Properties

Label 91.2.q.a.36.5
Level $91$
Weight $2$
Character 91.36
Analytic conductor $0.727$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 36.5
Root \(1.40744 + 0.138282i\) of defining polynomial
Character \(\chi\) \(=\) 91.36
Dual form 91.2.q.a.43.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.10554 - 0.638282i) q^{2} +(0.583963 + 1.01145i) q^{3} +(-0.185192 + 0.320762i) q^{4} -1.81487i q^{5} +(1.29118 + 0.745466i) q^{6} +(-0.866025 - 0.500000i) q^{7} +3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +O(q^{10})\) \(q+(1.10554 - 0.638282i) q^{2} +(0.583963 + 1.01145i) q^{3} +(-0.185192 + 0.320762i) q^{4} -1.81487i q^{5} +(1.29118 + 0.745466i) q^{6} +(-0.866025 - 0.500000i) q^{7} +3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +(-1.15840 - 2.00641i) q^{10} +(-2.40625 + 1.38925i) q^{11} -0.432581 q^{12} +(-3.58305 - 0.402155i) q^{13} -1.27656 q^{14} +(1.83566 - 1.05982i) q^{15} +(1.56102 + 2.70377i) q^{16} +(1.37198 - 2.37634i) q^{17} -2.08840i q^{18} +(-5.08351 - 2.93497i) q^{19} +(0.582143 + 0.336100i) q^{20} -1.16793i q^{21} +(-1.77346 + 3.07173i) q^{22} +(3.49955 + 6.06139i) q^{23} +(-3.06060 + 1.76704i) q^{24} +1.70623 q^{25} +(-4.21789 + 1.84240i) q^{26} +5.41444 q^{27} +(0.320762 - 0.185192i) q^{28} +(1.75806 + 3.04505i) q^{29} +(1.35293 - 2.34334i) q^{30} +2.06697i q^{31} +(-1.78956 - 1.03320i) q^{32} +(-2.81031 - 1.62254i) q^{33} -3.50284i q^{34} +(-0.907437 + 1.57173i) q^{35} +(0.302965 + 0.524751i) q^{36} +(1.50950 - 0.871512i) q^{37} -7.49334 q^{38} +(-1.68561 - 3.85893i) q^{39} +5.49171 q^{40} +(5.51406 - 3.18355i) q^{41} +(-0.745466 - 1.29118i) q^{42} +(4.55195 - 7.88422i) q^{43} -1.02911i q^{44} +(-2.57127 - 1.48452i) q^{45} +(7.73776 + 4.46740i) q^{46} +6.65932i q^{47} +(-1.82316 + 3.15780i) q^{48} +(0.500000 + 0.866025i) q^{49} +(1.88631 - 1.08906i) q^{50} +3.20474 q^{51} +(0.792549 - 1.07483i) q^{52} -10.4879 q^{53} +(5.98587 - 3.45594i) q^{54} +(2.52131 + 4.36703i) q^{55} +(1.51297 - 2.62055i) q^{56} -6.85564i q^{57} +(3.88720 + 2.24427i) q^{58} +(2.66212 + 1.53698i) q^{59} +0.785080i q^{60} +(-0.540892 + 0.936853i) q^{61} +(1.31931 + 2.28511i) q^{62} +(-1.41677 + 0.817975i) q^{63} -8.88199 q^{64} +(-0.729860 + 6.50279i) q^{65} -4.14254 q^{66} +(4.34568 - 2.50898i) q^{67} +(0.508159 + 0.880158i) q^{68} +(-4.08721 + 7.07925i) q^{69} +2.31680i q^{70} +(2.35453 + 1.35939i) q^{71} +(4.28709 + 2.47515i) q^{72} -7.67213i q^{73} +(1.11254 - 1.92698i) q^{74} +(0.996377 + 1.72578i) q^{75} +(1.88285 - 1.08706i) q^{76} +2.77849 q^{77} +(-4.32659 - 3.19030i) q^{78} -15.7399 q^{79} +(4.90700 - 2.83306i) q^{80} +(0.707906 + 1.22613i) q^{81} +(4.06400 - 7.03905i) q^{82} +7.97408i q^{83} +(0.374626 + 0.216290i) q^{84} +(-4.31275 - 2.48997i) q^{85} -11.6217i q^{86} +(-2.05328 + 3.55639i) q^{87} +(-4.20379 - 7.28117i) q^{88} +(-13.9118 + 8.03198i) q^{89} -3.79017 q^{90} +(2.90194 + 2.13980i) q^{91} -2.59235 q^{92} +(-2.09064 + 1.20703i) q^{93} +(4.25052 + 7.36212i) q^{94} +(-5.32659 + 9.22592i) q^{95} -2.41340i q^{96} +(-12.3209 - 7.11347i) q^{97} +(1.10554 + 0.638282i) q^{98} +4.54548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{4} - 18q^{6} - 4q^{9} + O(q^{10}) \) \( 12q + 4q^{4} - 18q^{6} - 4q^{9} + 12q^{10} + 6q^{11} - 4q^{12} + 4q^{13} - 8q^{14} + 6q^{15} - 8q^{16} - 4q^{17} - 12q^{20} + 6q^{22} - 12q^{23} + 12q^{24} - 20q^{25} - 42q^{26} + 12q^{27} + 8q^{29} + 8q^{30} + 36q^{32} - 30q^{33} + 6q^{35} - 10q^{36} - 42q^{37} + 4q^{38} - 4q^{39} + 92q^{40} + 30q^{41} + 4q^{42} + 2q^{43} + 12q^{46} - 2q^{48} + 6q^{49} - 18q^{50} + 52q^{51} + 2q^{52} - 44q^{53} + 12q^{54} - 6q^{55} - 12q^{56} - 12q^{58} + 18q^{59} + 14q^{61} - 4q^{62} + 12q^{63} - 52q^{64} + 60q^{65} - 52q^{66} - 24q^{67} - 8q^{68} + 4q^{69} - 24q^{71} + 60q^{72} + 6q^{74} + 46q^{75} - 18q^{76} + 8q^{77} - 10q^{78} - 56q^{79} - 72q^{80} + 2q^{81} + 14q^{82} + 18q^{84} - 48q^{85} - 2q^{87} - 14q^{88} - 12q^{89} + 24q^{90} + 14q^{91} + 24q^{92} - 18q^{93} + 4q^{94} - 22q^{95} + 6q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.10554 0.638282i 0.781733 0.451334i −0.0553113 0.998469i \(-0.517615\pi\)
0.837044 + 0.547136i \(0.184282\pi\)
\(3\) 0.583963 + 1.01145i 0.337151 + 0.583963i 0.983896 0.178744i \(-0.0572034\pi\)
−0.646745 + 0.762707i \(0.723870\pi\)
\(4\) −0.185192 + 0.320762i −0.0925960 + 0.160381i
\(5\) 1.81487i 0.811636i −0.913954 0.405818i \(-0.866987\pi\)
0.913954 0.405818i \(-0.133013\pi\)
\(6\) 1.29118 + 0.745466i 0.527124 + 0.304335i
\(7\) −0.866025 0.500000i −0.327327 0.188982i
\(8\) 3.02595i 1.06983i
\(9\) 0.817975 1.41677i 0.272658 0.472258i
\(10\) −1.15840 2.00641i −0.366319 0.634482i
\(11\) −2.40625 + 1.38925i −0.725510 + 0.418874i −0.816777 0.576953i \(-0.804242\pi\)
0.0912671 + 0.995826i \(0.470908\pi\)
\(12\) −0.432581 −0.124875
\(13\) −3.58305 0.402155i −0.993760 0.111538i
\(14\) −1.27656 −0.341176
\(15\) 1.83566 1.05982i 0.473965 0.273644i
\(16\) 1.56102 + 2.70377i 0.390256 + 0.675943i
\(17\) 1.37198 2.37634i 0.332754 0.576347i −0.650297 0.759680i \(-0.725355\pi\)
0.983051 + 0.183334i \(0.0586888\pi\)
\(18\) 2.08840i 0.492240i
\(19\) −5.08351 2.93497i −1.16624 0.673327i −0.213446 0.976955i \(-0.568469\pi\)
−0.952791 + 0.303628i \(0.901802\pi\)
\(20\) 0.582143 + 0.336100i 0.130171 + 0.0751543i
\(21\) 1.16793i 0.254862i
\(22\) −1.77346 + 3.07173i −0.378103 + 0.654894i
\(23\) 3.49955 + 6.06139i 0.729706 + 1.26389i 0.957007 + 0.290063i \(0.0936763\pi\)
−0.227302 + 0.973824i \(0.572990\pi\)
\(24\) −3.06060 + 1.76704i −0.624743 + 0.360696i
\(25\) 1.70623 0.341247
\(26\) −4.21789 + 1.84240i −0.827195 + 0.361325i
\(27\) 5.41444 1.04201
\(28\) 0.320762 0.185192i 0.0606183 0.0349980i
\(29\) 1.75806 + 3.04505i 0.326463 + 0.565451i 0.981807 0.189879i \(-0.0608097\pi\)
−0.655344 + 0.755330i \(0.727476\pi\)
\(30\) 1.35293 2.34334i 0.247009 0.427833i
\(31\) 2.06697i 0.371238i 0.982622 + 0.185619i \(0.0594290\pi\)
−0.982622 + 0.185619i \(0.940571\pi\)
\(32\) −1.78956 1.03320i −0.316352 0.182646i
\(33\) −2.81031 1.62254i −0.489213 0.282447i
\(34\) 3.50284i 0.600732i
\(35\) −0.907437 + 1.57173i −0.153385 + 0.265670i
\(36\) 0.302965 + 0.524751i 0.0504942 + 0.0874585i
\(37\) 1.50950 0.871512i 0.248161 0.143276i −0.370761 0.928728i \(-0.620903\pi\)
0.618922 + 0.785453i \(0.287570\pi\)
\(38\) −7.49334 −1.21558
\(39\) −1.68561 3.85893i −0.269913 0.617924i
\(40\) 5.49171 0.868316
\(41\) 5.51406 3.18355i 0.861152 0.497186i −0.00324599 0.999995i \(-0.501033\pi\)
0.864398 + 0.502808i \(0.167700\pi\)
\(42\) −0.745466 1.29118i −0.115028 0.199234i
\(43\) 4.55195 7.88422i 0.694167 1.20233i −0.276294 0.961073i \(-0.589106\pi\)
0.970461 0.241259i \(-0.0775603\pi\)
\(44\) 1.02911i 0.155144i
\(45\) −2.57127 1.48452i −0.383302 0.221299i
\(46\) 7.73776 + 4.46740i 1.14087 + 0.658681i
\(47\) 6.65932i 0.971361i 0.874136 + 0.485681i \(0.161428\pi\)
−0.874136 + 0.485681i \(0.838572\pi\)
\(48\) −1.82316 + 3.15780i −0.263150 + 0.455790i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 1.88631 1.08906i 0.266764 0.154016i
\(51\) 3.20474 0.448753
\(52\) 0.792549 1.07483i 0.109907 0.149052i
\(53\) −10.4879 −1.44063 −0.720313 0.693649i \(-0.756002\pi\)
−0.720313 + 0.693649i \(0.756002\pi\)
\(54\) 5.98587 3.45594i 0.814573 0.470294i
\(55\) 2.52131 + 4.36703i 0.339973 + 0.588850i
\(56\) 1.51297 2.62055i 0.202180 0.350185i
\(57\) 6.85564i 0.908052i
\(58\) 3.88720 + 2.24427i 0.510414 + 0.294688i
\(59\) 2.66212 + 1.53698i 0.346579 + 0.200097i 0.663177 0.748462i \(-0.269207\pi\)
−0.316598 + 0.948560i \(0.602541\pi\)
\(60\) 0.785080i 0.101353i
\(61\) −0.540892 + 0.936853i −0.0692541 + 0.119952i −0.898573 0.438824i \(-0.855395\pi\)
0.829319 + 0.558775i \(0.188729\pi\)
\(62\) 1.31931 + 2.28511i 0.167552 + 0.290209i
\(63\) −1.41677 + 0.817975i −0.178497 + 0.103055i
\(64\) −8.88199 −1.11025
\(65\) −0.729860 + 6.50279i −0.0905280 + 0.806572i
\(66\) −4.14254 −0.509912
\(67\) 4.34568 2.50898i 0.530910 0.306521i −0.210477 0.977599i \(-0.567502\pi\)
0.741387 + 0.671078i \(0.234168\pi\)
\(68\) 0.508159 + 0.880158i 0.0616234 + 0.106735i
\(69\) −4.08721 + 7.07925i −0.492042 + 0.852242i
\(70\) 2.31680i 0.276911i
\(71\) 2.35453 + 1.35939i 0.279431 + 0.161330i 0.633166 0.774016i \(-0.281755\pi\)
−0.353735 + 0.935346i \(0.615088\pi\)
\(72\) 4.28709 + 2.47515i 0.505238 + 0.291699i
\(73\) 7.67213i 0.897955i −0.893543 0.448978i \(-0.851788\pi\)
0.893543 0.448978i \(-0.148212\pi\)
\(74\) 1.11254 1.92698i 0.129330 0.224006i
\(75\) 0.996377 + 1.72578i 0.115052 + 0.199275i
\(76\) 1.88285 1.08706i 0.215978 0.124695i
\(77\) 2.77849 0.316639
\(78\) −4.32659 3.19030i −0.489890 0.361230i
\(79\) −15.7399 −1.77087 −0.885436 0.464761i \(-0.846140\pi\)
−0.885436 + 0.464761i \(0.846140\pi\)
\(80\) 4.90700 2.83306i 0.548620 0.316746i
\(81\) 0.707906 + 1.22613i 0.0786563 + 0.136237i
\(82\) 4.06400 7.03905i 0.448794 0.777333i
\(83\) 7.97408i 0.875269i 0.899153 + 0.437635i \(0.144184\pi\)
−0.899153 + 0.437635i \(0.855816\pi\)
\(84\) 0.374626 + 0.216290i 0.0408751 + 0.0235992i
\(85\) −4.31275 2.48997i −0.467784 0.270075i
\(86\) 11.6217i 1.25320i
\(87\) −2.05328 + 3.55639i −0.220135 + 0.381285i
\(88\) −4.20379 7.28117i −0.448125 0.776176i
\(89\) −13.9118 + 8.03198i −1.47465 + 0.851388i −0.999592 0.0285683i \(-0.990905\pi\)
−0.475055 + 0.879956i \(0.657572\pi\)
\(90\) −3.79017 −0.399519
\(91\) 2.90194 + 2.13980i 0.304206 + 0.224312i
\(92\) −2.59235 −0.270271
\(93\) −2.09064 + 1.20703i −0.216789 + 0.125163i
\(94\) 4.25052 + 7.36212i 0.438408 + 0.759345i
\(95\) −5.32659 + 9.22592i −0.546497 + 0.946560i
\(96\) 2.41340i 0.246317i
\(97\) −12.3209 7.11347i −1.25100 0.722263i −0.279689 0.960091i \(-0.590231\pi\)
−0.971307 + 0.237827i \(0.923565\pi\)
\(98\) 1.10554 + 0.638282i 0.111676 + 0.0644762i
\(99\) 4.54548i 0.456838i
\(100\) −0.315981 + 0.547295i −0.0315981 + 0.0547295i
\(101\) −0.0365612 0.0633259i −0.00363798 0.00630117i 0.864201 0.503147i \(-0.167825\pi\)
−0.867839 + 0.496846i \(0.834491\pi\)
\(102\) 3.54296 2.04553i 0.350805 0.202537i
\(103\) 12.9196 1.27301 0.636503 0.771275i \(-0.280380\pi\)
0.636503 + 0.771275i \(0.280380\pi\)
\(104\) 1.21690 10.8421i 0.119327 1.06316i
\(105\) −2.11964 −0.206855
\(106\) −11.5948 + 6.69425i −1.12618 + 0.650203i
\(107\) −2.00427 3.47150i −0.193761 0.335603i 0.752733 0.658326i \(-0.228735\pi\)
−0.946493 + 0.322723i \(0.895402\pi\)
\(108\) −1.00271 + 1.73675i −0.0964860 + 0.167119i
\(109\) 1.98589i 0.190214i −0.995467 0.0951071i \(-0.969681\pi\)
0.995467 0.0951071i \(-0.0303194\pi\)
\(110\) 5.57479 + 3.21861i 0.531536 + 0.306882i
\(111\) 1.76299 + 1.01786i 0.167335 + 0.0966110i
\(112\) 3.12205i 0.295006i
\(113\) 5.28711 9.15754i 0.497369 0.861469i −0.502626 0.864504i \(-0.667633\pi\)
0.999995 + 0.00303506i \(0.000966090\pi\)
\(114\) −4.37583 7.57916i −0.409834 0.709854i
\(115\) 11.0007 6.35123i 1.02582 0.592256i
\(116\) −1.30231 −0.120917
\(117\) −3.50061 + 4.74743i −0.323632 + 0.438900i
\(118\) 3.92410 0.361243
\(119\) −2.37634 + 1.37198i −0.217839 + 0.125769i
\(120\) 3.20695 + 5.55461i 0.292753 + 0.507064i
\(121\) −1.63999 + 2.84054i −0.149090 + 0.258231i
\(122\) 1.38097i 0.125027i
\(123\) 6.44001 + 3.71814i 0.580676 + 0.335254i
\(124\) −0.663004 0.382786i −0.0595395 0.0343752i
\(125\) 12.1710i 1.08860i
\(126\) −1.04420 + 1.80860i −0.0930246 + 0.161123i
\(127\) 5.63478 + 9.75972i 0.500006 + 0.866035i 1.00000 6.53271e-6i \(2.07943e-6\pi\)
−0.499994 + 0.866029i \(0.666665\pi\)
\(128\) −6.24025 + 3.60281i −0.551566 + 0.318447i
\(129\) 10.6327 0.936156
\(130\) 3.34373 + 7.65493i 0.293264 + 0.671382i
\(131\) 3.06481 0.267774 0.133887 0.990997i \(-0.457254\pi\)
0.133887 + 0.990997i \(0.457254\pi\)
\(132\) 1.04090 0.600962i 0.0905984 0.0523070i
\(133\) 2.93497 + 5.08351i 0.254494 + 0.440796i
\(134\) 3.20288 5.54754i 0.276686 0.479235i
\(135\) 9.82653i 0.845733i
\(136\) 7.19067 + 4.15154i 0.616595 + 0.355991i
\(137\) 18.9512 + 10.9415i 1.61911 + 0.934796i 0.987150 + 0.159799i \(0.0510845\pi\)
0.631965 + 0.774997i \(0.282249\pi\)
\(138\) 10.4352i 0.888300i
\(139\) −5.53535 + 9.58750i −0.469502 + 0.813201i −0.999392 0.0348652i \(-0.988900\pi\)
0.529890 + 0.848066i \(0.322233\pi\)
\(140\) −0.336100 0.582143i −0.0284056 0.0492000i
\(141\) −6.73559 + 3.88879i −0.567239 + 0.327495i
\(142\) 3.47069 0.291254
\(143\) 9.18040 4.01006i 0.767703 0.335338i
\(144\) 5.10752 0.425626
\(145\) 5.52637 3.19065i 0.458940 0.264969i
\(146\) −4.89699 8.48183i −0.405277 0.701961i
\(147\) −0.583963 + 1.01145i −0.0481644 + 0.0834232i
\(148\) 0.645588i 0.0530670i
\(149\) −1.99824 1.15369i −0.163702 0.0945136i 0.415911 0.909406i \(-0.363463\pi\)
−0.579613 + 0.814892i \(0.696796\pi\)
\(150\) 2.20306 + 1.27194i 0.179879 + 0.103853i
\(151\) 20.6158i 1.67769i −0.544371 0.838845i \(-0.683232\pi\)
0.544371 0.838845i \(-0.316768\pi\)
\(152\) 8.88105 15.3824i 0.720348 1.24768i
\(153\) −2.24449 3.88757i −0.181456 0.314292i
\(154\) 3.07173 1.77346i 0.247527 0.142910i
\(155\) 3.75128 0.301310
\(156\) 1.54996 + 0.173964i 0.124096 + 0.0139283i
\(157\) 2.89649 0.231165 0.115582 0.993298i \(-0.463127\pi\)
0.115582 + 0.993298i \(0.463127\pi\)
\(158\) −17.4010 + 10.0465i −1.38435 + 0.799254i
\(159\) −6.12455 10.6080i −0.485709 0.841272i
\(160\) −1.87513 + 3.24782i −0.148242 + 0.256763i
\(161\) 6.99909i 0.551606i
\(162\) 1.56523 + 0.903688i 0.122976 + 0.0710004i
\(163\) −20.2944 11.7170i −1.58958 0.917743i −0.993376 0.114907i \(-0.963343\pi\)
−0.596201 0.802835i \(-0.703324\pi\)
\(164\) 2.35827i 0.184150i
\(165\) −2.94470 + 5.10037i −0.229244 + 0.397063i
\(166\) 5.08971 + 8.81564i 0.395038 + 0.684226i
\(167\) 6.58349 3.80098i 0.509446 0.294129i −0.223160 0.974782i \(-0.571637\pi\)
0.732606 + 0.680653i \(0.238304\pi\)
\(168\) 3.53408 0.272660
\(169\) 12.6765 + 2.88188i 0.975119 + 0.221683i
\(170\) −6.35721 −0.487576
\(171\) −8.31637 + 4.80146i −0.635969 + 0.367177i
\(172\) 1.68597 + 2.92019i 0.128554 + 0.222662i
\(173\) 2.69861 4.67412i 0.205171 0.355367i −0.745016 0.667047i \(-0.767558\pi\)
0.950187 + 0.311679i \(0.100892\pi\)
\(174\) 5.24229i 0.397417i
\(175\) −1.47764 0.853117i −0.111699 0.0644896i
\(176\) −7.51241 4.33729i −0.566269 0.326936i
\(177\) 3.59015i 0.269852i
\(178\) −10.2533 + 17.7593i −0.768520 + 1.33112i
\(179\) −6.14571 10.6447i −0.459352 0.795621i 0.539575 0.841938i \(-0.318585\pi\)
−0.998927 + 0.0463168i \(0.985252\pi\)
\(180\) 0.952357 0.549843i 0.0709845 0.0409829i
\(181\) −21.8525 −1.62428 −0.812140 0.583463i \(-0.801697\pi\)
−0.812140 + 0.583463i \(0.801697\pi\)
\(182\) 4.57400 + 0.513376i 0.339047 + 0.0380540i
\(183\) −1.26344 −0.0933964
\(184\) −18.3415 + 10.5894i −1.35215 + 0.780664i
\(185\) −1.58168 2.73956i −0.116288 0.201416i
\(186\) −1.54085 + 2.66883i −0.112981 + 0.195688i
\(187\) 7.62407i 0.557527i
\(188\) −2.13606 1.23325i −0.155788 0.0899442i
\(189\) −4.68905 2.70722i −0.341078 0.196921i
\(190\) 13.5995i 0.986609i
\(191\) −1.37858 + 2.38777i −0.0997507 + 0.172773i −0.911581 0.411120i \(-0.865138\pi\)
0.811831 + 0.583893i \(0.198471\pi\)
\(192\) −5.18675 8.98371i −0.374321 0.648344i
\(193\) 11.2491 6.49467i 0.809728 0.467497i −0.0371334 0.999310i \(-0.511823\pi\)
0.846861 + 0.531814i \(0.178489\pi\)
\(194\) −18.1616 −1.30393
\(195\) −7.00347 + 3.05917i −0.501529 + 0.219071i
\(196\) −0.370384 −0.0264560
\(197\) 16.4772 9.51312i 1.17395 0.677781i 0.219344 0.975648i \(-0.429608\pi\)
0.954608 + 0.297866i \(0.0962749\pi\)
\(198\) 2.90130 + 5.02519i 0.206186 + 0.357125i
\(199\) −10.0159 + 17.3480i −0.710006 + 1.22977i 0.254848 + 0.966981i \(0.417975\pi\)
−0.964854 + 0.262786i \(0.915359\pi\)
\(200\) 5.16298i 0.365078i
\(201\) 5.07543 + 2.93030i 0.357993 + 0.206688i
\(202\) −0.0808396 0.0466728i −0.00568785 0.00328388i
\(203\) 3.51612i 0.246783i
\(204\) −0.593492 + 1.02796i −0.0415528 + 0.0719715i
\(205\) −5.77773 10.0073i −0.403534 0.698942i
\(206\) 14.2831 8.24634i 0.995150 0.574550i
\(207\) 11.4502 0.795842
\(208\) −4.50590 10.3155i −0.312428 0.715254i
\(209\) 16.3096 1.12816
\(210\) −2.34334 + 1.35293i −0.161706 + 0.0933608i
\(211\) −5.00015 8.66052i −0.344225 0.596215i 0.640988 0.767551i \(-0.278525\pi\)
−0.985213 + 0.171336i \(0.945192\pi\)
\(212\) 1.94228 3.36413i 0.133396 0.231049i
\(213\) 3.17532i 0.217570i
\(214\) −4.43160 2.55858i −0.302938 0.174901i
\(215\) −14.3089 8.26122i −0.975856 0.563411i
\(216\) 16.3838i 1.11478i
\(217\) 1.03348 1.79004i 0.0701574 0.121516i
\(218\) −1.26756 2.19548i −0.0858501 0.148697i
\(219\) 7.76000 4.48024i 0.524372 0.302747i
\(220\) −1.86770 −0.125921
\(221\) −5.87153 + 7.96280i −0.394962 + 0.535636i
\(222\) 2.59873 0.174415
\(223\) 7.25954 4.19130i 0.486135 0.280670i −0.236835 0.971550i \(-0.576110\pi\)
0.722970 + 0.690880i \(0.242777\pi\)
\(224\) 1.03320 + 1.78956i 0.0690336 + 0.119570i
\(225\) 1.39566 2.41735i 0.0930439 0.161157i
\(226\) 13.4987i 0.897918i
\(227\) −0.796500 0.459860i −0.0528656 0.0305220i 0.473334 0.880883i \(-0.343050\pi\)
−0.526200 + 0.850361i \(0.676384\pi\)
\(228\) 2.19903 + 1.26961i 0.145634 + 0.0840820i
\(229\) 24.6208i 1.62699i 0.581574 + 0.813494i \(0.302437\pi\)
−0.581574 + 0.813494i \(0.697563\pi\)
\(230\) 8.10776 14.0430i 0.534610 0.925971i
\(231\) 1.62254 + 2.81031i 0.106755 + 0.184905i
\(232\) −9.21415 + 5.31979i −0.604939 + 0.349261i
\(233\) 17.2769 1.13185 0.565925 0.824457i \(-0.308519\pi\)
0.565925 + 0.824457i \(0.308519\pi\)
\(234\) −0.839858 + 7.48283i −0.0549032 + 0.489168i
\(235\) 12.0858 0.788392
\(236\) −0.986008 + 0.569272i −0.0641837 + 0.0370565i
\(237\) −9.19149 15.9201i −0.597051 1.03412i
\(238\) −1.75142 + 3.03355i −0.113528 + 0.196636i
\(239\) 14.4828i 0.936816i 0.883512 + 0.468408i \(0.155172\pi\)
−0.883512 + 0.468408i \(0.844828\pi\)
\(240\) 5.73101 + 3.30880i 0.369935 + 0.213582i
\(241\) −7.30441 4.21720i −0.470518 0.271654i 0.245938 0.969285i \(-0.420904\pi\)
−0.716457 + 0.697632i \(0.754237\pi\)
\(242\) 4.18710i 0.269157i
\(243\) 7.29488 12.6351i 0.467967 0.810543i
\(244\) −0.200338 0.346995i −0.0128253 0.0222141i
\(245\) 1.57173 0.907437i 0.100414 0.0579740i
\(246\) 9.49290 0.605245
\(247\) 17.0342 + 12.5605i 1.08386 + 0.799205i
\(248\) −6.25453 −0.397163
\(249\) −8.06541 + 4.65657i −0.511124 + 0.295098i
\(250\) −7.76851 13.4555i −0.491324 0.850998i
\(251\) −7.33631 + 12.7069i −0.463064 + 0.802050i −0.999112 0.0421373i \(-0.986583\pi\)
0.536048 + 0.844188i \(0.319917\pi\)
\(252\) 0.605930i 0.0381700i
\(253\) −16.8415 9.72346i −1.05882 0.611309i
\(254\) 12.4589 + 7.19315i 0.781742 + 0.451339i
\(255\) 5.81620i 0.364224i
\(256\) 4.28277 7.41797i 0.267673 0.463623i
\(257\) 14.6643 + 25.3993i 0.914733 + 1.58436i 0.807292 + 0.590152i \(0.200932\pi\)
0.107441 + 0.994211i \(0.465734\pi\)
\(258\) 11.7548 6.78665i 0.731824 0.422519i
\(259\) −1.74302 −0.108306
\(260\) −1.95068 1.43838i −0.120976 0.0892043i
\(261\) 5.75219 0.356052
\(262\) 3.38826 1.95622i 0.209328 0.120855i
\(263\) −9.95747 17.2468i −0.614004 1.06349i −0.990558 0.137091i \(-0.956225\pi\)
0.376555 0.926394i \(-0.377109\pi\)
\(264\) 4.90971 8.50386i 0.302172 0.523377i
\(265\) 19.0342i 1.16926i
\(266\) 6.48942 + 3.74667i 0.397892 + 0.229723i
\(267\) −16.2479 9.38075i −0.994357 0.574092i
\(268\) 1.85857i 0.113530i
\(269\) 11.1625 19.3340i 0.680589 1.17881i −0.294213 0.955740i \(-0.595057\pi\)
0.974801 0.223074i \(-0.0716093\pi\)
\(270\) −6.27210 10.8636i −0.381708 0.661137i
\(271\) −8.14054 + 4.69994i −0.494502 + 0.285501i −0.726440 0.687230i \(-0.758827\pi\)
0.231938 + 0.972731i \(0.425493\pi\)
\(272\) 8.56677 0.519437
\(273\) −0.469686 + 4.18474i −0.0284267 + 0.253272i
\(274\) 27.9351 1.68762
\(275\) −4.10562 + 2.37038i −0.247578 + 0.142939i
\(276\) −1.51384 2.62204i −0.0911223 0.157828i
\(277\) −7.17133 + 12.4211i −0.430883 + 0.746312i −0.996950 0.0780478i \(-0.975131\pi\)
0.566066 + 0.824360i \(0.308465\pi\)
\(278\) 14.1324i 0.847608i
\(279\) 2.92842 + 1.69073i 0.175320 + 0.101221i
\(280\) −4.75596 2.74586i −0.284223 0.164096i
\(281\) 0.0988416i 0.00589640i 0.999996 + 0.00294820i \(0.000938442\pi\)
−0.999996 + 0.00294820i \(0.999062\pi\)
\(282\) −4.96429 + 8.59841i −0.295619 + 0.512028i
\(283\) −0.310336 0.537518i −0.0184476 0.0319521i 0.856654 0.515891i \(-0.172539\pi\)
−0.875102 + 0.483939i \(0.839206\pi\)
\(284\) −0.872079 + 0.503495i −0.0517484 + 0.0298769i
\(285\) −12.4421 −0.737007
\(286\) 7.58972 10.2930i 0.448789 0.608635i
\(287\) −6.36709 −0.375837
\(288\) −2.92763 + 1.69027i −0.172512 + 0.0995998i
\(289\) 4.73534 + 8.20186i 0.278550 + 0.482462i
\(290\) 4.07307 7.05477i 0.239179 0.414270i
\(291\) 16.6160i 0.974047i
\(292\) 2.46093 + 1.42082i 0.144015 + 0.0831471i
\(293\) 21.5586 + 12.4469i 1.25947 + 0.727153i 0.972971 0.230928i \(-0.0741762\pi\)
0.286496 + 0.958082i \(0.407510\pi\)
\(294\) 1.49093i 0.0869529i
\(295\) 2.78942 4.83142i 0.162406 0.281296i
\(296\) 2.63715 + 4.56767i 0.153281 + 0.265491i
\(297\) −13.0285 + 7.52200i −0.755989 + 0.436471i
\(298\) −2.94551 −0.170629
\(299\) −10.1014 23.1256i −0.584182 1.33739i
\(300\) −0.738085 −0.0426133
\(301\) −7.88422 + 4.55195i −0.454439 + 0.262370i
\(302\) −13.1587 22.7915i −0.757197 1.31150i
\(303\) 0.0427008 0.0739599i 0.00245310 0.00424889i
\(304\) 18.3262i 1.05108i
\(305\) 1.70027 + 0.981651i 0.0973571 + 0.0562091i
\(306\) −4.96274 2.86524i −0.283701 0.163795i
\(307\) 9.89767i 0.564890i 0.959284 + 0.282445i \(0.0911455\pi\)
−0.959284 + 0.282445i \(0.908855\pi\)
\(308\) −0.514555 + 0.891235i −0.0293195 + 0.0507828i
\(309\) 7.54456 + 13.0676i 0.429195 + 0.743387i
\(310\) 4.14718 2.39437i 0.235544 0.135991i
\(311\) −7.23790 −0.410423 −0.205212 0.978718i \(-0.565788\pi\)
−0.205212 + 0.978718i \(0.565788\pi\)
\(312\) 11.6769 5.10056i 0.661076 0.288763i
\(313\) 32.6606 1.84609 0.923043 0.384696i \(-0.125694\pi\)
0.923043 + 0.384696i \(0.125694\pi\)
\(314\) 3.20217 1.84877i 0.180709 0.104332i
\(315\) 1.48452 + 2.57127i 0.0836433 + 0.144874i
\(316\) 2.91490 5.04875i 0.163976 0.284014i
\(317\) 17.1744i 0.964608i 0.876004 + 0.482304i \(0.160200\pi\)
−0.876004 + 0.482304i \(0.839800\pi\)
\(318\) −13.5418 7.81838i −0.759388 0.438433i
\(319\) −8.46064 4.88475i −0.473705 0.273494i
\(320\) 16.1197i 0.901118i
\(321\) 2.34084 4.05446i 0.130653 0.226298i
\(322\) −4.46740 7.73776i −0.248958 0.431208i
\(323\) −13.9489 + 8.05342i −0.776140 + 0.448105i
\(324\) −0.524395 −0.0291330
\(325\) −6.11353 0.686170i −0.339118 0.0380619i
\(326\) −29.9149 −1.65683
\(327\) 2.00864 1.15969i 0.111078 0.0641309i
\(328\) 9.63324 + 16.6853i 0.531907 + 0.921289i
\(329\) 3.32966 5.76714i 0.183570 0.317953i
\(330\) 7.51819i 0.413863i
\(331\) 17.2633 + 9.96698i 0.948877 + 0.547835i 0.892732 0.450588i \(-0.148786\pi\)
0.0561454 + 0.998423i \(0.482119\pi\)
\(332\) −2.55778 1.47674i −0.140377 0.0810465i
\(333\) 2.85150i 0.156261i
\(334\) 4.85219 8.40424i 0.265500 0.459860i
\(335\) −4.55348 7.88687i −0.248783 0.430905i
\(336\) 3.15780 1.82316i 0.172272 0.0994615i
\(337\) 1.27189 0.0692842 0.0346421 0.999400i \(-0.488971\pi\)
0.0346421 + 0.999400i \(0.488971\pi\)
\(338\) 15.8538 4.90518i 0.862335 0.266807i
\(339\) 12.3499 0.670754
\(340\) 1.59738 0.922245i 0.0866298 0.0500158i
\(341\) −2.87152 4.97363i −0.155502 0.269337i
\(342\) −6.12937 + 10.6164i −0.331438 + 0.574068i
\(343\) 1.00000i 0.0539949i
\(344\) 23.8572 + 13.7740i 1.28630 + 0.742643i
\(345\) 12.8479 + 7.41777i 0.691710 + 0.399359i
\(346\) 6.88989i 0.370403i
\(347\) −12.9417 + 22.4156i −0.694744 + 1.20333i 0.275522 + 0.961295i \(0.411149\pi\)
−0.970267 + 0.242038i \(0.922184\pi\)
\(348\) −0.760503 1.31723i −0.0407672 0.0706109i
\(349\) −14.9967 + 8.65837i −0.802757 + 0.463472i −0.844434 0.535659i \(-0.820063\pi\)
0.0416774 + 0.999131i \(0.486730\pi\)
\(350\) −2.17812 −0.116425
\(351\) −19.4002 2.17744i −1.03551 0.116223i
\(352\) 5.74148 0.306022
\(353\) −21.9533 + 12.6747i −1.16846 + 0.674608i −0.953316 0.301975i \(-0.902354\pi\)
−0.215140 + 0.976583i \(0.569021\pi\)
\(354\) 2.29153 + 3.96904i 0.121793 + 0.210952i
\(355\) 2.46711 4.27317i 0.130941 0.226796i
\(356\) 5.94983i 0.315341i
\(357\) −2.77539 1.60237i −0.146889 0.0848064i
\(358\) −13.5886 7.84539i −0.718181 0.414642i
\(359\) 5.27044i 0.278163i −0.990281 0.139082i \(-0.955585\pi\)
0.990281 0.139082i \(-0.0444151\pi\)
\(360\) 4.49208 7.78052i 0.236754 0.410069i
\(361\) 7.72804 + 13.3854i 0.406739 + 0.704493i
\(362\) −24.1587 + 13.9480i −1.26975 + 0.733092i
\(363\) −3.83077 −0.201063
\(364\) −1.22378 + 0.534557i −0.0641437 + 0.0280184i
\(365\) −13.9240 −0.728813
\(366\) −1.39678 + 0.806433i −0.0730110 + 0.0421529i
\(367\) −12.6588 21.9257i −0.660783 1.14451i −0.980410 0.196967i \(-0.936891\pi\)
0.319627 0.947544i \(-0.396443\pi\)
\(368\) −10.9257 + 18.9240i −0.569544 + 0.986479i
\(369\) 10.4162i 0.542248i
\(370\) −3.49722 2.01912i −0.181812 0.104969i
\(371\) 9.08280 + 5.24396i 0.471556 + 0.272253i
\(372\) 0.894130i 0.0463585i
\(373\) 3.39391 5.87842i 0.175730 0.304373i −0.764684 0.644406i \(-0.777105\pi\)
0.940414 + 0.340033i \(0.110438\pi\)
\(374\) 4.86631 + 8.42869i 0.251631 + 0.435837i
\(375\) 12.3104 7.10739i 0.635704 0.367024i
\(376\) −20.1507 −1.03920
\(377\) −5.07464 11.6176i −0.261357 0.598336i
\(378\) −6.91188 −0.355509
\(379\) 10.6717 6.16130i 0.548168 0.316485i −0.200215 0.979752i \(-0.564164\pi\)
0.748383 + 0.663267i \(0.230831\pi\)
\(380\) −1.97288 3.41714i −0.101207 0.175295i
\(381\) −6.58100 + 11.3986i −0.337155 + 0.583969i
\(382\) 3.51970i 0.180083i
\(383\) −6.28662 3.62958i −0.321232 0.185463i 0.330710 0.943732i \(-0.392712\pi\)
−0.651941 + 0.758269i \(0.726045\pi\)
\(384\) −7.28815 4.20782i −0.371922 0.214729i
\(385\) 5.04261i 0.256995i
\(386\) 8.29086 14.3602i 0.421994 0.730915i
\(387\) −7.44677 12.8982i −0.378541 0.655652i
\(388\) 4.56346 2.63472i 0.231675 0.133757i
\(389\) 7.14811 0.362424 0.181212 0.983444i \(-0.441998\pi\)
0.181212 + 0.983444i \(0.441998\pi\)
\(390\) −5.78999 + 7.85221i −0.293187 + 0.397612i
\(391\) 19.2052 0.971250
\(392\) −2.62055 + 1.51297i −0.132358 + 0.0764167i
\(393\) 1.78974 + 3.09991i 0.0902802 + 0.156370i
\(394\) 12.1441 21.0342i 0.611811 1.05969i
\(395\) 28.5659i 1.43730i
\(396\) −1.45802 0.841786i −0.0732681 0.0423014i
\(397\) −19.4520 11.2306i −0.976266 0.563647i −0.0751252 0.997174i \(-0.523936\pi\)
−0.901141 + 0.433527i \(0.857269\pi\)
\(398\) 25.5718i 1.28180i
\(399\) −3.42782 + 5.93716i −0.171606 + 0.297230i
\(400\) 2.66347 + 4.61327i 0.133174 + 0.230663i
\(401\) −2.64547 + 1.52736i −0.132108 + 0.0762729i −0.564598 0.825366i \(-0.690969\pi\)
0.432489 + 0.901639i \(0.357635\pi\)
\(402\) 7.48144 0.373140
\(403\) 0.831240 7.40605i 0.0414070 0.368921i
\(404\) 0.0270834 0.00134745
\(405\) 2.22527 1.28476i 0.110575 0.0638403i
\(406\) −2.24427 3.88720i −0.111381 0.192918i
\(407\) −2.42149 + 4.19414i −0.120029 + 0.207896i
\(408\) 9.69737i 0.480091i
\(409\) 4.85482 + 2.80293i 0.240055 + 0.138596i 0.615202 0.788369i \(-0.289074\pi\)
−0.375147 + 0.926965i \(0.622408\pi\)
\(410\) −12.7750 7.37564i −0.630912 0.364257i
\(411\) 25.5577i 1.26067i
\(412\) −2.39261 + 4.14412i −0.117875 + 0.204166i
\(413\) −1.53698 2.66212i −0.0756297 0.130995i
\(414\) 12.6586 7.30844i 0.622136 0.359190i
\(415\) 14.4719 0.710400
\(416\) 5.99657 + 4.42169i 0.294006 + 0.216791i
\(417\) −12.9297 −0.633172
\(418\) 18.0308 10.4101i 0.881916 0.509175i
\(419\) −3.06969 5.31687i −0.149964 0.259746i 0.781250 0.624219i \(-0.214583\pi\)
−0.931214 + 0.364473i \(0.881249\pi\)
\(420\) 0.392540 0.679899i 0.0191540 0.0331757i
\(421\) 1.92589i 0.0938622i −0.998898 0.0469311i \(-0.985056\pi\)
0.998898 0.0469311i \(-0.0149441\pi\)
\(422\) −11.0557 6.38302i −0.538184 0.310720i
\(423\) 9.43475 + 5.44716i 0.458733 + 0.264850i
\(424\) 31.7359i 1.54123i
\(425\) 2.34092 4.05459i 0.113551 0.196677i
\(426\) 2.02675 + 3.51044i 0.0981965 + 0.170081i
\(427\) 0.936853 0.540892i 0.0453375 0.0261756i
\(428\) 1.48470 0.0717658
\(429\) 9.41700 + 6.94381i 0.454657 + 0.335250i
\(430\) −21.0920 −1.01714
\(431\) 9.30923 5.37469i 0.448410 0.258890i −0.258749 0.965945i \(-0.583310\pi\)
0.707158 + 0.707055i \(0.249977\pi\)
\(432\) 8.45207 + 14.6394i 0.406651 + 0.704340i
\(433\) 20.1328 34.8710i 0.967520 1.67579i 0.264835 0.964294i \(-0.414682\pi\)
0.702685 0.711501i \(-0.251984\pi\)
\(434\) 2.63861i 0.126658i
\(435\) 6.45439 + 3.72644i 0.309464 + 0.178669i
\(436\) 0.637000 + 0.367772i 0.0305068 + 0.0176131i
\(437\) 41.0842i 1.96532i
\(438\) 5.71931 9.90614i 0.273279 0.473334i
\(439\) −10.9754 19.0099i −0.523826 0.907294i −0.999615 0.0277345i \(-0.991171\pi\)
0.475789 0.879560i \(-0.342163\pi\)
\(440\) −13.2144 + 7.62934i −0.629972 + 0.363715i
\(441\) 1.63595 0.0779024
\(442\) −1.40868 + 12.5509i −0.0670042 + 0.596984i
\(443\) −27.8963 −1.32539 −0.662697 0.748887i \(-0.730588\pi\)
−0.662697 + 0.748887i \(0.730588\pi\)
\(444\) −0.652982 + 0.376999i −0.0309892 + 0.0178916i
\(445\) 14.5770 + 25.2481i 0.691017 + 1.19688i
\(446\) 5.35046 9.26727i 0.253352 0.438818i
\(447\) 2.69484i 0.127461i
\(448\) 7.69203 + 4.44099i 0.363414 + 0.209817i
\(449\) 19.1056 + 11.0306i 0.901648 + 0.520567i 0.877734 0.479147i \(-0.159054\pi\)
0.0239134 + 0.999714i \(0.492387\pi\)
\(450\) 3.56329i 0.167975i
\(451\) −8.84546 + 15.3208i −0.416516 + 0.721427i
\(452\) 1.95826 + 3.39181i 0.0921088 + 0.159537i
\(453\) 20.8519 12.0389i 0.979708 0.565635i
\(454\) −1.17408 −0.0551023
\(455\) 3.88347 5.26665i 0.182060 0.246904i
\(456\) 20.7448 0.971464
\(457\) 4.77724 2.75814i 0.223470 0.129020i −0.384086 0.923297i \(-0.625483\pi\)
0.607556 + 0.794277i \(0.292150\pi\)
\(458\) 15.7150 + 27.2192i 0.734314 + 1.27187i
\(459\) 7.42851 12.8665i 0.346733 0.600559i
\(460\) 4.70479i 0.219362i
\(461\) 25.0092 + 14.4391i 1.16479 + 0.672494i 0.952448 0.304700i \(-0.0985562\pi\)
0.212346 + 0.977195i \(0.431890\pi\)
\(462\) 3.58755 + 2.07127i 0.166908 + 0.0963643i
\(463\) 14.2284i 0.661251i 0.943762 + 0.330625i \(0.107260\pi\)
−0.943762 + 0.330625i \(0.892740\pi\)
\(464\) −5.48874 + 9.50678i −0.254808 + 0.441341i
\(465\) 2.19061 + 3.79424i 0.101587 + 0.175954i
\(466\) 19.1003 11.0276i 0.884804 0.510842i
\(467\) 4.54326 0.210237 0.105118 0.994460i \(-0.466478\pi\)
0.105118 + 0.994460i \(0.466478\pi\)
\(468\) −0.874509 2.00205i −0.0404242 0.0925448i
\(469\) −5.01796 −0.231708
\(470\) 13.3613 7.71416i 0.616312 0.355828i
\(471\) 1.69144 + 2.92966i 0.0779374 + 0.134992i
\(472\) −4.65081 + 8.05545i −0.214071 + 0.370782i
\(473\) 25.2951i 1.16307i
\(474\) −20.3231 11.7335i −0.933469 0.538939i
\(475\) −8.67366 5.00774i −0.397975 0.229771i
\(476\) 1.01632i 0.0465829i
\(477\) −8.57886 + 14.8590i −0.392799 + 0.680348i
\(478\) 9.24413 + 16.0113i 0.422817 + 0.732340i
\(479\) −1.44239 + 0.832764i −0.0659044 + 0.0380499i −0.532590 0.846373i \(-0.678781\pi\)
0.466686 + 0.884423i \(0.345448\pi\)
\(480\) −4.38002 −0.199920
\(481\) −5.75911 + 2.51562i −0.262593 + 0.114702i
\(482\) −10.7671 −0.490426
\(483\) 7.07925 4.08721i 0.322117 0.185974i
\(484\) −0.607426 1.05209i −0.0276103 0.0478224i
\(485\) −12.9100 + 22.3608i −0.586215 + 1.01535i
\(486\) 18.6248i 0.844837i
\(487\) −1.28598 0.742463i −0.0582735 0.0336442i 0.470580 0.882357i \(-0.344045\pi\)
−0.528854 + 0.848713i \(0.677378\pi\)
\(488\) −2.83487 1.63671i −0.128328 0.0740904i
\(489\) 27.3691i 1.23767i
\(490\) 1.15840 2.00641i 0.0523312 0.0906403i
\(491\) 7.99791 + 13.8528i 0.360941 + 0.625167i 0.988116 0.153711i \(-0.0491224\pi\)
−0.627175 + 0.778878i \(0.715789\pi\)
\(492\) −2.38528 + 1.37714i −0.107537 + 0.0620863i
\(493\) 9.64808 0.434528
\(494\) 26.8490 + 3.01348i 1.20800 + 0.135583i
\(495\) 8.24947 0.370786
\(496\) −5.58860 + 3.22658i −0.250936 + 0.144878i
\(497\) −1.35939 2.35453i −0.0609768 0.105615i
\(498\) −5.94440 + 10.2960i −0.266375 + 0.461375i
\(499\) 17.7199i 0.793253i −0.917980 0.396627i \(-0.870181\pi\)
0.917980 0.396627i \(-0.129819\pi\)
\(500\) 3.90398 + 2.25397i 0.174591 + 0.100800i
\(501\) 7.68902 + 4.43926i 0.343520 + 0.198331i
\(502\) 18.7305i 0.835985i
\(503\) 0.598451 1.03655i 0.0266836 0.0462174i −0.852375 0.522931i \(-0.824839\pi\)
0.879059 + 0.476713i \(0.158172\pi\)
\(504\) −2.47515 4.28709i −0.110252 0.190962i
\(505\) −0.114929 + 0.0663540i −0.00511425 + 0.00295272i
\(506\) −24.8253 −1.10362
\(507\) 4.48774 + 14.5046i 0.199307 + 0.644174i
\(508\) −4.17406 −0.185194
\(509\) 5.44396 3.14307i 0.241299 0.139314i −0.374474 0.927237i \(-0.622177\pi\)
0.615774 + 0.787923i \(0.288844\pi\)
\(510\) −3.71237 6.43002i −0.164387 0.284726i
\(511\) −3.83607 + 6.64426i −0.169698 + 0.293925i
\(512\) 25.3457i 1.12013i
\(513\) −27.5244 15.8912i −1.21523 0.701614i
\(514\) 32.4238 + 18.7199i 1.43015 + 0.825699i
\(515\) 23.4474i 1.03322i
\(516\) −1.96909 + 3.41056i −0.0866843 + 0.150142i
\(517\) −9.25143 16.0240i −0.406878 0.704733i
\(518\) −1.92698 + 1.11254i −0.0846665 + 0.0488822i
\(519\) 6.30354 0.276695
\(520\) −19.6771 2.20852i −0.862898 0.0968499i
\(521\) −10.8473 −0.475230 −0.237615 0.971359i \(-0.576366\pi\)
−0.237615 + 0.971359i \(0.576366\pi\)
\(522\) 6.35926 3.67152i 0.278337 0.160698i
\(523\) −0.673629 1.16676i −0.0294557 0.0510188i 0.850922 0.525292i \(-0.176044\pi\)
−0.880377 + 0.474274i \(0.842711\pi\)
\(524\) −0.567579 + 0.983076i −0.0247948 + 0.0429459i
\(525\) 1.99275i 0.0869709i
\(526\) −22.0167 12.7113i −0.959974 0.554241i
\(527\) 4.91181 + 2.83583i 0.213962 + 0.123531i
\(528\) 10.1313i 0.440907i
\(529\) −12.9936 + 22.5057i −0.564941 + 0.978507i
\(530\) 12.1492 + 21.0431i 0.527728 + 0.914052i
\(531\) 4.35510 2.51442i 0.188995 0.109117i
\(532\) −2.17413 −0.0942605
\(533\) −21.0375 + 9.18931i −0.911233 + 0.398033i
\(534\) −23.9502 −1.03643
\(535\) −6.30034 + 3.63750i −0.272388 + 0.157263i
\(536\) 7.59205 + 13.1498i 0.327926 + 0.567985i
\(537\) 7.17773 12.4322i 0.309742 0.536489i
\(538\) 28.4993i 1.22869i
\(539\) −2.40625 1.38925i −0.103644 0.0598391i
\(540\) 3.15198 + 1.81980i 0.135640 + 0.0783115i
\(541\) 20.1571i 0.866621i −0.901245 0.433310i \(-0.857345\pi\)
0.901245 0.433310i \(-0.142655\pi\)
\(542\) −5.99978 + 10.3919i −0.257712 + 0.446371i
\(543\) −12.7610 22.1027i −0.547628 0.948519i
\(544\) −4.91047 + 2.83506i −0.210535 + 0.121552i
\(545\) −3.60415 −0.154385
\(546\) 2.15179 + 4.92618i 0.0920880 + 0.210821i
\(547\) −3.42286 −0.146351 −0.0731755 0.997319i \(-0.523313\pi\)
−0.0731755 + 0.997319i \(0.523313\pi\)
\(548\) −7.01924 + 4.05256i −0.299847 + 0.173117i
\(549\) 0.884873 + 1.53264i 0.0377654 + 0.0654117i
\(550\) −3.02594 + 5.24109i −0.129027 + 0.223481i
\(551\) 20.6394i 0.879266i
\(552\) −21.4214 12.3677i −0.911757 0.526403i
\(553\) 13.6311 + 7.86993i 0.579654 + 0.334663i
\(554\) 18.3093i 0.777889i
\(555\) 1.84729 3.19960i 0.0784130 0.135815i
\(556\) −2.05020 3.55106i −0.0869480 0.150598i
\(557\) −20.4948 + 11.8327i −0.868394 + 0.501367i −0.866814 0.498631i \(-0.833836\pi\)
−0.00157977 + 0.999999i \(0.500503\pi\)
\(558\) 4.31664 0.182738
\(559\) −19.4806 + 26.4190i −0.823940 + 1.11740i
\(560\) −5.66612 −0.239437
\(561\) −7.71139 + 4.45217i −0.325575 + 0.187971i
\(562\) 0.0630888 + 0.109273i 0.00266124 + 0.00460941i
\(563\) 14.4037 24.9480i 0.607045 1.05143i −0.384680 0.923050i \(-0.625688\pi\)
0.991725 0.128382i \(-0.0409784\pi\)
\(564\) 2.88069i 0.121299i
\(565\) −16.6198 9.59543i −0.699199 0.403683i
\(566\) −0.686177 0.396164i −0.0288422 0.0166520i
\(567\) 1.41581i 0.0594585i
\(568\) −4.11343 + 7.12467i −0.172596 + 0.298945i
\(569\) −13.8361 23.9648i −0.580040 1.00466i −0.995474 0.0950353i \(-0.969704\pi\)
0.415434 0.909623i \(-0.363630\pi\)
\(570\) −13.7552 + 7.94158i −0.576143 + 0.332636i
\(571\) −12.9655 −0.542588 −0.271294 0.962497i \(-0.587452\pi\)
−0.271294 + 0.962497i \(0.587452\pi\)
\(572\) −0.413861 + 3.68736i −0.0173044 + 0.154176i
\(573\) −3.22016 −0.134524
\(574\) −7.03905 + 4.06400i −0.293804 + 0.169628i
\(575\) 5.97105 + 10.3422i 0.249010 + 0.431298i
\(576\) −7.26525 + 12.5838i −0.302719 + 0.524324i
\(577\) 9.46047i 0.393844i −0.980419 0.196922i \(-0.936905\pi\)
0.980419 0.196922i \(-0.0630947\pi\)
\(578\) 10.4702 + 6.04497i 0.435503 + 0.251438i
\(579\) 13.1381 + 7.58529i 0.546001 + 0.315234i
\(580\) 2.36354i 0.0981405i
\(581\) 3.98704 6.90576i 0.165410 0.286499i
\(582\) −10.6057 18.3696i −0.439620 0.761444i
\(583\) 25.2365 14.5703i 1.04519 0.603440i
\(584\) 23.2155 0.960663
\(585\) 8.61598 + 6.35317i 0.356227 + 0.262671i
\(586\) 31.7784 1.31275
\(587\) −18.6673 + 10.7776i −0.770481 + 0.444837i −0.833046 0.553204i \(-0.813405\pi\)
0.0625654 + 0.998041i \(0.480072\pi\)
\(588\) −0.216290 0.374626i −0.00891967 0.0154493i
\(589\) 6.06647 10.5074i 0.249965 0.432951i
\(590\) 7.12175i 0.293198i
\(591\) 19.2441 + 11.1106i 0.791598 + 0.457029i
\(592\) 4.71274 + 2.72090i 0.193692 + 0.111828i
\(593\) 3.97234i 0.163124i −0.996668 0.0815622i \(-0.974009\pi\)
0.996668 0.0815622i \(-0.0259909\pi\)
\(594\) −9.60231 + 16.6317i −0.393988 + 0.682407i
\(595\) 2.48997 + 4.31275i 0.102079 + 0.176806i
\(596\) 0.740117 0.427307i 0.0303164 0.0175032i
\(597\) −23.3956 −0.957517
\(598\) −25.9282 19.1187i −1.06028 0.781821i
\(599\) −19.5049 −0.796950 −0.398475 0.917179i \(-0.630460\pi\)
−0.398475 + 0.917179i \(0.630460\pi\)
\(600\) −5.22211 + 3.01498i −0.213192 + 0.123086i
\(601\) 13.4368 + 23.2733i 0.548100 + 0.949336i 0.998405 + 0.0564616i \(0.0179818\pi\)
−0.450305 + 0.892875i \(0.648685\pi\)
\(602\) −5.81086 + 10.0647i −0.236833 + 0.410207i
\(603\) 8.20914i 0.334302i
\(604\) 6.61276 + 3.81788i 0.269070 + 0.155347i
\(605\) 5.15523 + 2.97637i 0.209590 + 0.121007i
\(606\) 0.109021i 0.00442866i
\(607\) −12.5102 + 21.6682i −0.507772 + 0.879487i 0.492187 + 0.870489i \(0.336197\pi\)
−0.999960 + 0.00899773i \(0.997136\pi\)
\(608\) 6.06482 + 10.5046i 0.245961 + 0.426016i
\(609\) 3.55639 2.05328i 0.144112 0.0832031i
\(610\) 2.50628 0.101476
\(611\) 2.67808 23.8607i 0.108343 0.965300i
\(612\) 1.66265 0.0672086
\(613\) −18.4970 + 10.6793i −0.747088 + 0.431332i −0.824641 0.565657i \(-0.808623\pi\)
0.0775527 + 0.996988i \(0.475289\pi\)
\(614\) 6.31751 + 10.9422i 0.254954 + 0.441593i
\(615\) 6.74796 11.6878i 0.272104 0.471298i
\(616\) 8.40757i 0.338751i
\(617\) −28.5425 16.4790i −1.14908 0.663420i −0.200415 0.979711i \(-0.564229\pi\)
−0.948662 + 0.316291i \(0.897562\pi\)
\(618\) 16.6816 + 9.63111i 0.671031 + 0.387420i
\(619\) 48.9117i 1.96593i 0.183795 + 0.982965i \(0.441162\pi\)
−0.183795 + 0.982965i \(0.558838\pi\)
\(620\) −0.694707 + 1.20327i −0.0279001 + 0.0483244i
\(621\) 18.9481 + 32.8191i 0.760361 + 1.31698i
\(622\) −8.00176 + 4.61982i −0.320841 + 0.185238i
\(623\) 16.0640 0.643589
\(624\) 7.80240 10.5814i 0.312346 0.423595i
\(625\) −13.5576 −0.542304
\(626\) 36.1075 20.8467i 1.44315 0.833201i
\(627\) 9.52417 + 16.4964i 0.380359 + 0.658801i
\(628\) −0.536406 + 0.929083i −0.0214049 + 0.0370744i
\(629\) 4.78278i 0.190702i
\(630\) 3.28239 + 1.89509i 0.130773 + 0.0755021i
\(631\) 4.65076 + 2.68512i 0.185144 + 0.106893i 0.589707 0.807617i \(-0.299243\pi\)
−0.404563 + 0.914510i \(0.632576\pi\)
\(632\) 47.6280i 1.89454i
\(633\) 5.83981 10.1148i 0.232111 0.402029i
\(634\) 10.9621 + 18.9869i 0.435360 + 0.754066i
\(635\) 17.7127 10.2264i 0.702905 0.405823i
\(636\) 4.53687 0.179899
\(637\) −1.44325 3.30409i −0.0571837 0.130913i
\(638\) −12.4714 −0.493747
\(639\) 3.85189 2.22389i 0.152378 0.0879757i
\(640\) 6.53865 + 11.3253i 0.258463 + 0.447671i
\(641\) 19.8510 34.3829i 0.784066 1.35804i −0.145489 0.989360i \(-0.546475\pi\)
0.929555 0.368683i \(-0.120191\pi\)
\(642\) 5.97647i 0.235872i
\(643\) 27.8388 + 16.0727i 1.09785 + 0.633847i 0.935657 0.352911i \(-0.114808\pi\)
0.162198 + 0.986758i \(0.448142\pi\)
\(644\) 2.24504 + 1.29618i 0.0884671 + 0.0510765i
\(645\) 19.2970i 0.759818i
\(646\) −10.2807 + 17.8067i −0.404489 + 0.700596i
\(647\) −9.92502 17.1906i −0.390193 0.675833i 0.602282 0.798283i \(-0.294258\pi\)
−0.992475 + 0.122450i \(0.960925\pi\)
\(648\) −3.71020 + 2.14209i −0.145751 + 0.0841491i
\(649\) −8.54096 −0.335262
\(650\) −7.19670 + 3.14357i −0.282278 + 0.123301i
\(651\) 2.41406 0.0946145
\(652\) 7.51671 4.33977i 0.294377 0.169959i
\(653\) 9.50024 + 16.4549i 0.371773 + 0.643930i 0.989838 0.142197i \(-0.0454165\pi\)
−0.618065 + 0.786127i \(0.712083\pi\)
\(654\) 1.48042 2.56416i 0.0578889 0.100266i
\(655\) 5.56225i 0.217335i
\(656\) 17.2152 + 9.93918i 0.672139 + 0.388060i
\(657\) −10.8697 6.27562i −0.424067 0.244835i
\(658\) 8.50105i 0.331405i
\(659\) 3.60729 6.24801i 0.140520 0.243388i −0.787173 0.616733i \(-0.788456\pi\)
0.927693 + 0.373345i \(0.121789\pi\)
\(660\) −1.09067 1.88909i −0.0424542 0.0735329i
\(661\) 14.5068 8.37548i 0.564248 0.325769i −0.190601 0.981668i \(-0.561044\pi\)
0.754849 + 0.655899i \(0.227710\pi\)
\(662\) 25.4470 0.989025
\(663\) −11.4828 1.28880i −0.445953 0.0500529i
\(664\) −24.1291 −0.936393
\(665\) 9.22592 5.32659i 0.357766 0.206556i
\(666\) −1.82006 3.15244i −0.0705259 0.122155i
\(667\) −12.3048 + 21.3126i −0.476444 + 0.825226i
\(668\) 2.81564i 0.108941i
\(669\) 8.47860 + 4.89512i 0.327802 + 0.189256i
\(670\) −10.0681 5.81281i −0.388964 0.224569i
\(671\) 3.00573i 0.116035i
\(672\) −1.20670 + 2.09007i −0.0465495 + 0.0806261i
\(673\) −18.6684 32.3346i −0.719614 1.24641i −0.961153 0.276016i \(-0.910986\pi\)
0.241539 0.970391i \(-0.422348\pi\)
\(674\) 1.40612 0.811824i 0.0541618 0.0312703i
\(675\) 9.23831 0.355583
\(676\) −3.27199 + 3.53245i −0.125846 + 0.135864i
\(677\) 28.1341 1.08128 0.540641 0.841253i \(-0.318182\pi\)
0.540641 + 0.841253i \(0.318182\pi\)
\(678\) 13.6533 7.88271i 0.524350 0.302734i
\(679\) 7.11347 + 12.3209i 0.272990 + 0.472832i
\(680\) 7.53452 13.0502i 0.288935 0.500451i
\(681\) 1.07416i 0.0411620i
\(682\) −6.34915 3.66568i −0.243122 0.140366i
\(683\) −1.79295 1.03516i −0.0686053 0.0396093i 0.465305 0.885150i \(-0.345945\pi\)
−0.533910 + 0.845541i \(0.679278\pi\)
\(684\) 3.55677i 0.135996i
\(685\) 19.8574 34.3941i 0.758714 1.31413i
\(686\) −0.638282 1.10554i −0.0243697 0.0422096i
\(687\) −24.9028 + 14.3776i −0.950100 + 0.548540i
\(688\) 28.4228 1.08361
\(689\) 37.5788 + 4.21776i 1.43164 + 0.160684i
\(690\) 18.9385 0.720977
\(691\) 31.0542 17.9291i 1.18136 0.682057i 0.225029 0.974352i \(-0.427752\pi\)
0.956328 + 0.292295i \(0.0944190\pi\)
\(692\) 0.999521 + 1.73122i 0.0379961 + 0.0658112i
\(693\) 2.27274 3.93650i 0.0863342 0.149535i
\(694\) 33.0417i 1.25425i
\(695\) 17.4001 + 10.0460i 0.660023 + 0.381065i
\(696\) −10.7614 6.21312i −0.407911 0.235508i
\(697\) 17.4710i 0.661763i
\(698\) −11.0530 + 19.1443i −0.418361 + 0.724622i
\(699\) 10.0891 + 17.4748i 0.381604 + 0.660958i
\(700\) 0.547295 0.315981i 0.0206858 0.0119430i
\(701\) −44.8940 −1.69562 −0.847812 0.530297i \(-0.822081\pi\)
−0.847812 + 0.530297i \(0.822081\pi\)
\(702\) −22.8375 + 9.97558i −0.861946 + 0.376504i
\(703\) −10.2314 −0.385885
\(704\) 21.3722 12.3393i 0.805497 0.465054i
\(705\) 7.05767 + 12.2242i 0.265807 + 0.460391i
\(706\) −16.1801 + 28.0248i −0.608947 + 1.05473i
\(707\) 0.0731225i 0.00275005i
\(708\) −1.15158 0.664867i −0.0432792 0.0249872i
\(709\) −14.0864 8.13279i −0.529026 0.305433i 0.211594 0.977358i \(-0.432135\pi\)
−0.740620 + 0.671924i \(0.765468\pi\)
\(710\) 6.29886i 0.236392i
\(711\) −12.8748 + 22.2998i −0.482843 + 0.836309i
\(712\) −24.3043 42.0963i −0.910843 1.57763i
\(713\) −12.5287 + 7.23344i −0.469203 + 0.270894i
\(714\) −4.09105 −0.153104
\(715\) −7.27775 16.6613i −0.272173 0.623096i
\(716\) 4.55255 0.170137
\(717\) −14.6487 + 8.45743i −0.547066 + 0.315849i
\(718\) −3.36403 5.82667i −0.125544 0.217449i
\(719\) −5.00744 + 8.67314i −0.186746 + 0.323454i −0.944164 0.329477i \(-0.893127\pi\)
0.757417 + 0.652931i \(0.226461\pi\)
\(720\) 9.26949i 0.345454i
\(721\) −11.1887 6.45980i −0.416689 0.240575i
\(722\) 17.0873 + 9.86534i 0.635922 + 0.367150i
\(723\) 9.85076i 0.366354i
\(724\) 4.04690 7.00944i 0.150402 0.260504i
\(725\) 2.99966 + 5.19556i 0.111405 + 0.192958i
\(726\) −4.23506 + 2.44511i −0.157178 + 0.0907466i
\(727\) 34.5299 1.28064 0.640322 0.768106i \(-0.278801\pi\)
0.640322 + 0.768106i \(0.278801\pi\)
\(728\) −6.47493 + 8.78111i −0.239977 + 0.325450i
\(729\) 21.2872 0.788415
\(730\) −15.3934 + 8.88741i −0.569737 + 0.328938i
\(731\) −12.4904 21.6340i −0.461973 0.800161i
\(732\) 0.233980 0.405265i 0.00864814 0.0149790i
\(733\) 33.1360i 1.22391i 0.790894 + 0.611953i \(0.209616\pi\)
−0.790894 + 0.611953i \(0.790384\pi\)
\(734\) −27.9895 16.1598i −1.03311 0.596468i
\(735\) 1.83566 + 1.05982i 0.0677093 + 0.0390920i
\(736\) 14.4629i 0.533111i
\(737\) −6.97119 + 12.0745i −0.256787 + 0.444768i
\(738\) −6.64850 11.5155i −0.244735 0.423893i
\(739\) −3.47767 + 2.00784i −0.127928 + 0.0738594i −0.562598 0.826730i \(-0.690198\pi\)
0.434670 + 0.900590i \(0.356865\pi\)
\(740\) 1.17166 0.0430711
\(741\) −2.75703 + 24.5641i −0.101282 + 0.902386i
\(742\) 13.3885 0.491507
\(743\) 10.8361 6.25622i 0.397538 0.229519i −0.287883 0.957666i \(-0.592952\pi\)
0.685421 + 0.728147i \(0.259618\pi\)
\(744\) −3.65241 6.32616i −0.133904 0.231928i
\(745\) −2.09379 + 3.62656i −0.0767107 + 0.132867i
\(746\) 8.66508i 0.317251i
\(747\) 11.2975 + 6.52260i 0.413353 + 0.238650i
\(748\) −2.44551 1.41192i −0.0894168 0.0516248i
\(749\) 4.00855i 0.146469i
\(750\) 9.07304 15.7150i 0.331300 0.573829i
\(751\) 18.7579 + 32.4896i 0.684486 + 1.18556i 0.973598 + 0.228269i \(0.0733065\pi\)
−0.289112 + 0.957295i \(0.593360\pi\)
\(752\) −18.0053 + 10.3954i −0.656585 + 0.379080i
\(753\) −17.1365 −0.624490
\(754\) −13.0255 9.60461i −0.474360 0.349779i
\(755\) −37.4150 −1.36167
\(756\) 1.73675 1.00271i 0.0631649 0.0364683i
\(757\) 17.5223 + 30.3496i 0.636860 + 1.10307i 0.986118 + 0.166047i \(0.0531004\pi\)
−0.349258 + 0.937027i \(0.613566\pi\)
\(758\) 7.86530 13.6231i 0.285680 0.494813i
\(759\) 22.7126i 0.824414i
\(760\) −27.9172 16.1180i −1.01266 0.584661i
\(761\) −3.72586 2.15113i −0.135062 0.0779782i 0.430946 0.902378i \(-0.358180\pi\)
−0.566009 + 0.824399i \(0.691513\pi\)
\(762\) 16.8021i 0.608677i
\(763\) −0.992947 + 1.71984i −0.0359471 + 0.0622622i
\(764\) −0.510605 0.884394i −0.0184730 0.0319962i
\(765\) −7.05545 + 4.07347i −0.255090 + 0.147277i
\(766\) −9.26679 −0.334823
\(767\) −8.92043 6.57766i −0.322098 0.237506i
\(768\) 10.0039 0.360985
\(769\) 10.6146 6.12834i 0.382772 0.220994i −0.296251 0.955110i \(-0.595737\pi\)
0.679024 + 0.734116i \(0.262403\pi\)
\(770\) −3.21861 5.57479i −0.115991 0.200902i
\(771\) −17.1268 + 29.6645i −0.616806 + 1.06834i
\(772\) 4.81105i 0.173153i
\(773\) −3.29372 1.90163i −0.118467 0.0683970i 0.439596 0.898196i \(-0.355122\pi\)
−0.558063 + 0.829799i \(0.688455\pi\)
\(774\) −16.4654 9.50628i −0.591835 0.341696i
\(775\) 3.52673i 0.126684i
\(776\)