0.0848535 + 0.996393i \(0.527042\pi\)
\(294\) −21496.5 + 3964.63i −0.248699 + 0.0458678i
\(295\) 0 0
\(296\) 40453.8 + 66406.7i 0.461718 + 0.757929i
\(297\) 22024.9 0.249690
\(298\) 4439.09 + 24069.1i 0.0499875 + 0.271037i
\(299\) 35521.8i 0.397331i
\(300\) 0 0
\(301\) 96804.8 1.06847
\(302\) −119119. + 21969.3i −1.30608 + 0.240881i
\(303\) 68530.3i 0.746445i
\(304\) 41425.8 + 46334.2i 0.448253 + 0.501366i
\(305\) 0 0
\(306\) 6003.64 + 32552.2i 0.0641168 + 0.347647i
\(307\) 103447.i 1.09759i −0.835956 0.548796i \(-0.815086\pi\)
0.835956 0.548796i \(-0.184914\pi\)
\(308\) 86196.1 32914.0i 0.908628 0.346960i
\(309\) −11368.0 −0.119060
\(310\) 0 0
\(311\) 140701.i 1.45471i −0.686262 0.727354i \(-0.740750\pi\)
0.686262 0.727354i \(-0.259250\pi\)
\(312\) −17661.4 + 10759.0i −0.181433 + 0.110526i
\(313\) 100063. 1.02138 0.510688 0.859766i \(-0.329391\pi\)
0.510688 + 0.859766i \(0.329391\pi\)
\(314\) −8263.14 44803.4i −0.0838080 0.454414i
\(315\) 0 0
\(316\) −48776.1 127736.i −0.488464 1.27920i
\(317\) −15226.6 −0.151525 −0.0757623 0.997126i \(-0.524139\pi\)
−0.0757623 + 0.997126i \(0.524139\pi\)
\(318\) 28543.8 5264.36i 0.282265 0.0520585i
\(319\) 41843.5i 0.411194i
\(320\) 0 0
\(321\) 64512.3 0.626084
\(322\) 15222.3 + 82536.8i 0.146815 + 0.796042i
\(323\) 74411.5i 0.713239i
\(324\) −10896.6 + 4160.87i −0.103801 + 0.0396364i
\(325\) 0 0
\(326\) −41703.6 + 7691.44i −0.392409 + 0.0723723i
\(327\) 70172.9i 0.656257i
\(328\) −89153.5 146349.i −0.828687 1.36033i
\(329\) −87220.7 −0.805801
\(330\) 0 0
\(331\) 174253.i 1.59047i 0.606304 + 0.795233i \(0.292652\pi\)
−0.606304 + 0.795233i \(0.707348\pi\)
\(332\) 12406.4 + 32490.3i 0.112557 + 0.294766i
\(333\) 32804.3 0.295830
\(334\) 60316.6 11124.2i 0.540684 0.0997189i
\(335\) 0 0
\(336\) −36426.6 + 32567.7i −0.322656 + 0.288476i
\(337\) 202345. 1.78170 0.890848 0.454302i \(-0.150111\pi\)
0.890848 + 0.454302i \(0.150111\pi\)
\(338\) −17915.1 97136.9i −0.156814 0.850259i
\(339\) 127287.i 1.10760i
\(340\) 0 0
\(341\) 119197. 1.02508
\(342\) 25785.8 4755.70i 0.220459 0.0406595i
\(343\) 126827.i 1.07802i
\(344\) −144041. + 87747.4i −1.21722 + 0.741511i
\(345\) 0 0
\(346\) −27360.0 148348.i −0.228541 1.23917i
\(347\) 106576.i 0.885115i 0.896740 + 0.442558i \(0.145929\pi\)
−0.896740 + 0.442558i \(0.854071\pi\)
\(348\) 7904.93 + 20701.6i 0.0652739 + 0.170941i
\(349\) −192354. −1.57925 −0.789624 0.613590i \(-0.789725\pi\)
−0.789624 + 0.613590i \(0.789725\pi\)
\(350\) 0 0
\(351\) 8724.57i 0.0708158i
\(352\) −98421.4 + 127106.i −0.794336 + 1.02584i
\(353\) 76180.9 0.611360 0.305680 0.952134i \(-0.401116\pi\)
0.305680 + 0.952134i \(0.401116\pi\)
\(354\) 10938.9 + 59311.4i 0.0872902 + 0.473295i
\(355\) 0 0
\(356\) −99155.8 + 37862.7i −0.782380 + 0.298752i
\(357\) 58500.2 0.459008
\(358\) −102734. + 18947.3i −0.801582 + 0.147837i
\(359\) 169799.i 1.31749i −0.752368 0.658743i \(-0.771088\pi\)
0.752368 0.658743i \(-0.228912\pi\)
\(360\) 0 0
\(361\) 71377.0 0.547701
\(362\) −31924.4 173097.i −0.243616 1.32091i
\(363\) 51985.0i 0.394516i
\(364\) 13038.0 + 34144.2i 0.0984029 + 0.257700i
\(365\) 0 0
\(366\) 97845.1 18045.7i 0.730427 0.134713i
\(367\) 7980.18i 0.0592489i 0.999561 + 0.0296245i \(0.00943114\pi\)
−0.999561 + 0.0296245i \(0.990569\pi\)
\(368\) −97464.6 109013.i −0.719700 0.804976i
\(369\) −72295.2 −0.530954
\(370\) 0 0
\(371\) 51296.6i 0.372684i
\(372\) −58971.5 + 22518.3i −0.426144 + 0.162723i
\(373\) −259277. −1.86357 −0.931786 0.363007i \(-0.881750\pi\)
−0.931786 + 0.363007i \(0.881750\pi\)
\(374\) 189272. 34907.6i 1.35314 0.249561i
\(375\) 0 0
\(376\) 129780. 79060.1i 0.917981 0.559219i
\(377\) 16575.2 0.116621
\(378\) 3738.79 + 20272.0i 0.0261666 + 0.141878i
\(379\) 11693.1i 0.0814048i 0.999171 + 0.0407024i \(0.0129596\pi\)
−0.999171 + 0.0407024i \(0.987040\pi\)
\(380\) 0 0
\(381\) 35995.4 0.247969
\(382\) −134153. + 24741.9i −0.919334 + 0.169554i
\(383\) 34931.5i 0.238133i −0.992886 0.119067i \(-0.962010\pi\)
0.992886 0.119067i \(-0.0379902\pi\)
\(384\) 24680.6 81477.8i 0.167376 0.552557i
\(385\) 0 0
\(386\) −20004.7 108467.i −0.134263 0.727986i
\(387\) 71155.0i 0.475098i
\(388\) 234734. 89633.4i 1.55924 0.595397i
\(389\) 110218. 0.728375 0.364187 0.931326i \(-0.381347\pi\)
0.364187 + 0.931326i \(0.381347\pi\)
\(390\) 0 0
\(391\) 175072.i 1.14515i
\(392\) −35017.3 57482.4i −0.227882 0.374079i
\(393\) 9836.99 0.0636909
\(394\) −32764.9 177654.i −0.211065 1.14441i
\(395\) 0 0
\(396\) 24193.0 + 63357.3i 0.154276 + 0.404023i
\(397\) 44836.0 0.284476 0.142238 0.989832i \(-0.454570\pi\)
0.142238 + 0.989832i \(0.454570\pi\)
\(398\) −222543. + 41043.9i −1.40491 + 0.259109i
\(399\) 46340.1i 0.291079i
\(400\) 0 0
\(401\) 183752. 1.14273 0.571364 0.820697i \(-0.306414\pi\)
0.571364 + 0.820697i \(0.306414\pi\)
\(402\) −17553.6 95177.0i −0.108621 0.588952i
\(403\) 47216.7i 0.290727i
\(404\) 197135. 75276.3i 1.20782 0.461206i
\(405\) 0 0
\(406\) 38513.3 7103.05i 0.233646 0.0430916i
\(407\) 190738.i 1.15146i
\(408\) −87045.6 + 53026.7i −0.522910 + 0.318548i
\(409\) −116120. −0.694160 −0.347080 0.937836i \(-0.612827\pi\)
−0.347080 + 0.937836i \(0.612827\pi\)
\(410\) 0 0
\(411\) 187052.i 1.10734i
\(412\) −12487.0 32701.3i −0.0735638 0.192651i
\(413\) 106590. 0.624906
\(414\) −60667.6 + 11189.0i −0.353961 + 0.0652815i
\(415\) 0 0
\(416\) −50349.5 38987.0i −0.290944 0.225285i
\(417\) −9870.37 −0.0567625
\(418\) −27651.5 149929.i −0.158258 0.858090i
\(419\) 26586.3i 0.151436i 0.997129 + 0.0757181i \(0.0241249\pi\)
−0.997129 + 0.0757181i \(0.975875\pi\)
\(420\) 0 0
\(421\) −41926.6 −0.236551 −0.118276 0.992981i \(-0.537737\pi\)
−0.118276 + 0.992981i \(0.537737\pi\)
\(422\) −298822. + 55112.0i −1.67798 + 0.309472i
\(423\) 64110.4i 0.358301i
\(424\) 46497.1 + 76327.0i 0.258639 + 0.424567i
\(425\) 0 0
\(426\) 25512.1 + 138328.i 0.140581 + 0.762241i
\(427\) 175839.i 0.964406i
\(428\) 70862.7 + 185577.i 0.386839 + 1.01306i
\(429\) 50728.2 0.275635
\(430\) 0 0
\(431\) 258465.i 1.39138i −0.718340 0.695692i \(-0.755098\pi\)
0.718340 0.695692i \(-0.244902\pi\)
\(432\) −23938.5 26774.9i −0.128271 0.143470i
\(433\) 35539.8 0.189557 0.0947784 0.995498i \(-0.469786\pi\)
0.0947784 + 0.995498i \(0.469786\pi\)
\(434\) 20234.0 + 109711.i 0.107424 + 0.582464i
\(435\) 0 0
\(436\) −201861. + 77080.6i −1.06189 + 0.405482i
\(437\) 138681. 0.726195
\(438\) −134534. + 24812.3i −0.701269 + 0.129336i
\(439\) 238795.i 1.23907i 0.784969 + 0.619535i \(0.212679\pi\)
−0.784969 + 0.619535i \(0.787321\pi\)
\(440\) 0 0
\(441\) −28395.8 −0.146008
\(442\) 13827.7 + 74974.8i 0.0707791 + 0.383770i
\(443\) 133181.i 0.678632i 0.940672 + 0.339316i \(0.110196\pi\)
−0.940672 + 0.339316i \(0.889804\pi\)
\(444\) 36033.5 + 94365.4i 0.182785 + 0.478682i
\(445\) 0 0
\(446\) −364722. + 67266.0i −1.83355 + 0.338163i
\(447\) 31794.0i 0.159122i
\(448\) −133697. 69011.8i −0.666141 0.343848i
\(449\) 190392. 0.944398 0.472199 0.881492i \(-0.343460\pi\)
0.472199 + 0.881492i \(0.343460\pi\)
\(450\) 0 0
\(451\) 420354.i 2.06662i
\(452\) 366156. 139817.i 1.79221 0.684356i
\(453\) −157350. −0.766781
\(454\) −140298. + 25875.3i −0.680675 + 0.125538i
\(455\) 0 0
\(456\) 42004.4 + 68951.9i 0.202006 + 0.331602i
\(457\) −4305.85 −0.0206171 −0.0103085 0.999947i \(-0.503281\pi\)
−0.0103085 + 0.999947i \(0.503281\pi\)
\(458\) 75277.0 + 408158.i 0.358865 + 1.94580i
\(459\) 42999.8i 0.204099i
\(460\) 0 0
\(461\) −346295. −1.62946 −0.814730 0.579840i \(-0.803115\pi\)
−0.814730 + 0.579840i \(0.803115\pi\)
\(462\) 117870. 21738.8i 0.552228 0.101848i
\(463\) 148212.i 0.691388i −0.938347 0.345694i \(-0.887643\pi\)
0.938347 0.345694i \(-0.112357\pi\)
\(464\) −50867.6 + 45478.9i −0.236268 + 0.211239i
\(465\) 0 0
\(466\) −12777.8 69282.4i −0.0588417 0.319044i
\(467\) 171205.i 0.785023i 0.919747 + 0.392512i \(0.128394\pi\)
−0.919747 + 0.392512i \(0.871606\pi\)
\(468\) −25097.2 + 9583.40i −0.114587 + 0.0437550i
\(469\) −171044. −0.777611
\(470\) 0 0
\(471\) 59182.9i 0.266781i
\(472\) −158601. + 96616.8i −0.711903 + 0.433679i
\(473\) 413724. 1.84922
\(474\) −32215.3 174674.i −0.143386 0.777448i
\(475\) 0 0
\(476\) 64258.8 + 168283.i 0.283608 + 0.742720i
\(477\) 37704.9 0.165714
\(478\) 224982. 41493.6i 0.984672 0.181604i
\(479\) 55603.3i 0.242342i 0.992632 + 0.121171i \(0.0386650\pi\)
−0.992632 + 0.121171i \(0.961335\pi\)
\(480\) 0 0
\(481\) 75555.4 0.326569
\(482\) −23786.9 128975.i −0.102387 0.555150i
\(483\) 109027.i 0.467346i
\(484\) 149541. 57102.3i 0.638365 0.243760i
\(485\) 0 0
\(486\) −14900.7 + 2748.15i −0.0630861 + 0.0116350i
\(487\) 191414.i 0.807077i 0.914963 + 0.403538i \(0.132220\pi\)
−0.914963 + 0.403538i \(0.867780\pi\)
\(488\) 159387. + 261641.i 0.669289 + 1.09867i
\(489\) −55088.3 −0.230378
\(490\) 0 0
\(491\) 234139.i 0.971206i 0.874179 + 0.485603i \(0.161400\pi\)
−0.874179 + 0.485603i \(0.838600\pi\)
\(492\) −79411.7 207966.i −0.328061 0.859134i
\(493\) 81692.0 0.336113
\(494\) 59390.2 10953.4i 0.243367 0.0448844i
\(495\) 0 0
\(496\) −129553. 144903.i −0.526604 0.589000i
\(497\) 248592. 1.00641
\(498\) 8194.13 + 44429.2i 0.0330403 + 0.179147i
\(499\) 397603.i 1.59679i 0.602133 + 0.798396i \(0.294318\pi\)
−0.602133 + 0.798396i \(0.705682\pi\)
\(500\) 0 0
\(501\) 79675.0 0.317429
\(502\) 113303. 20896.5i 0.449607 0.0829215i
\(503\) 34902.1i 0.137948i 0.997618 + 0.0689741i \(0.0219726\pi\)
−0.997618 + 0.0689741i \(0.978027\pi\)
\(504\) −54208.0 + 33022.6i −0.213404 + 0.130002i
\(505\) 0 0
\(506\) 65057.3 + 352746.i 0.254094 + 1.37772i
\(507\) 128313.i 0.499176i
\(508\) 39538.7 + 103545.i 0.153213 + 0.401237i
\(509\) 14871.2 0.0573997 0.0286999 0.999588i \(-0.490863\pi\)
0.0286999 + 0.999588i \(0.490863\pi\)
\(510\) 0 0
\(511\) 241774.i 0.925907i
\(512\) 261490. 18501.7i 0.997506 0.0705785i
\(513\) 34061.6 0.129429
\(514\) 70710.7 + 383399.i 0.267645 + 1.45119i
\(515\) 0 0
\(516\) −204686. + 78159.3i −0.768755 + 0.293550i
\(517\) −372764. −1.39461
\(518\) 175557. 32378.2i 0.654273 0.120668i
\(519\) 195960.i 0.727500i
\(520\) 0 0
\(521\) −396677. −1.46137 −0.730687 0.682713i \(-0.760800\pi\)
−0.730687 + 0.682713i \(0.760800\pi\)
\(522\) 5221.00 + 28308.7i 0.0191607 + 0.103891i
\(523\) 492462.i 1.80040i 0.435474 + 0.900201i \(0.356581\pi\)
−0.435474 + 0.900201i \(0.643419\pi\)
\(524\) 10805.3 + 28297.2i 0.0393527 + 0.103058i
\(525\) 0 0
\(526\) 326301. 60179.9i 1.17936 0.217511i
\(527\) 232711.i 0.837907i
\(528\) −155680. + 139188.i −0.558425 + 0.499268i
\(529\) −46440.6 −0.165954
\(530\) 0 0
\(531\) 78347.2i 0.277866i
\(532\) 133303. 50901.7i 0.470994 0.179849i
\(533\) −166512. −0.586125
\(534\) −135592. + 25007.3i −0.475500 + 0.0876969i
\(535\) 0 0
\(536\) 254506. 155041.i 0.885867 0.539655i
\(537\) −135706. −0.470599
\(538\) −55818.5 302653.i −0.192847 1.04563i
\(539\) 165105.i 0.568305i
\(540\) 0 0
\(541\) −350781. −1.19851 −0.599255 0.800559i \(-0.704536\pi\)
−0.599255 + 0.800559i \(0.704536\pi\)
\(542\) 291058. 53680.1i 0.990788 0.182732i
\(543\) 228651.i 0.775487i
\(544\) −248152. 192150.i −0.838532 0.649297i
\(545\) 0 0
\(546\) 8611.24 + 46690.9i 0.0288855 + 0.156620i
\(547\) 426263.i 1.42463i −0.701858 0.712317i \(-0.747646\pi\)
0.701858 0.712317i \(-0.252354\pi\)
\(548\) 538078. 205465.i 1.79178 0.684191i
\(549\) 129248. 0.428825
\(550\) 0 0
\(551\) 64711.1i 0.213145i
\(552\) −98825.9 162227.i −0.324334 0.532408i
\(553\) −313910. −1.02649
\(554\) 29256.9 + 158634.i 0.0953255 + 0.516863i
\(555\) 0 0
\(556\) −10842.0 28393.3i −0.0350719 0.0918471i
\(557\) 46325.5 0.149317 0.0746585 0.997209i \(-0.476213\pi\)
0.0746585 + 0.997209i \(0.476213\pi\)
\(558\) −80641.2 + 14872.7i −0.258993 + 0.0477664i
\(559\) 163885.i 0.524465i
\(560\) 0 0
\(561\) 250018. 0.794411
\(562\) 28873.6 + 156555.i 0.0914172 + 0.495672i
\(563\) 155857.i 0.491711i 0.969306 + 0.245855i \(0.0790689\pi\)
−0.969306 + 0.245855i \(0.920931\pi\)
\(564\) 184421. 70421.2i 0.579765 0.221384i
\(565\) 0 0
\(566\) −115144. + 21236.0i −0.359424 + 0.0662889i
\(567\) 26778.3i 0.0832945i
\(568\) −369894. + 225333.i −1.14652 + 0.698440i
\(569\) 115079. 0.355443 0.177722 0.984081i \(-0.443127\pi\)
0.177722 + 0.984081i \(0.443127\pi\)
\(570\) 0 0
\(571\) 297667.i 0.912973i 0.889730 + 0.456487i \(0.150892\pi\)
−0.889730 + 0.456487i \(0.849108\pi\)
\(572\) 55721.7 + 145926.i 0.170307 + 0.446004i
\(573\) −177209. −0.539729
\(574\) −386899. + 71356.1i −1.17428 + 0.216575i
\(575\) 0 0
\(576\) 50726.2 98272.3i 0.152893 0.296201i
\(577\) −56864.8 −0.170802 −0.0854008 0.996347i \(-0.527217\pi\)
−0.0854008 + 0.996347i \(0.527217\pi\)
\(578\) 7557.32 + 40976.4i 0.0226210 + 0.122653i
\(579\) 143279.i 0.427391i
\(580\) 0 0
\(581\) 79844.5 0.236534
\(582\) 320990. 59200.5i 0.947644 0.174775i
\(583\) 219231.i 0.645008i
\(584\) −219153. 359748.i −0.642571 1.05481i
\(585\) 0 0
\(586\) −10569.8 57310.2i −0.0307801 0.166892i
\(587\) 265441.i 0.770358i −0.922842 0.385179i \(-0.874140\pi\)
0.922842 0.385179i \(-0.125860\pi\)
\(588\) −31191.0 81683.8i −0.0902141 0.236255i
\(589\) 184339. 0.531357
\(590\) 0 0
\(591\) 234671.i 0.671870i
\(592\) −231872. + 207309.i −0.661616 + 0.591527i
\(593\) 16961.6 0.0482343 0.0241172 0.999709i \(-0.492323\pi\)
0.0241172 + 0.999709i \(0.492323\pi\)
\(594\) 15978.8 + 86638.6i 0.0452869 + 0.245549i
\(595\) 0 0
\(596\) −91459.2 + 34923.8i −0.257475 + 0.0983170i
\(597\) −293968. −0.824804
\(598\) −139731. + 25770.6i −0.390741 + 0.0720648i
\(599\) 236573.i 0.659342i −0.944096 0.329671i \(-0.893062\pi\)
0.944096 0.329671i \(-0.106938\pi\)
\(600\) 0 0
\(601\) 60822.4 0.168389 0.0841947 0.996449i \(-0.473168\pi\)
0.0841947 + 0.996449i \(0.473168\pi\)
\(602\) 70230.7 + 380797.i 0.193791 + 1.05075i
\(603\) 125724.i 0.345766i
\(604\) −172839. 452636.i −0.473772 1.24073i
\(605\) 0 0
\(606\) 269575. 49718.0i 0.734065 0.135384i
\(607\) 507342.i 1.37697i −0.725252 0.688484i \(-0.758277\pi\)
0.725252 0.688484i \(-0.241723\pi\)
\(608\) −152209. + 196570.i −0.411750 + 0.531753i
\(609\) 50874.0 0.137171
\(610\) 0 0
\(611\) 147660.i 0.395531i
\(612\) −123694. + 47232.5i −0.330252 + 0.126107i
\(613\) −73376.7 −0.195271 −0.0976354 0.995222i \(-0.531128\pi\)
−0.0976354 + 0.995222i \(0.531128\pi\)
\(614\) 406925. 75049.6i 1.07939 0.199073i
\(615\) 0 0
\(616\) 192007. + 315187.i 0.506005 + 0.830629i
\(617\) −288711. −0.758391 −0.379195 0.925317i \(-0.623799\pi\)
−0.379195 + 0.925317i \(0.623799\pi\)
\(618\) −8247.34 44717.8i −0.0215942 0.117086i
\(619\) 241450.i 0.630153i −0.949066 0.315077i \(-0.897970\pi\)
0.949066 0.315077i \(-0.102030\pi\)
\(620\) 0 0
\(621\) −80138.6 −0.207806
\(622\) 553469. 102077.i 1.43058 0.263843i
\(623\) 243674.i 0.627817i
\(624\) −55135.5 61668.4i −0.141600 0.158377i
\(625\) 0 0
\(626\) 72594.6 + 393614.i 0.185249 + 1.00444i
\(627\) 198048.i 0.503774i
\(628\) 170247. 65008.7i 0.431677 0.164836i
\(629\) 372381. 0.941209
\(630\) 0 0
\(631\) 28166.1i 0.0707404i −0.999374 0.0353702i \(-0.988739\pi\)
0.999374 0.0353702i \(-0.0112610\pi\)
\(632\) 467084. 284539.i 1.16939 0.712374i
\(633\) −394727. −0.985122
\(634\) −11046.7 59896.1i −0.0274823 0.149011i
\(635\) 0 0
\(636\) 41416.4 + 108462.i 0.102390 + 0.268142i
\(637\) −65401.7 −0.161180
\(638\) 164598. 30357.0i 0.404374 0.0745791i
\(639\) 182725.i 0.447502i
\(640\) 0 0
\(641\) −265522. −0.646226 −0.323113 0.946360i \(-0.604729\pi\)
−0.323113 + 0.946360i \(0.604729\pi\)
\(642\) 46803.0 + 253769.i 0.113554 + 0.615700i
\(643\) 38089.8i 0.0921271i −0.998939 0.0460635i \(-0.985332\pi\)
0.998939 0.0460635i \(-0.0146677\pi\)
\(644\) −313628. + 119759.i −0.756211 + 0.288760i
\(645\) 0 0
\(646\) 292710. 53984.7i 0.701410 0.129362i
\(647\) 290269.i 0.693414i 0.937974 + 0.346707i \(0.112700\pi\)
−0.937974 + 0.346707i \(0.887300\pi\)
\(648\) −24272.8 39844.9i −0.0578056 0.0948904i
\(649\) 455542. 1.08153
\(650\) 0 0
\(651\) 144922.i 0.341957i
\(652\) −60511.0 158468.i −0.142344 0.372774i
\(653\) 145213. 0.340549 0.170275 0.985397i \(-0.445534\pi\)
0.170275 + 0.985397i \(0.445534\pi\)
\(654\) −276036. + 50909.7i −0.645373 + 0.119027i
\(655\) 0 0
\(656\) 511008. 456874.i 1.18746 1.06167i
\(657\) −177712. −0.411706
\(658\) −63277.6 343096.i −0.146150 0.792436i
\(659\) 27644.5i 0.0636559i −0.999493 0.0318279i \(-0.989867\pi\)
0.999493 0.0318279i \(-0.0101329\pi\)
\(660\) 0 0
\(661\) −368306. −0.842958 −0.421479 0.906838i \(-0.638489\pi\)
−0.421479 + 0.906838i \(0.638489\pi\)
\(662\) −685452. + 126419.i −1.56409 + 0.288466i
\(663\) 99037.8i 0.225307i
\(664\) −118805. + 72374.1i −0.269463 + 0.164152i
\(665\) 0 0
\(666\) 23799.1 + 129041.i 0.0536553 + 0.290924i
\(667\) 152249.i 0.342219i
\(668\) 87518.0 + 229194.i 0.196130 + 0.513631i
\(669\) −481778. −1.07645
\(670\) 0 0
\(671\) 751501.i 1.66911i
\(672\) −154537. 119662.i −0.342212 0.264984i
\(673\) −560984. −1.23857 −0.619285 0.785166i \(-0.712577\pi\)
−0.619285 + 0.785166i \(0.712577\pi\)
\(674\) 146799. + 795957.i 0.323150 + 1.75215i
\(675\) 0 0
\(676\) 369106. 140943.i 0.807715 0.308426i
\(677\) −887674. −1.93676 −0.968381 0.249475i \(-0.919742\pi\)
−0.968381 + 0.249475i \(0.919742\pi\)
\(678\) 500703. 92345.2i 1.08923 0.200888i
\(679\) 576856.i 1.25120i
\(680\) 0 0
\(681\) −185326. −0.399616
\(682\) 86476.1 + 468881.i 0.185921 + 1.00808i
\(683\) 673933.i 1.44469i −0.691532 0.722346i \(-0.743064\pi\)
0.691532 0.722346i \(-0.256936\pi\)
\(684\) 37414.6 + 97982.2i 0.0799703 + 0.209428i
\(685\) 0 0
\(686\) −498896. + 92011.8i −1.06014 + 0.195522i
\(687\) 539155.i 1.14235i
\(688\) −449669. 502949.i −0.949983 1.06254i
\(689\) 86842.5 0.182934
\(690\) 0 0
\(691\) 608132.i 1.27363i −0.771019 0.636813i \(-0.780253\pi\)
0.771019 0.636813i \(-0.219747\pi\)
\(692\) 563702. 215250.i 1.17717 0.449501i
\(693\) 155700. 0.324206
\(694\) −419233. + 77319.5i −0.870435 + 0.160535i
\(695\) 0 0
\(696\) −75698.2 + 46114.1i −0.156267 + 0.0951953i
\(697\) −820665. −1.68928
\(698\) −139551. 756655.i −0.286432 1.55306i
\(699\) 91518.4i 0.187307i
\(700\) 0 0
\(701\) 429210. 0.873442 0.436721 0.899597i \(-0.356140\pi\)
0.436721 + 0.899597i \(0.356140\pi\)
\(702\) −34319.5 + 6329.58i −0.0696413 + 0.0128440i
\(703\) 294976.i 0.596865i
\(704\) −571395. 294942.i −1.15290 0.595103i
\(705\) 0 0
\(706\) 55268.4 + 299670.i 0.110884 + 0.601220i
\(707\) 484458.i 0.969208i
\(708\) −225375. + 86059.5i −0.449613 + 0.171685i
\(709\) 196746. 0.391392 0.195696 0.980665i \(-0.437303\pi\)
0.195696 + 0.980665i \(0.437303\pi\)
\(710\) 0 0
\(711\) 230735.i 0.456430i
\(712\) −220875. 362576.i −0.435699 0.715219i
\(713\) −433704. −0.853128
\(714\) 42441.2 + 230120.i 0.0832513 + 0.451396i
\(715\) 0 0
\(716\) −149065. 390374.i −0.290769 0.761474i
\(717\) 297189. 0.578089
\(718\) 667931. 123187.i 1.29564 0.238955i
\(719\) 176676.i 0.341758i −0.985292 0.170879i \(-0.945339\pi\)
0.985292 0.170879i \(-0.0546607\pi\)
\(720\) 0 0
\(721\) −80363.1 −0.154592
\(722\) 51783.2 + 280773.i 0.0993377 + 0.538617i
\(723\) 170369.i 0.325921i
\(724\) 657742. 251159.i 1.25481 0.479151i
\(725\) 0 0
\(726\) 204491. 37714.5i 0.387973 0.0715542i
\(727\) 773494.i 1.46348i 0.681582 + 0.731742i \(0.261292\pi\)
−0.681582 + 0.731742i \(0.738708\pi\)
\(728\) −124853. + 76058.2i −0.235578 + 0.143510i
\(729\) −19683.0 −0.0370370
\(730\) 0 0
\(731\) 807722.i 1.51157i
\(732\) 141971. + 371797.i 0.264958 + 0.693880i
\(733\) 405112. 0.753992 0.376996 0.926215i \(-0.376957\pi\)
0.376996 + 0.926215i \(0.376957\pi\)
\(734\) −31391.3 + 5789.53i −0.0582663 + 0.0107461i
\(735\) 0 0
\(736\) 358110. 462480.i 0.661091 0.853763i
\(737\) −731008. −1.34582
\(738\) −52449.3 284385.i −0.0963002 0.522148i
\(739\) 12430.2i 0.0227609i −0.999935 0.0113805i \(-0.996377\pi\)
0.999935 0.0113805i \(-0.00362259\pi\)
\(740\) 0 0
\(741\) 78451.3 0.142878
\(742\) 201783. 37215.1i 0.366503 0.0675945i
\(743\) 642523.i 1.16389i −0.813229 0.581944i \(-0.802292\pi\)
0.813229 0.581944i \(-0.197708\pi\)
\(744\) −131362. 215637.i −0.237315 0.389563i
\(745\) 0 0
\(746\) −188102. 1.01991e6i −0.338000 1.83266i
\(747\) 58688.6i 0.105175i
\(748\) 274629. + 719206.i 0.490844 + 1.28543i
\(749\) 456054. 0.812928
\(750\) 0 0
\(751\) 1.01784e6i 1.80468i −0.431022 0.902342i \(-0.641847\pi\)
0.431022 0.902342i \(-0.358153\pi\)
\(752\) 405150. + 453155.i 0.716440 + 0.801329i
\(753\) 149667. 0.263959
\(754\) 12025.1 + 65201.0i 0.0211517 + 0.114686i
\(755\) 0 0
\(756\) −77030.8 + 29414.2i −0.134779 + 0.0514652i
\(757\) 386917. 0.675191 0.337595 0.941291i \(-0.390386\pi\)
0.337595 + 0.941291i \(0.390386\pi\)
\(758\) −45996.5 + 8483.19i −0.0800547 + 0.0147646i
\(759\) 465958.i 0.808842i
\(760\) 0 0
\(761\) −424041. −0.732215 −0.366108 0.930572i \(-0.619310\pi\)
−0.366108 + 0.930572i \(0.619310\pi\)
\(762\) 26114.2 + 141594.i 0.0449746 + 0.243856i
\(763\) 496070.i 0.852106i
\(764\) −194653. 509762.i −0.333483 0.873334i
\(765\) 0 0
\(766\) 137409. 25342.4i 0.234183 0.0431907i
\(767\) 180451.i 0.306738i
\(768\) 338411. + 37973.7i 0.573749 + 0.0643814i
\(769\) −267929. −0.453072 −0.226536 0.974003i \(-0.572740\pi\)
−0.226536 + 0.974003i \(0.572740\pi\)
\(770\) 0 0
\(771\) 506450.i 0.851977i
\(772\) 412159. 157383.i 0.691560 0.264073i
\(773\) 576873. 0.965431 0.482715 0.875777i \(-0.339651\pi\)
0.482715 + 0.875777i \(0.339651\pi\)
\(774\) −279900. + 51622.1i −0.467219 + 0.0861696i
\(775\) 0 0
\(776\) 522884. + 858336.i 0.868324 + 1.42539i
\(777\) 231902. 0.384116
\(778\) 79962.2 + 433561.i 0.132107 + 0.716294i
\(779\) 650078.i 1.07125i
\(780\) 0 0
\(781\) 1.06243e6 1.74181
\(782\) −688673. + 127013.i −1.12616 + 0.207699i
\(783\) 37394.3i 0.0609932i