Properties

Label 45.4.e.c.16.5
Level $45$
Weight $4$
Character 45.16
Analytic conductor $2.655$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,4,Mod(16,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.16");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.e (of order \(3\), 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: \(2.65508595026\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + 209529 x^{6} - 55412 x^{5} + 765088 x^{4} + 276096 x^{3} + 1572480 x^{2} + \cdots + 82944 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.5
Root \(1.09722 + 1.90044i\) of defining polynomial
Character \(\chi\) \(=\) 45.16
Dual form 45.4.e.c.31.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.09722 - 1.90044i) q^{2} +(0.206141 + 5.19206i) q^{3} +(1.59221 + 2.75778i) q^{4} +(2.50000 + 4.33013i) q^{5} +(10.0934 + 5.30509i) q^{6} +(-1.38302 + 2.39547i) q^{7} +24.5436 q^{8} +(-26.9150 + 2.14059i) q^{9} +O(q^{10})\) \(q+(1.09722 - 1.90044i) q^{2} +(0.206141 + 5.19206i) q^{3} +(1.59221 + 2.75778i) q^{4} +(2.50000 + 4.33013i) q^{5} +(10.0934 + 5.30509i) q^{6} +(-1.38302 + 2.39547i) q^{7} +24.5436 q^{8} +(-26.9150 + 2.14059i) q^{9} +10.9722 q^{10} +(26.3295 - 45.6040i) q^{11} +(-13.9904 + 8.83533i) q^{12} +(-10.2267 - 17.7132i) q^{13} +(3.03497 + 5.25672i) q^{14} +(-21.9669 + 13.8728i) q^{15} +(14.1921 - 24.5814i) q^{16} +3.66084 q^{17} +(-25.4637 + 53.4992i) q^{18} -95.6705 q^{19} +(-7.96104 + 13.7889i) q^{20} +(-12.7225 - 6.68694i) q^{21} +(-57.7786 - 100.075i) q^{22} +(44.9206 + 77.8047i) q^{23} +(5.05943 + 127.432i) q^{24} +(-12.5000 + 21.6506i) q^{25} -44.8840 q^{26} +(-16.6623 - 139.303i) q^{27} -8.80825 q^{28} +(113.890 - 197.264i) q^{29} +(2.26182 + 56.9684i) q^{30} +(-139.569 - 241.741i) q^{31} +(67.0306 + 116.100i) q^{32} +(242.206 + 127.303i) q^{33} +(4.01675 - 6.95722i) q^{34} -13.8302 q^{35} +(-48.7576 - 70.8175i) q^{36} +273.725 q^{37} +(-104.972 + 181.816i) q^{38} +(89.8599 - 56.7492i) q^{39} +(61.3589 + 106.277i) q^{40} +(-32.4323 - 56.1744i) q^{41} +(-26.6676 + 16.8414i) q^{42} +(-209.381 + 362.658i) q^{43} +167.688 q^{44} +(-76.5566 - 111.194i) q^{45} +197.151 q^{46} +(-69.3544 + 120.125i) q^{47} +(130.554 + 68.6190i) q^{48} +(167.674 + 290.421i) q^{49} +(27.4306 + 47.5111i) q^{50} +(0.754647 + 19.0073i) q^{51} +(32.5661 - 56.4062i) q^{52} -197.063 q^{53} +(-283.020 - 121.181i) q^{54} +263.295 q^{55} +(-33.9444 + 58.7934i) q^{56} +(-19.7216 - 496.727i) q^{57} +(-249.926 - 432.884i) q^{58} +(-370.552 - 641.814i) q^{59} +(-73.2340 - 38.4917i) q^{60} +(-244.234 + 423.026i) q^{61} -612.554 q^{62} +(32.0964 - 67.4346i) q^{63} +521.263 q^{64} +(51.1336 - 88.5660i) q^{65} +(507.687 - 320.620i) q^{66} +(205.734 + 356.341i) q^{67} +(5.82882 + 10.0958i) q^{68} +(-394.707 + 249.269i) q^{69} +(-15.1748 + 26.2836i) q^{70} -310.343 q^{71} +(-660.591 + 52.5377i) q^{72} -51.0260 q^{73} +(300.338 - 520.200i) q^{74} +(-114.988 - 60.4377i) q^{75} +(-152.327 - 263.839i) q^{76} +(72.8286 + 126.143i) q^{77} +(-9.25240 - 233.040i) q^{78} +(-603.999 + 1046.16i) q^{79} +141.921 q^{80} +(719.836 - 115.228i) q^{81} -142.342 q^{82} +(-452.611 + 783.945i) q^{83} +(-1.81574 - 45.7330i) q^{84} +(9.15210 + 15.8519i) q^{85} +(459.475 + 795.833i) q^{86} +(1047.68 + 550.661i) q^{87} +(646.220 - 1119.29i) q^{88} +663.633 q^{89} +(-295.317 + 23.4870i) q^{90} +56.5752 q^{91} +(-143.046 + 247.763i) q^{92} +(1226.36 - 774.485i) q^{93} +(152.194 + 263.608i) q^{94} +(-239.176 - 414.265i) q^{95} +(-588.982 + 371.960i) q^{96} +(362.668 - 628.159i) q^{97} +735.905 q^{98} +(-611.039 + 1283.79i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18} + 558 q^{19} + 180 q^{20} + 180 q^{21} - 311 q^{22} + 96 q^{23} + 48 q^{24} - 175 q^{25} + 716 q^{26} - 470 q^{27} + 674 q^{28} - 296 q^{29} + 80 q^{30} - 244 q^{31} - 314 q^{32} - 211 q^{33} - 125 q^{34} - 220 q^{35} - 2399 q^{36} + 808 q^{37} + 305 q^{38} + 634 q^{39} - 90 q^{40} - 47 q^{41} + 1941 q^{42} - 525 q^{43} - 110 q^{44} + 185 q^{45} + 1434 q^{46} + 164 q^{47} + 2051 q^{48} - 1225 q^{49} + 50 q^{50} + 1517 q^{51} - 1682 q^{52} - 1012 q^{53} - 4066 q^{54} + 230 q^{55} - 981 q^{56} + 337 q^{57} - 1183 q^{58} - 85 q^{59} + 65 q^{60} - 828 q^{61} + 1572 q^{62} - 828 q^{63} + 4472 q^{64} + 480 q^{65} + 4930 q^{66} - 1093 q^{67} + 2473 q^{68} - 822 q^{69} + 105 q^{70} - 656 q^{71} - 4626 q^{72} + 4170 q^{73} - 1316 q^{74} + 25 q^{75} - 2789 q^{76} + 24 q^{77} - 5314 q^{78} - 2110 q^{79} - 3240 q^{80} - 2167 q^{81} - 124 q^{82} + 1290 q^{83} + 5775 q^{84} - 805 q^{85} - 2569 q^{86} + 3604 q^{87} - 2271 q^{88} + 6096 q^{89} + 730 q^{90} + 6676 q^{91} + 2763 q^{92} - 696 q^{93} + 517 q^{94} + 1395 q^{95} - 593 q^{96} - 1787 q^{97} - 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.09722 1.90044i 0.387927 0.671909i −0.604244 0.796799i \(-0.706525\pi\)
0.992170 + 0.124891i \(0.0398581\pi\)
\(3\) 0.206141 + 5.19206i 0.0396718 + 0.999213i
\(4\) 1.59221 + 2.75778i 0.199026 + 0.344723i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 10.0934 + 5.30509i 0.686769 + 0.360965i
\(7\) −1.38302 + 2.39547i −0.0746763 + 0.129343i −0.900945 0.433932i \(-0.857126\pi\)
0.826269 + 0.563275i \(0.190459\pi\)
\(8\) 24.5436 1.08468
\(9\) −26.9150 + 2.14059i −0.996852 + 0.0792811i
\(10\) 10.9722 0.346972
\(11\) 26.3295 45.6040i 0.721694 1.25001i −0.238626 0.971112i \(-0.576697\pi\)
0.960320 0.278900i \(-0.0899698\pi\)
\(12\) −13.9904 + 8.83533i −0.336556 + 0.212545i
\(13\) −10.2267 17.7132i −0.218183 0.377905i 0.736069 0.676906i \(-0.236680\pi\)
−0.954253 + 0.299002i \(0.903346\pi\)
\(14\) 3.03497 + 5.25672i 0.0579378 + 0.100351i
\(15\) −21.9669 + 13.8728i −0.378123 + 0.238796i
\(16\) 14.1921 24.5814i 0.221751 0.384085i
\(17\) 3.66084 0.0522285 0.0261142 0.999659i \(-0.491687\pi\)
0.0261142 + 0.999659i \(0.491687\pi\)
\(18\) −25.4637 + 53.4992i −0.333436 + 0.700549i
\(19\) −95.6705 −1.15517 −0.577587 0.816329i \(-0.696006\pi\)
−0.577587 + 0.816329i \(0.696006\pi\)
\(20\) −7.96104 + 13.7889i −0.0890071 + 0.154165i
\(21\) −12.7225 6.68694i −0.132204 0.0694862i
\(22\) −57.7786 100.075i −0.559929 0.969825i
\(23\) 44.9206 + 77.8047i 0.407243 + 0.705365i 0.994580 0.103977i \(-0.0331569\pi\)
−0.587337 + 0.809343i \(0.699824\pi\)
\(24\) 5.05943 + 127.432i 0.0430313 + 1.08383i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −44.8840 −0.338556
\(27\) −16.6623 139.303i −0.118766 0.992922i
\(28\) −8.80825 −0.0594501
\(29\) 113.890 197.264i 0.729272 1.26314i −0.227919 0.973680i \(-0.573192\pi\)
0.957191 0.289456i \(-0.0934744\pi\)
\(30\) 2.26182 + 56.9684i 0.0137650 + 0.346699i
\(31\) −139.569 241.741i −0.808625 1.40058i −0.913816 0.406128i \(-0.866879\pi\)
0.105191 0.994452i \(-0.466455\pi\)
\(32\) 67.0306 + 116.100i 0.370295 + 0.641370i
\(33\) 242.206 + 127.303i 1.27766 + 0.671536i
\(34\) 4.01675 6.95722i 0.0202608 0.0350928i
\(35\) −13.8302 −0.0667925
\(36\) −48.7576 70.8175i −0.225730 0.327859i
\(37\) 273.725 1.21622 0.608110 0.793852i \(-0.291928\pi\)
0.608110 + 0.793852i \(0.291928\pi\)
\(38\) −104.972 + 181.816i −0.448123 + 0.776172i
\(39\) 89.8599 56.7492i 0.368951 0.233004i
\(40\) 61.3589 + 106.277i 0.242542 + 0.420096i
\(41\) −32.4323 56.1744i −0.123539 0.213975i 0.797622 0.603157i \(-0.206091\pi\)
−0.921161 + 0.389182i \(0.872758\pi\)
\(42\) −26.6676 + 16.8414i −0.0979738 + 0.0618733i
\(43\) −209.381 + 362.658i −0.742565 + 1.28616i 0.208759 + 0.977967i \(0.433057\pi\)
−0.951324 + 0.308193i \(0.900276\pi\)
\(44\) 167.688 0.574544
\(45\) −76.5566 111.194i −0.253608 0.368351i
\(46\) 197.151 0.631921
\(47\) −69.3544 + 120.125i −0.215242 + 0.372810i −0.953347 0.301875i \(-0.902387\pi\)
0.738105 + 0.674685i \(0.235721\pi\)
\(48\) 130.554 + 68.6190i 0.392580 + 0.206339i
\(49\) 167.674 + 290.421i 0.488847 + 0.846708i
\(50\) 27.4306 + 47.5111i 0.0775853 + 0.134382i
\(51\) 0.754647 + 19.0073i 0.00207200 + 0.0521874i
\(52\) 32.5661 56.4062i 0.0868483 0.150426i
\(53\) −197.063 −0.510730 −0.255365 0.966845i \(-0.582196\pi\)
−0.255365 + 0.966845i \(0.582196\pi\)
\(54\) −283.020 121.181i −0.713225 0.305381i
\(55\) 263.295 0.645503
\(56\) −33.9444 + 58.7934i −0.0810001 + 0.140296i
\(57\) −19.7216 496.727i −0.0458278 1.15427i
\(58\) −249.926 432.884i −0.565808 0.980008i
\(59\) −370.552 641.814i −0.817656 1.41622i −0.907405 0.420257i \(-0.861940\pi\)
0.0897490 0.995964i \(-0.471394\pi\)
\(60\) −73.2340 38.4917i −0.157575 0.0828211i
\(61\) −244.234 + 423.026i −0.512639 + 0.887916i 0.487254 + 0.873260i \(0.337999\pi\)
−0.999893 + 0.0146560i \(0.995335\pi\)
\(62\) −612.554 −1.25475
\(63\) 32.0964 67.4346i 0.0641868 0.134856i
\(64\) 521.263 1.01809
\(65\) 51.1336 88.5660i 0.0975746 0.169004i
\(66\) 507.687 320.620i 0.946848 0.597963i
\(67\) 205.734 + 356.341i 0.375140 + 0.649762i 0.990348 0.138603i \(-0.0442613\pi\)
−0.615208 + 0.788365i \(0.710928\pi\)
\(68\) 5.82882 + 10.0958i 0.0103948 + 0.0180044i
\(69\) −394.707 + 249.269i −0.688654 + 0.434905i
\(70\) −15.1748 + 26.2836i −0.0259106 + 0.0448785i
\(71\) −310.343 −0.518746 −0.259373 0.965777i \(-0.583516\pi\)
−0.259373 + 0.965777i \(0.583516\pi\)
\(72\) −660.591 + 52.5377i −1.08127 + 0.0859948i
\(73\) −51.0260 −0.0818101 −0.0409051 0.999163i \(-0.513024\pi\)
−0.0409051 + 0.999163i \(0.513024\pi\)
\(74\) 300.338 520.200i 0.471804 0.817189i
\(75\) −114.988 60.4377i −0.177036 0.0930499i
\(76\) −152.327 263.839i −0.229910 0.398215i
\(77\) 72.8286 + 126.143i 0.107787 + 0.186692i
\(78\) −9.25240 233.040i −0.0134311 0.338290i
\(79\) −603.999 + 1046.16i −0.860193 + 1.48990i 0.0115496 + 0.999933i \(0.496324\pi\)
−0.871742 + 0.489964i \(0.837010\pi\)
\(80\) 141.921 0.198340
\(81\) 719.836 115.228i 0.987429 0.158063i
\(82\) −142.342 −0.191695
\(83\) −452.611 + 783.945i −0.598560 + 1.03674i 0.394474 + 0.918907i \(0.370927\pi\)
−0.993034 + 0.117829i \(0.962406\pi\)
\(84\) −1.81574 45.7330i −0.00235849 0.0594033i
\(85\) 9.15210 + 15.8519i 0.0116786 + 0.0202280i
\(86\) 459.475 + 795.833i 0.576121 + 0.997871i
\(87\) 1047.68 + 550.661i 1.29107 + 0.678587i
\(88\) 646.220 1119.29i 0.782810 1.35587i
\(89\) 663.633 0.790393 0.395197 0.918597i \(-0.370676\pi\)
0.395197 + 0.918597i \(0.370676\pi\)
\(90\) −295.317 + 23.4870i −0.345880 + 0.0275083i
\(91\) 56.5752 0.0651725
\(92\) −143.046 + 247.763i −0.162104 + 0.280772i
\(93\) 1226.36 774.485i 1.36740 0.863552i
\(94\) 152.194 + 263.608i 0.166996 + 0.289246i
\(95\) −239.176 414.265i −0.258305 0.447397i
\(96\) −588.982 + 371.960i −0.626175 + 0.395448i
\(97\) 362.668 628.159i 0.379622 0.657525i −0.611385 0.791333i \(-0.709387\pi\)
0.991007 + 0.133809i \(0.0427207\pi\)
\(98\) 735.905 0.758547
\(99\) −611.039 + 1283.79i −0.620321 + 1.30329i
\(100\) −79.6104 −0.0796104
\(101\) −488.891 + 846.784i −0.481648 + 0.834239i −0.999778 0.0210629i \(-0.993295\pi\)
0.518130 + 0.855302i \(0.326628\pi\)
\(102\) 36.9503 + 19.4211i 0.0358689 + 0.0188527i
\(103\) −793.852 1374.99i −0.759423 1.31536i −0.943145 0.332381i \(-0.892148\pi\)
0.183722 0.982978i \(-0.441185\pi\)
\(104\) −251.000 434.745i −0.236660 0.409907i
\(105\) −2.85097 71.8075i −0.00264978 0.0667399i
\(106\) −216.222 + 374.507i −0.198126 + 0.343164i
\(107\) 897.731 0.811093 0.405546 0.914074i \(-0.367081\pi\)
0.405546 + 0.914074i \(0.367081\pi\)
\(108\) 357.638 267.751i 0.318646 0.238559i
\(109\) 855.492 0.751754 0.375877 0.926669i \(-0.377341\pi\)
0.375877 + 0.926669i \(0.377341\pi\)
\(110\) 288.893 500.377i 0.250408 0.433719i
\(111\) 56.4259 + 1421.20i 0.0482496 + 1.21526i
\(112\) 39.2560 + 67.9934i 0.0331191 + 0.0573640i
\(113\) −455.121 788.292i −0.378886 0.656250i 0.612014 0.790847i \(-0.290359\pi\)
−0.990900 + 0.134597i \(0.957026\pi\)
\(114\) −965.641 507.540i −0.793339 0.416978i
\(115\) −224.603 + 389.024i −0.182125 + 0.315449i
\(116\) 725.348 0.580576
\(117\) 313.169 + 454.860i 0.247457 + 0.359417i
\(118\) −1626.31 −1.26876
\(119\) −5.06303 + 8.76943i −0.00390023 + 0.00675539i
\(120\) −539.147 + 340.487i −0.410143 + 0.259017i
\(121\) −720.984 1248.78i −0.541686 0.938227i
\(122\) 535.958 + 928.306i 0.397732 + 0.688893i
\(123\) 284.976 179.971i 0.208906 0.131930i
\(124\) 444.447 769.804i 0.321875 0.557504i
\(125\) −125.000 −0.0894427
\(126\) −92.9387 134.988i −0.0657114 0.0954420i
\(127\) −2038.25 −1.42414 −0.712068 0.702111i \(-0.752241\pi\)
−0.712068 + 0.702111i \(0.752241\pi\)
\(128\) 35.6968 61.8287i 0.0246499 0.0426948i
\(129\) −1926.11 1012.36i −1.31461 0.690956i
\(130\) −112.210 194.353i −0.0757035 0.131122i
\(131\) −117.823 204.075i −0.0785817 0.136108i 0.824057 0.566508i \(-0.191706\pi\)
−0.902638 + 0.430400i \(0.858372\pi\)
\(132\) 34.5673 + 870.647i 0.0227932 + 0.574091i
\(133\) 132.315 229.176i 0.0862642 0.149414i
\(134\) 902.942 0.582107
\(135\) 561.544 420.408i 0.358000 0.268022i
\(136\) 89.8501 0.0566513
\(137\) 1486.45 2574.60i 0.926975 1.60557i 0.138621 0.990345i \(-0.455733\pi\)
0.788354 0.615222i \(-0.210934\pi\)
\(138\) 40.6409 + 1023.62i 0.0250694 + 0.631424i
\(139\) 1047.32 + 1814.00i 0.639080 + 1.10692i 0.985635 + 0.168890i \(0.0540182\pi\)
−0.346555 + 0.938030i \(0.612648\pi\)
\(140\) −22.0206 38.1408i −0.0132934 0.0230249i
\(141\) −637.995 335.330i −0.381056 0.200283i
\(142\) −340.515 + 589.790i −0.201235 + 0.348550i
\(143\) −1077.06 −0.629847
\(144\) −329.362 + 691.989i −0.190603 + 0.400456i
\(145\) 1138.90 0.652281
\(146\) −55.9868 + 96.9720i −0.0317363 + 0.0549689i
\(147\) −1473.32 + 930.444i −0.826648 + 0.522052i
\(148\) 435.828 + 754.876i 0.242060 + 0.419259i
\(149\) −136.969 237.237i −0.0753081 0.130437i 0.825912 0.563799i \(-0.190661\pi\)
−0.901220 + 0.433361i \(0.857327\pi\)
\(150\) −241.026 + 152.215i −0.131198 + 0.0828554i
\(151\) 468.422 811.331i 0.252448 0.437253i −0.711751 0.702432i \(-0.752098\pi\)
0.964199 + 0.265179i \(0.0854310\pi\)
\(152\) −2348.10 −1.25300
\(153\) −98.5315 + 7.83635i −0.0520641 + 0.00414073i
\(154\) 319.637 0.167254
\(155\) 697.846 1208.71i 0.361628 0.626358i
\(156\) 299.578 + 157.458i 0.153753 + 0.0808123i
\(157\) −199.218 345.055i −0.101269 0.175404i 0.810938 0.585131i \(-0.198957\pi\)
−0.912208 + 0.409728i \(0.865624\pi\)
\(158\) 1325.44 + 2295.73i 0.667383 + 1.15594i
\(159\) −40.6227 1023.16i −0.0202616 0.510328i
\(160\) −335.153 + 580.502i −0.165601 + 0.286829i
\(161\) −248.505 −0.121646
\(162\) 570.835 1494.44i 0.276846 0.724779i
\(163\) 478.154 0.229766 0.114883 0.993379i \(-0.463351\pi\)
0.114883 + 0.993379i \(0.463351\pi\)
\(164\) 103.278 178.883i 0.0491747 0.0851732i
\(165\) 54.2757 + 1367.04i 0.0256082 + 0.644995i
\(166\) 993.229 + 1720.32i 0.464395 + 0.804355i
\(167\) 170.181 + 294.763i 0.0788564 + 0.136583i 0.902757 0.430151i \(-0.141540\pi\)
−0.823900 + 0.566735i \(0.808206\pi\)
\(168\) −312.256 164.122i −0.143399 0.0753705i
\(169\) 889.328 1540.36i 0.404792 0.701120i
\(170\) 40.1675 0.0181218
\(171\) 2574.97 204.791i 1.15154 0.0915835i
\(172\) −1333.51 −0.591159
\(173\) −1888.03 + 3270.17i −0.829738 + 1.43715i 0.0685065 + 0.997651i \(0.478177\pi\)
−0.898244 + 0.439497i \(0.855157\pi\)
\(174\) 2196.04 1386.87i 0.956790 0.604241i
\(175\) −34.5756 59.8867i −0.0149353 0.0258686i
\(176\) −747.341 1294.43i −0.320073 0.554384i
\(177\) 3255.95 2056.23i 1.38267 0.873196i
\(178\) 728.153 1261.20i 0.306615 0.531072i
\(179\) 186.652 0.0779385 0.0389693 0.999240i \(-0.487593\pi\)
0.0389693 + 0.999240i \(0.487593\pi\)
\(180\) 184.755 388.170i 0.0765046 0.160736i
\(181\) 1438.75 0.590837 0.295418 0.955368i \(-0.404541\pi\)
0.295418 + 0.955368i \(0.404541\pi\)
\(182\) 62.0756 107.518i 0.0252821 0.0437900i
\(183\) −2246.72 1180.88i −0.907555 0.477010i
\(184\) 1102.51 + 1909.61i 0.441729 + 0.765098i
\(185\) 684.313 + 1185.27i 0.271955 + 0.471040i
\(186\) −126.272 3180.42i −0.0497781 1.25376i
\(187\) 96.3880 166.949i 0.0376930 0.0652862i
\(188\) −441.706 −0.171355
\(189\) 356.741 + 152.746i 0.137297 + 0.0587863i
\(190\) −1049.72 −0.400813
\(191\) 195.218 338.127i 0.0739552 0.128094i −0.826676 0.562678i \(-0.809771\pi\)
0.900631 + 0.434584i \(0.143104\pi\)
\(192\) 107.453 + 2706.43i 0.0403895 + 1.01729i
\(193\) 1957.52 + 3390.53i 0.730081 + 1.26454i 0.956848 + 0.290588i \(0.0938510\pi\)
−0.226767 + 0.973949i \(0.572816\pi\)
\(194\) −795.854 1378.46i −0.294531 0.510143i
\(195\) 470.381 + 247.232i 0.172742 + 0.0907930i
\(196\) −533.945 + 924.820i −0.194586 + 0.337034i
\(197\) −892.680 −0.322847 −0.161423 0.986885i \(-0.551608\pi\)
−0.161423 + 0.986885i \(0.551608\pi\)
\(198\) 1769.33 + 2569.85i 0.635055 + 0.922381i
\(199\) −2770.50 −0.986913 −0.493457 0.869770i \(-0.664267\pi\)
−0.493457 + 0.869770i \(0.664267\pi\)
\(200\) −306.795 + 531.384i −0.108468 + 0.187873i
\(201\) −1807.74 + 1141.64i −0.634368 + 0.400622i
\(202\) 1072.84 + 1858.22i 0.373688 + 0.647247i
\(203\) 315.026 + 545.641i 0.108919 + 0.188653i
\(204\) −51.2165 + 32.3447i −0.0175778 + 0.0111009i
\(205\) 162.162 280.872i 0.0552481 0.0956925i
\(206\) −3484.13 −1.17840
\(207\) −1375.59 1997.96i −0.461883 0.670859i
\(208\) −580.554 −0.193530
\(209\) −2518.96 + 4362.96i −0.833683 + 1.44398i
\(210\) −139.594 73.3706i −0.0458710 0.0241098i
\(211\) −2291.25 3968.57i −0.747566 1.29482i −0.948986 0.315318i \(-0.897889\pi\)
0.201420 0.979505i \(-0.435444\pi\)
\(212\) −313.765 543.458i −0.101649 0.176060i
\(213\) −63.9743 1611.32i −0.0205796 0.518338i
\(214\) 985.010 1706.09i 0.314644 0.544980i
\(215\) −2093.81 −0.664170
\(216\) −408.953 3419.00i −0.128823 1.07701i
\(217\) 772.111 0.241541
\(218\) 938.664 1625.81i 0.291626 0.505110i
\(219\) −10.5185 264.930i −0.00324555 0.0817457i
\(220\) 419.220 + 726.111i 0.128472 + 0.222520i
\(221\) −37.4384 64.8452i −0.0113954 0.0197374i
\(222\) 2762.82 + 1452.14i 0.835263 + 0.439014i
\(223\) −2047.67 + 3546.66i −0.614897 + 1.06503i 0.375506 + 0.926820i \(0.377469\pi\)
−0.990403 + 0.138212i \(0.955864\pi\)
\(224\) −370.820 −0.110609
\(225\) 290.093 609.484i 0.0859533 0.180588i
\(226\) −1997.47 −0.587920
\(227\) 1934.68 3350.96i 0.565678 0.979784i −0.431308 0.902205i \(-0.641948\pi\)
0.996986 0.0775789i \(-0.0247190\pi\)
\(228\) 1338.47 845.281i 0.388781 0.245527i
\(229\) −618.006 1070.42i −0.178336 0.308887i 0.762975 0.646429i \(-0.223738\pi\)
−0.941311 + 0.337541i \(0.890405\pi\)
\(230\) 492.878 + 853.690i 0.141302 + 0.244742i
\(231\) −639.929 + 404.134i −0.182269 + 0.115109i
\(232\) 2795.27 4841.56i 0.791029 1.37010i
\(233\) 2207.05 0.620552 0.310276 0.950647i \(-0.399579\pi\)
0.310276 + 0.950647i \(0.399579\pi\)
\(234\) 1208.05 96.0781i 0.337491 0.0268411i
\(235\) −693.544 −0.192518
\(236\) 1179.99 2043.80i 0.325470 0.563730i
\(237\) −5556.22 2920.35i −1.52285 0.800409i
\(238\) 11.1105 + 19.2440i 0.00302600 + 0.00524119i
\(239\) −438.324 759.199i −0.118631 0.205475i 0.800594 0.599207i \(-0.204517\pi\)
−0.919225 + 0.393732i \(0.871184\pi\)
\(240\) 29.2556 + 736.862i 0.00786852 + 0.198184i
\(241\) 238.931 413.840i 0.0638626 0.110613i −0.832326 0.554286i \(-0.812991\pi\)
0.896189 + 0.443673i \(0.146325\pi\)
\(242\) −3164.32 −0.840537
\(243\) 746.658 + 3713.68i 0.197112 + 0.980381i
\(244\) −1555.49 −0.408114
\(245\) −838.372 + 1452.10i −0.218619 + 0.378659i
\(246\) −29.3424 739.048i −0.00760490 0.191545i
\(247\) 978.396 + 1694.63i 0.252040 + 0.436546i
\(248\) −3425.53 5933.19i −0.877102 1.51919i
\(249\) −4163.59 2188.38i −1.05967 0.556960i
\(250\) −137.153 + 237.556i −0.0346972 + 0.0600973i
\(251\) 6892.28 1.73322 0.866608 0.498990i \(-0.166296\pi\)
0.866608 + 0.498990i \(0.166296\pi\)
\(252\) 237.074 18.8548i 0.0592630 0.00471327i
\(253\) 4730.94 1.17562
\(254\) −2236.41 + 3873.57i −0.552460 + 0.956889i
\(255\) −80.4174 + 50.7860i −0.0197488 + 0.0124719i
\(256\) 2006.72 + 3475.74i 0.489921 + 0.848568i
\(257\) 3628.35 + 6284.49i 0.880664 + 1.52535i 0.850605 + 0.525806i \(0.176236\pi\)
0.0300589 + 0.999548i \(0.490431\pi\)
\(258\) −4037.30 + 2549.67i −0.974230 + 0.615255i
\(259\) −378.569 + 655.701i −0.0908229 + 0.157310i
\(260\) 325.661 0.0776795
\(261\) −2643.10 + 5553.15i −0.626834 + 1.31698i
\(262\) −517.110 −0.121936
\(263\) 3158.78 5471.16i 0.740603 1.28276i −0.211618 0.977352i \(-0.567873\pi\)
0.952221 0.305409i \(-0.0987933\pi\)
\(264\) 5944.61 + 3124.48i 1.38585 + 0.728404i
\(265\) −492.658 853.308i −0.114203 0.197805i
\(266\) −290.357 502.913i −0.0669283 0.115923i
\(267\) 136.802 + 3445.63i 0.0313563 + 0.789771i
\(268\) −655.142 + 1134.74i −0.149325 + 0.258639i
\(269\) 5746.22 1.30243 0.651214 0.758894i \(-0.274260\pi\)
0.651214 + 0.758894i \(0.274260\pi\)
\(270\) −182.823 1528.46i −0.0412083 0.344516i
\(271\) 4925.20 1.10400 0.552001 0.833844i \(-0.313865\pi\)
0.552001 + 0.833844i \(0.313865\pi\)
\(272\) 51.9550 89.9886i 0.0115817 0.0200602i
\(273\) 11.6625 + 293.742i 0.00258551 + 0.0651212i
\(274\) −3261.92 5649.81i −0.719196 1.24568i
\(275\) 658.237 + 1140.10i 0.144339 + 0.250002i
\(276\) −1315.89 691.629i −0.286982 0.150837i
\(277\) −1162.94 + 2014.27i −0.252254 + 0.436917i −0.964146 0.265372i \(-0.914505\pi\)
0.711892 + 0.702289i \(0.247839\pi\)
\(278\) 4596.55 0.991665
\(279\) 4273.98 + 6207.70i 0.917119 + 1.33206i
\(280\) −339.444 −0.0724487
\(281\) −1641.71 + 2843.52i −0.348527 + 0.603667i −0.985988 0.166816i \(-0.946652\pi\)
0.637461 + 0.770483i \(0.279985\pi\)
\(282\) −1337.30 + 844.543i −0.282393 + 0.178340i
\(283\) −1007.11 1744.36i −0.211541 0.366400i 0.740656 0.671885i \(-0.234515\pi\)
−0.952197 + 0.305484i \(0.901182\pi\)
\(284\) −494.131 855.860i −0.103244 0.178824i
\(285\) 2101.59 1327.21i 0.436798 0.275851i
\(286\) −1181.77 + 2046.89i −0.244334 + 0.423199i
\(287\) 179.419 0.0369016
\(288\) −2052.65 2981.36i −0.419978 0.609994i
\(289\) −4899.60 −0.997272
\(290\) 1249.63 2164.42i 0.253037 0.438273i
\(291\) 3336.20 + 1753.50i 0.672067 + 0.353238i
\(292\) −81.2440 140.719i −0.0162823 0.0282018i
\(293\) −240.348 416.295i −0.0479225 0.0830042i 0.841069 0.540928i \(-0.181927\pi\)
−0.888992 + 0.457923i \(0.848593\pi\)
\(294\) 151.700 + 3820.86i 0.0300929 + 0.757950i
\(295\) 1852.76 3209.07i 0.365667 0.633354i
\(296\) 6718.20 1.31921
\(297\) −6791.49 2907.91i −1.32688 0.568128i
\(298\) −601.140 −0.116856
\(299\) 918.781 1591.37i 0.177707 0.307798i
\(300\) −16.4109 413.342i −0.00315828 0.0795477i
\(301\) −579.158 1003.13i −0.110904 0.192091i
\(302\) −1027.93 1780.42i −0.195863 0.339244i
\(303\) −4497.33 2363.79i −0.852690 0.448173i
\(304\) −1357.76 + 2351.72i −0.256162 + 0.443685i
\(305\) −2442.34 −0.458518
\(306\) −93.2184 + 195.852i −0.0174148 + 0.0365886i
\(307\) 3222.21 0.599026 0.299513 0.954092i \(-0.403176\pi\)
0.299513 + 0.954092i \(0.403176\pi\)
\(308\) −231.917 + 401.691i −0.0429048 + 0.0743133i
\(309\) 6975.40 4405.17i 1.28420 0.811008i
\(310\) −1531.38 2652.44i −0.280570 0.485962i
\(311\) −1207.00 2090.59i −0.220074 0.381179i 0.734757 0.678331i \(-0.237296\pi\)
−0.954830 + 0.297152i \(0.903963\pi\)
\(312\) 2205.48 1392.83i 0.400195 0.252735i
\(313\) 1253.47 2171.07i 0.226359 0.392065i −0.730368 0.683054i \(-0.760651\pi\)
0.956726 + 0.290990i \(0.0939846\pi\)
\(314\) −874.344 −0.157140
\(315\) 372.241 29.6049i 0.0665823 0.00529538i
\(316\) −3846.77 −0.684803
\(317\) −1853.56 + 3210.46i −0.328411 + 0.568825i −0.982197 0.187855i \(-0.939846\pi\)
0.653786 + 0.756680i \(0.273180\pi\)
\(318\) −1989.04 1045.44i −0.350754 0.184356i
\(319\) −5997.34 10387.7i −1.05262 1.82320i
\(320\) 1303.16 + 2257.13i 0.227652 + 0.394305i
\(321\) 185.059 + 4661.07i 0.0321775 + 0.810454i
\(322\) −272.665 + 472.270i −0.0471895 + 0.0817347i
\(323\) −350.234 −0.0603330
\(324\) 1463.90 + 1801.69i 0.251012 + 0.308931i
\(325\) 511.336 0.0872733
\(326\) 524.641 908.704i 0.0891324 0.154382i
\(327\) 176.352 + 4441.77i 0.0298234 + 0.751163i
\(328\) −796.005 1378.72i −0.134000 0.232095i
\(329\) −191.838 332.272i −0.0321470 0.0556802i
\(330\) 2657.54 + 1396.80i 0.443312 + 0.233004i
\(331\) −1276.72 + 2211.35i −0.212009 + 0.367211i −0.952343 0.305029i \(-0.901334\pi\)
0.740334 + 0.672239i \(0.234667\pi\)
\(332\) −2882.60 −0.476516
\(333\) −7367.32 + 585.933i −1.21239 + 0.0964233i
\(334\) 746.906 0.122362
\(335\) −1028.67 + 1781.71i −0.167768 + 0.290582i
\(336\) −344.934 + 217.836i −0.0560050 + 0.0353688i
\(337\) −1776.44 3076.89i −0.287148 0.497356i 0.685979 0.727621i \(-0.259374\pi\)
−0.973128 + 0.230265i \(0.926041\pi\)
\(338\) −1951.58 3380.24i −0.314059 0.543966i
\(339\) 3999.04 2525.51i 0.640702 0.404623i
\(340\) −29.1441 + 50.4790i −0.00464871 + 0.00805179i
\(341\) −14699.2 −2.33432
\(342\) 2436.12 5118.29i 0.385177 0.809256i
\(343\) −1876.35 −0.295374
\(344\) −5138.95 + 8900.93i −0.805447 + 1.39508i
\(345\) −2066.13 1085.96i −0.322426 0.169467i
\(346\) 4143.19 + 7176.21i 0.643754 + 1.11502i
\(347\) 3884.01 + 6727.30i 0.600878 + 1.04075i 0.992688 + 0.120705i \(0.0385155\pi\)
−0.391811 + 0.920046i \(0.628151\pi\)
\(348\) 149.524 + 3766.05i 0.0230325 + 0.580119i
\(349\) −348.003 + 602.760i −0.0533759 + 0.0924498i −0.891479 0.453062i \(-0.850331\pi\)
0.838103 + 0.545512i \(0.183665\pi\)
\(350\) −151.748 −0.0231751
\(351\) −2297.10 + 1719.76i −0.349317 + 0.261521i
\(352\) 7059.52 1.06896
\(353\) 2725.94 4721.46i 0.411011 0.711892i −0.583990 0.811761i \(-0.698509\pi\)
0.995001 + 0.0998692i \(0.0318424\pi\)
\(354\) −335.248 8443.90i −0.0503340 1.26776i
\(355\) −775.858 1343.83i −0.115995 0.200909i
\(356\) 1056.64 + 1830.16i 0.157309 + 0.272467i
\(357\) −46.5751 24.4798i −0.00690481 0.00362916i
\(358\) 204.798 354.721i 0.0302344 0.0523675i
\(359\) 4036.41 0.593408 0.296704 0.954969i \(-0.404113\pi\)
0.296704 + 0.954969i \(0.404113\pi\)
\(360\) −1878.97 2729.10i −0.275085 0.399545i
\(361\) 2293.85 0.334429
\(362\) 1578.63 2734.26i 0.229201 0.396988i
\(363\) 6335.12 4000.82i 0.915999 0.578481i
\(364\) 90.0795 + 156.022i 0.0129710 + 0.0224665i
\(365\) −127.565 220.949i −0.0182933 0.0316849i
\(366\) −4709.34 + 2974.09i −0.672572 + 0.424749i
\(367\) −5619.96 + 9734.06i −0.799345 + 1.38451i 0.120698 + 0.992689i \(0.461487\pi\)
−0.920043 + 0.391817i \(0.871847\pi\)
\(368\) 2550.07 0.361227
\(369\) 993.163 + 1442.51i 0.140114 + 0.203507i
\(370\) 3003.38 0.421995
\(371\) 272.543 472.059i 0.0381394 0.0660595i
\(372\) 4088.49 + 2148.91i 0.569834 + 0.299504i
\(373\) 3160.36 + 5473.90i 0.438706 + 0.759860i 0.997590 0.0693853i \(-0.0221038\pi\)
−0.558884 + 0.829246i \(0.688770\pi\)
\(374\) −211.518 366.360i −0.0292442 0.0506525i
\(375\) −25.7676 649.008i −0.00354835 0.0893723i
\(376\) −1702.20 + 2948.30i −0.233469 + 0.404381i
\(377\) −4658.90 −0.636460
\(378\) 681.708 510.370i 0.0927600 0.0694460i
\(379\) 9325.49 1.26390 0.631950 0.775009i \(-0.282255\pi\)
0.631950 + 0.775009i \(0.282255\pi\)
\(380\) 761.637 1319.19i 0.102819 0.178087i
\(381\) −420.165 10582.7i −0.0564980 1.42301i
\(382\) −428.394 742.000i −0.0573784 0.0993823i
\(383\) −5574.01 9654.47i −0.743652 1.28804i −0.950822 0.309738i \(-0.899759\pi\)
0.207170 0.978305i \(-0.433575\pi\)
\(384\) 328.377 + 172.595i 0.0436391 + 0.0229367i
\(385\) −364.143 + 630.715i −0.0482038 + 0.0834914i
\(386\) 8591.35 1.13287
\(387\) 4859.19 10209.1i 0.638259 1.34098i
\(388\) 2309.77 0.302219
\(389\) −3285.41 + 5690.49i −0.428218 + 0.741695i −0.996715 0.0809902i \(-0.974192\pi\)
0.568497 + 0.822685i \(0.307525\pi\)
\(390\) 985.963 622.665i 0.128016 0.0808458i
\(391\) 164.447 + 284.831i 0.0212697 + 0.0368402i
\(392\) 4115.33 + 7127.96i 0.530244 + 0.918409i
\(393\) 1035.28 653.810i 0.132883 0.0839195i
\(394\) −979.469 + 1696.49i −0.125241 + 0.216924i
\(395\) −6039.99 −0.769380
\(396\) −4513.33 + 358.951i −0.572735 + 0.0455504i
\(397\) 3969.33 0.501800 0.250900 0.968013i \(-0.419273\pi\)
0.250900 + 0.968013i \(0.419273\pi\)
\(398\) −3039.86 + 5265.19i −0.382850 + 0.663115i
\(399\) 1217.17 + 639.743i 0.152719 + 0.0802687i
\(400\) 354.802 + 614.535i 0.0443503 + 0.0768169i
\(401\) −2187.35 3788.60i −0.272396 0.471804i 0.697079 0.716995i \(-0.254483\pi\)
−0.969475 + 0.245190i \(0.921150\pi\)
\(402\) 186.133 + 4688.13i 0.0230932 + 0.581649i
\(403\) −2854.67 + 4944.44i −0.352857 + 0.611166i
\(404\) −3113.66 −0.383442
\(405\) 2298.54 + 2828.91i 0.282013 + 0.347086i
\(406\) 1382.61 0.169010
\(407\) 7207.05 12483.0i 0.877740 1.52029i
\(408\) 18.5217 + 466.507i 0.00224746 + 0.0566067i
\(409\) 4436.16 + 7683.66i 0.536318 + 0.928930i 0.999098 + 0.0424573i \(0.0135186\pi\)
−0.462780 + 0.886473i \(0.653148\pi\)
\(410\) −355.855 616.358i −0.0428644 0.0742433i
\(411\) 13673.9 + 7186.99i 1.64108 + 0.862550i
\(412\) 2527.95 4378.55i 0.302290 0.523581i
\(413\) 2049.93 0.244238
\(414\) −5306.33 + 422.020i −0.629932 + 0.0500994i
\(415\) −4526.11 −0.535368
\(416\) 1371.01 2374.65i 0.161584 0.279872i
\(417\) −9202.53 + 5811.67i −1.08069 + 0.682491i
\(418\) 5527.71 + 9574.27i 0.646816 + 1.12032i
\(419\) 507.087 + 878.300i 0.0591236 + 0.102405i 0.894072 0.447923i \(-0.147836\pi\)
−0.834949 + 0.550328i \(0.814503\pi\)
\(420\) 193.490 122.195i 0.0224794 0.0141964i
\(421\) 7446.57 12897.8i 0.862051 1.49312i −0.00789511 0.999969i \(-0.502513\pi\)
0.869946 0.493147i \(-0.164154\pi\)
\(422\) −10056.1 −1.16000
\(423\) 1609.54 3381.63i 0.185008 0.388701i
\(424\) −4836.63 −0.553980
\(425\) −45.7605 + 79.2595i −0.00522285 + 0.00904624i
\(426\) −3132.42 1646.40i −0.356259 0.187249i
\(427\) −675.563 1170.11i −0.0765639 0.132613i
\(428\) 1429.37 + 2475.75i 0.161429 + 0.279602i
\(429\) −222.025 5592.15i −0.0249871 0.629351i
\(430\) −2297.37 + 3979.17i −0.257649 + 0.446261i
\(431\) −4363.90 −0.487707 −0.243853 0.969812i \(-0.578412\pi\)
−0.243853 + 0.969812i \(0.578412\pi\)
\(432\) −3660.74 1567.42i −0.407703 0.174566i
\(433\) 9301.59 1.03235 0.516173 0.856484i \(-0.327356\pi\)
0.516173 + 0.856484i \(0.327356\pi\)
\(434\) 847.177 1467.35i 0.0937000 0.162293i
\(435\) 234.774 + 5913.25i 0.0258771 + 0.651767i
\(436\) 1362.12 + 2359.26i 0.149619 + 0.259147i
\(437\) −4297.57 7443.62i −0.470437 0.814820i
\(438\) −515.026 270.697i −0.0561847 0.0295306i
\(439\) −760.076 + 1316.49i −0.0826343 + 0.143127i −0.904381 0.426727i \(-0.859667\pi\)
0.821746 + 0.569853i \(0.193000\pi\)
\(440\) 6462.20 0.700166
\(441\) −5134.63 7457.76i −0.554436 0.805286i
\(442\) −164.313 −0.0176823
\(443\) −2231.24 + 3864.62i −0.239299 + 0.414478i −0.960513 0.278234i \(-0.910251\pi\)
0.721214 + 0.692712i \(0.243584\pi\)
\(444\) −3829.52 + 2418.45i −0.409326 + 0.258502i
\(445\) 1659.08 + 2873.62i 0.176737 + 0.306118i
\(446\) 4493.49 + 7782.96i 0.477070 + 0.826309i
\(447\) 1203.51 760.053i 0.127347 0.0804235i
\(448\) −720.919 + 1248.67i −0.0760273 + 0.131683i
\(449\) −5371.66 −0.564598 −0.282299 0.959326i \(-0.591097\pi\)
−0.282299 + 0.959326i \(0.591097\pi\)
\(450\) −839.995 1220.04i −0.0879950 0.127808i
\(451\) −3415.71 −0.356628
\(452\) 1449.29 2510.25i 0.150816 0.261222i
\(453\) 4309.04 + 2264.83i 0.446923 + 0.234903i
\(454\) −4245.54 7353.49i −0.438883 0.760168i
\(455\) 141.438 + 244.978i 0.0145730 + 0.0252412i
\(456\) −484.038 12191.5i −0.0497087 1.25201i
\(457\) −7762.71 + 13445.4i −0.794583 + 1.37626i 0.128520 + 0.991707i \(0.458977\pi\)
−0.923104 + 0.384551i \(0.874356\pi\)
\(458\) −2712.36 −0.276725
\(459\) −60.9982 509.966i −0.00620294 0.0518588i
\(460\) −1430.46 −0.144990
\(461\) 28.2090 48.8594i 0.00284994 0.00493624i −0.864597 0.502466i \(-0.832426\pi\)
0.867447 + 0.497530i \(0.165760\pi\)
\(462\) 65.8901 + 1659.57i 0.00663525 + 0.167122i
\(463\) −6686.89 11582.0i −0.671201 1.16255i −0.977564 0.210640i \(-0.932445\pi\)
0.306363 0.951915i \(-0.400888\pi\)
\(464\) −3232.68 5599.17i −0.323434 0.560204i
\(465\) 6419.53 + 3374.10i 0.640212 + 0.336495i
\(466\) 2421.62 4194.37i 0.240729 0.416954i
\(467\) 2677.46 0.265306 0.132653 0.991163i \(-0.457650\pi\)
0.132653 + 0.991163i \(0.457650\pi\)
\(468\) −755.776 + 1587.88i −0.0746490 + 0.156838i
\(469\) −1138.14 −0.112056
\(470\) −760.972 + 1318.04i −0.0746830 + 0.129355i
\(471\) 1750.48 1105.48i 0.171248 0.108148i
\(472\) −9094.66 15752.4i −0.886898 1.53615i
\(473\) 11025.8 + 19097.2i 1.07181 + 1.85643i
\(474\) −11646.4 + 7355.02i −1.12856 + 0.712716i
\(475\) 1195.88 2071.33i 0.115517 0.200082i
\(476\) −32.2456 −0.00310499
\(477\) 5303.96 421.831i 0.509123 0.0404912i
\(478\) −1923.75 −0.184080
\(479\) 1734.96 3005.05i 0.165496 0.286647i −0.771335 0.636429i \(-0.780411\pi\)
0.936831 + 0.349782i \(0.113744\pi\)
\(480\) −3083.09 1620.47i −0.293173 0.154092i
\(481\) −2799.31 4848.55i −0.265359 0.459616i
\(482\) −524.320 908.149i −0.0495480 0.0858196i
\(483\) −51.2270 1290.25i −0.00482589 0.121550i
\(484\) 2295.91 3976.64i 0.215619 0.373463i
\(485\) 3626.68 0.339544
\(486\) 7876.89 + 2655.75i 0.735191 + 0.247875i
\(487\) −14040.6 −1.30645 −0.653224 0.757165i \(-0.726584\pi\)
−0.653224 + 0.757165i \(0.726584\pi\)
\(488\) −5994.38 + 10382.6i −0.556051 + 0.963108i
\(489\) 98.5669 + 2482.60i 0.00911523 + 0.229585i
\(490\) 1839.76 + 3186.56i 0.169616 + 0.293784i
\(491\) −4907.72 8500.42i −0.451084 0.781301i 0.547369 0.836891i \(-0.315629\pi\)
−0.998454 + 0.0555902i \(0.982296\pi\)
\(492\) 950.060 + 499.351i 0.0870570 + 0.0457571i
\(493\) 416.934 722.151i 0.0380888 0.0659717i
\(494\) 4294.07 0.391092
\(495\) −7086.58 + 563.606i −0.643471 + 0.0511762i
\(496\) −7923.12 −0.717255
\(497\) 429.212 743.418i 0.0387380 0.0670962i
\(498\) −8727.28 + 5511.53i −0.785299 + 0.495939i
\(499\) 6026.00 + 10437.3i 0.540603 + 0.936351i 0.998869 + 0.0475367i \(0.0151371\pi\)
−0.458267 + 0.888815i \(0.651530\pi\)
\(500\) −199.026 344.723i −0.0178014 0.0308330i
\(501\) −1495.34 + 944.354i −0.133347 + 0.0842128i
\(502\) 7562.36 13098.4i 0.672360 1.16456i
\(503\) −4695.09 −0.416191 −0.208095 0.978109i \(-0.566726\pi\)
−0.208095 + 0.978109i \(0.566726\pi\)
\(504\) 787.760 1655.08i 0.0696223 0.146276i
\(505\) −4888.91 −0.430799
\(506\) 5190.89 8990.89i 0.456054 0.789909i
\(507\) 8180.98 + 4299.92i 0.716627 + 0.376659i
\(508\) −3245.31 5621.05i −0.283440 0.490932i
\(509\) 409.907 + 709.979i 0.0356951 + 0.0618257i 0.883321 0.468769i \(-0.155302\pi\)
−0.847626 + 0.530594i \(0.821969\pi\)
\(510\) 8.28016 + 208.552i 0.000718925 + 0.0181076i
\(511\) 70.5702 122.231i 0.00610928 0.0105816i
\(512\) 9378.41 0.809514
\(513\) 1594.09 + 13327.2i 0.137195 + 1.14700i
\(514\) 15924.4 1.36653
\(515\) 3969.26 6874.96i 0.339624 0.588247i
\(516\) −274.891 6923.67i −0.0234523 0.590693i
\(517\) 3652.13 + 6325.68i 0.310678 + 0.538110i
\(518\) 830.748 + 1438.90i 0.0704652 + 0.122049i
\(519\) −17368.1 9128.68i −1.46893 0.772070i
\(520\) 1255.00 2173.73i 0.105837 0.183316i
\(521\) 3282.80 0.276050 0.138025 0.990429i \(-0.455925\pi\)
0.138025 + 0.990429i \(0.455925\pi\)
\(522\) 7653.38 + 11116.1i 0.641723 + 0.932066i
\(523\) −10768.1 −0.900300 −0.450150 0.892953i \(-0.648629\pi\)
−0.450150 + 0.892953i \(0.648629\pi\)
\(524\) 375.196 649.859i 0.0312796 0.0541779i
\(525\) 303.808 191.864i 0.0252558 0.0159498i
\(526\) −6931.76 12006.2i −0.574599 0.995235i
\(527\) −510.941 884.975i −0.0422333 0.0731502i
\(528\) 6566.71 4147.07i 0.541249 0.341815i
\(529\) 2047.78 3546.87i 0.168306 0.291515i
\(530\) −2162.22 −0.177209
\(531\) 11347.3 + 16481.2i 0.927362 + 1.34694i
\(532\) 842.690 0.0686752
\(533\) −663.353 + 1148.96i −0.0539081 + 0.0933716i
\(534\) 6698.32 + 3520.63i 0.542818 + 0.285305i
\(535\) 2244.33 + 3887.29i 0.181366 + 0.314135i
\(536\) 5049.44 + 8745.89i 0.406908 + 0.704785i
\(537\) 38.4765 + 969.106i 0.00309196 + 0.0778771i
\(538\) 6304.88 10920.4i 0.505247 0.875113i
\(539\) 17659.1 1.41119
\(540\) 2053.49 + 879.242i 0.163645 + 0.0700677i
\(541\) −16037.9 −1.27453 −0.637266 0.770644i \(-0.719935\pi\)
−0.637266 + 0.770644i \(0.719935\pi\)
\(542\) 5404.04 9360.06i 0.428272 0.741788i
\(543\) 296.585 + 7470.08i 0.0234395 + 0.590372i
\(544\) 245.388 + 425.025i 0.0193399 + 0.0334978i
\(545\) 2138.73 + 3704.39i 0.168097 + 0.291153i
\(546\) 571.037 + 300.137i 0.0447585 + 0.0235250i
\(547\) −1024.56 + 1774.59i −0.0800862 + 0.138713i −0.903287 0.429037i \(-0.858853\pi\)
0.823201 + 0.567751i \(0.192186\pi\)
\(548\) 9466.92 0.737968
\(549\) 5668.04 11908.5i 0.440630 0.925764i
\(550\) 2888.93 0.223972
\(551\) −10895.9 + 18872.3i −0.842437 + 1.45914i
\(552\) −9687.52 + 6117.95i −0.746971 + 0.471734i
\(553\) −1670.69 2893.72i −0.128472 0.222520i
\(554\) 2552.01 + 4420.21i 0.195712 + 0.338983i
\(555\) −6012.91 + 3797.33i −0.459881 + 0.290428i
\(556\) −3335.09 + 5776.54i −0.254387 + 0.440611i
\(557\) 3644.07 0.277207 0.138603 0.990348i \(-0.455739\pi\)
0.138603 + 0.990348i \(0.455739\pi\)
\(558\) 16486.9 1311.23i 1.25080 0.0994778i
\(559\) 8565.12 0.648061
\(560\) −196.280 + 339.967i −0.0148113 + 0.0256540i
\(561\) 886.679 + 466.038i 0.0667301 + 0.0350733i
\(562\) 3602.64 + 6239.96i 0.270406 + 0.468357i
\(563\) −175.368 303.746i −0.0131277 0.0227378i 0.859387 0.511326i \(-0.170845\pi\)
−0.872515 + 0.488588i \(0.837512\pi\)
\(564\) −91.0536 2293.37i −0.00679796 0.171220i
\(565\) 2275.60 3941.46i 0.169443 0.293484i
\(566\) −4420.07 −0.328250
\(567\) −719.525 + 1883.71i −0.0532932 + 0.139521i
\(568\) −7616.93 −0.562675
\(569\) 9724.34 16843.1i 0.716460 1.24095i −0.245934 0.969287i \(-0.579095\pi\)
0.962394 0.271658i \(-0.0875721\pi\)
\(570\) −216.389 5450.20i −0.0159010 0.400498i
\(571\) 7572.97 + 13116.8i 0.555024 + 0.961330i 0.997902 + 0.0647480i \(0.0206244\pi\)
−0.442877 + 0.896582i \(0.646042\pi\)
\(572\) −1714.90 2970.29i −0.125356 0.217123i
\(573\) 1795.82 + 943.880i 0.130927 + 0.0688153i
\(574\) 196.862 340.975i 0.0143151 0.0247945i
\(575\) −2246.03 −0.162897
\(576\) −14029.8 + 1115.81i −1.01489 + 0.0807154i
\(577\) −6365.11 −0.459243 −0.229621 0.973280i \(-0.573749\pi\)
−0.229621 + 0.973280i \(0.573749\pi\)
\(578\) −5375.95 + 9311.41i −0.386868 + 0.670076i
\(579\) −17200.3 + 10862.5i −1.23458 + 0.779673i
\(580\) 1813.37 + 3140.85i 0.129821 + 0.224856i
\(581\) −1251.94 2168.43i −0.0893965 0.154839i
\(582\) 6992.99 4416.28i 0.498056 0.314537i
\(583\) −5188.57 + 8986.87i −0.368591 + 0.638419i
\(584\) −1252.36 −0.0887381
\(585\) −1186.68 + 2493.21i −0.0838686 + 0.176208i
\(586\) −1054.86 −0.0743617
\(587\) −5142.18 + 8906.52i −0.361568 + 0.626254i −0.988219 0.153046i \(-0.951092\pi\)
0.626651 + 0.779300i \(0.284425\pi\)
\(588\) −4911.79 2581.63i −0.344488 0.181063i
\(589\) 13352.7 + 23127.5i 0.934103 + 1.61791i
\(590\) −4065.77 7042.13i −0.283704 0.491389i
\(591\) −184.018 4634.85i −0.0128079 0.322593i
\(592\) 3884.73 6728.56i 0.269699 0.467132i
\(593\) 666.566 0.0461595 0.0230798 0.999734i \(-0.492653\pi\)
0.0230798 + 0.999734i \(0.492653\pi\)
\(594\) −12978.1 + 9716.23i −0.896461 + 0.671148i
\(595\) −50.6303 −0.00348847
\(596\) 436.165 755.460i 0.0299765 0.0519209i
\(597\) −571.113 14384.6i −0.0391526 0.986136i
\(598\) −2016.21 3492.18i −0.137875 0.238806i
\(599\) −12606.6 21835.3i −0.859922 1.48943i −0.872003 0.489501i \(-0.837179\pi\)
0.0120807 0.999927i \(-0.496155\pi\)
\(600\) −2822.22 1483.36i −0.192028 0.100930i
\(601\) 10309.3 17856.3i 0.699712 1.21194i −0.268855 0.963181i \(-0.586645\pi\)
0.968566 0.248755i \(-0.0800215\pi\)
\(602\) −2541.86 −0.172090
\(603\) −6300.11 9150.54i −0.425473 0.617975i
\(604\) 2983.30 0.200975
\(605\) 3604.92 6243.90i 0.242249 0.419588i
\(606\) −9426.83 + 5953.32i −0.631912 + 0.399071i
\(607\) 2541.76 + 4402.45i 0.169962 + 0.294382i 0.938406 0.345534i \(-0.112302\pi\)
−0.768444 + 0.639916i \(0.778969\pi\)
\(608\) −6412.85 11107.4i −0.427755 0.740894i
\(609\) −2768.06 + 1748.11i −0.184183 + 0.116317i
\(610\) −2679.79 + 4641.53i −0.177871 + 0.308082i
\(611\) 2837.07 0.187849
\(612\) −178.494 259.252i −0.0117895 0.0171236i
\(613\) 2625.18 0.172969 0.0864845 0.996253i \(-0.472437\pi\)
0.0864845 + 0.996253i \(0.472437\pi\)
\(614\) 3535.47 6123.62i 0.232378 0.402491i
\(615\) 1491.73 + 784.054i 0.0978090 + 0.0514083i
\(616\) 1787.48 + 3096.00i 0.116915 + 0.202502i
\(617\) 815.659 + 1412.76i 0.0532208 + 0.0921811i 0.891408 0.453201i \(-0.149718\pi\)
−0.838188 + 0.545382i \(0.816385\pi\)
\(618\) −718.220 18089.8i −0.0467493 1.17747i
\(619\) −1592.33 + 2758.00i −0.103395 + 0.179085i −0.913081 0.407778i \(-0.866304\pi\)
0.809687 + 0.586863i \(0.199637\pi\)
\(620\) 4444.47 0.287894
\(621\) 10090.0 7553.99i 0.652007 0.488134i
\(622\) −5297.40 −0.341489
\(623\) −917.821 + 1589.71i −0.0590236 + 0.102232i
\(624\) −119.676 3014.27i −0.00767767 0.193377i
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −2750.67 4764.29i −0.175621 0.304184i
\(627\) −23172.0 12179.2i −1.47592 0.775742i
\(628\) 634.392 1098.80i 0.0403105 0.0698199i
\(629\) 1002.06 0.0635214
\(630\) 352.169 739.907i 0.0222710 0.0467914i
\(631\) 10436.7 0.658447 0.329223 0.944252i \(-0.393213\pi\)
0.329223 + 0.944252i \(0.393213\pi\)
\(632\) −14824.3 + 25676.4i −0.933037 + 1.61607i
\(633\) 20132.7 12714.4i 1.26415 0.798346i
\(634\) 4067.54 + 7045.18i 0.254799 + 0.441325i
\(635\) −5095.62 8825.87i −0.318446 0.551565i
\(636\) 2756.99 1741.12i 0.171889 0.108553i
\(637\) 3429.52 5940.11i 0.213316 0.369475i
\(638\) −26321.7 −1.63336
\(639\) 8352.89 664.317i 0.517113 0.0411267i
\(640\) 356.968 0.0220475
\(641\) −4541.73 + 7866.50i −0.279856 + 0.484724i −0.971349 0.237659i \(-0.923620\pi\)
0.691493 + 0.722383i \(0.256953\pi\)
\(642\) 9061.16 + 4762.54i 0.557034 + 0.292776i
\(643\) −8593.81 14884.9i −0.527071 0.912914i −0.999502 0.0315465i \(-0.989957\pi\)
0.472431 0.881368i \(-0.343377\pi\)
\(644\) −395.672 685.323i −0.0242106 0.0419340i
\(645\) −431.619 10871.2i −0.0263488 0.663647i
\(646\) −384.285 + 665.601i −0.0234048 + 0.0405383i
\(647\) 2359.17 0.143352 0.0716758 0.997428i \(-0.477165\pi\)
0.0716758 + 0.997428i \(0.477165\pi\)
\(648\) 17667.3 2828.11i 1.07105 0.171448i
\(649\) −39025.7 −2.36039
\(650\) 561.049 971.766i 0.0338556 0.0586397i
\(651\) 159.163 + 4008.85i 0.00958234 + 0.241350i
\(652\) 761.320 + 1318.64i 0.0457294 + 0.0792057i
\(653\) −2718.06 4707.81i −0.162888 0.282130i 0.773015 0.634387i \(-0.218748\pi\)
−0.935903 + 0.352257i \(0.885414\pi\)
\(654\) 8634.82 + 4538.46i 0.516282 + 0.271357i
\(655\) 589.113 1020.37i 0.0351428 0.0608691i
\(656\) −1841.13 −0.109579
\(657\) 1373.36 109.226i 0.0815526 0.00648599i
\(658\) −841.954 −0.0498826
\(659\) −1544.45 + 2675.07i −0.0912950 + 0.158128i −0.908056 0.418848i \(-0.862434\pi\)
0.816761 + 0.576976i \(0.195767\pi\)
\(660\) −3683.59 + 2326.30i −0.217248 + 0.137199i
\(661\) 9526.94 + 16501.2i 0.560598 + 0.970984i 0.997444 + 0.0714479i \(0.0227620\pi\)
−0.436846 + 0.899536i \(0.643905\pi\)
\(662\) 2801.70 + 4852.68i 0.164488 + 0.284902i
\(663\) 328.963 207.750i 0.0192698 0.0121694i
\(664\) −11108.7 + 19240.8i −0.649248 + 1.12453i
\(665\) 1323.15 0.0771570
\(666\) −6970.05 + 14644.1i −0.405532 + 0.852022i
\(667\) 20464.1 1.18796
\(668\) −541.928 + 938.646i −0.0313889 + 0.0543672i
\(669\) −18836.6 9900.51i −1.08859 0.572161i
\(670\) 2257.36 + 3909.86i 0.130163 + 0.225449i
\(671\) 12861.1 + 22276.1i 0.739937 + 1.28161i
\(672\) −76.4409 1925.32i −0.00438806 0.110522i
\(673\) 14618.7 25320.4i 0.837312 1.45027i −0.0548215 0.998496i \(-0.517459\pi\)
0.892134 0.451771i \(-0.149208\pi\)
\(674\) −7796.61 −0.445570
\(675\) 3224.28 + 1380.54i 0.183856 + 0.0787214i
\(676\) 5663.98 0.322257
\(677\) −7235.62 + 12532.5i −0.410764 + 0.711465i −0.994974 0.100138i \(-0.968071\pi\)
0.584209 + 0.811603i \(0.301405\pi\)
\(678\) −411.760 10371.0i −0.0233238 0.587457i
\(679\) 1003.16 + 1737.52i 0.0566975 + 0.0982030i
\(680\) 224.625 + 389.062i 0.0126676 + 0.0219410i
\(681\) 17797.2 + 9354.19i 1.00145 + 0.526363i
\(682\) −16128.2 + 27934.9i −0.905545 + 1.56845i
\(683\) 5782.94 0.323980 0.161990 0.986792i \(-0.448209\pi\)
0.161990 + 0.986792i \(0.448209\pi\)
\(684\) 4664.66 + 6775.15i 0.260757 + 0.378734i
\(685\) 14864.5 0.829112
\(686\) −2058.77 + 3565.89i −0.114583 + 0.198464i
\(687\) 5430.28 3429.38i 0.301569 0.190450i
\(688\) 5943.10 + 10293.8i 0.329329 + 0.570415i
\(689\) 2015.31 + 3490.62i 0.111433 + 0.193007i
\(690\) −4330.81 + 2735.04i −0.238944 + 0.150900i
\(691\) −5527.56 + 9574.01i −0.304310 + 0.527080i −0.977107 0.212746i \(-0.931759\pi\)
0.672797 + 0.739827i \(0.265093\pi\)
\(692\) −12024.6 −0.660557
\(693\) −2230.20 3239.24i −0.122249 0.177559i
\(694\) 17046.5 0.932386
\(695\) −5236.58 + 9070.02i −0.285805 + 0.495029i
\(696\) 25713.9 + 13515.2i 1.40041 + 0.736052i
\(697\) −118.730 205.646i −0.00645223 0.0111756i
\(698\) 763.674 + 1322.72i 0.0414119 + 0.0717275i
\(699\) 454.962 + 11459.1i 0.0246184 + 0.620064i
\(700\) 110.103 190.704i 0.00594501 0.0102971i
\(701\) −13554.2 −0.730294 −0.365147 0.930950i \(-0.618981\pi\)
−0.365147 + 0.930950i \(0.618981\pi\)
\(702\) 747.872 + 6252.48i 0.0402088 + 0.336160i
\(703\) −26187.4 −1.40495
\(704\) 13724.6 23771.7i 0.734751 1.27263i
\(705\) −142.967 3600.92i −0.00763754 0.192367i
\(706\) −5981.91 10361.0i −0.318884 0.552324i
\(707\) −1352.30 2342.25i −0.0719354 0.124596i
\(708\) 10854.8 + 5705.27i 0.576198 + 0.302849i
\(709\) 4694.58 8131.26i 0.248672 0.430713i −0.714485 0.699650i \(-0.753339\pi\)
0.963158 + 0.268937i \(0.0866724\pi\)
\(710\) −3405.15 −0.179990
\(711\) 14017.3 29450.3i 0.739365 1.55340i
\(712\) 16287.9 0.857326
\(713\) 12539.1 21718.3i 0.658614 1.14075i
\(714\) −97.6258 + 61.6536i −0.00511702 + 0.00323155i
\(715\) −2692.64 4663.80i −0.140838 0.243939i
\(716\) 297.188 + 514.745i 0.0155118 + 0.0268672i
\(717\) 3851.45 2432.31i 0.200607 0.126689i
\(718\) 4428.84 7670.97i 0.230199 0.398716i
\(719\) −26301.8 −1.36424 −0.682122 0.731238i \(-0.738943\pi\)
−0.682122 + 0.731238i \(0.738943\pi\)
\(720\) −3819.80 + 303.794i −0.197716 + 0.0157246i
\(721\) 4391.67 0.226844
\(722\) 2516.86 4359.33i 0.129734 0.224705i
\(723\) 2197.94 + 1155.23i 0.113060 + 0.0594241i
\(724\) 2290.79 + 3967.76i 0.117592 + 0.203675i
\(725\) 2847.26 + 4931.59i 0.145854 + 0.252627i
\(726\) −652.294 16429.3i −0.0333456 0.839876i
\(727\) 12769.3 22117.1i 0.651427 1.12830i −0.331350 0.943508i \(-0.607504\pi\)
0.982777 0.184797i \(-0.0591626\pi\)
\(728\) 1388.56 0.0706915
\(729\) −19127.7 + 4642.23i −0.971789 + 0.235850i
\(730\) −559.868 −0.0283858
\(731\) −766.510 + 1327.63i −0.0387830 + 0.0671742i
\(732\) −320.649 8076.18i −0.0161906 0.407792i
\(733\) −3491.06 6046.70i −0.175914 0.304693i 0.764563 0.644549i \(-0.222955\pi\)
−0.940477 + 0.339856i \(0.889622\pi\)
\(734\) 12332.7 + 21360.8i 0.620174 + 1.07417i
\(735\) −7712.23 4053.54i −0.387034 0.203425i
\(736\) −6022.10 + 10430.6i −0.301600 + 0.522387i
\(737\) 21667.5 1.08295
\(738\) 3831.13 304.695i 0.191092 0.0151978i
\(739\) 8863.91 0.441224 0.220612 0.975362i \(-0.429195\pi\)
0.220612 + 0.975362i \(0.429195\pi\)
\(740\) −2179.14 + 3774.38i −0.108252 + 0.187499i
\(741\) −8596.94 + 5429.22i −0.426203 + 0.269160i
\(742\) −598.081 1035.91i −0.0295906 0.0512524i
\(743\) 19472.4 + 33727.3i 0.961473 + 1.66532i 0.718806 + 0.695211i \(0.244689\pi\)
0.242668 + 0.970110i \(0.421978\pi\)
\(744\) 30099.3 19008.6i 1.48319 0.936680i
\(745\) 684.843 1186.18i 0.0336788 0.0583334i
\(746\) 13870.5 0.680742
\(747\) 10503.9 22068.7i 0.514482 1.08093i
\(748\) 613.879 0.0300075
\(749\) −1241.58 + 2150.49i −0.0605694 + 0.104909i
\(750\) −1261.68 663.136i −0.0614265 0.0322857i
\(751\) −8795.16 15233.7i −0.427350 0.740192i 0.569287 0.822139i \(-0.307220\pi\)
−0.996637 + 0.0819470i \(0.973886\pi\)
\(752\) 1968.57 + 3409.66i 0.0954604 + 0.165342i
\(753\) 1420.78 + 35785.2i 0.0687597 + 1.73185i
\(754\) −5111.84 + 8853.97i −0.246900 + 0.427643i
\(755\) 4684.22 0.225796
\(756\) 146.766 + 1227.02i 0.00706062 + 0.0590293i
\(757\) −4075.85 −0.195693 −0.0978463 0.995202i \(-0.531195\pi\)
−0.0978463 + 0.995202i \(0.531195\pi\)
\(758\) 10232.1 17722.6i 0.490300 0.849225i
\(759\) 975.239 + 24563.3i 0.0466389 + 1.17469i
\(760\) −5870.24 10167.6i −0.280179 0.485284i
\(761\) −20268.5 35106.1i −0.965483 1.67227i −0.708312 0.705899i \(-0.750543\pi\)
−0.257171 0.966366i \(-0.582790\pi\)
\(762\) −20572.9 10813.1i −0.978052 0.514064i
\(763\) −1183.17 + 2049.30i −0.0561382 + 0.0972343i
\(764\) 1243.31 0.0588761
\(765\) −280.261 407.063i −0.0132456 0.0192384i
\(766\) −24463.7 −1.15393
\(767\) −7579.06 + 13127.3i −0.356798 + 0.617992i
\(768\) −17632.6 + 11135.5i −0.828464 + 0.523200i
\(769\) −12016.3 20812.9i −0.563485 0.975985i −0.997189 0.0749293i \(-0.976127\pi\)
0.433704 0.901056i \(-0.357206\pi\)
\(770\) 799.092 + 1384.07i 0.0373991 + 0.0647771i
\(771\) −31881.5 + 20134.1i −1.48922 + 0.940484i
\(772\) −6233.57 + 10796.9i −0.290610 + 0.503351i
\(773\) −20881.5 −0.971611 −0.485805 0.874067i \(-0.661474\pi\)
−0.485805 + 0.874067i \(0.661474\pi\)
\(774\) −14070.3 20436.3i −0.653420 0.949055i
\(775\) 6978.46 0.323450
\(776\) 8901.16 15417.3i 0.411770 0.713206i
\(777\) −3482.48 1830.39i −0.160789 0.0845106i
\(778\) 7209.64 + 12487.5i 0.332234 + 0.575446i
\(779\) 3102.82 + 5374.24i 0.142709 + 0.247179i
\(780\) 67.1320 + 1690.85i 0.00308168 + 0.0776183i
\(781\) −8171.18 + 14152.9i −0.374376 + 0.648439i
\(782\) 721.740 0.0330043
\(783\) −29377.1 12578.4i −1.34081 0.574093i
\(784\) 9518.60 0.433610
\(785\) 996.089 1725.28i 0.0452891 0.0784430i
\(786\) −106.597 2684.87i −0.00483741 0.121840i
\(787\) 2568.20 + 4448.25i 0.116323 + 0.201478i 0.918308 0.395867i \(-0.129556\pi\)
−0.801985 + 0.597345i \(0.796223\pi\)
\(788\) −1421.33 2461.82i −0.0642549 0.111293i
\(789\) 29057.8 + 15272.7i 1.31113 + 0.689130i
\(790\) −6627.21 + 11478.7i −0.298463 + 0.516953i
\(791\) 2517.77 0.113175
\(792\) −14997.1 + 31508.9i −0.672851 + 1.41366i
\(793\) 9990.86 0.447397
\(794\) 4355.23 7543.48i 0.194662 0.337164i
\(795\) 4328.87 2733.81i 0.193119 0.121960i
\(796\) −4411.22 7640.45i −0.196421 0.340212i
\(797\) −10998.0 19049.1i −0.488794 0.846615i 0.511123 0.859507i \(-0.329230\pi\)
−0.999917 + 0.0128922i \(0.995896\pi\)
\(798\) 2551.30 1611.22i 0.113177 0.0714745i
\(799\) −253.895 + 439.760i −0.0112418 + 0.0194713i
\(800\) −3351.53 −0.148118
\(801\) −17861.7 + 1420.57i −0.787905 + 0.0626632i
\(802\) −9600.03 −0.422679
\(803\) −1343.49 + 2326.99i −0.0590419 + 0.102264i
\(804\) −6026.69 3167.62i −0.264359 0.138947i
\(805\) −621.262 1076.06i −0.0272008 0.0471131i
\(806\) 6264.42 + 10850.3i 0.273765 + 0.474175i
\(807\) 1184.53 + 29834.7i 0.0516696 + 1.30140i
\(808\) −11999.1 + 20783.1i −0.522435 + 0.904885i
\(809\) 31094.2 1.35132 0.675658 0.737215i \(-0.263860\pi\)
0.675658 + 0.737215i \(0.263860\pi\)
\(810\) 7898.20 1264.31i 0.342610 0.0548435i
\(811\) 19130.6 0.828320 0.414160 0.910204i \(-0.364075\pi\)
0.414160 + 0.910204i \(0.364075\pi\)
\(812\) −1003.17 + 1737.55i −0.0433553 + 0.0750936i
\(813\) 1015.28 + 25571.9i 0.0437977 + 1.10313i
\(814\) −15815.5 27393.2i −0.680997 1.17952i
\(815\) 1195.38 + 2070.47i 0.0513773 + 0.0889881i
\(816\) 477.937 + 251.203i 0.0205038 + 0.0107768i
\(817\) 20031.6 34695.7i 0.857792 1.48574i
\(818\) 19469.8 0.832208
\(819\) −1522.72 + 121.104i −0.0649674 + 0.00516694i
\(820\) 1032.78 0.0439832
\(821\) 1778.81 3080.99i 0.0756162 0.130971i −0.825738 0.564054i \(-0.809241\pi\)
0.901354 + 0.433083i \(0.142574\pi\)
\(822\) 28661.8 18100.7i 1.21617 0.768049i
\(823\) −3074.69 5325.52i −0.130227 0.225560i 0.793537 0.608522i \(-0.208237\pi\)
−0.923764 + 0.382962i \(0.874904\pi\)
\(824\) −19484.0 33747.2i −0.823733 1.42675i
\(825\) −5783.78 + 3652.63i −0.244079 + 0.154143i
\(826\) 2249.23 3895.77i 0.0947464 0.164106i
\(827\) 21152.8 0.889425 0.444713 0.895673i \(-0.353306\pi\)
0.444713 + 0.895673i \(0.353306\pi\)
\(828\) 3319.72 6974.73i 0.139334 0.292740i
\(829\) −17402.4 −0.729083 −0.364541 0.931187i \(-0.618774\pi\)
−0.364541 + 0.931187i \(0.618774\pi\)
\(830\) −4966.14 + 8601.61i −0.207684 + 0.359719i
\(831\) −10698.0 5622.84i −0.446580 0.234722i
\(832\) −5330.81 9233.24i −0.222131 0.384742i
\(833\) 613.829 + 1063.18i 0.0255317 + 0.0442222i
\(834\) 947.536 + 23865.6i 0.0393411 + 0.990884i
\(835\) −850.906 + 1473.81i −0.0352657 + 0.0610819i
\(836\) −16042.8 −0.663698
\(837\) −31349.7 + 23470.4i −1.29463 + 0.969243i
\(838\) 2225.55 0.0917425
\(839\) 9037.12 15652.8i 0.371867 0.644092i −0.617986 0.786189i \(-0.712051\pi\)
0.989853 + 0.142097i \(0.0453845\pi\)
\(840\) −69.9731 1762.41i −0.00287417 0.0723917i
\(841\) −13747.5 23811.3i −0.563675 0.976314i
\(842\) −16341.1 28303.6i −0.668825 1.15844i
\(843\) −15102.2 7937.69i −0.617019 0.324304i
\(844\) 7296.31 12637.6i 0.297570 0.515407i
\(845\) 8893.28 0.362057
\(846\) −4660.59 6769.23i −0.189402 0.275096i
\(847\) 3988.55 0.161804
\(848\) −2796.74 + 4844.09i −0.113255 + 0.196164i
\(849\) 8849.21 5588.54i 0.357720 0.225911i
\(850\) 100.419 + 173.931i 0.00405216 + 0.00701855i
\(851\) 12295.9 + 21297.1i 0.495297 + 0.857880i
\(852\) 4341.82 2741.99i 0.174587 0.110257i
\(853\) −20396.1 + 35327.2i −0.818699 + 1.41803i 0.0879416 + 0.996126i \(0.471971\pi\)
−0.906641 + 0.421903i \(0.861362\pi\)
\(854\) −2964.97 −0.118805
\(855\) 7324.20 + 10638.0i 0.292962 + 0.425510i
\(856\) 22033.5 0.879778
\(857\) 5528.93 9576.39i 0.220379 0.381707i −0.734544 0.678561i \(-0.762604\pi\)
0.954923 + 0.296854i \(0.0959373\pi\)
\(858\) −10871.2 5713.88i −0.432559 0.227353i
\(859\) 876.815 + 1518.69i 0.0348272 + 0.0603224i 0.882914 0.469535i \(-0.155579\pi\)
−0.848086 + 0.529858i \(0.822245\pi\)
\(860\) −3333.78 5774.27i −0.132187 0.228955i
\(861\) 36.9855 + 931.554i 0.00146395 + 0.0368725i
\(862\) −4788.17 + 8293.35i −0.189194 + 0.327694i
\(863\) −19186.5 −0.756796 −0.378398 0.925643i \(-0.623525\pi\)
−0.378398 + 0.925643i \(0.623525\pi\)
\(864\) 15056.3 11272.1i 0.592852 0.443847i
\(865\) −18880.3 −0.742140
\(866\) 10205.9 17677.2i 0.400475 0.693642i
\(867\) −1010.01 25439.0i −0.0395635 0.996487i
\(868\) 1229.36 + 2129.32i 0.0480728 + 0.0832646i
\(869\) 31806.0 + 55089.6i 1.24159 + 2.15050i
\(870\) 11495.4 + 6041.98i 0.447966 + 0.235451i
\(871\) 4207.97 7288.41i 0.163699 0.283534i
\(872\) 20996.8 0.815415
\(873\) −8416.58 + 17683.2i −0.326298 + 0.685552i
\(874\) −18861.6 −0.729980
\(875\) 172.878 299.434i 0.00667925 0.0115688i
\(876\) 713.872 450.831i 0.0275337 0.0173883i
\(877\) 4257.30 + 7373.86i 0.163921 + 0.283920i 0.936272 0.351277i \(-0.114252\pi\)
−0.772350 + 0.635197i \(0.780919\pi\)
\(878\) 1667.94 + 2888.96i 0.0641121 + 0.111045i
\(879\) 2111.89 1333.72i 0.0810377 0.0511777i
\(880\) 3736.70 6472.16i 0.143141 0.247928i
\(881\) 41177.0 1.57467 0.787337 0.616522i \(-0.211459\pi\)
0.787337 + 0.616522i \(0.211459\pi\)
\(882\) −19806.9 + 1575.27i −0.756159 + 0.0601384i
\(883\) 32540.4 1.24017 0.620086 0.784533i \(-0.287098\pi\)
0.620086 + 0.784533i \(0.287098\pi\)
\(884\) 119.219 206.494i 0.00453595 0.00785650i
\(885\) 17043.6 + 8958.11i 0.647362 + 0.340253i
\(886\) 4896.34 + 8480.70i 0.185661 + 0.321574i
\(887\) −1083.05 1875.90i −0.0409980 0.0710106i 0.844798 0.535085i \(-0.179720\pi\)
−0.885796 + 0.464074i \(0.846387\pi\)
\(888\) 1384.89 + 34881.3i 0.0523356 + 1.31818i
\(889\) 2818.95 4882.56i 0.106349 0.184202i
\(890\) 7281.53 0.274244
\(891\) 13698.1 35861.3i 0.515041 1.34837i
\(892\) −13041.2 −0.489522
\(893\) 6635.17 11492.4i 0.248642 0.430661i
\(894\) −123.919 3121.15i −0.00463588 0.116764i
\(895\) 466.629 + 808.225i 0.0174276 + 0.0301855i
\(896\) 98.7391 + 171.021i 0.00368152 + 0.00637658i
\(897\) 8451.92 + 4442.32i 0.314606 + 0.165356i
\(898\) −5893.91 + 10208.5i −0.219023 + 0.379358i
\(899\) −63582.3 −2.35883
\(900\) 2142.71 170.413i 0.0793598 0.00631160i
\(901\) −721.416 −0.0266747
\(902\) −3747.79 + 6491.36i −0.138346 + 0.239622i
\(903\) 5088.93 3213.81i 0.187540 0.118437i
\(904\) −11170.3 19347.5i −0.410971 0.711823i
\(905\) 3596.88 + 6229.97i 0.132115 + 0.228830i
\(906\) 9032.15 5704.07i 0.331207 0.209167i
\(907\) 353.031 611.468i 0.0129241 0.0223853i −0.859491 0.511151i \(-0.829219\pi\)
0.872415 + 0.488766i \(0.162553\pi\)
\(908\) 12321.6 0.450339
\(909\) 11345.9 23837.7i 0.413993 0.869799i
\(910\) 620.756 0.0226130
\(911\) 247.743 429.103i 0.00900997 0.0156057i −0.861485 0.507783i \(-0.830465\pi\)
0.870495 + 0.492177i \(0.163799\pi\)
\(912\) −12490.1 6564.81i −0.453498 0.238358i
\(913\) 23834.0 + 41281.7i 0.863955 + 1.49641i
\(914\) 17034.8 + 29505.2i 0.616480 + 1.06777i
\(915\) −503.465 12680.8i −0.0181902 0.458157i
\(916\) 1967.99 3408.66i 0.0709871 0.122953i
\(917\) 651.806 0.0234728
\(918\) −1036.09 443.623i −0.0372507 0.0159496i
\(919\) 20473.6 0.734889 0.367445 0.930045i \(-0.380233\pi\)
0.367445 + 0.930045i \(0.380233\pi\)
\(920\) −5512.56 + 9548.03i −0.197547 + 0.342162i
\(921\) 664.227 + 16729.9i 0.0237644 + 0.598554i
\(922\) −61.9030 107.219i −0.00221114 0.00382980i
\(923\) 3173.80 + 5497.17i 0.113182 + 0.196037i
\(924\) −2133.41 1121.32i −0.0759569 0.0399229i
\(925\) −3421.57 + 5926.33i −0.121622 + 0.210656i
\(926\) −29348.0 −1.04151
\(927\) 24309.8 + 35308.6i 0.861316 + 1.25101i
\(928\) 30536.5 1.08018
\(929\) −24857.7 + 43054.7i −0.877883 + 1.52054i −0.0242231 + 0.999707i \(0.507711\pi\)
−0.853660 + 0.520831i \(0.825622\pi\)
\(930\) 13455.9 8497.82i 0.474449 0.299628i
\(931\) −16041.5 27784.7i −0.564704 0.978095i
\(932\) 3514.08 + 6086.57i 0.123506 + 0.213919i
\(933\) 10605.7 6697.79i 0.372148 0.235022i
\(934\) 2937.77 5088.36i 0.102919 0.178261i
\(935\) 963.880 0.0337136
\(936\) 7686.29 + 11163.9i 0.268413 + 0.389854i
\(937\) −31524.9 −1.09912 −0.549560 0.835454i \(-0.685204\pi\)
−0.549560 + 0.835454i \(0.685204\pi\)
\(938\) −1248.79 + 2162.97i −0.0434696 + 0.0752916i
\(939\) 11530.7 + 6060.54i 0.400736 + 0.210626i
\(940\) −1104.27 1912.64i −0.0383161 0.0663655i
\(941\) −18764.2 32500.6i −0.650050 1.12592i −0.983110 0.183014i \(-0.941415\pi\)
0.333060 0.942905i \(-0.391919\pi\)
\(942\) −180.238 4539.65i −0.00623404 0.157017i
\(943\) 2913.76 5046.78i 0.100620 0.174280i
\(944\) −21035.6 −0.725265
\(945\) 230.444 + 1926.60i 0.00793265 + 0.0663198i
\(946\) 48390.9 1.66313
\(947\) −12931.7 + 22398.3i −0.443741 + 0.768582i −0.997964 0.0637862i \(-0.979682\pi\)
0.554222 + 0.832369i \(0.313016\pi\)
\(948\) −792.975 19972.7i −0.0271673 0.684264i
\(949\) 521.829 + 903.834i 0.0178496 + 0.0309164i
\(950\) −2624.29 4545.41i −0.0896246 0.155234i
\(951\) −17051.0 8962.00i −0.581406 0.305586i
\(952\) −124.265 + 215.233i −0.00423051 + 0.00732746i
\(953\) 1060.03 0.0360312 0.0180156 0.999838i \(-0.494265\pi\)
0.0180156 + 0.999838i \(0.494265\pi\)
\(954\) 5017.95 10542.7i 0.170296 0.357791i
\(955\) 1952.18 0.0661476
\(956\) 1395.81 2417.61i 0.0472213 0.0817897i
\(957\) 52697.3 33279.9i 1.78000 1.12412i
\(958\) −3807.28 6594.40i −0.128400 0.222396i
\(959\) 4111.58 + 7121.46i 0.138446 + 0.239796i
\(960\) −11450.6 + 7231.36i −0.384963 + 0.243116i
\(961\) −24063.7 + 41679.5i −0.807750 + 1.39906i
\(962\) −12285.9 −0.411759
\(963\) −24162.4 + 1921.67i −0.808540 + 0.0643043i
\(964\) 1521.71 0.0508412
\(965\) −9787.62 + 16952.6i −0.326502 + 0.565518i
\(966\) −2508.26 1318.34i −0.0835424 0.0439098i
\(967\) 2592.51 + 4490.35i 0.0862145 + 0.149328i 0.905908 0.423474i \(-0.139190\pi\)
−0.819694 + 0.572802i \(0.805856\pi\)
\(968\) −17695.5 30649.5i −0.587557 1.01768i
\(969\) −72.1975 1818.44i −0.00239352 0.0602855i
\(970\) 3979.27 6892.30i 0.131718 0.228143i
\(971\) 28314.9 0.935805 0.467903 0.883780i \(-0.345010\pi\)
0.467903 + 0.883780i \(0.345010\pi\)
\(972\) −9052.69 + 7972.07i −0.298730 + 0.263070i
\(973\) −5793.85 −0.190897
\(974\) −15405.6 + 26683.4i −0.506806 + 0.877813i
\(975\) 105.407 + 2654.89i 0.00346229 + 0.0872046i
\(976\) 6932.38 + 12007.2i 0.227357 + 0.393793i
\(977\) −22448.3 38881.6i −0.735093 1.27322i −0.954683 0.297626i \(-0.903805\pi\)
0.219590 0.975592i \(-0.429528\pi\)
\(978\) 4826.20 + 2536.65i 0.157796 + 0.0829376i
\(979\) 17473.1 30264.3i 0.570422 0.988001i
\(980\) −5339.45 −0.174043
\(981\) −23025.6 + 1831.26i −0.749388 + 0.0595999i
\(982\) −21539.4 −0.699950
\(983\) 7286.40 12620.4i 0.236419 0.409490i −0.723265 0.690571i \(-0.757360\pi\)
0.959684 + 0.281081i \(0.0906928\pi\)
\(984\) 6994.32 4417.12i 0.226596 0.143102i
\(985\) −2231.70 3865.42i −0.0721908 0.125038i
\(986\) −914.938 1584.72i −0.0295513 0.0511843i
\(987\) 1685.63 1064.53i 0.0543610 0.0343306i
\(988\) −3115.62 + 5396.41i −0.100325 + 0.173768i
\(989\) −37622.0 −1.20962
\(990\) −6704.45 + 14086.1i −0.215234 + 0.452206i
\(991\) 10602.1 0.339844 0.169922 0.985457i \(-0.445648\pi\)
0.169922 + 0.985457i \(0.445648\pi\)
\(992\) 18710.8 32408.1i 0.598860 1.03726i
\(993\) −11744.6 6172.98i −0.375332 0.197274i
\(994\) −941.882 1631.39i −0.0300550 0.0520568i
\(995\) −6926.26 11996.6i −0.220681 0.382230i
\(996\) −594.221 14966.6i −0.0189042 0.476141i
\(997\) −13948.5 + 24159.5i −0.443082 + 0.767441i −0.997916 0.0645202i \(-0.979448\pi\)
0.554834 + 0.831961i \(0.312782\pi\)
\(998\) 26447.4 0.838857
\(999\) −4560.91 38130.8i −0.144445 1.20761i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 45.4.e.c.16.5 14
3.2 odd 2 135.4.e.c.46.3 14
5.2 odd 4 225.4.k.d.124.10 28
5.3 odd 4 225.4.k.d.124.5 28
5.4 even 2 225.4.e.d.151.3 14
9.2 odd 6 405.4.a.n.1.5 7
9.4 even 3 inner 45.4.e.c.31.5 yes 14
9.5 odd 6 135.4.e.c.91.3 14
9.7 even 3 405.4.a.m.1.3 7
45.4 even 6 225.4.e.d.76.3 14
45.13 odd 12 225.4.k.d.49.10 28
45.22 odd 12 225.4.k.d.49.5 28
45.29 odd 6 2025.4.a.ba.1.3 7
45.34 even 6 2025.4.a.bb.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.c.16.5 14 1.1 even 1 trivial
45.4.e.c.31.5 yes 14 9.4 even 3 inner
135.4.e.c.46.3 14 3.2 odd 2
135.4.e.c.91.3 14 9.5 odd 6
225.4.e.d.76.3 14 45.4 even 6
225.4.e.d.151.3 14 5.4 even 2
225.4.k.d.49.5 28 45.22 odd 12
225.4.k.d.49.10 28 45.13 odd 12
225.4.k.d.124.5 28 5.3 odd 4
225.4.k.d.124.10 28 5.2 odd 4
405.4.a.m.1.3 7 9.7 even 3
405.4.a.n.1.5 7 9.2 odd 6
2025.4.a.ba.1.3 7 45.29 odd 6
2025.4.a.bb.1.5 7 45.34 even 6