Properties

Label 76.2.i.a.73.2
Level $76$
Weight $2$
Character 76.73
Analytic conductor $0.607$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.606863055362\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} - 3969 x^{3} - 2088 x^{2} + 4446 x + 4161\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 73.2
Root \(2.25236 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 76.73
Dual form 76.2.i.a.25.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.456991 - 0.166331i) q^{3} +(0.485063 - 2.75093i) q^{5} +(1.68285 + 2.91479i) q^{7} +(-2.11696 + 1.77634i) q^{9} +O(q^{10})\) \(q+(0.456991 - 0.166331i) q^{3} +(0.485063 - 2.75093i) q^{5} +(1.68285 + 2.91479i) q^{7} +(-2.11696 + 1.77634i) q^{9} +(0.258097 - 0.447037i) q^{11} +(-4.37365 - 1.59188i) q^{13} +(-0.235896 - 1.33783i) q^{15} +(-0.735881 - 0.617477i) q^{17} +(-3.12016 + 3.04379i) q^{19} +(1.25387 + 1.05212i) q^{21} +(0.629673 + 3.57105i) q^{23} +(-2.63386 - 0.958648i) q^{25} +(-1.40145 + 2.42738i) q^{27} +(6.21450 - 5.21459i) q^{29} +(-2.38969 - 4.13907i) q^{31} +(0.0435918 - 0.247221i) q^{33} +(8.83466 - 3.21555i) q^{35} +9.13084 q^{37} -2.26350 q^{39} +(-6.54978 + 2.38392i) q^{41} +(-0.817138 + 4.63422i) q^{43} +(3.85973 + 6.68524i) q^{45} +(10.4172 - 8.74111i) q^{47} +(-2.16398 + 3.74813i) q^{49} +(-0.438996 - 0.159782i) q^{51} +(-1.20127 - 6.81274i) q^{53} +(-1.10457 - 0.926847i) q^{55} +(-0.919606 + 1.90996i) q^{57} +(-10.9602 - 9.19667i) q^{59} +(1.05803 + 6.00040i) q^{61} +(-8.74018 - 3.18116i) q^{63} +(-6.50065 + 11.2594i) q^{65} +(3.38541 - 2.84069i) q^{67} +(0.881732 + 1.52720i) q^{69} +(-1.66206 + 9.42601i) q^{71} +(5.65102 - 2.05680i) q^{73} -1.36310 q^{75} +1.73735 q^{77} +(-9.85305 + 3.58622i) q^{79} +(1.20293 - 6.82213i) q^{81} +(2.39066 + 4.14075i) q^{83} +(-2.05558 + 1.72484i) q^{85} +(1.97262 - 3.41669i) q^{87} +(-8.30245 - 3.02185i) q^{89} +(-2.72022 - 15.4272i) q^{91} +(-1.78053 - 1.49404i) q^{93} +(6.85977 + 10.0598i) q^{95} +(8.46492 + 7.10291i) q^{97} +(0.247709 + 1.40483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 3q^{3} + 3q^{7} - 3q^{9} + O(q^{10}) \) \( 12q - 3q^{3} + 3q^{7} - 3q^{9} + 3q^{11} - 9q^{13} - 15q^{15} - 3q^{17} - 12q^{19} - 15q^{21} - 12q^{23} - 18q^{25} - 9q^{27} + 27q^{29} + 6q^{31} + 48q^{33} + 33q^{35} - 12q^{37} + 60q^{39} + 3q^{41} + 27q^{43} + 24q^{45} - 15q^{47} + 9q^{49} - 33q^{51} - 21q^{53} - 27q^{55} - 42q^{57} - 48q^{59} - 6q^{61} - 9q^{63} - 33q^{65} + 24q^{67} - 33q^{69} + 30q^{73} + 42q^{75} + 24q^{77} + 3q^{79} + 3q^{81} + 3q^{83} - 42q^{85} - 18q^{87} - 18q^{89} - 24q^{91} - 78q^{93} + 9q^{95} + 12q^{97} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.456991 0.166331i 0.263844 0.0960313i −0.206711 0.978402i \(-0.566276\pi\)
0.470555 + 0.882371i \(0.344054\pi\)
\(4\) 0 0
\(5\) 0.485063 2.75093i 0.216927 1.23025i −0.660605 0.750734i \(-0.729700\pi\)
0.877531 0.479519i \(-0.159189\pi\)
\(6\) 0 0
\(7\) 1.68285 + 2.91479i 0.636058 + 1.10169i 0.986290 + 0.165022i \(0.0527696\pi\)
−0.350231 + 0.936663i \(0.613897\pi\)
\(8\) 0 0
\(9\) −2.11696 + 1.77634i −0.705653 + 0.592113i
\(10\) 0 0
\(11\) 0.258097 0.447037i 0.0778191 0.134787i −0.824490 0.565877i \(-0.808538\pi\)
0.902309 + 0.431090i \(0.141871\pi\)
\(12\) 0 0
\(13\) −4.37365 1.59188i −1.21303 0.441508i −0.345278 0.938500i \(-0.612215\pi\)
−0.867755 + 0.496993i \(0.834438\pi\)
\(14\) 0 0
\(15\) −0.235896 1.33783i −0.0609080 0.345426i
\(16\) 0 0
\(17\) −0.735881 0.617477i −0.178477 0.149760i 0.549173 0.835709i \(-0.314943\pi\)
−0.727650 + 0.685949i \(0.759387\pi\)
\(18\) 0 0
\(19\) −3.12016 + 3.04379i −0.715813 + 0.698292i
\(20\) 0 0
\(21\) 1.25387 + 1.05212i 0.273616 + 0.229591i
\(22\) 0 0
\(23\) 0.629673 + 3.57105i 0.131296 + 0.744616i 0.977368 + 0.211547i \(0.0678501\pi\)
−0.846072 + 0.533069i \(0.821039\pi\)
\(24\) 0 0
\(25\) −2.63386 0.958648i −0.526773 0.191730i
\(26\) 0 0
\(27\) −1.40145 + 2.42738i −0.269709 + 0.467150i
\(28\) 0 0
\(29\) 6.21450 5.21459i 1.15400 0.968325i 0.154199 0.988040i \(-0.450720\pi\)
0.999806 + 0.0197150i \(0.00627588\pi\)
\(30\) 0 0
\(31\) −2.38969 4.13907i −0.429202 0.743399i 0.567601 0.823304i \(-0.307872\pi\)
−0.996803 + 0.0799047i \(0.974538\pi\)
\(32\) 0 0
\(33\) 0.0435918 0.247221i 0.00758835 0.0430357i
\(34\) 0 0
\(35\) 8.83466 3.21555i 1.49333 0.543528i
\(36\) 0 0
\(37\) 9.13084 1.50110 0.750550 0.660813i \(-0.229789\pi\)
0.750550 + 0.660813i \(0.229789\pi\)
\(38\) 0 0
\(39\) −2.26350 −0.362450
\(40\) 0 0
\(41\) −6.54978 + 2.38392i −1.02290 + 0.372306i −0.798375 0.602161i \(-0.794306\pi\)
−0.224529 + 0.974467i \(0.572084\pi\)
\(42\) 0 0
\(43\) −0.817138 + 4.63422i −0.124612 + 0.706712i 0.856925 + 0.515441i \(0.172372\pi\)
−0.981537 + 0.191271i \(0.938739\pi\)
\(44\) 0 0
\(45\) 3.85973 + 6.68524i 0.575374 + 0.996577i
\(46\) 0 0
\(47\) 10.4172 8.74111i 1.51951 1.27502i 0.677562 0.735466i \(-0.263037\pi\)
0.841950 0.539555i \(-0.181408\pi\)
\(48\) 0 0
\(49\) −2.16398 + 3.74813i −0.309141 + 0.535447i
\(50\) 0 0
\(51\) −0.438996 0.159782i −0.0614718 0.0223739i
\(52\) 0 0
\(53\) −1.20127 6.81274i −0.165007 0.935802i −0.949057 0.315104i \(-0.897960\pi\)
0.784050 0.620698i \(-0.213151\pi\)
\(54\) 0 0
\(55\) −1.10457 0.926847i −0.148941 0.124976i
\(56\) 0 0
\(57\) −0.919606 + 1.90996i −0.121805 + 0.252981i
\(58\) 0 0
\(59\) −10.9602 9.19667i −1.42689 1.19730i −0.947522 0.319691i \(-0.896421\pi\)
−0.479370 0.877613i \(-0.659135\pi\)
\(60\) 0 0
\(61\) 1.05803 + 6.00040i 0.135467 + 0.768272i 0.974533 + 0.224243i \(0.0719908\pi\)
−0.839066 + 0.544029i \(0.816898\pi\)
\(62\) 0 0
\(63\) −8.74018 3.18116i −1.10116 0.400789i
\(64\) 0 0
\(65\) −6.50065 + 11.2594i −0.806306 + 1.39656i
\(66\) 0 0
\(67\) 3.38541 2.84069i 0.413593 0.347046i −0.412126 0.911127i \(-0.635214\pi\)
0.825720 + 0.564081i \(0.190769\pi\)
\(68\) 0 0
\(69\) 0.881732 + 1.52720i 0.106148 + 0.183854i
\(70\) 0 0
\(71\) −1.66206 + 9.42601i −0.197250 + 1.11866i 0.711928 + 0.702253i \(0.247822\pi\)
−0.909178 + 0.416408i \(0.863289\pi\)
\(72\) 0 0
\(73\) 5.65102 2.05680i 0.661401 0.240730i 0.0105601 0.999944i \(-0.496639\pi\)
0.650841 + 0.759214i \(0.274416\pi\)
\(74\) 0 0
\(75\) −1.36310 −0.157398
\(76\) 0 0
\(77\) 1.73735 0.197990
\(78\) 0 0
\(79\) −9.85305 + 3.58622i −1.10856 + 0.403481i −0.830463 0.557073i \(-0.811924\pi\)
−0.278092 + 0.960554i \(0.589702\pi\)
\(80\) 0 0
\(81\) 1.20293 6.82213i 0.133658 0.758015i
\(82\) 0 0
\(83\) 2.39066 + 4.14075i 0.262409 + 0.454506i 0.966882 0.255225i \(-0.0821497\pi\)
−0.704472 + 0.709731i \(0.748816\pi\)
\(84\) 0 0
\(85\) −2.05558 + 1.72484i −0.222959 + 0.187085i
\(86\) 0 0
\(87\) 1.97262 3.41669i 0.211487 0.366307i
\(88\) 0 0
\(89\) −8.30245 3.02185i −0.880058 0.320315i −0.137825 0.990457i \(-0.544011\pi\)
−0.742233 + 0.670142i \(0.766233\pi\)
\(90\) 0 0
\(91\) −2.72022 15.4272i −0.285157 1.61721i
\(92\) 0 0
\(93\) −1.78053 1.49404i −0.184632 0.154925i
\(94\) 0 0
\(95\) 6.85977 + 10.0598i 0.703797 + 1.03211i
\(96\) 0 0
\(97\) 8.46492 + 7.10291i 0.859482 + 0.721191i 0.961856 0.273555i \(-0.0881994\pi\)
−0.102374 + 0.994746i \(0.532644\pi\)
\(98\) 0 0
\(99\) 0.247709 + 1.40483i 0.0248956 + 0.141190i
\(100\) 0 0
\(101\) −0.382988 0.139396i −0.0381087 0.0138704i 0.322895 0.946435i \(-0.395344\pi\)
−0.361004 + 0.932564i \(0.617566\pi\)
\(102\) 0 0
\(103\) 2.40104 4.15872i 0.236581 0.409770i −0.723150 0.690691i \(-0.757306\pi\)
0.959731 + 0.280921i \(0.0906398\pi\)
\(104\) 0 0
\(105\) 3.50251 2.93896i 0.341810 0.286813i
\(106\) 0 0
\(107\) 4.53236 + 7.85028i 0.438160 + 0.758916i 0.997548 0.0699906i \(-0.0222969\pi\)
−0.559387 + 0.828906i \(0.688964\pi\)
\(108\) 0 0
\(109\) 1.35374 7.67741i 0.129664 0.735363i −0.848763 0.528773i \(-0.822652\pi\)
0.978428 0.206590i \(-0.0662366\pi\)
\(110\) 0 0
\(111\) 4.17271 1.51874i 0.396056 0.144153i
\(112\) 0 0
\(113\) −3.07308 −0.289091 −0.144546 0.989498i \(-0.546172\pi\)
−0.144546 + 0.989498i \(0.546172\pi\)
\(114\) 0 0
\(115\) 10.1291 0.944547
\(116\) 0 0
\(117\) 12.0866 4.39915i 1.11740 0.406701i
\(118\) 0 0
\(119\) 0.561435 3.18406i 0.0514667 0.291882i
\(120\) 0 0
\(121\) 5.36677 + 9.29552i 0.487888 + 0.845047i
\(122\) 0 0
\(123\) −2.59667 + 2.17886i −0.234134 + 0.196461i
\(124\) 0 0
\(125\) 3.06865 5.31506i 0.274469 0.475394i
\(126\) 0 0
\(127\) −9.77012 3.55603i −0.866958 0.315547i −0.130023 0.991511i \(-0.541505\pi\)
−0.736935 + 0.675964i \(0.763727\pi\)
\(128\) 0 0
\(129\) 0.397390 + 2.25371i 0.0349882 + 0.198428i
\(130\) 0 0
\(131\) 2.54356 + 2.13430i 0.222232 + 0.186475i 0.747106 0.664705i \(-0.231443\pi\)
−0.524874 + 0.851180i \(0.675887\pi\)
\(132\) 0 0
\(133\) −14.1227 3.97234i −1.22460 0.344446i
\(134\) 0 0
\(135\) 5.99777 + 5.03272i 0.516206 + 0.433148i
\(136\) 0 0
\(137\) 0.738982 + 4.19097i 0.0631355 + 0.358059i 0.999966 + 0.00827481i \(0.00263398\pi\)
−0.936830 + 0.349784i \(0.886255\pi\)
\(138\) 0 0
\(139\) 4.85603 + 1.76745i 0.411883 + 0.149913i 0.539647 0.841892i \(-0.318558\pi\)
−0.127764 + 0.991805i \(0.540780\pi\)
\(140\) 0 0
\(141\) 3.30667 5.72732i 0.278472 0.482327i
\(142\) 0 0
\(143\) −1.84045 + 1.54432i −0.153906 + 0.129143i
\(144\) 0 0
\(145\) −11.3305 19.6251i −0.940950 1.62977i
\(146\) 0 0
\(147\) −0.365491 + 2.07280i −0.0301451 + 0.170962i
\(148\) 0 0
\(149\) −17.5930 + 6.40331i −1.44127 + 0.524580i −0.940139 0.340791i \(-0.889305\pi\)
−0.501132 + 0.865371i \(0.667083\pi\)
\(150\) 0 0
\(151\) 9.08388 0.739235 0.369618 0.929184i \(-0.379489\pi\)
0.369618 + 0.929184i \(0.379489\pi\)
\(152\) 0 0
\(153\) 2.65468 0.214618
\(154\) 0 0
\(155\) −12.5454 + 4.56617i −1.00767 + 0.366764i
\(156\) 0 0
\(157\) −0.531125 + 3.01216i −0.0423884 + 0.240397i −0.998639 0.0521517i \(-0.983392\pi\)
0.956251 + 0.292548i \(0.0945032\pi\)
\(158\) 0 0
\(159\) −1.68214 2.91355i −0.133402 0.231060i
\(160\) 0 0
\(161\) −9.34920 + 7.84491i −0.736820 + 0.618266i
\(162\) 0 0
\(163\) −7.64442 + 13.2405i −0.598757 + 1.03708i 0.394248 + 0.919004i \(0.371005\pi\)
−0.993005 + 0.118074i \(0.962328\pi\)
\(164\) 0 0
\(165\) −0.658943 0.239836i −0.0512987 0.0186712i
\(166\) 0 0
\(167\) 2.57778 + 14.6193i 0.199475 + 1.13128i 0.905901 + 0.423491i \(0.139195\pi\)
−0.706426 + 0.707787i \(0.749694\pi\)
\(168\) 0 0
\(169\) 6.63618 + 5.56842i 0.510475 + 0.428340i
\(170\) 0 0
\(171\) 1.19844 11.9860i 0.0916473 0.916594i
\(172\) 0 0
\(173\) −4.06288 3.40916i −0.308895 0.259194i 0.475140 0.879910i \(-0.342397\pi\)
−0.784035 + 0.620716i \(0.786842\pi\)
\(174\) 0 0
\(175\) −1.63815 9.29041i −0.123833 0.702289i
\(176\) 0 0
\(177\) −6.53839 2.37978i −0.491455 0.178875i
\(178\) 0 0
\(179\) −5.46494 + 9.46556i −0.408469 + 0.707489i −0.994718 0.102641i \(-0.967271\pi\)
0.586249 + 0.810131i \(0.300604\pi\)
\(180\) 0 0
\(181\) −2.57271 + 2.15876i −0.191228 + 0.160460i −0.733375 0.679824i \(-0.762056\pi\)
0.542147 + 0.840284i \(0.317612\pi\)
\(182\) 0 0
\(183\) 1.48156 + 2.56614i 0.109520 + 0.189695i
\(184\) 0 0
\(185\) 4.42903 25.1183i 0.325629 1.84673i
\(186\) 0 0
\(187\) −0.465963 + 0.169597i −0.0340746 + 0.0124021i
\(188\) 0 0
\(189\) −9.43373 −0.686203
\(190\) 0 0
\(191\) −17.6763 −1.27902 −0.639508 0.768785i \(-0.720862\pi\)
−0.639508 + 0.768785i \(0.720862\pi\)
\(192\) 0 0
\(193\) 23.3296 8.49127i 1.67930 0.611215i 0.686086 0.727521i \(-0.259328\pi\)
0.993213 + 0.116306i \(0.0371053\pi\)
\(194\) 0 0
\(195\) −1.09794 + 6.22672i −0.0786251 + 0.445905i
\(196\) 0 0
\(197\) −0.599101 1.03767i −0.0426842 0.0739311i 0.843894 0.536510i \(-0.180258\pi\)
−0.886578 + 0.462579i \(0.846924\pi\)
\(198\) 0 0
\(199\) 10.0334 8.41899i 0.711246 0.596806i −0.213703 0.976899i \(-0.568552\pi\)
0.924948 + 0.380093i \(0.124108\pi\)
\(200\) 0 0
\(201\) 1.07460 1.86127i 0.0757968 0.131284i
\(202\) 0 0
\(203\) 25.6575 + 9.33857i 1.80080 + 0.655439i
\(204\) 0 0
\(205\) 3.38095 + 19.1743i 0.236136 + 1.33919i
\(206\) 0 0
\(207\) −7.67639 6.44126i −0.533546 0.447698i
\(208\) 0 0
\(209\) 0.555382 + 2.18041i 0.0384166 + 0.150822i
\(210\) 0 0
\(211\) 0.362133 + 0.303866i 0.0249303 + 0.0209190i 0.655168 0.755484i \(-0.272598\pi\)
−0.630237 + 0.776403i \(0.717042\pi\)
\(212\) 0 0
\(213\) 0.808292 + 4.58405i 0.0553833 + 0.314094i
\(214\) 0 0
\(215\) 12.3520 + 4.49578i 0.842402 + 0.306609i
\(216\) 0 0
\(217\) 8.04301 13.9309i 0.545995 0.945691i
\(218\) 0 0
\(219\) 2.24035 1.87988i 0.151389 0.127030i
\(220\) 0 0
\(221\) 2.23554 + 3.87206i 0.150378 + 0.260463i
\(222\) 0 0
\(223\) −3.40576 + 19.3150i −0.228066 + 1.29343i 0.628669 + 0.777673i \(0.283600\pi\)
−0.856736 + 0.515756i \(0.827511\pi\)
\(224\) 0 0
\(225\) 7.27867 2.64922i 0.485244 0.176615i
\(226\) 0 0
\(227\) 0.929069 0.0616645 0.0308322 0.999525i \(-0.490184\pi\)
0.0308322 + 0.999525i \(0.490184\pi\)
\(228\) 0 0
\(229\) −7.58741 −0.501390 −0.250695 0.968066i \(-0.580659\pi\)
−0.250695 + 0.968066i \(0.580659\pi\)
\(230\) 0 0
\(231\) 0.793955 0.288976i 0.0522384 0.0190132i
\(232\) 0 0
\(233\) 0.646394 3.66588i 0.0423467 0.240160i −0.956286 0.292433i \(-0.905535\pi\)
0.998633 + 0.0522725i \(0.0166464\pi\)
\(234\) 0 0
\(235\) −18.9931 32.8971i −1.23898 2.14597i
\(236\) 0 0
\(237\) −3.90626 + 3.27774i −0.253739 + 0.212912i
\(238\) 0 0
\(239\) 9.65144 16.7168i 0.624300 1.08132i −0.364376 0.931252i \(-0.618718\pi\)
0.988676 0.150067i \(-0.0479490\pi\)
\(240\) 0 0
\(241\) 12.8080 + 4.66174i 0.825037 + 0.300289i 0.719821 0.694160i \(-0.244224\pi\)
0.105217 + 0.994449i \(0.466446\pi\)
\(242\) 0 0
\(243\) −2.04516 11.5987i −0.131197 0.744056i
\(244\) 0 0
\(245\) 9.26118 + 7.77105i 0.591675 + 0.496474i
\(246\) 0 0
\(247\) 18.4918 8.34555i 1.17661 0.531015i
\(248\) 0 0
\(249\) 1.78125 + 1.49464i 0.112882 + 0.0947191i
\(250\) 0 0
\(251\) −2.99329 16.9758i −0.188935 1.07150i −0.920794 0.390048i \(-0.872458\pi\)
0.731859 0.681456i \(-0.238653\pi\)
\(252\) 0 0
\(253\) 1.75891 + 0.640190i 0.110582 + 0.0402484i
\(254\) 0 0
\(255\) −0.652489 + 1.13014i −0.0408604 + 0.0707724i
\(256\) 0 0
\(257\) −10.4154 + 8.73957i −0.649695 + 0.545159i −0.906979 0.421177i \(-0.861617\pi\)
0.257283 + 0.966336i \(0.417173\pi\)
\(258\) 0 0
\(259\) 15.3659 + 26.6144i 0.954788 + 1.65374i
\(260\) 0 0
\(261\) −3.89297 + 22.0781i −0.240969 + 1.36660i
\(262\) 0 0
\(263\) −7.53896 + 2.74396i −0.464872 + 0.169200i −0.563828 0.825892i \(-0.690672\pi\)
0.0989559 + 0.995092i \(0.468450\pi\)
\(264\) 0 0
\(265\) −19.3241 −1.18707
\(266\) 0 0
\(267\) −4.29677 −0.262958
\(268\) 0 0
\(269\) 0.158312 0.0576210i 0.00965248 0.00351322i −0.337189 0.941437i \(-0.609476\pi\)
0.346842 + 0.937924i \(0.387254\pi\)
\(270\) 0 0
\(271\) −2.06021 + 11.6841i −0.125149 + 0.709756i 0.856070 + 0.516860i \(0.172899\pi\)
−0.981219 + 0.192896i \(0.938212\pi\)
\(272\) 0 0
\(273\) −3.80913 6.59761i −0.230539 0.399306i
\(274\) 0 0
\(275\) −1.10834 + 0.930010i −0.0668356 + 0.0560817i
\(276\) 0 0
\(277\) −1.34766 + 2.33422i −0.0809733 + 0.140250i −0.903668 0.428233i \(-0.859136\pi\)
0.822695 + 0.568483i \(0.192470\pi\)
\(278\) 0 0
\(279\) 12.4113 + 4.51734i 0.743044 + 0.270446i
\(280\) 0 0
\(281\) 3.33967 + 18.9402i 0.199228 + 1.12988i 0.906267 + 0.422705i \(0.138919\pi\)
−0.707039 + 0.707174i \(0.749970\pi\)
\(282\) 0 0
\(283\) −21.2293 17.8135i −1.26195 1.05890i −0.995471 0.0950608i \(-0.969695\pi\)
−0.266478 0.963841i \(-0.585860\pi\)
\(284\) 0 0
\(285\) 4.80810 + 3.45622i 0.284807 + 0.204729i
\(286\) 0 0
\(287\) −17.9709 15.0794i −1.06079 0.890109i
\(288\) 0 0
\(289\) −2.79178 15.8330i −0.164222 0.931350i
\(290\) 0 0
\(291\) 5.04983 + 1.83799i 0.296026 + 0.107745i
\(292\) 0 0
\(293\) 8.84253 15.3157i 0.516586 0.894754i −0.483228 0.875494i \(-0.660536\pi\)
0.999815 0.0192592i \(-0.00613078\pi\)
\(294\) 0 0
\(295\) −30.6158 + 25.6897i −1.78252 + 1.49571i
\(296\) 0 0
\(297\) 0.723419 + 1.25300i 0.0419770 + 0.0727064i
\(298\) 0 0
\(299\) 2.93071 16.6209i 0.169488 0.961211i
\(300\) 0 0
\(301\) −14.8829 + 5.41692i −0.857835 + 0.312226i
\(302\) 0 0
\(303\) −0.198208 −0.0113868
\(304\) 0 0
\(305\) 17.0199 0.974555
\(306\) 0 0
\(307\) −9.96657 + 3.62753i −0.568822 + 0.207034i −0.610389 0.792101i \(-0.708987\pi\)
0.0415675 + 0.999136i \(0.486765\pi\)
\(308\) 0 0
\(309\) 0.405528 2.29986i 0.0230697 0.130835i
\(310\) 0 0
\(311\) −13.1081 22.7039i −0.743292 1.28742i −0.950989 0.309226i \(-0.899930\pi\)
0.207697 0.978193i \(-0.433403\pi\)
\(312\) 0 0
\(313\) −6.73987 + 5.65542i −0.380960 + 0.319663i −0.813079 0.582153i \(-0.802210\pi\)
0.432119 + 0.901817i \(0.357766\pi\)
\(314\) 0 0
\(315\) −12.9907 + 22.5005i −0.731943 + 1.26776i
\(316\) 0 0
\(317\) −15.5280 5.65174i −0.872140 0.317433i −0.133107 0.991102i \(-0.542495\pi\)
−0.739034 + 0.673669i \(0.764718\pi\)
\(318\) 0 0
\(319\) −0.727169 4.12398i −0.0407136 0.230898i
\(320\) 0 0
\(321\) 3.37700 + 2.83364i 0.188486 + 0.158158i
\(322\) 0 0
\(323\) 4.17553 0.313238i 0.232333 0.0174290i
\(324\) 0 0
\(325\) 9.99355 + 8.38559i 0.554343 + 0.465149i
\(326\) 0 0
\(327\) −0.658348 3.73368i −0.0364067 0.206473i
\(328\) 0 0
\(329\) 43.0091 + 15.6540i 2.37117 + 0.863036i
\(330\) 0 0
\(331\) 3.22922 5.59317i 0.177494 0.307429i −0.763528 0.645775i \(-0.776534\pi\)
0.941022 + 0.338347i \(0.109868\pi\)
\(332\) 0 0
\(333\) −19.3296 + 16.2195i −1.05926 + 0.888821i
\(334\) 0 0
\(335\) −6.17241 10.6909i −0.337235 0.584108i
\(336\) 0 0
\(337\) −1.92728 + 10.9302i −0.104986 + 0.595404i 0.886240 + 0.463226i \(0.153308\pi\)
−0.991226 + 0.132178i \(0.957803\pi\)
\(338\) 0 0
\(339\) −1.40437 + 0.511149i −0.0762750 + 0.0277618i
\(340\) 0 0
\(341\) −2.46709 −0.133600
\(342\) 0 0
\(343\) 8.99327 0.485591
\(344\) 0 0
\(345\) 4.62893 1.68479i 0.249213 0.0907061i
\(346\) 0 0
\(347\) 0.526344 2.98505i 0.0282556 0.160246i −0.967415 0.253195i \(-0.918518\pi\)
0.995671 + 0.0929497i \(0.0296296\pi\)
\(348\) 0 0
\(349\) 2.04290 + 3.53842i 0.109354 + 0.189407i 0.915509 0.402298i \(-0.131788\pi\)
−0.806155 + 0.591705i \(0.798455\pi\)
\(350\) 0 0
\(351\) 9.99355 8.38559i 0.533416 0.447590i
\(352\) 0 0
\(353\) 8.04626 13.9365i 0.428259 0.741767i −0.568459 0.822711i \(-0.692460\pi\)
0.996719 + 0.0809447i \(0.0257937\pi\)
\(354\) 0 0
\(355\) 25.1241 + 9.14442i 1.33345 + 0.485335i
\(356\) 0 0
\(357\) −0.273037 1.54847i −0.0144506 0.0819537i
\(358\) 0 0
\(359\) 22.4035 + 18.7988i 1.18241 + 0.992160i 0.999960 + 0.00894547i \(0.00284747\pi\)
0.182451 + 0.983215i \(0.441597\pi\)
\(360\) 0 0
\(361\) 0.470738 18.9942i 0.0247757 0.999693i
\(362\) 0 0
\(363\) 3.99870 + 3.35531i 0.209877 + 0.176108i
\(364\) 0 0
\(365\) −2.91702 16.5432i −0.152684 0.865912i
\(366\) 0 0
\(367\) −7.57969 2.75878i −0.395657 0.144007i 0.136527 0.990636i \(-0.456406\pi\)
−0.532183 + 0.846629i \(0.678628\pi\)
\(368\) 0 0
\(369\) 9.63095 16.6813i 0.501367 0.868393i
\(370\) 0 0
\(371\) 17.8361 14.9663i 0.926006 0.777011i
\(372\) 0 0
\(373\) 0.0909149 + 0.157469i 0.00470740 + 0.00815345i 0.868370 0.495918i \(-0.165168\pi\)
−0.863662 + 0.504071i \(0.831835\pi\)
\(374\) 0 0
\(375\) 0.518286 2.93935i 0.0267642 0.151787i
\(376\) 0 0
\(377\) −35.4811 + 12.9141i −1.82737 + 0.665108i
\(378\) 0 0
\(379\) 2.82977 0.145355 0.0726777 0.997355i \(-0.476846\pi\)
0.0726777 + 0.997355i \(0.476846\pi\)
\(380\) 0 0
\(381\) −5.05633 −0.259044
\(382\) 0 0
\(383\) 24.5927 8.95103i 1.25663 0.457376i 0.373994 0.927431i \(-0.377988\pi\)
0.882637 + 0.470055i \(0.155766\pi\)
\(384\) 0 0
\(385\) 0.842727 4.77934i 0.0429493 0.243578i
\(386\) 0 0
\(387\) −6.50210 11.2620i −0.330520 0.572478i
\(388\) 0 0
\(389\) −13.7179 + 11.5107i −0.695528 + 0.583617i −0.920497 0.390749i \(-0.872216\pi\)
0.224970 + 0.974366i \(0.427772\pi\)
\(390\) 0 0
\(391\) 1.74168 3.01668i 0.0880805 0.152560i
\(392\) 0 0
\(393\) 1.51739 + 0.552283i 0.0765420 + 0.0278590i
\(394\) 0 0
\(395\) 5.08608 + 28.8446i 0.255909 + 1.45133i
\(396\) 0 0
\(397\) 2.05186 + 1.72171i 0.102980 + 0.0864103i 0.692824 0.721107i \(-0.256366\pi\)
−0.589844 + 0.807517i \(0.700811\pi\)
\(398\) 0 0
\(399\) −7.11469 + 0.533727i −0.356180 + 0.0267198i
\(400\) 0 0
\(401\) 23.8632 + 20.0236i 1.19167 + 0.999929i 0.999829 + 0.0185028i \(0.00588995\pi\)
0.191840 + 0.981426i \(0.438554\pi\)
\(402\) 0 0
\(403\) 3.86279 + 21.9070i 0.192419 + 1.09126i
\(404\) 0 0
\(405\) −18.1837 6.61833i −0.903556 0.328867i
\(406\) 0 0
\(407\) 2.35664 4.08182i 0.116814 0.202328i
\(408\) 0 0
\(409\) 8.46492 7.10291i 0.418563 0.351216i −0.409053 0.912511i \(-0.634141\pi\)
0.827616 + 0.561294i \(0.189696\pi\)
\(410\) 0 0
\(411\) 1.03480 + 1.79232i 0.0510428 + 0.0884087i
\(412\) 0 0
\(413\) 8.36198 47.4232i 0.411466 2.33354i
\(414\) 0 0
\(415\) 12.5505 4.56802i 0.616081 0.224235i
\(416\) 0 0
\(417\) 2.51314 0.123069
\(418\) 0 0
\(419\) −8.02242 −0.391921 −0.195960 0.980612i \(-0.562782\pi\)
−0.195960 + 0.980612i \(0.562782\pi\)
\(420\) 0 0
\(421\) 17.7095 6.44572i 0.863107 0.314145i 0.127734 0.991808i \(-0.459230\pi\)
0.735372 + 0.677663i \(0.237007\pi\)
\(422\) 0 0
\(423\) −6.52571 + 37.0091i −0.317291 + 1.79945i
\(424\) 0 0
\(425\) 1.34627 + 2.33180i 0.0653035 + 0.113109i
\(426\) 0 0
\(427\) −15.7094 + 13.1817i −0.760229 + 0.637908i
\(428\) 0 0
\(429\) −0.584201 + 1.01187i −0.0282055 + 0.0488534i
\(430\) 0 0
\(431\) −14.3859 5.23604i −0.692945 0.252211i −0.0285491 0.999592i \(-0.509089\pi\)
−0.664395 + 0.747381i \(0.731311\pi\)
\(432\) 0 0
\(433\) 0.647150 + 3.67017i 0.0311000 + 0.176377i 0.996401 0.0847620i \(-0.0270130\pi\)
−0.965301 + 0.261139i \(0.915902\pi\)
\(434\) 0 0
\(435\) −8.44221 7.08386i −0.404773 0.339645i
\(436\) 0 0
\(437\) −12.8342 9.22565i −0.613943 0.441322i
\(438\) 0 0
\(439\) −6.52228 5.47284i −0.311292 0.261205i 0.473734 0.880668i \(-0.342906\pi\)
−0.785026 + 0.619463i \(0.787350\pi\)
\(440\) 0 0
\(441\) −2.07689 11.7786i −0.0988994 0.560886i
\(442\) 0 0
\(443\) 10.2321 + 3.72417i 0.486141 + 0.176941i 0.573450 0.819241i \(-0.305605\pi\)
−0.0873095 + 0.996181i \(0.527827\pi\)
\(444\) 0 0
\(445\) −12.3401 + 21.3737i −0.584977 + 1.01321i
\(446\) 0 0
\(447\) −6.97475 + 5.85251i −0.329894 + 0.276814i
\(448\) 0 0
\(449\) −3.42967 5.94036i −0.161856 0.280343i 0.773678 0.633579i \(-0.218415\pi\)
−0.935534 + 0.353236i \(0.885081\pi\)
\(450\) 0 0
\(451\) −0.624774 + 3.54327i −0.0294195 + 0.166846i
\(452\) 0 0
\(453\) 4.15125 1.51093i 0.195043 0.0709897i
\(454\) 0 0
\(455\) −43.7585 −2.05143
\(456\) 0 0
\(457\) −32.5371 −1.52202 −0.761010 0.648740i \(-0.775296\pi\)
−0.761010 + 0.648740i \(0.775296\pi\)
\(458\) 0 0
\(459\) 2.53015 0.920900i 0.118097 0.0429839i
\(460\) 0 0
\(461\) 3.42346 19.4154i 0.159446 0.904265i −0.795161 0.606398i \(-0.792614\pi\)
0.954608 0.297867i \(-0.0962751\pi\)
\(462\) 0 0
\(463\) 10.5884 + 18.3396i 0.492084 + 0.852314i 0.999958 0.00911693i \(-0.00290205\pi\)
−0.507875 + 0.861431i \(0.669569\pi\)
\(464\) 0 0
\(465\) −4.97366 + 4.17340i −0.230648 + 0.193537i
\(466\) 0 0
\(467\) 5.61175 9.71984i 0.259681 0.449781i −0.706475 0.707738i \(-0.749716\pi\)
0.966156 + 0.257957i \(0.0830492\pi\)
\(468\) 0 0
\(469\) 13.9772 + 5.08727i 0.645405 + 0.234908i
\(470\) 0 0
\(471\) 0.258296 + 1.46487i 0.0119017 + 0.0674977i
\(472\) 0 0
\(473\) 1.86076 + 1.56137i 0.0855580 + 0.0717917i
\(474\) 0 0
\(475\) 11.1360 5.02579i 0.510954 0.230599i
\(476\) 0 0
\(477\) 14.6448 + 12.2884i 0.670539 + 0.562649i
\(478\) 0 0
\(479\) 3.86409 + 21.9143i 0.176555 + 1.00129i 0.936334 + 0.351110i \(0.114196\pi\)
−0.759779 + 0.650181i \(0.774693\pi\)
\(480\) 0 0
\(481\) −39.9351 14.5352i −1.82088 0.662748i
\(482\) 0 0
\(483\) −2.96765 + 5.14012i −0.135033 + 0.233883i
\(484\) 0 0
\(485\) 23.6456 19.8410i 1.07369 0.900935i
\(486\) 0 0
\(487\) −2.74337 4.75166i −0.124314 0.215318i 0.797151 0.603781i \(-0.206340\pi\)
−0.921465 + 0.388462i \(0.873006\pi\)
\(488\) 0 0
\(489\) −1.29112 + 7.32230i −0.0583865 + 0.331126i
\(490\) 0 0
\(491\) −25.4961 + 9.27982i −1.15062 + 0.418792i −0.845739 0.533597i \(-0.820840\pi\)
−0.304884 + 0.952390i \(0.598618\pi\)
\(492\) 0 0
\(493\) −7.79302 −0.350980
\(494\) 0 0
\(495\) 3.98473 0.179100
\(496\) 0 0
\(497\) −30.2718 + 11.0180i −1.35788 + 0.494226i
\(498\) 0 0
\(499\) 2.79671 15.8609i 0.125198 0.710032i −0.855992 0.516988i \(-0.827053\pi\)
0.981190 0.193044i \(-0.0618359\pi\)
\(500\) 0 0
\(501\) 3.60967 + 6.25214i 0.161268 + 0.279325i
\(502\) 0 0
\(503\) 17.2137 14.4440i 0.767523 0.644028i −0.172550 0.985001i \(-0.555201\pi\)
0.940073 + 0.340973i \(0.110756\pi\)
\(504\) 0 0
\(505\) −0.569243 + 0.985957i −0.0253310 + 0.0438745i
\(506\) 0 0
\(507\) 3.95887 + 1.44091i 0.175820 + 0.0639932i
\(508\) 0 0
\(509\) 3.46194 + 19.6336i 0.153448 + 0.870246i 0.960191 + 0.279344i \(0.0901169\pi\)
−0.806743 + 0.590902i \(0.798772\pi\)
\(510\) 0 0
\(511\) 15.5050 + 13.0102i 0.685899 + 0.575538i
\(512\) 0 0
\(513\) −3.01569 11.8395i −0.133146 0.522728i
\(514\) 0 0
\(515\) −10.2757 8.62232i −0.452801 0.379945i
\(516\) 0 0
\(517\) −1.21894 6.91294i −0.0536088 0.304031i
\(518\) 0 0
\(519\) −2.42375 0.882173i −0.106391 0.0387231i
\(520\) 0 0
\(521\) −8.39608 + 14.5424i −0.367839 + 0.637116i −0.989227 0.146387i \(-0.953236\pi\)
0.621388 + 0.783503i \(0.286569\pi\)
\(522\) 0 0
\(523\) −11.8256 + 9.92282i −0.517096 + 0.433895i −0.863618 0.504147i \(-0.831807\pi\)
0.346522 + 0.938042i \(0.387363\pi\)
\(524\) 0 0
\(525\) −2.29390 3.97316i −0.100114 0.173403i
\(526\) 0 0
\(527\) −0.797253 + 4.52144i −0.0347289 + 0.196957i
\(528\) 0 0
\(529\) 9.25701 3.36928i 0.402479 0.146490i
\(530\) 0 0
\(531\) 39.5386 1.71583
\(532\) 0 0
\(533\) 32.4414 1.40519
\(534\) 0 0
\(535\) 23.7941 8.66033i 1.02871 0.374419i
\(536\) 0 0
\(537\) −0.923013 + 5.23467i −0.0398309 + 0.225892i
\(538\) 0 0
\(539\) 1.11703 + 1.93476i 0.0481141 + 0.0833360i
\(540\) 0 0
\(541\) 10.5437 8.84722i 0.453309 0.380372i −0.387353 0.921932i \(-0.626610\pi\)
0.840662 + 0.541560i \(0.182166\pi\)
\(542\) 0 0
\(543\) −0.816637 + 1.41446i −0.0350453 + 0.0607002i
\(544\) 0 0
\(545\) −20.4634 7.44806i −0.876555 0.319040i
\(546\) 0 0
\(547\) −6.60558 37.4621i −0.282434 1.60176i −0.714310 0.699830i \(-0.753259\pi\)
0.431875 0.901933i \(-0.357852\pi\)
\(548\) 0 0
\(549\) −12.8985 10.8232i −0.550497 0.461921i
\(550\) 0 0
\(551\) −3.51813 + 35.1859i −0.149877 + 1.49897i
\(552\) 0 0
\(553\) −27.0343 22.6845i −1.14962 0.964642i
\(554\) 0 0
\(555\) −2.15393 12.2155i −0.0914290 0.518520i
\(556\) 0 0
\(557\) 35.8744 + 13.0572i 1.52005 + 0.553251i 0.961160 0.275993i \(-0.0890068\pi\)
0.558886 + 0.829245i \(0.311229\pi\)
\(558\) 0 0
\(559\) 10.9510 18.9677i 0.463178 0.802247i
\(560\) 0 0
\(561\) −0.184732 + 0.155008i −0.00779938 + 0.00654446i
\(562\) 0 0
\(563\) 1.24788 + 2.16139i 0.0525919 + 0.0910919i 0.891123 0.453762i \(-0.149918\pi\)
−0.838531 + 0.544854i \(0.816585\pi\)
\(564\) 0 0
\(565\) −1.49064 + 8.45384i −0.0627117 + 0.355656i
\(566\) 0 0
\(567\) 21.9094 7.97437i 0.920108 0.334892i
\(568\) 0 0
\(569\) 36.7113 1.53902 0.769509 0.638636i \(-0.220501\pi\)
0.769509 + 0.638636i \(0.220501\pi\)
\(570\) 0 0
\(571\) 17.9010 0.749133 0.374567 0.927200i \(-0.377792\pi\)
0.374567 + 0.927200i \(0.377792\pi\)
\(572\) 0 0
\(573\) −8.07793 + 2.94012i −0.337460 + 0.122825i
\(574\) 0 0
\(575\) 1.76491 10.0093i 0.0736018 0.417417i
\(576\) 0 0
\(577\) 6.61207 + 11.4524i 0.275264 + 0.476771i 0.970202 0.242299i \(-0.0779014\pi\)
−0.694938 + 0.719070i \(0.744568\pi\)
\(578\) 0 0
\(579\) 9.24904 7.76087i 0.384377 0.322531i
\(580\) 0 0
\(581\) −8.04626 + 13.9365i −0.333815 + 0.578185i
\(582\) 0 0
\(583\) −3.35559 1.22133i −0.138974 0.0505825i
\(584\) 0 0
\(585\) −6.23900 35.3831i −0.257951 1.46291i
\(586\) 0 0
\(587\) 1.65952 + 1.39250i 0.0684957 + 0.0574747i 0.676393 0.736541i \(-0.263542\pi\)
−0.607897 + 0.794016i \(0.707987\pi\)
\(588\) 0 0
\(589\) 20.0547 + 5.64083i 0.826338 + 0.232426i
\(590\) 0 0
\(591\) −0.446381 0.374558i −0.0183617 0.0154073i
\(592\) 0 0
\(593\) 7.84333 + 44.4818i 0.322087 + 1.82665i 0.529400 + 0.848372i \(0.322417\pi\)
−0.207313 + 0.978275i \(0.566472\pi\)
\(594\) 0 0
\(595\) −8.48679 3.08894i −0.347924 0.126634i
\(596\) 0 0
\(597\) 3.18481 5.51626i 0.130346 0.225766i
\(598\) 0 0
\(599\) −7.79340 + 6.53944i −0.318430 + 0.267194i −0.787966 0.615719i \(-0.788866\pi\)
0.469536 + 0.882913i \(0.344421\pi\)
\(600\) 0 0
\(601\) 16.7570 + 29.0241i 0.683534 + 1.18392i 0.973895 + 0.226999i \(0.0728914\pi\)
−0.290361 + 0.956917i \(0.593775\pi\)
\(602\) 0 0
\(603\) −2.12073 + 12.0273i −0.0863629 + 0.489788i
\(604\) 0 0
\(605\) 28.1745 10.2547i 1.14546 0.416913i
\(606\) 0 0
\(607\) −17.0948 −0.693856 −0.346928 0.937892i \(-0.612775\pi\)
−0.346928 + 0.937892i \(0.612775\pi\)
\(608\) 0 0
\(609\) 13.2785 0.538074
\(610\) 0 0
\(611\) −59.4762 + 21.6476i −2.40615 + 0.875767i
\(612\) 0 0
\(613\) −1.92635 + 10.9248i −0.0778043 + 0.441250i 0.920874 + 0.389860i \(0.127476\pi\)
−0.998679 + 0.0513907i \(0.983635\pi\)
\(614\) 0 0
\(615\) 4.73435 + 8.20014i 0.190907 + 0.330661i
\(616\) 0 0
\(617\) 2.39215 2.00725i 0.0963042 0.0808088i −0.593364 0.804934i \(-0.702201\pi\)
0.689669 + 0.724125i \(0.257756\pi\)
\(618\) 0 0
\(619\) 0.214658 0.371798i 0.00862783 0.0149438i −0.861679 0.507453i \(-0.830587\pi\)
0.870307 + 0.492509i \(0.163920\pi\)
\(620\) 0 0
\(621\) −9.55076 3.47619i −0.383259 0.139495i
\(622\) 0 0
\(623\) −5.16377 29.2852i −0.206882 1.17329i
\(624\) 0 0
\(625\) −23.8686 20.0281i −0.954744 0.801126i
\(626\) 0 0
\(627\) 0.616475 + 0.904052i 0.0246196 + 0.0361044i
\(628\) 0 0
\(629\) −6.71921 5.63808i −0.267912 0.224805i
\(630\) 0 0
\(631\) −5.64012 31.9867i −0.224530 1.27337i −0.863582 0.504208i \(-0.831784\pi\)
0.639052 0.769163i \(-0.279327\pi\)
\(632\) 0 0
\(633\) 0.216034 + 0.0786299i 0.00858658 + 0.00312526i
\(634\) 0 0
\(635\) −14.5215 + 25.1520i −0.576269 + 0.998127i
\(636\) 0 0
\(637\) 15.4311 12.9482i 0.611402 0.513027i
\(638\) 0 0
\(639\) −13.2253 22.9068i −0.523184 0.906181i
\(640\) 0 0
\(641\) −3.22929 + 18.3142i −0.127549 + 0.723368i 0.852212 + 0.523197i \(0.175261\pi\)
−0.979761 + 0.200171i \(0.935850\pi\)
\(642\) 0 0
\(643\) 27.0472 9.84439i 1.06664 0.388225i 0.251720 0.967800i \(-0.419004\pi\)
0.814919 + 0.579575i \(0.196782\pi\)
\(644\) 0 0
\(645\) 6.39256 0.251707
\(646\) 0 0
\(647\) −36.0213 −1.41614 −0.708071 0.706141i \(-0.750435\pi\)
−0.708071 + 0.706141i \(0.750435\pi\)
\(648\) 0 0
\(649\) −6.94003 + 2.52596i −0.272420 + 0.0991528i
\(650\) 0 0
\(651\) 1.35844 7.70409i 0.0532414 0.301947i
\(652\) 0 0
\(653\) −14.4702 25.0631i −0.566262 0.980795i −0.996931 0.0782852i \(-0.975056\pi\)
0.430669 0.902510i \(-0.358278\pi\)
\(654\) 0 0
\(655\) 7.10510 5.96189i 0.277619 0.232950i
\(656\) 0 0
\(657\) −8.30939 + 14.3923i −0.324180 + 0.561497i
\(658\) 0 0
\(659\) −45.1158 16.4208i −1.75746 0.639664i −0.757550 0.652778i \(-0.773604\pi\)
−0.999914 + 0.0131131i \(0.995826\pi\)
\(660\) 0 0
\(661\) −1.64069 9.30480i −0.0638154 0.361915i −0.999947 0.0102659i \(-0.996732\pi\)
0.936132 0.351649i \(-0.114379\pi\)
\(662\) 0 0
\(663\) 1.66566 + 1.39766i 0.0646891 + 0.0542806i
\(664\) 0 0
\(665\) −17.7781 + 36.9238i −0.689403 + 1.43185i
\(666\) 0 0
\(667\) 22.5347 + 18.9088i 0.872546 + 0.732153i
\(668\) 0 0
\(669\) 1.65629 + 9.39327i 0.0640357 + 0.363165i
\(670\) 0 0
\(671\) 2.95547 + 1.07570i 0.114095 + 0.0415271i
\(672\) 0 0
\(673\) −9.60353 + 16.6338i −0.370189 + 0.641186i −0.989594 0.143885i \(-0.954040\pi\)
0.619406 + 0.785071i \(0.287374\pi\)
\(674\) 0 0
\(675\) 6.01823 5.04990i 0.231642 0.194371i
\(676\) 0 0
\(677\) −0.226932 0.393058i −0.00872171 0.0151064i 0.861632 0.507534i \(-0.169443\pi\)
−0.870353 + 0.492428i \(0.836110\pi\)
\(678\) 0 0
\(679\) −6.45825 + 36.6266i −0.247845 + 1.40560i
\(680\) 0 0
\(681\) 0.424576 0.154533i 0.0162698 0.00592172i
\(682\) 0 0
\(683\) 6.53688 0.250127 0.125063 0.992149i \(-0.460087\pi\)
0.125063 + 0.992149i \(0.460087\pi\)
\(684\) 0 0
\(685\) 11.8875 0.454199
\(686\) 0 0
\(687\) −3.46738 + 1.26202i −0.132289 + 0.0481491i
\(688\) 0 0
\(689\) −5.59113 + 31.7089i −0.213005 + 1.20801i
\(690\) 0 0
\(691\) 10.9350 + 18.9400i 0.415987 + 0.720510i 0.995531 0.0944301i \(-0.0301029\pi\)
−0.579545 + 0.814941i \(0.696770\pi\)
\(692\) 0 0
\(693\) −3.67791 + 3.08613i −0.139712 + 0.117232i
\(694\) 0 0
\(695\) 7.21761 12.5013i 0.273779 0.474200i
\(696\) 0 0
\(697\) 6.29187 + 2.29005i 0.238322 + 0.0867420i
\(698\) 0 0
\(699\) −0.314354 1.78279i −0.0118900 0.0674314i
\(700\) 0 0
\(701\) 3.84736 + 3.22832i 0.145313 + 0.121932i 0.712546 0.701625i \(-0.247542\pi\)
−0.567233 + 0.823557i \(0.691986\pi\)
\(702\) 0 0
\(703\) −28.4896 + 27.7923i −1.07451 + 1.04821i
\(704\) 0 0
\(705\) −14.1515 11.8745i −0.532977 0.447220i
\(706\) 0 0
\(707\) −0.238202 1.35091i −0.00895851 0.0508062i
\(708\) 0 0
\(709\) −47.1948 17.1775i −1.77244 0.645115i −0.999949 0.0100871i \(-0.996789\pi\)
−0.772489 0.635028i \(-0.780989\pi\)
\(710\) 0 0
\(711\) 14.4882 25.0942i 0.543349 0.941108i
\(712\) 0 0
\(713\) 13.2761 11.1400i 0.497194 0.417196i
\(714\) 0 0
\(715\) 3.35559 + 5.81205i 0.125492 + 0.217358i
\(716\) 0 0
\(717\) 1.63010 9.24476i 0.0608772 0.345252i
\(718\) 0 0
\(719\) 10.9561 3.98770i 0.408594 0.148716i −0.129542 0.991574i \(-0.541351\pi\)
0.538136 + 0.842858i \(0.319129\pi\)
\(720\) 0 0
\(721\) 16.1624 0.601918
\(722\) 0 0
\(723\) 6.62854 0.246518
\(724\) 0 0
\(725\) −21.3671 + 7.77699i −0.793555 + 0.288830i
\(726\) 0 0
\(727\) 6.57741 37.3023i 0.243942 1.38347i −0.578993 0.815332i \(-0.696554\pi\)
0.822936 0.568134i \(-0.192335\pi\)
\(728\) 0 0
\(729\) 7.52722 + 13.0375i 0.278786 + 0.482871i
\(730\) 0 0
\(731\) 3.46284 2.90567i 0.128078 0.107470i
\(732\) 0 0
\(733\) 8.45973 14.6527i 0.312467 0.541209i −0.666429 0.745569i \(-0.732178\pi\)
0.978896 + 0.204360i \(0.0655112\pi\)
\(734\) 0 0
\(735\) 5.52484 + 2.01088i 0.203787 + 0.0741723i
\(736\) 0 0
\(737\) −0.396132 2.24658i −0.0145917 0.0827537i
\(738\) 0 0
\(739\) −26.7418 22.4390i −0.983712 0.825432i 0.000933516 1.00000i \(-0.499703\pi\)
−0.984645 + 0.174567i \(0.944147\pi\)
\(740\) 0 0
\(741\) 7.06247 6.88960i 0.259446 0.253096i
\(742\) 0 0
\(743\) −31.8275 26.7064i −1.16764 0.979765i −0.167656 0.985845i \(-0.553620\pi\)
−0.999982 + 0.00608086i \(0.998064\pi\)
\(744\) 0 0
\(745\) 9.08137 + 51.5030i 0.332716 + 1.88692i
\(746\) 0 0
\(747\) −12.4163 4.51916i −0.454289 0.165348i
\(748\) 0 0
\(749\) −15.2546 + 26.4217i −0.557391 + 0.965429i
\(750\) 0 0
\(751\) 38.7302 32.4985i 1.41328 1.18589i 0.458461 0.888715i \(-0.348401\pi\)
0.954824 0.297172i \(-0.0960435\pi\)
\(752\) 0 0
\(753\) −4.19151 7.25991i −0.152747 0.264566i
\(754\) 0 0
\(755\) 4.40625 24.9891i 0.160360 0.909447i
\(756\) 0 0
\(757\) 36.3326 13.2240i 1.32053 0.480634i 0.416902 0.908951i \(-0.363116\pi\)
0.903628 + 0.428318i \(0.140894\pi\)
\(758\) 0 0
\(759\) 0.910288 0.0330414
\(760\) 0 0
\(761\) −22.8058 −0.826711 −0.413355 0.910570i \(-0.635643\pi\)
−0.413355 + 0.910570i \(0.635643\pi\)
\(762\) 0 0
\(763\) 24.6562 8.97411i 0.892613 0.324884i
\(764\) 0 0
\(765\) 1.28769 7.30283i 0.0465564 0.264034i
\(766\) 0 0
\(767\) 33.2960 + 57.6703i 1.20225 + 2.08235i
\(768\) 0 0
\(769\) 5.37493 4.51010i 0.193825 0.162638i −0.540711 0.841209i \(-0.681845\pi\)
0.734535 + 0.678570i \(0.237400\pi\)
\(770\) 0 0
\(771\) −3.30609 + 5.72631i −0.119066 + 0.206228i
\(772\) 0 0
\(773\) 20.2329 + 7.36419i 0.727728 + 0.264871i 0.679203 0.733950i \(-0.262326\pi\)
0.0485254 + 0.998822i \(0.484548\pi\)
\(774\) 0 0
\(775\) 2.32622 + 13.1926i 0.0835602 + 0.473893i
\(776\) 0 0
\(777\) 11.4489 + 9.60674i 0.410726 + 0.344640i
\(778\) 0 0
\(779\) 13.1802 27.3743i 0.472228 0.980787i
\(780\) 0 0
\(781\) 3.78480 + 3.17582i 0.135431 + 0.113640i
\(782\) 0 0
\(783\) 3.94848 + 22.3930i 0.141107 + 0.800259i
\(784\) 0 0
\(785\) 8.02861 + 2.92218i 0.286553 + 0.104297i
\(786\) 0 0
\(787\) −20.7212 + 35.8901i −0.738630 + 1.27934i 0.214483 + 0.976728i \(0.431193\pi\)
−0.953112 + 0.302616i \(0.902140\pi\)
\(788\) 0 0
\(789\) −2.98883 + 2.50793i −0.106405 + 0.0892846i
\(790\) 0 0
\(791\) −5.17155 8.95738i −0.183879 0.318488i
\(792\) 0 0
\(793\) 4.92444 27.9279i 0.174872 0.991749i
\(794\) 0 0