Properties

Label 400.2.l.g.301.3
Level $400$
Weight $2$
Character 400.301
Analytic conductor $3.194$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
Defining polynomial: \(x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 301.3
Root \(0.618969 - 1.27156i\) of defining polynomial
Character \(\chi\) \(=\) 400.301
Dual form 400.2.l.g.101.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.618969 - 1.27156i) q^{2} +(2.16859 + 2.16859i) q^{3} +(-1.23375 - 1.57412i) q^{4} +(4.09979 - 1.41521i) q^{6} +3.30519i q^{7} +(-2.76525 + 0.594467i) q^{8} +6.40553i q^{9} +O(q^{10})\) \(q+(0.618969 - 1.27156i) q^{2} +(2.16859 + 2.16859i) q^{3} +(-1.23375 - 1.57412i) q^{4} +(4.09979 - 1.41521i) q^{6} +3.30519i q^{7} +(-2.76525 + 0.594467i) q^{8} +6.40553i q^{9} +(2.01163 - 2.01163i) q^{11} +(0.738111 - 6.08911i) q^{12} +(0.794042 + 0.794042i) q^{13} +(4.20276 + 2.04581i) q^{14} +(-0.955702 + 3.88415i) q^{16} +4.61575 q^{17} +(8.14504 + 3.96483i) q^{18} +(-3.48786 - 3.48786i) q^{19} +(-7.16759 + 7.16759i) q^{21} +(-1.31278 - 3.80306i) q^{22} -7.99801i q^{23} +(-7.28583 - 4.70753i) q^{24} +(1.50116 - 0.518188i) q^{26} +(-7.38518 + 7.38518i) q^{27} +(5.20276 - 4.07779i) q^{28} +(-1.95065 - 1.95065i) q^{29} -5.12695 q^{31} +(4.34740 + 3.61941i) q^{32} +8.72480 q^{33} +(2.85701 - 5.86922i) q^{34} +(10.0831 - 7.90285i) q^{36} +(0.448156 - 0.448156i) q^{37} +(-6.59391 + 2.27616i) q^{38} +3.44390i q^{39} +4.02230i q^{41} +(4.67754 + 13.5506i) q^{42} +(4.97000 - 4.97000i) q^{43} +(-5.64841 - 0.684690i) q^{44} +(-10.1700 - 4.95052i) q^{46} -5.49112 q^{47} +(-10.4956 + 6.35059i) q^{48} -3.92429 q^{49} +(10.0096 + 10.0096i) q^{51} +(0.270264 - 2.22957i) q^{52} +(-3.35125 + 3.35125i) q^{53} +(4.81954 + 13.9619i) q^{54} +(-1.96483 - 9.13968i) q^{56} -15.1274i q^{57} +(-3.68777 + 1.27299i) q^{58} +(2.07673 - 2.07673i) q^{59} +(-0.557208 - 0.557208i) q^{61} +(-3.17343 + 6.51925i) q^{62} -21.1715 q^{63} +(7.29322 - 3.28770i) q^{64} +(5.40038 - 11.0941i) q^{66} +(-0.636094 - 0.636094i) q^{67} +(-5.69470 - 7.26573i) q^{68} +(17.3444 - 17.3444i) q^{69} -6.85258i q^{71} +(-3.80787 - 17.7129i) q^{72} -10.5177i q^{73} +(-0.292465 - 0.847255i) q^{74} +(-1.18714 + 9.79346i) q^{76} +(6.64883 + 6.64883i) q^{77} +(4.37914 + 2.13167i) q^{78} -17.3005 q^{79} -12.8142 q^{81} +(5.11461 + 2.48968i) q^{82} +(9.48015 + 9.48015i) q^{83} +(20.1257 + 2.43960i) q^{84} +(-3.24340 - 9.39596i) q^{86} -8.46030i q^{87} +(-4.36682 + 6.75852i) q^{88} +7.62073i q^{89} +(-2.62446 + 2.62446i) q^{91} +(-12.5898 + 9.86757i) q^{92} +(-11.1182 - 11.1182i) q^{93} +(-3.39883 + 6.98231i) q^{94} +(1.57871 + 17.2767i) q^{96} +0.709082 q^{97} +(-2.42901 + 4.98999i) q^{98} +(12.8856 + 12.8856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{2} + 2q^{3} + 2q^{4} + 6q^{6} - 8q^{8} + O(q^{10}) \) \( 12q + 4q^{2} + 2q^{3} + 2q^{4} + 6q^{6} - 8q^{8} - 2q^{11} + 8q^{12} - 4q^{13} + 14q^{14} + 2q^{16} - 8q^{17} + 18q^{18} - 14q^{19} - 20q^{21} + 2q^{22} - 14q^{24} - 16q^{26} - 10q^{27} + 26q^{28} - 4q^{31} - 16q^{32} + 28q^{33} - 6q^{34} + 2q^{36} + 8q^{37} + 10q^{38} + 10q^{42} - 44q^{44} - 10q^{46} + 8q^{47} - 28q^{48} + 4q^{49} + 10q^{51} - 12q^{52} - 16q^{53} + 10q^{54} + 6q^{56} - 60q^{58} + 20q^{59} + 4q^{61} - 18q^{62} - 8q^{63} + 38q^{64} + 32q^{66} + 50q^{67} - 60q^{68} - 14q^{72} + 10q^{74} + 60q^{76} - 8q^{77} + 4q^{78} + 12q^{79} - 8q^{81} + 42q^{82} - 2q^{83} + 34q^{84} + 6q^{86} + 30q^{88} - 2q^{92} - 44q^{93} + 32q^{94} - 34q^{96} + 64q^{98} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618969 1.27156i 0.437677 0.899132i
\(3\) 2.16859 + 2.16859i 1.25203 + 1.25203i 0.954807 + 0.297227i \(0.0960617\pi\)
0.297227 + 0.954807i \(0.403938\pi\)
\(4\) −1.23375 1.57412i −0.616877 0.787060i
\(5\) 0 0
\(6\) 4.09979 1.41521i 1.67373 0.577757i
\(7\) 3.30519i 1.24924i 0.780927 + 0.624622i \(0.214747\pi\)
−0.780927 + 0.624622i \(0.785253\pi\)
\(8\) −2.76525 + 0.594467i −0.977664 + 0.210176i
\(9\) 6.40553i 2.13518i
\(10\) 0 0
\(11\) 2.01163 2.01163i 0.606530 0.606530i −0.335507 0.942038i \(-0.608908\pi\)
0.942038 + 0.335507i \(0.108908\pi\)
\(12\) 0.738111 6.08911i 0.213074 1.75778i
\(13\) 0.794042 + 0.794042i 0.220228 + 0.220228i 0.808594 0.588367i \(-0.200229\pi\)
−0.588367 + 0.808594i \(0.700229\pi\)
\(14\) 4.20276 + 2.04581i 1.12324 + 0.546766i
\(15\) 0 0
\(16\) −0.955702 + 3.88415i −0.238926 + 0.971038i
\(17\) 4.61575 1.11948 0.559741 0.828667i \(-0.310900\pi\)
0.559741 + 0.828667i \(0.310900\pi\)
\(18\) 8.14504 + 3.96483i 1.91981 + 0.934518i
\(19\) −3.48786 3.48786i −0.800169 0.800169i 0.182953 0.983122i \(-0.441434\pi\)
−0.983122 + 0.182953i \(0.941434\pi\)
\(20\) 0 0
\(21\) −7.16759 + 7.16759i −1.56410 + 1.56410i
\(22\) −1.31278 3.80306i −0.279886 0.810815i
\(23\) 7.99801i 1.66770i −0.551991 0.833850i \(-0.686132\pi\)
0.551991 0.833850i \(-0.313868\pi\)
\(24\) −7.28583 4.70753i −1.48721 0.960921i
\(25\) 0 0
\(26\) 1.50116 0.518188i 0.294402 0.101625i
\(27\) −7.38518 + 7.38518i −1.42128 + 1.42128i
\(28\) 5.20276 4.07779i 0.983230 0.770630i
\(29\) −1.95065 1.95065i −0.362227 0.362227i 0.502406 0.864632i \(-0.332448\pi\)
−0.864632 + 0.502406i \(0.832448\pi\)
\(30\) 0 0
\(31\) −5.12695 −0.920828 −0.460414 0.887704i \(-0.652299\pi\)
−0.460414 + 0.887704i \(0.652299\pi\)
\(32\) 4.34740 + 3.61941i 0.768519 + 0.639827i
\(33\) 8.72480 1.51879
\(34\) 2.85701 5.86922i 0.489972 1.00656i
\(35\) 0 0
\(36\) 10.0831 7.90285i 1.68051 1.31714i
\(37\) 0.448156 0.448156i 0.0736764 0.0736764i −0.669308 0.742985i \(-0.733409\pi\)
0.742985 + 0.669308i \(0.233409\pi\)
\(38\) −6.59391 + 2.27616i −1.06967 + 0.369242i
\(39\) 3.44390i 0.551465i
\(40\) 0 0
\(41\) 4.02230i 0.628177i 0.949394 + 0.314089i \(0.101699\pi\)
−0.949394 + 0.314089i \(0.898301\pi\)
\(42\) 4.67754 + 13.5506i 0.721760 + 2.09090i
\(43\) 4.97000 4.97000i 0.757918 0.757918i −0.218025 0.975943i \(-0.569961\pi\)
0.975943 + 0.218025i \(0.0699615\pi\)
\(44\) −5.64841 0.684690i −0.851530 0.103221i
\(45\) 0 0
\(46\) −10.1700 4.95052i −1.49948 0.729915i
\(47\) −5.49112 −0.800962 −0.400481 0.916305i \(-0.631157\pi\)
−0.400481 + 0.916305i \(0.631157\pi\)
\(48\) −10.4956 + 6.35059i −1.51491 + 0.916629i
\(49\) −3.92429 −0.560612
\(50\) 0 0
\(51\) 10.0096 + 10.0096i 1.40163 + 1.40163i
\(52\) 0.270264 2.22957i 0.0374789 0.309186i
\(53\) −3.35125 + 3.35125i −0.460330 + 0.460330i −0.898763 0.438434i \(-0.855533\pi\)
0.438434 + 0.898763i \(0.355533\pi\)
\(54\) 4.81954 + 13.9619i 0.655856 + 1.89998i
\(55\) 0 0
\(56\) −1.96483 9.13968i −0.262561 1.22134i
\(57\) 15.1274i 2.00368i
\(58\) −3.68777 + 1.27299i −0.484228 + 0.167151i
\(59\) 2.07673 2.07673i 0.270367 0.270367i −0.558881 0.829248i \(-0.688769\pi\)
0.829248 + 0.558881i \(0.188769\pi\)
\(60\) 0 0
\(61\) −0.557208 0.557208i −0.0713432 0.0713432i 0.670535 0.741878i \(-0.266065\pi\)
−0.741878 + 0.670535i \(0.766065\pi\)
\(62\) −3.17343 + 6.51925i −0.403026 + 0.827946i
\(63\) −21.1715 −2.66736
\(64\) 7.29322 3.28770i 0.911652 0.410962i
\(65\) 0 0
\(66\) 5.40038 11.0941i 0.664741 1.36560i
\(67\) −0.636094 0.636094i −0.0777112 0.0777112i 0.667183 0.744894i \(-0.267500\pi\)
−0.744894 + 0.667183i \(0.767500\pi\)
\(68\) −5.69470 7.26573i −0.690583 0.881100i
\(69\) 17.3444 17.3444i 2.08802 2.08802i
\(70\) 0 0
\(71\) 6.85258i 0.813252i −0.913595 0.406626i \(-0.866705\pi\)
0.913595 0.406626i \(-0.133295\pi\)
\(72\) −3.80787 17.7129i −0.448762 2.08748i
\(73\) 10.5177i 1.23101i −0.788134 0.615504i \(-0.788953\pi\)
0.788134 0.615504i \(-0.211047\pi\)
\(74\) −0.292465 0.847255i −0.0339983 0.0984913i
\(75\) 0 0
\(76\) −1.18714 + 9.79346i −0.136175 + 1.12339i
\(77\) 6.64883 + 6.64883i 0.757705 + 0.757705i
\(78\) 4.37914 + 2.13167i 0.495840 + 0.241364i
\(79\) −17.3005 −1.94646 −0.973230 0.229833i \(-0.926182\pi\)
−0.973230 + 0.229833i \(0.926182\pi\)
\(80\) 0 0
\(81\) −12.8142 −1.42380
\(82\) 5.11461 + 2.48968i 0.564814 + 0.274939i
\(83\) 9.48015 + 9.48015i 1.04058 + 1.04058i 0.999141 + 0.0414412i \(0.0131949\pi\)
0.0414412 + 0.999141i \(0.486805\pi\)
\(84\) 20.1257 + 2.43960i 2.19589 + 0.266182i
\(85\) 0 0
\(86\) −3.24340 9.39596i −0.349745 1.01319i
\(87\) 8.46030i 0.907040i
\(88\) −4.36682 + 6.75852i −0.465505 + 0.720460i
\(89\) 7.62073i 0.807796i 0.914804 + 0.403898i \(0.132345\pi\)
−0.914804 + 0.403898i \(0.867655\pi\)
\(90\) 0 0
\(91\) −2.62446 + 2.62446i −0.275118 + 0.275118i
\(92\) −12.5898 + 9.86757i −1.31258 + 1.02877i
\(93\) −11.1182 11.1182i −1.15291 1.15291i
\(94\) −3.39883 + 6.98231i −0.350563 + 0.720171i
\(95\) 0 0
\(96\) 1.57871 + 17.2767i 0.161127 + 1.76330i
\(97\) 0.709082 0.0719964 0.0359982 0.999352i \(-0.488539\pi\)
0.0359982 + 0.999352i \(0.488539\pi\)
\(98\) −2.42901 + 4.98999i −0.245367 + 0.504065i
\(99\) 12.8856 + 12.8856i 1.29505 + 1.29505i
\(100\) 0 0
\(101\) 6.16223 6.16223i 0.613164 0.613164i −0.330605 0.943769i \(-0.607253\pi\)
0.943769 + 0.330605i \(0.107253\pi\)
\(102\) 18.9236 6.53225i 1.87371 0.646789i
\(103\) 15.9410i 1.57072i 0.619040 + 0.785359i \(0.287522\pi\)
−0.619040 + 0.785359i \(0.712478\pi\)
\(104\) −2.66776 1.72369i −0.261595 0.169022i
\(105\) 0 0
\(106\) 2.18701 + 6.33565i 0.212421 + 0.615373i
\(107\) −3.38717 + 3.38717i −0.327450 + 0.327450i −0.851616 0.524166i \(-0.824377\pi\)
0.524166 + 0.851616i \(0.324377\pi\)
\(108\) 20.7367 + 2.51366i 1.99539 + 0.241877i
\(109\) −2.43964 2.43964i −0.233675 0.233675i 0.580550 0.814225i \(-0.302838\pi\)
−0.814225 + 0.580550i \(0.802838\pi\)
\(110\) 0 0
\(111\) 1.94373 0.184491
\(112\) −12.8379 3.15878i −1.21306 0.298477i
\(113\) 1.09801 0.103292 0.0516461 0.998665i \(-0.483553\pi\)
0.0516461 + 0.998665i \(0.483553\pi\)
\(114\) −19.2355 9.36341i −1.80157 0.876964i
\(115\) 0 0
\(116\) −0.663933 + 5.47718i −0.0616447 + 0.508543i
\(117\) −5.08626 + 5.08626i −0.470225 + 0.470225i
\(118\) −1.35526 3.92612i −0.124762 0.361429i
\(119\) 15.2559i 1.39851i
\(120\) 0 0
\(121\) 2.90666i 0.264242i
\(122\) −1.05342 + 0.363632i −0.0953723 + 0.0329217i
\(123\) −8.72270 + 8.72270i −0.786499 + 0.786499i
\(124\) 6.32540 + 8.07044i 0.568038 + 0.724747i
\(125\) 0 0
\(126\) −13.1045 + 26.9209i −1.16744 + 2.39831i
\(127\) −1.51159 −0.134131 −0.0670657 0.997749i \(-0.521364\pi\)
−0.0670657 + 0.997749i \(0.521364\pi\)
\(128\) 0.333758 11.3088i 0.0295003 0.999565i
\(129\) 21.5557 1.89788
\(130\) 0 0
\(131\) −9.21660 9.21660i −0.805258 0.805258i 0.178654 0.983912i \(-0.442826\pi\)
−0.983912 + 0.178654i \(0.942826\pi\)
\(132\) −10.7643 13.7339i −0.936908 1.19538i
\(133\) 11.5280 11.5280i 0.999607 0.999607i
\(134\) −1.20256 + 0.415112i −0.103885 + 0.0358602i
\(135\) 0 0
\(136\) −12.7637 + 2.74391i −1.09448 + 0.235288i
\(137\) 3.38639i 0.289318i 0.989482 + 0.144659i \(0.0462086\pi\)
−0.989482 + 0.144659i \(0.953791\pi\)
\(138\) −11.3189 32.7901i −0.963525 2.79128i
\(139\) −2.09626 + 2.09626i −0.177802 + 0.177802i −0.790397 0.612595i \(-0.790126\pi\)
0.612595 + 0.790397i \(0.290126\pi\)
\(140\) 0 0
\(141\) −11.9080 11.9080i −1.00283 1.00283i
\(142\) −8.71350 4.24154i −0.731221 0.355942i
\(143\) 3.19464 0.267149
\(144\) −24.8800 6.12178i −2.07334 0.510148i
\(145\) 0 0
\(146\) −13.3740 6.51016i −1.10684 0.538784i
\(147\) −8.51015 8.51015i −0.701906 0.701906i
\(148\) −1.25837 0.152537i −0.103437 0.0125384i
\(149\) −2.45247 + 2.45247i −0.200915 + 0.200915i −0.800392 0.599477i \(-0.795375\pi\)
0.599477 + 0.800392i \(0.295375\pi\)
\(150\) 0 0
\(151\) 1.11727i 0.0909222i −0.998966 0.0454611i \(-0.985524\pi\)
0.998966 0.0454611i \(-0.0144757\pi\)
\(152\) 11.7182 + 7.57138i 0.950472 + 0.614120i
\(153\) 29.5663i 2.39029i
\(154\) 12.5698 4.33900i 1.01291 0.349646i
\(155\) 0 0
\(156\) 5.42110 4.24892i 0.434036 0.340186i
\(157\) 15.8377 + 15.8377i 1.26398 + 1.26398i 0.949145 + 0.314839i \(0.101950\pi\)
0.314839 + 0.949145i \(0.398050\pi\)
\(158\) −10.7085 + 21.9987i −0.851922 + 1.75012i
\(159\) −14.5349 −1.15270
\(160\) 0 0
\(161\) 26.4349 2.08337
\(162\) −7.93160 + 16.2941i −0.623166 + 1.28019i
\(163\) −7.22102 7.22102i −0.565594 0.565594i 0.365297 0.930891i \(-0.380967\pi\)
−0.930891 + 0.365297i \(0.880967\pi\)
\(164\) 6.33158 4.96253i 0.494413 0.387508i
\(165\) 0 0
\(166\) 17.9226 6.18671i 1.39106 0.480182i
\(167\) 13.2304i 1.02380i 0.859044 + 0.511901i \(0.171059\pi\)
−0.859044 + 0.511901i \(0.828941\pi\)
\(168\) 15.5593 24.0811i 1.20043 1.85790i
\(169\) 11.7390i 0.903000i
\(170\) 0 0
\(171\) 22.3416 22.3416i 1.70850 1.70850i
\(172\) −13.9551 1.69162i −1.06407 0.128984i
\(173\) 11.7503 + 11.7503i 0.893355 + 0.893355i 0.994837 0.101482i \(-0.0323585\pi\)
−0.101482 + 0.994837i \(0.532359\pi\)
\(174\) −10.7578 5.23667i −0.815548 0.396991i
\(175\) 0 0
\(176\) 5.89097 + 9.73601i 0.444048 + 0.733879i
\(177\) 9.00712 0.677017
\(178\) 9.69026 + 4.71700i 0.726315 + 0.353554i
\(179\) 4.84732 + 4.84732i 0.362306 + 0.362306i 0.864661 0.502355i \(-0.167533\pi\)
−0.502355 + 0.864661i \(0.667533\pi\)
\(180\) 0 0
\(181\) 10.5742 10.5742i 0.785976 0.785976i −0.194856 0.980832i \(-0.562424\pi\)
0.980832 + 0.194856i \(0.0624240\pi\)
\(182\) 1.71271 + 4.96163i 0.126955 + 0.367781i
\(183\) 2.41671i 0.178648i
\(184\) 4.75455 + 22.1165i 0.350510 + 1.63045i
\(185\) 0 0
\(186\) −21.0194 + 7.25571i −1.54122 + 0.532015i
\(187\) 9.28519 9.28519i 0.679000 0.679000i
\(188\) 6.77469 + 8.64368i 0.494095 + 0.630405i
\(189\) −24.4094 24.4094i −1.77553 1.77553i
\(190\) 0 0
\(191\) 7.94268 0.574712 0.287356 0.957824i \(-0.407224\pi\)
0.287356 + 0.957824i \(0.407224\pi\)
\(192\) 22.9456 + 8.68632i 1.65596 + 0.626881i
\(193\) −20.8617 −1.50166 −0.750829 0.660496i \(-0.770346\pi\)
−0.750829 + 0.660496i \(0.770346\pi\)
\(194\) 0.438900 0.901644i 0.0315112 0.0647343i
\(195\) 0 0
\(196\) 4.84160 + 6.17730i 0.345829 + 0.441235i
\(197\) 2.07707 2.07707i 0.147985 0.147985i −0.629232 0.777217i \(-0.716631\pi\)
0.777217 + 0.629232i \(0.216631\pi\)
\(198\) 24.3606 8.40907i 1.73123 0.597606i
\(199\) 23.2807i 1.65033i −0.564893 0.825164i \(-0.691083\pi\)
0.564893 0.825164i \(-0.308917\pi\)
\(200\) 0 0
\(201\) 2.75885i 0.194594i
\(202\) −4.02144 11.6499i −0.282948 0.819684i
\(203\) 6.44727 6.44727i 0.452510 0.452510i
\(204\) 3.40693 28.1058i 0.238533 1.96780i
\(205\) 0 0
\(206\) 20.2701 + 9.86702i 1.41228 + 0.687468i
\(207\) 51.2315 3.56083
\(208\) −3.84305 + 2.32531i −0.266467 + 0.161231i
\(209\) −14.0326 −0.970653
\(210\) 0 0
\(211\) −2.51586 2.51586i −0.173199 0.173199i 0.615184 0.788383i \(-0.289082\pi\)
−0.788383 + 0.615184i \(0.789082\pi\)
\(212\) 9.40989 + 1.14065i 0.646274 + 0.0783401i
\(213\) 14.8604 14.8604i 1.01822 1.01822i
\(214\) 2.21045 + 6.40357i 0.151103 + 0.437739i
\(215\) 0 0
\(216\) 16.0316 24.8121i 1.09081 1.68825i
\(217\) 16.9456i 1.15034i
\(218\) −4.61222 + 1.59210i −0.312379 + 0.107830i
\(219\) 22.8086 22.8086i 1.54126 1.54126i
\(220\) 0 0
\(221\) 3.66510 + 3.66510i 0.246541 + 0.246541i
\(222\) 1.20311 2.47158i 0.0807474 0.165882i
\(223\) 10.9088 0.730507 0.365253 0.930908i \(-0.380982\pi\)
0.365253 + 0.930908i \(0.380982\pi\)
\(224\) −11.9628 + 14.3690i −0.799300 + 0.960068i
\(225\) 0 0
\(226\) 0.679635 1.39619i 0.0452086 0.0928733i
\(227\) −11.6347 11.6347i −0.772220 0.772220i 0.206275 0.978494i \(-0.433866\pi\)
−0.978494 + 0.206275i \(0.933866\pi\)
\(228\) −23.8124 + 18.6635i −1.57701 + 1.23602i
\(229\) −1.60760 + 1.60760i −0.106233 + 0.106233i −0.758226 0.651992i \(-0.773933\pi\)
0.651992 + 0.758226i \(0.273933\pi\)
\(230\) 0 0
\(231\) 28.8371i 1.89734i
\(232\) 6.55363 + 4.23444i 0.430267 + 0.278005i
\(233\) 23.8100i 1.55985i 0.625875 + 0.779924i \(0.284742\pi\)
−0.625875 + 0.779924i \(0.715258\pi\)
\(234\) 3.31927 + 9.61575i 0.216987 + 0.628601i
\(235\) 0 0
\(236\) −5.83118 0.706845i −0.379578 0.0460117i
\(237\) −37.5177 37.5177i −2.43703 2.43703i
\(238\) 19.3989 + 9.44295i 1.25744 + 0.612095i
\(239\) −0.199630 −0.0129130 −0.00645649 0.999979i \(-0.502055\pi\)
−0.00645649 + 0.999979i \(0.502055\pi\)
\(240\) 0 0
\(241\) −16.8755 −1.08705 −0.543525 0.839393i \(-0.682911\pi\)
−0.543525 + 0.839393i \(0.682911\pi\)
\(242\) 3.69601 + 1.79914i 0.237589 + 0.115653i
\(243\) −5.63317 5.63317i −0.361368 0.361368i
\(244\) −0.189654 + 1.56457i −0.0121414 + 0.100161i
\(245\) 0 0
\(246\) 5.69239 + 16.4906i 0.362934 + 1.05140i
\(247\) 5.53901i 0.352439i
\(248\) 14.1773 3.04780i 0.900260 0.193536i
\(249\) 41.1171i 2.60569i
\(250\) 0 0
\(251\) −6.10023 + 6.10023i −0.385043 + 0.385043i −0.872915 0.487872i \(-0.837773\pi\)
0.487872 + 0.872915i \(0.337773\pi\)
\(252\) 26.1204 + 33.3265i 1.64543 + 2.09937i
\(253\) −16.0891 16.0891i −1.01151 1.01151i
\(254\) −0.935625 + 1.92208i −0.0587063 + 0.120602i
\(255\) 0 0
\(256\) −14.1733 7.42418i −0.885829 0.464012i
\(257\) −19.8360 −1.23733 −0.618667 0.785653i \(-0.712327\pi\)
−0.618667 + 0.785653i \(0.712327\pi\)
\(258\) 13.3423 27.4095i 0.830658 1.70644i
\(259\) 1.48124 + 1.48124i 0.0920399 + 0.0920399i
\(260\) 0 0
\(261\) 12.4949 12.4949i 0.773418 0.773418i
\(262\) −17.4243 + 6.01471i −1.07648 + 0.371590i
\(263\) 7.14438i 0.440542i 0.975439 + 0.220271i \(0.0706941\pi\)
−0.975439 + 0.220271i \(0.929306\pi\)
\(264\) −24.1263 + 5.18660i −1.48487 + 0.319213i
\(265\) 0 0
\(266\) −7.52314 21.7941i −0.461273 1.33628i
\(267\) −16.5262 + 16.5262i −1.01139 + 1.01139i
\(268\) −0.216504 + 1.78607i −0.0132251 + 0.109102i
\(269\) 21.7716 + 21.7716i 1.32744 + 1.32744i 0.907596 + 0.419844i \(0.137915\pi\)
0.419844 + 0.907596i \(0.362085\pi\)
\(270\) 0 0
\(271\) −4.71328 −0.286312 −0.143156 0.989700i \(-0.545725\pi\)
−0.143156 + 0.989700i \(0.545725\pi\)
\(272\) −4.41128 + 17.9283i −0.267473 + 1.08706i
\(273\) −11.3827 −0.688915
\(274\) 4.30601 + 2.09607i 0.260136 + 0.126628i
\(275\) 0 0
\(276\) −48.7008 5.90342i −2.93144 0.355344i
\(277\) 20.4588 20.4588i 1.22925 1.22925i 0.265006 0.964247i \(-0.414626\pi\)
0.964247 0.265006i \(-0.0853739\pi\)
\(278\) 1.36801 + 3.96304i 0.0820476 + 0.237687i
\(279\) 32.8409i 1.96613i
\(280\) 0 0
\(281\) 17.6481i 1.05280i 0.850239 + 0.526398i \(0.176458\pi\)
−0.850239 + 0.526398i \(0.823542\pi\)
\(282\) −22.5124 + 7.77108i −1.34059 + 0.462761i
\(283\) 18.1525 18.1525i 1.07906 1.07906i 0.0824607 0.996594i \(-0.473722\pi\)
0.996594 0.0824607i \(-0.0262779\pi\)
\(284\) −10.7868 + 8.45440i −0.640077 + 0.501676i
\(285\) 0 0
\(286\) 1.97739 4.06220i 0.116925 0.240203i
\(287\) −13.2945 −0.784747
\(288\) −23.1842 + 27.8474i −1.36614 + 1.64092i
\(289\) 4.30511 0.253242
\(290\) 0 0
\(291\) 1.53771 + 1.53771i 0.0901419 + 0.0901419i
\(292\) −16.5562 + 12.9763i −0.968877 + 0.759380i
\(293\) −0.638480 + 0.638480i −0.0373004 + 0.0373004i −0.725511 0.688211i \(-0.758397\pi\)
0.688211 + 0.725511i \(0.258397\pi\)
\(294\) −16.0887 + 5.55369i −0.938314 + 0.323898i
\(295\) 0 0
\(296\) −0.972850 + 1.50568i −0.0565458 + 0.0875157i
\(297\) 29.7126i 1.72410i
\(298\) 1.60047 + 4.63649i 0.0927130 + 0.268584i
\(299\) 6.35076 6.35076i 0.367274 0.367274i
\(300\) 0 0
\(301\) 16.4268 + 16.4268i 0.946825 + 0.946825i
\(302\) −1.42068 0.691557i −0.0817511 0.0397946i
\(303\) 26.7266 1.53540
\(304\) 16.8807 10.2140i 0.968175 0.585814i
\(305\) 0 0
\(306\) 37.5955 + 18.3006i 2.14919 + 1.04618i
\(307\) 4.52224 + 4.52224i 0.258098 + 0.258098i 0.824280 0.566182i \(-0.191580\pi\)
−0.566182 + 0.824280i \(0.691580\pi\)
\(308\) 2.26303 18.6691i 0.128948 1.06377i
\(309\) −34.5695 + 34.5695i −1.96659 + 1.96659i
\(310\) 0 0
\(311\) 14.1014i 0.799620i −0.916598 0.399810i \(-0.869076\pi\)
0.916598 0.399810i \(-0.130924\pi\)
\(312\) −2.04728 9.52324i −0.115904 0.539147i
\(313\) 11.9204i 0.673779i 0.941544 + 0.336889i \(0.109375\pi\)
−0.941544 + 0.336889i \(0.890625\pi\)
\(314\) 29.9417 10.3356i 1.68971 0.583271i
\(315\) 0 0
\(316\) 21.3446 + 27.2331i 1.20073 + 1.53198i
\(317\) 17.6516 + 17.6516i 0.991410 + 0.991410i 0.999963 0.00855359i \(-0.00272272\pi\)
−0.00855359 + 0.999963i \(0.502723\pi\)
\(318\) −8.99669 + 18.4821i −0.504509 + 1.03643i
\(319\) −7.84798 −0.439403
\(320\) 0 0
\(321\) −14.6907 −0.819958
\(322\) 16.3624 33.6137i 0.911842 1.87322i
\(323\) −16.0991 16.0991i −0.895775 0.895775i
\(324\) 15.8096 + 20.1711i 0.878310 + 1.12062i
\(325\) 0 0
\(326\) −13.6516 + 4.71241i −0.756092 + 0.260996i
\(327\) 10.5811i 0.585138i
\(328\) −2.39112 11.1227i −0.132028 0.614146i
\(329\) 18.1492i 1.00060i
\(330\) 0 0
\(331\) −24.9785 + 24.9785i −1.37294 + 1.37294i −0.516888 + 0.856053i \(0.672910\pi\)
−0.856053 + 0.516888i \(0.827090\pi\)
\(332\) 3.22671 26.6191i 0.177089 1.46091i
\(333\) 2.87068 + 2.87068i 0.157312 + 0.157312i
\(334\) 16.8234 + 8.18924i 0.920534 + 0.448095i
\(335\) 0 0
\(336\) −20.9899 34.6901i −1.14509 1.89250i
\(337\) −24.3167 −1.32462 −0.662308 0.749231i \(-0.730423\pi\)
−0.662308 + 0.749231i \(0.730423\pi\)
\(338\) −14.9269 7.26608i −0.811916 0.395223i
\(339\) 2.38113 + 2.38113i 0.129325 + 0.129325i
\(340\) 0 0
\(341\) −10.3136 + 10.3136i −0.558510 + 0.558510i
\(342\) −14.5800 42.2375i −0.788396 2.28394i
\(343\) 10.1658i 0.548903i
\(344\) −10.7888 + 16.6978i −0.581693 + 0.900285i
\(345\) 0 0
\(346\) 22.2142 7.66816i 1.19425 0.412243i
\(347\) 17.3818 17.3818i 0.933106 0.933106i −0.0647931 0.997899i \(-0.520639\pi\)
0.997899 + 0.0647931i \(0.0206387\pi\)
\(348\) −13.3175 + 10.4379i −0.713894 + 0.559532i
\(349\) −0.773103 0.773103i −0.0413832 0.0413832i 0.686112 0.727496i \(-0.259316\pi\)
−0.727496 + 0.686112i \(0.759316\pi\)
\(350\) 0 0
\(351\) −11.7283 −0.626010
\(352\) 16.0263 1.46445i 0.854204 0.0780556i
\(353\) 13.3720 0.711720 0.355860 0.934539i \(-0.384188\pi\)
0.355860 + 0.934539i \(0.384188\pi\)
\(354\) 5.57513 11.4531i 0.296315 0.608727i
\(355\) 0 0
\(356\) 11.9959 9.40211i 0.635784 0.498311i
\(357\) −33.0838 + 33.0838i −1.75098 + 1.75098i
\(358\) 9.16403 3.16334i 0.484334 0.167188i
\(359\) 28.5413i 1.50635i 0.657818 + 0.753177i \(0.271480\pi\)
−0.657818 + 0.753177i \(0.728520\pi\)
\(360\) 0 0
\(361\) 5.33027i 0.280541i
\(362\) −6.90069 19.9909i −0.362692 1.05070i
\(363\) −6.30335 + 6.30335i −0.330840 + 0.330840i
\(364\) 7.36915 + 0.893275i 0.386249 + 0.0468203i
\(365\) 0 0
\(366\) −3.07300 1.49587i −0.160628 0.0781903i
\(367\) −0.909186 −0.0474591 −0.0237296 0.999718i \(-0.507554\pi\)
−0.0237296 + 0.999718i \(0.507554\pi\)
\(368\) 31.0655 + 7.64371i 1.61940 + 0.398456i
\(369\) −25.7649 −1.34127
\(370\) 0 0
\(371\) −11.0765 11.0765i −0.575064 0.575064i
\(372\) −3.78426 + 31.2186i −0.196205 + 1.61861i
\(373\) −26.5010 + 26.5010i −1.37217 + 1.37217i −0.514946 + 0.857223i \(0.672188\pi\)
−0.857223 + 0.514946i \(0.827812\pi\)
\(374\) −6.05947 17.5540i −0.313328 0.907694i
\(375\) 0 0
\(376\) 15.1843 3.26429i 0.783071 0.168343i
\(377\) 3.09780i 0.159545i
\(378\) −46.1469 + 15.9295i −2.37354 + 0.819324i
\(379\) 1.23724 1.23724i 0.0635529 0.0635529i −0.674616 0.738169i \(-0.735691\pi\)
0.738169 + 0.674616i \(0.235691\pi\)
\(380\) 0 0
\(381\) −3.27800 3.27800i −0.167937 0.167937i
\(382\) 4.91628 10.0996i 0.251539 0.516742i
\(383\) −15.7161 −0.803057 −0.401529 0.915846i \(-0.631521\pi\)
−0.401529 + 0.915846i \(0.631521\pi\)
\(384\) 25.2479 23.8003i 1.28842 1.21455i
\(385\) 0 0
\(386\) −12.9128 + 26.5270i −0.657242 + 1.35019i
\(387\) 31.8355 + 31.8355i 1.61829 + 1.61829i
\(388\) −0.874833 1.11618i −0.0444129 0.0566655i
\(389\) 16.2799 16.2799i 0.825423 0.825423i −0.161457 0.986880i \(-0.551619\pi\)
0.986880 + 0.161457i \(0.0516193\pi\)
\(390\) 0 0
\(391\) 36.9168i 1.86696i
\(392\) 10.8516 2.33286i 0.548090 0.117827i
\(393\) 39.9740i 2.01642i
\(394\) −1.35549 3.92677i −0.0682885 0.197828i
\(395\) 0 0
\(396\) 4.38580 36.1811i 0.220395 1.81817i
\(397\) 22.8944 + 22.8944i 1.14903 + 1.14903i 0.986743 + 0.162292i \(0.0518887\pi\)
0.162292 + 0.986743i \(0.448111\pi\)
\(398\) −29.6030 14.4101i −1.48386 0.722311i
\(399\) 49.9990 2.50308
\(400\) 0 0
\(401\) 15.8553 0.791778 0.395889 0.918298i \(-0.370437\pi\)
0.395889 + 0.918298i \(0.370437\pi\)
\(402\) −3.50805 1.70764i −0.174966 0.0851694i
\(403\) −4.07102 4.07102i −0.202792 0.202792i
\(404\) −17.3027 2.09741i −0.860844 0.104350i
\(405\) 0 0
\(406\) −4.20746 12.1888i −0.208813 0.604919i
\(407\) 1.80305i 0.0893740i
\(408\) −33.6296 21.7288i −1.66491 1.07573i
\(409\) 10.0220i 0.495557i 0.968817 + 0.247779i \(0.0797006\pi\)
−0.968817 + 0.247779i \(0.920299\pi\)
\(410\) 0 0
\(411\) −7.34367 + 7.34367i −0.362236 + 0.362236i
\(412\) 25.0931 19.6673i 1.23625 0.968940i
\(413\) 6.86398 + 6.86398i 0.337754 + 0.337754i
\(414\) 31.7107 65.1441i 1.55850 3.20166i
\(415\) 0 0
\(416\) 0.578056 + 6.32598i 0.0283415 + 0.310157i
\(417\) −9.09182 −0.445228
\(418\) −8.68573 + 17.8433i −0.424833 + 0.872745i
\(419\) 14.4998 + 14.4998i 0.708362 + 0.708362i 0.966191 0.257829i \(-0.0830071\pi\)
−0.257829 + 0.966191i \(0.583007\pi\)
\(420\) 0 0
\(421\) 12.9983 12.9983i 0.633498 0.633498i −0.315446 0.948944i \(-0.602154\pi\)
0.948944 + 0.315446i \(0.102154\pi\)
\(422\) −4.75632 + 1.64184i −0.231534 + 0.0799235i
\(423\) 35.1735i 1.71020i
\(424\) 7.27484 11.2593i 0.353297 0.546798i
\(425\) 0 0
\(426\) −9.69783 28.0941i −0.469862 1.36116i
\(427\) 1.84168 1.84168i 0.0891251 0.0891251i
\(428\) 9.51075 + 1.15288i 0.459720 + 0.0557263i
\(429\) 6.92786 + 6.92786i 0.334480 + 0.334480i
\(430\) 0 0
\(431\) −34.4404 −1.65894 −0.829469 0.558553i \(-0.811357\pi\)
−0.829469 + 0.558553i \(0.811357\pi\)
\(432\) −21.6271 35.7432i −1.04054 1.71970i
\(433\) −14.5895 −0.701128 −0.350564 0.936539i \(-0.614010\pi\)
−0.350564 + 0.936539i \(0.614010\pi\)
\(434\) −21.5474 10.4888i −1.03431 0.503478i
\(435\) 0 0
\(436\) −0.830368 + 6.85019i −0.0397674 + 0.328065i
\(437\) −27.8959 + 27.8959i −1.33444 + 1.33444i
\(438\) −14.8848 43.1205i −0.711223 2.06038i
\(439\) 5.70179i 0.272131i −0.990700 0.136066i \(-0.956554\pi\)
0.990700 0.136066i \(-0.0434458\pi\)
\(440\) 0 0
\(441\) 25.1371i 1.19701i
\(442\) 6.92899 2.39183i 0.329578 0.113768i
\(443\) 5.03375 5.03375i 0.239161 0.239161i −0.577342 0.816503i \(-0.695910\pi\)
0.816503 + 0.577342i \(0.195910\pi\)
\(444\) −2.39808 3.05966i −0.113808 0.145205i
\(445\) 0 0
\(446\) 6.75221 13.8712i 0.319726 0.656822i
\(447\) −10.6368 −0.503104
\(448\) 10.8665 + 24.1055i 0.513392 + 1.13888i
\(449\) 22.2502 1.05005 0.525025 0.851087i \(-0.324056\pi\)
0.525025 + 0.851087i \(0.324056\pi\)
\(450\) 0 0
\(451\) 8.09139 + 8.09139i 0.381009 + 0.381009i
\(452\) −1.35468 1.72840i −0.0637186 0.0812971i
\(453\) 2.42290 2.42290i 0.113838 0.113838i
\(454\) −21.9957 + 7.59273i −1.03231 + 0.356344i
\(455\) 0 0
\(456\) 8.99275 + 41.8311i 0.421124 + 1.95892i
\(457\) 8.92927i 0.417694i 0.977948 + 0.208847i \(0.0669710\pi\)
−0.977948 + 0.208847i \(0.933029\pi\)
\(458\) 1.04912 + 3.03923i 0.0490219 + 0.142014i
\(459\) −34.0881 + 34.0881i −1.59110 + 1.59110i
\(460\) 0 0
\(461\) −8.14776 8.14776i −0.379479 0.379479i 0.491435 0.870914i \(-0.336472\pi\)
−0.870914 + 0.491435i \(0.836472\pi\)
\(462\) 36.6683 + 17.8493i 1.70596 + 0.830424i
\(463\) −31.7058 −1.47349 −0.736747 0.676168i \(-0.763639\pi\)
−0.736747 + 0.676168i \(0.763639\pi\)
\(464\) 9.44086 5.71238i 0.438281 0.265191i
\(465\) 0 0
\(466\) 30.2760 + 14.7377i 1.40251 + 0.682710i
\(467\) −17.7683 17.7683i −0.822219 0.822219i 0.164207 0.986426i \(-0.447494\pi\)
−0.986426 + 0.164207i \(0.947494\pi\)
\(468\) 14.2816 + 1.73119i 0.660166 + 0.0800241i
\(469\) 2.10241 2.10241i 0.0970803 0.0970803i
\(470\) 0 0
\(471\) 68.6907i 3.16510i
\(472\) −4.50812 + 6.97721i −0.207503 + 0.321152i
\(473\) 19.9956i 0.919401i
\(474\) −70.9284 + 24.4839i −3.25785 + 1.12458i
\(475\) 0 0
\(476\) 24.0146 18.8221i 1.10071 0.862707i
\(477\) −21.4665 21.4665i −0.982885 0.982885i
\(478\) −0.123565 + 0.253842i −0.00565172 + 0.0116105i
\(479\) −7.80806 −0.356759 −0.178380 0.983962i \(-0.557086\pi\)
−0.178380 + 0.983962i \(0.557086\pi\)
\(480\) 0 0
\(481\) 0.711710 0.0324512
\(482\) −10.4454 + 21.4584i −0.475777 + 0.977401i
\(483\) 57.3264 + 57.3264i 2.60844 + 2.60844i
\(484\) 4.57544 3.58611i 0.207974 0.163005i
\(485\) 0 0
\(486\) −10.6497 + 3.67618i −0.483081 + 0.166755i
\(487\) 27.6753i 1.25409i 0.778984 + 0.627044i \(0.215735\pi\)
−0.778984 + 0.627044i \(0.784265\pi\)
\(488\) 1.87206 + 1.20958i 0.0847443 + 0.0547551i
\(489\) 31.3188i 1.41629i
\(490\) 0 0
\(491\) −11.7995 + 11.7995i −0.532505 + 0.532505i −0.921317 0.388812i \(-0.872886\pi\)
0.388812 + 0.921317i \(0.372886\pi\)
\(492\) 24.4922 + 2.96890i 1.10419 + 0.133848i
\(493\) −9.00370 9.00370i −0.405506 0.405506i
\(494\) −7.04321 3.42848i −0.316889 0.154254i
\(495\) 0 0
\(496\) 4.89984 19.9139i 0.220009 0.894159i
\(497\) 22.6491 1.01595
\(498\) 52.2830 + 25.4502i 2.34286 + 1.14045i
\(499\) −25.0477 25.0477i −1.12129 1.12129i −0.991548 0.129743i \(-0.958585\pi\)
−0.129743 0.991548i \(-0.541415\pi\)
\(500\) 0 0
\(501\) −28.6914 + 28.6914i −1.28184 + 1.28184i
\(502\) 3.98098 + 11.5327i 0.177680 + 0.514729i
\(503\) 22.8644i 1.01947i −0.860331 0.509736i \(-0.829743\pi\)
0.860331 0.509736i \(-0.170257\pi\)
\(504\) 58.5445 12.5857i 2.60778 0.560614i
\(505\) 0 0
\(506\) −30.4169 + 10.4996i −1.35220 + 0.466766i
\(507\) 25.4570 25.4570i 1.13059 1.13059i
\(508\) 1.86492 + 2.37942i 0.0827426 + 0.105569i
\(509\) −17.1633 17.1633i −0.760748 0.760748i 0.215710 0.976458i \(-0.430794\pi\)
−0.976458 + 0.215710i \(0.930794\pi\)
\(510\) 0 0
\(511\) 34.7631 1.53783
\(512\) −18.2131 + 13.4269i −0.804915 + 0.593390i
\(513\) 51.5169 2.27453
\(514\) −12.2779 + 25.2227i −0.541553 + 1.11253i
\(515\) 0 0
\(516\) −26.5945 33.9313i −1.17076 1.49374i
\(517\) −11.0461 + 11.0461i −0.485808 + 0.485808i
\(518\) 2.80034 0.966652i 0.123040 0.0424722i
\(519\) 50.9629i 2.23702i
\(520\) 0 0
\(521\) 11.5206i 0.504726i −0.967633 0.252363i \(-0.918792\pi\)
0.967633 0.252363i \(-0.0812077\pi\)
\(522\) −8.15414 23.6221i −0.356897 1.03391i
\(523\) −25.4249 + 25.4249i −1.11175 + 1.11175i −0.118841 + 0.992913i \(0.537918\pi\)
−0.992913 + 0.118841i \(0.962082\pi\)
\(524\) −3.13701 + 25.8790i −0.137041 + 1.13053i
\(525\) 0 0
\(526\) 9.08455 + 4.42215i 0.396105 + 0.192815i
\(527\) −23.6647 −1.03085
\(528\) −8.33831 + 33.8884i −0.362878 + 1.47481i
\(529\) −40.9681 −1.78122
\(530\) 0 0
\(531\) 13.3025 + 13.3025i 0.577281 + 0.577281i
\(532\) −32.3692 3.92374i −1.40338 0.170116i
\(533\) −3.19387 + 3.19387i −0.138342 + 0.138342i
\(534\) 10.7849 + 31.2434i 0.466710 + 1.35203i
\(535\) 0 0
\(536\) 2.13709 + 1.38082i 0.0923084 + 0.0596424i
\(537\) 21.0237i 0.907239i
\(538\) 41.1600 14.2081i 1.77454 0.612554i
\(539\) −7.89423 + 7.89423i −0.340028 + 0.340028i
\(540\) 0 0
\(541\) −29.7997 29.7997i −1.28119 1.28119i −0.939992 0.341196i \(-0.889168\pi\)
−0.341196 0.939992i \(-0.610832\pi\)
\(542\) −2.91738 + 5.99325i −0.125312 + 0.257432i
\(543\) 45.8622 1.96814
\(544\) 20.0665 + 16.7063i 0.860344 + 0.716275i
\(545\) 0 0
\(546\) −7.04556 + 14.4739i −0.301522 + 0.619425i
\(547\) 28.3699 + 28.3699i 1.21301 + 1.21301i 0.970032 + 0.242979i \(0.0781246\pi\)
0.242979 + 0.970032i \(0.421875\pi\)
\(548\) 5.33057 4.17797i 0.227711 0.178474i
\(549\) 3.56921 3.56921i 0.152330 0.152330i
\(550\) 0 0
\(551\) 13.6072i 0.579685i
\(552\) −37.6509 + 58.2722i −1.60253 + 2.48023i
\(553\) 57.1815i 2.43161i
\(554\) −13.3513 38.6781i −0.567244 1.64328i
\(555\) 0 0
\(556\) 5.88602 + 0.713492i 0.249623 + 0.0302588i
\(557\) −21.7769 21.7769i −0.922718 0.922718i 0.0745028 0.997221i \(-0.476263\pi\)
−0.997221 + 0.0745028i \(0.976263\pi\)
\(558\) −41.7593 20.3275i −1.76781 0.860531i
\(559\) 7.89278 0.333829
\(560\) 0 0
\(561\) 40.2715 1.70026
\(562\) 22.4407 + 10.9236i 0.946602 + 0.460785i
\(563\) −10.9022 10.9022i −0.459473 0.459473i 0.439010 0.898482i \(-0.355329\pi\)
−0.898482 + 0.439010i \(0.855329\pi\)
\(564\) −4.05306 + 33.4361i −0.170664 + 1.40791i
\(565\) 0 0
\(566\) −11.8462 34.3179i −0.497935 1.44249i
\(567\) 42.3534i 1.77868i
\(568\) 4.07363 + 18.9491i 0.170926 + 0.795087i
\(569\) 31.1881i 1.30747i −0.756723 0.653736i \(-0.773201\pi\)
0.756723 0.653736i \(-0.226799\pi\)
\(570\) 0 0
\(571\) −2.20354 + 2.20354i −0.0922153 + 0.0922153i −0.751710 0.659494i \(-0.770770\pi\)
0.659494 + 0.751710i \(0.270770\pi\)
\(572\) −3.94140 5.02875i −0.164798 0.210263i
\(573\) 17.2244 + 17.2244i 0.719559 + 0.719559i
\(574\) −8.22886 + 16.9048i −0.343466 + 0.705591i
\(575\) 0 0
\(576\) 21.0594 + 46.7169i 0.877477 + 1.94654i
\(577\) −8.42524 −0.350747 −0.175374 0.984502i \(-0.556113\pi\)
−0.175374 + 0.984502i \(0.556113\pi\)
\(578\) 2.66473 5.47423i 0.110838 0.227698i
\(579\) −45.2404 45.2404i −1.88013 1.88013i
\(580\) 0 0
\(581\) −31.3337 + 31.3337i −1.29994 + 1.29994i
\(582\) 2.90709 1.00350i 0.120503 0.0415964i
\(583\) 13.4830i 0.558408i
\(584\) 6.25244 + 29.0842i 0.258728 + 1.20351i
\(585\) 0 0
\(586\) 0.416669 + 1.20707i 0.0172125 + 0.0498636i
\(587\) 19.3370 19.3370i 0.798125 0.798125i −0.184675 0.982800i \(-0.559123\pi\)
0.982800 + 0.184675i \(0.0591231\pi\)
\(588\) −2.89656 + 23.8954i −0.119452 + 0.985431i
\(589\) 17.8821 + 17.8821i 0.736818 + 0.736818i
\(590\) 0 0
\(591\) 9.00862 0.370565
\(592\) 1.31240 + 2.16901i 0.0539394 + 0.0891458i
\(593\) −18.1804 −0.746580 −0.373290 0.927715i \(-0.621770\pi\)
−0.373290 + 0.927715i \(0.621770\pi\)
\(594\) 37.7814 + 18.3912i 1.55019 + 0.754598i
\(595\) 0 0
\(596\) 6.88624 + 0.834737i 0.282071 + 0.0341922i
\(597\) 50.4863 50.4863i 2.06627 2.06627i
\(598\) −4.14447 12.0063i −0.169480 0.490975i
\(599\) 1.64695i 0.0672927i 0.999434 + 0.0336463i \(0.0107120\pi\)
−0.999434 + 0.0336463i \(0.989288\pi\)
\(600\) 0 0
\(601\) 12.7485i 0.520021i −0.965606 0.260011i \(-0.916274\pi\)
0.965606 0.260011i \(-0.0837261\pi\)
\(602\) 31.0554 10.7201i 1.26572 0.436917i
\(603\) 4.07452 4.07452i 0.165927 0.165927i
\(604\) −1.75872 + 1.37844i −0.0715612 + 0.0560878i
\(605\) 0 0
\(606\) 16.5430 33.9846i 0.672012 1.38053i
\(607\) −15.6773 −0.636322 −0.318161 0.948037i \(-0.603065\pi\)
−0.318161 + 0.948037i \(0.603065\pi\)
\(608\) −2.53913 27.7871i −0.102975 1.12691i
\(609\) 27.9629 1.13311
\(610\) 0 0
\(611\) −4.36018 4.36018i −0.176394 0.176394i
\(612\) 46.5409 36.4775i 1.88130 1.47452i
\(613\) −8.29399 + 8.29399i −0.334991 + 0.334991i −0.854478 0.519487i \(-0.826123\pi\)
0.519487 + 0.854478i \(0.326123\pi\)
\(614\) 8.54945 2.95119i 0.345028 0.119100i
\(615\) 0 0
\(616\) −22.3382 14.4332i −0.900031 0.581529i
\(617\) 20.3330i 0.818575i −0.912406 0.409287i \(-0.865777\pi\)
0.912406 0.409287i \(-0.134223\pi\)
\(618\) 22.5599 + 65.3549i 0.907493 + 2.62896i
\(619\) 12.5878 12.5878i 0.505946 0.505946i −0.407333 0.913280i \(-0.633541\pi\)
0.913280 + 0.407333i \(0.133541\pi\)
\(620\) 0 0
\(621\) 59.0667 + 59.0667i 2.37027 + 2.37027i
\(622\) −17.9309 8.72836i −0.718964 0.349975i
\(623\) −25.1880 −1.00914
\(624\) −13.3766 3.29134i −0.535493 0.131759i
\(625\) 0 0
\(626\) 15.1575 + 7.37834i 0.605816 + 0.294898i
\(627\) −30.4308 30.4308i −1.21529 1.21529i
\(628\) 5.39059 44.4702i 0.215108 1.77455i
\(629\) 2.06858 2.06858i 0.0824795 0.0824795i
\(630\) 0 0
\(631\) 21.4887i 0.855453i −0.903908 0.427726i \(-0.859315\pi\)
0.903908 0.427726i \(-0.140685\pi\)
\(632\) 47.8403 10.2846i 1.90298 0.409099i
\(633\) 10.9117i 0.433702i
\(634\) 33.3709 11.5193i 1.32533 0.457491i
\(635\) 0 0
\(636\) 17.9325 + 22.8797i 0.711072 + 0.907241i
\(637\) −3.11605 3.11605i −0.123462 0.123462i
\(638\) −4.85766 + 9.97922i −0.192317 + 0.395081i
\(639\) 43.8944 1.73644
\(640\) 0 0
\(641\) 26.1687 1.03360 0.516800 0.856106i \(-0.327123\pi\)
0.516800 + 0.856106i \(0.327123\pi\)
\(642\) −9.09312 + 18.6802i −0.358877 + 0.737250i
\(643\) 14.6501 + 14.6501i 0.577743 + 0.577743i 0.934281 0.356538i \(-0.116043\pi\)
−0.356538 + 0.934281i \(0.616043\pi\)
\(644\) −32.6142 41.6118i −1.28518 1.63973i
\(645\) 0 0
\(646\) −30.4358 + 10.5062i −1.19748 + 0.413360i
\(647\) 16.2623i 0.639337i −0.947530 0.319668i \(-0.896429\pi\)
0.947530 0.319668i \(-0.103571\pi\)
\(648\) 35.4345 7.61762i 1.39200 0.299248i
\(649\) 8.35522i 0.327971i
\(650\) 0 0
\(651\) 36.7479 36.7479i 1.44026 1.44026i
\(652\) −2.45778 + 20.2757i −0.0962543 + 0.794058i
\(653\) 32.0639 + 32.0639i 1.25476 + 1.25476i 0.953563 + 0.301194i \(0.0973851\pi\)
0.301194 + 0.953563i \(0.402615\pi\)
\(654\) −13.4546 6.54939i −0.526116 0.256101i
\(655\) 0 0
\(656\) −15.6232 3.84412i −0.609984 0.150088i
\(657\) 67.3717 2.62842
\(658\) −23.0779 11.2338i −0.899669 0.437939i
\(659\) −7.04696 7.04696i −0.274511 0.274511i 0.556402 0.830913i \(-0.312181\pi\)
−0.830913 + 0.556402i \(0.812181\pi\)
\(660\) 0 0
\(661\) 5.78655 5.78655i 0.225071 0.225071i −0.585559 0.810630i \(-0.699125\pi\)
0.810630 + 0.585559i \(0.199125\pi\)
\(662\) 16.3008 + 47.2226i 0.633550 + 1.83536i
\(663\) 15.8962i 0.617355i
\(664\) −31.8506 20.5794i −1.23604 0.798634i
\(665\) 0 0
\(666\) 5.42711 1.87339i 0.210296 0.0725924i
\(667\) −15.6013 + 15.6013i −0.604085 + 0.604085i
\(668\) 20.8263 16.3231i 0.805794 0.631560i
\(669\) 23.6567 + 23.6567i 0.914619 + 0.914619i
\(670\) 0 0
\(671\) −2.24180 −0.0865436
\(672\) −57.1028 + 5.21795i −2.20279 + 0.201287i
\(673\) 35.3380 1.36218 0.681090 0.732200i \(-0.261506\pi\)
0.681090 + 0.732200i \(0.261506\pi\)
\(674\) −15.0513 + 30.9203i −0.579755 + 1.19101i
\(675\) 0 0
\(676\) −18.4786 + 14.4830i −0.710714 + 0.557040i
\(677\) 7.72259 7.72259i 0.296803 0.296803i −0.542957 0.839760i \(-0.682695\pi\)
0.839760 + 0.542957i \(0.182695\pi\)
\(678\) 4.50161 1.55391i 0.172883 0.0596777i
\(679\) 2.34365i 0.0899411i
\(680\) 0 0
\(681\) 50.4615i 1.93369i
\(682\) 6.73058 + 19.4981i 0.257727 + 0.746622i
\(683\) −15.6011 + 15.6011i −0.596958 + 0.596958i −0.939502 0.342544i \(-0.888711\pi\)
0.342544 + 0.939502i \(0.388711\pi\)
\(684\) −62.7323 7.60429i −2.39863 0.290757i
\(685\) 0 0
\(686\) 12.9265 + 6.29233i 0.493536 + 0.240242i
\(687\) −6.97246 −0.266016
\(688\) 14.5544 + 24.0541i 0.554881 + 0.917053i
\(689\) −5.32207 −0.202755
\(690\) 0 0
\(691\) 30.0975 + 30.0975i 1.14496 + 1.14496i 0.987530 + 0.157433i \(0.0503218\pi\)
0.157433 + 0.987530i \(0.449678\pi\)
\(692\) 3.99938 32.9932i 0.152033 1.25421i
\(693\) −42.5893 + 42.5893i −1.61783 + 1.61783i
\(694\) −11.3433 32.8609i −0.430586 1.24738i
\(695\) 0 0
\(696\) 5.02937 + 23.3949i 0.190638 + 0.886780i
\(697\) 18.5659i 0.703234i
\(698\) −1.46158 + 0.504523i −0.0553215 + 0.0190965i
\(699\) −51.6341 + 51.6341i −1.95298 + 1.95298i
\(700\) 0 0
\(701\) 14.8151 + 14.8151i 0.559559 + 0.559559i 0.929182 0.369623i \(-0.120513\pi\)
−0.369623 + 0.929182i \(0.620513\pi\)
\(702\) −7.25945 + 14.9133i −0.273990 + 0.562865i
\(703\) −3.12621 −0.117907
\(704\) 8.05764 21.2849i 0.303684 0.802206i
\(705\) 0 0
\(706\) 8.27686 17.0034i 0.311504 0.639930i
\(707\) 20.3673 + 20.3673i 0.765992 + 0.765992i
\(708\) −11.1126 14.1783i −0.417636 0.532852i
\(709\) 9.26566 9.26566i 0.347979 0.347979i −0.511377 0.859356i \(-0.670864\pi\)
0.859356 + 0.511377i \(0.170864\pi\)
\(710\) 0 0
\(711\) 110.819i 4.15604i
\(712\) −4.53027 21.0732i −0.169779 0.789753i
\(713\) 41.0054i 1.53567i
\(714\) 21.5903 + 62.5460i 0.807998 + 2.34073i
\(715\) 0 0
\(716\) 1.64986 13.6107i 0.0616582 0.508655i
\(717\) −0.432914 0.432914i −0.0161675 0.0161675i
\(718\) 36.2922 + 17.6662i 1.35441 + 0.659297i
\(719\) 40.8143 1.52212 0.761058 0.648684i \(-0.224680\pi\)
0.761058 + 0.648684i \(0.224680\pi\)
\(720\) 0 0
\(721\) −52.6882 −1.96221
\(722\) 6.77778 + 3.29927i 0.252243 + 0.122786i
\(723\) −36.5961 36.5961i −1.36102 1.36102i
\(724\) −29.6911 3.59910i −1.10346 0.133759i
\(725\) 0 0
\(726\) 4.11354 + 11.9167i 0.152668 + 0.442270i
\(727\) 5.20944i 0.193208i −0.995323 0.0966038i \(-0.969202\pi\)
0.995323 0.0966038i \(-0.0307980\pi\)
\(728\) 5.69714 8.81744i 0.211150 0.326796i
\(729\) 14.0106i 0.518911i
\(730\) 0 0
\(731\) 22.9403 22.9403i 0.848476 0.848476i
\(732\) −3.80419 + 2.98162i −0.140607 + 0.110204i
\(733\) −14.7039 14.7039i −0.543099 0.543099i 0.381337 0.924436i \(-0.375464\pi\)
−0.924436 + 0.381337i \(0.875464\pi\)
\(734\) −0.562758 + 1.15609i −0.0207718 + 0.0426720i
\(735\) 0 0
\(736\) 28.9481 34.7705i 1.06704 1.28166i
\(737\) −2.55917 −0.0942684
\(738\) −15.9477 + 32.7618i −0.587043 + 1.20598i
\(739\) 7.68017 + 7.68017i 0.282520 + 0.282520i 0.834113 0.551594i \(-0.185980\pi\)
−0.551594 + 0.834113i \(0.685980\pi\)
\(740\) 0 0
\(741\) 12.0118 12.0118i 0.441265 0.441265i
\(742\) −20.9405 + 7.22849i −0.768752 + 0.265366i
\(743\) 34.9882i 1.28359i −0.766876 0.641796i \(-0.778190\pi\)
0.766876 0.641796i \(-0.221810\pi\)
\(744\) 37.3541 + 24.1353i 1.36947 + 0.884843i
\(745\) 0 0
\(746\) 17.2944 + 50.1010i 0.633194 + 1.83433i
\(747\) −60.7254 + 60.7254i −2.22183 + 2.22183i
\(748\) −26.0716 3.16035i −0.953273 0.115554i
\(749\) −11.1953 11.1953i −0.409066 0.409066i
\(750\) 0 0
\(751\) −33.1447 −1.20947 −0.604733 0.796428i \(-0.706720\pi\)
−0.604733 + 0.796428i \(0.706720\pi\)
\(752\) 5.24788 21.3283i 0.191370 0.777765i
\(753\) −26.4577 −0.964174
\(754\) −3.93905 1.91744i −0.143452 0.0698291i
\(755\) 0 0
\(756\) −8.30812 + 68.5386i −0.302163 + 2.49272i
\(757\) 22.1553 22.1553i 0.805248 0.805248i −0.178663 0.983910i \(-0.557177\pi\)
0.983910 + 0.178663i \(0.0571771\pi\)
\(758\) −0.807419 2.33905i −0.0293268 0.0849581i
\(759\) 69.7810i 2.53289i
\(760\) 0 0
\(761\) 48.1426i 1.74517i 0.488466 + 0.872583i \(0.337557\pi\)
−0.488466 + 0.872583i \(0.662443\pi\)
\(762\) −6.19717 + 2.13921i −0.224500 + 0.0774954i
\(763\) 8.06347 8.06347i 0.291917 0.291917i
\(764\) −9.79932 12.5027i −0.354527 0.452333i
\(765\) 0 0
\(766\) −9.72781 + 19.9841i −0.351480 + 0.722055i
\(767\) 3.29802 0.119084
\(768\) −14.6360 46.8359i −0.528130 1.69005i
\(769\) −41.1054 −1.48230 −0.741150 0.671339i \(-0.765719\pi\)
−0.741150 + 0.671339i \(0.765719\pi\)
\(770\) 0 0
\(771\) −43.0160 43.0160i −1.54918 1.54918i
\(772\) 25.7382 + 32.8388i 0.926339 + 1.18189i
\(773\) 10.8044 10.8044i 0.388607 0.388607i −0.485583 0.874190i \(-0.661393\pi\)
0.874190 + 0.485583i \(0.161393\pi\)
\(774\) 60.1861 20.7757i 2.16334 0.746767i
\(775\) 0 0
\(776\) −1.96079 + 0.421526i −0.0703883 + 0.0151319i
\(777\) 6.42440i 0.230474i
\(778\) −10.6242 30.7777i −0.380895 1.10343i
\(779\) 14.0292 14.0292i 0.502648 0.502648i
\(780\) 0 0
\(781\) −13.7849 13.7849i −0.493262 0.493262i
\(782\) −46.9421 22.8504i −1.67865 0.817127i
\(783\) 28.8118 1.02965