Properties

Label 400.2.l.f.101.4
Level $400$
Weight $2$
Character 400.101
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 101.4
Root \(0.618969 + 1.27156i\) of defining polynomial
Character \(\chi\) \(=\) 400.101
Dual form 400.2.l.f.301.4

$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

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

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 −0.297227 + 0.954807i \(0.596062\pi\)
−0.954807 + 0.297227i \(0.903938\pi\)
\(4\) −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 0.942038 0.335507i \(-0.108908\pi\)
−0.335507 + 0.942038i \(0.608908\pi\)
\(12\) −0.738111 6.08911i −0.213074 1.75778i
\(13\) −0.794042 + 0.794042i −0.220228 + 0.220228i −0.808594 0.588367i \(-0.799771\pi\)
0.588367 + 0.808594i \(0.299771\pi\)
\(14\) 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 \(-0.689100\pi\)
−0.559741 + 0.828667i \(0.689100\pi\)
\(18\) −8.14504 + 3.96483i −1.91981 + 0.934518i
\(19\) −3.48786 + 3.48786i −0.800169 + 0.800169i −0.983122 0.182953i \(-0.941434\pi\)
0.182953 + 0.983122i \(0.441434\pi\)
\(20\) 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 −0.864632 0.502406i \(-0.832448\pi\)
0.502406 + 0.864632i \(0.332448\pi\)
\(30\) 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 \(-0.266591\pi\)
−0.742985 + 0.669308i \(0.766591\pi\)
\(38\) 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 \(-0.898301\pi\)
0.949394 0.314089i \(-0.101699\pi\)
\(42\) −4.67754 + 13.5506i −0.721760 + 2.09090i
\(43\) −4.97000 4.97000i −0.757918 0.757918i 0.218025 0.975943i \(-0.430039\pi\)
−0.975943 + 0.218025i \(0.930039\pi\)
\(44\) −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 \(-0.368843\pi\)
0.400481 + 0.916305i \(0.368843\pi\)
\(48\) 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 \(-0.144467\pi\)
−0.438434 + 0.898763i \(0.644467\pi\)
\(54\) 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 0.829248 0.558881i \(-0.188769\pi\)
−0.558881 + 0.829248i \(0.688769\pi\)
\(60\) 0 0
\(61\) −0.557208 + 0.557208i −0.0713432 + 0.0713432i −0.741878 0.670535i \(-0.766065\pi\)
0.670535 + 0.741878i \(0.266065\pi\)
\(62\) 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 \(-0.732500\pi\)
0.744894 + 0.667183i \(0.232500\pi\)
\(68\) 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 \(0.133295\pi\)
−0.913595 + 0.406626i \(0.866705\pi\)
\(72\) 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 −0.0414412 + 0.999141i \(0.513195\pi\)
−0.999141 + 0.0414412i \(0.986805\pi\)
\(84\) 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 \(-0.867655\pi\)
0.914804 0.403898i \(-0.132345\pi\)
\(90\) 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 \(-0.511461\pi\)
−0.0359982 + 0.999352i \(0.511461\pi\)
\(98\) 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 0.943769 0.330605i \(-0.107253\pi\)
−0.330605 + 0.943769i \(0.607253\pi\)
\(102\) −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 \(-0.175623\pi\)
−0.524166 + 0.851616i \(0.675623\pi\)
\(108\) −20.7367 + 2.51366i −1.99539 + 0.241877i
\(109\) −2.43964 + 2.43964i −0.233675 + 0.233675i −0.814225 0.580550i \(-0.802838\pi\)
0.580550 + 0.814225i \(0.302838\pi\)
\(110\) 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 \(-0.516447\pi\)
−0.0516461 + 0.998665i \(0.516447\pi\)
\(114\) −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 \(-0.478636\pi\)
0.0670657 + 0.997749i \(0.478636\pi\)
\(128\) −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 −0.983912 0.178654i \(-0.942826\pi\)
0.178654 + 0.983912i \(0.442826\pi\)
\(132\) 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 0.612595 0.790397i \(-0.290126\pi\)
−0.790397 + 0.612595i \(0.790126\pi\)
\(140\) 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 0.599477 0.800392i \(-0.295375\pi\)
−0.800392 + 0.599477i \(0.795375\pi\)
\(150\) 0 0
\(151\) 1.11727i 0.0909222i 0.998966 + 0.0454611i \(0.0144757\pi\)
−0.998966 + 0.0454611i \(0.985524\pi\)
\(152\) −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 −0.314839 + 0.949145i \(0.601950\pi\)
−0.949145 + 0.314839i \(0.898050\pi\)
\(158\) 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 \(-0.619033\pi\)
0.930891 + 0.365297i \(0.119033\pi\)
\(164\) 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 \(-0.967641\pi\)
0.101482 + 0.994837i \(0.467641\pi\)
\(174\) −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 −0.502355 0.864661i \(-0.667533\pi\)
0.864661 + 0.502355i \(0.167533\pi\)
\(180\) 0 0
\(181\) 10.5742 + 10.5742i 0.785976 + 0.785976i 0.980832 0.194856i \(-0.0624240\pi\)
−0.194856 + 0.980832i \(0.562424\pi\)
\(182\) −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 \(-0.229654\pi\)
0.750829 + 0.660496i \(0.229654\pi\)
\(194\) 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 \(-0.283369\pi\)
−0.777217 + 0.629232i \(0.783369\pi\)
\(198\) −24.3606 8.40907i −1.73123 0.597606i
\(199\) 23.2807i 1.65033i 0.564893 + 0.825164i \(0.308917\pi\)
−0.564893 + 0.825164i \(0.691083\pi\)
\(200\) 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 −0.788383 0.615184i \(-0.789082\pi\)
0.615184 + 0.788383i \(0.289082\pi\)
\(212\) −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 \(-0.619018\pi\)
−0.365253 + 0.930908i \(0.619018\pi\)
\(224\) −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 \(-0.566134\pi\)
0.978494 + 0.206275i \(0.0661340\pi\)
\(228\) 23.8124 + 18.6635i 1.57701 + 1.23602i
\(229\) −1.60760 1.60760i −0.106233 0.106233i 0.651992 0.758226i \(-0.273933\pi\)
−0.758226 + 0.651992i \(0.773933\pi\)
\(230\) 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 0.487872 0.872915i \(-0.337773\pi\)
−0.872915 + 0.487872i \(0.837773\pi\)
\(252\) −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 \(-0.287673\pi\)
0.618667 + 0.785653i \(0.287673\pi\)
\(258\) −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 0.419844 0.907596i \(-0.362085\pi\)
0.907596 0.419844i \(-0.137915\pi\)
\(270\) 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 −0.964247 0.265006i \(-0.914626\pi\)
−0.265006 0.964247i \(-0.585374\pi\)
\(278\) −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 \(-0.823542\pi\)
0.850239 0.526398i \(-0.176458\pi\)
\(282\) 22.5124 + 7.77108i 1.34059 + 0.462761i
\(283\) −18.1525 18.1525i −1.07906 1.07906i −0.996594 0.0824607i \(-0.973722\pi\)
−0.0824607 0.996594i \(-0.526278\pi\)
\(284\) −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 \(-0.241603\pi\)
−0.688211 + 0.725511i \(0.741603\pi\)
\(294\) −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 \(-0.808420\pi\)
0.566182 + 0.824280i \(0.308420\pi\)
\(308\) −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 \(0.130924\pi\)
−0.916598 + 0.399810i \(0.869076\pi\)
\(312\) 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 \(-0.997277\pi\)
0.00855359 + 0.999963i \(0.497277\pi\)
\(318\) 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 −0.856053 0.516888i \(-0.827090\pi\)
−0.516888 0.856053i \(-0.672910\pi\)
\(332\) −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 \(-0.269577\pi\)
0.662308 + 0.749231i \(0.269577\pi\)
\(338\) 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 \(-0.479361\pi\)
−0.997899 + 0.0647931i \(0.979361\pi\)
\(348\) 13.3175 + 10.4379i 0.713894 + 0.559532i
\(349\) −0.773103 + 0.773103i −0.0413832 + 0.0413832i −0.727496 0.686112i \(-0.759316\pi\)
0.686112 + 0.727496i \(0.259316\pi\)
\(350\) 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 \(-0.615812\pi\)
−0.355860 + 0.934539i \(0.615812\pi\)
\(354\) 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 \(-0.728520\pi\)
0.657818 0.753177i \(-0.271480\pi\)
\(360\) 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 \(-0.492446\pi\)
0.0237296 + 0.999718i \(0.492446\pi\)
\(368\) −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 0.857223 + 0.514946i \(0.172188\pi\)
0.514946 + 0.857223i \(0.327812\pi\)
\(374\) −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 0.738169 0.674616i \(-0.235691\pi\)
−0.674616 + 0.738169i \(0.735691\pi\)
\(380\) 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 \(-0.368479\pi\)
0.401529 + 0.915846i \(0.368479\pi\)
\(384\) 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 0.986880 0.161457i \(-0.0516193\pi\)
−0.161457 + 0.986880i \(0.551619\pi\)
\(390\) 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 −0.162292 + 0.986743i \(0.551889\pi\)
−0.986743 + 0.162292i \(0.948111\pi\)
\(398\) 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 \(-0.920299\pi\)
0.968817 0.247779i \(-0.0797006\pi\)
\(410\) 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 −0.257829 0.966191i \(-0.583007\pi\)
0.966191 + 0.257829i \(0.0830071\pi\)
\(420\) 0 0
\(421\) 12.9983 + 12.9983i 0.633498 + 0.633498i 0.948944 0.315446i \(-0.102154\pi\)
−0.315446 + 0.948944i \(0.602154\pi\)
\(422\) 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 \(-0.385990\pi\)
0.350564 + 0.936539i \(0.385990\pi\)
\(434\) −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 \(0.0434458\pi\)
−0.990700 + 0.136066i \(0.956554\pi\)
\(440\) 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 \(-0.304090\pi\)
−0.816503 + 0.577342i \(0.804090\pi\)
\(444\) −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 −0.870914 0.491435i \(-0.836472\pi\)
0.491435 + 0.870914i \(0.336472\pi\)
\(462\) −36.6683 + 17.8493i −1.70596 + 0.830424i
\(463\) 31.7058 1.47349 0.736747 0.676168i \(-0.236361\pi\)
0.736747 + 0.676168i \(0.236361\pi\)
\(464\) 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 \(-0.552506\pi\)
0.986426 + 0.164207i \(0.0525065\pi\)
\(468\) −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 0.388812 0.921317i \(-0.372886\pi\)
−0.921317 + 0.388812i \(0.872886\pi\)
\(492\) −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 −0.129743 + 0.991548i \(0.541415\pi\)
−0.991548 + 0.129743i \(0.958585\pi\)
\(500\) 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 −0.976458 0.215710i \(-0.930794\pi\)
0.215710 + 0.976458i \(0.430794\pi\)
\(510\) 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 \(0.0812077\pi\)
−0.967633 + 0.252363i \(0.918792\pi\)
\(522\) 8.15414 23.6221i 0.356897 1.03391i
\(523\) 25.4249 + 25.4249i 1.11175 + 1.11175i 0.992913 + 0.118841i \(0.0379180\pi\)
0.118841 + 0.992913i \(0.462082\pi\)
\(524\) −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 −0.341196 + 0.939992i \(0.610832\pi\)
−0.939992 + 0.341196i \(0.889168\pi\)
\(542\) 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 −0.242979 + 0.970032i \(0.578125\pi\)
−0.970032 + 0.242979i \(0.921875\pi\)
\(548\) −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 \(-0.523737\pi\)
0.997221 + 0.0745028i \(0.0237370\pi\)
\(558\) 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 \(-0.644671\pi\)
0.898482 + 0.439010i \(0.144671\pi\)
\(564\) −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 \(0.226799\pi\)
−0.756723 + 0.653736i \(0.773201\pi\)
\(570\) 0 0
\(571\) −2.20354 2.20354i −0.0922153 0.0922153i 0.659494 0.751710i \(-0.270770\pi\)
−0.751710 + 0.659494i \(0.770770\pi\)
\(572\) 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 \(-0.443887\pi\)
0.175374 + 0.984502i \(0.443887\pi\)
\(578\) −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 \(-0.440877\pi\)
−0.982800 + 0.184675i \(0.940877\pi\)
\(588\) 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 \(-0.378230\pi\)
0.373290 + 0.927715i \(0.378230\pi\)
\(594\) 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 \(-0.989288\pi\)
0.999434 0.0336463i \(-0.0107120\pi\)
\(600\) 0 0
\(601\) 12.7485i 0.520021i 0.965606 + 0.260011i \(0.0837261\pi\)
−0.965606 + 0.260011i \(0.916274\pi\)
\(602\) −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 \(-0.396935\pi\)
0.318161 + 0.948037i \(0.396935\pi\)
\(608\) 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 \(-0.173877\pi\)
−0.519487 + 0.854478i \(0.673877\pi\)
\(614\) 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 0.913280 0.407333i \(-0.133541\pi\)
−0.407333 + 0.913280i \(0.633541\pi\)
\(620\) 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 \(0.140685\pi\)
−0.903908 + 0.427726i \(0.859315\pi\)
\(632\) −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 \(-0.883957\pi\)
0.356538 + 0.934281i \(0.383957\pi\)
\(644\) −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 −0.301194 + 0.953563i \(0.597385\pi\)
−0.953563 + 0.301194i \(0.902615\pi\)
\(654\) −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 −0.830913 0.556402i \(-0.812181\pi\)
0.556402 + 0.830913i \(0.312181\pi\)
\(660\) 0 0
\(661\) 5.78655 + 5.78655i 0.225071 + 0.225071i 0.810630 0.585559i \(-0.199125\pi\)
−0.585559 + 0.810630i \(0.699125\pi\)
\(662\) −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 \(-0.738494\pi\)
−0.681090 + 0.732200i \(0.738494\pi\)
\(674\) −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 \(-0.317305\pi\)
−0.839760 + 0.542957i \(0.817305\pi\)
\(678\) −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 \(-0.111289\pi\)
−0.342544 + 0.939502i \(0.611289\pi\)
\(684\) −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 0.157433 0.987530i \(-0.449678\pi\)
0.987530 0.157433i \(-0.0503218\pi\)
\(692\) −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 −0.369623 0.929182i \(-0.620513\pi\)
0.929182 + 0.369623i \(0.120513\pi\)
\(702\) 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 0.859356 0.511377i \(-0.170864\pi\)
−0.511377 + 0.859356i \(0.670864\pi\)
\(710\) 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 \(-0.624536\pi\)
0.924436 + 0.381337i \(0.124536\pi\)
\(734\) −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 −0.551594 0.834113i \(-0.685980\pi\)
0.834113 + 0.551594i \(0.185980\pi\)
\(740\) 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 \(-0.442823\pi\)
−0.983910 + 0.178663i \(0.942823\pi\)
\(758\) 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 \(-0.662443\pi\)
0.488466 0.872583i \(-0.337557\pi\)
\(762\) 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 \(-0.338607\pi\)
−0.874190 + 0.485583i \(0.838607\pi\)
\(774\) 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