Properties

Label 45.3.g.a.37.2
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 37.2
Root \(1.58114 + 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 45.37
Dual form 45.3.g.a.28.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.58114 + 1.58114i) q^{2} +1.00000i q^{4} +(1.58114 + 4.74342i) q^{5} +(-5.00000 - 5.00000i) q^{7} +(4.74342 - 4.74342i) q^{8} +(-5.00000 + 10.0000i) q^{10} -15.8114 q^{11} +(10.0000 - 10.0000i) q^{13} -15.8114i q^{14} +19.0000 q^{16} +(-3.16228 - 3.16228i) q^{17} +18.0000i q^{19} +(-4.74342 + 1.58114i) q^{20} +(-25.0000 - 25.0000i) q^{22} +(-3.16228 + 3.16228i) q^{23} +(-20.0000 + 15.0000i) q^{25} +31.6228 q^{26} +(5.00000 - 5.00000i) q^{28} +47.4342i q^{29} +8.00000 q^{31} +(11.0680 + 11.0680i) q^{32} -10.0000i q^{34} +(15.8114 - 31.6228i) q^{35} +(10.0000 + 10.0000i) q^{37} +(-28.4605 + 28.4605i) q^{38} +(30.0000 + 15.0000i) q^{40} +31.6228 q^{41} +(10.0000 - 10.0000i) q^{43} -15.8114i q^{44} -10.0000 q^{46} +(-41.1096 - 41.1096i) q^{47} +1.00000i q^{49} +(-55.3399 - 7.90569i) q^{50} +(10.0000 + 10.0000i) q^{52} +(25.2982 - 25.2982i) q^{53} +(-25.0000 - 75.0000i) q^{55} -47.4342 q^{56} +(-75.0000 + 75.0000i) q^{58} -47.4342i q^{59} -58.0000 q^{61} +(12.6491 + 12.6491i) q^{62} -41.0000i q^{64} +(63.2456 + 31.6228i) q^{65} +(70.0000 + 70.0000i) q^{67} +(3.16228 - 3.16228i) q^{68} +(75.0000 - 25.0000i) q^{70} -63.2456 q^{71} +(55.0000 - 55.0000i) q^{73} +31.6228i q^{74} -18.0000 q^{76} +(79.0569 + 79.0569i) q^{77} +12.0000i q^{79} +(30.0416 + 90.1249i) q^{80} +(50.0000 + 50.0000i) q^{82} +(53.7587 - 53.7587i) q^{83} +(10.0000 - 20.0000i) q^{85} +31.6228 q^{86} +(-75.0000 + 75.0000i) q^{88} -100.000 q^{91} +(-3.16228 - 3.16228i) q^{92} -130.000i q^{94} +(-85.3815 + 28.4605i) q^{95} +(-5.00000 - 5.00000i) q^{97} +(-1.58114 + 1.58114i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 20 q^{7} - 20 q^{10} + 40 q^{13} + 76 q^{16} - 100 q^{22} - 80 q^{25} + 20 q^{28} + 32 q^{31} + 40 q^{37} + 120 q^{40} + 40 q^{43} - 40 q^{46} + 40 q^{52} - 100 q^{55} - 300 q^{58} - 232 q^{61} + 280 q^{67}+ \cdots - 20 q^{97}+O(q^{100}) \) 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 0.981587 0.191017i \(-0.0611786\pi\)
−0.191017 + 0.981587i \(0.561179\pi\)
\(3\) 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 \(-0.755262\pi\)
−0.718699 + 0.695321i \(0.755262\pi\)
\(12\) 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 0.607955 0.793971i \(-0.291990\pi\)
−0.793971 + 0.607955i \(0.791990\pi\)
\(18\) 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 −0.772502 0.635012i \(-0.780995\pi\)
0.635012 + 0.772502i \(0.280995\pi\)
\(24\) 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 \(0.304823\pi\)
−0.575459 + 0.817830i \(0.695177\pi\)
\(30\) 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 \(-0.373979\pi\)
0.385644 + 0.922648i \(0.373979\pi\)
\(42\) 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 0.118305 0.992977i \(-0.462254\pi\)
−0.992977 + 0.118305i \(0.962254\pi\)
\(48\) 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 −0.426950 0.904275i \(-0.640412\pi\)
0.904275 + 0.426950i \(0.140412\pi\)
\(54\) 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 \(-0.868321\pi\)
0.915646 0.401984i \(-0.131679\pi\)
\(60\) 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 \(-0.646935\pi\)
−0.445391 + 0.895336i \(0.646935\pi\)
\(72\) 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 −0.304740 0.952436i \(-0.598570\pi\)
0.952436 + 0.304740i \(0.0985696\pi\)
\(84\) 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 \(-0.524941\pi\)
−0.0782742 + 0.996932i \(0.524941\pi\)
\(102\) 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 0.368215 0.929741i \(-0.379969\pi\)
−0.929741 + 0.368215i \(0.879969\pi\)
\(108\) 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 \(0.511489\pi\)
−0.999349 + 0.0360874i \(0.988511\pi\)
\(114\) 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 \(-0.268927\pi\)
0.663837 + 0.747877i \(0.268927\pi\)
\(132\) 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 0.762454 0.647042i \(-0.223994\pi\)
−0.647042 + 0.762454i \(0.723994\pi\)
\(138\) 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 \(-0.949117\pi\)
0.987250 0.159175i \(-0.0508834\pi\)
\(150\) 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 0.994521 0.104539i \(-0.0333365\pi\)
−0.104539 + 0.994521i \(0.533337\pi\)
\(168\) 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 −0.310731 0.950498i \(-0.600574\pi\)
0.950498 + 0.310731i \(0.100574\pi\)
\(174\) 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 \(-0.869880\pi\)
0.917605 0.397493i \(-0.130120\pi\)
\(180\) 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 \(-0.635837\pi\)
−0.413911 + 0.910317i \(0.635837\pi\)
\(192\) 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 0.233868 0.972268i \(-0.424862\pi\)
−0.972268 + 0.233868i \(0.924862\pi\)
\(198\) 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 \(0.0716803\pi\)
0.223292 + 0.974752i \(0.428320\pi\)
\(228\) 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 −0.428515 0.903535i \(-0.640963\pi\)
0.903535 + 0.428515i \(0.140963\pi\)
\(234\) 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 \(0.291941\pi\)
−0.608078 + 0.793877i \(0.708059\pi\)
\(240\) 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 \(-0.242105\pi\)
0.724426 + 0.689352i \(0.242105\pi\)
\(252\) 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 \(-0.930216\pi\)
−0.217480 0.976065i \(-0.569784\pi\)
\(258\) 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 \(0.531594\pi\)
−0.995078 + 0.0990940i \(0.968406\pi\)
\(264\) 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 \(0.0852078\pi\)
−0.964385 + 0.264503i \(0.914792\pi\)
\(270\) 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 \(-0.590779\pi\)
−0.281341 + 0.959608i \(0.590779\pi\)
\(282\) 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 −0.962394 0.271658i \(-0.912428\pi\)
0.271658 + 0.962394i \(0.412428\pi\)
\(294\) 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 \(-0.633329\pi\)
−0.406724 + 0.913551i \(0.633329\pi\)
\(312\) 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 0.731606 0.681728i \(-0.238771\pi\)
−0.681728 + 0.731606i \(0.738771\pi\)
\(318\) 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 0.429284 0.903170i \(-0.358766\pi\)
−0.903170 + 0.429284i \(0.858766\pi\)
\(348\) 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 −0.313537 0.949576i \(-0.601514\pi\)
0.949576 + 0.313537i \(0.101514\pi\)
\(354\) 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 \(0.129736\pi\)
−0.918084 + 0.396386i \(0.870264\pi\)
\(360\) 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 −0.236737 0.971574i \(-0.576078\pi\)
0.971574 + 0.236737i \(0.0760778\pi\)
\(384\) 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 \(-0.766010\pi\)
0.741762 0.670663i \(-0.233990\pi\)
\(390\) 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 \(-0.602152\pi\)
−0.315439 + 0.948946i \(0.602152\pi\)
\(402\) 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 \(-0.736782\pi\)
0.677142 0.735852i \(-0.263218\pi\)
\(420\) 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 \(-0.417333\pi\)
0.256797 + 0.966465i \(0.417333\pi\)
\(432\) 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 −0.450301 0.892877i \(-0.648683\pi\)
0.892877 + 0.450301i \(0.148683\pi\)
\(444\) 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 \(0.102653\pi\)
−0.948448 + 0.316932i \(0.897347\pi\)
\(450\) 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 \(-0.136925\pi\)
0.908898 + 0.417019i \(0.136925\pi\)
\(462\) 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 0.570649 0.821194i \(-0.306692\pi\)
−0.821194 + 0.570649i \(0.806692\pi\)
\(468\) 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 \(-0.870360\pi\)
0.918203 0.396110i \(-0.129640\pi\)
\(480\) 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 \(-0.345358\pi\)
0.466935 + 0.884292i \(0.345358\pi\)
\(492\) 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 −0.996397 0.0848065i \(-0.972973\pi\)
0.0848065 + 0.996397i \(0.472973\pi\)
\(504\) 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 \(0.0748468\pi\)
−0.972482 + 0.232977i \(0.925153\pi\)
\(510\) 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 \(-0.225833\pi\)
0.758704 + 0.651436i \(0.225833\pi\)
\(522\) 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 0.896742 0.442555i \(-0.145928\pi\)
−0.442555 + 0.896742i \(0.645928\pi\)
\(558\) 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 −0.863620 0.504143i \(-0.831808\pi\)
0.504143 + 0.863620i \(0.331808\pi\)
\(564\) 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 \(0.0533202\pi\)
−0.986003 + 0.166728i \(0.946680\pi\)
\(570\) 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 0.562694 0.826666i \(-0.309765\pi\)
−0.826666 + 0.562694i \(0.809765\pi\)
\(588\) 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 −0.551526 0.834158i \(-0.685954\pi\)
0.834158 + 0.551526i \(0.185954\pi\)
\(594\) 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 \(-0.663421\pi\)
0.491144 0.871078i \(-0.336579\pi\)
\(600\) 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 0.734734 0.678356i \(-0.237307\pi\)
−0.678356 + 0.734734i \(0.737307\pi\)
\(618\) 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 \(-0.612235\pi\)
−0.345335 + 0.938480i \(0.612235\pi\)
\(642\) 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 \(0.0166225\pi\)
0.0521974 + 0.998637i \(0.483378\pi\)
\(648\) 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 −0.981389 0.192030i \(-0.938493\pi\)
0.192030 + 0.981389i \(0.438493\pi\)
\(654\) 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 \(0.239674\pi\)
−0.729669 + 0.683801i \(0.760326\pi\)
\(660\) 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 0.237932 0.971282i \(-0.423530\pi\)
−0.971282 + 0.237932i \(0.923530\pi\)
\(678\) 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 −0.749722 0.661753i \(-0.769813\pi\)
0.661753 + 0.749722i \(0.269813\pi\)
\(684\) 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 \(-0.416479\pi\)
0.259388 + 0.965773i \(0.416479\pi\)
\(702\) 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 \(0.129545\pi\)
−0.918322 + 0.395834i \(0.870455\pi\)
\(720\) 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 \(-0.379882\pi\)
0.929640 0.368468i \(-0.120118\pi\)
\(744\) 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 \(-0.493386\pi\)
0.0207771 + 0.999784i \(0.493386\pi\)
\(762\) 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 −0.351272 0.936273i \(-0.614251\pi\)
0.936273 + 0.351272i \(0.114251\pi\)
\(774\) 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
\(783\) 0 0
\(784\) 19.0000i