Properties

Label 45.3.g.a.37.1
Level $45$
Weight $3$
Character 45.37
Analytic conductor $1.226$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,3,Mod(28,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.28");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 45.g (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.22616118962\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.1
Root \(-1.58114 - 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 45.37
Dual form 45.3.g.a.28.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.58114 - 1.58114i) q^{2} +1.00000i q^{4} +(-1.58114 - 4.74342i) q^{5} +(-5.00000 - 5.00000i) q^{7} +(-4.74342 + 4.74342i) q^{8} +O(q^{10})\) \(q+(-1.58114 - 1.58114i) q^{2} +1.00000i q^{4} +(-1.58114 - 4.74342i) q^{5} +(-5.00000 - 5.00000i) q^{7} +(-4.74342 + 4.74342i) q^{8} +(-5.00000 + 10.0000i) q^{10} +15.8114 q^{11} +(10.0000 - 10.0000i) q^{13} +15.8114i q^{14} +19.0000 q^{16} +(3.16228 + 3.16228i) q^{17} +18.0000i q^{19} +(4.74342 - 1.58114i) q^{20} +(-25.0000 - 25.0000i) q^{22} +(3.16228 - 3.16228i) q^{23} +(-20.0000 + 15.0000i) q^{25} -31.6228 q^{26} +(5.00000 - 5.00000i) q^{28} -47.4342i q^{29} +8.00000 q^{31} +(-11.0680 - 11.0680i) q^{32} -10.0000i q^{34} +(-15.8114 + 31.6228i) q^{35} +(10.0000 + 10.0000i) q^{37} +(28.4605 - 28.4605i) q^{38} +(30.0000 + 15.0000i) q^{40} -31.6228 q^{41} +(10.0000 - 10.0000i) q^{43} +15.8114i q^{44} -10.0000 q^{46} +(41.1096 + 41.1096i) q^{47} +1.00000i q^{49} +(55.3399 + 7.90569i) q^{50} +(10.0000 + 10.0000i) q^{52} +(-25.2982 + 25.2982i) q^{53} +(-25.0000 - 75.0000i) q^{55} +47.4342 q^{56} +(-75.0000 + 75.0000i) q^{58} +47.4342i q^{59} -58.0000 q^{61} +(-12.6491 - 12.6491i) q^{62} -41.0000i q^{64} +(-63.2456 - 31.6228i) q^{65} +(70.0000 + 70.0000i) q^{67} +(-3.16228 + 3.16228i) q^{68} +(75.0000 - 25.0000i) q^{70} +63.2456 q^{71} +(55.0000 - 55.0000i) q^{73} -31.6228i q^{74} -18.0000 q^{76} +(-79.0569 - 79.0569i) q^{77} +12.0000i q^{79} +(-30.0416 - 90.1249i) q^{80} +(50.0000 + 50.0000i) q^{82} +(-53.7587 + 53.7587i) q^{83} +(10.0000 - 20.0000i) q^{85} -31.6228 q^{86} +(-75.0000 + 75.0000i) q^{88} -100.000 q^{91} +(3.16228 + 3.16228i) q^{92} -130.000i q^{94} +(85.3815 - 28.4605i) q^{95} +(-5.00000 - 5.00000i) q^{97} +(1.58114 - 1.58114i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 20 q^{7} - 20 q^{10} + 40 q^{13} + 76 q^{16} - 100 q^{22} - 80 q^{25} + 20 q^{28} + 32 q^{31} + 40 q^{37} + 120 q^{40} + 40 q^{43} - 40 q^{46} + 40 q^{52} - 100 q^{55} - 300 q^{58} - 232 q^{61} + 280 q^{67} + 300 q^{70} + 220 q^{73} - 72 q^{76} + 200 q^{82} + 40 q^{85} - 300 q^{88} - 400 q^{91} - 20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58114 1.58114i −0.790569 0.790569i 0.191017 0.981587i \(-0.438821\pi\)
−0.981587 + 0.191017i \(0.938821\pi\)
\(3\) 0 0
\(4\) 1.00000i 0.250000i
\(5\) −1.58114 4.74342i −0.316228 0.948683i
\(6\) 0 0
\(7\) −5.00000 5.00000i −0.714286 0.714286i 0.253143 0.967429i \(-0.418536\pi\)
−0.967429 + 0.253143i \(0.918536\pi\)
\(8\) −4.74342 + 4.74342i −0.592927 + 0.592927i
\(9\) 0 0
\(10\) −5.00000 + 10.0000i −0.500000 + 1.00000i
\(11\) 15.8114 1.43740 0.718699 0.695321i \(-0.244738\pi\)
0.718699 + 0.695321i \(0.244738\pi\)
\(12\) 0 0
\(13\) 10.0000 10.0000i 0.769231 0.769231i −0.208740 0.977971i \(-0.566936\pi\)
0.977971 + 0.208740i \(0.0669363\pi\)
\(14\) 15.8114i 1.12938i
\(15\) 0 0
\(16\) 19.0000 1.18750
\(17\) 3.16228 + 3.16228i 0.186016 + 0.186016i 0.793971 0.607955i \(-0.208010\pi\)
−0.607955 + 0.793971i \(0.708010\pi\)
\(18\) 0 0
\(19\) 18.0000i 0.947368i 0.880695 + 0.473684i \(0.157076\pi\)
−0.880695 + 0.473684i \(0.842924\pi\)
\(20\) 4.74342 1.58114i 0.237171 0.0790569i
\(21\) 0 0
\(22\) −25.0000 25.0000i −1.13636 1.13636i
\(23\) 3.16228 3.16228i 0.137490 0.137490i −0.635012 0.772502i \(-0.719005\pi\)
0.772502 + 0.635012i \(0.219005\pi\)
\(24\) 0 0
\(25\) −20.0000 + 15.0000i −0.800000 + 0.600000i
\(26\) −31.6228 −1.21626
\(27\) 0 0
\(28\) 5.00000 5.00000i 0.178571 0.178571i
\(29\) 47.4342i 1.63566i −0.575459 0.817830i \(-0.695177\pi\)
0.575459 0.817830i \(-0.304823\pi\)
\(30\) 0 0
\(31\) 8.00000 0.258065 0.129032 0.991640i \(-0.458813\pi\)
0.129032 + 0.991640i \(0.458813\pi\)
\(32\) −11.0680 11.0680i −0.345874 0.345874i
\(33\) 0 0
\(34\) 10.0000i 0.294118i
\(35\) −15.8114 + 31.6228i −0.451754 + 0.903508i
\(36\) 0 0
\(37\) 10.0000 + 10.0000i 0.270270 + 0.270270i 0.829209 0.558939i \(-0.188791\pi\)
−0.558939 + 0.829209i \(0.688791\pi\)
\(38\) 28.4605 28.4605i 0.748960 0.748960i
\(39\) 0 0
\(40\) 30.0000 + 15.0000i 0.750000 + 0.375000i
\(41\) −31.6228 −0.771287 −0.385644 0.922648i \(-0.626021\pi\)
−0.385644 + 0.922648i \(0.626021\pi\)
\(42\) 0 0
\(43\) 10.0000 10.0000i 0.232558 0.232558i −0.581202 0.813760i \(-0.697417\pi\)
0.813760 + 0.581202i \(0.197417\pi\)
\(44\) 15.8114i 0.359350i
\(45\) 0 0
\(46\) −10.0000 −0.217391
\(47\) 41.1096 + 41.1096i 0.874673 + 0.874673i 0.992977 0.118305i \(-0.0377460\pi\)
−0.118305 + 0.992977i \(0.537746\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.0204082i
\(50\) 55.3399 + 7.90569i 1.10680 + 0.158114i
\(51\) 0 0
\(52\) 10.0000 + 10.0000i 0.192308 + 0.192308i
\(53\) −25.2982 + 25.2982i −0.477325 + 0.477325i −0.904275 0.426950i \(-0.859588\pi\)
0.426950 + 0.904275i \(0.359588\pi\)
\(54\) 0 0
\(55\) −25.0000 75.0000i −0.454545 1.36364i
\(56\) 47.4342 0.847039
\(57\) 0 0
\(58\) −75.0000 + 75.0000i −1.29310 + 1.29310i
\(59\) 47.4342i 0.803969i 0.915646 + 0.401984i \(0.131679\pi\)
−0.915646 + 0.401984i \(0.868321\pi\)
\(60\) 0 0
\(61\) −58.0000 −0.950820 −0.475410 0.879764i \(-0.657700\pi\)
−0.475410 + 0.879764i \(0.657700\pi\)
\(62\) −12.6491 12.6491i −0.204018 0.204018i
\(63\) 0 0
\(64\) 41.0000i 0.640625i
\(65\) −63.2456 31.6228i −0.973009 0.486504i
\(66\) 0 0
\(67\) 70.0000 + 70.0000i 1.04478 + 1.04478i 0.998949 + 0.0458267i \(0.0145922\pi\)
0.0458267 + 0.998949i \(0.485408\pi\)
\(68\) −3.16228 + 3.16228i −0.0465041 + 0.0465041i
\(69\) 0 0
\(70\) 75.0000 25.0000i 1.07143 0.357143i
\(71\) 63.2456 0.890782 0.445391 0.895336i \(-0.353065\pi\)
0.445391 + 0.895336i \(0.353065\pi\)
\(72\) 0 0
\(73\) 55.0000 55.0000i 0.753425 0.753425i −0.221692 0.975117i \(-0.571158\pi\)
0.975117 + 0.221692i \(0.0711580\pi\)
\(74\) 31.6228i 0.427335i
\(75\) 0 0
\(76\) −18.0000 −0.236842
\(77\) −79.0569 79.0569i −1.02671 1.02671i
\(78\) 0 0
\(79\) 12.0000i 0.151899i 0.997112 + 0.0759494i \(0.0241987\pi\)
−0.997112 + 0.0759494i \(0.975801\pi\)
\(80\) −30.0416 90.1249i −0.375520 1.12656i
\(81\) 0 0
\(82\) 50.0000 + 50.0000i 0.609756 + 0.609756i
\(83\) −53.7587 + 53.7587i −0.647695 + 0.647695i −0.952436 0.304740i \(-0.901430\pi\)
0.304740 + 0.952436i \(0.401430\pi\)
\(84\) 0 0
\(85\) 10.0000 20.0000i 0.117647 0.235294i
\(86\) −31.6228 −0.367707
\(87\) 0 0
\(88\) −75.0000 + 75.0000i −0.852273 + 0.852273i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −100.000 −1.09890
\(92\) 3.16228 + 3.16228i 0.0343726 + 0.0343726i
\(93\) 0 0
\(94\) 130.000i 1.38298i
\(95\) 85.3815 28.4605i 0.898753 0.299584i
\(96\) 0 0
\(97\) −5.00000 5.00000i −0.0515464 0.0515464i 0.680864 0.732410i \(-0.261605\pi\)
−0.732410 + 0.680864i \(0.761605\pi\)
\(98\) 1.58114 1.58114i 0.0161341 0.0161341i
\(99\) 0 0
\(100\) −15.0000 20.0000i −0.150000 0.200000i
\(101\) 15.8114 0.156548 0.0782742 0.996932i \(-0.475059\pi\)
0.0782742 + 0.996932i \(0.475059\pi\)
\(102\) 0 0
\(103\) −35.0000 + 35.0000i −0.339806 + 0.339806i −0.856294 0.516488i \(-0.827239\pi\)
0.516488 + 0.856294i \(0.327239\pi\)
\(104\) 94.8683i 0.912195i
\(105\) 0 0
\(106\) 80.0000 0.754717
\(107\) 60.0833 + 60.0833i 0.561526 + 0.561526i 0.929741 0.368215i \(-0.120031\pi\)
−0.368215 + 0.929741i \(0.620031\pi\)
\(108\) 0 0
\(109\) 162.000i 1.48624i 0.669159 + 0.743119i \(0.266655\pi\)
−0.669159 + 0.743119i \(0.733345\pi\)
\(110\) −79.0569 + 158.114i −0.718699 + 1.43740i
\(111\) 0 0
\(112\) −95.0000 95.0000i −0.848214 0.848214i
\(113\) 117.004 117.004i 1.03544 1.03544i 0.0360874 0.999349i \(-0.488511\pi\)
0.999349 0.0360874i \(-0.0114895\pi\)
\(114\) 0 0
\(115\) −20.0000 10.0000i −0.173913 0.0869565i
\(116\) 47.4342 0.408915
\(117\) 0 0
\(118\) 75.0000 75.0000i 0.635593 0.635593i
\(119\) 31.6228i 0.265738i
\(120\) 0 0
\(121\) 129.000 1.06612
\(122\) 91.7061 + 91.7061i 0.751689 + 0.751689i
\(123\) 0 0
\(124\) 8.00000i 0.0645161i
\(125\) 102.774 + 71.1512i 0.822192 + 0.569210i
\(126\) 0 0
\(127\) 55.0000 + 55.0000i 0.433071 + 0.433071i 0.889672 0.456601i \(-0.150933\pi\)
−0.456601 + 0.889672i \(0.650933\pi\)
\(128\) −109.099 + 109.099i −0.852333 + 0.852333i
\(129\) 0 0
\(130\) 50.0000 + 150.000i 0.384615 + 1.15385i
\(131\) −173.925 −1.32767 −0.663837 0.747877i \(-0.731073\pi\)
−0.663837 + 0.747877i \(0.731073\pi\)
\(132\) 0 0
\(133\) 90.0000 90.0000i 0.676692 0.676692i
\(134\) 221.359i 1.65194i
\(135\) 0 0
\(136\) −30.0000 −0.220588
\(137\) −15.8114 15.8114i −0.115412 0.115412i 0.647042 0.762454i \(-0.276006\pi\)
−0.762454 + 0.647042i \(0.776006\pi\)
\(138\) 0 0
\(139\) 102.000i 0.733813i −0.930258 0.366906i \(-0.880417\pi\)
0.930258 0.366906i \(-0.119583\pi\)
\(140\) −31.6228 15.8114i −0.225877 0.112938i
\(141\) 0 0
\(142\) −100.000 100.000i −0.704225 0.704225i
\(143\) 158.114 158.114i 1.10569 1.10569i
\(144\) 0 0
\(145\) −225.000 + 75.0000i −1.55172 + 0.517241i
\(146\) −173.925 −1.19127
\(147\) 0 0
\(148\) −10.0000 + 10.0000i −0.0675676 + 0.0675676i
\(149\) 47.4342i 0.318350i 0.987250 + 0.159175i \(0.0508834\pi\)
−0.987250 + 0.159175i \(0.949117\pi\)
\(150\) 0 0
\(151\) −22.0000 −0.145695 −0.0728477 0.997343i \(-0.523209\pi\)
−0.0728477 + 0.997343i \(0.523209\pi\)
\(152\) −85.3815 85.3815i −0.561720 0.561720i
\(153\) 0 0
\(154\) 250.000i 1.62338i
\(155\) −12.6491 37.9473i −0.0816072 0.244821i
\(156\) 0 0
\(157\) −200.000 200.000i −1.27389 1.27389i −0.944032 0.329853i \(-0.893001\pi\)
−0.329853 0.944032i \(-0.606999\pi\)
\(158\) 18.9737 18.9737i 0.120086 0.120086i
\(159\) 0 0
\(160\) −35.0000 + 70.0000i −0.218750 + 0.437500i
\(161\) −31.6228 −0.196415
\(162\) 0 0
\(163\) 100.000 100.000i 0.613497 0.613497i −0.330359 0.943856i \(-0.607170\pi\)
0.943856 + 0.330359i \(0.107170\pi\)
\(164\) 31.6228i 0.192822i
\(165\) 0 0
\(166\) 170.000 1.02410
\(167\) −148.627 148.627i −0.889982 0.889982i 0.104539 0.994521i \(-0.466663\pi\)
−0.994521 + 0.104539i \(0.966663\pi\)
\(168\) 0 0
\(169\) 31.0000i 0.183432i
\(170\) −47.4342 + 15.8114i −0.279024 + 0.0930082i
\(171\) 0 0
\(172\) 10.0000 + 10.0000i 0.0581395 + 0.0581395i
\(173\) −110.680 + 110.680i −0.639767 + 0.639767i −0.950498 0.310731i \(-0.899426\pi\)
0.310731 + 0.950498i \(0.399426\pi\)
\(174\) 0 0
\(175\) 175.000 + 25.0000i 1.00000 + 0.142857i
\(176\) 300.416 1.70691
\(177\) 0 0
\(178\) 0 0
\(179\) 142.302i 0.794986i 0.917605 + 0.397493i \(0.130120\pi\)
−0.917605 + 0.397493i \(0.869880\pi\)
\(180\) 0 0
\(181\) 218.000 1.20442 0.602210 0.798338i \(-0.294287\pi\)
0.602210 + 0.798338i \(0.294287\pi\)
\(182\) 158.114 + 158.114i 0.868758 + 0.868758i
\(183\) 0 0
\(184\) 30.0000i 0.163043i
\(185\) 31.6228 63.2456i 0.170934 0.341868i
\(186\) 0 0
\(187\) 50.0000 + 50.0000i 0.267380 + 0.267380i
\(188\) −41.1096 + 41.1096i −0.218668 + 0.218668i
\(189\) 0 0
\(190\) −180.000 90.0000i −0.947368 0.473684i
\(191\) 158.114 0.827821 0.413911 0.910317i \(-0.364163\pi\)
0.413911 + 0.910317i \(0.364163\pi\)
\(192\) 0 0
\(193\) −125.000 + 125.000i −0.647668 + 0.647668i −0.952429 0.304761i \(-0.901424\pi\)
0.304761 + 0.952429i \(0.401424\pi\)
\(194\) 15.8114i 0.0815020i
\(195\) 0 0
\(196\) −1.00000 −0.00510204
\(197\) 145.465 + 145.465i 0.738400 + 0.738400i 0.972268 0.233868i \(-0.0751385\pi\)
−0.233868 + 0.972268i \(0.575138\pi\)
\(198\) 0 0
\(199\) 18.0000i 0.0904523i −0.998977 0.0452261i \(-0.985599\pi\)
0.998977 0.0452261i \(-0.0144008\pi\)
\(200\) 23.7171 166.020i 0.118585 0.830098i
\(201\) 0 0
\(202\) −25.0000 25.0000i −0.123762 0.123762i
\(203\) −237.171 + 237.171i −1.16833 + 1.16833i
\(204\) 0 0
\(205\) 50.0000 + 150.000i 0.243902 + 0.731707i
\(206\) 110.680 0.537280
\(207\) 0 0
\(208\) 190.000 190.000i 0.913462 0.913462i
\(209\) 284.605i 1.36175i
\(210\) 0 0
\(211\) −298.000 −1.41232 −0.706161 0.708051i \(-0.749575\pi\)
−0.706161 + 0.708051i \(0.749575\pi\)
\(212\) −25.2982 25.2982i −0.119331 0.119331i
\(213\) 0 0
\(214\) 190.000i 0.887850i
\(215\) −63.2456 31.6228i −0.294165 0.147083i
\(216\) 0 0
\(217\) −40.0000 40.0000i −0.184332 0.184332i
\(218\) 256.144 256.144i 1.17497 1.17497i
\(219\) 0 0
\(220\) 75.0000 25.0000i 0.340909 0.113636i
\(221\) 63.2456 0.286179
\(222\) 0 0
\(223\) −215.000 + 215.000i −0.964126 + 0.964126i −0.999378 0.0352529i \(-0.988776\pi\)
0.0352529 + 0.999378i \(0.488776\pi\)
\(224\) 110.680i 0.494106i
\(225\) 0 0
\(226\) −370.000 −1.63717
\(227\) −271.956 271.956i −1.19804 1.19804i −0.974752 0.223292i \(-0.928320\pi\)
−0.223292 0.974752i \(-0.571680\pi\)
\(228\) 0 0
\(229\) 78.0000i 0.340611i 0.985391 + 0.170306i \(0.0544755\pi\)
−0.985391 + 0.170306i \(0.945524\pi\)
\(230\) 15.8114 + 47.4342i 0.0687452 + 0.206235i
\(231\) 0 0
\(232\) 225.000 + 225.000i 0.969828 + 0.969828i
\(233\) −110.680 + 110.680i −0.475020 + 0.475020i −0.903535 0.428515i \(-0.859037\pi\)
0.428515 + 0.903535i \(0.359037\pi\)
\(234\) 0 0
\(235\) 130.000 260.000i 0.553191 1.10638i
\(236\) −47.4342 −0.200992
\(237\) 0 0
\(238\) −50.0000 + 50.0000i −0.210084 + 0.210084i
\(239\) 379.473i 1.58775i −0.608078 0.793877i \(-0.708059\pi\)
0.608078 0.793877i \(-0.291941\pi\)
\(240\) 0 0
\(241\) 212.000 0.879668 0.439834 0.898079i \(-0.355037\pi\)
0.439834 + 0.898079i \(0.355037\pi\)
\(242\) −203.967 203.967i −0.842838 0.842838i
\(243\) 0 0
\(244\) 58.0000i 0.237705i
\(245\) 4.74342 1.58114i 0.0193609 0.00645363i
\(246\) 0 0
\(247\) 180.000 + 180.000i 0.728745 + 0.728745i
\(248\) −37.9473 + 37.9473i −0.153013 + 0.153013i
\(249\) 0 0
\(250\) −50.0000 275.000i −0.200000 1.10000i
\(251\) −363.662 −1.44885 −0.724426 0.689352i \(-0.757895\pi\)
−0.724426 + 0.689352i \(0.757895\pi\)
\(252\) 0 0
\(253\) 50.0000 50.0000i 0.197628 0.197628i
\(254\) 173.925i 0.684745i
\(255\) 0 0
\(256\) 181.000 0.707031
\(257\) 306.741 + 306.741i 1.19354 + 1.19354i 0.976065 + 0.217480i \(0.0697836\pi\)
0.217480 + 0.976065i \(0.430216\pi\)
\(258\) 0 0
\(259\) 100.000i 0.386100i
\(260\) 31.6228 63.2456i 0.121626 0.243252i
\(261\) 0 0
\(262\) 275.000 + 275.000i 1.04962 + 1.04962i
\(263\) 287.767 287.767i 1.09417 1.09417i 0.0990940 0.995078i \(-0.468406\pi\)
0.995078 0.0990940i \(-0.0315945\pi\)
\(264\) 0 0
\(265\) 160.000 + 80.0000i 0.603774 + 0.301887i
\(266\) −284.605 −1.06994
\(267\) 0 0
\(268\) −70.0000 + 70.0000i −0.261194 + 0.261194i
\(269\) 142.302i 0.529006i −0.964385 0.264503i \(-0.914792\pi\)
0.964385 0.264503i \(-0.0852078\pi\)
\(270\) 0 0
\(271\) −178.000 −0.656827 −0.328413 0.944534i \(-0.606514\pi\)
−0.328413 + 0.944534i \(0.606514\pi\)
\(272\) 60.0833 + 60.0833i 0.220894 + 0.220894i
\(273\) 0 0
\(274\) 50.0000i 0.182482i
\(275\) −316.228 + 237.171i −1.14992 + 0.862439i
\(276\) 0 0
\(277\) −230.000 230.000i −0.830325 0.830325i 0.157236 0.987561i \(-0.449742\pi\)
−0.987561 + 0.157236i \(0.949742\pi\)
\(278\) −161.276 + 161.276i −0.580130 + 0.580130i
\(279\) 0 0
\(280\) −75.0000 225.000i −0.267857 0.803571i
\(281\) 158.114 0.562683 0.281341 0.959608i \(-0.409221\pi\)
0.281341 + 0.959608i \(0.409221\pi\)
\(282\) 0 0
\(283\) −350.000 + 350.000i −1.23675 + 1.23675i −0.275427 + 0.961322i \(0.588819\pi\)
−0.961322 + 0.275427i \(0.911181\pi\)
\(284\) 63.2456i 0.222696i
\(285\) 0 0
\(286\) −500.000 −1.74825
\(287\) 158.114 + 158.114i 0.550919 + 0.550919i
\(288\) 0 0
\(289\) 269.000i 0.930796i
\(290\) 474.342 + 237.171i 1.63566 + 0.817830i
\(291\) 0 0
\(292\) 55.0000 + 55.0000i 0.188356 + 0.188356i
\(293\) 202.386 202.386i 0.690736 0.690736i −0.271658 0.962394i \(-0.587572\pi\)
0.962394 + 0.271658i \(0.0875718\pi\)
\(294\) 0 0
\(295\) 225.000 75.0000i 0.762712 0.254237i
\(296\) −94.8683 −0.320501
\(297\) 0 0
\(298\) 75.0000 75.0000i 0.251678 0.251678i
\(299\) 63.2456i 0.211524i
\(300\) 0 0
\(301\) −100.000 −0.332226
\(302\) 34.7851 + 34.7851i 0.115182 + 0.115182i
\(303\) 0 0
\(304\) 342.000i 1.12500i
\(305\) 91.7061 + 275.118i 0.300676 + 0.902027i
\(306\) 0 0
\(307\) 190.000 + 190.000i 0.618893 + 0.618893i 0.945247 0.326355i \(-0.105820\pi\)
−0.326355 + 0.945247i \(0.605820\pi\)
\(308\) 79.0569 79.0569i 0.256678 0.256678i
\(309\) 0 0
\(310\) −40.0000 + 80.0000i −0.129032 + 0.258065i
\(311\) 252.982 0.813448 0.406724 0.913551i \(-0.366671\pi\)
0.406724 + 0.913551i \(0.366671\pi\)
\(312\) 0 0
\(313\) 145.000 145.000i 0.463259 0.463259i −0.436463 0.899722i \(-0.643769\pi\)
0.899722 + 0.436463i \(0.143769\pi\)
\(314\) 632.456i 2.01419i
\(315\) 0 0
\(316\) −12.0000 −0.0379747
\(317\) −15.8114 15.8114i −0.0498782 0.0498782i 0.681728 0.731606i \(-0.261229\pi\)
−0.731606 + 0.681728i \(0.761229\pi\)
\(318\) 0 0
\(319\) 750.000i 2.35110i
\(320\) −194.480 + 64.8267i −0.607750 + 0.202583i
\(321\) 0 0
\(322\) 50.0000 + 50.0000i 0.155280 + 0.155280i
\(323\) −56.9210 + 56.9210i −0.176226 + 0.176226i
\(324\) 0 0
\(325\) −50.0000 + 350.000i −0.153846 + 1.07692i
\(326\) −316.228 −0.970024
\(327\) 0 0
\(328\) 150.000 150.000i 0.457317 0.457317i
\(329\) 411.096i 1.24953i
\(330\) 0 0
\(331\) 482.000 1.45619 0.728097 0.685474i \(-0.240405\pi\)
0.728097 + 0.685474i \(0.240405\pi\)
\(332\) −53.7587 53.7587i −0.161924 0.161924i
\(333\) 0 0
\(334\) 470.000i 1.40719i
\(335\) 221.359 442.719i 0.660774 1.32155i
\(336\) 0 0
\(337\) −155.000 155.000i −0.459941 0.459941i 0.438695 0.898636i \(-0.355441\pi\)
−0.898636 + 0.438695i \(0.855441\pi\)
\(338\) −49.0153 + 49.0153i −0.145016 + 0.145016i
\(339\) 0 0
\(340\) 20.0000 + 10.0000i 0.0588235 + 0.0294118i
\(341\) 126.491 0.370942
\(342\) 0 0
\(343\) −240.000 + 240.000i −0.699708 + 0.699708i
\(344\) 94.8683i 0.275780i
\(345\) 0 0
\(346\) 350.000 1.01156
\(347\) 164.438 + 164.438i 0.473886 + 0.473886i 0.903170 0.429284i \(-0.141234\pi\)
−0.429284 + 0.903170i \(0.641234\pi\)
\(348\) 0 0
\(349\) 318.000i 0.911175i 0.890191 + 0.455587i \(0.150571\pi\)
−0.890191 + 0.455587i \(0.849429\pi\)
\(350\) −237.171 316.228i −0.677631 0.903508i
\(351\) 0 0
\(352\) −175.000 175.000i −0.497159 0.497159i
\(353\) −224.522 + 224.522i −0.636039 + 0.636039i −0.949576 0.313537i \(-0.898486\pi\)
0.313537 + 0.949576i \(0.398486\pi\)
\(354\) 0 0
\(355\) −100.000 300.000i −0.281690 0.845070i
\(356\) 0 0
\(357\) 0 0
\(358\) 225.000 225.000i 0.628492 0.628492i
\(359\) 284.605i 0.792772i −0.918084 0.396386i \(-0.870264\pi\)
0.918084 0.396386i \(-0.129736\pi\)
\(360\) 0 0
\(361\) 37.0000 0.102493
\(362\) −344.688 344.688i −0.952178 0.952178i
\(363\) 0 0
\(364\) 100.000i 0.274725i
\(365\) −347.851 173.925i −0.953015 0.476508i
\(366\) 0 0
\(367\) −185.000 185.000i −0.504087 0.504087i 0.408618 0.912705i \(-0.366011\pi\)
−0.912705 + 0.408618i \(0.866011\pi\)
\(368\) 60.0833 60.0833i 0.163270 0.163270i
\(369\) 0 0
\(370\) −150.000 + 50.0000i −0.405405 + 0.135135i
\(371\) 252.982 0.681893
\(372\) 0 0
\(373\) 100.000 100.000i 0.268097 0.268097i −0.560236 0.828333i \(-0.689290\pi\)
0.828333 + 0.560236i \(0.189290\pi\)
\(374\) 158.114i 0.422764i
\(375\) 0 0
\(376\) −390.000 −1.03723
\(377\) −474.342 474.342i −1.25820 1.25820i
\(378\) 0 0
\(379\) 558.000i 1.47230i 0.676821 + 0.736148i \(0.263357\pi\)
−0.676821 + 0.736148i \(0.736643\pi\)
\(380\) 28.4605 + 85.3815i 0.0748960 + 0.224688i
\(381\) 0 0
\(382\) −250.000 250.000i −0.654450 0.654450i
\(383\) −281.443 + 281.443i −0.734837 + 0.734837i −0.971574 0.236737i \(-0.923922\pi\)
0.236737 + 0.971574i \(0.423922\pi\)
\(384\) 0 0
\(385\) −250.000 + 500.000i −0.649351 + 1.29870i
\(386\) 395.285 1.02405
\(387\) 0 0
\(388\) 5.00000 5.00000i 0.0128866 0.0128866i
\(389\) 521.776i 1.34133i 0.741762 + 0.670663i \(0.233990\pi\)
−0.741762 + 0.670663i \(0.766010\pi\)
\(390\) 0 0
\(391\) 20.0000 0.0511509
\(392\) −4.74342 4.74342i −0.0121006 0.0121006i
\(393\) 0 0
\(394\) 460.000i 1.16751i
\(395\) 56.9210 18.9737i 0.144104 0.0480346i
\(396\) 0 0
\(397\) −260.000 260.000i −0.654912 0.654912i 0.299260 0.954172i \(-0.403260\pi\)
−0.954172 + 0.299260i \(0.903260\pi\)
\(398\) −28.4605 + 28.4605i −0.0715088 + 0.0715088i
\(399\) 0 0
\(400\) −380.000 + 285.000i −0.950000 + 0.712500i
\(401\) 252.982 0.630878 0.315439 0.948946i \(-0.397848\pi\)
0.315439 + 0.948946i \(0.397848\pi\)
\(402\) 0 0
\(403\) 80.0000 80.0000i 0.198511 0.198511i
\(404\) 15.8114i 0.0391371i
\(405\) 0 0
\(406\) 750.000 1.84729
\(407\) 158.114 + 158.114i 0.388486 + 0.388486i
\(408\) 0 0
\(409\) 348.000i 0.850856i 0.904992 + 0.425428i \(0.139876\pi\)
−0.904992 + 0.425428i \(0.860124\pi\)
\(410\) 158.114 316.228i 0.385644 0.771287i
\(411\) 0 0
\(412\) −35.0000 35.0000i −0.0849515 0.0849515i
\(413\) 237.171 237.171i 0.574263 0.574263i
\(414\) 0 0
\(415\) 340.000 + 170.000i 0.819277 + 0.409639i
\(416\) −221.359 −0.532114
\(417\) 0 0
\(418\) 450.000 450.000i 1.07656 1.07656i
\(419\) 616.644i 1.47170i 0.677142 + 0.735852i \(0.263218\pi\)
−0.677142 + 0.735852i \(0.736782\pi\)
\(420\) 0 0
\(421\) 338.000 0.802850 0.401425 0.915892i \(-0.368515\pi\)
0.401425 + 0.915892i \(0.368515\pi\)
\(422\) 471.179 + 471.179i 1.11654 + 1.11654i
\(423\) 0 0
\(424\) 240.000i 0.566038i
\(425\) −110.680 15.8114i −0.260423 0.0372033i
\(426\) 0 0
\(427\) 290.000 + 290.000i 0.679157 + 0.679157i
\(428\) −60.0833 + 60.0833i −0.140381 + 0.140381i
\(429\) 0 0
\(430\) 50.0000 + 150.000i 0.116279 + 0.348837i
\(431\) −221.359 −0.513595 −0.256797 0.966465i \(-0.582667\pi\)
−0.256797 + 0.966465i \(0.582667\pi\)
\(432\) 0 0
\(433\) 145.000 145.000i 0.334873 0.334873i −0.519561 0.854434i \(-0.673904\pi\)
0.854434 + 0.519561i \(0.173904\pi\)
\(434\) 126.491i 0.291454i
\(435\) 0 0
\(436\) −162.000 −0.371560
\(437\) 56.9210 + 56.9210i 0.130254 + 0.130254i
\(438\) 0 0
\(439\) 78.0000i 0.177677i −0.996046 0.0888383i \(-0.971685\pi\)
0.996046 0.0888383i \(-0.0283154\pi\)
\(440\) 474.342 + 237.171i 1.07805 + 0.539025i
\(441\) 0 0
\(442\) −100.000 100.000i −0.226244 0.226244i
\(443\) −196.061 + 196.061i −0.442576 + 0.442576i −0.892877 0.450301i \(-0.851317\pi\)
0.450301 + 0.892877i \(0.351317\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 679.890 1.52442
\(447\) 0 0
\(448\) −205.000 + 205.000i −0.457589 + 0.457589i
\(449\) 284.605i 0.633864i −0.948448 0.316932i \(-0.897347\pi\)
0.948448 0.316932i \(-0.102653\pi\)
\(450\) 0 0
\(451\) −500.000 −1.10865
\(452\) 117.004 + 117.004i 0.258859 + 0.258859i
\(453\) 0 0
\(454\) 860.000i 1.89427i
\(455\) 158.114 + 474.342i 0.347503 + 1.04251i
\(456\) 0 0
\(457\) −365.000 365.000i −0.798687 0.798687i 0.184201 0.982889i \(-0.441030\pi\)
−0.982889 + 0.184201i \(0.941030\pi\)
\(458\) 123.329 123.329i 0.269277 0.269277i
\(459\) 0 0
\(460\) 10.0000 20.0000i 0.0217391 0.0434783i
\(461\) −838.004 −1.81780 −0.908898 0.417019i \(-0.863075\pi\)
−0.908898 + 0.417019i \(0.863075\pi\)
\(462\) 0 0
\(463\) −35.0000 + 35.0000i −0.0755940 + 0.0755940i −0.743893 0.668299i \(-0.767023\pi\)
0.668299 + 0.743893i \(0.267023\pi\)
\(464\) 901.249i 1.94235i
\(465\) 0 0
\(466\) 350.000 0.751073
\(467\) 117.004 + 117.004i 0.250544 + 0.250544i 0.821194 0.570649i \(-0.193308\pi\)
−0.570649 + 0.821194i \(0.693308\pi\)
\(468\) 0 0
\(469\) 700.000i 1.49254i
\(470\) −616.644 + 205.548i −1.31201 + 0.437336i
\(471\) 0 0
\(472\) −225.000 225.000i −0.476695 0.476695i
\(473\) 158.114 158.114i 0.334279 0.334279i
\(474\) 0 0
\(475\) −270.000 360.000i −0.568421 0.757895i
\(476\) 31.6228 0.0664344
\(477\) 0 0
\(478\) −600.000 + 600.000i −1.25523 + 1.25523i
\(479\) 379.473i 0.792220i 0.918203 + 0.396110i \(0.129640\pi\)
−0.918203 + 0.396110i \(0.870360\pi\)
\(480\) 0 0
\(481\) 200.000 0.415800
\(482\) −335.201 335.201i −0.695439 0.695439i
\(483\) 0 0
\(484\) 129.000i 0.266529i
\(485\) −15.8114 + 31.6228i −0.0326008 + 0.0652016i
\(486\) 0 0
\(487\) −125.000 125.000i −0.256674 0.256674i 0.567026 0.823700i \(-0.308094\pi\)
−0.823700 + 0.567026i \(0.808094\pi\)
\(488\) 275.118 275.118i 0.563767 0.563767i
\(489\) 0 0
\(490\) −10.0000 5.00000i −0.0204082 0.0102041i
\(491\) −458.530 −0.933870 −0.466935 0.884292i \(-0.654642\pi\)
−0.466935 + 0.884292i \(0.654642\pi\)
\(492\) 0 0
\(493\) 150.000 150.000i 0.304260 0.304260i
\(494\) 569.210i 1.15225i
\(495\) 0 0
\(496\) 152.000 0.306452
\(497\) −316.228 316.228i −0.636273 0.636273i
\(498\) 0 0
\(499\) 222.000i 0.444890i 0.974945 + 0.222445i \(0.0714037\pi\)
−0.974945 + 0.222445i \(0.928596\pi\)
\(500\) −71.1512 + 102.774i −0.142302 + 0.205548i
\(501\) 0 0
\(502\) 575.000 + 575.000i 1.14542 + 1.14542i
\(503\) 458.530 458.530i 0.911591 0.911591i −0.0848065 0.996397i \(-0.527027\pi\)
0.996397 + 0.0848065i \(0.0270272\pi\)
\(504\) 0 0
\(505\) −25.0000 75.0000i −0.0495050 0.148515i
\(506\) −158.114 −0.312478
\(507\) 0 0
\(508\) −55.0000 + 55.0000i −0.108268 + 0.108268i
\(509\) 237.171i 0.465954i −0.972482 0.232977i \(-0.925153\pi\)
0.972482 0.232977i \(-0.0748468\pi\)
\(510\) 0 0
\(511\) −550.000 −1.07632
\(512\) 150.208 + 150.208i 0.293375 + 0.293375i
\(513\) 0 0
\(514\) 970.000i 1.88716i
\(515\) 221.359 + 110.680i 0.429824 + 0.214912i
\(516\) 0 0
\(517\) 650.000 + 650.000i 1.25725 + 1.25725i
\(518\) −158.114 + 158.114i −0.305239 + 0.305239i
\(519\) 0 0
\(520\) 450.000 150.000i 0.865385 0.288462i
\(521\) −790.569 −1.51741 −0.758704 0.651436i \(-0.774167\pi\)
−0.758704 + 0.651436i \(0.774167\pi\)
\(522\) 0 0
\(523\) 370.000 370.000i 0.707457 0.707457i −0.258543 0.966000i \(-0.583242\pi\)
0.966000 + 0.258543i \(0.0832423\pi\)
\(524\) 173.925i 0.331918i
\(525\) 0 0
\(526\) −910.000 −1.73004
\(527\) 25.2982 + 25.2982i 0.0480042 + 0.0480042i
\(528\) 0 0
\(529\) 509.000i 0.962193i
\(530\) −126.491 379.473i −0.238662 0.715987i
\(531\) 0 0
\(532\) 90.0000 + 90.0000i 0.169173 + 0.169173i
\(533\) −316.228 + 316.228i −0.593298 + 0.593298i
\(534\) 0 0
\(535\) 190.000 380.000i 0.355140 0.710280i
\(536\) −664.078 −1.23895
\(537\) 0 0
\(538\) −225.000 + 225.000i −0.418216 + 0.418216i
\(539\) 15.8114i 0.0293347i
\(540\) 0 0
\(541\) 362.000 0.669131 0.334566 0.942372i \(-0.391410\pi\)
0.334566 + 0.942372i \(0.391410\pi\)
\(542\) 281.443 + 281.443i 0.519267 + 0.519267i
\(543\) 0 0
\(544\) 70.0000i 0.128676i
\(545\) 768.433 256.144i 1.40997 0.469990i
\(546\) 0 0
\(547\) 490.000 + 490.000i 0.895795 + 0.895795i 0.995061 0.0992657i \(-0.0316494\pi\)
−0.0992657 + 0.995061i \(0.531649\pi\)
\(548\) 15.8114 15.8114i 0.0288529 0.0288529i
\(549\) 0 0
\(550\) 875.000 + 125.000i 1.59091 + 0.227273i
\(551\) 853.815 1.54957
\(552\) 0 0
\(553\) 60.0000 60.0000i 0.108499 0.108499i
\(554\) 727.324i 1.31286i
\(555\) 0 0
\(556\) 102.000 0.183453
\(557\) −252.982 252.982i −0.454187 0.454187i 0.442555 0.896742i \(-0.354072\pi\)
−0.896742 + 0.442555i \(0.854072\pi\)
\(558\) 0 0
\(559\) 200.000i 0.357782i
\(560\) −300.416 + 600.833i −0.536458 + 1.07292i
\(561\) 0 0
\(562\) −250.000 250.000i −0.444840 0.444840i
\(563\) 202.386 202.386i 0.359477 0.359477i −0.504143 0.863620i \(-0.668192\pi\)
0.863620 + 0.504143i \(0.168192\pi\)
\(564\) 0 0
\(565\) −740.000 370.000i −1.30973 0.654867i
\(566\) 1106.80 1.95547
\(567\) 0 0
\(568\) −300.000 + 300.000i −0.528169 + 0.528169i
\(569\) 189.737i 0.333456i −0.986003 0.166728i \(-0.946680\pi\)
0.986003 0.166728i \(-0.0533202\pi\)
\(570\) 0 0
\(571\) −658.000 −1.15236 −0.576182 0.817321i \(-0.695458\pi\)
−0.576182 + 0.817321i \(0.695458\pi\)
\(572\) 158.114 + 158.114i 0.276423 + 0.276423i
\(573\) 0 0
\(574\) 500.000i 0.871080i
\(575\) −15.8114 + 110.680i −0.0274981 + 0.192486i
\(576\) 0 0
\(577\) −35.0000 35.0000i −0.0606586 0.0606586i 0.676127 0.736785i \(-0.263657\pi\)
−0.736785 + 0.676127i \(0.763657\pi\)
\(578\) −425.326 + 425.326i −0.735859 + 0.735859i
\(579\) 0 0
\(580\) −75.0000 225.000i −0.129310 0.387931i
\(581\) 537.587 0.925279
\(582\) 0 0
\(583\) −400.000 + 400.000i −0.686106 + 0.686106i
\(584\) 521.776i 0.893452i
\(585\) 0 0
\(586\) −640.000 −1.09215
\(587\) 154.952 + 154.952i 0.263972 + 0.263972i 0.826666 0.562694i \(-0.190235\pi\)
−0.562694 + 0.826666i \(0.690235\pi\)
\(588\) 0 0
\(589\) 144.000i 0.244482i
\(590\) −474.342 237.171i −0.803969 0.401984i
\(591\) 0 0
\(592\) 190.000 + 190.000i 0.320946 + 0.320946i
\(593\) −167.601 + 167.601i −0.282632 + 0.282632i −0.834158 0.551526i \(-0.814046\pi\)
0.551526 + 0.834158i \(0.314046\pi\)
\(594\) 0 0
\(595\) −150.000 + 50.0000i −0.252101 + 0.0840336i
\(596\) −47.4342 −0.0795875
\(597\) 0 0
\(598\) −100.000 + 100.000i −0.167224 + 0.167224i
\(599\) 1043.55i 1.74216i 0.491144 + 0.871078i \(0.336579\pi\)
−0.491144 + 0.871078i \(0.663421\pi\)
\(600\) 0 0
\(601\) −382.000 −0.635607 −0.317804 0.948157i \(-0.602945\pi\)
−0.317804 + 0.948157i \(0.602945\pi\)
\(602\) 158.114 + 158.114i 0.262648 + 0.262648i
\(603\) 0 0
\(604\) 22.0000i 0.0364238i
\(605\) −203.967 611.901i −0.337135 1.01141i
\(606\) 0 0
\(607\) 655.000 + 655.000i 1.07908 + 1.07908i 0.996592 + 0.0824851i \(0.0262857\pi\)
0.0824851 + 0.996592i \(0.473714\pi\)
\(608\) 199.223 199.223i 0.327670 0.327670i
\(609\) 0 0
\(610\) 290.000 580.000i 0.475410 0.950820i
\(611\) 822.192 1.34565
\(612\) 0 0
\(613\) −620.000 + 620.000i −1.01142 + 1.01142i −0.0114852 + 0.999934i \(0.503656\pi\)
−0.999934 + 0.0114852i \(0.996344\pi\)
\(614\) 600.833i 0.978555i
\(615\) 0 0
\(616\) 750.000 1.21753
\(617\) −34.7851 34.7851i −0.0563777 0.0563777i 0.678356 0.734734i \(-0.262693\pi\)
−0.734734 + 0.678356i \(0.762693\pi\)
\(618\) 0 0
\(619\) 258.000i 0.416801i −0.978044 0.208401i \(-0.933174\pi\)
0.978044 0.208401i \(-0.0668258\pi\)
\(620\) 37.9473 12.6491i 0.0612054 0.0204018i
\(621\) 0 0
\(622\) −400.000 400.000i −0.643087 0.643087i
\(623\) 0 0
\(624\) 0 0
\(625\) 175.000 600.000i 0.280000 0.960000i
\(626\) −458.530 −0.732476
\(627\) 0 0
\(628\) 200.000 200.000i 0.318471 0.318471i
\(629\) 63.2456i 0.100549i
\(630\) 0 0
\(631\) 812.000 1.28685 0.643423 0.765511i \(-0.277514\pi\)
0.643423 + 0.765511i \(0.277514\pi\)
\(632\) −56.9210 56.9210i −0.0900649 0.0900649i
\(633\) 0 0
\(634\) 50.0000i 0.0788644i
\(635\) 173.925 347.851i 0.273898 0.547796i
\(636\) 0 0
\(637\) 10.0000 + 10.0000i 0.0156986 + 0.0156986i
\(638\) −1185.85 + 1185.85i −1.85871 + 1.85871i
\(639\) 0 0
\(640\) 690.000 + 345.000i 1.07812 + 0.539062i
\(641\) 442.719 0.690669 0.345335 0.938480i \(-0.387765\pi\)
0.345335 + 0.938480i \(0.387765\pi\)
\(642\) 0 0
\(643\) 820.000 820.000i 1.27527 1.27527i 0.331989 0.943283i \(-0.392280\pi\)
0.943283 0.331989i \(-0.107720\pi\)
\(644\) 31.6228i 0.0491037i
\(645\) 0 0
\(646\) 180.000 0.278638
\(647\) −679.890 679.890i −1.05083 1.05083i −0.998637 0.0521974i \(-0.983378\pi\)
−0.0521974 0.998637i \(-0.516622\pi\)
\(648\) 0 0
\(649\) 750.000i 1.15562i
\(650\) 632.456 474.342i 0.973009 0.729756i
\(651\) 0 0
\(652\) 100.000 + 100.000i 0.153374 + 0.153374i
\(653\) 515.451 515.451i 0.789359 0.789359i −0.192030 0.981389i \(-0.561507\pi\)
0.981389 + 0.192030i \(0.0615072\pi\)
\(654\) 0 0
\(655\) 275.000 + 825.000i 0.419847 + 1.25954i
\(656\) −600.833 −0.915904
\(657\) 0 0
\(658\) −650.000 + 650.000i −0.987842 + 0.987842i
\(659\) 901.249i 1.36760i −0.729669 0.683801i \(-0.760326\pi\)
0.729669 0.683801i \(-0.239674\pi\)
\(660\) 0 0
\(661\) −802.000 −1.21331 −0.606657 0.794964i \(-0.707490\pi\)
−0.606657 + 0.794964i \(0.707490\pi\)
\(662\) −762.109 762.109i −1.15122 1.15122i
\(663\) 0 0
\(664\) 510.000i 0.768072i
\(665\) −569.210 284.605i −0.855955 0.427977i
\(666\) 0 0
\(667\) −150.000 150.000i −0.224888 0.224888i
\(668\) 148.627 148.627i 0.222496 0.222496i
\(669\) 0 0
\(670\) −1050.00 + 350.000i −1.56716 + 0.522388i
\(671\) −917.061 −1.36671
\(672\) 0 0
\(673\) 775.000 775.000i 1.15156 1.15156i 0.165320 0.986240i \(-0.447134\pi\)
0.986240 0.165320i \(-0.0528658\pi\)
\(674\) 490.153i 0.727230i
\(675\) 0 0
\(676\) 31.0000 0.0458580
\(677\) 496.478 + 496.478i 0.733349 + 0.733349i 0.971282 0.237932i \(-0.0764696\pi\)
−0.237932 + 0.971282i \(0.576470\pi\)
\(678\) 0 0
\(679\) 50.0000i 0.0736377i
\(680\) 47.4342 + 142.302i 0.0697561 + 0.209268i
\(681\) 0 0
\(682\) −200.000 200.000i −0.293255 0.293255i
\(683\) 60.0833 60.0833i 0.0879697 0.0879697i −0.661753 0.749722i \(-0.730187\pi\)
0.749722 + 0.661753i \(0.230187\pi\)
\(684\) 0 0
\(685\) −50.0000 + 100.000i −0.0729927 + 0.145985i
\(686\) 758.947 1.10634
\(687\) 0 0
\(688\) 190.000 190.000i 0.276163 0.276163i
\(689\) 505.964i 0.734346i
\(690\) 0 0
\(691\) −562.000 −0.813314 −0.406657 0.913581i \(-0.633306\pi\)
−0.406657 + 0.913581i \(0.633306\pi\)
\(692\) −110.680 110.680i −0.159942 0.159942i
\(693\) 0 0
\(694\) 520.000i 0.749280i
\(695\) −483.828 + 161.276i −0.696156 + 0.232052i
\(696\) 0 0
\(697\) −100.000 100.000i −0.143472 0.143472i
\(698\) 502.802 502.802i 0.720347 0.720347i
\(699\) 0 0
\(700\) −25.0000 + 175.000i −0.0357143 + 0.250000i
\(701\) −363.662 −0.518776 −0.259388 0.965773i \(-0.583521\pi\)
−0.259388 + 0.965773i \(0.583521\pi\)
\(702\) 0 0
\(703\) −180.000 + 180.000i −0.256046 + 0.256046i
\(704\) 648.267i 0.920834i
\(705\) 0 0
\(706\) 710.000 1.00567
\(707\) −79.0569 79.0569i −0.111820 0.111820i
\(708\) 0 0
\(709\) 498.000i 0.702398i 0.936301 + 0.351199i \(0.114226\pi\)
−0.936301 + 0.351199i \(0.885774\pi\)
\(710\) −316.228 + 632.456i −0.445391 + 0.890782i
\(711\) 0 0
\(712\) 0 0
\(713\) 25.2982 25.2982i 0.0354814 0.0354814i
\(714\) 0 0
\(715\) −1000.00 500.000i −1.39860 0.699301i
\(716\) −142.302 −0.198747
\(717\) 0 0
\(718\) −450.000 + 450.000i −0.626741 + 0.626741i
\(719\) 569.210i 0.791669i −0.918322 0.395834i \(-0.870455\pi\)
0.918322 0.395834i \(-0.129545\pi\)
\(720\) 0 0
\(721\) 350.000 0.485437
\(722\) −58.5021 58.5021i −0.0810279 0.0810279i
\(723\) 0 0
\(724\) 218.000i 0.301105i
\(725\) 711.512 + 948.683i 0.981397 + 1.30853i
\(726\) 0 0
\(727\) −905.000 905.000i −1.24484 1.24484i −0.957969 0.286873i \(-0.907384\pi\)
−0.286873 0.957969i \(-0.592616\pi\)
\(728\) 474.342 474.342i 0.651568 0.651568i
\(729\) 0 0
\(730\) 275.000 + 825.000i 0.376712 + 1.13014i
\(731\) 63.2456 0.0865192
\(732\) 0 0
\(733\) 550.000 550.000i 0.750341 0.750341i −0.224202 0.974543i \(-0.571977\pi\)
0.974543 + 0.224202i \(0.0719774\pi\)
\(734\) 585.021i 0.797032i
\(735\) 0 0
\(736\) −70.0000 −0.0951087
\(737\) 1106.80 + 1106.80i 1.50176 + 1.50176i
\(738\) 0 0
\(739\) 198.000i 0.267930i 0.990986 + 0.133965i \(0.0427709\pi\)
−0.990986 + 0.133965i \(0.957229\pi\)
\(740\) 63.2456 + 31.6228i 0.0854670 + 0.0427335i
\(741\) 0 0
\(742\) −400.000 400.000i −0.539084 0.539084i
\(743\) −964.495 + 964.495i −1.29811 + 1.29811i −0.368468 + 0.929640i \(0.620118\pi\)
−0.929640 + 0.368468i \(0.879882\pi\)
\(744\) 0 0
\(745\) 225.000 75.0000i 0.302013 0.100671i
\(746\) −316.228 −0.423898
\(747\) 0 0
\(748\) −50.0000 + 50.0000i −0.0668449 + 0.0668449i
\(749\) 600.833i 0.802180i
\(750\) 0 0
\(751\) 728.000 0.969374 0.484687 0.874688i \(-0.338933\pi\)
0.484687 + 0.874688i \(0.338933\pi\)
\(752\) 781.083 + 781.083i 1.03867 + 1.03867i
\(753\) 0 0
\(754\) 1500.00i 1.98939i
\(755\) 34.7851 + 104.355i 0.0460729 + 0.138219i
\(756\) 0 0
\(757\) −170.000 170.000i −0.224571 0.224571i 0.585849 0.810420i \(-0.300761\pi\)
−0.810420 + 0.585849i \(0.800761\pi\)
\(758\) 882.275 882.275i 1.16395 1.16395i
\(759\) 0 0
\(760\) −270.000 + 540.000i −0.355263 + 0.710526i
\(761\) −31.6228 −0.0415542 −0.0207771 0.999784i \(-0.506614\pi\)
−0.0207771 + 0.999784i \(0.506614\pi\)
\(762\) 0 0
\(763\) 810.000 810.000i 1.06160 1.06160i
\(764\) 158.114i 0.206955i
\(765\) 0 0
\(766\) 890.000 1.16188
\(767\) 474.342 + 474.342i 0.618438 + 0.618438i
\(768\) 0 0
\(769\) 318.000i 0.413524i −0.978391 0.206762i \(-0.933707\pi\)
0.978391 0.206762i \(-0.0662926\pi\)
\(770\) 1185.85 395.285i 1.54007 0.513357i
\(771\) 0 0
\(772\) −125.000 125.000i −0.161917 0.161917i
\(773\) −452.206 + 452.206i −0.585001 + 0.585001i −0.936273 0.351272i \(-0.885749\pi\)
0.351272 + 0.936273i \(0.385749\pi\)
\(774\) 0 0
\(775\) −160.000 + 120.000i −0.206452 + 0.154839i
\(776\) 47.4342 0.0611265
\(777\) 0 0
\(778\) 825.000 825.000i 1.06041 1.06041i
\(779\) 569.210i 0.730693i
\(780\) 0 0
\(781\) 1000.00 1.28041
\(782\) −31.6228 31.6228i −0.0404383 0.0404383i