Properties

Label 1400.2.bh.i.249.2
Level $1400$
Weight $2$
Character 1400.249
Analytic conductor $11.179$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.bh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.32905425960566784.37
Defining polynomial: \(x^{12} + 36 x^{10} + 432 x^{8} + 2040 x^{6} + 3780 x^{4} + 2592 x^{2} + 576\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 249.2
Root \(-0.802567i\) of defining polynomial
Character \(\chi\) \(=\) 1400.249
Dual form 1400.2.bh.i.849.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.23800 - 1.29211i) q^{3} +(2.62958 + 0.292113i) q^{7} +(1.83911 + 3.18543i) q^{9} +O(q^{10})\) \(q+(-2.23800 - 1.29211i) q^{3} +(2.62958 + 0.292113i) q^{7} +(1.83911 + 3.18543i) q^{9} +(-0.839111 + 1.45338i) q^{11} -4.84667i q^{13} +(1.73205 + 1.00000i) q^{17} +(3.42334 + 5.92939i) q^{19} +(-5.50756 - 4.05146i) q^{21} +(-1.95934 + 1.13122i) q^{23} -1.75268i q^{27} -3.32178 q^{29} +(-4.58423 + 7.94011i) q^{31} +(3.75587 - 2.16845i) q^{33} +(2.46529 - 1.42334i) q^{37} +(-6.26245 + 10.8469i) q^{39} +9.52489 q^{41} +6.58423i q^{43} +(10.5682 - 6.10156i) q^{47} +(6.82934 + 1.53627i) q^{49} +(-2.58423 - 4.47601i) q^{51} +(-6.48673 - 3.74511i) q^{53} -17.6933i q^{57} +(4.00000 - 6.92820i) q^{59} +(3.24511 + 5.62070i) q^{61} +(3.90558 + 8.91357i) q^{63} +(-4.98196 - 2.87634i) q^{67} +5.84667 q^{69} +(10.1267 + 5.84667i) q^{73} +(-2.63106 + 3.57666i) q^{77} +(2.84667 + 4.93058i) q^{79} +(3.25268 - 5.63380i) q^{81} -12.5842i q^{83} +(7.43416 + 4.29211i) q^{87} +(-2.92334 - 5.06337i) q^{89} +(1.41577 - 12.7447i) q^{91} +(20.5190 - 11.8467i) q^{93} +2.00000i q^{97} -6.17287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 18q^{9} + O(q^{10}) \) \( 12q + 18q^{9} - 6q^{11} + 6q^{19} - 48q^{29} - 24q^{31} - 36q^{39} + 36q^{41} + 24q^{49} + 48q^{59} + 12q^{61} - 36q^{79} - 54q^{81} + 48q^{91} - 252q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 0
\(3\) −2.23800 1.29211i −1.29211 0.746002i −0.313084 0.949725i \(-0.601362\pi\)
−0.979028 + 0.203724i \(0.934696\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.62958 + 0.292113i 0.993886 + 0.110408i
\(8\) 0 0
\(9\) 1.83911 + 3.18543i 0.613037 + 1.06181i
\(10\) 0 0
\(11\) −0.839111 + 1.45338i −0.253001 + 0.438211i −0.964351 0.264627i \(-0.914751\pi\)
0.711349 + 0.702839i \(0.248084\pi\)
\(12\) 0 0
\(13\) 4.84667i 1.34422i −0.740449 0.672112i \(-0.765387\pi\)
0.740449 0.672112i \(-0.234613\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.73205 + 1.00000i 0.420084 + 0.242536i 0.695113 0.718900i \(-0.255354\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(18\) 0 0
\(19\) 3.42334 + 5.92939i 0.785367 + 1.36030i 0.928779 + 0.370633i \(0.120859\pi\)
−0.143412 + 0.989663i \(0.545808\pi\)
\(20\) 0 0
\(21\) −5.50756 4.05146i −1.20185 0.884101i
\(22\) 0 0
\(23\) −1.95934 + 1.13122i −0.408550 + 0.235876i −0.690166 0.723651i \(-0.742463\pi\)
0.281617 + 0.959527i \(0.409129\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.75268i 0.337303i
\(28\) 0 0
\(29\) −3.32178 −0.616839 −0.308419 0.951250i \(-0.599800\pi\)
−0.308419 + 0.951250i \(0.599800\pi\)
\(30\) 0 0
\(31\) −4.58423 + 7.94011i −0.823351 + 1.42609i 0.0798217 + 0.996809i \(0.474565\pi\)
−0.903173 + 0.429277i \(0.858768\pi\)
\(32\) 0 0
\(33\) 3.75587 2.16845i 0.653813 0.377479i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.46529 1.42334i 0.405291 0.233995i −0.283473 0.958980i \(-0.591487\pi\)
0.688765 + 0.724985i \(0.258153\pi\)
\(38\) 0 0
\(39\) −6.26245 + 10.8469i −1.00279 + 1.73689i
\(40\) 0 0
\(41\) 9.52489 1.48754 0.743769 0.668437i \(-0.233036\pi\)
0.743769 + 0.668437i \(0.233036\pi\)
\(42\) 0 0
\(43\) 6.58423i 1.00408i 0.864843 + 0.502042i \(0.167418\pi\)
−0.864843 + 0.502042i \(0.832582\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.5682 6.10156i 1.54153 0.890004i 0.542789 0.839869i \(-0.317368\pi\)
0.998742 0.0501344i \(-0.0159650\pi\)
\(48\) 0 0
\(49\) 6.82934 + 1.53627i 0.975620 + 0.219466i
\(50\) 0 0
\(51\) −2.58423 4.47601i −0.361864 0.626767i
\(52\) 0 0
\(53\) −6.48673 3.74511i −0.891021 0.514431i −0.0167445 0.999860i \(-0.505330\pi\)
−0.874276 + 0.485429i \(0.838664\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 17.6933i 2.34354i
\(58\) 0 0
\(59\) 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i \(-0.658984\pi\)
0.999709 0.0241347i \(-0.00768307\pi\)
\(60\) 0 0
\(61\) 3.24511 + 5.62070i 0.415494 + 0.719657i 0.995480 0.0949692i \(-0.0302753\pi\)
−0.579986 + 0.814627i \(0.696942\pi\)
\(62\) 0 0
\(63\) 3.90558 + 8.91357i 0.492056 + 1.12300i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.98196 2.87634i −0.608644 0.351401i 0.163791 0.986495i \(-0.447628\pi\)
−0.772434 + 0.635094i \(0.780961\pi\)
\(68\) 0 0
\(69\) 5.84667 0.703857
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 10.1267 + 5.84667i 1.18524 + 0.684301i 0.957222 0.289355i \(-0.0934407\pi\)
0.228022 + 0.973656i \(0.426774\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.63106 + 3.57666i −0.299837 + 0.407599i
\(78\) 0 0
\(79\) 2.84667 + 4.93058i 0.320276 + 0.554734i 0.980545 0.196295i \(-0.0628911\pi\)
−0.660269 + 0.751029i \(0.729558\pi\)
\(80\) 0 0
\(81\) 3.25268 5.63380i 0.361408 0.625978i
\(82\) 0 0
\(83\) 12.5842i 1.38130i −0.723190 0.690649i \(-0.757325\pi\)
0.723190 0.690649i \(-0.242675\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 7.43416 + 4.29211i 0.797025 + 0.460163i
\(88\) 0 0
\(89\) −2.92334 5.06337i −0.309873 0.536716i 0.668461 0.743747i \(-0.266953\pi\)
−0.978334 + 0.207031i \(0.933620\pi\)
\(90\) 0 0
\(91\) 1.41577 12.7447i 0.148414 1.33601i
\(92\) 0 0
\(93\) 20.5190 11.8467i 2.12773 1.22844i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000i 0.203069i 0.994832 + 0.101535i \(0.0323753\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) 0 0
\(99\) −6.17287 −0.620397
\(100\) 0 0
\(101\) 8.50756 14.7355i 0.846534 1.46624i −0.0377483 0.999287i \(-0.512019\pi\)
0.884282 0.466953i \(-0.154648\pi\)
\(102\) 0 0
\(103\) 6.15668 3.55456i 0.606635 0.350241i −0.165012 0.986292i \(-0.552766\pi\)
0.771648 + 0.636050i \(0.219433\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.51786 0.876338i 0.146737 0.0847188i −0.424834 0.905271i \(-0.639667\pi\)
0.571571 + 0.820553i \(0.306334\pi\)
\(108\) 0 0
\(109\) 9.77001 16.9222i 0.935797 1.62085i 0.162591 0.986694i \(-0.448015\pi\)
0.773206 0.634154i \(-0.218652\pi\)
\(110\) 0 0
\(111\) −7.35644 −0.698243
\(112\) 0 0
\(113\) 10.3369i 0.972414i 0.873844 + 0.486207i \(0.161620\pi\)
−0.873844 + 0.486207i \(0.838380\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 15.4387 8.91357i 1.42731 0.824059i
\(118\) 0 0
\(119\) 4.26245 + 3.13553i 0.390738 + 0.287434i
\(120\) 0 0
\(121\) 4.09179 + 7.08718i 0.371981 + 0.644289i
\(122\) 0 0
\(123\) −21.3168 12.3072i −1.92207 1.10971i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 19.1836i 1.70227i 0.524949 + 0.851133i \(0.324084\pi\)
−0.524949 + 0.851133i \(0.675916\pi\)
\(128\) 0 0
\(129\) 8.50756 14.7355i 0.749049 1.29739i
\(130\) 0 0
\(131\) 8.91357 + 15.4387i 0.778782 + 1.34889i 0.932644 + 0.360797i \(0.117495\pi\)
−0.153862 + 0.988092i \(0.549171\pi\)
\(132\) 0 0
\(133\) 7.26987 + 16.5918i 0.630378 + 1.43869i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.46410 + 2.00000i 0.295958 + 0.170872i 0.640626 0.767853i \(-0.278675\pi\)
−0.344668 + 0.938725i \(0.612008\pi\)
\(138\) 0 0
\(139\) 5.16845 0.438382 0.219191 0.975682i \(-0.429658\pi\)
0.219191 + 0.975682i \(0.429658\pi\)
\(140\) 0 0
\(141\) −31.5356 −2.65578
\(142\) 0 0
\(143\) 7.04407 + 4.06689i 0.589054 + 0.340091i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −13.2991 12.2624i −1.09689 1.01139i
\(148\) 0 0
\(149\) 0.398443 + 0.690123i 0.0326417 + 0.0565371i 0.881885 0.471465i \(-0.156275\pi\)
−0.849243 + 0.528002i \(0.822941\pi\)
\(150\) 0 0
\(151\) 8.26245 14.3110i 0.672388 1.16461i −0.304837 0.952405i \(-0.598602\pi\)
0.977225 0.212206i \(-0.0680648\pi\)
\(152\) 0 0
\(153\) 7.35644i 0.594733i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 7.10411 + 4.10156i 0.566969 + 0.327340i 0.755938 0.654643i \(-0.227181\pi\)
−0.188969 + 0.981983i \(0.560514\pi\)
\(158\) 0 0
\(159\) 9.67822 + 16.7632i 0.767533 + 1.32941i
\(160\) 0 0
\(161\) −5.48267 + 2.40229i −0.432095 + 0.189327i
\(162\) 0 0
\(163\) 3.19853 1.84667i 0.250528 0.144643i −0.369478 0.929240i \(-0.620463\pi\)
0.620006 + 0.784597i \(0.287130\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.262447i 0.0203087i 0.999948 + 0.0101544i \(0.00323229\pi\)
−0.999948 + 0.0101544i \(0.996768\pi\)
\(168\) 0 0
\(169\) −10.4902 −0.806941
\(170\) 0 0
\(171\) −12.5918 + 21.8096i −0.962918 + 1.66782i
\(172\) 0 0
\(173\) −16.3217 + 9.42334i −1.24092 + 0.716443i −0.969281 0.245957i \(-0.920898\pi\)
−0.271635 + 0.962400i \(0.587564\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −17.9040 + 10.3369i −1.34575 + 0.776969i
\(178\) 0 0
\(179\) −6.00756 + 10.4054i −0.449026 + 0.777736i −0.998323 0.0578912i \(-0.981562\pi\)
0.549297 + 0.835627i \(0.314896\pi\)
\(180\) 0 0
\(181\) −6.03466 −0.448553 −0.224276 0.974526i \(-0.572002\pi\)
−0.224276 + 0.974526i \(0.572002\pi\)
\(182\) 0 0
\(183\) 16.7722i 1.23984i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.90676 + 1.67822i −0.212564 + 0.122724i
\(188\) 0 0
\(189\) 0.511979 4.60880i 0.0372410 0.335241i
\(190\) 0 0
\(191\) −1.41577 2.45219i −0.102442 0.177434i 0.810248 0.586087i \(-0.199332\pi\)
−0.912690 + 0.408652i \(0.865999\pi\)
\(192\) 0 0
\(193\) −11.2414 6.49023i −0.809174 0.467177i 0.0374948 0.999297i \(-0.488062\pi\)
−0.846669 + 0.532120i \(0.821396\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.84667i 0.345311i 0.984982 + 0.172656i \(0.0552347\pi\)
−0.984982 + 0.172656i \(0.944765\pi\)
\(198\) 0 0
\(199\) −7.69334 + 13.3253i −0.545367 + 0.944603i 0.453217 + 0.891400i \(0.350276\pi\)
−0.998584 + 0.0532026i \(0.983057\pi\)
\(200\) 0 0
\(201\) 7.43311 + 12.8745i 0.524291 + 0.908098i
\(202\) 0 0
\(203\) −8.73487 0.970334i −0.613068 0.0681041i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −7.20687 4.16089i −0.500912 0.289202i
\(208\) 0 0
\(209\) −11.4902 −0.794796
\(210\) 0 0
\(211\) 9.18357 0.632223 0.316112 0.948722i \(-0.397623\pi\)
0.316112 + 0.948722i \(0.397623\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −14.3740 + 19.5400i −0.975769 + 1.32646i
\(218\) 0 0
\(219\) −15.1091 26.1698i −1.02098 1.76839i
\(220\) 0 0
\(221\) 4.84667 8.39468i 0.326022 0.564687i
\(222\) 0 0
\(223\) 12.9805i 0.869236i −0.900615 0.434618i \(-0.856883\pi\)
0.900615 0.434618i \(-0.143117\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −19.0788 11.0151i −1.26630 0.731099i −0.292015 0.956414i \(-0.594326\pi\)
−0.974286 + 0.225314i \(0.927659\pi\)
\(228\) 0 0
\(229\) 2.15333 + 3.72967i 0.142296 + 0.246464i 0.928361 0.371680i \(-0.121218\pi\)
−0.786065 + 0.618144i \(0.787885\pi\)
\(230\) 0 0
\(231\) 10.5098 4.60497i 0.691492 0.302985i
\(232\) 0 0
\(233\) 15.5885 9.00000i 1.02123 0.589610i 0.106773 0.994283i \(-0.465948\pi\)
0.914461 + 0.404674i \(0.132615\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 14.7129i 0.955705i
\(238\) 0 0
\(239\) −10.8618 −0.702591 −0.351296 0.936265i \(-0.614259\pi\)
−0.351296 + 0.936265i \(0.614259\pi\)
\(240\) 0 0
\(241\) −0.101557 + 0.175902i −0.00654187 + 0.0113309i −0.869278 0.494324i \(-0.835416\pi\)
0.862736 + 0.505655i \(0.168749\pi\)
\(242\) 0 0
\(243\) −19.1126 + 11.0347i −1.22607 + 0.707874i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 28.7378 16.5918i 1.82854 1.05571i
\(248\) 0 0
\(249\) −16.2602 + 28.1636i −1.03045 + 1.78479i
\(250\) 0 0
\(251\) 5.03466 0.317785 0.158893 0.987296i \(-0.449208\pi\)
0.158893 + 0.987296i \(0.449208\pi\)
\(252\) 0 0
\(253\) 3.79689i 0.238708i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −20.2535 + 11.6933i −1.26338 + 0.729411i −0.973726 0.227722i \(-0.926872\pi\)
−0.289650 + 0.957133i \(0.593539\pi\)
\(258\) 0 0
\(259\) 6.89844 3.02263i 0.428648 0.187817i
\(260\) 0 0
\(261\) −6.10912 10.5813i −0.378145 0.654966i
\(262\) 0 0
\(263\) −23.4772 13.5546i −1.44767 0.835810i −0.449323 0.893369i \(-0.648335\pi\)
−0.998342 + 0.0575594i \(0.981668\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 15.1091i 0.924663i
\(268\) 0 0
\(269\) 3.24511 5.62070i 0.197858 0.342700i −0.749976 0.661466i \(-0.769935\pi\)
0.947834 + 0.318765i \(0.103268\pi\)
\(270\) 0 0
\(271\) 11.6933 + 20.2535i 0.710320 + 1.23031i 0.964737 + 0.263216i \(0.0847831\pi\)
−0.254417 + 0.967095i \(0.581884\pi\)
\(272\) 0 0
\(273\) −19.6361 + 26.6933i −1.18843 + 1.61555i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 3.17234 + 1.83155i 0.190607 + 0.110047i 0.592267 0.805742i \(-0.298233\pi\)
−0.401660 + 0.915789i \(0.631566\pi\)
\(278\) 0 0
\(279\) −33.7236 −2.01898
\(280\) 0 0
\(281\) 13.8965 0.828993 0.414497 0.910051i \(-0.363958\pi\)
0.414497 + 0.910051i \(0.363958\pi\)
\(282\) 0 0
\(283\) 17.6123 + 10.1685i 1.04694 + 0.604452i 0.921791 0.387686i \(-0.126726\pi\)
0.125150 + 0.992138i \(0.460059\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 25.0464 + 2.78234i 1.47844 + 0.164236i
\(288\) 0 0
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) 0 0
\(291\) 2.58423 4.47601i 0.151490 0.262388i
\(292\) 0 0
\(293\) 18.8467i 1.10103i 0.834824 + 0.550517i \(0.185569\pi\)
−0.834824 + 0.550517i \(0.814431\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 2.54731 + 1.47069i 0.147810 + 0.0853380i
\(298\) 0 0
\(299\) 5.48267 + 9.49626i 0.317071 + 0.549183i
\(300\) 0 0
\(301\) −1.92334 + 17.3137i −0.110859 + 0.997946i
\(302\) 0 0
\(303\) −38.0799 + 21.9855i −2.18763 + 1.26303i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.39623i 0.136760i 0.997659 + 0.0683802i \(0.0217831\pi\)
−0.997659 + 0.0683802i \(0.978217\pi\)
\(308\) 0 0
\(309\) −18.3716 −1.04512
\(310\) 0 0
\(311\) 2.83155 4.90439i 0.160562 0.278102i −0.774508 0.632564i \(-0.782003\pi\)
0.935071 + 0.354462i \(0.115336\pi\)
\(312\) 0 0
\(313\) 25.7414 14.8618i 1.45499 0.840038i 0.456231 0.889861i \(-0.349199\pi\)
0.998758 + 0.0498231i \(0.0158657\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −16.4976 + 9.52489i −0.926597 + 0.534971i −0.885734 0.464193i \(-0.846344\pi\)
−0.0408636 + 0.999165i \(0.513011\pi\)
\(318\) 0 0
\(319\) 2.78734 4.82781i 0.156061 0.270306i
\(320\) 0 0
\(321\) −4.52931 −0.252801
\(322\) 0 0
\(323\) 13.6933i 0.761918i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −43.7307 + 25.2479i −2.41831 + 1.39621i
\(328\) 0 0
\(329\) 29.5722 12.9574i 1.63037 0.714365i
\(330\) 0 0
\(331\) −1.16089 2.01072i −0.0638083 0.110519i 0.832356 0.554241i \(-0.186991\pi\)
−0.896165 + 0.443722i \(0.853658\pi\)
\(332\) 0 0
\(333\) 9.06788 + 5.23534i 0.496917 + 0.286895i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 16.4062i 0.893704i 0.894608 + 0.446852i \(0.147455\pi\)
−0.894608 + 0.446852i \(0.852545\pi\)
\(338\) 0 0
\(339\) 13.3564 23.1340i 0.725422 1.25647i
\(340\) 0 0
\(341\) −7.69334 13.3253i −0.416618 0.721603i
\(342\) 0 0
\(343\) 17.5095 + 6.03466i 0.945425 + 0.325841i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.97006 + 2.29211i 0.213124 + 0.123047i 0.602762 0.797921i \(-0.294067\pi\)
−0.389639 + 0.920968i \(0.627400\pi\)
\(348\) 0 0
\(349\) −12.3716 −0.662235 −0.331117 0.943590i \(-0.607426\pi\)
−0.331117 + 0.943590i \(0.607426\pi\)
\(350\) 0 0
\(351\) −8.49465 −0.453411
\(352\) 0 0
\(353\) −16.7894 9.69334i −0.893608 0.515925i −0.0184869 0.999829i \(-0.505885\pi\)
−0.875121 + 0.483904i \(0.839218\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −5.48792 12.5249i −0.290451 0.662888i
\(358\) 0 0
\(359\) −4.90600 8.49745i −0.258929 0.448478i 0.707026 0.707187i \(-0.250036\pi\)
−0.965955 + 0.258709i \(0.916703\pi\)
\(360\) 0 0
\(361\) −13.9385 + 24.1421i −0.733603 + 1.27064i
\(362\) 0 0
\(363\) 21.1482i 1.10999i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −11.0141 6.35901i −0.574933 0.331937i 0.184184 0.982892i \(-0.441036\pi\)
−0.759117 + 0.650954i \(0.774369\pi\)
\(368\) 0 0
\(369\) 17.5173 + 30.3409i 0.911916 + 1.57948i
\(370\) 0 0
\(371\) −15.9634 11.7429i −0.828776 0.609662i
\(372\) 0 0
\(373\) −14.2082 + 8.20311i −0.735673 + 0.424741i −0.820494 0.571655i \(-0.806302\pi\)
0.0848208 + 0.996396i \(0.472968\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 16.0996i 0.829170i
\(378\) 0 0
\(379\) −14.4707 −0.743309 −0.371655 0.928371i \(-0.621209\pi\)
−0.371655 + 0.928371i \(0.621209\pi\)
\(380\) 0 0
\(381\) 24.7873 42.9329i 1.26989 2.19952i
\(382\) 0 0
\(383\) −3.07401 + 1.77478i −0.157075 + 0.0906871i −0.576477 0.817113i \(-0.695573\pi\)
0.419402 + 0.907800i \(0.362240\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −20.9736 + 12.1091i −1.06615 + 0.615541i
\(388\) 0 0
\(389\) 4.49023 7.77731i 0.227664 0.394325i −0.729452 0.684032i \(-0.760225\pi\)
0.957115 + 0.289707i \(0.0935580\pi\)
\(390\) 0 0
\(391\) −4.52489 −0.228834
\(392\) 0 0
\(393\) 46.0693i 2.32389i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 24.3349 14.0498i 1.22134 0.705139i 0.256133 0.966642i \(-0.417551\pi\)
0.965203 + 0.261503i \(0.0842181\pi\)
\(398\) 0 0
\(399\) 5.16845 46.5260i 0.258746 2.32921i
\(400\) 0 0
\(401\) 13.3467 + 23.1171i 0.666501 + 1.15441i 0.978876 + 0.204455i \(0.0655421\pi\)
−0.312375 + 0.949959i \(0.601125\pi\)
\(402\) 0 0
\(403\) 38.4831 + 22.2182i 1.91698 + 1.10677i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.77735i 0.236804i
\(408\) 0 0
\(409\) 14.0325 24.3049i 0.693860 1.20180i −0.276703 0.960955i \(-0.589242\pi\)
0.970563 0.240846i \(-0.0774248\pi\)
\(410\) 0 0
\(411\) −5.16845 8.95202i −0.254941 0.441571i
\(412\) 0 0
\(413\) 12.5421 17.0498i 0.617157 0.838965i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −11.5670 6.67822i −0.566439 0.327034i
\(418\) 0 0
\(419\) 18.8769 0.922198 0.461099 0.887349i \(-0.347455\pi\)
0.461099 + 0.887349i \(0.347455\pi\)
\(420\) 0 0
\(421\) −28.1836 −1.37358 −0.686792 0.726854i \(-0.740982\pi\)
−0.686792 + 0.726854i \(0.740982\pi\)
\(422\) 0 0
\(423\) 38.8722 + 22.4429i 1.89003 + 1.09121i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 6.89140 + 15.7280i 0.333498 + 0.761132i
\(428\) 0 0
\(429\) −10.5098 18.2035i −0.507416 0.878871i
\(430\) 0 0
\(431\) −1.41577 + 2.45219i −0.0681955 + 0.118118i −0.898107 0.439777i \(-0.855057\pi\)
0.829912 + 0.557895i \(0.188391\pi\)
\(432\) 0 0
\(433\) 2.33690i 0.112304i −0.998422 0.0561522i \(-0.982117\pi\)
0.998422 0.0561522i \(-0.0178832\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −13.4149 7.74511i −0.641723 0.370499i
\(438\) 0 0
\(439\) −3.03466 5.25619i −0.144837 0.250864i 0.784475 0.620160i \(-0.212932\pi\)
−0.929312 + 0.369296i \(0.879599\pi\)
\(440\) 0 0
\(441\) 7.66624 + 24.5798i 0.365059 + 1.17047i
\(442\) 0 0
\(443\) 10.0492 5.80188i 0.477450 0.275656i −0.241903 0.970300i \(-0.577772\pi\)
0.719353 + 0.694645i \(0.244438\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 2.05933i 0.0974031i
\(448\) 0 0
\(449\) −4.13821 −0.195294 −0.0976470 0.995221i \(-0.531132\pi\)
−0.0976470 + 0.995221i \(0.531132\pi\)
\(450\) 0 0
\(451\) −7.99244 + 13.8433i −0.376349 + 0.651856i
\(452\) 0 0
\(453\) −36.9828 + 21.3520i −1.73760 + 1.00321i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 10.9496 6.32178i 0.512203 0.295720i −0.221536 0.975152i \(-0.571107\pi\)
0.733739 + 0.679432i \(0.237774\pi\)
\(458\) 0 0
\(459\) 1.75268 3.03572i 0.0818079 0.141695i
\(460\) 0 0
\(461\) 20.7129 0.964695 0.482348 0.875980i \(-0.339784\pi\)
0.482348 + 0.875980i \(0.339784\pi\)
\(462\) 0 0
\(463\) 16.3811i 0.761295i −0.924720 0.380647i \(-0.875701\pi\)
0.924720 0.380647i \(-0.124299\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.49167 0.861215i 0.0690262 0.0398523i −0.465090 0.885264i \(-0.653978\pi\)
0.534116 + 0.845411i \(0.320645\pi\)
\(468\) 0 0
\(469\) −12.2602 9.01884i −0.566125 0.416452i
\(470\) 0 0
\(471\) −10.5993 18.3586i −0.488392 0.845920i
\(472\) 0 0
\(473\) −9.56940 5.52489i −0.440001 0.254035i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 27.5507i 1.26146i
\(478\) 0 0
\(479\) −0.890881 + 1.54305i −0.0407054 + 0.0705038i −0.885660 0.464334i \(-0.846294\pi\)
0.844955 + 0.534838i \(0.179627\pi\)
\(480\) 0 0
\(481\) −6.89844 11.9485i −0.314542 0.544803i
\(482\) 0 0
\(483\) 15.3743 + 1.70789i 0.699553 + 0.0777116i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −9.54320 5.50977i −0.432444 0.249672i 0.267943 0.963435i \(-0.413656\pi\)
−0.700387 + 0.713763i \(0.746989\pi\)
\(488\) 0 0
\(489\) −9.54443 −0.431614
\(490\) 0 0
\(491\) −20.9311 −0.944608 −0.472304 0.881436i \(-0.656578\pi\)
−0.472304 + 0.881436i \(0.656578\pi\)
\(492\) 0 0
\(493\) −5.75349 3.32178i −0.259124 0.149605i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −3.75268 6.49983i −0.167993 0.290972i 0.769721 0.638380i \(-0.220395\pi\)
−0.937714 + 0.347408i \(0.887062\pi\)
\(500\) 0 0
\(501\) 0.339111 0.587357i 0.0151503 0.0262412i
\(502\) 0 0
\(503\) 20.5842i 0.917805i 0.888487 + 0.458903i \(0.151757\pi\)
−0.888487 + 0.458903i \(0.848243\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 23.4772 + 13.5546i 1.04266 + 0.601979i
\(508\) 0 0
\(509\) 6.82934 + 11.8288i 0.302705 + 0.524301i 0.976748 0.214392i \(-0.0687769\pi\)
−0.674043 + 0.738693i \(0.735444\pi\)
\(510\) 0 0
\(511\) 24.9211 + 18.3324i 1.10245 + 0.810978i
\(512\) 0 0
\(513\) 10.3923 6.00000i 0.458831 0.264906i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 20.4795i 0.900688i
\(518\) 0 0
\(519\) 48.7040 2.13787
\(520\) 0 0
\(521\) 21.0820 36.5151i 0.923620 1.59976i 0.129854 0.991533i \(-0.458549\pi\)
0.793766 0.608224i \(-0.208118\pi\)
\(522\) 0 0
\(523\) −26.5381 + 15.3218i −1.16043 + 0.669975i −0.951407 0.307936i \(-0.900362\pi\)
−0.209023 + 0.977911i \(0.567028\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −15.8802 + 9.16845i −0.691753 + 0.399384i
\(528\) 0 0
\(529\) −8.94067 + 15.4857i −0.388725 + 0.673291i
\(530\) 0 0
\(531\) 29.4258 1.27697
\(532\) 0 0
\(533\) 46.1640i 1.99959i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 26.8899 15.5249i 1.16038 0.669949i
\(538\) 0 0
\(539\) −7.96335 + 8.63654i −0.343006 + 0.372002i
\(540\) 0 0
\(541\) 16.8445 + 29.1755i 0.724200 + 1.25435i 0.959302 + 0.282381i \(0.0911241\pi\)
−0.235102 + 0.971971i \(0.575543\pi\)
\(542\) 0 0
\(543\) 13.5056 + 7.79747i 0.579581 + 0.334621i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 3.03979i 0.129972i 0.997886 + 0.0649861i \(0.0207003\pi\)
−0.997886 + 0.0649861i \(0.979300\pi\)
\(548\) 0 0
\(549\) −11.9363 + 20.6742i −0.509427 + 0.882353i
\(550\) 0 0
\(551\) −11.3716 19.6961i −0.484445 0.839083i
\(552\) 0 0
\(553\) 6.04526 + 13.7969i 0.257070 + 0.586703i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 15.7305 + 9.08202i 0.666523 + 0.384817i 0.794758 0.606926i \(-0.207598\pi\)
−0.128235 + 0.991744i \(0.540931\pi\)
\(558\) 0 0
\(559\) 31.9116 1.34972
\(560\) 0 0
\(561\) 8.67380 0.366208
\(562\) 0 0
\(563\) 32.0347 + 18.4952i 1.35010 + 0.779481i 0.988263 0.152760i \(-0.0488163\pi\)
0.361837 + 0.932241i \(0.382150\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 10.1989 13.8644i 0.428312 0.582248i
\(568\) 0 0
\(569\) 16.3047 + 28.2405i 0.683527 + 1.18390i 0.973897 + 0.226990i \(0.0728884\pi\)
−0.290370 + 0.956915i \(0.593778\pi\)
\(570\) 0 0
\(571\) −20.2182 + 35.0190i −0.846107 + 1.46550i 0.0385496 + 0.999257i \(0.487726\pi\)
−0.884656 + 0.466243i \(0.845607\pi\)
\(572\) 0 0
\(573\) 7.31736i 0.305687i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −32.9352 19.0151i −1.37111 0.791610i −0.380041 0.924970i \(-0.624090\pi\)
−0.991068 + 0.133360i \(0.957423\pi\)
\(578\) 0 0
\(579\) 16.7722 + 29.0503i 0.697030 + 1.20729i
\(580\) 0 0
\(581\) 3.67601 33.0912i 0.152507 1.37285i
\(582\) 0 0
\(583\) 10.8862 6.28513i 0.450859 0.260304i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 34.0302i 1.40458i −0.711892 0.702289i \(-0.752161\pi\)
0.711892 0.702289i \(-0.247839\pi\)
\(588\) 0 0
\(589\) −62.7734 −2.58653
\(590\) 0 0
\(591\) 6.26245 10.8469i 0.257603 0.446181i
\(592\) 0 0
\(593\) −29.2055 + 16.8618i −1.19933 + 0.692431i −0.960405 0.278608i \(-0.910127\pi\)
−0.238921 + 0.971039i \(0.576794\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 34.4355 19.8813i 1.40935 0.813689i
\(598\) 0 0
\(599\) 3.15333 5.46172i 0.128841 0.223160i −0.794387 0.607413i \(-0.792207\pi\)
0.923228 + 0.384253i \(0.125541\pi\)
\(600\) 0 0
\(601\) −11.2871 −0.460411 −0.230206 0.973142i \(-0.573940\pi\)
−0.230206 + 0.973142i \(0.573940\pi\)
\(602\) 0 0
\(603\) 21.1596i 0.861686i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 13.3897 7.73057i 0.543473 0.313774i −0.203012 0.979176i \(-0.565073\pi\)
0.746485 + 0.665402i \(0.231740\pi\)
\(608\) 0 0
\(609\) 18.2949 + 13.4580i 0.741347 + 0.545348i
\(610\) 0 0
\(611\) −29.5722 51.2206i −1.19637 2.07217i
\(612\) 0 0
\(613\) 19.1946 + 11.0820i 0.775263 + 0.447598i 0.834749 0.550631i \(-0.185613\pi\)
−0.0594857 + 0.998229i \(0.518946\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.9805i 0.603091i 0.953452 + 0.301545i \(0.0975024\pi\)
−0.953452 + 0.301545i \(0.902498\pi\)
\(618\) 0 0
\(619\) 11.8196 20.4721i 0.475069 0.822843i −0.524524 0.851396i \(-0.675757\pi\)
0.999592 + 0.0285529i \(0.00908990\pi\)
\(620\) 0 0
\(621\) 1.98267 + 3.43408i 0.0795617 + 0.137805i
\(622\) 0 0
\(623\) −6.20806 14.1685i −0.248721 0.567647i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 25.7152 + 14.8467i 1.02697 + 0.592919i
\(628\) 0 0
\(629\) 5.69334 0.227008
\(630\) 0 0
\(631\) −13.7818 −0.548643 −0.274322 0.961638i \(-0.588453\pi\)
−0.274322 + 0.961638i \(0.588453\pi\)
\(632\) 0 0
\(633\) −20.5529 11.8662i −0.816904 0.471640i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 7.44577 33.0996i 0.295012 1.31145i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −21.9309 + 37.9854i −0.866218 + 1.50033i −0.000386062 1.00000i \(0.500123\pi\)
−0.865832 + 0.500334i \(0.833210\pi\)
\(642\) 0 0
\(643\) 7.04979i 0.278016i 0.990291 + 0.139008i \(0.0443914\pi\)
−0.990291 + 0.139008i \(0.955609\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −21.2009 12.2403i −0.833493 0.481217i 0.0215540 0.999768i \(-0.493139\pi\)
−0.855047 + 0.518550i \(0.826472\pi\)
\(648\) 0 0
\(649\) 6.71288 + 11.6271i 0.263504 + 0.456402i
\(650\) 0 0
\(651\) 57.4169 25.1579i 2.25035 0.986014i
\(652\) 0 0
\(653\) 0.707046 0.408213i 0.0276688 0.0159746i −0.486102 0.873902i \(-0.661582\pi\)
0.513771 + 0.857928i \(0.328248\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 43.0107i 1.67801i
\(658\) 0 0
\(659\) −21.2871 −0.829228 −0.414614 0.909997i \(-0.636083\pi\)
−0.414614 + 0.909997i \(0.636083\pi\)
\(660\) 0 0
\(661\) −12.9731 + 22.4701i −0.504596 + 0.873986i 0.495390 + 0.868671i \(0.335025\pi\)
−0.999986 + 0.00531513i \(0.998308\pi\)
\(662\) 0 0
\(663\) −21.6938 + 12.5249i −0.842515 + 0.486427i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.50848 3.75767i 0.252009 0.145498i
\(668\) 0 0
\(669\) −16.7722 + 29.0503i −0.648451 + 1.12315i
\(670\) 0 0
\(671\) −10.8920 −0.420483
\(672\) 0 0
\(673\) 22.0693i 0.850710i 0.905027 + 0.425355i \(0.139851\pi\)
−0.905027 + 0.425355i \(0.860149\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −4.75468 + 2.74511i −0.182737 + 0.105503i −0.588578 0.808440i \(-0.700312\pi\)
0.405841 + 0.913944i \(0.366979\pi\)
\(678\) 0 0
\(679\) −0.584225 + 5.25915i −0.0224205 + 0.201828i
\(680\) 0 0
\(681\) 28.4656 + 49.3038i 1.09080 + 1.88933i
\(682\) 0 0
\(683\) −16.6517 9.61389i −0.637161 0.367865i 0.146359 0.989232i \(-0.453245\pi\)
−0.783520 + 0.621366i \(0.786578\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 11.1294i 0.424612i
\(688\) 0 0
\(689\) −18.1513 + 31.4390i −0.691511 + 1.19773i
\(690\) 0 0
\(691\) −7.10912 12.3134i −0.270444 0.468422i 0.698532 0.715579i \(-0.253837\pi\)
−0.968975 + 0.247157i \(0.920504\pi\)
\(692\) 0 0
\(693\) −16.2320 1.80317i −0.616604 0.0684969i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 16.4976 + 9.52489i 0.624891 + 0.360781i
\(698\) 0 0
\(699\) −46.5161 −1.75940
\(700\) 0 0
\(701\) 14.1533 0.534564 0.267282 0.963618i \(-0.413875\pi\)
0.267282 + 0.963618i \(0.413875\pi\)
\(702\) 0 0
\(703\) 16.8790 + 9.74511i 0.636605 + 0.367544i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 26.6757 36.2630i 1.00324 1.36381i
\(708\) 0 0
\(709\) 8.52268 + 14.7617i 0.320076 + 0.554388i 0.980503 0.196502i \(-0.0629582\pi\)
−0.660427 + 0.750890i \(0.729625\pi\)
\(710\) 0 0
\(711\) −10.4707 + 18.1358i −0.392682 + 0.680144i
\(712\) 0 0
\(713\) 20.7431i 0.776836i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 24.3088 + 14.0347i 0.907827 + 0.524134i
\(718\) 0 0
\(719\) −5.75268 9.96393i −0.214539 0.371592i 0.738591 0.674154i \(-0.235491\pi\)
−0.953130 + 0.302562i \(0.902158\pi\)
\(720\) 0 0
\(721\) 17.2278 7.54854i 0.641596 0.281122i
\(722\) 0 0
\(723\) 0.454571 0.262447i 0.0169057 0.00976049i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 16.4114i 0.608664i −0.952566 0.304332i \(-0.901567\pi\)
0.952566 0.304332i \(-0.0984331\pi\)
\(728\) 0 0
\(729\) 37.5161 1.38948
\(730\) 0 0
\(731\) −6.58423 + 11.4042i −0.243526 + 0.421800i
\(732\) 0 0
\(733\) −7.89317 + 4.55712i −0.291541 + 0.168321i −0.638637 0.769509i \(-0.720501\pi\)
0.347096 + 0.937830i \(0.387168\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.36084 4.82713i 0.307975 0.177810i
\(738\) 0 0
\(739\) −17.4978 + 30.3071i −0.643667 + 1.11486i 0.340941 + 0.940085i \(0.389254\pi\)
−0.984608 + 0.174779i \(0.944079\pi\)
\(740\) 0 0
\(741\) −85.7538 −3.15025
\(742\) 0 0
\(743\) 43.5305i 1.59698i −0.602009 0.798489i \(-0.705633\pi\)
0.602009 0.798489i \(-0.294367\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 40.0862 23.1438i 1.46668 0.846787i
\(748\) 0 0
\(749\) 4.24732 1.86101i 0.155194 0.0679999i
\(750\) 0 0
\(751\) −3.15333 5.46172i −0.115067 0.199301i 0.802740 0.596329i \(-0.203375\pi\)
−0.917806 + 0.397028i \(0.870041\pi\)
\(752\) 0 0
\(753\) −11.2676 6.50535i −0.410614 0.237068i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 24.3369i 0.884540i −0.896882 0.442270i \(-0.854173\pi\)
0.896882 0.442270i \(-0.145827\pi\)
\(758\) 0 0
\(759\) −4.90600 + 8.49745i −0.178077 + 0.308438i
\(760\) 0 0
\(761\) 14.1016 + 24.4246i 0.511181 + 0.885392i 0.999916 + 0.0129592i \(0.00412517\pi\)
−0.488735 + 0.872432i \(0.662541\pi\)
\(762\) 0 0
\(763\) 30.6342 41.6441i 1.10903 1.50762i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −33.5787 19.3867i −1.21246 0.700013i
\(768\) 0 0
\(769\) 41.8965 1.51082 0.755412 0.655250i \(-0.227437\pi\)
0.755412 + 0.655250i \(0.227437\pi\)
\(770\) 0 0
\(771\) 60.4365 2.17657
\(772\) 0 0
\(773\) −34.5175 19.9287i −1.24151 0.716785i −0.272107 0.962267i \(-0.587720\pi\)
−0.969401 + 0.245482i \(0.921054\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −19.3443 2.14891i −0.693974 0.0770917i
\(778\) 0 0
\(779\) 32.6069 + 56.4768i 1.16826 + 2.02349i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 5.82200i 0.208061i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 30.5944 + 17.6637i 1.09057 + 0.629642i 0.933729 0.357981i \(-0.116535\pi\)
0.156843 + 0.987623i \(0.449868\pi\)
\(788\) 0 0
\(789\) 35.0280 + 60.6703i 1.24703 + 2.15992i
\(790\) 0 0
\(791\) −3.01954 + 27.1817i −0.107363 + 0.966469i
\(792\) 0 0
\(793\) 27.2417 15.7280i 0.967381 0.558518i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 29.6933i 1.05179i −0.850549 0.525896i \(-0.823730\pi\)
0.850549 0.525896i \(-0.176270\pi\)
\(798\) 0 0
\(799\) 24.4062 0.863430
\(800\) 0 0