Properties

Label 585.2.bu.c.361.3
Level $585$
Weight $2$
Character 585.361
Analytic conductor $4.671$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bu (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.3
Root \(-1.27597 - 0.609843i\) of defining polynomial
Character \(\chi\) \(=\) 585.361
Dual form 585.2.bu.c.316.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.190254 - 0.109843i) q^{2} +(-0.975869 + 1.69025i) q^{4} +1.00000i q^{5} +(-0.287734 - 0.166123i) q^{7} +0.868145i q^{8} +O(q^{10})\) \(q+(0.190254 - 0.109843i) q^{2} +(-0.975869 + 1.69025i) q^{4} +1.00000i q^{5} +(-0.287734 - 0.166123i) q^{7} +0.868145i q^{8} +(0.109843 + 0.190254i) q^{10} +(-4.65213 + 2.68591i) q^{11} +(-3.55193 - 0.619491i) q^{13} -0.0729902 q^{14} +(-1.85638 - 3.21534i) q^{16} +(2.53215 - 4.38581i) q^{17} +(-1.96410 - 1.13397i) q^{19} +(-1.69025 - 0.975869i) q^{20} +(-0.590059 + 1.02201i) q^{22} +(1.41959 + 2.45880i) q^{23} -1.00000 q^{25} +(-0.743818 + 0.272296i) q^{26} +(0.561581 - 0.324229i) q^{28} +(-1.45174 - 2.51448i) q^{29} +5.46410i q^{31} +(-2.21004 - 1.27597i) q^{32} -1.11256i q^{34} +(0.166123 - 0.287734i) q^{35} +(-5.17191 + 2.98601i) q^{37} -0.498239 q^{38} -0.868145 q^{40} +(-3.23205 + 1.86603i) q^{41} +(-2.53215 + 4.38581i) q^{43} -10.4844i q^{44} +(0.540166 + 0.311865i) q^{46} +8.34285i q^{47} +(-3.44481 - 5.96658i) q^{49} +(-0.190254 + 0.109843i) q^{50} +(4.51332 - 5.39913i) q^{52} +1.56063 q^{53} +(-2.68591 - 4.65213i) q^{55} +(0.144219 - 0.249795i) q^{56} +(-0.552399 - 0.318928i) q^{58} +(-2.34461 - 1.35366i) q^{59} +(-7.05193 + 12.2143i) q^{61} +(0.600196 + 1.03957i) q^{62} +6.86488 q^{64} +(0.619491 - 3.55193i) q^{65} +(8.94799 - 5.16612i) q^{67} +(4.94209 + 8.55995i) q^{68} -0.0729902i q^{70} +(11.0828 + 6.39866i) q^{71} +9.68922i q^{73} +(-0.655986 + 1.13620i) q^{74} +(3.83341 - 2.21322i) q^{76} +1.78477 q^{77} +4.51851 q^{79} +(3.21534 - 1.85638i) q^{80} +(-0.409941 + 0.710039i) q^{82} +4.26371i q^{83} +(4.38581 + 2.53215i) q^{85} +1.11256i q^{86} +(-2.33176 - 4.03872i) q^{88} +(2.79366 - 1.61292i) q^{89} +(0.919100 + 0.768307i) q^{91} -5.54133 q^{92} +(0.916407 + 1.58726i) q^{94} +(1.13397 - 1.96410i) q^{95} +(2.17191 + 1.25396i) q^{97} +(-1.31078 - 0.756779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{4} - 6q^{7} + O(q^{10}) \) \( 8q + 2q^{4} - 6q^{7} - 2q^{10} - 4q^{14} - 2q^{16} + 2q^{17} + 12q^{19} - 12q^{20} - 12q^{22} + 10q^{23} - 8q^{25} - 10q^{26} - 18q^{28} + 8q^{29} - 6q^{32} - 10q^{35} + 6q^{37} + 16q^{38} - 12q^{40} - 12q^{41} - 2q^{43} - 42q^{46} + 12q^{49} - 6q^{52} + 24q^{53} - 12q^{56} + 36q^{58} + 12q^{59} - 28q^{61} - 4q^{62} - 8q^{64} + 8q^{65} + 6q^{67} + 14q^{68} - 10q^{74} + 54q^{76} + 36q^{77} - 16q^{79} + 4q^{82} + 18q^{85} - 18q^{88} - 24q^{89} + 28q^{91} - 44q^{92} + 32q^{94} + 16q^{95} - 30q^{97} - 72q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.190254 0.109843i 0.134530 0.0776710i −0.431224 0.902245i \(-0.641918\pi\)
0.565755 + 0.824574i \(0.308585\pi\)
\(3\) 0 0
\(4\) −0.975869 + 1.69025i −0.487934 + 0.845127i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −0.287734 0.166123i −0.108753 0.0627887i 0.444637 0.895711i \(-0.353333\pi\)
−0.553390 + 0.832922i \(0.686666\pi\)
\(8\) 0.868145i 0.306936i
\(9\) 0 0
\(10\) 0.109843 + 0.190254i 0.0347355 + 0.0601637i
\(11\) −4.65213 + 2.68591i −1.40267 + 0.809832i −0.994666 0.103149i \(-0.967108\pi\)
−0.408004 + 0.912980i \(0.633775\pi\)
\(12\) 0 0
\(13\) −3.55193 0.619491i −0.985129 0.171816i
\(14\) −0.0729902 −0.0195074
\(15\) 0 0
\(16\) −1.85638 3.21534i −0.464094 0.803835i
\(17\) 2.53215 4.38581i 0.614136 1.06372i −0.376399 0.926458i \(-0.622838\pi\)
0.990535 0.137258i \(-0.0438288\pi\)
\(18\) 0 0
\(19\) −1.96410 1.13397i −0.450596 0.260152i 0.257486 0.966282i \(-0.417106\pi\)
−0.708082 + 0.706130i \(0.750439\pi\)
\(20\) −1.69025 0.975869i −0.377952 0.218211i
\(21\) 0 0
\(22\) −0.590059 + 1.02201i −0.125801 + 0.217894i
\(23\) 1.41959 + 2.45880i 0.296005 + 0.512695i 0.975218 0.221246i \(-0.0710122\pi\)
−0.679213 + 0.733941i \(0.737679\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −0.743818 + 0.272296i −0.145875 + 0.0534016i
\(27\) 0 0
\(28\) 0.561581 0.324229i 0.106129 0.0612735i
\(29\) −1.45174 2.51448i −0.269581 0.466928i 0.699173 0.714953i \(-0.253552\pi\)
−0.968754 + 0.248025i \(0.920219\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i 0.871334 + 0.490691i \(0.163256\pi\)
−0.871334 + 0.490691i \(0.836744\pi\)
\(32\) −2.21004 1.27597i −0.390683 0.225561i
\(33\) 0 0
\(34\) 1.11256i 0.190802i
\(35\) 0.166123 0.287734i 0.0280800 0.0486359i
\(36\) 0 0
\(37\) −5.17191 + 2.98601i −0.850257 + 0.490896i −0.860738 0.509049i \(-0.829997\pi\)
0.0104803 + 0.999945i \(0.496664\pi\)
\(38\) −0.498239 −0.0808250
\(39\) 0 0
\(40\) −0.868145 −0.137266
\(41\) −3.23205 + 1.86603i −0.504762 + 0.291424i −0.730678 0.682723i \(-0.760796\pi\)
0.225916 + 0.974147i \(0.427462\pi\)
\(42\) 0 0
\(43\) −2.53215 + 4.38581i −0.386149 + 0.668830i −0.991928 0.126803i \(-0.959528\pi\)
0.605779 + 0.795633i \(0.292862\pi\)
\(44\) 10.4844i 1.58058i
\(45\) 0 0
\(46\) 0.540166 + 0.311865i 0.0796432 + 0.0459820i
\(47\) 8.34285i 1.21693i 0.793581 + 0.608465i \(0.208214\pi\)
−0.793581 + 0.608465i \(0.791786\pi\)
\(48\) 0 0
\(49\) −3.44481 5.96658i −0.492115 0.852368i
\(50\) −0.190254 + 0.109843i −0.0269060 + 0.0155342i
\(51\) 0 0
\(52\) 4.51332 5.39913i 0.625885 0.748724i
\(53\) 1.56063 0.214369 0.107184 0.994239i \(-0.465817\pi\)
0.107184 + 0.994239i \(0.465817\pi\)
\(54\) 0 0
\(55\) −2.68591 4.65213i −0.362168 0.627293i
\(56\) 0.144219 0.249795i 0.0192721 0.0333802i
\(57\) 0 0
\(58\) −0.552399 0.318928i −0.0725335 0.0418773i
\(59\) −2.34461 1.35366i −0.305242 0.176232i 0.339553 0.940587i \(-0.389724\pi\)
−0.644795 + 0.764355i \(0.723057\pi\)
\(60\) 0 0
\(61\) −7.05193 + 12.2143i −0.902908 + 1.56388i −0.0792059 + 0.996858i \(0.525238\pi\)
−0.823702 + 0.567023i \(0.808095\pi\)
\(62\) 0.600196 + 1.03957i 0.0762249 + 0.132025i
\(63\) 0 0
\(64\) 6.86488 0.858111
\(65\) 0.619491 3.55193i 0.0768384 0.440563i
\(66\) 0 0
\(67\) 8.94799 5.16612i 1.09317 0.631142i 0.158752 0.987319i \(-0.449253\pi\)
0.934419 + 0.356176i \(0.115920\pi\)
\(68\) 4.94209 + 8.55995i 0.599316 + 1.03805i
\(69\) 0 0
\(70\) 0.0729902i 0.00872400i
\(71\) 11.0828 + 6.39866i 1.31529 + 0.759382i 0.982967 0.183785i \(-0.0588349\pi\)
0.332321 + 0.943166i \(0.392168\pi\)
\(72\) 0 0
\(73\) 9.68922i 1.13404i 0.823705 + 0.567019i \(0.191903\pi\)
−0.823705 + 0.567019i \(0.808097\pi\)
\(74\) −0.655986 + 1.13620i −0.0762569 + 0.132081i
\(75\) 0 0
\(76\) 3.83341 2.21322i 0.439722 0.253874i
\(77\) 1.78477 0.203393
\(78\) 0 0
\(79\) 4.51851 0.508372 0.254186 0.967155i \(-0.418192\pi\)
0.254186 + 0.967155i \(0.418192\pi\)
\(80\) 3.21534 1.85638i 0.359486 0.207549i
\(81\) 0 0
\(82\) −0.409941 + 0.710039i −0.0452704 + 0.0784107i
\(83\) 4.26371i 0.468003i 0.972236 + 0.234001i \(0.0751821\pi\)
−0.972236 + 0.234001i \(0.924818\pi\)
\(84\) 0 0
\(85\) 4.38581 + 2.53215i 0.475708 + 0.274650i
\(86\) 1.11256i 0.119970i
\(87\) 0 0
\(88\) −2.33176 4.03872i −0.248566 0.430529i
\(89\) 2.79366 1.61292i 0.296127 0.170969i −0.344575 0.938759i \(-0.611977\pi\)
0.640702 + 0.767790i \(0.278644\pi\)
\(90\) 0 0
\(91\) 0.919100 + 0.768307i 0.0963478 + 0.0805405i
\(92\) −5.54133 −0.577724
\(93\) 0 0
\(94\) 0.916407 + 1.58726i 0.0945202 + 0.163714i
\(95\) 1.13397 1.96410i 0.116343 0.201513i
\(96\) 0 0
\(97\) 2.17191 + 1.25396i 0.220524 + 0.127320i 0.606193 0.795318i \(-0.292696\pi\)
−0.385669 + 0.922637i \(0.626029\pi\)
\(98\) −1.31078 0.756779i −0.132409 0.0764462i
\(99\) 0 0
\(100\) 0.975869 1.69025i 0.0975869 0.169025i
\(101\) −6.22336 10.7792i −0.619247 1.07257i −0.989623 0.143686i \(-0.954105\pi\)
0.370376 0.928882i \(-0.379229\pi\)
\(102\) 0 0
\(103\) 15.0247 1.48043 0.740215 0.672370i \(-0.234724\pi\)
0.740215 + 0.672370i \(0.234724\pi\)
\(104\) 0.537808 3.08359i 0.0527364 0.302371i
\(105\) 0 0
\(106\) 0.296916 0.171425i 0.0288390 0.0166502i
\(107\) −6.53215 11.3140i −0.631487 1.09377i −0.987248 0.159190i \(-0.949112\pi\)
0.355761 0.934577i \(-0.384222\pi\)
\(108\) 0 0
\(109\) 11.2325i 1.07587i −0.842985 0.537937i \(-0.819204\pi\)
0.842985 0.537937i \(-0.180796\pi\)
\(110\) −1.02201 0.590059i −0.0974450 0.0562599i
\(111\) 0 0
\(112\) 1.23355i 0.116560i
\(113\) −9.17191 + 15.8862i −0.862821 + 1.49445i 0.00637349 + 0.999980i \(0.497971\pi\)
−0.869195 + 0.494470i \(0.835362\pi\)
\(114\) 0 0
\(115\) −2.45880 + 1.41959i −0.229284 + 0.132377i
\(116\) 5.66682 0.526151
\(117\) 0 0
\(118\) −0.594763 −0.0547524
\(119\) −1.45717 + 0.841298i −0.133579 + 0.0771216i
\(120\) 0 0
\(121\) 8.92820 15.4641i 0.811655 1.40583i
\(122\) 3.09843i 0.280519i
\(123\) 0 0
\(124\) −9.23572 5.33225i −0.829392 0.478850i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 1.61998 + 2.80589i 0.143750 + 0.248982i 0.928906 0.370316i \(-0.120751\pi\)
−0.785156 + 0.619298i \(0.787417\pi\)
\(128\) 5.72615 3.30600i 0.506125 0.292212i
\(129\) 0 0
\(130\) −0.272296 0.743818i −0.0238819 0.0652372i
\(131\) −0.175664 −0.0153478 −0.00767390 0.999971i \(-0.502443\pi\)
−0.00767390 + 0.999971i \(0.502443\pi\)
\(132\) 0 0
\(133\) 0.376759 + 0.652566i 0.0326692 + 0.0565846i
\(134\) 1.13493 1.96576i 0.0980430 0.169815i
\(135\) 0 0
\(136\) 3.80752 + 2.19827i 0.326492 + 0.188500i
\(137\) 15.5736 + 8.99144i 1.33054 + 0.768190i 0.985383 0.170353i \(-0.0544907\pi\)
0.345162 + 0.938543i \(0.387824\pi\)
\(138\) 0 0
\(139\) −5.99307 + 10.3803i −0.508325 + 0.880445i 0.491628 + 0.870805i \(0.336402\pi\)
−0.999954 + 0.00964021i \(0.996931\pi\)
\(140\) 0.324229 + 0.561581i 0.0274024 + 0.0474623i
\(141\) 0 0
\(142\) 2.81140 0.235928
\(143\) 18.1879 6.65821i 1.52095 0.556788i
\(144\) 0 0
\(145\) 2.51448 1.45174i 0.208816 0.120560i
\(146\) 1.06430 + 1.84342i 0.0880819 + 0.152562i
\(147\) 0 0
\(148\) 11.6558i 0.958101i
\(149\) −2.95350 1.70520i −0.241960 0.139696i 0.374117 0.927381i \(-0.377946\pi\)
−0.616077 + 0.787686i \(0.711279\pi\)
\(150\) 0 0
\(151\) 7.96141i 0.647890i −0.946076 0.323945i \(-0.894991\pi\)
0.946076 0.323945i \(-0.105009\pi\)
\(152\) 0.984454 1.70512i 0.0798498 0.138304i
\(153\) 0 0
\(154\) 0.339560 0.196045i 0.0273625 0.0157978i
\(155\) −5.46410 −0.438887
\(156\) 0 0
\(157\) −16.4329 −1.31148 −0.655742 0.754985i \(-0.727644\pi\)
−0.655742 + 0.754985i \(0.727644\pi\)
\(158\) 0.859667 0.496329i 0.0683914 0.0394858i
\(159\) 0 0
\(160\) 1.27597 2.21004i 0.100874 0.174719i
\(161\) 0.943307i 0.0743430i
\(162\) 0 0
\(163\) 15.4215 + 8.90361i 1.20791 + 0.697384i 0.962301 0.271986i \(-0.0876804\pi\)
0.245604 + 0.969370i \(0.421014\pi\)
\(164\) 7.28398i 0.568784i
\(165\) 0 0
\(166\) 0.468341 + 0.811190i 0.0363503 + 0.0629605i
\(167\) −5.45047 + 3.14683i −0.421770 + 0.243509i −0.695834 0.718202i \(-0.744965\pi\)
0.274064 + 0.961711i \(0.411632\pi\)
\(168\) 0 0
\(169\) 12.2325 + 4.40078i 0.940959 + 0.338522i
\(170\) 1.11256 0.0853294
\(171\) 0 0
\(172\) −4.94209 8.55995i −0.376831 0.652690i
\(173\) −7.98756 + 13.8349i −0.607283 + 1.05184i 0.384404 + 0.923165i \(0.374407\pi\)
−0.991686 + 0.128679i \(0.958926\pi\)
\(174\) 0 0
\(175\) 0.287734 + 0.166123i 0.0217506 + 0.0125577i
\(176\) 17.2722 + 9.97212i 1.30194 + 0.751677i
\(177\) 0 0
\(178\) 0.354337 0.613729i 0.0265587 0.0460010i
\(179\) −11.8087 20.4533i −0.882625 1.52875i −0.848412 0.529336i \(-0.822441\pi\)
−0.0342123 0.999415i \(-0.510892\pi\)
\(180\) 0 0
\(181\) 2.62590 0.195182 0.0975909 0.995227i \(-0.468886\pi\)
0.0975909 + 0.995227i \(0.468886\pi\)
\(182\) 0.259256 + 0.0452168i 0.0192174 + 0.00335169i
\(183\) 0 0
\(184\) −2.13459 + 1.23241i −0.157364 + 0.0908544i
\(185\) −2.98601 5.17191i −0.219536 0.380247i
\(186\) 0 0
\(187\) 27.2045i 1.98939i
\(188\) −14.1015 8.14153i −1.02846 0.593782i
\(189\) 0 0
\(190\) 0.498239i 0.0361460i
\(191\) −1.00791 + 1.74575i −0.0729298 + 0.126318i −0.900184 0.435509i \(-0.856568\pi\)
0.827254 + 0.561828i \(0.189902\pi\)
\(192\) 0 0
\(193\) −19.7636 + 11.4105i −1.42262 + 0.821348i −0.996522 0.0833298i \(-0.973445\pi\)
−0.426095 + 0.904678i \(0.640111\pi\)
\(194\) 0.550955 0.0395563
\(195\) 0 0
\(196\) 13.4467 0.960480
\(197\) 0.556877 0.321513i 0.0396758 0.0229068i −0.480031 0.877252i \(-0.659375\pi\)
0.519707 + 0.854345i \(0.326041\pi\)
\(198\) 0 0
\(199\) 1.53342 2.65596i 0.108701 0.188276i −0.806543 0.591175i \(-0.798664\pi\)
0.915244 + 0.402899i \(0.131997\pi\)
\(200\) 0.868145i 0.0613871i
\(201\) 0 0
\(202\) −2.36804 1.36719i −0.166615 0.0961952i
\(203\) 0.964670i 0.0677065i
\(204\) 0 0
\(205\) −1.86603 3.23205i −0.130329 0.225736i
\(206\) 2.85852 1.65037i 0.199163 0.114987i
\(207\) 0 0
\(208\) 4.60185 + 12.5707i 0.319081 + 0.871620i
\(209\) 12.1830 0.842716
\(210\) 0 0
\(211\) 4.10020 + 7.10175i 0.282269 + 0.488904i 0.971943 0.235215i \(-0.0755796\pi\)
−0.689674 + 0.724120i \(0.742246\pi\)
\(212\) −1.52297 + 2.63786i −0.104598 + 0.181169i
\(213\) 0 0
\(214\) −2.48554 1.43503i −0.169908 0.0980964i
\(215\) −4.38581 2.53215i −0.299110 0.172691i
\(216\) 0 0
\(217\) 0.907714 1.57221i 0.0616197 0.106728i
\(218\) −1.23381 2.13703i −0.0835643 0.144738i
\(219\) 0 0
\(220\) 10.4844 0.706856
\(221\) −11.7110 + 14.0095i −0.787767 + 0.942378i
\(222\) 0 0
\(223\) 8.87174 5.12210i 0.594095 0.343001i −0.172620 0.984989i \(-0.555223\pi\)
0.766715 + 0.641987i \(0.221890\pi\)
\(224\) 0.423935 + 0.734278i 0.0283254 + 0.0490610i
\(225\) 0 0
\(226\) 4.02990i 0.268065i
\(227\) 6.10012 + 3.52190i 0.404879 + 0.233757i 0.688587 0.725154i \(-0.258231\pi\)
−0.283708 + 0.958911i \(0.591565\pi\)
\(228\) 0 0
\(229\) 1.32899i 0.0878219i −0.999035 0.0439109i \(-0.986018\pi\)
0.999035 0.0439109i \(-0.0139818\pi\)
\(230\) −0.311865 + 0.540166i −0.0205638 + 0.0356175i
\(231\) 0 0
\(232\) 2.18294 1.26032i 0.143317 0.0827440i
\(233\) −1.24746 −0.0817238 −0.0408619 0.999165i \(-0.513010\pi\)
−0.0408619 + 0.999165i \(0.513010\pi\)
\(234\) 0 0
\(235\) −8.34285 −0.544227
\(236\) 4.57606 2.64199i 0.297876 0.171979i
\(237\) 0 0
\(238\) −0.184822 + 0.320121i −0.0119802 + 0.0207504i
\(239\) 9.94207i 0.643099i 0.946893 + 0.321549i \(0.104204\pi\)
−0.946893 + 0.321549i \(0.895796\pi\)
\(240\) 0 0
\(241\) −19.5608 11.2934i −1.26002 0.727475i −0.286944 0.957947i \(-0.592640\pi\)
−0.973079 + 0.230472i \(0.925973\pi\)
\(242\) 3.92282i 0.252168i
\(243\) 0 0
\(244\) −13.7635 23.8391i −0.881119 1.52614i
\(245\) 5.96658 3.44481i 0.381191 0.220081i
\(246\) 0 0
\(247\) 6.27387 + 5.24455i 0.399197 + 0.333702i
\(248\) −4.74363 −0.301221
\(249\) 0 0
\(250\) −0.109843 0.190254i −0.00694711 0.0120327i
\(251\) 3.38418 5.86157i 0.213608 0.369979i −0.739233 0.673449i \(-0.764812\pi\)
0.952841 + 0.303470i \(0.0981453\pi\)
\(252\) 0 0
\(253\) −13.2082 7.62577i −0.830394 0.479428i
\(254\) 0.616417 + 0.355888i 0.0386774 + 0.0223304i
\(255\) 0 0
\(256\) −6.13860 + 10.6324i −0.383663 + 0.664523i
\(257\) 5.12691 + 8.88007i 0.319808 + 0.553924i 0.980448 0.196779i \(-0.0630483\pi\)
−0.660640 + 0.750703i \(0.729715\pi\)
\(258\) 0 0
\(259\) 1.98418 0.123291
\(260\) 5.39913 + 4.51332i 0.334840 + 0.279904i
\(261\) 0 0
\(262\) −0.0334208 + 0.0192955i −0.00206474 + 0.00119208i
\(263\) 9.32850 + 16.1574i 0.575220 + 0.996310i 0.996018 + 0.0891555i \(0.0284168\pi\)
−0.420798 + 0.907154i \(0.638250\pi\)
\(264\) 0 0
\(265\) 1.56063i 0.0958685i
\(266\) 0.143360 + 0.0827690i 0.00878998 + 0.00507489i
\(267\) 0 0
\(268\) 20.1658i 1.23182i
\(269\) 8.97894 15.5520i 0.547456 0.948221i −0.450992 0.892528i \(-0.648930\pi\)
0.998448 0.0556934i \(-0.0177369\pi\)
\(270\) 0 0
\(271\) −26.7582 + 15.4488i −1.62544 + 0.938450i −0.640014 + 0.768363i \(0.721071\pi\)
−0.985429 + 0.170086i \(0.945595\pi\)
\(272\) −18.8025 −1.14007
\(273\) 0 0
\(274\) 3.95060 0.238665
\(275\) 4.65213 2.68591i 0.280534 0.161966i
\(276\) 0 0
\(277\) 13.2522 22.9536i 0.796250 1.37915i −0.125792 0.992057i \(-0.540147\pi\)
0.922042 0.387089i \(-0.126519\pi\)
\(278\) 2.63320i 0.157929i
\(279\) 0 0
\(280\) 0.249795 + 0.144219i 0.0149281 + 0.00861874i
\(281\) 4.97766i 0.296942i 0.988917 + 0.148471i \(0.0474352\pi\)
−0.988917 + 0.148471i \(0.952565\pi\)
\(282\) 0 0
\(283\) −6.29317 10.9001i −0.374090 0.647943i 0.616100 0.787668i \(-0.288712\pi\)
−0.990190 + 0.139725i \(0.955378\pi\)
\(284\) −21.6307 + 12.4885i −1.28355 + 0.741057i
\(285\) 0 0
\(286\) 2.72898 3.26458i 0.161368 0.193039i
\(287\) 1.23996 0.0731926
\(288\) 0 0
\(289\) −4.32355 7.48861i −0.254327 0.440507i
\(290\) 0.318928 0.552399i 0.0187281 0.0324380i
\(291\) 0 0
\(292\) −16.3772 9.45541i −0.958406 0.553336i
\(293\) −14.6511 8.45880i −0.855925 0.494168i 0.00672072 0.999977i \(-0.497861\pi\)
−0.862645 + 0.505809i \(0.831194\pi\)
\(294\) 0 0
\(295\) 1.35366 2.34461i 0.0788132 0.136508i
\(296\) −2.59229 4.48997i −0.150674 0.260974i
\(297\) 0 0
\(298\) −0.749222 −0.0434012
\(299\) −3.51908 9.61292i −0.203514 0.555929i
\(300\) 0 0
\(301\) 1.45717 0.841298i 0.0839899 0.0484916i
\(302\) −0.874509 1.51469i −0.0503223 0.0871608i
\(303\) 0 0
\(304\) 8.42034i 0.482940i
\(305\) −12.2143 7.05193i −0.699389 0.403793i
\(306\) 0 0
\(307\) 4.30426i 0.245657i 0.992428 + 0.122828i \(0.0391965\pi\)
−0.992428 + 0.122828i \(0.960803\pi\)
\(308\) −1.74170 + 3.01671i −0.0992425 + 0.171893i
\(309\) 0 0
\(310\) −1.03957 + 0.600196i −0.0590436 + 0.0340888i
\(311\) −2.22512 −0.126175 −0.0630875 0.998008i \(-0.520095\pi\)
−0.0630875 + 0.998008i \(0.520095\pi\)
\(312\) 0 0
\(313\) 7.20887 0.407469 0.203735 0.979026i \(-0.434692\pi\)
0.203735 + 0.979026i \(0.434692\pi\)
\(314\) −3.12642 + 1.80504i −0.176434 + 0.101864i
\(315\) 0 0
\(316\) −4.40948 + 7.63744i −0.248052 + 0.429639i
\(317\) 0.321644i 0.0180653i 0.999959 + 0.00903266i \(0.00287522\pi\)
−0.999959 + 0.00903266i \(0.997125\pi\)
\(318\) 0 0
\(319\) 13.5073 + 7.79847i 0.756266 + 0.436630i
\(320\) 6.86488i 0.383759i
\(321\) 0 0
\(322\) −0.103616 0.179468i −0.00577430 0.0100014i
\(323\) −9.94679 + 5.74278i −0.553454 + 0.319537i
\(324\) 0 0
\(325\) 3.55193 + 0.619491i 0.197026 + 0.0343632i
\(326\) 3.91201 0.216666
\(327\) 0 0
\(328\) −1.61998 2.80589i −0.0894485 0.154929i
\(329\) 1.38594 2.40052i 0.0764094 0.132345i
\(330\) 0 0
\(331\) −14.4037 8.31600i −0.791701 0.457089i 0.0488600 0.998806i \(-0.484441\pi\)
−0.840561 + 0.541717i \(0.817775\pi\)
\(332\) −7.20676 4.16082i −0.395522 0.228355i
\(333\) 0 0
\(334\) −0.691317 + 1.19740i −0.0378272 + 0.0655186i
\(335\) 5.16612 + 8.94799i 0.282255 + 0.488881i
\(336\) 0 0
\(337\) −24.2186 −1.31927 −0.659636 0.751586i \(-0.729289\pi\)
−0.659636 + 0.751586i \(0.729289\pi\)
\(338\) 2.81068 0.506387i 0.152881 0.0275438i
\(339\) 0 0
\(340\) −8.55995 + 4.94209i −0.464229 + 0.268022i
\(341\) −14.6761 25.4197i −0.794754 1.37655i
\(342\) 0 0
\(343\) 4.61478i 0.249174i
\(344\) −3.80752 2.19827i −0.205288 0.118523i
\(345\) 0 0
\(346\) 3.50952i 0.188673i
\(347\) −3.13680 + 5.43309i −0.168392 + 0.291664i −0.937855 0.347028i \(-0.887191\pi\)
0.769463 + 0.638692i \(0.220524\pi\)
\(348\) 0 0
\(349\) −6.12275 + 3.53497i −0.327743 + 0.189223i −0.654839 0.755769i \(-0.727263\pi\)
0.327095 + 0.944991i \(0.393930\pi\)
\(350\) 0.0729902 0.00390149
\(351\) 0 0
\(352\) 13.7085 0.730666
\(353\) 18.8705 10.8949i 1.00438 0.579878i 0.0948371 0.995493i \(-0.469767\pi\)
0.909541 + 0.415615i \(0.136434\pi\)
\(354\) 0 0
\(355\) −6.39866 + 11.0828i −0.339606 + 0.588214i
\(356\) 6.29598i 0.333687i
\(357\) 0 0
\(358\) −4.49332 2.59422i −0.237479 0.137109i
\(359\) 23.9737i 1.26528i 0.774444 + 0.632642i \(0.218029\pi\)
−0.774444 + 0.632642i \(0.781971\pi\)
\(360\) 0 0
\(361\) −6.92820 12.0000i −0.364642 0.631579i
\(362\) 0.499589 0.288438i 0.0262578 0.0151600i
\(363\) 0 0
\(364\) −2.19556 + 0.803745i −0.115078 + 0.0421277i
\(365\) −9.68922 −0.507157
\(366\) 0 0
\(367\) −3.19566 5.53505i −0.166812 0.288927i 0.770485 0.637458i \(-0.220014\pi\)
−0.937297 + 0.348531i \(0.886681\pi\)
\(368\) 5.27059 9.12892i 0.274748 0.475878i
\(369\) 0 0
\(370\) −1.13620 0.655986i −0.0590683 0.0341031i
\(371\) −0.449045 0.259256i −0.0233133 0.0134599i
\(372\) 0 0
\(373\) 10.0401 17.3899i 0.519855 0.900414i −0.479879 0.877335i \(-0.659319\pi\)
0.999734 0.0230798i \(-0.00734719\pi\)
\(374\) 2.98823 + 5.17577i 0.154518 + 0.267633i
\(375\) 0 0
\(376\) −7.24280 −0.373519
\(377\) 3.59878 + 9.83062i 0.185346 + 0.506302i
\(378\) 0 0
\(379\) −4.73007 + 2.73091i −0.242968 + 0.140277i −0.616540 0.787324i \(-0.711466\pi\)
0.373572 + 0.927601i \(0.378133\pi\)
\(380\) 2.21322 + 3.83341i 0.113536 + 0.196650i
\(381\) 0 0
\(382\) 0.442849i 0.0226581i
\(383\) −4.90842 2.83388i −0.250808 0.144804i 0.369326 0.929300i \(-0.379589\pi\)
−0.620134 + 0.784496i \(0.712922\pi\)
\(384\) 0 0
\(385\) 1.78477i 0.0909602i
\(386\) −2.50675 + 4.34181i −0.127590 + 0.220992i
\(387\) 0 0
\(388\) −4.23901 + 2.44739i −0.215203 + 0.124247i
\(389\) 10.6174 0.538325 0.269162 0.963095i \(-0.413253\pi\)
0.269162 + 0.963095i \(0.413253\pi\)
\(390\) 0 0
\(391\) 14.3784 0.727149
\(392\) 5.17986 2.99059i 0.261622 0.151048i
\(393\) 0 0
\(394\) 0.0706321 0.122338i 0.00355840 0.00616332i
\(395\) 4.51851i 0.227351i
\(396\) 0 0
\(397\) 24.2780 + 14.0169i 1.21848 + 0.703487i 0.964592 0.263748i \(-0.0849586\pi\)
0.253884 + 0.967235i \(0.418292\pi\)
\(398\) 0.673745i 0.0337718i
\(399\) 0 0
\(400\) 1.85638 + 3.21534i 0.0928189 + 0.160767i
\(401\) −19.4979 + 11.2571i −0.973680 + 0.562155i −0.900356 0.435154i \(-0.856694\pi\)
−0.0733241 + 0.997308i \(0.523361\pi\)
\(402\) 0 0
\(403\) 3.38496 19.4081i 0.168617 0.966788i
\(404\) 24.2927 1.20861
\(405\) 0 0
\(406\) 0.105963 + 0.183533i 0.00525884 + 0.00910857i
\(407\) 16.0403 27.7826i 0.795087 1.37713i
\(408\) 0 0
\(409\) −3.71328 2.14386i −0.183610 0.106007i 0.405378 0.914149i \(-0.367140\pi\)
−0.588988 + 0.808142i \(0.700473\pi\)
\(410\) −0.710039 0.409941i −0.0350663 0.0202456i
\(411\) 0 0
\(412\) −14.6622 + 25.3956i −0.722353 + 1.25115i
\(413\) 0.449749 + 0.778989i 0.0221307 + 0.0383315i
\(414\) 0 0
\(415\) −4.26371 −0.209297
\(416\) 7.05946 + 5.90125i 0.346119 + 0.289333i
\(417\) 0 0
\(418\) 2.31787 1.33822i 0.113371 0.0654546i
\(419\) 8.85578 + 15.3387i 0.432633 + 0.749343i 0.997099 0.0761137i \(-0.0242512\pi\)
−0.564466 + 0.825456i \(0.690918\pi\)
\(420\) 0 0
\(421\) 12.8787i 0.627672i 0.949477 + 0.313836i \(0.101614\pi\)
−0.949477 + 0.313836i \(0.898386\pi\)
\(422\) 1.56016 + 0.900759i 0.0759474 + 0.0438483i
\(423\) 0 0
\(424\) 1.35485i 0.0657973i
\(425\) −2.53215 + 4.38581i −0.122827 + 0.212743i
\(426\) 0 0
\(427\) 4.05816 2.34298i 0.196388 0.113385i
\(428\) 25.4981 1.23250
\(429\) 0 0
\(430\) −1.11256 −0.0536524
\(431\) −8.22590 + 4.74923i −0.396228 + 0.228762i −0.684855 0.728679i \(-0.740134\pi\)
0.288627 + 0.957442i \(0.406801\pi\)
\(432\) 0 0
\(433\) −0.698141 + 1.20922i −0.0335505 + 0.0581112i −0.882313 0.470663i \(-0.844015\pi\)
0.848763 + 0.528774i \(0.177348\pi\)
\(434\) 0.398826i 0.0191443i
\(435\) 0 0
\(436\) 18.9857 + 10.9614i 0.909251 + 0.524956i
\(437\) 6.43911i 0.308024i
\(438\) 0 0
\(439\) 2.08090 + 3.60422i 0.0993159 + 0.172020i 0.911402 0.411518i \(-0.135001\pi\)
−0.812086 + 0.583538i \(0.801668\pi\)
\(440\) 4.03872 2.33176i 0.192539 0.111162i
\(441\) 0 0
\(442\) −0.689221 + 3.95174i −0.0327829 + 0.187965i
\(443\) −9.54563 −0.453526 −0.226763 0.973950i \(-0.572814\pi\)
−0.226763 + 0.973950i \(0.572814\pi\)
\(444\) 0 0
\(445\) 1.61292 + 2.79366i 0.0764596 + 0.132432i
\(446\) 1.12526 1.94900i 0.0532825 0.0922880i
\(447\) 0 0
\(448\) −1.97526 1.14042i −0.0933223 0.0538796i
\(449\) −18.8075 10.8585i −0.887582 0.512446i −0.0144310 0.999896i \(-0.504594\pi\)
−0.873151 + 0.487450i \(0.837927\pi\)
\(450\) 0 0
\(451\) 10.0239 17.3620i 0.472009 0.817544i
\(452\) −17.9012 31.0057i −0.842000 1.45839i
\(453\) 0 0
\(454\) 1.54743 0.0726246
\(455\) −0.768307 + 0.919100i −0.0360188 + 0.0430881i
\(456\) 0 0
\(457\) 4.08989 2.36130i 0.191317 0.110457i −0.401282 0.915955i \(-0.631435\pi\)
0.592599 + 0.805498i \(0.298102\pi\)
\(458\) −0.145980 0.252845i −0.00682122 0.0118147i
\(459\) 0 0
\(460\) 5.54133i 0.258366i
\(461\) −1.54283 0.890753i −0.0718568 0.0414865i 0.463641 0.886023i \(-0.346543\pi\)
−0.535498 + 0.844537i \(0.679876\pi\)
\(462\) 0 0
\(463\) 6.80200i 0.316116i −0.987430 0.158058i \(-0.949477\pi\)
0.987430 0.158058i \(-0.0505232\pi\)
\(464\) −5.38995 + 9.33566i −0.250222 + 0.433397i
\(465\) 0 0
\(466\) −0.237335 + 0.137025i −0.0109943 + 0.00634758i
\(467\) 18.2374 0.843927 0.421963 0.906613i \(-0.361341\pi\)
0.421963 + 0.906613i \(0.361341\pi\)
\(468\) 0 0
\(469\) −3.43285 −0.158514
\(470\) −1.58726 + 0.916407i −0.0732150 + 0.0422707i
\(471\) 0 0
\(472\) 1.17517 2.03546i 0.0540918 0.0936897i
\(473\) 27.2045i 1.25086i
\(474\) 0 0
\(475\) 1.96410 + 1.13397i 0.0901192 + 0.0520303i
\(476\) 3.28398i 0.150521i
\(477\) 0 0
\(478\) 1.09207 + 1.89152i 0.0499502 + 0.0865162i
\(479\) −30.4674 + 17.5904i −1.39209 + 0.803724i −0.993547 0.113425i \(-0.963818\pi\)
−0.398544 + 0.917149i \(0.630485\pi\)
\(480\) 0 0
\(481\) 20.2201 7.40214i 0.921957 0.337508i
\(482\) −4.96204 −0.226015
\(483\) 0 0
\(484\) 17.4255 + 30.1819i 0.792069 + 1.37190i
\(485\) −1.25396 + 2.17191i −0.0569392 + 0.0986215i
\(486\) 0 0
\(487\) 8.92352 + 5.15200i 0.404363 + 0.233459i 0.688365 0.725364i \(-0.258329\pi\)
−0.284002 + 0.958824i \(0.591662\pi\)
\(488\) −10.6038 6.12210i −0.480011 0.277134i
\(489\) 0 0
\(490\) 0.756779 1.31078i 0.0341878 0.0592150i
\(491\) −4.66599 8.08174i −0.210573 0.364724i 0.741321 0.671151i \(-0.234200\pi\)
−0.951894 + 0.306427i \(0.900866\pi\)
\(492\) 0 0
\(493\) −14.7041 −0.662238
\(494\) 1.76971 + 0.308654i 0.0796230 + 0.0138870i
\(495\) 0 0
\(496\) 17.5689 10.1434i 0.788869 0.455454i
\(497\) −2.12593 3.68222i −0.0953611 0.165170i
\(498\) 0 0
\(499\) 23.9421i 1.07179i 0.844283 + 0.535897i \(0.180026\pi\)
−0.844283 + 0.535897i \(0.819974\pi\)
\(500\) 1.69025 + 0.975869i 0.0755905 + 0.0436422i
\(501\) 0 0
\(502\) 1.48692i 0.0663645i
\(503\) 21.0721 36.4980i 0.939560 1.62737i 0.173266 0.984875i \(-0.444568\pi\)
0.766294 0.642490i \(-0.222099\pi\)
\(504\) 0 0
\(505\) 10.7792 6.22336i 0.479667 0.276936i
\(506\) −3.35056 −0.148951
\(507\) 0 0
\(508\) −6.32355 −0.280562
\(509\) 29.0640 16.7801i 1.28824 0.743765i 0.309899 0.950770i \(-0.399705\pi\)
0.978340 + 0.207005i \(0.0663715\pi\)
\(510\) 0 0
\(511\) 1.60960 2.78792i 0.0712047 0.123330i
\(512\) 15.9211i 0.703621i
\(513\) 0 0
\(514\) 1.95084 + 1.12632i 0.0860477 + 0.0496796i
\(515\) 15.0247i 0.662069i
\(516\) 0 0
\(517\) −22.4081 38.8120i −0.985508 1.70695i
\(518\) 0.377499 0.217949i 0.0165864 0.00957614i
\(519\) 0 0
\(520\) 3.08359 + 0.537808i 0.135224 + 0.0235844i
\(521\) −12.4649 −0.546098 −0.273049 0.962000i \(-0.588032\pi\)
−0.273049 + 0.962000i \(0.588032\pi\)
\(522\) 0 0
\(523\) 2.82978 + 4.90132i 0.123738 + 0.214320i 0.921239 0.388998i \(-0.127179\pi\)
−0.797501 + 0.603317i \(0.793845\pi\)
\(524\) 0.171425 0.296916i 0.00748872 0.0129708i
\(525\) 0 0
\(526\) 3.54958 + 2.04935i 0.154769 + 0.0893558i
\(527\) 23.9645 + 13.8359i 1.04391 + 0.602702i
\(528\) 0 0
\(529\) 7.46953 12.9376i 0.324762 0.562505i
\(530\) 0.171425 + 0.296916i 0.00744621 + 0.0128972i
\(531\) 0 0
\(532\) −1.47067 −0.0637616
\(533\) 12.6360 4.62577i 0.547327 0.200364i
\(534\) 0 0
\(535\) 11.3140 6.53215i 0.489147 0.282409i
\(536\) 4.48494 + 7.76815i 0.193720 + 0.335533i
\(537\) 0 0
\(538\) 3.94511i 0.170086i
\(539\) 32.0514 + 18.5049i 1.38055 + 0.797061i
\(540\) 0 0
\(541\) 15.4750i 0.665321i 0.943047 + 0.332660i \(0.107946\pi\)
−0.943047 + 0.332660i \(0.892054\pi\)
\(542\) −3.39391 + 5.87842i −0.145781 + 0.252500i
\(543\) 0 0
\(544\) −11.1923 + 6.46187i −0.479866 + 0.277051i
\(545\) 11.2325 0.481146
\(546\) 0 0
\(547\) 25.1765 1.07647 0.538234 0.842795i \(-0.319092\pi\)
0.538234 + 0.842795i \(0.319092\pi\)
\(548\) −30.3956 + 17.5489i −1.29844 + 0.749653i
\(549\) 0 0
\(550\) 0.590059 1.02201i 0.0251602 0.0435787i
\(551\) 6.58493i 0.280528i
\(552\) 0 0
\(553\) −1.30013 0.750630i −0.0552871 0.0319200i
\(554\) 5.82269i 0.247382i
\(555\) 0 0
\(556\) −11.6969 20.2596i −0.496059 0.859199i
\(557\) 36.6752 21.1744i 1.55398 0.897190i 0.556167 0.831071i \(-0.312272\pi\)
0.997812 0.0661194i \(-0.0210618\pi\)
\(558\) 0 0
\(559\) 11.7110 14.0095i 0.495322 0.592537i
\(560\) −1.23355 −0.0521270
\(561\) 0 0
\(562\) 0.546763 + 0.947022i 0.0230638 + 0.0399477i
\(563\) −11.8953 + 20.6032i −0.501326 + 0.868322i 0.498673 + 0.866790i \(0.333821\pi\)
−0.999999 + 0.00153173i \(0.999512\pi\)
\(564\) 0 0
\(565\) −15.8862 9.17191i −0.668338 0.385865i
\(566\) −2.39461 1.38253i −0.100653 0.0581119i
\(567\) 0 0
\(568\) −5.55497 + 9.62148i −0.233081 + 0.403709i
\(569\) 13.3710 + 23.1593i 0.560543 + 0.970889i 0.997449 + 0.0713817i \(0.0227408\pi\)
−0.436906 + 0.899507i \(0.643926\pi\)
\(570\) 0 0
\(571\) 16.7159 0.699539 0.349769 0.936836i \(-0.386260\pi\)
0.349769 + 0.936836i \(0.386260\pi\)
\(572\) −6.49498 + 37.2398i −0.271569 + 1.55707i
\(573\) 0 0
\(574\) 0.235908 0.136202i 0.00984661 0.00568494i
\(575\) −1.41959 2.45880i −0.0592010 0.102539i
\(576\) 0 0
\(577\) 20.6768i 0.860786i −0.902642 0.430393i \(-0.858375\pi\)
0.902642 0.430393i \(-0.141625\pi\)
\(578\) −1.64515 0.949828i −0.0684292 0.0395076i
\(579\) 0 0
\(580\) 5.66682i 0.235302i
\(581\) 0.708301 1.22681i 0.0293853 0.0508968i
\(582\) 0 0
\(583\) −7.26023 + 4.19170i −0.300688 + 0.173602i
\(584\) −8.41165 −0.348076
\(585\) 0 0
\(586\) −3.71657 −0.153530
\(587\) −18.0109 + 10.3986i −0.743388 + 0.429196i −0.823300 0.567606i \(-0.807870\pi\)
0.0799116 + 0.996802i \(0.474536\pi\)
\(588\) 0 0
\(589\) 6.19615 10.7321i 0.255308 0.442206i
\(590\) 0.594763i 0.0244860i
\(591\) 0 0
\(592\) 19.2021 + 11.0863i 0.789199 + 0.455644i
\(593\) 21.8475i 0.897169i −0.893740 0.448585i \(-0.851928\pi\)
0.893740 0.448585i \(-0.148072\pi\)
\(594\) 0 0
\(595\) −0.841298 1.45717i −0.0344898 0.0597381i
\(596\) 5.76446 3.32811i 0.236121 0.136325i
\(597\) 0 0
\(598\) −1.72544 1.44235i −0.0705583 0.0589822i
\(599\) 3.58040 0.146291 0.0731456 0.997321i \(-0.476696\pi\)
0.0731456 + 0.997321i \(0.476696\pi\)
\(600\) 0 0
\(601\) −10.6743 18.4885i −0.435414 0.754160i 0.561915 0.827195i \(-0.310065\pi\)
−0.997329 + 0.0730352i \(0.976731\pi\)
\(602\) 0.184822 0.320121i 0.00753278 0.0130472i
\(603\) 0 0
\(604\) 13.4568 + 7.76929i 0.547550 + 0.316128i
\(605\) 15.4641 + 8.92820i 0.628705 + 0.362983i
\(606\) 0 0
\(607\) 1.64988 2.85767i 0.0669665 0.115989i −0.830598 0.556872i \(-0.812001\pi\)
0.897565 + 0.440883i \(0.145335\pi\)
\(608\) 2.89383 + 5.01226i 0.117360 + 0.203274i
\(609\) 0 0
\(610\) −3.09843 −0.125452
\(611\) 5.16832 29.6332i 0.209088 1.19883i
\(612\) 0 0
\(613\) 8.56183 4.94318i 0.345809 0.199653i −0.317029 0.948416i \(-0.602685\pi\)
0.662838 + 0.748763i \(0.269352\pi\)
\(614\) 0.472795 + 0.818904i 0.0190804 + 0.0330483i
\(615\) 0 0
\(616\) 1.54944i 0.0624286i
\(617\) −39.5920 22.8584i −1.59391 0.920246i −0.992626 0.121213i \(-0.961321\pi\)
−0.601287 0.799033i \(-0.705345\pi\)
\(618\) 0 0
\(619\) 19.9143i 0.800425i −0.916422 0.400212i \(-0.868936\pi\)
0.916422 0.400212i \(-0.131064\pi\)
\(620\) 5.33225 9.23572i 0.214148 0.370916i
\(621\) 0 0
\(622\) −0.423339 + 0.244415i −0.0169743 + 0.00980014i
\(623\) −1.07177 −0.0429397
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 1.37152 0.791847i 0.0548169 0.0316486i
\(627\) 0 0
\(628\) 16.0363 27.7757i 0.639918 1.10837i
\(629\) 30.2440i 1.20591i
\(630\) 0 0
\(631\) 12.6403 + 7.29790i 0.503204 + 0.290525i 0.730036 0.683409i \(-0.239503\pi\)
−0.226832 + 0.973934i \(0.572837\pi\)
\(632\) 3.92272i 0.156038i
\(633\) 0 0
\(634\) 0.0353305 + 0.0611942i 0.00140315 + 0.00243033i
\(635\) −2.80589 + 1.61998i −0.111348 + 0.0642870i
\(636\) 0 0
\(637\) 8.53948 + 23.3269i 0.338346 + 0.924246i
\(638\) 3.42644 0.135654
\(639\) 0 0
\(640\) 3.30600 + 5.72615i 0.130681 + 0.226346i
\(641\) 7.08183 12.2661i 0.279716 0.484482i −0.691598 0.722282i \(-0.743093\pi\)
0.971314 + 0.237801i \(0.0764265\pi\)
\(642\) 0 0
\(643\) −14.5246 8.38581i −0.572796 0.330704i 0.185469 0.982650i \(-0.440620\pi\)
−0.758265 + 0.651946i \(0.773953\pi\)
\(644\) 1.59443 + 0.920544i 0.0628293 + 0.0362745i
\(645\) 0 0
\(646\) −1.26161 + 2.18518i −0.0496376 + 0.0859748i
\(647\) 1.49584 + 2.59087i 0.0588075 + 0.101858i 0.893930 0.448206i \(-0.147937\pi\)
−0.835123 + 0.550063i \(0.814604\pi\)
\(648\) 0 0
\(649\) 14.5432 0.570872
\(650\) 0.743818 0.272296i 0.0291749 0.0106803i
\(651\) 0 0
\(652\) −30.0987 + 17.3775i −1.17876 + 0.680556i
\(653\) −5.83217 10.1016i −0.228230 0.395307i 0.729053 0.684457i \(-0.239961\pi\)
−0.957284 + 0.289150i \(0.906627\pi\)
\(654\) 0 0
\(655\) 0.175664i 0.00686374i
\(656\) 11.9998 + 6.92810i 0.468514 + 0.270497i
\(657\) 0 0
\(658\) 0.608946i 0.0237392i
\(659\) −0.905237 + 1.56792i −0.0352630 + 0.0610773i −0.883118 0.469150i \(-0.844560\pi\)
0.847855 + 0.530228i \(0.177894\pi\)
\(660\) 0 0
\(661\) 10.6872 6.17028i 0.415686 0.239996i −0.277544 0.960713i \(-0.589520\pi\)
0.693230 + 0.720717i \(0.256187\pi\)
\(662\) −3.65383 −0.142010
\(663\) 0 0
\(664\) −3.70152 −0.143647
\(665\) −0.652566 + 0.376759i −0.0253054 + 0.0146101i
\(666\) 0 0
\(667\) 4.12174 7.13907i 0.159594 0.276426i
\(668\) 12.2836i 0.475265i
\(669\) 0 0
\(670\) 1.96576 + 1.13493i 0.0759438 + 0.0438461i
\(671\) 75.7634i 2.92481i
\(672\) 0 0
\(673\) 4.63313 + 8.02481i 0.178594 + 0.309334i 0.941399 0.337295i \(-0.109512\pi\)
−0.762805 + 0.646628i \(0.776178\pi\)
\(674\) −4.60770 + 2.66025i −0.177482 + 0.102469i
\(675\) 0 0
\(676\) −19.3757 + 16.3814i −0.745220 + 0.630053i
\(677\) −13.8984 −0.534158 −0.267079 0.963675i \(-0.586059\pi\)
−0.267079 + 0.963675i \(0.586059\pi\)
\(678\) 0 0
\(679\) −0.416622 0.721611i −0.0159885 0.0276929i
\(680\) −2.19827 + 3.80752i −0.0842999 + 0.146012i
\(681\) 0 0
\(682\) −5.58438 3.22414i −0.213837 0.123459i
\(683\) 32.6935 + 18.8756i 1.25098 + 0.722255i 0.971305 0.237838i \(-0.0764388\pi\)
0.279678 + 0.960094i \(0.409772\pi\)
\(684\) 0 0
\(685\) −8.99144 + 15.5736i −0.343545 + 0.595038i
\(686\) 0.506903 + 0.877981i 0.0193536 + 0.0335215i
\(687\) 0 0
\(688\) 18.8025 0.716838
\(689\) −5.54324 0.966794i −0.211181 0.0368319i
\(690\) 0 0
\(691\) −1.43146 + 0.826456i −0.0544554 + 0.0314399i −0.526981 0.849877i \(-0.676676\pi\)
0.472525 + 0.881317i \(0.343343\pi\)
\(692\) −15.5896 27.0020i −0.592628 1.02646i
\(693\) 0 0
\(694\) 1.37823i 0.0523168i
\(695\) −10.3803 5.99307i −0.393747 0.227330i
\(696\) 0 0
\(697\) 18.9002i 0.715897i
\(698\) −0.776587 + 1.34509i −0.0293943 + 0.0509123i
\(699\) 0 0
\(700\) −0.561581 + 0.324229i −0.0212258 + 0.0122547i
\(701\) 20.4819 0.773590 0.386795 0.922166i \(-0.373582\pi\)
0.386795 + 0.922166i \(0.373582\pi\)
\(702\) 0 0
\(703\) 13.5442 0.510830
\(704\) −31.9363 + 18.4384i −1.20365 + 0.694925i
\(705\) 0 0
\(706\) 2.39347 4.14561i 0.0900794 0.156022i
\(707\) 4.13538i 0.155527i
\(708\) 0 0
\(709\) 19.0021 + 10.9709i 0.713639 + 0.412020i 0.812407 0.583091i \(-0.198157\pi\)
−0.0987679 + 0.995110i \(0.531490\pi\)
\(710\) 2.81140i 0.105510i
\(711\) 0 0
\(712\) 1.40025 + 2.42530i 0.0524764 + 0.0908919i
\(713\) −13.4351 + 7.75678i −0.503150 + 0.290494i
\(714\) 0 0
\(715\) 6.65821 + 18.1879i 0.249003 + 0.680191i
\(716\) 46.0950 1.72265
\(717\) 0 0
\(718\) 2.63335 + 4.56110i 0.0982759 + 0.170219i
\(719\) −19.4237 + 33.6429i −0.724384 + 1.25467i 0.234844 + 0.972033i \(0.424542\pi\)
−0.959227 + 0.282636i \(0.908791\pi\)
\(720\) 0 0
\(721\) −4.32312 2.49596i −0.161002 0.0929543i
\(722\) −2.63624 1.52204i −0.0981108 0.0566443i
\(723\) 0 0
\(724\) −2.56254 + 4.43844i −0.0952359 + 0.164953i
\(725\) 1.45174 + 2.51448i 0.0539162 + 0.0933856i
\(726\) 0 0
\(727\) 30.6598 1.13711 0.568555 0.822645i \(-0.307503\pi\)
0.568555 + 0.822645i \(0.307503\pi\)
\(728\) −0.667002 + 0.797912i −0.0247207 + 0.0295726i
\(729\) 0 0
\(730\) −1.84342 + 1.06430i −0.0682279 + 0.0393914i
\(731\) 12.8236 + 22.2110i 0.474296 + 0.821505i
\(732\) 0 0
\(733\) 24.3858i 0.900709i 0.892850 + 0.450355i \(0.148702\pi\)
−0.892850 + 0.450355i \(0.851298\pi\)
\(734\) −1.21598 0.702045i −0.0448826 0.0259130i
\(735\) 0 0
\(736\) 7.24539i 0.267069i
\(737\) −27.7515 + 48.0669i −1.02224 + 1.77057i
\(738\) 0 0
\(739\) −33.1504 + 19.1394i −1.21946 + 0.704054i −0.964802 0.262977i \(-0.915296\pi\)
−0.254656 + 0.967032i \(0.581962\pi\)
\(740\) 11.6558 0.428476
\(741\) 0 0
\(742\) −0.113910 −0.00418178
\(743\) 34.6479 20.0040i 1.27111 0.733874i 0.295910 0.955216i \(-0.404377\pi\)
0.975196 + 0.221342i \(0.0710437\pi\)
\(744\) 0 0
\(745\) 1.70520 2.95350i 0.0624738 0.108208i
\(746\) 4.41134i 0.161511i
\(747\) 0 0
\(748\) −45.9825 26.5480i −1.68129 0.970691i
\(749\) 4.34057i 0.158601i
\(750\) 0 0
\(751\) 12.8010 + 22.1720i 0.467115 + 0.809067i 0.999294 0.0375648i \(-0.0119601\pi\)
−0.532179 + 0.846632i \(0.678627\pi\)
\(752\) 26.8251 15.4875i 0.978211 0.564770i
\(753\) 0 0
\(754\) 1.76451 + 1.47502i 0.0642597 + 0.0537169i
\(755\) 7.96141 0.289745
\(756\) 0 0
\(757\) 0.924239 + 1.60083i 0.0335920 + 0.0581831i 0.882333 0.470626i \(-0.155972\pi\)
−0.848741 + 0.528809i \(0.822639\pi\)
\(758\) −0.599945 + 1.03914i −0.0217910 + 0.0377431i
\(759\) 0 0
\(760\) 1.70512 + 0.984454i 0.0618514 + 0.0357099i
\(761\) −22.7006 13.1062i −0.822896 0.475099i 0.0285179 0.999593i \(-0.490921\pi\)
−0.851414 + 0.524494i \(0.824255\pi\)
\(762\) 0 0
\(763\) −1.86597 + 3.23196i −0.0675528 + 0.117005i
\(764\) −1.96718 3.40725i −0.0711699 0.123270i
\(765\) 0 0
\(766\) −1.24513 −0.0449884
\(767\) 7.48932 + 6.26058i 0.270424 + 0.226056i
\(768\) 0 0
\(769\) −38.4078 + 22.1747i −1.38502 + 0.799641i −0.992749 0.120208i \(-0.961644\pi\)
−0.392271 + 0.919850i \(0.628310\pi\)
\(770\) 0.196045 + 0.339560i 0.00706497 + 0.0122369i
\(771\) 0 0
\(772\) 44.5408i 1.60306i
\(773\) −20.1471 11.6319i −0.724640 0.418371i 0.0918181 0.995776i \(-0.470732\pi\)
−0.816458 + 0.577405i \(0.804065\pi\)
\(774\) 0 0
\(775\) 5.46410i 0.196276i
\(776\) −1.08861 + 1.88554i −0.0390790 + 0.0676868i
\(777\) 0 0
\(778\) 2.02001 1.16625i 0.0724209 0.0418122i
\(779\) 8.46410 0.303258
\(780\) 0 0
\(781\) −68.7449 −2.45989
\(782\) 2.73556 1.57938i 0.0978235 0.0564784i
\(783\) 0 0
\(784\) −12.7897 + 22.1524i −0.456776 + 0.791159i
\(785\) 16.4329i 0.586514i
\(786\) 0 0
\(787\) −41.4942 23.9567i −1.47911 0.853963i −0.479387 0.877604i \(-0.659141\pi\)
−0.999721 + 0.0236408i \(0.992474\pi\)
\(788\) 1.25502i 0.0447081i
\(789\) 0 0