Properties

Label 45.3.g.a.28.2
Level $45$
Weight $3$
Character 45.28
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 28.2
Root \(1.58114 - 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 45.28
Dual form 45.3.g.a.37.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.58114 - 1.58114i) q^{2} -1.00000i q^{4} +(1.58114 - 4.74342i) q^{5} +(-5.00000 + 5.00000i) q^{7} +(4.74342 + 4.74342i) q^{8} +O(q^{10})\) \(q+(1.58114 - 1.58114i) q^{2} -1.00000i q^{4} +(1.58114 - 4.74342i) q^{5} +(-5.00000 + 5.00000i) q^{7} +(4.74342 + 4.74342i) q^{8} +(-5.00000 - 10.0000i) q^{10} -15.8114 q^{11} +(10.0000 + 10.0000i) q^{13} +15.8114i q^{14} +19.0000 q^{16} +(-3.16228 + 3.16228i) q^{17} -18.0000i q^{19} +(-4.74342 - 1.58114i) q^{20} +(-25.0000 + 25.0000i) q^{22} +(-3.16228 - 3.16228i) q^{23} +(-20.0000 - 15.0000i) q^{25} +31.6228 q^{26} +(5.00000 + 5.00000i) q^{28} -47.4342i q^{29} +8.00000 q^{31} +(11.0680 - 11.0680i) q^{32} +10.0000i q^{34} +(15.8114 + 31.6228i) q^{35} +(10.0000 - 10.0000i) q^{37} +(-28.4605 - 28.4605i) q^{38} +(30.0000 - 15.0000i) q^{40} +31.6228 q^{41} +(10.0000 + 10.0000i) q^{43} +15.8114i q^{44} -10.0000 q^{46} +(-41.1096 + 41.1096i) q^{47} -1.00000i q^{49} +(-55.3399 + 7.90569i) q^{50} +(10.0000 - 10.0000i) q^{52} +(25.2982 + 25.2982i) q^{53} +(-25.0000 + 75.0000i) q^{55} -47.4342 q^{56} +(-75.0000 - 75.0000i) q^{58} +47.4342i q^{59} -58.0000 q^{61} +(12.6491 - 12.6491i) q^{62} +41.0000i q^{64} +(63.2456 - 31.6228i) q^{65} +(70.0000 - 70.0000i) q^{67} +(3.16228 + 3.16228i) q^{68} +(75.0000 + 25.0000i) q^{70} -63.2456 q^{71} +(55.0000 + 55.0000i) q^{73} -31.6228i q^{74} -18.0000 q^{76} +(79.0569 - 79.0569i) q^{77} -12.0000i q^{79} +(30.0416 - 90.1249i) q^{80} +(50.0000 - 50.0000i) q^{82} +(53.7587 + 53.7587i) q^{83} +(10.0000 + 20.0000i) q^{85} +31.6228 q^{86} +(-75.0000 - 75.0000i) q^{88} -100.000 q^{91} +(-3.16228 + 3.16228i) q^{92} +130.000i q^{94} +(-85.3815 - 28.4605i) q^{95} +(-5.00000 + 5.00000i) q^{97} +(-1.58114 - 1.58114i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 20 q^{7}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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 \(-0.561179\pi\)
0.981587 + 0.191017i \(0.0611786\pi\)
\(3\) 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 −0.967429 0.253143i \(-0.918536\pi\)
0.253143 + 0.967429i \(0.418536\pi\)
\(8\) 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 0.977971 0.208740i \(-0.0669363\pi\)
−0.208740 + 0.977971i \(0.566936\pi\)
\(14\) 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 \(-0.791990\pi\)
0.607955 + 0.793971i \(0.291990\pi\)
\(18\) 0 0
\(19\) 18.0000i 0.947368i −0.880695 0.473684i \(-0.842924\pi\)
0.880695 0.473684i \(-0.157076\pi\)
\(20\) −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 \(-0.280995\pi\)
−0.772502 + 0.635012i \(0.780995\pi\)
\(24\) 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 −0.558939 0.829209i \(-0.688791\pi\)
0.829209 + 0.558939i \(0.188791\pi\)
\(38\) −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 0.813760 0.581202i \(-0.197417\pi\)
−0.581202 + 0.813760i \(0.697417\pi\)
\(44\) 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 \(-0.962254\pi\)
0.118305 + 0.992977i \(0.462254\pi\)
\(48\) 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 \(-0.140412\pi\)
−0.426950 + 0.904275i \(0.640412\pi\)
\(54\) 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 0.0458267 0.998949i \(-0.485408\pi\)
0.998949 0.0458267i \(-0.0145922\pi\)
\(68\) 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 0.975117 0.221692i \(-0.0711580\pi\)
−0.221692 + 0.975117i \(0.571158\pi\)
\(74\) 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 \(-0.975801\pi\)
0.997112 0.0759494i \(-0.0241987\pi\)
\(80\) 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 \(-0.0985696\pi\)
−0.304740 + 0.952436i \(0.598570\pi\)
\(84\) 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 −0.732410 0.680864i \(-0.761605\pi\)
0.680864 + 0.732410i \(0.261605\pi\)
\(98\) −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 0.516488 0.856294i \(-0.327239\pi\)
−0.856294 + 0.516488i \(0.827239\pi\)
\(104\) 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 \(-0.879969\pi\)
0.368215 + 0.929741i \(0.379969\pi\)
\(108\) 0 0
\(109\) 162.000i 1.48624i −0.669159 0.743119i \(-0.733345\pi\)
0.669159 0.743119i \(-0.266655\pi\)
\(110\) 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 −0.999349 0.0360874i \(-0.988511\pi\)
−0.0360874 0.999349i \(-0.511489\pi\)
\(114\) 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 −0.456601 0.889672i \(-0.650933\pi\)
0.889672 + 0.456601i \(0.150933\pi\)
\(128\) 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 −0.647042 0.762454i \(-0.723994\pi\)
0.762454 + 0.647042i \(0.223994\pi\)
\(138\) 0 0
\(139\) 102.000i 0.733813i 0.930258 + 0.366906i \(0.119583\pi\)
−0.930258 + 0.366906i \(0.880417\pi\)
\(140\) 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 −0.329853 + 0.944032i \(0.606999\pi\)
−0.944032 + 0.329853i \(0.893001\pi\)
\(158\) −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 0.943856 0.330359i \(-0.107170\pi\)
−0.330359 + 0.943856i \(0.607170\pi\)
\(164\) 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 \(-0.533337\pi\)
0.994521 + 0.104539i \(0.0333365\pi\)
\(168\) 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 \(-0.100574\pi\)
−0.310731 + 0.950498i \(0.600574\pi\)
\(174\) 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 \(-0.635837\pi\)
−0.413911 + 0.910317i \(0.635837\pi\)
\(192\) 0 0
\(193\) −125.000 125.000i −0.647668 0.647668i 0.304761 0.952429i \(-0.401424\pi\)
−0.952429 + 0.304761i \(0.901424\pi\)
\(194\) 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 \(-0.924862\pi\)
0.233868 + 0.972268i \(0.424862\pi\)
\(198\) 0 0
\(199\) 18.0000i 0.0904523i 0.998977 + 0.0452261i \(0.0144008\pi\)
−0.998977 + 0.0452261i \(0.985599\pi\)
\(200\) −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 0.0352529 0.999378i \(-0.488776\pi\)
−0.999378 + 0.0352529i \(0.988776\pi\)
\(224\) 110.680i 0.494106i
\(225\) 0 0
\(226\) −370.000 −1.63717
\(227\) 271.956 271.956i 1.19804 1.19804i 0.223292 0.974752i \(-0.428320\pi\)
0.974752 0.223292i \(-0.0716803\pi\)
\(228\) 0 0
\(229\) 78.0000i 0.340611i −0.985391 0.170306i \(-0.945524\pi\)
0.985391 0.170306i \(-0.0544755\pi\)
\(230\) −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 \(-0.140963\pi\)
−0.428515 + 0.903535i \(0.640963\pi\)
\(234\) 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 \(-0.242105\pi\)
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 −0.217480 + 0.976065i \(0.569784\pi\)
−0.976065 + 0.217480i \(0.930216\pi\)
\(258\) 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 −0.995078 0.0990940i \(-0.968406\pi\)
−0.0990940 0.995078i \(-0.531594\pi\)
\(264\) 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 −0.987561 0.157236i \(-0.949742\pi\)
0.157236 + 0.987561i \(0.449742\pi\)
\(278\) 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 −0.961322 0.275427i \(-0.911181\pi\)
−0.275427 0.961322i \(-0.588819\pi\)
\(284\) 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 \(-0.412428\pi\)
−0.962394 + 0.271658i \(0.912428\pi\)
\(294\) 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 −0.326355 0.945247i \(-0.605820\pi\)
0.945247 + 0.326355i \(0.105820\pi\)
\(308\) −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 0.899722 0.436463i \(-0.143769\pi\)
−0.436463 + 0.899722i \(0.643769\pi\)
\(314\) 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 \(-0.738771\pi\)
0.731606 + 0.681728i \(0.238771\pi\)
\(318\) 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 −0.898636 0.438695i \(-0.855441\pi\)
0.438695 + 0.898636i \(0.355441\pi\)
\(338\) 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 \(-0.858766\pi\)
0.429284 + 0.903170i \(0.358766\pi\)
\(348\) 0 0
\(349\) 318.000i 0.911175i −0.890191 0.455587i \(-0.849429\pi\)
0.890191 0.455587i \(-0.150571\pi\)
\(350\) 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 \(-0.101514\pi\)
−0.313537 + 0.949576i \(0.601514\pi\)
\(354\) 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 −0.912705 0.408618i \(-0.866011\pi\)
0.408618 + 0.912705i \(0.366011\pi\)
\(368\) −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 0.828333 0.560236i \(-0.189290\pi\)
−0.560236 + 0.828333i \(0.689290\pi\)
\(374\) 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 \(-0.736643\pi\)
0.676821 0.736148i \(-0.263357\pi\)
\(380\) −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 \(-0.0760778\pi\)
−0.236737 + 0.971574i \(0.576078\pi\)
\(384\) 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 −0.954172 0.299260i \(-0.903260\pi\)
0.299260 + 0.954172i \(0.403260\pi\)
\(398\) 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 \(-0.860124\pi\)
0.904992 0.425428i \(-0.139876\pi\)
\(410\) −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 \(-0.417333\pi\)
0.256797 + 0.966465i \(0.417333\pi\)
\(432\) 0 0
\(433\) 145.000 + 145.000i 0.334873 + 0.334873i 0.854434 0.519561i \(-0.173904\pi\)
−0.519561 + 0.854434i \(0.673904\pi\)
\(434\) 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 \(0.0283154\pi\)
−0.996046 + 0.0888383i \(0.971685\pi\)
\(440\) −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 \(-0.148683\pi\)
−0.450301 + 0.892877i \(0.648683\pi\)
\(444\) 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 −0.982889 0.184201i \(-0.941030\pi\)
0.184201 + 0.982889i \(0.441030\pi\)
\(458\) −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 0.668299 0.743893i \(-0.267023\pi\)
−0.743893 + 0.668299i \(0.767023\pi\)
\(464\) 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 \(-0.806692\pi\)
0.570649 + 0.821194i \(0.306692\pi\)
\(468\) 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 −0.823700 0.567026i \(-0.808094\pi\)
0.567026 + 0.823700i \(0.308094\pi\)
\(488\) −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 \(-0.928596\pi\)
0.974945 0.222445i \(-0.0714037\pi\)
\(500\) 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 \(-0.472973\pi\)
−0.996397 + 0.0848065i \(0.972973\pi\)
\(504\) 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 \(-0.225833\pi\)
0.758704 + 0.651436i \(0.225833\pi\)
\(522\) 0 0
\(523\) 370.000 + 370.000i 0.707457 + 0.707457i 0.966000 0.258543i \(-0.0832423\pi\)
−0.258543 + 0.966000i \(0.583242\pi\)
\(524\) 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 −0.0992657 0.995061i \(-0.531649\pi\)
0.995061 + 0.0992657i \(0.0316494\pi\)
\(548\) −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 \(-0.645928\pi\)
0.896742 + 0.442555i \(0.145928\pi\)
\(558\) 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 \(-0.331808\pi\)
−0.863620 + 0.504143i \(0.831808\pi\)
\(564\) 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 −0.736785 0.676127i \(-0.763657\pi\)
0.676127 + 0.736785i \(0.263657\pi\)
\(578\) 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 \(-0.809765\pi\)
0.562694 + 0.826666i \(0.309765\pi\)
\(588\) 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 \(-0.185954\pi\)
−0.551526 + 0.834158i \(0.685954\pi\)
\(594\) 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 0.0824851 0.996592i \(-0.473714\pi\)
0.996592 0.0824851i \(-0.0262857\pi\)
\(608\) −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 −0.999934 0.0114852i \(-0.996344\pi\)
−0.0114852 0.999934i \(-0.503656\pi\)
\(614\) 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 \(-0.737307\pi\)
0.734734 + 0.678356i \(0.237307\pi\)
\(618\) 0 0
\(619\) 258.000i 0.416801i 0.978044 + 0.208401i \(0.0668258\pi\)
−0.978044 + 0.208401i \(0.933174\pi\)
\(620\) −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 0.943283 + 0.331989i \(0.107720\pi\)
0.331989 + 0.943283i \(0.392280\pi\)
\(644\) 31.6228i 0.0491037i
\(645\) 0 0
\(646\) 180.000 0.278638
\(647\) 679.890 679.890i 1.05083 1.05083i 0.0521974 0.998637i \(-0.483378\pi\)
0.998637 0.0521974i \(-0.0166225\pi\)
\(648\) 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 \(-0.438493\pi\)
−0.981389 + 0.192030i \(0.938493\pi\)
\(654\) 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 0.986240 + 0.165320i \(0.0528658\pi\)
0.165320 + 0.986240i \(0.447134\pi\)
\(674\) 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 \(-0.923530\pi\)
0.237932 + 0.971282i \(0.423530\pi\)
\(678\) 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 \(-0.269813\pi\)
−0.749722 + 0.661753i \(0.769813\pi\)
\(684\) 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 \(-0.885774\pi\)
0.936301 0.351199i \(-0.114226\pi\)
\(710\) 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 −0.286873 + 0.957969i \(0.592616\pi\)
−0.957969 + 0.286873i \(0.907384\pi\)
\(728\) −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 0.974543 0.224202i \(-0.0719774\pi\)
−0.224202 + 0.974543i \(0.571977\pi\)
\(734\) 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 \(-0.957229\pi\)
0.990986 0.133965i \(-0.0427709\pi\)
\(740\) −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 0.929640 + 0.368468i \(0.120118\pi\)
0.368468 + 0.929640i \(0.379882\pi\)
\(744\) 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 −0.810420 0.585849i \(-0.800761\pi\)
0.585849 + 0.810420i \(0.300761\pi\)
\(758\) −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 \(0.0662926\pi\)
−0.978391 + 0.206762i \(0.933707\pi\)
\(770\) −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 \(-0.114251\pi\)
−0.351272 + 0.936273i \(0.614251\pi\)
\(774\) 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