Properties

Label 91.2.i.a.34.2
Level $91$
Weight $2$
Character 91.34
Analytic conductor $0.727$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 35 x^{8} + 295 x^{4} + 169\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 34.2
Root \(0.626770 - 0.626770i\) of defining polynomial
Character \(\chi\) \(=\) 91.34
Dual form 91.2.i.a.83.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.45161 - 1.45161i) q^{2} +1.81964i q^{3} +2.21432i q^{4} +(-2.01464 + 2.01464i) q^{5} +(2.64141 - 2.64141i) q^{6} +(-1.13594 + 2.38948i) q^{7} +(0.311108 - 0.311108i) q^{8} -0.311108 q^{9} +O(q^{10})\) \(q+(-1.45161 - 1.45161i) q^{2} +1.81964i q^{3} +2.21432i q^{4} +(-2.01464 + 2.01464i) q^{5} +(2.64141 - 2.64141i) q^{6} +(-1.13594 + 2.38948i) q^{7} +(0.311108 - 0.311108i) q^{8} -0.311108 q^{9} +5.84892 q^{10} +(0.451606 - 0.451606i) q^{11} -4.02928 q^{12} +(3.40251 - 1.19288i) q^{13} +(5.11753 - 1.81964i) q^{14} +(-3.66593 - 3.66593i) q^{15} +3.52543 q^{16} -4.32672 q^{17} +(0.451606 + 0.451606i) q^{18} +(-3.40251 + 3.40251i) q^{19} +(-4.46105 - 4.46105i) q^{20} +(-4.34801 - 2.06702i) q^{21} -1.31111 q^{22} -0.933323i q^{23} +(0.566106 + 0.566106i) q^{24} -3.11753i q^{25} +(-6.67068 - 3.20751i) q^{26} +4.89283i q^{27} +(-5.29108 - 2.51534i) q^{28} +6.33185 q^{29} +10.6430i q^{30} +(5.47781 - 5.47781i) q^{31} +(-5.73975 - 5.73975i) q^{32} +(0.821763 + 0.821763i) q^{33} +(6.28070 + 6.28070i) q^{34} +(-2.52543 - 7.10246i) q^{35} -0.688892i q^{36} +(2.14050 - 2.14050i) q^{37} +9.87820 q^{38} +(2.17061 + 6.19135i) q^{39} +1.25354i q^{40} +(1.81964 - 1.81964i) q^{41} +(3.31111 + 9.31209i) q^{42} +10.4795i q^{43} +(1.00000 + 1.00000i) q^{44} +(0.626770 - 0.626770i) q^{45} +(-1.35482 + 1.35482i) q^{46} +(5.90958 + 5.90958i) q^{47} +6.41503i q^{48} +(-4.41926 - 5.42864i) q^{49} +(-4.52543 + 4.52543i) q^{50} -7.87310i q^{51} +(2.64141 + 7.53424i) q^{52} +3.36196 q^{53} +(7.10246 - 7.10246i) q^{54} +1.81964i q^{55} +(0.389986 + 1.09679i) q^{56} +(-6.19135 - 6.19135i) q^{57} +(-9.19135 - 9.19135i) q^{58} +(-0.255657 - 0.255657i) q^{59} +(8.11753 - 8.11753i) q^{60} -7.78989i q^{61} -15.9032 q^{62} +(0.353401 - 0.743387i) q^{63} +9.61285i q^{64} +(-4.45161 + 9.25803i) q^{65} -2.38575i q^{66} +(7.28100 + 7.28100i) q^{67} -9.58075i q^{68} +1.69832 q^{69} +(-6.64405 + 13.9759i) q^{70} +(5.56914 + 5.56914i) q^{71} +(-0.0967881 + 0.0967881i) q^{72} +(-8.86144 - 8.86144i) q^{73} -6.21432 q^{74} +5.67280 q^{75} +(-7.53424 - 7.53424i) q^{76} +(0.566106 + 1.59210i) q^{77} +(5.83654 - 12.1383i) q^{78} -13.7971 q^{79} +(-7.10246 + 7.10246i) q^{80} -9.83654 q^{81} -5.28281 q^{82} +(4.30785 - 4.30785i) q^{83} +(4.57703 - 9.62789i) q^{84} +(8.71678 - 8.71678i) q^{85} +(15.2121 - 15.2121i) q^{86} +11.5217i q^{87} -0.280996i q^{88} +(5.61214 + 5.61214i) q^{89} -1.81964 q^{90} +(-1.01470 + 9.48527i) q^{91} +2.06668 q^{92} +(9.96767 + 9.96767i) q^{93} -17.1568i q^{94} -13.7096i q^{95} +(10.4443 - 10.4443i) q^{96} +(-0.236784 + 0.236784i) q^{97} +(-1.46522 + 14.2953i) q^{98} +(-0.140498 + 0.140498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - 8q^{7} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 12q - 4q^{2} - 8q^{7} + 4q^{8} - 4q^{9} - 8q^{11} + 8q^{14} - 4q^{15} + 16q^{16} - 8q^{18} - 16q^{22} - 20q^{28} - 4q^{29} - 16q^{32} - 4q^{35} + 12q^{37} + 40q^{39} + 40q^{42} + 12q^{44} + 24q^{46} - 28q^{50} - 12q^{53} - 8q^{57} - 44q^{58} + 44q^{60} + 20q^{63} - 40q^{65} + 60q^{67} + 4q^{70} - 28q^{72} - 48q^{74} + 44q^{78} - 4q^{79} - 92q^{81} - 4q^{84} + 12q^{85} + 36q^{86} - 32q^{91} + 24q^{92} - 28q^{93} - 28q^{98} + 12q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45161 1.45161i −1.02644 1.02644i −0.999641 0.0267996i \(-0.991468\pi\)
−0.0267996 0.999641i \(-0.508532\pi\)
\(3\) 1.81964i 1.05057i 0.850926 + 0.525286i \(0.176042\pi\)
−0.850926 + 0.525286i \(0.823958\pi\)
\(4\) 2.21432i 1.10716i
\(5\) −2.01464 + 2.01464i −0.900973 + 0.900973i −0.995520 0.0945469i \(-0.969860\pi\)
0.0945469 + 0.995520i \(0.469860\pi\)
\(6\) 2.64141 2.64141i 1.07835 1.07835i
\(7\) −1.13594 + 2.38948i −0.429347 + 0.903140i
\(8\) 0.311108 0.311108i 0.109993 0.109993i
\(9\) −0.311108 −0.103703
\(10\) 5.84892 1.84959
\(11\) 0.451606 0.451606i 0.136164 0.136164i −0.635739 0.771904i \(-0.719305\pi\)
0.771904 + 0.635739i \(0.219305\pi\)
\(12\) −4.02928 −1.16315
\(13\) 3.40251 1.19288i 0.943685 0.330844i
\(14\) 5.11753 1.81964i 1.36772 0.486321i
\(15\) −3.66593 3.66593i −0.946538 0.946538i
\(16\) 3.52543 0.881357
\(17\) −4.32672 −1.04938 −0.524692 0.851292i \(-0.675820\pi\)
−0.524692 + 0.851292i \(0.675820\pi\)
\(18\) 0.451606 + 0.451606i 0.106445 + 0.106445i
\(19\) −3.40251 + 3.40251i −0.780588 + 0.780588i −0.979930 0.199342i \(-0.936120\pi\)
0.199342 + 0.979930i \(0.436120\pi\)
\(20\) −4.46105 4.46105i −0.997522 0.997522i
\(21\) −4.34801 2.06702i −0.948814 0.451060i
\(22\) −1.31111 −0.279529
\(23\) 0.933323i 0.194611i −0.995255 0.0973057i \(-0.968978\pi\)
0.995255 0.0973057i \(-0.0310225\pi\)
\(24\) 0.566106 + 0.566106i 0.115556 + 0.115556i
\(25\) 3.11753i 0.623506i
\(26\) −6.67068 3.20751i −1.30823 0.629045i
\(27\) 4.89283i 0.941625i
\(28\) −5.29108 2.51534i −0.999920 0.475355i
\(29\) 6.33185 1.17580 0.587898 0.808935i \(-0.299956\pi\)
0.587898 + 0.808935i \(0.299956\pi\)
\(30\) 10.6430i 1.94313i
\(31\) 5.47781 5.47781i 0.983843 0.983843i −0.0160282 0.999872i \(-0.505102\pi\)
0.999872 + 0.0160282i \(0.00510215\pi\)
\(32\) −5.73975 5.73975i −1.01465 1.01465i
\(33\) 0.821763 + 0.821763i 0.143050 + 0.143050i
\(34\) 6.28070 + 6.28070i 1.07713 + 1.07713i
\(35\) −2.52543 7.10246i −0.426875 1.20053i
\(36\) 0.688892i 0.114815i
\(37\) 2.14050 2.14050i 0.351896 0.351896i −0.508919 0.860815i \(-0.669955\pi\)
0.860815 + 0.508919i \(0.169955\pi\)
\(38\) 9.87820 1.60246
\(39\) 2.17061 + 6.19135i 0.347576 + 0.991410i
\(40\) 1.25354i 0.198202i
\(41\) 1.81964 1.81964i 0.284181 0.284181i −0.550593 0.834774i \(-0.685598\pi\)
0.834774 + 0.550593i \(0.185598\pi\)
\(42\) 3.31111 + 9.31209i 0.510915 + 1.43689i
\(43\) 10.4795i 1.59811i 0.601259 + 0.799054i \(0.294666\pi\)
−0.601259 + 0.799054i \(0.705334\pi\)
\(44\) 1.00000 + 1.00000i 0.150756 + 0.150756i
\(45\) 0.626770 0.626770i 0.0934333 0.0934333i
\(46\) −1.35482 + 1.35482i −0.199757 + 0.199757i
\(47\) 5.90958 + 5.90958i 0.862002 + 0.862002i 0.991570 0.129569i \(-0.0413593\pi\)
−0.129569 + 0.991570i \(0.541359\pi\)
\(48\) 6.41503i 0.925929i
\(49\) −4.41926 5.42864i −0.631323 0.775520i
\(50\) −4.52543 + 4.52543i −0.639992 + 0.639992i
\(51\) 7.87310i 1.10245i
\(52\) 2.64141 + 7.53424i 0.366297 + 1.04481i
\(53\) 3.36196 0.461801 0.230901 0.972977i \(-0.425833\pi\)
0.230901 + 0.972977i \(0.425833\pi\)
\(54\) 7.10246 7.10246i 0.966522 0.966522i
\(55\) 1.81964i 0.245361i
\(56\) 0.389986 + 1.09679i 0.0521141 + 0.146564i
\(57\) −6.19135 6.19135i −0.820065 0.820065i
\(58\) −9.19135 9.19135i −1.20688 1.20688i
\(59\) −0.255657 0.255657i −0.0332837 0.0332837i 0.690269 0.723553i \(-0.257492\pi\)
−0.723553 + 0.690269i \(0.757492\pi\)
\(60\) 8.11753 8.11753i 1.04797 1.04797i
\(61\) 7.78989i 0.997394i −0.866776 0.498697i \(-0.833812\pi\)
0.866776 0.498697i \(-0.166188\pi\)
\(62\) −15.9032 −2.01971
\(63\) 0.353401 0.743387i 0.0445244 0.0936580i
\(64\) 9.61285i 1.20161i
\(65\) −4.45161 + 9.25803i −0.552154 + 1.14832i
\(66\) 2.38575i 0.293666i
\(67\) 7.28100 + 7.28100i 0.889515 + 0.889515i 0.994476 0.104961i \(-0.0334718\pi\)
−0.104961 + 0.994476i \(0.533472\pi\)
\(68\) 9.58075i 1.16184i
\(69\) 1.69832 0.204453
\(70\) −6.64405 + 13.9759i −0.794116 + 1.67044i
\(71\) 5.56914 + 5.56914i 0.660935 + 0.660935i 0.955600 0.294665i \(-0.0952082\pi\)
−0.294665 + 0.955600i \(0.595208\pi\)
\(72\) −0.0967881 + 0.0967881i −0.0114066 + 0.0114066i
\(73\) −8.86144 8.86144i −1.03715 1.03715i −0.999283 0.0378706i \(-0.987943\pi\)
−0.0378706 0.999283i \(-0.512057\pi\)
\(74\) −6.21432 −0.722400
\(75\) 5.67280 0.655039
\(76\) −7.53424 7.53424i −0.864236 0.864236i
\(77\) 0.566106 + 1.59210i 0.0645137 + 0.181437i
\(78\) 5.83654 12.1383i 0.660857 1.37439i
\(79\) −13.7971 −1.55229 −0.776145 0.630554i \(-0.782828\pi\)
−0.776145 + 0.630554i \(0.782828\pi\)
\(80\) −7.10246 + 7.10246i −0.794079 + 0.794079i
\(81\) −9.83654 −1.09295
\(82\) −5.28281 −0.583389
\(83\) 4.30785 4.30785i 0.472848 0.472848i −0.429987 0.902835i \(-0.641482\pi\)
0.902835 + 0.429987i \(0.141482\pi\)
\(84\) 4.57703 9.62789i 0.499395 1.05049i
\(85\) 8.71678 8.71678i 0.945468 0.945468i
\(86\) 15.2121 15.2121i 1.64036 1.64036i
\(87\) 11.5217i 1.23526i
\(88\) 0.280996i 0.0299543i
\(89\) 5.61214 + 5.61214i 0.594885 + 0.594885i 0.938947 0.344062i \(-0.111803\pi\)
−0.344062 + 0.938947i \(0.611803\pi\)
\(90\) −1.81964 −0.191807
\(91\) −1.01470 + 9.48527i −0.106370 + 0.994327i
\(92\) 2.06668 0.215466
\(93\) 9.96767 + 9.96767i 1.03360 + 1.03360i
\(94\) 17.1568i 1.76959i
\(95\) 13.7096i 1.40658i
\(96\) 10.4443 10.4443i 1.06597 1.06597i
\(97\) −0.236784 + 0.236784i −0.0240417 + 0.0240417i −0.719025 0.694984i \(-0.755412\pi\)
0.694984 + 0.719025i \(0.255412\pi\)
\(98\) −1.46522 + 14.2953i −0.148009 + 1.44404i
\(99\) −0.140498 + 0.140498i −0.0141206 + 0.0141206i
\(100\) 6.90321 0.690321
\(101\) 9.21955 0.917380 0.458690 0.888596i \(-0.348319\pi\)
0.458690 + 0.888596i \(0.348319\pi\)
\(102\) −11.4286 + 11.4286i −1.13160 + 1.13160i
\(103\) −2.50708 −0.247030 −0.123515 0.992343i \(-0.539417\pi\)
−0.123515 + 0.992343i \(0.539417\pi\)
\(104\) 0.687433 1.42966i 0.0674084 0.140190i
\(105\) 12.9240 4.59538i 1.26125 0.448463i
\(106\) −4.88025 4.88025i −0.474011 0.474011i
\(107\) 2.88247 0.278659 0.139329 0.990246i \(-0.455505\pi\)
0.139329 + 0.990246i \(0.455505\pi\)
\(108\) −10.8343 −1.04253
\(109\) −3.54839 3.54839i −0.339875 0.339875i 0.516446 0.856320i \(-0.327255\pi\)
−0.856320 + 0.516446i \(0.827255\pi\)
\(110\) 2.64141 2.64141i 0.251848 0.251848i
\(111\) 3.89495 + 3.89495i 0.369692 + 0.369692i
\(112\) −4.00469 + 8.42395i −0.378408 + 0.795989i
\(113\) −16.3526 −1.53832 −0.769161 0.639055i \(-0.779326\pi\)
−0.769161 + 0.639055i \(0.779326\pi\)
\(114\) 17.9748i 1.68350i
\(115\) 1.88031 + 1.88031i 0.175340 + 0.175340i
\(116\) 14.0207i 1.30179i
\(117\) −1.05855 + 0.371113i −0.0978626 + 0.0343094i
\(118\) 0.742226i 0.0683274i
\(119\) 4.91492 10.3386i 0.450550 0.947741i
\(120\) −2.28100 −0.208226
\(121\) 10.5921i 0.962919i
\(122\) −11.3079 + 11.3079i −1.02377 + 1.02377i
\(123\) 3.31111 + 3.31111i 0.298553 + 0.298553i
\(124\) 12.1296 + 12.1296i 1.08927 + 1.08927i
\(125\) −3.79249 3.79249i −0.339211 0.339211i
\(126\) −1.59210 + 0.566106i −0.141836 + 0.0504327i
\(127\) 13.8272i 1.22696i −0.789709 0.613481i \(-0.789769\pi\)
0.789709 0.613481i \(-0.210231\pi\)
\(128\) 2.47457 2.47457i 0.218723 0.218723i
\(129\) −19.0690 −1.67893
\(130\) 19.9010 6.97703i 1.74543 0.611926i
\(131\) 12.8301i 1.12097i 0.828166 + 0.560483i \(0.189385\pi\)
−0.828166 + 0.560483i \(0.810615\pi\)
\(132\) −1.81964 + 1.81964i −0.158380 + 0.158380i
\(133\) −4.26517 11.9953i −0.369838 1.04012i
\(134\) 21.1383i 1.82607i
\(135\) −9.85728 9.85728i −0.848379 0.848379i
\(136\) −1.34608 + 1.34608i −0.115425 + 0.115425i
\(137\) 2.40075 2.40075i 0.205110 0.205110i −0.597075 0.802185i \(-0.703671\pi\)
0.802185 + 0.597075i \(0.203671\pi\)
\(138\) −2.46529 2.46529i −0.209859 0.209859i
\(139\) 3.34184i 0.283451i −0.989906 0.141726i \(-0.954735\pi\)
0.989906 0.141726i \(-0.0452651\pi\)
\(140\) 15.7271 5.59210i 1.32918 0.472619i
\(141\) −10.7533 + 10.7533i −0.905595 + 0.905595i
\(142\) 16.1684i 1.35682i
\(143\) 0.997882 2.07530i 0.0834471 0.173545i
\(144\) −1.09679 −0.0913990
\(145\) −12.7564 + 12.7564i −1.05936 + 1.05936i
\(146\) 25.7266i 2.12915i
\(147\) 9.87820 8.04149i 0.814740 0.663251i
\(148\) 4.73975 + 4.73975i 0.389605 + 0.389605i
\(149\) 2.62936 + 2.62936i 0.215406 + 0.215406i 0.806559 0.591153i \(-0.201327\pi\)
−0.591153 + 0.806559i \(0.701327\pi\)
\(150\) −8.23467 8.23467i −0.672358 0.672358i
\(151\) −4.78346 + 4.78346i −0.389272 + 0.389272i −0.874428 0.485156i \(-0.838763\pi\)
0.485156 + 0.874428i \(0.338763\pi\)
\(152\) 2.11709i 0.171719i
\(153\) 1.34608 0.108824
\(154\) 1.48935 3.13287i 0.120015 0.252454i
\(155\) 22.0716i 1.77283i
\(156\) −13.7096 + 4.80642i −1.09765 + 0.384822i
\(157\) 3.42542i 0.273379i −0.990614 0.136689i \(-0.956354\pi\)
0.990614 0.136689i \(-0.0436462\pi\)
\(158\) 20.0279 + 20.0279i 1.59333 + 1.59333i
\(159\) 6.11758i 0.485156i
\(160\) 23.1270 1.82835
\(161\) 2.23016 + 1.06020i 0.175761 + 0.0835557i
\(162\) 14.2788 + 14.2788i 1.12185 + 1.12185i
\(163\) 10.4494 10.4494i 0.818459 0.818459i −0.167426 0.985885i \(-0.553545\pi\)
0.985885 + 0.167426i \(0.0535455\pi\)
\(164\) 4.02928 + 4.02928i 0.314634 + 0.314634i
\(165\) −3.31111 −0.257769
\(166\) −12.5066 −0.970701
\(167\) −16.2326 16.2326i −1.25611 1.25611i −0.952933 0.303180i \(-0.901952\pi\)
−0.303180 0.952933i \(-0.598048\pi\)
\(168\) −1.99576 + 0.709636i −0.153977 + 0.0547496i
\(169\) 10.1541 8.11753i 0.781084 0.624426i
\(170\) −25.3067 −1.94093
\(171\) 1.05855 1.05855i 0.0809491 0.0809491i
\(172\) −23.2050 −1.76936
\(173\) 14.3810 1.09337 0.546685 0.837338i \(-0.315889\pi\)
0.546685 + 0.837338i \(0.315889\pi\)
\(174\) 16.7250 16.7250i 1.26792 1.26792i
\(175\) 7.44929 + 3.54134i 0.563113 + 0.267700i
\(176\) 1.59210 1.59210i 0.120009 0.120009i
\(177\) 0.465205 0.465205i 0.0349669 0.0349669i
\(178\) 16.2932i 1.22123i
\(179\) 4.11108i 0.307276i −0.988127 0.153638i \(-0.950901\pi\)
0.988127 0.153638i \(-0.0490990\pi\)
\(180\) 1.38787 + 1.38787i 0.103446 + 0.103446i
\(181\) 21.5760 1.60373 0.801867 0.597502i \(-0.203840\pi\)
0.801867 + 0.597502i \(0.203840\pi\)
\(182\) 15.2418 12.2959i 1.12980 0.911435i
\(183\) 14.1748 1.04783
\(184\) −0.290364 0.290364i −0.0214059 0.0214059i
\(185\) 8.62466i 0.634097i
\(186\) 28.9382i 2.12186i
\(187\) −1.95397 + 1.95397i −0.142889 + 0.142889i
\(188\) −13.0857 + 13.0857i −0.954373 + 0.954373i
\(189\) −11.6913 5.55798i −0.850419 0.404284i
\(190\) −19.9010 + 19.9010i −1.44377 + 1.44377i
\(191\) 10.3017 0.745408 0.372704 0.927950i \(-0.378431\pi\)
0.372704 + 0.927950i \(0.378431\pi\)
\(192\) −17.4920 −1.26237
\(193\) 6.28592 6.28592i 0.452470 0.452470i −0.443703 0.896174i \(-0.646336\pi\)
0.896174 + 0.443703i \(0.146336\pi\)
\(194\) 0.687433 0.0493548
\(195\) −16.8463 8.10034i −1.20639 0.580078i
\(196\) 12.0207 9.78566i 0.858625 0.698976i
\(197\) −3.25088 3.25088i −0.231616 0.231616i 0.581751 0.813367i \(-0.302368\pi\)
−0.813367 + 0.581751i \(0.802368\pi\)
\(198\) 0.407896 0.0289879
\(199\) −6.20116 −0.439589 −0.219794 0.975546i \(-0.570539\pi\)
−0.219794 + 0.975546i \(0.570539\pi\)
\(200\) −0.969888 0.969888i −0.0685815 0.0685815i
\(201\) −13.2488 + 13.2488i −0.934500 + 0.934500i
\(202\) −13.3832 13.3832i −0.941636 0.941636i
\(203\) −7.19263 + 15.1299i −0.504824 + 1.06191i
\(204\) 17.4336 1.22059
\(205\) 7.33185i 0.512079i
\(206\) 3.63929 + 3.63929i 0.253561 + 0.253561i
\(207\) 0.290364i 0.0201817i
\(208\) 11.9953 4.20540i 0.831724 0.291592i
\(209\) 3.07318i 0.212577i
\(210\) −25.4312 12.0898i −1.75492 0.834276i
\(211\) −9.55554 −0.657830 −0.328915 0.944359i \(-0.606683\pi\)
−0.328915 + 0.944359i \(0.606683\pi\)
\(212\) 7.44446i 0.511288i
\(213\) −10.1339 + 10.1339i −0.694360 + 0.694360i
\(214\) −4.18421 4.18421i −0.286027 0.286027i
\(215\) −21.1124 21.1124i −1.43985 1.43985i
\(216\) 1.52220 + 1.52220i 0.103572 + 0.103572i
\(217\) 6.86665 + 19.3116i 0.466138 + 1.31096i
\(218\) 10.3017i 0.697722i
\(219\) 16.1247 16.1247i 1.08960 1.08960i
\(220\) −4.02928 −0.271654
\(221\) −14.7217 + 5.16124i −0.990289 + 0.347183i
\(222\) 11.3079i 0.758934i
\(223\) −2.58074 + 2.58074i −0.172819 + 0.172819i −0.788217 0.615398i \(-0.788995\pi\)
0.615398 + 0.788217i \(0.288995\pi\)
\(224\) 20.2351 7.19500i 1.35201 0.480736i
\(225\) 0.969888i 0.0646592i
\(226\) 23.7375 + 23.7375i 1.57900 + 1.57900i
\(227\) 5.25403 5.25403i 0.348722 0.348722i −0.510911 0.859633i \(-0.670692\pi\)
0.859633 + 0.510911i \(0.170692\pi\)
\(228\) 13.7096 13.7096i 0.907943 0.907943i
\(229\) −0.729224 0.729224i −0.0481885 0.0481885i 0.682602 0.730790i \(-0.260848\pi\)
−0.730790 + 0.682602i \(0.760848\pi\)
\(230\) 5.45893i 0.359952i
\(231\) −2.89706 + 1.03011i −0.190613 + 0.0677764i
\(232\) 1.96989 1.96989i 0.129330 0.129330i
\(233\) 24.6128i 1.61244i −0.591615 0.806221i \(-0.701509\pi\)
0.591615 0.806221i \(-0.298491\pi\)
\(234\) 2.07530 + 0.997882i 0.135667 + 0.0652336i
\(235\) −23.8113 −1.55328
\(236\) 0.566106 0.566106i 0.0368503 0.0368503i
\(237\) 25.1057i 1.63079i
\(238\) −22.1421 + 7.87310i −1.43526 + 0.510337i
\(239\) −6.52543 6.52543i −0.422095 0.422095i 0.463830 0.885924i \(-0.346475\pi\)
−0.885924 + 0.463830i \(0.846475\pi\)
\(240\) −12.9240 12.9240i −0.834238 0.834238i
\(241\) 20.1563 + 20.1563i 1.29838 + 1.29838i 0.929461 + 0.368920i \(0.120272\pi\)
0.368920 + 0.929461i \(0.379728\pi\)
\(242\) 15.3756 15.3756i 0.988379 0.988379i
\(243\) 3.22051i 0.206596i
\(244\) 17.2493 1.10427
\(245\) 19.8400 + 2.03353i 1.26753 + 0.129918i
\(246\) 9.61285i 0.612893i
\(247\) −7.51828 + 15.6358i −0.478377 + 0.994883i
\(248\) 3.40838i 0.216432i
\(249\) 7.83876 + 7.83876i 0.496761 + 0.496761i
\(250\) 11.0104i 0.696359i
\(251\) −14.4448 −0.911747 −0.455873 0.890045i \(-0.650673\pi\)
−0.455873 + 0.890045i \(0.650673\pi\)
\(252\) 1.64610 + 0.782543i 0.103694 + 0.0492956i
\(253\) −0.421494 0.421494i −0.0264991 0.0264991i
\(254\) −20.0716 + 20.0716i −1.25940 + 1.25940i
\(255\) 15.8614 + 15.8614i 0.993282 + 0.993282i
\(256\) 12.0415 0.752593
\(257\) 14.6237 0.912201 0.456101 0.889928i \(-0.349246\pi\)
0.456101 + 0.889928i \(0.349246\pi\)
\(258\) 27.6806 + 27.6806i 1.72332 + 1.72332i
\(259\) 2.68320 + 7.54617i 0.166726 + 0.468896i
\(260\) −20.5002 9.85728i −1.27137 0.611322i
\(261\) −1.96989 −0.121933
\(262\) 18.6242 18.6242i 1.15061 1.15061i
\(263\) −2.61729 −0.161389 −0.0806946 0.996739i \(-0.525714\pi\)
−0.0806946 + 0.996739i \(0.525714\pi\)
\(264\) 0.511313 0.0314692
\(265\) −6.77314 + 6.77314i −0.416071 + 0.416071i
\(266\) −11.2211 + 23.6038i −0.688009 + 1.44724i
\(267\) −10.2121 + 10.2121i −0.624970 + 0.624970i
\(268\) −16.1225 + 16.1225i −0.984836 + 0.984836i
\(269\) 9.82340i 0.598944i −0.954105 0.299472i \(-0.903190\pi\)
0.954105 0.299472i \(-0.0968104\pi\)
\(270\) 28.6178i 1.74162i
\(271\) −3.43438 3.43438i −0.208624 0.208624i 0.595059 0.803682i \(-0.297129\pi\)
−0.803682 + 0.595059i \(0.797129\pi\)
\(272\) −15.2535 −0.924882
\(273\) −17.2598 1.84640i −1.04461 0.111749i
\(274\) −6.96989 −0.421066
\(275\) −1.40790 1.40790i −0.0848993 0.0848993i
\(276\) 3.76062i 0.226363i
\(277\) 5.89877i 0.354423i 0.984173 + 0.177211i \(0.0567076\pi\)
−0.984173 + 0.177211i \(0.943292\pi\)
\(278\) −4.85104 + 4.85104i −0.290946 + 0.290946i
\(279\) −1.70419 + 1.70419i −0.102027 + 0.102027i
\(280\) −2.99531 1.42395i −0.179004 0.0850973i
\(281\) 9.23729 9.23729i 0.551050 0.551050i −0.375694 0.926744i \(-0.622595\pi\)
0.926744 + 0.375694i \(0.122595\pi\)
\(282\) 31.2192 1.85908
\(283\) 8.32721 0.495001 0.247501 0.968888i \(-0.420391\pi\)
0.247501 + 0.968888i \(0.420391\pi\)
\(284\) −12.3319 + 12.3319i −0.731761 + 0.731761i
\(285\) 24.9467 1.47771
\(286\) −4.46105 + 1.56399i −0.263788 + 0.0924806i
\(287\) 2.28100 + 6.41503i 0.134643 + 0.378667i
\(288\) 1.78568 + 1.78568i 0.105222 + 0.105222i
\(289\) 1.72054 0.101208
\(290\) 37.0345 2.17474
\(291\) −0.430862 0.430862i −0.0252576 0.0252576i
\(292\) 19.6221 19.6221i 1.14829 1.14829i
\(293\) 15.4903 + 15.4903i 0.904955 + 0.904955i 0.995860 0.0909047i \(-0.0289759\pi\)
−0.0909047 + 0.995860i \(0.528976\pi\)
\(294\) −26.0123 2.66618i −1.51707 0.155495i
\(295\) 1.03011 0.0599754
\(296\) 1.33185i 0.0774123i
\(297\) 2.20963 + 2.20963i 0.128216 + 0.128216i
\(298\) 7.63359i 0.442202i
\(299\) −1.11334 3.17564i −0.0643860 0.183652i
\(300\) 12.5614i 0.725232i
\(301\) −25.0406 11.9041i −1.44331 0.686142i
\(302\) 13.8874 0.799130
\(303\) 16.7763i 0.963774i
\(304\) −11.9953 + 11.9953i −0.687977 + 0.687977i
\(305\) 15.6938 + 15.6938i 0.898625 + 0.898625i
\(306\) −1.95397 1.95397i −0.111701 0.111701i
\(307\) −5.77526 5.77526i −0.329611 0.329611i 0.522827 0.852439i \(-0.324877\pi\)
−0.852439 + 0.522827i \(0.824877\pi\)
\(308\) −3.52543 + 1.25354i −0.200880 + 0.0714270i
\(309\) 4.56199i 0.259523i
\(310\) 32.0393 32.0393i 1.81971 1.81971i
\(311\) 2.62562 0.148885 0.0744426 0.997225i \(-0.476282\pi\)
0.0744426 + 0.997225i \(0.476282\pi\)
\(312\) 2.60147 + 1.25088i 0.147279 + 0.0708174i
\(313\) 19.8489i 1.12193i −0.827840 0.560964i \(-0.810431\pi\)
0.827840 0.560964i \(-0.189569\pi\)
\(314\) −4.97237 + 4.97237i −0.280607 + 0.280607i
\(315\) 0.785680 + 2.20963i 0.0442681 + 0.124499i
\(316\) 30.5511i 1.71863i
\(317\) 1.14764 + 1.14764i 0.0644581 + 0.0644581i 0.738601 0.674143i \(-0.235487\pi\)
−0.674143 + 0.738601i \(0.735487\pi\)
\(318\) 8.88031 8.88031i 0.497983 0.497983i
\(319\) 2.85950 2.85950i 0.160101 0.160101i
\(320\) −19.3664 19.3664i −1.08262 1.08262i
\(321\) 5.24507i 0.292751i
\(322\) −1.69832 4.77631i −0.0946435 0.266173i
\(323\) 14.7217 14.7217i 0.819137 0.819137i
\(324\) 21.7812i 1.21007i
\(325\) −3.71883 10.6074i −0.206283 0.588394i
\(326\) −30.3368 −1.68020
\(327\) 6.45682 6.45682i 0.357063 0.357063i
\(328\) 1.13221i 0.0625159i
\(329\) −20.8338 + 7.40790i −1.14861 + 0.408411i
\(330\) 4.80642 + 4.80642i 0.264585 + 0.264585i
\(331\) −2.90321 2.90321i −0.159575 0.159575i 0.622803 0.782378i \(-0.285994\pi\)
−0.782378 + 0.622803i \(0.785994\pi\)
\(332\) 9.53896 + 9.53896i 0.523518 + 0.523518i
\(333\) −0.665926 + 0.665926i −0.0364925 + 0.0364925i
\(334\) 47.1266i 2.57865i
\(335\) −29.3371 −1.60286
\(336\) −15.3286 7.28711i −0.836244 0.397545i
\(337\) 4.47304i 0.243662i −0.992551 0.121831i \(-0.961123\pi\)
0.992551 0.121831i \(-0.0388766\pi\)
\(338\) −26.5232 2.95629i −1.44267 0.160801i
\(339\) 29.7559i 1.61612i
\(340\) 19.3017 + 19.3017i 1.04678 + 1.04678i
\(341\) 4.94762i 0.267929i
\(342\) −3.07318 −0.166179
\(343\) 17.9917 4.39312i 0.971459 0.237206i
\(344\) 3.26025 + 3.26025i 0.175781 + 0.175781i
\(345\) −3.42149 + 3.42149i −0.184207 + 0.184207i
\(346\) −20.8756 20.8756i −1.12228 1.12228i
\(347\) 8.81135 0.473018 0.236509 0.971629i \(-0.423997\pi\)
0.236509 + 0.971629i \(0.423997\pi\)
\(348\) −25.5128 −1.36763
\(349\) 11.8133 + 11.8133i 0.632351 + 0.632351i 0.948657 0.316306i \(-0.102443\pi\)
−0.316306 + 0.948657i \(0.602443\pi\)
\(350\) −5.67280 15.9541i −0.303224 0.852781i
\(351\) 5.83654 + 16.6479i 0.311531 + 0.888598i
\(352\) −5.18421 −0.276319
\(353\) 2.91007 2.91007i 0.154887 0.154887i −0.625410 0.780297i \(-0.715068\pi\)
0.780297 + 0.625410i \(0.215068\pi\)
\(354\) −1.35059 −0.0717829
\(355\) −22.4396 −1.19097
\(356\) −12.4271 + 12.4271i −0.658633 + 0.658633i
\(357\) 18.8126 + 8.94340i 0.995671 + 0.473335i
\(358\) −5.96767 + 5.96767i −0.315401 + 0.315401i
\(359\) 3.52320 3.52320i 0.185948 0.185948i −0.607994 0.793942i \(-0.708026\pi\)
0.793942 + 0.607994i \(0.208026\pi\)
\(360\) 0.389986i 0.0205541i
\(361\) 4.15410i 0.218637i
\(362\) −31.3199 31.3199i −1.64614 1.64614i
\(363\) −19.2739 −1.01162
\(364\) −21.0034 2.24687i −1.10088 0.117768i
\(365\) 35.7052 1.86890
\(366\) −20.5763 20.5763i −1.07554 1.07554i
\(367\) 19.8112i 1.03414i 0.855944 + 0.517068i \(0.172976\pi\)
−0.855944 + 0.517068i \(0.827024\pi\)
\(368\) 3.29036i 0.171522i
\(369\) −0.566106 + 0.566106i −0.0294703 + 0.0294703i
\(370\) 12.5196 12.5196i 0.650863 0.650863i
\(371\) −3.81900 + 8.03335i −0.198273 + 0.417071i
\(372\) −22.0716 + 22.0716i −1.14436 + 1.14436i
\(373\) −24.5368 −1.27047 −0.635234 0.772320i \(-0.719096\pi\)
−0.635234 + 0.772320i \(0.719096\pi\)
\(374\) 5.67280 0.293334
\(375\) 6.90099 6.90099i 0.356366 0.356366i
\(376\) 3.67704 0.189629
\(377\) 21.5442 7.55311i 1.10958 0.389005i
\(378\) 8.90321 + 25.0392i 0.457932 + 1.28788i
\(379\) −8.78346 8.78346i −0.451176 0.451176i 0.444569 0.895745i \(-0.353357\pi\)
−0.895745 + 0.444569i \(0.853357\pi\)
\(380\) 30.3575 1.55731
\(381\) 25.1605 1.28901
\(382\) −14.9541 14.9541i −0.765117 0.765117i
\(383\) 17.8990 17.8990i 0.914596 0.914596i −0.0820333 0.996630i \(-0.526141\pi\)
0.996630 + 0.0820333i \(0.0261414\pi\)
\(384\) 4.50284 + 4.50284i 0.229785 + 0.229785i
\(385\) −4.34801 2.06702i −0.221595 0.105345i
\(386\) −18.2494 −0.928868
\(387\) 3.26025i 0.165728i
\(388\) −0.524315 0.524315i −0.0266181 0.0266181i
\(389\) 12.0667i 0.611805i 0.952063 + 0.305902i \(0.0989581\pi\)
−0.952063 + 0.305902i \(0.901042\pi\)
\(390\) 12.6957 + 36.2127i 0.642873 + 1.83370i
\(391\) 4.03823i 0.204222i
\(392\) −3.06376 0.314025i −0.154743 0.0158607i
\(393\) −23.3461 −1.17766
\(394\) 9.43801i 0.475480i
\(395\) 27.7961 27.7961i 1.39857 1.39857i
\(396\) −0.311108 0.311108i −0.0156338 0.0156338i
\(397\) −7.82177 7.82177i −0.392563 0.392563i 0.483037 0.875600i \(-0.339534\pi\)
−0.875600 + 0.483037i \(0.839534\pi\)
\(398\) 9.00164 + 9.00164i 0.451212 + 0.451212i
\(399\) 21.8272 7.76110i 1.09273 0.388541i
\(400\) 10.9906i 0.549532i
\(401\) −17.6178 + 17.6178i −0.879789 + 0.879789i −0.993512 0.113723i \(-0.963722\pi\)
0.113723 + 0.993512i \(0.463722\pi\)
\(402\) 38.4642 1.91842
\(403\) 12.1039 25.1726i 0.602940 1.25394i
\(404\) 20.4150i 1.01569i
\(405\) 19.8171 19.8171i 0.984717 0.984717i
\(406\) 32.4035 11.5217i 1.60816 0.571813i
\(407\) 1.93332i 0.0958313i
\(408\) −2.44938 2.44938i −0.121263 0.121263i
\(409\) −24.0225 + 24.0225i −1.18783 + 1.18783i −0.210169 + 0.977665i \(0.567401\pi\)
−0.977665 + 0.210169i \(0.932599\pi\)
\(410\) 10.6430 10.6430i 0.525618 0.525618i
\(411\) 4.36851 + 4.36851i 0.215483 + 0.215483i
\(412\) 5.55147i 0.273501i
\(413\) 0.901299 0.320476i 0.0443500 0.0157696i
\(414\) 0.421494 0.421494i 0.0207153 0.0207153i
\(415\) 17.3575i 0.852047i
\(416\) −26.3763 12.6827i −1.29321 0.621822i
\(417\) 6.08097 0.297786
\(418\) 4.46105 4.46105i 0.218197 0.218197i
\(419\) 19.6899i 0.961912i −0.876745 0.480956i \(-0.840290\pi\)
0.876745 0.480956i \(-0.159710\pi\)
\(420\) 10.1756 + 28.6178i 0.496521 + 1.39640i
\(421\) 26.6042 + 26.6042i 1.29661 + 1.29661i 0.930619 + 0.365989i \(0.119269\pi\)
0.365989 + 0.930619i \(0.380731\pi\)
\(422\) 13.8709 + 13.8709i 0.675224 + 0.675224i
\(423\) −1.83852 1.83852i −0.0893918 0.0893918i
\(424\) 1.04593 1.04593i 0.0507950 0.0507950i
\(425\) 13.4887i 0.654298i
\(426\) 29.4207 1.42544
\(427\) 18.6138 + 8.84888i 0.900786 + 0.428228i
\(428\) 6.38271i 0.308520i
\(429\) 3.77631 + 1.81579i 0.182322 + 0.0876673i
\(430\) 61.2937i 2.95585i
\(431\) −4.81135 4.81135i −0.231754 0.231754i 0.581670 0.813425i \(-0.302399\pi\)
−0.813425 + 0.581670i \(0.802399\pi\)
\(432\) 17.2493i 0.829908i
\(433\) −8.34704 −0.401133 −0.200567 0.979680i \(-0.564278\pi\)
−0.200567 + 0.979680i \(0.564278\pi\)
\(434\) 18.0652 38.0005i 0.867157 1.82408i
\(435\) −23.2121 23.2121i −1.11293 1.11293i
\(436\) 7.85728 7.85728i 0.376295 0.376295i
\(437\) 3.17564 + 3.17564i 0.151911 + 0.151911i
\(438\) −46.8134 −2.23683
\(439\) −2.42350 −0.115667 −0.0578336 0.998326i \(-0.518419\pi\)
−0.0578336 + 0.998326i \(0.518419\pi\)
\(440\) 0.566106 + 0.566106i 0.0269880 + 0.0269880i
\(441\) 1.37487 + 1.68889i 0.0654698 + 0.0804234i
\(442\) 28.8622 + 13.8780i 1.37283 + 0.660110i
\(443\) 13.7763 0.654532 0.327266 0.944932i \(-0.393873\pi\)
0.327266 + 0.944932i \(0.393873\pi\)
\(444\) −8.62466 + 8.62466i −0.409308 + 0.409308i
\(445\) −22.6128 −1.07195
\(446\) 7.49245 0.354778
\(447\) −4.78450 + 4.78450i −0.226299 + 0.226299i
\(448\) −22.9697 10.9197i −1.08522 0.515905i
\(449\) −24.7447 + 24.7447i −1.16777 + 1.16777i −0.185043 + 0.982730i \(0.559242\pi\)
−0.982730 + 0.185043i \(0.940758\pi\)
\(450\) 1.40790 1.40790i 0.0663688 0.0663688i
\(451\) 1.64353i 0.0773906i
\(452\) 36.2099i 1.70317i
\(453\) −8.70419 8.70419i −0.408959 0.408959i
\(454\) −15.2535 −0.715885
\(455\) −17.0651 21.1536i −0.800026 0.991698i
\(456\) −3.85236 −0.180403
\(457\) −2.84521 2.84521i −0.133093 0.133093i 0.637422 0.770515i \(-0.280001\pi\)
−0.770515 + 0.637422i \(0.780001\pi\)
\(458\) 2.11709i 0.0989252i
\(459\) 21.1699i 0.988127i
\(460\) −4.16360 + 4.16360i −0.194129 + 0.194129i
\(461\) −2.38575 + 2.38575i −0.111115 + 0.111115i −0.760479 0.649363i \(-0.775036\pi\)
0.649363 + 0.760479i \(0.275036\pi\)
\(462\) 5.70071 + 2.71008i 0.265221 + 0.126084i
\(463\) 17.5899 17.5899i 0.817471 0.817471i −0.168270 0.985741i \(-0.553818\pi\)
0.985741 + 0.168270i \(0.0538180\pi\)
\(464\) 22.3225 1.03630
\(465\) −40.1625 −1.86249
\(466\) −35.7282 + 35.7282i −1.65507 + 1.65507i
\(467\) −21.4287 −0.991602 −0.495801 0.868436i \(-0.665126\pi\)
−0.495801 + 0.868436i \(0.665126\pi\)
\(468\) −0.821763 2.34396i −0.0379860 0.108350i
\(469\) −25.6686 + 9.12701i −1.18527 + 0.421446i
\(470\) 34.5647 + 34.5647i 1.59435 + 1.59435i
\(471\) 6.23306 0.287204
\(472\) −0.159074 −0.00732196
\(473\) 4.73260 + 4.73260i 0.217605 + 0.217605i
\(474\) −36.4436 + 36.4436i −1.67391 + 1.67391i
\(475\) 10.6074 + 10.6074i 0.486702 + 0.486702i
\(476\) 22.8930 + 10.8832i 1.04930 + 0.498830i
\(477\) −1.04593 −0.0478900
\(478\) 18.9447i 0.866510i
\(479\) 4.61425 + 4.61425i 0.210831 + 0.210831i 0.804620 0.593790i \(-0.202369\pi\)
−0.593790 + 0.804620i \(0.702369\pi\)
\(480\) 42.0830i 1.92082i
\(481\) 4.72971 9.83641i 0.215656 0.448501i
\(482\) 58.5180i 2.66542i
\(483\) −1.92919 + 4.05810i −0.0877814 + 0.184650i
\(484\) −23.4543 −1.06610
\(485\) 0.954067i 0.0433220i
\(486\) −4.67492 + 4.67492i −0.212059 + 0.212059i
\(487\) 9.62867 + 9.62867i 0.436317 + 0.436317i 0.890770 0.454454i \(-0.150166\pi\)
−0.454454 + 0.890770i \(0.650166\pi\)
\(488\) −2.42350 2.42350i −0.109707 0.109707i
\(489\) 19.0142 + 19.0142i 0.859850 + 0.859850i
\(490\) −25.8479 31.7517i −1.16769 1.43439i
\(491\) 9.21924i 0.416059i −0.978123 0.208029i \(-0.933295\pi\)
0.978123 0.208029i \(-0.0667049\pi\)
\(492\) −7.33185 + 7.33185i −0.330545 + 0.330545i
\(493\) −27.3962 −1.23386
\(494\) 33.6106 11.7835i 1.51221 0.530163i
\(495\) 0.566106i 0.0254446i
\(496\) 19.3116 19.3116i 0.867117 0.867117i
\(497\) −19.6336 + 6.98113i −0.880687 + 0.313147i
\(498\) 22.7576i 1.01979i
\(499\) −6.65947 6.65947i −0.298119 0.298119i 0.542158 0.840277i \(-0.317608\pi\)
−0.840277 + 0.542158i \(0.817608\pi\)
\(500\) 8.39779 8.39779i 0.375561 0.375561i
\(501\) 29.5375 29.5375i 1.31964 1.31964i
\(502\) 20.9681 + 20.9681i 0.935854 + 0.935854i
\(503\) 1.81069i 0.0807346i −0.999185 0.0403673i \(-0.987147\pi\)
0.999185 0.0403673i \(-0.0128528\pi\)
\(504\) −0.121328 0.341219i −0.00540436 0.0151991i
\(505\) −18.5741 + 18.5741i −0.826535 + 0.826535i
\(506\) 1.22369i 0.0543996i
\(507\) 14.7710 + 18.4769i 0.656004 + 0.820586i
\(508\) 30.6178 1.35844
\(509\) −22.2864 + 22.2864i −0.987827 + 0.987827i −0.999927 0.0121000i \(-0.996148\pi\)
0.0121000 + 0.999927i \(0.496148\pi\)
\(510\) 46.0491i 2.03909i
\(511\) 31.2404 11.1082i 1.38199 0.491396i
\(512\) −22.4286 22.4286i −0.991215 0.991215i
\(513\) −16.6479 16.6479i −0.735022 0.735022i
\(514\) −21.2278 21.2278i −0.936320 0.936320i
\(515\) 5.05086 5.05086i 0.222567 0.222567i
\(516\) 42.2248i 1.85884i
\(517\) 5.33761 0.234748
\(518\) 7.05912 14.8490i 0.310160 0.652428i
\(519\) 26.1684i 1.14866i
\(520\) 1.49532 + 4.26517i 0.0655739 + 0.187040i
\(521\) 15.8744i 0.695472i −0.937592 0.347736i \(-0.886951\pi\)
0.937592 0.347736i \(-0.113049\pi\)
\(522\) 2.85950 + 2.85950i 0.125157 + 0.125157i
\(523\) 3.90795i 0.170883i −0.996343 0.0854413i \(-0.972770\pi\)
0.996343 0.0854413i \(-0.0272300\pi\)
\(524\) −28.4098 −1.24109
\(525\) −6.44399 + 13.5551i −0.281239 + 0.591591i
\(526\) 3.79928 + 3.79928i 0.165656 + 0.165656i
\(527\) −23.7010 + 23.7010i −1.03243 + 1.03243i
\(528\) 2.89706 + 2.89706i 0.126079 + 0.126079i
\(529\) 22.1289 0.962126
\(530\) 19.6639 0.854143
\(531\) 0.0795368 + 0.0795368i 0.00345160 + 0.00345160i
\(532\) 26.5614 9.44446i 1.15158 0.409469i
\(533\) 4.02074 8.36196i 0.174158 0.362197i
\(534\) 29.6479 1.28299
\(535\) −5.80713 + 5.80713i −0.251064 + 0.251064i
\(536\) 4.53035 0.195681
\(537\) 7.48070 0.322816
\(538\) −14.2597 + 14.2597i −0.614780 + 0.614780i
\(539\) −4.44737 0.455841i −0.191562 0.0196345i
\(540\) 21.8272 21.8272i 0.939292 0.939292i
\(541\) 8.57406 8.57406i 0.368628 0.368628i −0.498349 0.866977i \(-0.666060\pi\)
0.866977 + 0.498349i \(0.166060\pi\)
\(542\) 9.97073i 0.428280i
\(543\) 39.2607i 1.68484i
\(544\) 24.8343 + 24.8343i 1.06476 + 1.06476i
\(545\) 14.2975 0.612436
\(546\) 22.3742 + 27.7347i 0.957529 + 1.18694i
\(547\) −4.72546 −0.202046 −0.101023 0.994884i \(-0.532212\pi\)
−0.101023 + 0.994884i \(0.532212\pi\)
\(548\) 5.31603 + 5.31603i 0.227090 + 0.227090i
\(549\) 2.42350i 0.103432i
\(550\) 4.08742i 0.174288i
\(551\) −21.5442 + 21.5442i −0.917812 + 0.917812i
\(552\) 0.528360 0.528360i 0.0224885 0.0224885i
\(553\) 15.6727 32.9678i 0.666470 1.40193i
\(554\) 8.56268 8.56268i 0.363794 0.363794i
\(555\) −15.6938 −0.666165
\(556\) 7.39991 0.313826
\(557\) −23.8415 + 23.8415i −1.01019 + 1.01019i −0.0102475 + 0.999947i \(0.503262\pi\)
−0.999947 + 0.0102475i \(0.996738\pi\)
\(558\) 4.94762 0.209450
\(559\) 12.5007 + 35.6565i 0.528725 + 1.50811i
\(560\) −8.90321 25.0392i −0.376229 1.05810i
\(561\) −3.55554 3.55554i −0.150115 0.150115i
\(562\) −26.8178 −1.13124
\(563\) −41.2776 −1.73965 −0.869823 0.493365i \(-0.835767\pi\)
−0.869823 + 0.493365i \(0.835767\pi\)
\(564\) −23.8113 23.8113i −1.00264 1.00264i
\(565\) 32.9446 32.9446i 1.38599 1.38599i
\(566\) −12.0878 12.0878i −0.508089 0.508089i
\(567\) 11.1738 23.5042i 0.469254 0.987085i
\(568\) 3.46520 0.145397
\(569\) 43.5402i 1.82530i −0.408742 0.912650i \(-0.634032\pi\)
0.408742 0.912650i \(-0.365968\pi\)
\(570\) −36.2127 36.2127i −1.51678 1.51678i
\(571\) 21.2701i 0.890126i 0.895499 + 0.445063i \(0.146819\pi\)
−0.895499 + 0.445063i \(0.853181\pi\)
\(572\) 4.59538 + 2.20963i 0.192143 + 0.0923893i
\(573\) 18.7455i 0.783105i
\(574\) 6.00098 12.6232i 0.250476 0.526882i
\(575\) −2.90967 −0.121341
\(576\) 2.99063i 0.124610i
\(577\) 8.73703 8.73703i 0.363727 0.363727i −0.501456 0.865183i \(-0.667202\pi\)
0.865183 + 0.501456i \(0.167202\pi\)
\(578\) −2.49754 2.49754i −0.103884 0.103884i
\(579\) 11.4381 + 11.4381i 0.475353 + 0.475353i
\(580\) −28.2467 28.2467i −1.17288 1.17288i
\(581\) 5.40006 + 15.1870i 0.224032 + 0.630064i
\(582\) 1.25088i 0.0518508i
\(583\) 1.51828 1.51828i 0.0628808 0.0628808i
\(584\) −5.51373 −0.228160
\(585\) 1.38493 2.88025i 0.0572598 0.119083i
\(586\) 44.9717i 1.85776i
\(587\) −30.6931 + 30.6931i −1.26684 + 1.26684i −0.319131 + 0.947711i \(0.603391\pi\)
−0.947711 + 0.319131i \(0.896609\pi\)
\(588\) 17.8064 + 21.8735i 0.734325 + 0.902047i
\(589\) 37.2766i 1.53595i
\(590\) −1.49532 1.49532i −0.0615612 0.0615612i
\(591\) 5.91546 5.91546i 0.243329 0.243329i
\(592\) 7.54617 7.54617i 0.310146 0.310146i
\(593\) −5.18036 5.18036i −0.212732 0.212732i 0.592695 0.805427i \(-0.298064\pi\)
−0.805427 + 0.592695i \(0.798064\pi\)
\(594\) 6.41503i 0.263212i
\(595\) 10.9268 + 30.7304i 0.447956 + 1.25982i
\(596\) −5.82225 + 5.82225i −0.238488 + 0.238488i
\(597\) 11.2839i 0.461820i
\(598\) −2.99365 + 6.22591i −0.122419 + 0.254596i
\(599\) −18.5254 −0.756928 −0.378464 0.925616i \(-0.623548\pi\)
−0.378464 + 0.925616i \(0.623548\pi\)
\(600\) 1.76485 1.76485i 0.0720498 0.0720498i
\(601\) 30.9807i 1.26373i 0.775079 + 0.631864i \(0.217710\pi\)
−0.775079 + 0.631864i \(0.782290\pi\)
\(602\) 19.0690 + 53.6291i 0.777193 + 2.18576i
\(603\) −2.26517 2.26517i −0.0922451 0.0922451i
\(604\) −10.5921 10.5921i −0.430987 0.430987i
\(605\) −21.3393 21.3393i −0.867564 0.867564i
\(606\) 24.3526 24.3526i 0.989257 0.989257i
\(607\) 29.4674i 1.19605i −0.801479 0.598023i \(-0.795953\pi\)
0.801479 0.598023i \(-0.204047\pi\)
\(608\) 39.0591 1.58405
\(609\) −27.5310 13.0880i −1.11561 0.530354i
\(610\) 45.5625i 1.84477i
\(611\) 27.1568 + 13.0580i 1.09865 + 0.528270i
\(612\) 2.98065i 0.120485i
\(613\) 13.9398 + 13.9398i 0.563022 + 0.563022i 0.930165 0.367142i \(-0.119664\pi\)
−0.367142 + 0.930165i \(0.619664\pi\)
\(614\) 16.7668i 0.676653i
\(615\) −13.3414 −0.537976
\(616\) 0.671436 + 0.319196i 0.0270529 + 0.0128608i
\(617\) −27.7052 27.7052i −1.11537 1.11537i −0.992412 0.122957i \(-0.960762\pi\)
−0.122957 0.992412i \(-0.539238\pi\)
\(618\) −6.62222 + 6.62222i −0.266385 + 0.266385i
\(619\) 4.58642 + 4.58642i 0.184344 + 0.184344i 0.793246 0.608902i \(-0.208390\pi\)
−0.608902 + 0.793246i \(0.708390\pi\)
\(620\) −48.8736 −1.96281
\(621\) 4.56659 0.183251
\(622\) −3.81137 3.81137i −0.152822 0.152822i
\(623\) −19.7852 + 7.03503i −0.792677 + 0.281853i
\(624\) 7.65233 + 21.8272i 0.306338 + 0.873786i
\(625\) 30.8687 1.23475
\(626\) −28.8128 + 28.8128i −1.15159 + 1.15159i
\(627\) −5.59210 −0.223327
\(628\) 7.58498 0.302674
\(629\) −9.26134 + 9.26134i −0.369274 + 0.369274i
\(630\) 2.06702 4.34801i 0.0823519 0.173229i
\(631\) 11.1175 11.1175i 0.442582 0.442582i −0.450297 0.892879i \(-0.648682\pi\)
0.892879 + 0.450297i \(0.148682\pi\)
\(632\) −4.29237 + 4.29237i −0.170741 + 0.170741i
\(633\) 17.3877i 0.691099i
\(634\) 3.33185i 0.132325i
\(635\) 27.8567 + 27.8567i 1.10546 + 1.10546i
\(636\) −13.5463 −0.537145
\(637\) −21.5123 13.1994i −0.852347 0.522977i
\(638\) −8.30174 −0.328669
\(639\) −1.73260 1.73260i −0.0685407 0.0685407i
\(640\) 9.97073i 0.394128i
\(641\) 22.3590i 0.883129i −0.897229 0.441565i \(-0.854424\pi\)
0.897229 0.441565i \(-0.145576\pi\)
\(642\) 7.61377 7.61377i 0.300492 0.300492i
\(643\) −5.69880 + 5.69880i −0.224739 + 0.224739i −0.810491 0.585752i \(-0.800799\pi\)
0.585752 + 0.810491i \(0.300799\pi\)
\(644\) −2.34763 + 4.93829i −0.0925096 + 0.194596i
\(645\) 38.4170 38.4170i 1.51267 1.51267i
\(646\) −42.7402 −1.68159
\(647\) 7.73510 0.304098 0.152049 0.988373i \(-0.451413\pi\)
0.152049 + 0.988373i \(0.451413\pi\)
\(648\) −3.06022 + 3.06022i −0.120217 + 0.120217i
\(649\) −0.230912 −0.00906410
\(650\) −9.99952 + 20.7961i −0.392214 + 0.815689i
\(651\) −35.1403 + 12.4949i −1.37726 + 0.489712i
\(652\) 23.1383 + 23.1383i 0.906165 + 0.906165i
\(653\) 21.3921 0.837137 0.418568 0.908185i \(-0.362532\pi\)
0.418568 + 0.908185i \(0.362532\pi\)
\(654\) −18.7455 −0.733007
\(655\) −25.8479 25.8479i −1.00996 1.00996i
\(656\) 6.41503 6.41503i 0.250465 0.250465i
\(657\) 2.75686 + 2.75686i 0.107555 + 0.107555i
\(658\) 40.9958 + 19.4891i 1.59818 + 0.759766i
\(659\) −1.68445 −0.0656167 −0.0328084 0.999462i \(-0.510445\pi\)
−0.0328084 + 0.999462i \(0.510445\pi\)
\(660\) 7.33185i 0.285392i
\(661\) −23.4056 23.4056i −0.910372 0.910372i 0.0859290 0.996301i \(-0.472614\pi\)
−0.996301 + 0.0859290i \(0.972614\pi\)
\(662\) 8.42864i 0.327588i
\(663\) −9.39163 26.7883i −0.364741 1.04037i
\(664\) 2.68041i 0.104020i
\(665\) 32.7589 + 15.5734i 1.27034 + 0.603910i
\(666\) 1.93332 0.0749148
\(667\) 5.90967i 0.228823i
\(668\) 35.9441 35.9441i 1.39072 1.39072i
\(669\) −4.69604 4.69604i −0.181559 0.181559i
\(670\) 42.5860 + 42.5860i 1.64524 + 1.64524i
\(671\) −3.51796 3.51796i −0.135809 0.135809i
\(672\) 13.0923 + 36.8206i 0.505048 + 1.42039i
\(673\) 26.2464i 1.01173i 0.862614 + 0.505863i \(0.168826\pi\)
−0.862614 + 0.505863i \(0.831174\pi\)
\(674\) −6.49309 + 6.49309i −0.250105 + 0.250105i
\(675\) 15.2535 0.587109
\(676\) 17.9748 + 22.4844i 0.691339 + 0.864785i
\(677\) 36.7658i 1.41303i 0.707700 + 0.706513i \(0.249733\pi\)
−0.707700 + 0.706513i \(0.750267\pi\)
\(678\) −43.1939 + 43.1939i −1.65885 + 1.65885i
\(679\) −0.296818 0.834764i −0.0113908 0.0320353i
\(680\) 5.42372i 0.207990i
\(681\) 9.56046 + 9.56046i 0.366358 + 0.366358i
\(682\) −7.18200 + 7.18200i −0.275013 + 0.275013i
\(683\) −14.5812 + 14.5812i −0.557934 + 0.557934i −0.928719 0.370785i \(-0.879089\pi\)
0.370785 + 0.928719i \(0.379089\pi\)
\(684\) 2.34396 + 2.34396i 0.0896235 + 0.0896235i
\(685\) 9.67329i 0.369597i
\(686\) −32.4939 19.7397i −1.24062 0.753667i
\(687\) 1.32693 1.32693i 0.0506255 0.0506255i
\(688\) 36.9447i 1.40850i
\(689\) 11.4391 4.01040i 0.435795 0.152784i
\(690\) 9.93332 0.378155
\(691\) 30.4663 30.4663i 1.15899 1.15899i 0.174299 0.984693i \(-0.444234\pi\)
0.984693 0.174299i \(-0.0557658\pi\)
\(692\) 31.8442i 1.21054i
\(693\) −0.176120 0.495316i −0.00669024 0.0188155i
\(694\) −12.7906 12.7906i −0.485525 0.485525i
\(695\) 6.73260 + 6.73260i 0.255382 + 0.255382i
\(696\) 3.58450 + 3.58450i 0.135870 + 0.135870i
\(697\) −7.87310 + 7.87310i −0.298215 + 0.298215i
\(698\) 34.2965i 1.29814i
\(699\) 44.7866 1.69399
\(700\) −7.84166 + 16.4951i −0.296387 + 0.623457i
\(701\) 17.7368i 0.669911i −0.942234 0.334955i \(-0.891279\pi\)
0.942234 0.334955i \(-0.108721\pi\)
\(702\) 15.6938 32.6385i 0.592325 1.23186i
\(703\) 14.5661i 0.549371i
\(704\) 4.34122 + 4.34122i 0.163616 + 0.163616i
\(705\) 43.3282i 1.63183i
\(706\) −8.44854 −0.317965
\(707\) −10.4729 + 22.0300i −0.393874 + 0.828522i
\(708\) 1.03011 + 1.03011i 0.0387140 + 0.0387140i
\(709\) 19.2422 19.2422i 0.722656 0.722656i −0.246489 0.969146i \(-0.579277\pi\)
0.969146 + 0.246489i \(0.0792770\pi\)
\(710\) 32.5734 + 32.5734i 1.22246 + 1.22246i
\(711\) 4.29237 0.160977
\(712\) 3.49196 0.130867
\(713\) −5.11257 5.11257i −0.191467 0.191467i
\(714\) −14.3262 40.2908i −0.536146 1.50785i
\(715\) 2.17061 + 6.19135i 0.0811762 + 0.231543i
\(716\) 9.10324 0.340204
\(717\) 11.8740 11.8740i 0.443441 0.443441i
\(718\) −10.2286 −0.381728
\(719\) 42.3551 1.57958 0.789789 0.613379i \(-0.210190\pi\)
0.789789 + 0.613379i \(0.210190\pi\)
\(720\) 2.20963 2.20963i 0.0823481 0.0823481i
\(721\) 2.84790 5.99062i 0.106061 0.223102i
\(722\) −6.03011 + 6.03011i −0.224418 + 0.224418i
\(723\) −36.6773 + 36.6773i −1.36404 + 1.36404i
\(724\) 47.7762i 1.77559i
\(725\) 19.7397i 0.733116i
\(726\) 27.9781 + 27.9781i 1.03836 + 1.03836i
\(727\) 23.2484 0.862234 0.431117 0.902296i \(-0.358120\pi\)
0.431117 + 0.902296i \(0.358120\pi\)
\(728\) 2.63526 + 3.26662i 0.0976693 + 0.121069i
\(729\) −23.6494 −0.875904
\(730\) −51.8299 51.8299i −1.91831 1.91831i
\(731\) 45.3419i 1.67703i
\(732\) 31.3876i 1.16012i
\(733\) 24.1280 24.1280i 0.891188 0.891188i −0.103447 0.994635i \(-0.532987\pi\)
0.994635 + 0.103447i \(0.0329873\pi\)
\(734\) 28.7580 28.7580i 1.06148 1.06148i
\(735\) −3.70030 + 36.1017i −0.136488 + 1.33163i
\(736\) −5.35704 + 5.35704i −0.197463 + 0.197463i
\(737\) 6.57628 0.242240
\(738\) 1.64353 0.0604990
\(739\) 4.46590 4.46590i 0.164281 0.164281i −0.620179 0.784460i \(-0.712940\pi\)
0.784460 + 0.620179i \(0.212940\pi\)
\(740\) −19.0977 −0.702047
\(741\) −28.4516 13.6806i −1.04520 0.502570i
\(742\) 17.2050 6.11758i 0.631614 0.224583i
\(743\) 10.0114 + 10.0114i 0.367282 + 0.367282i 0.866485 0.499203i \(-0.166374\pi\)
−0.499203 + 0.866485i \(0.666374\pi\)
\(744\) 6.20204 0.227378
\(745\) −10.5944 −0.388149
\(746\) 35.6178 + 35.6178i 1.30406 + 1.30406i
\(747\) −1.34021 + 1.34021i −0.0490356 + 0.0490356i
\(748\) −4.32672 4.32672i −0.158201 0.158201i
\(749\) −3.27432 + 6.88761i −0.119641 + 0.251668i
\(750\) −20.0350 −0.731576
\(751\) 8.16686i 0.298013i 0.988836 + 0.149006i \(0.0476075\pi\)
−0.988836 + 0.149006i \(0.952392\pi\)
\(752\) 20.8338 + 20.8338i 0.759731 + 0.759731i
\(753\) 26.2844i 0.957856i
\(754\) −42.2378 20.3095i −1.53821 0.739628i
\(755\) 19.2739i 0.701448i
\(756\) 12.3071 25.8884i 0.447607 0.941550i
\(757\) 10.5210 0.382392 0.191196 0.981552i \(-0.438763\pi\)
0.191196 + 0.981552i \(0.438763\pi\)
\(758\) 25.5002i 0.926210i
\(759\) 0.766970 0.766970i 0.0278393 0.0278393i
\(760\) −4.26517 4.26517i −0.154714 0.154714i
\(761\) 5.95138 + 5.95138i 0.215737 + 0.215737i 0.806699 0.590962i \(-0.201252\pi\)
−0.590962 + 0.806699i \(0.701252\pi\)
\(762\) −36.5232 36.5232i −1.32310 1.32310i
\(763\) 12.5096 4.44805i 0.452878 0.161030i
\(764\) 22.8113i 0.825286i
\(765\) −2.71186 + 2.71186i −0.0980475 + 0.0980475i
\(766\) −51.9646 −1.87756
\(767\) −1.17484 0.564907i −0.0424210 0.0203976i
\(768\) 21.9112i 0.790653i
\(769\) 9.73800 9.73800i 0.351161 0.351161i −0.509380 0.860541i \(-0.670125\pi\)
0.860541 + 0.509380i \(0.170125\pi\)
\(770\) 3.31111 + 9.31209i 0.119324 + 0.335584i
\(771\) 26.6099i 0.958333i
\(772\) 13.9190 + 13.9190i 0.500957 + 0.500957i
\(773\) −16.0246 + 16.0246i −0.576364 + 0.576364i −0.933899 0.357536i \(-0.883617\pi\)
0.357536 + 0.933899i \(0.383617\pi\)
\(774\) −4.73260 + 4.73260i −0.170110 + 0.170110i
\(775\) −17.0772 17.0772i −0.613433 0.613433i
\(776\) 0.147331i 0.00528886i
\(777\) −13.7314 + 4.88247i −0.492610 + 0.175158i
\(778\) 17.5161 17.5161i 0.627981 0.627981i
\(779\) 12.3827i 0