Properties

Label 637.2.u.g.30.5
Level $637$
Weight $2$
Character 637.30
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.u (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 30.5
Root \(0.874681 - 1.11128i\) of defining polynomial
Character \(\chi\) \(=\) 637.30
Dual form 637.2.u.g.361.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.16500 - 0.672613i) q^{2} -2.05010 q^{3} +(-0.0951832 + 0.164862i) q^{4} +(3.08979 + 1.78389i) q^{5} +(-2.38837 + 1.37893i) q^{6} +2.94654i q^{8} +1.20292 q^{9} +O(q^{10})\) \(q+(1.16500 - 0.672613i) q^{2} -2.05010 q^{3} +(-0.0951832 + 0.164862i) q^{4} +(3.08979 + 1.78389i) q^{5} +(-2.38837 + 1.37893i) q^{6} +2.94654i q^{8} +1.20292 q^{9} +4.79947 q^{10} -1.27867i q^{11} +(0.195135 - 0.337984i) q^{12} +(-3.57420 - 0.474474i) q^{13} +(-6.33438 - 3.65716i) q^{15} +(1.79151 + 3.10299i) q^{16} +(-3.86960 + 6.70234i) q^{17} +(1.40141 - 0.809103i) q^{18} +0.943878i q^{19} +(-0.588191 + 0.339592i) q^{20} +(-0.860052 - 1.48965i) q^{22} +(0.823637 + 1.42658i) q^{23} -6.04071i q^{24} +(3.86451 + 6.69354i) q^{25} +(-4.48308 + 1.85129i) q^{26} +3.68419 q^{27} +(-2.02242 + 3.50293i) q^{29} -9.83940 q^{30} +(4.46193 - 2.57610i) q^{31} +(-0.929326 - 0.536547i) q^{32} +2.62141i q^{33} +10.4110i q^{34} +(-0.114498 + 0.198317i) q^{36} +(0.914594 - 0.528041i) q^{37} +(0.634865 + 1.09962i) q^{38} +(7.32747 + 0.972721i) q^{39} +(-5.25629 + 9.10417i) q^{40} +(3.63629 + 2.09941i) q^{41} +(1.91532 + 3.31744i) q^{43} +(0.210805 + 0.121708i) q^{44} +(3.71678 + 2.14588i) q^{45} +(1.91908 + 1.10798i) q^{46} +(0.774415 + 0.447109i) q^{47} +(-3.67279 - 6.36146i) q^{48} +(9.00432 + 5.19865i) q^{50} +(7.93308 - 13.7405i) q^{51} +(0.418426 - 0.544088i) q^{52} +(0.0399961 + 0.0692754i) q^{53} +(4.29208 - 2.47804i) q^{54} +(2.28101 - 3.95082i) q^{55} -1.93505i q^{57} +5.44122i q^{58} +(-9.68627 - 5.59237i) q^{59} +(1.20585 - 0.696200i) q^{60} +7.62392 q^{61} +(3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(-10.1971 - 7.84199i) q^{65} +(1.76319 + 3.05394i) q^{66} +6.32103i q^{67} +(-0.736641 - 1.27590i) q^{68} +(-1.68854 - 2.92464i) q^{69} +(9.89346 - 5.71199i) q^{71} +3.54446i q^{72} +(0.658617 - 0.380253i) q^{73} +(0.710335 - 1.23034i) q^{74} +(-7.92265 - 13.7224i) q^{75} +(-0.155610 - 0.0898413i) q^{76} +(9.19077 - 3.79533i) q^{78} +(1.42765 - 2.47277i) q^{79} +12.7834i q^{80} -11.1617 q^{81} +5.64837 q^{82} +2.32483i q^{83} +(-23.9125 + 13.8059i) q^{85} +(4.46270 + 2.57654i) q^{86} +(4.14617 - 7.18137i) q^{87} +3.76766 q^{88} +(-6.56124 + 3.78813i) q^{89} +5.77339 q^{90} -0.313586 q^{92} +(-9.14742 + 5.28127i) q^{93} +1.20292 q^{94} +(-1.68377 + 2.91638i) q^{95} +(1.90522 + 1.09998i) q^{96} +(0.414443 - 0.239279i) q^{97} -1.53815i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + O(q^{10}) \) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + 24q^{10} + q^{12} + 2q^{13} - 12q^{15} - 8q^{16} - 17q^{17} - 3q^{18} + 3q^{20} - 15q^{22} + 3q^{23} - 5q^{25} + 9q^{26} - 12q^{27} - q^{29} - 22q^{30} + 18q^{31} + 18q^{32} - 13q^{36} + 15q^{37} - 19q^{38} - q^{39} + q^{40} + 6q^{41} + 11q^{43} + 33q^{44} + 9q^{45} - 30q^{46} - 15q^{47} - 19q^{48} + 18q^{50} + 4q^{51} - 47q^{52} - 8q^{53} - 6q^{54} + 15q^{55} - 27q^{59} + 30q^{60} + 10q^{61} - 41q^{62} + 2q^{64} - 3q^{65} + 34q^{66} + 11q^{68} - 7q^{69} + 30q^{71} + 42q^{73} - 33q^{74} - q^{75} + 45q^{76} + 44q^{78} - 35q^{79} - 28q^{81} + 10q^{82} - 21q^{85} + 57q^{86} - 10q^{87} + 28q^{88} - 48q^{89} - 66q^{92} - 81q^{93} + 2q^{94} + 2q^{95} + 21q^{96} + 3q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.16500 0.672613i 0.823779 0.475609i −0.0279386 0.999610i \(-0.508894\pi\)
0.851718 + 0.524000i \(0.175561\pi\)
\(3\) −2.05010 −1.18363 −0.591814 0.806075i \(-0.701588\pi\)
−0.591814 + 0.806075i \(0.701588\pi\)
\(4\) −0.0951832 + 0.164862i −0.0475916 + 0.0824311i
\(5\) 3.08979 + 1.78389i 1.38179 + 0.797779i 0.992372 0.123280i \(-0.0393415\pi\)
0.389422 + 0.921059i \(0.372675\pi\)
\(6\) −2.38837 + 1.37893i −0.975048 + 0.562944i
\(7\) 0 0
\(8\) 2.94654i 1.04176i
\(9\) 1.20292 0.400975
\(10\) 4.79947 1.51772
\(11\) 1.27867i 0.385534i −0.981245 0.192767i \(-0.938254\pi\)
0.981245 0.192767i \(-0.0617462\pi\)
\(12\) 0.195135 0.337984i 0.0563307 0.0975677i
\(13\) −3.57420 0.474474i −0.991304 0.131595i
\(14\) 0 0
\(15\) −6.33438 3.65716i −1.63553 0.944273i
\(16\) 1.79151 + 3.10299i 0.447878 + 0.775748i
\(17\) −3.86960 + 6.70234i −0.938515 + 1.62556i −0.170273 + 0.985397i \(0.554465\pi\)
−0.768242 + 0.640159i \(0.778868\pi\)
\(18\) 1.40141 0.809103i 0.330315 0.190707i
\(19\) 0.943878i 0.216540i 0.994121 + 0.108270i \(0.0345312\pi\)
−0.994121 + 0.108270i \(0.965469\pi\)
\(20\) −0.588191 + 0.339592i −0.131524 + 0.0759352i
\(21\) 0 0
\(22\) −0.860052 1.48965i −0.183364 0.317595i
\(23\) 0.823637 + 1.42658i 0.171740 + 0.297463i 0.939028 0.343840i \(-0.111728\pi\)
−0.767288 + 0.641303i \(0.778394\pi\)
\(24\) 6.04071i 1.23305i
\(25\) 3.86451 + 6.69354i 0.772903 + 1.33871i
\(26\) −4.48308 + 1.85129i −0.879203 + 0.363068i
\(27\) 3.68419 0.709023
\(28\) 0 0
\(29\) −2.02242 + 3.50293i −0.375554 + 0.650478i −0.990410 0.138161i \(-0.955881\pi\)
0.614856 + 0.788639i \(0.289214\pi\)
\(30\) −9.83940 −1.79642
\(31\) 4.46193 2.57610i 0.801387 0.462681i −0.0425691 0.999094i \(-0.513554\pi\)
0.843956 + 0.536413i \(0.180221\pi\)
\(32\) −0.929326 0.536547i −0.164283 0.0948490i
\(33\) 2.62141i 0.456329i
\(34\) 10.4110i 1.78547i
\(35\) 0 0
\(36\) −0.114498 + 0.198317i −0.0190830 + 0.0330528i
\(37\) 0.914594 0.528041i 0.150358 0.0868094i −0.422933 0.906161i \(-0.639000\pi\)
0.573292 + 0.819351i \(0.305666\pi\)
\(38\) 0.634865 + 1.09962i 0.102989 + 0.178382i
\(39\) 7.32747 + 0.972721i 1.17333 + 0.155760i
\(40\) −5.25629 + 9.10417i −0.831093 + 1.43950i
\(41\) 3.63629 + 2.09941i 0.567893 + 0.327873i 0.756307 0.654217i \(-0.227002\pi\)
−0.188415 + 0.982090i \(0.560335\pi\)
\(42\) 0 0
\(43\) 1.91532 + 3.31744i 0.292084 + 0.505904i 0.974302 0.225244i \(-0.0723180\pi\)
−0.682218 + 0.731148i \(0.738985\pi\)
\(44\) 0.210805 + 0.121708i 0.0317800 + 0.0183482i
\(45\) 3.71678 + 2.14588i 0.554064 + 0.319889i
\(46\) 1.91908 + 1.10798i 0.282952 + 0.163363i
\(47\) 0.774415 + 0.447109i 0.112960 + 0.0652175i 0.555416 0.831573i \(-0.312559\pi\)
−0.442456 + 0.896790i \(0.645893\pi\)
\(48\) −3.67279 6.36146i −0.530121 0.918197i
\(49\) 0 0
\(50\) 9.00432 + 5.19865i 1.27340 + 0.735200i
\(51\) 7.93308 13.7405i 1.11085 1.92405i
\(52\) 0.418426 0.544088i 0.0580253 0.0754514i
\(53\) 0.0399961 + 0.0692754i 0.00549389 + 0.00951570i 0.868759 0.495235i \(-0.164918\pi\)
−0.863265 + 0.504750i \(0.831585\pi\)
\(54\) 4.29208 2.47804i 0.584079 0.337218i
\(55\) 2.28101 3.95082i 0.307571 0.532729i
\(56\) 0 0
\(57\) 1.93505i 0.256303i
\(58\) 5.44122i 0.714467i
\(59\) −9.68627 5.59237i −1.26104 0.728064i −0.287768 0.957700i \(-0.592913\pi\)
−0.973277 + 0.229636i \(0.926246\pi\)
\(60\) 1.20585 0.696200i 0.155675 0.0898790i
\(61\) 7.62392 0.976143 0.488072 0.872804i \(-0.337701\pi\)
0.488072 + 0.872804i \(0.337701\pi\)
\(62\) 3.46543 6.00231i 0.440111 0.762294i
\(63\) 0 0
\(64\) −8.60961 −1.07620
\(65\) −10.1971 7.84199i −1.26479 0.972679i
\(66\) 1.76319 + 3.05394i 0.217034 + 0.375914i
\(67\) 6.32103i 0.772237i 0.922449 + 0.386119i \(0.126184\pi\)
−0.922449 + 0.386119i \(0.873816\pi\)
\(68\) −0.736641 1.27590i −0.0893309 0.154726i
\(69\) −1.68854 2.92464i −0.203277 0.352085i
\(70\) 0 0
\(71\) 9.89346 5.71199i 1.17414 0.677889i 0.219487 0.975616i \(-0.429562\pi\)
0.954651 + 0.297727i \(0.0962285\pi\)
\(72\) 3.54446i 0.417719i
\(73\) 0.658617 0.380253i 0.0770853 0.0445052i −0.460962 0.887420i \(-0.652496\pi\)
0.538047 + 0.842915i \(0.319162\pi\)
\(74\) 0.710335 1.23034i 0.0825747 0.143024i
\(75\) −7.92265 13.7224i −0.914829 1.58453i
\(76\) −0.155610 0.0898413i −0.0178497 0.0103055i
\(77\) 0 0
\(78\) 9.19077 3.79533i 1.04065 0.429737i
\(79\) 1.42765 2.47277i 0.160624 0.278208i −0.774469 0.632612i \(-0.781983\pi\)
0.935093 + 0.354404i \(0.115316\pi\)
\(80\) 12.7834i 1.42923i
\(81\) −11.1617 −1.24019
\(82\) 5.64837 0.623758
\(83\) 2.32483i 0.255183i 0.991827 + 0.127591i \(0.0407246\pi\)
−0.991827 + 0.127591i \(0.959275\pi\)
\(84\) 0 0
\(85\) −23.9125 + 13.8059i −2.59367 + 1.49746i
\(86\) 4.46270 + 2.57654i 0.481226 + 0.277836i
\(87\) 4.14617 7.18137i 0.444516 0.769924i
\(88\) 3.76766 0.401634
\(89\) −6.56124 + 3.78813i −0.695490 + 0.401541i −0.805665 0.592371i \(-0.798192\pi\)
0.110176 + 0.993912i \(0.464859\pi\)
\(90\) 5.77339 0.608569
\(91\) 0 0
\(92\) −0.313586 −0.0326936
\(93\) −9.14742 + 5.28127i −0.948544 + 0.547642i
\(94\) 1.20292 0.124072
\(95\) −1.68377 + 2.91638i −0.172751 + 0.299214i
\(96\) 1.90522 + 1.09998i 0.194450 + 0.112266i
\(97\) 0.414443 0.239279i 0.0420803 0.0242951i −0.478812 0.877917i \(-0.658933\pi\)
0.520893 + 0.853622i \(0.325599\pi\)
\(98\) 0 0
\(99\) 1.53815i 0.154589i
\(100\) −1.47135 −0.147135
\(101\) 2.87836 0.286407 0.143204 0.989693i \(-0.454260\pi\)
0.143204 + 0.989693i \(0.454260\pi\)
\(102\) 21.3436i 2.11333i
\(103\) 5.66755 9.81649i 0.558441 0.967248i −0.439186 0.898396i \(-0.644733\pi\)
0.997627 0.0688516i \(-0.0219335\pi\)
\(104\) 1.39806 10.5315i 0.137091 1.03270i
\(105\) 0 0
\(106\) 0.0931910 + 0.0538039i 0.00905151 + 0.00522589i
\(107\) 3.28603 + 5.69157i 0.317673 + 0.550225i 0.980002 0.198988i \(-0.0637653\pi\)
−0.662329 + 0.749213i \(0.730432\pi\)
\(108\) −0.350673 + 0.607384i −0.0337435 + 0.0584455i
\(109\) 5.05684 2.91957i 0.484358 0.279644i −0.237873 0.971296i \(-0.576450\pi\)
0.722231 + 0.691652i \(0.243117\pi\)
\(110\) 6.13694i 0.585135i
\(111\) −1.87501 + 1.08254i −0.177968 + 0.102750i
\(112\) 0 0
\(113\) −3.26617 5.65717i −0.307255 0.532181i 0.670506 0.741904i \(-0.266077\pi\)
−0.977761 + 0.209723i \(0.932744\pi\)
\(114\) −1.30154 2.25433i −0.121900 0.211137i
\(115\) 5.87711i 0.548043i
\(116\) −0.385001 0.666841i −0.0357464 0.0619146i
\(117\) −4.29949 0.570756i −0.397488 0.0527664i
\(118\) −15.0460 −1.38510
\(119\) 0 0
\(120\) 10.7759 18.6645i 0.983705 1.70383i
\(121\) 9.36500 0.851363
\(122\) 8.88187 5.12795i 0.804127 0.464263i
\(123\) −7.45477 4.30401i −0.672174 0.388080i
\(124\) 0.980805i 0.0880789i
\(125\) 9.73656i 0.870865i
\(126\) 0 0
\(127\) 7.35818 12.7447i 0.652932 1.13091i −0.329475 0.944164i \(-0.606872\pi\)
0.982408 0.186748i \(-0.0597948\pi\)
\(128\) −8.17154 + 4.71784i −0.722269 + 0.417002i
\(129\) −3.92661 6.80109i −0.345719 0.598802i
\(130\) −17.1542 2.27722i −1.50453 0.199726i
\(131\) 5.59335 9.68796i 0.488693 0.846441i −0.511222 0.859448i \(-0.670807\pi\)
0.999915 + 0.0130074i \(0.00414049\pi\)
\(132\) −0.432171 0.249514i −0.0376157 0.0217174i
\(133\) 0 0
\(134\) 4.25161 + 7.36400i 0.367283 + 0.636153i
\(135\) 11.3834 + 6.57219i 0.979724 + 0.565644i
\(136\) −19.7487 11.4019i −1.69344 0.977706i
\(137\) −15.2687 8.81541i −1.30450 0.753151i −0.323324 0.946288i \(-0.604800\pi\)
−0.981172 + 0.193137i \(0.938134\pi\)
\(138\) −3.93430 2.27147i −0.334910 0.193360i
\(139\) −2.92855 5.07240i −0.248396 0.430235i 0.714685 0.699447i \(-0.246570\pi\)
−0.963081 + 0.269212i \(0.913237\pi\)
\(140\) 0 0
\(141\) −1.58763 0.916619i −0.133703 0.0771932i
\(142\) 7.68392 13.3089i 0.644820 1.11686i
\(143\) −0.606697 + 4.57022i −0.0507345 + 0.382181i
\(144\) 2.15506 + 3.73267i 0.179588 + 0.311055i
\(145\) −12.4977 + 7.21554i −1.03788 + 0.599218i
\(146\) 0.511526 0.885989i 0.0423342 0.0733250i
\(147\) 0 0
\(148\) 0.201043i 0.0165256i
\(149\) 10.4790i 0.858470i −0.903193 0.429235i \(-0.858783\pi\)
0.903193 0.429235i \(-0.141217\pi\)
\(150\) −18.4598 10.6578i −1.50724 0.870203i
\(151\) 4.08249 2.35703i 0.332229 0.191812i −0.324602 0.945851i \(-0.605230\pi\)
0.656830 + 0.754039i \(0.271897\pi\)
\(152\) −2.78117 −0.225583
\(153\) −4.65483 + 8.06241i −0.376321 + 0.651807i
\(154\) 0 0
\(155\) 18.3819 1.47647
\(156\) −0.857817 + 1.11544i −0.0686803 + 0.0893063i
\(157\) 4.50105 + 7.79604i 0.359223 + 0.622192i 0.987831 0.155530i \(-0.0497085\pi\)
−0.628608 + 0.777722i \(0.716375\pi\)
\(158\) 3.84103i 0.305576i
\(159\) −0.0819962 0.142022i −0.00650272 0.0112630i
\(160\) −1.91428 3.31563i −0.151337 0.262123i
\(161\) 0 0
\(162\) −13.0034 + 7.50754i −1.02165 + 0.589848i
\(163\) 12.0324i 0.942449i −0.882013 0.471224i \(-0.843812\pi\)
0.882013 0.471224i \(-0.156188\pi\)
\(164\) −0.692227 + 0.399657i −0.0540538 + 0.0312080i
\(165\) −4.67630 + 8.09959i −0.364050 + 0.630553i
\(166\) 1.56371 + 2.70842i 0.121367 + 0.210214i
\(167\) 16.8199 + 9.71099i 1.30157 + 0.751459i 0.980672 0.195657i \(-0.0626838\pi\)
0.320893 + 0.947116i \(0.396017\pi\)
\(168\) 0 0
\(169\) 12.5497 + 3.39173i 0.965365 + 0.260902i
\(170\) −18.5720 + 32.1677i −1.42441 + 2.46715i
\(171\) 1.13541i 0.0868273i
\(172\) −0.729226 −0.0556030
\(173\) 14.3795 1.09325 0.546627 0.837376i \(-0.315912\pi\)
0.546627 + 0.837376i \(0.315912\pi\)
\(174\) 11.1551i 0.845663i
\(175\) 0 0
\(176\) 3.96771 2.29076i 0.299077 0.172672i
\(177\) 19.8578 + 11.4649i 1.49261 + 0.861757i
\(178\) −5.09589 + 8.82635i −0.381953 + 0.661563i
\(179\) −5.42606 −0.405563 −0.202781 0.979224i \(-0.564998\pi\)
−0.202781 + 0.979224i \(0.564998\pi\)
\(180\) −0.707550 + 0.408504i −0.0527376 + 0.0304481i
\(181\) 15.4902 1.15138 0.575688 0.817669i \(-0.304734\pi\)
0.575688 + 0.817669i \(0.304734\pi\)
\(182\) 0 0
\(183\) −15.6298 −1.15539
\(184\) −4.20348 + 2.42688i −0.309885 + 0.178912i
\(185\) 3.76786 0.277019
\(186\) −7.10450 + 12.3054i −0.520927 + 0.902272i
\(187\) 8.57010 + 4.94795i 0.626707 + 0.361830i
\(188\) −0.147423 + 0.0851144i −0.0107519 + 0.00620761i
\(189\) 0 0
\(190\) 4.53011i 0.328649i
\(191\) 4.74622 0.343425 0.171712 0.985147i \(-0.445070\pi\)
0.171712 + 0.985147i \(0.445070\pi\)
\(192\) 17.6506 1.27382
\(193\) 21.0391i 1.51443i 0.653166 + 0.757215i \(0.273441\pi\)
−0.653166 + 0.757215i \(0.726559\pi\)
\(194\) 0.321884 0.557519i 0.0231099 0.0400276i
\(195\) 20.9051 + 16.0769i 1.49704 + 1.15129i
\(196\) 0 0
\(197\) 5.03342 + 2.90604i 0.358616 + 0.207047i 0.668474 0.743736i \(-0.266948\pi\)
−0.309857 + 0.950783i \(0.600281\pi\)
\(198\) −1.03458 1.79194i −0.0735242 0.127348i
\(199\) −5.30909 + 9.19562i −0.376352 + 0.651860i −0.990528 0.137309i \(-0.956155\pi\)
0.614177 + 0.789168i \(0.289488\pi\)
\(200\) −19.7228 + 11.3869i −1.39461 + 0.805178i
\(201\) 12.9588i 0.914041i
\(202\) 3.35329 1.93602i 0.235936 0.136218i
\(203\) 0 0
\(204\) 1.51019 + 2.61573i 0.105735 + 0.183138i
\(205\) 7.49023 + 12.9735i 0.523140 + 0.906106i
\(206\) 15.2483i 1.06240i
\(207\) 0.990773 + 1.71607i 0.0688635 + 0.119275i
\(208\) −4.93093 11.9407i −0.341899 0.827941i
\(209\) 1.20691 0.0834837
\(210\) 0 0
\(211\) 2.33275 4.04043i 0.160593 0.278155i −0.774489 0.632588i \(-0.781993\pi\)
0.935081 + 0.354433i \(0.115326\pi\)
\(212\) −0.0152278 −0.00104585
\(213\) −20.2826 + 11.7102i −1.38974 + 0.802368i
\(214\) 7.65645 + 4.42046i 0.523384 + 0.302176i
\(215\) 13.6669i 0.932074i
\(216\) 10.8556i 0.738631i
\(217\) 0 0
\(218\) 3.92748 6.80260i 0.266003 0.460730i
\(219\) −1.35023 + 0.779558i −0.0912403 + 0.0526776i
\(220\) 0.434227 + 0.752104i 0.0292756 + 0.0507068i
\(221\) 17.0108 22.1195i 1.14427 1.48792i
\(222\) −1.45626 + 2.52232i −0.0977377 + 0.169287i
\(223\) −20.9798 12.1127i −1.40491 0.811126i −0.410020 0.912076i \(-0.634478\pi\)
−0.994891 + 0.100950i \(0.967812\pi\)
\(224\) 0 0
\(225\) 4.64872 + 8.05182i 0.309915 + 0.536788i
\(226\) −7.61017 4.39373i −0.506221 0.292267i
\(227\) 13.3154 + 7.68764i 0.883773 + 0.510247i 0.871901 0.489683i \(-0.162887\pi\)
0.0118726 + 0.999930i \(0.496221\pi\)
\(228\) 0.319016 + 0.184184i 0.0211274 + 0.0121979i
\(229\) −14.1608 8.17573i −0.935771 0.540268i −0.0471389 0.998888i \(-0.515010\pi\)
−0.888632 + 0.458621i \(0.848344\pi\)
\(230\) 3.95302 + 6.84683i 0.260654 + 0.451467i
\(231\) 0 0
\(232\) −10.3215 5.95913i −0.677641 0.391236i
\(233\) −14.5554 + 25.2106i −0.953554 + 1.65160i −0.215911 + 0.976413i \(0.569272\pi\)
−0.737643 + 0.675191i \(0.764061\pi\)
\(234\) −5.39280 + 2.22696i −0.352538 + 0.145581i
\(235\) 1.59518 + 2.76294i 0.104058 + 0.180234i
\(236\) 1.84394 1.06460i 0.120030 0.0692995i
\(237\) −2.92684 + 5.06943i −0.190119 + 0.329295i
\(238\) 0 0
\(239\) 8.65409i 0.559787i 0.960031 + 0.279893i \(0.0902991\pi\)
−0.960031 + 0.279893i \(0.909701\pi\)
\(240\) 26.2074i 1.69168i
\(241\) −15.7601 9.09909i −1.01520 0.586124i −0.102487 0.994734i \(-0.532680\pi\)
−0.912709 + 0.408611i \(0.866013\pi\)
\(242\) 10.9102 6.29902i 0.701336 0.404916i
\(243\) 11.8302 0.758905
\(244\) −0.725669 + 1.25690i −0.0464562 + 0.0804645i
\(245\) 0 0
\(246\) −11.5797 −0.738297
\(247\) 0.447846 3.37360i 0.0284957 0.214657i
\(248\) 7.59057 + 13.1473i 0.482002 + 0.834851i
\(249\) 4.76614i 0.302042i
\(250\) 6.54894 + 11.3431i 0.414191 + 0.717400i
\(251\) −7.93598 13.7455i −0.500915 0.867610i −0.999999 0.00105678i \(-0.999664\pi\)
0.499085 0.866553i \(-0.333670\pi\)
\(252\) 0 0
\(253\) 1.82413 1.05316i 0.114682 0.0662117i
\(254\) 19.7968i 1.24216i
\(255\) 49.0230 28.3034i 3.06994 1.77243i
\(256\) 2.26304 3.91971i 0.141440 0.244982i
\(257\) 12.1634 + 21.0676i 0.758730 + 1.31416i 0.943499 + 0.331376i \(0.107513\pi\)
−0.184769 + 0.982782i \(0.559154\pi\)
\(258\) −9.14900 5.28218i −0.569592 0.328854i
\(259\) 0 0
\(260\) 2.26344 0.934688i 0.140372 0.0579669i
\(261\) −2.43282 + 4.21376i −0.150588 + 0.260825i
\(262\) 15.0486i 0.929708i
\(263\) 15.4345 0.951734 0.475867 0.879517i \(-0.342134\pi\)
0.475867 + 0.879517i \(0.342134\pi\)
\(264\) −7.72409 −0.475385
\(265\) 0.285395i 0.0175317i
\(266\) 0 0
\(267\) 13.4512 7.76606i 0.823201 0.475275i
\(268\) −1.04210 0.601656i −0.0636563 0.0367520i
\(269\) −6.52035 + 11.2936i −0.397553 + 0.688582i −0.993423 0.114499i \(-0.963474\pi\)
0.595870 + 0.803081i \(0.296807\pi\)
\(270\) 17.6822 1.07610
\(271\) −23.3572 + 13.4853i −1.41885 + 0.819174i −0.996198 0.0871168i \(-0.972235\pi\)
−0.422654 + 0.906291i \(0.638901\pi\)
\(272\) −27.7298 −1.68136
\(273\) 0 0
\(274\) −23.7174 −1.43282
\(275\) 8.55884 4.94145i 0.516117 0.297980i
\(276\) 0.642883 0.0386970
\(277\) 6.35073 10.9998i 0.381578 0.660913i −0.609710 0.792625i \(-0.708714\pi\)
0.991288 + 0.131712i \(0.0420474\pi\)
\(278\) −6.82352 3.93956i −0.409248 0.236279i
\(279\) 5.36737 3.09885i 0.321336 0.185523i
\(280\) 0 0
\(281\) 26.7216i 1.59408i 0.603930 + 0.797038i \(0.293601\pi\)
−0.603930 + 0.797038i \(0.706399\pi\)
\(282\) −2.46612 −0.146855
\(283\) 14.7423 0.876336 0.438168 0.898893i \(-0.355627\pi\)
0.438168 + 0.898893i \(0.355627\pi\)
\(284\) 2.17474i 0.129047i
\(285\) 3.45191 5.97888i 0.204473 0.354158i
\(286\) 2.36719 + 5.73238i 0.139975 + 0.338963i
\(287\) 0 0
\(288\) −1.11791 0.645425i −0.0658734 0.0380320i
\(289\) −21.4476 37.1483i −1.26162 2.18519i
\(290\) −9.70653 + 16.8122i −0.569987 + 0.987247i
\(291\) −0.849651 + 0.490546i −0.0498074 + 0.0287563i
\(292\) 0.144775i 0.00847230i
\(293\) 10.0312 5.79153i 0.586030 0.338345i −0.177496 0.984121i \(-0.556800\pi\)
0.763526 + 0.645777i \(0.223466\pi\)
\(294\) 0 0
\(295\) −19.9523 34.5584i −1.16167 2.01207i
\(296\) 1.55589 + 2.69489i 0.0904344 + 0.156637i
\(297\) 4.71087i 0.273353i
\(298\) −7.04829 12.2080i −0.408297 0.707190i
\(299\) −2.26697 5.48968i −0.131102 0.317476i
\(300\) 3.01641 0.174153
\(301\) 0 0
\(302\) 3.17074 5.49188i 0.182455 0.316022i
\(303\) −5.90093 −0.339000
\(304\) −2.92885 + 1.69097i −0.167981 + 0.0969838i
\(305\) 23.5563 + 13.6002i 1.34883 + 0.778746i
\(306\) 12.5236i 0.715927i
\(307\) 29.3335i 1.67415i −0.547086 0.837076i \(-0.684263\pi\)
0.547086 0.837076i \(-0.315737\pi\)
\(308\) 0 0
\(309\) −11.6191 + 20.1248i −0.660986 + 1.14486i
\(310\) 21.4149 12.3639i 1.21628 0.702222i
\(311\) 0.0753271 + 0.130470i 0.00427141 + 0.00739830i 0.868153 0.496296i \(-0.165307\pi\)
−0.863882 + 0.503695i \(0.831974\pi\)
\(312\) −2.86616 + 21.5907i −0.162264 + 1.22233i
\(313\) −5.26057 + 9.11157i −0.297345 + 0.515016i −0.975528 0.219877i \(-0.929434\pi\)
0.678183 + 0.734893i \(0.262768\pi\)
\(314\) 10.4874 + 6.05493i 0.591841 + 0.341699i
\(315\) 0 0
\(316\) 0.271777 + 0.470732i 0.0152887 + 0.0264808i
\(317\) −1.30489 0.753380i −0.0732901 0.0423140i 0.462907 0.886407i \(-0.346806\pi\)
−0.536197 + 0.844093i \(0.680140\pi\)
\(318\) −0.191051 0.110303i −0.0107136 0.00618551i
\(319\) 4.47910 + 2.58601i 0.250782 + 0.144789i
\(320\) −26.6018 15.3586i −1.48709 0.858571i
\(321\) −6.73671 11.6683i −0.376006 0.651262i
\(322\) 0 0
\(323\) −6.32619 3.65243i −0.351999 0.203227i
\(324\) 1.06241 1.84015i 0.0590228 0.102231i
\(325\) −10.6366 25.7576i −0.590014 1.42878i
\(326\) −8.09314 14.0177i −0.448237 0.776370i
\(327\) −10.3671 + 5.98542i −0.573299 + 0.330995i
\(328\) −6.18600 + 10.7145i −0.341565 + 0.591607i
\(329\) 0 0
\(330\) 12.5814i 0.692582i
\(331\) 25.2509i 1.38791i 0.720017 + 0.693957i \(0.244134\pi\)
−0.720017 + 0.693957i \(0.755866\pi\)
\(332\) −0.383276 0.221284i −0.0210350 0.0121446i
\(333\) 1.10019 0.635193i 0.0602899 0.0348084i
\(334\) 26.1270 1.42960
\(335\) −11.2760 + 19.5306i −0.616075 + 1.06707i
\(336\) 0 0
\(337\) 32.1811 1.75302 0.876509 0.481386i \(-0.159866\pi\)
0.876509 + 0.481386i \(0.159866\pi\)
\(338\) 16.9018 4.48977i 0.919335 0.244211i
\(339\) 6.69598 + 11.5978i 0.363676 + 0.629905i
\(340\) 5.25634i 0.285065i
\(341\) −3.29398 5.70535i −0.178379 0.308962i
\(342\) 0.763694 + 1.32276i 0.0412959 + 0.0715265i
\(343\) 0 0
\(344\) −9.77495 + 5.64357i −0.527030 + 0.304281i
\(345\) 12.0487i 0.648679i
\(346\) 16.7521 9.67185i 0.900600 0.519962i
\(347\) −12.3819 + 21.4461i −0.664695 + 1.15128i 0.314673 + 0.949200i \(0.398105\pi\)
−0.979368 + 0.202085i \(0.935228\pi\)
\(348\) 0.789291 + 1.36709i 0.0423104 + 0.0732838i
\(349\) 10.0075 + 5.77782i 0.535688 + 0.309280i 0.743330 0.668925i \(-0.233245\pi\)
−0.207642 + 0.978205i \(0.566579\pi\)
\(350\) 0 0
\(351\) −13.1680 1.74805i −0.702857 0.0933042i
\(352\) −0.686067 + 1.18830i −0.0365675 + 0.0633368i
\(353\) 20.0884i 1.06920i 0.845106 + 0.534599i \(0.179537\pi\)
−0.845106 + 0.534599i \(0.820463\pi\)
\(354\) 30.8459 1.63944
\(355\) 40.7582 2.16322
\(356\) 1.44227i 0.0764399i
\(357\) 0 0
\(358\) −6.32136 + 3.64964i −0.334094 + 0.192890i
\(359\) −13.0346 7.52551i −0.687938 0.397181i 0.114901 0.993377i \(-0.463345\pi\)
−0.802839 + 0.596196i \(0.796678\pi\)
\(360\) −6.32292 + 10.9516i −0.333247 + 0.577201i
\(361\) 18.1091 0.953110
\(362\) 18.0461 10.4189i 0.948481 0.547606i
\(363\) −19.1992 −1.00770
\(364\) 0 0
\(365\) 2.71331 0.142021
\(366\) −18.2087 + 10.5128i −0.951787 + 0.549514i
\(367\) −9.00355 −0.469982 −0.234991 0.971998i \(-0.575506\pi\)
−0.234991 + 0.971998i \(0.575506\pi\)
\(368\) −2.95112 + 5.11148i −0.153838 + 0.266454i
\(369\) 4.37418 + 2.52543i 0.227711 + 0.131469i
\(370\) 4.38956 2.53431i 0.228202 0.131753i
\(371\) 0 0
\(372\) 2.01075i 0.104253i
\(373\) −16.1391 −0.835649 −0.417824 0.908528i \(-0.637207\pi\)
−0.417824 + 0.908528i \(0.637207\pi\)
\(374\) 13.3122 0.688358
\(375\) 19.9610i 1.03078i
\(376\) −1.31742 + 2.28184i −0.0679409 + 0.117677i
\(377\) 8.89057 11.5606i 0.457888 0.595400i
\(378\) 0 0
\(379\) −13.5668 7.83277i −0.696878 0.402342i 0.109306 0.994008i \(-0.465137\pi\)
−0.806183 + 0.591666i \(0.798471\pi\)
\(380\) −0.320534 0.555181i −0.0164430 0.0284802i
\(381\) −15.0850 + 26.1280i −0.772829 + 1.33858i
\(382\) 5.52935 3.19237i 0.282906 0.163336i
\(383\) 24.6328i 1.25868i 0.777131 + 0.629339i \(0.216674\pi\)
−0.777131 + 0.629339i \(0.783326\pi\)
\(384\) 16.7525 9.67207i 0.854898 0.493576i
\(385\) 0 0
\(386\) 14.1512 + 24.5106i 0.720277 + 1.24756i
\(387\) 2.30399 + 3.99062i 0.117118 + 0.202855i
\(388\) 0.0911013i 0.00462497i
\(389\) −9.42834 16.3304i −0.478036 0.827982i 0.521647 0.853161i \(-0.325318\pi\)
−0.999683 + 0.0251791i \(0.991984\pi\)
\(390\) 35.1680 + 4.66854i 1.78080 + 0.236401i
\(391\) −12.7486 −0.644724
\(392\) 0 0
\(393\) −11.4669 + 19.8613i −0.578431 + 1.00187i
\(394\) 7.81857 0.393894
\(395\) 8.82229 5.09355i 0.443897 0.256284i
\(396\) 0.253582 + 0.146406i 0.0127430 + 0.00735716i
\(397\) 14.5030i 0.727884i −0.931422 0.363942i \(-0.881431\pi\)
0.931422 0.363942i \(-0.118569\pi\)
\(398\) 14.2839i 0.715985i
\(399\) 0 0
\(400\) −13.8467 + 23.9831i −0.692333 + 1.19916i
\(401\) 18.1770 10.4945i 0.907714 0.524069i 0.0280189 0.999607i \(-0.491080\pi\)
0.879695 + 0.475539i \(0.157747\pi\)
\(402\) −8.71624 15.0970i −0.434727 0.752968i
\(403\) −17.1701 + 7.09041i −0.855304 + 0.353198i
\(404\) −0.273971 + 0.474532i −0.0136306 + 0.0236089i
\(405\) −34.4874 19.9113i −1.71369 0.989401i
\(406\) 0 0
\(407\) −0.675191 1.16947i −0.0334680 0.0579683i
\(408\) 40.4869 + 23.3751i 2.00440 + 1.15724i
\(409\) 18.5568 + 10.7138i 0.917576 + 0.529763i 0.882861 0.469635i \(-0.155614\pi\)
0.0347148 + 0.999397i \(0.488948\pi\)
\(410\) 17.4522 + 10.0761i 0.861905 + 0.497621i
\(411\) 31.3025 + 18.0725i 1.54404 + 0.891451i
\(412\) 1.07891 + 1.86873i 0.0531542 + 0.0920657i
\(413\) 0 0
\(414\) 2.30850 + 1.33281i 0.113457 + 0.0655043i
\(415\) −4.14723 + 7.18321i −0.203580 + 0.352610i
\(416\) 3.06702 + 2.35866i 0.150373 + 0.115643i
\(417\) 6.00383 + 10.3989i 0.294009 + 0.509238i
\(418\) 1.40605 0.811784i 0.0687722 0.0397056i
\(419\) 3.98203 6.89708i 0.194535 0.336944i −0.752213 0.658920i \(-0.771014\pi\)
0.946748 + 0.321976i \(0.104347\pi\)
\(420\) 0 0
\(421\) 2.81786i 0.137334i −0.997640 0.0686670i \(-0.978125\pi\)
0.997640 0.0686670i \(-0.0218746\pi\)
\(422\) 6.27614i 0.305518i
\(423\) 0.931562 + 0.537838i 0.0452941 + 0.0261506i
\(424\) −0.204122 + 0.117850i −0.00991306 + 0.00572331i
\(425\) −59.8165 −2.90152
\(426\) −15.7528 + 27.2847i −0.763227 + 1.32195i
\(427\) 0 0
\(428\) −1.25110 −0.0604742
\(429\) 1.24379 9.36943i 0.0600508 0.452360i
\(430\) 9.19253 + 15.9219i 0.443303 + 0.767823i
\(431\) 5.73626i 0.276306i 0.990411 + 0.138153i \(0.0441166\pi\)
−0.990411 + 0.138153i \(0.955883\pi\)
\(432\) 6.60028 + 11.4320i 0.317556 + 0.550023i
\(433\) 12.2628 + 21.2398i 0.589314 + 1.02072i 0.994322 + 0.106409i \(0.0339351\pi\)
−0.405009 + 0.914313i \(0.632732\pi\)
\(434\) 0 0
\(435\) 25.6215 14.7926i 1.22846 0.709251i
\(436\) 1.11158i 0.0532349i
\(437\) −1.34652 + 0.777413i −0.0644128 + 0.0371887i
\(438\) −1.04868 + 1.81637i −0.0501079 + 0.0867895i
\(439\) −18.3211 31.7332i −0.874420 1.51454i −0.857379 0.514686i \(-0.827909\pi\)
−0.0170416 0.999855i \(-0.505425\pi\)
\(440\) 11.6412 + 6.72108i 0.554975 + 0.320415i
\(441\) 0 0
\(442\) 4.93973 37.2108i 0.234959 1.76994i
\(443\) −13.5467 + 23.4635i −0.643622 + 1.11479i 0.340996 + 0.940065i \(0.389236\pi\)
−0.984618 + 0.174721i \(0.944098\pi\)
\(444\) 0.412158i 0.0195602i
\(445\) −27.0304 −1.28136
\(446\) −32.5886 −1.54312
\(447\) 21.4830i 1.01611i
\(448\) 0 0
\(449\) 23.7571 13.7162i 1.12117 0.647307i 0.179470 0.983764i \(-0.442562\pi\)
0.941699 + 0.336456i \(0.109228\pi\)
\(450\) 10.8315 + 6.25358i 0.510602 + 0.294796i
\(451\) 2.68446 4.64962i 0.126406 0.218942i
\(452\) 1.24354 0.0584911
\(453\) −8.36953 + 4.83215i −0.393235 + 0.227034i
\(454\) 20.6832 0.970712
\(455\) 0 0
\(456\) 5.70169 0.267006
\(457\) −34.3500 + 19.8320i −1.60682 + 0.927700i −0.616748 + 0.787161i \(0.711550\pi\)
−0.990075 + 0.140539i \(0.955116\pi\)
\(458\) −21.9964 −1.02783
\(459\) −14.2563 + 24.6927i −0.665429 + 1.15256i
\(460\) −0.968913 0.559402i −0.0451758 0.0260823i
\(461\) 4.23988 2.44790i 0.197471 0.114010i −0.398004 0.917384i \(-0.630297\pi\)
0.595475 + 0.803374i \(0.296964\pi\)
\(462\) 0 0
\(463\) 4.71193i 0.218982i 0.993988 + 0.109491i \(0.0349221\pi\)
−0.993988 + 0.109491i \(0.965078\pi\)
\(464\) −14.4928 −0.672810
\(465\) −37.6848 −1.74759
\(466\) 39.1605i 1.81408i
\(467\) −16.0081 + 27.7268i −0.740765 + 1.28304i 0.211383 + 0.977403i \(0.432203\pi\)
−0.952147 + 0.305639i \(0.901130\pi\)
\(468\) 0.503335 0.654496i 0.0232667 0.0302541i
\(469\) 0 0
\(470\) 3.71678 + 2.14588i 0.171442 + 0.0989822i
\(471\) −9.22761 15.9827i −0.425186 0.736444i
\(472\) 16.4781 28.5410i 0.758467 1.31370i
\(473\) 4.24191 2.44907i 0.195043 0.112608i
\(474\) 7.87452i 0.361689i
\(475\) −6.31788 + 3.64763i −0.289884 + 0.167365i
\(476\) 0 0
\(477\) 0.0481123 + 0.0833330i 0.00220291 + 0.00381556i
\(478\) 5.82086 + 10.0820i 0.266240 + 0.461141i
\(479\) 18.0245i 0.823560i −0.911283 0.411780i \(-0.864907\pi\)
0.911283 0.411780i \(-0.135093\pi\)
\(480\) 3.92447 + 6.79738i 0.179127 + 0.310257i
\(481\) −3.51948 + 1.45337i −0.160474 + 0.0662680i
\(482\) −24.4807 −1.11506
\(483\) 0 0
\(484\) −0.891390 + 1.54393i −0.0405177 + 0.0701788i
\(485\) 1.70739 0.0775284
\(486\) 13.7821 7.95712i 0.625170 0.360942i
\(487\) −15.2424 8.80020i −0.690699 0.398775i 0.113175 0.993575i \(-0.463898\pi\)
−0.803874 + 0.594800i \(0.797231\pi\)
\(488\) 22.4642i 1.01691i
\(489\) 24.6676i 1.11551i
\(490\) 0 0
\(491\) 1.93180 3.34598i 0.0871810 0.151002i −0.819138 0.573597i \(-0.805547\pi\)
0.906318 + 0.422595i \(0.138881\pi\)
\(492\) 1.41914 0.819339i 0.0639796 0.0369387i
\(493\) −15.6519 27.1099i −0.704926 1.22097i
\(494\) −1.74739 4.23148i −0.0786188 0.190383i
\(495\) 2.74388 4.75254i 0.123328 0.213611i
\(496\) 15.9872 + 9.23023i 0.717848 + 0.414450i
\(497\) 0 0
\(498\) −3.20576 5.55255i −0.143654 0.248816i
\(499\) 10.9528 + 6.32363i 0.490317 + 0.283084i 0.724706 0.689058i \(-0.241976\pi\)
−0.234389 + 0.972143i \(0.575309\pi\)
\(500\) −1.60519 0.926757i −0.0717863 0.0414458i
\(501\) −34.4826 19.9085i −1.54057 0.889448i
\(502\) −18.4908 10.6757i −0.825287 0.476480i
\(503\) 11.0180 + 19.0837i 0.491268 + 0.850902i 0.999949 0.0100533i \(-0.00320011\pi\)
−0.508681 + 0.860955i \(0.669867\pi\)
\(504\) 0 0
\(505\) 8.89351 + 5.13467i 0.395756 + 0.228490i
\(506\) 1.41674 2.45387i 0.0629818 0.109088i
\(507\) −25.7283 6.95339i −1.14263 0.308811i
\(508\) 1.40075 + 2.42617i 0.0621482 + 0.107644i
\(509\) 13.5708 7.83509i 0.601514 0.347284i −0.168123 0.985766i \(-0.553771\pi\)
0.769637 + 0.638482i \(0.220437\pi\)
\(510\) 38.0745 65.9470i 1.68597 2.92018i
\(511\) 0 0
\(512\) 24.9600i 1.10309i
\(513\) 3.47743i 0.153532i
\(514\) 28.3406 + 16.3625i 1.25005 + 0.721718i
\(515\) 35.0230 20.2206i 1.54330 0.891025i
\(516\) 1.49499 0.0658132
\(517\) 0.571705 0.990222i 0.0251436 0.0435499i
\(518\) 0 0
\(519\) −29.4795 −1.29401
\(520\) 23.1067 30.0461i 1.01330 1.31761i
\(521\) −12.6207 21.8598i −0.552925 0.957694i −0.998062 0.0622317i \(-0.980178\pi\)
0.445137 0.895463i \(-0.353155\pi\)
\(522\) 6.54538i 0.286483i
\(523\) −6.62383 11.4728i −0.289640 0.501671i 0.684084 0.729403i \(-0.260202\pi\)
−0.973724 + 0.227733i \(0.926869\pi\)
\(524\) 1.06479 + 1.84426i 0.0465154 + 0.0805670i
\(525\) 0 0
\(526\) 17.9812 10.3815i 0.784019 0.452654i
\(527\) 39.8738i 1.73693i
\(528\) −8.13422 + 4.69629i −0.353996 + 0.204380i
\(529\) 10.1432 17.5686i 0.441011 0.763853i
\(530\) 0.191960 + 0.332485i 0.00833822 + 0.0144422i
\(531\) −11.6518 6.72720i −0.505647 0.291935i
\(532\) 0 0
\(533\) −12.0007 9.22903i −0.519807 0.399754i
\(534\) 10.4471 18.0949i 0.452091 0.783044i
\(535\) 23.4477i 1.01373i
\(536\) −18.6252 −0.804485
\(537\) 11.1240 0.480036
\(538\) 17.5427i 0.756320i
\(539\) 0 0
\(540\) −2.16701 + 1.25112i −0.0932532 + 0.0538398i
\(541\) 12.4737 + 7.20170i 0.536287 + 0.309625i 0.743573 0.668655i \(-0.233130\pi\)
−0.207286 + 0.978280i \(0.566463\pi\)
\(542\) −18.1408 + 31.4208i −0.779214 + 1.34964i
\(543\) −31.7565 −1.36280
\(544\) 7.19224 4.15244i 0.308365 0.178034i
\(545\) 20.8328 0.892377
\(546\) 0 0
\(547\) 2.00679 0.0858042 0.0429021 0.999079i \(-0.486340\pi\)
0.0429021 + 0.999079i \(0.486340\pi\)
\(548\) 2.90665 1.67816i 0.124166 0.0716873i
\(549\) 9.17100 0.391409
\(550\) 6.64736 11.5136i 0.283445 0.490940i
\(551\) −3.30634 1.90892i −0.140855 0.0813226i
\(552\) 8.61757 4.97535i 0.366788 0.211765i
\(553\) 0 0
\(554\) 17.0863i 0.725928i
\(555\) −7.72451 −0.327887
\(556\) 1.11499 0.0472863
\(557\) 8.57916i 0.363511i −0.983344 0.181755i \(-0.941822\pi\)
0.983344 0.181755i \(-0.0581779\pi\)
\(558\) 4.16865 7.22032i 0.176473 0.305661i
\(559\) −5.27170 12.7659i −0.222969 0.539942i
\(560\) 0 0
\(561\) −17.5696 10.1438i −0.741788 0.428272i
\(562\) 17.9733 + 31.1306i 0.758157 + 1.31317i
\(563\) 6.38718 11.0629i 0.269188 0.466247i −0.699465 0.714667i \(-0.746578\pi\)
0.968652 + 0.248421i \(0.0799115\pi\)
\(564\) 0.302231 0.174493i 0.0127262 0.00734750i
\(565\) 23.3059i 0.980487i
\(566\) 17.1747 9.91583i 0.721908 0.416794i
\(567\) 0 0
\(568\) 16.8306 + 29.1515i 0.706196 + 1.22317i
\(569\) −2.89558 5.01530i −0.121389 0.210252i 0.798927 0.601429i \(-0.205402\pi\)
−0.920316 + 0.391176i \(0.872068\pi\)
\(570\) 9.28720i 0.388998i
\(571\) −22.0666 38.2204i −0.923458 1.59948i −0.794023 0.607888i \(-0.792017\pi\)
−0.129435 0.991588i \(-0.541316\pi\)
\(572\) −0.695710 0.535030i −0.0290891 0.0223707i
\(573\) −9.73025 −0.406487
\(574\) 0 0
\(575\) −6.36592 + 11.0261i −0.265477 + 0.459820i
\(576\) −10.3567 −0.431529
\(577\) 10.3343 5.96649i 0.430221 0.248388i −0.269220 0.963079i \(-0.586766\pi\)
0.699441 + 0.714691i \(0.253432\pi\)
\(578\) −49.9729 28.8518i −2.07860 1.20008i
\(579\) 43.1324i 1.79252i
\(580\) 2.74719i 0.114071i
\(581\) 0 0
\(582\) −0.659895 + 1.14297i −0.0273535 + 0.0473777i
\(583\) 0.0885805 0.0511420i 0.00366863 0.00211808i
\(584\) 1.12043 + 1.94064i 0.0463637 + 0.0803043i
\(585\) −12.2663 9.43332i −0.507150 0.390020i
\(586\) 7.79091 13.4943i 0.321840 0.557443i
\(587\) −17.6250 10.1758i −0.727462 0.420000i 0.0900312 0.995939i \(-0.471303\pi\)
−0.817493 + 0.575939i \(0.804637\pi\)
\(588\) 0 0
\(589\) 2.43152 + 4.21152i 0.100189 + 0.173533i
\(590\) −46.4889 26.8404i −1.91392 1.10500i
\(591\) −10.3190 5.95769i −0.424468 0.245067i
\(592\) 3.27701 + 1.89199i 0.134684 + 0.0777601i
\(593\) 15.7443 + 9.09000i 0.646543 + 0.373282i 0.787130 0.616787i \(-0.211566\pi\)
−0.140588 + 0.990068i \(0.544899\pi\)
\(594\) −3.16859 5.48817i −0.130009 0.225182i
\(595\) 0 0
\(596\) 1.72759 + 0.997422i 0.0707646 + 0.0408560i
\(597\) 10.8842 18.8520i 0.445460 0.771560i
\(598\) −6.33344 4.87068i −0.258994 0.199177i
\(599\) 19.1341 + 33.1412i 0.781797 + 1.35411i 0.930894 + 0.365290i \(0.119030\pi\)
−0.149096 + 0.988823i \(0.547636\pi\)
\(600\) 40.4337 23.3444i 1.65070 0.953031i
\(601\) −13.4360 + 23.2718i −0.548064 + 0.949275i 0.450343 + 0.892856i \(0.351302\pi\)
−0.998407 + 0.0564195i \(0.982032\pi\)
\(602\) 0 0
\(603\) 7.60372i 0.309648i
\(604\) 0.897398i 0.0365146i
\(605\) 28.9358 + 16.7061i 1.17641 + 0.679200i
\(606\) −6.87459 + 3.96904i −0.279261 + 0.161231i
\(607\) 9.40209 0.381619 0.190810 0.981627i \(-0.438889\pi\)
0.190810 + 0.981627i \(0.438889\pi\)
\(608\) 0.506435 0.877171i 0.0205386 0.0355740i
\(609\) 0 0
\(610\) 36.5908 1.48152
\(611\) −2.55577 1.96549i −0.103395 0.0795153i
\(612\) −0.886124 1.53481i −0.0358194 0.0620411i
\(613\) 13.2894i 0.536753i 0.963314 + 0.268376i \(0.0864871\pi\)
−0.963314 + 0.268376i \(0.913513\pi\)
\(614\) −19.7301 34.1735i −0.796242 1.37913i
\(615\) −15.3557 26.5969i −0.619204 1.07249i
\(616\) 0 0
\(617\) −9.72211 + 5.61306i −0.391397 + 0.225973i −0.682765 0.730638i \(-0.739223\pi\)
0.291368 + 0.956611i \(0.405890\pi\)
\(618\) 31.2606i 1.25748i
\(619\) −8.04109 + 4.64253i −0.323199 + 0.186599i −0.652817 0.757515i \(-0.726413\pi\)
0.329619 + 0.944114i \(0.393080\pi\)
\(620\) −1.74965 + 3.03048i −0.0702675 + 0.121707i
\(621\) 3.03444 + 5.25580i 0.121768 + 0.210908i
\(622\) 0.175512 + 0.101332i 0.00703740 + 0.00406304i
\(623\) 0 0
\(624\) 10.1089 + 24.4797i 0.404681 + 0.979974i
\(625\) 1.95363 3.38379i 0.0781452 0.135351i
\(626\) 14.1533i 0.565680i
\(627\) −2.47429 −0.0988137
\(628\) −1.71370 −0.0683839
\(629\) 8.17322i 0.325888i
\(630\) 0 0
\(631\) 9.00894 5.20132i 0.358640 0.207061i −0.309844 0.950787i \(-0.600277\pi\)
0.668484 + 0.743726i \(0.266943\pi\)
\(632\) 7.28611 + 4.20664i 0.289826 + 0.167331i
\(633\) −4.78237 + 8.28331i −0.190082 + 0.329232i
\(634\) −2.02693 −0.0804998
\(635\) 45.4704 26.2523i 1.80444 1.04179i
\(636\) 0.0312187 0.00123790
\(637\) 0 0
\(638\) 6.95754 0.275452
\(639\) 11.9011 6.87109i 0.470800 0.271816i
\(640\) −33.6644 −1.33070
\(641\) 7.42955 12.8684i 0.293449 0.508269i −0.681174 0.732122i \(-0.738530\pi\)
0.974623 + 0.223853i \(0.0718634\pi\)
\(642\) −15.6965 9.06239i −0.619492 0.357664i
\(643\) −1.98945 + 1.14861i −0.0784563 + 0.0452968i −0.538715 0.842488i \(-0.681090\pi\)
0.460259 + 0.887785i \(0.347757\pi\)
\(644\) 0 0
\(645\) 28.0185i 1.10323i
\(646\) −9.82669 −0.386626
\(647\) 7.99865 0.314459 0.157230 0.987562i \(-0.449744\pi\)
0.157230 + 0.987562i \(0.449744\pi\)
\(648\) 32.8885i 1.29198i
\(649\) −7.15081 + 12.3856i −0.280694 + 0.486176i
\(650\) −29.7166 22.8533i −1.16558 0.896380i
\(651\) 0 0
\(652\) 1.98368 + 1.14528i 0.0776871 + 0.0448526i
\(653\) −1.99222 3.45062i −0.0779615 0.135033i 0.824409 0.565995i \(-0.191508\pi\)
−0.902370 + 0.430962i \(0.858174\pi\)
\(654\) −8.05175 + 13.9460i −0.314848 + 0.545333i
\(655\) 34.5645 19.9558i 1.35055 0.779738i
\(656\) 15.0445i 0.587389i
\(657\) 0.792267 0.457415i 0.0309093 0.0178455i
\(658\) 0 0
\(659\) 13.7501 + 23.8159i 0.535629 + 0.927737i 0.999133 + 0.0416417i \(0.0132588\pi\)
−0.463504 + 0.886095i \(0.653408\pi\)
\(660\) −0.890211 1.54189i −0.0346514 0.0600180i
\(661\) 6.98621i 0.271732i −0.990727 0.135866i \(-0.956618\pi\)
0.990727 0.135866i \(-0.0433817\pi\)
\(662\) 16.9841 + 29.4173i 0.660105 + 1.14333i
\(663\) −34.8739 + 45.3472i −1.35439 + 1.76114i
\(664\) −6.85019 −0.265839
\(665\) 0 0
\(666\) 0.854479 1.48000i 0.0331104 0.0573488i
\(667\) −6.66296 −0.257991
\(668\) −3.20195 + 1.84865i −0.123887 + 0.0715263i
\(669\) 43.0108 + 24.8323i 1.66289 + 0.960071i
\(670\) 30.3376i 1.17204i
\(671\) 9.74849i 0.376336i
\(672\) 0 0
\(673\) 2.72783 4.72474i 0.105150 0.182125i −0.808649 0.588291i \(-0.799801\pi\)
0.913800 + 0.406166i \(0.133134\pi\)
\(674\) 37.4910 21.6455i 1.44410 0.833752i
\(675\) 14.2376 + 24.6603i 0.548006 + 0.949174i
\(676\) −1.75369 + 1.74614i −0.0674497 + 0.0671594i
\(677\) 16.8961 29.2649i 0.649371 1.12474i −0.333903 0.942607i \(-0.608366\pi\)
0.983273 0.182135i \(-0.0583009\pi\)
\(678\) 15.6016 + 9.00761i 0.599177 + 0.345935i
\(679\) 0 0
\(680\) −40.6795 70.4590i −1.55999 2.70198i
\(681\) −27.2979 15.7605i −1.04606 0.603942i
\(682\) −7.67498 4.43115i −0.293890 0.169678i
\(683\) −10.6511 6.14942i −0.407553 0.235301i 0.282185 0.959360i \(-0.408941\pi\)
−0.689738 + 0.724059i \(0.742274\pi\)
\(684\) −0.187187 0.108072i −0.00715726 0.00413225i
\(685\) −31.4514 54.4754i −1.20170 2.08140i
\(686\) 0 0
\(687\) 29.0311 + 16.7611i 1.10760 + 0.639476i
\(688\) −6.86265 + 11.8865i −0.261636 + 0.453167i
\(689\) −0.110085 0.266581i −0.00419389 0.0101559i
\(690\) −8.10410 14.0367i −0.308518 0.534369i
\(691\) −9.60393 + 5.54483i −0.365351 + 0.210935i −0.671425 0.741072i \(-0.734318\pi\)
0.306075 + 0.952008i \(0.400984\pi\)
\(692\) −1.36869 + 2.37064i −0.0520297 + 0.0901181i
\(693\) 0 0
\(694\) 33.3129i 1.26454i
\(695\) 20.8968i 0.792662i
\(696\) 21.1602 + 12.2168i 0.802075 + 0.463078i
\(697\) −28.1419 + 16.2478i −1.06595 + 0.615428i
\(698\) 15.5449 0.588385
\(699\) 29.8400 51.6844i 1.12865 1.95488i
\(700\) 0 0
\(701\) 10.6470 0.402133 0.201066 0.979578i \(-0.435559\pi\)
0.201066 + 0.979578i \(0.435559\pi\)
\(702\) −16.5165 + 6.82050i −0.623375 + 0.257423i
\(703\) 0.498406 + 0.863265i 0.0187977 + 0.0325587i
\(704\) 11.0089i 0.414912i
\(705\) −3.27029 5.66431i −0.123166 0.213330i
\(706\) 13.5117 + 23.4030i 0.508521 + 0.880784i
\(707\) 0 0
\(708\) −3.78027 + 2.18254i −0.142071 + 0.0820248i
\(709\) 40.7069i 1.52878i −0.644754 0.764391i \(-0.723040\pi\)
0.644754 0.764391i \(-0.276960\pi\)
\(710\) 47.4833 27.4145i 1.78202 1.02885i
\(711\) 1.71736 2.97455i 0.0644060 0.111554i
\(712\) −11.1619 19.3329i −0.418309 0.724532i
\(713\) 7.35003 + 4.24354i 0.275261 + 0.158922i
\(714\) 0 0
\(715\) −10.0273 + 13.0387i −0.375001 + 0.487621i
\(716\) 0.516470 0.894552i 0.0193014 0.0334310i
\(717\) 17.7418i 0.662579i
\(718\) −20.2470 −0.755612
\(719\) −9.77537 −0.364560 −0.182280 0.983247i \(-0.558348\pi\)
−0.182280 + 0.983247i \(0.558348\pi\)
\(720\) 15.3775i 0.573086i
\(721\) 0 0
\(722\) 21.0971 12.1804i 0.785153 0.453308i
\(723\) 32.3098 + 18.6541i 1.20161 + 0.693752i
\(724\) −1.47441 + 2.55375i −0.0547959 + 0.0949092i
\(725\) −31.2627 −1.16107
\(726\) −22.3671 + 12.9136i −0.830120 + 0.479270i
\(727\) 12.2091 0.452811 0.226406 0.974033i \(-0.427303\pi\)
0.226406 + 0.974033i \(0.427303\pi\)
\(728\) 0 0
\(729\) 9.23219 0.341933
\(730\) 3.16101 1.82501i 0.116994 0.0675467i
\(731\) −29.6461 −1.09650
\(732\) 1.48770 2.57677i 0.0549869 0.0952400i
\(733\) −19.3256 11.1577i −0.713809 0.412118i 0.0986608 0.995121i \(-0.468544\pi\)
−0.812470 + 0.583003i \(0.801877\pi\)
\(734\) −10.4891 + 6.05591i −0.387161 + 0.223528i
\(735\) 0 0
\(736\) 1.76768i 0.0651576i
\(737\) 8.08253 0.297724
\(738\) 6.79456 0.250111
\(739\) 42.3729i 1.55871i −0.626580 0.779357i \(-0.715546\pi\)
0.626580 0.779357i \(-0.284454\pi\)
\(740\) −0.358637 + 0.621178i −0.0131838 + 0.0228350i
\(741\) −0.918130 + 6.91624i −0.0337283 + 0.254074i
\(742\) 0 0
\(743\) −26.8296 15.4901i −0.984282 0.568276i −0.0807220 0.996737i \(-0.525723\pi\)
−0.903560 + 0.428461i \(0.859056\pi\)
\(744\) −15.5615 26.9532i −0.570511 0.988153i
\(745\) 18.6933 32.3778i 0.684870 1.18623i
\(746\) −18.8020 + 10.8553i −0.688390 + 0.397442i
\(747\) 2.79659i 0.102322i
\(748\) −1.63146 + 0.941923i −0.0596520 + 0.0344401i
\(749\) 0 0
\(750\) −13.4260 23.2545i −0.490248 0.849135i
\(751\) 11.2830 + 19.5427i 0.411722 + 0.713123i 0.995078 0.0990930i \(-0.0315941\pi\)
−0.583356 + 0.812216i \(0.698261\pi\)
\(752\) 3.20400i 0.116838i
\(753\) 16.2696 + 28.1798i 0.592897 + 1.02693i
\(754\) 2.58172 19.4480i 0.0940206 0.708254i
\(755\) 16.8187 0.612095
\(756\) 0 0
\(757\) −16.1404 + 27.9560i −0.586633 + 1.01608i 0.408037 + 0.912965i \(0.366213\pi\)
−0.994670 + 0.103112i \(0.967120\pi\)
\(758\) −21.0737 −0.765431
\(759\) −3.73966 + 2.15909i −0.135741 + 0.0783701i
\(760\) −8.59323 4.96130i −0.311709 0.179965i
\(761\) 29.7517i 1.07850i −0.842147 0.539249i \(-0.818708\pi\)
0.842147 0.539249i \(-0.181292\pi\)
\(762\) 40.5855i 1.47026i
\(763\) 0 0
\(764\) −0.451761 + 0.782473i −0.0163441 + 0.0283089i
\(765\) −28.7649 + 16.6074i −1.04000 + 0.600442i
\(766\) 16.5684 + 28.6972i 0.598639 + 1.03687i
\(767\) 31.9672 + 24.5841i 1.15427 + 0.887680i
\(768\) −4.63947 + 8.03581i −0.167413 + 0.289967i
\(769\) 36.2090 + 20.9053i 1.30573 + 0.753863i 0.981380 0.192075i \(-0.0615215\pi\)
0.324349 + 0.945938i \(0.394855\pi\)
\(770\) 0 0
\(771\) −24.9361 43.1907i −0.898053 1.55547i
\(772\) −3.46856 2.00257i −0.124836 0.0720742i
\(773\) −35.8826 20.7168i −1.29061 0.745132i −0.311845 0.950133i \(-0.600947\pi\)
−0.978762 + 0.205001i \(0.934280\pi\)
\(774\) 5.36829 + 3.09938i 0.192959 + 0.111405i
\(775\) 34.4864 + 19.9107i 1.23879 + 0.715215i
\(776\) 0.705044 + 1.22117i 0.0253096 + 0.0438375i
\(777\) 0 0
\(778\) −21.9680 12.6832i −0.787592 0.454716i
\(779\) −1.98159 + 3.43221i −0.0709978 + 0.122972i
\(780\) −4.64028 + 1.91621i −0.166149 + 0.0686112i
\(781\) −7.30376 12.6505i −0.261349