Properties

Label 91.2.q.a.43.5
Level $91$
Weight $2$
Character 91.43
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 43.5
Root \(1.40744 - 0.138282i\) of defining polynomial
Character \(\chi\) \(=\) 91.43
Dual form 91.2.q.a.36.5

$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

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

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 0.837044 0.547136i \(-0.184282\pi\)
−0.0553113 + 0.998469i \(0.517615\pi\)
\(3\) 0.583963 1.01145i 0.337151 0.583963i −0.646745 0.762707i \(-0.723870\pi\)
0.983896 + 0.178744i \(0.0572034\pi\)
\(4\) −0.185192 0.320762i −0.0925960 0.160381i
\(5\) 1.81487i 0.811636i 0.913954 + 0.405818i \(0.133013\pi\)
−0.913954 + 0.405818i \(0.866987\pi\)
\(6\) 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 0.0912671 0.995826i \(-0.470908\pi\)
−0.816777 + 0.576953i \(0.804242\pi\)
\(12\) −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 0.983051 0.183334i \(-0.0586888\pi\)
−0.650297 + 0.759680i \(0.725355\pi\)
\(18\) 2.08840i 0.492240i
\(19\) −5.08351 + 2.93497i −1.16624 + 0.673327i −0.952791 0.303628i \(-0.901802\pi\)
−0.213446 + 0.976955i \(0.568469\pi\)
\(20\) 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 −0.227302 0.973824i \(-0.572990\pi\)
0.957007 0.290063i \(-0.0936763\pi\)
\(24\) −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 −0.655344 0.755330i \(-0.727476\pi\)
0.981807 + 0.189879i \(0.0608097\pi\)
\(30\) 1.35293 + 2.34334i 0.247009 + 0.427833i
\(31\) 2.06697i 0.371238i −0.982622 0.185619i \(-0.940571\pi\)
0.982622 0.185619i \(-0.0594290\pi\)
\(32\) −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 0.618922 0.785453i \(-0.287570\pi\)
−0.370761 + 0.928728i \(0.620903\pi\)
\(38\) −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 0.864398 0.502808i \(-0.167700\pi\)
−0.00324599 + 0.999995i \(0.501033\pi\)
\(42\) −0.745466 + 1.29118i −0.115028 + 0.199234i
\(43\) 4.55195 + 7.88422i 0.694167 + 1.20233i 0.970461 + 0.241259i \(0.0775603\pi\)
−0.276294 + 0.961073i \(0.589106\pi\)
\(44\) 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 \(-0.838572\pi\)
0.874136 0.485681i \(-0.161428\pi\)
\(48\) −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 −0.316598 0.948560i \(-0.602541\pi\)
0.663177 + 0.748462i \(0.269207\pi\)
\(60\) 0.785080i 0.101353i
\(61\) −0.540892 0.936853i −0.0692541 0.119952i 0.829319 0.558775i \(-0.188729\pi\)
−0.898573 + 0.438824i \(0.855395\pi\)
\(62\) 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 0.741387 0.671078i \(-0.234168\pi\)
−0.210477 + 0.977599i \(0.567502\pi\)
\(68\) 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 −0.353735 0.935346i \(-0.615088\pi\)
0.633166 + 0.774016i \(0.281755\pi\)
\(72\) 4.28709 2.47515i 0.505238 0.291699i
\(73\) 7.67213i 0.897955i 0.893543 + 0.448978i \(0.148212\pi\)
−0.893543 + 0.448978i \(0.851788\pi\)
\(74\) 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 \(-0.855816\pi\)
0.899153 0.437635i \(-0.144184\pi\)
\(84\) 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 −0.475055 0.879956i \(-0.657572\pi\)
−0.999592 + 0.0285683i \(0.990905\pi\)
\(90\) −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 −0.971307 0.237827i \(-0.923565\pi\)
−0.279689 + 0.960091i \(0.590231\pi\)
\(98\) 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 −0.867839 0.496846i \(-0.834491\pi\)
0.864201 + 0.503147i \(0.167825\pi\)
\(102\) 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 −0.946493 0.322723i \(-0.895402\pi\)
0.752733 + 0.658326i \(0.228735\pi\)
\(108\) −1.00271 1.73675i −0.0964860 0.167119i
\(109\) 1.98589i 0.190214i 0.995467 + 0.0951071i \(0.0303194\pi\)
−0.995467 + 0.0951071i \(0.969681\pi\)
\(110\) 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 0.999995 0.00303506i \(-0.000966090\pi\)
−0.502626 + 0.864504i \(0.667633\pi\)
\(114\) −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 −0.499994 0.866029i \(-0.666665\pi\)
1.00000 6.53271e-6i \(-2.07943e-6\pi\)
\(128\) −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 0.631965 0.774997i \(-0.282249\pi\)
0.987150 0.159799i \(-0.0510845\pi\)
\(138\) 10.4352i 0.888300i
\(139\) −5.53535 9.58750i −0.469502 0.813201i 0.529890 0.848066i \(-0.322233\pi\)
−0.999392 + 0.0348652i \(0.988900\pi\)
\(140\) −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 −0.579613 0.814892i \(-0.696796\pi\)
0.415911 + 0.909406i \(0.363463\pi\)
\(150\) 2.20306 1.27194i 0.179879 0.103853i
\(151\) 20.6158i 1.67769i 0.544371 + 0.838845i \(0.316768\pi\)
−0.544371 + 0.838845i \(0.683232\pi\)
\(152\) 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 −0.596201 + 0.802835i \(0.703324\pi\)
−0.993376 + 0.114907i \(0.963343\pi\)
\(164\) 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 0.732606 0.680653i \(-0.238304\pi\)
−0.223160 + 0.974782i \(0.571637\pi\)
\(168\) 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 0.950187 0.311679i \(-0.100892\pi\)
−0.745016 + 0.667047i \(0.767558\pi\)
\(174\) 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 −0.998927 0.0463168i \(-0.985252\pi\)
0.539575 + 0.841938i \(0.318585\pi\)
\(180\) 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 0.811831 0.583893i \(-0.198471\pi\)
−0.911581 + 0.411120i \(0.865138\pi\)
\(192\) −5.18675 + 8.98371i −0.374321 + 0.648344i
\(193\) 11.2491 + 6.49467i 0.809728 + 0.467497i 0.846861 0.531814i \(-0.178489\pi\)
−0.0371334 + 0.999310i \(0.511823\pi\)
\(194\) −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 0.954608 0.297866i \(-0.0962749\pi\)
0.219344 + 0.975648i \(0.429608\pi\)
\(198\) 2.90130 5.02519i 0.206186 0.357125i
\(199\) −10.0159 17.3480i −0.710006 1.22977i −0.964854 0.262786i \(-0.915359\pi\)
0.254848 0.966981i \(-0.417975\pi\)
\(200\) 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 −0.985213 0.171336i \(-0.945192\pi\)
0.640988 + 0.767551i \(0.278525\pi\)
\(212\) 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 0.722970 0.690880i \(-0.242777\pi\)
−0.236835 + 0.971550i \(0.576110\pi\)
\(224\) 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 −0.526200 0.850361i \(-0.676384\pi\)
0.473334 + 0.880883i \(0.343050\pi\)
\(228\) 2.19903 1.26961i 0.145634 0.0840820i
\(229\) 24.6208i 1.62699i −0.581574 0.813494i \(-0.697563\pi\)
0.581574 0.813494i \(-0.302437\pi\)
\(230\) 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 \(-0.844828\pi\)
0.883512 0.468408i \(-0.155172\pi\)
\(240\) 5.73101 3.30880i 0.369935 0.213582i
\(241\) −7.30441 + 4.21720i −0.470518 + 0.271654i −0.716457 0.697632i \(-0.754237\pi\)
0.245938 + 0.969285i \(0.420904\pi\)
\(242\) 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 0.536048 0.844188i \(-0.319917\pi\)
−0.999112 + 0.0421373i \(0.986583\pi\)
\(252\) 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 0.107441 0.994211i \(-0.465734\pi\)
0.807292 0.590152i \(-0.200932\pi\)
\(258\) 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 0.376555 + 0.926394i \(0.377109\pi\)
−0.990558 + 0.137091i \(0.956225\pi\)
\(264\) 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 0.974801 + 0.223074i \(0.0716093\pi\)
−0.294213 + 0.955740i \(0.595057\pi\)
\(270\) −6.27210 + 10.8636i −0.381708 + 0.661137i
\(271\) −8.14054 4.69994i −0.494502 0.285501i 0.231938 0.972731i \(-0.425493\pi\)
−0.726440 + 0.687230i \(0.758827\pi\)
\(272\) 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 0.566066 0.824360i \(-0.308465\pi\)
−0.996950 + 0.0780478i \(0.975131\pi\)
\(278\) 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 \(-0.999062\pi\)
0.999996 0.00294820i \(-0.000938442\pi\)
\(282\) −4.96429 8.59841i −0.295619 0.512028i
\(283\) −0.310336 + 0.537518i −0.0184476 + 0.0319521i −0.875102 0.483939i \(-0.839206\pi\)
0.856654 + 0.515891i \(0.172539\pi\)
\(284\) −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 0.286496 0.958082i \(-0.407510\pi\)
0.972971 + 0.230928i \(0.0741762\pi\)
\(294\) 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 \(-0.908855\pi\)
0.959284 0.282445i \(-0.0911455\pi\)
\(308\) −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 \(-0.839800\pi\)
0.876004 0.482304i \(-0.160200\pi\)
\(318\) −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 0.0561454 0.998423i \(-0.482119\pi\)
0.892732 + 0.450588i \(0.148786\pi\)
\(332\) −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 −0.970267 0.242038i \(-0.922184\pi\)
0.275522 0.961295i \(-0.411149\pi\)
\(348\) −0.760503 + 1.31723i −0.0407672 + 0.0706109i
\(349\) −14.9967 8.65837i −0.802757 0.463472i 0.0416774 0.999131i \(-0.486730\pi\)
−0.844434 + 0.535659i \(0.820063\pi\)
\(350\) −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 −0.215140 0.976583i \(-0.569021\pi\)
−0.953316 + 0.301975i \(0.902354\pi\)
\(354\) 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 \(0.0444151\pi\)
−0.990281 + 0.139082i \(0.955585\pi\)
\(360\) 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 0.319627 + 0.947544i \(0.396443\pi\)
−0.980410 + 0.196967i \(0.936891\pi\)
\(368\) −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 0.940414 0.340033i \(-0.110438\pi\)
−0.764684 + 0.644406i \(0.777105\pi\)
\(374\) 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 0.748383 0.663267i \(-0.230831\pi\)
−0.200215 + 0.979752i \(0.564164\pi\)
\(380\) −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 −0.651941 0.758269i \(-0.726045\pi\)
0.330710 + 0.943732i \(0.392712\pi\)
\(384\) −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 −0.901141 0.433527i \(-0.857269\pi\)
−0.0751252 + 0.997174i \(0.523936\pi\)
\(398\) 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 0.432489 0.901639i \(-0.357635\pi\)
−0.564598 + 0.825366i \(0.690969\pi\)
\(402\) 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 −0.375147 0.926965i \(-0.622408\pi\)
0.615202 + 0.788369i \(0.289074\pi\)
\(410\) −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 −0.931214 0.364473i \(-0.881249\pi\)
0.781250 + 0.624219i \(0.214583\pi\)
\(420\) 0.392540 + 0.679899i 0.0191540 + 0.0331757i
\(421\) 1.92589i 0.0938622i 0.998898 + 0.0469311i \(0.0149441\pi\)
−0.998898 + 0.0469311i \(0.985056\pi\)
\(422\) −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 0.707158 0.707055i \(-0.249977\pi\)
−0.258749 + 0.965945i \(0.583310\pi\)
\(432\) 8.45207 14.6394i 0.406651 0.704340i
\(433\) 20.1328 + 34.8710i 0.967520 + 1.67579i 0.702685 + 0.711501i \(0.251984\pi\)
0.264835 + 0.964294i \(0.414682\pi\)
\(434\) 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 0.475789 + 0.879560i \(0.342163\pi\)
−0.999615 + 0.0277345i \(0.991171\pi\)
\(440\) −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 0.0239134 0.999714i \(-0.492387\pi\)
0.877734 + 0.479147i \(0.159054\pi\)
\(450\) 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 0.607556 0.794277i \(-0.292150\pi\)
−0.384086 + 0.923297i \(0.625483\pi\)
\(458\) 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 0.212346 0.977195i \(-0.431890\pi\)
0.952448 + 0.304700i \(0.0985562\pi\)
\(462\) 3.58755 2.07127i 0.166908 0.0963643i
\(463\) 14.2284i 0.661251i −0.943762 0.330625i \(-0.892740\pi\)
0.943762 0.330625i \(-0.107260\pi\)
\(464\) −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 0.466686 0.884423i \(-0.345448\pi\)
−0.532590 + 0.846373i \(0.678781\pi\)
\(480\) −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 −0.528854 0.848713i \(-0.677378\pi\)
0.470580 + 0.882357i \(0.344045\pi\)
\(488\) −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 −0.627175 0.778878i \(-0.715789\pi\)
0.988116 + 0.153711i \(0.0491224\pi\)
\(492\) −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 \(0.129819\pi\)
−0.917980 + 0.396627i \(0.870181\pi\)
\(500\) 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 0.879059 0.476713i \(-0.158172\pi\)
−0.852375 + 0.522931i \(0.824839\pi\)
\(504\) −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 0.615774 0.787923i \(-0.288844\pi\)
−0.374474 + 0.927237i \(0.622177\pi\)
\(510\) −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 −0.880377 0.474274i \(-0.842711\pi\)
0.850922 + 0.525292i \(0.176044\pi\)
\(524\) −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 \(0.142655\pi\)
−0.901245 + 0.433310i \(0.857345\pi\)
\(542\) −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 −0.00157977 0.999999i \(-0.500503\pi\)
−0.866814 + 0.498631i \(0.833836\pi\)
\(558\) 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 0.991725 + 0.128382i \(0.0409784\pi\)
−0.384680 + 0.923050i \(0.625688\pi\)
\(564\) 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 0.415434 + 0.909623i \(0.363630\pi\)
−0.995474 + 0.0950353i \(0.969704\pi\)
\(570\) −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 \(0.0630947\pi\)
−0.980419 + 0.196922i \(0.936905\pi\)
\(578\) 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 0.0625654 0.998041i \(-0.480072\pi\)
−0.833046 + 0.553204i \(0.813405\pi\)
\(588\) −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 \(0.0259909\pi\)
−0.996668 + 0.0815622i \(0.974009\pi\)
\(594\) −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 −0.450305 0.892875i \(-0.648685\pi\)
0.998405 0.0564616i \(-0.0179818\pi\)
\(602\) −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 −0.999960 0.00899773i \(-0.997136\pi\)
0.492187 0.870489i \(-0.336197\pi\)
\(608\) 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 0.0775527 0.996988i \(-0.475289\pi\)
−0.824641 + 0.565657i \(0.808623\pi\)
\(614\) 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 −0.948662 0.316291i \(-0.897562\pi\)
−0.200415 + 0.979711i \(0.564229\pi\)
\(618\) 16.6816 9.63111i 0.671031 0.387420i
\(619\) 48.9117i 1.96593i −0.183795 0.982965i \(-0.558838\pi\)
0.183795 0.982965i \(-0.441162\pi\)
\(620\) −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 −0.404563 0.914510i \(-0.632576\pi\)
0.589707 + 0.807617i \(0.299243\pi\)
\(632\) 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 0.929555 + 0.368683i \(0.120191\pi\)
−0.145489 + 0.989360i \(0.546475\pi\)
\(642\) 5.97647i 0.235872i
\(643\) 27.8388 16.0727i 1.09785 0.633847i 0.162198 0.986758i \(-0.448142\pi\)
0.935657 + 0.352911i \(0.114808\pi\)
\(644\) 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 −0.992475 0.122450i \(-0.960925\pi\)
0.602282 + 0.798283i \(0.294258\pi\)
\(648\) −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 −0.618065 0.786127i \(-0.712083\pi\)
0.989838 + 0.142197i \(0.0454165\pi\)
\(654\) 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 0.927693 0.373345i \(-0.121789\pi\)
−0.787173 + 0.616733i \(0.788456\pi\)
\(660\) −1.09067 + 1.88909i −0.0424542 + 0.0735329i
\(661\) 14.5068 + 8.37548i 0.564248 + 0.325769i 0.754849 0.655899i \(-0.227710\pi\)
−0.190601 + 0.981668i \(0.561044\pi\)
\(662\) 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 0.241539 + 0.970391i \(0.422348\pi\)
−0.961153 + 0.276016i \(0.910986\pi\)
\(674\) 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 −0.533910 0.845541i \(-0.679278\pi\)
0.465305 + 0.885150i \(0.345945\pi\)
\(684\) 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 0.956328 0.292295i \(-0.0944190\pi\)
0.225029 + 0.974352i \(0.427752\pi\)
\(692\) 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 −0.740620 0.671924i \(-0.765468\pi\)
0.211594 + 0.977358i \(0.432135\pi\)
\(710\) 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 0.757417 0.652931i \(-0.226461\pi\)
−0.944164 + 0.329477i \(0.893127\pi\)
\(720\) 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 \(-0.790384\pi\)
0.790894 0.611953i \(-0.209616\pi\)
\(734\) −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 0.434670 0.900590i \(-0.356865\pi\)
−0.562598 + 0.826730i \(0.690198\pi\)
\(740\) 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 0.685421 0.728147i \(-0.259618\pi\)
−0.287883 + 0.957666i \(0.592952\pi\)
\(744\) −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 −0.289112 0.957295i \(-0.593360\pi\)
0.973598 0.228269i \(-0.0733065\pi\)
\(752\) −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 −0.349258 0.937027i \(-0.613566\pi\)
0.986118 0.166047i \(-0.0531004\pi\)
\(758\) 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 −0.566009 0.824399i \(-0.691513\pi\)
0.430946 + 0.902378i \(0.358180\pi\)
\(762\) 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 0.679024 0.734116i \(-0.262403\pi\)
−0.296251 + 0.955110i \(0.595737\pi\)
\(770\) −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 −0.558063 0.829799i \(-0.688455\pi\)
0.439596 + 0.898196i \(0.355122\pi\)
\(774\) −16.4654 + 9.50628i −0.591835 + 0.341696i
\(775\) 3.52673i 0.126684i
\(776\)