Properties

Label 25.3.c.a.18.1
Level 25
Weight 3
Character 25.18
Analytic conductor 0.681
Analytic rank 0
Dimension 4
CM No
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 25.c (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.681200660901\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 18.1
Root \(-1.22474 + 1.22474i\)
Character \(\chi\) = 25.18
Dual form 25.3.c.a.7.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(-1.22474 + 1.22474i) q^{2}\) \(+(1.22474 + 1.22474i) q^{3}\) \(+1.00000i q^{4}\) \(-3.00000 q^{6}\) \(+(4.89898 - 4.89898i) q^{7}\) \(+(-6.12372 - 6.12372i) q^{8}\) \(-6.00000i q^{9}\) \(+O(q^{10})\) \(q\)\(+(-1.22474 + 1.22474i) q^{2}\) \(+(1.22474 + 1.22474i) q^{3}\) \(+1.00000i q^{4}\) \(-3.00000 q^{6}\) \(+(4.89898 - 4.89898i) q^{7}\) \(+(-6.12372 - 6.12372i) q^{8}\) \(-6.00000i q^{9}\) \(-3.00000 q^{11}\) \(+(-1.22474 + 1.22474i) q^{12}\) \(+(7.34847 + 7.34847i) q^{13}\) \(+12.0000i q^{14}\) \(+11.0000 q^{16}\) \(+(-13.4722 + 13.4722i) q^{17}\) \(+(7.34847 + 7.34847i) q^{18}\) \(-5.00000i q^{19}\) \(+12.0000 q^{21}\) \(+(3.67423 - 3.67423i) q^{22}\) \(+(-17.1464 - 17.1464i) q^{23}\) \(-15.0000i q^{24}\) \(-18.0000 q^{26}\) \(+(18.3712 - 18.3712i) q^{27}\) \(+(4.89898 + 4.89898i) q^{28}\) \(+30.0000i q^{29}\) \(-38.0000 q^{31}\) \(+(11.0227 - 11.0227i) q^{32}\) \(+(-3.67423 - 3.67423i) q^{33}\) \(-33.0000i q^{34}\) \(+6.00000 q^{36}\) \(+(-19.5959 + 19.5959i) q^{37}\) \(+(6.12372 + 6.12372i) q^{38}\) \(+18.0000i q^{39}\) \(+57.0000 q^{41}\) \(+(-14.6969 + 14.6969i) q^{42}\) \(+(-4.89898 - 4.89898i) q^{43}\) \(-3.00000i q^{44}\) \(+42.0000 q^{46}\) \(+(-7.34847 + 7.34847i) q^{47}\) \(+(13.4722 + 13.4722i) q^{48}\) \(+1.00000i q^{49}\) \(-33.0000 q^{51}\) \(+(-7.34847 + 7.34847i) q^{52}\) \(+(31.8434 + 31.8434i) q^{53}\) \(+45.0000i q^{54}\) \(-60.0000 q^{56}\) \(+(6.12372 - 6.12372i) q^{57}\) \(+(-36.7423 - 36.7423i) q^{58}\) \(-90.0000i q^{59}\) \(-28.0000 q^{61}\) \(+(46.5403 - 46.5403i) q^{62}\) \(+(-29.3939 - 29.3939i) q^{63}\) \(+71.0000i q^{64}\) \(+9.00000 q^{66}\) \(+(47.7650 - 47.7650i) q^{67}\) \(+(-13.4722 - 13.4722i) q^{68}\) \(-42.0000i q^{69}\) \(+42.0000 q^{71}\) \(+(-36.7423 + 36.7423i) q^{72}\) \(+(13.4722 + 13.4722i) q^{73}\) \(-48.0000i q^{74}\) \(+5.00000 q^{76}\) \(+(-14.6969 + 14.6969i) q^{77}\) \(+(-22.0454 - 22.0454i) q^{78}\) \(+80.0000i q^{79}\) \(-9.00000 q^{81}\) \(+(-69.8105 + 69.8105i) q^{82}\) \(+(111.452 + 111.452i) q^{83}\) \(+12.0000i q^{84}\) \(+12.0000 q^{86}\) \(+(-36.7423 + 36.7423i) q^{87}\) \(+(18.3712 + 18.3712i) q^{88}\) \(+15.0000i q^{89}\) \(+72.0000 q^{91}\) \(+(17.1464 - 17.1464i) q^{92}\) \(+(-46.5403 - 46.5403i) q^{93}\) \(-18.0000i q^{94}\) \(+27.0000 q^{96}\) \(+(53.8888 - 53.8888i) q^{97}\) \(+(-1.22474 - 1.22474i) q^{98}\) \(+18.0000i q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 44q^{16} \) \(\mathstrut +\mathstrut 48q^{21} \) \(\mathstrut -\mathstrut 72q^{26} \) \(\mathstrut -\mathstrut 152q^{31} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut +\mathstrut 228q^{41} \) \(\mathstrut +\mathstrut 168q^{46} \) \(\mathstrut -\mathstrut 132q^{51} \) \(\mathstrut -\mathstrut 240q^{56} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut +\mathstrut 36q^{66} \) \(\mathstrut +\mathstrut 168q^{71} \) \(\mathstrut +\mathstrut 20q^{76} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 288q^{91} \) \(\mathstrut +\mathstrut 108q^{96} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 + 1.22474i −0.612372 + 0.612372i −0.943564 0.331191i \(-0.892549\pi\)
0.331191 + 0.943564i \(0.392549\pi\)
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i 0.881127 0.472879i \(-0.156785\pi\)
−0.472879 + 0.881127i \(0.656785\pi\)
\(4\) 1.00000i 0.250000i
\(5\) 0 0
\(6\) −3.00000 −0.500000
\(7\) 4.89898 4.89898i 0.699854 0.699854i −0.264525 0.964379i \(-0.585215\pi\)
0.964379 + 0.264525i \(0.0852151\pi\)
\(8\) −6.12372 6.12372i −0.765466 0.765466i
\(9\) 6.00000i 0.666667i
\(10\) 0 0
\(11\) −3.00000 −0.272727 −0.136364 0.990659i \(-0.543542\pi\)
−0.136364 + 0.990659i \(0.543542\pi\)
\(12\) −1.22474 + 1.22474i −0.102062 + 0.102062i
\(13\) 7.34847 + 7.34847i 0.565267 + 0.565267i 0.930799 0.365532i \(-0.119113\pi\)
−0.365532 + 0.930799i \(0.619113\pi\)
\(14\) 12.0000i 0.857143i
\(15\) 0 0
\(16\) 11.0000 0.687500
\(17\) −13.4722 + 13.4722i −0.792482 + 0.792482i −0.981897 0.189415i \(-0.939341\pi\)
0.189415 + 0.981897i \(0.439341\pi\)
\(18\) 7.34847 + 7.34847i 0.408248 + 0.408248i
\(19\) 5.00000i 0.263158i −0.991306 0.131579i \(-0.957995\pi\)
0.991306 0.131579i \(-0.0420047\pi\)
\(20\) 0 0
\(21\) 12.0000 0.571429
\(22\) 3.67423 3.67423i 0.167011 0.167011i
\(23\) −17.1464 17.1464i −0.745497 0.745497i 0.228133 0.973630i \(-0.426738\pi\)
−0.973630 + 0.228133i \(0.926738\pi\)
\(24\) 15.0000i 0.625000i
\(25\) 0 0
\(26\) −18.0000 −0.692308
\(27\) 18.3712 18.3712i 0.680414 0.680414i
\(28\) 4.89898 + 4.89898i 0.174964 + 0.174964i
\(29\) 30.0000i 1.03448i 0.855840 + 0.517241i \(0.173041\pi\)
−0.855840 + 0.517241i \(0.826959\pi\)
\(30\) 0 0
\(31\) −38.0000 −1.22581 −0.612903 0.790158i \(-0.709998\pi\)
−0.612903 + 0.790158i \(0.709998\pi\)
\(32\) 11.0227 11.0227i 0.344459 0.344459i
\(33\) −3.67423 3.67423i −0.111340 0.111340i
\(34\) 33.0000i 0.970588i
\(35\) 0 0
\(36\) 6.00000 0.166667
\(37\) −19.5959 + 19.5959i −0.529619 + 0.529619i −0.920459 0.390839i \(-0.872185\pi\)
0.390839 + 0.920459i \(0.372185\pi\)
\(38\) 6.12372 + 6.12372i 0.161151 + 0.161151i
\(39\) 18.0000i 0.461538i
\(40\) 0 0
\(41\) 57.0000 1.39024 0.695122 0.718892i \(-0.255350\pi\)
0.695122 + 0.718892i \(0.255350\pi\)
\(42\) −14.6969 + 14.6969i −0.349927 + 0.349927i
\(43\) −4.89898 4.89898i −0.113930 0.113930i 0.647844 0.761773i \(-0.275671\pi\)
−0.761773 + 0.647844i \(0.775671\pi\)
\(44\) 3.00000i 0.0681818i
\(45\) 0 0
\(46\) 42.0000 0.913043
\(47\) −7.34847 + 7.34847i −0.156350 + 0.156350i −0.780947 0.624597i \(-0.785263\pi\)
0.624597 + 0.780947i \(0.285263\pi\)
\(48\) 13.4722 + 13.4722i 0.280671 + 0.280671i
\(49\) 1.00000i 0.0204082i
\(50\) 0 0
\(51\) −33.0000 −0.647059
\(52\) −7.34847 + 7.34847i −0.141317 + 0.141317i
\(53\) 31.8434 + 31.8434i 0.600818 + 0.600818i 0.940530 0.339711i \(-0.110329\pi\)
−0.339711 + 0.940530i \(0.610329\pi\)
\(54\) 45.0000i 0.833333i
\(55\) 0 0
\(56\) −60.0000 −1.07143
\(57\) 6.12372 6.12372i 0.107434 0.107434i
\(58\) −36.7423 36.7423i −0.633489 0.633489i
\(59\) 90.0000i 1.52542i −0.646738 0.762712i \(-0.723867\pi\)
0.646738 0.762712i \(-0.276133\pi\)
\(60\) 0 0
\(61\) −28.0000 −0.459016 −0.229508 0.973307i \(-0.573712\pi\)
−0.229508 + 0.973307i \(0.573712\pi\)
\(62\) 46.5403 46.5403i 0.750650 0.750650i
\(63\) −29.3939 29.3939i −0.466569 0.466569i
\(64\) 71.0000i 1.10938i
\(65\) 0 0
\(66\) 9.00000 0.136364
\(67\) 47.7650 47.7650i 0.712911 0.712911i −0.254232 0.967143i \(-0.581823\pi\)
0.967143 + 0.254232i \(0.0818227\pi\)
\(68\) −13.4722 13.4722i −0.198120 0.198120i
\(69\) 42.0000i 0.608696i
\(70\) 0 0
\(71\) 42.0000 0.591549 0.295775 0.955258i \(-0.404422\pi\)
0.295775 + 0.955258i \(0.404422\pi\)
\(72\) −36.7423 + 36.7423i −0.510310 + 0.510310i
\(73\) 13.4722 + 13.4722i 0.184551 + 0.184551i 0.793335 0.608785i \(-0.208343\pi\)
−0.608785 + 0.793335i \(0.708343\pi\)
\(74\) 48.0000i 0.648649i
\(75\) 0 0
\(76\) 5.00000 0.0657895
\(77\) −14.6969 + 14.6969i −0.190869 + 0.190869i
\(78\) −22.0454 22.0454i −0.282633 0.282633i
\(79\) 80.0000i 1.01266i 0.862340 + 0.506329i \(0.168998\pi\)
−0.862340 + 0.506329i \(0.831002\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) −69.8105 + 69.8105i −0.851347 + 0.851347i
\(83\) 111.452 + 111.452i 1.34279 + 1.34279i 0.893268 + 0.449525i \(0.148407\pi\)
0.449525 + 0.893268i \(0.351593\pi\)
\(84\) 12.0000i 0.142857i
\(85\) 0 0
\(86\) 12.0000 0.139535
\(87\) −36.7423 + 36.7423i −0.422326 + 0.422326i
\(88\) 18.3712 + 18.3712i 0.208763 + 0.208763i
\(89\) 15.0000i 0.168539i 0.996443 + 0.0842697i \(0.0268557\pi\)
−0.996443 + 0.0842697i \(0.973144\pi\)
\(90\) 0 0
\(91\) 72.0000 0.791209
\(92\) 17.1464 17.1464i 0.186374 0.186374i
\(93\) −46.5403 46.5403i −0.500433 0.500433i
\(94\) 18.0000i 0.191489i
\(95\) 0 0
\(96\) 27.0000 0.281250
\(97\) 53.8888 53.8888i 0.555554 0.555554i −0.372484 0.928039i \(-0.621494\pi\)
0.928039 + 0.372484i \(0.121494\pi\)
\(98\) −1.22474 1.22474i −0.0124974 0.0124974i
\(99\) 18.0000i 0.181818i
\(100\) 0 0
\(101\) −48.0000 −0.475248 −0.237624 0.971357i \(-0.576369\pi\)
−0.237624 + 0.971357i \(0.576369\pi\)
\(102\) 40.4166 40.4166i 0.396241 0.396241i
\(103\) −90.6311 90.6311i −0.879914 0.879914i 0.113611 0.993525i \(-0.463758\pi\)
−0.993525 + 0.113611i \(0.963758\pi\)
\(104\) 90.0000i 0.865385i
\(105\) 0 0
\(106\) −78.0000 −0.735849
\(107\) −25.7196 + 25.7196i −0.240370 + 0.240370i −0.817003 0.576633i \(-0.804366\pi\)
0.576633 + 0.817003i \(0.304366\pi\)
\(108\) 18.3712 + 18.3712i 0.170103 + 0.170103i
\(109\) 40.0000i 0.366972i −0.983022 0.183486i \(-0.941262\pi\)
0.983022 0.183486i \(-0.0587383\pi\)
\(110\) 0 0
\(111\) −48.0000 −0.432432
\(112\) 53.8888 53.8888i 0.481150 0.481150i
\(113\) −84.5074 84.5074i −0.747853 0.747853i 0.226223 0.974076i \(-0.427362\pi\)
−0.974076 + 0.226223i \(0.927362\pi\)
\(114\) 15.0000i 0.131579i
\(115\) 0 0
\(116\) −30.0000 −0.258621
\(117\) 44.0908 44.0908i 0.376845 0.376845i
\(118\) 110.227 + 110.227i 0.934127 + 0.934127i
\(119\) 132.000i 1.10924i
\(120\) 0 0
\(121\) −112.000 −0.925620
\(122\) 34.2929 34.2929i 0.281089 0.281089i
\(123\) 69.8105 + 69.8105i 0.567565 + 0.567565i
\(124\) 38.0000i 0.306452i
\(125\) 0 0
\(126\) 72.0000 0.571429
\(127\) −154.318 + 154.318i −1.21510 + 1.21510i −0.245774 + 0.969327i \(0.579042\pi\)
−0.969327 + 0.245774i \(0.920958\pi\)
\(128\) −42.8661 42.8661i −0.334891 0.334891i
\(129\) 12.0000i 0.0930233i
\(130\) 0 0
\(131\) 162.000 1.23664 0.618321 0.785926i \(-0.287813\pi\)
0.618321 + 0.785926i \(0.287813\pi\)
\(132\) 3.67423 3.67423i 0.0278351 0.0278351i
\(133\) −24.4949 24.4949i −0.184172 0.184172i
\(134\) 117.000i 0.873134i
\(135\) 0 0
\(136\) 165.000 1.21324
\(137\) −50.2145 + 50.2145i −0.366529 + 0.366529i −0.866210 0.499680i \(-0.833451\pi\)
0.499680 + 0.866210i \(0.333451\pi\)
\(138\) 51.4393 + 51.4393i 0.372748 + 0.372748i
\(139\) 185.000i 1.33094i −0.746427 0.665468i \(-0.768232\pi\)
0.746427 0.665468i \(-0.231768\pi\)
\(140\) 0 0
\(141\) −18.0000 −0.127660
\(142\) −51.4393 + 51.4393i −0.362248 + 0.362248i
\(143\) −22.0454 22.0454i −0.154164 0.154164i
\(144\) 66.0000i 0.458333i
\(145\) 0 0
\(146\) −33.0000 −0.226027
\(147\) −1.22474 + 1.22474i −0.00833160 + 0.00833160i
\(148\) −19.5959 19.5959i −0.132405 0.132405i
\(149\) 150.000i 1.00671i 0.864079 + 0.503356i \(0.167901\pi\)
−0.864079 + 0.503356i \(0.832099\pi\)
\(150\) 0 0
\(151\) 52.0000 0.344371 0.172185 0.985065i \(-0.444917\pi\)
0.172185 + 0.985065i \(0.444917\pi\)
\(152\) −30.6186 + 30.6186i −0.201438 + 0.201438i
\(153\) 80.8332 + 80.8332i 0.528321 + 0.528321i
\(154\) 36.0000i 0.233766i
\(155\) 0 0
\(156\) −18.0000 −0.115385
\(157\) 188.611 188.611i 1.20134 1.20134i 0.227584 0.973759i \(-0.426918\pi\)
0.973759 0.227584i \(-0.0730825\pi\)
\(158\) −97.9796 97.9796i −0.620124 0.620124i
\(159\) 78.0000i 0.490566i
\(160\) 0 0
\(161\) −168.000 −1.04348
\(162\) 11.0227 11.0227i 0.0680414 0.0680414i
\(163\) 99.2043 + 99.2043i 0.608616 + 0.608616i 0.942584 0.333969i \(-0.108388\pi\)
−0.333969 + 0.942584i \(0.608388\pi\)
\(164\) 57.0000i 0.347561i
\(165\) 0 0
\(166\) −273.000 −1.64458
\(167\) 17.1464 17.1464i 0.102673 0.102673i −0.653904 0.756577i \(-0.726870\pi\)
0.756577 + 0.653904i \(0.226870\pi\)
\(168\) −73.4847 73.4847i −0.437409 0.437409i
\(169\) 61.0000i 0.360947i
\(170\) 0 0
\(171\) −30.0000 −0.175439
\(172\) 4.89898 4.89898i 0.0284824 0.0284824i
\(173\) −78.3837 78.3837i −0.453085 0.453085i 0.443292 0.896377i \(-0.353810\pi\)
−0.896377 + 0.443292i \(0.853810\pi\)
\(174\) 90.0000i 0.517241i
\(175\) 0 0
\(176\) −33.0000 −0.187500
\(177\) 110.227 110.227i 0.622752 0.622752i
\(178\) −18.3712 18.3712i −0.103209 0.103209i
\(179\) 195.000i 1.08939i −0.838636 0.544693i \(-0.816646\pi\)
0.838636 0.544693i \(-0.183354\pi\)
\(180\) 0 0
\(181\) 262.000 1.44751 0.723757 0.690055i \(-0.242414\pi\)
0.723757 + 0.690055i \(0.242414\pi\)
\(182\) −88.1816 + 88.1816i −0.484514 + 0.484514i
\(183\) −34.2929 34.2929i −0.187393 0.187393i
\(184\) 210.000i 1.14130i
\(185\) 0 0
\(186\) 114.000 0.612903
\(187\) 40.4166 40.4166i 0.216131 0.216131i
\(188\) −7.34847 7.34847i −0.0390876 0.0390876i
\(189\) 180.000i 0.952381i
\(190\) 0 0
\(191\) −18.0000 −0.0942408 −0.0471204 0.998889i \(-0.515004\pi\)
−0.0471204 + 0.998889i \(0.515004\pi\)
\(192\) −86.9569 + 86.9569i −0.452900 + 0.452900i
\(193\) 86.9569 + 86.9569i 0.450554 + 0.450554i 0.895538 0.444984i \(-0.146791\pi\)
−0.444984 + 0.895538i \(0.646791\pi\)
\(194\) 132.000i 0.680412i
\(195\) 0 0
\(196\) −1.00000 −0.00510204
\(197\) −129.823 + 129.823i −0.659000 + 0.659000i −0.955143 0.296144i \(-0.904299\pi\)
0.296144 + 0.955143i \(0.404299\pi\)
\(198\) −22.0454 22.0454i −0.111340 0.111340i
\(199\) 200.000i 1.00503i 0.864570 + 0.502513i \(0.167591\pi\)
−0.864570 + 0.502513i \(0.832409\pi\)
\(200\) 0 0
\(201\) 117.000 0.582090
\(202\) 58.7878 58.7878i 0.291028 0.291028i
\(203\) 146.969 + 146.969i 0.723987 + 0.723987i
\(204\) 33.0000i 0.161765i
\(205\) 0 0
\(206\) 222.000 1.07767
\(207\) −102.879 + 102.879i −0.496998 + 0.496998i
\(208\) 80.8332 + 80.8332i 0.388621 + 0.388621i
\(209\) 15.0000i 0.0717703i
\(210\) 0 0
\(211\) −103.000 −0.488152 −0.244076 0.969756i \(-0.578485\pi\)
−0.244076 + 0.969756i \(0.578485\pi\)
\(212\) −31.8434 + 31.8434i −0.150205 + 0.150205i
\(213\) 51.4393 + 51.4393i 0.241499 + 0.241499i
\(214\) 63.0000i 0.294393i
\(215\) 0 0
\(216\) −225.000 −1.04167
\(217\) −186.161 + 186.161i −0.857886 + 0.857886i
\(218\) 48.9898 + 48.9898i 0.224724 + 0.224724i
\(219\) 33.0000i 0.150685i
\(220\) 0 0
\(221\) −198.000 −0.895928
\(222\) 58.7878 58.7878i 0.264810 0.264810i
\(223\) −200.858 200.858i −0.900709 0.900709i 0.0947882 0.995497i \(-0.469783\pi\)
−0.995497 + 0.0947882i \(0.969783\pi\)
\(224\) 108.000i 0.482143i
\(225\) 0 0
\(226\) 207.000 0.915929
\(227\) 274.343 274.343i 1.20856 1.20856i 0.237065 0.971494i \(-0.423815\pi\)
0.971494 0.237065i \(-0.0761854\pi\)
\(228\) 6.12372 + 6.12372i 0.0268584 + 0.0268584i
\(229\) 20.0000i 0.0873362i −0.999046 0.0436681i \(-0.986096\pi\)
0.999046 0.0436681i \(-0.0139044\pi\)
\(230\) 0 0
\(231\) −36.0000 −0.155844
\(232\) 183.712 183.712i 0.791861 0.791861i
\(233\) −102.879 102.879i −0.441539 0.441539i 0.450990 0.892529i \(-0.351071\pi\)
−0.892529 + 0.450990i \(0.851071\pi\)
\(234\) 108.000i 0.461538i
\(235\) 0 0
\(236\) 90.0000 0.381356
\(237\) −97.9796 + 97.9796i −0.413416 + 0.413416i
\(238\) −161.666 161.666i −0.679270 0.679270i
\(239\) 210.000i 0.878661i −0.898325 0.439331i \(-0.855216\pi\)
0.898325 0.439331i \(-0.144784\pi\)
\(240\) 0 0
\(241\) −43.0000 −0.178423 −0.0892116 0.996013i \(-0.528435\pi\)
−0.0892116 + 0.996013i \(0.528435\pi\)
\(242\) 137.171 137.171i 0.566824 0.566824i
\(243\) −176.363 176.363i −0.725775 0.725775i
\(244\) 28.0000i 0.114754i
\(245\) 0 0
\(246\) −171.000 −0.695122
\(247\) 36.7423 36.7423i 0.148754 0.148754i
\(248\) 232.702 + 232.702i 0.938313 + 0.938313i
\(249\) 273.000i 1.09639i
\(250\) 0 0
\(251\) −123.000 −0.490040 −0.245020 0.969518i \(-0.578795\pi\)
−0.245020 + 0.969518i \(0.578795\pi\)
\(252\) 29.3939 29.3939i 0.116642 0.116642i
\(253\) 51.4393 + 51.4393i 0.203317 + 0.203317i
\(254\) 378.000i 1.48819i
\(255\) 0 0
\(256\) −179.000 −0.699219
\(257\) 4.89898 4.89898i 0.0190622 0.0190622i −0.697511 0.716574i \(-0.745709\pi\)
0.716574 + 0.697511i \(0.245709\pi\)
\(258\) 14.6969 + 14.6969i 0.0569649 + 0.0569649i
\(259\) 192.000i 0.741313i
\(260\) 0 0
\(261\) 180.000 0.689655
\(262\) −198.409 + 198.409i −0.757285 + 0.757285i
\(263\) 7.34847 + 7.34847i 0.0279409 + 0.0279409i 0.720939 0.692998i \(-0.243711\pi\)
−0.692998 + 0.720939i \(0.743711\pi\)
\(264\) 45.0000i 0.170455i
\(265\) 0 0
\(266\) 60.0000 0.225564
\(267\) −18.3712 + 18.3712i −0.0688059 + 0.0688059i
\(268\) 47.7650 + 47.7650i 0.178228 + 0.178228i
\(269\) 120.000i 0.446097i 0.974807 + 0.223048i \(0.0716008\pi\)
−0.974807 + 0.223048i \(0.928399\pi\)
\(270\) 0 0
\(271\) −58.0000 −0.214022 −0.107011 0.994258i \(-0.534128\pi\)
−0.107011 + 0.994258i \(0.534128\pi\)
\(272\) −148.194 + 148.194i −0.544831 + 0.544831i
\(273\) 88.1816 + 88.1816i 0.323010 + 0.323010i
\(274\) 123.000i 0.448905i
\(275\) 0 0
\(276\) 42.0000 0.152174
\(277\) −276.792 + 276.792i −0.999250 + 0.999250i −1.00000 0.000749391i \(-0.999761\pi\)
0.000749391 1.00000i \(0.499761\pi\)
\(278\) 226.578 + 226.578i 0.815028 + 0.815028i
\(279\) 228.000i 0.817204i
\(280\) 0 0
\(281\) 462.000 1.64413 0.822064 0.569395i \(-0.192822\pi\)
0.822064 + 0.569395i \(0.192822\pi\)
\(282\) 22.0454 22.0454i 0.0781752 0.0781752i
\(283\) −72.2599 72.2599i −0.255336 0.255336i 0.567818 0.823154i \(-0.307788\pi\)
−0.823154 + 0.567818i \(0.807788\pi\)
\(284\) 42.0000i 0.147887i
\(285\) 0 0
\(286\) 54.0000 0.188811
\(287\) 279.242 279.242i 0.972968 0.972968i
\(288\) −66.1362 66.1362i −0.229640 0.229640i
\(289\) 74.0000i 0.256055i
\(290\) 0 0
\(291\) 132.000 0.453608
\(292\) −13.4722 + 13.4722i −0.0461376 + 0.0461376i
\(293\) −4.89898 4.89898i −0.0167201 0.0167201i 0.698697 0.715417i \(-0.253763\pi\)
−0.715417 + 0.698697i \(0.753763\pi\)
\(294\) 3.00000i 0.0102041i
\(295\) 0 0
\(296\) 240.000 0.810811
\(297\) −55.1135 + 55.1135i −0.185567 + 0.185567i
\(298\) −183.712 183.712i −0.616482 0.616482i
\(299\) 252.000i 0.842809i
\(300\) 0 0
\(301\) −48.0000 −0.159468
\(302\) −63.6867 + 63.6867i −0.210883 + 0.210883i
\(303\) −58.7878 58.7878i −0.194019 0.194019i
\(304\) 55.0000i 0.180921i
\(305\) 0 0
\(306\) −198.000 −0.647059
\(307\) −86.9569 + 86.9569i −0.283247 + 0.283247i −0.834403 0.551155i \(-0.814187\pi\)
0.551155 + 0.834403i \(0.314187\pi\)
\(308\) −14.6969 14.6969i −0.0477173 0.0477173i
\(309\) 222.000i 0.718447i
\(310\) 0 0
\(311\) −528.000 −1.69775 −0.848875 0.528594i \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(312\) 110.227 110.227i 0.353292 0.353292i
\(313\) 191.060 + 191.060i 0.610416 + 0.610416i 0.943054 0.332638i \(-0.107939\pi\)
−0.332638 + 0.943054i \(0.607939\pi\)
\(314\) 462.000i 1.47134i
\(315\) 0 0
\(316\) −80.0000 −0.253165
\(317\) 200.858 200.858i 0.633622 0.633622i −0.315353 0.948975i \(-0.602123\pi\)
0.948975 + 0.315353i \(0.102123\pi\)
\(318\) −95.5301 95.5301i −0.300409 0.300409i
\(319\) 90.0000i 0.282132i
\(320\) 0 0
\(321\) −63.0000 −0.196262
\(322\) 205.757 205.757i 0.638997 0.638997i
\(323\) 67.3610 + 67.3610i 0.208548 + 0.208548i
\(324\) 9.00000i 0.0277778i
\(325\) 0 0
\(326\) −243.000 −0.745399
\(327\) 48.9898 48.9898i 0.149816 0.149816i
\(328\) −349.052 349.052i −1.06418 1.06418i
\(329\) 72.0000i 0.218845i
\(330\) 0 0
\(331\) −313.000 −0.945619 −0.472810 0.881165i \(-0.656760\pi\)
−0.472810 + 0.881165i \(0.656760\pi\)
\(332\) −111.452 + 111.452i −0.335698 + 0.335698i
\(333\) 117.576 + 117.576i 0.353080 + 0.353080i
\(334\) 42.0000i 0.125749i
\(335\) 0 0
\(336\) 132.000 0.392857
\(337\) 194.734 194.734i 0.577847 0.577847i −0.356463 0.934310i \(-0.616017\pi\)
0.934310 + 0.356463i \(0.116017\pi\)
\(338\) 74.7094 + 74.7094i 0.221034 + 0.221034i
\(339\) 207.000i 0.610619i
\(340\) 0 0
\(341\) 114.000 0.334311
\(342\) 36.7423 36.7423i 0.107434 0.107434i
\(343\) 244.949 + 244.949i 0.714137 + 0.714137i
\(344\) 60.0000i 0.174419i
\(345\) 0 0
\(346\) 192.000 0.554913
\(347\) −99.2043 + 99.2043i −0.285891 + 0.285891i −0.835453 0.549562i \(-0.814795\pi\)
0.549562 + 0.835453i \(0.314795\pi\)
\(348\) −36.7423 36.7423i −0.105581 0.105581i
\(349\) 100.000i 0.286533i 0.989684 + 0.143266i \(0.0457606\pi\)
−0.989684 + 0.143266i \(0.954239\pi\)
\(350\) 0 0
\(351\) 270.000 0.769231
\(352\) −33.0681 + 33.0681i −0.0939435 + 0.0939435i
\(353\) −396.817 396.817i −1.12413 1.12413i −0.991114 0.133014i \(-0.957534\pi\)
−0.133014 0.991114i \(-0.542466\pi\)
\(354\) 270.000i 0.762712i
\(355\) 0 0
\(356\) −15.0000 −0.0421348
\(357\) −161.666 + 161.666i −0.452847 + 0.452847i
\(358\) 238.825 + 238.825i 0.667110 + 0.667110i
\(359\) 540.000i 1.50418i −0.659061 0.752089i \(-0.729046\pi\)
0.659061 0.752089i \(-0.270954\pi\)
\(360\) 0 0
\(361\) 336.000 0.930748
\(362\) −320.883 + 320.883i −0.886418 + 0.886418i
\(363\) −137.171 137.171i −0.377883 0.377883i
\(364\) 72.0000i 0.197802i
\(365\) 0 0
\(366\) 84.0000 0.229508
\(367\) −44.0908 + 44.0908i −0.120138 + 0.120138i −0.764620 0.644481i \(-0.777073\pi\)
0.644481 + 0.764620i \(0.277073\pi\)
\(368\) −188.611 188.611i −0.512529 0.512529i
\(369\) 342.000i 0.926829i
\(370\) 0 0
\(371\) 312.000 0.840970
\(372\) 46.5403 46.5403i 0.125108 0.125108i
\(373\) 350.277 + 350.277i 0.939081 + 0.939081i 0.998248 0.0591675i \(-0.0188446\pi\)
−0.0591675 + 0.998248i \(0.518845\pi\)
\(374\) 99.0000i 0.264706i
\(375\) 0 0
\(376\) 90.0000 0.239362
\(377\) −220.454 + 220.454i −0.584759 + 0.584759i
\(378\) 220.454 + 220.454i 0.583212 + 0.583212i
\(379\) 505.000i 1.33245i 0.745749 + 0.666227i \(0.232092\pi\)
−0.745749 + 0.666227i \(0.767908\pi\)
\(380\) 0 0
\(381\) −378.000 −0.992126
\(382\) 22.0454 22.0454i 0.0577105 0.0577105i
\(383\) 142.070 + 142.070i 0.370941 + 0.370941i 0.867820 0.496879i \(-0.165521\pi\)
−0.496879 + 0.867820i \(0.665521\pi\)
\(384\) 105.000i 0.273438i
\(385\) 0 0
\(386\) −213.000 −0.551813
\(387\) −29.3939 + 29.3939i −0.0759532 + 0.0759532i
\(388\) 53.8888 + 53.8888i 0.138889 + 0.138889i
\(389\) 690.000i 1.77378i 0.461982 + 0.886889i \(0.347139\pi\)
−0.461982 + 0.886889i \(0.652861\pi\)
\(390\) 0 0
\(391\) 462.000 1.18159
\(392\) 6.12372 6.12372i 0.0156217 0.0156217i
\(393\) 198.409 + 198.409i 0.504857 + 0.504857i
\(394\) 318.000i 0.807107i
\(395\) 0 0
\(396\) −18.0000 −0.0454545
\(397\) 421.312 421.312i 1.06124 1.06124i 0.0632416 0.997998i \(-0.479856\pi\)
0.997998 0.0632416i \(-0.0201439\pi\)
\(398\) −244.949 244.949i −0.615450 0.615450i
\(399\) 60.0000i 0.150376i
\(400\) 0 0
\(401\) −573.000 −1.42893 −0.714464 0.699672i \(-0.753329\pi\)
−0.714464 + 0.699672i \(0.753329\pi\)
\(402\) −143.295 + 143.295i −0.356456 + 0.356456i
\(403\) −279.242 279.242i −0.692908 0.692908i
\(404\) 48.0000i 0.118812i
\(405\) 0 0
\(406\) −360.000 −0.886700
\(407\) 58.7878 58.7878i 0.144442 0.144442i
\(408\) 202.083 + 202.083i 0.495301 + 0.495301i
\(409\) 365.000i 0.892421i −0.894928 0.446210i \(-0.852773\pi\)
0.894928 0.446210i \(-0.147227\pi\)
\(410\) 0 0
\(411\) −123.000 −0.299270
\(412\) 90.6311 90.6311i 0.219978 0.219978i
\(413\) −440.908 440.908i −1.06757 1.06757i
\(414\) 252.000i 0.608696i
\(415\) 0 0
\(416\) 162.000 0.389423
\(417\) 226.578 226.578i 0.543352 0.543352i
\(418\) −18.3712 18.3712i −0.0439502 0.0439502i
\(419\) 645.000i 1.53938i 0.638418 + 0.769690i \(0.279589\pi\)
−0.638418 + 0.769690i \(0.720411\pi\)
\(420\) 0 0
\(421\) −8.00000 −0.0190024 −0.00950119 0.999955i \(-0.503024\pi\)
−0.00950119 + 0.999955i \(0.503024\pi\)
\(422\) 126.149 126.149i 0.298931 0.298931i
\(423\) 44.0908 + 44.0908i 0.104234 + 0.104234i
\(424\) 390.000i 0.919811i
\(425\) 0 0
\(426\) −126.000 −0.295775
\(427\) −137.171 + 137.171i −0.321245 + 0.321245i
\(428\) −25.7196 25.7196i −0.0600926 0.0600926i
\(429\) 54.0000i 0.125874i
\(430\) 0 0
\(431\) 12.0000 0.0278422 0.0139211 0.999903i \(-0.495569\pi\)
0.0139211 + 0.999903i \(0.495569\pi\)
\(432\) 202.083 202.083i 0.467784 0.467784i
\(433\) −439.683 439.683i −1.01544 1.01544i −0.999879 0.0155561i \(-0.995048\pi\)
−0.0155561 0.999879i \(-0.504952\pi\)
\(434\) 456.000i 1.05069i
\(435\) 0 0
\(436\) 40.0000 0.0917431
\(437\) −85.7321 + 85.7321i −0.196183 + 0.196183i
\(438\) −40.4166 40.4166i −0.0922753 0.0922753i
\(439\) 10.0000i 0.0227790i −0.999935 0.0113895i \(-0.996375\pi\)
0.999935 0.0113895i \(-0.00362548\pi\)
\(440\) 0 0
\(441\) 6.00000 0.0136054
\(442\) 242.499 242.499i 0.548641 0.548641i
\(443\) 86.9569 + 86.9569i 0.196291 + 0.196291i 0.798408 0.602117i \(-0.205676\pi\)
−0.602117 + 0.798408i \(0.705676\pi\)
\(444\) 48.0000i 0.108108i
\(445\) 0 0
\(446\) 492.000 1.10314
\(447\) −183.712 + 183.712i −0.410988 + 0.410988i
\(448\) 347.828 + 347.828i 0.776401 + 0.776401i
\(449\) 75.0000i 0.167038i 0.996506 + 0.0835189i \(0.0266159\pi\)
−0.996506 + 0.0835189i \(0.973384\pi\)
\(450\) 0 0
\(451\) −171.000 −0.379157
\(452\) 84.5074 84.5074i 0.186963 0.186963i
\(453\) 63.6867 + 63.6867i 0.140589 + 0.140589i
\(454\) 672.000i 1.48018i
\(455\) 0 0
\(456\) −75.0000 −0.164474
\(457\) −209.431 + 209.431i −0.458274 + 0.458274i −0.898089 0.439814i \(-0.855044\pi\)
0.439814 + 0.898089i \(0.355044\pi\)
\(458\) 24.4949 + 24.4949i 0.0534823 + 0.0534823i
\(459\) 495.000i 1.07843i
\(460\) 0 0
\(461\) −228.000 −0.494577 −0.247289 0.968942i \(-0.579540\pi\)
−0.247289 + 0.968942i \(0.579540\pi\)
\(462\) 44.0908 44.0908i 0.0954347 0.0954347i
\(463\) 436.009 + 436.009i 0.941704 + 0.941704i 0.998392 0.0566875i \(-0.0180539\pi\)
−0.0566875 + 0.998392i \(0.518054\pi\)
\(464\) 330.000i 0.711207i
\(465\) 0 0
\(466\) 252.000 0.540773
\(467\) −533.989 + 533.989i −1.14344 + 1.14344i −0.155629 + 0.987816i \(0.549741\pi\)
−0.987816 + 0.155629i \(0.950259\pi\)
\(468\) 44.0908 + 44.0908i 0.0942111 + 0.0942111i
\(469\) 468.000i 0.997868i
\(470\) 0 0
\(471\) 462.000 0.980892
\(472\) −551.135 + 551.135i −1.16766 + 1.16766i
\(473\) 14.6969 + 14.6969i 0.0310718 + 0.0310718i
\(474\) 240.000i 0.506329i
\(475\) 0 0
\(476\) −132.000 −0.277311
\(477\) 191.060 191.060i 0.400545 0.400545i
\(478\) 257.196 + 257.196i 0.538068 + 0.538068i
\(479\) 270.000i 0.563674i −0.959462 0.281837i \(-0.909056\pi\)
0.959462 0.281837i \(-0.0909438\pi\)
\(480\) 0 0
\(481\) −288.000 −0.598753
\(482\) 52.6640 52.6640i 0.109261 0.109261i
\(483\) −205.757 205.757i −0.425998 0.425998i
\(484\) 112.000i 0.231405i
\(485\) 0 0
\(486\) 432.000 0.888889
\(487\) −80.8332 + 80.8332i −0.165982 + 0.165982i −0.785211 0.619229i \(-0.787445\pi\)
0.619229 + 0.785211i \(0.287445\pi\)
\(488\) 171.464 + 171.464i 0.351361 + 0.351361i
\(489\) 243.000i 0.496933i
\(490\) 0 0
\(491\) 582.000 1.18534 0.592668 0.805447i \(-0.298075\pi\)
0.592668 + 0.805447i \(0.298075\pi\)
\(492\) −69.8105 + 69.8105i −0.141891 + 0.141891i
\(493\) −404.166 404.166i −0.819809 0.819809i
\(494\) 90.0000i 0.182186i
\(495\) 0 0
\(496\) −418.000 −0.842742
\(497\) 205.757 205.757i 0.413998 0.413998i
\(498\) −334.355 334.355i −0.671396 0.671396i
\(499\) 250.000i 0.501002i −0.968116 0.250501i \(-0.919405\pi\)
0.968116 0.250501i \(-0.0805953\pi\)
\(500\) 0 0
\(501\) 42.0000 0.0838323
\(502\) 150.644 150.644i 0.300087 0.300087i
\(503\) 460.504 + 460.504i 0.915515 + 0.915515i 0.996699 0.0811841i \(-0.0258702\pi\)
−0.0811841 + 0.996699i \(0.525870\pi\)
\(504\) 360.000i 0.714286i
\(505\) 0 0
\(506\) −126.000 −0.249012
\(507\) 74.7094 74.7094i 0.147356 0.147356i
\(508\) −154.318 154.318i −0.303775 0.303775i
\(509\) 390.000i 0.766208i −0.923705 0.383104i \(-0.874855\pi\)
0.923705 0.383104i \(-0.125145\pi\)
\(510\) 0 0
\(511\) 132.000 0.258317
\(512\) 390.694 390.694i 0.763073 0.763073i
\(513\) −91.8559 91.8559i −0.179056 0.179056i
\(514\) 12.0000i 0.0233463i
\(515\) 0 0
\(516\) 12.0000 0.0232558
\(517\) 22.0454 22.0454i 0.0426410 0.0426410i
\(518\) −235.151 235.151i −0.453959 0.453959i
\(519\) 192.000i 0.369942i
\(520\) 0 0
\(521\) −183.000 −0.351248 −0.175624 0.984457i \(-0.556194\pi\)
−0.175624 + 0.984457i \(0.556194\pi\)
\(522\) −220.454 + 220.454i −0.422326 + 0.422326i
\(523\) −476.426 476.426i −0.910948 0.910948i 0.0853989 0.996347i \(-0.472784\pi\)
−0.996347 + 0.0853989i \(0.972784\pi\)
\(524\) 162.000i 0.309160i
\(525\) 0 0
\(526\) −18.0000 −0.0342205
\(527\) 511.943 511.943i 0.971430 0.971430i
\(528\) −40.4166 40.4166i −0.0765466 0.0765466i
\(529\) 59.0000i 0.111531i
\(530\) 0 0
\(531\) −540.000 −1.01695
\(532\) 24.4949 24.4949i 0.0460430 0.0460430i
\(533\) 418.863 + 418.863i 0.785859 + 0.785859i
\(534\) 45.0000i 0.0842697i
\(535\) 0 0
\(536\) −585.000 −1.09142
\(537\) 238.825 238.825i 0.444740 0.444740i
\(538\) −146.969 146.969i −0.273177 0.273177i
\(539\) 3.00000i 0.00556586i
\(540\) 0 0
\(541\) −568.000 −1.04991 −0.524954 0.851131i \(-0.675917\pi\)
−0.524954 + 0.851131i \(0.675917\pi\)
\(542\) 71.0352 71.0352i 0.131061 0.131061i
\(543\) 320.883 + 320.883i 0.590945 + 0.590945i
\(544\) 297.000i 0.545956i
\(545\) 0 0
\(546\) −216.000 −0.395604
\(547\) −160.442 + 160.442i −0.293312 + 0.293312i −0.838387 0.545075i \(-0.816501\pi\)
0.545075 + 0.838387i \(0.316501\pi\)
\(548\) −50.2145 50.2145i −0.0916324 0.0916324i
\(549\) 168.000i 0.306011i
\(550\) 0 0
\(551\) 150.000 0.272232
\(552\) −257.196 + 257.196i −0.465936 + 0.465936i
\(553\) 391.918 + 391.918i 0.708713 + 0.708713i
\(554\) 678.000i 1.22383i
\(555\) 0 0
\(556\) 185.000 0.332734
\(557\) 66.1362 66.1362i 0.118736 0.118736i −0.645242 0.763978i \(-0.723243\pi\)
0.763978 + 0.645242i \(0.223243\pi\)
\(558\) −279.242 279.242i −0.500433 0.500433i
\(559\) 72.0000i 0.128801i
\(560\) 0 0
\(561\) 99.0000 0.176471
\(562\) −565.832 + 565.832i −1.00682 + 1.00682i
\(563\) 191.060 + 191.060i 0.339361 + 0.339361i 0.856127 0.516766i \(-0.172864\pi\)
−0.516766 + 0.856127i \(0.672864\pi\)
\(564\) 18.0000i 0.0319149i
\(565\) 0 0
\(566\) 177.000 0.312721
\(567\) −44.0908 + 44.0908i −0.0777616 + 0.0777616i
\(568\) −257.196 257.196i −0.452811 0.452811i
\(569\) 45.0000i 0.0790861i 0.999218 + 0.0395431i \(0.0125902\pi\)
−0.999218 + 0.0395431i \(0.987410\pi\)
\(570\) 0 0
\(571\) 542.000 0.949212 0.474606 0.880198i \(-0.342591\pi\)
0.474606 + 0.880198i \(0.342591\pi\)
\(572\) 22.0454 22.0454i 0.0385409 0.0385409i
\(573\) −22.0454 22.0454i −0.0384737 0.0384737i
\(574\) 684.000i 1.19164i
\(575\) 0 0
\(576\) 426.000 0.739583
\(577\) 549.910 549.910i 0.953051 0.953051i −0.0458952 0.998946i \(-0.514614\pi\)
0.998946 + 0.0458952i \(0.0146140\pi\)
\(578\) 90.6311 + 90.6311i 0.156801 + 0.156801i
\(579\) 213.000i 0.367876i
\(580\) 0 0
\(581\) 1092.00 1.87952
\(582\) −161.666 + 161.666i −0.277777 + 0.277777i
\(583\) −95.5301 95.5301i −0.163860 0.163860i
\(584\) 165.000i 0.282534i
\(585\) 0 0
\(586\) 12.0000 0.0204778
\(587\) −417.638 + 417.638i −0.711479 + 0.711479i −0.966845 0.255366i \(-0.917804\pi\)
0.255366 + 0.966845i \(0.417804\pi\)
\(588\) −1.22474 1.22474i −0.00208290 0.00208290i
\(589\) 190.000i 0.322581i
\(590\) 0 0
\(591\) −318.000 −0.538071
\(592\) −215.555 + 215.555i −0.364113 + 0.364113i
\(593\) 331.906 + 331.906i 0.559706 + 0.559706i 0.929224 0.369517i \(-0.120477\pi\)
−0.369517 + 0.929224i \(0.620477\pi\)
\(594\) 135.000i 0.227273i
\(595\) 0 0
\(596\) −150.000 −0.251678
\(597\) −244.949 + 244.949i −0.410300 + 0.410300i
\(598\) 308.636 + 308.636i 0.516113 + 0.516113i
\(599\) 900.000i 1.50250i −0.660015 0.751252i \(-0.729450\pi\)
0.660015 0.751252i \(-0.270550\pi\)
\(600\) 0 0
\(601\) 577.000 0.960067 0.480033 0.877250i \(-0.340625\pi\)
0.480033 + 0.877250i \(0.340625\pi\)
\(602\) 58.7878 58.7878i 0.0976541 0.0976541i
\(603\) −286.590 286.590i −0.475274 0.475274i
\(604\) 52.0000i 0.0860927i
\(605\) 0 0
\(606\) 144.000 0.237624
\(607\) 127.373 127.373i 0.209841 0.209841i −0.594359 0.804200i \(-0.702594\pi\)
0.804200 + 0.594359i \(0.202594\pi\)
\(608\) −55.1135 55.1135i −0.0906472 0.0906472i
\(609\) 360.000i 0.591133i
\(610\) 0 0
\(611\) −108.000 −0.176759
\(612\) −80.8332 + 80.8332i −0.132080 + 0.132080i
\(613\) −237.601 237.601i −0.387603 0.387603i 0.486229 0.873832i \(-0.338372\pi\)
−0.873832 + 0.486229i \(0.838372\pi\)
\(614\) 213.000i 0.346906i
\(615\) 0 0
\(616\) 180.000 0.292208
\(617\) −656.463 + 656.463i −1.06396 + 1.06396i −0.0661502 + 0.997810i \(0.521072\pi\)
−0.997810 + 0.0661502i \(0.978928\pi\)
\(618\) 271.893 + 271.893i 0.439957 + 0.439957i
\(619\) 470.000i 0.759289i 0.925132 + 0.379645i \(0.123954\pi\)
−0.925132 + 0.379645i \(0.876046\pi\)
\(620\) 0 0
\(621\) −630.000 −1.01449
\(622\) 646.665 646.665i 1.03965 1.03965i
\(623\) 73.4847 + 73.4847i 0.117953 + 0.117953i
\(624\) 198.000i 0.317308i
\(625\) 0 0
\(626\) −468.000 −0.747604
\(627\) −18.3712 + 18.3712i −0.0293001 + 0.0293001i
\(628\) 188.611 + 188.611i 0.300336 + 0.300336i
\(629\) 528.000i 0.839428i
\(630\) 0 0
\(631\) −838.000 −1.32805 −0.664025 0.747710i \(-0.731153\pi\)
−0.664025 + 0.747710i \(0.731153\pi\)
\(632\) 489.898 489.898i 0.775155 0.775155i
\(633\) −126.149 126.149i −0.199287 0.199287i
\(634\) 492.000i 0.776025i
\(635\) 0 0
\(636\) −78.0000 −0.122642
\(637\) −7.34847 + 7.34847i −0.0115361 + 0.0115361i
\(638\) 110.227 + 110.227i 0.172770 + 0.172770i
\(639\) 252.000i 0.394366i
\(640\) 0 0
\(641\) −618.000 −0.964119 −0.482059 0.876139i \(-0.660111\pi\)
−0.482059 + 0.876139i \(0.660111\pi\)
\(642\) 77.1589 77.1589i 0.120185 0.120185i
\(643\) −249.848 249.848i −0.388566 0.388566i 0.485610 0.874176i \(-0.338598\pi\)
−0.874176 + 0.485610i \(0.838598\pi\)
\(644\) 168.000i 0.260870i
\(645\) 0 0
\(646\) −165.000 −0.255418
\(647\) 421.312 421.312i 0.651178 0.651178i −0.302099 0.953277i \(-0.597687\pi\)
0.953277 + 0.302099i \(0.0976872\pi\)
\(648\) 55.1135 + 55.1135i 0.0850517 + 0.0850517i
\(649\) 270.000i 0.416025i
\(650\) 0 0
\(651\) −456.000 −0.700461
\(652\) −99.2043 + 99.2043i −0.152154 + 0.152154i
\(653\) −519.292 519.292i −0.795240 0.795240i 0.187101 0.982341i \(-0.440091\pi\)
−0.982341 + 0.187101i \(0.940091\pi\)
\(654\) 120.000i 0.183486i
\(655\) 0 0
\(656\) 627.000 0.955793
\(657\) 80.8332 80.8332i 0.123034 0.123034i
\(658\) −88.1816 88.1816i −0.134015 0.134015i
\(659\) 885.000i 1.34294i 0.741030 + 0.671472i \(0.234338\pi\)
−0.741030 + 0.671472i \(0.765662\pi\)
\(660\) 0 0
\(661\) 922.000 1.39486 0.697428 0.716655i \(-0.254328\pi\)
0.697428 + 0.716655i \(0.254328\pi\)
\(662\) 383.345 383.345i 0.579071 0.579071i
\(663\) −242.499 242.499i −0.365761 0.365761i
\(664\) 1365.00i 2.05572i
\(665\) 0 0
\(666\) −288.000 −0.432432
\(667\) 514.393 514.393i 0.771204 0.771204i
\(668\) 17.1464 + 17.1464i 0.0256683 + 0.0256683i
\(669\) 492.000i 0.735426i
\(670\) 0 0
\(671\) 84.0000 0.125186
\(672\) 132.272 132.272i 0.196834 0.196834i
\(673\) −78.3837 78.3837i −0.116469 0.116469i 0.646470 0.762939i \(-0.276244\pi\)
−0.762939 + 0.646470i \(0.776244\pi\)
\(674\) 477.000i 0.707715i
\(675\) 0 0
\(676\) 61.0000 0.0902367
\(677\) −705.453 + 705.453i −1.04203 + 1.04203i −0.0429510 + 0.999077i \(0.513676\pi\)
−0.999077 + 0.0429510i \(0.986324\pi\)
\(678\) 253.522 + 253.522i 0.373927 + 0.373927i
\(679\) 528.000i 0.777614i
\(680\) 0 0
\(681\) 672.000 0.986784
\(682\) −139.621 + 139.621i −0.204723 + 0.204723i
\(683\) −133.497 133.497i −0.195457 0.195457i 0.602592 0.798049i \(-0.294135\pi\)
−0.798049 + 0.602592i \(0.794135\pi\)
\(684\) 30.0000i 0.0438596i
\(685\) 0 0
\(686\) −600.000 −0.874636
\(687\) 24.4949 24.4949i 0.0356549 0.0356549i
\(688\) −53.8888 53.8888i −0.0783267 0.0783267i
\(689\) 468.000i 0.679245i
\(690\) 0 0
\(691\) −893.000 −1.29233 −0.646165 0.763198i \(-0.723628\pi\)
−0.646165 + 0.763198i \(0.723628\pi\)
\(692\) 78.3837 78.3837i 0.113271 0.113271i
\(693\) 88.1816 + 88.1816i 0.127246 + 0.127246i
\(694\) 243.000i 0.350144i
\(695\) 0 0
\(696\) 450.000 0.646552
\(697\) −767.915 + 767.915i −1.10174 + 1.10174i
\(698\) −122.474 122.474i −0.175465 0.175465i
\(699\) 252.000i 0.360515i
\(700\) 0 0
\(701\) 402.000 0.573466 0.286733 0.958010i \(-0.407431\pi\)
0.286733 + 0.958010i \(0.407431\pi\)
\(702\) −330.681 + 330.681i −0.471056 + 0.471056i
\(703\) 97.9796 + 97.9796i 0.139374 + 0.139374i
\(704\) 213.000i 0.302557i
\(705\) 0 0
\(706\) 972.000 1.37677
\(707\) −235.151 + 235.151i −0.332604 + 0.332604i
\(708\) 110.227 + 110.227i 0.155688 + 0.155688i
\(709\) 1060.00i 1.49506i 0.664226 + 0.747532i \(0.268761\pi\)
−0.664226 + 0.747532i \(0.731239\pi\)
\(710\) 0 0
\(711\) 480.000 0.675105
\(712\) 91.8559 91.8559i 0.129011 0.129011i
\(713\) 651.564 + 651.564i 0.913835 + 0.913835i
\(714\) 396.000i 0.554622i
\(715\) 0 0
\(716\) 195.000 0.272346
\(717\) 257.196 257.196i 0.358712 0.358712i
\(718\) 661.362 + 661.362i 0.921117 + 0.921117i
\(719\) 1320.00i 1.83588i 0.396716 + 0.917942i \(0.370150\pi\)
−0.396716 + 0.917942i \(0.629850\pi\)
\(720\) 0 0
\(721\) −888.000 −1.23162
\(722\) −411.514 + 411.514i −0.569964 + 0.569964i
\(723\) −52.6640 52.6640i −0.0728410 0.0728410i
\(724\) 262.000i 0.361878i
\(725\) 0 0
\(726\) 336.000 0.462810
\(727\) −31.8434 + 31.8434i −0.0438011 + 0.0438011i −0.728668 0.684867i \(-0.759860\pi\)
0.684867 + 0.728668i \(0.259860\pi\)
\(728\) −440.908 440.908i −0.605643 0.605643i
\(729\) 351.000i 0.481481i
\(730\) 0 0
\(731\) 132.000 0.180575
\(732\) 34.2929 34.2929i 0.0468482 0.0468482i
\(733\) 815.680 + 815.680i 1.11280 + 1.11280i 0.992771 + 0.120026i \(0.0382978\pi\)
0.120026 + 0.992771i \(0.461702\pi\)
\(734\) 108.000i 0.147139i
\(735\) 0 0
\(736\) −378.000 −0.513587
\(737\) −143.295 + 143.295i −0.194430 + 0.194430i
\(738\) 418.863 + 418.863i 0.567565 + 0.567565i
\(739\) 710.000i 0.960758i −0.877061 0.480379i \(-0.840499\pi\)
0.877061 0.480379i \(-0.159501\pi\)
\(740\) 0 0
\(741\) 90.0000 0.121457
\(742\) −382.120 + 382.120i −0.514987 + 0.514987i
\(743\) −800.983 800.983i −1.07804 1.07804i −0.996685 0.0813540i \(-0.974076\pi\)
−0.0813540 0.996685i \(-0.525924\pi\)
\(744\) 570.000i 0.766129i
\(745\) 0 0
\(746\) −858.000 −1.15013
\(747\) 668.711 668.711i 0.895195 0.895195i
\(748\) 40.4166 + 40.4166i 0.0540329 + 0.0540329i
\(749\) 252.000i 0.336449i
\(750\) 0 0
\(751\) 502.000 0.668442 0.334221 0.942495i \(-0.391527\pi\)
0.334221 + 0.942495i \(0.391527\pi\)
\(752\) −80.8332 + 80.8332i −0.107491 + 0.107491i
\(753\) −150.644 150.644i −0.200058 0.200058i
\(754\) 540.000i 0.716180i
\(755\) 0 0
\(756\) 180.000 0.238095
\(757\) 4.89898 4.89898i 0.00647157 0.00647157i −0.703864 0.710335i \(-0.748543\pi\)
0.710335 + 0.703864i \(0.248543\pi\)
\(758\) −618.496 618.496i −0.815958 0.815958i
\(759\) 126.000i 0.166008i
\(760\) 0 0
\(761\) 747.000 0.981603 0.490802 0.871271i \(-0.336704\pi\)
0.490802 + 0.871271i \(0.336704\pi\)
\(762\) 462.954 462.954i 0.607551 0.607551i
\(763\) −195.959 195.959i −0.256827 0.256827i
\(764\) 18.0000i 0.0235602i
\(765\) 0 0
\(766\) −348.000 −0.454308
\(767\) 661.362 661.362i 0.862271 0.862271i
\(768\) −219.229 219.229i −0.285455 0.285455i
\(769\) 1255.00i 1.63199i −0.578059 0.815995i \(-0.696190\pi\)
0.578059 0.815995i \(-0.303810\pi\)
\(770\) 0 0
\(771\) 12.0000 0.0155642
\(772\) −86.9569 + 86.9569i −0.112638 + 0.112638i
\(773\) −17.1464 17.1464i −0.0221817 0.0221817i 0.695929 0.718111i \(-0.254993\pi\)
−0.718111 + 0.695929i \(0.754993\pi\)
\(774\) 72.0000i 0.0930233i
\(775\) 0 0
\(776\) −660.000 −0.850515
\(777\) −235.151 + 235.151i −0.302640 + 0.302640i
\(778\) −845.074 845.074i −1.08621 1.08621i
\(779\) 285.000i 0.365854i
\(780\) 0 0
\(781\) −126.000 −0.161332
\(782\) −565.832 + 565.832i −0.723570 + 0.723570i
\(783\) 551.135 + 551.135i 0.703876 + 0.703876i
\(784\) 11.0000i 0.0140306i
\(785\) 0 0
\(786\) −486.000 −0.618321
\(787\) 592.777 592.777i 0.753210 0.753210i −0.221867 0.975077i \(-0.571215\pi\)
0.975077 + 0.221867i \(0.0712150\pi\)
\(788\) −129.823 129.823i −0.164750 0.164750i
\(789\) 18.0000i 0.0228137i
\(790\) 0 0
\(791\) −828.000 −1.04678
\(792\) 110.227 110.227i 0.139176 0.139176i
\(793\) −205.757 205.757i −0.259467 0.259467i