Properties

Label 400.2.be.a.21.5
Level $400$
Weight $2$
Character 400.21
Analytic conductor $3.194$
Analytic rank $0$
Dimension $464$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [400,2,Mod(21,400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(400, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 5, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.21");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.be (of order \(20\), degree \(8\), 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: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(464\)
Relative dimension: \(58\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 21.5
Character \(\chi\) \(=\) 400.21
Dual form 400.2.be.a.381.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37167 + 0.344287i) q^{2} +(-2.96765 + 0.470029i) q^{3} +(1.76293 - 0.944493i) q^{4} +(-1.94195 - 1.10853i) q^{5} +(3.90880 - 1.66645i) q^{6} -4.09088i q^{7} +(-2.09298 + 1.90248i) q^{8} +(5.73284 - 1.86271i) q^{9} +O(q^{10})\) \(q+(-1.37167 + 0.344287i) q^{2} +(-2.96765 + 0.470029i) q^{3} +(1.76293 - 0.944493i) q^{4} +(-1.94195 - 1.10853i) q^{5} +(3.90880 - 1.66645i) q^{6} -4.09088i q^{7} +(-2.09298 + 1.90248i) q^{8} +(5.73284 - 1.86271i) q^{9} +(3.04536 + 0.851938i) q^{10} +(-1.46658 + 0.747262i) q^{11} +(-4.78782 + 3.63155i) q^{12} +(1.12061 + 0.570980i) q^{13} +(1.40844 + 5.61132i) q^{14} +(6.28406 + 2.37694i) q^{15} +(2.21586 - 3.33016i) q^{16} +(0.719264 - 0.522576i) q^{17} +(-7.22223 + 4.52876i) q^{18} +(0.637923 - 4.02769i) q^{19} +(-4.47052 - 0.120097i) q^{20} +(1.92283 + 12.1403i) q^{21} +(1.75439 - 1.52992i) q^{22} +(-5.73101 - 1.86212i) q^{23} +(5.31700 - 6.62966i) q^{24} +(2.54234 + 4.30540i) q^{25} +(-1.73368 - 0.397382i) q^{26} +(-8.10605 + 4.13024i) q^{27} +(-3.86381 - 7.21195i) q^{28} +(-6.97747 + 1.10512i) q^{29} +(-9.43798 - 1.09685i) q^{30} +(-8.04316 + 5.84370i) q^{31} +(-1.89290 + 5.33075i) q^{32} +(4.00107 - 2.90695i) q^{33} +(-0.806673 + 0.964432i) q^{34} +(-4.53485 + 7.94429i) q^{35} +(8.34729 - 8.69846i) q^{36} +(-2.73824 + 5.37411i) q^{37} +(0.511663 + 5.74427i) q^{38} +(-3.59396 - 1.16775i) q^{39} +(6.17341 - 1.37441i) q^{40} +(11.9488 - 3.88241i) q^{41} +(-6.81723 - 15.9904i) q^{42} +(1.35517 + 1.35517i) q^{43} +(-1.87971 + 2.70255i) q^{44} +(-13.1977 - 2.73770i) q^{45} +(8.50213 + 0.581091i) q^{46} +(5.57096 + 4.04754i) q^{47} +(-5.01064 + 10.9243i) q^{48} -9.73530 q^{49} +(-4.96954 - 5.03028i) q^{50} +(-1.88890 + 1.88890i) q^{51} +(2.51485 - 0.0518104i) q^{52} +(0.956719 + 6.04049i) q^{53} +(9.69680 - 8.45612i) q^{54} +(3.67639 + 0.174601i) q^{55} +(7.78283 + 8.56212i) q^{56} +12.2526i q^{57} +(9.19027 - 3.91811i) q^{58} +(-1.17975 + 2.31539i) q^{59} +(13.3234 - 1.74487i) q^{60} +(-0.313384 - 0.615051i) q^{61} +(9.02062 - 10.7848i) q^{62} +(-7.62013 - 23.4524i) q^{63} +(0.761111 - 7.96371i) q^{64} +(-1.54322 - 2.35104i) q^{65} +(-4.48731 + 5.36488i) q^{66} +(0.490167 - 3.09479i) q^{67} +(0.774444 - 1.60061i) q^{68} +(17.8829 + 2.83237i) q^{69} +(3.48518 - 12.4582i) q^{70} +(-8.03785 + 11.0631i) q^{71} +(-8.45492 + 14.8052i) q^{72} +(-0.484873 - 0.157545i) q^{73} +(1.90572 - 8.31422i) q^{74} +(-9.56844 - 11.5819i) q^{75} +(-2.67951 - 7.70306i) q^{76} +(3.05696 + 5.99962i) q^{77} +(5.33175 + 0.364406i) q^{78} +(0.632723 + 0.459700i) q^{79} +(-7.99466 + 4.01066i) q^{80} +(7.48465 - 5.43791i) q^{81} +(-15.0531 + 9.43919i) q^{82} +(0.536986 - 3.39040i) q^{83} +(14.8563 + 19.5864i) q^{84} +(-1.97606 + 0.217494i) q^{85} +(-2.32541 - 1.39227i) q^{86} +(20.1872 - 6.55923i) q^{87} +(1.64787 - 4.35416i) q^{88} +(-5.42062 - 1.76127i) q^{89} +(19.0455 - 0.788599i) q^{90} +(2.33581 - 4.58429i) q^{91} +(-11.8621 + 2.13011i) q^{92} +(21.1226 - 21.1226i) q^{93} +(-9.03502 - 3.63386i) q^{94} +(-5.70361 + 7.11442i) q^{95} +(3.11184 - 16.7095i) q^{96} +(3.80085 + 2.76148i) q^{97} +(13.3536 - 3.35174i) q^{98} +(-7.01576 + 7.01576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8} - 14 q^{10} - 6 q^{11} + 10 q^{12} - 6 q^{13} + 6 q^{14} - 16 q^{15} - 6 q^{16} - 12 q^{17} - 24 q^{18} - 6 q^{19} - 22 q^{20} + 12 q^{21} + 10 q^{22} - 16 q^{24} + 4 q^{26} - 18 q^{27} + 18 q^{28} - 6 q^{29} - 6 q^{30} + 12 q^{31} - 36 q^{32} - 12 q^{33} - 30 q^{34} + 44 q^{35} - 82 q^{36} - 6 q^{37} - 76 q^{38} - 52 q^{40} - 10 q^{42} - 48 q^{43} + 36 q^{44} - 12 q^{45} - 14 q^{46} - 12 q^{47} - 116 q^{48} - 400 q^{49} + 10 q^{50} - 4 q^{51} + 32 q^{52} - 6 q^{53} - 30 q^{54} + 36 q^{56} + 26 q^{58} - 6 q^{59} + 48 q^{60} - 6 q^{61} - 34 q^{62} + 72 q^{63} - 24 q^{64} + 16 q^{65} + 92 q^{66} + 30 q^{67} + 28 q^{68} - 18 q^{69} + 60 q^{70} + 22 q^{72} + 28 q^{74} - 26 q^{75} - 76 q^{76} + 36 q^{77} + 14 q^{78} - 52 q^{79} - 34 q^{80} + 72 q^{81} + 56 q^{82} - 46 q^{83} + 112 q^{84} + 2 q^{85} - 46 q^{86} - 136 q^{88} - 42 q^{90} + 36 q^{91} - 4 q^{93} + 50 q^{94} - 40 q^{95} - 66 q^{96} - 12 q^{97} - 8 q^{98} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37167 + 0.344287i −0.969914 + 0.243448i
\(3\) −2.96765 + 0.470029i −1.71337 + 0.271372i −0.934539 0.355860i \(-0.884188\pi\)
−0.778833 + 0.627231i \(0.784188\pi\)
\(4\) 1.76293 0.944493i 0.881466 0.472247i
\(5\) −1.94195 1.10853i −0.868467 0.495748i
\(6\) 3.90880 1.66645i 1.59576 0.680324i
\(7\) 4.09088i 1.54621i −0.634280 0.773104i \(-0.718703\pi\)
0.634280 0.773104i \(-0.281297\pi\)
\(8\) −2.09298 + 1.90248i −0.739979 + 0.672630i
\(9\) 5.73284 1.86271i 1.91095 0.620904i
\(10\) 3.04536 + 0.851938i 0.963027 + 0.269407i
\(11\) −1.46658 + 0.747262i −0.442192 + 0.225308i −0.660887 0.750485i \(-0.729820\pi\)
0.218695 + 0.975793i \(0.429820\pi\)
\(12\) −4.78782 + 3.63155i −1.38213 + 1.04834i
\(13\) 1.12061 + 0.570980i 0.310802 + 0.158361i 0.602433 0.798169i \(-0.294198\pi\)
−0.291631 + 0.956531i \(0.594198\pi\)
\(14\) 1.40844 + 5.61132i 0.376421 + 1.49969i
\(15\) 6.28406 + 2.37694i 1.62254 + 0.613723i
\(16\) 2.21586 3.33016i 0.553966 0.832539i
\(17\) 0.719264 0.522576i 0.174447 0.126743i −0.497136 0.867673i \(-0.665615\pi\)
0.671583 + 0.740930i \(0.265615\pi\)
\(18\) −7.22223 + 4.52876i −1.70230 + 1.06744i
\(19\) 0.637923 4.02769i 0.146350 0.924015i −0.799796 0.600272i \(-0.795059\pi\)
0.946145 0.323743i \(-0.104941\pi\)
\(20\) −4.47052 0.120097i −0.999639 0.0268546i
\(21\) 1.92283 + 12.1403i 0.419597 + 2.64923i
\(22\) 1.75439 1.52992i 0.374037 0.326180i
\(23\) −5.73101 1.86212i −1.19500 0.388278i −0.357080 0.934074i \(-0.616228\pi\)
−0.837918 + 0.545795i \(0.816228\pi\)
\(24\) 5.31700 6.62966i 1.08533 1.35327i
\(25\) 2.54234 + 4.30540i 0.508468 + 0.861081i
\(26\) −1.73368 0.397382i −0.340003 0.0779329i
\(27\) −8.10605 + 4.13024i −1.56001 + 0.794865i
\(28\) −3.86381 7.21195i −0.730191 1.36293i
\(29\) −6.97747 + 1.10512i −1.29568 + 0.205216i −0.765924 0.642932i \(-0.777718\pi\)
−0.529760 + 0.848148i \(0.677718\pi\)
\(30\) −9.43798 1.09685i −1.72313 0.200256i
\(31\) −8.04316 + 5.84370i −1.44459 + 1.04956i −0.457537 + 0.889191i \(0.651268\pi\)
−0.987057 + 0.160368i \(0.948732\pi\)
\(32\) −1.89290 + 5.33075i −0.334620 + 0.942353i
\(33\) 4.00107 2.90695i 0.696497 0.506035i
\(34\) −0.806673 + 0.964432i −0.138343 + 0.165399i
\(35\) −4.53485 + 7.94429i −0.766529 + 1.34283i
\(36\) 8.34729 8.69846i 1.39121 1.44974i
\(37\) −2.73824 + 5.37411i −0.450164 + 0.883498i 0.548708 + 0.836014i \(0.315120\pi\)
−0.998872 + 0.0474832i \(0.984880\pi\)
\(38\) 0.511663 + 5.74427i 0.0830028 + 0.931844i
\(39\) −3.59396 1.16775i −0.575494 0.186989i
\(40\) 6.17341 1.37441i 0.976102 0.217313i
\(41\) 11.9488 3.88241i 1.86609 0.606330i 0.873193 0.487375i \(-0.162046\pi\)
0.992900 0.118955i \(-0.0379544\pi\)
\(42\) −6.81723 15.9904i −1.05192 2.46737i
\(43\) 1.35517 + 1.35517i 0.206662 + 0.206662i 0.802847 0.596185i \(-0.203318\pi\)
−0.596185 + 0.802847i \(0.703318\pi\)
\(44\) −1.87971 + 2.70255i −0.283376 + 0.407425i
\(45\) −13.1977 2.73770i −1.96740 0.408113i
\(46\) 8.50213 + 0.581091i 1.25357 + 0.0856772i
\(47\) 5.57096 + 4.04754i 0.812609 + 0.590395i 0.914586 0.404392i \(-0.132517\pi\)
−0.101977 + 0.994787i \(0.532517\pi\)
\(48\) −5.01064 + 10.9243i −0.723223 + 1.57678i
\(49\) −9.73530 −1.39076
\(50\) −4.96954 5.03028i −0.702799 0.711389i
\(51\) −1.88890 + 1.88890i −0.264498 + 0.264498i
\(52\) 2.51485 0.0518104i 0.348747 0.00718481i
\(53\) 0.956719 + 6.04049i 0.131416 + 0.829725i 0.962043 + 0.272897i \(0.0879818\pi\)
−0.830628 + 0.556828i \(0.812018\pi\)
\(54\) 9.69680 8.45612i 1.31957 1.15073i
\(55\) 3.67639 + 0.174601i 0.495725 + 0.0235432i
\(56\) 7.78283 + 8.56212i 1.04002 + 1.14416i
\(57\) 12.2526i 1.62290i
\(58\) 9.19027 3.91811i 1.20674 0.514473i
\(59\) −1.17975 + 2.31539i −0.153590 + 0.301438i −0.954962 0.296729i \(-0.904104\pi\)
0.801371 + 0.598167i \(0.204104\pi\)
\(60\) 13.3234 1.74487i 1.72004 0.225262i
\(61\) −0.313384 0.615051i −0.0401248 0.0787493i 0.870074 0.492922i \(-0.164071\pi\)
−0.910198 + 0.414172i \(0.864071\pi\)
\(62\) 9.02062 10.7848i 1.14562 1.36967i
\(63\) −7.62013 23.4524i −0.960046 2.95472i
\(64\) 0.761111 7.96371i 0.0951388 0.995464i
\(65\) −1.54322 2.35104i −0.191413 0.291611i
\(66\) −4.48731 + 5.36488i −0.552349 + 0.660371i
\(67\) 0.490167 3.09479i 0.0598834 0.378089i −0.939486 0.342587i \(-0.888697\pi\)
0.999370 0.0355022i \(-0.0113031\pi\)
\(68\) 0.774444 1.60061i 0.0939152 0.194102i
\(69\) 17.8829 + 2.83237i 2.15284 + 0.340977i
\(70\) 3.48518 12.4582i 0.416558 1.48904i
\(71\) −8.03785 + 11.0631i −0.953917 + 1.31295i −0.00415130 + 0.999991i \(0.501321\pi\)
−0.949765 + 0.312962i \(0.898679\pi\)
\(72\) −8.45492 + 14.8052i −0.996422 + 1.74481i
\(73\) −0.484873 0.157545i −0.0567501 0.0184392i 0.280504 0.959853i \(-0.409498\pi\)
−0.337254 + 0.941414i \(0.609498\pi\)
\(74\) 1.90572 8.31422i 0.221535 0.966508i
\(75\) −9.56844 11.5819i −1.10487 1.33737i
\(76\) −2.67951 7.70306i −0.307361 0.883601i
\(77\) 3.05696 + 5.99962i 0.348373 + 0.683720i
\(78\) 5.33175 + 0.364406i 0.603701 + 0.0412609i
\(79\) 0.632723 + 0.459700i 0.0711869 + 0.0517203i 0.622810 0.782373i \(-0.285991\pi\)
−0.551623 + 0.834094i \(0.685991\pi\)
\(80\) −7.99466 + 4.01066i −0.893831 + 0.448405i
\(81\) 7.48465 5.43791i 0.831627 0.604213i
\(82\) −15.0531 + 9.43919i −1.66234 + 1.04238i
\(83\) 0.536986 3.39040i 0.0589419 0.372144i −0.940532 0.339706i \(-0.889673\pi\)
0.999474 0.0324389i \(-0.0103274\pi\)
\(84\) 14.8563 + 19.5864i 1.62095 + 2.13705i
\(85\) −1.97606 + 0.217494i −0.214334 + 0.0235905i
\(86\) −2.32541 1.39227i −0.250756 0.150133i
\(87\) 20.1872 6.55923i 2.16430 0.703223i
\(88\) 1.64787 4.35416i 0.175664 0.464155i
\(89\) −5.42062 1.76127i −0.574584 0.186694i 0.00728873 0.999973i \(-0.497680\pi\)
−0.581873 + 0.813280i \(0.697680\pi\)
\(90\) 19.0455 0.788599i 2.00757 0.0831257i
\(91\) 2.33581 4.58429i 0.244859 0.480564i
\(92\) −11.8621 + 2.13011i −1.23671 + 0.222079i
\(93\) 21.1226 21.1226i 2.19031 2.19031i
\(94\) −9.03502 3.63386i −0.931891 0.374805i
\(95\) −5.70361 + 7.11442i −0.585178 + 0.729924i
\(96\) 3.11184 16.7095i 0.317601 1.70541i
\(97\) 3.80085 + 2.76148i 0.385918 + 0.280386i 0.763781 0.645476i \(-0.223341\pi\)
−0.377863 + 0.925862i \(0.623341\pi\)
\(98\) 13.3536 3.35174i 1.34892 0.338577i
\(99\) −7.01576 + 7.01576i −0.705110 + 0.705110i
\(100\) 8.54840 + 5.18891i 0.854840 + 0.518891i
\(101\) 2.20763 + 2.20763i 0.219667 + 0.219667i 0.808358 0.588691i \(-0.200357\pi\)
−0.588691 + 0.808358i \(0.700357\pi\)
\(102\) 1.94061 3.24125i 0.192149 0.320932i
\(103\) 4.66549 6.42150i 0.459704 0.632729i −0.514743 0.857344i \(-0.672113\pi\)
0.974447 + 0.224616i \(0.0721127\pi\)
\(104\) −3.43169 + 0.936896i −0.336505 + 0.0918702i
\(105\) 9.72378 25.7074i 0.948944 2.50878i
\(106\) −3.39196 7.95614i −0.329456 0.772769i
\(107\) 12.6150 + 12.6150i 1.21954 + 1.21954i 0.967793 + 0.251747i \(0.0810049\pi\)
0.251747 + 0.967793i \(0.418995\pi\)
\(108\) −10.3894 + 14.9374i −0.999725 + 1.43736i
\(109\) 4.38838 + 2.23599i 0.420330 + 0.214169i 0.651346 0.758781i \(-0.274205\pi\)
−0.231015 + 0.972950i \(0.574205\pi\)
\(110\) −5.10290 + 1.02624i −0.486542 + 0.0978482i
\(111\) 5.60016 17.2355i 0.531543 1.63592i
\(112\) −13.6233 9.06484i −1.28728 0.856547i
\(113\) −1.71710 5.28469i −0.161531 0.497142i 0.837233 0.546847i \(-0.184172\pi\)
−0.998764 + 0.0497048i \(0.984172\pi\)
\(114\) −4.21841 16.8065i −0.395090 1.57407i
\(115\) 9.06513 + 9.96911i 0.845328 + 0.929624i
\(116\) −11.2570 + 8.53843i −1.04519 + 0.792773i
\(117\) 7.48785 + 1.18596i 0.692252 + 0.109642i
\(118\) 0.821063 3.58211i 0.0755849 0.329760i
\(119\) −2.13779 2.94242i −0.195971 0.269731i
\(120\) −17.6745 + 6.98045i −1.61345 + 0.637225i
\(121\) −4.87317 + 6.70734i −0.443015 + 0.609758i
\(122\) 0.641613 + 0.735751i 0.0580889 + 0.0666117i
\(123\) −33.6350 + 17.1379i −3.03277 + 1.54527i
\(124\) −8.66022 + 17.8988i −0.777710 + 1.60736i
\(125\) −0.164451 11.1791i −0.0147089 0.999892i
\(126\) 18.5266 + 29.5453i 1.65048 + 2.63210i
\(127\) −3.74652 + 11.5306i −0.332449 + 1.02317i 0.635515 + 0.772088i \(0.280788\pi\)
−0.967965 + 0.251086i \(0.919212\pi\)
\(128\) 1.69781 + 11.1856i 0.150067 + 0.988676i
\(129\) −4.65864 3.38470i −0.410171 0.298007i
\(130\) 2.92622 + 2.69353i 0.256647 + 0.236238i
\(131\) 1.23539 7.79997i 0.107937 0.681487i −0.873082 0.487574i \(-0.837882\pi\)
0.981019 0.193913i \(-0.0621179\pi\)
\(132\) 4.30803 8.90374i 0.374966 0.774971i
\(133\) −16.4768 2.60967i −1.42872 0.226287i
\(134\) 0.393152 + 4.41378i 0.0339631 + 0.381292i
\(135\) 20.3200 + 0.965047i 1.74887 + 0.0830580i
\(136\) −0.511211 + 2.46213i −0.0438360 + 0.211126i
\(137\) −10.3101 + 3.34995i −0.880850 + 0.286205i −0.714310 0.699829i \(-0.753259\pi\)
−0.166540 + 0.986035i \(0.553259\pi\)
\(138\) −25.5045 + 2.27178i −2.17108 + 0.193387i
\(139\) 1.32419 0.674707i 0.112316 0.0572279i −0.396930 0.917849i \(-0.629924\pi\)
0.509246 + 0.860621i \(0.329924\pi\)
\(140\) −0.491304 + 18.2884i −0.0415228 + 1.54565i
\(141\) −18.4351 9.39317i −1.55252 0.791047i
\(142\) 7.21634 17.9423i 0.605582 1.50568i
\(143\) −2.07014 −0.173114
\(144\) 6.50007 23.2188i 0.541673 1.93490i
\(145\) 14.7750 + 5.58861i 1.22699 + 0.464109i
\(146\) 0.719324 + 0.0491633i 0.0595317 + 0.00406878i
\(147\) 28.8910 4.57588i 2.38289 0.377412i
\(148\) 0.248467 + 12.0604i 0.0204239 + 0.991362i
\(149\) −6.21423 6.21423i −0.509090 0.509090i 0.405157 0.914247i \(-0.367217\pi\)
−0.914247 + 0.405157i \(0.867217\pi\)
\(150\) 17.1122 + 12.5923i 1.39721 + 1.02815i
\(151\) 13.8133i 1.12411i 0.827099 + 0.562056i \(0.189989\pi\)
−0.827099 + 0.562056i \(0.810011\pi\)
\(152\) 6.32745 + 9.64350i 0.513224 + 0.782191i
\(153\) 3.15001 4.33562i 0.254663 0.350514i
\(154\) −6.25872 7.17700i −0.504342 0.578339i
\(155\) 22.0973 2.43212i 1.77490 0.195353i
\(156\) −7.43883 + 1.33581i −0.595583 + 0.106950i
\(157\) −14.0619 + 14.0619i −1.12226 + 1.12226i −0.130859 + 0.991401i \(0.541774\pi\)
−0.991401 + 0.130859i \(0.958226\pi\)
\(158\) −1.02615 0.412716i −0.0816363 0.0328339i
\(159\) −5.67841 17.4764i −0.450327 1.38597i
\(160\) 9.58519 8.25374i 0.757776 0.652515i
\(161\) −7.61770 + 23.4449i −0.600359 + 1.84772i
\(162\) −8.39423 + 10.0359i −0.659513 + 0.788492i
\(163\) 17.0658 + 8.69548i 1.33670 + 0.681083i 0.968581 0.248696i \(-0.0800021\pi\)
0.368118 + 0.929779i \(0.380002\pi\)
\(164\) 17.3981 18.1300i 1.35856 1.41572i
\(165\) −10.9923 + 1.20986i −0.855750 + 0.0941874i
\(166\) 0.430704 + 4.83537i 0.0334291 + 0.375297i
\(167\) −9.72487 13.3851i −0.752533 1.03577i −0.997799 0.0663170i \(-0.978875\pi\)
0.245266 0.969456i \(-0.421125\pi\)
\(168\) −27.1212 21.7512i −2.09244 1.67814i
\(169\) −6.71146 9.23753i −0.516266 0.710579i
\(170\) 2.63562 0.978661i 0.202143 0.0750599i
\(171\) −3.84531 24.2783i −0.294058 1.85661i
\(172\) 3.66903 + 1.10913i 0.279761 + 0.0845701i
\(173\) −5.00185 9.81669i −0.380284 0.746349i 0.618952 0.785429i \(-0.287557\pi\)
−0.999236 + 0.0390797i \(0.987557\pi\)
\(174\) −25.4319 + 15.9473i −1.92799 + 1.20896i
\(175\) 17.6129 10.4004i 1.33141 0.786198i
\(176\) −0.761253 + 6.53979i −0.0573816 + 0.492955i
\(177\) 2.41278 7.42577i 0.181356 0.558155i
\(178\) 8.04165 + 0.549619i 0.602747 + 0.0411957i
\(179\) −15.6009 + 2.47094i −1.16607 + 0.184687i −0.709304 0.704903i \(-0.750991\pi\)
−0.456762 + 0.889589i \(0.650991\pi\)
\(180\) −25.8525 + 7.63880i −1.92693 + 0.569362i
\(181\) −9.24117 1.46366i −0.686891 0.108793i −0.196773 0.980449i \(-0.563046\pi\)
−0.490118 + 0.871656i \(0.663046\pi\)
\(182\) −1.62564 + 7.09230i −0.120500 + 0.525716i
\(183\) 1.21911 + 1.67796i 0.0901190 + 0.124038i
\(184\) 15.5375 7.00578i 1.14544 0.516473i
\(185\) 11.2749 7.40083i 0.828945 0.544120i
\(186\) −21.7009 + 36.2453i −1.59118 + 2.65763i
\(187\) −0.664360 + 1.30388i −0.0485828 + 0.0953491i
\(188\) 13.6441 + 1.87381i 0.995099 + 0.136661i
\(189\) 16.8963 + 33.1609i 1.22903 + 2.41210i
\(190\) 5.37405 11.7223i 0.389874 0.850423i
\(191\) 1.74414 + 5.36792i 0.126202 + 0.388409i 0.994118 0.108301i \(-0.0345411\pi\)
−0.867916 + 0.496710i \(0.834541\pi\)
\(192\) 1.48447 + 23.9912i 0.107132 + 1.73142i
\(193\) −1.91961 −0.138176 −0.0690881 0.997611i \(-0.522009\pi\)
−0.0690881 + 0.997611i \(0.522009\pi\)
\(194\) −6.16424 2.47924i −0.442567 0.177999i
\(195\) 5.68481 + 6.25170i 0.407097 + 0.447693i
\(196\) −17.1627 + 9.19493i −1.22591 + 0.656781i
\(197\) −3.91917 24.7447i −0.279229 1.76298i −0.585148 0.810926i \(-0.698964\pi\)
0.305919 0.952058i \(-0.401036\pi\)
\(198\) 7.20784 12.0387i 0.512239 0.855554i
\(199\) 2.81161i 0.199310i −0.995022 0.0996548i \(-0.968226\pi\)
0.995022 0.0996548i \(-0.0317739\pi\)
\(200\) −13.5120 4.17435i −0.955444 0.295171i
\(201\) 9.41465i 0.664058i
\(202\) −3.78818 2.26807i −0.266536 0.159581i
\(203\) 4.52092 + 28.5440i 0.317307 + 2.00340i
\(204\) −1.54595 + 5.11404i −0.108238 + 0.358055i
\(205\) −27.5078 5.70613i −1.92123 0.398534i
\(206\) −4.18865 + 10.4144i −0.291837 + 0.725606i
\(207\) −36.3235 −2.52466
\(208\) 4.38457 2.46660i 0.304016 0.171028i
\(209\) 2.07417 + 6.38364i 0.143473 + 0.441566i
\(210\) −4.48707 + 38.6097i −0.309637 + 2.66432i
\(211\) −5.84538 11.4722i −0.402413 0.789779i 0.597514 0.801858i \(-0.296155\pi\)
−0.999927 + 0.0120789i \(0.996155\pi\)
\(212\) 7.39183 + 9.74536i 0.507673 + 0.669314i
\(213\) 18.6535 36.6095i 1.27812 2.50844i
\(214\) −21.6468 12.9604i −1.47974 0.885955i
\(215\) −1.12943 4.13392i −0.0770267 0.281931i
\(216\) 9.10807 24.0661i 0.619726 1.63749i
\(217\) 23.9059 + 32.9036i 1.62284 + 2.23364i
\(218\) −6.78921 1.55617i −0.459823 0.105397i
\(219\) 1.51298 + 0.239633i 0.102238 + 0.0161929i
\(220\) 6.64614 3.16452i 0.448083 0.213352i
\(221\) 1.10439 0.174919i 0.0742896 0.0117663i
\(222\) −1.74758 + 25.5694i −0.117290 + 1.71611i
\(223\) −0.922924 + 2.84047i −0.0618036 + 0.190212i −0.977191 0.212362i \(-0.931884\pi\)
0.915387 + 0.402574i \(0.131884\pi\)
\(224\) 21.8075 + 7.74361i 1.45707 + 0.517392i
\(225\) 22.5946 + 19.9465i 1.50630 + 1.32977i
\(226\) 4.17474 + 6.65765i 0.277699 + 0.442860i
\(227\) −2.86977 5.63224i −0.190473 0.373825i 0.775944 0.630801i \(-0.217274\pi\)
−0.966418 + 0.256976i \(0.917274\pi\)
\(228\) 11.5725 + 21.6005i 0.766408 + 1.43053i
\(229\) −3.10595 19.6102i −0.205247 1.29588i −0.848079 0.529870i \(-0.822241\pi\)
0.642832 0.766007i \(-0.277759\pi\)
\(230\) −15.8666 10.5533i −1.04621 0.695863i
\(231\) −11.8920 16.3679i −0.782435 1.07693i
\(232\) 12.5012 15.5875i 0.820745 1.02337i
\(233\) 4.77010 + 6.56548i 0.312500 + 0.430119i 0.936159 0.351577i \(-0.114355\pi\)
−0.623659 + 0.781697i \(0.714355\pi\)
\(234\) −10.6791 + 0.951231i −0.698117 + 0.0621839i
\(235\) −6.33173 14.0357i −0.413037 0.915587i
\(236\) 0.107050 + 5.19614i 0.00696835 + 0.338240i
\(237\) −2.09377 1.06683i −0.136005 0.0692980i
\(238\) 3.94538 + 3.30000i 0.255741 + 0.213907i
\(239\) −0.508630 + 1.56540i −0.0329006 + 0.101258i −0.966158 0.257950i \(-0.916953\pi\)
0.933258 + 0.359208i \(0.116953\pi\)
\(240\) 21.8402 15.6599i 1.40978 1.01084i
\(241\) −2.08108 6.40490i −0.134054 0.412576i 0.861388 0.507948i \(-0.169596\pi\)
−0.995442 + 0.0953722i \(0.969596\pi\)
\(242\) 4.37511 10.8780i 0.281243 0.699264i
\(243\) −0.356820 + 0.356820i −0.0228900 + 0.0228900i
\(244\) −1.13339 0.788305i −0.0725577 0.0504661i
\(245\) 18.9055 + 10.7918i 1.20783 + 0.689465i
\(246\) 40.2357 35.0876i 2.56533 2.23710i
\(247\) 3.01459 4.14923i 0.191814 0.264009i
\(248\) 5.71661 27.5327i 0.363005 1.74833i
\(249\) 10.3139i 0.653617i
\(250\) 4.07440 + 15.2774i 0.257688 + 0.966228i
\(251\) 1.96932 + 1.96932i 0.124303 + 0.124303i 0.766521 0.642219i \(-0.221986\pi\)
−0.642219 + 0.766521i \(0.721986\pi\)
\(252\) −35.5844 34.1478i −2.24160 2.15111i
\(253\) 9.79650 1.55161i 0.615901 0.0975491i
\(254\) 1.16913 17.1060i 0.0733580 1.07333i
\(255\) 5.76203 1.57425i 0.360832 0.0985835i
\(256\) −6.17989 14.7584i −0.386243 0.922397i
\(257\) −13.0841 −0.816162 −0.408081 0.912946i \(-0.633802\pi\)
−0.408081 + 0.912946i \(0.633802\pi\)
\(258\) 7.55541 + 3.03877i 0.470379 + 0.189186i
\(259\) 21.9848 + 11.2018i 1.36607 + 0.696048i
\(260\) −4.94114 2.68716i −0.306437 0.166651i
\(261\) −37.9422 + 19.3325i −2.34856 + 1.19665i
\(262\) 0.990881 + 11.1243i 0.0612168 + 0.687260i
\(263\) −20.1253 + 6.53911i −1.24098 + 0.403219i −0.854680 0.519155i \(-0.826247\pi\)
−0.386300 + 0.922373i \(0.626247\pi\)
\(264\) −2.84373 + 13.6962i −0.175020 + 0.842940i
\(265\) 4.83814 12.7909i 0.297204 0.785737i
\(266\) 23.4991 2.09315i 1.44082 0.128340i
\(267\) 16.9143 + 2.67897i 1.03514 + 0.163950i
\(268\) −2.05888 5.91887i −0.125766 0.361553i
\(269\) −2.48855 + 15.7121i −0.151730 + 0.957983i 0.787903 + 0.615799i \(0.211167\pi\)
−0.939633 + 0.342184i \(0.888833\pi\)
\(270\) −28.2045 + 5.67220i −1.71647 + 0.345199i
\(271\) 21.9193 + 15.9253i 1.33151 + 0.967395i 0.999711 + 0.0240439i \(0.00765415\pi\)
0.331795 + 0.943352i \(0.392346\pi\)
\(272\) −0.146468 3.55322i −0.00888090 0.215445i
\(273\) −4.77711 + 14.7024i −0.289124 + 0.889832i
\(274\) 12.9886 8.14464i 0.784672 0.492035i
\(275\) −6.94582 4.41444i −0.418849 0.266201i
\(276\) 34.2015 11.8970i 2.05869 0.716114i
\(277\) −9.90984 + 5.04932i −0.595425 + 0.303384i −0.725611 0.688106i \(-0.758443\pi\)
0.130186 + 0.991490i \(0.458443\pi\)
\(278\) −1.58405 + 1.38137i −0.0950049 + 0.0828492i
\(279\) −35.2250 + 48.4830i −2.10887 + 2.90260i
\(280\) −5.62255 25.2547i −0.336011 1.50926i
\(281\) 7.24408 + 9.97062i 0.432145 + 0.594797i 0.968444 0.249231i \(-0.0801779\pi\)
−0.536299 + 0.844028i \(0.680178\pi\)
\(282\) 28.5208 + 6.53731i 1.69839 + 0.389291i
\(283\) −21.7077 3.43816i −1.29039 0.204377i −0.526749 0.850021i \(-0.676589\pi\)
−0.763639 + 0.645643i \(0.776589\pi\)
\(284\) −3.72112 + 27.0953i −0.220808 + 1.60781i
\(285\) 13.5823 23.7939i 0.804547 1.40943i
\(286\) 2.83954 0.712723i 0.167906 0.0421442i
\(287\) −15.8825 48.8812i −0.937512 2.88537i
\(288\) −0.922006 + 34.0863i −0.0543297 + 2.00855i
\(289\) −5.00903 + 15.4162i −0.294649 + 0.906837i
\(290\) −22.1904 2.57888i −1.30306 0.151437i
\(291\) −12.5776 6.40859i −0.737310 0.375678i
\(292\) −1.00360 + 0.180218i −0.0587312 + 0.0105465i
\(293\) 21.9915 + 21.9915i 1.28476 + 1.28476i 0.937929 + 0.346827i \(0.112741\pi\)
0.346827 + 0.937929i \(0.387259\pi\)
\(294\) −38.0533 + 16.2234i −2.21931 + 0.946165i
\(295\) 4.85768 3.18858i 0.282825 0.185647i
\(296\) −4.49307 16.4573i −0.261154 0.956564i
\(297\) 8.80184 12.1147i 0.510734 0.702966i
\(298\) 10.6633 + 6.38437i 0.617710 + 0.369837i
\(299\) −5.35900 5.35900i −0.309919 0.309919i
\(300\) −27.8076 11.3809i −1.60547 0.657075i
\(301\) 5.54385 5.54385i 0.319542 0.319542i
\(302\) −4.75575 18.9473i −0.273662 1.09029i
\(303\) −7.58911 5.51381i −0.435983 0.316760i
\(304\) −11.9993 11.0492i −0.688206 0.633715i
\(305\) −0.0732235 + 1.54179i −0.00419276 + 0.0882829i
\(306\) −2.82807 + 7.03153i −0.161670 + 0.401966i
\(307\) 1.62340 1.62340i 0.0926523 0.0926523i −0.659261 0.751914i \(-0.729131\pi\)
0.751914 + 0.659261i \(0.229131\pi\)
\(308\) 11.0558 + 7.68965i 0.629964 + 0.438159i
\(309\) −10.8272 + 21.2497i −0.615940 + 1.20885i
\(310\) −29.4728 + 10.9439i −1.67394 + 0.621570i
\(311\) 17.7505 + 5.76749i 1.00654 + 0.327044i 0.765476 0.643465i \(-0.222504\pi\)
0.241063 + 0.970509i \(0.422504\pi\)
\(312\) 9.74369 4.39337i 0.551628 0.248726i
\(313\) −15.0648 + 4.89484i −0.851511 + 0.276673i −0.702079 0.712099i \(-0.747745\pi\)
−0.149432 + 0.988772i \(0.547745\pi\)
\(314\) 14.4469 24.1295i 0.815284 1.36171i
\(315\) −11.1996 + 53.9904i −0.631027 + 3.04202i
\(316\) 1.54963 + 0.212818i 0.0871736 + 0.0119719i
\(317\) 3.56301 22.4960i 0.200119 1.26350i −0.659165 0.751999i \(-0.729090\pi\)
0.859283 0.511500i \(-0.170910\pi\)
\(318\) 13.8058 + 22.0167i 0.774189 + 1.23464i
\(319\) 9.40723 6.83475i 0.526704 0.382673i
\(320\) −10.3060 + 14.6214i −0.576124 + 0.817362i
\(321\) −43.3664 31.5075i −2.42047 1.75858i
\(322\) 2.37717 34.7812i 0.132475 1.93828i
\(323\) −1.64594 3.23033i −0.0915824 0.179740i
\(324\) 8.05886 16.6559i 0.447714 0.925326i
\(325\) 0.390677 + 6.27631i 0.0216709 + 0.348147i
\(326\) −26.4024 6.05174i −1.46229 0.335175i
\(327\) −14.0741 4.57297i −0.778302 0.252886i
\(328\) −17.6224 + 30.8582i −0.973034 + 1.70386i
\(329\) 16.5580 22.7902i 0.912873 1.25646i
\(330\) 14.6612 5.44403i 0.807074 0.299684i
\(331\) 14.8941 + 2.35899i 0.818653 + 0.129662i 0.551695 0.834046i \(-0.313981\pi\)
0.266958 + 0.963708i \(0.413981\pi\)
\(332\) −2.25554 6.48422i −0.123789 0.355868i
\(333\) −5.68750 + 35.9094i −0.311673 + 1.96782i
\(334\) 17.9476 + 15.0118i 0.982049 + 0.821408i
\(335\) −4.38254 + 5.46657i −0.239444 + 0.298671i
\(336\) 44.6898 + 20.4979i 2.43803 + 1.11825i
\(337\) 1.70316 + 5.24178i 0.0927768 + 0.285538i 0.986668 0.162746i \(-0.0520353\pi\)
−0.893891 + 0.448284i \(0.852035\pi\)
\(338\) 12.3862 + 10.3601i 0.673722 + 0.563517i
\(339\) 7.57971 + 14.8760i 0.411673 + 0.807954i
\(340\) −3.27824 + 2.24980i −0.177788 + 0.122013i
\(341\) 7.42920 14.5806i 0.402314 0.789585i
\(342\) 13.6332 + 31.9779i 0.737199 + 1.72917i
\(343\) 11.1898i 0.604193i
\(344\) −5.41454 0.258152i −0.291932 0.0139186i
\(345\) −31.5879 25.3239i −1.70063 1.36339i
\(346\) 10.2406 + 11.7431i 0.550539 + 0.631315i
\(347\) −2.81855 17.7956i −0.151308 0.955318i −0.940159 0.340735i \(-0.889324\pi\)
0.788852 0.614583i \(-0.210676\pi\)
\(348\) 29.3936 30.6302i 1.57566 1.64195i
\(349\) 4.48855 4.48855i 0.240266 0.240266i −0.576694 0.816960i \(-0.695657\pi\)
0.816960 + 0.576694i \(0.195657\pi\)
\(350\) −20.5783 + 20.3298i −1.09995 + 1.08667i
\(351\) −11.4420 −0.610730
\(352\) −1.20738 9.23249i −0.0643535 0.492093i
\(353\) −12.6421 9.18499i −0.672869 0.488868i 0.198115 0.980179i \(-0.436518\pi\)
−0.870984 + 0.491311i \(0.836518\pi\)
\(354\) −0.752929 + 11.0164i −0.0400178 + 0.585513i
\(355\) 27.8729 12.5739i 1.47934 0.667354i
\(356\) −11.2197 + 2.01474i −0.594642 + 0.106781i
\(357\) 7.72725 + 7.72725i 0.408969 + 0.408969i
\(358\) 20.5485 8.76049i 1.08602 0.463006i
\(359\) 21.8634 7.10386i 1.15391 0.374928i 0.331294 0.943527i \(-0.392515\pi\)
0.822614 + 0.568600i \(0.192515\pi\)
\(360\) 32.8310 19.3785i 1.73035 1.02134i
\(361\) 2.25475 + 0.732613i 0.118671 + 0.0385586i
\(362\) 13.1797 1.17397i 0.692710 0.0617023i
\(363\) 11.3092 22.1956i 0.593579 1.16496i
\(364\) −0.211950 10.2879i −0.0111092 0.539235i
\(365\) 0.766957 + 0.843438i 0.0401443 + 0.0441476i
\(366\) −2.24991 1.88187i −0.117604 0.0983670i
\(367\) −9.63679 + 7.00153i −0.503036 + 0.365477i −0.810175 0.586187i \(-0.800628\pi\)
0.307139 + 0.951665i \(0.400628\pi\)
\(368\) −18.9003 + 14.9590i −0.985246 + 0.779790i
\(369\) 61.2688 44.5144i 3.18953 2.31733i
\(370\) −12.9173 + 14.0333i −0.671540 + 0.729554i
\(371\) 24.7109 3.91383i 1.28293 0.203196i
\(372\) 17.2875 57.1878i 0.896317 2.96505i
\(373\) 7.10665 3.62102i 0.367968 0.187489i −0.260222 0.965549i \(-0.583796\pi\)
0.628191 + 0.778060i \(0.283796\pi\)
\(374\) 0.462371 2.01722i 0.0239086 0.104308i
\(375\) 5.74255 + 33.0984i 0.296544 + 1.70920i
\(376\) −19.3603 + 2.12725i −0.998431 + 0.109705i
\(377\) −8.45003 2.74558i −0.435199 0.141405i
\(378\) −34.5930 39.6685i −1.77927 2.04033i
\(379\) 3.62864 + 22.9104i 0.186391 + 1.17683i 0.886479 + 0.462769i \(0.153144\pi\)
−0.700088 + 0.714057i \(0.746856\pi\)
\(380\) −3.33557 + 17.9293i −0.171111 + 0.919752i
\(381\) 5.69862 35.9797i 0.291949 1.84330i
\(382\) −4.24049 6.76251i −0.216962 0.346000i
\(383\) 21.6248 15.7113i 1.10497 0.802810i 0.123109 0.992393i \(-0.460714\pi\)
0.981865 + 0.189583i \(0.0607135\pi\)
\(384\) −10.2961 32.3969i −0.525419 1.65325i
\(385\) 0.714271 15.0397i 0.0364026 0.766493i
\(386\) 2.63306 0.660895i 0.134019 0.0336387i
\(387\) 10.2933 + 5.24469i 0.523237 + 0.266602i
\(388\) 9.30885 + 1.27843i 0.472585 + 0.0649022i
\(389\) −6.25384 + 3.18649i −0.317082 + 0.161562i −0.605287 0.796007i \(-0.706942\pi\)
0.288205 + 0.957569i \(0.406942\pi\)
\(390\) −9.95003 6.61804i −0.503839 0.335117i
\(391\) −5.09520 + 1.65553i −0.257676 + 0.0837239i
\(392\) 20.3758 18.5213i 1.02913 0.935465i
\(393\) 23.7282i 1.19693i
\(394\) 13.8951 + 32.5921i 0.700023 + 1.64197i
\(395\) −0.719127 1.59410i −0.0361832 0.0802081i
\(396\) −5.74197 + 18.9946i −0.288545 + 0.954517i
\(397\) −13.6062 + 2.15501i −0.682874 + 0.108157i −0.488227 0.872717i \(-0.662356\pi\)
−0.194647 + 0.980873i \(0.562356\pi\)
\(398\) 0.968000 + 3.85659i 0.0485215 + 0.193313i
\(399\) 50.1239 2.50934
\(400\) 19.9712 + 1.07380i 0.998558 + 0.0536899i
\(401\) 24.8287 1.23989 0.619943 0.784647i \(-0.287156\pi\)
0.619943 + 0.784647i \(0.287156\pi\)
\(402\) −3.24134 12.9137i −0.161663 0.644079i
\(403\) −12.3499 + 1.95603i −0.615192 + 0.0974368i
\(404\) 5.97699 + 1.80681i 0.297366 + 0.0898921i
\(405\) −20.5629 + 2.26324i −1.02178 + 0.112461i
\(406\) −16.0285 37.5963i −0.795482 1.86587i
\(407\) 9.92777i 0.492101i
\(408\) 0.359823 7.54701i 0.0178139 0.373633i
\(409\) 7.94465 2.58137i 0.392837 0.127641i −0.105936 0.994373i \(-0.533784\pi\)
0.498774 + 0.866732i \(0.333784\pi\)
\(410\) 39.6960 1.64366i 1.96045 0.0811745i
\(411\) 29.0221 14.7875i 1.43156 0.729414i
\(412\) 2.15989 15.7272i 0.106410 0.774823i
\(413\) 9.47197 + 4.82621i 0.466085 + 0.237482i
\(414\) 49.8237 12.5057i 2.44870 0.614623i
\(415\) −4.80114 + 5.98872i −0.235679 + 0.293975i
\(416\) −5.16495 + 4.89290i −0.253233 + 0.239894i
\(417\) −3.61259 + 2.62470i −0.176909 + 0.128532i
\(418\) −5.04287 8.04211i −0.246655 0.393352i
\(419\) −1.54140 + 9.73200i −0.0753022 + 0.475439i 0.921003 + 0.389556i \(0.127371\pi\)
−0.996305 + 0.0858838i \(0.972629\pi\)
\(420\) −7.13805 54.5044i −0.348301 2.65954i
\(421\) −3.12363 19.7218i −0.152236 0.961183i −0.938997 0.343925i \(-0.888243\pi\)
0.786761 0.617258i \(-0.211757\pi\)
\(422\) 11.9676 + 13.7235i 0.582576 + 0.668052i
\(423\) 39.4768 + 12.8268i 1.91943 + 0.623661i
\(424\) −13.4943 10.8225i −0.655342 0.525585i
\(425\) 4.07851 + 1.76815i 0.197837 + 0.0857681i
\(426\) −12.9822 + 56.6382i −0.628988 + 2.74413i
\(427\) −2.51610 + 1.28202i −0.121763 + 0.0620412i
\(428\) 34.1542 + 10.3246i 1.65091 + 0.499060i
\(429\) 6.14345 0.973027i 0.296609 0.0469782i
\(430\) 2.97246 + 5.28151i 0.143345 + 0.254697i
\(431\) −15.9804 + 11.6104i −0.769747 + 0.559254i −0.901885 0.431977i \(-0.857816\pi\)
0.132137 + 0.991231i \(0.457816\pi\)
\(432\) −4.20757 + 36.1465i −0.202437 + 1.73910i
\(433\) −23.2534 + 16.8946i −1.11749 + 0.811902i −0.983826 0.179126i \(-0.942673\pi\)
−0.133660 + 0.991027i \(0.542673\pi\)
\(434\) −44.1191 36.9023i −2.11779 1.77137i
\(435\) −46.4737 9.64037i −2.22824 0.462220i
\(436\) 9.84829 0.202893i 0.471648 0.00971680i
\(437\) −11.1560 + 21.8948i −0.533663 + 1.04737i
\(438\) −2.15781 + 0.192204i −0.103104 + 0.00918387i
\(439\) −29.5368 9.59708i −1.40971 0.458044i −0.497395 0.867524i \(-0.665710\pi\)
−0.912319 + 0.409480i \(0.865710\pi\)
\(440\) −8.02678 + 6.62884i −0.382662 + 0.316018i
\(441\) −55.8109 + 18.1341i −2.65766 + 0.863527i
\(442\) −1.45464 + 0.620159i −0.0691901 + 0.0294980i
\(443\) −1.54302 1.54302i −0.0733111 0.0733111i 0.669501 0.742812i \(-0.266508\pi\)
−0.742812 + 0.669501i \(0.766508\pi\)
\(444\) −6.40612 35.6744i −0.304021 1.69303i
\(445\) 8.57416 + 9.42918i 0.406454 + 0.446986i
\(446\) 0.288007 4.21392i 0.0136375 0.199535i
\(447\) 21.3625 + 15.5208i 1.01041 + 0.734108i
\(448\) −32.5786 3.11361i −1.53919 0.147104i
\(449\) −23.0290 −1.08681 −0.543403 0.839472i \(-0.682864\pi\)
−0.543403 + 0.839472i \(0.682864\pi\)
\(450\) −37.8595 19.5810i −1.78471 0.923055i
\(451\) −14.6228 + 14.6228i −0.688560 + 0.688560i
\(452\) −8.01849 7.69477i −0.377158 0.361931i
\(453\) −6.49266 40.9931i −0.305052 1.92602i
\(454\) 5.87547 + 6.73753i 0.275750 + 0.316208i
\(455\) −9.61783 + 6.31315i −0.450891 + 0.295965i
\(456\) −23.3104 25.6444i −1.09161 1.20091i
\(457\) 0.0323799i 0.00151467i 1.00000 0.000757333i \(0.000241067\pi\)
−1.00000 0.000757333i \(0.999759\pi\)
\(458\) 11.0119 + 25.8293i 0.514550 + 1.20692i
\(459\) −3.67203 + 7.20676i −0.171395 + 0.336383i
\(460\) 25.3970 + 9.01292i 1.18414 + 0.420230i
\(461\) 1.63852 + 3.21577i 0.0763133 + 0.149773i 0.926011 0.377498i \(-0.123215\pi\)
−0.849697 + 0.527271i \(0.823215\pi\)
\(462\) 21.9471 + 18.3570i 1.02107 + 0.854047i
\(463\) 1.69557 + 5.21843i 0.0787999 + 0.242521i 0.982694 0.185234i \(-0.0593044\pi\)
−0.903894 + 0.427755i \(0.859304\pi\)
\(464\) −11.7809 + 25.6849i −0.546914 + 1.19239i
\(465\) −64.4338 + 17.6041i −2.98805 + 0.816369i
\(466\) −8.80340 7.36336i −0.407809 0.341101i
\(467\) −3.18102 + 20.0842i −0.147200 + 0.929385i 0.797944 + 0.602731i \(0.205921\pi\)
−0.945144 + 0.326653i \(0.894079\pi\)
\(468\) 14.3207 4.98146i 0.661975 0.230268i
\(469\) −12.6604 2.00521i −0.584604 0.0925922i
\(470\) 13.5173 + 17.0723i 0.623508 + 0.787488i
\(471\) 35.1212 48.3402i 1.61830 2.22740i
\(472\) −1.93580 7.09050i −0.0891023 0.326367i
\(473\) −3.00014 0.974806i −0.137947 0.0448216i
\(474\) 3.23925 + 0.742475i 0.148784 + 0.0341030i
\(475\) 18.9626 7.49324i 0.870066 0.343814i
\(476\) −6.54789 3.16816i −0.300122 0.145212i
\(477\) 16.7364 + 32.8470i 0.766307 + 1.50396i
\(478\) 0.158723 2.32232i 0.00725981 0.106221i
\(479\) 4.45138 + 3.23411i 0.203389 + 0.147770i 0.684817 0.728715i \(-0.259882\pi\)
−0.481429 + 0.876485i \(0.659882\pi\)
\(480\) −24.5660 + 28.9995i −1.12128 + 1.32364i
\(481\) −6.13701 + 4.45880i −0.279824 + 0.203304i
\(482\) 5.05967 + 8.06890i 0.230462 + 0.367528i
\(483\) 11.5869 73.1567i 0.527221 3.32874i
\(484\) −2.25603 + 16.4273i −0.102547 + 0.746694i
\(485\) −4.31989 9.57600i −0.196156 0.434824i
\(486\) 0.366589 0.612286i 0.0166288 0.0277739i
\(487\) −5.76881 + 1.87440i −0.261410 + 0.0849372i −0.436790 0.899564i \(-0.643885\pi\)
0.175380 + 0.984501i \(0.443885\pi\)
\(488\) 1.82603 + 0.691080i 0.0826606 + 0.0312837i
\(489\) −54.7325 17.7837i −2.47509 0.804206i
\(490\) −29.6475 8.29388i −1.33934 0.374679i
\(491\) 13.3362 26.1737i 0.601854 1.18120i −0.366218 0.930529i \(-0.619347\pi\)
0.968071 0.250675i \(-0.0806525\pi\)
\(492\) −43.1097 + 61.9811i −1.94353 + 2.79432i
\(493\) −4.44113 + 4.44113i −0.200018 + 0.200018i
\(494\) −2.70649 + 6.72924i −0.121771 + 0.302763i
\(495\) 21.4014 5.84710i 0.961921 0.262808i
\(496\) 1.63787 + 39.7338i 0.0735426 + 1.78410i
\(497\) 45.2580 + 32.8819i 2.03010 + 1.47495i
\(498\) −3.55094 14.1472i −0.159122 0.633953i
\(499\) −29.8174 + 29.8174i −1.33481 + 1.33481i −0.433801 + 0.901009i \(0.642828\pi\)
−0.901009 + 0.433801i \(0.857172\pi\)
\(500\) −10.8485 19.5527i −0.485161 0.874425i
\(501\) 35.1514 + 35.1514i 1.57045 + 1.57045i
\(502\) −3.37926 2.02324i −0.150824 0.0903016i
\(503\) −6.40313 + 8.81316i −0.285502 + 0.392959i −0.927547 0.373708i \(-0.878086\pi\)
0.642045 + 0.766667i \(0.278086\pi\)
\(504\) 60.5665 + 34.5881i 2.69785 + 1.54068i
\(505\) −1.83989 6.73431i −0.0818740 0.299673i
\(506\) −12.9033 + 5.50110i −0.573623 + 0.244554i
\(507\) 24.2592 + 24.2592i 1.07739 + 1.07739i
\(508\) 4.28571 + 23.8662i 0.190148 + 1.05889i
\(509\) −10.6842 5.44386i −0.473568 0.241295i 0.200882 0.979615i \(-0.435619\pi\)
−0.674450 + 0.738321i \(0.735619\pi\)
\(510\) −7.36158 + 4.14314i −0.325976 + 0.183461i
\(511\) −0.644497 + 1.98356i −0.0285109 + 0.0877474i
\(512\) 13.5578 + 18.1159i 0.599178 + 0.800616i
\(513\) 11.4643 + 35.2834i 0.506160 + 1.55780i
\(514\) 17.9470 4.50468i 0.791607 0.198693i
\(515\) −16.1785 + 7.29841i −0.712912 + 0.321606i
\(516\) −11.4097 1.56695i −0.502284 0.0689810i
\(517\) −11.1949 1.77309i −0.492350 0.0779805i
\(518\) −34.0125 7.79607i −1.49442 0.342540i
\(519\) 19.4579 + 26.7815i 0.854105 + 1.17558i
\(520\) 7.70275 + 1.98471i 0.337788 + 0.0870355i
\(521\) −7.94775 + 10.9391i −0.348197 + 0.479253i −0.946813 0.321784i \(-0.895718\pi\)
0.598616 + 0.801036i \(0.295718\pi\)
\(522\) 45.3880 39.5807i 1.98658 1.73240i
\(523\) −9.56832 + 4.87530i −0.418393 + 0.213182i −0.650497 0.759509i \(-0.725439\pi\)
0.232103 + 0.972691i \(0.425439\pi\)
\(524\) −5.18910 14.9176i −0.226687 0.651680i
\(525\) −47.3804 + 39.1433i −2.06785 + 1.70836i
\(526\) 25.3539 15.8984i 1.10548 0.693201i
\(527\) −2.73138 + 8.40632i −0.118981 + 0.366185i
\(528\) −0.814760 19.7656i −0.0354579 0.860187i
\(529\) 10.7696 + 7.82457i 0.468243 + 0.340199i
\(530\) −2.23257 + 19.2105i −0.0969767 + 0.834451i
\(531\) −2.45041 + 15.4713i −0.106339 + 0.671396i
\(532\) −31.5123 + 10.9615i −1.36623 + 0.475243i
\(533\) 15.6068 + 2.47187i 0.676004 + 0.107068i
\(534\) −24.1231 + 2.14874i −1.04391 + 0.0929850i
\(535\) −10.5137 38.4818i −0.454545 1.66371i
\(536\) 4.86188 + 7.40987i 0.210001 + 0.320057i
\(537\) 45.1366 14.6658i 1.94779 0.632874i
\(538\) −1.99601 22.4085i −0.0860540 0.966099i
\(539\) 14.2776 7.27482i 0.614982 0.313349i
\(540\) 36.7343 17.4908i 1.58079 0.752685i
\(541\) −29.5167 15.0395i −1.26902 0.646600i −0.315788 0.948830i \(-0.602269\pi\)
−0.953235 + 0.302230i \(0.902269\pi\)
\(542\) −35.5489 14.2977i −1.52696 0.614138i
\(543\) 28.1125 1.20642
\(544\) 1.42423 + 4.82340i 0.0610634 + 0.206802i
\(545\) −6.04336 9.20681i −0.258869 0.394377i
\(546\) 1.49074 21.8115i 0.0637979 0.933448i
\(547\) −29.8544 + 4.72848i −1.27648 + 0.202175i −0.757628 0.652686i \(-0.773642\pi\)
−0.518856 + 0.854862i \(0.673642\pi\)
\(548\) −15.0120 + 15.6435i −0.641280 + 0.668259i
\(549\) −2.94224 2.94224i −0.125572 0.125572i
\(550\) 11.0472 + 3.66378i 0.471053 + 0.156224i
\(551\) 28.8081i 1.22726i
\(552\) −42.8170 + 28.0938i −1.82241 + 1.19575i
\(553\) 1.88058 2.58839i 0.0799703 0.110070i
\(554\) 11.8546 10.3378i 0.503653 0.439211i
\(555\) −29.9812 + 27.2626i −1.27263 + 1.15723i
\(556\) 1.69720 2.44015i 0.0719771 0.103485i
\(557\) −2.86672 + 2.86672i −0.121467 + 0.121467i −0.765227 0.643760i \(-0.777373\pi\)
0.643760 + 0.765227i \(0.277373\pi\)
\(558\) 31.6248 78.6300i 1.33879 3.32867i
\(559\) 0.744845 + 2.29240i 0.0315036 + 0.0969580i
\(560\) 16.4071 + 32.7052i 0.693327 + 1.38205i
\(561\) 1.35872 4.18172i 0.0573654 0.176553i
\(562\) −13.3692 11.1823i −0.563946 0.471697i
\(563\) −27.0677 13.7917i −1.14077 0.581251i −0.221609 0.975136i \(-0.571131\pi\)
−0.919160 + 0.393885i \(0.871131\pi\)
\(564\) −41.3717 + 0.852331i −1.74206 + 0.0358896i
\(565\) −2.52369 + 12.1661i −0.106173 + 0.511830i
\(566\) 30.9594 2.75767i 1.30132 0.115913i
\(567\) −22.2459 30.6188i −0.934238 1.28587i
\(568\) −4.22442 38.4468i −0.177253 1.61319i
\(569\) −20.7899 28.6149i −0.871559 1.19960i −0.978688 0.205352i \(-0.934166\pi\)
0.107129 0.994245i \(-0.465834\pi\)
\(570\) −10.4385 + 37.3136i −0.437219 + 1.56289i
\(571\) 4.17584 + 26.3652i 0.174753 + 1.10335i 0.906634 + 0.421917i \(0.138643\pi\)
−0.731881 + 0.681433i \(0.761357\pi\)
\(572\) −3.64952 + 1.95524i −0.152594 + 0.0817525i
\(573\) −7.69908 15.1103i −0.321634 0.631242i
\(574\) 38.6146 + 61.5805i 1.61174 + 2.57032i
\(575\) −6.55302 29.4084i −0.273280 1.22642i
\(576\) −10.4708 47.0724i −0.436282 1.96135i
\(577\) 13.7410 42.2905i 0.572046 1.76058i −0.0739786 0.997260i \(-0.523570\pi\)
0.646025 0.763317i \(-0.276430\pi\)
\(578\) 1.56311 22.8704i 0.0650170 0.951285i
\(579\) 5.69671 0.902271i 0.236747 0.0374971i
\(580\) 31.3257 4.10250i 1.30073 0.170347i
\(581\) −13.8697 2.19675i −0.575413 0.0911364i
\(582\) 19.4586 + 4.46015i 0.806585 + 0.184879i
\(583\) −5.91694 8.14397i −0.245055 0.337289i
\(584\) 1.31455 0.592725i 0.0543967 0.0245271i
\(585\) −13.2264 10.6035i −0.546843 0.438403i
\(586\) −37.7363 22.5936i −1.55887 0.933332i
\(587\) 10.4447 20.4988i 0.431098 0.846077i −0.568627 0.822596i \(-0.692525\pi\)
0.999724 0.0234811i \(-0.00747496\pi\)
\(588\) 46.6109 35.3543i 1.92220 1.45799i
\(589\) 18.4057 + 36.1232i 0.758392 + 1.48843i
\(590\) −5.56532 + 6.04611i −0.229121 + 0.248914i
\(591\) 23.2614 + 71.5913i 0.956847 + 2.94487i
\(592\) 11.8290 + 21.0271i 0.486170 + 0.864207i
\(593\) 3.62324 0.148789 0.0743943 0.997229i \(-0.476298\pi\)
0.0743943 + 0.997229i \(0.476298\pi\)
\(594\) −7.90225 + 19.6477i −0.324233 + 0.806153i
\(595\) 0.889740 + 8.08384i 0.0364758 + 0.331405i
\(596\) −16.8246 5.08597i −0.689162 0.208330i
\(597\) 1.32154 + 8.34386i 0.0540870 + 0.341492i
\(598\) 9.19579 + 5.50572i 0.376044 + 0.225146i
\(599\) 2.10759i 0.0861140i −0.999073 0.0430570i \(-0.986290\pi\)
0.999073 0.0430570i \(-0.0137097\pi\)
\(600\) 42.0610 + 6.03695i 1.71713 + 0.246458i
\(601\) 2.49399i 0.101732i −0.998705 0.0508660i \(-0.983802\pi\)
0.998705 0.0508660i \(-0.0161981\pi\)
\(602\) −5.69563 + 9.51298i −0.232137 + 0.387720i
\(603\) −2.95466 18.6550i −0.120323 0.759690i
\(604\) 13.0466 + 24.3520i 0.530858 + 0.990867i
\(605\) 16.8987 7.62329i 0.687030 0.309931i
\(606\) 12.3081 + 4.95027i 0.499980 + 0.201091i
\(607\) −41.0789 −1.66734 −0.833670 0.552263i \(-0.813764\pi\)
−0.833670 + 0.552263i \(0.813764\pi\)
\(608\) 20.2631 + 11.0246i 0.821777 + 0.447107i
\(609\) −26.8330 82.5836i −1.08733 3.34645i
\(610\) −0.430381 2.14004i −0.0174256 0.0866475i
\(611\) 3.93182 + 7.71663i 0.159064 + 0.312181i
\(612\) 1.45830 10.6186i 0.0589482 0.429231i
\(613\) −13.6883 + 26.8647i −0.552864 + 1.08506i 0.430361 + 0.902657i \(0.358386\pi\)
−0.983225 + 0.182399i \(0.941614\pi\)
\(614\) −1.66785 + 2.78568i −0.0673088 + 0.112421i
\(615\) 84.3154 + 4.00434i 3.39993 + 0.161471i
\(616\) −17.8123 6.74126i −0.717679 0.271613i
\(617\) −11.3521 15.6248i −0.457017 0.629030i 0.516870 0.856064i \(-0.327097\pi\)
−0.973887 + 0.227034i \(0.927097\pi\)
\(618\) 7.53537 32.8751i 0.303117 1.32243i
\(619\) 28.9706 + 4.58849i 1.16443 + 0.184427i 0.708580 0.705631i \(-0.249336\pi\)
0.455848 + 0.890058i \(0.349336\pi\)
\(620\) 36.6589 25.1584i 1.47226 1.01039i
\(621\) 54.1469 8.57602i 2.17284 0.344144i
\(622\) −26.3334 1.79980i −1.05587 0.0721653i
\(623\) −7.20513 + 22.1751i −0.288667 + 0.888426i
\(624\) −11.8525 + 9.38087i −0.474480 + 0.375535i
\(625\) −12.0730 + 21.8916i −0.482920 + 0.875665i
\(626\) 18.9786 11.9007i 0.758537 0.475647i
\(627\) −9.15591 17.9695i −0.365652 0.717632i
\(628\) −11.5088 + 38.0715i −0.459251 + 1.51922i
\(629\) 0.838858 + 5.29634i 0.0334474 + 0.211179i
\(630\) −3.22607 77.9127i −0.128530 3.10412i
\(631\) −6.72598 9.25752i −0.267757 0.368536i 0.653874 0.756604i \(-0.273143\pi\)
−0.921631 + 0.388068i \(0.873143\pi\)
\(632\) −2.19885 + 0.241603i −0.0874654 + 0.00961045i
\(633\) 22.7393 + 31.2980i 0.903806 + 1.24398i
\(634\) 2.85781 + 32.0836i 0.113498 + 1.27420i
\(635\) 20.0575 18.2387i 0.795958 0.723782i
\(636\) −26.5170 25.4464i −1.05147 1.00902i
\(637\) −10.9095 5.55866i −0.432250 0.220242i
\(638\) −10.5505 + 12.6138i −0.417697 + 0.499385i
\(639\) −25.4722 + 78.3954i −1.00767 + 3.10127i
\(640\) 9.10245 23.6039i 0.359806 0.933027i
\(641\) 2.97985 + 9.17103i 0.117697 + 0.362234i 0.992500 0.122245i \(-0.0390093\pi\)
−0.874803 + 0.484479i \(0.839009\pi\)
\(642\) 70.3318 + 28.2873i 2.77577 + 1.11641i
\(643\) −9.92867 + 9.92867i −0.391549 + 0.391549i −0.875239 0.483691i \(-0.839296\pi\)
0.483691 + 0.875239i \(0.339296\pi\)
\(644\) 8.71403 + 48.5266i 0.343381 + 1.91222i
\(645\) 5.29483 + 11.7372i 0.208484 + 0.462150i
\(646\) 3.36984 + 3.86426i 0.132584 + 0.152037i
\(647\) −8.30294 + 11.4280i −0.326422 + 0.449282i −0.940414 0.340030i \(-0.889563\pi\)
0.613992 + 0.789312i \(0.289563\pi\)
\(648\) −5.31965 + 25.6209i −0.208976 + 1.00648i
\(649\) 4.27729i 0.167898i
\(650\) −2.69673 8.47449i −0.105774 0.332397i
\(651\) −86.4099 86.4099i −3.38667 3.38667i
\(652\) 38.2988 0.789024i 1.49990 0.0309005i
\(653\) 12.5903 1.99411i 0.492698 0.0780356i 0.0948583 0.995491i \(-0.469760\pi\)
0.397839 + 0.917455i \(0.369760\pi\)
\(654\) 20.8794 + 1.42704i 0.816450 + 0.0558015i
\(655\) −11.0455 + 13.7777i −0.431585 + 0.538339i
\(656\) 13.5479 48.3943i 0.528959 1.88948i
\(657\) −3.07316 −0.119895
\(658\) −14.8657 + 36.9612i −0.579526 + 1.44090i
\(659\) −45.5085 23.1877i −1.77276 0.903266i −0.932585 0.360951i \(-0.882452\pi\)
−0.840175 0.542315i \(-0.817548\pi\)
\(660\) −18.2360 + 12.5151i −0.709835 + 0.487148i
\(661\) 9.95826 5.07399i 0.387331 0.197355i −0.249471 0.968382i \(-0.580257\pi\)
0.636802 + 0.771027i \(0.280257\pi\)
\(662\) −21.2419 + 1.89209i −0.825589 + 0.0735383i
\(663\) −3.19524 + 1.03820i −0.124093 + 0.0403202i
\(664\) 5.32628 + 8.11763i 0.206700 + 0.315025i
\(665\) 29.1042 + 23.3328i 1.12861 + 0.904807i
\(666\) −4.56181 51.2139i −0.176767 1.98450i
\(667\) 42.0458 + 6.65940i 1.62802 + 0.257853i
\(668\) −29.7865 14.4120i −1.15247 0.557618i
\(669\) 1.40381 8.86331i 0.0542744 0.342675i
\(670\) 4.12931 9.00716i 0.159529 0.347977i
\(671\) 0.919209 + 0.667845i 0.0354857 + 0.0257819i
\(672\) −68.3567 12.7302i −2.63692 0.491077i
\(673\) 7.06591 21.7466i 0.272371 0.838272i −0.717532 0.696525i \(-0.754728\pi\)
0.989903 0.141746i \(-0.0452717\pi\)
\(674\) −4.14084 6.60359i −0.159499 0.254361i
\(675\) −38.3907 24.3993i −1.47766 0.939131i
\(676\) −20.5566 9.94622i −0.790640 0.382547i
\(677\) 35.3566 18.0151i 1.35886 0.692376i 0.385729 0.922612i \(-0.373950\pi\)
0.973135 + 0.230236i \(0.0739500\pi\)
\(678\) −15.5184 17.7953i −0.595982 0.683425i
\(679\) 11.2969 15.5488i 0.433535 0.596709i
\(680\) 3.72208 4.21464i 0.142735 0.161624i
\(681\) 11.1638 + 15.3656i 0.427797 + 0.588812i
\(682\) −5.17046 + 22.5575i −0.197987 + 0.863772i
\(683\) −15.0791 2.38829i −0.576984 0.0913854i −0.138880 0.990309i \(-0.544350\pi\)
−0.438105 + 0.898924i \(0.644350\pi\)
\(684\) −29.7098 39.1692i −1.13598 1.49767i
\(685\) 23.7352 + 4.92356i 0.906874 + 0.188119i
\(686\) −3.85250 15.3487i −0.147089 0.586015i
\(687\) 18.4347 + 56.7363i 0.703329 + 2.16462i
\(688\) 7.51581 1.51006i 0.286538 0.0575704i
\(689\) −2.37689 + 7.31531i −0.0905522 + 0.278691i
\(690\) 52.0467 + 23.8607i 1.98138 + 0.908360i
\(691\) 35.2506 + 17.9611i 1.34100 + 0.683272i 0.969484 0.245156i \(-0.0788393\pi\)
0.371512 + 0.928428i \(0.378839\pi\)
\(692\) −18.0897 12.5819i −0.687668 0.478294i
\(693\) 28.7006 + 28.7006i 1.09025 + 1.09025i
\(694\) 9.99290 + 23.4392i 0.379325 + 0.889741i
\(695\) −3.31943 0.157648i −0.125913 0.00597992i
\(696\) −29.7726 + 52.1342i −1.12853 + 1.97614i
\(697\) 6.56550 9.03664i 0.248686 0.342287i
\(698\) −4.61144 + 7.70213i −0.174545 + 0.291530i
\(699\) −17.2420 17.2420i −0.652151 0.652151i
\(700\) 21.2272 34.9705i 0.802314 1.32176i
\(701\) 9.04961 9.04961i 0.341799 0.341799i −0.515244 0.857043i \(-0.672299\pi\)
0.857043 + 0.515244i \(0.172299\pi\)
\(702\) 15.6946 3.93934i 0.592355 0.148681i
\(703\) 19.8984 + 14.4571i 0.750484 + 0.545258i
\(704\) 4.83475 + 12.2482i 0.182216 + 0.461622i
\(705\) 25.3875 + 38.6769i 0.956150 + 1.45666i
\(706\) 20.5030 + 8.24624i 0.771639 + 0.310351i
\(707\) 9.03114 9.03114i 0.339651 0.339651i
\(708\) −2.76002 15.3700i −0.103728 0.577639i
\(709\) 7.06142 13.8588i 0.265197 0.520479i −0.719556 0.694434i \(-0.755655\pi\)
0.984754 + 0.173955i \(0.0556548\pi\)
\(710\) −33.9032 + 26.8435i −1.27237 + 1.00742i
\(711\) 4.48358 + 1.45680i 0.168148 + 0.0546344i
\(712\) 14.6960 6.62635i 0.550756 0.248333i
\(713\) 56.9771 18.5130i 2.13381 0.693316i
\(714\) −13.2596 7.93881i −0.496228 0.297102i
\(715\) 4.02011 + 2.29481i 0.150344 + 0.0858209i
\(716\) −25.1695 + 19.0910i −0.940630 + 0.713466i
\(717\) 0.773650 4.88464i 0.0288925 0.182420i
\(718\) −27.5436 + 17.2714i −1.02792 + 0.644564i
\(719\) −39.0864 + 28.3979i −1.45768 + 1.05906i −0.473716 + 0.880678i \(0.657088\pi\)
−0.983961 + 0.178386i \(0.942912\pi\)
\(720\) −38.3614 + 37.8842i −1.42965 + 1.41186i
\(721\) −26.2696 19.0860i −0.978330 0.710798i
\(722\) −3.34499 0.228618i −0.124488 0.00850830i
\(723\) 9.18640 + 18.0293i 0.341646 + 0.670518i
\(724\) −17.6740 + 6.14789i −0.656848 + 0.228485i
\(725\) −22.4971 27.2312i −0.835522 1.01134i
\(726\) −7.87080 + 34.3385i −0.292113 + 1.27442i
\(727\) 13.8829 + 4.51081i 0.514887 + 0.167297i 0.554923 0.831901i \(-0.312748\pi\)
−0.0400369 + 0.999198i \(0.512748\pi\)
\(728\) 3.83273 + 14.0386i 0.142050 + 0.520307i
\(729\) −15.4225 + 21.2273i −0.571205 + 0.786197i
\(730\) −1.34239 0.892862i −0.0496842 0.0330463i
\(731\) 1.68291 + 0.266546i 0.0622445 + 0.00985856i
\(732\) 3.73402 + 1.80669i 0.138013 + 0.0667770i
\(733\) −2.19237 + 13.8421i −0.0809769 + 0.511268i 0.913545 + 0.406738i \(0.133334\pi\)
−0.994522 + 0.104530i \(0.966666\pi\)
\(734\) 10.8079 12.9216i 0.398927 0.476944i
\(735\) −61.1773 23.1402i −2.25656 0.853541i
\(736\) 20.7747 27.0258i 0.765766 0.996185i
\(737\) 1.59375 + 4.90506i 0.0587065 + 0.180680i
\(738\) −68.7146 + 82.1530i −2.52942 + 3.02409i
\(739\) −1.30869 2.56845i −0.0481409 0.0944819i 0.865683 0.500593i \(-0.166885\pi\)
−0.913824 + 0.406111i \(0.866885\pi\)
\(740\) 12.8868 23.6962i 0.473728 0.871090i
\(741\) −6.99599 + 13.7304i −0.257004 + 0.504399i
\(742\) −32.5476 + 13.8761i −1.19486 + 0.509408i
\(743\) 22.1960i 0.814293i −0.913363 0.407146i \(-0.866524\pi\)
0.913363 0.407146i \(-0.133476\pi\)
\(744\) −4.02372 + 84.3944i −0.147517 + 3.09405i
\(745\) 5.17909 + 18.9564i 0.189747 + 0.694508i
\(746\) −8.50127 + 7.41355i −0.311254 + 0.271429i
\(747\) −3.23688 20.4368i −0.118431 0.747745i
\(748\) 0.0602837 + 2.92614i 0.00220419 + 0.106990i
\(749\) 51.6065 51.6065i 1.88566 1.88566i
\(750\) −19.2722 43.4229i −0.703722 1.58558i
\(751\) 13.6146 0.496805 0.248403 0.968657i \(-0.420094\pi\)
0.248403 + 0.968657i \(0.420094\pi\)
\(752\) 25.8235 9.58338i 0.941685 0.349470i
\(753\) −6.76990 4.91862i −0.246709 0.179244i
\(754\) 12.5359 + 0.856784i 0.456530 + 0.0312022i
\(755\) 15.3124 26.8248i 0.557276 0.976254i
\(756\) 61.1073 + 42.5020i 2.22245 + 1.54578i
\(757\) 16.3029 + 16.3029i 0.592540 + 0.592540i 0.938317 0.345777i \(-0.112385\pi\)
−0.345777 + 0.938317i \(0.612385\pi\)
\(758\) −12.8650 30.1761i −0.467279 1.09604i
\(759\) −28.3433 + 9.20928i −1.02880 + 0.334276i
\(760\) −1.59753 25.7413i −0.0579485 0.933736i
\(761\) −24.9329 8.10120i −0.903818 0.293668i −0.180006 0.983666i \(-0.557612\pi\)
−0.723812 + 0.689997i \(0.757612\pi\)
\(762\) 4.57074 + 51.3141i 0.165580 + 1.85891i
\(763\) 9.14717 17.9523i 0.331150 0.649918i
\(764\) 8.14477 + 7.81595i 0.294668 + 0.282771i
\(765\) −10.9233 + 4.92769i −0.394933 + 0.178161i
\(766\) −24.2527 + 28.9958i −0.876287 + 1.04766i
\(767\) −2.64408 + 1.92103i −0.0954721 + 0.0693645i
\(768\) 25.2766 + 40.8929i 0.912090 + 1.47559i
\(769\) 5.79986 4.21384i 0.209148 0.151955i −0.478280 0.878207i \(-0.658740\pi\)
0.687428 + 0.726252i \(0.258740\pi\)
\(770\) 4.19823 + 20.8753i 0.151294 + 0.752295i
\(771\) 38.8289 6.14990i 1.39839 0.221483i
\(772\) −3.38414 + 1.81305i −0.121798 + 0.0652533i
\(773\) 19.1698 9.76751i 0.689491 0.351313i −0.0738860 0.997267i \(-0.523540\pi\)
0.763377 + 0.645954i \(0.223540\pi\)
\(774\) −15.9246 3.65011i −0.572398 0.131201i
\(775\) −45.6079 19.7724i −1.63829 0.710245i
\(776\) −13.2088 + 1.45134i −0.474167 + 0.0521001i
\(777\) −70.5084 22.9096i −2.52948 0.821876i
\(778\) 7.48111 6.52392i 0.268211 0.233894i
\(779\) −8.01470 50.6028i −0.287156 1.81303i
\(780\) 15.9266 + 5.65207i 0.570264 + 0.202376i
\(781\) 3.52111 22.2314i 0.125995 0.795503i
\(782\) 6.41894 4.02505i 0.229541 0.143935i
\(783\) 51.9953 37.7768i 1.85816 1.35003i
\(784\) −21.5721 + 32.4201i −0.770433 + 1.15786i
\(785\) 42.8954 11.7195i 1.53100 0.418287i
\(786\) −8.16932 32.5472i −0.291390 1.16092i
\(787\) −25.1782 12.8290i −0.897507 0.457303i −0.0565471 0.998400i \(-0.518009\pi\)
−0.840960 + 0.541097i \(0.818009\pi\)
\(788\) −30.2804 39.9215i −1.07869 1.42215i
\(789\) 56.6513 28.8653i 2.01684 1.02763i
\(790\) 1.53523 + 1.93899i 0.0546211 + 0.0689862i
\(791\) −21.6190 + 7.02445i −0.768685 + 0.249761i
\(792\) 1.33646 28.0312i 0.0474890 0.996045i
\(793\) 0.868169i 0.0308296i
\(794\) 17.9212 7.64038i 0.635999 0.271147i
\(795\) −8.34580 + 40.2329i −0.295995 + 1.42691i
\(796\) −2.65555 4.95668i −0.0941233 0.175685i
\(797\) −11.8286 + 1.87346i −0.418989 + 0.0663614i −0.362370 0.932034i \(-0.618032\pi\)
−0.0566197 + 0.998396i \(0.518032\pi\)
\(798\) −68.7533 + 17.2570i −2.43384 + 0.610892i
\(799\) 6.12214 0.216586
\(800\) −27.7634 + 5.40292i −0.981586 + 0.191022i
\(801\) −34.3562 −1.21392
\(802\) −34.0567 + 8.54820i −1.20258 + 0.301847i
\(803\) 0.828834 0.131274i 0.0292489 0.00463258i
\(804\) 8.89207 + 16.5974i 0.313599 + 0.585345i
\(805\) 40.7824 37.0844i 1.43739 1.30705i
\(806\) 16.2665 6.93492i 0.572962 0.244272i
\(807\) 47.7976i 1.68256i
\(808\) −8.82049 0.420539i −0.310304 0.0147945i
\(809\) −27.7401 + 9.01329i −0.975288 + 0.316890i −0.752949 0.658079i \(-0.771369\pi\)
−0.222339 + 0.974969i \(0.571369\pi\)
\(810\) 27.4262 10.1839i 0.963658 0.357827i
\(811\) 13.1691 6.70998i 0.462429 0.235619i −0.207224 0.978294i \(-0.566443\pi\)
0.669653 + 0.742674i \(0.266443\pi\)
\(812\) 34.9297 + 46.0512i 1.22579 + 1.61608i
\(813\) −72.5343 36.9581i −2.54389 1.29618i
\(814\) 3.41800 + 13.6176i 0.119801 + 0.477296i
\(815\) −23.5019 35.8041i −0.823234 1.25416i
\(816\) 2.10478 + 10.4759i 0.0736820 + 0.366728i
\(817\) 6.32271 4.59371i 0.221203 0.160714i
\(818\) −10.0087 + 6.27602i −0.349945 + 0.219436i
\(819\) 4.85162 30.6319i 0.169529 1.07037i
\(820\) −53.8837 + 15.9214i −1.88170 + 0.555998i
\(821\) 0.351422 + 2.21879i 0.0122647 + 0.0774364i 0.993062 0.117596i \(-0.0375188\pi\)
−0.980797 + 0.195032i \(0.937519\pi\)
\(822\) −34.7175 + 30.2754i −1.21091 + 1.05598i
\(823\) −12.7855 4.15426i −0.445674 0.144808i 0.0775778 0.996986i \(-0.475281\pi\)
−0.523252 + 0.852178i \(0.675281\pi\)
\(824\) 2.45203 + 22.3161i 0.0854204 + 0.777417i
\(825\) 22.6877 + 9.83577i 0.789884 + 0.342438i
\(826\) −14.6540 3.35887i −0.509877 0.116870i
\(827\) −31.7037 + 16.1539i −1.10245 + 0.561724i −0.907908 0.419170i \(-0.862321\pi\)
−0.194539 + 0.980895i \(0.562321\pi\)
\(828\) −64.0360 + 34.3073i −2.22540 + 1.19226i
\(829\) 2.41010 0.381722i 0.0837061 0.0132577i −0.114441 0.993430i \(-0.536508\pi\)
0.198147 + 0.980172i \(0.436508\pi\)
\(830\) 4.52372 9.86749i 0.157021 0.342506i
\(831\) 27.0356 19.6425i 0.937854 0.681391i
\(832\) 5.40003 8.48964i 0.187212 0.294325i
\(833\) −7.00225 + 5.08743i −0.242614 + 0.176269i
\(834\) 4.05161 4.84397i 0.140296 0.167733i
\(835\) 4.04745 + 36.7735i 0.140068 + 1.27260i
\(836\) 9.68593 + 9.29489i 0.334995 + 0.321470i
\(837\) 41.0624 80.5895i 1.41932 2.78558i
\(838\) −1.23632 13.8797i −0.0427080 0.479468i
\(839\) −12.2786 3.98957i −0.423905 0.137735i 0.0892928 0.996005i \(-0.471539\pi\)
−0.513198 + 0.858270i \(0.671539\pi\)
\(840\) 28.5562 + 72.3043i 0.985282 + 2.49473i
\(841\) 19.8831 6.46042i 0.685626 0.222773i
\(842\) 11.0745 + 25.9763i 0.381654 + 0.895203i
\(843\) −26.1844 26.1844i −0.901837 0.901837i
\(844\) −21.1404 14.7038i −0.727684 0.506126i
\(845\) 2.79328 + 25.3786i 0.0960917 + 0.873052i
\(846\) −58.5651 4.00272i −2.01351 0.137616i
\(847\) 27.4389 + 19.9355i 0.942813 + 0.684994i
\(848\) 22.2357 + 10.1989i 0.763578 + 0.350231i
\(849\) 66.0368 2.26638
\(850\) −6.20311 1.02114i −0.212765 0.0350247i
\(851\) 25.7001 25.7001i 0.880989 0.880989i
\(852\) −1.69261 82.1583i −0.0579878 2.81470i
\(853\) 0.177521 + 1.12083i 0.00607822 + 0.0383764i 0.990541 0.137217i \(-0.0438157\pi\)
−0.984463 + 0.175593i \(0.943816\pi\)
\(854\) 3.00987 2.62476i 0.102996 0.0898175i
\(855\) −19.4458 + 51.4100i −0.665031 + 1.75818i
\(856\) −50.4028 2.40308i −1.72273 0.0821357i
\(857\) 3.36706i 0.115016i −0.998345 0.0575082i \(-0.981684\pi\)
0.998345 0.0575082i \(-0.0183155\pi\)
\(858\) −8.09176 + 3.44978i −0.276248 + 0.117774i
\(859\) 12.4528 24.4400i 0.424884 0.833882i −0.574992 0.818159i \(-0.694995\pi\)
0.999876 0.0157234i \(-0.00500511\pi\)
\(860\) −5.89558 6.22108i −0.201037 0.212137i
\(861\) 70.1092 + 137.597i 2.38931 + 4.68929i
\(862\) 17.9224 21.4274i 0.610440 0.729822i
\(863\) −3.18469 9.80148i −0.108408 0.333646i 0.882107 0.471049i \(-0.156125\pi\)
−0.990515 + 0.137403i \(0.956125\pi\)
\(864\) −6.67338 51.0295i −0.227033 1.73606i
\(865\) −1.16870 + 24.6082i −0.0397371 + 0.836704i
\(866\) 26.0793 31.1796i 0.886210 1.05952i
\(867\) 7.61897 48.1043i 0.258754 1.63371i
\(868\) 73.2217 + 35.4279i 2.48531 + 1.20250i
\(869\) −1.27146 0.201379i −0.0431312 0.00683132i
\(870\) 67.0654 2.77692i 2.27373 0.0941464i
\(871\) 2.31635 3.18818i 0.0784865 0.108027i
\(872\) −13.4387 + 3.66894i −0.455092 + 0.124246i
\(873\) 26.9335 + 8.75123i 0.911561 + 0.296184i
\(874\) 7.76416 33.8732i 0.262627 1.14578i
\(875\) −45.7325 + 0.672747i −1.54604 + 0.0227430i
\(876\) 2.89362 1.00655i 0.0977663 0.0340080i
\(877\) 20.9949 + 41.2048i 0.708948 + 1.39139i 0.911162 + 0.412048i \(0.135186\pi\)
−0.202214 + 0.979341i \(0.564814\pi\)
\(878\) 43.8187 + 2.99486i 1.47881 + 0.101072i
\(879\) −75.5996 54.9263i −2.54991 1.85262i
\(880\) 8.72784 11.8561i 0.294215 0.399668i
\(881\) −26.4651 + 19.2280i −0.891633 + 0.647809i −0.936303 0.351193i \(-0.885776\pi\)
0.0446705 + 0.999002i \(0.485776\pi\)
\(882\) 70.3106 44.0888i 2.36748 1.48455i
\(883\) −4.17157 + 26.3383i −0.140385 + 0.886354i 0.812487 + 0.582980i \(0.198113\pi\)
−0.952871 + 0.303374i \(0.901887\pi\)
\(884\) 1.78176 1.35146i 0.0599272 0.0454546i
\(885\) −12.9171 + 11.7458i −0.434205 + 0.394832i
\(886\) 2.64775 + 1.58527i 0.0889528 + 0.0532580i
\(887\) −14.7069 + 4.77857i −0.493811 + 0.160449i −0.545327 0.838223i \(-0.683595\pi\)
0.0515164 + 0.998672i \(0.483595\pi\)
\(888\) 21.0693 + 46.7277i 0.707039 + 1.56808i
\(889\) 47.1703 + 15.3265i 1.58204 + 0.514036i
\(890\) −15.0072 9.98171i −0.503043 0.334588i
\(891\) −6.91332 + 13.5682i −0.231605 + 0.454550i
\(892\) 1.05575 + 5.87925i 0.0353491 + 0.196852i
\(893\) 19.8561 19.8561i 0.664459 0.664459i
\(894\) −34.6458 13.9345i −1.15873 0.466039i
\(895\) 33.0353 + 12.4956i 1.10425 + 0.417680i
\(896\) 45.7589 6.94555i 1.52870 0.232035i
\(897\) 18.4225 + 13.3847i 0.615110 + 0.446903i
\(898\) 31.5881 7.92858i 1.05411 0.264580i
\(899\) 49.6629 49.6629i 1.65635 1.65635i
\(900\) 58.6720 + 13.8240i 1.95573 + 0.460799i
\(901\) 3.84475 + 3.84475i 0.128087 + 0.128087i
\(902\) 15.0231 25.0920i 0.500216 0.835472i
\(903\) −13.8464 + 19.0580i −0.460780 + 0.634209i
\(904\) 13.6479 + 7.79398i 0.453922 + 0.259224i
\(905\) 16.3234 + 13.0864i 0.542608 + 0.435007i
\(906\) 23.0191 + 53.9934i 0.764760 + 1.79381i
\(907\) −5.60394 5.60394i −0.186076 0.186076i 0.607921 0.793997i \(-0.292004\pi\)
−0.793997 + 0.607921i \(0.792004\pi\)
\(908\) −10.3788 7.21878i −0.344433 0.239564i
\(909\) 16.7681 + 8.54379i 0.556164 + 0.283380i
\(910\) 11.0189 11.9708i 0.365273 0.396829i
\(911\) 6.61779 20.3675i 0.219257 0.674804i −0.779567 0.626319i \(-0.784561\pi\)
0.998824 0.0484850i \(-0.0154393\pi\)
\(912\) 40.8031 + 27.1501i 1.35113 + 0.899030i
\(913\) 1.74598 + 5.37357i 0.0577835 + 0.177839i
\(914\) −0.0111480 0.0444144i −0.000368742 0.00146910i
\(915\) −0.507387 4.60992i −0.0167737 0.152399i
\(916\) −23.9973 31.6379i −0.792892 1.04535i
\(917\) −31.9087 5.05385i −1.05372 0.166893i
\(918\) 2.55560 11.1495i 0.0843473 0.367988i
\(919\) −14.7354 20.2815i −0.486076 0.669026i 0.493583 0.869699i \(-0.335687\pi\)
−0.979658 + 0.200673i \(0.935687\pi\)
\(920\) −37.9392 3.61886i −1.25082 0.119310i
\(921\) −4.05463 + 5.58072i −0.133605 + 0.183891i
\(922\) −3.35464 3.84684i −0.110479 0.126689i
\(923\) −15.3241 + 7.80803i −0.504400 + 0.257005i
\(924\) −36.4241 17.6236i −1.19827 0.579775i
\(925\) −30.0992 + 1.87357i −0.989657 + 0.0616026i
\(926\) −4.12239 6.57418i −0.135470 0.216041i
\(927\) 14.7851 45.5038i 0.485606 1.49454i
\(928\) 7.31649 39.2871i 0.240175 1.28966i
\(929\) −23.6824 17.2063i −0.776994 0.564519i 0.127081 0.991892i \(-0.459439\pi\)
−0.904075 + 0.427373i \(0.859439\pi\)
\(930\) 82.3208 46.3306i 2.69941 1.51924i
\(931\) −6.21038 + 39.2108i −0.203537 + 1.28508i
\(932\) 14.6104 + 7.06918i 0.478580 + 0.231559i
\(933\) −55.3882 8.77262i −1.81333 0.287203i
\(934\) −2.55142 28.6439i −0.0834851 0.937259i
\(935\) 2.73554 1.79561i 0.0894617 0.0587227i
\(936\) −17.9282 + 11.7633i −0.586001 + 0.384496i
\(937\) −44.7234 + 14.5315i −1.46105 + 0.474723i −0.928390 0.371607i \(-0.878807\pi\)
−0.532658 + 0.846330i \(0.678807\pi\)
\(938\) 18.0562 1.60834i 0.589557 0.0525141i
\(939\) 42.4062 21.6070i 1.38387 0.705119i
\(940\) −24.4190 18.7637i −0.796461 0.612004i
\(941\) 27.5230 + 14.0237i 0.897226 + 0.457159i 0.840861 0.541251i \(-0.182049\pi\)
0.0563646 + 0.998410i \(0.482049\pi\)
\(942\) −31.5317 + 78.3984i −1.02736 + 2.55436i
\(943\) −75.7083 −2.46540
\(944\) 5.09644 + 9.05933i 0.165875 + 0.294856i
\(945\) 3.94789 83.1268i 0.128425 2.70412i
\(946\) 4.45081 + 0.304197i 0.144708 + 0.00989030i
\(947\) −21.7995 + 3.45270i −0.708388 + 0.112198i −0.500224 0.865896i \(-0.666749\pi\)
−0.208164 + 0.978094i \(0.566749\pi\)
\(948\) −4.69879 + 0.0968036i −0.152610 + 0.00314403i
\(949\) −0.453399 0.453399i −0.0147180 0.0147180i
\(950\) −23.4306 + 16.8068i −0.760188 + 0.545285i
\(951\) 68.4348i 2.21915i
\(952\) 10.0723 + 2.09130i 0.326444 + 0.0677795i
\(953\) −5.65569 + 7.78439i −0.183206 + 0.252161i −0.890735 0.454523i \(-0.849810\pi\)
0.707529 + 0.706684i \(0.249810\pi\)
\(954\) −34.2656 39.2930i −1.10939 1.27216i
\(955\) 2.56344 12.3577i 0.0829509 0.399885i
\(956\) 0.581832 + 3.24010i 0.0188178 + 0.104792i
\(957\) −24.7048 + 24.7048i −0.798593 + 0.798593i
\(958\) −7.21926 2.90357i −0.233244 0.0938102i
\(959\) 13.7042 + 42.1773i 0.442533 + 1.36198i
\(960\) 23.7121 48.2354i 0.765306 1.55679i
\(961\) 20.9641 64.5208i 0.676261 2.08132i
\(962\) 6.88282 8.22888i 0.221911 0.265310i
\(963\) 95.8180 + 48.8217i 3.08769 + 1.57326i
\(964\) −9.71819 9.32585i −0.313002 0.300365i
\(965\) 3.72778 + 2.12793i 0.120001 + 0.0685006i
\(966\) 9.29357 + 104.336i 0.299016 + 3.35695i
\(967\) −14.6957 20.2269i −0.472581 0.650452i 0.504477 0.863425i \(-0.331685\pi\)
−0.977058 + 0.212973i \(0.931685\pi\)
\(968\) −2.56117 23.3094i −0.0823193 0.749194i
\(969\) 6.40291 + 8.81285i 0.205691 + 0.283110i
\(970\) 9.22234 + 11.6478i 0.296112 + 0.373988i
\(971\) 9.25297 + 58.4209i 0.296942 + 1.87482i 0.459588 + 0.888132i \(0.347997\pi\)
−0.162646 + 0.986684i \(0.552003\pi\)
\(972\) −0.292035 + 0.966063i −0.00936704 + 0.0309865i
\(973\) −2.76014 5.41709i −0.0884862 0.173664i
\(974\) 7.26755 4.55718i 0.232867 0.146021i
\(975\) −4.10944 18.4422i −0.131607 0.590624i
\(976\) −2.74263 0.319252i −0.0877896 0.0102190i
\(977\) −1.03872 + 3.19684i −0.0332315 + 0.102276i −0.966296 0.257432i \(-0.917124\pi\)
0.933065 + 0.359708i \(0.117124\pi\)
\(978\) 81.1974 + 5.54956i 2.59641 + 0.177455i
\(979\) 9.26592 1.46758i 0.296140 0.0469040i
\(980\) 43.5219 + 1.16919i 1.39026 + 0.0373483i
\(981\) 29.3229 + 4.64429i 0.936207 + 0.148281i
\(982\) −9.28151 + 40.4931i −0.296185 + 1.29219i
\(983\) 10.4604 + 14.3974i 0.333634 + 0.459207i 0.942568 0.334013i \(-0.108403\pi\)
−0.608935 + 0.793220i \(0.708403\pi\)
\(984\) 37.7928 99.8594i 1.20479 3.18340i
\(985\) −19.8193 + 52.3974i −0.631494 + 1.66952i
\(986\) 4.56272 7.62077i 0.145307 0.242695i
\(987\) −38.4263 + 75.4159i −1.22312 + 2.40051i
\(988\) 1.39560 10.1621i 0.0444001 0.323299i
\(989\) −5.24301 10.2900i −0.166718 0.327203i
\(990\) −27.3425 + 15.3885i −0.869001 + 0.489078i
\(991\) −16.3018 50.1718i −0.517844 1.59376i −0.778047 0.628205i \(-0.783790\pi\)
0.260204 0.965554i \(-0.416210\pi\)
\(992\) −15.9265 53.9376i −0.505665 1.71252i
\(993\) −45.3092 −1.43784
\(994\) −73.3997 29.5212i −2.32810 0.936355i
\(995\) −3.11674 + 5.46000i −0.0988073 + 0.173094i
\(996\) 9.74141 + 18.1827i 0.308669 + 0.576142i
\(997\) 7.29239 + 46.0423i 0.230952 + 1.45818i 0.781779 + 0.623556i \(0.214313\pi\)
−0.550827 + 0.834620i \(0.685687\pi\)
\(998\) 30.6337 51.1652i 0.969694 1.61961i
\(999\) 54.8724i 1.73609i
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 400.2.be.a.21.5 464
16.13 even 4 inner 400.2.be.a.221.42 yes 464
25.6 even 5 inner 400.2.be.a.181.42 yes 464
400.381 even 20 inner 400.2.be.a.381.5 yes 464
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
400.2.be.a.21.5 464 1.1 even 1 trivial
400.2.be.a.181.42 yes 464 25.6 even 5 inner
400.2.be.a.221.42 yes 464 16.13 even 4 inner
400.2.be.a.381.5 yes 464 400.381 even 20 inner