Properties

Label 570.2.k.a.533.2
Level $570$
Weight $2$
Character 570.533
Analytic conductor $4.551$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 533.2
Character \(\chi\) \(=\) 570.533
Dual form 570.2.k.a.77.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.35438 + 1.07966i) q^{3} +1.00000i q^{4} +(1.25473 - 1.85086i) q^{5} +(1.72112 + 0.194257i) q^{6} +(-3.56316 + 3.56316i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.668679 - 2.92453i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.35438 + 1.07966i) q^{3} +1.00000i q^{4} +(1.25473 - 1.85086i) q^{5} +(1.72112 + 0.194257i) q^{6} +(-3.56316 + 3.56316i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.668679 - 2.92453i) q^{9} +(-2.19598 + 0.421528i) q^{10} -3.35156i q^{11} +(-1.07966 - 1.35438i) q^{12} +(0.759044 + 0.759044i) q^{13} +5.03907 q^{14} +(0.298918 + 3.86143i) q^{15} -1.00000 q^{16} +(0.534673 + 0.534673i) q^{17} +(-2.54078 + 1.59513i) q^{18} -1.00000i q^{19} +(1.85086 + 1.25473i) q^{20} +(0.978873 - 8.67286i) q^{21} +(-2.36991 + 2.36991i) q^{22} +(3.95419 - 3.95419i) q^{23} +(-0.194257 + 1.72112i) q^{24} +(-1.85133 - 4.64463i) q^{25} -1.07345i q^{26} +(2.25184 + 4.68286i) q^{27} +(-3.56316 - 3.56316i) q^{28} -3.01104 q^{29} +(2.51908 - 2.94181i) q^{30} +8.18480 q^{31} +(0.707107 + 0.707107i) q^{32} +(3.61853 + 4.53927i) q^{33} -0.756142i q^{34} +(2.12411 + 11.0657i) q^{35} +(2.92453 + 0.668679i) q^{36} +(5.57606 - 5.57606i) q^{37} +(-0.707107 + 0.707107i) q^{38} +(-1.84754 - 0.208525i) q^{39} +(-0.421528 - 2.19598i) q^{40} -8.43195i q^{41} +(-6.82480 + 5.44047i) q^{42} +(4.29665 + 4.29665i) q^{43} +3.35156 q^{44} +(-4.57387 - 4.90711i) q^{45} -5.59207 q^{46} +(-8.00851 - 8.00851i) q^{47} +(1.35438 - 1.07966i) q^{48} -18.3922i q^{49} +(-1.97516 + 4.59334i) q^{50} +(-1.30141 - 0.146886i) q^{51} +(-0.759044 + 0.759044i) q^{52} +(7.04762 - 7.04762i) q^{53} +(1.71899 - 4.90358i) q^{54} +(-6.20325 - 4.20528i) q^{55} +5.03907i q^{56} +(1.07966 + 1.35438i) q^{57} +(2.12913 + 2.12913i) q^{58} -4.32394 q^{59} +(-3.86143 + 0.298918i) q^{60} +1.35764 q^{61} +(-5.78753 - 5.78753i) q^{62} +(8.03795 + 12.8032i) q^{63} -1.00000i q^{64} +(2.35727 - 0.452489i) q^{65} +(0.651062 - 5.76844i) q^{66} +(5.23044 - 5.23044i) q^{67} +(-0.534673 + 0.534673i) q^{68} +(-1.08630 + 9.62464i) q^{69} +(6.32265 - 9.32659i) q^{70} +4.74757i q^{71} +(-1.59513 - 2.54078i) q^{72} +(-5.12695 - 5.12695i) q^{73} -7.88574 q^{74} +(7.52201 + 4.29178i) q^{75} +1.00000 q^{76} +(11.9421 + 11.9421i) q^{77} +(1.15896 + 1.45386i) q^{78} -0.256451i q^{79} +(-1.25473 + 1.85086i) q^{80} +(-8.10574 - 3.91114i) q^{81} +(-5.96229 + 5.96229i) q^{82} +(-4.73252 + 4.73252i) q^{83} +(8.67286 + 0.978873i) q^{84} +(1.66047 - 0.318735i) q^{85} -6.07639i q^{86} +(4.07809 - 3.25089i) q^{87} +(-2.36991 - 2.36991i) q^{88} +15.2064 q^{89} +(-0.235635 + 6.70406i) q^{90} -5.40919 q^{91} +(3.95419 + 3.95419i) q^{92} +(-11.0853 + 8.83678i) q^{93} +11.3257i q^{94} +(-1.85086 - 1.25473i) q^{95} +(-1.72112 - 0.194257i) q^{96} +(-9.73496 + 9.73496i) q^{97} +(-13.0053 + 13.0053i) q^{98} +(-9.80172 - 2.24112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} - 32q^{21} - 4q^{22} + 32q^{25} + 28q^{27} - 12q^{28} - 8q^{30} + 8q^{31} + 36q^{33} + 4q^{36} - 32q^{37} - 8q^{40} + 12q^{42} - 24q^{43} - 28q^{45} - 16q^{46} - 4q^{48} - 40q^{51} - 8q^{52} - 4q^{55} + 4q^{57} - 4q^{58} - 24q^{60} + 200q^{61} + 28q^{63} + 12q^{70} - 68q^{73} - 36q^{75} + 36q^{76} + 24q^{78} - 92q^{81} + 24q^{82} + 24q^{85} + 28q^{87} - 4q^{88} - 68q^{90} + 64q^{91} + 16q^{93} - 4q^{96} - 148q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) −1.35438 + 1.07966i −0.781950 + 0.623341i
\(4\) 1.00000i 0.500000i
\(5\) 1.25473 1.85086i 0.561130 0.827728i
\(6\) 1.72112 + 0.194257i 0.702646 + 0.0793050i
\(7\) −3.56316 + 3.56316i −1.34675 + 1.34675i −0.457579 + 0.889169i \(0.651283\pi\)
−0.889169 + 0.457579i \(0.848717\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0.668679 2.92453i 0.222893 0.974843i
\(10\) −2.19598 + 0.421528i −0.694429 + 0.133299i
\(11\) 3.35156i 1.01053i −0.862964 0.505266i \(-0.831394\pi\)
0.862964 0.505266i \(-0.168606\pi\)
\(12\) −1.07966 1.35438i −0.311670 0.390975i
\(13\) 0.759044 + 0.759044i 0.210521 + 0.210521i 0.804489 0.593968i \(-0.202439\pi\)
−0.593968 + 0.804489i \(0.702439\pi\)
\(14\) 5.03907 1.34675
\(15\) 0.298918 + 3.86143i 0.0771802 + 0.997017i
\(16\) −1.00000 −0.250000
\(17\) 0.534673 + 0.534673i 0.129677 + 0.129677i 0.768966 0.639289i \(-0.220771\pi\)
−0.639289 + 0.768966i \(0.720771\pi\)
\(18\) −2.54078 + 1.59513i −0.598868 + 0.375975i
\(19\) 1.00000i 0.229416i
\(20\) 1.85086 + 1.25473i 0.413864 + 0.280565i
\(21\) 0.978873 8.67286i 0.213608 1.89257i
\(22\) −2.36991 + 2.36991i −0.505266 + 0.505266i
\(23\) 3.95419 3.95419i 0.824506 0.824506i −0.162245 0.986751i \(-0.551873\pi\)
0.986751 + 0.162245i \(0.0518734\pi\)
\(24\) −0.194257 + 1.72112i −0.0396525 + 0.351323i
\(25\) −1.85133 4.64463i −0.370266 0.928926i
\(26\) 1.07345i 0.210521i
\(27\) 2.25184 + 4.68286i 0.433368 + 0.901217i
\(28\) −3.56316 3.56316i −0.673374 0.673374i
\(29\) −3.01104 −0.559137 −0.279568 0.960126i \(-0.590191\pi\)
−0.279568 + 0.960126i \(0.590191\pi\)
\(30\) 2.51908 2.94181i 0.459918 0.537099i
\(31\) 8.18480 1.47003 0.735017 0.678049i \(-0.237174\pi\)
0.735017 + 0.678049i \(0.237174\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 3.61853 + 4.53927i 0.629906 + 0.790186i
\(34\) 0.756142i 0.129677i
\(35\) 2.12411 + 11.0657i 0.359040 + 1.87044i
\(36\) 2.92453 + 0.668679i 0.487421 + 0.111447i
\(37\) 5.57606 5.57606i 0.916699 0.916699i −0.0800886 0.996788i \(-0.525520\pi\)
0.996788 + 0.0800886i \(0.0255203\pi\)
\(38\) −0.707107 + 0.707107i −0.114708 + 0.114708i
\(39\) −1.84754 0.208525i −0.295843 0.0333907i
\(40\) −0.421528 2.19598i −0.0666494 0.347214i
\(41\) 8.43195i 1.31685i −0.752647 0.658425i \(-0.771223\pi\)
0.752647 0.658425i \(-0.228777\pi\)
\(42\) −6.82480 + 5.44047i −1.05309 + 0.839483i
\(43\) 4.29665 + 4.29665i 0.655234 + 0.655234i 0.954248 0.299015i \(-0.0966580\pi\)
−0.299015 + 0.954248i \(0.596658\pi\)
\(44\) 3.35156 0.505266
\(45\) −4.57387 4.90711i −0.681832 0.731509i
\(46\) −5.59207 −0.824506
\(47\) −8.00851 8.00851i −1.16816 1.16816i −0.982640 0.185522i \(-0.940603\pi\)
−0.185522 0.982640i \(-0.559397\pi\)
\(48\) 1.35438 1.07966i 0.195488 0.155835i
\(49\) 18.3922i 2.62746i
\(50\) −1.97516 + 4.59334i −0.279330 + 0.649596i
\(51\) −1.30141 0.146886i −0.182234 0.0205681i
\(52\) −0.759044 + 0.759044i −0.105260 + 0.105260i
\(53\) 7.04762 7.04762i 0.968064 0.968064i −0.0314411 0.999506i \(-0.510010\pi\)
0.999506 + 0.0314411i \(0.0100097\pi\)
\(54\) 1.71899 4.90358i 0.233925 0.667292i
\(55\) −6.20325 4.20528i −0.836446 0.567040i
\(56\) 5.03907i 0.673374i
\(57\) 1.07966 + 1.35438i 0.143004 + 0.179392i
\(58\) 2.12913 + 2.12913i 0.279568 + 0.279568i
\(59\) −4.32394 −0.562928 −0.281464 0.959572i \(-0.590820\pi\)
−0.281464 + 0.959572i \(0.590820\pi\)
\(60\) −3.86143 + 0.298918i −0.498509 + 0.0385901i
\(61\) 1.35764 0.173828 0.0869138 0.996216i \(-0.472300\pi\)
0.0869138 + 0.996216i \(0.472300\pi\)
\(62\) −5.78753 5.78753i −0.735017 0.735017i
\(63\) 8.03795 + 12.8032i 1.01269 + 1.61305i
\(64\) 1.00000i 0.125000i
\(65\) 2.35727 0.452489i 0.292384 0.0561243i
\(66\) 0.651062 5.76844i 0.0801402 0.710046i
\(67\) 5.23044 5.23044i 0.639000 0.639000i −0.311309 0.950309i \(-0.600767\pi\)
0.950309 + 0.311309i \(0.100767\pi\)
\(68\) −0.534673 + 0.534673i −0.0648386 + 0.0648386i
\(69\) −1.08630 + 9.62464i −0.130775 + 1.15867i
\(70\) 6.32265 9.32659i 0.755701 1.11474i
\(71\) 4.74757i 0.563433i 0.959498 + 0.281716i \(0.0909038\pi\)
−0.959498 + 0.281716i \(0.909096\pi\)
\(72\) −1.59513 2.54078i −0.187987 0.299434i
\(73\) −5.12695 5.12695i −0.600064 0.600064i 0.340265 0.940330i \(-0.389483\pi\)
−0.940330 + 0.340265i \(0.889483\pi\)
\(74\) −7.88574 −0.916699
\(75\) 7.52201 + 4.29178i 0.868567 + 0.495572i
\(76\) 1.00000 0.114708
\(77\) 11.9421 + 11.9421i 1.36093 + 1.36093i
\(78\) 1.15896 + 1.45386i 0.131226 + 0.164617i
\(79\) 0.256451i 0.0288529i −0.999896 0.0144265i \(-0.995408\pi\)
0.999896 0.0144265i \(-0.00459225\pi\)
\(80\) −1.25473 + 1.85086i −0.140283 + 0.206932i
\(81\) −8.10574 3.91114i −0.900637 0.434572i
\(82\) −5.96229 + 5.96229i −0.658425 + 0.658425i
\(83\) −4.73252 + 4.73252i −0.519462 + 0.519462i −0.917408 0.397947i \(-0.869723\pi\)
0.397947 + 0.917408i \(0.369723\pi\)
\(84\) 8.67286 + 0.978873i 0.946286 + 0.106804i
\(85\) 1.66047 0.318735i 0.180103 0.0345716i
\(86\) 6.07639i 0.655234i
\(87\) 4.07809 3.25089i 0.437217 0.348533i
\(88\) −2.36991 2.36991i −0.252633 0.252633i
\(89\) 15.2064 1.61188 0.805938 0.592000i \(-0.201662\pi\)
0.805938 + 0.592000i \(0.201662\pi\)
\(90\) −0.235635 + 6.70406i −0.0248381 + 0.706670i
\(91\) −5.40919 −0.567037
\(92\) 3.95419 + 3.95419i 0.412253 + 0.412253i
\(93\) −11.0853 + 8.83678i −1.14949 + 0.916332i
\(94\) 11.3257i 1.16816i
\(95\) −1.85086 1.25473i −0.189894 0.128732i
\(96\) −1.72112 0.194257i −0.175661 0.0198262i
\(97\) −9.73496 + 9.73496i −0.988435 + 0.988435i −0.999934 0.0114985i \(-0.996340\pi\)
0.0114985 + 0.999934i \(0.496340\pi\)
\(98\) −13.0053 + 13.0053i −1.31373 + 1.31373i
\(99\) −9.80172 2.24112i −0.985110 0.225241i
\(100\) 4.64463 1.85133i 0.464463 0.185133i
\(101\) 12.3184i 1.22573i 0.790189 + 0.612863i \(0.209982\pi\)
−0.790189 + 0.612863i \(0.790018\pi\)
\(102\) 0.816374 + 1.02410i 0.0808331 + 0.101401i
\(103\) 0.357091 + 0.357091i 0.0351852 + 0.0351852i 0.724481 0.689295i \(-0.242080\pi\)
−0.689295 + 0.724481i \(0.742080\pi\)
\(104\) 1.07345 0.105260
\(105\) −14.8240 12.6938i −1.44667 1.23879i
\(106\) −9.96683 −0.968064
\(107\) −2.15869 2.15869i −0.208688 0.208688i 0.595022 0.803710i \(-0.297143\pi\)
−0.803710 + 0.595022i \(0.797143\pi\)
\(108\) −4.68286 + 2.25184i −0.450609 + 0.216684i
\(109\) 2.96084i 0.283597i 0.989896 + 0.141798i \(0.0452885\pi\)
−0.989896 + 0.141798i \(0.954712\pi\)
\(110\) 1.41277 + 7.35994i 0.134703 + 0.701743i
\(111\) −1.53186 + 13.5723i −0.145398 + 1.28823i
\(112\) 3.56316 3.56316i 0.336687 0.336687i
\(113\) 0.894915 0.894915i 0.0841865 0.0841865i −0.663760 0.747946i \(-0.731040\pi\)
0.747946 + 0.663760i \(0.231040\pi\)
\(114\) 0.194257 1.72112i 0.0181938 0.161198i
\(115\) −2.35721 12.2801i −0.219811 1.14512i
\(116\) 3.01104i 0.279568i
\(117\) 2.72740 1.71229i 0.252149 0.158301i
\(118\) 3.05748 + 3.05748i 0.281464 + 0.281464i
\(119\) −3.81025 −0.349285
\(120\) 2.94181 + 2.51908i 0.268549 + 0.229959i
\(121\) −0.232932 −0.0211757
\(122\) −0.959995 0.959995i −0.0869138 0.0869138i
\(123\) 9.10362 + 11.4200i 0.820846 + 1.02971i
\(124\) 8.18480i 0.735017i
\(125\) −10.9194 2.40119i −0.976665 0.214769i
\(126\) 3.36952 14.7369i 0.300181 1.31287i
\(127\) −6.70476 + 6.70476i −0.594951 + 0.594951i −0.938965 0.344014i \(-0.888213\pi\)
0.344014 + 0.938965i \(0.388213\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −10.4582 1.18038i −0.920794 0.103927i
\(130\) −1.98680 1.34689i −0.174254 0.118130i
\(131\) 1.53144i 0.133802i −0.997760 0.0669011i \(-0.978689\pi\)
0.997760 0.0669011i \(-0.0213112\pi\)
\(132\) −4.53927 + 3.61853i −0.395093 + 0.314953i
\(133\) 3.56316 + 3.56316i 0.308965 + 0.308965i
\(134\) −7.39695 −0.639000
\(135\) 11.4927 + 1.70787i 0.989138 + 0.146990i
\(136\) 0.756142 0.0648386
\(137\) −4.76164 4.76164i −0.406814 0.406814i 0.473812 0.880626i \(-0.342878\pi\)
−0.880626 + 0.473812i \(0.842878\pi\)
\(138\) 7.57378 6.03752i 0.644723 0.513948i
\(139\) 9.84417i 0.834971i 0.908684 + 0.417486i \(0.137089\pi\)
−0.908684 + 0.417486i \(0.862911\pi\)
\(140\) −11.0657 + 2.12411i −0.935221 + 0.179520i
\(141\) 19.4930 + 2.20010i 1.64161 + 0.185282i
\(142\) 3.35704 3.35704i 0.281716 0.281716i
\(143\) 2.54398 2.54398i 0.212738 0.212738i
\(144\) −0.668679 + 2.92453i −0.0557233 + 0.243711i
\(145\) −3.77803 + 5.57300i −0.313748 + 0.462813i
\(146\) 7.25060i 0.600064i
\(147\) 19.8573 + 24.9100i 1.63780 + 2.05454i
\(148\) 5.57606 + 5.57606i 0.458350 + 0.458350i
\(149\) 1.98019 0.162224 0.0811118 0.996705i \(-0.474153\pi\)
0.0811118 + 0.996705i \(0.474153\pi\)
\(150\) −2.28412 8.35361i −0.186497 0.682069i
\(151\) 20.6241 1.67837 0.839185 0.543847i \(-0.183033\pi\)
0.839185 + 0.543847i \(0.183033\pi\)
\(152\) −0.707107 0.707107i −0.0573539 0.0573539i
\(153\) 1.92119 1.20614i 0.155319 0.0975108i
\(154\) 16.8887i 1.36093i
\(155\) 10.2697 15.1489i 0.824880 1.21679i
\(156\) 0.208525 1.84754i 0.0166954 0.147922i
\(157\) −16.6468 + 16.6468i −1.32856 + 1.32856i −0.421939 + 0.906624i \(0.638650\pi\)
−0.906624 + 0.421939i \(0.861350\pi\)
\(158\) −0.181338 + 0.181338i −0.0144265 + 0.0144265i
\(159\) −1.93612 + 17.1541i −0.153545 + 1.36041i
\(160\) 2.19598 0.421528i 0.173607 0.0333247i
\(161\) 28.1788i 2.22080i
\(162\) 2.96602 + 8.49722i 0.233033 + 0.667604i
\(163\) −10.0274 10.0274i −0.785406 0.785406i 0.195331 0.980737i \(-0.437422\pi\)
−0.980737 + 0.195331i \(0.937422\pi\)
\(164\) 8.43195 0.658425
\(165\) 12.9418 1.00184i 1.00752 0.0779931i
\(166\) 6.69279 0.519462
\(167\) −6.15920 6.15920i −0.476613 0.476613i 0.427434 0.904047i \(-0.359418\pi\)
−0.904047 + 0.427434i \(0.859418\pi\)
\(168\) −5.44047 6.82480i −0.419741 0.526545i
\(169\) 11.8477i 0.911362i
\(170\) −1.39951 0.948750i −0.107337 0.0727658i
\(171\) −2.92453 0.668679i −0.223644 0.0511352i
\(172\) −4.29665 + 4.29665i −0.327617 + 0.327617i
\(173\) 1.69599 1.69599i 0.128944 0.128944i −0.639690 0.768633i \(-0.720937\pi\)
0.768633 + 0.639690i \(0.220937\pi\)
\(174\) −5.18237 0.584915i −0.392875 0.0443423i
\(175\) 23.1461 + 9.95297i 1.74968 + 0.752374i
\(176\) 3.35156i 0.252633i
\(177\) 5.85624 4.66837i 0.440182 0.350896i
\(178\) −10.7526 10.7526i −0.805938 0.805938i
\(179\) −11.4970 −0.859323 −0.429662 0.902990i \(-0.641367\pi\)
−0.429662 + 0.902990i \(0.641367\pi\)
\(180\) 4.90711 4.57387i 0.365754 0.340916i
\(181\) 22.3294 1.65973 0.829867 0.557961i \(-0.188416\pi\)
0.829867 + 0.557961i \(0.188416\pi\)
\(182\) 3.82488 + 3.82488i 0.283519 + 0.283519i
\(183\) −1.83875 + 1.46578i −0.135925 + 0.108354i
\(184\) 5.59207i 0.412253i
\(185\) −3.32406 17.3169i −0.244390 1.27316i
\(186\) 14.0871 + 1.58995i 1.03291 + 0.116581i
\(187\) 1.79199 1.79199i 0.131043 0.131043i
\(188\) 8.00851 8.00851i 0.584081 0.584081i
\(189\) −24.7095 8.66210i −1.79735 0.630075i
\(190\) 0.421528 + 2.19598i 0.0305808 + 0.159313i
\(191\) 7.92842i 0.573680i −0.957978 0.286840i \(-0.907395\pi\)
0.957978 0.286840i \(-0.0926048\pi\)
\(192\) 1.07966 + 1.35438i 0.0779176 + 0.0977438i
\(193\) 4.68979 + 4.68979i 0.337578 + 0.337578i 0.855455 0.517877i \(-0.173277\pi\)
−0.517877 + 0.855455i \(0.673277\pi\)
\(194\) 13.7673 0.988435
\(195\) −2.70410 + 3.15789i −0.193645 + 0.226141i
\(196\) 18.3922 1.31373
\(197\) −4.72215 4.72215i −0.336439 0.336439i 0.518586 0.855025i \(-0.326459\pi\)
−0.855025 + 0.518586i \(0.826459\pi\)
\(198\) 5.34616 + 8.51557i 0.379935 + 0.605176i
\(199\) 10.0047i 0.709217i −0.935015 0.354609i \(-0.884614\pi\)
0.935015 0.354609i \(-0.115386\pi\)
\(200\) −4.59334 1.97516i −0.324798 0.139665i
\(201\) −1.43691 + 12.7311i −0.101352 + 0.897980i
\(202\) 8.71043 8.71043i 0.612863 0.612863i
\(203\) 10.7288 10.7288i 0.753016 0.753016i
\(204\) 0.146886 1.30141i 0.0102841 0.0911171i
\(205\) −15.6063 10.5798i −1.08999 0.738924i
\(206\) 0.505003i 0.0351852i
\(207\) −8.92006 14.2082i −0.619987 0.987540i
\(208\) −0.759044 0.759044i −0.0526302 0.0526302i
\(209\) −3.35156 −0.231832
\(210\) 1.50627 + 19.4580i 0.103942 + 1.34273i
\(211\) 0.338632 0.0233124 0.0116562 0.999932i \(-0.496290\pi\)
0.0116562 + 0.999932i \(0.496290\pi\)
\(212\) 7.04762 + 7.04762i 0.484032 + 0.484032i
\(213\) −5.12575 6.43000i −0.351211 0.440577i
\(214\) 3.05284i 0.208688i
\(215\) 13.3436 2.56136i 0.910026 0.174684i
\(216\) 4.90358 + 1.71899i 0.333646 + 0.116962i
\(217\) −29.1638 + 29.1638i −1.97977 + 1.97977i
\(218\) 2.09363 2.09363i 0.141798 0.141798i
\(219\) 12.4792 + 1.40848i 0.843265 + 0.0951762i
\(220\) 4.20528 6.20325i 0.283520 0.418223i
\(221\) 0.811681i 0.0545996i
\(222\) 10.6803 8.51390i 0.716813 0.571416i
\(223\) −6.58383 6.58383i −0.440886 0.440886i 0.451424 0.892310i \(-0.350916\pi\)
−0.892310 + 0.451424i \(0.850916\pi\)
\(224\) −5.03907 −0.336687
\(225\) −14.8213 + 2.30850i −0.988086 + 0.153900i
\(226\) −1.26560 −0.0841865
\(227\) −15.0913 15.0913i −1.00164 1.00164i −0.999999 0.00164481i \(-0.999476\pi\)
−0.00164481 0.999999i \(-0.500524\pi\)
\(228\) −1.35438 + 1.07966i −0.0896959 + 0.0715021i
\(229\) 13.2052i 0.872626i −0.899795 0.436313i \(-0.856284\pi\)
0.899795 0.436313i \(-0.143716\pi\)
\(230\) −7.01651 + 10.3501i −0.462655 + 0.682466i
\(231\) −29.0676 3.28075i −1.91251 0.215857i
\(232\) −2.12913 + 2.12913i −0.139784 + 0.139784i
\(233\) −17.7744 + 17.7744i −1.16444 + 1.16444i −0.180943 + 0.983494i \(0.557915\pi\)
−0.983494 + 0.180943i \(0.942085\pi\)
\(234\) −3.13934 0.717794i −0.205225 0.0469237i
\(235\) −24.8711 + 4.77412i −1.62241 + 0.311429i
\(236\) 4.32394i 0.281464i
\(237\) 0.276879 + 0.347331i 0.0179852 + 0.0225616i
\(238\) 2.69425 + 2.69425i 0.174643 + 0.174643i
\(239\) −8.08746 −0.523134 −0.261567 0.965185i \(-0.584239\pi\)
−0.261567 + 0.965185i \(0.584239\pi\)
\(240\) −0.298918 3.86143i −0.0192950 0.249254i
\(241\) 17.4598 1.12468 0.562341 0.826905i \(-0.309901\pi\)
0.562341 + 0.826905i \(0.309901\pi\)
\(242\) 0.164708 + 0.164708i 0.0105878 + 0.0105878i
\(243\) 15.2009 3.45425i 0.975140 0.221590i
\(244\) 1.35764i 0.0869138i
\(245\) −34.0413 23.0772i −2.17482 1.47435i
\(246\) 1.63796 14.5124i 0.104433 0.925278i
\(247\) 0.759044 0.759044i 0.0482968 0.0482968i
\(248\) 5.78753 5.78753i 0.367508 0.367508i
\(249\) 1.30012 11.5191i 0.0823918 0.729995i
\(250\) 6.02332 + 9.41911i 0.380948 + 0.595717i
\(251\) 2.20006i 0.138867i 0.997587 + 0.0694333i \(0.0221191\pi\)
−0.997587 + 0.0694333i \(0.977881\pi\)
\(252\) −12.8032 + 8.03795i −0.806524 + 0.506343i
\(253\) −13.2527 13.2527i −0.833190 0.833190i
\(254\) 9.48196 0.594951
\(255\) −1.90478 + 2.22443i −0.119282 + 0.139299i
\(256\) 1.00000 0.0625000
\(257\) 18.3829 + 18.3829i 1.14670 + 1.14670i 0.987198 + 0.159499i \(0.0509877\pi\)
0.159499 + 0.987198i \(0.449012\pi\)
\(258\) 6.56042 + 8.22972i 0.408434 + 0.512360i
\(259\) 39.7368i 2.46913i
\(260\) 0.452489 + 2.35727i 0.0280622 + 0.146192i
\(261\) −2.01342 + 8.80588i −0.124628 + 0.545070i
\(262\) −1.08289 + 1.08289i −0.0669011 + 0.0669011i
\(263\) 17.6465 17.6465i 1.08813 1.08813i 0.0924109 0.995721i \(-0.470543\pi\)
0.995721 0.0924109i \(-0.0294573\pi\)
\(264\) 5.76844 + 0.651062i 0.355023 + 0.0400701i
\(265\) −4.20130 21.8869i −0.258084 1.34450i
\(266\) 5.03907i 0.308965i
\(267\) −20.5952 + 16.4177i −1.26041 + 1.00475i
\(268\) 5.23044 + 5.23044i 0.319500 + 0.319500i
\(269\) −12.7863 −0.779593 −0.389796 0.920901i \(-0.627455\pi\)
−0.389796 + 0.920901i \(0.627455\pi\)
\(270\) −6.91895 9.33424i −0.421074 0.568064i
\(271\) −8.21287 −0.498897 −0.249448 0.968388i \(-0.580249\pi\)
−0.249448 + 0.968388i \(0.580249\pi\)
\(272\) −0.534673 0.534673i −0.0324193 0.0324193i
\(273\) 7.32609 5.84007i 0.443395 0.353457i
\(274\) 6.73398i 0.406814i
\(275\) −15.5667 + 6.20484i −0.938710 + 0.374166i
\(276\) −9.62464 1.08630i −0.579335 0.0653874i
\(277\) 4.32961 4.32961i 0.260141 0.260141i −0.564970 0.825111i \(-0.691112\pi\)
0.825111 + 0.564970i \(0.191112\pi\)
\(278\) 6.96088 6.96088i 0.417486 0.417486i
\(279\) 5.47301 23.9367i 0.327660 1.43305i
\(280\) 9.32659 + 6.32265i 0.557370 + 0.377850i
\(281\) 11.0222i 0.657530i 0.944412 + 0.328765i \(0.106632\pi\)
−0.944412 + 0.328765i \(0.893368\pi\)
\(282\) −12.2279 15.3393i −0.728163 0.913445i
\(283\) −12.1343 12.1343i −0.721309 0.721309i 0.247563 0.968872i \(-0.420370\pi\)
−0.968872 + 0.247563i \(0.920370\pi\)
\(284\) −4.74757 −0.281716
\(285\) 3.86143 0.298918i 0.228731 0.0177063i
\(286\) −3.59773 −0.212738
\(287\) 30.0444 + 30.0444i 1.77346 + 1.77346i
\(288\) 2.54078 1.59513i 0.149717 0.0939937i
\(289\) 16.4282i 0.966368i
\(290\) 6.61218 1.26924i 0.388281 0.0745322i
\(291\) 2.67439 23.6952i 0.156776 1.38904i
\(292\) 5.12695 5.12695i 0.300032 0.300032i
\(293\) 17.4542 17.4542i 1.01968 1.01968i 0.0198825 0.999802i \(-0.493671\pi\)
0.999802 0.0198825i \(-0.00632920\pi\)
\(294\) 3.57281 31.6553i 0.208371 1.84617i
\(295\) −5.42535 + 8.00298i −0.315876 + 0.465951i
\(296\) 7.88574i 0.458350i
\(297\) 15.6949 7.54718i 0.910709 0.437932i
\(298\) −1.40021 1.40021i −0.0811118 0.0811118i
\(299\) 6.00281 0.347151
\(300\) −4.29178 + 7.52201i −0.247786 + 0.434283i
\(301\) −30.6193 −1.76487
\(302\) −14.5835 14.5835i −0.839185 0.839185i
\(303\) −13.2997 16.6838i −0.764045 0.958458i
\(304\) 1.00000i 0.0573539i
\(305\) 1.70346 2.51279i 0.0975399 0.143882i
\(306\) −2.21136 0.505616i −0.126415 0.0289042i
\(307\) −5.85378 + 5.85378i −0.334093 + 0.334093i −0.854138 0.520046i \(-0.825915\pi\)
0.520046 + 0.854138i \(0.325915\pi\)
\(308\) −11.9421 + 11.9421i −0.680466 + 0.680466i
\(309\) −0.869172 0.0981002i −0.0494455 0.00558073i
\(310\) −17.9736 + 3.45012i −1.02083 + 0.195954i
\(311\) 14.2142i 0.806015i −0.915197 0.403008i \(-0.867965\pi\)
0.915197 0.403008i \(-0.132035\pi\)
\(312\) −1.45386 + 1.15896i −0.0823085 + 0.0656131i
\(313\) 23.2992 + 23.2992i 1.31695 + 1.31695i 0.916180 + 0.400766i \(0.131256\pi\)
0.400766 + 0.916180i \(0.368744\pi\)
\(314\) 23.5422 1.32856
\(315\) 33.7822 + 1.18738i 1.90341 + 0.0669014i
\(316\) 0.256451 0.0144265
\(317\) 9.99115 + 9.99115i 0.561159 + 0.561159i 0.929637 0.368478i \(-0.120121\pi\)
−0.368478 + 0.929637i \(0.620121\pi\)
\(318\) 13.4989 10.7608i 0.756978 0.603434i
\(319\) 10.0917i 0.565026i
\(320\) −1.85086 1.25473i −0.103466 0.0701413i
\(321\) 5.25432 + 0.593035i 0.293267 + 0.0331000i
\(322\) 19.9254 19.9254i 1.11040 1.11040i
\(323\) 0.534673 0.534673i 0.0297500 0.0297500i
\(324\) 3.91114 8.10574i 0.217286 0.450319i
\(325\) 2.12024 4.93072i 0.117610 0.273507i
\(326\) 14.1809i 0.785406i
\(327\) −3.19669 4.01009i −0.176777 0.221759i
\(328\) −5.96229 5.96229i −0.329212 0.329212i
\(329\) 57.0712 3.14644
\(330\) −9.85964 8.44283i −0.542756 0.464763i
\(331\) −8.73786 −0.480276 −0.240138 0.970739i \(-0.577193\pi\)
−0.240138 + 0.970739i \(0.577193\pi\)
\(332\) −4.73252 4.73252i −0.259731 0.259731i
\(333\) −12.5788 20.0360i −0.689312 1.09796i
\(334\) 8.71042i 0.476613i
\(335\) −3.11802 16.2435i −0.170356 0.887479i
\(336\) −0.978873 + 8.67286i −0.0534019 + 0.473143i
\(337\) 18.7714 18.7714i 1.02254 1.02254i 0.0228016 0.999740i \(-0.492741\pi\)
0.999740 0.0228016i \(-0.00725861\pi\)
\(338\) −8.37759 + 8.37759i −0.455681 + 0.455681i
\(339\) −0.245851 + 2.17825i −0.0133528 + 0.118307i
\(340\) 0.318735 + 1.66047i 0.0172858 + 0.0900516i
\(341\) 27.4318i 1.48552i
\(342\) 1.59513 + 2.54078i 0.0862546 + 0.137390i
\(343\) 40.5923 + 40.5923i 2.19178 + 2.19178i
\(344\) 6.07639 0.327617
\(345\) 16.4508 + 14.0869i 0.885682 + 0.758411i
\(346\) −2.39849 −0.128944
\(347\) −5.40165 5.40165i −0.289976 0.289976i 0.547095 0.837071i \(-0.315734\pi\)
−0.837071 + 0.547095i \(0.815734\pi\)
\(348\) 3.25089 + 4.07809i 0.174266 + 0.218609i
\(349\) 19.1590i 1.02556i 0.858521 + 0.512778i \(0.171384\pi\)
−0.858521 + 0.512778i \(0.828616\pi\)
\(350\) −9.32898 23.4046i −0.498655 1.25103i
\(351\) −1.84525 + 5.26375i −0.0984921 + 0.280958i
\(352\) 2.36991 2.36991i 0.126317 0.126317i
\(353\) −0.366441 + 0.366441i −0.0195037 + 0.0195037i −0.716791 0.697288i \(-0.754390\pi\)
0.697288 + 0.716791i \(0.254390\pi\)
\(354\) −7.44203 0.839954i −0.395539 0.0446430i
\(355\) 8.78707 + 5.95690i 0.466369 + 0.316159i
\(356\) 15.2064i 0.805938i
\(357\) 5.16052 4.11377i 0.273124 0.217724i
\(358\) 8.12958 + 8.12958i 0.429662 + 0.429662i
\(359\) −16.4393 −0.867631 −0.433815 0.901002i \(-0.642833\pi\)
−0.433815 + 0.901002i \(0.642833\pi\)
\(360\) −6.70406 0.235635i −0.353335 0.0124191i
\(361\) −1.00000 −0.0526316
\(362\) −15.7893 15.7893i −0.829867 0.829867i
\(363\) 0.315478 0.251487i 0.0165583 0.0131996i
\(364\) 5.40919i 0.283519i
\(365\) −15.9222 + 3.05633i −0.833404 + 0.159976i
\(366\) 2.33666 + 0.263730i 0.122139 + 0.0137854i
\(367\) 13.3725 13.3725i 0.698039 0.698039i −0.265948 0.963987i \(-0.585685\pi\)
0.963987 + 0.265948i \(0.0856851\pi\)
\(368\) −3.95419 + 3.95419i −0.206126 + 0.206126i
\(369\) −24.6595 5.63827i −1.28372 0.293517i
\(370\) −9.89444 + 14.5954i −0.514387 + 0.758777i
\(371\) 50.2236i 2.60748i
\(372\) −8.83678 11.0853i −0.458166 0.574747i
\(373\) −2.80556 2.80556i −0.145266 0.145266i 0.630733 0.776000i \(-0.282754\pi\)
−0.776000 + 0.630733i \(0.782754\pi\)
\(374\) −2.53425 −0.131043
\(375\) 17.3815 8.53714i 0.897578 0.440856i
\(376\) −11.3257 −0.584081
\(377\) −2.28551 2.28551i −0.117710 0.117710i
\(378\) 11.3472 + 23.5973i 0.583637 + 1.21371i
\(379\) 35.0537i 1.80059i 0.435284 + 0.900293i \(0.356648\pi\)
−0.435284 + 0.900293i \(0.643352\pi\)
\(380\) 1.25473 1.85086i 0.0643660 0.0949469i
\(381\) 1.84193 16.3196i 0.0943651 0.836079i
\(382\) −5.60624 + 5.60624i −0.286840 + 0.286840i
\(383\) −0.786561 + 0.786561i −0.0401914 + 0.0401914i −0.726917 0.686725i \(-0.759047\pi\)
0.686725 + 0.726917i \(0.259047\pi\)
\(384\) 0.194257 1.72112i 0.00991312 0.0878307i
\(385\) 37.0873 7.11906i 1.89014 0.362821i
\(386\) 6.63236i 0.337578i
\(387\) 15.4388 9.69260i 0.784797 0.492703i
\(388\) −9.73496 9.73496i −0.494218 0.494218i
\(389\) 1.39333 0.0706444 0.0353222 0.999376i \(-0.488754\pi\)
0.0353222 + 0.999376i \(0.488754\pi\)
\(390\) 4.14505 0.320873i 0.209893 0.0162480i
\(391\) 4.22840 0.213839
\(392\) −13.0053 13.0053i −0.656865 0.656865i
\(393\) 1.65343 + 2.07414i 0.0834043 + 0.104627i
\(394\) 6.67813i 0.336439i
\(395\) −0.474653 0.321775i −0.0238824 0.0161903i
\(396\) 2.24112 9.80172i 0.112620 0.492555i
\(397\) −10.5012 + 10.5012i −0.527041 + 0.527041i −0.919689 0.392648i \(-0.871559\pi\)
0.392648 + 0.919689i \(0.371559\pi\)
\(398\) −7.07442 + 7.07442i −0.354609 + 0.354609i
\(399\) −8.67286 0.978873i −0.434186 0.0490049i
\(400\) 1.85133 + 4.64463i 0.0925665 + 0.232231i
\(401\) 19.6404i 0.980792i 0.871500 + 0.490396i \(0.163148\pi\)
−0.871500 + 0.490396i \(0.836852\pi\)
\(402\) 10.0183 7.98618i 0.499666 0.398314i
\(403\) 6.21263 + 6.21263i 0.309473 + 0.309473i
\(404\) −12.3184 −0.612863
\(405\) −17.4094 + 10.0951i −0.865082 + 0.501631i
\(406\) −15.1729 −0.753016
\(407\) −18.6885 18.6885i −0.926354 0.926354i
\(408\) −1.02410 + 0.816374i −0.0507006 + 0.0404165i
\(409\) 8.61457i 0.425963i 0.977056 + 0.212981i \(0.0683174\pi\)
−0.977056 + 0.212981i \(0.931683\pi\)
\(410\) 3.55430 + 18.5164i 0.175534 + 0.914458i
\(411\) 11.5900 + 1.30812i 0.571693 + 0.0645248i
\(412\) −0.357091 + 0.357091i −0.0175926 + 0.0175926i
\(413\) 15.4069 15.4069i 0.758123 0.758123i
\(414\) −3.73930 + 16.3542i −0.183777 + 0.803764i
\(415\) 2.82120 + 14.6972i 0.138487 + 0.721458i
\(416\) 1.07345i 0.0526302i
\(417\) −10.6283 13.3327i −0.520471 0.652906i
\(418\) 2.36991 + 2.36991i 0.115916 + 0.115916i
\(419\) −0.0254108 −0.00124140 −0.000620699 1.00000i \(-0.500198\pi\)
−0.000620699 1.00000i \(0.500198\pi\)
\(420\) 12.6938 14.8240i 0.619394 0.723337i
\(421\) 5.45966 0.266087 0.133044 0.991110i \(-0.457525\pi\)
0.133044 + 0.991110i \(0.457525\pi\)
\(422\) −0.239449 0.239449i −0.0116562 0.0116562i
\(423\) −28.7763 + 18.0660i −1.39915 + 0.878399i
\(424\) 9.96683i 0.484032i
\(425\) 1.49350 3.47321i 0.0724455 0.168476i
\(426\) −0.922247 + 8.17115i −0.0446830 + 0.395894i
\(427\) −4.83748 + 4.83748i −0.234102 + 0.234102i
\(428\) 2.15869 2.15869i 0.104344 0.104344i
\(429\) −0.698883 + 6.19214i −0.0337424 + 0.298959i
\(430\) −11.2465 7.62419i −0.542355 0.367671i
\(431\) 2.80348i 0.135039i −0.997718 0.0675195i \(-0.978491\pi\)
0.997718 0.0675195i \(-0.0215085\pi\)
\(432\) −2.25184 4.68286i −0.108342 0.225304i
\(433\) −8.33316 8.33316i −0.400466 0.400466i 0.477931 0.878397i \(-0.341387\pi\)
−0.878397 + 0.477931i \(0.841387\pi\)
\(434\) 41.2438 1.97977
\(435\) −0.900054 11.6269i −0.0431543 0.557469i
\(436\) −2.96084 −0.141798
\(437\) −3.95419 3.95419i −0.189155 0.189155i
\(438\) −7.82817 9.82006i −0.374044 0.469221i
\(439\) 12.5841i 0.600607i −0.953844 0.300304i \(-0.902912\pi\)
0.953844 0.300304i \(-0.0970880\pi\)
\(440\) −7.35994 + 1.41277i −0.350871 + 0.0673513i
\(441\) −53.7886 12.2985i −2.56136 0.585643i
\(442\) 0.573945 0.573945i 0.0272998 0.0272998i
\(443\) −9.22581 + 9.22581i −0.438331 + 0.438331i −0.891450 0.453119i \(-0.850311\pi\)
0.453119 + 0.891450i \(0.350311\pi\)
\(444\) −13.5723 1.53186i −0.644115 0.0726988i
\(445\) 19.0799 28.1448i 0.904472 1.33419i
\(446\) 9.31094i 0.440886i
\(447\) −2.68193 + 2.13793i −0.126851 + 0.101120i
\(448\) 3.56316 + 3.56316i 0.168343 + 0.168343i
\(449\) 8.74214 0.412567 0.206283 0.978492i \(-0.433863\pi\)
0.206283 + 0.978492i \(0.433863\pi\)
\(450\) 12.1126 + 8.84788i 0.570993 + 0.417093i
\(451\) −28.2602 −1.33072
\(452\) 0.894915 + 0.894915i 0.0420933 + 0.0420933i
\(453\) −27.9329 + 22.2670i −1.31240 + 1.04620i
\(454\) 21.3423i 1.00164i
\(455\) −6.78705 + 10.0116i −0.318182 + 0.469352i
\(456\) 1.72112 + 0.194257i 0.0805990 + 0.00909690i
\(457\) 10.4440 10.4440i 0.488549 0.488549i −0.419299 0.907848i \(-0.637724\pi\)
0.907848 + 0.419299i \(0.137724\pi\)
\(458\) −9.33750 + 9.33750i −0.436313 + 0.436313i
\(459\) −1.29980 + 3.70780i −0.0606694 + 0.173065i
\(460\) 12.2801 2.35721i 0.572561 0.109906i
\(461\) 15.6610i 0.729407i 0.931124 + 0.364704i \(0.118830\pi\)
−0.931124 + 0.364704i \(0.881170\pi\)
\(462\) 18.2340 + 22.8737i 0.848324 + 1.06418i
\(463\) −3.40622 3.40622i −0.158301 0.158301i 0.623513 0.781813i \(-0.285705\pi\)
−0.781813 + 0.623513i \(0.785705\pi\)
\(464\) 3.01104 0.139784
\(465\) 2.44658 + 31.6050i 0.113457 + 1.46565i
\(466\) 25.1367 1.16444
\(467\) 26.4385 + 26.4385i 1.22343 + 1.22343i 0.966405 + 0.257025i \(0.0827421\pi\)
0.257025 + 0.966405i \(0.417258\pi\)
\(468\) 1.71229 + 2.72740i 0.0791506 + 0.126074i
\(469\) 37.2738i 1.72114i
\(470\) 20.9623 + 14.2107i 0.966920 + 0.655491i
\(471\) 4.57323 40.5190i 0.210723 1.86702i
\(472\) −3.05748 + 3.05748i −0.140732 + 0.140732i
\(473\) 14.4005 14.4005i 0.662135 0.662135i
\(474\) 0.0498172 0.441383i 0.00228818 0.0202734i
\(475\) −4.64463 + 1.85133i −0.213110 + 0.0849448i
\(476\) 3.81025i 0.174643i
\(477\) −15.8984 25.3236i −0.727936 1.15949i
\(478\) 5.71869 + 5.71869i 0.261567 + 0.261567i
\(479\) 22.6245 1.03374 0.516871 0.856063i \(-0.327097\pi\)
0.516871 + 0.856063i \(0.327097\pi\)
\(480\) −2.51908 + 2.94181i −0.114980 + 0.134275i
\(481\) 8.46495 0.385969
\(482\) −12.3459 12.3459i −0.562341 0.562341i
\(483\) −30.4235 38.1648i −1.38432 1.73656i
\(484\) 0.232932i 0.0105878i
\(485\) 5.80330 + 30.2327i 0.263514 + 1.37280i
\(486\) −13.1912 8.30615i −0.598365 0.376775i
\(487\) 19.6380 19.6380i 0.889884 0.889884i −0.104627 0.994511i \(-0.533365\pi\)
0.994511 + 0.104627i \(0.0333650\pi\)
\(488\) 0.959995 0.959995i 0.0434569 0.0434569i
\(489\) 24.4070 + 2.75473i 1.10372 + 0.124573i
\(490\) 7.75283 + 40.3889i 0.350237 + 1.82458i
\(491\) 7.22196i 0.325922i −0.986632 0.162961i \(-0.947895\pi\)
0.986632 0.162961i \(-0.0521045\pi\)
\(492\) −11.4200 + 9.10362i −0.514856 + 0.410423i
\(493\) −1.60992 1.60992i −0.0725073 0.0725073i
\(494\) −1.07345 −0.0482968
\(495\) −16.4465 + 15.3296i −0.739213 + 0.689014i
\(496\) −8.18480 −0.367508
\(497\) −16.9164 16.9164i −0.758802 0.758802i
\(498\) −9.06457 + 7.22593i −0.406193 + 0.323801i
\(499\) 29.0605i 1.30093i −0.759538 0.650463i \(-0.774575\pi\)
0.759538 0.650463i \(-0.225425\pi\)
\(500\) 2.40119 10.9194i 0.107384 0.488332i
\(501\) 14.9917 + 1.69206i 0.669780 + 0.0755956i
\(502\) 1.55568 1.55568i 0.0694333 0.0694333i
\(503\) 23.3678 23.3678i 1.04192 1.04192i 0.0428359 0.999082i \(-0.486361\pi\)
0.999082 0.0428359i \(-0.0136392\pi\)
\(504\) 14.7369 + 3.36952i 0.656434 + 0.150090i
\(505\) 22.7996 + 15.4562i 1.01457 + 0.687792i
\(506\) 18.7421i 0.833190i
\(507\) 12.7915 + 16.0463i 0.568089 + 0.712640i
\(508\) −6.70476 6.70476i −0.297475 0.297475i
\(509\) 15.9405 0.706550 0.353275 0.935520i \(-0.385068\pi\)
0.353275 + 0.935520i \(0.385068\pi\)
\(510\) 2.91979 0.226024i 0.129290 0.0100085i
\(511\) 36.5363 1.61627
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 4.68286 2.25184i 0.206753 0.0994214i
\(514\) 25.9974i 1.14670i
\(515\) 1.10897 0.212873i 0.0488673 0.00938029i
\(516\) 1.18038 10.4582i 0.0519633 0.460397i
\(517\) −26.8410 + 26.8410i −1.18047 + 1.18047i
\(518\) 28.0982 28.0982i 1.23456 1.23456i
\(519\) −0.465923 + 4.12810i −0.0204517 + 0.181203i
\(520\) 1.34689 1.98680i 0.0590648 0.0871270i
\(521\) 39.2764i 1.72073i 0.509679 + 0.860365i \(0.329764\pi\)
−0.509679 + 0.860365i \(0.670236\pi\)
\(522\) 7.65040 4.80299i 0.334849 0.210221i
\(523\) −7.29624 7.29624i −0.319042 0.319042i 0.529357 0.848399i \(-0.322433\pi\)
−0.848399 + 0.529357i \(0.822433\pi\)
\(524\) 1.53144 0.0669011
\(525\) −42.0944 + 11.5098i −1.83715 + 0.502330i
\(526\) −24.9560 −1.08813
\(527\) 4.37619 + 4.37619i 0.190630 + 0.190630i
\(528\) −3.61853 4.53927i −0.157476 0.197547i
\(529\) 8.27125i 0.359620i
\(530\) −12.5056 + 18.4472i −0.543210 + 0.801294i
\(531\) −2.89133 + 12.6455i −0.125473 + 0.548767i
\(532\) −3.56316 + 3.56316i −0.154483 + 0.154483i
\(533\) 6.40022 6.40022i 0.277224 0.277224i
\(534\) 26.1721 + 2.95395i 1.13258 + 0.127830i
\(535\) −6.70397 + 1.28686i −0.289838 + 0.0556357i
\(536\) 7.39695i 0.319500i
\(537\) 15.5712 12.4128i 0.671948 0.535651i
\(538\) 9.04126 + 9.04126i 0.389796 + 0.389796i
\(539\) −61.6426 −2.65513
\(540\) −1.70787 + 11.4927i −0.0734949 + 0.494569i
\(541\) −18.2326 −0.783881 −0.391940 0.919991i \(-0.628196\pi\)
−0.391940 + 0.919991i \(0.628196\pi\)
\(542\) 5.80738 + 5.80738i 0.249448 + 0.249448i
\(543\) −30.2425 + 24.1081i −1.29783 + 1.03458i
\(544\) 0.756142i 0.0324193i
\(545\) 5.48008 + 3.71504i 0.234741 + 0.159135i
\(546\) −9.30988 1.05077i −0.398426 0.0449689i
\(547\) 15.9706 15.9706i 0.682854 0.682854i −0.277788 0.960642i \(-0.589601\pi\)
0.960642 + 0.277788i \(0.0896013\pi\)
\(548\) 4.76164 4.76164i 0.203407 0.203407i
\(549\) 0.907824 3.97045i 0.0387450 0.169455i
\(550\) 15.3948 + 6.61986i 0.656438 + 0.282272i
\(551\) 3.01104i 0.128275i
\(552\) 6.03752 + 7.57378i 0.256974 + 0.322361i
\(553\) 0.913774 + 0.913774i 0.0388576 + 0.0388576i
\(554\) −6.12299 −0.260141
\(555\) 23.1984 + 19.8648i 0.984716 + 0.843214i
\(556\) −9.84417 −0.417486
\(557\) 12.9276 + 12.9276i 0.547758 + 0.547758i 0.925792 0.378034i \(-0.123400\pi\)
−0.378034 + 0.925792i \(0.623400\pi\)
\(558\) −20.7958 + 13.0558i −0.880356 + 0.552696i
\(559\) 6.52270i 0.275881i
\(560\) −2.12411 11.0657i −0.0897599 0.467610i
\(561\) −0.492296 + 4.36176i −0.0207847 + 0.184154i
\(562\) 7.79389 7.79389i 0.328765 0.328765i
\(563\) −26.9809 + 26.9809i −1.13711 + 1.13711i −0.148145 + 0.988966i \(0.547330\pi\)
−0.988966 + 0.148145i \(0.952670\pi\)
\(564\) −2.20010 + 19.4930i −0.0926410 + 0.820804i
\(565\) −0.533486 2.77923i −0.0224439 0.116923i
\(566\) 17.1605i 0.721309i
\(567\) 42.8181 14.9460i 1.79819 0.627673i
\(568\) 3.35704 + 3.35704i 0.140858 + 0.140858i
\(569\) −30.1015 −1.26192 −0.630961 0.775814i \(-0.717339\pi\)
−0.630961 + 0.775814i \(0.717339\pi\)
\(570\) −2.94181 2.51908i −0.123219 0.105513i
\(571\) −2.85189 −0.119348 −0.0596740 0.998218i \(-0.519006\pi\)
−0.0596740 + 0.998218i \(0.519006\pi\)
\(572\) 2.54398 + 2.54398i 0.106369 + 0.106369i
\(573\) 8.55997 + 10.7381i 0.357598 + 0.448589i
\(574\) 42.4892i 1.77346i
\(575\) −25.6863 11.0452i −1.07119 0.460618i
\(576\) −2.92453 0.668679i −0.121855 0.0278616i
\(577\) −2.60285 + 2.60285i −0.108358 + 0.108358i −0.759207 0.650849i \(-0.774413\pi\)
0.650849 + 0.759207i \(0.274413\pi\)
\(578\) −11.6165 + 11.6165i −0.483184 + 0.483184i
\(579\) −11.4151 1.28838i −0.474396 0.0535433i
\(580\) −5.57300 3.77803i −0.231406 0.156874i
\(581\) 33.7255i 1.39917i
\(582\) −18.6461 + 14.8640i −0.772908 + 0.616132i
\(583\) −23.6205 23.6205i −0.978260 0.978260i
\(584\) −7.25060 −0.300032
\(585\) 0.252943 7.19648i 0.0104579 0.297538i
\(586\) −24.6840 −1.01968
\(587\) 9.92177 + 9.92177i 0.409515 + 0.409515i 0.881569 0.472054i \(-0.156487\pi\)
−0.472054 + 0.881569i \(0.656487\pi\)
\(588\) −24.9100 + 19.8573i −1.02727 + 0.818901i
\(589\) 8.18480i 0.337249i
\(590\) 9.49526 1.82266i 0.390914 0.0750377i
\(591\) 11.4939 + 1.29727i 0.472795 + 0.0533626i
\(592\) −5.57606 + 5.57606i −0.229175 + 0.229175i
\(593\) −0.851881 + 0.851881i −0.0349826 + 0.0349826i −0.724382 0.689399i \(-0.757875\pi\)
0.689399 + 0.724382i \(0.257875\pi\)
\(594\) −16.4346 5.76129i −0.674321 0.236389i
\(595\) −4.78082 + 7.05222i −0.195994 + 0.289113i
\(596\) 1.98019i 0.0811118i
\(597\) 10.8017 + 13.5502i 0.442084 + 0.554573i
\(598\) −4.24463 4.24463i −0.173576 0.173576i
\(599\) −3.99004 −0.163028 −0.0815142 0.996672i \(-0.525976\pi\)
−0.0815142 + 0.996672i \(0.525976\pi\)
\(600\) 8.35361 2.28412i 0.341035 0.0932486i
\(601\) 6.42813 0.262209 0.131104 0.991369i \(-0.458148\pi\)
0.131104 + 0.991369i \(0.458148\pi\)
\(602\) 21.6511 + 21.6511i 0.882435 + 0.882435i
\(603\) −11.7991 18.7940i −0.480496 0.765353i
\(604\) 20.6241i 0.839185i
\(605\) −0.292266 + 0.431124i −0.0118823 + 0.0175277i
\(606\) −2.39293 + 21.2015i −0.0972062 + 0.861252i
\(607\) 18.0117 18.0117i 0.731071 0.731071i −0.239761 0.970832i \(-0.577069\pi\)
0.970832 + 0.239761i \(0.0770690\pi\)
\(608\) 0.707107 0.707107i 0.0286770 0.0286770i
\(609\) −2.94743 + 26.1143i −0.119436 + 1.05821i
\(610\) −2.98134 + 0.572282i −0.120711 + 0.0231710i
\(611\) 12.1576i 0.491845i
\(612\) 1.20614 + 1.92119i 0.0487554 + 0.0776596i
\(613\) −24.1414 24.1414i −0.975063 0.975063i 0.0246339 0.999697i \(-0.492158\pi\)
−0.999697 + 0.0246339i \(0.992158\pi\)
\(614\) 8.27850 0.334093
\(615\) 32.5594 2.52046i 1.31292 0.101635i
\(616\) 16.8887 0.680466
\(617\) −27.8433 27.8433i −1.12093 1.12093i −0.991602 0.129329i \(-0.958718\pi\)
−0.129329 0.991602i \(-0.541282\pi\)
\(618\) 0.545230 + 0.683965i 0.0219324 + 0.0275131i
\(619\) 26.3475i 1.05899i 0.848312 + 0.529497i \(0.177619\pi\)
−0.848312 + 0.529497i \(0.822381\pi\)
\(620\) 15.1489 + 10.2697i 0.608394 + 0.412440i
\(621\) 27.4212 + 9.61271i 1.10037 + 0.385745i
\(622\) −10.0510 + 10.0510i −0.403008 + 0.403008i
\(623\) −54.1828 + 54.1828i −2.17079 + 2.17079i
\(624\) 1.84754 + 0.208525i 0.0739608 + 0.00834768i
\(625\) −18.1452 + 17.1975i −0.725806 + 0.687899i
\(626\) 32.9500i 1.31695i
\(627\) 4.53927 3.61853i 0.181281 0.144510i
\(628\) −16.6468 16.6468i −0.664282 0.664282i
\(629\) 5.96274 0.237750
\(630\) −23.0480 24.7273i −0.918256 0.985158i
\(631\) 34.9462 1.39119 0.695593 0.718436i \(-0.255142\pi\)
0.695593 + 0.718436i \(0.255142\pi\)
\(632\) −0.181338 0.181338i −0.00721324 0.00721324i
\(633\) −0.458636 + 0.365606i −0.0182291 + 0.0145316i
\(634\) 14.1296i 0.561159i
\(635\) 3.99691 + 20.8222i 0.158612 + 0.826302i
\(636\) −17.1541 1.93612i −0.680206 0.0767723i
\(637\) 13.9605 13.9605i 0.553135 0.553135i
\(638\) 7.13590 7.13590i 0.282513 0.282513i
\(639\) 13.8844 + 3.17460i 0.549259 + 0.125585i
\(640\) 0.421528 + 2.19598i 0.0166623 + 0.0868036i
\(641\) 46.8388i 1.85002i 0.379943 + 0.925010i \(0.375944\pi\)
−0.379943 + 0.925010i \(0.624056\pi\)
\(642\) −3.29602 4.13470i −0.130084 0.163184i
\(643\) 22.8114 + 22.8114i 0.899592 + 0.899592i 0.995400 0.0958078i \(-0.0305434\pi\)
−0.0958078 + 0.995400i \(0.530543\pi\)
\(644\) −28.1788 −1.11040
\(645\) −15.3069 + 17.8756i −0.602708 + 0.703850i
\(646\) −0.756142 −0.0297500
\(647\) 10.8816 + 10.8816i 0.427801 + 0.427801i 0.887879 0.460078i \(-0.152179\pi\)
−0.460078 + 0.887879i \(0.652179\pi\)
\(648\) −8.49722 + 2.96602i −0.333802 + 0.116516i
\(649\) 14.4919i 0.568857i
\(650\) −4.98578 + 1.98731i −0.195558 + 0.0779487i
\(651\) 8.01188 70.9856i 0.314010 2.78215i
\(652\) 10.0274 10.0274i 0.392703 0.392703i
\(653\) 0.0974665 0.0974665i 0.00381416 0.00381416i −0.705197 0.709011i \(-0.749142\pi\)
0.709011 + 0.705197i \(0.249142\pi\)
\(654\) −0.575163 + 5.09597i −0.0224906 + 0.199268i
\(655\) −2.83447 1.92153i −0.110752 0.0750804i
\(656\) 8.43195i 0.329212i
\(657\) −18.4222 + 11.5656i −0.718719 + 0.451218i
\(658\) −40.3555 40.3555i −1.57322 1.57322i
\(659\) 4.39566 0.171231 0.0856153 0.996328i \(-0.472714\pi\)
0.0856153 + 0.996328i \(0.472714\pi\)
\(660\) 1.00184 + 12.9418i 0.0389965 + 0.503759i
\(661\) −36.4313 −1.41701 −0.708507 0.705704i \(-0.750631\pi\)
−0.708507 + 0.705704i \(0.750631\pi\)
\(662\) 6.17860 + 6.17860i 0.240138 + 0.240138i
\(663\) −0.876337 1.09932i −0.0340341 0.0426941i
\(664\) 6.69279i 0.259731i
\(665\) 11.0657 2.12411i 0.429109 0.0823693i
\(666\) −5.27303 + 23.0621i −0.204326 + 0.893638i
\(667\) −11.9062 + 11.9062i −0.461011 + 0.461011i
\(668\) 6.15920 6.15920i 0.238307 0.238307i
\(669\) 16.0253 + 1.80871i 0.619573 + 0.0699289i
\(670\) −9.28114 + 13.6907i −0.358562 + 0.528918i
\(671\) 4.55020i 0.175658i
\(672\) 6.82480 5.44047i 0.263273 0.209871i
\(673\) 12.9562 + 12.9562i 0.499425 + 0.499425i 0.911259 0.411834i \(-0.135112\pi\)
−0.411834 + 0.911259i \(0.635112\pi\)
\(674\) −26.5467 −1.02254
\(675\) 17.5812 19.1285i 0.676703 0.736256i
\(676\) 11.8477 0.455681
\(677\) −21.1304 21.1304i −0.812109 0.812109i 0.172841 0.984950i \(-0.444705\pi\)
−0.984950 + 0.172841i \(0.944705\pi\)
\(678\) 1.71410 1.36642i 0.0658297 0.0524769i
\(679\) 69.3744i 2.66235i
\(680\) 0.948750 1.39951i 0.0363829 0.0536687i
\(681\) 36.7327 + 4.14588i 1.40760 + 0.158871i
\(682\) −19.3972 + 19.3972i −0.742758 + 0.742758i
\(683\) −9.66304 + 9.66304i −0.369746 + 0.369746i −0.867385 0.497638i \(-0.834201\pi\)
0.497638 + 0.867385i \(0.334201\pi\)
\(684\) 0.668679 2.92453i 0.0255676 0.111822i
\(685\) −14.7877 + 2.83856i −0.565007 + 0.108456i
\(686\) 57.4062i 2.19178i
\(687\) 14.2571 + 17.8849i 0.543943 + 0.682350i
\(688\) −4.29665 4.29665i −0.163808 0.163808i
\(689\) 10.6989 0.407596
\(690\) −1.67157 21.5934i −0.0636355 0.822046i
\(691\) −5.64130 −0.214605 −0.107303 0.994226i \(-0.534221\pi\)
−0.107303 + 0.994226i \(0.534221\pi\)
\(692\) 1.69599 + 1.69599i 0.0644718 + 0.0644718i
\(693\) 42.9106 26.9397i 1.63004 1.02335i
\(694\) 7.63909i 0.289976i
\(695\) 18.2201 + 12.3517i 0.691129 + 0.468527i
\(696\) 0.584915 5.18237i 0.0221712 0.196437i
\(697\) 4.50834 4.50834i 0.170765 0.170765i
\(698\) 13.5474 13.5474i 0.512778 0.512778i
\(699\) 4.88298 43.2634i 0.184691 1.63637i
\(700\) −9.95297 + 23.1461i −0.376187 + 0.874842i
\(701\) 5.68210i 0.214610i 0.994226 + 0.107305i \(0.0342221\pi\)
−0.994226 + 0.107305i \(0.965778\pi\)
\(702\) 5.02682 2.41724i 0.189725 0.0912330i
\(703\) −5.57606 5.57606i −0.210305 0.210305i
\(704\) −3.35156 −0.126317
\(705\) 28.5304 33.3182i 1.07452 1.25484i
\(706\) 0.518226 0.0195037
\(707\) −43.8924 43.8924i −1.65075 1.65075i
\(708\) 4.66837 + 5.85624i 0.175448 + 0.220091i
\(709\) 29.4977i 1.10781i −0.832580 0.553906i \(-0.813137\pi\)
0.832580 0.553906i \(-0.186863\pi\)
\(710\) −2.00123 10.4256i −0.0751049 0.391264i
\(711\) −0.749997 0.171483i −0.0281271 0.00643112i
\(712\) 10.7526 10.7526i 0.402969 0.402969i
\(713\) 32.3643 32.3643i 1.21205 1.21205i
\(714\) −6.55791 0.740167i −0.245424 0.0277000i
\(715\) −1.51654 7.90053i −0.0567155 0.295463i
\(716\) 11.4970i 0.429662i
\(717\) 10.9535 8.73168i 0.409065 0.326091i
\(718\) 11.6243 + 11.6243i 0.433815 + 0.433815i
\(719\) 38.3623 1.43067 0.715337 0.698780i \(-0.246273\pi\)
0.715337 + 0.698780i \(0.246273\pi\)
\(720\) 4.57387 + 4.90711i 0.170458 + 0.182877i
\(721\) −2.54474 −0.0947712
\(722\) 0.707107 + 0.707107i 0.0263158 + 0.0263158i
\(723\) −23.6471 + 18.8506i −0.879446 + 0.701060i
\(724\) 22.3294i 0.829867i
\(725\) 5.57443 + 13.9852i 0.207029 + 0.519396i
\(726\) −0.400905 0.0452486i −0.0148790 0.00167933i
\(727\) −12.1887 + 12.1887i −0.452054 + 0.452054i −0.896036 0.443982i \(-0.853565\pi\)
0.443982 + 0.896036i \(0.353565\pi\)
\(728\) −3.82488 + 3.82488i −0.141759 + 0.141759i
\(729\) −16.8584 + 21.0902i −0.624385 + 0.781117i
\(730\) 13.4198 + 9.09752i 0.496690 + 0.336714i
\(731\) 4.59461i 0.169938i
\(732\) −1.46578 1.83875i −0.0541769 0.0679623i
\(733\) 21.4518 + 21.4518i 0.792340 + 0.792340i 0.981874 0.189534i \(-0.0606977\pi\)
−0.189534 + 0.981874i \(0.560698\pi\)
\(734\) −18.9116 −0.698039
\(735\) 71.0203 5.49776i 2.61962 0.202788i
\(736\) 5.59207 0.206126
\(737\) −17.5301 17.5301i −0.645730 0.645730i
\(738\) 13.4500 + 21.4237i 0.495102 + 0.788619i
\(739\) 1.62124i 0.0596381i −0.999555 0.0298191i \(-0.990507\pi\)
0.999555 0.0298191i \(-0.00949311\pi\)
\(740\) 17.3169 3.32406i 0.636582 0.122195i
\(741\) −0.208525 + 1.84754i −0.00766036 + 0.0678711i
\(742\) 35.5134 35.5134i 1.30374 1.30374i
\(743\) −4.47847 + 4.47847i −0.164299 + 0.164299i −0.784468 0.620169i \(-0.787064\pi\)
0.620169 + 0.784468i \(0.287064\pi\)
\(744\) −1.58995 + 14.0871i −0.0582905 + 0.516456i
\(745\) 2.48459 3.66505i 0.0910285 0.134277i
\(746\) 3.96766i 0.145266i
\(747\) 10.6759 + 17.0049i 0.390609 + 0.622178i
\(748\) 1.79199 + 1.79199i 0.0655215 + 0.0655215i
\(749\) 15.3835 0.562100
\(750\) −18.3273 6.25392i −0.669217 0.228361i
\(751\) −21.5949 −0.788010 −0.394005 0.919108i \(-0.628911\pi\)
−0.394005 + 0.919108i \(0.628911\pi\)
\(752\) 8.00851 + 8.00851i 0.292040 + 0.292040i
\(753\) −2.37531 2.97971i −0.0865612 0.108587i
\(754\) 3.23220i 0.117710i
\(755\) 25.8776 38.1723i 0.941784 1.38923i
\(756\) 8.66210 24.7095i 0.315038 0.898675i
\(757\) −11.6792 + 11.6792i −0.424488 + 0.424488i −0.886746 0.462258i \(-0.847040\pi\)
0.462258 + 0.886746i \(0.347040\pi\)
\(758\) 24.7867 24.7867i 0.900293 0.900293i
\(759\) 32.2575 + 3.64079i 1.17087 + 0.132152i
\(760\) −2.19598 + 0.421528i −0.0796565 + 0.0152904i
\(761\) 21.6915i 0.786317i 0.919471 + 0.393159i \(0.128618\pi\)
−0.919471 + 0.393159i \(0.871382\pi\)
\(762\) −12.8422 + 10.2373i −0.465222 + 0.370857i
\(763\) −10.5499 10.5499i −0.381933 0.381933i
\(764\) 7.92842 0.286840
\(765\) 0.178174 5.06922i 0.00644188 0.183278i
\(766\) 1.11237 0.0401914
\(767\) −3.28206 3.28206i −0.118508 0.118508i
\(768\) −1.35438 + 1.07966i −0.0488719 + 0.0389588i
\(769\) 24.6155i 0.887659i −0.896111 0.443830i \(-0.853620\pi\)
0.896111 0.443830i \(-0.146380\pi\)
\(770\) −31.2586 21.1907i −1.12648 0.763660i
\(771\) −44.7447 5.05017i −1.61144 0.181878i
\(772\) −4.68979 + 4.68979i −0.168789 + 0.168789i
\(773\) 3.36652 3.36652i 0.121085 0.121085i −0.643968 0.765053i \(-0.722713\pi\)
0.765053 + 0.643968i \(0.222713\pi\)
\(774\) −17.7706 4.06315i −0.638750 0.146047i
\(775\) −15.1528 38.0154i −0.544303 1.36555i
\(776\) 13.7673i 0.494218i
\(777\) −42.9021 53.8187i −1.53911 1.93073i