Properties

Label 637.2.x.b.19.3
Level $637$
Weight $2$
Character 637.19
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 19.3
Character \(\chi\) \(=\) 637.19
Dual form 637.2.x.b.570.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.813723 - 0.218036i) q^{2} -1.43324i q^{3} +(-1.11745 - 0.645157i) q^{4} +(1.38386 - 0.370805i) q^{5} +(-0.312498 + 1.16626i) q^{6} +(1.96000 + 1.96000i) q^{8} +0.945832 q^{9} +O(q^{10})\) \(q+(-0.813723 - 0.218036i) q^{2} -1.43324i q^{3} +(-1.11745 - 0.645157i) q^{4} +(1.38386 - 0.370805i) q^{5} +(-0.312498 + 1.16626i) q^{6} +(1.96000 + 1.96000i) q^{8} +0.945832 q^{9} -1.20693 q^{10} +(3.43228 + 3.43228i) q^{11} +(-0.924663 + 1.60156i) q^{12} +(1.04975 + 3.44935i) q^{13} +(-0.531452 - 1.98341i) q^{15} +(0.122771 + 0.212645i) q^{16} +(1.49151 - 2.58338i) q^{17} +(-0.769645 - 0.206226i) q^{18} +(4.44020 + 4.44020i) q^{19} +(-1.78562 - 0.478455i) q^{20} +(-2.04457 - 3.54129i) q^{22} +(1.02242 - 0.590296i) q^{23} +(2.80914 - 2.80914i) q^{24} +(-2.55254 + 1.47371i) q^{25} +(-0.102119 - 3.03570i) q^{26} -5.65531i q^{27} +(-2.77911 + 4.81356i) q^{29} +1.72982i q^{30} +(1.75449 - 6.54786i) q^{31} +(-1.48835 - 5.55461i) q^{32} +(4.91928 - 4.91928i) q^{33} +(-1.77695 + 1.77695i) q^{34} +(-1.05692 - 0.610210i) q^{36} +(-1.44737 + 5.40165i) q^{37} +(-2.64497 - 4.58121i) q^{38} +(4.94374 - 1.50454i) q^{39} +(3.43915 + 1.98559i) q^{40} +(4.71621 - 1.26371i) q^{41} +(-2.90941 + 1.67975i) q^{43} +(-1.62103 - 6.04975i) q^{44} +(1.30890 - 0.350719i) q^{45} +(-0.960674 + 0.257412i) q^{46} +(-1.51103 - 5.63925i) q^{47} +(0.304771 - 0.175960i) q^{48} +(2.39839 - 0.642646i) q^{50} +(-3.70259 - 2.13769i) q^{51} +(1.05234 - 4.53171i) q^{52} +(-2.89658 - 5.01702i) q^{53} +(-1.23306 + 4.60186i) q^{54} +(6.02252 + 3.47711i) q^{55} +(6.36385 - 6.36385i) q^{57} +(3.31096 - 3.31096i) q^{58} +(2.88250 + 10.7576i) q^{59} +(-0.685740 + 2.55922i) q^{60} -9.18124i q^{61} +(-2.85534 + 4.94560i) q^{62} +4.35335i q^{64} +(2.73174 + 4.38418i) q^{65} +(-5.07551 + 2.93035i) q^{66} +(-1.38921 + 1.38921i) q^{67} +(-3.33337 + 1.92452i) q^{68} +(-0.846033 - 1.46537i) q^{69} +(-3.19094 - 0.855010i) q^{71} +(1.85383 + 1.85383i) q^{72} +(0.482220 + 0.129211i) q^{73} +(2.35552 - 4.07987i) q^{74} +(2.11218 + 3.65840i) q^{75} +(-2.09705 - 7.82630i) q^{76} +(-4.35088 + 0.146360i) q^{78} +(3.47711 - 6.02254i) q^{79} +(0.248748 + 0.248748i) q^{80} -5.26791 q^{81} -4.11322 q^{82} +(3.22886 + 3.22886i) q^{83} +(1.10612 - 4.12811i) q^{85} +(2.73370 - 0.732493i) q^{86} +(6.89897 + 3.98312i) q^{87} +13.4545i q^{88} +(0.237487 + 0.0636346i) q^{89} -1.14155 q^{90} -1.52333 q^{92} +(-9.38464 - 2.51461i) q^{93} +4.91825i q^{94} +(7.79107 + 4.49818i) q^{95} +(-7.96108 + 2.13316i) q^{96} +(2.43374 - 9.08284i) q^{97} +(3.24636 + 3.24636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + O(q^{10}) \) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + 20q^{11} - 8q^{15} + 12q^{16} - 64q^{18} + 4q^{22} + 12q^{23} + 4q^{29} + 64q^{32} + 4q^{37} + 36q^{39} - 48q^{43} - 84q^{44} - 108q^{46} - 44q^{50} + 12q^{51} - 36q^{53} - 92q^{57} + 44q^{58} + 28q^{60} + 28q^{65} + 64q^{67} + 84q^{71} + 4q^{72} - 24q^{74} + 148q^{78} + 40q^{79} - 56q^{81} + 36q^{85} + 108q^{86} + 24q^{92} - 24q^{93} + 84q^{95} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.813723 0.218036i −0.575389 0.154175i −0.0406221 0.999175i \(-0.512934\pi\)
−0.534767 + 0.845000i \(0.679601\pi\)
\(3\) 1.43324i 0.827480i −0.910395 0.413740i \(-0.864222\pi\)
0.910395 0.413740i \(-0.135778\pi\)
\(4\) −1.11745 0.645157i −0.558723 0.322579i
\(5\) 1.38386 0.370805i 0.618883 0.165829i 0.0642629 0.997933i \(-0.479530\pi\)
0.554620 + 0.832104i \(0.312864\pi\)
\(6\) −0.312498 + 1.16626i −0.127577 + 0.476123i
\(7\) 0 0
\(8\) 1.96000 + 1.96000i 0.692963 + 0.692963i
\(9\) 0.945832 0.315277
\(10\) −1.20693 −0.381665
\(11\) 3.43228 + 3.43228i 1.03487 + 1.03487i 0.999370 + 0.0355032i \(0.0113034\pi\)
0.0355032 + 0.999370i \(0.488697\pi\)
\(12\) −0.924663 + 1.60156i −0.266927 + 0.462332i
\(13\) 1.04975 + 3.44935i 0.291147 + 0.956678i
\(14\) 0 0
\(15\) −0.531452 1.98341i −0.137220 0.512113i
\(16\) 0.122771 + 0.212645i 0.0306927 + 0.0531613i
\(17\) 1.49151 2.58338i 0.361745 0.626561i −0.626503 0.779419i \(-0.715514\pi\)
0.988248 + 0.152858i \(0.0488477\pi\)
\(18\) −0.769645 0.206226i −0.181407 0.0486079i
\(19\) 4.44020 + 4.44020i 1.01865 + 1.01865i 0.999823 + 0.0188279i \(0.00599346\pi\)
0.0188279 + 0.999823i \(0.494007\pi\)
\(20\) −1.78562 0.478455i −0.399277 0.106986i
\(21\) 0 0
\(22\) −2.04457 3.54129i −0.435903 0.755006i
\(23\) 1.02242 0.590296i 0.213190 0.123085i −0.389603 0.920983i \(-0.627388\pi\)
0.602793 + 0.797898i \(0.294055\pi\)
\(24\) 2.80914 2.80914i 0.573413 0.573413i
\(25\) −2.55254 + 1.47371i −0.510509 + 0.294742i
\(26\) −0.102119 3.03570i −0.0200271 0.595350i
\(27\) 5.65531i 1.08837i
\(28\) 0 0
\(29\) −2.77911 + 4.81356i −0.516068 + 0.893856i 0.483758 + 0.875202i \(0.339271\pi\)
−0.999826 + 0.0186541i \(0.994062\pi\)
\(30\) 1.72982i 0.315820i
\(31\) 1.75449 6.54786i 0.315116 1.17603i −0.608765 0.793351i \(-0.708335\pi\)
0.923881 0.382680i \(-0.124999\pi\)
\(32\) −1.48835 5.55461i −0.263106 0.981926i
\(33\) 4.91928 4.91928i 0.856336 0.856336i
\(34\) −1.77695 + 1.77695i −0.304744 + 0.304744i
\(35\) 0 0
\(36\) −1.05692 0.610210i −0.176153 0.101702i
\(37\) −1.44737 + 5.40165i −0.237946 + 0.888027i 0.738853 + 0.673867i \(0.235368\pi\)
−0.976799 + 0.214160i \(0.931299\pi\)
\(38\) −2.64497 4.58121i −0.429070 0.743171i
\(39\) 4.94374 1.50454i 0.791632 0.240919i
\(40\) 3.43915 + 1.98559i 0.543777 + 0.313950i
\(41\) 4.71621 1.26371i 0.736549 0.197358i 0.129005 0.991644i \(-0.458822\pi\)
0.607544 + 0.794286i \(0.292155\pi\)
\(42\) 0 0
\(43\) −2.90941 + 1.67975i −0.443681 + 0.256159i −0.705158 0.709050i \(-0.749124\pi\)
0.261477 + 0.965210i \(0.415790\pi\)
\(44\) −1.62103 6.04975i −0.244379 0.912035i
\(45\) 1.30890 0.350719i 0.195120 0.0522822i
\(46\) −0.960674 + 0.257412i −0.141644 + 0.0379533i
\(47\) −1.51103 5.63925i −0.220407 0.822570i −0.984193 0.177100i \(-0.943328\pi\)
0.763786 0.645470i \(-0.223338\pi\)
\(48\) 0.304771 0.175960i 0.0439899 0.0253976i
\(49\) 0 0
\(50\) 2.39839 0.642646i 0.339183 0.0908839i
\(51\) −3.70259 2.13769i −0.518467 0.299337i
\(52\) 1.05234 4.53171i 0.145933 0.628436i
\(53\) −2.89658 5.01702i −0.397875 0.689141i 0.595588 0.803290i \(-0.296919\pi\)
−0.993464 + 0.114149i \(0.963586\pi\)
\(54\) −1.23306 + 4.60186i −0.167799 + 0.626234i
\(55\) 6.02252 + 3.47711i 0.812077 + 0.468853i
\(56\) 0 0
\(57\) 6.36385 6.36385i 0.842913 0.842913i
\(58\) 3.31096 3.31096i 0.434750 0.434750i
\(59\) 2.88250 + 10.7576i 0.375270 + 1.40053i 0.852950 + 0.521992i \(0.174811\pi\)
−0.477681 + 0.878534i \(0.658522\pi\)
\(60\) −0.685740 + 2.55922i −0.0885287 + 0.330393i
\(61\) 9.18124i 1.17554i −0.809029 0.587768i \(-0.800007\pi\)
0.809029 0.587768i \(-0.199993\pi\)
\(62\) −2.85534 + 4.94560i −0.362629 + 0.628092i
\(63\) 0 0
\(64\) 4.35335i 0.544169i
\(65\) 2.73174 + 4.38418i 0.338831 + 0.543791i
\(66\) −5.07551 + 2.93035i −0.624752 + 0.360701i
\(67\) −1.38921 + 1.38921i −0.169719 + 0.169719i −0.786856 0.617137i \(-0.788292\pi\)
0.617137 + 0.786856i \(0.288292\pi\)
\(68\) −3.33337 + 1.92452i −0.404231 + 0.233383i
\(69\) −0.846033 1.46537i −0.101850 0.176410i
\(70\) 0 0
\(71\) −3.19094 0.855010i −0.378695 0.101471i 0.0644501 0.997921i \(-0.479471\pi\)
−0.443145 + 0.896450i \(0.646137\pi\)
\(72\) 1.85383 + 1.85383i 0.218476 + 0.218476i
\(73\) 0.482220 + 0.129211i 0.0564396 + 0.0151230i 0.286928 0.957952i \(-0.407366\pi\)
−0.230489 + 0.973075i \(0.574032\pi\)
\(74\) 2.35552 4.07987i 0.273823 0.474275i
\(75\) 2.11218 + 3.65840i 0.243893 + 0.422436i
\(76\) −2.09705 7.82630i −0.240548 0.897738i
\(77\) 0 0
\(78\) −4.35088 + 0.146360i −0.492640 + 0.0165720i
\(79\) 3.47711 6.02254i 0.391206 0.677588i −0.601403 0.798946i \(-0.705391\pi\)
0.992609 + 0.121357i \(0.0387247\pi\)
\(80\) 0.248748 + 0.248748i 0.0278109 + 0.0278109i
\(81\) −5.26791 −0.585323
\(82\) −4.11322 −0.454230
\(83\) 3.22886 + 3.22886i 0.354413 + 0.354413i 0.861749 0.507335i \(-0.169369\pi\)
−0.507335 + 0.861749i \(0.669369\pi\)
\(84\) 0 0
\(85\) 1.10612 4.12811i 0.119976 0.447756i
\(86\) 2.73370 0.732493i 0.294783 0.0789867i
\(87\) 6.89897 + 3.98312i 0.739648 + 0.427036i
\(88\) 13.4545i 1.43426i
\(89\) 0.237487 + 0.0636346i 0.0251736 + 0.00674525i 0.271384 0.962471i \(-0.412519\pi\)
−0.246210 + 0.969216i \(0.579185\pi\)
\(90\) −1.14155 −0.120330
\(91\) 0 0
\(92\) −1.52333 −0.158819
\(93\) −9.38464 2.51461i −0.973141 0.260752i
\(94\) 4.91825i 0.507279i
\(95\) 7.79107 + 4.49818i 0.799347 + 0.461503i
\(96\) −7.96108 + 2.13316i −0.812524 + 0.217715i
\(97\) 2.43374 9.08284i 0.247109 0.922223i −0.725203 0.688535i \(-0.758254\pi\)
0.972312 0.233688i \(-0.0750793\pi\)
\(98\) 0 0
\(99\) 3.24636 + 3.24636i 0.326272 + 0.326272i
\(100\) 3.80310 0.380310
\(101\) −14.2869 −1.42160 −0.710799 0.703396i \(-0.751666\pi\)
−0.710799 + 0.703396i \(0.751666\pi\)
\(102\) 2.54679 + 2.54679i 0.252170 + 0.252170i
\(103\) 3.72565 6.45301i 0.367099 0.635834i −0.622012 0.783008i \(-0.713684\pi\)
0.989111 + 0.147174i \(0.0470177\pi\)
\(104\) −4.70322 + 8.81822i −0.461189 + 0.864698i
\(105\) 0 0
\(106\) 1.26312 + 4.71402i 0.122685 + 0.457866i
\(107\) 2.34132 + 4.05528i 0.226344 + 0.392039i 0.956722 0.291004i \(-0.0939894\pi\)
−0.730378 + 0.683043i \(0.760656\pi\)
\(108\) −3.64857 + 6.31950i −0.351083 + 0.608094i
\(109\) 4.15534 + 1.11342i 0.398009 + 0.106646i 0.452271 0.891880i \(-0.350614\pi\)
−0.0542619 + 0.998527i \(0.517281\pi\)
\(110\) −4.14253 4.14253i −0.394975 0.394975i
\(111\) 7.74185 + 2.07442i 0.734824 + 0.196895i
\(112\) 0 0
\(113\) 2.02372 + 3.50518i 0.190375 + 0.329740i 0.945375 0.325986i \(-0.105696\pi\)
−0.754999 + 0.655725i \(0.772363\pi\)
\(114\) −6.56597 + 3.79086i −0.614959 + 0.355047i
\(115\) 1.19601 1.19601i 0.111528 0.111528i
\(116\) 6.21101 3.58593i 0.576678 0.332945i
\(117\) 0.992884 + 3.26251i 0.0917921 + 0.301619i
\(118\) 9.38223i 0.863705i
\(119\) 0 0
\(120\) 2.84582 4.92911i 0.259787 0.449964i
\(121\) 12.5612i 1.14192i
\(122\) −2.00184 + 7.47099i −0.181238 + 0.676391i
\(123\) −1.81119 6.75945i −0.163309 0.609479i
\(124\) −6.18495 + 6.18495i −0.555425 + 0.555425i
\(125\) −8.05121 + 8.05121i −0.720122 + 0.720122i
\(126\) 0 0
\(127\) 10.6871 + 6.17021i 0.948328 + 0.547518i 0.892561 0.450926i \(-0.148906\pi\)
0.0557671 + 0.998444i \(0.482240\pi\)
\(128\) −2.02752 + 7.56681i −0.179209 + 0.668817i
\(129\) 2.40748 + 4.16987i 0.211967 + 0.367137i
\(130\) −1.26697 4.16313i −0.111121 0.365131i
\(131\) −5.81415 3.35680i −0.507985 0.293285i 0.224020 0.974584i \(-0.428082\pi\)
−0.732005 + 0.681299i \(0.761415\pi\)
\(132\) −8.67073 + 2.32332i −0.754690 + 0.202219i
\(133\) 0 0
\(134\) 1.43333 0.827533i 0.123821 0.0714879i
\(135\) −2.09702 7.82618i −0.180483 0.673571i
\(136\) 7.98678 2.14005i 0.684860 0.183508i
\(137\) −21.1477 + 5.66652i −1.80677 + 0.484124i −0.995002 0.0998520i \(-0.968163\pi\)
−0.811771 + 0.583976i \(0.801496\pi\)
\(138\) 0.368932 + 1.37687i 0.0314056 + 0.117207i
\(139\) 3.49682 2.01889i 0.296597 0.171240i −0.344316 0.938854i \(-0.611889\pi\)
0.640913 + 0.767614i \(0.278556\pi\)
\(140\) 0 0
\(141\) −8.08239 + 2.16567i −0.680660 + 0.182382i
\(142\) 2.41012 + 1.39148i 0.202253 + 0.116771i
\(143\) −8.23613 + 15.4422i −0.688740 + 1.29134i
\(144\) 0.116121 + 0.201127i 0.00967671 + 0.0167606i
\(145\) −2.06102 + 7.69182i −0.171158 + 0.638771i
\(146\) −0.364221 0.210283i −0.0301432 0.0174032i
\(147\) 0 0
\(148\) 5.10227 5.10227i 0.419404 0.419404i
\(149\) 2.00586 2.00586i 0.164327 0.164327i −0.620154 0.784480i \(-0.712930\pi\)
0.784480 + 0.620154i \(0.212930\pi\)
\(150\) −0.921064 3.43746i −0.0752045 0.280667i
\(151\) 4.33327 16.1720i 0.352636 1.31606i −0.530796 0.847499i \(-0.678107\pi\)
0.883433 0.468558i \(-0.155226\pi\)
\(152\) 17.4055i 1.41178i
\(153\) 1.41072 2.44344i 0.114050 0.197541i
\(154\) 0 0
\(155\) 9.71192i 0.780080i
\(156\) −6.49502 1.50825i −0.520018 0.120757i
\(157\) 2.48434 1.43433i 0.198272 0.114472i −0.397577 0.917569i \(-0.630149\pi\)
0.595849 + 0.803096i \(0.296816\pi\)
\(158\) −4.14254 + 4.14254i −0.329563 + 0.329563i
\(159\) −7.19058 + 4.15148i −0.570250 + 0.329234i
\(160\) −4.11936 7.13494i −0.325664 0.564067i
\(161\) 0 0
\(162\) 4.28662 + 1.14860i 0.336789 + 0.0902422i
\(163\) −17.0408 17.0408i −1.33474 1.33474i −0.901076 0.433660i \(-0.857222\pi\)
−0.433660 0.901076i \(-0.642778\pi\)
\(164\) −6.08540 1.63058i −0.475190 0.127327i
\(165\) 4.98352 8.63170i 0.387966 0.671977i
\(166\) −1.92339 3.33141i −0.149284 0.258567i
\(167\) −2.53997 9.47931i −0.196549 0.733531i −0.991860 0.127330i \(-0.959359\pi\)
0.795311 0.606201i \(-0.207307\pi\)
\(168\) 0 0
\(169\) −10.7961 + 7.24189i −0.830466 + 0.557069i
\(170\) −1.80016 + 3.11796i −0.138066 + 0.239137i
\(171\) 4.19968 + 4.19968i 0.321157 + 0.321157i
\(172\) 4.33481 0.330526
\(173\) −5.23766 −0.398212 −0.199106 0.979978i \(-0.563804\pi\)
−0.199106 + 0.979978i \(0.563804\pi\)
\(174\) −4.74539 4.74539i −0.359747 0.359747i
\(175\) 0 0
\(176\) −0.308475 + 1.15124i −0.0232522 + 0.0867783i
\(177\) 15.4183 4.13131i 1.15891 0.310528i
\(178\) −0.179374 0.103562i −0.0134447 0.00776229i
\(179\) 22.5733i 1.68721i 0.536965 + 0.843605i \(0.319571\pi\)
−0.536965 + 0.843605i \(0.680429\pi\)
\(180\) −1.68890 0.452538i −0.125883 0.0337302i
\(181\) −22.4803 −1.67095 −0.835474 0.549530i \(-0.814807\pi\)
−0.835474 + 0.549530i \(0.814807\pi\)
\(182\) 0 0
\(183\) −13.1589 −0.972733
\(184\) 3.16092 + 0.846966i 0.233026 + 0.0624392i
\(185\) 8.01185i 0.589043i
\(186\) 7.08822 + 4.09239i 0.519733 + 0.300068i
\(187\) 13.9862 3.74759i 1.02277 0.274051i
\(188\) −1.94971 + 7.27641i −0.142197 + 0.530687i
\(189\) 0 0
\(190\) −5.35901 5.35901i −0.388783 0.388783i
\(191\) 24.6708 1.78511 0.892557 0.450935i \(-0.148909\pi\)
0.892557 + 0.450935i \(0.148909\pi\)
\(192\) 6.23938 0.450289
\(193\) −2.43183 2.43183i −0.175047 0.175047i 0.614146 0.789193i \(-0.289501\pi\)
−0.789193 + 0.614146i \(0.789501\pi\)
\(194\) −3.96078 + 6.86027i −0.284367 + 0.492539i
\(195\) 6.28357 3.91524i 0.449976 0.280376i
\(196\) 0 0
\(197\) −1.03338 3.85664i −0.0736255 0.274774i 0.919293 0.393575i \(-0.128762\pi\)
−0.992918 + 0.118801i \(0.962095\pi\)
\(198\) −1.93382 3.34947i −0.137430 0.238036i
\(199\) −0.511550 + 0.886031i −0.0362628 + 0.0628091i −0.883587 0.468267i \(-0.844879\pi\)
0.847324 + 0.531076i \(0.178212\pi\)
\(200\) −7.89145 2.11451i −0.558010 0.149518i
\(201\) 1.99106 + 1.99106i 0.140439 + 0.140439i
\(202\) 11.6256 + 3.11506i 0.817972 + 0.219175i
\(203\) 0 0
\(204\) 2.75830 + 4.77751i 0.193119 + 0.334493i
\(205\) 6.05801 3.49759i 0.423110 0.244282i
\(206\) −4.43864 + 4.43864i −0.309255 + 0.309255i
\(207\) 0.967039 0.558320i 0.0672139 0.0388059i
\(208\) −0.604610 + 0.646704i −0.0419222 + 0.0448408i
\(209\) 30.4800i 2.10835i
\(210\) 0 0
\(211\) 2.70061 4.67759i 0.185918 0.322019i −0.757968 0.652292i \(-0.773808\pi\)
0.943885 + 0.330273i \(0.107141\pi\)
\(212\) 7.47499i 0.513385i
\(213\) −1.22543 + 4.57337i −0.0839652 + 0.313362i
\(214\) −1.02099 3.81037i −0.0697932 0.260472i
\(215\) −3.40337 + 3.40337i −0.232108 + 0.232108i
\(216\) 11.0844 11.0844i 0.754197 0.754197i
\(217\) 0 0
\(218\) −3.13853 1.81203i −0.212568 0.122726i
\(219\) 0.185189 0.691136i 0.0125139 0.0467026i
\(220\) −4.48656 7.77095i −0.302484 0.523917i
\(221\) 10.4767 + 2.43287i 0.704739 + 0.163652i
\(222\) −5.84742 3.37601i −0.392453 0.226583i
\(223\) 16.6138 4.45165i 1.11254 0.298105i 0.344680 0.938720i \(-0.387987\pi\)
0.767862 + 0.640616i \(0.221321\pi\)
\(224\) 0 0
\(225\) −2.41428 + 1.39388i −0.160952 + 0.0929256i
\(226\) −0.882488 3.29349i −0.0587022 0.219080i
\(227\) −9.62310 + 2.57850i −0.638707 + 0.171141i −0.563618 0.826036i \(-0.690591\pi\)
−0.0750896 + 0.997177i \(0.523924\pi\)
\(228\) −11.2169 + 3.00557i −0.742860 + 0.199049i
\(229\) 1.07935 + 4.02820i 0.0713257 + 0.266191i 0.992375 0.123255i \(-0.0393332\pi\)
−0.921049 + 0.389446i \(0.872667\pi\)
\(230\) −1.23399 + 0.712446i −0.0813671 + 0.0469773i
\(231\) 0 0
\(232\) −14.8816 + 3.98752i −0.977026 + 0.261793i
\(233\) −5.47860 3.16307i −0.358915 0.207220i 0.309690 0.950838i \(-0.399775\pi\)
−0.668605 + 0.743618i \(0.733108\pi\)
\(234\) −0.0965870 2.87126i −0.00631409 0.187700i
\(235\) −4.18213 7.24366i −0.272812 0.472524i
\(236\) 3.71933 13.8807i 0.242108 0.903560i
\(237\) −8.63172 4.98353i −0.560691 0.323715i
\(238\) 0 0
\(239\) 7.84175 7.84175i 0.507241 0.507241i −0.406438 0.913679i \(-0.633229\pi\)
0.913679 + 0.406438i \(0.133229\pi\)
\(240\) 0.356515 0.356515i 0.0230129 0.0230129i
\(241\) −3.61892 13.5060i −0.233115 0.869996i −0.978990 0.203910i \(-0.934635\pi\)
0.745875 0.666086i \(-0.232032\pi\)
\(242\) 2.73879 10.2213i 0.176056 0.657050i
\(243\) 9.41578i 0.604022i
\(244\) −5.92334 + 10.2595i −0.379203 + 0.656799i
\(245\) 0 0
\(246\) 5.89523i 0.375866i
\(247\) −10.6547 + 19.9769i −0.677943 + 1.27110i
\(248\) 16.2726 9.39498i 1.03331 0.596582i
\(249\) 4.62772 4.62772i 0.293270 0.293270i
\(250\) 8.30691 4.79600i 0.525375 0.303325i
\(251\) 13.1784 + 22.8256i 0.831813 + 1.44074i 0.896599 + 0.442843i \(0.146030\pi\)
−0.0647865 + 0.997899i \(0.520637\pi\)
\(252\) 0 0
\(253\) 5.53531 + 1.48318i 0.348002 + 0.0932468i
\(254\) −7.35102 7.35102i −0.461244 0.461244i
\(255\) −5.91655 1.58534i −0.370509 0.0992776i
\(256\) 7.65303 13.2554i 0.478314 0.828465i
\(257\) −5.39025 9.33618i −0.336234 0.582375i 0.647487 0.762077i \(-0.275820\pi\)
−0.983721 + 0.179702i \(0.942487\pi\)
\(258\) −1.04984 3.91804i −0.0653599 0.243927i
\(259\) 0 0
\(260\) −0.224087 6.66149i −0.0138973 0.413128i
\(261\) −2.62857 + 4.55282i −0.162704 + 0.281812i
\(262\) 3.99920 + 3.99920i 0.247072 + 0.247072i
\(263\) −15.4912 −0.955231 −0.477616 0.878569i \(-0.658499\pi\)
−0.477616 + 0.878569i \(0.658499\pi\)
\(264\) 19.2835 1.18682
\(265\) −5.86881 5.86881i −0.360518 0.360518i
\(266\) 0 0
\(267\) 0.0912034 0.340376i 0.00558156 0.0208307i
\(268\) 2.44862 0.656106i 0.149573 0.0400781i
\(269\) −22.6324 13.0668i −1.37992 0.796697i −0.387770 0.921756i \(-0.626754\pi\)
−0.992149 + 0.125060i \(0.960088\pi\)
\(270\) 6.82557i 0.415391i
\(271\) 6.35804 + 1.70363i 0.386223 + 0.103488i 0.446706 0.894681i \(-0.352597\pi\)
−0.0604821 + 0.998169i \(0.519264\pi\)
\(272\) 0.732458 0.0444118
\(273\) 0 0
\(274\) 18.4439 1.11424
\(275\) −13.8193 3.70286i −0.833333 0.223291i
\(276\) 2.18330i 0.131419i
\(277\) 25.2681 + 14.5885i 1.51821 + 0.876540i 0.999770 + 0.0214270i \(0.00682096\pi\)
0.518442 + 0.855113i \(0.326512\pi\)
\(278\) −3.28564 + 0.880384i −0.197059 + 0.0528019i
\(279\) 1.65946 6.19317i 0.0993490 0.370776i
\(280\) 0 0
\(281\) 8.85369 + 8.85369i 0.528167 + 0.528167i 0.920025 0.391859i \(-0.128168\pi\)
−0.391859 + 0.920025i \(0.628168\pi\)
\(282\) 7.04902 0.419763
\(283\) 31.9411 1.89870 0.949351 0.314217i \(-0.101742\pi\)
0.949351 + 0.314217i \(0.101742\pi\)
\(284\) 3.01408 + 3.01408i 0.178853 + 0.178853i
\(285\) 6.44696 11.1665i 0.381885 0.661444i
\(286\) 10.0689 10.7699i 0.595386 0.636837i
\(287\) 0 0
\(288\) −1.40773 5.25373i −0.0829514 0.309579i
\(289\) 4.05077 + 7.01614i 0.238281 + 0.412714i
\(290\) 3.35420 5.80964i 0.196965 0.341154i
\(291\) −13.0179 3.48813i −0.763121 0.204478i
\(292\) −0.455494 0.455494i −0.0266558 0.0266558i
\(293\) −12.4822 3.34459i −0.729218 0.195393i −0.124937 0.992165i \(-0.539873\pi\)
−0.604281 + 0.796771i \(0.706540\pi\)
\(294\) 0 0
\(295\) 7.97798 + 13.8183i 0.464496 + 0.804531i
\(296\) −13.4241 + 7.75039i −0.780258 + 0.450482i
\(297\) 19.4106 19.4106i 1.12632 1.12632i
\(298\) −2.06957 + 1.19486i −0.119887 + 0.0692167i
\(299\) 3.10942 + 2.90703i 0.179822 + 0.168118i
\(300\) 5.45075i 0.314699i
\(301\) 0 0
\(302\) −7.05216 + 12.2147i −0.405806 + 0.702877i
\(303\) 20.4765i 1.17634i
\(304\) −0.399060 + 1.48931i −0.0228877 + 0.0854180i
\(305\) −3.40445 12.7056i −0.194938 0.727520i
\(306\) −1.68070 + 1.68070i −0.0960790 + 0.0960790i
\(307\) 5.42520 5.42520i 0.309632 0.309632i −0.535135 0.844767i \(-0.679739\pi\)
0.844767 + 0.535135i \(0.179739\pi\)
\(308\) 0 0
\(309\) −9.24869 5.33974i −0.526140 0.303767i
\(310\) −2.11755 + 7.90282i −0.120269 + 0.448850i
\(311\) −0.241688 0.418616i −0.0137049 0.0237375i 0.859092 0.511822i \(-0.171029\pi\)
−0.872797 + 0.488084i \(0.837696\pi\)
\(312\) 12.6386 + 6.74083i 0.715520 + 0.381624i
\(313\) 0.385666 + 0.222664i 0.0217991 + 0.0125857i 0.510860 0.859664i \(-0.329327\pi\)
−0.489061 + 0.872250i \(0.662660\pi\)
\(314\) −2.33430 + 0.625474i −0.131732 + 0.0352976i
\(315\) 0 0
\(316\) −7.77097 + 4.48657i −0.437151 + 0.252389i
\(317\) −6.42697 23.9858i −0.360975 1.34718i −0.872797 0.488084i \(-0.837696\pi\)
0.511822 0.859091i \(-0.328971\pi\)
\(318\) 6.75631 1.81035i 0.378875 0.101519i
\(319\) −26.0602 + 6.98281i −1.45909 + 0.390962i
\(320\) 1.61424 + 6.02444i 0.0902390 + 0.336777i
\(321\) 5.81218 3.35567i 0.324404 0.187295i
\(322\) 0 0
\(323\) 18.0933 4.84809i 1.00674 0.269755i
\(324\) 5.88660 + 3.39863i 0.327033 + 0.188813i
\(325\) −7.76288 7.25760i −0.430607 0.402579i
\(326\) 10.1510 + 17.5820i 0.562210 + 0.973776i
\(327\) 1.59579 5.95559i 0.0882476 0.329345i
\(328\) 11.7206 + 6.76690i 0.647163 + 0.373640i
\(329\) 0 0
\(330\) −5.93723 + 5.93723i −0.326834 + 0.326834i
\(331\) 10.5285 10.5285i 0.578699 0.578699i −0.355846 0.934545i \(-0.615807\pi\)
0.934545 + 0.355846i \(0.115807\pi\)
\(332\) −1.52495 5.69120i −0.0836926 0.312345i
\(333\) −1.36897 + 5.10906i −0.0750190 + 0.279975i
\(334\) 8.26734i 0.452369i
\(335\) −1.40735 + 2.43760i −0.0768917 + 0.133180i
\(336\) 0 0
\(337\) 7.23643i 0.394194i −0.980384 0.197097i \(-0.936849\pi\)
0.980384 0.197097i \(-0.0631513\pi\)
\(338\) 10.3640 3.53896i 0.563727 0.192494i
\(339\) 5.02375 2.90046i 0.272853 0.157532i
\(340\) −3.89931 + 3.89931i −0.211470 + 0.211470i
\(341\) 28.4960 16.4522i 1.54315 0.890936i
\(342\) −2.50169 4.33306i −0.135276 0.234305i
\(343\) 0 0
\(344\) −8.99474 2.41013i −0.484964 0.129946i
\(345\) −1.71416 1.71416i −0.0922874 0.0922874i
\(346\) 4.26201 + 1.14200i 0.229127 + 0.0613944i
\(347\) 6.28405 10.8843i 0.337345 0.584299i −0.646587 0.762840i \(-0.723804\pi\)
0.983933 + 0.178541i \(0.0571376\pi\)
\(348\) −5.13948 8.90185i −0.275505 0.477189i
\(349\) 4.81774 + 17.9800i 0.257888 + 0.962450i 0.966461 + 0.256813i \(0.0826723\pi\)
−0.708574 + 0.705637i \(0.750661\pi\)
\(350\) 0 0
\(351\) 19.5072 5.93665i 1.04122 0.316875i
\(352\) 13.9566 24.1735i 0.743887 1.28845i
\(353\) −4.42576 4.42576i −0.235559 0.235559i 0.579449 0.815008i \(-0.303268\pi\)
−0.815008 + 0.579449i \(0.803268\pi\)
\(354\) −13.4470 −0.714698
\(355\) −4.73287 −0.251195
\(356\) −0.224325 0.224325i −0.0118892 0.0118892i
\(357\) 0 0
\(358\) 4.92181 18.3684i 0.260126 0.970802i
\(359\) 2.27568 0.609768i 0.120106 0.0321823i −0.198265 0.980148i \(-0.563531\pi\)
0.318371 + 0.947966i \(0.396864\pi\)
\(360\) 3.25285 + 1.87804i 0.171440 + 0.0989812i
\(361\) 20.4307i 1.07530i
\(362\) 18.2928 + 4.90153i 0.961446 + 0.257619i
\(363\) 18.0031 0.944918
\(364\) 0 0
\(365\) 0.715239 0.0374373
\(366\) 10.7077 + 2.86912i 0.559700 + 0.149971i
\(367\) 19.3296i 1.00900i −0.863412 0.504499i \(-0.831677\pi\)
0.863412 0.504499i \(-0.168323\pi\)
\(368\) 0.251047 + 0.144942i 0.0130867 + 0.00755563i
\(369\) 4.46074 1.19525i 0.232217 0.0622224i
\(370\) 1.74687 6.51943i 0.0908157 0.338929i
\(371\) 0 0
\(372\) 8.86450 + 8.86450i 0.459603 + 0.459603i
\(373\) −8.34749 −0.432217 −0.216108 0.976369i \(-0.569336\pi\)
−0.216108 + 0.976369i \(0.569336\pi\)
\(374\) −12.1980 −0.630743
\(375\) 11.5393 + 11.5393i 0.595886 + 0.595886i
\(376\) 8.09130 14.0145i 0.417277 0.722745i
\(377\) −19.5210 4.53311i −1.00538 0.233467i
\(378\) 0 0
\(379\) −4.99923 18.6574i −0.256793 0.958365i −0.967084 0.254457i \(-0.918103\pi\)
0.710291 0.703908i \(-0.248563\pi\)
\(380\) −5.80407 10.0529i −0.297742 0.515705i
\(381\) 8.84337 15.3172i 0.453060 0.784723i
\(382\) −20.0752 5.37912i −1.02713 0.275220i
\(383\) −16.6391 16.6391i −0.850219 0.850219i 0.139941 0.990160i \(-0.455309\pi\)
−0.990160 + 0.139941i \(0.955309\pi\)
\(384\) 10.8450 + 2.90592i 0.553433 + 0.148292i
\(385\) 0 0
\(386\) 1.44861 + 2.50906i 0.0737323 + 0.127708i
\(387\) −2.75181 + 1.58876i −0.139882 + 0.0807612i
\(388\) −8.57943 + 8.57943i −0.435555 + 0.435555i
\(389\) 24.2127 13.9792i 1.22763 0.708775i 0.261100 0.965312i \(-0.415915\pi\)
0.966535 + 0.256536i \(0.0825813\pi\)
\(390\) −5.96675 + 1.81587i −0.302138 + 0.0919502i
\(391\) 3.52174i 0.178102i
\(392\) 0 0
\(393\) −4.81109 + 8.33305i −0.242687 + 0.420347i
\(394\) 3.36355i 0.169453i
\(395\) 2.57866 9.62371i 0.129747 0.484221i
\(396\) −1.53322 5.72205i −0.0770471 0.287544i
\(397\) −8.48258 + 8.48258i −0.425729 + 0.425729i −0.887170 0.461442i \(-0.847332\pi\)
0.461442 + 0.887170i \(0.347332\pi\)
\(398\) 0.609447 0.609447i 0.0305488 0.0305488i
\(399\) 0 0
\(400\) −0.626756 0.361858i −0.0313378 0.0180929i
\(401\) −5.12441 + 19.1246i −0.255901 + 0.955035i 0.711686 + 0.702497i \(0.247932\pi\)
−0.967587 + 0.252537i \(0.918735\pi\)
\(402\) −1.18605 2.05430i −0.0591548 0.102459i
\(403\) 24.4277 0.821727i 1.21683 0.0409332i
\(404\) 15.9648 + 9.21728i 0.794279 + 0.458577i
\(405\) −7.29007 + 1.95337i −0.362246 + 0.0970636i
\(406\) 0 0
\(407\) −23.5078 + 13.5722i −1.16524 + 0.672751i
\(408\) −3.06720 11.4469i −0.151849 0.566708i
\(409\) −17.1952 + 4.60743i −0.850247 + 0.227823i −0.657527 0.753431i \(-0.728398\pi\)
−0.192720 + 0.981254i \(0.561731\pi\)
\(410\) −5.69214 + 1.52521i −0.281115 + 0.0753245i
\(411\) 8.12147 + 30.3097i 0.400602 + 1.49507i
\(412\) −8.32642 + 4.80726i −0.410213 + 0.236837i
\(413\) 0 0
\(414\) −0.908636 + 0.243468i −0.0446570 + 0.0119658i
\(415\) 5.66558 + 3.27102i 0.278112 + 0.160568i
\(416\) 17.5974 10.9648i 0.862785 0.537593i
\(417\) −2.89355 5.01178i −0.141698 0.245428i
\(418\) 6.64576 24.8023i 0.325055 1.21312i
\(419\) −8.03474 4.63886i −0.392523 0.226623i 0.290730 0.956805i \(-0.406102\pi\)
−0.683253 + 0.730182i \(0.739435\pi\)
\(420\) 0 0
\(421\) −13.2205 + 13.2205i −0.644329 + 0.644329i −0.951617 0.307288i \(-0.900579\pi\)
0.307288 + 0.951617i \(0.400579\pi\)
\(422\) −3.21743 + 3.21743i −0.156622 + 0.156622i
\(423\) −1.42918 5.33379i −0.0694893 0.259338i
\(424\) 4.15606 15.5106i 0.201836 0.753262i
\(425\) 8.79225i 0.426487i
\(426\) 1.99432 3.45427i 0.0966253 0.167360i
\(427\) 0 0
\(428\) 6.04208i 0.292055i
\(429\) 22.1323 + 11.8043i 1.06856 + 0.569918i
\(430\) 3.51146 2.02734i 0.169338 0.0977671i
\(431\) 4.19200 4.19200i 0.201921 0.201921i −0.598901 0.800823i \(-0.704396\pi\)
0.800823 + 0.598901i \(0.204396\pi\)
\(432\) 1.20258 0.694307i 0.0578589 0.0334049i
\(433\) −6.32385 10.9532i −0.303905 0.526379i 0.673112 0.739541i \(-0.264957\pi\)
−0.977017 + 0.213162i \(0.931624\pi\)
\(434\) 0 0
\(435\) 11.0242 + 2.95393i 0.528570 + 0.141630i
\(436\) −3.92503 3.92503i −0.187975 0.187975i
\(437\) 7.16078 + 1.91873i 0.342547 + 0.0917851i
\(438\) −0.301386 + 0.522015i −0.0144008 + 0.0249429i
\(439\) 12.8788 + 22.3067i 0.614670 + 1.06464i 0.990442 + 0.137928i \(0.0440442\pi\)
−0.375772 + 0.926712i \(0.622622\pi\)
\(440\) 4.98901 + 18.6192i 0.237842 + 0.887638i
\(441\) 0 0
\(442\) −7.99468 4.26398i −0.380268 0.202817i
\(443\) −8.62206 + 14.9338i −0.409647 + 0.709529i −0.994850 0.101358i \(-0.967681\pi\)
0.585203 + 0.810886i \(0.301015\pi\)
\(444\) −7.31277 7.31277i −0.347049 0.347049i
\(445\) 0.352246 0.0166981
\(446\) −14.4896 −0.686105
\(447\) −2.87487 2.87487i −0.135977 0.135977i
\(448\) 0 0
\(449\) −1.50842 + 5.62952i −0.0711870 + 0.265673i −0.992342 0.123523i \(-0.960581\pi\)
0.921155 + 0.389197i \(0.127247\pi\)
\(450\) 2.26847 0.607835i 0.106937 0.0286536i
\(451\) 20.5248 + 11.8500i 0.966474 + 0.557994i
\(452\) 5.22246i 0.245644i
\(453\) −23.1783 6.21060i −1.08901 0.291800i
\(454\) 8.39274 0.393891
\(455\) 0 0
\(456\) 24.9463 1.16822
\(457\) −21.4480 5.74697i −1.00329 0.268832i −0.280469 0.959863i \(-0.590490\pi\)
−0.722825 + 0.691031i \(0.757157\pi\)
\(458\) 3.51318i 0.164160i
\(459\) −14.6098 8.43498i −0.681928 0.393711i
\(460\) −2.10809 + 0.564860i −0.0982901 + 0.0263367i
\(461\) −5.52093 + 20.6044i −0.257135 + 0.959642i 0.709755 + 0.704449i \(0.248806\pi\)
−0.966890 + 0.255193i \(0.917861\pi\)
\(462\) 0 0
\(463\) −5.14657 5.14657i −0.239181 0.239181i 0.577330 0.816511i \(-0.304095\pi\)
−0.816511 + 0.577330i \(0.804095\pi\)
\(464\) −1.36477 −0.0633581
\(465\) −13.9195 −0.645501
\(466\) 3.76840 + 3.76840i 0.174568 + 0.174568i
\(467\) −14.2554 + 24.6911i −0.659661 + 1.14257i 0.321042 + 0.947065i \(0.395967\pi\)
−0.980703 + 0.195502i \(0.937366\pi\)
\(468\) 0.995337 4.28624i 0.0460095 0.198131i
\(469\) 0 0
\(470\) 1.82371 + 6.80619i 0.0841216 + 0.313946i
\(471\) −2.05574 3.56065i −0.0947235 0.164066i
\(472\) −15.4352 + 26.7346i −0.710465 + 1.23056i
\(473\) −15.7513 4.22055i −0.724245 0.194061i
\(474\) 5.93724 + 5.93724i 0.272707 + 0.272707i
\(475\) −17.8774 4.79022i −0.820270 0.219791i
\(476\) 0 0
\(477\) −2.73967 4.74526i −0.125441 0.217270i
\(478\) −8.09080 + 4.67123i −0.370065 + 0.213657i
\(479\) −23.2801 + 23.2801i −1.06369 + 1.06369i −0.0658656 + 0.997829i \(0.520981\pi\)
−0.997829 + 0.0658656i \(0.979019\pi\)
\(480\) −10.2261 + 5.90402i −0.466754 + 0.269480i
\(481\) −20.1516 + 0.677884i −0.918833 + 0.0309088i
\(482\) 11.7792i 0.536527i
\(483\) 0 0
\(484\) 8.10392 14.0364i 0.368360 0.638018i
\(485\) 13.4719i 0.611726i
\(486\) −2.05298 + 7.66184i −0.0931252 + 0.347548i
\(487\) −3.66858 13.6913i −0.166239 0.620414i −0.997879 0.0650979i \(-0.979264\pi\)
0.831640 0.555316i \(-0.187403\pi\)
\(488\) 17.9952 17.9952i 0.814604 0.814604i
\(489\) −24.4235 + 24.4235i −1.10447 + 1.10447i
\(490\) 0 0
\(491\) −25.7788 14.8834i −1.16338 0.671678i −0.211269 0.977428i \(-0.567759\pi\)
−0.952112 + 0.305750i \(0.901093\pi\)
\(492\) −2.33700 + 8.72182i −0.105360 + 0.393210i
\(493\) 8.29017 + 14.3590i 0.373370 + 0.646696i
\(494\) 13.0257 13.9325i 0.586053 0.626854i
\(495\) 5.69629 + 3.28876i 0.256029 + 0.147819i
\(496\) 1.60777 0.430801i 0.0721911 0.0193435i
\(497\) 0 0
\(498\) −4.77470 + 2.75667i −0.213959 + 0.123529i
\(499\) 4.78371 + 17.8531i 0.214148 + 0.799213i 0.986465 + 0.163974i \(0.0524314\pi\)
−0.772316 + 0.635238i \(0.780902\pi\)
\(500\) 14.1911 3.80249i 0.634644 0.170052i
\(501\) −13.5861 + 3.64039i −0.606982 + 0.162640i
\(502\) −5.74674 21.4471i −0.256490 0.957232i
\(503\) 5.05931 2.92099i 0.225583 0.130241i −0.382949 0.923769i \(-0.625092\pi\)
0.608533 + 0.793529i \(0.291758\pi\)
\(504\) 0 0
\(505\) −19.7711 + 5.29765i −0.879802 + 0.235742i
\(506\) −4.18082 2.41380i −0.185860 0.107306i
\(507\) 10.3793 + 15.4733i 0.460963 + 0.687194i
\(508\) −7.96151 13.7897i −0.353235 0.611821i
\(509\) −7.59031 + 28.3274i −0.336435 + 1.25559i 0.565871 + 0.824494i \(0.308540\pi\)
−0.902306 + 0.431097i \(0.858127\pi\)
\(510\) 4.46878 + 2.58005i 0.197881 + 0.114246i
\(511\) 0 0
\(512\) 1.96096 1.96096i 0.0866629 0.0866629i
\(513\) 25.1107 25.1107i 1.10866 1.10866i
\(514\) 2.35054 + 8.77234i 0.103678 + 0.386931i
\(515\) 2.76298 10.3116i 0.121751 0.454382i
\(516\) 6.21281i 0.273504i
\(517\) 14.1692 24.5418i 0.623162 1.07935i
\(518\) 0 0
\(519\) 7.50681i 0.329513i
\(520\) −3.23877 + 13.9472i −0.142030 + 0.611625i
\(521\) −35.5182 + 20.5064i −1.55608 + 0.898402i −0.558453 + 0.829536i \(0.688605\pi\)
−0.997626 + 0.0688659i \(0.978062\pi\)
\(522\) 3.13161 3.13161i 0.137067 0.137067i
\(523\) −38.4309 + 22.1881i −1.68047 + 0.970217i −0.719114 + 0.694892i \(0.755452\pi\)
−0.961351 + 0.275325i \(0.911215\pi\)
\(524\) 4.33133 + 7.50208i 0.189215 + 0.327730i
\(525\) 0 0
\(526\) 12.6056 + 3.37766i 0.549630 + 0.147273i
\(527\) −14.2987 14.2987i −0.622863 0.622863i
\(528\) 1.65000 + 0.442118i 0.0718072 + 0.0192407i
\(529\) −10.8031 + 18.7115i −0.469700 + 0.813544i
\(530\) 3.49597 + 6.05520i 0.151855 + 0.263021i
\(531\) 2.72636 + 10.1749i 0.118314 + 0.441554i
\(532\) 0 0
\(533\) 9.30979 + 14.9413i 0.403252 + 0.647180i
\(534\) −0.148429 + 0.257086i −0.00642314 + 0.0111252i
\(535\) 4.74379 + 4.74379i 0.205092 + 0.205092i
\(536\) −5.44569 −0.235218
\(537\) 32.3529 1.39613
\(538\) 15.5674 + 15.5674i 0.671160 + 0.671160i
\(539\) 0 0
\(540\) −2.70581 + 10.0982i −0.116440 + 0.434559i
\(541\) 6.62524 1.77523i 0.284841 0.0763230i −0.113570 0.993530i \(-0.536228\pi\)
0.398411 + 0.917207i \(0.369562\pi\)
\(542\) −4.80223 2.77257i −0.206273 0.119092i
\(543\) 32.2196i 1.38268i
\(544\) −16.5696 4.43980i −0.710414 0.190355i
\(545\) 6.16329 0.264006
\(546\) 0 0
\(547\) −16.7670 −0.716904 −0.358452 0.933548i \(-0.616695\pi\)
−0.358452 + 0.933548i \(0.616695\pi\)
\(548\) 27.2872 + 7.31159i 1.16565 + 0.312336i
\(549\) 8.68391i 0.370620i
\(550\) 10.4377 + 6.02620i 0.445065 + 0.256958i
\(551\) −33.7129 + 9.03336i −1.43622 + 0.384834i
\(552\) 1.21390 4.53035i 0.0516672 0.192824i
\(553\) 0 0
\(554\) −17.3804 17.3804i −0.738422 0.738422i
\(555\) 11.4829 0.487421
\(556\) −5.21001 −0.220954
\(557\) 27.8578 + 27.8578i 1.18037 + 1.18037i 0.979648 + 0.200725i \(0.0643298\pi\)
0.200725 + 0.979648i \(0.435670\pi\)
\(558\) −2.70068 + 4.67771i −0.114329 + 0.198023i
\(559\) −8.84819 8.27227i −0.374238 0.349880i
\(560\) 0 0
\(561\) −5.37118 20.0455i −0.226772 0.846323i
\(562\) −5.27402 9.13488i −0.222471 0.385332i
\(563\) −1.05586 + 1.82880i −0.0444991 + 0.0770748i −0.887417 0.460967i \(-0.847503\pi\)
0.842918 + 0.538042i \(0.180836\pi\)
\(564\) 10.4288 + 2.79440i 0.439133 + 0.117665i
\(565\) 4.10029 + 4.10029i 0.172500 + 0.172500i
\(566\) −25.9912 6.96433i −1.09249 0.292733i
\(567\) 0 0
\(568\) −4.57841 7.93005i −0.192106 0.332737i
\(569\) −31.5451 + 18.2126i −1.32244 + 0.763512i −0.984117 0.177518i \(-0.943193\pi\)
−0.338323 + 0.941030i \(0.609860\pi\)
\(570\) −7.68073 + 7.68073i −0.321710 + 0.321710i
\(571\) −13.1672 + 7.60209i −0.551030 + 0.318138i −0.749537 0.661962i \(-0.769724\pi\)
0.198507 + 0.980099i \(0.436391\pi\)
\(572\) 19.1661 11.9422i 0.801374 0.499329i
\(573\) 35.3590i 1.47715i
\(574\) 0 0
\(575\) −1.73985 + 3.01351i −0.0725568 + 0.125672i
\(576\) 4.11754i 0.171564i
\(577\) 2.93081 10.9379i 0.122011 0.455352i −0.877704 0.479202i \(-0.840926\pi\)
0.999716 + 0.0238508i \(0.00759266\pi\)
\(578\) −1.76643 6.59241i −0.0734739 0.274208i
\(579\) −3.48539 + 3.48539i −0.144848 + 0.144848i
\(580\) 7.26551 7.26551i 0.301684 0.301684i
\(581\) 0 0
\(582\) 9.83240 + 5.67674i 0.407566 + 0.235308i
\(583\) 7.27796 27.1617i 0.301422 1.12492i
\(584\) 0.691898 + 1.19840i 0.0286309 + 0.0495902i
\(585\) 2.58377 + 4.14670i 0.106826 + 0.171445i
\(586\) 9.42781 + 5.44315i 0.389459 + 0.224854i
\(587\) −3.32195 + 0.890113i −0.137111 + 0.0367389i −0.326722 0.945120i \(-0.605944\pi\)
0.189611 + 0.981859i \(0.439277\pi\)
\(588\) 0 0
\(589\) 36.8641 21.2835i 1.51896 0.876971i
\(590\) −3.47898 12.9837i −0.143227 0.534532i
\(591\) −5.52747 + 1.48108i −0.227370 + 0.0609236i
\(592\) −1.32633 + 0.355389i −0.0545119 + 0.0146064i
\(593\) −12.0428 44.9445i −0.494540 1.84565i −0.532589 0.846374i \(-0.678781\pi\)
0.0380481 0.999276i \(-0.487886\pi\)
\(594\) −20.0271 + 11.5627i −0.821722 + 0.474422i
\(595\) 0 0
\(596\) −3.53554 + 0.947344i −0.144821 + 0.0388047i
\(597\) 1.26989 + 0.733173i 0.0519732 + 0.0300068i
\(598\) −1.89637 3.04349i −0.0775483 0.124457i
\(599\) −3.80885 6.59712i −0.155625 0.269551i 0.777661 0.628684i \(-0.216406\pi\)
−0.933287 + 0.359133i \(0.883073\pi\)
\(600\) −3.03059 + 11.3103i −0.123723 + 0.461742i
\(601\) −32.3774 18.6931i −1.32070 0.762508i −0.336863 0.941554i \(-0.609366\pi\)
−0.983841 + 0.179045i \(0.942699\pi\)
\(602\) 0 0
\(603\) −1.31396 + 1.31396i −0.0535085 + 0.0535085i
\(604\) −15.2757 + 15.2757i −0.621558 + 0.621558i
\(605\) 4.65774 + 17.3829i 0.189364 + 0.706717i
\(606\) 4.46462 16.6622i 0.181363 0.676855i
\(607\) 18.9804i 0.770390i −0.922835 0.385195i \(-0.874134\pi\)
0.922835 0.385195i \(-0.125866\pi\)
\(608\) 18.0550 31.2722i 0.732226 1.26825i
\(609\) 0 0
\(610\) 11.0811i 0.448661i
\(611\) 17.8656 11.1319i 0.722764 0.450348i
\(612\) −3.15281 + 1.82027i −0.127445 + 0.0735802i
\(613\) −3.10787 + 3.10787i −0.125526 + 0.125526i −0.767079 0.641553i \(-0.778290\pi\)
0.641553 + 0.767079i \(0.278290\pi\)
\(614\) −5.59750 + 3.23172i −0.225897 + 0.130421i
\(615\) −5.01288 8.68256i −0.202139 0.350115i
\(616\) 0 0
\(617\) 23.9468 + 6.41652i 0.964061 + 0.258319i 0.706318 0.707894i \(-0.250355\pi\)
0.257743 + 0.966214i \(0.417021\pi\)
\(618\) 6.36162 + 6.36162i 0.255902 + 0.255902i
\(619\) 23.5480 + 6.30966i 0.946473 + 0.253607i 0.698865 0.715254i \(-0.253689\pi\)
0.247608 + 0.968860i \(0.420355\pi\)
\(620\) −6.26572 + 10.8525i −0.251637 + 0.435849i
\(621\) −3.33831 5.78211i −0.133962 0.232028i
\(622\) 0.105394 + 0.393334i 0.00422590 + 0.0157713i
\(623\) 0 0
\(624\) 0.926879 + 0.866550i 0.0371049 + 0.0346898i
\(625\) −0.787786 + 1.36449i −0.0315115 + 0.0545794i
\(626\) −0.265276 0.265276i −0.0106026 0.0106026i
\(627\) 43.6851 1.74461
\(628\) −3.70149 −0.147705
\(629\) 11.7957 + 11.7957i 0.470327 + 0.470327i
\(630\) 0 0
\(631\) 0.701056 2.61638i 0.0279086 0.104156i −0.950567 0.310521i \(-0.899497\pi\)
0.978475 + 0.206364i \(0.0661633\pi\)
\(632\) 18.6193 4.98902i 0.740635 0.198453i
\(633\) −6.70410 3.87061i −0.266464 0.153843i
\(634\) 20.9191i 0.830803i
\(635\) 17.0775 + 4.57589i 0.677698 + 0.181589i
\(636\) 10.7134 0.424815
\(637\) 0 0
\(638\) 22.7283 0.899822
\(639\) −3.01809 0.808695i −0.119394 0.0319915i
\(640\) 11.2232i 0.443638i
\(641\) −2.71103 1.56522i −0.107079 0.0618223i 0.445504 0.895280i \(-0.353025\pi\)
−0.552583 + 0.833458i \(0.686358\pi\)
\(642\) −5.46117 + 1.46331i −0.215535 + 0.0577524i
\(643\) 0.747638 2.79022i 0.0294840 0.110036i −0.949616 0.313417i \(-0.898526\pi\)
0.979100 + 0.203381i \(0.0651930\pi\)
\(644\) 0 0
\(645\) 4.87783 + 4.87783i 0.192064 + 0.192064i
\(646\) −15.7800 −0.620856
\(647\) 17.7360 0.697275 0.348637 0.937258i \(-0.386645\pi\)
0.348637 + 0.937258i \(0.386645\pi\)
\(648\) −10.3251 10.3251i −0.405607 0.405607i
\(649\) −27.0297 + 46.8169i −1.06101 + 1.83772i
\(650\) 4.73441 + 7.59827i 0.185699 + 0.298029i
\(651\) 0 0
\(652\) 8.04815 + 30.0361i 0.315190 + 1.17631i
\(653\) 11.0978 + 19.2219i 0.434289 + 0.752211i 0.997237 0.0742811i \(-0.0236662\pi\)
−0.562948 + 0.826492i \(0.690333\pi\)
\(654\) −2.59707 + 4.49826i −0.101553 + 0.175896i
\(655\) −9.29071 2.48944i −0.363018 0.0972704i
\(656\) 0.847734 + 0.847734i 0.0330985 + 0.0330985i
\(657\) 0.456099 + 0.122211i 0.0177941 + 0.00476792i
\(658\) 0 0
\(659\) 14.4500 + 25.0282i 0.562893 + 0.974960i 0.997242 + 0.0742153i \(0.0236452\pi\)
−0.434349 + 0.900745i \(0.643021\pi\)
\(660\) −11.1376 + 6.43031i −0.433531 + 0.250299i
\(661\) −2.74283 + 2.74283i −0.106684 + 0.106684i −0.758434 0.651750i \(-0.774035\pi\)
0.651750 + 0.758434i \(0.274035\pi\)
\(662\) −10.8629 + 6.27169i −0.422198 + 0.243756i
\(663\) 3.48687 15.0156i 0.135419 0.583157i
\(664\) 12.6571i 0.491191i
\(665\) 0 0
\(666\) 2.22792 3.85887i 0.0863302 0.149528i
\(667\) 6.56199i 0.254081i
\(668\) −3.27737 + 12.2313i −0.126805 + 0.473243i
\(669\) −6.38027 23.8115i −0.246676 0.920606i
\(670\) 1.67668 1.67668i 0.0647757 0.0647757i
\(671\) 31.5126 31.5126i 1.21653 1.21653i
\(672\) 0 0
\(673\) 14.8015 + 8.54566i 0.570557 + 0.329411i 0.757372 0.652984i \(-0.226483\pi\)
−0.186815 + 0.982395i \(0.559816\pi\)
\(674\) −1.57781 + 5.88845i −0.0607748 + 0.226815i
\(675\) 8.33430 + 14.4354i 0.320787 + 0.555620i
\(676\) 16.7362 1.12726i 0.643699 0.0433561i
\(677\) −26.4773 15.2867i −1.01760 0.587514i −0.104195 0.994557i \(-0.533227\pi\)
−0.913409 + 0.407043i \(0.866560\pi\)
\(678\) −4.72035 + 1.26481i −0.181284 + 0.0485749i
\(679\) 0 0
\(680\) 10.2591 5.92308i 0.393417 0.227140i
\(681\) 3.69560 + 13.7922i 0.141616 + 0.528517i
\(682\) −26.7751 + 7.17436i −1.02527 + 0.274720i
\(683\) −6.12129 + 1.64019i −0.234224 + 0.0627603i −0.374022 0.927420i \(-0.622022\pi\)
0.139797 + 0.990180i \(0.455355\pi\)
\(684\) −1.98346 7.40236i −0.0758394 0.283036i
\(685\) −27.1644 + 15.6834i −1.03790 + 0.599231i
\(686\) 0 0
\(687\) 5.77337 1.54697i 0.220268 0.0590206i
\(688\) −0.714381 0.412448i −0.0272355 0.0157244i
\(689\) 14.2648 15.2579i 0.543445 0.581280i
\(690\) 1.02110 + 1.76860i 0.0388728 + 0.0673296i
\(691\) 1.23455 4.60739i 0.0469643 0.175273i −0.938460 0.345388i \(-0.887747\pi\)
0.985424 + 0.170115i \(0.0544139\pi\)
\(692\) 5.85280 + 3.37912i 0.222490 + 0.128455i
\(693\) 0 0
\(694\) −7.48665 + 7.48665i −0.284189 + 0.284189i
\(695\) 4.09051 4.09051i 0.155162 0.155162i
\(696\) 5.71506 + 21.3289i 0.216629 + 0.808469i
\(697\) 3.76967 14.0686i 0.142786 0.532886i
\(698\) 15.6812i 0.593543i
\(699\) −4.53343 + 7.85213i −0.171470 + 0.296995i
\(700\) 0 0
\(701\) 29.4647i 1.11287i −0.830892 0.556433i \(-0.812169\pi\)
0.830892 0.556433i \(-0.187831\pi\)
\(702\) −17.1678 + 0.577513i −0.647958 + 0.0217968i
\(703\) −30.4110 + 17.5578i −1.14697 + 0.662205i
\(704\) −14.9419 + 14.9419i −0.563145 + 0.563145i
\(705\) −10.3819 + 5.99398i −0.391004 + 0.225746i
\(706\) 2.63637 + 4.56632i 0.0992209 + 0.171856i
\(707\) 0 0
\(708\) −19.8944 5.33069i −0.747677 0.200340i
\(709\) −11.8528 11.8528i −0.445140 0.445140i 0.448595 0.893735i \(-0.351925\pi\)
−0.893735 + 0.448595i \(0.851925\pi\)
\(710\) 3.85124 + 1.03194i 0.144535 + 0.0387279i
\(711\) 3.28876 5.69631i 0.123338 0.213628i
\(712\) 0.340751 + 0.590198i 0.0127702 + 0.0221186i
\(713\) −2.07134 7.73035i −0.0775723 0.289504i
\(714\) 0 0
\(715\) −5.67164 + 24.4239i −0.212107 + 0.913402i
\(716\) 14.5633 25.2245i 0.544258 0.942682i
\(717\) −11.2391 11.2391i −0.419732 0.419732i
\(718\) −1.98473 −0.0740694
\(719\) −17.9279 −0.668598 −0.334299 0.942467i \(-0.608500\pi\)
−0.334299 + 0.942467i \(0.608500\pi\)
\(720\) 0.235274 + 0.235274i 0.00876814 + 0.00876814i
\(721\) 0 0
\(722\) 4.45463 16.6249i 0.165784 0.618715i
\(723\) −19.3573 + 5.18676i −0.719904 + 0.192898i
\(724\) 25.1205 + 14.5033i 0.933597 + 0.539012i
\(725\) 16.3824i 0.608428i
\(726\) −14.6496 3.92534i −0.543696 0.145683i
\(727\) 32.6548 1.21110 0.605549 0.795808i \(-0.292954\pi\)
0.605549 + 0.795808i \(0.292954\pi\)
\(728\) 0 0
\(729\) −29.2988 −1.08514
\(730\) −0.582007 0.155948i −0.0215410 0.00577190i
\(731\) 10.0215i 0.370658i
\(732\) 14.7043 + 8.48955i 0.543488 + 0.313783i
\(733\) 34.2658 9.18149i 1.26564 0.339126i 0.437279 0.899326i \(-0.355942\pi\)
0.828358 + 0.560200i \(0.189276\pi\)
\(734\) −4.21456 + 15.7290i −0.155562 + 0.580567i
\(735\) 0 0
\(736\) −4.80059 4.80059i −0.176952 0.176952i
\(737\) −9.53631 −0.351275
\(738\) −3.89042 −0.143208
\(739\) −10.1559 10.1559i −0.373590 0.373590i 0.495193 0.868783i \(-0.335097\pi\)
−0.868783 + 0.495193i \(0.835097\pi\)
\(740\) 5.16890 8.95280i 0.190013 0.329112i
\(741\) 28.6316 + 15.2707i 1.05181 + 0.560984i
\(742\) 0 0
\(743\) 6.76509 + 25.2477i 0.248187 + 0.926247i 0.971755 + 0.235993i \(0.0758344\pi\)
−0.723568 + 0.690254i \(0.757499\pi\)
\(744\) −13.4652 23.3225i −0.493659 0.855043i
\(745\) 2.03206 3.51962i 0.0744487 0.128949i
\(746\) 6.79255 + 1.82006i 0.248693 + 0.0666370i
\(747\) 3.05396 + 3.05396i 0.111738 + 0.111738i
\(748\) −18.0466 4.83557i −0.659849 0.176806i
\(749\) 0 0
\(750\) −6.87380 11.9058i −0.250996 0.434737i
\(751\) −10.2898 + 5.94079i −0.375479 + 0.216783i −0.675849 0.737040i \(-0.736223\pi\)
0.300371 + 0.953823i \(0.402890\pi\)
\(752\) 1.01365 1.01365i 0.0369640 0.0369640i
\(753\) 32.7146 18.8878i 1.19218 0.688308i
\(754\) 14.8963 + 7.94500i 0.542492 + 0.289340i
\(755\) 23.9866i 0.872963i
\(756\) 0 0
\(757\) 21.1088 36.5615i 0.767212 1.32885i −0.171857 0.985122i \(-0.554977\pi\)
0.939069 0.343729i \(-0.111690\pi\)
\(758\) 16.2720i 0.591024i
\(759\) 2.12575 7.93340i 0.0771598 0.287964i
\(760\) 6.45406 + 24.0869i 0.234114 + 0.873723i
\(761\) 20.3544 20.3544i 0.737845 0.737845i −0.234316 0.972161i \(-0.575285\pi\)
0.972161 + 0.234316i \(0.0752849\pi\)
\(762\) −10.5358 + 10.5358i −0.381670 + 0.381670i
\(763\) 0 0
\(764\) −27.5682 15.9165i −0.997383 0.575840i
\(765\) 1.04621 3.90449i 0.0378257 0.141167i
\(766\) 9.91170 + 17.1676i 0.358124 + 0.620290i
\(767\) −34.0810 + 21.2356i −1.23059 + 0.766772i
\(768\) −18.9982 10.9686i −0.685538 0.395795i
\(769\) −33.9039 + 9.08451i −1.22260 + 0.327596i −0.811696 0.584081i \(-0.801455\pi\)
−0.410909 + 0.911676i \(0.634789\pi\)
\(770\) 0 0
\(771\) −13.3810 + 7.72550i −0.481903 + 0.278227i
\(772\) 1.14852 + 4.28635i 0.0413363 + 0.154269i
\(773\) 29.3542 7.86544i 1.05580 0.282900i 0.311152 0.950360i \(-0.399285\pi\)
0.744646 + 0.667460i \(0.232619\pi\)
\(774\) 2.58562 0.692815i 0.0929382 0.0249027i
\(775\) 5.17124 + 19.2993i 0.185756 + 0.693252i
\(776\) 22.5725 13.0322i 0.810304 0.467829i
\(777\) 0 0
\(778\) −22.7505 + 6.09597i −0.815643 + 0.218551i
\(779\) 26.5520 + 15.3298i 0.951324 + 0.549247i
\(780\) −9.54749 + 0.321170i −0.341855 + 0.0114997i